Trait RealField 

pub trait RealField:
    Field
    + PartialOrd
    + Neg<Output = Self>
    + Copy
    + Clone
    + AddAssign
    + SubAssign
    + MulAssign
    + DivAssign {
    // Required methods
    fn nan() -> Self;
    fn is_nan(self) -> bool;
    fn is_infinite(self) -> bool;
    fn is_finite(self) -> bool;
    fn clamp(self, min: Self, max: Self) -> Self;
    fn sqrt(self) -> Self;
    fn abs(self) -> Self;
    fn floor(self) -> Self;
    fn ceil(self) -> Self;
    fn round(self) -> Self;
    fn exp(self) -> Self;
    fn ln(self) -> Self;
    fn log(self, base: Self) -> Self;
    fn powf(self, n: Self) -> Self;
    fn sin(self) -> Self;
    fn asin(self) -> Self;
    fn cos(self) -> Self;
    fn acos(self) -> Self;
    fn tan(self) -> Self;
    fn sinh(self) -> Self;
    fn cosh(self) -> Self;
    fn tanh(self) -> Self;
    fn atan(self) -> Self;
    fn atan2(self, other: Self) -> Self;
    fn pi() -> Self;
    fn e() -> Self;
    fn epsilon() -> Self;
}

Represents an ordered Field with additional operations for calculus and analysis.

A RealField extends the algebraic definition of a Field with properties and functions characteristic of the real numbers, such as ordering (PartialOrd) and transcendental functions (sin, exp, ln, etc.).

This trait abstracts over concrete floating-point types like f32 and f64, and could be implemented for other types like dual numbers (for automatic differentiation) or custom fixed-point types.

Required Methods

fn nan() -> Self

Returns the NaN value.

fn is_nan(self) -> bool

Returns true if this value is NaN and false otherwise.

use deep_causality_num::Float;
use core::f64;

let nan = f64::NAN;
let f = 7.0;

assert!(nan.is_nan());
assert!(!f.is_nan());

fn is_infinite(self) -> bool

Returns true if this value is positive infinity or negative infinity and false otherwise.

use deep_causality_num::Float;
use core::f32;

let f = 7.0f32;
let inf: f32 = Float::infinity();
let neg_inf: f32 = Float::neg_infinity();
let nan: f32 = f32::NAN;

assert!(!f.is_infinite());
assert!(!nan.is_infinite());

assert!(inf.is_infinite());
assert!(neg_inf.is_infinite());

fn is_finite(self) -> bool

Returns true if this number is neither infinite nor NaN.

use deep_causality_num::Float;
use core::f32;

let f = 7.0f32;
let inf: f32 = Float::infinity();
let neg_inf: f32 = Float::neg_infinity();
let nan: f32 = f32::NAN;

assert!(f.is_finite());

assert!(!nan.is_finite());
assert!(!inf.is_finite());
assert!(!neg_inf.is_finite());

fn clamp(self, min: Self, max: Self) -> Self

fn sqrt(self) -> Self

Computes the principal square root of a number. For negative numbers, it returns NaN.

Example

use deep_causality_num::RealField;
assert_eq!(4.0f64.sqrt(), 2.0);

fn abs(self) -> Self

Computes the absolute value of a number.

Example

use deep_causality_num::RealField;
let x = -4.0f64;
assert_eq!(x.abs(), 4.0);

fn floor(self) -> Self

Returns the largest integer less than or equal to a number.

Example

use deep_causality_num::RealField;
assert_eq!(2.99f64.floor(), 2.0);

fn ceil(self) -> Self

Returns the smallest integer greater than or equal to a number.

Example

use deep_causality_num::RealField;
assert_eq!(2.01f64.ceil(), 3.0);

fn round(self) -> Self

Returns the nearest integer to a number. Rounds half-way cases away from 0.0.

Example

use deep_causality_num::RealField;
assert_eq!(2.5f64.round(), 3.0);
assert_eq!(-2.5f64.round(), -3.0);

fn exp(self) -> Self

Returns e^(self), (the exponential function).

Example

use deep_causality_num::RealField;
use std::f64::consts;
assert_eq!(1.0f64.exp(), consts::E);

fn ln(self) -> Self

Returns the natural logarithm of the number.

Example

use deep_causality_num::RealField;
use std::f64::consts;
assert_eq!(consts::E.ln(), 1.0);

fn log(self, base: Self) -> Self

Returns the logarithm of the number with respect to an arbitrary base.

Example

use deep_causality_num::RealField;
assert_eq!(8.0f64.log(2.0), 3.0);

fn powf(self, n: Self) -> Self

Raises a number to a floating point power.

Example

use deep_causality_num::RealField;
assert_eq!(2.0f64.powf(3.0), 8.0);

fn sin(self) -> Self

Computes the sine of a number (in radians).

Example

use deep_causality_num::RealField;
use std::f64::consts;
assert!((consts::PI / 2.0).sin() - 1.0 < 1e-9);

fn asin(self) -> Self

Computes the arcsine of a number. Return value is in radians in the range [-pi/2, pi/2] or NaN if the number is outside the range [-1, 1].

Example

use deep_causality_num::RealField;
use std::f64::consts;
let val = 1.0f64;
assert!((val.asin() - consts::FRAC_PI_2).abs() < 1e-9);

fn cos(self) -> Self

Computes the cosine of a number (in radians).

Example

use deep_causality_num::RealField;
use std::f64::consts;
assert!((consts::PI.cos() - (-1.0)).abs() < 1e-9);

fn acos(self) -> Self

Computes the arccosine of a number. Return value is in radians in the range [0, pi] or NaN if the number is outside the range [-1, 1].

Example

use deep_causality_num::RealField;
use std::f64::consts;
let val = 1.0f64;
assert!((val.acos() - 0.0).abs() < 1e-9);

fn tan(self) -> Self

Computes the tangent of a number (in radians).

Example

use deep_causality_num::RealField;
use std::f64::consts;
assert!((consts::FRAC_PI_4.tan() - 1.0).abs() < 1e-9);

fn sinh(self) -> Self

Computes the hyperbolic sine of a number.

fn cosh(self) -> Self

Computes the hyperbolic cosine of a number.

fn tanh(self) -> Self

Computes the hyperbolic tangent of a number.

Example

use deep_causality_num::RealField;
assert!(0.0f64.tanh() == 0.0);

fn atan(self) -> Self

Computes the arctangent of a number. Return value is in radians in the range [-pi/2, pi/2];

use deep_causality_num::RealField;

let f = 1.0;

// atan(tan(1))
let abs_difference = (f.tan().atan() - 1.0).abs();

assert!(abs_difference < 1e-10);

fn atan2(self, other: Self) -> Self

Computes the four-quadrant arctangent of self (y) and other (x).

Example

use deep_causality_num::RealField;
use std::f64::consts;
let y = 1.0f64;
let x = -1.0f64;
assert!((y.atan2(x) - (3.0 * consts::PI / 4.0)).abs() < 1e-9);

fn pi() -> Self

Returns the constant π.

fn e() -> Self

Returns the Euler number e, the base of the natural logarithm.

fn epsilon() -> Self

Machine epsilon. Used for comparison comparisons to zero.

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

Implementations on Foreign Types

impl RealField for f32

fn nan() -> Self

fn is_nan(self) -> bool

fn is_infinite(self) -> bool

fn is_finite(self) -> bool

fn clamp(self, min: Self, max: Self) -> Self

fn sqrt(self) -> Self

fn abs(self) -> Self

fn floor(self) -> Self

fn ceil(self) -> Self

fn round(self) -> Self

fn exp(self) -> Self

fn ln(self) -> Self

fn log(self, base: Self) -> Self

fn powf(self, n: Self) -> Self

fn sin(self) -> Self

fn asin(self) -> Self

fn cos(self) -> Self

fn acos(self) -> Self

fn tan(self) -> Self

fn sinh(self) -> Self

fn cosh(self) -> Self

fn tanh(self) -> Self

fn atan(self) -> Self

fn atan2(self, other: Self) -> Self

fn pi() -> Self

fn e() -> Self

fn epsilon() -> Self

impl RealField for f64

fn nan() -> Self

fn clamp(self, min: Self, max: Self) -> Self

fn abs(self) -> Self

fn sqrt(self) -> Self

fn floor(self) -> Self

fn ceil(self) -> Self

fn round(self) -> Self

fn exp(self) -> Self

fn ln(self) -> Self

fn log(self, base: Self) -> Self

fn powf(self, n: Self) -> Self

fn sin(self) -> Self

fn cos(self) -> Self

fn acos(self) -> Self

fn tan(self) -> Self

fn sinh(self) -> Self

fn cosh(self) -> Self

fn tanh(self) -> Self

fn atan2(self, other: Self) -> Self

fn pi() -> Self

fn e() -> Self

fn epsilon() -> Self

fn atan(self) -> Self

fn asin(self) -> Self

fn is_nan(self) -> bool

fn is_infinite(self) -> bool

fn is_finite(self) -> bool

Implementors

impl RealField for Float106