144 lines
4.8 KiB
C
144 lines
4.8 KiB
C
/* cosh.c - hyperbolic routines */
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/* Copyright 1992-1993 Wind River Systems, Inc. */
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/*
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modification history
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--------------------
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01e,05feb93,jdi doc changes based on kdl review.
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01d,02dec92,jdi doc tweaks.
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01c,28oct92,jdi documentation cleanup.
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01b,20sep92,smb documentation additions
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01a,08jul92,smb documentation
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*/
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/*
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DESCRIPTION
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* Copyright (c) 1985 Regents of the University of California.
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms are permitted
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* provided that the above copyright notice and this paragraph are
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* duplicated in all such forms and that any documentation,
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* advertising materials, and other materials related to such
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* distribution and use acknowledge that the software was developed
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* by the University of California, Berkeley. The name of the
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* University may not be used to endorse or promote products derived
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* from this software without specific prior written permission.
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* THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
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* IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
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* WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE.
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*
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* All recipients should regard themselves as participants in an ongoing
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* research project and hence should feel obligated to report their
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* experiences (good or bad) with these elementary function codes, using
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* the sendbug(8) program, to the authors.
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*
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SEE ALSO: American National Standard X3.159-1989
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NOMANUAL
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*/
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#include "vxWorks.h"
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#include "math.h"
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#if defined(vax)||defined(tahoe)
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#ifdef vax
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#define _0x(A,B) 0x/**/A/**/B
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#else /* vax */
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#define _0x(A,B) 0x/**/B/**/A
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#endif /* vax */
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/* static double */
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/* mln2hi = 8.8029691931113054792E1 , Hex 2^ 7 * .B00F33C7E22BDB */
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/* mln2lo = -4.9650192275318476525E-16 , Hex 2^-50 * -.8F1B60279E582A */
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/* lnovfl = 8.8029691931113053016E1 ; Hex 2^ 7 * .B00F33C7E22BDA */
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static long mln2hix[] = { _0x(0f33,43b0), _0x(2bdb,c7e2)};
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static long mln2lox[] = { _0x(1b60,a70f), _0x(582a,279e)};
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static long lnovflx[] = { _0x(0f33,43b0), _0x(2bda,c7e2)};
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#define mln2hi (*(double*)mln2hix)
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#define mln2lo (*(double*)mln2lox)
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#define lnovfl (*(double*)lnovflx)
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#else /* defined(vax)||defined(tahoe) */
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static double
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mln2hi = 7.0978271289338397310E2 , /*Hex 2^ 10 * 1.62E42FEFA39EF */
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mln2lo = 2.3747039373786107478E-14 , /*Hex 2^-45 * 1.ABC9E3B39803F */
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lnovfl = 7.0978271289338397310E2 ; /*Hex 2^ 9 * 1.62E42FEFA39EF */
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#endif /* defined(vax)||defined(tahoe) */
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#if defined(vax)||defined(tahoe)
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static max = 126 ;
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#else /* defined(vax)||defined(tahoe) */
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static max = 1023 ;
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#endif /* defined(vax)||defined(tahoe) */
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/*******************************************************************************
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*
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* cosh - compute a hyperbolic cosine (ANSI)
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*
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* This routine returns the hyperbolic cosine of <x> in
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* double precision (IEEE double, 53 bits).
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*
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* A range error occurs if <x> is too large.
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*
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* INTERNAL:
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* Method:
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* (1) Replace <x> by |x|.
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* (2)
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* [ exp(x) - 1 ]^2
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* 0 <= x <= 0.3465 : cosh(x) := 1 + -------------------
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* 2*exp(x)
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*
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* exp(x) + 1/exp(x)
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* 0.3465 <= x <= 22 : cosh(x) := -------------------
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* 2
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* 22 <= x <= lnovfl : cosh(x) := exp(x)/2
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* lnovfl <= x <= lnovfl+log(2)
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* : cosh(x) := exp(x)/2 (avoid overflow)
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* log(2)+lnovfl < x < INF: overflow to INF
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*
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* Note: .3465 is a number near one half of ln2.
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*
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* INCLUDE FILES: math.h
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*
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* RETURNS:
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* The double-precision hyperbolic cosine of <x>.
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*
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* Special cases:
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* If <x> is +INF, -INF, or NaN, cosh() returns <x>.
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*
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* SEE ALSO: mathALib
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*
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* INTERNAL:
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* Coded in C by K.C. Ng, 1/8/85;
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* Revised by K.C. Ng on 2/8/85, 2/23/85, 3/7/85, 3/29/85, 4/16/85.
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*/
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double cosh
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(
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double x /* value to compute the hyperbolic cosine of */
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)
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{
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static double half=1.0/2.0,one=1.0, small=1.0E-18; /* fl(1+small)==1 */
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double scalb(),copysign(),exp(),exp__E(),t;
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#if !defined(vax)&&!defined(tahoe)
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if(x!=x) return(x); /* x is NaN */
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#endif /* !defined(vax)&&!defined(tahoe) */
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if((x=copysign(x,one)) <= 22)
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if(x<0.3465)
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if(x<small) return(one+x);
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else {t=x+exp__E(x,0.0);x=t+t; return(one+t*t/(2.0+x)); }
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else /* for x lies in [0.3465,22] */
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{ t=exp(x); return((t+one/t)*half); }
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if( lnovfl <= x && x <= (lnovfl+0.7))
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/* for x lies in [lnovfl, lnovfl+ln2], decrease x by ln(2^(max+1))
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* and return 2^max*exp(x) to avoid unnecessary overflow
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*/
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return(scalb(exp((x-mln2hi)-mln2lo), max));
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else
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return(exp(x)*half); /* for large x, cosh(x)=exp(x)/2 */
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}
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