Fixed Point

This library has been modified from cubit library by influenceth and adjusted to match with other fixed point implementations.

This API provides basic some operations for signed fixed point numbers. Fixed point numbers are represented as a struct with a magnitude and a sign.

The magnitude represents the absolute value of the number, and the sign indicates whether the number is positive or negative.

struct FP8x23 {
    mag: u32,
    sign: bool
}

Data types

Orion supports currently these fixed point types:

Data type	dtype
Q8.23	FP8x23
Q16.16	FP16x16
Q32.32	FP32x32
Q64.64	FP64x64

Fixed Trait

use orion::numbers::fixed_point::core::FixedTrait;

Fixed trait defines the operations that can be performed on a fixed point.

function	description
fp.new	Constructs a new fixed point instance.
fp.new_unscaled	Creates a new fixed point instance with the specified unscaled magnitude and sign.
fp.from_felt	Creates a new fixed point instance from a felt252 value.
fp.abs	Returns the absolute value of the fixed point number.
fp.ceil	Returns the smallest integer greater than or equal to the fixed point number.
fp.exp	Returns the value of e raised to the power of the fixed point number.
fp.exp2	Returns the value of 2 raised to the power of the fixed point number.
fp.floor	Returns the largest integer less than or equal to the fixed point number.
fp.ln	Returns the natural logarithm of the fixed point number.
fp.log2	Returns the base-2 logarithm of the fixed point number.
fp.log10	Returns the base-10 logarithm of the fixed point number.
fp.pow	Returns the result of raising the fixed point number to the power of another fixed point number.
fp.round	Rounds the fixed point number to the nearest whole number.
fp.sqrt	Returns the square root of the fixed point number.
fp.acos	Returns the arccosine (inverse of cosine) of the fixed point number.
fp.acos_fast	Returns the arccosine (inverse of cosine) of the fixed point number faster with LUT.
fp.asin	Returns the arcsine (inverse of sine) of the fixed point number.
fp.asin_fast	Returns the arcsine (inverse of sine) of the fixed point number faster with LUT.
fp.atan	Returns the arctangent (inverse of tangent) of the input fixed point number.
fp.atan_fast	Returns the arctangent (inverse of tangent) of the input fixed point number faster with LUT.
fp.cos	Returns the cosine of the fixed point number.
fp.cos_fast	Returns the cosine of the fixed point number fast with LUT.
fp.sin	Returns the sine of the fixed point number.
fp.sin_fast	Returns the sine of the fixed point number faster with LUT.
fp.tan	Returns the tangent of the fixed point number.
fp.tan_fast	Returns the tangent of the fixed point number faster with LUT.
fp.acosh	Returns the value of the inverse hyperbolic cosine of the fixed point number.
fp.asinh	Returns the value of the inverse hyperbolic sine of the fixed point number.
fp.atanh	Returns the value of the inverse hyperbolic tangent of the fixed point number.
fp.cosh	Returns the value of the hyperbolic cosine of the fixed point number.
fp.sinh	Returns the value of the hyperbolic sine of the fixed point number.
fp.tanh	Returns the value of the hyperbolic tangent of the fixed point number.
fp.sign	Returns the element-wise indication of the sign of the input fixed point number.
fp.erf	Returns the error function of the input fixed point number computed element-wise.

Arithmetic & Comparison operators

FixedType implements arithmetic and comparison traits. This allows you to perform basic arithmetic operations using the associated operators. (+,+= -,-= *,*= / , /= ), as well as relational operators (>, >= ,< , <= , ==, != ).

Examples

fn add_fp_example() {
    // We instantiate two fixed point from here.
    // a = 1
    // b = 2
    let a = Fixed::new_unscaled(1, false);
    let b = Fixed::new_unscaled(2, false);

    // We can add two fixed point as follows.
    let result = a + b;

    assert(result == Fixed::new_unscaled(3), 'invalid result');
}

fn compare_fp_example() -> bool {
    // We instantiate two fixed point from here.
    // a = 42
    // b = -10
    let a = Fixed::new_unscaled(42, false);
    let b = Fixed::new_unscaled(10, true);

    // We can compare two fixed point as follows.
    return a > b;
}
>>> true