static PyObject *
GMPy_MPZ_Function_IsSquare(PyObject *self, PyObject *other)
{
int res;
MPZ_Object *tempx;
if (MPZ_Check(other)) {
res = mpz_perfect_square_p(MPZ(other));
}
else {
if (!(tempx = GMPy_MPZ_From_Integer(other, NULL))) {
TYPE_ERROR("is_square() requires 'mpz' argument");
return NULL;
}
else {
res = mpz_perfect_square_p(tempx->z);
Py_DECREF((PyObject*)tempx);
}
}
if (res)
Py_RETURN_TRUE;
else
Py_RETURN_FALSE;
}
/* See Cohen 1.5.3 */
int modified_cornacchia(mpz_t x, mpz_t y, mpz_t D, mpz_t p)
{
int result = 0;
mpz_t a, b, c, d;
if (mpz_cmp_ui(p, 2) == 0) {
mpz_add_ui(x, D, 8);
if (mpz_perfect_square_p(x)) {
mpz_sqrt(x, x);
mpz_set_ui(y, 1);
result = 1;
}
return result;
}
if (mpz_jacobi(D, p) == -1) /* No solution */
return 0;
mpz_init(a);
mpz_init(b);
mpz_init(c);
mpz_init(d);
sqrtmod(x, D, p, a, b, c, d);
if ( (mpz_even_p(D) && mpz_odd_p(x)) || (mpz_odd_p(D) && mpz_even_p(x)) )
mpz_sub(x, p, x);
mpz_mul_ui(a, p, 2);
mpz_set(b, x);
mpz_sqrt(c, p);
mpz_mul_ui(c, c, 2);
/* Euclidean algorithm */
while (mpz_cmp(b, c) > 0) {
mpz_set(d, a);
mpz_set(a, b);
mpz_mod(b, d, b);
}
mpz_mul_ui(c, p, 4);
mpz_mul(a, b, b);
mpz_sub(a, c, a); /* a = 4p - b^2 */
mpz_abs(d, D); /* d = |D| */
if (mpz_divisible_p(a, d)) {
mpz_divexact(c, a, d);
if (mpz_perfect_square_p(c)) {
mpz_set(x, b);
mpz_sqrt(y, c);
result = 1;
}
}
mpz_clear(a);
mpz_clear(b);
mpz_clear(c);
mpz_clear(d);
return result;
}
int main(int argc, const char **argv) {
char str[100];
uint64_t n, maxn;
if(argc > 1)
maxn=atoll(argv[1]);
else
maxn=1000;
mpz_t fac;
mpz_t fac_plus;
mpz_init_set_ui(fac, 1UL);
mpz_init_set_ui(fac_plus, 1UL);
for(n = 2; n < maxn; n++) {
// fac *= n;
mpz_mul_ui(fac, fac, n);
// fac_plus = fac + 1;
mpz_add_ui(fac_plus, fac, 1UL);
if(mpz_perfect_square_p(fac_plus))
printf("found %" PRIu64 "\n", n);
else if(0){
mpz_get_str(str, 10, fac_plus);
printf("n=1: n!+1=%s\n", str);
}
}
printf("last checked n=%" PRIu64 "\n", n);
return 0;
}
int main() {
unsigned long long a,b;
mpz_t a2, b3, v, sum;
mpz_init(a2);
mpz_init(b3);
mpz_init(v);
mpz_init_set_ui(sum, 0);
for (b = 1; b < sqrt(MAX); b++) {
mpz_ui_pow_ui(b3, b, 3);
for (a = 1; a < b ; a++) {
mpz_ui_pow_ui(a2, a, 2);
mpz_add(v, a2, b3);
if (!mpz_divisible_ui_p(v, a)) {
continue;
}
mpz_div_ui(v, v, a);
if (mpz_perfect_square_p(v)) {
mpz_add(sum, sum, v);
printf("%s %llu %llu\n", mpz_get_str(NULL, 10, v), a, b);
}
}
}
return(0);
}
// NOTE: Runs in 1 minutes. Not satisfactory.
//
// Gotta redo this using Pythagorean triples
int main() {
const int N = 1000000000;
mpz_class sumOfPerimeters = 0, p = 0;
for (int n = 3; 3 * n + 1 <= N; n += 2) { // HACK
p = 3 * n - 1;
p *= n + 1;
if (mpz_perfect_square_p(p.get_mpz_t())) sumOfPerimeters += 3 * n - 1;
p = 3 * n + 1;
p *= n - 1;
if (mpz_perfect_square_p(p.get_mpz_t())) sumOfPerimeters += 3 * n + 1;
}
std::cout << sumOfPerimeters << "\n";
return 0;
}
int
main(int argc, char **argv)
{
char line[INTEGER_LIMIT];
if (argc > 1)
strncpy(&line[0], argv[1], INTEGER_LIMIT);
else if (scanf("%s\n", &line[0]) != 1) {
fprintf(stderr, "factor: unable to read number from stdin\n");
return 1;
}
mpz_t n;
mpz_init(n);
if (mpz_set_str(n, &line[0], 0) == -1 || mpz_cmp_ui(n, 1) < 0) {
fprintf(stderr, "factor: input must be a positive integer\n");
mpz_clear(n);
return 1;
}
if (mpz_cmp_ui(n, 1) == 0 || mpz_probab_prime_p(n, MILLERRABIN_REPEATS) > 0) {
gmp_printf("%Zd: %Zd\n", n, n);
mpz_clear(n);
return 0;
}
mpz_t t;
mpz_init(t);
mpz_sqrt(t, n);
struct factors *f = factors_create();
struct prime_sieve *ps = prime_sieve_create(MIN(TRIALDIVISION_LIMIT, mpz_get_ui(t)));
if (mpz_perfect_square_p(n)) {
factors_push(f, t);
factors_push(f, t);
} else {
mpz_set(t, n);
factors_push(f, t);
}
/* run trial division to find find small factors */
while (factors_remove_composite(f, t) && trial_division(t, f, ps));
prime_sieve_destroy(ps);
/* run quadratic sieve until factorized into only prime numbers */
while (factors_remove_composite(f, t) && quadratic_sieve(t, f, QUADRATIC_SIEVE_SIZE));
factors_sort(f);
print_result(n, f);
mpz_clears(n, t, NULL);
factors_destroy(f);
return 0;
}
// Factor using lehman method.
int _factor_lehman_method(mpz_class &rop, const mpz_class &n)
{
if (n < 21)
throw std::runtime_error("Require n >= 21 to use lehman method");
int ret_val = 0;
mpz_class u_bound;
mpz_root(u_bound.get_mpz_t(), n.get_mpz_t(), 3);
u_bound = u_bound + 1;
Sieve::iterator pi(u_bound.get_ui());
unsigned p;
while ((p = pi.next_prime()) <= u_bound.get_ui()) {
if (n % p == 0) {
rop = n / p;
ret_val = 1;
break;
}
}
if (!ret_val) {
mpz_class k, a, b, l;
mpf_class t;
k = 1;
while (k <= u_bound) {
t = 2 * sqrt(k * n);
mpz_set_f(a.get_mpz_t(), t.get_mpf_t());
mpz_root(b.get_mpz_t(), n.get_mpz_t(), 6);
mpz_root(l.get_mpz_t(), k.get_mpz_t(), 2);
b = b / (4 * l);
b = b + a;
while (a <= b) {
l = a * a - 4 * k * n;
if (mpz_perfect_square_p(l.get_mpz_t())) {
mpz_sqrt(b.get_mpz_t(), l.get_mpz_t());
b = a + b;
mpz_gcd(rop.get_mpz_t(), n.get_mpz_t(), b.get_mpz_t());
ret_val = 1;
break;
}
a = a + 1;
}
if (ret_val)
break;
k = k + 1;
}
}
return ret_val;
}
/* Return non-zero iff c+i*d is an exact square (a+i*b)^2,
with a, b both of the form m*2^e with m, e integers.
If so, returns in a+i*b the corresponding square root, with a >= 0.
The variables a, b must not overlap with c, d.
We have c = a^2 - b^2 and d = 2*a*b.
If one of a, b is exact, then both are (see algorithms.tex).
Case 1: a <> 0 and b <> 0.
Let a = m*2^e and b = n*2^f with m, e, n, f integers, m and n odd
(we will treat apart the case a = 0 or b = 0).
Then 2*a*b = m*n*2^(e+f+1), thus necessarily e+f >= -1.
Assume e < 0, then f >= 0, then a^2 - b^2 = m^2*2^(2e) - n^2*2^(2f) cannot
be an integer, since n^2*2^(2f) is an integer, and m^2*2^(2e) is not.
Similarly when f < 0 (and thus e >= 0).
Thus we have e, f >= 0, and a, b are both integers.
Let A = 2a^2, then eliminating b between c = a^2 - b^2 and d = 2*a*b
gives A^2 - 2c*A - d^2 = 0, which has solutions c +/- sqrt(c^2+d^2).
We thus need c^2+d^2 to be a square, and c + sqrt(c^2+d^2) --- the solution
we are interested in --- to be two times a square. Then b = d/(2a) is
necessarily an integer.
Case 2: a = 0. Then d is necessarily zero, thus it suffices to check
whether c = -b^2, i.e., if -c is a square.
Case 3: b = 0. Then d is necessarily zero, thus it suffices to check
whether c = a^2, i.e., if c is a square.
*/
static int
mpc_perfect_square_p (mpz_t a, mpz_t b, mpz_t c, mpz_t d)
{
if (mpz_cmp_ui (d, 0) == 0) /* case a = 0 or b = 0 */
{
/* necessarily c < 0 here, since we have already considered the case
where x is real non-negative and y is real */
MPC_ASSERT (mpz_cmp_ui (c, 0) < 0);
mpz_neg (b, c);
if (mpz_perfect_square_p (b)) /* case 2 above */
{
mpz_sqrt (b, b);
mpz_set_ui (a, 0);
return 1; /* c + i*d = (0 + i*b)^2 */
}
}
else /* both a and b are non-zero */
{
if (mpz_divisible_2exp_p (d, 1) == 0)
return 0; /* d must be even */
mpz_mul (a, c, c);
mpz_addmul (a, d, d); /* c^2 + d^2 */
if (mpz_perfect_square_p (a))
{
mpz_sqrt (a, a);
mpz_add (a, c, a); /* c + sqrt(c^2+d^2) */
if (mpz_divisible_2exp_p (a, 1))
{
mpz_tdiv_q_2exp (a, a, 1);
if (mpz_perfect_square_p (a))
{
mpz_sqrt (a, a);
mpz_tdiv_q_2exp (b, d, 1); /* d/2 */
mpz_divexact (b, b, a); /* d/(2a) */
return 1;
}
}
}
}
return 0; /* not a square */
}
static PyObject *
GMPy_MPZ_Method_IsSquare(PyObject *self, PyObject *other)
{
int res;
res = mpz_perfect_square_p(MPZ(self));
if (res)
Py_RETURN_TRUE;
else
Py_RETURN_FALSE;
}
/* return non zero iff x^y is exact.
Assumes x and y are ordinary numbers (neither NaN nor Inf),
and y is not zero.
*/
int
mpfr_pow_is_exact (mpfr_srcptr x, mpfr_srcptr y)
{
mp_exp_t d;
unsigned long i, c;
mp_limb_t *yp;
if ((mpfr_sgn (x) < 0) && (mpfr_isinteger (y) == 0))
return 0;
if (mpfr_sgn (y) < 0)
return mpfr_cmp_si_2exp (x, MPFR_SIGN(x), MPFR_EXP(x) - 1) == 0;
/* compute d such that y = c*2^d with c odd integer */
d = MPFR_EXP(y) - MPFR_PREC(y);
/* since y is not zero, necessarily one of the mantissa limbs is not zero,
thus we can simply loop until we find a non zero limb */
yp = MPFR_MANT(y);
for (i = 0; yp[i] == 0; i++, d += BITS_PER_MP_LIMB);
/* now yp[i] is not zero */
count_trailing_zeros (c, yp[i]);
d += c;
if (d < 0)
{
mpz_t a;
mp_exp_t b;
mpz_init (a);
b = mpfr_get_z_exp (a, x); /* x = a * 2^b */
c = mpz_scan1 (a, 0);
mpz_div_2exp (a, a, c);
b += c;
/* now a is odd */
while (d != 0)
{
if (mpz_perfect_square_p (a))
{
d++;
mpz_sqrt (a, a);
}
else
{
mpz_clear (a);
return 0;
}
}
mpz_clear (a);
}
return 1;
}
static bool HHVM_FUNCTION(gmp_perfect_square,
const Variant& data) {
mpz_t gmpData;
if (!variantToGMPData(cs_GMP_FUNC_NAME_GMP_PERFECT_SQUARE, gmpData, data)) {
return false;
}
bool isPerfectSquare = (mpz_perfect_square_p(gmpData) != 0);
mpz_clear(gmpData);
return isPerfectSquare;
}
int
main(void)
{
int i, result;
FLINT_TEST_INIT(state);
flint_printf("is_square....");
fflush(stdout);
for (i = 0; i < 10000 * flint_test_multiplier(); i++)
{
fmpz_t a;
mpz_t b;
int r1, r2;
fmpz_init(a);
mpz_init(b);
fmpz_randtest(a, state, 200);
if (n_randint(state, 2) == 0)
fmpz_mul(a, a, a);
fmpz_get_mpz(b, a);
r1 = fmpz_is_square(a);
r2 = mpz_perfect_square_p(b);
result = (r1 == r2);
if (!result)
{
flint_printf("FAIL:\n");
gmp_printf("b = %Zd\n", b);
abort();
}
fmpz_clear(a);
mpz_clear(b);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
/* Exercise mpz_perfect_square_p compared to what mpz_sqrt says. */
void
check_sqrt (int reps)
{
mpz_t x2, x2t, x;
mp_size_t x2n;
int res;
int i;
/* int cnt = 0; */
gmp_randstate_ptr rands = RANDS;
mpz_t bs;
mpz_init (bs);
mpz_init (x2);
mpz_init (x);
mpz_init (x2t);
for (i = 0; i < reps; i++)
{
mpz_urandomb (bs, rands, 9);
x2n = mpz_get_ui (bs);
mpz_rrandomb (x2, rands, x2n);
/* mpz_out_str (stdout, -16, x2); puts (""); */
res = mpz_perfect_square_p (x2);
mpz_sqrt (x, x2);
mpz_mul (x2t, x, x);
if (res != (mpz_cmp (x2, x2t) == 0))
{
printf ("mpz_perfect_square_p and mpz_sqrt differ\n");
mpz_trace (" x ", x);
mpz_trace (" x2 ", x2);
mpz_trace (" x2t", x2t);
printf (" mpz_perfect_square_p %d\n", res);
printf (" mpz_sqrt %d\n", mpz_cmp (x2, x2t) == 0);
abort ();
}
/* cnt += res != 0; */
}
/* printf ("%d/%d perfect squares\n", cnt, reps); */
mpz_clear (bs);
mpz_clear (x2);
mpz_clear (x);
mpz_clear (x2t);
}
//------------------------------------------------------------------------------
// Name: sqrt
//------------------------------------------------------------------------------
knumber_base *knumber_integer::sqrt() {
if(sign() < 0) {
delete this;
return new knumber_error(knumber_error::ERROR_UNDEFINED);
}
if(mpz_perfect_square_p(mpz_)) {
mpz_sqrt(mpz_, mpz_);
return this;
} else {
knumber_float *f = new knumber_float(this);
delete this;
return f->sqrt();
}
}
/* See Cohen 1.5.2 */
int cornacchia(mpz_t x, mpz_t y, mpz_t D, mpz_t p)
{
int result = 0;
mpz_t a, b, c, d;
if (mpz_jacobi(D, p) < 0) /* No solution */
return 0;
mpz_init(a);
mpz_init(b);
mpz_init(c);
mpz_init(d);
sqrtmod(x, D, p, a, b, c, d);
mpz_set(a, p);
mpz_set(b, x);
mpz_sqrt(c, p);
while (mpz_cmp(b,c) > 0) {
mpz_set(d, a);
mpz_set(a, b);
mpz_mod(b, d, b);
}
mpz_mul(a, b, b);
mpz_sub(a, p, a); /* a = p - b^2 */
mpz_abs(d, D); /* d = |D| */
if (mpz_divisible_p(a, d)) {
mpz_divexact(c, a, d);
if (mpz_perfect_square_p(c)) {
mpz_set(x, b);
mpz_sqrt(y, c);
result = 1;
}
}
mpz_clear(a);
mpz_clear(b);
mpz_clear(c);
mpz_clear(d);
return result;
}
void
check_modulo (void)
{
static const unsigned long divisor[] = PERFSQR_DIVISORS;
unsigned long i, j;
mpz_t alldiv, others, n;
mpz_init (alldiv);
mpz_init (others);
mpz_init (n);
/* product of all divisors */
mpz_set_ui (alldiv, 1L);
for (i = 0; i < numberof (divisor); i++)
mpz_mul_ui (alldiv, alldiv, divisor[i]);
for (i = 0; i < numberof (divisor); i++)
{
/* product of all divisors except i */
mpz_set_ui (others, 1L);
for (j = 0; j < numberof (divisor); j++)
if (i != j)
mpz_mul_ui (others, others, divisor[j]);
for (j = 1; j <= divisor[i]; j++)
{
/* square */
mpz_mul_ui (n, others, j);
mpz_mul (n, n, n);
if (! mpz_perfect_square_p (n))
{
printf ("mpz_perfect_square_p got 0, want 1\n");
mpz_trace (" n", n);
abort ();
}
}
}
mpz_clear (alldiv);
mpz_clear (others);
mpz_clear (n);
}
int check_specialcase(FILE *sieve_log, fact_obj_t *fobj)
{
//check for some special cases of input number
//sieve_log is passed in already open, and should return open
if (mpz_even_p(fobj->qs_obj.gmp_n))
{
printf("input must be odd\n");
return 1;
}
if (mpz_probab_prime_p(fobj->qs_obj.gmp_n, NUM_WITNESSES))
{
add_to_factor_list(fobj, fobj->qs_obj.gmp_n);
if (sieve_log != NULL)
logprint(sieve_log,"prp%d = %s\n", gmp_base10(fobj->qs_obj.gmp_n),
mpz_conv2str(&gstr1.s, 10, fobj->qs_obj.gmp_n));
mpz_set_ui(fobj->qs_obj.gmp_n,1);
return 1;
}
if (mpz_perfect_square_p(fobj->qs_obj.gmp_n))
{
mpz_sqrt(fobj->qs_obj.gmp_n,fobj->qs_obj.gmp_n);
add_to_factor_list(fobj, fobj->qs_obj.gmp_n);
if (sieve_log != NULL)
logprint(sieve_log,"prp%d = %s\n",gmp_base10(fobj->qs_obj.gmp_n),
mpz_conv2str(&gstr1.s, 10, fobj->qs_obj.gmp_n));
add_to_factor_list(fobj, fobj->qs_obj.gmp_n);
if (sieve_log != NULL)
logprint(sieve_log,"prp%d = %s\n",gmp_base10(fobj->qs_obj.gmp_n),
mpz_conv2str(&gstr1.s, 10, fobj->qs_obj.gmp_n));
mpz_set_ui(fobj->qs_obj.gmp_n,1);
return 1;
}
if (mpz_perfect_power_p(fobj->qs_obj.gmp_n))
{
if (VFLAG > 0)
printf("input is a perfect power\n");
factor_perfect_power(fobj, fobj->qs_obj.gmp_n);
if (sieve_log != NULL)
{
uint32 j;
logprint(sieve_log,"input is a perfect power\n");
for (j=0; j<fobj->num_factors; j++)
{
uint32 k;
for (k=0; k<fobj->fobj_factors[j].count; k++)
{
logprint(sieve_log,"prp%d = %s\n",gmp_base10(fobj->fobj_factors[j].factor),
mpz_conv2str(&gstr1.s, 10, fobj->fobj_factors[j].factor));
}
}
}
return 1;
}
if (mpz_sizeinbase(fobj->qs_obj.gmp_n,2) < 115)
{
//run MPQS, as SIQS doesn't work for smaller inputs
//MPQS will take over the log file, so close it now.
int i;
// we've verified that the input is not odd or prime. also
// do some very quick trial division before calling smallmpqs, which
// does none of these things.
for (i=1; i<25; i++)
{
if (mpz_tdiv_ui(fobj->qs_obj.gmp_n, spSOEprimes[i]) == 0)
mpz_tdiv_q_ui(fobj->qs_obj.gmp_n, fobj->qs_obj.gmp_n, spSOEprimes[i]);
}
smallmpqs(fobj);
return 1; //tells SIQS to not try to close the logfile
}
if (gmp_base10(fobj->qs_obj.gmp_n) > 140)
{
printf("input too big for SIQS\n");
return 1;
}
return 0;
}
/* return non zero iff x^y is exact.
Assumes x and y are ordinary numbers,
y is not an integer, x is not a power of 2 and x is positive
If x^y is exact, it computes it and sets *inexact.
*/
static int
mpfr_pow_is_exact (mpfr_ptr z, mpfr_srcptr x, mpfr_srcptr y,
mpfr_rnd_t rnd_mode, int *inexact)
{
mpz_t a, c;
mpfr_exp_t d, b;
unsigned long i;
int res;
MPFR_ASSERTD (!MPFR_IS_SINGULAR (y));
MPFR_ASSERTD (!MPFR_IS_SINGULAR (x));
MPFR_ASSERTD (!mpfr_integer_p (y));
MPFR_ASSERTD (mpfr_cmp_si_2exp (x, MPFR_INT_SIGN (x),
MPFR_GET_EXP (x) - 1) != 0);
MPFR_ASSERTD (MPFR_IS_POS (x));
if (MPFR_IS_NEG (y))
return 0; /* x is not a power of two => x^-y is not exact */
/* compute d such that y = c*2^d with c odd integer */
mpz_init (c);
d = mpfr_get_z_2exp (c, y);
i = mpz_scan1 (c, 0);
mpz_fdiv_q_2exp (c, c, i);
d += i;
/* now y=c*2^d with c odd */
/* Since y is not an integer, d is necessarily < 0 */
MPFR_ASSERTD (d < 0);
/* Compute a,b such that x=a*2^b */
mpz_init (a);
b = mpfr_get_z_2exp (a, x);
i = mpz_scan1 (a, 0);
mpz_fdiv_q_2exp (a, a, i);
b += i;
/* now x=a*2^b with a is odd */
for (res = 1 ; d != 0 ; d++)
{
/* a*2^b is a square iff
(i) a is a square when b is even
(ii) 2*a is a square when b is odd */
if (b % 2 != 0)
{
mpz_mul_2exp (a, a, 1); /* 2*a */
b --;
}
MPFR_ASSERTD ((b % 2) == 0);
if (!mpz_perfect_square_p (a))
{
res = 0;
goto end;
}
mpz_sqrt (a, a);
b = b / 2;
}
/* Now x = (a'*2^b')^(2^-d) with d < 0
so x^y = ((a'*2^b')^(2^-d))^(c*2^d)
= ((a'*2^b')^c with c odd integer */
{
mpfr_t tmp;
mpfr_prec_t p;
MPFR_MPZ_SIZEINBASE2 (p, a);
mpfr_init2 (tmp, p); /* prec = 1 should not be possible */
res = mpfr_set_z (tmp, a, MPFR_RNDN);
MPFR_ASSERTD (res == 0);
res = mpfr_mul_2si (tmp, tmp, b, MPFR_RNDN);
MPFR_ASSERTD (res == 0);
*inexact = mpfr_pow_z (z, tmp, c, rnd_mode);
mpfr_clear (tmp);
res = 1;
}
end:
mpz_clear (a);
mpz_clear (c);
return res;
}
static PyObject *
GMPY_mpz_is_strongselfridge_prp(PyObject *self, PyObject *args)
{
MPZ_Object *n;
PyObject *result = 0, *temp = 0;
long d = 5, p = 1, q = 0, max_d = 1000000;
int jacobi = 0;
mpz_t zD;
if (PyTuple_Size(args) != 1) {
TYPE_ERROR("is_strong_selfridge_prp() requires 1 integer argument");
return NULL;
}
mpz_init(zD);
n = GMPy_MPZ_From_Integer(PyTuple_GET_ITEM(args, 0), NULL);
if (!n) {
TYPE_ERROR("is_strong_selfridge_prp() requires 1 integer argument");
goto cleanup;
}
/* Require n > 0. */
if (mpz_sgn(n->z) <= 0) {
VALUE_ERROR("is_strong_selfridge_prp() requires 'n' be greater than 0");
goto cleanup;
}
/* Check for n == 1 */
if (mpz_cmp_ui(n->z, 1) == 0) {
result = Py_False;
goto cleanup;
}
/* Handle n even. */
if (mpz_divisible_ui_p(n->z, 2)) {
if (mpz_cmp_ui(n->z, 2) == 0)
result = Py_True;
else
result = Py_False;
goto cleanup;
}
mpz_set_ui(zD, d);
while (1) {
jacobi = mpz_jacobi(zD, n->z);
/* if jacobi == 0, d is a factor of n, therefore n is composite... */
/* if d == n, then either n is either prime or 9... */
if (jacobi == 0) {
if ((mpz_cmpabs(zD, n->z) == 0) && (mpz_cmp_ui(zD, 9) != 0)) {
result = Py_True;
goto cleanup;
}
else {
result = Py_False;
goto cleanup;
}
}
if (jacobi == -1)
break;
/* if we get to the 5th d, make sure we aren't dealing with a square... */
if (d == 13) {
if (mpz_perfect_square_p(n->z)) {
result = Py_False;
goto cleanup;
}
}
if (d < 0) {
d *= -1;
d += 2;
}
else {
d += 2;
d *= -1;
}
/* make sure we don't search forever */
if (d >= max_d) {
VALUE_ERROR("appropriate value for D cannot be found in is_strong_selfridge_prp()");
goto cleanup;
}
mpz_set_si(zD, d);
}
q = (1-d)/4;
/* Since "O" is used, the refcount for n is incremented so deleting
* temp will not delete n.
*/
temp = Py_BuildValue("Oll", n, p, q);
if (!temp)
goto cleanup;
result = GMPY_mpz_is_stronglucas_prp(NULL, temp);
Py_DECREF(temp);
goto return_result;
cleanup:
Py_XINCREF(result);
return_result:
mpz_clear(zD);
Py_DECREF((PyObject*)n);
return result;
}
int perfect_square(const Integer &n)
{
return mpz_perfect_square_p(n.as_mpz().get_mpz_t());
}
//----------------------- NFS ENTRY POINT ------------------------------------//
void nfs(fact_obj_t *fobj)
{
//expect the input in fobj->nfs_obj.gmp_n
char *input;
msieve_obj *obj = NULL;
char *nfs_args = NULL; // unused as yet
enum cpu_type cpu = yafu_get_cpu_type();
mp_t mpN;
factor_list_t factor_list;
uint32 flags = 0;
nfs_job_t job;
uint32 relations_needed = 1;
uint32 last_specialq = 0;
struct timeval stop; // stop time of this job
struct timeval start; // start time of this job
struct timeval bstop; // stop time of sieving batch
struct timeval bstart; // start time of sieving batch
TIME_DIFF * difference;
double t_time;
uint32 pre_batch_rels = 0;
char tmpstr[GSTR_MAXSIZE];
int process_done;
enum nfs_state_e nfs_state;
// initialize some job parameters
memset(&job, 0, sizeof(nfs_job_t));
obj_ptr = NULL;
//below a certain amount, revert to SIQS
if (gmp_base10(fobj->nfs_obj.gmp_n) < fobj->nfs_obj.min_digits)
{
mpz_set(fobj->qs_obj.gmp_n, fobj->nfs_obj.gmp_n);
SIQS(fobj);
mpz_set(fobj->nfs_obj.gmp_n, fobj->qs_obj.gmp_n);
return;
}
if (mpz_probab_prime_p(fobj->nfs_obj.gmp_n, NUM_WITNESSES))
{
add_to_factor_list(fobj, fobj->nfs_obj.gmp_n);
if (VFLAG >= 0)
gmp_printf("PRP%d = %Zd\n", gmp_base10(fobj->nfs_obj.gmp_n),
fobj->nfs_obj.gmp_n);
logprint_oc(fobj->flogname, "a", "PRP%d = %s\n",
gmp_base10(fobj->nfs_obj.gmp_n),
mpz_conv2str(&gstr1.s, 10, fobj->nfs_obj.gmp_n));
mpz_set_ui(fobj->nfs_obj.gmp_n, 1);
return;
}
if (mpz_perfect_square_p(fobj->nfs_obj.gmp_n))
{
mpz_sqrt(fobj->nfs_obj.gmp_n, fobj->nfs_obj.gmp_n);
add_to_factor_list(fobj, fobj->nfs_obj.gmp_n);
logprint_oc(fobj->flogname, "a", "prp%d = %s\n",
gmp_base10(fobj->nfs_obj.gmp_n),
mpz_conv2str(&gstr1.s, 10, fobj->nfs_obj.gmp_n));
add_to_factor_list(fobj, fobj->nfs_obj.gmp_n);
logprint_oc(fobj->flogname, "a", "prp%d = %s\n",
gmp_base10(fobj->nfs_obj.gmp_n),
mpz_conv2str(&gstr1.s, 10, fobj->nfs_obj.gmp_n));
mpz_set_ui(fobj->nfs_obj.gmp_n, 1);
return;
}
if (mpz_perfect_power_p(fobj->nfs_obj.gmp_n))
{
FILE *flog;
uint32 j;
if (VFLAG > 0)
printf("input is a perfect power\n");
factor_perfect_power(fobj, fobj->nfs_obj.gmp_n);
flog = fopen(fobj->flogname, "a");
if (flog == NULL)
{
printf("fopen error: %s\n", strerror(errno));
printf("could not open %s for appending\n", fobj->flogname);
exit(1);
}
logprint(flog,"input is a perfect power\n");
for (j=0; j<fobj->num_factors; j++)
{
uint32 k;
for (k=0; k<fobj->fobj_factors[j].count; k++)
{
logprint(flog,"prp%d = %s\n",gmp_base10(fobj->fobj_factors[j].factor),
mpz_conv2str(&gstr1.s, 10, fobj->fobj_factors[j].factor));
}
}
fclose(flog);
return;
}
if (fobj->nfs_obj.filearg[0] != '\0')
{
if (VFLAG > 0) printf("test: starting trial sieving\n");
trial_sieve(fobj);
return;
}
//initialize the flag to watch for interrupts, and set the
//pointer to the function to call if we see a user interrupt
NFS_ABORT = 0;
signal(SIGINT,nfsexit);
//start a counter for the whole job
gettimeofday(&start, NULL);
//nfs state machine:
input = (char *)malloc(GSTR_MAXSIZE * sizeof(char));
nfs_state = NFS_STATE_INIT;
process_done = 0;
while (!process_done)
{
switch (nfs_state)
{
case NFS_STATE_INIT:
// write the input bigint as a string
input = mpz_conv2str(&input, 10, fobj->nfs_obj.gmp_n);
// create an msieve_obj
// this will initialize the savefile to the outputfile name provided
obj = msieve_obj_new(input, flags, fobj->nfs_obj.outputfile, fobj->nfs_obj.logfile,
fobj->nfs_obj.fbfile, g_rand.low, g_rand.hi, (uint32)0, cpu,
(uint32)L1CACHE, (uint32)L2CACHE, (uint32)THREADS, (uint32)0, nfs_args);
fobj->nfs_obj.mobj = obj;
// initialize these before checking existing files. If poly
// select is resumed they will be changed by check_existing_files.
job.last_leading_coeff = 0;
job.poly_time = 0;
job.use_max_rels = 0;
job.snfs = NULL;
// determine what to do next based on the state of various files.
// this will set job.current_rels if it finds any
nfs_state = check_existing_files(fobj, &last_specialq, &job);
// before we get started, check to make sure we can find ggnfs sievers
// if we are going to be doing sieving
if (check_for_sievers(fobj, 1) == 1)
nfs_state = NFS_STATE_DONE;
if (VFLAG >= 0 && nfs_state != NFS_STATE_DONE)
gmp_printf("nfs: commencing nfs on c%d: %Zd\n",
gmp_base10(fobj->nfs_obj.gmp_n), fobj->nfs_obj.gmp_n);
if (nfs_state != NFS_STATE_DONE)
logprint_oc(fobj->flogname, "a", "nfs: commencing nfs on c%d: %s\n",
gmp_base10(fobj->nfs_obj.gmp_n),
mpz_conv2str(&gstr1.s, 10, fobj->nfs_obj.gmp_n));
// convert input to msieve bigint notation and initialize a list of factors
gmp2mp_t(fobj->nfs_obj.gmp_n,&mpN);
factor_list_init(&factor_list);
if (fobj->nfs_obj.rangeq > 0)
job.qrange = ceil((double)fobj->nfs_obj.rangeq / (double)THREADS);
break;
case NFS_STATE_POLY:
if ((fobj->nfs_obj.nfs_phases == NFS_DEFAULT_PHASES) ||
(fobj->nfs_obj.nfs_phases & NFS_PHASE_POLY))
{
// always check snfs forms (it is fast)
snfs_choose_poly(fobj, &job);
if( job.snfs == NULL )
{
// either we never were doing snfs, or snfs form detect failed.
// if the latter then bail with an error because the user
// explicitly wants to run snfs...
if (fobj->nfs_obj.snfs)
{
printf("nfs: failed to find snfs polynomial!\n");
exit(-1);
}
// init job.poly for gnfs
job.poly = (mpz_polys_t*)malloc(sizeof(mpz_polys_t));
if (job.poly == NULL)
{
printf("nfs: couldn't allocate memory!\n");
exit(-1);
}
mpz_polys_init(job.poly);
job.poly->rat.degree = 1; // maybe way off in the future this isn't true
// assume gnfs for now
job.poly->side = ALGEBRAIC_SPQ;
do_msieve_polyselect(fobj, obj, &job, &mpN, &factor_list);
}
else
{
fobj->nfs_obj.snfs = 1;
mpz_set(fobj->nfs_obj.gmp_n, job.snfs->n);
}
}
nfs_state = NFS_STATE_SIEVE;
break;
case NFS_STATE_SIEVE:
pre_batch_rels = job.current_rels;
gettimeofday(&bstart, NULL);
// sieve if the user has requested to (or by default). else,
// set the done sieving flag. this will prevent some infinite loops,
// for instance if we only want to post-process, but filtering
// doesn't produce a matrix. if we don't want to sieve in that case,
// then we're done.
if (((fobj->nfs_obj.nfs_phases == NFS_DEFAULT_PHASES) ||
(fobj->nfs_obj.nfs_phases & NFS_PHASE_SIEVE)) &&
!(fobj->nfs_obj.nfs_phases & NFS_DONE_SIEVING))
do_sieving(fobj, &job);
else
fobj->nfs_obj.nfs_phases |= NFS_DONE_SIEVING;
// if this has been previously marked, then go ahead and exit.
if (fobj->nfs_obj.nfs_phases & NFS_DONE_SIEVING)
process_done = 1;
// if user specified -ns with a fixed start and range,
// then mark that we're done sieving.
if (fobj->nfs_obj.rangeq > 0)
{
// we're done sieving the requested range, but there may be
// more phases to check, so don't exit yet
fobj->nfs_obj.nfs_phases |= NFS_DONE_SIEVING;
}
// then move on to the next phase
nfs_state = NFS_STATE_FILTCHECK;
break;
case NFS_STATE_FILTER:
// if we've flagged not to do filtering, then assume we have
// enough relations and move on to linear algebra
if ((fobj->nfs_obj.nfs_phases == NFS_DEFAULT_PHASES) ||
(fobj->nfs_obj.nfs_phases & NFS_PHASE_FILTER))
relations_needed = do_msieve_filtering(fobj, obj, &job);
else
relations_needed = 0;
if (relations_needed == 0)
nfs_state = NFS_STATE_LINALG;
else
{
// if we filtered, but didn't produce a matrix, raise the target
// min rels by a few percent. this will prevent too frequent
// filtering attempts while allowing the q_batch size to remain small.
if (job.current_rels > job.min_rels)
job.min_rels = job.current_rels * fobj->nfs_obj.filter_min_rels_nudge;
else
job.min_rels *= fobj->nfs_obj.filter_min_rels_nudge;
if (VFLAG > 0)
printf("nfs: raising min_rels by %1.2f percent to %u\n",
100*(fobj->nfs_obj.filter_min_rels_nudge-1), job.min_rels);
nfs_state = NFS_STATE_SIEVE;
}
break;
case NFS_STATE_LINALG:
if ((fobj->nfs_obj.nfs_phases == NFS_DEFAULT_PHASES) ||
(fobj->nfs_obj.nfs_phases & NFS_PHASE_LA) ||
(fobj->nfs_obj.nfs_phases & NFS_PHASE_LA_RESUME))
{
// msieve: build matrix
flags = 0;
flags = flags | MSIEVE_FLAG_USE_LOGFILE;
if (VFLAG > 0)
flags = flags | MSIEVE_FLAG_LOG_TO_STDOUT;
flags = flags | MSIEVE_FLAG_NFS_LA;
// add restart flag if requested
if (fobj->nfs_obj.nfs_phases & NFS_PHASE_LA_RESUME)
flags |= MSIEVE_FLAG_NFS_LA_RESTART;
obj->flags = flags;
if (VFLAG >= 0)
printf("nfs: commencing msieve linear algebra\n");
logprint_oc(fobj->flogname, "a", "nfs: commencing msieve linear algebra\n");
// use a different number of threads for the LA, if requested
if (LATHREADS > 0)
{
msieve_obj_free(obj);
obj = msieve_obj_new(input, flags, fobj->nfs_obj.outputfile, fobj->nfs_obj.logfile,
fobj->nfs_obj.fbfile, g_rand.low, g_rand.hi, (uint32)0, cpu,
(uint32)L1CACHE, (uint32)L2CACHE, (uint32)LATHREADS, (uint32)0, nfs_args);
}
// try this hack - store a pointer to the msieve obj so that
// we can change a flag on abort in order to interrupt the LA.
obj_ptr = obj;
nfs_solve_linear_system(obj, fobj->nfs_obj.gmp_n);
if (obj_ptr->flags & MSIEVE_FLAG_STOP_SIEVING)
nfs_state = NFS_STATE_DONE;
else
{
// check for a .dat.deps file. if we don't have one, assume
// its because the job was way oversieved and only trivial
// dependencies were found. try again from filtering with
// 20% less relations.
FILE *t;
sprintf(tmpstr, "%s.dep", fobj->nfs_obj.outputfile);
if ((t = fopen(tmpstr, "r")) == NULL)
{
if (job.use_max_rels > 0)
{
// we've already tried again with an attempted fix to the trivial
// dependencies problem, so either that wasn't the problem or
// it didn't work. either way, give up.
printf("nfs: no dependency file retry failed\n");
fobj->flags |= FACTOR_INTERRUPT;
nfs_state = NFS_STATE_DONE;
}
else
{
// this should be sufficient to produce a matrix, but not too much
// to trigger the assumed failure mode.
if (job.min_rels == 0)
{
// if min_rels is not set, then we need to parse the .job file to compute it.
parse_job_file(fobj, &job);
nfs_set_min_rels(&job);
}
job.use_max_rels = job.min_rels * 1.5;
printf("nfs: no dependency file found - trying again with %u relations\n",
job.use_max_rels);
nfs_state = NFS_STATE_FILTER;
}
}
else
{
fclose(t);
nfs_state = NFS_STATE_SQRT;
}
}
// set the msieve threads back to where it was if we used
// a different amount for linalg
if (LATHREADS > 0)
{
msieve_obj_free(obj);
obj = msieve_obj_new(input, flags, fobj->nfs_obj.outputfile, fobj->nfs_obj.logfile,
fobj->nfs_obj.fbfile, g_rand.low, g_rand.hi, (uint32)0, cpu,
(uint32)L1CACHE, (uint32)L2CACHE, (uint32)THREADS, (uint32)0, nfs_args);
}
obj_ptr = NULL;
}
else // not doing linalg
nfs_state = NFS_STATE_SQRT;
break;
case NFS_STATE_SQRT:
if ((fobj->nfs_obj.nfs_phases == NFS_DEFAULT_PHASES) ||
(fobj->nfs_obj.nfs_phases & NFS_PHASE_SQRT))
{
uint32 retcode;
// msieve: find factors
flags = 0;
flags = flags | MSIEVE_FLAG_USE_LOGFILE;
if (VFLAG > 0)
flags = flags | MSIEVE_FLAG_LOG_TO_STDOUT;
flags = flags | MSIEVE_FLAG_NFS_SQRT;
obj->flags = flags;
if (VFLAG >= 0)
printf("nfs: commencing msieve sqrt\n");
logprint_oc(fobj->flogname, "a", "nfs: commencing msieve sqrt\n");
// try this hack - store a pointer to the msieve obj so that
// we can change a flag on abort in order to interrupt the sqrt.
obj_ptr = obj;
retcode = nfs_find_factors(obj, fobj->nfs_obj.gmp_n, &factor_list);
obj_ptr = NULL;
if (retcode)
{
extract_factors(&factor_list,fobj);
if (mpz_cmp_ui(fobj->nfs_obj.gmp_n, 1) == 0)
nfs_state = NFS_STATE_CLEANUP; //completely factored, clean up everything
else
nfs_state = NFS_STATE_DONE; //not factored completely, keep files and stop
}
else
{
if (VFLAG >= 0)
{
printf("nfs: failed to find factors... possibly no dependencies found\n");
printf("nfs: continuing with sieving\n");
}
logprint_oc(fobj->flogname, "a", "nfs: failed to find factors... "
"possibly no dependencies found\n"
"nfs: continuing with sieving\n");
nfs_state = NFS_STATE_SIEVE;
}
}
else
nfs_state = NFS_STATE_DONE; //not factored completely, keep files and stop
break;
case NFS_STATE_CLEANUP:
remove(fobj->nfs_obj.outputfile);
remove(fobj->nfs_obj.fbfile);
sprintf(tmpstr, "%s.p",fobj->nfs_obj.outputfile); remove(tmpstr);
sprintf(tmpstr, "%s.br",fobj->nfs_obj.outputfile); remove(tmpstr);
sprintf(tmpstr, "%s.cyc",fobj->nfs_obj.outputfile); remove(tmpstr);
sprintf(tmpstr, "%s.dep",fobj->nfs_obj.outputfile); remove(tmpstr);
sprintf(tmpstr, "%s.hc",fobj->nfs_obj.outputfile); remove(tmpstr);
sprintf(tmpstr, "%s.mat",fobj->nfs_obj.outputfile); remove(tmpstr);
sprintf(tmpstr, "%s.lp",fobj->nfs_obj.outputfile); remove(tmpstr);
sprintf(tmpstr, "%s.d",fobj->nfs_obj.outputfile); remove(tmpstr);
sprintf(tmpstr, "%s.mat.chk",fobj->nfs_obj.outputfile); remove(tmpstr);
gettimeofday(&stop, NULL);
difference = my_difftime (&start, &stop);
t_time = ((double)difference->secs + (double)difference->usecs / 1000000);
free(difference);
if (VFLAG >= 0)
printf("NFS elapsed time = %6.4f seconds.\n",t_time);
logprint_oc(fobj->flogname, "a", "NFS elapsed time = %6.4f seconds.\n",t_time);
logprint_oc(fobj->flogname, "a", "\n");
logprint_oc(fobj->flogname, "a", "\n");
// free stuff
nfs_state = NFS_STATE_DONE;
break;
case NFS_STATE_DONE:
process_done = 1;
break;
case NFS_STATE_FILTCHECK:
if (job.current_rels >= job.min_rels)
{
if (VFLAG > 0)
printf("nfs: found %u relations, need at least %u, proceeding with filtering ...\n",
job.current_rels, job.min_rels);
nfs_state = NFS_STATE_FILTER;
}
else
{
// compute eta by dividing how many rels we have left to find
// by the average time per relation. we have average time
// per relation because we've saved the time it took to do
// the last batch of sieving and we know how many relations we
// found in that batch.
uint32 est_time;
gettimeofday(&bstop, NULL);
difference = my_difftime (&bstart, &bstop);
t_time = ((double)difference->secs + (double)difference->usecs / 1000000);
free(difference);
est_time = (uint32)((job.min_rels - job.current_rels) *
(t_time / (job.current_rels - pre_batch_rels)));
// if the user doesn't want to sieve, then we can't make progress.
if ((fobj->nfs_obj.nfs_phases == NFS_DEFAULT_PHASES) ||
(fobj->nfs_obj.nfs_phases & NFS_PHASE_SIEVE))
{
if (VFLAG > 0)
printf("nfs: found %u relations, need at least %u "
"(filtering ETA: %uh %um), continuing with sieving ...\n", // uh... um... hmm... idk *shrug*
job.current_rels, job.min_rels, est_time / 3600,
(est_time % 3600) / 60);
nfs_state = NFS_STATE_SIEVE;
}
else
{
if (VFLAG > 0)
printf("nfs: found %u relations, need at least %u "
"(filtering ETA: %uh %um), sieving not selected, finishing ...\n",
job.current_rels, job.min_rels, est_time / 3600,
(est_time % 3600) / 60);
nfs_state = NFS_STATE_DONE;
}
}
break;
case NFS_STATE_STARTNEW:
nfs_state = NFS_STATE_POLY;
// create a new directory for this job
//#ifdef _WIN32
// sprintf(tmpstr, "%s\%s", fobj->nfs_obj.ggnfs_dir,
// mpz_conv2str(&gstr1.s, 10, fobj->nfs_obj.gmp_n));
// mkdir(tmpstr);
//#else
// sprintf(tmpstr, "%s/%s", fobj->nfs_obj.ggnfs_dir,
// mpz_conv2str(&gstr1.s, 10, fobj->nfs_obj.gmp_n));
// mkdir(tmpstr, S_IRWXU);
//#endif
// point msieve and ggnfs to the new directory
//#ifdef _WIN32
// sprintf(fobj->nfs_obj.outputfile, "%s\%s",
// tmpstr, fobj->nfs_obj.outputfile);
// sprintf(fobj->nfs_obj.logfile, "%s\%s",
// tmpstr, fobj->nfs_obj.logfile);
// sprintf(fobj->nfs_obj.fbfile, "%s\%s",
// tmpstr, fobj->nfs_obj.fbfile);
//#else
// sprintf(fobj->nfs_obj.outputfile, "%s%s",
// tmpstr, fobj->nfs_obj.outputfile);
// sprintf(fobj->nfs_obj.logfile, "%s%s",
// tmpstr, fobj->nfs_obj.logfile);
// sprintf(fobj->nfs_obj.fbfile, "%s%s",
// tmpstr, fobj->nfs_obj.fbfile);
//
//#endif
//
// msieve_obj_free(fobj->nfs_obj.mobj);
// obj = msieve_obj_new(input, flags, fobj->nfs_obj.outputfile, fobj->nfs_obj.logfile,
// fobj->nfs_obj.fbfile, g_rand.low, g_rand.hi, (uint32)0, nfs_lower, nfs_upper, cpu,
// (uint32)L1CACHE, (uint32)L2CACHE, (uint32)THREADS, (uint32)0, (uint32)0, 0.0);
// fobj->nfs_obj.mobj = obj;
//
// printf("output: %s\n", fobj->nfs_obj.mobj->savefile.name);
// printf("log: %s\n", fobj->nfs_obj.mobj->logfile_name);
// printf("fb: %s\n", fobj->nfs_obj.mobj->nfs_fbfile_name);
break;
// should really be "resume_job", since we do more than just resume sieving...
case NFS_STATE_RESUMESIEVE:
// last_specialq == 0 if:
// 1) user specifies -R and -ns with params
// 2) user specifies post processing steps only
// 3) user wants to resume sieving (either with a solo -ns or no arguements)
// but no data file or special-q was found
// 4) -R was not specified (but then we won't be in this state, we'll be in DONE)
// last_specialq > 1 if:
// 5) user wants to resume sieving (either with a solo -ns or no arguements)
// and a data file and special-q was found
// 6) it contains poly->time info (in which case we'll be in NFS_STATE_RESUMEPOLY)
strcpy(tmpstr, "");
if ((last_specialq == 0) &&
((fobj->nfs_obj.nfs_phases == NFS_DEFAULT_PHASES) ||
(fobj->nfs_obj.nfs_phases & NFS_PHASE_SIEVE)))
{
// this if-block catches cases 1 and 3 from above
uint32 missing_params = parse_job_file(fobj, &job);
// set min_rels.
get_ggnfs_params(fobj, &job);
fill_job_file(fobj, &job, missing_params);
// if any ggnfs params are missing, fill them
// this means the user can provide an SNFS poly or external GNFS poly,
// but let YAFU choose the other params
// this won't override any params in the file.
if (fobj->nfs_obj.startq > 0)
{
job.startq = fobj->nfs_obj.startq;
sprintf(tmpstr, "nfs: resuming with sieving at user specified special-q %u\n",
job.startq);
}
else
{
// this is a guess, may be completely wrong
job.startq = (job.poly->side == RATIONAL_SPQ ? job.rlim : job.alim) / 2;
sprintf(tmpstr, "nfs: continuing with sieving - could not determine "
"last special q; using default startq\n");
}
// next step is sieving
nfs_state = NFS_STATE_SIEVE;
}
else if ((last_specialq == 0) &&
((fobj->nfs_obj.nfs_phases & NFS_PHASE_FILTER) ||
(fobj->nfs_obj.nfs_phases & NFS_PHASE_LA) ||
(fobj->nfs_obj.nfs_phases & NFS_PHASE_LA_RESUME) ||
(fobj->nfs_obj.nfs_phases & NFS_PHASE_SQRT)))
{
// this if-block catches case 2 from above
// with these options we don't check for the last special-q, so this isn't
// really a new factorization
if ((fobj->nfs_obj.nfs_phases & NFS_PHASE_FILTER))
{
nfs_state = NFS_STATE_FILTCHECK;
sprintf(tmpstr, "nfs: resuming with filtering\n");
}
else if ((fobj->nfs_obj.nfs_phases & NFS_PHASE_LA) ||
(fobj->nfs_obj.nfs_phases & NFS_PHASE_LA_RESUME))
{
nfs_state = NFS_STATE_LINALG;
sprintf(tmpstr, "nfs: resuming with linear algebra\n");
}
else if (fobj->nfs_obj.nfs_phases & NFS_PHASE_SQRT)
{
nfs_state = NFS_STATE_SQRT;
sprintf(tmpstr, "nfs: resuming with sqrt\n");
}
}
else // data file already exists
{
// this if-block catches case 5 from above
(void) parse_job_file(fobj, &job);
// set min_rels.
get_ggnfs_params(fobj, &job);
if (fobj->nfs_obj.startq > 0)
{
// user wants to resume sieving.
// i don't believe this case is ever executed...
// because if startq is > 0, then last_specialq will be 0...
job.startq = fobj->nfs_obj.startq;
nfs_state = NFS_STATE_SIEVE;
}
else
{
job.startq = last_specialq;
// we found some relations - find the appropriate state
// given user input
if ((fobj->nfs_obj.nfs_phases == NFS_DEFAULT_PHASES) ||
(fobj->nfs_obj.nfs_phases & NFS_PHASE_FILTER))
{
nfs_state = NFS_STATE_FILTCHECK;
sprintf(tmpstr, "nfs: resuming with filtering\n");
}
else if (fobj->nfs_obj.nfs_phases & NFS_PHASE_SIEVE)
{
nfs_state = NFS_STATE_SIEVE;
sprintf(tmpstr, "nfs: resuming with sieving at special-q = %u\n",
last_specialq);
}
else if ((fobj->nfs_obj.nfs_phases & NFS_PHASE_LA) ||
(fobj->nfs_obj.nfs_phases & NFS_PHASE_LA_RESUME))
{
nfs_state = NFS_STATE_LINALG;
sprintf(tmpstr, "nfs: resuming with linear algebra\n");
}
else if (fobj->nfs_obj.nfs_phases & NFS_PHASE_SQRT)
{
nfs_state = NFS_STATE_SQRT;
sprintf(tmpstr, "nfs: resuming with sqrt\n");
}
}
}
if (VFLAG >= 0)
printf("%s", tmpstr);
logprint_oc(fobj->flogname, "a", "%s", tmpstr);
// if there is a job file and the user has specified -np, print
// this warning.
if (fobj->nfs_obj.nfs_phases & NFS_PHASE_POLY)
{
printf("WARNING: .job file exists! If you really want to redo poly selection,"
" delete the .job file.\n");
// non ideal solution to infinite loop in factor() if we return without factors
// (should return error code instead)
NFS_ABORT = 1;
process_done = 1;
}
break;
case NFS_STATE_RESUMEPOLY:
if (VFLAG > 1) printf("nfs: resuming poly select\n");
fobj->nfs_obj.polystart = job.last_leading_coeff;
nfs_state = NFS_STATE_POLY;
break;
default:
printf("unknown state, bailing\n");
// non ideal solution to infinite loop in factor() if we return without factors
// (should return error code instead)
NFS_ABORT = 1;
break;
}
//after every state, check elasped time against a specified timeout value
gettimeofday(&stop, NULL);
difference = my_difftime (&start, &stop);
t_time = ((double)difference->secs + (double)difference->usecs / 1000000);
free(difference);
if ((fobj->nfs_obj.timeout > 0) && (t_time > (double)fobj->nfs_obj.timeout))
{
if (VFLAG >= 0)
printf("NFS timeout after %6.4f seconds.\n",t_time);
logprint_oc(fobj->flogname, "a", "NFS timeout after %6.4f seconds.\n",t_time);
process_done = 1;
}
if (NFS_ABORT)
{
print_factors(fobj);
exit(1);
}
}
//reset signal handler to default (no handler).
signal(SIGINT,NULL);
if (obj != NULL)
msieve_obj_free(obj);
free(input);
if( job.snfs )
{
snfs_clear(job.snfs);
free(job.snfs);
}
else if( job.poly )
{
mpz_polys_free(job.poly);
free(job.poly);
}
return;
}
int shankSquares(mpz_t *n)
{
mpz_t myN, constA, constB, tmp, tmp2;
mpz_t Pi, Qi, Plast, Qlast, Qnext, bi;
long counter = 1;
int status = FAIL;
printf("[INFO ] Trying shank squares\n");
mpz_init_set(myN, *n);
mpz_init(tmp); mpz_init(tmp2);
mpz_init(bi); mpz_init(Qnext);
mpz_init(Pi);
mpz_mul_ui(tmp, myN, SHANKQUAREK); // constA = k*N
mpz_init_set(constA, tmp);
mpz_sqrt(tmp, constA); // constB = floor(sqrt(constA))
mpz_init_set(constB, tmp);
mpz_init_set(Plast, constB);
mpz_pow_ui(tmp, Plast, 2); // Qi = (constA) - (Pi**2)
mpz_sub(tmp, constA, tmp);
mpz_init_set(Qi, tmp);
mpz_init_set_ui(Qlast, 1);
while (counter < SHANKQUAREMAX)
{
mpz_add(tmp, constB, Plast); //bi = floor( (constB) + (Plast) / Qi )
mpz_fdiv_q(bi, tmp, Qi);
mpz_mul(tmp, bi, Qi); //Pi = (bi * Qi) - (Plast)
mpz_sub(Pi, tmp, Plast);
mpz_sub(tmp, Plast, Pi); //Qnext = Qlast + (bi * (Plast - Pi))
mpz_mul(tmp, tmp, bi);
mpz_add(Qnext, Qlast, tmp);
if (mpz_perfect_square_p(Qi) != 0 && counter % 2 == 0)
{
break;
}
else
{
mpz_set(Plast, Pi);
mpz_set(Qlast, Qi);
mpz_set(Qi, Qnext);
}
counter += 1;
}
mpz_sub(tmp, constB, Plast); //bi = floor( ( constB - Plast ) / sqrt(Qi) )
mpz_sqrt(tmp2, Qi);
mpz_fdiv_q(bi, tmp, tmp2);
mpz_sqrt(tmp, Qi); //Plast = (bi * sqrt(Qi)) + Plast
mpz_mul(tmp, tmp, bi);
mpz_add(Plast, tmp, Plast);
mpz_sqrt(Qlast, Qi);
mpz_pow_ui(tmp2, Plast, 2); //Qnext = ((constA) - Plast**2) / Qlast
mpz_sub(tmp, constA, tmp2);
mpz_div(Qnext, tmp, Qlast);
mpz_set(Qi, Qnext);
counter = 0;
while (counter < SHANKQUAREMAX)
{
mpz_add(tmp, constB, Plast); //bi = floor( ( constB + Plast ) / Qi )
mpz_fdiv_q(bi, tmp, Qi);
mpz_mul(tmp, bi, Qi); //Pi = (bi*Qi) - Plast
mpz_sub(Pi, tmp, Plast);
mpz_sub(tmp, Plast, Pi); //Qnext = Qlast + (bi * (Plast - Pi))
mpz_mul(tmp, tmp, bi);
mpz_add(Qnext, Qlast, tmp);
if (mpz_cmp(Pi, Plast) == 0)
{
break;
}
mpz_set(Plast, Pi);
mpz_set(Qlast, Qi);
mpz_set(Qi, Qnext);
counter += 1;
}
mpz_gcd(tmp, myN, Pi);
if (mpz_cmp_ui(tmp, 1) != 0 && mpz_cmp(tmp, myN) != 0)
{
printWin(&tmp, "Shanks squares");
status = WIN;
}
mpz_clear(myN); mpz_clear(constA);
mpz_clear(constB); mpz_clear(tmp); mpz_clear(tmp2);
mpz_clear(Pi); mpz_clear(Qi); mpz_clear(Plast);
mpz_clear(Qlast); mpz_clear(Qnext); mpz_clear(bi);
return status;
}
void zFermat(uint64 limit, uint32 mult, fact_obj_t *fobj)
{
// Fermat's factorization method with a sieve-based improvement
// provided by 'neonsignal'
mpz_t a, b2, tmp, multN, a2;
int i;
int numChars;
uint64 reportIt, reportInc;
uint64 count;
uint64 i64;
FILE *flog = NULL;
uint32 M = 2 * 2 * 2 * 2 * 3 * 3 * 5 * 5 * 7 * 7; //176400u
uint32 M1 = 11 * 17 * 23 * 31; //133331u
uint32 M2 = 13 * 19 * 29 * 37; //265031u
uint8 *sqr, *sqr1, *sqr2, *mod, *mod1, *mod2;
uint16 *skip;
uint32 m, mmn, s, d;
uint8 masks[8] = {0xfe, 0xfd, 0xfb, 0xf7, 0xef, 0xdf, 0xbf, 0x7f};
uint8 nmasks[8];
uint32 iM = 0, iM1 = 0, iM2 = 0;
if (mpz_even_p(fobj->div_obj.gmp_n))
{
mpz_init(tmp);
mpz_set_ui(tmp, 2);
mpz_tdiv_q_2exp(fobj->div_obj.gmp_n, fobj->div_obj.gmp_n, 1);
add_to_factor_list(fobj, tmp);
mpz_clear(tmp);
return;
}
if (mpz_perfect_square_p(fobj->div_obj.gmp_n))
{
//open the log file
flog = fopen(fobj->flogname,"a");
if (flog == NULL)
{
printf("fopen error: %s\n", strerror(errno));
printf("could not open %s for writing\n",fobj->flogname);
return;
}
mpz_sqrt(fobj->div_obj.gmp_n, fobj->div_obj.gmp_n);
if (is_mpz_prp(fobj->div_obj.gmp_n))
{
logprint(flog, "Fermat method found perfect square factorization:\n");
logprint(flog,"prp%d = %s\n",
gmp_base10(fobj->div_obj.gmp_n),
mpz_conv2str(&gstr1.s, 10, fobj->div_obj.gmp_n));
logprint(flog,"prp%d = %s\n",
gmp_base10(fobj->div_obj.gmp_n),
mpz_conv2str(&gstr1.s, 10, fobj->div_obj.gmp_n));
}
else
{
logprint(flog, "Fermat method found perfect square factorization:\n");
logprint(flog,"c%d = %s\n",
gmp_base10(fobj->div_obj.gmp_n),
mpz_conv2str(&gstr1.s, 10, fobj->div_obj.gmp_n));
logprint(flog,"c%d = %s\n",
gmp_base10(fobj->div_obj.gmp_n),
mpz_conv2str(&gstr1.s, 10, fobj->div_obj.gmp_n));
}
add_to_factor_list(fobj, fobj->div_obj.gmp_n);
add_to_factor_list(fobj, fobj->div_obj.gmp_n);
mpz_set_ui(fobj->div_obj.gmp_n, 1);
fclose(flog);
return;
}
mpz_init(a);
mpz_init(b2);
mpz_init(tmp);
mpz_init(multN);
mpz_init(a2);
// apply the user supplied multiplier
mpz_mul_ui(multN, fobj->div_obj.gmp_n, mult);
// compute ceil(sqrt(multN))
mpz_sqrt(a, multN);
// form b^2
mpz_mul(b2, a, a);
mpz_sub(b2, b2, multN);
// test successive 'a' values using a sieve-based approach.
// the idea is that not all 'a' values allow a^2 or b^2 to be square.
// we pre-compute allowable 'a' values modulo various smooth numbers and
// build tables to allow us to quickly iterate over 'a' values that are
// more likely to produce squares.
// init sieve structures
sqr = (uint8 *)calloc((M / 8 + 1) , sizeof(uint8));
sqr1 = (uint8 *)calloc((M1 / 8 + 1) , sizeof(uint8));
sqr2 = (uint8 *)calloc((M2 / 8 + 1) , sizeof(uint8));
mod = (uint8 *)calloc((M / 8 + 1) , sizeof(uint8));
mod1 = (uint8 *)calloc((M1 / 8 + 1) , sizeof(uint8));
mod2 = (uint8 *)calloc((M2 / 8 + 1) , sizeof(uint8));
skip = (uint16 *)malloc(M * sizeof(uint16));
// test it. This will be good enough if |u*p-v*q| < 2 * N^(1/4), where
// mult = u*v
count = 0;
if (mpz_perfect_square_p(b2))
goto found;
for (i=0; i<8; i++)
nmasks[i] = ~masks[i];
// marks locations where squares can occur mod M, M1, M2
for (i64 = 0; i64 < M; ++i64)
setbit(sqr, (i64*i64)%M);
for (i64 = 0; i64 < M1; ++i64)
setbit(sqr1, (i64*i64)%M1);
for (i64 = 0; i64 < M2; ++i64)
setbit(sqr2, (i64*i64)%M2);
// for the modular sequence of b*b = a*a - n values
// (where b2_2 = b2_1 * 2a + 1), mark locations where
// b^2 can be a square
m = mpz_mod_ui(tmp, a, M);
mmn = mpz_mod_ui(tmp, b2, M);
for (i = 0; i < M; ++i)
{
if (getbit(sqr, mmn)) setbit(mod, i);
mmn = (mmn+m+m+1)%M;
m = (m+1)%M;
}
// we only consider locations where the modular sequence mod M can
// be square, so compute the distance to the next square location
// at each possible value of i mod M.
s = 0;
d = 0;
for (i = 0; !getbit(mod,i); ++i)
++s;
for (i = M; i > 0;)
{
--i;
++s;
skip[i] = s;
if (s > d) d = s;
if (getbit(mod,i)) s = 0;
}
//printf("maxSkip = %u\n", d);
// for the modular sequence of b*b = a*a - n values
// (where b2_2 = b2_1 * 2a + 1), mark locations where the
// modular sequence can be a square mod M1. These will
// generally differ from the sequence mod M.
m = mpz_mod_ui(tmp, a, M1);
mmn = mpz_mod_ui(tmp, b2, M1);
for (i = 0; i < M1; ++i)
{
if (getbit(sqr1, mmn)) setbit(mod1, i);
mmn = (mmn+m+m+1)%M1;
m = (m+1)%M1;
}
// for the modular sequence of b*b = a*a - n values
// (where b2_2 = b2_1 * 2a + 1), mark locations where the
// modular sequence can be a square mod M2. These will
// generally differ from the sequence mod M or M1.
m = mpz_mod_ui(tmp, a, M2);
mmn = mpz_mod_ui(tmp, b2, M2);
for (i = 0; i < M2; ++i)
{
if (getbit(sqr2, mmn)) setbit(mod2, i);
mmn = (mmn+m+m+1)%M2;
m = (m+1)%M2;
}
// loop, checking for perfect squares
mpz_mul_2exp(a2, a, 1);
count = 0;
numChars = 0;
reportIt = limit / 100;
reportInc = reportIt;
do
{
d = 0;
i64 = 0;
do
{
// skip to the next possible square residue of b*b mod M
s = skip[iM];
// remember how far we skipped
d += s;
// update the other residue indices
if ((iM1 += s) >= M1) iM1 -= M1;
if ((iM2 += s) >= M2) iM2 -= M2;
if ((iM += s) >= M) iM -= M;
// some multpliers can lead to infinite loops. bail out
// if so.
if (++i64 > M) goto done;
// continue if either of the other residues indicates
// non-square.
} while (!getbit(mod1,iM1) || !getbit(mod2,iM2));
// form b^2 by incrementing by many factors of 2*a+1
mpz_add_ui(tmp, a2, d);
mpz_mul_ui(tmp, tmp, d);
mpz_add(b2, b2, tmp);
// accumulate so that we can reset d
// (and thus keep it single precision)
mpz_add_ui(a2, a2, d*2);
count += d;
if (count > limit)
break;
//progress report
if ((count > reportIt) && (VFLAG > 1))
{
for (i=0; i< numChars; i++)
printf("\b");
numChars = printf("%" PRIu64 "%%",(uint64)((double)count / (double)limit * 100));
fflush(stdout);
reportIt += reportInc;
}
} while (!mpz_perfect_square_p(b2));
found:
// 'count' is how far we had to scan 'a' to find a square b
mpz_add_ui(a, a, count);
//printf("count is %" PRIu64 "\n", count);
if ((mpz_size(b2) > 0) && mpz_perfect_square_p(b2))
{
//printf("found square at count = %d: a = %s, b2 = %s",count,
// z2decstr(&a,&gstr1),z2decstr(&b2,&gstr2));
mpz_sqrt(tmp, b2);
mpz_add(tmp, a, tmp);
mpz_gcd(tmp, fobj->div_obj.gmp_n, tmp);
flog = fopen(fobj->flogname,"a");
if (flog == NULL)
{
printf("fopen error: %s\n", strerror(errno));
printf("could not open %s for writing\n",fobj->flogname);
goto done;
}
logprint(flog, "Fermat method found factors:\n");
add_to_factor_list(fobj, tmp);
if (is_mpz_prp(tmp))
{
logprint(flog,"prp%d = %s\n",
gmp_base10(tmp),
mpz_conv2str(&gstr1.s, 10, tmp));
}
else
{
logprint(flog,"c%d = %s\n",
gmp_base10(tmp),
mpz_conv2str(&gstr1.s, 10, tmp));
}
mpz_tdiv_q(fobj->div_obj.gmp_n, fobj->div_obj.gmp_n, tmp);
mpz_sqrt(tmp, b2);
mpz_sub(tmp, a, tmp);
mpz_gcd(tmp, fobj->div_obj.gmp_n, tmp);
add_to_factor_list(fobj, tmp);
if (is_mpz_prp(tmp))
{
logprint(flog,"prp%d = %s\n",
gmp_base10(tmp),
mpz_conv2str(&gstr1.s, 10, tmp));
}
else
{
logprint(flog,"c%d = %s\n",
gmp_base10(tmp),
mpz_conv2str(&gstr1.s, 10, tmp));
}
mpz_tdiv_q(fobj->div_obj.gmp_n, fobj->div_obj.gmp_n, tmp);
}
done:
mpz_clear(tmp);
mpz_clear(a);
mpz_clear(b2);
mpz_clear(multN);
mpz_clear(a2);
free(sqr);
free(sqr1);
free(sqr2);
free(mod);
free(mod1);
free(mod2);
free(skip);
if (flog != NULL)
fclose(flog);
return;
}
/* ***********************************************************************************************
* mpz_selfridge_prp:
* A "Lucas-Selfridge pseudoprime" n is a "Lucas pseudoprime" using Selfridge parameters of:
* Find the first element D in the sequence {5, -7, 9, -11, 13, ...} such that Jacobi(D,n) = -1
* Then use P=1 and Q=(1-D)/4 in the Lucas pseudoprime test.
* Make sure n is not a perfect square, otherwise the search for D will only stop when D=n.
* ***********************************************************************************************/
int mpz_selfridge_prp(mpz_t n)
{
long int d = 5, p = 1, q = 0;
int max_d = 1000000;
int jacobi = 0;
mpz_t zD;
if (mpz_cmp_ui(n, 2) < 0)
return PRP_COMPOSITE;
if (mpz_divisible_ui_p(n, 2))
{
if (mpz_cmp_ui(n, 2) == 0)
return PRP_PRIME;
else
return PRP_COMPOSITE;
}
mpz_init_set_ui(zD, d);
while (1)
{
jacobi = mpz_jacobi(zD, n);
/* if jacobi == 0, d is a factor of n, therefore n is composite... */
/* if d == n, then either n is either prime or 9... */
if (jacobi == 0)
{
if ((mpz_cmpabs(zD, n) == 0) && (mpz_cmp_ui(zD, 9) != 0))
{
mpz_clear(zD);
return PRP_PRIME;
}
else
{
mpz_clear(zD);
return PRP_COMPOSITE;
}
}
if (jacobi == -1)
break;
/* if we get to the 5th d, make sure we aren't dealing with a square... */
if (d == 13)
{
if (mpz_perfect_square_p(n))
{
mpz_clear(zD);
return PRP_COMPOSITE;
}
}
if (d < 0)
{
d *= -1;
d += 2;
}
else
{
d += 2;
d *= -1;
}
/* make sure we don't search forever */
if (d >= max_d)
{
mpz_clear(zD);
return PRP_ERROR;
}
mpz_set_si(zD, d);
}
mpz_clear(zD);
q = (1-d)/4;
return mpz_lucas_prp(n, p, q);
}/* method mpz_selfridge_prp */
/*
* Run the randomized quadratic frobenius test to check whether [n] is a a
* prime. The Parameter [k] determines how many times the test will be run at
* most. If the test returns "composite", it will not be run again.
*/
int main(int argc, char *argv[])
{
Primality result;
#define VARS n, b, c, bb4c
mpz_t VARS;
uint64_t n_, b_ = 0, c_;
uint64_t false_positives = 0;
uint64_t lower_bound = 5, upper_bound = 1000000;
mpz_inits(VARS, NULL);
if (argc > 2)
lower_bound = strtoul(argv[1], NULL, 10);
if (argc > 1)
upper_bound = strtoul(argv[argc > 2 ? 2 : 1], NULL, 10);
printf("%lu to %lu\n", lower_bound, upper_bound);
for (n_ = lower_bound | 1; n_ <= upper_bound; n_+=2) {
mpz_set_ui(n, n_);
if (mpz_perfect_square_p(n) || mpz_probab_prime_p(n, 100))
continue;
#ifdef SMALL_C
for (c_ = 2; c_ < n_; c_++) {
if (jacobi(n_ - c_, n_) != 1)
continue;
#else
c_ = n_ - 4;
mpz_sub_ui(c, n, 4);
#endif
for (b_ = 1; b_ < n_; b_++) {
mpz_mul(bb4c, b, b);
mpz_addmul_ui(bb4c, c, 4);
mpz_mod(bb4c, bb4c, n);
if (mpz_jacobi(bb4c, n) == -1)
break;
if (b_ % 1000 == 999) {
fprintf(stderr, "Could not find a valid parameter pair (b, c)\n");
goto next_n;
}
}
#ifdef SMALL_C
break;
}
#endif
result = steps_3_4_5(n, b, c);
if (result != composite) {
false_positives++;
fflush(stdout);
printf("Found a false positive: n = %lu, b = %lu, c = %lu\n", n_, b_, c_);
}
if (n_ % 10000000 == 1) {
fprintf(stderr, ".");
fflush(stderr);
}
next_n:
;
}
printf("\nA total number of %lu false positives were found among the numbers %lu,...,%lu\n",
false_positives, lower_bound, upper_bound);
mpz_clears(VARS, NULL);
return 0;
}