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 #ifndef lint 17 static char rcsid[] = "$FreeBSD$"; 18 #endif 19 20 #include "math.h" 21 #include "math_private.h" 22 23 static const float atanhi[] = { 24 4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */ 25 7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */ 26 9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */ 27 1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */ 28 }; 29 30 static const float atanlo[] = { 31 5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */ 32 3.7748947079e-08, /* atan(1.0)lo 0x33222168 */ 33 3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */ 34 7.5497894159e-08, /* atan(inf)lo 0x33a22168 */ 35 }; 36 37 static const float aT[] = { 38 3.3333334327e-01, /* 0x3eaaaaaa */ 39 -2.0000000298e-01, /* 0xbe4ccccd */ 40 1.4285714924e-01, /* 0x3e124925 */ 41 -1.1111110449e-01, /* 0xbde38e38 */ 42 9.0908870101e-02, /* 0x3dba2e6e */ 43 -7.6918758452e-02, /* 0xbd9d8795 */ 44 6.6610731184e-02, /* 0x3d886b35 */ 45 -5.8335702866e-02, /* 0xbd6ef16b */ 46 4.9768779427e-02, /* 0x3d4bda59 */ 47 -3.6531571299e-02, /* 0xbd15a221 */ 48 1.6285819933e-02, /* 0x3c8569d7 */ 49 }; 50 51 static const float 52 one = 1.0, 53 huge = 1.0e30; 54 55 float 56 atanf(float x) 57 { 58 float w,s1,s2,z; 59 int32_t ix,hx,id; 60 61 GET_FLOAT_WORD(hx,x); 62 ix = hx&0x7fffffff; 63 if(ix>=0x50800000) { /* if |x| >= 2^34 */ 64 if(ix>0x7f800000) 65 return x+x; /* NaN */ 66 if(hx>0) return atanhi[3]+atanlo[3]; 67 else return -atanhi[3]-atanlo[3]; 68 } if (ix < 0x3ee00000) { /* |x| < 0.4375 */ 69 if (ix < 0x31000000) { /* |x| < 2^-29 */ 70 if(huge+x>one) return x; /* raise inexact */ 71 } 72 id = -1; 73 } else { 74 x = fabsf(x); 75 if (ix < 0x3f980000) { /* |x| < 1.1875 */ 76 if (ix < 0x3f300000) { /* 7/16 <=|x|<11/16 */ 77 id = 0; x = ((float)2.0*x-one)/((float)2.0+x); 78 } else { /* 11/16<=|x|< 19/16 */ 79 id = 1; x = (x-one)/(x+one); 80 } 81 } else { 82 if (ix < 0x401c0000) { /* |x| < 2.4375 */ 83 id = 2; x = (x-(float)1.5)/(one+(float)1.5*x); 84 } else { /* 2.4375 <= |x| < 2^66 */ 85 id = 3; x = -(float)1.0/x; 86 } 87 }} 88 /* end of argument reduction */ 89 z = x*x; 90 w = z*z; 91 /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ 92 s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10]))))); 93 s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9])))); 94 if (id<0) return x - x*(s1+s2); 95 else { 96 z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); 97 return (hx<0)? -z:z; 98 } 99 } 100