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remove two obsolete helper functions

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This commit is contained in:
Fredrik Johansson 2014-12-07 03:16:25 +01:00
parent 0214f750d7
commit e3f7ef1f66
1 changed files with 0 additions and 76 deletions
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76
hypgeom/bound.c
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@ -27,82 +27,6 @@
#include "double_extras.h"
#include "hypgeom.h"
void
fmpr_gamma_ui_lbound(fmpr_t x, ulong n, long prec)
{
if (n == 0) abort();
if (n < 250)
{
fmpz_t t;
fmpz_init(t);
fmpz_fac_ui(t, n - 1);
fmpr_set_round_fmpz(x, t, prec, FMPR_RND_DOWN);
fmpz_clear(t);
}
else
{
/* (2 pi/x)^(1/2) * (x/e)^x < Gamma(x) */
fmpr_t t, u;
fmpr_init(t);
fmpr_init(u);
/* lower bound for 2 pi */
fmpr_set_ui_2exp_si(t, 843314855, -27);
fmpr_div_ui(t, t, n, prec, FMPR_RND_DOWN);
fmpr_sqrt(t, t, prec, FMPR_RND_DOWN);
/* lower bound for 1/e */
fmpr_set_ui_2exp_si(u, 197503771, -29);
fmpr_mul_ui(u, u, n, prec, FMPR_RND_DOWN);
fmpr_pow_sloppy_ui(u, u, n, prec, FMPR_RND_DOWN);
fmpr_mul(x, t, u, prec, FMPR_RND_DOWN);
fmpr_clear(t);
fmpr_clear(u);
}
}
void
fmpr_gamma_ui_ubound(fmpr_t x, ulong n, long prec)
{
if (n == 0) abort();
if (n < 250)
{
fmpz_t t;
fmpz_init(t);
fmpz_fac_ui(t, n - 1);
fmpr_set_round_fmpz(x, t, prec, FMPR_RND_UP);
fmpz_clear(t);
}
else
{
fmpr_t t, u;
fmpr_init(t);
/* Gamma(x) < e * (x / e)^x -- TODO: use a tighter bound */
fmpr_init(t);
fmpr_init(u);
/* upper bound for 1/e */
fmpr_set_ui_2exp_si(u, 197503773, -29);
fmpr_mul_ui(u, u, n, prec, FMPR_RND_UP);
fmpr_pow_sloppy_ui(u, u, n, prec, FMPR_RND_UP);
/* upper bound for e */
fmpr_set_ui_2exp_si(t, 364841613, -27);
fmpr_mul(x, t, u, prec, FMPR_RND_UP);
fmpr_clear(t);
fmpr_clear(u);
}
}
long
hypgeom_root_bound(const mag_t z, int r)
{