toom63_mul.c
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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 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 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.
- 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 Lesser General Public
- License for more details.
- You should have received a copy of the GNU Lesser General Public License
- along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */
- #include "gmp.h"
- #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] = 0;
- v1[n] = 0;
- sign = ~sign;
- }
- else
- {
- mp_limb_t cy2;
- cy2 = mpn_add_n_sub_n (v3, v1, ws, b1, n);
- w3[n] = cy + (cy2 >> 1);
- w1[n] = cy - (cy & 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
- }