1/* Implementation of the algorithm for Toom-Cook 4.5-way.
2
3   Contributed to the GNU project by 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
9Copyright 2009, 2012 Free Software Foundation, Inc.
10
11This file is part of the GNU MP Library.
12
13The GNU MP Library is free software; you can redistribute it and/or modify
14it 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
20or
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
26or both in parallel, as here.
27
28The GNU MP Library is distributed in the hope that it will be useful, but
29WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
30or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
31for more details.
32
33You should have received copies of the GNU General Public License and the
34GNU Lesser General Public License along with the GNU MP Library.  If not,
35see https://www.gnu.org/licenses/.  */
36
37#include "gmp-impl.h"
38
39
40/* Toom-4.5, the splitting 5x4 unbalanced version.
41   Evaluate in: infinity, +4, -4, +2, -2, +1, -1, 0.
42
43  <--s-><--n--><--n--><--n--><--n-->
44   ____ ______ ______ ______ ______
45  |_a4_|__a3__|__a2__|__a1__|__a0__|
46	  |b3_|__b2__|__b1__|__b0__|
47	  <-t-><--n--><--n--><--n-->
48
49*/
50#define TOOM_54_MUL_N_REC(p, a, b, n, ws)		\
51  do {	mpn_mul_n (p, a, b, n);				\
52  } while (0)
53
54#define TOOM_54_MUL_REC(p, a, na, b, nb, ws)		\
55  do {	mpn_mul (p, a, na, b, nb);			\
56  } while (0)
57
58void
59mpn_toom54_mul (mp_ptr pp,
60		mp_srcptr ap, mp_size_t an,
61		mp_srcptr bp, mp_size_t bn, mp_ptr scratch)
62{
63  mp_size_t n, s, t;
64  int sign;
65
66  /***************************** decomposition *******************************/
67#define a4  (ap + 4 * n)
68#define b3  (bp + 3 * n)
69
70  ASSERT (an >= bn);
71  n = 1 + (4 * an >= 5 * bn ? (an - 1) / (size_t) 5 : (bn - 1) / (size_t) 4);
72
73  s = an - 4 * n;
74  t = bn - 3 * n;
75
76  ASSERT (0 < s && s <= n);
77  ASSERT (0 < t && t <= n);
78  /* Required by mpn_toom_interpolate_8pts. */
79  ASSERT ( s + t >= n );
80  ASSERT ( s + t > 4);
81  ASSERT ( n > 2);
82
83#define   r8    pp				/* 2n   */
84#define   r7    scratch				/* 3n+1 */
85#define   r5    (pp + 3*n)			/* 3n+1 */
86#define   v0    (pp + 3*n)			/* n+1 */
87#define   v1    (pp + 4*n+1)			/* n+1 */
88#define   v2    (pp + 5*n+2)			/* n+1 */
89#define   v3    (pp + 6*n+3)			/* n+1 */
90#define   r3    (scratch + 3 * n + 1)		/* 3n+1 */
91#define   r1    (pp + 7*n)			/* s+t <= 2*n */
92#define   ws    (scratch + 6 * n + 2)		/* ??? */
93
94  /* Alloc also 3n+1 limbs for ws... mpn_toom_interpolate_8pts may
95     need all of them, when DO_mpn_sublsh_n usea a scratch  */
96  /********************** evaluation and recursive calls *********************/
97  /* $\pm4$ */
98  sign = mpn_toom_eval_pm2exp (v2, v0, 4, ap, n, s, 2, pp)
99       ^ mpn_toom_eval_pm2exp (v3, v1, 3, bp, n, t, 2, pp);
100  TOOM_54_MUL_N_REC(pp, v0, v1, n + 1, ws); /* A(-4)*B(-4) */
101  TOOM_54_MUL_N_REC(r3, v2, v3, n + 1, ws); /* A(+4)*B(+4) */
102  mpn_toom_couple_handling (r3, 2*n+1, pp, sign, n, 2, 4);
103
104  /* $\pm1$ */
105  sign = mpn_toom_eval_pm1 (v2, v0, 4, ap, n, s,    pp)
106       ^ mpn_toom_eval_dgr3_pm1 (v3, v1, bp, n, t,    pp);
107  TOOM_54_MUL_N_REC(pp, v0, v1, n + 1, ws); /* A(-1)*B(-1) */
108  TOOM_54_MUL_N_REC(r7, v2, v3, n + 1, ws); /* A(1)*B(1) */
109  mpn_toom_couple_handling (r7, 2*n+1, pp, sign, n, 0, 0);
110
111  /* $\pm2$ */
112  sign = mpn_toom_eval_pm2 (v2, v0, 4, ap, n, s, pp)
113       ^ mpn_toom_eval_dgr3_pm2 (v3, v1, bp, n, t, pp);
114  TOOM_54_MUL_N_REC(pp, v0, v1, n + 1, ws); /* A(-2)*B(-2) */
115  TOOM_54_MUL_N_REC(r5, v2, v3, n + 1, ws); /* A(+2)*B(+2) */
116  mpn_toom_couple_handling (r5, 2*n+1, pp, sign, n, 1, 2);
117
118  /* A(0)*B(0) */
119  TOOM_54_MUL_N_REC(pp, ap, bp, n, ws);
120
121  /* Infinity */
122  if (s > t) {
123    TOOM_54_MUL_REC(r1, a4, s, b3, t, ws);
124  } else {
125    TOOM_54_MUL_REC(r1, b3, t, a4, s, ws);
126  };
127
128  mpn_toom_interpolate_8pts (pp, n, r3, r7, s + t, ws);
129
130#undef a4
131#undef b3
132#undef r1
133#undef r3
134#undef r5
135#undef v0
136#undef v1
137#undef v2
138#undef v3
139#undef r7
140#undef r8
141#undef ws
142}
143