1 /* mpn_toom_interpolate_5pts -- Interpolate for toom3, 33, 42.
2
3 Contributed to the GNU project by Robert Harley.
4 Improvements by Paul Zimmermann and 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 2000-2003, 2005-2007, 2009 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 #include "gmp-impl.h"
39
40 void
41 mpn_toom_interpolate_5pts (mp_ptr c, mp_ptr v2, mp_ptr vm1,
42 mp_size_t k, mp_size_t twor, int sa,
43 mp_limb_t vinf0)
44 {
45 mp_limb_t cy, saved;
46 mp_size_t twok;
47 mp_size_t kk1;
48 mp_ptr c1, v1, c3, vinf;
49
50 twok = k + k;
51 kk1 = twok + 1;
52
53 c1 = c + k;
54 v1 = c1 + k;
55 c3 = v1 + k;
56 vinf = c3 + k;
57
58 #define v0 (c)
59 /* (1) v2 <- v2-vm1 < v2+|vm1|, (16 8 4 2 1) - (1 -1 1 -1 1) =
60 thus 0 <= v2 < 50*B^(2k) < 2^6*B^(2k) (15 9 3 3 0)
61 */
62 if (sa)
63 ASSERT_NOCARRY (mpn_add_n (v2, v2, vm1, kk1));
64 else
65 ASSERT_NOCARRY (mpn_sub_n (v2, v2, vm1, kk1));
66
67 /* {c,2k} {c+2k,2k+1} {c+4k+1,2r-1} {t,2k+1} {t+2k+1,2k+1} {t+4k+2,2r}
68 v0 v1 hi(vinf) |vm1| v2-vm1 EMPTY */
69
70 ASSERT_NOCARRY (mpn_divexact_by3 (v2, v2, kk1)); /* v2 <- v2 / 3 */
71 /* (5 3 1 1 0)*/
72
73 /* {c,2k} {c+2k,2k+1} {c+4k+1,2r-1} {t,2k+1} {t+2k+1,2k+1} {t+4k+2,2r}
74 v0 v1 hi(vinf) |vm1| (v2-vm1)/3 EMPTY */
75
76 /* (2) vm1 <- tm1 := (v1 - vm1) / 2 [(1 1 1 1 1) - (1 -1 1 -1 1)] / 2 =
77 tm1 >= 0 (0 1 0 1 0)
78 No carry comes out from {v1, kk1} +/- {vm1, kk1},
79 and the division by two is exact.
80 If (sa!=0) the sign of vm1 is negative */
81 if (sa)
82 {
83 #ifdef HAVE_NATIVE_mpn_rsh1add_n
84 mpn_rsh1add_n (vm1, v1, vm1, kk1);
85 #else
86 ASSERT_NOCARRY (mpn_add_n (vm1, v1, vm1, kk1));
87 ASSERT_NOCARRY (mpn_rshift (vm1, vm1, kk1, 1));
88 #endif
89 }
90 else
91 {
92 #ifdef HAVE_NATIVE_mpn_rsh1sub_n
93 mpn_rsh1sub_n (vm1, v1, vm1, kk1);
94 #else
95 ASSERT_NOCARRY (mpn_sub_n (vm1, v1, vm1, kk1));
96 ASSERT_NOCARRY (mpn_rshift (vm1, vm1, kk1, 1));
97 #endif
98 }
99
100 /* {c,2k} {c+2k,2k+1} {c+4k+1,2r-1} {t,2k+1} {t+2k+1,2k+1} {t+4k+2,2r}
101 v0 v1 hi(vinf) tm1 (v2-vm1)/3 EMPTY */
102
103 /* (3) v1 <- t1 := v1 - v0 (1 1 1 1 1) - (0 0 0 0 1) = (1 1 1 1 0)
104 t1 >= 0
105 */
106 vinf[0] -= mpn_sub_n (v1, v1, c, twok);
107
108 /* {c,2k} {c+2k,2k+1} {c+4k+1,2r-1} {t,2k+1} {t+2k+1,2k+1} {t+4k+2,2r}
109 v0 v1-v0 hi(vinf) tm1 (v2-vm1)/3 EMPTY */
110
111 /* (4) v2 <- t2 := ((v2-vm1)/3-t1)/2 = (v2-vm1-3*t1)/6
112 t2 >= 0 [(5 3 1 1 0) - (1 1 1 1 0)]/2 = (2 1 0 0 0)
113 */
114 #ifdef HAVE_NATIVE_mpn_rsh1sub_n
115 mpn_rsh1sub_n (v2, v2, v1, kk1);
116 #else
117 ASSERT_NOCARRY (mpn_sub_n (v2, v2, v1, kk1));
118 ASSERT_NOCARRY (mpn_rshift (v2, v2, kk1, 1));
119 #endif
120
121 /* {c,2k} {c+2k,2k+1} {c+4k+1,2r-1} {t,2k+1} {t+2k+1,2k+1} {t+4k+2,2r}
122 v0 v1-v0 hi(vinf) tm1 (v2-vm1-3t1)/6 EMPTY */
123
124 /* (5) v1 <- t1-tm1 (1 1 1 1 0) - (0 1 0 1 0) = (1 0 1 0 0)
125 result is v1 >= 0
126 */
127 ASSERT_NOCARRY (mpn_sub_n (v1, v1, vm1, kk1));
128
129 /* We do not need to read the value in vm1, so we add it in {c+k, ...} */
130 cy = mpn_add_n (c1, c1, vm1, kk1);
131 MPN_INCR_U (c3 + 1, twor + k - 1, cy); /* 2n-(3k+1) = 2r+k-1 */
132 /* Memory allocated for vm1 is now free, it can be recycled ...*/
133
134 /* (6) v2 <- v2 - 2*vinf, (2 1 0 0 0) - 2*(1 0 0 0 0) = (0 1 0 0 0)
135 result is v2 >= 0 */
136 saved = vinf[0]; /* Remember v1's highest byte (will be overwritten). */
137 vinf[0] = vinf0; /* Set the right value for vinf0 */
138 #ifdef HAVE_NATIVE_mpn_sublsh1_n_ip1
139 cy = mpn_sublsh1_n_ip1 (v2, vinf, twor);
140 #else
141 /* Overwrite unused vm1 */
142 cy = mpn_lshift (vm1, vinf, twor, 1);
143 cy += mpn_sub_n (v2, v2, vm1, twor);
144 #endif
145 MPN_DECR_U (v2 + twor, kk1 - twor, cy);
146
147 /* Current matrix is
148 [1 0 0 0 0; vinf
149 0 1 0 0 0; v2
150 1 0 1 0 0; v1
151 0 1 0 1 0; vm1
152 0 0 0 0 1] v0
153 Some values already are in-place (we added vm1 in the correct position)
154 | vinf| v1 | v0 |
155 | vm1 |
156 One still is in a separated area
157 | +v2 |
158 We have to compute v1-=vinf; vm1 -= v2,
159 |-vinf|
160 | -v2 |
161 Carefully reordering operations we can avoid to compute twice the sum
162 of the high half of v2 plus the low half of vinf.
163 */
164
165 /* Add the high half of t2 in {vinf} */
166 if ( LIKELY(twor > k + 1) ) { /* This is the expected flow */
167 cy = mpn_add_n (vinf, vinf, v2 + k, k + 1);
168 MPN_INCR_U (c3 + kk1, twor - k - 1, cy); /* 2n-(5k+1) = 2r-k-1 */
169 } else { /* triggered only by very unbalanced cases like
170 (k+k+(k-2))x(k+k+1) , should be handled by toom32 */
171 ASSERT_NOCARRY (mpn_add_n (vinf, vinf, v2 + k, twor));
172 }
173 /* (7) v1 <- v1 - vinf, (1 0 1 0 0) - (1 0 0 0 0) = (0 0 1 0 0)
174 result is >= 0 */
175 /* Side effect: we also subtracted (high half) vm1 -= v2 */
176 cy = mpn_sub_n (v1, v1, vinf, twor); /* vinf is at most twor long. */
177 vinf0 = vinf[0]; /* Save again the right value for vinf0 */
178 vinf[0] = saved;
179 MPN_DECR_U (v1 + twor, kk1 - twor, cy); /* Treat the last bytes. */
180
181 /* (8) vm1 <- vm1-v2 (0 1 0 1 0) - (0 1 0 0 0) = (0 0 0 1 0)
182 Operate only on the low half.
183 */
184 cy = mpn_sub_n (c1, c1, v2, k);
185 MPN_DECR_U (v1, kk1, cy);
186
187 /********************* Beginning the final phase **********************/
188
189 /* Most of the recomposition was done */
190
191 /* add t2 in {c+3k, ...}, but only the low half */
192 cy = mpn_add_n (c3, c3, v2, k);
193 vinf[0] += cy;
194 ASSERT(vinf[0] >= cy); /* No carry */
195 MPN_INCR_U (vinf, twor, vinf0); /* Add vinf0, propagate carry. */
196
197 #undef v0
198 }