diff options
| -rw-r--r-- | src/math/fma.c | 146 | ||||
| -rw-r--r-- | src/math/fmal.c | 8 |
2 files changed, 143 insertions, 11 deletions
diff --git a/src/math/fma.c b/src/math/fma.c index f44ecda7..87d450c7 100644 --- a/src/math/fma.c +++ b/src/math/fma.c @@ -1,3 +1,137 @@ +#include <fenv.h> +#include "libm.h" + +#if LDBL_MANT_DIG==64 && LDBL_MAX_EXP==16384 +union ld80 { + long double x; + struct { + uint64_t m; + uint16_t e : 15; + uint16_t s : 1; + uint16_t pad; + } bits; +}; + +/* exact add, assumes exponent_x >= exponent_y */ +static void add(long double *hi, long double *lo, long double x, long double y) +{ + long double r; + + r = x + y; + *hi = r; + r -= x; + *lo = y - r; +} + +/* exact mul, assumes no over/underflow */ +static void mul(long double *hi, long double *lo, long double x, long double y) +{ + static const long double c = 1.0 + 0x1p32L; + long double cx, xh, xl, cy, yh, yl; + + cx = c*x; + xh = (x - cx) + cx; + xl = x - xh; + cy = c*y; + yh = (y - cy) + cy; + yl = y - yh; + *hi = x*y; + *lo = (xh*yh - *hi) + xh*yl + xl*yh + xl*yl; +} + +/* +assume (long double)(hi+lo) == hi +return an adjusted hi so that rounding it to double is correct +*/ +static long double adjust(long double hi, long double lo) +{ + union ld80 uhi, ulo; + + if (lo == 0) + return hi; + uhi.x = hi; + if (uhi.bits.m & 0x3ff) + return hi; + ulo.x = lo; + if (uhi.bits.s == ulo.bits.s) + uhi.bits.m++; + else + uhi.bits.m--; + return uhi.x; +} + +static long double dadd(long double x, long double y) +{ + add(&x, &y, x, y); + return adjust(x, y); +} + +static long double dmul(long double x, long double y) +{ + mul(&x, &y, x, y); + return adjust(x, y); +} + +static int getexp(long double x) +{ + union ld80 u; + u.x = x; + return u.bits.e; +} + +double fma(double x, double y, double z) +{ + long double hi, lo1, lo2, xy; + int round, ez, exy; + + /* handle +-inf,nan */ + if (!isfinite(x) || !isfinite(y)) + return x*y + z; + if (!isfinite(z)) + return z; + /* handle +-0 */ + if (x == 0.0 || y == 0.0) + return x*y + z; + round = fegetround(); + if (z == 0.0) { + if (round == FE_TONEAREST) + return dmul(x, y); + return x*y; + } + + /* exact mul and add require nearest rounding */ + /* spurious inexact exceptions may be raised */ + fesetround(FE_TONEAREST); + mul(&xy, &lo1, x, y); + exy = getexp(xy); + ez = getexp(z); + if (ez > exy) { + add(&hi, &lo2, z, xy); + } else if (ez > exy - 12) { + add(&hi, &lo2, xy, z); + if (hi == 0) { + fesetround(round); + /* make sure that the sign of 0 is correct */ + return (xy + z) + lo1; + } + } else { + /* + ez <= exy - 12 + the 12 extra bits (1guard, 11round+sticky) are needed so with + lo = dadd(lo1, lo2) + elo <= ehi - 11, and we use the last 10 bits in adjust so + dadd(hi, lo) + gives correct result when rounded to double + */ + hi = xy; + lo2 = z; + } + fesetround(round); + if (round == FE_TONEAREST) + return dadd(hi, dadd(lo1, lo2)); + return hi + (lo1 + lo2); +} +#else /* origin: FreeBSD /usr/src/lib/msun/src/s_fma.c */ /*- * Copyright (c) 2005-2011 David Schultz <das@FreeBSD.ORG> @@ -25,9 +159,6 @@ * SUCH DAMAGE. */ -#include <fenv.h> -#include "libm.h" - /* * A struct dd represents a floating-point number with twice the precision * of a double. We maintain the invariant that "hi" stores the 53 high-order @@ -178,14 +309,14 @@ double fma(double x, double y, double z) * return values here are crucial in handling special cases involving * infinities, NaNs, overflows, and signed zeroes correctly. */ - if (x == 0.0 || y == 0.0) - return (x * y + z); - if (z == 0.0) - return (x * y); if (!isfinite(x) || !isfinite(y)) return (x * y + z); if (!isfinite(z)) return (z); + if (x == 0.0 || y == 0.0) + return (x * y + z); + if (z == 0.0) + return (x * y); xs = frexp(x, &ex); ys = frexp(y, &ey); @@ -278,3 +409,4 @@ double fma(double x, double y, double z) else return (add_and_denormalize(r.hi, adj, spread)); } +#endif diff --git a/src/math/fmal.c b/src/math/fmal.c index 3944c292..cbaf46eb 100644 --- a/src/math/fmal.c +++ b/src/math/fmal.c @@ -173,14 +173,14 @@ long double fmal(long double x, long double y, long double z) * return values here are crucial in handling special cases involving * infinities, NaNs, overflows, and signed zeroes correctly. */ - if (x == 0.0 || y == 0.0) - return (x * y + z); - if (z == 0.0) - return (x * y); if (!isfinite(x) || !isfinite(y)) return (x * y + z); if (!isfinite(z)) return (z); + if (x == 0.0 || y == 0.0) + return (x * y + z); + if (z == 0.0) + return (x * y); xs = frexpl(x, &ex); ys = frexpl(y, &ey); |