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60 lines
1.1 KiB
C
60 lines
1.1 KiB
C
#include "f2c.h"
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#undef abs
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#include "math.h"
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extern double f__cabs (double, double);
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void
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z_log (doublecomplex * r, doublecomplex * z)
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{
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double s, s0, t, t2, u, v;
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double zi = z->i, zr = z->r;
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r->i = atan2 (zi, zr);
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#ifdef Pre20000310
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r->r = log (f__cabs (zr, zi));
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#else
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if (zi < 0)
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zi = -zi;
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if (zr < 0)
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zr = -zr;
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if (zr < zi)
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{
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t = zi;
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zi = zr;
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zr = t;
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}
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t = zi / zr;
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s = zr * sqrt (1 + t * t);
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/* now s = f__cabs(zi,zr), and zr = |zr| >= |zi| = zi */
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if ((t = s - 1) < 0)
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t = -t;
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if (t > .01)
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r->r = log (s);
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else
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{
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#ifdef Comment
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log (1 + x) = x - x ^ 2 / 2 + x ^ 3 / 3 - x ^ 4 / 4 + -...
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= x (1 - x / 2 + x ^ 2 / 3 - +...)
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[sqrt (y ^ 2 + z ^ 2) - 1] *[sqrt (y ^ 2 + z ^ 2) + 1] =
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y ^ 2 + z ^ 2 - 1, so sqrt (y ^ 2 + z ^ 2) - 1 =
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(y ^ 2 + z ^ 2 - 1) /[sqrt (y ^ 2 + z ^ 2) + 1]
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#endif /*Comment */
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t = ((zr * zr - 1.) + zi * zi) / (s + 1);
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t2 = t * t;
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s = 1. - 0.5 * t;
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u = v = 1;
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do
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{
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s0 = s;
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u *= t2;
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v += 2;
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s += u / v - t * u / (v + 1);
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}
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while (s > s0);
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r->r = s * t;
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}
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#endif
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}
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