I met this problem when I tried to compute 3**557 in irb. Ruby and MacRuby both are installed in my Mac (OS X 10.8). And the version of ruby is 1.8.7, of MacRuby 0.12 (ruby 1.9.2). rib and macirb gave me two different answers on computation of 3**557. (macirb's is right.)
$ irb
>> 3**557
=> 54755702179342762063551440788945541007926808765326951193810107165429610423703291760740244724326099993131913104272587572918520442872536889724676586931200965615875242243330408150984753872526006744122187638040962508934109837755428764447134683114539218909666971979603
$ macirb
irb(main):001:0> 3**557
=> 57087217942658063217290581978966727348872586279944803346410228520919738045995056049600505293676159316424182057188730248707922985741467061108015301244570536546607487919981026877250949414156613856336341922395385463291076789878575326012378057561766997352898452974964563
And then I tried something bigger, e.g. 3**5337, and I got the same answer this time.
So, is this a bug in Ruby 1.8.7, or I should use another way to compute exponentiation?
When calculating, Ruby is supposed to convert from Fixnum to Bignum when the numbers go beyond the bounds of Fixnum. For older versions of Ruby, this fails with the ** operator:
$ ruby --version
ruby 1.8.7 (2012-02-08 patchlevel 358) [universal-darwin12.0]
$ irb
>> 2 ** 62
=> 4611686018427387904
>> 2 ** 63
=> -9223372036854775808
>> 2 ** 64
=> 0
Where it fails depends on the word size of the architecture. 64-bit words on the iMac in this example. Internally, the Fixnum is cast to a long integer, and the operator is handled with longs. The longs overflow at word size, and Ruby is ungracefully handling this by returning 0.
Note that the * operator works correctly (converting to Bignum), where the ** fails:
>> a = 2 ** 62
=> 4611686018427387904
>> 2 ** 63
=> -9223372036854775808
>> a * 2
=> 9223372036854775808
>> 2 ** 64
=> 0
>> a * 4
=> 18446744073709551616
Moving to a newer version of Ruby will fix this. If you can't move to a newer version, then avoid using Fixnum and ** with large powers.