# Janet numbers are "doubles" representing each int up to 2^53 (9007199254740992) # Above this, they can't, so these both eval to the same thing! (math/exp2 53) (+ 1 (math/exp2 53)) # After 2^53, doubles only represent even numbers # Janet prints numbers above 2^53 in exponent form, hiding the end (+ 2 (math/exp2 53)) # 9.00719925474099e+15 # But the odd numbers round interestingly! # 2^53 + 2, 2^53 + 4 etc. are slots. We choose which to round e.g. 2^53 + 3 into. # In school, we round .5 up, doubles above 2^53 round .5 to the neighbor divisible by 4! (def p53 (math/exp2 53)) (= (+ p53 1) p53) # true (= (+ p53 2) p53) # false (= (+ p53 1) (+ p53 2)) # false (= (+ p53 3) (+ p53 2)) # false (= (+ p53 3) (+ p53 4)) # true (= (+ p53 5) (+ p53 4)) # true (= (+ p53 5) (+ p53 6)) # false (= (+ p53 7) (+ p53 8)) # true (= (+ p53 9) (+ p53 8)) # true # After 2^54, it's the neighbor divisible by 8. # After 2^55, it's the neighbor divisible by 16! # It continues this way until 2^1024, which overflows to infinity (= math/inf (math/exp2 1024)) # true