pub trait Float: Sized {
Show 39 methods
// Required methods
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 copysign(self, y: Self) -> Self;
fn mul_add(self, a: Self, b: Self) -> Self;
fn div_euc(self, rhs: Self) -> Self;
fn mod_euc(self, rhs: 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 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)
where Self: Sized;
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
Copy and pasted from Rust std
Required Methods§
sourcefn floor(self) -> Self
fn floor(self) -> Self
Returns the largest integer less than or equal to a number.
§Examples
let f = 3.99_f64;
let g = 3.0_f64;
assert_eq!(f.floor(), 3.0);
assert_eq!(g.floor(), 3.0);
sourcefn ceil(self) -> Self
fn ceil(self) -> Self
Returns the smallest integer greater than or equal to a number.
§Examples
let f = 3.01_f64;
let g = 4.0_f64;
assert_eq!(f.ceil(), 4.0);
assert_eq!(g.ceil(), 4.0);
sourcefn round(self) -> Self
fn round(self) -> Self
Returns the nearest integer to a number. Round half-way cases away from
0.0
.
§Examples
let f = 3.3_f64;
let g = -3.3_f64;
assert_eq!(f.round(), 3.0);
assert_eq!(g.round(), -3.0);
sourcefn trunc(self) -> Self
fn trunc(self) -> Self
Returns the integer part of a number.
§Examples
let f = 3.3_f64;
let g = -3.7_f64;
assert_eq!(f.trunc(), 3.0);
assert_eq!(g.trunc(), -3.0);
sourcefn fract(self) -> Self
fn fract(self) -> Self
Returns the fractional part of a number.
§Examples
let x = 3.5_f64;
let y = -3.5_f64;
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);
sourcefn abs(self) -> Self
fn abs(self) -> Self
Computes the absolute value of self
. Returns NAN
if the
number is NAN
.
§Examples
use std::f64;
let x = 3.5_f64;
let y = -3.5_f64;
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!(f64::NAN.abs().is_nan());
sourcefn signum(self) -> Self
fn signum(self) -> Self
Returns a number that represents the sign of self
.
1.0
if the number is positive,+0.0
orINFINITY
-1.0
if the number is negative,-0.0
orNEG_INFINITY
NAN
if the number isNAN
§Examples
use std::f64;
let f = 3.5_f64;
assert_eq!(f.signum(), 1.0);
assert_eq!(f64::NEG_INFINITY.signum(), -1.0);
assert!(f64::NAN.signum().is_nan());
sourcefn copysign(self, y: Self) -> Self
fn copysign(self, y: Self) -> Self
Returns a number composed of the magnitude of self
and the sign of
y
.
Equal to self
if the sign of self
and y
are the same, otherwise
equal to -self
. If self
is a NAN
, then a NAN
with the sign of
y
is returned.
§Examples
#![feature(copysign)]
use std::f64;
let f = 3.5_f64;
assert_eq!(f.copysign(0.42), 3.5_f64);
assert_eq!(f.copysign(-0.42), -3.5_f64);
assert_eq!((-f).copysign(0.42), 3.5_f64);
assert_eq!((-f).copysign(-0.42), -3.5_f64);
assert!(f64::NAN.copysign(1.0).is_nan());
sourcefn mul_add(self, a: Self, b: Self) -> Self
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.
§Examples
let m = 10.0_f64;
let x = 4.0_f64;
let b = 60.0_f64;
// 100.0
let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs();
assert!(abs_difference < 1e-10);
sourcefn div_euc(self, rhs: Self) -> Self
fn div_euc(self, rhs: Self) -> Self
Calculates Euclidean division, the matching method for mod_euc
.
This computes the integer n
such that
self = n * rhs + self.mod_euc(rhs)
.
In other words, the result is self / rhs
rounded to the integer n
such that self >= n * rhs
.
§Examples
#![feature(euclidean_division)]
let a: f64 = 7.0;
let b = 4.0;
assert_eq!(a.div_euc(b), 1.0); // 7.0 > 4.0 * 1.0
assert_eq!((-a).div_euc(b), -2.0); // -7.0 >= 4.0 * -2.0
assert_eq!(a.div_euc(-b), -1.0); // 7.0 >= -4.0 * -1.0
assert_eq!((-a).div_euc(-b), 2.0); // -7.0 >= -4.0 * 2.0
sourcefn mod_euc(self, rhs: Self) -> Self
fn mod_euc(self, rhs: Self) -> Self
Calculates the Euclidean modulo (self mod rhs), which is never negative.
In particular, the return value r
satisfies 0.0 <= r < rhs.abs()
in
most cases. However, due to a floating point round-off error it can
result in r == rhs.abs()
, violating the mathematical definition, if
self
is much smaller than rhs.abs()
in magnitude and self < 0.0
.
This result is not an element of the function’s codomain, but it is the
closest floating point number in the real numbers and thus fulfills the
property self == self.div_euc(rhs) * rhs + self.mod_euc(rhs)
approximatively.
§Examples
#![feature(euclidean_division)]
let a: f64 = 7.0;
let b = 4.0;
assert_eq!(a.mod_euc(b), 3.0);
assert_eq!((-a).mod_euc(b), 1.0);
assert_eq!(a.mod_euc(-b), 3.0);
assert_eq!((-a).mod_euc(-b), 1.0);
// limitation due to round-off error
assert_ne!((-std::f64::EPSILON).mod_euc(3.0), 0.0);
sourcefn powi(self, n: i32) -> Self
fn powi(self, n: i32) -> Self
Raises a number to an integer power.
Using this function is generally faster than using powf
§Examples
let x = 2.0_f64;
let abs_difference = (x.powi(2) - x*x).abs();
assert!(abs_difference < 1e-10);
sourcefn powf(self, n: Self) -> Self
fn powf(self, n: Self) -> Self
Raises a number to a floating point power.
§Examples
let x = 2.0_f64;
let abs_difference = (x.powf(2.0) - x*x).abs();
assert!(abs_difference < 1e-10);
sourcefn sqrt(self) -> Self
fn sqrt(self) -> Self
Takes the square root of a number.
Returns NaN if self
is a negative number.
§Examples
let positive = 4.0_f64;
let negative = -4.0_f64;
let abs_difference = (positive.sqrt() - 2.0).abs();
assert!(abs_difference < 1e-10);
assert!(negative.sqrt().is_nan());
sourcefn exp(self) -> Self
fn exp(self) -> Self
Returns e^(self)
, (the exponential function).
§Examples
let one = 1.0_f64;
// e^1
let e = one.exp();
// ln(e) - 1 == 0
let abs_difference = (e.ln() - 1.0).abs();
assert!(abs_difference < 1e-10);
sourcefn exp2(self) -> Self
fn exp2(self) -> Self
Returns 2^(self)
.
§Examples
let f = 2.0_f64;
// 2^2 - 4 == 0
let abs_difference = (f.exp2() - 4.0).abs();
assert!(abs_difference < 1e-10);
sourcefn ln(self) -> Self
fn ln(self) -> Self
Returns the natural logarithm of the number.
§Examples
let one = 1.0_f64;
// e^1
let e = one.exp();
// ln(e) - 1 == 0
let abs_difference = (e.ln() - 1.0).abs();
assert!(abs_difference < 1e-10);
sourcefn log(self, base: Self) -> Self
fn log(self, base: Self) -> Self
Returns the logarithm of the number with respect to an arbitrary base.
The result may not be correctly rounded owing to implementation details;
self.log2()
can produce more accurate results for base 2, and
self.log10()
can produce more accurate results for base 10.
§Examples
let five = 5.0_f64;
// log5(5) - 1 == 0
let abs_difference = (five.log(5.0) - 1.0).abs();
assert!(abs_difference < 1e-10);
sourcefn log2(self) -> Self
fn log2(self) -> Self
Returns the base 2 logarithm of the number.
§Examples
let two = 2.0_f64;
// log2(2) - 1 == 0
let abs_difference = (two.log2() - 1.0).abs();
assert!(abs_difference < 1e-10);
sourcefn log10(self) -> Self
fn log10(self) -> Self
Returns the base 10 logarithm of the number.
§Examples
let ten = 10.0_f64;
// log10(10) - 1 == 0
let abs_difference = (ten.log10() - 1.0).abs();
assert!(abs_difference < 1e-10);
sourcefn abs_sub(self, other: Self) -> Self
fn abs_sub(self, other: Self) -> Self
(self - other).abs()
: this operation is (self - other).max(0.0)
(also known as fdim
in C). If you truly need the positive difference, consider using that expression or the C function fdim
, depending on how you wish to handle NaN (please consider filing an issue describing your use-case too).The positive difference of two numbers.
- If
self <= other
:0:0
- Else:
self - other
§Examples
let x = 3.0_f64;
let y = -3.0_f64;
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);
sourcefn cbrt(self) -> Self
fn cbrt(self) -> Self
Takes the cubic root of a number.
§Examples
let x = 8.0_f64;
// x^(1/3) - 2 == 0
let abs_difference = (x.cbrt() - 2.0).abs();
assert!(abs_difference < 1e-10);
sourcefn hypot(self, other: Self) -> Self
fn hypot(self, other: Self) -> Self
Calculates the length of the hypotenuse of a right-angle triangle given
legs of length x
and y
.
§Examples
let x = 2.0_f64;
let y = 3.0_f64;
// sqrt(x^2 + y^2)
let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();
assert!(abs_difference < 1e-10);
sourcefn sin(self) -> Self
fn sin(self) -> Self
Computes the sine of a number (in radians).
§Examples
use std::f64;
let x = f64::consts::PI/2.0;
let abs_difference = (x.sin() - 1.0).abs();
assert!(abs_difference < 1e-10);
sourcefn cos(self) -> Self
fn cos(self) -> Self
Computes the cosine of a number (in radians).
§Examples
use std::f64;
let x = 2.0*f64::consts::PI;
let abs_difference = (x.cos() - 1.0).abs();
assert!(abs_difference < 1e-10);
sourcefn tan(self) -> Self
fn tan(self) -> Self
Computes the tangent of a number (in radians).
§Examples
use std::f64;
let x = f64::consts::PI/4.0;
let abs_difference = (x.tan() - 1.0).abs();
assert!(abs_difference < 1e-14);
sourcefn asin(self) -> Self
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].
§Examples
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);
sourcefn acos(self) -> Self
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].
§Examples
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);
sourcefn atan(self) -> Self
fn atan(self) -> Self
Computes the arctangent of a number. Return value is in radians in the range [-pi/2, pi/2];
§Examples
let f = 1.0_f64;
// atan(tan(1))
let abs_difference = (f.tan().atan() - 1.0).abs();
assert!(abs_difference < 1e-10);
sourcefn atan2(self, other: Self) -> Self
fn atan2(self, other: Self) -> Self
Computes the four quadrant arctangent of self
(y
) and other
(x
) in radians.
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)
§Examples
use std::f64;
let pi = f64::consts::PI;
// Positive angles measured counter-clockwise
// from positive x axis
// -pi/4 radians (45 deg clockwise)
let x1 = 3.0_f64;
let y1 = -3.0_f64;
// 3pi/4 radians (135 deg counter-clockwise)
let x2 = -3.0_f64;
let y2 = 3.0_f64;
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);
sourcefn sin_cos(self) -> (Self, Self)where
Self: Sized,
fn sin_cos(self) -> (Self, Self)where
Self: Sized,
Simultaneously computes the sine and cosine of the number, x
. Returns
(sin(x), cos(x))
.
§Examples
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_1 < 1e-10);
sourcefn exp_m1(self) -> Self
fn exp_m1(self) -> Self
Returns e^(self) - 1
in a way that is accurate even if the
number is close to zero.
§Examples
let x = 7.0_f64;
// e^(ln(7)) - 1
let abs_difference = (x.ln().exp_m1() - 6.0).abs();
assert!(abs_difference < 1e-10);
sourcefn ln_1p(self) -> Self
fn ln_1p(self) -> Self
Returns ln(1+n)
(natural logarithm) more accurately than if
the operations were performed separately.
§Examples
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);
sourcefn sinh(self) -> Self
fn sinh(self) -> Self
Hyperbolic sine function.
§Examples
use std::f64;
let e = f64::consts::E;
let x = 1.0_f64;
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);
sourcefn cosh(self) -> Self
fn cosh(self) -> Self
Hyperbolic cosine function.
§Examples
use std::f64;
let e = f64::consts::E;
let x = 1.0_f64;
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);
sourcefn tanh(self) -> Self
fn tanh(self) -> Self
Hyperbolic tangent function.
§Examples
use std::f64;
let e = f64::consts::E;
let x = 1.0_f64;
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);
sourcefn asinh(self) -> Self
fn asinh(self) -> Self
Inverse hyperbolic sine function.
§Examples
let x = 1.0_f64;
let f = x.sinh().asinh();
let abs_difference = (f - x).abs();
assert!(abs_difference < 1.0e-10);
Object Safety§
Implementations on Foreign Types§
source§impl Float for f32
impl Float for f32
fn floor(self) -> f32
fn ceil(self) -> f32
fn round(self) -> f32
fn trunc(self) -> f32
fn fract(self) -> f32
fn abs(self) -> f32
fn signum(self) -> f32
fn copysign(self, y: f32) -> f32
fn mul_add(self, a: f32, b: f32) -> f32
fn div_euc(self, rhs: f32) -> f32
fn mod_euc(self, rhs: f32) -> f32
fn powi(self, n: i32) -> f32
fn powf(self, n: f32) -> f32
fn sqrt(self) -> f32
fn exp(self) -> f32
fn exp2(self) -> f32
fn ln(self) -> f32
fn log(self, base: f32) -> f32
fn log2(self) -> f32
fn log10(self) -> f32
source§fn abs_sub(self, other: f32) -> f32
fn abs_sub(self, other: f32) -> f32
(self - other).abs()
: this operation is (self - other).max(0.0)
(also known as fdim
in C). If you truly need the positive difference, consider using that expression or the C function fdim
, depending on how you wish to handle NaN (please consider filing an issue describing your use-case too).fn cbrt(self) -> f32
fn hypot(self, other: f32) -> f32
fn sin(self) -> f32
fn cos(self) -> f32
fn tan(self) -> f32
fn asin(self) -> f32
fn acos(self) -> f32
fn atan(self) -> f32
fn atan2(self, other: f32) -> f32
fn sin_cos(self) -> (f32, f32)
fn exp_m1(self) -> f32
fn ln_1p(self) -> f32
fn sinh(self) -> f32
fn cosh(self) -> f32
fn tanh(self) -> f32
fn asinh(self) -> f32
fn acosh(self) -> f32
fn atanh(self) -> f32
source§impl Float for f64
impl Float for f64
fn floor(self) -> f64
fn ceil(self) -> f64
fn round(self) -> f64
fn trunc(self) -> f64
fn fract(self) -> f64
fn abs(self) -> f64
fn signum(self) -> f64
fn copysign(self, y: f64) -> f64
fn mul_add(self, a: f64, b: f64) -> f64
fn div_euc(self, rhs: f64) -> f64
fn mod_euc(self, rhs: f64) -> f64
fn powi(self, n: i32) -> f64
fn powf(self, n: f64) -> f64
fn sqrt(self) -> f64
fn exp(self) -> f64
fn exp2(self) -> f64
fn ln(self) -> f64
fn log(self, base: f64) -> f64
fn log2(self) -> f64
fn log10(self) -> f64
source§fn abs_sub(self, other: f64) -> f64
fn abs_sub(self, other: f64) -> f64
(self - other).abs()
: this operation is (self - other).max(0.0)
(also known as fdim
in C). If you truly need the positive difference, consider using that expression or the C function fdim
, depending on how you wish to handle NaN (please consider filing an issue describing your use-case too).