1 /* crypto/bn/bn_sqr.c */
2 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
5 * This package is an SSL implementation written
6 * by Eric Young (eay@cryptsoft.com).
7 * The implementation was written so as to conform with Netscapes SSL.
9 * This library is free for commercial and non-commercial use as long as
10 * the following conditions are aheared to. The following conditions
11 * apply to all code found in this distribution, be it the RC4, RSA,
12 * lhash, DES, etc., code; not just the SSL code. The SSL documentation
13 * included with this distribution is covered by the same copyright terms
14 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
16 * Copyright remains Eric Young's, and as such any Copyright notices in
17 * the code are not to be removed.
18 * If this package is used in a product, Eric Young should be given attribution
19 * as the author of the parts of the library used.
20 * This can be in the form of a textual message at program startup or
21 * in documentation (online or textual) provided with the package.
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
26 * 1. Redistributions of source code must retain the copyright
27 * notice, this list of conditions and the following disclaimer.
28 * 2. Redistributions in binary form must reproduce the above copyright
29 * notice, this list of conditions and the following disclaimer in the
30 * documentation and/or other materials provided with the distribution.
31 * 3. All advertising materials mentioning features or use of this software
32 * must display the following acknowledgement:
33 * "This product includes cryptographic software written by
34 * Eric Young (eay@cryptsoft.com)"
35 * The word 'cryptographic' can be left out if the rouines from the library
36 * being used are not cryptographic related :-).
37 * 4. If you include any Windows specific code (or a derivative thereof) from
38 * the apps directory (application code) you must include an acknowledgement:
39 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
41 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
42 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
43 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
44 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
45 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
46 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
47 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
48 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
49 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
50 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
53 * The licence and distribution terms for any publically available version or
54 * derivative of this code cannot be changed. i.e. this code cannot simply be
55 * copied and put under another distribution licence
56 * [including the GNU Public Licence.]
65 * I've just gone over this and it is now %20 faster on x86 - eay - 27 Jun 96
67 int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
74 fprintf(stderr, "BN_sqr %d * %d\n", a->top, a->top);
86 rr = (a != r) ? r : BN_CTX_get(ctx);
87 tmp = BN_CTX_get(ctx);
91 max = 2 * al; /* Non-zero (from above) */
92 if (bn_wexpand(rr, max) == NULL)
98 bn_sqr_normal(rr->d, a->d, 4, t);
100 bn_sqr_comba4(rr->d, a->d);
102 } else if (al == 8) {
105 bn_sqr_normal(rr->d, a->d, 8, t);
107 bn_sqr_comba8(rr->d, a->d);
110 #if defined(BN_RECURSION)
111 if (al < BN_SQR_RECURSIVE_SIZE_NORMAL) {
112 BN_ULONG t[BN_SQR_RECURSIVE_SIZE_NORMAL * 2];
113 bn_sqr_normal(rr->d, a->d, al, t);
117 j = BN_num_bits_word((BN_ULONG)al);
121 if (bn_wexpand(tmp, k * 2) == NULL)
123 bn_sqr_recursive(rr->d, a->d, al, tmp->d);
125 if (bn_wexpand(tmp, max) == NULL)
127 bn_sqr_normal(rr->d, a->d, al, tmp->d);
131 if (bn_wexpand(tmp, max) == NULL)
133 bn_sqr_normal(rr->d, a->d, al, tmp->d);
139 * If the most-significant half of the top word of 'a' is zero, then the
140 * square of 'a' will max-1 words.
142 if (a->d[al - 1] == (a->d[al - 1] & BN_MASK2l))
146 if (r != rr && BN_copy(r, rr) == NULL)
157 /* tmp must have 2*n words */
158 void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp)
167 rp[0] = rp[max - 1] = 0;
173 rp[j] = bn_mul_words(rp, ap, j, ap[-1]);
177 for (i = n - 2; i > 0; i--) {
180 rp[j] = bn_mul_add_words(rp, ap, j, ap[-1]);
184 bn_add_words(r, r, r, max);
186 /* There will not be a carry */
188 bn_sqr_words(tmp, a, n);
190 bn_add_words(r, r, tmp, max);
195 * r is 2*n words in size,
196 * a and b are both n words in size. (There's not actually a 'b' here ...)
197 * n must be a power of 2.
198 * We multiply and return the result.
199 * t must be 2*n words in size
202 * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
205 void bn_sqr_recursive(BN_ULONG *r, const BN_ULONG *a, int n2, BN_ULONG *t)
212 fprintf(stderr, " bn_sqr_recursive %d * %d\n", n2, n2);
215 # ifndef BN_SQR_COMBA
216 bn_sqr_normal(r, a, 4, t);
221 } else if (n2 == 8) {
222 # ifndef BN_SQR_COMBA
223 bn_sqr_normal(r, a, 8, t);
229 if (n2 < BN_SQR_RECURSIVE_SIZE_NORMAL) {
230 bn_sqr_normal(r, a, n2, t);
233 /* r=(a[0]-a[1])*(a[1]-a[0]) */
234 c1 = bn_cmp_words(a, &(a[n]), n);
237 bn_sub_words(t, a, &(a[n]), n);
239 bn_sub_words(t, &(a[n]), a, n);
243 /* The result will always be negative unless it is zero */
247 bn_sqr_recursive(&(t[n2]), t, n, p);
249 memset(&(t[n2]), 0, n2 * sizeof(BN_ULONG));
250 bn_sqr_recursive(r, a, n, p);
251 bn_sqr_recursive(&(r[n2]), &(a[n]), n, p);
254 * t[32] holds (a[0]-a[1])*(a[1]-a[0]), it is negative or zero
255 * r[10] holds (a[0]*b[0])
256 * r[32] holds (b[1]*b[1])
259 c1 = (int)(bn_add_words(t, r, &(r[n2]), n2));
261 /* t[32] is negative */
262 c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2));
265 * t[32] holds (a[0]-a[1])*(a[1]-a[0])+(a[0]*a[0])+(a[1]*a[1])
266 * r[10] holds (a[0]*a[0])
267 * r[32] holds (a[1]*a[1])
268 * c1 holds the carry bits
270 c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2));
274 ln = (lo + c1) & BN_MASK2;
278 * The overflow will stop before we over write words we should not
281 if (ln < (BN_ULONG)c1) {
285 ln = (lo + 1) & BN_MASK2;