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/* 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;
mp_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;
}
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