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+/* acoshf.c
+ *
+ * Inverse hyperbolic cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, acoshf();
+ *
+ * y = acoshf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns inverse hyperbolic cosine of argument.
+ *
+ * If 1 <= x < 1.5, a polynomial approximation
+ *
+ * sqrt(z) * P(z)
+ *
+ * where z = x-1, is used. Otherwise,
+ *
+ * acosh(x) = log( x + sqrt( (x-1)(x+1) ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 1,3 100000 1.8e-7 3.9e-8
+ * IEEE 1,2000 100000 3.0e-8
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * acoshf domain |x| < 1 0.0
+ *
+ */
+
+/* acosh.c */
+
+/*
+Cephes Math Library Release 2.2: June, 1992
+Copyright 1984, 1987, 1988, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+/* Single precision inverse hyperbolic cosine
+ * test interval: [1.0, 1.5]
+ * trials: 10000
+ * peak relative error: 1.7e-7
+ * rms relative error: 5.0e-8
+ *
+ * Copyright (C) 1989 by Stephen L. Moshier. All rights reserved.
+ */
+#include <math.h>
+extern float LOGE2F;
+
+float sqrtf( float );
+float logf( float );
+
+float acoshf( float xx )
+{
+float x, z;
+
+x = xx;
+if( x < 1.0 )
+ {
+ mtherr( "acoshf", DOMAIN );
+ return(0.0);
+ }
+
+if( x > 1500.0 )
+ return( logf(x) + LOGE2F );
+
+z = x - 1.0;
+
+if( z < 0.5 )
+ {
+ z =
+ (((( 1.7596881071E-3 * z
+ - 7.5272886713E-3) * z
+ + 2.6454905019E-2) * z
+ - 1.1784741703E-1) * z
+ + 1.4142135263E0) * sqrtf( z );
+ }
+else
+ {
+ z = sqrtf( z*(x+1.0) );
+ z = logf(x + z);
+ }
+return( z );
+}