Trait num_traits::real::Real

source ·
pub trait Real: Num + Copy + NumCast + PartialOrd + Neg<Output = Self> {
Show 47 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;
}
Expand description

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

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);

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);

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.

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);

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);

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);

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);

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);

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);

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()));

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());

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());

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());

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);

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);

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);

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);

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()));

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);

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);

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);

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);

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);

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);

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);

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);

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);

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);

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);

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);

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);

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);

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);

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);

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);

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);

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);

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);

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);

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);

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);

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);

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);

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);

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);

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);

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);

Implementors