#!/usr/local/bin/bc -l

### SRR.BC - Sum of Repeated Roots (less one);
###          calculate the value of sum[n=1..oo] x^(2^(-n))-1

define srr(x) {
  auto s,t,os;
  if(x<=0){print "srr: Negative Infinity\n";return 1-A^scale}
  scale+=6
  s=x ; os=s+1
  t=0;while(os!=s){
    os=s
    s=sqrt(s)
    t+=s-1
  }
  scale-=6;t/=1
  return(t);
}

define srr_n(n,x) { # Generalisation of srr; srr(x) == srr_n(2,x)
  auto s,t,os;
  if(x<=0){print "srr_n: Negative Infinity\n";return 1-A^scale}
  if(n==2)return(srr(x))
  if(n<=1){print "srr_n: Infinity\n";return A^scale-1}
  scale+=6
  s=x ; os=s+1
  t=0;while(os!=s){
    os=s
    s=e(l(s)/n)
    t+=s-1
  }
  scale-=6;t/=1
  return(t);
}