Crate fpa

Expand description

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§

I1F7: Checked cast
I1F15: Checked cast
I1F31: Checked cast
I2F6: Checked cast
I2F14: Checked cast
I2F30: 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
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
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
I30F2: Checked cast
I31F1: Checked cast

Type Aliases§

I1F7: Fixed point number
I1F15: Fixed point number
I1F31: Fixed point number
I2F6: Fixed point number
I2F14: Fixed point number
I2F30: 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
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
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
I30F2: Fixed point number
I31F1: Fixed point number

Crate fpaCopy item path

§Examples

Structs§

Functions§

Type Aliases§

Crate fpa