--- /dev/null
+/* 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>
+ */
+#undef bn_div_words
+# 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>
+ */
+# undef bn_div_words
+# 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;
+ int no_branch=0;
+
+ /* 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))
+ {
+ no_branch=1;
+ }
+
+ 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 (!no_branch && 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;
+
+ if (no_branch)
+ {
+ /* 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-no_branch;
+ resp= &(res->d[loop-1]);
+
+ /* space for temp */
+ if (!bn_wexpand(tmp,(div_n+1))) goto err;
+
+ if (!no_branch)
+ {
+ 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);
+ }
+ if (no_branch) bn_correct_top(res);
+ BN_CTX_end(ctx);
+ return(1);
+err:
+ bn_check_top(rm);
+ BN_CTX_end(ctx);
+ return(0);
+ }
+#endif
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