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factor.c
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factor.c
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/*
This file is part of Alpertron Calculators.
Copyright 2015 Dario Alejandro Alpern
Alpertron Calculators is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
Alpertron Calculators is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with Alpertron Calculators. If not, see <http://www.gnu.org/licenses/>.
*/
#include <string.h>
#include <stdio.h>
#include <stdint.h>
#include <math.h>
#include "bignbr.h"
#include "expression.h"
#include "factor.h"
int yieldFreq;
#ifdef __EMSCRIPTEN__
char upperText[30000];
char lowerText[30000];
char *ptrLowerText;
extern mmCback modmultCallback;
extern long long lModularMult;
extern char *ptrInputText;
#endif
#define TYP_AURIF 100000000
#define TYP_TABLE 150000000
#define TYP_SIQS 200000000
#define TYP_LEHMAN 250000000
#define TYP_RABIN 300000000
#define TYP_EC 350000000
#define MAX_PRIME_SIEVE 7 // Only numbers 7 or 11 are accepted here.
#if MAX_PRIME_SIEVE == 11
#define SIEVE_SIZE (2*3*5*7*11)
#define GROUP_SIZE ((2-1)*(3-1)*(5-1)*(7-1)*(11-1))
#else
#define SIEVE_SIZE (2*3*5*7)
#define GROUP_SIZE ((2-1)*(3-1)*(5-1)*(7-1))
#endif
#define HALF_SIEVE_SIZE (SIEVE_SIZE/2)
char factorsAscii[10000];
static int nbrPrimes, indexPrimes, StepECM, DegreeAurif;
static int FactorIndex;
static BigInteger power, prime;
int *factorArr[FACTOR_ARRSIZE];
static int Typ[4000];
static int indexM, maxIndexM;
static int foundByLehman, performLehman;
static int SmallPrime[670]; /* Primes < 5000 */
int NextEC;
static int EC;
static limb A0[MAX_LEN];
static limb A02[MAX_LEN];
static limb A03[MAX_LEN];
static limb AA[MAX_LEN];
static limb DX[MAX_LEN];
static limb DZ[MAX_LEN];
static limb GD[MAX_LEN];
static limb M[MAX_LEN];
static limb TX[MAX_LEN];
static limb TZ[MAX_LEN];
static limb UX[MAX_LEN];
static limb UZ[MAX_LEN];
static limb W1[MAX_LEN];
static limb W2[MAX_LEN];
static limb W3[MAX_LEN];
static limb W4[MAX_LEN];
static limb WX[MAX_LEN];
static limb WZ[MAX_LEN];
static limb X[MAX_LEN];
static limb Z[MAX_LEN];
static limb Aux1[MAX_LEN];
static limb Aux2[MAX_LEN];
static limb Aux3[MAX_LEN];
static limb Aux4[MAX_LEN];
static limb Xaux[MAX_LEN];
static limb Zaux[MAX_LEN];
static limb root[GROUP_SIZE][MAX_LEN];
static unsigned char sieve[10*SIEVE_SIZE];
static unsigned char sieve2310[SIEVE_SIZE];
static int sieveidx[GROUP_SIZE];
static limb GcdAccumulated[MAX_LEN];
static limb *fieldAA, *fieldTX, *fieldTZ, *fieldUX, *fieldUZ;
static void add3(limb *x3, limb *z3, limb *x2, limb *z2, limb *x1, limb *z1, limb *x, limb *z);
static void duplicate(limb *x2, limb *z2, limb *x1, limb *z1);
static BigInteger Temp1, Temp2, Temp3, Temp4;
BigInteger factorValue, tofactor;
char verbose, prettyprint, cunningham, hexadecimal;
long long Gamma[386];
long long Delta[386];
long long AurifQ[386];
char tofactorDec[30000];
extern int q[MAX_LEN];
int nbrToFactor[MAX_LEN];
struct sFactors astFactorsMod[1000];
int factorsMod[10000];
static void insertBigFactor(struct sFactors *pstFactors, BigInteger *divisor);
static char *findChar(char *str, char c);
enum eEcmResult
{
FACTOR_NOT_FOUND = 0,
FACTOR_FOUND,
CHANGE_TO_SIQS,
};
/* ECM limits for 30, 35, ..., 95 digits */
static int limits[] = { 10, 10, 10, 10, 10, 15, 22, 26, 35, 50, 100, 150, 250 };
/******************************************************/
/* Start of code adapted from Paul Zimmermann's ECM4C */
/******************************************************/
#define ADD 6 /* number of multiplications in an addition */
#define DUP 5 /* number of multiplications in a duplicate */
static void GetYieldFrequency(void)
{
yieldFreq = 1000000 / (NumberLength * NumberLength) + 1;
if (yieldFreq > 100000)
{
yieldFreq = yieldFreq / 100000 * 100000;
}
else if (yieldFreq > 10000)
{
yieldFreq = yieldFreq / 10000 * 10000;
}
else if (yieldFreq > 1000)
{
yieldFreq = yieldFreq / 1000 * 1000;
}
else if (yieldFreq > 100)
{
yieldFreq = yieldFreq / 100 * 100;
}
}
/* returns the number of modular multiplications */
static int lucas_cost(int n, double v)
{
int c, d, e, r;
d = n;
r = (int)((double)d / v + 0.5);
if (r >= n)
{
return (ADD * n);
}
d = n - r;
e = 2 * r - n;
c = DUP + ADD; /* initial duplicate and final addition */
while (d != e)
{
if (d < e)
{
r = d;
d = e;
e = r;
}
if (4 * d <= 5 * e && ((d + e) % 3) == 0)
{ /* condition 1 */
r = (2 * d - e) / 3;
e = (2 * e - d) / 3;
d = r;
c += 3 * ADD; /* 3 additions */
}
else if (4 * d <= 5 * e && (d - e) % 6 == 0)
{ /* condition 2 */
d = (d - e) / 2;
c += ADD + DUP; /* one addition, one duplicate */
}
else if (d <= (4 * e))
{ /* condition 3 */
d -= e;
c += ADD; /* one addition */
}
else if ((d + e) % 2 == 0)
{ /* condition 4 */
d = (d - e) / 2;
c += ADD + DUP; /* one addition, one duplicate */
}
else if (d % 2 == 0)
{ /* condition 5 */
d /= 2;
c += ADD + DUP; /* one addition, one duplicate */
}
else if (d % 3 == 0)
{ /* condition 6 */
d = d / 3 - e;
c += 3 * ADD + DUP; /* three additions, one duplicate */
}
else if ((d + e) % 3 == 0)
{ /* condition 7 */
d = (d - 2 * e) / 3;
c += 3 * ADD + DUP; /* three additions, one duplicate */
}
else if ((d - e) % 3 == 0)
{ /* condition 8 */
d = (d - e) / 3;
c += 3 * ADD + DUP; /* three additions, one duplicate */
}
else if (e % 2 == 0)
{ /* condition 9 */
e /= 2;
c += ADD + DUP; /* one addition, one duplicate */
}
}
return c;
}
/* computes nP from P=(x:z) and puts the result in (x:z). Assumes n>2. */
void prac(int n, limb *x, limb *z, limb *xT, limb *zT, limb *xT2, limb *zT2)
{
int d, e, r, i;
limb *t;
limb *xA = x, *zA = z;
limb *xB = Aux1, *zB = Aux2;
limb *xC = Aux3, *zC = Aux4;
double v[] =
{
1.61803398875,
1.72360679775,
1.618347119656,
1.617914406529,
1.612429949509,
1.632839806089,
1.620181980807,
1.580178728295,
1.617214616534,
1.38196601125 };
/* chooses the best value of v */
r = lucas_cost(n, v[0]);
i = 0;
for (d = 1; d < 10; d++)
{
e = lucas_cost(n, v[d]);
if (e < r)
{
r = e;
i = d;
}
}
d = n;
r = (int)((double)d / v[i] + 0.5);
/* first iteration always begins by Condition 3, then a swap */
d = n - r;
e = 2 * r - n;
memcpy(xB, xA, NumberLength * sizeof(limb)); // B <- A
memcpy(zB, zA, NumberLength * sizeof(limb));
memcpy(xC, xA, NumberLength * sizeof(limb)); // C <- A
memcpy(zC, zA, NumberLength * sizeof(limb));
duplicate(xA, zA, xA, zA); /* A=2*A */
while (d != e)
{
if (d < e)
{
r = d;
d = e;
e = r;
t = xA;
xA = xB;
xB = t;
t = zA;
zA = zB;
zB = t;
}
/* do the first line of Table 4 whose condition qualifies */
if (4 * d <= 5 * e && ((d + e) % 3) == 0)
{ /* condition 1 */
r = (2 * d - e) / 3;
e = (2 * e - d) / 3;
d = r;
add3(xT, zT, xA, zA, xB, zB, xC, zC); /* T = f(A,B,C) */
add3(xT2, zT2, xT, zT, xA, zA, xB, zB); /* T2 = f(T,A,B) */
add3(xB, zB, xB, zB, xT, zT, xA, zA); /* B = f(B,T,A) */
t = xA;
xA = xT2;
xT2 = t;
t = zA;
zA = zT2;
zT2 = t; /* swap A and T2 */
}
else if (4 * d <= 5 * e && (d - e) % 6 == 0)
{ /* condition 2 */
d = (d - e) / 2;
add3(xB, zB, xA, zA, xB, zB, xC, zC); /* B = f(A,B,C) */
duplicate(xA, zA, xA, zA); /* A = 2*A */
}
else if (d <= (4 * e))
{ /* condition 3 */
d -= e;
add3(xT, zT, xB, zB, xA, zA, xC, zC); /* T = f(B,A,C) */
t = xB;
xB = xT;
xT = xC;
xC = t;
t = zB;
zB = zT;
zT = zC;
zC = t; /* circular permutation (B,T,C) */
}
else if ((d + e) % 2 == 0)
{ /* condition 4 */
d = (d - e) / 2;
add3(xB, zB, xB, zB, xA, zA, xC, zC); /* B = f(B,A,C) */
duplicate(xA, zA, xA, zA); /* A = 2*A */
}
else if (d % 2 == 0)
{ /* condition 5 */
d /= 2;
add3(xC, zC, xC, zC, xA, zA, xB, zB); /* C = f(C,A,B) */
duplicate(xA, zA, xA, zA); /* A = 2*A */
}
else if (d % 3 == 0)
{ /* condition 6 */
d = d / 3 - e;
duplicate(xT, zT, xA, zA); /* T1 = 2*A */
add3(xT2, zT2, xA, zA, xB, zB, xC, zC); /* T2 = f(A,B,C) */
add3(xA, zA, xT, zT, xA, zA, xA, zA); /* A = f(T1,A,A) */
add3(xT, zT, xT, zT, xT2, zT2, xC, zC); /* T1 = f(T1,T2,C) */
t = xC;
xC = xB;
xB = xT;
xT = t;
t = zC;
zC = zB;
zB = zT;
zT = t; /* circular permutation (C,B,T) */
}
else if ((d + e) % 3 == 0)
{ /* condition 7 */
d = (d - 2 * e) / 3;
add3(xT, zT, xA, zA, xB, zB, xC, zC); /* T1 = f(A,B,C) */
add3(xB, zB, xT, zT, xA, zA, xB, zB); /* B = f(T1,A,B) */
duplicate(xT, zT, xA, zA);
add3(xA, zA, xA, zA, xT, zT, xA, zA); /* A = 3*A */
}
else if ((d - e) % 3 == 0)
{ /* condition 8 */
d = (d - e) / 3;
add3(xT, zT, xA, zA, xB, zB, xC, zC); /* T1 = f(A,B,C) */
add3(xC, zC, xC, zC, xA, zA, xB, zB); /* C = f(A,C,B) */
t = xB;
xB = xT;
xT = t;
t = zB;
zB = zT;
zT = t; /* swap B and T */
duplicate(xT, zT, xA, zA);
add3(xA, zA, xA, zA, xT, zT, xA, zA); /* A = 3*A */
}
else if (e % 2 == 0)
{ /* condition 9 */
e /= 2;
add3(xC, zC, xC, zC, xB, zB, xA, zA); /* C = f(C,B,A) */
duplicate(xB, zB, xB, zB); /* B = 2*B */
}
}
add3(x, z, xA, zA, xB, zB, xC, zC);
}
/* adds Q=(x2:z2) and R=(x1:z1) and puts the result in (x3:z3),
using 5/6 mul, 6 add/sub and 6 mod. One assumes that Q-R=P or R-Q=P where P=(x:z).
Uses the following global variables:
- n : number to factor
- x, z : coordinates of P
- u, v, w : auxiliary variables
Modifies: x3, z3, u, v, w.
(x3,z3) may be identical to (x2,z2) and to (x,z)
*/
static void add3(limb *x3, limb *z3, limb *x2, limb *z2,
limb *x1, limb *z1, limb *x, limb *z)
{
limb *t = fieldTX;
limb *u = fieldTZ;
limb *v = fieldUX;
limb *w = fieldUZ;
SubtBigNbrModN(x2, z2, v, TestNbr, NumberLength); // v = x2-z2
AddBigNbrModN(x1, z1, w, TestNbr, NumberLength); // w = x1+z1
modmult(v, w, u); // u = (x2-z2)*(x1+z1)
AddBigNbrModN(x2, z2, w, TestNbr, NumberLength); // w = x2+z2
SubtBigNbrModN(x1, z1, t, TestNbr, NumberLength); // t = x1-z1
modmult(t, w, v); // v = (x2+z2)*(x1-z1)
AddBigNbrModN(u, v, t, TestNbr, NumberLength); // t = 2*(x1*x2-z1*z2)
modmult(t, t, w); // w = 4*(x1*x2-z1*z2)^2
SubtBigNbrModN(u, v, t, TestNbr, NumberLength); // t = 2*(x2*z1-x1*z2)
modmult(t, t, v); // v = 4*(x2*z1-x1*z2)^2
if (!memcmp(x, x3, NumberLength*sizeof(limb)))
{
memcpy(u, x, NumberLength * sizeof(int));
memcpy(t, w, NumberLength * sizeof(int));
modmult(z, t, w);
modmult(v, u, z3);
memcpy(x3, w, NumberLength * sizeof(int));
}
else
{
modmult(w, z, x3); // x3 = 4*z*(x1*x2-z1*z2)^2
modmult(x, v, z3); // z3 = 4*x*(x2*z1-x1*z2)^2
}
}
/* computes 2P=(x2:z2) from P=(x1:z1), with 5 mul, 4 add/sub, 5 mod.
Uses the following global variables:
- n : number to factor
- b : (a+2)/4 mod n
- u, v, w : auxiliary variables
Modifies: x2, z2, u, v, w
*/
#if 0
void print(limb *w)
{
char pepe[1000];
Bin2Dec(w, pepe, NumberLength, 0);
printf("%s\n", pepe);
memset(Xaux, 0, NumberLength * sizeof(limb));
Xaux[0].x = 1;
modmult(Xaux, w, Zaux);
Bin2Dec(Zaux, pepe, NumberLength, 0);
printf("%s\n\n", pepe);
}
#endif
static void duplicate(limb *x2, limb *z2, limb *x1, limb *z1)
{
limb *u = fieldUZ;
limb *v = fieldTX;
limb *w = fieldTZ;
AddBigNbrModN(x1, z1, w, TestNbr, NumberLength); // w = x1+z1
modmult(w, w, u); // u = (x1+z1)^2
SubtBigNbrModN(x1, z1, w, TestNbr, NumberLength); // w = x1-z1
modmult(w, w, v); // v = (x1-z1)^2
modmult(u, v, x2); // x2 = u*v = (x1^2 - z1^2)^2
SubtBigNbrModN(u, v, w, TestNbr, NumberLength); // w = u-v = 4*x1*z1
modmult(fieldAA, w, u);
AddBigNbrModN(u, v, u, TestNbr, NumberLength); // u = (v+b*w)
modmult(w, u, z2); // z2 = (w*u)
}
/* End of code adapted from Paul Zimmermann's ECM4C */
static int gcdIsOne(limb *value)
{
UncompressLimbsBigInteger(value, &Temp1);
UncompressLimbsBigInteger(TestNbr, &Temp2);
// Return zero if value is zero or both numbers are equal.
if (Temp1.nbrLimbs == 1 && Temp1.limbs[0].x == 0)
{
return 0;
}
BigIntSubt(&Temp1, &Temp2, &Temp3);
if (Temp3.nbrLimbs == 1 && Temp3.limbs[0].x == 0)
{
return 0;
}
BigIntGcd(&Temp1, &Temp2, &Temp3);
CompressLimbsBigInteger(GD, &Temp3);
if (Temp3.nbrLimbs == 1 && Temp3.limbs[0].x < 2)
{
return Temp3.limbs[0].x; // GCD is less than 2.
}
return 2; // GCD is greater than one.
}
static void GenerateSieve(int initial)
{
int i, j, Q, initModQ;
for (i = 0; i < 10*SIEVE_SIZE; i += SIEVE_SIZE)
{
memcpy(&sieve[i], sieve2310, SIEVE_SIZE);
}
#if MAX_PRIME_SIEVE == 11
j = 5;
Q = 13; /* Point to prime 13 */
#else
j = 4;
Q = 11; /* Point to prime 11 */
#endif
do
{
if (initial > Q * Q)
{
initModQ = initial % Q;
if (initModQ & 1)
{ // initModQ is odd
i = (Q - initModQ) >> 1;
}
else if (initModQ == 0)
{
i = 0;
}
else
{ // initModQ is even
i = Q - (initModQ >> 1);
}
for (; i < 10*SIEVE_SIZE; i += Q)
{
sieve[i] = 1; /* Composite */
}
}
else
{
i = Q * Q - initial;
if (i < 20*SIEVE_SIZE)
{
for (i = i / 2; i < 10*SIEVE_SIZE; i += Q)
{
sieve[i] = 1; /* Composite */
}
}
else
{
break;
}
}
Q = SmallPrime[++j];
#if MAX_PRIME_SIEVE == 11
} while (Q < 5000);
#else
} while (Q < 10*SIEVE_SIZE);
#endif
}
static int Cos(int N)
{
switch (N % 8)
{
case 0:
return 1;
case 4:
return -1;
}
return 0;
}
static int intTotient(int N)
{
int totient, q, k;
totient = q = N;
if (q % 2 == 0)
{
totient /= 2;
do
{
q /= 2;
} while (q % 2 == 0);
}
if (q % 3 == 0)
{
totient = totient * 2 / 3;
do
{
q /= 3;
} while (q % 3 == 0);
}
k = 5;
while (k * k <= q)
{
if (k % 3 != 0 && q % k == 0)
{
totient = totient * (k - 1) / k;
do
{
q /= k;
} while (q % k == 0);
}
k += 2;
}
if (q > 1)
{
totient = totient * (q - 1) / q;
}
return totient;
}
int Moebius(int N)
{
int moebius, q, k;
moebius = 1;
q = N;
if (q % 2 == 0)
{
moebius = -moebius;
q /= 2;
if (q % 2 == 0)
{
return 0;
}
}
if (q % 3 == 0)
{
moebius = -moebius;
q /= 3;
if (q % 3 == 0)
{
return 0;
}
}
k = 5;
while (k * k <= q)
{
if (k % 3 != 0)
{
while (q % k == 0)
{
moebius = -moebius;
q /= k;
if (q % k == 0)
{
return 0;
}
}
}
k += 2;
}
if (q > 1)
{
moebius = -moebius;
}
return moebius;
}
void GetAurifeuilleFactor(struct sFactors *pstFactors, int L, BigInteger *BigBase)
{
BigInteger x, Csal, Dsal, Nbr1;
int k;
BigIntPowerIntExp(BigBase, L, &x); // x <- BigBase^L.
intToBigInteger(&Csal, 1);
intToBigInteger(&Dsal, 1);
for (k = 1; k < DegreeAurif; k++)
{
longToBigInteger(&Nbr1, Gamma[k]);
BigIntMultiply(&Csal, &x, &Csal);
BigIntAdd(&Csal, &Nbr1, &Csal); // Csal <- Csal * x + Gamma[k]
longToBigInteger(&Nbr1, Delta[k]);
BigIntMultiply(&Dsal, &x, &Dsal);
BigIntAdd(&Dsal, &Nbr1, &Dsal); // Dsal <- Dsal * x + Gamma[k]
}
longToBigInteger(&Nbr1, Gamma[k]);
BigIntMultiply(&Csal, &x, &Csal);
BigIntAdd(&Csal, &Nbr1, &Csal); // Csal <- Csal * x + Gamma[k]
BigIntPowerIntExp(BigBase, (L + 1) / 2, &Nbr1); // Nbr1 <- Dsal * base^((L+1)/2)
BigIntMultiply(&Dsal, &Nbr1, &Nbr1);
BigIntAdd(&Csal, &Nbr1, &Dsal);
insertBigFactor(pstFactors, &Dsal);
BigIntSubt(&Csal, &Nbr1, &Dsal);
insertBigFactor(pstFactors, &Dsal);
}
// Get Aurifeuille factors.
void InsertAurifFactors(struct sFactors *pstFactors, BigInteger *BigBase, int Expon, int Incre)
{
int Base = BigBase->limbs[0].x;
if (BigBase->nbrLimbs != 1 || Base >= 386)
{
return; // Base is very big, so go out.
}
if (Expon % 2 == 0 && Incre == -1)
{
do
{
Expon /= 2;
} while (Expon % 2 == 0);
Incre = Base % 4 - 2;
}
if (Expon % Base == 0
&& Expon / Base % 2 != 0
&& ((Base % 4 != 1 && Incre == 1) || (Base % 4 == 1 && Incre == -1)))
{
int N1, q, L, k;
int N = Base;
if (N % 4 == 1)
{
N1 = N;
}
else
{
N1 = 2 * N;
}
DegreeAurif = intTotient(N1) / 2;
for (k = 1; k <= DegreeAurif; k += 2)
{
AurifQ[k] = JacobiSymbol(N, k);
}
for (k = 2; k <= DegreeAurif; k += 2)
{
int t1 = k; // Calculate t2 = gcd(k, N1)
int t2 = N1;
while (t1 != 0)
{
int t3 = t2 % t1;
t2 = t1;
t1 = t3;
}
AurifQ[k] = Moebius(N1 / t2) * intTotient(t2) * Cos((N - 1) * k);
}
Gamma[0] = Delta[0] = 1;
for (k = 1; k <= DegreeAurif / 2; k++)
{
int j;
Gamma[k] = Delta[k] = 0;
for (j = 0; j < k; j++)
{
Gamma[k] =
Gamma[k]
+ N * AurifQ[2 * k
- 2 * j
- 1] * Delta[j]
- AurifQ[2 * k
- 2 * j] * Gamma[j];
Delta[k] =
Delta[k]
+ AurifQ[2 * k
+ 1
- 2 * j] * Gamma[j]
- AurifQ[2 * k
- 2 * j] * Delta[j];
}
Gamma[k] /= 2 * k;
Delta[k] = (Delta[k] + Gamma[k]) / (2 * k + 1);
}
for (k = DegreeAurif / 2 + 1; k <= DegreeAurif; k++)
{
Gamma[k] = Gamma[DegreeAurif - k];
}
for (k = (DegreeAurif + 1) / 2; k < DegreeAurif; k++)
{
Delta[k] = Delta[DegreeAurif - k - 1];
}
q = Expon / Base;
L = 1;
while (L * L <= q)
{
if (q % L == 0)
{
GetAurifeuilleFactor(pstFactors,L, BigBase);
if (q != L * L)
{
GetAurifeuilleFactor(pstFactors, q / L, BigBase);
}
}
L += 2;
}
}
}
void copyString(char *textFromServer)
{
strcpy(factorsAscii, textFromServer);
}
void Cunningham(struct sFactors *pstFactors, BigInteger *BigBase, int Expon,
int increment, BigInteger *BigOriginal)
{
#ifdef __EMSCRIPTEN__
char url[200];
char *ptrUrl;
#endif
int Expon2, k;
char *ptrFactorsAscii;
BigInteger Nbr1, Nbr2;
factorsAscii[0] = 0; // Indicate no new factor found in advance.
Expon2 = Expon;
if (cunningham && BigOriginal->nbrLimbs > 4)
{ // Enter here on numbers of more than 40 digits if the user selected
// get Cunningham factors from server.
#ifdef __EMSCRIPTEN__
databack(lang ? "4<p>Obteniendo los factores primitivos conocidos del servidor Web.</p>":
"4<p>Requesting known primitive factors from Web server.</p>");
// Format URL.
ptrUrl = url;
strcpy(ptrUrl, "factors.pl?base=");
ptrUrl += strlen(ptrUrl);
int2dec(&ptrUrl, BigBase->limbs[0].x);
strcpy(ptrUrl, "&expon=");
ptrUrl += strlen(ptrUrl);
int2dec(&ptrUrl, Expon);
strcpy(ptrUrl, "&type=");
ptrUrl += strlen(ptrUrl);
*ptrUrl++ = (increment > 0? 'p': 'm');
*ptrUrl = 0;
getCunn(url, factorsAscii);
#endif
}
ptrFactorsAscii = factorsAscii;
while (*ptrFactorsAscii > ' ')
{ // Loop through factors found in server.
int nbrDigits;
char *ptrEndFactor = findChar(ptrFactorsAscii, '*');
if (ptrEndFactor == NULL)
{
nbrDigits = (int)strlen(ptrFactorsAscii);
ptrEndFactor = ptrFactorsAscii + nbrDigits;
}
else
{
nbrDigits = (int)(ptrEndFactor - ptrFactorsAscii);
ptrEndFactor++;
}
Dec2Bin(ptrFactorsAscii, Nbr1.limbs, nbrDigits, &Nbr1.nbrLimbs);
Nbr1.sign = SIGN_POSITIVE;
ptrFactorsAscii = ptrEndFactor;
insertBigFactor(pstFactors, &Nbr1);
}
while (Expon2 % 2 == 0 && increment == -1)
{
Expon2 /= 2;
BigIntPowerIntExp(BigBase, Expon2, &Nbr1);
addbigint(&Nbr1, increment);
insertBigFactor(pstFactors, &Nbr1);
InsertAurifFactors(pstFactors,BigBase, Expon2, 1);
}
k = 1;
while (k * k <= Expon)
{
if (Expon % k == 0)
{
if (k % 2 != 0)
{ /* Only for odd exponent */
BigIntPowerIntExp(BigBase, Expon / k, &Nbr1);
addbigint(&Nbr1, increment);
BigIntGcd(&Nbr1, BigOriginal, &Nbr2); // Nbr2 <- gcd(Base^(Expon/k)+incre, original)
insertBigFactor(pstFactors, &Nbr2);
CopyBigInt(&Temp1, BigOriginal);
BigIntDivide(&Temp1, &Nbr2, &Nbr1);
insertBigFactor(pstFactors, &Nbr1);
InsertAurifFactors(pstFactors, BigBase, Expon / k, increment);
}
if ((Expon / k) % 2 != 0)
{ /* Only for odd exponent */
BigIntPowerIntExp(BigBase, k, &Nbr1);
addbigint(&Nbr1, increment);
BigIntGcd(&Nbr1, BigOriginal, &Nbr2); // Nbr2 <- gcd(Base^k+incre, original)
insertBigFactor(pstFactors, &Nbr2);
CopyBigInt(&Temp1, BigOriginal);
BigIntDivide(&Temp1, &Nbr2, &Nbr1);
insertBigFactor(pstFactors, &Nbr1);
InsertAurifFactors(pstFactors, BigBase, k, increment);
}
}
k++;
}
}
static boolean ProcessExponent(struct sFactors *pstFactors, BigInteger *nbrToFactor, int Exponent)
{
#ifdef __EMSCRIPTEN__
char status[200];
char *ptrStatus;
#endif
BigInteger NFp1, NFm1, nthRoot, rootN1, rootN, rootbak;
BigInteger nextroot, dif;
double log2N;
#ifdef __EMSCRIPTEN__
int elapsedTime = (int)(tenths() - originalTenthSecond);
if (elapsedTime / 10 != oldTimeElapsed / 10)
{
oldTimeElapsed = elapsedTime;
ptrStatus = status;
strcpy(ptrStatus, lang ? "4<p>Transcurrió " : "4<p>Time elapsed: ");
ptrStatus += strlen(ptrStatus);
GetDHMS(&ptrStatus, elapsedTime / 10);
strcpy(ptrStatus, lang ? " Exponente potencia +/- 1: " :
" Power +/- 1 exponent: ");
ptrStatus += strlen(ptrStatus);
int2dec(&ptrStatus, Exponent);
*ptrStatus = 0; // Add string terminator.
databack(status);
}
#endif
CopyBigInt(&NFp1, nbrToFactor);
addbigint(&NFp1, 1); // NFp1 <- NumberToFactor + 1
CopyBigInt(&NFm1, nbrToFactor);
addbigint(&NFm1, -1); // NFm1 <- NumberToFactor - 1
log2N = logBigNbr(&NFp1) / Exponent; // Find nth root of number to factor.
expBigNbr(&nthRoot, log2N);
rootbak = nthRoot;
for (;;)
{
BigIntPowerIntExp(&nthRoot, Exponent - 1, &rootN1); // rootN1 <- nthRoot ^ (Exponent-1)
BigIntMultiply(&nthRoot, &rootN1, &rootN); // rootN <- nthRoot ^ Exponent
BigIntSubt(&NFp1, &rootN, &dif); // dif <- NFp1 - rootN
if (dif.nbrLimbs == 1 && dif.limbs[0].x == 0)
{ // Perfect power
Cunningham(pstFactors, &nthRoot, Exponent, -1, nbrToFactor);
return TRUE;
}
addbigint(&dif, 1); // dif <- dif + 1
BigIntDivide(&dif, &rootN1, &Temp1); // Temp1 <- dif / rootN1
subtractdivide(&Temp1, 0, Exponent); // Temp1 <- Temp1 / Exponent
BigIntAdd(&Temp1, &nthRoot, &nextroot); // nextroot <- Temp1 + nthRoot
addbigint(&nextroot, -1); // nextroot <- nextroot - 1
BigIntSubt(&nextroot, &nthRoot, &nthRoot); // nthRoot <- nextroot - nthRoot
if (nthRoot.sign == SIGN_POSITIVE)
{
break; // Not a perfect power
}
CopyBigInt(&nthRoot, &nextroot);
}
nthRoot = rootbak;
for (;;)
{
BigIntPowerIntExp(&nthRoot, Exponent - 1, &rootN1); // rootN1 <- nthRoot ^ (Exponent-1)
BigIntMultiply(&nthRoot, &rootN1, &rootN); // rootN <- nthRoot ^ Exponent
BigIntSubt(&NFm1, &rootN, &dif); // dif <- NFm1 - rootN
if (dif.nbrLimbs == 1 && dif.limbs[0].x == 0)
{ // Perfect power
Cunningham(pstFactors, &nthRoot, Exponent, 1, nbrToFactor);
return TRUE;
}
addbigint(&dif, 1); // dif <- dif + 1
BigIntDivide(&dif, &rootN1, &Temp1); // Temp1 <- dif / rootN1
subtractdivide(&Temp1, 0, Exponent); // Temp1 <- Temp1 / Exponent
BigIntAdd(&Temp1, &nthRoot, &nextroot); // nextroot <- Temp1 + nthRoot
addbigint(&nextroot, -1); // nextroot <- nextroot - 1
BigIntSubt(&nextroot, &nthRoot, &nthRoot); // nthRoot <- nextroot - nthRoot
if (nthRoot.sign == SIGN_POSITIVE)
{
break; // Not a perfect power
}
CopyBigInt(&nthRoot, &nextroot);
}
return FALSE;
}
static void PowerPM1Check(struct sFactors *pstFactors, BigInteger *nbrToFactor)
{
char plus1 = FALSE;
char minus1 = FALSE;
int Exponent = 0;
int i, j;
int modulus;
int mod9 = getRemainder(nbrToFactor, 9);
int maxExpon = nbrToFactor->nbrLimbs * BITS_PER_GROUP;
int numPrimes = 2 * maxExpon + 3;
double logar = logBigNbr(nbrToFactor);
// 33219 = logarithm base 2 of max number supported = 10^10000.
unsigned char ProcessExpon[(33219+7)/8];
unsigned char primes[(2*33219+3+7)/8];
memset(ProcessExpon, 0xFF, sizeof(ProcessExpon));
memset(primes, 0xFF, sizeof(primes));
for (i = 2; i * i < numPrimes; i++)
{ // Generation of primes using sieve of Eratosthenes.
if (primes[i >> 3] & (1 << (i & 7)))
{ // Number i is prime.
for (j = i * i; j < numPrimes; j += i)
{ // Mark multiple of i as composite.
primes[j >> 3] &= ~(1 << (j & 7));
}
}
}
// If the number +/- 1 is multiple of a prime but not a multiple
// of its square then the number +/- 1 cannot be a perfect power.
for (i = 2; i < numPrimes; i++)
{
if (primes[i>>3] & (1 << (i & 7)))
{ // i is prime according to sieve.
unsigned int remainder;
int index;
longToBigInteger(&Temp1, (unsigned int)i*(unsigned int)i);
BigIntRemainder(nbrToFactor, &Temp1, &Temp2); // Temp2 <- nbrToFactor % (i*i)
remainder = (unsigned int)Temp2.limbs[0].x;
if (Temp2.nbrLimbs > 1)
{
remainder += (unsigned int)Temp2.limbs[1].x << BITS_PER_GROUP;
}
if (remainder % i == 1 && remainder != 1)
{
plus1 = TRUE; // NumberFactor cannot be a power + 1
}
if (remainder % i == (unsigned int)i-1 &&
remainder != (unsigned int)i*(unsigned int)i-1)
{
minus1 = TRUE; // NumberFactor cannot be a power - 1
}
if (minus1 && plus1)
{
return;
}
index = i / 2;
if (!(ProcessExpon[index >> 3] & (1<<(index&7))))
{
continue;
}
modulus = remainder % i;
if (modulus > (plus1 ? 1 : 2) && modulus < (minus1 ? i - 1 : i - 2))
{