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 /* atan(x) 16 * Method 17 * 1. Reduce x to positive by atan(x) = -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] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...) 23 * [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) ) 24 * [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) ) 25 * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) ) 26 * [39/16,INF] atan(x) = atan(INF) + 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 #ifndef _DOUBLE_IS_32BITS 38 39 #ifdef __STDC__ 40 static const double atanhi[] = { 41 #else 42 static double atanhi[] = { 43 #endif 44 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */ 45 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */ 46 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */ 47 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */ 48 }; 49 50 #ifdef __STDC__ 51 static const double atanlo[] = { 52 #else 53 static double atanlo[] = { 54 #endif 55 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */ 56 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */ 57 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */ 58 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */ 59 }; 60 61 #ifdef __STDC__ 62 static const double aT[] = { 63 #else 64 static double aT[] = { 65 #endif 66 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */ 67 -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */ 68 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */ 69 -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */ 70 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */ 71 -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */ 72 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */ 73 -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */ 74 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */ 75 -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */ 76 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */ 77 }; 78 79 #ifdef __STDC__ 80 static const double 81 #else 82 static double 83 #endif 84 one = 1.0, 85 huge = 1.0e300; 86 87 #ifdef __STDC__ atan(double x)88 double atan(double x) 89 #else 90 double atan(x) 91 double x; 92 #endif 93 { 94 double w,s1,s2,z; 95 int32_t ix,hx,id; 96 97 GET_HIGH_WORD(hx,x); 98 ix = hx&0x7fffffff; 99 if(ix>=0x44100000) { /* if |x| >= 2^66 */ 100 uint32_t low; 101 102 GET_LOW_WORD(low,x); 103 if(ix>0x7ff00000|| 104 (ix==0x7ff00000&&(low!=0))) 105 return x+x; /* NaN */ 106 if(hx>0) return atanhi[3]+atanlo[3]; 107 else return -atanhi[3]-atanlo[3]; 108 } if (ix < 0x3fdc0000) { /* |x| < 0.4375 */ 109 if (ix < 0x3e200000) { /* |x| < 2^-29 */ 110 if(huge+x>one) return x; /* raise inexact */ 111 } 112 id = -1; 113 } else { 114 x = fabs(x); 115 if (ix < 0x3ff30000) { /* |x| < 1.1875 */ 116 if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */ 117 id = 0; x = (2.0*x-one)/(2.0+x); 118 } else { /* 11/16<=|x|< 19/16 */ 119 id = 1; x = (x-one)/(x+one); 120 } 121 } else { 122 if (ix < 0x40038000) { /* |x| < 2.4375 */ 123 id = 2; x = (x-1.5)/(one+1.5*x); 124 } else { /* 2.4375 <= |x| < 2^66 */ 125 id = 3; x = -1.0/x; 126 } 127 }} 128 /* end of argument reduction */ 129 z = x*x; 130 w = z*z; 131 /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ 132 s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10]))))); 133 s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9])))); 134 if (id<0) return x - x*(s1+s2); 135 else { 136 z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); 137 return (hx<0)? -z:z; 138 } 139 } 140 #endif /* _DOUBLE_IS_32BITS */ 141