650 lines
17 KiB
C
650 lines
17 KiB
C
/* crypto/bn/bn_div.c */
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/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
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* All rights reserved.
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*
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* This package is an SSL implementation written
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* by Eric Young (eay@cryptsoft.com).
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* The implementation was written so as to conform with Netscapes SSL.
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*
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* This library is free for commercial and non-commercial use as long as
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* the following conditions are aheared to. The following conditions
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* apply to all code found in this distribution, be it the RC4, RSA,
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* lhash, DES, etc., code; not just the SSL code. The SSL documentation
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* included with this distribution is covered by the same copyright terms
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* except that the holder is Tim Hudson (tjh@cryptsoft.com).
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*
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* Copyright remains Eric Young's, and as such any Copyright notices in
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* the code are not to be removed.
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* If this package is used in a product, Eric Young should be given attribution
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* as the author of the parts of the library used.
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* This can be in the form of a textual message at program startup or
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* in documentation (online or textual) provided with the package.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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* 3. All advertising materials mentioning features or use of this software
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* must display the following acknowledgement:
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* "This product includes cryptographic software written by
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* Eric Young (eay@cryptsoft.com)"
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* The word 'cryptographic' can be left out if the rouines from the library
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* being used are not cryptographic related :-).
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* 4. If you include any Windows specific code (or a derivative thereof) from
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* the apps directory (application code) you must include an acknowledgement:
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* "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
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*
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* THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*
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* The licence and distribution terms for any publically available version or
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* derivative of this code cannot be changed. i.e. this code cannot simply be
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* copied and put under another distribution licence
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* [including the GNU Public Licence.]
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*/
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#include <stdio.h>
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#include <openssl/bn.h>
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#include "cryptlib.h"
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#include "bn_lcl.h"
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/* The old slow way */
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#if 0
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int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
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BN_CTX *ctx)
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{
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int i,nm,nd;
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int ret = 0;
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BIGNUM *D;
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bn_check_top(m);
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bn_check_top(d);
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if (BN_is_zero(d))
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{
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BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
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return(0);
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}
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if (BN_ucmp(m,d) < 0)
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{
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if (rem != NULL)
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{ if (BN_copy(rem,m) == NULL) return(0); }
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if (dv != NULL) BN_zero(dv);
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return(1);
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}
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BN_CTX_start(ctx);
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D = BN_CTX_get(ctx);
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if (dv == NULL) dv = BN_CTX_get(ctx);
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if (rem == NULL) rem = BN_CTX_get(ctx);
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if (D == NULL || dv == NULL || rem == NULL)
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goto end;
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nd=BN_num_bits(d);
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nm=BN_num_bits(m);
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if (BN_copy(D,d) == NULL) goto end;
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if (BN_copy(rem,m) == NULL) goto end;
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/* The next 2 are needed so we can do a dv->d[0]|=1 later
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* since BN_lshift1 will only work once there is a value :-) */
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BN_zero(dv);
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bn_wexpand(dv,1);
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dv->top=1;
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if (!BN_lshift(D,D,nm-nd)) goto end;
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for (i=nm-nd; i>=0; i--)
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{
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if (!BN_lshift1(dv,dv)) goto end;
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if (BN_ucmp(rem,D) >= 0)
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{
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dv->d[0]|=1;
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if (!BN_usub(rem,rem,D)) goto end;
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}
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/* CAN IMPROVE (and have now :=) */
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if (!BN_rshift1(D,D)) goto end;
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}
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rem->neg=BN_is_zero(rem)?0:m->neg;
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dv->neg=m->neg^d->neg;
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ret = 1;
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end:
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BN_CTX_end(ctx);
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return(ret);
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}
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#else
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#if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) \
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&& !defined(PEDANTIC) && !defined(BN_DIV3W)
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# if defined(__GNUC__) && __GNUC__>=2
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# if defined(__i386) || defined (__i386__)
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/*
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* There were two reasons for implementing this template:
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* - GNU C generates a call to a function (__udivdi3 to be exact)
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* in reply to ((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0 (I fail to
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* understand why...);
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* - divl doesn't only calculate quotient, but also leaves
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* remainder in %edx which we can definitely use here:-)
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*
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* <appro@fy.chalmers.se>
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*/
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# define bn_div_words(n0,n1,d0) \
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({ asm volatile ( \
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"divl %4" \
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: "=a"(q), "=d"(rem) \
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: "a"(n1), "d"(n0), "g"(d0) \
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: "cc"); \
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q; \
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})
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# define REMAINDER_IS_ALREADY_CALCULATED
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# elif defined(__x86_64) && defined(SIXTY_FOUR_BIT_LONG)
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/*
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* Same story here, but it's 128-bit by 64-bit division. Wow!
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* <appro@fy.chalmers.se>
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*/
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# define bn_div_words(n0,n1,d0) \
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({ asm volatile ( \
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"divq %4" \
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: "=a"(q), "=d"(rem) \
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: "a"(n1), "d"(n0), "g"(d0) \
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: "cc"); \
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q; \
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})
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# define REMAINDER_IS_ALREADY_CALCULATED
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# endif /* __<cpu> */
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# endif /* __GNUC__ */
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#endif /* OPENSSL_NO_ASM */
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/* BN_div[_no_branch] computes dv := num / divisor, rounding towards
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* zero, and sets up rm such that dv*divisor + rm = num holds.
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* Thus:
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* dv->neg == num->neg ^ divisor->neg (unless the result is zero)
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* rm->neg == num->neg (unless the remainder is zero)
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* If 'dv' or 'rm' is NULL, the respective value is not returned.
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*/
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static int BN_div_no_branch(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num,
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const BIGNUM *divisor, BN_CTX *ctx);
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int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
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BN_CTX *ctx)
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{
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int norm_shift,i,loop;
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BIGNUM *tmp,wnum,*snum,*sdiv,*res;
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BN_ULONG *resp,*wnump;
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BN_ULONG d0,d1;
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int num_n,div_n;
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/* Invalid zero-padding would have particularly bad consequences
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* in the case of 'num', so don't just rely on bn_check_top() for this one
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* (bn_check_top() works only for BN_DEBUG builds) */
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if (num->top > 0 && num->d[num->top - 1] == 0)
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{
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BNerr(BN_F_BN_DIV,BN_R_NOT_INITIALIZED);
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return 0;
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}
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bn_check_top(num);
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if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0) || (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0))
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{
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return BN_div_no_branch(dv, rm, num, divisor, ctx);
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}
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bn_check_top(dv);
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bn_check_top(rm);
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/* bn_check_top(num); */ /* 'num' has been checked already */
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bn_check_top(divisor);
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if (BN_is_zero(divisor))
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{
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BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
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return(0);
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}
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if (BN_ucmp(num,divisor) < 0)
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{
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if (rm != NULL)
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{ if (BN_copy(rm,num) == NULL) return(0); }
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if (dv != NULL) BN_zero(dv);
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return(1);
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}
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BN_CTX_start(ctx);
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tmp=BN_CTX_get(ctx);
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snum=BN_CTX_get(ctx);
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sdiv=BN_CTX_get(ctx);
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if (dv == NULL)
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res=BN_CTX_get(ctx);
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else res=dv;
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if (sdiv == NULL || res == NULL || tmp == NULL || snum == NULL)
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goto err;
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/* First we normalise the numbers */
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norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
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if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
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sdiv->neg=0;
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norm_shift+=BN_BITS2;
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if (!(BN_lshift(snum,num,norm_shift))) goto err;
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snum->neg=0;
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div_n=sdiv->top;
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num_n=snum->top;
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loop=num_n-div_n;
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/* Lets setup a 'window' into snum
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* This is the part that corresponds to the current
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* 'area' being divided */
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wnum.neg = 0;
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wnum.d = &(snum->d[loop]);
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wnum.top = div_n;
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/* only needed when BN_ucmp messes up the values between top and max */
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wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */
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/* Get the top 2 words of sdiv */
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/* div_n=sdiv->top; */
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d0=sdiv->d[div_n-1];
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d1=(div_n == 1)?0:sdiv->d[div_n-2];
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/* pointer to the 'top' of snum */
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wnump= &(snum->d[num_n-1]);
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/* Setup to 'res' */
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res->neg= (num->neg^divisor->neg);
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if (!bn_wexpand(res,(loop+1))) goto err;
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res->top=loop;
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resp= &(res->d[loop-1]);
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/* space for temp */
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if (!bn_wexpand(tmp,(div_n+1))) goto err;
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if (BN_ucmp(&wnum,sdiv) >= 0)
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{
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/* If BN_DEBUG_RAND is defined BN_ucmp changes (via
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* bn_pollute) the const bignum arguments =>
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* clean the values between top and max again */
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bn_clear_top2max(&wnum);
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bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n);
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*resp=1;
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}
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else
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res->top--;
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/* if res->top == 0 then clear the neg value otherwise decrease
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* the resp pointer */
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if (res->top == 0)
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res->neg = 0;
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else
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resp--;
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for (i=0; i<loop-1; i++, wnump--, resp--)
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{
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BN_ULONG q,l0;
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/* the first part of the loop uses the top two words of
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* snum and sdiv to calculate a BN_ULONG q such that
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* | wnum - sdiv * q | < sdiv */
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#if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
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BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG);
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q=bn_div_3_words(wnump,d1,d0);
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#else
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BN_ULONG n0,n1,rem=0;
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n0=wnump[0];
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n1=wnump[-1];
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if (n0 == d0)
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q=BN_MASK2;
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else /* n0 < d0 */
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{
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#ifdef BN_LLONG
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BN_ULLONG t2;
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#if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
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q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
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#else
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q=bn_div_words(n0,n1,d0);
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#ifdef BN_DEBUG_LEVITTE
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fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
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X) -> 0x%08X\n",
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n0, n1, d0, q);
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#endif
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#endif
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#ifndef REMAINDER_IS_ALREADY_CALCULATED
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/*
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* rem doesn't have to be BN_ULLONG. The least we
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* know it's less that d0, isn't it?
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*/
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rem=(n1-q*d0)&BN_MASK2;
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#endif
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t2=(BN_ULLONG)d1*q;
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for (;;)
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{
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if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
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break;
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q--;
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rem += d0;
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if (rem < d0) break; /* don't let rem overflow */
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t2 -= d1;
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}
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#else /* !BN_LLONG */
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BN_ULONG t2l,t2h;
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q=bn_div_words(n0,n1,d0);
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#ifdef BN_DEBUG_LEVITTE
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fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
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X) -> 0x%08X\n",
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n0, n1, d0, q);
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#endif
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#ifndef REMAINDER_IS_ALREADY_CALCULATED
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rem=(n1-q*d0)&BN_MASK2;
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#endif
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#if defined(BN_UMULT_LOHI)
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BN_UMULT_LOHI(t2l,t2h,d1,q);
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#elif defined(BN_UMULT_HIGH)
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t2l = d1 * q;
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t2h = BN_UMULT_HIGH(d1,q);
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#else
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{
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BN_ULONG ql, qh;
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t2l=LBITS(d1); t2h=HBITS(d1);
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ql =LBITS(q); qh =HBITS(q);
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mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
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}
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#endif
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for (;;)
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{
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if ((t2h < rem) ||
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((t2h == rem) && (t2l <= wnump[-2])))
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break;
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q--;
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rem += d0;
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if (rem < d0) break; /* don't let rem overflow */
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if (t2l < d1) t2h--; t2l -= d1;
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}
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#endif /* !BN_LLONG */
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}
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#endif /* !BN_DIV3W */
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l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
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tmp->d[div_n]=l0;
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wnum.d--;
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/* ingore top values of the bignums just sub the two
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* BN_ULONG arrays with bn_sub_words */
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if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1))
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{
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/* Note: As we have considered only the leading
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* two BN_ULONGs in the calculation of q, sdiv * q
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* might be greater than wnum (but then (q-1) * sdiv
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* is less or equal than wnum)
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*/
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q--;
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if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
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/* we can't have an overflow here (assuming
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* that q != 0, but if q == 0 then tmp is
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* zero anyway) */
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(*wnump)++;
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}
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/* store part of the result */
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*resp = q;
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}
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bn_correct_top(snum);
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if (rm != NULL)
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{
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/* Keep a copy of the neg flag in num because if rm==num
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* BN_rshift() will overwrite it.
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*/
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int neg = num->neg;
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BN_rshift(rm,snum,norm_shift);
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if (!BN_is_zero(rm))
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rm->neg = neg;
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bn_check_top(rm);
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}
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BN_CTX_end(ctx);
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return(1);
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err:
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bn_check_top(rm);
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BN_CTX_end(ctx);
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return(0);
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}
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/* BN_div_no_branch is a special version of BN_div. It does not contain
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* branches that may leak sensitive information.
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*/
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static int BN_div_no_branch(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num,
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const BIGNUM *divisor, BN_CTX *ctx)
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{
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int norm_shift,i,loop;
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BIGNUM *tmp,wnum,*snum,*sdiv,*res;
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BN_ULONG *resp,*wnump;
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BN_ULONG d0,d1;
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int num_n,div_n;
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bn_check_top(dv);
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bn_check_top(rm);
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/* bn_check_top(num); */ /* 'num' has been checked in BN_div() */
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bn_check_top(divisor);
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if (BN_is_zero(divisor))
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{
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BNerr(BN_F_BN_DIV_NO_BRANCH,BN_R_DIV_BY_ZERO);
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return(0);
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}
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BN_CTX_start(ctx);
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tmp=BN_CTX_get(ctx);
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snum=BN_CTX_get(ctx);
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sdiv=BN_CTX_get(ctx);
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if (dv == NULL)
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res=BN_CTX_get(ctx);
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else res=dv;
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if (sdiv == NULL || res == NULL) goto err;
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/* First we normalise the numbers */
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norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
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if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
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sdiv->neg=0;
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norm_shift+=BN_BITS2;
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if (!(BN_lshift(snum,num,norm_shift))) goto err;
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snum->neg=0;
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/* Since we don't know whether snum is larger than sdiv,
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* we pad snum with enough zeroes without changing its
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* value.
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*/
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if (snum->top <= sdiv->top+1)
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{
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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-1;
|
|
resp= &(res->d[loop-1]);
|
|
|
|
/* space for temp */
|
|
if (!bn_wexpand(tmp,(div_n+1))) goto err;
|
|
|
|
/* 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);
|
|
}
|
|
bn_correct_top(res);
|
|
BN_CTX_end(ctx);
|
|
return(1);
|
|
err:
|
|
bn_check_top(rm);
|
|
BN_CTX_end(ctx);
|
|
return(0);
|
|
}
|
|
|
|
#endif
|