1 2 /* @(#)s_atan.c 1.3 95/01/18 */ 3 /* 4 * ==================================================== 5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6 * 7 * Developed at SunSoft, a Sun Microsystems, Inc. business. 8 * Permission to use, copy, modify, and distribute this 9 * software is freely granted, provided that this notice 10 * is preserved. 11 * ==================================================== 12 * 13 */ 14 15 /* ieee_atan(x) 16 * Method 17 * 1. Reduce x to positive by ieee_atan(x) = -ieee_atan(-x). 18 * 2. According to the integer k=4t+0.25 chopped, t=x, the argument 19 * is further reduced to one of the following intervals and the 20 * arctangent of t is evaluated by the corresponding formula: 21 * 22 * [0,7/16] ieee_atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...) 23 * [7/16,11/16] ieee_atan(x) = ieee_atan(1/2) + ieee_atan( (t-0.5)/(1+t/2) ) 24 * [11/16.19/16] ieee_atan(x) = ieee_atan( 1 ) + ieee_atan( (t-1)/(1+t) ) 25 * [19/16,39/16] ieee_atan(x) = ieee_atan(3/2) + ieee_atan( (t-1.5)/(1+1.5t) ) 26 * [39/16,INF] ieee_atan(x) = ieee_atan(INF) + ieee_atan( -1/t ) 27 * 28 * Constants: 29 * The hexadecimal values are the intended ones for the following 30 * constants. The decimal values may be used, provided that the 31 * compiler will convert from decimal to binary accurately enough 32 * to produce the hexadecimal values shown. 33 */ 34 35 #include "fdlibm.h" 36 37 #ifdef __STDC__ 38 static const double atanhi[] = { 39 #else 40 static double atanhi[] = { 41 #endif 42 4.63647609000806093515e-01, /* ieee_atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */ 43 7.85398163397448278999e-01, /* ieee_atan(1.0)hi 0x3FE921FB, 0x54442D18 */ 44 9.82793723247329054082e-01, /* ieee_atan(1.5)hi 0x3FEF730B, 0xD281F69B */ 45 1.57079632679489655800e+00, /* ieee_atan(inf)hi 0x3FF921FB, 0x54442D18 */ 46 }; 47 48 #ifdef __STDC__ 49 static const double atanlo[] = { 50 #else 51 static double atanlo[] = { 52 #endif 53 2.26987774529616870924e-17, /* ieee_atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */ 54 3.06161699786838301793e-17, /* ieee_atan(1.0)lo 0x3C81A626, 0x33145C07 */ 55 1.39033110312309984516e-17, /* ieee_atan(1.5)lo 0x3C700788, 0x7AF0CBBD */ 56 6.12323399573676603587e-17, /* ieee_atan(inf)lo 0x3C91A626, 0x33145C07 */ 57 }; 58 59 #ifdef __STDC__ 60 static const double aT[] = { 61 #else 62 static double aT[] = { 63 #endif 64 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */ 65 -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */ 66 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */ 67 -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */ 68 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */ 69 -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */ 70 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */ 71 -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */ 72 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */ 73 -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */ 74 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */ 75 }; 76 77 #ifdef __STDC__ 78 static const double 79 #else 80 static double 81 #endif 82 one = 1.0, 83 huge = 1.0e300; 84 85 #ifdef __STDC__ ieee_atan(double x)86 double ieee_atan(double x) 87 #else 88 double ieee_atan(x) 89 double x; 90 #endif 91 { 92 double w,s1,s2,z; 93 int ix,hx,id; 94 95 hx = __HI(x); 96 ix = hx&0x7fffffff; 97 if(ix>=0x44100000) { /* if |x| >= 2^66 */ 98 if(ix>0x7ff00000|| 99 (ix==0x7ff00000&&(__LO(x)!=0))) 100 return x+x; /* NaN */ 101 if(hx>0) return atanhi[3]+atanlo[3]; 102 else return -atanhi[3]-atanlo[3]; 103 } if (ix < 0x3fdc0000) { /* |x| < 0.4375 */ 104 if (ix < 0x3e200000) { /* |x| < 2^-29 */ 105 if(huge+x>one) return x; /* raise inexact */ 106 } 107 id = -1; 108 } else { 109 x = ieee_fabs(x); 110 if (ix < 0x3ff30000) { /* |x| < 1.1875 */ 111 if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */ 112 id = 0; x = (2.0*x-one)/(2.0+x); 113 } else { /* 11/16<=|x|< 19/16 */ 114 id = 1; x = (x-one)/(x+one); 115 } 116 } else { 117 if (ix < 0x40038000) { /* |x| < 2.4375 */ 118 id = 2; x = (x-1.5)/(one+1.5*x); 119 } else { /* 2.4375 <= |x| < 2^66 */ 120 id = 3; x = -1.0/x; 121 } 122 }} 123 /* end of argument reduction */ 124 z = x*x; 125 w = z*z; 126 /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ 127 s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10]))))); 128 s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9])))); 129 if (id<0) return x - x*(s1+s2); 130 else { 131 z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); 132 return (hx<0)? -z:z; 133 } 134 } 135