1 | /* origin: FreeBSD /usr/src/lib/msun/src/s_atanf.c */
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2 | /*
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3 | * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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4 | */
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5 | /*
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6 | * ====================================================
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7 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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8 | *
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9 | * Developed at SunPro, a Sun Microsystems, Inc. business.
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10 | * Permission to use, copy, modify, and distribute this
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11 | * software is freely granted, provided that this notice
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12 | * is preserved.
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13 | * ====================================================
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14 | */
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15 |
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16 |
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17 | #include "libm.h"
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18 |
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19 | static const float atanhi[] = {
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20 | 4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */
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21 | 7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */
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22 | 9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */
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23 | 1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */
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24 | };
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25 |
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26 | static const float atanlo[] = {
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27 | 5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */
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28 | 3.7748947079e-08, /* atan(1.0)lo 0x33222168 */
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29 | 3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */
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30 | 7.5497894159e-08, /* atan(inf)lo 0x33a22168 */
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31 | };
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32 |
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33 | static const float aT[] = {
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34 | 3.3333328366e-01,
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35 | -1.9999158382e-01,
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36 | 1.4253635705e-01,
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37 | -1.0648017377e-01,
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38 | 6.1687607318e-02,
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39 | };
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40 |
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41 | float atanf(float x)
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42 | {
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43 | float_t w,s1,s2,z;
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44 | uint32_t ix,sign;
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45 | int id;
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46 |
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47 | GET_FLOAT_WORD(ix, x);
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48 | sign = ix>>31;
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49 | ix &= 0x7fffffff;
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50 | if (ix >= 0x4c800000) { /* if |x| >= 2**26 */
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51 | if (isnan(x))
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52 | return x;
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53 | z = atanhi[3] + 0x1p-120f;
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54 | return sign ? -z : z;
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55 | }
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56 | if (ix < 0x3ee00000) { /* |x| < 0.4375 */
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57 | if (ix < 0x39800000) { /* |x| < 2**-12 */
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58 | if (ix < 0x00800000)
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59 | /* raise underflow for subnormal x */
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60 | FORCE_EVAL(x*x);
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61 | return x;
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62 | }
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63 | id = -1;
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64 | } else {
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65 | x = fabsf(x);
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66 | if (ix < 0x3f980000) { /* |x| < 1.1875 */
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67 | if (ix < 0x3f300000) { /* 7/16 <= |x| < 11/16 */
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68 | id = 0;
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69 | x = (2.0f*x - 1.0f)/(2.0f + x);
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70 | } else { /* 11/16 <= |x| < 19/16 */
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71 | id = 1;
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72 | x = (x - 1.0f)/(x + 1.0f);
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73 | }
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74 | } else {
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75 | if (ix < 0x401c0000) { /* |x| < 2.4375 */
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76 | id = 2;
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77 | x = (x - 1.5f)/(1.0f + 1.5f*x);
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78 | } else { /* 2.4375 <= |x| < 2**26 */
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79 | id = 3;
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80 | x = -1.0f/x;
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81 | }
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82 | }
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83 | }
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84 | /* end of argument reduction */
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85 | z = x*x;
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86 | w = z*z;
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87 | /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
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88 | s1 = z*(aT[0]+w*(aT[2]+w*aT[4]));
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89 | s2 = w*(aT[1]+w*aT[3]);
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90 | if (id < 0)
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91 | return x - x*(s1+s2);
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92 | z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
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93 | return sign ? -z : z;
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94 | }
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