--- /dev/null
+/* Use mpz_kronecker_ui() to calculate an estimate for the quadratic
+ class number h(d), for a given negative fundamental discriminant, using
+ Dirichlet's analytic formula.
+
+Copyright 1999, 2000, 2001, 2002 Free Software Foundation, Inc.
+
+This file is part of the GNU MP Library.
+
+This program 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.
+
+This program 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
+this program. If not, see http://www.gnu.org/licenses/. */
+
+
+/* Usage: qcn [-p limit] <discriminant>...
+
+ A fundamental discriminant means one of the form D or 4*D with D
+ square-free. Each argument is checked to see it's congruent to 0 or 1
+ mod 4 (as all discriminants must be), and that it's negative, but there's
+ no check on D being square-free.
+
+ This program is a bit of a toy, there are better methods for calculating
+ the class number and class group structure.
+
+ Reference:
+
+ Daniel Shanks, "Class Number, A Theory of Factorization, and Genera",
+ Proc. Symp. Pure Math., vol 20, 1970, pages 415-440.
+
+*/
+
+#include <math.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+
+#include "gmp.h"
+
+#ifndef M_PI
+#define M_PI 3.14159265358979323846
+#endif
+
+
+/* A simple but slow primality test. */
+int
+prime_p (unsigned long n)
+{
+ unsigned long i, limit;
+
+ if (n == 2)
+ return 1;
+ if (n < 2 || !(n&1))
+ return 0;
+
+ limit = (unsigned long) floor (sqrt ((double) n));
+ for (i = 3; i <= limit; i+=2)
+ if ((n % i) == 0)
+ return 0;
+
+ return 1;
+}
+
+
+/* The formula is as follows, with d < 0.
+
+ w * sqrt(-d) inf p
+ h(d) = ------------ * product --------
+ 2 * pi p=2 p - (d/p)
+
+
+ (d/p) is the Kronecker symbol and the product is over primes p. w is 6
+ when d=-3, 4 when d=-4, or 2 otherwise.
+
+ Calculating the product up to p=infinity would take a long time, so for
+ the estimate primes up to 132,000 are used. Shanks found this giving an
+ accuracy of about 1 part in 1000, in normal cases. */
+
+unsigned long p_limit = 132000;
+
+double
+qcn_estimate (mpz_t d)
+{
+ double h;
+ unsigned long p;
+
+ /* p=2 */
+ h = sqrt (-mpz_get_d (d)) / M_PI
+ * 2.0 / (2.0 - mpz_kronecker_ui (d, 2));
+
+ if (mpz_cmp_si (d, -3) == 0) h *= 3;
+ else if (mpz_cmp_si (d, -4) == 0) h *= 2;
+
+ for (p = 3; p <= p_limit; p += 2)
+ if (prime_p (p))
+ h *= (double) p / (double) (p - mpz_kronecker_ui (d, p));
+
+ return h;
+}
+
+
+void
+qcn_str (char *num)
+{
+ mpz_t z;
+
+ mpz_init_set_str (z, num, 0);
+
+ if (mpz_sgn (z) >= 0)
+ {
+ mpz_out_str (stdout, 0, z);
+ printf (" is not supported (negatives only)\n");
+ }
+ else if (mpz_fdiv_ui (z, 4) != 0 && mpz_fdiv_ui (z, 4) != 1)
+ {
+ mpz_out_str (stdout, 0, z);
+ printf (" is not a discriminant (must == 0 or 1 mod 4)\n");
+ }
+ else
+ {
+ printf ("h(");
+ mpz_out_str (stdout, 0, z);
+ printf (") approx %.1f\n", qcn_estimate (z));
+ }
+ mpz_clear (z);
+}
+
+
+int
+main (int argc, char *argv[])
+{
+ int i;
+ int saw_number = 0;
+
+ for (i = 1; i < argc; i++)
+ {
+ if (strcmp (argv[i], "-p") == 0)
+ {
+ i++;
+ if (i >= argc)
+ {
+ fprintf (stderr, "Missing argument to -p\n");
+ exit (1);
+ }
+ p_limit = atoi (argv[i]);
+ }
+ else
+ {
+ qcn_str (argv[i]);
+ saw_number = 1;
+ }
+ }
+
+ if (! saw_number)
+ {
+ /* some default output */
+ qcn_str ("-85702502803"); /* is 16259 */
+ qcn_str ("-328878692999"); /* is 1499699 */
+ qcn_str ("-928185925902146563"); /* is 52739552 */
+ qcn_str ("-84148631888752647283"); /* is 496652272 */
+ return 0;
+ }
+
+ return 0;
+}
projects / msp430-gcc.git / blobdiff