Use Kahan's formula in cacosh

3 files changed, 17 insertions, 0 deletions

diff --git a/math/s_cacosh.c b/math/s_cacosh.c
index df5ce69..cb01ca8 100644
--- a/math/s_cacosh.c
+++ b/math/s_cacosh.c
@@ -65,6 +65,11 @@ __cacosh (__complex__ double x)
       __real__ res = 0.0;
       __imag__ res = __copysign (M_PI_2, __imag__ x);
     }
+  /* The factor 16 is just a guess.  */
+  else if (16.0 * fabs (__imag__ x) < fabs (__real__ x))
+    /* Kahan's formula which avoid cancellation through subtraction in
+       some cases.  */
+    res = 2.0 * __clog (__csqrt ((x + 1.0) / 2.0) + __csqrt ((x - 1.0) / 2.0));
   else
     {
       __complex__ double y;
diff --git a/math/s_cacoshf.c b/math/s_cacoshf.c
index aa4696f..fe04692 100644
--- a/math/s_cacoshf.c
+++ b/math/s_cacoshf.c
@@ -65,6 +65,12 @@ __cacoshf (__complex__ float x)
       __real__ res = 0.0;
       __imag__ res = __copysignf (M_PI_2, __imag__ x);
     }
+  /* The factor 16 is just a guess.  */
+  else if (16.0 * fabsf (__imag__ x) < fabsf (__real__ x))
+    /* Kahan's formula which avoid cancellation through subtraction in
+       some cases.  */
+    res = 2.0 * __clogf (__csqrtf ((x + 1.0) / 2.0)
+			 + __csqrtf ((x - 1.0) / 2.0));
   else
     {
       __complex__ float y;
diff --git a/math/s_cacoshl.c b/math/s_cacoshl.c
index b90b196..84c2715 100644
--- a/math/s_cacoshl.c
+++ b/math/s_cacoshl.c
@@ -65,6 +65,12 @@ __cacoshl (__complex__ long double x)
       __real__ res = 0.0;
       __imag__ res = __copysignl (M_PI_2l, __imag__ x);
     }
+  /* The factor 16 is just a guess.  */
+  else if (16.0L * fabsl (__imag__ x) < fabsl (__real__ x))
+    /* Kahan's formula which avoid cancellation through subtraction in
+       some cases.  */
+    res = 2.0L * __clogl (__csqrtl ((x + 1.0L) / 2.0L)
+			  + __csqrtl ((x - 1.0L) / 2.0L));
   else
     {
       __complex__ long double y;