[352] | 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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