openssl/crypto/bn/bn_asm.c

/* crypto/bn/bn_asm.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.]
 */

#ifndef BN_DEBUG
# undef NDEBUG /* avoid conflicting definitions */
# define NDEBUG
#endif

#include <stdio.h>
#include <assert.h>
#include "cryptlib.h"
#include "bn_lcl.h"

#if defined(BN_LLONG) || defined(BN_UMULT_HIGH)

BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w)
	{
	BN_ULONG c1=0;

	assert(num >= 0);
	if (num <= 0) return(c1);

#ifndef OPENSSL_SMALL_FOOTPRINT
	while (num&~3)
		{
		mul_add(rp[0],ap[0],w,c1);
		mul_add(rp[1],ap[1],w,c1);
		mul_add(rp[2],ap[2],w,c1);
		mul_add(rp[3],ap[3],w,c1);
		ap+=4; rp+=4; num-=4;
		}
#endif
	while (num)
		{
		mul_add(rp[0],ap[0],w,c1);
		ap++; rp++; num--;
		}
	
	return(c1);
	} 

BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w)
	{
	BN_ULONG c1=0;

	assert(num >= 0);
	if (num <= 0) return(c1);

#ifndef OPENSSL_SMALL_FOOTPRINT
	while (num&~3)
		{
		mul(rp[0],ap[0],w,c1);
		mul(rp[1],ap[1],w,c1);
		mul(rp[2],ap[2],w,c1);
		mul(rp[3],ap[3],w,c1);
		ap+=4; rp+=4; num-=4;
		}
#endif
	while (num)
		{
		mul(rp[0],ap[0],w,c1);
		ap++; rp++; num--;
		}
	return(c1);
	} 

void bn_sqr_words(BN_ULONG *r, const BN_ULONG *a, int n)
        {
	assert(n >= 0);
	if (n <= 0) return;

#ifndef OPENSSL_SMALL_FOOTPRINT
	while (n&~3)
		{
		sqr(r[0],r[1],a[0]);
		sqr(r[2],r[3],a[1]);
		sqr(r[4],r[5],a[2]);
		sqr(r[6],r[7],a[3]);
		a+=4; r+=8; n-=4;
		}
#endif
	while (n)
		{
		sqr(r[0],r[1],a[0]);
		a++; r+=2; n--;
		}
	}

#else /* !(defined(BN_LLONG) || defined(BN_UMULT_HIGH)) */

BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w)
	{
	BN_ULONG c=0;
	BN_ULONG bl,bh;

	assert(num >= 0);
	if (num <= 0) return((BN_ULONG)0);

	bl=LBITS(w);
	bh=HBITS(w);

#ifndef OPENSSL_SMALL_FOOTPRINT
	while (num&~3)
		{
		mul_add(rp[0],ap[0],bl,bh,c);
		mul_add(rp[1],ap[1],bl,bh,c);
		mul_add(rp[2],ap[2],bl,bh,c);
		mul_add(rp[3],ap[3],bl,bh,c);
		ap+=4; rp+=4; num-=4;
		}
#endif
	while (num)
		{
		mul_add(rp[0],ap[0],bl,bh,c);
		ap++; rp++; num--;
		}
	return(c);
	} 

BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w)
	{
	BN_ULONG carry=0;
	BN_ULONG bl,bh;

	assert(num >= 0);
	if (num <= 0) return((BN_ULONG)0);

	bl=LBITS(w);
	bh=HBITS(w);

#ifndef OPENSSL_SMALL_FOOTPRINT
	while (num&~3)
		{
		mul(rp[0],ap[0],bl,bh,carry);
		mul(rp[1],ap[1],bl,bh,carry);
		mul(rp[2],ap[2],bl,bh,carry);
		mul(rp[3],ap[3],bl,bh,carry);
		ap+=4; rp+=4; num-=4;
		}
#endif
	while (num)
		{
		mul(rp[0],ap[0],bl,bh,carry);
		ap++; rp++; num--;
		}
	return(carry);
	} 

void bn_sqr_words(BN_ULONG *r, const BN_ULONG *a, int n)
        {
	assert(n >= 0);
	if (n <= 0) return;

#ifndef OPENSSL_SMALL_FOOTPRINT
	while (n&~3)
		{
		sqr64(r[0],r[1],a[0]);
		sqr64(r[2],r[3],a[1]);
		sqr64(r[4],r[5],a[2]);
		sqr64(r[6],r[7],a[3]);
		a+=4; r+=8; n-=4;
		}
#endif
	while (n)
		{
		sqr64(r[0],r[1],a[0]);
		a++; r+=2; n--;
		}
	}

#endif /* !(defined(BN_LLONG) || defined(BN_UMULT_HIGH)) */

#if defined(BN_LLONG) && defined(BN_DIV2W)

BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d)
	{
	return((BN_ULONG)(((((BN_ULLONG)h)<<BN_BITS2)|l)/(BN_ULLONG)d));
	}

#else

/* Divide h,l by d and return the result. */
/* I need to test this some more :-( */
BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d)
	{
	BN_ULONG dh,dl,q,ret=0,th,tl,t;
	int i,count=2;

	if (d == 0) return(BN_MASK2);

	i=BN_num_bits_word(d);
	assert((i == BN_BITS2) || (h <= (BN_ULONG)1<<i));

	i=BN_BITS2-i;
	if (h >= d) h-=d;

	if (i)
		{
		d<<=i;
		h=(h<<i)|(l>>(BN_BITS2-i));
		l<<=i;
		}
	dh=(d&BN_MASK2h)>>BN_BITS4;
	dl=(d&BN_MASK2l);
	for (;;)
		{
		if ((h>>BN_BITS4) == dh)
			q=BN_MASK2l;
		else
			q=h/dh;

		th=q*dh;
		tl=dl*q;
		for (;;)
			{
			t=h-th;
			if ((t&BN_MASK2h) ||
				((tl) <= (
					(t<<BN_BITS4)|
					((l&BN_MASK2h)>>BN_BITS4))))
				break;
			q--;
			th-=dh;
			tl-=dl;
			}
		t=(tl>>BN_BITS4);
		tl=(tl<<BN_BITS4)&BN_MASK2h;
		th+=t;

		if (l < tl) th++;
		l-=tl;
		if (h < th)
			{
			h+=d;
			q--;
			}
		h-=th;

		if (--count == 0) break;

		ret=q<<BN_BITS4;
		h=((h<<BN_BITS4)|(l>>BN_BITS4))&BN_MASK2;
		l=(l&BN_MASK2l)<<BN_BITS4;
		}
	ret|=q;
	return(ret);
	}
#endif /* !defined(BN_LLONG) && defined(BN_DIV2W) */

#ifdef BN_LLONG
BN_ULONG bn_add_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, int n)
        {
	BN_ULLONG ll=0;

	assert(n >= 0);
	if (n <= 0) return((BN_ULONG)0);

#ifndef OPENSSL_SMALL_FOOTPRINT
	while (n&~3)
		{
		ll+=(BN_ULLONG)a[0]+b[0];
		r[0]=(BN_ULONG)ll&BN_MASK2;
		ll>>=BN_BITS2;
		ll+=(BN_ULLONG)a[1]+b[1];
		r[1]=(BN_ULONG)ll&BN_MASK2;
		ll>>=BN_BITS2;
		ll+=(BN_ULLONG)a[2]+b[2];
		r[2]=(BN_ULONG)ll&BN_MASK2;
		ll>>=BN_BITS2;
		ll+=(BN_ULLONG)a[3]+b[3];
		r[3]=(BN_ULONG)ll&BN_MASK2;
		ll>>=BN_BITS2;
		a+=4; b+=4; r+=4; n-=4;
		}
#endif
	while (n)
		{
		ll+=(BN_ULLONG)a[0]+b[0];
		r[0]=(BN_ULONG)ll&BN_MASK2;
		ll>>=BN_BITS2;
		a++; b++; r++; n--;
		}
	return((BN_ULONG)ll);
	}
#else /* !BN_LLONG */
BN_ULONG bn_add_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, int n)
        {
	BN_ULONG c,l,t;

	assert(n >= 0);
	if (n <= 0) return((BN_ULONG)0);

	c=0;
#ifndef OPENSSL_SMALL_FOOTPRINT
	while (n&~3)
		{
		t=a[0];
		t=(t+c)&BN_MASK2;
		c=(t < c);
		l=(t+b[0])&BN_MASK2;
		c+=(l < t);
		r[0]=l;
		t=a[1];
		t=(t+c)&BN_MASK2;
		c=(t < c);
		l=(t+b[1])&BN_MASK2;
		c+=(l < t);
		r[1]=l;
		t=a[2];
		t=(t+c)&BN_MASK2;
		c=(t < c);
		l=(t+b[2])&BN_MASK2;
		c+=(l < t);
		r[2]=l;
		t=a[3];
		t=(t+c)&BN_MASK2;
		c=(t < c);
		l=(t+b[3])&BN_MASK2;
		c+=(l < t);
		r[3]=l;
		a+=4; b+=4; r+=4; n-=4;
		}
#endif
	while(n)
		{
		t=a[0];
		t=(t+c)&BN_MASK2;
		c=(t < c);
		l=(t+b[0])&BN_MASK2;
		c+=(l < t);
		r[0]=l;
		a++; b++; r++; n--;
		}
	return((BN_ULONG)c);
	}
#endif /* !BN_LLONG */

BN_ULONG bn_sub_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, int n)
        {
	BN_ULONG t1,t2;
	int c=0;

	assert(n >= 0);
	if (n <= 0) return((BN_ULONG)0);

#ifndef OPENSSL_SMALL_FOOTPRINT
	while (n&~3)
		{
		t1=a[0]; t2=b[0];
		r[0]=(t1-t2-c)&BN_MASK2;
		if (t1 != t2) c=(t1 < t2);
		t1=a[1]; t2=b[1];
		r[1]=(t1-t2-c)&BN_MASK2;
		if (t1 != t2) c=(t1 < t2);
		t1=a[2]; t2=b[2];
		r[2]=(t1-t2-c)&BN_MASK2;
		if (t1 != t2) c=(t1 < t2);
		t1=a[3]; t2=b[3];
		r[3]=(t1-t2-c)&BN_MASK2;
		if (t1 != t2) c=(t1 < t2);
		a+=4; b+=4; r+=4; n-=4;
		}
#endif
	while (n)
		{
		t1=a[0]; t2=b[0];
		r[0]=(t1-t2-c)&BN_MASK2;
		if (t1 != t2) c=(t1 < t2);
		a++; b++; r++; n--;
		}
	return(c);
	}

#if defined(BN_MUL_COMBA) && !defined(OPENSSL_SMALL_FOOTPRINT)

#undef bn_mul_comba8
#undef bn_mul_comba4
#undef bn_sqr_comba8
#undef bn_sqr_comba4

/* mul_add_c(a,b,c0,c1,c2)  -- c+=a*b for three word number c=(c2,c1,c0) */
/* mul_add_c2(a,b,c0,c1,c2) -- c+=2*a*b for three word number c=(c2,c1,c0) */
/* sqr_add_c(a,i,c0,c1,c2)  -- c+=a[i]^2 for three word number c=(c2,c1,c0) */
/* sqr_add_c2(a,i,c0,c1,c2) -- c+=2*a[i]*a[j] for three word number c=(c2,c1,c0) */

#ifdef BN_LLONG
#define mul_add_c(a,b,c0,c1,c2) \
	t=(BN_ULLONG)a*b; \
	t1=(BN_ULONG)Lw(t); \
	t2=(BN_ULONG)Hw(t); \
	c0=(c0+t1)&BN_MASK2; if ((c0) < t1) t2++; \
	c1=(c1+t2)&BN_MASK2; if ((c1) < t2) c2++;

#define mul_add_c2(a,b,c0,c1,c2) \
	t=(BN_ULLONG)a*b; \
	tt=(t+t)&BN_MASK; \
	if (tt < t) c2++; \
	t1=(BN_ULONG)Lw(tt); \
	t2=(BN_ULONG)Hw(tt); \
	c0=(c0+t1)&BN_MASK2;  \
	if ((c0 < t1) && (((++t2)&BN_MASK2) == 0)) c2++; \
	c1=(c1+t2)&BN_MASK2; if ((c1) < t2) c2++;

#define sqr_add_c(a,i,c0,c1,c2) \
	t=(BN_ULLONG)a[i]*a[i]; \
	t1=(BN_ULONG)Lw(t); \
	t2=(BN_ULONG)Hw(t); \
	c0=(c0+t1)&BN_MASK2; if ((c0) < t1) t2++; \
	c1=(c1+t2)&BN_MASK2; if ((c1) < t2) c2++;

#define sqr_add_c2(a,i,j,c0,c1,c2) \
	mul_add_c2((a)[i],(a)[j],c0,c1,c2)

#elif defined(BN_UMULT_LOHI)

#define mul_add_c(a,b,c0,c1,c2)	{	\
	BN_ULONG ta=(a),tb=(b);		\
	BN_UMULT_LOHI(t1,t2,ta,tb);	\
	c0 += t1; t2 += (c0<t1)?1:0;	\
	c1 += t2; c2 += (c1<t2)?1:0;	\
	}

#define mul_add_c2(a,b,c0,c1,c2) {	\
	BN_ULONG ta=(a),tb=(b),t0;	\
	BN_UMULT_LOHI(t0,t1,ta,tb);	\
	t2 = t1+t1; c2 += (t2<t1)?1:0;	\
	t1 = t0+t0; t2 += (t1<t0)?1:0;	\
	c0 += t1; t2 += (c0<t1)?1:0;	\
	c1 += t2; c2 += (c1<t2)?1:0;	\
	}

#define sqr_add_c(a,i,c0,c1,c2)	{	\
	BN_ULONG ta=(a)[i];		\
	BN_UMULT_LOHI(t1,t2,ta,ta);	\
	c0 += t1; t2 += (c0<t1)?1:0;	\
	c1 += t2; c2 += (c1<t2)?1:0;	\
	}

#define sqr_add_c2(a,i,j,c0,c1,c2)	\
	mul_add_c2((a)[i],(a)[j],c0,c1,c2)

#elif defined(BN_UMULT_HIGH)

#define mul_add_c(a,b,c0,c1,c2)	{	\
	BN_ULONG ta=(a),tb=(b);		\
	t1 = ta * tb;			\
	t2 = BN_UMULT_HIGH(ta,tb);	\
	c0 += t1; t2 += (c0<t1)?1:0;	\
	c1 += t2; c2 += (c1<t2)?1:0;	\
	}

#define mul_add_c2(a,b,c0,c1,c2) {	\
	BN_ULONG ta=(a),tb=(b),t0;	\
	t1 = BN_UMULT_HIGH(ta,tb);	\
	t0 = ta * tb;			\
	t2 = t1+t1; c2 += (t2<t1)?1:0;	\
	t1 = t0+t0; t2 += (t1<t0)?1:0;	\
	c0 += t1; t2 += (c0<t1)?1:0;	\
	c1 += t2; c2 += (c1<t2)?1:0;	\
	}

#define sqr_add_c(a,i,c0,c1,c2)	{	\
	BN_ULONG ta=(a)[i];		\
	t1 = ta * ta;			\
	t2 = BN_UMULT_HIGH(ta,ta);	\
	c0 += t1; t2 += (c0<t1)?1:0;	\
	c1 += t2; c2 += (c1<t2)?1:0;	\
	}

#define sqr_add_c2(a,i,j,c0,c1,c2)	\
	mul_add_c2((a)[i],(a)[j],c0,c1,c2)

#else /* !BN_LLONG */
#define mul_add_c(a,b,c0,c1,c2) \
	t1=LBITS(a); t2=HBITS(a); \
	bl=LBITS(b); bh=HBITS(b); \
	mul64(t1,t2,bl,bh); \
	c0=(c0+t1)&BN_MASK2; if ((c0) < t1) t2++; \
	c1=(c1+t2)&BN_MASK2; if ((c1) < t2) c2++;

#define mul_add_c2(a,b,c0,c1,c2) \
	t1=LBITS(a); t2=HBITS(a); \
	bl=LBITS(b); bh=HBITS(b); \
	mul64(t1,t2,bl,bh); \
	if (t2 & BN_TBIT) c2++; \
	t2=(t2+t2)&BN_MASK2; \
	if (t1 & BN_TBIT) t2++; \
	t1=(t1+t1)&BN_MASK2; \
	c0=(c0+t1)&BN_MASK2;  \
	if ((c0 < t1) && (((++t2)&BN_MASK2) == 0)) c2++; \
	c1=(c1+t2)&BN_MASK2; if ((c1) < t2) c2++;

#define sqr_add_c(a,i,c0,c1,c2) \
	sqr64(t1,t2,(a)[i]); \
	c0=(c0+t1)&BN_MASK2; if ((c0) < t1) t2++; \
	c1=(c1+t2)&BN_MASK2; if ((c1) < t2) c2++;

#define sqr_add_c2(a,i,j,c0,c1,c2) \
	mul_add_c2((a)[i],(a)[j],c0,c1,c2)
#endif /* !BN_LLONG */

void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
	{
#ifdef BN_LLONG
	BN_ULLONG t;
#else
	BN_ULONG bl,bh;
#endif
	BN_ULONG t1,t2;
	BN_ULONG c1,c2,c3;

	c1=0;
	c2=0;
	c3=0;
	mul_add_c(a[0],b[0],c1,c2,c3);
	r[0]=c1;
	c1=0;
	mul_add_c(a[0],b[1],c2,c3,c1);
	mul_add_c(a[1],b[0],c2,c3,c1);
	r[1]=c2;
	c2=0;
	mul_add_c(a[2],b[0],c3,c1,c2);
	mul_add_c(a[1],b[1],c3,c1,c2);
	mul_add_c(a[0],b[2],c3,c1,c2);
	r[2]=c3;
	c3=0;
	mul_add_c(a[0],b[3],c1,c2,c3);
	mul_add_c(a[1],b[2],c1,c2,c3);
	mul_add_c(a[2],b[1],c1,c2,c3);
	mul_add_c(a[3],b[0],c1,c2,c3);
	r[3]=c1;
	c1=0;
	mul_add_c(a[4],b[0],c2,c3,c1);
	mul_add_c(a[3],b[1],c2,c3,c1);
	mul_add_c(a[2],b[2],c2,c3,c1);
	mul_add_c(a[1],b[3],c2,c3,c1);
	mul_add_c(a[0],b[4],c2,c3,c1);
	r[4]=c2;
	c2=0;
	mul_add_c(a[0],b[5],c3,c1,c2);
	mul_add_c(a[1],b[4],c3,c1,c2);
	mul_add_c(a[2],b[3],c3,c1,c2);
	mul_add_c(a[3],b[2],c3,c1,c2);
	mul_add_c(a[4],b[1],c3,c1,c2);
	mul_add_c(a[5],b[0],c3,c1,c2);
	r[5]=c3;
	c3=0;
	mul_add_c(a[6],b[0],c1,c2,c3);
	mul_add_c(a[5],b[1],c1,c2,c3);
	mul_add_c(a[4],b[2],c1,c2,c3);
	mul_add_c(a[3],b[3],c1,c2,c3);
	mul_add_c(a[2],b[4],c1,c2,c3);
	mul_add_c(a[1],b[5],c1,c2,c3);
	mul_add_c(a[0],b[6],c1,c2,c3);
	r[6]=c1;
	c1=0;
	mul_add_c(a[0],b[7],c2,c3,c1);
	mul_add_c(a[1],b[6],c2,c3,c1);
	mul_add_c(a[2],b[5],c2,c3,c1);
	mul_add_c(a[3],b[4],c2,c3,c1);
	mul_add_c(a[4],b[3],c2,c3,c1);
	mul_add_c(a[5],b[2],c2,c3,c1);
	mul_add_c(a[6],b[1],c2,c3,c1);
	mul_add_c(a[7],b[0],c2,c3,c1);
	r[7]=c2;
	c2=0;
	mul_add_c(a[7],b[1],c3,c1,c2);
	mul_add_c(a[6],b[2],c3,c1,c2);
	mul_add_c(a[5],b[3],c3,c1,c2);
	mul_add_c(a[4],b[4],c3,c1,c2);
	mul_add_c(a[3],b[5],c3,c1,c2);
	mul_add_c(a[2],b[6],c3,c1,c2);
	mul_add_c(a[1],b[7],c3,c1,c2);
	r[8]=c3;
	c3=0;
	mul_add_c(a[2],b[7],c1,c2,c3);
	mul_add_c(a[3],b[6],c1,c2,c3);
	mul_add_c(a[4],b[5],c1,c2,c3);
	mul_add_c(a[5],b[4],c1,c2,c3);
	mul_add_c(a[6],b[3],c1,c2,c3);
	mul_add_c(a[7],b[2],c1,c2,c3);
	r[9]=c1;
	c1=0;
	mul_add_c(a[7],b[3],c2,c3,c1);
	mul_add_c(a[6],b[4],c2,c3,c1);
	mul_add_c(a[5],b[5],c2,c3,c1);
	mul_add_c(a[4],b[6],c2,c3,c1);
	mul_add_c(a[3],b[7],c2,c3,c1);
	r[10]=c2;
	c2=0;
	mul_add_c(a[4],b[7],c3,c1,c2);
	mul_add_c(a[5],b[6],c3,c1,c2);
	mul_add_c(a[6],b[5],c3,c1,c2);
	mul_add_c(a[7],b[4],c3,c1,c2);
	r[11]=c3;
	c3=0;
	mul_add_c(a[7],b[5],c1,c2,c3);
	mul_add_c(a[6],b[6],c1,c2,c3);
	mul_add_c(a[5],b[7],c1,c2,c3);
	r[12]=c1;
	c1=0;
	mul_add_c(a[6],b[7],c2,c3,c1);
	mul_add_c(a[7],b[6],c2,c3,c1);
	r[13]=c2;
	c2=0;
	mul_add_c(a[7],b[7],c3,c1,c2);
	r[14]=c3;
	r[15]=c1;
	}

void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
	{
#ifdef BN_LLONG
	BN_ULLONG t;
#else
	BN_ULONG bl,bh;
#endif
	BN_ULONG t1,t2;
	BN_ULONG c1,c2,c3;

	c1=0;
	c2=0;
	c3=0;
	mul_add_c(a[0],b[0],c1,c2,c3);
	r[0]=c1;
	c1=0;
	mul_add_c(a[0],b[1],c2,c3,c1);
	mul_add_c(a[1],b[0],c2,c3,c1);
	r[1]=c2;
	c2=0;
	mul_add_c(a[2],b[0],c3,c1,c2);
	mul_add_c(a[1],b[1],c3,c1,c2);
	mul_add_c(a[0],b[2],c3,c1,c2);
	r[2]=c3;
	c3=0;
	mul_add_c(a[0],b[3],c1,c2,c3);
	mul_add_c(a[1],b[2],c1,c2,c3);
	mul_add_c(a[2],b[1],c1,c2,c3);
	mul_add_c(a[3],b[0],c1,c2,c3);
	r[3]=c1;
	c1=0;
	mul_add_c(a[3],b[1],c2,c3,c1);
	mul_add_c(a[2],b[2],c2,c3,c1);
	mul_add_c(a[1],b[3],c2,c3,c1);
	r[4]=c2;
	c2=0;
	mul_add_c(a[2],b[3],c3,c1,c2);
	mul_add_c(a[3],b[2],c3,c1,c2);
	r[5]=c3;
	c3=0;
	mul_add_c(a[3],b[3],c1,c2,c3);
	r[6]=c1;
	r[7]=c2;
	}

void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a)
	{
#ifdef BN_LLONG
	BN_ULLONG t,tt;
#else
	BN_ULONG bl,bh;
#endif
	BN_ULONG t1,t2;
	BN_ULONG c1,c2,c3;

	c1=0;
	c2=0;
	c3=0;
	sqr_add_c(a,0,c1,c2,c3);
	r[0]=c1;
	c1=0;
	sqr_add_c2(a,1,0,c2,c3,c1);
	r[1]=c2;
	c2=0;
	sqr_add_c(a,1,c3,c1,c2);
	sqr_add_c2(a,2,0,c3,c1,c2);
	r[2]=c3;
	c3=0;
	sqr_add_c2(a,3,0,c1,c2,c3);
	sqr_add_c2(a,2,1,c1,c2,c3);
	r[3]=c1;
	c1=0;
	sqr_add_c(a,2,c2,c3,c1);
	sqr_add_c2(a,3,1,c2,c3,c1);
	sqr_add_c2(a,4,0,c2,c3,c1);
	r[4]=c2;
	c2=0;
	sqr_add_c2(a,5,0,c3,c1,c2);
	sqr_add_c2(a,4,1,c3,c1,c2);
	sqr_add_c2(a,3,2,c3,c1,c2);
	r[5]=c3;
	c3=0;
	sqr_add_c(a,3,c1,c2,c3);
	sqr_add_c2(a,4,2,c1,c2,c3);
	sqr_add_c2(a,5,1,c1,c2,c3);
	sqr_add_c2(a,6,0,c1,c2,c3);
	r[6]=c1;
	c1=0;
	sqr_add_c2(a,7,0,c2,c3,c1);
	sqr_add_c2(a,6,1,c2,c3,c1);
	sqr_add_c2(a,5,2,c2,c3,c1);
	sqr_add_c2(a,4,3,c2,c3,c1);
	r[7]=c2;
	c2=0;
	sqr_add_c(a,4,c3,c1,c2);
	sqr_add_c2(a,5,3,c3,c1,c2);
	sqr_add_c2(a,6,2,c3,c1,c2);
	sqr_add_c2(a,7,1,c3,c1,c2);
	r[8]=c3;
	c3=0;
	sqr_add_c2(a,7,2,c1,c2,c3);
	sqr_add_c2(a,6,3,c1,c2,c3);
	sqr_add_c2(a,5,4,c1,c2,c3);
	r[9]=c1;
	c1=0;
	sqr_add_c(a,5,c2,c3,c1);
	sqr_add_c2(a,6,4,c2,c3,c1);
	sqr_add_c2(a,7,3,c2,c3,c1);
	r[10]=c2;
	c2=0;
	sqr_add_c2(a,7,4,c3,c1,c2);
	sqr_add_c2(a,6,5,c3,c1,c2);
	r[11]=c3;
	c3=0;
	sqr_add_c(a,6,c1,c2,c3);
	sqr_add_c2(a,7,5,c1,c2,c3);
	r[12]=c1;
	c1=0;
	sqr_add_c2(a,7,6,c2,c3,c1);
	r[13]=c2;
	c2=0;
	sqr_add_c(a,7,c3,c1,c2);
	r[14]=c3;
	r[15]=c1;
	}

void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a)
	{
#ifdef BN_LLONG
	BN_ULLONG t,tt;
#else
	BN_ULONG bl,bh;
#endif
	BN_ULONG t1,t2;
	BN_ULONG c1,c2,c3;

	c1=0;
	c2=0;
	c3=0;
	sqr_add_c(a,0,c1,c2,c3);
	r[0]=c1;
	c1=0;
	sqr_add_c2(a,1,0,c2,c3,c1);
	r[1]=c2;
	c2=0;
	sqr_add_c(a,1,c3,c1,c2);
	sqr_add_c2(a,2,0,c3,c1,c2);
	r[2]=c3;
	c3=0;
	sqr_add_c2(a,3,0,c1,c2,c3);
	sqr_add_c2(a,2,1,c1,c2,c3);
	r[3]=c1;
	c1=0;
	sqr_add_c(a,2,c2,c3,c1);
	sqr_add_c2(a,3,1,c2,c3,c1);
	r[4]=c2;
	c2=0;
	sqr_add_c2(a,3,2,c3,c1,c2);
	r[5]=c3;
	c3=0;
	sqr_add_c(a,3,c1,c2,c3);
	r[6]=c1;
	r[7]=c2;
	}

#ifdef OPENSSL_NO_ASM
#ifdef OPENSSL_BN_ASM_MONT
#include <alloca.h>
/*
 * This is essentially reference implementation, which may or may not
 * result in performance improvement. E.g. on IA-32 this routine was
 * observed to give 40% faster rsa1024 private key operations and 10%
 * faster rsa4096 ones, while on AMD64 it improves rsa1024 sign only
 * by 10% and *worsens* rsa4096 sign by 15%. Once again, it's a
 * reference implementation, one to be used as starting point for
 * platform-specific assembler. Mentioned numbers apply to compiler
 * generated code compiled with and without -DOPENSSL_BN_ASM_MONT and
 * can vary not only from platform to platform, but even for compiler
 * versions. Assembler vs. assembler improvement coefficients can
 * [and are known to] differ and are to be documented elsewhere.
 */
int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, const BN_ULONG *np,const BN_ULONG *n0p, int num)
	{
	BN_ULONG c0,c1,ml,*tp,n0;
#ifdef mul64
	BN_ULONG mh;
#endif
	volatile BN_ULONG *vp;
	int i=0,j;

#if 0	/* template for platform-specific implementation */
	if (ap==bp)	return bn_sqr_mont(rp,ap,np,n0p,num);
#endif
	vp = tp = alloca((num+2)*sizeof(BN_ULONG));

	n0 = *n0p;

	c0 = 0;
	ml = bp[0];
#ifdef mul64
	mh = HBITS(ml);
	ml = LBITS(ml);
	for (j=0;j<num;++j)
		mul(tp[j],ap[j],ml,mh,c0);
#else
	for (j=0;j<num;++j)
		mul(tp[j],ap[j],ml,c0);
#endif

	tp[num]   = c0;
	tp[num+1] = 0;
	goto enter;

	for(i=0;i<num;i++)
		{
		c0 = 0;
		ml = bp[i];
#ifdef mul64
		mh = HBITS(ml);
		ml = LBITS(ml);
		for (j=0;j<num;++j)
			mul_add(tp[j],ap[j],ml,mh,c0);
#else
		for (j=0;j<num;++j)
			mul_add(tp[j],ap[j],ml,c0);
#endif
		c1 = (tp[num] + c0)&BN_MASK2;
		tp[num]   = c1;
		tp[num+1] = (c1<c0?1:0);
	enter:
		c1  = tp[0];
		ml = (c1*n0)&BN_MASK2;
		c0 = 0;
#ifdef mul64
		mh = HBITS(ml);
		ml = LBITS(ml);
		mul_add(c1,np[0],ml,mh,c0);
#else
		mul_add(c1,ml,np[0],c0);
#endif
		for(j=1;j<num;j++)
			{
			c1 = tp[j];
#ifdef mul64
			mul_add(c1,np[j],ml,mh,c0);
#else
			mul_add(c1,ml,np[j],c0);
#endif
			tp[j-1] = c1&BN_MASK2;
			}
		c1        = (tp[num] + c0)&BN_MASK2;
		tp[num-1] = c1;
		tp[num]   = tp[num+1] + (c1<c0?1:0);
		}

	if (tp[num]!=0 || tp[num-1]>=np[num-1])
		{
		c0 = bn_sub_words(rp,tp,np,num);
		if (tp[num]!=0 || c0==0)
			{
			for(i=0;i<num+2;i++)	vp[i] = 0;
			return 1;
			}
		}
	for(i=0;i<num;i++)	rp[i] = tp[i],	vp[i] = 0;
	vp[num]   = 0;
	vp[num+1] = 0;
	return 1;
	}
#else
/*
 * Return value of 0 indicates that multiplication/convolution was not
 * performed to signal the caller to fall down to alternative/original
 * code-path.
 */
int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, const BN_ULONG *np,const BN_ULONG *n0, int num)
{	return 0;	}
#endif /* OPENSSL_BN_ASM_MONT */
#endif

#else /* !BN_MUL_COMBA */

/* hmm... is it faster just to do a multiply? */
#undef bn_sqr_comba4
void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a)
	{
	BN_ULONG t[8];
	bn_sqr_normal(r,a,4,t);
	}

#undef bn_sqr_comba8
void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a)
	{
	BN_ULONG t[16];
	bn_sqr_normal(r,a,8,t);
	}

void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
	{
	r[4]=bn_mul_words(    &(r[0]),a,4,b[0]);
	r[5]=bn_mul_add_words(&(r[1]),a,4,b[1]);
	r[6]=bn_mul_add_words(&(r[2]),a,4,b[2]);
	r[7]=bn_mul_add_words(&(r[3]),a,4,b[3]);
	}

void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
	{
	r[ 8]=bn_mul_words(    &(r[0]),a,8,b[0]);
	r[ 9]=bn_mul_add_words(&(r[1]),a,8,b[1]);
	r[10]=bn_mul_add_words(&(r[2]),a,8,b[2]);
	r[11]=bn_mul_add_words(&(r[3]),a,8,b[3]);
	r[12]=bn_mul_add_words(&(r[4]),a,8,b[4]);
	r[13]=bn_mul_add_words(&(r[5]),a,8,b[5]);
	r[14]=bn_mul_add_words(&(r[6]),a,8,b[6]);
	r[15]=bn_mul_add_words(&(r[7]),a,8,b[7]);
	}

#ifdef OPENSSL_NO_ASM
#ifdef OPENSSL_BN_ASM_MONT
#include <alloca.h>
int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, const BN_ULONG *np,const BN_ULONG *n0p, int num)
	{
	BN_ULONG c0,c1,*tp,n0=*n0p;
	volatile BN_ULONG *vp;
	int i=0,j;

	vp = tp = alloca((num+2)*sizeof(BN_ULONG));

	for(i=0;i<=num;i++)	tp[i]=0;

	for(i=0;i<num;i++)
		{
		c0         = bn_mul_add_words(tp,ap,num,bp[i]);
		c1         = (tp[num] + c0)&BN_MASK2;
		tp[num]    = c1;
		tp[num+1]  = (c1<c0?1:0);

		c0         = bn_mul_add_words(tp,np,num,tp[0]*n0);
		c1         = (tp[num] + c0)&BN_MASK2;
		tp[num]    = c1;
		tp[num+1] += (c1<c0?1:0);
		for(j=0;j<=num;j++)	tp[j]=tp[j+1];
		}

	if (tp[num]!=0 || tp[num-1]>=np[num-1])
		{
		c0 = bn_sub_words(rp,tp,np,num);
		if (tp[num]!=0 || c0==0)
			{
			for(i=0;i<num+2;i++)	vp[i] = 0;
			return 1;
			}
		}
	for(i=0;i<num;i++)	rp[i] = tp[i],	vp[i] = 0;
	vp[num]   = 0;
	vp[num+1] = 0;
	return 1;
	}
#else
int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, const BN_ULONG *np,const BN_ULONG *n0, int num)
{	return 0;	}
#endif /* OPENSSL_BN_ASM_MONT */
#endif

#endif /* !BN_MUL_COMBA */