xref: /freebsd/crypto/openssl/crypto/bn/bn_div.c (revision 77a0943ded95b9e6438f7db70c4a28e4d93946d4)
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
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 		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 
155 int 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 	tmp->neg=0;
184 	snum=BN_CTX_get(ctx);
185 	sdiv=BN_CTX_get(ctx);
186 	if (dv == NULL)
187 		res=BN_CTX_get(ctx);
188 	else	res=dv;
189 	if (res == NULL) goto err;
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 #ifdef BN_DIV3W
241 		q=bn_div_3_words(wnump,d1,d0);
242 #else
243 		BN_ULONG n0,n1,rem=0;
244 
245 		n0=wnump[0];
246 		n1=wnump[-1];
247 		if (n0 == d0)
248 			q=BN_MASK2;
249 		else 			/* n0 < d0 */
250 			{
251 #ifdef BN_LLONG
252 			BN_ULLONG t2;
253 
254 #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
255 			q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
256 #else
257 			q=bn_div_words(n0,n1,d0);
258 #endif
259 
260 #ifndef REMAINDER_IS_ALREADY_CALCULATED
261 			/*
262 			 * rem doesn't have to be BN_ULLONG. The least we
263 			 * know it's less that d0, isn't it?
264 			 */
265 			rem=(n1-q*d0)&BN_MASK2;
266 #endif
267 			t2=(BN_ULLONG)d1*q;
268 
269 			for (;;)
270 				{
271 				if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
272 					break;
273 				q--;
274 				rem += d0;
275 				if (rem < d0) break; /* don't let rem overflow */
276 				t2 -= d1;
277 				}
278 #else /* !BN_LLONG */
279 			BN_ULONG t2l,t2h,ql,qh;
280 
281 			q=bn_div_words(n0,n1,d0);
282 #ifndef REMAINDER_IS_ALREADY_CALCULATED
283 			rem=(n1-q*d0)&BN_MASK2;
284 #endif
285 
286 #ifdef BN_UMULT_HIGH
287 			t2l = d1 * q;
288 			t2h = BN_UMULT_HIGH(d1,q);
289 #else
290 			t2l=LBITS(d1); t2h=HBITS(d1);
291 			ql =LBITS(q);  qh =HBITS(q);
292 			mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
293 #endif
294 
295 			for (;;)
296 				{
297 				if ((t2h < rem) ||
298 					((t2h == rem) && (t2l <= wnump[-2])))
299 					break;
300 				q--;
301 				rem += d0;
302 				if (rem < d0) break; /* don't let rem overflow */
303 				if (t2l < d1) t2h--; t2l -= d1;
304 				}
305 #endif /* !BN_LLONG */
306 			}
307 #endif /* !BN_DIV3W */
308 
309 		l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
310 		wnum.d--; wnum.top++;
311 		tmp->d[div_n]=l0;
312 		for (j=div_n+1; j>0; j--)
313 			if (tmp->d[j-1]) break;
314 		tmp->top=j;
315 
316 		j=wnum.top;
317 		BN_sub(&wnum,&wnum,tmp);
318 
319 		snum->top=snum->top+wnum.top-j;
320 
321 		if (wnum.neg)
322 			{
323 			q--;
324 			j=wnum.top;
325 			BN_add(&wnum,&wnum,sdiv);
326 			snum->top+=wnum.top-j;
327 			}
328 		*(resp--)=q;
329 		wnump--;
330 		}
331 	if (rm != NULL)
332 		{
333 		BN_rshift(rm,snum,norm_shift);
334 		rm->neg=num->neg;
335 		}
336 	BN_CTX_end(ctx);
337 	return(1);
338 err:
339 	BN_CTX_end(ctx);
340 	return(0);
341 	}
342 
343 #endif
344 
345 /* rem != m */
346 int BN_mod(BIGNUM *rem, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx)
347 	{
348 #if 0 /* The old slow way */
349 	int i,nm,nd;
350 	BIGNUM *dv;
351 
352 	if (BN_ucmp(m,d) < 0)
353 		return((BN_copy(rem,m) == NULL)?0:1);
354 
355 	BN_CTX_start(ctx);
356 	dv=BN_CTX_get(ctx);
357 
358 	if (!BN_copy(rem,m)) goto err;
359 
360 	nm=BN_num_bits(rem);
361 	nd=BN_num_bits(d);
362 	if (!BN_lshift(dv,d,nm-nd)) goto err;
363 	for (i=nm-nd; i>=0; i--)
364 		{
365 		if (BN_cmp(rem,dv) >= 0)
366 			{
367 			if (!BN_sub(rem,rem,dv)) goto err;
368 			}
369 		if (!BN_rshift1(dv,dv)) goto err;
370 		}
371 	BN_CTX_end(ctx);
372 	return(1);
373  err:
374 	BN_CTX_end(ctx);
375 	return(0);
376 #else
377 	return(BN_div(NULL,rem,m,d,ctx));
378 #endif
379 	}
380 
381