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slightly improve const_glaisher

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This commit is contained in:
Fredrik Johansson 2013-08-03 14:56:29 +02:00
parent 6e8e2d26ad
commit 9ddd9641eb
1 changed files with 20 additions and 29 deletions
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49
fmprb/const_glaisher.c
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@ -24,46 +24,37 @@
******************************************************************************/ ******************************************************************************/
#include "fmprb.h" #include "fmprb.h"
#include "fmprb_poly.h" #include "zeta.h"
void void
fmprb_const_glaisher_eval(fmprb_t y, long prec) fmprb_const_glaisher_eval(fmprb_t y, long prec)
{ {
fmprb_t t; fmpcb_struct z[2];
fmprb_struct z[2]; fmpcb_t s, a;
long wp; long wp;
fmprb_init(t); fmpcb_init(z + 0);
fmprb_init(z + 0); fmpcb_init(z + 1);
fmprb_init(z + 1); fmpcb_init(s);
fmpcb_init(a);
wp = prec + 20; wp = prec + 20;
fmprb_set_ui(z + 0, 2); /* directly evaluating at s = -1 is slightly faster
fmprb_one(z + 1); than evaluating at s = 2 */
fmprb_one(t); fmpcb_set_si(s, -1);
fmpcb_one(a);
zeta_series(z, s, a, 0, 2, wp);
_fmprb_poly_zeta_series(z, z, 2, t, 0, 2, wp); fmprb_one(y);
fmprb_div_ui(y, y, 12, wp);
fmprb_sub(y, y, fmpcb_realref(z + 1), wp);
fmprb_exp(y, y, wp);
fmprb_const_pi(z, wp); fmpcb_clear(z + 0);
fmprb_mul(z, z, z, wp); fmpcb_clear(z + 1);
fmprb_mul_2exp_si(z, z, 1); fmpcb_clear(s);
fmprb_div(z, z + 1, z, wp); fmpcb_clear(a);
fmprb_const_euler(t, wp);
fmprb_div_ui(t, t, 12, wp);
fmprb_sub(t, t, z, wp);
fmprb_exp(y, t, wp);
fmprb_const_pi(t, wp);
fmprb_mul_2exp_si(t, t, 1);
fmprb_root(t, t, 12, wp);
fmprb_mul(y, y, t, prec);
fmprb_clear(t);
fmprb_clear(z + 0);
fmprb_clear(z + 1);
} }
DEF_CACHED_CONSTANT(fmprb_const_glaisher, fmprb_const_glaisher_eval) DEF_CACHED_CONSTANT(fmprb_const_glaisher, fmprb_const_glaisher_eval)