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| 1 /* origin: FreeBSD /usr/src/lib/msun/src/s_atanf.c */ |
| 2 /* |
| 3 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. |
| 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 |
| 17 #include "libm.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 3.3333328366e-01, |
| 35 -1.9999158382e-01, |
| 36 1.4253635705e-01, |
| 37 -1.0648017377e-01, |
| 38 6.1687607318e-02, |
| 39 }; |
| 40 |
| 41 float atanf(float x) |
| 42 { |
| 43 float_t w,s1,s2,z; |
| 44 uint32_t ix,sign; |
| 45 int id; |
| 46 |
| 47 GET_FLOAT_WORD(ix, x); |
| 48 sign = ix>>31; |
| 49 ix &= 0x7fffffff; |
| 50 if (ix >= 0x4c800000) { /* if |x| >= 2**26 */ |
| 51 if (isnan(x)) |
| 52 return x; |
| 53 z = atanhi[3] + 0x1p-120f; |
| 54 return sign ? -z : z; |
| 55 } |
| 56 if (ix < 0x3ee00000) { /* |x| < 0.4375 */ |
| 57 if (ix < 0x39800000) { /* |x| < 2**-12 */ |
| 58 if (ix < 0x00800000) |
| 59 /* raise underflow for subnormal x */ |
| 60 FORCE_EVAL(x*x); |
| 61 return x; |
| 62 } |
| 63 id = -1; |
| 64 } else { |
| 65 x = fabsf(x); |
| 66 if (ix < 0x3f980000) { /* |x| < 1.1875 */ |
| 67 if (ix < 0x3f300000) { /* 7/16 <= |x| < 11/16 */ |
| 68 id = 0; |
| 69 x = (2.0f*x - 1.0f)/(2.0f + x); |
| 70 } else { /* 11/16 <= |x| < 19/16 */ |
| 71 id = 1; |
| 72 x = (x - 1.0f)/(x + 1.0f); |
| 73 } |
| 74 } else { |
| 75 if (ix < 0x401c0000) { /* |x| < 2.4375 */ |
| 76 id = 2; |
| 77 x = (x - 1.5f)/(1.0f + 1.5f*x); |
| 78 } else { /* 2.4375 <= |x| < 2**26 */ |
| 79 id = 3; |
| 80 x = -1.0f/x; |
| 81 } |
| 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])); |
| 89 s2 = w*(aT[1]+w*aT[3]); |
| 90 if (id < 0) |
| 91 return x - x*(s1+s2); |
| 92 z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); |
| 93 return sign ? -z : z; |
| 94 } |
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