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r=[],s=function(t,e,n,r){if(p(n))Object.keys(n).forEach((function(o){var i=n[o];p(i)?(r.push(o),r.push("."),s(t,e,i,r),r.pop(),r.pop()):(r.push(o),s(t,e,i,r),r.pop())}));else if(a(n))n.forEach((function(n,o){p(n)?(r.push("["+o+"]"),r.push("."),s(t,e,n,r),r.pop(),r.pop()):(r.push("["+o+"]"),s(t,e,n,r),r.pop())}));else if(u(n)){var c=_t.test(n);if(c){var l="Detected HTML in message '"+n+"' of keypath '"+r.join("")+"' at '"+e+"'. 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this._root.$i18n.vm.$watch("locale",(function(t){r.$set(r,"locale",t),r.$forceUpdate()}),{immediate:!0})},xt.prototype.onComponentInstanceCreated=function(t){this._componentInstanceCreatedListener&&this._componentInstanceCreatedListener(t,this)},Ot.vm.get=function(){return this._vm},Ot.messages.get=function(){return m(this._getMessages())},Ot.dateTimeFormats.get=function(){return m(this._getDateTimeFormats())},Ot.numberFormats.get=function(){return m(this._getNumberFormats())},Ot.availableLocales.get=function(){return Object.keys(this.messages).sort()},Ot.locale.get=function(){return this._vm.locale},Ot.locale.set=function(t){this._vm.$set(this._vm,"locale",t)},Ot.fallbackLocale.get=function(){return this._vm.fallbackLocale},Ot.fallbackLocale.set=function(t){this._localeChainCache={},this._vm.$set(this._vm,"fallbackLocale",t)},Ot.formatFallbackMessages.get=function(){return this._formatFallbackMessages},Ot.formatFallbackMessages.set=function(t){this._formatFallbackMessages=t},Ot.missing.get=function(){return this._missing},Ot.missing.set=function(t){this._missing=t},Ot.formatter.get=function(){return this._formatter},Ot.formatter.set=function(t){this._formatter=t},Ot.silentTranslationWarn.get=function(){return this._silentTranslationWarn},Ot.silentTranslationWarn.set=function(t){this._silentTranslationWarn=t},Ot.silentFallbackWarn.get=function(){return this._silentFallbackWarn},Ot.silentFallbackWarn.set=function(t){this._silentFallbackWarn=t},Ot.preserveDirectiveContent.get=function(){return this._preserveDirectiveContent},Ot.preserveDirectiveContent.set=function(t){this._preserveDirectiveContent=t},Ot.warnHtmlInMessage.get=function(){return this._warnHtmlInMessage},Ot.warnHtmlInMessage.set=function(t){var e=this,n=this._warnHtmlInMessage;if(this._warnHtmlInMessage=t,n!==t&&("warn"===t||"error"===t)){var r=this._getMessages();Object.keys(r).forEach((function(t){e._checkLocaleMessage(t,e._warnHtmlInMessage,r[t])}))}},Ot.postTranslation.get=function(){return this._postTranslation},Ot.postTranslation.set=function(t){this._postTranslation=t},Ot.sync.get=function(){return this._sync},Ot.sync.set=function(t){this._sync=t},xt.prototype._getMessages=function(){return this._vm.messages},xt.prototype._getDateTimeFormats=function(){return this._vm.dateTimeFormats},xt.prototype._getNumberFormats=function(){return this._vm.numberFormats},xt.prototype._warnDefault=function(t,e,n,r,o,i){if(!h(n))return n;if(this._missing){var a=this._missing.apply(null,[t,e,r,o]);if(u(a))return a}else 0;if(this._formatFallbackMessages){var s=v.apply(void 0,o);return this._render(e,i,s.params,e)}return e},xt.prototype._isFallbackRoot=function(t){return(this._fallbackRootWithEmptyString?!t:h(t))&&!h(this._root)&&this._fallbackRoot},xt.prototype._isSilentFallbackWarn=function(t){return this._silentFallbackWarn 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i=this._translate(n,e,this.fallbackLocale,t,r,"raw",o);if(this._isFallbackRoot(i)){if(!this._root)throw Error("unexpected error");return this._root.$i18n.i(t,e,o)}return this._warnDefault(e,t,i,r,[o],"raw")},xt.prototype.i=function(t,e,n){return t?(u(e)||(e=this.locale),this._i(t,e,this._getMessages(),null,n)):""},xt.prototype._tc=function(t,e,n,r,o){var i,a=[],s=arguments.length-5;while(s-- >0)a[s]=arguments[s+5];if(!t)return"";void 0===o&&(o=1);var c={count:o,n:o},u=v.apply(void 0,a);return u.params=Object.assign(c,u.params),a=null===u.locale?[u.params]:[u.locale,u.params],this.fetchChoice((i=this)._t.apply(i,[t,e,n,r].concat(a)),o)},xt.prototype.fetchChoice=function(t,e){if(!t||!u(t))return null;var n=t.split("|");return e=this.getChoiceIndex(e,n.length),n[e]?n[e].trim():t},xt.prototype.tc=function(t,e){var n,r=[],o=arguments.length-2;while(o-- 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")]):e._e()],2)])},qr=[],Fr={name:"Tag",props:{name:{type:String,required:!0},isFocused:{type:Boolean,default:()=>!1},isRemovableTag:{type:Boolean,default:!1},isTranslatableTag:{type:Boolean,default:!1},isActiveTag:{type:Boolean,default:!1},activeTags:{type:Array,required:!1},keyboardIsVirtual:{type:Boolean,default:!1}},watch:{isFocused(e){e&&this.focusButton()}},mounted(){document.addEventListener("copy",this.handleCopy),document.addEventListener("cut",this.handleCut),document.addEventListener("paste",this.handlePaste),this.$once("hook:beforeDestroy",(()=>{document.removeEventListener("copy",this.handleCopy),document.removeEventListener("cut",this.handleCut),document.removeEventListener("paste",this.handlePaste)}))},methods:{isCurrentlyActiveElement(){return document.activeElement===this.$refs.button},handleCopy(e){if(!this.isCurrentlyActiveElement())return;e.preventDefault();let t=[];t=this.activeTags.length>0?this.activeTags:[this.name],e.clipboardData.setData("text/html",Ir({tags:t})),e.clipboardData.setData("text/plain",t.join(" "))},handleCut(e){this.isCurrentlyActiveElement()&&this.isRemovableTag&&(this.handleCopy(e),this.deleteTag(e))},handlePaste(e){this.isCurrentlyActiveElement()&&this.isRemovableTag&&(e.preventDefault(),this.deleteTag(e),this.$emit("paste-content",e))},deleteTag(e){this.$emit("delete-tag",{tagName:this.name,event:e}),this.$emit("prevent-blur")},focusButton(e={}){this.keyboardIsVirtual||this.$refs.button.focus(),0===e.buttons&&this.isFocused&&this.deleteTag(e)}},computed:{ariaSelected:({isActiveTag:e,isRemovableTag:t})=>t?e?"true":"false":null}},Hr=Fr,Vr=(0,Z.Z)(Hr,jr,qr,!1,null,"7e76f326",null),Wr=Vr.exports,Ur={name:"Tags",mixins:[Ar,Zr],props:{tags:{type:Array,default:()=>[]},activeTags:{type:Array,default:()=>[]},translatableTags:{type:Array,default:()=>[]},ariaLabel:{type:String,required:!1},id:{type:String,required:!1},input:{type:String,default:null},areTagsRemovable:{type:Boolean,default:!1},keyboardIsVirtual:{type:Boolean,default:!1}},components:{Tag:Wr},methods:{focusTag(e){this.focusIndex(this.tags.indexOf(e))},startingPointHook(){this.$emit("focus-prev")},handleFocus(e,t){this.focusIndex(t),this.isScrolling=!1,this.$emit("focus",e)},endingPointHook(){this.$emit("focus-next")},resetScroll(){this.$refs["scroll-wrapper"].scrollLeft=0},handleKeydown(e){const{key:t}=e,n=this.tags[this.focusedIndex];kr(t)&&n&&this.$emit("delete-tag",{tagName:n.label||n,event:e})}},computed:{totalItemsToNavigate:({tags:e})=>e.length}},Gr=Ur,Qr=(0,Z.Z)(Gr,zr,Kr,!1,null,"1f2bd813",null),Jr=Qr.exports;const Yr=5,Xr="filter-input",eo="selected-tags",to="suggested-tags",no={autocorrect:"off",autocapitalize:"off",spellcheck:"false",role:"combobox","aria-haspopup":"true","aria-autocomplete":"none","aria-owns":"suggestedTags","aria-controls":"suggestedTags"};var io,so,ao={name:"FilterInput",mixins:[Ar,Pr],constants:{FilterInputId:Xr,SelectedTagsId:eo,SuggestedTagsId:to,AXinputProperties:no,TagLimit:Yr},components:{TagList:Jr,ClearRoundedIcon:Tr,FilterIcon:Mr},props:{positionReversed:{type:Boolean,default:()=>!1},tags:{type:Array,default:()=>[]},selectedTags:{type:Array,default:()=>[]},preventedBlur:{type:Boolean,default:()=>!1},placeholder:{type:String,default:()=>""},disabled:{type:Boolean,default:()=>!1},value:{type:String,default:()=>""},shouldTruncateTags:{type:Boolean,default:!1},focusInputWhenCreated:{type:Boolean,default:!1},focusInputWhenEmpty:{type:Boolean,default:!1},selectInputOnFocus:{type:Boolean,default:!1},clearFilterOnTagSelect:{type:Boolean,default:!0},preventBorderStyle:{type:Boolean,default:!1},translatableTags:{type:Array,default:()=>[]}},data(){return{resetedTagsViaDeleteButton:!1,FilterInputId:Xr,SelectedTagsId:eo,SuggestedTagsId:to,AXinputProperties:no,showSuggestedTags:!1}},computed:{hasSuggestedTags:({suggestedTags:e})=>e.length,hasSelectedTags:({selectedTags:e})=>e.length,inputIsNotEmpty:({input:e,hasSelectedTags:t})=>e.length||t,searchAriaLabelledBy:({hasSelectedTags:e})=>e?Xr.concat(" ",eo):Xr,modelValue:{get:({value:e})=>e,set(e){this.$emit("input",e)}},input:({value:e})=>e,suggestedTags:({tags:e,selectedTags:t,shouldTruncateTags:n})=>{const i=e.filter((e=>!t.includes(e)));return n?i.slice(0,Yr):i},displaySuggestedTags:({showSuggestedTags:e,suggestedTags:t})=>e&&t.length>0,inputMultipleSelectionListeners:({resetActiveTags:e,handleCopy:t,handleCut:n,handlePaste:i})=>({click:e,copy:t,cut:n,paste:i}),selectedTagsMultipleSelectionListeners:({handleSingleTagClick:e,selectInputAndTags:t,handleDeleteTag:n,selectedTagsKeydownHandler:i,focusTagHandler:s,handlePaste:a})=>({"click-tags":e,"select-all":t,"delete-tag":n,keydown:i,focus:s,"paste-tags":a})},watch:{async selectedTags(){this.resetedTagsViaDeleteButton?this.resetedTagsViaDeleteButton=!1:this.$el.contains(document.activeElement)&&await this.focusInput(),this.displaySuggestedTags&&this.hasSuggestedTags&&this.$refs.suggestedTags.resetScroll()},suggestedTags:{immediate:!0,handler(e){this.$emit("suggested-tags",e)}},showSuggestedTags(e){this.$emit("show-suggested-tags",e)}},methods:{async focusInput(){await this.$nextTick(),this.$refs.input.focus(),!this.input&&this.resetActiveTags&&this.resetActiveTags()},async resetFilters(e=!1){if(this.setFilterInput(""),this.setSelectedTags([]),!e)return this.$emit("update:preventedBlur",!0),this.resetActiveTags&&this.resetActiveTags(),void await this.focusInput();this.resetedTagsViaDeleteButton=!0,this.showSuggestedTags=!1,this.$refs.input.blur()},focusFirstTag(e=(()=>{})){this.showSuggestedTags||(this.showSuggestedTags=!0),this.hasSuggestedTags&&this.$refs.suggestedTags?this.$refs.suggestedTags.focusFirst():e()},setFilterInput(e){this.$emit("input",e)},setSelectedTags(e){this.$emit("update:selectedTags",e)},deleteTags(e){this.setSelectedTags(this.selectedTags.filter((t=>!e.includes(t))))},async handleBlur(e){const t=e.relatedTarget;t&&t.matches&&t.matches("button, input, ul")&&this.$el.contains(t)||(await this.$nextTick(),this.resetActiveTags(),this.preventedBlur?this.$emit("update:preventedBlur",!1):(this.showSuggestedTags=!1,this.$emit("blur")))},downHandler(e){const t=()=>this.$emit("focus-next",e);this.positionReversed?t():this.focusFirstTag(t)},upHandler(e){const t=()=>this.$emit("focus-prev",e);this.positionReversed?this.focusFirstTag(t):t()},handleFocusPrevOnSelectedTags(){this.positionReversed?this.focusFirstTag((()=>this.$emit("focus-prev"))):this.$emit("focus-prev")},handleFocus(){this.showSuggestedTags=!0,this.$emit("focus")}},created(){this.focusInputWhenCreated&&document.activeElement!==this.$refs.input&&(this.inputIsNotEmpty||this.focusInputWhenEmpty)&&this.focusInput()}},ro=ao,oo=(0,Z.Z)(ro,hr,pr,!1,null,"7a79f6ea",null),lo=oo.exports,co=n(5590),uo={name:"QuickNavigationHighlighter",props:{text:{type:String,required:!0},matcherText:{type:String,default:""}},render(e){const{matcherText:t,text:n}=this,i=[];let s=0;return t?([...t].forEach((t=>{const a=n.toLowerCase().indexOf(t.toLowerCase(),s);s&&i.push(e("span",n.slice(s,a)));const r=a+1;i.push(e("span",{class:"match"},n.slice(a,r))),s=r})),e("p",{class:"highlight"},i)):e("span",{class:"highlight"},n)}},ho=uo,po=(0,Z.Z)(ho,io,so,!1,null,"4a2ce75d",null),go=po.exports,fo=function(){var e=this,t=e._self._c;return t("SVGIcon",{staticClass:"magnifier-icon",attrs:{viewBox:"0 0 14 14",themeId:"magnifier"}},[t("path",{attrs:{d:"M15.0013 14.0319L10.9437 9.97424C11.8165 8.88933 12.2925 7.53885 12.2929 6.14645C12.2929 2.75841 9.53449 0 6.14645 0C2.75841 0 0 2.75841 0 6.14645C0 9.53449 2.75841 12.2929 6.14645 12.2929C7.57562 12.2929 8.89486 11.7932 9.94425 10.9637L14.0019 15.0213L15.0013 14.0319ZM6.13645 11.0736C4.83315 11.071 3.58399 10.5521 2.66241 9.63048C1.74084 8.70891 1.22194 7.45974 1.2193 6.15644C1.2193 3.44801 3.41802 1.23928 6.13645 1.23928C8.85488 1.23928 11.0536 3.44801 11.0536 6.15644C11.0636 8.86488 8.85488 11.0736 6.13645 11.0736Z"}})])},mo=[],yo={name:"MagnifierIcon",components:{SVGIcon:mr.Z}},vo=yo,bo=(0,Z.Z)(vo,fo,mo,!1,null,null,null),To=bo.exports,So=function(){var e=this,t=e._self._c;return t("div",{staticClass:"preview"},[e.state===e.STATE.success?t("DocumentationTopic",e._b({attrs:{enableMinimized:""}},"DocumentationTopic",e.topicProps,!1)):e.state===e.STATE.loadingSlowly?t("div",{staticClass:"loading"},e._l(e.LOADER_ROW_STYLES,(function(e){return t("div",{key:e["--index"],staticClass:"loading-row",style:e})})),0):e.state===e.STATE.error?t("div",{staticClass:"unavailable"},[t("p",[e._v(e._s(e.$t("quicknav.preview-unavailable")))])]):e._e()],1)},_o=[];const{extractProps:Co}=xa.methods,ko="hero",wo={error:"error",loading:"loading",loadingSlowly:"loadingSlowly",success:"success"},Io={...Ea,state:(0,w.d9)(Ea.state)};var xo={name:"QuickNavigationPreview",components:{DocumentationTopic:xa},constants:{PreviewState:wo,PreviewStore:Io},data(){return{store:Io}},provide(){return{store:this.store}},props:{json:{type:Object,required:!1},state:{type:String,required:!0,validator:e=>Object.hasOwnProperty.call(wo,e)}},computed:{LOADER_ROW_STYLES:()=>[{"--index":0,width:"30%"},{"--index":1,width:"80%"},{"--index":2,width:"50%"}],STATE:()=>wo,topicProps:({json:e})=>{const t=Co(e),{sections:n=[]}=e;let{abstract:i}=t;const s=n.find((({kind:e})=>e===ko));return!i&&s&&(i=s.content),{...t,abstract:i}}}},$o=xo,Do=(0,Z.Z)($o,So,_o,!1,null,"779b8b01",null),Po=Do.exports;class Lo{constructor(e){this.map=new Map,this.maxSize=e}get size(){return this.map.size}get(e){if(!this.map.has(e))return;const t=this.map.get(e);return this.map.delete(e),this.map.set(e,t),t}has(e){return this.map.has(e)}set(e,t){if(this.map.has(e)&&this.map.delete(e),this.map.set(e,t),this.map.size>this.maxSize){const e=this.map.keys().next().value;this.map.delete(e)}}*[Symbol.iterator](){yield*this.map}}var Ao=n(9652);const{PreviewState:Oo}=Po.constants,No="AbortError",Ro=20,Bo=1e3;var Eo={name:"QuickNavigationModal",components:{FilterInput:lo,GenericModal:co.Z,MagnifierIcon:To,TopicTypeIcon:_e.Z,QuickNavigationHighlighter:go,Reference:$s.Z,Preview:Po},mixins:[Zr],created(){this.abortController=null,this.$cachedSymbolResults=new Lo(Ro),this.loadingTimeout=null},data(){return{debouncedInput:"",userInput:"",focusedInput:!1,cachedSymbolResults:{},previewIsLoadingSlowly:!1,SCROLL_LOCK_DISABLE_ATTR:Ao.n}},props:{children:{type:Array,required:!0},showQuickNavigationModal:{type:Boolean,required:!0},technology:{type:String,required:!0}},computed:{childrenMap({children:e}){return Va(e)},filteredSymbols:({constructFuzzyRegex:e,children:t,fuzzyMatch:n,processedUserInput:i,childrenMap:s,orderSymbolsByPriority:a})=>{const r=t.filter((e=>"groupMarker"!==e.type&&null!=e.title));if(!i)return[];const o=n({inputLength:i.length,symbols:r,processedInputRegex:new RegExp(e(i),"i"),childrenMap:s}),l=[...new Map(o.map((e=>[e.path,e]))).values()];return a(l).slice(0,Ro)},isVisible:{get:({showQuickNavigationModal:e})=>e,set(e){this.$emit("update:showQuickNavigationModal",e)}},noResultsWereFound:({processedUserInput:e,totalItemsToNavigate:t})=>e.length&&!t,processedUserInput:({debouncedInput:e})=>e.replace(/\s/g,""),totalItemsToNavigate:({filteredSymbols:e})=>e.length,selectedSymbol:({filteredSymbols:e,focusedIndex:t})=>null!==t?e[t]:null,nextSymbol:({filteredSymbols:e,focusedIndex:t})=>{if(null===t)return null;let n=t+1;return n>=e.length&&(n=0),e[n]},focusedMatchElement:({$refs:e,focusedIndex:t})=>e.match[t].$el,previewJSON:({cachedSymbolResults:e,selectedSymbol:t})=>t?(e[t.uid]||{}).json:null,previewState:({cachedSymbolResults:e,previewIsLoadingSlowly:t,selectedSymbol:n})=>n&&Object.hasOwnProperty.call(e,n.uid)?e[n.uid].success?Oo.success:Oo.error:t?Oo.loadingSlowly:Oo.loading},watch:{userInput:"debounceInput",focusedIndex(){this.focusedInput||(this.scrollIntoView(),this.focusReference())},selectedSymbol:"fetchSelectedSymbolData",$route:"closeQuickNavigationModal"},methods:{closeQuickNavigationModal(){this.$emit("update:showQuickNavigationModal",!1)},constructFuzzyRegex(e){return[...e].reduce(((t,n,i)=>t.concat(`[${n}]`).concat(i{const s=n.exec(t.title);if(!s)return!1;const a=s[0].length;return!(a>3*e)&&{uid:t.uid,title:t.title,path:t.path,parents:Qa(t.parent,i),type:t.type,inputLengthDifference:t.title.length-e,matchLength:a,matchLengthDifference:a-e,start:s.index,substring:s[0]}})).filter(Boolean)},handleKeyEnter(){!this.noResultsWereFound&&this.userInput.length&&(this.$router.push(this.filteredSymbols[this.focusedIndex].path),this.closeQuickNavigationModal())},orderSymbolsByPriority(e){return e.sort(((e,t)=>e.matchLengthDifference>t.matchLengthDifference?1:e.matchLengthDifferencet.start?1:e.startt.inputLengthDifference?1:e.inputLengthDifference{this.previewState===Oo.loading&&(this.previewIsLoadingSlowly=!0)}),Bo),!this.selectedSymbol||this.$cachedSymbolResults.has(this.selectedSymbol.uid))return clearTimeout(this.loadingTimeout),void(this.previewIsLoadingSlowly=!1);const e=async e=>{if(e&&!this.$cachedSymbolResults.has(e.uid))try{const t=await(0,w.k_)(e.path,{signal:this.abortController.signal});this.$cachedSymbolResults.set(e.uid,{success:!0,json:t})}catch(t){t.name!==No&&this.$cachedSymbolResults.set(e.uid,{success:!1})}finally{this.cachedSymbolResults=Object.freeze(Object.fromEntries(this.$cachedSymbolResults))}};this.abortController&&this.abortController.abort(),this.abortController=new AbortController,await Promise.all([e(this.selectedSymbol).finally((()=>{clearTimeout(this.loadingTimeout),this.previewIsLoadingSlowly=!1})),e(this.nextSymbol)])}}},Mo=Eo,zo=(0,Z.Z)(Mo,dr,ur,!1,null,"479a2da8",null),Ko=zo.exports,Zo=function(){var e=this,t=e._self._c;return t("div",{staticClass:"adjustable-sidebar-width",class:{dragging:e.isDragging,"sidebar-hidden":e.hiddenOnLarge}},[t("div",{ref:"sidebar",staticClass:"sidebar"},[t("div",{ref:"aside",staticClass:"aside",class:e.asideClasses,style:e.asideStyles,attrs:{"aria-hidden":e.hiddenOnLarge?"true":null},on:{transitionstart:function(t){return t.target!==t.currentTarget?null:e.trackTransitionStart.apply(null,arguments)},transitionend:function(t){return t.target!==t.currentTarget?null:e.trackTransitionEnd.apply(null,arguments)}}},[e._t("aside",null,{animationClass:"aside-animated-child",scrollLockID:e.scrollLockID,breakpoint:e.breakpoint})],2),e.fixedWidth?e._e():t("div",{staticClass:"resize-handle",on:{mousedown:function(t){return t.preventDefault(),e.startDrag.apply(null,arguments)},touchstart:function(t){return t.preventDefault(),e.startDrag.apply(null,arguments)}}})]),t("div",{ref:"content",staticClass:"content"},[e._t("default")],2),t("BreakpointEmitter",{attrs:{scope:e.BreakpointScopes.nav},on:{change:function(t){e.breakpoint=t}}})],1)},jo=[],qo=n(7247),Fo=n(7188),Ho=n(5381),Vo=n(114),Wo=n(1147),Uo=n(1716);const Go="sidebar",Qo=1921,Jo=543,Yo=400,Xo={touch:{move:"touchmove",end:"touchend"},mouse:{move:"mousemove",end:"mouseup"}},el=(e,t=window.innerWidth)=>{const n=Math.min(t,Qo);return Math.floor(Math.min(n*(e/100),n))},tl={medium:30,large:20},nl={medium:50,large:50},il="sidebar-scroll-lock";var sl={name:"AdjustableSidebarWidth",constants:{SCROLL_LOCK_ID:il},components:{BreakpointEmitter:Fo["default"]},inject:["store"],props:{shownOnMobile:{type:Boolean,default:!1},hiddenOnLarge:{type:Boolean,default:!1},fixedWidth:{type:Number,default:null}},data(){const e=window.innerWidth,t=window.innerHeight,n=Ho.L3.large,i=el(tl[n]),s=el(nl[n]),a=e>=Qo?Jo:Yo,r=qo.tO.get(Go,a);return{isDragging:!1,width:this.fixedWidth||Math.min(Math.max(r,i),s),isTouch:!1,windowWidth:e,windowHeight:t,breakpoint:n,noTransition:!1,isTransitioning:!1,isOpeningOnLarge:!1,focusTrapInstance:null,mobileTopOffset:0,topOffset:0}},computed:{minWidthPercent:({breakpoint:e})=>tl[e]||0,maxWidthPercent:({breakpoint:e})=>nl[e]||100,maxWidth:({maxWidthPercent:e,windowWidth:t,fixedWidth:n})=>Math.max(n,el(e,t)),minWidth:({minWidthPercent:e,windowWidth:t,fixedWidth:n})=>Math.min(n||t,el(e,t)),widthInPx:({width:e})=>`${e}px`,hiddenOnLargeThreshold:({minWidth:e})=>e/2,events:({isTouch:e})=>e?Xo.touch:Xo.mouse,asideStyles:({widthInPx:e,mobileTopOffset:t,topOffset:n,windowHeight:i})=>({width:e,"--top-offset":n?`${n}px`:null,"--top-offset-mobile":`${t}px`,"--app-height":`${i}px`}),asideClasses:({isDragging:e,shownOnMobile:t,noTransition:n,isTransitioning:i,hiddenOnLarge:s,mobileTopOffset:a,isOpeningOnLarge:r})=>({dragging:e,"show-on-mobile":t,"hide-on-large":s,"is-opening-on-large":r,"no-transition":n,"sidebar-transitioning":i,"has-mobile-top-offset":a}),scrollLockID:()=>il,BreakpointScopes:()=>Ho.lU},async mounted(){window.addEventListener("keydown",this.onEscapeKeydown),window.addEventListener("resize",this.storeWindowSize,{passive:!0}),window.addEventListener("orientationchange",this.storeWindowSize,{passive:!0}),this.storeTopOffset(),0===this.topOffset&&0===window.scrollY||window.addEventListener("scroll",this.storeTopOffset,{passive:!0}),this.$once("hook:beforeDestroy",(()=>{window.removeEventListener("keydown",this.onEscapeKeydown),window.removeEventListener("resize",this.storeWindowSize),window.removeEventListener("orientationchange",this.storeWindowSize),window.removeEventListener("scroll",this.storeTopOffset),this.shownOnMobile&&this.toggleScrollLock(!1),this.focusTrapInstance&&this.focusTrapInstance.destroy()})),await this.$nextTick(),this.focusTrapInstance=new Vo.Z(this.$refs.aside)},watch:{$route:"closeMobileSidebar",width:{immediate:!0,handler:Ne((function(e){this.emitEventChange(e)}),150)},windowWidth:"getWidthInCheck",async breakpoint(e){this.getWidthInCheck(),e===Ho.L3.large&&this.closeMobileSidebar(),this.noTransition=!0,await(0,Re.J)(5),this.noTransition=!1},shownOnMobile:"handleExternalOpen",async isTransitioning(e){e?(await(0,Re.X)(1e3),this.isTransitioning=!1):this.updateContentWidthInStore()},hiddenOnLarge(){this.isTransitioning=!0}},methods:{getWidthInCheck:xr((function(){this.width>this.maxWidth?this.width=this.maxWidth:this.widththis.maxWidth&&(i=this.maxWidth),this.hiddenOnLarge&&i>=this.hiddenOnLargeThreshold&&(this.$emit("update:hiddenOnLarge",!1),this.isOpeningOnLarge=!0),this.width=Math.max(i,this.minWidth),i<=this.hiddenOnLargeThreshold&&this.$emit("update:hiddenOnLarge",!0)},stopDrag(e){e.preventDefault(),this.isDragging&&(this.isDragging=!1,qo.tO.set(Go,this.width),document.removeEventListener(this.events.move,this.handleDrag),document.removeEventListener(this.events.end,this.stopDrag),this.emitEventChange(this.width))},emitEventChange(e){this.$emit("width-change",e),this.updateContentWidthInStore()},getTopOffset(){const e=document.getElementById(Uo.EA);if(!e)return 0;const{y:t}=e.getBoundingClientRect();return Math.max(t,0)},handleExternalOpen(e){e&&(this.mobileTopOffset=this.getTopOffset()),this.toggleScrollLock(e)},async updateContentWidthInStore(){await this.$nextTick(),this.store.setContentWidth(this.$refs.content.offsetWidth)},async toggleScrollLock(e){const t=document.getElementById(this.scrollLockID);e?(await this.$nextTick(),Ao.Z.lockScroll(t),this.focusTrapInstance.start(),Wo.Z.hide(this.$refs.aside)):(Ao.Z.unlockScroll(t),this.focusTrapInstance.stop(),Wo.Z.show(this.$refs.aside))},storeTopOffset:Ne((function(){this.topOffset=this.getTopOffset()}),60),async trackTransitionStart({propertyName:e}){"width"!==e&&"transform"!==e||(this.isTransitioning=!0)},trackTransitionEnd({propertyName:e}){"width"!==e&&"transform"!==e||(this.isTransitioning=!1,this.isOpeningOnLarge=!1)}}},al=sl,rl=(0,Z.Z)(al,Zo,jo,!1,null,"5cd50784",null),ol=rl.exports,ll=function(){var e=this,t=e._self._c;return 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bc(e,t){e.component(`${t}recycle-scroller`,tc),e.component(`${t}RecycleScroller`,tc),e.component(`${t}dynamic-scroller`,dc),e.component(`${t}DynamicScroller`,dc),e.component(`${t}dynamic-scroller-item`,yc),e.component(`${t}DynamicScrollerItem`,yc)}const Tc={version:"1.1.2",install(e,t){const n=Object.assign({},{installComponents:!0,componentsPrefix:""},t);for(const i in n)"undefined"!==typeof n[i]&&(Kl[i]=n[i]);n.installComponents&&bc(e,n.componentsPrefix)}};let Sc=null;function _c(e){const t=(0,nn.RL)((0,nn.hr)(e));return new RegExp(t,"ig")}"undefined"!==typeof window?Sc=window.Vue:"undefined"!==typeof n.g&&(Sc=n.g.Vue),Sc&&Sc.use(Tc);var Cc,kc,wc=function(){var e=this,t=e._self._c;return 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t("div",{staticClass:"navigator-card-item"},[t("div",{staticClass:"head-wrapper"},[t("div",{staticClass:"depth-spacer"},[e._t("depth-spacer")],2),e.hideNavigatorIcon?e._e():t("div",{staticClass:"navigator-icon-wrapper"},[e._t("navigator-icon",null,{className:"navigator-icon"})],2),t("div",{staticClass:"title-container"},[e._t("title-container")],2)])])},Dc=[],Pc={name:"BaseNavigatorCardItem",props:{hideNavigatorIcon:{type:Boolean,default:()=>!1}}},Lc=Pc,Ac=(0,Z.Z)(Lc,$c,Dc,!1,null,"41ab423b",null),Oc=Ac.exports,Nc={name:"HighlightMatch",props:{text:{type:String,required:!0},matcher:{type:RegExp,default:void 0}},render(e){const{matcher:t,text:n}=this;if(!t)return e("p",{class:"highlight"},n);const i=[];let s=0,a=null;const r=new RegExp(t,"gi");while(null!==(a=r.exec(n))){const t=a[0].length,r=a.index+t,o=n.slice(s,a.index);o&&i.push(e("span",o));const l=n.slice(a.index,r);l&&i.push(e("span",{class:"match"},l)),s=r}const o=n.slice(s,n.length);return o&&i.push(e("span",o)),e("p",{class:"highlight"},i)}},Rc=Nc,Bc=(0,Z.Z)(Rc,Cc,kc,!1,null,"7b81ca08",null),Ec=Bc.exports,Mc={name:"NavigatorCardItem",mixins:[vc({idProp:e=>e.item.uid})],components:{BaseNavigatorCardItem:Oc,HighlightMatches:Ec,TopicTypeIcon:_e.Z,InlineChevronRightIcon:xc.Z,Reference:$s.Z,Badge:ei.Z},props:{isRendered:{type:Boolean,default:!1},item:{type:Object,required:!0},expanded:{type:Boolean,default:!1},filterPattern:{type:RegExp,default:void 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hd={name:"NavigatorCard",constants:{STORAGE_KEY:nd,FILTER_TAGS:id,FILTER_TAGS_TO_LABELS:sd,FILTER_LABELS_TO_TAGS:ad,TOPIC_TYPE_TO_TAG:rd,ERROR_FETCHING:cd,ITEMS_FOUND:dd,HIDE_DEPRECATED:ud},components:{FilterInput:lo,NavigatorCardItem:Zc,DynamicScroller:dc,DynamicScrollerItem:yc,BaseNavigatorCard:Xc},props:{...Xc.props,children:{type:Array,required:!0},activePath:{type:Array,required:!0},type:{type:String,required:!0},scrollLockID:{type:String,default:""},errorFetching:{type:Boolean,default:!1},apiChanges:{type:Object,default:null},isTechnologyBeta:{type:Boolean,default:!1},navigatorReferences:{type:Object,default:()=>{}},renderFilterOnTop:{type:Boolean,default:!1},hideAvailableTags:{type:Boolean,default:!1}},mixins:[Zr],data(){return{filter:"",debouncedFilter:"",selectedTags:[],openNodes:Object.freeze({}),nodesToRender:Object.freeze([]),activeUID:null,lastFocusTarget:null,allNodesToggled:!1,translatableTags:[ud]}},computed:{politeAriaLive(){const{hasNodes:e,nodesToRender:t}=this;return e?this.$tc(dd,t.length,{number:t.length}):""},assertiveAriaLive:({hasNodes:e,hasFilter:t,errorFetching:n})=>e?"":t?od:n?cd:ld,availableTags({selectedTags:e,renderableChildNodesMap:t,apiChangesObject:n,hideAvailableTags:i}){if(i||e.length)return[];const s=new Set(Object.values(n)),a=new Set(Object.values(sd)),r=new Set([ud]);s.size&&r.delete(ud);const o={type:[],changes:[],other:[]};for(const l in t){if(!Object.hasOwnProperty.call(t,l))continue;if(!a.size&&!s.size&&!r.size)break;const{type:e,path:i,deprecated:c}=t[l],d=sd[rd[e]],u=n[i];a.has(d)&&(o.type.push(d),a.delete(d)),u&&s.has(u)&&(o.changes.push(this.$t(It.Ag[u])),s.delete(u)),c&&r.has(ud)&&(o.other.push(ud),r.delete(ud))}return o.type.concat(o.changes,o.other)},selectedTagsModelValue:{get(){return this.selectedTags.map((e=>sd[e]||this.$t(It.Ag[e])||e))},set(e){(this.selectedTags.length||e.length)&&(this.selectedTags=e.map((e=>ad[e]||It.ct[e]||e)))}},filterPattern:({debouncedFilter:e})=>e?new RegExp(_c(e),"i"):null,itemSize:()=>qa,childrenMap({children:e}){return Va(e)},activePathChildren({activeUID:e,childrenMap:t}){return e&&t[e]?Qa(e,t):[]},activePathMap:({activePathChildren:e})=>Object.fromEntries(e.map((({uid:e})=>[e,!0]))),activeIndex:({activeUID:e,nodesToRender:t})=>t.findIndex((t=>t.uid===e)),filteredChildren({hasFilter:e,children:t,filterPattern:n,selectedTags:i,apiChanges:s}){if(!e)return[];const a=new Set(i);return t.filter((({title:e,path:t,type:i,deprecated:r,deprecatedChildrenCount:o,childUIDs:l})=>{const c=r||o===l.length,d=!n||n.test(e);let u=!0;a.size&&(u=a.has(rd[i]),s&&!u&&(u=a.has(s[t])),!c&&a.has(ud)&&(u=!0));const h=!s||!!s[t];return d&&u&&h}))},renderableChildNodesMap({hasFilter:e,childrenMap:t,deprecatedHidden:n,filteredChildren:i,removeDeprecated:s}){if(!e)return t;const a=i.length-1,r=new Set([]);for(let o=a;o>=0;o-=1){const e=i[o],a=t[e.groupMarkerUID];if(a&&r.add(a),r.has(e))continue;if(r.has(t[e.parent])&&e.type!==Ce.t.groupMarker){r.add(e);continue}let l=[];e.childUIDs.length&&(l=s(Ua(e.uid,t),n)),l.concat(Qa(e.uid,t)).forEach((e=>r.add(e)))}return Va([...r])},nodeChangeDeps:({filteredChildren:e,activePathChildren:t,debouncedFilter:n,selectedTags:i})=>[e,t,n,i],hasFilter({debouncedFilter:e,selectedTags:t,apiChanges:n}){return Boolean(e.length||t.length||n)},deprecatedHidden:({selectedTags:e})=>e[0]===ud,apiChangesObject(){return this.apiChanges||{}},hasNodes:({nodesToRender:e})=>!!e.length,totalItemsToNavigate:({nodesToRender:e})=>e.length,lastActivePathItem:({activePath:e})=>ed(e)},created(){this.restorePersistedState()},watch:{filter:"debounceInput",nodeChangeDeps:"trackOpenNodes",activePath:"handleActivePathChange",apiChanges(e){e||(this.selectedTags=this.selectedTags.filter((e=>!this.$t(It.Ag[e]))))},async activeUID(e,t){await this.$nextTick();const n=this.$refs[`dynamicScroller_${t}`];n&&n.updateSize&&n.updateSize()}},methods:{setUnlessEqual(e,t){td(t,this[e])||(this[e]=Object.freeze(t))},toggleAllNodes(){const e=this.children.filter((e=>e.parent===ja&&e.type!==Ce.t.groupMarker&&e.childUIDs.length));this.allNodesToggled=!this.allNodesToggled,this.allNodesToggled&&(this.openNodes={},this.generateNodesToRender()),e.forEach((e=>{this.toggleFullTree(e)}))},clearFilters(){this.filter="",this.debouncedFilter="",this.selectedTags=[]},scrollToFocus(){this.$refs.scroller.scrollToItem(this.focusedIndex)},debounceInput:xr((function(e){this.debouncedFilter=e,this.lastFocusTarget=null}),200),trackOpenNodes([e,t,n,i],[,s=[],a="",r=[]]=[]){if(n!==a&&!a&&this.getFromStorage("filter")||!td(i,r)&&!r.length&&this.getFromStorage("selectedTags",[]).length)return;const o=!td(s,t),{childrenMap:l}=this;let c=t;if(!(this.deprecatedHidden&&!this.debouncedFilter.length||o&&this.hasFilter)&&this.hasFilter){const t=new Set,n=e.length-1;for(let i=n;i>=0;i-=1){const n=e[i];t.has(l[n.parent])||t.has(n)||Qa(n.uid,l).slice(0,-1).forEach((e=>t.add(e)))}c=[...t]}const d=o?{...this.openNodes}:{},u=c.reduce(((e,t)=>(e[t.uid]=!0,e)),d);this.setUnlessEqual("openNodes",u),this.generateNodesToRender(),this.updateFocusIndexExternally()},toggle(e){const t=this.openNodes[e.uid];let n=[],i=[];if(t){const t=(0,w.d9)(this.openNodes),n=Ua(e.uid,this.childrenMap);n.forEach((({uid:e})=>{delete t[e]})),this.setUnlessEqual("openNodes",t),i=n.slice(1)}else this.setUnlessEqual("openNodes",{...this.openNodes,[e.uid]:!0}),n=Ga(e.uid,this.childrenMap,this.children).filter((e=>this.renderableChildNodesMap[e.uid]));this.augmentRenderNodes({uid:e.uid,include:n,exclude:i})},toggleFullTree(e){const t=this.openNodes[e.uid],n=(0,w.d9)(this.openNodes),i=Ua(e.uid,this.childrenMap);let s=[],a=[];i.forEach((({uid:e})=>{t?delete 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0;const{paddingTop:t,paddingBottom:n}=getComputedStyle(this.$refs.scroller.$el),i={top:parseInt(t,10)||0,bottom:parseInt(n,10)||0},{y:s,height:a}=this.$refs.scroller.$el.getBoundingClientRect(),{y:r}=e.getBoundingClientRect(),o=e.offsetParent.offsetHeight,l=r-s-i.top;return l<0?-1:l+o>=a-i.bottom?1:0},isInsideScroller(e){return this.$refs.scroller.$el.contains(e)},handleFocusIn({target:e}){this.lastFocusTarget=e;const t=this.getChildPositionInScroller(e);if(0===t)return;const{offsetHeight:n}=e.offsetParent;this.$refs.scroller.$el.scrollBy({top:n*t,left:0})},handleFocusOut(e){e.relatedTarget&&(this.isInsideScroller(e.relatedTarget)||(this.lastFocusTarget=null))},handleScrollerUpdate:xr((async 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wd={name:"LoadingNavigatorCard",components:{BaseNavigatorCard:Xc,LoadingNavigatorItem:Cd},props:{...Xc.props},data(){return{LOADER_ROWS:kd}}},Id=wd,xd=(0,Z.Z)(Id,md,yd,!1,null,"4b6d345f",null),$d=xd.exports,Dd={name:"Navigator",components:{NavigatorCard:fd,LoadingNavigatorCard:$d},data(){return{INDEX_ROOT_KEY:ja}},props:{flatChildren:{type:Array,required:!0},parentTopicIdentifiers:{type:Array,required:!0},technology:{type:Object,required:!0},isFetching:{type:Boolean,default:!1},references:{type:Object,default:()=>{}},navigatorReferences:{type:Object,default:()=>{}},scrollLockID:{type:String,default:""},errorFetching:{type:Boolean,default:!1},renderFilterOnTop:{type:Boolean,default:!1},apiChanges:{type:Object,default:null},allowHiding:{type:Boolean,default:!0}},computed:{parentTopicReferences({references:e,parentTopicIdentifiers:t}){return t.reduce(((t,n)=>{const i=e[n];return i?t.concat(i):(console.error(`Reference for "${n}" is missing`),t)}),[])},activePath({parentTopicReferences:e,$route:{path:t}}){if(t=t.replace(/\/$/,"").toLowerCase(),!e.length)return[t];let n=1;return"technologies"===e[0].kind&&(n=2),e.slice(n).map((e=>e.url)).concat(t)},type:()=>Ce.t.module,technologyProps:({technology:e})=>({technology:e.title,technologyPath:e.path||e.url,isTechnologyBeta:e.beta})}},Pd=Dd,Ld=(0,Z.Z)(Pd,ll,cl,!1,null,"159b9764",null),Ad=Ld.exports,Od=function(){var e=this,t=e._self._c;return t("NavBase",{staticClass:"documentation-nav",attrs:{breakpoint:e.BreakpointName.medium,hasOverlay:!1,hasSolidBackground:"",hasNoBorder:e.hasNoBorder,isDark:e.isDark,isWideFormat:"",hasFullWidthBorder:"","aria-label":e.$t("api-reference")},scopedSlots:e._u([e.displaySidenav?{key:"pre-title",fn:function({closeNav:n,isOpen:i,currentBreakpoint:s,className:a}){return[t("div",{class:a},[t("transition",{attrs:{name:"sidenav-toggle"}},[t("div",{directives:[{name:"show",rawName:"v-show",value:e.sidenavHiddenOnLarge,expression:"sidenavHiddenOnLarge"}],staticClass:"sidenav-toggle-wrapper"},[t("button",{staticClass:"sidenav-toggle",attrs:{"aria-label":e.$t("navigator.open-navigator"),id:e.baseNavOpenSidenavButtonId,tabindex:i?-1:null},on:{click:function(t){return t.preventDefault(),e.handleSidenavToggle(n,s)}}},[t("span",{staticClass:"sidenav-icon-wrapper"},[t("SidenavIcon",{staticClass:"icon-inline 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t("NavMenuItems",{staticClass:"hierarchy",class:{"has-badge":e.hasBadge},attrs:{"aria-label":e.$t("documentation.nav.breadcrumbs")}},[e.root?t("HierarchyItem",{key:e.root.title,staticClass:"root-hierarchy",attrs:{url:e.addQueryParamsToUrl(e.root.url)}},[e._v(" "+e._s(e.root.title)+" ")]):e._e(),e._l(e.collapsibleItems,(function(n){return t("HierarchyItem",{key:n.title,attrs:{isCollapsed:"",url:e.addQueryParamsToUrl(n.url)}},[e._v(" "+e._s(n.title)+" ")])})),e.collapsibleItems.length?t("HierarchyCollapsedItems",{attrs:{topics:e.collapsibleItems}}):e._e(),e._l(e.nonCollapsibleItems,(function(n){return t("HierarchyItem",{key:n.title,attrs:{url:e.addQueryParamsToUrl(n.url)}},[e._v(" "+e._s(n.title)+" ")])})),t("HierarchyItem",{scopedSlots:e._u([{key:"tags",fn:function(){return[e.isSymbolDeprecated?t("Badge",{attrs:{variant:"deprecated"}}):e.isSymbolBeta?t("Badge",{attrs:{variant:"beta"}}):e._e(),e._l(e.currentTopicTags,(function(n){return t("Badge",{key:`${n.type}-${n.text}`,attrs:{variant:n.type}},[e._v(" "+e._s(n.text)+" ")])}))]},proxy:!0}])},[e._v(" "+e._s(e.currentTopicTitle)+" ")])],2)},Md=[],zd=function(){var e=this,t=e._self._c;return t("li",{staticClass:"hierarchy-collapsed-items"},[t("span",{staticClass:"hierarchy-item-icon icon-inline"},[e._v("/")]),t("button",{ref:"btn",staticClass:"toggle",class:{focused:!e.collapsed},on:{click:e.toggleCollapsed}},[t("span",{staticClass:"indicator"},[t("EllipsisIcon",{staticClass:"icon-inline toggle-icon"})],1)]),t("ul",{ref:"dropdown",staticClass:"dropdown",class:{collapsed:e.collapsed}},e._l(e.topicsWithUrls,(function(n){return t("li",{key:n.title,staticClass:"dropdown-item"},[t("router-link",{staticClass:"nav-menu-link",attrs:{to:n.url}},[e._v(e._s(n.title))])],1)})),0)])},Kd=[],Zd=function(){var e=this,t=e._self._c;return t("SVGIcon",{staticClass:"ellipsis-icon",attrs:{viewBox:"0 0 14 14",themeId:"ellipsis"}},[t("path",{attrs:{d:"m12.439 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e(t.$options.components.NavMenuItemBase,{tag:"component",staticClass:"hierarchy-item",class:[{collapsed:t.props.isCollapsed},t.data.staticClass]},[e("span",{staticClass:"hierarchy-item-icon icon-inline"},[t._v("/")]),t.props.url?e("router-link",{staticClass:"parent item nav-menu-link",attrs:{to:t.props.url}},[t._t("default")],2):[e("span",{staticClass:"current item"},[t._t("default")],2),t._t("tags")]],2)},Yd=[],Xd=n(3822),eu={name:"HierarchyItem",components:{NavMenuItemBase:Xd.Z,InlineChevronRightIcon:xc.Z},props:{isCollapsed:Boolean,url:{type:String,required:!1}}},tu=eu,nu=(0,Z.Z)(tu,Jd,Yd,!0,null,"6cf5f1d1",null),iu=nu.exports;const su=3;var au={name:"Hierarchy",components:{Badge:ei.Z,NavMenuItems:Bd.Z,HierarchyCollapsedItems:Qd,HierarchyItem:iu},constants:{MaxVisibleLinks:su},inject:["store"],props:{isSymbolDeprecated:Boolean,isSymbolBeta:Boolean,references:Object,currentTopicTitle:{type:String,required:!0},parentTopicIdentifiers:{type:Array,default:()=>[]},currentTopicTags:{type:Array,default:()=>[]}},computed:{windowWidth:({store:e})=>e.state.contentWidth,parentTopics(){return this.parentTopicIdentifiers.reduce(((e,t)=>{const n=this.references[t];if(n){const{title:t,url:i}=n;return e.concat({title:t,url:i})}return console.error(`Reference for "${t}" is missing`),e}),[])},root:({parentTopics:e,windowWidth:t})=>t<=1e3?null:e[0],firstItemSlice:({root:e})=>e?1:0,linksAfterCollapse:({windowWidth:e,hasBadge:t})=>{const n=t?1:0;return e>1200?su-n:e>1e3?su-1-n:e>=800?su-2-n:0},collapsibleItems:({parentTopics:e,linksAfterCollapse:t,firstItemSlice:n})=>t?e.slice(n,-t):e.slice(n),nonCollapsibleItems:({parentTopics:e,linksAfterCollapse:t,firstItemSlice:n})=>t?e.slice(n).slice(-t):[],hasBadge:({isSymbolDeprecated:e,isSymbolBeta:t,currentTopicTags:n})=>e||t||n.length},methods:{addQueryParamsToUrl(e){return(0,L.Q2)(e,this.$route.query)}}},ru=au,ou=(0,Z.Z)(ru,Ed,Md,!1,null,"069ffff2",null),lu=ou.exports,cu=function(){var e=this,t=e._self._c;return t("NavMenuItemBase",{staticClass:"nav-menu-setting language-container"},[t("div",{class:{"language-toggle-container":e.hasLanguages}},[t("select",{ref:"language-sizer",staticClass:"language-dropdown 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")])])})),0)]):e._e()])},du=[],uu=n(5151),hu={name:"LanguageToggle",components:{InlineChevronDownIcon:uu.Z,NavMenuItemBase:Xd.Z},inject:{store:{default(){return{setPreferredLanguage(){}}}}},props:{interfaceLanguage:{type:String,required:!0},objcPath:{type:String,required:!1},swiftPath:{type:String,required:!1},closeNav:{type:Function,default:()=>{}}},data(){return{languageModel:null,adjustedWidth:0}},mounted(){const e=Ne((async()=>{await(0,Re.J)(3),this.calculateSelectWidth()}),150);window.addEventListener("resize",e),window.addEventListener("orientationchange",e),this.$once("hook:beforeDestroy",(()=>{window.removeEventListener("resize",e),window.removeEventListener("orientationchange",e)}))},watch:{interfaceLanguage:{immediate:!0,handler(e){this.languageModel=e}},currentLanguage:{immediate:!0,handler:"calculateSelectWidth"}},methods:{getRoute(e){const t=e.query===D.Z.swift.key.url?void 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\ No newline at end of file diff --git a/BigInt.doccarchive/metadata.json b/BigInt.doccarchive/metadata.json new file mode 100644 index 0000000..c6ad35d --- /dev/null +++ b/BigInt.doccarchive/metadata.json @@ -0,0 +1 @@ +{"bundleIdentifier":"BigInt","schemaVersion":{"major":0,"patch":0,"minor":1},"bundleDisplayName":"BigInt"} \ No newline at end of file diff --git a/Package.swift b/Package.swift index a6faf15..b5f3c9d 100644 --- a/Package.swift +++ b/Package.swift @@ -1,4 +1,4 @@ -// swift-tools-version: 5.7 +// swift-tools-version: 5.9 // The swift-tools-version declares the minimum version of Swift required to build this package. import PackageDescription @@ -11,10 +11,6 @@ let package = Package( name: "BigInt", targets: ["BigInt"]), ], - dependencies: [ - // Dependencies declare other packages that this package depends on. - // .package(url: /* package url */, from: "1.0.0"), - ], targets: [ // Targets are the basic building blocks of a package. A target can define a module or a test suite. // Targets can depend on other targets in this package, and on products in packages this package depends on. diff --git a/README.md b/README.md index 6a2e6c4..db0d5fb 100644 --- a/README.md +++ b/README.md @@ -1,314 +1,23 @@

BigInt

-

Contents:

- The BigInt package provides arbitrary-precision integer arithmetic in Swift. Its functionality falls in the following categories:
    -
  • Arithmetic: add, subtract, multiply, divide, remainder and exponentiation
    • -
  • Comparison: the six standard operations == != < <= > >=
    • -
  • Shifting: logical left shift and rigth shift
    • -
  • Logical: bitwise and, or, xor, and not
    • -
  • Modulo: normal modulus, inverse modulus, and modular exponentiation
    • -
  • Conversion: to double, to integer, to string, to magnitude byte array, and to 2's complement byte array
    • -
  • Primes: prime number testing, probable prime number generation and primorial
    • -
  • Miscellaneous: random number generation, greatest common divisor, least common multiple, n-th root, square root modulo an odd prime, +
  • Arithmetic: add, subtract, multiply, divide, remainder and exponentiation
    • +
  • Comparison: the six standard operations == != < <= > >=
    • +
  • Shifting: logical left shift and rigth shift
    • +
  • Logical: bitwise and, or, xor, and not
    • +
  • Modulo: normal modulus, inverse modulus, and modular exponentiation
    • +
  • Conversion: to double, to integer, to string, to magnitude byte array, and to 2's complement byte array
    • +
  • Primes: prime number testing, probable prime number generation and primorial
    • +
  • Miscellaneous: random number generation, greatest common divisor, least common multiple, n-th root, square root modulo an odd prime, Jacobi symbol, Kronecker symbol, Factorial function, Binomial function, Fibonacci numbers, Lucas numbers and Bernoulli numbers
    • -
  • Fractions: Standard arithmetic on fractions whose numerators and denominators are of unbounded size
    • +
  • Fractions: Standard arithmetic on fractions whose numerators and denominators are of unbounded size
BigInt requires Swift 5.0. It also requires that the Int and UInt types be 64 bit types. -

Usage

-In your projects Package.swift file add a dependency like
- - dependencies: [ - .package(url: "https://github.com/leif-ibsen/BigInt", from: "1.14.0"), - ] - -

Examples

-

Creating BInt's

- - // From an integer - let a = BInt(27) - - // From a decimal value - let x = BInt(1.12345e30) // x = 1123450000000000064996914495488 - - // From string literals - let b = BInt("123456789012345678901234567890")! - let c = BInt("1234567890abcdef1234567890abcdef", radix: 16)! - - // From magnitude and sign - let m: Limbs = [1, 2, 3] - let d = BInt(m) // d = 1020847100762815390427017310442723737601 - let e = BInt(m, true) // e = -1020847100762815390427017310442723737601 - - // From a big-endian 2's complement byte array - let f = BInt(signed: [255, 255, 127]) // f = -129 - - // From a big-endian magnitude byte array - let g = BInt(magnitude: [255, 255, 127]) // g = 16777087 - - // Random value with specified bitwidth - let h = BInt(bitWidth: 43) // For example h = 3965245974702 (=0b111001101100111011000100111110100010101110) - - // Random value less than a given value - let i = h.randomLessThan() // For example i = 583464003284 - - -

Converting BInt's

- - let x = BInt(16777087) - - // To double - let d = x.asDouble() // d = 16777087.0 - - // To strings - let s1 = x.asString() // s1 = "16777087" - let s2 = x.asString(radix: 16) // s2 = "ffff7f" - - // To big-endian magnitude byte array - let b1 = x.asMagnitudeBytes() // b1 = [255, 255, 127] - - // To big-endian 2's complement byte array - let b2 = x.asSignedBytes() // b2 = [0, 255, 255, 127] - - -

Performance

- -To assess the performance of BigInt, the execution times for a number of common operations were measured on an iMac 2021, Apple M1 chip. -The results are in the table below. It shows the operation being measured and the time it took (in microseconds or milliseconds). - -Four large numbers 'a1000', 'b1000', 'c2000' and 'p1000' were used throughout the measurements. Their actual values are shown under the table. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
OperationSwift codeTime
As stringc2000.asString()13 uSec
As signed bytesc2000.asSignedBytes()0.30 uSec
Bitwise anda1000 & b10000.083 uSec
Bitwise ora1000 | b10000.083 uSec
Bitwise xora1000 ^ b10000.082 uSec
Bitwise not~c20000.087 uSec
Test bitc2000.testBit(701)0.017 uSec
Flip bitc2000.flipBit(701)0.018 uSec
Set bitc2000.setBit(701)0.018 uSec
Clear bitc2000.clearBit(701)0.018 uSec
Additiona1000 + b10000.07 uSec
Subtractiona1000 - b10000.08 uSec
Multiplicationa1000 * b10000.32 uSec
Divisionc2000 / a10002.2 uSec
Modulusc2000.mod(a1000)2.2 uSec
Inverse modulusc2000.modInverse(p1000)83 uSec
Modular exponentiationa1000.expMod(b1000, c2000)3.5 mSec
Equalc2000 + 1 == c20000.017 uSec
Less thanb1000 + 1 < b10000.021 uSec
Shift 1 leftc2000 <<= 10.05 uSec
Shift 1 rightc2000 >>= 10.06 uSec
Shift 100 leftc2000 <<= 1000.14 uSec
Shift 100 rightc2000 >>= 1000.11 uSec
Is probably primep1000.isProbablyPrime()5.8 mSec
Make probable 1000 bit primeBInt.probablePrime(1000)60 mSec
Next probable primec2000.nextPrime()730 mSec
PrimorialBInt.primorial(100000)8.5 mSec
BinomialBInt.binomial(100000, 10000)22 mSec
FactorialBInt.factorial(100000)57 mSec
FibonacciBInt.fibonacci(100000)0.22 mSec
Greatest common divisora1000.gcd(b1000)29 uSec
Extended gcda1000.gcdExtended(b1000)81 uSec
Least common multiplea1000.lcm(b1000)32 uSec
Make random numberc2000.randomLessThan()1.2 uSec
Squarec2000 ** 20.68 uSec
Square rootc2000.sqrt()13 uSec
Square root and remainderc2000.sqrtRemainder()13 uSec
Is perfect square(c2000 * c2000).isPerfectSquare()16 uSec
Square root modulob1000.sqrtMod(p1000)1.6 mSec
Powerc2000 ** 1111.9 mSec
Rootc2000.root(111)15 uSec
Root and remainderc2000.rootRemainder(111)17 uSec
Is perfect rootc2000.isPerfectRoot()13 mSec
Jacobi symbolc2000.jacobiSymbol(p1000)0.15 mSec
Kronecker symbolc2000.kroneckerSymbol(p1000)0.15 mSec
Bernoulli numberBFraction.bernoulli(1000)83 mSec
- -a1000 = 3187705437890850041662973758105262878153514794996698172406519277876060364087986868049465132757493318066301987043192958841748826350731448419937544810921786918975580180410200630645469411588934094075222404396990984350815153163569041641732160380739556436955287671287935796642478260435292021117614349253825
-b1000 = 9159373012373110951130589007821321098436345855865428979299172149373720601254669552044211236974571462005332583657082428026625366060511329189733296464187785766230514564038057370938741745651937465362625449921195096442684523511715110908407508139315000469851121118117438147266381183636498494901233452870695
-c2000 = 1190583332681083129323588684910845359379915367459759242106618067261956856381281184752008892106576666833853411939711280970145570546868549934865719229538926506588929417873149597614787608112658086250354719939407543740242931571462165384138560315454455247539461818779966171917173966217706187439870264672508450210272481951994459523586160979759782950984370978171111340529321052541588344733968902238813379990628157732181128074253104347868153860527298911917508606081710893794973605227829729403843750412766366804402629686458092685235454222856584200220355212623917637542398554907364450159627359316156463617143173
-p1000 (probably a prime) = 7662841304438384296568220077355872003841475576593385710590818274399706072141018649398767137142090308734613594718593893634649122767374115742644499040193270857876678047220373151142747088797516044505739487695946446362769947024029728822155570722524629197074319602110260674029276185098937139753025851896997
- -

Fractions

-Fractions are represented as BFraction values consisting of a numerator BInt value and a denominator BInt value. The representation is normalized: -
    -
  • The numerator and denominator have no common factors except 1
    • -
  • The denominator is always positive
    • -
  • Zero is represented as 0/1
    • -
-

Creating BFraction's

-Fractions are created by -
    -
  • Specifying the numerator and denominator explicitly f.ex. BFraction(17, 4)
    • -
  • Specifying the decimal value explictly f.ex. BFraction(4.25)
    • -
  • Using a string representation f.ex. BFraction("4.25")! or equivalently BFraction("425E-2")!
    • -
  • Specifying a continued fraction like BFraction([3, 4, 12, 4]) equivalent to 649 / 200
    • -
-Defining a fraction by giving its decimal value (like 4.25) might lead to surprises, -because not all decimal values can be represented exactly as a floating point number. -For example, one might think that BFraction(0.1) would equal 1/10, -but in fact it equals 3602879701896397 / 36028797018963968 = 0.1000000000000000055511151231257827021181583404541015625
-

Converting BFraction's

-BFraction values can be converted to String values, to decimal String values, to Double values and to Continued Fraction values. - - let x = BFraction(1000, 7) - - // To String - let s1 = x.asString() // s1 = "1000 / 7" - - // To decimal String - let s1 = x.asDecimalString(precision: 8, exponential: false) // s1 = "142.85714" - let s2 = x.asDecimalString(precision: 8, exponential: true) // s2 = "1.4285714E+2" - - // To Double - let d = x.asDouble() // d = 142.8571428571429 - - // To Continued Fraction - let f = x.asContinuedFraction() // f = [BInt(142), BInt(1), BInt(6)] - -

Operations

-The operations available to fractions are: -
    -
  • Arithmetic -
      -
    • addition
      • -
    • subtraction
      • -
    • multiplication
      • -
    • division
      • -
    • modulo an integer
      • -
    • exponentiation
      • -
    -
    • -
  • Rounding to an integer -
      -
    • round - to nearest integer
      • -
    • truncate - towards 0
      • -
    • ceil - towards +infinity
      • -
    • floor - towards -infinity
      • -
    -
    • -
  • Comparison - the six standard operations == != < <= > >=
    • -
-

Bernoulli Numbers

-The static function
+Its documentation is build with Apple's DocC tool and published on GitHub Pages at this location - let bn = BFraction.bernoulli(n) +https://leif-ibsen.github.io/BigInt/documentation/bigint -computes the n'th (n >= 0) Bernoulli number, which is a rational number.
-For example
- - print(BFraction.bernoulli(60)) - print(BFraction.bernoulli(60).asDecimalString(precision: 20, exponential: true)) - -would print
- - -1215233140483755572040304994079820246041491 / 56786730 - -2.1399949257225333665E+34 - -The static function
- - let x = BFraction.bernoulliSequence(n) - -computes the n even numbered Bernoulli numbers B(0), B(2) ... B(2 * n - 2).
- -

Harmonic Numbers

-The static function
- - let Hn = BFraction.harmonic(n) - -computes the n'th harmonic number, that is, 1 + 1/2 + ... + 1/n
-The static function
- - let x = BFraction.harmonicSequence(n) - -returns an array containing the first n harmonic numbers. -

Chinese Remainder Theorem

-The CRT structure implements the Chinese Remainder Theorem. Construct a CRT instance from a given set of moduli, -and then use the *compute* method to compute the CRT value for a given set of residues. The same instance can be reused -for any set of input data, as long as the moduli are the same. -This is relevant because it takes longer time to create the CRT instance than to compute the CRT value.
-For example
- - let moduli = [3, 5, 7] - let residues = [2, 2, 6] - let crt = CRT(moduli)! - print("CRT value:", crt.compute(residues)) - -would print
- - CRT value: 62 - -

References

- -Algorithms from the following books and papers have been used in the implementation. -There are references in the source code where appropriate. - -
    -
  • [BRENT] - Brent and Zimmermann: Modern Computer Arithmetic, 2010
    • -
  • [BURNIKEL] - Burnikel and Ziegler: Fast Recursive Division, October 1998
    • -
  • [CRANDALL] - Crandall and Pomerance: Prime Numbers - A Computational Perspective. Second Edition, Springer 2005
    • -
  • [GRANLUND] - Moller and Granlund: Improved Division by Invariant Integers, 2011
    • -
  • [HACKER] - Henry S. Warren, Jr.: Hacker's Delight. Second Edition, Addison-Wesley
    • -
  • [HANDBOOK] - Menezes, Oorschot, Vanstone: Handbook of Applied Cryptography. CRC Press 1996
    • -
  • [JEBELEAN] - Tudor Jebelean: An Algorithm for Exact Division. Journal of Symbolic Computation, volume 15, 1993
    • -
  • [KNUTH] - Donald E. Knuth: Seminumerical Algorithms, Third Edition
    • -
  • [KOC] - Cetin Kaya Koc: A New Algorithm for Inversion mod p^k
    • -
- -

Algorithms

-Some of the algorithms used in BigInt are described below. -

Multiplication

-
    -
  • Schonhage-Strassen FFT based algorithm for numbers above 384000 bits
    • -
  • ToomCook-3 algorithm for numbers above 12800 bits
    • -
  • Karatsuba algorithm for numbers above 6400 bits
    • -
  • Basecase - Knuth algorithm M
    • -
-

Division and Remainder

-
    -
  • Burnikel-Ziegler algorithm for divisors above 3840 bits provided the dividend has at least 3840 bits more than the divisor
    • -
  • Basecase - Knuth algorithm D
    • -
  • Exact Division - Jebelean's exact division algorithm
    • -
-

Greatest Common Divisor and Extended Greatest Common Divisor

-Lehmer's algorithm [KNUTH] chapter 4.5.2, with binary GCD basecase. -

Modular Exponentiation

-Sliding window algorithm 14.85 from [HANDBOOK] using Barrett reduction for exponents with fewer than 2048 bits -and Montgomery reduction for larger exponents. -

Inverse Modulus

-If the modulus is a (not too large) power of 2, the algorithm from [KOC] section 7. -Else, it is computed via the extended GCD algorithm. -

Square Root

-Algorithm 1.12 (SqrtRem) from [BRENT] with algorithm 9.2.11 from [CRANDALL] as basecase. -

Square Root Modulo a Prime Number

-Algorithm 2.3.8 from [CRANDALL]. -

Prime Number Test

-Miller-Rabin test. -

Prime Number Generation

-The algorithm from Java BigInteger translated to Swift. -

Factorial

-The 'SplitRecursive' algorithm from Peter Luschny: https://www.luschny.de -

Fibonacci

-The 'fastDoubling' algorithm from Project Nayuki: https://www.nayuki.io -

Jacobi and Kronecker symbols

-Algorithm 2.3.5 from [CRANDALL]. -

Bernoulli Numbers

-Computed via Tangent numbers which is fast because it only involves integer arithmetic -but no fractional arithmetic. -

Chinese Remainder Theorem

-The Garner algorithm 2.1.7 from [CRANDALL]. \ No newline at end of file +The documentation is also available in the BigInt.doccarchive file. \ No newline at end of file diff --git a/Sources/BigInt/BigFrac.swift b/Sources/BigInt/BigFrac.swift index 9622c52..9eaece9 100644 --- a/Sources/BigInt/BigFrac.swift +++ b/Sources/BigInt/BigFrac.swift @@ -513,7 +513,12 @@ public struct BFraction: CustomStringConvertible, Comparable, Equatable { public prefix static func -(x: BFraction) -> BFraction { return BFraction(-x.numerator, x.denominator) } - + + /// Negates *self* + public mutating func negate() { + self.numerator.negate() + } + /// Subtraction /// /// - Parameters: @@ -826,7 +831,7 @@ public struct BFraction: CustomStringConvertible, Comparable, Equatable { // MARK: Rounding functions - /// Round + /// Round to nearest /// /// Returns: *self* rounded to the nearest integer public func round() -> BInt { @@ -838,14 +843,14 @@ public struct BFraction: CustomStringConvertible, Comparable, Equatable { } } - /// Truncate + /// Round towards 0 /// /// Returns: *self* rounded to an integer towards 0 public func truncate() -> BInt { return self.isPositive ? self.floor() : self.ceil() } - /// Ceil + /// Round towards +Infinity /// /// Returns: *self* rounded to an integer towards +Infinity public func ceil() -> BInt { @@ -853,7 +858,7 @@ public struct BFraction: CustomStringConvertible, Comparable, Equatable { return r.isPositive ? q + 1 : q } - /// Floor + /// Round towards -Infinity /// /// Returns: *self* rounded to an integer towards -Infinity public func floor() -> BInt { diff --git a/Sources/BigInt/BigInt.docc/Articles/Algorithms.md b/Sources/BigInt/BigInt.docc/Articles/Algorithms.md new file mode 100644 index 0000000..448f70f --- /dev/null +++ b/Sources/BigInt/BigInt.docc/Articles/Algorithms.md @@ -0,0 +1,55 @@ +# Algorithms + +## + +Some of the algorithms used in BigInt are described below. + +### Multiplication +* Schonhage-Strassen FFT based algorithm for numbers above 384000 bits +* ToomCook-3 algorithm for numbers above 12800 bits +* Karatsuba algorithm for numbers above 6400 bits +* Basecase - Knuth algorithm M + +### Division and Remainder +* Burnikel-Ziegler algorithm for divisors above 3840 bits provided the dividend has at least 3840 bits more than the divisor +* Basecase - Knuth algorithm D +* Exact Division - Jebelean's exact division algorithm + +### Greatest Common Divisor and Extended Greatest Common Divisor +Lehmer's algorithm [KNUTH] chapter 4.5.2, with binary GCD basecase. + +### Modular Exponentiation +Sliding window algorithm 14.85 from [HANDBOOK] using Barrett reduction for exponents with fewer than 2048 bits +and Montgomery reduction for larger exponents. + +### Inverse Modulus +If the modulus is a (not too large) power of 2, the algorithm from [KOC] section 7. +Else, it is computed via the extended GCD algorithm. + +### Square Root +Algorithm 1.12 (SqrtRem) from [BRENT] with algorithm 9.2.11 from [CRANDALL] as basecase. + +### Square Root Modulo a Prime Number +Algorithm 2.3.8 from [CRANDALL]. + +### Prime Number Test +Miller-Rabin test. + +### Prime Number Generation +The algorithm from Java BigInteger translated to Swift. + +### Factorial +The *SplitRecursive* algorithm from Peter Luschny: https://www.luschny.de + +### Fibonacci +The *fastDoubling* algorithm from Project Nayuki: https://www.nayuki.io + +### Jacobi and Kronecker symbols +Algorithm 2.3.5 from [CRANDALL]. + +### Bernoulli Numbers +Computed via Tangent numbers which is fast because it only involves integer arithmetic +but no fractional arithmetic. + +### Chinese Remainder Theorem +The Garner algorithm 2.1.7 from [CRANDALL]. diff --git a/Sources/BigInt/BigInt.docc/Articles/Chinese.md b/Sources/BigInt/BigInt.docc/Articles/Chinese.md new file mode 100644 index 0000000..887cff8 --- /dev/null +++ b/Sources/BigInt/BigInt.docc/Articles/Chinese.md @@ -0,0 +1,20 @@ +# Chinese Remainder Theorem + +## + +The CRT structure implements the Chinese Remainder Theorem. Construct a CRT instance from a given set of moduli, +and then use the *compute* method to compute the CRT value for a given set of residues. The same instance can be reused +for any set of input data, as long as the moduli are the same. +This is relevant because it takes longer time to create the CRT instance than to compute the CRT value. + +For example +```swift +let moduli = [3, 5, 7] +let residues = [2, 2, 6] +let crt = CRT(moduli)! +print("CRT value:", crt.compute(residues)) +``` +would print +```swift +CRT value: 62 +``` diff --git a/Sources/BigInt/BigInt.docc/Articles/Dependencies.md b/Sources/BigInt/BigInt.docc/Articles/Dependencies.md new file mode 100644 index 0000000..ea42f76 --- /dev/null +++ b/Sources/BigInt/BigInt.docc/Articles/Dependencies.md @@ -0,0 +1,4 @@ +# Dependencies + +## +BigInt does not depend on other packages. diff --git a/Sources/BigInt/BigInt.docc/Articles/Examples.md b/Sources/BigInt/BigInt.docc/Articles/Examples.md new file mode 100644 index 0000000..e2136b9 --- /dev/null +++ b/Sources/BigInt/BigInt.docc/Articles/Examples.md @@ -0,0 +1,51 @@ +# Examples + +## + +### Creating BInt's +```swift +// From an integer +let a = BInt(27) + +// From a decimal value +let x = BInt(1.12345e30) // x = 1123450000000000064996914495488 + +// From string literals +let b = BInt("123456789012345678901234567890")! +let c = BInt("1234567890abcdef1234567890abcdef", radix: 16)! + +// From magnitude and sign +let m: Limbs = [1, 2, 3] +let d = BInt(m) // d = 1020847100762815390427017310442723737601 +let e = BInt(m, true) // e = -1020847100762815390427017310442723737601 + +// From a big-endian 2's complement byte array +let f = BInt(signed: [255, 255, 127]) // f = -129 + +// From a big-endian magnitude byte array +let g = BInt(magnitude: [255, 255, 127]) // g = 16777087 + +// Random value with specified bitwidth +let h = BInt(bitWidth: 43) // For example h = 3965245974702 (=0b111001101100111011000100111110100010101110) + +// Random value less than a given value +let i = h.randomLessThan() // For example i = 583464003284 +``` + +### Converting BInt's +```swift +let x = BInt(16777087) + +// To double +let d = x.asDouble() // d = 16777087.0 + +// To strings +let s1 = x.asString() // s1 = "16777087" +let s2 = x.asString(radix: 16) // s2 = "ffff7f" + +// To big-endian magnitude byte array +let b1 = x.asMagnitudeBytes() // b1 = [255, 255, 127] + +// To big-endian 2's complement byte array +let b2 = x.asSignedBytes() // b2 = [0, 255, 255, 127] +``` diff --git a/Sources/BigInt/BigInt.docc/Articles/Fractions.md b/Sources/BigInt/BigInt.docc/Articles/Fractions.md new file mode 100644 index 0000000..e78c759 --- /dev/null +++ b/Sources/BigInt/BigInt.docc/Articles/Fractions.md @@ -0,0 +1,91 @@ +# Fractions + +## +Fractions are represented as BFraction values consisting of a numerator BInt value and a denominator BInt value. The representation is normalized: +* The numerator and denominator have no common factors except 1 +* The denominator is always positive +* Zero is represented as 0/1 + +### Creating BFraction's +Fractions are created by +* Specifying the numerator and denominator explicitly f.ex. BFraction(17, 4) +* Specifying the decimal value explictly f.ex. BFraction(4.25) +* Using a string representation f.ex. BFraction("4.25")! or equivalently BFraction("425E-2")! +* Specifying a continued fraction like BFraction([3, 4, 12, 4]) equivalent to 649 / 200 + +Defining a fraction by giving its decimal value (like 4.25) might lead to surprises, +because not all decimal values can be represented exactly as a floating point number. +For example, one might think that BFraction(0.1) would equal 1/10, +but in fact it equals 3602879701896397 / 36028797018963968 = 0.1000000000000000055511151231257827021181583404541015625 + +### Converting BFraction's +BFraction values can be converted to String values, to decimal String values, to Double values and to Continued Fraction values. +```swift +let x = BFraction(1000, 7) + +// To String +let s1 = x.asString() // s1 = "1000 / 7" + +// To decimal String +let s1 = x.asDecimalString(precision: 8, exponential: false) // s1 = "142.85714" +let s2 = x.asDecimalString(precision: 8, exponential: true) // s2 = "1.4285714E+2" + +// To Double +let d = x.asDouble() // d = 142.8571428571429 + +// To Continued Fraction +let f = x.asContinuedFraction() // f = [BInt(142), BInt(1), BInt(6)] +``` + +### Operations +The operations available to fractions are: +* Arithmetic + + addition + + subtraction + + multiplication + + division + + modulo an integer + + exponentiation +* Rounding to an integer + + round - to nearest integer + + truncate - towards 0 + + ceil - towards +infinity + + floor - towards -infinity +* Comparison - the six standard operations == != < <= > >= + +### Bernoulli Numbers +The static function +```swift +let bn = BFraction.bernoulli(n) +``` +computes the n'th (n >= 0) Bernoulli number, which is a rational number. + +For example +```swift +print(BFraction.bernoulli(60)) +print(BFraction.bernoulli(60).asDecimalString(precision: 20, exponential: true)) +``` +would print
+```swift +-1215233140483755572040304994079820246041491 / 56786730 +-2.1399949257225333665E+34 +``` +The static function +```swift +let x = BFraction.bernoulliSequence(n) +``` +computes the n even numbered Bernoulli numbers B(0), B(2) ... B(2 * n - 2). + +### Harmonic Numbers + +The static function +```swift +let Hn = BFraction.harmonic(n) +``` +computes the n'th harmonic number, that is, 1 + 1/2 + ... + 1/n + +The static function +```swift +let x = BFraction.harmonicSequence(n) +``` +returns an array containing the first n harmonic numbers. diff --git a/Sources/BigInt/BigInt.docc/Articles/Performance.md b/Sources/BigInt/BigInt.docc/Articles/Performance.md new file mode 100644 index 0000000..f3544c9 --- /dev/null +++ b/Sources/BigInt/BigInt.docc/Articles/Performance.md @@ -0,0 +1,66 @@ +# Performance + +## + +To assess the performance of BigInt, the execution times for a number of common operations were measured on an iMac 2021, Apple M1 chip. +The results are in the table below. It shows the operation being measured and the time it took (in microseconds or milliseconds). + +> Note: +Four large numbers *a1000*, *b1000*, *c2000* and *p1000* were used throughout the measurements. Their actual values are shown under the table. + +| Operation | Swift code | Time | +|-----------|------------|------| +| As string | c2000.asString() | 13 uSec | +| As signed bytes | c2000.asSignedBytes() | 0.30 uSec | +| Bitwise and | a1000 & b1000 | 0.083 uSec | +| Bitwise or | a1000 | b1000 | 0.083 uSec | +| Bitwise xor | a1000 ^ b1000 | 0.082 uSec | +| Bitwise not | ~c2000 | 0.087 uSec | +| Test bit | c2000.testBit(701) | 0.017 uSec | +| Flip bit | c2000.flipBit(701) | 0.018 uSec | +| Set bit | c2000.setBit(701) | 0.018 uSec | +| Clear bit | c2000.clearBit(701) | 0.018 uSec | +| Addition | a1000 + b1000 | 0.07 uSec | +| Subtraction | a1000 - b1000 | 0.08 uSec | +| Multiplication | a1000 \* b1000 | 0.32 uSec | +| Division | c2000 / a1000 | 2.2 uSec | +| Modulus | c2000.mod(a1000) | 2.2 uSec | +| Inverse modulus | c2000.modInverse(p1000) | 83 uSec | +| Modular exponentiation | a1000.expMod(b1000, c2000) | 3.5 mSec | +| Equal | c2000 + 1 == c2000 | 0.017 uSec | +| Less than | b1000 + 1 < b1000 | 0.021 uSec | +| Shift 1 left | c2000 <<= 1 | 0.05 uSec | +| Shift 1 right | c2000 >>= 1 | 0.06 uSec | +| Shift 100 left | c2000 <<= 100 | 0.14 uSec | +| Shift 100 right | c2000 >>= 100 | 0.11 uSec | +| Is probably prime | p1000.isProbablyPrime() | 5.8 mSec | +| Make probable 1000 bit prime | BInt.probablePrime(1000) | 60 mSec | +| Next probable prime | c2000.nextPrime() | 730 mSec | +| Primorial | BInt.primorial(100000) | 8.5 mSec | +| Binomial | BInt.binomial(100000, 10000) | 22 mSec | +| Factorial | BInt.factorial(100000) | 57 mSec | +| Fibonacci | BInt.fibonacci(100000) | 0.22 mSec | +| Greatest common divisor | a1000.gcd(b1000) | 29 uSec | +| Extended gcd | a1000.gcdExtended(b1000) | 81 uSec | +| Least common multiple | a1000.lcm(b1000) | 32 uSec | +| Make random number | c2000.randomLessThan() | 1.2 uSec | +| Square | c2000 \*\* 2 | 0.68 uSec | +| Square root | c2000.sqrt() | 13 uSec | +| Square root and remainder | c2000.sqrtRemainder() | 13 uSec | +| Is perfect square | (c2000 \* c2000).isPerfectSquare() | 16 uSec | +| Square root modulo | b1000.sqrtMod(p1000) | 1.6 mSec | +| Power | c2000 \*\* 111 | 1.9 mSec | +| Root | c2000.root(111) | 15 uSec | +| Root and remainder | c2000.rootRemainder(111) | 17 uSec | +| Is perfect root | c2000.isPerfectRoot() | 13 mSec | +| Jacobi symbol | c2000.jacobiSymbol(p1000) | 0.15 mSec | +| Kronecker symbol | c2000.kroneckerSymbol(p1000) | 0.15 mSec | +| Bernoulli number | BFraction.bernoulli(1000) | 83 mSec | + +a1000 = 3187705437890850041662973758105262878153514794996698172406519277876060364087986868049465132757493318066301987043192958841748826350731448419937544810921786918975580180410200630645469411588934094075222404396990984350815153163569041641732160380739556436955287671287935796642478260435292021117614349253825 + +b1000 = 9159373012373110951130589007821321098436345855865428979299172149373720601254669552044211236974571462005332583657082428026625366060511329189733296464187785766230514564038057370938741745651937465362625449921195096442684523511715110908407508139315000469851121118117438147266381183636498494901233452870695 + +c2000 = 1190583332681083129323588684910845359379915367459759242106618067261956856381281184752008892106576666833853411939711280970145570546868549934865719229538926506588929417873149597614787608112658086250354719939407543740242931571462165384138560315454455247539461818779966171917173966217706187439870264672508450210272481951994459523586160979759782950984370978171111340529321052541588344733968902238813379990628157732181128074253104347868153860527298911917508606081710893794973605227829729403843750412766366804402629686458092685235454222856584200220355212623917637542398554907364450159627359316156463617143173 + +p1000 (probably a prime) = 7662841304438384296568220077355872003841475576593385710590818274399706072141018649398767137142090308734613594718593893634649122767374115742644499040193270857876678047220373151142747088797516044505739487695946446362769947024029728822155570722524629197074319602110260674029276185098937139753025851896997 diff --git a/Sources/BigInt/BigInt.docc/Articles/References.md b/Sources/BigInt/BigInt.docc/Articles/References.md new file mode 100644 index 0000000..7029116 --- /dev/null +++ b/Sources/BigInt/BigInt.docc/Articles/References.md @@ -0,0 +1,16 @@ +# References + +## + +Algorithms from the following books and papers have been used in the implementation. +There are references in the source code where appropriate. +* [BRENT] - Brent and Zimmermann: Modern Computer Arithmetic, 2010 +* [BURNIKEL] - Burnikel and Ziegler: Fast Recursive Division, October 1998 +* [CRANDALL] - Crandall and Pomerance: Prime Numbers - A Computational Perspective. Second Edition, Springer 2005 +* [GRANLUND] - Moller and Granlund: Improved Division by Invariant Integers, 2011 +* [HACKER] - Henry S. Warren, Jr.: Hacker's Delight. Second Edition, Addison-Wesley +* [HANDBOOK] - Menezes, Oorschot, Vanstone: Handbook of Applied Cryptography. CRC Press 1996 +* [JEBELEAN] - Tudor Jebelean: An Algorithm for Exact Division. Journal of Symbolic Computation, volume 15, 1993 +* [KNUTH] - Donald E. Knuth: Seminumerical Algorithms, Third Edition +* [KOC] - Cetin Kaya Koc: A New Algorithm for Inversion mod p^k + diff --git a/Sources/BigInt/BigInt.docc/Articles/Usage.md b/Sources/BigInt/BigInt.docc/Articles/Usage.md new file mode 100644 index 0000000..1169cc4 --- /dev/null +++ b/Sources/BigInt/BigInt.docc/Articles/Usage.md @@ -0,0 +1,11 @@ +# Usage + +## + +In your project Package.swift file add a dependency like + +```swift +dependencies: [ + package(url: "https://github.com/leif-ibsen/BigInt", from: "1.15.0"), +] +``` diff --git a/Sources/BigInt/BigInt.docc/BigInt.md b/Sources/BigInt/BigInt.docc/BigInt.md new file mode 100644 index 0000000..b87bba24 --- /dev/null +++ b/Sources/BigInt/BigInt.docc/BigInt.md @@ -0,0 +1,31 @@ +# ``BigInt`` + +## Overview + +The BigInt package provides arbitrary-precision integer arithmetic in Swift. +Its functionality falls in the following categories: + +* **Arithmetic:** add, subtract, multiply, divide, remainder and exponentiation +* **Comparison:** the six standard operations == != < <= > >= +* **Shifting:** logical left shift and rigth shift +* **Logical:** bitwise and, or, xor, and not +* **Modulo:** normal modulus, inverse modulus, and modular exponentiation +* **Conversion:** to double, to integer, to string, to magnitude byte array, and to 2's complement byte array +* **Primes:** prime number testing, probable prime number generation and primorial +* **Miscellaneous:** random number generation, greatest common divisor, least common multiple, n-th root, square root modulo an odd prime, +Jacobi symbol, Kronecker symbol, Factorial function, Binomial function, Fibonacci numbers, Lucas numbers and Bernoulli numbers +* **Fractions:** Standard arithmetic on fractions whose numerators and denominators are of unbounded size + +> Important: +BigInt requires Swift 5.0. It also requires that the Int and UInt types be 64 bit types. + +## Topics + +- +- +- +- +- +- +- +- diff --git a/Sources/BigInt/BigInt.docc/Extensions/BFraction.md b/Sources/BigInt/BigInt.docc/Extensions/BFraction.md new file mode 100644 index 0000000..9bf5ed8 --- /dev/null +++ b/Sources/BigInt/BigInt.docc/Extensions/BFraction.md @@ -0,0 +1,146 @@ +# ``BigInt/BFraction`` + +## Topics + +### Constants + +- ``ZERO`` +- ``ONE`` + +### Properties + +- ``abs`` +- ``denominator`` +- ``description`` +- ``isInteger`` +- ``isNegative`` +- ``isPositive`` +- ``isZero`` +- ``numerator`` +- ``signum`` + +### Constructors + +- ``init(_:_:)-7sb75`` +- ``init(_:_:)-7j7w1`` +- ``init(_:_:)-1eivz`` +- ``init(_:_:)-q5rn`` +- ``init(_:)-7fk0z`` +- ``init(_:)-8d7x`` +- ``init(_:)-1nf7w`` +- ``init(_:)-3gknk`` + +### Conversion + +- ``asString()`` +- ``asDecimalString(precision:exponential:)`` +- ``asDouble()`` +- ``asContinuedFraction()`` + +### Addition + +- ``+(_:)`` +- ``+(_:_:)-8h9j5`` +- ``+(_:_:)-2s0hx`` +- ``+(_:_:)-2ifyp`` +- ``+(_:_:)-6y32m`` +- ``+(_:_:)-2jkh4`` +- ``+=(_:_:)-91tnu`` +- ``+=(_:_:)-4dmlm`` +- ``+=(_:_:)-8z5h1`` + +### Subtraction + +- ``-(_:_:)-7wxxx`` +- ``-(_:_:)-6t2so`` +- ``-(_:_:)-1789v`` +- ``-(_:_:)-7ge79`` +- ``-(_:_:)-3751b`` +- ``-=(_:_:)-8nvxh`` +- ``-=(_:_:)-11vza`` +- ``-=(_:_:)-6s118`` + +### Negation + +- ``-(_:)`` +- ``negate()`` + +### Multiplication + +- ``*(_:_:)-42r5a`` +- ``*(_:_:)-1m8z9`` +- ``*(_:_:)-5fsb0`` +- ``*(_:_:)-97qba`` +- ``*(_:_:)-9pekq`` +- ``*=(_:_:)-1b305`` +- ``*=(_:_:)-7engg`` +- ``*=(_:_:)-9rhyz`` + +### Division + +- ``/(_:_:)-3syd2`` +- ``/(_:_:)-36e09`` +- ``/(_:_:)-f4k1`` +- ``/(_:_:)-nbpu`` +- ``/(_:_:)-6s4x9`` +- ``/=(_:_:)-5kwdi`` +- ``/=(_:_:)-9882z`` +- ``/=(_:_:)-an0e`` +- ``invert()`` + +### Exponentiation + +- ``**(_:_:)`` + +### Modulus + +- ``mod(_:)-2n1yz`` +- ``mod(_:)-3uydm`` + +### Comparison + +- ``==(_:_:)-76frx`` +- ``==(_:_:)-5uozb`` +- ``==(_:_:)-57efs`` +- ``==(_:_:)-8pm8k`` +- ``==(_:_:)-iccd`` +- ``!=(_:_:)-21ytn`` +- ``!=(_:_:)-6d0go`` +- ``!=(_:_:)-1yd5f`` +- ``!=(_:_:)-7obdp`` +- ``!=(_:_:)-25fz4`` +- ``<(_:_:)-61olb`` +- ``<(_:_:)-co3`` +- ``<(_:_:)-4hmme`` +- ``<(_:_:)-64cso`` +- ``<(_:_:)-4tyit`` +- ``>(_:_:)-v3rz`` +- ``>(_:_:)-79llm`` +- ``>(_:_:)-4lokn`` +- ``>(_:_:)-8yu93`` +- ``>(_:_:)-9xtvu`` +- ``<=(_:_:)-65hym`` +- ``<=(_:_:)-8xefd`` +- ``<=(_:_:)-7mj6q`` +- ``<=(_:_:)-44c69`` +- ``<=(_:_:)-5zk4n`` +- ``>=(_:_:)-6uyhl`` +- ``>=(_:_:)-v34i`` +- ``>=(_:_:)-9fdw7`` +- ``>=(_:_:)-24s7g`` +- ``>=(_:_:)-4xk0g`` + +### Rounding + +- ``round()`` +- ``truncate()`` +- ``ceil()`` +- ``floor()`` + +### Miscellaneous + +- ``bernoulli(_:)`` +- ``bernoulliSequence(_:)`` +- ``harmonic(_:)`` +- ``harmonicSequence(_:)`` + diff --git a/Sources/BigInt/BigInt.docc/Extensions/BInt.md b/Sources/BigInt/BigInt.docc/Extensions/BInt.md new file mode 100644 index 0000000..bdf57b0 --- /dev/null +++ b/Sources/BigInt/BigInt.docc/Extensions/BInt.md @@ -0,0 +1,194 @@ +# ``BigInt/BInt`` + +## Topics + +### Contstants + +- ``ZERO`` +- ``ONE`` +- ``TWO`` +- ``THREE`` +- ``FOUR`` +- ``FIVE`` +- ``SIX`` +- ``SEVEN`` +- ``EIGHT`` +- ``NINE`` +- ``TEN`` + +### Properties + +- ``abs`` +- ``bitWidth`` +- ``description`` +- ``isEven`` +- ``isNegative`` +- ``isNotZero`` +- ``isOdd`` +- ``isOne`` +- ``isPositive`` +- ``isZero`` +- ``leadingZeroBitCount`` +- ``magnitude`` +- ``population`` +- ``signum`` +- ``trailingZeroBitCount`` + +### Constructors + +- ``init(_:_:)`` +- ``init(_:)-11k0r`` +- ``init(_:)-5ez2f`` +- ``init(_:radix:)`` +- ``init(bitWidth:)`` +- ``init(magnitude:)`` +- ``init(signed:)`` + +### Conversion + +- ``asDouble()`` +- ``asInt()`` +- ``asMagnitudeBytes()`` +- ``asSignedBytes()`` +- ``asString(radix:uppercase:)`` + +### Addition + +- ``+(_:)`` +- ``+(_:_:)-1ld7b`` +- ``+(_:_:)-5nydr`` +- ``+(_:_:)-16w9b`` +- ``+=(_:_:)-62vn`` +- ``+=(_:_:)-2d1k`` + +### Subtraction + +- ``-(_:_:)-frii`` +- ``-(_:_:)-u0sh`` +- ``-(_:_:)-68eee`` +- ``-=(_:_:)-9vi8d`` +- ``-=(_:_:)-38r8g`` + +### Negation + +- ``-(_:)`` +- ``negate()`` + +### Multiplication + +- ``*(_:_:)-6ix02`` +- ``*(_:_:)-2wzsq`` +- ``*(_:_:)-6gaof`` +- ``*=(_:_:)-162pt`` +- ``*=(_:_:)-58nlt`` + +### Division + +- ``/(_:_:)-m4w0`` +- ``/(_:_:)-965hy`` +- ``/(_:_:)-49klv`` +- ``/=(_:_:)-2y3x4`` +- ``/=(_:_:)-5xeas`` +- ``quotientAndRemainder(dividingBy:)-xgn0`` +- ``quotientAndRemainder(dividingBy:_:_:)-7yssj`` +- ``quotientAndRemainder(dividingBy:)-6j8yx`` +- ``quotientAndRemainder(dividingBy:_:_:)-83wsf`` +- ``quotientExact(dividingBy:)`` + +### Exponentiation + +- ``**(_:_:)`` + +### Remainder and Modulus + +- ``%(_:_:)-5wrfu`` +- ``%(_:_:)-5bnmh`` +- ``%(_:_:)-sgel`` +- ``%=(_:_:)-9xw8j`` +- ``%=(_:_:)-7wqfe`` +- ``mod(_:)-8df0q`` +- ``mod(_:)-45rbl`` +- ``modInverse(_:)-2w6ad`` +- ``modInverse(_:)-7493u`` + +### Comparison + +- ``==(_:_:)-9vw7b`` +- ``==(_:_:)-368tp`` +- ``==(_:_:)-6xz16`` +- ``!=(_:_:)-1f8kc`` +- ``!=(_:_:)-3im3p`` +- ``!=(_:_:)-8g1i`` +- ``<(_:_:)-2jdj6`` +- ``<(_:_:)-7tmyi`` +- ``<(_:_:)-9r6ru`` +- ``>(_:_:)-1az8o`` +- ``>(_:_:)-3sy8p`` +- ``>(_:_:)-93apb`` +- ``<=(_:_:)-80gxv`` +- ``<=(_:_:)-7768j`` +- ``<=(_:_:)-1oyt2`` +- ``>=(_:_:)-4ql0q`` +- ``>=(_:_:)-7c55v`` +- ``>=(_:_:)-44uln`` + +### Shift Operations + +- ``<<(_:_:)`` +- ``<<=(_:_:)`` +- ``>>(_:_:)`` +- ``>>=(_:_:)`` + +### Bit Operations + +- ``&(_:_:)`` +- ``&=(_:_:)`` +- ``|(_:_:)`` +- ``|=(_:_:)`` +- ``^(_:_:)`` +- ``^=(_:_:)`` +- ``~(_:)`` +- ``clearBit(_:)`` +- ``flipBit(_:)`` +- ``setBit(_:)`` +- ``testBit(_:)`` + +### Modular Exponentiation + +- ``expMod(_:_:)-4sp4z`` +- ``expMod(_:_:)-9n2n9`` + +### Root Extraction + +- ``root(_:)`` +- ``rootRemainder(_:)`` +- ``isPerfectRoot()`` +- ``sqrt()`` +- ``sqrtRemainder()`` +- ``isPerfectSquare()`` +- ``sqrtMod(_:)-44ev6`` +- ``sqrtMod(_:)-5foxz`` + +### Prime Number + +- ``isProbablyPrime(_:)`` +- ``nextPrime(_:)`` +- ``probablePrime(_:_:)`` +- ``primorial(_:)`` + +### Miscellaneous + +- ``binomial(_:_:)`` +- ``factorial(_:)`` +- ``fibonacci(_:)`` +- ``fibonacci2(_:)`` +- ``gcd(_:)`` +- ``gcdExtended(_:)`` +- ``jacobiSymbol(_:)-3695r`` +- ``jacobiSymbol(_:)-9whxs`` +- ``kroneckerSymbol(_:)-7ml1a`` +- ``kroneckerSymbol(_:)-6q1ca`` +- ``lcm(_:)`` +- ``lucas(_:)`` +- ``lucas2(_:)`` +- ``randomLessThan()`` diff --git a/Sources/BigInt/BigInt.docc/Extensions/CRT.md b/Sources/BigInt/BigInt.docc/Extensions/CRT.md new file mode 100644 index 0000000..5b1f7d1 --- /dev/null +++ b/Sources/BigInt/BigInt.docc/Extensions/CRT.md @@ -0,0 +1,13 @@ +# ``BigInt/CRT`` + +## Topics + +### Constructors + +- ``init(_:)-2467`` +- ``init(_:)-6ke5h`` + +### Methods + +- ``compute(_:)-9xjvk`` +- ``compute(_:)-5qe04`` diff --git a/docs/Structs.html b/docs/Structs.html deleted file mode 100644 index 57c5d57..0000000 --- a/docs/Structs.html +++ /dev/null @@ -1,198 +0,0 @@ - - - - Structures Reference - - - - - - - - - - - - - -
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    A signed fraction with numerator and denominator of unbounded size.

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    A signed integer of unbounded size.

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    -

    CRT instances implement the Chinese Remainder Theorem

    - -

    Create an instance from a given set of moduli which fullfill the following conditions:

    - -
      -
    • at least two moduli
      • -
    • all moduli are positive
      • -
    • the moduli are pairwise coprime
      • -
    - -

    Then use the compute method to compute the CRT value for a given set of residues. -The same CRT instance can be used for different inputs, as long as the moduli are the same.

    - - See more -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public struct CRT
    - -
    -
    -
    -
    -
    • -
-
-
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- -
-
- - diff --git a/docs/Structs/BFraction.html b/docs/Structs/BFraction.html deleted file mode 100644 index 2d05cb1..0000000 --- a/docs/Structs/BFraction.html +++ /dev/null @@ -1,5689 +0,0 @@ - - - - BFraction Structure Reference - - - - - - - - - - - - - -
-
-

BigInt Docs (100% documented)

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- -
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-

BFraction

-
-
- - 
public struct BFraction : CustomStringConvertible, Comparable, Equatable
- -
-
-

A signed fraction with numerator and denominator of unbounded size.

- -

A BFraction value is represented by a BInt numerator and a BInt denominator. -The representation is normalized, so that numerator and denominator has no common divisors except 1. -The denominator is always positive, 0 has the representation 0/1

- -
-
-
-
- - -
- -

Constants -

-
-
-
    -
  • -
    - - - - ZERO - -
    -
    -
    -
    -
    -
    -

    BFraction(0, 1)

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static let ZERO: BFraction
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - ONE - -
    -
    -
    -
    -
    -
    -

    BFraction(1, 1)

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static let ONE: BFraction
    - -
    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Initializers -

-
-
-
    -
  • -
    - - - - init(_:_:) - -
    -
    -
    -
    -
    -
    -

    Constructs a BFraction from numerator and denominator

    -
    -

    Precondition

    - Denominator is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public init(_ n: BInt, _ d: BInt)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - n - - -
    -

    The numerator

    -
    -
    - - d - - -
    -

    The denominator

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - init(_:_:) - -
    -
    -
    -
    -
    -
    -

    Constructs a BFraction from numerator and denominator

    -
    -

    Precondition

    - Denominator is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public init(_ n: BInt, _ d: Int)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - n - - -
    -

    The numerator

    -
    -
    - - d - - -
    -

    The denominator

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - init(_:_:) - -
    -
    -
    -
    -
    -
    -

    Constructs a BFraction from numerator and denominator

    -
    -

    Precondition

    - Denominator is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public init(_ n: Int, _ d: BInt)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - n - - -
    -

    The numerator

    -
    -
    - - d - - -
    -

    The denominator

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - init(_:_:) - -
    -
    -
    -
    -
    -
    -

    Constructs a BFraction from numerator and denominator

    -
    -

    Precondition

    - Denominator is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public init(_ n: Int, _ d: Int)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - n - - -
    -

    The numerator

    -
    -
    - - d - - -
    -

    The denominator

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - init(_:) - -
    -
    -
    -
    -
    -
    -

    Constructs a BFraction from its decimal value

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public init?(_ d: Double)
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - d - - -
    -

    The decimal value

    -
    -
    -
    -
    -

    Return Value

    -

    The BFraction corresponding to d, nil if d is infinite or NaN

    -
    -
    -
    -
    • -
  • -
    - - - - init(_:) - -
    -
    -
    -
    -
    -
    -

    Constructs a BFraction from a String representation

    - -

    Examples:

    - -
      -
    • BFraction(“3.1415”) = 6283 / 2000
      • -
    • BFraction(“-12345E-3”) = -2469 / 200
      • -
    • BFraction(“12345e3”) = 12345000 / 1
      • -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public init?(_ x: String)
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - x - - -
    -

    The String representation

    -
    -
    -
    -
    -

    Return Value

    -

    The BFraction represented by x, nil if x does not represent a decimal number

    -
    -
    -
    -
    • -
  • -
    - - - - init(_:) - -
    -
    -
    -
    -
    -
    -

    Constructs a BFraction from a continued fraction - BInt version

    -
    -

    Precondition

    - x contains at least one element, all elements except possibly the first are positive - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public init(_ x: [BInt])
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - x - - -
    -

    The continued fraction

    -
    -
    -
    -
    -

    Return Value

    -

    The BFraction represented by x

    -
    -
    -
    -
    • -
  • -
    - - - - init(_:) - -
    -
    -
    -
    -
    -
    -

    Constructs a BFraction from a continued fraction - Int version

    -
    -

    Precondition

    - x contains at least one element, all elements except possibly the first are positive - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public init(_ x: [Int])
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - x - - -
    -

    The continued fraction

    -
    -
    -
    -
    -

    Return Value

    -

    The BFraction represented by x

    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Stored properties -

-
-
-
    -
  • -
    - - - - numerator - -
    -
    -
    -
    -
    -
    -

    The numerator - a BInt value

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public internal(set) var numerator: BInt { get }
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - denominator - -
    -
    -
    -
    -
    -
    -

    The denominator - a positive BInt value

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public internal(set) var denominator: BInt { get }
    - -
    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Computed properties -

-
-
-
    -
  • -
    - - - - abs - -
    -
    -
    -
    -
    -
    -

    The absolute value of self

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public var abs: BFraction { get }
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - description - -
    -
    -
    -
    -
    -
    -

    String value of self

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public var description: String { get }
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - isInteger - -
    -
    -
    -
    -
    -
    -

    Is true if self is an integer, that is, the denominator is 1

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public var isInteger: Bool { get }
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - isNegative - -
    -
    -
    -
    -
    -
    -

    Is true if self < 0, false otherwise

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public var isNegative: Bool { get }
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - isPositive - -
    -
    -
    -
    -
    -
    -

    Is true if self > 0, false otherwise

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public var isPositive: Bool { get }
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - isZero - -
    -
    -
    -
    -
    -
    -

    Is true if self = 0, false otherwise

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public var isZero: Bool { get }
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - signum - -
    -
    -
    -
    -
    -
    -

    Is 0 if self = 0, 1 if self > 0, and -1 if self < 0

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public var signum: Int { get }
    - -
    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Conversion functions to String, Decimal String, Double and Continued Fractions -

-
-
-
    -
  • -
    - - - - asString() - -
    -
    -
    -
    -
    -
    -

    self as a String
    -Examples: BFraction(-97, 100).asString() is “-97 / 100”

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func asString() -> String
    - -
    -
    -
    -

    Return Value

    -

    self as a String

    -
    -
    -
    -
    • -
  • - -
    -
    -
    -
    -
    -

    self as a Decimal String with a specified precision, possibly using exponential notation

    -
    -

    Precondition

    - precision > 0 - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func asDecimalString(precision: Int, exponential: Bool = false) -> String
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - precision - - -
    -

    The number of significant digits

    -
    -
    - - exponential - - -
    -

    true to use exponential notation, false to use plain notation, default is false

    -
    -
    -
    -
    -

    Return Value

    -

    self as a decimal String

    -
    -
    -
    -
    • -
  • -
    - - - - asDouble() - -
    -
    -
    -
    -
    -
    -

    self as a Double

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func asDouble() -> Double
    - -
    -
    -
    -

    Return Value

    -

    self as a Double or Infinity if self is not representable as a Double

    -
    -
    -
    -
    • -
  • -
    - - - - asContinuedFraction() - -
    -
    -
    -
    -
    -
    -

    self as a Continued Fraction

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func asContinuedFraction() -> [BInt]
    - -
    -
    -
    -

    Return Value

    -

    self as a Continued Fraction

    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Addition functions -

-
-
-
    -
  • -
    - - - - +(_:) - -
    -
    -
    -
    -
    -
    -

    Prefix plus

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public prefix static func + (x: BFraction) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - x - - -
    -

    BFraction value

    -
    -
    -
    -
    -

    Return Value

    -

    x

    -
    -
    -
    -
    • -
  • -
    - - - - +(_:_:) - -
    -
    -
    -
    -
    -
    -

    Addition

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func + (x: BFraction, y: BFraction) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First addend

    -
    -
    - - y - - -
    -

    Second addend

    -
    -
    -
    -
    -

    Return Value

    -

    x + y

    -
    -
    -
    -
    • -
  • -
    - - - - +(_:_:) - -
    -
    -
    -
    -
    -
    -

    Addition

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func + (x: BFraction, y: BInt) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First addend

    -
    -
    - - y - - -
    -

    Second addend

    -
    -
    -
    -
    -

    Return Value

    -

    x + y

    -
    -
    -
    -
    • -
  • -
    - - - - +(_:_:) - -
    -
    -
    -
    -
    -
    -

    Addition

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func + (x: BInt, y: BFraction) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First addend

    -
    -
    - - y - - -
    -

    Second addend

    -
    -
    -
    -
    -

    Return Value

    -

    x + y

    -
    -
    -
    -
    • -
  • -
    - - - - +(_:_:) - -
    -
    -
    -
    -
    -
    -

    Addition

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func + (x: BFraction, y: Int) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First addend

    -
    -
    - - y - - -
    -

    Second addend

    -
    -
    -
    -
    -

    Return Value

    -

    x + y

    -
    -
    -
    -
    • -
  • -
    - - - - +(_:_:) - -
    -
    -
    -
    -
    -
    -

    Addition

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func + (x: Int, y: BFraction) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First addend

    -
    -
    - - y - - -
    -

    Second addend

    -
    -
    -
    -
    -

    Return Value

    -

    x + y

    -
    -
    -
    -
    • -
  • -
    - - - - +=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x + y

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func += (x: inout BFraction, y: BFraction)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand addend

    -
    -
    - - y - - -
    -

    Right hand addend

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - +=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x + y

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func += (x: inout BFraction, y: BInt)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand addend

    -
    -
    - - y - - -
    -

    Right hand addend

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - +=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x + y

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func += (x: inout BFraction, y: Int)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand addend

    -
    -
    - - y - - -
    -

    Right hand addend

    -
    -
    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Subtraction functions -

-
-
-
    -
  • -
    - - - - -(_:) - -
    -
    -
    -
    -
    -
    -

    Negation

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public prefix static func - (x: BFraction) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - x - - -
    -

    Operand

    -
    -
    -
    -
    -

    Return Value

    -

    -x

    -
    -
    -
    -
    • -
  • -
    - - - - -(_:_:) - -
    -
    -
    -
    -
    -
    -

    Subtraction

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func - (x: BFraction, y: BFraction) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Minuend

    -
    -
    - - y - - -
    -

    Subtrahend

    -
    -
    -
    -
    -

    Return Value

    -

    x - y

    -
    -
    -
    -
    • -
  • -
    - - - - -(_:_:) - -
    -
    -
    -
    -
    -
    -

    Subtraction

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func - (x: BFraction, y: BInt) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Minuend

    -
    -
    - - y - - -
    -

    Subtrahend

    -
    -
    -
    -
    -

    Return Value

    -

    x - y

    -
    -
    -
    -
    • -
  • -
    - - - - -(_:_:) - -
    -
    -
    -
    -
    -
    -

    Subtraction

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func - (x: BInt, y: BFraction) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Minuend

    -
    -
    - - y - - -
    -

    Subtrahend

    -
    -
    -
    -
    -

    Return Value

    -

    x - y

    -
    -
    -
    -
    • -
  • -
    - - - - -(_:_:) - -
    -
    -
    -
    -
    -
    -

    Subtraction

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func - (x: BFraction, y: Int) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Minuend

    -
    -
    - - y - - -
    -

    Subtrahend

    -
    -
    -
    -
    -

    Return Value

    -

    x - y

    -
    -
    -
    -
    • -
  • -
    - - - - -(_:_:) - -
    -
    -
    -
    -
    -
    -

    Subtraction

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func - (x: Int, y: BFraction) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Minuend

    -
    -
    - - y - - -
    -

    Subtrahend

    -
    -
    -
    -
    -

    Return Value

    -

    x - y

    -
    -
    -
    -
    • -
  • -
    - - - - -=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x - y

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func -= (x: inout BFraction, y: BFraction)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand minuend

    -
    -
    - - y - - -
    -

    Right hand subtrahend

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - -=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x - y

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func -= (x: inout BFraction, y: BInt)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand minuend

    -
    -
    - - y - - -
    -

    Right hand subtrahend

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - -=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x - y

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func -= (x: inout BFraction, y: Int)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand minuend

    -
    -
    - - y - - -
    -

    Right hand subtrahend

    -
    -
    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Multiplication functions -

-
-
-
    -
  • -
    - - - - *(_:_:) - -
    -
    -
    -
    -
    -
    -

    Multiplication

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func * (x: BFraction, y: BFraction) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Multiplier

    -
    -
    - - y - - -
    -

    Multiplicand

    -
    -
    -
    -
    -

    Return Value

    -

    x * y

    -
    -
    -
    -
    • -
  • -
    - - - - *(_:_:) - -
    -
    -
    -
    -
    -
    -

    Multiplication

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func * (x: BFraction, y: BInt) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Multiplier

    -
    -
    - - y - - -
    -

    Multiplicand

    -
    -
    -
    -
    -

    Return Value

    -

    x * y

    -
    -
    -
    -
    • -
  • -
    - - - - *(_:_:) - -
    -
    -
    -
    -
    -
    -

    Multiplication

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func * (x: BInt, y: BFraction) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Multiplier

    -
    -
    - - y - - -
    -

    Multiplicand

    -
    -
    -
    -
    -

    Return Value

    -

    x * y

    -
    -
    -
    -
    • -
  • -
    - - - - *(_:_:) - -
    -
    -
    -
    -
    -
    -

    Multiplication

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func * (x: BFraction, y: Int) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Multiplier

    -
    -
    - - y - - -
    -

    Multiplicand

    -
    -
    -
    -
    -

    Return Value

    -

    x * y

    -
    -
    -
    -
    • -
  • -
    - - - - *(_:_:) - -
    -
    -
    -
    -
    -
    -

    Multiplication

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func * (x: Int, y: BFraction) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Multiplier

    -
    -
    - - y - - -
    -

    Multiplicand

    -
    -
    -
    -
    -

    Return Value

    -

    x * y

    -
    -
    -
    -
    • -
  • -
    - - - - *=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x * y

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func *= (x: inout BFraction, y: BFraction)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand multiplier

    -
    -
    - - y - - -
    -

    Right hand multiplicand

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - *=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x * y

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func *= (x: inout BFraction, y: BInt)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand multiplier

    -
    -
    - - y - - -
    -

    Right hand multiplicand

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - *=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x * y

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func *= (x: inout BFraction, y: Int)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand multiplier

    -
    -
    - - y - - -
    -

    Right hand multiplicand

    -
    -
    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Division functions -

-
-
-
    -
  • -
    - - - - /(_:_:) - -
    -
    -
    -
    -
    -
    -

    Division

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func / (x: BFraction, y: BFraction) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Dividend

    -
    -
    - - y - - -
    -

    Divisor

    -
    -
    -
    -
    -

    Return Value

    -

    x / y

    -
    -
    -
    -
    • -
  • -
    - - - - /(_:_:) - -
    -
    -
    -
    -
    -
    -

    Division

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func / (x: BFraction, y: BInt) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Dividend

    -
    -
    - - y - - -
    -

    Divisor

    -
    -
    -
    -
    -

    Return Value

    -

    x / y

    -
    -
    -
    -
    • -
  • -
    - - - - /(_:_:) - -
    -
    -
    -
    -
    -
    -

    Division

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func / (x: BInt, y: BFraction) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Dividend

    -
    -
    - - y - - -
    -

    Divisor

    -
    -
    -
    -
    -

    Return Value

    -

    x / y

    -
    -
    -
    -
    • -
  • -
    - - - - /(_:_:) - -
    -
    -
    -
    -
    -
    -

    Division

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func / (x: BFraction, y: Int) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Dividend

    -
    -
    - - y - - -
    -

    Divisor

    -
    -
    -
    -
    -

    Return Value

    -

    x / y

    -
    -
    -
    -
    • -
  • -
    - - - - /(_:_:) - -
    -
    -
    -
    -
    -
    -

    Division

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func / (x: Int, y: BFraction) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Dividend

    -
    -
    - - y - - -
    -

    Divisor

    -
    -
    -
    -
    -

    Return Value

    -

    x / y

    -
    -
    -
    -
    • -
  • -
    - - - - /=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x / y

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func /= (x: inout BFraction, y: BFraction)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand dividend

    -
    -
    - - y - - -
    -

    Right hand divisor

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - /=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x / y

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func /= (x: inout BFraction, y: BInt)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand dividend

    -
    -
    - - y - - -
    -

    Right hand divisor

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - /=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x / y

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func /= (x: inout BFraction, y: Int)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand dividend

    -
    -
    - - y - - -
    -

    Right hand divisor

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - invert() - -
    -
    -
    -
    -
    -
    -

    Invert self

    -
    -

    Precondition

    - self is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func invert() -> BFraction
    - -
    -
    -
    -

    Return Value

    -

    1 / self

    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Modulus functions -

-
-
-
    -
  • -
    - - - - mod(_:) - -
    -
    -
    -
    -
    -
    -

    Modulus - BInt parameter

    -
    -

    Precondition

    - Modulus is positive - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func mod(_ m: BInt) -> BInt?
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - m - - -
    -

    Modulus

    -
    -
    -
    -
    -

    Return Value

    -

    self mod m, a non-negative value or nil if the denominator and modulus are not coprime

    -
    -
    -
    -
    • -
  • -
    - - - - mod(_:) - -
    -
    -
    -
    -
    -
    -

    Modulus - Int parameter

    -
    -

    Precondition

    - Modulus is positive - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func mod(_ m: Int) -> Int?
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - m - - -
    -

    Modulus

    -
    -
    -
    -
    -

    Return Value

    -

    self mod x, a non-negative value or nil if the denominator and modulus are not coprime

    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Exponentiation functions -

-
-
-
    -
  • -
    - - - - **(_:_:) - -
    -
    -
    -
    -
    -
    -

    Exponentiation

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func ** (a: BFraction, x: Int) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - a - - -
    -

    Operand

    -
    -
    - - x - - -
    -

    Exponent

    -
    -
    -
    -
    -

    Return Value

    -

    a^x

    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Rounding functions -

-
-
-
    -
  • -
    - - - - round() - -
    -
    -
    -
    -
    -
    -

    Round

    - -

    Returns: self rounded to the nearest integer

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func round() -> BInt
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - truncate() - -
    -
    -
    -
    -
    -
    -

    Truncate

    - -

    Returns: self rounded to an integer towards 0

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func truncate() -> BInt
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - ceil() - -
    -
    -
    -
    -
    -
    -

    Ceil

    - -

    Returns: self rounded to an integer towards +Infinity

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func ceil() -> BInt
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - floor() - -
    -
    -
    -
    -
    -
    -

    Floor

    - -

    Returns: self rounded to an integer towards -Infinity

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func floor() -> BInt
    - -
    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Comparison functions -

-
-
-
    -
  • -
    - - - - ==(_:_:) - -
    -
    -
    -
    -
    -
    -

    Equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func == (x: BFraction, y: BFraction) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x = y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - ==(_:_:) - -
    -
    -
    -
    -
    -
    -

    Equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func == (x: BFraction, y: BInt) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x = y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - ==(_:_:) - -
    -
    -
    -
    -
    -
    -

    Equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func == (x: BInt, y: BFraction) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x = y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - ==(_:_:) - -
    -
    -
    -
    -
    -
    -

    Equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func == (x: BFraction, y: Int) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x = y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - ==(_:_:) - -
    -
    -
    -
    -
    -
    -

    Equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func == (x: Int, y: BFraction) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x = y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - !=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Not equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func != (x: BFraction, y: BFraction) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x != y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - !=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Not equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func != (x: BFraction, y: BInt) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x != y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - !=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Not equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func != (x: BInt, y: BFraction) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x != y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - !=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Not equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func != (x: BFraction, y: Int) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x != y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - !=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Not equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func != (x: Int, y: BFraction) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x != y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - <(_:_:) - -
    -
    -
    -
    -
    -
    -

    Less than

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func < (x: BFraction, y: BFraction) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x < y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - <(_:_:) - -
    -
    -
    -
    -
    -
    -

    Less than

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func < (x: BFraction, y: BInt) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x < y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - <(_:_:) - -
    -
    -
    -
    -
    -
    -

    Less than

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func < (x: BInt, y: BFraction) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x < y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - <(_:_:) - -
    -
    -
    -
    -
    -
    -

    Less than

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func < (x: BFraction, y: Int) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x < y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - <(_:_:) - -
    -
    -
    -
    -
    -
    -

    Less than

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func < (x: Int, y: BFraction) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x < y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - >(_:_:) - -
    -
    -
    -
    -
    -
    -

    Greater than

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func > (x: BFraction, y: BFraction) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x > y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - >(_:_:) - -
    -
    -
    -
    -
    -
    -

    Greater than

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func > (x: BFraction, y: BInt) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x > y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - >(_:_:) - -
    -
    -
    -
    -
    -
    -

    Greater than

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func > (x: BInt, y: BFraction) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x > y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - >(_:_:) - -
    -
    -
    -
    -
    -
    -

    Greater than

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func > (x: BFraction, y: Int) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x > y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - >(_:_:) - -
    -
    -
    -
    -
    -
    -

    Greater than

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func > (x: Int, y: BFraction) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x > y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - <=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Less than or equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func <= (x: BFraction, y: BFraction) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x <= y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - <=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Less than or equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func <= (x: BFraction, y: BInt) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x <= y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - <=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Less than or equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func <= (x: BInt, y: BFraction) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x <= y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - <=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Less than or equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func <= (x: BFraction, y: Int) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x <= y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - <=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Less than or equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func <= (x: Int, y: BFraction) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x <= y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - >=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Greater than or equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func >= (x: BFraction, y: BFraction) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x >= y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - >=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Greater than or equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func >= (x: BFraction, y: BInt) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x >= y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - >=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Greater than or equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func >= (x: BInt, y: BFraction) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x >= y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - >=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Greater than or equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func >= (x: BFraction, y: Int) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x >= y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - >=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Greater than or equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func >= (x: Int, y: BFraction) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x >= y, false otherwise

    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Miscellaneous functions -

-
-
-
    -
  • -
    - - - - bernoulli(_:) - -
    -
    -
    -
    -
    -
    -

    Bernoulli number

    -
    -

    Precondition

    - n >= 0 - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func bernoulli(_ n: Int) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - n - - -
    -

    The Bernoulli index

    -
    -
    -
    -
    -

    Return Value

    -

    The n'th Bernoulli number

    -
    -
    -
    -
    • -
  • -
    - - - - bernoulliSequence(_:) - -
    -
    -
    -
    -
    -
    -

    Bernoulli numbers

    -
    -

    Precondition

    - n > 0 - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func bernoulliSequence(_ n: Int) -> [BFraction]
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - n - - -
    -

    The number of Bernoulli numbers to compute

    -
    -
    -
    -
    -

    Return Value

    -

    The even numbered Bernoulli numbers B(0), B(2), B(4) … B(2 * n - 2)

    -
    -
    -
    -
    • -
  • -
    - - - - harmonic(_:) - -
    -
    -
    -
    -
    -
    -

    Harmonic number: 1 + 1 / 2 + … + 1 / n

    -
    -

    Precondition

    - n > 0 - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func harmonic(_ n: Int) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - n - - -
    -

    The number of fractions to add

    -
    -
    -
    -
    -

    Return Value

    -

    The n'th harmonic number

    -
    -
    -
    -
    • -
  • -
    - - - - harmonicSequence(_:) - -
    -
    -
    -
    -
    -
    -

    Harmonic sequence: The first n harmonic numbers

    -
    -

    Precondition

    - n > 0 - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func harmonicSequence(_ n: Int) -> [BFraction]
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - n - - -
    -

    The number of harmonic numbers

    -
    -
    -
    -
    -

    Return Value

    -

    The harmonic numbers: H1, H2 … Hn

    -
    -
    -
    -
    • -
-
-
-
- -
-
- - diff --git a/docs/Structs/BInt.html b/docs/Structs/BInt.html deleted file mode 100644 index 2412c34..0000000 --- a/docs/Structs/BInt.html +++ /dev/null @@ -1,7346 +0,0 @@ - - - - BInt Structure Reference - - - - - - - - - - - - - -
-
-

BigInt Docs (100% documented)

-
-
- -
-
-
-
-
- -
-
- -
-
-
-

BInt

-
-
- - 
public struct BInt : CustomStringConvertible, Comparable, Equatable, Hashable
- -
-
-

A signed integer of unbounded size.

- -

A BInt value is represented with magnitude and sign. -The magnitude is an array of unsigned 64 bit integers (a.k.a. Limbs). -The sign is a boolean value, true means value < 0, false means value >= 0 -The representation is little-endian, least significant Limb has index 0. -The representation is minimal, there is no leading zero Limbs. -The exception is that the value 0 is represented as a single 64 bit zero Limb and sign false

- -
-
-
-
- - -
- -

Constants -

-
-
-
    -
  • -
    - - - - ZERO - -
    -
    -
    -
    -
    -
    -

    BInt(0)

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static let ZERO: BInt
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - ONE - -
    -
    -
    -
    -
    -
    -

    BInt(1)

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static let ONE: BInt
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - TWO - -
    -
    -
    -
    -
    -
    -

    BInt(2)

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static let TWO: BInt
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - THREE - -
    -
    -
    -
    -
    -
    -

    BInt(3)

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static let THREE: BInt
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - FOUR - -
    -
    -
    -
    -
    -
    -

    BInt(4)

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static let FOUR: BInt
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - FIVE - -
    -
    -
    -
    -
    -
    -

    BInt(5)

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static let FIVE: BInt
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - SIX - -
    -
    -
    -
    -
    -
    -

    BInt(6)

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static let SIX: BInt
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - SEVEN - -
    -
    -
    -
    -
    -
    -

    BInt(7)

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static let SEVEN: BInt
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - EIGHT - -
    -
    -
    -
    -
    -
    -

    BInt(8)

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static let EIGHT: BInt
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - NINE - -
    -
    -
    -
    -
    -
    -

    BInt(9)

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static let NINE: BInt
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - TEN - -
    -
    -
    -
    -
    -
    -

    BInt(10)

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static let TEN: BInt
    - -
    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Initializers -

-
-
-
    -
  • -
    - - - - init(_:_:) - -
    -
    -
    -
    -
    -
    -

    Constructs a BInt from magnitude and sign

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public init(_ magnitude: Limbs, _ isNegative: Bool = false)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - magnitude - - -
    -

    magnitude of value

    -
    -
    - - isNegative - - -
    -

    true means negative value, false means 0 or positive value, default is false

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - init(_:) - -
    -
    -
    -
    -
    -
    -

    Constructs a BInt from an Int value

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public init(_ x: Int)
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - x - - -
    -

    Int value

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - init(_:) - -
    -
    -
    -
    -
    -
    -

    Constructs a BInt from a decimal value

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public init?(_ d: Double)
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - d - - -
    -

    The decimal value

    -
    -
    -
    -
    -

    Return Value

    -

    The BInt corresponding to d truncated to an integer value, nil if d is infinite or NaN

    -
    -
    -
    -
    • -
  • -
    - - - - init(_:radix:) - -
    -
    -
    -
    -
    -
    -

    Constructs a BInt from a String value and radix

    - -

    Examples:

    - -
      -
    • BInt(“90abcdef”, radix = 16)
      • -
    • BInt(“111110010”, radix = 2)
      • -
    • BInt(“1cdefghijk44”, radix = 26)
      • -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public init?(_ x: String, radix: Int = 10)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    String value to be converted

    -
    -
    - - radix - - -
    -

    Radix of x, from 2 to 36 inclusive, default is 10 -Returns: The BInt corresponding to x, nil if x does not designate an integer in the given radix

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - init(bitWidth:) - -
    -
    -
    -
    -
    -
    -

    Constructs a random BInt with a specified number of bits

    -
    -

    Precondition

    - bitWidth is positive - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public init(bitWidth: Int)
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - bitWidth - - -
    -

    Number of bits

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - init(magnitude:) - -
    -
    -
    -
    -
    -
    -

    Constructs a BInt from a big-endian magnitude byte array representation

    -
    -

    Precondition

    - Byte array is not empty - -
    - -

    Examples:

    - -
      -
    • The byte array [1, 0, 0] represents BInt value 65536
      • -
    • The byte array [128, 0] represents BInt value 32768
      • -
    • The byte array [255, 127] represents BInt value 65407
      • -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public init(magnitude x: Bytes)
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - x - - -
    -

    Magnitude big-endian byte array

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - init(signed:) - -
    -
    -
    -
    -
    -
    -

    Constructs a BInt from a big-endian 2’s complement byte array representation

    -
    -

    Precondition

    - Byte array is not empty - -
    - -

    Examples:

    - -
      -
    • The byte array [1, 0, 0] represents BInt value 65536
      • -
    • The byte array [128, 0] represents BInt value -32768
      • -
    • The byte array [255, 127] represents BInt value -129
      • -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public init(signed x: Bytes)
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - x - - -
    -

    2’s complement big-endian byte array

    -
    -
    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Stored properties -

-
-
-
    -
  • -
    - - - - isNegative - -
    -
    -
    -
    -
    -
    -

    The sign, true if self < 0, false otherwise

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public internal(set) var isNegative: Bool { get }
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - magnitude - -
    -
    -
    -
    -
    -
    -

    The magnitude limb array

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public internal(set) var magnitude: Limbs { get }
    - -
    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Computed properties -

-
-
-
    -
  • -
    - - - - abs - -
    -
    -
    -
    -
    -
    -

    The absolute value of self

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public var abs: BInt { get }
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - bitWidth - -
    -
    -
    -
    -
    -
    -

    The number of bits in the binary representation of the magnitude of self. 0 if self = 0

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public var bitWidth: Int { get }
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - description - -
    -
    -
    -
    -
    -
    -

    Base 10 string value of self

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public var description: String { get }
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - isEven - -
    -
    -
    -
    -
    -
    -

    Is true if self is even, false if self is odd

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public var isEven: Bool { get }
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - isNotZero - -
    -
    -
    -
    -
    -
    -

    Is false if self = 0, true otherwise

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public var isNotZero: Bool { get }
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - isOdd - -
    -
    -
    -
    -
    -
    -

    Is true if self is odd, false if self is even

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public var isOdd: Bool { get }
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - isOne - -
    -
    -
    -
    -
    -
    -

    Is true if self = 1, false otherwise

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public var isOne: Bool { get }
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - isPositive - -
    -
    -
    -
    -
    -
    -

    Is true if self > 0, false otherwise

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public var isPositive: Bool { get }
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - isZero - -
    -
    -
    -
    -
    -
    -

    Is true if self = 0, false otherwise

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public var isZero: Bool { get }
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - leadingZeroBitCount - -
    -
    -
    -
    -
    -
    -

    The number of leading zero bits in the magnitude of self. 0 if self = 0

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public var leadingZeroBitCount: Int { get }
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - population - -
    -
    -
    -
    -
    -
    -

    The number of 1 bits in the magnitude of self

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public var population: Int { get }
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - signum - -
    -
    -
    -
    -
    -
    -

    Is 0 if self = 0, 1 if self > 0, and -1 if self < 0

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public var signum: Int { get }
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - trailingZeroBitCount - -
    -
    -
    -
    -
    -
    -

    The number of trailing zero bits in the magnitude of self. 0 if self = 0

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public var trailingZeroBitCount: Int { get }
    - -
    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Conversion functions to Double, Int, String, and Bytes -

-
-
-
    -
  • -
    - - - - asDouble() - -
    -
    -
    -
    -
    -
    -

    self as a Double

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func asDouble() -> Double
    - -
    -
    -
    -

    Return Value

    -

    self as a Double or Infinity if self is not representable as a Double

    -
    -
    -
    -
    • -
  • -
    - - - - asInt() - -
    -
    -
    -
    -
    -
    -

    self as an Int

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func asInt() -> Int?
    - -
    -
    -
    -

    Return Value

    -

    self as an Int or nil if self is not representable as an Int

    -
    -
    -
    -
    • -
  • -
    - - - - asMagnitudeBytes() - -
    -
    -
    -
    -
    -
    -

    Byte array representation of magnitude value

    - -

    Examples:

    - -
      -
    • BInt(1).asMagnitudeBytes() = [1]
      • -
    • BInt(-1).asMagnitudeBytes() = [1]
      • -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func asMagnitudeBytes() -> Bytes
    - -
    -
    -
    -

    Return Value

    -

    Minimal big-endian magnitude byte array representation

    -
    -
    -
    -
    • -
  • -
    - - - - asSignedBytes() - -
    -
    -
    -
    -
    -
    -

    Byte array representation of 2’s complement value

    - -

    Examples:

    - -
      -
    • BInt(1).asSignedBytes() = [1]
      • -
    • BInt(-1).asSignedBytes() = [255]
      • -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func asSignedBytes() -> Bytes
    - -
    -
    -
    -

    Return Value

    -

    Minimal big-endian 2’s complement byte array representation

    -
    -
    -
    -
    • -
  • - -
    -
    -
    -
    -
    -

    self as a String with a given radix

    -
    -

    Precondition

    - Radix between 2 and 36 inclusive - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func asString(radix: Int = 10, uppercase: Bool = false) -> String
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - radix - - -
    -

    Radix from 2 to 36 inclusive

    -
    -
    - - uppercase - - -
    -

    true to use uppercase letters, false to use lowercase letters, default is false

    -
    -
    -
    -
    -

    Return Value

    -

    self as a String in the given radix

    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Bit operation functions -

-
-
-
    -
  • -
    - - - - &(_:_:) - -
    -
    -
    -
    -
    -
    -

    Bitwise and operator - behaves as if two’s complement representation were used,
    -although this is not actually the case

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func & (x: BInt, y: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First value

    -
    -
    - - y - - -
    -

    Second value

    -
    -
    -
    -
    -

    Return Value

    -

    BInt(signed: bx & by) where - -

      -
    • bx = x.asSignedBytes()
      • -
    • by = y.asSignedBytes()
      • -

    -
    -
    -
    -
    • -
  • -
    - - - - &=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x & y

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func &= (x: inout BInt, y: BInt)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand parameter

    -
    -
    - - y - - -
    -

    Right hand parameter

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - |(_:_:) - -
    -
    -
    -
    -
    -
    -

    Bitwise or operator - behaves as if two’s complement representation were used,
    -although this is not actually the case

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func | (x: BInt, y: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First value

    -
    -
    - - y - - -
    -

    Second value

    -
    -
    -
    -
    -

    Return Value

    -

    BInt(signed: bx | by) where - -

      -
    • bx = x.asSignedBytes()
      • -
    • by = y.asSignedBytes()
      • -

    -
    -
    -
    -
    • -
  • -
    - - - - |=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x | y

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func |= (x: inout BInt, y: BInt)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand parameter

    -
    -
    - - y - - -
    -

    Right hand parameter

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - ^(_:_:) - -
    -
    -
    -
    -
    -
    -

    Bitwise xor operator - behaves as if two’s complement representation were used,
    -although this is not actually the case

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func ^ (x: BInt, y: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First value

    -
    -
    - - y - - -
    -

    Second value

    -
    -
    -
    -
    -

    Return Value

    -

    BInt(signed: bx ^ by) where - -

      -
    • bx = x.asSignedBytes()
      • -
    • by = y.asSignedBytes()
      • -

    -
    -
    -
    -
    • -
  • -
    - - - - ^=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x ^ y

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func ^= (x: inout BInt, y: BInt)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand parameter

    -
    -
    - - y - - -
    -

    Right hand parameter

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - ~(_:) - -
    -
    -
    -
    -
    -
    -

    Bitwise not operator - behaves as if two’s complement arithmetic were used,
    -although this is not actually the case

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public prefix static func ~ (x: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - x - - -
    -

    BInt value

    -
    -
    -
    -
    -

    Return Value

    -

    -x - 1

    -
    -
    -
    -
    • -
  • -
    - - - - clearBit(_:) - -
    -
    -
    -
    -
    -
    -

    Clear a specified bit - a no-op if bit number < 0

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public mutating func clearBit(_ n: Int)
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - n - - -
    -

    Bit number

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - flipBit(_:) - -
    -
    -
    -
    -
    -
    -

    Invert a specified bit - a no-op if bit number < 0

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public mutating func flipBit(_ n: Int)
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - n - - -
    -

    Bit number

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - setBit(_:) - -
    -
    -
    -
    -
    -
    -

    Set a specified bit - a no-op if bit number < 0

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public mutating func setBit(_ n: Int)
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - n - - -
    -

    Bit number

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - testBit(_:) - -
    -
    -
    -
    -
    -
    -

    Test a specified bit - false if bit number < 0

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func testBit(_ n: Int) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - n - - -
    -

    Bit number

    -
    -
    -
    -
    -

    Return Value

    -

    true if bit is set, false otherwise

    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Addition functions -

-
-
-
    -
  • -
    - - - - +(_:) - -
    -
    -
    -
    -
    -
    -

    Prefix plus

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public prefix static func + (x: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - x - - -
    -

    BInt value

    -
    -
    -
    -
    -

    Return Value

    -

    x

    -
    -
    -
    -
    • -
  • -
    - - - - +(_:_:) - -
    -
    -
    -
    -
    -
    -

    Addition

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func + (x: BInt, y: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First addend

    -
    -
    - - y - - -
    -

    Second addend

    -
    -
    -
    -
    -

    Return Value

    -

    x + y

    -
    -
    -
    -
    • -
  • -
    - - - - +(_:_:) - -
    -
    -
    -
    -
    -
    -

    Addition

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func + (x: Int, y: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First addend

    -
    -
    - - y - - -
    -

    Second addend

    -
    -
    -
    -
    -

    Return Value

    -

    x + y

    -
    -
    -
    -
    • -
  • -
    - - - - +(_:_:) - -
    -
    -
    -
    -
    -
    -

    Addition

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func + (x: BInt, y: Int) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First addend

    -
    -
    - - y - - -
    -

    Second addend

    -
    -
    -
    -
    -

    Return Value

    -

    x + y

    -
    -
    -
    -
    • -
  • -
    - - - - +=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x + y

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func += (x: inout BInt, y: BInt)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand addend

    -
    -
    - - y - - -
    -

    Right hand addend

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - +=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x + y

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func += (x: inout BInt, y: Int)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand addend

    -
    -
    - - y - - -
    -

    Right hand addend

    -
    -
    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Negation functions -

-
-
-
    -
  • -
    - - - - negate() - -
    -
    -
    -
    -
    -
    -

    Negates self

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public mutating func negate()
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - -(_:) - -
    -
    -
    -
    -
    -
    -

    Negation

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public prefix static func - (x: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - x - - -
    -

    Operand

    -
    -
    -
    -
    -

    Return Value

    -

    -x

    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Subtraction functions -

-
-
-
    -
  • -
    - - - - -(_:_:) - -
    -
    -
    -
    -
    -
    -

    Subtraction

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func - (x: BInt, y: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Minuend

    -
    -
    - - y - - -
    -

    Subtrahend

    -
    -
    -
    -
    -

    Return Value

    -

    x - y

    -
    -
    -
    -
    • -
  • -
    - - - - -(_:_:) - -
    -
    -
    -
    -
    -
    -

    Subtraction

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func - (x: Int, y: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Minuend

    -
    -
    - - y - - -
    -

    Subtrahend

    -
    -
    -
    -
    -

    Return Value

    -

    x - y

    -
    -
    -
    -
    • -
  • -
    - - - - -(_:_:) - -
    -
    -
    -
    -
    -
    -

    Subtraction

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func - (x: BInt, y: Int) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Minuend

    -
    -
    - - y - - -
    -

    Subtrahend

    -
    -
    -
    -
    -

    Return Value

    -

    x - y

    -
    -
    -
    -
    • -
  • -
    - - - - -=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x - y

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func -= (x: inout BInt, y: BInt)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand minuend

    -
    -
    - - y - - -
    -

    Right hand subtrahend

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - -=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x - y

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func -= (x: inout BInt, y: Int)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand minuend

    -
    -
    - - y - - -
    -

    Right hand subtrahend

    -
    -
    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Multiplication functions -

-
-
-
    -
  • -
    - - - - *(_:_:) - -
    -
    -
    -
    -
    -
    -

    Multiplication

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func * (x: BInt, y: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Multiplier

    -
    -
    - - y - - -
    -

    Multiplicand

    -
    -
    -
    -
    -

    Return Value

    -

    x * y

    -
    -
    -
    -
    • -
  • -
    - - - - *(_:_:) - -
    -
    -
    -
    -
    -
    -

    Multiplication

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func * (x: Int, y: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Multiplier

    -
    -
    - - y - - -
    -

    Multiplicand

    -
    -
    -
    -
    -

    Return Value

    -

    x * y

    -
    -
    -
    -
    • -
  • -
    - - - - *(_:_:) - -
    -
    -
    -
    -
    -
    -

    Multiplication

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func * (x: BInt, y: Int) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Multiplier

    -
    -
    - - y - - -
    -

    Multiplicand

    -
    -
    -
    -
    -

    Return Value

    -

    x * y

    -
    -
    -
    -
    • -
  • -
    - - - - *=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x * y

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func *= (x: inout BInt, y: BInt)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand multiplier

    -
    -
    - - y - - -
    -

    Right hand multiplicand

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - *=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x * y

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func *= (x: inout BInt, y: Int)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand multiplier

    -
    -
    - - y - - -
    -

    Right hand multiplicand

    -
    -
    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Division functions -

-
-
-
    -
  • - -
    -
    -
    -
    -
    -

    Division

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func quotientAndRemainder(dividingBy x: BInt) -> (quotient: BInt, remainder: BInt)
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - x - - -
    -

    Divisor - a BInt value

    -
    -
    -
    -
    -

    Return Value

    -

    Quotient and remainder of self / x

    -
    -
    -
    -
    • -
  • - -
    -
    -
    -
    -
    -

    Division

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func quotientAndRemainder(dividingBy x: BInt, _ quotient: inout BInt, _ remainder: inout BInt)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - - - - - -
    - - x - - -
    -

    Divisor - a BInt value

    -
    -
    - - quotient - - -
    -

    Set to the quotient of self / x

    -
    -
    - - remainder - - -
    -

    Set to the remainder of self / x

    -
    -
    -
    -
    -
    -
    • -
  • - -
    -
    -
    -
    -
    -

    Division

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func quotientAndRemainder(dividingBy x: Int) -> (quotient: BInt, remainder: Int)
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - x - - -
    -

    Divisor - an Int value

    -
    -
    -
    -
    -

    Return Value

    -

    Quotient and remainder of self / x

    -
    -
    -
    -
    • -
  • - -
    -
    -
    -
    -
    -

    Division

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func quotientAndRemainder(dividingBy x: Int, _ quotient: inout BInt, _ remainder: inout Int)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - - - - - -
    - - x - - -
    -

    Divisor - an Int value

    -
    -
    - - quotient - - -
    -

    Set to the quotient of self / x

    -
    -
    - - remainder - - -
    -

    Set to the remainder of self / x

    -
    -
    -
    -
    -
    -
    • -
  • - -
    -
    -
    -
    -
    -

    Exact division - that is, the remainder of the division is known to be 0

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func quotientExact(dividingBy x: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - x - - -
    -

    Divisor - a BInt value

    -
    -
    -
    -
    -

    Return Value

    -

    Quotient of self / x - undefined if the remainder is in fact not 0

    -
    -
    -
    -
    • -
  • -
    - - - - /(_:_:) - -
    -
    -
    -
    -
    -
    -

    Division

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func / (x: BInt, y: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Dividend

    -
    -
    - - y - - -
    -

    Divisor

    -
    -
    -
    -
    -

    Return Value

    -

    x / y

    -
    -
    -
    -
    • -
  • -
    - - - - /(_:_:) - -
    -
    -
    -
    -
    -
    -

    Division

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func / (x: Int, y: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Dividend

    -
    -
    - - y - - -
    -

    Divisor

    -
    -
    -
    -
    -

    Return Value

    -

    x / y

    -
    -
    -
    -
    • -
  • -
    - - - - /(_:_:) - -
    -
    -
    -
    -
    -
    -

    Division

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func / (x: BInt, y: Int) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Dividend

    -
    -
    - - y - - -
    -

    Divisor

    -
    -
    -
    -
    -

    Return Value

    -

    x / y

    -
    -
    -
    -
    • -
  • -
    - - - - /=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x / y

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func /= (x: inout BInt, y: BInt)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand dividend

    -
    -
    - - y - - -
    -

    Right hand divisor

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - /=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x / y

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func /= (x: inout BInt, y: Int)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand dividend

    -
    -
    - - y - - -
    -

    Right hand divisor

    -
    -
    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Remainder and modulus functions -

-
-
-
    -
  • -
    - - - - %(_:_:) - -
    -
    -
    -
    -
    -
    -

    Remainder

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func % (x: BInt, y: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Dividend

    -
    -
    - - y - - -
    -

    Divisor

    -
    -
    -
    -
    -

    Return Value

    -

    x % y

    -
    -
    -
    -
    • -
  • -
    - - - - %(_:_:) - -
    -
    -
    -
    -
    -
    -

    Remainder

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func % (x: Int, y: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Dividend

    -
    -
    - - y - - -
    -

    Divisor

    -
    -
    -
    -
    -

    Return Value

    -

    x % y

    -
    -
    -
    -
    • -
  • -
    - - - - %(_:_:) - -
    -
    -
    -
    -
    -
    -

    Remainder

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func % (x: BInt, y: Int) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Dividend

    -
    -
    - - y - - -
    -

    Divisor

    -
    -
    -
    -
    -

    Return Value

    -

    x % y

    -
    -
    -
    -
    • -
  • -
    - - - - %=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x % y

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func %= (x: inout BInt, y: BInt)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Dividend

    -
    -
    - - y - - -
    -

    Divisor

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - %=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x % y

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func %= (x: inout BInt, y: Int)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Dividend

    -
    -
    - - y - - -
    -

    Divisor

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - mod(_:) - -
    -
    -
    -
    -
    -
    -

    Modulus - BInt parameter

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func mod(_ x: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - x - - -
    -

    Divisor

    -
    -
    -
    -
    -

    Return Value

    -

    self mod x, a non-negative value

    -
    -
    -
    -
    • -
  • -
    - - - - mod(_:) - -
    -
    -
    -
    -
    -
    -

    Modulus - Int parameter

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func mod(_ x: Int) -> Int
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - x - - -
    -

    Divisor

    -
    -
    -
    -
    -

    Return Value

    -

    self mod x, a non-negative value

    -
    -
    -
    -
    • -
  • -
    - - - - modInverse(_:) - -
    -
    -
    -
    -
    -
    -

    Inverse modulus - BInt parameter

    -
    -

    Precondition

    - self and modulus are coprime, modulus is positive - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func modInverse(_ m: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - m - - -
    -

    Modulus

    -
    -
    -
    -
    -

    Return Value

    -

    If self and m are coprime, x such that (self * x) mod m = 1

    -
    -
    -
    -
    • -
  • -
    - - - - modInverse(_:) - -
    -
    -
    -
    -
    -
    -

    Inverse modulus - Int parameter

    -
    -

    Precondition

    - self and modulus are coprime, modulus is positive - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func modInverse(_ m: Int) -> Int
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - m - - -
    -

    Modulus

    -
    -
    -
    -
    -

    Return Value

    -

    If self and m are coprime, x such that (self * x) mod m = 1

    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Exponentiation functions -

-
-
-
    -
  • -
    - - - - **(_:_:) - -
    -
    -
    -
    -
    -
    -

    Exponentiation

    -
    -

    Precondition

    - Exponent is non-negative - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func ** (a: BInt, x: Int) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - a - - -
    -

    Operand

    -
    -
    - - x - - -
    -

    Non-negative exponent

    -
    -
    -
    -
    -

    Return Value

    -

    a^x

    -
    -
    -
    -
    • -
  • -
    - - - - expMod(_:_:) - -
    -
    -
    -
    -
    -
    -

    Modular exponentiation - BInt modulus

    -
    -

    Precondition

    - Modulus is positive - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func expMod(_ x: BInt, _ m: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    The exponent

    -
    -
    - - m - - -
    -

    The modulus, a positive number

    -
    -
    -
    -
    -

    Return Value

    -

    (self^x) mod m for positive x, ((self^-x) mod m) modInverse m for negative x

    -
    -
    -
    -
    • -
  • -
    - - - - expMod(_:_:) - -
    -
    -
    -
    -
    -
    -

    Modular exponentiation - Int modulus

    -
    -

    Precondition

    - Modulus is positive - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func expMod(_ x: BInt, _ m: Int) -> Int
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    The exponent

    -
    -
    - - m - - -
    -

    The modulus, a positive integer

    -
    -
    -
    -
    -

    Return Value

    -

    (self^x) mod m for positive x, ((self^-x) mod m) modInverse m for negative x

    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Comparison functions -

-
-
-
    -
  • -
    - - - - ==(_:_:) - -
    -
    -
    -
    -
    -
    -

    Equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func == (x: BInt, y: BInt) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x = y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - ==(_:_:) - -
    -
    -
    -
    -
    -
    -

    Equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func == (x: BInt, y: Int) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x = y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - ==(_:_:) - -
    -
    -
    -
    -
    -
    -

    Equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func == (x: Int, y: BInt) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x = y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - !=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Not equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func != (x: BInt, y: BInt) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x != y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - !=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Not equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func != (x: BInt, y: Int) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x != y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - !=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Not equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func != (x: Int, y: BInt) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x != y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - <(_:_:) - -
    -
    -
    -
    -
    -
    -

    Less than

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func < (x: BInt, y: BInt) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x < y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - <(_:_:) - -
    -
    -
    -
    -
    -
    -

    Less than

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func < (x: BInt, y: Int) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x < y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - <(_:_:) - -
    -
    -
    -
    -
    -
    -

    Less than

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func < (x: Int, y: BInt) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x < y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - >(_:_:) - -
    -
    -
    -
    -
    -
    -

    Greater than

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func > (x: BInt, y: BInt) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x > y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - >(_:_:) - -
    -
    -
    -
    -
    -
    -

    Greater than

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func > (x: Int, y: BInt) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x > y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - >(_:_:) - -
    -
    -
    -
    -
    -
    -

    Greater than

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func > (x: BInt, y: Int) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x > y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - <=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Less than or equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func <= (x: BInt, y: BInt) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x <= y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - <=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Less than or equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func <= (x: Int, y: BInt) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x <= y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - <=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Less than or equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func <= (x: BInt, y: Int) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x <= y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - >=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Greater than or equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func >= (x: BInt, y: BInt) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x >= y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - >=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Greater than or equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func >= (x: Int, y: BInt) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x >= y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - >=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Greater than or equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func >= (x: BInt, y: Int) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x >= y, false otherwise

    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Shift functions -

-
-
-
    -
  • -
    - - - - <<(_:_:) - -
    -
    -
    -
    -
    -
    -

    Logical left shift

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func << (x: BInt, n: Int) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Operand

    -
    -
    - - n - - -
    -

    Shift count

    -
    -
    -
    -
    -

    Return Value

    -

      -
    • BInt(x.magnitude << n, x.isNegative) if n > 0
      • -
    • BInt(x.magnitude >> -n, x.isNegative) if n < 0
      • -
    • x if n = 0
      • -

    -
    -
    -
    -
    • -
  • -
    - - - - <<=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x << n

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func <<= (x: inout BInt, n: Int)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Operand

    -
    -
    - - n - - -
    -

    Shift count

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - >>(_:_:) - -
    -
    -
    -
    -
    -
    -

    Logical right shift

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func >> (x: BInt, n: Int) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Operand

    -
    -
    - - n - - -
    -

    Shift count

    -
    -
    -
    -
    -

    Return Value

    -

      -
    • BInt(x.magnitude >> n, x.isNegative) if n > 0
      • -
    • BInt(x.magnitude << -n, x.isNegative) if n < 0
      • -
    • x if n = 0
      • -

    -
    -
    -
    -
    • -
  • -
    - - - - >>=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x >> n

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func >>= (x: inout BInt, n: Int)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Operand

    -
    -
    - - n - - -
    -

    Shift count

    -
    -
    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Prime number functions -

-
-
-
    -
  • -
    - - - - isProbablyPrime(_:) - -
    -
    -
    -
    -
    -
    -

    Checks whether self is prime using the Miller-Rabin algorithm

    -
    -

    Precondition

    - Probability parameter is positive - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func isProbablyPrime(_ p: Int = 30) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - p - - -
    -

    If true is returned, self is prime with probability > 1-½^p

    -
    -
    -
    -
    -

    Return Value

    -

    true if self is probably prime, false if self is definitely not prime

    -
    -
    -
    -
    • -
  • -
    - - - - nextPrime(_:) - -
    -
    -
    -
    -
    -
    -

    The next probable prime greater than self

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func nextPrime(_ p: Int = 30) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - p - - -
    -

    The returned number is prime with probability > 1-½^p, default value is 30

    -
    -
    -
    -
    -

    Return Value

    -

    The smallest probable prime greater than self, returns 2 if self is negative

    -
    -
    -
    -
    • -
  • -
    - - - - probablePrime(_:_:) - -
    -
    -
    -
    -
    -
    -

    A probable prime number with a given bitwidth

    -
    -

    Precondition

    - bitWidth > 1 - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func probablePrime(_ bitWidth: Int, _ p: Int = 30) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - bitWidth - - -
    -

    The bitWidth - must be > 1

    -
    -
    - - p - - -
    -

    The returned number is prime with probability > 1-½^p, default value is 30

    -
    -
    -
    -
    -

    Return Value

    -

    A prime number with the specified bitwidth and probability

    -
    -
    -
    -
    • -
  • -
    - - - - primorial(_:) - -
    -
    -
    -
    -
    -
    -

    Product of primes up to n

    -
    -

    Precondition

    - n >= 0 - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func primorial(_ n: Int) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - n - - -
    -

    number to compute primorial for

    -
    -
    -
    -
    -

    Return Value

    -

    The product of primes less than or equal to n

    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Root extraction functions -

-
-
-
    -
  • -
    - - - - root(_:) - -
    -
    -
    -
    -
    -
    -

    n'th root

    -
    -

    Precondition

    -
      -
    • self is non-negative or n is odd
      • -
    • n is positive
      • -
    - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func root(_ n: Int) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - n - - -
    -

    The root

    -
    -
    -
    -
    -

    Return Value

    -

    The integer part of the n'th root of self

    -
    -
    -
    -
    • -
  • -
    - - - - rootRemainder(_:) - -
    -
    -
    -
    -
    -
    -

    n'th root and remainder

    -
    -

    Precondition

    -
      -
    • self is non-negative or n is odd
      • -
    • n is positive
      • -
    - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func rootRemainder(_ n: Int) -> (root: BInt, rem: BInt)
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - n - - -
    -

    The root

    -
    -
    -
    -
    -

    Return Value

    -

    root = the integer part of the n'th root of self, rem = self - root^n

    -
    -
    -
    -
    • -
  • -
    - - - - isPerfectRoot() - -
    -
    -
    -
    -
    -
    -

    Check whether self is a perfect root, that is, for some integer x and n > 1 self = x^n

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func isPerfectRoot() -> Bool
    - -
    -
    -
    -

    Return Value

    -

    true iff self is a perfect root

    -
    -
    -
    -
    • -
  • -
    - - - - sqrt() - -
    -
    -
    -
    -
    -
    -

    Square root of a non-negative number

    -
    -

    Precondition

    - self is non-negative - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func sqrt() -> BInt
    - -
    -
    -
    -

    Return Value

    -

    The integer part of the square root of self

    -
    -
    -
    -
    • -
  • -
    - - - - sqrtRemainder() - -
    -
    -
    -
    -
    -
    -

    Square root and remainder of a non-negative number

    -
    -

    Precondition

    - self is non-negative - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func sqrtRemainder() -> (root: BInt, rem: BInt)
    - -
    -
    -
    -

    Return Value

    -

    root = the integer part of the square root of self, rem = self - root^2

    -
    -
    -
    -
    • -
  • -
    - - - - isPerfectSquare() - -
    -
    -
    -
    -
    -
    -

    Check whether self is a perfect square, that is, for some integer x self = x^2

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func isPerfectSquare() -> Bool
    - -
    -
    -
    -

    Return Value

    -

    true iff self is a perfect square

    -
    -
    -
    -
    • -
  • -
    - - - - sqrtMod(_:) - -
    -
    -
    -
    -
    -
    -

    Square root modulo a prime number - BInt prime

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func sqrtMod(_ p: BInt) -> BInt?
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - p - - -
    -

    An odd prime number

    -
    -
    -
    -
    -

    Return Value

    -

    x, such that x^2 = self (mod p), or nil if no such x exists

    -
    -
    -
    -
    • -
  • -
    - - - - sqrtMod(_:) - -
    -
    -
    -
    -
    -
    -

    Square root modulo a prime number - Int prime

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func sqrtMod(_ p: Int) -> Int?
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - p - - -
    -

    An odd prime number

    -
    -
    -
    -
    -

    Return Value

    -

    x, such that x^2 = self (mod p), or nil if no such x exists

    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Miscellaneous functions -

-
-
-
    -
  • -
    - - - - binomial(_:_:) - -
    -
    -
    -
    -
    -
    -

    Compute binomial coefficient n over k

    -
    -

    Precondition

    - n >= k and k >= 0 - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func binomial(_ n: Int, _ k: Int) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - n - - -
    -

    First binomial parameter

    -
    -
    - - k - - -
    -

    Second binomial parameter

    -
    -
    -
    -
    -

    Return Value

    -

    Binomial coefficient n over k

    -
    -
    -
    -
    • -
  • -
    - - - - factorial(_:) - -
    -
    -
    -
    -
    -
    -

    Factorial function

    -
    -

    Precondition

    - n >= 0 - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func factorial(_ n: Int) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - n - - -
    -

    Number to compute factorial for

    -
    -
    -
    -
    -

    Return Value

    -

    n!

    -
    -
    -
    -
    • -
  • -
    - - - - fibonacci(_:) - -
    -
    -
    -
    -
    -
    -

    n'th Fibonacci number

    -
    -

    Precondition

    - n >= 0 - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func fibonacci(_ n: Int) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - n - - -
    -

    The fibonacci index

    -
    -
    -
    -
    -

    Return Value

    -

    The n'th fibonacci number

    -
    -
    -
    -
    • -
  • -
    - - - - fibonacci2(_:) - -
    -
    -
    -
    -
    -
    -

    Fibonacci pair, n'th and n'th + 1 Fibonacci number

    - -

    Precondition: n >= 0

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func fibonacci2(_ n: Int) -> (BInt, BInt)
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - n - - -
    -

    The fibonacci index

    -
    -
    -
    -
    -

    Return Value

    -

    The n'th and n'th + 1 fibonacci number

    -
    -
    -
    -
    • -
  • -
    - - - - gcd(_:) - -
    -
    -
    -
    -
    -
    -

    Greatest common divisor

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func gcd(_ x: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - x - - -
    -

    Operand

    -
    -
    -
    -
    -

    Return Value

    -

    Greatest common divisor of self and x

    -
    -
    -
    -
    • -
  • -
    - - - - gcdExtended(_:) - -
    -
    -
    -
    -
    -
    -

    Extended greatest common divisor

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func gcdExtended(_ x: BInt) -> (g: BInt, a: BInt, b: BInt)
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - x - - -
    -

    Operand

    -
    -
    -
    -
    -

    Return Value

    -

    Greatest common divisor g of self and x, and a and b such that a * self + b * x = g

    -
    -
    -
    -
    • -
  • -
    - - - - jacobiSymbol(_:) - -
    -
    -
    -
    -
    -
    -

    Jacobi symbol - BInt parameter. If m is an odd prime, this is also the Legendre symbol

    -
    -

    Precondition

    - m is positive and odd - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func jacobiSymbol(_ m: BInt) -> Int
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - m - - -
    -

    A positive, odd integer

    -
    -
    -
    -
    -

    Return Value

    -

    The Jacobi symbol of self and m: -1, 0, or 1

    -
    -
    -
    -
    • -
  • -
    - - - - jacobiSymbol(_:) - -
    -
    -
    -
    -
    -
    -

    Jacobi symbol - Int parameter. If m is an odd prime, this is also the Legendre symbol

    -
    -

    Precondition

    - m is positive and odd - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func jacobiSymbol(_ m: Int) -> Int
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - m - - -
    -

    A positive, odd integer

    -
    -
    -
    -
    -

    Return Value

    -

    The Jacobi symbol of self and m: -1, 0, or 1

    -
    -
    -
    -
    • -
  • -
    - - - - kroneckerSymbol(_:) - -
    -
    -
    -
    -
    -
    -

    Kronecker symbol - BInt parameter. If m is positive and odd, this is also the Jacobi symbol

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func kroneckerSymbol(_ m: BInt) -> Int
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - m - - -
    -

    An integer value

    -
    -
    -
    -
    -

    Return Value

    -

    The Kronecker symbol of self and m: -1, 0, or 1

    -
    -
    -
    -
    • -
  • -
    - - - - kroneckerSymbol(_:) - -
    -
    -
    -
    -
    -
    -

    Kronecker symbol - Int parameter. If m is positive and odd, this is also the Jacobi symbol

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func kroneckerSymbol(_ m: Int) -> Int
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - m - - -
    -

    An integer value

    -
    -
    -
    -
    -

    Return Value

    -

    The Kronecker symbol of self and m: -1, 0, or 1

    -
    -
    -
    -
    • -
  • -
    - - - - lcm(_:) - -
    -
    -
    -
    -
    -
    -

    Least common multiple

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func lcm(_ x: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - x - - -
    -

    Operand

    -
    -
    -
    -
    -

    Return Value

    -

    Least common multiple of self and x - a non-negative number

    -
    -
    -
    -
    • -
  • -
    - - - - lucas(_:) - -
    -
    -
    -
    -
    -
    -

    n'th Lucas number

    -
    -

    Precondition

    - n >= 0 - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func lucas(_ n: Int) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - n - - -
    -

    The lucas index

    -
    -
    -
    -
    -

    Return Value

    -

    The n'th lucas number

    -
    -
    -
    -
    • -
  • -
    - - - - lucas2(_:) - -
    -
    -
    -
    -
    -
    -

    Lucas pair, n'th and n'th + 1 Lucas number

    - -

    Precondition: n >= 0

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func lucas2(_ n: Int) -> (BInt, BInt)
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - n - - -
    -

    The lucas index

    -
    -
    -
    -
    -

    Return Value

    -

    The n'th and n'th + 1 lucas number

    -
    -
    -
    -
    • -
  • -
    - - - - randomLessThan() - -
    -
    -
    -
    -
    -
    -

    Random value

    -
    -

    Precondition

    - self is positive - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func randomLessThan() -> BInt
    - -
    -
    -
    -

    Return Value

    -

    A random value < absolute value of self

    -
    -
    -
    -
    • -
-
-
-
- -
-
- - diff --git a/docs/Structs/CRT.html b/docs/Structs/CRT.html deleted file mode 100644 index 8b112b1..0000000 --- a/docs/Structs/CRT.html +++ /dev/null @@ -1,342 +0,0 @@ - - - - CRT Structure Reference - - - - - - - - - - - - - -
-
-

BigInt Docs (100% documented)

-
-
- -
-
-
-
-
- -
-
- -
-
-
-

CRT

-
-
- - 
public struct CRT
- -
-
-

CRT instances implement the Chinese Remainder Theorem

- -

Create an instance from a given set of moduli which fullfill the following conditions:

- -
    -
  • at least two moduli
    • -
  • all moduli are positive
    • -
  • the moduli are pairwise coprime
    • -
- -

Then use the compute method to compute the CRT value for a given set of residues. -The same CRT instance can be used for different inputs, as long as the moduli are the same.

- -
-
-
-
- - -
- -

Initializers -

-
-
-
    -
  • -
    - - - - init(_:) - -
    -
    -
    -
    -
    -
    -

    Constructs a CRT instance from the moduli - BInt version

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public init?(_ m: [BInt])
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - m - - -
    -

    The moduli

    -
    -
    -
    -
    -

    Return Value

    -

    The CRT instance for the moduli, nil if they do not fullfill the conditions

    -
    -
    -
    -
    • -
  • -
    - - - - init(_:) - -
    -
    -
    -
    -
    -
    -

    Constructs a CRT instance from the moduli - Int version

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public init?(_ m: [Int])
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - m - - -
    -

    The moduli

    -
    -
    -
    -
    -

    Return Value

    -

    The CRT instance for the moduli, nil if they do not fullfill the conditions

    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Instance methods -

-
-
-
    -
  • -
    - - - - compute(_:) - -
    -
    -
    -
    -
    -
    -

    Compute the CRT value - BInt version

    -
    -

    Precondition

    - r.count = number of moduli - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func compute(_ r: [BInt]) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - r - - -
    -

    The residues

    -
    -
    -
    -
    -

    Return Value

    -

    The CRT value

    -
    -
    -
    -
    • -
  • -
    - - - - compute(_:) - -
    -
    -
    -
    -
    -
    -

    Compute the CRT value - Int version

    -
    -

    Precondition

    - r.count = number of moduli - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func compute(_ r: [Int]) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - r - - -
    -

    The residues

    -
    -
    -
    -
    -

    Return Value

    -

    The CRT value

    -
    -
    -
    -
    • -
-
-
-
- -
-
- - diff --git a/docs/Typealiases.html b/docs/Typealiases.html deleted file mode 100644 index b52857b..0000000 --- a/docs/Typealiases.html +++ /dev/null @@ -1,200 +0,0 @@ - - - - Type Aliases Reference - - - - - - - - - - - - - -
-
-

BigInt Docs (100% documented)

-
-
- -
-
-
-
-
- -
-
- -
-
-
-

Type Aliases

-

The following type aliases are available globally.

- -
-
-
-
    -
  • -
    - - - - Byte - -
    -
    -
    -
    -
    -
    -

    Unsigned 8 bit value

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public typealias Byte = UInt8
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - Bytes - -
    -
    -
    -
    -
    -
    -

    Array of unsigned 8 bit values

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public typealias Bytes = [UInt8]
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - Limb - -
    -
    -
    -
    -
    -
    -

    Unsigned 64 bit value

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public typealias Limb = UInt64
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - Limbs - -
    -
    -
    -
    -
    -
    -

    Array of unsigned 64 bit values

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public typealias Limbs = [UInt64]
    - -
    -
    -
    -
    -
    • -
-
-
-
- -
-
- - diff --git a/docs/badge.svg b/docs/badge.svg deleted file mode 100644 index a096fec..0000000 --- a/docs/badge.svg +++ /dev/null @@ -1,28 +0,0 @@ - - - - - - - - - - - - - - - - documentation - - - documentation - - - 100% - - - 100% - - - diff --git a/docs/css/523.e9a069b0.css b/docs/css/523.e9a069b0.css new file mode 100644 index 0000000..1b2d801 --- /dev/null +++ b/docs/css/523.e9a069b0.css @@ -0,0 +1,9 @@ +/*! + * This source file is part of the Swift.org open source project + * + * Copyright (c) 2021 Apple Inc. and the Swift project authors + * Licensed under Apache License v2.0 with Runtime Library Exception + * + * See https://swift.org/LICENSE.txt for license information + * See https://swift.org/CONTRIBUTORS.txt for Swift project authors + */aside[data-v-3ccce809]{-moz-column-break-inside:avoid;break-inside:avoid;border-radius:var(--aside-border-radius,var(--border-radius,4px));border-style:var(--aside-border-style,solid);border-width:var(--aside-border-width,0 0 0 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Remainder Theorem"}}} \ No newline at end of file diff --git a/docs/data/documentation/bigint/fractions.json b/docs/data/documentation/bigint/fractions.json new file mode 100644 index 0000000..81014e9 --- /dev/null +++ b/docs/data/documentation/bigint/fractions.json @@ -0,0 +1 @@ +{"identifier":{"interfaceLanguage":"swift","url":"doc:\/\/BigInt\/documentation\/BigInt\/Fractions"},"primaryContentSections":[{"content":[{"level":2,"anchor":"","type":"heading","text":""},{"inlineContent":[{"type":"text","text":"Fractions are represented as BFraction values consisting of a numerator BInt value and a denominator BInt value. 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BFraction(4.25)"}],"type":"paragraph"}]},{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"Using a string representation f.ex. BFraction(“4.25”)! or equivalently BFraction(“425E-2”)!"}]}]},{"content":[{"inlineContent":[{"text":"Specifying a continued fraction like BFraction([3, 4, 12, 4]) equivalent to 649 \/ 200","type":"text"}],"type":"paragraph"}]}],"type":"unorderedList"},{"inlineContent":[{"type":"text","text":"Defining a fraction by giving its decimal value (like 4.25) might lead to surprises,"},{"type":"text","text":" "},{"type":"text","text":"because not all decimal values can be represented exactly as a floating point number."},{"type":"text","text":" "},{"text":"For example, one might think that BFraction(0.1) would equal 1\/10,","type":"text"},{"type":"text","text":" "},{"text":"but in fact it equals 3602879701896397 \/ 36028797018963968 = 0.1000000000000000055511151231257827021181583404541015625","type":"text"}],"type":"paragraph"},{"anchor":"Converting-BFractions","level":3,"type":"heading","text":"Converting BFraction’s"},{"inlineContent":[{"type":"text","text":"BFraction values can be converted 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of file diff --git a/docs/data/documentation/bigint/limbs.json b/docs/data/documentation/bigint/limbs.json new file mode 100644 index 0000000..e2d24c0 --- /dev/null +++ b/docs/data/documentation/bigint/limbs.json @@ -0,0 +1 @@ +{"sections":[],"identifier":{"interfaceLanguage":"swift","url":"doc:\/\/BigInt\/documentation\/BigInt\/Limbs"},"hierarchy":{"paths":[["doc:\/\/BigInt\/documentation\/BigInt"]]},"metadata":{"modules":[{"name":"BigInt"}],"role":"symbol","symbolKind":"typealias","title":"Limbs","externalID":"s:6BigInt5Limbsa","navigatorTitle":[{"kind":"identifier","text":"Limbs"}],"fragments":[{"kind":"keyword","text":"typealias"},{"text":" ","kind":"text"},{"kind":"identifier","text":"Limbs"}],"roleHeading":"Type Alias"},"schemaVersion":{"major":0,"minor":3,"patch":0},"primaryContentSections":[{"declarations":[{"platforms":["macOS"],"tokens":[{"text":"typealias","kind":"keyword"},{"kind":"text","text":" "},{"text":"Limbs","kind":"identifier"},{"kind":"text","text":" = 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a/docs/docsets/BigInt.docset/Contents/Resources/Documents/Structs.html b/docs/docsets/BigInt.docset/Contents/Resources/Documents/Structs.html deleted file mode 100644 index 57c5d57..0000000 --- a/docs/docsets/BigInt.docset/Contents/Resources/Documents/Structs.html +++ /dev/null @@ -1,198 +0,0 @@ - - - - Structures Reference - - - - - - - - - - - - - -
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BigInt Docs (100% documented)

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Structures

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The following structures are available globally.

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    A signed fraction with numerator and denominator of unbounded size.

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    A BFraction value is represented by a BInt numerator and a BInt denominator. -The representation is normalized, so that numerator and denominator has no common divisors except 1. -The denominator is always positive, 0 has the representation 0/1

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    Declaration

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    public struct BFraction : CustomStringConvertible, Comparable, Equatable
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    A signed integer of unbounded size.

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    A BInt value is represented with magnitude and sign. -The magnitude is an array of unsigned 64 bit integers (a.k.a. Limbs). -The sign is a boolean value, true means value < 0, false means value >= 0 -The representation is little-endian, least significant Limb has index 0. -The representation is minimal, there is no leading zero Limbs. -The exception is that the value 0 is represented as a single 64 bit zero Limb and sign false

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    public struct BInt : CustomStringConvertible, Comparable, Equatable, Hashable
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    CRT instances implement the Chinese Remainder Theorem

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    Create an instance from a given set of moduli which fullfill the following conditions:

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    • at least two moduli
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    Then use the compute method to compute the CRT value for a given set of residues. -The same CRT instance can be used for different inputs, as long as the moduli are the same.

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    public struct CRT
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BigInt Docs (100% documented)

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BFraction

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public struct BFraction : CustomStringConvertible, Comparable, Equatable
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A signed fraction with numerator and denominator of unbounded size.

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A BFraction value is represented by a BInt numerator and a BInt denominator. -The representation is normalized, so that numerator and denominator has no common divisors except 1. -The denominator is always positive, 0 has the representation 0/1

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Constants -

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    BFraction(0, 1)

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    public static let ZERO: BFraction
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    BFraction(1, 1)

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    Constructs a BFraction from numerator and denominator

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    Precondition

    - Denominator is not zero - -
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    Declaration

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    public init(_ n: BInt, _ d: BInt)
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    Parameters

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    The numerator

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    The denominator

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    Constructs a BFraction from numerator and denominator

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    Precondition

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    Declaration

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    public init(_ n: BInt, _ d: Int)
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    Parameters

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    The numerator

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    The denominator

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    Constructs a BFraction from numerator and denominator

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    Precondition

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    Declaration

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    public init(_ n: Int, _ d: BInt)
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    Parameters

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    The numerator

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    The denominator

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    Constructs a BFraction from numerator and denominator

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    Precondition

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    Declaration

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    public init(_ n: Int, _ d: Int)
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    Parameters

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    The numerator

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    The denominator

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    Constructs a BFraction from its decimal value

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    Parameters

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    The decimal value

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    Return Value

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    The BFraction corresponding to d, nil if d is infinite or NaN

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    Constructs a BFraction from a String representation

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    Examples:

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    • BFraction(“3.1415”) = 6283 / 2000
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    • BFraction(“-12345E-3”) = -2469 / 200
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    • BFraction(“12345e3”) = 12345000 / 1
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    The String representation

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    Return Value

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    The BFraction represented by x, nil if x does not represent a decimal number

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    Constructs a BFraction from a continued fraction - BInt version

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    Precondition

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    Parameters

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    The continued fraction

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    Return Value

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    The BFraction represented by x

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    Constructs a BFraction from a continued fraction - Int version

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    Precondition

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    Parameters

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    The continued fraction

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    Return Value

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    The BFraction represented by x

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Stored properties -

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    The numerator - a BInt value

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    Declaration

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    public internal(set) var numerator: BInt { get }
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    The denominator - a positive BInt value

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    Declaration

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    public internal(set) var denominator: BInt { get }
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Computed properties -

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    The absolute value of self

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    Declaration

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    public var abs: BFraction { get }
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    String value of self

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    Is true if self is an integer, that is, the denominator is 1

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    Declaration

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    public var isInteger: Bool { get }
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    Is true if self < 0, false otherwise

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    Declaration

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    public var isNegative: Bool { get }
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    Is true if self > 0, false otherwise

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    Declaration

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    public var isPositive: Bool { get }
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    Is true if self = 0, false otherwise

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    Declaration

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    - - - - signum - -
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    Is 0 if self = 0, 1 if self > 0, and -1 if self < 0

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    Declaration

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    public var signum: Int { get }
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Conversion functions to String, Decimal String, Double and Continued Fractions -

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    self as a String
    -Examples: BFraction(-97, 100).asString() is “-97 / 100”

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    Declaration

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    public func asString() -> String
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    Return Value

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    self as a String

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    self as a Decimal String with a specified precision, possibly using exponential notation

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    Precondition

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    Declaration

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    public func asDecimalString(precision: Int, exponential: Bool = false) -> String
    - -
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    Parameters

    - - - - - - - - - - - -
    - - precision - - -
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    The number of significant digits

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    true to use exponential notation, false to use plain notation, default is false

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    Return Value

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    self as a decimal String

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  • -
    - - - - asDouble() - -
    -
    -
    -
    -
    -
    -

    self as a Double

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func asDouble() -> Double
    - -
    -
    -
    -

    Return Value

    -

    self as a Double or Infinity if self is not representable as a Double

    -
    -
    -
    -
    • -
  • -
    - - - - asContinuedFraction() - -
    -
    -
    -
    -
    -
    -

    self as a Continued Fraction

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func asContinuedFraction() -> [BInt]
    - -
    -
    -
    -

    Return Value

    -

    self as a Continued Fraction

    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Addition functions -

-
-
-
    -
  • -
    - - - - +(_:) - -
    -
    -
    -
    -
    -
    -

    Prefix plus

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public prefix static func + (x: BFraction) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - x - - -
    -

    BFraction value

    -
    -
    -
    -
    -

    Return Value

    -

    x

    -
    -
    -
    -
    • -
  • -
    - - - - +(_:_:) - -
    -
    -
    -
    -
    -
    -

    Addition

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func + (x: BFraction, y: BFraction) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First addend

    -
    -
    - - y - - -
    -

    Second addend

    -
    -
    -
    -
    -

    Return Value

    -

    x + y

    -
    -
    -
    -
    • -
  • -
    - - - - +(_:_:) - -
    -
    -
    -
    -
    -
    -

    Addition

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func + (x: BFraction, y: BInt) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First addend

    -
    -
    - - y - - -
    -

    Second addend

    -
    -
    -
    -
    -

    Return Value

    -

    x + y

    -
    -
    -
    -
    • -
  • -
    - - - - +(_:_:) - -
    -
    -
    -
    -
    -
    -

    Addition

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func + (x: BInt, y: BFraction) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First addend

    -
    -
    - - y - - -
    -

    Second addend

    -
    -
    -
    -
    -

    Return Value

    -

    x + y

    -
    -
    -
    -
    • -
  • -
    - - - - +(_:_:) - -
    -
    -
    -
    -
    -
    -

    Addition

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func + (x: BFraction, y: Int) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First addend

    -
    -
    - - y - - -
    -

    Second addend

    -
    -
    -
    -
    -

    Return Value

    -

    x + y

    -
    -
    -
    -
    • -
  • -
    - - - - +(_:_:) - -
    -
    -
    -
    -
    -
    -

    Addition

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func + (x: Int, y: BFraction) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First addend

    -
    -
    - - y - - -
    -

    Second addend

    -
    -
    -
    -
    -

    Return Value

    -

    x + y

    -
    -
    -
    -
    • -
  • -
    - - - - +=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x + y

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func += (x: inout BFraction, y: BFraction)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand addend

    -
    -
    - - y - - -
    -

    Right hand addend

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - +=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x + y

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func += (x: inout BFraction, y: BInt)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand addend

    -
    -
    - - y - - -
    -

    Right hand addend

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - +=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x + y

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func += (x: inout BFraction, y: Int)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand addend

    -
    -
    - - y - - -
    -

    Right hand addend

    -
    -
    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Subtraction functions -

-
-
-
    -
  • -
    - - - - -(_:) - -
    -
    -
    -
    -
    -
    -

    Negation

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public prefix static func - (x: BFraction) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - x - - -
    -

    Operand

    -
    -
    -
    -
    -

    Return Value

    -

    -x

    -
    -
    -
    -
    • -
  • -
    - - - - -(_:_:) - -
    -
    -
    -
    -
    -
    -

    Subtraction

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func - (x: BFraction, y: BFraction) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Minuend

    -
    -
    - - y - - -
    -

    Subtrahend

    -
    -
    -
    -
    -

    Return Value

    -

    x - y

    -
    -
    -
    -
    • -
  • -
    - - - - -(_:_:) - -
    -
    -
    -
    -
    -
    -

    Subtraction

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func - (x: BFraction, y: BInt) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Minuend

    -
    -
    - - y - - -
    -

    Subtrahend

    -
    -
    -
    -
    -

    Return Value

    -

    x - y

    -
    -
    -
    -
    • -
  • -
    - - - - -(_:_:) - -
    -
    -
    -
    -
    -
    -

    Subtraction

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func - (x: BInt, y: BFraction) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Minuend

    -
    -
    - - y - - -
    -

    Subtrahend

    -
    -
    -
    -
    -

    Return Value

    -

    x - y

    -
    -
    -
    -
    • -
  • -
    - - - - -(_:_:) - -
    -
    -
    -
    -
    -
    -

    Subtraction

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func - (x: BFraction, y: Int) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Minuend

    -
    -
    - - y - - -
    -

    Subtrahend

    -
    -
    -
    -
    -

    Return Value

    -

    x - y

    -
    -
    -
    -
    • -
  • -
    - - - - -(_:_:) - -
    -
    -
    -
    -
    -
    -

    Subtraction

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func - (x: Int, y: BFraction) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Minuend

    -
    -
    - - y - - -
    -

    Subtrahend

    -
    -
    -
    -
    -

    Return Value

    -

    x - y

    -
    -
    -
    -
    • -
  • -
    - - - - -=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x - y

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func -= (x: inout BFraction, y: BFraction)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand minuend

    -
    -
    - - y - - -
    -

    Right hand subtrahend

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - -=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x - y

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func -= (x: inout BFraction, y: BInt)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand minuend

    -
    -
    - - y - - -
    -

    Right hand subtrahend

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - -=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x - y

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func -= (x: inout BFraction, y: Int)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand minuend

    -
    -
    - - y - - -
    -

    Right hand subtrahend

    -
    -
    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Multiplication functions -

-
-
-
    -
  • -
    - - - - *(_:_:) - -
    -
    -
    -
    -
    -
    -

    Multiplication

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func * (x: BFraction, y: BFraction) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Multiplier

    -
    -
    - - y - - -
    -

    Multiplicand

    -
    -
    -
    -
    -

    Return Value

    -

    x * y

    -
    -
    -
    -
    • -
  • -
    - - - - *(_:_:) - -
    -
    -
    -
    -
    -
    -

    Multiplication

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func * (x: BFraction, y: BInt) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Multiplier

    -
    -
    - - y - - -
    -

    Multiplicand

    -
    -
    -
    -
    -

    Return Value

    -

    x * y

    -
    -
    -
    -
    • -
  • -
    - - - - *(_:_:) - -
    -
    -
    -
    -
    -
    -

    Multiplication

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func * (x: BInt, y: BFraction) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Multiplier

    -
    -
    - - y - - -
    -

    Multiplicand

    -
    -
    -
    -
    -

    Return Value

    -

    x * y

    -
    -
    -
    -
    • -
  • -
    - - - - *(_:_:) - -
    -
    -
    -
    -
    -
    -

    Multiplication

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func * (x: BFraction, y: Int) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Multiplier

    -
    -
    - - y - - -
    -

    Multiplicand

    -
    -
    -
    -
    -

    Return Value

    -

    x * y

    -
    -
    -
    -
    • -
  • -
    - - - - *(_:_:) - -
    -
    -
    -
    -
    -
    -

    Multiplication

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func * (x: Int, y: BFraction) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Multiplier

    -
    -
    - - y - - -
    -

    Multiplicand

    -
    -
    -
    -
    -

    Return Value

    -

    x * y

    -
    -
    -
    -
    • -
  • -
    - - - - *=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x * y

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func *= (x: inout BFraction, y: BFraction)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand multiplier

    -
    -
    - - y - - -
    -

    Right hand multiplicand

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - *=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x * y

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func *= (x: inout BFraction, y: BInt)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand multiplier

    -
    -
    - - y - - -
    -

    Right hand multiplicand

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - *=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x * y

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func *= (x: inout BFraction, y: Int)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand multiplier

    -
    -
    - - y - - -
    -

    Right hand multiplicand

    -
    -
    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Division functions -

-
-
-
    -
  • -
    - - - - /(_:_:) - -
    -
    -
    -
    -
    -
    -

    Division

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func / (x: BFraction, y: BFraction) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Dividend

    -
    -
    - - y - - -
    -

    Divisor

    -
    -
    -
    -
    -

    Return Value

    -

    x / y

    -
    -
    -
    -
    • -
  • -
    - - - - /(_:_:) - -
    -
    -
    -
    -
    -
    -

    Division

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func / (x: BFraction, y: BInt) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Dividend

    -
    -
    - - y - - -
    -

    Divisor

    -
    -
    -
    -
    -

    Return Value

    -

    x / y

    -
    -
    -
    -
    • -
  • -
    - - - - /(_:_:) - -
    -
    -
    -
    -
    -
    -

    Division

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func / (x: BInt, y: BFraction) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Dividend

    -
    -
    - - y - - -
    -

    Divisor

    -
    -
    -
    -
    -

    Return Value

    -

    x / y

    -
    -
    -
    -
    • -
  • -
    - - - - /(_:_:) - -
    -
    -
    -
    -
    -
    -

    Division

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func / (x: BFraction, y: Int) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Dividend

    -
    -
    - - y - - -
    -

    Divisor

    -
    -
    -
    -
    -

    Return Value

    -

    x / y

    -
    -
    -
    -
    • -
  • -
    - - - - /(_:_:) - -
    -
    -
    -
    -
    -
    -

    Division

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func / (x: Int, y: BFraction) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Dividend

    -
    -
    - - y - - -
    -

    Divisor

    -
    -
    -
    -
    -

    Return Value

    -

    x / y

    -
    -
    -
    -
    • -
  • -
    - - - - /=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x / y

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func /= (x: inout BFraction, y: BFraction)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand dividend

    -
    -
    - - y - - -
    -

    Right hand divisor

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - /=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x / y

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func /= (x: inout BFraction, y: BInt)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand dividend

    -
    -
    - - y - - -
    -

    Right hand divisor

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - /=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x / y

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func /= (x: inout BFraction, y: Int)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand dividend

    -
    -
    - - y - - -
    -

    Right hand divisor

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - invert() - -
    -
    -
    -
    -
    -
    -

    Invert self

    -
    -

    Precondition

    - self is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func invert() -> BFraction
    - -
    -
    -
    -

    Return Value

    -

    1 / self

    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Modulus functions -

-
-
-
    -
  • -
    - - - - mod(_:) - -
    -
    -
    -
    -
    -
    -

    Modulus - BInt parameter

    -
    -

    Precondition

    - Modulus is positive - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func mod(_ m: BInt) -> BInt?
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - m - - -
    -

    Modulus

    -
    -
    -
    -
    -

    Return Value

    -

    self mod m, a non-negative value or nil if the denominator and modulus are not coprime

    -
    -
    -
    -
    • -
  • -
    - - - - mod(_:) - -
    -
    -
    -
    -
    -
    -

    Modulus - Int parameter

    -
    -

    Precondition

    - Modulus is positive - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func mod(_ m: Int) -> Int?
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - m - - -
    -

    Modulus

    -
    -
    -
    -
    -

    Return Value

    -

    self mod x, a non-negative value or nil if the denominator and modulus are not coprime

    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Exponentiation functions -

-
-
-
    -
  • -
    - - - - **(_:_:) - -
    -
    -
    -
    -
    -
    -

    Exponentiation

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func ** (a: BFraction, x: Int) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - a - - -
    -

    Operand

    -
    -
    - - x - - -
    -

    Exponent

    -
    -
    -
    -
    -

    Return Value

    -

    a^x

    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Rounding functions -

-
-
-
    -
  • -
    - - - - round() - -
    -
    -
    -
    -
    -
    -

    Round

    - -

    Returns: self rounded to the nearest integer

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func round() -> BInt
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - truncate() - -
    -
    -
    -
    -
    -
    -

    Truncate

    - -

    Returns: self rounded to an integer towards 0

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func truncate() -> BInt
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - ceil() - -
    -
    -
    -
    -
    -
    -

    Ceil

    - -

    Returns: self rounded to an integer towards +Infinity

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func ceil() -> BInt
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - floor() - -
    -
    -
    -
    -
    -
    -

    Floor

    - -

    Returns: self rounded to an integer towards -Infinity

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func floor() -> BInt
    - -
    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Comparison functions -

-
-
-
    -
  • -
    - - - - ==(_:_:) - -
    -
    -
    -
    -
    -
    -

    Equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func == (x: BFraction, y: BFraction) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x = y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - ==(_:_:) - -
    -
    -
    -
    -
    -
    -

    Equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func == (x: BFraction, y: BInt) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x = y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - ==(_:_:) - -
    -
    -
    -
    -
    -
    -

    Equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func == (x: BInt, y: BFraction) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x = y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - ==(_:_:) - -
    -
    -
    -
    -
    -
    -

    Equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func == (x: BFraction, y: Int) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x = y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - ==(_:_:) - -
    -
    -
    -
    -
    -
    -

    Equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func == (x: Int, y: BFraction) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x = y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - !=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Not equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func != (x: BFraction, y: BFraction) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x != y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - !=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Not equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func != (x: BFraction, y: BInt) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x != y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - !=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Not equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func != (x: BInt, y: BFraction) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x != y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - !=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Not equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func != (x: BFraction, y: Int) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x != y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - !=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Not equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func != (x: Int, y: BFraction) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x != y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - <(_:_:) - -
    -
    -
    -
    -
    -
    -

    Less than

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func < (x: BFraction, y: BFraction) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x < y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - <(_:_:) - -
    -
    -
    -
    -
    -
    -

    Less than

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func < (x: BFraction, y: BInt) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x < y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - <(_:_:) - -
    -
    -
    -
    -
    -
    -

    Less than

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func < (x: BInt, y: BFraction) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x < y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - <(_:_:) - -
    -
    -
    -
    -
    -
    -

    Less than

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func < (x: BFraction, y: Int) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x < y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - <(_:_:) - -
    -
    -
    -
    -
    -
    -

    Less than

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func < (x: Int, y: BFraction) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x < y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - >(_:_:) - -
    -
    -
    -
    -
    -
    -

    Greater than

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func > (x: BFraction, y: BFraction) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x > y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - >(_:_:) - -
    -
    -
    -
    -
    -
    -

    Greater than

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func > (x: BFraction, y: BInt) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x > y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - >(_:_:) - -
    -
    -
    -
    -
    -
    -

    Greater than

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func > (x: BInt, y: BFraction) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x > y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - >(_:_:) - -
    -
    -
    -
    -
    -
    -

    Greater than

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func > (x: BFraction, y: Int) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x > y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - >(_:_:) - -
    -
    -
    -
    -
    -
    -

    Greater than

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func > (x: Int, y: BFraction) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x > y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - <=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Less than or equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func <= (x: BFraction, y: BFraction) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x <= y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - <=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Less than or equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func <= (x: BFraction, y: BInt) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x <= y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - <=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Less than or equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func <= (x: BInt, y: BFraction) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x <= y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - <=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Less than or equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func <= (x: BFraction, y: Int) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x <= y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - <=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Less than or equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func <= (x: Int, y: BFraction) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x <= y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - >=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Greater than or equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func >= (x: BFraction, y: BFraction) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x >= y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - >=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Greater than or equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func >= (x: BFraction, y: BInt) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x >= y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - >=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Greater than or equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func >= (x: BInt, y: BFraction) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x >= y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - >=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Greater than or equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func >= (x: BFraction, y: Int) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x >= y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - >=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Greater than or equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func >= (x: Int, y: BFraction) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x >= y, false otherwise

    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Miscellaneous functions -

-
-
-
    -
  • -
    - - - - bernoulli(_:) - -
    -
    -
    -
    -
    -
    -

    Bernoulli number

    -
    -

    Precondition

    - n >= 0 - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func bernoulli(_ n: Int) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - n - - -
    -

    The Bernoulli index

    -
    -
    -
    -
    -

    Return Value

    -

    The n'th Bernoulli number

    -
    -
    -
    -
    • -
  • -
    - - - - bernoulliSequence(_:) - -
    -
    -
    -
    -
    -
    -

    Bernoulli numbers

    -
    -

    Precondition

    - n > 0 - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func bernoulliSequence(_ n: Int) -> [BFraction]
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - n - - -
    -

    The number of Bernoulli numbers to compute

    -
    -
    -
    -
    -

    Return Value

    -

    The even numbered Bernoulli numbers B(0), B(2), B(4) … B(2 * n - 2)

    -
    -
    -
    -
    • -
  • -
    - - - - harmonic(_:) - -
    -
    -
    -
    -
    -
    -

    Harmonic number: 1 + 1 / 2 + … + 1 / n

    -
    -

    Precondition

    - n > 0 - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func harmonic(_ n: Int) -> BFraction
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - n - - -
    -

    The number of fractions to add

    -
    -
    -
    -
    -

    Return Value

    -

    The n'th harmonic number

    -
    -
    -
    -
    • -
  • -
    - - - - harmonicSequence(_:) - -
    -
    -
    -
    -
    -
    -

    Harmonic sequence: The first n harmonic numbers

    -
    -

    Precondition

    - n > 0 - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func harmonicSequence(_ n: Int) -> [BFraction]
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - n - - -
    -

    The number of harmonic numbers

    -
    -
    -
    -
    -

    Return Value

    -

    The harmonic numbers: H1, H2 … Hn

    -
    -
    -
    -
    • -
-
-
-
- -
-
- - diff --git a/docs/docsets/BigInt.docset/Contents/Resources/Documents/Structs/BInt.html b/docs/docsets/BigInt.docset/Contents/Resources/Documents/Structs/BInt.html deleted file mode 100644 index 2412c34..0000000 --- a/docs/docsets/BigInt.docset/Contents/Resources/Documents/Structs/BInt.html +++ /dev/null @@ -1,7346 +0,0 @@ - - - - BInt Structure Reference - - - - - - - - - - - - - -
-
-

BigInt Docs (100% documented)

-
-
- -
-
-
-
-
- -
-
- -
-
-
-

BInt

-
-
- - 
public struct BInt : CustomStringConvertible, Comparable, Equatable, Hashable
- -
-
-

A signed integer of unbounded size.

- -

A BInt value is represented with magnitude and sign. -The magnitude is an array of unsigned 64 bit integers (a.k.a. Limbs). -The sign is a boolean value, true means value < 0, false means value >= 0 -The representation is little-endian, least significant Limb has index 0. -The representation is minimal, there is no leading zero Limbs. -The exception is that the value 0 is represented as a single 64 bit zero Limb and sign false

- -
-
-
-
- - -
- -

Constants -

-
-
-
    -
  • -
    - - - - ZERO - -
    -
    -
    -
    -
    -
    -

    BInt(0)

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static let ZERO: BInt
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - ONE - -
    -
    -
    -
    -
    -
    -

    BInt(1)

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static let ONE: BInt
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - TWO - -
    -
    -
    -
    -
    -
    -

    BInt(2)

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static let TWO: BInt
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - THREE - -
    -
    -
    -
    -
    -
    -

    BInt(3)

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static let THREE: BInt
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - FOUR - -
    -
    -
    -
    -
    -
    -

    BInt(4)

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static let FOUR: BInt
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - FIVE - -
    -
    -
    -
    -
    -
    -

    BInt(5)

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static let FIVE: BInt
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - SIX - -
    -
    -
    -
    -
    -
    -

    BInt(6)

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static let SIX: BInt
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - SEVEN - -
    -
    -
    -
    -
    -
    -

    BInt(7)

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static let SEVEN: BInt
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - EIGHT - -
    -
    -
    -
    -
    -
    -

    BInt(8)

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static let EIGHT: BInt
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - NINE - -
    -
    -
    -
    -
    -
    -

    BInt(9)

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static let NINE: BInt
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - TEN - -
    -
    -
    -
    -
    -
    -

    BInt(10)

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static let TEN: BInt
    - -
    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Initializers -

-
-
-
    -
  • -
    - - - - init(_:_:) - -
    -
    -
    -
    -
    -
    -

    Constructs a BInt from magnitude and sign

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public init(_ magnitude: Limbs, _ isNegative: Bool = false)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - magnitude - - -
    -

    magnitude of value

    -
    -
    - - isNegative - - -
    -

    true means negative value, false means 0 or positive value, default is false

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - init(_:) - -
    -
    -
    -
    -
    -
    -

    Constructs a BInt from an Int value

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public init(_ x: Int)
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - x - - -
    -

    Int value

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - init(_:) - -
    -
    -
    -
    -
    -
    -

    Constructs a BInt from a decimal value

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public init?(_ d: Double)
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - d - - -
    -

    The decimal value

    -
    -
    -
    -
    -

    Return Value

    -

    The BInt corresponding to d truncated to an integer value, nil if d is infinite or NaN

    -
    -
    -
    -
    • -
  • -
    - - - - init(_:radix:) - -
    -
    -
    -
    -
    -
    -

    Constructs a BInt from a String value and radix

    - -

    Examples:

    - -
      -
    • BInt(“90abcdef”, radix = 16)
      • -
    • BInt(“111110010”, radix = 2)
      • -
    • BInt(“1cdefghijk44”, radix = 26)
      • -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public init?(_ x: String, radix: Int = 10)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    String value to be converted

    -
    -
    - - radix - - -
    -

    Radix of x, from 2 to 36 inclusive, default is 10 -Returns: The BInt corresponding to x, nil if x does not designate an integer in the given radix

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - init(bitWidth:) - -
    -
    -
    -
    -
    -
    -

    Constructs a random BInt with a specified number of bits

    -
    -

    Precondition

    - bitWidth is positive - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public init(bitWidth: Int)
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - bitWidth - - -
    -

    Number of bits

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - init(magnitude:) - -
    -
    -
    -
    -
    -
    -

    Constructs a BInt from a big-endian magnitude byte array representation

    -
    -

    Precondition

    - Byte array is not empty - -
    - -

    Examples:

    - -
      -
    • The byte array [1, 0, 0] represents BInt value 65536
      • -
    • The byte array [128, 0] represents BInt value 32768
      • -
    • The byte array [255, 127] represents BInt value 65407
      • -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public init(magnitude x: Bytes)
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - x - - -
    -

    Magnitude big-endian byte array

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - init(signed:) - -
    -
    -
    -
    -
    -
    -

    Constructs a BInt from a big-endian 2’s complement byte array representation

    -
    -

    Precondition

    - Byte array is not empty - -
    - -

    Examples:

    - -
      -
    • The byte array [1, 0, 0] represents BInt value 65536
      • -
    • The byte array [128, 0] represents BInt value -32768
      • -
    • The byte array [255, 127] represents BInt value -129
      • -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public init(signed x: Bytes)
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - x - - -
    -

    2’s complement big-endian byte array

    -
    -
    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Stored properties -

-
-
-
    -
  • -
    - - - - isNegative - -
    -
    -
    -
    -
    -
    -

    The sign, true if self < 0, false otherwise

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public internal(set) var isNegative: Bool { get }
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - magnitude - -
    -
    -
    -
    -
    -
    -

    The magnitude limb array

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public internal(set) var magnitude: Limbs { get }
    - -
    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Computed properties -

-
-
-
    -
  • -
    - - - - abs - -
    -
    -
    -
    -
    -
    -

    The absolute value of self

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public var abs: BInt { get }
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - bitWidth - -
    -
    -
    -
    -
    -
    -

    The number of bits in the binary representation of the magnitude of self. 0 if self = 0

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public var bitWidth: Int { get }
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - description - -
    -
    -
    -
    -
    -
    -

    Base 10 string value of self

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public var description: String { get }
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - isEven - -
    -
    -
    -
    -
    -
    -

    Is true if self is even, false if self is odd

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public var isEven: Bool { get }
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - isNotZero - -
    -
    -
    -
    -
    -
    -

    Is false if self = 0, true otherwise

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public var isNotZero: Bool { get }
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - isOdd - -
    -
    -
    -
    -
    -
    -

    Is true if self is odd, false if self is even

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public var isOdd: Bool { get }
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - isOne - -
    -
    -
    -
    -
    -
    -

    Is true if self = 1, false otherwise

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public var isOne: Bool { get }
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - isPositive - -
    -
    -
    -
    -
    -
    -

    Is true if self > 0, false otherwise

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public var isPositive: Bool { get }
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - isZero - -
    -
    -
    -
    -
    -
    -

    Is true if self = 0, false otherwise

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public var isZero: Bool { get }
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - leadingZeroBitCount - -
    -
    -
    -
    -
    -
    -

    The number of leading zero bits in the magnitude of self. 0 if self = 0

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public var leadingZeroBitCount: Int { get }
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - population - -
    -
    -
    -
    -
    -
    -

    The number of 1 bits in the magnitude of self

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public var population: Int { get }
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - signum - -
    -
    -
    -
    -
    -
    -

    Is 0 if self = 0, 1 if self > 0, and -1 if self < 0

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public var signum: Int { get }
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - trailingZeroBitCount - -
    -
    -
    -
    -
    -
    -

    The number of trailing zero bits in the magnitude of self. 0 if self = 0

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public var trailingZeroBitCount: Int { get }
    - -
    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Conversion functions to Double, Int, String, and Bytes -

-
-
-
    -
  • -
    - - - - asDouble() - -
    -
    -
    -
    -
    -
    -

    self as a Double

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func asDouble() -> Double
    - -
    -
    -
    -

    Return Value

    -

    self as a Double or Infinity if self is not representable as a Double

    -
    -
    -
    -
    • -
  • -
    - - - - asInt() - -
    -
    -
    -
    -
    -
    -

    self as an Int

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func asInt() -> Int?
    - -
    -
    -
    -

    Return Value

    -

    self as an Int or nil if self is not representable as an Int

    -
    -
    -
    -
    • -
  • -
    - - - - asMagnitudeBytes() - -
    -
    -
    -
    -
    -
    -

    Byte array representation of magnitude value

    - -

    Examples:

    - -
      -
    • BInt(1).asMagnitudeBytes() = [1]
      • -
    • BInt(-1).asMagnitudeBytes() = [1]
      • -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func asMagnitudeBytes() -> Bytes
    - -
    -
    -
    -

    Return Value

    -

    Minimal big-endian magnitude byte array representation

    -
    -
    -
    -
    • -
  • -
    - - - - asSignedBytes() - -
    -
    -
    -
    -
    -
    -

    Byte array representation of 2’s complement value

    - -

    Examples:

    - -
      -
    • BInt(1).asSignedBytes() = [1]
      • -
    • BInt(-1).asSignedBytes() = [255]
      • -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func asSignedBytes() -> Bytes
    - -
    -
    -
    -

    Return Value

    -

    Minimal big-endian 2’s complement byte array representation

    -
    -
    -
    -
    • -
  • - -
    -
    -
    -
    -
    -

    self as a String with a given radix

    -
    -

    Precondition

    - Radix between 2 and 36 inclusive - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func asString(radix: Int = 10, uppercase: Bool = false) -> String
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - radix - - -
    -

    Radix from 2 to 36 inclusive

    -
    -
    - - uppercase - - -
    -

    true to use uppercase letters, false to use lowercase letters, default is false

    -
    -
    -
    -
    -

    Return Value

    -

    self as a String in the given radix

    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Bit operation functions -

-
-
-
    -
  • -
    - - - - &(_:_:) - -
    -
    -
    -
    -
    -
    -

    Bitwise and operator - behaves as if two’s complement representation were used,
    -although this is not actually the case

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func & (x: BInt, y: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First value

    -
    -
    - - y - - -
    -

    Second value

    -
    -
    -
    -
    -

    Return Value

    -

    BInt(signed: bx & by) where - -

      -
    • bx = x.asSignedBytes()
      • -
    • by = y.asSignedBytes()
      • -

    -
    -
    -
    -
    • -
  • -
    - - - - &=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x & y

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func &= (x: inout BInt, y: BInt)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand parameter

    -
    -
    - - y - - -
    -

    Right hand parameter

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - |(_:_:) - -
    -
    -
    -
    -
    -
    -

    Bitwise or operator - behaves as if two’s complement representation were used,
    -although this is not actually the case

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func | (x: BInt, y: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First value

    -
    -
    - - y - - -
    -

    Second value

    -
    -
    -
    -
    -

    Return Value

    -

    BInt(signed: bx | by) where - -

      -
    • bx = x.asSignedBytes()
      • -
    • by = y.asSignedBytes()
      • -

    -
    -
    -
    -
    • -
  • -
    - - - - |=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x | y

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func |= (x: inout BInt, y: BInt)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand parameter

    -
    -
    - - y - - -
    -

    Right hand parameter

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - ^(_:_:) - -
    -
    -
    -
    -
    -
    -

    Bitwise xor operator - behaves as if two’s complement representation were used,
    -although this is not actually the case

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func ^ (x: BInt, y: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First value

    -
    -
    - - y - - -
    -

    Second value

    -
    -
    -
    -
    -

    Return Value

    -

    BInt(signed: bx ^ by) where - -

      -
    • bx = x.asSignedBytes()
      • -
    • by = y.asSignedBytes()
      • -

    -
    -
    -
    -
    • -
  • -
    - - - - ^=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x ^ y

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func ^= (x: inout BInt, y: BInt)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand parameter

    -
    -
    - - y - - -
    -

    Right hand parameter

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - ~(_:) - -
    -
    -
    -
    -
    -
    -

    Bitwise not operator - behaves as if two’s complement arithmetic were used,
    -although this is not actually the case

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public prefix static func ~ (x: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - x - - -
    -

    BInt value

    -
    -
    -
    -
    -

    Return Value

    -

    -x - 1

    -
    -
    -
    -
    • -
  • -
    - - - - clearBit(_:) - -
    -
    -
    -
    -
    -
    -

    Clear a specified bit - a no-op if bit number < 0

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public mutating func clearBit(_ n: Int)
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - n - - -
    -

    Bit number

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - flipBit(_:) - -
    -
    -
    -
    -
    -
    -

    Invert a specified bit - a no-op if bit number < 0

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public mutating func flipBit(_ n: Int)
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - n - - -
    -

    Bit number

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - setBit(_:) - -
    -
    -
    -
    -
    -
    -

    Set a specified bit - a no-op if bit number < 0

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public mutating func setBit(_ n: Int)
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - n - - -
    -

    Bit number

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - testBit(_:) - -
    -
    -
    -
    -
    -
    -

    Test a specified bit - false if bit number < 0

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func testBit(_ n: Int) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - n - - -
    -

    Bit number

    -
    -
    -
    -
    -

    Return Value

    -

    true if bit is set, false otherwise

    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Addition functions -

-
-
-
    -
  • -
    - - - - +(_:) - -
    -
    -
    -
    -
    -
    -

    Prefix plus

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public prefix static func + (x: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - x - - -
    -

    BInt value

    -
    -
    -
    -
    -

    Return Value

    -

    x

    -
    -
    -
    -
    • -
  • -
    - - - - +(_:_:) - -
    -
    -
    -
    -
    -
    -

    Addition

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func + (x: BInt, y: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First addend

    -
    -
    - - y - - -
    -

    Second addend

    -
    -
    -
    -
    -

    Return Value

    -

    x + y

    -
    -
    -
    -
    • -
  • -
    - - - - +(_:_:) - -
    -
    -
    -
    -
    -
    -

    Addition

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func + (x: Int, y: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First addend

    -
    -
    - - y - - -
    -

    Second addend

    -
    -
    -
    -
    -

    Return Value

    -

    x + y

    -
    -
    -
    -
    • -
  • -
    - - - - +(_:_:) - -
    -
    -
    -
    -
    -
    -

    Addition

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func + (x: BInt, y: Int) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First addend

    -
    -
    - - y - - -
    -

    Second addend

    -
    -
    -
    -
    -

    Return Value

    -

    x + y

    -
    -
    -
    -
    • -
  • -
    - - - - +=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x + y

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func += (x: inout BInt, y: BInt)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand addend

    -
    -
    - - y - - -
    -

    Right hand addend

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - +=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x + y

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func += (x: inout BInt, y: Int)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand addend

    -
    -
    - - y - - -
    -

    Right hand addend

    -
    -
    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Negation functions -

-
-
-
    -
  • -
    - - - - negate() - -
    -
    -
    -
    -
    -
    -

    Negates self

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public mutating func negate()
    - -
    -
    -
    -
    -
    • -
  • -
    - - - - -(_:) - -
    -
    -
    -
    -
    -
    -

    Negation

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public prefix static func - (x: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - x - - -
    -

    Operand

    -
    -
    -
    -
    -

    Return Value

    -

    -x

    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Subtraction functions -

-
-
-
    -
  • -
    - - - - -(_:_:) - -
    -
    -
    -
    -
    -
    -

    Subtraction

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func - (x: BInt, y: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Minuend

    -
    -
    - - y - - -
    -

    Subtrahend

    -
    -
    -
    -
    -

    Return Value

    -

    x - y

    -
    -
    -
    -
    • -
  • -
    - - - - -(_:_:) - -
    -
    -
    -
    -
    -
    -

    Subtraction

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func - (x: Int, y: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Minuend

    -
    -
    - - y - - -
    -

    Subtrahend

    -
    -
    -
    -
    -

    Return Value

    -

    x - y

    -
    -
    -
    -
    • -
  • -
    - - - - -(_:_:) - -
    -
    -
    -
    -
    -
    -

    Subtraction

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func - (x: BInt, y: Int) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Minuend

    -
    -
    - - y - - -
    -

    Subtrahend

    -
    -
    -
    -
    -

    Return Value

    -

    x - y

    -
    -
    -
    -
    • -
  • -
    - - - - -=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x - y

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func -= (x: inout BInt, y: BInt)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand minuend

    -
    -
    - - y - - -
    -

    Right hand subtrahend

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - -=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x - y

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func -= (x: inout BInt, y: Int)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand minuend

    -
    -
    - - y - - -
    -

    Right hand subtrahend

    -
    -
    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Multiplication functions -

-
-
-
    -
  • -
    - - - - *(_:_:) - -
    -
    -
    -
    -
    -
    -

    Multiplication

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func * (x: BInt, y: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Multiplier

    -
    -
    - - y - - -
    -

    Multiplicand

    -
    -
    -
    -
    -

    Return Value

    -

    x * y

    -
    -
    -
    -
    • -
  • -
    - - - - *(_:_:) - -
    -
    -
    -
    -
    -
    -

    Multiplication

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func * (x: Int, y: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Multiplier

    -
    -
    - - y - - -
    -

    Multiplicand

    -
    -
    -
    -
    -

    Return Value

    -

    x * y

    -
    -
    -
    -
    • -
  • -
    - - - - *(_:_:) - -
    -
    -
    -
    -
    -
    -

    Multiplication

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func * (x: BInt, y: Int) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Multiplier

    -
    -
    - - y - - -
    -

    Multiplicand

    -
    -
    -
    -
    -

    Return Value

    -

    x * y

    -
    -
    -
    -
    • -
  • -
    - - - - *=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x * y

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func *= (x: inout BInt, y: BInt)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand multiplier

    -
    -
    - - y - - -
    -

    Right hand multiplicand

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - *=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x * y

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func *= (x: inout BInt, y: Int)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand multiplier

    -
    -
    - - y - - -
    -

    Right hand multiplicand

    -
    -
    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Division functions -

-
-
-
    -
  • - -
    -
    -
    -
    -
    -

    Division

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func quotientAndRemainder(dividingBy x: BInt) -> (quotient: BInt, remainder: BInt)
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - x - - -
    -

    Divisor - a BInt value

    -
    -
    -
    -
    -

    Return Value

    -

    Quotient and remainder of self / x

    -
    -
    -
    -
    • -
  • - -
    -
    -
    -
    -
    -

    Division

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func quotientAndRemainder(dividingBy x: BInt, _ quotient: inout BInt, _ remainder: inout BInt)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - - - - - -
    - - x - - -
    -

    Divisor - a BInt value

    -
    -
    - - quotient - - -
    -

    Set to the quotient of self / x

    -
    -
    - - remainder - - -
    -

    Set to the remainder of self / x

    -
    -
    -
    -
    -
    -
    • -
  • - -
    -
    -
    -
    -
    -

    Division

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func quotientAndRemainder(dividingBy x: Int) -> (quotient: BInt, remainder: Int)
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - x - - -
    -

    Divisor - an Int value

    -
    -
    -
    -
    -

    Return Value

    -

    Quotient and remainder of self / x

    -
    -
    -
    -
    • -
  • - -
    -
    -
    -
    -
    -

    Division

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func quotientAndRemainder(dividingBy x: Int, _ quotient: inout BInt, _ remainder: inout Int)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - - - - - -
    - - x - - -
    -

    Divisor - an Int value

    -
    -
    - - quotient - - -
    -

    Set to the quotient of self / x

    -
    -
    - - remainder - - -
    -

    Set to the remainder of self / x

    -
    -
    -
    -
    -
    -
    • -
  • - -
    -
    -
    -
    -
    -

    Exact division - that is, the remainder of the division is known to be 0

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func quotientExact(dividingBy x: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - x - - -
    -

    Divisor - a BInt value

    -
    -
    -
    -
    -

    Return Value

    -

    Quotient of self / x - undefined if the remainder is in fact not 0

    -
    -
    -
    -
    • -
  • -
    - - - - /(_:_:) - -
    -
    -
    -
    -
    -
    -

    Division

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func / (x: BInt, y: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Dividend

    -
    -
    - - y - - -
    -

    Divisor

    -
    -
    -
    -
    -

    Return Value

    -

    x / y

    -
    -
    -
    -
    • -
  • -
    - - - - /(_:_:) - -
    -
    -
    -
    -
    -
    -

    Division

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func / (x: Int, y: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Dividend

    -
    -
    - - y - - -
    -

    Divisor

    -
    -
    -
    -
    -

    Return Value

    -

    x / y

    -
    -
    -
    -
    • -
  • -
    - - - - /(_:_:) - -
    -
    -
    -
    -
    -
    -

    Division

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func / (x: BInt, y: Int) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Dividend

    -
    -
    - - y - - -
    -

    Divisor

    -
    -
    -
    -
    -

    Return Value

    -

    x / y

    -
    -
    -
    -
    • -
  • -
    - - - - /=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x / y

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func /= (x: inout BInt, y: BInt)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand dividend

    -
    -
    - - y - - -
    -

    Right hand divisor

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - /=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x / y

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func /= (x: inout BInt, y: Int)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Left hand dividend

    -
    -
    - - y - - -
    -

    Right hand divisor

    -
    -
    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Remainder and modulus functions -

-
-
-
    -
  • -
    - - - - %(_:_:) - -
    -
    -
    -
    -
    -
    -

    Remainder

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func % (x: BInt, y: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Dividend

    -
    -
    - - y - - -
    -

    Divisor

    -
    -
    -
    -
    -

    Return Value

    -

    x % y

    -
    -
    -
    -
    • -
  • -
    - - - - %(_:_:) - -
    -
    -
    -
    -
    -
    -

    Remainder

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func % (x: Int, y: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Dividend

    -
    -
    - - y - - -
    -

    Divisor

    -
    -
    -
    -
    -

    Return Value

    -

    x % y

    -
    -
    -
    -
    • -
  • -
    - - - - %(_:_:) - -
    -
    -
    -
    -
    -
    -

    Remainder

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func % (x: BInt, y: Int) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Dividend

    -
    -
    - - y - - -
    -

    Divisor

    -
    -
    -
    -
    -

    Return Value

    -

    x % y

    -
    -
    -
    -
    • -
  • -
    - - - - %=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x % y

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func %= (x: inout BInt, y: BInt)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Dividend

    -
    -
    - - y - - -
    -

    Divisor

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - %=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x % y

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func %= (x: inout BInt, y: Int)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Dividend

    -
    -
    - - y - - -
    -

    Divisor

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - mod(_:) - -
    -
    -
    -
    -
    -
    -

    Modulus - BInt parameter

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func mod(_ x: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - x - - -
    -

    Divisor

    -
    -
    -
    -
    -

    Return Value

    -

    self mod x, a non-negative value

    -
    -
    -
    -
    • -
  • -
    - - - - mod(_:) - -
    -
    -
    -
    -
    -
    -

    Modulus - Int parameter

    -
    -

    Precondition

    - Divisor is not zero - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func mod(_ x: Int) -> Int
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - x - - -
    -

    Divisor

    -
    -
    -
    -
    -

    Return Value

    -

    self mod x, a non-negative value

    -
    -
    -
    -
    • -
  • -
    - - - - modInverse(_:) - -
    -
    -
    -
    -
    -
    -

    Inverse modulus - BInt parameter

    -
    -

    Precondition

    - self and modulus are coprime, modulus is positive - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func modInverse(_ m: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - m - - -
    -

    Modulus

    -
    -
    -
    -
    -

    Return Value

    -

    If self and m are coprime, x such that (self * x) mod m = 1

    -
    -
    -
    -
    • -
  • -
    - - - - modInverse(_:) - -
    -
    -
    -
    -
    -
    -

    Inverse modulus - Int parameter

    -
    -

    Precondition

    - self and modulus are coprime, modulus is positive - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func modInverse(_ m: Int) -> Int
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - m - - -
    -

    Modulus

    -
    -
    -
    -
    -

    Return Value

    -

    If self and m are coprime, x such that (self * x) mod m = 1

    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Exponentiation functions -

-
-
-
    -
  • -
    - - - - **(_:_:) - -
    -
    -
    -
    -
    -
    -

    Exponentiation

    -
    -

    Precondition

    - Exponent is non-negative - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func ** (a: BInt, x: Int) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - a - - -
    -

    Operand

    -
    -
    - - x - - -
    -

    Non-negative exponent

    -
    -
    -
    -
    -

    Return Value

    -

    a^x

    -
    -
    -
    -
    • -
  • -
    - - - - expMod(_:_:) - -
    -
    -
    -
    -
    -
    -

    Modular exponentiation - BInt modulus

    -
    -

    Precondition

    - Modulus is positive - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func expMod(_ x: BInt, _ m: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    The exponent

    -
    -
    - - m - - -
    -

    The modulus, a positive number

    -
    -
    -
    -
    -

    Return Value

    -

    (self^x) mod m for positive x, ((self^-x) mod m) modInverse m for negative x

    -
    -
    -
    -
    • -
  • -
    - - - - expMod(_:_:) - -
    -
    -
    -
    -
    -
    -

    Modular exponentiation - Int modulus

    -
    -

    Precondition

    - Modulus is positive - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func expMod(_ x: BInt, _ m: Int) -> Int
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    The exponent

    -
    -
    - - m - - -
    -

    The modulus, a positive integer

    -
    -
    -
    -
    -

    Return Value

    -

    (self^x) mod m for positive x, ((self^-x) mod m) modInverse m for negative x

    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Comparison functions -

-
-
-
    -
  • -
    - - - - ==(_:_:) - -
    -
    -
    -
    -
    -
    -

    Equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func == (x: BInt, y: BInt) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x = y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - ==(_:_:) - -
    -
    -
    -
    -
    -
    -

    Equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func == (x: BInt, y: Int) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x = y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - ==(_:_:) - -
    -
    -
    -
    -
    -
    -

    Equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func == (x: Int, y: BInt) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x = y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - !=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Not equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func != (x: BInt, y: BInt) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x != y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - !=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Not equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func != (x: BInt, y: Int) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x != y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - !=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Not equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func != (x: Int, y: BInt) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x != y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - <(_:_:) - -
    -
    -
    -
    -
    -
    -

    Less than

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func < (x: BInt, y: BInt) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x < y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - <(_:_:) - -
    -
    -
    -
    -
    -
    -

    Less than

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func < (x: BInt, y: Int) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x < y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - <(_:_:) - -
    -
    -
    -
    -
    -
    -

    Less than

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func < (x: Int, y: BInt) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x < y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - >(_:_:) - -
    -
    -
    -
    -
    -
    -

    Greater than

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func > (x: BInt, y: BInt) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x > y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - >(_:_:) - -
    -
    -
    -
    -
    -
    -

    Greater than

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func > (x: Int, y: BInt) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x > y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - >(_:_:) - -
    -
    -
    -
    -
    -
    -

    Greater than

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func > (x: BInt, y: Int) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x > y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - <=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Less than or equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func <= (x: BInt, y: BInt) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x <= y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - <=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Less than or equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func <= (x: Int, y: BInt) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x <= y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - <=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Less than or equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func <= (x: BInt, y: Int) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x <= y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - >=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Greater than or equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func >= (x: BInt, y: BInt) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x >= y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - >=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Greater than or equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func >= (x: Int, y: BInt) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x >= y, false otherwise

    -
    -
    -
    -
    • -
  • -
    - - - - >=(_:_:) - -
    -
    -
    -
    -
    -
    -

    Greater than or equal

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func >= (x: BInt, y: Int) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    First operand

    -
    -
    - - y - - -
    -

    Second operand

    -
    -
    -
    -
    -

    Return Value

    -

    true if x >= y, false otherwise

    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Shift functions -

-
-
-
    -
  • -
    - - - - <<(_:_:) - -
    -
    -
    -
    -
    -
    -

    Logical left shift

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func << (x: BInt, n: Int) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Operand

    -
    -
    - - n - - -
    -

    Shift count

    -
    -
    -
    -
    -

    Return Value

    -

      -
    • BInt(x.magnitude << n, x.isNegative) if n > 0
      • -
    • BInt(x.magnitude >> -n, x.isNegative) if n < 0
      • -
    • x if n = 0
      • -

    -
    -
    -
    -
    • -
  • -
    - - - - <<=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x << n

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func <<= (x: inout BInt, n: Int)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Operand

    -
    -
    - - n - - -
    -

    Shift count

    -
    -
    -
    -
    -
    -
    • -
  • -
    - - - - >>(_:_:) - -
    -
    -
    -
    -
    -
    -

    Logical right shift

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func >> (x: BInt, n: Int) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Operand

    -
    -
    - - n - - -
    -

    Shift count

    -
    -
    -
    -
    -

    Return Value

    -

      -
    • BInt(x.magnitude >> n, x.isNegative) if n > 0
      • -
    • BInt(x.magnitude << -n, x.isNegative) if n < 0
      • -
    • x if n = 0
      • -

    -
    -
    -
    -
    • -
  • -
    - - - - >>=(_:_:) - -
    -
    -
    -
    -
    -
    -

    x = x >> n

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func >>= (x: inout BInt, n: Int)
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - x - - -
    -

    Operand

    -
    -
    - - n - - -
    -

    Shift count

    -
    -
    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Prime number functions -

-
-
-
    -
  • -
    - - - - isProbablyPrime(_:) - -
    -
    -
    -
    -
    -
    -

    Checks whether self is prime using the Miller-Rabin algorithm

    -
    -

    Precondition

    - Probability parameter is positive - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func isProbablyPrime(_ p: Int = 30) -> Bool
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - p - - -
    -

    If true is returned, self is prime with probability > 1-½^p

    -
    -
    -
    -
    -

    Return Value

    -

    true if self is probably prime, false if self is definitely not prime

    -
    -
    -
    -
    • -
  • -
    - - - - nextPrime(_:) - -
    -
    -
    -
    -
    -
    -

    The next probable prime greater than self

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func nextPrime(_ p: Int = 30) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - p - - -
    -

    The returned number is prime with probability > 1-½^p, default value is 30

    -
    -
    -
    -
    -

    Return Value

    -

    The smallest probable prime greater than self, returns 2 if self is negative

    -
    -
    -
    -
    • -
  • -
    - - - - probablePrime(_:_:) - -
    -
    -
    -
    -
    -
    -

    A probable prime number with a given bitwidth

    -
    -

    Precondition

    - bitWidth > 1 - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func probablePrime(_ bitWidth: Int, _ p: Int = 30) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - bitWidth - - -
    -

    The bitWidth - must be > 1

    -
    -
    - - p - - -
    -

    The returned number is prime with probability > 1-½^p, default value is 30

    -
    -
    -
    -
    -

    Return Value

    -

    A prime number with the specified bitwidth and probability

    -
    -
    -
    -
    • -
  • -
    - - - - primorial(_:) - -
    -
    -
    -
    -
    -
    -

    Product of primes up to n

    -
    -

    Precondition

    - n >= 0 - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func primorial(_ n: Int) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - n - - -
    -

    number to compute primorial for

    -
    -
    -
    -
    -

    Return Value

    -

    The product of primes less than or equal to n

    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Root extraction functions -

-
-
-
    -
  • -
    - - - - root(_:) - -
    -
    -
    -
    -
    -
    -

    n'th root

    -
    -

    Precondition

    -
      -
    • self is non-negative or n is odd
      • -
    • n is positive
      • -
    - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func root(_ n: Int) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - n - - -
    -

    The root

    -
    -
    -
    -
    -

    Return Value

    -

    The integer part of the n'th root of self

    -
    -
    -
    -
    • -
  • -
    - - - - rootRemainder(_:) - -
    -
    -
    -
    -
    -
    -

    n'th root and remainder

    -
    -

    Precondition

    -
      -
    • self is non-negative or n is odd
      • -
    • n is positive
      • -
    - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func rootRemainder(_ n: Int) -> (root: BInt, rem: BInt)
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - n - - -
    -

    The root

    -
    -
    -
    -
    -

    Return Value

    -

    root = the integer part of the n'th root of self, rem = self - root^n

    -
    -
    -
    -
    • -
  • -
    - - - - isPerfectRoot() - -
    -
    -
    -
    -
    -
    -

    Check whether self is a perfect root, that is, for some integer x and n > 1 self = x^n

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func isPerfectRoot() -> Bool
    - -
    -
    -
    -

    Return Value

    -

    true iff self is a perfect root

    -
    -
    -
    -
    • -
  • -
    - - - - sqrt() - -
    -
    -
    -
    -
    -
    -

    Square root of a non-negative number

    -
    -

    Precondition

    - self is non-negative - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func sqrt() -> BInt
    - -
    -
    -
    -

    Return Value

    -

    The integer part of the square root of self

    -
    -
    -
    -
    • -
  • -
    - - - - sqrtRemainder() - -
    -
    -
    -
    -
    -
    -

    Square root and remainder of a non-negative number

    -
    -

    Precondition

    - self is non-negative - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func sqrtRemainder() -> (root: BInt, rem: BInt)
    - -
    -
    -
    -

    Return Value

    -

    root = the integer part of the square root of self, rem = self - root^2

    -
    -
    -
    -
    • -
  • -
    - - - - isPerfectSquare() - -
    -
    -
    -
    -
    -
    -

    Check whether self is a perfect square, that is, for some integer x self = x^2

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func isPerfectSquare() -> Bool
    - -
    -
    -
    -

    Return Value

    -

    true iff self is a perfect square

    -
    -
    -
    -
    • -
  • -
    - - - - sqrtMod(_:) - -
    -
    -
    -
    -
    -
    -

    Square root modulo a prime number - BInt prime

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func sqrtMod(_ p: BInt) -> BInt?
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - p - - -
    -

    An odd prime number

    -
    -
    -
    -
    -

    Return Value

    -

    x, such that x^2 = self (mod p), or nil if no such x exists

    -
    -
    -
    -
    • -
  • -
    - - - - sqrtMod(_:) - -
    -
    -
    -
    -
    -
    -

    Square root modulo a prime number - Int prime

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func sqrtMod(_ p: Int) -> Int?
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - p - - -
    -

    An odd prime number

    -
    -
    -
    -
    -

    Return Value

    -

    x, such that x^2 = self (mod p), or nil if no such x exists

    -
    -
    -
    -
    • -
-
-
-
- - -
- -

Miscellaneous functions -

-
-
-
    -
  • -
    - - - - binomial(_:_:) - -
    -
    -
    -
    -
    -
    -

    Compute binomial coefficient n over k

    -
    -

    Precondition

    - n >= k and k >= 0 - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func binomial(_ n: Int, _ k: Int) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - - - - - -
    - - n - - -
    -

    First binomial parameter

    -
    -
    - - k - - -
    -

    Second binomial parameter

    -
    -
    -
    -
    -

    Return Value

    -

    Binomial coefficient n over k

    -
    -
    -
    -
    • -
  • -
    - - - - factorial(_:) - -
    -
    -
    -
    -
    -
    -

    Factorial function

    -
    -

    Precondition

    - n >= 0 - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func factorial(_ n: Int) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - n - - -
    -

    Number to compute factorial for

    -
    -
    -
    -
    -

    Return Value

    -

    n!

    -
    -
    -
    -
    • -
  • -
    - - - - fibonacci(_:) - -
    -
    -
    -
    -
    -
    -

    n'th Fibonacci number

    -
    -

    Precondition

    - n >= 0 - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func fibonacci(_ n: Int) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - n - - -
    -

    The fibonacci index

    -
    -
    -
    -
    -

    Return Value

    -

    The n'th fibonacci number

    -
    -
    -
    -
    • -
  • -
    - - - - fibonacci2(_:) - -
    -
    -
    -
    -
    -
    -

    Fibonacci pair, n'th and n'th + 1 Fibonacci number

    - -

    Precondition: n >= 0

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func fibonacci2(_ n: Int) -> (BInt, BInt)
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - n - - -
    -

    The fibonacci index

    -
    -
    -
    -
    -

    Return Value

    -

    The n'th and n'th + 1 fibonacci number

    -
    -
    -
    -
    • -
  • -
    - - - - gcd(_:) - -
    -
    -
    -
    -
    -
    -

    Greatest common divisor

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func gcd(_ x: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - x - - -
    -

    Operand

    -
    -
    -
    -
    -

    Return Value

    -

    Greatest common divisor of self and x

    -
    -
    -
    -
    • -
  • -
    - - - - gcdExtended(_:) - -
    -
    -
    -
    -
    -
    -

    Extended greatest common divisor

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func gcdExtended(_ x: BInt) -> (g: BInt, a: BInt, b: BInt)
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - x - - -
    -

    Operand

    -
    -
    -
    -
    -

    Return Value

    -

    Greatest common divisor g of self and x, and a and b such that a * self + b * x = g

    -
    -
    -
    -
    • -
  • -
    - - - - jacobiSymbol(_:) - -
    -
    -
    -
    -
    -
    -

    Jacobi symbol - BInt parameter. If m is an odd prime, this is also the Legendre symbol

    -
    -

    Precondition

    - m is positive and odd - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func jacobiSymbol(_ m: BInt) -> Int
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - m - - -
    -

    A positive, odd integer

    -
    -
    -
    -
    -

    Return Value

    -

    The Jacobi symbol of self and m: -1, 0, or 1

    -
    -
    -
    -
    • -
  • -
    - - - - jacobiSymbol(_:) - -
    -
    -
    -
    -
    -
    -

    Jacobi symbol - Int parameter. If m is an odd prime, this is also the Legendre symbol

    -
    -

    Precondition

    - m is positive and odd - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func jacobiSymbol(_ m: Int) -> Int
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - m - - -
    -

    A positive, odd integer

    -
    -
    -
    -
    -

    Return Value

    -

    The Jacobi symbol of self and m: -1, 0, or 1

    -
    -
    -
    -
    • -
  • -
    - - - - kroneckerSymbol(_:) - -
    -
    -
    -
    -
    -
    -

    Kronecker symbol - BInt parameter. If m is positive and odd, this is also the Jacobi symbol

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func kroneckerSymbol(_ m: BInt) -> Int
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - m - - -
    -

    An integer value

    -
    -
    -
    -
    -

    Return Value

    -

    The Kronecker symbol of self and m: -1, 0, or 1

    -
    -
    -
    -
    • -
  • -
    - - - - kroneckerSymbol(_:) - -
    -
    -
    -
    -
    -
    -

    Kronecker symbol - Int parameter. If m is positive and odd, this is also the Jacobi symbol

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func kroneckerSymbol(_ m: Int) -> Int
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - m - - -
    -

    An integer value

    -
    -
    -
    -
    -

    Return Value

    -

    The Kronecker symbol of self and m: -1, 0, or 1

    -
    -
    -
    -
    • -
  • -
    - - - - lcm(_:) - -
    -
    -
    -
    -
    -
    -

    Least common multiple

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public func lcm(_ x: BInt) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - x - - -
    -

    Operand

    -
    -
    -
    -
    -

    Return Value

    -

    Least common multiple of self and x - a non-negative number

    -
    -
    -
    -
    • -
  • -
    - - - - lucas(_:) - -
    -
    -
    -
    -
    -
    -

    n'th Lucas number

    -
    -

    Precondition

    - n >= 0 - -
    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func lucas(_ n: Int) -> BInt
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - n - - -
    -

    The lucas index

    -
    -
    -
    -
    -

    Return Value

    -

    The n'th lucas number

    -
    -
    -
    -
    • -
  • -
    - - - - lucas2(_:) - -
    -
    -
    -
    -
    -
    -

    Lucas pair, n'th and n'th + 1 Lucas number

    - -

    Precondition: n >= 0

    - -
    -
    -

    Declaration

    -
    -

    Swift

    - 
    public static func lucas2(_ n: Int) -> (BInt, BInt)
    - -
    -
    -
    -

    Parameters

    - - - - - - - -
    - - n - - -
    -

    The lucas index

    -
    -
    -
    -
    -

    Return Value

    -

    The n'th and n'th + 1 lucas number

    -
    -
    -
    -
    • -
  • -
    - - - - randomLessThan() - -
    -
    -
    -
    -
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    Random value

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    Precondition

    - self is positive - -
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    Declaration

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    public func randomLessThan() -> BInt
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    Return Value

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    A random value < absolute value of self

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- - diff --git a/docs/docsets/BigInt.docset/Contents/Resources/Documents/Structs/CRT.html b/docs/docsets/BigInt.docset/Contents/Resources/Documents/Structs/CRT.html deleted file mode 100644 index 8b112b1..0000000 --- a/docs/docsets/BigInt.docset/Contents/Resources/Documents/Structs/CRT.html +++ /dev/null @@ -1,342 +0,0 @@ - - - - CRT Structure Reference - - - - - - - - - - - - - -
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BigInt Docs (100% documented)

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CRT

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public struct CRT
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CRT instances implement the Chinese Remainder Theorem

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Create an instance from a given set of moduli which fullfill the following conditions:

- -
    -
  • at least two moduli
    • -
  • all moduli are positive
    • -
  • the moduli are pairwise coprime
    • -
- -

Then use the compute method to compute the CRT value for a given set of residues. -The same CRT instance can be used for different inputs, as long as the moduli are the same.

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Initializers -

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    Constructs a CRT instance from the moduli - BInt version

    - -
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    Declaration

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    public init?(_ m: [BInt])
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    Parameters

    - - - - - - - -
    - - m - - -
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    The moduli

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    Return Value

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    The CRT instance for the moduli, nil if they do not fullfill the conditions

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    Constructs a CRT instance from the moduli - Int version

    - -
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    Declaration

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    public init?(_ m: [Int])
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    Parameters

    - - - - - - - -
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    The moduli

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    Return Value

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    The CRT instance for the moduli, nil if they do not fullfill the conditions

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Instance methods -

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    Compute the CRT value - BInt version

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    Precondition

    - r.count = number of moduli - -
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    Declaration

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    public func compute(_ r: [BInt]) -> BInt
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    Parameters

    - - - - - - - -
    - - r - - -
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    The residues

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    Return Value

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    The CRT value

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    - - - - compute(_:) - -
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    Compute the CRT value - Int version

    -
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    Precondition

    - r.count = number of moduli - -
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    Declaration

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    Swift

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    public func compute(_ r: [Int]) -> BInt
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    Parameters

    - - - - - - - -
    - - r - - -
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    The residues

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    Return Value

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    The CRT value

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- - diff --git a/docs/docsets/BigInt.docset/Contents/Resources/Documents/Typealiases.html b/docs/docsets/BigInt.docset/Contents/Resources/Documents/Typealiases.html deleted file mode 100644 index b52857b..0000000 --- a/docs/docsets/BigInt.docset/Contents/Resources/Documents/Typealiases.html +++ /dev/null @@ -1,200 +0,0 @@ - - - - Type Aliases Reference - - - - - - - - - - - - - -
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BigInt Docs (100% documented)

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Type Aliases

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The following type aliases are available globally.

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    Unsigned 8 bit value

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    - - - - Bytes - -
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    Array of unsigned 8 bit values

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    Declaration

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    - - - - Limb - -
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    Unsigned 64 bit value

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    Declaration

    -
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    public typealias Limb = UInt64
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    - - - - Limbs - -
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    Array of unsigned 64 bit values

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    Declaration

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    public typealias Limbs = [UInt64]
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BigInt Docs (100% documented)

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BigInt

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Contents:

- - - -

The BigInt package provides arbitrary-precision integer arithmetic in Swift. -Its functionality falls in the following categories:

- -
    -
  • Arithmetic: add, subtract, multiply, divide, remainder and exponentiation
    • -
  • Comparison: the six standard operations == != < <= > >=
    • -
  • Shifting: logical left shift and rigth shift
    • -
  • Logical: bitwise and, or, xor, and not
    • -
  • Modulo: normal modulus, inverse modulus, and modular exponentiation
    • -
  • Conversion: to double, to integer, to string, to magnitude byte array, and to 2’s complement byte array
    • -
  • Primes: prime number testing, probable prime number generation and primorial
    • -
  • Miscellaneous: random number generation, greatest common divisor, least common multiple, n-th root, square root modulo an odd prime, -Jacobi symbol, Kronecker symbol, Factorial function, Binomial function, Fibonacci numbers, Lucas numbers and Bernoulli numbers
    • -
  • Fractions: Standard arithmetic on fractions whose numerators and denominators are of unbounded size
    • -
- -

BigInt requires Swift 5.0. It also requires that the Int and UInt types be 64 bit types.

- -

Usage

- -

In your projects Package.swift file add a dependency like

-
  dependencies: [
-  .package(url: "https://github.com/leif-ibsen/BigInt", from: "1.14.0"),
-  ]
-
- -

Examples

- -

Creating BInt’s

-
  // From an integer
-  let a = BInt(27)
-
-  // From a decimal value
-  let x = BInt(1.12345e30) // x = 1123450000000000064996914495488
-
-  // From string literals
-  let b = BInt("123456789012345678901234567890")!
-  let c = BInt("1234567890abcdef1234567890abcdef", radix: 16)!
-
-  // From magnitude and sign
-  let m: Limbs = [1, 2, 3]
-  let d = BInt(m) // d = 1020847100762815390427017310442723737601
-  let e = BInt(m, true) // e = -1020847100762815390427017310442723737601
-
-  // From a big-endian 2's complement byte array
-  let f = BInt(signed: [255, 255, 127]) // f = -129
-
-  // From a big-endian magnitude byte array
-  let g = BInt(magnitude: [255, 255, 127]) // g = 16777087
-
-  // Random value with specified bitwidth
-  let h = BInt(bitWidth: 43) // For example h = 3965245974702 (=0b111001101100111011000100111110100010101110)
-
-  // Random value less than a given value
-  let i = h.randomLessThan() // For example i = 583464003284
-
- -

Converting BInt’s

-
  let x = BInt(16777087)
-
-  // To double
-  let d = x.asDouble() // d = 16777087.0
-
-  // To strings
-  let s1 = x.asString() // s1 = "16777087"
-  let s2 = x.asString(radix: 16) // s2 = "ffff7f"
-
-  // To big-endian magnitude byte array
-  let b1 = x.asMagnitudeBytes() // b1 = [255, 255, 127]
-
-  // To big-endian 2's complement byte array
-  let b2 = x.asSignedBytes() // b2 = [0, 255, 255, 127]
-
- -

Performance

- -

To assess the performance of BigInt, the execution times for a number of common operations were measured on an iMac 2021, Apple M1 chip. -The results are in the table below. It shows the operation being measured and the time it took (in microseconds or milliseconds).

- -

Four large numbers ‘a1000’, ‘b1000’, ‘c2000’ and ‘p1000’ were used throughout the measurements. Their actual values are shown under the table.

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OperationSwift codeTime
As stringc2000.asString()13 uSec
As signed bytesc2000.asSignedBytes()0.30 uSec
Bitwise anda1000 & b10000.083 uSec
Bitwise ora1000 | b10000.083 uSec
Bitwise xora1000 ^ b10000.082 uSec
Bitwise not~c20000.087 uSec
Test bitc2000.testBit(701)0.017 uSec
Flip bitc2000.flipBit(701)0.018 uSec
Set bitc2000.setBit(701)0.018 uSec
Clear bitc2000.clearBit(701)0.018 uSec
Additiona1000 + b10000.07 uSec
Subtractiona1000 - b10000.08 uSec
Multiplicationa1000 * b10000.32 uSec
Divisionc2000 / a10002.2 uSec
Modulusc2000.mod(a1000)2.2 uSec
Inverse modulusc2000.modInverse(p1000)83 uSec
Modular exponentiationa1000.expMod(b1000, c2000)3.5 mSec
Equalc2000 + 1 == c20000.017 uSec
Less thanb1000 + 1 < b10000.021 uSec
Shift 1 leftc2000 <<= 10.05 uSec
Shift 1 rightc2000 >>= 10.06 uSec
Shift 100 leftc2000 <<= 1000.14 uSec
Shift 100 rightc2000 >>= 1000.11 uSec
Is probably primep1000.isProbablyPrime()5.8 mSec
Make probable 1000 bit primeBInt.probablePrime(1000)60 mSec
Next probable primec2000.nextPrime()730 mSec
PrimorialBInt.primorial(100000)8.5 mSec
BinomialBInt.binomial(100000, 10000)22 mSec
FactorialBInt.factorial(100000)57 mSec
FibonacciBInt.fibonacci(100000)0.22 mSec
Greatest common divisora1000.gcd(b1000)29 uSec
Extended gcda1000.gcdExtended(b1000)81 uSec
Least common multiplea1000.lcm(b1000)32 uSec
Make random numberc2000.randomLessThan()1.2 uSec
Squarec2000 ** 20.68 uSec
Square rootc2000.sqrt()13 uSec
Square root and remainderc2000.sqrtRemainder()13 uSec
Is perfect square(c2000 * c2000).isPerfectSquare()16 uSec
Square root modulob1000.sqrtMod(p1000)1.6 mSec
Powerc2000 ** 1111.9 mSec
Rootc2000.root(111)15 uSec
Root and remainderc2000.rootRemainder(111)17 uSec
Is perfect rootc2000.isPerfectRoot()13 mSec
Jacobi symbolc2000.jacobiSymbol(p1000)0.15 mSec
Kronecker symbolc2000.kroneckerSymbol(p1000)0.15 mSec
Bernoulli numberBFraction.bernoulli(1000)83 mSec
- -

a1000 = 3187705437890850041662973758105262878153514794996698172406519277876060364087986868049465132757493318066301987043192958841748826350731448419937544810921786918975580180410200630645469411588934094075222404396990984350815153163569041641732160380739556436955287671287935796642478260435292021117614349253825
-b1000 = 9159373012373110951130589007821321098436345855865428979299172149373720601254669552044211236974571462005332583657082428026625366060511329189733296464187785766230514564038057370938741745651937465362625449921195096442684523511715110908407508139315000469851121118117438147266381183636498494901233452870695
-c2000 = 1190583332681083129323588684910845359379915367459759242106618067261956856381281184752008892106576666833853411939711280970145570546868549934865719229538926506588929417873149597614787608112658086250354719939407543740242931571462165384138560315454455247539461818779966171917173966217706187439870264672508450210272481951994459523586160979759782950984370978171111340529321052541588344733968902238813379990628157732181128074253104347868153860527298911917508606081710893794973605227829729403843750412766366804402629686458092685235454222856584200220355212623917637542398554907364450159627359316156463617143173
-p1000 (probably a prime) = 7662841304438384296568220077355872003841475576593385710590818274399706072141018649398767137142090308734613594718593893634649122767374115742644499040193270857876678047220373151142747088797516044505739487695946446362769947024029728822155570722524629197074319602110260674029276185098937139753025851896997

- -

Fractions

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Fractions are represented as BFraction values consisting of a numerator BInt value and a denominator BInt value. The representation is normalized:

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    -
  • The numerator and denominator have no common factors except 1
    • -
  • The denominator is always positive
    • -
  • Zero is represented as 0/1
    • -
- -

Creating BFraction’s

- -

Fractions are created by

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  • Specifying the numerator and denominator explicitly f.ex. BFraction(17, 4)
    • -
  • Specifying the decimal value explictly f.ex. BFraction(4.25)
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  • Using a string representation f.ex. BFraction(“4.25”)! or equivalently BFraction(“425E-2”)!
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  • Specifying a continued fraction like BFraction([3, 4, 12, 4]) equivalent to 649 / 200
    • -
- -

Defining a fraction by giving its decimal value (like 4.25) might lead to surprises, -because not all decimal values can be represented exactly as a floating point number. -For example, one might think that BFraction(0.1) would equal 1/10, -but in fact it equals 3602879701896397 / 36028797018963968 = 0.1000000000000000055511151231257827021181583404541015625

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Converting BFraction’s

- -

BFraction values can be converted to String values, to decimal String values, to Double values and to Continued Fraction values.

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  let x = BFraction(1000, 7)
-
-  // To String
-  let s1 = x.asString() // s1 = "1000 / 7"
-
-  // To decimal String
-  let s1 = x.asDecimalString(precision: 8, exponential: false) // s1 = "142.85714"
-  let s2 = x.asDecimalString(precision: 8, exponential: true) // s2 = "1.4285714E+2"
-
-  // To Double
-  let d = x.asDouble() // d = 142.8571428571429
-
-  // To Continued Fraction
-  let f = x.asContinuedFraction() // f = [BInt(142), BInt(1), BInt(6)]
-
- -

Operations

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The operations available to fractions are:

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    -
  • Arithmetic -
      -
    • addition
      • -
    • subtraction
      • -
    • multiplication
      • -
    • division
      • -
    • modulo an integer
      • -
    • exponentiation
      • -
    - -

    • -
  • Rounding to an integer

    - -
      -
    • round - to nearest integer
      • -
    • truncate - towards 0
      • -
    • ceil - towards +infinity
      • -
    • floor - towards -infinity
      • -
    - -

    • -
  • Comparison - the six standard operations == != < <= > >=
    • -

- -

Bernoulli Numbers

- -

The static function

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let bn = BFraction.bernoulli(n)
-
- -

computes the n'th (n >= 0) Bernoulli number, which is a rational number.
-For example

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print(BFraction.bernoulli(60))
-print(BFraction.bernoulli(60).asDecimalString(precision: 20, exponential: true))
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- -

would print

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-1215233140483755572040304994079820246041491 / 56786730
--2.1399949257225333665E+34
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- -

The static function

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let x = BFraction.bernoulliSequence(n)
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- -

computes the n even numbered Bernoulli numbers B(0), B(2) … B(2 * n - 2).

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Harmonic Numbers

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The static function

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let Hn = BFraction.harmonic(n)
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- -

computes the n'th harmonic number, that is, 1 + ½ + … + 1/n
-The static function

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let x = BFraction.harmonicSequence(n)
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- -

returns an array containing the first n harmonic numbers.

- -

Chinese Remainder Theorem

- -

The CRT structure implements the Chinese Remainder Theorem. Construct a CRT instance from a given set of moduli, -and then use the compute method to compute the CRT value for a given set of residues. The same instance can be reused -for any set of input data, as long as the moduli are the same. -This is relevant because it takes longer time to create the CRT instance than to compute the CRT value.
-For example

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let moduli = [3, 5, 7]
-let residues = [2, 2, 6]
-let crt = CRT(moduli)!
-print("CRT value:", crt.compute(residues))
-
- -

would print

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CRT value: 62
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- -

References

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Algorithms from the following books and papers have been used in the implementation. -There are references in the source code where appropriate.

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    -
  • [BRENT] - Brent and Zimmermann: Modern Computer Arithmetic, 2010
    • -
  • [BURNIKEL] - Burnikel and Ziegler: Fast Recursive Division, October 1998
    • -
  • [CRANDALL] - Crandall and Pomerance: Prime Numbers - A Computational Perspective. Second Edition, Springer 2005
    • -
  • [GRANLUND] - Moller and Granlund: Improved Division by Invariant Integers, 2011
    • -
  • [HACKER] - Henry S. Warren, Jr.: Hacker’s Delight. Second Edition, Addison-Wesley
    • -
  • [HANDBOOK] - Menezes, Oorschot, Vanstone: Handbook of Applied Cryptography. CRC Press 1996
    • -
  • [JEBELEAN] - Tudor Jebelean: An Algorithm for Exact Division. Journal of Symbolic Computation, volume 15, 1993
    • -
  • [KNUTH] - Donald E. Knuth: Seminumerical Algorithms, Third Edition
    • -
  • [KOC] - Cetin Kaya Koc: A New Algorithm for Inversion mod p^k
    • -
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Algorithms

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Some of the algorithms used in BigInt are described below.

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Multiplication

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  • Schonhage-Strassen FFT based algorithm for numbers above 384000 bits
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  • ToomCook-3 algorithm for numbers above 12800 bits
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  • Karatsuba algorithm for numbers above 6400 bits
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  • Basecase - Knuth algorithm M
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Division and Remainder

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  • Burnikel-Ziegler algorithm for divisors above 3840 bits provided the dividend has at least 3840 bits more than the divisor
    • -
  • Basecase - Knuth algorithm D
    • -
  • Exact Division - Jebelean’s exact division algorithm
    • -
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Greatest Common Divisor and Extended Greatest Common Divisor

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Lehmer’s algorithm [KNUTH] chapter 4.5.2, with binary GCD basecase.

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Modular Exponentiation

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Sliding window algorithm 14.85 from [HANDBOOK] using Barrett reduction for exponents with fewer than 2048 bits -and Montgomery reduction for larger exponents.

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Inverse Modulus

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If the modulus is a (not too large) power of 2, the algorithm from [KOC] section 7. -Else, it is computed via the extended GCD algorithm.

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Square Root

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Algorithm 1.12 (SqrtRem) from [BRENT] with algorithm 9.2.11 from [CRANDALL] as basecase.

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Square Root Modulo a Prime Number

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Algorithm 2.3.8 from [CRANDALL].

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Prime Number Test

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Miller-Rabin test.

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Prime Number Generation

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The algorithm from Java BigInteger translated to Swift.

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Factorial

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The ‘SplitRecursive’ algorithm from Peter Luschny: https://www.luschny.de

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Fibonacci

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The ‘fastDoubling’ algorithm from Project Nayuki: https://www.nayuki.io

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Jacobi and Kronecker symbols

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Algorithm 2.3.5 from [CRANDALL].

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Bernoulli Numbers

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Computed via Tangent numbers which is fast because it only involves integer arithmetic -but no fractional arithmetic.

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Chinese Remainder Theorem

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The Garner algorithm 2.1.7 from [CRANDALL].

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- -
-
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"" : s + ""; - }, - bind: $.proxy, - each: function(collection, cb) { - $.each(collection, reverseArgs); - function reverseArgs(index, value) { - return cb(value, index); - } - }, - map: $.map, - filter: $.grep, - every: function(obj, test) { - var result = true; - if (!obj) { - return result; - } - $.each(obj, function(key, val) { - if (!(result = test.call(null, val, key, obj))) { - return false; - } - }); - return !!result; - }, - some: function(obj, test) { - var result = false; - if (!obj) { - return result; - } - $.each(obj, function(key, val) { - if (result = test.call(null, val, key, obj)) { - return false; - } - }); - return !!result; - }, - mixin: $.extend, - identity: function(x) { - return x; - }, - clone: function(obj) { - return $.extend(true, {}, obj); - }, - getIdGenerator: function() { - var counter = 0; - return function() { - return counter++; - }; - }, - templatify: function templatify(obj) { - return $.isFunction(obj) ? obj : template; - function template() { - return String(obj); - } - }, - defer: function(fn) { - setTimeout(fn, 0); - }, - debounce: function(func, wait, immediate) { - var timeout, result; - return function() { - var context = this, args = arguments, later, callNow; - later = function() { - timeout = null; - if (!immediate) { - result = func.apply(context, args); - } - }; - callNow = immediate && !timeout; - clearTimeout(timeout); - timeout = setTimeout(later, wait); - if (callNow) { - result = func.apply(context, args); - } - return result; - }; - }, - throttle: function(func, wait) { - var context, args, timeout, result, previous, later; - previous = 0; - later = function() { - previous = new Date(); - timeout = null; - result = func.apply(context, args); - }; - return function() { - var now = new Date(), remaining = wait - (now - previous); - context = this; - args = arguments; - if (remaining <= 0) { - clearTimeout(timeout); - timeout = null; - previous = now; - result = func.apply(context, args); - } else if (!timeout) { - timeout = setTimeout(later, remaining); - } - return result; - }; - }, - stringify: function(val) { - return _.isString(val) ? val : JSON.stringify(val); - }, - guid: function() { - function _p8(s) { - var p = (Math.random().toString(16) + "000000000").substr(2, 8); - return s ? "-" + p.substr(0, 4) + "-" + p.substr(4, 4) : p; - } - return "tt-" + _p8() + _p8(true) + _p8(true) + _p8(); - }, - noop: function() {} - }; - }(); - var WWW = function() { - "use strict"; - var defaultClassNames = { - wrapper: "twitter-typeahead", - input: "tt-input", - hint: "tt-hint", - menu: "tt-menu", - dataset: "tt-dataset", - suggestion: "tt-suggestion", - selectable: "tt-selectable", - empty: "tt-empty", - open: "tt-open", - cursor: "tt-cursor", - highlight: "tt-highlight" - }; - return build; - function build(o) { - var www, classes; - classes = _.mixin({}, defaultClassNames, o); - www = { - css: buildCss(), - classes: classes, - html: buildHtml(classes), - selectors: buildSelectors(classes) - }; - return { - css: www.css, - html: www.html, - classes: www.classes, - selectors: www.selectors, - mixin: function(o) { - _.mixin(o, www); - } - }; - } - function buildHtml(c) { - return { - wrapper: '', - menu: '
' - }; - } - function buildSelectors(classes) { - var selectors = {}; - _.each(classes, function(v, k) { - selectors[k] = "." + v; - }); - return selectors; - } - function buildCss() { - var css = { - wrapper: { - position: "relative", - display: "inline-block" - }, - hint: { - position: "absolute", - top: "0", - left: "0", - borderColor: "transparent", - boxShadow: "none", - opacity: "1" - }, - input: { - position: "relative", - verticalAlign: "top", - backgroundColor: "transparent" - }, - inputWithNoHint: { - position: "relative", - verticalAlign: "top" - }, - menu: { - position: "absolute", - top: "100%", - left: "0", - zIndex: "100", - display: "none" - }, - ltr: { - left: "0", - right: "auto" - }, - rtl: { - left: "auto", - right: " 0" - } - }; - if (_.isMsie()) { - _.mixin(css.input, { - backgroundImage: "url(data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)" - }); - } - return css; - } - }(); - var EventBus = function() { - "use strict"; - var namespace, deprecationMap; - namespace = "typeahead:"; - deprecationMap = { - render: "rendered", - cursorchange: "cursorchanged", - select: "selected", - autocomplete: "autocompleted" - }; - function EventBus(o) { - if (!o || !o.el) { - $.error("EventBus initialized without el"); - } - this.$el = $(o.el); - } - _.mixin(EventBus.prototype, { - _trigger: function(type, args) { - var $e = $.Event(namespace + type); - this.$el.trigger.call(this.$el, $e, args || []); - return $e; - }, - before: function(type) { - var args, $e; - args = [].slice.call(arguments, 1); - $e = this._trigger("before" + type, args); - return $e.isDefaultPrevented(); - }, - trigger: function(type) { - var deprecatedType; - this._trigger(type, [].slice.call(arguments, 1)); - if (deprecatedType = deprecationMap[type]) { - this._trigger(deprecatedType, [].slice.call(arguments, 1)); - } - } - }); - return EventBus; - }(); - var EventEmitter = function() { - "use strict"; - var splitter = /\s+/, nextTick = getNextTick(); - return { - onSync: onSync, - onAsync: onAsync, - off: off, - trigger: trigger - }; - function on(method, types, cb, context) { - var type; - if (!cb) { - return this; - } - types = types.split(splitter); - cb = context ? bindContext(cb, context) : cb; - this._callbacks = this._callbacks || {}; - while (type = types.shift()) { - this._callbacks[type] = this._callbacks[type] || { - sync: [], - async: [] - }; - this._callbacks[type][method].push(cb); - } - return this; - } - function onAsync(types, cb, context) { - return on.call(this, "async", types, cb, context); - } - function onSync(types, cb, context) { - return on.call(this, "sync", types, cb, context); - } - function off(types) { - var type; - if (!this._callbacks) { - return this; - } - types = types.split(splitter); - while (type = types.shift()) { - delete this._callbacks[type]; - } - return this; - } - function trigger(types) { - var type, callbacks, args, syncFlush, asyncFlush; - if (!this._callbacks) { - return this; - } - types = types.split(splitter); - args = [].slice.call(arguments, 1); - while ((type = types.shift()) && (callbacks = this._callbacks[type])) { - syncFlush = getFlush(callbacks.sync, this, [ type ].concat(args)); - asyncFlush = getFlush(callbacks.async, this, [ type ].concat(args)); - syncFlush() && nextTick(asyncFlush); - } - return this; - } - function getFlush(callbacks, context, args) { - return flush; - function flush() { - var cancelled; - for (var i = 0, len = callbacks.length; !cancelled && i < len; i += 1) { - cancelled = callbacks[i].apply(context, args) === false; - } - return !cancelled; - } - } - function getNextTick() { - var nextTickFn; - if (window.setImmediate) { - nextTickFn = function nextTickSetImmediate(fn) { - setImmediate(function() { - fn(); - }); - }; - } else { - nextTickFn = function nextTickSetTimeout(fn) { - setTimeout(function() { - fn(); - }, 0); - }; - } - return nextTickFn; - } - function bindContext(fn, context) { - return fn.bind ? fn.bind(context) : function() { - fn.apply(context, [].slice.call(arguments, 0)); - }; - } - }(); - var highlight = function(doc) { - "use strict"; - var defaults = { - node: null, - pattern: null, - tagName: "strong", - className: null, - wordsOnly: false, - caseSensitive: false, - diacriticInsensitive: false - }; - var accented = { - A: "[AaªÀ-Åà-åĀ-ąǍǎȀ-ȃȦȧᴬᵃḀḁẚẠ-ảₐ℀℁℻⒜Ⓐⓐ㍱-㍴㎀-㎄㎈㎉㎩-㎯㏂㏊㏟㏿Ａａ]", - B: "[BbᴮᵇḂ-ḇℬ⒝Ⓑⓑ㍴㎅-㎇㏃㏈㏔㏝Ｂｂ]", - C: "[CcÇçĆ-čᶜ℀ℂ℃℅℆ℭⅭⅽ⒞Ⓒⓒ㍶㎈㎉㎝㎠㎤㏄-㏇Ｃｃ]", - D: "[DdĎďDŽ-džDZ-dzᴰᵈḊ-ḓⅅⅆⅮⅾ⒟Ⓓⓓ㋏㍲㍷-㍹㎗㎭-㎯㏅㏈Ｄｄ]", - E: "[EeÈ-Ëè-ëĒ-ěȄ-ȇȨȩᴱᵉḘ-ḛẸ-ẽₑ℡ℯℰⅇ⒠Ⓔⓔ㉐㋍㋎Ｅｅ]", - F: "[FfᶠḞḟ℉ℱ℻⒡Ⓕⓕ㎊-㎌㎙ff-fflＦｆ]", - G: "[GgĜ-ģǦǧǴǵᴳᵍḠḡℊ⒢Ⓖⓖ㋌㋍㎇㎍-㎏㎓㎬㏆㏉㏒㏿Ｇｇ]", - H: "[HhĤĥȞȟʰᴴḢ-ḫẖℋ-ℎ⒣Ⓗⓗ㋌㍱㎐-㎔㏊㏋㏗Ｈｈ]", - I: "[IiÌ-Ïì-ïĨ-İIJijǏǐȈ-ȋᴵᵢḬḭỈ-ịⁱℐℑℹⅈⅠ-ⅣⅥ-ⅨⅪⅫⅰ-ⅳⅵ-ⅸⅺⅻ⒤Ⓘⓘ㍺㏌㏕fiffiＩｉ]", - J: "[JjIJ-ĵLJ-njǰʲᴶⅉ⒥ⒿⓙⱼＪｊ]", - K: "[KkĶķǨǩᴷᵏḰ-ḵK⒦Ⓚⓚ㎄㎅㎉㎏㎑㎘㎞㎢㎦㎪㎸㎾㏀㏆㏍-㏏Ｋｋ]", - L: "[LlĹ-ŀLJ-ljˡᴸḶḷḺ-ḽℒℓ℡Ⅼⅼ⒧Ⓛⓛ㋏㎈㎉㏐-㏓㏕㏖㏿flfflＬｌ]", - M: "[MmᴹᵐḾ-ṃ℠™ℳⅯⅿ⒨Ⓜⓜ㍷-㍹㎃㎆㎎㎒㎖㎙-㎨㎫㎳㎷㎹㎽㎿㏁㏂㏎㏐㏔-㏖㏘㏙㏞㏟Ｍｍ]", - N: "[NnÑñŃ-ʼnNJ-njǸǹᴺṄ-ṋⁿℕ№⒩Ⓝⓝ㎁㎋㎚㎱㎵㎻㏌㏑Ｎｎ]", - O: "[OoºÒ-Öò-öŌ-őƠơǑǒǪǫȌ-ȏȮȯᴼᵒỌ-ỏₒ℅№ℴ⒪Ⓞⓞ㍵㏇㏒㏖Ｏｏ]", - P: "[PpᴾᵖṔ-ṗℙ⒫Ⓟⓟ㉐㍱㍶㎀㎊㎩-㎬㎰㎴㎺㏋㏗-㏚Ｐｐ]", - Q: "[Qqℚ⒬Ⓠⓠ㏃Ｑｑ]", - R: "[RrŔ-řȐ-ȓʳᴿᵣṘ-ṛṞṟ₨ℛ-ℝ⒭Ⓡⓡ㋍㍴㎭-㎯㏚㏛Ｒｒ]", - S: "[SsŚ-šſȘșˢṠ-ṣ₨℁℠⒮Ⓢⓢ㎧㎨㎮-㎳㏛㏜stＳｓ]", - T: "[TtŢ-ťȚțᵀᵗṪ-ṱẗ℡™⒯Ⓣⓣ㉐㋏㎔㏏ſtstＴｔ]", - U: "[UuÙ-Üù-üŨ-ųƯưǓǔȔ-ȗᵁᵘᵤṲ-ṷỤ-ủ℆⒰Ⓤⓤ㍳㍺Ｕｕ]", - V: "[VvᵛᵥṼ-ṿⅣ-Ⅷⅳ-ⅷ⒱Ⓥⓥⱽ㋎㍵㎴-㎹㏜㏞Ｖｖ]", - W: "[WwŴŵʷᵂẀ-ẉẘ⒲Ⓦⓦ㎺-㎿㏝Ｗｗ]", - X: "[XxˣẊ-ẍₓ℻Ⅸ-Ⅻⅸ-ⅻ⒳Ⓧⓧ㏓Ｘｘ]", - Y: "[YyÝýÿŶ-ŸȲȳʸẎẏẙỲ-ỹ⒴Ⓨⓨ㏉Ｙｙ]", - Z: "[ZzŹ-žDZ-dzᶻẐ-ẕℤℨ⒵Ⓩⓩ㎐-㎔Ｚｚ]" - }; - return function hightlight(o) { - var regex; - o = _.mixin({}, defaults, o); - if (!o.node || !o.pattern) { - return; - } - o.pattern = _.isArray(o.pattern) ? o.pattern : [ o.pattern ]; - regex = getRegex(o.pattern, o.caseSensitive, o.wordsOnly, o.diacriticInsensitive); - traverse(o.node, hightlightTextNode); - function hightlightTextNode(textNode) { - var match, patternNode, wrapperNode; - if (match = regex.exec(textNode.data)) { - wrapperNode = doc.createElement(o.tagName); - o.className && (wrapperNode.className = o.className); - patternNode = textNode.splitText(match.index); - patternNode.splitText(match[0].length); - wrapperNode.appendChild(patternNode.cloneNode(true)); - textNode.parentNode.replaceChild(wrapperNode, patternNode); - } - return !!match; - } - function traverse(el, hightlightTextNode) { - var childNode, TEXT_NODE_TYPE = 3; - for (var i = 0; i < el.childNodes.length; i++) { - childNode = el.childNodes[i]; - if (childNode.nodeType === TEXT_NODE_TYPE) { - i += hightlightTextNode(childNode) ? 1 : 0; - } else { - traverse(childNode, hightlightTextNode); - } - } - } - }; - function accent_replacer(chr) { - return accented[chr.toUpperCase()] || chr; - } - function getRegex(patterns, caseSensitive, wordsOnly, diacriticInsensitive) { - var escapedPatterns = [], regexStr; - for (var i = 0, len = patterns.length; i < len; i++) { - var escapedWord = _.escapeRegExChars(patterns[i]); - if (diacriticInsensitive) { - escapedWord = escapedWord.replace(/\S/g, accent_replacer); - } - escapedPatterns.push(escapedWord); - } - regexStr = wordsOnly ? "\\b(" + escapedPatterns.join("|") + ")\\b" : "(" + escapedPatterns.join("|") + ")"; - return caseSensitive ? new RegExp(regexStr) : new RegExp(regexStr, "i"); - } - }(window.document); - var Input = function() { - "use strict"; - var specialKeyCodeMap; - specialKeyCodeMap = { - 9: "tab", - 27: "esc", - 37: "left", - 39: "right", - 13: "enter", - 38: "up", - 40: "down" - }; - function Input(o, www) { - var id; - o = o || {}; - if (!o.input) { - $.error("input is missing"); - } - www.mixin(this); - this.$hint = $(o.hint); - this.$input = $(o.input); - this.$menu = $(o.menu); - id = this.$input.attr("id") || _.guid(); - this.$menu.attr("id", id + "_listbox"); - this.$hint.attr({ - "aria-hidden": true - }); - this.$input.attr({ - "aria-owns": id + "_listbox", - role: "combobox", - "aria-autocomplete": "list", - "aria-expanded": false - }); - this.query = this.$input.val(); - this.queryWhenFocused = this.hasFocus() ? this.query : null; - this.$overflowHelper = buildOverflowHelper(this.$input); - this._checkLanguageDirection(); - if (this.$hint.length === 0) { - this.setHint = this.getHint = this.clearHint = this.clearHintIfInvalid = _.noop; - } - this.onSync("cursorchange", this._updateDescendent); - } - Input.normalizeQuery = function(str) { - return _.toStr(str).replace(/^\s*/g, "").replace(/\s{2,}/g, " "); - }; - _.mixin(Input.prototype, EventEmitter, { - _onBlur: function onBlur() { - this.resetInputValue(); - this.trigger("blurred"); - }, - _onFocus: function onFocus() { - this.queryWhenFocused = this.query; - this.trigger("focused"); - }, - _onKeydown: function onKeydown($e) { - var keyName = specialKeyCodeMap[$e.which || $e.keyCode]; - this._managePreventDefault(keyName, $e); - if (keyName && this._shouldTrigger(keyName, $e)) { - this.trigger(keyName + "Keyed", $e); - } - }, - _onInput: function onInput() { - this._setQuery(this.getInputValue()); - this.clearHintIfInvalid(); - this._checkLanguageDirection(); - }, - _managePreventDefault: function managePreventDefault(keyName, $e) { - var preventDefault; - switch (keyName) { - case "up": - case "down": - preventDefault = !withModifier($e); - break; - - default: - preventDefault = false; - } - preventDefault && $e.preventDefault(); - }, - _shouldTrigger: function shouldTrigger(keyName, $e) { - var trigger; - switch (keyName) { - case "tab": - trigger = !withModifier($e); - break; - - default: - trigger = true; - } - return trigger; - }, - _checkLanguageDirection: function checkLanguageDirection() { - var dir = (this.$input.css("direction") || "ltr").toLowerCase(); - if (this.dir !== dir) { - this.dir = dir; - this.$hint.attr("dir", dir); - this.trigger("langDirChanged", dir); - } - }, - _setQuery: function setQuery(val, silent) { - var areEquivalent, hasDifferentWhitespace; - areEquivalent = areQueriesEquivalent(val, this.query); - hasDifferentWhitespace = areEquivalent ? this.query.length !== val.length : false; - this.query = val; - if (!silent && !areEquivalent) { - this.trigger("queryChanged", this.query); - } else if (!silent && hasDifferentWhitespace) { - this.trigger("whitespaceChanged", this.query); - } - }, - _updateDescendent: function updateDescendent(event, id) { - this.$input.attr("aria-activedescendant", id); - }, - bind: function() { - var that = this, onBlur, onFocus, onKeydown, onInput; - onBlur = _.bind(this._onBlur, this); - onFocus = _.bind(this._onFocus, this); - onKeydown = _.bind(this._onKeydown, this); - onInput = _.bind(this._onInput, this); - this.$input.on("blur.tt", onBlur).on("focus.tt", onFocus).on("keydown.tt", onKeydown); - if (!_.isMsie() || _.isMsie() > 9) { - this.$input.on("input.tt", onInput); - } else { - this.$input.on("keydown.tt keypress.tt cut.tt paste.tt", function($e) { - if (specialKeyCodeMap[$e.which || $e.keyCode]) { - return; - } - _.defer(_.bind(that._onInput, that, $e)); - }); - } - return this; - }, - focus: function focus() { - this.$input.focus(); - }, - blur: function blur() { - this.$input.blur(); - }, - getLangDir: function getLangDir() { - return this.dir; - }, - getQuery: function getQuery() { - return this.query || ""; - }, - setQuery: function setQuery(val, silent) { - this.setInputValue(val); - this._setQuery(val, silent); - }, - hasQueryChangedSinceLastFocus: function hasQueryChangedSinceLastFocus() { - return this.query !== this.queryWhenFocused; - }, - getInputValue: function getInputValue() { - return this.$input.val(); - }, - setInputValue: function setInputValue(value) { - this.$input.val(value); - this.clearHintIfInvalid(); - this._checkLanguageDirection(); - }, - resetInputValue: function resetInputValue() { - this.setInputValue(this.query); - }, - getHint: function getHint() { - return this.$hint.val(); - }, - setHint: function setHint(value) { - this.$hint.val(value); - }, - clearHint: function clearHint() { - this.setHint(""); - }, - clearHintIfInvalid: function clearHintIfInvalid() { - var val, hint, valIsPrefixOfHint, isValid; - val = this.getInputValue(); - hint = this.getHint(); - valIsPrefixOfHint = val !== hint && hint.indexOf(val) === 0; - isValid = val !== "" && valIsPrefixOfHint && !this.hasOverflow(); - !isValid && this.clearHint(); - }, - hasFocus: function hasFocus() { - return this.$input.is(":focus"); - }, - hasOverflow: function hasOverflow() { - var constraint = this.$input.width() - 2; - this.$overflowHelper.text(this.getInputValue()); - return this.$overflowHelper.width() >= constraint; - }, - isCursorAtEnd: function() { - var valueLength, selectionStart, range; - valueLength = this.$input.val().length; - selectionStart = this.$input[0].selectionStart; - if (_.isNumber(selectionStart)) { - return selectionStart === valueLength; - } else if (document.selection) { - range = document.selection.createRange(); - range.moveStart("character", -valueLength); - return valueLength === range.text.length; - } - return true; - }, - destroy: function destroy() { - this.$hint.off(".tt"); - this.$input.off(".tt"); - this.$overflowHelper.remove(); - this.$hint = this.$input = this.$overflowHelper = $("
"); - }, - setAriaExpanded: function setAriaExpanded(value) { - this.$input.attr("aria-expanded", value); - } - }); - return Input; - function buildOverflowHelper($input) { - return $('').css({ - position: "absolute", - visibility: "hidden", - whiteSpace: "pre", - fontFamily: $input.css("font-family"), - fontSize: $input.css("font-size"), - fontStyle: $input.css("font-style"), - fontVariant: $input.css("font-variant"), - fontWeight: $input.css("font-weight"), - wordSpacing: $input.css("word-spacing"), - letterSpacing: $input.css("letter-spacing"), - textIndent: $input.css("text-indent"), - textRendering: $input.css("text-rendering"), - textTransform: $input.css("text-transform") - }).insertAfter($input); - } - function areQueriesEquivalent(a, b) { - return Input.normalizeQuery(a) === Input.normalizeQuery(b); - } - function withModifier($e) { - return $e.altKey || $e.ctrlKey || $e.metaKey || $e.shiftKey; - } - }(); - var Dataset = function() { - "use strict"; - var keys, nameGenerator; - keys = { - dataset: "tt-selectable-dataset", - val: "tt-selectable-display", - obj: "tt-selectable-object" - }; - nameGenerator = _.getIdGenerator(); - function Dataset(o, www) { - o = o || {}; - o.templates = o.templates || {}; - o.templates.notFound = o.templates.notFound || o.templates.empty; - if (!o.source) { - $.error("missing source"); - } - if (!o.node) { - $.error("missing node"); - } - if (o.name && !isValidName(o.name)) { - $.error("invalid dataset name: " + o.name); - } - www.mixin(this); - this.highlight = !!o.highlight; - this.name = _.toStr(o.name || nameGenerator()); - this.limit = o.limit || 5; - this.displayFn = getDisplayFn(o.display || o.displayKey); - this.templates = getTemplates(o.templates, this.displayFn); - this.source = o.source.__ttAdapter ? o.source.__ttAdapter() : o.source; - this.async = _.isUndefined(o.async) ? this.source.length > 2 : !!o.async; - this._resetLastSuggestion(); - this.$el = $(o.node).attr("role", "presentation").addClass(this.classes.dataset).addClass(this.classes.dataset + "-" + this.name); - } - Dataset.extractData = function extractData(el) { - var $el = $(el); - if ($el.data(keys.obj)) { - return { - dataset: $el.data(keys.dataset) || "", - val: $el.data(keys.val) || "", - obj: $el.data(keys.obj) || null - }; - } - return null; - }; - _.mixin(Dataset.prototype, EventEmitter, { - _overwrite: function overwrite(query, suggestions) { - suggestions = suggestions || []; - if (suggestions.length) { - this._renderSuggestions(query, suggestions); - } else if (this.async && this.templates.pending) { - this._renderPending(query); - } else if (!this.async && this.templates.notFound) { - this._renderNotFound(query); - } else { - this._empty(); - } - this.trigger("rendered", suggestions, false, this.name); - }, - _append: function append(query, suggestions) { - suggestions = suggestions || []; - if (suggestions.length && this.$lastSuggestion.length) { - this._appendSuggestions(query, suggestions); - } else if (suggestions.length) { - this._renderSuggestions(query, suggestions); - } else if (!this.$lastSuggestion.length && this.templates.notFound) { - this._renderNotFound(query); - } - this.trigger("rendered", suggestions, true, this.name); - }, - _renderSuggestions: function renderSuggestions(query, suggestions) { - var $fragment; - $fragment = this._getSuggestionsFragment(query, suggestions); - this.$lastSuggestion = $fragment.children().last(); - this.$el.html($fragment).prepend(this._getHeader(query, suggestions)).append(this._getFooter(query, suggestions)); - }, - _appendSuggestions: function appendSuggestions(query, suggestions) { - var $fragment, $lastSuggestion; - $fragment = this._getSuggestionsFragment(query, suggestions); - $lastSuggestion = $fragment.children().last(); - this.$lastSuggestion.after($fragment); - this.$lastSuggestion = $lastSuggestion; - }, - _renderPending: function renderPending(query) { - var template = this.templates.pending; - this._resetLastSuggestion(); - template && this.$el.html(template({ - query: query, - dataset: this.name - })); - }, - _renderNotFound: function renderNotFound(query) { - var template = this.templates.notFound; - this._resetLastSuggestion(); - template && this.$el.html(template({ - query: query, - dataset: this.name - })); - }, - _empty: function empty() { - this.$el.empty(); - this._resetLastSuggestion(); - }, - _getSuggestionsFragment: function getSuggestionsFragment(query, suggestions) { - var that = this, fragment; - fragment = document.createDocumentFragment(); - _.each(suggestions, function getSuggestionNode(suggestion) { - var $el, context; - context = that._injectQuery(query, suggestion); - $el = $(that.templates.suggestion(context)).data(keys.dataset, that.name).data(keys.obj, suggestion).data(keys.val, that.displayFn(suggestion)).addClass(that.classes.suggestion + " " + that.classes.selectable); - fragment.appendChild($el[0]); - }); - this.highlight && highlight({ - className: this.classes.highlight, - node: fragment, - pattern: query - }); - return $(fragment); - }, - _getFooter: function getFooter(query, suggestions) { - return this.templates.footer ? this.templates.footer({ - query: query, - suggestions: suggestions, - dataset: this.name - }) : null; - }, - _getHeader: function getHeader(query, suggestions) { - return this.templates.header ? this.templates.header({ - query: query, - suggestions: suggestions, - dataset: this.name - }) : null; - }, - _resetLastSuggestion: function resetLastSuggestion() { - this.$lastSuggestion = $(); - }, - _injectQuery: function injectQuery(query, obj) { - return _.isObject(obj) ? _.mixin({ - _query: query - }, obj) : obj; - }, - update: function update(query) { - var that = this, canceled = false, syncCalled = false, rendered = 0; - this.cancel(); - this.cancel = function cancel() { - canceled = true; - that.cancel = $.noop; - that.async && that.trigger("asyncCanceled", query, that.name); - }; - this.source(query, sync, async); - !syncCalled && sync([]); - function sync(suggestions) { - if (syncCalled) { - return; - } - syncCalled = true; - suggestions = (suggestions || []).slice(0, that.limit); - rendered = suggestions.length; - that._overwrite(query, suggestions); - if (rendered < that.limit && that.async) { - that.trigger("asyncRequested", query, that.name); - } - } - function async(suggestions) { - suggestions = suggestions || []; - if (!canceled && rendered < that.limit) { - that.cancel = $.noop; - var idx = Math.abs(rendered - that.limit); - rendered += idx; - that._append(query, suggestions.slice(0, idx)); - that.async && that.trigger("asyncReceived", query, that.name); - } - } - }, - cancel: $.noop, - clear: function clear() { - this._empty(); - this.cancel(); - this.trigger("cleared"); - }, - isEmpty: function isEmpty() { - return this.$el.is(":empty"); - }, - destroy: function destroy() { - this.$el = $("
"); - } - }); - return Dataset; - function getDisplayFn(display) { - display = display || _.stringify; - return _.isFunction(display) ? display : displayFn; - function displayFn(obj) { - return obj[display]; - } - } - function getTemplates(templates, displayFn) { - return { - notFound: templates.notFound && _.templatify(templates.notFound), - pending: templates.pending && _.templatify(templates.pending), - header: templates.header && _.templatify(templates.header), - footer: templates.footer && _.templatify(templates.footer), - suggestion: templates.suggestion ? userSuggestionTemplate : suggestionTemplate - }; - function userSuggestionTemplate(context) { - var template = templates.suggestion; - return $(template(context)).attr("id", _.guid()); - } - function suggestionTemplate(context) { - return $('
').attr("id", _.guid()).text(displayFn(context)); - } - } - function isValidName(str) { - return /^[_a-zA-Z0-9-]+$/.test(str); - } - }(); - var Menu = function() { - "use strict"; - function Menu(o, www) { - var that = this; - o = o || {}; - if (!o.node) { - $.error("node is required"); - } - www.mixin(this); - this.$node = $(o.node); - this.query = null; - this.datasets = _.map(o.datasets, initializeDataset); - function initializeDataset(oDataset) { - var node = that.$node.find(oDataset.node).first(); - oDataset.node = node.length ? node : $("
").appendTo(that.$node); - return new Dataset(oDataset, www); - } - } - _.mixin(Menu.prototype, EventEmitter, { - _onSelectableClick: function onSelectableClick($e) { - this.trigger("selectableClicked", $($e.currentTarget)); - }, - _onRendered: function onRendered(type, dataset, suggestions, async) { - this.$node.toggleClass(this.classes.empty, this._allDatasetsEmpty()); - this.trigger("datasetRendered", dataset, suggestions, async); - }, - _onCleared: function onCleared() { - this.$node.toggleClass(this.classes.empty, this._allDatasetsEmpty()); - this.trigger("datasetCleared"); - }, - _propagate: function propagate() { - this.trigger.apply(this, arguments); - }, - _allDatasetsEmpty: function allDatasetsEmpty() { - return _.every(this.datasets, _.bind(function isDatasetEmpty(dataset) { - var isEmpty = dataset.isEmpty(); - this.$node.attr("aria-expanded", !isEmpty); - return isEmpty; - }, this)); - }, - _getSelectables: function getSelectables() { - return this.$node.find(this.selectors.selectable); - }, - _removeCursor: function _removeCursor() { - var $selectable = this.getActiveSelectable(); - $selectable && $selectable.removeClass(this.classes.cursor); - }, - _ensureVisible: function ensureVisible($el) { - var elTop, elBottom, nodeScrollTop, nodeHeight; - elTop = $el.position().top; - elBottom = elTop + $el.outerHeight(true); - nodeScrollTop = this.$node.scrollTop(); - nodeHeight = this.$node.height() + parseInt(this.$node.css("paddingTop"), 10) + parseInt(this.$node.css("paddingBottom"), 10); - if (elTop < 0) { - this.$node.scrollTop(nodeScrollTop + elTop); - } else if (nodeHeight < elBottom) { - this.$node.scrollTop(nodeScrollTop + (elBottom - nodeHeight)); - } - }, - bind: function() { - var that = this, onSelectableClick; - onSelectableClick = _.bind(this._onSelectableClick, this); - this.$node.on("click.tt", this.selectors.selectable, onSelectableClick); - this.$node.on("mouseover", this.selectors.selectable, function() { - that.setCursor($(this)); - }); - this.$node.on("mouseleave", function() { - that._removeCursor(); - }); - _.each(this.datasets, function(dataset) { - dataset.onSync("asyncRequested", that._propagate, that).onSync("asyncCanceled", that._propagate, that).onSync("asyncReceived", that._propagate, that).onSync("rendered", that._onRendered, that).onSync("cleared", that._onCleared, that); - }); - return this; - }, - isOpen: function isOpen() { - return this.$node.hasClass(this.classes.open); - }, - open: function open() { - this.$node.scrollTop(0); - this.$node.addClass(this.classes.open); - }, - close: function close() { - this.$node.attr("aria-expanded", false); - this.$node.removeClass(this.classes.open); - this._removeCursor(); - }, - setLanguageDirection: function setLanguageDirection(dir) { - this.$node.attr("dir", dir); - }, - selectableRelativeToCursor: function selectableRelativeToCursor(delta) { - var $selectables, $oldCursor, oldIndex, newIndex; - $oldCursor = this.getActiveSelectable(); - $selectables = this._getSelectables(); - oldIndex = $oldCursor ? $selectables.index($oldCursor) : -1; - newIndex = oldIndex + delta; - newIndex = (newIndex + 1) % ($selectables.length + 1) - 1; - newIndex = newIndex < -1 ? $selectables.length - 1 : newIndex; - return newIndex === -1 ? null : $selectables.eq(newIndex); - }, - setCursor: function setCursor($selectable) { - this._removeCursor(); - if ($selectable = $selectable && $selectable.first()) { - $selectable.addClass(this.classes.cursor); - this._ensureVisible($selectable); - } - }, - getSelectableData: function getSelectableData($el) { - return $el && $el.length ? Dataset.extractData($el) : null; - }, - getActiveSelectable: function getActiveSelectable() { - var $selectable = this._getSelectables().filter(this.selectors.cursor).first(); - return $selectable.length ? $selectable : null; - }, - getTopSelectable: function getTopSelectable() { - var $selectable = this._getSelectables().first(); - return $selectable.length ? $selectable : null; - }, - update: function update(query) { - var isValidUpdate = query !== this.query; - if (isValidUpdate) { - this.query = query; - _.each(this.datasets, updateDataset); - } - return isValidUpdate; - function updateDataset(dataset) { - dataset.update(query); - } - }, - empty: function empty() { - _.each(this.datasets, clearDataset); - this.query = null; - this.$node.addClass(this.classes.empty); - function clearDataset(dataset) { - dataset.clear(); - } - }, - destroy: function destroy() { - this.$node.off(".tt"); - this.$node = $("
"); - _.each(this.datasets, destroyDataset); - function destroyDataset(dataset) { - dataset.destroy(); - } - } - }); - return Menu; - }(); - var Status = function() { - "use strict"; - function Status(options) { - this.$el = $("", { - role: "status", - "aria-live": "polite" - }).css({ - position: "absolute", - padding: "0", - border: "0", - height: "1px", - width: "1px", - "margin-bottom": "-1px", - "margin-right": "-1px", - overflow: "hidden", - clip: "rect(0 0 0 0)", - "white-space": "nowrap" - }); - options.$input.after(this.$el); - _.each(options.menu.datasets, _.bind(function(dataset) { - if (dataset.onSync) { - dataset.onSync("rendered", _.bind(this.update, this)); - dataset.onSync("cleared", _.bind(this.cleared, this)); - } - }, this)); - } - _.mixin(Status.prototype, { - update: function update(event, suggestions) { - var length = suggestions.length; - var words; - if (length === 1) { - words = { - result: "result", - is: "is" - }; - } else { - words = { - result: "results", - is: "are" - }; - } - this.$el.text(length + " " + words.result + " " + words.is + " available, use up and down arrow keys to navigate."); - }, - cleared: function() { - this.$el.text(""); - } - }); - return Status; - }(); - var DefaultMenu = function() { - "use strict"; - var s = Menu.prototype; - function DefaultMenu() { - Menu.apply(this, [].slice.call(arguments, 0)); - } - _.mixin(DefaultMenu.prototype, Menu.prototype, { - open: function open() { - !this._allDatasetsEmpty() && this._show(); - return s.open.apply(this, [].slice.call(arguments, 0)); - }, - close: function close() { - this._hide(); - return s.close.apply(this, [].slice.call(arguments, 0)); - }, - _onRendered: function onRendered() { - if (this._allDatasetsEmpty()) { - this._hide(); - } else { - this.isOpen() && this._show(); - } - return s._onRendered.apply(this, [].slice.call(arguments, 0)); - }, - _onCleared: function onCleared() { - if (this._allDatasetsEmpty()) { - this._hide(); - } else { - this.isOpen() && this._show(); - } - return s._onCleared.apply(this, [].slice.call(arguments, 0)); - }, - setLanguageDirection: function setLanguageDirection(dir) { - this.$node.css(dir === "ltr" ? this.css.ltr : this.css.rtl); - return s.setLanguageDirection.apply(this, [].slice.call(arguments, 0)); - }, - _hide: function hide() { - this.$node.hide(); - }, - _show: function show() { - this.$node.css("display", "block"); - } - }); - return DefaultMenu; - }(); - var Typeahead = function() { - "use strict"; - function Typeahead(o, www) { - var onFocused, onBlurred, onEnterKeyed, onTabKeyed, onEscKeyed, onUpKeyed, onDownKeyed, onLeftKeyed, onRightKeyed, onQueryChanged, onWhitespaceChanged; - o = o || {}; - if (!o.input) { - $.error("missing input"); - } - if (!o.menu) { - $.error("missing menu"); - } - if (!o.eventBus) { - $.error("missing event bus"); - } - www.mixin(this); - this.eventBus = o.eventBus; - this.minLength = _.isNumber(o.minLength) ? o.minLength : 1; - this.input = o.input; - this.menu = o.menu; - this.enabled = true; - this.autoselect = !!o.autoselect; - this.active = false; - this.input.hasFocus() && this.activate(); - this.dir = this.input.getLangDir(); - this._hacks(); - this.menu.bind().onSync("selectableClicked", this._onSelectableClicked, this).onSync("asyncRequested", this._onAsyncRequested, this).onSync("asyncCanceled", this._onAsyncCanceled, this).onSync("asyncReceived", this._onAsyncReceived, this).onSync("datasetRendered", this._onDatasetRendered, this).onSync("datasetCleared", this._onDatasetCleared, this); - onFocused = c(this, "activate", "open", "_onFocused"); - onBlurred = c(this, "deactivate", "_onBlurred"); - onEnterKeyed = c(this, "isActive", "isOpen", "_onEnterKeyed"); - onTabKeyed = c(this, "isActive", "isOpen", "_onTabKeyed"); - onEscKeyed = c(this, "isActive", "_onEscKeyed"); - onUpKeyed = c(this, "isActive", "open", "_onUpKeyed"); - onDownKeyed = c(this, "isActive", "open", "_onDownKeyed"); - onLeftKeyed = c(this, "isActive", "isOpen", "_onLeftKeyed"); - onRightKeyed = c(this, "isActive", "isOpen", "_onRightKeyed"); - onQueryChanged = c(this, "_openIfActive", "_onQueryChanged"); - onWhitespaceChanged = c(this, "_openIfActive", "_onWhitespaceChanged"); - this.input.bind().onSync("focused", onFocused, this).onSync("blurred", onBlurred, this).onSync("enterKeyed", onEnterKeyed, this).onSync("tabKeyed", onTabKeyed, this).onSync("escKeyed", onEscKeyed, this).onSync("upKeyed", onUpKeyed, this).onSync("downKeyed", onDownKeyed, this).onSync("leftKeyed", onLeftKeyed, this).onSync("rightKeyed", onRightKeyed, this).onSync("queryChanged", onQueryChanged, this).onSync("whitespaceChanged", onWhitespaceChanged, this).onSync("langDirChanged", this._onLangDirChanged, this); - } - _.mixin(Typeahead.prototype, { - _hacks: function hacks() { - var $input, $menu; - $input = this.input.$input || $("
"); - $menu = this.menu.$node || $("
"); - $input.on("blur.tt", function($e) { - var active, isActive, hasActive; - active = document.activeElement; - isActive = $menu.is(active); - hasActive = $menu.has(active).length > 0; - if (_.isMsie() && (isActive || hasActive)) { - $e.preventDefault(); - $e.stopImmediatePropagation(); - _.defer(function() { - $input.focus(); - }); - } - }); - $menu.on("mousedown.tt", function($e) { - $e.preventDefault(); - }); - }, - _onSelectableClicked: function onSelectableClicked(type, $el) { - this.select($el); - }, - _onDatasetCleared: function onDatasetCleared() { - this._updateHint(); - }, - _onDatasetRendered: function onDatasetRendered(type, suggestions, async, dataset) { - this._updateHint(); - if (this.autoselect) { - var cursorClass = this.selectors.cursor.substr(1); - this.menu.$node.find(this.selectors.suggestion).first().addClass(cursorClass); - } - this.eventBus.trigger("render", suggestions, async, dataset); - }, - _onAsyncRequested: function onAsyncRequested(type, dataset, query) { - this.eventBus.trigger("asyncrequest", query, dataset); - }, - _onAsyncCanceled: function onAsyncCanceled(type, dataset, query) { - this.eventBus.trigger("asynccancel", query, dataset); - }, - _onAsyncReceived: function onAsyncReceived(type, dataset, query) { - this.eventBus.trigger("asyncreceive", query, dataset); - }, - _onFocused: function onFocused() { - this._minLengthMet() && this.menu.update(this.input.getQuery()); - }, - _onBlurred: function onBlurred() { - if (this.input.hasQueryChangedSinceLastFocus()) { - this.eventBus.trigger("change", this.input.getQuery()); - } - }, - _onEnterKeyed: function onEnterKeyed(type, $e) { - var $selectable; - if ($selectable = this.menu.getActiveSelectable()) { - if (this.select($selectable)) { - $e.preventDefault(); - $e.stopPropagation(); - } - } else if (this.autoselect) { - if (this.select(this.menu.getTopSelectable())) { - $e.preventDefault(); - $e.stopPropagation(); - } - } - }, - _onTabKeyed: function onTabKeyed(type, $e) { - var $selectable; - if ($selectable = this.menu.getActiveSelectable()) { - this.select($selectable) && $e.preventDefault(); - } else if (this.autoselect) { - if ($selectable = this.menu.getTopSelectable()) { - this.autocomplete($selectable) && $e.preventDefault(); - } - } - }, - _onEscKeyed: function onEscKeyed() { - this.close(); - }, - _onUpKeyed: function onUpKeyed() { - this.moveCursor(-1); - }, - _onDownKeyed: function onDownKeyed() { - this.moveCursor(+1); - }, - _onLeftKeyed: function onLeftKeyed() { - if (this.dir === "rtl" && this.input.isCursorAtEnd()) { - this.autocomplete(this.menu.getActiveSelectable() || this.menu.getTopSelectable()); - } - }, - _onRightKeyed: function onRightKeyed() { - if (this.dir === "ltr" && this.input.isCursorAtEnd()) { - this.autocomplete(this.menu.getActiveSelectable() || this.menu.getTopSelectable()); - } - }, - _onQueryChanged: function onQueryChanged(e, query) { - this._minLengthMet(query) ? this.menu.update(query) : this.menu.empty(); - }, - _onWhitespaceChanged: function onWhitespaceChanged() { - this._updateHint(); - }, - _onLangDirChanged: function onLangDirChanged(e, dir) { - if (this.dir !== dir) { - this.dir = dir; - this.menu.setLanguageDirection(dir); - } - }, - _openIfActive: function openIfActive() { - this.isActive() && this.open(); - }, - _minLengthMet: function minLengthMet(query) { - query = _.isString(query) ? query : this.input.getQuery() || ""; - return query.length >= this.minLength; - }, - _updateHint: function updateHint() { - var $selectable, data, val, query, escapedQuery, frontMatchRegEx, match; - $selectable = this.menu.getTopSelectable(); - data = this.menu.getSelectableData($selectable); - val = this.input.getInputValue(); - if (data && !_.isBlankString(val) && !this.input.hasOverflow()) { - query = Input.normalizeQuery(val); - escapedQuery = _.escapeRegExChars(query); - frontMatchRegEx = new RegExp("^(?:" + escapedQuery + ")(.+$)", "i"); - match = frontMatchRegEx.exec(data.val); - match && this.input.setHint(val + match[1]); - } else { - this.input.clearHint(); - } - }, - isEnabled: function isEnabled() { - return this.enabled; - }, - enable: function enable() { - this.enabled = true; - }, - disable: function disable() { - this.enabled = false; - }, - isActive: function isActive() { - return this.active; - }, - activate: function activate() { - if (this.isActive()) { - return true; - } else if (!this.isEnabled() || this.eventBus.before("active")) { - return false; - } else { - this.active = true; - this.eventBus.trigger("active"); - return true; - } - }, - deactivate: function deactivate() { - if (!this.isActive()) { - return true; - } else if (this.eventBus.before("idle")) { - return false; - } else { - this.active = false; - this.close(); - this.eventBus.trigger("idle"); - return true; - } - }, - isOpen: function isOpen() { - return this.menu.isOpen(); - }, - open: function open() { - if (!this.isOpen() && !this.eventBus.before("open")) { - this.input.setAriaExpanded(true); - this.menu.open(); - this._updateHint(); - this.eventBus.trigger("open"); - } - return this.isOpen(); - }, - close: function close() { - if (this.isOpen() && !this.eventBus.before("close")) { - this.input.setAriaExpanded(false); - this.menu.close(); - this.input.clearHint(); - this.input.resetInputValue(); - this.eventBus.trigger("close"); - } - return !this.isOpen(); - }, - setVal: function setVal(val) { - this.input.setQuery(_.toStr(val)); - }, - getVal: function getVal() { - return this.input.getQuery(); - }, - select: function select($selectable) { - var data = this.menu.getSelectableData($selectable); - if (data && !this.eventBus.before("select", data.obj, data.dataset)) { - this.input.setQuery(data.val, true); - this.eventBus.trigger("select", data.obj, data.dataset); - this.close(); - return true; - } - return false; - }, - autocomplete: function autocomplete($selectable) { - var query, data, isValid; - query = this.input.getQuery(); - data = this.menu.getSelectableData($selectable); - isValid = data && query !== data.val; - if (isValid && !this.eventBus.before("autocomplete", data.obj, data.dataset)) { - this.input.setQuery(data.val); - this.eventBus.trigger("autocomplete", data.obj, data.dataset); - return true; - } - return false; - }, - moveCursor: function moveCursor(delta) { - var query, $candidate, data, suggestion, datasetName, cancelMove, id; - query = this.input.getQuery(); - $candidate = this.menu.selectableRelativeToCursor(delta); - data = this.menu.getSelectableData($candidate); - suggestion = data ? data.obj : null; - datasetName = data ? data.dataset : null; - id = $candidate ? $candidate.attr("id") : null; - this.input.trigger("cursorchange", id); - cancelMove = this._minLengthMet() && this.menu.update(query); - if (!cancelMove && !this.eventBus.before("cursorchange", suggestion, datasetName)) { - this.menu.setCursor($candidate); - if (data) { - if (typeof data.val === "string") { - this.input.setInputValue(data.val); - } - } else { - this.input.resetInputValue(); - this._updateHint(); - } - this.eventBus.trigger("cursorchange", suggestion, datasetName); - return true; - } - return false; - }, - destroy: function destroy() { - this.input.destroy(); - this.menu.destroy(); - } - }); - return Typeahead; - function c(ctx) { - var methods = [].slice.call(arguments, 1); - return function() { - var args = [].slice.call(arguments); - _.each(methods, function(method) { - return ctx[method].apply(ctx, args); - }); - }; - } - }(); - (function() { - "use strict"; - var old, keys, methods; - old = $.fn.typeahead; - keys = { - www: "tt-www", - attrs: "tt-attrs", - typeahead: "tt-typeahead" - }; - methods = { - initialize: function initialize(o, datasets) { - var www; - datasets = _.isArray(datasets) ? datasets : [].slice.call(arguments, 1); - o = o || {}; - www = WWW(o.classNames); - return this.each(attach); - function attach() { - var $input, $wrapper, $hint, $menu, defaultHint, defaultMenu, eventBus, input, menu, status, typeahead, MenuConstructor; - _.each(datasets, function(d) { - d.highlight = !!o.highlight; - }); - $input = $(this); - $wrapper = $(www.html.wrapper); - $hint = $elOrNull(o.hint); - $menu = $elOrNull(o.menu); - defaultHint = o.hint !== false && !$hint; - defaultMenu = o.menu !== false && !$menu; - defaultHint && ($hint = buildHintFromInput($input, www)); - defaultMenu && ($menu = $(www.html.menu).css(www.css.menu)); - $hint && $hint.val(""); - $input = prepInput($input, www); - if (defaultHint || defaultMenu) { - $wrapper.css(www.css.wrapper); - $input.css(defaultHint ? www.css.input : www.css.inputWithNoHint); - $input.wrap($wrapper).parent().prepend(defaultHint ? $hint : null).append(defaultMenu ? $menu : null); - } - MenuConstructor = defaultMenu ? 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$input.removeAttr(key) : $input.attr(key, val); - }); - $input.removeData(keys.typeahead).removeData(keys.www).removeData(keys.attr).removeClass(www.classes.input); - if ($wrapper.length) { - $input.detach().insertAfter($wrapper); - $wrapper.remove(); - } - } - function $elOrNull(obj) { - var isValid, $el; - isValid = _.isJQuery(obj) || _.isElement(obj); - $el = isValid ? $(obj).first() : []; - return $el.length ? $el : null; - } - })(); -}); \ No newline at end of file diff --git a/docs/docsets/BigInt.docset/Contents/Resources/Documents/search.json b/docs/docsets/BigInt.docset/Contents/Resources/Documents/search.json deleted file mode 100644 index 9a860f0..0000000 --- a/docs/docsets/BigInt.docset/Contents/Resources/Documents/search.json +++ /dev/null @@ -1 +0,0 @@ -{"Typealiases.html#/s:6BigInt4Bytea":{"name":"Byte","abstract":"

Unsigned 8 bit value

"},"Typealiases.html#/s:6BigInt5Bytesa":{"name":"Bytes","abstract":"

Array of unsigned 8 bit values

"},"Typealiases.html#/s:6BigInt4Limba":{"name":"Limb","abstract":"

Unsigned 64 bit value

"},"Typealiases.html#/s:6BigInt5Limbsa":{"name":"Limbs","abstract":"

Array of unsigned 64 bit values

"},"Structs/CRT.html#/s:6BigInt3CRTVyACSgSayAA4BIntVGcfc":{"name":"init(_:)","abstract":"

Constructs a CRT instance from the moduli - BInt version

","parent_name":"CRT"},"Structs/CRT.html#/s:6BigInt3CRTVyACSgSaySiGcfc":{"name":"init(_:)","abstract":"

Constructs a CRT instance from the moduli - Int version

","parent_name":"CRT"},"Structs/CRT.html#/s:6BigInt3CRTV7computeyAA4BIntVSayAFGF":{"name":"compute(_:)","abstract":"

Compute the CRT value - BInt version

","parent_name":"CRT"},"Structs/CRT.html#/s:6BigInt3CRTV7computeyAA4BIntVSaySiGF":{"name":"compute(_:)","abstract":"

Compute the CRT value - Int version

","parent_name":"CRT"},"Structs/BInt.html#/s:6BigInt4BIntV4ZEROACvpZ":{"name":"ZERO","abstract":"

BInt(0)

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV3ONEACvpZ":{"name":"ONE","abstract":"

BInt(1)

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV3TWOACvpZ":{"name":"TWO","abstract":"

BInt(2)

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV5THREEACvpZ":{"name":"THREE","abstract":"

BInt(3)

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV4FOURACvpZ":{"name":"FOUR","abstract":"

BInt(4)

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV4FIVEACvpZ":{"name":"FIVE","abstract":"

BInt(5)

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV3SIXACvpZ":{"name":"SIX","abstract":"

BInt(6)

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV5SEVENACvpZ":{"name":"SEVEN","abstract":"

BInt(7)

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV5EIGHTACvpZ":{"name":"EIGHT","abstract":"

BInt(8)

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV4NINEACvpZ":{"name":"NINE","abstract":"

BInt(9)

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV3TENACvpZ":{"name":"TEN","abstract":"

BInt(10)

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntVyACSays6UInt64VG_Sbtcfc":{"name":"init(_:_:)","abstract":"

Constructs a BInt from magnitude and sign

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntVyACSicfc":{"name":"init(_:)","abstract":"

Constructs a BInt from an Int value

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntVyACSgSdcfc":{"name":"init(_:)","abstract":"

Constructs a BInt from a decimal value

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV_5radixACSgSS_Sitcfc":{"name":"init(_:radix:)","abstract":"

Constructs a BInt from a String value and radix

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV8bitWidthACSi_tcfc":{"name":"init(bitWidth:)","abstract":"

Constructs a random BInt with a specified number of bits

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV9magnitudeACSays5UInt8VG_tcfc":{"name":"init(magnitude:)","abstract":"

Constructs a BInt from a big-endian magnitude byte array representation

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV6signedACSays5UInt8VG_tcfc":{"name":"init(signed:)","abstract":"

Constructs a BInt from a big-endian 2’s complement byte array representation

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV10isNegativeSbvp":{"name":"isNegative","abstract":"

The sign, true if self < 0, false otherwise

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV9magnitudeSays6UInt64VGvp":{"name":"magnitude","abstract":"

The magnitude limb array

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV3absACvp":{"name":"abs","abstract":"

The absolute value of self

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV8bitWidthSivp":{"name":"bitWidth","abstract":"

The number of bits in the binary representation of the magnitude of self. 0 if self = 0

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV11descriptionSSvp":{"name":"description","abstract":"

Base 10 string value of self

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV6isEvenSbvp":{"name":"isEven","abstract":"

Is true if self is even, false if self is odd

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV9isNotZeroSbvp":{"name":"isNotZero","abstract":"

Is false if self = 0, true otherwise

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV5isOddSbvp":{"name":"isOdd","abstract":"

Is true if self is odd, false if self is even

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV5isOneSbvp":{"name":"isOne","abstract":"

Is true if self = 1, false otherwise

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV10isPositiveSbvp":{"name":"isPositive","abstract":"

Is true if self > 0, false otherwise

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV6isZeroSbvp":{"name":"isZero","abstract":"

Is true if self = 0, false otherwise

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV19leadingZeroBitCountSivp":{"name":"leadingZeroBitCount","abstract":"

The number of leading zero bits in the magnitude of self. 0 if self = 0

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV10populationSivp":{"name":"population","abstract":"

The number of 1 bits in the magnitude of self

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV6signumSivp":{"name":"signum","abstract":"

Is 0 if self = 0, 1 if self > 0, and -1 if self < 0

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV20trailingZeroBitCountSivp":{"name":"trailingZeroBitCount","abstract":"

The number of trailing zero bits in the magnitude of self. 0 if self = 0

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV8asDoubleSdyF":{"name":"asDouble()","abstract":"

self as a Double

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV02asB0SiSgyF":{"name":"asInt()","abstract":"

self as an Int

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV16asMagnitudeBytesSays5UInt8VGyF":{"name":"asMagnitudeBytes()","abstract":"

Byte array representation of magnitude value

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV13asSignedBytesSays5UInt8VGyF":{"name":"asSignedBytes()","abstract":"

Byte array representation of 2’s complement value

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV8asString5radix9uppercaseSSSi_SbtF":{"name":"asString(radix:uppercase:)","abstract":"

self as a String with a given radix

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV1aoiyA2C_ACtFZ":{"name":"&(_:_:)","abstract":"

Bitwise and operator - behaves as if two’s complement representation were used,
","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV2aeoiyyACz_ACtFZ":{"name":"&=(_:_:)","abstract":"

x = x & y

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV1ooiyA2C_ACtFZ":{"name":"|(_:_:)","abstract":"

Bitwise or operator - behaves as if two’s complement representation were used,
","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV2oeoiyyACz_ACtFZ":{"name":"|=(_:_:)","abstract":"

x = x | y

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV1xoiyA2C_ACtFZ":{"name":"^(_:_:)","abstract":"

Bitwise xor operator - behaves as if two’s complement representation were used,
","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV2xeoiyyACz_ACtFZ":{"name":"^=(_:_:)","abstract":"

x = x ^ y

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV1topyA2CFZ":{"name":"~(_:)","abstract":"

Bitwise not operator - behaves as if two’s complement arithmetic were used,
","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV8clearBityySiF":{"name":"clearBit(_:)","abstract":"

Clear a specified bit - a no-op if bit number < 0

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV7flipBityySiF":{"name":"flipBit(_:)","abstract":"

Invert a specified bit - a no-op if bit number < 0

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV6setBityySiF":{"name":"setBit(_:)","abstract":"

Set a specified bit - a no-op if bit number < 0

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV7testBitySbSiF":{"name":"testBit(_:)","abstract":"

Test a specified bit - false if bit number < 0

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV1popyA2CFZ":{"name":"+(_:)","abstract":"

Prefix plus

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV1poiyA2C_ACtFZ":{"name":"+(_:_:)","abstract":"

Addition

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV1poiyACSi_ACtFZ":{"name":"+(_:_:)","abstract":"

Addition

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV1poiyA2C_SitFZ":{"name":"+(_:_:)","abstract":"

Addition

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV2peoiyyACz_ACtFZ":{"name":"+=(_:_:)","abstract":"

x = x + y

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV2peoiyyACz_SitFZ":{"name":"+=(_:_:)","abstract":"

x = x + y

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV6negateyyF":{"name":"negate()","abstract":"

Negates self

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV1sopyA2CFZ":{"name":"-(_:)","abstract":"

Negation

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV1soiyA2C_ACtFZ":{"name":"-(_:_:)","abstract":"

Subtraction

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV1soiyACSi_ACtFZ":{"name":"-(_:_:)","abstract":"

Subtraction

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV1soiyA2C_SitFZ":{"name":"-(_:_:)","abstract":"

Subtraction

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV2seoiyyACz_ACtFZ":{"name":"-=(_:_:)","abstract":"

x = x - y

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV2seoiyyACz_SitFZ":{"name":"-=(_:_:)","abstract":"

x = x - y

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV1moiyA2C_ACtFZ":{"name":"*(_:_:)","abstract":"

Multiplication

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV1moiyACSi_ACtFZ":{"name":"*(_:_:)","abstract":"

Multiplication

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV1moiyA2C_SitFZ":{"name":"*(_:_:)","abstract":"

Multiplication

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV2meoiyyACz_ACtFZ":{"name":"*=(_:_:)","abstract":"

x = x * y

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV2meoiyyACz_SitFZ":{"name":"*=(_:_:)","abstract":"

x = x * y

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV20quotientAndRemainder10dividingByAC0D0_AC9remaindertAC_tF":{"name":"quotientAndRemainder(dividingBy:)","abstract":"

Division

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV20quotientAndRemainder10dividingBy__yAC_ACzACztF":{"name":"quotientAndRemainder(dividingBy:_:_:)","abstract":"

Division

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV20quotientAndRemainder10dividingByAC0D0_Si9remaindertSi_tF":{"name":"quotientAndRemainder(dividingBy:)","abstract":"

Division

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV20quotientAndRemainder10dividingBy__ySi_ACzSiztF":{"name":"quotientAndRemainder(dividingBy:_:_:)","abstract":"

Division

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV13quotientExact10dividingByA2C_tF":{"name":"quotientExact(dividingBy:)","abstract":"

Exact division - that is, the remainder of the division is known to be 0

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV1doiyA2C_ACtFZ":{"name":"/(_:_:)","abstract":"

Division

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV1doiyACSi_ACtFZ":{"name":"/(_:_:)","abstract":"

Division

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV1doiyA2C_SitFZ":{"name":"/(_:_:)","abstract":"

Division

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV2deoiyyACz_ACtFZ":{"name":"/=(_:_:)","abstract":"

x = x / y

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV2deoiyyACz_SitFZ":{"name":"/=(_:_:)","abstract":"

x = x / y

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV1roiyA2C_ACtFZ":{"name":"%(_:_:)","abstract":"

Remainder

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV1roiyACSi_ACtFZ":{"name":"%(_:_:)","abstract":"

Remainder

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV1roiyA2C_SitFZ":{"name":"%(_:_:)","abstract":"

Remainder

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV2reoiyyACz_ACtFZ":{"name":"%=(_:_:)","abstract":"

x = x % y

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV2reoiyyACz_SitFZ":{"name":"%=(_:_:)","abstract":"

x = x % y

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV3modyA2CF":{"name":"mod(_:)","abstract":"

Modulus - BInt parameter

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV3modyS2iF":{"name":"mod(_:)","abstract":"

Modulus - Int parameter

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV10modInverseyA2CF":{"name":"modInverse(_:)","abstract":"

Inverse modulus - BInt parameter

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV10modInverseyS2iF":{"name":"modInverse(_:)","abstract":"

Inverse modulus - Int parameter

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV2mmoiyA2C_SitFZ":{"name":"**(_:_:)","abstract":"

Exponentiation

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV6expModyA2C_ACtF":{"name":"expMod(_:_:)","abstract":"

Modular exponentiation - BInt modulus

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV6expModySiAC_SitF":{"name":"expMod(_:_:)","abstract":"

Modular exponentiation - Int modulus

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV2eeoiySbAC_ACtFZ":{"name":"==(_:_:)","abstract":"

Equal

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV2eeoiySbAC_SitFZ":{"name":"==(_:_:)","abstract":"

Equal

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV2eeoiySbSi_ACtFZ":{"name":"==(_:_:)","abstract":"

Equal

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV2neoiySbAC_ACtFZ":{"name":"!=(_:_:)","abstract":"

Not equal

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV2neoiySbAC_SitFZ":{"name":"!=(_:_:)","abstract":"

Not equal

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV2neoiySbSi_ACtFZ":{"name":"!=(_:_:)","abstract":"

Not equal

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV1loiySbAC_ACtFZ":{"name":"<(_:_:)","abstract":"

Less than

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Less than

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Less than

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Greater than

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Greater than

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Greater than

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Less than or equal

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Less than or equal

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Less than or equal

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV2geoiySbAC_ACtFZ":{"name":">=(_:_:)","abstract":"

Greater than or equal

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV2geoiySbSi_ACtFZ":{"name":">=(_:_:)","abstract":"

Greater than or equal

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV2geoiySbAC_SitFZ":{"name":">=(_:_:)","abstract":"

Greater than or equal

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV2lloiyA2C_SitFZ":{"name":"<<(_:_:)","abstract":"

Logical left shift

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x = x << n

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV2ggoiyA2C_SitFZ":{"name":">>(_:_:)","abstract":"

Logical right shift

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x = x >> n

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Checks whether self is prime using the Miller-Rabin algorithm

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The next probable prime greater than self

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A probable prime number with a given bitwidth

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Product of primes up to n

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n'th root

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n'th root and remainder

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Check whether self is a perfect root, that is, for some integer x and n > 1 self = x^n

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Square root of a non-negative number

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Square root and remainder of a non-negative number

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Check whether self is a perfect square, that is, for some integer x self = x^2

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Square root modulo a prime number - BInt prime

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Square root modulo a prime number - Int prime

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Compute binomial coefficient n over k

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Factorial function

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n'th Fibonacci number

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Fibonacci pair, n'th and n'th + 1 Fibonacci number

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Greatest common divisor

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Extended greatest common divisor

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Jacobi symbol - BInt parameter. If m is an odd prime, this is also the Legendre symbol

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Jacobi symbol - Int parameter. If m is an odd prime, this is also the Legendre symbol

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Kronecker symbol - BInt parameter. If m is positive and odd, this is also the Jacobi symbol

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Kronecker symbol - Int parameter. If m is positive and odd, this is also the Jacobi symbol

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV3lcmyA2CF":{"name":"lcm(_:)","abstract":"

Least common multiple

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV5lucasyACSiFZ":{"name":"lucas(_:)","abstract":"

n'th Lucas number

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV6lucas2yAC_ACtSiFZ":{"name":"lucas2(_:)","abstract":"

Lucas pair, n'th and n'th + 1 Lucas number

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV14randomLessThanACyF":{"name":"randomLessThan()","abstract":"

Random value

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BFraction(0, 1)

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV3ONEACvpZ":{"name":"ONE","abstract":"

BFraction(1, 1)

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionVyAcA4BIntV_AEtcfc":{"name":"init(_:_:)","abstract":"

Constructs a BFraction from numerator and denominator

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionVyAcA4BIntV_Sitcfc":{"name":"init(_:_:)","abstract":"

Constructs a BFraction from numerator and denominator

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionVyACSi_AA4BIntVtcfc":{"name":"init(_:_:)","abstract":"

Constructs a BFraction from numerator and denominator

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionVyACSi_Sitcfc":{"name":"init(_:_:)","abstract":"

Constructs a BFraction from numerator and denominator

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionVyACSgSdcfc":{"name":"init(_:)","abstract":"

Constructs a BFraction from its decimal value

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionVyACSgSScfc":{"name":"init(_:)","abstract":"

Constructs a BFraction from a String representation

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionVyACSayAA4BIntVGcfc":{"name":"init(_:)","abstract":"

Constructs a BFraction from a continued fraction - BInt version

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionVyACSaySiGcfc":{"name":"init(_:)","abstract":"

Constructs a BFraction from a continued fraction - Int version

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV9numeratorAA4BIntVvp":{"name":"numerator","abstract":"

The numerator - a BInt value

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV11denominatorAA4BIntVvp":{"name":"denominator","abstract":"

The denominator - a positive BInt value

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV3absACvp":{"name":"abs","abstract":"

The absolute value of self

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV11descriptionSSvp":{"name":"description","abstract":"

String value of self

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV9isIntegerSbvp":{"name":"isInteger","abstract":"

Is true if self is an integer, that is, the denominator is 1

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV10isNegativeSbvp":{"name":"isNegative","abstract":"

Is true if self < 0, false otherwise

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV10isPositiveSbvp":{"name":"isPositive","abstract":"

Is true if self > 0, false otherwise

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV6isZeroSbvp":{"name":"isZero","abstract":"

Is true if self = 0, false otherwise

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV6signumSivp":{"name":"signum","abstract":"

Is 0 if self = 0, 1 if self > 0, and -1 if self < 0

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV8asStringSSyF":{"name":"asString()","abstract":"

self as a String
","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV15asDecimalString9precision11exponentialSSSi_SbtF":{"name":"asDecimalString(precision:exponential:)","abstract":"

self as a Decimal String with a specified precision, possibly using exponential notation

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV8asDoubleSdyF":{"name":"asDouble()","abstract":"

self as a Double

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV19asContinuedFractionSayAA4BIntVGyF":{"name":"asContinuedFraction()","abstract":"

self as a Continued Fraction

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1popyA2CFZ":{"name":"+(_:)","abstract":"

Prefix plus

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1poiyA2C_ACtFZ":{"name":"+(_:_:)","abstract":"

Addition

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1poiyA2C_AA4BIntVtFZ":{"name":"+(_:_:)","abstract":"

Addition

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1poiyAcA4BIntV_ACtFZ":{"name":"+(_:_:)","abstract":"

Addition

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1poiyA2C_SitFZ":{"name":"+(_:_:)","abstract":"

Addition

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1poiyACSi_ACtFZ":{"name":"+(_:_:)","abstract":"

Addition

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2peoiyyACz_ACtFZ":{"name":"+=(_:_:)","abstract":"

x = x + y

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2peoiyyACz_AA4BIntVtFZ":{"name":"+=(_:_:)","abstract":"

x = x + y

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2peoiyyACz_SitFZ":{"name":"+=(_:_:)","abstract":"

x = x + y

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1sopyA2CFZ":{"name":"-(_:)","abstract":"

Negation

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1soiyA2C_ACtFZ":{"name":"-(_:_:)","abstract":"

Subtraction

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1soiyA2C_AA4BIntVtFZ":{"name":"-(_:_:)","abstract":"

Subtraction

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1soiyAcA4BIntV_ACtFZ":{"name":"-(_:_:)","abstract":"

Subtraction

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1soiyA2C_SitFZ":{"name":"-(_:_:)","abstract":"

Subtraction

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1soiyACSi_ACtFZ":{"name":"-(_:_:)","abstract":"

Subtraction

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2seoiyyACz_ACtFZ":{"name":"-=(_:_:)","abstract":"

x = x - y

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2seoiyyACz_AA4BIntVtFZ":{"name":"-=(_:_:)","abstract":"

x = x - y

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2seoiyyACz_SitFZ":{"name":"-=(_:_:)","abstract":"

x = x - y

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1moiyA2C_ACtFZ":{"name":"*(_:_:)","abstract":"

Multiplication

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1moiyA2C_AA4BIntVtFZ":{"name":"*(_:_:)","abstract":"

Multiplication

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1moiyAcA4BIntV_ACtFZ":{"name":"*(_:_:)","abstract":"

Multiplication

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1moiyA2C_SitFZ":{"name":"*(_:_:)","abstract":"

Multiplication

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1moiyACSi_ACtFZ":{"name":"*(_:_:)","abstract":"

Multiplication

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2meoiyyACz_ACtFZ":{"name":"*=(_:_:)","abstract":"

x = x * y

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2meoiyyACz_AA4BIntVtFZ":{"name":"*=(_:_:)","abstract":"

x = x * y

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2meoiyyACz_SitFZ":{"name":"*=(_:_:)","abstract":"

x = x * y

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1doiyA2C_ACtFZ":{"name":"/(_:_:)","abstract":"

Division

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1doiyA2C_AA4BIntVtFZ":{"name":"/(_:_:)","abstract":"

Division

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1doiyAcA4BIntV_ACtFZ":{"name":"/(_:_:)","abstract":"

Division

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1doiyA2C_SitFZ":{"name":"/(_:_:)","abstract":"

Division

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1doiyACSi_ACtFZ":{"name":"/(_:_:)","abstract":"

Division

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2deoiyyACz_ACtFZ":{"name":"/=(_:_:)","abstract":"

x = x / y

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2deoiyyACz_AA4BIntVtFZ":{"name":"/=(_:_:)","abstract":"

x = x / y

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2deoiyyACz_SitFZ":{"name":"/=(_:_:)","abstract":"

x = x / y

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV6invertACyF":{"name":"invert()","abstract":"

Invert self

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV3modyAA4BIntVSgAFF":{"name":"mod(_:)","abstract":"

Modulus - BInt parameter

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV3modySiSgSiF":{"name":"mod(_:)","abstract":"

Modulus - Int parameter

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2mmoiyA2C_SitFZ":{"name":"**(_:_:)","abstract":"

Exponentiation

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV5roundAA4BIntVyF":{"name":"round()","abstract":"

Round

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV8truncateAA4BIntVyF":{"name":"truncate()","abstract":"

Truncate

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV4ceilAA4BIntVyF":{"name":"ceil()","abstract":"

Ceil

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV5floorAA4BIntVyF":{"name":"floor()","abstract":"

Floor

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2eeoiySbAC_ACtFZ":{"name":"==(_:_:)","abstract":"

Equal

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2eeoiySbAC_AA4BIntVtFZ":{"name":"==(_:_:)","abstract":"

Equal

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2eeoiySbAA4BIntV_ACtFZ":{"name":"==(_:_:)","abstract":"

Equal

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2eeoiySbAC_SitFZ":{"name":"==(_:_:)","abstract":"

Equal

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2eeoiySbSi_ACtFZ":{"name":"==(_:_:)","abstract":"

Equal

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2neoiySbAC_ACtFZ":{"name":"!=(_:_:)","abstract":"

Not equal

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2neoiySbAC_AA4BIntVtFZ":{"name":"!=(_:_:)","abstract":"

Not equal

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2neoiySbAA4BIntV_ACtFZ":{"name":"!=(_:_:)","abstract":"

Not equal

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2neoiySbAC_SitFZ":{"name":"!=(_:_:)","abstract":"

Not equal

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2neoiySbSi_ACtFZ":{"name":"!=(_:_:)","abstract":"

Not equal

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1loiySbAC_ACtFZ":{"name":"<(_:_:)","abstract":"

Less than

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1loiySbAC_AA4BIntVtFZ":{"name":"<(_:_:)","abstract":"

Less than

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1loiySbAA4BIntV_ACtFZ":{"name":"<(_:_:)","abstract":"

Less than

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1loiySbAC_SitFZ":{"name":"<(_:_:)","abstract":"

Less than

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1loiySbSi_ACtFZ":{"name":"<(_:_:)","abstract":"

Less than

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1goiySbAC_ACtFZ":{"name":">(_:_:)","abstract":"

Greater than

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1goiySbAC_AA4BIntVtFZ":{"name":">(_:_:)","abstract":"

Greater than

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1goiySbAA4BIntV_ACtFZ":{"name":">(_:_:)","abstract":"

Greater than

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1goiySbAC_SitFZ":{"name":">(_:_:)","abstract":"

Greater than

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1goiySbSi_ACtFZ":{"name":">(_:_:)","abstract":"

Greater than

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2leoiySbAC_ACtFZ":{"name":"<=(_:_:)","abstract":"

Less than or equal

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2leoiySbAC_AA4BIntVtFZ":{"name":"<=(_:_:)","abstract":"

Less than or equal

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2leoiySbAA4BIntV_ACtFZ":{"name":"<=(_:_:)","abstract":"

Less than or equal

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2leoiySbAC_SitFZ":{"name":"<=(_:_:)","abstract":"

Less than or equal

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2leoiySbSi_ACtFZ":{"name":"<=(_:_:)","abstract":"

Less than or equal

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2geoiySbAC_ACtFZ":{"name":">=(_:_:)","abstract":"

Greater than or equal

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2geoiySbAC_AA4BIntVtFZ":{"name":">=(_:_:)","abstract":"

Greater than or equal

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2geoiySbAA4BIntV_ACtFZ":{"name":">=(_:_:)","abstract":"

Greater than or equal

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2geoiySbAC_SitFZ":{"name":">=(_:_:)","abstract":"

Greater than or equal

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2geoiySbSi_ACtFZ":{"name":">=(_:_:)","abstract":"

Greater than or equal

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV9bernoulliyACSiFZ":{"name":"bernoulli(_:)","abstract":"

Bernoulli number

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV17bernoulliSequenceySayACGSiFZ":{"name":"bernoulliSequence(_:)","abstract":"

Bernoulli numbers

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV8harmonicyACSiFZ":{"name":"harmonic(_:)","abstract":"

Harmonic number: 1 + 1 / 2 + … + 1 / n

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV16harmonicSequenceySayACGSiFZ":{"name":"harmonicSequence(_:)","abstract":"

Harmonic sequence: The first n harmonic numbers

","parent_name":"BFraction"},"Structs/BFraction.html":{"name":"BFraction","abstract":"

A signed fraction with numerator and denominator of unbounded size.

"},"Structs/BInt.html":{"name":"BInt","abstract":"

A signed integer of unbounded size.

"},"Structs/CRT.html":{"name":"CRT","abstract":"

CRT instances implement the Chinese Remainder Theorem

"},"Structs.html":{"name":"Structures","abstract":"

The following structures are available globally.

"},"Typealiases.html":{"name":"Type Aliases","abstract":"

The following type aliases are available globally.

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BigInt Docs (100% documented)

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BigInt

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Contents:

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The BigInt package provides arbitrary-precision integer arithmetic in Swift. -Its functionality falls in the following categories:

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  • Arithmetic: add, subtract, multiply, divide, remainder and exponentiation
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  • Comparison: the six standard operations == != < <= > >=
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  • Shifting: logical left shift and rigth shift
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  • Logical: bitwise and, or, xor, and not
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  • Modulo: normal modulus, inverse modulus, and modular exponentiation
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  • Conversion: to double, to integer, to string, to magnitude byte array, and to 2’s complement byte array
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  • Primes: prime number testing, probable prime number generation and primorial
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  • Miscellaneous: random number generation, greatest common divisor, least common multiple, n-th root, square root modulo an odd prime, -Jacobi symbol, Kronecker symbol, Factorial function, Binomial function, Fibonacci numbers, Lucas numbers and Bernoulli numbers
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  • Fractions: Standard arithmetic on fractions whose numerators and denominators are of unbounded size
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BigInt requires Swift 5.0. It also requires that the Int and UInt types be 64 bit types.

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Usage

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In your projects Package.swift file add a dependency like

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  dependencies: [
-  .package(url: "https://github.com/leif-ibsen/BigInt", from: "1.14.0"),
-  ]
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Examples

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Creating BInt’s

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  // From an integer
-  let a = BInt(27)
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-  // From a decimal value
-  let x = BInt(1.12345e30) // x = 1123450000000000064996914495488
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-  // From string literals
-  let b = BInt("123456789012345678901234567890")!
-  let c = BInt("1234567890abcdef1234567890abcdef", radix: 16)!
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-  // From magnitude and sign
-  let m: Limbs = [1, 2, 3]
-  let d = BInt(m) // d = 1020847100762815390427017310442723737601
-  let e = BInt(m, true) // e = -1020847100762815390427017310442723737601
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-  // From a big-endian 2's complement byte array
-  let f = BInt(signed: [255, 255, 127]) // f = -129
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-  // From a big-endian magnitude byte array
-  let g = BInt(magnitude: [255, 255, 127]) // g = 16777087
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-  // Random value with specified bitwidth
-  let h = BInt(bitWidth: 43) // For example h = 3965245974702 (=0b111001101100111011000100111110100010101110)
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-  // Random value less than a given value
-  let i = h.randomLessThan() // For example i = 583464003284
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- -

Converting BInt’s

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  let x = BInt(16777087)
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-  // To double
-  let d = x.asDouble() // d = 16777087.0
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-  // To strings
-  let s1 = x.asString() // s1 = "16777087"
-  let s2 = x.asString(radix: 16) // s2 = "ffff7f"
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-  // To big-endian magnitude byte array
-  let b1 = x.asMagnitudeBytes() // b1 = [255, 255, 127]
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-  // To big-endian 2's complement byte array
-  let b2 = x.asSignedBytes() // b2 = [0, 255, 255, 127]
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- -

Performance

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To assess the performance of BigInt, the execution times for a number of common operations were measured on an iMac 2021, Apple M1 chip. -The results are in the table below. It shows the operation being measured and the time it took (in microseconds or milliseconds).

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Four large numbers ‘a1000’, ‘b1000’, ‘c2000’ and ‘p1000’ were used throughout the measurements. Their actual values are shown under the table.

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OperationSwift codeTime
As stringc2000.asString()13 uSec
As signed bytesc2000.asSignedBytes()0.30 uSec
Bitwise anda1000 & b10000.083 uSec
Bitwise ora1000 | b10000.083 uSec
Bitwise xora1000 ^ b10000.082 uSec
Bitwise not~c20000.087 uSec
Test bitc2000.testBit(701)0.017 uSec
Flip bitc2000.flipBit(701)0.018 uSec
Set bitc2000.setBit(701)0.018 uSec
Clear bitc2000.clearBit(701)0.018 uSec
Additiona1000 + b10000.07 uSec
Subtractiona1000 - b10000.08 uSec
Multiplicationa1000 * b10000.32 uSec
Divisionc2000 / a10002.2 uSec
Modulusc2000.mod(a1000)2.2 uSec
Inverse modulusc2000.modInverse(p1000)83 uSec
Modular exponentiationa1000.expMod(b1000, c2000)3.5 mSec
Equalc2000 + 1 == c20000.017 uSec
Less thanb1000 + 1 < b10000.021 uSec
Shift 1 leftc2000 <<= 10.05 uSec
Shift 1 rightc2000 >>= 10.06 uSec
Shift 100 leftc2000 <<= 1000.14 uSec
Shift 100 rightc2000 >>= 1000.11 uSec
Is probably primep1000.isProbablyPrime()5.8 mSec
Make probable 1000 bit primeBInt.probablePrime(1000)60 mSec
Next probable primec2000.nextPrime()730 mSec
PrimorialBInt.primorial(100000)8.5 mSec
BinomialBInt.binomial(100000, 10000)22 mSec
FactorialBInt.factorial(100000)57 mSec
FibonacciBInt.fibonacci(100000)0.22 mSec
Greatest common divisora1000.gcd(b1000)29 uSec
Extended gcda1000.gcdExtended(b1000)81 uSec
Least common multiplea1000.lcm(b1000)32 uSec
Make random numberc2000.randomLessThan()1.2 uSec
Squarec2000 ** 20.68 uSec
Square rootc2000.sqrt()13 uSec
Square root and remainderc2000.sqrtRemainder()13 uSec
Is perfect square(c2000 * c2000).isPerfectSquare()16 uSec
Square root modulob1000.sqrtMod(p1000)1.6 mSec
Powerc2000 ** 1111.9 mSec
Rootc2000.root(111)15 uSec
Root and remainderc2000.rootRemainder(111)17 uSec
Is perfect rootc2000.isPerfectRoot()13 mSec
Jacobi symbolc2000.jacobiSymbol(p1000)0.15 mSec
Kronecker symbolc2000.kroneckerSymbol(p1000)0.15 mSec
Bernoulli numberBFraction.bernoulli(1000)83 mSec
- -

a1000 = 3187705437890850041662973758105262878153514794996698172406519277876060364087986868049465132757493318066301987043192958841748826350731448419937544810921786918975580180410200630645469411588934094075222404396990984350815153163569041641732160380739556436955287671287935796642478260435292021117614349253825
-b1000 = 9159373012373110951130589007821321098436345855865428979299172149373720601254669552044211236974571462005332583657082428026625366060511329189733296464187785766230514564038057370938741745651937465362625449921195096442684523511715110908407508139315000469851121118117438147266381183636498494901233452870695
-c2000 = 1190583332681083129323588684910845359379915367459759242106618067261956856381281184752008892106576666833853411939711280970145570546868549934865719229538926506588929417873149597614787608112658086250354719939407543740242931571462165384138560315454455247539461818779966171917173966217706187439870264672508450210272481951994459523586160979759782950984370978171111340529321052541588344733968902238813379990628157732181128074253104347868153860527298911917508606081710893794973605227829729403843750412766366804402629686458092685235454222856584200220355212623917637542398554907364450159627359316156463617143173
-p1000 (probably a prime) = 7662841304438384296568220077355872003841475576593385710590818274399706072141018649398767137142090308734613594718593893634649122767374115742644499040193270857876678047220373151142747088797516044505739487695946446362769947024029728822155570722524629197074319602110260674029276185098937139753025851896997

- -

Fractions

- -

Fractions are represented as BFraction values consisting of a numerator BInt value and a denominator BInt value. The representation is normalized:

- -
    -
  • The numerator and denominator have no common factors except 1
    • -
  • The denominator is always positive
    • -
  • Zero is represented as 0/1
    • -
- -

Creating BFraction’s

- -

Fractions are created by

- -
    -
  • Specifying the numerator and denominator explicitly f.ex. BFraction(17, 4)
    • -
  • Specifying the decimal value explictly f.ex. BFraction(4.25)
    • -
  • Using a string representation f.ex. BFraction(“4.25”)! or equivalently BFraction(“425E-2”)!
    • -
  • Specifying a continued fraction like BFraction([3, 4, 12, 4]) equivalent to 649 / 200
    • -
- -

Defining a fraction by giving its decimal value (like 4.25) might lead to surprises, -because not all decimal values can be represented exactly as a floating point number. -For example, one might think that BFraction(0.1) would equal 1/10, -but in fact it equals 3602879701896397 / 36028797018963968 = 0.1000000000000000055511151231257827021181583404541015625

- -

Converting BFraction’s

- -

BFraction values can be converted to String values, to decimal String values, to Double values and to Continued Fraction values.

-
  let x = BFraction(1000, 7)
-
-  // To String
-  let s1 = x.asString() // s1 = "1000 / 7"
-
-  // To decimal String
-  let s1 = x.asDecimalString(precision: 8, exponential: false) // s1 = "142.85714"
-  let s2 = x.asDecimalString(precision: 8, exponential: true) // s2 = "1.4285714E+2"
-
-  // To Double
-  let d = x.asDouble() // d = 142.8571428571429
-
-  // To Continued Fraction
-  let f = x.asContinuedFraction() // f = [BInt(142), BInt(1), BInt(6)]
-
- -

Operations

- -

The operations available to fractions are:

- -
    -
  • Arithmetic -
      -
    • addition
      • -
    • subtraction
      • -
    • multiplication
      • -
    • division
      • -
    • modulo an integer
      • -
    • exponentiation
      • -
    - -

    • -
  • Rounding to an integer

    - -
      -
    • round - to nearest integer
      • -
    • truncate - towards 0
      • -
    • ceil - towards +infinity
      • -
    • floor - towards -infinity
      • -
    - -

    • -
  • Comparison - the six standard operations == != < <= > >=
    • -

- -

Bernoulli Numbers

- -

The static function

-
let bn = BFraction.bernoulli(n)
-
- -

computes the n'th (n >= 0) Bernoulli number, which is a rational number.
-For example

-
print(BFraction.bernoulli(60))
-print(BFraction.bernoulli(60).asDecimalString(precision: 20, exponential: true))
-
- -

would print

-
-1215233140483755572040304994079820246041491 / 56786730
--2.1399949257225333665E+34
-
- -

The static function

-
let x = BFraction.bernoulliSequence(n)
-
- -

computes the n even numbered Bernoulli numbers B(0), B(2) … B(2 * n - 2).

- -

Harmonic Numbers

- -

The static function

-
let Hn = BFraction.harmonic(n)
-
- -

computes the n'th harmonic number, that is, 1 + ½ + … + 1/n
-The static function

-
let x = BFraction.harmonicSequence(n)
-
- -

returns an array containing the first n harmonic numbers.

- -

Chinese Remainder Theorem

- -

The CRT structure implements the Chinese Remainder Theorem. Construct a CRT instance from a given set of moduli, -and then use the compute method to compute the CRT value for a given set of residues. The same instance can be reused -for any set of input data, as long as the moduli are the same. -This is relevant because it takes longer time to create the CRT instance than to compute the CRT value.
-For example

-
let moduli = [3, 5, 7]
-let residues = [2, 2, 6]
-let crt = CRT(moduli)!
-print("CRT value:", crt.compute(residues))
-
- -

would print

-
CRT value: 62
-
- -

References

- -

Algorithms from the following books and papers have been used in the implementation. -There are references in the source code where appropriate.

- -
    -
  • [BRENT] - Brent and Zimmermann: Modern Computer Arithmetic, 2010
    • -
  • [BURNIKEL] - Burnikel and Ziegler: Fast Recursive Division, October 1998
    • -
  • [CRANDALL] - Crandall and Pomerance: Prime Numbers - A Computational Perspective. Second Edition, Springer 2005
    • -
  • [GRANLUND] - Moller and Granlund: Improved Division by Invariant Integers, 2011
    • -
  • [HACKER] - Henry S. Warren, Jr.: Hacker’s Delight. Second Edition, Addison-Wesley
    • -
  • [HANDBOOK] - Menezes, Oorschot, Vanstone: Handbook of Applied Cryptography. CRC Press 1996
    • -
  • [JEBELEAN] - Tudor Jebelean: An Algorithm for Exact Division. Journal of Symbolic Computation, volume 15, 1993
    • -
  • [KNUTH] - Donald E. Knuth: Seminumerical Algorithms, Third Edition
    • -
  • [KOC] - Cetin Kaya Koc: A New Algorithm for Inversion mod p^k
    • -
- -

Algorithms

- -

Some of the algorithms used in BigInt are described below.

- -

Multiplication

- -
    -
  • Schonhage-Strassen FFT based algorithm for numbers above 384000 bits
    • -
  • ToomCook-3 algorithm for numbers above 12800 bits
    • -
  • Karatsuba algorithm for numbers above 6400 bits
    • -
  • Basecase - Knuth algorithm M
    • -
- -

Division and Remainder

- -
    -
  • Burnikel-Ziegler algorithm for divisors above 3840 bits provided the dividend has at least 3840 bits more than the divisor
    • -
  • Basecase - Knuth algorithm D
    • -
  • Exact Division - Jebelean’s exact division algorithm
    • -
- -

Greatest Common Divisor and Extended Greatest Common Divisor

- -

Lehmer’s algorithm [KNUTH] chapter 4.5.2, with binary GCD basecase.

- -

Modular Exponentiation

- -

Sliding window algorithm 14.85 from [HANDBOOK] using Barrett reduction for exponents with fewer than 2048 bits -and Montgomery reduction for larger exponents.

- -

Inverse Modulus

- -

If the modulus is a (not too large) power of 2, the algorithm from [KOC] section 7. -Else, it is computed via the extended GCD algorithm.

- -

Square Root

- -

Algorithm 1.12 (SqrtRem) from [BRENT] with algorithm 9.2.11 from [CRANDALL] as basecase.

- -

Square Root Modulo a Prime Number

- -

Algorithm 2.3.8 from [CRANDALL].

- -

Prime Number Test

- -

Miller-Rabin test.

- -

Prime Number Generation

- -

The algorithm from Java BigInteger translated to Swift.

- -

Factorial

- -

The ‘SplitRecursive’ algorithm from Peter Luschny: https://www.luschny.de

- -

Fibonacci

- -

The ‘fastDoubling’ algorithm from Project Nayuki: https://www.nayuki.io

- -

Jacobi and Kronecker symbols

- -

Algorithm 2.3.5 from [CRANDALL].

- -

Bernoulli Numbers

- -

Computed via Tangent numbers which is fast because it only involves integer arithmetic -but no fractional arithmetic.

- -

Chinese Remainder Theorem

- -

The Garner algorithm 2.1.7 from [CRANDALL].

- -
-
- -
-
- - +Documentation
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r=[],s=function(t,e,n,r){if(p(n))Object.keys(n).forEach((function(o){var i=n[o];p(i)?(r.push(o),r.push("."),s(t,e,i,r),r.pop(),r.pop()):(r.push(o),s(t,e,i,r),r.pop())}));else if(a(n))n.forEach((function(n,o){p(n)?(r.push("["+o+"]"),r.push("."),s(t,e,n,r),r.pop(),r.pop()):(r.push("["+o+"]"),s(t,e,n,r),r.pop())}));else if(u(n)){var c=_t.test(n);if(c){var l="Detected HTML in message '"+n+"' of keypath '"+r.join("")+"' at '"+e+"'. 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this._root.$i18n.vm.$watch("locale",(function(t){r.$set(r,"locale",t),r.$forceUpdate()}),{immediate:!0})},xt.prototype.onComponentInstanceCreated=function(t){this._componentInstanceCreatedListener&&this._componentInstanceCreatedListener(t,this)},Ot.vm.get=function(){return this._vm},Ot.messages.get=function(){return m(this._getMessages())},Ot.dateTimeFormats.get=function(){return m(this._getDateTimeFormats())},Ot.numberFormats.get=function(){return m(this._getNumberFormats())},Ot.availableLocales.get=function(){return Object.keys(this.messages).sort()},Ot.locale.get=function(){return this._vm.locale},Ot.locale.set=function(t){this._vm.$set(this._vm,"locale",t)},Ot.fallbackLocale.get=function(){return this._vm.fallbackLocale},Ot.fallbackLocale.set=function(t){this._localeChainCache={},this._vm.$set(this._vm,"fallbackLocale",t)},Ot.formatFallbackMessages.get=function(){return this._formatFallbackMessages},Ot.formatFallbackMessages.set=function(t){this._formatFallbackMessages=t},Ot.missing.get=function(){return this._missing},Ot.missing.set=function(t){this._missing=t},Ot.formatter.get=function(){return this._formatter},Ot.formatter.set=function(t){this._formatter=t},Ot.silentTranslationWarn.get=function(){return this._silentTranslationWarn},Ot.silentTranslationWarn.set=function(t){this._silentTranslationWarn=t},Ot.silentFallbackWarn.get=function(){return this._silentFallbackWarn},Ot.silentFallbackWarn.set=function(t){this._silentFallbackWarn=t},Ot.preserveDirectiveContent.get=function(){return this._preserveDirectiveContent},Ot.preserveDirectiveContent.set=function(t){this._preserveDirectiveContent=t},Ot.warnHtmlInMessage.get=function(){return this._warnHtmlInMessage},Ot.warnHtmlInMessage.set=function(t){var e=this,n=this._warnHtmlInMessage;if(this._warnHtmlInMessage=t,n!==t&&("warn"===t||"error"===t)){var r=this._getMessages();Object.keys(r).forEach((function(t){e._checkLocaleMessage(t,e._warnHtmlInMessage,r[t])}))}},Ot.postTranslation.get=function(){return this._postTranslation},Ot.postTranslation.set=function(t){this._postTranslation=t},Ot.sync.get=function(){return this._sync},Ot.sync.set=function(t){this._sync=t},xt.prototype._getMessages=function(){return this._vm.messages},xt.prototype._getDateTimeFormats=function(){return this._vm.dateTimeFormats},xt.prototype._getNumberFormats=function(){return this._vm.numberFormats},xt.prototype._warnDefault=function(t,e,n,r,o,i){if(!h(n))return n;if(this._missing){var a=this._missing.apply(null,[t,e,r,o]);if(u(a))return a}else 0;if(this._formatFallbackMessages){var s=v.apply(void 0,o);return this._render(e,i,s.params,e)}return e},xt.prototype._isFallbackRoot=function(t){return(this._fallbackRootWithEmptyString?!t:h(t))&&!h(this._root)&&this._fallbackRoot},xt.prototype._isSilentFallbackWarn=function(t){return this._silentFallbackWarn 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i=this._translate(n,e,this.fallbackLocale,t,r,"raw",o);if(this._isFallbackRoot(i)){if(!this._root)throw Error("unexpected error");return this._root.$i18n.i(t,e,o)}return this._warnDefault(e,t,i,r,[o],"raw")},xt.prototype.i=function(t,e,n){return t?(u(e)||(e=this.locale),this._i(t,e,this._getMessages(),null,n)):""},xt.prototype._tc=function(t,e,n,r,o){var i,a=[],s=arguments.length-5;while(s-- >0)a[s]=arguments[s+5];if(!t)return"";void 0===o&&(o=1);var c={count:o,n:o},u=v.apply(void 0,a);return u.params=Object.assign(c,u.params),a=null===u.locale?[u.params]:[u.locale,u.params],this.fetchChoice((i=this)._t.apply(i,[t,e,n,r].concat(a)),o)},xt.prototype.fetchChoice=function(t,e){if(!t||!u(t))return null;var n=t.split("|");return e=this.getChoiceIndex(e,n.length),n[e]?n[e].trim():t},xt.prototype.tc=function(t,e){var n,r=[],o=arguments.length-2;while(o-- 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")]):e._e()],2)])},qr=[],Fr={name:"Tag",props:{name:{type:String,required:!0},isFocused:{type:Boolean,default:()=>!1},isRemovableTag:{type:Boolean,default:!1},isTranslatableTag:{type:Boolean,default:!1},isActiveTag:{type:Boolean,default:!1},activeTags:{type:Array,required:!1},keyboardIsVirtual:{type:Boolean,default:!1}},watch:{isFocused(e){e&&this.focusButton()}},mounted(){document.addEventListener("copy",this.handleCopy),document.addEventListener("cut",this.handleCut),document.addEventListener("paste",this.handlePaste),this.$once("hook:beforeDestroy",(()=>{document.removeEventListener("copy",this.handleCopy),document.removeEventListener("cut",this.handleCut),document.removeEventListener("paste",this.handlePaste)}))},methods:{isCurrentlyActiveElement(){return document.activeElement===this.$refs.button},handleCopy(e){if(!this.isCurrentlyActiveElement())return;e.preventDefault();let t=[];t=this.activeTags.length>0?this.activeTags:[this.name],e.clipboardData.setData("text/html",Ir({tags:t})),e.clipboardData.setData("text/plain",t.join(" "))},handleCut(e){this.isCurrentlyActiveElement()&&this.isRemovableTag&&(this.handleCopy(e),this.deleteTag(e))},handlePaste(e){this.isCurrentlyActiveElement()&&this.isRemovableTag&&(e.preventDefault(),this.deleteTag(e),this.$emit("paste-content",e))},deleteTag(e){this.$emit("delete-tag",{tagName:this.name,event:e}),this.$emit("prevent-blur")},focusButton(e={}){this.keyboardIsVirtual||this.$refs.button.focus(),0===e.buttons&&this.isFocused&&this.deleteTag(e)}},computed:{ariaSelected:({isActiveTag:e,isRemovableTag:t})=>t?e?"true":"false":null}},Hr=Fr,Vr=(0,Z.Z)(Hr,jr,qr,!1,null,"7e76f326",null),Wr=Vr.exports,Ur={name:"Tags",mixins:[Ar,Zr],props:{tags:{type:Array,default:()=>[]},activeTags:{type:Array,default:()=>[]},translatableTags:{type:Array,default:()=>[]},ariaLabel:{type:String,required:!1},id:{type:String,required:!1},input:{type:String,default:null},areTagsRemovable:{type:Boolean,default:!1},keyboardIsVirtual:{type:Boolean,default:!1}},components:{Tag:Wr},methods:{focusTag(e){this.focusIndex(this.tags.indexOf(e))},startingPointHook(){this.$emit("focus-prev")},handleFocus(e,t){this.focusIndex(t),this.isScrolling=!1,this.$emit("focus",e)},endingPointHook(){this.$emit("focus-next")},resetScroll(){this.$refs["scroll-wrapper"].scrollLeft=0},handleKeydown(e){const{key:t}=e,n=this.tags[this.focusedIndex];kr(t)&&n&&this.$emit("delete-tag",{tagName:n.label||n,event:e})}},computed:{totalItemsToNavigate:({tags:e})=>e.length}},Gr=Ur,Qr=(0,Z.Z)(Gr,zr,Kr,!1,null,"1f2bd813",null),Jr=Qr.exports;const Yr=5,Xr="filter-input",eo="selected-tags",to="suggested-tags",no={autocorrect:"off",autocapitalize:"off",spellcheck:"false",role:"combobox","aria-haspopup":"true","aria-autocomplete":"none","aria-owns":"suggestedTags","aria-controls":"suggestedTags"};var io,so,ao={name:"FilterInput",mixins:[Ar,Pr],constants:{FilterInputId:Xr,SelectedTagsId:eo,SuggestedTagsId:to,AXinputProperties:no,TagLimit:Yr},components:{TagList:Jr,ClearRoundedIcon:Tr,FilterIcon:Mr},props:{positionReversed:{type:Boolean,default:()=>!1},tags:{type:Array,default:()=>[]},selectedTags:{type:Array,default:()=>[]},preventedBlur:{type:Boolean,default:()=>!1},placeholder:{type:String,default:()=>""},disabled:{type:Boolean,default:()=>!1},value:{type:String,default:()=>""},shouldTruncateTags:{type:Boolean,default:!1},focusInputWhenCreated:{type:Boolean,default:!1},focusInputWhenEmpty:{type:Boolean,default:!1},selectInputOnFocus:{type:Boolean,default:!1},clearFilterOnTagSelect:{type:Boolean,default:!0},preventBorderStyle:{type:Boolean,default:!1},translatableTags:{type:Array,default:()=>[]}},data(){return{resetedTagsViaDeleteButton:!1,FilterInputId:Xr,SelectedTagsId:eo,SuggestedTagsId:to,AXinputProperties:no,showSuggestedTags:!1}},computed:{hasSuggestedTags:({suggestedTags:e})=>e.length,hasSelectedTags:({selectedTags:e})=>e.length,inputIsNotEmpty:({input:e,hasSelectedTags:t})=>e.length||t,searchAriaLabelledBy:({hasSelectedTags:e})=>e?Xr.concat(" ",eo):Xr,modelValue:{get:({value:e})=>e,set(e){this.$emit("input",e)}},input:({value:e})=>e,suggestedTags:({tags:e,selectedTags:t,shouldTruncateTags:n})=>{const i=e.filter((e=>!t.includes(e)));return n?i.slice(0,Yr):i},displaySuggestedTags:({showSuggestedTags:e,suggestedTags:t})=>e&&t.length>0,inputMultipleSelectionListeners:({resetActiveTags:e,handleCopy:t,handleCut:n,handlePaste:i})=>({click:e,copy:t,cut:n,paste:i}),selectedTagsMultipleSelectionListeners:({handleSingleTagClick:e,selectInputAndTags:t,handleDeleteTag:n,selectedTagsKeydownHandler:i,focusTagHandler:s,handlePaste:a})=>({"click-tags":e,"select-all":t,"delete-tag":n,keydown:i,focus:s,"paste-tags":a})},watch:{async selectedTags(){this.resetedTagsViaDeleteButton?this.resetedTagsViaDeleteButton=!1:this.$el.contains(document.activeElement)&&await this.focusInput(),this.displaySuggestedTags&&this.hasSuggestedTags&&this.$refs.suggestedTags.resetScroll()},suggestedTags:{immediate:!0,handler(e){this.$emit("suggested-tags",e)}},showSuggestedTags(e){this.$emit("show-suggested-tags",e)}},methods:{async focusInput(){await this.$nextTick(),this.$refs.input.focus(),!this.input&&this.resetActiveTags&&this.resetActiveTags()},async resetFilters(e=!1){if(this.setFilterInput(""),this.setSelectedTags([]),!e)return this.$emit("update:preventedBlur",!0),this.resetActiveTags&&this.resetActiveTags(),void await this.focusInput();this.resetedTagsViaDeleteButton=!0,this.showSuggestedTags=!1,this.$refs.input.blur()},focusFirstTag(e=(()=>{})){this.showSuggestedTags||(this.showSuggestedTags=!0),this.hasSuggestedTags&&this.$refs.suggestedTags?this.$refs.suggestedTags.focusFirst():e()},setFilterInput(e){this.$emit("input",e)},setSelectedTags(e){this.$emit("update:selectedTags",e)},deleteTags(e){this.setSelectedTags(this.selectedTags.filter((t=>!e.includes(t))))},async handleBlur(e){const t=e.relatedTarget;t&&t.matches&&t.matches("button, input, ul")&&this.$el.contains(t)||(await this.$nextTick(),this.resetActiveTags(),this.preventedBlur?this.$emit("update:preventedBlur",!1):(this.showSuggestedTags=!1,this.$emit("blur")))},downHandler(e){const t=()=>this.$emit("focus-next",e);this.positionReversed?t():this.focusFirstTag(t)},upHandler(e){const t=()=>this.$emit("focus-prev",e);this.positionReversed?this.focusFirstTag(t):t()},handleFocusPrevOnSelectedTags(){this.positionReversed?this.focusFirstTag((()=>this.$emit("focus-prev"))):this.$emit("focus-prev")},handleFocus(){this.showSuggestedTags=!0,this.$emit("focus")}},created(){this.focusInputWhenCreated&&document.activeElement!==this.$refs.input&&(this.inputIsNotEmpty||this.focusInputWhenEmpty)&&this.focusInput()}},ro=ao,oo=(0,Z.Z)(ro,hr,pr,!1,null,"7a79f6ea",null),lo=oo.exports,co=n(5590),uo={name:"QuickNavigationHighlighter",props:{text:{type:String,required:!0},matcherText:{type:String,default:""}},render(e){const{matcherText:t,text:n}=this,i=[];let s=0;return t?([...t].forEach((t=>{const a=n.toLowerCase().indexOf(t.toLowerCase(),s);s&&i.push(e("span",n.slice(s,a)));const r=a+1;i.push(e("span",{class:"match"},n.slice(a,r))),s=r})),e("p",{class:"highlight"},i)):e("span",{class:"highlight"},n)}},ho=uo,po=(0,Z.Z)(ho,io,so,!1,null,"4a2ce75d",null),go=po.exports,fo=function(){var e=this,t=e._self._c;return t("SVGIcon",{staticClass:"magnifier-icon",attrs:{viewBox:"0 0 14 14",themeId:"magnifier"}},[t("path",{attrs:{d:"M15.0013 14.0319L10.9437 9.97424C11.8165 8.88933 12.2925 7.53885 12.2929 6.14645C12.2929 2.75841 9.53449 0 6.14645 0C2.75841 0 0 2.75841 0 6.14645C0 9.53449 2.75841 12.2929 6.14645 12.2929C7.57562 12.2929 8.89486 11.7932 9.94425 10.9637L14.0019 15.0213L15.0013 14.0319ZM6.13645 11.0736C4.83315 11.071 3.58399 10.5521 2.66241 9.63048C1.74084 8.70891 1.22194 7.45974 1.2193 6.15644C1.2193 3.44801 3.41802 1.23928 6.13645 1.23928C8.85488 1.23928 11.0536 3.44801 11.0536 6.15644C11.0636 8.86488 8.85488 11.0736 6.13645 11.0736Z"}})])},mo=[],yo={name:"MagnifierIcon",components:{SVGIcon:mr.Z}},vo=yo,bo=(0,Z.Z)(vo,fo,mo,!1,null,null,null),To=bo.exports,So=function(){var e=this,t=e._self._c;return t("div",{staticClass:"preview"},[e.state===e.STATE.success?t("DocumentationTopic",e._b({attrs:{enableMinimized:""}},"DocumentationTopic",e.topicProps,!1)):e.state===e.STATE.loadingSlowly?t("div",{staticClass:"loading"},e._l(e.LOADER_ROW_STYLES,(function(e){return t("div",{key:e["--index"],staticClass:"loading-row",style:e})})),0):e.state===e.STATE.error?t("div",{staticClass:"unavailable"},[t("p",[e._v(e._s(e.$t("quicknav.preview-unavailable")))])]):e._e()],1)},_o=[];const{extractProps:Co}=xa.methods,ko="hero",wo={error:"error",loading:"loading",loadingSlowly:"loadingSlowly",success:"success"},Io={...Ea,state:(0,w.d9)(Ea.state)};var xo={name:"QuickNavigationPreview",components:{DocumentationTopic:xa},constants:{PreviewState:wo,PreviewStore:Io},data(){return{store:Io}},provide(){return{store:this.store}},props:{json:{type:Object,required:!1},state:{type:String,required:!0,validator:e=>Object.hasOwnProperty.call(wo,e)}},computed:{LOADER_ROW_STYLES:()=>[{"--index":0,width:"30%"},{"--index":1,width:"80%"},{"--index":2,width:"50%"}],STATE:()=>wo,topicProps:({json:e})=>{const t=Co(e),{sections:n=[]}=e;let{abstract:i}=t;const s=n.find((({kind:e})=>e===ko));return!i&&s&&(i=s.content),{...t,abstract:i}}}},$o=xo,Do=(0,Z.Z)($o,So,_o,!1,null,"779b8b01",null),Po=Do.exports;class Lo{constructor(e){this.map=new Map,this.maxSize=e}get size(){return this.map.size}get(e){if(!this.map.has(e))return;const t=this.map.get(e);return this.map.delete(e),this.map.set(e,t),t}has(e){return this.map.has(e)}set(e,t){if(this.map.has(e)&&this.map.delete(e),this.map.set(e,t),this.map.size>this.maxSize){const e=this.map.keys().next().value;this.map.delete(e)}}*[Symbol.iterator](){yield*this.map}}var Ao=n(9652);const{PreviewState:Oo}=Po.constants,No="AbortError",Ro=20,Bo=1e3;var Eo={name:"QuickNavigationModal",components:{FilterInput:lo,GenericModal:co.Z,MagnifierIcon:To,TopicTypeIcon:_e.Z,QuickNavigationHighlighter:go,Reference:$s.Z,Preview:Po},mixins:[Zr],created(){this.abortController=null,this.$cachedSymbolResults=new Lo(Ro),this.loadingTimeout=null},data(){return{debouncedInput:"",userInput:"",focusedInput:!1,cachedSymbolResults:{},previewIsLoadingSlowly:!1,SCROLL_LOCK_DISABLE_ATTR:Ao.n}},props:{children:{type:Array,required:!0},showQuickNavigationModal:{type:Boolean,required:!0},technology:{type:String,required:!0}},computed:{childrenMap({children:e}){return Va(e)},filteredSymbols:({constructFuzzyRegex:e,children:t,fuzzyMatch:n,processedUserInput:i,childrenMap:s,orderSymbolsByPriority:a})=>{const r=t.filter((e=>"groupMarker"!==e.type&&null!=e.title));if(!i)return[];const o=n({inputLength:i.length,symbols:r,processedInputRegex:new RegExp(e(i),"i"),childrenMap:s}),l=[...new Map(o.map((e=>[e.path,e]))).values()];return a(l).slice(0,Ro)},isVisible:{get:({showQuickNavigationModal:e})=>e,set(e){this.$emit("update:showQuickNavigationModal",e)}},noResultsWereFound:({processedUserInput:e,totalItemsToNavigate:t})=>e.length&&!t,processedUserInput:({debouncedInput:e})=>e.replace(/\s/g,""),totalItemsToNavigate:({filteredSymbols:e})=>e.length,selectedSymbol:({filteredSymbols:e,focusedIndex:t})=>null!==t?e[t]:null,nextSymbol:({filteredSymbols:e,focusedIndex:t})=>{if(null===t)return null;let n=t+1;return n>=e.length&&(n=0),e[n]},focusedMatchElement:({$refs:e,focusedIndex:t})=>e.match[t].$el,previewJSON:({cachedSymbolResults:e,selectedSymbol:t})=>t?(e[t.uid]||{}).json:null,previewState:({cachedSymbolResults:e,previewIsLoadingSlowly:t,selectedSymbol:n})=>n&&Object.hasOwnProperty.call(e,n.uid)?e[n.uid].success?Oo.success:Oo.error:t?Oo.loadingSlowly:Oo.loading},watch:{userInput:"debounceInput",focusedIndex(){this.focusedInput||(this.scrollIntoView(),this.focusReference())},selectedSymbol:"fetchSelectedSymbolData",$route:"closeQuickNavigationModal"},methods:{closeQuickNavigationModal(){this.$emit("update:showQuickNavigationModal",!1)},constructFuzzyRegex(e){return[...e].reduce(((t,n,i)=>t.concat(`[${n}]`).concat(i{const s=n.exec(t.title);if(!s)return!1;const a=s[0].length;return!(a>3*e)&&{uid:t.uid,title:t.title,path:t.path,parents:Qa(t.parent,i),type:t.type,inputLengthDifference:t.title.length-e,matchLength:a,matchLengthDifference:a-e,start:s.index,substring:s[0]}})).filter(Boolean)},handleKeyEnter(){!this.noResultsWereFound&&this.userInput.length&&(this.$router.push(this.filteredSymbols[this.focusedIndex].path),this.closeQuickNavigationModal())},orderSymbolsByPriority(e){return e.sort(((e,t)=>e.matchLengthDifference>t.matchLengthDifference?1:e.matchLengthDifferencet.start?1:e.startt.inputLengthDifference?1:e.inputLengthDifference{this.previewState===Oo.loading&&(this.previewIsLoadingSlowly=!0)}),Bo),!this.selectedSymbol||this.$cachedSymbolResults.has(this.selectedSymbol.uid))return clearTimeout(this.loadingTimeout),void(this.previewIsLoadingSlowly=!1);const e=async e=>{if(e&&!this.$cachedSymbolResults.has(e.uid))try{const t=await(0,w.k_)(e.path,{signal:this.abortController.signal});this.$cachedSymbolResults.set(e.uid,{success:!0,json:t})}catch(t){t.name!==No&&this.$cachedSymbolResults.set(e.uid,{success:!1})}finally{this.cachedSymbolResults=Object.freeze(Object.fromEntries(this.$cachedSymbolResults))}};this.abortController&&this.abortController.abort(),this.abortController=new AbortController,await Promise.all([e(this.selectedSymbol).finally((()=>{clearTimeout(this.loadingTimeout),this.previewIsLoadingSlowly=!1})),e(this.nextSymbol)])}}},Mo=Eo,zo=(0,Z.Z)(Mo,dr,ur,!1,null,"479a2da8",null),Ko=zo.exports,Zo=function(){var e=this,t=e._self._c;return t("div",{staticClass:"adjustable-sidebar-width",class:{dragging:e.isDragging,"sidebar-hidden":e.hiddenOnLarge}},[t("div",{ref:"sidebar",staticClass:"sidebar"},[t("div",{ref:"aside",staticClass:"aside",class:e.asideClasses,style:e.asideStyles,attrs:{"aria-hidden":e.hiddenOnLarge?"true":null},on:{transitionstart:function(t){return t.target!==t.currentTarget?null:e.trackTransitionStart.apply(null,arguments)},transitionend:function(t){return t.target!==t.currentTarget?null:e.trackTransitionEnd.apply(null,arguments)}}},[e._t("aside",null,{animationClass:"aside-animated-child",scrollLockID:e.scrollLockID,breakpoint:e.breakpoint})],2),e.fixedWidth?e._e():t("div",{staticClass:"resize-handle",on:{mousedown:function(t){return t.preventDefault(),e.startDrag.apply(null,arguments)},touchstart:function(t){return t.preventDefault(),e.startDrag.apply(null,arguments)}}})]),t("div",{ref:"content",staticClass:"content"},[e._t("default")],2),t("BreakpointEmitter",{attrs:{scope:e.BreakpointScopes.nav},on:{change:function(t){e.breakpoint=t}}})],1)},jo=[],qo=n(7247),Fo=n(7188),Ho=n(5381),Vo=n(114),Wo=n(1147),Uo=n(1716);const Go="sidebar",Qo=1921,Jo=543,Yo=400,Xo={touch:{move:"touchmove",end:"touchend"},mouse:{move:"mousemove",end:"mouseup"}},el=(e,t=window.innerWidth)=>{const n=Math.min(t,Qo);return Math.floor(Math.min(n*(e/100),n))},tl={medium:30,large:20},nl={medium:50,large:50},il="sidebar-scroll-lock";var sl={name:"AdjustableSidebarWidth",constants:{SCROLL_LOCK_ID:il},components:{BreakpointEmitter:Fo["default"]},inject:["store"],props:{shownOnMobile:{type:Boolean,default:!1},hiddenOnLarge:{type:Boolean,default:!1},fixedWidth:{type:Number,default:null}},data(){const e=window.innerWidth,t=window.innerHeight,n=Ho.L3.large,i=el(tl[n]),s=el(nl[n]),a=e>=Qo?Jo:Yo,r=qo.tO.get(Go,a);return{isDragging:!1,width:this.fixedWidth||Math.min(Math.max(r,i),s),isTouch:!1,windowWidth:e,windowHeight:t,breakpoint:n,noTransition:!1,isTransitioning:!1,isOpeningOnLarge:!1,focusTrapInstance:null,mobileTopOffset:0,topOffset:0}},computed:{minWidthPercent:({breakpoint:e})=>tl[e]||0,maxWidthPercent:({breakpoint:e})=>nl[e]||100,maxWidth:({maxWidthPercent:e,windowWidth:t,fixedWidth:n})=>Math.max(n,el(e,t)),minWidth:({minWidthPercent:e,windowWidth:t,fixedWidth:n})=>Math.min(n||t,el(e,t)),widthInPx:({width:e})=>`${e}px`,hiddenOnLargeThreshold:({minWidth:e})=>e/2,events:({isTouch:e})=>e?Xo.touch:Xo.mouse,asideStyles:({widthInPx:e,mobileTopOffset:t,topOffset:n,windowHeight:i})=>({width:e,"--top-offset":n?`${n}px`:null,"--top-offset-mobile":`${t}px`,"--app-height":`${i}px`}),asideClasses:({isDragging:e,shownOnMobile:t,noTransition:n,isTransitioning:i,hiddenOnLarge:s,mobileTopOffset:a,isOpeningOnLarge:r})=>({dragging:e,"show-on-mobile":t,"hide-on-large":s,"is-opening-on-large":r,"no-transition":n,"sidebar-transitioning":i,"has-mobile-top-offset":a}),scrollLockID:()=>il,BreakpointScopes:()=>Ho.lU},async mounted(){window.addEventListener("keydown",this.onEscapeKeydown),window.addEventListener("resize",this.storeWindowSize,{passive:!0}),window.addEventListener("orientationchange",this.storeWindowSize,{passive:!0}),this.storeTopOffset(),0===this.topOffset&&0===window.scrollY||window.addEventListener("scroll",this.storeTopOffset,{passive:!0}),this.$once("hook:beforeDestroy",(()=>{window.removeEventListener("keydown",this.onEscapeKeydown),window.removeEventListener("resize",this.storeWindowSize),window.removeEventListener("orientationchange",this.storeWindowSize),window.removeEventListener("scroll",this.storeTopOffset),this.shownOnMobile&&this.toggleScrollLock(!1),this.focusTrapInstance&&this.focusTrapInstance.destroy()})),await this.$nextTick(),this.focusTrapInstance=new Vo.Z(this.$refs.aside)},watch:{$route:"closeMobileSidebar",width:{immediate:!0,handler:Ne((function(e){this.emitEventChange(e)}),150)},windowWidth:"getWidthInCheck",async breakpoint(e){this.getWidthInCheck(),e===Ho.L3.large&&this.closeMobileSidebar(),this.noTransition=!0,await(0,Re.J)(5),this.noTransition=!1},shownOnMobile:"handleExternalOpen",async isTransitioning(e){e?(await(0,Re.X)(1e3),this.isTransitioning=!1):this.updateContentWidthInStore()},hiddenOnLarge(){this.isTransitioning=!0}},methods:{getWidthInCheck:xr((function(){this.width>this.maxWidth?this.width=this.maxWidth:this.widththis.maxWidth&&(i=this.maxWidth),this.hiddenOnLarge&&i>=this.hiddenOnLargeThreshold&&(this.$emit("update:hiddenOnLarge",!1),this.isOpeningOnLarge=!0),this.width=Math.max(i,this.minWidth),i<=this.hiddenOnLargeThreshold&&this.$emit("update:hiddenOnLarge",!0)},stopDrag(e){e.preventDefault(),this.isDragging&&(this.isDragging=!1,qo.tO.set(Go,this.width),document.removeEventListener(this.events.move,this.handleDrag),document.removeEventListener(this.events.end,this.stopDrag),this.emitEventChange(this.width))},emitEventChange(e){this.$emit("width-change",e),this.updateContentWidthInStore()},getTopOffset(){const e=document.getElementById(Uo.EA);if(!e)return 0;const{y:t}=e.getBoundingClientRect();return Math.max(t,0)},handleExternalOpen(e){e&&(this.mobileTopOffset=this.getTopOffset()),this.toggleScrollLock(e)},async updateContentWidthInStore(){await this.$nextTick(),this.store.setContentWidth(this.$refs.content.offsetWidth)},async toggleScrollLock(e){const t=document.getElementById(this.scrollLockID);e?(await this.$nextTick(),Ao.Z.lockScroll(t),this.focusTrapInstance.start(),Wo.Z.hide(this.$refs.aside)):(Ao.Z.unlockScroll(t),this.focusTrapInstance.stop(),Wo.Z.show(this.$refs.aside))},storeTopOffset:Ne((function(){this.topOffset=this.getTopOffset()}),60),async trackTransitionStart({propertyName:e}){"width"!==e&&"transform"!==e||(this.isTransitioning=!0)},trackTransitionEnd({propertyName:e}){"width"!==e&&"transform"!==e||(this.isTransitioning=!1,this.isOpeningOnLarge=!1)}}},al=sl,rl=(0,Z.Z)(al,Zo,jo,!1,null,"5cd50784",null),ol=rl.exports,ll=function(){var e=this,t=e._self._c;return 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bc(e,t){e.component(`${t}recycle-scroller`,tc),e.component(`${t}RecycleScroller`,tc),e.component(`${t}dynamic-scroller`,dc),e.component(`${t}DynamicScroller`,dc),e.component(`${t}dynamic-scroller-item`,yc),e.component(`${t}DynamicScrollerItem`,yc)}const Tc={version:"1.1.2",install(e,t){const n=Object.assign({},{installComponents:!0,componentsPrefix:""},t);for(const i in n)"undefined"!==typeof n[i]&&(Kl[i]=n[i]);n.installComponents&&bc(e,n.componentsPrefix)}};let Sc=null;function _c(e){const t=(0,nn.RL)((0,nn.hr)(e));return new RegExp(t,"ig")}"undefined"!==typeof window?Sc=window.Vue:"undefined"!==typeof n.g&&(Sc=n.g.Vue),Sc&&Sc.use(Tc);var Cc,kc,wc=function(){var e=this,t=e._self._c;return 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t("div",{staticClass:"navigator-card-item"},[t("div",{staticClass:"head-wrapper"},[t("div",{staticClass:"depth-spacer"},[e._t("depth-spacer")],2),e.hideNavigatorIcon?e._e():t("div",{staticClass:"navigator-icon-wrapper"},[e._t("navigator-icon",null,{className:"navigator-icon"})],2),t("div",{staticClass:"title-container"},[e._t("title-container")],2)])])},Dc=[],Pc={name:"BaseNavigatorCardItem",props:{hideNavigatorIcon:{type:Boolean,default:()=>!1}}},Lc=Pc,Ac=(0,Z.Z)(Lc,$c,Dc,!1,null,"41ab423b",null),Oc=Ac.exports,Nc={name:"HighlightMatch",props:{text:{type:String,required:!0},matcher:{type:RegExp,default:void 0}},render(e){const{matcher:t,text:n}=this;if(!t)return e("p",{class:"highlight"},n);const i=[];let s=0,a=null;const r=new RegExp(t,"gi");while(null!==(a=r.exec(n))){const t=a[0].length,r=a.index+t,o=n.slice(s,a.index);o&&i.push(e("span",o));const l=n.slice(a.index,r);l&&i.push(e("span",{class:"match"},l)),s=r}const o=n.slice(s,n.length);return o&&i.push(e("span",o)),e("p",{class:"highlight"},i)}},Rc=Nc,Bc=(0,Z.Z)(Rc,Cc,kc,!1,null,"7b81ca08",null),Ec=Bc.exports,Mc={name:"NavigatorCardItem",mixins:[vc({idProp:e=>e.item.uid})],components:{BaseNavigatorCardItem:Oc,HighlightMatches:Ec,TopicTypeIcon:_e.Z,InlineChevronRightIcon:xc.Z,Reference:$s.Z,Badge:ei.Z},props:{isRendered:{type:Boolean,default:!1},item:{type:Object,required:!0},expanded:{type:Boolean,default:!1},filterPattern:{type:RegExp,default:void 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hd={name:"NavigatorCard",constants:{STORAGE_KEY:nd,FILTER_TAGS:id,FILTER_TAGS_TO_LABELS:sd,FILTER_LABELS_TO_TAGS:ad,TOPIC_TYPE_TO_TAG:rd,ERROR_FETCHING:cd,ITEMS_FOUND:dd,HIDE_DEPRECATED:ud},components:{FilterInput:lo,NavigatorCardItem:Zc,DynamicScroller:dc,DynamicScrollerItem:yc,BaseNavigatorCard:Xc},props:{...Xc.props,children:{type:Array,required:!0},activePath:{type:Array,required:!0},type:{type:String,required:!0},scrollLockID:{type:String,default:""},errorFetching:{type:Boolean,default:!1},apiChanges:{type:Object,default:null},isTechnologyBeta:{type:Boolean,default:!1},navigatorReferences:{type:Object,default:()=>{}},renderFilterOnTop:{type:Boolean,default:!1},hideAvailableTags:{type:Boolean,default:!1}},mixins:[Zr],data(){return{filter:"",debouncedFilter:"",selectedTags:[],openNodes:Object.freeze({}),nodesToRender:Object.freeze([]),activeUID:null,lastFocusTarget:null,allNodesToggled:!1,translatableTags:[ud]}},computed:{politeAriaLive(){const{hasNodes:e,nodesToRender:t}=this;return e?this.$tc(dd,t.length,{number:t.length}):""},assertiveAriaLive:({hasNodes:e,hasFilter:t,errorFetching:n})=>e?"":t?od:n?cd:ld,availableTags({selectedTags:e,renderableChildNodesMap:t,apiChangesObject:n,hideAvailableTags:i}){if(i||e.length)return[];const s=new Set(Object.values(n)),a=new Set(Object.values(sd)),r=new Set([ud]);s.size&&r.delete(ud);const o={type:[],changes:[],other:[]};for(const l in t){if(!Object.hasOwnProperty.call(t,l))continue;if(!a.size&&!s.size&&!r.size)break;const{type:e,path:i,deprecated:c}=t[l],d=sd[rd[e]],u=n[i];a.has(d)&&(o.type.push(d),a.delete(d)),u&&s.has(u)&&(o.changes.push(this.$t(It.Ag[u])),s.delete(u)),c&&r.has(ud)&&(o.other.push(ud),r.delete(ud))}return o.type.concat(o.changes,o.other)},selectedTagsModelValue:{get(){return this.selectedTags.map((e=>sd[e]||this.$t(It.Ag[e])||e))},set(e){(this.selectedTags.length||e.length)&&(this.selectedTags=e.map((e=>ad[e]||It.ct[e]||e)))}},filterPattern:({debouncedFilter:e})=>e?new RegExp(_c(e),"i"):null,itemSize:()=>qa,childrenMap({children:e}){return Va(e)},activePathChildren({activeUID:e,childrenMap:t}){return e&&t[e]?Qa(e,t):[]},activePathMap:({activePathChildren:e})=>Object.fromEntries(e.map((({uid:e})=>[e,!0]))),activeIndex:({activeUID:e,nodesToRender:t})=>t.findIndex((t=>t.uid===e)),filteredChildren({hasFilter:e,children:t,filterPattern:n,selectedTags:i,apiChanges:s}){if(!e)return[];const a=new Set(i);return t.filter((({title:e,path:t,type:i,deprecated:r,deprecatedChildrenCount:o,childUIDs:l})=>{const c=r||o===l.length,d=!n||n.test(e);let u=!0;a.size&&(u=a.has(rd[i]),s&&!u&&(u=a.has(s[t])),!c&&a.has(ud)&&(u=!0));const h=!s||!!s[t];return d&&u&&h}))},renderableChildNodesMap({hasFilter:e,childrenMap:t,deprecatedHidden:n,filteredChildren:i,removeDeprecated:s}){if(!e)return t;const a=i.length-1,r=new Set([]);for(let o=a;o>=0;o-=1){const e=i[o],a=t[e.groupMarkerUID];if(a&&r.add(a),r.has(e))continue;if(r.has(t[e.parent])&&e.type!==Ce.t.groupMarker){r.add(e);continue}let l=[];e.childUIDs.length&&(l=s(Ua(e.uid,t),n)),l.concat(Qa(e.uid,t)).forEach((e=>r.add(e)))}return Va([...r])},nodeChangeDeps:({filteredChildren:e,activePathChildren:t,debouncedFilter:n,selectedTags:i})=>[e,t,n,i],hasFilter({debouncedFilter:e,selectedTags:t,apiChanges:n}){return Boolean(e.length||t.length||n)},deprecatedHidden:({selectedTags:e})=>e[0]===ud,apiChangesObject(){return this.apiChanges||{}},hasNodes:({nodesToRender:e})=>!!e.length,totalItemsToNavigate:({nodesToRender:e})=>e.length,lastActivePathItem:({activePath:e})=>ed(e)},created(){this.restorePersistedState()},watch:{filter:"debounceInput",nodeChangeDeps:"trackOpenNodes",activePath:"handleActivePathChange",apiChanges(e){e||(this.selectedTags=this.selectedTags.filter((e=>!this.$t(It.Ag[e]))))},async activeUID(e,t){await this.$nextTick();const n=this.$refs[`dynamicScroller_${t}`];n&&n.updateSize&&n.updateSize()}},methods:{setUnlessEqual(e,t){td(t,this[e])||(this[e]=Object.freeze(t))},toggleAllNodes(){const e=this.children.filter((e=>e.parent===ja&&e.type!==Ce.t.groupMarker&&e.childUIDs.length));this.allNodesToggled=!this.allNodesToggled,this.allNodesToggled&&(this.openNodes={},this.generateNodesToRender()),e.forEach((e=>{this.toggleFullTree(e)}))},clearFilters(){this.filter="",this.debouncedFilter="",this.selectedTags=[]},scrollToFocus(){this.$refs.scroller.scrollToItem(this.focusedIndex)},debounceInput:xr((function(e){this.debouncedFilter=e,this.lastFocusTarget=null}),200),trackOpenNodes([e,t,n,i],[,s=[],a="",r=[]]=[]){if(n!==a&&!a&&this.getFromStorage("filter")||!td(i,r)&&!r.length&&this.getFromStorage("selectedTags",[]).length)return;const o=!td(s,t),{childrenMap:l}=this;let c=t;if(!(this.deprecatedHidden&&!this.debouncedFilter.length||o&&this.hasFilter)&&this.hasFilter){const t=new Set,n=e.length-1;for(let i=n;i>=0;i-=1){const n=e[i];t.has(l[n.parent])||t.has(n)||Qa(n.uid,l).slice(0,-1).forEach((e=>t.add(e)))}c=[...t]}const d=o?{...this.openNodes}:{},u=c.reduce(((e,t)=>(e[t.uid]=!0,e)),d);this.setUnlessEqual("openNodes",u),this.generateNodesToRender(),this.updateFocusIndexExternally()},toggle(e){const t=this.openNodes[e.uid];let n=[],i=[];if(t){const t=(0,w.d9)(this.openNodes),n=Ua(e.uid,this.childrenMap);n.forEach((({uid:e})=>{delete t[e]})),this.setUnlessEqual("openNodes",t),i=n.slice(1)}else this.setUnlessEqual("openNodes",{...this.openNodes,[e.uid]:!0}),n=Ga(e.uid,this.childrenMap,this.children).filter((e=>this.renderableChildNodesMap[e.uid]));this.augmentRenderNodes({uid:e.uid,include:n,exclude:i})},toggleFullTree(e){const t=this.openNodes[e.uid],n=(0,w.d9)(this.openNodes),i=Ua(e.uid,this.childrenMap);let s=[],a=[];i.forEach((({uid:e})=>{t?delete 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0;const{paddingTop:t,paddingBottom:n}=getComputedStyle(this.$refs.scroller.$el),i={top:parseInt(t,10)||0,bottom:parseInt(n,10)||0},{y:s,height:a}=this.$refs.scroller.$el.getBoundingClientRect(),{y:r}=e.getBoundingClientRect(),o=e.offsetParent.offsetHeight,l=r-s-i.top;return l<0?-1:l+o>=a-i.bottom?1:0},isInsideScroller(e){return this.$refs.scroller.$el.contains(e)},handleFocusIn({target:e}){this.lastFocusTarget=e;const t=this.getChildPositionInScroller(e);if(0===t)return;const{offsetHeight:n}=e.offsetParent;this.$refs.scroller.$el.scrollBy({top:n*t,left:0})},handleFocusOut(e){e.relatedTarget&&(this.isInsideScroller(e.relatedTarget)||(this.lastFocusTarget=null))},handleScrollerUpdate:xr((async 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wd={name:"LoadingNavigatorCard",components:{BaseNavigatorCard:Xc,LoadingNavigatorItem:Cd},props:{...Xc.props},data(){return{LOADER_ROWS:kd}}},Id=wd,xd=(0,Z.Z)(Id,md,yd,!1,null,"4b6d345f",null),$d=xd.exports,Dd={name:"Navigator",components:{NavigatorCard:fd,LoadingNavigatorCard:$d},data(){return{INDEX_ROOT_KEY:ja}},props:{flatChildren:{type:Array,required:!0},parentTopicIdentifiers:{type:Array,required:!0},technology:{type:Object,required:!0},isFetching:{type:Boolean,default:!1},references:{type:Object,default:()=>{}},navigatorReferences:{type:Object,default:()=>{}},scrollLockID:{type:String,default:""},errorFetching:{type:Boolean,default:!1},renderFilterOnTop:{type:Boolean,default:!1},apiChanges:{type:Object,default:null},allowHiding:{type:Boolean,default:!0}},computed:{parentTopicReferences({references:e,parentTopicIdentifiers:t}){return t.reduce(((t,n)=>{const i=e[n];return i?t.concat(i):(console.error(`Reference for "${n}" is missing`),t)}),[])},activePath({parentTopicReferences:e,$route:{path:t}}){if(t=t.replace(/\/$/,"").toLowerCase(),!e.length)return[t];let n=1;return"technologies"===e[0].kind&&(n=2),e.slice(n).map((e=>e.url)).concat(t)},type:()=>Ce.t.module,technologyProps:({technology:e})=>({technology:e.title,technologyPath:e.path||e.url,isTechnologyBeta:e.beta})}},Pd=Dd,Ld=(0,Z.Z)(Pd,ll,cl,!1,null,"159b9764",null),Ad=Ld.exports,Od=function(){var e=this,t=e._self._c;return t("NavBase",{staticClass:"documentation-nav",attrs:{breakpoint:e.BreakpointName.medium,hasOverlay:!1,hasSolidBackground:"",hasNoBorder:e.hasNoBorder,isDark:e.isDark,isWideFormat:"",hasFullWidthBorder:"","aria-label":e.$t("api-reference")},scopedSlots:e._u([e.displaySidenav?{key:"pre-title",fn:function({closeNav:n,isOpen:i,currentBreakpoint:s,className:a}){return[t("div",{class:a},[t("transition",{attrs:{name:"sidenav-toggle"}},[t("div",{directives:[{name:"show",rawName:"v-show",value:e.sidenavHiddenOnLarge,expression:"sidenavHiddenOnLarge"}],staticClass:"sidenav-toggle-wrapper"},[t("button",{staticClass:"sidenav-toggle",attrs:{"aria-label":e.$t("navigator.open-navigator"),id:e.baseNavOpenSidenavButtonId,tabindex:i?-1:null},on:{click:function(t){return t.preventDefault(),e.handleSidenavToggle(n,s)}}},[t("span",{staticClass:"sidenav-icon-wrapper"},[t("SidenavIcon",{staticClass:"icon-inline 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t("NavMenuItems",{staticClass:"hierarchy",class:{"has-badge":e.hasBadge},attrs:{"aria-label":e.$t("documentation.nav.breadcrumbs")}},[e.root?t("HierarchyItem",{key:e.root.title,staticClass:"root-hierarchy",attrs:{url:e.addQueryParamsToUrl(e.root.url)}},[e._v(" "+e._s(e.root.title)+" ")]):e._e(),e._l(e.collapsibleItems,(function(n){return t("HierarchyItem",{key:n.title,attrs:{isCollapsed:"",url:e.addQueryParamsToUrl(n.url)}},[e._v(" "+e._s(n.title)+" ")])})),e.collapsibleItems.length?t("HierarchyCollapsedItems",{attrs:{topics:e.collapsibleItems}}):e._e(),e._l(e.nonCollapsibleItems,(function(n){return t("HierarchyItem",{key:n.title,attrs:{url:e.addQueryParamsToUrl(n.url)}},[e._v(" "+e._s(n.title)+" ")])})),t("HierarchyItem",{scopedSlots:e._u([{key:"tags",fn:function(){return[e.isSymbolDeprecated?t("Badge",{attrs:{variant:"deprecated"}}):e.isSymbolBeta?t("Badge",{attrs:{variant:"beta"}}):e._e(),e._l(e.currentTopicTags,(function(n){return t("Badge",{key:`${n.type}-${n.text}`,attrs:{variant:n.type}},[e._v(" "+e._s(n.text)+" ")])}))]},proxy:!0}])},[e._v(" "+e._s(e.currentTopicTitle)+" ")])],2)},Md=[],zd=function(){var e=this,t=e._self._c;return t("li",{staticClass:"hierarchy-collapsed-items"},[t("span",{staticClass:"hierarchy-item-icon icon-inline"},[e._v("/")]),t("button",{ref:"btn",staticClass:"toggle",class:{focused:!e.collapsed},on:{click:e.toggleCollapsed}},[t("span",{staticClass:"indicator"},[t("EllipsisIcon",{staticClass:"icon-inline toggle-icon"})],1)]),t("ul",{ref:"dropdown",staticClass:"dropdown",class:{collapsed:e.collapsed}},e._l(e.topicsWithUrls,(function(n){return t("li",{key:n.title,staticClass:"dropdown-item"},[t("router-link",{staticClass:"nav-menu-link",attrs:{to:n.url}},[e._v(e._s(n.title))])],1)})),0)])},Kd=[],Zd=function(){var e=this,t=e._self._c;return t("SVGIcon",{staticClass:"ellipsis-icon",attrs:{viewBox:"0 0 14 14",themeId:"ellipsis"}},[t("path",{attrs:{d:"m12.439 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e(t.$options.components.NavMenuItemBase,{tag:"component",staticClass:"hierarchy-item",class:[{collapsed:t.props.isCollapsed},t.data.staticClass]},[e("span",{staticClass:"hierarchy-item-icon icon-inline"},[t._v("/")]),t.props.url?e("router-link",{staticClass:"parent item nav-menu-link",attrs:{to:t.props.url}},[t._t("default")],2):[e("span",{staticClass:"current item"},[t._t("default")],2),t._t("tags")]],2)},Yd=[],Xd=n(3822),eu={name:"HierarchyItem",components:{NavMenuItemBase:Xd.Z,InlineChevronRightIcon:xc.Z},props:{isCollapsed:Boolean,url:{type:String,required:!1}}},tu=eu,nu=(0,Z.Z)(tu,Jd,Yd,!0,null,"6cf5f1d1",null),iu=nu.exports;const su=3;var au={name:"Hierarchy",components:{Badge:ei.Z,NavMenuItems:Bd.Z,HierarchyCollapsedItems:Qd,HierarchyItem:iu},constants:{MaxVisibleLinks:su},inject:["store"],props:{isSymbolDeprecated:Boolean,isSymbolBeta:Boolean,references:Object,currentTopicTitle:{type:String,required:!0},parentTopicIdentifiers:{type:Array,default:()=>[]},currentTopicTags:{type:Array,default:()=>[]}},computed:{windowWidth:({store:e})=>e.state.contentWidth,parentTopics(){return this.parentTopicIdentifiers.reduce(((e,t)=>{const n=this.references[t];if(n){const{title:t,url:i}=n;return e.concat({title:t,url:i})}return console.error(`Reference for "${t}" is missing`),e}),[])},root:({parentTopics:e,windowWidth:t})=>t<=1e3?null:e[0],firstItemSlice:({root:e})=>e?1:0,linksAfterCollapse:({windowWidth:e,hasBadge:t})=>{const n=t?1:0;return e>1200?su-n:e>1e3?su-1-n:e>=800?su-2-n:0},collapsibleItems:({parentTopics:e,linksAfterCollapse:t,firstItemSlice:n})=>t?e.slice(n,-t):e.slice(n),nonCollapsibleItems:({parentTopics:e,linksAfterCollapse:t,firstItemSlice:n})=>t?e.slice(n).slice(-t):[],hasBadge:({isSymbolDeprecated:e,isSymbolBeta:t,currentTopicTags:n})=>e||t||n.length},methods:{addQueryParamsToUrl(e){return(0,L.Q2)(e,this.$route.query)}}},ru=au,ou=(0,Z.Z)(ru,Ed,Md,!1,null,"069ffff2",null),lu=ou.exports,cu=function(){var e=this,t=e._self._c;return t("NavMenuItemBase",{staticClass:"nav-menu-setting language-container"},[t("div",{class:{"language-toggle-container":e.hasLanguages}},[t("select",{ref:"language-sizer",staticClass:"language-dropdown 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")])])})),0)]):e._e()])},du=[],uu=n(5151),hu={name:"LanguageToggle",components:{InlineChevronDownIcon:uu.Z,NavMenuItemBase:Xd.Z},inject:{store:{default(){return{setPreferredLanguage(){}}}}},props:{interfaceLanguage:{type:String,required:!0},objcPath:{type:String,required:!1},swiftPath:{type:String,required:!1},closeNav:{type:Function,default:()=>{}}},data(){return{languageModel:null,adjustedWidth:0}},mounted(){const e=Ne((async()=>{await(0,Re.J)(3),this.calculateSelectWidth()}),150);window.addEventListener("resize",e),window.addEventListener("orientationchange",e),this.$once("hook:beforeDestroy",(()=>{window.removeEventListener("resize",e),window.removeEventListener("orientationchange",e)}))},watch:{interfaceLanguage:{immediate:!0,handler(e){this.languageModel=e}},currentLanguage:{immediate:!0,handler:"calculateSelectWidth"}},methods:{getRoute(e){const t=e.query===D.Z.swift.key.url?void 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\ No newline at end of file diff --git a/docs/js/typeahead.jquery.js b/docs/js/typeahead.jquery.js deleted file mode 100644 index 3a2d2ab..0000000 --- a/docs/js/typeahead.jquery.js +++ /dev/null @@ -1,1694 +0,0 @@ -/*! - * typeahead.js 1.3.1 - * https://github.com/corejavascript/typeahead.js - * Copyright 2013-2020 Twitter, Inc. and other contributors; Licensed MIT - */ - - -(function(root, factory) { - if (typeof define === "function" && define.amd) { - define([ "jquery" ], function(a0) { - return factory(a0); - }); - } else if (typeof module === "object" && module.exports) { - module.exports = factory(require("jquery")); - } else { - factory(root["jQuery"]); - } -})(this, function($) { - var _ = function() { - "use strict"; - return { - isMsie: function() { - return /(msie|trident)/i.test(navigator.userAgent) ? navigator.userAgent.match(/(msie |rv:)(\d+(.\d+)?)/i)[2] : false; - }, - isBlankString: function(str) { - return !str || /^\s*$/.test(str); - }, - escapeRegExChars: function(str) { - return str.replace(/[\-\[\]\/\{\}\(\)\*\+\?\.\\\^\$\|]/g, "\\$&"); - }, - isString: function(obj) { - return typeof obj === "string"; - }, - isNumber: function(obj) { - return typeof obj === "number"; - }, - isArray: $.isArray, - isFunction: $.isFunction, - isObject: $.isPlainObject, - isUndefined: function(obj) { - return typeof obj === "undefined"; - }, - isElement: function(obj) { - return !!(obj && obj.nodeType === 1); - }, - isJQuery: function(obj) { - return obj instanceof $; - }, - toStr: function toStr(s) { - return _.isUndefined(s) || s === null ? "" : s + ""; - }, - bind: $.proxy, - each: function(collection, cb) { - $.each(collection, reverseArgs); - function reverseArgs(index, value) { - return cb(value, index); - } - }, - map: $.map, - filter: $.grep, - every: function(obj, test) { - var result = true; - if (!obj) { - return result; - } - $.each(obj, function(key, val) { - if (!(result = test.call(null, val, key, obj))) { - return false; - } - }); - return !!result; - }, - some: function(obj, test) { - var result = false; - if (!obj) { - return result; - } - $.each(obj, function(key, val) { - if (result = test.call(null, val, key, obj)) { - return false; - } - }); - return !!result; - }, - mixin: $.extend, - identity: function(x) { - return x; - }, - clone: function(obj) { - return $.extend(true, {}, obj); - }, - getIdGenerator: function() { - var counter = 0; - return function() { - return counter++; - }; - }, - templatify: function templatify(obj) { - return $.isFunction(obj) ? obj : template; - function template() { - return String(obj); - } - }, - defer: function(fn) { - setTimeout(fn, 0); - }, - debounce: function(func, wait, immediate) { - var timeout, result; - return function() { - var context = this, args = arguments, later, callNow; - later = function() { - timeout = null; - if (!immediate) { - result = func.apply(context, args); - } - }; - callNow = immediate && !timeout; - clearTimeout(timeout); - timeout = setTimeout(later, wait); - if (callNow) { - result = func.apply(context, args); - } - return result; - }; - }, - throttle: function(func, wait) { - var context, args, timeout, result, previous, later; - previous = 0; - later = function() { - previous = new Date(); - timeout = null; - result = func.apply(context, args); - }; - return function() { - var now = new Date(), remaining = wait - (now - previous); - context = this; - args = arguments; - if (remaining <= 0) { - clearTimeout(timeout); - timeout = null; - previous = now; - result = func.apply(context, args); - } else if (!timeout) { - timeout = setTimeout(later, remaining); - } - return result; - }; - }, - stringify: function(val) { - return _.isString(val) ? val : JSON.stringify(val); - }, - guid: function() { - function _p8(s) { - var p = (Math.random().toString(16) + "000000000").substr(2, 8); - return s ? "-" + p.substr(0, 4) + "-" + p.substr(4, 4) : p; - } - return "tt-" + _p8() + _p8(true) + _p8(true) + _p8(); - }, - noop: function() {} - }; - }(); - var WWW = function() { - "use strict"; - var defaultClassNames = { - wrapper: "twitter-typeahead", - input: "tt-input", - hint: "tt-hint", - menu: "tt-menu", - dataset: "tt-dataset", - suggestion: "tt-suggestion", - selectable: "tt-selectable", - empty: "tt-empty", - open: "tt-open", - cursor: "tt-cursor", - highlight: "tt-highlight" - }; - return build; - function build(o) { - var www, classes; - classes = _.mixin({}, defaultClassNames, o); - www = { - css: buildCss(), - classes: classes, - html: buildHtml(classes), - selectors: buildSelectors(classes) - }; - return { - css: www.css, - html: www.html, - classes: www.classes, - selectors: www.selectors, - mixin: function(o) { - _.mixin(o, www); - } - }; - } - function buildHtml(c) { - return { - wrapper: '', - menu: '
' - }; - } - function buildSelectors(classes) { - var selectors = {}; - _.each(classes, function(v, k) { - selectors[k] = "." + v; - }); - return selectors; - } - function buildCss() { - var css = { - wrapper: { - position: "relative", - display: "inline-block" - }, - hint: { - position: "absolute", - top: "0", - left: "0", - borderColor: "transparent", - boxShadow: "none", - opacity: "1" - }, - input: { - position: "relative", - verticalAlign: "top", - backgroundColor: "transparent" - }, - inputWithNoHint: { - position: "relative", - verticalAlign: "top" - }, - menu: { - position: "absolute", - top: "100%", - left: "0", - zIndex: "100", - display: "none" - }, - ltr: { - left: "0", - right: "auto" - }, - rtl: { - left: "auto", - right: " 0" - } - }; - if (_.isMsie()) { - _.mixin(css.input, { - backgroundImage: "url(data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)" - }); - } - return css; - } - }(); - var EventBus = function() { - "use strict"; - var namespace, deprecationMap; - namespace = "typeahead:"; - deprecationMap = { - render: "rendered", - cursorchange: "cursorchanged", - select: "selected", - autocomplete: "autocompleted" - }; - function EventBus(o) { - if (!o || !o.el) { - $.error("EventBus initialized without el"); - } - this.$el = $(o.el); - } - _.mixin(EventBus.prototype, { - _trigger: function(type, args) { - var $e = $.Event(namespace + type); - this.$el.trigger.call(this.$el, $e, args || []); - return $e; - }, - before: function(type) { - var args, $e; - args = [].slice.call(arguments, 1); - $e = this._trigger("before" + type, args); - return $e.isDefaultPrevented(); - }, - trigger: function(type) { - var deprecatedType; - this._trigger(type, [].slice.call(arguments, 1)); - if (deprecatedType = deprecationMap[type]) { - this._trigger(deprecatedType, [].slice.call(arguments, 1)); - } - } - }); - return EventBus; - }(); - var EventEmitter = function() { - "use strict"; - var splitter = /\s+/, nextTick = getNextTick(); - return { - onSync: onSync, - onAsync: onAsync, - off: off, - trigger: trigger - }; - function on(method, types, cb, context) { - var type; - if (!cb) { - return this; - } - types = types.split(splitter); - cb = context ? bindContext(cb, context) : cb; - this._callbacks = this._callbacks || {}; - while (type = types.shift()) { - this._callbacks[type] = this._callbacks[type] || { - sync: [], - async: [] - }; - this._callbacks[type][method].push(cb); - } - return this; - } - function onAsync(types, cb, context) { - return on.call(this, "async", types, cb, context); - } - function onSync(types, cb, context) { - return on.call(this, "sync", types, cb, context); - } - function off(types) { - var type; - if (!this._callbacks) { - return this; - } - types = types.split(splitter); - while (type = types.shift()) { - delete this._callbacks[type]; - } - return this; - } - function trigger(types) { - var type, callbacks, args, syncFlush, asyncFlush; - if (!this._callbacks) { - return this; - } - types = types.split(splitter); - args = [].slice.call(arguments, 1); - while ((type = types.shift()) && (callbacks = this._callbacks[type])) { - syncFlush = getFlush(callbacks.sync, this, [ type ].concat(args)); - asyncFlush = getFlush(callbacks.async, this, [ type ].concat(args)); - syncFlush() && nextTick(asyncFlush); - } - return this; - } - function getFlush(callbacks, context, args) { - return flush; - function flush() { - var cancelled; - for (var i = 0, len = callbacks.length; !cancelled && i < len; i += 1) { - cancelled = callbacks[i].apply(context, args) === false; - } - return !cancelled; - } - } - function getNextTick() { - var nextTickFn; - if (window.setImmediate) { - nextTickFn = function nextTickSetImmediate(fn) { - setImmediate(function() { - fn(); - }); - }; - } else { - nextTickFn = function nextTickSetTimeout(fn) { - setTimeout(function() { - fn(); - }, 0); - }; - } - return nextTickFn; - } - function bindContext(fn, context) { - return fn.bind ? fn.bind(context) : function() { - fn.apply(context, [].slice.call(arguments, 0)); - }; - } - }(); - var highlight = function(doc) { - "use strict"; - var defaults = { - node: null, - pattern: null, - tagName: "strong", - className: null, - wordsOnly: false, - caseSensitive: false, - diacriticInsensitive: false - }; - var accented = { - A: "[AaªÀ-Åà-åĀ-ąǍǎȀ-ȃȦȧᴬᵃḀḁẚẠ-ảₐ℀℁℻⒜Ⓐⓐ㍱-㍴㎀-㎄㎈㎉㎩-㎯㏂㏊㏟㏿Ａａ]", - B: "[BbᴮᵇḂ-ḇℬ⒝Ⓑⓑ㍴㎅-㎇㏃㏈㏔㏝Ｂｂ]", - C: "[CcÇçĆ-čᶜ℀ℂ℃℅℆ℭⅭⅽ⒞Ⓒⓒ㍶㎈㎉㎝㎠㎤㏄-㏇Ｃｃ]", - D: "[DdĎďDŽ-džDZ-dzᴰᵈḊ-ḓⅅⅆⅮⅾ⒟Ⓓⓓ㋏㍲㍷-㍹㎗㎭-㎯㏅㏈Ｄｄ]", - E: "[EeÈ-Ëè-ëĒ-ěȄ-ȇȨȩᴱᵉḘ-ḛẸ-ẽₑ℡ℯℰⅇ⒠Ⓔⓔ㉐㋍㋎Ｅｅ]", - F: "[FfᶠḞḟ℉ℱ℻⒡Ⓕⓕ㎊-㎌㎙ff-fflＦｆ]", - G: "[GgĜ-ģǦǧǴǵᴳᵍḠḡℊ⒢Ⓖⓖ㋌㋍㎇㎍-㎏㎓㎬㏆㏉㏒㏿Ｇｇ]", - H: "[HhĤĥȞȟʰᴴḢ-ḫẖℋ-ℎ⒣Ⓗⓗ㋌㍱㎐-㎔㏊㏋㏗Ｈｈ]", - I: "[IiÌ-Ïì-ïĨ-İIJijǏǐȈ-ȋᴵᵢḬḭỈ-ịⁱℐℑℹⅈⅠ-ⅣⅥ-ⅨⅪⅫⅰ-ⅳⅵ-ⅸⅺⅻ⒤Ⓘⓘ㍺㏌㏕fiffiＩｉ]", - J: "[JjIJ-ĵLJ-njǰʲᴶⅉ⒥ⒿⓙⱼＪｊ]", - K: "[KkĶķǨǩᴷᵏḰ-ḵK⒦Ⓚⓚ㎄㎅㎉㎏㎑㎘㎞㎢㎦㎪㎸㎾㏀㏆㏍-㏏Ｋｋ]", - L: "[LlĹ-ŀLJ-ljˡᴸḶḷḺ-ḽℒℓ℡Ⅼⅼ⒧Ⓛⓛ㋏㎈㎉㏐-㏓㏕㏖㏿flfflＬｌ]", - M: "[MmᴹᵐḾ-ṃ℠™ℳⅯⅿ⒨Ⓜⓜ㍷-㍹㎃㎆㎎㎒㎖㎙-㎨㎫㎳㎷㎹㎽㎿㏁㏂㏎㏐㏔-㏖㏘㏙㏞㏟Ｍｍ]", - N: "[NnÑñŃ-ʼnNJ-njǸǹᴺṄ-ṋⁿℕ№⒩Ⓝⓝ㎁㎋㎚㎱㎵㎻㏌㏑Ｎｎ]", - O: "[OoºÒ-Öò-öŌ-őƠơǑǒǪǫȌ-ȏȮȯᴼᵒỌ-ỏₒ℅№ℴ⒪Ⓞⓞ㍵㏇㏒㏖Ｏｏ]", - P: "[PpᴾᵖṔ-ṗℙ⒫Ⓟⓟ㉐㍱㍶㎀㎊㎩-㎬㎰㎴㎺㏋㏗-㏚Ｐｐ]", - Q: "[Qqℚ⒬Ⓠⓠ㏃Ｑｑ]", - R: "[RrŔ-řȐ-ȓʳᴿᵣṘ-ṛṞṟ₨ℛ-ℝ⒭Ⓡⓡ㋍㍴㎭-㎯㏚㏛Ｒｒ]", - S: "[SsŚ-šſȘșˢṠ-ṣ₨℁℠⒮Ⓢⓢ㎧㎨㎮-㎳㏛㏜stＳｓ]", - T: "[TtŢ-ťȚțᵀᵗṪ-ṱẗ℡™⒯Ⓣⓣ㉐㋏㎔㏏ſtstＴｔ]", - U: "[UuÙ-Üù-üŨ-ųƯưǓǔȔ-ȗᵁᵘᵤṲ-ṷỤ-ủ℆⒰Ⓤⓤ㍳㍺Ｕｕ]", - V: "[VvᵛᵥṼ-ṿⅣ-Ⅷⅳ-ⅷ⒱Ⓥⓥⱽ㋎㍵㎴-㎹㏜㏞Ｖｖ]", - W: "[WwŴŵʷᵂẀ-ẉẘ⒲Ⓦⓦ㎺-㎿㏝Ｗｗ]", - X: "[XxˣẊ-ẍₓ℻Ⅸ-Ⅻⅸ-ⅻ⒳Ⓧⓧ㏓Ｘｘ]", - Y: "[YyÝýÿŶ-ŸȲȳʸẎẏẙỲ-ỹ⒴Ⓨⓨ㏉Ｙｙ]", - Z: "[ZzŹ-žDZ-dzᶻẐ-ẕℤℨ⒵Ⓩⓩ㎐-㎔Ｚｚ]" - }; - return function hightlight(o) { - var regex; - o = _.mixin({}, defaults, o); - if (!o.node || !o.pattern) { - return; - } - o.pattern = _.isArray(o.pattern) ? o.pattern : [ o.pattern ]; - regex = getRegex(o.pattern, o.caseSensitive, o.wordsOnly, o.diacriticInsensitive); - traverse(o.node, hightlightTextNode); - function hightlightTextNode(textNode) { - var match, patternNode, wrapperNode; - if (match = regex.exec(textNode.data)) { - wrapperNode = doc.createElement(o.tagName); - o.className && (wrapperNode.className = o.className); - patternNode = textNode.splitText(match.index); - patternNode.splitText(match[0].length); - wrapperNode.appendChild(patternNode.cloneNode(true)); - textNode.parentNode.replaceChild(wrapperNode, patternNode); - } - return !!match; - } - function traverse(el, hightlightTextNode) { - var childNode, TEXT_NODE_TYPE = 3; - for (var i = 0; i < el.childNodes.length; i++) { - childNode = el.childNodes[i]; - if (childNode.nodeType === TEXT_NODE_TYPE) { - i += hightlightTextNode(childNode) ? 1 : 0; - } else { - traverse(childNode, hightlightTextNode); - } - } - } - }; - function accent_replacer(chr) { - return accented[chr.toUpperCase()] || chr; - } - function getRegex(patterns, caseSensitive, wordsOnly, diacriticInsensitive) { - var escapedPatterns = [], regexStr; - for (var i = 0, len = patterns.length; i < len; i++) { - var escapedWord = _.escapeRegExChars(patterns[i]); - if (diacriticInsensitive) { - escapedWord = escapedWord.replace(/\S/g, accent_replacer); - } - escapedPatterns.push(escapedWord); - } - regexStr = wordsOnly ? "\\b(" + escapedPatterns.join("|") + ")\\b" : "(" + escapedPatterns.join("|") + ")"; - return caseSensitive ? new RegExp(regexStr) : new RegExp(regexStr, "i"); - } - }(window.document); - var Input = function() { - "use strict"; - var specialKeyCodeMap; - specialKeyCodeMap = { - 9: "tab", - 27: "esc", - 37: "left", - 39: "right", - 13: "enter", - 38: "up", - 40: "down" - }; - function Input(o, www) { - var id; - o = o || {}; - if (!o.input) { - $.error("input is missing"); - } - www.mixin(this); - this.$hint = $(o.hint); - this.$input = $(o.input); - this.$menu = $(o.menu); - id = this.$input.attr("id") || _.guid(); - this.$menu.attr("id", id + "_listbox"); - this.$hint.attr({ - "aria-hidden": true - }); - this.$input.attr({ - "aria-owns": id + "_listbox", - role: "combobox", - "aria-autocomplete": "list", - "aria-expanded": false - }); - this.query = this.$input.val(); - this.queryWhenFocused = this.hasFocus() ? this.query : null; - this.$overflowHelper = buildOverflowHelper(this.$input); - this._checkLanguageDirection(); - if (this.$hint.length === 0) { - this.setHint = this.getHint = this.clearHint = this.clearHintIfInvalid = _.noop; - } - this.onSync("cursorchange", this._updateDescendent); - } - Input.normalizeQuery = function(str) { - return _.toStr(str).replace(/^\s*/g, "").replace(/\s{2,}/g, " "); - }; - _.mixin(Input.prototype, EventEmitter, { - _onBlur: function onBlur() { - this.resetInputValue(); - this.trigger("blurred"); - }, - _onFocus: function onFocus() { - this.queryWhenFocused = this.query; - this.trigger("focused"); - }, - _onKeydown: function onKeydown($e) { - var keyName = specialKeyCodeMap[$e.which || $e.keyCode]; - this._managePreventDefault(keyName, $e); - if (keyName && this._shouldTrigger(keyName, $e)) { - this.trigger(keyName + "Keyed", $e); - } - }, - _onInput: function onInput() { - this._setQuery(this.getInputValue()); - this.clearHintIfInvalid(); - this._checkLanguageDirection(); - }, - _managePreventDefault: function managePreventDefault(keyName, $e) { - var preventDefault; - switch (keyName) { - case "up": - case "down": - preventDefault = !withModifier($e); - break; - - default: - preventDefault = false; - } - preventDefault && $e.preventDefault(); - }, - _shouldTrigger: function shouldTrigger(keyName, $e) { - var trigger; - switch (keyName) { - case "tab": - trigger = !withModifier($e); - break; - - default: - trigger = true; - } - return trigger; - }, - _checkLanguageDirection: function checkLanguageDirection() { - var dir = (this.$input.css("direction") || "ltr").toLowerCase(); - if (this.dir !== dir) { - this.dir = dir; - this.$hint.attr("dir", dir); - this.trigger("langDirChanged", dir); - } - }, - _setQuery: function setQuery(val, silent) { - var areEquivalent, hasDifferentWhitespace; - areEquivalent = areQueriesEquivalent(val, this.query); - hasDifferentWhitespace = areEquivalent ? this.query.length !== val.length : false; - this.query = val; - if (!silent && !areEquivalent) { - this.trigger("queryChanged", this.query); - } else if (!silent && hasDifferentWhitespace) { - this.trigger("whitespaceChanged", this.query); - } - }, - _updateDescendent: function updateDescendent(event, id) { - this.$input.attr("aria-activedescendant", id); - }, - bind: function() { - var that = this, onBlur, onFocus, onKeydown, onInput; - onBlur = _.bind(this._onBlur, this); - onFocus = _.bind(this._onFocus, this); - onKeydown = _.bind(this._onKeydown, this); - onInput = _.bind(this._onInput, this); - this.$input.on("blur.tt", onBlur).on("focus.tt", onFocus).on("keydown.tt", onKeydown); - if (!_.isMsie() || _.isMsie() > 9) { - this.$input.on("input.tt", onInput); - } else { - this.$input.on("keydown.tt keypress.tt cut.tt paste.tt", function($e) { - if (specialKeyCodeMap[$e.which || $e.keyCode]) { - return; - } - _.defer(_.bind(that._onInput, that, $e)); - }); - } - return this; - }, - focus: function focus() { - this.$input.focus(); - }, - blur: function blur() { - this.$input.blur(); - }, - getLangDir: function getLangDir() { - return this.dir; - }, - getQuery: function getQuery() { - return this.query || ""; - }, - setQuery: function setQuery(val, silent) { - this.setInputValue(val); - this._setQuery(val, silent); - }, - hasQueryChangedSinceLastFocus: function hasQueryChangedSinceLastFocus() { - return this.query !== this.queryWhenFocused; - }, - getInputValue: function getInputValue() { - return this.$input.val(); - }, - setInputValue: function setInputValue(value) { - this.$input.val(value); - this.clearHintIfInvalid(); - this._checkLanguageDirection(); - }, - resetInputValue: function resetInputValue() { - this.setInputValue(this.query); - }, - getHint: function getHint() { - return this.$hint.val(); - }, - setHint: function setHint(value) { - this.$hint.val(value); - }, - clearHint: function clearHint() { - this.setHint(""); - }, - clearHintIfInvalid: function clearHintIfInvalid() { - var val, hint, valIsPrefixOfHint, isValid; - val = this.getInputValue(); - hint = this.getHint(); - valIsPrefixOfHint = val !== hint && hint.indexOf(val) === 0; - isValid = val !== "" && valIsPrefixOfHint && !this.hasOverflow(); - !isValid && this.clearHint(); - }, - hasFocus: function hasFocus() { - return this.$input.is(":focus"); - }, - hasOverflow: function hasOverflow() { - var constraint = this.$input.width() - 2; - this.$overflowHelper.text(this.getInputValue()); - return this.$overflowHelper.width() >= constraint; - }, - isCursorAtEnd: function() { - var valueLength, selectionStart, range; - valueLength = this.$input.val().length; - selectionStart = this.$input[0].selectionStart; - if (_.isNumber(selectionStart)) { - return selectionStart === valueLength; - } else if (document.selection) { - range = document.selection.createRange(); - range.moveStart("character", -valueLength); - return valueLength === range.text.length; - } - return true; - }, - destroy: function destroy() { - this.$hint.off(".tt"); - this.$input.off(".tt"); - this.$overflowHelper.remove(); - this.$hint = this.$input = this.$overflowHelper = $("
"); - }, - setAriaExpanded: function setAriaExpanded(value) { - this.$input.attr("aria-expanded", value); - } - }); - return Input; - function buildOverflowHelper($input) { - return $('').css({ - position: "absolute", - visibility: "hidden", - whiteSpace: "pre", - fontFamily: $input.css("font-family"), - fontSize: $input.css("font-size"), - fontStyle: $input.css("font-style"), - fontVariant: $input.css("font-variant"), - fontWeight: $input.css("font-weight"), - wordSpacing: $input.css("word-spacing"), - letterSpacing: $input.css("letter-spacing"), - textIndent: $input.css("text-indent"), - textRendering: $input.css("text-rendering"), - textTransform: $input.css("text-transform") - }).insertAfter($input); - } - function areQueriesEquivalent(a, b) { - return Input.normalizeQuery(a) === Input.normalizeQuery(b); - } - function withModifier($e) { - return $e.altKey || $e.ctrlKey || $e.metaKey || $e.shiftKey; - } - }(); - var Dataset = function() { - "use strict"; - var keys, nameGenerator; - keys = { - dataset: "tt-selectable-dataset", - val: "tt-selectable-display", - obj: "tt-selectable-object" - }; - nameGenerator = _.getIdGenerator(); - function Dataset(o, www) { - o = o || {}; - o.templates = o.templates || {}; - o.templates.notFound = o.templates.notFound || o.templates.empty; - if (!o.source) { - $.error("missing source"); - } - if (!o.node) { - $.error("missing node"); - } - if (o.name && !isValidName(o.name)) { - $.error("invalid dataset name: " + o.name); - } - www.mixin(this); - this.highlight = !!o.highlight; - this.name = _.toStr(o.name || nameGenerator()); - this.limit = o.limit || 5; - this.displayFn = getDisplayFn(o.display || o.displayKey); - this.templates = getTemplates(o.templates, this.displayFn); - this.source = o.source.__ttAdapter ? o.source.__ttAdapter() : o.source; - this.async = _.isUndefined(o.async) ? this.source.length > 2 : !!o.async; - this._resetLastSuggestion(); - this.$el = $(o.node).attr("role", "presentation").addClass(this.classes.dataset).addClass(this.classes.dataset + "-" + this.name); - } - Dataset.extractData = function extractData(el) { - var $el = $(el); - if ($el.data(keys.obj)) { - return { - dataset: $el.data(keys.dataset) || "", - val: $el.data(keys.val) || "", - obj: $el.data(keys.obj) || null - }; - } - return null; - }; - _.mixin(Dataset.prototype, EventEmitter, { - _overwrite: function overwrite(query, suggestions) { - suggestions = suggestions || []; - if (suggestions.length) { - this._renderSuggestions(query, suggestions); - } else if (this.async && this.templates.pending) { - this._renderPending(query); - } else if (!this.async && this.templates.notFound) { - this._renderNotFound(query); - } else { - this._empty(); - } - this.trigger("rendered", suggestions, false, this.name); - }, - _append: function append(query, suggestions) { - suggestions = suggestions || []; - if (suggestions.length && this.$lastSuggestion.length) { - this._appendSuggestions(query, suggestions); - } else if (suggestions.length) { - this._renderSuggestions(query, suggestions); - } else if (!this.$lastSuggestion.length && this.templates.notFound) { - this._renderNotFound(query); - } - this.trigger("rendered", suggestions, true, this.name); - }, - _renderSuggestions: function renderSuggestions(query, suggestions) { - var $fragment; - $fragment = this._getSuggestionsFragment(query, suggestions); - this.$lastSuggestion = $fragment.children().last(); - this.$el.html($fragment).prepend(this._getHeader(query, suggestions)).append(this._getFooter(query, suggestions)); - }, - _appendSuggestions: function appendSuggestions(query, suggestions) { - var $fragment, $lastSuggestion; - $fragment = this._getSuggestionsFragment(query, suggestions); - $lastSuggestion = $fragment.children().last(); - this.$lastSuggestion.after($fragment); - this.$lastSuggestion = $lastSuggestion; - }, - _renderPending: function renderPending(query) { - var template = this.templates.pending; - this._resetLastSuggestion(); - template && this.$el.html(template({ - query: query, - dataset: this.name - })); - }, - _renderNotFound: function renderNotFound(query) { - var template = this.templates.notFound; - this._resetLastSuggestion(); - template && this.$el.html(template({ - query: query, - dataset: this.name - })); - }, - _empty: function empty() { - this.$el.empty(); - this._resetLastSuggestion(); - }, - _getSuggestionsFragment: function getSuggestionsFragment(query, suggestions) { - var that = this, fragment; - fragment = document.createDocumentFragment(); - _.each(suggestions, function getSuggestionNode(suggestion) { - var $el, context; - context = that._injectQuery(query, suggestion); - $el = $(that.templates.suggestion(context)).data(keys.dataset, that.name).data(keys.obj, suggestion).data(keys.val, that.displayFn(suggestion)).addClass(that.classes.suggestion + " " + that.classes.selectable); - fragment.appendChild($el[0]); - }); - this.highlight && highlight({ - className: this.classes.highlight, - node: fragment, - pattern: query - }); - return $(fragment); - }, - _getFooter: function getFooter(query, suggestions) { - return this.templates.footer ? this.templates.footer({ - query: query, - suggestions: suggestions, - dataset: this.name - }) : null; - }, - _getHeader: function getHeader(query, suggestions) { - return this.templates.header ? this.templates.header({ - query: query, - suggestions: suggestions, - dataset: this.name - }) : null; - }, - _resetLastSuggestion: function resetLastSuggestion() { - this.$lastSuggestion = $(); - }, - _injectQuery: function injectQuery(query, obj) { - return _.isObject(obj) ? _.mixin({ - _query: query - }, obj) : obj; - }, - update: function update(query) { - var that = this, canceled = false, syncCalled = false, rendered = 0; - this.cancel(); - this.cancel = function cancel() { - canceled = true; - that.cancel = $.noop; - that.async && that.trigger("asyncCanceled", query, that.name); - }; - this.source(query, sync, async); - !syncCalled && sync([]); - function sync(suggestions) { - if (syncCalled) { - return; - } - syncCalled = true; - suggestions = (suggestions || []).slice(0, that.limit); - rendered = suggestions.length; - that._overwrite(query, suggestions); - if (rendered < that.limit && that.async) { - that.trigger("asyncRequested", query, that.name); - } - } - function async(suggestions) { - suggestions = suggestions || []; - if (!canceled && rendered < that.limit) { - that.cancel = $.noop; - var idx = Math.abs(rendered - that.limit); - rendered += idx; - that._append(query, suggestions.slice(0, idx)); - that.async && that.trigger("asyncReceived", query, that.name); - } - } - }, - cancel: $.noop, - clear: function clear() { - this._empty(); - this.cancel(); - this.trigger("cleared"); - }, - isEmpty: function isEmpty() { - return this.$el.is(":empty"); - }, - destroy: function destroy() { - this.$el = $("
"); - } - }); - return Dataset; - function getDisplayFn(display) { - display = display || _.stringify; - return _.isFunction(display) ? display : displayFn; - function displayFn(obj) { - return obj[display]; - } - } - function getTemplates(templates, displayFn) { - return { - notFound: templates.notFound && _.templatify(templates.notFound), - pending: templates.pending && _.templatify(templates.pending), - header: templates.header && _.templatify(templates.header), - footer: templates.footer && _.templatify(templates.footer), - suggestion: templates.suggestion ? userSuggestionTemplate : suggestionTemplate - }; - function userSuggestionTemplate(context) { - var template = templates.suggestion; - return $(template(context)).attr("id", _.guid()); - } - function suggestionTemplate(context) { - return $('
').attr("id", _.guid()).text(displayFn(context)); - } - } - function isValidName(str) { - return /^[_a-zA-Z0-9-]+$/.test(str); - } - }(); - var Menu = function() { - "use strict"; - function Menu(o, www) { - var that = this; - o = o || {}; - if (!o.node) { - $.error("node is required"); - } - www.mixin(this); - this.$node = $(o.node); - this.query = null; - this.datasets = _.map(o.datasets, initializeDataset); - function initializeDataset(oDataset) { - var node = that.$node.find(oDataset.node).first(); - oDataset.node = node.length ? node : $("
").appendTo(that.$node); - return new Dataset(oDataset, www); - } - } - _.mixin(Menu.prototype, EventEmitter, { - _onSelectableClick: function onSelectableClick($e) { - this.trigger("selectableClicked", $($e.currentTarget)); - }, - _onRendered: function onRendered(type, dataset, suggestions, async) { - this.$node.toggleClass(this.classes.empty, this._allDatasetsEmpty()); - this.trigger("datasetRendered", dataset, suggestions, async); - }, - _onCleared: function onCleared() { - this.$node.toggleClass(this.classes.empty, this._allDatasetsEmpty()); - this.trigger("datasetCleared"); - }, - _propagate: function propagate() { - this.trigger.apply(this, arguments); - }, - _allDatasetsEmpty: function allDatasetsEmpty() { - return _.every(this.datasets, _.bind(function isDatasetEmpty(dataset) { - var isEmpty = dataset.isEmpty(); - this.$node.attr("aria-expanded", !isEmpty); - return isEmpty; - }, this)); - }, - _getSelectables: function getSelectables() { - return this.$node.find(this.selectors.selectable); - }, - _removeCursor: function _removeCursor() { - var $selectable = this.getActiveSelectable(); - $selectable && $selectable.removeClass(this.classes.cursor); - }, - _ensureVisible: function ensureVisible($el) { - var elTop, elBottom, nodeScrollTop, nodeHeight; - elTop = $el.position().top; - elBottom = elTop + $el.outerHeight(true); - nodeScrollTop = this.$node.scrollTop(); - nodeHeight = this.$node.height() + parseInt(this.$node.css("paddingTop"), 10) + parseInt(this.$node.css("paddingBottom"), 10); - if (elTop < 0) { - this.$node.scrollTop(nodeScrollTop + elTop); - } else if (nodeHeight < elBottom) { - this.$node.scrollTop(nodeScrollTop + (elBottom - nodeHeight)); - } - }, - bind: function() { - var that = this, onSelectableClick; - onSelectableClick = _.bind(this._onSelectableClick, this); - this.$node.on("click.tt", this.selectors.selectable, onSelectableClick); - this.$node.on("mouseover", this.selectors.selectable, function() { - that.setCursor($(this)); - }); - this.$node.on("mouseleave", function() { - that._removeCursor(); - }); - _.each(this.datasets, function(dataset) { - dataset.onSync("asyncRequested", that._propagate, that).onSync("asyncCanceled", that._propagate, that).onSync("asyncReceived", that._propagate, that).onSync("rendered", that._onRendered, that).onSync("cleared", that._onCleared, that); - }); - return this; - }, - isOpen: function isOpen() { - return this.$node.hasClass(this.classes.open); - }, - open: function open() { - this.$node.scrollTop(0); - this.$node.addClass(this.classes.open); - }, - close: function close() { - this.$node.attr("aria-expanded", false); - this.$node.removeClass(this.classes.open); - this._removeCursor(); - }, - setLanguageDirection: function setLanguageDirection(dir) { - this.$node.attr("dir", dir); - }, - selectableRelativeToCursor: function selectableRelativeToCursor(delta) { - var $selectables, $oldCursor, oldIndex, newIndex; - $oldCursor = this.getActiveSelectable(); - $selectables = this._getSelectables(); - oldIndex = $oldCursor ? $selectables.index($oldCursor) : -1; - newIndex = oldIndex + delta; - newIndex = (newIndex + 1) % ($selectables.length + 1) - 1; - newIndex = newIndex < -1 ? $selectables.length - 1 : newIndex; - return newIndex === -1 ? null : $selectables.eq(newIndex); - }, - setCursor: function setCursor($selectable) { - this._removeCursor(); - if ($selectable = $selectable && $selectable.first()) { - $selectable.addClass(this.classes.cursor); - this._ensureVisible($selectable); - } - }, - getSelectableData: function getSelectableData($el) { - return $el && $el.length ? Dataset.extractData($el) : null; - }, - getActiveSelectable: function getActiveSelectable() { - var $selectable = this._getSelectables().filter(this.selectors.cursor).first(); - return $selectable.length ? $selectable : null; - }, - getTopSelectable: function getTopSelectable() { - var $selectable = this._getSelectables().first(); - return $selectable.length ? $selectable : null; - }, - update: function update(query) { - var isValidUpdate = query !== this.query; - if (isValidUpdate) { - this.query = query; - _.each(this.datasets, updateDataset); - } - return isValidUpdate; - function updateDataset(dataset) { - dataset.update(query); - } - }, - empty: function empty() { - _.each(this.datasets, clearDataset); - this.query = null; - this.$node.addClass(this.classes.empty); - function clearDataset(dataset) { - dataset.clear(); - } - }, - destroy: function destroy() { - this.$node.off(".tt"); - this.$node = $("
"); - _.each(this.datasets, destroyDataset); - function destroyDataset(dataset) { - dataset.destroy(); - } - } - }); - return Menu; - }(); - var Status = function() { - "use strict"; - function Status(options) { - this.$el = $("", { - role: "status", - "aria-live": "polite" - }).css({ - position: "absolute", - padding: "0", - border: "0", - height: "1px", - width: "1px", - "margin-bottom": "-1px", - "margin-right": "-1px", - overflow: "hidden", - clip: "rect(0 0 0 0)", - "white-space": "nowrap" - }); - options.$input.after(this.$el); - _.each(options.menu.datasets, _.bind(function(dataset) { - if (dataset.onSync) { - dataset.onSync("rendered", _.bind(this.update, this)); - dataset.onSync("cleared", _.bind(this.cleared, this)); - } - }, this)); - } - _.mixin(Status.prototype, { - update: function update(event, suggestions) { - var length = suggestions.length; - var words; - if (length === 1) { - words = { - result: "result", - is: "is" - }; - } else { - words = { - result: "results", - is: "are" - }; - } - this.$el.text(length + " " + words.result + " " + words.is + " available, use up and down arrow keys to navigate."); - }, - cleared: function() { - this.$el.text(""); - } - }); - return Status; - }(); - var DefaultMenu = function() { - "use strict"; - var s = Menu.prototype; - function DefaultMenu() { - Menu.apply(this, [].slice.call(arguments, 0)); - } - _.mixin(DefaultMenu.prototype, Menu.prototype, { - open: function open() { - !this._allDatasetsEmpty() && this._show(); - return s.open.apply(this, [].slice.call(arguments, 0)); - }, - close: function close() { - this._hide(); - return s.close.apply(this, [].slice.call(arguments, 0)); - }, - _onRendered: function onRendered() { - if (this._allDatasetsEmpty()) { - this._hide(); - } else { - this.isOpen() && this._show(); - } - return s._onRendered.apply(this, [].slice.call(arguments, 0)); - }, - _onCleared: function onCleared() { - if (this._allDatasetsEmpty()) { - this._hide(); - } else { - this.isOpen() && this._show(); - } - return s._onCleared.apply(this, [].slice.call(arguments, 0)); - }, - setLanguageDirection: function setLanguageDirection(dir) { - this.$node.css(dir === "ltr" ? this.css.ltr : this.css.rtl); - return s.setLanguageDirection.apply(this, [].slice.call(arguments, 0)); - }, - _hide: function hide() { - this.$node.hide(); - }, - _show: function show() { - this.$node.css("display", "block"); - } - }); - return DefaultMenu; - }(); - var Typeahead = function() { - "use strict"; - function Typeahead(o, www) { - var onFocused, onBlurred, onEnterKeyed, onTabKeyed, onEscKeyed, onUpKeyed, onDownKeyed, onLeftKeyed, onRightKeyed, onQueryChanged, onWhitespaceChanged; - o = o || {}; - if (!o.input) { - $.error("missing input"); - } - if (!o.menu) { - $.error("missing menu"); - } - if (!o.eventBus) { - $.error("missing event bus"); - } - www.mixin(this); - this.eventBus = o.eventBus; - this.minLength = _.isNumber(o.minLength) ? o.minLength : 1; - this.input = o.input; - this.menu = o.menu; - this.enabled = true; - this.autoselect = !!o.autoselect; - this.active = false; - this.input.hasFocus() && this.activate(); - this.dir = this.input.getLangDir(); - this._hacks(); - this.menu.bind().onSync("selectableClicked", this._onSelectableClicked, this).onSync("asyncRequested", this._onAsyncRequested, this).onSync("asyncCanceled", this._onAsyncCanceled, this).onSync("asyncReceived", this._onAsyncReceived, this).onSync("datasetRendered", this._onDatasetRendered, this).onSync("datasetCleared", this._onDatasetCleared, this); - onFocused = c(this, "activate", "open", "_onFocused"); - onBlurred = c(this, "deactivate", "_onBlurred"); - onEnterKeyed = c(this, "isActive", "isOpen", "_onEnterKeyed"); - onTabKeyed = c(this, "isActive", "isOpen", "_onTabKeyed"); - onEscKeyed = c(this, "isActive", "_onEscKeyed"); - onUpKeyed = c(this, "isActive", "open", "_onUpKeyed"); - onDownKeyed = c(this, "isActive", "open", "_onDownKeyed"); - onLeftKeyed = c(this, "isActive", "isOpen", "_onLeftKeyed"); - onRightKeyed = c(this, "isActive", "isOpen", "_onRightKeyed"); - onQueryChanged = c(this, "_openIfActive", "_onQueryChanged"); - onWhitespaceChanged = c(this, "_openIfActive", "_onWhitespaceChanged"); - this.input.bind().onSync("focused", onFocused, this).onSync("blurred", onBlurred, this).onSync("enterKeyed", onEnterKeyed, this).onSync("tabKeyed", onTabKeyed, this).onSync("escKeyed", onEscKeyed, this).onSync("upKeyed", onUpKeyed, this).onSync("downKeyed", onDownKeyed, this).onSync("leftKeyed", onLeftKeyed, this).onSync("rightKeyed", onRightKeyed, this).onSync("queryChanged", onQueryChanged, this).onSync("whitespaceChanged", onWhitespaceChanged, this).onSync("langDirChanged", this._onLangDirChanged, this); - } - _.mixin(Typeahead.prototype, { - _hacks: function hacks() { - var $input, $menu; - $input = this.input.$input || $("
"); - $menu = this.menu.$node || $("
"); - $input.on("blur.tt", function($e) { - var active, isActive, hasActive; - active = document.activeElement; - isActive = $menu.is(active); - hasActive = $menu.has(active).length > 0; - if (_.isMsie() && (isActive || hasActive)) { - $e.preventDefault(); - $e.stopImmediatePropagation(); - _.defer(function() { - $input.focus(); - }); - } - }); - $menu.on("mousedown.tt", function($e) { - $e.preventDefault(); - }); - }, - _onSelectableClicked: function onSelectableClicked(type, $el) { - this.select($el); - }, - _onDatasetCleared: function onDatasetCleared() { - this._updateHint(); - }, - _onDatasetRendered: function onDatasetRendered(type, suggestions, async, dataset) { - this._updateHint(); - if (this.autoselect) { - var cursorClass = this.selectors.cursor.substr(1); - this.menu.$node.find(this.selectors.suggestion).first().addClass(cursorClass); - } - this.eventBus.trigger("render", suggestions, async, dataset); - }, - _onAsyncRequested: function onAsyncRequested(type, dataset, query) { - this.eventBus.trigger("asyncrequest", query, dataset); - }, - _onAsyncCanceled: function onAsyncCanceled(type, dataset, query) { - this.eventBus.trigger("asynccancel", query, dataset); - }, - _onAsyncReceived: function onAsyncReceived(type, dataset, query) { - this.eventBus.trigger("asyncreceive", query, dataset); - }, - _onFocused: function onFocused() { - this._minLengthMet() && this.menu.update(this.input.getQuery()); - }, - _onBlurred: function onBlurred() { - if (this.input.hasQueryChangedSinceLastFocus()) { - this.eventBus.trigger("change", this.input.getQuery()); - } - }, - _onEnterKeyed: function onEnterKeyed(type, $e) { - var $selectable; - if ($selectable = this.menu.getActiveSelectable()) { - if (this.select($selectable)) { - $e.preventDefault(); - $e.stopPropagation(); - } - } else if (this.autoselect) { - if (this.select(this.menu.getTopSelectable())) { - $e.preventDefault(); - $e.stopPropagation(); - } - } - }, - _onTabKeyed: function onTabKeyed(type, $e) { - var $selectable; - if ($selectable = this.menu.getActiveSelectable()) { - this.select($selectable) && $e.preventDefault(); - } else if (this.autoselect) { - if ($selectable = this.menu.getTopSelectable()) { - this.autocomplete($selectable) && $e.preventDefault(); - } - } - }, - _onEscKeyed: function onEscKeyed() { - this.close(); - }, - _onUpKeyed: function onUpKeyed() { - this.moveCursor(-1); - }, - _onDownKeyed: function onDownKeyed() { - this.moveCursor(+1); - }, - _onLeftKeyed: function onLeftKeyed() { - if (this.dir === "rtl" && this.input.isCursorAtEnd()) { - this.autocomplete(this.menu.getActiveSelectable() || this.menu.getTopSelectable()); - } - }, - _onRightKeyed: function onRightKeyed() { - if (this.dir === "ltr" && this.input.isCursorAtEnd()) { - this.autocomplete(this.menu.getActiveSelectable() || this.menu.getTopSelectable()); - } - }, - _onQueryChanged: function onQueryChanged(e, query) { - this._minLengthMet(query) ? this.menu.update(query) : this.menu.empty(); - }, - _onWhitespaceChanged: function onWhitespaceChanged() { - this._updateHint(); - }, - _onLangDirChanged: function onLangDirChanged(e, dir) { - if (this.dir !== dir) { - this.dir = dir; - this.menu.setLanguageDirection(dir); - } - }, - _openIfActive: function openIfActive() { - this.isActive() && this.open(); - }, - _minLengthMet: function minLengthMet(query) { - query = _.isString(query) ? query : this.input.getQuery() || ""; - return query.length >= this.minLength; - }, - _updateHint: function updateHint() { - var $selectable, data, val, query, escapedQuery, frontMatchRegEx, match; - $selectable = this.menu.getTopSelectable(); - data = this.menu.getSelectableData($selectable); - val = this.input.getInputValue(); - if (data && !_.isBlankString(val) && !this.input.hasOverflow()) { - query = Input.normalizeQuery(val); - escapedQuery = _.escapeRegExChars(query); - frontMatchRegEx = new RegExp("^(?:" + escapedQuery + ")(.+$)", "i"); - match = frontMatchRegEx.exec(data.val); - match && this.input.setHint(val + match[1]); - } else { - this.input.clearHint(); - } - }, - isEnabled: function isEnabled() { - return this.enabled; - }, - enable: function enable() { - this.enabled = true; - }, - disable: function disable() { - this.enabled = false; - }, - isActive: function isActive() { - return this.active; - }, - activate: function activate() { - if (this.isActive()) { - return true; - } else if (!this.isEnabled() || this.eventBus.before("active")) { - return false; - } else { - this.active = true; - this.eventBus.trigger("active"); - return true; - } - }, - deactivate: function deactivate() { - if (!this.isActive()) { - return true; - } else if (this.eventBus.before("idle")) { - return false; - } else { - this.active = false; - this.close(); - this.eventBus.trigger("idle"); - return true; - } - }, - isOpen: function isOpen() { - return this.menu.isOpen(); - }, - open: function open() { - if (!this.isOpen() && !this.eventBus.before("open")) { - this.input.setAriaExpanded(true); - this.menu.open(); - this._updateHint(); - this.eventBus.trigger("open"); - } - return this.isOpen(); - }, - close: function close() { - if (this.isOpen() && !this.eventBus.before("close")) { - this.input.setAriaExpanded(false); - this.menu.close(); - this.input.clearHint(); - this.input.resetInputValue(); - this.eventBus.trigger("close"); - } - return !this.isOpen(); - }, - setVal: function setVal(val) { - this.input.setQuery(_.toStr(val)); - }, - getVal: function getVal() { - return this.input.getQuery(); - }, - select: function select($selectable) { - var data = this.menu.getSelectableData($selectable); - if (data && !this.eventBus.before("select", data.obj, data.dataset)) { - this.input.setQuery(data.val, true); - this.eventBus.trigger("select", data.obj, data.dataset); - this.close(); - return true; - } - return false; - }, - autocomplete: function autocomplete($selectable) { - var query, data, isValid; - query = this.input.getQuery(); - data = this.menu.getSelectableData($selectable); - isValid = data && query !== data.val; - if (isValid && !this.eventBus.before("autocomplete", data.obj, data.dataset)) { - this.input.setQuery(data.val); - this.eventBus.trigger("autocomplete", data.obj, data.dataset); - return true; - } - return false; - }, - moveCursor: function moveCursor(delta) { - var query, $candidate, data, suggestion, datasetName, cancelMove, id; - query = this.input.getQuery(); - $candidate = this.menu.selectableRelativeToCursor(delta); - data = this.menu.getSelectableData($candidate); - suggestion = data ? data.obj : null; - datasetName = data ? data.dataset : null; - id = $candidate ? $candidate.attr("id") : null; - this.input.trigger("cursorchange", id); - cancelMove = this._minLengthMet() && this.menu.update(query); - if (!cancelMove && !this.eventBus.before("cursorchange", suggestion, datasetName)) { - this.menu.setCursor($candidate); - if (data) { - if (typeof data.val === "string") { - this.input.setInputValue(data.val); - } - } else { - this.input.resetInputValue(); - this._updateHint(); - } - this.eventBus.trigger("cursorchange", suggestion, datasetName); - return true; - } - return false; - }, - destroy: function destroy() { - this.input.destroy(); - this.menu.destroy(); - } - }); - return Typeahead; - function c(ctx) { - var methods = [].slice.call(arguments, 1); - return function() { - var args = [].slice.call(arguments); - _.each(methods, function(method) { - return ctx[method].apply(ctx, args); - }); - }; - } - }(); - (function() { - "use strict"; - var old, keys, methods; - old = $.fn.typeahead; - keys = { - www: "tt-www", - attrs: "tt-attrs", - typeahead: "tt-typeahead" - }; - methods = { - initialize: function initialize(o, datasets) { - var www; - datasets = _.isArray(datasets) ? datasets : [].slice.call(arguments, 1); - o = o || {}; - www = WWW(o.classNames); - return this.each(attach); - function attach() { - var $input, $wrapper, $hint, $menu, defaultHint, defaultMenu, eventBus, input, menu, status, typeahead, MenuConstructor; - _.each(datasets, function(d) { - d.highlight = !!o.highlight; - }); - $input = $(this); - $wrapper = $(www.html.wrapper); - $hint = $elOrNull(o.hint); - $menu = $elOrNull(o.menu); - defaultHint = o.hint !== false && !$hint; - defaultMenu = o.menu !== false && !$menu; - defaultHint && ($hint = buildHintFromInput($input, www)); - defaultMenu && ($menu = $(www.html.menu).css(www.css.menu)); - $hint && $hint.val(""); - $input = prepInput($input, www); - if (defaultHint || defaultMenu) { - $wrapper.css(www.css.wrapper); - $input.css(defaultHint ? www.css.input : www.css.inputWithNoHint); - $input.wrap($wrapper).parent().prepend(defaultHint ? $hint : null).append(defaultMenu ? $menu : null); - } - MenuConstructor = defaultMenu ? DefaultMenu : Menu; - eventBus = new EventBus({ - el: $input - }); - input = new Input({ - hint: $hint, - input: $input, - menu: $menu - }, www); - menu = new MenuConstructor({ - node: $menu, - datasets: datasets - }, www); - status = new Status({ - $input: $input, - menu: menu - }); - typeahead = new Typeahead({ - input: input, - menu: menu, - eventBus: eventBus, - minLength: o.minLength, - autoselect: o.autoselect - }, www); - $input.data(keys.www, www); - $input.data(keys.typeahead, typeahead); - } - }, - isEnabled: function isEnabled() { - var enabled; - ttEach(this.first(), function(t) { - enabled = t.isEnabled(); - }); - return enabled; - }, - enable: function enable() { - ttEach(this, function(t) { - t.enable(); - }); - return this; - }, - disable: function disable() { - ttEach(this, function(t) { - t.disable(); - }); - return this; - }, - isActive: function isActive() { - var active; - ttEach(this.first(), function(t) { - active = t.isActive(); - }); - return active; - }, - activate: function activate() { - ttEach(this, function(t) { - t.activate(); - }); - return this; - }, - deactivate: function deactivate() { - ttEach(this, function(t) { - t.deactivate(); - }); - return this; - }, - isOpen: function isOpen() { - var open; - ttEach(this.first(), function(t) { - open = t.isOpen(); - }); - return open; - }, - open: function open() { - ttEach(this, function(t) { - t.open(); - }); - return this; - }, - close: function close() { - ttEach(this, function(t) { - t.close(); - }); - return this; - }, - select: function select(el) { - var success = false, $el = $(el); - ttEach(this.first(), function(t) { - success = t.select($el); - }); - return success; - }, - autocomplete: function autocomplete(el) { - var success = false, $el = $(el); - ttEach(this.first(), function(t) { - success = t.autocomplete($el); - }); - return success; - }, - moveCursor: function moveCursoe(delta) { - var success = false; - ttEach(this.first(), function(t) { - success = t.moveCursor(delta); - }); - return success; - }, - val: function val(newVal) { - var query; - if (!arguments.length) { - ttEach(this.first(), function(t) { - query = t.getVal(); - }); - return query; - } else { - ttEach(this, function(t) { - t.setVal(_.toStr(newVal)); - }); - return this; - } - }, - destroy: function destroy() { - ttEach(this, function(typeahead, $input) { - revert($input); - typeahead.destroy(); - }); - return this; - } - }; - $.fn.typeahead = function(method) { - if (methods[method]) { - return methods[method].apply(this, [].slice.call(arguments, 1)); - } else { - return methods.initialize.apply(this, arguments); - } - }; - $.fn.typeahead.noConflict = function noConflict() { - $.fn.typeahead = old; - return this; - }; - function ttEach($els, fn) { - $els.each(function() { - var $input = $(this), typeahead; - (typeahead = $input.data(keys.typeahead)) && fn(typeahead, $input); - }); - } - function buildHintFromInput($input, www) { - return $input.clone().addClass(www.classes.hint).removeData().css(www.css.hint).css(getBackgroundStyles($input)).prop({ - readonly: true, - required: false - }).removeAttr("id name placeholder").removeClass("required").attr({ - spellcheck: "false", - tabindex: -1 - }); - } - function prepInput($input, www) { - $input.data(keys.attrs, { - dir: $input.attr("dir"), - autocomplete: $input.attr("autocomplete"), - spellcheck: $input.attr("spellcheck"), - style: $input.attr("style") - }); - $input.addClass(www.classes.input).attr({ - spellcheck: false - }); - try { - !$input.attr("dir") && $input.attr("dir", "auto"); - } catch (e) {} - return $input; - } - function getBackgroundStyles($el) { - return { - backgroundAttachment: $el.css("background-attachment"), - backgroundClip: $el.css("background-clip"), - backgroundColor: $el.css("background-color"), - backgroundImage: $el.css("background-image"), - backgroundOrigin: $el.css("background-origin"), - backgroundPosition: $el.css("background-position"), - backgroundRepeat: $el.css("background-repeat"), - backgroundSize: $el.css("background-size") - }; - } - function revert($input) { - var www, $wrapper; - www = $input.data(keys.www); - $wrapper = $input.parent().filter(www.selectors.wrapper); - _.each($input.data(keys.attrs), function(val, key) { - _.isUndefined(val) ? $input.removeAttr(key) : $input.attr(key, val); - }); - $input.removeData(keys.typeahead).removeData(keys.www).removeData(keys.attr).removeClass(www.classes.input); - if ($wrapper.length) { - $input.detach().insertAfter($wrapper); - $wrapper.remove(); - } - } - function $elOrNull(obj) { - var isValid, $el; - isValid = _.isJQuery(obj) || _.isElement(obj); - $el = isValid ? $(obj).first() : []; - return $el.length ? $el : null; - } - })(); -}); \ No newline at end of file diff --git a/docs/metadata.json b/docs/metadata.json new file mode 100644 index 0000000..5991546 --- /dev/null +++ b/docs/metadata.json @@ -0,0 +1 @@ +{"bundleDisplayName":"BigInt","bundleIdentifier":"BigInt","schemaVersion":{"major":0,"minor":1,"patch":0}} \ No newline at end of file diff --git a/docs/search.json b/docs/search.json deleted file mode 100644 index 9a860f0..0000000 --- a/docs/search.json +++ /dev/null @@ -1 +0,0 @@ -{"Typealiases.html#/s:6BigInt4Bytea":{"name":"Byte","abstract":"

Unsigned 8 bit value

"},"Typealiases.html#/s:6BigInt5Bytesa":{"name":"Bytes","abstract":"

Array of unsigned 8 bit values

"},"Typealiases.html#/s:6BigInt4Limba":{"name":"Limb","abstract":"

Unsigned 64 bit value

"},"Typealiases.html#/s:6BigInt5Limbsa":{"name":"Limbs","abstract":"

Array of unsigned 64 bit values

"},"Structs/CRT.html#/s:6BigInt3CRTVyACSgSayAA4BIntVGcfc":{"name":"init(_:)","abstract":"

Constructs a CRT instance from the moduli - BInt version

","parent_name":"CRT"},"Structs/CRT.html#/s:6BigInt3CRTVyACSgSaySiGcfc":{"name":"init(_:)","abstract":"

Constructs a CRT instance from the moduli - Int version

","parent_name":"CRT"},"Structs/CRT.html#/s:6BigInt3CRTV7computeyAA4BIntVSayAFGF":{"name":"compute(_:)","abstract":"

Compute the CRT value - BInt version

","parent_name":"CRT"},"Structs/CRT.html#/s:6BigInt3CRTV7computeyAA4BIntVSaySiGF":{"name":"compute(_:)","abstract":"

Compute the CRT value - Int version

","parent_name":"CRT"},"Structs/BInt.html#/s:6BigInt4BIntV4ZEROACvpZ":{"name":"ZERO","abstract":"

BInt(0)

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV3ONEACvpZ":{"name":"ONE","abstract":"

BInt(1)

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV3TWOACvpZ":{"name":"TWO","abstract":"

BInt(2)

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV5THREEACvpZ":{"name":"THREE","abstract":"

BInt(3)

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV4FOURACvpZ":{"name":"FOUR","abstract":"

BInt(4)

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV4FIVEACvpZ":{"name":"FIVE","abstract":"

BInt(5)

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV3SIXACvpZ":{"name":"SIX","abstract":"

BInt(6)

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV5SEVENACvpZ":{"name":"SEVEN","abstract":"

BInt(7)

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV5EIGHTACvpZ":{"name":"EIGHT","abstract":"

BInt(8)

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV4NINEACvpZ":{"name":"NINE","abstract":"

BInt(9)

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV3TENACvpZ":{"name":"TEN","abstract":"

BInt(10)

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntVyACSays6UInt64VG_Sbtcfc":{"name":"init(_:_:)","abstract":"

Constructs a BInt from magnitude and sign

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntVyACSicfc":{"name":"init(_:)","abstract":"

Constructs a BInt from an Int value

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntVyACSgSdcfc":{"name":"init(_:)","abstract":"

Constructs a BInt from a decimal value

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV_5radixACSgSS_Sitcfc":{"name":"init(_:radix:)","abstract":"

Constructs a BInt from a String value and radix

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV8bitWidthACSi_tcfc":{"name":"init(bitWidth:)","abstract":"

Constructs a random BInt with a specified number of bits

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Constructs a BInt from a big-endian magnitude byte array representation

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Constructs a BInt from a big-endian 2’s complement byte array representation

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The sign, true if self < 0, false otherwise

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV9magnitudeSays6UInt64VGvp":{"name":"magnitude","abstract":"

The magnitude limb array

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV3absACvp":{"name":"abs","abstract":"

The absolute value of self

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV8bitWidthSivp":{"name":"bitWidth","abstract":"

The number of bits in the binary representation of the magnitude of self. 0 if self = 0

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV11descriptionSSvp":{"name":"description","abstract":"

Base 10 string value of self

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV6isEvenSbvp":{"name":"isEven","abstract":"

Is true if self is even, false if self is odd

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV9isNotZeroSbvp":{"name":"isNotZero","abstract":"

Is false if self = 0, true otherwise

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV5isOddSbvp":{"name":"isOdd","abstract":"

Is true if self is odd, false if self is even

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV5isOneSbvp":{"name":"isOne","abstract":"

Is true if self = 1, false otherwise

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV10isPositiveSbvp":{"name":"isPositive","abstract":"

Is true if self > 0, false otherwise

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV6isZeroSbvp":{"name":"isZero","abstract":"

Is true if self = 0, false otherwise

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV19leadingZeroBitCountSivp":{"name":"leadingZeroBitCount","abstract":"

The number of leading zero bits in the magnitude of self. 0 if self = 0

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV10populationSivp":{"name":"population","abstract":"

The number of 1 bits in the magnitude of self

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV6signumSivp":{"name":"signum","abstract":"

Is 0 if self = 0, 1 if self > 0, and -1 if self < 0

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV20trailingZeroBitCountSivp":{"name":"trailingZeroBitCount","abstract":"

The number of trailing zero bits in the magnitude of self. 0 if self = 0

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV8asDoubleSdyF":{"name":"asDouble()","abstract":"

self as a Double

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV02asB0SiSgyF":{"name":"asInt()","abstract":"

self as an Int

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV16asMagnitudeBytesSays5UInt8VGyF":{"name":"asMagnitudeBytes()","abstract":"

Byte array representation of magnitude value

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV13asSignedBytesSays5UInt8VGyF":{"name":"asSignedBytes()","abstract":"

Byte array representation of 2’s complement value

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV8asString5radix9uppercaseSSSi_SbtF":{"name":"asString(radix:uppercase:)","abstract":"

self as a String with a given radix

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV1aoiyA2C_ACtFZ":{"name":"&(_:_:)","abstract":"

Bitwise and operator - behaves as if two’s complement representation were used,
","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV2aeoiyyACz_ACtFZ":{"name":"&=(_:_:)","abstract":"

x = x & y

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV1ooiyA2C_ACtFZ":{"name":"|(_:_:)","abstract":"

Bitwise or operator - behaves as if two’s complement representation were used,
","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV2oeoiyyACz_ACtFZ":{"name":"|=(_:_:)","abstract":"

x = x | y

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV1xoiyA2C_ACtFZ":{"name":"^(_:_:)","abstract":"

Bitwise xor operator - behaves as if two’s complement representation were used,
","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV2xeoiyyACz_ACtFZ":{"name":"^=(_:_:)","abstract":"

x = x ^ y

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV1topyA2CFZ":{"name":"~(_:)","abstract":"

Bitwise not operator - behaves as if two’s complement arithmetic were used,
","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV8clearBityySiF":{"name":"clearBit(_:)","abstract":"

Clear a specified bit - a no-op if bit number < 0

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV7flipBityySiF":{"name":"flipBit(_:)","abstract":"

Invert a specified bit - a no-op if bit number < 0

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV6setBityySiF":{"name":"setBit(_:)","abstract":"

Set a specified bit - a no-op if bit number < 0

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV7testBitySbSiF":{"name":"testBit(_:)","abstract":"

Test a specified bit - false if bit number < 0

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV1popyA2CFZ":{"name":"+(_:)","abstract":"

Prefix plus

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV1poiyA2C_ACtFZ":{"name":"+(_:_:)","abstract":"

Addition

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV1poiyACSi_ACtFZ":{"name":"+(_:_:)","abstract":"

Addition

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV1poiyA2C_SitFZ":{"name":"+(_:_:)","abstract":"

Addition

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV2peoiyyACz_ACtFZ":{"name":"+=(_:_:)","abstract":"

x = x + y

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV2peoiyyACz_SitFZ":{"name":"+=(_:_:)","abstract":"

x = x + y

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV6negateyyF":{"name":"negate()","abstract":"

Negates self

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV1sopyA2CFZ":{"name":"-(_:)","abstract":"

Negation

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV1soiyA2C_ACtFZ":{"name":"-(_:_:)","abstract":"

Subtraction

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV1soiyACSi_ACtFZ":{"name":"-(_:_:)","abstract":"

Subtraction

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Subtraction

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x = x - y

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x = x - y

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Multiplication

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Multiplication

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Multiplication

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x = x * y

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x = x * y

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Division

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Division

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Division

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Division

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Exact division - that is, the remainder of the division is known to be 0

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Division

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Division

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Division

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x = x / y

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x = x / y

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Remainder

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Remainder

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Remainder

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x = x % y

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x = x % y

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Modulus - BInt parameter

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Modulus - Int parameter

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Inverse modulus - BInt parameter

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Inverse modulus - Int parameter

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Exponentiation

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Modular exponentiation - BInt modulus

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Modular exponentiation - Int modulus

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Equal

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Equal

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Equal

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Not equal

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Not equal

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Not equal

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Less than

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Less than

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Less than

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Greater than

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Greater than

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Greater than

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Less than or equal

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Less than or equal

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Less than or equal

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Greater than or equal

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Greater than or equal

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Greater than or equal

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Logical left shift

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x = x << n

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Logical right shift

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x = x >> n

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Checks whether self is prime using the Miller-Rabin algorithm

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The next probable prime greater than self

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A probable prime number with a given bitwidth

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Product of primes up to n

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n'th root

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n'th root and remainder

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Check whether self is a perfect root, that is, for some integer x and n > 1 self = x^n

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Square root of a non-negative number

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Square root and remainder of a non-negative number

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Check whether self is a perfect square, that is, for some integer x self = x^2

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Square root modulo a prime number - BInt prime

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Square root modulo a prime number - Int prime

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV8binomialyACSi_SitFZ":{"name":"binomial(_:_:)","abstract":"

Compute binomial coefficient n over k

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Factorial function

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n'th Fibonacci number

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Fibonacci pair, n'th and n'th + 1 Fibonacci number

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Greatest common divisor

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Extended greatest common divisor

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV12jacobiSymbolySiACF":{"name":"jacobiSymbol(_:)","abstract":"

Jacobi symbol - BInt parameter. If m is an odd prime, this is also the Legendre symbol

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Jacobi symbol - Int parameter. If m is an odd prime, this is also the Legendre symbol

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Kronecker symbol - BInt parameter. If m is positive and odd, this is also the Jacobi symbol

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Kronecker symbol - Int parameter. If m is positive and odd, this is also the Jacobi symbol

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Least common multiple

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV5lucasyACSiFZ":{"name":"lucas(_:)","abstract":"

n'th Lucas number

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV6lucas2yAC_ACtSiFZ":{"name":"lucas2(_:)","abstract":"

Lucas pair, n'th and n'th + 1 Lucas number

","parent_name":"BInt"},"Structs/BInt.html#/s:6BigInt4BIntV14randomLessThanACyF":{"name":"randomLessThan()","abstract":"

Random value

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BFraction(0, 1)

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BFraction(1, 1)

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Constructs a BFraction from numerator and denominator

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionVyAcA4BIntV_Sitcfc":{"name":"init(_:_:)","abstract":"

Constructs a BFraction from numerator and denominator

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionVyACSi_AA4BIntVtcfc":{"name":"init(_:_:)","abstract":"

Constructs a BFraction from numerator and denominator

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionVyACSi_Sitcfc":{"name":"init(_:_:)","abstract":"

Constructs a BFraction from numerator and denominator

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionVyACSgSdcfc":{"name":"init(_:)","abstract":"

Constructs a BFraction from its decimal value

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionVyACSgSScfc":{"name":"init(_:)","abstract":"

Constructs a BFraction from a String representation

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Constructs a BFraction from a continued fraction - BInt version

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionVyACSaySiGcfc":{"name":"init(_:)","abstract":"

Constructs a BFraction from a continued fraction - Int version

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The numerator - a BInt value

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV11denominatorAA4BIntVvp":{"name":"denominator","abstract":"

The denominator - a positive BInt value

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV3absACvp":{"name":"abs","abstract":"

The absolute value of self

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV11descriptionSSvp":{"name":"description","abstract":"

String value of self

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Is true if self is an integer, that is, the denominator is 1

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV10isNegativeSbvp":{"name":"isNegative","abstract":"

Is true if self < 0, false otherwise

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV10isPositiveSbvp":{"name":"isPositive","abstract":"

Is true if self > 0, false otherwise

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV6isZeroSbvp":{"name":"isZero","abstract":"

Is true if self = 0, false otherwise

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV6signumSivp":{"name":"signum","abstract":"

Is 0 if self = 0, 1 if self > 0, and -1 if self < 0

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self as a String
","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV15asDecimalString9precision11exponentialSSSi_SbtF":{"name":"asDecimalString(precision:exponential:)","abstract":"

self as a Decimal String with a specified precision, possibly using exponential notation

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self as a Double

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV19asContinuedFractionSayAA4BIntVGyF":{"name":"asContinuedFraction()","abstract":"

self as a Continued Fraction

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1popyA2CFZ":{"name":"+(_:)","abstract":"

Prefix plus

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1poiyA2C_ACtFZ":{"name":"+(_:_:)","abstract":"

Addition

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1poiyA2C_AA4BIntVtFZ":{"name":"+(_:_:)","abstract":"

Addition

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1poiyAcA4BIntV_ACtFZ":{"name":"+(_:_:)","abstract":"

Addition

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1poiyA2C_SitFZ":{"name":"+(_:_:)","abstract":"

Addition

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1poiyACSi_ACtFZ":{"name":"+(_:_:)","abstract":"

Addition

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2peoiyyACz_ACtFZ":{"name":"+=(_:_:)","abstract":"

x = x + y

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2peoiyyACz_AA4BIntVtFZ":{"name":"+=(_:_:)","abstract":"

x = x + y

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2peoiyyACz_SitFZ":{"name":"+=(_:_:)","abstract":"

x = x + y

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1sopyA2CFZ":{"name":"-(_:)","abstract":"

Negation

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1soiyA2C_ACtFZ":{"name":"-(_:_:)","abstract":"

Subtraction

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1soiyA2C_AA4BIntVtFZ":{"name":"-(_:_:)","abstract":"

Subtraction

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1soiyAcA4BIntV_ACtFZ":{"name":"-(_:_:)","abstract":"

Subtraction

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1soiyA2C_SitFZ":{"name":"-(_:_:)","abstract":"

Subtraction

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1soiyACSi_ACtFZ":{"name":"-(_:_:)","abstract":"

Subtraction

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2seoiyyACz_ACtFZ":{"name":"-=(_:_:)","abstract":"

x = x - y

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2seoiyyACz_AA4BIntVtFZ":{"name":"-=(_:_:)","abstract":"

x = x - y

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2seoiyyACz_SitFZ":{"name":"-=(_:_:)","abstract":"

x = x - y

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1moiyA2C_ACtFZ":{"name":"*(_:_:)","abstract":"

Multiplication

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1moiyA2C_AA4BIntVtFZ":{"name":"*(_:_:)","abstract":"

Multiplication

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1moiyAcA4BIntV_ACtFZ":{"name":"*(_:_:)","abstract":"

Multiplication

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1moiyA2C_SitFZ":{"name":"*(_:_:)","abstract":"

Multiplication

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1moiyACSi_ACtFZ":{"name":"*(_:_:)","abstract":"

Multiplication

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2meoiyyACz_ACtFZ":{"name":"*=(_:_:)","abstract":"

x = x * y

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2meoiyyACz_AA4BIntVtFZ":{"name":"*=(_:_:)","abstract":"

x = x * y

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2meoiyyACz_SitFZ":{"name":"*=(_:_:)","abstract":"

x = x * y

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1doiyA2C_ACtFZ":{"name":"/(_:_:)","abstract":"

Division

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1doiyA2C_AA4BIntVtFZ":{"name":"/(_:_:)","abstract":"

Division

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1doiyAcA4BIntV_ACtFZ":{"name":"/(_:_:)","abstract":"

Division

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1doiyA2C_SitFZ":{"name":"/(_:_:)","abstract":"

Division

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1doiyACSi_ACtFZ":{"name":"/(_:_:)","abstract":"

Division

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2deoiyyACz_ACtFZ":{"name":"/=(_:_:)","abstract":"

x = x / y

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2deoiyyACz_AA4BIntVtFZ":{"name":"/=(_:_:)","abstract":"

x = x / y

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2deoiyyACz_SitFZ":{"name":"/=(_:_:)","abstract":"

x = x / y

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV6invertACyF":{"name":"invert()","abstract":"

Invert self

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV3modyAA4BIntVSgAFF":{"name":"mod(_:)","abstract":"

Modulus - BInt parameter

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV3modySiSgSiF":{"name":"mod(_:)","abstract":"

Modulus - Int parameter

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2mmoiyA2C_SitFZ":{"name":"**(_:_:)","abstract":"

Exponentiation

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV5roundAA4BIntVyF":{"name":"round()","abstract":"

Round

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Truncate

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Ceil

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Floor

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Equal

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Equal

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Equal

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Equal

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Equal

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Not equal

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Not equal

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Not equal

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Not equal

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Not equal

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Less than

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Less than

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Less than

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Less than

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Less than

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV1goiySbAC_ACtFZ":{"name":">(_:_:)","abstract":"

Greater than

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Greater than

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Greater than

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Greater than

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Greater than

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Less than or equal

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2leoiySbAC_AA4BIntVtFZ":{"name":"<=(_:_:)","abstract":"

Less than or equal

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2leoiySbAA4BIntV_ACtFZ":{"name":"<=(_:_:)","abstract":"

Less than or equal

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2leoiySbAC_SitFZ":{"name":"<=(_:_:)","abstract":"

Less than or equal

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2leoiySbSi_ACtFZ":{"name":"<=(_:_:)","abstract":"

Less than or equal

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Greater than or equal

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Greater than or equal

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Greater than or equal

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2geoiySbAC_SitFZ":{"name":">=(_:_:)","abstract":"

Greater than or equal

","parent_name":"BFraction"},"Structs/BFraction.html#/s:6BigInt9BFractionV2geoiySbSi_ACtFZ":{"name":">=(_:_:)","abstract":"

Greater than or equal

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Bernoulli number

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Bernoulli numbers

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Harmonic number: 1 + 1 / 2 + … + 1 / n

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Harmonic sequence: The first n harmonic numbers

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A signed fraction with numerator and denominator of unbounded size.

"},"Structs/BInt.html":{"name":"BInt","abstract":"

A signed integer of unbounded size.

"},"Structs/CRT.html":{"name":"CRT","abstract":"

CRT instances implement the Chinese Remainder Theorem

"},"Structs.html":{"name":"Structures","abstract":"

The following structures are available globally.

"},"Typealiases.html":{"name":"Type Aliases","abstract":"

The following type aliases are available globally.

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