Optimized acosh for 64-bit platforms

ChangeLog

@@ -1,5 +1,7 @@
 2012-01-11  Ulrich Drepper  <drepper@gmail.com>
 
+	* sysdeps/ieee754/dbl-64/wordsize-64/e_acosh.c: New file.
+
 	* sysdeps/ieee754/dbl-64/s_scalbln.c: Add branch prediction.
 	* sysdeps/ieee754/flt-32/s_scalblnf.c: Likewise.
 	* sysdeps/ieee754/ldbl-96/s_scalblnl.c: Likewise.

sysdeps/ieee754/dbl-64/wordsize-64/e_acosh.c

@@ -0,0 +1,67 @@
+/* Optimized for 64-bit by Ulrich Drepper <drepper@gmail.com>, 2012 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+/* __ieee754_acosh(x)
+ * Method :
+ *	Based on
+ *		acosh(x) = log [ x + sqrt(x*x-1) ]
+ *	we have
+ *		acosh(x) := log(x)+ln2,	if x is large; else
+ *		acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
+ *		acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
+ *
+ * Special cases:
+ *	acosh(x) is NaN with signal if x<1.
+ *	acosh(NaN) is NaN without signal.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+static const double
+one	= 1.0,
+ln2	= 6.93147180559945286227e-01;  /* 0x3FE62E42, 0xFEFA39EF */
+
+double
+__ieee754_acosh (double x)
+{
+  int64_t hx;
+  EXTRACT_WORDS64 (hx, x);
+
+  if (hx > INT64_C (0x4000000000000000))
+    {
+      if (__builtin_expect (hx >= INT64_C (0x41b0000000000000), 0))
+	{
+	  /* x > 2**28 */
+	  if (hx >= INT64_C (0x7ff0000000000000))
+	    /* x is inf of NaN */
+	    return x + x;
+	  else
+	    return __ieee754_log (x) + ln2;/* acosh(huge)=log(2x) */
+	}
+
+      /* 2**28 > x > 2 */
+      double t = x * x;
+      return __ieee754_log (2.0 * x - one / (x + __ieee754_sqrt (t - one)));
+    }
+  else if (__builtin_expect (hx > INT64_C (0x3ff0000000000000), 1))
+    {
+      /* 1<x<2 */
+      double t = x - one;
+      return __log1p (t + __ieee754_sqrt (2.0 * t + t * t));
+    }
+  else if (__builtin_expect (hx == INT64_C (0x3ff0000000000000), 1))
+    return 0.0;				/* acosh(1) = 0 */
+  else					/* x < 1 */
+    return (x - x) / (x - x);
+}
+strong_alias (__ieee754_acosh, __acosh_finite)