[−][src]Trait ndless::prelude::Float
Copy and pasted from Rust std
Required methods
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);
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);
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);
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);
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);
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());
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());
#[must_use]
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());
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);
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
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);
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);
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);
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());
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);
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);
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);
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);
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);
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);
fn abs_sub(self, other: Self) -> Self
you probably meant (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);
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);
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);
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);
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);
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);
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);
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);
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);
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);
fn sin_cos(self) -> (Self, Self) where
Self: Sized,
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);
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);
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);
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);
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);
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);
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);
fn acosh(self) -> Self
Inverse hyperbolic cosine function.
Examples
let x = 1.0_f64; 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.
Examples
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);