[−][src]Trait num_traits::real::Real
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
orFloat::infinity()
-1.0
if the number is negative,-0.0
orFloat::neg_infinity()
Float::nan()
if the number isFloat::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);