Spigot

From Wiki

Algorithm

for(i=0;i<NUM;i++) a[i]=2;
for(loop=0;loop<DIGITS;loop++) {
	for(i=0;i<NUM;i++) a[i]*=10;
	for(i=NUM-1;i>=1;i--) {
		a[i]/(i*2+1)   ->   quotient,remainder
		a[i]=remainder;
		a[i-1]+=quotient*i;
	}
	output(a[0]/10);
	a[0]%=10;
}

Runthrough (NUM=10, DIGITS=3)

0	1	2	3	4	5	6	7	8	9	i
1	3	5	7	9	11	13	15	17	19	(i*2+1)
---------------------------------------------------------------------------
2	2	2	2	2	2	2	2	2	2	a
20	20	20	20	20	20	20	20	20	20	a
0	2	2	4	3	10	1	13	12	1	a
3
0	20	20	40	30	100	10	130	120	10	a
3	1	3	3	0	10	3	6	1	10	a
1
30	10	30	30	0	100	30	60	10	100	a
0	0	1	5	1	9	0	9	4	5	a
4

Sources

• Calculation of the Digits of π by the Spigot Algorithm of Rabinowitz and Wagon
• A Spigot Algorithm for the Digits of Pi