void sftbit(_MIPD_ big x,int n,big z)
{ /* shift x by n bits */
int m;
mr_small sm;
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
if (mr_mip->ERNUM) return;
copy(x,z);
if (n==0) return;
MR_IN(47)
m=mr_abs(n);
sm=mr_shiftbits((mr_small)1,m%mr_mip->lg2b);
if (n>0)
{ /* shift left */
#ifndef MR_ALWAYS_BINARY
if (mr_mip->base==mr_mip->base2)
{
#endif
mr_shift(_MIPP_ z,n/mr_mip->lg2b,z);
mr_pmul(_MIPP_ z,sm,z);
#ifndef MR_ALWAYS_BINARY
}
else
{
expb2(_MIPP_ m,mr_mip->w1);
multiply(_MIPP_ z,mr_mip->w1,z);
}
#endif
}
else
{ /* shift right */
#ifndef MR_ALWAYS_BINARY
if (mr_mip->base==mr_mip->base2)
{
#endif
mr_shift(_MIPP_ z,n/mr_mip->lg2b,z);
#ifdef MR_FP_ROUNDING
mr_sdiv(_MIPP_ z,sm,mr_invert(sm),z);
#else
mr_sdiv(_MIPP_ z,sm,z);
#endif
#ifndef MR_ALWAYS_BINARY
}
else
{
expb2(_MIPP_ m,mr_mip->w1);
divide(_MIPP_ z,mr_mip->w1,z);
}
#endif
}
MR_OUT
}
mr_small brand(_MIPDO_ )
{ /* Marsaglia & Zaman random number generator */
int i,k;
mr_unsign32 pdiff,t;
mr_small r;
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
if (mr_mip->lg2b>32)
{ /* underlying type is > 32 bits. Assume <= 64 bits */
mr_mip->rndptr+=2;
if (mr_mip->rndptr<NK-1)
{
r=(mr_small)mr_mip->ira[mr_mip->rndptr];
r=mr_shiftbits(r,mr_mip->lg2b-32);
r+=(mr_small)mr_mip->ira[mr_mip->rndptr+1];
return r;
}
}
else
{
mr_mip->rndptr++;
if (mr_mip->rndptr<NK) return (mr_small)mr_mip->ira[mr_mip->rndptr];
}
mr_mip->rndptr=0;
for (i=0,k=NK-NJ;i<NK;i++,k++)
{ /* calculate next NK values */
if (k==NK) k=0;
t=mr_mip->ira[k];
pdiff=t - mr_mip->ira[i] - mr_mip->borrow;
if (pdiff<t) mr_mip->borrow=0;
if (pdiff>t) mr_mip->borrow=1;
mr_mip->ira[i]=pdiff;
}
if (mr_mip->lg2b>32)
{ /* double up */
r=(mr_small)mr_mip->ira[0];
r=mr_shiftbits(r,mr_mip->lg2b-32);
r+=(mr_small)mr_mip->ira[1];
return r;
}
else return (mr_small)(mr_mip->ira[0]);
}
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;
}
if (n<0)
{
mr_berror(_MIPP_ MR_ERR_NEG_POWER);
MR_OUT
return;
}
r=n/mr_mip->lg2b;
p=n%mr_mip->lg2b;
#ifndef MR_ALWAYS_BINARY
if (mr_mip->base==mr_mip->base2)
{
#endif
mr_shift(_MIPP_ x,r,x);
x->w[x->len-1]=mr_shiftbits(x->w[x->len-1],p);
#ifndef MR_ALWAYS_BINARY
}
else
{
for (i=1;i<=r;i++)
mr_pmul(_MIPP_ x,mr_mip->base2,x);
mr_pmul(_MIPP_ x,mr_shiftbits((mr_small)1,p),x);
}
#endif
MR_OUT
}
void bigbits(_MIPD_ int n,big x)
{ /* sets x as random < 2^n */
mr_small r;
