FixedPointNumbers

This library exports fixed-point number types. A fixed-point number represents a fractional, or non-integral, number. In contrast with the more widely known floating-point numbers, fixed-point numbers have a fixed number of digits (bits) after the decimal (radix) point. They are effectively integers scaled by a constant factor.

Fixed-point numbers can be used to perform arithmetic. Another practical application is to implicitly rescale integers without modifying the underlying representation.

This library exports two categories of fixed-point types. Fixed-point types are used like any other number: they can be added, multiplied, raised to a power, etc. In many cases these operations result in conversion to floating-point types.

Type hierarchy

This library defines an abstract type FixedPoint{T <: Integer, f} as a subtype of Real. The parameter T is the underlying representation and f is the number of fraction bits.

For signed integers, there is a fixed-point type Fixed{T, f} and for unsigned integers, there is the UFixed{T, f} type.

These types, built with f fraction bits, map the closed interval [0.0,1.0] to the span of numbers with f bits. For example, the UFixed8 type is represented internally by a UInt8, and makes 0x00 equivalent to 0.0 and 0xff to 1.0. The types UFixed10, UFixed12, UFixed14, and UFixed16 are all based on UInt16 and reach the value 1.0 at 10, 12, 14, and 16 bits, respectively (0x03ff, 0x0fff, 0x3fff, and 0xffff).

To construct such a number, use convert(UFixed12, 1.3), ufixed12(1.3), or the literal syntax 0x14ccuf12. The latter syntax means to construct a UFixed12 (it ends in uf12) from the UInt16 value 0x14cc.

There currently is no literal syntax for signed Fixed numbers.