/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-│
│vi: set et ft=c ts=8 tw=8 fenc=utf-8 :vi│
╚──────────────────────────────────────────────────────────────────────────────╝
│ │
│ Musl Libc │
│ Copyright © 2005-2020 Rich Felker, et al. │
│ │
│ Permission is hereby granted, free of charge, to any person obtaining │
│ a copy of this software and associated documentation files (the │
│ "Software"), to deal in the Software without restriction, including │
│ without limitation the rights to use, copy, modify, merge, publish, │
│ distribute, sublicense, and/or sell copies of the Software, and to │
│ permit persons to whom the Software is furnished to do so, subject to │
│ the following conditions: │
│ │
│ The above copyright notice and this permission notice shall be │
│ included in all copies or substantial portions of the Software. │
│ │
│ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │
│ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │
│ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │
│ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │
│ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │
│ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │
│ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │
│ │
╚─────────────────────────────────────────────────────────────────────────────*/
#include "libc/math.h"
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
#define ASUINT64(x) ((union {double f; uint64_t i;}){x}).i
#define ZEROINFNAN (0x7ff-0x3ff-52-1)
static inline int a_clz_64(uint64_t x)
{
#ifdef __GNUC__
if (!x) return 63;
return __builtin_clzll(x);
#else
uint32_t y;
int r;
if (x>>32) y=x>>32, r=0; else y=x, r=32;
if (y>>16) y>>=16; else r |= 16;
if (y>>8) y>>=8; else r |= 8;
if (y>>4) y>>=4; else r |= 4;
if (y>>2) y>>=2; else r |= 2;
return r | !(y>>1);
#endif
}
struct num { uint64_t m; int e; int sign; };
static struct num normalize(double x)
{
uint64_t ix = ASUINT64(x);
int e = ix>>52;
int sign = e & 0x800;
e &= 0x7ff;
if (!e) {
ix = ASUINT64(x*0x1p63);
e = ix>>52 & 0x7ff;
e = e ? e-63 : 0x800;
}
ix &= (1ull<<52)-1;
ix |= 1ull<<52;
ix <<= 1;
e -= 0x3ff + 52 + 1;
return (struct num){ix,e,sign};
}
static void mul(uint64_t *hi, uint64_t *lo, uint64_t x, uint64_t y)
{
uint64_t t1,t2,t3;
uint64_t xlo = (uint32_t)x, xhi = x>>32;
uint64_t ylo = (uint32_t)y, yhi = y>>32;
t1 = xlo*ylo;
t2 = xlo*yhi + xhi*ylo;
t3 = xhi*yhi;
*lo = t1 + (t2<<32);
*hi = t3 + (t2>>32) + (t1 > *lo);
}
/**
* Performs fused multiply add.
*
* @return `𝑥 * 𝑦 + 𝑧` rounded as one ternary operation
*/
double fma(double x, double y, double z)
{
#if defined(__x86_64__) && defined(__FMA__)
// Intel Haswell+ (c. 2013)
// AMD Piledriver+ (c. 2011)
asm("vfmadd132sd\t%1,%2,%0" : "+x"(x) : "x"(y), "x"(z));
return x;
#elif defined(__x86_64__) && defined(__FMA4__)
// AMD Bulldozer+ (c. 2011)
asm("vfmaddsd\t%3,%2,%1,%0" : "=x"(x) : "x"(x), "x"(y), "x"(z));
return x;
#elif defined(__aarch64__)
asm("fmadd\t%d0,%d1,%d2,%d3" : "=w"(x) : "w"(x), "w"(y), "w"(z));
return x;
#elif defined(__powerpc64__)
asm("fmadd\t%0,%1,%2,%3" : "=d"(x) : "d"(x), "d"(y), "d"(z));
return x;
#elif defined(__riscv) && __riscv_flen >= 64
asm("fmadd.d\t%0,%1,%2,%3" : "=f"(x) : "f"(x), "f"(y), "f"(z));
return x;
#elif defined(__s390x__)
asm("madbr\t%0,\t%1,\t%2" : "+f"(z) : "f"(x), "f"(y));
return z;
#else
/* normalize so top 10bits and last bit are 0 */
struct num nx, ny, nz;
nx = normalize(x);
ny = normalize(y);
nz = normalize(z);
if (nx.e >= ZEROINFNAN || ny.e >= ZEROINFNAN)
return x*y + z;
if (nz.e >= ZEROINFNAN) {
if (nz.e > ZEROINFNAN) /* z==0 */
return x*y + z;
return z;
}
/* mul: r = x*y */
uint64_t rhi, rlo, zhi, zlo;
mul(&rhi, &rlo, nx.m, ny.m);
/* either top 20 or 21 bits of rhi and last 2 bits of rlo are 0 */
/* align exponents */
int e = nx.e + ny.e;
int d = nz.e - e;
/* shift bits z<<=kz, r>>=kr, so kz+kr == d, set e = e+kr (== ez-kz) */
if (d > 0) {
if (d < 64) {
zlo = nz.m<<d;
zhi = nz.m>>64-d;
} else {
zlo = 0;
zhi = nz.m;
e = nz.e - 64;
d -= 64;
if (d == 0) {
} else if (d < 64) {
rlo = rhi<<64-d | rlo>>d | !!(rlo<<64-d);
rhi = rhi>>d;
} else {
rlo = 1;
rhi = 0;
}
}
} else {
zhi = 0;
d = -d;
if (d == 0) {
zlo = nz.m;
} else if (d < 64) {
zlo = nz.m>>d | !!(nz.m<<64-d);
} else {
zlo = 1;
}
}
/* add */
int sign = nx.sign^ny.sign;
int samesign = !(sign^nz.sign);
int nonzero = 1;
if (samesign) {
/* r += z */
rlo += zlo;
rhi += zhi + (rlo < zlo);
} else {
/* r -= z */
uint64_t t = rlo;
rlo -= zlo;
rhi = rhi - zhi - (t < rlo);
if (rhi>>63) {
rlo = -rlo;
rhi = -rhi-!!rlo;
sign = !sign;
}
nonzero = !!rhi;
}
/* set rhi to top 63bit of the result (last bit is sticky) */
if (nonzero) {
e += 64;
d = a_clz_64(rhi)-1;
/* note: d > 0 */
rhi = rhi<<d | rlo>>64-d | !!(rlo<<d);
} else if (rlo) {
d = a_clz_64(rlo)-1;
if (d < 0)
rhi = rlo>>1 | (rlo&1);
else
rhi = rlo<<d;
} else {
/* exact +-0 */
return x*y + z;
}
e -= d;
/* convert to double */
int64_t i = rhi; /* i is in [1<<62,(1<<63)-1] */
if (sign)
i = -i;
double r = i; /* |r| is in [0x1p62,0x1p63] */
if (e < -1022-62) {
/* result is subnormal before rounding */
if (e == -1022-63) {
double c = 0x1p63;
if (sign)
c = -c;
if (r == c) {
/* min normal after rounding, underflow depends
on arch behaviour which can be imitated by
a double to float conversion */
float fltmin = 0x0.ffffff8p-63*FLT_MIN * r;
return DBL_MIN/FLT_MIN * fltmin;
}
/* one bit is lost when scaled, add another top bit to
only round once at conversion if it is inexact */
if (rhi << 53) {
i = rhi>>1 | (rhi&1) | 1ull<<62;
if (sign)
i = -i;
r = i;
r = 2*r - c; /* remove top bit */
/* raise underflow portably, such that it
cannot be optimized away */
{
double_t tiny = DBL_MIN/FLT_MIN * r;
r += (double)(tiny*tiny) * (r-r);
}
}
} else {
/* only round once when scaled */
d = 10;
i = ( rhi>>d | !!(rhi<<64-d) ) << d;
if (sign)
i = -i;
r = i;
}
}
return scalbn(r, e);
#endif /* __x86_64__ */
}