# Programming Ruby ### The Pragmatic Programmer's Guide
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class Bignum |
Parent: | Integer
Version: | 1.6

### Index:

Arithmetic operations Bit operations <=> [ ] size to_f to_i to_s

`Bignum` objects hold integers outside the range of `Fixnum`. `Bignum` objects are created automatically when integer calculations would otherwise overflow a `Fixnum`. When a calculation involving `Bignum` objects returns a result that will fit in a `Fixnum`, the result is automatically converted.

For the purposes of the bitwise operations and `[]`, a `Bignum` is treated as if it were an infinite-length bitstring with 2's complement representation.

While `Fixnum` values are immediate, `Bignum` objects are not---assignment and parameter passing work with references to objects, not the objects themselves.

instance methods
Arithmetic operations |
|  | Performs various arithmetic operations on big.
big | + | aNumeric | Addition
big | -- | aNumeric | Subtraction
big | * | aNumeric | Multiplication
big | / | aNumeric | Division
big | % | aNumeric | Modulo
big | ** | aNumeric | Exponentiation
Bit operations |
|  | Performs various operations on the binary representations of the `Bignum`.
~ big | Invert bits
big | | | aNumeric | Bitwise OR
big | & | aNumeric | Bitwise AND
big | ^ | aNumeric | Bitwise EXCLUSIVE OR
big | << | aNumeric | Left-shift aNumeric bits
big | >> | aNumeric | Right-shift aNumeric bits (with sign extension)
<=> | big <=> aNumeric -> -1, 0, +1
|  | Comparison---Returns -1, 0, or +1 depending on whether big is less than, equal to, or greater than aNumeric. This is the basis for the tests in `Comparable`.
[ ] | big[ n ] -> 0, 1
|  | Bit Reference---Returns the nth bit in the (assumed) binary representation of big, where big[0] is the least significant bit.
    a = 9**15
    50.downto(0) do |n|
      print a[n]
    end
produces:
    000101110110100000111000011110010100111100010111001
size | big.size -> anInteger
|  | Returns the number of bytes in the machine representation of big.
`(256**10 - 1).size` | » | `12`
`(256**20 - 1).size` | » | `20`
`(256**40 - 1).size` | » | `40`
to_f | big.to_f -> aFloat
|  | Converts big to a `Float`. If big doesn't fit in a `Float`, the result is infinity.
to_i | big.to_i -> big
|  | Returns big.
to_s | big.to_s -> aString
|  | Returns a string containing the decimal representation of big.

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Extracted from the book "Programming Ruby - The Pragmatic Programmer's Guide"
Copyright © 2001 by Addison Wesley Longman, Inc. This material may be distributed only subject to the terms and conditions set forth in the Open Publication License, v1.0 or later (the latest version is presently available at http://www.opencontent.org/openpub/)).

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