mirror of
https://github.com/RGBCube/serenity
synced 2025-10-31 08:52:44 +00:00
1416 lines
29 KiB
C++
1416 lines
29 KiB
C++
/*
|
|
* Copyright (c) 2018-2020, Andreas Kling <kling@serenityos.org>
|
|
* Copyright (c) 2021, Mițca Dumitru <dumitru0mitca@gmail.com>
|
|
*
|
|
* SPDX-License-Identifier: BSD-2-Clause
|
|
*/
|
|
|
|
#include <AK/ExtraMathConstants.h>
|
|
#include <AK/Platform.h>
|
|
#include <AK/StdLibExtras.h>
|
|
#include <LibC/assert.h>
|
|
#include <fenv.h>
|
|
#include <math.h>
|
|
#include <stdint.h>
|
|
#include <stdlib.h>
|
|
|
|
template<size_t>
|
|
constexpr double e_to_power();
|
|
template<>
|
|
constexpr double e_to_power<0>() { return 1; }
|
|
template<size_t exponent>
|
|
constexpr double e_to_power() { return M_E * e_to_power<exponent - 1>(); }
|
|
|
|
template<size_t>
|
|
constexpr size_t factorial();
|
|
template<>
|
|
constexpr size_t factorial<0>() { return 1; }
|
|
template<size_t value>
|
|
constexpr size_t factorial() { return value * factorial<value - 1>(); }
|
|
|
|
template<size_t>
|
|
constexpr size_t product_even();
|
|
template<>
|
|
constexpr size_t product_even<2>() { return 2; }
|
|
template<size_t value>
|
|
constexpr size_t product_even() { return value * product_even<value - 2>(); }
|
|
|
|
template<size_t>
|
|
constexpr size_t product_odd();
|
|
template<>
|
|
constexpr size_t product_odd<1>() { return 1; }
|
|
template<size_t value>
|
|
constexpr size_t product_odd() { return value * product_odd<value - 2>(); }
|
|
|
|
enum class RoundingMode {
|
|
ToZero = FE_TOWARDZERO,
|
|
Up = FE_UPWARD,
|
|
Down = FE_DOWNWARD,
|
|
ToEven = FE_TONEAREST
|
|
};
|
|
|
|
template<typename T>
|
|
union FloatExtractor;
|
|
|
|
#if ARCH(I386) || ARCH(X86_64)
|
|
// This assumes long double is 80 bits, which is true with GCC on Intel platforms
|
|
template<>
|
|
union FloatExtractor<long double> {
|
|
static const int mantissa_bits = 64;
|
|
static const unsigned long long mantissa_max = ~0u;
|
|
static const int exponent_bias = 16383;
|
|
static const int exponent_bits = 15;
|
|
static const unsigned exponent_max = 32767;
|
|
struct {
|
|
unsigned long long mantissa;
|
|
unsigned exponent : 15;
|
|
unsigned sign : 1;
|
|
};
|
|
long double d;
|
|
};
|
|
#endif
|
|
|
|
template<>
|
|
union FloatExtractor<double> {
|
|
static const int mantissa_bits = 52;
|
|
static const unsigned long long mantissa_max = (1ull << 52) - 1;
|
|
static const int exponent_bias = 1023;
|
|
static const int exponent_bits = 11;
|
|
static const unsigned exponent_max = 2047;
|
|
struct {
|
|
unsigned long long mantissa : 52;
|
|
unsigned exponent : 11;
|
|
unsigned sign : 1;
|
|
};
|
|
double d;
|
|
};
|
|
|
|
template<>
|
|
union FloatExtractor<float> {
|
|
static const int mantissa_bits = 23;
|
|
static const unsigned mantissa_max = (1 << 23) - 1;
|
|
static const int exponent_bias = 127;
|
|
static const int exponent_bits = 8;
|
|
static const unsigned exponent_max = 255;
|
|
struct {
|
|
unsigned long long mantissa : 23;
|
|
unsigned exponent : 8;
|
|
unsigned sign : 1;
|
|
};
|
|
float d;
|
|
};
|
|
|
|
// This is much branchier than it really needs to be
|
|
template<typename FloatType>
|
|
static FloatType internal_to_integer(FloatType x, RoundingMode rounding_mode)
|
|
{
|
|
if (!isfinite(x))
|
|
return x;
|
|
using Extractor = FloatExtractor<decltype(x)>;
|
|
Extractor extractor;
|
|
extractor.d = x;
|
|
auto unbiased_exponent = extractor.exponent - Extractor::exponent_bias;
|
|
bool round = false;
|
|
bool guard = false;
|
|
if (unbiased_exponent < 0) {
|
|
// it was easier to special case [0..1) as it saves us from
|
|
// handling subnormals, underflows, etc
|
|
if (unbiased_exponent == -1) {
|
|
round = true;
|
|
}
|
|
guard = extractor.mantissa != 0;
|
|
extractor.mantissa = 0;
|
|
extractor.exponent = 0;
|
|
} else {
|
|
if (unbiased_exponent >= Extractor::mantissa_bits)
|
|
return x;
|
|
auto dead_bitcount = Extractor::mantissa_bits - unbiased_exponent;
|
|
auto dead_mask = (1ull << dead_bitcount) - 1;
|
|
auto dead_bits = extractor.mantissa & dead_mask;
|
|
extractor.mantissa &= ~dead_mask;
|
|
|
|
auto guard_mask = dead_mask >> 1;
|
|
guard = (dead_bits & guard_mask) != 0;
|
|
round = (dead_bits & ~guard_mask) != 0;
|
|
}
|
|
bool should_round = false;
|
|
switch (rounding_mode) {
|
|
case RoundingMode::ToEven:
|
|
should_round = round;
|
|
break;
|
|
case RoundingMode::Up:
|
|
if (!extractor.sign)
|
|
should_round = guard || round;
|
|
break;
|
|
case RoundingMode::Down:
|
|
if (extractor.sign)
|
|
should_round = guard || round;
|
|
break;
|
|
case RoundingMode::ToZero:
|
|
break;
|
|
}
|
|
if (should_round) {
|
|
// We could do this ourselves, but this saves us from manually
|
|
// handling overflow.
|
|
if (extractor.sign)
|
|
extractor.d -= static_cast<FloatType>(1.0);
|
|
else
|
|
extractor.d += static_cast<FloatType>(1.0);
|
|
}
|
|
|
|
return extractor.d;
|
|
}
|
|
|
|
// This is much branchier than it really needs to be
|
|
template<typename FloatType>
|
|
static FloatType internal_nextafter(FloatType x, bool up)
|
|
{
|
|
if (!isfinite(x))
|
|
return x;
|
|
using Extractor = FloatExtractor<decltype(x)>;
|
|
Extractor extractor;
|
|
extractor.d = x;
|
|
if (x == 0) {
|
|
if (!extractor.sign) {
|
|
extractor.mantissa = 1;
|
|
extractor.sign = !up;
|
|
return extractor.d;
|
|
}
|
|
if (up) {
|
|
extractor.sign = false;
|
|
extractor.mantissa = 1;
|
|
return extractor.d;
|
|
}
|
|
extractor.mantissa = 1;
|
|
extractor.sign = up != extractor.sign;
|
|
return extractor.d;
|
|
}
|
|
if (up != extractor.sign) {
|
|
extractor.mantissa++;
|
|
if (!extractor.mantissa) {
|
|
// no need to normalize the mantissa as we just hit a power
|
|
// of two.
|
|
extractor.exponent++;
|
|
if (extractor.exponent == Extractor::exponent_max) {
|
|
extractor.exponent = Extractor::exponent_max - 1;
|
|
extractor.mantissa = Extractor::mantissa_max;
|
|
}
|
|
}
|
|
return extractor.d;
|
|
}
|
|
|
|
if (!extractor.mantissa) {
|
|
if (extractor.exponent) {
|
|
extractor.exponent--;
|
|
extractor.mantissa = Extractor::mantissa_max;
|
|
} else {
|
|
extractor.d = 0;
|
|
}
|
|
return extractor.d;
|
|
}
|
|
|
|
extractor.mantissa--;
|
|
if (extractor.mantissa != Extractor::mantissa_max)
|
|
return extractor.d;
|
|
if (extractor.exponent) {
|
|
extractor.exponent--;
|
|
// normalize
|
|
extractor.mantissa <<= 1;
|
|
} else {
|
|
if (extractor.sign) {
|
|
// Negative infinity
|
|
extractor.mantissa = 0;
|
|
extractor.exponent = Extractor::exponent_max;
|
|
}
|
|
}
|
|
return extractor.d;
|
|
}
|
|
|
|
template<typename FloatT>
|
|
static int internal_ilogb(FloatT x) NOEXCEPT
|
|
{
|
|
if (x == 0)
|
|
return FP_ILOGB0;
|
|
|
|
if (isnan(x))
|
|
return FP_ILOGNAN;
|
|
|
|
if (!isfinite(x))
|
|
return INT_MAX;
|
|
|
|
using Extractor = FloatExtractor<FloatT>;
|
|
|
|
Extractor extractor;
|
|
extractor.d = x;
|
|
|
|
return (int)extractor.exponent - Extractor::exponent_bias;
|
|
}
|
|
|
|
template<typename FloatT>
|
|
static FloatT internal_modf(FloatT x, FloatT* intpart) NOEXCEPT
|
|
{
|
|
FloatT integer_part = internal_to_integer(x, RoundingMode::ToZero);
|
|
*intpart = integer_part;
|
|
auto fraction = x - integer_part;
|
|
if (signbit(fraction) != signbit(x))
|
|
fraction = -fraction;
|
|
return fraction;
|
|
}
|
|
|
|
template<typename FloatT>
|
|
static FloatT internal_scalbn(FloatT x, int exponent) NOEXCEPT
|
|
{
|
|
if (x == 0 || !isfinite(x) || isnan(x) || exponent == 0)
|
|
return x;
|
|
|
|
using Extractor = FloatExtractor<FloatT>;
|
|
Extractor extractor;
|
|
extractor.d = x;
|
|
|
|
if (extractor.exponent != 0) {
|
|
extractor.exponent = clamp((int)extractor.exponent + exponent, 0, (int)Extractor::exponent_max);
|
|
return extractor.d;
|
|
}
|
|
|
|
unsigned leading_mantissa_zeroes = extractor.mantissa == 0 ? 32 : __builtin_clz(extractor.mantissa);
|
|
int shift = min((int)leading_mantissa_zeroes, exponent);
|
|
exponent = max(exponent - shift, 0);
|
|
|
|
extractor.exponent <<= shift;
|
|
extractor.exponent = exponent + 1;
|
|
|
|
return extractor.d;
|
|
}
|
|
|
|
template<typename FloatT>
|
|
static FloatT internal_copysign(FloatT x, FloatT y) NOEXCEPT
|
|
{
|
|
using Extractor = FloatExtractor<FloatT>;
|
|
Extractor ex, ey;
|
|
ex.d = x;
|
|
ey.d = y;
|
|
ex.sign = ey.sign;
|
|
return ex.d;
|
|
}
|
|
|
|
template<typename FloatT>
|
|
static FloatT internal_gamma(FloatT x) NOEXCEPT
|
|
{
|
|
if (isnan(x))
|
|
return (FloatT)NAN;
|
|
|
|
if (x == (FloatT)0.0)
|
|
return signbit(x) ? (FloatT)-INFINITY : (FloatT)INFINITY;
|
|
|
|
if (x < (FloatT)0 && (rintl(x) == x || isinf(x)))
|
|
return (FloatT)NAN;
|
|
|
|
if (isinf(x))
|
|
return (FloatT)INFINITY;
|
|
|
|
using Extractor = FloatExtractor<FloatT>;
|
|
// These constants were obtained through use of WolframAlpha
|
|
constexpr long long max_integer_whose_factorial_fits = (Extractor::mantissa_bits == FloatExtractor<long double>::mantissa_bits ? 20 : (Extractor::mantissa_bits == FloatExtractor<double>::mantissa_bits ? 18 : (Extractor::mantissa_bits == FloatExtractor<float>::mantissa_bits ? 10 : 0)));
|
|
static_assert(max_integer_whose_factorial_fits != 0, "internal_gamma needs to be aware of the integer factorial that fits in this floating point type.");
|
|
if (rintl(x) == (long double)x && x <= max_integer_whose_factorial_fits) {
|
|
long long result = 1;
|
|
for (long long cursor = 1; cursor <= min(max_integer_whose_factorial_fits, (long long)x); cursor++)
|
|
result *= cursor;
|
|
return (FloatT)result;
|
|
}
|
|
|
|
// Stirling approximation
|
|
return sqrtl(2.0 * M_PI / static_cast<long double>(x)) * powl(static_cast<long double>(x) / M_E, static_cast<long double>(x));
|
|
}
|
|
|
|
extern "C" {
|
|
|
|
float nanf(const char* s) NOEXCEPT
|
|
{
|
|
return __builtin_nanf(s);
|
|
}
|
|
|
|
double nan(const char* s) NOEXCEPT
|
|
{
|
|
return __builtin_nan(s);
|
|
}
|
|
|
|
long double nanl(const char* s) NOEXCEPT
|
|
{
|
|
return __builtin_nanl(s);
|
|
}
|
|
|
|
double trunc(double x) NOEXCEPT
|
|
{
|
|
return internal_to_integer(x, RoundingMode::ToZero);
|
|
}
|
|
|
|
float truncf(float x) NOEXCEPT
|
|
{
|
|
return internal_to_integer(x, RoundingMode::ToZero);
|
|
}
|
|
|
|
long double truncl(long double x) NOEXCEPT
|
|
{
|
|
return internal_to_integer(x, RoundingMode::ToZero);
|
|
}
|
|
|
|
long double cosl(long double angle) NOEXCEPT
|
|
{
|
|
return sinl(angle + M_PI_2);
|
|
}
|
|
|
|
double cos(double angle) NOEXCEPT
|
|
{
|
|
return sin(angle + M_PI_2);
|
|
}
|
|
|
|
float cosf(float angle) NOEXCEPT
|
|
{
|
|
return sinf(angle + static_cast<float>(M_PI_2));
|
|
}
|
|
|
|
long double sinl(long double angle) NOEXCEPT
|
|
{
|
|
long double ret = 0.0;
|
|
__asm__(
|
|
"fsin"
|
|
: "=t"(ret)
|
|
: "0"(angle));
|
|
|
|
return ret;
|
|
}
|
|
|
|
// This can also be done with a taylor expansion, but for
|
|
// now this works pretty well (and doesn't mess anything up
|
|
// in quake in particular, which is very Floating-Point precision
|
|
// heavy)
|
|
double sin(double angle) NOEXCEPT
|
|
{
|
|
double ret = 0.0;
|
|
__asm__(
|
|
"fsin"
|
|
: "=t"(ret)
|
|
: "0"(angle));
|
|
|
|
return ret;
|
|
}
|
|
|
|
float sinf(float angle) NOEXCEPT
|
|
{
|
|
float ret = 0.0f;
|
|
__asm__(
|
|
"fsin"
|
|
: "=t"(ret)
|
|
: "0"(angle));
|
|
return ret;
|
|
}
|
|
|
|
long double powl(long double x, long double y) NOEXCEPT
|
|
{
|
|
// FIXME: Please fix me. I am naive.
|
|
if (isnan(y))
|
|
return y;
|
|
if (y == 0)
|
|
return 1;
|
|
if (x == 0)
|
|
return 0;
|
|
if (y == 1)
|
|
return x;
|
|
int y_as_int = (int)y;
|
|
if (y == (long double)y_as_int) {
|
|
long double result = x;
|
|
for (int i = 0; i < fabsl(y) - 1; ++i)
|
|
result *= x;
|
|
if (y < 0)
|
|
result = 1.0l / result;
|
|
return result;
|
|
}
|
|
return exp2l(y * log2l(x));
|
|
}
|
|
|
|
double pow(double x, double y) NOEXCEPT
|
|
{
|
|
return (double)powl(x, y);
|
|
}
|
|
|
|
float powf(float x, float y) NOEXCEPT
|
|
{
|
|
return (float)powl(x, y);
|
|
}
|
|
|
|
// On systems where FLT_RADIX == 2, ldexp is equivalent to scalbn
|
|
long double ldexpl(long double x, int exp) NOEXCEPT
|
|
{
|
|
return internal_scalbn(x, exp);
|
|
}
|
|
|
|
double ldexp(double x, int exp) NOEXCEPT
|
|
{
|
|
return internal_scalbn(x, exp);
|
|
}
|
|
|
|
float ldexpf(float x, int exp) NOEXCEPT
|
|
{
|
|
return internal_scalbn(x, exp);
|
|
}
|
|
|
|
long double tanhl(long double x) NOEXCEPT
|
|
{
|
|
if (x > 0) {
|
|
long double exponentiated = expl(2 * x);
|
|
return (exponentiated - 1) / (exponentiated + 1);
|
|
}
|
|
long double plusX = expl(x);
|
|
long double minusX = 1 / plusX;
|
|
return (plusX - minusX) / (plusX + minusX);
|
|
}
|
|
|
|
double tanh(double x) NOEXCEPT
|
|
{
|
|
return (double)tanhl(x);
|
|
}
|
|
|
|
float tanhf(float x) NOEXCEPT
|
|
{
|
|
return (float)tanhl(x);
|
|
}
|
|
|
|
[[maybe_unused]] static long double ampsin(long double angle) NOEXCEPT
|
|
{
|
|
long double looped_angle = fmodl(M_PI + angle, M_TAU) - M_PI;
|
|
long double looped_angle_squared = looped_angle * looped_angle;
|
|
|
|
long double quadratic_term;
|
|
if (looped_angle > 0) {
|
|
quadratic_term = -looped_angle_squared;
|
|
} else {
|
|
quadratic_term = looped_angle_squared;
|
|
}
|
|
|
|
long double linear_term = M_PI * looped_angle;
|
|
|
|
return quadratic_term + linear_term;
|
|
}
|
|
|
|
long double tanl(long double angle) NOEXCEPT
|
|
{
|
|
long double ret = 0.0, one;
|
|
__asm__(
|
|
"fptan"
|
|
: "=t"(one), "=u"(ret)
|
|
: "0"(angle));
|
|
|
|
return ret;
|
|
}
|
|
|
|
double tan(double angle) NOEXCEPT
|
|
{
|
|
return (double)tanl(angle);
|
|
}
|
|
|
|
float tanf(float angle) NOEXCEPT
|
|
{
|
|
return (float)tanl(angle);
|
|
}
|
|
|
|
long double sqrtl(long double x) NOEXCEPT
|
|
{
|
|
long double res;
|
|
asm("fsqrt"
|
|
: "=t"(res)
|
|
: "0"(x));
|
|
return res;
|
|
}
|
|
|
|
double sqrt(double x) NOEXCEPT
|
|
{
|
|
double res;
|
|
__asm__("fsqrt"
|
|
: "=t"(res)
|
|
: "0"(x));
|
|
return res;
|
|
}
|
|
|
|
float sqrtf(float x) NOEXCEPT
|
|
{
|
|
float res;
|
|
__asm__("fsqrt"
|
|
: "=t"(res)
|
|
: "0"(x));
|
|
return res;
|
|
}
|
|
|
|
long double sinhl(long double x) NOEXCEPT
|
|
{
|
|
long double exponentiated = expl(x);
|
|
if (x > 0)
|
|
return (exponentiated * exponentiated - 1) / 2 / exponentiated;
|
|
return (exponentiated - 1 / exponentiated) / 2;
|
|
}
|
|
|
|
double sinh(double x) NOEXCEPT
|
|
{
|
|
return (double)sinhl(x);
|
|
}
|
|
|
|
float sinhf(float x) NOEXCEPT
|
|
{
|
|
return (float)sinhl(x);
|
|
}
|
|
|
|
long double log10l(long double x) NOEXCEPT
|
|
{
|
|
long double ret = 0.0l;
|
|
__asm__(
|
|
"fldlg2\n"
|
|
"fld %%st(1)\n"
|
|
"fyl2x\n"
|
|
"fstp %%st(1)"
|
|
: "=t"(ret)
|
|
: "0"(x));
|
|
return ret;
|
|
}
|
|
|
|
double log10(double x) NOEXCEPT
|
|
{
|
|
return (double)log10l(x);
|
|
}
|
|
|
|
float log10f(float x) NOEXCEPT
|
|
{
|
|
return (float)log10l(x);
|
|
}
|
|
|
|
long double logl(long double x) NOEXCEPT
|
|
{
|
|
long double ret = 0.0l;
|
|
asm(
|
|
"fldln2\n"
|
|
"fld %%st(1)\n"
|
|
"fyl2x\n"
|
|
"fstp %%st(1)"
|
|
: "=t"(ret)
|
|
: "0"(x));
|
|
return ret;
|
|
}
|
|
|
|
double log(double x) NOEXCEPT
|
|
{
|
|
return (double)logl(x);
|
|
}
|
|
|
|
float logf(float x) NOEXCEPT
|
|
{
|
|
return (float)logl(x);
|
|
}
|
|
|
|
long double fmodl(long double index, long double period) NOEXCEPT
|
|
{
|
|
return index - truncl(index / period) * period;
|
|
}
|
|
|
|
double fmod(double index, double period) NOEXCEPT
|
|
{
|
|
return index - trunc(index / period) * period;
|
|
}
|
|
|
|
float fmodf(float index, float period) NOEXCEPT
|
|
{
|
|
return index - truncf(index / period) * period;
|
|
}
|
|
|
|
// FIXME: These aren't exactly like fmod, but these definitions are probably good enough for now
|
|
long double remainderl(long double x, long double y) NOEXCEPT
|
|
{
|
|
return fmodl(x, y);
|
|
}
|
|
|
|
double remainder(double x, double y) NOEXCEPT
|
|
{
|
|
return fmod(x, y);
|
|
}
|
|
|
|
float remainderf(float x, float y) NOEXCEPT
|
|
{
|
|
return fmodf(x, y);
|
|
}
|
|
|
|
long double expl(long double exponent) NOEXCEPT
|
|
{
|
|
long double res = 0;
|
|
asm("fldl2e\n"
|
|
"fmulp\n"
|
|
"fld1\n"
|
|
"fld %%st(1)\n"
|
|
"fprem\n"
|
|
"f2xm1\n"
|
|
"faddp\n"
|
|
"fscale\n"
|
|
"fstp %%st(1)"
|
|
: "=t"(res)
|
|
: "0"(exponent));
|
|
return res;
|
|
}
|
|
|
|
double exp(double exponent) NOEXCEPT
|
|
{
|
|
return (double)expl(exponent);
|
|
}
|
|
|
|
float expf(float exponent) NOEXCEPT
|
|
{
|
|
return (float)expl(exponent);
|
|
}
|
|
|
|
long double exp2l(long double exponent) NOEXCEPT
|
|
{
|
|
long double res = 0;
|
|
asm("fld1\n"
|
|
"fld %%st(1)\n"
|
|
"fprem\n"
|
|
"f2xm1\n"
|
|
"faddp\n"
|
|
"fscale\n"
|
|
"fstp %%st(1)"
|
|
: "=t"(res)
|
|
: "0"(exponent));
|
|
return res;
|
|
}
|
|
|
|
double exp2(double exponent) NOEXCEPT
|
|
{
|
|
return (double)exp2l(exponent);
|
|
}
|
|
|
|
float exp2f(float exponent) NOEXCEPT
|
|
{
|
|
return (float)exp2l(exponent);
|
|
}
|
|
|
|
long double coshl(long double x) NOEXCEPT
|
|
{
|
|
long double exponentiated = expl(-x);
|
|
if (x < 0)
|
|
return (1 + exponentiated * exponentiated) / 2 / exponentiated;
|
|
return (1 / exponentiated + exponentiated) / 2;
|
|
}
|
|
|
|
double cosh(double x) NOEXCEPT
|
|
{
|
|
return (double)coshl(x);
|
|
}
|
|
|
|
float coshf(float x) NOEXCEPT
|
|
{
|
|
return (float)coshl(x);
|
|
}
|
|
|
|
long double atan2l(long double y, long double x) NOEXCEPT
|
|
{
|
|
if (x == 0) {
|
|
if (y > 0)
|
|
return M_PI_2;
|
|
if (y < 0)
|
|
return -M_PI_2;
|
|
return 0;
|
|
}
|
|
|
|
long double result = 0; //atanl(y / x);
|
|
__asm__("fpatan"
|
|
: "=t"(result)
|
|
: "0"(x), "u"(y)
|
|
: "st(1)");
|
|
return result;
|
|
}
|
|
|
|
double atan2(double y, double x) NOEXCEPT
|
|
{
|
|
return (double)atan2l(y, x);
|
|
}
|
|
|
|
float atan2f(float y, float x) NOEXCEPT
|
|
{
|
|
return (float)atan2l(y, x);
|
|
}
|
|
|
|
long double atanl(long double x) NOEXCEPT
|
|
{
|
|
if (x < 0)
|
|
return -atanl(-x);
|
|
if (x > 1)
|
|
return M_PI_2 - atanl(1 / x);
|
|
long double squared = x * x;
|
|
return x / (1 + 1 * 1 * squared / (3 + 2 * 2 * squared / (5 + 3 * 3 * squared / (7 + 4 * 4 * squared / (9 + 5 * 5 * squared / (11 + 6 * 6 * squared / (13 + 7 * 7 * squared)))))));
|
|
}
|
|
|
|
double atan(double x) NOEXCEPT
|
|
{
|
|
return (double)atanl(x);
|
|
}
|
|
|
|
float atanf(float x) NOEXCEPT
|
|
{
|
|
return (float)atanl(x);
|
|
}
|
|
|
|
long double asinl(long double x) NOEXCEPT
|
|
{
|
|
if (x > 1 || x < -1)
|
|
return NAN;
|
|
if (x > 0.5 || x < -0.5)
|
|
return 2 * atanl(x / (1 + sqrtl(1 - x * x)));
|
|
long double squared = x * x;
|
|
long double value = x;
|
|
long double i = x * squared;
|
|
value += i * product_odd<1>() / product_even<2>() / 3;
|
|
i *= squared;
|
|
value += i * product_odd<3>() / product_even<4>() / 5;
|
|
i *= squared;
|
|
value += i * product_odd<5>() / product_even<6>() / 7;
|
|
i *= squared;
|
|
value += i * product_odd<7>() / product_even<8>() / 9;
|
|
i *= squared;
|
|
value += i * product_odd<9>() / product_even<10>() / 11;
|
|
i *= squared;
|
|
value += i * product_odd<11>() / product_even<12>() / 13;
|
|
return value;
|
|
}
|
|
|
|
double asin(double x) NOEXCEPT
|
|
{
|
|
return (double)asinl(x);
|
|
}
|
|
|
|
float asinf(float x) NOEXCEPT
|
|
{
|
|
return (float)asinl(x);
|
|
}
|
|
|
|
long double acosl(long double x) NOEXCEPT
|
|
{
|
|
return M_PI_2 - asinl(x);
|
|
}
|
|
|
|
double acos(double x) NOEXCEPT
|
|
{
|
|
return M_PI_2 - asin(x);
|
|
}
|
|
|
|
float acosf(float x) NOEXCEPT
|
|
{
|
|
return static_cast<float>(M_PI_2) - asinf(x);
|
|
}
|
|
|
|
long double fabsl(long double value) NOEXCEPT
|
|
{
|
|
return value < 0 ? -value : value;
|
|
}
|
|
|
|
double fabs(double value) NOEXCEPT
|
|
{
|
|
return value < 0 ? -value : value;
|
|
}
|
|
|
|
float fabsf(float value) NOEXCEPT
|
|
{
|
|
return value < 0 ? -value : value;
|
|
}
|
|
|
|
int ilogbl(long double x) NOEXCEPT
|
|
{
|
|
return internal_ilogb(x);
|
|
}
|
|
|
|
int ilogb(double x) NOEXCEPT
|
|
{
|
|
return internal_ilogb(x);
|
|
}
|
|
|
|
int ilogbf(float x) NOEXCEPT
|
|
{
|
|
return internal_ilogb(x);
|
|
}
|
|
|
|
long double logbl(long double x) NOEXCEPT
|
|
{
|
|
return ilogbl(x);
|
|
}
|
|
|
|
double logb(double x) NOEXCEPT
|
|
{
|
|
return ilogb(x);
|
|
}
|
|
|
|
float logbf(float x) NOEXCEPT
|
|
{
|
|
return ilogbf(x);
|
|
}
|
|
|
|
long double log2l(long double x) NOEXCEPT
|
|
{
|
|
long double ret = 0.0;
|
|
asm(
|
|
"fld1\n"
|
|
"fld %%st(1)\n"
|
|
"fyl2x\n"
|
|
"fstp %%st(1)"
|
|
: "=t"(ret)
|
|
: "0"(x));
|
|
return ret;
|
|
}
|
|
|
|
double log2(double x) NOEXCEPT
|
|
{
|
|
return (double)log2l(x);
|
|
}
|
|
|
|
float log2f(float x) NOEXCEPT
|
|
{
|
|
return (float)log2l(x);
|
|
}
|
|
|
|
double frexp(double x, int* exp) NOEXCEPT
|
|
{
|
|
*exp = (x == 0) ? 0 : (1 + ilogb(x));
|
|
return scalbn(x, -(*exp));
|
|
}
|
|
|
|
float frexpf(float x, int* exp) NOEXCEPT
|
|
{
|
|
*exp = (x == 0) ? 0 : (1 + ilogbf(x));
|
|
return scalbnf(x, -(*exp));
|
|
}
|
|
|
|
long double frexpl(long double x, int* exp) NOEXCEPT
|
|
{
|
|
*exp = (x == 0) ? 0 : (1 + ilogbl(x));
|
|
return scalbnl(x, -(*exp));
|
|
}
|
|
|
|
double round(double value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode::ToEven);
|
|
}
|
|
|
|
float roundf(float value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode::ToEven);
|
|
}
|
|
|
|
long double roundl(long double value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode::ToEven);
|
|
}
|
|
|
|
long lroundf(float value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode::ToEven);
|
|
}
|
|
|
|
long lround(double value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode::ToEven);
|
|
}
|
|
|
|
long lroundl(long double value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode::ToEven);
|
|
}
|
|
|
|
long long llroundf(float value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode::ToEven);
|
|
}
|
|
|
|
long long llround(double value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode::ToEven);
|
|
}
|
|
|
|
long long llroundd(long double value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode::ToEven);
|
|
}
|
|
|
|
float floorf(float value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode::Down);
|
|
}
|
|
|
|
double floor(double value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode::Down);
|
|
}
|
|
|
|
long double floorl(long double value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode::Down);
|
|
}
|
|
|
|
long double rintl(long double value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode { fegetround() });
|
|
}
|
|
|
|
double rint(double value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode { fegetround() });
|
|
}
|
|
|
|
float rintf(float value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode { fegetround() });
|
|
}
|
|
|
|
long lrintl(long double value) NOEXCEPT
|
|
{
|
|
return (long)internal_to_integer(value, RoundingMode { fegetround() });
|
|
}
|
|
|
|
long lrint(double value) NOEXCEPT
|
|
{
|
|
return (long)internal_to_integer(value, RoundingMode { fegetround() });
|
|
}
|
|
|
|
long lrintf(float value) NOEXCEPT
|
|
{
|
|
return (long)internal_to_integer(value, RoundingMode { fegetround() });
|
|
}
|
|
|
|
long long llrintl(long double value) NOEXCEPT
|
|
{
|
|
return (long long)internal_to_integer(value, RoundingMode { fegetround() });
|
|
}
|
|
|
|
long long llrint(double value) NOEXCEPT
|
|
{
|
|
return (long long)internal_to_integer(value, RoundingMode { fegetround() });
|
|
}
|
|
|
|
long long llrintf(float value) NOEXCEPT
|
|
{
|
|
return (long long)internal_to_integer(value, RoundingMode { fegetround() });
|
|
}
|
|
|
|
float ceilf(float value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode::Up);
|
|
}
|
|
|
|
double ceil(double value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode::Up);
|
|
}
|
|
|
|
long double ceill(long double value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode::Up);
|
|
}
|
|
|
|
long double modfl(long double x, long double* intpart) NOEXCEPT
|
|
{
|
|
return internal_modf(x, intpart);
|
|
}
|
|
|
|
double modf(double x, double* intpart) NOEXCEPT
|
|
{
|
|
return internal_modf(x, intpart);
|
|
}
|
|
|
|
float modff(float x, float* intpart) NOEXCEPT
|
|
{
|
|
return internal_modf(x, intpart);
|
|
}
|
|
|
|
double gamma(double x) NOEXCEPT
|
|
{
|
|
// Stirling approximation
|
|
return sqrt(2.0 * M_PI / x) * pow(x / M_E, x);
|
|
}
|
|
|
|
long double tgammal(long double value) NOEXCEPT
|
|
{
|
|
return internal_gamma(value);
|
|
}
|
|
|
|
double tgamma(double value) NOEXCEPT
|
|
{
|
|
return internal_gamma(value);
|
|
}
|
|
|
|
float tgammaf(float value) NOEXCEPT
|
|
{
|
|
return internal_gamma(value);
|
|
}
|
|
|
|
int signgam = 0;
|
|
|
|
long double lgammal(long double value) NOEXCEPT
|
|
{
|
|
return lgammal_r(value, &signgam);
|
|
}
|
|
|
|
double lgamma(double value) NOEXCEPT
|
|
{
|
|
return lgamma_r(value, &signgam);
|
|
}
|
|
|
|
float lgammaf(float value) NOEXCEPT
|
|
{
|
|
return lgammaf_r(value, &signgam);
|
|
}
|
|
|
|
long double lgammal_r(long double value, int* sign) NOEXCEPT
|
|
{
|
|
if (value == 1.0 || value == 2.0)
|
|
return 0.0;
|
|
if (isinf(value) || value == 0.0)
|
|
return INFINITY;
|
|
long double result = logl(internal_gamma(value));
|
|
*sign = signbit(result) ? -1 : 1;
|
|
return result;
|
|
}
|
|
|
|
double lgamma_r(double value, int* sign) NOEXCEPT
|
|
{
|
|
if (value == 1.0 || value == 2.0)
|
|
return 0.0;
|
|
if (isinf(value) || value == 0.0)
|
|
return INFINITY;
|
|
double result = log(internal_gamma(value));
|
|
*sign = signbit(result) ? -1 : 1;
|
|
return result;
|
|
}
|
|
|
|
float lgammaf_r(float value, int* sign) NOEXCEPT
|
|
{
|
|
if (value == 1.0f || value == 2.0f)
|
|
return 0.0;
|
|
if (isinf(value) || value == 0.0f)
|
|
return INFINITY;
|
|
float result = logf(internal_gamma(value));
|
|
*sign = signbit(result) ? -1 : 1;
|
|
return result;
|
|
}
|
|
|
|
long double expm1l(long double x) NOEXCEPT
|
|
{
|
|
return expl(x) - 1;
|
|
}
|
|
|
|
double expm1(double x) NOEXCEPT
|
|
{
|
|
return exp(x) - 1;
|
|
}
|
|
|
|
float expm1f(float x) NOEXCEPT
|
|
{
|
|
return expf(x) - 1;
|
|
}
|
|
|
|
long double cbrtl(long double x) NOEXCEPT
|
|
{
|
|
if (isinf(x) || x == 0)
|
|
return x;
|
|
if (x < 0)
|
|
return -cbrtl(-x);
|
|
|
|
long double r = x;
|
|
long double ex = 0;
|
|
|
|
while (r < 0.125l) {
|
|
r *= 8;
|
|
ex--;
|
|
}
|
|
while (r > 1.0l) {
|
|
r *= 0.125l;
|
|
ex++;
|
|
}
|
|
|
|
r = (-0.46946116l * r + 1.072302l) * r + 0.3812513l;
|
|
|
|
while (ex < 0) {
|
|
r *= 0.5l;
|
|
ex++;
|
|
}
|
|
while (ex > 0) {
|
|
r *= 2.0l;
|
|
ex--;
|
|
}
|
|
|
|
r = (2.0l / 3.0l) * r + (1.0l / 3.0l) * x / (r * r);
|
|
r = (2.0l / 3.0l) * r + (1.0l / 3.0l) * x / (r * r);
|
|
r = (2.0l / 3.0l) * r + (1.0l / 3.0l) * x / (r * r);
|
|
r = (2.0l / 3.0l) * r + (1.0l / 3.0l) * x / (r * r);
|
|
|
|
return r;
|
|
}
|
|
|
|
double cbrt(double x) NOEXCEPT
|
|
{
|
|
return (double)cbrtl(x);
|
|
}
|
|
|
|
float cbrtf(float x) NOEXCEPT
|
|
{
|
|
return (float)cbrtl(x);
|
|
}
|
|
|
|
long double log1pl(long double x) NOEXCEPT
|
|
{
|
|
return logl(1 + x);
|
|
}
|
|
|
|
double log1p(double x) NOEXCEPT
|
|
{
|
|
return log(1 + x);
|
|
}
|
|
|
|
float log1pf(float x) NOEXCEPT
|
|
{
|
|
return logf(1 + x);
|
|
}
|
|
|
|
long double acoshl(long double x) NOEXCEPT
|
|
{
|
|
return logl(x + sqrtl(x * x - 1));
|
|
}
|
|
|
|
double acosh(double x) NOEXCEPT
|
|
{
|
|
return log(x + sqrt(x * x - 1));
|
|
}
|
|
|
|
float acoshf(float x) NOEXCEPT
|
|
{
|
|
return logf(x + sqrtf(x * x - 1));
|
|
}
|
|
|
|
long double asinhl(long double x) NOEXCEPT
|
|
{
|
|
return logl(x + sqrtl(x * x + 1));
|
|
}
|
|
|
|
double asinh(double x) NOEXCEPT
|
|
{
|
|
return log(x + sqrt(x * x + 1));
|
|
}
|
|
|
|
float asinhf(float x) NOEXCEPT
|
|
{
|
|
return logf(x + sqrtf(x * x + 1));
|
|
}
|
|
|
|
long double atanhl(long double x) NOEXCEPT
|
|
{
|
|
return logl((1 + x) / (1 - x)) / 2.0l;
|
|
}
|
|
|
|
double atanh(double x) NOEXCEPT
|
|
{
|
|
return log((1 + x) / (1 - x)) / 2.0;
|
|
}
|
|
|
|
float atanhf(float x) NOEXCEPT
|
|
{
|
|
return logf((1 + x) / (1 - x)) / 2.0f;
|
|
}
|
|
|
|
long double hypotl(long double x, long double y) NOEXCEPT
|
|
{
|
|
return sqrtl(x * x + y * y);
|
|
}
|
|
|
|
double hypot(double x, double y) NOEXCEPT
|
|
{
|
|
return sqrt(x * x + y * y);
|
|
}
|
|
|
|
float hypotf(float x, float y) NOEXCEPT
|
|
{
|
|
return sqrtf(x * x + y * y);
|
|
}
|
|
|
|
long double erfl(long double x) NOEXCEPT
|
|
{
|
|
// algorithm taken from Abramowitz and Stegun (no. 26.2.17)
|
|
long double t = 1 / (1 + 0.47047l * fabsl(x));
|
|
long double poly = t * (0.3480242l + t * (-0.958798l + t * 0.7478556l));
|
|
long double answer = 1 - poly * expl(-x * x);
|
|
if (x < 0)
|
|
return -answer;
|
|
|
|
return answer;
|
|
}
|
|
|
|
double erf(double x) NOEXCEPT
|
|
{
|
|
return (double)erfl(x);
|
|
}
|
|
|
|
float erff(float x) NOEXCEPT
|
|
{
|
|
return (float)erf(x);
|
|
}
|
|
|
|
long double erfcl(long double x) NOEXCEPT
|
|
{
|
|
return 1 - erfl(x);
|
|
}
|
|
|
|
double erfc(double x) NOEXCEPT
|
|
{
|
|
return 1 - erf(x);
|
|
}
|
|
|
|
float erfcf(float x) NOEXCEPT
|
|
{
|
|
return 1 - erff(x);
|
|
}
|
|
|
|
double nextafter(double x, double target) NOEXCEPT
|
|
{
|
|
if (x == target)
|
|
return target;
|
|
return internal_nextafter(x, target >= x);
|
|
}
|
|
|
|
float nextafterf(float x, float target) NOEXCEPT
|
|
{
|
|
if (x == target)
|
|
return target;
|
|
return internal_nextafter(x, target >= x);
|
|
}
|
|
|
|
long double nextafterl(long double x, long double target) NOEXCEPT
|
|
{
|
|
return internal_nextafter(x, target >= x);
|
|
}
|
|
|
|
double nexttoward(double x, long double target) NOEXCEPT
|
|
{
|
|
if (x == target)
|
|
return target;
|
|
return internal_nextafter(x, target >= x);
|
|
}
|
|
|
|
float nexttowardf(float x, long double target) NOEXCEPT
|
|
{
|
|
if (x == target)
|
|
return target;
|
|
return internal_nextafter(x, target >= x);
|
|
}
|
|
|
|
long double nexttowardl(long double x, long double target) NOEXCEPT
|
|
{
|
|
if (x == target)
|
|
return target;
|
|
return internal_nextafter(x, target >= x);
|
|
}
|
|
|
|
float copysignf(float x, float y) NOEXCEPT
|
|
{
|
|
return internal_copysign(x, y);
|
|
}
|
|
|
|
double copysign(double x, double y) NOEXCEPT
|
|
{
|
|
return internal_copysign(x, y);
|
|
}
|
|
|
|
long double copysignl(long double x, long double y) NOEXCEPT
|
|
{
|
|
return internal_copysign(x, y);
|
|
}
|
|
|
|
float scalbnf(float x, int exponent) NOEXCEPT
|
|
{
|
|
return internal_scalbn(x, exponent);
|
|
}
|
|
|
|
double scalbn(double x, int exponent) NOEXCEPT
|
|
{
|
|
return internal_scalbn(x, exponent);
|
|
}
|
|
|
|
long double scalbnl(long double x, int exponent) NOEXCEPT
|
|
{
|
|
return internal_scalbn(x, exponent);
|
|
}
|
|
|
|
float scalbnlf(float x, long exponent) NOEXCEPT
|
|
{
|
|
return internal_scalbn(x, exponent);
|
|
}
|
|
|
|
double scalbln(double x, long exponent) NOEXCEPT
|
|
{
|
|
return internal_scalbn(x, exponent);
|
|
}
|
|
|
|
long double scalblnl(long double x, long exponent) NOEXCEPT
|
|
{
|
|
return internal_scalbn(x, exponent);
|
|
}
|
|
|
|
long double fmaxl(long double x, long double y) NOEXCEPT
|
|
{
|
|
if (isnan(x))
|
|
return y;
|
|
if (isnan(y))
|
|
return x;
|
|
|
|
return x > y ? x : y;
|
|
}
|
|
|
|
double fmax(double x, double y) NOEXCEPT
|
|
{
|
|
if (isnan(x))
|
|
return y;
|
|
if (isnan(y))
|
|
return x;
|
|
|
|
return x > y ? x : y;
|
|
}
|
|
|
|
float fmaxf(float x, float y) NOEXCEPT
|
|
{
|
|
if (isnan(x))
|
|
return y;
|
|
if (isnan(y))
|
|
return x;
|
|
|
|
return x > y ? x : y;
|
|
}
|
|
|
|
long double fminl(long double x, long double y) NOEXCEPT
|
|
{
|
|
if (isnan(x))
|
|
return y;
|
|
if (isnan(y))
|
|
return x;
|
|
|
|
return x < y ? x : y;
|
|
}
|
|
|
|
double fmin(double x, double y) NOEXCEPT
|
|
{
|
|
if (isnan(x))
|
|
return y;
|
|
if (isnan(y))
|
|
return x;
|
|
|
|
return x < y ? x : y;
|
|
}
|
|
|
|
float fminf(float x, float y) NOEXCEPT
|
|
{
|
|
if (isnan(x))
|
|
return y;
|
|
if (isnan(y))
|
|
return x;
|
|
|
|
return x < y ? x : y;
|
|
}
|
|
}
|