1 | /* origin: OpenBSD /usr/src/lib/libm/src/s_catanl.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 | * long double complex catanl();
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24 | * long double complex z, w;
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25 | *
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26 | * w = catanl( 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 | *
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49 | * ACCURACY:
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50 | *
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51 | * Relative error:
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52 | * arithmetic domain # trials peak rms
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53 | * DEC -10,+10 5900 1.3e-16 7.8e-18
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54 | * IEEE -10,+10 30000 2.3e-15 8.5e-17
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55 | * The check catan( ctan(z) ) = z, with |x| and |y| < PI/2,
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56 | * had peak relative error 1.5e-16, rms relative error
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57 | * 2.9e-17. See also clog().
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58 | */
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59 |
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60 | #include <complex.h>
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61 | #include <float.h>
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62 | #include "libm.h"
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63 |
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64 | #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
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65 | long double complex catanl(long double complex z)
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66 | {
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67 | return catan(z);
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68 | }
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69 | #else
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70 | static const long double PIL = 3.141592653589793238462643383279502884197169L;
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71 | static const long double DP1 = 3.14159265358979323829596852490908531763125L;
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72 | static const long double DP2 = 1.6667485837041756656403424829301998703007e-19L;
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73 | static const long double DP3 = 1.8830410776607851167459095484560349402753e-39L;
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74 |
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75 | static long double redupil(long double x)
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76 | {
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77 | long double t;
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78 | long i;
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79 |
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80 | t = x / PIL;
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81 | if (t >= 0.0L)
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82 | t += 0.5L;
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83 | else
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84 | t -= 0.5L;
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85 |
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86 | i = t; /* the multiple */
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87 | t = i;
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88 | t = ((x - t * DP1) - t * DP2) - t * DP3;
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89 | return t;
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90 | }
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91 |
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92 | long double complex catanl(long double complex z)
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93 | {
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94 | long double complex w;
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95 | long double a, t, x, x2, y;
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96 |
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97 | x = creall(z);
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98 | y = cimagl(z);
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99 |
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100 | if ((x == 0.0L) && (y > 1.0L))
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101 | goto ovrf;
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102 |
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103 | x2 = x * x;
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104 | a = 1.0L - x2 - (y * y);
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105 | if (a == 0.0L)
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106 | goto ovrf;
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107 |
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108 | t = atan2l(2.0L * x, a) * 0.5L;
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109 | w = redupil(t);
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110 |
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111 | t = y - 1.0L;
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112 | a = x2 + (t * t);
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113 | if (a == 0.0L)
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114 | goto ovrf;
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115 |
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116 | t = y + 1.0L;
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117 | a = (x2 + (t * t)) / a;
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118 | w = w + (0.25L * logl(a)) * I;
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119 | return w;
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120 |
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121 | ovrf:
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122 | // FIXME
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123 | w = LDBL_MAX + LDBL_MAX * I;
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124 | return w;
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125 | }
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126 | #endif
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