blob: f56b12ed7e3957761ea41926baa8d5286c3e71f3 [file] [log] [blame]
 #include "f2c.h" #undef abs #include "math.h" extern double f__cabs (double, double); void z_log (doublecomplex * r, doublecomplex * z) { double s, s0, t, t2, u, v; double zi = z->i, zr = z->r; r->i = atan2 (zi, zr); #ifdef Pre20000310 r->r = log (f__cabs (zr, zi)); #else if (zi < 0) zi = -zi; if (zr < 0) zr = -zr; if (zr < zi) { t = zi; zi = zr; zr = t; } t = zi / zr; s = zr * sqrt (1 + t * t); /* now s = f__cabs(zi,zr), and zr = |zr| >= |zi| = zi */ if ((t = s - 1) < 0) t = -t; if (t > .01) r->r = log (s); else { #ifdef Comment log (1 + x) = x - x ^ 2 / 2 + x ^ 3 / 3 - x ^ 4 / 4 + -... = x (1 - x / 2 + x ^ 2 / 3 - +...) [sqrt (y ^ 2 + z ^ 2) - 1] *[sqrt (y ^ 2 + z ^ 2) + 1] = y ^ 2 + z ^ 2 - 1, so sqrt (y ^ 2 + z ^ 2) - 1 = (y ^ 2 + z ^ 2 - 1) /[sqrt (y ^ 2 + z ^ 2) + 1] #endif /*Comment */ t = ((zr * zr - 1.) + zi * zi) / (s + 1); t2 = t * t; s = 1. - 0.5 * t; u = v = 1; do { s0 = s; u *= t2; v += 2; s += u / v - t * u / (v + 1); } while (s > s0); r->r = s * t; } #endif }