s_atan.c (4072B)
1 /* 2 * ==================================================== 3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 4 * 5 * Developed at SunPro, a Sun Microsystems, Inc. business. 6 * Permission to use, copy, modify, and distribute this 7 * software is freely granted, provided that this notice 8 * is preserved. 9 * ==================================================== 10 */ 11 12 /* atan(x) 13 * Method 14 * 1. Reduce x to positive by atan(x) = -atan(-x). 15 * 2. According to the integer k=4t+0.25 chopped, t=x, the argument 16 * is further reduced to one of the following intervals and the 17 * arctangent of t is evaluated by the corresponding formula: 18 * 19 * [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...) 20 * [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) ) 21 * [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) ) 22 * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) ) 23 * [39/16,INF] atan(x) = atan(INF) + atan( -1/t ) 24 * 25 * Constants: 26 * The hexadecimal values are the intended ones for the following 27 * constants. The decimal values may be used, provided that the 28 * compiler will convert from decimal to binary accurately enough 29 * to produce the hexadecimal values shown. 30 */ 31 32 #include "math_libm.h" 33 #include "math_private.h" 34 35 static const double atanhi[] = { 36 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */ 37 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */ 38 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */ 39 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */ 40 }; 41 42 static const double atanlo[] = { 43 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */ 44 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */ 45 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */ 46 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */ 47 }; 48 49 static const double aT[] = { 50 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */ 51 -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */ 52 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */ 53 -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */ 54 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */ 55 -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */ 56 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */ 57 -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */ 58 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */ 59 -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */ 60 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */ 61 }; 62 63 #ifdef __WATCOMC__ /* Watcom defines huge=__huge */ 64 #undef huge 65 #endif 66 67 static const double 68 one = 1.0, 69 huge = 1.0e300; 70 71 double atan(double x) 72 { 73 double w,s1,s2,z; 74 int32_t ix,hx,id; 75 76 GET_HIGH_WORD(hx,x); 77 ix = hx&0x7fffffff; 78 if(ix>=0x44100000) { /* if |x| >= 2^66 */ 79 u_int32_t low; 80 GET_LOW_WORD(low,x); 81 if(ix>0x7ff00000|| 82 (ix==0x7ff00000&&(low!=0))) 83 return x+x; /* NaN */ 84 if(hx>0) return atanhi[3]+atanlo[3]; 85 else return -atanhi[3]-atanlo[3]; 86 } if (ix < 0x3fdc0000) { /* |x| < 0.4375 */ 87 if (ix < 0x3e200000) { /* |x| < 2^-29 */ 88 if(huge+x>one) return x; /* raise inexact */ 89 } 90 id = -1; 91 } else { 92 x = fabs(x); 93 if (ix < 0x3ff30000) { /* |x| < 1.1875 */ 94 if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */ 95 id = 0; x = (2.0*x-one)/(2.0+x); 96 } else { /* 11/16<=|x|< 19/16 */ 97 id = 1; x = (x-one)/(x+one); 98 } 99 } else { 100 if (ix < 0x40038000) { /* |x| < 2.4375 */ 101 id = 2; x = (x-1.5)/(one+1.5*x); 102 } else { /* 2.4375 <= |x| < 2^66 */ 103 id = 3; x = -1.0/x; 104 } 105 }} 106 /* end of argument reduction */ 107 z = x*x; 108 w = z*z; 109 /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ 110 s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10]))))); 111 s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9])))); 112 if (id<0) return x - x*(s1+s2); 113 else { 114 z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); 115 return (hx<0)? -z:z; 116 } 117 } 118 libm_hidden_def(atan)