diff options
Diffstat (limited to 'libc-top-half/musl/src/math/fma.c')
| -rw-r--r-- | libc-top-half/musl/src/math/fma.c | 183 |
1 files changed, 183 insertions, 0 deletions
diff --git a/libc-top-half/musl/src/math/fma.c b/libc-top-half/musl/src/math/fma.c new file mode 100644 index 0000000..0c6f90c --- /dev/null +++ b/libc-top-half/musl/src/math/fma.c @@ -0,0 +1,183 @@ +#include <stdint.h> +#include <float.h> +#include <math.h> +#include "atomic.h" + +#define ASUINT64(x) ((union {double f; uint64_t i;}){x}).i +#define ZEROINFNAN (0x7ff-0x3ff-52-1) + +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); +} + +double fma(double x, double y, double z) +{ + #pragma STDC FENV_ACCESS ON + + /* 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); +} |