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authorDuncan Wilkie <antigravityd@gmail.com>2023-11-18 06:11:09 -0600
committerDuncan Wilkie <antigravityd@gmail.com>2023-11-18 06:11:09 -0600
commit11da511c784eca003deb90c23570f0873954e0de (patch)
treee14fdd3d5d6345956d67e79ae771d0633d28362b /gmp-6.3.0/mpn/generic/toom42_mul.c
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+/* mpn_toom42_mul -- Multiply {ap,an} and {bp,bn} where an is nominally twice
+ as large as bn. Or more accurately, (3/2)bn < an < 4bn.
+
+ Contributed to the GNU project by Torbjorn Granlund.
+ Additional improvements by Marco Bodrato.
+
+ The idea of applying toom to unbalanced multiplication is due to Marco
+ Bodrato and Alberto Zanoni.
+
+ THE FUNCTION IN THIS FILE IS INTERNAL WITH A MUTABLE INTERFACE. IT IS ONLY
+ SAFE TO REACH IT THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
+ GUARANTEED THAT IT WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
+
+Copyright 2006-2008, 2012, 2014 Free Software Foundation, Inc.
+
+This file is part of the GNU MP Library.
+
+The GNU MP Library is free software; you can redistribute it and/or modify
+it under the terms of either:
+
+ * the GNU Lesser General Public License as published by the Free
+ Software Foundation; either version 3 of the License, or (at your
+ option) any later version.
+
+or
+
+ * the GNU General Public License as published by the Free Software
+ Foundation; either version 2 of the License, or (at your option) any
+ later version.
+
+or both in parallel, as here.
+
+The GNU MP Library is distributed in the hope that it will be useful, but
+WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
+for more details.
+
+You should have received copies of the GNU General Public License and the
+GNU Lesser General Public License along with the GNU MP Library. If not,
+see https://www.gnu.org/licenses/. */
+
+
+#include "gmp-impl.h"
+
+/* Evaluate in: -1, 0, +1, +2, +inf
+
+ <-s-><--n--><--n--><--n-->
+ ___ ______ ______ ______
+ |a3_|___a2_|___a1_|___a0_|
+ |_b1_|___b0_|
+ <-t--><--n-->
+
+ v0 = a0 * b0 # A(0)*B(0)
+ v1 = (a0+ a1+ a2+ a3)*(b0+ b1) # A(1)*B(1) ah <= 3 bh <= 1
+ vm1 = (a0- a1+ a2- a3)*(b0- b1) # A(-1)*B(-1) |ah| <= 1 bh = 0
+ v2 = (a0+2a1+4a2+8a3)*(b0+2b1) # A(2)*B(2) ah <= 14 bh <= 2
+ vinf= a3 * b1 # A(inf)*B(inf)
+*/
+
+#define TOOM42_MUL_N_REC(p, a, b, n, ws) \
+ do { \
+ mpn_mul_n (p, a, b, n); \
+ } while (0)
+
+void
+mpn_toom42_mul (mp_ptr pp,
+ mp_srcptr ap, mp_size_t an,
+ mp_srcptr bp, mp_size_t bn,
+ mp_ptr scratch)
+{
+ mp_size_t n, s, t;
+ int vm1_neg;
+ mp_limb_t cy, vinf0;
+ mp_ptr a0_a2;
+ mp_ptr as1, asm1, as2;
+ mp_ptr bs1, bsm1, bs2;
+ mp_ptr tmp;
+ TMP_DECL;
+
+#define a0 ap
+#define a1 (ap + n)
+#define a2 (ap + 2*n)
+#define a3 (ap + 3*n)
+#define b0 bp
+#define b1 (bp + n)
+
+ n = an >= 2 * bn ? (an + 3) >> 2 : (bn + 1) >> 1;
+
+ s = an - 3 * n;
+ t = bn - n;
+
+ ASSERT (0 < s && s <= n);
+ ASSERT (0 < t && t <= n);
+
+ TMP_MARK;
+
+ tmp = TMP_ALLOC_LIMBS (6 * n + 5);
+ as1 = tmp; tmp += n + 1;
+ asm1 = tmp; tmp += n + 1;
+ as2 = tmp; tmp += n + 1;
+ bs1 = tmp; tmp += n + 1;
+ bsm1 = tmp; tmp += n;
+ bs2 = tmp; tmp += n + 1;
+
+ a0_a2 = pp;
+
+ /* Compute as1 and asm1. */
+ vm1_neg = mpn_toom_eval_dgr3_pm1 (as1, asm1, ap, n, s, a0_a2) & 1;
+
+ /* Compute as2. */
+#if HAVE_NATIVE_mpn_addlsh1_n
+ cy = mpn_addlsh1_n (as2, a2, a3, s);
+ if (s != n)
+ cy = mpn_add_1 (as2 + s, a2 + s, n - s, cy);
+ cy = 2 * cy + mpn_addlsh1_n (as2, a1, as2, n);
+ cy = 2 * cy + mpn_addlsh1_n (as2, a0, as2, n);
+#else
+ cy = mpn_lshift (as2, a3, s, 1);
+ cy += mpn_add_n (as2, a2, as2, s);
+ if (s != n)
+ cy = mpn_add_1 (as2 + s, a2 + s, n - s, cy);
+ cy = 2 * cy + mpn_lshift (as2, as2, n, 1);
+ cy += mpn_add_n (as2, a1, as2, n);
+ cy = 2 * cy + mpn_lshift (as2, as2, n, 1);
+ cy += mpn_add_n (as2, a0, as2, n);
+#endif
+ as2[n] = cy;
+
+ /* Compute bs1 and bsm1. */
+ if (t == n)
+ {
+#if HAVE_NATIVE_mpn_add_n_sub_n
+ if (mpn_cmp (b0, b1, n) < 0)
+ {
+ cy = mpn_add_n_sub_n (bs1, bsm1, b1, b0, n);
+ vm1_neg ^= 1;
+ }
+ else
+ {
+ cy = mpn_add_n_sub_n (bs1, bsm1, b0, b1, n);
+ }
+ bs1[n] = cy >> 1;
+#else
+ bs1[n] = mpn_add_n (bs1, b0, b1, n);
+
+ if (mpn_cmp (b0, b1, n) < 0)
+ {
+ mpn_sub_n (bsm1, b1, b0, n);
+ vm1_neg ^= 1;
+ }
+ else
+ {
+ mpn_sub_n (bsm1, b0, b1, n);
+ }
+#endif
+ }
+ else
+ {
+ bs1[n] = mpn_add (bs1, b0, n, b1, t);
+
+ if (mpn_zero_p (b0 + t, n - t) && mpn_cmp (b0, b1, t) < 0)
+ {
+ mpn_sub_n (bsm1, b1, b0, t);
+ MPN_ZERO (bsm1 + t, n - t);
+ vm1_neg ^= 1;
+ }
+ else
+ {
+ mpn_sub (bsm1, b0, n, b1, t);
+ }
+ }
+
+ /* Compute bs2, recycling bs1. bs2=bs1+b1 */
+ mpn_add (bs2, bs1, n + 1, b1, t);
+
+ ASSERT (as1[n] <= 3);
+ ASSERT (bs1[n] <= 1);
+ ASSERT (asm1[n] <= 1);
+/*ASSERT (bsm1[n] == 0);*/
+ ASSERT (as2[n] <= 14);
+ ASSERT (bs2[n] <= 2);
+
+#define v0 pp /* 2n */
+#define v1 (pp + 2 * n) /* 2n+1 */
+#define vinf (pp + 4 * n) /* s+t */
+#define vm1 scratch /* 2n+1 */
+#define v2 (scratch + 2 * n + 1) /* 2n+2 */
+#define scratch_out scratch + 4 * n + 4 /* Currently unused. */
+
+ /* vm1, 2n+1 limbs */
+ TOOM42_MUL_N_REC (vm1, asm1, bsm1, n, scratch_out);
+ cy = 0;
+ if (asm1[n] != 0)
+ cy = mpn_add_n (vm1 + n, vm1 + n, bsm1, n);
+ vm1[2 * n] = cy;
+
+ TOOM42_MUL_N_REC (v2, as2, bs2, n + 1, scratch_out); /* v2, 2n+1 limbs */
+
+ /* vinf, s+t limbs */
+ if (s > t) mpn_mul (vinf, a3, s, b1, t);
+ else mpn_mul (vinf, b1, t, a3, s);
+
+ vinf0 = vinf[0]; /* v1 overlaps with this */
+
+ /* v1, 2n+1 limbs */
+ TOOM42_MUL_N_REC (v1, as1, bs1, n, scratch_out);
+ if (as1[n] == 1)
+ {
+ cy = mpn_add_n (v1 + n, v1 + n, bs1, n);
+ }
+ else if (as1[n] == 2)
+ {
+#if HAVE_NATIVE_mpn_addlsh1_n_ip1
+ cy = mpn_addlsh1_n_ip1 (v1 + n, bs1, n);
+#else
+ cy = mpn_addmul_1 (v1 + n, bs1, n, CNST_LIMB(2));
+#endif
+ }
+ else if (as1[n] == 3)
+ {
+ cy = mpn_addmul_1 (v1 + n, bs1, n, CNST_LIMB(3));
+ }
+ else
+ cy = 0;
+ if (bs1[n] != 0)
+ cy += as1[n] + mpn_add_n (v1 + n, v1 + n, as1, n);
+ v1[2 * n] = cy;
+
+ TOOM42_MUL_N_REC (v0, ap, bp, n, scratch_out); /* v0, 2n limbs */
+
+ mpn_toom_interpolate_5pts (pp, v2, vm1, n, s + t, vm1_neg, vinf0);
+
+ TMP_FREE;
+}