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matty |
32 |
/* 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 "bn.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; |
| 94 |
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| 95 |
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nd=BN_num_bits(d); |
| 96 |
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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; |
| 99 |
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| 100 |
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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 :-) */ |
| 102 |
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BN_zero(dv); |
| 103 |
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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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} |
| 115 |
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/* CAN IMPROVE (and have now :=) */ |
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if (!BN_rshift1(D,D)) goto end; |
| 117 |
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} |
| 118 |
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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: |
| 122 |
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BN_CTX_end(ctx); |
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return(ret); |
| 124 |
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} |
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| 126 |
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#else |
| 127 |
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| 128 |
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#if !defined(NO_ASM) && !defined(NO_INLINE_ASM) && !defined(PEDANTIC) && !defined(BN_DIV3W) |
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# if defined(__GNUC__) && __GNUC__>=2 |
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matthewc |
195 |
# if defined(__i386) || defined (__i386__) |
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matty |
32 |
/* |
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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...); |
| 136 |
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* - divl doesn't only calculate quotient, but also leaves |
| 137 |
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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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*/ |
| 141 |
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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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# endif /* __<cpu> */ |
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# endif /* __GNUC__ */ |
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#endif /* NO_ASM */ |
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| 154 |
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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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{ |
| 157 |
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int norm_shift,i,j,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(num); |
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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); |
| 178 |
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} |
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| 180 |
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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); |
| 184 |
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if (dv == NULL) |
| 185 |
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res=BN_CTX_get(ctx); |
| 186 |
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else res=dv; |
| 187 |
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if (sdiv==NULL || res == NULL) goto err; |
| 188 |
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tmp->neg=0; |
| 189 |
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| 190 |
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/* First we normalise the numbers */ |
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norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2); |
| 192 |
matthewc |
195 |
if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err; |
| 193 |
matty |
32 |
sdiv->neg=0; |
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norm_shift+=BN_BITS2; |
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matthewc |
195 |
if (!(BN_lshift(snum,num,norm_shift))) goto err; |
| 196 |
matty |
32 |
snum->neg=0; |
| 197 |
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div_n=sdiv->top; |
| 198 |
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num_n=snum->top; |
| 199 |
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loop=num_n-div_n; |
| 200 |
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| 201 |
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/* Lets setup a 'window' into snum |
| 202 |
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* This is the part that corresponds to the current |
| 203 |
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* 'area' being divided */ |
| 204 |
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BN_init(&wnum); |
| 205 |
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wnum.d= &(snum->d[loop]); |
| 206 |
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wnum.top= div_n; |
| 207 |
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wnum.dmax= snum->dmax+1; /* a bit of a lie */ |
| 208 |
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| 209 |
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/* Get the top 2 words of sdiv */ |
| 210 |
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/* i=sdiv->top; */ |
| 211 |
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d0=sdiv->d[div_n-1]; |
| 212 |
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d1=(div_n == 1)?0:sdiv->d[div_n-2]; |
| 213 |
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| 214 |
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/* pointer to the 'top' of snum */ |
| 215 |
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wnump= &(snum->d[num_n-1]); |
| 216 |
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| 217 |
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/* Setup to 'res' */ |
| 218 |
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res->neg= (num->neg^divisor->neg); |
| 219 |
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if (!bn_wexpand(res,(loop+1))) goto err; |
| 220 |
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res->top=loop; |
| 221 |
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resp= &(res->d[loop-1]); |
| 222 |
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| 223 |
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/* space for temp */ |
| 224 |
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if (!bn_wexpand(tmp,(div_n+1))) goto err; |
| 225 |
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| 226 |
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if (BN_ucmp(&wnum,sdiv) >= 0) |
| 227 |
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{ |
| 228 |
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if (!BN_usub(&wnum,&wnum,sdiv)) goto err; |
| 229 |
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*resp=1; |
| 230 |
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res->d[res->top-1]=1; |
| 231 |
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} |
| 232 |
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else |
| 233 |
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res->top--; |
| 234 |
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resp--; |
| 235 |
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| 236 |
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for (i=0; i<loop-1; i++) |
| 237 |
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{ |
| 238 |
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BN_ULONG q,l0; |
| 239 |
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#if defined(BN_DIV3W) && !defined(NO_ASM) |
| 240 |
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BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG); |
| 241 |
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q=bn_div_3_words(wnump,d1,d0); |
| 242 |
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#else |
| 243 |
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BN_ULONG n0,n1,rem=0; |
| 244 |
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| 245 |
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n0=wnump[0]; |
| 246 |
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n1=wnump[-1]; |
| 247 |
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if (n0 == d0) |
| 248 |
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q=BN_MASK2; |
| 249 |
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else /* n0 < d0 */ |
| 250 |
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{ |
| 251 |
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#ifdef BN_LLONG |
| 252 |
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BN_ULLONG t2; |
| 253 |
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| 254 |
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#if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words) |
| 255 |
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q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0); |
| 256 |
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#else |
| 257 |
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q=bn_div_words(n0,n1,d0); |
| 258 |
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#endif |
| 259 |
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| 260 |
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#ifndef REMAINDER_IS_ALREADY_CALCULATED |
| 261 |
|
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/* |
| 262 |
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* rem doesn't have to be BN_ULLONG. The least we |
| 263 |
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* know it's less that d0, isn't it? |
| 264 |
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*/ |
| 265 |
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rem=(n1-q*d0)&BN_MASK2; |
| 266 |
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#endif |
| 267 |
|
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t2=(BN_ULLONG)d1*q; |
| 268 |
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|
| 269 |
|
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for (;;) |
| 270 |
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{ |
| 271 |
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if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2])) |
| 272 |
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break; |
| 273 |
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q--; |
| 274 |
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rem += d0; |
| 275 |
|
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if (rem < d0) break; /* don't let rem overflow */ |
| 276 |
|
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t2 -= d1; |
| 277 |
|
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} |
| 278 |
|
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#else /* !BN_LLONG */ |
| 279 |
|
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BN_ULONG t2l,t2h,ql,qh; |
| 280 |
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|
| 281 |
|
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q=bn_div_words(n0,n1,d0); |
| 282 |
|
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#ifndef REMAINDER_IS_ALREADY_CALCULATED |
| 283 |
|
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rem=(n1-q*d0)&BN_MASK2; |
| 284 |
|
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#endif |
| 285 |
|
|
|
| 286 |
|
|
#ifdef BN_UMULT_HIGH |
| 287 |
|
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t2l = d1 * q; |
| 288 |
|
|
t2h = BN_UMULT_HIGH(d1,q); |
| 289 |
|
|
#else |
| 290 |
|
|
t2l=LBITS(d1); t2h=HBITS(d1); |
| 291 |
|
|
ql =LBITS(q); qh =HBITS(q); |
| 292 |
|
|
mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */ |
| 293 |
|
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#endif |
| 294 |
|
|
|
| 295 |
|
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for (;;) |
| 296 |
|
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{ |
| 297 |
|
|
if ((t2h < rem) || |
| 298 |
|
|
((t2h == rem) && (t2l <= wnump[-2]))) |
| 299 |
|
|
break; |
| 300 |
|
|
q--; |
| 301 |
|
|
rem += d0; |
| 302 |
|
|
if (rem < d0) break; /* don't let rem overflow */ |
| 303 |
|
|
if (t2l < d1) t2h--; t2l -= d1; |
| 304 |
|
|
} |
| 305 |
|
|
#endif /* !BN_LLONG */ |
| 306 |
|
|
} |
| 307 |
|
|
#endif /* !BN_DIV3W */ |
| 308 |
|
|
|
| 309 |
|
|
l0=bn_mul_words(tmp->d,sdiv->d,div_n,q); |
| 310 |
|
|
wnum.d--; wnum.top++; |
| 311 |
|
|
tmp->d[div_n]=l0; |
| 312 |
|
|
for (j=div_n+1; j>0; j--) |
| 313 |
|
|
if (tmp->d[j-1]) break; |
| 314 |
|
|
tmp->top=j; |
| 315 |
|
|
|
| 316 |
|
|
j=wnum.top; |
| 317 |
matthewc |
195 |
if (!BN_sub(&wnum,&wnum,tmp)) goto err; |
| 318 |
matty |
32 |
|
| 319 |
|
|
snum->top=snum->top+wnum.top-j; |
| 320 |
|
|
|
| 321 |
|
|
if (wnum.neg) |
| 322 |
|
|
{ |
| 323 |
|
|
q--; |
| 324 |
|
|
j=wnum.top; |
| 325 |
matthewc |
195 |
if (!BN_add(&wnum,&wnum,sdiv)) goto err; |
| 326 |
matty |
32 |
snum->top+=wnum.top-j; |
| 327 |
|
|
} |
| 328 |
|
|
*(resp--)=q; |
| 329 |
|
|
wnump--; |
| 330 |
|
|
} |
| 331 |
|
|
if (rm != NULL) |
| 332 |
|
|
{ |
| 333 |
|
|
BN_rshift(rm,snum,norm_shift); |
| 334 |
|
|
rm->neg=num->neg; |
| 335 |
|
|
} |
| 336 |
|
|
BN_CTX_end(ctx); |
| 337 |
|
|
return(1); |
| 338 |
|
|
err: |
| 339 |
|
|
BN_CTX_end(ctx); |
| 340 |
|
|
return(0); |
| 341 |
|
|
} |
| 342 |
|
|
|
| 343 |
|
|
#endif |
| 344 |
|
|
|
| 345 |
|
|
/* rem != m */ |
| 346 |
|
|
int BN_mod(BIGNUM *rem, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx) |
| 347 |
|
|
{ |
| 348 |
|
|
#if 0 /* The old slow way */ |
| 349 |
|
|
int i,nm,nd; |
| 350 |
|
|
BIGNUM *dv; |
| 351 |
|
|
|
| 352 |
|
|
if (BN_ucmp(m,d) < 0) |
| 353 |
|
|
return((BN_copy(rem,m) == NULL)?0:1); |
| 354 |
|
|
|
| 355 |
|
|
BN_CTX_start(ctx); |
| 356 |
|
|
dv=BN_CTX_get(ctx); |
| 357 |
|
|
|
| 358 |
|
|
if (!BN_copy(rem,m)) goto err; |
| 359 |
|
|
|
| 360 |
|
|
nm=BN_num_bits(rem); |
| 361 |
|
|
nd=BN_num_bits(d); |
| 362 |
|
|
if (!BN_lshift(dv,d,nm-nd)) goto err; |
| 363 |
|
|
for (i=nm-nd; i>=0; i--) |
| 364 |
|
|
{ |
| 365 |
|
|
if (BN_cmp(rem,dv) >= 0) |
| 366 |
|
|
{ |
| 367 |
|
|
if (!BN_sub(rem,rem,dv)) goto err; |
| 368 |
|
|
} |
| 369 |
|
|
if (!BN_rshift1(dv,dv)) goto err; |
| 370 |
|
|
} |
| 371 |
|
|
BN_CTX_end(ctx); |
| 372 |
|
|
return(1); |
| 373 |
|
|
err: |
| 374 |
|
|
BN_CTX_end(ctx); |
| 375 |
|
|
return(0); |
| 376 |
|
|
#else |
| 377 |
|
|
return(BN_div(NULL,rem,m,d,ctx)); |
| 378 |
|
|
#endif |
| 379 |
|
|
} |
| 380 |
|
|
|
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