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