Crate fpa [−] [src]

Fixed point arithmetic

A fixed point number is an alternative representation for a real number. IEEE floats, f32 and f64, being the standard format in processors with Floating Point Units (FPU). You should consider using fixed numbers on systems where there's no FPU and performance is critical as fixed point arithmetic is faster than software emulated IEEE float arithmetic. Do note that fixed point numbers tend to be more prone to overflows as they operate in ranges much smaller than floats.

The fixed point numbers exposed in this library use the following naming convention: IxFy, where x is the number of bits used for the integer part and y is the number of bits used for the fractional part.

Unlike IEEE floats, fixed points numbers have fixed precision. One can exchange range for precision by selecting different values for x and y:

Range: [-2 ^ (y - 1), 2 ^ (y - 1) - 2 ^ (-x)]
Precision: 2 ^ (-x)

For example, the type I1F7 has range [-1, 0.9921875] and precision 0.0078125.

Examples

Casts

// https://crates.io/crates/cast
extern crate cast;
extern crate fpa;

use cast::f64;
// 32-bit fixed point number, 16 bits for the integer part and 16 bits for
// the fractional part
use fpa::I16F16;

fn main() {
    // casts an integer into a fixed point number (infallible)
    let q = I16F16(1i8);

    // casts the fixed point number into a float (infallible)
    let f = f64(q);

    assert_eq!(f, 1.);
}

Arithmetic

use fpa::I16F16;

// NOTE the `f64` -> `I16F16` cast is fallible because of NaN and infinity
assert_eq!(I16F16(1.25_f64).unwrap() + I16F16(2.75_f64).unwrap(),
           I16F16(4_f64).unwrap());

assert_eq!(I16F16(2_f64).unwrap() / I16F16(0.5_f64).unwrap(),
           I16F16(4_f64).unwrap());

assert_eq!(I16F16(2_f64).unwrap() * I16F16(0.5_f64).unwrap(),
           I16F16(1_f64).unwrap());

Trigonometry

extern crate cast;
extern crate fpa;

use cast::f64;
use fpa::I2F30;

fn main() {
    let (r, _) = I2F30(0.3_f64).unwrap().polar(I2F30(0.4_f64).unwrap());
    assert!((f64(r) - 0.5).abs() < 1e-5);
}

Structs

Q	Fixed point number

Functions

I10F6	Checked cast
I10F22	Checked cast
I11F5	Checked cast
I11F21	Checked cast
I12F4	Checked cast
I12F20	Checked cast
I13F3	Checked cast
I13F19	Checked cast
I14F2	Checked cast
I14F18	Checked cast
I15F1	Checked cast
I15F17	Checked cast
I16F16	Checked cast
I17F15	Checked cast
I18F14	Checked cast
I19F13	Checked cast
I1F7	Checked cast
I1F15	Checked cast
I1F31	Checked cast
I20F12	Checked cast
I21F11	Checked cast
I22F10	Checked cast
I23F9	Checked cast
I24F8	Checked cast
I25F7	Checked cast
I26F6	Checked cast
I27F5	Checked cast
I28F4	Checked cast
I29F3	Checked cast
I2F6	Checked cast
I2F14	Checked cast
I2F30	Checked cast
I30F2	Checked cast
I31F1	Checked cast
I3F5	Checked cast
I3F13	Checked cast
I3F29	Checked cast
I4F4	Checked cast
I4F12	Checked cast
I4F28	Checked cast
I5F3	Checked cast
I5F11	Checked cast
I5F27	Checked cast
I6F2	Checked cast
I6F10	Checked cast
I6F26	Checked cast
I7F1	Checked cast
I7F9	Checked cast
I7F25	Checked cast
I8F8	Checked cast
I8F24	Checked cast
I9F7	Checked cast
I9F23	Checked cast

Type Definitions

I10F6	Fixed point number
I10F22	Fixed point number
I11F5	Fixed point number
I11F21	Fixed point number
I12F4	Fixed point number
I12F20	Fixed point number
I13F3	Fixed point number
I13F19	Fixed point number
I14F2	Fixed point number
I14F18	Fixed point number
I15F1	Fixed point number
I15F17	Fixed point number
I16F16	Fixed point number
I17F15	Fixed point number
I18F14	Fixed point number
I19F13	Fixed point number
I1F7	Fixed point number
I1F15	Fixed point number
I1F31	Fixed point number
I20F12	Fixed point number
I21F11	Fixed point number
I22F10	Fixed point number
I23F9	Fixed point number
I24F8	Fixed point number
I25F7	Fixed point number
I26F6	Fixed point number
I27F5	Fixed point number
I28F4	Fixed point number
I29F3	Fixed point number
I2F6	Fixed point number
I2F14	Fixed point number
I2F30	Fixed point number
I30F2	Fixed point number
I31F1	Fixed point number
I3F5	Fixed point number
I3F13	Fixed point number
I3F29	Fixed point number
I4F4	Fixed point number
I4F12	Fixed point number
I4F28	Fixed point number
I5F3	Fixed point number
I5F11	Fixed point number
I5F27	Fixed point number
I6F2	Fixed point number
I6F10	Fixed point number
I6F26	Fixed point number
I7F1	Fixed point number
I7F9	Fixed point number
I7F25	Fixed point number
I8F8	Fixed point number
I8F24	Fixed point number
I9F7	Fixed point number
I9F23	Fixed point number