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authorRoland McGrath <roland@gnu.org>1995-02-18 01:27:10 +0000
committerRoland McGrath <roland@gnu.org>1995-02-18 01:27:10 +0000
commit28f540f45bbacd939bfd07f213bcad2bf730b1bf (patch)
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+/*
+ * Copyright (c) 1985, 1993
+ * The Regents of the University of California. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ * notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ * notice, this list of conditions and the following disclaimer in the
+ * documentation and/or other materials provided with the distribution.
+ * 3. All advertising materials mentioning features or use of this software
+ * must display the following acknowledgement:
+ * This product includes software developed by the University of
+ * California, Berkeley and its contributors.
+ * 4. 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 BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+#ifndef lint
+static char sccsid[] = "@(#)cosh.c 8.1 (Berkeley) 6/4/93";
+#endif /* not lint */
+
+/* COSH(X)
+ * RETURN THE HYPERBOLIC COSINE 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, 2/23/85, 3/7/85, 3/29/85, 4/16/85.
+ *
+ * Required system supported functions :
+ * copysign(x,y)
+ * scalb(x,N)
+ *
+ * Required kernel function:
+ * exp(x)
+ * exp__E(x,c) ...return exp(x+c)-1-x for |x|<0.3465
+ *
+ * Method :
+ * 1. Replace x by |x|.
+ * 2.
+ * [ exp(x) - 1 ]^2
+ * 0 <= x <= 0.3465 : cosh(x) := 1 + -------------------
+ * 2*exp(x)
+ *
+ * exp(x) + 1/exp(x)
+ * 0.3465 <= x <= 22 : cosh(x) := -------------------
+ * 2
+ * 22 <= x <= lnovfl : cosh(x) := exp(x)/2
+ * lnovfl <= x <= lnovfl+log(2)
+ * : cosh(x) := exp(x)/2 (avoid overflow)
+ * log(2)+lnovfl < x < INF: overflow to INF
+ *
+ * Note: .3465 is a number near one half of ln2.
+ *
+ * Special cases:
+ * cosh(x) is x if x is +INF, -INF, or NaN.
+ * only cosh(0)=1 is exact for finite x.
+ *
+ * Accuracy:
+ * cosh(x) returns the exact hyperbolic cosine of x nearly rounded.
+ * In a test run with 768,000 random arguments on a VAX, the maximum
+ * observed error was 1.23 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 cosh(x)
+double x;
+{
+ static const double half=1.0/2.0,
+ one=1.0, small=1.0E-18; /* fl(1+small)==1 */
+ double t;
+
+#if !defined(vax)&&!defined(tahoe)
+ if(x!=x) return(x); /* x is NaN */
+#endif /* !defined(vax)&&!defined(tahoe) */
+ if((x=copysign(x,one)) <= 22)
+ if(x<0.3465)
+ if(x<small) return(one+x);
+ else {t=x+__exp__E(x,0.0);x=t+t; return(one+t*t/(2.0+x)); }
+
+ else /* for x lies in [0.3465,22] */
+ { t=exp(x); return((t+one/t)*half); }
+
+ if( lnovfl <= x && x <= (lnovfl+0.7))
+ /* for x lies in [lnovfl, lnovfl+ln2], decrease x by ln(2^(max+1))
+ * and return 2^max*exp(x) to avoid unnecessary overflow
+ */
+ return(scalb(exp((x-mln2hi)-mln2lo), max));
+
+ else
+ return(exp(x)*half); /* for large x, cosh(x)=exp(x)/2 */
+}