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add arb_rising_fmpq_ui

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This commit is contained in:
Fredrik Johansson 2014-06-04 13:02:45 +02:00
parent b014dbec80
commit befeb0ec50
3 changed files with 109 additions and 0 deletions
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1
arb.h
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@ -641,6 +641,7 @@ void arb_rising_ui_bs(arb_t y, const arb_t x, ulong n, long prec);
void arb_rising_ui_rs(arb_t y, const arb_t x, ulong n, ulong m, long prec);
void arb_rising_ui_rec(arb_t y, const arb_t x, ulong n, long prec);
void arb_rising_ui(arb_t z, const arb_t x, ulong n, long prec);
void arb_rising_fmpq_ui(arb_t y, const fmpq_t x, ulong n, long prec);
/* vector functions */

102
arb/rising_fmpq_ui.c Normal file
View file

@ -0,0 +1,102 @@
/*=============================================================================
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 "arb.h"
static void
bsplit(arb_t y, const fmpz_t p, const fmpz_t q, ulong a, ulong b, long prec)
{
if (b - a <= 8)
{
fmpz_t t, u;
ulong c;
fmpz_init(t);
fmpz_init(u);
fmpz_mul_ui(t, q, a);
fmpz_add(t, t, p);
fmpz_set(u, t);
for (c = a + 1; c < b; c++)
{
fmpz_add(u, u, q);
fmpz_mul(t, t, u);
}
arb_set_round_fmpz(y, t, prec);
fmpz_clear(t);
fmpz_clear(u);
}
else
{
arb_t w;
ulong m = a + (b - a) / 2;
arb_init(w);
bsplit(y, p, q, a, m, prec);
bsplit(w, p, q, m, b, prec);
arb_mul(y, y, w, prec);
arb_clear(w);
}
}
void
arb_rising_fmpq_ui(arb_t y, const fmpq_t x, ulong n, long prec)
{
if (n == 0)
{
arb_one(y);
}
else if (n == 1)
{
arb_set_fmpq(y, x, prec);
}
else
{
long wp;
wp = ARF_PREC_ADD(prec, FLINT_BIT_COUNT(n));
bsplit(y, fmpq_numref(x), fmpq_denref(x), 0, n, wp);
if (fmpz_is_one(fmpq_denref(x)))
{
arb_set_round(y, y, prec);
}
else
{
arb_t t;
arb_init(t);
arb_set_fmpz(t, fmpq_denref(x));
arb_pow_ui(t, t, n, wp);
arb_div(y, y, t, prec);
arb_clear(t);
}
}
}

6
doc/source/arb.rst
View file

@ -747,6 +747,12 @@ Rising factorials
The *rs* version takes an optional *step* parameter for tuning
purposes (to use the default step length, pass zero).
.. function:: void arb_rising_fmpq_ui(arb_t z, const fmpq_t x, ulong n, long prec)
Computes the rising factorial `z = x (x+1) (x+2) \cdots (x+n-1)` using
binary splitting. If the denominator or numerator of *x* is large
compared to *prec*, it is more efficient to convert *x* to an approximation
and use :func:`arb_rising_ui`.
Special functions
-------------------------------------------------------------------------------