// Integrating -log(1-x)/x once around branch point at 1.
#include <stdio.h>
#include <stdlib.h>
#include <complex.h>
#include <math.h>
typedef double _Complex C;
typedef double R;

static R  sq(R x){return x*x;}
static R m2(C x){return sq(creal(x)) + sq(cimag(x));}
static void pc(C a){printf("%20.16f + %19.16fi\n", creal(a),  cimag(a));}
C c(R x, R y){C a; __real__ a = x; __imag__ a = y; return a;}
static R const tp = 2*3.141592653589793238;
static int const N = 100000;
static C mem;
C ln(C z){
static int n = 0;
if(m2(z - mem) > 0.001) {pc(z); pc(mem); exit(printf("ouch\n"));}
if(creal(z) < 0 && (cimag(z)<0) != (cimag(mem)<0)) n += cimag(z)<0?1:-1;
mem = z; return clog(z) + c(0, n*tp);}
int main(){mem = 1;
if(0) {printf("ln(-1+0.01i) = "); pc(clog(-1+0.01i));
  printf("ln(-1-0.01i) = "); pc(clog(-1-0.01i));
  {int j; for(j=0; j<400; ++j) {R t = -0.01*j; C v = ln(c(cos(t), sin(t)));
    if(j>300) {printf("%d", j); pc(v);}}}}
else {C s = 0; int j; for(j=0; j<N; ++j) {R t = (j+0.5)*tp/N;
   C cis = c(cos(t), sin(t)), z = 1 - cis, v = -ln(1-z)/z;
   s += v*c(cimag(cis), -creal(cis));
   if(!(j%1000)) {printf("j=%7d\n", j); pc(z); pc(v); pc(s/N);}}
   printf("I = "); pc(s/N);}
  return 0;}


// http://en.wikipedia.org/wiki/Branch_point