bn_div.c revision 68651
1155852Sgallatin/* crypto/bn/bn_div.c */ 2155852Sgallatin/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com) 3247795Sgallatin * All rights reserved. 4155852Sgallatin * 5155852Sgallatin * This package is an SSL implementation written 6155852Sgallatin * by Eric Young (eay@cryptsoft.com). 7155852Sgallatin * The implementation was written so as to conform with Netscapes SSL. 8155852Sgallatin * 9155852Sgallatin * This library is free for commercial and non-commercial use as long as 10155852Sgallatin * the following conditions are aheared to. The following conditions 11155852Sgallatin * apply to all code found in this distribution, be it the RC4, RSA, 12171405Sgallatin * lhash, DES, etc., code; not just the SSL code. The SSL documentation 13155852Sgallatin * included with this distribution is covered by the same copyright terms 14155852Sgallatin * except that the holder is Tim Hudson (tjh@cryptsoft.com). 15155852Sgallatin * 16155852Sgallatin * Copyright remains Eric Young's, and as such any Copyright notices in 17155852Sgallatin * the code are not to be removed. 18155852Sgallatin * If this package is used in a product, Eric Young should be given attribution 19155852Sgallatin * as the author of the parts of the library used. 20155852Sgallatin * This can be in the form of a textual message at program startup or 21155852Sgallatin * in documentation (online or textual) provided with the package. 22155852Sgallatin * 23155852Sgallatin * Redistribution and use in source and binary forms, with or without 24155852Sgallatin * modification, are permitted provided that the following conditions 25155852Sgallatin * are met: 26155852Sgallatin * 1. Redistributions of source code must retain the copyright 27155852Sgallatin * notice, this list of conditions and the following disclaimer. 28155852Sgallatin * 2. Redistributions in binary form must reproduce the above copyright 29155852Sgallatin * notice, this list of conditions and the following disclaimer in the 30155852Sgallatin * documentation and/or other materials provided with the distribution. 31155852Sgallatin * 3. All advertising materials mentioning features or use of this software 32159571Sgallatin * must display the following acknowledgement: 33159571Sgallatin * "This product includes cryptographic software written by 34159571Sgallatin * Eric Young (eay@cryptsoft.com)" 35159571Sgallatin * The word 'cryptographic' can be left out if the rouines from the library 36159571Sgallatin * being used are not cryptographic related :-). 37155852Sgallatin * 4. If you include any Windows specific code (or a derivative thereof) from 38159571Sgallatin * the apps directory (application code) you must include an acknowledgement: 39159571Sgallatin * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)" 40169871Sgallatin * 41155852Sgallatin * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND 42181964Sgallatin * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 43181964Sgallatin * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 44175579Sgallatin * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 45175579Sgallatin * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 46175579Sgallatin * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 47175579Sgallatin * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 48175579Sgallatin * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 49193311Sgallatin * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 50193311Sgallatin * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 51193311Sgallatin * SUCH DAMAGE. 52193311Sgallatin * 53176261Sgallatin * The licence and distribution terms for any publically available version or 54176261Sgallatin * derivative of this code cannot be changed. i.e. this code cannot simply be 55176261Sgallatin * copied and put under another distribution licence 56176261Sgallatin * [including the GNU Public Licence.] 57176261Sgallatin */ 58176261Sgallatin 59176261Sgallatin#include <stdio.h> 60176261Sgallatin#include <openssl/bn.h> 61176261Sgallatin#include "cryptlib.h" 62176261Sgallatin#include "bn_lcl.h" 63176261Sgallatin 64176261Sgallatin/* The old slow way */ 65176261Sgallatin#if 0 66176261Sgallatinint BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d, 67176261Sgallatin BN_CTX *ctx) 68176261Sgallatin { 69176261Sgallatin int i,nm,nd; 70176261Sgallatin int ret = 0; 71176261Sgallatin BIGNUM *D; 72176261Sgallatin 73176261Sgallatin bn_check_top(m); 74176261Sgallatin bn_check_top(d); 75176261Sgallatin if (BN_is_zero(d)) 76247320Sgallatin { 77247320Sgallatin BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO); 78247320Sgallatin return(0); 79247320Sgallatin } 80247320Sgallatin 81247320Sgallatin if (BN_ucmp(m,d) < 0) 82247320Sgallatin { 83247320Sgallatin if (rem != NULL) 84247320Sgallatin { if (BN_copy(rem,m) == NULL) return(0); } 85247320Sgallatin if (dv != NULL) BN_zero(dv); 86247320Sgallatin return(1); 87247320Sgallatin } 88176261Sgallatin 89176261Sgallatin BN_CTX_start(ctx); 90176261Sgallatin D = BN_CTX_get(ctx); 91176261Sgallatin if (dv == NULL) dv = BN_CTX_get(ctx); 92247320Sgallatin if (rem == NULL) rem = BN_CTX_get(ctx); 93247320Sgallatin if (D == NULL || dv == NULL || rem == NULL) 94247320Sgallatin goto end; 95176261Sgallatin 96247320Sgallatin nd=BN_num_bits(d); 97247320Sgallatin nm=BN_num_bits(m); 98247320Sgallatin if (BN_copy(D,d) == NULL) goto end; 99247320Sgallatin if (BN_copy(rem,m) == NULL) goto end; 100247320Sgallatin 101247320Sgallatin /* The next 2 are needed so we can do a dv->d[0]|=1 later 102247320Sgallatin * since BN_lshift1 will only work once there is a value :-) */ 103247320Sgallatin BN_zero(dv); 104155852Sgallatin bn_wexpand(dv,1); 105155852Sgallatin dv->top=1; 106155852Sgallatin 107155852Sgallatin if (!BN_lshift(D,D,nm-nd)) goto end; 108155852Sgallatin for (i=nm-nd; i>=0; i--) 109159571Sgallatin { 110155852Sgallatin if (!BN_lshift1(dv,dv)) goto end; 111155852Sgallatin if (BN_ucmp(rem,D) >= 0) 112159612Sgallatin { 113159612Sgallatin dv->d[0]|=1; 114159612Sgallatin if (!BN_usub(rem,rem,D)) goto end; 115159612Sgallatin } 116159612Sgallatin/* CAN IMPROVE (and have now :=) */ 117169871Sgallatin if (!BN_rshift1(D,D)) goto end; 118159612Sgallatin } 119155852Sgallatin rem->neg=BN_is_zero(rem)?0:m->neg; 120155852Sgallatin dv->neg=m->neg^d->neg; 121155852Sgallatin ret = 1; 122155852Sgallatin end: 123155852Sgallatin BN_CTX_end(ctx); 124155852Sgallatin return(ret); 125159571Sgallatin } 126155852Sgallatin 127159612Sgallatin#else 128155852Sgallatin 129155852Sgallatin#if !defined(NO_ASM) && !defined(NO_INLINE_ASM) && !defined(PEDANTIC) && !defined(BN_DIV3W) 130155852Sgallatin# if defined(__GNUC__) && __GNUC__>=2 131155852Sgallatin# if defined(__i386) 132159612Sgallatin /* 133159612Sgallatin * There were two reasons for implementing this template: 134159612Sgallatin * - GNU C generates a call to a function (__udivdi3 to be exact) 135159612Sgallatin * in reply to ((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0 (I fail to 136159612Sgallatin * understand why...); 137159612Sgallatin * - divl doesn't only calculate quotient, but also leaves 138155852Sgallatin * remainder in %edx which we can definitely use here:-) 139155852Sgallatin * 140155852Sgallatin * <appro@fy.chalmers.se> 141155852Sgallatin */ 142159612Sgallatin# define bn_div_words(n0,n1,d0) \ 143155852Sgallatin ({ asm volatile ( \ 144155852Sgallatin "divl %4" \ 145155852Sgallatin : "=a"(q), "=d"(rem) \ 146169840Sgallatin : "a"(n1), "d"(n0), "g"(d0) \ 147169840Sgallatin : "cc"); \ 148155852Sgallatin q; \ 149155852Sgallatin }) 150193250Sgallatin# define REMAINDER_IS_ALREADY_CALCULATED 151175365Sgallatin# endif /* __<cpu> */ 152155852Sgallatin# endif /* __GNUC__ */ 153155852Sgallatin#endif /* NO_ASM */ 154155852Sgallatin 155175365Sgallatinint BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor, 156191567Sgallatin BN_CTX *ctx) 157191562Sgallatin { 158191562Sgallatin int norm_shift,i,j,loop; 159155852Sgallatin BIGNUM *tmp,wnum,*snum,*sdiv,*res; 160191562Sgallatin BN_ULONG *resp,*wnump; 161191562Sgallatin BN_ULONG d0,d1; 162155852Sgallatin int num_n,div_n; 163155852Sgallatin 164162322Sgallatin bn_check_top(num); 165159612Sgallatin bn_check_top(divisor); 166155852Sgallatin 167155852Sgallatin if (BN_is_zero(divisor)) 168155852Sgallatin { 169155852Sgallatin BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO); 170159612Sgallatin return(0); 171169871Sgallatin } 172191562Sgallatin 173191562Sgallatin if (BN_ucmp(num,divisor) < 0) 174191562Sgallatin { 175166345Sgallatin if (rm != NULL) 176166345Sgallatin { if (BN_copy(rm,num) == NULL) return(0); } 177166373Sgallatin if (dv != NULL) BN_zero(dv); 178166373Sgallatin return(1); 179171917Sgallatin } 180175365Sgallatin 181175365Sgallatin BN_CTX_start(ctx); 182175365Sgallatin tmp=BN_CTX_get(ctx); 183155852Sgallatin tmp->neg=0; 184175365Sgallatin snum=BN_CTX_get(ctx); 185175365Sgallatin sdiv=BN_CTX_get(ctx); 186175365Sgallatin if (dv == NULL) 187175365Sgallatin res=BN_CTX_get(ctx); 188175365Sgallatin else res=dv; 189175365Sgallatin if (res == NULL) goto err; 190175365Sgallatin 191175365Sgallatin /* First we normalise the numbers */ 192159612Sgallatin norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2); 193159612Sgallatin BN_lshift(sdiv,divisor,norm_shift); 194175365Sgallatin sdiv->neg=0; 195175365Sgallatin norm_shift+=BN_BITS2; 196191562Sgallatin BN_lshift(snum,num,norm_shift); 197194751Sgallatin snum->neg=0; 198194751Sgallatin div_n=sdiv->top; 199191562Sgallatin num_n=snum->top; 200191562Sgallatin loop=num_n-div_n; 201247472Sgallatin 202175365Sgallatin /* Lets setup a 'window' into snum 203175365Sgallatin * This is the part that corresponds to the current 204175365Sgallatin * 'area' being divided */ 205175365Sgallatin BN_init(&wnum); 206175365Sgallatin wnum.d= &(snum->d[loop]); 207175365Sgallatin wnum.top= div_n; 208175365Sgallatin wnum.dmax= snum->dmax+1; /* a bit of a lie */ 209175365Sgallatin 210175365Sgallatin /* Get the top 2 words of sdiv */ 211175365Sgallatin /* i=sdiv->top; */ 212169840Sgallatin d0=sdiv->d[div_n-1]; 213175365Sgallatin d1=(div_n == 1)?0:sdiv->d[div_n-2]; 214175365Sgallatin 215155852Sgallatin /* pointer to the 'top' of snum */ 216159612Sgallatin wnump= &(snum->d[num_n-1]); 217155852Sgallatin 218159571Sgallatin /* Setup to 'res' */ 219159571Sgallatin res->neg= (num->neg^divisor->neg); 220155852Sgallatin if (!bn_wexpand(res,(loop+1))) goto err; 221176281Sgallatin res->top=loop; 222155852Sgallatin resp= &(res->d[loop-1]); 223155852Sgallatin 224155852Sgallatin /* space for temp */ 225159612Sgallatin if (!bn_wexpand(tmp,(div_n+1))) goto err; 226155852Sgallatin 227166370Sgallatin if (BN_ucmp(&wnum,sdiv) >= 0) 228166370Sgallatin { 229155852Sgallatin if (!BN_usub(&wnum,&wnum,sdiv)) goto err; 230155852Sgallatin *resp=1; 231155852Sgallatin res->d[res->top-1]=1; 232155852Sgallatin } 233175365Sgallatin else 234155852Sgallatin res->top--; 235155852Sgallatin resp--; 236155852Sgallatin 237175365Sgallatin for (i=0; i<loop-1; i++) 238175365Sgallatin { 239175365Sgallatin BN_ULONG q,l0; 240155852Sgallatin#ifdef BN_DIV3W 241175365Sgallatin q=bn_div_3_words(wnump,d1,d0); 242155852Sgallatin#else 243159571Sgallatin BN_ULONG n0,n1,rem=0; 244155852Sgallatin 245166875Sgallatin n0=wnump[0]; 246166875Sgallatin n1=wnump[-1]; 247166875Sgallatin if (n0 == d0) 248166875Sgallatin q=BN_MASK2; 249155852Sgallatin else /* n0 < d0 */ 250155852Sgallatin { 251159612Sgallatin#ifdef BN_LLONG 252159612Sgallatin BN_ULLONG t2; 253159612Sgallatin 254162328Sgallatin#if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words) 255164513Sgallatin q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0); 256169840Sgallatin#else 257197391Sgallatin q=bn_div_words(n0,n1,d0); 258169871Sgallatin#endif 259171917Sgallatin 260171917Sgallatin#ifndef REMAINDER_IS_ALREADY_CALCULATED 261175365Sgallatin /* 262175365Sgallatin * rem doesn't have to be BN_ULLONG. The least we 263194909Sgallatin * know it's less that d0, isn't it? 264206662Sgallatin */ 265206662Sgallatin rem=(n1-q*d0)&BN_MASK2; 266247320Sgallatin#endif 267166370Sgallatin t2=(BN_ULLONG)d1*q; 268166373Sgallatin 269198250Sgallatin for (;;) 270198250Sgallatin { 271175365Sgallatin if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2])) 272175365Sgallatin break; 273159612Sgallatin q--; 274169871Sgallatin rem += d0; 275197645Sgallatin if (rem < d0) break; /* don't let rem overflow */ 276159612Sgallatin t2 -= d1; 277159612Sgallatin } 278166370Sgallatin#else /* !BN_LLONG */ 279166370Sgallatin BN_ULONG t2l,t2h,ql,qh; 280175365Sgallatin 281155852Sgallatin q=bn_div_words(n0,n1,d0); 282159571Sgallatin#ifndef REMAINDER_IS_ALREADY_CALCULATED 283159571Sgallatin rem=(n1-q*d0)&BN_MASK2; 284172162Sgallatin#endif 285188736Sgallatin 286188736Sgallatin#ifdef BN_UMULT_HIGH 287171917Sgallatin t2l = d1 * q; 288188736Sgallatin t2h = BN_UMULT_HIGH(d1,q); 289197391Sgallatin#else 290197391Sgallatin t2l=LBITS(d1); t2h=HBITS(d1); 291155852Sgallatin ql =LBITS(q); qh =HBITS(q); 292206662Sgallatin mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */ 293206662Sgallatin#endif 294206662Sgallatin 295206662Sgallatin for (;;) 296206662Sgallatin { 297206662Sgallatin if ((t2h < rem) || 298159571Sgallatin ((t2h == rem) && (t2l <= wnump[-2]))) 299155852Sgallatin break; 300159571Sgallatin q--; 301155852Sgallatin rem += d0; 302171917Sgallatin if (rem < d0) break; /* don't let rem overflow */ 303171917Sgallatin if (t2l < d1) t2h--; t2l -= d1; 304171917Sgallatin } 305171917Sgallatin#endif /* !BN_LLONG */ 306171917Sgallatin } 307171917Sgallatin#endif /* !BN_DIV3W */ 308155852Sgallatin 309247320Sgallatin l0=bn_mul_words(tmp->d,sdiv->d,div_n,q); 310247320Sgallatin wnum.d--; wnum.top++; 311247320Sgallatin tmp->d[div_n]=l0; 312247320Sgallatin for (j=div_n+1; j>0; j--) 313247320Sgallatin if (tmp->d[j-1]) break; 314247320Sgallatin tmp->top=j; 315247320Sgallatin 316247320Sgallatin j=wnum.top; 317247320Sgallatin BN_sub(&wnum,&wnum,tmp); 318155852Sgallatin 319155852Sgallatin snum->top=snum->top+wnum.top-j; 320155852Sgallatin 321185162Skmacy if (wnum.neg) 322185162Skmacy { 323155852Sgallatin q--; 324155852Sgallatin j=wnum.top; 325185255Sgallatin BN_add(&wnum,&wnum,sdiv); 326155852Sgallatin snum->top+=wnum.top-j; 327185255Sgallatin } 328155852Sgallatin *(resp--)=q; 329185255Sgallatin wnump--; 330155852Sgallatin } 331185255Sgallatin if (rm != NULL) 332155852Sgallatin { 333155852Sgallatin BN_rshift(rm,snum,norm_shift); 334155852Sgallatin rm->neg=num->neg; 335155852Sgallatin } 336155852Sgallatin BN_CTX_end(ctx); 337185162Skmacy return(1); 338185162Skmacyerr: 339155852Sgallatin BN_CTX_end(ctx); 340159571Sgallatin return(0); 341155852Sgallatin } 342155852Sgallatin 343155852Sgallatin#endif 344155852Sgallatin 345155852Sgallatin/* rem != m */ 346155852Sgallatinint BN_mod(BIGNUM *rem, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx) 347155852Sgallatin { 348155852Sgallatin#if 0 /* The old slow way */ 349155852Sgallatin int i,nm,nd; 350155852Sgallatin BIGNUM *dv; 351155852Sgallatin 352155852Sgallatin if (BN_ucmp(m,d) < 0) 353155852Sgallatin return((BN_copy(rem,m) == NULL)?0:1); 354155852Sgallatin 355155852Sgallatin BN_CTX_start(ctx); 356175365Sgallatin dv=BN_CTX_get(ctx); 357175365Sgallatin 358175365Sgallatin if (!BN_copy(rem,m)) goto err; 359169840Sgallatin 360155852Sgallatin nm=BN_num_bits(rem); 361169840Sgallatin nd=BN_num_bits(d); 362155852Sgallatin if (!BN_lshift(dv,d,nm-nd)) goto err; 363155852Sgallatin for (i=nm-nd; i>=0; i--) 364155852Sgallatin { 365155852Sgallatin if (BN_cmp(rem,dv) >= 0) 366155852Sgallatin { 367155852Sgallatin if (!BN_sub(rem,rem,dv)) goto err; 368155852Sgallatin } 369155852Sgallatin 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 } 380 381