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fix lgamma_series; add test code

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This commit is contained in:
Fredrik Johansson 2013-07-22 01:28:36 +02:00
parent 3bc81e2838
commit 4c0210196a
2 changed files with 141 additions and 43 deletions
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53
fmprb_poly/lgamma_series.c
View file

@ -27,16 +27,16 @@
#include "gamma.h" #include "gamma.h"
void void
_fmprb_poly_lgamma_cpx_series(fmprb_ptr res, const fmprb_t z, long len, long prec) _fmprb_poly_lgamma_series(fmprb_ptr res, fmprb_ptr h, long hlen, long len, long prec)
{ {
int reflect; int reflect;
long r, n, rflen, wp; long r, n, rflen, wp;
fmprb_t zr; fmprb_t zr;
fmprb_ptr t, u, f; fmprb_ptr t, u, f;
hlen = FLINT_MIN(hlen, len);
wp = prec + FLINT_BIT_COUNT(prec); wp = prec + FLINT_BIT_COUNT(prec);
gamma_stirling_choose_param_fmprb(&reflect, &r, &n, h, 0, 0, wp);
gamma_stirling_choose_param_fmprb(&reflect, &r, &n, z, 0, 0, wp);
t = _fmprb_vec_init(len); t = _fmprb_vec_init(len);
u = _fmprb_vec_init(len); u = _fmprb_vec_init(len);
@ -44,19 +44,26 @@ _fmprb_poly_lgamma_cpx_series(fmprb_ptr res, const fmprb_t z, long len, long pre
fmprb_init(zr); fmprb_init(zr);
/* log(gamma(z)) = log(gamma(z+r)) - log(rf(z,r)) */ /* log(gamma(z)) = log(gamma(z+r)) - log(rf(z,r)) */
fmprb_add_ui(zr, z, r, wp); fmprb_add_ui(zr, h, r, wp);
/* u = log(gamma(z+r)) */ /* u = log(gamma(z+r)) */
gamma_stirling_eval_fmprb_series(u, zr, n, len, wp); gamma_stirling_eval_fmprb_series(u, zr, n, len, wp);
/* t = rising factorial */ /* subtract t = log(rf(z,r)) */
fmprb_set(f, z); if (r != 0)
{
fmprb_set(f, h);
fmprb_one(f + 1); fmprb_one(f + 1);
rflen = FLINT_MIN(len, r + 1); rflen = FLINT_MIN(len, r + 1);
_fmprb_poly_rfac_series_ui(t, f, FLINT_MIN(2, len), r, rflen, prec); _fmprb_poly_rfac_series_ui(t, f, FLINT_MIN(2, len), r, rflen, prec);
_fmprb_poly_log_series(t, t, rflen, len, wp); _fmprb_poly_log_series(t, t, rflen, len, wp);
_fmprb_vec_sub(u, u, t, len, prec);
}
_fmprb_vec_sub(res, u, t, len, prec); /* compose with nonconstant part */
fmprb_zero(t);
_fmprb_vec_set(t + 1, h + 1, hlen - 1);
_fmprb_poly_compose_series(res, u, len, t, hlen, len, prec);
fmprb_clear(zr); fmprb_clear(zr);
_fmprb_vec_clear(t, len); _fmprb_vec_clear(t, len);
@ -64,38 +71,6 @@ _fmprb_poly_lgamma_cpx_series(fmprb_ptr res, const fmprb_t z, long len, long pre
_fmprb_vec_clear(f, 2); _fmprb_vec_clear(f, 2);
} }
void
fmprb_poly_lgamma_cpx_series(fmprb_poly_t res, const fmprb_t z, long num, long prec)
{
fmprb_poly_fit_length(res, num);
_fmprb_poly_lgamma_cpx_series(res->coeffs, z, num, prec);
_fmprb_poly_set_length(res, num);
_fmprb_poly_normalise(res);
}
void
_fmprb_poly_lgamma_series(fmprb_ptr res, fmprb_ptr h, long hlen, long len, long prec)
{
fmprb_ptr t, u;
fmprb_t z;
hlen = FLINT_MIN(hlen, len);
t = _fmprb_vec_init(hlen);
u = _fmprb_vec_init(len);
fmprb_init(z);
fmprb_set(z, h);
_fmprb_vec_set(t + 1, h + 1, hlen - 1);
_fmprb_poly_lgamma_cpx_series(u, z, len, prec);
_fmprb_poly_compose_series(res, u, len, t, hlen, len, prec);
fmprb_clear(z);
_fmprb_vec_clear(t, hlen);
_fmprb_vec_clear(u, len);
}
void void
fmprb_poly_lgamma_series(fmprb_poly_t res, const fmprb_poly_t f, long n, long prec) fmprb_poly_lgamma_series(fmprb_poly_t res, const fmprb_poly_t f, long n, long prec)
{ {

123
fmprb_poly/test/t-lgamma_series.c Normal file
View file

@ -0,0 +1,123 @@
/*=============================================================================
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, 2013 Fredrik Johansson
******************************************************************************/
#include "fmprb_poly.h"
int main()
{
long iter;
flint_rand_t state;
printf("lgamma_series....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000; iter++)
{
long m, n1, n2, qbits, rbits1, rbits2, rbits3;
fmpq_poly_t A;
fmprb_poly_t a, b, c, d;
qbits = 2 + n_randint(state, 200);
rbits1 = 2 + n_randint(state, 400);
rbits2 = 2 + n_randint(state, 400);
rbits3 = 2 + n_randint(state, 400);
m = 1 + n_randint(state, 30);
n1 = 1 + n_randint(state, 30);
n2 = 1 + n_randint(state, 30);
fmpq_poly_init(A);
fmprb_poly_init(a);
fmprb_poly_init(b);
fmprb_poly_init(c);
fmprb_poly_init(d);
fmpq_poly_randtest_not_zero(A, state, m, qbits);
fmpz_abs(A->coeffs, A->coeffs);
fmprb_poly_set_fmpq_poly(a, A, rbits1);
fmprb_poly_lgamma_series(b, a, n1, rbits2);
fmprb_poly_lgamma_series(c, a, n2, rbits3);
fmprb_poly_set(d, b);
fmprb_poly_truncate(d, FLINT_MIN(n1, n2));
fmprb_poly_truncate(c, FLINT_MIN(n1, n2));
if (!fmprb_poly_overlaps(c, d))
{
printf("FAIL\n\n");
printf("n1 = %ld, n2 = %ld, bits2 = %ld, bits3 = %ld\n", n1, n2, rbits2, rbits3);
printf("A = "); fmpq_poly_print(A); printf("\n\n");
printf("a = "); fmprb_poly_printd(a, 15); printf("\n\n");
printf("b = "); fmprb_poly_printd(b, 15); printf("\n\n");
printf("c = "); fmprb_poly_printd(c, 15); printf("\n\n");
abort();
}
/* check loggamma(a) + log(a) = loggamma(a+1) */
fmprb_poly_log_series(c, a, n1, rbits2);
fmprb_poly_add(c, b, c, rbits2);
fmprb_poly_set(d, a);
fmprb_add_ui(d->coeffs, d->coeffs, 1, rbits2);
fmprb_poly_lgamma_series(d, d, n1, rbits2);
if (!fmprb_poly_overlaps(c, d))
{
printf("FAIL (functional equation)\n\n");
printf("A = "); fmpq_poly_print(A); printf("\n\n");
printf("a = "); fmprb_poly_printd(a, 15); printf("\n\n");
printf("b = "); fmprb_poly_printd(b, 15); printf("\n\n");
printf("c = "); fmprb_poly_printd(c, 15); printf("\n\n");
printf("d = "); fmprb_poly_printd(d, 15); printf("\n\n");
abort();
}
fmprb_poly_lgamma_series(a, a, n1, rbits2);
if (!fmprb_poly_overlaps(a, b))
{
printf("FAIL (aliasing)\n\n");
abort();
}
fmpq_poly_clear(A);
fmprb_poly_clear(a);
fmprb_poly_clear(b);
fmprb_poly_clear(c);
fmprb_poly_clear(d);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}