mirror of git://sourceware.org/git/glibc.git
Merge common usage of mul_split function
A number of files share identical code for the mul_split function. This moves the duplicated function mul_split into its own header, and refactors the fma usage into a single selection macro. Likewise, mul_split when used by a long double implementation is renamed mul_splitl for clarity.
This commit is contained in:
Paul E. Murphy
parent
01ee387015
commit
4482ff226e
24
ChangeLog
24
ChangeLog
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@ -1,3 +1,27 @@
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2016-08-19 Paul E. Murphy <murphyp@linux.vnet.ibm.com>
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* sysdeps/ieee754/ldbl-128/gamma_productl.c:
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(mul_split) Remove, rename as mul_splitl, remove
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redundant float.h include, and include via mul_splitl.h
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* sysdeps/ieee754/ldbl-128/lgamma_productl.c: Likewise.
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* sysdeps/ieee754/ldbl-128/x2y2m1l.c: Likewise.
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* sysdeps/ieee754/ldbl-96/gamma_product.c: Likewise.
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* sysdeps/ieee754/ldbl-96/lgamma_product.c: Likewise.
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* sysdeps/ieee754/ldbl-96/x2y2m1.c: Likewise.
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* math/mul_splitl.h: New file.
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* sysdeps/ieee754/dbl-64/gamma_product.c (mul_split):
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Move into mul_split.h, and remove redundant float.h include.
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* sysdeps/ieee754/dbl-64/lgamma_product.c: Likewise.
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* sysdeps/ieee754/dbl-64/x2y2m1.c: Likewise.
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* sysdeps/ieee754/ldbl-128ibm/s_fmal.c: Likewise.
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* sysdeps/ieee754/ldbl-128ibm/x2y2m1.c: Likewise.
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* math/mul_split.h: New file.
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2016-08-19 Paul E. Murphy <murphyp@linux.vnet.ibm.com>
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* math/Makefile (libm-gen-calls): Move
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@ -0,0 +1,50 @@
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/* Compute full X * Y for double type.
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Copyright (C) 2013-2016 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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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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#ifndef _MUL_SPLIT_H
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#define _MUL_SPLIT_H
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#include <float.h>
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/* Calculate X * Y exactly and store the result in *HI + *LO. It is
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given that the values are small enough that no overflow occurs and
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large enough (or zero) that no underflow occurs. */
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static void
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mul_split (double *hi, double *lo, double x, double y)
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{
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#ifdef __FP_FAST_FMA
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/* Fast built-in fused multiply-add. */
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*hi = x * y;
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*lo = __builtin_fma (x, y, -*hi);
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#else
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/* Apply Dekker's algorithm. */
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*hi = x * y;
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# define C ((1 << (DBL_MANT_DIG + 1) / 2) + 1)
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double x1 = x * C;
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double y1 = y * C;
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# undef C
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x1 = (x - x1) + x1;
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y1 = (y - y1) + y1;
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double x2 = x - x1;
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double y2 = y - y1;
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*lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2;
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#endif
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}
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#endif /* _MUL_SPLIT_H */
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@ -0,0 +1,50 @@
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/* Compute full X * Y for long double type.
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Copyright (C) 2013-2016 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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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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#ifndef _MUL_SPLITL_H
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#define _MUL_SPLITL_H
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#include <float.h>
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/* Calculate X * Y exactly and store the result in *HI + *LO. It is
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given that the values are small enough that no overflow occurs and
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large enough (or zero) that no underflow occurs. */
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static inline void
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mul_splitl (long double *hi, long double *lo, long double x, long double y)
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{
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#ifdef __FP_FAST_FMAL
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/* Fast built-in fused multiply-add. */
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*hi = x * y;
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*lo = __builtin_fmal (x, y, -*hi);
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#else
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/* Apply Dekker's algorithm. */
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*hi = x * y;
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# define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1)
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long double x1 = x * C;
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long double y1 = y * C;
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# undef C
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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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*lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2;
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#endif
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}
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#endif /* _MUL_SPLITL_H */
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@ -18,37 +18,7 @@
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#include <math.h>
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#include <math_private.h>
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#include <float.h>
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/* Calculate X * Y exactly and store the result in *HI + *LO. It is
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given that the values are small enough that no overflow occurs and
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large enough (or zero) that no underflow occurs. */
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static void
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mul_split (double *hi, double *lo, double x, double y)
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{
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#ifdef __FP_FAST_FMA
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/* Fast built-in fused multiply-add. */
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*hi = x * y;
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*lo = __builtin_fma (x, y, -*hi);
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#elif defined FP_FAST_FMA
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/* Fast library fused multiply-add, compiler before GCC 4.6. */
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*hi = x * y;
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*lo = __fma (x, y, -*hi);
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#else
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/* Apply Dekker's algorithm. */
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*hi = x * y;
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# define C ((1 << (DBL_MANT_DIG + 1) / 2) + 1)
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double x1 = x * C;
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double y1 = y * C;
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# undef C
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x1 = (x - x1) + x1;
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y1 = (y - y1) + y1;
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double x2 = x - x1;
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double y2 = y - y1;
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*lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2;
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#endif
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}
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#include <mul_split.h>
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/* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N
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- 1, in the form R * (1 + *EPS) where the return value R is an
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@ -18,37 +18,7 @@
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#include <math.h>
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#include <math_private.h>
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#include <float.h>
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/* Calculate X * Y exactly and store the result in *HI + *LO. It is
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given that the values are small enough that no overflow occurs and
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large enough (or zero) that no underflow occurs. */
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static void
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mul_split (double *hi, double *lo, double x, double y)
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{
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#ifdef __FP_FAST_FMA
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/* Fast built-in fused multiply-add. */
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*hi = x * y;
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*lo = __builtin_fma (x, y, -*hi);
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#elif defined FP_FAST_FMA
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/* Fast library fused multiply-add, compiler before GCC 4.6. */
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*hi = x * y;
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*lo = __fma (x, y, -*hi);
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#else
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/* Apply Dekker's algorithm. */
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*hi = x * y;
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# define C ((1 << (DBL_MANT_DIG + 1) / 2) + 1)
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double x1 = x * C;
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double y1 = y * C;
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# undef C
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x1 = (x - x1) + x1;
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y1 = (y - y1) + y1;
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double x2 = x - x1;
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double y2 = y - y1;
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*lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2;
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#endif
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}
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#include <mul_split.h>
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/* Compute the product of 1 + (T / (X + X_EPS)), 1 + (T / (X + X_EPS +
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1)), ..., 1 + (T / (X + X_EPS + N - 1)), minus 1. X is such that
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@ -18,7 +18,7 @@
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#include <math.h>
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#include <math_private.h>
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#include <float.h>
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#include <mul_split.h>
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#include <stdlib.h>
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/* Calculate X + Y exactly and store the result in *HI + *LO. It is
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@ -33,36 +33,6 @@ add_split (double *hi, double *lo, double x, double y)
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*lo = (x - *hi) + y;
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}
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/* Calculate X * Y exactly and store the result in *HI + *LO. It is
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given that the values are small enough that no overflow occurs and
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large enough (or zero) that no underflow occurs. */
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static void
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mul_split (double *hi, double *lo, double x, double y)
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{
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#ifdef __FP_FAST_FMA
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/* Fast built-in fused multiply-add. */
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*hi = x * y;
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*lo = __builtin_fma (x, y, -*hi);
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#elif defined FP_FAST_FMA
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/* Fast library fused multiply-add, compiler before GCC 4.6. */
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*hi = x * y;
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*lo = __fma (x, y, -*hi);
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#else
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/* Apply Dekker's algorithm. */
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*hi = x * y;
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# define C ((1 << (DBL_MANT_DIG + 1) / 2) + 1)
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double x1 = x * C;
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double y1 = y * C;
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# undef C
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x1 = (x - x1) + x1;
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y1 = (y - y1) + y1;
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double x2 = x - x1;
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double y2 = y - y1;
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*lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2;
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#endif
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}
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/* Compare absolute values of floating-point values pointed to by P
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and Q for qsort. */
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@ -18,37 +18,7 @@
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#include <math.h>
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#include <math_private.h>
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#include <float.h>
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/* Calculate X * Y exactly and store the result in *HI + *LO. It is
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given that the values are small enough that no overflow occurs and
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large enough (or zero) that no underflow occurs. */
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static inline void
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mul_split (long double *hi, long double *lo, long double x, long double y)
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{
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#ifdef __FP_FAST_FMAL
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/* Fast built-in fused multiply-add. */
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*hi = x * y;
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*lo = __builtin_fmal (x, y, -*hi);
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#elif defined FP_FAST_FMAL
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/* Fast library fused multiply-add, compiler before GCC 4.6. */
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*hi = x * y;
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*lo = __fmal (x, y, -*hi);
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#else
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/* Apply Dekker's algorithm. */
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*hi = x * y;
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# define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1)
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long double x1 = x * C;
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long double y1 = y * C;
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# undef C
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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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*lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2;
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#endif
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}
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#include <mul_splitl.h>
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/* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N
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- 1, in the form R * (1 + *EPS) where the return value R is an
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@ -68,7 +38,7 @@ __gamma_productl (long double x, long double x_eps, int n, long double *eps)
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{
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*eps += x_eps / (x + i);
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long double lo;
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mul_split (&ret, &lo, ret, x + i);
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mul_splitl (&ret, &lo, ret, x + i);
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*eps += lo / ret;
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}
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return ret;
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@ -18,37 +18,7 @@
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#include <math.h>
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#include <math_private.h>
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#include <float.h>
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/* Calculate X * Y exactly and store the result in *HI + *LO. It is
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given that the values are small enough that no overflow occurs and
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large enough (or zero) that no underflow occurs. */
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static void
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mul_split (long double *hi, long double *lo, long double x, long double y)
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{
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#ifdef __FP_FAST_FMAL
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/* Fast built-in fused multiply-add. */
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*hi = x * y;
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*lo = __builtin_fmal (x, y, -*hi);
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#elif defined FP_FAST_FMAL
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/* Fast library fused multiply-add, compiler before GCC 4.6. */
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*hi = x * y;
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*lo = __fmal (x, y, -*hi);
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#else
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/* Apply Dekker's algorithm. */
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*hi = x * y;
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# define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1)
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long double x1 = x * C;
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long double y1 = y * C;
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# undef C
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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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*lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2;
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#endif
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}
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#include <mul_splitl.h>
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/* Compute the product of 1 + (T / (X + X_EPS)), 1 + (T / (X + X_EPS +
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1)), ..., 1 + (T / (X + X_EPS + N - 1)), minus 1. X is such that
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@ -65,11 +35,11 @@ __lgamma_productl (long double t, long double x, long double x_eps, int n)
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long double xi = x + i;
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long double quot = t / xi;
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long double mhi, mlo;
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mul_split (&mhi, &mlo, quot, xi);
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mul_splitl (&mhi, &mlo, quot, xi);
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long double quot_lo = (t - mhi - mlo) / xi - t * x_eps / (xi * xi);
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/* We want (1 + RET + RET_EPS) * (1 + QUOT + QUOT_LO) - 1. */
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long double rhi, rlo;
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mul_split (&rhi, &rlo, ret, quot);
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mul_splitl (&rhi, &rlo, ret, quot);
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long double rpq = ret + quot;
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long double rpq_eps = (ret - rpq) + quot;
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long double nret = rpq + rhi;
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@ -18,9 +18,10 @@
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#include <math.h>
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#include <math_private.h>
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#include <float.h>
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#include <mul_splitl.h>
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#include <stdlib.h>
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/* Calculate X + Y exactly and store the result in *HI + *LO. It is
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given that |X| >= |Y| and the values are small enough that no
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overflow occurs. */
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@ -33,36 +34,6 @@ add_split (long double *hi, long double *lo, long double x, long double y)
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*lo = (x - *hi) + y;
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}
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/* Calculate X * Y exactly and store the result in *HI + *LO. It is
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given that the values are small enough that no overflow occurs and
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large enough (or zero) that no underflow occurs. */
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static inline void
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mul_split (long double *hi, long double *lo, long double x, long double y)
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{
|
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#ifdef __FP_FAST_FMAL
|
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/* Fast built-in fused multiply-add. */
|
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*hi = x * y;
|
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*lo = __builtin_fmal (x, y, -*hi);
|
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#elif defined FP_FAST_FMAL
|
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/* Fast library fused multiply-add, compiler before GCC 4.6. */
|
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*hi = x * y;
|
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*lo = __fmal (x, y, -*hi);
|
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#else
|
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/* Apply Dekker's algorithm. */
|
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*hi = x * y;
|
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# define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1)
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long double x1 = x * C;
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long double y1 = y * C;
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# undef C
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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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*lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2;
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#endif
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}
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/* Compare absolute values of floating-point values pointed to by P
|
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and Q for qsort. */
|
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@ -88,8 +59,8 @@ __x2y2m1l (long double x, long double y)
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{
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long double vals[5];
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SET_RESTORE_ROUNDL (FE_TONEAREST);
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mul_split (&vals[1], &vals[0], x, x);
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mul_split (&vals[3], &vals[2], y, y);
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||||
mul_splitl (&vals[1], &vals[0], x, x);
|
||||
mul_splitl (&vals[3], &vals[2], y, y);
|
||||
vals[4] = -1.0L;
|
||||
qsort (vals, 5, sizeof (long double), compare);
|
||||
/* Add up the values so that each element of VALS has absolute value
|
||||
|
|
|
|||
|
|
@ -22,6 +22,7 @@
|
|||
#include <math.h>
|
||||
#include <math_private.h>
|
||||
#include <math_ldbl_opt.h>
|
||||
#include <mul_split.h>
|
||||
#include <stdlib.h>
|
||||
|
||||
/* Calculate X + Y exactly and store the result in *HI + *LO. It is
|
||||
|
|
@ -36,32 +37,6 @@ add_split (double *hi, double *lo, double x, double y)
|
|||
*lo = (x - *hi) + y;
|
||||
}
|
||||
|
||||
/* Calculate X * Y exactly and store the result in *HI + *LO. It is
|
||||
given that the values are small enough that no overflow occurs and
|
||||
large enough (or zero) that no underflow occurs. */
|
||||
|
||||
static void
|
||||
mul_split (double *hi, double *lo, double x, double y)
|
||||
{
|
||||
#ifdef __FP_FAST_FMA
|
||||
/* Fast built-in fused multiply-add. */
|
||||
*hi = x * y;
|
||||
*lo = __builtin_fma (x, y, -*hi);
|
||||
#else
|
||||
/* Apply Dekker's algorithm. */
|
||||
*hi = x * y;
|
||||
# define C ((1 << (DBL_MANT_DIG + 1) / 2) + 1)
|
||||
double x1 = x * C;
|
||||
double y1 = y * C;
|
||||
# undef C
|
||||
x1 = (x - x1) + x1;
|
||||
y1 = (y - y1) + y1;
|
||||
double x2 = x - x1;
|
||||
double y2 = y - y1;
|
||||
*lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2;
|
||||
#endif
|
||||
}
|
||||
|
||||
/* Value with extended range, used in intermediate computations. */
|
||||
typedef struct
|
||||
{
|
||||
|
|
|
|||
|
|
@ -18,7 +18,7 @@
|
|||
|
||||
#include <math.h>
|
||||
#include <math_private.h>
|
||||
#include <float.h>
|
||||
#include <mul_split.h>
|
||||
#include <stdlib.h>
|
||||
|
||||
/* Calculate X + Y exactly and store the result in *HI + *LO. It is
|
||||
|
|
@ -33,36 +33,6 @@ add_split (double *hi, double *lo, double x, double y)
|
|||
*lo = (x - *hi) + y;
|
||||
}
|
||||
|
||||
/* Calculate X * Y exactly and store the result in *HI + *LO. It is
|
||||
given that the values are small enough that no overflow occurs and
|
||||
large enough (or zero) that no underflow occurs. */
|
||||
|
||||
static inline void
|
||||
mul_split (double *hi, double *lo, double x, double y)
|
||||
{
|
||||
#ifdef __FP_FAST_FMA
|
||||
/* Fast built-in fused multiply-add. */
|
||||
*hi = x * y;
|
||||
*lo = __builtin_fma (x, y, -*hi);
|
||||
#elif defined FP_FAST_FMA
|
||||
/* Fast library fused multiply-add, compiler before GCC 4.6. */
|
||||
*hi = x * y;
|
||||
*lo = __fma (x, y, -*hi);
|
||||
#else
|
||||
/* Apply Dekker's algorithm. */
|
||||
*hi = x * y;
|
||||
# define C ((1 << (DBL_MANT_DIG + 1) / 2) + 1)
|
||||
double x1 = x * C;
|
||||
double y1 = y * C;
|
||||
# undef C
|
||||
x1 = (x - x1) + x1;
|
||||
y1 = (y - y1) + y1;
|
||||
double x2 = x - x1;
|
||||
double y2 = y - y1;
|
||||
*lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2;
|
||||
#endif
|
||||
}
|
||||
|
||||
/* Compare absolute values of floating-point values pointed to by P
|
||||
and Q for qsort. */
|
||||
|
||||
|
|
|
|||
|
|
@ -18,37 +18,7 @@
|
|||
|
||||
#include <math.h>
|
||||
#include <math_private.h>
|
||||
#include <float.h>
|
||||
|
||||
/* Calculate X * Y exactly and store the result in *HI + *LO. It is
|
||||
given that the values are small enough that no overflow occurs and
|
||||
large enough (or zero) that no underflow occurs. */
|
||||
|
||||
static inline void
|
||||
mul_split (long double *hi, long double *lo, long double x, long double y)
|
||||
{
|
||||
#ifdef __FP_FAST_FMAL
|
||||
/* Fast built-in fused multiply-add. */
|
||||
*hi = x * y;
|
||||
*lo = __builtin_fmal (x, y, -*hi);
|
||||
#elif defined FP_FAST_FMAL
|
||||
/* Fast library fused multiply-add, compiler before GCC 4.6. */
|
||||
*hi = x * y;
|
||||
*lo = __fmal (x, y, -*hi);
|
||||
#else
|
||||
/* Apply Dekker's algorithm. */
|
||||
*hi = x * y;
|
||||
# define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1)
|
||||
long double x1 = x * C;
|
||||
long double y1 = y * C;
|
||||
# undef C
|
||||
x1 = (x - x1) + x1;
|
||||
y1 = (y - y1) + y1;
|
||||
long double x2 = x - x1;
|
||||
long double y2 = y - y1;
|
||||
*lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2;
|
||||
#endif
|
||||
}
|
||||
#include <mul_splitl.h>
|
||||
|
||||
/* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N
|
||||
- 1, in the form R * (1 + *EPS) where the return value R is an
|
||||
|
|
@ -68,7 +38,7 @@ __gamma_productl (long double x, long double x_eps, int n, long double *eps)
|
|||
{
|
||||
*eps += x_eps / (x + i);
|
||||
long double lo;
|
||||
mul_split (&ret, &lo, ret, x + i);
|
||||
mul_splitl (&ret, &lo, ret, x + i);
|
||||
*eps += lo / ret;
|
||||
}
|
||||
return ret;
|
||||
|
|
|
|||
|
|
@ -18,37 +18,7 @@
|
|||
|
||||
#include <math.h>
|
||||
#include <math_private.h>
|
||||
#include <float.h>
|
||||
|
||||
/* Calculate X * Y exactly and store the result in *HI + *LO. It is
|
||||
given that the values are small enough that no overflow occurs and
|
||||
large enough (or zero) that no underflow occurs. */
|
||||
|
||||
static void
|
||||
mul_split (long double *hi, long double *lo, long double x, long double y)
|
||||
{
|
||||
#ifdef __FP_FAST_FMAL
|
||||
/* Fast built-in fused multiply-add. */
|
||||
*hi = x * y;
|
||||
*lo = __builtin_fmal (x, y, -*hi);
|
||||
#elif defined FP_FAST_FMAL
|
||||
/* Fast library fused multiply-add, compiler before GCC 4.6. */
|
||||
*hi = x * y;
|
||||
*lo = __fmal (x, y, -*hi);
|
||||
#else
|
||||
/* Apply Dekker's algorithm. */
|
||||
*hi = x * y;
|
||||
# define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1)
|
||||
long double x1 = x * C;
|
||||
long double y1 = y * C;
|
||||
# undef C
|
||||
x1 = (x - x1) + x1;
|
||||
y1 = (y - y1) + y1;
|
||||
long double x2 = x - x1;
|
||||
long double y2 = y - y1;
|
||||
*lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2;
|
||||
#endif
|
||||
}
|
||||
#include <mul_splitl.h>
|
||||
|
||||
/* Compute the product of 1 + (T / (X + X_EPS)), 1 + (T / (X + X_EPS +
|
||||
1)), ..., 1 + (T / (X + X_EPS + N - 1)), minus 1. X is such that
|
||||
|
|
@ -65,11 +35,11 @@ __lgamma_productl (long double t, long double x, long double x_eps, int n)
|
|||
long double xi = x + i;
|
||||
long double quot = t / xi;
|
||||
long double mhi, mlo;
|
||||
mul_split (&mhi, &mlo, quot, xi);
|
||||
mul_splitl (&mhi, &mlo, quot, xi);
|
||||
long double quot_lo = (t - mhi - mlo) / xi - t * x_eps / (xi * xi);
|
||||
/* We want (1 + RET + RET_EPS) * (1 + QUOT + QUOT_LO) - 1. */
|
||||
long double rhi, rlo;
|
||||
mul_split (&rhi, &rlo, ret, quot);
|
||||
mul_splitl (&rhi, &rlo, ret, quot);
|
||||
long double rpq = ret + quot;
|
||||
long double rpq_eps = (ret - rpq) + quot;
|
||||
long double nret = rpq + rhi;
|
||||
|
|
|
|||
|
|
@ -18,7 +18,7 @@
|
|||
|
||||
#include <math.h>
|
||||
#include <math_private.h>
|
||||
#include <float.h>
|
||||
#include <mul_splitl.h>
|
||||
#include <stdlib.h>
|
||||
|
||||
/* Calculate X + Y exactly and store the result in *HI + *LO. It is
|
||||
|
|
@ -33,36 +33,6 @@ add_split (long double *hi, long double *lo, long double x, long double y)
|
|||
*lo = (x - *hi) + y;
|
||||
}
|
||||
|
||||
/* Calculate X * Y exactly and store the result in *HI + *LO. It is
|
||||
given that the values are small enough that no overflow occurs and
|
||||
large enough (or zero) that no underflow occurs. */
|
||||
|
||||
static inline void
|
||||
mul_split (long double *hi, long double *lo, long double x, long double y)
|
||||
{
|
||||
#ifdef __FP_FAST_FMAL
|
||||
/* Fast built-in fused multiply-add. */
|
||||
*hi = x * y;
|
||||
*lo = __builtin_fmal (x, y, -*hi);
|
||||
#elif defined FP_FAST_FMAL
|
||||
/* Fast library fused multiply-add, compiler before GCC 4.6. */
|
||||
*hi = x * y;
|
||||
*lo = __fmal (x, y, -*hi);
|
||||
#else
|
||||
/* Apply Dekker's algorithm. */
|
||||
*hi = x * y;
|
||||
# define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1)
|
||||
long double x1 = x * C;
|
||||
long double y1 = y * C;
|
||||
# undef C
|
||||
x1 = (x - x1) + x1;
|
||||
y1 = (y - y1) + y1;
|
||||
long double x2 = x - x1;
|
||||
long double y2 = y - y1;
|
||||
*lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2;
|
||||
#endif
|
||||
}
|
||||
|
||||
/* Compare absolute values of floating-point values pointed to by P
|
||||
and Q for qsort. */
|
||||
|
||||
|
|
@ -88,8 +58,8 @@ __x2y2m1l (long double x, long double y)
|
|||
{
|
||||
long double vals[5];
|
||||
SET_RESTORE_ROUNDL (FE_TONEAREST);
|
||||
mul_split (&vals[1], &vals[0], x, x);
|
||||
mul_split (&vals[3], &vals[2], y, y);
|
||||
mul_splitl (&vals[1], &vals[0], x, x);
|
||||
mul_splitl (&vals[3], &vals[2], y, y);
|
||||
vals[4] = -1.0L;
|
||||
qsort (vals, 5, sizeof (long double), compare);
|
||||
/* Add up the values so that each element of VALS has absolute value
|
||||
|
|
|
|||
Loading…
Reference in New Issue