/* $OpenBSD: bn_div.c,v 1.25 2017/01/29 17:49:22 beck Exp $ */ /* 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/opensslconf.h> #include <openssl/bn.h> #include <openssl/err.h> #include "bn_lcl.h" #if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) \ && !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(_LP64) /* * 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. */ static int BN_div_internal(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor, BN_CTX *ctx, int ct) { 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 * in the case of 'num', so don't just rely on bn_check_top() for this one * (bn_check_top() works only for BN_DEBUG builds) */ if (num->top > 0 && num->d[num->top - 1] == 0) { BNerror(BN_R_NOT_INITIALIZED); return 0; } bn_check_top(num); if (ct) no_branch = 1; bn_check_top(dv); bn_check_top(rm); /* bn_check_top(num); */ /* 'num' has been checked already */ bn_check_top(divisor); if (BN_is_zero(divisor)) { BNerror(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 (tmp == NULL || snum == NULL || sdiv == NULL || res == 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 */ wnum.flags = snum->flags | BN_FLG_STATIC_DATA; /* 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_DIV2W) && !defined(bn_div_words) q = (BN_ULONG)(((((BN_ULLONG)n0) << BN_BITS2)|n1)/d0); #else q = bn_div_words(n0, n1, d0); #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); #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); } int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor, BN_CTX *ctx) { int ct = ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0) || (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0)); return BN_div_internal(dv, rm, num, divisor, ctx, ct); } int BN_div_nonct(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor, BN_CTX *ctx) { return BN_div_internal(dv, rm, num, divisor, ctx, 0); } int BN_div_ct(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor, BN_CTX *ctx) { return BN_div_internal(dv, rm, num, divisor, ctx, 1); }
