int logb2(_MIPD_ big x)
{ /* returns number of bits in x */
int xl,lg2;
mr_small top;
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
if (mr_mip->ERNUM || size(x)==0) return 0;
MR_IN(49)
#ifndef MR_ALWAYS_BINARY
if (mr_mip->base==mr_mip->base2)
{
#endif
xl=(int)(x->len&MR_OBITS);
lg2=mr_mip->lg2b*(xl-1);
top=x->w[xl-1];
while (top>=1)
{
lg2++;
top/=2;
}
#ifndef MR_ALWAYS_BINARY
}
else
{
copy(x,mr_mip->w0);
insign(PLUS,mr_mip->w0);
lg2=0;
while (mr_mip->w0->len>1)
{
#ifdef MR_FP_ROUNDING
mr_sdiv(_MIPP_ mr_mip->w0,mr_mip->base2,mr_invert(mr_mip->base2),mr_mip->w0);
#else
mr_sdiv(_MIPP_ mr_mip->w0,mr_mip->base2,mr_mip->w0);
#endif
lg2+=mr_mip->lg2b;
}
while (mr_mip->w0->w[0]>=1)
{
lg2++;
mr_mip->w0->w[0]/=2;
}
}
#endif
MR_OUT
return lg2;
}
double fdsize(_MIPD_ flash w)
{ /* express flash number as double. */
int i,s,en,ed;
double n,d,b,BIGGEST;
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
if (mr_mip->ERNUM || size(w)==0) return (0.0);
MR_IN(11)
BIGGEST=pow(2.0,(double)(1<<(MR_EBITS-4)));
mr_mip->EXACT=FALSE;
n=0.0;
d=0.0;
if (mr_mip->base==0) b=pow(2.0,(double)MIRACL);
else b=(double)mr_mip->base;
numer(_MIPP_ w,mr_mip->w1);
s=exsign(mr_mip->w1);
insign(PLUS,mr_mip->w1);
en=(int)mr_mip->w1->len;
for (i=0;i<en;i++)
n=(double)mr_mip->w1->w[i]+(n/b);
denom(_MIPP_ w,mr_mip->w1);
ed=(int)mr_mip->w1->len;
for (i=0;i<ed;i++)
d=(double)mr_mip->w1->w[i]+(d/b);
n/=d;
while (en!=ed)
{
if (en>ed)
{
ed++;
if (BIGGEST/b<n)
{
mr_berror(_MIPP_ MR_ERR_DOUBLE_FAIL);
MR_OUT
return (0.0);
}
n*=b;
}
void ftan(_MIPD_ flash x,flash y)
{ /* calculates y=tan(x) */
int i,n,nsq,m,sqrn,sgn,op[5];
#ifndef MR_GENERIC_MT
miracl *mr_mip=get_mip();
#endif
copy(x,y);
if (mr_mip->ERNUM || size(y)==0) return;
MR_IN(57)
sgn=norm(_MIPP_ TAN,y);
ftrunc(_MIPP_ y,y,mr_mip->w10);
n=size(y);
if (n!=0) build(_MIPP_ y,tan1);
if (size(mr_mip->w10)==0)
{
insign(sgn,y);
MR_OUT
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
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));
}
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));
}
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));
}
