mr_small mr_setbase(_MIPD_ mr_small nb)
{ /* set base. Pack as many digits as *
* possible into each computer word */
mr_small temp;
#ifdef MR_FP
mr_small dres;
#endif
#ifndef MR_NOFULLWIDTH
BOOL fits;
int bits;
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
fits=FALSE;
bits=MIRACL;
while (bits>1)
{
bits/=2;
temp=((mr_small)1<<bits);
if (temp==nb)
{
fits=TRUE;
break;
}
if (temp<nb || (bits%2)!=0) break;
}
if (fits)
{
mr_mip->apbase=nb;
mr_mip->pack=MIRACL/bits;
mr_mip->base=0;
return 0;
}
#endif
mr_mip->apbase=nb;
mr_mip->pack=1;
mr_mip->base=nb;
if (mr_mip->base==0) return 0;
temp=MR_DIV(MAXBASE,nb);
while (temp>=nb)
{
temp=MR_DIV(temp,nb);
mr_mip->base*=nb;
mr_mip->pack++;
}
#ifdef MR_FP_ROUNDING
mr_mip->inverse_base=mr_invert(mr_mip->base);
return mr_mip->inverse_base;
#else
return 0;
#endif
}
static mr_small qdiv(mr_large u,mr_large v)
{ /* fast division - small quotient expected. */
mr_large lq,x=u;
#ifdef MR_FP
mr_small dres;
#endif
x-=v;
if (x<v) return 1;
x-=v;
if (x<v) return 2;
x-=v;
if (x<v) return 3;
x-=v;
if (x<v) return 4;
x-=v;
if (x<v) return 5;
x-=v;
if (x<v) return 6;
x-=v;
if (x<v) return 7;
x-=v;
if (x<v) return 8;
/* do it the hard way! */
lq=8+MR_DIV(x,v);
if (lq>=MAXBASE) return 0;
return (mr_small)lq;
}
mr_small invers(mr_small x,mr_small y)
{ /* returns inverse of x mod y */
mr_small r,s,q,t,p;
#ifdef MR_FP
mr_small dres;
#endif
BOOL pos;
if (y!=0) x=MR_REMAIN(x,y);
r=1;
s=0;
p=y;
pos=TRUE;
#ifndef MR_NOFULLWIDTH
if (p==0)
{ /* if modulus is 0, assume its actually 2^MIRACL */
if (x==1) return (mr_small)1;
t=r; r=s; s=t;
p=x;
q=muldvm((mr_small)1,(mr_small)0,p,&t);
t=r+s*q; r=s; s=t;
t=0-p*q; x=p; p=t;
}
#endif
while (p!=0)
{ /* main euclidean loop */
q=MR_DIV(x,p);
t=r+s*q; r=s; s=t;
t=x-p*q; x=p; p=t;
pos=!pos;
}
if (!pos) r=y-r;
return r;
}
int jac(mr_small x,mr_small n)
{ /* finds (x/n) as (-1)^m */
int m,k,n8,u4;
mr_small t;
#ifdef MR_FP
mr_small dres;
#endif
if (x==0)
{
if (n==1) return 1;
else return 0;
}
if (MR_REMAIN(n,2)==0) return 0;
x=MR_REMAIN(x,n);
m=0;
while(n>1)
{ /* main loop */
if (x==0) return 0;
/* extract powers of 2 */
for (k=0;MR_REMAIN(x,2)==0;k++) x=MR_DIV(x,2);
n8=(int)MR_REMAIN(n,8);
if (k%2==1) m+=(n8*n8-1)/8;
/* quadratic reciprocity */
u4=(int)MR_REMAIN(x,4);
m+=(n8-1)*(u4-1)/4;
t=n; t=MR_REMAIN(t,x);
n=x; x=t;
m%=2;
}
if (m==0) return 1;
else return (-1);
}
static mr_small qdiv(mr_small u,mr_small v)
{ /* fast division - small quotient expected */
mr_small x=u;
x-=v;
if (x<v) return 1;
x-=v;
if (x<v) return 2;
return MR_DIV(u,v);
}
mr_small spmd(mr_small x,mr_small n,mr_small m)
{ /* returns x^n mod m */
mr_small r,sx;
#ifdef MR_FP
mr_small dres;
#endif
x=MR_REMAIN(x,m);
r=0;
if (x==0) return r;
r=1;
if (n==0) return r;
sx=x;
forever
{
if (MR_REMAIN(n,2)!=0) muldiv(r,sx,(mr_small)0,m,&r);
n=MR_DIV(n,2);
if (n==0) return r;
muldiv(sx,sx,(mr_small)0,m,&sx);
}
}
mr_small mr_shiftbits(mr_small x,int n)
{
#ifdef MR_FP
int i;
mr_small dres;
if (n==0) return x;
if (n>0)
{
for (i=0;i<n;i++) x=x+x;
return x;
}
n=-n;
for (i=0;i<n;i++) x=MR_DIV(x,2.0);
return x;
#else
if (n==0) return x;
if (n>0) x<<=n;
else x>>=n;
return x;
#endif
}
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
union doubleword uu,vv;
mr_large u,v,lr;
#else
mr_small u,v,lr;
#endif
BOOL last,dplus=TRUE;
big t;
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
if (mr_mip->ERNUM) return 0;
MR_IN(30)
#ifdef MR_COUNT_OPS
fpx++;
#endif
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= %I64u b= %I64u c= %I64u d= %I64u \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;
#ifndef MR_SIMPLE_BASE
if (mr_mip->base==0)
{
#endif
#ifndef MR_NOFULLWIDTH
#ifdef mr_dltype
/* use double length type if available */
if (n>2 && m!=0)
{ /* squeeze out as much significance as possible */
uu.h[MR_TOP]=muldvm(mr_mip->w1->w[n-1],mr_mip->w1->w[n-2],m,&sr);
uu.h[MR_BOT]=muldvm(sr,mr_mip->w1->w[n-3],m,&sr);
vv.h[MR_TOP]=muldvm(mr_mip->w2->w[n-1],mr_mip->w2->w[n-2],m,&sr);
vv.h[MR_BOT]=muldvm(sr,mr_mip->w2->w[n-3],m,&sr);
}
else
{
uu.h[MR_TOP]=mr_mip->w1->w[n-1];
uu.h[MR_BOT]=mr_mip->w1->w[n-2];
vv.h[MR_TOP]=mr_mip->w2->w[n-1];
vv.h[MR_BOT]=mr_mip->w2->w[n-2];
if (n==2) last=TRUE;
}
u=uu.d;
v=vv.d;
#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
#ifndef MR_SIMPLE_BASE
}
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
}
#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 ((mr_small)(v-c)==0 || (mr_small)(v+d)==0) break;
q=qdiv(u+a,v-c);
if (q==0) break;
if (q!=qdiv(u-b,v+d)) break;
}
else
{
if ((mr_small)(v+c)==0 || (mr_small)(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 ((mr_small)(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));
}
mr_small sqrmp(mr_small x,mr_small m)
{ /* square root mod a small prime by Shanks method *
* returns 0 if root does not exist or m not prime */
mr_small z,y,v,w,t,q;
#ifdef MR_FP
mr_small dres;
#endif
int i,e,n,r;
BOOL pp;
x=MR_REMAIN(x,m);
if (x==0) return 0;
if (x==1) return 1;
if (spmd(x,(mr_small)((m-1)/2),m)!=1) return 0; /* Legendre symbol not 1 */
if (MR_REMAIN(m,4)==3) return spmd(x,(mr_small)((m+1)/4),m); /* easy case for m=4.k+3 */
if (MR_REMAIN(m,8)==5)
{ /* also relatively easy */
t=spmd(x,(mr_small)((m-1)/4),m);
if (t==1) return spmd(x,(mr_small)((m+3)/8),m);
if (t==(mr_small)(m-1))
{
muldiv((mr_small)4,x,(mr_small)0,m,&t);
t=spmd(t,(mr_small)((m+3)/8),m);
muldiv(t,(mr_small)((m+1)/2),(mr_small)0,m,&t);
return t;
}
return 0;
}
q=m-1;
e=0;
while (MR_REMAIN(q,2)==0)
{
q=MR_DIV(q,2);
e++;
}
if (e==0) return 0; /* even m */
for (r=2;;r++)
{ /* find suitable z */
z=spmd((mr_small)r,q,m);
if (z==1) continue;
t=z;
pp=FALSE;
for (i=1;i<e;i++)
{ /* check for composite m */
if (t==(m-1)) pp=TRUE;
muldiv(t,t,(mr_small)0,m,&t);
if (t==1 && !pp) return 0;
}
if (t==(m-1)) break;
if (!pp) return 0; /* m is not prime */
}
y=z;
r=e;
v=spmd(x,(mr_small)((q+1)/2),m);
w=spmd(x,q,m);
while (w!=1)
{
t=w;
for (n=0;t!=1;n++) muldiv(t,t,(mr_small)0,m,&t);
if (n>=r) return 0;
y=spmd(y,mr_shiftbits(1,r-n-1),m);
muldiv(v,y,(mr_small)0,m,&v);
muldiv(y,y,(mr_small)0,m,&y);
muldiv(w,y,(mr_small)0,m,&w);
r=n;
}
return v;
}
int egcd(_MIPD_ big x,big y,big z)
{ /* greatest common divisor z=gcd(x,y) by Euclids *
* method using Lehmers algorithm for big numbers */
int q,r,a,b,c,d,n;
mr_small sr,m,sm;
mr_small u,v,lq,lr;
#ifdef MR_FP
mr_small dres;
#endif
big t;
#ifndef MR_GENERIC_MT
miracl *mr_mip=get_mip();
#endif
if (mr_mip->ERNUM) return 0;
MR_IN(12)
copy(x,mr_mip->w1);
copy(y,mr_mip->w2);
insign(PLUS,mr_mip->w1);
insign(PLUS,mr_mip->w2);
a=b=c=d=0;
while (size(mr_mip->w2)!=0)
{
if (b==0)
{ /* update w1 and w2 */
divide(_MIPP_ mr_mip->w1,mr_mip->w2,mr_mip->w2);
t=mr_mip->w1,mr_mip->w1=mr_mip->w2,mr_mip->w2=t; /* swap(w1,w2) */
}
else
{
premult(_MIPP_ mr_mip->w1,c,z);
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(_MIPP_ mr_mip->w1,mr_mip->w0,mr_mip->w1);
add(_MIPP_ mr_mip->w2,z,mr_mip->w2);
}
if (mr_mip->ERNUM || size(mr_mip->w2)==0) break;
n=(int)mr_mip->w1->len;
if (mr_mip->w2->len==1)
{ /* special case if mr_mip->w2 is now small */
sm=mr_mip->w2->w[0];
#ifdef MR_FP_ROUNDING
sr=mr_sdiv(_MIPP_ mr_mip->w1,sm,mr_invert(sm),mr_mip->w1);
#else
sr=mr_sdiv(_MIPP_ mr_mip->w1,sm,mr_mip->w1);
#endif
if (sr==0)
{
copy(mr_mip->w2,mr_mip->w1);
break;
}
zero(mr_mip->w1);
mr_mip->w1->len=1;
mr_mip->w1->w[0]=sr;
while ((sr=MR_REMAIN(mr_mip->w2->w[0],mr_mip->w1->w[0]))!=0)
mr_mip->w2->w[0]=mr_mip->w1->w[0],mr_mip->w1->w[0]=sr;
break;
}
a=1;
b=0;
c=0;
d=1;
m=mr_mip->w1->w[n-1]+1;
if (mr_mip->base==0)
{
#ifndef MR_NOFULLWIDTH
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
}
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);
}
forever
{ /* work only with most significant piece */
if (((v+c)==0) || ((v+d)==0)) break;
lq=MR_DIV((u+a),(v+c));
if (lq!=MR_DIV((u+b),(v+d))) break;
if (lq>=(mr_small)(MR_TOOBIG/mr_abs(d))) break;
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;
}
}
copy(mr_mip->w1,z);
MR_OUT
return (size(mr_mip->w1));
}
static int euclid(_MIPD_ big x,int num)
{ /* outputs next c.f. quotient from gcd(w5,w6) */
mr_small sr,m;
#ifdef MR_FP
mr_small dres;
#endif
mr_small lr,lq;
big t;
#ifndef MR_GENERIC_MT
miracl *mr_mip=get_mip();
#endif
if (num==0)
{
mr_mip->oldn=(-1);
mr_mip->carryon=FALSE;
mr_mip->last=FALSE;
if (compare(mr_mip->w6,mr_mip->w5)>0)
{ /* ensure w5>w6 */
t=mr_mip->w5,mr_mip->w5=mr_mip->w6,mr_mip->w6=t;
return (mr_mip->q=0);
}
}
else if (num==mr_mip->oldn || mr_mip->q<0) return mr_mip->q;
mr_mip->oldn=num;
if (mr_mip->carryon) goto middle;
start:
if (size(mr_mip->w6)==0) return (mr_mip->q=(-1));
mr_mip->ndig=(int)mr_mip->w5->len;
mr_mip->carryon=TRUE;
mr_mip->a=1;
mr_mip->b=0;
mr_mip->c=0;
mr_mip->d=1;
if (mr_mip->ndig==1)
{
mr_mip->last=TRUE;
mr_mip->u=mr_mip->w5->w[0];
mr_mip->v=mr_mip->w6->w[0];
}
else
{
m=mr_mip->w5->w[mr_mip->ndig-1]+1;
if (mr_mip->base==0)
{
#ifndef MR_NOFULLWIDTH
if (m==0)
{
mr_mip->u=mr_mip->w5->w[mr_mip->ndig-1];
mr_mip->v=mr_mip->w6->w[mr_mip->ndig-1];
}
else
{
mr_mip->u=muldvm(mr_mip->w5->w[mr_mip->ndig-1],mr_mip->w5->w[mr_mip->ndig-2],m,&sr);
mr_mip->v=muldvm(mr_mip->w6->w[mr_mip->ndig-1],mr_mip->w6->w[mr_mip->ndig-2],m,&sr);
}
#endif
}
else
{
mr_mip->u=muldiv(mr_mip->w5->w[mr_mip->ndig-1],mr_mip->base,mr_mip->w5->w[mr_mip->ndig-2],m,&sr);
mr_mip->v=muldiv(mr_mip->w6->w[mr_mip->ndig-1],mr_mip->base,mr_mip->w6->w[mr_mip->ndig-2],m,&sr);
}
}
mr_mip->ku=mr_mip->u;
mr_mip->kv=mr_mip->v;
middle:
forever
{ /* work only with most significant piece */
if (mr_mip->last)
{
if (mr_mip->v==0) return (mr_mip->q=(-1));
lq=MR_DIV(mr_mip->u,mr_mip->v);
}
else
{
if (((mr_mip->v+mr_mip->c)==0) || ((mr_mip->v+mr_mip->d)==0)) break;
lq=MR_DIV((mr_mip->u+mr_mip->a),(mr_mip->v+mr_mip->c));
if (lq!=MR_DIV((mr_mip->u+mr_mip->b),(mr_mip->v+mr_mip->d))) break;
}
if (lq>=(mr_small)(MR_TOOBIG/mr_abs(mr_mip->d))) break;
mr_mip->q=(int)lq;
mr_mip->r=mr_mip->a-mr_mip->q*mr_mip->c;
mr_mip->a=mr_mip->c;
mr_mip->c=mr_mip->r;
mr_mip->r=mr_mip->b-mr_mip->q*mr_mip->d;
mr_mip->b=mr_mip->d;
mr_mip->d=mr_mip->r;
lr=mr_mip->u-lq*mr_mip->v;
mr_mip->u=mr_mip->v;
mr_mip->v=lr;
return mr_mip->q;
}
mr_mip->carryon=FALSE;
if (mr_mip->b==0)
{ /* update w5 and w6 */
mr_mip->check=OFF;
divide(_MIPP_ mr_mip->w5,mr_mip->w6,mr_mip->w7);
mr_mip->check=ON;
if (mr_lent(mr_mip->w7)>mr_mip->nib) return (mr_mip->q=(-2));
t=mr_mip->w5,mr_mip->w5=mr_mip->w6,mr_mip->w6=t; /* swap(w5,w6) */
copy(mr_mip->w7,x);
return (mr_mip->q=size(x));
}
else
{
mr_mip->check=OFF;
premult(_MIPP_ mr_mip->w5,mr_mip->c,mr_mip->w7);
premult(_MIPP_ mr_mip->w5,mr_mip->a,mr_mip->w5);
premult(_MIPP_ mr_mip->w6,mr_mip->b,mr_mip->w0);
premult(_MIPP_ mr_mip->w6,mr_mip->d,mr_mip->w6);
add(_MIPP_ mr_mip->w5,mr_mip->w0,mr_mip->w5);
add(_MIPP_ mr_mip->w6,mr_mip->w7,mr_mip->w6);
mr_mip->check=ON;
}
goto start;
}
