Trait bonsaidb::core::num_traits::Float
source · pub trait Float: Num + Copy + NumCast + PartialOrd<Self> + Neg<Output = Self> {
Show 59 methods
// Required methods
fn nan() -> Self;
fn infinity() -> Self;
fn neg_infinity() -> Self;
fn neg_zero() -> Self;
fn min_value() -> Self;
fn min_positive_value() -> Self;
fn max_value() -> Self;
fn is_nan(self) -> bool;
fn is_infinite(self) -> bool;
fn is_finite(self) -> bool;
fn is_normal(self) -> bool;
fn classify(self) -> FpCategory;
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 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;
fn integer_decode(self) -> (u64, i16, i8);
// Provided methods
fn epsilon() -> Self { ... }
fn is_subnormal(self) -> bool { ... }
fn to_degrees(self) -> Self { ... }
fn to_radians(self) -> Self { ... }
fn copysign(self, sign: Self) -> Self { ... }
}
Expand description
Generic trait for floating point numbers
This trait is only available with the std
feature, or with the libm
feature otherwise.
Required Methods§
sourcefn nan() -> Self
fn nan() -> Self
Returns the NaN
value.
use num_traits::Float;
let nan: f32 = Float::nan();
assert!(nan.is_nan());
sourcefn infinity() -> Self
fn infinity() -> Self
Returns the infinite value.
use num_traits::Float;
use std::f32;
let infinity: f32 = Float::infinity();
assert!(infinity.is_infinite());
assert!(!infinity.is_finite());
assert!(infinity > f32::MAX);
sourcefn neg_infinity() -> Self
fn neg_infinity() -> Self
Returns the negative infinite value.
use num_traits::Float;
use std::f32;
let neg_infinity: f32 = Float::neg_infinity();
assert!(neg_infinity.is_infinite());
assert!(!neg_infinity.is_finite());
assert!(neg_infinity < f32::MIN);
sourcefn neg_zero() -> Self
fn neg_zero() -> Self
Returns -0.0
.
use num_traits::{Zero, Float};
let inf: f32 = Float::infinity();
let zero: f32 = Zero::zero();
let neg_zero: f32 = Float::neg_zero();
assert_eq!(zero, neg_zero);
assert_eq!(7.0f32/inf, zero);
assert_eq!(zero * 10.0, zero);
sourcefn min_value() -> Self
fn min_value() -> Self
Returns the smallest finite value that this type can represent.
use num_traits::Float;
use std::f64;
let x: f64 = Float::min_value();
assert_eq!(x, f64::MIN);
sourcefn min_positive_value() -> Self
fn min_positive_value() -> Self
Returns the smallest positive, normalized value that this type can represent.
use num_traits::Float;
use std::f64;
let x: f64 = Float::min_positive_value();
assert_eq!(x, f64::MIN_POSITIVE);
sourcefn max_value() -> Self
fn max_value() -> Self
Returns the largest finite value that this type can represent.
use num_traits::Float;
use std::f64;
let x: f64 = Float::max_value();
assert_eq!(x, f64::MAX);
sourcefn is_nan(self) -> bool
fn is_nan(self) -> bool
Returns true
if this value is NaN
and false otherwise.
use num_traits::Float;
use std::f64;
let nan = f64::NAN;
let f = 7.0;
assert!(nan.is_nan());
assert!(!f.is_nan());
sourcefn is_infinite(self) -> bool
fn is_infinite(self) -> bool
Returns true
if this value is positive infinity or negative infinity and
false otherwise.
use num_traits::Float;
use std::f32;
let f = 7.0f32;
let inf: f32 = Float::infinity();
let neg_inf: f32 = Float::neg_infinity();
let nan: f32 = f32::NAN;
assert!(!f.is_infinite());
assert!(!nan.is_infinite());
assert!(inf.is_infinite());
assert!(neg_inf.is_infinite());
sourcefn is_finite(self) -> bool
fn is_finite(self) -> bool
Returns true
if this number is neither infinite nor NaN
.
use num_traits::Float;
use std::f32;
let f = 7.0f32;
let inf: f32 = Float::infinity();
let neg_inf: f32 = Float::neg_infinity();
let nan: f32 = f32::NAN;
assert!(f.is_finite());
assert!(!nan.is_finite());
assert!(!inf.is_finite());
assert!(!neg_inf.is_finite());
sourcefn is_normal(self) -> bool
fn is_normal(self) -> bool
Returns true
if the number is neither zero, infinite,
subnormal, or NaN
.
use num_traits::Float;
use std::f32;
let min = f32::MIN_POSITIVE; // 1.17549435e-38f32
let max = f32::MAX;
let lower_than_min = 1.0e-40_f32;
let zero = 0.0f32;
assert!(min.is_normal());
assert!(max.is_normal());
assert!(!zero.is_normal());
assert!(!f32::NAN.is_normal());
assert!(!f32::INFINITY.is_normal());
// Values between `0` and `min` are Subnormal.
assert!(!lower_than_min.is_normal());
sourcefn classify(self) -> FpCategory
fn classify(self) -> FpCategory
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 num_traits::Float;
use std::num::FpCategory;
use std::f32;
let num = 12.4f32;
let inf = f32::INFINITY;
assert_eq!(num.classify(), FpCategory::Normal);
assert_eq!(inf.classify(), FpCategory::Infinite);
sourcefn floor(self) -> Self
fn floor(self) -> Self
Returns the largest integer less than or equal to a number.
use num_traits::Float;
let f = 3.99;
let g = 3.0;
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.
use num_traits::Float;
let f = 3.01;
let g = 4.0;
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
.
use num_traits::Float;
let f = 3.3;
let g = -3.3;
assert_eq!(f.round(), 3.0);
assert_eq!(g.round(), -3.0);
sourcefn trunc(self) -> Self
fn trunc(self) -> Self
Return the integer part of a number.
use num_traits::Float;
let f = 3.3;
let g = -3.7;
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.
use num_traits::Float;
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);
sourcefn abs(self) -> Self
fn abs(self) -> Self
Computes the absolute value of self
. Returns Float::nan()
if the
number is Float::nan()
.
use num_traits::Float;
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!(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
orFloat::infinity()
-1.0
if the number is negative,-0.0
orFloat::neg_infinity()
Float::nan()
if the number isFloat::nan()
use num_traits::Float;
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());
sourcefn is_sign_positive(self) -> bool
fn is_sign_positive(self) -> bool
Returns true
if self
is positive, including +0.0
,
Float::infinity()
, and Float::nan()
.
use num_traits::Float;
use std::f64;
let nan: f64 = f64::NAN;
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!(nan.is_sign_positive());
assert!(!neg_nan.is_sign_positive());
sourcefn is_sign_negative(self) -> bool
fn is_sign_negative(self) -> bool
Returns true
if self
is negative, including -0.0
,
Float::neg_infinity()
, and -Float::nan()
.
use num_traits::Float;
use std::f64;
let nan: f64 = f64::NAN;
let neg_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());
assert!(neg_nan.is_sign_negative());
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.
use num_traits::Float;
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);
sourcefn recip(self) -> Self
fn recip(self) -> Self
Take the reciprocal (inverse) of a number, 1/x
.
use num_traits::Float;
let x = 2.0;
let abs_difference = (x.recip() - (1.0/x)).abs();
assert!(abs_difference < 1e-10);
sourcefn powi(self, n: i32) -> Self
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::Float;
let x = 2.0;
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
Raise a number to a floating point power.
use num_traits::Float;
let x = 2.0;
let abs_difference = (x.powf(2.0) - x*x).abs();
assert!(abs_difference < 1e-10);
sourcefn sqrt(self) -> Self
fn sqrt(self) -> Self
Take the square root of a number.
Returns NaN if self
is a negative number.
use num_traits::Float;
let positive = 4.0;
let negative = -4.0;
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).
use num_traits::Float;
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);
sourcefn exp2(self) -> Self
fn exp2(self) -> Self
Returns 2^(self)
.
use num_traits::Float;
let f = 2.0;
// 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.
use num_traits::Float;
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);
sourcefn log(self, base: Self) -> Self
fn log(self, base: Self) -> Self
Returns the logarithm of the number with respect to an arbitrary base.
use num_traits::Float;
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);
sourcefn log2(self) -> Self
fn log2(self) -> Self
Returns the base 2 logarithm of the number.
use num_traits::Float;
let two = 2.0;
// 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.
use num_traits::Float;
let ten = 10.0;
// log10(10) - 1 == 0
let abs_difference = (ten.log10() - 1.0).abs();
assert!(abs_difference < 1e-10);
sourcefn max(self, other: Self) -> Self
fn max(self, other: Self) -> Self
Returns the maximum of the two numbers.
use num_traits::Float;
let x = 1.0;
let y = 2.0;
assert_eq!(x.max(y), y);
sourcefn min(self, other: Self) -> Self
fn min(self, other: Self) -> Self
Returns the minimum of the two numbers.
use num_traits::Float;
let x = 1.0;
let y = 2.0;
assert_eq!(x.min(y), x);
sourcefn abs_sub(self, other: Self) -> Self
fn abs_sub(self, other: Self) -> Self
The positive difference of two numbers.
- If
self <= other
:0:0
- Else:
self - other
use num_traits::Float;
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);
sourcefn cbrt(self) -> Self
fn cbrt(self) -> Self
Take the cubic root of a number.
use num_traits::Float;
let x = 8.0;
// 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
Calculate the length of the hypotenuse of a right-angle triangle given
legs of length x
and y
.
use num_traits::Float;
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);
sourcefn sin(self) -> Self
fn sin(self) -> Self
Computes the sine of a number (in radians).
use num_traits::Float;
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).
use num_traits::Float;
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).
use num_traits::Float;
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].
use num_traits::Float;
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].
use num_traits::Float;
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];
use num_traits::Float;
let f = 1.0;
// 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
).
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::Float;
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);
sourcefn sin_cos(self) -> (Self, Self)
fn sin_cos(self) -> (Self, Self)
Simultaneously computes the sine and cosine of the number, x
. Returns
(sin(x), cos(x))
.
use num_traits::Float;
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);
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.
use num_traits::Float;
let x = 7.0;
// 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.
use num_traits::Float;
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.
use num_traits::Float;
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);
sourcefn cosh(self) -> Self
fn cosh(self) -> Self
Hyperbolic cosine function.
use num_traits::Float;
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);
sourcefn tanh(self) -> Self
fn tanh(self) -> Self
Hyperbolic tangent function.
use num_traits::Float;
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);
sourcefn asinh(self) -> Self
fn asinh(self) -> Self
Inverse hyperbolic sine function.
use num_traits::Float;
let x = 1.0;
let f = x.sinh().asinh();
let abs_difference = (f - x).abs();
assert!(abs_difference < 1.0e-10);
sourcefn acosh(self) -> Self
fn acosh(self) -> Self
Inverse hyperbolic cosine function.
use num_traits::Float;
let x = 1.0;
let f = x.cosh().acosh();
let abs_difference = (f - x).abs();
assert!(abs_difference < 1.0e-10);
sourcefn atanh(self) -> Self
fn atanh(self) -> Self
Inverse hyperbolic tangent function.
use num_traits::Float;
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);
sourcefn integer_decode(self) -> (u64, i16, i8)
fn integer_decode(self) -> (u64, i16, i8)
Returns the mantissa, base 2 exponent, and sign as integers, respectively.
The original number can be recovered by sign * mantissa * 2 ^ exponent
.
use num_traits::Float;
let num = 2.0f32;
// (8388608, -22, 1)
let (mantissa, exponent, sign) = Float::integer_decode(num);
let sign_f = sign as f32;
let mantissa_f = mantissa as f32;
let exponent_f = num.powf(exponent as f32);
// 1 * 8388608 * 2^(-22) == 2
let abs_difference = (sign_f * mantissa_f * exponent_f - num).abs();
assert!(abs_difference < 1e-10);
Provided Methods§
sourcefn epsilon() -> Self
fn epsilon() -> Self
Returns epsilon, a small positive value.
use num_traits::Float;
use std::f64;
let x: f64 = Float::epsilon();
assert_eq!(x, f64::EPSILON);
Panics
The default implementation will panic if f32::EPSILON
cannot
be cast to Self
.
sourcefn is_subnormal(self) -> bool
fn is_subnormal(self) -> bool
Returns true
if the number is subnormal.
use num_traits::Float;
use std::f64;
let min = f64::MIN_POSITIVE; // 2.2250738585072014e-308_f64
let max = f64::MAX;
let lower_than_min = 1.0e-308_f64;
let zero = 0.0_f64;
assert!(!min.is_subnormal());
assert!(!max.is_subnormal());
assert!(!zero.is_subnormal());
assert!(!f64::NAN.is_subnormal());
assert!(!f64::INFINITY.is_subnormal());
// Values between `0` and `min` are Subnormal.
assert!(lower_than_min.is_subnormal());
sourcefn to_degrees(self) -> Self
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);
sourcefn to_radians(self) -> Self
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);
sourcefn copysign(self, sign: Self) -> Self
fn copysign(self, sign: Self) -> Self
Returns a number composed of the magnitude of self
and the sign of
sign
.
Equal to self
if the sign of self
and sign
are the same, otherwise
equal to -self
. If self
is a NAN
, then a NAN
with the sign of
sign
is returned.
Examples
use num_traits::Float;
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());