Trait Real

pub trait Real:
    Num
    + Copy
    + NumCast
    + PartialOrd
    + Neg<Output = Self> {
    // Required methods
    fn min_value() -> Self;
    fn min_positive_value() -> Self;
    fn epsilon() -> Self;
    fn max_value() -> Self;
    fn floor(self) -> Self;
    fn ceil(self) -> Self;
    fn round(self) -> Self;
    fn trunc(self) -> Self;
    fn fract(self) -> Self;
    fn abs(self) -> Self;
    fn signum(self) -> Self;
    fn is_sign_positive(self) -> bool;
    fn is_sign_negative(self) -> bool;
    fn mul_add(self, a: Self, b: Self) -> Self;
    fn recip(self) -> Self;
    fn powi(self, n: i32) -> Self;
    fn powf(self, n: Self) -> Self;
    fn sqrt(self) -> Self;
    fn exp(self) -> Self;
    fn exp2(self) -> Self;
    fn ln(self) -> Self;
    fn log(self, base: Self) -> Self;
    fn log2(self) -> Self;
    fn log10(self) -> Self;
    fn to_degrees(self) -> Self;
    fn to_radians(self) -> Self;
    fn max(self, other: Self) -> Self;
    fn min(self, other: Self) -> Self;
    fn abs_sub(self, other: Self) -> Self;
    fn cbrt(self) -> Self;
    fn hypot(self, other: Self) -> Self;
    fn sin(self) -> Self;
    fn cos(self) -> Self;
    fn tan(self) -> Self;
    fn asin(self) -> Self;
    fn acos(self) -> Self;
    fn atan(self) -> Self;
    fn atan2(self, other: Self) -> Self;
    fn sin_cos(self) -> (Self, Self);
    fn exp_m1(self) -> Self;
    fn ln_1p(self) -> Self;
    fn sinh(self) -> Self;
    fn cosh(self) -> Self;
    fn tanh(self) -> Self;
    fn asinh(self) -> Self;
    fn acosh(self) -> Self;
    fn atanh(self) -> Self;
}

A trait for real number types that do not necessarily have floating-point-specific characteristics such as NaN and infinity.

See this Wikipedia article for a list of data types that could meaningfully implement this trait.

This trait is only available with the std feature, or with the libm feature otherwise.

Required Methods

fn min_value() -> Self

Returns the smallest finite value that this type can represent.

use num_traits::real::Real;
use std::f64;

let x: f64 = Real::min_value();

assert_eq!(x, f64::MIN);

fn min_positive_value() -> Self

Returns the smallest positive, normalized value that this type can represent.

use num_traits::real::Real;
use std::f64;

let x: f64 = Real::min_positive_value();

assert_eq!(x, f64::MIN_POSITIVE);

fn epsilon() -> Self

Returns epsilon, a small positive value.

use num_traits::real::Real;
use std::f64;

let x: f64 = Real::epsilon();

assert_eq!(x, f64::EPSILON);

Panics

The default implementation will panic if f32::EPSILON cannot be cast to Self.

fn max_value() -> Self

Returns the largest finite value that this type can represent.

use num_traits::real::Real;
use std::f64;

let x: f64 = Real::max_value();
assert_eq!(x, f64::MAX);

fn floor(self) -> Self

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

use num_traits::real::Real;

let f = 3.99;
let g = 3.0;

assert_eq!(f.floor(), 3.0);
assert_eq!(g.floor(), 3.0);

fn ceil(self) -> Self

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

use num_traits::real::Real;

let f = 3.01;
let g = 4.0;

assert_eq!(f.ceil(), 4.0);
assert_eq!(g.ceil(), 4.0);

fn round(self) -> Self

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

use num_traits::real::Real;

let f = 3.3;
let g = -3.3;

assert_eq!(f.round(), 3.0);
assert_eq!(g.round(), -3.0);

fn trunc(self) -> Self

Return the integer part of a number.

use num_traits::real::Real;

let f = 3.3;
let g = -3.7;

assert_eq!(f.trunc(), 3.0);
assert_eq!(g.trunc(), -3.0);

fn fract(self) -> Self

Returns the fractional part of a number.

use num_traits::real::Real;

let x = 3.5;
let y = -3.5;
let abs_difference_x = (x.fract() - 0.5).abs();
let abs_difference_y = (y.fract() - (-0.5)).abs();

assert!(abs_difference_x < 1e-10);
assert!(abs_difference_y < 1e-10);

fn abs(self) -> Self

Computes the absolute value of self. Returns Float::nan() if the number is Float::nan().

use num_traits::real::Real;
use std::f64;

let x = 3.5;
let y = -3.5;

let abs_difference_x = (x.abs() - x).abs();
let abs_difference_y = (y.abs() - (-y)).abs();

assert!(abs_difference_x < 1e-10);
assert!(abs_difference_y < 1e-10);

assert!(::num_traits::Float::is_nan(f64::NAN.abs()));

fn signum(self) -> Self

Returns a number that represents the sign of self.

• 1.0 if the number is positive, +0.0 or Float::infinity()
• -1.0 if the number is negative, -0.0 or Float::neg_infinity()
• Float::nan() if the number is Float::nan()

use num_traits::real::Real;
use std::f64;

let f = 3.5;

assert_eq!(f.signum(), 1.0);
assert_eq!(f64::NEG_INFINITY.signum(), -1.0);

assert!(f64::NAN.signum().is_nan());

fn is_sign_positive(self) -> bool

Returns true if self is positive, including +0.0, Float::infinity(), and with newer versions of Rust f64::NAN.

use num_traits::real::Real;
use std::f64;

let neg_nan: f64 = -f64::NAN;

let f = 7.0;
let g = -7.0;

assert!(f.is_sign_positive());
assert!(!g.is_sign_positive());
assert!(!neg_nan.is_sign_positive());

fn is_sign_negative(self) -> bool

Returns true if self is negative, including -0.0, Float::neg_infinity(), and with newer versions of Rust -f64::NAN.

use num_traits::real::Real;
use std::f64;

let nan: f64 = f64::NAN;

let f = 7.0;
let g = -7.0;

assert!(!f.is_sign_negative());
assert!(g.is_sign_negative());
assert!(!nan.is_sign_negative());

fn mul_add(self, a: Self, b: Self) -> Self

Fused multiply-add. Computes (self * a) + b with only one rounding error, yielding a more accurate result than an unfused multiply-add.

Using mul_add can be more performant than an unfused multiply-add if the target architecture has a dedicated fma CPU instruction.

use num_traits::real::Real;

let m = 10.0;
let x = 4.0;
let b = 60.0;

// 100.0
let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs();

assert!(abs_difference < 1e-10);

fn recip(self) -> Self

Take the reciprocal (inverse) of a number, 1/x.

use num_traits::real::Real;

let x = 2.0;
let abs_difference = (x.recip() - (1.0/x)).abs();

assert!(abs_difference < 1e-10);

fn powi(self, n: i32) -> Self

Raise a number to an integer power.

Using this function is generally faster than using powf

use num_traits::real::Real;

let x = 2.0;
let abs_difference = (x.powi(2) - x*x).abs();

assert!(abs_difference < 1e-10);

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

Raise a number to a real number power.

use num_traits::real::Real;

let x = 2.0;
let abs_difference = (x.powf(2.0) - x*x).abs();

assert!(abs_difference < 1e-10);

fn sqrt(self) -> Self

Take the square root of a number.

Returns NaN if self is a negative floating-point number.

Panics

If the implementing type doesn’t support NaN, this method should panic if self < 0.

use num_traits::real::Real;

let positive = 4.0;
let negative = -4.0;

let abs_difference = (positive.sqrt() - 2.0).abs();

assert!(abs_difference < 1e-10);
assert!(::num_traits::Float::is_nan(negative.sqrt()));

fn exp(self) -> Self

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

use num_traits::real::Real;

let one = 1.0;
// e^1
let e = one.exp();

// ln(e) - 1 == 0
let abs_difference = (e.ln() - 1.0).abs();

assert!(abs_difference < 1e-10);

fn exp2(self) -> Self

Returns 2^(self).

use num_traits::real::Real;

let f = 2.0;

// 2^2 - 4 == 0
let abs_difference = (f.exp2() - 4.0).abs();

assert!(abs_difference < 1e-10);

fn ln(self) -> Self

Returns the natural logarithm of the number.

Panics

If self <= 0 and this type does not support a NaN representation, this function should panic.

use num_traits::real::Real;

let one = 1.0;
// e^1
let e = one.exp();

// ln(e) - 1 == 0
let abs_difference = (e.ln() - 1.0).abs();

assert!(abs_difference < 1e-10);

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

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

Panics

If self <= 0 and this type does not support a NaN representation, this function should panic.

use num_traits::real::Real;

let ten = 10.0;
let two = 2.0;

// log10(10) - 1 == 0
let abs_difference_10 = (ten.log(10.0) - 1.0).abs();

// log2(2) - 1 == 0
let abs_difference_2 = (two.log(2.0) - 1.0).abs();

assert!(abs_difference_10 < 1e-10);
assert!(abs_difference_2 < 1e-10);

fn log2(self) -> Self

Returns the base 2 logarithm of the number.

Panics

If self <= 0 and this type does not support a NaN representation, this function should panic.

use num_traits::real::Real;

let two = 2.0;

// log2(2) - 1 == 0
let abs_difference = (two.log2() - 1.0).abs();

assert!(abs_difference < 1e-10);

fn log10(self) -> Self

Returns the base 10 logarithm of the number.

Panics

If self <= 0 and this type does not support a NaN representation, this function should panic.

use num_traits::real::Real;

let ten = 10.0;

// log10(10) - 1 == 0
let abs_difference = (ten.log10() - 1.0).abs();

assert!(abs_difference < 1e-10);

fn to_degrees(self) -> Self

Converts radians to degrees.

use std::f64::consts;

let angle = consts::PI;

let abs_difference = (angle.to_degrees() - 180.0).abs();

assert!(abs_difference < 1e-10);

fn to_radians(self) -> Self

Converts degrees to radians.

use std::f64::consts;

let angle = 180.0_f64;

let abs_difference = (angle.to_radians() - consts::PI).abs();

assert!(abs_difference < 1e-10);

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

Returns the maximum of the two numbers.

use num_traits::real::Real;

let x = 1.0;
let y = 2.0;

assert_eq!(x.max(y), y);

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

Returns the minimum of the two numbers.

use num_traits::real::Real;

let x = 1.0;
let y = 2.0;

assert_eq!(x.min(y), x);

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

The positive difference of two numbers.

• If self <= other: 0:0
• Else: self - other

use num_traits::real::Real;

let x = 3.0;
let y = -3.0;

let abs_difference_x = (x.abs_sub(1.0) - 2.0).abs();
let abs_difference_y = (y.abs_sub(1.0) - 0.0).abs();

assert!(abs_difference_x < 1e-10);
assert!(abs_difference_y < 1e-10);

fn cbrt(self) -> Self

Take the cubic root of a number.

use num_traits::real::Real;

let x = 8.0;

// x^(1/3) - 2 == 0
let abs_difference = (x.cbrt() - 2.0).abs();

assert!(abs_difference < 1e-10);

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

Calculate the length of the hypotenuse of a right-angle triangle given legs of length x and y.

use num_traits::real::Real;

let x = 2.0;
let y = 3.0;

// sqrt(x^2 + y^2)
let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();

assert!(abs_difference < 1e-10);

fn sin(self) -> Self

Computes the sine of a number (in radians).

use num_traits::real::Real;
use std::f64;

let x = f64::consts::PI/2.0;

let abs_difference = (x.sin() - 1.0).abs();

assert!(abs_difference < 1e-10);

fn cos(self) -> Self

Computes the cosine of a number (in radians).

use num_traits::real::Real;
use std::f64;

let x = 2.0*f64::consts::PI;

let abs_difference = (x.cos() - 1.0).abs();

assert!(abs_difference < 1e-10);

fn tan(self) -> Self

Computes the tangent of a number (in radians).

use num_traits::real::Real;
use std::f64;

let x = f64::consts::PI/4.0;
let abs_difference = (x.tan() - 1.0).abs();

assert!(abs_difference < 1e-14);

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].

Panics

If this type does not support a NaN representation, this function should panic if the number is outside the range [-1, 1].

use num_traits::real::Real;
use std::f64;

let f = f64::consts::PI / 2.0;

// asin(sin(pi/2))
let abs_difference = (f.sin().asin() - f64::consts::PI / 2.0).abs();

assert!(abs_difference < 1e-10);

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].

Panics

If this type does not support a NaN representation, this function should panic if the number is outside the range [-1, 1].

use num_traits::real::Real;
use std::f64;

let f = f64::consts::PI / 4.0;

// acos(cos(pi/4))
let abs_difference = (f.cos().acos() - f64::consts::PI / 4.0).abs();

assert!(abs_difference < 1e-10);

fn atan(self) -> Self

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

use num_traits::real::Real;

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).

• x = 0, y = 0: 0
• x >= 0: arctan(y/x) -> [-pi/2, pi/2]
• y >= 0: arctan(y/x) + pi -> (pi/2, pi]
• y < 0: arctan(y/x) - pi -> (-pi, -pi/2)

use num_traits::real::Real;
use std::f64;

let pi = f64::consts::PI;
// All angles from horizontal right (+x)
// 45 deg counter-clockwise
let x1 = 3.0;
let y1 = -3.0;

// 135 deg clockwise
let x2 = -3.0;
let y2 = 3.0;

let abs_difference_1 = (y1.atan2(x1) - (-pi/4.0)).abs();
let abs_difference_2 = (y2.atan2(x2) - 3.0*pi/4.0).abs();

assert!(abs_difference_1 < 1e-10);
assert!(abs_difference_2 < 1e-10);

fn sin_cos(self) -> (Self, Self)

Simultaneously computes the sine and cosine of the number, x. Returns (sin(x), cos(x)).

use num_traits::real::Real;
use std::f64;

let x = f64::consts::PI/4.0;
let f = x.sin_cos();

let abs_difference_0 = (f.0 - x.sin()).abs();
let abs_difference_1 = (f.1 - x.cos()).abs();

assert!(abs_difference_0 < 1e-10);
assert!(abs_difference_0 < 1e-10);

fn exp_m1(self) -> Self

Returns e^(self) - 1 in a way that is accurate even if the number is close to zero.

use num_traits::real::Real;

let x = 7.0;

// e^(ln(7)) - 1
let abs_difference = (x.ln().exp_m1() - 6.0).abs();

assert!(abs_difference < 1e-10);

fn ln_1p(self) -> Self

Returns ln(1+n) (natural logarithm) more accurately than if the operations were performed separately.

Panics

If this type does not support a NaN representation, this function should panic if self-1 <= 0.

use num_traits::real::Real;
use std::f64;

let x = f64::consts::E - 1.0;

// ln(1 + (e - 1)) == ln(e) == 1
let abs_difference = (x.ln_1p() - 1.0).abs();

assert!(abs_difference < 1e-10);

fn sinh(self) -> Self

Hyperbolic sine function.

use num_traits::real::Real;
use std::f64;

let e = f64::consts::E;
let x = 1.0;

let f = x.sinh();
// Solving sinh() at 1 gives `(e^2-1)/(2e)`
let g = (e*e - 1.0)/(2.0*e);
let abs_difference = (f - g).abs();

assert!(abs_difference < 1e-10);

fn cosh(self) -> Self

Hyperbolic cosine function.

use num_traits::real::Real;
use std::f64;

let e = f64::consts::E;
let x = 1.0;
let f = x.cosh();
// Solving cosh() at 1 gives this result
let g = (e*e + 1.0)/(2.0*e);
let abs_difference = (f - g).abs();

// Same result
assert!(abs_difference < 1.0e-10);

fn tanh(self) -> Self

Hyperbolic tangent function.

use num_traits::real::Real;
use std::f64;

let e = f64::consts::E;
let x = 1.0;

let f = x.tanh();
// Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))`
let g = (1.0 - e.powi(-2))/(1.0 + e.powi(-2));
let abs_difference = (f - g).abs();

assert!(abs_difference < 1.0e-10);

fn asinh(self) -> Self

Inverse hyperbolic sine function.

use num_traits::real::Real;

let x = 1.0;
let f = x.sinh().asinh();

let abs_difference = (f - x).abs();

assert!(abs_difference < 1.0e-10);

fn acosh(self) -> Self

Inverse hyperbolic cosine function.

use num_traits::real::Real;

let x = 1.0;
let f = x.cosh().acosh();

let abs_difference = (f - x).abs();

assert!(abs_difference < 1.0e-10);

fn atanh(self) -> Self

Inverse hyperbolic tangent function.

use num_traits::real::Real;
use std::f64;

let e = f64::consts::E;
let f = e.tanh().atanh();

let abs_difference = (f - e).abs();

assert!(abs_difference < 1.0e-10);

Object Safety

This trait is not object safe.

Implementors

impl<T: Float> Real for T