1 /* s_atanf.c -- float version of s_atan.c. 2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. 3 */ 4 5 /* 6 * ==================================================== 7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 8 * 9 * Developed at SunPro, a Sun Microsystems, Inc. business. 10 * Permission to use, copy, modify, and distribute this 11 * software is freely granted, provided that this notice 12 * is preserved. 13 * ==================================================== 14 */ 15 16 #include "math.h" 17 #include "math_private.h" 18 19 static const float atanhi[] = { 20 4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */ 21 7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */ 22 9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */ 23 1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */ 24 }; 25 26 static const float atanlo[] = { 27 5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */ 28 3.7748947079e-08, /* atan(1.0)lo 0x33222168 */ 29 3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */ 30 7.5497894159e-08, /* atan(inf)lo 0x33a22168 */ 31 }; 32 33 static const float aT[] = { 34 3.3333334327e-01, /* 0x3eaaaaaa */ 35 -2.0000000298e-01, /* 0xbe4ccccd */ 36 1.4285714924e-01, /* 0x3e124925 */ 37 -1.1111110449e-01, /* 0xbde38e38 */ 38 9.0908870101e-02, /* 0x3dba2e6e */ 39 -7.6918758452e-02, /* 0xbd9d8795 */ 40 6.6610731184e-02, /* 0x3d886b35 */ 41 -5.8335702866e-02, /* 0xbd6ef16b */ 42 4.9768779427e-02, /* 0x3d4bda59 */ 43 -3.6531571299e-02, /* 0xbd15a221 */ 44 1.6285819933e-02, /* 0x3c8569d7 */ 45 }; 46 47 static const float 48 one = 1.0, 49 huge = 1.0e30; 50 51 float 52 atanf(float x) 53 { 54 float w,s1,s2,z; 55 int32_t ix,hx,id; 56 57 GET_FLOAT_WORD(hx,x); 58 ix = hx&0x7fffffff; 59 if(ix>=0x50800000) { /* if |x| >= 2^34 */ 60 if(ix>0x7f800000) 61 return x+x; /* NaN */ 62 if(hx>0) return atanhi[3]+atanlo[3]; 63 else return -atanhi[3]-atanlo[3]; 64 } if (ix < 0x3ee00000) { /* |x| < 0.4375 */ 65 if (ix < 0x31000000) { /* |x| < 2^-29 */ 66 if(huge+x>one) return x; /* raise inexact */ 67 } 68 id = -1; 69 } else { 70 x = fabsf(x); 71 if (ix < 0x3f980000) { /* |x| < 1.1875 */ 72 if (ix < 0x3f300000) { /* 7/16 <=|x|<11/16 */ 73 id = 0; x = ((float)2.0*x-one)/((float)2.0+x); 74 } else { /* 11/16<=|x|< 19/16 */ 75 id = 1; x = (x-one)/(x+one); 76 } 77 } else { 78 if (ix < 0x401c0000) { /* |x| < 2.4375 */ 79 id = 2; x = (x-(float)1.5)/(one+(float)1.5*x); 80 } else { /* 2.4375 <= |x| < 2^66 */ 81 id = 3; x = -(float)1.0/x; 82 } 83 }} 84 /* end of argument reduction */ 85 z = x*x; 86 w = z*z; 87 /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ 88 s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10]))))); 89 s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9])))); 90 if (id<0) return x - x*(s1+s2); 91 else { 92 z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); 93 return (hx<0)? -z:z; 94 } 95 } 96