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1/* crypto/bn/bn_div.c */
2/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
3 * All rights reserved.
4 *
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.
8 *
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).
15 *
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.
22 *
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
25 * are met:
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)"
40 *
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
51 * SUCH DAMAGE.
52 *
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.]
57 */
58
59#include <stdio.h>
60#include <openssl/bn.h>
61#include "cryptlib.h"
62#include "bn_lcl.h"
63
64/* The old slow way */
65#if 0
66int BN_div(BIGNUM *dv, BIGNUM *rem, BIGNUM *m, BIGNUM *d, BN_CTX *ctx)
67 {
68 int i,nm,nd;
69 BIGNUM *D;
70
71 bn_check_top(m);
72 bn_check_top(d);
73 if (BN_is_zero(d))
74 {
75 BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
76 return(0);
77 }
78
79 if (BN_ucmp(m,d) < 0)
80 {
81 if (rem != NULL)
82 { if (BN_copy(rem,m) == NULL) return(0); }
83 if (dv != NULL) BN_zero(dv);
84 return(1);
85 }
86
87 D= &(ctx->bn[ctx->tos]);
88 if (dv == NULL) dv= &(ctx->bn[ctx->tos+1]);
89 if (rem == NULL) rem= &(ctx->bn[ctx->tos+2]);
90
91 nd=BN_num_bits(d);
92 nm=BN_num_bits(m);
93 if (BN_copy(D,d) == NULL) return(0);
94 if (BN_copy(rem,m) == NULL) return(0);
95
96 /* The next 2 are needed so we can do a dv->d[0]|=1 later
97 * since BN_lshift1 will only work once there is a value :-) */
98 BN_zero(dv);
99 bn_wexpand(dv,1);
100 dv->top=1;
101
102 if (!BN_lshift(D,D,nm-nd)) return(0);
103 for (i=nm-nd; i>=0; i--)
104 {
105 if (!BN_lshift1(dv,dv)) return(0);
106 if (BN_ucmp(rem,D) >= 0)
107 {
108 dv->d[0]|=1;
109 if (!BN_usub(rem,rem,D)) return(0);
110 }
111/* CAN IMPROVE (and have now :=) */
112 if (!BN_rshift1(D,D)) return(0);
113 }
114 rem->neg=BN_is_zero(rem)?0:m->neg;
115 dv->neg=m->neg^d->neg;
116 return(1);
117 }
118
119#else
120
121int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
122 BN_CTX *ctx)
123 {
124 int norm_shift,i,j,loop;
125 BIGNUM *tmp,wnum,*snum,*sdiv,*res;
126 BN_ULONG *resp,*wnump;
127 BN_ULONG d0,d1;
128 int num_n,div_n;
129
130 bn_check_top(num);
131 bn_check_top(divisor);
132
133 if (BN_is_zero(divisor))
134 {
135 BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
136 return(0);
137 }
138
139 if (BN_ucmp(num,divisor) < 0)
140 {
141 if (rm != NULL)
142 { if (BN_copy(rm,num) == NULL) return(0); }
143 if (dv != NULL) BN_zero(dv);
144 return(1);
145 }
146
147 tmp= &(ctx->bn[ctx->tos]);
148 tmp->neg=0;
149 snum= &(ctx->bn[ctx->tos+1]);
150 sdiv= &(ctx->bn[ctx->tos+2]);
151 if (dv == NULL)
152 res= &(ctx->bn[ctx->tos+3]);
153 else res=dv;
154
155 /* First we normalise the numbers */
156 norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
157 BN_lshift(sdiv,divisor,norm_shift);
158 sdiv->neg=0;
159 norm_shift+=BN_BITS2;
160 BN_lshift(snum,num,norm_shift);
161 snum->neg=0;
162 div_n=sdiv->top;
163 num_n=snum->top;
164 loop=num_n-div_n;
165
166 /* Lets setup a 'window' into snum
167 * This is the part that corresponds to the current
168 * 'area' being divided */
169 BN_init(&wnum);
170 wnum.d= &(snum->d[loop]);
171 wnum.top= div_n;
172 wnum.max= snum->max+1; /* a bit of a lie */
173
174 /* Get the top 2 words of sdiv */
175 /* i=sdiv->top; */
176 d0=sdiv->d[div_n-1];
177 d1=(div_n == 1)?0:sdiv->d[div_n-2];
178
179 /* pointer to the 'top' of snum */
180 wnump= &(snum->d[num_n-1]);
181
182 /* Setup to 'res' */
183 res->neg= (num->neg^divisor->neg);
184 if (!bn_wexpand(res,(loop+1))) goto err;
185 res->top=loop;
186 resp= &(res->d[loop-1]);
187
188 /* space for temp */
189 if (!bn_wexpand(tmp,(div_n+1))) goto err;
190
191 if (BN_ucmp(&wnum,sdiv) >= 0)
192 {
193 if (!BN_usub(&wnum,&wnum,sdiv)) goto err;
194 *resp=1;
195 res->d[res->top-1]=1;
196 }
197 else
198 res->top--;
199 resp--;
200
201 for (i=0; i<loop-1; i++)
202 {
203 BN_ULONG q,l0;
204#ifdef BN_DIV3W
205 q=bn_div_3_words(wnump,d0,d1);
206#else
207
208#if !defined(NO_ASM) && !defined(PEDANTIC)
209# if defined(__GNUC__) && __GNUC__>=2
210# if defined(__i386)
211 /*
212 * There were two reasons for implementing this template:
213 * - GNU C generates a call to a function (__udivdi3 to be exact)
214 * in reply to ((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0 (I fail to
215 * understand why...);
216 * - divl doesn't only calculate quotient, but also leaves
217 * remainder in %edx which we can definitely use here:-)
218 *
219 * <appro@fy.chalmers.se>
220 */
221# define bn_div_words(n0,n1,d0) \
222 ({ asm volatile ( \
223 "divl %4" \
224 : "=a"(q), "=d"(rem) \
225 : "a"(n1), "d"(n0), "g"(d0) \
226 : "cc"); \
227 q; \
228 })
229# define REMINDER_IS_ALREADY_CALCULATED
230# endif /* __<cpu> */
231# endif /* __GNUC__ */
232#endif /* NO_ASM */
233 BN_ULONG n0,n1,rem=0;
234
235 n0=wnump[0];
236 n1=wnump[-1];
237 if (n0 == d0)
238 q=BN_MASK2;
239 else
240#if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
241 q=((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0;
242#else
243 q=bn_div_words(n0,n1,d0);
244#endif
245 {
246#ifdef BN_LLONG
247 BN_ULLONG t2;
248
249#ifndef REMINDER_IS_ALREADY_CALCULATED
250 /*
251 * rem doesn't have to be BN_ULLONG. The least we
252 * know it's less that d0, isn't it?
253 */
254 rem=(n1-q*d0)&BN_MASK2;
255#endif
256 t2=(BN_ULLONG)d1*q;
257
258 for (;;)
259 {
260 if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
261 break;
262 q--;
263 rem += d0;
264 if (rem < d0) break; /* don't let rem overflow */
265 t2 -= d1;
266 }
267#else
268 BN_ULONG t2l,t2h,ql,qh;
269
270#ifndef REMINDER_IS_ALREADY_CALCULATED
271 /*
272 * It's more than enough with the only multiplication.
273 * See the comment above in BN_LLONG section...
274 */
275 rem=(n1-q*d0)&BN_MASK2;
276#endif
277 t2l=LBITS(d1); t2h=HBITS(d1);
278 ql =LBITS(q); qh =HBITS(q);
279 mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
280
281 for (;;)
282 {
283 if ((t2h < rem) ||
284 ((t2h == rem) && (t2l <= wnump[-2])))
285 break;
286 q--;
287 rem += d0;
288 if (rem < d0) break; /* don't let rem overflow */
289 if (t2l < d1) t2h--; t2l -= d1;
290 }
291#endif
292 }
293#endif /* !BN_DIV3W */
294 wnum.d--; wnum.top++;
295 l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
296 tmp->d[div_n]=l0;
297 for (j=div_n+1; j>0; j--)
298 if (tmp->d[j-1]) break;
299 tmp->top=j;
300
301 j=wnum.top;
302 BN_sub(&wnum,&wnum,tmp);
303
304 snum->top=snum->top+wnum.top-j;
305
306 if (wnum.neg)
307 {
308 q--;
309 j=wnum.top;
310 BN_add(&wnum,&wnum,sdiv);
311 snum->top+=wnum.top-j;
312 }
313 *(resp--)=q;
314 wnump--;
315 }
316 if (rm != NULL)
317 {
318 BN_rshift(rm,snum,norm_shift);
319 rm->neg=num->neg;
320 }
321 return(1);
322err:
323 return(0);
324 }
325
326#endif
327
328/* rem != m */
329int BN_mod(BIGNUM *rem, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx)
330 {
331#if 0 /* The old slow way */
332 int i,nm,nd;
333 BIGNUM *dv;
334
335 if (BN_ucmp(m,d) < 0)
336 return((BN_copy(rem,m) == NULL)?0:1);
337
338 dv= &(ctx->bn[ctx->tos]);
339
340 if (!BN_copy(rem,m)) return(0);
341
342 nm=BN_num_bits(rem);
343 nd=BN_num_bits(d);
344 if (!BN_lshift(dv,d,nm-nd)) return(0);
345 for (i=nm-nd; i>=0; i--)
346 {
347 if (BN_cmp(rem,dv) >= 0)
348 {
349 if (!BN_sub(rem,rem,dv)) return(0);
350 }
351 if (!BN_rshift1(dv,dv)) return(0);
352 }
353 return(1);
354#else
355 return(BN_div(NULL,rem,m,d,ctx));
356#endif
357 }
358