Expand the README

Author: timholy

README.md

@@ -1,8 +1,41 @@
 # FixedPoint
 
-This library exports a 32-bit fixed-point type `Fixed32{f}`.
+This library exports fixed-point number types.
+A [fixed-point number][wikipedia] 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.
+
+## Fixed32 (signed fixed-point numbers)
+
+For signed integers, there is a 32-bit fixed-point type `Fixed32{f}`.
 The parameter `f` is the number of fraction bits. There is also an abstract subtype of
 `Real` called `Fixed`.
 
 To use it, convert numbers to a `Fixed32` type, or call `Fixed32(x)`, which will default
-to constructing a `Fixed32{16}`. Then use ordinary arithmetic.
+to constructing a `Fixed32{16}`.
+
+## Ufixed (unsigned fixed-point numbers)
+
+For unsigned integers, there is a family of subtypes of the abstract `Ufixed` 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)` or the literal syntax `0x14ccuf12`.
+The latter syntax means to construct a `Ufixed12` (it ends in `uf12`) from the `Uint16` value
+`0x14cc`.
+
+[wikipedia]: http://en.wikipedia.org/wiki/Fixed-point_arithmetic