bn_mul.c

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	case 0:
	case 1:
		zero=1;
		/* break; */
	case 2:
		bn_sub_part_words(t,      a,      &(a[n]),tna,n-tna); /* + */
		bn_sub_part_words(&(t[n]),b,      &(b[n]),tnb,n-tnb); /* - */
		neg=1;
		break;
	case 3:
		zero=1;
		/* break; */
	case 4:
		bn_sub_part_words(t,      a,      &(a[n]),tna,n-tna);
		bn_sub_part_words(&(t[n]),&(b[n]),b,      tnb,tnb-n);
		break;
		}
		/* The zero case isn't yet implemented here. The speedup
		   would probably be negligible. */
# if 0
	if (n == 4)
		{
		bn_mul_comba4(&(t[n2]),t,&(t[n]));
		bn_mul_comba4(r,a,b);
		bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
		memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
		}
	else
# endif
	if (n == 8)
		{
		bn_mul_comba8(&(t[n2]),t,&(t[n]));
		bn_mul_comba8(r,a,b);
		bn_mul_normal(&(r[n2]),&(a[n]),tna,&(b[n]),tnb);
		memset(&(r[n2+tna+tnb]),0,sizeof(BN_ULONG)*(n2-tna-tnb));
		}
	else
		{
		p= &(t[n2*2]);
		bn_mul_recursive(&(t[n2]),t,&(t[n]),n,0,0,p);
		bn_mul_recursive(r,a,b,n,0,0,p);
		i=n/2;
		/* If there is only a bottom half to the number,
		 * just do it */
		if (tna > tnb)
			j = tna - i;
		else
			j = tnb - i;
		if (j == 0)
			{
			bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),
				i,tna-i,tnb-i,p);
			memset(&(r[n2+i*2]),0,sizeof(BN_ULONG)*(n2-i*2));
			}
		else if (j > 0) /* eg, n == 16, i == 8 and tn == 11 */
				{
				bn_mul_part_recursive(&(r[n2]),&(a[n]),&(b[n]),
					i,tna-i,tnb-i,p);
				memset(&(r[n2+tna+tnb]),0,
					sizeof(BN_ULONG)*(n2-tna-tnb));
				}
		else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
			{
			memset(&(r[n2]),0,sizeof(BN_ULONG)*n2);
			if (tna < BN_MUL_RECURSIVE_SIZE_NORMAL
				&& tnb < BN_MUL_RECURSIVE_SIZE_NORMAL)
				{
				bn_mul_normal(&(r[n2]),&(a[n]),tna,&(b[n]),tnb);
				}
			else
				{
				for (;;)
					{
					i/=2;
					if (i < tna && i < tnb)
						{
						bn_mul_part_recursive(&(r[n2]),
							&(a[n]),&(b[n]),
							i,tna-i,tnb-i,p);
						break;
						}
					else if (i <= tna && i <= tnb)
						{
						bn_mul_recursive(&(r[n2]),
							&(a[n]),&(b[n]),
							i,tna-i,tnb-i,p);
						break;
						}
					}
				}
			}
		}

	/* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
	 * r[10] holds (a[0]*b[0])
	 * r[32] holds (b[1]*b[1])
	 */

	c1=(int)(bn_add_words(t,r,&(r[n2]),n2));

	if (neg) /* if t[32] is negative */
		{
		c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
		}
	else
		{
		/* Might have a carry */
		c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
		}

	/* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
	 * r[10] holds (a[0]*b[0])
	 * r[32] holds (b[1]*b[1])
	 * c1 holds the carry bits
	 */
	c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
	if (c1)
		{
		p= &(r[n+n2]);
		lo= *p;
		ln=(lo+c1)&BN_MASK2;
		*p=ln;

		/* The overflow will stop before we over write
		 * words we should not overwrite */
		if (ln < (BN_ULONG)c1)
			{
			do	{
				p++;
				lo= *p;
				ln=(lo+1)&BN_MASK2;
				*p=ln;
				} while (ln == 0);
			}
		}
	}

/* a and b must be the same size, which is n2.
 * r needs to be n2 words and t needs to be n2*2
 */
void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
	     BN_ULONG *t)
	{
	int n=n2/2;

# ifdef BN_COUNT
	fprintf(stderr," bn_mul_low_recursive %d * %d\n",n2,n2);
# endif

	bn_mul_recursive(r,a,b,n,0,0,&(t[0]));
	if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL)
		{
		bn_mul_low_recursive(&(t[0]),&(a[0]),&(b[n]),n,&(t[n2]));
		bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
		bn_mul_low_recursive(&(t[0]),&(a[n]),&(b[0]),n,&(t[n2]));
		bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
		}
	else
		{
		bn_mul_low_normal(&(t[0]),&(a[0]),&(b[n]),n);
		bn_mul_low_normal(&(t[n]),&(a[n]),&(b[0]),n);
		bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
		bn_add_words(&(r[n]),&(r[n]),&(t[n]),n);
		}
	}

/* a and b must be the same size, which is n2.
 * r needs to be n2 words and t needs to be n2*2
 * l is the low words of the output.
 * t needs to be n2*3
 */
void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
	     BN_ULONG *t)
	{
	int i,n;
	int c1,c2;
	int neg,oneg,zero;
	BN_ULONG ll,lc,*lp,*mp;

# ifdef BN_COUNT
	fprintf(stderr," bn_mul_high %d * %d\n",n2,n2);
# endif
	n=n2/2;

	/* Calculate (al-ah)*(bh-bl) */
	neg=zero=0;
	c1=bn_cmp_words(&(a[0]),&(a[n]),n);
	c2=bn_cmp_words(&(b[n]),&(b[0]),n);
	switch (c1*3+c2)
		{
	case -4:
		bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
		bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
		break;
	case -3:
		zero=1;
		break;
	case -2:
		bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
		bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
		neg=1;
		break;
	case -1:
	case 0:
	case 1:
		zero=1;
		break;
	case 2:
		bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
		bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
		neg=1;
		break;
	case 3:
		zero=1;
		break;
	case 4:
		bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
		bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
		break;
		}
		
	oneg=neg;
	/* t[10] = (a[0]-a[1])*(b[1]-b[0]) */
	/* r[10] = (a[1]*b[1]) */
# ifdef BN_MUL_COMBA
	if (n == 8)
		{
		bn_mul_comba8(&(t[0]),&(r[0]),&(r[n]));
		bn_mul_comba8(r,&(a[n]),&(b[n]));
		}
	else
# endif
		{
		bn_mul_recursive(&(t[0]),&(r[0]),&(r[n]),n,0,0,&(t[n2]));
		bn_mul_recursive(r,&(a[n]),&(b[n]),n,0,0,&(t[n2]));
		}

	/* s0 == low(al*bl)
	 * s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl)
	 * We know s0 and s1 so the only unknown is high(al*bl)
	 * high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl))
	 * high(al*bl) == s1 - (r[0]+l[0]+t[0])
	 */
	if (l != NULL)
		{
		lp= &(t[n2+n]);
		c1=(int)(bn_add_words(lp,&(r[0]),&(l[0]),n));
		}
	else
		{
		c1=0;
		lp= &(r[0]);
		}

	if (neg)
		neg=(int)(bn_sub_words(&(t[n2]),lp,&(t[0]),n));
	else
		{
		bn_add_words(&(t[n2]),lp,&(t[0]),n);
		neg=0;
		}

	if (l != NULL)
		{
		bn_sub_words(&(t[n2+n]),&(l[n]),&(t[n2]),n);
		}
	else
		{
		lp= &(t[n2+n]);
		mp= &(t[n2]);
		for (i=0; i<n; i++)
			lp[i]=((~mp[i])+1)&BN_MASK2;
		}

	/* s[0] = low(al*bl)
	 * t[3] = high(al*bl)
	 * t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign
	 * r[10] = (a[1]*b[1])
	 */
	/* R[10] = al*bl
	 * R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0])
	 * R[32] = ah*bh
	 */
	/* R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow)
	 * R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow)
	 * R[3]=r[1]+(carry/borrow)
	 */
	if (l != NULL)
		{
		lp= &(t[n2]);
		c1= (int)(bn_add_words(lp,&(t[n2+n]),&(l[0]),n));
		}
	else
		{
		lp= &(t[n2+n]);
		c1=0;
		}
	c1+=(int)(bn_add_words(&(t[n2]),lp,  &(r[0]),n));
	if (oneg)
		c1-=(int)(bn_sub_words(&(t[n2]),&(t[n2]),&(t[0]),n));
	else
		c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),&(t[0]),n));

	c2 =(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n2+n]),n));
	c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(r[n]),n));
	if (oneg)
		c2-=(int)(bn_sub_words(&(r[0]),&(r[0]),&(t[n]),n));
	else
		c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n]),n));
	
	if (c1 != 0) /* Add starting at r[0], could be +ve or -ve */
		{
		i=0;
		if (c1 > 0)
			{
			lc=c1;
			do	{
				ll=(r[i]+lc)&BN_MASK2;
				r[i++]=ll;
				lc=(lc > ll);
				} while (lc);
			}
		else
			{
			lc= -c1;
			do	{
				ll=r[i];
				r[i++]=(ll-lc)&BN_MASK2;
				lc=(lc > ll);
				} while (lc);
			}
		}
	if (c2 != 0) /* Add starting at r[1] */
		{
		i=n;
		if (c2 > 0)
			{
			lc=c2;
			do	{
				ll=(r[i]+lc)&BN_MASK2;
				r[i++]=ll;
				lc=(lc > ll);
				} while (lc);
			}
		else
			{
			lc= -c2;
			do	{
				ll=r[i];
				r[i++]=(ll-lc)&BN_MASK2;
				lc=(lc > ll);
				} while (lc);
			}
		}
	}
#endif /* BN_RECURSION */

int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
	{
	int ret=0;
	int top,al,bl;
	BIGNUM *rr;
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
	int i;
#endif
#ifdef BN_RECURSION
	BIGNUM *t=NULL;
	int j=0,k;
#endif

#ifdef BN_COUNT
	fprintf(stderr,"BN_mul %d * %d\n",a->top,b->top);
#endif

	bn_check_top(a);
	bn_check_top(b);
	bn_check_top(r);

	al=a->top;
	bl=b->top;

	if ((al == 0) || (bl == 0))
		{
		BN_zero(r);
		return(1);
		}
	top=al+bl;

	BN_CTX_start(ctx);
	if ((r == a) || (r == b))
		{
		if ((rr = BN_CTX_get(ctx)) == NULL) goto err;
		}
	else
		rr = r;
	rr->neg=a->neg^b->neg;

#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
	i = al-bl;
#endif
#ifdef BN_MUL_COMBA
	if (i == 0)
		{
# if 0
		if (al == 4)
			{
			if (bn_wexpand(rr,8) == NULL) goto err;
			rr->top=8;
			bn_mul_comba4(rr->d,a->d,b->d);
			goto end;
			}
# endif
		if (al == 8)
			{
			if (bn_wexpand(rr,16) == NULL) goto err;
			rr->top=16;
			bn_mul_comba8(rr->d,a->d,b->d);
			goto end;
			}
		}
#endif /* BN_MUL_COMBA */
#ifdef BN_RECURSION
	if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL))
		{
		if (i >= -1 && i <= 1)
			{
			int sav_j =0;
			/* Find out the power of two lower or equal
			   to the longest of the two numbers */
			if (i >= 0)
				{
				j = BN_num_bits_word((BN_ULONG)al);
				}
			if (i == -1)
				{
				j = BN_num_bits_word((BN_ULONG)bl);
				}
			sav_j = j;
			j = 1<<(j-1);
			assert(j <= al || j <= bl);
			k = j+j;
			t = BN_CTX_get(ctx);
			if (al > j || bl > j)
				{
				bn_wexpand(t,k*4);
				bn_wexpand(rr,k*4);
				bn_mul_part_recursive(rr->d,a->d,b->d,
					j,al-j,bl-j,t->d);
				}
			else	/* al <= j || bl <= j */
				{
				bn_wexpand(t,k*2);
				bn_wexpand(rr,k*2);
				bn_mul_recursive(rr->d,a->d,b->d,
					j,al-j,bl-j,t->d);
				}
			rr->top=top;
			goto end;
			}
#if 0
		if (i == 1 && !BN_get_flags(b,BN_FLG_STATIC_DATA))
			{
			BIGNUM *tmp_bn = (BIGNUM *)b;
			if (bn_wexpand(tmp_bn,al) == NULL) goto err;
			tmp_bn->d[bl]=0;
			bl++;
			i--;
			}
		else if (i == -1 && !BN_get_flags(a,BN_FLG_STATIC_DATA))
			{
			BIGNUM *tmp_bn = (BIGNUM *)a;
			if (bn_wexpand(tmp_bn,bl) == NULL) goto err;
			tmp_bn->d[al]=0;
			al++;
			i++;
			}
		if (i == 0)
			{
			/* symmetric and > 4 */
			/* 16 or larger */
			j=BN_num_bits_word((BN_ULONG)al);
			j=1<<(j-1);
			k=j+j;
			t = BN_CTX_get(ctx);
			if (al == j) /* exact multiple */
				{
				if (bn_wexpand(t,k*2) == NULL) goto err;
				if (bn_wexpand(rr,k*2) == NULL) goto err;
				bn_mul_recursive(rr->d,a->d,b->d,al,t->d);
				}
			else
				{
				if (bn_wexpand(t,k*4) == NULL) goto err;
				if (bn_wexpand(rr,k*4) == NULL) goto err;
				bn_mul_part_recursive(rr->d,a->d,b->d,al-j,j,t->d);
				}
			rr->top=top;
			goto end;
			}
#endif
		}
#endif /* BN_RECURSION */
	if (bn_wexpand(rr,top) == NULL) goto err;
	rr->top=top;
	bn_mul_normal(rr->d,a->d,al,b->d,bl);

#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
end:
#endif
	bn_correct_top(rr);
	if (r != rr) BN_copy(r,rr);
	ret=1;
err:
	bn_check_top(r);
	BN_CTX_end(ctx);
	return(ret);
	}

void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb)
	{
	BN_ULONG *rr;

#ifdef BN_COUNT
	fprintf(stderr," bn_mul_normal %d * %d\n",na,nb);
#endif

	if (na < nb)
		{
		int itmp;
		BN_ULONG *ltmp;

		itmp=na; na=nb; nb=itmp;
		ltmp=a;   a=b;   b=ltmp;

		}
	rr= &(r[na]);
	if (nb <= 0)
		{
		(void)bn_mul_words(r,a,na,0);
		return;
		}
	else
		rr[0]=bn_mul_words(r,a,na,b[0]);

	for (;;)
		{
		if (--nb <= 0) return;
		rr[1]=bn_mul_add_words(&(r[1]),a,na,b[1]);
		if (--nb <= 0) return;
		rr[2]=bn_mul_add_words(&(r[2]),a,na,b[2]);
		if (--nb <= 0) return;
		rr[3]=bn_mul_add_words(&(r[3]),a,na,b[3]);
		if (--nb <= 0) return;
		rr[4]=bn_mul_add_words(&(r[4]),a,na,b[4]);
		rr+=4;
		r+=4;
		b+=4;
		}
	}

void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
	{
#ifdef BN_COUNT
	fprintf(stderr," bn_mul_low_normal %d * %d\n",n,n);
#endif
	bn_mul_words(r,a,n,b[0]);

	for (;;)
		{
		if (--n <= 0) return;
		bn_mul_add_words(&(r[1]),a,n,b[1]);
		if (--n <= 0) return;
		bn_mul_add_words(&(r[2]),a,n,b[2]);
		if (--n <= 0) return;
		bn_mul_add_words(&(r[3]),a,n,b[3]);
		if (--n <= 0) return;
		bn_mul_add_words(&(r[4]),a,n,b[4]);
		r+=4;
		b+=4;
		}
	}