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101 lines
3.1 KiB
C
101 lines
3.1 KiB
C
/* Compute x * y + z as ternary operation.
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Copyright (C) 2010-2019 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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Contributed by Jakub Jelinek <jakub@redhat.com>, 2010.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<http://www.gnu.org/licenses/>. */
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#include <float.h>
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#include <math.h>
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#include <fenv.h>
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#include <ieee754.h>
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#include <math-barriers.h>
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#include <libm-alias-double.h>
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/* This implementation uses rounding to odd to avoid problems with
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double rounding. See a paper by Boldo and Melquiond:
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http://www.lri.fr/~melquion/doc/08-tc.pdf */
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double
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__fma (double x, double y, double z)
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{
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if (__glibc_unlikely (!isfinite (x) || !isfinite (y)))
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return x * y + z;
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else if (__glibc_unlikely (!isfinite (z)))
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/* If z is Inf, but x and y are finite, the result should be z
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rather than NaN. */
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return (z + x) + y;
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/* Ensure correct sign of exact 0 + 0. */
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if (__glibc_unlikely ((x == 0 || y == 0) && z == 0))
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{
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x = math_opt_barrier (x);
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return x * y + z;
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}
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fenv_t env;
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feholdexcept (&env);
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fesetround (FE_TONEAREST);
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/* Multiplication m1 + m2 = x * y using Dekker's algorithm. */
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#define C ((1ULL << (LDBL_MANT_DIG + 1) / 2) + 1)
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long double x1 = (long double) x * C;
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long double y1 = (long double) y * C;
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long double m1 = (long double) x * y;
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x1 = (x - x1) + x1;
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y1 = (y - y1) + y1;
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long double x2 = x - x1;
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long double y2 = y - y1;
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long double m2 = (((x1 * y1 - m1) + x1 * y2) + x2 * y1) + x2 * y2;
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/* Addition a1 + a2 = z + m1 using Knuth's algorithm. */
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long double a1 = z + m1;
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long double t1 = a1 - z;
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long double t2 = a1 - t1;
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t1 = m1 - t1;
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t2 = z - t2;
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long double a2 = t1 + t2;
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/* Ensure the arithmetic is not scheduled after feclearexcept call. */
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math_force_eval (m2);
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math_force_eval (a2);
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feclearexcept (FE_INEXACT);
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/* If the result is an exact zero, ensure it has the correct sign. */
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if (a1 == 0 && m2 == 0)
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{
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feupdateenv (&env);
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/* Ensure that round-to-nearest value of z + m1 is not reused. */
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z = math_opt_barrier (z);
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return z + m1;
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}
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fesetround (FE_TOWARDZERO);
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/* Perform m2 + a2 addition with round to odd. */
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a2 = a2 + m2;
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/* Add that to a1 again using rounding to odd. */
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union ieee854_long_double u;
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u.d = a1 + a2;
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if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7fff)
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u.ieee.mantissa1 |= fetestexcept (FE_INEXACT) != 0;
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feupdateenv (&env);
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/* Add finally round to double precision. */
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return u.d;
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}
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#ifndef __fma
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libm_alias_double (__fma, fma)
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#endif
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