1 | /* origin: OpenBSD /usr/src/lib/libm/src/s_catan.c */
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2 | /*
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3 | * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
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4 | *
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5 | * Permission to use, copy, modify, and distribute this software for any
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6 | * purpose with or without fee is hereby granted, provided that the above
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7 | * copyright notice and this permission notice appear in all copies.
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8 | *
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9 | * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
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10 | * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
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11 | * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
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12 | * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
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13 | * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
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14 | * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
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15 | * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
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16 | */
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17 | /*
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18 | * Complex circular arc tangent
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19 | *
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20 | *
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21 | * SYNOPSIS:
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22 | *
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23 | * double complex catan();
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24 | * double complex z, w;
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25 | *
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26 | * w = catan (z);
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27 | *
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28 | *
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29 | * DESCRIPTION:
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30 | *
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31 | * If
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32 | * z = x + iy,
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33 | *
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34 | * then
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35 | * 1 ( 2x )
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36 | * Re w = - arctan(-----------) + k PI
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37 | * 2 ( 2 2)
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38 | * (1 - x - y )
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39 | *
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40 | * ( 2 2)
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41 | * 1 (x + (y+1) )
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42 | * Im w = - log(------------)
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43 | * 4 ( 2 2)
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44 | * (x + (y-1) )
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45 | *
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46 | * Where k is an arbitrary integer.
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47 | *
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48 | * catan(z) = -i catanh(iz).
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49 | *
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50 | * ACCURACY:
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51 | *
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52 | * Relative error:
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53 | * arithmetic domain # trials peak rms
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54 | * DEC -10,+10 5900 1.3e-16 7.8e-18
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55 | * IEEE -10,+10 30000 2.3e-15 8.5e-17
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56 | * The check catan( ctan(z) ) = z, with |x| and |y| < PI/2,
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57 | * had peak relative error 1.5e-16, rms relative error
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58 | * 2.9e-17. See also clog().
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59 | */
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60 |
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61 | #include "libm.h"
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62 |
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63 | #define MAXNUM 1.0e308
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64 |
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65 | static const double DP1 = 3.14159265160560607910E0;
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66 | static const double DP2 = 1.98418714791870343106E-9;
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67 | static const double DP3 = 1.14423774522196636802E-17;
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68 |
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69 | static double _redupi(double x)
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70 | {
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71 | double t;
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72 | long i;
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73 |
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74 | t = x/M_PI;
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75 | if (t >= 0.0)
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76 | t += 0.5;
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77 | else
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78 | t -= 0.5;
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79 |
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80 | i = t; /* the multiple */
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81 | t = i;
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82 | t = ((x - t * DP1) - t * DP2) - t * DP3;
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83 | return t;
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84 | }
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85 |
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86 | double complex catan(double complex z)
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87 | {
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88 | double complex w;
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89 | double a, t, x, x2, y;
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90 |
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91 | x = creal(z);
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92 | y = cimag(z);
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93 |
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94 | if (x == 0.0 && y > 1.0)
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95 | goto ovrf;
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96 |
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97 | x2 = x * x;
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98 | a = 1.0 - x2 - (y * y);
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99 | if (a == 0.0)
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100 | goto ovrf;
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101 |
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102 | t = 0.5 * atan2(2.0 * x, a);
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103 | w = _redupi(t);
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104 |
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105 | t = y - 1.0;
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106 | a = x2 + (t * t);
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107 | if (a == 0.0)
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108 | goto ovrf;
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109 |
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110 | t = y + 1.0;
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111 | a = (x2 + t * t)/a;
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112 | w = w + (0.25 * log(a)) * I;
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113 | return w;
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114 |
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115 | ovrf:
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116 | // FIXME
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117 | w = MAXNUM + MAXNUM * I;
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118 | return w;
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119 | }
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