f16 - Rust (original) (raw)
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 f32hardware if it exists, and convert between f16 and f32 when performing math.
See also the std::f16::consts module.
🔬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);🔬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);🔬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);🔬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);🔬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);🔬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);🔬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 asfusedMultiplyAdd 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);🔬This is a nightly-only experimental API. (f16 #116909)
Calculates Euclidean division, the matching method for rem_euclid.
This computes the integer n such thatself = n * rhs + self.rem_euclid(rhs). In other words, the result is self / rhs rounded to the integer nsuch 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🔬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, ifself 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);🔬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);🔬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);🔬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 squareRootand 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);🔬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);🔬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);🔬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);🔬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, andself.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);🔬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);🔬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);🔬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);🔬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() andy.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);🔬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);🔬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);🔬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);🔬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);🔬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);🔬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);🔬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 = 0:0x >= 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);🔬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);🔬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);🔬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);🔬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);🔬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);🔬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);🔬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);🔬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);🔬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);🔬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);🔬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);🔬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);🔬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);🔬This is a nightly-only experimental API. (f16 #116909)
The radix or base of the internal representation of f16.
🔬This is a nightly-only experimental API. (f16 #116909)
Number of significant digits in base 2.
🔬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 2MANTISSA_DIGITS − 1).
🔬This is a nightly-only experimental API. (f16 #116909)
🔬This is a nightly-only experimental API. (f16 #116909)
Smallest finite f16 value.
Equal to −MAX.
🔬This is a nightly-only experimental API. (f16 #116909)
Smallest positive normal f16 value.
Equal to 2MIN_EXP − 1.
🔬This is a nightly-only experimental API. (f16 #116909)
🔬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_.
🔬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_.
🔬This is a nightly-only experimental API. (f16 #116909)
Minimum x for which 10_x_ is normal.
Equal to ceil(log10 MIN_POSITIVE).
🔬This is a nightly-only experimental API. (f16 #116909)
Maximum x for which 10_x_ is normal.
Equal to floor(log10 MAX).
🔬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.
🔬This is a nightly-only experimental API. (f16 #116909)
Infinity (∞).
🔬This is a nightly-only experimental API. (f16 #116909)
Negative infinity (−∞).
🔬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());🔬This is a nightly-only experimental API. (f16 #116909)
Returns true if this value is positive infinity or negative infinity, andfalse 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());🔬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());🔬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());🔬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());🔬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);🔬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() == 1.0if 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());🔬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() == -1.0if 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());🔬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 returnsself; - if
selfis NEG_INFINITY, this returns MIN; - if
selfis-TINY, this returns -0.0; - if
selfis -0.0 or +0.0, this returnsTINY; - if
selfis MAX or INFINITY, this returns INFINITY; - otherwise the unique least value greater than
selfis returned.
The identity x.next_up() == -(-x).next_down() holds for all non-NaN x. When xis 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.
🔬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 returnsself; - if
selfis INFINITY, this returns MAX; - if
selfisTINY, this returns 0.0; - if
selfis -0.0 or +0.0, this returns-TINY; - if
selfis MIN or NEG_INFINITY, this returns NEG_INFINITY; - otherwise the unique greatest value less than
selfis returned.
The identity x.next_down() == -(-x).next_up() holds for all non-NaN x. When xis 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.
🔬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);🔬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);🔬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);🔬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);🔬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);🔬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 tof16::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.
🔬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 tof16::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.
🔬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)]
assert_eq!(1f16.midpoint(4.0), 2.5);
assert_eq!((-5.5f16).midpoint(8.0), 1.25);🔬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
🔬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);🔬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);🔬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]);🔬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]);🔬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]
}
);🔬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);🔬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);🔬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);🔬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 thePartialOrd and PartialEq implementations of f16. For example, they consider negative and positive zero equal, while total_cmpdoesn’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()))
}🔬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());🔬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());🔬This is a nightly-only experimental API. (f16 #116909)
Returns a number that represents the sign of self.
1.0if the number is positive,+0.0orINFINITY-1.0if the number is negative,-0.0orNEG_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());🔬This is a nightly-only experimental API. (f16 #116909)
Returns a number composed of the magnitude of self and the sign ofsign.
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());