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add keiper-li coefficients example program

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This commit is contained in:
Fredrik Johansson 2013-09-19 18:15:55 +01:00
parent 707587b837
commit 62e3dced8c
1 changed files with 135 additions and 0 deletions
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135
examples/keiper_li.c Normal file
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#include <string.h>
#include "fmprb.h"
#include "fmpcb.h"
#include "fmprb_poly.h"
#include "zeta.h"
#include "profiler.h"
void
keiper_li_series(fmprb_ptr z, long len, long prec)
{
fmprb_ptr t, u, v;
t = _fmprb_vec_init(len);
u = _fmprb_vec_init(len);
v = _fmprb_vec_init(len);
/* -zeta(s) */
printf("zeta: ");
TIMEIT_ONCE_START
fmprb_zero(t + 0);
fmprb_one(t + 1);
fmprb_one(u);
_fmprb_poly_zeta_series(v, t, 2, u, 0, len, prec);
_fmprb_vec_neg(v, v, len);
TIMEIT_ONCE_STOP
SHOW_MEMORY_USAGE
/* logarithm */
printf("log: ");
TIMEIT_ONCE_START
_fmprb_poly_log_series(t, v, len, len, prec);
TIMEIT_ONCE_STOP
/* add log(gamma(1+s/2)) */
printf("gamma: ");
TIMEIT_ONCE_START
fmprb_one(u);
fmprb_one(u + 1);
fmprb_mul_2exp_si(u + 1, u + 1, -1);
_fmprb_poly_lgamma_series(v, u, 2, len, prec);
_fmprb_vec_add(t, t, v, len, prec);
TIMEIT_ONCE_STOP
/* subtract 0.5 s log(pi) */
fmprb_const_pi(u, prec);
fmprb_log(u, u, prec);
fmprb_mul_2exp_si(u, u, -1);
fmprb_sub(t + 1, t + 1, u, prec);
/* add log(1-s) */
fmprb_one(u);
fmprb_set_si(u + 1, -1);
_fmprb_poly_log_series(v, u, 2, len, prec);
_fmprb_vec_add(t, t, v, len, prec);
/* binomial transform */
printf("binomial transform: ");
TIMEIT_ONCE_START
fmprb_set(z, t);
_fmprb_vec_neg(t + 1, t + 1, len - 1);
_fmprb_poly_binomial_transform(z + 1, t + 1, len - 1, len - 1, prec);
TIMEIT_ONCE_STOP
_fmprb_vec_clear(t, len);
_fmprb_vec_clear(u, len);
_fmprb_vec_clear(v, len);
}
int main(int argc, char *argv[])
{
long i, len, prec, num_threads;
char * out_file;
fmprb_ptr z;
if (argc < 2)
{
printf("keiper_li n [-prec prec] [-threads num_threads] [-out out_file]\n");
return 1;
}
len = atol(argv[1]) + 1;
prec = 1.1 * len + 50;
num_threads = 1;
out_file = NULL;
for (i = 1; i < argc; i++)
{
if (!strcmp(argv[i], "-prec"))
prec = atol(argv[i+1]);
else if (!strcmp(argv[i], "-threads"))
num_threads = atol(argv[i+1]);
else if (!strcmp(argv[i], "-out"))
out_file = argv[i+1];
}
flint_set_num_threads(num_threads);
z = _fmprb_vec_init(len);
keiper_li_series(z, len, prec);
for (i = 0; i < len; i++)
{
if (i <= 10 || len - i <= 10)
{
printf("%ld: ", i); fmprb_printd(z + i, 50); printf("\n");
}
}
SHOW_MEMORY_USAGE
if (out_file != NULL)
{
FILE * fp = fopen(out_file, "w");
for (i = 0; i < len; i++)
{
fprintf(fp, "%ld ", i);
fmpz_fprint(fp, fmpr_manref(fmprb_midref(z + i)));
fprintf(fp, " ");
fmpz_fprint(fp, fmpr_expref(fmprb_midref(z + i)));
fprintf(fp, " ");
fmpz_fprint(fp, fmpr_manref(fmprb_radref(z + i)));
fprintf(fp, " ");
fmpz_fprint(fp, fmpr_expref(fmprb_radref(z + i)));
fprintf(fp, "\n");
}
fclose(fp);
}
_fmprb_vec_clear(z, len);
flint_cleanup();
return 0;
}