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