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Diffstat (limited to 'vendor/half/src/bfloat.rs')
| -rw-r--r-- | vendor/half/src/bfloat.rs | 1841 |
1 files changed, 1841 insertions, 0 deletions
diff --git a/vendor/half/src/bfloat.rs b/vendor/half/src/bfloat.rs new file mode 100644 index 0000000..8b23863 --- /dev/null +++ b/vendor/half/src/bfloat.rs @@ -0,0 +1,1841 @@ +#[cfg(feature = "bytemuck")] +use bytemuck::{Pod, Zeroable}; +use core::{ + cmp::Ordering, + iter::{Product, Sum}, + num::FpCategory, + ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Rem, RemAssign, Sub, SubAssign}, +}; +#[cfg(not(target_arch = "spirv"))] +use core::{ + fmt::{ + Binary, Debug, Display, Error, Formatter, LowerExp, LowerHex, Octal, UpperExp, UpperHex, + }, + num::ParseFloatError, + 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))] +#[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] + #[must_use] + 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] + #[must_use] + pub fn from_f32(value: f32) -> bf16 { + Self::from_f32_const(value) + } + + /// Constructs a [`bf16`] value from a 32-bit floating point value. + /// + /// This function is identical to [`from_f32`][Self::from_f32] except it never uses hardware + /// intrinsics, which allows it to be `const`. [`from_f32`][Self::from_f32] should be preferred + /// in any non-`const` context. + /// + /// 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] + #[must_use] + pub const fn from_f32_const(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] + #[must_use] + pub fn from_f64(value: f64) -> bf16 { + Self::from_f64_const(value) + } + + /// Constructs a [`bf16`] value from a 64-bit floating point value. + /// + /// This function is identical to [`from_f64`][Self::from_f64] except it never uses hardware + /// intrinsics, which allows it to be `const`. [`from_f64`][Self::from_f64] should be preferred + /// in any non-`const` context. + /// + /// 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] + #[must_use] + pub const fn from_f64_const(value: f64) -> bf16 { + bf16(convert::f64_to_bf16(value)) + } + + /// Converts a [`bf16`] into the underlying bit representation. + #[inline] + #[must_use] + 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] + #[must_use] + 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] + #[must_use] + 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] + #[must_use] + 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] + #[must_use] + 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] + #[must_use] + 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] + #[must_use] + 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] + #[must_use] + pub fn to_f32(self) -> f32 { + self.to_f32_const() + } + + /// Converts a [`bf16`] value into an [`f32`] value. + /// + /// This function is identical to [`to_f32`][Self::to_f32] except it never uses hardware + /// intrinsics, which allows it to be `const`. [`to_f32`][Self::to_f32] should be preferred + /// in any non-`const` context. + /// + /// This conversion is lossless as all values can be represented exactly in [`f32`]. + #[inline] + #[must_use] + pub const fn to_f32_const(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] + #[must_use] + pub fn to_f64(self) -> f64 { + self.to_f64_const() + } + + /// Converts a [`bf16`] value into an [`f64`] value. + /// + /// This function is identical to [`to_f64`][Self::to_f64] except it never uses hardware + /// intrinsics, which allows it to be `const`. [`to_f64`][Self::to_f64] should be preferred + /// in any non-`const` context. + /// + /// This conversion is lossless as all values can be represented exactly in [`f64`]. + #[inline] + #[must_use] + pub const fn to_f64_const(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] + #[must_use] + 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] + #[must_use] + 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] + #[must_use] + 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] + #[must_use] + 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); + /// ``` + #[must_use] + 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()); + /// ``` + #[must_use] + 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] + #[must_use] + 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] + #[must_use] + 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] + #[must_use] + 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] + #[must_use] + 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] + #[must_use] + 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] + #[must_use] + 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 + } + + /// Returns the ordering between `self` and `other`. + /// + /// Unlike the standard partial comparison between floating point numbers, + /// this comparison always produces an ordering in accordance to + /// the `totalOrder` predicate as defined in the IEEE 754 (2008 revision) + /// floating point standard. The values are ordered in the following sequence: + /// + /// - negative quiet NaN + /// - negative signaling NaN + /// - negative infinity + /// - negative numbers + /// - negative subnormal numbers + /// - negative zero + /// - positive zero + /// - positive subnormal numbers + /// - positive numbers + /// - positive infinity + /// - positive signaling NaN + /// - positive quiet NaN. + /// + /// The ordering established by this function does not always agree with the + /// [`PartialOrd`] and [`PartialEq`] implementations of `bf16`. For example, + /// they consider negative and positive zero equal, while `total_cmp` + /// doesn't. + /// + /// The interpretation of the signaling NaN bit follows the definition in + /// the IEEE 754 standard, which may not match the interpretation by some of + /// the older, non-conformant (e.g. MIPS) hardware implementations. + /// + /// # Examples + /// ``` + /// # use half::bf16; + /// let mut v: Vec<bf16> = vec![]; + /// v.push(bf16::ONE); + /// v.push(bf16::INFINITY); + /// v.push(bf16::NEG_INFINITY); + /// v.push(bf16::NAN); + /// v.push(bf16::MAX_SUBNORMAL); + /// v.push(-bf16::MAX_SUBNORMAL); + /// v.push(bf16::ZERO); + /// v.push(bf16::NEG_ZERO); + /// v.push(bf16::NEG_ONE); + /// v.push(bf16::MIN_POSITIVE); + /// + /// v.sort_by(|a, b| a.total_cmp(&b)); + /// + /// assert!(v + /// .into_iter() + /// .zip( + /// [ + /// bf16::NEG_INFINITY, + /// bf16::NEG_ONE, + /// -bf16::MAX_SUBNORMAL, + /// bf16::NEG_ZERO, + /// bf16::ZERO, + /// bf16::MAX_SUBNORMAL, + /// bf16::MIN_POSITIVE, + /// bf16::ONE, + /// bf16::INFINITY, + /// bf16::NAN + /// ] + /// .iter() + /// ) + /// .all(|(a, b)| a.to_bits() == b.to_bits())); + /// ``` + // Implementation based on: https://doc.rust-lang.org/std/primitive.f32.html#method.total_cmp + #[inline] + #[must_use] + pub fn total_cmp(&self, other: &Self) -> Ordering { + let mut left = self.to_bits() as i16; + let mut right = other.to_bits() as i16; + left ^= (((left >> 15) as u16) >> 1) as i16; + right ^= (((right >> 15) as u16) >> 1) as i16; + left.cmp(&right) + } + + /// Alternate serialize adapter for serializing as a float. + /// + /// By default, [`bf16`] serializes as a newtype of [`u16`]. This is an alternate serialize + /// implementation that serializes as an [`f32`] value. It is designed for use with + /// `serialize_with` serde attributes. Deserialization from `f32` values is already supported by + /// the default deserialize implementation. + /// + /// # Examples + /// + /// A demonstration on how to use this adapater: + /// + /// ``` + /// use serde::{Serialize, Deserialize}; + /// use half::bf16; + /// + /// #[derive(Serialize, Deserialize)] + /// struct MyStruct { + /// #[serde(serialize_with = "bf16::serialize_as_f32")] + /// value: bf16 // Will be serialized as f32 instead of u16 + /// } + /// ``` + #[cfg(feature = "serde")] + pub fn serialize_as_f32<S: serde::Serializer>(&self, serializer: S) -> Result<S::Ok, S::Error> { + serializer.serialize_f32(self.to_f32()) + } + + /// Alternate serialize adapter for serializing as a string. + /// + /// By default, [`bf16`] serializes as a newtype of [`u16`]. This is an alternate serialize + /// implementation that serializes as a string value. It is designed for use with + /// `serialize_with` serde attributes. Deserialization from string values is already supported + /// by the default deserialize implementation. + /// + /// # Examples + /// + /// A demonstration on how to use this adapater: + /// + /// ``` + /// use serde::{Serialize, Deserialize}; + /// use half::bf16; + /// + /// #[derive(Serialize, Deserialize)] + /// struct MyStruct { + /// #[serde(serialize_with = "bf16::serialize_as_string")] + /// value: bf16 // Will be serialized as a string instead of u16 + /// } + /// ``` + #[cfg(feature = "serde")] + pub fn serialize_as_string<S: serde::Serializer>( + &self, + serializer: S, + ) -> Result<S::Ok, S::Error> { + serializer.serialize_str(&self.to_string()) + } + + /// 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, + } + } + } +} + +#[cfg(not(target_arch = "spirv"))] +impl FromStr for bf16 { + type Err = ParseFloatError; + fn from_str(src: &str) -> Result<bf16, ParseFloatError> { + f32::from_str(src).map(bf16::from_f32) + } +} + +#[cfg(not(target_arch = "spirv"))] +impl Debug for bf16 { + fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> { + write!(f, "{:?}", self.to_f32()) + } +} + +#[cfg(not(target_arch = "spirv"))] +impl Display for bf16 { + fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> { + write!(f, "{}", self.to_f32()) + } +} + +#[cfg(not(target_arch = "spirv"))] +impl LowerExp for bf16 { + fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> { + write!(f, "{:e}", self.to_f32()) + } +} + +#[cfg(not(target_arch = "spirv"))] +impl UpperExp for bf16 { + fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> { + write!(f, "{:E}", self.to_f32()) + } +} + +#[cfg(not(target_arch = "spirv"))] +impl Binary for bf16 { + fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> { + write!(f, "{:b}", self.0) + } +} + +#[cfg(not(target_arch = "spirv"))] +impl Octal for bf16 { + fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> { + write!(f, "{:o}", self.0) + } +} + +#[cfg(not(target_arch = "spirv"))] +impl LowerHex for bf16 { + fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> { + write!(f, "{:x}", self.0) + } +} + +#[cfg(not(target_arch = "spirv"))] +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 Neg for &bf16 { + type Output = <bf16 as Neg>::Output; + + #[inline] + fn neg(self) -> Self::Output { + Neg::neg(*self) + } +} + +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()) + } +} + +#[cfg(feature = "serde")] +struct Visitor; + +#[cfg(feature = "serde")] +impl<'de> Deserialize<'de> for bf16 { + fn deserialize<D>(deserializer: D) -> Result<bf16, D::Error> + where + D: serde::de::Deserializer<'de>, + { + deserializer.deserialize_newtype_struct("bf16", Visitor) + } +} + +#[cfg(feature = "serde")] +impl<'de> serde::de::Visitor<'de> for Visitor { + type Value = bf16; + + fn expecting(&self, formatter: &mut alloc::fmt::Formatter) -> alloc::fmt::Result { + write!(formatter, "tuple struct bf16") + } + + fn visit_newtype_struct<D>(self, deserializer: D) -> Result<Self::Value, D::Error> + where + D: serde::Deserializer<'de>, + { + Ok(bf16(<u16 as Deserialize>::deserialize(deserializer)?)) + } + + fn visit_str<E>(self, v: &str) -> Result<Self::Value, E> + where + E: serde::de::Error, + { + v.parse().map_err(|_| { + serde::de::Error::invalid_value(serde::de::Unexpected::Str(v), &"a float string") + }) + } + + fn visit_f32<E>(self, v: f32) -> Result<Self::Value, E> + where + E: serde::de::Error, + { + Ok(bf16::from_f32(v)) + } + + fn visit_f64<E>(self, v: f64) -> Result<Self::Value, E> + where + E: serde::de::Error, + { + Ok(bf16::from_f64(v)) + } +} + +#[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 + } + } +} |