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
10Copyright 2000-2003, 2005-2007, 2009 Free Software Foundation, Inc.
11
12This file is part of the GNU MP Library.
13
14The GNU MP Library is free software; you can redistribute it and/or modify
15it 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
21or
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
27or both in parallel, as here.
28
29The GNU MP Library is distributed in the hope that it will be useful, but
30WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
31or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
32for more details.
33
34You should have received copies of the GNU General Public License and the
35GNU Lesser General Public License along with the GNU MP Library.  If not,
36see https://www.gnu.org/licenses/.  */
37
38#include "gmp-impl.h"
39
40void
41mpn_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}
199