ansimath.c

VXWORKS源代码

* return value.  A domain error may occur if both arguments are zero.
*
* INTERNAL:
* (1) Reduce <y> to positive by:
* 
*     atan2(y,x)=-atan2(-y,x)
* 
* (2) Reduce <x> to positive by (if <x> and <y> are unexceptional):
* 
*     ARG (x+iy) = arctan(y/x)   	 ... if x > 0
*     ARG (x+iy) = pi - arctan[y/(-x)]   ... if x < 0
*
* (3) According to the integer k=4t+0.25 truncated , t=y/x, the argument
*     is further reduced to one of the following intervals and the
*     arc tangent of y/x is evaluated by the corresponding formula:
*
*     [0,7/16]	      atan(y/x) = t - t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
*     [7/16,11/16]    atan(y/x) = atan(1/2) + atan( (y-x/2)/(x+y/2) )
*     [11/16.19/16]   atan(y/x) = atan( 1 ) + atan( (y-x)/(x+y) )
*     [19/16,39/16]   atan(y/x) = atan(3/2) + atan( (y-1.5x)/(x+1.5y) )
*     [39/16,INF]     atan(y/x) = atan(INF) + atan( -x/y )
*
* INCLUDE FILES: math.h
*
* RETURNS:
* The double-precision arc tangent of <y>/<x>, in the range [-pi,pi] radians.
*
* Special cases:
*     Notations: atan2(y,x) == ARG (x+iy) == ARG(x,y).
* 
* .TS
* tab(|);
* l0 c0 l.
*     ARG(NAN, (anything))                      | is | NaN
*     ARG((anything), NaN)                      | is | NaN
*     ARG(+(anything but NaN), +-0)             | is | +-0
*     ARG(-(anything but NaN), +-0)             | is | +-PI
*     ARG(0, +-(anything but 0 and NaN))        | is | +-PI/2
*     ARG(+INF, +-(anything but INF and NaN))   | is | +-0
*     ARG(-INF, +-(anything but INF and NaN))   | is | +-PI
*     ARG(+INF, +-INF)                          | is | +-PI/4
*     ARG(-INF, +-INF)                          | is | +-3PI/4
*     ARG((anything but 0, NaN, and INF),+-INF) | is | +-PI/2
* .TE
*
* SEE ALSO: mathALib
*
* INTERNAL:
* Coded in C by K.C. Ng, 1/8/85;
* Revised by K.C. Ng on 2/7/85, 2/13/85, 3/7/85, 3/30/85, 6/29/85.
*/

double atan2
    (
    double  y,	/* numerator   */
    double  x	/* denominator */
    )

    {
	static double zero=0, one=1, small=1.0E-9, big=1.0E18;
	double copysign(),logb(),scalb(),t,z,signy,signx,hi,lo;
	int finite(), k,m;

#if !defined(vax)&&!defined(tahoe)
    /* if x or y is NAN */
	if(x!=x) return(x); if(y!=y) return(y);
#endif	/* !defined(vax)&&!defined(tahoe) */

    /* copy down the sign of y and x */
	signy = copysign(one,y) ;
	signx = copysign(one,x) ;

    /* if x is 1.0, goto begin */
	if(x==1) { y=copysign(y,one); t=y; if(finite(t)) goto begin;}

    /* when y = 0 */
	if(y==zero) return((signx==one)?y:copysign(PI,signy));

    /* when x = 0 */
	if(x==zero) return(copysign(PIo2,signy));

    /* when x is INF */
	if(!finite(x))
	    if(!finite(y))
		return(copysign((signx==one)?PIo4:3*PIo4,signy));
	    else
		return(copysign((signx==one)?zero:PI,signy));

    /* when y is INF */
	if(!finite(y)) return(copysign(PIo2,signy));

    /* compute y/x */
	x=copysign(x,one);
	y=copysign(y,one);
	if((m=(k=logb(y))-logb(x)) > 60) t=big+big;
	    else if(m < -80 ) t=y/x;
	    else { t = y/x ; y = scalb(y,-k); x=scalb(x,-k); }

    /* begin argument reduction */
begin:
	if (t < 2.4375) {

	/* truncate 4(t+1/16) to integer for branching */
	    k = 4 * (t+0.0625);
	    switch (k) {

	    /* t is in [0,7/16] */
	    case 0:
	    case 1:
		if (t < small)
		    { big + small ;  /* raise inexact flag */
		      return (copysign((signx>zero)?t:PI-t,signy)); }

		hi = zero;  lo = zero;  break;

	    /* t is in [7/16,11/16] */
	    case 2:
		hi = athfhi; lo = athflo;
		z = x+x;
		t = ( (y+y) - x ) / ( z +  y ); break;

	    /* t is in [11/16,19/16] */
	    case 3:
	    case 4:
		hi = PIo4; lo = zero;
		t = ( y - x ) / ( x + y ); break;

	    /* t is in [19/16,39/16] */
	    default:
		hi = at1fhi; lo = at1flo;
		z = y-x; y=y+y+y; t = x+x;
		t = ( (z+z)-x ) / ( t + y ); break;
	    }
	}
	/* end of if (t < 2.4375) */

	else
	{
	    hi = PIo2; lo = zero;

	    /* t is in [2.4375, big] */
	    if (t <= big)  t = - x / y;

	    /* t is in [big, INF] */
	    else
	      { big+small;	/* raise inexact flag */
		t = zero; }
	}
    /* end of argument reduction */

    /* compute atan(t) for t in [-.4375, .4375] */
	z = t*t;
#if defined(vax)||defined(tahoe)
	z = t*(z*(a1+z*(a2+z*(a3+z*(a4+z*(a5+z*(a6+z*(a7+z*(a8+
			z*(a9+z*(a10+z*(a11+z*a12))))))))))));
#else	/* defined(vax)||defined(tahoe) */
	z = t*(z*(a1+z*(a2+z*(a3+z*(a4+z*(a5+z*(a6+z*(a7+z*(a8+
			z*(a9+z*(a10+z*a11)))))))))));
#endif	/* defined(vax)||defined(tahoe) */
	z = lo - z; z += t; z += hi;

	return(copysign((signx>zero)?z:PI-z,signy));
    }
/* ceil.c - ceil math routine */

/* Copyright 1992-1993 Wind River Systems, Inc. */

/*
modification history
--------------------
01f,05feb93,jdi  doc changes based on kdl review.
01e,02dec92,jdi  doc tweaks.
01d,28oct92,jdi  documentation cleanup.
01c,20sep92,smb  documentation additions
01b,30jul92,kdl  changed _d_type() calls to fpTypeGet().
01a,08jul92,smb  documentation.
*/

/*
DESCRIPTION
SEE ALSO: American National Standard X3.159-1989
NOMANUAL
*/

#include "vxWorks.h"
#include "math.h"
#include "stddef.h"
#include "errno.h"
#include "private/mathP.h"


/*******************************************************************************
*
* ceil - compute the smallest integer greater than or equal to a specified value (ANSI)
*
* This routine returns the smallest integer greater than or equal to <v>,
* in double precision.
*
* INCLUDE FILES: math.h
*
* RETURNS: The smallest integral value greater than or equal to <v>, in
* double precision.
*
* SEE ALSO: mathALib
*/

double ceil
    (
    double v	/* value to find the ceiling of */
    )

    {
    double r;

    switch (fpTypeGet (v, &r))		/* get the type of v */
        {
    	case ZERO:	/* ZERO */
    	case INF:	/* INFINITY */
            return (0.0);

    	case NAN:	/* NOT A NUMBER */
            return (v);

    	case INTEGER:	/* INTEGER */
            return (v);

    	case REAL:	/* REAL */
            return (((v < 0.0) || (v == r)) ? r : r + 1.0);

	default:
	    return (0.0);		/* this should never happen */
        }
    }
/* cosh.c - hyperbolic routines */

/* Copyright 1992-1993 Wind River Systems, Inc. */

/*
modification history
--------------------
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) */

/*******************************************************************************
*
* cosh - compute a hyperbolic cosine (ANSI)
*
* This routine returns the hyperbolic cosine of <x> in
* double precision (IEEE double, 53 bits).
*
* A range error occurs if <x> is too large.
*
* INTERNAL:
* 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.
*
* INCLUDE FILES: math.h
*
* RETURNS:
* The double-precision hyperbolic cosine of <x>.
*
* Special cases:
*     If <x> is +INF, -INF, or NaN, cosh() returns <x>.
*
* SEE ALSO: mathALib
*
* INTERNAL:
* 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.
*/

double cosh
    (
    double x	/* value to compute the hyperbolic cosine of */
    )

    {
	static double half=1.0/2.0,one=1.0, small=1.0E-18; /* fl(1+small)==1 */
	double scalb(),copysign(),exp(),exp__E(),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 */
    }
/* exp.c - math routines */

/* Copyright 1992-1993 Wind River Systems, Inc. */

/*
modification history
--------------------
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)	/* 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 */
/* ln2hi  =  6.9314718055829871446E-1    , Hex  2^  0   *  .B17217F7D00000 */
/* ln2lo  =  1.6465949582897081279E-12   , Hex  2^-39   *  .E7BCD5E4F1D9CC */
/* lnhuge =  9.4961163736712506989E1     , Hex  2^  7   *  .BDEC1DA73E9010 */
/* lntiny = -9.5654310917272452386E1     , Hex  2^  7   * -.BF4F01D72E33AF */
/* invln2 =  1.4426950408889634148E0     ; Hex  2^  1   *  .B8AA3B295C17F1 */
/* p1     =  1.6666666666666602251E-1    , Hex  2^-2    *  .AAAAAAAAAAA9F1 */
/* p2     = -2.7777777777015591216E-3    , Hex  2^-8    * -.B60B60B5F5EC94 */
/* p3     =  6.6137563214379341918E-5    , Hex  2^-13   *  .8AB355792EF15F */
/* p4     = -1.6533902205465250480E-6    , Hex  2^-19   * -.DDEA0E2E935F84 */
/* p5     =  4.1381367970572387085E-8    , Hex  2^-24   *  .B1BB4B95F52683 */
static long     ln2hix[] = { _0x(7217,4031), _0x(0000,f7d0)};
static long     ln2lox[] = { _0x(bcd5,2ce7), _0x(d9cc,e4f1)};
static long    lnhugex[] = { _0x(ec1d,43bd), _0x(9010,a73e)};
static long    lntinyx[] = { _0x(4f01,c3bf), _0x(33af,d72e)};
static long    invln2x[] = { _0x(aa3b,40b8), _0x(17f1,295c)};
static long        p1x[] = { _0x(aaaa,3f2a), _0x(a9f1,aaaa)};