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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/toom63_mul.c
Initial commit.
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+/* Implementation of the algorithm for Toom-Cook 4.5-way.
+
+ Contributed to the GNU project by Marco Bodrato.
+
+ 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 2009, 2012 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"
+
+/* Stores |{ap,n}-{bp,n}| in {rp,n}, returns the sign. */
+static int
+abs_sub_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n)
+{
+ mp_limb_t x, y;
+ while (--n >= 0)
+ {
+ x = ap[n];
+ y = bp[n];
+ if (x != y)
+ {
+ n++;
+ if (x > y)
+ {
+ mpn_sub_n (rp, ap, bp, n);
+ return 0;
+ }
+ else
+ {
+ mpn_sub_n (rp, bp, ap, n);
+ return ~0;
+ }
+ }
+ rp[n] = 0;
+ }
+ return 0;
+}
+
+static int
+abs_sub_add_n (mp_ptr rm, mp_ptr rp, mp_srcptr rs, mp_size_t n) {
+ int result;
+ result = abs_sub_n (rm, rp, rs, n);
+ ASSERT_NOCARRY(mpn_add_n (rp, rp, rs, n));
+ return result;
+}
+
+
+/* Toom-4.5, the splitting 6x3 unbalanced version.
+ Evaluate in: infinity, +4, -4, +2, -2, +1, -1, 0.
+
+ <--s-><--n--><--n--><--n--><--n--><--n-->
+ ____ ______ ______ ______ ______ ______
+ |_a5_|__a4__|__a3__|__a2__|__a1__|__a0__|
+ |b2_|__b1__|__b0__|
+ <-t-><--n--><--n-->
+
+*/
+#define TOOM_63_MUL_N_REC(p, a, b, n, ws) \
+ do { mpn_mul_n (p, a, b, n); \
+ } while (0)
+
+#define TOOM_63_MUL_REC(p, a, na, b, nb, ws) \
+ do { mpn_mul (p, a, na, b, nb); \
+ } while (0)
+
+void
+mpn_toom63_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;
+ mp_limb_t cy;
+ int sign;
+
+ /***************************** decomposition *******************************/
+#define a5 (ap + 5 * n)
+#define b0 (bp + 0 * n)
+#define b1 (bp + 1 * n)
+#define b2 (bp + 2 * n)
+
+ ASSERT (an >= bn);
+ n = 1 + (an >= 2 * bn ? (an - 1) / (size_t) 6 : (bn - 1) / (size_t) 3);
+
+ s = an - 5 * n;
+ t = bn - 2 * n;
+
+ ASSERT (0 < s && s <= n);
+ ASSERT (0 < t && t <= n);
+ /* WARNING! it assumes s+t>=n */
+ ASSERT ( s + t >= n );
+ ASSERT ( s + t > 4);
+ /* WARNING! it assumes n>1 */
+ ASSERT ( n > 2);
+
+#define r8 pp /* 2n */
+#define r7 scratch /* 3n+1 */
+#define r5 (pp + 3*n) /* 3n+1 */
+#define v0 (pp + 3*n) /* n+1 */
+#define v1 (pp + 4*n+1) /* n+1 */
+#define v2 (pp + 5*n+2) /* n+1 */
+#define v3 (pp + 6*n+3) /* n+1 */
+#define r3 (scratch + 3 * n + 1) /* 3n+1 */
+#define r1 (pp + 7*n) /* s+t <= 2*n */
+#define ws (scratch + 6 * n + 2) /* ??? */
+
+ /* Alloc also 3n+1 limbs for ws... mpn_toom_interpolate_8pts may
+ need all of them, when DO_mpn_sublsh_n usea a scratch */
+/* if (scratch == NULL) scratch = TMP_SALLOC_LIMBS (9 * n + 3); */
+
+ /********************** evaluation and recursive calls *********************/
+ /* $\pm4$ */
+ sign = mpn_toom_eval_pm2exp (v2, v0, 5, ap, n, s, 2, pp);
+ pp[n] = mpn_lshift (pp, b1, n, 2); /* 4b1 */
+ /* FIXME: use addlsh */
+ v3[t] = mpn_lshift (v3, b2, t, 4);/* 16b2 */
+ if ( n == t )
+ v3[n]+= mpn_add_n (v3, v3, b0, n); /* 16b2+b0 */
+ else
+ v3[n] = mpn_add (v3, b0, n, v3, t+1); /* 16b2+b0 */
+ sign ^= abs_sub_add_n (v1, v3, pp, n + 1);
+ TOOM_63_MUL_N_REC(pp, v0, v1, n + 1, ws); /* A(-4)*B(-4) */
+ TOOM_63_MUL_N_REC(r3, v2, v3, n + 1, ws); /* A(+4)*B(+4) */
+ mpn_toom_couple_handling (r3, 2*n+1, pp, sign, n, 2, 4);
+
+ /* $\pm1$ */
+ sign = mpn_toom_eval_pm1 (v2, v0, 5, ap, n, s, pp);
+ /* Compute bs1 and bsm1. Code taken from toom33 */
+ cy = mpn_add (ws, b0, n, b2, t);
+#if HAVE_NATIVE_mpn_add_n_sub_n
+ if (cy == 0 && mpn_cmp (ws, b1, n) < 0)
+ {
+ cy = mpn_add_n_sub_n (v3, v1, b1, ws, n);
+ v3[n] = cy >> 1;
+ v1[n] = 0;
+ sign = ~sign;
+ }
+ else
+ {
+ mp_limb_t cy2;
+ cy2 = mpn_add_n_sub_n (v3, v1, ws, b1, n);
+ v3[n] = cy + (cy2 >> 1);
+ v1[n] = cy - (cy2 & 1);
+ }
+#else
+ v3[n] = cy + mpn_add_n (v3, ws, b1, n);
+ if (cy == 0 && mpn_cmp (ws, b1, n) < 0)
+ {
+ mpn_sub_n (v1, b1, ws, n);
+ v1[n] = 0;
+ sign = ~sign;
+ }
+ else
+ {
+ cy -= mpn_sub_n (v1, ws, b1, n);
+ v1[n] = cy;
+ }
+#endif
+ TOOM_63_MUL_N_REC(pp, v0, v1, n + 1, ws); /* A(-1)*B(-1) */
+ TOOM_63_MUL_N_REC(r7, v2, v3, n + 1, ws); /* A(1)*B(1) */
+ mpn_toom_couple_handling (r7, 2*n+1, pp, sign, n, 0, 0);
+
+ /* $\pm2$ */
+ sign = mpn_toom_eval_pm2 (v2, v0, 5, ap, n, s, pp);
+ pp[n] = mpn_lshift (pp, b1, n, 1); /* 2b1 */
+ /* FIXME: use addlsh or addlsh2 */
+ v3[t] = mpn_lshift (v3, b2, t, 2);/* 4b2 */
+ if ( n == t )
+ v3[n]+= mpn_add_n (v3, v3, b0, n); /* 4b2+b0 */
+ else
+ v3[n] = mpn_add (v3, b0, n, v3, t+1); /* 4b2+b0 */
+ sign ^= abs_sub_add_n (v1, v3, pp, n + 1);
+ TOOM_63_MUL_N_REC(pp, v0, v1, n + 1, ws); /* A(-2)*B(-2) */
+ TOOM_63_MUL_N_REC(r5, v2, v3, n + 1, ws); /* A(+2)*B(+2) */
+ mpn_toom_couple_handling (r5, 2*n+1, pp, sign, n, 1, 2);
+
+ /* A(0)*B(0) */
+ TOOM_63_MUL_N_REC(pp, ap, bp, n, ws);
+
+ /* Infinity */
+ if (s > t) {
+ TOOM_63_MUL_REC(r1, a5, s, b2, t, ws);
+ } else {
+ TOOM_63_MUL_REC(r1, b2, t, a5, s, ws);
+ };
+
+ mpn_toom_interpolate_8pts (pp, n, r3, r7, s + t, ws);
+
+#undef a5
+#undef b0
+#undef b1
+#undef b2
+#undef r1
+#undef r3
+#undef r5
+#undef v0
+#undef v1
+#undef v2
+#undef v3
+#undef r7
+#undef r8
+#undef ws
+}