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Diffstat (limited to 'sysdeps/generic/acosh.c')
| -rw-r--r-- | sysdeps/generic/acosh.c | 102 |
1 files changed, 102 insertions, 0 deletions
diff --git a/sysdeps/generic/acosh.c b/sysdeps/generic/acosh.c new file mode 100644 index 0000000000..bc16cc7b46 --- /dev/null +++ b/sysdeps/generic/acosh.c @@ -0,0 +1,102 @@ +/* + * 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[] = "@(#)acosh.c 8.1 (Berkeley) 6/4/93"; +#endif /* not lint */ + +/* ACOSH(X) + * RETURN THE INVERSE HYPERBOLIC COSINE OF X + * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS) + * CODED IN C BY K.C. NG, 2/16/85; + * REVISED BY K.C. NG on 3/6/85, 3/24/85, 4/16/85, 8/17/85. + * + * Required system supported functions : + * sqrt(x) + * + * Required kernel function: + * log1p(x) ...return log(1+x) + * + * Method : + * Based on + * acosh(x) = log [ x + sqrt(x*x-1) ] + * we have + * acosh(x) := log1p(x)+ln2, if (x > 1.0E20); else + * acosh(x) := log1p( sqrt(x-1) * (sqrt(x-1) + sqrt(x+1)) ) . + * These formulae avoid the over/underflow complication. + * + * Special cases: + * acosh(x) is NaN with signal if x<1. + * acosh(NaN) is NaN without signal. + * + * Accuracy: + * acosh(x) returns the exact inverse hyperbolic cosine of x nearly + * rounded. In a test run with 512,000 random arguments on a VAX, the + * maximum observed error was 3.30 ulps (units of the last place) at + * x=1.0070493753568216 . + * + * 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(ln2hi, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0, 0, .B17217F7D00000) +vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC) + +ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000) +ic(ln2lo, 1.9082149292705877000E-10,-33, 1.A39EF35793C76) + +#ifdef vccast +#define ln2hi vccast(ln2hi) +#define ln2lo vccast(ln2lo) +#endif + +double acosh(x) +double x; +{ + double t,big=1.E20; /* big+1==big */ + +#if !defined(vax)&&!defined(tahoe) + if(x!=x) return(x); /* x is NaN */ +#endif /* !defined(vax)&&!defined(tahoe) */ + + /* return log1p(x) + log(2) if x is large */ + if(x>big) {t=log1p(x)+ln2lo; return(t+ln2hi);} + + t=sqrt(x-1.0); + return(log1p(t*(t+sqrt(x+1.0)))); +} |