1 /* mpn_toom22_mul -- Multiply {ap,an} and {bp,bn} where an >= bn. Or more
2 accurately, bn <= an < 2bn.
3
4 Contributed to the GNU project by Torbjorn Granlund.
5
6 THE FUNCTION IN THIS FILE IS INTERNAL WITH A MUTABLE INTERFACE. IT IS ONLY
7 SAFE TO REACH IT THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
8 GUARANTEED THAT IT WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
9
10 Copyright 2006-2010, 2012, 2014, 2018, 2020 Free Software Foundation, Inc.
11
12 This file is part of the GNU MP Library.
13
14 The GNU MP Library is free software; you can redistribute it and/or modify
15 it under the terms of either:
16
17 * the GNU Lesser General Public License as published by the Free
18 Software Foundation; either version 3 of the License, or (at your
19 option) any later version.
20
21 or
22
23 * the GNU General Public License as published by the Free Software
24 Foundation; either version 2 of the License, or (at your option) any
25 later version.
26
27 or both in parallel, as here.
28
29 The GNU MP Library is distributed in the hope that it will be useful, but
30 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
31 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
32 for more details.
33
34 You should have received copies of the GNU General Public License and the
35 GNU Lesser General Public License along with the GNU MP Library. If not,
36 see https://www.gnu.org/licenses/. */
37
38
39 #include "gmp-impl.h"
40
41 /* Evaluate in: -1, 0, +inf
42
43 <-s--><--n-->
44 ____ ______
45 |_a1_|___a0_|
46 |b1_|___b0_|
47 <-t-><--n-->
48
49 v0 = a0 * b0 # A(0)*B(0)
50 vm1 = (a0- a1)*(b0- b1) # A(-1)*B(-1)
51 vinf= a1 * b1 # A(inf)*B(inf)
52 */
53
54 #if TUNE_PROGRAM_BUILD || WANT_FAT_BINARY
55 #define MAYBE_mul_toom22 1
56 #else
57 #define MAYBE_mul_toom22 \
58 (MUL_TOOM33_THRESHOLD >= 2 * MUL_TOOM22_THRESHOLD)
59 #endif
60
61 #define TOOM22_MUL_N_REC(p, a, b, n, ws) \
62 do { \
63 if (! MAYBE_mul_toom22 \
64 || BELOW_THRESHOLD (n, MUL_TOOM22_THRESHOLD)) \
65 mpn_mul_basecase (p, a, n, b, n); \
66 else \
67 mpn_toom22_mul (p, a, n, b, n, ws); \
68 } while (0)
69
70 /* Normally, this calls mul_basecase or toom22_mul. But when when the fraction
71 MUL_TOOM33_THRESHOLD / MUL_TOOM22_THRESHOLD is large, an initially small
72 relative unbalance will become a larger and larger relative unbalance with
73 each recursion (the difference s-t will be invariant over recursive calls).
74 Therefore, we need to call toom32_mul. FIXME: Suppress depending on
75 MUL_TOOM33_THRESHOLD / MUL_TOOM22_THRESHOLD and on MUL_TOOM22_THRESHOLD. */
76 #define TOOM22_MUL_REC(p, a, an, b, bn, ws) \
77 do { \
78 if (! MAYBE_mul_toom22 \
79 || BELOW_THRESHOLD (bn, MUL_TOOM22_THRESHOLD)) \
80 mpn_mul_basecase (p, a, an, b, bn); \
81 else if (4 * an < 5 * bn) \
82 mpn_toom22_mul (p, a, an, b, bn, ws); \
83 else \
84 mpn_toom32_mul (p, a, an, b, bn, ws); \
85 } while (0)
86
87 void
88 mpn_toom22_mul (mp_ptr pp,
89 mp_srcptr ap, mp_size_t an,
90 mp_srcptr bp, mp_size_t bn,
91 mp_ptr scratch)
92 {
93 const int __gmpn_cpuvec_initialized = 1;
94 mp_size_t n, s, t;
95 int vm1_neg;
96 mp_limb_t cy, cy2;
97 mp_ptr asm1;
98 mp_ptr bsm1;
99
100 #define a0 ap
101 #define a1 (ap + n)
102 #define b0 bp
103 #define b1 (bp + n)
104
105 s = an >> 1;
106 n = an - s;
107 t = bn - n;
108
109 ASSERT (an >= bn);
110
111 ASSERT (0 < s && s <= n && (n - s) == (an & 1));
112 ASSERT (0 < t && t <= s);
113
114 asm1 = pp;
115 bsm1 = pp + n;
116
117 vm1_neg = 0;
118
119 /* Compute asm1. */
120 if ((an & 1) == 0) /* s == n */
121 {
122 if (mpn_cmp (a0, a1, n) < 0)
123 {
124 mpn_sub_n (asm1, a1, a0, n);
125 vm1_neg = 1;
126 }
127 else
128 {
129 mpn_sub_n (asm1, a0, a1, n);
130 }
131 }
132 else /* n - s == 1 */
133 {
134 if (a0[s] == 0 && mpn_cmp (a0, a1, s) < 0)
135 {
136 mpn_sub_n (asm1, a1, a0, s);
137 asm1[s] = 0;
138 vm1_neg = 1;
139 }
140 else
141 {
142 asm1[s] = a0[s] - mpn_sub_n (asm1, a0, a1, s);
143 }
144 }
145
146 /* Compute bsm1. */
147 if (t == n)
148 {
149 if (mpn_cmp (b0, b1, n) < 0)
150 {
151 mpn_sub_n (bsm1, b1, b0, n);
152 vm1_neg ^= 1;
153 }
154 else
155 {
156 mpn_sub_n (bsm1, b0, b1, n);
157 }
158 }
159 else
160 {
161 if (mpn_zero_p (b0 + t, n - t) && mpn_cmp (b0, b1, t) < 0)
162 {
163 mpn_sub_n (bsm1, b1, b0, t);
164 MPN_ZERO (bsm1 + t, n - t);
165 vm1_neg ^= 1;
166 }
167 else
168 {
169 mpn_sub (bsm1, b0, n, b1, t);
170 }
171 }
172
173 #define v0 pp /* 2n */
174 #define vinf (pp + 2 * n) /* s+t */
175 #define vm1 scratch /* 2n */
176 #define scratch_out scratch + 2 * n
177
178 /* vm1, 2n limbs */
179 TOOM22_MUL_N_REC (vm1, asm1, bsm1, n, scratch_out);
180
181 if (s > t) TOOM22_MUL_REC (vinf, a1, s, b1, t, scratch_out);
182 else TOOM22_MUL_N_REC (vinf, a1, b1, s, scratch_out);
183
184 /* v0, 2n limbs */
185 TOOM22_MUL_N_REC (v0, ap, bp, n, scratch_out);
186
187 /* H(v0) + L(vinf) */
188 cy = mpn_add_n (pp + 2 * n, v0 + n, vinf, n);
189
190 /* L(v0) + (H(v0) + L(vinf)) */
191 cy2 = cy + mpn_add_n (pp + n, pp + 2 * n, v0, n);
192
193 /* (H(v0) + L(vinf)) + H(vinf) */
194 cy += mpn_add (pp + 2 * n, pp + 2 * n, n, vinf + n, s + t - n);
195
196 if (vm1_neg)
197 cy += mpn_add_n (pp + n, pp + n, vm1, 2 * n);
198 else {
199 cy -= mpn_sub_n (pp + n, pp + n, vm1, 2 * n);
200 if (UNLIKELY (cy + 1 == 0)) { /* cy is negative */
201 /* The total contribution of v0+vinf-vm1 can not be negative. */
202 #if WANT_ASSERT
203 /* The borrow in cy stops the propagation of the carry cy2, */
204 ASSERT (cy2 == 1);
205 cy += mpn_add_1 (pp + 2 * n, pp + 2 * n, n, cy2);
206 ASSERT (cy == 0);
207 #else
208 /* we simply fill the area with zeros. */
209 MPN_FILL (pp + 2 * n, n, 0);
210 /* ASSERT (s + t == n || mpn_zero_p (pp + 3 * n, s + t - n)); */
211 #endif
212 return;
213 }
214 }
215
216 ASSERT (cy <= 2);
217 ASSERT (cy2 <= 2);
218
219 MPN_INCR_U (pp + 2 * n, s + t, cy2);
220 /* if s+t==n, cy is zero, but we should not access pp[3*n] at all. */
221 MPN_INCR_U (pp + 3 * n, s + t - n, cy);
222 }