sinh.c
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上传日期:2007-01-17
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- /* sinh.c - math routine */
- /* Copyright 1992-1994 Wind River Systems, Inc. */
- /*
- modification history
- --------------------
- 01f,09dec94,rhp fix descriptions of hyperbolic fns.
- 01e,05feb93,jdi doc changes based on kdl review.
- 01d,02dec92,jdi doc tweaks.
- 01c,28oct92,jdi documentation cleanup.
- 01b,20sep92,smb documentation additions
- 01a,08jul92,smb documentation.
- */
- /*
- DESCRIPTION
- * Copyright (c) 1985 Regents of the University of California.
- * All rights reserved.
- *
- * Redistribution and use in source and binary forms are permitted
- * provided that the above copyright notice and this paragraph are
- * duplicated in all such forms and that any documentation,
- * advertising materials, and other materials related to such
- * distribution and use acknowledge that the software was developed
- * by the University of California, Berkeley. The name of the
- * University may not 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 MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE.
- *
- * All recipients should regard themselves as participants in an ongoing
- * research project and hence should feel obligated to report their
- * experiences (good or bad) with these elementary function codes, using
- * the sendbug(8) program, to the authors.
- *
- SEE ALSO: American National Standard X3.159-1989
- NOMANUAL
- */
- #include "vxWorks.h"
- #include "math.h"
- #if defined(vax)||defined(tahoe)
- #ifdef vax
- #define _0x(A,B) 0x/**/A/**/B
- #else /* vax */
- #define _0x(A,B) 0x/**/B/**/A
- #endif /* vax */
- /* static double */
- /* mln2hi = 8.8029691931113054792E1 , Hex 2^ 7 * .B00F33C7E22BDB */
- /* mln2lo = -4.9650192275318476525E-16 , Hex 2^-50 * -.8F1B60279E582A */
- /* lnovfl = 8.8029691931113053016E1 ; Hex 2^ 7 * .B00F33C7E22BDA */
- static long mln2hix[] = { _0x(0f33,43b0), _0x(2bdb,c7e2)};
- static long mln2lox[] = { _0x(1b60,a70f), _0x(582a,279e)};
- static long lnovflx[] = { _0x(0f33,43b0), _0x(2bda,c7e2)};
- #define mln2hi (*(double*)mln2hix)
- #define mln2lo (*(double*)mln2lox)
- #define lnovfl (*(double*)lnovflx)
- #else /* defined(vax)||defined(tahoe) */
- static double
- mln2hi = 7.0978271289338397310E2 , /*Hex 2^ 10 * 1.62E42FEFA39EF */
- mln2lo = 2.3747039373786107478E-14 , /*Hex 2^-45 * 1.ABC9E3B39803F */
- lnovfl = 7.0978271289338397310E2 ; /*Hex 2^ 9 * 1.62E42FEFA39EF */
- #endif /* defined(vax)||defined(tahoe) */
- #if defined(vax)||defined(tahoe)
- static max = 126 ;
- #else /* defined(vax)||defined(tahoe) */
- static max = 1023 ;
- #endif /* defined(vax)||defined(tahoe) */
- /*******************************************************************************
- *
- * sinh - compute a hyperbolic sine (ANSI)
- *
- * This routine returns the hyperbolic sine of <x> in
- * double precision (IEEE double, 53 bits).
- *
- * A range error occurs if <x> is too large.
- *
- * INTERNAL:
- * 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
- *
- * INCLUDE FILES: math.h
- *
- * RETURNS:
- * The double-precision hyperbolic sine of <x>.
- *
- * Special cases:
- * If <x> is +INF, -INF, or NaN, sinh() returns <x>.
- *
- * SEE ALSO: mathALib
- */
- double sinh
- (
- double x /* number whose hyperbolic sine is required */
- )
- {
- static double one=1.0, half=1.0/2.0 ;
- double expm1(), t, scalb(), copysign(), 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 );
- }