Adding upstream version 115.7.0esr.upstream/115.7.0esrupstream

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

8 files changed, 6808 insertions, 0 deletions

diff --git a/third_party/rust/half/src/bfloat.rs b/third_party/rust/half/src/bfloat.rs
new file mode 100644
index 0000000000..f7a840ebe1
--- /dev/null
+++ b/third_party/rust/half/src/bfloat.rs
@@ -0,0 +1,1555 @@
+#[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 [`bfloat16`] format.
+///
+/// The [`bfloat16`] floating point format is a truncated 16-bit version of the IEEE 754 standard
+/// `binary32`, a.k.a [`f32`]. [`bf16`] has approximately the same dynamic range as [`f32`] by
+/// having a lower precision than [`f16`][crate::f16]. While [`f16`][crate::f16] has a precision of
+/// 11 bits, [`bf16`] has a precision of only 8 bits.
+///
+/// Like [`f16`][crate::f16], [`bf16`] does not offer arithmetic operations as it is intended for
+/// compact storage rather than calculations. Operations should be performed with [`f32`] or
+/// higher-precision types and converted to/from [`bf16`] as necessary.
+///
+/// [`bfloat16`]: https://en.wikipedia.org/wiki/Bfloat16_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 bf16(u16);
+
+impl bf16 {
+    /// Constructs a [`bf16`] value from the raw bits.
+    #[inline]
+    pub const fn from_bits(bits: u16) -> bf16 {
+        bf16(bits)
+    }
+
+    /// Constructs a [`bf16`] value from a 32-bit floating point value.
+    ///
+    /// If the 32-bit value is too large to fit, ±∞ will result. NaN values are preserved.
+    /// Subnormal values that are too tiny to be represented will result in ±0. All other values
+    /// are truncated and rounded to the nearest representable value.
+    #[inline]
+    pub fn from_f32(value: f32) -> bf16 {
+        bf16(convert::f32_to_bf16(value))
+    }
+
+    /// Constructs a [`bf16`] value from a 64-bit floating point value.
+    ///
+    /// If the 64-bit value is to large to fit, ±∞ will result. NaN values are preserved.
+    /// 64-bit subnormal values are too tiny to be represented and result in ±0. Exponents that
+    /// underflow the minimum exponent will result in subnormals or ±0. All other values are
+    /// truncated and rounded to the nearest representable value.
+    #[inline]
+    pub fn from_f64(value: f64) -> bf16 {
+        bf16(convert::f64_to_bf16(value))
+    }
+
+    /// Converts a [`bf16`] 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 = bf16::from_f32(12.5).to_le_bytes();
+    /// assert_eq!(bytes, [0x48, 0x41]);
+    /// ```
+    #[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 = bf16::from_f32(12.5).to_be_bytes();
+    /// assert_eq!(bytes, [0x41, 0x48]);
+    /// ```
+    #[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`][bf16::to_be_bytes] or [`to_le_bytes`][bf16::to_le_bytes], as appropriate,
+    /// instead.
+    ///
+    /// # Examples
+    ///
+    /// ```rust
+    /// # use half::prelude::*;
+    /// let bytes = bf16::from_f32(12.5).to_ne_bytes();
+    /// assert_eq!(bytes, if cfg!(target_endian = "big") {
+    ///     [0x41, 0x48]
+    /// } else {
+    ///     [0x48, 0x41]
+    /// });
+    /// ```
+    #[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 = bf16::from_le_bytes([0x48, 0x41]);
+    /// assert_eq!(value, bf16::from_f32(12.5));
+    /// ```
+    #[inline]
+    pub const fn from_le_bytes(bytes: [u8; 2]) -> bf16 {
+        bf16::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 = bf16::from_be_bytes([0x41, 0x48]);
+    /// assert_eq!(value, bf16::from_f32(12.5));
+    /// ```
+    #[inline]
+    pub const fn from_be_bytes(bytes: [u8; 2]) -> bf16 {
+        bf16::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`][bf16::from_be_bytes] or [`from_le_bytes`][bf16::from_le_bytes], as
+    /// appropriate instead.
+    ///
+    /// # Examples
+    ///
+    /// ```rust
+    /// # use half::prelude::*;
+    /// let value = bf16::from_ne_bytes(if cfg!(target_endian = "big") {
+    ///     [0x41, 0x48]
+    /// } else {
+    ///     [0x48, 0x41]
+    /// });
+    /// assert_eq!(value, bf16::from_f32(12.5));
+    /// ```
+    #[inline]
+    pub const fn from_ne_bytes(bytes: [u8; 2]) -> bf16 {
+        bf16::from_bits(u16::from_ne_bytes(bytes))
+    }
+
+    /// Converts a [`bf16`] value into an [`f32`] value.
+    ///
+    /// This conversion is lossless as all values can be represented exactly in [`f32`].
+    #[inline]
+    pub fn to_f32(self) -> f32 {
+        convert::bf16_to_f32(self.0)
+    }
+
+    /// Converts a [`bf16`] value into an [`f64`] value.
+    ///
+    /// This conversion is lossless as all values can be represented exactly in [`f64`].
+    #[inline]
+    pub fn to_f64(self) -> f64 {
+        convert::bf16_to_f64(self.0)
+    }
+
+    /// Returns `true` if this value is NaN and `false` otherwise.
+    ///
+    /// # Examples
+    ///
+    /// ```rust
+    /// # use half::prelude::*;
+    ///
+    /// let nan = bf16::NAN;
+    /// let f = bf16::from_f32(7.0_f32);
+    ///
+    /// assert!(nan.is_nan());
+    /// assert!(!f.is_nan());
+    /// ```
+    #[inline]
+    pub const fn is_nan(self) -> bool {
+        self.0 & 0x7FFFu16 > 0x7F80u16
+    }
+
+    /// Returns `true` if this value is ±∞ and `false` otherwise.
+    ///
+    /// # Examples
+    ///
+    /// ```rust
+    /// # use half::prelude::*;
+    ///
+    /// let f = bf16::from_f32(7.0f32);
+    /// let inf = bf16::INFINITY;
+    /// let neg_inf = bf16::NEG_INFINITY;
+    /// let nan = bf16::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 == 0x7F80u16
+    }
+
+    /// Returns `true` if this number is neither infinite nor NaN.
+    ///
+    /// # Examples
+    ///
+    /// ```rust
+    /// # use half::prelude::*;
+    ///
+    /// let f = bf16::from_f32(7.0f32);
+    /// let inf = bf16::INFINITY;
+    /// let neg_inf = bf16::NEG_INFINITY;
+    /// let nan = bf16::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 & 0x7F80u16 != 0x7F80u16
+    }
+
+    /// Returns `true` if the number is neither zero, infinite, subnormal, or NaN.
+    ///
+    /// # Examples
+    ///
+    /// ```rust
+    /// # use half::prelude::*;
+    ///
+    /// let min = bf16::MIN_POSITIVE;
+    /// let max = bf16::MAX;
+    /// let lower_than_min = bf16::from_f32(1.0e-39_f32);
+    /// let zero = bf16::from_f32(0.0_f32);
+    ///
+    /// assert!(min.is_normal());
+    /// assert!(max.is_normal());
+    ///
+    /// assert!(!zero.is_normal());
+    /// assert!(!bf16::NAN.is_normal());
+    /// assert!(!bf16::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 & 0x7F80u16;
+        exp != 0x7F80u16 && 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 = bf16::from_f32(12.4_f32);
+    /// let inf = bf16::INFINITY;
+    ///
+    /// assert_eq!(num.classify(), FpCategory::Normal);
+    /// assert_eq!(inf.classify(), FpCategory::Infinite);
+    /// ```
+    pub const fn classify(self) -> FpCategory {
+        let exp = self.0 & 0x7F80u16;
+        let man = self.0 & 0x007Fu16;
+        match (exp, man) {
+            (0, 0) => FpCategory::Zero,
+            (0, _) => FpCategory::Subnormal,
+            (0x7F80u16, 0) => FpCategory::Infinite,
+            (0x7F80u16, _) => FpCategory::Nan,
+            _ => FpCategory::Normal,
+        }
+    }
+
+    /// Returns a number that represents the sign of `self`.
+    ///
+    /// * 1.0 if the number is positive, +0.0 or [`INFINITY`][bf16::INFINITY]
+    /// * −1.0 if the number is negative, −0.0` or [`NEG_INFINITY`][bf16::NEG_INFINITY]
+    /// * [`NAN`][bf16::NAN] if the number is NaN
+    ///
+    /// # Examples
+    ///
+    /// ```rust
+    /// # use half::prelude::*;
+    ///
+    /// let f = bf16::from_f32(3.5_f32);
+    ///
+    /// assert_eq!(f.signum(), bf16::from_f32(1.0));
+    /// assert_eq!(bf16::NEG_INFINITY.signum(), bf16::from_f32(-1.0));
+    ///
+    /// assert!(bf16::NAN.signum().is_nan());
+    /// ```
+    pub const fn signum(self) -> bf16 {
+        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 = bf16::NAN;
+    /// let f = bf16::from_f32(7.0_f32);
+    /// let g = bf16::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 = bf16::NAN;
+    /// let f = bf16::from_f32(7.0f32);
+    /// let g = bf16::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 = bf16::from_f32(3.5);
+    ///
+    /// assert_eq!(f.copysign(bf16::from_f32(0.42)), bf16::from_f32(3.5));
+    /// assert_eq!(f.copysign(bf16::from_f32(-0.42)), bf16::from_f32(-3.5));
+    /// assert_eq!((-f).copysign(bf16::from_f32(0.42)), bf16::from_f32(3.5));
+    /// assert_eq!((-f).copysign(bf16::from_f32(-0.42)), bf16::from_f32(-3.5));
+    ///
+    /// assert!(bf16::NAN.copysign(bf16::from_f32(1.0)).is_nan());
+    /// ```
+    #[inline]
+    pub const fn copysign(self, sign: bf16) -> bf16 {
+        bf16((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 = bf16::from_f32(1.0);
+    /// let y = bf16::from_f32(2.0);
+    ///
+    /// assert_eq!(x.max(y), y);
+    /// ```
+    #[inline]
+    pub fn max(self, other: bf16) -> bf16 {
+        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 = bf16::from_f32(1.0);
+    /// let y = bf16::from_f32(2.0);
+    ///
+    /// assert_eq!(x.min(y), x);
+    /// ```
+    #[inline]
+    pub fn min(self, other: bf16) -> bf16 {
+        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!(bf16::from_f32(-3.0).clamp(bf16::from_f32(-2.0), bf16::from_f32(1.0)) == bf16::from_f32(-2.0));
+    /// assert!(bf16::from_f32(0.0).clamp(bf16::from_f32(-2.0), bf16::from_f32(1.0)) == bf16::from_f32(0.0));
+    /// assert!(bf16::from_f32(2.0).clamp(bf16::from_f32(-2.0), bf16::from_f32(1.0)) == bf16::from_f32(1.0));
+    /// assert!(bf16::NAN.clamp(bf16::from_f32(-2.0), bf16::from_f32(1.0)).is_nan());
+    /// ```
+    #[inline]
+    pub fn clamp(self, min: bf16, max: bf16) -> bf16 {
+        assert!(min <= max);
+        let mut x = self;
+        if x < min {
+            x = min;
+        }
+        if x > max {
+            x = max;
+        }
+        x
+    }
+
+    /// Approximate number of [`bf16`] significant digits in base 10
+    pub const DIGITS: u32 = 2;
+    /// [`bf16`]
+    /// [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: bf16 = bf16(0x3C00u16);
+    /// [`bf16`] positive Infinity (+∞)
+    pub const INFINITY: bf16 = bf16(0x7F80u16);
+    /// Number of [`bf16`] significant digits in base 2
+    pub const MANTISSA_DIGITS: u32 = 8;
+    /// Largest finite [`bf16`] value
+    pub const MAX: bf16 = bf16(0x7F7F);
+    /// Maximum possible [`bf16`] power of 10 exponent
+    pub const MAX_10_EXP: i32 = 38;
+    /// Maximum possible [`bf16`] power of 2 exponent
+    pub const MAX_EXP: i32 = 128;
+    /// Smallest finite [`bf16`] value
+    pub const MIN: bf16 = bf16(0xFF7F);
+    /// Minimum possible normal [`bf16`] power of 10 exponent
+    pub const MIN_10_EXP: i32 = -37;
+    /// One greater than the minimum possible normal [`bf16`] power of 2 exponent
+    pub const MIN_EXP: i32 = -125;
+    /// Smallest positive normal [`bf16`] value
+    pub const MIN_POSITIVE: bf16 = bf16(0x0080u16);
+    /// [`bf16`] Not a Number (NaN)
+    pub const NAN: bf16 = bf16(0x7FC0u16);
+    /// [`bf16`] negative infinity (-∞).
+    pub const NEG_INFINITY: bf16 = bf16(0xFF80u16);
+    /// The radix or base of the internal representation of [`bf16`]
+    pub const RADIX: u32 = 2;
+
+    /// Minimum positive subnormal [`bf16`] value
+    pub const MIN_POSITIVE_SUBNORMAL: bf16 = bf16(0x0001u16);
+    /// Maximum subnormal [`bf16`] value
+    pub const MAX_SUBNORMAL: bf16 = bf16(0x007Fu16);
+
+    /// [`bf16`] 1
+    pub const ONE: bf16 = bf16(0x3F80u16);
+    /// [`bf16`] 0
+    pub const ZERO: bf16 = bf16(0x0000u16);
+    /// [`bf16`] -0
+    pub const NEG_ZERO: bf16 = bf16(0x8000u16);
+    /// [`bf16`] -1
+    pub const NEG_ONE: bf16 = bf16(0xBF80u16);
+
+    /// [`bf16`] Euler's number (ℯ)
+    pub const E: bf16 = bf16(0x402Eu16);
+    /// [`bf16`] Archimedes' constant (π)
+    pub const PI: bf16 = bf16(0x4049u16);
+    /// [`bf16`] 1/π
+    pub const FRAC_1_PI: bf16 = bf16(0x3EA3u16);
+    /// [`bf16`] 1/√2
+    pub const FRAC_1_SQRT_2: bf16 = bf16(0x3F35u16);
+    /// [`bf16`] 2/π
+    pub const FRAC_2_PI: bf16 = bf16(0x3F23u16);
+    /// [`bf16`] 2/√π
+    pub const FRAC_2_SQRT_PI: bf16 = bf16(0x3F90u16);
+    /// [`bf16`] π/2
+    pub const FRAC_PI_2: bf16 = bf16(0x3FC9u16);
+    /// [`bf16`] π/3
+    pub const FRAC_PI_3: bf16 = bf16(0x3F86u16);
+    /// [`bf16`] π/4
+    pub const FRAC_PI_4: bf16 = bf16(0x3F49u16);
+    /// [`bf16`] π/6
+    pub const FRAC_PI_6: bf16 = bf16(0x3F06u16);
+    /// [`bf16`] π/8
+    pub const FRAC_PI_8: bf16 = bf16(0x3EC9u16);
+    /// [`bf16`] 𝗅𝗇 10
+    pub const LN_10: bf16 = bf16(0x4013u16);
+    /// [`bf16`] 𝗅𝗇 2
+    pub const LN_2: bf16 = bf16(0x3F31u16);
+    /// [`bf16`] 𝗅𝗈𝗀₁₀ℯ
+    pub const LOG10_E: bf16 = bf16(0x3EDEu16);
+    /// [`bf16`] 𝗅𝗈𝗀₁₀2
+    pub const LOG10_2: bf16 = bf16(0x3E9Au16);
+    /// [`bf16`] 𝗅𝗈𝗀₂ℯ
+    pub const LOG2_E: bf16 = bf16(0x3FB9u16);
+    /// [`bf16`] 𝗅𝗈𝗀₂10
+    pub const LOG2_10: bf16 = bf16(0x4055u16);
+    /// [`bf16`] √2
+    pub const SQRT_2: bf16 = bf16(0x3FB5u16);
+}
+
+impl From<bf16> for f32 {
+    #[inline]
+    fn from(x: bf16) -> f32 {
+        x.to_f32()
+    }
+}
+
+impl From<bf16> for f64 {
+    #[inline]
+    fn from(x: bf16) -> f64 {
+        x.to_f64()
+    }
+}
+
+impl From<i8> for bf16 {
+    #[inline]
+    fn from(x: i8) -> bf16 {
+        // Convert to f32, then to bf16
+        bf16::from_f32(f32::from(x))
+    }
+}
+
+impl From<u8> for bf16 {
+    #[inline]
+    fn from(x: u8) -> bf16 {
+        // Convert to f32, then to f16
+        bf16::from_f32(f32::from(x))
+    }
+}
+
+impl PartialEq for bf16 {
+    fn eq(&self, other: &bf16) -> bool {
+        if self.is_nan() || other.is_nan() {
+            false
+        } else {
+            (self.0 == other.0) || ((self.0 | other.0) & 0x7FFFu16 == 0)
+        }
+    }
+}
+
+impl PartialOrd for bf16 {
+    fn partial_cmp(&self, other: &bf16) -> 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: &bf16) -> 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: &bf16) -> 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: &bf16) -> 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: &bf16) -> 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 bf16 {
+    type Err = ParseFloatError;
+    fn from_str(src: &str) -> Result<bf16, ParseFloatError> {
+        f32::from_str(src).map(bf16::from_f32)
+    }
+}
+
+impl Debug for bf16 {
+    fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> {
+        write!(f, "{:?}", self.to_f32())
+    }
+}
+
+impl Display for bf16 {
+    fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> {
+        write!(f, "{}", self.to_f32())
+    }
+}
+
+impl LowerExp for bf16 {
+    fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> {
+        write!(f, "{:e}", self.to_f32())
+    }
+}
+
+impl UpperExp for bf16 {
+    fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> {
+        write!(f, "{:E}", self.to_f32())
+    }
+}
+
+impl Binary for bf16 {
+    fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> {
+        write!(f, "{:b}", self.0)
+    }
+}
+
+impl Octal for bf16 {
+    fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> {
+        write!(f, "{:o}", self.0)
+    }
+}
+
+impl LowerHex for bf16 {
+    fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> {
+        write!(f, "{:x}", self.0)
+    }
+}
+
+impl UpperHex for bf16 {
+    fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> {
+        write!(f, "{:X}", self.0)
+    }
+}
+
+impl Neg for bf16 {
+    type Output = Self;
+
+    fn neg(self) -> Self::Output {
+        Self(self.0 ^ 0x8000)
+    }
+}
+
+impl Add for bf16 {
+    type Output = Self;
+
+    fn add(self, rhs: Self) -> Self::Output {
+        Self::from_f32(Self::to_f32(self) + Self::to_f32(rhs))
+    }
+}
+
+impl Add<&bf16> for bf16 {
+    type Output = <bf16 as Add<bf16>>::Output;
+
+    #[inline]
+    fn add(self, rhs: &bf16) -> Self::Output {
+        self.add(*rhs)
+    }
+}
+
+impl Add<&bf16> for &bf16 {
+    type Output = <bf16 as Add<bf16>>::Output;
+
+    #[inline]
+    fn add(self, rhs: &bf16) -> Self::Output {
+        (*self).add(*rhs)
+    }
+}
+
+impl Add<bf16> for &bf16 {
+    type Output = <bf16 as Add<bf16>>::Output;
+
+    #[inline]
+    fn add(self, rhs: bf16) -> Self::Output {
+        (*self).add(rhs)
+    }
+}
+
+impl AddAssign for bf16 {
+    #[inline]
+    fn add_assign(&mut self, rhs: Self) {
+        *self = (*self).add(rhs);
+    }
+}
+
+impl AddAssign<&bf16> for bf16 {
+    #[inline]
+    fn add_assign(&mut self, rhs: &bf16) {
+        *self = (*self).add(rhs);
+    }
+}
+
+impl Sub for bf16 {
+    type Output = Self;
+
+    fn sub(self, rhs: Self) -> Self::Output {
+        Self::from_f32(Self::to_f32(self) - Self::to_f32(rhs))
+    }
+}
+
+impl Sub<&bf16> for bf16 {
+    type Output = <bf16 as Sub<bf16>>::Output;
+
+    #[inline]
+    fn sub(self, rhs: &bf16) -> Self::Output {
+        self.sub(*rhs)
+    }
+}
+
+impl Sub<&bf16> for &bf16 {
+    type Output = <bf16 as Sub<bf16>>::Output;
+
+    #[inline]
+    fn sub(self, rhs: &bf16) -> Self::Output {
+        (*self).sub(*rhs)
+    }
+}
+
+impl Sub<bf16> for &bf16 {
+    type Output = <bf16 as Sub<bf16>>::Output;
+
+    #[inline]
+    fn sub(self, rhs: bf16) -> Self::Output {
+        (*self).sub(rhs)
+    }
+}
+
+impl SubAssign for bf16 {
+    #[inline]
+    fn sub_assign(&mut self, rhs: Self) {
+        *self = (*self).sub(rhs);
+    }
+}
+
+impl SubAssign<&bf16> for bf16 {
+    #[inline]
+    fn sub_assign(&mut self, rhs: &bf16) {
+        *self = (*self).sub(rhs);
+    }
+}
+
+impl Mul for bf16 {
+    type Output = Self;
+
+    fn mul(self, rhs: Self) -> Self::Output {
+        Self::from_f32(Self::to_f32(self) * Self::to_f32(rhs))
+    }
+}
+
+impl Mul<&bf16> for bf16 {
+    type Output = <bf16 as Mul<bf16>>::Output;
+
+    #[inline]
+    fn mul(self, rhs: &bf16) -> Self::Output {
+        self.mul(*rhs)
+    }
+}
+
+impl Mul<&bf16> for &bf16 {
+    type Output = <bf16 as Mul<bf16>>::Output;
+
+    #[inline]
+    fn mul(self, rhs: &bf16) -> Self::Output {
+        (*self).mul(*rhs)
+    }
+}
+
+impl Mul<bf16> for &bf16 {
+    type Output = <bf16 as Mul<bf16>>::Output;
+
+    #[inline]
+    fn mul(self, rhs: bf16) -> Self::Output {
+        (*self).mul(rhs)
+    }
+}
+
+impl MulAssign for bf16 {
+    #[inline]
+    fn mul_assign(&mut self, rhs: Self) {
+        *self = (*self).mul(rhs);
+    }
+}
+
+impl MulAssign<&bf16> for bf16 {
+    #[inline]
+    fn mul_assign(&mut self, rhs: &bf16) {
+        *self = (*self).mul(rhs);
+    }
+}
+
+impl Div for bf16 {
+    type Output = Self;
+
+    fn div(self, rhs: Self) -> Self::Output {
+        Self::from_f32(Self::to_f32(self) / Self::to_f32(rhs))
+    }
+}
+
+impl Div<&bf16> for bf16 {
+    type Output = <bf16 as Div<bf16>>::Output;
+
+    #[inline]
+    fn div(self, rhs: &bf16) -> Self::Output {
+        self.div(*rhs)
+    }
+}
+
+impl Div<&bf16> for &bf16 {
+    type Output = <bf16 as Div<bf16>>::Output;
+
+    #[inline]
+    fn div(self, rhs: &bf16) -> Self::Output {
+        (*self).div(*rhs)
+    }
+}
+
+impl Div<bf16> for &bf16 {
+    type Output = <bf16 as Div<bf16>>::Output;
+
+    #[inline]
+    fn div(self, rhs: bf16) -> Self::Output {
+        (*self).div(rhs)
+    }
+}
+
+impl DivAssign for bf16 {
+    #[inline]
+    fn div_assign(&mut self, rhs: Self) {
+        *self = (*self).div(rhs);
+    }
+}
+
+impl DivAssign<&bf16> for bf16 {
+    #[inline]
+    fn div_assign(&mut self, rhs: &bf16) {
+        *self = (*self).div(rhs);
+    }
+}
+
+impl Rem for bf16 {
+    type Output = Self;
+
+    fn rem(self, rhs: Self) -> Self::Output {
+        Self::from_f32(Self::to_f32(self) % Self::to_f32(rhs))
+    }
+}
+
+impl Rem<&bf16> for bf16 {
+    type Output = <bf16 as Rem<bf16>>::Output;
+
+    #[inline]
+    fn rem(self, rhs: &bf16) -> Self::Output {
+        self.rem(*rhs)
+    }
+}
+
+impl Rem<&bf16> for &bf16 {
+    type Output = <bf16 as Rem<bf16>>::Output;
+
+    #[inline]
+    fn rem(self, rhs: &bf16) -> Self::Output {
+        (*self).rem(*rhs)
+    }
+}
+
+impl Rem<bf16> for &bf16 {
+    type Output = <bf16 as Rem<bf16>>::Output;
+
+    #[inline]
+    fn rem(self, rhs: bf16) -> Self::Output {
+        (*self).rem(rhs)
+    }
+}
+
+impl RemAssign for bf16 {
+    #[inline]
+    fn rem_assign(&mut self, rhs: Self) {
+        *self = (*self).rem(rhs);
+    }
+}
+
+impl RemAssign<&bf16> for bf16 {
+    #[inline]
+    fn rem_assign(&mut self, rhs: &bf16) {
+        *self = (*self).rem(rhs);
+    }
+}
+
+impl Product for bf16 {
+    #[inline]
+    fn product<I: Iterator<Item = Self>>(iter: I) -> Self {
+        bf16::from_f32(iter.map(|f| f.to_f32()).product())
+    }
+}
+
+impl<'a> Product<&'a bf16> for bf16 {
+    #[inline]
+    fn product<I: Iterator<Item = &'a bf16>>(iter: I) -> Self {
+        bf16::from_f32(iter.map(|f| f.to_f32()).product())
+    }
+}
+
+impl Sum for bf16 {
+    #[inline]
+    fn sum<I: Iterator<Item = Self>>(iter: I) -> Self {
+        bf16::from_f32(iter.map(|f| f.to_f32()).sum())
+    }
+}
+
+impl<'a> Sum<&'a bf16> for bf16 {
+    #[inline]
+    fn sum<I: Iterator<Item = &'a bf16>>(iter: I) -> Self {
+        bf16::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 = bf16::from_f32(2.0);
+        assert_eq!(<i32 as AsPrimitive<bf16>>::as_(2), two);
+        assert_eq!(<bf16 as AsPrimitive<i32>>::as_(two), 2);
+
+        assert_eq!(<f32 as AsPrimitive<bf16>>::as_(2.0), two);
+        assert_eq!(<bf16 as AsPrimitive<f32>>::as_(two), 2.0);
+
+        assert_eq!(<f64 as AsPrimitive<bf16>>::as_(2.0), two);
+        assert_eq!(<bf16 as AsPrimitive<f64>>::as_(two), 2.0);
+    }
+
+    #[cfg(feature = "num-traits")]
+    #[test]
+    fn to_primitive() {
+        let two = bf16::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 = bf16::from_f32(2.0);
+        assert_eq!(<bf16 as FromPrimitive>::from_i32(2).unwrap(), two);
+        assert_eq!(<bf16 as FromPrimitive>::from_f32(2.0).unwrap(), two);
+        assert_eq!(<bf16 as FromPrimitive>::from_f64(2.0).unwrap(), two);
+    }
+
+    #[test]
+    fn test_bf16_consts_from_f32() {
+        let one = bf16::from_f32(1.0);
+        let zero = bf16::from_f32(0.0);
+        let neg_zero = bf16::from_f32(-0.0);
+        let neg_one = bf16::from_f32(-1.0);
+        let inf = bf16::from_f32(core::f32::INFINITY);
+        let neg_inf = bf16::from_f32(core::f32::NEG_INFINITY);
+        let nan = bf16::from_f32(core::f32::NAN);
+
+        assert_eq!(bf16::ONE, one);
+        assert_eq!(bf16::ZERO, zero);
+        assert!(zero.is_sign_positive());
+        assert_eq!(bf16::NEG_ZERO, neg_zero);
+        assert!(neg_zero.is_sign_negative());
+        assert_eq!(bf16::NEG_ONE, neg_one);
+        assert!(neg_one.is_sign_negative());
+        assert_eq!(bf16::INFINITY, inf);
+        assert_eq!(bf16::NEG_INFINITY, neg_inf);
+        assert!(nan.is_nan());
+        assert!(bf16::NAN.is_nan());
+
+        let e = bf16::from_f32(core::f32::consts::E);
+        let pi = bf16::from_f32(core::f32::consts::PI);
+        let frac_1_pi = bf16::from_f32(core::f32::consts::FRAC_1_PI);
+        let frac_1_sqrt_2 = bf16::from_f32(core::f32::consts::FRAC_1_SQRT_2);
+        let frac_2_pi = bf16::from_f32(core::f32::consts::FRAC_2_PI);
+        let frac_2_sqrt_pi = bf16::from_f32(core::f32::consts::FRAC_2_SQRT_PI);
+        let frac_pi_2 = bf16::from_f32(core::f32::consts::FRAC_PI_2);
+        let frac_pi_3 = bf16::from_f32(core::f32::consts::FRAC_PI_3);
+        let frac_pi_4 = bf16::from_f32(core::f32::consts::FRAC_PI_4);
+        let frac_pi_6 = bf16::from_f32(core::f32::consts::FRAC_PI_6);
+        let frac_pi_8 = bf16::from_f32(core::f32::consts::FRAC_PI_8);
+        let ln_10 = bf16::from_f32(core::f32::consts::LN_10);
+        let ln_2 = bf16::from_f32(core::f32::consts::LN_2);
+        let log10_e = bf16::from_f32(core::f32::consts::LOG10_E);
+        // core::f32::consts::LOG10_2 requires rustc 1.43.0
+        let log10_2 = bf16::from_f32(2f32.log10());
+        let log2_e = bf16::from_f32(core::f32::consts::LOG2_E);
+        // core::f32::consts::LOG2_10 requires rustc 1.43.0
+        let log2_10 = bf16::from_f32(10f32.log2());
+        let sqrt_2 = bf16::from_f32(core::f32::consts::SQRT_2);
+
+        assert_eq!(bf16::E, e);
+        assert_eq!(bf16::PI, pi);
+        assert_eq!(bf16::FRAC_1_PI, frac_1_pi);
+        assert_eq!(bf16::FRAC_1_SQRT_2, frac_1_sqrt_2);
+        assert_eq!(bf16::FRAC_2_PI, frac_2_pi);
+        assert_eq!(bf16::FRAC_2_SQRT_PI, frac_2_sqrt_pi);
+        assert_eq!(bf16::FRAC_PI_2, frac_pi_2);
+        assert_eq!(bf16::FRAC_PI_3, frac_pi_3);
+        assert_eq!(bf16::FRAC_PI_4, frac_pi_4);
+        assert_eq!(bf16::FRAC_PI_6, frac_pi_6);
+        assert_eq!(bf16::FRAC_PI_8, frac_pi_8);
+        assert_eq!(bf16::LN_10, ln_10);
+        assert_eq!(bf16::LN_2, ln_2);
+        assert_eq!(bf16::LOG10_E, log10_e);
+        assert_eq!(bf16::LOG10_2, log10_2);
+        assert_eq!(bf16::LOG2_E, log2_e);
+        assert_eq!(bf16::LOG2_10, log2_10);
+        assert_eq!(bf16::SQRT_2, sqrt_2);
+    }
+
+    #[test]
+    fn test_bf16_consts_from_f64() {
+        let one = bf16::from_f64(1.0);
+        let zero = bf16::from_f64(0.0);
+        let neg_zero = bf16::from_f64(-0.0);
+        let inf = bf16::from_f64(core::f64::INFINITY);
+        let neg_inf = bf16::from_f64(core::f64::NEG_INFINITY);
+        let nan = bf16::from_f64(core::f64::NAN);
+
+        assert_eq!(bf16::ONE, one);
+        assert_eq!(bf16::ZERO, zero);
+        assert_eq!(bf16::NEG_ZERO, neg_zero);
+        assert_eq!(bf16::INFINITY, inf);
+        assert_eq!(bf16::NEG_INFINITY, neg_inf);
+        assert!(nan.is_nan());
+        assert!(bf16::NAN.is_nan());
+
+        let e = bf16::from_f64(core::f64::consts::E);
+        let pi = bf16::from_f64(core::f64::consts::PI);
+        let frac_1_pi = bf16::from_f64(core::f64::consts::FRAC_1_PI);
+        let frac_1_sqrt_2 = bf16::from_f64(core::f64::consts::FRAC_1_SQRT_2);
+        let frac_2_pi = bf16::from_f64(core::f64::consts::FRAC_2_PI);
+        let frac_2_sqrt_pi = bf16::from_f64(core::f64::consts::FRAC_2_SQRT_PI);
+        let frac_pi_2 = bf16::from_f64(core::f64::consts::FRAC_PI_2);
+        let frac_pi_3 = bf16::from_f64(core::f64::consts::FRAC_PI_3);
+        let frac_pi_4 = bf16::from_f64(core::f64::consts::FRAC_PI_4);
+        let frac_pi_6 = bf16::from_f64(core::f64::consts::FRAC_PI_6);
+        let frac_pi_8 = bf16::from_f64(core::f64::consts::FRAC_PI_8);
+        let ln_10 = bf16::from_f64(core::f64::consts::LN_10);
+        let ln_2 = bf16::from_f64(core::f64::consts::LN_2);
+        let log10_e = bf16::from_f64(core::f64::consts::LOG10_E);
+        // core::f64::consts::LOG10_2 requires rustc 1.43.0
+        let log10_2 = bf16::from_f64(2f64.log10());
+        let log2_e = bf16::from_f64(core::f64::consts::LOG2_E);
+        // core::f64::consts::LOG2_10 requires rustc 1.43.0
+        let log2_10 = bf16::from_f64(10f64.log2());
+        let sqrt_2 = bf16::from_f64(core::f64::consts::SQRT_2);
+
+        assert_eq!(bf16::E, e);
+        assert_eq!(bf16::PI, pi);
+        assert_eq!(bf16::FRAC_1_PI, frac_1_pi);
+        assert_eq!(bf16::FRAC_1_SQRT_2, frac_1_sqrt_2);
+        assert_eq!(bf16::FRAC_2_PI, frac_2_pi);
+        assert_eq!(bf16::FRAC_2_SQRT_PI, frac_2_sqrt_pi);
+        assert_eq!(bf16::FRAC_PI_2, frac_pi_2);
+        assert_eq!(bf16::FRAC_PI_3, frac_pi_3);
+        assert_eq!(bf16::FRAC_PI_4, frac_pi_4);
+        assert_eq!(bf16::FRAC_PI_6, frac_pi_6);
+        assert_eq!(bf16::FRAC_PI_8, frac_pi_8);
+        assert_eq!(bf16::LN_10, ln_10);
+        assert_eq!(bf16::LN_2, ln_2);
+        assert_eq!(bf16::LOG10_E, log10_e);
+        assert_eq!(bf16::LOG10_2, log10_2);
+        assert_eq!(bf16::LOG2_E, log2_e);
+        assert_eq!(bf16::LOG2_10, log2_10);
+        assert_eq!(bf16::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 = bf16::from_f64(nan64);
+        let neg_nan16_from_64 = bf16::from_f64(neg_nan64);
+        let nan16_from_32 = bf16::from_f32(nan32);
+        let neg_nan16_from_32 = bf16::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 = bf16::from_bits(0x7F81u16);
+        let neg_nan16 = bf16::from_bits(0xFF81u16);
+        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_bf16_to_f32() {
+        let f = bf16::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 = bf16::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 * bf16::EPSILON.to_f32());
+
+        let tiny32 = f32::from_bits(0x0001_0000u32);
+        assert_eq!(bf16::from_bits(0x0001).to_f32(), tiny32);
+        assert_eq!(bf16::from_bits(0x0005).to_f32(), 5.0 * tiny32);
+
+        assert_eq!(bf16::from_bits(0x0001), bf16::from_f32(tiny32));
+        assert_eq!(bf16::from_bits(0x0005), bf16::from_f32(5.0 * tiny32));
+    }
+
+    #[test]
+    fn test_bf16_to_f64() {
+        let f = bf16::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 = bf16::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 * bf16::EPSILON.to_f64());
+
+        let tiny64 = 2.0f64.powi(-133);
+        assert_eq!(bf16::from_bits(0x0001).to_f64(), tiny64);
+        assert_eq!(bf16::from_bits(0x0005).to_f64(), 5.0 * tiny64);
+
+        assert_eq!(bf16::from_bits(0x0001), bf16::from_f64(tiny64));
+        assert_eq!(bf16::from_bits(0x0005), bf16::from_f64(5.0 * tiny64));
+    }
+
+    #[test]
+    fn test_comparisons() {
+        let zero = bf16::from_f64(0.0);
+        let one = bf16::from_f64(1.0);
+        let neg_zero = bf16::from_f64(-0.0);
+        let neg_one = bf16::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_001 * 2^-126 = 2^-133
+        let min_sub = bf16::from_bits(1);
+        let min_sub_f = (-133f32).exp2();
+        assert_eq!(bf16::from_f32(min_sub_f).to_bits(), min_sub.to_bits());
+        assert_eq!(f32::from(min_sub).to_bits(), min_sub_f.to_bits());
+
+        // 0.0000000_011111 rounded to 0.0000000 (< tie, no rounding)
+        // 0.0000000_100000 rounded to 0.0000000 (tie and even, remains at even)
+        // 0.0000000_100001 rounded to 0.0000001 (> tie, rounds up)
+        assert_eq!(
+            bf16::from_f32(min_sub_f * 0.49).to_bits(),
+            min_sub.to_bits() * 0
+        );
+        assert_eq!(
+            bf16::from_f32(min_sub_f * 0.50).to_bits(),
+            min_sub.to_bits() * 0
+        );
+        assert_eq!(
+            bf16::from_f32(min_sub_f * 0.51).to_bits(),
+            min_sub.to_bits() * 1
+        );
+
+        // 0.0000001_011111 rounded to 0.0000001 (< tie, no rounding)
+        // 0.0000001_100000 rounded to 0.0000010 (tie and odd, rounds up to even)
+        // 0.0000001_100001 rounded to 0.0000010 (> tie, rounds up)
+        assert_eq!(
+            bf16::from_f32(min_sub_f * 1.49).to_bits(),
+            min_sub.to_bits() * 1
+        );
+        assert_eq!(
+            bf16::from_f32(min_sub_f * 1.50).to_bits(),
+            min_sub.to_bits() * 2
+        );
+        assert_eq!(
+            bf16::from_f32(min_sub_f * 1.51).to_bits(),
+            min_sub.to_bits() * 2
+        );
+
+        // 0.0000010_011111 rounded to 0.0000010 (< tie, no rounding)
+        // 0.0000010_100000 rounded to 0.0000010 (tie and even, remains at even)
+        // 0.0000010_100001 rounded to 0.0000011 (> tie, rounds up)
+        assert_eq!(
+            bf16::from_f32(min_sub_f * 2.49).to_bits(),
+            min_sub.to_bits() * 2
+        );
+        assert_eq!(
+            bf16::from_f32(min_sub_f * 2.50).to_bits(),
+            min_sub.to_bits() * 2
+        );
+        assert_eq!(
+            bf16::from_f32(min_sub_f * 2.51).to_bits(),
+            min_sub.to_bits() * 3
+        );
+
+        assert_eq!(
+            bf16::from_f32(250.49f32).to_bits(),
+            bf16::from_f32(250.0).to_bits()
+        );
+        assert_eq!(
+            bf16::from_f32(250.50f32).to_bits(),
+            bf16::from_f32(250.0).to_bits()
+        );
+        assert_eq!(
+            bf16::from_f32(250.51f32).to_bits(),
+            bf16::from_f32(251.0).to_bits()
+        );
+        assert_eq!(
+            bf16::from_f32(251.49f32).to_bits(),
+            bf16::from_f32(251.0).to_bits()
+        );
+        assert_eq!(
+            bf16::from_f32(251.50f32).to_bits(),
+            bf16::from_f32(252.0).to_bits()
+        );
+        assert_eq!(
+            bf16::from_f32(251.51f32).to_bits(),
+            bf16::from_f32(252.0).to_bits()
+        );
+        assert_eq!(
+            bf16::from_f32(252.49f32).to_bits(),
+            bf16::from_f32(252.0).to_bits()
+        );
+        assert_eq!(
+            bf16::from_f32(252.50f32).to_bits(),
+            bf16::from_f32(252.0).to_bits()
+        );
+        assert_eq!(
+            bf16::from_f32(252.51f32).to_bits(),
+            bf16::from_f32(253.0).to_bits()
+        );
+    }
+
+    #[test]
+    #[allow(clippy::erasing_op, clippy::identity_op)]
+    fn round_to_even_f64() {
+        // smallest positive subnormal = 0b0.0000_001 * 2^-126 = 2^-133
+        let min_sub = bf16::from_bits(1);
+        let min_sub_f = (-133f64).exp2();
+        assert_eq!(bf16::from_f64(min_sub_f).to_bits(), min_sub.to_bits());
+        assert_eq!(f64::from(min_sub).to_bits(), min_sub_f.to_bits());
+
+        // 0.0000000_011111 rounded to 0.0000000 (< tie, no rounding)
+        // 0.0000000_100000 rounded to 0.0000000 (tie and even, remains at even)
+        // 0.0000000_100001 rounded to 0.0000001 (> tie, rounds up)
+        assert_eq!(
+            bf16::from_f64(min_sub_f * 0.49).to_bits(),
+            min_sub.to_bits() * 0
+        );
+        assert_eq!(
+            bf16::from_f64(min_sub_f * 0.50).to_bits(),
+            min_sub.to_bits() * 0
+        );
+        assert_eq!(
+            bf16::from_f64(min_sub_f * 0.51).to_bits(),
+            min_sub.to_bits() * 1
+        );
+
+        // 0.0000001_011111 rounded to 0.0000001 (< tie, no rounding)
+        // 0.0000001_100000 rounded to 0.0000010 (tie and odd, rounds up to even)
+        // 0.0000001_100001 rounded to 0.0000010 (> tie, rounds up)
+        assert_eq!(
+            bf16::from_f64(min_sub_f * 1.49).to_bits(),
+            min_sub.to_bits() * 1
+        );
+        assert_eq!(
+            bf16::from_f64(min_sub_f * 1.50).to_bits(),
+            min_sub.to_bits() * 2
+        );
+        assert_eq!(
+            bf16::from_f64(min_sub_f * 1.51).to_bits(),
+            min_sub.to_bits() * 2
+        );
+
+        // 0.0000010_011111 rounded to 0.0000010 (< tie, no rounding)
+        // 0.0000010_100000 rounded to 0.0000010 (tie and even, remains at even)
+        // 0.0000010_100001 rounded to 0.0000011 (> tie, rounds up)
+        assert_eq!(
+            bf16::from_f64(min_sub_f * 2.49).to_bits(),
+            min_sub.to_bits() * 2
+        );
+        assert_eq!(
+            bf16::from_f64(min_sub_f * 2.50).to_bits(),
+            min_sub.to_bits() * 2
+        );
+        assert_eq!(
+            bf16::from_f64(min_sub_f * 2.51).to_bits(),
+            min_sub.to_bits() * 3
+        );
+
+        assert_eq!(
+            bf16::from_f64(250.49f64).to_bits(),
+            bf16::from_f64(250.0).to_bits()
+        );
+        assert_eq!(
+            bf16::from_f64(250.50f64).to_bits(),
+            bf16::from_f64(250.0).to_bits()
+        );
+        assert_eq!(
+            bf16::from_f64(250.51f64).to_bits(),
+            bf16::from_f64(251.0).to_bits()
+        );
+        assert_eq!(
+            bf16::from_f64(251.49f64).to_bits(),
+            bf16::from_f64(251.0).to_bits()
+        );
+        assert_eq!(
+            bf16::from_f64(251.50f64).to_bits(),
+            bf16::from_f64(252.0).to_bits()
+        );
+        assert_eq!(
+            bf16::from_f64(251.51f64).to_bits(),
+            bf16::from_f64(252.0).to_bits()
+        );
+        assert_eq!(
+            bf16::from_f64(252.49f64).to_bits(),
+            bf16::from_f64(252.0).to_bits()
+        );
+        assert_eq!(
+            bf16::from_f64(252.50f64).to_bits(),
+            bf16::from_f64(252.0).to_bits()
+        );
+        assert_eq!(
+            bf16::from_f64(252.51f64).to_bits(),
+            bf16::from_f64(253.0).to_bits()
+        );
+    }
+
+    impl quickcheck::Arbitrary for bf16 {
+        fn arbitrary(g: &mut quickcheck::Gen) -> Self {
+            bf16(u16::arbitrary(g))
+        }
+    }
+
+    #[quickcheck]
+    fn qc_roundtrip_bf16_f32_is_identity(f: bf16) -> bool {
+        let roundtrip = bf16::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_bf16_f64_is_identity(f: bf16) -> bool {
+        let roundtrip = bf16::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
+        }
+    }
+}
diff --git a/third_party/rust/half/src/bfloat/convert.rs b/third_party/rust/half/src/bfloat/convert.rs
new file mode 100644
index 0000000000..4aa0aec751
--- /dev/null
+++ b/third_party/rust/half/src/bfloat/convert.rs
@@ -0,0 +1,135 @@
+pub(crate) fn f32_to_bf16(value: f32) -> u16 {
+    // Convert to raw bytes
+    let x = value.to_bits();
+
+    // check for NaN
+    if x & 0x7FFF_FFFFu32 > 0x7F80_0000u32 {
+        // Keep high part of current mantissa but also set most significiant mantissa bit
+        return ((x >> 16) | 0x0040u32) as u16;
+    }
+
+    // round and shift
+    let round_bit = 0x0000_8000u32;
+    if (x & round_bit) != 0 && (x & (3 * round_bit - 1)) != 0 {
+        (x >> 16) as u16 + 1
+    } else {
+        (x >> 16) as u16
+    }
+}
+
+pub(crate) fn f64_to_bf16(value: f64) -> u16 {
+    // Convert to raw bytes, truncating the last 32-bits of mantissa; that precision will always
+    // be lost on half-precision.
+    let val = value.to_bits();
+    let x = (val >> 32) as u32;
+
+    // Extract IEEE754 components
+    let sign = x & 0x8000_0000u32;
+    let exp = x & 0x7FF0_0000u32;
+    let man = x & 0x000F_FFFFu32;
+
+    // Check for all exponent bits being set, which is Infinity or NaN
+    if exp == 0x7FF0_0000u32 {
+        // Set mantissa MSB for NaN (and also keep shifted mantissa bits).
+        // We also have to check the last 32 bits.
+        let nan_bit = if man == 0 && (val as u32 == 0) {
+            0
+        } else {
+            0x0040u32
+        };
+        return ((sign >> 16) | 0x7F80u32 | nan_bit | (man >> 13)) as u16;
+    }
+
+    // The number is normalized, start assembling half precision version
+    let half_sign = sign >> 16;
+    // Unbias the exponent, then bias for bfloat16 precision
+    let unbiased_exp = ((exp >> 20) as i64) - 1023;
+    let half_exp = unbiased_exp + 127;
+
+    // Check for exponent overflow, return +infinity
+    if half_exp >= 0xFF {
+        return (half_sign | 0x7F80u32) as u16;
+    }
+
+    // Check for underflow
+    if half_exp <= 0 {
+        // Check mantissa for what we can do
+        if 7 - half_exp > 21 {
+            // No rounding possibility, so this is a full underflow, return signed zero
+            return half_sign as u16;
+        }
+        // Don't forget about hidden leading mantissa bit when assembling mantissa
+        let man = man | 0x0010_0000u32;
+        let mut half_man = man >> (14 - half_exp);
+        // Check for rounding
+        let round_bit = 1 << (13 - half_exp);
+        if (man & round_bit) != 0 && (man & (3 * round_bit - 1)) != 0 {
+            half_man += 1;
+        }
+        // No exponent for subnormals
+        return (half_sign | half_man) as u16;
+    }
+
+    // Rebias the exponent
+    let half_exp = (half_exp as u32) << 7;
+    let half_man = man >> 13;
+    // Check for rounding
+    let round_bit = 0x0000_1000u32;
+    if (man & round_bit) != 0 && (man & (3 * round_bit - 1)) != 0 {
+        // Round it
+        ((half_sign | half_exp | half_man) + 1) as u16
+    } else {
+        (half_sign | half_exp | half_man) as u16
+    }
+}
+
+pub(crate) fn bf16_to_f32(i: u16) -> f32 {
+    // If NaN, keep current mantissa but also set most significiant mantissa bit
+    if i & 0x7FFFu16 > 0x7F80u16 {
+        f32::from_bits((i as u32 | 0x0040u32) << 16)
+    } else {
+        f32::from_bits((i as u32) << 16)
+    }
+}
+
+pub(crate) fn bf16_to_f64(i: u16) -> f64 {
+    // Check for signed zero
+    if i & 0x7FFFu16 == 0 {
+        return f64::from_bits((i as u64) << 48);
+    }
+
+    let half_sign = (i & 0x8000u16) as u64;
+    let half_exp = (i & 0x7F80u16) as u64;
+    let half_man = (i & 0x007Fu16) as u64;
+
+    // Check for an infinity or NaN when all exponent bits set
+    if half_exp == 0x7F80u64 {
+        // Check for signed infinity if mantissa is zero
+        if half_man == 0 {
+            return f64::from_bits((half_sign << 48) | 0x7FF0_0000_0000_0000u64);
+        } else {
+            // NaN, keep current mantissa but also set most significiant mantissa bit
+            return f64::from_bits((half_sign << 48) | 0x7FF8_0000_0000_0000u64 | (half_man << 45));
+        }
+    }
+
+    // Calculate double-precision components with adjusted exponent
+    let sign = half_sign << 48;
+    // Unbias exponent
+    let unbiased_exp = ((half_exp as i64) >> 7) - 127;
+
+    // Check for subnormals, which will be normalized by adjusting exponent
+    if half_exp == 0 {
+        // Calculate how much to adjust the exponent by
+        let e = (half_man as u16).leading_zeros() - 9;
+
+        // Rebias and adjust exponent
+        let exp = ((1023 - 127 - e) as u64) << 52;
+        let man = (half_man << (46 + e)) & 0xF_FFFF_FFFF_FFFFu64;
+        return f64::from_bits(sign | exp | man);
+    }
+    // Rebias exponent for a normalized normal
+    let exp = ((unbiased_exp + 1023) as u64) << 52;
+    let man = (half_man & 0x007Fu64) << 45;
+    f64::from_bits(sign | exp | man)
+}
diff --git a/third_party/rust/half/src/binary16.rs b/third_party/rust/half/src/binary16.rs
new file mode 100644
index 0000000000..8d3fad75e7
--- /dev/null
+++ b/third_party/rust/half/src/binary16.rs
@@ -0,0 +1,1711 @@
+#[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
+        }
+    }
+}
diff --git a/third_party/rust/half/src/binary16/convert.rs b/third_party/rust/half/src/binary16/convert.rs
new file mode 100644
index 0000000000..c2521d8d26
--- /dev/null
+++ b/third_party/rust/half/src/binary16/convert.rs
@@ -0,0 +1,491 @@
+#![allow(dead_code, unused_imports)]
+
+macro_rules! convert_fn {
+    (fn $name:ident($var:ident : $vartype:ty) -> $restype:ty {
+            if feature("f16c") { $f16c:expr }
+            else { $fallback:expr }}) => {
+        #[inline]
+        pub(crate) fn $name($var: $vartype) -> $restype {
+            // Use CPU feature detection if using std
+            #[cfg(all(
+                feature = "use-intrinsics",
+                feature = "std",
+                any(target_arch = "x86", target_arch = "x86_64"),
+                not(target_feature = "f16c")
+            ))]
+            {
+                if is_x86_feature_detected!("f16c") {
+                    $f16c
+                } else {
+                    $fallback
+                }
+            }
+            // Use intrinsics directly when a compile target or using no_std
+            #[cfg(all(
+                feature = "use-intrinsics",
+                any(target_arch = "x86", target_arch = "x86_64"),
+                target_feature = "f16c"
+            ))]
+            {
+                $f16c
+            }
+            // Fallback to software
+            #[cfg(any(
+                not(feature = "use-intrinsics"),
+                not(any(target_arch = "x86", target_arch = "x86_64")),
+                all(not(feature = "std"), not(target_feature = "f16c"))
+            ))]
+            {
+                $fallback
+            }
+        }
+    };
+}
+
+convert_fn! {
+    fn f32_to_f16(f: f32) -> u16 {
+        if feature("f16c") {
+            unsafe { x86::f32_to_f16_x86_f16c(f) }
+        } else {
+            f32_to_f16_fallback(f)
+        }
+    }
+}
+
+convert_fn! {
+    fn f64_to_f16(f: f64) -> u16 {
+        if feature("f16c") {
+            unsafe { x86::f32_to_f16_x86_f16c(f as f32) }
+        } else {
+            f64_to_f16_fallback(f)
+        }
+    }
+}
+
+convert_fn! {
+    fn f16_to_f32(i: u16) -> f32 {
+        if feature("f16c") {
+            unsafe { x86::f16_to_f32_x86_f16c(i) }
+        } else {
+            f16_to_f32_fallback(i)
+        }
+    }
+}
+
+convert_fn! {
+    fn f16_to_f64(i: u16) -> f64 {
+        if feature("f16c") {
+            unsafe { x86::f16_to_f32_x86_f16c(i) as f64 }
+        } else {
+            f16_to_f64_fallback(i)
+        }
+    }
+}
+
+// TODO: While SIMD versions are faster, further improvements can be made by doing runtime feature
+// detection once at beginning of convert slice method, rather than per chunk
+
+convert_fn! {
+    fn f32x4_to_f16x4(f: &[f32]) -> [u16; 4] {
+        if feature("f16c") {
+            unsafe { x86::f32x4_to_f16x4_x86_f16c(f) }
+        } else {
+            f32x4_to_f16x4_fallback(f)
+        }
+    }
+}
+
+convert_fn! {
+    fn f16x4_to_f32x4(i: &[u16]) -> [f32; 4] {
+        if feature("f16c") {
+            unsafe { x86::f16x4_to_f32x4_x86_f16c(i) }
+        } else {
+            f16x4_to_f32x4_fallback(i)
+        }
+    }
+}
+
+convert_fn! {
+    fn f64x4_to_f16x4(f: &[f64]) -> [u16; 4] {
+        if feature("f16c") {
+            unsafe { x86::f64x4_to_f16x4_x86_f16c(f) }
+        } else {
+            f64x4_to_f16x4_fallback(f)
+        }
+    }
+}
+
+convert_fn! {
+    fn f16x4_to_f64x4(i: &[u16]) -> [f64; 4] {
+        if feature("f16c") {
+            unsafe { x86::f16x4_to_f64x4_x86_f16c(i) }
+        } else {
+            f16x4_to_f64x4_fallback(i)
+        }
+    }
+}
+
+/////////////// Fallbacks ////////////////
+
+// In the below functions, round to nearest, with ties to even.
+// Let us call the most significant bit that will be shifted out the round_bit.
+//
+// Round up if either
+//  a) Removed part > tie.
+//     (mantissa & round_bit) != 0 && (mantissa & (round_bit - 1)) != 0
+//  b) Removed part == tie, and retained part is odd.
+//     (mantissa & round_bit) != 0 && (mantissa & (2 * round_bit)) != 0
+// (If removed part == tie and retained part is even, do not round up.)
+// These two conditions can be combined into one:
+//     (mantissa & round_bit) != 0 && (mantissa & ((round_bit - 1) | (2 * round_bit))) != 0
+// which can be simplified into
+//     (mantissa & round_bit) != 0 && (mantissa & (3 * round_bit - 1)) != 0
+
+fn f32_to_f16_fallback(value: f32) -> u16 {
+    // Convert to raw bytes
+    let x = value.to_bits();
+
+    // Extract IEEE754 components
+    let sign = x & 0x8000_0000u32;
+    let exp = x & 0x7F80_0000u32;
+    let man = x & 0x007F_FFFFu32;
+
+    // Check for all exponent bits being set, which is Infinity or NaN
+    if exp == 0x7F80_0000u32 {
+        // Set mantissa MSB for NaN (and also keep shifted mantissa bits)
+        let nan_bit = if man == 0 { 0 } else { 0x0200u32 };
+        return ((sign >> 16) | 0x7C00u32 | nan_bit | (man >> 13)) as u16;
+    }
+
+    // The number is normalized, start assembling half precision version
+    let half_sign = sign >> 16;
+    // Unbias the exponent, then bias for half precision
+    let unbiased_exp = ((exp >> 23) as i32) - 127;
+    let half_exp = unbiased_exp + 15;
+
+    // Check for exponent overflow, return +infinity
+    if half_exp >= 0x1F {
+        return (half_sign | 0x7C00u32) as u16;
+    }
+
+    // Check for underflow
+    if half_exp <= 0 {
+        // Check mantissa for what we can do
+        if 14 - half_exp > 24 {
+            // No rounding possibility, so this is a full underflow, return signed zero
+            return half_sign as u16;
+        }
+        // Don't forget about hidden leading mantissa bit when assembling mantissa
+        let man = man | 0x0080_0000u32;
+        let mut half_man = man >> (14 - half_exp);
+        // Check for rounding (see comment above functions)
+        let round_bit = 1 << (13 - half_exp);
+        if (man & round_bit) != 0 && (man & (3 * round_bit - 1)) != 0 {
+            half_man += 1;
+        }
+        // No exponent for subnormals
+        return (half_sign | half_man) as u16;
+    }
+
+    // Rebias the exponent
+    let half_exp = (half_exp as u32) << 10;
+    let half_man = man >> 13;
+    // Check for rounding (see comment above functions)
+    let round_bit = 0x0000_1000u32;
+    if (man & round_bit) != 0 && (man & (3 * round_bit - 1)) != 0 {
+        // Round it
+        ((half_sign | half_exp | half_man) + 1) as u16
+    } else {
+        (half_sign | half_exp | half_man) as u16
+    }
+}
+
+fn f64_to_f16_fallback(value: f64) -> u16 {
+    // Convert to raw bytes, truncating the last 32-bits of mantissa; that precision will always
+    // be lost on half-precision.
+    let val = value.to_bits();
+    let x = (val >> 32) as u32;
+
+    // Extract IEEE754 components
+    let sign = x & 0x8000_0000u32;
+    let exp = x & 0x7FF0_0000u32;
+    let man = x & 0x000F_FFFFu32;
+
+    // Check for all exponent bits being set, which is Infinity or NaN
+    if exp == 0x7FF0_0000u32 {
+        // Set mantissa MSB for NaN (and also keep shifted mantissa bits).
+        // We also have to check the last 32 bits.
+        let nan_bit = if man == 0 && (val as u32 == 0) {
+            0
+        } else {
+            0x0200u32
+        };
+        return ((sign >> 16) | 0x7C00u32 | nan_bit | (man >> 10)) as u16;
+    }
+
+    // The number is normalized, start assembling half precision version
+    let half_sign = sign >> 16;
+    // Unbias the exponent, then bias for half precision
+    let unbiased_exp = ((exp >> 20) as i64) - 1023;
+    let half_exp = unbiased_exp + 15;
+
+    // Check for exponent overflow, return +infinity
+    if half_exp >= 0x1F {
+        return (half_sign | 0x7C00u32) as u16;
+    }
+
+    // Check for underflow
+    if half_exp <= 0 {
+        // Check mantissa for what we can do
+        if 10 - half_exp > 21 {
+            // No rounding possibility, so this is a full underflow, return signed zero
+            return half_sign as u16;
+        }
+        // Don't forget about hidden leading mantissa bit when assembling mantissa
+        let man = man | 0x0010_0000u32;
+        let mut half_man = man >> (11 - half_exp);
+        // Check for rounding (see comment above functions)
+        let round_bit = 1 << (10 - half_exp);
+        if (man & round_bit) != 0 && (man & (3 * round_bit - 1)) != 0 {
+            half_man += 1;
+        }
+        // No exponent for subnormals
+        return (half_sign | half_man) as u16;
+    }
+
+    // Rebias the exponent
+    let half_exp = (half_exp as u32) << 10;
+    let half_man = man >> 10;
+    // Check for rounding (see comment above functions)
+    let round_bit = 0x0000_0200u32;
+    if (man & round_bit) != 0 && (man & (3 * round_bit - 1)) != 0 {
+        // Round it
+        ((half_sign | half_exp | half_man) + 1) as u16
+    } else {
+        (half_sign | half_exp | half_man) as u16
+    }
+}
+
+fn f16_to_f32_fallback(i: u16) -> f32 {
+    // Check for signed zero
+    if i & 0x7FFFu16 == 0 {
+        return f32::from_bits((i as u32) << 16);
+    }
+
+    let half_sign = (i & 0x8000u16) as u32;
+    let half_exp = (i & 0x7C00u16) as u32;
+    let half_man = (i & 0x03FFu16) as u32;
+
+    // Check for an infinity or NaN when all exponent bits set
+    if half_exp == 0x7C00u32 {
+        // Check for signed infinity if mantissa is zero
+        if half_man == 0 {
+            return f32::from_bits((half_sign << 16) | 0x7F80_0000u32);
+        } else {
+            // NaN, keep current mantissa but also set most significiant mantissa bit
+            return f32::from_bits((half_sign << 16) | 0x7FC0_0000u32 | (half_man << 13));
+        }
+    }
+
+    // Calculate single-precision components with adjusted exponent
+    let sign = half_sign << 16;
+    // Unbias exponent
+    let unbiased_exp = ((half_exp as i32) >> 10) - 15;
+
+    // Check for subnormals, which will be normalized by adjusting exponent
+    if half_exp == 0 {
+        // Calculate how much to adjust the exponent by
+        let e = (half_man as u16).leading_zeros() - 6;
+
+        // Rebias and adjust exponent
+        let exp = (127 - 15 - e) << 23;
+        let man = (half_man << (14 + e)) & 0x7F_FF_FFu32;
+        return f32::from_bits(sign | exp | man);
+    }
+
+    // Rebias exponent for a normalized normal
+    let exp = ((unbiased_exp + 127) as u32) << 23;
+    let man = (half_man & 0x03FFu32) << 13;
+    f32::from_bits(sign | exp | man)
+}
+
+fn f16_to_f64_fallback(i: u16) -> f64 {
+    // Check for signed zero
+    if i & 0x7FFFu16 == 0 {
+        return f64::from_bits((i as u64) << 48);
+    }
+
+    let half_sign = (i & 0x8000u16) as u64;
+    let half_exp = (i & 0x7C00u16) as u64;
+    let half_man = (i & 0x03FFu16) as u64;
+
+    // Check for an infinity or NaN when all exponent bits set
+    if half_exp == 0x7C00u64 {
+        // Check for signed infinity if mantissa is zero
+        if half_man == 0 {
+            return f64::from_bits((half_sign << 48) | 0x7FF0_0000_0000_0000u64);
+        } else {
+            // NaN, keep current mantissa but also set most significiant mantissa bit
+            return f64::from_bits((half_sign << 48) | 0x7FF8_0000_0000_0000u64 | (half_man << 42));
+        }
+    }
+
+    // Calculate double-precision components with adjusted exponent
+    let sign = half_sign << 48;
+    // Unbias exponent
+    let unbiased_exp = ((half_exp as i64) >> 10) - 15;
+
+    // Check for subnormals, which will be normalized by adjusting exponent
+    if half_exp == 0 {
+        // Calculate how much to adjust the exponent by
+        let e = (half_man as u16).leading_zeros() - 6;
+
+        // Rebias and adjust exponent
+        let exp = ((1023 - 15 - e) as u64) << 52;
+        let man = (half_man << (43 + e)) & 0xF_FFFF_FFFF_FFFFu64;
+        return f64::from_bits(sign | exp | man);
+    }
+
+    // Rebias exponent for a normalized normal
+    let exp = ((unbiased_exp + 1023) as u64) << 52;
+    let man = (half_man & 0x03FFu64) << 42;
+    f64::from_bits(sign | exp | man)
+}
+
+#[inline]
+fn f16x4_to_f32x4_fallback(v: &[u16]) -> [f32; 4] {
+    debug_assert!(v.len() >= 4);
+
+    [
+        f16_to_f32_fallback(v[0]),
+        f16_to_f32_fallback(v[1]),
+        f16_to_f32_fallback(v[2]),
+        f16_to_f32_fallback(v[3]),
+    ]
+}
+
+#[inline]
+fn f32x4_to_f16x4_fallback(v: &[f32]) -> [u16; 4] {
+    debug_assert!(v.len() >= 4);
+
+    [
+        f32_to_f16_fallback(v[0]),
+        f32_to_f16_fallback(v[1]),
+        f32_to_f16_fallback(v[2]),
+        f32_to_f16_fallback(v[3]),
+    ]
+}
+
+#[inline]
+fn f16x4_to_f64x4_fallback(v: &[u16]) -> [f64; 4] {
+    debug_assert!(v.len() >= 4);
+
+    [
+        f16_to_f64_fallback(v[0]),
+        f16_to_f64_fallback(v[1]),
+        f16_to_f64_fallback(v[2]),
+        f16_to_f64_fallback(v[3]),
+    ]
+}
+
+#[inline]
+fn f64x4_to_f16x4_fallback(v: &[f64]) -> [u16; 4] {
+    debug_assert!(v.len() >= 4);
+
+    [
+        f64_to_f16_fallback(v[0]),
+        f64_to_f16_fallback(v[1]),
+        f64_to_f16_fallback(v[2]),
+        f64_to_f16_fallback(v[3]),
+    ]
+}
+
+/////////////// x86/x86_64 f16c ////////////////
+#[cfg(all(
+    feature = "use-intrinsics",
+    any(target_arch = "x86", target_arch = "x86_64")
+))]
+mod x86 {
+    use core::{mem::MaybeUninit, ptr};
+
+    #[cfg(target_arch = "x86")]
+    use core::arch::x86::{__m128, __m128i, _mm_cvtph_ps, _mm_cvtps_ph, _MM_FROUND_TO_NEAREST_INT};
+    #[cfg(target_arch = "x86_64")]
+    use core::arch::x86_64::{
+        __m128, __m128i, _mm_cvtph_ps, _mm_cvtps_ph, _MM_FROUND_TO_NEAREST_INT,
+    };
+
+    #[target_feature(enable = "f16c")]
+    #[inline]
+    pub(super) unsafe fn f16_to_f32_x86_f16c(i: u16) -> f32 {
+        let mut vec = MaybeUninit::<__m128i>::zeroed();
+        vec.as_mut_ptr().cast::<u16>().write(i);
+        let retval = _mm_cvtph_ps(vec.assume_init());
+        *(&retval as *const __m128).cast()
+    }
+
+    #[target_feature(enable = "f16c")]
+    #[inline]
+    pub(super) unsafe fn f32_to_f16_x86_f16c(f: f32) -> u16 {
+        let mut vec = MaybeUninit::<__m128>::zeroed();
+        vec.as_mut_ptr().cast::<f32>().write(f);
+        let retval = _mm_cvtps_ph(vec.assume_init(), _MM_FROUND_TO_NEAREST_INT);
+        *(&retval as *const __m128i).cast()
+    }
+
+    #[target_feature(enable = "f16c")]
+    #[inline]
+    pub(super) unsafe fn f16x4_to_f32x4_x86_f16c(v: &[u16]) -> [f32; 4] {
+        debug_assert!(v.len() >= 4);
+
+        let mut vec = MaybeUninit::<__m128i>::zeroed();
+        ptr::copy_nonoverlapping(v.as_ptr(), vec.as_mut_ptr().cast(), 4);
+        let retval = _mm_cvtph_ps(vec.assume_init());
+        *(&retval as *const __m128).cast()
+    }
+
+    #[target_feature(enable = "f16c")]
+    #[inline]
+    pub(super) unsafe fn f32x4_to_f16x4_x86_f16c(v: &[f32]) -> [u16; 4] {
+        debug_assert!(v.len() >= 4);
+
+        let mut vec = MaybeUninit::<__m128>::uninit();
+        ptr::copy_nonoverlapping(v.as_ptr(), vec.as_mut_ptr().cast(), 4);
+        let retval = _mm_cvtps_ph(vec.assume_init(), _MM_FROUND_TO_NEAREST_INT);
+        *(&retval as *const __m128i).cast()
+    }
+
+    #[target_feature(enable = "f16c")]
+    #[inline]
+    pub(super) unsafe fn f16x4_to_f64x4_x86_f16c(v: &[u16]) -> [f64; 4] {
+        debug_assert!(v.len() >= 4);
+
+        let mut vec = MaybeUninit::<__m128i>::zeroed();
+        ptr::copy_nonoverlapping(v.as_ptr(), vec.as_mut_ptr().cast(), 4);
+        let retval = _mm_cvtph_ps(vec.assume_init());
+        let array = *(&retval as *const __m128).cast::<[f32; 4]>();
+        // Let compiler vectorize this regular cast for now.
+        // TODO: investigate auto-detecting sse2/avx convert features
+        [
+            array[0] as f64,
+            array[1] as f64,
+            array[2] as f64,
+            array[3] as f64,
+        ]
+    }
+
+    #[target_feature(enable = "f16c")]
+    #[inline]
+    pub(super) unsafe fn f64x4_to_f16x4_x86_f16c(v: &[f64]) -> [u16; 4] {
+        debug_assert!(v.len() >= 4);
+
+        // Let compiler vectorize this regular cast for now.
+        // TODO: investigate auto-detecting sse2/avx convert features
+        let v = [v[0] as f32, v[1] as f32, v[2] as f32, v[3] as f32];
+
+        let mut vec = MaybeUninit::<__m128>::uninit();
+        ptr::copy_nonoverlapping(v.as_ptr(), vec.as_mut_ptr().cast(), 4);
+        let retval = _mm_cvtps_ph(vec.assume_init(), _MM_FROUND_TO_NEAREST_INT);
+        *(&retval as *const __m128i).cast()
+    }
+}
diff --git a/third_party/rust/half/src/lib.rs b/third_party/rust/half/src/lib.rs
new file mode 100644
index 0000000000..2c5568b035
--- /dev/null
+++ b/third_party/rust/half/src/lib.rs
@@ -0,0 +1,217 @@
+//! A crate that provides support for half-precision 16-bit floating point types.
+//!
+//! This crate provides the [`f16`] type, which is an implementation of the IEEE 754-2008 standard
+//! [`binary16`] a.k.a `half` floating point type. 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. This is especially useful for image storage formats.
+//!
+//! This crate also provides a [`bf16`] type, an alternative 16-bit floating point format. The
+//! [`bfloat16`] format is a truncated IEEE 754 standard `binary32` float that preserves the
+//! exponent to allow the same range as [`f32`] but with only 8 bits of precision (instead of 11
+//! bits for [`f16`]). See the [`bf16`] type for details.
+//!
+//! Because [`f16`] and [`bf16`] are primarily for efficient storage, floating point operations such
+//! as addition, multiplication, etc. are not implemented by hardware. While this crate does provide
+//! the appropriate trait implementations for basic operations, they each convert the value to
+//! [`f32`] before performing the operation and then back afterward. When performing complex
+//! arithmetic, manually convert to and from [`f32`] before and after to reduce repeated conversions
+//! for each operation.
+//!
+//! This crate also provides a [`slice`][mod@slice] module for zero-copy in-place conversions of
+//! [`u16`] slices to both [`f16`] and [`bf16`], as well as efficient vectorized conversions of
+//! larger buffers of floating point values to and from these half formats.
+//!
+//! The crate uses `#[no_std]` by default, so can be used in embedded environments without using the
+//! Rust [`std`] library. A `std` feature to enable support for the standard library is available,
+//! see the [Cargo Features](#cargo-features) section below.
+//!
+//! A [`prelude`] module is provided for easy importing of available utility traits.
+//!
+//! # Cargo Features
+//!
+//! This crate supports a number of optional cargo features. None of these features are enabled by
+//! default, even `std`.
+//!
+//! - **`use-intrinsics`** -- Use [`core::arch`] hardware intrinsics for `f16` and `bf16` conversions
+//!   if available on the compiler target. This feature currently only works on nightly Rust
+//!   until the corresponding intrinsics are stabilized.
+//!
+//!   When this feature is enabled and the hardware supports it, the functions and traits in the
+//!   [`slice`][mod@slice] module will use vectorized SIMD intructions for increased efficiency.
+//!
+//!   By default, without this feature, conversions are done only in software, which will also be
+//!   the fallback if the target does not have hardware support. Note that without the `std`
+//!   feature enabled, no runtime CPU feature detection is used, so the hardware support is only
+//!   compiled if the compiler target supports the CPU feature.
+//!
+//! - **`alloc`** -- Enable use of the [`alloc`] crate when not using the `std` library.
+//!
+//!   Among other functions, this enables the [`vec`] module, which contains zero-copy
+//!   conversions for the [`Vec`] type. This allows fast conversion between raw `Vec<u16>` bits and
+//!   `Vec<f16>` or `Vec<bf16>` arrays, and vice versa.
+//!
+//! - **`std`** -- Enable features that depend on the Rust [`std`] library. This also enables the
+//!   `alloc` feature automatically.
+//!
+//!   Enabling the `std` feature also enables runtime CPU feature detection when the
+//!   `use-intrsincis` feature is also enabled. Without this feature detection, intrinsics are only
+//!   used when compiler target supports the target feature.
+//!
+//! - **`serde`** -- Adds support for the [`serde`] crate by implementing [`Serialize`] and
+//!   [`Deserialize`] traits for both [`f16`] and [`bf16`].
+//!
+//! - **`num-traits`** -- Adds support for the [`num-traits`] crate by implementing [`ToPrimitive`],
+//!   [`FromPrimitive`], [`AsPrimitive`], [`Num`], [`Float`], [`FloatCore`], and [`Bounded`] traits
+//!   for both [`f16`] and [`bf16`].
+//!
+//! - **`bytemuck`** -- Adds support for the [`bytemuck`] crate by implementing [`Zeroable`] and
+//!   [`Pod`] traits for both [`f16`] and [`bf16`].
+//!
+//! - **`zerocopy`** -- Adds support for the [`zerocopy`] crate by implementing [`AsBytes`] and
+//!   [`FromBytes`] traits for both [`f16`] and [`bf16`].
+//!
+//! [`alloc`]: https://doc.rust-lang.org/alloc/
+//! [`std`]: https://doc.rust-lang.org/std/
+//! [`binary16`]: https://en.wikipedia.org/wiki/Half-precision_floating-point_format
+//! [`bfloat16`]: https://en.wikipedia.org/wiki/Bfloat16_floating-point_format
+//! [`serde`]: https://crates.io/crates/serde
+//! [`bytemuck`]: https://crates.io/crates/bytemuck
+//! [`num-traits`]: https://crates.io/crates/num-traits
+//! [`zerocopy`]: https://crates.io/crates/zerocopy
+#![cfg_attr(
+    feature = "alloc",
+    doc = "
+[`vec`]: mod@vec"
+)]
+#![cfg_attr(
+    not(feature = "alloc"),
+    doc = "
+[`vec`]: #
+[`Vec`]: https://docs.rust-lang.org/stable/alloc/vec/struct.Vec.html"
+)]
+#![cfg_attr(
+    feature = "serde",
+    doc = "
+[`Serialize`]: serde::Serialize
+[`Deserialize`]: serde::Deserialize"
+)]
+#![cfg_attr(
+    not(feature = "serde"),
+    doc = "
+[`Serialize`]: https://docs.rs/serde/*/serde/trait.Serialize.html
+[`Deserialize`]: https://docs.rs/serde/*/serde/trait.Deserialize.html"
+)]
+#![cfg_attr(
+    feature = "num-traits",
+    doc = "
+[`ToPrimitive`]: ::num_traits::ToPrimitive
+[`FromPrimitive`]: ::num_traits::FromPrimitive
+[`AsPrimitive`]: ::num_traits::AsPrimitive
+[`Num`]: ::num_traits::Num
+[`Float`]: ::num_traits::Float
+[`FloatCore`]: ::num_traits::float::FloatCore
+[`Bounded`]: ::num_traits::Bounded"
+)]
+#![cfg_attr(
+    not(feature = "num-traits"),
+    doc = "
+[`ToPrimitive`]: https://docs.rs/num-traits/*/num_traits/cast/trait.ToPrimitive.html
+[`FromPrimitive`]: https://docs.rs/num-traits/*/num_traits/cast/trait.FromPrimitive.html
+[`AsPrimitive`]: https://docs.rs/num-traits/*/num_traits/cast/trait.AsPrimitive.html
+[`Num`]: https://docs.rs/num-traits/*/num_traits/trait.Num.html
+[`Float`]: https://docs.rs/num-traits/*/num_traits/float/trait.Float.html
+[`FloatCore`]: https://docs.rs/num-traits/*/num_traits/float/trait.FloatCore.html
+[`Bounded`]: https://docs.rs/num-traits/*/num_traits/bounds/trait.Bounded.html"
+)]
+#![cfg_attr(
+    feature = "bytemuck",
+    doc = "
+[`Zeroable`]: bytemuck::Zeroable
+[`Pod`]: bytemuck::Pod"
+)]
+#![cfg_attr(
+    not(feature = "bytemuck"),
+    doc = "
+[`Zeroable`]: https://docs.rs/bytemuck/*/bytemuck/trait.Zeroable.html
+[`Pod`]: https://docs.rs/bytemuck/*bytemuck/trait.Pod.html"
+)]
+#![cfg_attr(
+    feature = "zerocopy",
+    doc = "
+[`AsBytes`]: zerocopy::AsBytes
+[`FromBytes`]: zerocopy::FromBytes"
+)]
+#![cfg_attr(
+    not(feature = "zerocopy"),
+    doc = "
+[`AsBytes`]: https://docs.rs/zerocopy/*/zerocopy/trait.AsBytes.html
+[`FromBytes`]: https://docs.rs/zerocopy/*/zerocopy/trait.FromBytes.html"
+)]
+#![warn(
+    missing_docs,
+    missing_copy_implementations,
+    missing_debug_implementations,
+    trivial_numeric_casts,
+    future_incompatible
+)]
+#![allow(clippy::verbose_bit_mask, clippy::cast_lossless)]
+#![cfg_attr(not(feature = "std"), no_std)]
+#![cfg_attr(
+    all(
+        feature = "use-intrinsics",
+        any(target_arch = "x86", target_arch = "x86_64")
+    ),
+    feature(stdsimd, f16c_target_feature)
+)]
+#![doc(html_root_url = "https://docs.rs/half/1.8.2")]
+#![doc(test(attr(deny(warnings), allow(unused))))]
+#![cfg_attr(docsrs, feature(doc_cfg))]
+
+#[cfg(feature = "alloc")]
+extern crate alloc;
+
+mod bfloat;
+mod binary16;
+#[cfg(feature = "num-traits")]
+mod num_traits;
+
+pub mod slice;
+#[cfg(feature = "alloc")]
+#[cfg_attr(docsrs, doc(cfg(feature = "alloc")))]
+pub mod vec;
+
+pub use bfloat::bf16;
+#[doc(hidden)]
+#[allow(deprecated)]
+pub use binary16::consts;
+pub use binary16::f16;
+
+/// A collection of the most used items and traits in this crate for easy importing.
+///
+/// # Examples
+///
+/// ```rust
+/// use half::prelude::*;
+/// ```
+pub mod prelude {
+    #[doc(no_inline)]
+    pub use crate::{
+        bf16, f16,
+        slice::{HalfBitsSliceExt, HalfFloatSliceExt},
+    };
+
+    #[cfg(feature = "alloc")]
+    #[doc(no_inline)]
+    #[cfg_attr(docsrs, doc(cfg(feature = "alloc")))]
+    pub use crate::vec::{HalfBitsVecExt, HalfFloatVecExt};
+}
+
+// Keep this module private to crate
+mod private {
+    use crate::{bf16, f16};
+
+    pub trait SealedHalf {}
+
+    impl SealedHalf for f16 {}
+    impl SealedHalf for bf16 {}
+}
diff --git a/third_party/rust/half/src/num_traits.rs b/third_party/rust/half/src/num_traits.rs
new file mode 100644
index 0000000000..e5ee490a84
--- /dev/null
+++ b/third_party/rust/half/src/num_traits.rs
@@ -0,0 +1,1461 @@
+use crate::{bf16, f16};
+use core::cmp::Ordering;
+use core::{num::FpCategory, ops::Div};
+use num_traits::{
+    AsPrimitive, Bounded, FloatConst, FromPrimitive, Num, NumCast, One, ToPrimitive, Zero,
+};
+
+impl ToPrimitive for f16 {
+    #[inline]
+    fn to_i64(&self) -> Option<i64> {
+        Self::to_f32(*self).to_i64()
+    }
+    #[inline]
+    fn to_u64(&self) -> Option<u64> {
+        Self::to_f32(*self).to_u64()
+    }
+    #[inline]
+    fn to_i8(&self) -> Option<i8> {
+        Self::to_f32(*self).to_i8()
+    }
+    #[inline]
+    fn to_u8(&self) -> Option<u8> {
+        Self::to_f32(*self).to_u8()
+    }
+    #[inline]
+    fn to_i16(&self) -> Option<i16> {
+        Self::to_f32(*self).to_i16()
+    }
+    #[inline]
+    fn to_u16(&self) -> Option<u16> {
+        Self::to_f32(*self).to_u16()
+    }
+    #[inline]
+    fn to_i32(&self) -> Option<i32> {
+        Self::to_f32(*self).to_i32()
+    }
+    #[inline]
+    fn to_u32(&self) -> Option<u32> {
+        Self::to_f32(*self).to_u32()
+    }
+    #[inline]
+    fn to_f32(&self) -> Option<f32> {
+        Some(Self::to_f32(*self))
+    }
+    #[inline]
+    fn to_f64(&self) -> Option<f64> {
+        Some(Self::to_f64(*self))
+    }
+}
+
+impl FromPrimitive for f16 {
+    #[inline]
+    fn from_i64(n: i64) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+    #[inline]
+    fn from_u64(n: u64) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+    #[inline]
+    fn from_i8(n: i8) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+    #[inline]
+    fn from_u8(n: u8) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+    #[inline]
+    fn from_i16(n: i16) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+    #[inline]
+    fn from_u16(n: u16) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+    #[inline]
+    fn from_i32(n: i32) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+    #[inline]
+    fn from_u32(n: u32) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+    #[inline]
+    fn from_f32(n: f32) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+    #[inline]
+    fn from_f64(n: f64) -> Option<Self> {
+        n.to_f64().map(Self::from_f64)
+    }
+}
+
+impl Num for f16 {
+    type FromStrRadixErr = <f32 as Num>::FromStrRadixErr;
+
+    #[inline]
+    fn from_str_radix(str: &str, radix: u32) -> Result<Self, Self::FromStrRadixErr> {
+        Ok(Self::from_f32(f32::from_str_radix(str, radix)?))
+    }
+}
+
+impl One for f16 {
+    #[inline]
+    fn one() -> Self {
+        Self::ONE
+    }
+}
+
+impl Zero for f16 {
+    #[inline]
+    fn zero() -> Self {
+        Self::ZERO
+    }
+
+    #[inline]
+    fn is_zero(&self) -> bool {
+        *self == Self::ZERO
+    }
+}
+
+impl NumCast for f16 {
+    #[inline]
+    fn from<T: ToPrimitive>(n: T) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+}
+
+impl num_traits::float::FloatCore for f16 {
+    #[inline]
+    fn infinity() -> Self {
+        Self::INFINITY
+    }
+
+    #[inline]
+    fn neg_infinity() -> Self {
+        Self::NEG_INFINITY
+    }
+
+    #[inline]
+    fn nan() -> Self {
+        Self::NAN
+    }
+
+    #[inline]
+    fn neg_zero() -> Self {
+        Self::NEG_ZERO
+    }
+
+    #[inline]
+    fn min_value() -> Self {
+        Self::MIN
+    }
+
+    #[inline]
+    fn min_positive_value() -> Self {
+        Self::MIN_POSITIVE
+    }
+
+    #[inline]
+    fn epsilon() -> Self {
+        Self::EPSILON
+    }
+
+    #[inline]
+    fn max_value() -> Self {
+        Self::MAX
+    }
+
+    #[inline]
+    fn is_nan(self) -> bool {
+        self.is_nan()
+    }
+
+    #[inline]
+    fn is_infinite(self) -> bool {
+        self.is_infinite()
+    }
+
+    #[inline]
+    fn is_finite(self) -> bool {
+        self.is_finite()
+    }
+
+    #[inline]
+    fn is_normal(self) -> bool {
+        self.is_normal()
+    }
+
+    #[inline]
+    fn classify(self) -> FpCategory {
+        self.classify()
+    }
+
+    #[inline]
+    fn floor(self) -> Self {
+        Self::from_f32(self.to_f32().floor())
+    }
+
+    #[inline]
+    fn ceil(self) -> Self {
+        Self::from_f32(self.to_f32().ceil())
+    }
+
+    #[inline]
+    fn round(self) -> Self {
+        Self::from_f32(self.to_f32().round())
+    }
+
+    #[inline]
+    fn trunc(self) -> Self {
+        Self::from_f32(self.to_f32().trunc())
+    }
+
+    #[inline]
+    fn fract(self) -> Self {
+        Self::from_f32(self.to_f32().fract())
+    }
+
+    #[inline]
+    fn abs(self) -> Self {
+        Self::from_bits(self.to_bits() & 0x7FFF)
+    }
+
+    #[inline]
+    fn signum(self) -> Self {
+        self.signum()
+    }
+
+    #[inline]
+    fn is_sign_positive(self) -> bool {
+        self.is_sign_positive()
+    }
+
+    #[inline]
+    fn is_sign_negative(self) -> bool {
+        self.is_sign_negative()
+    }
+
+    fn min(self, other: Self) -> Self {
+        match self.partial_cmp(&other) {
+            None => {
+                if self.is_nan() {
+                    other
+                } else {
+                    self
+                }
+            }
+            Some(Ordering::Greater) | Some(Ordering::Equal) => other,
+            Some(Ordering::Less) => self,
+        }
+    }
+
+    fn max(self, other: Self) -> Self {
+        match self.partial_cmp(&other) {
+            None => {
+                if self.is_nan() {
+                    other
+                } else {
+                    self
+                }
+            }
+            Some(Ordering::Greater) | Some(Ordering::Equal) => self,
+            Some(Ordering::Less) => other,
+        }
+    }
+
+    #[inline]
+    fn recip(self) -> Self {
+        Self::from_f32(self.to_f32().recip())
+    }
+
+    #[inline]
+    fn powi(self, exp: i32) -> Self {
+        Self::from_f32(self.to_f32().powi(exp))
+    }
+
+    #[inline]
+    fn to_degrees(self) -> Self {
+        Self::from_f32(self.to_f32().to_degrees())
+    }
+
+    #[inline]
+    fn to_radians(self) -> Self {
+        Self::from_f32(self.to_f32().to_radians())
+    }
+
+    #[inline]
+    fn integer_decode(self) -> (u64, i16, i8) {
+        num_traits::float::FloatCore::integer_decode(self.to_f32())
+    }
+}
+
+impl num_traits::float::Float for f16 {
+    #[inline]
+    fn nan() -> Self {
+        Self::NAN
+    }
+
+    #[inline]
+    fn infinity() -> Self {
+        Self::INFINITY
+    }
+
+    #[inline]
+    fn neg_infinity() -> Self {
+        Self::NEG_INFINITY
+    }
+
+    #[inline]
+    fn neg_zero() -> Self {
+        Self::NEG_ZERO
+    }
+
+    #[inline]
+    fn min_value() -> Self {
+        Self::MIN
+    }
+
+    #[inline]
+    fn min_positive_value() -> Self {
+        Self::MIN_POSITIVE
+    }
+
+    #[inline]
+    fn epsilon() -> Self {
+        Self::EPSILON
+    }
+
+    #[inline]
+    fn max_value() -> Self {
+        Self::MAX
+    }
+
+    #[inline]
+    fn is_nan(self) -> bool {
+        self.is_nan()
+    }
+
+    #[inline]
+    fn is_infinite(self) -> bool {
+        self.is_infinite()
+    }
+
+    #[inline]
+    fn is_finite(self) -> bool {
+        self.is_finite()
+    }
+
+    #[inline]
+    fn is_normal(self) -> bool {
+        self.is_normal()
+    }
+
+    #[inline]
+    fn classify(self) -> FpCategory {
+        self.classify()
+    }
+
+    #[inline]
+    fn floor(self) -> Self {
+        Self::from_f32(self.to_f32().floor())
+    }
+
+    #[inline]
+    fn ceil(self) -> Self {
+        Self::from_f32(self.to_f32().ceil())
+    }
+
+    #[inline]
+    fn round(self) -> Self {
+        Self::from_f32(self.to_f32().round())
+    }
+
+    #[inline]
+    fn trunc(self) -> Self {
+        Self::from_f32(self.to_f32().trunc())
+    }
+
+    #[inline]
+    fn fract(self) -> Self {
+        Self::from_f32(self.to_f32().fract())
+    }
+
+    #[inline]
+    fn abs(self) -> Self {
+        Self::from_f32(self.to_f32().abs())
+    }
+
+    #[inline]
+    fn signum(self) -> Self {
+        Self::from_f32(self.to_f32().signum())
+    }
+
+    #[inline]
+    fn is_sign_positive(self) -> bool {
+        self.is_sign_positive()
+    }
+
+    #[inline]
+    fn is_sign_negative(self) -> bool {
+        self.is_sign_negative()
+    }
+
+    #[inline]
+    fn mul_add(self, a: Self, b: Self) -> Self {
+        Self::from_f32(self.to_f32().mul_add(a.to_f32(), b.to_f32()))
+    }
+
+    #[inline]
+    fn recip(self) -> Self {
+        Self::from_f32(self.to_f32().recip())
+    }
+
+    #[inline]
+    fn powi(self, n: i32) -> Self {
+        Self::from_f32(self.to_f32().powi(n))
+    }
+
+    #[inline]
+    fn powf(self, n: Self) -> Self {
+        Self::from_f32(self.to_f32().powf(n.to_f32()))
+    }
+
+    #[inline]
+    fn sqrt(self) -> Self {
+        Self::from_f32(self.to_f32().sqrt())
+    }
+
+    #[inline]
+    fn exp(self) -> Self {
+        Self::from_f32(self.to_f32().exp())
+    }
+
+    #[inline]
+    fn exp2(self) -> Self {
+        Self::from_f32(self.to_f32().exp2())
+    }
+
+    #[inline]
+    fn ln(self) -> Self {
+        Self::from_f32(self.to_f32().ln())
+    }
+
+    #[inline]
+    fn log(self, base: Self) -> Self {
+        Self::from_f32(self.to_f32().log(base.to_f32()))
+    }
+
+    #[inline]
+    fn log2(self) -> Self {
+        Self::from_f32(self.to_f32().log2())
+    }
+
+    #[inline]
+    fn log10(self) -> Self {
+        Self::from_f32(self.to_f32().log10())
+    }
+
+    #[inline]
+    fn to_degrees(self) -> Self {
+        Self::from_f32(self.to_f32().to_degrees())
+    }
+
+    #[inline]
+    fn to_radians(self) -> Self {
+        Self::from_f32(self.to_f32().to_radians())
+    }
+
+    #[inline]
+    fn max(self, other: Self) -> Self {
+        self.max(other)
+    }
+
+    #[inline]
+    fn min(self, other: Self) -> Self {
+        self.min(other)
+    }
+
+    #[inline]
+    fn abs_sub(self, other: Self) -> Self {
+        Self::from_f32((self.to_f32() - other.to_f32()).max(0.0))
+    }
+
+    #[inline]
+    fn cbrt(self) -> Self {
+        Self::from_f32(self.to_f32().cbrt())
+    }
+
+    #[inline]
+    fn hypot(self, other: Self) -> Self {
+        Self::from_f32(self.to_f32().hypot(other.to_f32()))
+    }
+
+    #[inline]
+    fn sin(self) -> Self {
+        Self::from_f32(self.to_f32().sin())
+    }
+
+    #[inline]
+    fn cos(self) -> Self {
+        Self::from_f32(self.to_f32().cos())
+    }
+
+    #[inline]
+    fn tan(self) -> Self {
+        Self::from_f32(self.to_f32().tan())
+    }
+
+    #[inline]
+    fn asin(self) -> Self {
+        Self::from_f32(self.to_f32().asin())
+    }
+
+    #[inline]
+    fn acos(self) -> Self {
+        Self::from_f32(self.to_f32().acos())
+    }
+
+    #[inline]
+    fn atan(self) -> Self {
+        Self::from_f32(self.to_f32().atan())
+    }
+
+    #[inline]
+    fn atan2(self, other: Self) -> Self {
+        Self::from_f32(self.to_f32().atan2(other.to_f32()))
+    }
+
+    #[inline]
+    fn sin_cos(self) -> (Self, Self) {
+        let (sin, cos) = self.to_f32().sin_cos();
+        (Self::from_f32(sin), Self::from_f32(cos))
+    }
+
+    #[inline]
+    fn exp_m1(self) -> Self {
+        Self::from_f32(self.to_f32().exp_m1())
+    }
+
+    #[inline]
+    fn ln_1p(self) -> Self {
+        Self::from_f32(self.to_f32().ln_1p())
+    }
+
+    #[inline]
+    fn sinh(self) -> Self {
+        Self::from_f32(self.to_f32().sinh())
+    }
+
+    #[inline]
+    fn cosh(self) -> Self {
+        Self::from_f32(self.to_f32().cosh())
+    }
+
+    #[inline]
+    fn tanh(self) -> Self {
+        Self::from_f32(self.to_f32().tanh())
+    }
+
+    #[inline]
+    fn asinh(self) -> Self {
+        Self::from_f32(self.to_f32().asinh())
+    }
+
+    #[inline]
+    fn acosh(self) -> Self {
+        Self::from_f32(self.to_f32().acosh())
+    }
+
+    #[inline]
+    fn atanh(self) -> Self {
+        Self::from_f32(self.to_f32().atanh())
+    }
+
+    #[inline]
+    fn integer_decode(self) -> (u64, i16, i8) {
+        num_traits::float::Float::integer_decode(self.to_f32())
+    }
+}
+
+impl FloatConst for f16 {
+    #[inline]
+    fn E() -> Self {
+        Self::E
+    }
+
+    #[inline]
+    fn FRAC_1_PI() -> Self {
+        Self::FRAC_1_PI
+    }
+
+    #[inline]
+    fn FRAC_1_SQRT_2() -> Self {
+        Self::FRAC_1_SQRT_2
+    }
+
+    #[inline]
+    fn FRAC_2_PI() -> Self {
+        Self::FRAC_2_PI
+    }
+
+    #[inline]
+    fn FRAC_2_SQRT_PI() -> Self {
+        Self::FRAC_2_SQRT_PI
+    }
+
+    #[inline]
+    fn FRAC_PI_2() -> Self {
+        Self::FRAC_PI_2
+    }
+
+    #[inline]
+    fn FRAC_PI_3() -> Self {
+        Self::FRAC_PI_3
+    }
+
+    #[inline]
+    fn FRAC_PI_4() -> Self {
+        Self::FRAC_PI_4
+    }
+
+    #[inline]
+    fn FRAC_PI_6() -> Self {
+        Self::FRAC_PI_6
+    }
+
+    #[inline]
+    fn FRAC_PI_8() -> Self {
+        Self::FRAC_PI_8
+    }
+
+    #[inline]
+    fn LN_10() -> Self {
+        Self::LN_10
+    }
+
+    #[inline]
+    fn LN_2() -> Self {
+        Self::LN_2
+    }
+
+    #[inline]
+    fn LOG10_E() -> Self {
+        Self::LOG10_E
+    }
+
+    #[inline]
+    fn LOG2_E() -> Self {
+        Self::LOG2_E
+    }
+
+    #[inline]
+    fn PI() -> Self {
+        Self::PI
+    }
+
+    fn SQRT_2() -> Self {
+        Self::SQRT_2
+    }
+
+    #[inline]
+    fn LOG10_2() -> Self
+    where
+        Self: Sized + Div<Self, Output = Self>,
+    {
+        Self::LOG10_2
+    }
+
+    #[inline]
+    fn LOG2_10() -> Self
+    where
+        Self: Sized + Div<Self, Output = Self>,
+    {
+        Self::LOG2_10
+    }
+}
+
+impl Bounded for f16 {
+    #[inline]
+    fn min_value() -> Self {
+        f16::MIN
+    }
+
+    #[inline]
+    fn max_value() -> Self {
+        f16::MAX
+    }
+}
+
+macro_rules! impl_as_primitive_to_f16 {
+    ($ty:ty, $meth:ident) => {
+        impl AsPrimitive<$ty> for f16 {
+            #[inline]
+            fn as_(self) -> $ty {
+                self.$meth().as_()
+            }
+        }
+    };
+}
+
+impl_as_primitive_to_f16!(i64, to_f32);
+impl_as_primitive_to_f16!(u64, to_f32);
+impl_as_primitive_to_f16!(i8, to_f32);
+impl_as_primitive_to_f16!(u8, to_f32);
+impl_as_primitive_to_f16!(i16, to_f32);
+impl_as_primitive_to_f16!(u16, to_f32);
+impl_as_primitive_to_f16!(i32, to_f32);
+impl_as_primitive_to_f16!(u32, to_f32);
+impl_as_primitive_to_f16!(f32, to_f32);
+impl_as_primitive_to_f16!(f64, to_f64);
+
+macro_rules! impl_as_primitive_f16_from {
+    ($ty:ty, $meth:ident) => {
+        impl AsPrimitive<f16> for $ty {
+            #[inline]
+            fn as_(self) -> f16 {
+                f16::$meth(self.as_())
+            }
+        }
+    };
+}
+
+impl_as_primitive_f16_from!(i64, from_f32);
+impl_as_primitive_f16_from!(u64, from_f32);
+impl_as_primitive_f16_from!(i8, from_f32);
+impl_as_primitive_f16_from!(u8, from_f32);
+impl_as_primitive_f16_from!(i16, from_f32);
+impl_as_primitive_f16_from!(u16, from_f32);
+impl_as_primitive_f16_from!(i32, from_f32);
+impl_as_primitive_f16_from!(u32, from_f32);
+impl_as_primitive_f16_from!(f32, from_f32);
+impl_as_primitive_f16_from!(f64, from_f64);
+
+impl ToPrimitive for bf16 {
+    #[inline]
+    fn to_i64(&self) -> Option<i64> {
+        Self::to_f32(*self).to_i64()
+    }
+    #[inline]
+    fn to_u64(&self) -> Option<u64> {
+        Self::to_f32(*self).to_u64()
+    }
+    #[inline]
+    fn to_i8(&self) -> Option<i8> {
+        Self::to_f32(*self).to_i8()
+    }
+    #[inline]
+    fn to_u8(&self) -> Option<u8> {
+        Self::to_f32(*self).to_u8()
+    }
+    #[inline]
+    fn to_i16(&self) -> Option<i16> {
+        Self::to_f32(*self).to_i16()
+    }
+    #[inline]
+    fn to_u16(&self) -> Option<u16> {
+        Self::to_f32(*self).to_u16()
+    }
+    #[inline]
+    fn to_i32(&self) -> Option<i32> {
+        Self::to_f32(*self).to_i32()
+    }
+    #[inline]
+    fn to_u32(&self) -> Option<u32> {
+        Self::to_f32(*self).to_u32()
+    }
+    #[inline]
+    fn to_f32(&self) -> Option<f32> {
+        Some(Self::to_f32(*self))
+    }
+    #[inline]
+    fn to_f64(&self) -> Option<f64> {
+        Some(Self::to_f64(*self))
+    }
+}
+
+impl FromPrimitive for bf16 {
+    #[inline]
+    fn from_i64(n: i64) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+    #[inline]
+    fn from_u64(n: u64) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+    #[inline]
+    fn from_i8(n: i8) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+    #[inline]
+    fn from_u8(n: u8) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+    #[inline]
+    fn from_i16(n: i16) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+    #[inline]
+    fn from_u16(n: u16) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+    #[inline]
+    fn from_i32(n: i32) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+    #[inline]
+    fn from_u32(n: u32) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+    #[inline]
+    fn from_f32(n: f32) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+    #[inline]
+    fn from_f64(n: f64) -> Option<Self> {
+        n.to_f64().map(Self::from_f64)
+    }
+}
+
+impl Num for bf16 {
+    type FromStrRadixErr = <f32 as Num>::FromStrRadixErr;
+
+    #[inline]
+    fn from_str_radix(str: &str, radix: u32) -> Result<Self, Self::FromStrRadixErr> {
+        Ok(Self::from_f32(f32::from_str_radix(str, radix)?))
+    }
+}
+
+impl One for bf16 {
+    #[inline]
+    fn one() -> Self {
+        Self::ONE
+    }
+}
+
+impl Zero for bf16 {
+    #[inline]
+    fn zero() -> Self {
+        Self::ZERO
+    }
+
+    #[inline]
+    fn is_zero(&self) -> bool {
+        *self == Self::ZERO
+    }
+}
+
+impl NumCast for bf16 {
+    #[inline]
+    fn from<T: ToPrimitive>(n: T) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+}
+
+impl num_traits::float::FloatCore for bf16 {
+    #[inline]
+    fn infinity() -> Self {
+        Self::INFINITY
+    }
+
+    #[inline]
+    fn neg_infinity() -> Self {
+        Self::NEG_INFINITY
+    }
+
+    #[inline]
+    fn nan() -> Self {
+        Self::NAN
+    }
+
+    #[inline]
+    fn neg_zero() -> Self {
+        Self::NEG_ZERO
+    }
+
+    #[inline]
+    fn min_value() -> Self {
+        Self::MIN
+    }
+
+    #[inline]
+    fn min_positive_value() -> Self {
+        Self::MIN_POSITIVE
+    }
+
+    #[inline]
+    fn epsilon() -> Self {
+        Self::EPSILON
+    }
+
+    #[inline]
+    fn max_value() -> Self {
+        Self::MAX
+    }
+
+    #[inline]
+    fn is_nan(self) -> bool {
+        self.is_nan()
+    }
+
+    #[inline]
+    fn is_infinite(self) -> bool {
+        self.is_infinite()
+    }
+
+    #[inline]
+    fn is_finite(self) -> bool {
+        self.is_finite()
+    }
+
+    #[inline]
+    fn is_normal(self) -> bool {
+        self.is_normal()
+    }
+
+    #[inline]
+    fn classify(self) -> FpCategory {
+        self.classify()
+    }
+
+    #[inline]
+    fn floor(self) -> Self {
+        Self::from_f32(self.to_f32().floor())
+    }
+
+    #[inline]
+    fn ceil(self) -> Self {
+        Self::from_f32(self.to_f32().ceil())
+    }
+
+    #[inline]
+    fn round(self) -> Self {
+        Self::from_f32(self.to_f32().round())
+    }
+
+    #[inline]
+    fn trunc(self) -> Self {
+        Self::from_f32(self.to_f32().trunc())
+    }
+
+    #[inline]
+    fn fract(self) -> Self {
+        Self::from_f32(self.to_f32().fract())
+    }
+
+    #[inline]
+    fn abs(self) -> Self {
+        Self::from_bits(self.to_bits() & 0x7FFF)
+    }
+
+    #[inline]
+    fn signum(self) -> Self {
+        self.signum()
+    }
+
+    #[inline]
+    fn is_sign_positive(self) -> bool {
+        self.is_sign_positive()
+    }
+
+    #[inline]
+    fn is_sign_negative(self) -> bool {
+        self.is_sign_negative()
+    }
+
+    fn min(self, other: Self) -> Self {
+        match self.partial_cmp(&other) {
+            None => {
+                if self.is_nan() {
+                    other
+                } else {
+                    self
+                }
+            }
+            Some(Ordering::Greater) | Some(Ordering::Equal) => other,
+            Some(Ordering::Less) => self,
+        }
+    }
+
+    fn max(self, other: Self) -> Self {
+        match self.partial_cmp(&other) {
+            None => {
+                if self.is_nan() {
+                    other
+                } else {
+                    self
+                }
+            }
+            Some(Ordering::Greater) | Some(Ordering::Equal) => self,
+            Some(Ordering::Less) => other,
+        }
+    }
+
+    #[inline]
+    fn recip(self) -> Self {
+        Self::from_f32(self.to_f32().recip())
+    }
+
+    #[inline]
+    fn powi(self, exp: i32) -> Self {
+        Self::from_f32(self.to_f32().powi(exp))
+    }
+
+    #[inline]
+    fn to_degrees(self) -> Self {
+        Self::from_f32(self.to_f32().to_degrees())
+    }
+
+    #[inline]
+    fn to_radians(self) -> Self {
+        Self::from_f32(self.to_f32().to_radians())
+    }
+
+    #[inline]
+    fn integer_decode(self) -> (u64, i16, i8) {
+        num_traits::float::FloatCore::integer_decode(self.to_f32())
+    }
+}
+
+impl num_traits::float::Float for bf16 {
+    #[inline]
+    fn nan() -> Self {
+        Self::NAN
+    }
+
+    #[inline]
+    fn infinity() -> Self {
+        Self::INFINITY
+    }
+
+    #[inline]
+    fn neg_infinity() -> Self {
+        Self::NEG_INFINITY
+    }
+
+    #[inline]
+    fn neg_zero() -> Self {
+        Self::NEG_ZERO
+    }
+
+    #[inline]
+    fn min_value() -> Self {
+        Self::MIN
+    }
+
+    #[inline]
+    fn min_positive_value() -> Self {
+        Self::MIN_POSITIVE
+    }
+
+    #[inline]
+    fn epsilon() -> Self {
+        Self::EPSILON
+    }
+
+    #[inline]
+    fn max_value() -> Self {
+        Self::MAX
+    }
+
+    #[inline]
+    fn is_nan(self) -> bool {
+        self.is_nan()
+    }
+
+    #[inline]
+    fn is_infinite(self) -> bool {
+        self.is_infinite()
+    }
+
+    #[inline]
+    fn is_finite(self) -> bool {
+        self.is_finite()
+    }
+
+    #[inline]
+    fn is_normal(self) -> bool {
+        self.is_normal()
+    }
+
+    #[inline]
+    fn classify(self) -> FpCategory {
+        self.classify()
+    }
+
+    #[inline]
+    fn floor(self) -> Self {
+        Self::from_f32(self.to_f32().floor())
+    }
+
+    #[inline]
+    fn ceil(self) -> Self {
+        Self::from_f32(self.to_f32().ceil())
+    }
+
+    #[inline]
+    fn round(self) -> Self {
+        Self::from_f32(self.to_f32().round())
+    }
+
+    #[inline]
+    fn trunc(self) -> Self {
+        Self::from_f32(self.to_f32().trunc())
+    }
+
+    #[inline]
+    fn fract(self) -> Self {
+        Self::from_f32(self.to_f32().fract())
+    }
+
+    #[inline]
+    fn abs(self) -> Self {
+        Self::from_f32(self.to_f32().abs())
+    }
+
+    #[inline]
+    fn signum(self) -> Self {
+        Self::from_f32(self.to_f32().signum())
+    }
+
+    #[inline]
+    fn is_sign_positive(self) -> bool {
+        self.is_sign_positive()
+    }
+
+    #[inline]
+    fn is_sign_negative(self) -> bool {
+        self.is_sign_negative()
+    }
+
+    #[inline]
+    fn mul_add(self, a: Self, b: Self) -> Self {
+        Self::from_f32(self.to_f32().mul_add(a.to_f32(), b.to_f32()))
+    }
+
+    #[inline]
+    fn recip(self) -> Self {
+        Self::from_f32(self.to_f32().recip())
+    }
+
+    #[inline]
+    fn powi(self, n: i32) -> Self {
+        Self::from_f32(self.to_f32().powi(n))
+    }
+
+    #[inline]
+    fn powf(self, n: Self) -> Self {
+        Self::from_f32(self.to_f32().powf(n.to_f32()))
+    }
+
+    #[inline]
+    fn sqrt(self) -> Self {
+        Self::from_f32(self.to_f32().sqrt())
+    }
+
+    #[inline]
+    fn exp(self) -> Self {
+        Self::from_f32(self.to_f32().exp())
+    }
+
+    #[inline]
+    fn exp2(self) -> Self {
+        Self::from_f32(self.to_f32().exp2())
+    }
+
+    #[inline]
+    fn ln(self) -> Self {
+        Self::from_f32(self.to_f32().ln())
+    }
+
+    #[inline]
+    fn log(self, base: Self) -> Self {
+        Self::from_f32(self.to_f32().log(base.to_f32()))
+    }
+
+    #[inline]
+    fn log2(self) -> Self {
+        Self::from_f32(self.to_f32().log2())
+    }
+
+    #[inline]
+    fn log10(self) -> Self {
+        Self::from_f32(self.to_f32().log10())
+    }
+
+    #[inline]
+    fn to_degrees(self) -> Self {
+        Self::from_f32(self.to_f32().to_degrees())
+    }
+
+    #[inline]
+    fn to_radians(self) -> Self {
+        Self::from_f32(self.to_f32().to_radians())
+    }
+
+    #[inline]
+    fn max(self, other: Self) -> Self {
+        self.max(other)
+    }
+
+    #[inline]
+    fn min(self, other: Self) -> Self {
+        self.min(other)
+    }
+
+    #[inline]
+    fn abs_sub(self, other: Self) -> Self {
+        Self::from_f32((self.to_f32() - other.to_f32()).max(0.0))
+    }
+
+    #[inline]
+    fn cbrt(self) -> Self {
+        Self::from_f32(self.to_f32().cbrt())
+    }
+
+    #[inline]
+    fn hypot(self, other: Self) -> Self {
+        Self::from_f32(self.to_f32().hypot(other.to_f32()))
+    }
+
+    #[inline]
+    fn sin(self) -> Self {
+        Self::from_f32(self.to_f32().sin())
+    }
+
+    #[inline]
+    fn cos(self) -> Self {
+        Self::from_f32(self.to_f32().cos())
+    }
+
+    #[inline]
+    fn tan(self) -> Self {
+        Self::from_f32(self.to_f32().tan())
+    }
+
+    #[inline]
+    fn asin(self) -> Self {
+        Self::from_f32(self.to_f32().asin())
+    }
+
+    #[inline]
+    fn acos(self) -> Self {
+        Self::from_f32(self.to_f32().acos())
+    }
+
+    #[inline]
+    fn atan(self) -> Self {
+        Self::from_f32(self.to_f32().atan())
+    }
+
+    #[inline]
+    fn atan2(self, other: Self) -> Self {
+        Self::from_f32(self.to_f32().atan2(other.to_f32()))
+    }
+
+    #[inline]
+    fn sin_cos(self) -> (Self, Self) {
+        let (sin, cos) = self.to_f32().sin_cos();
+        (Self::from_f32(sin), Self::from_f32(cos))
+    }
+
+    #[inline]
+    fn exp_m1(self) -> Self {
+        Self::from_f32(self.to_f32().exp_m1())
+    }
+
+    #[inline]
+    fn ln_1p(self) -> Self {
+        Self::from_f32(self.to_f32().ln_1p())
+    }
+
+    #[inline]
+    fn sinh(self) -> Self {
+        Self::from_f32(self.to_f32().sinh())
+    }
+
+    #[inline]
+    fn cosh(self) -> Self {
+        Self::from_f32(self.to_f32().cosh())
+    }
+
+    #[inline]
+    fn tanh(self) -> Self {
+        Self::from_f32(self.to_f32().tanh())
+    }
+
+    #[inline]
+    fn asinh(self) -> Self {
+        Self::from_f32(self.to_f32().asinh())
+    }
+
+    #[inline]
+    fn acosh(self) -> Self {
+        Self::from_f32(self.to_f32().acosh())
+    }
+
+    #[inline]
+    fn atanh(self) -> Self {
+        Self::from_f32(self.to_f32().atanh())
+    }
+
+    #[inline]
+    fn integer_decode(self) -> (u64, i16, i8) {
+        num_traits::float::Float::integer_decode(self.to_f32())
+    }
+}
+
+impl FloatConst for bf16 {
+    #[inline]
+    fn E() -> Self {
+        Self::E
+    }
+
+    #[inline]
+    fn FRAC_1_PI() -> Self {
+        Self::FRAC_1_PI
+    }
+
+    #[inline]
+    fn FRAC_1_SQRT_2() -> Self {
+        Self::FRAC_1_SQRT_2
+    }
+
+    #[inline]
+    fn FRAC_2_PI() -> Self {
+        Self::FRAC_2_PI
+    }
+
+    #[inline]
+    fn FRAC_2_SQRT_PI() -> Self {
+        Self::FRAC_2_SQRT_PI
+    }
+
+    #[inline]
+    fn FRAC_PI_2() -> Self {
+        Self::FRAC_PI_2
+    }
+
+    #[inline]
+    fn FRAC_PI_3() -> Self {
+        Self::FRAC_PI_3
+    }
+
+    #[inline]
+    fn FRAC_PI_4() -> Self {
+        Self::FRAC_PI_4
+    }
+
+    #[inline]
+    fn FRAC_PI_6() -> Self {
+        Self::FRAC_PI_6
+    }
+
+    #[inline]
+    fn FRAC_PI_8() -> Self {
+        Self::FRAC_PI_8
+    }
+
+    #[inline]
+    fn LN_10() -> Self {
+        Self::LN_10
+    }
+
+    #[inline]
+    fn LN_2() -> Self {
+        Self::LN_2
+    }
+
+    #[inline]
+    fn LOG10_E() -> Self {
+        Self::LOG10_E
+    }
+
+    #[inline]
+    fn LOG2_E() -> Self {
+        Self::LOG2_E
+    }
+
+    #[inline]
+    fn PI() -> Self {
+        Self::PI
+    }
+
+    #[inline]
+    fn SQRT_2() -> Self {
+        Self::SQRT_2
+    }
+
+    #[inline]
+    fn LOG10_2() -> Self
+    where
+        Self: Sized + Div<Self, Output = Self>,
+    {
+        Self::LOG10_2
+    }
+
+    #[inline]
+    fn LOG2_10() -> Self
+    where
+        Self: Sized + Div<Self, Output = Self>,
+    {
+        Self::LOG2_10
+    }
+}
+
+impl Bounded for bf16 {
+    #[inline]
+    fn min_value() -> Self {
+        bf16::MIN
+    }
+
+    #[inline]
+    fn max_value() -> Self {
+        bf16::MAX
+    }
+}
+
+macro_rules! impl_as_primitive_to_bf16 {
+    ($ty:ty, $meth:ident) => {
+        impl AsPrimitive<$ty> for bf16 {
+            #[inline]
+            fn as_(self) -> $ty {
+                self.$meth().as_()
+            }
+        }
+    };
+}
+
+impl_as_primitive_to_bf16!(i64, to_f32);
+impl_as_primitive_to_bf16!(u64, to_f32);
+impl_as_primitive_to_bf16!(i8, to_f32);
+impl_as_primitive_to_bf16!(u8, to_f32);
+impl_as_primitive_to_bf16!(i16, to_f32);
+impl_as_primitive_to_bf16!(u16, to_f32);
+impl_as_primitive_to_bf16!(i32, to_f32);
+impl_as_primitive_to_bf16!(u32, to_f32);
+impl_as_primitive_to_bf16!(f32, to_f32);
+impl_as_primitive_to_bf16!(f64, to_f64);
+
+macro_rules! impl_as_primitive_bf16_from {
+    ($ty:ty, $meth:ident) => {
+        impl AsPrimitive<bf16> for $ty {
+            #[inline]
+            fn as_(self) -> bf16 {
+                bf16::$meth(self.as_())
+            }
+        }
+    };
+}
+
+impl_as_primitive_bf16_from!(i64, from_f32);
+impl_as_primitive_bf16_from!(u64, from_f32);
+impl_as_primitive_bf16_from!(i8, from_f32);
+impl_as_primitive_bf16_from!(u8, from_f32);
+impl_as_primitive_bf16_from!(i16, from_f32);
+impl_as_primitive_bf16_from!(u16, from_f32);
+impl_as_primitive_bf16_from!(i32, from_f32);
+impl_as_primitive_bf16_from!(u32, from_f32);
+impl_as_primitive_bf16_from!(f32, from_f32);
+impl_as_primitive_bf16_from!(f64, from_f64);
diff --git a/third_party/rust/half/src/slice.rs b/third_party/rust/half/src/slice.rs
new file mode 100644
index 0000000000..3157e6a355
--- /dev/null
+++ b/third_party/rust/half/src/slice.rs
@@ -0,0 +1,952 @@
+//! Contains utility functions and traits to convert between slices of [`u16`] bits and [`f16`] or
+//! [`bf16`] numbers.
+//!
+//! The utility [`HalfBitsSliceExt`] sealed extension trait is implemented for `[u16]` slices,
+//! while the utility [`HalfFloatSliceExt`] sealed extension trait is implemented for both `[f16]`
+//! and `[bf16]` slices. These traits provide efficient conversions and reinterpret casting of
+//! larger buffers of floating point values, and are automatically included in the
+//! [`prelude`][crate::prelude] module.
+
+use crate::{bf16, binary16::convert, f16};
+#[cfg(feature = "alloc")]
+use alloc::vec::Vec;
+use core::slice;
+
+/// Extensions to `[f16]` and `[bf16]` slices to support conversion and reinterpret operations.
+///
+/// This trait is sealed and cannot be implemented outside of this crate.
+pub trait HalfFloatSliceExt: private::SealedHalfFloatSlice {
+    /// Reinterprets a slice of [`f16`] or [`bf16`] numbers as a slice of [`u16`] bits.
+    ///
+    /// This is a zero-copy operation. The reinterpreted slice has the same lifetime and memory
+    /// location as `self`.
+    ///
+    /// # Examples
+    ///
+    /// ```rust
+    /// # use half::prelude::*;
+    /// let float_buffer = [f16::from_f32(1.), f16::from_f32(2.), f16::from_f32(3.)];
+    /// let int_buffer = float_buffer.reinterpret_cast();
+    ///
+    /// assert_eq!(int_buffer, [float_buffer[0].to_bits(), float_buffer[1].to_bits(), float_buffer[2].to_bits()]);
+    /// ```
+    fn reinterpret_cast(&self) -> &[u16];
+
+    /// Reinterprets a mutable slice of [`f16`] or [`bf16`] numbers as a mutable slice of [`u16`].
+    /// bits
+    ///
+    /// This is a zero-copy operation. The transmuted slice has the same lifetime as the original,
+    /// which prevents mutating `self` as long as the returned `&mut [u16]` is borrowed.
+    ///
+    /// # Examples
+    ///
+    /// ```rust
+    /// # use half::prelude::*;
+    /// let mut float_buffer = [f16::from_f32(1.), f16::from_f32(2.), f16::from_f32(3.)];
+    ///
+    /// {
+    ///     let int_buffer = float_buffer.reinterpret_cast_mut();
+    ///
+    ///     assert_eq!(int_buffer, [f16::from_f32(1.).to_bits(), f16::from_f32(2.).to_bits(), f16::from_f32(3.).to_bits()]);
+    ///
+    ///     // Mutating the u16 slice will mutating the original
+    ///     int_buffer[0] = 0;
+    /// }
+    ///
+    /// // Note that we need to drop int_buffer before using float_buffer again or we will get a borrow error.
+    /// assert_eq!(float_buffer, [f16::from_f32(0.), f16::from_f32(2.), f16::from_f32(3.)]);
+    /// ```
+    fn reinterpret_cast_mut(&mut self) -> &mut [u16];
+
+    /// Converts all of the elements of a `[f32]` slice into [`f16`] or [`bf16`] values in `self`.
+    ///
+    /// The length of `src` must be the same as `self`.
+    ///
+    /// The conversion operation is vectorized over the slice, meaning the conversion may be more
+    /// efficient than converting individual elements on some hardware that supports SIMD
+    /// conversions. See [crate documentation](crate) for more information on hardware conversion
+    /// support.
+    ///
+    /// # Panics
+    ///
+    /// This function will panic if the two slices have different lengths.
+    ///
+    /// # Examples
+    /// ```rust
+    /// # use half::prelude::*;
+    /// // Initialize an empty buffer
+    /// let mut buffer = [0u16; 4];
+    /// let buffer = buffer.reinterpret_cast_mut::<f16>();
+    ///
+    /// let float_values = [1., 2., 3., 4.];
+    ///
+    /// // Now convert
+    /// buffer.convert_from_f32_slice(&float_values);
+    ///
+    /// assert_eq!(buffer, [f16::from_f32(1.), f16::from_f32(2.), f16::from_f32(3.), f16::from_f32(4.)]);
+    /// ```
+    fn convert_from_f32_slice(&mut self, src: &[f32]);
+
+    /// Converts all of the elements of a `[f64]` slice into [`f16`] or [`bf16`] values in `self`.
+    ///
+    /// The length of `src` must be the same as `self`.
+    ///
+    /// The conversion operation is vectorized over the slice, meaning the conversion may be more
+    /// efficient than converting individual elements on some hardware that supports SIMD
+    /// conversions. See [crate documentation](crate) for more information on hardware conversion
+    /// support.
+    ///
+    /// # Panics
+    ///
+    /// This function will panic if the two slices have different lengths.
+    ///
+    /// # Examples
+    /// ```rust
+    /// # use half::prelude::*;
+    /// // Initialize an empty buffer
+    /// let mut buffer = [0u16; 4];
+    /// let buffer = buffer.reinterpret_cast_mut::<f16>();
+    ///
+    /// let float_values = [1., 2., 3., 4.];
+    ///
+    /// // Now convert
+    /// buffer.convert_from_f64_slice(&float_values);
+    ///
+    /// assert_eq!(buffer, [f16::from_f64(1.), f16::from_f64(2.), f16::from_f64(3.), f16::from_f64(4.)]);
+    /// ```
+    fn convert_from_f64_slice(&mut self, src: &[f64]);
+
+    /// Converts all of the [`f16`] or [`bf16`] elements of `self` into [`f32`] values in `dst`.
+    ///
+    /// The length of `src` must be the same as `self`.
+    ///
+    /// The conversion operation is vectorized over the slice, meaning the conversion may be more
+    /// efficient than converting individual elements on some hardware that supports SIMD
+    /// conversions. See [crate documentation](crate) for more information on hardware conversion
+    /// support.
+    ///
+    /// # Panics
+    ///
+    /// This function will panic if the two slices have different lengths.
+    ///
+    /// # Examples
+    /// ```rust
+    /// # use half::prelude::*;
+    /// // Initialize an empty buffer
+    /// let mut buffer = [0f32; 4];
+    ///
+    /// let half_values = [f16::from_f32(1.), f16::from_f32(2.), f16::from_f32(3.), f16::from_f32(4.)];
+    ///
+    /// // Now convert
+    /// half_values.convert_to_f32_slice(&mut buffer);
+    ///
+    /// assert_eq!(buffer, [1., 2., 3., 4.]);
+    /// ```
+    fn convert_to_f32_slice(&self, dst: &mut [f32]);
+
+    /// Converts all of the [`f16`] or [`bf16`] elements of `self` into [`f64`] values in `dst`.
+    ///
+    /// The length of `src` must be the same as `self`.
+    ///
+    /// The conversion operation is vectorized over the slice, meaning the conversion may be more
+    /// efficient than converting individual elements on some hardware that supports SIMD
+    /// conversions. See [crate documentation](crate) for more information on hardware conversion
+    /// support.
+    ///
+    /// # Panics
+    ///
+    /// This function will panic if the two slices have different lengths.
+    ///
+    /// # Examples
+    /// ```rust
+    /// # use half::prelude::*;
+    /// // Initialize an empty buffer
+    /// let mut buffer = [0f64; 4];
+    ///
+    /// let half_values = [f16::from_f64(1.), f16::from_f64(2.), f16::from_f64(3.), f16::from_f64(4.)];
+    ///
+    /// // Now convert
+    /// half_values.convert_to_f64_slice(&mut buffer);
+    ///
+    /// assert_eq!(buffer, [1., 2., 3., 4.]);
+    /// ```
+    fn convert_to_f64_slice(&self, dst: &mut [f64]);
+
+    // Because trait is sealed, we can get away with different interfaces between features.
+
+    /// Converts all of the [`f16`] or [`bf16`] elements of `self` into [`f32`] values in a new
+    /// vector
+    ///
+    /// The conversion operation is vectorized over the slice, meaning the conversion may be more
+    /// efficient than converting individual elements on some hardware that supports SIMD
+    /// conversions. See [crate documentation](crate) for more information on hardware conversion
+    /// support.
+    ///
+    /// This method is only available with the `std` or `alloc` feature.
+    ///
+    /// # Examples
+    /// ```rust
+    /// # use half::prelude::*;
+    /// let half_values = [f16::from_f32(1.), f16::from_f32(2.), f16::from_f32(3.), f16::from_f32(4.)];
+    /// let vec = half_values.to_f32_vec();
+    ///
+    /// assert_eq!(vec, vec![1., 2., 3., 4.]);
+    /// ```
+    #[cfg(any(feature = "alloc", feature = "std"))]
+    #[cfg_attr(docsrs, doc(cfg(feature = "alloc")))]
+    fn to_f32_vec(&self) -> Vec<f32>;
+
+    /// Converts all of the [`f16`] or [`bf16`] elements of `self` into [`f64`] values in a new
+    /// vector.
+    ///
+    /// The conversion operation is vectorized over the slice, meaning the conversion may be more
+    /// efficient than converting individual elements on some hardware that supports SIMD
+    /// conversions. See [crate documentation](crate) for more information on hardware conversion
+    /// support.
+    ///
+    /// This method is only available with the `std` or `alloc` feature.
+    ///
+    /// # Examples
+    /// ```rust
+    /// # use half::prelude::*;
+    /// let half_values = [f16::from_f64(1.), f16::from_f64(2.), f16::from_f64(3.), f16::from_f64(4.)];
+    /// let vec = half_values.to_f64_vec();
+    ///
+    /// assert_eq!(vec, vec![1., 2., 3., 4.]);
+    /// ```
+    #[cfg(feature = "alloc")]
+    #[cfg_attr(docsrs, doc(cfg(feature = "alloc")))]
+    fn to_f64_vec(&self) -> Vec<f64>;
+}
+
+/// Extensions to `[u16]` slices to support reinterpret operations.
+///
+/// This trait is sealed and cannot be implemented outside of this crate.
+pub trait HalfBitsSliceExt: private::SealedHalfBitsSlice {
+    /// Reinterprets a slice of [`u16`] bits as a slice of [`f16`] or [`bf16`] numbers.
+    ///
+    /// `H` is the type to cast to, and must be either the [`f16`] or [`bf16`] type.
+    ///
+    /// This is a zero-copy operation. The reinterpreted slice has the same lifetime and memory
+    /// location as `self`.
+    ///
+    /// # Examples
+    ///
+    /// ```rust
+    /// # use half::prelude::*;
+    /// let int_buffer = [f16::from_f32(1.).to_bits(), f16::from_f32(2.).to_bits(), f16::from_f32(3.).to_bits()];
+    /// let float_buffer: &[f16] = int_buffer.reinterpret_cast();
+    ///
+    /// assert_eq!(float_buffer, [f16::from_f32(1.), f16::from_f32(2.), f16::from_f32(3.)]);
+    ///
+    /// // You may have to specify the cast type directly if the compiler can't infer the type.
+    /// // The following is also valid in Rust.
+    /// let typed_buffer = int_buffer.reinterpret_cast::<f16>();
+    /// ```
+    fn reinterpret_cast<H>(&self) -> &[H]
+    where
+        H: crate::private::SealedHalf;
+
+    /// Reinterprets a mutable slice of [`u16`] bits as a mutable slice of [`f16`] or [`bf16`]
+    /// numbers.
+    ///
+    /// `H` is the type to cast to, and must be either the [`f16`] or [`bf16`] type.
+    ///
+    /// This is a zero-copy operation. The transmuted slice has the same lifetime as the original,
+    /// which prevents mutating `self` as long as the returned `&mut [f16]` is borrowed.
+    ///
+    /// # Examples
+    ///
+    /// ```rust
+    /// # use half::prelude::*;
+    /// let mut int_buffer = [f16::from_f32(1.).to_bits(), f16::from_f32(2.).to_bits(), f16::from_f32(3.).to_bits()];
+    ///
+    /// {
+    ///     let float_buffer: &mut [f16] = int_buffer.reinterpret_cast_mut();
+    ///
+    ///     assert_eq!(float_buffer, [f16::from_f32(1.), f16::from_f32(2.), f16::from_f32(3.)]);
+    ///
+    ///     // Mutating the f16 slice will mutating the original
+    ///     float_buffer[0] = f16::from_f32(0.);
+    /// }
+    ///
+    /// // Note that we need to drop float_buffer before using int_buffer again or we will get a borrow error.
+    /// assert_eq!(int_buffer, [f16::from_f32(0.).to_bits(), f16::from_f32(2.).to_bits(), f16::from_f32(3.).to_bits()]);
+    ///
+    /// // You may have to specify the cast type directly if the compiler can't infer the type.
+    /// // The following is also valid in Rust.
+    /// let typed_buffer = int_buffer.reinterpret_cast_mut::<f16>();
+    /// ```
+    fn reinterpret_cast_mut<H>(&mut self) -> &mut [H]
+    where
+        H: crate::private::SealedHalf;
+}
+
+mod private {
+    use crate::{bf16, f16};
+
+    pub trait SealedHalfFloatSlice {}
+    impl SealedHalfFloatSlice for [f16] {}
+    impl SealedHalfFloatSlice for [bf16] {}
+
+    pub trait SealedHalfBitsSlice {}
+    impl SealedHalfBitsSlice for [u16] {}
+}
+
+impl HalfFloatSliceExt for [f16] {
+    #[inline]
+    fn reinterpret_cast(&self) -> &[u16] {
+        let pointer = self.as_ptr() as *const u16;
+        let length = self.len();
+        // SAFETY: We are reconstructing full length of original slice, using its same lifetime,
+        // and the size of elements are identical
+        unsafe { slice::from_raw_parts(pointer, length) }
+    }
+
+    #[inline]
+    fn reinterpret_cast_mut(&mut self) -> &mut [u16] {
+        let pointer = self.as_ptr() as *mut u16;
+        let length = self.len();
+        // SAFETY: We are reconstructing full length of original slice, using its same lifetime,
+        // and the size of elements are identical
+        unsafe { slice::from_raw_parts_mut(pointer, length) }
+    }
+
+    fn convert_from_f32_slice(&mut self, src: &[f32]) {
+        assert_eq!(
+            self.len(),
+            src.len(),
+            "destination and source slices have different lengths"
+        );
+
+        let mut chunks = src.chunks_exact(4);
+        let mut chunk_count = 0usize; // Not using .enumerate() because we need this value for remainder
+        for chunk in &mut chunks {
+            let vec = convert::f32x4_to_f16x4(chunk);
+            let dst_idx = chunk_count * 4;
+            self[dst_idx..dst_idx + 4].copy_from_slice(vec.reinterpret_cast());
+            chunk_count += 1;
+        }
+
+        // Process remainder
+        if !chunks.remainder().is_empty() {
+            let mut buf = [0f32; 4];
+            buf[..chunks.remainder().len()].copy_from_slice(chunks.remainder());
+            let vec = convert::f32x4_to_f16x4(&buf);
+            let dst_idx = chunk_count * 4;
+            self[dst_idx..dst_idx + chunks.remainder().len()]
+                .copy_from_slice(vec[..chunks.remainder().len()].reinterpret_cast());
+        }
+    }
+
+    fn convert_from_f64_slice(&mut self, src: &[f64]) {
+        assert_eq!(
+            self.len(),
+            src.len(),
+            "destination and source slices have different lengths"
+        );
+
+        let mut chunks = src.chunks_exact(4);
+        let mut chunk_count = 0usize; // Not using .enumerate() because we need this value for remainder
+        for chunk in &mut chunks {
+            let vec = convert::f64x4_to_f16x4(chunk);
+            let dst_idx = chunk_count * 4;
+            self[dst_idx..dst_idx + 4].copy_from_slice(vec.reinterpret_cast());
+            chunk_count += 1;
+        }
+
+        // Process remainder
+        if !chunks.remainder().is_empty() {
+            let mut buf = [0f64; 4];
+            buf[..chunks.remainder().len()].copy_from_slice(chunks.remainder());
+            let vec = convert::f64x4_to_f16x4(&buf);
+            let dst_idx = chunk_count * 4;
+            self[dst_idx..dst_idx + chunks.remainder().len()]
+                .copy_from_slice(vec[..chunks.remainder().len()].reinterpret_cast());
+        }
+    }
+
+    fn convert_to_f32_slice(&self, dst: &mut [f32]) {
+        assert_eq!(
+            self.len(),
+            dst.len(),
+            "destination and source slices have different lengths"
+        );
+
+        let mut chunks = self.chunks_exact(4);
+        let mut chunk_count = 0usize; // Not using .enumerate() because we need this value for remainder
+        for chunk in &mut chunks {
+            let vec = convert::f16x4_to_f32x4(chunk.reinterpret_cast());
+            let dst_idx = chunk_count * 4;
+            dst[dst_idx..dst_idx + 4].copy_from_slice(&vec);
+            chunk_count += 1;
+        }
+
+        // Process remainder
+        if !chunks.remainder().is_empty() {
+            let mut buf = [0u16; 4];
+            buf[..chunks.remainder().len()].copy_from_slice(chunks.remainder().reinterpret_cast());
+            let vec = convert::f16x4_to_f32x4(&buf);
+            let dst_idx = chunk_count * 4;
+            dst[dst_idx..dst_idx + chunks.remainder().len()]
+                .copy_from_slice(&vec[..chunks.remainder().len()]);
+        }
+    }
+
+    fn convert_to_f64_slice(&self, dst: &mut [f64]) {
+        assert_eq!(
+            self.len(),
+            dst.len(),
+            "destination and source slices have different lengths"
+        );
+
+        let mut chunks = self.chunks_exact(4);
+        let mut chunk_count = 0usize; // Not using .enumerate() because we need this value for remainder
+        for chunk in &mut chunks {
+            let vec = convert::f16x4_to_f64x4(chunk.reinterpret_cast());
+            let dst_idx = chunk_count * 4;
+            dst[dst_idx..dst_idx + 4].copy_from_slice(&vec);
+            chunk_count += 1;
+        }
+
+        // Process remainder
+        if !chunks.remainder().is_empty() {
+            let mut buf = [0u16; 4];
+            buf[..chunks.remainder().len()].copy_from_slice(chunks.remainder().reinterpret_cast());
+            let vec = convert::f16x4_to_f64x4(&buf);
+            let dst_idx = chunk_count * 4;
+            dst[dst_idx..dst_idx + chunks.remainder().len()]
+                .copy_from_slice(&vec[..chunks.remainder().len()]);
+        }
+    }
+
+    #[cfg(any(feature = "alloc", feature = "std"))]
+    #[inline]
+    fn to_f32_vec(&self) -> Vec<f32> {
+        let mut vec = Vec::with_capacity(self.len());
+        // SAFETY: convert will initialize every value in the vector without reading them,
+        // so this is safe to do instead of double initialize from resize, and we're setting it to
+        // same value as capacity.
+        unsafe { vec.set_len(self.len()) };
+        self.convert_to_f32_slice(&mut vec);
+        vec
+    }
+
+    #[cfg(any(feature = "alloc", feature = "std"))]
+    #[inline]
+    fn to_f64_vec(&self) -> Vec<f64> {
+        let mut vec = Vec::with_capacity(self.len());
+        // SAFETY: convert will initialize every value in the vector without reading them,
+        // so this is safe to do instead of double initialize from resize, and we're setting it to
+        // same value as capacity.
+        unsafe { vec.set_len(self.len()) };
+        self.convert_to_f64_slice(&mut vec);
+        vec
+    }
+}
+
+impl HalfFloatSliceExt for [bf16] {
+    #[inline]
+    fn reinterpret_cast(&self) -> &[u16] {
+        let pointer = self.as_ptr() as *const u16;
+        let length = self.len();
+        // SAFETY: We are reconstructing full length of original slice, using its same lifetime,
+        // and the size of elements are identical
+        unsafe { slice::from_raw_parts(pointer, length) }
+    }
+
+    #[inline]
+    fn reinterpret_cast_mut(&mut self) -> &mut [u16] {
+        let pointer = self.as_ptr() as *mut u16;
+        let length = self.len();
+        // SAFETY: We are reconstructing full length of original slice, using its same lifetime,
+        // and the size of elements are identical
+        unsafe { slice::from_raw_parts_mut(pointer, length) }
+    }
+
+    fn convert_from_f32_slice(&mut self, src: &[f32]) {
+        assert_eq!(
+            self.len(),
+            src.len(),
+            "destination and source slices have different lengths"
+        );
+
+        // Just use regular loop here until there's any bf16 SIMD support.
+        for (i, f) in src.iter().enumerate() {
+            self[i] = bf16::from_f32(*f);
+        }
+    }
+
+    fn convert_from_f64_slice(&mut self, src: &[f64]) {
+        assert_eq!(
+            self.len(),
+            src.len(),
+            "destination and source slices have different lengths"
+        );
+
+        // Just use regular loop here until there's any bf16 SIMD support.
+        for (i, f) in src.iter().enumerate() {
+            self[i] = bf16::from_f64(*f);
+        }
+    }
+
+    fn convert_to_f32_slice(&self, dst: &mut [f32]) {
+        assert_eq!(
+            self.len(),
+            dst.len(),
+            "destination and source slices have different lengths"
+        );
+
+        // Just use regular loop here until there's any bf16 SIMD support.
+        for (i, f) in self.iter().enumerate() {
+            dst[i] = f.to_f32();
+        }
+    }
+
+    fn convert_to_f64_slice(&self, dst: &mut [f64]) {
+        assert_eq!(
+            self.len(),
+            dst.len(),
+            "destination and source slices have different lengths"
+        );
+
+        // Just use regular loop here until there's any bf16 SIMD support.
+        for (i, f) in self.iter().enumerate() {
+            dst[i] = f.to_f64();
+        }
+    }
+
+    #[cfg(any(feature = "alloc", feature = "std"))]
+    #[inline]
+    fn to_f32_vec(&self) -> Vec<f32> {
+        let mut vec = Vec::with_capacity(self.len());
+        // SAFETY: convert will initialize every value in the vector without reading them,
+        // so this is safe to do instead of double initialize from resize, and we're setting it to
+        // same value as capacity.
+        unsafe { vec.set_len(self.len()) };
+        self.convert_to_f32_slice(&mut vec);
+        vec
+    }
+
+    #[cfg(any(feature = "alloc", feature = "std"))]
+    #[inline]
+    fn to_f64_vec(&self) -> Vec<f64> {
+        let mut vec = Vec::with_capacity(self.len());
+        // SAFETY: convert will initialize every value in the vector without reading them,
+        // so this is safe to do instead of double initialize from resize, and we're setting it to
+        // same value as capacity.
+        unsafe { vec.set_len(self.len()) };
+        self.convert_to_f64_slice(&mut vec);
+        vec
+    }
+}
+
+impl HalfBitsSliceExt for [u16] {
+    // Since we sealed all the traits involved, these are safe.
+    #[inline]
+    fn reinterpret_cast<H>(&self) -> &[H]
+    where
+        H: crate::private::SealedHalf,
+    {
+        let pointer = self.as_ptr() as *const H;
+        let length = self.len();
+        // SAFETY: We are reconstructing full length of original slice, using its same lifetime,
+        // and the size of elements are identical
+        unsafe { slice::from_raw_parts(pointer, length) }
+    }
+
+    #[inline]
+    fn reinterpret_cast_mut<H>(&mut self) -> &mut [H]
+    where
+        H: crate::private::SealedHalf,
+    {
+        let pointer = self.as_mut_ptr() as *mut H;
+        let length = self.len();
+        // SAFETY: We are reconstructing full length of original slice, using its same lifetime,
+        // and the size of elements are identical
+        unsafe { slice::from_raw_parts_mut(pointer, length) }
+    }
+}
+
+#[doc(hidden)]
+#[deprecated(
+    since = "1.4.0",
+    note = "use `HalfBitsSliceExt::reinterpret_cast_mut` instead"
+)]
+#[inline]
+pub fn from_bits_mut(bits: &mut [u16]) -> &mut [f16] {
+    bits.reinterpret_cast_mut()
+}
+
+#[doc(hidden)]
+#[deprecated(
+    since = "1.4.0",
+    note = "use `HalfFloatSliceExt::reinterpret_cast_mut` instead"
+)]
+#[inline]
+pub fn to_bits_mut(bits: &mut [f16]) -> &mut [u16] {
+    bits.reinterpret_cast_mut()
+}
+
+#[doc(hidden)]
+#[deprecated(
+    since = "1.4.0",
+    note = "use `HalfBitsSliceExt::reinterpret_cast` instead"
+)]
+#[inline]
+pub fn from_bits(bits: &[u16]) -> &[f16] {
+    bits.reinterpret_cast()
+}
+
+#[doc(hidden)]
+#[deprecated(
+    since = "1.4.0",
+    note = "use `HalfFloatSliceExt::reinterpret_cast` instead"
+)]
+#[inline]
+pub fn to_bits(bits: &[f16]) -> &[u16] {
+    bits.reinterpret_cast()
+}
+
+#[allow(clippy::float_cmp)]
+#[cfg(test)]
+mod test {
+    use super::{HalfBitsSliceExt, HalfFloatSliceExt};
+    use crate::{bf16, f16};
+
+    #[test]
+    fn test_slice_conversions_f16() {
+        let bits = &[
+            f16::E.to_bits(),
+            f16::PI.to_bits(),
+            f16::EPSILON.to_bits(),
+            f16::FRAC_1_SQRT_2.to_bits(),
+        ];
+        let numbers = &[f16::E, f16::PI, f16::EPSILON, f16::FRAC_1_SQRT_2];
+
+        // Convert from bits to numbers
+        let from_bits = bits.reinterpret_cast::<f16>();
+        assert_eq!(from_bits, numbers);
+
+        // Convert from numbers back to bits
+        let to_bits = from_bits.reinterpret_cast();
+        assert_eq!(to_bits, bits);
+    }
+
+    #[test]
+    fn test_mutablility_f16() {
+        let mut bits_array = [f16::PI.to_bits()];
+        let bits = &mut bits_array[..];
+
+        {
+            // would not compile without these braces
+            let numbers = bits.reinterpret_cast_mut();
+            numbers[0] = f16::E;
+        }
+
+        assert_eq!(bits, &[f16::E.to_bits()]);
+
+        bits[0] = f16::LN_2.to_bits();
+        assert_eq!(bits, &[f16::LN_2.to_bits()]);
+    }
+
+    #[test]
+    fn test_slice_conversions_bf16() {
+        let bits = &[
+            bf16::E.to_bits(),
+            bf16::PI.to_bits(),
+            bf16::EPSILON.to_bits(),
+            bf16::FRAC_1_SQRT_2.to_bits(),
+        ];
+        let numbers = &[bf16::E, bf16::PI, bf16::EPSILON, bf16::FRAC_1_SQRT_2];
+
+        // Convert from bits to numbers
+        let from_bits = bits.reinterpret_cast::<bf16>();
+        assert_eq!(from_bits, numbers);
+
+        // Convert from numbers back to bits
+        let to_bits = from_bits.reinterpret_cast();
+        assert_eq!(to_bits, bits);
+    }
+
+    #[test]
+    fn test_mutablility_bf16() {
+        let mut bits_array = [bf16::PI.to_bits()];
+        let bits = &mut bits_array[..];
+
+        {
+            // would not compile without these braces
+            let numbers = bits.reinterpret_cast_mut();
+            numbers[0] = bf16::E;
+        }
+
+        assert_eq!(bits, &[bf16::E.to_bits()]);
+
+        bits[0] = bf16::LN_2.to_bits();
+        assert_eq!(bits, &[bf16::LN_2.to_bits()]);
+    }
+
+    #[test]
+    fn slice_convert_f16_f32() {
+        // Exact chunks
+        let vf32 = [1., 2., 3., 4., 5., 6., 7., 8.];
+        let vf16 = [
+            f16::from_f32(1.),
+            f16::from_f32(2.),
+            f16::from_f32(3.),
+            f16::from_f32(4.),
+            f16::from_f32(5.),
+            f16::from_f32(6.),
+            f16::from_f32(7.),
+            f16::from_f32(8.),
+        ];
+        let mut buf32 = vf32;
+        let mut buf16 = vf16;
+
+        vf16.convert_to_f32_slice(&mut buf32);
+        assert_eq!(&vf32, &buf32);
+
+        buf16.convert_from_f32_slice(&vf32);
+        assert_eq!(&vf16, &buf16);
+
+        // Partial with chunks
+        let vf32 = [1., 2., 3., 4., 5., 6., 7., 8., 9.];
+        let vf16 = [
+            f16::from_f32(1.),
+            f16::from_f32(2.),
+            f16::from_f32(3.),
+            f16::from_f32(4.),
+            f16::from_f32(5.),
+            f16::from_f32(6.),
+            f16::from_f32(7.),
+            f16::from_f32(8.),
+            f16::from_f32(9.),
+        ];
+        let mut buf32 = vf32;
+        let mut buf16 = vf16;
+
+        vf16.convert_to_f32_slice(&mut buf32);
+        assert_eq!(&vf32, &buf32);
+
+        buf16.convert_from_f32_slice(&vf32);
+        assert_eq!(&vf16, &buf16);
+
+        // Partial with chunks
+        let vf32 = [1., 2.];
+        let vf16 = [f16::from_f32(1.), f16::from_f32(2.)];
+        let mut buf32 = vf32;
+        let mut buf16 = vf16;
+
+        vf16.convert_to_f32_slice(&mut buf32);
+        assert_eq!(&vf32, &buf32);
+
+        buf16.convert_from_f32_slice(&vf32);
+        assert_eq!(&vf16, &buf16);
+    }
+
+    #[test]
+    fn slice_convert_bf16_f32() {
+        // Exact chunks
+        let vf32 = [1., 2., 3., 4., 5., 6., 7., 8.];
+        let vf16 = [
+            bf16::from_f32(1.),
+            bf16::from_f32(2.),
+            bf16::from_f32(3.),
+            bf16::from_f32(4.),
+            bf16::from_f32(5.),
+            bf16::from_f32(6.),
+            bf16::from_f32(7.),
+            bf16::from_f32(8.),
+        ];
+        let mut buf32 = vf32;
+        let mut buf16 = vf16;
+
+        vf16.convert_to_f32_slice(&mut buf32);
+        assert_eq!(&vf32, &buf32);
+
+        buf16.convert_from_f32_slice(&vf32);
+        assert_eq!(&vf16, &buf16);
+
+        // Partial with chunks
+        let vf32 = [1., 2., 3., 4., 5., 6., 7., 8., 9.];
+        let vf16 = [
+            bf16::from_f32(1.),
+            bf16::from_f32(2.),
+            bf16::from_f32(3.),
+            bf16::from_f32(4.),
+            bf16::from_f32(5.),
+            bf16::from_f32(6.),
+            bf16::from_f32(7.),
+            bf16::from_f32(8.),
+            bf16::from_f32(9.),
+        ];
+        let mut buf32 = vf32;
+        let mut buf16 = vf16;
+
+        vf16.convert_to_f32_slice(&mut buf32);
+        assert_eq!(&vf32, &buf32);
+
+        buf16.convert_from_f32_slice(&vf32);
+        assert_eq!(&vf16, &buf16);
+
+        // Partial with chunks
+        let vf32 = [1., 2.];
+        let vf16 = [bf16::from_f32(1.), bf16::from_f32(2.)];
+        let mut buf32 = vf32;
+        let mut buf16 = vf16;
+
+        vf16.convert_to_f32_slice(&mut buf32);
+        assert_eq!(&vf32, &buf32);
+
+        buf16.convert_from_f32_slice(&vf32);
+        assert_eq!(&vf16, &buf16);
+    }
+
+    #[test]
+    fn slice_convert_f16_f64() {
+        // Exact chunks
+        let vf64 = [1., 2., 3., 4., 5., 6., 7., 8.];
+        let vf16 = [
+            f16::from_f64(1.),
+            f16::from_f64(2.),
+            f16::from_f64(3.),
+            f16::from_f64(4.),
+            f16::from_f64(5.),
+            f16::from_f64(6.),
+            f16::from_f64(7.),
+            f16::from_f64(8.),
+        ];
+        let mut buf64 = vf64;
+        let mut buf16 = vf16;
+
+        vf16.convert_to_f64_slice(&mut buf64);
+        assert_eq!(&vf64, &buf64);
+
+        buf16.convert_from_f64_slice(&vf64);
+        assert_eq!(&vf16, &buf16);
+
+        // Partial with chunks
+        let vf64 = [1., 2., 3., 4., 5., 6., 7., 8., 9.];
+        let vf16 = [
+            f16::from_f64(1.),
+            f16::from_f64(2.),
+            f16::from_f64(3.),
+            f16::from_f64(4.),
+            f16::from_f64(5.),
+            f16::from_f64(6.),
+            f16::from_f64(7.),
+            f16::from_f64(8.),
+            f16::from_f64(9.),
+        ];
+        let mut buf64 = vf64;
+        let mut buf16 = vf16;
+
+        vf16.convert_to_f64_slice(&mut buf64);
+        assert_eq!(&vf64, &buf64);
+
+        buf16.convert_from_f64_slice(&vf64);
+        assert_eq!(&vf16, &buf16);
+
+        // Partial with chunks
+        let vf64 = [1., 2.];
+        let vf16 = [f16::from_f64(1.), f16::from_f64(2.)];
+        let mut buf64 = vf64;
+        let mut buf16 = vf16;
+
+        vf16.convert_to_f64_slice(&mut buf64);
+        assert_eq!(&vf64, &buf64);
+
+        buf16.convert_from_f64_slice(&vf64);
+        assert_eq!(&vf16, &buf16);
+    }
+
+    #[test]
+    fn slice_convert_bf16_f64() {
+        // Exact chunks
+        let vf64 = [1., 2., 3., 4., 5., 6., 7., 8.];
+        let vf16 = [
+            bf16::from_f64(1.),
+            bf16::from_f64(2.),
+            bf16::from_f64(3.),
+            bf16::from_f64(4.),
+            bf16::from_f64(5.),
+            bf16::from_f64(6.),
+            bf16::from_f64(7.),
+            bf16::from_f64(8.),
+        ];
+        let mut buf64 = vf64;
+        let mut buf16 = vf16;
+
+        vf16.convert_to_f64_slice(&mut buf64);
+        assert_eq!(&vf64, &buf64);
+
+        buf16.convert_from_f64_slice(&vf64);
+        assert_eq!(&vf16, &buf16);
+
+        // Partial with chunks
+        let vf64 = [1., 2., 3., 4., 5., 6., 7., 8., 9.];
+        let vf16 = [
+            bf16::from_f64(1.),
+            bf16::from_f64(2.),
+            bf16::from_f64(3.),
+            bf16::from_f64(4.),
+            bf16::from_f64(5.),
+            bf16::from_f64(6.),
+            bf16::from_f64(7.),
+            bf16::from_f64(8.),
+            bf16::from_f64(9.),
+        ];
+        let mut buf64 = vf64;
+        let mut buf16 = vf16;
+
+        vf16.convert_to_f64_slice(&mut buf64);
+        assert_eq!(&vf64, &buf64);
+
+        buf16.convert_from_f64_slice(&vf64);
+        assert_eq!(&vf16, &buf16);
+
+        // Partial with chunks
+        let vf64 = [1., 2.];
+        let vf16 = [bf16::from_f64(1.), bf16::from_f64(2.)];
+        let mut buf64 = vf64;
+        let mut buf16 = vf16;
+
+        vf16.convert_to_f64_slice(&mut buf64);
+        assert_eq!(&vf64, &buf64);
+
+        buf16.convert_from_f64_slice(&vf64);
+        assert_eq!(&vf16, &buf16);
+    }
+
+    #[test]
+    #[should_panic]
+    fn convert_from_f32_slice_len_mismatch_panics() {
+        let mut slice1 = [f16::ZERO; 3];
+        let slice2 = [0f32; 4];
+        slice1.convert_from_f32_slice(&slice2);
+    }
+
+    #[test]
+    #[should_panic]
+    fn convert_from_f64_slice_len_mismatch_panics() {
+        let mut slice1 = [f16::ZERO; 3];
+        let slice2 = [0f64; 4];
+        slice1.convert_from_f64_slice(&slice2);
+    }
+
+    #[test]
+    #[should_panic]
+    fn convert_to_f32_slice_len_mismatch_panics() {
+        let slice1 = [f16::ZERO; 3];
+        let mut slice2 = [0f32; 4];
+        slice1.convert_to_f32_slice(&mut slice2);
+    }
+
+    #[test]
+    #[should_panic]
+    fn convert_to_f64_slice_len_mismatch_panics() {
+        let slice1 = [f16::ZERO; 3];
+        let mut slice2 = [0f64; 4];
+        slice1.convert_to_f64_slice(&mut slice2);
+    }
+}
diff --git a/third_party/rust/half/src/vec.rs b/third_party/rust/half/src/vec.rs
new file mode 100644
index 0000000000..6967656e4d
--- /dev/null
+++ b/third_party/rust/half/src/vec.rs
@@ -0,0 +1,286 @@
+//! Contains utility functions and traits to convert between vectors of [`u16`] bits and [`f16`] or
+//! [`bf16`] vectors.
+//!
+//! The utility [`HalfBitsVecExt`] sealed extension trait is implemented for [`Vec<u16>`] vectors,
+//! while the utility [`HalfFloatVecExt`] sealed extension trait is implemented for both
+//! [`Vec<f16>`] and [`Vec<bf16>`] vectors. These traits provide efficient conversions and
+//! reinterpret casting of larger buffers of floating point values, and are automatically included
+//! in the [`prelude`][crate::prelude] module.
+//!
+//! This module is only available with the `std` or `alloc` feature.
+
+use super::{bf16, f16, slice::HalfFloatSliceExt};
+#[cfg(feature = "alloc")]
+use alloc::vec::Vec;
+use core::mem;
+
+/// Extensions to [`Vec<f16>`] and [`Vec<bf16>`] to support reinterpret operations.
+///
+/// This trait is sealed and cannot be implemented outside of this crate.
+pub trait HalfFloatVecExt: private::SealedHalfFloatVec {
+    /// Reinterprets a vector of [`f16`]or [`bf16`] numbers as a vector of [`u16`] bits.
+    ///
+    /// This is a zero-copy operation. The reinterpreted vector has the same memory location as
+    /// `self`.
+    ///
+    /// # Examples
+    ///
+    /// ```rust
+    /// # use half::prelude::*;
+    /// let float_buffer = vec![f16::from_f32(1.), f16::from_f32(2.), f16::from_f32(3.)];
+    /// let int_buffer = float_buffer.reinterpret_into();
+    ///
+    /// assert_eq!(int_buffer, [f16::from_f32(1.).to_bits(), f16::from_f32(2.).to_bits(), f16::from_f32(3.).to_bits()]);
+    /// ```
+    fn reinterpret_into(self) -> Vec<u16>;
+
+    /// Converts all of the elements of a `[f32]` slice into a new [`f16`] or [`bf16`] vector.
+    ///
+    /// The conversion operation is vectorized over the slice, meaning the conversion may be more
+    /// efficient than converting individual elements on some hardware that supports SIMD
+    /// conversions. See [crate documentation][crate] for more information on hardware conversion
+    /// support.
+    ///
+    /// # Examples
+    /// ```rust
+    /// # use half::prelude::*;
+    /// let float_values = [1., 2., 3., 4.];
+    /// let vec: Vec<f16> = Vec::from_f32_slice(&float_values);
+    ///
+    /// assert_eq!(vec, vec![f16::from_f32(1.), f16::from_f32(2.), f16::from_f32(3.), f16::from_f32(4.)]);
+    /// ```
+    fn from_f32_slice(slice: &[f32]) -> Self;
+
+    /// Converts all of the elements of a `[f64]` slice into a new [`f16`] or [`bf16`] vector.
+    ///
+    /// The conversion operation is vectorized over the slice, meaning the conversion may be more
+    /// efficient than converting individual elements on some hardware that supports SIMD
+    /// conversions. See [crate documentation][crate] for more information on hardware conversion
+    /// support.
+    ///
+    /// # Examples
+    /// ```rust
+    /// # use half::prelude::*;
+    /// let float_values = [1., 2., 3., 4.];
+    /// let vec: Vec<f16> = Vec::from_f64_slice(&float_values);
+    ///
+    /// assert_eq!(vec, vec![f16::from_f64(1.), f16::from_f64(2.), f16::from_f64(3.), f16::from_f64(4.)]);
+    /// ```
+    fn from_f64_slice(slice: &[f64]) -> Self;
+}
+
+/// Extensions to [`Vec<u16>`] to support reinterpret operations.
+///
+/// This trait is sealed and cannot be implemented outside of this crate.
+pub trait HalfBitsVecExt: private::SealedHalfBitsVec {
+    /// Reinterprets a vector of [`u16`] bits as a vector of [`f16`] or [`bf16`] numbers.
+    ///
+    /// `H` is the type to cast to, and must be either the [`f16`] or [`bf16`] type.
+    ///
+    /// This is a zero-copy operation. The reinterpreted vector has the same memory location as
+    /// `self`.
+    ///
+    /// # Examples
+    ///
+    /// ```rust
+    /// # use half::prelude::*;
+    /// let int_buffer = vec![f16::from_f32(1.).to_bits(), f16::from_f32(2.).to_bits(), f16::from_f32(3.).to_bits()];
+    /// let float_buffer = int_buffer.reinterpret_into::<f16>();
+    ///
+    /// assert_eq!(float_buffer, [f16::from_f32(1.), f16::from_f32(2.), f16::from_f32(3.)]);
+    /// ```
+    fn reinterpret_into<H>(self) -> Vec<H>
+    where
+        H: crate::private::SealedHalf;
+}
+
+mod private {
+    use crate::{bf16, f16};
+    #[cfg(feature = "alloc")]
+    use alloc::vec::Vec;
+
+    pub trait SealedHalfFloatVec {}
+    impl SealedHalfFloatVec for Vec<f16> {}
+    impl SealedHalfFloatVec for Vec<bf16> {}
+
+    pub trait SealedHalfBitsVec {}
+    impl SealedHalfBitsVec for Vec<u16> {}
+}
+
+impl HalfFloatVecExt for Vec<f16> {
+    #[inline]
+    fn reinterpret_into(mut self) -> Vec<u16> {
+        // An f16 array has same length and capacity as u16 array
+        let length = self.len();
+        let capacity = self.capacity();
+
+        // Actually reinterpret the contents of the Vec<f16> as u16,
+        // knowing that structs are represented as only their members in memory,
+        // which is the u16 part of `f16(u16)`
+        let pointer = self.as_mut_ptr() as *mut u16;
+
+        // Prevent running a destructor on the old Vec<u16>, so the pointer won't be deleted
+        mem::forget(self);
+
+        // Finally construct a new Vec<f16> from the raw pointer
+        // SAFETY: We are reconstructing full length and capacity of original vector,
+        // using its original pointer, and the size of elements are identical.
+        unsafe { Vec::from_raw_parts(pointer, length, capacity) }
+    }
+
+    fn from_f32_slice(slice: &[f32]) -> Self {
+        let mut vec = Vec::with_capacity(slice.len());
+        // SAFETY: convert will initialize every value in the vector without reading them,
+        // so this is safe to do instead of double initialize from resize, and we're setting it to
+        // same value as capacity.
+        unsafe { vec.set_len(slice.len()) };
+        vec.convert_from_f32_slice(slice);
+        vec
+    }
+
+    fn from_f64_slice(slice: &[f64]) -> Self {
+        let mut vec = Vec::with_capacity(slice.len());
+        // SAFETY: convert will initialize every value in the vector without reading them,
+        // so this is safe to do instead of double initialize from resize, and we're setting it to
+        // same value as capacity.
+        unsafe { vec.set_len(slice.len()) };
+        vec.convert_from_f64_slice(slice);
+        vec
+    }
+}
+
+impl HalfFloatVecExt for Vec<bf16> {
+    #[inline]
+    fn reinterpret_into(mut self) -> Vec<u16> {
+        // An f16 array has same length and capacity as u16 array
+        let length = self.len();
+        let capacity = self.capacity();
+
+        // Actually reinterpret the contents of the Vec<f16> as u16,
+        // knowing that structs are represented as only their members in memory,
+        // which is the u16 part of `f16(u16)`
+        let pointer = self.as_mut_ptr() as *mut u16;
+
+        // Prevent running a destructor on the old Vec<u16>, so the pointer won't be deleted
+        mem::forget(self);
+
+        // Finally construct a new Vec<f16> from the raw pointer
+        // SAFETY: We are reconstructing full length and capacity of original vector,
+        // using its original pointer, and the size of elements are identical.
+        unsafe { Vec::from_raw_parts(pointer, length, capacity) }
+    }
+
+    fn from_f32_slice(slice: &[f32]) -> Self {
+        let mut vec = Vec::with_capacity(slice.len());
+        // SAFETY: convert will initialize every value in the vector without reading them,
+        // so this is safe to do instead of double initialize from resize, and we're setting it to
+        // same value as capacity.
+        unsafe { vec.set_len(slice.len()) };
+        vec.convert_from_f32_slice(slice);
+        vec
+    }
+
+    fn from_f64_slice(slice: &[f64]) -> Self {
+        let mut vec = Vec::with_capacity(slice.len());
+        // SAFETY: convert will initialize every value in the vector without reading them,
+        // so this is safe to do instead of double initialize from resize, and we're setting it to
+        // same value as capacity.
+        unsafe { vec.set_len(slice.len()) };
+        vec.convert_from_f64_slice(slice);
+        vec
+    }
+}
+
+impl HalfBitsVecExt for Vec<u16> {
+    // This is safe because all traits are sealed
+    #[inline]
+    fn reinterpret_into<H>(mut self) -> Vec<H>
+    where
+        H: crate::private::SealedHalf,
+    {
+        // An f16 array has same length and capacity as u16 array
+        let length = self.len();
+        let capacity = self.capacity();
+
+        // Actually reinterpret the contents of the Vec<u16> as f16,
+        // knowing that structs are represented as only their members in memory,
+        // which is the u16 part of `f16(u16)`
+        let pointer = self.as_mut_ptr() as *mut H;
+
+        // Prevent running a destructor on the old Vec<u16>, so the pointer won't be deleted
+        mem::forget(self);
+
+        // Finally construct a new Vec<f16> from the raw pointer
+        // SAFETY: We are reconstructing full length and capacity of original vector,
+        // using its original pointer, and the size of elements are identical.
+        unsafe { Vec::from_raw_parts(pointer, length, capacity) }
+    }
+}
+
+#[doc(hidden)]
+#[deprecated(
+    since = "1.4.0",
+    note = "use `HalfBitsVecExt::reinterpret_into` instead"
+)]
+#[inline]
+pub fn from_bits(bits: Vec<u16>) -> Vec<f16> {
+    bits.reinterpret_into()
+}
+
+#[doc(hidden)]
+#[deprecated(
+    since = "1.4.0",
+    note = "use `HalfFloatVecExt::reinterpret_into` instead"
+)]
+#[inline]
+pub fn to_bits(numbers: Vec<f16>) -> Vec<u16> {
+    numbers.reinterpret_into()
+}
+
+#[cfg(test)]
+mod test {
+    use super::{HalfBitsVecExt, HalfFloatVecExt};
+    use crate::{bf16, f16};
+    #[cfg(all(feature = "alloc", not(feature = "std")))]
+    use alloc::vec;
+
+    #[test]
+    fn test_vec_conversions_f16() {
+        let numbers = vec![f16::E, f16::PI, f16::EPSILON, f16::FRAC_1_SQRT_2];
+        let bits = vec![
+            f16::E.to_bits(),
+            f16::PI.to_bits(),
+            f16::EPSILON.to_bits(),
+            f16::FRAC_1_SQRT_2.to_bits(),
+        ];
+        let bits_cloned = bits.clone();
+
+        // Convert from bits to numbers
+        let from_bits = bits.reinterpret_into::<f16>();
+        assert_eq!(&from_bits[..], &numbers[..]);
+
+        // Convert from numbers back to bits
+        let to_bits = from_bits.reinterpret_into();
+        assert_eq!(&to_bits[..], &bits_cloned[..]);
+    }
+
+    #[test]
+    fn test_vec_conversions_bf16() {
+        let numbers = vec![bf16::E, bf16::PI, bf16::EPSILON, bf16::FRAC_1_SQRT_2];
+        let bits = vec![
+            bf16::E.to_bits(),
+            bf16::PI.to_bits(),
+            bf16::EPSILON.to_bits(),
+            bf16::FRAC_1_SQRT_2.to_bits(),
+        ];
+        let bits_cloned = bits.clone();
+
+        // Convert from bits to numbers
+        let from_bits = bits.reinterpret_into::<bf16>();
+        assert_eq!(&from_bits[..], &numbers[..]);
+
+        // Convert from numbers back to bits
+        let to_bits = from_bits.reinterpret_into();
+        assert_eq!(&to_bits[..], &bits_cloned[..]);
+    }
+}