1 files changed, 61 insertions, 2 deletions
diff --git a/math/k_casinhl.c b/math/k_casinhl.c
index 110ae33dee..8e5bbd4385 100644
--- a/math/k_casinhl.c
+++ b/math/k_casinhl.c
@@ -84,10 +84,69 @@ __kernel_casinhl (__complex__ long double x, int adj)
       else
 	__imag__ res = __ieee754_atan2l (s, rx);
     }
+  else if (ix > 1.0L && ix < 1.5L && rx < 0.5L)
+    {
+      if (rx < LDBL_EPSILON * LDBL_EPSILON)
+	{
+	  long double ix2m1 = (ix + 1.0L) * (ix - 1.0L);
+	  long double s = __ieee754_sqrtl (ix2m1);
+
+	  __real__ res = __log1pl (2.0L * (ix2m1 + ix * s)) / 2.0L;
+	  if (adj)
+	    __imag__ res = __ieee754_atan2l (rx, __copysignl (s, __imag__ x));
+	  else
+	    __imag__ res = __ieee754_atan2l (s, rx);
+	}
+      else
+	{
+	  long double ix2m1 = (ix + 1.0L) * (ix - 1.0L);
+	  long double rx2 = rx * rx;
+	  long double f = rx2 * (2.0L + rx2 + 2.0L * ix * ix);
+	  long double d = __ieee754_sqrtl (ix2m1 * ix2m1 + f);
+	  long double dp = d + ix2m1;
+	  long double dm = f / dp;
+	  long double r1 = __ieee754_sqrtl ((dm + rx2) / 2.0L);
+	  long double r2 = rx * ix / r1;
+
+	  __real__ res
+	    = __log1pl (rx2 + dp + 2.0L * (rx * r1 + ix * r2)) / 2.0L;
+	  if (adj)
+	    __imag__ res = __ieee754_atan2l (rx + r1, __copysignl (ix + r2,
+								   __imag__ x));
+	  else
+	    __imag__ res = __ieee754_atan2l (ix + r2, rx + r1);
+	}
+    }
+  else if (ix == 1.0L && rx < 0.5L)
+    {
+      if (rx < LDBL_EPSILON / 8.0L)
+	{
+	  __real__ res = __log1pl (2.0L * (rx + __ieee754_sqrtl (rx))) / 2.0L;
+	  if (adj)
+	    __imag__ res = __ieee754_atan2l (__ieee754_sqrtl (rx),
+					     __copysignl (1.0L, __imag__ x));
+	  else
+	    __imag__ res = __ieee754_atan2l (1.0L, __ieee754_sqrtl (rx));
+	}
+      else
+	{
+	  long double d = rx * __ieee754_sqrtl (4.0L + rx * rx);
+	  long double s1 = __ieee754_sqrtl ((d + rx * rx) / 2.0L);
+	  long double s2 = __ieee754_sqrtl ((d - rx * rx) / 2.0L);
+
+	  __real__ res = __log1pl (rx * rx + d + 2.0L * (rx * s1 + s2)) / 2.0L;
+	  if (adj)
+	    __imag__ res = __ieee754_atan2l (rx + s1,
+					     __copysignl (1.0L + s2,
+							  __imag__ x));
+	  else
+	    __imag__ res = __ieee754_atan2l (1.0L + s2, rx + s1);
+	}
+    }
   else
     {
-      __real__ y = (rx - ix) * (rx + ix) + 1.0;
-      __imag__ y = 2.0 * rx * ix;
+      __real__ y = (rx - ix) * (rx + ix) + 1.0L;
+      __imag__ y = 2.0L * rx * ix;
 
       y = __csqrtl (y);