void fexp(_MIPD_ flash x,flash y)
{ /* calculates y=exp(x) */
int i,n,nsq,m,sqrn,op[5];
BOOL minus,rem;
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
if (mr_mip->ERNUM) return;
if (size(x)==0)
{
convert(_MIPP_ 1,y);
return;
}
copy(x,y);
MR_IN(54)
minus=FALSE;
if (size(y)<0)
{
minus=TRUE;
negify(y,y);
}
ftrunc(_MIPP_ y,y,mr_mip->w9);
n=size(y);
if (n==MR_TOOBIG)
{
mr_berror(_MIPP_ MR_ERR_FLASH_OVERFLOW);
MR_OUT
return;
}
static int norm(_MIPD_ int type,flash y)
{ /* convert y to first quadrant angle *
* and return sign of result */
int s;
#ifndef MR_GENERIC_MT
miracl *mr_mip=get_mip();
#endif
if (mr_mip->ERNUM) return 0;
s=PLUS;
if (size(y)<0)
{
negify(y,y);
if (type!=COS) s=(-s);
}
fpi(_MIPP_ mr_mip->pi);
fpmul(_MIPP_ mr_mip->pi,1,2,mr_mip->w8);
if (fcomp(_MIPP_ y,mr_mip->w8)<=0) return s;
fpmul(_MIPP_ mr_mip->pi,2,1,mr_mip->w8);
if (fcomp(_MIPP_ y,mr_mip->w8)>0)
{ /* reduce mod 2.pi */
fdiv(_MIPP_ y,mr_mip->w8,mr_mip->w9);
ftrunc(_MIPP_ mr_mip->w9,mr_mip->w9,mr_mip->w9);
fmul(_MIPP_ mr_mip->w9,mr_mip->w8,mr_mip->w9);
fsub(_MIPP_ y,mr_mip->w9,y);
}
if (fcomp(_MIPP_ y,mr_mip->pi)>0)
{ /* if greater than pi */
fsub(_MIPP_ y,mr_mip->pi,y);
if (type!=TAN) s=(-s);
}
fpmul(_MIPP_ mr_mip->pi,1,2,mr_mip->w8);
if (fcomp(_MIPP_ y,mr_mip->w8)>0)
{ /* if greater than pi/2 */
fsub(_MIPP_ mr_mip->pi,y,y);
if (type!=SIN) s=(-s);
}
return s;
}
static BOOL act(int p,int q)
{ /* act on selected key */
int k,n,c;
aprint(PRESSED,4+5*p,6+3*q,keys[q][p]);
switch(p+7*q)
{
case 0: if (degrees) fmul(x,radeg,x);
if (hyp) fsinh(x,x);
else fsin(x,x);
newx=TRUE;
break;
case 1: if (degrees) fmul(x,radeg,x);
if (hyp) fcosh(x,x);
else fcos(x,x);
newx=TRUE;
break;
case 2: if (degrees) fmul(x,radeg,x);
if (hyp) ftanh(x,x);
else ftan(x,x);
newx=TRUE;
break;
case 3: if (lgbase>0)
{
n=size(x);
if (abs(n)<MR_TOOBIG)
{
convert(lgbase,x);
if (n<0) frecip(x,x);
fpower(x,abs(n),x);
newx=TRUE;
break;
}
if (lgbase==2) fmul(x,loge2,x);
if (lgbase==10) fmul(x,loge10,x);
}
fexp(x,x);
newx=TRUE;
break;
case 4: mip->RPOINT=!mip->RPOINT;
newx=TRUE;
break;
case 5: clrall();
newx=TRUE;
break;
case 6: return TRUE;
case 7: if (hyp) fasinh(x,x);
else fasin(x,x);
if (degrees) fdiv(x,radeg,x);
newx=TRUE;
break;
case 8: if (hyp) facosh(x,x);
else facos(x,x);
if (degrees) fdiv(x,radeg,x);
newx=TRUE;
break;
case 9: if (hyp) fatanh(x,x);
else fatan(x,x);
if (degrees) fdiv(x,radeg,x);
newx=TRUE;
break;
case 10: flog(x,x);
if (lgbase==2) fdiv(x,loge2,x);
if (lgbase==10) fdiv(x,loge10,x);
newx=TRUE;
break;
case 11: newx=TRUE;
k=3;
forever
{
aprint(INVER,2+stptr[k],2,settings[k][option[k]]);
curser(2+stptr[k],2);
c=arrow(gethit());
if (c==1)
{
if (option[k]==nops[k]) option[k]=0;
else option[k]+=1;
continue;
}
aprint(STATCOL,2+stptr[k],2,settings[k][option[k]]);
if (c==0 || c==2) break;
if (c==4 && k>0) k--;
if (c==3 && k<3) k++;
}
setopts();
break;
case 12: chekit(7);
break;
case 13: result=FALSE;
if (ipt==0) break;
ipt--;
mybuff[ipt]='\0';
if (ipt==0) clr();
just(mybuff);
cinstr(x,mybuff);
newx=TRUE;
break;
case 14: if (!next('7')) putchar(BELL);
break;
case 15: if (!next('8')) putchar(BELL);
break;
case 16: if (!next('9')) putchar(BELL);
break;
case 17: chekit(6);
break;
case 18: chekit(5);
break;
case 19: chekit(4);
break;
case 20: copy(m,x);
newx=TRUE;
break;
case 21: if (!next('4')) putchar(BELL);
break;
case 22: if (!next('5')) putchar(BELL);
break;
case 23: if (!next('6')) putchar(BELL);
break;
case 24: fmul(x,x,x);
newx=TRUE;
break;
case 25: froot(x,2,x);
newx=TRUE;
break;
case 26: chekit(3);
break;
case 27: brkt=0;
chekit(0);
flag=OFF;
fadd(m,x,m);
newx=TRUE;
break;
case 28: if (!next('1')) putchar(BELL);
break;
case 29: if (!next('2')) putchar(BELL);
break;
case 30: if (!next('3')) putchar(BELL);
break;
case 31: frecip(x,x);
newx=TRUE;
break;
case 32: fpi(x);
newx=TRUE;
break;
case 33: chekit(2);
break;
case 34: negify(x,x);
newx=TRUE;
break;
case 35: if (!next('0')) putchar(BELL);
break;
case 36: if (!next('/')) putchar(BELL);
break;
case 37: if (!next('.')) putchar(BELL);
break;
case 38: if (ipt>0)
{
putchar(BELL);
result=FALSE;
}
else
{
zero(x);
brkt+=1;
newx=TRUE;
}
break;
case 39: if (brkt>0)
{
chekit(0);
brkt-=1;
}
else
{
putchar(BELL);
result=FALSE;
}
break;
case 40: chekit(1);
break;
case 41: brkt=0;
equals(0);
flag=OFF;
break;
}
return FALSE;
}
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));
}
Big operator-(int i, const Big& b)
{Big mib;decr(b.fn, i, mib.fn);negify(mib.fn,mib.fn);return mib;}
Big operator-(const Big& b)
{Big nb; negify(b.fn,nb.fn); return nb;}
void Big::negate() const
{ negify(fn,fn); }
int main()
{ /* factoring program using Williams (p+1) method */
int k,phase,m,nt,iv,pos,btch;
long i,p,pa,interval;
big b,q,n,fp,fvw,fd,fn,t;
static big fu[1+MULT/2];
static BOOL cp[1+MULT/2];
mip=mirsys(30,0);
b=mirvar(0);
q=mirvar(0);
n=mirvar(0);
t=mirvar(0);
fp=mirvar(0);
fvw=mirvar(0);
fd=mirvar(0);
fn=mirvar(0);
gprime(LIMIT1);
for (m=1;m<=MULT/2;m+=2)
if (igcd(MULT,m)==1)
{
fu[m]=mirvar(0);
cp[m]=TRUE;
}
else cp[m]=FALSE;
printf("input number to be factored\n");
cinnum(n,stdin);
if (isprime(n))
{
printf("this number is prime!\n");
return 0;
}
for (nt=0,k=3;k<10;k++)
{ /* try more than once for p+1 condition (may be p-1) */
convert(k,b); /* try b=3,4,5.. */
convert((k*k-4),t);
if (egcd(t,n,t)!=1) continue; /* check (b*b-4,n)!=0 */
nt++;
phase=1;
p=0;
btch=50;
i=0;
printf("phase 1 - trying all primes less than %d\n",LIMIT1);
printf("prime= %8ld",p);
forever
{ /* main loop */
if (phase==1)
{ /* looking for all factors of p+1 < LIMIT1 */
p=mip->PRIMES[i];
if (mip->PRIMES[i+1]==0)
{ /* now change gear */
phase=2;
printf("\nphase 2 - trying last prime less than %ld\n"
,LIMIT2);
printf("prime= %8ld",p);
copy(b,fu[1]);
copy(b,fp);
mad(b,b,b,n,n,fd);
decr(fd,2,fd);
negify(b,t);
mad(fd,b,t,n,n,fn);
for (m=5;m<=MULT/2;m+=2)
{ /* store fu[m] = Vm(b) */
negify(fp,t);
mad(fn,fd,t,n,n,t);
copy(fn,fp);
copy(t,fn);
if (!cp[m]) continue;
copy(t,fu[m]);
}
convert(MULT,t);
lucas(b,t,n,fp,fd);
iv=(int)(p/MULT);
if (p%MULT>MULT/2) iv++;
interval=(long)iv*MULT;
p=interval+1;
convert(iv,t);
lucas(fd,t,n,fp,fvw);
negify(fp,fp);
subtract(fvw,fu[p%MULT],q);
marks(interval);
btch*=100;
i++;
continue;
}
pa=p;
while ((LIMIT1/p) > pa) pa*=p;
convert((int)pa,t);
lucas(b,t,n,fp,q);
copy(q,b);
decr(q,2,q);
}
else
{ /* phase 2 - looking for last large prime factor of (p+1) */
p+=2;
pos=(int)(p%MULT);
if (pos>MULT/2)
{ /* increment giant step */
iv++;
interval=(long)iv*MULT;
p=interval+1;
marks(interval);
pos=1;
copy(fvw,t);
mad(fvw,fd,fp,n,n,fvw);
negify(t,fp);
}
if (!cp[pos]) continue;
/* if neither interval+/-pos is prime, don't bother */
if (!plus[pos] && !minus[pos]) continue;
subtract(fvw,fu[pos],t);
mad(q,t,t,n,n,q); /* batching gcds */
}
if (i++%btch==0)
{ /* try for a solution */
printf("\b\b\b\b\b\b\b\b%8ld",p);
fflush(stdout);
egcd(q,n,t);
if (size(t)==1)
{
if (p>LIMIT2) break;
else continue;
}
if (compare(t,n)==0)
{
printf("\ndegenerate case");
break;
}
printf("\nfactors are\n");
if (isprime(t)) printf("prime factor ");
else printf("composite factor ");
cotnum(t,stdout);
divide(n,t,n);
if (isprime(n)) printf("prime factor ");
else printf("composite factor ");
cotnum(n,stdout);
return 0;
}
}
if (nt>=NTRYS) break;
printf("\ntrying again\n");
}
printf("\nfailed to factor\n");
return 0;
}
void build(_MIPD_ flash x,int (*gen)(_MIPT_ big,int))
{ /* Build x from its regular c.f. *
* generated by gen() */
mr_small ex1,ex2,ex,st,sr;
int a,b,c,d,rm,q,n,prc,lw2,lw4,lz;
BOOL finoff,last;
big t;
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
if (mr_mip->ERNUM) return;
MR_IN(48)
zero(mr_mip->w1);
convert(_MIPP_ 1,mr_mip->w2);
convert(_MIPP_ 1,mr_mip->w3);
zero(mr_mip->w4);
finoff=FALSE;
last=FALSE;
n=0;
q=(*gen)(_MIPP_ x,n); /* Note - first quotient may be zero */
ex=mr_mip->base-1;
if (mr_mip->nib==mr_mip->workprec) prc=mr_mip->nib;
else prc=mr_mip->workprec+1;
while (!mr_mip->ERNUM && q>=0)
{
if (q==MR_TOOBIG || n==0 || finoff)
{
if (q!=MR_TOOBIG) convert(_MIPP_ q,x);
else last=FALSE;
mr_mip->check=OFF;
multiply(_MIPP_ mr_mip->w2,x,mr_mip->w0);
subtract(_MIPP_ mr_mip->w1,mr_mip->w0,mr_mip->w7);
mr_mip->check=ON;
if ((int)(mr_mip->w7->len&MR_OBITS)>mr_mip->nib) break;
copy(mr_mip->w7,mr_mip->w1);
t=mr_mip->w1,mr_mip->w1=mr_mip->w2,mr_mip->w2=t; /* swap(w1,w2) */
mr_mip->check=OFF;
multiply(_MIPP_ mr_mip->w4,x,mr_mip->w0);
subtract(_MIPP_ mr_mip->w3,mr_mip->w0,mr_mip->w7);
mr_mip->check=ON;
if ((int)(mr_mip->w7->len&MR_OBITS)>mr_mip->nib)
{ /* oops! */
fpack(_MIPP_ mr_mip->w1,mr_mip->w4,x);
negify(x,x);
mr_mip->EXACT=FALSE;
MR_OUT
return;
}
copy(mr_mip->w7,mr_mip->w3);
t=mr_mip->w3,mr_mip->w3=mr_mip->w4,mr_mip->w4=t; /* swap(w3,w4) */
n++;
}
lw2=(int)(mr_mip->w2->len&MR_OBITS);
lw4=(int)(mr_mip->w4->len&MR_OBITS);
lz=lw2+lw4;
if (lz > prc) break; /* too big - exit */
if (last)
{
if (finoff) break;
finoff=TRUE;
q=(*gen)(_MIPP_ x,n);
continue;
}
if (lz>=prc-1)
{ /* nearly finished - so be careful not to overshoot */
if (mr_mip->base==0)
{
#ifndef MR_NOFULLWIDTH
st=mr_mip->w2->w[lw2-1]+1;
if (st==0) ex1=1;
else ex1=muldvm((mr_small)1,(mr_small)0,st,&sr);
st=mr_mip->w4->w[lw4-1]+1;
if (st==0) ex2=1;
else ex2=muldvm((mr_small)1,(mr_small)0,st,&sr);
#endif
}
else
{
ex1=mr_mip->base/(mr_mip->w2->w[lw2-1]+1);
ex2=mr_mip->base/(mr_mip->w4->w[lw4-1]+1);
}
if (ex2>ex1) ex=ex1,ex1=ex2,ex2=ex;
if (lz==prc) ex=ex2;
else ex=ex1;
last=TRUE;
}
a=1;
b=0;
c=0;
d=1;
forever
{
q=(*gen)(_MIPP_ x,n);
if (q<0 || q>=MR_TOOBIG/mr_abs(d))
{ /* there could be more.... *** V3.21 mod *** */
last=FALSE;
break;
}
rm=b-q*d;
b=d;
d=rm;
rm=a-q*c;
a=c;
c=rm;
n++;
if ((mr_small)(mr_abs(c-d))>ex) break;
}
premult(_MIPP_ mr_mip->w1,c,mr_mip->w7);
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,mr_mip->w7,mr_mip->w2);
premult(_MIPP_ mr_mip->w3,c,mr_mip->w7);
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(_MIPP_ mr_mip->w3,mr_mip->w0,mr_mip->w3);
add(_MIPP_ mr_mip->w4,mr_mip->w7,mr_mip->w4);
}
