first implementation of mpc_sin (not tested yet)

git-svn-id: svn://scm.gforge.inria.fr/svn/mpc/trunk@48 211d60ee-9f03-0410-a15a-8952a2c7a4e4

1 files changed, 91 insertions, 0 deletions

diff --git a/sin.c b/sin.c
new file mode 100644
index 0000000..cf33180
--- /dev/null
+++ b/sin.c
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+/* mpc_sin -- sine of a complex number.
+
+Copyright (C) 2007 Andreas Enge, 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 */
+  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;
+    }
+
+  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);
+}