1 /* mpn_toom4_sqr -- Square {ap,an}.
2
3 Contributed to the GNU project by Torbjorn Granlund and 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 2006-2010, 2013, 2021 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-impl.h"
39
40 /* Evaluate in: -2, -1, 0, +1/2, +1, +2, +inf
41
42 <-s--><--n--><--n--><--n-->
43 ____ ______ ______ ______
44 |_a3_|___a2_|___a1_|___a0_|
45
46 v0 = a0 ^2 # A(0)^2
47 v1 = ( a0+ a1+ a2+ a3)^2 # A(1)^2 ah <= 3
48 vm1 = ( a0- a1+ a2- a3)^2 # A(-1)^2 |ah| <= 1
49 v2 = ( a0+2a1+4a2+8a3)^2 # A(2)^2 ah <= 14
50 vm2 = ( a0-2a1+4a2-8a3)^2 # A(-2)^2 -9<=ah<=4
51 vh = (8a0+4a1+2a2+ a3)^2 # A(1/2)^2 ah <= 14
52 vinf= a3 ^2 # A(inf)^2
53 */
54
55 #if TUNE_PROGRAM_BUILD
56 #define MAYBE_sqr_basecase 1
57 #define MAYBE_sqr_toom2 1
58 #define MAYBE_sqr_toom4 1
59 #else
60 #define MAYBE_sqr_basecase \
61 (SQR_TOOM4_THRESHOLD < 4 * SQR_TOOM2_THRESHOLD)
62 #define MAYBE_sqr_toom2 \
63 (SQR_TOOM4_THRESHOLD < 4 * SQR_TOOM3_THRESHOLD)
64 #define MAYBE_sqr_toom4 \
65 (SQR_TOOM6_THRESHOLD >= 4 * SQR_TOOM4_THRESHOLD)
66 #endif
67
68 #define TOOM4_SQR_REC(p, a, n, ws) \
69 do { \
70 if (MAYBE_sqr_basecase \
71 && BELOW_THRESHOLD (n, SQR_TOOM2_THRESHOLD)) \
72 mpn_sqr_basecase (p, a, n); \
73 else if (MAYBE_sqr_toom2 \
74 && BELOW_THRESHOLD (n, SQR_TOOM3_THRESHOLD)) \
75 mpn_toom2_sqr (p, a, n, ws); \
76 else if (! MAYBE_sqr_toom4 \
77 || BELOW_THRESHOLD (n, SQR_TOOM4_THRESHOLD)) \
78 mpn_toom3_sqr (p, a, n, ws); \
79 else \
80 mpn_toom4_sqr (p, a, n, ws); \
81 } while (0)
82
83 void
84 mpn_toom4_sqr (mp_ptr pp,
85 mp_srcptr ap, mp_size_t an,
86 mp_ptr scratch)
87 {
88 mp_size_t n, s;
89 mp_limb_t cy;
90
91 #define a0 ap
92 #define a1 (ap + n)
93 #define a2 (ap + 2*n)
94 #define a3 (ap + 3*n)
95
96 n = (an + 3) >> 2;
97
98 s = an - 3 * n;
99
100 ASSERT (0 < s && s <= n);
101
102 /* NOTE: The multiplications to v2, vm2, vh and vm1 overwrites the
103 * following limb, so these must be computed in order, and we need a
104 * one limb gap to tp. */
105 #define v0 pp /* 2n */
106 #define v1 (pp + 2 * n) /* 2n+1 */
107 #define vinf (pp + 6 * n) /* s+t */
108 #define v2 scratch /* 2n+1 */
109 #define vm2 (scratch + 2 * n + 1) /* 2n+1 */
110 #define vh (scratch + 4 * n + 2) /* 2n+1 */
111 #define vm1 (scratch + 6 * n + 3) /* 2n+1 */
112 #define tp (scratch + 8*n + 5)
113
114 /* No overlap with v1 */
115 #define apx pp /* n+1 */
116 #define amx (pp + 4*n + 2) /* n+1 */
117
118 /* Total scratch need: 8*n + 5 + scratch for recursive calls. This
119 gives roughly 32 n/3 + log term. */
120
121 /* Compute apx = a0 + 2 a1 + 4 a2 + 8 a3 and amx = a0 - 2 a1 + 4 a2 - 8 a3. */
122 mpn_toom_eval_dgr3_pm2 (apx, amx, ap, n, s, tp);
123
124 TOOM4_SQR_REC (v2, apx, n + 1, tp); /* v2, 2n+1 limbs */
125 TOOM4_SQR_REC (vm2, amx, n + 1, tp); /* vm2, 2n+1 limbs */
126
127 /* Compute apx = 8 a0 + 4 a1 + 2 a2 + a3 = (((2*a0 + a1) * 2 + a2) * 2 + a3 */
128 #if HAVE_NATIVE_mpn_addlsh1_n
129 cy = mpn_addlsh1_n (apx, a1, a0, n);
130 cy = 2*cy + mpn_addlsh1_n (apx, a2, apx, n);
131 if (s < n)
132 {
133 mp_limb_t cy2;
134 cy2 = mpn_addlsh1_n (apx, a3, apx, s);
135 apx[n] = 2*cy + mpn_lshift (apx + s, apx + s, n - s, 1);
136 MPN_INCR_U (apx + s, n+1-s, cy2);
137 }
138 else
139 apx[n] = 2*cy + mpn_addlsh1_n (apx, a3, apx, n);
140 #else
141 cy = mpn_lshift (apx, a0, n, 1);
142 cy += mpn_add_n (apx, apx, a1, n);
143 cy = 2*cy + mpn_lshift (apx, apx, n, 1);
144 cy += mpn_add_n (apx, apx, a2, n);
145 cy = 2*cy + mpn_lshift (apx, apx, n, 1);
146 apx[n] = cy + mpn_add (apx, apx, n, a3, s);
147 #endif
148
149 ASSERT (apx[n] < 15);
150
151 TOOM4_SQR_REC (vh, apx, n + 1, tp); /* vh, 2n+1 limbs */
152
153 /* Compute apx = a0 + a1 + a2 + a3 and amx = a0 - a1 + a2 - a3. */
154 mpn_toom_eval_dgr3_pm1 (apx, amx, ap, n, s, tp);
155
156 TOOM4_SQR_REC (v1, apx, n + 1, tp); /* v1, 2n+1 limbs */
157 vm1 [2 * n] = 0;
158 TOOM4_SQR_REC (vm1, amx, n + amx[n], tp); /* vm1, 2n+1 limbs */
159
160 TOOM4_SQR_REC (v0, a0, n, tp);
161 TOOM4_SQR_REC (vinf, a3, s, tp); /* vinf, 2s limbs */
162
163 mpn_toom_interpolate_7pts (pp, n, (enum toom7_flags) 0, vm2, vm1, v2, vh, 2*s, tp);
164 }