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diff --git a/vendor/half/src/bfloat.rs b/vendor/half/src/bfloat.rs
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+++ b/vendor/half/src/bfloat.rs
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+#[cfg(feature = "bytemuck")]
+use bytemuck::{Pod, Zeroable};
+use core::{
+ cmp::Ordering,
+ fmt::{
+ Binary, Debug, Display, Error, Formatter, LowerExp, LowerHex, Octal, UpperExp, UpperHex,
+ },
+ iter::{Product, Sum},
+ num::{FpCategory, ParseFloatError},
+ ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Rem, RemAssign, Sub, SubAssign},
+ str::FromStr,
+};
+#[cfg(feature = "serde")]
+use serde::{Deserialize, Serialize};
+#[cfg(feature = "zerocopy")]
+use zerocopy::{AsBytes, FromBytes};
+
+pub(crate) mod convert;
+
+/// A 16-bit floating point type implementing the [`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
+ }
+ }
+}
generated by cgit v1.2.3 (git 2.39.1) at 2024-12-25 22:23:39 +0000