Primitive Type f16

🔬This is a nightly-only experimental API. (f16 #116909)

A 16-bit floating point type (specifically, the “binary16” type defined in IEEE 754-2008).

This type is very similar to f32 but has decreased precision because it uses half as many bits. Please see [the documentation for f32 or Wikipedia on half-precision values for more information.

Note that most common platforms will not support f16 in hardware without enabling extra target features, with the notable exception of Apple Silicon (also known as M1, M2, etc.) processors. Hardware support on x86-64 requires the avx512fp16 feature, while RISC-V requires Zhf. Usually the fallback implementation will be to use f32 hardware if it exists, and convert between f16 and f32 when performing math.

See also the std::f16::consts module.

Implementations

impl f16

pub fn floor(self) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Returns the largest integer less than or equal to self.

This function always returns the precise result.

Examples

#![feature(f16)]

let f = 3.7_f16;
let g = 3.0_f16;
let h = -3.7_f16;

assert_eq!(f.floor(), 3.0);
assert_eq!(g.floor(), 3.0);
assert_eq!(h.floor(), -4.0);

pub fn ceil(self) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Returns the smallest integer greater than or equal to self.

This function always returns the precise result.

Examples

#![feature(f16)]

let f = 3.01_f16;
let g = 4.0_f16;

assert_eq!(f.ceil(), 4.0);
assert_eq!(g.ceil(), 4.0);

pub fn round(self) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Returns the nearest integer to self. If a value is half-way between two integers, round away from 0.0.

This function always returns the precise result.

Examples

#![feature(f16)]

let f = 3.3_f16;
let g = -3.3_f16;
let h = -3.7_f16;
let i = 3.5_f16;
let j = 4.5_f16;

assert_eq!(f.round(), 3.0);
assert_eq!(g.round(), -3.0);
assert_eq!(h.round(), -4.0);
assert_eq!(i.round(), 4.0);
assert_eq!(j.round(), 5.0);

pub fn round_ties_even(self) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Returns the nearest integer to a number. Rounds half-way cases to the number with an even least significant digit.

This function always returns the precise result.

Examples

#![feature(f16)]

let f = 3.3_f16;
let g = -3.3_f16;
let h = 3.5_f16;
let i = 4.5_f16;

assert_eq!(f.round_ties_even(), 3.0);
assert_eq!(g.round_ties_even(), -3.0);
assert_eq!(h.round_ties_even(), 4.0);
assert_eq!(i.round_ties_even(), 4.0);

pub fn trunc(self) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Returns the integer part of self. This means that non-integer numbers are always truncated towards zero.

This function always returns the precise result.

Examples

#![feature(f16)]

let f = 3.7_f16;
let g = 3.0_f16;
let h = -3.7_f16;

assert_eq!(f.trunc(), 3.0);
assert_eq!(g.trunc(), 3.0);
assert_eq!(h.trunc(), -3.0);

pub fn fract(self) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Returns the fractional part of self.

This function always returns the precise result.

Examples

#![feature(f16)]

let x = 3.6_f16;
let y = -3.6_f16;
let abs_difference_x = (x.fract() - 0.6).abs();
let abs_difference_y = (y.fract() - (-0.6)).abs();

assert!(abs_difference_x <= f16::EPSILON);
assert!(abs_difference_y <= f16::EPSILON);

pub fn abs(self) -> Self

🔬This is a nightly-only experimental API. (f16 #116909)

Computes the absolute value of self.

This function always returns the precise result.

Examples

#![feature(f16)]

let x = 3.5_f16;
let y = -3.5_f16;

assert_eq!(x.abs(), x);
assert_eq!(y.abs(), -y);

assert!(f16::NAN.abs().is_nan());

pub fn signum(self) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

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

Examples

#![feature(f16)]

let f = 3.5_f16;

assert_eq!(f.signum(), 1.0);
assert_eq!(f16::NEG_INFINITY.signum(), -1.0);

assert!(f16::NAN.signum().is_nan());

pub fn copysign(self, sign: f16) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

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 bit of sign is returned. Note, however, that conserving the sign bit on NaN across arithmetical operations is not generally guaranteed. See explanation of NaN as a special value for more info.

Examples

#![feature(f16)]

let f = 3.5_f16;

assert_eq!(f.copysign(0.42), 3.5_f16);
assert_eq!(f.copysign(-0.42), -3.5_f16);
assert_eq!((-f).copysign(0.42), 3.5_f16);
assert_eq!((-f).copysign(-0.42), -3.5_f16);

assert!(f16::NAN.copysign(1.0).is_nan());

pub fn mul_add(self, a: f16, b: f16) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

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 may be more performant than an unfused multiply-add if the target architecture has a dedicated fma CPU instruction. However, this is not always true, and will be heavily dependant on designing algorithms with specific target hardware in mind.

Precision

The result of this operation is guaranteed to be the rounded infinite-precision result. It is specified by IEEE 754 as fusedMultiplyAdd and guaranteed not to change.

Examples

#![feature(f16)]

let m = 10.0_f16;
let x = 4.0_f16;
let b = 60.0_f16;

assert_eq!(m.mul_add(x, b), 100.0);
assert_eq!(m * x + b, 100.0);

let one_plus_eps = 1.0_f16 + f16::EPSILON;
let one_minus_eps = 1.0_f16 - f16::EPSILON;
let minus_one = -1.0_f16;

// The exact result (1 + eps) * (1 - eps) = 1 - eps * eps.
assert_eq!(one_plus_eps.mul_add(one_minus_eps, minus_one), -f16::EPSILON * f16::EPSILON);
// Different rounding with the non-fused multiply and add.
assert_eq!(one_plus_eps * one_minus_eps + minus_one, 0.0);

pub fn div_euclid(self, rhs: f16) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

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.

Precision

The result of this operation is guaranteed to be the rounded infinite-precision result.

Examples

#![feature(f16)]

let a: f16 = 7.0;
let b = 4.0;
assert_eq!(a.div_euclid(b), 1.0); // 7.0 > 4.0 * 1.0
assert_eq!((-a).div_euclid(b), -2.0); // -7.0 >= 4.0 * -2.0
assert_eq!(a.div_euclid(-b), -1.0); // 7.0 >= -4.0 * -1.0
assert_eq!((-a).div_euclid(-b), 2.0); // -7.0 >= -4.0 * 2.0

pub fn rem_euclid(self, rhs: f16) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

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) approximately.

Precision

The result of this operation is guaranteed to be the rounded infinite-precision result.

Examples

#![feature(f16)]

let a: f16 = 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);
// limitation due to round-off error
assert!((-f16::EPSILON).rem_euclid(3.0) != 0.0);

pub fn powi(self, n: i32) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Raises a number to an integer power.

Using this function is generally faster than using powf. It might have a different sequence of rounding operations than powf, so the results are not guaranteed to agree.

Unspecified precision

The precision of this function is non-deterministic. This means it varies by platform, Rust version, and can even differ within the same execution from one invocation to the next.

pub fn powf(self, n: f16) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Raises a number to a floating point power.

Unspecified precision

The precision of this function is non-deterministic. This means it varies by platform, Rust version, and can even differ within the same execution from one invocation to the next.

Examples

#![feature(f16)]

let x = 2.0_f16;
let abs_difference = (x.powf(2.0) - (x * x)).abs();

assert!(abs_difference <= f16::EPSILON);

pub fn sqrt(self) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Returns the square root of a number.

Returns NaN if self is a negative number other than -0.0.

Precision

The result of this operation is guaranteed to be the rounded infinite-precision result. It is specified by IEEE 754 as squareRoot and guaranteed not to change.

Examples

#![feature(f16)]

let positive = 4.0_f16;
let negative = -4.0_f16;
let negative_zero = -0.0_f16;

assert_eq!(positive.sqrt(), 2.0);
assert!(negative.sqrt().is_nan());
assert!(negative_zero.sqrt() == negative_zero);

pub fn exp(self) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Returns e^(self), (the exponential function).

Unspecified precision

The precision of this function is non-deterministic. This means it varies by platform, Rust version, and can even differ within the same execution from one invocation to the next.

Examples

#![feature(f16)]

let one = 1.0f16;
// e^1
let e = one.exp();

// ln(e) - 1 == 0
let abs_difference = (e.ln() - 1.0).abs();

assert!(abs_difference <= f16::EPSILON);

pub fn exp2(self) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Returns 2^(self).

Unspecified precision

The precision of this function is non-deterministic. This means it varies by platform, Rust version, and can even differ within the same execution from one invocation to the next.

Examples

#![feature(f16)]

let f = 2.0f16;

// 2^2 - 4 == 0
let abs_difference = (f.exp2() - 4.0).abs();

assert!(abs_difference <= f16::EPSILON);

pub fn ln(self) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Returns the natural logarithm of the number.

Unspecified precision

The precision of this function is non-deterministic. This means it varies by platform, Rust version, and can even differ within the same execution from one invocation to the next.

Examples

#![feature(f16)]

let one = 1.0f16;
// e^1
let e = one.exp();

// ln(e) - 1 == 0
let abs_difference = (e.ln() - 1.0).abs();

assert!(abs_difference <= f16::EPSILON);

pub fn log(self, base: f16) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Returns the logarithm of the number with respect to an arbitrary base.

The result might 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.

Unspecified precision

The precision of this function is non-deterministic. This means it varies by platform, Rust version, and can even differ within the same execution from one invocation to the next.

Examples

#![feature(f16)]

let five = 5.0f16;

// log5(5) - 1 == 0
let abs_difference = (five.log(5.0) - 1.0).abs();

assert!(abs_difference <= f16::EPSILON);

pub fn log2(self) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Returns the base 2 logarithm of the number.

Unspecified precision

The precision of this function is non-deterministic. This means it varies by platform, Rust version, and can even differ within the same execution from one invocation to the next.

Examples

#![feature(f16)]

let two = 2.0f16;

// log2(2) - 1 == 0
let abs_difference = (two.log2() - 1.0).abs();

assert!(abs_difference <= f16::EPSILON);

pub fn log10(self) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Returns the base 10 logarithm of the number.

Unspecified precision

The precision of this function is non-deterministic. This means it varies by platform, Rust version, and can even differ within the same execution from one invocation to the next.

Examples

#![feature(f16)]

let ten = 10.0f16;

// log10(10) - 1 == 0
let abs_difference = (ten.log10() - 1.0).abs();

assert!(abs_difference <= f16::EPSILON);

pub fn cbrt(self) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Returns the cube root of a number.

Unspecified precision

The precision of this function is non-deterministic. This means it varies by platform, Rust version, and can even differ within the same execution from one invocation to the next.

This function currently corresponds to the cbrtf from libc on Unix and Windows. Note that this might change in the future.

Examples

#![feature(f16)]

let x = 8.0f16;

// x^(1/3) - 2 == 0
let abs_difference = (x.cbrt() - 2.0).abs();

assert!(abs_difference <= f16::EPSILON);

pub fn hypot(self, other: f16) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Compute the distance between the origin and a point (x, y) on the Euclidean plane. Equivalently, compute the length of the hypotenuse of a right-angle triangle with other sides having length x.abs() and y.abs().

Unspecified precision

The precision of this function is non-deterministic. This means it varies by platform, Rust version, and can even differ within the same execution from one invocation to the next.

This function currently corresponds to the hypotf from libc on Unix and Windows. Note that this might change in the future.

Examples

#![feature(f16)]

let x = 2.0f16;
let y = 3.0f16;

// sqrt(x^2 + y^2)
let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();

assert!(abs_difference <= f16::EPSILON);

pub fn sin(self) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Computes the sine of a number (in radians).

Unspecified precision

The precision of this function is non-deterministic. This means it varies by platform, Rust version, and can even differ within the same execution from one invocation to the next.

Examples

#![feature(f16)]

let x = std::f16::consts::FRAC_PI_2;

let abs_difference = (x.sin() - 1.0).abs();

assert!(abs_difference <= f16::EPSILON);

pub fn cos(self) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Computes the cosine of a number (in radians).

Unspecified precision

The precision of this function is non-deterministic. This means it varies by platform, Rust version, and can even differ within the same execution from one invocation to the next.

Examples

#![feature(f16)]

let x = 2.0 * std::f16::consts::PI;

let abs_difference = (x.cos() - 1.0).abs();

assert!(abs_difference <= f16::EPSILON);

pub fn tan(self) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Computes the tangent of a number (in radians).

Unspecified precision

The precision of this function is non-deterministic. This means it varies by platform, Rust version, and can even differ within the same execution from one invocation to the next.

This function currently corresponds to the tanf from libc on Unix and Windows. Note that this might change in the future.

Examples

#![feature(f16)]

let x = std::f16::consts::FRAC_PI_4;
let abs_difference = (x.tan() - 1.0).abs();

assert!(abs_difference <= f16::EPSILON);

pub fn asin(self) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

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].

Unspecified precision

The precision of this function is non-deterministic. This means it varies by platform, Rust version, and can even differ within the same execution from one invocation to the next.

This function currently corresponds to the asinf from libc on Unix and Windows. Note that this might change in the future.

Examples

#![feature(f16)]

let f = std::f16::consts::FRAC_PI_2;

// asin(sin(pi/2))
let abs_difference = (f.sin().asin() - std::f16::consts::FRAC_PI_2).abs();

assert!(abs_difference <= f16::EPSILON);

pub fn acos(self) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

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].

Unspecified precision

The precision of this function is non-deterministic. This means it varies by platform, Rust version, and can even differ within the same execution from one invocation to the next.

This function currently corresponds to the acosf from libc on Unix and Windows. Note that this might change in the future.

Examples

#![feature(f16)]

let f = std::f16::consts::FRAC_PI_4;

// acos(cos(pi/4))
let abs_difference = (f.cos().acos() - std::f16::consts::FRAC_PI_4).abs();

assert!(abs_difference <= f16::EPSILON);

pub fn atan(self) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Computes the arctangent of a number. Return value is in radians in the range [-pi/2, pi/2];

Unspecified precision

The precision of this function is non-deterministic. This means it varies by platform, Rust version, and can even differ within the same execution from one invocation to the next.

This function currently corresponds to the atanf from libc on Unix and Windows. Note that this might change in the future.

Examples

#![feature(f16)]

let f = 1.0f16;

// atan(tan(1))
let abs_difference = (f.tan().atan() - 1.0).abs();

assert!(abs_difference <= f16::EPSILON);

pub fn atan2(self, other: f16) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

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)

Unspecified precision

The precision of this function is non-deterministic. This means it varies by platform, Rust version, and can even differ within the same execution from one invocation to the next.

This function currently corresponds to the atan2f from libc on Unix and Windows. Note that this might change in the future.

Examples

#![feature(f16)]

// Positive angles measured counter-clockwise
// from positive x axis
// -pi/4 radians (45 deg clockwise)
let x1 = 3.0f16;
let y1 = -3.0f16;

// 3pi/4 radians (135 deg counter-clockwise)
let x2 = -3.0f16;
let y2 = 3.0f16;

let abs_difference_1 = (y1.atan2(x1) - (-std::f16::consts::FRAC_PI_4)).abs();
let abs_difference_2 = (y2.atan2(x2) - (3.0 * std::f16::consts::FRAC_PI_4)).abs();

assert!(abs_difference_1 <= f16::EPSILON);
assert!(abs_difference_2 <= f16::EPSILON);

pub fn sin_cos(self) -> (f16, f16)

🔬This is a nightly-only experimental API. (f16 #116909)

Simultaneously computes the sine and cosine of the number, x. Returns (sin(x), cos(x)).

Unspecified precision

The precision of this function is non-deterministic. This means it varies by platform, Rust version, and can even differ within the same execution from one invocation to the next.

This function currently corresponds to the (f16::sin(x), f16::cos(x)). Note that this might change in the future.

Examples

#![feature(f16)]

let x = std::f16::consts::FRAC_PI_4;
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 <= f16::EPSILON);
assert!(abs_difference_1 <= f16::EPSILON);

pub fn exp_m1(self) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Returns e^(self) - 1 in a way that is accurate even if the number is close to zero.

Unspecified precision

The precision of this function is non-deterministic. This means it varies by platform, Rust version, and can even differ within the same execution from one invocation to the next.

This function currently corresponds to the expm1f from libc on Unix and Windows. Note that this might change in the future.

Examples

#![feature(f16)]

let x = 1e-4_f16;

// for very small x, e^x is approximately 1 + x + x^2 / 2
let approx = x + x * x / 2.0;
let abs_difference = (x.exp_m1() - approx).abs();

assert!(abs_difference < 1e-4);

pub fn ln_1p(self) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Returns ln(1+n) (natural logarithm) more accurately than if the operations were performed separately.

Unspecified precision

The precision of this function is non-deterministic. This means it varies by platform, Rust version, and can even differ within the same execution from one invocation to the next.

This function currently corresponds to the log1pf from libc on Unix and Windows. Note that this might change in the future.

Examples

#![feature(f16)]

let x = 1e-4_f16;

// for very small x, ln(1 + x) is approximately x - x^2 / 2
let approx = x - x * x / 2.0;
let abs_difference = (x.ln_1p() - approx).abs();

assert!(abs_difference < 1e-4);

pub fn sinh(self) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Hyperbolic sine function.

Unspecified precision

The precision of this function is non-deterministic. This means it varies by platform, Rust version, and can even differ within the same execution from one invocation to the next.

This function currently corresponds to the sinhf from libc on Unix and Windows. Note that this might change in the future.

Examples

#![feature(f16)]

let e = std::f16::consts::E;
let x = 1.0f16;

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 <= f16::EPSILON);

pub fn cosh(self) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Hyperbolic cosine function.

Unspecified precision

The precision of this function is non-deterministic. This means it varies by platform, Rust version, and can even differ within the same execution from one invocation to the next.

This function currently corresponds to the coshf from libc on Unix and Windows. Note that this might change in the future.

Examples

#![feature(f16)]

let e = std::f16::consts::E;
let x = 1.0f16;
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 <= f16::EPSILON);

pub fn tanh(self) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Hyperbolic tangent function.

Unspecified precision

The precision of this function is non-deterministic. This means it varies by platform, Rust version, and can even differ within the same execution from one invocation to the next.

This function currently corresponds to the tanhf from libc on Unix and Windows. Note that this might change in the future.

Examples

#![feature(f16)]

let e = std::f16::consts::E;
let x = 1.0f16;

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 <= f16::EPSILON);

pub fn asinh(self) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Inverse hyperbolic sine function.

Unspecified precision

The precision of this function is non-deterministic. This means it varies by platform, Rust version, and can even differ within the same execution from one invocation to the next.

Examples

#![feature(f16)]

let x = 1.0f16;
let f = x.sinh().asinh();

let abs_difference = (f - x).abs();

assert!(abs_difference <= f16::EPSILON);

pub fn acosh(self) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Inverse hyperbolic cosine function.

Unspecified precision

The precision of this function is non-deterministic. This means it varies by platform, Rust version, and can even differ within the same execution from one invocation to the next.

Examples

#![feature(f16)]

let x = 1.0f16;
let f = x.cosh().acosh();

let abs_difference = (f - x).abs();

assert!(abs_difference <= f16::EPSILON);

pub fn atanh(self) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Inverse hyperbolic tangent function.

Unspecified precision

The precision of this function is non-deterministic. This means it varies by platform, Rust version, and can even differ within the same execution from one invocation to the next.

Examples

#![feature(f16)]

let e = std::f16::consts::E;
let f = e.tanh().atanh();

let abs_difference = (f - e).abs();

assert!(abs_difference <= 0.01);

pub fn gamma(self) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Gamma function.

Unspecified precision

The precision of this function is non-deterministic. This means it varies by platform, Rust version, and can even differ within the same execution from one invocation to the next.

This function currently corresponds to the tgammaf from libc on Unix and Windows. Note that this might change in the future.

Examples

#![feature(f16)]
#![feature(float_gamma)]

let x = 5.0f16;

let abs_difference = (x.gamma() - 24.0).abs();

assert!(abs_difference <= f16::EPSILON);

pub fn ln_gamma(self) -> (f16, i32)

🔬This is a nightly-only experimental API. (f16 #116909)

Natural logarithm of the absolute value of the gamma function

The integer part of the tuple indicates the sign of the gamma function.

Unspecified precision

The precision of this function is non-deterministic. This means it varies by platform, Rust version, and can even differ within the same execution from one invocation to the next.

This function currently corresponds to the lgamma_r from libc on Unix and Windows. Note that this might change in the future.

Examples

#![feature(f16)]
#![feature(float_gamma)]

let x = 2.0f16;

let abs_difference = (x.ln_gamma().0 - 0.0).abs();

assert!(abs_difference <= f16::EPSILON);

impl f16

pub const RADIX: u32 = 2u32

🔬This is a nightly-only experimental API. (f16 #116909)

The radix or base of the internal representation of f16.

pub const MANTISSA_DIGITS: u32 = 11u32

🔬This is a nightly-only experimental API. (f16 #116909)

Number of significant digits in base 2.

pub const DIGITS: u32 = 3u32

🔬This is a nightly-only experimental API. (f16 #116909)

Approximate number of significant digits in base 10.

This is the maximum x such that any decimal number with x significant digits can be converted to f16 and back without loss.

Equal to floor(log₁₀ 2^{MANTISSA_DIGITS − 1}).

pub const EPSILON: f16 = 9.7656E-4f16

🔬This is a nightly-only experimental API. (f16 #116909)

Machine epsilon value for f16.

This is the difference between 1.0 and the next larger representable number.

Equal to 2^{1 − MANTISSA_DIGITS}.

pub const MIN: f16 = -65504f16

🔬This is a nightly-only experimental API. (f16 #116909)

Smallest finite f16 value.

Equal to −MAX.

pub const MIN_POSITIVE: f16 = 6.1035E-5f16

🔬This is a nightly-only experimental API. (f16 #116909)

Smallest positive normal f16 value.

Equal to 2^{MIN_EXP − 1}.

pub const MAX: f16 = 65504f16

🔬This is a nightly-only experimental API. (f16 #116909)

Largest finite f16 value.

Equal to (1 − 2^{−MANTISSA_DIGITS}) 2^MAX_EXP.

pub const MIN_EXP: i32 = -13i32

🔬This is a nightly-only experimental API. (f16 #116909)

One greater than the minimum possible normal power of 2 exponent.

If x = MIN_EXP, then normal numbers ≥ 0.5 × 2^x.

pub const MAX_EXP: i32 = 16i32

🔬This is a nightly-only experimental API. (f16 #116909)

Maximum possible power of 2 exponent.

If x = MAX_EXP, then normal numbers < 1 × 2^x.

pub const MIN_10_EXP: i32 = -4i32

🔬This is a nightly-only experimental API. (f16 #116909)

Minimum x for which 10^x is normal.

Equal to ceil(log₁₀ MIN_POSITIVE).

pub const MAX_10_EXP: i32 = 4i32

🔬This is a nightly-only experimental API. (f16 #116909)

Maximum x for which 10^x is normal.

Equal to floor(log₁₀ MAX).

pub const NAN: f16 = NaN_f16

🔬This is a nightly-only experimental API. (f16 #116909)

Not a Number (NaN).

Note that IEEE 754 doesn’t define just a single NaN value; a plethora of bit patterns are considered to be NaN. Furthermore, the standard makes a difference between a “signaling” and a “quiet” NaN, and allows inspecting its “payload” (the unspecified bits in the bit pattern). This constant isn’t guaranteed to equal to any specific NaN bitpattern, and the stability of its representation over Rust versions and target platforms isn’t guaranteed.

pub const INFINITY: f16 = +Inf_f16

🔬This is a nightly-only experimental API. (f16 #116909)

Infinity (∞).

pub const NEG_INFINITY: f16 = -Inf_f16

🔬This is a nightly-only experimental API. (f16 #116909)

Negative infinity (−∞).

pub const fn is_nan(self) -> bool

🔬This is a nightly-only experimental API. (f16 #116909)

Returns true if this value is NaN.

#![feature(f16)]

let nan = f16::NAN;
let f = 7.0_f16;

assert!(nan.is_nan());
assert!(!f.is_nan());

pub const fn is_infinite(self) -> bool

🔬This is a nightly-only experimental API. (f16 #116909)

Returns true if this value is positive infinity or negative infinity, and false otherwise.

#![feature(f16)]

let f = 7.0f16;
let inf = f16::INFINITY;
let neg_inf = f16::NEG_INFINITY;
let nan = f16::NAN;

assert!(!f.is_infinite());
assert!(!nan.is_infinite());

assert!(inf.is_infinite());
assert!(neg_inf.is_infinite());

pub const fn is_finite(self) -> bool

🔬This is a nightly-only experimental API. (f16 #116909)

Returns true if this number is neither infinite nor NaN.

#![feature(f16)]

let f = 7.0f16;
let inf: f16 = f16::INFINITY;
let neg_inf: f16 = f16::NEG_INFINITY;
let nan: f16 = f16::NAN;

assert!(f.is_finite());

assert!(!nan.is_finite());
assert!(!inf.is_finite());
assert!(!neg_inf.is_finite());

pub const fn is_subnormal(self) -> bool

🔬This is a nightly-only experimental API. (f16 #116909)

Returns true if the number is subnormal.

#![feature(f16)]

let min = f16::MIN_POSITIVE; // 6.1035e-5
let max = f16::MAX;
let lower_than_min = 1.0e-7_f16;
let zero = 0.0_f16;

assert!(!min.is_subnormal());
assert!(!max.is_subnormal());

assert!(!zero.is_subnormal());
assert!(!f16::NAN.is_subnormal());
assert!(!f16::INFINITY.is_subnormal());
// Values between `0` and `min` are Subnormal.
assert!(lower_than_min.is_subnormal());

pub const fn is_normal(self) -> bool

🔬This is a nightly-only experimental API. (f16 #116909)

Returns true if the number is neither zero, infinite, subnormal, or NaN.

#![feature(f16)]

let min = f16::MIN_POSITIVE; // 6.1035e-5
let max = f16::MAX;
let lower_than_min = 1.0e-7_f16;
let zero = 0.0_f16;

assert!(min.is_normal());
assert!(max.is_normal());

assert!(!zero.is_normal());
assert!(!f16::NAN.is_normal());
assert!(!f16::INFINITY.is_normal());
// Values between `0` and `min` are Subnormal.
assert!(!lower_than_min.is_normal());

pub const fn classify(self) -> FpCategory

🔬This is a nightly-only experimental API. (f16 #116909)

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.

#![feature(f16)]

use std::num::FpCategory;

let num = 12.4_f16;
let inf = f16::INFINITY;

assert_eq!(num.classify(), FpCategory::Normal);
assert_eq!(inf.classify(), FpCategory::Infinite);

pub fn is_sign_positive(self) -> bool

🔬This is a nightly-only experimental API. (f16 #116909)

Returns true if self has a positive sign, including +0.0, NaNs with positive sign bit and positive infinity. Note that IEEE 754 doesn’t assign any meaning to the sign bit in case of a NaN, and as Rust doesn’t guarantee that the bit pattern of NaNs are conserved over arithmetic operations, the result of is_sign_positive on a NaN might produce an unexpected result in some cases. See explanation of NaN as a special value for more info.

#![feature(f16)]

let f = 7.0_f16;
let g = -7.0_f16;

assert!(f.is_sign_positive());
assert!(!g.is_sign_positive());

pub fn is_sign_negative(self) -> bool

🔬This is a nightly-only experimental API. (f16 #116909)

Returns true if self has a negative sign, including -0.0, NaNs with negative sign bit and negative infinity. Note that IEEE 754 doesn’t assign any meaning to the sign bit in case of a NaN, and as Rust doesn’t guarantee that the bit pattern of NaNs are conserved over arithmetic operations, the result of is_sign_negative on a NaN might produce an unexpected result in some cases. See explanation of NaN as a special value for more info.

#![feature(f16)]

let f = 7.0_f16;
let g = -7.0_f16;

assert!(!f.is_sign_negative());
assert!(g.is_sign_negative());

pub fn next_up(self) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Returns the least number greater than self.

Let TINY be the smallest representable positive f16. Then,

• if self.is_nan(), this returns self;
• if self is NEG_INFINITY, this returns MIN;
• if self is -TINY, this returns -0.0;
• if self is -0.0 or +0.0, this returns TINY;
• if self is MAX or INFINITY, this returns INFINITY;
• otherwise the unique least value greater than self is returned.

The identity x.next_up() == -(-x).next_down() holds for all non-NaN x. When x is finite x == x.next_up().next_down() also holds.

#![feature(f16)]
#![feature(float_next_up_down)]

// f16::EPSILON is the difference between 1.0 and the next number up.
assert_eq!(1.0f16.next_up(), 1.0 + f16::EPSILON);
// But not for most numbers.
assert!(0.1f16.next_up() < 0.1 + f16::EPSILON);
assert_eq!(4356f16.next_up(), 4360.0);

pub fn next_down(self) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Returns the greatest number less than self.

Let TINY be the smallest representable positive f16. Then,

• if self.is_nan(), this returns self;
• if self is INFINITY, this returns MAX;
• if self is TINY, this returns 0.0;
• if self is -0.0 or +0.0, this returns -TINY;
• if self is MIN or NEG_INFINITY, this returns NEG_INFINITY;
• otherwise the unique greatest value less than self is returned.

The identity x.next_down() == -(-x).next_up() holds for all non-NaN x. When x is finite x == x.next_down().next_up() also holds.

#![feature(f16)]
#![feature(float_next_up_down)]

let x = 1.0f16;
// Clamp value into range [0, 1).
let clamped = x.clamp(0.0, 1.0f16.next_down());
assert!(clamped < 1.0);
assert_eq!(clamped.next_up(), 1.0);

pub fn recip(self) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Takes the reciprocal (inverse) of a number, 1/x.

#![feature(f16)]

let x = 2.0_f16;
let abs_difference = (x.recip() - (1.0 / x)).abs();

assert!(abs_difference <= f16::EPSILON);

pub fn to_degrees(self) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Converts radians to degrees.

#![feature(f16)]

let angle = std::f16::consts::PI;

let abs_difference = (angle.to_degrees() - 180.0).abs();
assert!(abs_difference <= 0.5);

pub fn to_radians(self) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Converts degrees to radians.

#![feature(f16)]

let angle = 180.0f16;

let abs_difference = (angle.to_radians() - std::f16::consts::PI).abs();

assert!(abs_difference <= 0.01);

pub fn max(self, other: f16) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Returns the maximum of the two numbers, ignoring NaN.

If one of the arguments is NaN, then the other argument is returned. This follows the IEEE 754-2008 semantics for maxNum, except for handling of signaling NaNs; this function handles all NaNs the same way and avoids maxNum’s problems with associativity. This also matches the behavior of libm’s fmax.

#![feature(f16)]

let x = 1.0f16;
let y = 2.0f16;

assert_eq!(x.max(y), y);

pub fn min(self, other: f16) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Returns the minimum of the two numbers, ignoring NaN.

If one of the arguments is NaN, then the other argument is returned. This follows the IEEE 754-2008 semantics for minNum, except for handling of signaling NaNs; this function handles all NaNs the same way and avoids minNum’s problems with associativity. This also matches the behavior of libm’s fmin.

#![feature(f16)]

let x = 1.0f16;
let y = 2.0f16;

assert_eq!(x.min(y), x);

pub fn maximum(self, other: f16) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Returns the maximum of the two numbers, propagating NaN.

This returns NaN when either argument is NaN, as opposed to f16::max which only returns NaN when both arguments are NaN.

#![feature(f16)]
#![feature(float_minimum_maximum)]

let x = 1.0f16;
let y = 2.0f16;

assert_eq!(x.maximum(y), y);
assert!(x.maximum(f16::NAN).is_nan());

If one of the arguments is NaN, then NaN is returned. Otherwise this returns the greater of the two numbers. For this operation, -0.0 is considered to be less than +0.0. Note that this follows the semantics specified in IEEE 754-2019.

Also note that “propagation” of NaNs here doesn’t necessarily mean that the bitpattern of a NaN operand is conserved; see explanation of NaN as a special value for more info.

pub fn minimum(self, other: f16) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Returns the minimum of the two numbers, propagating NaN.

This returns NaN when either argument is NaN, as opposed to f16::min which only returns NaN when both arguments are NaN.

#![feature(f16)]
#![feature(float_minimum_maximum)]

let x = 1.0f16;
let y = 2.0f16;

assert_eq!(x.minimum(y), x);
assert!(x.minimum(f16::NAN).is_nan());

If one of the arguments is NaN, then NaN is returned. Otherwise this returns the lesser of the two numbers. For this operation, -0.0 is considered to be less than +0.0. Note that this follows the semantics specified in IEEE 754-2019.

Also note that “propagation” of NaNs here doesn’t necessarily mean that the bitpattern of a NaN operand is conserved; see explanation of NaN as a special value for more info.

pub fn midpoint(self, other: f16) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Calculates the middle point of self and rhs.

This returns NaN when either argument is NaN or if a combination of +inf and -inf is provided as arguments.

Examples

#![feature(f16)]
#![feature(num_midpoint)]

assert_eq!(1f16.midpoint(4.0), 2.5);
assert_eq!((-5.5f16).midpoint(8.0), 1.25);

pub unsafe fn to_int_unchecked<Int>(self) -> Int

where f16: FloatToInt<Int>,

🔬This is a nightly-only experimental API. (f16 #116909)

Rounds toward zero and converts to any primitive integer type, assuming that the value is finite and fits in that type.

#![feature(f16)]

let value = 4.6_f16;
let rounded = unsafe { value.to_int_unchecked::<u16>() };
assert_eq!(rounded, 4);

let value = -128.9_f16;
let rounded = unsafe { value.to_int_unchecked::<i8>() };
assert_eq!(rounded, i8::MIN);

Safety

The value must:

• Not be NaN
• Not be infinite
• Be representable in the return type Int, after truncating off its fractional part

pub const fn to_bits(self) -> u16

🔬This is a nightly-only experimental API. (f16 #116909)

Raw transmutation to u16.

This is currently identical to transmute::<f16, u16>(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.

#![feature(f16)]

assert_eq!((12.5f16).to_bits(), 0x4a40);

pub const fn from_bits(v: u16) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Raw transmutation from u16.

This is currently identical to transmute::<u16, f16>(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.

#![feature(f16)]

let v = f16::from_bits(0x4a40);
assert_eq!(v, 12.5);

pub const fn to_be_bytes(self) -> [u8; 2]

🔬This is a nightly-only experimental API. (f16 #116909)

Returns the memory representation of this floating point number as a byte array in big-endian (network) byte order.

See from_bits for some discussion of the portability of this operation (there are almost no issues).

Examples

#![feature(f16)]

let bytes = 12.5f16.to_be_bytes();
assert_eq!(bytes, [0x4a, 0x40]);

pub const fn to_le_bytes(self) -> [u8; 2]

🔬This is a nightly-only experimental API. (f16 #116909)

Returns the memory representation of this floating point number as a byte array in little-endian byte order.

See from_bits for some discussion of the portability of this operation (there are almost no issues).

Examples

#![feature(f16)]

let bytes = 12.5f16.to_le_bytes();
assert_eq!(bytes, [0x40, 0x4a]);

pub const fn to_ne_bytes(self) -> [u8; 2]

🔬This is a nightly-only experimental API. (f16 #116909)

Returns the memory representation of this floating point number as a byte array in native byte order.

As the target platform’s native endianness is used, portable code should use to_be_bytes or to_le_bytes, as appropriate, instead.

See from_bits for some discussion of the portability of this operation (there are almost no issues).

Examples

#![feature(f16)]

let bytes = 12.5f16.to_ne_bytes();
assert_eq!(
    bytes,
    if cfg!(target_endian = "big") {
        [0x4a, 0x40]
    } else {
        [0x40, 0x4a]
    }
);

pub const fn from_be_bytes(bytes: [u8; 2]) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Creates a floating point value from its representation as a byte array in big endian.

See from_bits for some discussion of the portability of this operation (there are almost no issues).

Examples

#![feature(f16)]

let value = f16::from_be_bytes([0x4a, 0x40]);
assert_eq!(value, 12.5);

pub const fn from_le_bytes(bytes: [u8; 2]) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Creates a floating point value from its representation as a byte array in little endian.

See from_bits for some discussion of the portability of this operation (there are almost no issues).

Examples

#![feature(f16)]

let value = f16::from_le_bytes([0x40, 0x4a]);
assert_eq!(value, 12.5);

pub const fn from_ne_bytes(bytes: [u8; 2]) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Creates a floating point value from its representation as a byte array in native endian.

As the target platform’s native endianness is used, portable code likely wants to use from_be_bytes or from_le_bytes, as appropriate instead.

See from_bits for some discussion of the portability of this operation (there are almost no issues).

Examples

#![feature(f16)]

let value = f16::from_ne_bytes(if cfg!(target_endian = "big") {
    [0x4a, 0x40]
} else {
    [0x40, 0x4a]
});
assert_eq!(value, 12.5);

pub fn total_cmp(&self, other: &f16) -> Ordering

🔬This is a nightly-only experimental API. (f16 #116909)

Returns the ordering between self and other.

Unlike the standard partial comparison between floating point numbers, this comparison always produces an ordering in accordance to the totalOrder predicate as defined in the IEEE 754 (2008 revision) floating point standard. The values are ordered in the following sequence:

• negative quiet NaN
• negative signaling NaN
• negative infinity
• negative numbers
• negative subnormal numbers
• negative zero
• positive zero
• positive subnormal numbers
• positive numbers
• positive infinity
• positive signaling NaN
• positive quiet NaN.

The ordering established by this function does not always agree with the PartialOrd and PartialEq implementations of f16. For example, they consider negative and positive zero equal, while total_cmp doesn’t.

The interpretation of the signaling NaN bit follows the definition in the IEEE 754 standard, which may not match the interpretation by some of the older, non-conformant (e.g. MIPS) hardware implementations.

Example

#![feature(f16)]

struct GoodBoy {
    name: &'static str,
    weight: f16,
}

let mut bois = vec![
    GoodBoy { name: "Pucci", weight: 0.1 },
    GoodBoy { name: "Woofer", weight: 99.0 },
    GoodBoy { name: "Yapper", weight: 10.0 },
    GoodBoy { name: "Chonk", weight: f16::INFINITY },
    GoodBoy { name: "Abs. Unit", weight: f16::NAN },
    GoodBoy { name: "Floaty", weight: -5.0 },
];

bois.sort_by(|a, b| a.weight.total_cmp(&b.weight));

// `f16::NAN` could be positive or negative, which will affect the sort order.
if f16::NAN.is_sign_negative() {
    bois.into_iter().map(|b| b.weight)
        .zip([f16::NAN, -5.0, 0.1, 10.0, 99.0, f16::INFINITY].iter())
        .for_each(|(a, b)| assert_eq!(a.to_bits(), b.to_bits()))
} else {
    bois.into_iter().map(|b| b.weight)
        .zip([-5.0, 0.1, 10.0, 99.0, f16::INFINITY, f16::NAN].iter())
        .for_each(|(a, b)| assert_eq!(a.to_bits(), b.to_bits()))
}

pub fn clamp(self, min: f16, max: f16) -> f16

🔬This is a nightly-only experimental API. (f16 #116909)

Restrict a value to a certain interval unless it is NaN.

Returns max if self is greater than max, and min if self is less than min. Otherwise this returns self.

Note that this function returns NaN if the initial value was NaN as well.

Panics

Panics if min > max, min is NaN, or max is NaN.

Examples

#![feature(f16)]

assert!((-3.0f16).clamp(-2.0, 1.0) == -2.0);
assert!((0.0f16).clamp(-2.0, 1.0) == 0.0);
assert!((2.0f16).clamp(-2.0, 1.0) == 1.0);
assert!((f16::NAN).clamp(-2.0, 1.0).is_nan());

Trait Implementations

impl Add<&f16> for &f16

type Output = <f16 as Add>::Output

The resulting type after applying the + operator.

fn add(self, other: &f16) -> <f16 as Add>::Output

Performs the + operation.

impl Add<&f16> for f16

type Output = <f16 as Add>::Output

The resulting type after applying the + operator.

fn add(self, other: &f16) -> <f16 as Add>::Output

Performs the + operation.

impl<'a> Add<f16> for &'a f16

type Output = <f16 as Add>::Output

The resulting type after applying the + operator.

fn add(self, other: f16) -> <f16 as Add>::Output

Performs the + operation.

impl Add for f16

type Output = f16

The resulting type after applying the + operator.

fn add(self, other: f16) -> f16

Performs the + operation.

impl AddAssign<&f16> for f16

fn add_assign(&mut self, other: &f16)

Performs the += operation.

impl AddAssign for f16

fn add_assign(&mut self, other: f16)

Performs the += operation.

impl Clone for f16

fn clone(&self) -> f16

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for f16

fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter.

impl Default for f16

fn default() -> f16

Returns the default value of 0.0

impl Div<&f16> for &f16

type Output = <f16 as Div>::Output

The resulting type after applying the / operator.

fn div(self, other: &f16) -> <f16 as Div>::Output

Performs the / operation.

impl Div<&f16> for f16

type Output = <f16 as Div>::Output

The resulting type after applying the / operator.

fn div(self, other: &f16) -> <f16 as Div>::Output

Performs the / operation.

impl<'a> Div<f16> for &'a f16

type Output = <f16 as Div>::Output

The resulting type after applying the / operator.

fn div(self, other: f16) -> <f16 as Div>::Output

Performs the / operation.

impl Div for f16

type Output = f16

The resulting type after applying the / operator.

fn div(self, other: f16) -> f16

Performs the / operation.

impl DivAssign<&f16> for f16

fn div_assign(&mut self, other: &f16)

Performs the /= operation.

impl DivAssign for f16

fn div_assign(&mut self, other: f16)

Performs the /= operation.

impl From<f16> for f128

fn from(small: f16) -> f128

Converts f16 to f128 losslessly.

impl From<f16> for f64

fn from(small: f16) -> f64

Converts f16 to f64 losslessly.

impl Mul<&f16> for &f16

type Output = <f16 as Mul>::Output

The resulting type after applying the * operator.

fn mul(self, other: &f16) -> <f16 as Mul>::Output

Performs the * operation.

impl Mul<&f16> for f16

type Output = <f16 as Mul>::Output

The resulting type after applying the * operator.

fn mul(self, other: &f16) -> <f16 as Mul>::Output

Performs the * operation.

impl<'a> Mul<f16> for &'a f16

type Output = <f16 as Mul>::Output

The resulting type after applying the * operator.

fn mul(self, other: f16) -> <f16 as Mul>::Output

Performs the * operation.

impl Mul for f16

type Output = f16

The resulting type after applying the * operator.

fn mul(self, other: f16) -> f16

Performs the * operation.

impl MulAssign<&f16> for f16

fn mul_assign(&mut self, other: &f16)

Performs the *= operation.

impl MulAssign for f16

fn mul_assign(&mut self, other: f16)

Performs the *= operation.

impl Neg for &f16

type Output = <f16 as Neg>::Output

The resulting type after applying the - operator.

fn neg(self) -> <f16 as Neg>::Output

Performs the unary - operation.

impl Neg for f16

type Output = f16

The resulting type after applying the - operator.

fn neg(self) -> f16

Performs the unary - operation.

impl PartialEq for f16

fn eq(&self, other: &f16) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &f16) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl PartialOrd for f16

fn partial_cmp(&self, other: &f16) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

fn lt(&self, other: &f16) -> bool

Tests less than (for self and other) and is used by the < operator.

fn le(&self, other: &f16) -> bool

Tests less than or equal to (for self and other) and is used by the <= operator.

fn ge(&self, other: &f16) -> bool

Tests greater than or equal to (for self and other) and is used by the >= operator.

fn gt(&self, other: &f16) -> bool

Tests greater than (for self and other) and is used by the > operator.

impl Rem<&f16> for &f16

type Output = <f16 as Rem>::Output

The resulting type after applying the % operator.

fn rem(self, other: &f16) -> <f16 as Rem>::Output

Performs the % operation.

impl Rem<&f16> for f16

type Output = <f16 as Rem>::Output

The resulting type after applying the % operator.

fn rem(self, other: &f16) -> <f16 as Rem>::Output

Performs the % operation.

impl<'a> Rem<f16> for &'a f16

type Output = <f16 as Rem>::Output

The resulting type after applying the % operator.

fn rem(self, other: f16) -> <f16 as Rem>::Output

Performs the % operation.

impl Rem for f16

The remainder from the division of two floats.

The remainder has the same sign as the dividend and is computed as: x - (x / y).trunc() * y.

Examples

let x: f32 = 50.50;
let y: f32 = 8.125;
let remainder = x - (x / y).trunc() * y;

// The answer to both operations is 1.75
assert_eq!(x % y, remainder);

type Output = f16

The resulting type after applying the % operator.

fn rem(self, other: f16) -> f16

Performs the % operation.

impl RemAssign<&f16> for f16

fn rem_assign(&mut self, other: &f16)

Performs the %= operation.

impl RemAssign for f16

fn rem_assign(&mut self, other: f16)

Performs the %= operation.

impl Sub<&f16> for &f16

type Output = <f16 as Sub>::Output

The resulting type after applying the - operator.

fn sub(self, other: &f16) -> <f16 as Sub>::Output

Performs the - operation.

impl Sub<&f16> for f16

type Output = <f16 as Sub>::Output

The resulting type after applying the - operator.

fn sub(self, other: &f16) -> <f16 as Sub>::Output

Performs the - operation.

impl<'a> Sub<f16> for &'a f16

type Output = <f16 as Sub>::Output

The resulting type after applying the - operator.

fn sub(self, other: f16) -> <f16 as Sub>::Output

Performs the - operation.

impl Sub for f16

type Output = f16

The resulting type after applying the - operator.

fn sub(self, other: f16) -> f16

Performs the - operation.

impl SubAssign<&f16> for f16

fn sub_assign(&mut self, other: &f16)

Performs the -= operation.

impl SubAssign for f16

fn sub_assign(&mut self, other: f16)

Performs the -= operation.

impl Copy for f16

impl FloatToInt<i128> for f16

impl FloatToInt<i16> for f16

impl FloatToInt<i32> for f16

impl FloatToInt<i64> for f16

impl FloatToInt<i8> for f16

impl FloatToInt<isize> for f16

impl FloatToInt<u128> for f16

impl FloatToInt<u16> for f16

impl FloatToInt<u32> for f16

impl FloatToInt<u64> for f16

impl FloatToInt<u8> for f16

impl FloatToInt<usize> for f16