#include <complex.h>
#include <stdio.h>
#include <math.h>
typedef double _Complex C;
typedef double R;

static R  sq(R x){return x*x;}
static C csq(C x){return x*x;}
static R m2(C x){return sq(creal(x)) + sq(cimag(x));}
static int t(C x){return fabs(creal(x)) < 1.e-16 && fabs(cimag(x)) < 1.e-16;}
static R const pi = 3.141592653589793238, p2 = pi*pi;
static void pc(C a){printf("%19.16f + %19.16fi\n", creal(a),  cimag(a));}
int wrk, wrkD;
C dilog(C z){R r = m2(z);
  if(r > 1) {C r = 1/z; return - dilog(r) - p2/6 - 0.5*csq(clog(-r));}
  if(creal(z) > 0.6) return - dilog(1-z) + p2/6 - (z==1?0:clog(1-z)*clog(z));
  if(r > 0.4) if(creal(z) < 0.15) return -dilog(z/(z-1))-0.5*csq(clog(1-z));
              else return 0.5*dilog(z*z) - dilog(-z);
  if(m2(z + 0.268) < 0.0049){C s = 0; C w = z; R a = 1, b = 3;
     while(1) {C T = w/a; s += T; ++wrk; if(t(T)) break; w *= z; a += b; b += 2;}
     return s;}
 {C z2=z*z, s = z + 1.4375*z2 + 0.75*(1-z2)*clog(1-z), f = z*z2; R J=6, K=18, L=18;
    while(1){C a = f/(J*J); s+=a; ++wrk; if(t(a)) break; f *= z; J+=K; K+=L; L+=6;}
    return 4*s/(1+4*z+z2);}}

C dilogD(C z){long double _Complex s = 0; C w = z; R a = 1, b = 3;
  if(m2(z)>1) {C r = 1/z; return - dilogD(r) - p2/6 - 0.5*csq(clog(-r));}
  while(1) {C T = w/a; s += T; ++wrkD; if(t(T)) break; w *= z; a += b; b += 2;}
  return s;}

void pr(R a, char * m){printf("%19.16f %s\n", a, m);}
void tst(C z, R v, char * m){pc(z); pr(v, m); wrkD=0; pc(dilogD(z));
  wrk=0; pc(dilog(z)); printf("w=%9d %4d\n", wrkD, wrk);}
C c(R x, R y){C a; __real__ a = x; __imag__ a = y; return a;}
int main(){if (1) { // Ad-hoc tests
  R r5 = sqrt(5), v = sq(log((1+r5)/2));
  printf("Three functional equations corroborated:\n");
  {C z = -1.27-0.93i; tst(1/z, 0, "rel1"); pc(-dilog(z) - p2/6 - 0.5*csq(clog(-z)));}
  {C z = 0.162+0.13i; tst(1-z, 0, "rel2"); pc(-dilog(z) + p2/6 - clog(z)*clog(1-z));}
  {C z = -0.9+0.12i; tst(z, 0, "xx"); pc(-dilogD(z/(z-1))-0.5*csq(clog(1-z)));}
  printf("Mostly known values for increasing argments on the real line:\n");
  tst(-(r5+1)/2, -p2/10 - v, "-(r5+1)/2");
  tst(-(r5+1)/2, -p2/15 + sq(log((r5-1)/2))/2, "-(r5+1)/2 W");
  tst(-(r5+1)/2, -p2/10 + v/2, "-(r5+1)/2 W"); // note to Zagier
  tst(-1, -p2/12., "-1");
  tst((1-r5)/2, -p2/15 + v/2, "(1-r5)/2");
  tst(-0.269, 0, "-0.269");
  tst(-0.268, 0, "-0.268");
  tst(0, 0, "0");
  tst((3-r5)/2, p2/15 - v, "(3-r5)/2");
  tst(0.5, p2/12 - sq(log(2))/2., "1/2");
  tst((r5-1)/2, p2/10 - v, "(r5-1)/2");
  tst(0.89999, 0, "0.89999");
  tst(0.90001, 0, "0.90001");
  tst(0.99999, 0, ".99999"); // only three digits!!
  tst(1, p2/6, "1"); // note peculiar error in 8th digit.
  tst((r5+1)/2, (11*p2)/15 - v/2, "(r5+1)/2 W"); // note to W polylog
  tst(2, 0, "2");
  tst((r5+3)/2, -(11*p2)/15 - v, "(r5+3)/2 W"); // note to W polylog
  printf("Some ad-hoc probes\n");

  printf("Li2(2) = \n"); pc(dilog(2)); pc(p2/4+(0.+1i)*pi*log(2));
  tst(c( 0.5, sqrt(3)/2), 0, "c(0.5, sqrt(3)/2)");
  tst(c(-0.5, sqrt(3)/2), 0, "c(-0.5, sqrt(3)/2)");
  tst(csqrt(c(0.5, sqrt(3)/2)), 0, "csqrt(c(0.5, sqrt(3)/2))");
  tst(0+0.5i, 0, "0+0.5i");
  tst(0+1.i, 0, "0+1.i");
  tst(0.23-0.4i, 0, "0.23-0.4i");
  tst(2.+3i, 0, "2.+3i");
  tst(0.5+0.8660254037844386i, 0, "0.5+0.8660254037844386i");
  tst(0.999+0.001i, 0, "0.999+0.001i");
  tst(0.999-0.001i, 0, "0.999-0.001i");
  tst(1.001+0.001i, 0, "1.001+0.001i");
  tst(1.001-0.001i, 0, "1.001-0.001i");
  tst(0.11+0.9i, 0, "0.11+0.9i");}
  else {C pa; int tc = 0, tw=0; 
  R x = -1.01; while(x < 1.011) {R y = -0.02; while (y < 1.011){
    wrk = 0; dilog(c(x, y)); if(wrk > tc) {pa = c(x, y); tc = wrk;}
      tw += wrk; y += 0.001;} x += 0.001;}
  printf("Max count, tw = %d, %5.2f\n", tc, tw/2083651.); pc(pa);}
return 0;}

/*
Three functional equations corroborated:
-0.5125514569376060 +  0.3753329566550972i
 0.0000000000000000 rel1
-0.4783427691711131 +  0.3007754948400878i
-0.4783427691711135 +  0.3007754948400879i
w=       63   19
-0.4783427691711135 +  0.3007754948400879i
 0.8380000000000000 + -0.1300000000000000i
 0.0000000000000000 rel2
 1.1180086749729419 + -0.2718669089150707i
 1.1180086749729423 + -0.2718669089150709i
w=      162   12
 1.1180086749729423 + -0.2718669089150709i
-0.9000000000000000 +  0.1200000000000000i
 0.0000000000000000 xx
-0.7536563997933813 +  0.0855363530169917i
-0.7536563997933812 +  0.0855363530169917i
w=      265   23
-0.7536563997933813 +  0.0855363530169917i
Mostly known values for increasing argments on the real line:
-1.6180339887498949 +  0.0000000000000000i
-1.2185252606861301 -(r5+1)/2
-1.2185252606861301 + -0.0000000000000000i
-1.2185252606861305 +  0.0000000000000000i
w=       60   32
-1.6180339887498949 +  0.0000000000000000i
-0.5421912164506933 -(r5+1)/2 W
-1.2185252606861301 + -0.0000000000000000i
-1.2185252606861305 +  0.0000000000000000i
w=       60   32
-1.6180339887498949 +  0.0000000000000000i
-0.8711780298203387 -(r5+1)/2 W
-1.2185252606861301 + -0.0000000000000000i
-1.2185252606861305 +  0.0000000000000000i
w=       60   32
-1.0000000000000000 +  0.0000000000000000i
-0.8224670334241132 -1
-0.8224670334241133 +  0.0000000000000000i
-0.8224670334241131 + -0.0000000000000000i
w=100000001   24
-0.6180339887498949 +  0.0000000000000000i
-0.5421912164506932 (1-r5)/2
-0.5421912164506933 +  0.0000000000000000i
-0.5421912164506930 + -0.0000000000000000i
w=       60   32
-0.2690000000000000 +  0.0000000000000000i
 0.0000000000000000 -0.269
-0.2527928250522439 +  0.0000000000000000i
-0.2527928250522439 +  0.0000000000000000i
w=       24   24
-0.2680000000000000 +  0.0000000000000000i
 0.0000000000000000 -0.268
-0.2519070332294852 +  0.0000000000000000i
-0.2519070332294851 +  0.0000000000000000i
w=       24   24
 0.0000000000000000 +  0.0000000000000000i
 0.0000000000000000 0
 0.0000000000000000 +  0.0000000000000000i
 0.0000000000000000 +  0.0000000000000000i
w=        1    1
 0.3819660112501051 +  0.0000000000000000i
 0.4264088061620961 (3-r5)/2
 0.4264088061620961 +  0.0000000000000000i
 0.4264088061620960 +  0.0000000000000000i
w=       32   18
 0.5000000000000000 +  0.0000000000000000i
 0.5822405264650126 1/2
 0.5822405264650125 +  0.0000000000000000i
 0.5822405264650123 +  0.0000000000000000i
w=       43   24
 0.6180339887498949 +  0.0000000000000000i
 0.7553956195317414 (r5-1)/2
 0.7553956195317414 +  0.0000000000000000i
 0.7553956195317415 +  0.0000000000000000i
w=       60   18
 0.8999900000000000 +  0.0000000000000000i
 0.0000000000000000 0.89999
 1.2996891391395520 +  0.0000000000000000i
 1.2996891391395529 +  0.0000000000000000i
w=      246    9
 0.9000100000000000 +  0.0000000000000000i
 0.0000000000000000 0.90001
 1.2997403076972049 +  0.0000000000000000i
 1.2997403076972058 +  0.0000000000000000i
w=      246    9
 0.9999900000000000 +  0.0000000000000000i
 0.0000000000000000 .99999
 1.6448089369845762 +  0.0000000000000000i
 1.6448089369929271 +  0.0000000000000000i
w=   934565    1
 1.0000000000000000 +  0.0000000000000000i
 1.6449340668482264 1
 1.6449340568482267 +  0.0000000000000000i
 1.6449340668482264 +  0.0000000000000000i
w=100000001    1
 1.6180339887498949 +  0.0000000000000000i
 7.1219274838435984 (r5+1)/2 W
 2.4186901038761142 + -1.5117715344277867i
 2.4186901038761137 + -1.5117715344277867i
w=       60   18
 2.0000000000000000 +  0.0000000000000000i
 0.0000000000000000 2
 2.4674011002723399 + -2.1775860903036022i
 2.4674011002723399 + -2.1775860903036022i
w=       43   24
 2.6180339887498949 +  0.0000000000000000i
-7.4692747147093899 (r5+3)/2 W
 2.4003296863799677 + -3.0235430688555738i
 2.4003296863799677 + -3.0235430688555738i
w=       32   18
Some ad-hoc probes
Li2(2) = 
 2.4674011002723399 + -2.1775860903036022i
 2.4674011002723395 +  2.1775860903036022i
 0.5000000000000000 +  0.8660254037844386i
 0.0000000000000000 c(0.5, sqrt(3)/2)
 0.2741556778080378 +  1.0149416064096535i
 0.2741556778080378 +  1.0149416064096535i
w= 93060487   58
-0.5000000000000000 +  0.8660254037844386i
 0.0000000000000000 c(-0.5, sqrt(3)/2)
-0.5483113556160755 +  0.6766277376064358i
-0.5483113556160755 +  0.6766277376064358i
w= 93060487   29
 0.8660254037844386 +  0.5000000000000000i
 0.0000000000000000 csqrt(c(0.5, sqrt(3)/2))
 0.8910059528761225 +  0.8643791310538929i
 0.8910059528761227 +  0.8643791310538929i
w= 93060487   25
 0.0000000000000000 +  0.5000000000000000i
 0.0000000000000000 0+0.5i
-0.0589750744215659 +  0.4872223582945224i
-0.0589750744215659 +  0.4872223582945226i
w=       43   24
 0.0000000000000000 +  1.0000000000000000i
 0.0000000000000000 0+1.i
-0.2056167583560283 +  0.9159655941772190i
-0.2056167583560283 +  0.9159655941772193i
w=100000001   45
 0.2300000000000000 + -0.4000000000000000i
 0.0000000000000000 0.23-0.4i
 0.1916195524960158 + -0.4428626779408241i
 0.1916195524960156 + -0.4428626779408241i
w=       38   22
 2.0000000000000000 +  3.0000000000000000i
 0.0000000000000000 2.+3i
-0.2809880553780608 +  3.0172512063694064i
-0.2809880553780608 +  3.0172512063694064i
w=       24   15
 0.5000000000000000 +  0.8660254037844386i
 0.0000000000000000 0.5+0.8660254037844386i
 0.2741556778080378 +  1.0149416064096535i
 0.2741556778080378 +  1.0149416064096535i
w= 93060487   58
 0.9990000000000000 +  0.0010000000000000i
 0.0000000000000000 0.999+0.001i
 1.6365867056774774 +  0.0067828498277630i
 1.6365867056775252 +  0.0067828498277161i
w=    17321    3
 0.9990000000000000 + -0.0010000000000000i
 0.0000000000000000 0.999-0.001i
 1.6365867056774774 + -0.0067828498277630i
 1.6365867056775252 + -0.0067828498277161i
w=    17321    3
 1.0009999999999999 +  0.0010000000000000i
 0.0000000000000000 1.001+0.001i
 1.6501414040809399 +  0.0099103180251496i
 1.6501414040808937 +  0.0099103180251011i
w=    17322    3
 1.0009999999999999 + -0.0010000000000000i
 0.0000000000000000 1.001-0.001i
 1.6501414040809399 + -0.0099103180251496i
 1.6501414040808937 + -0.0099103180251011i
w=    17322    3
 0.1100000000000000 +  0.9000000000000000i
 0.0000000000000000 0.11+0.9i
-0.0810971714351589 +  0.8740867676634512i
-0.0810971714351590 +  0.8740867676634509i
w=      262   47
*/