1 /* Implementation of the algorithm for Toom-Cook 4.5-way.
2
3 Contributed to the GNU project by Marco Bodrato.
4
5 THE FUNCTION IN THIS FILE IS INTERNAL WITH A MUTABLE INTERFACE. IT IS ONLY
6 SAFE TO REACH IT THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
7 GUARANTEED THAT IT WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
8
9 Copyright 2009, 2012 Free Software Foundation, Inc.
10
11 This file is part of the GNU MP Library.
12
13 The GNU MP Library is free software; you can redistribute it and/or modify
14 it under the terms of either:
15
16 * the GNU Lesser General Public License as published by the Free
17 Software Foundation; either version 3 of the License, or (at your
18 option) any later version.
19
20 or
21
22 * the GNU General Public License as published by the Free Software
23 Foundation; either version 2 of the License, or (at your option) any
24 later version.
25
26 or both in parallel, as here.
27
28 The GNU MP Library is distributed in the hope that it will be useful, but
29 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
30 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
31 for more details.
32
33 You should have received copies of the GNU General Public License and the
34 GNU Lesser General Public License along with the GNU MP Library. If not,
35 see https://www.gnu.org/licenses/. */
36
37
38 #include "gmp.h"
39 #include "gmp-impl.h"
40
41 /* Stores |{ap,n}-{bp,n}| in {rp,n}, returns the sign. */
42 static int
abs_sub_n(mp_ptr rp,mp_srcptr ap,mp_srcptr bp,mp_size_t n)43 abs_sub_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n)
44 {
45 mp_limb_t x, y;
46 while (--n >= 0)
47 {
48 x = ap[n];
49 y = bp[n];
50 if (x != y)
51 {
52 n++;
53 if (x > y)
54 {
55 mpn_sub_n (rp, ap, bp, n);
56 return 0;
57 }
58 else
59 {
60 mpn_sub_n (rp, bp, ap, n);
61 return ~0;
62 }
63 }
64 rp[n] = 0;
65 }
66 return 0;
67 }
68
69 static int
abs_sub_add_n(mp_ptr rm,mp_ptr rp,mp_srcptr rs,mp_size_t n)70 abs_sub_add_n (mp_ptr rm, mp_ptr rp, mp_srcptr rs, mp_size_t n) {
71 int result;
72 result = abs_sub_n (rm, rp, rs, n);
73 ASSERT_NOCARRY(mpn_add_n (rp, rp, rs, n));
74 return result;
75 }
76
77
78 /* Toom-4.5, the splitting 6x3 unbalanced version.
79 Evaluate in: infinity, +4, -4, +2, -2, +1, -1, 0.
80
81 <--s-><--n--><--n--><--n--><--n--><--n-->
82 ____ ______ ______ ______ ______ ______
83 |_a5_|__a4__|__a3__|__a2__|__a1__|__a0__|
84 |b2_|__b1__|__b0__|
85 <-t-><--n--><--n-->
86
87 */
88 #define TOOM_63_MUL_N_REC(p, a, b, n, ws) \
89 do { mpn_mul_n (p, a, b, n); \
90 } while (0)
91
92 #define TOOM_63_MUL_REC(p, a, na, b, nb, ws) \
93 do { mpn_mul (p, a, na, b, nb); \
94 } while (0)
95
96 void
mpn_toom63_mul(mp_ptr pp,mp_srcptr ap,mp_size_t an,mp_srcptr bp,mp_size_t bn,mp_ptr scratch)97 mpn_toom63_mul (mp_ptr pp,
98 mp_srcptr ap, mp_size_t an,
99 mp_srcptr bp, mp_size_t bn, mp_ptr scratch)
100 {
101 mp_size_t n, s, t;
102 mp_limb_t cy;
103 int sign;
104
105 /***************************** decomposition *******************************/
106 #define a5 (ap + 5 * n)
107 #define b0 (bp + 0 * n)
108 #define b1 (bp + 1 * n)
109 #define b2 (bp + 2 * n)
110
111 ASSERT (an >= bn);
112 n = 1 + (an >= 2 * bn ? (an - 1) / (size_t) 6 : (bn - 1) / (size_t) 3);
113
114 s = an - 5 * n;
115 t = bn - 2 * n;
116
117 ASSERT (0 < s && s <= n);
118 ASSERT (0 < t && t <= n);
119 /* WARNING! it assumes s+t>=n */
120 ASSERT ( s + t >= n );
121 ASSERT ( s + t > 4);
122 /* WARNING! it assumes n>1 */
123 ASSERT ( n > 2);
124
125 #define r8 pp /* 2n */
126 #define r7 scratch /* 3n+1 */
127 #define r5 (pp + 3*n) /* 3n+1 */
128 #define v0 (pp + 3*n) /* n+1 */
129 #define v1 (pp + 4*n+1) /* n+1 */
130 #define v2 (pp + 5*n+2) /* n+1 */
131 #define v3 (pp + 6*n+3) /* n+1 */
132 #define r3 (scratch + 3 * n + 1) /* 3n+1 */
133 #define r1 (pp + 7*n) /* s+t <= 2*n */
134 #define ws (scratch + 6 * n + 2) /* ??? */
135
136 /* Alloc also 3n+1 limbs for ws... mpn_toom_interpolate_8pts may
137 need all of them, when DO_mpn_sublsh_n usea a scratch */
138 /* if (scratch == NULL) scratch = TMP_SALLOC_LIMBS (9 * n + 3); */
139
140 /********************** evaluation and recursive calls *********************/
141 /* $\pm4$ */
142 sign = mpn_toom_eval_pm2exp (v2, v0, 5, ap, n, s, 2, pp);
143 pp[n] = mpn_lshift (pp, b1, n, 2); /* 4b1 */
144 /* FIXME: use addlsh */
145 v3[t] = mpn_lshift (v3, b2, t, 4);/* 16b2 */
146 if ( n == t )
147 v3[n]+= mpn_add_n (v3, v3, b0, n); /* 16b2+b0 */
148 else
149 v3[n] = mpn_add (v3, b0, n, v3, t+1); /* 16b2+b0 */
150 sign ^= abs_sub_add_n (v1, v3, pp, n + 1);
151 TOOM_63_MUL_N_REC(pp, v0, v1, n + 1, ws); /* A(-4)*B(-4) */
152 TOOM_63_MUL_N_REC(r3, v2, v3, n + 1, ws); /* A(+4)*B(+4) */
153 mpn_toom_couple_handling (r3, 2*n+1, pp, sign, n, 2, 4);
154
155 /* $\pm1$ */
156 sign = mpn_toom_eval_pm1 (v2, v0, 5, ap, n, s, pp);
157 /* Compute bs1 and bsm1. Code taken from toom33 */
158 cy = mpn_add (ws, b0, n, b2, t);
159 #if HAVE_NATIVE_mpn_add_n_sub_n
160 if (cy == 0 && mpn_cmp (ws, b1, n) < 0)
161 {
162 cy = mpn_add_n_sub_n (v3, v1, b1, ws, n);
163 v3[n] = cy >> 1;
164 v1[n] = 0;
165 sign = ~sign;
166 }
167 else
168 {
169 mp_limb_t cy2;
170 cy2 = mpn_add_n_sub_n (v3, v1, ws, b1, n);
171 v3[n] = cy + (cy2 >> 1);
172 v1[n] = cy - (cy2 & 1);
173 }
174 #else
175 v3[n] = cy + mpn_add_n (v3, ws, b1, n);
176 if (cy == 0 && mpn_cmp (ws, b1, n) < 0)
177 {
178 mpn_sub_n (v1, b1, ws, n);
179 v1[n] = 0;
180 sign = ~sign;
181 }
182 else
183 {
184 cy -= mpn_sub_n (v1, ws, b1, n);
185 v1[n] = cy;
186 }
187 #endif
188 TOOM_63_MUL_N_REC(pp, v0, v1, n + 1, ws); /* A(-1)*B(-1) */
189 TOOM_63_MUL_N_REC(r7, v2, v3, n + 1, ws); /* A(1)*B(1) */
190 mpn_toom_couple_handling (r7, 2*n+1, pp, sign, n, 0, 0);
191
192 /* $\pm2$ */
193 sign = mpn_toom_eval_pm2 (v2, v0, 5, ap, n, s, pp);
194 pp[n] = mpn_lshift (pp, b1, n, 1); /* 2b1 */
195 /* FIXME: use addlsh or addlsh2 */
196 v3[t] = mpn_lshift (v3, b2, t, 2);/* 4b2 */
197 if ( n == t )
198 v3[n]+= mpn_add_n (v3, v3, b0, n); /* 4b2+b0 */
199 else
200 v3[n] = mpn_add (v3, b0, n, v3, t+1); /* 4b2+b0 */
201 sign ^= abs_sub_add_n (v1, v3, pp, n + 1);
202 TOOM_63_MUL_N_REC(pp, v0, v1, n + 1, ws); /* A(-2)*B(-2) */
203 TOOM_63_MUL_N_REC(r5, v2, v3, n + 1, ws); /* A(+2)*B(+2) */
204 mpn_toom_couple_handling (r5, 2*n+1, pp, sign, n, 1, 2);
205
206 /* A(0)*B(0) */
207 TOOM_63_MUL_N_REC(pp, ap, bp, n, ws);
208
209 /* Infinity */
210 if (s > t) {
211 TOOM_63_MUL_REC(r1, a5, s, b2, t, ws);
212 } else {
213 TOOM_63_MUL_REC(r1, b2, t, a5, s, ws);
214 };
215
216 mpn_toom_interpolate_8pts (pp, n, r3, r7, s + t, ws);
217
218 #undef a5
219 #undef b0
220 #undef b1
221 #undef b2
222 #undef r1
223 #undef r3
224 #undef r5
225 #undef v0
226 #undef v1
227 #undef v2
228 #undef v3
229 #undef r7
230 #undef r8
231 #undef ws
232 }
233