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>
65 /* The old slow way */
67 int BN_div(BIGNUM
*dv
, BIGNUM
*rem
, const BIGNUM
*m
, const BIGNUM
*d
,
78 BNerr(BN_F_BN_DIV
,BN_R_DIV_BY_ZERO
);
85 { if (BN_copy(rem
,m
) == NULL
) return(0); }
86 if (dv
!= NULL
) BN_zero(dv
);
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
)
99 if (BN_copy(D
,d
) == NULL
) goto end
;
100 if (BN_copy(rem
,m
) == NULL
) goto end
;
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 :-) */
108 if (!BN_lshift(D
,D
,nm
-nd
)) goto end
;
109 for (i
=nm
-nd
; i
>=0; i
--)
111 if (!BN_lshift1(dv
,dv
)) goto end
;
112 if (BN_ucmp(rem
,D
) >= 0)
115 if (!BN_usub(rem
,rem
,D
)) goto end
;
117 /* CAN IMPROVE (and have now :=) */
118 if (!BN_rshift1(D
,D
)) goto end
;
120 rem
->neg
=BN_is_zero(rem
)?0:m
->neg
;
121 dv
->neg
=m
->neg
^d
->neg
;
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__)
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:-)
142 * <appro@fy.chalmers.se>
144 # define bn_div_words(n0,n1,d0) \
147 : "=a"(q), "=d"(rem) \
148 : "a"(n1), "d"(n0), "g"(d0) \
152 # define REMAINDER_IS_ALREADY_CALCULATED
153 # elif defined(__x86_64) && defined(SIXTY_FOUR_BIT_LONG)
155 * Same story here, but it's 128-bit by 64-bit division. Wow!
156 * <appro@fy.chalmers.se>
158 # define bn_div_words(n0,n1,d0) \
161 : "=a"(q), "=d"(rem) \
162 : "a"(n1), "d"(n0), "g"(d0) \
166 # define REMAINDER_IS_ALREADY_CALCULATED
167 # endif /* __<cpu> */
168 # endif /* __GNUC__ */
169 #endif /* OPENSSL_NO_ASM */
172 /* BN_div[_no_branch] computes dv := num / divisor, rounding towards
173 * zero, and sets up rm such that dv*divisor + rm = num holds.
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.
179 static int BN_div_no_branch(BIGNUM
*dv
, BIGNUM
*rm
, const BIGNUM
*num
,
180 const BIGNUM
*divisor
, BN_CTX
*ctx
);
181 int BN_div(BIGNUM
*dv
, BIGNUM
*rm
, const BIGNUM
*num
, const BIGNUM
*divisor
,
184 int norm_shift
,i
,loop
;
185 BIGNUM
*tmp
,wnum
,*snum
,*sdiv
,*res
;
186 BN_ULONG
*resp
,*wnump
;
190 /* Invalid zero-padding would have particularly bad consequences
191 * in the case of 'num', so don't just rely on bn_check_top() for this one
192 * (bn_check_top() works only for BN_DEBUG builds) */
193 if (num
->top
> 0 && num
->d
[num
->top
- 1] == 0)
195 BNerr(BN_F_BN_DIV
,BN_R_NOT_INITIALIZED
);
201 if ((BN_get_flags(num
, BN_FLG_CONSTTIME
) != 0) || (BN_get_flags(divisor
, BN_FLG_CONSTTIME
) != 0))
203 return BN_div_no_branch(dv
, rm
, num
, divisor
, ctx
);
208 /* bn_check_top(num); */ /* 'num' has been checked already */
209 bn_check_top(divisor
);
211 if (BN_is_zero(divisor
))
213 BNerr(BN_F_BN_DIV
,BN_R_DIV_BY_ZERO
);
217 if (BN_ucmp(num
,divisor
) < 0)
220 { if (BN_copy(rm
,num
) == NULL
) return(0); }
221 if (dv
!= NULL
) BN_zero(dv
);
227 snum
=BN_CTX_get(ctx
);
228 sdiv
=BN_CTX_get(ctx
);
232 if (sdiv
== NULL
|| res
== NULL
) goto err
;
234 /* First we normalise the numbers */
235 norm_shift
=BN_BITS2
-((BN_num_bits(divisor
))%BN_BITS2
);
236 if (!(BN_lshift(sdiv
,divisor
,norm_shift
))) goto err
;
238 norm_shift
+=BN_BITS2
;
239 if (!(BN_lshift(snum
,num
,norm_shift
))) goto err
;
244 /* Lets setup a 'window' into snum
245 * This is the part that corresponds to the current
246 * 'area' being divided */
248 wnum
.d
= &(snum
->d
[loop
]);
250 /* only needed when BN_ucmp messes up the values between top and max */
251 wnum
.dmax
= snum
->dmax
- loop
; /* so we don't step out of bounds */
253 /* Get the top 2 words of sdiv */
254 /* div_n=sdiv->top; */
256 d1
=(div_n
== 1)?0:sdiv
->d
[div_n
-2];
258 /* pointer to the 'top' of snum */
259 wnump
= &(snum
->d
[num_n
-1]);
262 res
->neg
= (num
->neg
^divisor
->neg
);
263 if (!bn_wexpand(res
,(loop
+1))) goto err
;
265 resp
= &(res
->d
[loop
-1]);
268 if (!bn_wexpand(tmp
,(div_n
+1))) goto err
;
270 if (BN_ucmp(&wnum
,sdiv
) >= 0)
272 /* If BN_DEBUG_RAND is defined BN_ucmp changes (via
273 * bn_pollute) the const bignum arguments =>
274 * clean the values between top and max again */
275 bn_clear_top2max(&wnum
);
276 bn_sub_words(wnum
.d
, wnum
.d
, sdiv
->d
, div_n
);
281 /* if res->top == 0 then clear the neg value otherwise decrease
282 * the resp pointer */
288 for (i
=0; i
<loop
-1; i
++, wnump
--, resp
--)
291 /* the first part of the loop uses the top two words of
292 * snum and sdiv to calculate a BN_ULONG q such that
293 * | wnum - sdiv * q | < sdiv */
294 #if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
295 BN_ULONG
bn_div_3_words(BN_ULONG
*,BN_ULONG
,BN_ULONG
);
296 q
=bn_div_3_words(wnump
,d1
,d0
);
298 BN_ULONG n0
,n1
,rem
=0;
309 #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
310 q
=(BN_ULONG
)(((((BN_ULLONG
)n0
)<<BN_BITS2
)|n1
)/d0
);
312 q
=bn_div_words(n0
,n1
,d0
);
313 #ifdef BN_DEBUG_LEVITTE
314 fprintf(stderr
,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
320 #ifndef REMAINDER_IS_ALREADY_CALCULATED
322 * rem doesn't have to be BN_ULLONG. The least we
323 * know it's less that d0, isn't it?
325 rem
=(n1
-q
*d0
)&BN_MASK2
;
331 if (t2
<= ((((BN_ULLONG
)rem
)<<BN_BITS2
)|wnump
[-2]))
335 if (rem
< d0
) break; /* don't let rem overflow */
338 #else /* !BN_LLONG */
339 BN_ULONG t2l
,t2h
,ql
,qh
;
341 q
=bn_div_words(n0
,n1
,d0
);
342 #ifdef BN_DEBUG_LEVITTE
343 fprintf(stderr
,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
347 #ifndef REMAINDER_IS_ALREADY_CALCULATED
348 rem
=(n1
-q
*d0
)&BN_MASK2
;
351 #if defined(BN_UMULT_LOHI)
352 BN_UMULT_LOHI(t2l
,t2h
,d1
,q
);
353 #elif defined(BN_UMULT_HIGH)
355 t2h
= BN_UMULT_HIGH(d1
,q
);
357 t2l
=LBITS(d1
); t2h
=HBITS(d1
);
358 ql
=LBITS(q
); qh
=HBITS(q
);
359 mul64(t2l
,t2h
,ql
,qh
); /* t2=(BN_ULLONG)d1*q; */
365 ((t2h
== rem
) && (t2l
<= wnump
[-2])))
369 if (rem
< d0
) break; /* don't let rem overflow */
370 if (t2l
< d1
) t2h
--; t2l
-= d1
;
372 #endif /* !BN_LLONG */
374 #endif /* !BN_DIV3W */
376 l0
=bn_mul_words(tmp
->d
,sdiv
->d
,div_n
,q
);
379 /* ingore top values of the bignums just sub the two
380 * BN_ULONG arrays with bn_sub_words */
381 if (bn_sub_words(wnum
.d
, wnum
.d
, tmp
->d
, div_n
+1))
383 /* Note: As we have considered only the leading
384 * two BN_ULONGs in the calculation of q, sdiv * q
385 * might be greater than wnum (but then (q-1) * sdiv
386 * is less or equal than wnum)
389 if (bn_add_words(wnum
.d
, wnum
.d
, sdiv
->d
, div_n
))
390 /* we can't have an overflow here (assuming
391 * that q != 0, but if q == 0 then tmp is
395 /* store part of the result */
398 bn_correct_top(snum
);
401 /* Keep a copy of the neg flag in num because if rm==num
402 * BN_rshift() will overwrite it.
405 BN_rshift(rm
,snum
,norm_shift
);
419 /* BN_div_no_branch is a special version of BN_div. It does not contain
420 * branches that may leak sensitive information.
422 static int BN_div_no_branch(BIGNUM
*dv
, BIGNUM
*rm
, const BIGNUM
*num
,
423 const BIGNUM
*divisor
, BN_CTX
*ctx
)
425 int norm_shift
,i
,loop
;
426 BIGNUM
*tmp
,wnum
,*snum
,*sdiv
,*res
;
427 BN_ULONG
*resp
,*wnump
;
433 /* bn_check_top(num); */ /* 'num' has been checked in BN_div() */
434 bn_check_top(divisor
);
436 if (BN_is_zero(divisor
))
438 BNerr(BN_F_BN_DIV_NO_BRANCH
,BN_R_DIV_BY_ZERO
);
444 snum
=BN_CTX_get(ctx
);
445 sdiv
=BN_CTX_get(ctx
);
449 if (sdiv
== NULL
|| res
== NULL
) goto err
;
451 /* First we normalise the numbers */
452 norm_shift
=BN_BITS2
-((BN_num_bits(divisor
))%BN_BITS2
);
453 if (!(BN_lshift(sdiv
,divisor
,norm_shift
))) goto err
;
455 norm_shift
+=BN_BITS2
;
456 if (!(BN_lshift(snum
,num
,norm_shift
))) goto err
;
459 /* Since we don't know whether snum is larger than sdiv,
460 * we pad snum with enough zeroes without changing its
463 if (snum
->top
<= sdiv
->top
+1)
465 if (bn_wexpand(snum
, sdiv
->top
+ 2) == NULL
) goto err
;
466 for (i
= snum
->top
; i
< sdiv
->top
+ 2; i
++) snum
->d
[i
] = 0;
467 snum
->top
= sdiv
->top
+ 2;
471 if (bn_wexpand(snum
, snum
->top
+ 1) == NULL
) goto err
;
472 snum
->d
[snum
->top
] = 0;
479 /* Lets setup a 'window' into snum
480 * This is the part that corresponds to the current
481 * 'area' being divided */
483 wnum
.d
= &(snum
->d
[loop
]);
485 /* only needed when BN_ucmp messes up the values between top and max */
486 wnum
.dmax
= snum
->dmax
- loop
; /* so we don't step out of bounds */
488 /* Get the top 2 words of sdiv */
489 /* div_n=sdiv->top; */
491 d1
=(div_n
== 1)?0:sdiv
->d
[div_n
-2];
493 /* pointer to the 'top' of snum */
494 wnump
= &(snum
->d
[num_n
-1]);
497 res
->neg
= (num
->neg
^divisor
->neg
);
498 if (!bn_wexpand(res
,(loop
+1))) goto err
;
500 resp
= &(res
->d
[loop
-1]);
503 if (!bn_wexpand(tmp
,(div_n
+1))) goto err
;
505 /* if res->top == 0 then clear the neg value otherwise decrease
506 * the resp pointer */
512 for (i
=0; i
<loop
-1; i
++, wnump
--, resp
--)
515 /* the first part of the loop uses the top two words of
516 * snum and sdiv to calculate a BN_ULONG q such that
517 * | wnum - sdiv * q | < sdiv */
518 #if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
519 BN_ULONG
bn_div_3_words(BN_ULONG
*,BN_ULONG
,BN_ULONG
);
520 q
=bn_div_3_words(wnump
,d1
,d0
);
522 BN_ULONG n0
,n1
,rem
=0;
533 #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
534 q
=(BN_ULONG
)(((((BN_ULLONG
)n0
)<<BN_BITS2
)|n1
)/d0
);
536 q
=bn_div_words(n0
,n1
,d0
);
537 #ifdef BN_DEBUG_LEVITTE
538 fprintf(stderr
,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
544 #ifndef REMAINDER_IS_ALREADY_CALCULATED
546 * rem doesn't have to be BN_ULLONG. The least we
547 * know it's less that d0, isn't it?
549 rem
=(n1
-q
*d0
)&BN_MASK2
;
555 if (t2
<= ((((BN_ULLONG
)rem
)<<BN_BITS2
)|wnump
[-2]))
559 if (rem
< d0
) break; /* don't let rem overflow */
562 #else /* !BN_LLONG */
563 BN_ULONG t2l
,t2h
,ql
,qh
;
565 q
=bn_div_words(n0
,n1
,d0
);
566 #ifdef BN_DEBUG_LEVITTE
567 fprintf(stderr
,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
571 #ifndef REMAINDER_IS_ALREADY_CALCULATED
572 rem
=(n1
-q
*d0
)&BN_MASK2
;
575 #if defined(BN_UMULT_LOHI)
576 BN_UMULT_LOHI(t2l
,t2h
,d1
,q
);
577 #elif defined(BN_UMULT_HIGH)
579 t2h
= BN_UMULT_HIGH(d1
,q
);
581 t2l
=LBITS(d1
); t2h
=HBITS(d1
);
582 ql
=LBITS(q
); qh
=HBITS(q
);
583 mul64(t2l
,t2h
,ql
,qh
); /* t2=(BN_ULLONG)d1*q; */
589 ((t2h
== rem
) && (t2l
<= wnump
[-2])))
593 if (rem
< d0
) break; /* don't let rem overflow */
594 if (t2l
< d1
) t2h
--; t2l
-= d1
;
596 #endif /* !BN_LLONG */
598 #endif /* !BN_DIV3W */
600 l0
=bn_mul_words(tmp
->d
,sdiv
->d
,div_n
,q
);
603 /* ingore top values of the bignums just sub the two
604 * BN_ULONG arrays with bn_sub_words */
605 if (bn_sub_words(wnum
.d
, wnum
.d
, tmp
->d
, div_n
+1))
607 /* Note: As we have considered only the leading
608 * two BN_ULONGs in the calculation of q, sdiv * q
609 * might be greater than wnum (but then (q-1) * sdiv
610 * is less or equal than wnum)
613 if (bn_add_words(wnum
.d
, wnum
.d
, sdiv
->d
, div_n
))
614 /* we can't have an overflow here (assuming
615 * that q != 0, but if q == 0 then tmp is
619 /* store part of the result */
622 bn_correct_top(snum
);
625 /* Keep a copy of the neg flag in num because if rm==num
626 * BN_rshift() will overwrite it.
629 BN_rshift(rm
,snum
,norm_shift
);