ladybird/Userland/Libraries/LibM/math.cpp
2021-03-06 09:42:06 +01:00

755 lines
17 KiB
C++

/*
* Copyright (c) 2018-2020, Andreas Kling <kling@serenityos.org>
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* 1. Redistributions of source code must retain the above copyright notice, this
* list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#include <LibC/assert.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,
Up,
Down,
ToEven
};
template<typename T>
union FloatExtractor;
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 -= 1.0;
else
extractor.d += 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;
}
extern "C" {
double trunc(double x) NOEXCEPT
{
return internal_to_integer(x, RoundingMode::ToZero);
}
double cos(double angle) NOEXCEPT
{
return sin(angle + M_PI_2);
}
float cosf(float angle) NOEXCEPT
{
return sinf(angle + M_PI_2);
}
// 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;
}
double pow(double x, 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 == (double)y_as_int) {
double result = x;
for (int i = 0; i < fabs(y) - 1; ++i)
result *= x;
if (y < 0)
result = 1.0 / result;
return result;
}
return exp2(y * log2(x));
}
float powf(float x, float y) NOEXCEPT
{
return (float)pow(x, y);
}
double ldexp(double x, int exp) NOEXCEPT
{
return x * exp2(exp);
}
float ldexpf(float x, int exp) NOEXCEPT
{
return x * exp2f(exp);
}
double tanh(double x) NOEXCEPT
{
if (x > 0) {
double exponentiated = exp(2 * x);
return (exponentiated - 1) / (exponentiated + 1);
}
double plusX = exp(x);
double minusX = 1 / plusX;
return (plusX - minusX) / (plusX + minusX);
}
static double ampsin(double angle) NOEXCEPT
{
double looped_angle = fmod(M_PI + angle, M_TAU) - M_PI;
double looped_angle_squared = looped_angle * looped_angle;
double quadratic_term;
if (looped_angle > 0) {
quadratic_term = -looped_angle_squared;
} else {
quadratic_term = looped_angle_squared;
}
double linear_term = M_PI * looped_angle;
return quadratic_term + linear_term;
}
double tan(double angle) NOEXCEPT
{
return ampsin(angle) / ampsin(M_PI_2 + angle);
}
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;
}
double sinh(double x) NOEXCEPT
{
double exponentiated = exp(x);
if (x > 0)
return (exponentiated * exponentiated - 1) / 2 / exponentiated;
return (exponentiated - 1 / exponentiated) / 2;
}
double log10(double x) NOEXCEPT
{
double ret = 0.0;
__asm__(
"fldlg2\n"
"fld %%st(1)\n"
"fyl2x\n"
"fstp %%st(1)"
: "=t"(ret)
: "0"(x));
return ret;
}
double log(double x) NOEXCEPT
{
double ret = 0.0;
__asm__(
"fldln2\n"
"fld %%st(1)\n"
"fyl2x\n"
"fstp %%st(1)"
: "=t"(ret)
: "0"(x));
return ret;
}
float logf(float x) NOEXCEPT
{
return (float)log(x);
}
double fmod(double index, double period) NOEXCEPT
{
return index - trunc(index / period) * period;
}
float fmodf(float index, float period) NOEXCEPT
{
return index - trunc(index / period) * period;
}
double exp(double exponent) NOEXCEPT
{
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;
}
float expf(float exponent) NOEXCEPT
{
return (float)exp(exponent);
}
double exp2(double exponent) NOEXCEPT
{
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;
}
float exp2f(float exponent) NOEXCEPT
{
return (float)exp2(exponent);
}
double cosh(double x) NOEXCEPT
{
double exponentiated = exp(-x);
if (x < 0)
return (1 + exponentiated * exponentiated) / 2 / exponentiated;
return (1 / exponentiated + exponentiated) / 2;
}
double atan2(double y, double x) NOEXCEPT
{
if (x > 0)
return atan(y / x);
if (x == 0) {
if (y > 0)
return M_PI_2;
if (y < 0)
return -M_PI_2;
return 0;
}
if (y >= 0)
return atan(y / x) + M_PI;
return atan(y / x) - M_PI;
}
float atan2f(float y, float x) NOEXCEPT
{
return (float)atan2(y, x);
}
double atan(double x) NOEXCEPT
{
if (x < 0)
return -atan(-x);
if (x > 1)
return M_PI_2 - atan(1 / x);
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 asin(double x) NOEXCEPT
{
if (x > 1 || x < -1)
return NAN;
if (x > 0.5 || x < -0.5)
return 2 * atan(x / (1 + sqrt(1 - x * x)));
double squared = x * x;
double value = x;
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;
}
float asinf(float x) NOEXCEPT
{
return (float)asin(x);
}
double acos(double x) NOEXCEPT
{
return M_PI_2 - asin(x);
}
float acosf(float x) NOEXCEPT
{
return M_PI_2 - asinf(x);
}
double fabs(double value) NOEXCEPT
{
return value < 0 ? -value : value;
}
double log2(double x) NOEXCEPT
{
double ret = 0.0;
__asm__(
"fld1\n"
"fld %%st(1)\n"
"fyl2x\n"
"fstp %%st(1)"
: "=t"(ret)
: "0"(x));
return ret;
}
float log2f(float x) NOEXCEPT
{
return log2(x);
}
long double log2l(long double x) NOEXCEPT
{
return log2(x);
}
double frexp(double, int*) NOEXCEPT
{
VERIFY_NOT_REACHED();
return 0;
}
float frexpf(float, int*) NOEXCEPT
{
VERIFY_NOT_REACHED();
return 0;
}
long double frexpl(long double, int*) NOEXCEPT
{
VERIFY_NOT_REACHED();
return 0;
}
double round(double value) NOEXCEPT
{
return internal_to_integer(value, RoundingMode::ToEven);
}
float roundf(float 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);
}
double rint(double value) NOEXCEPT
{
// This should be the current rounding mode
return internal_to_integer(value, RoundingMode::ToEven);
}
float ceilf(float value) NOEXCEPT
{
return internal_to_integer(value, RoundingMode::Up);
}
double ceil(double value) NOEXCEPT
{
return internal_to_integer(value, RoundingMode::Up);
}
double modf(double x, double* intpart) NOEXCEPT
{
double 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;
}
double gamma(double x) NOEXCEPT
{
// Stirling approximation
return sqrt(2.0 * M_PI / x) * pow(x / M_E, x);
}
double expm1(double x) NOEXCEPT
{
return exp(x) - 1;
}
double cbrt(double x) NOEXCEPT
{
if (isinf(x) || x == 0)
return x;
if (x < 0)
return -cbrt(-x);
double r = x;
double ex = 0;
while (r < 0.125) {
r *= 8;
ex--;
}
while (r > 1.0) {
r *= 0.125;
ex++;
}
r = (-0.46946116 * r + 1.072302) * r + 0.3812513;
while (ex < 0) {
r *= 0.5;
ex++;
}
while (ex > 0) {
r *= 2;
ex--;
}
r = (2.0 / 3.0) * r + (1.0 / 3.0) * x / (r * r);
r = (2.0 / 3.0) * r + (1.0 / 3.0) * x / (r * r);
r = (2.0 / 3.0) * r + (1.0 / 3.0) * x / (r * r);
r = (2.0 / 3.0) * r + (1.0 / 3.0) * x / (r * r);
return r;
}
double log1p(double x) NOEXCEPT
{
return log(1 + x);
}
double acosh(double x) NOEXCEPT
{
return log(x + sqrt(x * x - 1));
}
double asinh(double x) NOEXCEPT
{
return log(x + sqrt(x * x + 1));
}
double atanh(double x) NOEXCEPT
{
return log((1 + x) / (1 - x)) / 2.0;
}
double hypot(double x, double y) NOEXCEPT
{
return sqrt(x * x + y * y);
}
double erf(double x) NOEXCEPT
{
// algorithm taken from Abramowitz and Stegun (no. 26.2.17)
double t = 1 / (1 + 0.47047 * fabs(x));
double poly = t * (0.3480242 + t * (-0.958798 + t * 0.7478556));
double answer = 1 - poly * exp(-x * x);
if (x < 0)
return -answer;
return answer;
}
double erfc(double x) NOEXCEPT
{
return 1 - erf(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, long double) NOEXCEPT
{
TODO();
}
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, long double) NOEXCEPT
{
TODO();
}
double copysign(double x, double y)
{
using Extractor = FloatExtractor<decltype(x)>;
Extractor ex, ey;
ex.d = x;
ey.d = y;
ex.sign = ey.sign;
return ex.d;
}
}