Returns the largest integer less than or equal to a number.
let f = 3.99_f32;
let g = 3.0_f32;
assert_eq!(f.floor(), 3.0);
assert_eq!(g.floor(), 3.0);Run
Returns the smallest integer greater than or equal to a number.
let f = 3.01_f32;
let g = 4.0_f32;
assert_eq!(f.ceil(), 4.0);
assert_eq!(g.ceil(), 4.0);Run
Returns the nearest integer to a number. Round half-way cases away from
0.0.
let f = 3.3_f32;
let g = -3.3_f32;
assert_eq!(f.round(), 3.0);
assert_eq!(g.round(), -3.0);Run
Returns the integer part of a number.
let f = 3.3_f32;
let g = -3.7_f32;
assert_eq!(f.trunc(), 3.0);
assert_eq!(g.trunc(), -3.0);Run
Returns the fractional part of a number.
use std::f32;
let x = 3.5_f32;
let y = -3.5_f32;
let abs_difference_x = (x.fract() - 0.5).abs();
let abs_difference_y = (y.fract() - (-0.5)).abs();
assert!(abs_difference_x <= f32::EPSILON);
assert!(abs_difference_y <= f32::EPSILON);Run
Computes the absolute value of self. Returns NAN if the
number is NAN.
use std::f32;
let x = 3.5_f32;
let y = -3.5_f32;
let abs_difference_x = (x.abs() - x).abs();
let abs_difference_y = (y.abs() - (-y)).abs();
assert!(abs_difference_x <= f32::EPSILON);
assert!(abs_difference_y <= f32::EPSILON);
assert!(f32::NAN.abs().is_nan());Run
Returns a number that represents the sign of self.
1.0 if the number is positive, +0.0 or INFINITY
-1.0 if the number is negative, -0.0 or NEG_INFINITY
NAN if the number is NAN
use std::f32;
let f = 3.5_f32;
assert_eq!(f.signum(), 1.0);
assert_eq!(f32::NEG_INFINITY.signum(), -1.0);
assert!(f32::NAN.signum().is_nan());Run
🔬 This is a nightly-only experimental API. (
copysign #55169)
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.
#![feature(copysign)]
use std::f32;
let f = 3.5_f32;
assert_eq!(f.copysign(0.42), 3.5_f32);
assert_eq!(f.copysign(-0.42), -3.5_f32);
assert_eq!((-f).copysign(0.42), 3.5_f32);
assert_eq!((-f).copysign(-0.42), -3.5_f32);
assert!(f32::NAN.copysign(1.0).is_nan());Run
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 std::f32;
let m = 10.0_f32;
let x = 4.0_f32;
let b = 60.0_f32;
let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs();
assert!(abs_difference <= f32::EPSILON);Run
🔬 This is a nightly-only experimental API. (
euclidean_division #49048)
Calculates Euclidean division, the matching method for rem_euclid.
This computes the integer n such that
self = n * rhs + self.rem_euclid(rhs).
In other words, the result is self / rhs rounded to the integer n
such that self >= n * rhs.
#![feature(euclidean_division)]
let a: f32 = 7.0;
let b = 4.0;
assert_eq!(a.div_euclid(b), 1.0);
assert_eq!((-a).div_euclid(b), -2.0);
assert_eq!(a.div_euclid(-b), -1.0);
assert_eq!((-a).div_euclid(-b), 2.0); Run
🔬 This is a nightly-only experimental API. (
euclidean_division #49048)
Calculates the least nonnegative remainder of self (mod rhs).
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_euclid(rhs) * rhs + self.rem_euclid(rhs)
approximatively.
#![feature(euclidean_division)]
let a: f32 = 7.0;
let b = 4.0;
assert_eq!(a.rem_euclid(b), 3.0);
assert_eq!((-a).rem_euclid(b), 1.0);
assert_eq!(a.rem_euclid(-b), 3.0);
assert_eq!((-a).rem_euclid(-b), 1.0);
assert!((-std::f32::EPSILON).rem_euclid(3.0) != 0.0);Run
Raises a number to an integer power.
Using this function is generally faster than using powf
use std::f32;
let x = 2.0_f32;
let abs_difference = (x.powi(2) - x*x).abs();
assert!(abs_difference <= f32::EPSILON);Run
Raises a number to a floating point power.
use std::f32;
let x = 2.0_f32;
let abs_difference = (x.powf(2.0) - x*x).abs();
assert!(abs_difference <= f32::EPSILON);Run
Takes the square root of a number.
Returns NaN if self is a negative number.
use std::f32;
let positive = 4.0_f32;
let negative = -4.0_f32;
let abs_difference = (positive.sqrt() - 2.0).abs();
assert!(abs_difference <= f32::EPSILON);
assert!(negative.sqrt().is_nan());Run
Returns e^(self), (the exponential function).
use std::f32;
let one = 1.0f32;
let e = one.exp();
let abs_difference = (e.ln() - 1.0).abs();
assert!(abs_difference <= f32::EPSILON);Run
Returns 2^(self).
use std::f32;
let f = 2.0f32;
let abs_difference = (f.exp2() - 4.0).abs();
assert!(abs_difference <= f32::EPSILON);Run
Returns the natural logarithm of the number.
use std::f32;
let one = 1.0f32;
let e = one.exp();
let abs_difference = (e.ln() - 1.0).abs();
assert!(abs_difference <= f32::EPSILON);Run
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.
use std::f32;
let five = 5.0f32;
let abs_difference = (five.log(5.0) - 1.0).abs();
assert!(abs_difference <= f32::EPSILON);Run
Returns the base 2 logarithm of the number.
use std::f32;
let two = 2.0f32;
let abs_difference = (two.log2() - 1.0).abs();
assert!(abs_difference <= f32::EPSILON);Run
Returns the base 10 logarithm of the number.
use std::f32;
let ten = 10.0f32;
let abs_difference = (ten.log10() - 1.0).abs();
assert!(abs_difference <= f32::EPSILON);Run
Deprecated since 1.10.0:
you probably meant (self - other).abs(): this operation is (self - other).max(0.0) except that abs_sub also propagates NaNs (also known as fdimf in C). If you truly need the positive difference, consider using that expression or the C function fdimf, 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
use std::f32;
let x = 3.0f32;
let y = -3.0f32;
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 <= f32::EPSILON);
assert!(abs_difference_y <= f32::EPSILON);Run
Takes the cubic root of a number.
use std::f32;
let x = 8.0f32;
let abs_difference = (x.cbrt() - 2.0).abs();
assert!(abs_difference <= f32::EPSILON);Run
Calculates the length of the hypotenuse of a right-angle triangle given
legs of length x and y.
use std::f32;
let x = 2.0f32;
let y = 3.0f32;
let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();
assert!(abs_difference <= f32::EPSILON);Run
Computes the sine of a number (in radians).
use std::f32;
let x = f32::consts::PI/2.0;
let abs_difference = (x.sin() - 1.0).abs();
assert!(abs_difference <= f32::EPSILON);Run
Computes the cosine of a number (in radians).
use std::f32;
let x = 2.0*f32::consts::PI;
let abs_difference = (x.cos() - 1.0).abs();
assert!(abs_difference <= f32::EPSILON);Run
Computes the tangent of a number (in radians).
use std::f32;
let x = f32::consts::PI / 4.0;
let abs_difference = (x.tan() - 1.0).abs();
assert!(abs_difference <= f32::EPSILON);Run
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].
use std::f32;
let f = f32::consts::PI / 2.0;
let abs_difference = (f.sin().asin() - f32::consts::PI / 2.0).abs();
assert!(abs_difference <= f32::EPSILON);Run
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].
use std::f32;
let f = f32::consts::PI / 4.0;
let abs_difference = (f.cos().acos() - f32::consts::PI / 4.0).abs();
assert!(abs_difference <= f32::EPSILON);Run
Computes the arctangent of a number. Return value is in radians in the
range [-pi/2, pi/2];
use std::f32;
let f = 1.0f32;
let abs_difference = (f.tan().atan() - 1.0).abs();
assert!(abs_difference <= f32::EPSILON);Run
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)
use std::f32;
let pi = f32::consts::PI;
let x1 = 3.0f32;
let y1 = -3.0f32;
let x2 = -3.0f32;
let y2 = 3.0f32;
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 <= f32::EPSILON);
assert!(abs_difference_2 <= f32::EPSILON);Run
Simultaneously computes the sine and cosine of the number, x. Returns
(sin(x), cos(x)).
use std::f32;
let x = f32::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 <= f32::EPSILON);
assert!(abs_difference_1 <= f32::EPSILON);Run
Returns e^(self) - 1 in a way that is accurate even if the
number is close to zero.
use std::f32;
let x = 6.0f32;
let abs_difference = (x.ln().exp_m1() - 5.0).abs();
assert!(abs_difference <= f32::EPSILON);Run
Returns ln(1+n) (natural logarithm) more accurately than if
the operations were performed separately.
use std::f32;
let x = f32::consts::E - 1.0;
let abs_difference = (x.ln_1p() - 1.0).abs();
assert!(abs_difference <= f32::EPSILON);Run
Hyperbolic sine function.
use std::f32;
let e = f32::consts::E;
let x = 1.0f32;
let f = x.sinh();
let g = (e*e - 1.0)/(2.0*e);
let abs_difference = (f - g).abs();
assert!(abs_difference <= f32::EPSILON);Run
Hyperbolic cosine function.
use std::f32;
let e = f32::consts::E;
let x = 1.0f32;
let f = x.cosh();
let g = (e*e + 1.0)/(2.0*e);
let abs_difference = (f - g).abs();
assert!(abs_difference <= f32::EPSILON);Run
Hyperbolic tangent function.
use std::f32;
let e = f32::consts::E;
let x = 1.0f32;
let f = x.tanh();
let g = (1.0 - e.powi(-2))/(1.0 + e.powi(-2));
let abs_difference = (f - g).abs();
assert!(abs_difference <= f32::EPSILON);Run
Inverse hyperbolic sine function.
use std::f32;
let x = 1.0f32;
let f = x.sinh().asinh();
let abs_difference = (f - x).abs();
assert!(abs_difference <= f32::EPSILON);Run
Inverse hyperbolic cosine function.
use std::f32;
let x = 1.0f32;
let f = x.cosh().acosh();
let abs_difference = (f - x).abs();
assert!(abs_difference <= f32::EPSILON);Run
Inverse hyperbolic tangent function.
use std::f32;
let e = f32::consts::E;
let f = e.tanh().atanh();
let abs_difference = (f - e).abs();
assert!(abs_difference <= 1e-5);Run
Returns true if this value is NaN and false otherwise.
use std::f32;
let nan = f32::NAN;
let f = 7.0_f32;
assert!(nan.is_nan());
assert!(!f.is_nan());Run
Returns true if this value is positive infinity or negative infinity and
false otherwise.
use std::f32;
let f = 7.0f32;
let inf = f32::INFINITY;
let neg_inf = f32::NEG_INFINITY;
let nan = f32::NAN;
assert!(!f.is_infinite());
assert!(!nan.is_infinite());
assert!(inf.is_infinite());
assert!(neg_inf.is_infinite());Run
Returns true if this number is neither infinite nor NaN.
use std::f32;
let f = 7.0f32;
let inf = f32::INFINITY;
let neg_inf = f32::NEG_INFINITY;
let nan = f32::NAN;
assert!(f.is_finite());
assert!(!nan.is_finite());
assert!(!inf.is_finite());
assert!(!neg_inf.is_finite());Run
Returns true if the number is neither zero, infinite,
subnormal, or NaN.
use std::f32;
let min = f32::MIN_POSITIVE;
let max = f32::MAX;
let lower_than_min = 1.0e-40_f32;
let zero = 0.0_f32;
assert!(min.is_normal());
assert!(max.is_normal());
assert!(!zero.is_normal());
assert!(!f32::NAN.is_normal());
assert!(!f32::INFINITY.is_normal());
assert!(!lower_than_min.is_normal());Run
Returns the floating point category of the number. If only one property
is going to be tested, it is generally faster to use the specific
predicate instead.
use std::num::FpCategory;
use std::f32;
let num = 12.4_f32;
let inf = f32::INFINITY;
assert_eq!(num.classify(), FpCategory::Normal);
assert_eq!(inf.classify(), FpCategory::Infinite);Run
Returns true if and only if self has a positive sign, including +0.0, NaNs with
positive sign bit and positive infinity.
let f = 7.0_f32;
let g = -7.0_f32;
assert!(f.is_sign_positive());
assert!(!g.is_sign_positive());Run
Returns true if and only if self has a negative sign, including -0.0, NaNs with
negative sign bit and negative infinity.
let f = 7.0f32;
let g = -7.0f32;
assert!(!f.is_sign_negative());
assert!(g.is_sign_negative());Run
Takes the reciprocal (inverse) of a number, 1/x.
use std::f32;
let x = 2.0_f32;
let abs_difference = (x.recip() - (1.0/x)).abs();
assert!(abs_difference <= f32::EPSILON);Run
Converts radians to degrees.
use std::f32::{self, consts};
let angle = consts::PI;
let abs_difference = (angle.to_degrees() - 180.0).abs();
assert!(abs_difference <= f32::EPSILON);Run
Converts degrees to radians.
use std::f32::{self, consts};
let angle = 180.0f32;
let abs_difference = (angle.to_radians() - consts::PI).abs();
assert!(abs_difference <= f32::EPSILON);Run
Returns the maximum of the two numbers.
let x = 1.0f32;
let y = 2.0f32;
assert_eq!(x.max(y), y);Run
If one of the arguments is NaN, then the other argument is returned.
Returns the minimum of the two numbers.
let x = 1.0f32;
let y = 2.0f32;
assert_eq!(x.min(y), x);Run
If one of the arguments is NaN, then the other argument is returned.
Raw transmutation to u32.
This is currently identical to transmute::<f32, u32>(self) on all platforms.
See from_bits for some discussion of the portability of this operation
(there are almost no issues).
Note that this function is distinct from as casting, which attempts to
preserve the numeric value, and not the bitwise value.
assert_ne!((1f32).to_bits(), 1f32 as u32);
assert_eq!((12.5f32).to_bits(), 0x41480000);
Run
Raw transmutation from u32.
This is currently identical to transmute::<u32, f32>(v) on all platforms.
It turns out this is incredibly portable, for two reasons:
- Floats and Ints have the same endianness on all supported platforms.
- IEEE-754 very precisely specifies the bit layout of floats.
However there is one caveat: prior to the 2008 version of IEEE-754, how
to interpret the NaN signaling bit wasn't actually specified. Most platforms
(notably x86 and ARM) picked the interpretation that was ultimately
standardized in 2008, but some didn't (notably MIPS). As a result, all
signaling NaNs on MIPS are quiet NaNs on x86, and vice-versa.
Rather than trying to preserve signaling-ness cross-platform, this
implementation favors preserving the exact bits. This means that
any payloads encoded in NaNs will be preserved even if the result of
this method is sent over the network from an x86 machine to a MIPS one.
If the results of this method are only manipulated by the same
architecture that produced them, then there is no portability concern.
If the input isn't NaN, then there is no portability concern.
If you don't care about signalingness (very likely), then there is no
portability concern.
Note that this function is distinct from as casting, which attempts to
preserve the numeric value, and not the bitwise value.
use std::f32;
let v = f32::from_bits(0x41480000);
let difference = (v - 12.5).abs();
assert!(difference <= 1e-5);Run