haskell-mpfr-0.1: deps/mpfr/src/sum.c
/* Sum -- efficiently sum a list of floating-point numbers
Copyright 2004-2015 Free Software Foundation, Inc.
Contributed by the AriC and Caramel projects, INRIA.
This file is part of the GNU MPFR Library.
The GNU MPFR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 3 of the License, or (at your
option) any later version.
The GNU MPFR Library 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 Lesser General Public
License for more details.
You should have received a copy of the GNU Lesser General Public License
along with the GNU MPFR Library; see the file COPYING.LESSER. If not, see
http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
/* Reference: James Demmel and Yozo Hida, Fast and accurate floating-point
summation with application to computational geometry, Numerical Algorithms,
volume 37, number 1-4, pages 101--112, 2004. */
#define MPFR_NEED_LONGLONG_H
#include "mpfr-impl.h"
/* I would really like to use "mpfr_srcptr const []" but the norm is buggy:
it doesn't automaticaly cast a "mpfr_ptr []" to "mpfr_srcptr const []"
if necessary. So the choice are:
mpfr_s ** : ok
mpfr_s *const* : ok
mpfr_s **const : ok
mpfr_s *const*const : ok
const mpfr_s *const* : no
const mpfr_s **const : no
const mpfr_s *const*const: no
VL: this is not a bug, but a feature. See the reason here:
http://c-faq.com/ansi/constmismatch.html
*/
static void heap_sort (mpfr_srcptr *const, unsigned long, mpfr_srcptr *);
static void count_sort (mpfr_srcptr *const, unsigned long, mpfr_srcptr *,
mpfr_exp_t, mpfr_uexp_t);
/* Either sort the tab in perm and returns 0
Or returns 1 for +INF, -1 for -INF and 2 for NAN */
int
mpfr_sum_sort (mpfr_srcptr *const tab, unsigned long n, mpfr_srcptr *perm)
{
mpfr_exp_t min, max;
mpfr_uexp_t exp_num;
unsigned long i;
int sign_inf;
sign_inf = 0;
min = MPFR_EMIN_MAX;
max = MPFR_EMAX_MIN;
for (i = 0; i < n; i++)
{
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (tab[i])))
{
if (MPFR_IS_NAN (tab[i]))
return 2; /* Return NAN code */
else if (MPFR_IS_INF (tab[i]))
{
if (sign_inf == 0) /* No previous INF */
sign_inf = MPFR_SIGN (tab[i]);
else if (sign_inf != MPFR_SIGN (tab[i]))
return 2; /* Return NAN */
}
}
else
{
MPFR_ASSERTD (MPFR_IS_PURE_FP (tab[i]));
if (MPFR_GET_EXP (tab[i]) < min)
min = MPFR_GET_EXP(tab[i]);
if (MPFR_GET_EXP (tab[i]) > max)
max = MPFR_GET_EXP(tab[i]);
}
}
if (MPFR_UNLIKELY (sign_inf != 0))
return sign_inf;
exp_num = max - min + 1;
/* FIXME : better test */
if (exp_num > n * MPFR_INT_CEIL_LOG2 (n))
heap_sort (tab, n, perm);
else
count_sort (tab, n, perm, min, exp_num);
return 0;
}
#define GET_EXP1(x) (MPFR_IS_ZERO (x) ? min : MPFR_GET_EXP (x))
/* Performs a count sort of the entries */
static void
count_sort (mpfr_srcptr *const tab, unsigned long n,
mpfr_srcptr *perm, mpfr_exp_t min, mpfr_uexp_t exp_num)
{
unsigned long *account;
unsigned long target_rank, i;
MPFR_TMP_DECL(marker);
/* Reserve a place for potential 0 (with EXP min-1)
If there is no zero, we only lose one unused entry */
min--;
exp_num++;
/* Performs a counting sort of the entries */
MPFR_TMP_MARK (marker);
account = (unsigned long *) MPFR_TMP_ALLOC (exp_num * sizeof *account);
for (i = 0; i < exp_num; i++)
account[i] = 0;
for (i = 0; i < n; i++)
account[GET_EXP1 (tab[i]) - min]++;
for (i = exp_num - 1; i >= 1; i--)
account[i - 1] += account[i];
for (i = 0; i < n; i++)
{
target_rank = --account[GET_EXP1 (tab[i]) - min];
perm[target_rank] = tab[i];
}
MPFR_TMP_FREE (marker);
}
#define GET_EXP2(x) (MPFR_IS_ZERO (x) ? MPFR_EMIN_MIN : MPFR_GET_EXP (x))
/* Performs a heap sort of the entries */
static void
heap_sort (mpfr_srcptr *const tab, unsigned long n, mpfr_srcptr *perm)
{
unsigned long dernier_traite;
unsigned long i, pere;
mpfr_srcptr tmp;
unsigned long fils_gauche, fils_droit, fils_indigne;
/* Reminder of a heap structure :
node(i) has for left son node(2i +1) and right son node(2i)
and father(node(i)) = node((i - 1) / 2)
*/
/* initialize the permutation to identity */
for (i = 0; i < n; i++)
perm[i] = tab[i];
/* insertion phase */
for (dernier_traite = 1; dernier_traite < n; dernier_traite++)
{
i = dernier_traite;
while (i > 0)
{
pere = (i - 1) / 2;
if (GET_EXP2 (perm[pere]) > GET_EXP2 (perm[i]))
{
tmp = perm[pere];
perm[pere] = perm[i];
perm[i] = tmp;
i = pere;
}
else
break;
}
}
/* extraction phase */
for (dernier_traite = n - 1; dernier_traite > 0; dernier_traite--)
{
tmp = perm[0];
perm[0] = perm[dernier_traite];
perm[dernier_traite] = tmp;
i = 0;
while (1)
{
fils_gauche = 2 * i + 1;
fils_droit = fils_gauche + 1;
if (fils_gauche < dernier_traite)
{
if (fils_droit < dernier_traite)
{
if (GET_EXP2(perm[fils_droit]) < GET_EXP2(perm[fils_gauche]))
fils_indigne = fils_droit;
else
fils_indigne = fils_gauche;
if (GET_EXP2 (perm[i]) > GET_EXP2 (perm[fils_indigne]))
{
tmp = perm[i];
perm[i] = perm[fils_indigne];
perm[fils_indigne] = tmp;
i = fils_indigne;
}
else
break;
}
else /* on a un fils gauche, pas de fils droit */
{
if (GET_EXP2 (perm[i]) > GET_EXP2 (perm[fils_gauche]))
{
tmp = perm[i];
perm[i] = perm[fils_gauche];
perm[fils_gauche] = tmp;
}
break;
}
}
else /* on n'a pas de fils */
break;
}
}
}
/* Sum a list of float with order given by permutation perm,
* intermediate size set to F.
* Internal use function.
*/
static int
sum_once (mpfr_ptr ret, mpfr_srcptr *const tab, unsigned long n, mpfr_prec_t F)
{
mpfr_t sum;
unsigned long i;
int error_trap;
MPFR_ASSERTD (n >= 2);
mpfr_init2 (sum, F);
error_trap = mpfr_set (sum, tab[0], MPFR_RNDN);
for (i = 1; i < n - 1; i++)
{
MPFR_ASSERTD (!MPFR_IS_NAN (sum) && !MPFR_IS_INF (sum));
error_trap |= mpfr_add (sum, sum, tab[i], MPFR_RNDN);
}
error_trap |= mpfr_add (ret, sum, tab[n - 1], MPFR_RNDN);
mpfr_clear (sum);
return error_trap;
}
/* Sum a list of floating-point numbers.
*/
int
mpfr_sum (mpfr_ptr ret, mpfr_ptr *const tab_p, unsigned long n, mpfr_rnd_t rnd)
{
mpfr_t cur_sum;
mpfr_prec_t prec;
mpfr_srcptr *perm, *const tab = (mpfr_srcptr *) tab_p;
int k, error_trap;
MPFR_ZIV_DECL (loop);
MPFR_SAVE_EXPO_DECL (expo);
MPFR_TMP_DECL (marker);
if (MPFR_UNLIKELY (n <= 1))
{
if (n < 1)
{
MPFR_SET_ZERO (ret);
MPFR_SET_POS (ret);
return 0;
}
else
return mpfr_set (ret, tab[0], rnd);
}
/* Sort and treat special cases */
MPFR_TMP_MARK (marker);
perm = (mpfr_srcptr *) MPFR_TMP_ALLOC (n * sizeof *perm);
error_trap = mpfr_sum_sort (tab, n, perm);
/* Check if there was a NAN or a INF */
if (MPFR_UNLIKELY (error_trap != 0))
{
MPFR_TMP_FREE (marker);
if (error_trap == 2)
{
MPFR_SET_NAN (ret);
MPFR_RET_NAN;
}
MPFR_SET_INF (ret);
MPFR_SET_SIGN (ret, error_trap);
MPFR_RET (0);
}
/* Initial precision */
prec = MAX (MPFR_PREC (tab[0]), MPFR_PREC (ret));
k = MPFR_INT_CEIL_LOG2 (n) + 1;
prec += k + 2;
mpfr_init2 (cur_sum, prec);
/* Ziv Loop */
MPFR_SAVE_EXPO_MARK (expo);
MPFR_ZIV_INIT (loop, prec);
for (;;)
{
error_trap = sum_once (cur_sum, perm, n, prec + k);
if (MPFR_LIKELY (error_trap == 0 ||
(!MPFR_IS_ZERO (cur_sum) &&
mpfr_can_round (cur_sum,
MPFR_GET_EXP (cur_sum) - prec + 2,
MPFR_RNDN, rnd, MPFR_PREC (ret)))))
break;
MPFR_ZIV_NEXT (loop, prec);
mpfr_set_prec (cur_sum, prec);
}
MPFR_ZIV_FREE (loop);
MPFR_TMP_FREE (marker);
error_trap |= mpfr_set (ret, cur_sum, rnd);
mpfr_clear (cur_sum);
MPFR_SAVE_EXPO_FREE (expo);
error_trap |= mpfr_check_range (ret, 0, rnd);
return error_trap; /* It doesn't return the ternary value */
}
/* __END__ */