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authorThe Android Open Source Project <initial-contribution@android.com>2008-10-21 07:00:00 -0700
committerThe Android Open Source Project <initial-contribution@android.com>2008-10-21 07:00:00 -0700
commit8771baa10b2dc5bbedb08231d99c72cfd6abcb5b (patch)
tree87dbea36a0e5ed0f2f8e2a499b9c1014af6a38b5 /e_acosh.c
downloadfdlibm-8771baa10b2dc5bbedb08231d99c72cfd6abcb5b.tar.gz
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+
+/* @(#)e_acosh.c 1.3 95/01/18 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunSoft, 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 + ieee_sqrt(x*x-1) ]
+ * we have
+ * acosh(x) := ieee_log(x)+ln2, if x is large; else
+ * acosh(x) := ieee_log(2x-1/(ieee_sqrt(x*x-1)+x)) if x>2; else
+ * acosh(x) := ieee_log1p(t+ieee_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 "fdlibm.h"
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+one = 1.0,
+ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */
+
+#ifdef __STDC__
+ double __ieee754_acosh(double x)
+#else
+ double __ieee754_acosh(x)
+ double x;
+#endif
+{
+ double t;
+ int hx;
+ hx = __HI(x);
+ if(hx<0x3ff00000) { /* x < 1 */
+ return (x-x)/(x-x);
+ } else if(hx >=0x41b00000) { /* x > 2**28 */
+ if(hx >=0x7ff00000) { /* x is inf of NaN */
+ return x+x;
+ } else
+ return __ieee754_log(x)+ln2; /* acosh(huge)=ieee_log(2x) */
+ } else if(((hx-0x3ff00000)|__LO(x))==0) {
+ return 0.0; /* acosh(1) = 0 */
+ } else if (hx > 0x40000000) { /* 2**28 > x > 2 */
+ t=x*x;
+ return __ieee754_log(2.0*x-one/(x+ieee_sqrt(t-one)));
+ } else { /* 1<x<2 */
+ t = x-one;
+ return ieee_log1p(t+ieee_sqrt(2.0*t+t*t));
+ }
+}