s_atan.c revision 176451 
1/* @(#)s_atan.c 5.1 93/09/24 */
2/*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
9 * is preserved.
10 * ====================================================
11 */
12
13#include <sys/cdefs.h>
14__FBSDID("$FreeBSD: head/lib/msun/src/s_atan.c 176451 2008-02-22 02:30:36Z das $");
15
16/* atan(x)
17 * Method
18 *   1. Reduce x to positive by atan(x) = -atan(-x).
19 *   2. According to the integer k=4t+0.25 chopped, t=x, the argument
20 *      is further reduced to one of the following intervals and the
21 *      arctangent of t is evaluated by the corresponding formula:
22 *
23 *      [0,7/16]      atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
24 *      [7/16,11/16]  atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
25 *      [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
26 *      [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
27 *      [39/16,INF]   atan(x) = atan(INF) + atan( -1/t )
28 *
29 * Constants:
30 * The hexadecimal values are the intended ones for the following
31 * constants. The decimal values may be used, provided that the
32 * compiler will convert from decimal to binary accurately enough
33 * to produce the hexadecimal values shown.
34 */
35
36#include "math.h"
37#include "math_private.h"
38
39static const double atanhi[] = {
40  4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
41  7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
42  9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
43  1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
44};
45
46static const double atanlo[] = {
47  2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
48  3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
49  1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
50  6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
51};
52
53static const double aT[] = {
54  3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
55 -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
56  1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
57 -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
58  9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
59 -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
60  6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
61 -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
62  4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
63 -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
64  1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
65};
66
67	static const double
68one   = 1.0,
69huge   = 1.0e300;
70
71double
72atan(double x)
73{
74	double w,s1,s2,z;
75	int32_t ix,hx,id;
76
77	GET_HIGH_WORD(hx,x);
78	ix = hx&0x7fffffff;
79	if(ix>=0x44100000) {	/* if |x| >= 2^66 */
80	    u_int32_t low;
81	    GET_LOW_WORD(low,x);
82	    if(ix>0x7ff00000||
83		(ix==0x7ff00000&&(low!=0)))
84		return x+x;		/* NaN */
85	    if(hx>0) return  atanhi[3]+atanlo[3];
86	    else     return -atanhi[3]-atanlo[3];
87	} if (ix < 0x3fdc0000) {	/* |x| < 0.4375 */
88	    if (ix < 0x3e200000) {	/* |x| < 2^-29 */
89		if(huge+x>one) return x;	/* raise inexact */
90	    }
91	    id = -1;
92	} else {
93	x = fabs(x);
94	if (ix < 0x3ff30000) {		/* |x| < 1.1875 */
95	    if (ix < 0x3fe60000) {	/* 7/16 <=|x|<11/16 */
96		id = 0; x = (2.0*x-one)/(2.0+x);
97	    } else {			/* 11/16<=|x|< 19/16 */
98		id = 1; x  = (x-one)/(x+one);
99	    }
100	} else {
101	    if (ix < 0x40038000) {	/* |x| < 2.4375 */
102		id = 2; x  = (x-1.5)/(one+1.5*x);
103	    } else {			/* 2.4375 <= |x| < 2^66 */
104		id = 3; x  = -1.0/x;
105	    }
106	}}
107    /* end of argument reduction */
108	z = x*x;
109	w = z*z;
110    /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
111	s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
112	s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
113	if (id<0) return x - x*(s1+s2);
114	else {
115	    z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
116	    return (hx<0)? -z:z;
117	}
118}
119