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 #if defined(LIBM_SCCS) && !defined(lint) 18 __RCSID("$NetBSD: s_atanf.c,v 1.7 2002/05/26 22:01:54 wiz Exp $"); 19 #endif 20 21 #include "math.h" 22 #include "math_private.h" 23 24 static const float atanhi[] = { 25 4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */ 26 7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */ 27 9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */ 28 1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */ 29 }; 30 31 static const float atanlo[] = { 32 5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */ 33 3.7748947079e-08, /* atan(1.0)lo 0x33222168 */ 34 3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */ 35 7.5497894159e-08, /* atan(inf)lo 0x33a22168 */ 36 }; 37 38 static const float aT[] = { 39 3.3333334327e-01, /* 0x3eaaaaaa */ 40 -2.0000000298e-01, /* 0xbe4ccccd */ 41 1.4285714924e-01, /* 0x3e124925 */ 42 -1.1111110449e-01, /* 0xbde38e38 */ 43 9.0908870101e-02, /* 0x3dba2e6e */ 44 -7.6918758452e-02, /* 0xbd9d8795 */ 45 6.6610731184e-02, /* 0x3d886b35 */ 46 -5.8335702866e-02, /* 0xbd6ef16b */ 47 4.9768779427e-02, /* 0x3d4bda59 */ 48 -3.6531571299e-02, /* 0xbd15a221 */ 49 1.6285819933e-02, /* 0x3c8569d7 */ 50 }; 51 52 static const float 53 one = 1.0, 54 huge = 1.0e30; 55 56 float 57 atanf(float x) 58 { 59 float w,s1,s2,z; 60 int32_t ix,hx,id; 61 62 GET_FLOAT_WORD(hx,x); 63 ix = hx&0x7fffffff; 64 if(ix>=0x50800000) { /* if |x| >= 2^34 */ 65 if(ix>0x7f800000) 66 return x+x; /* NaN */ 67 if(hx>0) return atanhi[3]+atanlo[3]; 68 else return -atanhi[3]-atanlo[3]; 69 } if (ix < 0x3ee00000) { /* |x| < 0.4375 */ 70 if (ix < 0x31000000) { /* |x| < 2^-29 */ 71 if(huge+x>one) return x; /* raise inexact */ 72 } 73 id = -1; 74 } else { 75 x = fabsf(x); 76 if (ix < 0x3f980000) { /* |x| < 1.1875 */ 77 if (ix < 0x3f300000) { /* 7/16 <=|x|<11/16 */ 78 id = 0; x = ((float)2.0*x-one)/((float)2.0+x); 79 } else { /* 11/16<=|x|< 19/16 */ 80 id = 1; x = (x-one)/(x+one); 81 } 82 } else { 83 if (ix < 0x401c0000) { /* |x| < 2.4375 */ 84 id = 2; x = (x-(float)1.5)/(one+(float)1.5*x); 85 } else { /* 2.4375 <= |x| < 2^66 */ 86 id = 3; x = -(float)1.0/x; 87 } 88 }} 89 /* end of argument reduction */ 90 z = x*x; 91 w = z*z; 92 /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ 93 s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10]))))); 94 s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9])))); 95 if (id<0) return x - x*(s1+s2); 96 else { 97 z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); 98 return (hx<0)? -z:z; 99 } 100 } 101