258 lines
7.0 KiB
C
258 lines
7.0 KiB
C
/* Compute x * y + z as ternary operation.
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Copyright (C) 2011-2017 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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Contributed by David Flaherty <flaherty@linux.vnet.ibm.com>.
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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 <fenv.h>
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#include <float.h>
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#include <math.h>
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#include <math_private.h>
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#include <math_ldbl_opt.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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given that |X| >= |Y| and the values are small enough that no
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overflow occurs. */
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static void
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add_split (double *hi, double *lo, double x, double y)
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{
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/* Apply Dekker's algorithm. */
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*hi = x + y;
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*lo = (x - *hi) + y;
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}
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/* Value with extended range, used in intermediate computations. */
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typedef struct
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{
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/* Value in [0.5, 1), as from frexp, or 0. */
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double val;
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/* Exponent of power of 2 it is multiplied by, or 0 for zero. */
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int exp;
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} ext_val;
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/* Store D as an ext_val value. */
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static void
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store_ext_val (ext_val *v, double d)
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{
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v->val = __frexp (d, &v->exp);
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}
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/* Store X * Y as ext_val values *V0 and *V1. */
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static void
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mul_ext_val (ext_val *v0, ext_val *v1, double x, double y)
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{
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int xexp, yexp;
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x = __frexp (x, &xexp);
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y = __frexp (y, &yexp);
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double hi, lo;
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mul_split (&hi, &lo, x, y);
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store_ext_val (v0, hi);
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if (hi != 0)
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v0->exp += xexp + yexp;
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store_ext_val (v1, lo);
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if (lo != 0)
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v1->exp += xexp + yexp;
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}
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/* Compare absolute values of ext_val values pointed to by P and Q for
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qsort. */
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static int
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compare (const void *p, const void *q)
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{
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const ext_val *pe = p;
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const ext_val *qe = q;
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if (pe->val == 0)
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return qe->val == 0 ? 0 : -1;
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else if (qe->val == 0)
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return 1;
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else if (pe->exp < qe->exp)
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return -1;
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else if (pe->exp > qe->exp)
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return 1;
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else
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{
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double pd = fabs (pe->val);
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double qd = fabs (qe->val);
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if (pd < qd)
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return -1;
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else if (pd == qd)
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return 0;
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else
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return 1;
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}
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}
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/* Calculate *X + *Y exactly, storing the high part in *X (rounded to
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nearest) and the low part in *Y. It is given that |X| >= |Y|. */
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static void
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add_split_ext (ext_val *x, ext_val *y)
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{
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int xexp = x->exp, yexp = y->exp;
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if (y->val == 0 || xexp - yexp > 53)
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return;
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double hi = x->val;
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double lo = __scalbn (y->val, yexp - xexp);
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add_split (&hi, &lo, hi, lo);
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store_ext_val (x, hi);
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if (hi != 0)
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x->exp += xexp;
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store_ext_val (y, lo);
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if (lo != 0)
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y->exp += xexp;
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}
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long double
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__fmal (long double x, long double y, long double z)
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{
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double xhi, xlo, yhi, ylo, zhi, zlo;
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int64_t hx, hy, hz;
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int xexp, yexp, zexp;
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double scale_val;
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int scale_exp;
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ldbl_unpack (x, &xhi, &xlo);
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EXTRACT_WORDS64 (hx, xhi);
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xexp = (hx & 0x7ff0000000000000LL) >> 52;
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ldbl_unpack (y, &yhi, &ylo);
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EXTRACT_WORDS64 (hy, yhi);
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yexp = (hy & 0x7ff0000000000000LL) >> 52;
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ldbl_unpack (z, &zhi, &zlo);
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EXTRACT_WORDS64 (hz, zhi);
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zexp = (hz & 0x7ff0000000000000LL) >> 52;
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/* If z is Inf or NaN, but x and y are finite, avoid any exceptions
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from computing x * y. */
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if (zexp == 0x7ff && xexp != 0x7ff && yexp != 0x7ff)
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return (z + x) + y;
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/* If z is zero and x are y are nonzero, compute the result as x * y
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to avoid the wrong sign of a zero result if x * y underflows to
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0. */
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if (z == 0 && x != 0 && y != 0)
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return x * y;
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/* If x or y or z is Inf/NaN, or if x * y is zero, compute as x * y
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+ z. */
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if (xexp == 0x7ff || yexp == 0x7ff || zexp == 0x7ff
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|| x == 0 || y == 0)
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return (x * y) + z;
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{
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SET_RESTORE_ROUND (FE_TONEAREST);
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ext_val vals[10];
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store_ext_val (&vals[0], zhi);
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store_ext_val (&vals[1], zlo);
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mul_ext_val (&vals[2], &vals[3], xhi, yhi);
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mul_ext_val (&vals[4], &vals[5], xhi, ylo);
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mul_ext_val (&vals[6], &vals[7], xlo, yhi);
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mul_ext_val (&vals[8], &vals[9], xlo, ylo);
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qsort (vals, 10, sizeof (ext_val), compare);
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/* Add up the values so that each element of VALS has absolute
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value at most equal to the last set bit of the next nonzero
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element. */
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for (size_t i = 0; i <= 8; i++)
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{
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add_split_ext (&vals[i + 1], &vals[i]);
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qsort (vals + i + 1, 9 - i, sizeof (ext_val), compare);
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}
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/* Add up the values in the other direction, so that each element
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of VALS has absolute value less than 5ulp of the next
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value. */
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size_t dstpos = 9;
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for (size_t i = 1; i <= 9; i++)
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{
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if (vals[dstpos].val == 0)
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{
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vals[dstpos] = vals[9 - i];
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vals[9 - i].val = 0;
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vals[9 - i].exp = 0;
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}
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else
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{
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add_split_ext (&vals[dstpos], &vals[9 - i]);
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if (vals[9 - i].val != 0)
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{
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if (9 - i < dstpos - 1)
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{
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vals[dstpos - 1] = vals[9 - i];
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vals[9 - i].val = 0;
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vals[9 - i].exp = 0;
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}
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dstpos--;
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}
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}
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}
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/* If the result is an exact zero, it results from adding two
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values with opposite signs; recompute in the original rounding
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mode. */
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if (vals[9].val == 0)
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goto zero_out;
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/* Adding the top three values will now give a result as accurate
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as the underlying long double arithmetic. */
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add_split_ext (&vals[9], &vals[8]);
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if (compare (&vals[8], &vals[7]) < 0)
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{
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ext_val tmp = vals[7];
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vals[7] = vals[8];
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vals[8] = tmp;
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}
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add_split_ext (&vals[8], &vals[7]);
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add_split_ext (&vals[9], &vals[8]);
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if (vals[9].exp > DBL_MAX_EXP || vals[9].exp < DBL_MIN_EXP)
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{
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/* Overflow or underflow, with the result depending on the
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original rounding mode, but not on the low part computed
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here. */
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scale_val = vals[9].val;
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scale_exp = vals[9].exp;
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goto scale_out;
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}
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double hi = __scalbn (vals[9].val, vals[9].exp);
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double lo = __scalbn (vals[8].val, vals[8].exp);
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/* It is possible that the low part became subnormal and was
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rounded so that the result is no longer canonical. */
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ldbl_canonicalize (&hi, &lo);
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long double ret = ldbl_pack (hi, lo);
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math_check_force_underflow (ret);
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return ret;
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}
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scale_out:
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scale_val = math_opt_barrier (scale_val);
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scale_val = __scalbn (scale_val, scale_exp);
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if (fabs (scale_val) == DBL_MAX)
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return __copysignl (LDBL_MAX, scale_val);
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math_check_force_underflow (scale_val);
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return scale_val;
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zero_out:;
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double zero = 0.0;
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zero = math_opt_barrier (zero);
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return zero - zero;
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}
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#if IS_IN (libm)
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long_double_symbol (libm, __fmal, fmal);
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#else
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long_double_symbol (libc, __fmal, fmal);
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#endif
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