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