64 lines
1.1 KiB
C
64 lines
1.1 KiB
C
#include "f2c.h"
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#ifdef KR_headers
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double log(), f__cabs(), atan2();
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VOID z_log(r, z) doublecomplex *r, *z;
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#else
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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 z_log(doublecomplex *r, doublecomplex *z)
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#endif
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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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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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#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] = y^2 + z^2 - 1, so
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sqrt(y^2 + z^2) - 1 = (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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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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} 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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