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Diffstat (limited to 'libm/src/s_fma.c')
| -rw-r--r-- | libm/src/s_fma.c | 202 |
1 files changed, 202 insertions, 0 deletions
diff --git a/libm/src/s_fma.c b/libm/src/s_fma.c new file mode 100644 index 0000000..1fcc26c --- /dev/null +++ b/libm/src/s_fma.c @@ -0,0 +1,202 @@ +/*- + * Copyright (c) 2005 David Schultz <das@FreeBSD.ORG> + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include <sys/cdefs.h> +/* __FBSDID("$FreeBSD: src/lib/msun/src/s_fma.c,v 1.4 2005/03/18 02:27:59 das Exp $"); */ + +#include <fenv.h> +#include <float.h> +#include <math.h> + +/* + * Fused multiply-add: Compute x * y + z with a single rounding error. + * + * We use scaling to avoid overflow/underflow, along with the + * canonical precision-doubling technique adapted from: + * + * Dekker, T. A Floating-Point Technique for Extending the + * Available Precision. Numer. Math. 18, 224-242 (1971). + * + * This algorithm is sensitive to the rounding precision. FPUs such + * as the i387 must be set in double-precision mode if variables are + * to be stored in FP registers in order to avoid incorrect results. + * This is the default on FreeBSD, but not on many other systems. + * + * Hardware instructions should be used on architectures that support it, + * since this implementation will likely be several times slower. + */ +#if LDBL_MANT_DIG != 113 +double +fma(double x, double y, double z) +{ + static const double split = 0x1p27 + 1.0; + double xs, ys, zs; + double c, cc, hx, hy, p, q, tx, ty; + double r, rr, s; + int oround; + int ex, ey, ez; + int spread; + + if (z == 0.0) + return (x * y); + if (x == 0.0 || y == 0.0) + return (x * y + z); + + /* Results of frexp() are undefined for these cases. */ + if (!isfinite(x) || !isfinite(y) || !isfinite(z)) + return (x * y + z); + + xs = frexp(x, &ex); + ys = frexp(y, &ey); + zs = frexp(z, &ez); + oround = fegetround(); + spread = ex + ey - ez; + + /* + * If x * y and z are many orders of magnitude apart, the scaling + * will overflow, so we handle these cases specially. Rounding + * modes other than FE_TONEAREST are painful. + */ + if (spread > DBL_MANT_DIG * 2) { + fenv_t env; + feraiseexcept(FE_INEXACT); + switch(oround) { + case FE_TONEAREST: + return (x * y); + case FE_TOWARDZERO: + if (x > 0.0 ^ y < 0.0 ^ z < 0.0) + return (x * y); + feholdexcept(&env); + r = x * y; + if (!fetestexcept(FE_INEXACT)) + r = nextafter(r, 0); + feupdateenv(&env); + return (r); + case FE_DOWNWARD: + if (z > 0.0) + return (x * y); + feholdexcept(&env); + r = x * y; + if (!fetestexcept(FE_INEXACT)) + r = nextafter(r, -INFINITY); + feupdateenv(&env); + return (r); + default: /* FE_UPWARD */ + if (z < 0.0) + return (x * y); + feholdexcept(&env); + r = x * y; + if (!fetestexcept(FE_INEXACT)) + r = nextafter(r, INFINITY); + feupdateenv(&env); + return (r); + } + } + if (spread < -DBL_MANT_DIG) { + feraiseexcept(FE_INEXACT); + if (!isnormal(z)) + feraiseexcept(FE_UNDERFLOW); + switch (oround) { + case FE_TONEAREST: + return (z); + case FE_TOWARDZERO: + if (x > 0.0 ^ y < 0.0 ^ z < 0.0) + return (z); + else + return (nextafter(z, 0)); + case FE_DOWNWARD: + if (x > 0.0 ^ y < 0.0) + return (z); + else + return (nextafter(z, -INFINITY)); + default: /* FE_UPWARD */ + if (x > 0.0 ^ y < 0.0) + return (nextafter(z, INFINITY)); + else + return (z); + } + } + + /* + * Use Dekker's algorithm to perform the multiplication and + * subsequent addition in twice the machine precision. + * Arrange so that x * y = c + cc, and x * y + z = r + rr. + */ + fesetround(FE_TONEAREST); + + p = xs * split; + hx = xs - p; + hx += p; + tx = xs - hx; + + p = ys * split; + hy = ys - p; + hy += p; + ty = ys - hy; + + p = hx * hy; + q = hx * ty + tx * hy; + c = p + q; + cc = p - c + q + tx * ty; + + zs = ldexp(zs, -spread); + r = c + zs; + s = r - c; + rr = (c - (r - s)) + (zs - s) + cc; + + spread = ex + ey; + if (spread + ilogb(r) > -1023) { + fesetround(oround); + r = r + rr; + } else { + /* + * The result is subnormal, so we round before scaling to + * avoid double rounding. + */ + p = ldexp(copysign(0x1p-1022, r), -spread); + c = r + p; + s = c - r; + cc = (r - (c - s)) + (p - s) + rr; + fesetround(oround); + r = (c + cc) - p; + } + return (ldexp(r, spread)); +} +#else /* LDBL_MANT_DIG == 113 */ +/* + * 113 bits of precision is more than twice the precision of a double, + * so it is enough to represent the intermediate product exactly. + */ +double +fma(double x, double y, double z) +{ + return ((long double)x * y + z); +} +#endif /* LDBL_MANT_DIG != 113 */ + +#if (LDBL_MANT_DIG == 53) +__weak_reference(fma, fmal); +#endif |