1 /* mpn_toom3_sqr -- Square {ap,an}.
2
3 Contributed to the GNU project by Torbjorn Granlund.
4 Additional improvements by Marco Bodrato.
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, 2015, 2021 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, +1, +2, +inf
42
43 <-s--><--n--><--n-->
44 ____ ______ ______
45 |_a2_|___a1_|___a0_|
46
47 v0 = a0 ^2 # A(0)^2
48 v1 = (a0+ a1+ a2)^2 # A(1)^2 ah <= 2
49 vm1 = (a0- a1+ a2)^2 # A(-1)^2 |ah| <= 1
50 v2 = (a0+2a1+4a2)^2 # A(2)^2 ah <= 6
51 vinf= a2 ^2 # A(inf)^2
52 */
53
54 #if TUNE_PROGRAM_BUILD || WANT_FAT_BINARY
55 #define MAYBE_sqr_basecase 1
56 #define MAYBE_sqr_toom3 1
57 #else
58 #define MAYBE_sqr_basecase \
59 (SQR_TOOM3_THRESHOLD < 3 * SQR_TOOM2_THRESHOLD)
60 #define MAYBE_sqr_toom3 \
61 (SQR_TOOM4_THRESHOLD >= 3 * SQR_TOOM3_THRESHOLD)
62 #endif
63
64 #define TOOM3_SQR_REC(p, a, n, ws) \
65 do { \
66 if (MAYBE_sqr_basecase \
67 && BELOW_THRESHOLD (n, SQR_TOOM2_THRESHOLD)) \
68 mpn_sqr_basecase (p, a, n); \
69 else if (! MAYBE_sqr_toom3 \
70 || BELOW_THRESHOLD (n, SQR_TOOM3_THRESHOLD)) \
71 mpn_toom2_sqr (p, a, n, ws); \
72 else \
73 mpn_toom3_sqr (p, a, n, ws); \
74 } while (0)
75
76 void
77 mpn_toom3_sqr (mp_ptr pp,
78 mp_srcptr ap, mp_size_t an,
79 mp_ptr scratch)
80 {
81 const int __gmpn_cpuvec_initialized = 1;
82 mp_size_t n, s;
83 mp_limb_t cy, vinf0;
84 mp_ptr gp;
85 mp_ptr as1, asm1, as2;
86
87 #define a0 ap
88 #define a1 (ap + n)
89 #define a2 (ap + 2*n)
90
91 n = (an + 2) / (size_t) 3;
92
93 s = an - 2 * n;
94
95 ASSERT (0 < s && s <= n);
96
97 as1 = scratch + 4 * n + 4;
98 asm1 = scratch + 2 * n + 2;
99 as2 = pp + n + 1;
100
101 gp = scratch;
102
103 /* Compute as1 and asm1. */
104 cy = mpn_add (gp, a0, n, a2, s);
105 #if HAVE_NATIVE_mpn_add_n_sub_n
106 if (cy == 0 && mpn_cmp (gp, a1, n) < 0)
107 {
108 cy = mpn_add_n_sub_n (as1, asm1, a1, gp, n);
109 as1[n] = cy >> 1;
110 asm1[n] = 0;
111 }
112 else
113 {
114 mp_limb_t cy2;
115 cy2 = mpn_add_n_sub_n (as1, asm1, gp, a1, n);
116 as1[n] = cy + (cy2 >> 1);
117 asm1[n] = cy - (cy2 & 1);
118 }
119 #else
120 as1[n] = cy + mpn_add_n (as1, gp, a1, n);
121 if (cy == 0 && mpn_cmp (gp, a1, n) < 0)
122 {
123 mpn_sub_n (asm1, a1, gp, n);
124 asm1[n] = 0;
125 }
126 else
127 {
128 cy -= mpn_sub_n (asm1, gp, a1, n);
129 asm1[n] = cy;
130 }
131 #endif
132
133 /* Compute as2. */
134 #if HAVE_NATIVE_mpn_rsblsh1_n
135 cy = mpn_add_n (as2, a2, as1, s);
136 if (s != n)
137 cy = mpn_add_1 (as2 + s, as1 + s, n - s, cy);
138 cy += as1[n];
139 cy = 2 * cy + mpn_rsblsh1_n (as2, a0, as2, n);
140 #else
141 #if HAVE_NATIVE_mpn_addlsh1_n
142 cy = mpn_addlsh1_n (as2, a1, a2, s);
143 if (s != n)
144 cy = mpn_add_1 (as2 + s, a1 + s, n - s, cy);
145 cy = 2 * cy + mpn_addlsh1_n (as2, a0, as2, n);
146 #else
147 cy = mpn_add_n (as2, a2, as1, s);
148 if (s != n)
149 cy = mpn_add_1 (as2 + s, as1 + s, n - s, cy);
150 cy += as1[n];
151 cy = 2 * cy + mpn_lshift (as2, as2, n, 1);
152 cy -= mpn_sub_n (as2, as2, a0, n);
153 #endif
154 #endif
155 as2[n] = cy;
156
157 ASSERT (as1[n] <= 2);
158 ASSERT (asm1[n] <= 1);
159
160 #define v0 pp /* 2n */
161 #define v1 (pp + 2 * n) /* 2n+1 */
162 #define vinf (pp + 4 * n) /* s+s */
163 #define vm1 scratch /* 2n+1 */
164 #define v2 (scratch + 2 * n + 1) /* 2n+2 */
165 #define scratch_out (scratch + 5 * n + 5)
166
167 /* vm1, 2n+1 limbs */
168 #ifdef SMALLER_RECURSION
169 TOOM3_SQR_REC (vm1, asm1, n, scratch_out);
170 cy = asm1[n];
171 if (cy != 0)
172 {
173 #if HAVE_NATIVE_mpn_addlsh1_n_ip1
174 cy += mpn_addlsh1_n_ip1 (vm1 + n, asm1, n);
175 #else
176 cy += mpn_addmul_1 (vm1 + n, asm1, n, CNST_LIMB(2));
177 #endif
178 }
179 vm1[2 * n] = cy;
180 #else
181 vm1[2 * n] = 0;
182 TOOM3_SQR_REC (vm1, asm1, n + asm1[n], scratch_out);
183 #endif
184
185 TOOM3_SQR_REC (v2, as2, n + 1, scratch_out); /* v2, 2n+1 limbs */
186
187 TOOM3_SQR_REC (vinf, a2, s, scratch_out); /* vinf, s+s limbs */
188
189 vinf0 = vinf[0]; /* v1 overlaps with this */
190
191 #ifdef SMALLER_RECURSION
192 /* v1, 2n+1 limbs */
193 TOOM3_SQR_REC (v1, as1, n, scratch_out);
194 cy = as1[n];
195 if (cy == 1)
196 {
197 #if HAVE_NATIVE_mpn_addlsh1_n_ip1
198 cy += mpn_addlsh1_n_ip1 (v1 + n, as1, n);
199 #else
200 cy += mpn_addmul_1 (v1 + n, as1, n, CNST_LIMB(2));
201 #endif
202 }
203 else if (cy != 0)
204 {
205 #if HAVE_NATIVE_mpn_addlsh2_n_ip1
206 cy = 4 + mpn_addlsh2_n_ip1 (v1 + n, as1, n);
207 #else
208 cy = 4 + mpn_addmul_1 (v1 + n, as1, n, CNST_LIMB(4));
209 #endif
210 }
211 v1[2 * n] = cy;
212 #else
213 cy = vinf[1];
214 TOOM3_SQR_REC (v1, as1, n + 1, scratch_out);
215 vinf[1] = cy;
216 #endif
217
218 TOOM3_SQR_REC (v0, ap, n, scratch_out); /* v0, 2n limbs */
219
220 mpn_toom_interpolate_5pts (pp, v2, vm1, n, s + s, 0, vinf0);
221 }