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Diffstat (limited to 'Build/source/libs/mpfi/mpfi-src/src/sec.c')
-rw-r--r-- | Build/source/libs/mpfi/mpfi-src/src/sec.c | 136 |
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; +} |