Fix casinh, casin inaccuracy from cancellation (bug 14994).

1 files changed, 10 insertions, 6 deletions

diff --git a/math/s_casinh.c b/math/s_casinh.c
index 8c4aa19..acdf1a1 100644
--- a/math/s_casinh.c
+++ b/math/s_casinh.c
@@ -62,20 +62,24 @@ __casinh (__complex__ double x)
     }
   else
     {
+      double rx, ix;
       __complex__ double y;
 
-      __real__ y = (__real__ x - __imag__ x) * (__real__ x + __imag__ x) + 1.0;
-      __imag__ y = 2.0 * __real__ x * __imag__ x;
+      /* Avoid cancellation by reducing to the first quadrant.  */
+      rx = fabs (__real__ x);
+      ix = fabs (__imag__ x);
+
+      __real__ y = (rx - ix) * (rx + ix) + 1.0;
+      __imag__ y = 2.0 * rx * ix;
 
       y = __csqrt (y);
 
-      __real__ y += __real__ x;
-      __imag__ y += __imag__ x;
+      __real__ y += rx;
+      __imag__ y += ix;
 
       res = __clog (y);
 
-      /* Ensure zeros have correct sign and results are correct if
-	 very close to branch cuts.  */
+      /* Give results the correct sign for the original argument.  */
       __real__ res = __copysign (__real__ res, __real__ x);
       __imag__ res = __copysign (__imag__ res, __imag__ x);
     }