Annotation of src/lib/libm/src/s_atan.c, Revision 1.11
1.1 jtc 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
1.10 simonb 8: * software is freely granted, provided that this notice
1.1 jtc 9: * is preserved.
10: * ====================================================
11: */
1.3 jtc 12:
1.9 lukem 13: #include <sys/cdefs.h>
1.7 jtc 14: #if defined(LIBM_SCCS) && !defined(lint)
1.11 ! wiz 15: __RCSID("$NetBSD: s_atan.c,v 1.10 1999/07/02 15:37:42 simonb Exp $");
1.3 jtc 16: #endif
1.1 jtc 17:
18: /* atan(x)
19: * Method
20: * 1. Reduce x to positive by atan(x) = -atan(-x).
21: * 2. According to the integer k=4t+0.25 chopped, t=x, the argument
22: * is further reduced to one of the following intervals and the
23: * arctangent of t is evaluated by the corresponding formula:
24: *
25: * [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
26: * [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
27: * [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
28: * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
29: * [39/16,INF] atan(x) = atan(INF) + atan( -1/t )
30: *
31: * Constants:
1.10 simonb 32: * The hexadecimal values are the intended ones for the following
33: * constants. The decimal values may be used, provided that the
34: * compiler will convert from decimal to binary accurately enough
1.1 jtc 35: * to produce the hexadecimal values shown.
36: */
37:
1.5 jtc 38: #include "math.h"
39: #include "math_private.h"
1.1 jtc 40:
41: static const double atanhi[] = {
42: 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
43: 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
44: 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
45: 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
46: };
47:
48: static const double atanlo[] = {
49: 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
50: 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
51: 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
52: 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
53: };
54:
55: static const double aT[] = {
56: 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
57: -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
58: 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
59: -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
60: 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
61: -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
62: 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
63: -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
64: 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
65: -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
66: 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
67: };
68:
1.10 simonb 69: static const double
1.1 jtc 70: one = 1.0,
71: huge = 1.0e300;
72:
1.11 ! wiz 73: double
! 74: atan(double x)
1.1 jtc 75: {
76: double w,s1,s2,z;
1.6 jtc 77: int32_t ix,hx,id;
1.1 jtc 78:
1.5 jtc 79: GET_HIGH_WORD(hx,x);
1.1 jtc 80: ix = hx&0x7fffffff;
81: if(ix>=0x44100000) { /* if |x| >= 2^66 */
1.6 jtc 82: u_int32_t low;
1.5 jtc 83: GET_LOW_WORD(low,x);
1.1 jtc 84: if(ix>0x7ff00000||
1.5 jtc 85: (ix==0x7ff00000&&(low!=0)))
1.1 jtc 86: return x+x; /* NaN */
87: if(hx>0) return atanhi[3]+atanlo[3];
88: else return -atanhi[3]-atanlo[3];
89: } if (ix < 0x3fdc0000) { /* |x| < 0.4375 */
90: if (ix < 0x3e200000) { /* |x| < 2^-29 */
91: if(huge+x>one) return x; /* raise inexact */
92: }
93: id = -1;
94: } else {
95: x = fabs(x);
96: if (ix < 0x3ff30000) { /* |x| < 1.1875 */
97: if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */
1.10 simonb 98: id = 0; x = (2.0*x-one)/(2.0+x);
1.1 jtc 99: } else { /* 11/16<=|x|< 19/16 */
1.10 simonb 100: id = 1; x = (x-one)/(x+one);
1.1 jtc 101: }
102: } else {
103: if (ix < 0x40038000) { /* |x| < 2.4375 */
104: id = 2; x = (x-1.5)/(one+1.5*x);
105: } else { /* 2.4375 <= |x| < 2^66 */
106: id = 3; x = -1.0/x;
107: }
108: }}
109: /* end of argument reduction */
110: z = x*x;
111: w = z*z;
112: /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
113: s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
114: s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
115: if (id<0) return x - x*(s1+s2);
116: else {
117: z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
118: return (hx<0)? -z:z;
119: }
120: }
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