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+#[cfg(feature = "bytemuck")]
+use bytemuck::{Pod, Zeroable};
+use core::{
+ cmp::Ordering,
+ fmt::{
+ Binary, Debug, Display, Error, Formatter, LowerExp, LowerHex, Octal, UpperExp, UpperHex,
+ },
+ iter::{Product, Sum},
+ num::{FpCategory, ParseFloatError},
+ ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Rem, RemAssign, Sub, SubAssign},
+ str::FromStr,
+};
+#[cfg(feature = "serde")]
+use serde::{Deserialize, Serialize};
+#[cfg(feature = "zerocopy")]
+use zerocopy::{AsBytes, FromBytes};
+
+pub(crate) mod convert;
+
+/// A 16-bit floating point type implementing the IEEE 754-2008 standard [`binary16`] a.k.a `half`
+/// format.
+///
+/// This 16-bit floating point type is intended for efficient storage where the full range and
+/// precision of a larger floating point value is not required. Because [`f16`] is primarily for
+/// efficient storage, floating point operations such as addition, multiplication, etc. are not
+/// implemented. Operations should be performed with [`f32`] or higher-precision types and converted
+/// to/from [`f16`] as necessary.
+///
+/// [`binary16`]: https://en.wikipedia.org/wiki/Half-precision_floating-point_format
+#[allow(non_camel_case_types)]
+#[derive(Clone, Copy, Default)]
+#[repr(transparent)]
+#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
+#[cfg_attr(feature = "bytemuck", derive(Zeroable, Pod))]
+#[cfg_attr(feature = "zerocopy", derive(AsBytes, FromBytes))]
+pub struct f16(u16);
+
+#[doc(hidden)]
+#[deprecated(
+ since = "1.4.0",
+ note = "all constants moved to associated constants of `f16`"
+)]
+pub mod consts {
+ use super::f16;
+
+ #[deprecated(since = "1.4.0", note = "moved to `f16::DIGITS`")]
+ pub const DIGITS: u32 = f16::DIGITS;
+ #[deprecated(since = "1.4.0", note = "moved to `f16::EPSILON`")]
+ pub const EPSILON: f16 = f16::EPSILON;
+ #[deprecated(since = "1.4.0", note = "moved to `f16::INFINITY`")]
+ pub const INFINITY: f16 = f16::INFINITY;
+ #[deprecated(since = "1.4.0", note = "moved to `f16::MANTISSA_DIGITS`")]
+ pub const MANTISSA_DIGITS: u32 = f16::MANTISSA_DIGITS;
+ #[deprecated(since = "1.4.0", note = "moved to `f16::MAX`")]
+ pub const MAX: f16 = f16::MAX;
+ #[deprecated(since = "1.4.0", note = "moved to `f16::MAX_10_EXP`")]
+ pub const MAX_10_EXP: i32 = f16::MAX_10_EXP;
+ #[deprecated(since = "1.4.0", note = "moved to `f16::MAX_EXP`")]
+ pub const MAX_EXP: i32 = f16::MAX_EXP;
+ #[deprecated(since = "1.4.0", note = "moved to `f16::MIN`")]
+ pub const MIN: f16 = f16::MIN;
+ #[deprecated(since = "1.4.0", note = "moved to `f16::MIN_10_EXP`")]
+ pub const MIN_10_EXP: i32 = f16::MIN_10_EXP;
+ #[deprecated(since = "1.4.0", note = "moved to `f16::MIN_EXP`")]
+ pub const MIN_EXP: i32 = f16::MIN_EXP;
+ #[deprecated(since = "1.4.0", note = "moved to `f16::MIN_POSITIVE`")]
+ pub const MIN_POSITIVE: f16 = f16::MIN_POSITIVE;
+ #[deprecated(since = "1.4.0", note = "moved to `f16::NAN`")]
+ pub const NAN: f16 = f16::NAN;
+ #[deprecated(since = "1.4.0", note = "moved to `f16::NEG_INFINITY`")]
+ pub const NEG_INFINITY: f16 = f16::NEG_INFINITY;
+ #[deprecated(since = "1.4.0", note = "moved to `f16::RADIX`")]
+ pub const RADIX: u32 = f16::RADIX;
+
+ #[deprecated(since = "1.4.0", note = "moved to `f16::MIN_POSITIVE_SUBNORMAL`")]
+ pub const MIN_POSITIVE_SUBNORMAL: f16 = f16::MIN_POSITIVE_SUBNORMAL;
+ #[deprecated(since = "1.4.0", note = "moved to `f16::MAX_SUBNORMAL`")]
+ pub const MAX_SUBNORMAL: f16 = f16::MAX_SUBNORMAL;
+
+ #[deprecated(since = "1.4.0", note = "moved to `f16::ONE`")]
+ pub const ONE: f16 = f16::ONE;
+ #[deprecated(since = "1.4.0", note = "moved to `f16::ZERO`")]
+ pub const ZERO: f16 = f16::ZERO;
+ #[deprecated(since = "1.4.0", note = "moved to `f16::NEG_ZERO`")]
+ pub const NEG_ZERO: f16 = f16::NEG_ZERO;
+
+ #[deprecated(since = "1.4.0", note = "moved to `f16::E`")]
+ pub const E: f16 = f16::E;
+ #[deprecated(since = "1.4.0", note = "moved to `f16::PI`")]
+ pub const PI: f16 = f16::PI;
+ #[deprecated(since = "1.4.0", note = "moved to `f16::FRAC_1_PI`")]
+ pub const FRAC_1_PI: f16 = f16::FRAC_1_PI;
+ #[deprecated(since = "1.4.0", note = "moved to `f16::FRAC_1_SQRT_2`")]
+ pub const FRAC_1_SQRT_2: f16 = f16::FRAC_1_SQRT_2;
+ #[deprecated(since = "1.4.0", note = "moved to `f16::FRAC_2_PI`")]
+ pub const FRAC_2_PI: f16 = f16::FRAC_2_PI;
+ #[deprecated(since = "1.4.0", note = "moved to `f16::FRAC_2_SQRT_PI`")]
+ pub const FRAC_2_SQRT_PI: f16 = f16::FRAC_2_SQRT_PI;
+ #[deprecated(since = "1.4.0", note = "moved to `f16::FRAC_PI_2`")]
+ pub const FRAC_PI_2: f16 = f16::FRAC_PI_2;
+ #[deprecated(since = "1.4.0", note = "moved to `f16::FRAC_PI_3`")]
+ pub const FRAC_PI_3: f16 = f16::FRAC_PI_3;
+ #[deprecated(since = "1.4.0", note = "moved to `f16::FRAC_PI_4`")]
+ pub const FRAC_PI_4: f16 = f16::FRAC_PI_4;
+ #[deprecated(since = "1.4.0", note = "moved to `f16::FRAC_PI_6`")]
+ pub const FRAC_PI_6: f16 = f16::FRAC_PI_6;
+ #[deprecated(since = "1.4.0", note = "moved to `f16::FRAC_PI_8`")]
+ pub const FRAC_PI_8: f16 = f16::FRAC_PI_8;
+ #[deprecated(since = "1.4.0", note = "moved to `f16::LN_10`")]
+ pub const LN_10: f16 = f16::LN_10;
+ #[deprecated(since = "1.4.0", note = "moved to `f16::LN_2`")]
+ pub const LN_2: f16 = f16::LN_2;
+ #[deprecated(since = "1.4.0", note = "moved to `f16::LOG10_E`")]
+ pub const LOG10_E: f16 = f16::LOG10_E;
+ #[deprecated(since = "1.4.0", note = "moved to `f16::LOG2_E`")]
+ pub const LOG2_E: f16 = f16::LOG2_E;
+ #[deprecated(since = "1.4.0", note = "moved to `f16::SQRT_2`")]
+ pub const SQRT_2: f16 = f16::SQRT_2;
+}
+
+impl f16 {
+ /// Constructs a 16-bit floating point value from the raw bits.
+ #[inline]
+ pub const fn from_bits(bits: u16) -> f16 {
+ f16(bits)
+ }
+
+ /// Constructs a 16-bit floating point value from a 32-bit floating point value.
+ ///
+ /// If the 32-bit value is to large to fit in 16-bits, ±∞ will result. NaN values are
+ /// preserved. 32-bit subnormal values are too tiny to be represented in 16-bits and result in
+ /// ±0. Exponents that underflow the minimum 16-bit exponent will result in 16-bit subnormals
+ /// or ±0. All other values are truncated and rounded to the nearest representable 16-bit
+ /// value.
+ #[inline]
+ pub fn from_f32(value: f32) -> f16 {
+ f16(convert::f32_to_f16(value))
+ }
+
+ /// Constructs a 16-bit floating point value from a 64-bit floating point value.
+ ///
+ /// If the 64-bit value is to large to fit in 16-bits, ±∞ will result. NaN values are
+ /// preserved. 64-bit subnormal values are too tiny to be represented in 16-bits and result in
+ /// ±0. Exponents that underflow the minimum 16-bit exponent will result in 16-bit subnormals
+ /// or ±0. All other values are truncated and rounded to the nearest representable 16-bit
+ /// value.
+ #[inline]
+ pub fn from_f64(value: f64) -> f16 {
+ f16(convert::f64_to_f16(value))
+ }
+
+ /// Converts a [`f16`] into the underlying bit representation.
+ #[inline]
+ pub const fn to_bits(self) -> u16 {
+ self.0
+ }
+
+ /// Returns the memory representation of the underlying bit representation as a byte array in
+ /// little-endian byte order.
+ ///
+ /// # Examples
+ ///
+ /// ```rust
+ /// # use half::prelude::*;
+ /// let bytes = f16::from_f32(12.5).to_le_bytes();
+ /// assert_eq!(bytes, [0x40, 0x4A]);
+ /// ```
+ #[inline]
+ pub const fn to_le_bytes(self) -> [u8; 2] {
+ self.0.to_le_bytes()
+ }
+
+ /// Returns the memory representation of the underlying bit representation as a byte array in
+ /// big-endian (network) byte order.
+ ///
+ /// # Examples
+ ///
+ /// ```rust
+ /// # use half::prelude::*;
+ /// let bytes = f16::from_f32(12.5).to_be_bytes();
+ /// assert_eq!(bytes, [0x4A, 0x40]);
+ /// ```
+ #[inline]
+ pub const fn to_be_bytes(self) -> [u8; 2] {
+ self.0.to_be_bytes()
+ }
+
+ /// Returns the memory representation of the underlying bit representation as a byte array in
+ /// native byte order.
+ ///
+ /// As the target platform's native endianness is used, portable code should use
+ /// [`to_be_bytes`][Self::to_be_bytes] or [`to_le_bytes`][Self::to_le_bytes], as appropriate,
+ /// instead.
+ ///
+ /// # Examples
+ ///
+ /// ```rust
+ /// # use half::prelude::*;
+ /// let bytes = f16::from_f32(12.5).to_ne_bytes();
+ /// assert_eq!(bytes, if cfg!(target_endian = "big") {
+ /// [0x4A, 0x40]
+ /// } else {
+ /// [0x40, 0x4A]
+ /// });
+ /// ```
+ #[inline]
+ pub const fn to_ne_bytes(self) -> [u8; 2] {
+ self.0.to_ne_bytes()
+ }
+
+ /// Creates a floating point value from its representation as a byte array in little endian.
+ ///
+ /// # Examples
+ ///
+ /// ```rust
+ /// # use half::prelude::*;
+ /// let value = f16::from_le_bytes([0x40, 0x4A]);
+ /// assert_eq!(value, f16::from_f32(12.5));
+ /// ```
+ #[inline]
+ pub const fn from_le_bytes(bytes: [u8; 2]) -> f16 {
+ f16::from_bits(u16::from_le_bytes(bytes))
+ }
+
+ /// Creates a floating point value from its representation as a byte array in big endian.
+ ///
+ /// # Examples
+ ///
+ /// ```rust
+ /// # use half::prelude::*;
+ /// let value = f16::from_be_bytes([0x4A, 0x40]);
+ /// assert_eq!(value, f16::from_f32(12.5));
+ /// ```
+ #[inline]
+ pub const fn from_be_bytes(bytes: [u8; 2]) -> f16 {
+ f16::from_bits(u16::from_be_bytes(bytes))
+ }
+
+ /// 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`][Self::from_be_bytes] or [`from_le_bytes`][Self::from_le_bytes], as
+ /// appropriate instead.
+ ///
+ /// # Examples
+ ///
+ /// ```rust
+ /// # use half::prelude::*;
+ /// let value = f16::from_ne_bytes(if cfg!(target_endian = "big") {
+ /// [0x4A, 0x40]
+ /// } else {
+ /// [0x40, 0x4A]
+ /// });
+ /// assert_eq!(value, f16::from_f32(12.5));
+ /// ```
+ #[inline]
+ pub const fn from_ne_bytes(bytes: [u8; 2]) -> f16 {
+ f16::from_bits(u16::from_ne_bytes(bytes))
+ }
+
+ #[doc(hidden)]
+ #[deprecated(since = "1.2.0", note = "renamed to `to_bits`")]
+ #[inline]
+ pub fn as_bits(self) -> u16 {
+ self.to_bits()
+ }
+
+ /// Converts a [`f16`] value into a `f32` value.
+ ///
+ /// This conversion is lossless as all 16-bit floating point values can be represented exactly
+ /// in 32-bit floating point.
+ #[inline]
+ pub fn to_f32(self) -> f32 {
+ convert::f16_to_f32(self.0)
+ }
+
+ /// Converts a [`f16`] value into a `f64` value.
+ ///
+ /// This conversion is lossless as all 16-bit floating point values can be represented exactly
+ /// in 64-bit floating point.
+ #[inline]
+ pub fn to_f64(self) -> f64 {
+ convert::f16_to_f64(self.0)
+ }
+
+ /// Returns `true` if this value is `NaN` and `false` otherwise.
+ ///
+ /// # Examples
+ ///
+ /// ```rust
+ /// # use half::prelude::*;
+ ///
+ /// let nan = f16::NAN;
+ /// let f = f16::from_f32(7.0_f32);
+ ///
+ /// assert!(nan.is_nan());
+ /// assert!(!f.is_nan());
+ /// ```
+ #[inline]
+ pub const fn is_nan(self) -> bool {
+ self.0 & 0x7FFFu16 > 0x7C00u16
+ }
+
+ /// Returns `true` if this value is ±∞ and `false`.
+ /// otherwise.
+ ///
+ /// # Examples
+ ///
+ /// ```rust
+ /// # use half::prelude::*;
+ ///
+ /// let f = f16::from_f32(7.0f32);
+ /// 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());
+ /// ```
+ #[inline]
+ pub const fn is_infinite(self) -> bool {
+ self.0 & 0x7FFFu16 == 0x7C00u16
+ }
+
+ /// Returns `true` if this number is neither infinite nor `NaN`.
+ ///
+ /// # Examples
+ ///
+ /// ```rust
+ /// # use half::prelude::*;
+ ///
+ /// let f = f16::from_f32(7.0f32);
+ /// let inf = f16::INFINITY;
+ /// let neg_inf = f16::NEG_INFINITY;
+ /// let nan = f16::NAN;
+ ///
+ /// assert!(f.is_finite());
+ ///
+ /// assert!(!nan.is_finite());
+ /// assert!(!inf.is_finite());
+ /// assert!(!neg_inf.is_finite());
+ /// ```
+ #[inline]
+ pub const fn is_finite(self) -> bool {
+ self.0 & 0x7C00u16 != 0x7C00u16
+ }
+
+ /// Returns `true` if the number is neither zero, infinite, subnormal, or `NaN`.
+ ///
+ /// # Examples
+ ///
+ /// ```rust
+ /// # use half::prelude::*;
+ ///
+ /// let min = f16::MIN_POSITIVE;
+ /// let max = f16::MAX;
+ /// let lower_than_min = f16::from_f32(1.0e-10_f32);
+ /// let zero = f16::from_f32(0.0_f32);
+ ///
+ /// 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());
+ /// ```
+ #[inline]
+ pub const fn is_normal(self) -> bool {
+ let exp = self.0 & 0x7C00u16;
+ exp != 0x7C00u16 && exp != 0
+ }
+
+ /// 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.
+ ///
+ /// # Examples
+ ///
+ /// ```rust
+ /// use std::num::FpCategory;
+ /// # use half::prelude::*;
+ ///
+ /// let num = f16::from_f32(12.4_f32);
+ /// let inf = f16::INFINITY;
+ ///
+ /// assert_eq!(num.classify(), FpCategory::Normal);
+ /// assert_eq!(inf.classify(), FpCategory::Infinite);
+ /// ```
+ pub const fn classify(self) -> FpCategory {
+ let exp = self.0 & 0x7C00u16;
+ let man = self.0 & 0x03FFu16;
+ match (exp, man) {
+ (0, 0) => FpCategory::Zero,
+ (0, _) => FpCategory::Subnormal,
+ (0x7C00u16, 0) => FpCategory::Infinite,
+ (0x7C00u16, _) => FpCategory::Nan,
+ _ => FpCategory::Normal,
+ }
+ }
+
+ /// Returns a number that represents the sign of `self`.
+ ///
+ /// * `1.0` if the number is positive, `+0.0` or [`INFINITY`][f16::INFINITY]
+ /// * `-1.0` if the number is negative, `-0.0` or [`NEG_INFINITY`][f16::NEG_INFINITY]
+ /// * [`NAN`][f16::NAN] if the number is `NaN`
+ ///
+ /// # Examples
+ ///
+ /// ```rust
+ /// # use half::prelude::*;
+ ///
+ /// let f = f16::from_f32(3.5_f32);
+ ///
+ /// assert_eq!(f.signum(), f16::from_f32(1.0));
+ /// assert_eq!(f16::NEG_INFINITY.signum(), f16::from_f32(-1.0));
+ ///
+ /// assert!(f16::NAN.signum().is_nan());
+ /// ```
+ pub const fn signum(self) -> f16 {
+ if self.is_nan() {
+ self
+ } else if self.0 & 0x8000u16 != 0 {
+ Self::NEG_ONE
+ } else {
+ Self::ONE
+ }
+ }
+
+ /// Returns `true` if and only if `self` has a positive sign, including `+0.0`, `NaNs` with a
+ /// positive sign bit and +∞.
+ ///
+ /// # Examples
+ ///
+ /// ```rust
+ /// # use half::prelude::*;
+ ///
+ /// let nan = f16::NAN;
+ /// let f = f16::from_f32(7.0_f32);
+ /// let g = f16::from_f32(-7.0_f32);
+ ///
+ /// assert!(f.is_sign_positive());
+ /// assert!(!g.is_sign_positive());
+ /// // `NaN` can be either positive or negative
+ /// assert!(nan.is_sign_positive() != nan.is_sign_negative());
+ /// ```
+ #[inline]
+ pub const fn is_sign_positive(self) -> bool {
+ self.0 & 0x8000u16 == 0
+ }
+
+ /// Returns `true` if and only if `self` has a negative sign, including `-0.0`, `NaNs` with a
+ /// negative sign bit and −∞.
+ ///
+ /// # Examples
+ ///
+ /// ```rust
+ /// # use half::prelude::*;
+ ///
+ /// let nan = f16::NAN;
+ /// let f = f16::from_f32(7.0f32);
+ /// let g = f16::from_f32(-7.0f32);
+ ///
+ /// assert!(!f.is_sign_negative());
+ /// assert!(g.is_sign_negative());
+ /// // `NaN` can be either positive or negative
+ /// assert!(nan.is_sign_positive() != nan.is_sign_negative());
+ /// ```
+ #[inline]
+ pub const fn is_sign_negative(self) -> bool {
+ self.0 & 0x8000u16 != 0
+ }
+
+ /// 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 NaN, then NaN with the sign of `sign` is returned.
+ ///
+ /// # Examples
+ ///
+ /// ```
+ /// # use half::prelude::*;
+ /// let f = f16::from_f32(3.5);
+ ///
+ /// assert_eq!(f.copysign(f16::from_f32(0.42)), f16::from_f32(3.5));
+ /// assert_eq!(f.copysign(f16::from_f32(-0.42)), f16::from_f32(-3.5));
+ /// assert_eq!((-f).copysign(f16::from_f32(0.42)), f16::from_f32(3.5));
+ /// assert_eq!((-f).copysign(f16::from_f32(-0.42)), f16::from_f32(-3.5));
+ ///
+ /// assert!(f16::NAN.copysign(f16::from_f32(1.0)).is_nan());
+ /// ```
+ #[inline]
+ pub const fn copysign(self, sign: f16) -> f16 {
+ f16((sign.0 & 0x8000u16) | (self.0 & 0x7FFFu16))
+ }
+
+ /// Returns the maximum of the two numbers.
+ ///
+ /// If one of the arguments is NaN, then the other argument is returned.
+ ///
+ /// # Examples
+ ///
+ /// ```
+ /// # use half::prelude::*;
+ /// let x = f16::from_f32(1.0);
+ /// let y = f16::from_f32(2.0);
+ ///
+ /// assert_eq!(x.max(y), y);
+ /// ```
+ #[inline]
+ pub fn max(self, other: f16) -> f16 {
+ if other > self && !other.is_nan() {
+ other
+ } else {
+ self
+ }
+ }
+
+ /// Returns the minimum of the two numbers.
+ ///
+ /// If one of the arguments is NaN, then the other argument is returned.
+ ///
+ /// # Examples
+ ///
+ /// ```
+ /// # use half::prelude::*;
+ /// let x = f16::from_f32(1.0);
+ /// let y = f16::from_f32(2.0);
+ ///
+ /// assert_eq!(x.min(y), x);
+ /// ```
+ #[inline]
+ pub fn min(self, other: f16) -> f16 {
+ if other < self && !other.is_nan() {
+ other
+ } else {
+ self
+ }
+ }
+
+ /// 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
+ ///
+ /// ```
+ /// # use half::prelude::*;
+ /// assert!(f16::from_f32(-3.0).clamp(f16::from_f32(-2.0), f16::from_f32(1.0)) == f16::from_f32(-2.0));
+ /// assert!(f16::from_f32(0.0).clamp(f16::from_f32(-2.0), f16::from_f32(1.0)) == f16::from_f32(0.0));
+ /// assert!(f16::from_f32(2.0).clamp(f16::from_f32(-2.0), f16::from_f32(1.0)) == f16::from_f32(1.0));
+ /// assert!(f16::NAN.clamp(f16::from_f32(-2.0), f16::from_f32(1.0)).is_nan());
+ /// ```
+ #[inline]
+ pub fn clamp(self, min: f16, max: f16) -> f16 {
+ assert!(min <= max);
+ let mut x = self;
+ if x < min {
+ x = min;
+ }
+ if x > max {
+ x = max;
+ }
+ x
+ }
+
+ /// Approximate number of [`f16`] significant digits in base 10
+ pub const DIGITS: u32 = 3;
+ /// [`f16`]
+ /// [machine epsilon](https://en.wikipedia.org/wiki/Machine_epsilon) value
+ ///
+ /// This is the difference between 1.0 and the next largest representable number.
+ pub const EPSILON: f16 = f16(0x1400u16);
+ /// [`f16`] positive Infinity (+∞)
+ pub const INFINITY: f16 = f16(0x7C00u16);
+ /// Number of [`f16`] significant digits in base 2
+ pub const MANTISSA_DIGITS: u32 = 11;
+ /// Largest finite [`f16`] value
+ pub const MAX: f16 = f16(0x7BFF);
+ /// Maximum possible [`f16`] power of 10 exponent
+ pub const MAX_10_EXP: i32 = 4;
+ /// Maximum possible [`f16`] power of 2 exponent
+ pub const MAX_EXP: i32 = 16;
+ /// Smallest finite [`f16`] value
+ pub const MIN: f16 = f16(0xFBFF);
+ /// Minimum possible normal [`f16`] power of 10 exponent
+ pub const MIN_10_EXP: i32 = -4;
+ /// One greater than the minimum possible normal [`f16`] power of 2 exponent
+ pub const MIN_EXP: i32 = -13;
+ /// Smallest positive normal [`f16`] value
+ pub const MIN_POSITIVE: f16 = f16(0x0400u16);
+ /// [`f16`] Not a Number (NaN)
+ pub const NAN: f16 = f16(0x7E00u16);
+ /// [`f16`] negative infinity (-∞)
+ pub const NEG_INFINITY: f16 = f16(0xFC00u16);
+ /// The radix or base of the internal representation of [`f16`]
+ pub const RADIX: u32 = 2;
+
+ /// Minimum positive subnormal [`f16`] value
+ pub const MIN_POSITIVE_SUBNORMAL: f16 = f16(0x0001u16);
+ /// Maximum subnormal [`f16`] value
+ pub const MAX_SUBNORMAL: f16 = f16(0x03FFu16);
+
+ /// [`f16`] 1
+ pub const ONE: f16 = f16(0x3C00u16);
+ /// [`f16`] 0
+ pub const ZERO: f16 = f16(0x0000u16);
+ /// [`f16`] -0
+ pub const NEG_ZERO: f16 = f16(0x8000u16);
+ /// [`f16`] -1
+ pub const NEG_ONE: f16 = f16(0xBC00u16);
+
+ /// [`f16`] Euler's number (ℯ)
+ pub const E: f16 = f16(0x4170u16);
+ /// [`f16`] Archimedes' constant (π)
+ pub const PI: f16 = f16(0x4248u16);
+ /// [`f16`] 1/π
+ pub const FRAC_1_PI: f16 = f16(0x3518u16);
+ /// [`f16`] 1/√2
+ pub const FRAC_1_SQRT_2: f16 = f16(0x39A8u16);
+ /// [`f16`] 2/π
+ pub const FRAC_2_PI: f16 = f16(0x3918u16);
+ /// [`f16`] 2/√π
+ pub const FRAC_2_SQRT_PI: f16 = f16(0x3C83u16);
+ /// [`f16`] π/2
+ pub const FRAC_PI_2: f16 = f16(0x3E48u16);
+ /// [`f16`] π/3
+ pub const FRAC_PI_3: f16 = f16(0x3C30u16);
+ /// [`f16`] π/4
+ pub const FRAC_PI_4: f16 = f16(0x3A48u16);
+ /// [`f16`] π/6
+ pub const FRAC_PI_6: f16 = f16(0x3830u16);
+ /// [`f16`] π/8
+ pub const FRAC_PI_8: f16 = f16(0x3648u16);
+ /// [`f16`] 𝗅𝗇 10
+ pub const LN_10: f16 = f16(0x409Bu16);
+ /// [`f16`] 𝗅𝗇 2
+ pub const LN_2: f16 = f16(0x398Cu16);
+ /// [`f16`] 𝗅𝗈𝗀₁₀ℯ
+ pub const LOG10_E: f16 = f16(0x36F3u16);
+ /// [`f16`] 𝗅𝗈𝗀₁₀2
+ pub const LOG10_2: f16 = f16(0x34D1u16);
+ /// [`f16`] 𝗅𝗈𝗀₂ℯ
+ pub const LOG2_E: f16 = f16(0x3DC5u16);
+ /// [`f16`] 𝗅𝗈𝗀₂10
+ pub const LOG2_10: f16 = f16(0x42A5u16);
+ /// [`f16`] √2
+ pub const SQRT_2: f16 = f16(0x3DA8u16);
+}
+
+impl From<f16> for f32 {
+ #[inline]
+ fn from(x: f16) -> f32 {
+ x.to_f32()
+ }
+}
+
+impl From<f16> for f64 {
+ #[inline]
+ fn from(x: f16) -> f64 {
+ x.to_f64()
+ }
+}
+
+impl From<i8> for f16 {
+ #[inline]
+ fn from(x: i8) -> f16 {
+ // Convert to f32, then to f16
+ f16::from_f32(f32::from(x))
+ }
+}
+
+impl From<u8> for f16 {
+ #[inline]
+ fn from(x: u8) -> f16 {
+ // Convert to f32, then to f16
+ f16::from_f32(f32::from(x))
+ }
+}
+
+impl PartialEq for f16 {
+ fn eq(&self, other: &f16) -> bool {
+ if self.is_nan() || other.is_nan() {
+ false
+ } else {
+ (self.0 == other.0) || ((self.0 | other.0) & 0x7FFFu16 == 0)
+ }
+ }
+}
+
+impl PartialOrd for f16 {
+ fn partial_cmp(&self, other: &f16) -> Option<Ordering> {
+ if self.is_nan() || other.is_nan() {
+ None
+ } else {
+ let neg = self.0 & 0x8000u16 != 0;
+ let other_neg = other.0 & 0x8000u16 != 0;
+ match (neg, other_neg) {
+ (false, false) => Some(self.0.cmp(&other.0)),
+ (false, true) => {
+ if (self.0 | other.0) & 0x7FFFu16 == 0 {
+ Some(Ordering::Equal)
+ } else {
+ Some(Ordering::Greater)
+ }
+ }
+ (true, false) => {
+ if (self.0 | other.0) & 0x7FFFu16 == 0 {
+ Some(Ordering::Equal)
+ } else {
+ Some(Ordering::Less)
+ }
+ }
+ (true, true) => Some(other.0.cmp(&self.0)),
+ }
+ }
+ }
+
+ fn lt(&self, other: &f16) -> bool {
+ if self.is_nan() || other.is_nan() {
+ false
+ } else {
+ let neg = self.0 & 0x8000u16 != 0;
+ let other_neg = other.0 & 0x8000u16 != 0;
+ match (neg, other_neg) {
+ (false, false) => self.0 < other.0,
+ (false, true) => false,
+ (true, false) => (self.0 | other.0) & 0x7FFFu16 != 0,
+ (true, true) => self.0 > other.0,
+ }
+ }
+ }
+
+ fn le(&self, other: &f16) -> bool {
+ if self.is_nan() || other.is_nan() {
+ false
+ } else {
+ let neg = self.0 & 0x8000u16 != 0;
+ let other_neg = other.0 & 0x8000u16 != 0;
+ match (neg, other_neg) {
+ (false, false) => self.0 <= other.0,
+ (false, true) => (self.0 | other.0) & 0x7FFFu16 == 0,
+ (true, false) => true,
+ (true, true) => self.0 >= other.0,
+ }
+ }
+ }
+
+ fn gt(&self, other: &f16) -> bool {
+ if self.is_nan() || other.is_nan() {
+ false
+ } else {
+ let neg = self.0 & 0x8000u16 != 0;
+ let other_neg = other.0 & 0x8000u16 != 0;
+ match (neg, other_neg) {
+ (false, false) => self.0 > other.0,
+ (false, true) => (self.0 | other.0) & 0x7FFFu16 != 0,
+ (true, false) => false,
+ (true, true) => self.0 < other.0,
+ }
+ }
+ }
+
+ fn ge(&self, other: &f16) -> bool {
+ if self.is_nan() || other.is_nan() {
+ false
+ } else {
+ let neg = self.0 & 0x8000u16 != 0;
+ let other_neg = other.0 & 0x8000u16 != 0;
+ match (neg, other_neg) {
+ (false, false) => self.0 >= other.0,
+ (false, true) => true,
+ (true, false) => (self.0 | other.0) & 0x7FFFu16 == 0,
+ (true, true) => self.0 <= other.0,
+ }
+ }
+ }
+}
+
+impl FromStr for f16 {
+ type Err = ParseFloatError;
+ fn from_str(src: &str) -> Result<f16, ParseFloatError> {
+ f32::from_str(src).map(f16::from_f32)
+ }
+}
+
+impl Debug for f16 {
+ fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> {
+ write!(f, "{:?}", self.to_f32())
+ }
+}
+
+impl Display for f16 {
+ fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> {
+ write!(f, "{}", self.to_f32())
+ }
+}
+
+impl LowerExp for f16 {
+ fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> {
+ write!(f, "{:e}", self.to_f32())
+ }
+}
+
+impl UpperExp for f16 {
+ fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> {
+ write!(f, "{:E}", self.to_f32())
+ }
+}
+
+impl Binary for f16 {
+ fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> {
+ write!(f, "{:b}", self.0)
+ }
+}
+
+impl Octal for f16 {
+ fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> {
+ write!(f, "{:o}", self.0)
+ }
+}
+
+impl LowerHex for f16 {
+ fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> {
+ write!(f, "{:x}", self.0)
+ }
+}
+
+impl UpperHex for f16 {
+ fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> {
+ write!(f, "{:X}", self.0)
+ }
+}
+
+impl Neg for f16 {
+ type Output = Self;
+
+ #[inline]
+ fn neg(self) -> Self::Output {
+ Self(self.0 ^ 0x8000)
+ }
+}
+
+impl Add for f16 {
+ type Output = Self;
+
+ #[inline]
+ fn add(self, rhs: Self) -> Self::Output {
+ Self::from_f32(Self::to_f32(self) + Self::to_f32(rhs))
+ }
+}
+
+impl Add<&f16> for f16 {
+ type Output = <f16 as Add<f16>>::Output;
+
+ #[inline]
+ fn add(self, rhs: &f16) -> Self::Output {
+ self.add(*rhs)
+ }
+}
+
+impl Add<&f16> for &f16 {
+ type Output = <f16 as Add<f16>>::Output;
+
+ #[inline]
+ fn add(self, rhs: &f16) -> Self::Output {
+ (*self).add(*rhs)
+ }
+}
+
+impl Add<f16> for &f16 {
+ type Output = <f16 as Add<f16>>::Output;
+
+ #[inline]
+ fn add(self, rhs: f16) -> Self::Output {
+ (*self).add(rhs)
+ }
+}
+
+impl AddAssign for f16 {
+ #[inline]
+ fn add_assign(&mut self, rhs: Self) {
+ *self = (*self).add(rhs);
+ }
+}
+
+impl AddAssign<&f16> for f16 {
+ #[inline]
+ fn add_assign(&mut self, rhs: &f16) {
+ *self = (*self).add(rhs);
+ }
+}
+
+impl Sub for f16 {
+ type Output = Self;
+
+ #[inline]
+ fn sub(self, rhs: Self) -> Self::Output {
+ Self::from_f32(Self::to_f32(self) - Self::to_f32(rhs))
+ }
+}
+
+impl Sub<&f16> for f16 {
+ type Output = <f16 as Sub<f16>>::Output;
+
+ #[inline]
+ fn sub(self, rhs: &f16) -> Self::Output {
+ self.sub(*rhs)
+ }
+}
+
+impl Sub<&f16> for &f16 {
+ type Output = <f16 as Sub<f16>>::Output;
+
+ #[inline]
+ fn sub(self, rhs: &f16) -> Self::Output {
+ (*self).sub(*rhs)
+ }
+}
+
+impl Sub<f16> for &f16 {
+ type Output = <f16 as Sub<f16>>::Output;
+
+ #[inline]
+ fn sub(self, rhs: f16) -> Self::Output {
+ (*self).sub(rhs)
+ }
+}
+
+impl SubAssign for f16 {
+ #[inline]
+ fn sub_assign(&mut self, rhs: Self) {
+ *self = (*self).sub(rhs);
+ }
+}
+
+impl SubAssign<&f16> for f16 {
+ #[inline]
+ fn sub_assign(&mut self, rhs: &f16) {
+ *self = (*self).sub(rhs);
+ }
+}
+
+impl Mul for f16 {
+ type Output = Self;
+
+ #[inline]
+ fn mul(self, rhs: Self) -> Self::Output {
+ Self::from_f32(Self::to_f32(self) * Self::to_f32(rhs))
+ }
+}
+
+impl Mul<&f16> for f16 {
+ type Output = <f16 as Mul<f16>>::Output;
+
+ #[inline]
+ fn mul(self, rhs: &f16) -> Self::Output {
+ self.mul(*rhs)
+ }
+}
+
+impl Mul<&f16> for &f16 {
+ type Output = <f16 as Mul<f16>>::Output;
+
+ #[inline]
+ fn mul(self, rhs: &f16) -> Self::Output {
+ (*self).mul(*rhs)
+ }
+}
+
+impl Mul<f16> for &f16 {
+ type Output = <f16 as Mul<f16>>::Output;
+
+ #[inline]
+ fn mul(self, rhs: f16) -> Self::Output {
+ (*self).mul(rhs)
+ }
+}
+
+impl MulAssign for f16 {
+ #[inline]
+ fn mul_assign(&mut self, rhs: Self) {
+ *self = (*self).mul(rhs);
+ }
+}
+
+impl MulAssign<&f16> for f16 {
+ #[inline]
+ fn mul_assign(&mut self, rhs: &f16) {
+ *self = (*self).mul(rhs);
+ }
+}
+
+impl Div for f16 {
+ type Output = Self;
+
+ #[inline]
+ fn div(self, rhs: Self) -> Self::Output {
+ Self::from_f32(Self::to_f32(self) / Self::to_f32(rhs))
+ }
+}
+
+impl Div<&f16> for f16 {
+ type Output = <f16 as Div<f16>>::Output;
+
+ #[inline]
+ fn div(self, rhs: &f16) -> Self::Output {
+ self.div(*rhs)
+ }
+}
+
+impl Div<&f16> for &f16 {
+ type Output = <f16 as Div<f16>>::Output;
+
+ #[inline]
+ fn div(self, rhs: &f16) -> Self::Output {
+ (*self).div(*rhs)
+ }
+}
+
+impl Div<f16> for &f16 {
+ type Output = <f16 as Div<f16>>::Output;
+
+ #[inline]
+ fn div(self, rhs: f16) -> Self::Output {
+ (*self).div(rhs)
+ }
+}
+
+impl DivAssign for f16 {
+ #[inline]
+ fn div_assign(&mut self, rhs: Self) {
+ *self = (*self).div(rhs);
+ }
+}
+
+impl DivAssign<&f16> for f16 {
+ #[inline]
+ fn div_assign(&mut self, rhs: &f16) {
+ *self = (*self).div(rhs);
+ }
+}
+
+impl Rem for f16 {
+ type Output = Self;
+
+ #[inline]
+ fn rem(self, rhs: Self) -> Self::Output {
+ Self::from_f32(Self::to_f32(self) % Self::to_f32(rhs))
+ }
+}
+
+impl Rem<&f16> for f16 {
+ type Output = <f16 as Rem<f16>>::Output;
+
+ #[inline]
+ fn rem(self, rhs: &f16) -> Self::Output {
+ self.rem(*rhs)
+ }
+}
+
+impl Rem<&f16> for &f16 {
+ type Output = <f16 as Rem<f16>>::Output;
+
+ #[inline]
+ fn rem(self, rhs: &f16) -> Self::Output {
+ (*self).rem(*rhs)
+ }
+}
+
+impl Rem<f16> for &f16 {
+ type Output = <f16 as Rem<f16>>::Output;
+
+ #[inline]
+ fn rem(self, rhs: f16) -> Self::Output {
+ (*self).rem(rhs)
+ }
+}
+
+impl RemAssign for f16 {
+ #[inline]
+ fn rem_assign(&mut self, rhs: Self) {
+ *self = (*self).rem(rhs);
+ }
+}
+
+impl RemAssign<&f16> for f16 {
+ #[inline]
+ fn rem_assign(&mut self, rhs: &f16) {
+ *self = (*self).rem(rhs);
+ }
+}
+
+impl Product for f16 {
+ #[inline]
+ fn product<I: Iterator<Item = Self>>(iter: I) -> Self {
+ f16::from_f32(iter.map(|f| f.to_f32()).product())
+ }
+}
+
+impl<'a> Product<&'a f16> for f16 {
+ #[inline]
+ fn product<I: Iterator<Item = &'a f16>>(iter: I) -> Self {
+ f16::from_f32(iter.map(|f| f.to_f32()).product())
+ }
+}
+
+impl Sum for f16 {
+ #[inline]
+ fn sum<I: Iterator<Item = Self>>(iter: I) -> Self {
+ f16::from_f32(iter.map(|f| f.to_f32()).sum())
+ }
+}
+
+impl<'a> Sum<&'a f16> for f16 {
+ #[inline]
+ fn sum<I: Iterator<Item = &'a f16>>(iter: I) -> Self {
+ f16::from_f32(iter.map(|f| f.to_f32()).product())
+ }
+}
+
+#[allow(
+ clippy::cognitive_complexity,
+ clippy::float_cmp,
+ clippy::neg_cmp_op_on_partial_ord
+)]
+#[cfg(test)]
+mod test {
+ use super::*;
+ use core::cmp::Ordering;
+ #[cfg(feature = "num-traits")]
+ use num_traits::{AsPrimitive, FromPrimitive, ToPrimitive};
+ use quickcheck_macros::quickcheck;
+
+ #[cfg(feature = "num-traits")]
+ #[test]
+ fn as_primitive() {
+ let two = f16::from_f32(2.0);
+ assert_eq!(<i32 as AsPrimitive<f16>>::as_(2), two);
+ assert_eq!(<f16 as AsPrimitive<i32>>::as_(two), 2);
+
+ assert_eq!(<f32 as AsPrimitive<f16>>::as_(2.0), two);
+ assert_eq!(<f16 as AsPrimitive<f32>>::as_(two), 2.0);
+
+ assert_eq!(<f64 as AsPrimitive<f16>>::as_(2.0), two);
+ assert_eq!(<f16 as AsPrimitive<f64>>::as_(two), 2.0);
+ }
+
+ #[cfg(feature = "num-traits")]
+ #[test]
+ fn to_primitive() {
+ let two = f16::from_f32(2.0);
+ assert_eq!(ToPrimitive::to_i32(&two).unwrap(), 2i32);
+ assert_eq!(ToPrimitive::to_f32(&two).unwrap(), 2.0f32);
+ assert_eq!(ToPrimitive::to_f64(&two).unwrap(), 2.0f64);
+ }
+
+ #[cfg(feature = "num-traits")]
+ #[test]
+ fn from_primitive() {
+ let two = f16::from_f32(2.0);
+ assert_eq!(<f16 as FromPrimitive>::from_i32(2).unwrap(), two);
+ assert_eq!(<f16 as FromPrimitive>::from_f32(2.0).unwrap(), two);
+ assert_eq!(<f16 as FromPrimitive>::from_f64(2.0).unwrap(), two);
+ }
+
+ #[test]
+ fn test_f16_consts() {
+ // DIGITS
+ let digits = ((f16::MANTISSA_DIGITS as f32 - 1.0) * 2f32.log10()).floor() as u32;
+ assert_eq!(f16::DIGITS, digits);
+ // sanity check to show test is good
+ let digits32 = ((core::f32::MANTISSA_DIGITS as f32 - 1.0) * 2f32.log10()).floor() as u32;
+ assert_eq!(core::f32::DIGITS, digits32);
+
+ // EPSILON
+ let one = f16::from_f32(1.0);
+ let one_plus_epsilon = f16::from_bits(one.to_bits() + 1);
+ let epsilon = f16::from_f32(one_plus_epsilon.to_f32() - 1.0);
+ assert_eq!(f16::EPSILON, epsilon);
+ // sanity check to show test is good
+ let one_plus_epsilon32 = f32::from_bits(1.0f32.to_bits() + 1);
+ let epsilon32 = one_plus_epsilon32 - 1f32;
+ assert_eq!(core::f32::EPSILON, epsilon32);
+
+ // MAX, MIN and MIN_POSITIVE
+ let max = f16::from_bits(f16::INFINITY.to_bits() - 1);
+ let min = f16::from_bits(f16::NEG_INFINITY.to_bits() - 1);
+ let min_pos = f16::from_f32(2f32.powi(f16::MIN_EXP - 1));
+ assert_eq!(f16::MAX, max);
+ assert_eq!(f16::MIN, min);
+ assert_eq!(f16::MIN_POSITIVE, min_pos);
+ // sanity check to show test is good
+ let max32 = f32::from_bits(core::f32::INFINITY.to_bits() - 1);
+ let min32 = f32::from_bits(core::f32::NEG_INFINITY.to_bits() - 1);
+ let min_pos32 = 2f32.powi(core::f32::MIN_EXP - 1);
+ assert_eq!(core::f32::MAX, max32);
+ assert_eq!(core::f32::MIN, min32);
+ assert_eq!(core::f32::MIN_POSITIVE, min_pos32);
+
+ // MIN_10_EXP and MAX_10_EXP
+ let ten_to_min = 10f32.powi(f16::MIN_10_EXP);
+ assert!(ten_to_min / 10.0 < f16::MIN_POSITIVE.to_f32());
+ assert!(ten_to_min > f16::MIN_POSITIVE.to_f32());
+ let ten_to_max = 10f32.powi(f16::MAX_10_EXP);
+ assert!(ten_to_max < f16::MAX.to_f32());
+ assert!(ten_to_max * 10.0 > f16::MAX.to_f32());
+ // sanity check to show test is good
+ let ten_to_min32 = 10f64.powi(core::f32::MIN_10_EXP);
+ assert!(ten_to_min32 / 10.0 < f64::from(core::f32::MIN_POSITIVE));
+ assert!(ten_to_min32 > f64::from(core::f32::MIN_POSITIVE));
+ let ten_to_max32 = 10f64.powi(core::f32::MAX_10_EXP);
+ assert!(ten_to_max32 < f64::from(core::f32::MAX));
+ assert!(ten_to_max32 * 10.0 > f64::from(core::f32::MAX));
+ }
+
+ #[test]
+ fn test_f16_consts_from_f32() {
+ let one = f16::from_f32(1.0);
+ let zero = f16::from_f32(0.0);
+ let neg_zero = f16::from_f32(-0.0);
+ let neg_one = f16::from_f32(-1.0);
+ let inf = f16::from_f32(core::f32::INFINITY);
+ let neg_inf = f16::from_f32(core::f32::NEG_INFINITY);
+ let nan = f16::from_f32(core::f32::NAN);
+
+ assert_eq!(f16::ONE, one);
+ assert_eq!(f16::ZERO, zero);
+ assert!(zero.is_sign_positive());
+ assert_eq!(f16::NEG_ZERO, neg_zero);
+ assert!(neg_zero.is_sign_negative());
+ assert_eq!(f16::NEG_ONE, neg_one);
+ assert!(neg_one.is_sign_negative());
+ assert_eq!(f16::INFINITY, inf);
+ assert_eq!(f16::NEG_INFINITY, neg_inf);
+ assert!(nan.is_nan());
+ assert!(f16::NAN.is_nan());
+
+ let e = f16::from_f32(core::f32::consts::E);
+ let pi = f16::from_f32(core::f32::consts::PI);
+ let frac_1_pi = f16::from_f32(core::f32::consts::FRAC_1_PI);
+ let frac_1_sqrt_2 = f16::from_f32(core::f32::consts::FRAC_1_SQRT_2);
+ let frac_2_pi = f16::from_f32(core::f32::consts::FRAC_2_PI);
+ let frac_2_sqrt_pi = f16::from_f32(core::f32::consts::FRAC_2_SQRT_PI);
+ let frac_pi_2 = f16::from_f32(core::f32::consts::FRAC_PI_2);
+ let frac_pi_3 = f16::from_f32(core::f32::consts::FRAC_PI_3);
+ let frac_pi_4 = f16::from_f32(core::f32::consts::FRAC_PI_4);
+ let frac_pi_6 = f16::from_f32(core::f32::consts::FRAC_PI_6);
+ let frac_pi_8 = f16::from_f32(core::f32::consts::FRAC_PI_8);
+ let ln_10 = f16::from_f32(core::f32::consts::LN_10);
+ let ln_2 = f16::from_f32(core::f32::consts::LN_2);
+ let log10_e = f16::from_f32(core::f32::consts::LOG10_E);
+ // core::f32::consts::LOG10_2 requires rustc 1.43.0
+ let log10_2 = f16::from_f32(2f32.log10());
+ let log2_e = f16::from_f32(core::f32::consts::LOG2_E);
+ // core::f32::consts::LOG2_10 requires rustc 1.43.0
+ let log2_10 = f16::from_f32(10f32.log2());
+ let sqrt_2 = f16::from_f32(core::f32::consts::SQRT_2);
+
+ assert_eq!(f16::E, e);
+ assert_eq!(f16::PI, pi);
+ assert_eq!(f16::FRAC_1_PI, frac_1_pi);
+ assert_eq!(f16::FRAC_1_SQRT_2, frac_1_sqrt_2);
+ assert_eq!(f16::FRAC_2_PI, frac_2_pi);
+ assert_eq!(f16::FRAC_2_SQRT_PI, frac_2_sqrt_pi);
+ assert_eq!(f16::FRAC_PI_2, frac_pi_2);
+ assert_eq!(f16::FRAC_PI_3, frac_pi_3);
+ assert_eq!(f16::FRAC_PI_4, frac_pi_4);
+ assert_eq!(f16::FRAC_PI_6, frac_pi_6);
+ assert_eq!(f16::FRAC_PI_8, frac_pi_8);
+ assert_eq!(f16::LN_10, ln_10);
+ assert_eq!(f16::LN_2, ln_2);
+ assert_eq!(f16::LOG10_E, log10_e);
+ assert_eq!(f16::LOG10_2, log10_2);
+ assert_eq!(f16::LOG2_E, log2_e);
+ assert_eq!(f16::LOG2_10, log2_10);
+ assert_eq!(f16::SQRT_2, sqrt_2);
+ }
+
+ #[test]
+ fn test_f16_consts_from_f64() {
+ let one = f16::from_f64(1.0);
+ let zero = f16::from_f64(0.0);
+ let neg_zero = f16::from_f64(-0.0);
+ let inf = f16::from_f64(core::f64::INFINITY);
+ let neg_inf = f16::from_f64(core::f64::NEG_INFINITY);
+ let nan = f16::from_f64(core::f64::NAN);
+
+ assert_eq!(f16::ONE, one);
+ assert_eq!(f16::ZERO, zero);
+ assert!(zero.is_sign_positive());
+ assert_eq!(f16::NEG_ZERO, neg_zero);
+ assert!(neg_zero.is_sign_negative());
+ assert_eq!(f16::INFINITY, inf);
+ assert_eq!(f16::NEG_INFINITY, neg_inf);
+ assert!(nan.is_nan());
+ assert!(f16::NAN.is_nan());
+
+ let e = f16::from_f64(core::f64::consts::E);
+ let pi = f16::from_f64(core::f64::consts::PI);
+ let frac_1_pi = f16::from_f64(core::f64::consts::FRAC_1_PI);
+ let frac_1_sqrt_2 = f16::from_f64(core::f64::consts::FRAC_1_SQRT_2);
+ let frac_2_pi = f16::from_f64(core::f64::consts::FRAC_2_PI);
+ let frac_2_sqrt_pi = f16::from_f64(core::f64::consts::FRAC_2_SQRT_PI);
+ let frac_pi_2 = f16::from_f64(core::f64::consts::FRAC_PI_2);
+ let frac_pi_3 = f16::from_f64(core::f64::consts::FRAC_PI_3);
+ let frac_pi_4 = f16::from_f64(core::f64::consts::FRAC_PI_4);
+ let frac_pi_6 = f16::from_f64(core::f64::consts::FRAC_PI_6);
+ let frac_pi_8 = f16::from_f64(core::f64::consts::FRAC_PI_8);
+ let ln_10 = f16::from_f64(core::f64::consts::LN_10);
+ let ln_2 = f16::from_f64(core::f64::consts::LN_2);
+ let log10_e = f16::from_f64(core::f64::consts::LOG10_E);
+ // core::f64::consts::LOG10_2 requires rustc 1.43.0
+ let log10_2 = f16::from_f64(2f64.log10());
+ let log2_e = f16::from_f64(core::f64::consts::LOG2_E);
+ // core::f64::consts::LOG2_10 requires rustc 1.43.0
+ let log2_10 = f16::from_f64(10f64.log2());
+ let sqrt_2 = f16::from_f64(core::f64::consts::SQRT_2);
+
+ assert_eq!(f16::E, e);
+ assert_eq!(f16::PI, pi);
+ assert_eq!(f16::FRAC_1_PI, frac_1_pi);
+ assert_eq!(f16::FRAC_1_SQRT_2, frac_1_sqrt_2);
+ assert_eq!(f16::FRAC_2_PI, frac_2_pi);
+ assert_eq!(f16::FRAC_2_SQRT_PI, frac_2_sqrt_pi);
+ assert_eq!(f16::FRAC_PI_2, frac_pi_2);
+ assert_eq!(f16::FRAC_PI_3, frac_pi_3);
+ assert_eq!(f16::FRAC_PI_4, frac_pi_4);
+ assert_eq!(f16::FRAC_PI_6, frac_pi_6);
+ assert_eq!(f16::FRAC_PI_8, frac_pi_8);
+ assert_eq!(f16::LN_10, ln_10);
+ assert_eq!(f16::LN_2, ln_2);
+ assert_eq!(f16::LOG10_E, log10_e);
+ assert_eq!(f16::LOG10_2, log10_2);
+ assert_eq!(f16::LOG2_E, log2_e);
+ assert_eq!(f16::LOG2_10, log2_10);
+ assert_eq!(f16::SQRT_2, sqrt_2);
+ }
+
+ #[test]
+ fn test_nan_conversion_to_smaller() {
+ let nan64 = f64::from_bits(0x7FF0_0000_0000_0001u64);
+ let neg_nan64 = f64::from_bits(0xFFF0_0000_0000_0001u64);
+ let nan32 = f32::from_bits(0x7F80_0001u32);
+ let neg_nan32 = f32::from_bits(0xFF80_0001u32);
+ let nan32_from_64 = nan64 as f32;
+ let neg_nan32_from_64 = neg_nan64 as f32;
+ let nan16_from_64 = f16::from_f64(nan64);
+ let neg_nan16_from_64 = f16::from_f64(neg_nan64);
+ let nan16_from_32 = f16::from_f32(nan32);
+ let neg_nan16_from_32 = f16::from_f32(neg_nan32);
+
+ assert!(nan64.is_nan() && nan64.is_sign_positive());
+ assert!(neg_nan64.is_nan() && neg_nan64.is_sign_negative());
+ assert!(nan32.is_nan() && nan32.is_sign_positive());
+ assert!(neg_nan32.is_nan() && neg_nan32.is_sign_negative());
+ assert!(nan32_from_64.is_nan() && nan32_from_64.is_sign_positive());
+ assert!(neg_nan32_from_64.is_nan() && neg_nan32_from_64.is_sign_negative());
+ assert!(nan16_from_64.is_nan() && nan16_from_64.is_sign_positive());
+ assert!(neg_nan16_from_64.is_nan() && neg_nan16_from_64.is_sign_negative());
+ assert!(nan16_from_32.is_nan() && nan16_from_32.is_sign_positive());
+ assert!(neg_nan16_from_32.is_nan() && neg_nan16_from_32.is_sign_negative());
+ }
+
+ #[test]
+ fn test_nan_conversion_to_larger() {
+ let nan16 = f16::from_bits(0x7C01u16);
+ let neg_nan16 = f16::from_bits(0xFC01u16);
+ let nan32 = f32::from_bits(0x7F80_0001u32);
+ let neg_nan32 = f32::from_bits(0xFF80_0001u32);
+ let nan32_from_16 = f32::from(nan16);
+ let neg_nan32_from_16 = f32::from(neg_nan16);
+ let nan64_from_16 = f64::from(nan16);
+ let neg_nan64_from_16 = f64::from(neg_nan16);
+ let nan64_from_32 = f64::from(nan32);
+ let neg_nan64_from_32 = f64::from(neg_nan32);
+
+ assert!(nan16.is_nan() && nan16.is_sign_positive());
+ assert!(neg_nan16.is_nan() && neg_nan16.is_sign_negative());
+ assert!(nan32.is_nan() && nan32.is_sign_positive());
+ assert!(neg_nan32.is_nan() && neg_nan32.is_sign_negative());
+ assert!(nan32_from_16.is_nan() && nan32_from_16.is_sign_positive());
+ assert!(neg_nan32_from_16.is_nan() && neg_nan32_from_16.is_sign_negative());
+ assert!(nan64_from_16.is_nan() && nan64_from_16.is_sign_positive());
+ assert!(neg_nan64_from_16.is_nan() && neg_nan64_from_16.is_sign_negative());
+ assert!(nan64_from_32.is_nan() && nan64_from_32.is_sign_positive());
+ assert!(neg_nan64_from_32.is_nan() && neg_nan64_from_32.is_sign_negative());
+ }
+
+ #[test]
+ fn test_f16_to_f32() {
+ let f = f16::from_f32(7.0);
+ assert_eq!(f.to_f32(), 7.0f32);
+
+ // 7.1 is NOT exactly representable in 16-bit, it's rounded
+ let f = f16::from_f32(7.1);
+ let diff = (f.to_f32() - 7.1f32).abs();
+ // diff must be <= 4 * EPSILON, as 7 has two more significant bits than 1
+ assert!(diff <= 4.0 * f16::EPSILON.to_f32());
+
+ assert_eq!(f16::from_bits(0x0000_0001).to_f32(), 2.0f32.powi(-24));
+ assert_eq!(f16::from_bits(0x0000_0005).to_f32(), 5.0 * 2.0f32.powi(-24));
+
+ assert_eq!(f16::from_bits(0x0000_0001), f16::from_f32(2.0f32.powi(-24)));
+ assert_eq!(
+ f16::from_bits(0x0000_0005),
+ f16::from_f32(5.0 * 2.0f32.powi(-24))
+ );
+ }
+
+ #[test]
+ fn test_f16_to_f64() {
+ let f = f16::from_f64(7.0);
+ assert_eq!(f.to_f64(), 7.0f64);
+
+ // 7.1 is NOT exactly representable in 16-bit, it's rounded
+ let f = f16::from_f64(7.1);
+ let diff = (f.to_f64() - 7.1f64).abs();
+ // diff must be <= 4 * EPSILON, as 7 has two more significant bits than 1
+ assert!(diff <= 4.0 * f16::EPSILON.to_f64());
+
+ assert_eq!(f16::from_bits(0x0000_0001).to_f64(), 2.0f64.powi(-24));
+ assert_eq!(f16::from_bits(0x0000_0005).to_f64(), 5.0 * 2.0f64.powi(-24));
+
+ assert_eq!(f16::from_bits(0x0000_0001), f16::from_f64(2.0f64.powi(-24)));
+ assert_eq!(
+ f16::from_bits(0x0000_0005),
+ f16::from_f64(5.0 * 2.0f64.powi(-24))
+ );
+ }
+
+ #[test]
+ fn test_comparisons() {
+ let zero = f16::from_f64(0.0);
+ let one = f16::from_f64(1.0);
+ let neg_zero = f16::from_f64(-0.0);
+ let neg_one = f16::from_f64(-1.0);
+
+ assert_eq!(zero.partial_cmp(&neg_zero), Some(Ordering::Equal));
+ assert_eq!(neg_zero.partial_cmp(&zero), Some(Ordering::Equal));
+ assert!(zero == neg_zero);
+ assert!(neg_zero == zero);
+ assert!(!(zero != neg_zero));
+ assert!(!(neg_zero != zero));
+ assert!(!(zero < neg_zero));
+ assert!(!(neg_zero < zero));
+ assert!(zero <= neg_zero);
+ assert!(neg_zero <= zero);
+ assert!(!(zero > neg_zero));
+ assert!(!(neg_zero > zero));
+ assert!(zero >= neg_zero);
+ assert!(neg_zero >= zero);
+
+ assert_eq!(one.partial_cmp(&neg_zero), Some(Ordering::Greater));
+ assert_eq!(neg_zero.partial_cmp(&one), Some(Ordering::Less));
+ assert!(!(one == neg_zero));
+ assert!(!(neg_zero == one));
+ assert!(one != neg_zero);
+ assert!(neg_zero != one);
+ assert!(!(one < neg_zero));
+ assert!(neg_zero < one);
+ assert!(!(one <= neg_zero));
+ assert!(neg_zero <= one);
+ assert!(one > neg_zero);
+ assert!(!(neg_zero > one));
+ assert!(one >= neg_zero);
+ assert!(!(neg_zero >= one));
+
+ assert_eq!(one.partial_cmp(&neg_one), Some(Ordering::Greater));
+ assert_eq!(neg_one.partial_cmp(&one), Some(Ordering::Less));
+ assert!(!(one == neg_one));
+ assert!(!(neg_one == one));
+ assert!(one != neg_one);
+ assert!(neg_one != one);
+ assert!(!(one < neg_one));
+ assert!(neg_one < one);
+ assert!(!(one <= neg_one));
+ assert!(neg_one <= one);
+ assert!(one > neg_one);
+ assert!(!(neg_one > one));
+ assert!(one >= neg_one);
+ assert!(!(neg_one >= one));
+ }
+
+ #[test]
+ #[allow(clippy::erasing_op, clippy::identity_op)]
+ fn round_to_even_f32() {
+ // smallest positive subnormal = 0b0.0000_0000_01 * 2^-14 = 2^-24
+ let min_sub = f16::from_bits(1);
+ let min_sub_f = (-24f32).exp2();
+ assert_eq!(f16::from_f32(min_sub_f).to_bits(), min_sub.to_bits());
+ assert_eq!(f32::from(min_sub).to_bits(), min_sub_f.to_bits());
+
+ // 0.0000000000_011111 rounded to 0.0000000000 (< tie, no rounding)
+ // 0.0000000000_100000 rounded to 0.0000000000 (tie and even, remains at even)
+ // 0.0000000000_100001 rounded to 0.0000000001 (> tie, rounds up)
+ assert_eq!(
+ f16::from_f32(min_sub_f * 0.49).to_bits(),
+ min_sub.to_bits() * 0
+ );
+ assert_eq!(
+ f16::from_f32(min_sub_f * 0.50).to_bits(),
+ min_sub.to_bits() * 0
+ );
+ assert_eq!(
+ f16::from_f32(min_sub_f * 0.51).to_bits(),
+ min_sub.to_bits() * 1
+ );
+
+ // 0.0000000001_011111 rounded to 0.0000000001 (< tie, no rounding)
+ // 0.0000000001_100000 rounded to 0.0000000010 (tie and odd, rounds up to even)
+ // 0.0000000001_100001 rounded to 0.0000000010 (> tie, rounds up)
+ assert_eq!(
+ f16::from_f32(min_sub_f * 1.49).to_bits(),
+ min_sub.to_bits() * 1
+ );
+ assert_eq!(
+ f16::from_f32(min_sub_f * 1.50).to_bits(),
+ min_sub.to_bits() * 2
+ );
+ assert_eq!(
+ f16::from_f32(min_sub_f * 1.51).to_bits(),
+ min_sub.to_bits() * 2
+ );
+
+ // 0.0000000010_011111 rounded to 0.0000000010 (< tie, no rounding)
+ // 0.0000000010_100000 rounded to 0.0000000010 (tie and even, remains at even)
+ // 0.0000000010_100001 rounded to 0.0000000011 (> tie, rounds up)
+ assert_eq!(
+ f16::from_f32(min_sub_f * 2.49).to_bits(),
+ min_sub.to_bits() * 2
+ );
+ assert_eq!(
+ f16::from_f32(min_sub_f * 2.50).to_bits(),
+ min_sub.to_bits() * 2
+ );
+ assert_eq!(
+ f16::from_f32(min_sub_f * 2.51).to_bits(),
+ min_sub.to_bits() * 3
+ );
+
+ assert_eq!(
+ f16::from_f32(2000.49f32).to_bits(),
+ f16::from_f32(2000.0).to_bits()
+ );
+ assert_eq!(
+ f16::from_f32(2000.50f32).to_bits(),
+ f16::from_f32(2000.0).to_bits()
+ );
+ assert_eq!(
+ f16::from_f32(2000.51f32).to_bits(),
+ f16::from_f32(2001.0).to_bits()
+ );
+ assert_eq!(
+ f16::from_f32(2001.49f32).to_bits(),
+ f16::from_f32(2001.0).to_bits()
+ );
+ assert_eq!(
+ f16::from_f32(2001.50f32).to_bits(),
+ f16::from_f32(2002.0).to_bits()
+ );
+ assert_eq!(
+ f16::from_f32(2001.51f32).to_bits(),
+ f16::from_f32(2002.0).to_bits()
+ );
+ assert_eq!(
+ f16::from_f32(2002.49f32).to_bits(),
+ f16::from_f32(2002.0).to_bits()
+ );
+ assert_eq!(
+ f16::from_f32(2002.50f32).to_bits(),
+ f16::from_f32(2002.0).to_bits()
+ );
+ assert_eq!(
+ f16::from_f32(2002.51f32).to_bits(),
+ f16::from_f32(2003.0).to_bits()
+ );
+ }
+
+ #[test]
+ #[allow(clippy::erasing_op, clippy::identity_op)]
+ fn round_to_even_f64() {
+ // smallest positive subnormal = 0b0.0000_0000_01 * 2^-14 = 2^-24
+ let min_sub = f16::from_bits(1);
+ let min_sub_f = (-24f64).exp2();
+ assert_eq!(f16::from_f64(min_sub_f).to_bits(), min_sub.to_bits());
+ assert_eq!(f64::from(min_sub).to_bits(), min_sub_f.to_bits());
+
+ // 0.0000000000_011111 rounded to 0.0000000000 (< tie, no rounding)
+ // 0.0000000000_100000 rounded to 0.0000000000 (tie and even, remains at even)
+ // 0.0000000000_100001 rounded to 0.0000000001 (> tie, rounds up)
+ assert_eq!(
+ f16::from_f64(min_sub_f * 0.49).to_bits(),
+ min_sub.to_bits() * 0
+ );
+ assert_eq!(
+ f16::from_f64(min_sub_f * 0.50).to_bits(),
+ min_sub.to_bits() * 0
+ );
+ assert_eq!(
+ f16::from_f64(min_sub_f * 0.51).to_bits(),
+ min_sub.to_bits() * 1
+ );
+
+ // 0.0000000001_011111 rounded to 0.0000000001 (< tie, no rounding)
+ // 0.0000000001_100000 rounded to 0.0000000010 (tie and odd, rounds up to even)
+ // 0.0000000001_100001 rounded to 0.0000000010 (> tie, rounds up)
+ assert_eq!(
+ f16::from_f64(min_sub_f * 1.49).to_bits(),
+ min_sub.to_bits() * 1
+ );
+ assert_eq!(
+ f16::from_f64(min_sub_f * 1.50).to_bits(),
+ min_sub.to_bits() * 2
+ );
+ assert_eq!(
+ f16::from_f64(min_sub_f * 1.51).to_bits(),
+ min_sub.to_bits() * 2
+ );
+
+ // 0.0000000010_011111 rounded to 0.0000000010 (< tie, no rounding)
+ // 0.0000000010_100000 rounded to 0.0000000010 (tie and even, remains at even)
+ // 0.0000000010_100001 rounded to 0.0000000011 (> tie, rounds up)
+ assert_eq!(
+ f16::from_f64(min_sub_f * 2.49).to_bits(),
+ min_sub.to_bits() * 2
+ );
+ assert_eq!(
+ f16::from_f64(min_sub_f * 2.50).to_bits(),
+ min_sub.to_bits() * 2
+ );
+ assert_eq!(
+ f16::from_f64(min_sub_f * 2.51).to_bits(),
+ min_sub.to_bits() * 3
+ );
+
+ assert_eq!(
+ f16::from_f64(2000.49f64).to_bits(),
+ f16::from_f64(2000.0).to_bits()
+ );
+ assert_eq!(
+ f16::from_f64(2000.50f64).to_bits(),
+ f16::from_f64(2000.0).to_bits()
+ );
+ assert_eq!(
+ f16::from_f64(2000.51f64).to_bits(),
+ f16::from_f64(2001.0).to_bits()
+ );
+ assert_eq!(
+ f16::from_f64(2001.49f64).to_bits(),
+ f16::from_f64(2001.0).to_bits()
+ );
+ assert_eq!(
+ f16::from_f64(2001.50f64).to_bits(),
+ f16::from_f64(2002.0).to_bits()
+ );
+ assert_eq!(
+ f16::from_f64(2001.51f64).to_bits(),
+ f16::from_f64(2002.0).to_bits()
+ );
+ assert_eq!(
+ f16::from_f64(2002.49f64).to_bits(),
+ f16::from_f64(2002.0).to_bits()
+ );
+ assert_eq!(
+ f16::from_f64(2002.50f64).to_bits(),
+ f16::from_f64(2002.0).to_bits()
+ );
+ assert_eq!(
+ f16::from_f64(2002.51f64).to_bits(),
+ f16::from_f64(2003.0).to_bits()
+ );
+ }
+
+ impl quickcheck::Arbitrary for f16 {
+ fn arbitrary(g: &mut quickcheck::Gen) -> Self {
+ f16(u16::arbitrary(g))
+ }
+ }
+
+ #[quickcheck]
+ fn qc_roundtrip_f16_f32_is_identity(f: f16) -> bool {
+ let roundtrip = f16::from_f32(f.to_f32());
+ if f.is_nan() {
+ roundtrip.is_nan() && f.is_sign_negative() == roundtrip.is_sign_negative()
+ } else {
+ f.0 == roundtrip.0
+ }
+ }
+
+ #[quickcheck]
+ fn qc_roundtrip_f16_f64_is_identity(f: f16) -> bool {
+ let roundtrip = f16::from_f64(f.to_f64());
+ if f.is_nan() {
+ roundtrip.is_nan() && f.is_sign_negative() == roundtrip.is_sign_negative()
+ } else {
+ f.0 == roundtrip.0
+ }
+ }
+}
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-12 00:25:31 +0000