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Revision 1.11, Sun May 26 22:01:54 2002 UTC (12 years, 2 months ago) by wiz
Branch: MAIN
CVS Tags: yamt-pf42-baseX, yamt-pf42-base4, yamt-pf42-base3, yamt-pf42-base2, yamt-pf42-base, yamt-pf42, yamt-pagecache-tag8, yamt-pagecache-base9, yamt-pagecache-base8, yamt-pagecache-base7, yamt-pagecache-base6, yamt-pagecache-base5, yamt-pagecache-base4, yamt-pagecache-base3, yamt-pagecache-base2, yamt-pagecache-base, yamt-pagecache, wrstuden-revivesa-base-3, wrstuden-revivesa-base-2, wrstuden-revivesa-base-1, wrstuden-revivesa-base, wrstuden-revivesa, wrstuden-fixsa-newbase, wrstuden-fixsa-base-1, wrstuden-fixsa-base, wrstuden-fixsa, tls-maxphys-nbase, tls-maxphys-base, tls-maxphys, tls-earlyentropy-base, tls-earlyentropy, riastradh-xf86-video-intel-2-7-1-pre-2-21-15, riastradh-drm2-base3, riastradh-drm2-base2, riastradh-drm2-base1, riastradh-drm2-base, riastradh-drm2, netbsd-7-base, netbsd-7, netbsd-6-base, netbsd-6-1-RELEASE, netbsd-6-1-RC4, netbsd-6-1-RC3, netbsd-6-1-RC2, netbsd-6-1-RC1, netbsd-6-1-4-RELEASE, netbsd-6-1-3-RELEASE, netbsd-6-1-2-RELEASE, netbsd-6-1-1-RELEASE, netbsd-6-1, netbsd-6-0-RELEASE, netbsd-6-0-RC2, netbsd-6-0-RC1, netbsd-6-0-5-RELEASE, netbsd-6-0-4-RELEASE, netbsd-6-0-3-RELEASE, netbsd-6-0-2-RELEASE, netbsd-6-0-1-RELEASE, netbsd-6-0, netbsd-6, netbsd-5-base, netbsd-5-2-RELEASE, netbsd-5-2-RC1, netbsd-5-2-2-RELEASE, netbsd-5-2-1-RELEASE, netbsd-5-2, netbsd-5-1-RELEASE, netbsd-5-1-RC4, netbsd-5-1-RC3, netbsd-5-1-RC2, netbsd-5-1-RC1, netbsd-5-1-4-RELEASE, netbsd-5-1-3-RELEASE, netbsd-5-1-2-RELEASE, netbsd-5-1-1-RELEASE, netbsd-5-1, netbsd-5-0-RELEASE, netbsd-5-0-RC4, netbsd-5-0-RC3, netbsd-5-0-RC2, netbsd-5-0-RC1, netbsd-5-0-2-RELEASE, netbsd-5-0-1-RELEASE, netbsd-5-0, netbsd-5, netbsd-4-base, netbsd-4-0-RELEASE, netbsd-4-0-RC5, netbsd-4-0-RC4, netbsd-4-0-RC3, netbsd-4-0-RC2, netbsd-4-0-RC1, netbsd-4-0-1-RELEASE, netbsd-4-0, netbsd-4, netbsd-3-base, netbsd-3-1-RELEASE, netbsd-3-1-RC4, netbsd-3-1-RC3, netbsd-3-1-RC2, netbsd-3-1-RC1, netbsd-3-1-1-RELEASE, netbsd-3-1, netbsd-3-0-RELEASE, netbsd-3-0-RC6, netbsd-3-0-RC5, netbsd-3-0-RC4, netbsd-3-0-RC3, netbsd-3-0-RC2, netbsd-3-0-RC1, netbsd-3-0-3-RELEASE, netbsd-3-0-2-RELEASE, netbsd-3-0-1-RELEASE, netbsd-3-0, netbsd-3, netbsd-2-base, netbsd-2-1-RELEASE, netbsd-2-1-RC6, netbsd-2-1-RC5, netbsd-2-1-RC4, netbsd-2-1-RC3, netbsd-2-1-RC2, netbsd-2-1-RC1, netbsd-2-1, netbsd-2-0-base, netbsd-2-0-RELEASE, netbsd-2-0-RC5, netbsd-2-0-RC4, netbsd-2-0-RC3, netbsd-2-0-RC2, netbsd-2-0-RC1, netbsd-2-0-3-RELEASE, netbsd-2-0-2-RELEASE, netbsd-2-0-1-RELEASE, netbsd-2-0, netbsd-2, mjf-devfs2-base, mjf-devfs2, matt-premerge-20091211, matt-nb6-plus-nbase, matt-nb6-plus-base, matt-nb6-plus, matt-nb5-pq3-base, matt-nb5-pq3, matt-nb5-mips64-u2-k2-k4-k7-k8-k9, matt-nb5-mips64-u1-k1-k5, matt-nb5-mips64-premerge-20101231, matt-nb5-mips64-premerge-20091211, matt-nb5-mips64-k15, matt-nb5-mips64, matt-nb4-mips64-k7-u2a-k9b, matt-mips64-premerge-20101231, matt-mips64-base2, matt-mips64-base, matt-mips64, matt-armv6-prevmlocking, matt-armv6-nbase, matt-armv6-base, matt-armv6, keiichi-mipv6-base, keiichi-mipv6, jym-xensuspend-nbase, jym-xensuspend-base, jym-xensuspend, hpcarm-cleanup-nbase, hpcarm-cleanup-base, hpcarm-cleanup, fvdl_fs64_base, cube-autoconf-base, cube-autoconf, cherry-xenmp-base, cherry-xenmp, bouyer-quota2-nbase, bouyer-quota2-base, bouyer-quota2, agc-symver-base, agc-symver, abandoned-netbsd-4-base, abandoned-netbsd-4, HEAD
Changes since 1.10: +3 -23 lines

__STDC__ is always defined on NetBSD.

/* @(#)s_atan.c 5.1 93/09/24 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */

#include <sys/cdefs.h>
#if defined(LIBM_SCCS) && !defined(lint)
__RCSID("$NetBSD: s_atan.c,v 1.11 2002/05/26 22:01:54 wiz Exp $");
#endif

/* atan(x)
 * Method
 *   1. Reduce x to positive by atan(x) = -atan(-x).
 *   2. According to the integer k=4t+0.25 chopped, t=x, the argument
 *      is further reduced to one of the following intervals and the
 *      arctangent of t is evaluated by the corresponding formula:
 *
 *      [0,7/16]      atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
 *      [7/16,11/16]  atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
 *      [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
 *      [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
 *      [39/16,INF]   atan(x) = atan(INF) + atan( -1/t )
 *
 * 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 "math.h"
#include "math_private.h"

static const double atanhi[] = {
  4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
  7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
  9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
  1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
};

static const double atanlo[] = {
  2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
  3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
  1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
  6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
};

static const double aT[] = {
  3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
 -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
  1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
 -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
  9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
 -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
  6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
 -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
  4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
 -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
  1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
};

	static const double
one   = 1.0,
huge   = 1.0e300;

double
atan(double x)
{
	double w,s1,s2,z;
	int32_t ix,hx,id;

	GET_HIGH_WORD(hx,x);
	ix = hx&0x7fffffff;
	if(ix>=0x44100000) {	/* if |x| >= 2^66 */
	    u_int32_t low;
	    GET_LOW_WORD(low,x);
	    if(ix>0x7ff00000||
		(ix==0x7ff00000&&(low!=0)))
		return x+x;		/* NaN */
	    if(hx>0) return  atanhi[3]+atanlo[3];
	    else     return -atanhi[3]-atanlo[3];
	} if (ix < 0x3fdc0000) {	/* |x| < 0.4375 */
	    if (ix < 0x3e200000) {	/* |x| < 2^-29 */
		if(huge+x>one) return x;	/* raise inexact */
	    }
	    id = -1;
	} else {
	x = fabs(x);
	if (ix < 0x3ff30000) {		/* |x| < 1.1875 */
	    if (ix < 0x3fe60000) {	/* 7/16 <=|x|<11/16 */
		id = 0; x = (2.0*x-one)/(2.0+x);
	    } else {			/* 11/16<=|x|< 19/16 */
		id = 1; x  = (x-one)/(x+one);
	    }
	} else {
	    if (ix < 0x40038000) {	/* |x| < 2.4375 */
		id = 2; x  = (x-1.5)/(one+1.5*x);
	    } else {			/* 2.4375 <= |x| < 2^66 */
		id = 3; x  = -1.0/x;
	    }
	}}
    /* end of argument reduction */
	z = x*x;
	w = z*z;
    /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
	s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
	s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
	if (id<0) return x - x*(s1+s2);
	else {
	    z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
	    return (hx<0)? -z:z;
	}
}