/* mpc_sin -- sine of a complex number.
-Copyright (C) 2010, 2011 INRIA
+Copyright (C) 2007, 2009 Paul Zimmermann, Philippe Th\'eveny
-This file is part of GNU MPC.
+This file is part of the MPC Library.
-GNU MPC 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 3 of the License, or (at your
+The MPC 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.
-GNU MPC 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.
+The MPC 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 this program. If not, see http://www.gnu.org/licenses/ .
-*/
+along with the MPC Library; see the file COPYING.LIB. If not, write to
+the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+MA 02111-1307, USA. */
#include "mpc-impl.h"
int
mpc_sin (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
{
- return MPC_INEX1 (mpc_sin_cos (rop, NULL, op, rnd, 0));
+ mpfr_t x, y, z;
+ mp_prec_t prec;
+ int ok = 0;
+ int inex_re, inex_im;
+
+ /* special values */
+ if (!mpfr_number_p (MPC_RE (op)) || !mpfr_number_p (MPC_IM (op)))
+ {
+ if (mpfr_nan_p (MPC_RE (op)) || mpfr_nan_p (MPC_IM (op)))
+ {
+ mpc_set (rop, op, rnd);
+
+ if (mpfr_nan_p (MPC_IM (op)))
+ {
+ /* sin(x +i*NaN) = NaN +i*NaN, except for x=0 */
+ /* sin(-0 +i*NaN) = -0 +i*NaN */
+ /* sin(+0 +i*NaN) = +0 +i*NaN */
+ if (!mpfr_zero_p (MPC_RE (op)))
+ mpfr_set_nan (MPC_RE (rop));
+ else if (!mpfr_inf_p (MPC_IM (op))
+ && !mpfr_zero_p (MPC_IM (op)))
+ /* sin(NaN -i*Inf) = NaN -i*Inf */
+ /* sin(NaN -i*0) = NaN -i*0 */
+ /* sin(NaN +i*0) = NaN +i*0 */
+ /* sin(NaN +i*Inf) = NaN +i*Inf */
+ /* sin(NaN +i*y) = NaN +i*NaN, when 0<|y|<Inf */
+ mpfr_set_nan (MPC_IM (rop));
+ }
+ }
+ else if (mpfr_inf_p (MPC_RE (op)))
+ {
+ mpfr_set_nan (MPC_RE (rop));
+
+ if (!mpfr_inf_p (MPC_IM (op)) && !mpfr_zero_p (MPC_IM (op)))
+ /* sin(+/-Inf -i*Inf) = NaN -i*Inf */
+ /* sin(+/-Inf +i*Inf) = NaN +i*Inf */
+ /* sin(+/-Inf +i*y) = NaN +i*NaN, when 0<|y|<Inf */
+ mpfr_set_nan (MPC_IM (rop));
+ else
+ /* sin(+/-Inf -i*0) = NaN -i*0 */
+ /* sin(+/-Inf +i*0) = NaN +i*0 */
+ mpfr_set (MPC_IM (rop), MPC_IM (op), MPC_RND_IM (rnd));
+ }
+ else if (mpfr_zero_p (MPC_RE (op)))
+ /* sin(-0 -i*Inf) = -0 -i*Inf */
+ /* sin(+0 -i*Inf) = +0 -i*Inf */
+ /* sin(-0 +i*Inf) = -0 +i*Inf */
+ /* sin(+0 +i*Inf) = +0 +i*Inf */
+ {
+ mpc_set (rop, op, rnd);
+ }
+ else
+ /* sin(x -i*Inf) = +Inf*(sin(x) -i*cos(x)) */
+ /* sin(x +i*Inf) = +Inf*(sin(x) +i*cos(x)) */
+ {
+ mpfr_init2 (x, 2);
+ mpfr_init2 (y, 2);
+ mpfr_sin_cos (x, y, MPC_RE (op), GMP_RNDZ);
+ mpfr_set_inf (MPC_RE (rop), MPFR_SIGN (x));
+ mpfr_set_inf (MPC_IM (rop), MPFR_SIGN (y)*MPFR_SIGN (MPC_IM (op)));
+ mpfr_clear (y);
+ mpfr_clear(x);
+ }
+
+ return MPC_INEX (0, 0); /* exact in all cases*/
+ }
+
+ /* special case when the input is real: */
+ /* sin(x -0*i) = sin(x) -0*i*cos(x) */
+ /* sin(x +0*i) = sin(x) +0*i*cos(x) */
+ if (mpfr_cmp_ui (MPC_IM(op), 0) == 0)
+ {
+ mpfr_init2 (x, 2);
+ mpfr_cos (x, MPC_RE (op), MPC_RND_RE (rnd));
+ inex_re = mpfr_sin (MPC_RE (rop), MPC_RE (op), MPC_RND_RE (rnd));
+ mpfr_mul (MPC_IM(rop), MPC_IM(op), x, MPC_RND_IM(rnd));
+ mpfr_clear (x);
+
+ return MPC_INEX (inex_re, 0);
+ }
+
+ /* special case when the input is imaginary:
+ sin(+/-O +i*y) = +/-0 +i*sinh(y) */
+ if (mpfr_cmp_ui (MPC_RE(op), 0) == 0)
+ {
+ mpfr_set (MPC_RE(rop), MPC_RE(op), MPC_RND_RE(rnd));
+ inex_im = mpfr_sinh (MPC_IM(rop), MPC_IM(op), MPC_RND_IM(rnd));
+
+ return MPC_INEX (0, inex_im);
+ }
+
+ /* let op = a + i*b, then sin(op) = sin(a)*cosh(b) + i*cos(a)*sinh(b).
+
+ We use the following algorithm (same for the imaginary part),
+ with rounding to nearest for all operations, and working precision w:
+
+ (1) x = o(sin(a))
+ (2) y = o(cosh(b))
+ (3) r = o(x*y)
+ then the error on r is at most 4 ulps, since we can write
+ r = sin(a)*cosh(b)*(1+t)^3 with |t| <= 2^(-w),
+ thus for w >= 2, r = sin(a)*cosh(b)*(1+4*t) with |t| <= 2^(-w),
+ thus the relative error is bounded by 4*2^(-w) <= 4*ulp(r).
+ */
+
+ prec = MPC_MAX_PREC(rop);
+
+ mpfr_init2 (x, 2);
+ mpfr_init2 (y, 2);
+ mpfr_init2 (z, 2);
+
+ do
+ {
+ prec += mpc_ceil_log2 (prec) + 5;
+
+ mpfr_set_prec (x, prec);
+ mpfr_set_prec (y, prec);
+ mpfr_set_prec (z, prec);
+
+ mpfr_sin_cos (x, y, MPC_RE(op), GMP_RNDN);
+ mpfr_cosh (z, MPC_IM(op), GMP_RNDN);
+ mpfr_mul (x, x, z, GMP_RNDN);
+ ok = mpfr_can_round (x, prec - 2, GMP_RNDN, GMP_RNDZ,
+ MPFR_PREC(MPC_RE(rop)) + (MPC_RND_RE(rnd) == GMP_RNDN));
+ if (ok) /* compute imaginary part */
+ {
+ mpfr_sinh (z, MPC_IM(op), GMP_RNDN);
+ mpfr_mul (y, y, z, GMP_RNDN);
+ ok = mpfr_can_round (y, prec - 2, GMP_RNDN, GMP_RNDZ,
+ MPFR_PREC(MPC_IM(rop)) + (MPC_RND_IM(rnd) == GMP_RNDN));
+ }
+ }
+ while (ok == 0);
+
+ inex_re = mpfr_set (MPC_RE(rop), x, MPC_RND_RE(rnd));
+ inex_im = mpfr_set (MPC_IM(rop), y, MPC_RND_IM(rnd));
+
+ mpfr_clear (x);
+ mpfr_clear (y);
+ mpfr_clear (z);
+
+ return MPC_INEX (inex_re, inex_im);
}
projects / platform / upstream / mpc.git / blobdiff