tan: use sin_cos, gains about a third of the running time in ttan

git-svn-id: svn://scm.gforge.inria.fr/svn/mpc/trunk@862 211d60ee-9f03-0410-a15a-8952a2c7a4e4

3 files changed, 14 insertions, 22 deletions

diff --git a/NEWS b/NEWS
index 95fe789..21b98cc 100644
--- a/NEWS
+++ b/NEWS
@@ -4,8 +4,10 @@ Changes in version 0.8.3:
       between mpc type variables and C variables of type double _Complex
       or long double _Complex
     - mpc_sin_cos, computing simultaneously the sine and cosine
-  - Speed-up of mpc_pow_si through binary exponentiation, and of
-    mpc_pow_z when the exponent fits in a long
+  - Speed-ups:
+    - mpc_pow_si through binary exponentiation
+    - mpc_pow_z when the exponent fits in a long
+    - mpc_tan through the use of mpc_sin_cos
   - Bug fixes:
     - trigonometric functions: infinite loop due to overflow for large arguments
     - exp: close to infinite loop for argument close to 0
diff --git a/TODO b/TODO
index 84620bc..a6abca2 100644
--- a/TODO
+++ b/TODO
@@ -3,13 +3,7 @@ Bench:
   Scripts and web page comparing timings with different systems,
   as done for mpfr at http://www.mpfr.org/mpfr-2.4.0/timings.html
 
-Efficiency:
-- from Andreas Enge 16 September 2008:
-  Once mpc_sin_cos exists, improve mpc_tan to use it
-
 New functions to implement:
-- from Andreas Enge 16 September 2008:
-  mpc_sin_cos (needs mpfr_sinh_cosh)
 - from Mickael Gastineau <gastineau@imcce.fr> 14 Apr 2008:
   mpc_fma: d=a*b+c
 - from Andreas Enge and Philippe Théveny 17 July 2008
diff --git a/src/tan.c b/src/tan.c
index d730a06..5301128 100644
--- a/src/tan.c
+++ b/src/tan.c
@@ -1,6 +1,6 @@
 /* mpc_tan -- tangent of a complex number.
 
-Copyright (C) 2008, 2009, 2010 Philippe Th\'eveny, Andreas Enge, Paul Zimmermann
+Copyright (C) 2008, 2009, 2010, 2011 Philippe Th\'eveny, Andreas Enge, Paul Zimmermann
 
 This file is part of the MPC Library.
 
@@ -183,7 +183,6 @@ mpc_tan (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
   do
     {
       mpfr_exp_t k, exr, eyr, eyi, ezr;
-      int isinf = 0;
 
       ok = 0;
 
@@ -195,23 +194,19 @@ mpc_tan (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
       /* rounding away from zero: except in the cases x=0 or y=0 (processed
          above), sin x and cos y are never exact, so rounding away from 0 is
          rounding towards 0 and adding one ulp to the absolute value */
-      mpc_sin (x, op, MPC_RNDZZ);
-      isinf = mpfr_inf_p (MPC_RE (x)) || mpfr_inf_p (MPC_IM (x));
-      /* if the real or imaginary part of x is infinite, it means that Im(op)
-         was large, in which case the result is
-         sign(tan(Re(op)))*0 + sign(Im(op))*I,
-         where sign(tan(Re(op))) = sign(Re(x))*sign(Re(y)) */
+      mpc_sin_cos (x, y, op, MPC_RNDZZ, MPC_RNDZZ);
       MPFR_ADD_ONE_ULP (MPC_RE (x));
       MPFR_ADD_ONE_ULP (MPC_IM (x));
-      MPC_ASSERT (mpfr_zero_p (MPC_RE (x)) == 0);
-      exr = mpfr_get_exp (MPC_RE (x));
-      mpc_cos (y, op, MPC_RNDZZ);
-      isinf = isinf || mpfr_inf_p (MPC_RE (y)) || mpfr_inf_p (MPC_IM (y));
       MPFR_ADD_ONE_ULP (MPC_RE (y));
       MPFR_ADD_ONE_ULP (MPC_IM (y));
+      MPC_ASSERT (mpfr_zero_p (MPC_RE (x)) == 0);
 
-      if (isinf)
-        {
+      if (   mpfr_inf_p (MPC_RE (x)) || mpfr_inf_p (MPC_IM (x))
+          || mpfr_inf_p (MPC_RE (y)) || mpfr_inf_p (MPC_IM (y))) {
+         /* If the real or imaginary part of x is infinite, it means that
+            Im(op) was large, in which case the result is
+            sign(tan(Re(op)))*0 + sign(Im(op))*I,
+            where sign(tan(Re(op))) = sign(Re(x))*sign(Re(y)). */
           int inex_re, inex_im;
           mpfr_set_ui (MPC_RE (rop), 0, GMP_RNDN);
           if (mpfr_sgn (MPC_RE (x)) * mpfr_sgn (MPC_RE (y)) < 0)
@@ -235,6 +230,7 @@ mpc_tan (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
           goto end;
         }
 
+      exr = mpfr_get_exp (MPC_RE (x));
       eyr = mpfr_get_exp (MPC_RE (y));
       eyi = mpfr_get_exp (MPC_IM (y));