/* cabs.c - math routines *//* Copyright 1992 Wind River Systems, Inc. *//*modification history--------------------01d,15feb93,jdi  made hypot() NOMANUAL.01c,14oct92,jdi  made cabs() NOMANUAL.01b,13oct92,jdi  mangen fixes.01a,30jul92,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.*#ifndef lintstatic char sccsid[] = "@(#)cabs.c	5.3 (Berkeley) 6/30/88";#endif	* not lint *SEE ALSO: American National Standard X3.159-1989NOMANUAL*/#include "vxWorks.h"#include "math.h"#if defined(vax)||defined(tahoe)	/* VAX D format */#ifdef vax#define _0x(A,B)	0x/**/A/**/B#else	/* vax */#define _0x(A,B)	0x/**/B/**/A#endif	/* vax *//* static double *//* r2p1hi =  2.4142135623730950345E0     , Hex  2^  2   *  .9A827999FCEF32 *//* r2p1lo =  1.4349369327986523769E-17   , Hex  2^-55   *  .84597D89B3754B *//* sqrt2  =  1.4142135623730950622E0     ; Hex  2^  1   *  .B504F333F9DE65 */static long    r2p1hix[] = { _0x(8279,411a), _0x(ef32,99fc)};static long    r2p1lox[] = { _0x(597d,2484), _0x(754b,89b3)};static long     sqrt2x[] = { _0x(04f3,40b5), _0x(de65,33f9)};#define   r2p1hi    (*(double*)r2p1hix)#define   r2p1lo    (*(double*)r2p1lox)#define    sqrt2    (*(double*)sqrt2x)#else	/* defined(vax)||defined(tahoe) */static doubler2p1hi =  2.4142135623730949234E0     , /*Hex  2^1     *  1.3504F333F9DE6 */r2p1lo =  1.2537167179050217666E-16   , /*Hex  2^-53   *  1.21165F626CDD5 */sqrt2  =  1.4142135623730951455E0     ; /*Hex  2^  0   *  1.6A09E667F3BCD */#endif	/* defined(vax)||defined(tahoe) *//******************************************************************************** hypot - return the square root of X^2 + Y^2 where Z = X + iY** This routine returns the square root of X^2 + Y^2 where Z=X+iY* in double precision (VAX D format 56 bits, IEEE double 53 bits).** Required system support functions: copysign(), finite(), scalb(), sqrt().** Method:* 1. replace x by |x| and y by |y|, and swap x and*    y if y > x (hence x is never smaller than y).* 2. Hypot(x,y) is computed by:* .CS*   Case I, x/y > 2**			       y*	hypot = x + -----------------------------*				    2*		    sqrt ( 1 + [x/y]  )  +  x/y**   Case II, x/y <= 2*					   y*	hypot = x + --------------------------------------------------*						     2*						[x/y]   -  2*		   (sqrt(2)+1) + (x-y)/y + -----------------------------*							  2*					  sqrt ( 1 + [x/y]  )  + sqrt(2)* .CE** Special cases:* .CS*	hypot(x,y) is INF if x or y is +INF or -INF; else*	hypot(x,y) is NAN if x or y is NAN.* .CE** ACCURACY:* hypot() returns the sqrt(x^2+y^2) with error less than 1 ulps (units* in the last place).  See Kahan's "Interval Arithmetic Options in the* Proposed IEEE Floating Point Arithmetic Standard", Interval Mathematics* 1980, Edited by Karl L.E. Nickel, pp 99-128.  (A faster but less accurate* code follows in comments.)  In a test run with 500,000 random arguments* on a VAX, the maximum observed error was 0.959 ulps.** 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.** RETURNS: The square root of X^2 + Y^2 where Z = X + iY.** INTERNAL:* Coded in C by K.C. Ng, 11/28/84;* Revised by K.C. Ng, 7/12/85.*/double hypot(x,y)    double x, y;{	static double zero=0, one=1,		      small=1.0E-18;	/* fl(1+small)==1 */	static ibig=30;	/* fl(1+2**(2*ibig))==1 */	double copysign(),scalb(),logb(),sqrt(),t,r;	int finite(), exp;	if(finite(x))	    if(finite(y))	    {		x=copysign(x,one);		y=copysign(y,one);		if(y > x)		    { t=x; x=y; y=t; }		if(x == zero) return(zero);		if(y == zero) return(x);		exp= logb(x);		if(exp-(int)logb(y) > ibig )			/* raise inexact flag and return |x| */		   { one+small; return(x); }	    /* start computing sqrt(x^2 + y^2) */		r=x-y;		if(r>y) { 	/* x/y > 2 */		    r=x/y;		    r=r+sqrt(one+r*r); }		else {		/* 1 <= x/y <= 2 */		    r/=y; t=r*(r+2.0);		    r+=t/(sqrt2+sqrt(2.0+t));		    r+=r2p1lo; r+=r2p1hi; }		r=y/r;		return(x+r);	    }	    else if(y==y)   	   /* y is +-INF */		     return(copysign(y,one));	    else		     return(y);	   /* y is NaN and x is finite */	else if(x==x) 		   /* x is +-INF */	         return (copysign(x,one));	else if(finite(y))	         return(x);		   /* x is NaN, y is finite */#if !defined(vax)&&!defined(tahoe)	else if(y!=y) return(y);  /* x and y is NaN */#endif	/* !defined(vax)&&!defined(tahoe) */	else return(copysign(y,one));   /* y is INF */}/******************************************************************************* cabs - return the absolute value of the complex number Z = X + iY** This routine returns the absolute value of the complex number Z = X + iY,* in double precision (VAX D format 56 bits, IEEE double 53 bits).** Required kernel function:  hypot()** Method :* .CS*	cabs(z) = hypot(x,y) .* .CE** RETURNS: The absolute value of Z = X + iY.** INTERNAL:* Coded in C by K.C. Ng, 11/28/84.* Revised by K.C. Ng, 7/12/85.** NOMANUAL*/double cabs(z)    struct { double x, y;} z;{	return hypot(z.x,z.y);}doublez_abs(z)struct { double x,y;} *z;{	return hypot(z->x,z->y);}