ladybird/AK/Math.h

/*
 * 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/NumericLimits.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;
template<FloatingPoint T>
constexpr T Sqrt2 = 1.414213562373095048801688724209698079L;
template<FloatingPoint T>
constexpr T Sqrt1_2 = 0.707106781186547524400844362104849039L;

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); \
    }

#define AARCH64_INSTRUCTION(instruction, arg) \
    if constexpr (IsSame<T, long double>)     \
        TODO();                               \
    if constexpr (IsSame<T, double>) {        \
        double res;                           \
        asm(#instruction " %d0, %d1"          \
            : "=w"(res)                       \
            : "w"(arg));                      \
        return res;                           \
    }                                         \
    if constexpr (IsSame<T, float>) {         \
        float res;                            \
        asm(#instruction " %s0, %s1"          \
            : "=w"(res)                       \
            : "w"(arg));                      \
        return res;                           \
    }

namespace Division {
template<FloatingPoint T>
constexpr T fmod(T x, T y)
{
    CONSTEXPR_STATE(fmod, x, y);

#if 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
#    if defined(AK_OS_SERENITY)
    // TODO: Add implementation for this function.
    TODO();
#    endif
    return __builtin_fmod(x, y);
#endif
}
template<FloatingPoint T>
constexpr T remainder(T x, T y)
{
    CONSTEXPR_STATE(remainder, x, y);

#if 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
#    if defined(AK_OS_SERENITY)
    // TODO: Add implementation for this function.
    TODO();
#    endif
    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(X86_64)
    if constexpr (IsSame<T, float>) {
        float res;
        asm("sqrtss %1, %0"
            : "=x"(res)
            : "x"(x));
        return res;
    }
    if constexpr (IsSame<T, double>) {
        double res;
        asm("sqrtsd %1, %0"
            : "=x"(res)
            : "x"(x));
        return res;
    }
    T res;
    asm("fsqrt"
        : "=t"(res)
        : "0"(x));
    return res;
#elif ARCH(AARCH64)
    AARCH64_INSTRUCTION(fsqrt, x);
#else
    return __builtin_sqrt(x);
#endif
}

template<FloatingPoint T>
constexpr T rsqrt(T x)
{
#if ARCH(AARCH64)
    AARCH64_INSTRUCTION(frsqrte, x);
#elif ARCH(X86_64)
    if constexpr (IsSame<T, float>) {
        float res;
        asm("rsqrtss %1, %0"
            : "=x"(res)
            : "x"(x));
        return res;
    }
#endif
    return (T)1. / sqrt(x);
}

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(X86_64)
    asm(
        "fabs"
        : "+t"(x));
    return x;
#elif ARCH(AARCH64)
    AARCH64_INSTRUCTION(fabs, 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(X86_64)
    T ret;
    asm(
        "fsin"
        : "=t"(ret)
        : "0"(angle));
    return ret;
#else
#    if defined(AK_OS_SERENITY)
    // FIXME: This is a very naive implementation, and is only valid for small x.
    //        Probably a good idea to use a better algorithm in the future, such as a taylor approximation.
    return angle;
#    else
    return __builtin_sin(angle);
#    endif
#endif
}

template<FloatingPoint T>
constexpr T cos(T angle)
{
    CONSTEXPR_STATE(cos, angle);

#if ARCH(X86_64)
    T ret;
    asm(
        "fcos"
        : "=t"(ret)
        : "0"(angle));
    return ret;
#else
#    if defined(AK_OS_SERENITY)
    // FIXME: This is a very naive implementation, and is only valid for small x.
    //        Probably a good idea to use a better algorithm in the future, such as a taylor approximation.
    return 1 - ((angle * angle) / 2);
#    else
    return __builtin_cos(angle);
#    endif
#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(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(X86_64)
    T ret, one;
    asm(
        "fptan"
        : "=t"(one), "=u"(ret)
        : "0"(angle));

    return ret;
#else
#    if defined(AK_OS_SERENITY)
    // FIXME: This is a very naive implementation, and is only valid for small x.
    //        Probably a good idea to use a better algorithm in the future, such as a taylor approximation.
    return angle;
#    else
    return __builtin_tan(angle);
#    endif
#endif
}

template<FloatingPoint T>
constexpr T atan(T value)
{
    CONSTEXPR_STATE(atan, value);

#if ARCH(X86_64)
    T ret;
    asm(
        "fld1\n"
        "fpatan\n"
        : "=t"(ret)
        : "0"(value));
    return ret;
#else
#    if defined(AK_OS_SERENITY)
    // TODO: Add implementation for this function.
    TODO();
#    endif
    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(X86_64)
    T ret;
    asm("fpatan"
        : "=t"(ret)
        : "0"(x), "u"(y)
        : "st(1)");
    return ret;
#else
#    if defined(AK_OS_SERENITY)
    // TODO: Add implementation for this function.
    TODO();
#    endif
    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(X86_64)
    T ret;
    asm(
        "fldln2\n"
        "fxch %%st(1)\n"
        "fyl2x\n"
        : "=t"(ret)
        : "0"(x));
    return ret;
#else
#    if defined(AK_OS_SERENITY)
    // TODO: Add implementation for this function.
    TODO();
#    endif
    return __builtin_log(x);
#endif
}

template<FloatingPoint T>
constexpr T log2(T x)
{
    CONSTEXPR_STATE(log2, x);

#if ARCH(X86_64)
    T ret;
    asm(
        "fld1\n"
        "fxch %%st(1)\n"
        "fyl2x\n"
        : "=t"(ret)
        : "0"(x));
    return ret;
#else
#    if defined(AK_OS_SERENITY)
    // TODO: Add implementation for this function.
    TODO();
#    endif
    return __builtin_log2(x);
#endif
}

template<FloatingPoint T>
constexpr T log10(T x)
{
    CONSTEXPR_STATE(log10, x);

#if ARCH(X86_64)
    T ret;
    asm(
        "fldlg2\n"
        "fxch %%st(1)\n"
        "fyl2x\n"
        : "=t"(ret)
        : "0"(x));
    return ret;
#else
#    if defined(AK_OS_SERENITY)
    // TODO: Add implementation for this function.
    TODO();
#    endif
    return __builtin_log10(x);
#endif
}

template<FloatingPoint T>
constexpr T exp(T exponent)
{
    CONSTEXPR_STATE(exp, exponent);

#if 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
#    if defined(AK_OS_SERENITY)
    // TODO: Add implementation for this function.
    TODO();
#    endif
    return __builtin_exp(exponent);
#endif
}

template<FloatingPoint T>
constexpr T exp2(T exponent)
{
    CONSTEXPR_STATE(exp2, exponent);

#if 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
#    if defined(AK_OS_SERENITY)
    // TODO: Add implementation for this function.
    TODO();
#    endif
    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(X86_64)
template<Integral I>
ALWAYS_INLINE I round_to(long double value)
{
    // 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);
}

template<Integral I>
ALWAYS_INLINE I round_to(float value)
{
    // FIXME: round_to<u64> might will cause issues, aka the indefinite value being set,
    //        if the value surpasses the i64 limit, even if the result could fit into an u64
    //        To solve this we would either need to detect that value or do a range check and
    //        then do a more specialized conversion, which might include a division (which is expensive)
    if constexpr (sizeof(I) == sizeof(i64) || IsSame<I, u32>) {
        i64 ret;
        asm("cvtss2si %1, %0"
            : "=r"(ret)
            : "xm"(value));
        return static_cast<I>(ret);
    }
    i32 ret;
    asm("cvtss2si %1, %0"
        : "=r"(ret)
        : "xm"(value));
    return static_cast<I>(ret);
}

template<Integral I>
ALWAYS_INLINE I round_to(double value)
{
    // FIXME: round_to<u64> might will cause issues, aka the indefinite value being set,
    //        if the value surpasses the i64 limit, even if the result could fit into an u64
    //        To solve this we would either need to detect that value or do a range check and
    //        then do a more specialized conversion, which might include a division (which is expensive)
    if constexpr (sizeof(I) == sizeof(i64) || IsSame<I, u32>) {
        i64 ret;
        asm("cvtsd2si %1, %0"
            : "=r"(ret)
            : "xm"(value));
        return static_cast<I>(ret);
    }
    i32 ret;
    asm("cvtsd2si %1, %0"
        : "=r"(ret)
        : "xm"(value));
    return static_cast<I>(ret);
}

#elif ARCH(AARCH64)
template<Signed I>
ALWAYS_INLINE I round_to(float value)
{
    if constexpr (sizeof(I) <= sizeof(u32)) {
        i32 res;
        asm("fcvtns %w0, %s1"
            : "=r"(res)
            : "w"(value));
        return static_cast<I>(res);
    }
    i64 res;
    asm("fcvtns %0, %s1"
        : "=r"(res)
        : "w"(value));
    return static_cast<I>(res);
}

template<Signed I>
ALWAYS_INLINE I round_to(double value)
{
    if constexpr (sizeof(I) <= sizeof(u32)) {
        i32 res;
        asm("fcvtns %w0, %d1"
            : "=r"(res)
            : "w"(value));
        return static_cast<I>(res);
    }
    i64 res;
    asm("fcvtns %0, %d1"
        : "=r"(res)
        : "w"(value));
    return static_cast<I>(res);
}

template<Unsigned U>
ALWAYS_INLINE U round_to(float value)
{
    if constexpr (sizeof(U) <= sizeof(u32)) {
        u32 res;
        asm("fcvtnu %w0, %s1"
            : "=r"(res)
            : "w"(value));
        return static_cast<U>(res);
    }
    i64 res;
    asm("fcvtnu %0, %s1"
        : "=r"(res)
        : "w"(value));
    return static_cast<U>(res);
}

template<Unsigned U>
ALWAYS_INLINE U round_to(double value)
{
    if constexpr (sizeof(U) <= sizeof(u32)) {
        u32 res;
        asm("fcvtns %w0, %d1"
            : "=r"(res)
            : "w"(value));
        return static_cast<U>(res);
    }
    i64 res;
    asm("fcvtns %0, %d1"
        : "=r"(res)
        : "w"(value));
    return static_cast<U>(res);
}

#else
template<Integral I, FloatingPoint P>
ALWAYS_INLINE I round_to(P value)
{
    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

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<T>(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
}

template<FloatingPoint T>
constexpr T floor(T num)
{
    if (is_constant_evaluated()) {
        if (num < NumericLimits<i64>::min() || num > NumericLimits<i64>::max())
            return num;
        return (static_cast<T>(static_cast<i64>(num)) == num)
            ? static_cast<i64>(num)
            : static_cast<i64>(num) - ((num > 0) ? 0 : 1);
    }
#if ARCH(AARCH64)
    AARCH64_INSTRUCTION(frintm, num);
#else
    return __builtin_floor(num);
#endif
}

template<FloatingPoint T>
constexpr T round(T x)
{
    CONSTEXPR_STATE(round, x);
    // Note: This is break-tie-away-from-zero, so not the hw's understanding of
    //       "nearest", which would be towards even.
    if (x == 0.)
        return x;
    if (x > 0.)
        return floor(x + .5);
    return ceil(x - .5);
}

#undef CONSTEXPR_STATE
#undef AARCH64_INSTRUCTION
}

#if USING_AK_GLOBALLY
using AK::round_to;
#endif