text: /* $OpenBSD: bn_asm.c,v 1.13 2014/07/11 08:44:47 jsing Exp $ */
  /* 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 <assert.h>
  #include <stdio.h>
  
  #include <openssl/opensslconf.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
  /*
   * Keep in mind that additions to multiplication result can not
   * overflow, because its high half cannot be all-ones.
   */
  #define mul_add_c(a,b,c0,c1,c2)		do {	\
  	BN_ULONG hi;				\
  	BN_ULLONG t = (BN_ULLONG)(a)*(b);	\
  	t += c0;		/* no carry */	\
  	c0 = (BN_ULONG)Lw(t);			\
  	hi = (BN_ULONG)Hw(t);			\
  	c1 = (c1+hi)&BN_MASK2; if (c1<hi) c2++;	\
  	} while(0)
  
  #define mul_add_c2(a,b,c0,c1,c2)	do {	\
  	BN_ULONG hi;				\
  	BN_ULLONG t = (BN_ULLONG)(a)*(b);	\
  	BN_ULLONG tt = t+c0;	/* no carry */	\
  	c0 = (BN_ULONG)Lw(tt);			\
  	hi = (BN_ULONG)Hw(tt);			\
  	c1 = (c1+hi)&BN_MASK2; if (c1<hi) c2++;	\
  	t += c0;		/* no carry */	\
  	c0 = (BN_ULONG)Lw(t);			\
  	hi = (BN_ULONG)Hw(t);			\
  	c1 = (c1+hi)&BN_MASK2; if (c1<hi) c2++;	\
  	} while(0)
  
  #define sqr_add_c(a,i,c0,c1,c2)		do {	\
  	BN_ULONG hi;				\
  	BN_ULLONG t = (BN_ULLONG)a[i]*a[i];	\
  	t += c0;		/* no carry */	\
  	c0 = (BN_ULONG)Lw(t);			\
  	hi = (BN_ULONG)Hw(t);			\
  	c1 = (c1+hi)&BN_MASK2; if (c1<hi) c2++;	\
  	} while(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_LOHI)
  /*
   * Keep in mind that additions to hi can not overflow, because
   * the high word of a multiplication result cannot be all-ones.
   */
  #define mul_add_c(a,b,c0,c1,c2)		do {	\
  	BN_ULONG ta = (a), tb = (b);		\
  	BN_ULONG lo, hi;			\
  	BN_UMULT_LOHI(lo,hi,ta,tb);		\
  	c0 += lo; hi += (c0<lo)?1:0;		\
  	c1 += hi; c2 += (c1<hi)?1:0;		\
  	} while(0)
  
  #define mul_add_c2(a,b,c0,c1,c2)	do {	\
  	BN_ULONG ta = (a), tb = (b);		\
  	BN_ULONG lo, hi, tt;			\
  	BN_UMULT_LOHI(lo,hi,ta,tb);		\
  	c0 += lo; tt = hi+((c0<lo)?1:0);	\
  	c1 += tt; c2 += (c1<tt)?1:0;		\
  	c0 += lo; hi += (c0<lo)?1:0;		\
  	c1 += hi; c2 += (c1<hi)?1:0;		\
  	} while(0)
  
  #define sqr_add_c(a,i,c0,c1,c2)		do {	\
  	BN_ULONG ta = (a)[i];			\
  	BN_ULONG lo, hi;			\
  	BN_UMULT_LOHI(lo,hi,ta,ta);		\
  	c0 += lo; hi += (c0<lo)?1:0;		\
  	c1 += hi; c2 += (c1<hi)?1:0;		\
  	} while(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)
  /*
   * Keep in mind that additions to hi can not overflow, because
   * the high word of a multiplication result cannot be all-ones.
   */
  #define mul_add_c(a,b,c0,c1,c2)		do {	\
  	BN_ULONG ta = (a), tb = (b);		\
  	BN_ULONG lo = ta * tb;			\
  	BN_ULONG hi = BN_UMULT_HIGH(ta,tb);	\
  	c0 += lo; hi += (c0<lo)?1:0;		\
  	c1 += hi; c2 += (c1<hi)?1:0;		\
  	} while(0)
  
  #define mul_add_c2(a,b,c0,c1,c2)	do {	\
  	BN_ULONG ta = (a), tb = (b), tt;	\
  	BN_ULONG lo = ta * tb;			\
  	BN_ULONG hi = BN_UMULT_HIGH(ta,tb);	\
  	c0 += lo; tt = hi + ((c0<lo)?1:0);	\
  	c1 += tt; c2 += (c1<tt)?1:0;		\
  	c0 += lo; hi += (c0<lo)?1:0;		\
  	c1 += hi; c2 += (c1<hi)?1:0;		\
  	} while(0)
  
  #define sqr_add_c(a,i,c0,c1,c2)		do {	\
  	BN_ULONG ta = (a)[i];			\
  	BN_ULONG lo = ta * ta;			\
  	BN_ULONG hi = BN_UMULT_HIGH(ta,ta);	\
  	c0 += lo; hi += (c0<lo)?1:0;		\
  	c1 += hi; c2 += (c1<hi)?1:0;		\
  	} while(0)
  
  #define sqr_add_c2(a,i,j,c0,c1,c2)	\
  	mul_add_c2((a)[i],(a)[j],c0,c1,c2)
  
  #else /* !BN_LLONG */
  /*
   * Keep in mind that additions to hi can not overflow, because
   * the high word of a multiplication result cannot be all-ones.
   */
  #define mul_add_c(a,b,c0,c1,c2)		do {	\
  	BN_ULONG lo = LBITS(a), hi = HBITS(a);	\
  	BN_ULONG bl = LBITS(b), bh = HBITS(b);	\
  	mul64(lo,hi,bl,bh);			\
  	c0 = (c0+lo)&BN_MASK2; if (c0<lo) hi++;	\
  	c1 = (c1+hi)&BN_MASK2; if (c1<hi) c2++;	\
  	} while(0)
  
  #define mul_add_c2(a,b,c0,c1,c2)	do {	\
  	BN_ULONG tt;				\
  	BN_ULONG lo = LBITS(a), hi = HBITS(a);	\
  	BN_ULONG bl = LBITS(b), bh = HBITS(b);	\
  	mul64(lo,hi,bl,bh);			\
  	tt = hi;				\
  	c0 = (c0+lo)&BN_MASK2; if (c0<lo) tt++;	\
  	c1 = (c1+tt)&BN_MASK2; if (c1<tt) c2++;	\
  	c0 = (c0+lo)&BN_MASK2; if (c0<lo) hi++;	\
  	c1 = (c1+hi)&BN_MASK2; if (c1<hi) c2++;	\
  	} while(0)
  
  #define sqr_add_c(a,i,c0,c1,c2)		do {	\
  	BN_ULONG lo, hi;			\
  	sqr64(lo,hi,(a)[i]);			\
  	c0 = (c0+lo)&BN_MASK2; if (c0<lo) hi++;	\
  	c1 = (c1+hi)&BN_MASK2; if (c1<hi) c2++;	\
  	} while(0)
  
  #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)
  {
  	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)
  {
  	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)
  {
  	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)
  {
  	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
  /*
   * 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
  	int i = 0, j;
  
  #if 0	/* template for platform-specific implementation */
  	if (ap == bp)
  		return bn_sqr_mont(rp, ap, np, n0p, num);
  #endif
  	tp = reallocarray(NULL, num + 2, sizeof(BN_ULONG));
  	if (tp == NULL)
  		return 0;
  
  	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) {
  			goto out;
  		}
  	}
  	memcpy(rp, tp, num * sizeof(BN_ULONG));
  out:
  	explicit_bzero(tp, (num + 2) * sizeof(BN_ULONG));
  	free(tp);
  	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
  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;
  	int i = 0, j;
  
  	tp = calloc(NULL, num + 2, sizeof(BN_ULONG));
  	if (tp == NULL)
  		return 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) {
  			goto out;
  		}
  	}
  	memcpy(rp, tp, num * sizeof(BN_ULONG));
  out:
  	explicit_bzero(tp, (num + 2) * sizeof(BN_ULONG));
  	free(tp);
  	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 */
  