You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
650 lines
17 KiB
650 lines
17 KiB
/* crypto/bn/bn_div.c */
|
|
/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
|
|
* All rights reserved.
|
|
*
|
|
* This package is an SSL implementation written
|
|
* by Eric Young (eay@cryptsoft.com).
|
|
* The implementation was written so as to conform with Netscapes SSL.
|
|
*
|
|
* This library is free for commercial and non-commercial use as long as
|
|
* the following conditions are aheared to. The following conditions
|
|
* apply to all code found in this distribution, be it the RC4, RSA,
|
|
* lhash, DES, etc., code; not just the SSL code. The SSL documentation
|
|
* included with this distribution is covered by the same copyright terms
|
|
* except that the holder is Tim Hudson (tjh@cryptsoft.com).
|
|
*
|
|
* Copyright remains Eric Young's, and as such any Copyright notices in
|
|
* the code are not to be removed.
|
|
* If this package is used in a product, Eric Young should be given attribution
|
|
* as the author of the parts of the library used.
|
|
* This can be in the form of a textual message at program startup or
|
|
* in documentation (online or textual) provided with the package.
|
|
*
|
|
* Redistribution and use in source and binary forms, with or without
|
|
* modification, are permitted provided that the following conditions
|
|
* are met:
|
|
* 1. Redistributions of source code must retain the copyright
|
|
* notice, this list of conditions and the following disclaimer.
|
|
* 2. Redistributions in binary form must reproduce the above copyright
|
|
* notice, this list of conditions and the following disclaimer in the
|
|
* documentation and/or other materials provided with the distribution.
|
|
* 3. All advertising materials mentioning features or use of this software
|
|
* must display the following acknowledgement:
|
|
* "This product includes cryptographic software written by
|
|
* Eric Young (eay@cryptsoft.com)"
|
|
* The word 'cryptographic' can be left out if the rouines from the library
|
|
* being used are not cryptographic related :-).
|
|
* 4. If you include any Windows specific code (or a derivative thereof) from
|
|
* the apps directory (application code) you must include an acknowledgement:
|
|
* "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
|
|
*
|
|
* THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
|
|
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
|
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
|
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
|
|
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
|
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
|
|
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
|
|
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
|
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
|
|
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
|
|
* SUCH DAMAGE.
|
|
*
|
|
* The licence and distribution terms for any publically available version or
|
|
* derivative of this code cannot be changed. i.e. this code cannot simply be
|
|
* copied and put under another distribution licence
|
|
* [including the GNU Public Licence.]
|
|
*/
|
|
|
|
#include <stdio.h>
|
|
#include <openssl/bn.h>
|
|
#include "cryptlib.h"
|
|
#include "bn_lcl.h"
|
|
|
|
|
|
/* The old slow way */
|
|
#if 0
|
|
int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
|
|
BN_CTX *ctx)
|
|
{
|
|
int i,nm,nd;
|
|
int ret = 0;
|
|
BIGNUM *D;
|
|
|
|
bn_check_top(m);
|
|
bn_check_top(d);
|
|
if (BN_is_zero(d))
|
|
{
|
|
BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
|
|
return(0);
|
|
}
|
|
|
|
if (BN_ucmp(m,d) < 0)
|
|
{
|
|
if (rem != NULL)
|
|
{ if (BN_copy(rem,m) == NULL) return(0); }
|
|
if (dv != NULL) BN_zero(dv);
|
|
return(1);
|
|
}
|
|
|
|
BN_CTX_start(ctx);
|
|
D = BN_CTX_get(ctx);
|
|
if (dv == NULL) dv = BN_CTX_get(ctx);
|
|
if (rem == NULL) rem = BN_CTX_get(ctx);
|
|
if (D == NULL || dv == NULL || rem == NULL)
|
|
goto end;
|
|
|
|
nd=BN_num_bits(d);
|
|
nm=BN_num_bits(m);
|
|
if (BN_copy(D,d) == NULL) goto end;
|
|
if (BN_copy(rem,m) == NULL) goto end;
|
|
|
|
/* The next 2 are needed so we can do a dv->d[0]|=1 later
|
|
* since BN_lshift1 will only work once there is a value :-) */
|
|
BN_zero(dv);
|
|
if(bn_wexpand(dv,1) == NULL) goto end;
|
|
dv->top=1;
|
|
|
|
if (!BN_lshift(D,D,nm-nd)) goto end;
|
|
for (i=nm-nd; i>=0; i--)
|
|
{
|
|
if (!BN_lshift1(dv,dv)) goto end;
|
|
if (BN_ucmp(rem,D) >= 0)
|
|
{
|
|
dv->d[0]|=1;
|
|
if (!BN_usub(rem,rem,D)) goto end;
|
|
}
|
|
/* CAN IMPROVE (and have now :=) */
|
|
if (!BN_rshift1(D,D)) goto end;
|
|
}
|
|
rem->neg=BN_is_zero(rem)?0:m->neg;
|
|
dv->neg=m->neg^d->neg;
|
|
ret = 1;
|
|
end:
|
|
BN_CTX_end(ctx);
|
|
return(ret);
|
|
}
|
|
|
|
#else
|
|
|
|
#if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) \
|
|
&& !defined(PEDANTIC) && !defined(BN_DIV3W)
|
|
# if defined(__GNUC__) && __GNUC__>=2
|
|
# if defined(__i386) || defined (__i386__)
|
|
/*
|
|
* There were two reasons for implementing this template:
|
|
* - GNU C generates a call to a function (__udivdi3 to be exact)
|
|
* in reply to ((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0 (I fail to
|
|
* understand why...);
|
|
* - divl doesn't only calculate quotient, but also leaves
|
|
* remainder in %edx which we can definitely use here:-)
|
|
*
|
|
* <appro@fy.chalmers.se>
|
|
*/
|
|
# define bn_div_words(n0,n1,d0) \
|
|
({ asm volatile ( \
|
|
"divl %4" \
|
|
: "=a"(q), "=d"(rem) \
|
|
: "a"(n1), "d"(n0), "g"(d0) \
|
|
: "cc"); \
|
|
q; \
|
|
})
|
|
# define REMAINDER_IS_ALREADY_CALCULATED
|
|
# elif defined(__x86_64) && defined(SIXTY_FOUR_BIT_LONG)
|
|
/*
|
|
* Same story here, but it's 128-bit by 64-bit division. Wow!
|
|
* <appro@fy.chalmers.se>
|
|
*/
|
|
# define bn_div_words(n0,n1,d0) \
|
|
({ asm volatile ( \
|
|
"divq %4" \
|
|
: "=a"(q), "=d"(rem) \
|
|
: "a"(n1), "d"(n0), "g"(d0) \
|
|
: "cc"); \
|
|
q; \
|
|
})
|
|
# define REMAINDER_IS_ALREADY_CALCULATED
|
|
# endif /* __<cpu> */
|
|
# endif /* __GNUC__ */
|
|
#endif /* OPENSSL_NO_ASM */
|
|
|
|
|
|
/* BN_div[_no_branch] computes dv := num / divisor, rounding towards
|
|
* zero, and sets up rm such that dv*divisor + rm = num holds.
|
|
* Thus:
|
|
* dv->neg == num->neg ^ divisor->neg (unless the result is zero)
|
|
* rm->neg == num->neg (unless the remainder is zero)
|
|
* If 'dv' or 'rm' is NULL, the respective value is not returned.
|
|
*/
|
|
static int BN_div_no_branch(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num,
|
|
const BIGNUM *divisor, BN_CTX *ctx);
|
|
int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
|
|
BN_CTX *ctx)
|
|
{
|
|
int norm_shift,i,loop;
|
|
BIGNUM *tmp,wnum,*snum,*sdiv,*res;
|
|
BN_ULONG *resp,*wnump;
|
|
BN_ULONG d0,d1;
|
|
int num_n,div_n;
|
|
|
|
/* Invalid zero-padding would have particularly bad consequences
|
|
* in the case of 'num', so don't just rely on bn_check_top() for this one
|
|
* (bn_check_top() works only for BN_DEBUG builds) */
|
|
if (num->top > 0 && num->d[num->top - 1] == 0)
|
|
{
|
|
BNerr(BN_F_BN_DIV,BN_R_NOT_INITIALIZED);
|
|
return 0;
|
|
}
|
|
|
|
bn_check_top(num);
|
|
|
|
if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0) || (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0))
|
|
{
|
|
return BN_div_no_branch(dv, rm, num, divisor, ctx);
|
|
}
|
|
|
|
bn_check_top(dv);
|
|
bn_check_top(rm);
|
|
/* bn_check_top(num); */ /* 'num' has been checked already */
|
|
bn_check_top(divisor);
|
|
|
|
if (BN_is_zero(divisor))
|
|
{
|
|
BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
|
|
return(0);
|
|
}
|
|
|
|
if (BN_ucmp(num,divisor) < 0)
|
|
{
|
|
if (rm != NULL)
|
|
{ if (BN_copy(rm,num) == NULL) return(0); }
|
|
if (dv != NULL) BN_zero(dv);
|
|
return(1);
|
|
}
|
|
|
|
BN_CTX_start(ctx);
|
|
tmp=BN_CTX_get(ctx);
|
|
snum=BN_CTX_get(ctx);
|
|
sdiv=BN_CTX_get(ctx);
|
|
if (dv == NULL)
|
|
res=BN_CTX_get(ctx);
|
|
else res=dv;
|
|
if (sdiv == NULL || res == NULL || tmp == NULL || snum == NULL)
|
|
goto err;
|
|
|
|
/* First we normalise the numbers */
|
|
norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
|
|
if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
|
|
sdiv->neg=0;
|
|
norm_shift+=BN_BITS2;
|
|
if (!(BN_lshift(snum,num,norm_shift))) goto err;
|
|
snum->neg=0;
|
|
div_n=sdiv->top;
|
|
num_n=snum->top;
|
|
loop=num_n-div_n;
|
|
/* Lets setup a 'window' into snum
|
|
* This is the part that corresponds to the current
|
|
* 'area' being divided */
|
|
wnum.neg = 0;
|
|
wnum.d = &(snum->d[loop]);
|
|
wnum.top = div_n;
|
|
/* only needed when BN_ucmp messes up the values between top and max */
|
|
wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */
|
|
|
|
/* Get the top 2 words of sdiv */
|
|
/* div_n=sdiv->top; */
|
|
d0=sdiv->d[div_n-1];
|
|
d1=(div_n == 1)?0:sdiv->d[div_n-2];
|
|
|
|
/* pointer to the 'top' of snum */
|
|
wnump= &(snum->d[num_n-1]);
|
|
|
|
/* Setup to 'res' */
|
|
res->neg= (num->neg^divisor->neg);
|
|
if (!bn_wexpand(res,(loop+1))) goto err;
|
|
res->top=loop;
|
|
resp= &(res->d[loop-1]);
|
|
|
|
/* space for temp */
|
|
if (!bn_wexpand(tmp,(div_n+1))) goto err;
|
|
|
|
if (BN_ucmp(&wnum,sdiv) >= 0)
|
|
{
|
|
/* If BN_DEBUG_RAND is defined BN_ucmp changes (via
|
|
* bn_pollute) the const bignum arguments =>
|
|
* clean the values between top and max again */
|
|
bn_clear_top2max(&wnum);
|
|
bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n);
|
|
*resp=1;
|
|
}
|
|
else
|
|
res->top--;
|
|
/* if res->top == 0 then clear the neg value otherwise decrease
|
|
* the resp pointer */
|
|
if (res->top == 0)
|
|
res->neg = 0;
|
|
else
|
|
resp--;
|
|
|
|
for (i=0; i<loop-1; i++, wnump--, resp--)
|
|
{
|
|
BN_ULONG q,l0;
|
|
/* the first part of the loop uses the top two words of
|
|
* snum and sdiv to calculate a BN_ULONG q such that
|
|
* | wnum - sdiv * q | < sdiv */
|
|
#if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
|
|
BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG);
|
|
q=bn_div_3_words(wnump,d1,d0);
|
|
#else
|
|
BN_ULONG n0,n1,rem=0;
|
|
|
|
n0=wnump[0];
|
|
n1=wnump[-1];
|
|
if (n0 == d0)
|
|
q=BN_MASK2;
|
|
else /* n0 < d0 */
|
|
{
|
|
#ifdef BN_LLONG
|
|
BN_ULLONG t2;
|
|
|
|
#if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
|
|
q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
|
|
#else
|
|
q=bn_div_words(n0,n1,d0);
|
|
#ifdef BN_DEBUG_LEVITTE
|
|
fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
|
|
X) -> 0x%08X\n",
|
|
n0, n1, d0, q);
|
|
#endif
|
|
#endif
|
|
|
|
#ifndef REMAINDER_IS_ALREADY_CALCULATED
|
|
/*
|
|
* rem doesn't have to be BN_ULLONG. The least we
|
|
* know it's less that d0, isn't it?
|
|
*/
|
|
rem=(n1-q*d0)&BN_MASK2;
|
|
#endif
|
|
t2=(BN_ULLONG)d1*q;
|
|
|
|
for (;;)
|
|
{
|
|
if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
|
|
break;
|
|
q--;
|
|
rem += d0;
|
|
if (rem < d0) break; /* don't let rem overflow */
|
|
t2 -= d1;
|
|
}
|
|
#else /* !BN_LLONG */
|
|
BN_ULONG t2l,t2h;
|
|
|
|
q=bn_div_words(n0,n1,d0);
|
|
#ifdef BN_DEBUG_LEVITTE
|
|
fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
|
|
X) -> 0x%08X\n",
|
|
n0, n1, d0, q);
|
|
#endif
|
|
#ifndef REMAINDER_IS_ALREADY_CALCULATED
|
|
rem=(n1-q*d0)&BN_MASK2;
|
|
#endif
|
|
|
|
#if defined(BN_UMULT_LOHI)
|
|
BN_UMULT_LOHI(t2l,t2h,d1,q);
|
|
#elif defined(BN_UMULT_HIGH)
|
|
t2l = d1 * q;
|
|
t2h = BN_UMULT_HIGH(d1,q);
|
|
#else
|
|
{
|
|
BN_ULONG ql, qh;
|
|
t2l=LBITS(d1); t2h=HBITS(d1);
|
|
ql =LBITS(q); qh =HBITS(q);
|
|
mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
|
|
}
|
|
#endif
|
|
|
|
for (;;)
|
|
{
|
|
if ((t2h < rem) ||
|
|
((t2h == rem) && (t2l <= wnump[-2])))
|
|
break;
|
|
q--;
|
|
rem += d0;
|
|
if (rem < d0) break; /* don't let rem overflow */
|
|
if (t2l < d1) t2h--; t2l -= d1;
|
|
}
|
|
#endif /* !BN_LLONG */
|
|
}
|
|
#endif /* !BN_DIV3W */
|
|
|
|
l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
|
|
tmp->d[div_n]=l0;
|
|
wnum.d--;
|
|
/* ingore top values of the bignums just sub the two
|
|
* BN_ULONG arrays with bn_sub_words */
|
|
if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1))
|
|
{
|
|
/* Note: As we have considered only the leading
|
|
* two BN_ULONGs in the calculation of q, sdiv * q
|
|
* might be greater than wnum (but then (q-1) * sdiv
|
|
* is less or equal than wnum)
|
|
*/
|
|
q--;
|
|
if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
|
|
/* we can't have an overflow here (assuming
|
|
* that q != 0, but if q == 0 then tmp is
|
|
* zero anyway) */
|
|
(*wnump)++;
|
|
}
|
|
/* store part of the result */
|
|
*resp = q;
|
|
}
|
|
bn_correct_top(snum);
|
|
if (rm != NULL)
|
|
{
|
|
/* Keep a copy of the neg flag in num because if rm==num
|
|
* BN_rshift() will overwrite it.
|
|
*/
|
|
int neg = num->neg;
|
|
BN_rshift(rm,snum,norm_shift);
|
|
if (!BN_is_zero(rm))
|
|
rm->neg = neg;
|
|
bn_check_top(rm);
|
|
}
|
|
BN_CTX_end(ctx);
|
|
return(1);
|
|
err:
|
|
bn_check_top(rm);
|
|
BN_CTX_end(ctx);
|
|
return(0);
|
|
}
|
|
|
|
|
|
/* BN_div_no_branch is a special version of BN_div. It does not contain
|
|
* branches that may leak sensitive information.
|
|
*/
|
|
static int BN_div_no_branch(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num,
|
|
const BIGNUM *divisor, BN_CTX *ctx)
|
|
{
|
|
int norm_shift,i,loop;
|
|
BIGNUM *tmp,wnum,*snum,*sdiv,*res;
|
|
BN_ULONG *resp,*wnump;
|
|
BN_ULONG d0,d1;
|
|
int num_n,div_n;
|
|
|
|
bn_check_top(dv);
|
|
bn_check_top(rm);
|
|
/* bn_check_top(num); */ /* 'num' has been checked in BN_div() */
|
|
bn_check_top(divisor);
|
|
|
|
if (BN_is_zero(divisor))
|
|
{
|
|
BNerr(BN_F_BN_DIV_NO_BRANCH,BN_R_DIV_BY_ZERO);
|
|
return(0);
|
|
}
|
|
|
|
BN_CTX_start(ctx);
|
|
tmp=BN_CTX_get(ctx);
|
|
snum=BN_CTX_get(ctx);
|
|
sdiv=BN_CTX_get(ctx);
|
|
if (dv == NULL)
|
|
res=BN_CTX_get(ctx);
|
|
else res=dv;
|
|
if (sdiv == NULL || res == NULL) goto err;
|
|
|
|
/* First we normalise the numbers */
|
|
norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
|
|
if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
|
|
sdiv->neg=0;
|
|
norm_shift+=BN_BITS2;
|
|
if (!(BN_lshift(snum,num,norm_shift))) goto err;
|
|
snum->neg=0;
|
|
|
|
/* Since we don't know whether snum is larger than sdiv,
|
|
* we pad snum with enough zeroes without changing its
|
|
* value.
|
|
*/
|
|
if (snum->top <= sdiv->top+1)
|
|
{
|
|
if (bn_wexpand(snum, sdiv->top + 2) == NULL) goto err;
|
|
for (i = snum->top; i < sdiv->top + 2; i++) snum->d[i] = 0;
|
|
snum->top = sdiv->top + 2;
|
|
}
|
|
else
|
|
{
|
|
if (bn_wexpand(snum, snum->top + 1) == NULL) goto err;
|
|
snum->d[snum->top] = 0;
|
|
snum->top ++;
|
|
}
|
|
|
|
div_n=sdiv->top;
|
|
num_n=snum->top;
|
|
loop=num_n-div_n;
|
|
/* Lets setup a 'window' into snum
|
|
* This is the part that corresponds to the current
|
|
* 'area' being divided */
|
|
wnum.neg = 0;
|
|
wnum.d = &(snum->d[loop]);
|
|
wnum.top = div_n;
|
|
/* only needed when BN_ucmp messes up the values between top and max */
|
|
wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */
|
|
|
|
/* Get the top 2 words of sdiv */
|
|
/* div_n=sdiv->top; */
|
|
d0=sdiv->d[div_n-1];
|
|
d1=(div_n == 1)?0:sdiv->d[div_n-2];
|
|
|
|
/* pointer to the 'top' of snum */
|
|
wnump= &(snum->d[num_n-1]);
|
|
|
|
/* Setup to 'res' */
|
|
res->neg= (num->neg^divisor->neg);
|
|
if (!bn_wexpand(res,(loop+1))) goto err;
|
|
res->top=loop-1;
|
|
resp= &(res->d[loop-1]);
|
|
|
|
/* space for temp */
|
|
if (!bn_wexpand(tmp,(div_n+1))) goto err;
|
|
|
|
/* if res->top == 0 then clear the neg value otherwise decrease
|
|
* the resp pointer */
|
|
if (res->top == 0)
|
|
res->neg = 0;
|
|
else
|
|
resp--;
|
|
|
|
for (i=0; i<loop-1; i++, wnump--, resp--)
|
|
{
|
|
BN_ULONG q,l0;
|
|
/* the first part of the loop uses the top two words of
|
|
* snum and sdiv to calculate a BN_ULONG q such that
|
|
* | wnum - sdiv * q | < sdiv */
|
|
#if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
|
|
BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG);
|
|
q=bn_div_3_words(wnump,d1,d0);
|
|
#else
|
|
BN_ULONG n0,n1,rem=0;
|
|
|
|
n0=wnump[0];
|
|
n1=wnump[-1];
|
|
if (n0 == d0)
|
|
q=BN_MASK2;
|
|
else /* n0 < d0 */
|
|
{
|
|
#ifdef BN_LLONG
|
|
BN_ULLONG t2;
|
|
|
|
#if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
|
|
q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
|
|
#else
|
|
q=bn_div_words(n0,n1,d0);
|
|
#ifdef BN_DEBUG_LEVITTE
|
|
fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
|
|
X) -> 0x%08X\n",
|
|
n0, n1, d0, q);
|
|
#endif
|
|
#endif
|
|
|
|
#ifndef REMAINDER_IS_ALREADY_CALCULATED
|
|
/*
|
|
* rem doesn't have to be BN_ULLONG. The least we
|
|
* know it's less that d0, isn't it?
|
|
*/
|
|
rem=(n1-q*d0)&BN_MASK2;
|
|
#endif
|
|
t2=(BN_ULLONG)d1*q;
|
|
|
|
for (;;)
|
|
{
|
|
if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
|
|
break;
|
|
q--;
|
|
rem += d0;
|
|
if (rem < d0) break; /* don't let rem overflow */
|
|
t2 -= d1;
|
|
}
|
|
#else /* !BN_LLONG */
|
|
BN_ULONG t2l,t2h;
|
|
|
|
q=bn_div_words(n0,n1,d0);
|
|
#ifdef BN_DEBUG_LEVITTE
|
|
fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
|
|
X) -> 0x%08X\n",
|
|
n0, n1, d0, q);
|
|
#endif
|
|
#ifndef REMAINDER_IS_ALREADY_CALCULATED
|
|
rem=(n1-q*d0)&BN_MASK2;
|
|
#endif
|
|
|
|
#if defined(BN_UMULT_LOHI)
|
|
BN_UMULT_LOHI(t2l,t2h,d1,q);
|
|
#elif defined(BN_UMULT_HIGH)
|
|
t2l = d1 * q;
|
|
t2h = BN_UMULT_HIGH(d1,q);
|
|
#else
|
|
{
|
|
BN_ULONG ql, qh;
|
|
t2l=LBITS(d1); t2h=HBITS(d1);
|
|
ql =LBITS(q); qh =HBITS(q);
|
|
mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
|
|
}
|
|
#endif
|
|
|
|
for (;;)
|
|
{
|
|
if ((t2h < rem) ||
|
|
((t2h == rem) && (t2l <= wnump[-2])))
|
|
break;
|
|
q--;
|
|
rem += d0;
|
|
if (rem < d0) break; /* don't let rem overflow */
|
|
if (t2l < d1) t2h--; t2l -= d1;
|
|
}
|
|
#endif /* !BN_LLONG */
|
|
}
|
|
#endif /* !BN_DIV3W */
|
|
|
|
l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
|
|
tmp->d[div_n]=l0;
|
|
wnum.d--;
|
|
/* ingore top values of the bignums just sub the two
|
|
* BN_ULONG arrays with bn_sub_words */
|
|
if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1))
|
|
{
|
|
/* Note: As we have considered only the leading
|
|
* two BN_ULONGs in the calculation of q, sdiv * q
|
|
* might be greater than wnum (but then (q-1) * sdiv
|
|
* is less or equal than wnum)
|
|
*/
|
|
q--;
|
|
if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
|
|
/* we can't have an overflow here (assuming
|
|
* that q != 0, but if q == 0 then tmp is
|
|
* zero anyway) */
|
|
(*wnump)++;
|
|
}
|
|
/* store part of the result */
|
|
*resp = q;
|
|
}
|
|
bn_correct_top(snum);
|
|
if (rm != NULL)
|
|
{
|
|
/* Keep a copy of the neg flag in num because if rm==num
|
|
* BN_rshift() will overwrite it.
|
|
*/
|
|
int neg = num->neg;
|
|
BN_rshift(rm,snum,norm_shift);
|
|
if (!BN_is_zero(rm))
|
|
rm->neg = neg;
|
|
bn_check_top(rm);
|
|
}
|
|
bn_correct_top(res);
|
|
BN_CTX_end(ctx);
|
|
return(1);
|
|
err:
|
|
bn_check_top(rm);
|
|
BN_CTX_end(ctx);
|
|
return(0);
|
|
}
|
|
|
|
#endif
|
|
|