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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
65/* The old slow way */
66#if 0
67int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
68 BN_CTX *ctx)
69 {
70 int i,nm,nd;
71 int ret = 0;
72 BIGNUM *D;
73
74 bn_check_top(m);
75 bn_check_top(d);
76 if (BN_is_zero(d))
77 {
78 BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
79 return(0);
80 }
81
82 if (BN_ucmp(m,d) < 0)
83 {
84 if (rem != NULL)
85 { if (BN_copy(rem,m) == NULL) return(0); }
86 if (dv != NULL) BN_zero(dv);
87 return(1);
88 }
89
90 BN_CTX_start(ctx);
91 D = BN_CTX_get(ctx);
92 if (dv == NULL) dv = BN_CTX_get(ctx);
93 if (rem == NULL) rem = BN_CTX_get(ctx);
94 if (D == NULL || dv == NULL || rem == NULL)
95 goto end;
96
97 nd=BN_num_bits(d);
98 nm=BN_num_bits(m);
99 if (BN_copy(D,d) == NULL) goto end;
100 if (BN_copy(rem,m) == NULL) goto end;
101
102 /* The next 2 are needed so we can do a dv->d[0]|=1 later
103 * since BN_lshift1 will only work once there is a value :-) */
104 BN_zero(dv);
105 bn_wexpand(dv,1);
106 dv->top=1;
107
108 if (!BN_lshift(D,D,nm-nd)) goto end;
109 for (i=nm-nd; i>=0; i--)
110 {
111 if (!BN_lshift1(dv,dv)) goto end;
112 if (BN_ucmp(rem,D) >= 0)
113 {
114 dv->d[0]|=1;
115 if (!BN_usub(rem,rem,D)) goto end;
116 }
117/* CAN IMPROVE (and have now :=) */
118 if (!BN_rshift1(D,D)) goto end;
119 }
120 rem->neg=BN_is_zero(rem)?0:m->neg;
121 dv->neg=m->neg^d->neg;
122 ret = 1;
123 end:
124 BN_CTX_end(ctx);
125 return(ret);
126 }
127
128#else
129
130#if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) \
131 && !defined(PEDANTIC) && !defined(BN_DIV3W)
132# if defined(__GNUC__) && __GNUC__>=2
133# if defined(__i386) || defined (__i386__)
134 /*
135 * There were two reasons for implementing this template:
136 * - GNU C generates a call to a function (__udivdi3 to be exact)
137 * in reply to ((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0 (I fail to
138 * understand why...);
139 * - divl doesn't only calculate quotient, but also leaves
140 * remainder in %edx which we can definitely use here:-)
141 *
142 * <appro@fy.chalmers.se>
143 */
144# define bn_div_words(n0,n1,d0) \
145 ({ asm volatile ( \
146 "divl %4" \
147 : "=a"(q), "=d"(rem) \
148 : "a"(n1), "d"(n0), "g"(d0) \
149 : "cc"); \
150 q; \
151 })
152# define REMAINDER_IS_ALREADY_CALCULATED
153# elif defined(__x86_64) && defined(SIXTY_FOUR_BIT_LONG)
154 /*
155 * Same story here, but it's 128-bit by 64-bit division. Wow!
156 * <appro@fy.chalmers.se>
157 */
158# define bn_div_words(n0,n1,d0) \
159 ({ asm volatile ( \
160 "divq %4" \
161 : "=a"(q), "=d"(rem) \
162 : "a"(n1), "d"(n0), "g"(d0) \
163 : "cc"); \
164 q; \
165 })
166# define REMAINDER_IS_ALREADY_CALCULATED
167# endif /* __<cpu> */
168# endif /* __GNUC__ */
169#endif /* OPENSSL_NO_ASM */
170
171
172/* BN_div computes dv := num / divisor, rounding towards zero, and sets up
173 * rm such that dv*divisor + rm = num holds.
174 * Thus:
175 * dv->neg == num->neg ^ divisor->neg (unless the result is zero)
176 * rm->neg == num->neg (unless the remainder is zero)
177 * If 'dv' or 'rm' is NULL, the respective value is not returned.
178 */
179int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
180 BN_CTX *ctx)
181 {
182 int norm_shift,i,j,loop;
183 BIGNUM *tmp,wnum,*snum,*sdiv,*res;
184 BN_ULONG *resp,*wnump;
185 BN_ULONG d0,d1;
186 int num_n,div_n;
187
188 bn_check_top(num);
189 bn_check_top(divisor);
190
191 if (BN_is_zero(divisor))
192 {
193 BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
194 return(0);
195 }
196
197 if (BN_ucmp(num,divisor) < 0)
198 {
199 if (rm != NULL)
200 { if (BN_copy(rm,num) == NULL) return(0); }
201 if (dv != NULL) BN_zero(dv);
202 return(1);
203 }
204
205 BN_CTX_start(ctx);
206 tmp=BN_CTX_get(ctx);
207 snum=BN_CTX_get(ctx);
208 sdiv=BN_CTX_get(ctx);
209 if (dv == NULL)
210 res=BN_CTX_get(ctx);
211 else res=dv;
212 if (sdiv == NULL || res == NULL) goto err;
213 tmp->neg=0;
214
215 /* First we normalise the numbers */
216 norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
217 if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
218 sdiv->neg=0;
219 norm_shift+=BN_BITS2;
220 if (!(BN_lshift(snum,num,norm_shift))) goto err;
221 snum->neg=0;
222 div_n=sdiv->top;
223 num_n=snum->top;
224 loop=num_n-div_n;
225
226 /* Lets setup a 'window' into snum
227 * This is the part that corresponds to the current
228 * 'area' being divided */
229 BN_init(&wnum);
230 wnum.d= &(snum->d[loop]);
231 wnum.top= div_n;
232 wnum.dmax= snum->dmax+1; /* a bit of a lie */
233
234 /* Get the top 2 words of sdiv */
235 /* i=sdiv->top; */
236 d0=sdiv->d[div_n-1];
237 d1=(div_n == 1)?0:sdiv->d[div_n-2];
238
239 /* pointer to the 'top' of snum */
240 wnump= &(snum->d[num_n-1]);
241
242 /* Setup to 'res' */
243 res->neg= (num->neg^divisor->neg);
244 if (!bn_wexpand(res,(loop+1))) goto err;
245 res->top=loop;
246 resp= &(res->d[loop-1]);
247
248 /* space for temp */
249 if (!bn_wexpand(tmp,(div_n+1))) goto err;
250
251 if (BN_ucmp(&wnum,sdiv) >= 0)
252 {
253 if (!BN_usub(&wnum,&wnum,sdiv)) goto err;
254 *resp=1;
255 res->d[res->top-1]=1;
256 }
257 else
258 res->top--;
259 if (res->top == 0)
260 res->neg = 0;
261 resp--;
262
263 for (i=0; i<loop-1; i++)
264 {
265 BN_ULONG q,l0;
266#if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
267 BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG);
268 q=bn_div_3_words(wnump,d1,d0);
269#else
270 BN_ULONG n0,n1,rem=0;
271
272 n0=wnump[0];
273 n1=wnump[-1];
274 if (n0 == d0)
275 q=BN_MASK2;
276 else /* n0 < d0 */
277 {
278#ifdef BN_LLONG
279 BN_ULLONG t2;
280
281#if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
282 q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
283#else
284 q=bn_div_words(n0,n1,d0);
285#ifdef BN_DEBUG_LEVITTE
286 fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
287X) -> 0x%08X\n",
288 n0, n1, d0, q);
289#endif
290#endif
291
292#ifndef REMAINDER_IS_ALREADY_CALCULATED
293 /*
294 * rem doesn't have to be BN_ULLONG. The least we
295 * know it's less that d0, isn't it?
296 */
297 rem=(n1-q*d0)&BN_MASK2;
298#endif
299 t2=(BN_ULLONG)d1*q;
300
301 for (;;)
302 {
303 if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
304 break;
305 q--;
306 rem += d0;
307 if (rem < d0) break; /* don't let rem overflow */
308 t2 -= d1;
309 }
310#else /* !BN_LLONG */
311 BN_ULONG t2l,t2h,ql,qh;
312
313 q=bn_div_words(n0,n1,d0);
314#ifdef BN_DEBUG_LEVITTE
315 fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
316X) -> 0x%08X\n",
317 n0, n1, d0, q);
318#endif
319#ifndef REMAINDER_IS_ALREADY_CALCULATED
320 rem=(n1-q*d0)&BN_MASK2;
321#endif
322
323#if defined(BN_UMULT_LOHI)
324 BN_UMULT_LOHI(t2l,t2h,d1,q);
325#elif defined(BN_UMULT_HIGH)
326 t2l = d1 * q;
327 t2h = BN_UMULT_HIGH(d1,q);
328#else
329 t2l=LBITS(d1); t2h=HBITS(d1);
330 ql =LBITS(q); qh =HBITS(q);
331 mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
332#endif
333
334 for (;;)
335 {
336 if ((t2h < rem) ||
337 ((t2h == rem) && (t2l <= wnump[-2])))
338 break;
339 q--;
340 rem += d0;
341 if (rem < d0) break; /* don't let rem overflow */
342 if (t2l < d1) t2h--; t2l -= d1;
343 }
344#endif /* !BN_LLONG */
345 }
346#endif /* !BN_DIV3W */
347
348 l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
349 wnum.d--; wnum.top++;
350 tmp->d[div_n]=l0;
351 for (j=div_n+1; j>0; j--)
352 if (tmp->d[j-1]) break;
353 tmp->top=j;
354
355 j=wnum.top;
356 if (!BN_sub(&wnum,&wnum,tmp)) goto err;
357
358 snum->top=snum->top+wnum.top-j;
359
360 if (wnum.neg)
361 {
362 q--;
363 j=wnum.top;
364 if (!BN_add(&wnum,&wnum,sdiv)) goto err;
365 snum->top+=wnum.top-j;
366 }
367 *(resp--)=q;
368 wnump--;
369 }
370 if (rm != NULL)
371 {
372 /* Keep a copy of the neg flag in num because if rm==num
373 * BN_rshift() will overwrite it.
374 */
375 int neg = num->neg;
376 BN_rshift(rm,snum,norm_shift);
377 if (!BN_is_zero(rm))
378 rm->neg = neg;
379 }
380 BN_CTX_end(ctx);
381 return(1);
382err:
383 BN_CTX_end(ctx);
384 return(0);
385 }
386
387#endif
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