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fixed.h
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fixed.h
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// Copyright © 2008-2024 Pioneer Developers. See AUTHORS.txt for details
// Licensed under the terms of the GPL v3. See licenses/GPL-3.txt
#ifndef _FIXED_H
#define _FIXED_H
#include <SDL_stdinc.h>
#include <cassert>
template <int FRAC_BITS>
class fixedf {
public:
static const int FRAC = FRAC_BITS;
static const Uint64 MASK = (Uint64(1UL) << FRAC_BITS) - 1;
fixedf() :
v(0) {}
// template <int bits>
// fixedf(fixedf<bits> f) { *this = f; }
constexpr fixedf(Sint64 raw) :
v(raw) {}
constexpr fixedf(Sint64 num, Sint64 denom) :
v((num << FRAC) / denom) {}
// ^^ this is fucking shit
fixedf Abs() const { return fixedf(v >= 0 ? v : -v); }
friend fixedf operator+(const fixedf &a, const Sint64 b) { return a + fixedf(b << FRAC); }
friend fixedf operator-(const fixedf &a, const Sint64 b) { return a - fixedf(b << FRAC); }
friend fixedf operator*(const fixedf &a, const Sint64 b) { return a * fixedf(b << FRAC); }
friend fixedf operator/(const fixedf &a, const Sint64 b) { return a / fixedf(b << FRAC); }
friend fixedf operator+(const Sint64 a, const fixedf &b) { return fixedf(a << FRAC) + b; }
friend fixedf operator-(const Sint64 a, const fixedf &b) { return fixedf(a << FRAC) - b; }
friend fixedf operator*(const Sint64 a, const fixedf &b) { return fixedf(a << FRAC) * b; }
friend fixedf operator/(const Sint64 a, const fixedf &b) { return fixedf(a << FRAC) / b; }
friend bool operator==(const fixedf &a, const Sint64 b) { return a == fixedf(b << FRAC); }
friend bool operator==(const Sint64 a, const fixedf &b) { return b == fixedf(a << FRAC); }
friend bool operator!=(const fixedf &a, const Sint64 b) { return a != fixedf(b << FRAC); }
friend bool operator!=(const Sint64 a, const fixedf &b) { return b != fixedf(a << FRAC); }
friend bool operator>=(const fixedf &a, const Sint64 b) { return a >= fixedf(b << FRAC); }
friend bool operator>=(const Sint64 a, const fixedf &b) { return b >= fixedf(a << FRAC); }
friend bool operator<=(const fixedf &a, const Sint64 b) { return a <= fixedf(b << FRAC); }
friend bool operator<=(const Sint64 a, const fixedf &b) { return b <= fixedf(a << FRAC); }
friend bool operator>(const fixedf &a, const Sint64 b) { return a > fixedf(b << FRAC); }
friend bool operator>(const Sint64 a, const fixedf &b) { return b > fixedf(a << FRAC); }
friend bool operator<(const fixedf &a, const Sint64 b) { return a < fixedf(b << FRAC); }
friend bool operator<(const Sint64 a, const fixedf &b) { return b < fixedf(a << FRAC); }
friend fixedf operator>>(const fixedf &a, const int b) { return fixedf(a.v >> b); }
friend fixedf operator<<(const fixedf &a, const int b) { return fixedf(a.v << b); }
fixedf &operator*=(const fixedf &a)
{
(*this) = (*this) * a;
return (*this);
}
fixedf &operator*=(const Sint64 a)
{
(*this) = (*this) * a;
return (*this);
}
fixedf &operator/=(const fixedf &a)
{
(*this) = (*this) / a;
return (*this);
}
fixedf &operator/=(const Sint64 a)
{
(*this) = (*this) / a;
return (*this);
}
fixedf &operator+=(const fixedf &a)
{
(*this) = (*this) + a;
return (*this);
}
fixedf &operator+=(const Sint64 a)
{
(*this) = (*this) + a;
return (*this);
}
fixedf &operator-=(const fixedf &a)
{
(*this) = (*this) - a;
return (*this);
}
fixedf &operator-=(const Sint64 a)
{
(*this) = (*this) - a;
return (*this);
}
fixedf &operator>>=(const int a)
{
v >>= a;
return (*this);
}
fixedf &operator<<=(const int a)
{
v <<= a;
return (*this);
}
friend fixedf operator-(const fixedf &a) { return fixedf(-a.v); }
friend fixedf operator+(const fixedf &a, const fixedf &b) { return fixedf(a.v + b.v); }
friend fixedf operator-(const fixedf &a, const fixedf &b) { return fixedf(a.v - b.v); }
friend fixedf operator*(const fixedf &a, const fixedf &b)
{
// 64*64 = (128bit>>FRAC) & ((1<<64)-1)
//return fixedf(a.v*b.v >> FRAC);
Sint64 hi = 0;
Uint64 a0, a1, b0, b1;
Uint64 lo = 0;
Uint64 oldlo;
int isneg = 0;
if (a.v < 0) {
a0 = (-a.v) & 0xffffffff;
a1 = (-a.v) >> 32;
isneg = !isneg;
} else {
a0 = a.v & 0xffffffff;
a1 = a.v >> 32;
}
if (b.v < 0) {
b0 = (-b.v) & 0xffffffff;
b1 = (-b.v) >> 32;
isneg = !isneg;
} else {
b0 = b.v & 0xffffffff;
b1 = b.v >> 32;
}
Uint64 x;
// a0 * b;
lo = a0 * b0;
oldlo = lo;
x = a0 * b1;
lo += x << 32;
if (lo < oldlo) hi++;
oldlo = lo;
hi += (x >> 32);
// a1 * b;
x = a1 * b0;
lo += x << 32;
if (lo < oldlo) hi++;
oldlo = lo;
hi += x >> 32;
hi += a1 * b1;
Sint64 out = (lo >> FRAC) + ((hi & MASK) << (64 - FRAC));
return isneg ? -out : out;
}
friend fixedf operator/(const fixedf &a, const fixedf &b)
{
// 128-bit divided by 64-bit, to make sure high bits are not lost
Sint64 quotient_hi = a.v >> (64 - FRAC);
Uint64 quotient_lo = a.v << FRAC;
Sint64 d = b.v;
int isneg = 0;
Sint64 remainder = 0;
if (d < 0) {
d = -d;
isneg = 1;
}
for (int i = 0; i < 128; i++) {
Uint64 sbit = (Uint64(1) << 63) & quotient_hi;
remainder <<= 1;
if (sbit) remainder |= 1;
// shift quotient left 1
{
quotient_hi <<= 1;
if (quotient_lo & (Uint64(1) << 63)) quotient_hi |= 1;
quotient_lo <<= 1;
}
if (remainder >= d) {
remainder -= d;
quotient_lo |= 1;
}
}
return (isneg ? -Sint64(quotient_lo) : quotient_lo);
}
friend bool operator==(const fixedf &a, const fixedf &b) { return a.v == b.v; }
friend bool operator!=(const fixedf &a, const fixedf &b) { return a.v != b.v; }
friend bool operator>(const fixedf &a, const fixedf &b) { return a.v > b.v; }
friend bool operator<(const fixedf &a, const fixedf &b) { return a.v < b.v; }
friend bool operator>=(const fixedf &a, const fixedf &b) { return a.v >= b.v; }
friend bool operator<=(const fixedf &a, const fixedf &b) { return a.v <= b.v; }
/* implicit operator float() bad */
inline int ToInt32() const { return int(v >> FRAC); }
inline Sint64 ToInt64() const { return v >> FRAC; }
inline float ToFloat() const { return v / float(Sint64(1) << FRAC); }
inline double ToDouble() const { return v / double(Sint64(1) << FRAC); }
static fixedf FromDouble(const double val) { return fixedf(Sint64(((val) * double(Sint64(1) << FRAC)))); }
template <int NEW_FRAC_BITS>
operator fixedf<NEW_FRAC_BITS>() const
{
int shift = NEW_FRAC_BITS - FRAC_BITS;
if (shift > 0)
return fixedf<NEW_FRAC_BITS>(v << shift);
else
return fixedf<NEW_FRAC_BITS>(v >> (-shift));
}
static fixedf SqrtOf(const fixedf &a)
{
/* only works on even-numbered fractional bits */
assert(!(FRAC & 1));
Uint64 root, remHi, remLo, testDiv, count;
root = 0;
remHi = 0;
remLo = a.v;
count = 32 + (FRAC >> 1) - 1;
do {
remHi = (remHi << 2) | (remLo >> 62);
remLo <<= 2;
root <<= 1;
testDiv = (root << 1) + 1;
if (remHi >= testDiv) {
remHi -= testDiv;
root++;
}
} while (count-- != 0);
return (fixedf(root));
}
static fixedf CubeRootOf(const fixedf &a)
{
/* NR method. XXX very bad initial estimate (we get there in
* the end... XXX */
fixedf x = a;
for (int i = 0; i < 48; i++)
x = fixedf(1, 3) * ((a / (x * x)) + 2 * x);
return x;
}
Sint64 v;
};
typedef fixedf<32> fixed;
#endif /* _FIXED_H */