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 #if defined(LIBM_SCCS) && !defined(lint) 15 __RCSID("$NetBSD: s_atan.c,v 1.9 1997/10/09 11:30:56 lukem Exp $"); 16 #endif 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: 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 35 * to produce the hexadecimal values shown. 36 */ 37 38 #include "math.h" 39 #include "math_private.h" 40 41 #ifdef __STDC__ 42 static const double atanhi[] = { 43 #else 44 static double atanhi[] = { 45 #endif 46 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */ 47 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */ 48 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */ 49 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */ 50 }; 51 52 #ifdef __STDC__ 53 static const double atanlo[] = { 54 #else 55 static double atanlo[] = { 56 #endif 57 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */ 58 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */ 59 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */ 60 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */ 61 }; 62 63 #ifdef __STDC__ 64 static const double aT[] = { 65 #else 66 static double aT[] = { 67 #endif 68 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */ 69 -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */ 70 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */ 71 -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */ 72 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */ 73 -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */ 74 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */ 75 -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */ 76 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */ 77 -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */ 78 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */ 79 }; 80 81 #ifdef __STDC__ 82 static const double 83 #else 84 static double 85 #endif 86 one = 1.0, 87 huge = 1.0e300; 88 89 #ifdef __STDC__ 90 double atan(double x) 91 #else 92 double atan(x) 93 double x; 94 #endif 95 { 96 double w,s1,s2,z; 97 int32_t ix,hx,id; 98 99 GET_HIGH_WORD(hx,x); 100 ix = hx&0x7fffffff; 101 if(ix>=0x44100000) { /* if |x| >= 2^66 */ 102 u_int32_t low; 103 GET_LOW_WORD(low,x); 104 if(ix>0x7ff00000|| 105 (ix==0x7ff00000&&(low!=0))) 106 return x+x; /* NaN */ 107 if(hx>0) return atanhi[3]+atanlo[3]; 108 else return -atanhi[3]-atanlo[3]; 109 } if (ix < 0x3fdc0000) { /* |x| < 0.4375 */ 110 if (ix < 0x3e200000) { /* |x| < 2^-29 */ 111 if(huge+x>one) return x; /* raise inexact */ 112 } 113 id = -1; 114 } else { 115 x = fabs(x); 116 if (ix < 0x3ff30000) { /* |x| < 1.1875 */ 117 if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */ 118 id = 0; x = (2.0*x-one)/(2.0+x); 119 } else { /* 11/16<=|x|< 19/16 */ 120 id = 1; x = (x-one)/(x+one); 121 } 122 } else { 123 if (ix < 0x40038000) { /* |x| < 2.4375 */ 124 id = 2; x = (x-1.5)/(one+1.5*x); 125 } else { /* 2.4375 <= |x| < 2^66 */ 126 id = 3; x = -1.0/x; 127 } 128 }} 129 /* end of argument reduction */ 130 z = x*x; 131 w = z*z; 132 /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ 133 s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10]))))); 134 s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9])))); 135 if (id<0) return x - x*(s1+s2); 136 else { 137 z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); 138 return (hx<0)? -z:z; 139 } 140 } 141