# Question about Fixnum **URL:** \ **Category:** Ruby\ **Created:** [April 13, 2007, 7:09pm UTC](https://www.ruby-forum.com/t/question-about-fixnum/91954 "2007-04-13T19:09:56Z")\ **Posts on this page:** 6\ **Page:** 1
**Author:** ![huang\_zhimin](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/h/54ee81/32.png) [@huang\_zhimin](https://www.ruby-forum.com/u/huang_zhimin)\ **Post date:** [April 13, 2007, 7:09pm UTC](https://www.ruby-forum.com/t/question-about-fixnum/91954/1 "2007-04-13T19:09:56Z")
Why the range of Fixnum is -2^30 ~ 2^30 rather than -2^31 ~2^31 ? ---
**Author:** ![huang\_zhimin](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/h/54ee81/32.png) [@huang\_zhimin](https://www.ruby-forum.com/u/huang_zhimin)\ **Post date:** [April 13, 2007, 7:12pm UTC](https://www.ruby-forum.com/t/question-about-fixnum/91954/2 "2007-04-13T19:12:57Z")
On 4/14/07, huang zhimin [removed\_email\_address@domain.invalid](mailto:removed_email_address@domain.invalid) wrote: > Why the range of Fixnum is -2^30 ~ 2^30 rather than -2^31 ~2^31 ? ``` ~~~~ should be ``` 2^30-1 ~~~~ 2^31-1 – ---
**Author:** ![huang\_zhimin](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/h/54ee81/32.png) [@huang\_zhimin](https://www.ruby-forum.com/u/huang_zhimin)\ **Post date:** [April 13, 2007, 7:33pm UTC](https://www.ruby-forum.com/t/question-about-fixnum/91954/3 "2007-04-13T19:33:59Z")
Because a bit is used to differentiate fixnums from other value types appearing in the same context, such as object pointers. A regular Ruby object has its own memory space which Ruby interpreter has access via a pointer. Allocating memory for each number is obviously too expensive, so Matz decided to store “small” numbers in a pointer itself. This is Fixnum. This means you have to distinguish a fixnum from a pointer somehow. The bit I mentioned is used for the purpose. LSB of a fixnum is set to 1 because an object pointer’s LSB is guaranteed to be 0 on a 32bit/64bit system. -Mak ---
**Author:** ![huang\_zhimin](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/h/54ee81/32.png) [@huang\_zhimin](https://www.ruby-forum.com/u/huang_zhimin)\ **Post date:** [April 13, 2007, 7:36pm UTC](https://www.ruby-forum.com/t/question-about-fixnum/91954/4 "2007-04-13T19:36:59Z")
On 4/13/07, huang zhimin [removed\_email\_address@domain.invalid](mailto:removed_email_address@domain.invalid) wrote: > Why the range of Fixnum is -2^30 ~ 2^30 rather than -2^31 ~2^31 ? > > – > removed\_email\_address@domain.invalid Fixnum objects are immediate objects in the Ruy source code (other immediate objects are nil, true, false, and symbols). These immediate objects occupy 4 bytes of storage (unsigned long) on most machines. They are accessed by casting and bit shifting in the Ruby source code. The other core types (String, Hash, Array, Object, Class, etc.) are structures and are accessed by pointer dereference. The sneaky part is that all these objects are referenced as VALUE types in the source code. The allocated structures are 4-byte aligned such that the bottom two bits will always be zero. If bit zero is set to 1, then you have a Fixnum. The consequence is that you have to right shift your Fixnum VALUE to get an integer, and hence, you loose one bit of precision for Fixnum. Read more here … [http://rhg.rubyforge.org/chapter02.html](http://rhg.rubyforge.org/chapter02.html). Scroll down to the secion on “Small Integers”. Blessings, TwP ---
**Author:** ![huang\_zhimin](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/h/54ee81/32.png) [@huang\_zhimin](https://www.ruby-forum.com/u/huang_zhimin)\ **Post date:** [April 13, 2007, 8:32pm UTC](https://www.ruby-forum.com/t/question-about-fixnum/91954/5 "2007-04-13T20:32:02Z")
On Apr 13, 2007, at 1:36 PM, Tim P. wrote: > Fixnum objects are immediate objects in the Ruy source code (other > immediate objects are nil, true, false, and symbols). These immediate > objects occupy 4 bytes of storage (unsigned long) on most machines. > They are accessed by casting and bit shifting in the Ruby source code. As long as you think of this description (‘immediate objects’) as entirely an implementation issue, I think it is useful. When you switch to talking about Ruby language semantics, I think it is better to simply think of Fixnum objects and references as the same as all other Ruby objects and references. Same for NilClass, FalseClass, and TrueClass. The differences are that the language provides literal representations of these references (-1,0,1,nil,false,true) and also ensures that object identity and object equivalence are the same for their respective classes (for example, #dup has no meaning for these objects and you can’t create new instances of NilClass, FalseClass, and TrueClass). Gary W. ---
**Author:** ![huang\_zhimin](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/h/54ee81/32.png) [@huang\_zhimin](https://www.ruby-forum.com/u/huang_zhimin)\ **Post date:** [April 14, 2007, 1:28am UTC](https://www.ruby-forum.com/t/question-about-fixnum/91954/6 "2007-04-14T01:28:36Z")
Hah! Much makes sense now. I was often curious as to why Fixnums’ object IDs are always equal to 2\*n+1; the ID is also the storage mechanism. Thanks for this. Harrison R.