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More double_fp syntax improvements

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This commit is contained in:
ckormanyos
2025-09-22 16:05:07 +02:00
parent f40742cc3c
commit 6ffeac8e45
3 changed files with 121 additions and 106 deletions
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17
include/boost/multiprecision/cpp_df_qf/cpp_df_qf_detail_ccmath_log.hpp
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@@ -125,6 +125,8 @@ constexpr auto log_impl(Real x) noexcept -> Real
{
int n2 { };
// Scale the argument down.
Real x2 { ::boost::multiprecision::backends::cpp_df_qf_detail::ccmath::detail::frexp_impl(x, &n2) };
if (x2 > static_cast<Real>(0.875L))
@@ -134,18 +136,17 @@ constexpr auto log_impl(Real x) noexcept -> Real
++n2;
}
Real s { log_impl_pade(x2) };
// Estimate the logarithm of the argument to roughly half
// the precision of Real.
const Real s { log_impl_pade(x2) };
// Compute the exponent function to the full precision of Real.
const Real E { exp_impl(s) };
// Do one single step of Newton-Raphson iteration.
s = s + ((x2 - E) / E);
// Perform one single step of Newton-Raphson iteration
// and scale the result back up.
Real xn2 { static_cast<Real>(n2) * constant_ln_two<Real>() };
s += xn2;
return s;
return (s + ((x2 - E) / E)) + Real { static_cast<Real>(n2) * constant_ln_two<Real>() };
}
// LCOV_EXCL_STOP

208
include/boost/multiprecision/cpp_double_fp.hpp
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@@ -382,8 +382,6 @@ class cpp_double_fp_backend
constexpr auto hash() const -> ::std::size_t
{
std::size_t result { UINT8_C(0) };
#if defined(BOOST_MP_CPP_DOUBLE_FP_HAS_FLOAT128)
using local_float_type = typename std::conditional<::std::is_same<float_type, ::boost::float128_type>::value,
long double,
@@ -392,8 +390,15 @@ class cpp_double_fp_backend
using local_float_type = float_type;
#endif
boost::multiprecision::detail::hash_combine(result, static_cast<local_float_type>(data.first));
boost::multiprecision::detail::hash_combine(result, static_cast<local_float_type>(data.second));
std::size_t result { UINT8_C(0) };
int n_first { };
int n_second { };
boost::multiprecision::detail::hash_combine(result, static_cast<local_float_type>(cpp_df_qf_detail::ccmath::frexp(data.first, &n_first)));
boost::multiprecision::detail::hash_combine(result, static_cast<local_float_type>(cpp_df_qf_detail::ccmath::frexp(data.second, &n_second)));
boost::multiprecision::detail::hash_combine(result, n_first);
boost::multiprecision::detail::hash_combine(result, n_second);
return result;
}
@@ -408,8 +413,8 @@ class cpp_double_fp_backend
{
return
(
(data.second == float_type { 0.0F })
&& (data.first == float_type { 1.0F })
(data.second == float_type { 0.0F })
&& (data.first == float_type { 1.0F })
);
}
@@ -425,13 +430,9 @@ class cpp_double_fp_backend
}
else
{
data.first = -data.first;
if (!iszero_unchecked())
{
data.second = -data.second;
data = arithmetic::normalize(data.first, data.second);
data = arithmetic::normalize(-data.first, -data.second);
}
}
}
@@ -725,23 +726,17 @@ class cpp_double_fp_backend
float_type u { cpp_df_qf_detail::split_maker<float_type>::value * v.data.first };
float_type hv { };
if (cpp_df_qf_detail::ccmath::isinf(u))
{
// Handle overflow by scaling down (and then back up) with the split.
hv =
cpp_df_qf_detail::ccmath::ldexp
(
v.data.first - float_type { v.data.first - cpp_df_qf_detail::ccmath::ldexp(v.data.first, -cpp_df_qf_detail::split_maker<float_type>::n_shl) },
cpp_df_qf_detail::split_maker<float_type>::n_shl
);
}
else
{
hv = u - float_type { u - v.data.first };
}
const float_type hv =
(
cpp_df_qf_detail::ccmath::isinf(u)
? cpp_df_qf_detail::ccmath::ldexp
(
// Handle overflow by scaling down (and then back up) with the split.
v.data.first - float_type { v.data.first - cpp_df_qf_detail::ccmath::ldexp(v.data.first, -cpp_df_qf_detail::split_maker<float_type>::n_shl) },
cpp_df_qf_detail::split_maker<float_type>::n_shl
)
: u - float_type { u - v.data.first }
);
const float_type U { C * v.data.first };
@@ -1016,7 +1011,18 @@ class cpp_double_fp_backend
);
}
private:
constexpr auto add_unchecked_limb(const float_type v_first) -> void
{
const float_type thi { data.second };
data = arithmetic::two_sum(data.first, v_first);
data = arithmetic::two_hilo_sum(data.first, data.second + thi);
data = arithmetic::two_hilo_sum(data.first, data.second);
}
private:
rep_type data;
using cpp_bin_float_read_write_backend_type = boost::multiprecision::backends::cpp_bin_float<static_cast<unsigned>(my_digits), digit_base_2, void, int, cpp_df_qf_detail::ccmath::numeric_limits<float_type>::min_exponent, cpp_df_qf_detail::ccmath::numeric_limits<float_type>::max_exponent>;
@@ -1049,17 +1055,6 @@ class cpp_double_fp_backend
data = arithmetic::two_hilo_sum(data.first, thi_tlo.second + data.second);
}
constexpr auto add_unchecked_limb(const float_type v_first) -> void
{
const float_type thi { data.second };
data = arithmetic::two_sum(data.first, v_first);
data = arithmetic::two_hilo_sum(data.first, data.second + thi);
data = arithmetic::two_hilo_sum(data.first, data.second);
}
constexpr auto mul_unchecked(const cpp_double_fp_backend& v) -> void
{
// The multiplication algorithm has been taken from Victor Shoup,
@@ -1219,20 +1214,17 @@ constexpr auto cpp_double_fp_backend<FloatingPointType>::rd_string(const char* p
bool is_definitely_inf { ((fpc == FP_INFINITE) || cpp_df_qf_detail::ccmath::isinf(flt_inf_check_first)) };
if (!is_definitely_inf)
if ((!is_definitely_inf) && (flt_inf_check_first > my_value_max().my_first()))
{
if (flt_inf_check_first > my_value_max().my_first())
{
cpp_bin_float_read_write_backend_type f_bin_inf_check(f_bin);
cpp_bin_float_read_write_backend_type f_bin_inf_check(f_bin);
eval_subtract(f_bin_inf_check, cpp_bin_float_read_write_backend_type(flt_inf_check_first));
eval_subtract(f_bin_inf_check, cpp_bin_float_read_write_backend_type(flt_inf_check_first));
float_type flt_inf_check_second { };
float_type flt_inf_check_second { };
eval_convert_to(&flt_inf_check_second, f_bin_inf_check);
eval_convert_to(&flt_inf_check_second, f_bin_inf_check);
is_definitely_inf = eval_gt(local_double_fp_type(flt_inf_check_first, flt_inf_check_second), my_value_max());
}
is_definitely_inf = eval_gt(local_double_fp_type(flt_inf_check_first, flt_inf_check_second), my_value_max());
};
if (is_definitely_inf)
@@ -1252,12 +1244,15 @@ constexpr auto cpp_double_fp_backend<FloatingPointType>::rd_string(const char* p
data.first = float_type { 0.0F };
data.second = float_type { 0.0F };
// Handle small input values. Scale (and re-scale them below) if possible.
constexpr int pow2_scaling_for_small_input { cpp_df_qf_detail::ccmath::numeric_limits<float_type>::digits };
const auto has_pow2_scaling_for_small_input =
(
expval_from_f_bin < static_cast<int>(local_double_fp_type::my_min_exponent + pow2_scaling_for_small_input)
);
const bool
has_pow2_scaling_for_small_input
{
(expval_from_f_bin < static_cast<int>(local_double_fp_type::my_min_exponent + pow2_scaling_for_small_input))
};
if (has_pow2_scaling_for_small_input)
{
@@ -1755,10 +1750,14 @@ constexpr auto eval_exp(cpp_double_fp_backend<FloatingPointType>& result, const
}
else if (xx.is_one())
{
result =
((!b_neg)
? cpp_df_qf_detail::constant_df_exp1<local_float_type>()
: double_float_type(1U) / cpp_df_qf_detail::constant_df_exp1<local_float_type>());
if(!b_neg)
{
result = cpp_df_qf_detail::constant_df_exp1<local_float_type>();
}
else
{
eval_divide(result, one, cpp_df_qf_detail::constant_df_exp1<local_float_type>());
}
}
else
{
@@ -1766,15 +1765,15 @@ constexpr auto eval_exp(cpp_double_fp_backend<FloatingPointType>& result, const
double_float_type nf { };
eval_floor(nf, xx / cpp_df_qf_detail::constant_df_ln_two<local_float_type>());
// Prepare the scaled variables.
const auto b_scale = (xx.order02() > -1);
const bool b_scale { (xx.order02() > -1) };
double_float_type r { };
if (b_scale)
{
eval_floor(nf, xx / cpp_df_qf_detail::constant_df_ln_two<local_float_type>());
eval_ldexp(r, xx - (nf * cpp_df_qf_detail::constant_df_ln_two<local_float_type>()), -2);
}
else
@@ -1801,10 +1800,11 @@ constexpr auto eval_exp(cpp_double_fp_backend<FloatingPointType>& result, const
const double_float_type r2 { r * r };
// Use the small-argument Pade approximation having coefficients shown above.
const double_float_type top = (n84 * r * (n7920 + (n240 + r2) * r2));
result = (n84 * r * (n7920 + (n240 + r2) * r2));
const double_float_type bot = (n665280 + r * (-n332640 + r * (n75600 + r * (-n10080 + r * (n840 + (-n42 + r) * r)))));
result = one + (top / bot);
eval_divide(result, bot);
result.add_unchecked_limb(local_float_type { 1.0F });
// Rescale the result.
if (b_scale)
@@ -1820,13 +1820,13 @@ constexpr auto eval_exp(cpp_double_fp_backend<FloatingPointType>& result, const
if (n > 0)
{
eval_ldexp(result, double_float_type(result), n);
eval_ldexp(result, result, n);
}
}
if (b_neg)
{
result = one / result;
eval_divide(result, one, result);
}
}
}
@@ -1877,10 +1877,14 @@ constexpr auto eval_exp(cpp_double_fp_backend<FloatingPointType>& result, const
}
else if (xx.is_one())
{
result =
((!b_neg)
? cpp_df_qf_detail::constant_df_exp1<local_float_type>()
: double_float_type(1U) / cpp_df_qf_detail::constant_df_exp1<local_float_type>());
if(!b_neg)
{
result = cpp_df_qf_detail::constant_df_exp1<local_float_type>();
}
else
{
eval_divide(result, one, cpp_df_qf_detail::constant_df_exp1<local_float_type>());
}
}
else
{
@@ -1888,15 +1892,15 @@ constexpr auto eval_exp(cpp_double_fp_backend<FloatingPointType>& result, const
double_float_type nf { };
eval_floor(nf, xx / cpp_df_qf_detail::constant_df_ln_two<local_float_type>());
// Prepare the scaled variables.
const auto b_scale = (xx.order02() > -4);
const bool b_scale { (xx.order02() > -4) };
double_float_type r { };
if (b_scale)
{
eval_floor(nf, xx / cpp_df_qf_detail::constant_df_ln_two<local_float_type>());
eval_ldexp(r, xx - (nf * cpp_df_qf_detail::constant_df_ln_two<local_float_type>()), -4);
}
else
@@ -1923,10 +1927,11 @@ constexpr auto eval_exp(cpp_double_fp_backend<FloatingPointType>& result, const
const double_float_type r2 { r * r };
const double_float_type top = (n144 * r) * (n3603600 + r2 * (n120120 + r2 * (n770 + r2)));
result = (n144 * r) * (n3603600 + r2 * (n120120 + r2 * (n770 + r2)));
const double_float_type bot = (n518918400 + r * (-n259459200 + r * (n60540480 + r * (-n8648640 + r * (n831600 + r * (-n55440 + r * (n2520 + r * (-n72 + r))))))));
result = one + (top / bot);
eval_divide(result, bot);
result.add_unchecked_limb(local_float_type { 1.0F });
// Rescale the result.
if (b_scale)
@@ -1944,13 +1949,13 @@ constexpr auto eval_exp(cpp_double_fp_backend<FloatingPointType>& result, const
if (n > 0)
{
eval_ldexp(result, double_float_type(result), n);
eval_ldexp(result, result, n);
}
}
if (b_neg)
{
result = one / result;
eval_divide(result, one, result);
}
}
}
@@ -2001,10 +2006,14 @@ constexpr auto eval_exp(cpp_double_fp_backend<FloatingPointType>& result, const
}
else if (xx.is_one())
{
result =
((!b_neg)
? cpp_df_qf_detail::constant_df_exp1<local_float_type>()
: double_float_type(1U) / cpp_df_qf_detail::constant_df_exp1<local_float_type>());
if(!b_neg)
{
result = cpp_df_qf_detail::constant_df_exp1<local_float_type>();
}
else
{
eval_divide(result, one, cpp_df_qf_detail::constant_df_exp1<local_float_type>());
}
}
else
{
@@ -2012,15 +2021,15 @@ constexpr auto eval_exp(cpp_double_fp_backend<FloatingPointType>& result, const
double_float_type nf { };
eval_floor(nf, xx / cpp_df_qf_detail::constant_df_ln_two<local_float_type>());
// Prepare the scaled variables.
const auto b_scale = (xx.order02() > -4);
const bool b_scale { (xx.order02() > -4) };
double_float_type xh { };
if (b_scale)
{
eval_floor(nf, xx / cpp_df_qf_detail::constant_df_ln_two<local_float_type>());
eval_ldexp(xh, xx - (nf * cpp_df_qf_detail::constant_df_ln_two<local_float_type>()), -4);
}
else
@@ -2030,29 +2039,30 @@ constexpr auto eval_exp(cpp_double_fp_backend<FloatingPointType>& result, const
double_float_type x_pow_n_div_n_fact(xh);
result = one + x_pow_n_div_n_fact;
result = x_pow_n_div_n_fact;
result.add_unchecked_limb(local_float_type { 1.0F });
double_float_type dummy { };
// Series expansion of hypergeometric_0f0(; ; x).
// Use the Taylor series expansion of hypergeometric_0f0(; ; x).
// For this high(er) digit count, a scaled argument with subsequent
// Taylor series expansion is actually more precise than Pade approximation.
for (unsigned n { 2U }; n < 64U; ++n)
for (unsigned n { UINT8_C(2) }; n < unsigned { UINT8_C(64) }; ++n)
{
x_pow_n_div_n_fact *= xh;
eval_multiply(x_pow_n_div_n_fact, xh);
x_pow_n_div_n_fact /= typename double_float_type::float_type(n);
eval_divide(x_pow_n_div_n_fact, double_float_type(n));
int n_tol { };
eval_frexp(dummy, x_pow_n_div_n_fact, &n_tol);
if ((n > 4U) && (n_tol < -(double_float_type::my_digits - 2)))
if ((n > 4U) && (n_tol < -(double_float_type::my_digits - 1)))
{
break;
}
result += x_pow_n_div_n_fact;
eval_add(result, x_pow_n_div_n_fact);
}
// Rescale the result.
@@ -2071,13 +2081,13 @@ constexpr auto eval_exp(cpp_double_fp_backend<FloatingPointType>& result, const
if (n > 0)
{
eval_ldexp(result, double_float_type(result), n);
eval_ldexp(result, result, n);
}
}
if (b_neg)
{
result = one / result;
eval_divide(result, one, result);
}
}
}
@@ -2129,19 +2139,23 @@ constexpr auto eval_log(cpp_double_fp_backend<FloatingPointType>& result, const
eval_frexp(x2, x, &n2);
// Get initial estimate using the self-written, detail math function log.
const double_float_type s(cpp_df_qf_detail::ccmath::log(x2.my_first()));
using local_float_type = typename double_float_type::float_type;
const local_float_type s { cpp_df_qf_detail::ccmath::log(x2.my_first()) };
double_float_type E { };
eval_exp(E, s);
eval_exp(E, double_float_type(s));
// Do one single step of Newton-Raphson iteration.
result = s + ((x2 - E) / E);
// Perform one single step of Newton-Raphson iteration.
// result = s + (x2 - E) / E;
eval_subtract(result, x2, E);
eval_divide(result, E);
result.add_unchecked_limb(s);
double_float_type xn2 { n2 };
using local_float_type = typename double_float_type::float_type;
eval_multiply(xn2, cpp_df_qf_detail::constant_df_ln_two<local_float_type>());
eval_add(result, xn2);

2
performance/performance_test_df.cpp
View File

@@ -226,7 +226,7 @@ void local::test32()
static_assert(digits10_for_performance_test >= 32, "Error: Too few digits for performance comparison");
using cpp_bin_float_type =
boost::multiprecision::number<boost::multiprecision::backends::cpp_bin_float<digits10_for_performance_test>,
boost::multiprecision::number<boost::multiprecision::backends::cpp_bin_float<digits10_for_performance_test, boost::multiprecision::digit_base_10, void>,
boost::multiprecision::et_off>;
test<cpp_bin_float_type>("cpp_bin_float", digits10_for_performance_test);