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, 2007, 2008, 2009, 2010 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 the GNU Lesser General Public License as published by
16 the Free Software Foundation; either version 3 of the License, or (at your
17 option) any later version.
18
19 The GNU MP Library is distributed in the hope that it will be useful, but
20 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
21 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
22 License for more details.
23
24 You should have received a copy of the GNU Lesser General Public License
25 along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */
26
27
28 #include "gmp.h"
29 #include "gmp-impl.h"
30
31 /* Evaluate in: -1, 0, +inf
32
33 <-s--><--n-->
34 ____ ______
35 |_a1_|___a0_|
36 |b1_|___b0_|
37 <-t-><--n-->
38
39 v0 = a0 * b0 # A(0)*B(0)
40 vm1 = (a0- a1)*(b0- b1) # A(-1)*B(-1)
41 vinf= a1 * b1 # A(inf)*B(inf)
42 */
43
44 #if TUNE_PROGRAM_BUILD
45 #define MAYBE_mul_toom22 1
46 #else
47 #define MAYBE_mul_toom22 \
48 (MUL_TOOM33_THRESHOLD >= 2 * MUL_TOOM22_THRESHOLD)
49 #endif
50
51 #define TOOM22_MUL_N_REC(p, a, b, n, ws) \
52 do { \
53 if (! MAYBE_mul_toom22 \
54 || BELOW_THRESHOLD (n, MUL_TOOM22_THRESHOLD)) \
55 mpn_mul_basecase (p, a, n, b, n); \
56 else \
57 mpn_toom22_mul (p, a, n, b, n, ws); \
58 } while (0)
59
60 /* Normally, this calls mul_basecase or toom22_mul. But when when the fraction
61 MUL_TOOM33_THRESHOLD / MUL_TOOM22_THRESHOLD is large, an initially small
62 relative unbalance will become a larger and larger relative unbalance with
63 each recursion (the difference s-t will be invariant over recursive calls).
64 Therefore, we need to call toom32_mul. FIXME: Suppress depending on
65 MUL_TOOM33_THRESHOLD / MUL_TOOM22_THRESHOLD and on MUL_TOOM22_THRESHOLD. */
66 #define TOOM22_MUL_REC(p, a, an, b, bn, ws) \
67 do { \
68 if (! MAYBE_mul_toom22 \
69 || BELOW_THRESHOLD (bn, MUL_TOOM22_THRESHOLD)) \
70 mpn_mul_basecase (p, a, an, b, bn); \
71 else if (4 * an < 5 * bn) \
72 mpn_toom22_mul (p, a, an, b, bn, ws); \
73 else \
74 mpn_toom32_mul (p, a, an, b, bn, ws); \
75 } while (0)
76
77 void
mpn_toom22_mul(mp_ptr pp,mp_srcptr ap,mp_size_t an,mp_srcptr bp,mp_size_t bn,mp_ptr scratch)78 mpn_toom22_mul (mp_ptr pp,
79 mp_srcptr ap, mp_size_t an,
80 mp_srcptr bp, mp_size_t bn,
81 mp_ptr scratch)
82 {
83 mp_size_t n, s, t;
84 int vm1_neg;
85 mp_limb_t cy, cy2;
86 mp_ptr asm1;
87 mp_ptr bsm1;
88
89 #define a0 ap
90 #define a1 (ap + n)
91 #define b0 bp
92 #define b1 (bp + n)
93
94 s = an >> 1;
95 n = an - s;
96 t = bn - n;
97
98 ASSERT (an >= bn);
99
100 ASSERT (0 < s && s <= n);
101 ASSERT (0 < t && t <= s);
102
103 asm1 = pp;
104 bsm1 = pp + n;
105
106 vm1_neg = 0;
107
108 /* Compute asm1. */
109 if (s == n)
110 {
111 if (mpn_cmp (a0, a1, n) < 0)
112 {
113 mpn_sub_n (asm1, a1, a0, n);
114 vm1_neg = 1;
115 }
116 else
117 {
118 mpn_sub_n (asm1, a0, a1, n);
119 }
120 }
121 else
122 {
123 if (mpn_zero_p (a0 + s, n - s) && mpn_cmp (a0, a1, s) < 0)
124 {
125 mpn_sub_n (asm1, a1, a0, s);
126 MPN_ZERO (asm1 + s, n - s);
127 vm1_neg = 1;
128 }
129 else
130 {
131 mpn_sub (asm1, a0, n, a1, s);
132 }
133 }
134
135 /* Compute bsm1. */
136 if (t == n)
137 {
138 if (mpn_cmp (b0, b1, n) < 0)
139 {
140 mpn_sub_n (bsm1, b1, b0, n);
141 vm1_neg ^= 1;
142 }
143 else
144 {
145 mpn_sub_n (bsm1, b0, b1, n);
146 }
147 }
148 else
149 {
150 if (mpn_zero_p (b0 + t, n - t) && mpn_cmp (b0, b1, t) < 0)
151 {
152 mpn_sub_n (bsm1, b1, b0, t);
153 MPN_ZERO (bsm1 + t, n - t);
154 vm1_neg ^= 1;
155 }
156 else
157 {
158 mpn_sub (bsm1, b0, n, b1, t);
159 }
160 }
161
162 #define v0 pp /* 2n */
163 #define vinf (pp + 2 * n) /* s+t */
164 #define vm1 scratch /* 2n */
165 #define scratch_out scratch + 2 * n
166
167 /* vm1, 2n limbs */
168 TOOM22_MUL_N_REC (vm1, asm1, bsm1, n, scratch_out);
169
170 if (s > t) TOOM22_MUL_REC (vinf, a1, s, b1, t, scratch_out);
171 else TOOM22_MUL_N_REC (vinf, a1, b1, s, scratch_out);
172
173 /* v0, 2n limbs */
174 TOOM22_MUL_N_REC (v0, ap, bp, n, scratch_out);
175
176 /* H(v0) + L(vinf) */
177 cy = mpn_add_n (pp + 2 * n, v0 + n, vinf, n);
178
179 /* L(v0) + H(v0) */
180 cy2 = cy + mpn_add_n (pp + n, pp + 2 * n, v0, n);
181
182 /* L(vinf) + H(vinf) */
183 cy += mpn_add (pp + 2 * n, pp + 2 * n, n, vinf + n, s + t - n);
184
185 if (vm1_neg)
186 cy += mpn_add_n (pp + n, pp + n, vm1, 2 * n);
187 else
188 cy -= mpn_sub_n (pp + n, pp + n, vm1, 2 * n);
189
190 ASSERT (cy + 1 <= 3);
191 ASSERT (cy2 <= 2);
192
193 mpn_incr_u (pp + 2 * n, cy2);
194 if (LIKELY (cy <= 2))
195 mpn_incr_u (pp + 3 * n, cy);
196 else
197 mpn_decr_u (pp + 3 * n, 1);
198 }
199