1 | |
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2 | /* @(#)z_sqrt.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 | <<sqrt>>, <<sqrtf>>---positive square root |
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13 | |
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14 | INDEX |
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15 | sqrt |
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16 | INDEX |
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17 | sqrtf |
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18 | |
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19 | SYNOPSIS |
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20 | #include <math.h> |
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21 | double sqrt(double <[x]>); |
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22 | float sqrtf(float <[x]>); |
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23 | |
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24 | DESCRIPTION |
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25 | <<sqrt>> computes the positive square root of the argument. |
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26 | |
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27 | RETURNS |
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28 | On success, the square root is returned. If <[x]> is real and |
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29 | positive, then the result is positive. If <[x]> is real and |
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30 | negative, the global value <<errno>> is set to <<EDOM>> (domain error). |
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31 | |
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32 | |
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33 | PORTABILITY |
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34 | <<sqrt>> is ANSI C. <<sqrtf>> is an extension. |
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35 | */ |
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36 | |
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37 | /****************************************************************** |
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38 | * Square Root |
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39 | * |
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40 | * Input: |
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41 | * x - floating point value |
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42 | * |
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43 | * Output: |
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44 | * square-root of x |
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45 | * |
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46 | * Description: |
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47 | * This routine performs floating point square root. |
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48 | * |
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49 | * The initial approximation is computed as |
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50 | * y0 = 0.41731 + 0.59016 * f |
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51 | * where f is a fraction such that x = f * 2^exp. |
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52 | * |
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53 | * Three Newton iterations in the form of Heron's formula |
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54 | * are then performed to obtain the final value: |
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55 | * y[i] = (y[i-1] + f / y[i-1]) / 2, i = 1, 2, 3. |
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56 | * |
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57 | *****************************************************************/ |
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58 | |
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59 | #include "fdlibm.h" |
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60 | #include "zmath.h" |
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61 | |
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62 | #ifndef _DOUBLE_IS_32BITS |
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63 | |
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64 | double |
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65 | sqrt (double x) |
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66 | { |
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67 | double f, y; |
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68 | int exp, i, odd; |
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69 | |
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70 | /* Check for special values. */ |
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71 | switch (numtest (x)) |
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72 | { |
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73 | case NAN: |
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74 | errno = EDOM; |
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75 | return (x); |
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76 | case INF: |
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77 | if (ispos (x)) |
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78 | { |
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79 | errno = EDOM; |
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80 | return (z_notanum.d); |
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81 | } |
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82 | else |
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83 | { |
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84 | errno = ERANGE; |
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85 | return (z_infinity.d); |
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86 | } |
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87 | } |
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88 | |
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89 | /* Initial checks are performed here. */ |
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90 | if (x == 0.0) |
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91 | return (0.0); |
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92 | if (x < 0) |
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93 | { |
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94 | errno = EDOM; |
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95 | return (z_notanum.d); |
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96 | } |
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97 | |
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98 | /* Find the exponent and mantissa for the form x = f * 2^exp. */ |
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99 | f = frexp (x, &exp); |
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100 | |
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101 | odd = exp & 1; |
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102 | |
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103 | /* Get the initial approximation. */ |
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104 | y = 0.41731 + 0.59016 * f; |
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105 | |
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106 | f /= 2.0; |
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107 | /* Calculate the remaining iterations. */ |
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108 | for (i = 0; i < 3; ++i) |
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109 | y = y / 2.0 + f / y; |
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110 | |
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111 | /* Calculate the final value. */ |
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112 | if (odd) |
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113 | { |
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114 | y *= __SQRT_HALF; |
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115 | exp++; |
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116 | } |
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117 | exp >>= 1; |
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118 | y = ldexp (y, exp); |
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119 | |
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120 | return (y); |
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121 | } |
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122 | |
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123 | #endif /* _DOUBLE_IS_32BITS */ |
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