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Diffstat (limited to 'libm/src/s_fma.c')
| -rw-r--r-- | libm/src/s_fma.c | 202 |
1 files changed, 0 insertions, 202 deletions
diff --git a/libm/src/s_fma.c b/libm/src/s_fma.c deleted file mode 100644 index 1fcc26c..0000000 --- a/libm/src/s_fma.c +++ /dev/null @@ -1,202 +0,0 @@ -/*- - * 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 |