bn_div.c

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/* crypto/bn/bn_div.c */
/* Copyright (C) 1995-1998 Eric Young ([email protected])
 * All rights reserved.
 *
 * This package is an SSL implementation written
 * by Eric Young ([email protected]).
 * 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 ([email protected]).
 *
 * 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 ([email protected])"
 *    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 ([email protected])"
 *
 * 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>
#if defined( INC_ALL )
  #include "bn_lcl.h"
#else
  #include "bn/bn_lcl.h"
#endif /* Compiler-specific includes */

/* Apple ship their own private fork of gcc rather than any standard version,
   and going by its behaviour across several releases they must be basing it 
   on alpha versions that they dig up somewhere.  One of the things that 
   version 4.0.1 on Intel 32-bit shows up is an optimiser bug with -O3 where 
   the output generated for the code just before the bn_div loop bears no 
   relation whatsoever to the source code.  Dropping in a printf() at -03 
   resolves this, with the output being identical to what it would be with 
   -O2.  There's at least one silver lining with Apple's buggy custom version 
   of gcc, it gives you the ability to selectively turn off optimisation on 
   a per-function level (which standard gcc doesn't), see 
   http://developer.apple.com/documentation/DeveloperTools/gcc-4.0.1/gcc/Darwin-Pragmas.html
   So we use the following pragma to reduce the optimisation level from -O3 
   (produces garbled output) to -O2 (produces output identical to -O3 but 
   without the garbling) for Apple's buggy gcc on 32-bit x86 */

#if defined( __APPLE__ ) && defined( __GNUC__ ) && \
        ( __GNUC__ == 4 ) && ( __GNUC_MINOR__ == 0 ) && defined( __i386__ )
  #pragma optimization_level 2
#endif /* Apple gcc 4.0.x with buggy optimisation - pcg */

/* 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);
    bn_wexpand(dv,1);
    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:-)
    *
    *                   <[email protected]>
    */
#  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!
    *                   <[email protected]>
    */
#  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 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.
 */
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;

    if (dv)
        bn_check_top(dv);
    if (rm)
        bn_check_top(rm);
    bn_check_top(num);
    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 0                                           /* pcg */
    if (sdiv == NULL || res == NULL) goto err;
#else
    if (sdiv == NULL || res == NULL || \
        tmp == NULL || snum == NULL) goto err;  /* pcg */
#endif /* 0 */

    /* 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;
#if !defined( BN_UMULT_LOHI ) && !defined( BN_UMULT_HIGH )  /* pcg */
            BN_ULONG ql,qh;
#endif 

            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
            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:
    if (rm)
        bn_check_top(rm);
    BN_CTX_end(ctx);
    return(0);
    }

#endif