summaryrefslogtreecommitdiff
path: root/Build/source/libs/mpfi/mpfi-src/src/sec.c
diff options
context:
space:
mode:
Diffstat (limited to 'Build/source/libs/mpfi/mpfi-src/src/sec.c')
-rw-r--r--Build/source/libs/mpfi/mpfi-src/src/sec.c136
1 files changed, 136 insertions, 0 deletions
diff --git a/Build/source/libs/mpfi/mpfi-src/src/sec.c b/Build/source/libs/mpfi/mpfi-src/src/sec.c
new file mode 100644
index 00000000000..eeb7f559998
--- /dev/null
+++ b/Build/source/libs/mpfi/mpfi-src/src/sec.c
@@ -0,0 +1,136 @@
+/* sec.c -- Secant of an interval.
+
+Copyright 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2010,
+ Spaces project, Inria Lorraine
+ and Salsa project, INRIA Rocquencourt,
+ and Arenaire project, Inria Rhone-Alpes, France
+ and Lab. ANO, USTL (Univ. of Lille), France
+
+This file is part of the MPFI Library.
+
+The MPFI 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 2.1 of the License, or (at your
+option) any later version.
+
+The MPFI 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 MPFI Library; see the file COPYING.LIB. If not, write to
+the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston,
+MA 02110-1301, USA. */
+
+#include "mpfi-impl.h"
+
+int
+mpfi_sec (mpfi_ptr a, mpfi_srcptr b)
+{
+ int inexact_left, inexact_right, inexact = 0;
+ mpfr_prec_t prec, prec_left, prec_right;
+ mpfr_t tmp;
+ mpz_t z_left, z_right;
+ mpz_t z, zmod4;
+ int ql_mod4, qr_mod4;
+
+ if (MPFI_NAN_P (b)) {
+ mpfr_set_nan (&(a->left));
+ mpfr_set_nan (&(a->right));
+ MPFR_RET_NAN;
+ }
+
+ if (MPFI_INF_P (b)) {
+ /* the two endpoints are the same infinite */
+ if ( mpfr_cmp (&(b->left), &(b->right)) == 0) {
+ mpfr_set_nan (&(a->left));
+ mpfr_set_nan (&(a->right));
+ MPFR_RET_NAN;
+ }
+ mpfr_set_inf (&(a->left), -1);
+ mpfr_set_inf (&(a->right), 1);
+ return 0;
+ }
+
+ mpz_init (z_left);
+ mpz_init (z_right);
+ mpz_init (z);
+
+ prec_left = mpfi_quadrant (z_left, &(b->left));
+ prec_right = mpfi_quadrant (z_right, &(b->right));
+
+ /* if there is at least one period in b or if b contains a Pi/2 + k*Pi, */
+ /* then a = ]-oo, +oo[ */
+ mpz_sub (z, z_right, z_left);
+ if ( (mpz_cmp_ui (z, 2) >= 0) ||
+ (mpz_even_p (z_left) && mpz_odd_p (z_right)) ) {
+ mpfr_set_inf (&(a->left), -1);
+ mpfr_set_inf (&(a->right), 1);
+ inexact = 0;
+ }
+ else {
+ /* computing precision = maximal precision required to determine the */
+ /* relative position of the endpoints of b and of integer multiples of Pi / 2 */
+ prec = mpfi_get_prec (a);
+ if (prec_left > prec) prec = prec_left;
+ if (prec_right > prec) prec = prec_right;
+
+ mpz_init (zmod4);
+
+ /* qr_mod4 gives the quadrant where the right endpoint of b is */
+ /* qr_mod4 = floor (2 b->right / pi) mod 4 */
+ mpz_mod_ui (zmod4, z_right, 4);
+ qr_mod4 = mpz_get_ui (zmod4);
+
+ /* z_left gives the quadrant where the left endpoint of b is */
+ /* z_left = floor (2 b->left / pi) mod 4 */
+ mpz_mod_ui (zmod4, z_left, 4);
+ ql_mod4 = mpz_get_ui (zmod4);
+
+
+ if (qr_mod4 == ql_mod4) {
+ if (qr_mod4 == 0 || qr_mod4 == 1) {
+ /* sec is increasing on b */
+ inexact_left = mpfr_sec (&(a->left), &(b->left), MPFI_RNDD);
+ inexact_right = mpfr_sec (&(a->right), &(b->right), MPFI_RNDU);
+ }
+ else {
+ /* sec is decreasing on b */
+ mpfr_init2 (tmp, mpfr_get_prec (&(a->left)));
+ inexact_left = mpfr_sec (tmp, &(b->right), MPFI_RNDD);
+ inexact_right = mpfr_sec (&(a->right), &(b->left), MPFI_RNDU);
+ mpfr_set (&(a->left), tmp, MPFI_RNDD); /* exact */
+ mpfr_clear (tmp);
+ }
+ }
+ else if (ql_mod4 == 1) {
+ mpz_add (z, z_left, z_right);
+ mpz_add_ui (z, z, 1);
+ if (mpfi_cmp_sym_pi (z, &(b->right), &(b->left), prec) >= 0)
+ inexact_left = mpfr_sec (&(a->left), &(b->left), MPFI_RNDD);
+ else
+ inexact_left = mpfr_sec (&(a->left), &(b->right), MPFI_RNDD);
+ inexact_right = mpfr_set_si (&(a->right), -1, MPFI_RNDU);
+ }
+ else {
+ mpz_add (z, z_left, z_right);
+ mpz_add_ui (z, z, 1);
+ if (mpfi_cmp_sym_pi (z, &(b->right), &(b->left), prec) >= 0)
+ inexact_right = mpfr_sec (&(a->right), &(b->left), MPFI_RNDU);
+ else
+ inexact_right = mpfr_sec (&(a->right), &(b->right), MPFI_RNDU);
+ inexact_left = mpfr_set_ui (&(a->left), +1, MPFI_RNDD);
+ }
+
+ if (inexact_left) inexact = 1;
+ if (inexact_right) inexact += 2;
+
+ mpz_clear (zmod4);
+ }
+
+ mpz_clear (z_left);
+ mpz_clear (z_right);
+
+ return inexact;
+}