Numbers

In number.diesel:

Numbers support the standard arithmetic operations, plus the protocol of totally-ordered objects (=, <, min, etc.). This contract implies that all subclasses of number are freely mixable at run-time.

extend module Stdlib;

module Number;
abstract class num isa ordered_hashable[num];

as_int converts its argument to an integer, possibly rounding up or down if not already an integer.

  fun as_int(:num):integer;

as_float converts its argument to a float representation. Related operations exist to specify the kind of float to produce.

  fun as_float(n:num):float;
  fun as_single_float(:num):single_float;
  fun as_double_float(:num):double_float;

Standard arithmetic operations. When invoked on a small integer (an int), they might overflow and wrap around. (Use the _ov versions below to get correct answers in the face of overflow.)

  fun +(:`T <= num, :T):T;
  fun -(:`T <= num, :T):T;
  fun *(:`T <= num, :T):T;

/ returns an integer if applied to integers, rounding towards zero. Use /_float to yield a (precise) float result.

  fun /(:`T <= num, :T):T;
  fun /_float(:`T <= num, :T):T & float;

Unary arithmetic operators:

  fun negate(n:`T <= num):T;
  fun -(n:`T <= num):T;  - same as negate
  fun +(n:`T <= num):T;  - silly no-op

These arithmetic operators handle int overflow by converting to arbitrary-precision integers (big_ints):

  fun -_ov(l:num):num;
  fun +_ov(l:num,r:num):num;
  fun -_ov(l:num,r:num):num;
  fun *_ov(l:num,r:num):num;
  fun /_ov(l:num,r:num):num;
  fun /_float_ov(l:num,r:num):num;

Simple convenience functions:

  fun pred(i:`T <= num):T;  - i-1
  fun succ(i:`T <= num):T;  - i+1
  fun square(n:`T <= num):T;  - n2
  fun cube(n:`T <= num):T;  - n3
  fun abs(n:`T <= num):T;  - absolute value
  fun sign(x:num):int;  - return -1, 0, or 1 depending on sign of argument
  fun average(n1:`T <= num, n2:`T):T|int;  - arithmetic average: (n1+n2)/2
  fun power(x:`T <= num, power:integer):S where *_ov(:T,:T):`S <= T;  - exponentiation
  fun **(x:`T <= num, power:integer):S where *_ov(:T,:T):`S <= T;  - same as power

end module Number;