1 /* crypto/bn/bn_div.c */
2 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
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.
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).
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.
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
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)"
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
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.]
60 #include <openssl/bn.h>
64 /* The old slow way */
66 int BN_div(BIGNUM
*dv
, BIGNUM
*rem
, const BIGNUM
*m
, const BIGNUM
*d
,
76 BNerr(BN_F_BN_DIV
, BN_R_DIV_BY_ZERO
);
80 if (BN_ucmp(m
, d
) < 0) {
82 if (BN_copy(rem
, m
) == NULL
)
95 rem
= BN_CTX_get(ctx
);
96 if (D
== NULL
|| dv
== NULL
|| rem
== NULL
)
101 if (BN_copy(D
, d
) == NULL
)
103 if (BN_copy(rem
, m
) == NULL
)
107 * The next 2 are needed so we can do a dv->d[0]|=1 later since
108 * BN_lshift1 will only work once there is a value :-)
111 if (bn_wexpand(dv
, 1) == NULL
)
115 if (!BN_lshift(D
, D
, nm
- nd
))
117 for (i
= nm
- nd
; i
>= 0; i
--) {
118 if (!BN_lshift1(dv
, dv
))
120 if (BN_ucmp(rem
, D
) >= 0) {
122 if (!BN_usub(rem
, rem
, D
))
125 /* CAN IMPROVE (and have now :=) */
126 if (!BN_rshift1(D
, D
))
129 rem
->neg
= BN_is_zero(rem
) ? 0 : m
->neg
;
130 dv
->neg
= m
->neg
^ d
->neg
;
139 # if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) \
140 && !defined(PEDANTIC) && !defined(BN_DIV3W)
141 # if defined(__GNUC__) && __GNUC__>=2
142 # if defined(__i386) || defined (__i386__)
144 * There were two reasons for implementing this template:
145 * - GNU C generates a call to a function (__udivdi3 to be exact)
146 * in reply to ((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0 (I fail to
147 * understand why...);
148 * - divl doesn't only calculate quotient, but also leaves
149 * remainder in %edx which we can definitely use here:-)
151 * <appro@fy.chalmers.se>
154 # define bn_div_words(n0,n1,d0) \
157 : "=a"(q), "=d"(rem) \
158 : "a"(n1), "d"(n0), "g"(d0) \
162 # define REMAINDER_IS_ALREADY_CALCULATED
163 # elif defined(__x86_64) && defined(SIXTY_FOUR_BIT_LONG)
165 * Same story here, but it's 128-bit by 64-bit division. Wow!
166 * <appro@fy.chalmers.se>
169 # define bn_div_words(n0,n1,d0) \
172 : "=a"(q), "=d"(rem) \
173 : "a"(n1), "d"(n0), "g"(d0) \
177 # define REMAINDER_IS_ALREADY_CALCULATED
178 # endif /* __<cpu> */
179 # endif /* __GNUC__ */
180 # endif /* OPENSSL_NO_ASM */
183 * BN_div computes dv := num / divisor, rounding towards
184 * zero, and sets up rm such that dv*divisor + rm = num holds.
186 * dv->neg == num->neg ^ divisor->neg (unless the result is zero)
187 * rm->neg == num->neg (unless the remainder is zero)
188 * If 'dv' or 'rm' is NULL, the respective value is not returned.
190 int BN_div(BIGNUM
*dv
, BIGNUM
*rm
, const BIGNUM
*num
, const BIGNUM
*divisor
,
193 int norm_shift
, i
, loop
;
194 BIGNUM
*tmp
, wnum
, *snum
, *sdiv
, *res
;
195 BN_ULONG
*resp
, *wnump
;
201 * Invalid zero-padding would have particularly bad consequences so don't
202 * just rely on bn_check_top() here (bn_check_top() works only for
205 if ((num
->top
> 0 && num
->d
[num
->top
- 1] == 0) ||
206 (divisor
->top
> 0 && divisor
->d
[divisor
->top
- 1] == 0)) {
207 BNerr(BN_F_BN_DIV
, BN_R_NOT_INITIALIZED
);
212 bn_check_top(divisor
);
214 if ((BN_get_flags(num
, BN_FLG_CONSTTIME
) != 0)
215 || (BN_get_flags(divisor
, BN_FLG_CONSTTIME
) != 0)) {
221 /*- bn_check_top(num); *//*
222 * 'num' has been checked already
224 /*- bn_check_top(divisor); *//*
225 * 'divisor' has been checked already
228 if (BN_is_zero(divisor
)) {
229 BNerr(BN_F_BN_DIV
, BN_R_DIV_BY_ZERO
);
233 if (!no_branch
&& BN_ucmp(num
, divisor
) < 0) {
235 if (BN_copy(rm
, num
) == NULL
)
244 tmp
= BN_CTX_get(ctx
);
245 snum
= BN_CTX_get(ctx
);
246 sdiv
= BN_CTX_get(ctx
);
248 res
= BN_CTX_get(ctx
);
251 if (sdiv
== NULL
|| res
== NULL
|| tmp
== NULL
|| snum
== NULL
)
254 /* First we normalise the numbers */
255 norm_shift
= BN_BITS2
- ((BN_num_bits(divisor
)) % BN_BITS2
);
256 if (!(BN_lshift(sdiv
, divisor
, norm_shift
)))
259 norm_shift
+= BN_BITS2
;
260 if (!(BN_lshift(snum
, num
, norm_shift
)))
266 * Since we don't know whether snum is larger than sdiv, we pad snum
267 * with enough zeroes without changing its value.
269 if (snum
->top
<= sdiv
->top
+ 1) {
270 if (bn_wexpand(snum
, sdiv
->top
+ 2) == NULL
)
272 for (i
= snum
->top
; i
< sdiv
->top
+ 2; i
++)
274 snum
->top
= sdiv
->top
+ 2;
276 if (bn_wexpand(snum
, snum
->top
+ 1) == NULL
)
278 snum
->d
[snum
->top
] = 0;
285 loop
= num_n
- div_n
;
287 * Lets setup a 'window' into snum This is the part that corresponds to
288 * the current 'area' being divided
291 wnum
.d
= &(snum
->d
[loop
]);
294 * only needed when BN_ucmp messes up the values between top and max
296 wnum
.dmax
= snum
->dmax
- loop
; /* so we don't step out of bounds */
298 /* Get the top 2 words of sdiv */
299 /* div_n=sdiv->top; */
300 d0
= sdiv
->d
[div_n
- 1];
301 d1
= (div_n
== 1) ? 0 : sdiv
->d
[div_n
- 2];
303 /* pointer to the 'top' of snum */
304 wnump
= &(snum
->d
[num_n
- 1]);
307 res
->neg
= (num
->neg
^ divisor
->neg
);
308 if (!bn_wexpand(res
, (loop
+ 1)))
310 res
->top
= loop
- no_branch
;
311 resp
= &(res
->d
[loop
- 1]);
314 if (!bn_wexpand(tmp
, (div_n
+ 1)))
318 if (BN_ucmp(&wnum
, sdiv
) >= 0) {
320 * If BN_DEBUG_RAND is defined BN_ucmp changes (via bn_pollute)
321 * the const bignum arguments => clean the values between top and
324 bn_clear_top2max(&wnum
);
325 bn_sub_words(wnum
.d
, wnum
.d
, sdiv
->d
, div_n
);
332 * if res->top == 0 then clear the neg value otherwise decrease the resp
340 for (i
= 0; i
< loop
- 1; i
++, wnump
--, resp
--) {
343 * the first part of the loop uses the top two words of snum and sdiv
344 * to calculate a BN_ULONG q such that | wnum - sdiv * q | < sdiv
346 # if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
347 BN_ULONG
bn_div_3_words(BN_ULONG
*, BN_ULONG
, BN_ULONG
);
348 q
= bn_div_3_words(wnump
, d1
, d0
);
350 BN_ULONG n0
, n1
, rem
= 0;
361 # if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
362 q
= (BN_ULONG
)(((((BN_ULLONG
) n0
) << BN_BITS2
) | n1
) / d0
);
364 q
= bn_div_words(n0
, n1
, d0
);
365 # ifdef BN_DEBUG_LEVITTE
366 fprintf(stderr
, "DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
367 X) -> 0x%08X\n", n0
, n1
, d0
, q
);
371 # ifndef REMAINDER_IS_ALREADY_CALCULATED
373 * rem doesn't have to be BN_ULLONG. The least we
374 * know it's less that d0, isn't it?
376 rem
= (n1
- q
* d0
) & BN_MASK2
;
378 t2
= (BN_ULLONG
) d1
*q
;
381 if (t2
<= ((((BN_ULLONG
) rem
) << BN_BITS2
) | wnump
[-2]))
386 break; /* don't let rem overflow */
389 # else /* !BN_LLONG */
392 q
= bn_div_words(n0
, n1
, d0
);
393 # ifdef BN_DEBUG_LEVITTE
394 fprintf(stderr
, "DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
395 X) -> 0x%08X\n", n0
, n1
, d0
, q
);
397 # ifndef REMAINDER_IS_ALREADY_CALCULATED
398 rem
= (n1
- q
* d0
) & BN_MASK2
;
401 # if defined(BN_UMULT_LOHI)
402 BN_UMULT_LOHI(t2l
, t2h
, d1
, q
);
403 # elif defined(BN_UMULT_HIGH)
405 t2h
= BN_UMULT_HIGH(d1
, q
);
413 mul64(t2l
, t2h
, ql
, qh
); /* t2=(BN_ULLONG)d1*q; */
418 if ((t2h
< rem
) || ((t2h
== rem
) && (t2l
<= wnump
[-2])))
423 break; /* don't let rem overflow */
428 # endif /* !BN_LLONG */
430 # endif /* !BN_DIV3W */
432 l0
= bn_mul_words(tmp
->d
, sdiv
->d
, div_n
, q
);
436 * ingore top values of the bignums just sub the two BN_ULONG arrays
439 if (bn_sub_words(wnum
.d
, wnum
.d
, tmp
->d
, div_n
+ 1)) {
441 * Note: As we have considered only the leading two BN_ULONGs in
442 * the calculation of q, sdiv * q might be greater than wnum (but
443 * then (q-1) * sdiv is less or equal than wnum)
446 if (bn_add_words(wnum
.d
, wnum
.d
, sdiv
->d
, div_n
))
448 * we can't have an overflow here (assuming that q != 0, but
449 * if q == 0 then tmp is zero anyway)
453 /* store part of the result */
456 bn_correct_top(snum
);
459 * Keep a copy of the neg flag in num because if rm==num BN_rshift()
463 BN_rshift(rm
, snum
, norm_shift
);