q-num

This library provides the define_q_num! procedural macro (evaluated at compile time) to define a signed/unsigned binary fixed-point number type. It uses ARM-style Q notation: Qm.n (signed) or UQm.n (unsigned), where:

• m is the number of integer bits, and
• n is the number of fractional bits.

Internally, the macro chooses the narrowest primitive integer type that can hold m + n bits, up to u64 (unsigned) and i64 (signed). More internal details are discussed below.

Q Number Value

A Q number's value is the ratio of the stored number (having n + m bits) and a fixed denominator (equal to 2 ^ n).

For example, using the UQ3.2 specification, the bit pattern 0b10111 represents the value 5.75. Keeping in mind the denominator is 2 ^ 2 = 4, there are two ways to see this:

• 0b10111 / 4 == 23 / 4 == 5.75
• 0b101 + 0b11 / 4 == 5 + 3/4 == 5.75

Example Macro Usage

Here is one example:

define_q_num!(MyQ, Q6.2);
let a = MyQ::from(13.75);
let b = MyQ::from(-2.25);
let c = a + b; // 11.5