first shot at approximating floats with ratios

run-tests.coffee

@@ -42,6 +42,7 @@ selftest  = ->
 	test_abs()
 	test_adj()
 	test_arg()
+	test_approxratio()
 	test_besselj()
 	test_bessely()
 	test_ceiling()

runtime/defs.coffee

@@ -80,6 +80,7 @@ ABS = counter++
 ADD = counter++
 ADJ = counter++
 AND = counter++
+APPROXRATIO = counter++
 ARCCOS = counter++
 ARCCOSH = counter++
 ARCSIN = counter++

runtime/init.coffee

@@ -64,6 +64,7 @@ defn = ->
 	std_symbol("add", ADD)
 	std_symbol("adj", ADJ)
 	std_symbol("and", AND)
+	std_symbol("approxratio", APPROXRATIO)
 	std_symbol("arccos", ARCCOS)
 	std_symbol("arccosh", ARCCOSH)
 	std_symbol("arcsin", ARCSIN)

runtime/zombocom.coffee

@@ -97,7 +97,7 @@ $.exec = exec
 $.parse = parse
 
 do ->
-	builtin_fns = ["abs", "add", "adj", "and", "arccos", "arccosh", "arcsin", "arcsinh", "arctan", "arctanh", "arg", "atomize", "besselj", "bessely", "binding", "binomial", "ceiling", "check", "choose", "circexp", "clear", "clearall", "clearpatterns", "clock", "coeff", "cofactor", "condense", "conj", "contract", "cos", "cosh", "decomp", "defint", "deg", "denominator", "det", "derivative", "dim", "dirac", "display", "divisors", "do", "dot", "draw", "dsolve", "eigen", "eigenval", "eigenvec", "erf", "erfc", "eval", "exp", "expand", "expcos", "expsin", "factor", "factorial", "factorpoly", "filter", "float", "floor", "for", "Gamma", "gcd", "hermite", "hilbert", "imag", "component", "inner", "integral", "inv", "invg", "isinteger", "isprime", "laguerre", "lcm", "leading", "legendre", "log", "mag", "mod", "multiply", "not", "nroots", "number", "numerator", "operator", "or", "outer", "pattern", "patternsinfo", "polar", "power", "prime", "print", "product", "quote", "quotient", "rank", "rationalize", "real", "rect", "roots", "equals", "shape", "sgn", "silentpattern", "simplify", "sin", "sinh", "sqrt", "stop", "subst", "sum", "symbolsinfo", "tan", "tanh", "taylor", "test", "testeq", "testge", "testgt", "testle", "testlt", "transpose", "unit", "zero"]
+	builtin_fns = ["abs", "add", "adj", "and", "approxratio", "arccos", "arccosh", "arcsin", "arcsinh", "arctan", "arctanh", "arg", "atomize", "besselj", "bessely", "binding", "binomial", "ceiling", "check", "choose", "circexp", "clear", "clearall", "clearpatterns", "clock", "coeff", "cofactor", "condense", "conj", "contract", "cos", "cosh", "decomp", "defint", "deg", "denominator", "det", "derivative", "dim", "dirac", "display", "divisors", "do", "dot", "draw", "dsolve", "eigen", "eigenval", "eigenvec", "erf", "erfc", "eval", "exp", "expand", "expcos", "expsin", "factor", "factorial", "factorpoly", "filter", "float", "floor", "for", "Gamma", "gcd", "hermite", "hilbert", "imag", "component", "inner", "integral", "inv", "invg", "isinteger", "isprime", "laguerre", "lcm", "leading", "legendre", "log", "mag", "mod", "multiply", "not", "nroots", "number", "numerator", "operator", "or", "outer", "pattern", "patternsinfo", "polar", "power", "prime", "print", "product", "quote", "quotient", "rank", "rationalize", "real", "rect", "roots", "equals", "shape", "sgn", "silentpattern", "simplify", "sin", "sinh", "sqrt", "stop", "subst", "sum", "symbolsinfo", "tan", "tanh", "taylor", "test", "testeq", "testge", "testgt", "testle", "testlt", "transpose", "unit", "zero"]
 
 	for fn in builtin_fns
 		$[fn] = exec.bind(this, fn)

sources/approxratio.coffee

@@ -0,0 +1,101 @@
+###
+ Guesses a rational for a given float.
+###
+
+Eval_approxratio = ->
+	theArgument = cadr(p1)
+	push(theArgument)
+	zzfloat()
+	supposedlyTheFloat = pop()
+	if supposedlyTheFloat.k == DOUBLE
+    theFloat = supposedlyTheFloat.d
+    splitBeforeAndAfterDot = theFloat.toString().split(".")
+    if splitBeforeAndAfterDot.length == 2
+    	numberOfDigitsAfterTheDot = splitBeforeAndAfterDot[1].length
+    	precision = 1/Math.pow(10,numberOfDigitsAfterTheDot)
+    	theRatio = approxratio(theFloat,precision)
+    	push_rational(theRatio[0], theRatio[1])
+    else
+      push_integer(theFloat)
+    return
+
+	# we didn't manage, just leave unexpressed
+	push_symbol(APPROXRATIO)
+	push(theArgument)
+	list(2)
+
+
+# courtesy of Michael Borcherds
+# who ported this to JavaScript under MIT licence
+# also see
+# https://github.com/geogebra/geogebra/blob/master/common/src/main/java/org/geogebra/common/kernel/algos/AlgoFractionText.java
+# potential other ways to do this:
+#   https://rosettacode.org/wiki/Convert_decimal_number_to_rational
+#   http://www.homeschoolmath.net/teaching/rational_numbers.php
+#   http://stackoverflow.com/questions/95727/how-to-convert-floats-to-human-readable-fractions
+
+approxratio = (decimal, AccuracyFactor) ->
+  FractionNumerator = undefined
+  FractionDenominator = undefined
+  DecimalSign = undefined
+  Z = undefined
+  PreviousDenominator = undefined
+  ScratchValue = undefined
+  ret = [
+    0
+    0
+  ]
+  if isNaN(decimal)
+    return ret
+  # return 0/0 
+  if decimal == Infinity
+    ret[0] = 1
+    ret[1] = 0
+    # 1/0
+    return ret
+  if decimal == -Infinity
+    ret[0] = -1
+    ret[1] = 0
+    # -1/0
+    return ret
+  if decimal < 0.0
+    DecimalSign = -1.0
+  else
+    DecimalSign = 1.0
+  decimal = Math.abs(decimal)
+  if Math.abs(decimal - Math.floor(decimal)) < AccuracyFactor
+    # handles exact integers including 0 
+    FractionNumerator = decimal * DecimalSign
+    FractionDenominator = 1.0
+    ret[0] = FractionNumerator
+    ret[1] = FractionDenominator
+    return ret
+  if decimal < 1.0e-19
+    # X = 0 already taken care of 
+    FractionNumerator = DecimalSign
+    FractionDenominator = 9999999999999999999.0
+    ret[0] = FractionNumerator
+    ret[1] = FractionDenominator
+    return ret
+  if decimal > 1.0e19
+    FractionNumerator = 9999999999999999999.0 * DecimalSign
+    FractionDenominator = 1.0
+    ret[0] = FractionNumerator
+    ret[1] = FractionDenominator
+    return ret
+  Z = decimal
+  PreviousDenominator = 0.0
+  FractionDenominator = 1.0
+  loop
+    Z = 1.0 / (Z - Math.floor(Z))
+    ScratchValue = FractionDenominator
+    FractionDenominator = FractionDenominator * Math.floor(Z) + PreviousDenominator
+    PreviousDenominator = ScratchValue
+    FractionNumerator = Math.floor(decimal * FractionDenominator + 0.5)
+    # Rounding Function
+    unless Math.abs(decimal - (FractionNumerator / FractionDenominator)) > AccuracyFactor and Z != Math.floor(Z)
+      break
+  FractionNumerator = DecimalSign * FractionNumerator
+  ret[0] = FractionNumerator
+  ret[1] = FractionDenominator
+  ret

sources/eval.coffee

@@ -151,6 +151,7 @@ Eval_cons = ->
 		when FACTORPOLY then Eval_factorpoly()
 		when FILTER then Eval_filter()
 		when FLOATF then Eval_float()
+		when APPROXRATIO then Eval_approxratio()
 		when FLOOR then Eval_floor()
 		when FOR then Eval_for()
 		# this is invoked only when we

tests/approxratio.coffee

@@ -0,0 +1,44 @@
+test_approxratio = ->
+	run_test [
+		"approxratio(0.9054054)",
+		"67/74",
+
+		"approxratio(0.518518)",
+		"14/27",
+
+		"approxratio(0.3333)",
+		"1/3",
+
+		"approxratio(0.5)",
+		"1/2",
+
+		"approxratio(3.14159)",
+		"355/113",
+
+		"approxratio(a*3.14)",
+		"approxratio(a*3.14)",
+
+		"approxratio(3.14)",
+		"22/7",
+
+		# see http://davidbau.com/archives/2010/03/14/the_mystery_of_355113.html
+		"approxratio(3.14159)",
+		"355/113",
+
+		"approxratio(-3.14159)",
+		"-355/113",
+
+		"approxratio(0)",
+		"0",
+
+		"approxratio(0.0)",
+		"0",
+
+		"approxratio(2)",
+		"2",
+
+		"approxratio(2.0)",
+		"2",
+
+	]
+