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authorthevenyp <thevenyp@211d60ee-9f03-0410-a15a-8952a2c7a4e4>2008-04-09 10:47:19 +0000
committerthevenyp <thevenyp@211d60ee-9f03-0410-a15a-8952a2c7a4e4>2008-04-09 10:47:19 +0000
commit08edcef1c32fdc936f0b2a1e3d49317513145887 (patch)
tree7c77abc85f4e757e2bd3a02fe41557744a990565 /src/sin.c
parentafea999b442052808beb14b22f17252e67a2da8c (diff)
downloadmpc-08edcef1c32fdc936f0b2a1e3d49317513145887.tar.gz
File reorganisation into three new directories: src, tests and doc.
git-svn-id: svn://scm.gforge.inria.fr/svn/mpc/trunk@82 211d60ee-9f03-0410-a15a-8952a2c7a4e4
Diffstat (limited to 'src/sin.c')
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diff --git a/src/sin.c b/src/sin.c
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+/* mpc_sin -- sine of a complex number.
+
+Copyright (C) 2007 Paul Zimmermann
+
+This file is part of the MPC Library.
+
+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.
+
+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 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 "gmp.h"
+#include "mpfr.h"
+#include "mpc.h"
+#include "mpc-impl.h"
+
+void
+mpc_sin (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
+{
+ mpfr_t x, y, z;
+ mp_prec_t prec;
+ int ok = 0;
+
+ /* 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).
+ */
+
+ /* special case when the input is real: sin(x) = sin(x) */
+ if (mpfr_cmp_ui (MPC_IM(op), 0) == 0)
+ {
+ mpfr_sin (MPC_RE(rop), MPC_RE(op), MPC_RND_RE(rnd));
+ mpfr_set_ui (MPC_IM(rop), 0, MPC_RND_IM(rnd));
+ return;
+ }
+
+ /* special case when the input is imaginary: sin(I*y) = sinh(y)*I */
+ if (mpfr_cmp_ui (MPC_RE(op), 0) == 0)
+ {
+ mpfr_set_ui (MPC_RE(rop), 0, MPC_RND_RE(rnd));
+ mpfr_sinh (MPC_IM(rop), MPC_IM(op), MPC_RND_IM(rnd));
+ return;
+ }
+
+ 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, MPC_RND_RE(rnd),
+ MPFR_PREC(MPC_RE(rop)));
+ 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, MPC_RND_IM(rnd),
+ MPFR_PREC(MPC_IM(rop)));
+ }
+ }
+ while (ok == 0);
+
+ mpfr_set (MPC_RE(rop), x, MPC_RND_RE(rnd));
+ mpfr_set (MPC_IM(rop), y, MPC_RND_IM(rnd));
+
+ mpfr_clear (x);
+ mpfr_clear (y);
+ mpfr_clear (z);
+}