[PATCH v2] improve cexp performance for imaginary inputs

[Julian Taylor <jtaylor dot debian at googlemail dot com>]

cexp(x) can avoid the exponential from the exp(x_r) * (cos(x_i) + i sin(x_i))
when the real part of the input is zero.
This is a common enough input to be worth optimizing, e.g. twiddle factors in
fast fourier transforms.

Even though the exp function has a fast path for the zero input case it
does still impose about 15% overhead on the computation of cexp on amd64.
For 10000 uniform imaginary inputs from -pi to pi performance improved
from 350 cycles to 300 cycles per call on an amd phenom 2X4.

In the case of real and imaginary input it just adds one branch to the
already existing 6 branches and sincos computation so it has no
measurable negative effect on amd64 and likely also most other cpus.
---
 math/s_cexp.c  | 6 +++++-
 math/s_cexpf.c | 6 +++++-
 math/s_cexpl.c | 6 +++++-
 3 files changed, 15 insertions(+), 3 deletions(-)

diff --git a/math/s_cexp.c b/math/s_cexp.c
index 9116e2b..2472708 100644
--- a/math/s_cexp.c
+++ b/math/s_cexp.c
@@ -70,7 +70,11 @@ __cexp (__complex__ double x)
 	    }
 	  else
 	    {
-	      double exp_val = __ieee754_exp (__real__ x);
+	      double exp_val = 1.;
+	      if (__real__ x != 0.)
+	        {
+	          exp_val= __ieee754_exp (__real__ x);
+	        }
 	      __real__ retval = exp_val * cosix;
 	      __imag__ retval = exp_val * sinix;
 	    }
diff --git a/math/s_cexpf.c b/math/s_cexpf.c
index fac1a17..84b7b56 100644
--- a/math/s_cexpf.c
+++ b/math/s_cexpf.c
@@ -70,7 +70,11 @@ __cexpf (__complex__ float x)
 	    }
 	  else
 	    {
-	      float exp_val = __ieee754_expf (__real__ x);
+	      float exp_val = 1.;
+	      if (__real__ x != 0.)
+	        {
+	          exp_val= __ieee754_expf (__real__ x);
+	        }
 	      __real__ retval = exp_val * cosix;
 	      __imag__ retval = exp_val * sinix;
 	    }
diff --git a/math/s_cexpl.c b/math/s_cexpl.c
index 9309b1f..0e9d515 100644
--- a/math/s_cexpl.c
+++ b/math/s_cexpl.c
@@ -70,7 +70,11 @@ __cexpl (__complex__ long double x)
 	    }
 	  else
 	    {
-	      long double exp_val = __ieee754_expl (__real__ x);
+	      long double exp_val = 1.;
+	      if (__real__ x != 0.)
+	        {
+	          exp_val= __ieee754_expl (__real__ x);
+	        }
 	      __real__ retval = exp_val * cosix;
 	      __imag__ retval = exp_val * sinix;
 	    }
-- 
2.1.0