1 /* mpn_toom4_sqr -- Square {ap,an}.
3 Contributed to the GNU project by Torbjorn Granlund and Marco Bodrato.
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.
9 Copyright 2006, 2007, 2008, 2009, 2010 Free Software Foundation, Inc.
11 This file is part of the GNU MP Library.
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.
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.
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/. */
30 /* Evaluate in: -1, -1/2, 0, +1/2, +1, +2, +inf
32 <-s--><--n--><--n--><--n-->
33 ____ ______ ______ ______
34 |_a3_|___a2_|___a1_|___a0_|
37 v1 = ( a0+ a1+ a2+ a3)^2 # A(1)^2 ah <= 3
38 vm1 = ( a0- a1+ a2- a3)^2 # A(-1)^2 |ah| <= 1
39 v2 = ( a0+2a1+4a2+8a3)^2 # A(2)^2 ah <= 14
40 vh = (8a0+4a1+2a2+ a3)^2 # A(1/2)^2 ah <= 14
41 vmh = (8a0-4a1+2a2- a3)^2 # A(-1/2)^2 -4<=ah<=9
42 vinf= a3 ^2 # A(inf)^2
45 #if TUNE_PROGRAM_BUILD
46 #define MAYBE_sqr_basecase 1
47 #define MAYBE_sqr_toom2 1
48 #define MAYBE_sqr_toom4 1
50 #define MAYBE_sqr_basecase \
51 (SQR_TOOM4_THRESHOLD < 4 * SQR_TOOM2_THRESHOLD)
52 #define MAYBE_sqr_toom2 \
53 (SQR_TOOM4_THRESHOLD < 4 * SQR_TOOM3_THRESHOLD)
54 #define MAYBE_sqr_toom4 \
55 (SQR_FFT_THRESHOLD >= 4 * SQR_TOOM4_THRESHOLD)
58 #define TOOM4_SQR_REC(p, a, n, ws) \
60 if (MAYBE_sqr_basecase \
61 && BELOW_THRESHOLD (n, SQR_TOOM2_THRESHOLD)) \
62 mpn_sqr_basecase (p, a, n); \
63 else if (MAYBE_sqr_toom2 \
64 && BELOW_THRESHOLD (n, SQR_TOOM3_THRESHOLD)) \
65 mpn_toom2_sqr (p, a, n, ws); \
66 else if (! MAYBE_sqr_toom4 \
67 || BELOW_THRESHOLD (n, SQR_TOOM4_THRESHOLD)) \
68 mpn_toom3_sqr (p, a, n, ws); \
70 mpn_toom4_sqr (p, a, n, ws); \
74 mpn_toom4_sqr (mp_ptr pp,
75 mp_srcptr ap, mp_size_t an,
90 ASSERT (0 < s && s <= n);
92 /* NOTE: The multiplications to v2, vm2, vh and vm1 overwrites the
93 * following limb, so these must be computed in order, and we need a
94 * one limb gap to tp. */
95 #define v0 pp /* 2n */
96 #define v1 (pp + 2 * n) /* 2n+1 */
97 #define vinf (pp + 6 * n) /* s+t */
98 #define v2 scratch /* 2n+1 */
99 #define vm2 (scratch + 2 * n + 1) /* 2n+1 */
100 #define vh (scratch + 4 * n + 2) /* 2n+1 */
101 #define vm1 (scratch + 6 * n + 3) /* 2n+1 */
102 #define tp (scratch + 8*n + 5)
104 /* No overlap with v1 */
105 #define apx pp /* n+1 */
106 #define amx (pp + 4*n + 2) /* n+1 */
108 /* Total scratch need: 8*n + 5 + scratch for recursive calls. This
109 gives roughly 32 n/3 + log term. */
111 /* Compute apx = a0 + 2 a1 + 4 a2 + 8 a3 and amx = a0 - 2 a1 + 4 a2 - 8 a3. */
112 mpn_toom_eval_dgr3_pm2 (apx, amx, ap, n, s, tp);
114 TOOM4_SQR_REC (v2, apx, n + 1, tp); /* v2, 2n+1 limbs */
115 TOOM4_SQR_REC (vm2, amx, n + 1, tp); /* vm2, 2n+1 limbs */
117 /* Compute apx = 8 a0 + 4 a1 + 2 a2 + a3 = (((2*a0 + a1) * 2 + a2) * 2 + a3 */
118 #if HAVE_NATIVE_mpn_addlsh1_n
119 cy = mpn_addlsh1_n (apx, a1, a0, n);
120 cy = 2*cy + mpn_addlsh1_n (apx, a2, apx, n);
124 cy2 = mpn_addlsh1_n (apx, a3, apx, s);
125 apx[n] = 2*cy + mpn_lshift (apx + s, apx + s, n - s, 1);
126 MPN_INCR_U (apx + s, n+1-s, cy2);
129 apx[n] = 2*cy + mpn_addlsh1_n (apx, a3, apx, n);
131 cy = mpn_lshift (apx, a0, n, 1);
132 cy += mpn_add_n (apx, apx, a1, n);
133 cy = 2*cy + mpn_lshift (apx, apx, n, 1);
134 cy += mpn_add_n (apx, apx, a2, n);
135 cy = 2*cy + mpn_lshift (apx, apx, n, 1);
136 apx[n] = cy + mpn_add (apx, apx, n, a3, s);
139 ASSERT (apx[n] < 15);
141 TOOM4_SQR_REC (vh, apx, n + 1, tp); /* vh, 2n+1 limbs */
143 /* Compute apx = a0 + a1 + a2 + a3 and amx = a0 - a1 + a2 - a3. */
144 mpn_toom_eval_dgr3_pm1 (apx, amx, ap, n, s, tp);
146 TOOM4_SQR_REC (v1, apx, n + 1, tp); /* v1, 2n+1 limbs */
147 TOOM4_SQR_REC (vm1, amx, n + 1, tp); /* vm1, 2n+1 limbs */
149 TOOM4_SQR_REC (v0, a0, n, tp);
150 TOOM4_SQR_REC (vinf, a3, s, tp); /* vinf, 2s limbs */
152 mpn_toom_interpolate_7pts (pp, n, 0, vm2, vm1, v2, vh, 2*s, tp);