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@fredrik-johansson
fredrik-johansson committed Oct 9, 2023
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287 changes: 287 additions & 0 deletions BPTJCubes.c
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/*============================================================================
This file is part of FLINT.
FLINT 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 2 of the License, or
(at your option) any later version.
FLINT 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 FLINT; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
===============================================================================*/
/****************************************************************************
BPTJ_cubes.c: Finds solutions to x^3 + y^3 + z^3 = k
Based on the algorithm of Beck, Pine, Tarrant and Jensen
Simultaneously searches for solutions for k = k1, k2, k3
Searches from T = START to STOP
Copyright (C) 2007, William Hart
*****************************************************************************/

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <gmp.h>
#include "long_extras.h"

#define START 1000000
#define STOP 200000000
#define k1 1965
#define k2 1986
#define k3 1991

#define NUMPRIMES 4000
#define TABLESIZE 1800000 // Must be a multiple of CACHEBLOCK
#define CACHEBLOCK 60000
#define RABIN 6

mpz_t temp, temp2, D;

gmp_randstate_t randstate;

static inline
int test_root(unsigned long root, unsigned long T, unsigned long k)
{
long d;

if (root > T/2)
{
mpz_set_ui(D, root);
mpz_pow_ui(D, D, 3);
mpz_sub_ui(D, D, k);
} else
{
mpz_set_ui(D, T-root);
mpz_pow_ui(D, D, 3);
mpz_add_ui(D, D, k);
}

mpz_mul_2exp(D, D, 2);
mpz_divexact_ui(D, D, T);
mpz_set_ui(temp2, T);
mpz_submul_ui(D, temp2, T);
mpz_mul_ui(D, D, 3);

if (mpz_sgn(D) >= 0)
{
mpz_sqrtrem(D, temp2, D);
if (!mpz_sgn(temp2))
{
if (!mpz_fdiv_r_ui(temp, D, 3))
{
d = mpz_fdiv_r_ui(temp, D, 6);
if ((((3*T)%6) == d) || (((3*T)%6) == 6-d)) return 1;
}
}
}

return 0;

}

int main()
{
gmp_randinit_default(randstate);

FILE * file1 = fopen("output.log","w");

unsigned long T = z_nextprime(START, 0);
double Tinv;
unsigned long cuberoot1;
unsigned long root1, root2, root3;
unsigned long s = 0, t, p;
unsigned char * current;

unsigned char * table = (unsigned char *) malloc(TABLESIZE);
unsigned long * mod = (unsigned long *) malloc(NUMPRIMES*sizeof(unsigned long));
unsigned long * prime = (unsigned long *) malloc(NUMPRIMES*sizeof(unsigned long));

s = 3;
unsigned long i;
for (i = 0; i < NUMPRIMES; i++)
{
prime[i] = s;
s = z_nextprime(s, 0);
}
unsigned long i;
for (i = 0; i < NUMPRIMES; i++)
{
s = (T%prime[i]);
if (s == 0) s = prime[i];
mod[i] = prime[i]-s;
}


mpz_init(temp);
mpz_init(temp2);
mpz_init(D);

unsigned long Ttab = 0;

while (T < STOP)
{
memset(table, 0, TABLESIZE);
unsigned long offset;
for (offset = 0; offset < TABLESIZE; offset+=CACHEBLOCK)
{
unsigned long i;
for (i = 0; i < NUMPRIMES; i++)
{
s = mod[i];
p = prime[i];
current = table + offset;
for ( ; s < CACHEBLOCK; s += p) current[s] = 1;
s -= CACHEBLOCK;
mod[i] = s;
}
}

mpz_set_ui(temp, T);
while (!mpz_probab_prime_p(temp,3))
{
T += 2;
Ttab += 2;
while (table[Ttab])
{
T += 2;
Ttab += 2;
}
mpz_set_ui(temp, T);
}
Tinv = z_precompute_inverse(T);

while (Ttab < TABLESIZE)
{
root1 = z_cuberootmod(&cuberoot1, k1, T);
if (root1)
{
if (cuberoot1 != 1)
{
root2 = z_mulmod_precomp(root1, cuberoot1, Tinv, T);
root3 = z_mulmod_precomp(root2, cuberoot1, Tinv, T);
}
if (test_root(root1, T, k1))
{
fprintf(file1,"k = %ld, T = %ld, root = %ld\n", k1, T, root1);
fflush(file1);
abort();
}

if (cuberoot1 != 1)
{
if (test_root(root2, T, k1))
{
fprintf(file1,"k = %ld, T = %ld, root = %ld\n", k1, T, root2);
fflush(file1);
abort();
}
if (test_root(root3, T, k1))
{
fprintf(file1,"k = %ld, T = %ld, root = %ld\n", k1, T, root3);
fflush(file1);
abort();
}
}
}
root1 = z_cuberootmod(&cuberoot1, k2, T);
if (root1)
{
if (cuberoot1 != 1)
{
root2 = z_mulmod_precomp(root1, cuberoot1, Tinv, T);
root3 = z_mulmod_precomp(root2, cuberoot1, Tinv, T);
}
if (test_root(root1, T, k2))
{
fprintf(file1,"k = %ld, T = %ld, root = %ld\n", k2, T, root1);
fflush(file1);
abort();
}

if (cuberoot1 != 1)
{
if (test_root(root2, T, k2))
{
fprintf(file1,"k = %ld, T = %ld, root = %ld\n", k2, T, root2);
fflush(file1);
abort();
}
if (test_root(root3, T, k2))
{
fprintf(file1,"k = %ld, T = %ld, root = %ld\n", k2, T, root3);
fflush(file1);
abort();
}
}
}
root1 = z_cuberootmod(&cuberoot1, k3, T);
if (root1)
{
if (cuberoot1 != 1)
{
root2 = z_mulmod_precomp(root1, cuberoot1, Tinv, T);
root3 = z_mulmod_precomp(root2, cuberoot1, Tinv, T);
}
if (test_root(root1, T, k3))
{
fprintf(file1,"k = %ld, T = %ld, root = %ld\n", k3, T, root1);
fflush(file1);
abort();
}

if (cuberoot1 != 1)
{
if (test_root(root2, T, k3))
{
fprintf(file1,"k = %ld, T = %ld, root = %ld\n", k3, T, root2);
fflush(file1);
abort();
}
if (test_root(root3, T, k3))
{
fprintf(file1,"k = %ld, T = %ld, root = %ld\n", k3, T, root3);
fflush(file1);
abort();
}
}
}

do
{
do
{
T += 2;
Ttab += 2;
} while (table[Ttab] && (Ttab < TABLESIZE));
Tinv = z_precompute_inverse(T);
} while (!z_isprime_precomp(T, Tinv) && (Ttab < TABLESIZE));

t++;
if ((t%1000000UL) == 0)
{
fprintf(file1,"Checkpoint T = %ld\n", T);
fflush(file1);
}

}
Ttab -= TABLESIZE;
}

mpz_clear(temp);
mpz_clear(temp2);
mpz_clear(D);
gmp_randclear(randstate);

return 0;
}
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