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|
/*
* 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/Math.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>
#ifdef __clang__
# pragma clang diagnostic push
# pragma clang diagnostic ignored "-Wdouble-promotion"
#endif
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 ((int)x == x && x <= max_integer_whose_factorial_fits + 1) {
long long result = 1;
for (long long cursor = 2; cursor < (long long)x; cursor++)
result *= cursor;
return (FloatT)result;
}
// Stirling approximation
return sqrtl(2.0 * M_PIl / static_cast<long double>(x)) * powl(static_cast<long double>(x) / M_El, 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);
}
#define MAKE_AK_BACKED1(name) \
long double name##l(long double arg) NOEXCEPT \
{ \
return AK::name<long double>(arg); \
} \
double name(double arg) NOEXCEPT \
{ \
return AK::name<double>(arg); \
} \
float name##f(float arg) NOEXCEPT \
{ \
return AK::name<float>(arg); \
}
#define MAKE_AK_BACKED2(name) \
long double name##l(long double arg1, long double arg2) NOEXCEPT \
{ \
return AK::name<long double>(arg1, arg2); \
} \
double name(double arg1, double arg2) NOEXCEPT \
{ \
return AK::name<double>(arg1, arg2); \
} \
float name##f(float arg1, float arg2) NOEXCEPT \
{ \
return AK::name<float>(arg1, arg2); \
}
MAKE_AK_BACKED1(sin);
MAKE_AK_BACKED1(cos);
MAKE_AK_BACKED1(tan);
MAKE_AK_BACKED1(asin);
MAKE_AK_BACKED1(acos);
MAKE_AK_BACKED1(atan);
MAKE_AK_BACKED1(sinh);
MAKE_AK_BACKED1(cosh);
MAKE_AK_BACKED1(tanh);
MAKE_AK_BACKED1(asinh);
MAKE_AK_BACKED1(acosh);
MAKE_AK_BACKED1(atanh);
MAKE_AK_BACKED1(sqrt);
MAKE_AK_BACKED1(cbrt);
MAKE_AK_BACKED1(log);
MAKE_AK_BACKED1(log2);
MAKE_AK_BACKED1(log10);
MAKE_AK_BACKED1(exp);
MAKE_AK_BACKED1(exp2);
MAKE_AK_BACKED1(fabs);
MAKE_AK_BACKED2(atan2);
MAKE_AK_BACKED2(hypot);
MAKE_AK_BACKED2(fmod);
MAKE_AK_BACKED2(pow);
MAKE_AK_BACKED2(remainder);
long double truncl(long double x) NOEXCEPT
{
if (fabsl(x) < LONG_LONG_MAX) {
// This is 1.6 times faster than the implemenation using the "internal_to_integer"
// helper (on x86_64)
// https://quick-bench.com/q/xBmxuY8am9qibSYVna90Y6PIvqA
u64 temp;
asm(
"fisttpq %[temp]\n"
"fildq %[temp]"
: "+t"(x)
: [temp] "m"(temp));
return x;
}
return internal_to_integer(x, RoundingMode::ToZero);
}
double trunc(double x) NOEXCEPT
{
if (fabs(x) < LONG_LONG_MAX) {
u64 temp;
asm(
"fisttpq %[temp]\n"
"fildq %[temp]"
: "+t"(x)
: [temp] "m"(temp));
return x;
}
return internal_to_integer(x, RoundingMode::ToZero);
}
float truncf(float x) NOEXCEPT
{
if (fabsf(x) < LONG_LONG_MAX) {
u64 temp;
asm(
"fisttpq %[temp]\n"
"fildq %[temp]"
: "+t"(x)
: [temp] "m"(temp));
return x;
}
return internal_to_integer(x, RoundingMode::ToZero);
}
long double rintl(long double value)
{
double res;
asm(
"frndint\n"
: "=t"(res)
: "0"(value));
return res;
}
double rint(double value)
{
double res;
asm(
"frndint\n"
: "=t"(res)
: "0"(value));
return res;
}
float rintf(float value)
{
double res;
asm(
"frndint\n"
: "=t"(res)
: "0"(value));
return res;
}
long lrintl(long double value)
{
long res;
asm(
"fistpl %0\n"
: "+m"(res)
: "t"(value)
: "st");
return res;
}
long lrint(double value)
{
long res;
asm(
"fistpl %0\n"
: "+m"(res)
: "t"(value)
: "st");
return res;
}
long lrintf(float value)
{
long res;
asm(
"fistpl %0\n"
: "+m"(res)
: "t"(value)
: "st");
return res;
}
long long llrintl(long double value)
{
long long res;
asm(
"fistpq %0\n"
: "+m"(res)
: "t"(value)
: "st");
return res;
}
long long llrint(double value)
{
long long res;
asm(
"fistpq %0\n"
: "+m"(res)
: "t"(value)
: "st");
return res;
}
long long llrintf(float value)
{
long long res;
asm(
"fistpq %0\n"
: "+m"(res)
: "t"(value)
: "st");
return res;
}
// 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);
}
[[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;
}
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);
}
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);
}
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 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 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;
}
long double nearbyintl(long double value) NOEXCEPT
{
return internal_to_integer(value, RoundingMode { fegetround() });
}
double nearbyint(double value) NOEXCEPT
{
return internal_to_integer(value, RoundingMode { fegetround() });
}
float nearbyintf(float value) NOEXCEPT
{
return internal_to_integer(value, RoundingMode { fegetround() });
}
}
#ifdef __clang__
# pragma clang diagnostic pop
#endif
|