| /* crypto/bn/bn_div.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.] |
| */ |
| |
| #include <stdio.h> |
| #include <openssl/bn.h> |
| #include "cryptlib.h" |
| #include "bn_lcl.h" |
| |
| /* The old slow way */ |
| #if 0 |
| int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d, |
| BN_CTX *ctx) |
| { |
| int i, nm, nd; |
| int ret = 0; |
| BIGNUM *D; |
| |
| bn_check_top(m); |
| bn_check_top(d); |
| if (BN_is_zero(d)) { |
| BNerr(BN_F_BN_DIV, BN_R_DIV_BY_ZERO); |
| return (0); |
| } |
| |
| if (BN_ucmp(m, d) < 0) { |
| if (rem != NULL) { |
| if (BN_copy(rem, m) == NULL) |
| return (0); |
| } |
| if (dv != NULL) |
| BN_zero(dv); |
| return (1); |
| } |
| |
| BN_CTX_start(ctx); |
| D = BN_CTX_get(ctx); |
| if (dv == NULL) |
| dv = BN_CTX_get(ctx); |
| if (rem == NULL) |
| rem = BN_CTX_get(ctx); |
| if (D == NULL || dv == NULL || rem == NULL) |
| goto end; |
| |
| nd = BN_num_bits(d); |
| nm = BN_num_bits(m); |
| if (BN_copy(D, d) == NULL) |
| goto end; |
| if (BN_copy(rem, m) == NULL) |
| goto end; |
| |
| /* |
| * The next 2 are needed so we can do a dv->d[0]|=1 later since |
| * BN_lshift1 will only work once there is a value :-) |
| */ |
| BN_zero(dv); |
| if (bn_wexpand(dv, 1) == NULL) |
| goto end; |
| dv->top = 1; |
| |
| if (!BN_lshift(D, D, nm - nd)) |
| goto end; |
| for (i = nm - nd; i >= 0; i--) { |
| if (!BN_lshift1(dv, dv)) |
| goto end; |
| if (BN_ucmp(rem, D) >= 0) { |
| dv->d[0] |= 1; |
| if (!BN_usub(rem, rem, D)) |
| goto end; |
| } |
| /* CAN IMPROVE (and have now :=) */ |
| if (!BN_rshift1(D, D)) |
| goto end; |
| } |
| rem->neg = BN_is_zero(rem) ? 0 : m->neg; |
| dv->neg = m->neg ^ d->neg; |
| ret = 1; |
| end: |
| BN_CTX_end(ctx); |
| return (ret); |
| } |
| |
| #else |
| |
| # if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) \ |
| && !defined(PEDANTIC) && !defined(BN_DIV3W) |
| # if defined(__GNUC__) && __GNUC__>=2 |
| # if defined(__i386) || defined (__i386__) |
| /*- |
| * There were two reasons for implementing this template: |
| * - GNU C generates a call to a function (__udivdi3 to be exact) |
| * in reply to ((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0 (I fail to |
| * understand why...); |
| * - divl doesn't only calculate quotient, but also leaves |
| * remainder in %edx which we can definitely use here:-) |
| * |
| * <appro@fy.chalmers.se> |
| */ |
| # undef bn_div_words |
| # define bn_div_words(n0,n1,d0) \ |
| ({ asm volatile ( \ |
| "divl %4" \ |
| : "=a"(q), "=d"(rem) \ |
| : "a"(n1), "d"(n0), "g"(d0) \ |
| : "cc"); \ |
| q; \ |
| }) |
| # define REMAINDER_IS_ALREADY_CALCULATED |
| # elif defined(__x86_64) && defined(SIXTY_FOUR_BIT_LONG) |
| /* |
| * Same story here, but it's 128-bit by 64-bit division. Wow! |
| * <appro@fy.chalmers.se> |
| */ |
| # undef bn_div_words |
| # define bn_div_words(n0,n1,d0) \ |
| ({ asm volatile ( \ |
| "divq %4" \ |
| : "=a"(q), "=d"(rem) \ |
| : "a"(n1), "d"(n0), "g"(d0) \ |
| : "cc"); \ |
| q; \ |
| }) |
| # define REMAINDER_IS_ALREADY_CALCULATED |
| # endif /* __<cpu> */ |
| # endif /* __GNUC__ */ |
| # endif /* OPENSSL_NO_ASM */ |
| |
| /*- |
| * BN_div computes dv := num / divisor, rounding towards |
| * zero, and sets up rm such that dv*divisor + rm = num holds. |
| * Thus: |
| * dv->neg == num->neg ^ divisor->neg (unless the result is zero) |
| * rm->neg == num->neg (unless the remainder is zero) |
| * If 'dv' or 'rm' is NULL, the respective value is not returned. |
| */ |
| int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor, |
| BN_CTX *ctx) |
| { |
| int norm_shift, i, loop; |
| BIGNUM *tmp, wnum, *snum, *sdiv, *res; |
| BN_ULONG *resp, *wnump; |
| BN_ULONG d0, d1; |
| int num_n, div_n; |
| int no_branch = 0; |
| |
| /* |
| * Invalid zero-padding would have particularly bad consequences so don't |
| * just rely on bn_check_top() here (bn_check_top() works only for |
| * BN_DEBUG builds) |
| */ |
| if ((num->top > 0 && num->d[num->top - 1] == 0) || |
| (divisor->top > 0 && divisor->d[divisor->top - 1] == 0)) { |
| BNerr(BN_F_BN_DIV, BN_R_NOT_INITIALIZED); |
| return 0; |
| } |
| |
| bn_check_top(num); |
| bn_check_top(divisor); |
| |
| if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0) |
| || (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0)) { |
| no_branch = 1; |
| } |
| |
| bn_check_top(dv); |
| bn_check_top(rm); |
| /*- bn_check_top(num); *//* |
| * 'num' has been checked already |
| */ |
| /*- bn_check_top(divisor); *//* |
| * 'divisor' has been checked already |
| */ |
| |
| if (BN_is_zero(divisor)) { |
| BNerr(BN_F_BN_DIV, BN_R_DIV_BY_ZERO); |
| return (0); |
| } |
| |
| if (!no_branch && BN_ucmp(num, divisor) < 0) { |
| if (rm != NULL) { |
| if (BN_copy(rm, num) == NULL) |
| return (0); |
| } |
| if (dv != NULL) |
| BN_zero(dv); |
| return (1); |
| } |
| |
| BN_CTX_start(ctx); |
| tmp = BN_CTX_get(ctx); |
| snum = BN_CTX_get(ctx); |
| sdiv = BN_CTX_get(ctx); |
| if (dv == NULL) |
| res = BN_CTX_get(ctx); |
| else |
| res = dv; |
| if (sdiv == NULL || res == NULL || tmp == NULL || snum == NULL) |
| goto err; |
| |
| /* First we normalise the numbers */ |
| norm_shift = BN_BITS2 - ((BN_num_bits(divisor)) % BN_BITS2); |
| if (!(BN_lshift(sdiv, divisor, norm_shift))) |
| goto err; |
| sdiv->neg = 0; |
| norm_shift += BN_BITS2; |
| if (!(BN_lshift(snum, num, norm_shift))) |
| goto err; |
| snum->neg = 0; |
| |
| if (no_branch) { |
| /* |
| * Since we don't know whether snum is larger than sdiv, we pad snum |
| * with enough zeroes without changing its value. |
| */ |
| if (snum->top <= sdiv->top + 1) { |
| if (bn_wexpand(snum, sdiv->top + 2) == NULL) |
| goto err; |
| for (i = snum->top; i < sdiv->top + 2; i++) |
| snum->d[i] = 0; |
| snum->top = sdiv->top + 2; |
| } else { |
| if (bn_wexpand(snum, snum->top + 1) == NULL) |
| goto err; |
| snum->d[snum->top] = 0; |
| snum->top++; |
| } |
| } |
| |
| div_n = sdiv->top; |
| num_n = snum->top; |
| loop = num_n - div_n; |
| /* |
| * Lets setup a 'window' into snum This is the part that corresponds to |
| * the current 'area' being divided |
| */ |
| wnum.neg = 0; |
| wnum.d = &(snum->d[loop]); |
| wnum.top = div_n; |
| /* |
| * only needed when BN_ucmp messes up the values between top and max |
| */ |
| wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */ |
| |
| /* Get the top 2 words of sdiv */ |
| /* div_n=sdiv->top; */ |
| d0 = sdiv->d[div_n - 1]; |
| d1 = (div_n == 1) ? 0 : sdiv->d[div_n - 2]; |
| |
| /* pointer to the 'top' of snum */ |
| wnump = &(snum->d[num_n - 1]); |
| |
| /* Setup to 'res' */ |
| res->neg = (num->neg ^ divisor->neg); |
| if (!bn_wexpand(res, (loop + 1))) |
| goto err; |
| res->top = loop - no_branch; |
| resp = &(res->d[loop - 1]); |
| |
| /* space for temp */ |
| if (!bn_wexpand(tmp, (div_n + 1))) |
| goto err; |
| |
| if (!no_branch) { |
| if (BN_ucmp(&wnum, sdiv) >= 0) { |
| /* |
| * If BN_DEBUG_RAND is defined BN_ucmp changes (via bn_pollute) |
| * the const bignum arguments => clean the values between top and |
| * max again |
| */ |
| bn_clear_top2max(&wnum); |
| bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n); |
| *resp = 1; |
| } else |
| res->top--; |
| } |
| |
| /* |
| * if res->top == 0 then clear the neg value otherwise decrease the resp |
| * pointer |
| */ |
| if (res->top == 0) |
| res->neg = 0; |
| else |
| resp--; |
| |
| for (i = 0; i < loop - 1; i++, wnump--, resp--) { |
| BN_ULONG q, l0; |
| /* |
| * the first part of the loop uses the top two words of snum and sdiv |
| * to calculate a BN_ULONG q such that | wnum - sdiv * q | < sdiv |
| */ |
| # if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM) |
| BN_ULONG bn_div_3_words(BN_ULONG *, BN_ULONG, BN_ULONG); |
| q = bn_div_3_words(wnump, d1, d0); |
| # else |
| BN_ULONG n0, n1, rem = 0; |
| |
| n0 = wnump[0]; |
| n1 = wnump[-1]; |
| if (n0 == d0) |
| q = BN_MASK2; |
| else { /* n0 < d0 */ |
| |
| # ifdef BN_LLONG |
| BN_ULLONG t2; |
| |
| # if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words) |
| q = (BN_ULONG)(((((BN_ULLONG) n0) << BN_BITS2) | n1) / d0); |
| # else |
| q = bn_div_words(n0, n1, d0); |
| # ifdef BN_DEBUG_LEVITTE |
| fprintf(stderr, "DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\ |
| X) -> 0x%08X\n", n0, n1, d0, q); |
| # endif |
| # endif |
| |
| # ifndef REMAINDER_IS_ALREADY_CALCULATED |
| /* |
| * rem doesn't have to be BN_ULLONG. The least we |
| * know it's less that d0, isn't it? |
| */ |
| rem = (n1 - q * d0) & BN_MASK2; |
| # endif |
| t2 = (BN_ULLONG) d1 *q; |
| |
| for (;;) { |
| if (t2 <= ((((BN_ULLONG) rem) << BN_BITS2) | wnump[-2])) |
| break; |
| q--; |
| rem += d0; |
| if (rem < d0) |
| break; /* don't let rem overflow */ |
| t2 -= d1; |
| } |
| # else /* !BN_LLONG */ |
| BN_ULONG t2l, t2h; |
| |
| q = bn_div_words(n0, n1, d0); |
| # ifdef BN_DEBUG_LEVITTE |
| fprintf(stderr, "DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\ |
| X) -> 0x%08X\n", n0, n1, d0, q); |
| # endif |
| # ifndef REMAINDER_IS_ALREADY_CALCULATED |
| rem = (n1 - q * d0) & BN_MASK2; |
| # endif |
| |
| # if defined(BN_UMULT_LOHI) |
| BN_UMULT_LOHI(t2l, t2h, d1, q); |
| # elif defined(BN_UMULT_HIGH) |
| t2l = d1 * q; |
| t2h = BN_UMULT_HIGH(d1, q); |
| # else |
| { |
| BN_ULONG ql, qh; |
| t2l = LBITS(d1); |
| t2h = HBITS(d1); |
| ql = LBITS(q); |
| qh = HBITS(q); |
| mul64(t2l, t2h, ql, qh); /* t2=(BN_ULLONG)d1*q; */ |
| } |
| # endif |
| |
| for (;;) { |
| if ((t2h < rem) || ((t2h == rem) && (t2l <= wnump[-2]))) |
| break; |
| q--; |
| rem += d0; |
| if (rem < d0) |
| break; /* don't let rem overflow */ |
| if (t2l < d1) |
| t2h--; |
| t2l -= d1; |
| } |
| # endif /* !BN_LLONG */ |
| } |
| # endif /* !BN_DIV3W */ |
| |
| l0 = bn_mul_words(tmp->d, sdiv->d, div_n, q); |
| tmp->d[div_n] = l0; |
| wnum.d--; |
| /* |
| * ingore top values of the bignums just sub the two BN_ULONG arrays |
| * with bn_sub_words |
| */ |
| if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n + 1)) { |
| /* |
| * Note: As we have considered only the leading two BN_ULONGs in |
| * the calculation of q, sdiv * q might be greater than wnum (but |
| * then (q-1) * sdiv is less or equal than wnum) |
| */ |
| q--; |
| if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n)) |
| /* |
| * we can't have an overflow here (assuming that q != 0, but |
| * if q == 0 then tmp is zero anyway) |
| */ |
| (*wnump)++; |
| } |
| /* store part of the result */ |
| *resp = q; |
| } |
| bn_correct_top(snum); |
| if (rm != NULL) { |
| /* |
| * Keep a copy of the neg flag in num because if rm==num BN_rshift() |
| * will overwrite it. |
| */ |
| int neg = num->neg; |
| BN_rshift(rm, snum, norm_shift); |
| if (!BN_is_zero(rm)) |
| rm->neg = neg; |
| bn_check_top(rm); |
| } |
| if (no_branch) |
| bn_correct_top(res); |
| BN_CTX_end(ctx); |
| return (1); |
| err: |
| bn_check_top(rm); |
| BN_CTX_end(ctx); |
| return (0); |
| } |
| #endif |
