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SingleInteger examples
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The SingleInteger domain is intended to provide support in Axiom
for machine integer arithmetic.  It is generally much faster than
(bignum) Integer arithmetic but suffers from a limited range of
values.  Since Axiom can be implemented on top of various dialects of
Lisp, the actual representation of small integers may not correspond
exactly to the host machines integer representation.

You can discover the minimum and maximum values in your implementation
by using min and max.

  min()$SingleInteger
    - 2147483648
                              Type: SingleInteger

  max()$SingleInteger
    2147483647
                              Type: SingleInteger

To avoid confusion with Integer, which is the default type for
integers, you usually need to work with declared variables.

  a := 1234 :: SingleInteger
    1234
                              Type: SingleInteger

or use package calling

  b := 124$SingleInteger
    124
                              Type: SingleInteger

You can add, multiply and subtract SingleInteger objects, and ask for
the greatest common divisor (gcd).

  gcd(a,b)
    2
                              Type: SingleInteger

The least common multiple (lcm) is also available.

  lcm(a,b)
    76508
                              Type: SingleInteger

Operations mulmod, addmod, submod, and invmod are similar - they provide
arithmetic modulo a given small integer.
Here is 5 * 6 mod 13.

  mulmod(5,6,13)$SingleInteger
    4
                              Type: SingleInteger

To reduce a small integer modulo a prime, use positiveRemainder.

  positiveRemainder(37,13)$SingleInteger
    11
                              Type: SingleInteger

Operations And, Or, xor, and Not provide bit level operations on small
integers.

  And(3,4)$SingleInteger
    0
                              Type: SingleInteger

Use shift(int,numToShift) to shift bits, where i is shifted left if
numToShift is positive, right if negative.

  shift(1,4)$SingleInteger
    16
                              Type: SingleInteger

  shift(31,-1)$SingleInteger
    15
                              Type: SingleInteger

Many other operations are available for small integers, including many
of those provided for Integer.  

See Also:
o )help Integer
o )show SingleInteger

