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Logarithmic funcs #536

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merged 5 commits into from
May 5, 2024
Merged

Logarithmic funcs #536

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fc7058c
Preliminary logarightmic funcs improve
ckormanyos May 5, 2024
8cab9e6
Merge branch 'develop' into logarithmic_funcs
ckormanyos May 5, 2024
e4c3c7d
Simplify log and add 128-bit coefs/tests
ckormanyos May 5, 2024
b9c37b7
Finish log1p impl/tests 128
ckormanyos May 5, 2024
a001179
Simplify logarithmic functions
ckormanyos May 5, 2024
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2 changes: 1 addition & 1 deletion include/boost/decimal/detail/cmath/impl/cosh_impl.hpp
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Expand Up @@ -99,7 +99,7 @@ constexpr typename cosh_table_imp<b>::d128_coeffs_t cosh_table_imp<b>::d128_coef
using cosh_table = cosh_detail::cosh_table_imp<true>;

template <BOOST_DECIMAL_DECIMAL_FLOATING_TYPE T>
constexpr auto cosh_series_expansion(T z) noexcept;
constexpr auto cosh_series_expansion(T z2) noexcept;

template <>
constexpr auto cosh_series_expansion<decimal32>(decimal32 z2) noexcept
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162 changes: 162 additions & 0 deletions include/boost/decimal/detail/cmath/impl/log1p_impl.hpp
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@@ -0,0 +1,162 @@
// Copyright 2023 - 2024 Matt Borland
// Copyright 2023 - 2024 Christopher Kormanyos
// Distributed under the Boost Software License, Version 1.0.
// https://www.boost.org/LICENSE_1_0.txt

#ifndef BOOST_DECIMAL_DETAIL_CMATH_IMPL_LOG1P_IMPL_HPP
#define BOOST_DECIMAL_DETAIL_CMATH_IMPL_LOG1P_IMPL_HPP

#include <boost/decimal/detail/concepts.hpp>
#include <boost/decimal/detail/cmath/impl/taylor_series_result.hpp>

#ifndef BOOST_DECIMAL_BUILD_MODULE
#include <array>
#include <cstddef>
#include <cstdint>
#endif

namespace boost {
namespace decimal {
namespace detail {

namespace log1p_detail {

template <bool b>
struct log1p_table_imp
{
private:
using d32_coeffs_t = std::array<decimal32, 12>;
using d64_coeffs_t = std::array<decimal64, 20>;
using d128_coeffs_t = std::array<decimal128, 36>;

public:
static constexpr d32_coeffs_t d32_coeffs =
{{
// Series[Log[1 + x], {x, 0, 13}]
// (1), // * z
-boost::decimal::decimal32 { 5, -1 }, // * z^2
boost::decimal::decimal32 { UINT64_C(3333333333333333333), -19 }, // * z^3
-boost::decimal::decimal32 { 25, -2 }, // * z^4
boost::decimal::decimal32 { 2, -1 }, // * z^5
-boost::decimal::decimal32 { UINT64_C(1666666666666666667), -19 }, // * z^6
boost::decimal::decimal32 { UINT64_C(1428571428571428571), -19 }, // * z^7
-boost::decimal::decimal32 { 125, -3 }, // * z^8
boost::decimal::decimal32 { UINT64_C(1111111111111111111), -19 }, // * z^9
-boost::decimal::decimal32 { 1, -1 }, // * z^10
boost::decimal::decimal32 { UINT64_C(9090909090909090909), -19 - 1 }, // * z^11
-boost::decimal::decimal32 { UINT64_C(8333333333333333333), -19 - 1 }, // * z^12
boost::decimal::decimal32 { UINT64_C(7692307692307692308), -19 - 1 }, // * z^13
}};

static constexpr d64_coeffs_t d64_coeffs =
{{
// Series[Log[1 + x], {x, 0, 21}]
// (1), // * z
-boost::decimal::decimal64 { 5, -1 }, // * z^2
boost::decimal::decimal64 { UINT64_C(3333333333333333333), -19 }, // * z^3
-boost::decimal::decimal64 { 25, -2 }, // * z^4
boost::decimal::decimal64 { 2, -1 }, // * z^5
-boost::decimal::decimal64 { UINT64_C(1666666666666666667), -19 }, // * z^6
boost::decimal::decimal64 { UINT64_C(1428571428571428571), -19 }, // * z^7
-boost::decimal::decimal64 { 125, -3 }, // * z^8
boost::decimal::decimal64 { UINT64_C(1111111111111111111), -19 }, // * z^9
-boost::decimal::decimal64 { 1, -1 }, // * z^10
boost::decimal::decimal64 { UINT64_C(9090909090909090909), -19 - 1 }, // * z^11
-boost::decimal::decimal64 { UINT64_C(8333333333333333333), -19 - 1 }, // * z^12
boost::decimal::decimal64 { UINT64_C(7692307692307692308), -19 - 1 }, // * z^13
-boost::decimal::decimal64 { UINT64_C(7142857142857142857), -19 - 1 }, // * z^14
boost::decimal::decimal64 { UINT64_C(6666666666666666667), -19 - 1 }, // * z^15
-boost::decimal::decimal64 { UINT64_C(6250000000000000000), -19 - 1 }, // * z^16
boost::decimal::decimal64 { UINT64_C(5882352941176470588), -19 - 1 }, // * z^17
-boost::decimal::decimal64 { UINT64_C(5555555555555555556), -19 - 1 }, // * z^18
boost::decimal::decimal64 { UINT64_C(5263157894736842105), -19 - 1 }, // * z^19
-boost::decimal::decimal64 { 5, -2 }, // * z^20
boost::decimal::decimal64 { UINT64_C(4761904761904761905), -19 - 1 }, // * z^21
}};

static constexpr d128_coeffs_t d128_coeffs =
{{
// Series[Log[(1 + (z/2))/(1 - (z/2))], {z, 0, 43}]
// (1), // * z
-::boost::decimal::decimal128 { 5, -1 }, // * z^2
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(180700362080917), UINT64_C(7483252092553221458) }, -34 }, // * z^3
-::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(135525271560688), UINT64_C(1000753050987528192) }, -34 }, // * z^4
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(108420217248550), UINT64_C(8179300070273843200) }, -34 }, // * z^5
-::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(90350181040458), UINT64_C(12964998083131386532) }, -34 }, // * z^6
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(77443012320393), UINT64_C(3207108039665666332) }, -34 }, // * z^7
-::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(67762635780344), UINT64_C(500376525493764096) }, -34 }, // * z^8
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(60233454026972), UINT64_C(8643332055420924359) }, -34 }, // * z^9
-::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(54210108624275), UINT64_C(4089650035136921600) }, -34 }, // * z^10
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(492819169311592), UINT64_C(17054915875379776418) }, -35 }, // * z^11
-::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(451750905202293), UINT64_C(9484758194528277842) }, -35 }, // * z^12
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(417000835571347), UINT64_C(15850062977145160938) }, -35 }, // * z^13
-::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(387215061601965), UINT64_C(16035540198328331700) }, -35 }, // * z^14
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(361400724161834), UINT64_C(14966504185106442916) }, -35 }, // * z^15
-::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(338813178901720), UINT64_C(2501882627468820480) }, -35 }, // * z^16
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(318882991907501), UINT64_C(5610020838860575434) }, -35 }, // * z^17
-::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(301167270134862), UINT64_C(6323172129685518558) }, -35 }, // * z^18
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(285316361180395), UINT64_C(16670067533954968520) }, -35 }, // * z^19
-::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(271050543121376), UINT64_C(2001506101975056384) }, -35 }, // * z^20
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(258143374401310), UINT64_C(10690360132218887800) }, -35 }, // * z^21
-::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(246409584655796), UINT64_C(8527457937689888204) }, -35 }, // * z^22
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(235696124453370), UINT64_C(9760763598982462770) }, -35 }, // * z^23
-::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(225875452601146), UINT64_C(13965751134118914724) }, -35 }, // * z^24
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(216840434497100), UINT64_C(16358600140547686400) }, -35 }, // * z^25
-::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(208500417785673), UINT64_C(17148403525427356272) }, -35 }, // * z^26
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(200778180089908), UINT64_C(4215448086457012372) }, -35 }, // * z^27
-::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(193607530800982), UINT64_C(17241142136018941658) }, -35 }, // * z^28
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(186931409049224), UINT64_C(16646619993397598836) }, -35 }, // * z^29
-::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(180700362080917), UINT64_C(7483252092553221458) }, -35 }, // * z^30
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(174871318142823), UINT64_C(5456688082434451252) }, -35 }, // * z^31
-::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(169406589450860), UINT64_C(1250941313734410240) }, -35 }, // * z^32
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(164273056437197), UINT64_C(11833886649696442678) }, -35 }, // * z^33
-::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(159441495953750), UINT64_C(12028382456285063520) }, -35 }, // * z^34
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(154886024640786), UINT64_C(6414216079331332674) }, -35 }, // * z^35
-::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(150583635067431), UINT64_C(3161586064842759274) }, -35 }, // * z^36
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(146513807092635), UINT64_C(13545911456276754540) }, -35 }, // * z^37
}};
};

#if !(defined(__cpp_inline_variables) && __cpp_inline_variables >= 201606L) && (!defined(_MSC_VER) || _MSC_VER != 1900)

template <bool b>
constexpr typename log1p_table_imp<b>::d32_coeffs_t log1p_table_imp<b>::d32_coeffs;

template <bool b>
constexpr typename log1p_table_imp<b>::d64_coeffs_t log1p_table_imp<b>::d64_coeffs;

template <bool b>
constexpr typename log1p_table_imp<b>::d128_coeffs_t log1p_table_imp<b>::d128_coeffs;

#endif

} //namespace log1p_detail

using log1p_table = log1p_detail::log1p_table_imp<true>;

template <BOOST_DECIMAL_DECIMAL_FLOATING_TYPE T>
constexpr auto log1p_series_expansion(T z2) noexcept;

template <>
constexpr auto log1p_series_expansion<decimal32>(decimal32 z2) noexcept
{
return taylor_series_result(z2, log1p_table::d32_coeffs);
}

template <>
constexpr auto log1p_series_expansion<decimal64>(decimal64 z2) noexcept
{
return taylor_series_result(z2, log1p_table::d64_coeffs);
}

template <>
constexpr auto log1p_series_expansion<decimal128>(decimal128 z2) noexcept
{
return taylor_series_result(z2, log1p_table::d128_coeffs);
}

} //namespace detail
} //namespace decimal
} //namespace boost

#endif //BOOST_DECIMAL_DETAIL_CMATH_IMPL_LOG1P_IMPL_HPP
134 changes: 134 additions & 0 deletions include/boost/decimal/detail/cmath/impl/log_impl.hpp
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@@ -0,0 +1,134 @@
// Copyright 2023 - 2024 Matt Borland
// Copyright 2023 - 2024 Christopher Kormanyos
// Distributed under the Boost Software License, Version 1.0.
// https://www.boost.org/LICENSE_1_0.txt

#ifndef BOOST_DECIMAL_DETAIL_CMATH_IMPL_LOG_IMPL_HPP
#define BOOST_DECIMAL_DETAIL_CMATH_IMPL_LOG_IMPL_HPP

#include <boost/decimal/detail/concepts.hpp>
#include <boost/decimal/detail/cmath/impl/taylor_series_result.hpp>

#ifndef BOOST_DECIMAL_BUILD_MODULE
#include <array>
#include <cstddef>
#include <cstdint>
#endif

namespace boost {
namespace decimal {
namespace detail {

namespace log_detail {

template <bool b>
struct log_table_imp
{
private:
using d32_coeffs_t = std::array<decimal32, 8>;
using d64_coeffs_t = std::array<decimal64, 11>;
using d128_coeffs_t = std::array<decimal128, 21>;

public:
static constexpr d32_coeffs_t d32_coeffs =
{{
// Series[Log[(1 + (z/2))/(1 - (z/2))], {z, 0, 17}]
// (1), // * z
::boost::decimal::decimal32 { UINT64_C(8333333333333333333), - 19 - 1 }, // * z^3
::boost::decimal::decimal32 { UINT64_C(1250000000000000000), - 19 - 1 }, // * z^5
::boost::decimal::decimal32 { UINT64_C(2232142857142857143), - 19 - 2 }, // * z^7
::boost::decimal::decimal32 { UINT64_C(4340277777777777778), - 19 - 3 }, // * z^9
::boost::decimal::decimal32 { UINT64_C(8877840909090909091), - 19 - 4 }, // * z^11
::boost::decimal::decimal32 { UINT64_C(1878004807692307692), - 19 - 4 }, // * z^13
::boost::decimal::decimal32 { UINT64_C(4069010416666666667), - 19 - 5 }, // * z^15
::boost::decimal::decimal32 { UINT64_C(8975758272058823529), - 19 - 6 }, // * z^17
}};

static constexpr d64_coeffs_t d64_coeffs =
{{
// Series[Log[(1 + (z/2))/(1 - (z/2))], {z, 0, 23}]
// (1), // * z
::boost::decimal::decimal64 { UINT64_C(8333333333333333333), - 19 - 1 }, // * z^3
::boost::decimal::decimal64 { UINT64_C(1250000000000000000), - 19 - 1 }, // * z^5
::boost::decimal::decimal64 { UINT64_C(2232142857142857143), - 19 - 2 }, // * z^7
::boost::decimal::decimal64 { UINT64_C(4340277777777777778), - 19 - 3 }, // * z^9
::boost::decimal::decimal64 { UINT64_C(8877840909090909091), - 19 - 4 }, // * z^11
::boost::decimal::decimal64 { UINT64_C(1878004807692307692), - 19 - 4 }, // * z^13
::boost::decimal::decimal64 { UINT64_C(4069010416666666667), - 19 - 5 }, // * z^15
::boost::decimal::decimal64 { UINT64_C(8975758272058823529), - 19 - 6 }, // * z^17
::boost::decimal::decimal64 { UINT64_C(2007735402960526316), - 19 - 6 }, // * z^19
::boost::decimal::decimal64 { UINT64_C(4541306268601190476), - 19 - 7 }, // * z^21
::boost::decimal::decimal64 { UINT64_C(1036602517832880435), - 19 - 7 }, // * z^23
}};

static constexpr d128_coeffs_t d128_coeffs =
{{
// Series[Log[(1 + (z/2))/(1 - (z/2))], {z, 0, 43}]
// (1), // * z
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(451750905202293), UINT64_C(9484758194528277842) }, -35 }, // * z^3
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(67762635780344), UINT64_C(500376525493764096) }, -35 }, // * z^5
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(121004706750614), UINT64_C(6164027816584450626) }, -36 }, // * z^7
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(235286929792861), UINT64_C(3787056721709964394) }, -37 }, // * z^9
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(481268720030852), UINT64_C(8584740752302634068) }, -38 }, // * z^11
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(101806844621911), UINT64_C(1816002851448634124) }, -38 }, // * z^13
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(220581496680807), UINT64_C(7009130190423632548) }, -39 }, // * z^15
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(486576830913545), UINT64_C(12748560115094843630) }, -40 }, // * z^17
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(108839554283293), UINT64_C(2123490654414259032) }, -40 }, // * z^19
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(246184706116972), UINT64_C(9634423737622849438) }, -41 }, // * z^21
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(56194335091917), UINT64_C(11823550152479764302) }, -41 }, // * z^23
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(129246970711410), UINT64_C(10592095684364861440) }, -42 }, // * z^25
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(299182802572709), UINT64_C(12220910627630811506) }, -43 }, // * z^27
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(69637376460889), UINT64_C(5865971761607874066) }, -43 }, // * z^29
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(162861606239176), UINT64_C(11636108014793143194) }, -44 }, // * z^31
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(382478014652611), UINT64_C(14470401740943906374) }, -45 }, // * z^33
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(90155532025258), UINT64_C(9076666090147568782) }, -45 }, // * z^35
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(213205650059732), UINT64_C(16978042870933143358) }, -46 }, // * z^37
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(505680067449366), UINT64_C(9996854995997550184) }, -47 }, // * z^39
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(120253186771495), UINT64_C(12950434681540257980) }, -47 }, // * z^41
::boost::decimal::decimal128 { boost::decimal::detail::uint128 { UINT64_C(286650038234379), UINT64_C(5345076336561816786) }, -48 }, // * z^43
}};
};

#if !(defined(__cpp_inline_variables) && __cpp_inline_variables >= 201606L) && (!defined(_MSC_VER) || _MSC_VER != 1900)

template <bool b>
constexpr typename log_table_imp<b>::d32_coeffs_t log_table_imp<b>::d32_coeffs;

template <bool b>
constexpr typename log_table_imp<b>::d64_coeffs_t log_table_imp<b>::d64_coeffs;

template <bool b>
constexpr typename log_table_imp<b>::d128_coeffs_t log_table_imp<b>::d128_coeffs;

#endif

} //namespace log_detail

using log_table = log_detail::log_table_imp<true>;

template <BOOST_DECIMAL_DECIMAL_FLOATING_TYPE T>
constexpr auto log_series_expansion(T z2) noexcept;

template <>
constexpr auto log_series_expansion<decimal32>(decimal32 z2) noexcept
{
return taylor_series_result(z2, log_table::d32_coeffs);
}

template <>
constexpr auto log_series_expansion<decimal64>(decimal64 z2) noexcept
{
return taylor_series_result(z2, log_table::d64_coeffs);
}

template <>
constexpr auto log_series_expansion<decimal128>(decimal128 z2) noexcept
{
return taylor_series_result(z2, log_table::d128_coeffs);
}

} //namespace detail
} //namespace decimal
} //namespace boost

#endif //BOOST_DECIMAL_DETAIL_CMATH_IMPL_LOG_IMPL_HPP
2 changes: 1 addition & 1 deletion include/boost/decimal/detail/cmath/impl/sinh_impl.hpp
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Expand Up @@ -99,7 +99,7 @@ constexpr typename sinh_table_imp<b>::d128_coeffs_t sinh_table_imp<b>::d128_coef
using sinh_table = sinh_detail::sinh_table_imp<true>;

template <BOOST_DECIMAL_DECIMAL_FLOATING_TYPE T>
constexpr auto sinh_series_expansion(T z) noexcept;
constexpr auto sinh_series_expansion(T z2) noexcept;

template <>
constexpr auto sinh_series_expansion<decimal32>(decimal32 z2) noexcept
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2 changes: 1 addition & 1 deletion include/boost/decimal/detail/cmath/impl/tanh_impl.hpp
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Expand Up @@ -107,7 +107,7 @@ constexpr typename tanh_table_imp<b>::d128_coeffs_t tanh_table_imp<b>::d128_coef
using tanh_table = tanh_detail::tanh_table_imp<true>;

template <BOOST_DECIMAL_DECIMAL_FLOATING_TYPE T>
constexpr auto tanh_series_expansion(T z) noexcept;
constexpr auto tanh_series_expansion(T z2) noexcept;

template <>
constexpr auto tanh_series_expansion<decimal32>(decimal32 z2) noexcept
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