define 0^0 as (1,+0), since the sign of the imaginary part cannot be determined

git-svn-id: svn://scm.gforge.inria.fr/svn/mpc/trunk@1121 211d60ee-9f03-0410-a15a-8952a2c7a4e4

4 files changed, 17 insertions, 43 deletions

diff --git a/NEWS b/NEWS
index b018daa..f4ca2d7 100644
--- a/NEWS
+++ b/NEWS
@@ -1,9 +1,7 @@
 Changes in version 1.0:
   - First release as a GNU package
   - License change: LGPLv3+ for code, GFDLv1.3+ for documentation
-  - 0^0, which returned (NaN,NaN) previously, now returns (1,0),
-    with the sign of the imaginary part of the result being the opposite of
-    the sign of the imaginary part of the exponent
+  - 0^0, which returned (NaN,NaN) previously, now returns (1,+0),
   - Bug fixes:
     - div and norm now return a value indicating the effective rounding
       direction, as the other functions.
diff --git a/src/pow.c b/src/pow.c
index f6d54a8..3c4e8dc 100644
--- a/src/pow.c
+++ b/src/pow.c
@@ -1,6 +1,6 @@
 /* mpc_pow -- Raise a complex number to the power of another complex number.
 
-Copyright (C) 2009, 2010, 2011 INRIA
+Copyright (C) 2009, 2010, 2011, 2012 INRIA
 
 This file is part of GNU MPC.
 
@@ -491,34 +491,10 @@ mpc_pow (mpc_ptr z, mpc_srcptr x, mpc_srcptr y, mpc_rnd_t rnd)
     {
       if (x_real && mpfr_zero_p (mpc_realref(x)))
         {
-          /* we define 0^0 to be (1, -sign(Im(y))*0) since the real part is
+          /* we define 0^0 to be (1, +0) since the real part is
              coherent with MPFR where 0^0 gives 1, and the sign of the
-             imaginary part is the most frequent one obtained for random
-             tiny x and y, for example with the following Sage program:
-             D = dict()
-             for sa in [-1,1]:
-               for sb in [-1,1]:
-                 for sc in [-1,1]:
-                   for sd in [-1,1]:
-                     D[(sa,sb,sc,sd)] = [0,0]
-             def tiny():
-               return (random() - 0.5) * 1e-3
-             for n in range(10^4):
-               a = tiny()
-               b = tiny()
-               c = tiny()
-               d = tiny()
-               x = a+I*b
-               y = c+I*d
-               z = x^y
-               t = sign(a),sign(b),sign(c),sign(d)
-               if sign(z.imag()) == 1:
-                 D[t] = [D[t][0],D[t][1]+1]
-               else:
-                 D[t] = [D[t][0]+1,D[t][1]] */
-          mpfr_set_ui (mpc_realref(z), 1, GMP_RNDZ);
-          mpfr_set_zero (mpc_imagref(z),
-                         mpfr_signbit (mpc_imagref(y)) ? 1 : -1);
+             imaginary part cannot be determined                       */
+          mpc_set_ui_ui (z, 1, 0, MPC_RNDNN);
           return 0;
         }
       else /* x^0 = 1 +/- i*0 even for x=NaN see algorithms.tex for the
diff --git a/tests/pow.dat b/tests/pow.dat
index 6331496..9d14b5d 100644
--- a/tests/pow.dat
+++ b/tests/pow.dat
@@ -1,6 +1,6 @@
 # Data file for mpc_pow.
 #
-# Copyright (C) 2009 INRIA
+# Copyright (C) 2009, 2011, 2012 INRIA
 #
 # This file is part of GNU MPC.
 #
@@ -133,14 +133,14 @@
 0 0 53    0 53    0    53 -inf 53   -1  53 -inf 53   +1 N N 
 0 0 53    0 53    0    53 -inf 53   -1  53 -inf 53   -1 N N 
 
-0 0 53    1 53   -0    53   +0 53   +0  53   +0 53   +0 N N 
-0 0 53    1 53   -0    53   +0 53   +0  53   -0 53   +0 N N 
-0 0 53    1 53   -0    53   +0 53   -0  53   +0 53   +0 N N 
-0 0 53    1 53   -0    53   +0 53   -0  53   -0 53   +0 N N 
-0 0 53    1 53   -0    53   -0 53   +0  53   +0 53   +0 N N 
-0 0 53    1 53   -0    53   -0 53   +0  53   -0 53   +0 N N 
-0 0 53    1 53   -0    53   -0 53   -0  53   +0 53   +0 N N 
-0 0 53    1 53   -0    53   -0 53   -0  53   -0 53   +0 N N 
+0 0 53    1 53   +0    53   +0 53   +0  53   +0 53   +0 N N
+0 0 53    1 53   +0    53   +0 53   +0  53   -0 53   +0 N N
+0 0 53    1 53   +0    53   +0 53   -0  53   +0 53   +0 N N
+0 0 53    1 53   +0    53   +0 53   -0  53   -0 53   +0 N N
+0 0 53    1 53   +0    53   -0 53   +0  53   +0 53   +0 N N
+0 0 53    1 53   +0    53   -0 53   +0  53   -0 53   +0 N N
+0 0 53    1 53   +0    53   -0 53   -0  53   +0 53   +0 N N
+0 0 53    1 53   +0    53   -0 53   -0  53   -0 53   +0 N N
 0 0 53    1 53   +0    53   +0 53   +0  53   +0 53   -0 N N 
 0 0 53    1 53   +0    53   +0 53   +0  53   -0 53   -0 N N 
 0 0 53    1 53   +0    53   +0 53   -0  53   +0 53   -0 N N 
diff --git a/tests/pow_ui.dat b/tests/pow_ui.dat
index 9ecde18..2a82700 100644
--- a/tests/pow_ui.dat
+++ b/tests/pow_ui.dat
@@ -1,6 +1,6 @@
 # Data file for mpc_pow_ui.
 #
-# Copyright (C) 2010, 2011 INRIA
+# Copyright (C) 2010, 2011, 2012 INRIA
 #
 # This file is part of GNU MPC.
 #
@@ -34,8 +34,8 @@
 0 0 53 +inf 53  nan    53 -inf 53   +1  +1 N N
 0 0 53 +inf 53  nan    53 -inf 53   -1  +1 N N
 
-0 0 53   +1 53   -0    53   +0 53   +0  +0 N N
-0 0 53    0 53    0    53   +0 53   +0  +1 N N
+0 0 53   +1 53   +0    53   +0 53   +0  +0 N N
+0 0 53   +0 53   +0    53   +0 53   +0  +1 N N
 
 0 0 53   +1 53   +0    53   +0 53   +1  +0 N N
 0 0 53   +1 53   -0    53   +0 53   +1  +0 N D