mirror of
https://github.com/SerenityOS/serenity
synced 2024-09-06 08:56:40 +00:00
![EWouters](/assets/img/avatar_default.png)
This fixes the lagom build on aarch64, as `__builtin_sincosf` doesn't take double arguments.
668 lines
13 KiB
C++
668 lines
13 KiB
C++
/*
|
|
* Copyright (c) 2021, Leon Albrecht <leon2002.la@gmail.com>.
|
|
*
|
|
* SPDX-License-Identifier: BSD-2-Clause
|
|
*/
|
|
|
|
#pragma once
|
|
|
|
#include <AK/BuiltinWrappers.h>
|
|
#include <AK/Concepts.h>
|
|
#include <AK/StdLibExtraDetails.h>
|
|
#include <AK/Types.h>
|
|
|
|
#ifdef KERNEL
|
|
# error "Including AK/Math.h from the Kernel is never correct! Floating point is disabled."
|
|
#endif
|
|
|
|
namespace AK {
|
|
|
|
template<FloatingPoint T>
|
|
constexpr T NaN = __builtin_nan("");
|
|
template<FloatingPoint T>
|
|
constexpr T Pi = 3.141592653589793238462643383279502884L;
|
|
template<FloatingPoint T>
|
|
constexpr T E = 2.718281828459045235360287471352662498L;
|
|
|
|
namespace Details {
|
|
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>(); }
|
|
}
|
|
|
|
#define CONSTEXPR_STATE(function, args...) \
|
|
if (is_constant_evaluated()) { \
|
|
if (IsSame<T, long double>) \
|
|
return __builtin_##function##l(args); \
|
|
if (IsSame<T, double>) \
|
|
return __builtin_##function(args); \
|
|
if (IsSame<T, float>) \
|
|
return __builtin_##function##f(args); \
|
|
}
|
|
|
|
namespace Division {
|
|
template<FloatingPoint T>
|
|
constexpr T fmod(T x, T y)
|
|
{
|
|
CONSTEXPR_STATE(fmod, x, y);
|
|
|
|
#if ARCH(I386) || ARCH(X86_64)
|
|
u16 fpu_status;
|
|
do {
|
|
asm(
|
|
"fprem\n"
|
|
"fnstsw %%ax\n"
|
|
: "+t"(x), "=a"(fpu_status)
|
|
: "u"(y));
|
|
} while (fpu_status & 0x400);
|
|
return x;
|
|
#else
|
|
return __builtin_fmod(x, y);
|
|
#endif
|
|
}
|
|
template<FloatingPoint T>
|
|
constexpr T remainder(T x, T y)
|
|
{
|
|
CONSTEXPR_STATE(remainder, x, y);
|
|
|
|
#if ARCH(I386) || ARCH(X86_64)
|
|
u16 fpu_status;
|
|
do {
|
|
asm(
|
|
"fprem1\n"
|
|
"fnstsw %%ax\n"
|
|
: "+t"(x), "=a"(fpu_status)
|
|
: "u"(y));
|
|
} while (fpu_status & 0x400);
|
|
return x;
|
|
#else
|
|
return __builtin_fmod(x, y);
|
|
#endif
|
|
}
|
|
}
|
|
|
|
using Division::fmod;
|
|
using Division::remainder;
|
|
|
|
template<FloatingPoint T>
|
|
constexpr T sqrt(T x)
|
|
{
|
|
CONSTEXPR_STATE(sqrt, x);
|
|
|
|
#if ARCH(I386) || ARCH(X86_64)
|
|
T res;
|
|
asm("fsqrt"
|
|
: "=t"(res)
|
|
: "0"(x));
|
|
return res;
|
|
#else
|
|
return __builtin_sqrt(x);
|
|
#endif
|
|
}
|
|
|
|
template<FloatingPoint T>
|
|
constexpr T rsqrt(T x)
|
|
{
|
|
return (T)1. / sqrt(x);
|
|
}
|
|
|
|
#ifdef __SSE__
|
|
template<>
|
|
constexpr float sqrt(float x)
|
|
{
|
|
if (is_constant_evaluated())
|
|
return __builtin_sqrtf(x);
|
|
|
|
float res;
|
|
asm("sqrtss %1, %0"
|
|
: "=x"(res)
|
|
: "x"(x));
|
|
return res;
|
|
}
|
|
|
|
# ifdef __SSE2__
|
|
template<>
|
|
constexpr double sqrt(double x)
|
|
{
|
|
if (is_constant_evaluated())
|
|
return __builtin_sqrt(x);
|
|
|
|
double res;
|
|
asm("sqrtsd %1, %0"
|
|
: "=x"(res)
|
|
: "x"(x));
|
|
return res;
|
|
}
|
|
# endif
|
|
|
|
template<>
|
|
constexpr float rsqrt(float x)
|
|
{
|
|
if (is_constant_evaluated())
|
|
return 1.f / __builtin_sqrtf(x);
|
|
|
|
float res;
|
|
asm("rsqrtss %1, %0"
|
|
: "=x"(res)
|
|
: "x"(x));
|
|
return res;
|
|
}
|
|
#endif
|
|
|
|
template<FloatingPoint T>
|
|
constexpr T cbrt(T x)
|
|
{
|
|
CONSTEXPR_STATE(cbrt, x);
|
|
if (__builtin_isinf(x) || x == 0)
|
|
return x;
|
|
if (x < 0)
|
|
return -cbrt(-x);
|
|
|
|
T r = x;
|
|
T 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;
|
|
}
|
|
|
|
template<FloatingPoint T>
|
|
constexpr T fabs(T x)
|
|
{
|
|
if (is_constant_evaluated())
|
|
return x < 0 ? -x : x;
|
|
#if ARCH(I386) || ARCH(X86_64)
|
|
asm(
|
|
"fabs"
|
|
: "+t"(x));
|
|
return x;
|
|
#else
|
|
return __builtin_fabs(x);
|
|
#endif
|
|
}
|
|
|
|
namespace Trigonometry {
|
|
|
|
template<FloatingPoint T>
|
|
constexpr T hypot(T x, T y)
|
|
{
|
|
return sqrt(x * x + y * y);
|
|
}
|
|
|
|
template<FloatingPoint T>
|
|
constexpr T sin(T angle)
|
|
{
|
|
CONSTEXPR_STATE(sin, angle);
|
|
|
|
#if ARCH(I386) || ARCH(X86_64)
|
|
T ret;
|
|
asm(
|
|
"fsin"
|
|
: "=t"(ret)
|
|
: "0"(angle));
|
|
return ret;
|
|
#else
|
|
return __builtin_sin(angle);
|
|
#endif
|
|
}
|
|
|
|
template<FloatingPoint T>
|
|
constexpr T cos(T angle)
|
|
{
|
|
CONSTEXPR_STATE(cos, angle);
|
|
|
|
#if ARCH(I386) || ARCH(X86_64)
|
|
T ret;
|
|
asm(
|
|
"fcos"
|
|
: "=t"(ret)
|
|
: "0"(angle));
|
|
return ret;
|
|
#else
|
|
return __builtin_cos(angle);
|
|
#endif
|
|
}
|
|
|
|
template<FloatingPoint T>
|
|
constexpr void sincos(T angle, T& sin_val, T& cos_val)
|
|
{
|
|
if (is_constant_evaluated()) {
|
|
sin_val = sin(angle);
|
|
cos_val = cos(angle);
|
|
return;
|
|
}
|
|
#if ARCH(I386) || ARCH(X86_64)
|
|
asm(
|
|
"fsincos"
|
|
: "=t"(cos_val), "=u"(sin_val)
|
|
: "0"(angle));
|
|
#else
|
|
sin_val = sin(angle);
|
|
cos_val = cos(angle);
|
|
#endif
|
|
}
|
|
|
|
template<FloatingPoint T>
|
|
constexpr T tan(T angle)
|
|
{
|
|
CONSTEXPR_STATE(tan, angle);
|
|
|
|
#if ARCH(I386) || ARCH(X86_64)
|
|
T ret, one;
|
|
asm(
|
|
"fptan"
|
|
: "=t"(one), "=u"(ret)
|
|
: "0"(angle));
|
|
|
|
return ret;
|
|
#else
|
|
return __builtin_tan(angle);
|
|
#endif
|
|
}
|
|
|
|
template<FloatingPoint T>
|
|
constexpr T atan(T value)
|
|
{
|
|
CONSTEXPR_STATE(atan, value);
|
|
|
|
#if ARCH(I386) || ARCH(X86_64)
|
|
T ret;
|
|
asm(
|
|
"fld1\n"
|
|
"fpatan\n"
|
|
: "=t"(ret)
|
|
: "0"(value));
|
|
return ret;
|
|
#else
|
|
return __builtin_atan(value);
|
|
#endif
|
|
}
|
|
|
|
template<FloatingPoint T>
|
|
constexpr T asin(T x)
|
|
{
|
|
CONSTEXPR_STATE(asin, x);
|
|
if (x > 1 || x < -1)
|
|
return NaN<T>;
|
|
if (x > (T)0.5 || x < (T)-0.5)
|
|
return 2 * atan<T>(x / (1 + sqrt<T>(1 - x * x)));
|
|
T squared = x * x;
|
|
T value = x;
|
|
T i = x * squared;
|
|
value += i * Details::product_odd<1>() / Details::product_even<2>() / 3;
|
|
i *= squared;
|
|
value += i * Details::product_odd<3>() / Details::product_even<4>() / 5;
|
|
i *= squared;
|
|
value += i * Details::product_odd<5>() / Details::product_even<6>() / 7;
|
|
i *= squared;
|
|
value += i * Details::product_odd<7>() / Details::product_even<8>() / 9;
|
|
i *= squared;
|
|
value += i * Details::product_odd<9>() / Details::product_even<10>() / 11;
|
|
i *= squared;
|
|
value += i * Details::product_odd<11>() / Details::product_even<12>() / 13;
|
|
i *= squared;
|
|
value += i * Details::product_odd<13>() / Details::product_even<14>() / 15;
|
|
i *= squared;
|
|
value += i * Details::product_odd<15>() / Details::product_even<16>() / 17;
|
|
return value;
|
|
}
|
|
|
|
template<FloatingPoint T>
|
|
constexpr T acos(T value)
|
|
{
|
|
CONSTEXPR_STATE(acos, value);
|
|
|
|
// FIXME: I am naive
|
|
return static_cast<T>(0.5) * Pi<T> - asin<T>(value);
|
|
}
|
|
|
|
template<FloatingPoint T>
|
|
constexpr T atan2(T y, T x)
|
|
{
|
|
CONSTEXPR_STATE(atan2, y, x);
|
|
|
|
#if ARCH(I386) || ARCH(X86_64)
|
|
T ret;
|
|
asm("fpatan"
|
|
: "=t"(ret)
|
|
: "0"(x), "u"(y)
|
|
: "st(1)");
|
|
return ret;
|
|
#else
|
|
return __builtin_atan2(y, x);
|
|
#endif
|
|
}
|
|
|
|
}
|
|
|
|
using Trigonometry::acos;
|
|
using Trigonometry::asin;
|
|
using Trigonometry::atan;
|
|
using Trigonometry::atan2;
|
|
using Trigonometry::cos;
|
|
using Trigonometry::hypot;
|
|
using Trigonometry::sin;
|
|
using Trigonometry::sincos;
|
|
using Trigonometry::tan;
|
|
|
|
namespace Exponentials {
|
|
|
|
template<FloatingPoint T>
|
|
constexpr T log(T x)
|
|
{
|
|
CONSTEXPR_STATE(log, x);
|
|
|
|
#if ARCH(I386) || ARCH(X86_64)
|
|
T ret;
|
|
asm(
|
|
"fldln2\n"
|
|
"fxch %%st(1)\n"
|
|
"fyl2x\n"
|
|
: "=t"(ret)
|
|
: "0"(x));
|
|
return ret;
|
|
#else
|
|
return __builtin_log(x);
|
|
#endif
|
|
}
|
|
|
|
template<FloatingPoint T>
|
|
constexpr T log2(T x)
|
|
{
|
|
CONSTEXPR_STATE(log2, x);
|
|
|
|
#if ARCH(I386) || ARCH(X86_64)
|
|
T ret;
|
|
asm(
|
|
"fld1\n"
|
|
"fxch %%st(1)\n"
|
|
"fyl2x\n"
|
|
: "=t"(ret)
|
|
: "0"(x));
|
|
return ret;
|
|
#else
|
|
return __builtin_log2(x);
|
|
#endif
|
|
}
|
|
|
|
template<FloatingPoint T>
|
|
constexpr T log10(T x)
|
|
{
|
|
CONSTEXPR_STATE(log10, x);
|
|
|
|
#if ARCH(I386) || ARCH(X86_64)
|
|
T ret;
|
|
asm(
|
|
"fldlg2\n"
|
|
"fxch %%st(1)\n"
|
|
"fyl2x\n"
|
|
: "=t"(ret)
|
|
: "0"(x));
|
|
return ret;
|
|
#else
|
|
return __builtin_log10(x);
|
|
#endif
|
|
}
|
|
|
|
template<FloatingPoint T>
|
|
constexpr T exp(T exponent)
|
|
{
|
|
CONSTEXPR_STATE(exp, exponent);
|
|
|
|
#if ARCH(I386) || ARCH(X86_64)
|
|
T res;
|
|
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;
|
|
#else
|
|
return __builtin_exp(exponent);
|
|
#endif
|
|
}
|
|
|
|
template<FloatingPoint T>
|
|
constexpr T exp2(T exponent)
|
|
{
|
|
CONSTEXPR_STATE(exp2, exponent);
|
|
|
|
#if ARCH(I386) || ARCH(X86_64)
|
|
T res;
|
|
asm("fld1\n"
|
|
"fld %%st(1)\n"
|
|
"fprem\n"
|
|
"f2xm1\n"
|
|
"faddp\n"
|
|
"fscale\n"
|
|
"fstp %%st(1)"
|
|
: "=t"(res)
|
|
: "0"(exponent));
|
|
return res;
|
|
#else
|
|
return __builtin_exp2(exponent);
|
|
#endif
|
|
}
|
|
|
|
}
|
|
|
|
using Exponentials::exp;
|
|
using Exponentials::exp2;
|
|
using Exponentials::log;
|
|
using Exponentials::log10;
|
|
using Exponentials::log2;
|
|
|
|
namespace Hyperbolic {
|
|
|
|
template<FloatingPoint T>
|
|
constexpr T sinh(T x)
|
|
{
|
|
T exponentiated = exp<T>(x);
|
|
if (x > 0)
|
|
return (exponentiated * exponentiated - 1) / 2 / exponentiated;
|
|
return (exponentiated - 1 / exponentiated) / 2;
|
|
}
|
|
|
|
template<FloatingPoint T>
|
|
constexpr T cosh(T x)
|
|
{
|
|
CONSTEXPR_STATE(cosh, x);
|
|
|
|
T exponentiated = exp(-x);
|
|
if (x < 0)
|
|
return (1 + exponentiated * exponentiated) / 2 / exponentiated;
|
|
return (1 / exponentiated + exponentiated) / 2;
|
|
}
|
|
|
|
template<FloatingPoint T>
|
|
constexpr T tanh(T x)
|
|
{
|
|
if (x > 0) {
|
|
T exponentiated = exp<T>(2 * x);
|
|
return (exponentiated - 1) / (exponentiated + 1);
|
|
}
|
|
T plusX = exp<T>(x);
|
|
T minusX = 1 / plusX;
|
|
return (plusX - minusX) / (plusX + minusX);
|
|
}
|
|
|
|
template<FloatingPoint T>
|
|
constexpr T asinh(T x)
|
|
{
|
|
return log<T>(x + sqrt<T>(x * x + 1));
|
|
}
|
|
|
|
template<FloatingPoint T>
|
|
constexpr T acosh(T x)
|
|
{
|
|
return log<T>(x + sqrt<T>(x * x - 1));
|
|
}
|
|
|
|
template<FloatingPoint T>
|
|
constexpr T atanh(T x)
|
|
{
|
|
return log<T>((1 + x) / (1 - x)) / (T)2.0l;
|
|
}
|
|
|
|
}
|
|
|
|
using Hyperbolic::acosh;
|
|
using Hyperbolic::asinh;
|
|
using Hyperbolic::atanh;
|
|
using Hyperbolic::cosh;
|
|
using Hyperbolic::sinh;
|
|
using Hyperbolic::tanh;
|
|
|
|
template<Integral I, FloatingPoint P>
|
|
ALWAYS_INLINE I round_to(P value)
|
|
{
|
|
#if ARCH(I386) || ARCH(X86_64)
|
|
// Note: fistps outputs into a signed integer location (i16, i32, i64),
|
|
// so lets be nice and tell the compiler that.
|
|
Conditional<sizeof(I) >= sizeof(i16), MakeSigned<I>, i16> ret;
|
|
if constexpr (sizeof(I) == sizeof(i64)) {
|
|
asm("fistpll %0"
|
|
: "=m"(ret)
|
|
: "t"(value)
|
|
: "st");
|
|
} else if constexpr (sizeof(I) == sizeof(i32)) {
|
|
asm("fistpl %0"
|
|
: "=m"(ret)
|
|
: "t"(value)
|
|
: "st");
|
|
} else {
|
|
asm("fistps %0"
|
|
: "=m"(ret)
|
|
: "t"(value)
|
|
: "st");
|
|
}
|
|
return static_cast<I>(ret);
|
|
#else
|
|
if constexpr (IsSame<P, long double>)
|
|
return static_cast<I>(__builtin_llrintl(value));
|
|
if constexpr (IsSame<P, double>)
|
|
return static_cast<I>(__builtin_llrint(value));
|
|
if constexpr (IsSame<P, float>)
|
|
return static_cast<I>(__builtin_llrintf(value));
|
|
#endif
|
|
}
|
|
|
|
#ifdef __SSE__
|
|
template<Integral I>
|
|
ALWAYS_INLINE I round_to(float value)
|
|
{
|
|
if constexpr (sizeof(I) == sizeof(i64)) {
|
|
// Note: Outputting into 64-bit registers or memory locations requires the
|
|
// REX prefix, so we have to fall back to long doubles on i686
|
|
# if ARCH(X86_64)
|
|
i64 ret;
|
|
asm("cvtss2si %1, %0"
|
|
: "=r"(ret)
|
|
: "xm"(value));
|
|
return static_cast<I>(ret);
|
|
# else
|
|
return round_to<I, long double>(value);
|
|
# endif
|
|
}
|
|
i32 ret;
|
|
asm("cvtss2si %1, %0"
|
|
: "=r"(ret)
|
|
: "xm"(value));
|
|
return static_cast<I>(ret);
|
|
}
|
|
#endif
|
|
#ifdef __SSE2__
|
|
template<Integral I>
|
|
ALWAYS_INLINE I round_to(double value)
|
|
{
|
|
if constexpr (sizeof(I) == sizeof(i64)) {
|
|
// Note: Outputting into 64-bit registers or memory locations requires the
|
|
// REX prefix, so we have to fall back to long doubles on i686
|
|
# if ARCH(X86_64)
|
|
i64 ret;
|
|
asm("cvtsd2si %1, %0"
|
|
: "=r"(ret)
|
|
: "xm"(value));
|
|
return static_cast<I>(ret);
|
|
# else
|
|
return round_to<I, long double>(value);
|
|
# endif
|
|
}
|
|
i32 ret;
|
|
asm("cvtsd2si %1, %0"
|
|
: "=r"(ret)
|
|
: "xm"(value));
|
|
return static_cast<I>(ret);
|
|
}
|
|
#endif
|
|
|
|
template<FloatingPoint T>
|
|
constexpr T pow(T x, T y)
|
|
{
|
|
CONSTEXPR_STATE(pow, x, y);
|
|
// fixme I am naive
|
|
if (__builtin_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 == (T)y_as_int) {
|
|
T result = x;
|
|
for (int i = 0; i < fabs<T>(y) - 1; ++i)
|
|
result *= x;
|
|
if (y < 0)
|
|
result = 1.0l / result;
|
|
return result;
|
|
}
|
|
|
|
return exp2<T>(y * log2<T>(x));
|
|
}
|
|
|
|
#undef CONSTEXPR_STATE
|
|
}
|
|
|
|
using AK::round_to;
|