1/* mpn_toom3_sqr -- Square {ap,an}.
2
3   Contributed to the GNU project by Torbjorn Granlund.
4   Additional improvements by 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 2006, 2007, 2008, 2009, 2010 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 the GNU Lesser General Public License as published by
16the Free Software Foundation; either version 3 of the License, or (at your
17option) any later version.
18
19The GNU MP Library is distributed in the hope that it will be useful, but
20WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
21or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
22License for more details.
23
24You should have received a copy of the GNU Lesser General Public License
25along with the GNU MP Library.  If not, see http://www.gnu.org/licenses/.  */
26
27
28#include "gmp.h"
29#include "gmp-impl.h"
30
31/* Evaluate in: -1, 0, +1, +2, +inf
32
33  <-s--><--n--><--n-->
34   ____ ______ ______
35  |_a2_|___a1_|___a0_|
36
37  v0  =  a0         ^2 #   A(0)^2
38  v1  = (a0+ a1+ a2)^2 #   A(1)^2    ah  <= 2
39  vm1 = (a0- a1+ a2)^2 #  A(-1)^2   |ah| <= 1
40  v2  = (a0+2a1+4a2)^2 #   A(2)^2    ah  <= 6
41  vinf=          a2 ^2 # A(inf)^2
42*/
43
44#if TUNE_PROGRAM_BUILD
45#define MAYBE_sqr_basecase 1
46#define MAYBE_sqr_toom3   1
47#else
48#define MAYBE_sqr_basecase						\
49  (SQR_TOOM3_THRESHOLD < 3 * SQR_TOOM2_THRESHOLD)
50#define MAYBE_sqr_toom3							\
51  (SQR_TOOM4_THRESHOLD >= 3 * SQR_TOOM3_THRESHOLD)
52#endif
53
54#define TOOM3_SQR_REC(p, a, n, ws)					\
55  do {									\
56    if (MAYBE_sqr_basecase						\
57	&& BELOW_THRESHOLD (n, SQR_TOOM2_THRESHOLD))			\
58      mpn_sqr_basecase (p, a, n);					\
59    else if (! MAYBE_sqr_toom3						\
60	     || BELOW_THRESHOLD (n, SQR_TOOM3_THRESHOLD))		\
61      mpn_toom2_sqr (p, a, n, ws);					\
62    else								\
63      mpn_toom3_sqr (p, a, n, ws);					\
64  } while (0)
65
66void
67mpn_toom3_sqr (mp_ptr pp,
68	       mp_srcptr ap, mp_size_t an,
69	       mp_ptr scratch)
70{
71  mp_size_t n, s;
72  mp_limb_t cy, vinf0;
73  mp_ptr gp;
74  mp_ptr as1, asm1, as2;
75
76#define a0  ap
77#define a1  (ap + n)
78#define a2  (ap + 2*n)
79
80  n = (an + 2) / (size_t) 3;
81
82  s = an - 2 * n;
83
84  ASSERT (0 < s && s <= n);
85
86  as1 = scratch + 4 * n + 4;
87  asm1 = scratch + 2 * n + 2;
88  as2 = pp + n + 1;
89
90  gp = scratch;
91
92  /* Compute as1 and asm1.  */
93  cy = mpn_add (gp, a0, n, a2, s);
94#if HAVE_NATIVE_mpn_add_n_sub_n
95  if (cy == 0 && mpn_cmp (gp, a1, n) < 0)
96    {
97      cy = mpn_add_n_sub_n (as1, asm1, a1, gp, n);
98      as1[n] = cy >> 1;
99      asm1[n] = 0;
100    }
101  else
102    {
103      mp_limb_t cy2;
104      cy2 = mpn_add_n_sub_n (as1, asm1, gp, a1, n);
105      as1[n] = cy + (cy2 >> 1);
106      asm1[n] = cy - (cy2 & 1);
107    }
108#else
109  as1[n] = cy + mpn_add_n (as1, gp, a1, n);
110  if (cy == 0 && mpn_cmp (gp, a1, n) < 0)
111    {
112      mpn_sub_n (asm1, a1, gp, n);
113      asm1[n] = 0;
114    }
115  else
116    {
117      cy -= mpn_sub_n (asm1, gp, a1, n);
118      asm1[n] = cy;
119    }
120#endif
121
122  /* Compute as2.  */
123#if HAVE_NATIVE_mpn_rsblsh1_n
124  cy = mpn_add_n (as2, a2, as1, s);
125  if (s != n)
126    cy = mpn_add_1 (as2 + s, as1 + s, n - s, cy);
127  cy += as1[n];
128  cy = 2 * cy + mpn_rsblsh1_n (as2, a0, as2, n);
129#else
130#if HAVE_NATIVE_mpn_addlsh1_n
131  cy  = mpn_addlsh1_n (as2, a1, a2, s);
132  if (s != n)
133    cy = mpn_add_1 (as2 + s, a1 + s, n - s, cy);
134  cy = 2 * cy + mpn_addlsh1_n (as2, a0, as2, n);
135#else
136  cy = mpn_add_n (as2, a2, as1, s);
137  if (s != n)
138    cy = mpn_add_1 (as2 + s, as1 + s, n - s, cy);
139  cy += as1[n];
140  cy = 2 * cy + mpn_lshift (as2, as2, n, 1);
141  cy -= mpn_sub_n (as2, as2, a0, n);
142#endif
143#endif
144  as2[n] = cy;
145
146  ASSERT (as1[n] <= 2);
147  ASSERT (asm1[n] <= 1);
148
149#define v0    pp				/* 2n */
150#define v1    (pp + 2 * n)			/* 2n+1 */
151#define vinf  (pp + 4 * n)			/* s+s */
152#define vm1   scratch				/* 2n+1 */
153#define v2    (scratch + 2 * n + 1)		/* 2n+2 */
154#define scratch_out  (scratch + 5 * n + 5)
155
156  /* vm1, 2n+1 limbs */
157#ifdef SMALLER_RECURSION
158  TOOM3_SQR_REC (vm1, asm1, n, scratch_out);
159  cy = 0;
160  if (asm1[n] != 0)
161    cy = asm1[n] + mpn_add_n (vm1 + n, vm1 + n, asm1, n);
162  if (asm1[n] != 0)
163    cy += mpn_add_n (vm1 + n, vm1 + n, asm1, n);
164  vm1[2 * n] = cy;
165#else
166  TOOM3_SQR_REC (vm1, asm1, n + 1, scratch_out);
167#endif
168
169  TOOM3_SQR_REC (v2, as2, n + 1, scratch_out);	/* v2, 2n+1 limbs */
170
171  TOOM3_SQR_REC (vinf, a2, s, scratch_out);	/* vinf, s+s limbs */
172
173  vinf0 = vinf[0];				/* v1 overlaps with this */
174
175#ifdef SMALLER_RECURSION
176  /* v1, 2n+1 limbs */
177  TOOM3_SQR_REC (v1, as1, n, scratch_out);
178  if (as1[n] == 1)
179    {
180      cy = as1[n] + mpn_add_n (v1 + n, v1 + n, as1, n);
181    }
182  else if (as1[n] != 0)
183    {
184#if HAVE_NATIVE_mpn_addlsh1_n
185      cy = 2 * as1[n] + mpn_addlsh1_n (v1 + n, v1 + n, as1, n);
186#else
187      cy = 2 * as1[n] + mpn_addmul_1 (v1 + n, as1, n, CNST_LIMB(2));
188#endif
189    }
190  else
191    cy = 0;
192  if (as1[n] == 1)
193    {
194      cy += mpn_add_n (v1 + n, v1 + n, as1, n);
195    }
196  else if (as1[n] != 0)
197    {
198#if HAVE_NATIVE_mpn_addlsh1_n
199      cy += mpn_addlsh1_n (v1 + n, v1 + n, as1, n);
200#else
201      cy += mpn_addmul_1 (v1 + n, as1, n, CNST_LIMB(2));
202#endif
203    }
204  v1[2 * n] = cy;
205#else
206  cy = vinf[1];
207  TOOM3_SQR_REC (v1, as1, n + 1, scratch_out);
208  vinf[1] = cy;
209#endif
210
211  TOOM3_SQR_REC (v0, ap, n, scratch_out);	/* v0, 2n limbs */
212
213  mpn_toom_interpolate_5pts (pp, v2, vm1, n, s + s, 0, vinf0);
214}
215