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add fmprb_const_log10

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This commit is contained in:
Fredrik Johansson 2013-03-04 16:24:27 +01:00
parent 74b2c9dc55
commit 79143c1c7e
4 changed files with 157 additions and 0 deletions
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7
doc/source/fmprb.rst
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@ -642,6 +642,13 @@ Constants
\log 2 = \frac{3}{4} \sum_{k=0}^{\infty} \frac{(-1)^k (k!)^2}{2^k (2k+1)!}
.. function:: void fmprb_const_log10(fmprb_t s, long prec)
Sets *x* to `\log 10`. The value is cached for repeated use.
Uses the generic hypergeometric series code to evaluate the
Machin-like formula
`\log 10 = 46 \operatorname{atanh}(1/31) + 34 \operatorname{atanh}(1/49) + 20 \operatorname{atanh}(1/161)`.
.. function:: void fmprb_const_e(fmprb_t s, long prec)
Sets *x* to Euler's number `e = \sum_{n=0}^{\infty} 1/n!`, evaluated

1
fmprb.h
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@ -307,6 +307,7 @@ void fmprb_const_pi(fmprb_t x, long prec);
void fmprb_const_sqrt_pi(fmprb_t t, long prec);
void fmprb_const_log_sqrt2pi(fmprb_t t, long prec);
void fmprb_const_log2(fmprb_t s, long prec);
void fmprb_const_log10(fmprb_t s, long prec);
void fmprb_const_catalan(fmprb_t s, long prec);
void fmprb_const_e(fmprb_t s, long prec);

70
fmprb/const_log10.c Normal file
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@ -0,0 +1,70 @@
/*=============================================================================
This file is part of ARB.
ARB 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 2 of the License, or
(at your option) any later version.
ARB 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 ARB; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2013 Fredrik Johansson
******************************************************************************/
#include "fmprb.h"
#include "hypgeom.h"
static void
atanh_bsplit(fmprb_t s, ulong c, long a, long prec)
{
fmprb_t t;
hypgeom_t series;
hypgeom_init(series);
fmprb_init(t);
fmpz_poly_set_ui(series->A, 1);
fmpz_poly_set_coeff_ui(series->B, 0, 1);
fmpz_poly_set_coeff_ui(series->B, 1, 2);
fmpz_poly_set_ui(series->P, 1);
fmpz_poly_set_ui(series->Q, c * c);
fmprb_hypgeom_infsum(s, t, series, prec, prec);
fmprb_mul_si(s, s, a, prec);
fmprb_mul_ui(t, t, c, prec);
fmprb_div(s, s, t, prec);
fmprb_clear(t);
hypgeom_clear(series);
}
void
fmprb_const_log10_eval(fmprb_t s, long prec)
{
fmprb_t t;
fmprb_init(t);
prec += FLINT_CLOG2(prec);
atanh_bsplit(s, 31, 46, prec);
atanh_bsplit(t, 49, 34, prec);
fmprb_add(s, s, t, prec);
atanh_bsplit(t, 161, 20, prec);
fmprb_add(s, s, t, prec);
fmprb_clear(t);
}
DEF_CACHED_CONSTANT(fmprb_const_log10, fmprb_const_log10_eval)

79
fmprb/test/t-const_log10.c Normal file
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@ -0,0 +1,79 @@
/*=============================================================================
This file is part of ARB.
ARB 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 2 of the License, or
(at your option) any later version.
ARB 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 ARB; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2012 Fredrik Johansson
******************************************************************************/
#include "fmprb.h"
int main()
{
long iter;
flint_rand_t state;
printf("const_log10....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 250; iter++)
{
fmprb_t r;
mpfr_t s;
long accuracy, prec;
prec = 2 + n_randint(state, 1 << n_randint(state, 16));
fmprb_init(r);
mpfr_init2(s, prec + 1000);
fmprb_const_log10(r, prec);
mpfr_set_ui(s, 10, MPFR_RNDN);
mpfr_log(s, s, MPFR_RNDN);
if (!fmprb_contains_mpfr(r, s))
{
printf("FAIL: containment\n\n");
printf("prec = %ld\n", prec);
printf("r = "); fmprb_printd(r, prec / 3.33); printf("\n\n");
abort();
}
accuracy = fmprb_rel_accuracy_bits(r);
if (accuracy < prec - 4)
{
printf("FAIL: poor accuracy\n\n");
printf("prec = %ld\n", prec);
printf("r = "); fmprb_printd(r, prec / 3.33); printf("\n\n");
abort();
}
fmprb_clear(r);
mpfr_clear(s);
}
flint_randclear(state);
_fmpz_cleanup();
mpfr_free_cache();
printf("PASS\n");
return EXIT_SUCCESS;
}