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Diffstat (limited to 'Build/source/libs/mpfi/mpfi-src/src/cot.c')
-rw-r--r-- | Build/source/libs/mpfi/mpfi-src/src/cot.c | 115 |
1 files changed, 115 insertions, 0 deletions
diff --git a/Build/source/libs/mpfi/mpfi-src/src/cot.c b/Build/source/libs/mpfi/mpfi-src/src/cot.c new file mode 100644 index 00000000000..722c5aa25b7 --- /dev/null +++ b/Build/source/libs/mpfi/mpfi-src/src/cot.c @@ -0,0 +1,115 @@ +/* cot.c -- Cotangent 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_cot (mpfi_ptr a, mpfi_srcptr b) +{ + int inexact_left, inexact_right, inexact=0; + mpz_t z_left, z_right, z; + + 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); + + mpfi_quadrant (z_left, &(b->left)); + mpfi_quadrant (z_right, &(b->right)); + mpz_sub (z, z_right, z_left); + + if (mpfr_zero_p (&(b->left)) || mpfr_zero_p (&(b->right))) { + /* one end point is zero, this is the only multiple of Pi to be exact */ + if (mpfr_zero_p (&(b->left)) && mpfr_zero_p (&(b->right))) { + /* cot([+0, -0] = [NaN, NaN] */ + mpfr_set_nan (&(a->left)); + mpfr_set_nan (&(a->right)); + MPFR_RET_NAN; + } + + if ((mpfr_zero_p (&(b->left)) && mpz_cmp_ui (z_right, 1) > 0) + || (mpfr_zero_p (&(b->right)) && mpz_cmp_si (z_left, -2) < 0)) { + /* b contains more than one period */ + mpfr_set_inf (&(a->left), -1); + mpfr_set_inf (&(a->right), 1); + inexact = 0; + } + else if (mpfr_zero_p (&(b->left))) { + /* cot([+0, x]) = [cot(x), +oo] */ + inexact_left = mpfr_cot (&(a->left), &(b->right), MPFI_RNDD); + inexact = inexact_left ? MPFI_FLAGS_LEFT_ENDPOINT_INEXACT : 0; + mpfr_set_inf (&(a->right), 1); + } + else { + /* cot([x, -0]) = [-oo, cot(x)] */ + inexact_right = mpfr_cot (&(a->right), &(b->left), MPFI_RNDU); + inexact = inexact_right ? MPFI_FLAGS_RIGHT_ENDPOINT_INEXACT : 0; + mpfr_set_inf (&(a->left), -1); + } + } + else if ((mpz_cmp_ui (z, 2) >= 0) + || (mpz_odd_p (z_left) && mpz_even_p (z_right))) { + /* there is at least one period in b or if b contains a k*Pi, */ + /* then a = ]-oo, +oo[ */ + mpfr_set_inf (&(a->left), -1); + mpfr_set_inf (&(a->right), 1); + inexact = 0; + } + else { /* within one period, cot is decreasing */ + mpfr_t tmp; + + mpfr_init2 (tmp, mpfr_get_prec (&(a->left))); + inexact_left = mpfr_cot (tmp, &(b->right), MPFI_RNDD); + inexact_right = mpfr_cot (&(a->right), &(b->left), MPFI_RNDU); + mpfr_set (&(a->left), tmp, MPFI_RNDD); /* exact */ + mpfr_clear (tmp); + + if (inexact_left) inexact += 1; + if (inexact_right) inexact += 2; + } + + mpz_clear (z_left); + mpz_clear (z_right); + mpz_clear (z); + + return inexact; +} |