1 | |
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2 | /* @(#)z_asinef.c 1.0 98/08/13 */ |
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3 | /****************************************************************** |
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4 | * The following routines are coded directly from the algorithms |
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5 | * and coefficients given in "Software Manual for the Elementary |
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6 | * Functions" by William J. Cody, Jr. and William Waite, Prentice |
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7 | * Hall, 1980. |
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8 | ******************************************************************/ |
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9 | /****************************************************************** |
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10 | * Arcsine |
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11 | * |
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12 | * Input: |
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13 | * x - floating point value |
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14 | * acosine - indicates acos calculation |
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15 | * |
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16 | * Output: |
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17 | * Arcsine of x. |
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18 | * |
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19 | * Description: |
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20 | * This routine calculates arcsine / arccosine. |
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21 | * |
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22 | *****************************************************************/ |
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23 | |
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24 | #include "fdlibm.h" |
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25 | #include "zmath.h" |
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26 | |
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27 | static const float p[] = { 0.933935835, -0.504400557 }; |
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28 | static const float q[] = { 0.560363004e+1, -0.554846723e+1 }; |
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29 | static const float a[] = { 0.0, 0.785398163 }; |
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30 | static const float b[] = { 1.570796326, 0.785398163 }; |
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31 | |
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32 | float |
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33 | asinef (float x, |
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34 | int acosine) |
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35 | { |
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36 | int flag, i; |
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37 | int branch = 0; |
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38 | float g, res, R, P, Q, y; |
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39 | |
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40 | /* Check for special values. */ |
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41 | i = numtestf (x); |
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42 | if (i == NAN || i == INF) |
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43 | { |
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44 | errno = EDOM; |
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45 | if (i == NAN) |
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46 | return (x); |
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47 | else |
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48 | return (z_infinity_f.f); |
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49 | } |
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50 | |
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51 | y = fabsf (x); |
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52 | flag = acosine; |
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53 | |
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54 | if (y > 0.5) |
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55 | { |
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56 | i = 1 - flag; |
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57 | |
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58 | /* Check for range error. */ |
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59 | if (y > 1.0) |
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60 | { |
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61 | errno = ERANGE; |
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62 | return (z_notanum_f.f); |
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63 | } |
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64 | |
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65 | g = (1 - y) / 2.0; |
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66 | y = -2 * sqrt (g); |
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67 | branch = 1; |
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68 | } |
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69 | else |
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70 | { |
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71 | i = flag; |
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72 | if (y < z_rooteps_f) |
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73 | res = y; |
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74 | else |
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75 | g = y * y; |
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76 | } |
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77 | |
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78 | if (y >= z_rooteps_f || branch == 1) |
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79 | { |
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80 | /* Calculate the Taylor series. */ |
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81 | P = (p[1] * g + p[0]) * g; |
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82 | Q = (g + q[1]) * g + q[0]; |
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83 | R = P / Q; |
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84 | |
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85 | res = y + y * R; |
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86 | } |
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87 | |
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88 | /* Calculate asine or acose. */ |
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89 | if (flag == 0) |
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90 | { |
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91 | res = (a[i] + res) + a[i]; |
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92 | if (x < 0.0) |
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93 | res = -res; |
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94 | } |
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95 | else |
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96 | { |
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97 | if (x < 0.0) |
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98 | res = (b[i] + res) + b[i]; |
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99 | else |
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100 | res = (a[i] - res) + a[i]; |
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101 | } |
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102 | |
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103 | return (res); |
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104 | } |
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