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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, const BIGNUM *m, const BIGNUM *d,
67 BN_CTX *ctx)
68 {
69 int i,nm,nd;
70 int ret = 0;
71 BIGNUM *D;
72
73 bn_check_top(m);
74 bn_check_top(d);
75 if (BN_is_zero(d))
76 {
77 BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
78 return(0);
79 }
80
81 if (BN_ucmp(m,d) < 0)
82 {
83 if (rem != NULL)
84 { if (BN_copy(rem,m) == NULL) return(0); }
85 if (dv != NULL) BN_zero(dv);
86 return(1);
87 }
88
89 BN_CTX_start(ctx);
90 D = BN_CTX_get(ctx);
91 if (dv == NULL) dv = BN_CTX_get(ctx);
92 if (rem == NULL) rem = BN_CTX_get(ctx);
93 if (D == NULL || dv == NULL || rem == NULL)
94 goto end;
95
96 nd=BN_num_bits(d);
97 nm=BN_num_bits(m);
98 if (BN_copy(D,d) == NULL) goto end;
99 if (BN_copy(rem,m) == NULL) goto end;
100
101 /* The next 2 are needed so we can do a dv->d[0]|=1 later
102 * since BN_lshift1 will only work once there is a value :-) */
103 BN_zero(dv);
104 bn_wexpand(dv,1);
105 dv->top=1;
106
107 if (!BN_lshift(D,D,nm-nd)) goto end;
108 for (i=nm-nd; i>=0; i--)
109 {
110 if (!BN_lshift1(dv,dv)) goto end;
111 if (BN_ucmp(rem,D) >= 0)
112 {
113 dv->d[0]|=1;
114 if (!BN_usub(rem,rem,D)) goto end;
115 }
116/* CAN IMPROVE (and have now :=) */
117 if (!BN_rshift1(D,D)) goto end;
118 }
119 rem->neg=BN_is_zero(rem)?0:m->neg;
120 dv->neg=m->neg^d->neg;
121 ret = 1;
122 end:
123 BN_CTX_end(ctx);
124 return(ret);
125 }
126
127#else
128
129#if !defined(NO_ASM) && !defined(NO_INLINE_ASM) && !defined(PEDANTIC) && !defined(BN_DIV3W)
130# if defined(__GNUC__) && __GNUC__>=2
131# if defined(__i386)
132 /*
133 * There were two reasons for implementing this template:
134 * - GNU C generates a call to a function (__udivdi3 to be exact)
135 * in reply to ((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0 (I fail to
136 * understand why...);
137 * - divl doesn't only calculate quotient, but also leaves
138 * remainder in %edx which we can definitely use here:-)
139 *
140 * <appro@fy.chalmers.se>
141 */
142# define bn_div_words(n0,n1,d0) \
143 ({ asm volatile ( \
144 "divl %4" \
145 : "=a"(q), "=d"(rem) \
146 : "a"(n1), "d"(n0), "g"(d0) \
147 : "cc"); \
148 q; \
149 })
150# define REMAINDER_IS_ALREADY_CALCULATED
151# endif /* __<cpu> */
152# endif /* __GNUC__ */
153#endif /* NO_ASM */
154
155int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
156 BN_CTX *ctx)
157 {
158 int norm_shift,i,j,loop;
159 BIGNUM *tmp,wnum,*snum,*sdiv,*res;
160 BN_ULONG *resp,*wnump;
161 BN_ULONG d0,d1;
162 int num_n,div_n;
163
164 bn_check_top(num);
165 bn_check_top(divisor);
166
167 if (BN_is_zero(divisor))
168 {
169 BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
170 return(0);
171 }
172
173 if (BN_ucmp(num,divisor) < 0)
174 {
175 if (rm != NULL)
176 { if (BN_copy(rm,num) == NULL) return(0); }
177 if (dv != NULL) BN_zero(dv);
178 return(1);
179 }
180
181 BN_CTX_start(ctx);
182 tmp=BN_CTX_get(ctx);
183 snum=BN_CTX_get(ctx);
184 sdiv=BN_CTX_get(ctx);
185 if (dv == NULL)
186 res=BN_CTX_get(ctx);
187 else res=dv;
188 if (sdiv==NULL || res == NULL) goto err;
189 tmp->neg=0;
190
191 /* First we normalise the numbers */
192 norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
193 BN_lshift(sdiv,divisor,norm_shift);
194 sdiv->neg=0;
195 norm_shift+=BN_BITS2;
196 BN_lshift(snum,num,norm_shift);
197 snum->neg=0;
198 div_n=sdiv->top;
199 num_n=snum->top;
200 loop=num_n-div_n;
201
202 /* Lets setup a 'window' into snum
203 * This is the part that corresponds to the current
204 * 'area' being divided */
205 BN_init(&wnum);
206 wnum.d= &(snum->d[loop]);
207 wnum.top= div_n;
208 wnum.dmax= snum->dmax+1; /* a bit of a lie */
209
210 /* Get the top 2 words of sdiv */
211 /* i=sdiv->top; */
212 d0=sdiv->d[div_n-1];
213 d1=(div_n == 1)?0:sdiv->d[div_n-2];
214
215 /* pointer to the 'top' of snum */
216 wnump= &(snum->d[num_n-1]);
217
218 /* Setup to 'res' */
219 res->neg= (num->neg^divisor->neg);
220 if (!bn_wexpand(res,(loop+1))) goto err;
221 res->top=loop;
222 resp= &(res->d[loop-1]);
223
224 /* space for temp */
225 if (!bn_wexpand(tmp,(div_n+1))) goto err;
226
227 if (BN_ucmp(&wnum,sdiv) >= 0)
228 {
229 if (!BN_usub(&wnum,&wnum,sdiv)) goto err;
230 *resp=1;
231 res->d[res->top-1]=1;
232 }
233 else
234 res->top--;
235 resp--;
236
237 for (i=0; i<loop-1; i++)
238 {
239 BN_ULONG q,l0;
240#if defined(BN_DIV3W) && !defined(NO_ASM)
241 BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG);
242 q=bn_div_3_words(wnump,d1,d0);
243#else
244 BN_ULONG n0,n1,rem=0;
245
246 n0=wnump[0];
247 n1=wnump[-1];
248 if (n0 == d0)
249 q=BN_MASK2;
250 else /* n0 < d0 */
251 {
252#ifdef BN_LLONG
253 BN_ULLONG t2;
254
255#if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
256 q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
257#else
258 q=bn_div_words(n0,n1,d0);
259#endif
260
261#ifndef REMAINDER_IS_ALREADY_CALCULATED
262 /*
263 * rem doesn't have to be BN_ULLONG. The least we
264 * know it's less that d0, isn't it?
265 */
266 rem=(n1-q*d0)&BN_MASK2;
267#endif
268 t2=(BN_ULLONG)d1*q;
269
270 for (;;)
271 {
272 if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
273 break;
274 q--;
275 rem += d0;
276 if (rem < d0) break; /* don't let rem overflow */
277 t2 -= d1;
278 }
279#else /* !BN_LLONG */
280 BN_ULONG t2l,t2h,ql,qh;
281
282 q=bn_div_words(n0,n1,d0);
283#ifndef REMAINDER_IS_ALREADY_CALCULATED
284 rem=(n1-q*d0)&BN_MASK2;
285#endif
286
287#ifdef BN_UMULT_HIGH
288 t2l = d1 * q;
289 t2h = BN_UMULT_HIGH(d1,q);
290#else
291 t2l=LBITS(d1); t2h=HBITS(d1);
292 ql =LBITS(q); qh =HBITS(q);
293 mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
294#endif
295
296 for (;;)
297 {
298 if ((t2h < rem) ||
299 ((t2h == rem) && (t2l <= wnump[-2])))
300 break;
301 q--;
302 rem += d0;
303 if (rem < d0) break; /* don't let rem overflow */
304 if (t2l < d1) t2h--; t2l -= d1;
305 }
306#endif /* !BN_LLONG */
307 }
308#endif /* !BN_DIV3W */
309
310 l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
311 wnum.d--; wnum.top++;
312 tmp->d[div_n]=l0;
313 for (j=div_n+1; j>0; j--)
314 if (tmp->d[j-1]) break;
315 tmp->top=j;
316
317 j=wnum.top;
318 BN_sub(&wnum,&wnum,tmp);
319
320 snum->top=snum->top+wnum.top-j;
321
322 if (wnum.neg)
323 {
324 q--;
325 j=wnum.top;
326 BN_add(&wnum,&wnum,sdiv);
327 snum->top+=wnum.top-j;
328 }
329 *(resp--)=q;
330 wnump--;
331 }
332 if (rm != NULL)
333 {
334 BN_rshift(rm,snum,norm_shift);
335 rm->neg=num->neg;
336 }
337 BN_CTX_end(ctx);
338 return(1);
339err:
340 BN_CTX_end(ctx);
341 return(0);
342 }
343
344#endif
345
346/* rem != m */
347int BN_mod(BIGNUM *rem, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx)
348 {
349#if 0 /* The old slow way */
350 int i,nm,nd;
351 BIGNUM *dv;
352
353 if (BN_ucmp(m,d) < 0)
354 return((BN_copy(rem,m) == NULL)?0:1);
355
356 BN_CTX_start(ctx);
357 dv=BN_CTX_get(ctx);
358
359 if (!BN_copy(rem,m)) goto err;
360
361 nm=BN_num_bits(rem);
362 nd=BN_num_bits(d);
363 if (!BN_lshift(dv,d,nm-nd)) goto err;
364 for (i=nm-nd; i>=0; i--)
365 {
366 if (BN_cmp(rem,dv) >= 0)
367 {
368 if (!BN_sub(rem,rem,dv)) goto err;
369 }
370 if (!BN_rshift1(dv,dv)) goto err;
371 }
372 BN_CTX_end(ctx);
373 return(1);
374 err:
375 BN_CTX_end(ctx);
376 return(0);
377#else
378 return(BN_div(NULL,rem,m,d,ctx));
379#endif
380 }
381
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