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1 office 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 "bn_lcl.h"
61  
62 #define NO_ASM
63  
64 /* The old slow way */
65 #if 0
66 int 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 return(0);
78 }
79  
80 if (BN_ucmp(m,d) < 0)
81 {
82 if (rem != NULL)
83 { if (BN_copy(rem,m) == NULL) return(0); }
84 if (dv != NULL) BN_zero(dv);
85 return(1);
86 }
87  
88 BN_CTX_start(ctx);
89 D = BN_CTX_get(ctx);
90 if (dv == NULL) dv = BN_CTX_get(ctx);
91 if (rem == NULL) rem = BN_CTX_get(ctx);
92 if (D == NULL || dv == NULL || rem == NULL)
93 goto end;
94  
95 nd=BN_num_bits(d);
96 nm=BN_num_bits(m);
97 if (BN_copy(D,d) == NULL) goto end;
98 if (BN_copy(rem,m) == NULL) goto end;
99  
100 /* The next 2 are needed so we can do a dv->d[0]|=1 later
101 * since BN_lshift1 will only work once there is a value :-) */
102 BN_zero(dv);
103 bn_wexpand(dv,1);
104 dv->top=1;
105  
106 if (!BN_lshift(D,D,nm-nd)) goto end;
107 for (i=nm-nd; i>=0; i--)
108 {
109 if (!BN_lshift1(dv,dv)) goto end;
110 if (BN_ucmp(rem,D) >= 0)
111 {
112 dv->d[0]|=1;
113 if (!BN_usub(rem,rem,D)) goto end;
114 }
115 /* CAN IMPROVE (and have now :=) */
116 if (!BN_rshift1(D,D)) goto end;
117 }
118 rem->neg=BN_is_zero(rem)?0:m->neg;
119 dv->neg=m->neg^d->neg;
120 ret = 1;
121 end:
122 BN_CTX_end(ctx);
123 return(ret);
124 }
125  
126 #else
127  
128 #if !defined(NO_ASM) && !defined(NO_INLINE_ASM) && !defined(PEDANTIC) && !defined(BN_DIV3W)
129 # if defined(__GNUC__) && __GNUC__>=2
130 # if defined(__i386)
131 /*
132 * There were two reasons for implementing this template:
133 * - GNU C generates a call to a function (__udivdi3 to be exact)
134 * in reply to ((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0 (I fail to
135 * understand why...);
136 * - divl doesn't only calculate quotient, but also leaves
137 * remainder in %edx which we can definitely use here:-)
138 *
139 * <appro@fy.chalmers.se>
140 */
141 # define bn_div_words(n0,n1,d0) \
142 ({ asm volatile ( \
143 "divl %4" \
144 : "=a"(q), "=d"(rem) \
145 : "a"(n1), "d"(n0), "g"(d0) \
146 : "cc"); \
147 q; \
148 })
149 # define REMAINDER_IS_ALREADY_CALCULATED
150 # endif /* __<cpu> */
151 # endif /* __GNUC__ */
152 #endif /* NO_ASM */
153  
154 int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
155 BN_CTX *ctx)
156 {
157 int norm_shift,i,j,loop;
158 BIGNUM *tmp,wnum,*snum,*sdiv,*res;
159 BN_ULONG *resp,*wnump;
160 BN_ULONG d0,d1;
161 int num_n,div_n;
162  
163 bn_check_top(num);
164 bn_check_top(divisor);
165  
166 if (BN_is_zero(divisor))
167 {
168 return(0);
169 }
170  
171 if (BN_ucmp(num,divisor) < 0)
172 {
173 if (rm != NULL)
174 { if (BN_copy(rm,num) == NULL) return(0); }
175 if (dv != NULL) BN_zero(dv);
176 return(1);
177 }
178  
179 BN_CTX_start(ctx);
180 tmp=BN_CTX_get(ctx);
181 tmp->neg=0;
182 snum=BN_CTX_get(ctx);
183 sdiv=BN_CTX_get(ctx);
184 if (dv == NULL)
185 res=BN_CTX_get(ctx);
186 else res=dv;
187 if (res == NULL) goto err;
188  
189 /* First we normalise the numbers */
190 norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
191 BN_lshift(sdiv,divisor,norm_shift);
192 sdiv->neg=0;
193 norm_shift+=BN_BITS2;
194 BN_lshift(snum,num,norm_shift);
195 snum->neg=0;
196 div_n=sdiv->top;
197 num_n=snum->top;
198 loop=num_n-div_n;
199  
200 /* Lets setup a 'window' into snum
201 * This is the part that corresponds to the current
202 * 'area' being divided */
203 BN_init(&wnum);
204 wnum.d= &(snum->d[loop]);
205 wnum.top= div_n;
206 wnum.dmax= snum->dmax+1; /* a bit of a lie */
207  
208 /* Get the top 2 words of sdiv */
209 /* i=sdiv->top; */
210 d0=sdiv->d[div_n-1];
211 d1=(div_n == 1)?0:sdiv->d[div_n-2];
212  
213 /* pointer to the 'top' of snum */
214 wnump= &(snum->d[num_n-1]);
215  
216 /* Setup to 'res' */
217 res->neg= (num->neg^divisor->neg);
218 if (!bn_wexpand(res,(loop+1))) goto err;
219 res->top=loop;
220 resp= &(res->d[loop-1]);
221  
222 /* space for temp */
223 if (!bn_wexpand(tmp,(div_n+1))) goto err;
224  
225 if (BN_ucmp(&wnum,sdiv) >= 0)
226 {
227 if (!BN_usub(&wnum,&wnum,sdiv)) goto err;
228 *resp=1;
229 res->d[res->top-1]=1;
230 }
231 else
232 res->top--;
233 resp--;
234  
235 for (i=0; i<loop-1; i++)
236 {
237 BN_ULONG q,l0;
238 #ifdef BN_DIV3W
239 q=bn_div_3_words(wnump,d1,d0);
240 #else
241 BN_ULONG n0,n1,rem=0;
242  
243 n0=wnump[0];
244 n1=wnump[-1];
245 if (n0 == d0)
246 q=BN_MASK2;
247 else /* n0 < d0 */
248 {
249 #ifdef BN_LLONG
250 BN_ULLONG t2;
251  
252 #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
253 q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
254 #else
255 q=bn_div_words(n0,n1,d0);
256 #endif
257  
258 #ifndef REMAINDER_IS_ALREADY_CALCULATED
259 /*
260 * rem doesn't have to be BN_ULLONG. The least we
261 * know it's less that d0, isn't it?
262 */
263 rem=(n1-q*d0)&BN_MASK2;
264 #endif
265 t2=(BN_ULLONG)d1*q;
266  
267 for (;;)
268 {
269 if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
270 break;
271 q--;
272 rem += d0;
273 if (rem < d0) break; /* don't let rem overflow */
274 t2 -= d1;
275 }
276 #else /* !BN_LLONG */
277 BN_ULONG t2l,t2h,ql,qh;
278  
279 q=bn_div_words(n0,n1,d0);
280 #ifndef REMAINDER_IS_ALREADY_CALCULATED
281 rem=(n1-q*d0)&BN_MASK2;
282 #endif
283  
284 #ifdef BN_UMULT_HIGH
285 t2l = d1 * q;
286 t2h = BN_UMULT_HIGH(d1,q);
287 #else
288 t2l=LBITS(d1); t2h=HBITS(d1);
289 ql =LBITS(q); qh =HBITS(q);
290 mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
291 #endif
292  
293 for (;;)
294 {
295 if ((t2h < rem) ||
296 ((t2h == rem) && (t2l <= wnump[-2])))
297 break;
298 q--;
299 rem += d0;
300 if (rem < d0) break; /* don't let rem overflow */
301 if (t2l < d1) t2h--; t2l -= d1;
302 }
303 #endif /* !BN_LLONG */
304 }
305 #endif /* !BN_DIV3W */
306  
307 l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
308 wnum.d--; wnum.top++;
309 tmp->d[div_n]=l0;
310 for (j=div_n+1; j>0; j--)
311 if (tmp->d[j-1]) break;
312 tmp->top=j;
313  
314 j=wnum.top;
315 BN_sub(&wnum,&wnum,tmp);
316  
317 snum->top=snum->top+wnum.top-j;
318  
319 if (wnum.neg)
320 {
321 q--;
322 j=wnum.top;
323 BN_add(&wnum,&wnum,sdiv);
324 snum->top+=wnum.top-j;
325 }
326 *(resp--)=q;
327 wnump--;
328 }
329 if (rm != NULL)
330 {
331 BN_rshift(rm,snum,norm_shift);
332 rm->neg=num->neg;
333 }
334 BN_CTX_end(ctx);
335 return(1);
336 err:
337 BN_CTX_end(ctx);
338 return(0);
339 }
340  
341 #endif
342  
343 /* rem != m */
344 int BN_mod(BIGNUM *rem, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx)
345 {
346 #if 0 /* The old slow way */
347 int i,nm,nd;
348 BIGNUM *dv;
349  
350 if (BN_ucmp(m,d) < 0)
351 return((BN_copy(rem,m) == NULL)?0:1);
352  
353 BN_CTX_start(ctx);
354 dv=BN_CTX_get(ctx);
355  
356 if (!BN_copy(rem,m)) goto err;
357  
358 nm=BN_num_bits(rem);
359 nd=BN_num_bits(d);
360 if (!BN_lshift(dv,d,nm-nd)) goto err;
361 for (i=nm-nd; i>=0; i--)
362 {
363 if (BN_cmp(rem,dv) >= 0)
364 {
365 if (!BN_sub(rem,rem,dv)) goto err;
366 }
367 if (!BN_rshift1(dv,dv)) goto err;
368 }
369 BN_CTX_end(ctx);
370 return(1);
371 err:
372 BN_CTX_end(ctx);
373 return(0);
374 #else
375 return(BN_div(NULL,rem,m,d,ctx));
376 #endif
377 }
378