2007-06-03 23:20:06 +02:00
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/*
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* IBM Accurate Mathematical Library
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* written by International Business Machines Corp.
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2013-01-02 20:01:50 +01:00
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* Copyright (C) 2001-2013 Free Software Foundation, Inc.
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2007-06-03 23:20:06 +02:00
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU Lesser General Public License as published by
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* the Free Software Foundation; either version 2.1 of the License, or
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* (at your option) any later version.
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*
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* This program 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
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* GNU Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public License
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2012-02-10 00:18:22 +01:00
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* along with this program; if not, see <http://www.gnu.org/licenses/>.
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2007-06-03 23:20:06 +02:00
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*/
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2013-03-07 07:53:29 +01:00
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/* Define __mul and __sqr and use the rest from generic code. */
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#define NO__MUL
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#define NO__SQR
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2007-06-03 23:20:06 +02:00
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2013-03-07 07:53:29 +01:00
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#include <sysdeps/ieee754/dbl-64/mpa.c>
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2007-06-03 23:20:06 +02:00
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2013-01-09 14:37:15 +01:00
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/* Multiply *X and *Y and store result in *Z. X and Y may overlap but not X
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and Z or Y and Z. For P in [1, 2, 3], the exact result is truncated to P
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digits. In case P > 3 the error is bounded by 1.001 ULP. */
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2013-01-14 17:01:25 +01:00
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void
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__mul (const mp_no *x, const mp_no *y, mp_no *z, int p)
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{
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2007-06-03 23:20:06 +02:00
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long i, i1, i2, j, k, k2;
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long p2 = p;
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double u, zk, zk2;
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2013-02-20 14:26:20 +01:00
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/* Is z=0? */
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2013-02-21 07:47:29 +01:00
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if (__glibc_unlikely (X[0] * Y[0] == ZERO))
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2013-01-14 17:01:25 +01:00
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{
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Z[0] = ZERO;
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return;
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}
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2007-06-03 23:20:06 +02:00
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2013-01-14 17:01:25 +01:00
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/* Multiply, add and carry */
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k2 = (p2 < 3) ? p2 + p2 : p2 + 3;
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zk = Z[k2] = ZERO;
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for (k = k2; k > 1;)
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2007-06-03 23:20:06 +02:00
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{
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2013-01-14 17:01:25 +01:00
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if (k > p2)
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2007-06-03 23:20:06 +02:00
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{
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2013-01-14 17:01:25 +01:00
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i1 = k - p2;
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i2 = p2 + 1;
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2007-06-03 23:20:06 +02:00
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}
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2013-01-14 17:01:25 +01:00
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else
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2007-06-03 23:20:06 +02:00
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{
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2013-01-14 17:01:25 +01:00
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i1 = 1;
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i2 = k;
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}
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#if 1
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/* Rearrange this inner loop to allow the fmadd instructions to be
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independent and execute in parallel on processors that have
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dual symmetrical FP pipelines. */
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if (i1 < (i2 - 1))
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{
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/* Make sure we have at least 2 iterations. */
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if (((i2 - i1) & 1L) == 1L)
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{
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/* Handle the odd iterations case. */
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zk2 = x->d[i2 - 1] * y->d[i1];
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}
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else
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zk2 = 0.0;
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/* Do two multiply/adds per loop iteration, using independent
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accumulators; zk and zk2. */
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for (i = i1, j = i2 - 1; i < i2 - 1; i += 2, j -= 2)
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{
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zk += x->d[i] * y->d[j];
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zk2 += x->d[i + 1] * y->d[j - 1];
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}
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zk += zk2; /* Final sum. */
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}
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else
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{
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/* Special case when iterations is 1. */
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zk += x->d[i1] * y->d[i1];
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2007-06-03 23:20:06 +02:00
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}
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#else
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2013-01-14 17:01:25 +01:00
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/* The original code. */
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for (i = i1, j = i2 - 1; i < i2; i++, j--)
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zk += X[i] * Y[j];
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2007-06-03 23:20:06 +02:00
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#endif
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2013-01-14 17:01:25 +01:00
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u = (zk + CUTTER) - CUTTER;
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if (u > zk)
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u -= RADIX;
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Z[k] = zk - u;
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zk = u * RADIXI;
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--k;
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}
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2007-06-03 23:20:06 +02:00
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Z[k] = zk;
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2013-01-09 14:37:15 +01:00
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/* Is there a carry beyond the most significant digit? */
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2013-01-14 17:01:25 +01:00
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if (Z[1] == ZERO)
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{
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for (i = 1; i <= p2; i++)
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Z[i] = Z[i + 1];
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EZ = EX + EY - 1;
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}
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2007-06-03 23:20:06 +02:00
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else
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EZ = EX + EY;
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Z[0] = X[0] * Y[0];
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}
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2013-02-14 06:01:09 +01:00
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/* Square *X and store result in *Y. X and Y may not overlap. For P in
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[1, 2, 3], the exact result is truncated to P digits. In case P > 3 the
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error is bounded by 1.001 ULP. This is a faster special case of
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multiplication. */
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void
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__sqr (const mp_no *x, mp_no *y, int p)
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{
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long i, j, k, ip;
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double u, yk;
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/* Is z=0? */
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if (__glibc_unlikely (X[0] == ZERO))
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{
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Y[0] = ZERO;
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return;
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}
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/* We need not iterate through all X's since it's pointless to
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multiply zeroes. */
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for (ip = p; ip > 0; ip--)
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if (X[ip] != ZERO)
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break;
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k = (__glibc_unlikely (p < 3)) ? p + p : p + 3;
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while (k > 2 * ip + 1)
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Y[k--] = ZERO;
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yk = ZERO;
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while (k > p)
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{
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double yk2 = 0.0;
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long lim = k / 2;
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if (k % 2 == 0)
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{
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yk += X[lim] * X[lim];
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lim--;
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}
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/* In __mul, this loop (and the one within the next while loop) run
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between a range to calculate the mantissa as follows:
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Z[k] = X[k] * Y[n] + X[k+1] * Y[n-1] ... + X[n-1] * Y[k+1]
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+ X[n] * Y[k]
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For X == Y, we can get away with summing halfway and doubling the
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result. For cases where the range size is even, the mid-point needs
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to be added separately (above). */
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for (i = k - p, j = p; i <= lim; i++, j--)
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yk2 += X[i] * X[j];
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yk += 2.0 * yk2;
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u = (yk + CUTTER) - CUTTER;
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if (u > yk)
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u -= RADIX;
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Y[k--] = yk - u;
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yk = u * RADIXI;
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}
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while (k > 1)
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{
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double yk2 = 0.0;
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long lim = k / 2;
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if (k % 2 == 0)
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{
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yk += X[lim] * X[lim];
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lim--;
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}
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/* Likewise for this loop. */
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for (i = 1, j = k - 1; i <= lim; i++, j--)
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yk2 += X[i] * X[j];
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yk += 2.0 * yk2;
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u = (yk + CUTTER) - CUTTER;
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if (u > yk)
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u -= RADIX;
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Y[k--] = yk - u;
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yk = u * RADIXI;
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}
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Y[k] = yk;
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/* Squares are always positive. */
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Y[0] = 1.0;
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EY = 2 * EX;
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/* Is there a carry beyond the most significant digit? */
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if (__glibc_unlikely (Y[1] == ZERO))
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{
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for (i = 1; i <= p; i++)
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Y[i] = Y[i + 1];
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EY--;
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}
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}
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