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Diffstat (limited to 'Build/source/libs/mpfi/mpfi-src/src/sin.c')
-rw-r--r-- | Build/source/libs/mpfi/mpfi-src/src/sin.c | 209 |
1 files changed, 209 insertions, 0 deletions
diff --git a/Build/source/libs/mpfi/mpfi-src/src/sin.c b/Build/source/libs/mpfi/mpfi-src/src/sin.c new file mode 100644 index 00000000000..dbf2205b71d --- /dev/null +++ b/Build/source/libs/mpfi/mpfi-src/src/sin.c @@ -0,0 +1,209 @@ +/* sin.c -- Sine 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_sin (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, zmod4; + mpz_t quad_left, quad_right; + 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_si (&(a->left), -1, MPFI_RNDD); + mpfr_set_si (&(a->right), 1, MPFI_RNDU); + return 0; + } + + mpz_init (quad_left); + mpz_init (quad_right); + mpz_init (z); + /* quad_left gives the quadrant where the left endpoint of b is */ + /* quad_left = floor (2 b->left / pi) */ + /* idem for quad_right and b->right */ + prec_left = mpfi_quadrant (quad_left, &(b->left)); + prec_right = mpfi_quadrant (quad_right, &(b->right)); + + + /* if there is at least one period in b, then a = [-1, 1] */ + mpz_sub (z, quad_right, quad_left); + if (mpz_cmp_ui (z, 4) >= 0) { + mpfr_set_si (&(a->left), -1, MPFI_RNDD); + mpfr_set_si (&(a->right), 1, MPFI_RNDU); + inexact = 0; + } + else { + /* there is less than one period in b */ + /* let us discuss according to the position (quadrant) of the endpoints of b */ + + /* 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_add (z, quad_left, quad_right); + /* z = quad_right + quad_left */ + + 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, quad_right, 4); + qr_mod4 = mpz_get_ui (zmod4); + + /* quad_left gives the quadrant where the left endpoint of b is */ + /* quad_left = floor (2 b->left / pi) mod 4 */ + mpz_mod_ui (zmod4, quad_left, 4); + ql_mod4 = mpz_get_ui (zmod4); + + + switch (qr_mod4) { + case 0: + switch (ql_mod4) { + case 0: + case 3: + inexact_left = mpfr_sin (&(a->left), &(b->left), MPFI_RNDD); + inexact_right = mpfr_sin (&(a->right), &(b->right), MPFI_RNDU); + break; + case 1: + mpz_add_ui (z, z, 1); + if (mpfi_cmp_sym_pi (z, &(b->left), &(b->right), prec) >= 0) + inexact_right = mpfr_sin (&(a->right), &(b->left), MPFI_RNDU); + else + inexact_right = mpfr_sin (&(a->right), &(b->right), MPFI_RNDU); + inexact_left = mpfr_set_si (&(a->left), -1, MPFI_RNDD); + break; + case 2: + inexact_left = mpfr_set_si (&(a->left), -1, MPFI_RNDD); + inexact_right = mpfr_sin (&(a->right), &(b->right), MPFI_RNDU); + break; + } + break; + case 1: + switch (ql_mod4) { + case 0: + mpz_add_ui (z, z, 1); + if (mpfi_cmp_sym_pi (z, &(b->right), &(b->left), prec) >= 0) + inexact_left = mpfr_sin (&(a->left), &(b->left), MPFI_RNDD); + else + inexact_left = mpfr_sin (&(a->left), &(b->right), MPFI_RNDD); + inexact_right = mpfr_set_si (&(a->right), 1, MPFI_RNDU); + break; + case 1: + mpfr_init2 (tmp, mpfr_get_prec (&(a->left))); + inexact_left = mpfr_sin (tmp, &(b->right), MPFI_RNDD); + inexact_right = mpfr_sin (&(a->right), &(b->left), MPFI_RNDU); + mpfr_set (&(a->left), tmp, MPFI_RNDD); /* exact */ + mpfr_clear (tmp); + break; + case 2: + inexact_left = mpfr_set_si (&(a->left), -1, MPFI_RNDD); + inexact_right = mpfr_set_si (&(a->right), 1, MPFI_RNDU); + break; + case 3: + inexact_left = mpfr_sin (&(a->left), &(b->left), MPFI_RNDD); + inexact_right = mpfr_set_si (&(a->right), 1, MPFI_RNDU); + break; + } + break; + case 2: + switch (ql_mod4) { + case 0: + inexact_left = mpfr_sin (&(a->left), &(b->right), MPFI_RNDD); + inexact_right = mpfr_set_si (&(a->right), 1, MPFI_RNDU); + break; + case 1: + case 2: + mpfr_init2 (tmp, mpfr_get_prec (&(a->left))); + inexact_left = mpfr_sin (tmp, &(b->right), MPFI_RNDD); + inexact_right = mpfr_sin (&(a->right), &(b->left), MPFI_RNDU); + mpfr_set (&(a->left), tmp, MPFI_RNDD); /* exact */ + mpfr_clear (tmp); + break; + case 3: + mpz_add_ui (z, z, 1); + if (mpfi_cmp_sym_pi (z, &(b->left), &(b->right), prec) >= 0) + inexact_left = mpfr_sin (&(a->left), &(b->left), MPFI_RNDD); + else + inexact_left = mpfr_sin (&(a->left), &(b->right), MPFI_RNDD); + inexact_right = mpfr_set_si (&(a->right), 1, MPFI_RNDU); + break; + } + break; + case 3: + switch (ql_mod4) { + case 0: + inexact_left = mpfr_set_si (&(a->left), -1, MPFI_RNDD); + inexact_right = mpfr_set_si (&(a->right), 1, MPFI_RNDU); + break; + case 1: + inexact_right = mpfr_sin (&(a->right), &(b->left), MPFI_RNDU); + inexact_left = mpfr_set_si (&(a->left), -1, MPFI_RNDD); + break; + case 2: + mpz_add_ui (z, z, 1); + if (mpfi_cmp_sym_pi (z, &(b->right), &(b->left), prec) >= 0) + inexact_right = mpfr_sin (&(a->right), &(b->left), MPFI_RNDU); + else + inexact_right = mpfr_sin (&(a->right), &(b->right), MPFI_RNDU); + inexact_left = mpfr_set_si (&(a->left), -1, MPFI_RNDD); + break; + case 3: + inexact_left = mpfr_sin (&(a->left), &(b->left), MPFI_RNDD); + inexact_right = mpfr_sin (&(a->right), &(b->right), MPFI_RNDU); + break; + } + break; + } + + if (inexact_left) inexact = 1; + if (inexact_right) inexact += 2; + + mpz_clear (zmod4); + } + + mpz_clear (quad_left); + mpz_clear (quad_right); + mpz_clear (z); + + return inexact; +} |