Ruby

The new Integer.sqrt method produces wrong results, e.g. for

38815036599065022652481536 38904514499428047971680256 

and (many) other numbers.

Note that these numbers were picked selectively (these are not the 2 smallest examples), and also that they are well in the range where Math.sqrt(n).to_i still gives correct results (Float precision still sufficient). However, the latter point is only incidental, I also found much bigger examples, in the range where Math.sqrt is useless.

numbers = [ 38815036599065022652481534, 38815036599065022652481535, 38815036599065022652481536, # fails 38815036599065022652481537, # fails 38904514499428047971680254, 38904514499428047971680255, 38904514499428047971680256, # fails 38904514499428047971680257, # fails 40271703432545948091285502, 40271703432545948091285503, 40271703432545948091285504, # fails 40271703432545948091285505, # fails 1442115351524865087017488818362939538217338142719, 1442115351524865087017488818362939538217338142720, # fails ] def validate(number, root) root**2 <= number && (root+1)**2 > number end numbers.map {|n| [Integer.sqrt(n), validate(n, Integer.sqrt(n))] } # => [[6230171474290, true], # [6230171474290, true], # [6230171582464, false], # [6230171582464, false], # [6237348354824, true], # [6237348354824, true], # [6237348429824, false], # [6237348429824, false], # [6345999009812, true], # [6345999009812, true], # [6345999122432, false], # [6345999122432, false], # [1200881073014669961418100, true], # [1200881075629054276665344, false]] numbers.map {|n| [Math.sqrt(n).to_i, validate(n, Math.sqrt(n).to_i)] } # => [[6230171474290, true], # [6230171474290, true], # [6230171474290, true], # [6230171474290, true], # [6237348354824, true], # [6237348354824, true], # [6237348354824, true], # [6237348354824, true], # [6345999009812, true], # [6345999009812, true], # [6345999009812, true], # [6345999009812, true], # [1200881073014669968408576, false], # [1200881073014669968408576, false]] 1.size # => 4 (32-bit system) 

Interestingly, I found only examples (yet) where Integer.sqrt produces results that are (much) too big.

It was rather too easy to find those; here's what I did:

too_big, too_small = [], [] total = 0 0.step(to: 50, by: 0.001) do |i| n = (10**i).to_i raise unless n.class == Integer # just to make sure... int_root = Integer.sqrt(n) total += 1 too_big << n if int_root*int_root > n too_small << n if (int_root+1)*(int_root+1) <= n end puts "total: #{total}" puts puts "too small (#{too_small.size}):", too_small puts puts "too big (#{too_big.size}):" puts too_big[0..9] puts "..." puts too_big[-10..-1] # >> total: 50001 # >>  # >> too small (0): # >>  # >> too big (3579): # >> 38815036599065022652481536 # >> 38904514499428047971680256 # >> 38994198667654436652843008 # >> 39810717055349854497144832 # >> 40271703432545948091285504 # >> 40364539296760648765014016 # >> 40457589169744204087164928 # >> 40644332916521443952427008 # >> 40926065973001261821198336 # >> 42169650342858222399913984 # >> ... # >> 1324341535194664238462783233069825155347351863296 # >> 1367728825595857894544027656111101204949201059840 # >> 1370881766164855075247880701478883966489888555008 # >> 1409288798421877644341184857286932334307738386432 # >> 1412537544622749693814622477014802231398687047680 # >> 1415793779957092451680042925874609046246970621952 # >> 1422328787122815537257372883177955123216529752064 # >> 1432187899273539462185319204962288499459270639616 # >> 1438798578255849634982033297755877609401625870336 # >> 1442115351524865087017488818362939538217338142720