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.h"
39 #include "gmp-impl.h"
40 
41 void
mpn_toom_interpolate_5pts(mp_ptr c,mp_ptr v2,mp_ptr vm1,mp_size_t k,mp_size_t twor,int sa,mp_limb_t vinf0)42 mpn_toom_interpolate_5pts (mp_ptr c, mp_ptr v2, mp_ptr vm1,
43 			   mp_size_t k, mp_size_t twor, int sa,
44 			   mp_limb_t vinf0)
45 {
46   mp_limb_t cy, saved;
47   mp_size_t twok;
48   mp_size_t kk1;
49   mp_ptr c1, v1, c3, vinf;
50 
51   twok = k + k;
52   kk1 = twok + 1;
53 
54   c1 = c  + k;
55   v1 = c1 + k;
56   c3 = v1 + k;
57   vinf = c3 + k;
58 
59 #define v0 (c)
60   /* (1) v2 <- v2-vm1 < v2+|vm1|,       (16 8 4 2 1) - (1 -1 1 -1  1) =
61      thus 0 <= v2 < 50*B^(2k) < 2^6*B^(2k)             (15 9 3  3  0)
62   */
63   if (sa)
64     ASSERT_NOCARRY (mpn_add_n (v2, v2, vm1, kk1));
65   else
66     ASSERT_NOCARRY (mpn_sub_n (v2, v2, vm1, kk1));
67 
68   /* {c,2k} {c+2k,2k+1} {c+4k+1,2r-1} {t,2k+1} {t+2k+1,2k+1} {t+4k+2,2r}
69        v0       v1       hi(vinf)       |vm1|     v2-vm1      EMPTY */
70 
71   ASSERT_NOCARRY (mpn_divexact_by3 (v2, v2, kk1));    /* v2 <- v2 / 3 */
72 						      /* (5 3 1 1 0)*/
73 
74   /* {c,2k} {c+2k,2k+1} {c+4k+1,2r-1} {t,2k+1} {t+2k+1,2k+1} {t+4k+2,2r}
75        v0       v1      hi(vinf)       |vm1|     (v2-vm1)/3    EMPTY */
76 
77   /* (2) vm1 <- tm1 := (v1 - vm1) / 2  [(1 1 1 1 1) - (1 -1 1 -1 1)] / 2 =
78      tm1 >= 0                                         (0  1 0  1 0)
79      No carry comes out from {v1, kk1} +/- {vm1, kk1},
80      and the division by two is exact.
81      If (sa!=0) the sign of vm1 is negative */
82   if (sa)
83     {
84 #ifdef HAVE_NATIVE_mpn_rsh1add_n
85       mpn_rsh1add_n (vm1, v1, vm1, kk1);
86 #else
87       ASSERT_NOCARRY (mpn_add_n (vm1, v1, vm1, kk1));
88       ASSERT_NOCARRY (mpn_rshift (vm1, vm1, kk1, 1));
89 #endif
90     }
91   else
92     {
93 #ifdef HAVE_NATIVE_mpn_rsh1sub_n
94       mpn_rsh1sub_n (vm1, v1, vm1, kk1);
95 #else
96       ASSERT_NOCARRY (mpn_sub_n (vm1, v1, vm1, kk1));
97       ASSERT_NOCARRY (mpn_rshift (vm1, vm1, kk1, 1));
98 #endif
99     }
100 
101   /* {c,2k} {c+2k,2k+1} {c+4k+1,2r-1} {t,2k+1} {t+2k+1,2k+1} {t+4k+2,2r}
102        v0       v1        hi(vinf)       tm1     (v2-vm1)/3    EMPTY */
103 
104   /* (3) v1 <- t1 := v1 - v0    (1 1 1 1 1) - (0 0 0 0 1) = (1 1 1 1 0)
105      t1 >= 0
106   */
107   vinf[0] -= mpn_sub_n (v1, v1, c, twok);
108 
109   /* {c,2k} {c+2k,2k+1} {c+4k+1,2r-1} {t,2k+1} {t+2k+1,2k+1} {t+4k+2,2r}
110        v0     v1-v0        hi(vinf)       tm1     (v2-vm1)/3    EMPTY */
111 
112   /* (4) v2 <- t2 := ((v2-vm1)/3-t1)/2 = (v2-vm1-3*t1)/6
113      t2 >= 0                  [(5 3 1 1 0) - (1 1 1 1 0)]/2 = (2 1 0 0 0)
114   */
115 #ifdef HAVE_NATIVE_mpn_rsh1sub_n
116   mpn_rsh1sub_n (v2, v2, v1, kk1);
117 #else
118   ASSERT_NOCARRY (mpn_sub_n (v2, v2, v1, kk1));
119   ASSERT_NOCARRY (mpn_rshift (v2, v2, kk1, 1));
120 #endif
121 
122   /* {c,2k} {c+2k,2k+1} {c+4k+1,2r-1} {t,2k+1} {t+2k+1,2k+1} {t+4k+2,2r}
123        v0     v1-v0        hi(vinf)     tm1    (v2-vm1-3t1)/6    EMPTY */
124 
125   /* (5) v1 <- t1-tm1           (1 1 1 1 0) - (0 1 0 1 0) = (1 0 1 0 0)
126      result is v1 >= 0
127   */
128   ASSERT_NOCARRY (mpn_sub_n (v1, v1, vm1, kk1));
129 
130   /* We do not need to read the value in vm1, so we add it in {c+k, ...} */
131   cy = mpn_add_n (c1, c1, vm1, kk1);
132   MPN_INCR_U (c3 + 1, twor + k - 1, cy); /* 2n-(3k+1) = 2r+k-1 */
133   /* Memory allocated for vm1 is now free, it can be recycled ...*/
134 
135   /* (6) v2 <- v2 - 2*vinf,     (2 1 0 0 0) - 2*(1 0 0 0 0) = (0 1 0 0 0)
136      result is v2 >= 0 */
137   saved = vinf[0];       /* Remember v1's highest byte (will be overwritten). */
138   vinf[0] = vinf0;       /* Set the right value for vinf0                     */
139 #ifdef HAVE_NATIVE_mpn_sublsh1_n_ip1
140   cy = mpn_sublsh1_n_ip1 (v2, vinf, twor);
141 #else
142   /* Overwrite unused vm1 */
143   cy = mpn_lshift (vm1, vinf, twor, 1);
144   cy += mpn_sub_n (v2, v2, vm1, twor);
145 #endif
146   MPN_DECR_U (v2 + twor, kk1 - twor, cy);
147 
148   /* Current matrix is
149      [1 0 0 0 0; vinf
150       0 1 0 0 0; v2
151       1 0 1 0 0; v1
152       0 1 0 1 0; vm1
153       0 0 0 0 1] v0
154      Some values already are in-place (we added vm1 in the correct position)
155      | vinf|  v1 |  v0 |
156 	      | vm1 |
157      One still is in a separated area
158 	| +v2 |
159      We have to compute v1-=vinf; vm1 -= v2,
160 	   |-vinf|
161 	      | -v2 |
162      Carefully reordering operations we can avoid to compute twice the sum
163      of the high half of v2 plus the low half of vinf.
164   */
165 
166   /* Add the high half of t2 in {vinf} */
167   if ( LIKELY(twor > k + 1) ) { /* This is the expected flow  */
168     cy = mpn_add_n (vinf, vinf, v2 + k, k + 1);
169     MPN_INCR_U (c3 + kk1, twor - k - 1, cy); /* 2n-(5k+1) = 2r-k-1 */
170   } else { /* triggered only by very unbalanced cases like
171 	      (k+k+(k-2))x(k+k+1) , should be handled by toom32 */
172     ASSERT_NOCARRY (mpn_add_n (vinf, vinf, v2 + k, twor));
173   }
174   /* (7) v1 <- v1 - vinf,       (1 0 1 0 0) - (1 0 0 0 0) = (0 0 1 0 0)
175      result is >= 0 */
176   /* Side effect: we also subtracted (high half) vm1 -= v2 */
177   cy = mpn_sub_n (v1, v1, vinf, twor);          /* vinf is at most twor long.  */
178   vinf0 = vinf[0];                     /* Save again the right value for vinf0 */
179   vinf[0] = saved;
180   MPN_DECR_U (v1 + twor, kk1 - twor, cy);       /* Treat the last bytes.       */
181 
182   /* (8) vm1 <- vm1-v2          (0 1 0 1 0) - (0 1 0 0 0) = (0 0 0 1 0)
183      Operate only on the low half.
184   */
185   cy = mpn_sub_n (c1, c1, v2, k);
186   MPN_DECR_U (v1, kk1, cy);
187 
188   /********************* Beginning the final phase **********************/
189 
190   /* Most of the recomposition was done */
191 
192   /* add t2 in {c+3k, ...}, but only the low half */
193   cy = mpn_add_n (c3, c3, v2, k);
194   vinf[0] += cy;
195   ASSERT(vinf[0] >= cy); /* No carry */
196   MPN_INCR_U (vinf, twor, vinf0); /* Add vinf0, propagate carry. */
197 
198 #undef v0
199 }
200