>>12656803An interesting new method was recently proposed by David Bailey, Peter Borwein and Simon Plouffe. It can compute the Nth hexadecimal digit of Pi efficiently without the previous N-1 digits. The method is based on the formula:
pi = sum_(i = 0)^oo (1 16^i) ((4 8i + 1) - (2 8i + 4) - (1 8i + 5) - (1 8i + 6))
in O(N) time and O(log N) space. (See references.)
The following 160 character C program, written by Dik T. Winter at CWI, computes pi to 800 decimal digits.
int a=10000,b,c=2800,d,e,f[2801],g;main(){for(;b-c;)f[b++]=a/5;
for(;d=0,g=c*2;c-=14,printf("%.4d",e+d/a),e=d%a)for(b=c;d+=f
*a,
f=d%--g,d/=g--,--b;d*=b);}
https://cs.uwaterloo.ca/~alopez-o/math-faq/mathtext/node12.html 
