add directory gnu

gnu/glibc/glibc-1.03/math/bsd/common_source/sinh.c

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+/*
+ * Copyright (c) 1985 Regents of the University of California.
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms are permitted provided
+ * that: (1) source distributions retain this entire copyright notice and
+ * comment, and (2) distributions including binaries display the following
+ * acknowledgement:  ``This product includes software developed by the
+ * University of California, Berkeley and its contributors'' in the
+ * documentation or other materials provided with the distribution and in
+ * all advertising materials mentioning features or use of this software.
+ * Neither the name of the University nor the names of its contributors may
+ * be used to endorse or promote products derived from this software without
+ * specific prior written permission.
+ * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR IMPLIED
+ * WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED WARRANTIES OF
+ * MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
+ */
+
+#ifndef lint
+static char sccsid[] = "@(#)sinh.c	5.6 (Berkeley) 10/9/90";
+#endif /* not lint */
+
+/* SINH(X)
+ * RETURN THE HYPERBOLIC SINE OF X
+ * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
+ * CODED IN C BY K.C. NG, 1/8/85; 
+ * REVISED BY K.C. NG on 2/8/85, 3/7/85, 3/24/85, 4/16/85.
+ *
+ * Required system supported functions :
+ *	copysign(x,y)
+ *	scalb(x,N)
+ *
+ * Required kernel functions:
+ *	expm1(x)	...return exp(x)-1
+ *
+ * Method :
+ *	1. reduce x to non-negative by sinh(-x) = - sinh(x).
+ *	2. 
+ *
+ *	                                      expm1(x) + expm1(x)/(expm1(x)+1)
+ *	    0 <= x <= lnovfl     : sinh(x) := --------------------------------
+ *			       		                      2
+ *     lnovfl <= x <= lnovfl+ln2 : sinh(x) := expm1(x)/2 (avoid overflow)
+ * lnovfl+ln2 <  x <  INF        :  overflow to INF
+ *	
+ *
+ * Special cases:
+ *	sinh(x) is x if x is +INF, -INF, or NaN.
+ *	only sinh(0)=0 is exact for finite argument.
+ *
+ * Accuracy:
+ *	sinh(x) returns the exact hyperbolic sine of x nearly rounded. In
+ *	a test run with 1,024,000 random arguments on a VAX, the maximum
+ *	observed error was 1.93 ulps (units in the last place).
+ *
+ * Constants:
+ * The hexadecimal values are the intended ones for the following constants.
+ * The decimal values may be used, provided that the compiler will convert
+ * from decimal to binary accurately enough to produce the hexadecimal values
+ * shown.
+ */
+
+#include "mathimpl.h"
+
+vc(mln2hi, 8.8029691931113054792E1   ,0f33,43b0,2bdb,c7e2,   7, .B00F33C7E22BDB)
+vc(mln2lo,-4.9650192275318476525E-16 ,1b60,a70f,582a,279e, -50,-.8F1B60279E582A)
+vc(lnovfl, 8.8029691931113053016E1   ,0f33,43b0,2bda,c7e2,   7, .B00F33C7E22BDA)
+
+ic(mln2hi, 7.0978271289338397310E2,    10, 1.62E42FEFA39EF)
+ic(mln2lo, 2.3747039373786107478E-14, -45, 1.ABC9E3B39803F)
+ic(lnovfl, 7.0978271289338397310E2,     9, 1.62E42FEFA39EF)
+
+#ifdef vccast
+#define	mln2hi	vccast(mln2hi)
+#define	mln2lo	vccast(mln2lo)
+#define	lnovfl	vccast(lnovfl)
+#endif
+
+#if defined(vax)||defined(tahoe)
+static max = 126                      ;
+#else	/* defined(vax)||defined(tahoe) */
+static max = 1023                     ;
+#endif	/* defined(vax)||defined(tahoe) */
+
+
+double sinh(x)
+double x;
+{
+	static const double  one=1.0, half=1.0/2.0 ;
+	double t, sign;
+#if !defined(vax)&&!defined(tahoe)
+	if(x!=x) return(x);	/* x is NaN */
+#endif	/* !defined(vax)&&!defined(tahoe) */
+	sign=copysign(one,x);
+	x=copysign(x,one);
+	if(x<lnovfl)
+	    {t=expm1(x); return(copysign((t+t/(one+t))*half,sign));}
+
+	else if(x <= lnovfl+0.7)
+		/* subtract x by ln(2^(max+1)) and return 2^max*exp(x) 
+	    		to avoid unnecessary overflow */
+	    return(copysign(scalb(one+expm1((x-mln2hi)-mln2lo),max),sign));
+
+	else  /* sinh(+-INF) = +-INF, sinh(+-big no.) overflow to +-INF */
+	    return( expm1(x)*sign );
+}