1 /* mpn_toom42_mul -- Multiply {ap,an} and {bp,bn} where an is nominally twice
2 as large as bn. Or more accurately, (3/2)bn < an < 4bn.
4 Contributed to the GNU project by Torbjorn Granlund.
5 Additional improvements by Marco Bodrato.
7 The idea of applying toom to unbalanced multiplication is due to Marco
8 Bodrato and Alberto Zanoni.
10 THE FUNCTION IN THIS FILE IS INTERNAL WITH A MUTABLE INTERFACE. IT IS ONLY
11 SAFE TO REACH IT THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
12 GUARANTEED THAT IT WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
14 Copyright 2006, 2007, 2008 Free Software Foundation, Inc.
16 This file is part of the GNU MP Library.
18 The GNU MP Library is free software; you can redistribute it and/or modify
19 it under the terms of the GNU Lesser General Public License as published by
20 the Free Software Foundation; either version 3 of the License, or (at your
21 option) any later version.
23 The GNU MP Library is distributed in the hope that it will be useful, but
24 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
25 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
26 License for more details.
28 You should have received a copy of the GNU Lesser General Public License
29 along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */
35 /* Evaluate in: -1, 0, +1, +2, +inf
37 <-s-><--n--><--n--><--n-->
38 ___ ______ ______ ______
39 |a3_|___a2_|___a1_|___a0_|
43 v0 = a0 * b0 # A(0)*B(0)
44 v1 = (a0+ a1+ a2+ a3)*(b0+ b1) # A(1)*B(1) ah <= 3 bh <= 1
45 vm1 = (a0- a1+ a2- a3)*(b0- b1) # A(-1)*B(-1) |ah| <= 1 bh = 0
46 v2 = (a0+2a1+4a2+8a3)*(b0+2b1) # A(2)*B(2) ah <= 14 bh <= 2
47 vinf= a3 * b1 # A(inf)*B(inf)
50 #define TOOM42_MUL_N_REC(p, a, b, n, ws) \
52 mpn_mul_n (p, a, b, n); \
56 mpn_toom42_mul (mp_ptr pp,
57 mp_srcptr ap, mp_size_t an,
58 mp_srcptr bp, mp_size_t bn,
65 mp_ptr as1, asm1, as2;
66 mp_ptr bs1, bsm1, bs2;
76 n = an >= 2 * bn ? (an + 3) >> 2 : (bn + 1) >> 1;
81 ASSERT (0 < s && s <= n);
82 ASSERT (0 < t && t <= n);
86 as1 = TMP_SALLOC_LIMBS (n + 1);
87 asm1 = TMP_SALLOC_LIMBS (n + 1);
88 as2 = TMP_SALLOC_LIMBS (n + 1);
90 bs1 = TMP_SALLOC_LIMBS (n + 1);
91 bsm1 = TMP_SALLOC_LIMBS (n);
92 bs2 = TMP_SALLOC_LIMBS (n + 1);
97 /* Compute as1 and asm1. */
98 vm1_neg = mpn_toom_eval_dgr3_pm1 (as1, asm1, ap, n, s, a0_a2) & 1;
101 #if HAVE_NATIVE_mpn_addlsh1_n
102 cy = mpn_addlsh1_n (as2, a2, a3, s);
104 cy = mpn_add_1 (as2 + s, a2 + s, n - s, cy);
105 cy = 2 * cy + mpn_addlsh1_n (as2, a1, as2, n);
106 cy = 2 * cy + mpn_addlsh1_n (as2, a0, as2, n);
108 cy = mpn_lshift (as2, a3, s, 1);
109 cy += mpn_add_n (as2, a2, as2, s);
111 cy = mpn_add_1 (as2 + s, a2 + s, n - s, cy);
112 cy = 2 * cy + mpn_lshift (as2, as2, n, 1);
113 cy += mpn_add_n (as2, a1, as2, n);
114 cy = 2 * cy + mpn_lshift (as2, as2, n, 1);
115 cy += mpn_add_n (as2, a0, as2, n);
119 /* Compute bs1 and bsm1. */
122 #if HAVE_NATIVE_mpn_add_n_sub_n
123 if (mpn_cmp (b0, b1, n) < 0)
125 cy = mpn_add_n_sub_n (bs1, bsm1, b1, b0, n);
130 cy = mpn_add_n_sub_n (bs1, bsm1, b0, b1, n);
134 bs1[n] = mpn_add_n (bs1, b0, b1, n);
136 if (mpn_cmp (b0, b1, n) < 0)
138 mpn_sub_n (bsm1, b1, b0, n);
143 mpn_sub_n (bsm1, b0, b1, n);
149 bs1[n] = mpn_add (bs1, b0, n, b1, t);
151 if (mpn_zero_p (b0 + t, n - t) && mpn_cmp (b0, b1, t) < 0)
153 mpn_sub_n (bsm1, b1, b0, t);
154 MPN_ZERO (bsm1 + t, n - t);
159 mpn_sub (bsm1, b0, n, b1, t);
163 /* Compute bs2, recycling bs1. bs2=bs1+b1 */
164 mpn_add (bs2, bs1, n + 1, b1, t);
166 ASSERT (as1[n] <= 3);
167 ASSERT (bs1[n] <= 1);
168 ASSERT (asm1[n] <= 1);
169 /*ASSERT (bsm1[n] == 0);*/
170 ASSERT (as2[n] <= 14);
171 ASSERT (bs2[n] <= 2);
173 #define v0 pp /* 2n */
174 #define v1 (pp + 2 * n) /* 2n+1 */
175 #define vinf (pp + 4 * n) /* s+t */
176 #define vm1 scratch /* 2n+1 */
177 #define v2 (scratch + 2 * n + 1) /* 2n+2 */
178 #define scratch_out scratch + 4 * n + 4 /* Currently unused. */
180 /* vm1, 2n+1 limbs */
181 TOOM42_MUL_N_REC (vm1, asm1, bsm1, n, scratch_out);
184 cy = mpn_add_n (vm1 + n, vm1 + n, bsm1, n);
187 TOOM42_MUL_N_REC (v2, as2, bs2, n + 1, scratch_out); /* v2, 2n+1 limbs */
189 /* vinf, s+t limbs */
190 if (s > t) mpn_mul (vinf, a3, s, b1, t);
191 else mpn_mul (vinf, b1, t, a3, s);
193 vinf0 = vinf[0]; /* v1 overlaps with this */
196 TOOM42_MUL_N_REC (v1, as1, bs1, n, scratch_out);
199 cy = bs1[n] + mpn_add_n (v1 + n, v1 + n, bs1, n);
201 else if (as1[n] == 2)
203 #if HAVE_NATIVE_mpn_addlsh1_n
204 cy = 2 * bs1[n] + mpn_addlsh1_n (v1 + n, v1 + n, bs1, n);
206 cy = 2 * bs1[n] + mpn_addmul_1 (v1 + n, bs1, n, CNST_LIMB(2));
209 else if (as1[n] == 3)
211 cy = 3 * bs1[n] + mpn_addmul_1 (v1 + n, bs1, n, CNST_LIMB(3));
216 cy += mpn_add_n (v1 + n, v1 + n, as1, n);
219 TOOM42_MUL_N_REC (v0, ap, bp, n, scratch_out); /* v0, 2n limbs */
221 mpn_toom_interpolate_5pts (pp, v2, vm1, n, s + t, vm1_neg, vinf0);