static void mr_comba_halfm(big x,big y,big z)
{
mr_small extra;
mr_large dig,carry;
carry=(mr_large)x[0]*y[0];
z[0]=(mr_small)carry;
carry=MR_TOP(carry);
extra=0;
carry=(mr_large)x[1]*y[0]+carry;
dig=(mr_large)x[0]*y[1];
carry+=dig;
if (carry<dig) extra=1;
z[1]=(mr_small)carry;
carry=MR_TOP(carry);
MR_TOP(carry)=extra;
extra=0;
carry+=(mr_large)x[2]*y[0];
dig=(mr_large)x[1]*y[1];
carry+=dig;
if (carry<dig) extra=1;
dig=(mr_large)x[0]*y[2];
carry+=dig;
if (carry<dig) extra++;
z[2]=(mr_small)carry;
carry=MR_TOP(carry);
MR_TOP(carry)=extra;
extra=0;
dig=(mr_large)x[3]*y[0];
carry+=dig;
dig=(mr_large)x[2]*y[1];
carry+=dig;
dig=(mr_large)x[1]*y[2];
carry+=dig;
dig=(mr_large)x[0]*y[3];
carry+=dig;
z[3]=(mr_small)carry;
return;
}
static int mr_decn(big y,big z,int n)
{ /* subtract from an array of length n*4 */
int m;
mr_small borrow=0;
mr_large u;
for (m=0;m<4*n;m+=4)
{
u=(mr_large)z[m]-y[m]-borrow;
z[m]=(mr_small)u;
borrow=0-MR_TOP(u);
u=(mr_large)z[m+1]-y[m+1]-borrow;
z[m+1]=(mr_small)u;
borrow=0-MR_TOP(u);
u=(mr_large)z[m+2]-y[m+2]-borrow;
z[m+2]=(mr_small)u;
borrow=0-MR_TOP(u);
u=(mr_large)z[m+3]-y[m+3]-borrow;
z[m+3]=(mr_small)u;
borrow=0-MR_TOP(u);
}
return borrow;
}
static int mr_incn(big y,big z,int n)
{ /* add to an array of length n*4 */
int m;
mr_small carry=0;
mr_large u;
for (m=0;m<4*n;m+=4)
{
u=(mr_large)carry+z[m]+y[m];
z[m]=(mr_small)u;
carry=MR_TOP(u);
u=(mr_large)carry+z[m+1]+y[m+1];
z[m+1]=(mr_small)u;
carry=MR_TOP(u);
u=(mr_large)carry+z[m+2]+y[m+2];
z[m+2]=(mr_small)u;
carry=MR_TOP(u);
u=(mr_large)carry+z[m+3]+y[m+3];
z[m+3]=(mr_small)u;
carry=MR_TOP(u);
}
return carry;
}
static int mr_addn(big x,big y,big z,int n)
{ /* add two arrays of length n*4 */
int m;
mr_small carry=0;
mr_large u;
for (m=0;m<4*n;m+=4)
{ /* unroll the loops 4 times and hope to God for a decent compiler.... */
u=(mr_large)carry+x[m]+y[m];
z[m]=(mr_small)u;
carry=MR_TOP(u);
u=(mr_large)carry+x[m+1]+y[m+1];
z[m+1]=(mr_small)u;
carry=MR_TOP(u);
u=(mr_large)carry+x[m+2]+y[m+2];
z[m+2]=(mr_small)u;
carry=MR_TOP(u);
u=(mr_large)carry+x[m+3]+y[m+3];
z[m+3]=(mr_small)u;
carry=MR_TOP(u);
}
return carry;
}
static void mr_comba_sqr(big x,big z)
{ /* square an array of length MR_KCM */
mr_small extra;
mr_large dig,carry;
/* going up the pyramid of partial products.... */
carry=(mr_large)x[0]*x[0];
z[0]=(mr_small)carry;
carry=MR_TOP(carry);
extra=0;
dig=(mr_large)x[0]*x[1];
carry+=dig;
carry+=dig;
if (carry<dig) extra=1;
z[1]=(mr_small)carry;
carry=MR_TOP(carry);
MR_TOP(carry)=extra;
extra=0;
dig=(mr_large)x[2]*x[0];
carry+=dig;
carry+=dig;
if (carry<dig) extra=1;
dig=(mr_large)x[1]*x[1];
carry+=dig;
if (carry<dig) extra++;
z[2]=(mr_small)carry;
carry=MR_TOP(carry);
MR_TOP(carry)=extra;
extra=0;
dig=(mr_large)x[3]*x[0];
carry+=dig;
if (carry<dig) extra=1;
carry+=dig;
if (carry<dig) extra++;
dig=(mr_large)x[2]*x[1];
carry+=dig;
if (carry<dig) extra++;
carry+=dig;
if (carry<dig) extra++;
z[3]=(mr_small)carry;
carry=MR_TOP(carry);
MR_TOP(carry)=extra;
extra=0;
dig=(mr_large)x[3]*x[1];
carry+=dig;
if (carry<dig) extra=1;
carry+=dig;
if (carry<dig) extra++;
dig=(mr_large)x[2]*x[2];
carry+=dig;
if (carry<dig) extra++;
z[4]=(mr_small)carry;
carry=MR_TOP(carry);
MR_TOP(carry)=extra;
extra=0;
dig=(mr_large)x[3]*x[2];
carry+=dig;
if (carry<dig) extra=1;
carry+=dig;
if (carry<dig) extra++;
z[5]=(mr_small)carry;
carry=MR_TOP(carry);
MR_TOP(carry)=extra;
dig=(mr_large)x[3]*x[3];
carry+=dig;
z[6]=(mr_small)carry;
z[7]=MR_TOP(carry);
return;
}
static void mr_comba_mul(big x,big y,big z)
{ /* unwound Comba code for 4x4 multiply */
mr_small extra;
mr_large dig,carry;
/* going up the pyramid of partial products.... */
carry=(mr_large)x[0]*y[0];
z[0]=(mr_small)carry;
carry=MR_TOP(carry);
extra=0;
carry+=(mr_large)x[1]*y[0];
dig=(mr_large)x[0]*y[1];
carry+=dig;
if (carry<dig) extra=1;
z[1]=(mr_small)carry;
carry=MR_TOP(carry);
MR_TOP(carry)=extra;
extra=0;
carry+=(mr_large)x[2]*y[0]; /* never overflows! */
dig=(mr_large)x[1]*y[1];
carry+=dig;
if (carry<dig) extra=1;
dig=(mr_large)x[0]*y[2];
carry+=dig;
if (carry<dig) extra++;
z[2]=(mr_small)carry;
carry=MR_TOP(carry);
MR_TOP(carry)=extra;
extra=0;
dig=(mr_large)x[3]*y[0];
carry+=dig;
if (carry<dig) extra=1;
dig=(mr_large)x[2]*y[1];
carry+=dig;
if (carry<dig) extra++;
dig=(mr_large)x[1]*y[2];
carry+=dig;
if (carry<dig) extra++;
dig=(mr_large)x[0]*y[3];
carry+=dig;
if (carry<dig) extra++;
z[3]=(mr_small)carry;
carry=MR_TOP(carry);
MR_TOP(carry)=extra;
extra=0;
dig=(mr_large)x[3]*y[1];
carry+=dig;
if (carry<dig) extra=1;
dig=(mr_large)x[2]*y[2];
carry+=dig;
if (carry<dig) extra++;
dig=(mr_large)x[1]*y[3];
carry+=dig;
if (carry<dig) extra++;
z[4]=(mr_small)carry;
carry=MR_TOP(carry);
MR_TOP(carry)=extra;
extra=0;
dig=(mr_large)x[3]*y[2];
carry+=dig;
if (carry<dig) extra=1;
dig=(mr_large)x[2]*y[3];
carry+=dig;
if (carry<dig) extra++;
z[5]=(mr_small)carry;
carry=MR_TOP(carry);
MR_TOP(carry)=extra;
dig=(mr_large)x[3]*y[3];
carry+=dig;
z[6]=(mr_small)carry;
z[7]=MR_TOP(carry);
return;
}
int xgcd(_MIPD_ big x,big y,big xd,big yd,big z)
{ /* greatest common divisor by Euclids method *
* extended to also calculate xd and yd where *
* z = x.xd + y.yd = gcd(x,y) *
* if xd, yd not distinct, only xd calculated *
* z only returned if distinct from xd and yd *
* xd will always be positive, yd negative */
int s,n,iter;
mr_small r,a,b,c,d;
mr_small q,m,sr;
#ifdef MR_FP
mr_small dres;
#endif
#ifdef mr_dltype
mr_large u,v,lr;
#else
mr_small u,v,lr;
#endif
BOOL last,dplus=TRUE;
big t;
#ifndef MR_GENERIC_MT
miracl *mr_mip=get_mip();
#endif
if (mr_mip->ERNUM) return 0;
MR_IN(30)
copy(x,mr_mip->w1);
copy(y,mr_mip->w2);
s=exsign(mr_mip->w1);
insign(PLUS,mr_mip->w1);
insign(PLUS,mr_mip->w2);
convert(_MIPP_ 1,mr_mip->w3);
zero(mr_mip->w4);
last=FALSE;
a=b=c=d=0;
iter=0;
while (size(mr_mip->w2)!=0)
{
if (b==0)
{ /* update mr_mip->w1 and mr_mip->w2 */
divide(_MIPP_ mr_mip->w1,mr_mip->w2,mr_mip->w5);
t=mr_mip->w1,mr_mip->w1=mr_mip->w2,mr_mip->w2=t; /* swap(mr_mip->w1,mr_mip->w2) */
multiply(_MIPP_ mr_mip->w4,mr_mip->w5,mr_mip->w0);
add(_MIPP_ mr_mip->w3,mr_mip->w0,mr_mip->w3);
t=mr_mip->w3,mr_mip->w3=mr_mip->w4,mr_mip->w4=t; /* swap(xd,yd) */
iter++;
}
else
{
/* printf("a= %d b= %d c= %d d= %d \n",a,b,c,d); */
mr_pmul(_MIPP_ mr_mip->w1,c,mr_mip->w5); /* c*w1 */
mr_pmul(_MIPP_ mr_mip->w1,a,mr_mip->w1); /* a*w1 */
mr_pmul(_MIPP_ mr_mip->w2,b,mr_mip->w0); /* b*w2 */
mr_pmul(_MIPP_ mr_mip->w2,d,mr_mip->w2); /* d*w2 */
if (!dplus)
{
mr_psub(_MIPP_ mr_mip->w0,mr_mip->w1,mr_mip->w1); /* b*w2-a*w1 */
mr_psub(_MIPP_ mr_mip->w5,mr_mip->w2,mr_mip->w2); /* c*w1-d*w2 */
}
else
{
mr_psub(_MIPP_ mr_mip->w1,mr_mip->w0,mr_mip->w1); /* a*w1-b*w2 */
mr_psub(_MIPP_ mr_mip->w2,mr_mip->w5,mr_mip->w2); /* d*w2-c*w1 */
}
mr_pmul(_MIPP_ mr_mip->w3,c,mr_mip->w5);
mr_pmul(_MIPP_ mr_mip->w3,a,mr_mip->w3);
mr_pmul(_MIPP_ mr_mip->w4,b,mr_mip->w0);
mr_pmul(_MIPP_ mr_mip->w4,d,mr_mip->w4);
if (a==0) copy(mr_mip->w0,mr_mip->w3);
else mr_padd(_MIPP_ mr_mip->w3,mr_mip->w0,mr_mip->w3);
mr_padd(_MIPP_ mr_mip->w4,mr_mip->w5,mr_mip->w4);
}
if (mr_mip->ERNUM || size(mr_mip->w2)==0) break;
n=(int)mr_mip->w1->len;
if (n==1)
{
last=TRUE;
u=mr_mip->w1->w[0];
v=mr_mip->w2->w[0];
}
else
{
m=mr_mip->w1->w[n-1]+1;
if (mr_mip->base==0)
{
#ifndef MR_NOFULLWIDTH
#ifdef mr_dltype
/* use double length type if available */
if (n>2 && m!=0)
{ /* squeeze out as much significance as possible */
MR_TOP(u)=muldvm(mr_mip->w1->w[n-1],mr_mip->w1->w[n-2],m,&sr);
MR_BOT(u)=muldvm(sr,mr_mip->w1->w[n-3],m,&sr);
MR_TOP(v)=muldvm(mr_mip->w2->w[n-1],mr_mip->w2->w[n-2],m,&sr);
MR_BOT(v)=muldvm(sr,mr_mip->w2->w[n-3],m,&sr);
}
else
{
MR_TOP(u)=mr_mip->w1->w[n-1];
MR_BOT(u)=mr_mip->w1->w[n-2];
MR_TOP(v)=mr_mip->w2->w[n-1];
MR_BOT(v)=mr_mip->w2->w[n-2];
if (n==2) last=TRUE;
}
#else
if (m==0)
{
u=mr_mip->w1->w[n-1];
v=mr_mip->w2->w[n-1];
}
else
{
u=muldvm(mr_mip->w1->w[n-1],mr_mip->w1->w[n-2],m,&sr);
v=muldvm(mr_mip->w2->w[n-1],mr_mip->w2->w[n-2],m,&sr);
}
#endif
#endif
}
else
{
#ifdef mr_dltype
if (n>2)
{ /* squeeze out as much significance as possible */
u=muldiv(mr_mip->w1->w[n-1],mr_mip->base,mr_mip->w1->w[n-2],m,&sr);
u=u*mr_mip->base+muldiv(sr,mr_mip->base,mr_mip->w1->w[n-3],m,&sr);
v=muldiv(mr_mip->w2->w[n-1],mr_mip->base,mr_mip->w2->w[n-2],m,&sr);
v=v*mr_mip->base+muldiv(sr,mr_mip->base,mr_mip->w2->w[n-3],m,&sr);
}
else
{
u=(mr_large)mr_mip->base*mr_mip->w1->w[n-1]+mr_mip->w1->w[n-2];
v=(mr_large)mr_mip->base*mr_mip->w2->w[n-1]+mr_mip->w2->w[n-2];
last=TRUE;
}
#else
u=muldiv(mr_mip->w1->w[n-1],mr_mip->base,mr_mip->w1->w[n-2],m,&sr);
v=muldiv(mr_mip->w2->w[n-1],mr_mip->base,mr_mip->w2->w[n-2],m,&sr);
#endif
}
}
dplus=TRUE;
a=1;
b=0;
c=0;
d=1;
forever
{ /* work only with most significant piece */
if (last)
{
if (v==0) break;
q=qdiv(u,v);
if (q==0) break;
}
else
{
if (dplus)
{
if (v-c==0 || v+d==0) break;
q=qdiv(u+a,v-c);
if (q==0) break;
if (q!=qdiv(u-b,v+d)) break;
}
else
{
if (v+c==0 || v-d==0) break;
q=qdiv(u-a,v+c);
if (q==0) break;
if (q!=qdiv(u+b,v-d)) break;
}
}
if (q==1)
{
if (b+d >= MAXBASE) break;
r=a+c;
a=c;
c=r;
r=b+d;
b=d;
d=r;
lr=u-v;
u=v;
v=lr;
}
else
{
if (q>=MR_DIV(MAXBASE-b,d)) break;
r=a+q*c;
a=c;
c=r;
r=b+q*d;
b=d;
d=r;
lr=u-q*v;
u=v;
v=lr;
}
iter++;
dplus=!dplus;
}
iter%=2;
}
if (s==MINUS) iter++;
if (iter%2==1) subtract(_MIPP_ y,mr_mip->w3,mr_mip->w3);
if (xd!=yd)
{
negify(x,mr_mip->w2);
mad(_MIPP_ mr_mip->w2,mr_mip->w3,mr_mip->w1,y,mr_mip->w4,mr_mip->w4);
copy(mr_mip->w4,yd);
}
copy(mr_mip->w3,xd);
if (z!=xd && z!=yd) copy(mr_mip->w1,z);
MR_OUT
return (size(mr_mip->w1));
}
int xgcd(_MIPD_ big x,big y,big xd,big yd,big z)
{ /* greatest common divisor by Euclids method *
* extended to also calculate xd and yd where *
* z = x.xd + y.yd = gcd(x,y) *
* if xd, yd not distinct, only xd calculated *
* z only returned if distinct from xd and yd *
* xd will always be positive, yd negative */
int q,r,a,b,c,d,s,n;
mr_small m,sr;
#ifdef mr_dltype
mr_large u,v,lq,lr;
#else
mr_small u,v,lq,lr;
#endif
BOOL last;
big t;
#ifndef MR_GENERIC_MT
miracl *mr_mip=get_mip();
#endif
if (mr_mip->ERNUM) return 0;
MR_IN(30)
copy(x,mr_mip->w1);
copy(y,mr_mip->w2);
s=exsign(mr_mip->w1);
insign(PLUS,mr_mip->w1);
insign(PLUS,mr_mip->w2);
/* copy(mr_mip->w1,mr_mip->w3);
copy(mr_mip->w2,mr_mip->w4); */
convert(_MIPP_ 1,mr_mip->w3);
zero(mr_mip->w4);
last=FALSE;
a=b=c=d=0;
while (size(mr_mip->w2)!=0)
{
if (b==0)
{ /* update mr_mip->w1 and mr_mip->w2 */
divide(_MIPP_ mr_mip->w1,mr_mip->w2,mr_mip->w5);
t=mr_mip->w1,mr_mip->w1=mr_mip->w2,mr_mip->w2=t; /* swap(mr_mip->w1,mr_mip->w2) */
multiply(_MIPP_ mr_mip->w4,mr_mip->w5,mr_mip->w0);
subtract(_MIPP_ mr_mip->w3,mr_mip->w0,mr_mip->w3);
t=mr_mip->w3,mr_mip->w3=mr_mip->w4,mr_mip->w4=t; /* swap(xd,yd) */
}
else
{
premult(_MIPP_ mr_mip->w1,c,mr_mip->w5);
premult(_MIPP_ mr_mip->w1,a,mr_mip->w1);
premult(_MIPP_ mr_mip->w2,b,mr_mip->w0);
premult(_MIPP_ mr_mip->w2,d,mr_mip->w2);
add_r(_MIPP_ mr_mip->w1,mr_mip->w0,mr_mip->w1);
add_r(_MIPP_ mr_mip->w2,mr_mip->w5,mr_mip->w2);
premult(_MIPP_ mr_mip->w3,c,mr_mip->w5);
premult(_MIPP_ mr_mip->w3,a,mr_mip->w3);
premult(_MIPP_ mr_mip->w4,b,mr_mip->w0);
premult(_MIPP_ mr_mip->w4,d,mr_mip->w4);
add_r(_MIPP_ mr_mip->w3,mr_mip->w0,mr_mip->w3);
add_r(_MIPP_ mr_mip->w4,mr_mip->w5,mr_mip->w4);
}
if (mr_mip->ERNUM || size(mr_mip->w2)==0) break;
n=(int)mr_mip->w1[0];
a=1;
b=0;
c=0;
d=1;
if (n==1)
{
last=TRUE;
u=mr_mip->w1[1];
v=mr_mip->w2[1];
}
else
{
m=mr_mip->w1[n]+1;
if (mr_mip->base==0)
{
#ifdef mr_dltype
/* use double length type if available */
if (n>2 && m!=0)
{ /* squeeze out as much significance as possible */
MR_TOP(u)=muldvm(mr_mip->w1[n],mr_mip->w1[n-1],m,&sr);
MR_BOT(u)=muldvm(sr,mr_mip->w1[n-2],m,&sr);
MR_TOP(v)=muldvm(mr_mip->w2[n],mr_mip->w2[n-1],m,&sr);
MR_BOT(v)=muldvm(sr,mr_mip->w2[n-2],m,&sr);
}
else
{
MR_TOP(u)=mr_mip->w1[n];
MR_BOT(u)=mr_mip->w1[n-1];
MR_TOP(v)=mr_mip->w2[n];
MR_BOT(v)=mr_mip->w2[n-1];
if (n==2) last=TRUE;
}
#else
if (m==0)
{
u=mr_mip->w1[n];
v=mr_mip->w2[n];
}
else
{
u=muldvm(mr_mip->w1[n],mr_mip->w1[n-1],m,&sr);
v=muldvm(mr_mip->w2[n],mr_mip->w2[n-1],m,&sr);
}
#endif
}
else
{
#ifdef mr_dltype
/* use double length type if available */
if (n>2)
{ /* squeeze out as much significance as possible */
u=muldiv(mr_mip->w1[n],mr_mip->base,mr_mip->w1[n-1],m,&sr);
u=u*mr_mip->base+muldiv(sr,mr_mip->base,mr_mip->w1[n-2],m,&sr);
v=muldiv(mr_mip->w2[n],mr_mip->base,mr_mip->w2[n-1],m,&sr);
v=v*mr_mip->base+muldiv(sr,mr_mip->base,mr_mip->w2[n-2],m,&sr);
}
else
{
u=(mr_large)mr_mip->base*mr_mip->w1[n]+mr_mip->w1[n-1];
v=(mr_large)mr_mip->base*mr_mip->w2[n]+mr_mip->w2[n-1];
last=TRUE;
}
#else
u=muldiv(mr_mip->w1[n],mr_mip->base,mr_mip->w1[n-1],m,&sr);
v=muldiv(mr_mip->w2[n],mr_mip->base,mr_mip->w2[n-1],m,&sr);
#endif
}
}
forever
{ /* work only with most significant piece */
if (last)
{
if (v==0) break;
lq=u/v;
}
else
{
if (((v+c)==0) || ((v+d)==0)) break;
lq=(u+a)/(v+c);
if (lq!=(u+b)/(v+d)) break;
}
#ifdef mr_dltype
if (lq>=(mr_large)(MR_TOOBIG/abs(d))) break;
#else
if (lq>=(mr_small)(MR_TOOBIG/abs(d))) break;
#endif
q=(int)lq;
r=a-q*c;
a=c;
c=r;
r=b-q*d;
b=d;
d=r;
lr=u-lq*v;
u=v;
v=lr;
}
}
if (s==MINUS) negate(mr_mip->w3,mr_mip->w3);
if (size(mr_mip->w3)<=0) add_r(_MIPP_ mr_mip->w3,y,mr_mip->w3);
if (xd!=yd)
{
negate(x,mr_mip->w2);
mad(_MIPP_ mr_mip->w2,mr_mip->w3,mr_mip->w1,y,mr_mip->w4,mr_mip->w4);
copy(mr_mip->w4,yd);
}
copy(mr_mip->w3,xd);
if (z!=xd && z!=yd) copy(mr_mip->w1,z);
MR_OUT
return (size(mr_mip->w1));
}