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778 lines
17 KiB
C++
778 lines
17 KiB
C++
/*
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* Copyright (c) 2021, Leon Albrecht <leon2002.la@gmail.com>.
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*
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* SPDX-License-Identifier: BSD-2-Clause
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*/
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#pragma once
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#include <AK/BuiltinWrappers.h>
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#include <AK/Concepts.h>
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#include <AK/NumericLimits.h>
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#include <AK/StdLibExtraDetails.h>
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#include <AK/Types.h>
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#ifdef KERNEL
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# error "Including AK/Math.h from the Kernel is never correct! Floating point is disabled."
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#endif
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namespace AK {
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template<FloatingPoint T>
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constexpr T NaN = __builtin_nan("");
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template<FloatingPoint T>
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constexpr T Pi = 3.141592653589793238462643383279502884L;
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template<FloatingPoint T>
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constexpr T E = 2.718281828459045235360287471352662498L;
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template<FloatingPoint T>
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constexpr T Sqrt2 = 1.414213562373095048801688724209698079L;
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template<FloatingPoint T>
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constexpr T Sqrt1_2 = 0.707106781186547524400844362104849039L;
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namespace Details {
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template<size_t>
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constexpr size_t product_even();
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template<>
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constexpr size_t product_even<2>() { return 2; }
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template<size_t value>
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constexpr size_t product_even() { return value * product_even<value - 2>(); }
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template<size_t>
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constexpr size_t product_odd();
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template<>
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constexpr size_t product_odd<1>() { return 1; }
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template<size_t value>
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constexpr size_t product_odd() { return value * product_odd<value - 2>(); }
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}
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#define CONSTEXPR_STATE(function, args...) \
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if (is_constant_evaluated()) { \
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if (IsSame<T, long double>) \
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return __builtin_##function##l(args); \
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if (IsSame<T, double>) \
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return __builtin_##function(args); \
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if (IsSame<T, float>) \
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return __builtin_##function##f(args); \
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}
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#define AARCH64_INSTRUCTION(instruction, arg) \
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if constexpr (IsSame<T, long double>) \
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TODO(); \
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if constexpr (IsSame<T, double>) { \
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double res; \
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asm(#instruction " %d0, %d1" \
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: "=w"(res) \
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: "w"(arg)); \
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return res; \
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} \
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if constexpr (IsSame<T, float>) { \
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float res; \
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asm(#instruction " %s0, %s1" \
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: "=w"(res) \
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: "w"(arg)); \
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return res; \
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}
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namespace Division {
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template<FloatingPoint T>
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constexpr T fmod(T x, T y)
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{
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CONSTEXPR_STATE(fmod, x, y);
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#if ARCH(I386) || ARCH(X86_64)
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u16 fpu_status;
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do {
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asm(
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"fprem\n"
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"fnstsw %%ax\n"
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: "+t"(x), "=a"(fpu_status)
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: "u"(y));
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} while (fpu_status & 0x400);
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return x;
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#else
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return __builtin_fmod(x, y);
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#endif
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}
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template<FloatingPoint T>
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constexpr T remainder(T x, T y)
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{
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CONSTEXPR_STATE(remainder, x, y);
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#if ARCH(I386) || ARCH(X86_64)
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u16 fpu_status;
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do {
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asm(
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"fprem1\n"
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"fnstsw %%ax\n"
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: "+t"(x), "=a"(fpu_status)
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: "u"(y));
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} while (fpu_status & 0x400);
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return x;
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#else
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return __builtin_fmod(x, y);
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#endif
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}
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}
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using Division::fmod;
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using Division::remainder;
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template<FloatingPoint T>
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constexpr T sqrt(T x)
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{
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CONSTEXPR_STATE(sqrt, x);
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#if ARCH(I386) || ARCH(X86_64)
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T res;
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asm("fsqrt"
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: "=t"(res)
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: "0"(x));
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return res;
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#elif ARCH(AARCH64)
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AARCH64_INSTRUCTION(fsqrt, x);
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#else
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return __builtin_sqrt(x);
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#endif
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}
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template<FloatingPoint T>
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constexpr T rsqrt(T x)
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{
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#if ARCH(AARCH64)
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AARCH64_INSTRUCTION(frsqrte, x);
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#endif
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return (T)1. / sqrt(x);
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}
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#ifdef __SSE__
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template<>
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constexpr float sqrt(float x)
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{
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if (is_constant_evaluated())
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return __builtin_sqrtf(x);
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float res;
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asm("sqrtss %1, %0"
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: "=x"(res)
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: "x"(x));
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return res;
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}
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# ifdef __SSE2__
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template<>
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constexpr double sqrt(double x)
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{
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if (is_constant_evaluated())
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return __builtin_sqrt(x);
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double res;
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asm("sqrtsd %1, %0"
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: "=x"(res)
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: "x"(x));
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return res;
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}
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# endif
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template<>
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constexpr float rsqrt(float x)
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{
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if (is_constant_evaluated())
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return 1.f / __builtin_sqrtf(x);
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float res;
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asm("rsqrtss %1, %0"
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: "=x"(res)
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: "x"(x));
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return res;
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}
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#endif
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template<FloatingPoint T>
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constexpr T cbrt(T x)
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{
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CONSTEXPR_STATE(cbrt, x);
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if (__builtin_isinf(x) || x == 0)
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return x;
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if (x < 0)
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return -cbrt(-x);
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T r = x;
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T ex = 0;
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while (r < 0.125l) {
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r *= 8;
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ex--;
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}
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while (r > 1.0l) {
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r *= 0.125l;
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ex++;
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}
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r = (-0.46946116l * r + 1.072302l) * r + 0.3812513l;
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while (ex < 0) {
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r *= 0.5l;
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ex++;
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}
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while (ex > 0) {
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r *= 2.0l;
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ex--;
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}
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r = (2.0l / 3.0l) * r + (1.0l / 3.0l) * x / (r * r);
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r = (2.0l / 3.0l) * r + (1.0l / 3.0l) * x / (r * r);
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r = (2.0l / 3.0l) * r + (1.0l / 3.0l) * x / (r * r);
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r = (2.0l / 3.0l) * r + (1.0l / 3.0l) * x / (r * r);
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return r;
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}
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template<FloatingPoint T>
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constexpr T fabs(T x)
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{
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if (is_constant_evaluated())
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return x < 0 ? -x : x;
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#if ARCH(I386) || ARCH(X86_64)
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asm(
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"fabs"
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: "+t"(x));
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return x;
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#elif ARCH(AARCH64)
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AARCH64_INSTRUCTION(fabs, x);
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#else
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return __builtin_fabs(x);
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#endif
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}
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namespace Trigonometry {
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template<FloatingPoint T>
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constexpr T hypot(T x, T y)
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{
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return sqrt(x * x + y * y);
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}
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template<FloatingPoint T>
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constexpr T sin(T angle)
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{
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CONSTEXPR_STATE(sin, angle);
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#if ARCH(I386) || ARCH(X86_64)
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T ret;
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asm(
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"fsin"
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: "=t"(ret)
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: "0"(angle));
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return ret;
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#else
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return __builtin_sin(angle);
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#endif
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}
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template<FloatingPoint T>
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constexpr T cos(T angle)
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{
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CONSTEXPR_STATE(cos, angle);
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#if ARCH(I386) || ARCH(X86_64)
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T ret;
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asm(
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"fcos"
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: "=t"(ret)
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: "0"(angle));
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return ret;
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#else
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return __builtin_cos(angle);
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#endif
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}
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template<FloatingPoint T>
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constexpr void sincos(T angle, T& sin_val, T& cos_val)
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{
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if (is_constant_evaluated()) {
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sin_val = sin(angle);
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cos_val = cos(angle);
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return;
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}
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#if ARCH(I386) || ARCH(X86_64)
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asm(
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"fsincos"
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: "=t"(cos_val), "=u"(sin_val)
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: "0"(angle));
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#else
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sin_val = sin(angle);
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cos_val = cos(angle);
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#endif
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}
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template<FloatingPoint T>
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constexpr T tan(T angle)
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{
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CONSTEXPR_STATE(tan, angle);
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#if ARCH(I386) || ARCH(X86_64)
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T ret, one;
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asm(
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"fptan"
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: "=t"(one), "=u"(ret)
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: "0"(angle));
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return ret;
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#else
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return __builtin_tan(angle);
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#endif
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}
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template<FloatingPoint T>
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constexpr T atan(T value)
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{
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CONSTEXPR_STATE(atan, value);
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#if ARCH(I386) || ARCH(X86_64)
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T ret;
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asm(
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"fld1\n"
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"fpatan\n"
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: "=t"(ret)
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: "0"(value));
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return ret;
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#else
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return __builtin_atan(value);
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#endif
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}
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template<FloatingPoint T>
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constexpr T asin(T x)
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{
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CONSTEXPR_STATE(asin, x);
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if (x > 1 || x < -1)
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return NaN<T>;
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if (x > (T)0.5 || x < (T)-0.5)
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return 2 * atan<T>(x / (1 + sqrt<T>(1 - x * x)));
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T squared = x * x;
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T value = x;
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T i = x * squared;
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value += i * Details::product_odd<1>() / Details::product_even<2>() / 3;
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i *= squared;
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value += i * Details::product_odd<3>() / Details::product_even<4>() / 5;
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i *= squared;
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value += i * Details::product_odd<5>() / Details::product_even<6>() / 7;
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i *= squared;
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value += i * Details::product_odd<7>() / Details::product_even<8>() / 9;
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i *= squared;
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value += i * Details::product_odd<9>() / Details::product_even<10>() / 11;
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i *= squared;
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value += i * Details::product_odd<11>() / Details::product_even<12>() / 13;
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i *= squared;
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value += i * Details::product_odd<13>() / Details::product_even<14>() / 15;
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i *= squared;
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value += i * Details::product_odd<15>() / Details::product_even<16>() / 17;
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return value;
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}
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template<FloatingPoint T>
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constexpr T acos(T value)
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{
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CONSTEXPR_STATE(acos, value);
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// FIXME: I am naive
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return static_cast<T>(0.5) * Pi<T> - asin<T>(value);
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}
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template<FloatingPoint T>
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constexpr T atan2(T y, T x)
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{
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CONSTEXPR_STATE(atan2, y, x);
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#if ARCH(I386) || ARCH(X86_64)
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T ret;
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asm("fpatan"
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: "=t"(ret)
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: "0"(x), "u"(y)
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: "st(1)");
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return ret;
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#else
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return __builtin_atan2(y, x);
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#endif
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}
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}
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using Trigonometry::acos;
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using Trigonometry::asin;
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using Trigonometry::atan;
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using Trigonometry::atan2;
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using Trigonometry::cos;
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using Trigonometry::hypot;
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using Trigonometry::sin;
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using Trigonometry::sincos;
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using Trigonometry::tan;
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namespace Exponentials {
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template<FloatingPoint T>
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constexpr T log(T x)
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{
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CONSTEXPR_STATE(log, x);
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#if ARCH(I386) || ARCH(X86_64)
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T ret;
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asm(
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"fldln2\n"
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"fxch %%st(1)\n"
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"fyl2x\n"
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: "=t"(ret)
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: "0"(x));
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return ret;
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#else
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return __builtin_log(x);
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#endif
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}
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template<FloatingPoint T>
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constexpr T log2(T x)
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{
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CONSTEXPR_STATE(log2, x);
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#if ARCH(I386) || ARCH(X86_64)
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T ret;
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asm(
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"fld1\n"
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"fxch %%st(1)\n"
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"fyl2x\n"
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: "=t"(ret)
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: "0"(x));
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return ret;
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#else
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return __builtin_log2(x);
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#endif
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}
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template<FloatingPoint T>
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constexpr T log10(T x)
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{
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CONSTEXPR_STATE(log10, x);
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#if ARCH(I386) || ARCH(X86_64)
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T ret;
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asm(
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"fldlg2\n"
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"fxch %%st(1)\n"
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"fyl2x\n"
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: "=t"(ret)
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: "0"(x));
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return ret;
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#else
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return __builtin_log10(x);
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#endif
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}
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template<FloatingPoint T>
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constexpr T exp(T exponent)
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{
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CONSTEXPR_STATE(exp, exponent);
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#if ARCH(I386) || ARCH(X86_64)
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T res;
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asm("fldl2e\n"
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"fmulp\n"
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"fld1\n"
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"fld %%st(1)\n"
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"fprem\n"
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"f2xm1\n"
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"faddp\n"
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"fscale\n"
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"fstp %%st(1)"
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: "=t"(res)
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: "0"(exponent));
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return res;
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#else
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return __builtin_exp(exponent);
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#endif
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}
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template<FloatingPoint T>
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constexpr T exp2(T exponent)
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{
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CONSTEXPR_STATE(exp2, exponent);
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#if ARCH(I386) || ARCH(X86_64)
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T res;
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asm("fld1\n"
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"fld %%st(1)\n"
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"fprem\n"
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"f2xm1\n"
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"faddp\n"
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"fscale\n"
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"fstp %%st(1)"
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: "=t"(res)
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: "0"(exponent));
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return res;
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#else
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return __builtin_exp2(exponent);
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#endif
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}
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}
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using Exponentials::exp;
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using Exponentials::exp2;
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using Exponentials::log;
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using Exponentials::log10;
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using Exponentials::log2;
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namespace Hyperbolic {
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template<FloatingPoint T>
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constexpr T sinh(T x)
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{
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T exponentiated = exp<T>(x);
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if (x > 0)
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return (exponentiated * exponentiated - 1) / 2 / exponentiated;
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return (exponentiated - 1 / exponentiated) / 2;
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}
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template<FloatingPoint T>
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constexpr T cosh(T x)
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{
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CONSTEXPR_STATE(cosh, x);
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T exponentiated = exp(-x);
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if (x < 0)
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return (1 + exponentiated * exponentiated) / 2 / exponentiated;
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return (1 / exponentiated + exponentiated) / 2;
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}
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template<FloatingPoint T>
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constexpr T tanh(T x)
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{
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if (x > 0) {
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T exponentiated = exp<T>(2 * x);
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return (exponentiated - 1) / (exponentiated + 1);
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}
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T plusX = exp<T>(x);
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T minusX = 1 / plusX;
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return (plusX - minusX) / (plusX + minusX);
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}
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template<FloatingPoint T>
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constexpr T asinh(T x)
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{
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return log<T>(x + sqrt<T>(x * x + 1));
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}
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template<FloatingPoint T>
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constexpr T acosh(T x)
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{
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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);
|
|
#elif ARCH(AARCH64)
|
|
if constexpr (IsSigned<I>) {
|
|
if constexpr (sizeof(I) <= sizeof(i32)) {
|
|
i32 res;
|
|
if constexpr (IsSame<P, float>) {
|
|
asm("fcvtns %w0, %s1"
|
|
: "=r"(res)
|
|
: "w"(value));
|
|
} else if constexpr (IsSame<P, double>) {
|
|
asm("fcvtns %w0, %d1"
|
|
: "=r"(res)
|
|
: "w"(value));
|
|
} else if constexpr (IsSame<P, long double>) {
|
|
TODO();
|
|
}
|
|
return static_cast<I>(res);
|
|
}
|
|
// either long or long long aka i64
|
|
i64 res;
|
|
if constexpr (IsSame<P, float>) {
|
|
asm("fcvtns %0, %s1"
|
|
: "=r"(res)
|
|
: "w"(value));
|
|
} else if constexpr (IsSame<P, double>) {
|
|
asm("fcvtns %0, %d1"
|
|
: "=r"(res)
|
|
: "w"(value));
|
|
} else if constexpr (IsSame<P, long double>) {
|
|
TODO();
|
|
}
|
|
return static_cast<I>(res);
|
|
}
|
|
|
|
if constexpr (sizeof(I) <= sizeof(u32)) {
|
|
u32 res;
|
|
if constexpr (IsSame<P, float>) {
|
|
asm("fcvtnu %w0, %s1"
|
|
: "=r"(res)
|
|
: "w"(value));
|
|
} else if constexpr (IsSame<P, double>) {
|
|
asm("fcvtnu %w0, %d1"
|
|
: "=r"(res)
|
|
: "w"(value));
|
|
} else if constexpr (IsSame<P, long double>) {
|
|
TODO();
|
|
}
|
|
return static_cast<I>(res);
|
|
}
|
|
|
|
// either unsigned long or unsigned long long aka u64
|
|
u64 res;
|
|
if constexpr (IsSame<P, float>) {
|
|
asm("fcvtnu %0, %s1"
|
|
: "=r"(res)
|
|
: "w"(value));
|
|
} else if constexpr (IsSame<P, double>) {
|
|
asm("fcvtnu %0, %d1"
|
|
: "=r"(res)
|
|
: "w"(value));
|
|
} else if constexpr (IsSame<P, long double>) {
|
|
TODO();
|
|
}
|
|
return static_cast<I>(res);
|
|
#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));
|
|
}
|
|
|
|
template<FloatingPoint T>
|
|
constexpr T ceil(T num)
|
|
{
|
|
if (is_constant_evaluated()) {
|
|
if (num < NumericLimits<i64>::min() || num > NumericLimits<i64>::max())
|
|
return num;
|
|
return (static_cast<double>(static_cast<i64>(num)) == num)
|
|
? static_cast<i64>(num)
|
|
: static_cast<i64>(num) + ((num > 0) ? 1 : 0);
|
|
}
|
|
#if ARCH(AARCH64)
|
|
AARCH64_INSTRUCTION(frintp, num);
|
|
#else
|
|
return __builtin_ceil(num);
|
|
#endif
|
|
}
|
|
|
|
#undef CONSTEXPR_STATE
|
|
#undef AARCH64_INSTRUCTION
|
|
}
|
|
|
|
using AK::round_to;
|