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Diffstat (limited to 'openssl/crypto/bn/bn_mul.c')
| -rw-r--r-- | openssl/crypto/bn/bn_mul.c | 1165 |
1 files changed, 1165 insertions, 0 deletions
diff --git a/openssl/crypto/bn/bn_mul.c b/openssl/crypto/bn/bn_mul.c new file mode 100644 index 0000000..3c618dc --- /dev/null +++ b/openssl/crypto/bn/bn_mul.c @@ -0,0 +1,1165 @@ +/* crypto/bn/bn_mul.c */ +/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com) + * All rights reserved. + * + * This package is an SSL implementation written + * by Eric Young (eay@cryptsoft.com). + * The implementation was written so as to conform with Netscapes SSL. + * + * This library is free for commercial and non-commercial use as long as + * the following conditions are aheared to. The following conditions + * apply to all code found in this distribution, be it the RC4, RSA, + * lhash, DES, etc., code; not just the SSL code. The SSL documentation + * included with this distribution is covered by the same copyright terms + * except that the holder is Tim Hudson (tjh@cryptsoft.com). + * + * Copyright remains Eric Young's, and as such any Copyright notices in + * the code are not to be removed. + * If this package is used in a product, Eric Young should be given attribution + * as the author of the parts of the library used. + * This can be in the form of a textual message at program startup or + * in documentation (online or textual) provided with the package. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. All advertising materials mentioning features or use of this software + * must display the following acknowledgement: + * "This product includes cryptographic software written by + * Eric Young (eay@cryptsoft.com)" + * The word 'cryptographic' can be left out if the rouines from the library + * being used are not cryptographic related :-). + * 4. If you include any Windows specific code (or a derivative thereof) from + * the apps directory (application code) you must include an acknowledgement: + * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)" + * + * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * The licence and distribution terms for any publically available version or + * derivative of this code cannot be changed. i.e. this code cannot simply be + * copied and put under another distribution licence + * [including the GNU Public Licence.] + */ + +#ifndef BN_DEBUG +# undef NDEBUG /* avoid conflicting definitions */ +# define NDEBUG +#endif + +#include <stdio.h> +#include <assert.h> +#include "cryptlib.h" +#include "bn_lcl.h" + +#if defined(OPENSSL_NO_ASM) || !defined(OPENSSL_BN_ASM_PART_WORDS) +/* + * Here follows specialised variants of bn_add_words() and bn_sub_words(). + * They have the property performing operations on arrays of different sizes. + * The sizes of those arrays is expressed through cl, which is the common + * length ( basicall, min(len(a),len(b)) ), and dl, which is the delta + * between the two lengths, calculated as len(a)-len(b). All lengths are the + * number of BN_ULONGs... For the operations that require a result array as + * parameter, it must have the length cl+abs(dl). These functions should + * probably end up in bn_asm.c as soon as there are assembler counterparts + * for the systems that use assembler files. + */ + +BN_ULONG bn_sub_part_words(BN_ULONG *r, + const BN_ULONG *a, const BN_ULONG *b, + int cl, int dl) +{ + BN_ULONG c, t; + + assert(cl >= 0); + c = bn_sub_words(r, a, b, cl); + + if (dl == 0) + return c; + + r += cl; + a += cl; + b += cl; + + if (dl < 0) { +# ifdef BN_COUNT + fprintf(stderr, " bn_sub_part_words %d + %d (dl < 0, c = %d)\n", cl, + dl, c); +# endif + for (;;) { + t = b[0]; + r[0] = (0 - t - c) & BN_MASK2; + if (t != 0) + c = 1; + if (++dl >= 0) + break; + + t = b[1]; + r[1] = (0 - t - c) & BN_MASK2; + if (t != 0) + c = 1; + if (++dl >= 0) + break; + + t = b[2]; + r[2] = (0 - t - c) & BN_MASK2; + if (t != 0) + c = 1; + if (++dl >= 0) + break; + + t = b[3]; + r[3] = (0 - t - c) & BN_MASK2; + if (t != 0) + c = 1; + if (++dl >= 0) + break; + + b += 4; + r += 4; + } + } else { + int save_dl = dl; +# ifdef BN_COUNT + fprintf(stderr, " bn_sub_part_words %d + %d (dl > 0, c = %d)\n", cl, + dl, c); +# endif + while (c) { + t = a[0]; + r[0] = (t - c) & BN_MASK2; + if (t != 0) + c = 0; + if (--dl <= 0) + break; + + t = a[1]; + r[1] = (t - c) & BN_MASK2; + if (t != 0) + c = 0; + if (--dl <= 0) + break; + + t = a[2]; + r[2] = (t - c) & BN_MASK2; + if (t != 0) + c = 0; + if (--dl <= 0) + break; + + t = a[3]; + r[3] = (t - c) & BN_MASK2; + if (t != 0) + c = 0; + if (--dl <= 0) + break; + + save_dl = dl; + a += 4; + r += 4; + } + if (dl > 0) { +# ifdef BN_COUNT + fprintf(stderr, " bn_sub_part_words %d + %d (dl > 0, c == 0)\n", + cl, dl); +# endif + if (save_dl > dl) { + switch (save_dl - dl) { + case 1: + r[1] = a[1]; + if (--dl <= 0) + break; + case 2: + r[2] = a[2]; + if (--dl <= 0) + break; + case 3: + r[3] = a[3]; + if (--dl <= 0) + break; + } + a += 4; + r += 4; + } + } + if (dl > 0) { +# ifdef BN_COUNT + fprintf(stderr, " bn_sub_part_words %d + %d (dl > 0, copy)\n", + cl, dl); +# endif + for (;;) { + r[0] = a[0]; + if (--dl <= 0) + break; + r[1] = a[1]; + if (--dl <= 0) + break; + r[2] = a[2]; + if (--dl <= 0) + break; + r[3] = a[3]; + if (--dl <= 0) + break; + + a += 4; + r += 4; + } + } + } + return c; +} +#endif + +BN_ULONG bn_add_part_words(BN_ULONG *r, + const BN_ULONG *a, const BN_ULONG *b, + int cl, int dl) +{ + BN_ULONG c, l, t; + + assert(cl >= 0); + c = bn_add_words(r, a, b, cl); + + if (dl == 0) + return c; + + r += cl; + a += cl; + b += cl; + + if (dl < 0) { + int save_dl = dl; +#ifdef BN_COUNT + fprintf(stderr, " bn_add_part_words %d + %d (dl < 0, c = %d)\n", cl, + dl, c); +#endif + while (c) { + l = (c + b[0]) & BN_MASK2; + c = (l < c); + r[0] = l; + if (++dl >= 0) + break; + + l = (c + b[1]) & BN_MASK2; + c = (l < c); + r[1] = l; + if (++dl >= 0) + break; + + l = (c + b[2]) & BN_MASK2; + c = (l < c); + r[2] = l; + if (++dl >= 0) + break; + + l = (c + b[3]) & BN_MASK2; + c = (l < c); + r[3] = l; + if (++dl >= 0) + break; + + save_dl = dl; + b += 4; + r += 4; + } + if (dl < 0) { +#ifdef BN_COUNT + fprintf(stderr, " bn_add_part_words %d + %d (dl < 0, c == 0)\n", + cl, dl); +#endif + if (save_dl < dl) { + switch (dl - save_dl) { + case 1: + r[1] = b[1]; + if (++dl >= 0) + break; + case 2: + r[2] = b[2]; + if (++dl >= 0) + break; + case 3: + r[3] = b[3]; + if (++dl >= 0) + break; + } + b += 4; + r += 4; + } + } + if (dl < 0) { +#ifdef BN_COUNT + fprintf(stderr, " bn_add_part_words %d + %d (dl < 0, copy)\n", + cl, dl); +#endif + for (;;) { + r[0] = b[0]; + if (++dl >= 0) + break; + r[1] = b[1]; + if (++dl >= 0) + break; + r[2] = b[2]; + if (++dl >= 0) + break; + r[3] = b[3]; + if (++dl >= 0) + break; + + b += 4; + r += 4; + } + } + } else { + int save_dl = dl; +#ifdef BN_COUNT + fprintf(stderr, " bn_add_part_words %d + %d (dl > 0)\n", cl, dl); +#endif + while (c) { + t = (a[0] + c) & BN_MASK2; + c = (t < c); + r[0] = t; + if (--dl <= 0) + break; + + t = (a[1] + c) & BN_MASK2; + c = (t < c); + r[1] = t; + if (--dl <= 0) + break; + + t = (a[2] + c) & BN_MASK2; + c = (t < c); + r[2] = t; + if (--dl <= 0) + break; + + t = (a[3] + c) & BN_MASK2; + c = (t < c); + r[3] = t; + if (--dl <= 0) + break; + + save_dl = dl; + a += 4; + r += 4; + } +#ifdef BN_COUNT + fprintf(stderr, " bn_add_part_words %d + %d (dl > 0, c == 0)\n", cl, + dl); +#endif + if (dl > 0) { + if (save_dl > dl) { + switch (save_dl - dl) { + case 1: + r[1] = a[1]; + if (--dl <= 0) + break; + case 2: + r[2] = a[2]; + if (--dl <= 0) + break; + case 3: + r[3] = a[3]; + if (--dl <= 0) + break; + } + a += 4; + r += 4; + } + } + if (dl > 0) { +#ifdef BN_COUNT + fprintf(stderr, " bn_add_part_words %d + %d (dl > 0, copy)\n", + cl, dl); +#endif + for (;;) { + r[0] = a[0]; + if (--dl <= 0) + break; + r[1] = a[1]; + if (--dl <= 0) + break; + r[2] = a[2]; + if (--dl <= 0) + break; + r[3] = a[3]; + if (--dl <= 0) + break; + + a += 4; + r += 4; + } + } + } + return c; +} + +#ifdef BN_RECURSION +/* + * Karatsuba recursive multiplication algorithm (cf. Knuth, The Art of + * Computer Programming, Vol. 2) + */ + +/*- + * r is 2*n2 words in size, + * a and b are both n2 words in size. + * n2 must be a power of 2. + * We multiply and return the result. + * t must be 2*n2 words in size + * We calculate + * a[0]*b[0] + * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0]) + * a[1]*b[1] + */ +/* dnX may not be positive, but n2/2+dnX has to be */ +void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2, + int dna, int dnb, BN_ULONG *t) +{ + int n = n2 / 2, c1, c2; + int tna = n + dna, tnb = n + dnb; + unsigned int neg, zero; + BN_ULONG ln, lo, *p; + +# ifdef BN_COUNT + fprintf(stderr, " bn_mul_recursive %d%+d * %d%+d\n", n2, dna, n2, dnb); +# endif +# ifdef BN_MUL_COMBA +# if 0 + if (n2 == 4) { + bn_mul_comba4(r, a, b); + return; + } +# endif + /* + * Only call bn_mul_comba 8 if n2 == 8 and the two arrays are complete + * [steve] + */ + if (n2 == 8 && dna == 0 && dnb == 0) { + bn_mul_comba8(r, a, b); + return; + } +# endif /* BN_MUL_COMBA */ + /* Else do normal multiply */ + if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL) { + bn_mul_normal(r, a, n2 + dna, b, n2 + dnb); + if ((dna + dnb) < 0) + memset(&r[2 * n2 + dna + dnb], 0, + sizeof(BN_ULONG) * -(dna + dnb)); + return; + } + /* r=(a[0]-a[1])*(b[1]-b[0]) */ + c1 = bn_cmp_part_words(a, &(a[n]), tna, n - tna); + c2 = bn_cmp_part_words(&(b[n]), b, tnb, tnb - n); + zero = neg = 0; + switch (c1 * 3 + c2) { + case -4: + bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */ + bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */ + break; + case -3: + zero = 1; + break; + case -2: + bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */ + bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); /* + */ + neg = 1; + break; + case -1: + case 0: + case 1: + zero = 1; + break; + case 2: + bn_sub_part_words(t, a, &(a[n]), tna, n - tna); /* + */ + bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */ + neg = 1; + break; + case 3: + zero = 1; + break; + case 4: + bn_sub_part_words(t, a, &(a[n]), tna, n - tna); + bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); + break; + } + +# ifdef BN_MUL_COMBA + if (n == 4 && dna == 0 && dnb == 0) { /* XXX: bn_mul_comba4 could take + * extra args to do this well */ + if (!zero) + bn_mul_comba4(&(t[n2]), t, &(t[n])); + else + memset(&(t[n2]), 0, 8 * sizeof(BN_ULONG)); + + bn_mul_comba4(r, a, b); + bn_mul_comba4(&(r[n2]), &(a[n]), &(b[n])); + } else if (n == 8 && dna == 0 && dnb == 0) { /* XXX: bn_mul_comba8 could + * take extra args to do + * this well */ + if (!zero) + bn_mul_comba8(&(t[n2]), t, &(t[n])); + else + memset(&(t[n2]), 0, 16 * sizeof(BN_ULONG)); + + bn_mul_comba8(r, a, b); + bn_mul_comba8(&(r[n2]), &(a[n]), &(b[n])); + } else +# endif /* BN_MUL_COMBA */ + { + p = &(t[n2 * 2]); + if (!zero) + bn_mul_recursive(&(t[n2]), t, &(t[n]), n, 0, 0, p); + else + memset(&(t[n2]), 0, n2 * sizeof(BN_ULONG)); + bn_mul_recursive(r, a, b, n, 0, 0, p); + bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]), n, dna, dnb, p); + } + + /*- + * t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign + * r[10] holds (a[0]*b[0]) + * r[32] holds (b[1]*b[1]) + */ + + c1 = (int)(bn_add_words(t, r, &(r[n2]), n2)); + + if (neg) { /* if t[32] is negative */ + c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2)); + } else { + /* Might have a carry */ + c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), t, n2)); + } + + /*- + * t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1]) + * r[10] holds (a[0]*b[0]) + * r[32] holds (b[1]*b[1]) + * c1 holds the carry bits + */ + c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2)); + if (c1) { + p = &(r[n + n2]); + lo = *p; + ln = (lo + c1) & BN_MASK2; + *p = ln; + + /* + * The overflow will stop before we over write words we should not + * overwrite + */ + if (ln < (BN_ULONG)c1) { + do { + p++; + lo = *p; + ln = (lo + 1) & BN_MASK2; + *p = ln; + } while (ln == 0); + } + } +} + +/* + * n+tn is the word length t needs to be n*4 is size, as does r + */ +/* tnX may not be negative but less than n */ +void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n, + int tna, int tnb, BN_ULONG *t) +{ + int i, j, n2 = n * 2; + int c1, c2, neg; + BN_ULONG ln, lo, *p; + +# ifdef BN_COUNT + fprintf(stderr, " bn_mul_part_recursive (%d%+d) * (%d%+d)\n", + n, tna, n, tnb); +# endif + if (n < 8) { + bn_mul_normal(r, a, n + tna, b, n + tnb); + return; + } + + /* r=(a[0]-a[1])*(b[1]-b[0]) */ + c1 = bn_cmp_part_words(a, &(a[n]), tna, n - tna); + c2 = bn_cmp_part_words(&(b[n]), b, tnb, tnb - n); + neg = 0; + switch (c1 * 3 + c2) { + case -4: + bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */ + bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */ + break; + case -3: + /* break; */ + case -2: + bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */ + bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); /* + */ + neg = 1; + break; + case -1: + case 0: + case 1: + /* break; */ + case 2: + bn_sub_part_words(t, a, &(a[n]), tna, n - tna); /* + */ + bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */ + neg = 1; + break; + case 3: + /* break; */ + case 4: + bn_sub_part_words(t, a, &(a[n]), tna, n - tna); + bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); + break; + } + /* + * The zero case isn't yet implemented here. The speedup would probably + * be negligible. + */ +# if 0 + if (n == 4) { + bn_mul_comba4(&(t[n2]), t, &(t[n])); + bn_mul_comba4(r, a, b); + bn_mul_normal(&(r[n2]), &(a[n]), tn, &(b[n]), tn); + memset(&(r[n2 + tn * 2]), 0, sizeof(BN_ULONG) * (n2 - tn * 2)); + } else +# endif + if (n == 8) { + bn_mul_comba8(&(t[n2]), t, &(t[n])); + bn_mul_comba8(r, a, b); + bn_mul_normal(&(r[n2]), &(a[n]), tna, &(b[n]), tnb); + memset(&(r[n2 + tna + tnb]), 0, sizeof(BN_ULONG) * (n2 - tna - tnb)); + } else { + p = &(t[n2 * 2]); + bn_mul_recursive(&(t[n2]), t, &(t[n]), n, 0, 0, p); + bn_mul_recursive(r, a, b, n, 0, 0, p); + i = n / 2; + /* + * If there is only a bottom half to the number, just do it + */ + if (tna > tnb) + j = tna - i; + else + j = tnb - i; + if (j == 0) { + bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]), + i, tna - i, tnb - i, p); + memset(&(r[n2 + i * 2]), 0, sizeof(BN_ULONG) * (n2 - i * 2)); + } else if (j > 0) { /* eg, n == 16, i == 8 and tn == 11 */ + bn_mul_part_recursive(&(r[n2]), &(a[n]), &(b[n]), + i, tna - i, tnb - i, p); + memset(&(r[n2 + tna + tnb]), 0, + sizeof(BN_ULONG) * (n2 - tna - tnb)); + } else { /* (j < 0) eg, n == 16, i == 8 and tn == 5 */ + + memset(&(r[n2]), 0, sizeof(BN_ULONG) * n2); + if (tna < BN_MUL_RECURSIVE_SIZE_NORMAL + && tnb < BN_MUL_RECURSIVE_SIZE_NORMAL) { + bn_mul_normal(&(r[n2]), &(a[n]), tna, &(b[n]), tnb); + } else { + for (;;) { + i /= 2; + /* + * these simplified conditions work exclusively because + * difference between tna and tnb is 1 or 0 + */ + if (i < tna || i < tnb) { + bn_mul_part_recursive(&(r[n2]), + &(a[n]), &(b[n]), + i, tna - i, tnb - i, p); + break; + } else if (i == tna || i == tnb) { + bn_mul_recursive(&(r[n2]), + &(a[n]), &(b[n]), + i, tna - i, tnb - i, p); + break; + } + } + } + } + } + + /*- + * t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign + * r[10] holds (a[0]*b[0]) + * r[32] holds (b[1]*b[1]) + */ + + c1 = (int)(bn_add_words(t, r, &(r[n2]), n2)); + + if (neg) { /* if t[32] is negative */ + c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2)); + } else { + /* Might have a carry */ + c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), t, n2)); + } + + /*- + * t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1]) + * r[10] holds (a[0]*b[0]) + * r[32] holds (b[1]*b[1]) + * c1 holds the carry bits + */ + c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2)); + if (c1) { + p = &(r[n + n2]); + lo = *p; + ln = (lo + c1) & BN_MASK2; + *p = ln; + + /* + * The overflow will stop before we over write words we should not + * overwrite + */ + if (ln < (BN_ULONG)c1) { + do { + p++; + lo = *p; + ln = (lo + 1) & BN_MASK2; + *p = ln; + } while (ln == 0); + } + } +} + +/*- + * a and b must be the same size, which is n2. + * r needs to be n2 words and t needs to be n2*2 + */ +void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2, + BN_ULONG *t) +{ + int n = n2 / 2; + +# ifdef BN_COUNT + fprintf(stderr, " bn_mul_low_recursive %d * %d\n", n2, n2); +# endif + + bn_mul_recursive(r, a, b, n, 0, 0, &(t[0])); + if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL) { + bn_mul_low_recursive(&(t[0]), &(a[0]), &(b[n]), n, &(t[n2])); + bn_add_words(&(r[n]), &(r[n]), &(t[0]), n); + bn_mul_low_recursive(&(t[0]), &(a[n]), &(b[0]), n, &(t[n2])); + bn_add_words(&(r[n]), &(r[n]), &(t[0]), n); + } else { + bn_mul_low_normal(&(t[0]), &(a[0]), &(b[n]), n); + bn_mul_low_normal(&(t[n]), &(a[n]), &(b[0]), n); + bn_add_words(&(r[n]), &(r[n]), &(t[0]), n); + bn_add_words(&(r[n]), &(r[n]), &(t[n]), n); + } +} + +/*- + * a and b must be the same size, which is n2. + * r needs to be n2 words and t needs to be n2*2 + * l is the low words of the output. + * t needs to be n2*3 + */ +void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2, + BN_ULONG *t) +{ + int i, n; + int c1, c2; + int neg, oneg, zero; + BN_ULONG ll, lc, *lp, *mp; + +# ifdef BN_COUNT + fprintf(stderr, " bn_mul_high %d * %d\n", n2, n2); +# endif + n = n2 / 2; + + /* Calculate (al-ah)*(bh-bl) */ + neg = zero = 0; + c1 = bn_cmp_words(&(a[0]), &(a[n]), n); + c2 = bn_cmp_words(&(b[n]), &(b[0]), n); + switch (c1 * 3 + c2) { + case -4: + bn_sub_words(&(r[0]), &(a[n]), &(a[0]), n); + bn_sub_words(&(r[n]), &(b[0]), &(b[n]), n); + break; + case -3: + zero = 1; + break; + case -2: + bn_sub_words(&(r[0]), &(a[n]), &(a[0]), n); + bn_sub_words(&(r[n]), &(b[n]), &(b[0]), n); + neg = 1; + break; + case -1: + case 0: + case 1: + zero = 1; + break; + case 2: + bn_sub_words(&(r[0]), &(a[0]), &(a[n]), n); + bn_sub_words(&(r[n]), &(b[0]), &(b[n]), n); + neg = 1; + break; + case 3: + zero = 1; + break; + case 4: + bn_sub_words(&(r[0]), &(a[0]), &(a[n]), n); + bn_sub_words(&(r[n]), &(b[n]), &(b[0]), n); + break; + } + + oneg = neg; + /* t[10] = (a[0]-a[1])*(b[1]-b[0]) */ + /* r[10] = (a[1]*b[1]) */ +# ifdef BN_MUL_COMBA + if (n == 8) { + bn_mul_comba8(&(t[0]), &(r[0]), &(r[n])); + bn_mul_comba8(r, &(a[n]), &(b[n])); + } else +# endif + { + bn_mul_recursive(&(t[0]), &(r[0]), &(r[n]), n, 0, 0, &(t[n2])); + bn_mul_recursive(r, &(a[n]), &(b[n]), n, 0, 0, &(t[n2])); + } + + /*- + * s0 == low(al*bl) + * s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl) + * We know s0 and s1 so the only unknown is high(al*bl) + * high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl)) + * high(al*bl) == s1 - (r[0]+l[0]+t[0]) + */ + if (l != NULL) { + lp = &(t[n2 + n]); + c1 = (int)(bn_add_words(lp, &(r[0]), &(l[0]), n)); + } else { + c1 = 0; + lp = &(r[0]); + } + + if (neg) + neg = (int)(bn_sub_words(&(t[n2]), lp, &(t[0]), n)); + else { + bn_add_words(&(t[n2]), lp, &(t[0]), n); + neg = 0; + } + + if (l != NULL) { + bn_sub_words(&(t[n2 + n]), &(l[n]), &(t[n2]), n); + } else { + lp = &(t[n2 + n]); + mp = &(t[n2]); + for (i = 0; i < n; i++) + lp[i] = ((~mp[i]) + 1) & BN_MASK2; + } + + /*- + * s[0] = low(al*bl) + * t[3] = high(al*bl) + * t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign + * r[10] = (a[1]*b[1]) + */ + /*- + * R[10] = al*bl + * R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0]) + * R[32] = ah*bh + */ + /*- + * R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow) + * R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow) + * R[3]=r[1]+(carry/borrow) + */ + if (l != NULL) { + lp = &(t[n2]); + c1 = (int)(bn_add_words(lp, &(t[n2 + n]), &(l[0]), n)); + } else { + lp = &(t[n2 + n]); + c1 = 0; + } + c1 += (int)(bn_add_words(&(t[n2]), lp, &(r[0]), n)); + if (oneg) + c1 -= (int)(bn_sub_words(&(t[n2]), &(t[n2]), &(t[0]), n)); + else + c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), &(t[0]), n)); + + c2 = (int)(bn_add_words(&(r[0]), &(r[0]), &(t[n2 + n]), n)); + c2 += (int)(bn_add_words(&(r[0]), &(r[0]), &(r[n]), n)); + if (oneg) + c2 -= (int)(bn_sub_words(&(r[0]), &(r[0]), &(t[n]), n)); + else + c2 += (int)(bn_add_words(&(r[0]), &(r[0]), &(t[n]), n)); + + if (c1 != 0) { /* Add starting at r[0], could be +ve or -ve */ + i = 0; + if (c1 > 0) { + lc = c1; + do { + ll = (r[i] + lc) & BN_MASK2; + r[i++] = ll; + lc = (lc > ll); + } while (lc); + } else { + lc = -c1; + do { + ll = r[i]; + r[i++] = (ll - lc) & BN_MASK2; + lc = (lc > ll); + } while (lc); + } + } + if (c2 != 0) { /* Add starting at r[1] */ + i = n; + if (c2 > 0) { + lc = c2; + do { + ll = (r[i] + lc) & BN_MASK2; + r[i++] = ll; + lc = (lc > ll); + } while (lc); + } else { + lc = -c2; + do { + ll = r[i]; + r[i++] = (ll - lc) & BN_MASK2; + lc = (lc > ll); + } while (lc); + } + } +} +#endif /* BN_RECURSION */ + +int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) +{ + int ret = 0; + int top, al, bl; + BIGNUM *rr; +#if defined(BN_MUL_COMBA) || defined(BN_RECURSION) + int i; +#endif +#ifdef BN_RECURSION + BIGNUM *t = NULL; + int j = 0, k; +#endif + +#ifdef BN_COUNT + fprintf(stderr, "BN_mul %d * %d\n", a->top, b->top); +#endif + + bn_check_top(a); + bn_check_top(b); + bn_check_top(r); + + al = a->top; + bl = b->top; + + if ((al == 0) || (bl == 0)) { + BN_zero(r); + return (1); + } + top = al + bl; + + BN_CTX_start(ctx); + if ((r == a) || (r == b)) { + if ((rr = BN_CTX_get(ctx)) == NULL) + goto err; + } else + rr = r; + rr->neg = a->neg ^ b->neg; + +#if defined(BN_MUL_COMBA) || defined(BN_RECURSION) + i = al - bl; +#endif +#ifdef BN_MUL_COMBA + if (i == 0) { +# if 0 + if (al == 4) { + if (bn_wexpand(rr, 8) == NULL) + goto err; + rr->top = 8; + bn_mul_comba4(rr->d, a->d, b->d); + goto end; + } +# endif + if (al == 8) { + if (bn_wexpand(rr, 16) == NULL) + goto err; + rr->top = 16; + bn_mul_comba8(rr->d, a->d, b->d); + goto end; + } + } +#endif /* BN_MUL_COMBA */ +#ifdef BN_RECURSION + if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL)) { + if (i >= -1 && i <= 1) { + /* + * Find out the power of two lower or equal to the longest of the + * two numbers + */ + if (i >= 0) { + j = BN_num_bits_word((BN_ULONG)al); + } + if (i == -1) { + j = BN_num_bits_word((BN_ULONG)bl); + } + j = 1 << (j - 1); + assert(j <= al || j <= bl); + k = j + j; + t = BN_CTX_get(ctx); + if (t == NULL) + goto err; + if (al > j || bl > j) { + if (bn_wexpand(t, k * 4) == NULL) + goto err; + if (bn_wexpand(rr, k * 4) == NULL) + goto err; + bn_mul_part_recursive(rr->d, a->d, b->d, + j, al - j, bl - j, t->d); + } else { /* al <= j || bl <= j */ + + if (bn_wexpand(t, k * 2) == NULL) + goto err; + if (bn_wexpand(rr, k * 2) == NULL) + goto err; + bn_mul_recursive(rr->d, a->d, b->d, j, al - j, bl - j, t->d); + } + rr->top = top; + goto end; + } +# if 0 + if (i == 1 && !BN_get_flags(b, BN_FLG_STATIC_DATA)) { + BIGNUM *tmp_bn = (BIGNUM *)b; + if (bn_wexpand(tmp_bn, al) == NULL) + goto err; + tmp_bn->d[bl] = 0; + bl++; + i--; + } else if (i == -1 && !BN_get_flags(a, BN_FLG_STATIC_DATA)) { + BIGNUM *tmp_bn = (BIGNUM *)a; + if (bn_wexpand(tmp_bn, bl) == NULL) + goto err; + tmp_bn->d[al] = 0; + al++; + i++; + } + if (i == 0) { + /* symmetric and > 4 */ + /* 16 or larger */ + j = BN_num_bits_word((BN_ULONG)al); + j = 1 << (j - 1); + k = j + j; + t = BN_CTX_get(ctx); + if (al == j) { /* exact multiple */ + if (bn_wexpand(t, k * 2) == NULL) + goto err; + if (bn_wexpand(rr, k * 2) == NULL) + goto err; + bn_mul_recursive(rr->d, a->d, b->d, al, t->d); + } else { + if (bn_wexpand(t, k * 4) == NULL) + goto err; + if (bn_wexpand(rr, k * 4) == NULL) + goto err; + bn_mul_part_recursive(rr->d, a->d, b->d, al - j, j, t->d); + } + rr->top = top; + goto end; + } +# endif + } +#endif /* BN_RECURSION */ + if (bn_wexpand(rr, top) == NULL) + goto err; + rr->top = top; + bn_mul_normal(rr->d, a->d, al, b->d, bl); + +#if defined(BN_MUL_COMBA) || defined(BN_RECURSION) + end: +#endif + bn_correct_top(rr); + if (r != rr && BN_copy(r, rr) == NULL) + goto err; + + ret = 1; + err: + bn_check_top(r); + BN_CTX_end(ctx); + return (ret); +} + +void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb) +{ + BN_ULONG *rr; + +#ifdef BN_COUNT + fprintf(stderr, " bn_mul_normal %d * %d\n", na, nb); +#endif + + if (na < nb) { + int itmp; + BN_ULONG *ltmp; + + itmp = na; + na = nb; + nb = itmp; + ltmp = a; + a = b; + b = ltmp; + + } + rr = &(r[na]); + if (nb <= 0) { + (void)bn_mul_words(r, a, na, 0); + return; + } else + rr[0] = bn_mul_words(r, a, na, b[0]); + + for (;;) { + if (--nb <= 0) + return; + rr[1] = bn_mul_add_words(&(r[1]), a, na, b[1]); + if (--nb <= 0) + return; + rr[2] = bn_mul_add_words(&(r[2]), a, na, b[2]); + if (--nb <= 0) + return; + rr[3] = bn_mul_add_words(&(r[3]), a, na, b[3]); + if (--nb <= 0) + return; + rr[4] = bn_mul_add_words(&(r[4]), a, na, b[4]); + rr += 4; + r += 4; + b += 4; + } +} + +void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n) +{ +#ifdef BN_COUNT + fprintf(stderr, " bn_mul_low_normal %d * %d\n", n, n); +#endif + bn_mul_words(r, a, n, b[0]); + + for (;;) { + if (--n <= 0) + return; + bn_mul_add_words(&(r[1]), a, n, b[1]); + if (--n <= 0) + return; + bn_mul_add_words(&(r[2]), a, n, b[2]); + if (--n <= 0) + return; + bn_mul_add_words(&(r[3]), a, n, b[3]); + if (--n <= 0) + return; + bn_mul_add_words(&(r[4]), a, n, b[4]); + r += 4; + b += 4; + } +} |