/*
  Author:  Pate Williams (c) 1997

  "Exercise 2.1. Computing li x.
  Write a function li(x) for li x, utilizing the
  continued fraction expansion
  li(exp(z)) = exp(z) / z - 1 / 1 - 1 / z - ...
  Compute the continued fraction backwards,
  starting with the term 10 / z. Test values can
  be found in Table 3 (compute li x as pi(x)
  + (li x - pi(x))." -Hans Riesel-
  See "Primes Numbers and Computer Methods for
  Factorization" by Hans Riesel second edition
  page 43.
*/

#include <math.h>
#include <stdio.h>

#define SIZE 256

double li(long x)
{
  double A0, A1, Am1, B0, B1, Bm1, z = log(x);
  double a[SIZE], b[SIZE];
  long i, i2;

  a[1] = x;
  for (i = 1; i <= 10; i++) {
    i2 = 2 * i;
    a[i2] = - i;
    a[i2 + 1] = - i;
  }
  for (i = 1; i <= 21; i += 2) b[i] = z;
  for (i = 2; i <= 22; i += 2) b[i] = 1;
  Am1 = 1;
  A0 = 0;
  B0 = 1;
  Bm1 = 0;
  for (i = 1; i <= 20; i++) {
    A1 = b[i] * A0 + a[i] * Am1;
    B1 = b[i] * B0 + a[i] * Bm1;
    Am1 = A0;
    Bm1 = B0;
    A0 = A1;
    B0 = B1;
  }
  return A1 / B1;
}

int main(void)
{
  long x;

  printf("x = ");
  scanf("%ld", &x);
  printf("li %ld = %lf\n", x, li(x));
  return 0;
}