1 | |
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2 | /* @(#)z_logarithm.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 | /* |
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11 | FUNCTION |
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12 | <<log>>, <<logf>>, <<log10>>, <<log10f>>, <<logarithm>>, <<logarithmf>>---natural or base 10 logarithms |
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13 | |
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14 | INDEX |
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15 | log |
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16 | INDEX |
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17 | logf |
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18 | INDEX |
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19 | log10 |
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20 | INDEX |
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21 | log10f |
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22 | |
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23 | SYNOPSIS |
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24 | #include <math.h> |
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25 | double log(double <[x]>); |
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26 | float logf(float <[x]>); |
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27 | double log10(double <[x]>); |
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28 | float log10f(float <[x]>); |
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29 | |
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30 | DESCRIPTION |
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31 | Return the natural or base 10 logarithm of <[x]>, that is, its logarithm base e |
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32 | (where e is the base of the natural system of logarithms, 2.71828@dots{}) or |
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33 | base 10. |
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34 | <<log>> and <<logf>> are identical save for the return and argument types. |
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35 | <<log10>> and <<log10f>> are identical save for the return and argument types. |
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36 | |
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37 | RETURNS |
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38 | Normally, returns the calculated value. When <[x]> is zero, the |
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39 | returned value is <<-HUGE_VAL>> and <<errno>> is set to <<ERANGE>>. |
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40 | When <[x]> is negative, the returned value is <<-HUGE_VAL>> and |
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41 | <<errno>> is set to <<EDOM>>. You can control the error behavior via |
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42 | <<matherr>>. |
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43 | |
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44 | PORTABILITY |
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45 | <<log>> is ANSI. <<logf>> is an extension. |
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46 | |
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47 | <<log10>> is ANSI. <<log10f>> is an extension. |
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48 | */ |
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49 | |
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50 | |
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51 | /****************************************************************** |
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52 | * Logarithm |
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53 | * |
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54 | * Input: |
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55 | * x - floating point value |
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56 | * ten - indicates base ten numbers |
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57 | * |
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58 | * Output: |
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59 | * logarithm of x |
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60 | * |
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61 | * Description: |
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62 | * This routine calculates logarithms. |
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63 | * |
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64 | *****************************************************************/ |
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65 | |
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66 | #include "fdlibm.h" |
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67 | #include "zmath.h" |
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68 | |
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69 | #ifndef _DOUBLE_IS_32BITS |
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70 | |
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71 | static const double a[] = { -0.64124943423745581147e+02, |
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72 | 0.16383943563021534222e+02, |
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73 | -0.78956112887481257267 }; |
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74 | static const double b[] = { -0.76949932108494879777e+03, |
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75 | 0.31203222091924532844e+03, |
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76 | -0.35667977739034646171e+02 }; |
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77 | static const double C1 = 22713.0 / 32768.0; |
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78 | static const double C2 = 1.428606820309417232e-06; |
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79 | static const double C3 = 0.43429448190325182765; |
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80 | |
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81 | double |
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82 | logarithm (double x, |
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83 | int ten) |
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84 | { |
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85 | int N; |
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86 | double f, w, z; |
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87 | |
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88 | /* Check for range and domain errors here. */ |
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89 | if (x == 0.0) |
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90 | { |
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91 | errno = ERANGE; |
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92 | return (-z_infinity.d); |
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93 | } |
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94 | else if (x < 0.0) |
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95 | { |
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96 | errno = EDOM; |
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97 | return (z_notanum.d); |
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98 | } |
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99 | else if (!isfinite(x)) |
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100 | { |
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101 | if (isnan(x)) |
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102 | return (z_notanum.d); |
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103 | else |
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104 | return (z_infinity.d); |
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105 | } |
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106 | |
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107 | /* Get the exponent and mantissa where x = f * 2^N. */ |
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108 | f = frexp (x, &N); |
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109 | |
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110 | z = f - 0.5; |
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111 | |
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112 | if (f > __SQRT_HALF) |
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113 | z = (z - 0.5) / (f * 0.5 + 0.5); |
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114 | else |
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115 | { |
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116 | N--; |
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117 | z /= (z * 0.5 + 0.5); |
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118 | } |
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119 | w = z * z; |
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120 | |
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121 | /* Use Newton's method with 4 terms. */ |
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122 | z += z * w * ((a[2] * w + a[1]) * w + a[0]) / (((w + b[2]) * w + b[1]) * w + b[0]); |
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123 | |
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124 | if (N != 0) |
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125 | z = (N * C2 + z) + N * C1; |
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126 | |
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127 | if (ten) |
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128 | z *= C3; |
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129 | |
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130 | return (z); |
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131 | } |
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132 | |
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133 | #endif /* _DOUBLE_IS_32BITS */ |
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