/*****************************************************************************/
/* */
/* FACTOR (a**p+b**p)/(a+b) (when [(a**p+b**p)/(a+b)] is a pth power) */
/* 11/03/06 (dkc) */
/* */
/* This program factors (a**p+b**p)/(a+b). Use "table3b" (same as "table3")*/
/* for a<1000000. Use "table4b" (same as "table4" except for the range of */
/* a) for 1000000<a<2000000. Use "table6b" (same as "table6") for 2000000< */
/* a<2500000. (Modify "insize" accordingly.) */
/* */
/* Note: [(a**p+b**p)/(a+b)] can have only two distinct prime factors. */
/* */
/* The output is a, b, (factor0<<16)|factor1, (power0<<20)|(power1<<4)|code */
/* where "factor0" and "factor1" are the distinct prime factors of */
/* [(a**p+b**p)/(a+b)], "power0" and "power1" are the powers of these */
/* factors, and "code" is set to 1 if p divides a+b, or 0 otherwise. */
/* */
/* If a is even, p does not divide a, and (a/2)**(p-1) is not congruent to */
/* 1 modulus p**3, then an error is indicated ("error[1]" is set to 9). b */
/* is treated similarly. */
/* */
/* If a is odd, p divides a+b, and a**(p-1) is not congruent to 1 modulus */
/* p**3, then an error is indicated ("error[1]" is set to 9). b and a-b */
/* are treated similarly. */
/* */
/* If p**3 divides a, b, a-b or p**4 divides a+b, 2 does not divide a, and */
/* a**(p-1) is not congruent to 1 modulus p**3, then an error is indicated */
/* ("error[1]" is set to 8). b and a-b are treated similarly. If p**3 */
/* divides a, b, or a-b or p**4 divides a+b, 2 does not divide a+b, p does */
/* not divide a+b, and (a+b)**(p-1) is not congruent to 1 modulus p**3, */
/* then an error is indicated. If p**3 divides a, b, or a-b or p**4 */
/* divides a+b, 2 does not divide a+b, p divides a+b, and [(a+b)/p]**(p-1) */
/* is not congruent to 1 modulus p**3, then an error is indicated. */
/* */
/* Output of this program is input to "prop28d.c". */
/* */
/*****************************************************************************/
#include <stdio.h>
#include <math.h>
#include "table6b.h"
void bigprod(unsigned int a, unsigned int b, unsigned int c, unsigned int *p);
void quotient(unsigned int *a, unsigned int *b, unsigned int);
void bigbigs(unsigned int *a, unsigned int *b);
void bigbigd(unsigned int *a, unsigned int *b);
void bigbigq(unsigned int a, unsigned int b, unsigned int c, unsigned int d,
unsigned int *e, unsigned int f, unsigned int g);
int main ()
{
unsigned int p=3; // input prime
extern unsigned short table[];
extern unsigned int tmptab[];
extern unsigned int input[];
extern unsigned int output[];
extern unsigned int error[];
extern unsigned int tmpsav;
unsigned int c,ps,pc,pf;
unsigned int tsize=1228;
unsigned int tmpsiz;
unsigned int insiz=1068; // table6b
//unsigned int insiz=2534; // table4b
//unsigned int insiz=4284; // table3b
unsigned int outsiz=5000*3;
unsigned int d,e,temp,qflag;
unsigned int i,j,k,l,m;
unsigned int flag,sflag,tflag,iters,sumdif;
int pflag;
unsigned int S[2],T[2],V[2],X[3],Y[4],Z[4];
unsigned int n=0;
FILE *Outfp;
Outfp = fopen("out28e.dat","w");
/*********************************/
/* extend prime look-up table */
/*********************************/
for (i=0; i<tsize; i++) tmptab[i] = (int)(table[i]);
tmpsiz=tsize;
for (d=10001; d<160000; d++) {
if(d==(d/2)*2) continue;
if(d==(d/3)*3) continue;
if(d==(d/5)*5) continue;
if(d==(d/7)*7) continue;
if(d==(d/11)*11) continue;
if(d==(d/13)*13) continue;
if(d==(d/17)*17) continue;
if(d==(d/19)*19) continue;
/************************************************/
/* look for prime factors using look-up table */
/************************************************/
l = (int)(100.0 + sqrt((double)d));
k=0;
if (l>table[tsize-1]) {
error[0]=1;
aspin: goto aspin;
}
else {
for (i=0; i<tsize; i++) {
if (table[i] < l) k=i;
else break;
}
}
flag=1;
l=k;
for (i=0; i<=l; i++) {
k = table[i];
if ((d/k)*k == d) {
flag=0;
break;
}
}
if (flag==1) {
tmptab[tmpsiz]=d;
tmpsiz = tmpsiz + 1;
}
}
/***********************************/
/* factor (d**p + e**p)/(d + e) */
/***********************************/
ps=p*p;
pc=ps*p;
pf=pc*p;
pflag=0;
error[0]=0; // clear error array
error[1]=0;
error[2]=0;
for (j=0; j<insiz; j++) {
zloop:if (pflag<2) {
d=input[3*j];
e=input[3*j+1];
c=input[3*j+2];
sumdif=1;
}
else {
d=input[3*(j-1)+1];
e=input[3*j+1];
c=input[3*j+2];
sumdif=0;
}
if (c!=2)
goto askip;
if (sumdif==1) {
if (((d+e)/p)*p==(d+e))
qflag=1;
else
qflag=0;
}
else {
if (((d-e)/p)*p==(d-e))
qflag=1;
else
qflag=0;
}
/**********************************************************/
/* check if p**3 divides a, b, or a-b or p**4 divides a+b */
/**********************************************************/
qflag=0;
if ((d/pc)*pc==d)
qflag=1;
if ((e/pc)*pc==e)
qflag=1;
if (sumdif==1) {
if (((d+e)/pf)*pf==(d+e))
qflag=1;
if (((d-e)/pc)*pc==(d-e))
qflag=1;
}
if (sumdif==0) {
if (((d-e)/pf)*pf==(d-e))
qflag=1;
if (((d+e)/pc)*pc==(d+e))
qflag=1;
}
/************************************/
/* compute (d**p + e**p)/(d + e) */
/************************************/
Y[0] = 0;
Y[1] = 0;
Y[2] = 0;
Y[3] = d;
for (i=0; i<p-1; i++) {
bigprod(Y[2], Y[3], d, X);
Y[1]=X[0];
Y[2]=X[1];
Y[3]=X[2];
}
Z[0] = 0;
Z[1] = 0;
Z[2] = 0;
Z[3] = e;
for (i=0; i<p-1; i++) {
bigprod(Z[2], Z[3], e, X);
Z[1]=X[0];
Z[2]=X[1];
Z[3]=X[2];
}
if (sumdif!=0)
bigbigs(Y, Z);
else
bigbigd(Y, Z);
if (sumdif!=0) {
temp=d+e;
if (((d+e)/p)*p==(d+e))
temp=temp*p;
}
else {
temp=d-e;
if (((d-e)/p)*p==(d-e))
temp=temp*p;
}
bigbigq(Z[0], Z[1], Z[2], Z[3], Y, 0, temp);
S[0]=Y[2];
S[1]=Y[3];
/************************************************/
/* look for prime factors using look-up table */
/************************************************/
iters=0;
for (i=0; i<tmpsiz; i++) {
m=0;
k = tmptab[i];
quotient(S, T, k);
V[0]=T[0];
V[1]=T[1];
bigprod(T[0], T[1], k, X);
if ((S[0]!=X[1]) || (S[1]!=X[2]))
continue;
if (((k-1)/ps)*ps!=(k-1))
goto askip;
aloop: S[0]=V[0];
S[1]=V[1];
m=m+1;
quotient(S, T, k);
V[0]=T[0];
V[1]=T[1];
bigprod(T[0], T[1], k, X);
if ((S[0]==X[1]) && (S[1]==X[2])) goto aloop;
if ((m/3)*3!=m) {
error[0]=2;
goto bskip;
}
iters=iters+1;
if (iters==2)
break;
sflag=k;
tflag=m;
}
if ((S[0]!=0)||(S[1]!=1)) {
error[0]=3;
goto bskip;
}
sflag=(k<<16)|sflag;
tflag=(m<<8)|tflag;
tflag=(tflag<<16)|qflag;
/***********************************************/
/* output prime factors satisfying criterion */
/***********************************************/
if (qflag!=0) {
if ((d/2)*2!=d) {
flag=0;
if (((d-1)/pc)*pc==(d-1))
flag=1;
if (((d+1)/pc)*pc==(d+1))
flag=1;
if (flag==0)
error[1]=8;
}
if ((e/2)*2!=e) {
flag=0;
if (((e-1)/pc)*pc==(e-1))
flag=1;
if (((e+1)/pc)*pc==(e+1))
flag=1;
if (flag==0)
error[1]=8;
}
if (sumdif==1) {
if (((d-e)/2)*2!=(d-e)) {
flag=0;
if ((((d-e)-1)/pc)*pc==((d-e)-1))
flag=1;
if ((((d-e)+1)/pc)*pc==((d-e)+1))
flag=1;
if (flag==0)
error[1]=8;
}
if (((d+e)/2)*2!=(d+e)) {
if (((d+e)/p)*p==(d+e)) {
flag=0;
if (((((d+e)/p)-1)/pc)*pc==(((d+e)/p)-1))
flag=1;
if (((((d+e)/p)+1)/pc)*pc==(((d+e)/p)+1))
flag=1;
if (flag==0)
error[1]=8;
}
else {
flag=0;
if ((((d+e)-1)/pc)*pc==((d+e)-1))
flag=1;
if ((((d+e)+1)/pc)*pc==((d+e)+1))
flag=1;
if (flag==0)
error[1]=8;
}
}
}
else {
if (((d+e)/2)*2!=(d+e)) {
flag=0;
if ((((d+e)-1)/pc)*pc==((d+e)-1))
flag=1;
if ((((d+e)+1)/pc)*pc==((d+e)+1))
flag=1;
if (flag==0)
error[1]=8;
}
if (((d-e)/2)*2!=(d-e)) {
if (((d-e)/p)*p==(d-e)) {
flag=0;
if (((((d-e)/p)-1)/pc)*pc==(((d-e)/p)-1))
flag=1;
if (((((d-e)/p)+1)/pc)*pc==(((d-e)/p)+1))
flag=1;
if (flag==0)
error[1]=8;
}
else {
flag=0;
if ((((d-e)-1)/pc)*pc==((d-e)-1))
flag=1;
if ((((d-e)+1)/pc)*pc==((d-e)+1))
flag=1;
if (flag==0)
error[1]=8;
}
}
}
}
//
// "split" tests
//
if ((d/2)*2==d) {
if ((d/p)*p!=d) {
flag=0;
if ((((d/2)-1)/pc)*pc==((d/2)-1))
flag=1;
if ((((d/2)+1)/pc)*pc==((d/2)+1))
flag=1;
if (flag==0)
error[1]=9;
}
}
else {
if (sumdif==1) {
if (((d+e)/p)*p==(d+e)) {
flag=0;
if (((d-1)/pc)*pc==(d-1))
flag=1;
if (((d+1)/pc)*pc==(d+1))
flag=1;
if (flag==0)
error[1]=9;
}
}
else {
if (((d-e)/p)*p==(d-e)) {
flag=0;
if (((d-1)/pc)*pc==(d-1))
flag=1;
if (((d+1)/pc)*pc==(d+1))
flag=1;
if (flag==0)
error[1]=9;
}
}
}
if ((e/2)*2==e) {
if ((e/p)*p!=e) {
flag=0;
if ((((e/2)-1)/pc)*pc==((e/2)-1))
flag=1;
if ((((e/2)+1)/pc)*pc==((e/2)+1))
flag=1;
if (flag==0)
error[1]=9;
}
}
else {
if (sumdif==1) {
if (((d+e)/p)*p==(d+e)) {
flag=0;
if (((e-1)/pc)*pc==(e-1))
flag=1;
if (((e+1)/pc)*pc==(e+1))
flag=1;
if (flag==0)
error[1]=9;
}
}
else {
if (((d-e)/p)*p==(d-e)) {
flag=0;
if (((e-1)/pc)*pc==(e-1))
flag=1;
if (((e+1)/pc)*pc==(e+1))
flag=1;
if (flag==0)
error[1]=9;
}
}
}
if (sumdif==1) {
if (((d-e)/2)*2!=(d-e)) {
if (((d+e)/p)*p==(d+e)) {
flag=0;
if ((((d-e)-1)/pc)*pc==((d-e)-1))
flag=1;
if ((((d-e)+1)/pc)*pc==((d-e)+1))
flag=1;
if (flag==0)
error[1]=9;
}
}
}
else {
if (((d+e)/2)*2!=(d+e)) {
if (((d-e)/p)*p==(d-e)) {
flag=0;
if ((((d+e)-1)/pc)*pc==((d+e)-1))
flag=1;
if ((((d+e)+1)/pc)*pc==((d+e)+1))
flag=1;
if (flag==0)
error[1]=9;
}
}
}
if (n+4>outsiz) {
error[0]=6;
goto cskip;
}
output[n]=d;
output[n+1]=e;
output[n+2]=sflag;
output[n+3]=tflag;
n=n+4;
askip:if (pflag==2)
pflag=-1;
pflag+=1;
if (pflag==2)
goto zloop;
}
goto cskip;
bskip:
error[1]=d;
error[2]=e;
cskip:
output[n]=0xffffffff;
fprintf(Outfp," error0=%d error1=%d \n",error[0],error[1]);
fprintf(Outfp," count=%d \n",(n+1)/4);
for (i=0; i<(n+1)/4; i++)
fprintf(Outfp," %#10x, %#10x, %#10x, %#10x, \n",output[4*i],output[4*i+1],
output[4*i+2],output[4*i+3]);
fclose(Outfp);
if (error[1]!=0)
printf(" error \n");
return(0);
}