## f16

# Primitive Type f16

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

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/x86-64 requires the avx512fp16 or avx10.1 features, while RISC-V requires Zfh, and Arm/AArch64 requires FEAT_FP16. 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§

Source§

### impl f16

Source

#### 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);

    assert_eq!(f16::powf(1.0, f16::NAN), 1.0);
    assert_eq!(f16::powf(f16::NAN, 0.0), 1.0);
    assert_eq!(f16::powf(0.0, 0.0), 1.0);

Source

#### 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);

Source

#### 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);

Source

#### pub fn ln(self) -> f16

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

Returns the natural logarithm of the number.

This returns NaN when the number is negative, and negative infinity when number is 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.

##### §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);

Non-positive values:

    #![feature(f16)]

    assert_eq!(0_f16.ln(), f16::NEG_INFINITY);
    assert!((-42_f16).ln().is_nan());

Source

#### 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.

This returns NaN when the number is negative, and negative infinity when number is zero.

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);

Non-positive values:

    #![feature(f16)]

    assert_eq!(0_f16.log(10.0), f16::NEG_INFINITY);
    assert!((-42_f16).log(10.0).is_nan());

Source

#### pub fn log2(self) -> f16

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

Returns the base 2 logarithm of the number.

This returns NaN when the number is negative, and negative infinity when number is 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.

##### §Examples

    #![feature(f16)]

    let two = 2.0f16;

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

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

Non-positive values:

    #![feature(f16)]

    assert_eq!(0_f16.log2(), f16::NEG_INFINITY);
    assert!((-42_f16).log2().is_nan());

Source

#### pub fn log10(self) -> f16

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

Returns the base 10 logarithm of the number.

This returns NaN when the number is negative, and negative infinity when number is 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.

##### §Examples

    #![feature(f16)]

    let ten = 10.0f16;

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

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

Non-positive values:

    #![feature(f16)]

    assert_eq!(0_f16.log10(), f16::NEG_INFINITY);
    assert!((-42_f16).log10().is_nan());

Source

#### 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);

Source

#### 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);

Source

#### 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);

Source

#### 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);

Source

#### 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_4;

    // asin(sin(pi/2))
    let abs_difference = (f.sin().asin() - f).abs();

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

Source

#### 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);

Source

#### 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);

Source

#### 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` | `y` | Piecewise Definition | Range
--- | --- | --- | ---
`>= +0` | `>= +0` | `arctan(y/x)` | `[+0, +pi/2]`
`>= +0` | `<= -0` | `arctan(y/x)` | `[-pi/2, -0]`
`<= -0` | `>= +0` | `arctan(y/x) + pi` | `[+pi/2, +pi]`
`<= -0` | `<= -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);

Source

#### 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);

Source

#### 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);

Source

#### 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.

This returns NaN when `n < -1.0`, and negative infinity when `n == -1.0`.

##### §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);

Out-of-range values:

    #![feature(f16)]

    assert_eq!((-1.0_f16).ln_1p(), f16::NEG_INFINITY);
    assert!((-2.0_f16).ln_1p().is_nan());

Source

#### 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);

Source

#### 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);

Source

#### 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);

Source

#### 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);

Source

#### 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);

Source

#### 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 x = std::f16::consts::FRAC_PI_6;
    let f = x.tanh().atanh();

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

    assert!(abs_difference <= 0.01);

Source

#### 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);

Source

#### 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);

Source

#### pub fn erf(self) -> f16

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

Error 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 `erff` from libc on Unix and Windows. Note that this might change in the future.

##### §Examples

    #![feature(f16)]
    #![feature(float_erf)]
    /// The error function relates what percent of a normal distribution lies
    /// within `x` standard deviations (scaled by `1/sqrt(2)`).
    fn within_standard_deviations(x: f16) -> f16 {
        (x * std::f16::consts::FRAC_1_SQRT_2).erf() * 100.0
    }

    // 68% of a normal distribution is within one standard deviation
    assert!((within_standard_deviations(1.0) - 68.269).abs() < 0.1);
    // 95% of a normal distribution is within two standard deviations
    assert!((within_standard_deviations(2.0) - 95.450).abs() < 0.1);
    // 99.7% of a normal distribution is within three standard deviations
    assert!((within_standard_deviations(3.0) - 99.730).abs() < 0.1);

Source

#### pub fn erfc(self) -> f16

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

Complementary error 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 `erfcf` from libc on Unix and Windows. Note that this might change in the future.

##### §Examples

    #![feature(f16)]
    #![feature(float_erf)]
    let x: f16 = 0.123;

    let one = x.erf() + x.erfc();
    let abs_difference = (one - 1.0).abs();

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

Source§

### impl f16

Source

#### pub const RADIX: u32 = 2u32

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

The radix or base of the internal representation of `f16`.

Source

#### pub const MANTISSA_DIGITS: u32 = 11u32

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

Number of significant digits in base 2.

Note that the size of the mantissa in the bitwise representation is one smaller than this since the leading 1 is not stored explicitly.

Source

#### 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).

Source

#### 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 21 − `MANTISSA_DIGITS`.

Source

#### pub const MIN: f16 = -65504f16

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

Smallest finite `f16` value.

Equal to −`MAX`.

Source

#### 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.

Source

#### 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`.

Source

#### 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 for a significand bounded by 1 ≤ x < 2 (i.e. the IEEE definition).

This corresponds to the exact minimum possible normal power of 2 exponent for a significand bounded by 0.5 ≤ x < 1 (i.e. the C definition). In other words, all normal numbers representable by this type are greater than or equal to 0.5 × 2MIN_EXP.

Source

#### pub const MAX_EXP: i32 = 16i32

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

One greater than the maximum possible power of 2 exponent for a significand bounded by 1 ≤ x < 2 (i.e. the IEEE definition).

This corresponds to the exact maximum possible power of 2 exponent for a significand bounded by 0.5 ≤ x < 1 (i.e. the C definition). In other words, all numbers representable by this type are strictly less than 2MAX_EXP.

Source

#### pub const MIN_10_EXP: i32 = -4i32

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

Minimum x for which 10x is normal.

Equal to ceil(log10 `MIN_POSITIVE`).

Source

#### pub const MAX_10_EXP: i32 = 4i32

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

Maximum x for which 10x is normal.

Equal to floor(log10 `MAX`).

Source

#### 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) and its sign. See the specification of NaN bit patterns for more info.

This constant is guaranteed to be a quiet NaN (on targets that follow the Rust assumptions that the quiet/signaling bit being set to 1 indicates a quiet NaN). Beyond that, nothing is guaranteed about the specific bit pattern chosen here: both payload and sign are arbitrary. The concrete bit pattern may change across Rust versions and target platforms.

Source

#### pub const INFINITY: f16 = +Inf_f16

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

Infinity (∞).

Source

#### pub const NEG_INFINITY: f16 = -Inf_f16

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

Negative infinity (−∞).

Source

#### 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());

Source

#### 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());

Source

#### 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());

Source

#### 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());

Source

#### 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());

Source

#### 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);

Source

#### pub const 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 or non-portable result. See the specification of NaN bit patterns for more info. Use `self.signum() == 1.0` if you need fully portable behavior (will return `false` for all NaNs).

    #![feature(f16)]

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

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

Source

#### pub const 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 or non-portable result. See the specification of NaN bit patterns for more info. Use `self.signum() == -1.0` if you need fully portable behavior (will return `false` for all NaNs).

    #![feature(f16)]

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

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

Source

#### pub const 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)]

    // 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);

This operation corresponds to IEEE-754 `nextUp`.

Source

#### pub const 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)]

    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);

This operation corresponds to IEEE-754 `nextDown`.

Source

#### pub const 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);

Source

#### pub const fn to_degrees(self) -> f16

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

Converts radians to degrees.

##### §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 angle = std::f16::consts::PI;

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

Source

#### pub const fn to_radians(self) -> f16

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

Converts degrees to 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 angle = 180.0f16;

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

    assert!(abs_difference <= 0.01);

Source

#### pub const 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. In particular, if the inputs compare equal (such as for the case of `+0.0` and `-0.0`), either input may be returned non-deterministically.

    #![feature(f16)]

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

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

Source

#### pub const 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. In particular, if the inputs compare equal (such as for the case of `+0.0` and `-0.0`), either input may be returned non-deterministically.

    #![feature(f16)]

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

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

Source

#### pub const 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 the specification of NaN bit patterns for more info.

Source

#### pub const 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 the specification of NaN bit patterns for more info.

Source

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

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

Calculates the midpoint (average) between `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)]

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

Source

#### 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

Source

#### 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);

Source

#### 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);

Source

#### 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]);

Source

#### 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]);

Source

#### 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]
        }
    );

Source

#### 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);

Source

#### 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);

Source

#### 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);

Source

#### pub const 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()))
    }

Source

#### pub const 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());

Source

#### pub const fn abs(self) -> f16

🔬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());

Source

#### pub const 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());

Source

#### pub const 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 same payload as `self` and the sign bit of `sign` is returned.

If `sign` is a NaN, then this operation will still carry over its sign into the result. 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 `copysign` with `sign` being a NaN might produce an unexpected or non-portable result. See the specification of NaN bit patterns 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());

Source

#### pub const fn algebraic_add(self, rhs: f16) -> f16

🔬This is a nightly-only experimental API. (`float_algebraic` #136469)

Float addition that allows optimizations based on algebraic rules.

See algebraic operators for more info.

Source

#### pub const fn algebraic_sub(self, rhs: f16) -> f16

🔬This is a nightly-only experimental API. (`float_algebraic` #136469)

Float subtraction that allows optimizations based on algebraic rules.

See algebraic operators for more info.

Source

#### pub const fn algebraic_mul(self, rhs: f16) -> f16

🔬This is a nightly-only experimental API. (`float_algebraic` #136469)

Float multiplication that allows optimizations based on algebraic rules.

See algebraic operators for more info.

Source

#### pub const fn algebraic_div(self, rhs: f16) -> f16

🔬This is a nightly-only experimental API. (`float_algebraic` #136469)

Float division that allows optimizations based on algebraic rules.

See algebraic operators for more info.

Source

#### pub const fn algebraic_rem(self, rhs: f16) -> f16

🔬This is a nightly-only experimental API. (`float_algebraic` #136469)

Float remainder that allows optimizations based on algebraic rules.

See algebraic operators for more info.

Source§

### impl f16

Source

#### pub const 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);

Source

#### pub const 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);

Source

#### pub const 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);

Source

#### pub const 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);

Source

#### pub const 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);

Source

#### pub const 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);

Source

#### pub const 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);

Source

#### 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

Source

#### 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);

Source

#### 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.

##### §Examples

    #![feature(f16)]

    let x = 2.0_f16;
    let abs_difference = (x.powi(2) - (x * x)).abs();
    assert!(abs_difference <= f16::EPSILON);

    assert_eq!(f16::powi(f16::NAN, 0), 1.0);
    assert_eq!(f16::powi(0.0, 0), 1.0);

Source

#### 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);

Source

#### 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);

## Trait Implementations§

1.0.0 (const: unstable) · Source§

### impl Add<&f16> for &f16

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#### type Output = <f16 as Add>::Output

The resulting type after applying the `+` operator.
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#### fn add(self, other: &f16) -> <f16 as Add>::Output

Performs the `+` operation. Read more
1.0.0 (const: unstable) · Source§

### impl Add<&f16> for f16

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#### type Output = <f16 as Add>::Output

The resulting type after applying the `+` operator.
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#### fn add(self, other: &f16) -> <f16 as Add>::Output

Performs the `+` operation. Read more
1.0.0 (const: unstable) · Source§

### impl Add<f16> for &f16

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#### type Output = <f16 as Add>::Output

The resulting type after applying the `+` operator.
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#### fn add(self, other: f16) -> <f16 as Add>::Output

Performs the `+` operation. Read more
1.0.0 (const: unstable) · Source§

### impl Add for f16

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#### type Output = f16

The resulting type after applying the `+` operator.
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#### fn add(self, other: f16) -> f16

Performs the `+` operation. Read more
1.22.0 (const: unstable) · Source§

### impl AddAssign<&f16> for f16

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

Performs the `+=` operation. Read more
1.8.0 (const: unstable) · Source§

### impl AddAssign for f16

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

Performs the `+=` operation. Read more
1.0.0 (const: unstable) · Source§

### impl Clone for f16

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#### fn clone(&self) -> f16

Returns a duplicate of the value. Read more
1.0.0 · Source§

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

Performs copy-assignment from `source`. Read more
1.0.0 · Source§

### impl Debug for f16

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

Formats the value using the given formatter. Read more
1.0.0 (const: unstable) · Source§

### impl Default for f16

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#### fn default() -> f16

Returns the default value of `0.0`

1.0.0 · Source§

### impl Display for f16

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

Formats the value using the given formatter. Read more
1.0.0 (const: unstable) · Source§

### impl Div<&f16> for &f16

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#### type Output = <f16 as Div>::Output

The resulting type after applying the `/` operator.
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#### fn div(self, other: &f16) -> <f16 as Div>::Output

Performs the `/` operation. Read more
1.0.0 (const: unstable) · Source§

### impl Div<&f16> for f16

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#### type Output = <f16 as Div>::Output

The resulting type after applying the `/` operator.
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#### fn div(self, other: &f16) -> <f16 as Div>::Output

Performs the `/` operation. Read more
1.0.0 (const: unstable) · Source§

### impl Div<f16> for &f16

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#### type Output = <f16 as Div>::Output

The resulting type after applying the `/` operator.
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#### fn div(self, other: f16) -> <f16 as Div>::Output

Performs the `/` operation. Read more
1.0.0 (const: unstable) · Source§

### impl Div for f16

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#### type Output = f16

The resulting type after applying the `/` operator.
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#### fn div(self, other: f16) -> f16

Performs the `/` operation. Read more
1.22.0 (const: unstable) · Source§

### impl DivAssign<&f16> for f16

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

Performs the `/=` operation. Read more
1.8.0 (const: unstable) · Source§

### impl DivAssign for f16

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

Performs the `/=` operation. Read more
1.68.0 (const: unstable) · Source§

### impl From<bool> for f16

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#### fn from(small: bool) -> f16

Converts a `bool` to `f16` losslessly. The resulting value is positive `0.0` for `false` and `1.0` for `true` values.

##### §Examples

    #![feature(f16)]

    let x: f16 = false.into();
    assert_eq!(x, 0.0);
    assert!(x.is_sign_positive());

    let y: f16 = true.into();
    assert_eq!(y, 1.0);

1.6.0 (const: unstable) · Source§

### impl From<f16> for f128

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#### fn from(small: f16) -> f128

Converts `f16` to `f128` losslessly.

1.6.0 (const: unstable) · Source§

### impl From<f16> for f64

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#### fn from(small: f16) -> f64

Converts `f16` to `f64` losslessly.

1.6.0 (const: unstable) · Source§

### impl From<i8> for f16

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#### fn from(small: i8) -> f16

Converts `i8` to `f16` losslessly.

1.6.0 (const: unstable) · Source§

### impl From<u8> for f16

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#### fn from(small: u8) -> f16

Converts `u8` to `f16` losslessly.

1.0.0 · Source§

### impl FromStr for f16

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#### fn from_str(src: &str) -> Result<f16, ParseFloatError>

Converts a string in base 10 to a float. Accepts an optional decimal exponent.

This function accepts strings such as

- ‘3.14’
- ‘-3.14’
- ‘2.5E10’, or equivalently, ‘2.5e10’
- ‘2.5E-10’
- ‘5.’
- ‘.5’, or, equivalently, ‘0.5’
- ‘7’
- ‘007’
- ‘inf’, ‘-inf’, ‘+infinity’, ‘NaN’

Note that alphabetical characters are not case-sensitive.

Leading and trailing whitespace represent an error.

##### §Grammar

All strings that adhere to the following EBNF grammar when lowercased will result in an `Ok` being returned:

    Float  ::= Sign? ( 'inf' | 'infinity' | 'nan' | Number )
    Number ::= ( Digit+ |
                 Digit+ '.' Digit* |
                 Digit* '.' Digit+ ) Exp?
    Exp    ::= 'e' Sign? Digit+
    Sign   ::= [+-]
    Digit  ::= [0-9]

##### §Arguments

- src - A string

##### §Return value

`Err(ParseFloatError)` if the string did not represent a valid number. Otherwise, `Ok(n)` where `n` is the closest representable floating-point number to the number represented by `src` (following the same rules for rounding as for the results of primitive operations).

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#### type Err = ParseFloatError

The associated error which can be returned from parsing.
1.0.0 · Source§

### impl LowerExp for f16

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

Formats the value using the given formatter. Read more
1.0.0 (const: unstable) · Source§

### impl Mul<&f16> for &f16

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#### type Output = <f16 as Mul>::Output

The resulting type after applying the `*` operator.
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#### fn mul(self, other: &f16) -> <f16 as Mul>::Output

Performs the `*` operation. Read more
1.0.0 (const: unstable) · Source§

### impl Mul<&f16> for f16

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#### type Output = <f16 as Mul>::Output

The resulting type after applying the `*` operator.
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#### fn mul(self, other: &f16) -> <f16 as Mul>::Output

Performs the `*` operation. Read more
1.0.0 (const: unstable) · Source§

### impl Mul<f16> for &f16

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#### type Output = <f16 as Mul>::Output

The resulting type after applying the `*` operator.
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#### fn mul(self, other: f16) -> <f16 as Mul>::Output

Performs the `*` operation. Read more
1.0.0 (const: unstable) · Source§

### impl Mul for f16

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#### type Output = f16

The resulting type after applying the `*` operator.
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#### fn mul(self, other: f16) -> f16

Performs the `*` operation. Read more
1.22.0 (const: unstable) · Source§

### impl MulAssign<&f16> for f16

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

Performs the `*=` operation. Read more
1.8.0 (const: unstable) · Source§

### impl MulAssign for f16

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

Performs the `*=` operation. Read more
1.0.0 (const: unstable) · Source§

### impl Neg for &f16

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#### type Output = <f16 as Neg>::Output

The resulting type after applying the `-` operator.
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#### fn neg(self) -> <f16 as Neg>::Output

Performs the unary `-` operation. Read more
1.0.0 (const: unstable) · Source§

### impl Neg for f16

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#### type Output = f16

The resulting type after applying the `-` operator.
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#### fn neg(self) -> f16

Performs the unary `-` operation. Read more
1.0.0 (const: unstable) · Source§

### impl PartialEq for f16

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

Tests for `self` and `other` values to be equal, and is used by `==`.
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#### fn ne(&self, other: &f16) -> bool

Tests for `!=`. The default implementation is almost always sufficient, and should not be overridden without very good reason.
1.0.0 (const: unstable) · Source§

### impl PartialOrd for f16

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

This method returns an ordering between `self` and `other` values if one exists. Read more
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#### fn lt(&self, other: &f16) -> bool

Tests less than (for `self` and `other`) and is used by the `<` operator. Read more
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#### fn le(&self, other: &f16) -> bool

Tests less than or equal to (for `self` and `other`) and is used by the `<=` operator. Read more
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#### fn gt(&self, other: &f16) -> bool

Tests greater than (for `self` and `other`) and is used by the `>` operator. Read more
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#### fn ge(&self, other: &f16) -> bool

Tests greater than or equal to (for `self` and `other`) and is used by the `>=` operator. Read more
1.12.0 · Source§

### impl<'a> Product<&'a f16> for f16

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#### fn product<I>(iter: I) -> f16
where I: Iterator<Item = &'a f16>,

Takes an iterator and generates `Self` from the elements by multiplying the items.
1.12.0 · Source§

### impl Product for f16

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#### fn product<I>(iter: I) -> f16
where I: Iterator<Item = f16>,

Takes an iterator and generates `Self` from the elements by multiplying the items.
1.0.0 (const: unstable) · Source§

### impl Rem<&f16> for &f16

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#### type Output = <f16 as Rem>::Output

The resulting type after applying the `%` operator.
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#### fn rem(self, other: &f16) -> <f16 as Rem>::Output

Performs the `%` operation. Read more
1.0.0 (const: unstable) · Source§

### impl Rem<&f16> for f16

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#### type Output = <f16 as Rem>::Output

The resulting type after applying the `%` operator.
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#### fn rem(self, other: &f16) -> <f16 as Rem>::Output

Performs the `%` operation. Read more
1.0.0 (const: unstable) · Source§

### impl Rem<f16> for &f16

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#### type Output = <f16 as Rem>::Output

The resulting type after applying the `%` operator.
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#### fn rem(self, other: f16) -> <f16 as Rem>::Output

Performs the `%` operation. Read more
1.0.0 (const: unstable) · Source§

### 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);

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#### type Output = f16

The resulting type after applying the `%` operator.
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#### fn rem(self, other: f16) -> f16

Performs the `%` operation. Read more
1.22.0 (const: unstable) · Source§

### impl RemAssign<&f16> for f16

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

Performs the `%=` operation. Read more
1.8.0 (const: unstable) · Source§

### impl RemAssign for f16

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

Performs the `%=` operation. Read more
1.0.0 (const: unstable) · Source§

### impl Sub<&f16> for &f16

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#### type Output = <f16 as Sub>::Output

The resulting type after applying the `-` operator.
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#### fn sub(self, other: &f16) -> <f16 as Sub>::Output

Performs the `-` operation. Read more
1.0.0 (const: unstable) · Source§

### impl Sub<&f16> for f16

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#### type Output = <f16 as Sub>::Output

The resulting type after applying the `-` operator.
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#### fn sub(self, other: &f16) -> <f16 as Sub>::Output

Performs the `-` operation. Read more
1.0.0 (const: unstable) · Source§

### impl Sub<f16> for &f16

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#### type Output = <f16 as Sub>::Output

The resulting type after applying the `-` operator.
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#### fn sub(self, other: f16) -> <f16 as Sub>::Output

Performs the `-` operation. Read more
1.0.0 (const: unstable) · Source§

### impl Sub for f16

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#### type Output = f16

The resulting type after applying the `-` operator.
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#### fn sub(self, other: f16) -> f16

Performs the `-` operation. Read more
1.22.0 (const: unstable) · Source§

### impl SubAssign<&f16> for f16

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

Performs the `-=` operation. Read more
1.8.0 (const: unstable) · Source§

### impl SubAssign for f16

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

Performs the `-=` operation. Read more
1.12.0 · Source§

### impl<'a> Sum<&'a f16> for f16

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#### fn sum<I>(iter: I) -> f16
where I: Iterator<Item = &'a f16>,

Takes an iterator and generates `Self` from the elements by “summing up” the items.
1.12.0 · Source§

### impl Sum for f16

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#### fn sum<I>(iter: I) -> f16
where I: Iterator<Item = f16>,

Takes an iterator and generates `Self` from the elements by “summing up” the items.
1.0.0 · Source§

### impl UpperExp for f16

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

Formats the value using the given formatter. Read more
1.0.0 · Source§

### impl Copy for f16

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### impl FloatToInt<i128> for f16

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### impl FloatToInt<i16> for f16

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### impl FloatToInt<i32> for f16

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### impl FloatToInt<i64> for f16

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### impl FloatToInt<i8> for f16

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### impl FloatToInt<isize> for f16

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### impl FloatToInt<u128> for f16

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### impl FloatToInt<u16> for f16

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### impl FloatToInt<u32> for f16

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### impl FloatToInt<u64> for f16

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### impl FloatToInt<u8> for f16

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### impl FloatToInt<usize> for f16

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### impl UseCloned for f16

## Auto Trait Implementations§

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### impl Freeze for f16

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### impl RefUnwindSafe for f16

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### impl Send for f16

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### impl Sync for f16

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### impl Unpin for f16

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### impl UnwindSafe for f16

## Blanket Implementations§

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### impl<T> Any for T
where T: 'static + ?Sized,

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#### fn type_id(&self) -> TypeId

Gets the `TypeId` of `self`. Read more
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### impl<T> Borrow<T> for T
where T: ?Sized,

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#### fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more
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### impl<T> BorrowMut<T> for T
where T: ?Sized,

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#### fn borrow_mut(&mut self) -> &mut T

Mutably borrows from an owned value. Read more
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### impl<T> CloneToUninit for T
where T: Clone,

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#### unsafe fn clone_to_uninit(&self, dest: *mut u8)

🔬This is a nightly-only experimental API. (`clone_to_uninit` #126799)
Performs copy-assignment from `self` to `dest`. Read more
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### impl<T> From<T> for T

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#### fn from(t: T) -> T

Returns the argument unchanged.

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### impl<T, U> Into<U> for T
where U: From<T>,

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#### fn into(self) -> U

Calls `U::from(self)`.

That is, this conversion is whatever the implementation of `From<T> for U` chooses to do.

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### impl<T> ToOwned for T
where T: Clone,

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#### type Owned = T

The resulting type after obtaining ownership.
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#### fn to_owned(&self) -> T

Creates owned data from borrowed data, usually by cloning. Read more
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#### fn clone_into(&self, target: &mut T)

Uses borrowed data to replace owned data, usually by cloning. Read more
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### impl<T> ToString for T
where T: Display + ?Sized,

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#### fn to_string(&self) -> String

Converts the given value to a `String`. Read more
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### impl<T, U> TryFrom<U> for T
where U: Into<T>,

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#### type Error = Infallible

The type returned in the event of a conversion error.
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#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.
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### impl<T, U> TryInto<U> for T
where U: TryFrom<T>,

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#### type Error = <U as TryFrom<T>>::Error

The type returned in the event of a conversion error.
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#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.