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Logs #376

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merged 7 commits into from
Jan 15, 2024
Merged

Logs #376

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4434a05
Add trivial log2 impl
mborland Jan 12, 2024
ac57ba7
Add log2 and log10 test sets
mborland Jan 12, 2024
9de0015
Reduce number of trials in cmath
mborland Jan 12, 2024
978c035
Add coefficients for decimal128 log calculations
mborland Jan 12, 2024
88e5aec
Add decimal128 tests
mborland Jan 12, 2024
5466ebf
Fix ADL error
mborland Jan 12, 2024
67d6b40
Fix for MSVC variable shadowing warning
mborland Jan 12, 2024
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1 change: 1 addition & 0 deletions include/boost/decimal/cmath.hpp
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Expand Up @@ -37,6 +37,7 @@
#include <boost/decimal/detail/cmath/log.hpp>
#include <boost/decimal/detail/cmath/log1p.hpp>
#include <boost/decimal/detail/cmath/log10.hpp>
#include <boost/decimal/detail/cmath/log2.hpp>
#include <boost/decimal/detail/cmath/modf.hpp>
#include <boost/decimal/detail/cmath/nearbyint.hpp>
#include <boost/decimal/detail/cmath/next.hpp>
Expand Down
97 changes: 58 additions & 39 deletions include/boost/decimal/detail/cmath/log.hpp
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Expand Up @@ -12,11 +12,67 @@
#include <boost/decimal/fwd.hpp>
#include <boost/decimal/detail/type_traits.hpp>
#include <boost/decimal/detail/concepts.hpp>
#include <boost/decimal/detail/emulated128.hpp>
#include <boost/decimal/numbers.hpp>

namespace boost {
namespace decimal {

namespace detail {

#if (defined(__clang__) && (__clang__ < 6))
# pragma clang diagnostic push
# pragma clang diagnostic ignored "-Wmissing-braces"
#endif

template <typename T>
static constexpr std::array<T, 11> small_coefficient_table {
// (1,) 12, 80, 448, 2304, 11264, 53248, 245760, 1114112, 4980736, 22020096, 96468992, ...
// See also Sloane's A058962 at: https://oeis.org/A058962

// See also
// Series[Log[(1 + (z/2))/(1 - (z/2))], {z, 0, 23}]
// Or at Wolfram Alpha: https://www.wolframalpha.com/input?i=Series%5BLog%5B%281+%2B+%28z%2F2%29%29%2F%281+-+%28z%2F2%29%29%5D%2C+%7Bz%2C+0%2C+21%7D%5D

// TODO(ckormanyos)
// Consider also Pade expansion of Log[1 + z/2].
// PadeApproximant[Log[1 + z/2], {z, 6, 6}]
// FullSimplify[%].

T { UINT64_C(833333333333333333), -18 - 1 }, // * z^3
T { UINT64_C(125000000000000000), -18 - 1 }, // * z^5
T { UINT64_C(223214285714285714), -18 - 2 }, // * z^7
T { UINT64_C(434027777777777778), -18 - 3 }, // * z^9
T { UINT64_C(887784090909090909), -18 - 4 }, // * z^11
T { UINT64_C(187800480769230769), -18 - 4 }, // * z^13
T { UINT64_C(406901041666666667), -18 - 5 }, // * z^15
T { UINT64_C(897575827205882353), -18 - 6 }, // * z^17
T { UINT64_C(200773540296052632), -18 - 6 }, // * z^19
T { UINT64_C(454130626860119048), -18 - 7 }, // * z^21
T { UINT64_C(103660251783288043), -18 - 7 } // * z^23
};

template <typename T>
static constexpr std::array<T, 11> large_coefficient_table {
T{uint128{UINT64_C(451750905202293), UINT64_C(9484758194528277842)}, -35}, // z^3
T{uint128{UINT64_C(67762635780344), UINT64_C(500376525493764096)}, -35}, // z^5
T{uint128{UINT64_C(121004706750614), UINT64_C(6164027816584450626)}, -36}, // z^7
T{uint128{UINT64_C(235286929792861), UINT64_C(3787056721709964394)}, -37}, // z^9
T{uint128{UINT64_C(481268720030852), UINT64_C(8584740752302634068)}, -38}, // z^11
T{uint128{UINT64_C(101806844621911), UINT64_C(1816002851448634124)}, -38}, // z^13
T{uint128{UINT64_C(220581496680807), UINT64_C(7009130190423632548)}, -40}, // z^15
T{uint128{UINT64_C(486576830913545), UINT64_C(12748560115094843630)}, -41}, // z^17
T{uint128{UINT64_C(108839554283293), UINT64_C(2123490654414259032)}, -41}, // z^19
T{uint128{UINT64_C(246184706116972), UINT64_C(9634423737622849438)}, -42}, // z^21
T{uint128{UINT64_C(56194335091917), UINT64_C(11823550152479764302)}, -42} // z^23
};

#if (defined(__clang__) && (__clang__ < 6))
# pragma clang diagnostic pop
#endif

} //namespace detail

template <BOOST_DECIMAL_DECIMAL_FLOATING_TYPE T>
constexpr auto log(T x) noexcept -> std::enable_if_t<detail::is_decimal_floating_point_v<T>, T> // NOLINT(misc-no-recursion)
{
Expand Down Expand Up @@ -76,49 +132,12 @@ constexpr auto log(T x) noexcept -> std::enable_if_t<detail::is_decimal_floating
--exp2val;
}

using coefficient_array_type = std::array<T, static_cast<std::size_t>(UINT8_C(11))>;

#if (defined(__clang__) && (__clang__ < 6))
# pragma clang diagnostic push
# pragma clang diagnostic ignored "-Wmissing-braces"
#endif

constexpr auto coefficient_table =
coefficient_array_type
{
// (1,) 12, 80, 448, 2304, 11264, 53248, 245760, 1114112, 4980736, 22020096, 96468992, ...
// See also Sloane's A058962 at: https://oeis.org/A058962

// See also
// Series[Log[(1 + (z/2))/(1 - (z/2))], {z, 0, 23}]
// Or at Wolfram Alpha: https://www.wolframalpha.com/input?i=Series%5BLog%5B%281+%2B+%28z%2F2%29%29%2F%281+-+%28z%2F2%29%29%5D%2C+%7Bz%2C+0%2C+21%7D%5D

// TODO(ckormanyos)
// Consider also Pade expansion of Log[1 + z/2].
// PadeApproximant[Log[1 + z/2], {z, 6, 6}]
// FullSimplify[%].

T { UINT64_C(833333333333333333), -18 - 1 }, // * z^3
T { UINT64_C(125000000000000000), -18 - 1 }, // * z^5
T { UINT64_C(223214285714285714), -18 - 2 }, // * z^7
T { UINT64_C(434027777777777778), -18 - 3 }, // * z^9
T { UINT64_C(887784090909090909), -18 - 4 }, // * z^11
T { UINT64_C(187800480769230769), -18 - 4 }, // * z^13
T { UINT64_C(406901041666666667), -18 - 5 }, // * z^15
T { UINT64_C(897575827205882353), -18 - 6 }, // * z^17
T { UINT64_C(200773540296052632), -18 - 6 }, // * z^19
T { UINT64_C(454130626860119048), -18 - 7 }, // * z^21
T { UINT64_C(103660251783288043), -18 - 7 } // * z^23
};

#if (defined(__clang__) && (__clang__ < 6))
# pragma clang diagnostic pop
#endif

const auto s = (g - one) / (g + one);
const auto z = s + s;
const auto zsq = z * z;

auto& coefficient_table = std::is_same<T, decimal128>::value ? detail::large_coefficient_table<T> : detail::small_coefficient_table<T>;

auto rit = coefficient_table.crbegin() + static_cast<std::size_t>((sizeof(T) == 4U) ? 5U : 0U);

result = *rit;
Expand Down
30 changes: 30 additions & 0 deletions include/boost/decimal/detail/cmath/log2.hpp
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@@ -0,0 +1,30 @@
// Copyright 2024 Matt Borland
// Copyright 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_LOG2_HPP
#define BOOST_DECIMAL_DETAIL_CMATH_LOG2_HPP

#include <cmath>
#include <type_traits>

#include <boost/decimal/fwd.hpp> // NOLINT(llvm-include-order)
#include <boost/decimal/detail/type_traits.hpp>
#include <boost/decimal/detail/concepts.hpp>
#include <boost/decimal/numbers.hpp>
#include <boost/decimal/detail/cmath/log.hpp>

namespace boost {
namespace decimal {

template <BOOST_DECIMAL_DECIMAL_FLOATING_TYPE T>
constexpr auto log2(T x) noexcept -> std::enable_if_t<detail::is_decimal_floating_point_v<T>, T>
{
return log(x) / numbers::ln2_v<T>;
}

} //namespace decimal
} //namespace boost

#endif //BOOST_DECIMAL_DETAIL_CMATH_LOG2_HPP
83 changes: 80 additions & 3 deletions test/test_cmath.cpp
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Expand Up @@ -13,10 +13,10 @@
#include <cmath>


#if !defined(BOOST_DECIMAL_REDUCE_TEST_DEPTH)
static constexpr auto N = static_cast<std::size_t>(512U); // Number of trials
#if !defined(BOOST_DECIMAL_REDUCE_TEST_DEPTH) && !defined(_WIN32)
static constexpr auto N = static_cast<std::size_t>(128U); // Number of trials
#else
static constexpr auto N = static_cast<std::size_t>(512U >> 4U); // Number of trials
static constexpr auto N = static_cast<std::size_t>(128U >> 4U); // Number of trials
#endif

static std::mt19937_64 rng(42);
Expand Down Expand Up @@ -1556,6 +1556,72 @@ void test_nan()
}
#endif

template <typename Dec>
void test_log2()
{
std::uniform_real_distribution<float> dist(-0.5F, 0.5F);

constexpr auto max_iter {std::is_same<Dec, decimal128>::value ? N / 4 : N};
for (std::size_t n {}; n < max_iter; ++n)
{
const auto val1 {dist(rng)};
Dec d1 {val1};

auto ret_val {std::log2(val1)};
auto ret_dec {static_cast<float>(log2(d1))};

if (!std::isfinite(ret_val) && !std::isfinite(ret_dec))
{
continue;
}

const auto distance {std::fabs(boost::math::float_distance(ret_val, ret_dec))};
if (!BOOST_TEST(distance < 100))
{
// LCOV_EXCL_START
std::cerr << "Val 1: " << val1
<< "\nDec 1: " << d1
<< "\nRet val: " << ret_val
<< "\nRet dec: " << ret_dec
<< "\nDist: " << distance << std::endl;
// LCOV_EXCL_STOP
}
}
}

template <typename Dec>
void test_log10()
{
std::uniform_real_distribution<float> dist(-0.5F, 0.5F);

constexpr auto max_iter {std::is_same<Dec, decimal128>::value ? N / 4 : N};
for (std::size_t n {}; n < max_iter; ++n)
{
const auto val1 {dist(rng)};
Dec d1 {val1};

auto ret_val {std::log10(val1)};
auto ret_dec {static_cast<float>(log10(d1))};

if (!std::isfinite(ret_val) && !std::isfinite(ret_dec))
{
continue;
}

const auto distance {std::fabs(boost::math::float_distance(ret_val, ret_dec))};
if (!BOOST_TEST(distance < 100))
{
// LCOV_EXCL_START
std::cerr << "Val 1: " << val1
<< "\nDec 1: " << d1
<< "\nRet val: " << ret_val
<< "\nRet dec: " << ret_dec
<< "\nDist: " << distance << std::endl;
// LCOV_EXCL_STOP
}
}
}

int main()
{
test_fmax<decimal32>();
Expand Down Expand Up @@ -1686,5 +1752,16 @@ int main()
test_nan<decimal128>();
#endif

test_log2<decimal32>();
test_log2<decimal64>();

test_log10<decimal32>();
test_log10<decimal64>();

#if !defined(BOOST_DECIMAL_REDUCE_TEST_DEPTH)
test_log2<decimal128>();
test_log10<decimal128>();
#endif

return boost::report_errors();
}