1 /* crypto/bn/bn_div.c */
2 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
5 * This package is an SSL implementation written
6 * by Eric Young (eay@cryptsoft.com).
7 * The implementation was written so as to conform with Netscapes SSL.
9 * This library is free for commercial and non-commercial use as long as
10 * the following conditions are aheared to. The following conditions
11 * apply to all code found in this distribution, be it the RC4, RSA,
12 * lhash, DES, etc., code; not just the SSL code. The SSL documentation
13 * included with this distribution is covered by the same copyright terms
14 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
16 * Copyright remains Eric Young's, and as such any Copyright notices in
17 * the code are not to be removed.
18 * If this package is used in a product, Eric Young should be given attribution
19 * as the author of the parts of the library used.
20 * This can be in the form of a textual message at program startup or
21 * in documentation (online or textual) provided with the package.
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
26 * 1. Redistributions of source code must retain the copyright
27 * notice, this list of conditions and the following disclaimer.
28 * 2. Redistributions in binary form must reproduce the above copyright
29 * notice, this list of conditions and the following disclaimer in the
30 * documentation and/or other materials provided with the distribution.
31 * 3. All advertising materials mentioning features or use of this software
32 * must display the following acknowledgement:
33 * "This product includes cryptographic software written by
34 * Eric Young (eay@cryptsoft.com)"
35 * The word 'cryptographic' can be left out if the rouines from the library
36 * being used are not cryptographic related :-).
37 * 4. If you include any Windows specific code (or a derivative thereof) from
38 * the apps directory (application code) you must include an acknowledgement:
39 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
41 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
42 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
43 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
44 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
45 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
46 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
47 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
48 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
49 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
50 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
53 * The licence and distribution terms for any publically available version or
54 * derivative of this code cannot be changed. i.e. this code cannot simply be
55 * copied and put under another distribution licence
56 * [including the GNU Public Licence.]
60 #include <openssl/bn.h>
64 /* The old slow way */
66 int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
76 BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
83 { if (BN_copy(rem,m) == NULL) return(0); }
84 if (dv != NULL) BN_zero(dv);
88 D= &(ctx->bn[ctx->tos]);
89 if (dv == NULL) dv= &(ctx->bn[ctx->tos+1]);
90 if (rem == NULL) rem= &(ctx->bn[ctx->tos+2]);
94 if (BN_copy(D,d) == NULL) return(0);
95 if (BN_copy(rem,m) == NULL) return(0);
97 /* The next 2 are needed so we can do a dv->d[0]|=1 later
98 * since BN_lshift1 will only work once there is a value :-) */
103 if (!BN_lshift(D,D,nm-nd)) return(0);
104 for (i=nm-nd; i>=0; i--)
106 if (!BN_lshift1(dv,dv)) return(0);
107 if (BN_ucmp(rem,D) >= 0)
110 if (!BN_usub(rem,rem,D)) return(0);
112 /* CAN IMPROVE (and have now :=) */
113 if (!BN_rshift1(D,D)) return(0);
115 rem->neg=BN_is_zero(rem)?0:m->neg;
116 dv->neg=m->neg^d->neg;
122 int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
125 int norm_shift,i,j,loop;
126 BIGNUM *tmp,wnum,*snum,*sdiv,*res;
127 BN_ULONG *resp,*wnump;
132 bn_check_top(divisor);
134 if (BN_is_zero(divisor))
136 BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
140 if (BN_ucmp(num,divisor) < 0)
143 { if (BN_copy(rm,num) == NULL) return(0); }
144 if (dv != NULL) BN_zero(dv);
148 tmp= &(ctx->bn[ctx->tos]);
150 snum= &(ctx->bn[ctx->tos+1]);
151 sdiv= &(ctx->bn[ctx->tos+2]);
153 res= &(ctx->bn[ctx->tos+3]);
156 /* First we normalise the numbers */
157 norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
158 BN_lshift(sdiv,divisor,norm_shift);
160 norm_shift+=BN_BITS2;
161 BN_lshift(snum,num,norm_shift);
167 /* Lets setup a 'window' into snum
168 * This is the part that corresponds to the current
169 * 'area' being divided */
171 wnum.d= &(snum->d[loop]);
173 wnum.max= snum->max+1; /* a bit of a lie */
175 /* Get the top 2 words of sdiv */
178 d1=(div_n == 1)?0:sdiv->d[div_n-2];
180 /* pointer to the 'top' of snum */
181 wnump= &(snum->d[num_n-1]);
184 res->neg= (num->neg^divisor->neg);
185 if (!bn_wexpand(res,(loop+1))) goto err;
187 resp= &(res->d[loop-1]);
190 if (!bn_wexpand(tmp,(div_n+1))) goto err;
192 if (BN_ucmp(&wnum,sdiv) >= 0)
194 if (!BN_usub(&wnum,&wnum,sdiv)) goto err;
196 res->d[res->top-1]=1;
202 for (i=0; i<loop-1; i++)
206 q=bn_div_3_words(wnump,d1,d0);
209 #if !defined(NO_ASM) && !defined(PEDANTIC)
210 # if defined(__GNUC__) && __GNUC__>=2
213 * There were two reasons for implementing this template:
214 * - GNU C generates a call to a function (__udivdi3 to be exact)
215 * in reply to ((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0 (I fail to
216 * understand why...);
217 * - divl doesn't only calculate quotient, but also leaves
218 * remainder in %edx which we can definitely use here:-)
220 * <appro@fy.chalmers.se>
222 # define bn_div_words(n0,n1,d0) \
225 : "=a"(q), "=d"(rem) \
226 : "a"(n1), "d"(n0), "g"(d0) \
230 # define REMAINDER_IS_ALREADY_CALCULATED
231 # endif /* __<cpu> */
232 # endif /* __GNUC__ */
234 BN_ULONG n0,n1,rem=0;
241 #ifdef REMAINDER_IS_ALREADY_CALCULATED /* in this case it isn't */
242 rem=(n1-q*d0)&BN_MASK2;
246 #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
247 q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
249 q=bn_div_words(n0,n1,d0);
255 #ifndef REMAINDER_IS_ALREADY_CALCULATED
257 * rem doesn't have to be BN_ULLONG. The least we
258 * know it's less that d0, isn't it?
260 rem=(n1-q*d0)&BN_MASK2;
266 if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
270 if (rem < d0) break; /* don't let rem overflow */
274 BN_ULONG t2l,t2h,ql,qh;
276 #ifndef REMAINDER_IS_ALREADY_CALCULATED
278 * It's more than enough with the only multiplication.
279 * See the comment above in BN_LLONG section...
281 rem=(n1-q*d0)&BN_MASK2;
283 t2l=LBITS(d1); t2h=HBITS(d1);
284 ql =LBITS(q); qh =HBITS(q);
285 mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
290 ((t2h == rem) && (t2l <= wnump[-2])))
294 if (rem < d0) break; /* don't let rem overflow */
295 if (t2l < d1) t2h--; t2l -= d1;
299 #endif /* !BN_DIV3W */
300 l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
301 wnum.d--; wnum.top++;
303 for (j=div_n+1; j>0; j--)
304 if (tmp->d[j-1]) break;
308 BN_sub(&wnum,&wnum,tmp);
310 snum->top=snum->top+wnum.top-j;
316 BN_add(&wnum,&wnum,sdiv);
317 snum->top+=wnum.top-j;
324 BN_rshift(rm,snum,norm_shift);
335 int BN_mod(BIGNUM *rem, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx)
337 #if 0 /* The old slow way */
341 if (BN_ucmp(m,d) < 0)
342 return((BN_copy(rem,m) == NULL)?0:1);
344 dv= &(ctx->bn[ctx->tos]);
346 if (!BN_copy(rem,m)) return(0);
350 if (!BN_lshift(dv,d,nm-nd)) return(0);
351 for (i=nm-nd; i>=0; i--)
353 if (BN_cmp(rem,dv) >= 0)
355 if (!BN_sub(rem,rem,dv)) return(0);
357 if (!BN_rshift1(dv,dv)) return(0);
361 return(BN_div(NULL,rem,m,d,ctx));