nth_digit_of_fraction.sf

#!/usr/bin/ruby

# An efficient formula for computing the n-th decimal digit of a given fraction expression x/y.

# Formula from:
#   https://stackoverflow.com/questions/804934/getting-a-specific-digit-from-a-ratio-expansion-in-any-base-nth-digit-of-x-y

# See also:
#   https://projecteuler.net/problem=820

func nth_digit_of_fraction(n,x,y,base=10) {
     idiv(base * powmod(base, n-1, y) * x, y) % base
}

say sum(1..7, {|k| nth_digit_of_fraction(7, 1, k) })        #=> 10
say sum(1..100, {|k| nth_digit_of_fraction(100, 1, k) })    #=> 418

assert_eq(nth_digit_of_fraction(5, 13, 7, 5), 3)
assert_eq(nth_digit_of_fraction(6, 13, 7, 5), 2)
assert_eq(nth_digit_of_fraction(7, 13, 7, 5), 4)
assert_eq(nth_digit_of_fraction(8, 13, 7, 5), 1)