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Diffstat (limited to 'vendor/half/src/binary16.rs')
| -rw-r--r-- | vendor/half/src/binary16.rs | 1912 |
1 files changed, 0 insertions, 1912 deletions
diff --git a/vendor/half/src/binary16.rs b/vendor/half/src/binary16.rs deleted file mode 100644 index b622f01..0000000 --- a/vendor/half/src/binary16.rs +++ /dev/null @@ -1,1912 +0,0 @@ -#[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 IEEE 754-2008 standard [`binary16`] a.k.a `half` -/// format. -/// -/// This 16-bit floating point type is intended for efficient storage where the full range and -/// precision of a larger floating point value is not required. Because [`f16`] is primarily for -/// efficient storage, floating point operations such as addition, multiplication, etc. are not -/// implemented. Operations should be performed with [`f32`] or higher-precision types and converted -/// to/from [`f16`] as necessary. -/// -/// [`binary16`]: https://en.wikipedia.org/wiki/Half-precision_floating-point_format -#[allow(non_camel_case_types)] -#[derive(Clone, Copy, Default)] -#[repr(transparent)] -#[cfg_attr(feature = "serde", derive(Serialize))] -#[cfg_attr(feature = "bytemuck", derive(Zeroable, Pod))] -#[cfg_attr(feature = "zerocopy", derive(AsBytes, FromBytes))] -pub struct f16(u16); - -impl f16 { - /// Constructs a 16-bit floating point value from the raw bits. - #[inline] - #[must_use] - pub const fn from_bits(bits: u16) -> f16 { - f16(bits) - } - - /// Constructs a 16-bit floating point value from a 32-bit floating point value. - /// - /// If the 32-bit value is to large to fit in 16-bits, ±∞ will result. NaN values are - /// preserved. 32-bit subnormal values are too tiny to be represented in 16-bits and result in - /// ±0. Exponents that underflow the minimum 16-bit exponent will result in 16-bit subnormals - /// or ±0. All other values are truncated and rounded to the nearest representable 16-bit - /// value. - #[inline] - #[must_use] - pub fn from_f32(value: f32) -> f16 { - f16(convert::f32_to_f16(value)) - } - - /// Constructs a 16-bit floating point 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 to large to fit in 16-bits, ±∞ will result. NaN values are - /// preserved. 32-bit subnormal values are too tiny to be represented in 16-bits and result in - /// ±0. Exponents that underflow the minimum 16-bit exponent will result in 16-bit subnormals - /// or ±0. All other values are truncated and rounded to the nearest representable 16-bit - /// value. - #[inline] - #[must_use] - pub const fn from_f32_const(value: f32) -> f16 { - f16(convert::f32_to_f16_fallback(value)) - } - - /// Constructs a 16-bit floating point value from a 64-bit floating point value. - /// - /// If the 64-bit value is to large to fit in 16-bits, ±∞ will result. NaN values are - /// preserved. 64-bit subnormal values are too tiny to be represented in 16-bits and result in - /// ±0. Exponents that underflow the minimum 16-bit exponent will result in 16-bit subnormals - /// or ±0. All other values are truncated and rounded to the nearest representable 16-bit - /// value. - #[inline] - #[must_use] - pub fn from_f64(value: f64) -> f16 { - f16(convert::f64_to_f16(value)) - } - - /// Constructs a 16-bit floating point 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 in 16-bits, ±∞ will result. NaN values are - /// preserved. 64-bit subnormal values are too tiny to be represented in 16-bits and result in - /// ±0. Exponents that underflow the minimum 16-bit exponent will result in 16-bit subnormals - /// or ±0. All other values are truncated and rounded to the nearest representable 16-bit - /// value. - #[inline] - #[must_use] - pub const fn from_f64_const(value: f64) -> f16 { - f16(convert::f64_to_f16_fallback(value)) - } - - /// Converts a [`f16`] 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 = f16::from_f32(12.5).to_le_bytes(); - /// assert_eq!(bytes, [0x40, 0x4A]); - /// ``` - #[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 = f16::from_f32(12.5).to_be_bytes(); - /// assert_eq!(bytes, [0x4A, 0x40]); - /// ``` - #[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`][Self::to_be_bytes] or [`to_le_bytes`][Self::to_le_bytes], as appropriate, - /// instead. - /// - /// # Examples - /// - /// ```rust - /// # use half::prelude::*; - /// let bytes = f16::from_f32(12.5).to_ne_bytes(); - /// assert_eq!(bytes, if cfg!(target_endian = "big") { - /// [0x4A, 0x40] - /// } else { - /// [0x40, 0x4A] - /// }); - /// ``` - #[inline] - #[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 = f16::from_le_bytes([0x40, 0x4A]); - /// assert_eq!(value, f16::from_f32(12.5)); - /// ``` - #[inline] - #[must_use] - pub const fn from_le_bytes(bytes: [u8; 2]) -> f16 { - f16::from_bits(u16::from_le_bytes(bytes)) - } - - /// Creates a floating point value from its representation as a byte array in big endian. - /// - /// # Examples - /// - /// ```rust - /// # use half::prelude::*; - /// let value = f16::from_be_bytes([0x4A, 0x40]); - /// assert_eq!(value, f16::from_f32(12.5)); - /// ``` - #[inline] - #[must_use] - pub const fn from_be_bytes(bytes: [u8; 2]) -> f16 { - f16::from_bits(u16::from_be_bytes(bytes)) - } - - /// Creates a floating point value from its representation as a byte array in native endian. - /// - /// As the target platform's native endianness is used, portable code likely wants to use - /// [`from_be_bytes`][Self::from_be_bytes] or [`from_le_bytes`][Self::from_le_bytes], as - /// appropriate instead. - /// - /// # Examples - /// - /// ```rust - /// # use half::prelude::*; - /// let value = f16::from_ne_bytes(if cfg!(target_endian = "big") { - /// [0x4A, 0x40] - /// } else { - /// [0x40, 0x4A] - /// }); - /// assert_eq!(value, f16::from_f32(12.5)); - /// ``` - #[inline] - #[must_use] - pub const fn from_ne_bytes(bytes: [u8; 2]) -> f16 { - f16::from_bits(u16::from_ne_bytes(bytes)) - } - - /// Converts a [`f16`] value into a `f32` value. - /// - /// This conversion is lossless as all 16-bit floating point values can be represented exactly - /// in 32-bit floating point. - #[inline] - #[must_use] - pub fn to_f32(self) -> f32 { - convert::f16_to_f32(self.0) - } - - /// Converts a [`f16`] value into a `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 16-bit floating point values can be represented exactly - /// in 32-bit floating point. - #[inline] - #[must_use] - pub const fn to_f32_const(self) -> f32 { - convert::f16_to_f32_fallback(self.0) - } - - /// Converts a [`f16`] value into a `f64` value. - /// - /// This conversion is lossless as all 16-bit floating point values can be represented exactly - /// in 64-bit floating point. - #[inline] - #[must_use] - pub fn to_f64(self) -> f64 { - convert::f16_to_f64(self.0) - } - - /// Converts a [`f16`] value into a `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 16-bit floating point values can be represented exactly - /// in 64-bit floating point. - #[inline] - #[must_use] - pub const fn to_f64_const(self) -> f64 { - convert::f16_to_f64_fallback(self.0) - } - - /// Returns `true` if this value is `NaN` and `false` otherwise. - /// - /// # Examples - /// - /// ```rust - /// # use half::prelude::*; - /// - /// let nan = f16::NAN; - /// let f = f16::from_f32(7.0_f32); - /// - /// assert!(nan.is_nan()); - /// assert!(!f.is_nan()); - /// ``` - #[inline] - #[must_use] - pub const fn is_nan(self) -> bool { - self.0 & 0x7FFFu16 > 0x7C00u16 - } - - /// Returns `true` if this value is ±∞ and `false`. - /// otherwise. - /// - /// # Examples - /// - /// ```rust - /// # use half::prelude::*; - /// - /// let f = f16::from_f32(7.0f32); - /// let inf = f16::INFINITY; - /// let neg_inf = f16::NEG_INFINITY; - /// let nan = f16::NAN; - /// - /// assert!(!f.is_infinite()); - /// assert!(!nan.is_infinite()); - /// - /// assert!(inf.is_infinite()); - /// assert!(neg_inf.is_infinite()); - /// ``` - #[inline] - #[must_use] - pub const fn is_infinite(self) -> bool { - self.0 & 0x7FFFu16 == 0x7C00u16 - } - - /// Returns `true` if this number is neither infinite nor `NaN`. - /// - /// # Examples - /// - /// ```rust - /// # use half::prelude::*; - /// - /// let f = f16::from_f32(7.0f32); - /// let inf = f16::INFINITY; - /// let neg_inf = f16::NEG_INFINITY; - /// let nan = f16::NAN; - /// - /// assert!(f.is_finite()); - /// - /// assert!(!nan.is_finite()); - /// assert!(!inf.is_finite()); - /// assert!(!neg_inf.is_finite()); - /// ``` - #[inline] - #[must_use] - pub const fn is_finite(self) -> bool { - self.0 & 0x7C00u16 != 0x7C00u16 - } - - /// Returns `true` if the number is neither zero, infinite, subnormal, or `NaN`. - /// - /// # Examples - /// - /// ```rust - /// # use half::prelude::*; - /// - /// let min = f16::MIN_POSITIVE; - /// let max = f16::MAX; - /// let lower_than_min = f16::from_f32(1.0e-10_f32); - /// let zero = f16::from_f32(0.0_f32); - /// - /// assert!(min.is_normal()); - /// assert!(max.is_normal()); - /// - /// assert!(!zero.is_normal()); - /// assert!(!f16::NAN.is_normal()); - /// assert!(!f16::INFINITY.is_normal()); - /// // Values between `0` and `min` are Subnormal. - /// assert!(!lower_than_min.is_normal()); - /// ``` - #[inline] - #[must_use] - pub const fn is_normal(self) -> bool { - let exp = self.0 & 0x7C00u16; - exp != 0x7C00u16 && exp != 0 - } - - /// Returns the floating point category of the number. - /// - /// If only one property is going to be tested, it is generally faster to use the specific - /// predicate instead. - /// - /// # Examples - /// - /// ```rust - /// use std::num::FpCategory; - /// # use half::prelude::*; - /// - /// let num = f16::from_f32(12.4_f32); - /// let inf = f16::INFINITY; - /// - /// assert_eq!(num.classify(), FpCategory::Normal); - /// assert_eq!(inf.classify(), FpCategory::Infinite); - /// ``` - #[must_use] - pub const fn classify(self) -> FpCategory { - let exp = self.0 & 0x7C00u16; - let man = self.0 & 0x03FFu16; - match (exp, man) { - (0, 0) => FpCategory::Zero, - (0, _) => FpCategory::Subnormal, - (0x7C00u16, 0) => FpCategory::Infinite, - (0x7C00u16, _) => FpCategory::Nan, - _ => FpCategory::Normal, - } - } - - /// Returns a number that represents the sign of `self`. - /// - /// * `1.0` if the number is positive, `+0.0` or [`INFINITY`][f16::INFINITY] - /// * `-1.0` if the number is negative, `-0.0` or [`NEG_INFINITY`][f16::NEG_INFINITY] - /// * [`NAN`][f16::NAN] if the number is `NaN` - /// - /// # Examples - /// - /// ```rust - /// # use half::prelude::*; - /// - /// let f = f16::from_f32(3.5_f32); - /// - /// assert_eq!(f.signum(), f16::from_f32(1.0)); - /// assert_eq!(f16::NEG_INFINITY.signum(), f16::from_f32(-1.0)); - /// - /// assert!(f16::NAN.signum().is_nan()); - /// ``` - #[must_use] - pub const fn signum(self) -> f16 { - if self.is_nan() { - self - } else if self.0 & 0x8000u16 != 0 { - Self::NEG_ONE - } else { - Self::ONE - } - } - - /// Returns `true` if and only if `self` has a positive sign, including `+0.0`, `NaNs` with a - /// positive sign bit and +∞. - /// - /// # Examples - /// - /// ```rust - /// # use half::prelude::*; - /// - /// let nan = f16::NAN; - /// let f = f16::from_f32(7.0_f32); - /// let g = f16::from_f32(-7.0_f32); - /// - /// assert!(f.is_sign_positive()); - /// assert!(!g.is_sign_positive()); - /// // `NaN` can be either positive or negative - /// assert!(nan.is_sign_positive() != nan.is_sign_negative()); - /// ``` - #[inline] - #[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 = f16::NAN; - /// let f = f16::from_f32(7.0f32); - /// let g = f16::from_f32(-7.0f32); - /// - /// assert!(!f.is_sign_negative()); - /// assert!(g.is_sign_negative()); - /// // `NaN` can be either positive or negative - /// assert!(nan.is_sign_positive() != nan.is_sign_negative()); - /// ``` - #[inline] - #[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 = f16::from_f32(3.5); - /// - /// assert_eq!(f.copysign(f16::from_f32(0.42)), f16::from_f32(3.5)); - /// assert_eq!(f.copysign(f16::from_f32(-0.42)), f16::from_f32(-3.5)); - /// assert_eq!((-f).copysign(f16::from_f32(0.42)), f16::from_f32(3.5)); - /// assert_eq!((-f).copysign(f16::from_f32(-0.42)), f16::from_f32(-3.5)); - /// - /// assert!(f16::NAN.copysign(f16::from_f32(1.0)).is_nan()); - /// ``` - #[inline] - #[must_use] - pub const fn copysign(self, sign: f16) -> f16 { - f16((sign.0 & 0x8000u16) | (self.0 & 0x7FFFu16)) - } - - /// Returns the maximum of the two numbers. - /// - /// If one of the arguments is NaN, then the other argument is returned. - /// - /// # Examples - /// - /// ``` - /// # use half::prelude::*; - /// let x = f16::from_f32(1.0); - /// let y = f16::from_f32(2.0); - /// - /// assert_eq!(x.max(y), y); - /// ``` - #[inline] - #[must_use] - pub fn max(self, other: f16) -> f16 { - if other > self && !other.is_nan() { - other - } else { - self - } - } - - /// Returns the minimum of the two numbers. - /// - /// If one of the arguments is NaN, then the other argument is returned. - /// - /// # Examples - /// - /// ``` - /// # use half::prelude::*; - /// let x = f16::from_f32(1.0); - /// let y = f16::from_f32(2.0); - /// - /// assert_eq!(x.min(y), x); - /// ``` - #[inline] - #[must_use] - pub fn min(self, other: f16) -> f16 { - if other < self && !other.is_nan() { - other - } else { - self - } - } - - /// Restrict a value to a certain interval unless it is NaN. - /// - /// Returns `max` if `self` is greater than `max`, and `min` if `self` is less than `min`. - /// Otherwise this returns `self`. - /// - /// Note that this function returns NaN if the initial value was NaN as well. - /// - /// # Panics - /// Panics if `min > max`, `min` is NaN, or `max` is NaN. - /// - /// # Examples - /// - /// ``` - /// # use half::prelude::*; - /// assert!(f16::from_f32(-3.0).clamp(f16::from_f32(-2.0), f16::from_f32(1.0)) == f16::from_f32(-2.0)); - /// assert!(f16::from_f32(0.0).clamp(f16::from_f32(-2.0), f16::from_f32(1.0)) == f16::from_f32(0.0)); - /// assert!(f16::from_f32(2.0).clamp(f16::from_f32(-2.0), f16::from_f32(1.0)) == f16::from_f32(1.0)); - /// assert!(f16::NAN.clamp(f16::from_f32(-2.0), f16::from_f32(1.0)).is_nan()); - /// ``` - #[inline] - #[must_use] - pub fn clamp(self, min: f16, max: f16) -> f16 { - assert!(min <= max); - let mut x = self; - if x < min { - x = min; - } - if x > max { - x = max; - } - x - } - - /// 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 `f16`. 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::f16; - /// let mut v: Vec<f16> = vec![]; - /// v.push(f16::ONE); - /// v.push(f16::INFINITY); - /// v.push(f16::NEG_INFINITY); - /// v.push(f16::NAN); - /// v.push(f16::MAX_SUBNORMAL); - /// v.push(-f16::MAX_SUBNORMAL); - /// v.push(f16::ZERO); - /// v.push(f16::NEG_ZERO); - /// v.push(f16::NEG_ONE); - /// v.push(f16::MIN_POSITIVE); - /// - /// v.sort_by(|a, b| a.total_cmp(&b)); - /// - /// assert!(v - /// .into_iter() - /// .zip( - /// [ - /// f16::NEG_INFINITY, - /// f16::NEG_ONE, - /// -f16::MAX_SUBNORMAL, - /// f16::NEG_ZERO, - /// f16::ZERO, - /// f16::MAX_SUBNORMAL, - /// f16::MIN_POSITIVE, - /// f16::ONE, - /// f16::INFINITY, - /// f16::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, [`f16`] 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::f16; - /// - /// #[derive(Serialize, Deserialize)] - /// struct MyStruct { - /// #[serde(serialize_with = "f16::serialize_as_f32")] - /// value: f16 // 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, [`f16`] 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::f16; - /// - /// #[derive(Serialize, Deserialize)] - /// struct MyStruct { - /// #[serde(serialize_with = "f16::serialize_as_string")] - /// value: f16 // 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 [`f16`] significant digits in base 10 - pub const DIGITS: u32 = 3; - /// [`f16`] - /// [machine epsilon](https://en.wikipedia.org/wiki/Machine_epsilon) value - /// - /// This is the difference between 1.0 and the next largest representable number. - pub const EPSILON: f16 = f16(0x1400u16); - /// [`f16`] positive Infinity (+∞) - pub const INFINITY: f16 = f16(0x7C00u16); - /// Number of [`f16`] significant digits in base 2 - pub const MANTISSA_DIGITS: u32 = 11; - /// Largest finite [`f16`] value - pub const MAX: f16 = f16(0x7BFF); - /// Maximum possible [`f16`] power of 10 exponent - pub const MAX_10_EXP: i32 = 4; - /// Maximum possible [`f16`] power of 2 exponent - pub const MAX_EXP: i32 = 16; - /// Smallest finite [`f16`] value - pub const MIN: f16 = f16(0xFBFF); - /// Minimum possible normal [`f16`] power of 10 exponent - pub const MIN_10_EXP: i32 = -4; - /// One greater than the minimum possible normal [`f16`] power of 2 exponent - pub const MIN_EXP: i32 = -13; - /// Smallest positive normal [`f16`] value - pub const MIN_POSITIVE: f16 = f16(0x0400u16); - /// [`f16`] Not a Number (NaN) - pub const NAN: f16 = f16(0x7E00u16); - /// [`f16`] negative infinity (-∞) - pub const NEG_INFINITY: f16 = f16(0xFC00u16); - /// The radix or base of the internal representation of [`f16`] - pub const RADIX: u32 = 2; - - /// Minimum positive subnormal [`f16`] value - pub const MIN_POSITIVE_SUBNORMAL: f16 = f16(0x0001u16); - /// Maximum subnormal [`f16`] value - pub const MAX_SUBNORMAL: f16 = f16(0x03FFu16); - - /// [`f16`] 1 - pub const ONE: f16 = f16(0x3C00u16); - /// [`f16`] 0 - pub const ZERO: f16 = f16(0x0000u16); - /// [`f16`] -0 - pub const NEG_ZERO: f16 = f16(0x8000u16); - /// [`f16`] -1 - pub const NEG_ONE: f16 = f16(0xBC00u16); - - /// [`f16`] Euler's number (ℯ) - pub const E: f16 = f16(0x4170u16); - /// [`f16`] Archimedes' constant (π) - pub const PI: f16 = f16(0x4248u16); - /// [`f16`] 1/π - pub const FRAC_1_PI: f16 = f16(0x3518u16); - /// [`f16`] 1/√2 - pub const FRAC_1_SQRT_2: f16 = f16(0x39A8u16); - /// [`f16`] 2/π - pub const FRAC_2_PI: f16 = f16(0x3918u16); - /// [`f16`] 2/√π - pub const FRAC_2_SQRT_PI: f16 = f16(0x3C83u16); - /// [`f16`] π/2 - pub const FRAC_PI_2: f16 = f16(0x3E48u16); - /// [`f16`] π/3 - pub const FRAC_PI_3: f16 = f16(0x3C30u16); - /// [`f16`] π/4 - pub const FRAC_PI_4: f16 = f16(0x3A48u16); - /// [`f16`] π/6 - pub const FRAC_PI_6: f16 = f16(0x3830u16); - /// [`f16`] π/8 - pub const FRAC_PI_8: f16 = f16(0x3648u16); - /// [`f16`] 𝗅𝗇 10 - pub const LN_10: f16 = f16(0x409Bu16); - /// [`f16`] 𝗅𝗇 2 - pub const LN_2: f16 = f16(0x398Cu16); - /// [`f16`] 𝗅𝗈𝗀₁₀ℯ - pub const LOG10_E: f16 = f16(0x36F3u16); - /// [`f16`] 𝗅𝗈𝗀₁₀2 - pub const LOG10_2: f16 = f16(0x34D1u16); - /// [`f16`] 𝗅𝗈𝗀₂ℯ - pub const LOG2_E: f16 = f16(0x3DC5u16); - /// [`f16`] 𝗅𝗈𝗀₂10 - pub const LOG2_10: f16 = f16(0x42A5u16); - /// [`f16`] √2 - pub const SQRT_2: f16 = f16(0x3DA8u16); -} - -impl From<f16> for f32 { - #[inline] - fn from(x: f16) -> f32 { - x.to_f32() - } -} - -impl From<f16> for f64 { - #[inline] - fn from(x: f16) -> f64 { - x.to_f64() - } -} - -impl From<i8> for f16 { - #[inline] - fn from(x: i8) -> f16 { - // Convert to f32, then to f16 - f16::from_f32(f32::from(x)) - } -} - -impl From<u8> for f16 { - #[inline] - fn from(x: u8) -> f16 { - // Convert to f32, then to f16 - f16::from_f32(f32::from(x)) - } -} - -impl PartialEq for f16 { - fn eq(&self, other: &f16) -> bool { - if self.is_nan() || other.is_nan() { - false - } else { - (self.0 == other.0) || ((self.0 | other.0) & 0x7FFFu16 == 0) - } - } -} - -impl PartialOrd for f16 { - fn partial_cmp(&self, other: &f16) -> Option<Ordering> { - if self.is_nan() || other.is_nan() { - None - } else { - let neg = self.0 & 0x8000u16 != 0; - let other_neg = other.0 & 0x8000u16 != 0; - match (neg, other_neg) { - (false, false) => Some(self.0.cmp(&other.0)), - (false, true) => { - if (self.0 | other.0) & 0x7FFFu16 == 0 { - Some(Ordering::Equal) - } else { - Some(Ordering::Greater) - } - } - (true, false) => { - if (self.0 | other.0) & 0x7FFFu16 == 0 { - Some(Ordering::Equal) - } else { - Some(Ordering::Less) - } - } - (true, true) => Some(other.0.cmp(&self.0)), - } - } - } - - fn lt(&self, other: &f16) -> bool { - if self.is_nan() || other.is_nan() { - false - } else { - let neg = self.0 & 0x8000u16 != 0; - let other_neg = other.0 & 0x8000u16 != 0; - match (neg, other_neg) { - (false, false) => self.0 < other.0, - (false, true) => false, - (true, false) => (self.0 | other.0) & 0x7FFFu16 != 0, - (true, true) => self.0 > other.0, - } - } - } - - fn le(&self, other: &f16) -> bool { - if self.is_nan() || other.is_nan() { - false - } else { - let neg = self.0 & 0x8000u16 != 0; - let other_neg = other.0 & 0x8000u16 != 0; - match (neg, other_neg) { - (false, false) => self.0 <= other.0, - (false, true) => (self.0 | other.0) & 0x7FFFu16 == 0, - (true, false) => true, - (true, true) => self.0 >= other.0, - } - } - } - - fn gt(&self, other: &f16) -> bool { - if self.is_nan() || other.is_nan() { - false - } else { - let neg = self.0 & 0x8000u16 != 0; - let other_neg = other.0 & 0x8000u16 != 0; - match (neg, other_neg) { - (false, false) => self.0 > other.0, - (false, true) => (self.0 | other.0) & 0x7FFFu16 != 0, - (true, false) => false, - (true, true) => self.0 < other.0, - } - } - } - - fn ge(&self, other: &f16) -> bool { - if self.is_nan() || other.is_nan() { - false - } else { - let neg = self.0 & 0x8000u16 != 0; - let other_neg = other.0 & 0x8000u16 != 0; - match (neg, other_neg) { - (false, false) => self.0 >= other.0, - (false, true) => true, - (true, false) => (self.0 | other.0) & 0x7FFFu16 == 0, - (true, true) => self.0 <= other.0, - } - } - } -} - -#[cfg(not(target_arch = "spirv"))] -impl FromStr for f16 { - type Err = ParseFloatError; - fn from_str(src: &str) -> Result<f16, ParseFloatError> { - f32::from_str(src).map(f16::from_f32) - } -} - -#[cfg(not(target_arch = "spirv"))] -impl Debug for f16 { - fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> { - write!(f, "{:?}", self.to_f32()) - } -} - -#[cfg(not(target_arch = "spirv"))] -impl Display for f16 { - fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> { - write!(f, "{}", self.to_f32()) - } -} - -#[cfg(not(target_arch = "spirv"))] -impl LowerExp for f16 { - fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> { - write!(f, "{:e}", self.to_f32()) - } -} - -#[cfg(not(target_arch = "spirv"))] -impl UpperExp for f16 { - fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> { - write!(f, "{:E}", self.to_f32()) - } -} - -#[cfg(not(target_arch = "spirv"))] -impl Binary for f16 { - fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> { - write!(f, "{:b}", self.0) - } -} - -#[cfg(not(target_arch = "spirv"))] -impl Octal for f16 { - fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> { - write!(f, "{:o}", self.0) - } -} - -#[cfg(not(target_arch = "spirv"))] -impl LowerHex for f16 { - fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> { - write!(f, "{:x}", self.0) - } -} - -#[cfg(not(target_arch = "spirv"))] -impl UpperHex for f16 { - fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> { - write!(f, "{:X}", self.0) - } -} - -impl Neg for f16 { - type Output = Self; - - #[inline] - fn neg(self) -> Self::Output { - Self(self.0 ^ 0x8000) - } -} - -impl Neg for &f16 { - type Output = <f16 as Neg>::Output; - - #[inline] - fn neg(self) -> Self::Output { - Neg::neg(*self) - } -} - -impl Add for f16 { - type Output = Self; - - #[inline] - fn add(self, rhs: Self) -> Self::Output { - Self::from_f32(Self::to_f32(self) + Self::to_f32(rhs)) - } -} - -impl Add<&f16> for f16 { - type Output = <f16 as Add<f16>>::Output; - - #[inline] - fn add(self, rhs: &f16) -> Self::Output { - self.add(*rhs) - } -} - -impl Add<&f16> for &f16 { - type Output = <f16 as Add<f16>>::Output; - - #[inline] - fn add(self, rhs: &f16) -> Self::Output { - (*self).add(*rhs) - } -} - -impl Add<f16> for &f16 { - type Output = <f16 as Add<f16>>::Output; - - #[inline] - fn add(self, rhs: f16) -> Self::Output { - (*self).add(rhs) - } -} - -impl AddAssign for f16 { - #[inline] - fn add_assign(&mut self, rhs: Self) { - *self = (*self).add(rhs); - } -} - -impl AddAssign<&f16> for f16 { - #[inline] - fn add_assign(&mut self, rhs: &f16) { - *self = (*self).add(rhs); - } -} - -impl Sub for f16 { - type Output = Self; - - #[inline] - fn sub(self, rhs: Self) -> Self::Output { - Self::from_f32(Self::to_f32(self) - Self::to_f32(rhs)) - } -} - -impl Sub<&f16> for f16 { - type Output = <f16 as Sub<f16>>::Output; - - #[inline] - fn sub(self, rhs: &f16) -> Self::Output { - self.sub(*rhs) - } -} - -impl Sub<&f16> for &f16 { - type Output = <f16 as Sub<f16>>::Output; - - #[inline] - fn sub(self, rhs: &f16) -> Self::Output { - (*self).sub(*rhs) - } -} - -impl Sub<f16> for &f16 { - type Output = <f16 as Sub<f16>>::Output; - - #[inline] - fn sub(self, rhs: f16) -> Self::Output { - (*self).sub(rhs) - } -} - -impl SubAssign for f16 { - #[inline] - fn sub_assign(&mut self, rhs: Self) { - *self = (*self).sub(rhs); - } -} - -impl SubAssign<&f16> for f16 { - #[inline] - fn sub_assign(&mut self, rhs: &f16) { - *self = (*self).sub(rhs); - } -} - -impl Mul for f16 { - type Output = Self; - - #[inline] - fn mul(self, rhs: Self) -> Self::Output { - Self::from_f32(Self::to_f32(self) * Self::to_f32(rhs)) - } -} - -impl Mul<&f16> for f16 { - type Output = <f16 as Mul<f16>>::Output; - - #[inline] - fn mul(self, rhs: &f16) -> Self::Output { - self.mul(*rhs) - } -} - -impl Mul<&f16> for &f16 { - type Output = <f16 as Mul<f16>>::Output; - - #[inline] - fn mul(self, rhs: &f16) -> Self::Output { - (*self).mul(*rhs) - } -} - -impl Mul<f16> for &f16 { - type Output = <f16 as Mul<f16>>::Output; - - #[inline] - fn mul(self, rhs: f16) -> Self::Output { - (*self).mul(rhs) - } -} - -impl MulAssign for f16 { - #[inline] - fn mul_assign(&mut self, rhs: Self) { - *self = (*self).mul(rhs); - } -} - -impl MulAssign<&f16> for f16 { - #[inline] - fn mul_assign(&mut self, rhs: &f16) { - *self = (*self).mul(rhs); - } -} - -impl Div for f16 { - type Output = Self; - - #[inline] - fn div(self, rhs: Self) -> Self::Output { - Self::from_f32(Self::to_f32(self) / Self::to_f32(rhs)) - } -} - -impl Div<&f16> for f16 { - type Output = <f16 as Div<f16>>::Output; - - #[inline] - fn div(self, rhs: &f16) -> Self::Output { - self.div(*rhs) - } -} - -impl Div<&f16> for &f16 { - type Output = <f16 as Div<f16>>::Output; - - #[inline] - fn div(self, rhs: &f16) -> Self::Output { - (*self).div(*rhs) - } -} - -impl Div<f16> for &f16 { - type Output = <f16 as Div<f16>>::Output; - - #[inline] - fn div(self, rhs: f16) -> Self::Output { - (*self).div(rhs) - } -} - -impl DivAssign for f16 { - #[inline] - fn div_assign(&mut self, rhs: Self) { - *self = (*self).div(rhs); - } -} - -impl DivAssign<&f16> for f16 { - #[inline] - fn div_assign(&mut self, rhs: &f16) { - *self = (*self).div(rhs); - } -} - -impl Rem for f16 { - type Output = Self; - - #[inline] - fn rem(self, rhs: Self) -> Self::Output { - Self::from_f32(Self::to_f32(self) % Self::to_f32(rhs)) - } -} - -impl Rem<&f16> for f16 { - type Output = <f16 as Rem<f16>>::Output; - - #[inline] - fn rem(self, rhs: &f16) -> Self::Output { - self.rem(*rhs) - } -} - -impl Rem<&f16> for &f16 { - type Output = <f16 as Rem<f16>>::Output; - - #[inline] - fn rem(self, rhs: &f16) -> Self::Output { - (*self).rem(*rhs) - } -} - -impl Rem<f16> for &f16 { - type Output = <f16 as Rem<f16>>::Output; - - #[inline] - fn rem(self, rhs: f16) -> Self::Output { - (*self).rem(rhs) - } -} - -impl RemAssign for f16 { - #[inline] - fn rem_assign(&mut self, rhs: Self) { - *self = (*self).rem(rhs); - } -} - -impl RemAssign<&f16> for f16 { - #[inline] - fn rem_assign(&mut self, rhs: &f16) { - *self = (*self).rem(rhs); - } -} - -impl Product for f16 { - #[inline] - fn product<I: Iterator<Item = Self>>(iter: I) -> Self { - f16::from_f32(iter.map(|f| f.to_f32()).product()) - } -} - -impl<'a> Product<&'a f16> for f16 { - #[inline] - fn product<I: Iterator<Item = &'a f16>>(iter: I) -> Self { - f16::from_f32(iter.map(|f| f.to_f32()).product()) - } -} - -impl Sum for f16 { - #[inline] - fn sum<I: Iterator<Item = Self>>(iter: I) -> Self { - f16::from_f32(iter.map(|f| f.to_f32()).sum()) - } -} - -impl<'a> Sum<&'a f16> for f16 { - #[inline] - fn sum<I: Iterator<Item = &'a f16>>(iter: I) -> Self { - f16::from_f32(iter.map(|f| f.to_f32()).product()) - } -} - -#[cfg(feature = "serde")] -struct Visitor; - -#[cfg(feature = "serde")] -impl<'de> Deserialize<'de> for f16 { - fn deserialize<D>(deserializer: D) -> Result<f16, D::Error> - where - D: serde::de::Deserializer<'de>, - { - deserializer.deserialize_newtype_struct("f16", Visitor) - } -} - -#[cfg(feature = "serde")] -impl<'de> serde::de::Visitor<'de> for Visitor { - type Value = f16; - - fn expecting(&self, formatter: &mut alloc::fmt::Formatter) -> alloc::fmt::Result { - write!(formatter, "tuple struct f16") - } - - fn visit_newtype_struct<D>(self, deserializer: D) -> Result<Self::Value, D::Error> - where - D: serde::Deserializer<'de>, - { - Ok(f16(<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(f16::from_f32(v)) - } - - fn visit_f64<E>(self, v: f64) -> Result<Self::Value, E> - where - E: serde::de::Error, - { - Ok(f16::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 = f16::from_f32(2.0); - assert_eq!(<i32 as AsPrimitive<f16>>::as_(2), two); - assert_eq!(<f16 as AsPrimitive<i32>>::as_(two), 2); - - assert_eq!(<f32 as AsPrimitive<f16>>::as_(2.0), two); - assert_eq!(<f16 as AsPrimitive<f32>>::as_(two), 2.0); - - assert_eq!(<f64 as AsPrimitive<f16>>::as_(2.0), two); - assert_eq!(<f16 as AsPrimitive<f64>>::as_(two), 2.0); - } - - #[cfg(feature = "num-traits")] - #[test] - fn to_primitive() { - let two = f16::from_f32(2.0); - assert_eq!(ToPrimitive::to_i32(&two).unwrap(), 2i32); - assert_eq!(ToPrimitive::to_f32(&two).unwrap(), 2.0f32); - assert_eq!(ToPrimitive::to_f64(&two).unwrap(), 2.0f64); - } - - #[cfg(feature = "num-traits")] - #[test] - fn from_primitive() { - let two = f16::from_f32(2.0); - assert_eq!(<f16 as FromPrimitive>::from_i32(2).unwrap(), two); - assert_eq!(<f16 as FromPrimitive>::from_f32(2.0).unwrap(), two); - assert_eq!(<f16 as FromPrimitive>::from_f64(2.0).unwrap(), two); - } - - #[test] - fn test_f16_consts() { - // DIGITS - let digits = ((f16::MANTISSA_DIGITS as f32 - 1.0) * 2f32.log10()).floor() as u32; - assert_eq!(f16::DIGITS, digits); - // sanity check to show test is good - let digits32 = ((core::f32::MANTISSA_DIGITS as f32 - 1.0) * 2f32.log10()).floor() as u32; - assert_eq!(core::f32::DIGITS, digits32); - - // EPSILON - let one = f16::from_f32(1.0); - let one_plus_epsilon = f16::from_bits(one.to_bits() + 1); - let epsilon = f16::from_f32(one_plus_epsilon.to_f32() - 1.0); - assert_eq!(f16::EPSILON, epsilon); - // sanity check to show test is good - let one_plus_epsilon32 = f32::from_bits(1.0f32.to_bits() + 1); - let epsilon32 = one_plus_epsilon32 - 1f32; - assert_eq!(core::f32::EPSILON, epsilon32); - - // MAX, MIN and MIN_POSITIVE - let max = f16::from_bits(f16::INFINITY.to_bits() - 1); - let min = f16::from_bits(f16::NEG_INFINITY.to_bits() - 1); - let min_pos = f16::from_f32(2f32.powi(f16::MIN_EXP - 1)); - assert_eq!(f16::MAX, max); - assert_eq!(f16::MIN, min); - assert_eq!(f16::MIN_POSITIVE, min_pos); - // sanity check to show test is good - let max32 = f32::from_bits(core::f32::INFINITY.to_bits() - 1); - let min32 = f32::from_bits(core::f32::NEG_INFINITY.to_bits() - 1); - let min_pos32 = 2f32.powi(core::f32::MIN_EXP - 1); - assert_eq!(core::f32::MAX, max32); - assert_eq!(core::f32::MIN, min32); - assert_eq!(core::f32::MIN_POSITIVE, min_pos32); - - // MIN_10_EXP and MAX_10_EXP - let ten_to_min = 10f32.powi(f16::MIN_10_EXP); - assert!(ten_to_min / 10.0 < f16::MIN_POSITIVE.to_f32()); - assert!(ten_to_min > f16::MIN_POSITIVE.to_f32()); - let ten_to_max = 10f32.powi(f16::MAX_10_EXP); - assert!(ten_to_max < f16::MAX.to_f32()); - assert!(ten_to_max * 10.0 > f16::MAX.to_f32()); - // sanity check to show test is good - let ten_to_min32 = 10f64.powi(core::f32::MIN_10_EXP); - assert!(ten_to_min32 / 10.0 < f64::from(core::f32::MIN_POSITIVE)); - assert!(ten_to_min32 > f64::from(core::f32::MIN_POSITIVE)); - let ten_to_max32 = 10f64.powi(core::f32::MAX_10_EXP); - assert!(ten_to_max32 < f64::from(core::f32::MAX)); - assert!(ten_to_max32 * 10.0 > f64::from(core::f32::MAX)); - } - - #[test] - fn test_f16_consts_from_f32() { - let one = f16::from_f32(1.0); - let zero = f16::from_f32(0.0); - let neg_zero = f16::from_f32(-0.0); - let neg_one = f16::from_f32(-1.0); - let inf = f16::from_f32(core::f32::INFINITY); - let neg_inf = f16::from_f32(core::f32::NEG_INFINITY); - let nan = f16::from_f32(core::f32::NAN); - - assert_eq!(f16::ONE, one); - assert_eq!(f16::ZERO, zero); - assert!(zero.is_sign_positive()); - assert_eq!(f16::NEG_ZERO, neg_zero); - assert!(neg_zero.is_sign_negative()); - assert_eq!(f16::NEG_ONE, neg_one); - assert!(neg_one.is_sign_negative()); - assert_eq!(f16::INFINITY, inf); - assert_eq!(f16::NEG_INFINITY, neg_inf); - assert!(nan.is_nan()); - assert!(f16::NAN.is_nan()); - - let e = f16::from_f32(core::f32::consts::E); - let pi = f16::from_f32(core::f32::consts::PI); - let frac_1_pi = f16::from_f32(core::f32::consts::FRAC_1_PI); - let frac_1_sqrt_2 = f16::from_f32(core::f32::consts::FRAC_1_SQRT_2); - let frac_2_pi = f16::from_f32(core::f32::consts::FRAC_2_PI); - let frac_2_sqrt_pi = f16::from_f32(core::f32::consts::FRAC_2_SQRT_PI); - let frac_pi_2 = f16::from_f32(core::f32::consts::FRAC_PI_2); - let frac_pi_3 = f16::from_f32(core::f32::consts::FRAC_PI_3); - let frac_pi_4 = f16::from_f32(core::f32::consts::FRAC_PI_4); - let frac_pi_6 = f16::from_f32(core::f32::consts::FRAC_PI_6); - let frac_pi_8 = f16::from_f32(core::f32::consts::FRAC_PI_8); - let ln_10 = f16::from_f32(core::f32::consts::LN_10); - let ln_2 = f16::from_f32(core::f32::consts::LN_2); - let log10_e = f16::from_f32(core::f32::consts::LOG10_E); - // core::f32::consts::LOG10_2 requires rustc 1.43.0 - let log10_2 = f16::from_f32(2f32.log10()); - let log2_e = f16::from_f32(core::f32::consts::LOG2_E); - // core::f32::consts::LOG2_10 requires rustc 1.43.0 - let log2_10 = f16::from_f32(10f32.log2()); - let sqrt_2 = f16::from_f32(core::f32::consts::SQRT_2); - - assert_eq!(f16::E, e); - assert_eq!(f16::PI, pi); - assert_eq!(f16::FRAC_1_PI, frac_1_pi); - assert_eq!(f16::FRAC_1_SQRT_2, frac_1_sqrt_2); - assert_eq!(f16::FRAC_2_PI, frac_2_pi); - assert_eq!(f16::FRAC_2_SQRT_PI, frac_2_sqrt_pi); - assert_eq!(f16::FRAC_PI_2, frac_pi_2); - assert_eq!(f16::FRAC_PI_3, frac_pi_3); - assert_eq!(f16::FRAC_PI_4, frac_pi_4); - assert_eq!(f16::FRAC_PI_6, frac_pi_6); - assert_eq!(f16::FRAC_PI_8, frac_pi_8); - assert_eq!(f16::LN_10, ln_10); - assert_eq!(f16::LN_2, ln_2); - assert_eq!(f16::LOG10_E, log10_e); - assert_eq!(f16::LOG10_2, log10_2); - assert_eq!(f16::LOG2_E, log2_e); - assert_eq!(f16::LOG2_10, log2_10); - assert_eq!(f16::SQRT_2, sqrt_2); - } - - #[test] - fn test_f16_consts_from_f64() { - let one = f16::from_f64(1.0); - let zero = f16::from_f64(0.0); - let neg_zero = f16::from_f64(-0.0); - let inf = f16::from_f64(core::f64::INFINITY); - let neg_inf = f16::from_f64(core::f64::NEG_INFINITY); - let nan = f16::from_f64(core::f64::NAN); - - assert_eq!(f16::ONE, one); - assert_eq!(f16::ZERO, zero); - assert!(zero.is_sign_positive()); - assert_eq!(f16::NEG_ZERO, neg_zero); - assert!(neg_zero.is_sign_negative()); - assert_eq!(f16::INFINITY, inf); - assert_eq!(f16::NEG_INFINITY, neg_inf); - assert!(nan.is_nan()); - assert!(f16::NAN.is_nan()); - - let e = f16::from_f64(core::f64::consts::E); - let pi = f16::from_f64(core::f64::consts::PI); - let frac_1_pi = f16::from_f64(core::f64::consts::FRAC_1_PI); - let frac_1_sqrt_2 = f16::from_f64(core::f64::consts::FRAC_1_SQRT_2); - let frac_2_pi = f16::from_f64(core::f64::consts::FRAC_2_PI); - let frac_2_sqrt_pi = f16::from_f64(core::f64::consts::FRAC_2_SQRT_PI); - let frac_pi_2 = f16::from_f64(core::f64::consts::FRAC_PI_2); - let frac_pi_3 = f16::from_f64(core::f64::consts::FRAC_PI_3); - let frac_pi_4 = f16::from_f64(core::f64::consts::FRAC_PI_4); - let frac_pi_6 = f16::from_f64(core::f64::consts::FRAC_PI_6); - let frac_pi_8 = f16::from_f64(core::f64::consts::FRAC_PI_8); - let ln_10 = f16::from_f64(core::f64::consts::LN_10); - let ln_2 = f16::from_f64(core::f64::consts::LN_2); - let log10_e = f16::from_f64(core::f64::consts::LOG10_E); - // core::f64::consts::LOG10_2 requires rustc 1.43.0 - let log10_2 = f16::from_f64(2f64.log10()); - let log2_e = f16::from_f64(core::f64::consts::LOG2_E); - // core::f64::consts::LOG2_10 requires rustc 1.43.0 - let log2_10 = f16::from_f64(10f64.log2()); - let sqrt_2 = f16::from_f64(core::f64::consts::SQRT_2); - - assert_eq!(f16::E, e); - assert_eq!(f16::PI, pi); - assert_eq!(f16::FRAC_1_PI, frac_1_pi); - assert_eq!(f16::FRAC_1_SQRT_2, frac_1_sqrt_2); - assert_eq!(f16::FRAC_2_PI, frac_2_pi); - assert_eq!(f16::FRAC_2_SQRT_PI, frac_2_sqrt_pi); - assert_eq!(f16::FRAC_PI_2, frac_pi_2); - assert_eq!(f16::FRAC_PI_3, frac_pi_3); - assert_eq!(f16::FRAC_PI_4, frac_pi_4); - assert_eq!(f16::FRAC_PI_6, frac_pi_6); - assert_eq!(f16::FRAC_PI_8, frac_pi_8); - assert_eq!(f16::LN_10, ln_10); - assert_eq!(f16::LN_2, ln_2); - assert_eq!(f16::LOG10_E, log10_e); - assert_eq!(f16::LOG10_2, log10_2); - assert_eq!(f16::LOG2_E, log2_e); - assert_eq!(f16::LOG2_10, log2_10); - assert_eq!(f16::SQRT_2, sqrt_2); - } - - #[test] - fn test_nan_conversion_to_smaller() { - let nan64 = f64::from_bits(0x7FF0_0000_0000_0001u64); - let neg_nan64 = f64::from_bits(0xFFF0_0000_0000_0001u64); - let nan32 = f32::from_bits(0x7F80_0001u32); - let neg_nan32 = f32::from_bits(0xFF80_0001u32); - let nan32_from_64 = nan64 as f32; - let neg_nan32_from_64 = neg_nan64 as f32; - let nan16_from_64 = f16::from_f64(nan64); - let neg_nan16_from_64 = f16::from_f64(neg_nan64); - let nan16_from_32 = f16::from_f32(nan32); - let neg_nan16_from_32 = f16::from_f32(neg_nan32); - - assert!(nan64.is_nan() && nan64.is_sign_positive()); - assert!(neg_nan64.is_nan() && neg_nan64.is_sign_negative()); - assert!(nan32.is_nan() && nan32.is_sign_positive()); - assert!(neg_nan32.is_nan() && neg_nan32.is_sign_negative()); - assert!(nan32_from_64.is_nan() && nan32_from_64.is_sign_positive()); - assert!(neg_nan32_from_64.is_nan() && neg_nan32_from_64.is_sign_negative()); - assert!(nan16_from_64.is_nan() && nan16_from_64.is_sign_positive()); - assert!(neg_nan16_from_64.is_nan() && neg_nan16_from_64.is_sign_negative()); - assert!(nan16_from_32.is_nan() && nan16_from_32.is_sign_positive()); - assert!(neg_nan16_from_32.is_nan() && neg_nan16_from_32.is_sign_negative()); - } - - #[test] - fn test_nan_conversion_to_larger() { - let nan16 = f16::from_bits(0x7C01u16); - let neg_nan16 = f16::from_bits(0xFC01u16); - let nan32 = f32::from_bits(0x7F80_0001u32); - let neg_nan32 = f32::from_bits(0xFF80_0001u32); - let nan32_from_16 = f32::from(nan16); - let neg_nan32_from_16 = f32::from(neg_nan16); - let nan64_from_16 = f64::from(nan16); - let neg_nan64_from_16 = f64::from(neg_nan16); - let nan64_from_32 = f64::from(nan32); - let neg_nan64_from_32 = f64::from(neg_nan32); - - assert!(nan16.is_nan() && nan16.is_sign_positive()); - assert!(neg_nan16.is_nan() && neg_nan16.is_sign_negative()); - assert!(nan32.is_nan() && nan32.is_sign_positive()); - assert!(neg_nan32.is_nan() && neg_nan32.is_sign_negative()); - assert!(nan32_from_16.is_nan() && nan32_from_16.is_sign_positive()); - assert!(neg_nan32_from_16.is_nan() && neg_nan32_from_16.is_sign_negative()); - assert!(nan64_from_16.is_nan() && nan64_from_16.is_sign_positive()); - assert!(neg_nan64_from_16.is_nan() && neg_nan64_from_16.is_sign_negative()); - assert!(nan64_from_32.is_nan() && nan64_from_32.is_sign_positive()); - assert!(neg_nan64_from_32.is_nan() && neg_nan64_from_32.is_sign_negative()); - } - - #[test] - fn test_f16_to_f32() { - let f = f16::from_f32(7.0); - assert_eq!(f.to_f32(), 7.0f32); - - // 7.1 is NOT exactly representable in 16-bit, it's rounded - let f = f16::from_f32(7.1); - let diff = (f.to_f32() - 7.1f32).abs(); - // diff must be <= 4 * EPSILON, as 7 has two more significant bits than 1 - assert!(diff <= 4.0 * f16::EPSILON.to_f32()); - - assert_eq!(f16::from_bits(0x0000_0001).to_f32(), 2.0f32.powi(-24)); - assert_eq!(f16::from_bits(0x0000_0005).to_f32(), 5.0 * 2.0f32.powi(-24)); - - assert_eq!(f16::from_bits(0x0000_0001), f16::from_f32(2.0f32.powi(-24))); - assert_eq!( - f16::from_bits(0x0000_0005), - f16::from_f32(5.0 * 2.0f32.powi(-24)) - ); - } - - #[test] - fn test_f16_to_f64() { - let f = f16::from_f64(7.0); - assert_eq!(f.to_f64(), 7.0f64); - - // 7.1 is NOT exactly representable in 16-bit, it's rounded - let f = f16::from_f64(7.1); - let diff = (f.to_f64() - 7.1f64).abs(); - // diff must be <= 4 * EPSILON, as 7 has two more significant bits than 1 - assert!(diff <= 4.0 * f16::EPSILON.to_f64()); - - assert_eq!(f16::from_bits(0x0000_0001).to_f64(), 2.0f64.powi(-24)); - assert_eq!(f16::from_bits(0x0000_0005).to_f64(), 5.0 * 2.0f64.powi(-24)); - - assert_eq!(f16::from_bits(0x0000_0001), f16::from_f64(2.0f64.powi(-24))); - assert_eq!( - f16::from_bits(0x0000_0005), - f16::from_f64(5.0 * 2.0f64.powi(-24)) - ); - } - - #[test] - fn test_comparisons() { - let zero = f16::from_f64(0.0); - let one = f16::from_f64(1.0); - let neg_zero = f16::from_f64(-0.0); - let neg_one = f16::from_f64(-1.0); - - assert_eq!(zero.partial_cmp(&neg_zero), Some(Ordering::Equal)); - assert_eq!(neg_zero.partial_cmp(&zero), Some(Ordering::Equal)); - assert!(zero == neg_zero); - assert!(neg_zero == zero); - assert!(!(zero != neg_zero)); - assert!(!(neg_zero != zero)); - assert!(!(zero < neg_zero)); - assert!(!(neg_zero < zero)); - assert!(zero <= neg_zero); - assert!(neg_zero <= zero); - assert!(!(zero > neg_zero)); - assert!(!(neg_zero > zero)); - assert!(zero >= neg_zero); - assert!(neg_zero >= zero); - - assert_eq!(one.partial_cmp(&neg_zero), Some(Ordering::Greater)); - assert_eq!(neg_zero.partial_cmp(&one), Some(Ordering::Less)); - assert!(!(one == neg_zero)); - assert!(!(neg_zero == one)); - assert!(one != neg_zero); - assert!(neg_zero != one); - assert!(!(one < neg_zero)); - assert!(neg_zero < one); - assert!(!(one <= neg_zero)); - assert!(neg_zero <= one); - assert!(one > neg_zero); - assert!(!(neg_zero > one)); - assert!(one >= neg_zero); - assert!(!(neg_zero >= one)); - - assert_eq!(one.partial_cmp(&neg_one), Some(Ordering::Greater)); - assert_eq!(neg_one.partial_cmp(&one), Some(Ordering::Less)); - assert!(!(one == neg_one)); - assert!(!(neg_one == one)); - assert!(one != neg_one); - assert!(neg_one != one); - assert!(!(one < neg_one)); - assert!(neg_one < one); - assert!(!(one <= neg_one)); - assert!(neg_one <= one); - assert!(one > neg_one); - assert!(!(neg_one > one)); - assert!(one >= neg_one); - assert!(!(neg_one >= one)); - } - - #[test] - #[allow(clippy::erasing_op, clippy::identity_op)] - fn round_to_even_f32() { - // smallest positive subnormal = 0b0.0000_0000_01 * 2^-14 = 2^-24 - let min_sub = f16::from_bits(1); - let min_sub_f = (-24f32).exp2(); - assert_eq!(f16::from_f32(min_sub_f).to_bits(), min_sub.to_bits()); - assert_eq!(f32::from(min_sub).to_bits(), min_sub_f.to_bits()); - - // 0.0000000000_011111 rounded to 0.0000000000 (< tie, no rounding) - // 0.0000000000_100000 rounded to 0.0000000000 (tie and even, remains at even) - // 0.0000000000_100001 rounded to 0.0000000001 (> tie, rounds up) - assert_eq!( - f16::from_f32(min_sub_f * 0.49).to_bits(), - min_sub.to_bits() * 0 - ); - assert_eq!( - f16::from_f32(min_sub_f * 0.50).to_bits(), - min_sub.to_bits() * 0 - ); - assert_eq!( - f16::from_f32(min_sub_f * 0.51).to_bits(), - min_sub.to_bits() * 1 - ); - - // 0.0000000001_011111 rounded to 0.0000000001 (< tie, no rounding) - // 0.0000000001_100000 rounded to 0.0000000010 (tie and odd, rounds up to even) - // 0.0000000001_100001 rounded to 0.0000000010 (> tie, rounds up) - assert_eq!( - f16::from_f32(min_sub_f * 1.49).to_bits(), - min_sub.to_bits() * 1 - ); - assert_eq!( - f16::from_f32(min_sub_f * 1.50).to_bits(), - min_sub.to_bits() * 2 - ); - assert_eq!( - f16::from_f32(min_sub_f * 1.51).to_bits(), - min_sub.to_bits() * 2 - ); - - // 0.0000000010_011111 rounded to 0.0000000010 (< tie, no rounding) - // 0.0000000010_100000 rounded to 0.0000000010 (tie and even, remains at even) - // 0.0000000010_100001 rounded to 0.0000000011 (> tie, rounds up) - assert_eq!( - f16::from_f32(min_sub_f * 2.49).to_bits(), - min_sub.to_bits() * 2 - ); - assert_eq!( - f16::from_f32(min_sub_f * 2.50).to_bits(), - min_sub.to_bits() * 2 - ); - assert_eq!( - f16::from_f32(min_sub_f * 2.51).to_bits(), - min_sub.to_bits() * 3 - ); - - assert_eq!( - f16::from_f32(2000.49f32).to_bits(), - f16::from_f32(2000.0).to_bits() - ); - assert_eq!( - f16::from_f32(2000.50f32).to_bits(), - f16::from_f32(2000.0).to_bits() - ); - assert_eq!( - f16::from_f32(2000.51f32).to_bits(), - f16::from_f32(2001.0).to_bits() - ); - assert_eq!( - f16::from_f32(2001.49f32).to_bits(), - f16::from_f32(2001.0).to_bits() - ); - assert_eq!( - f16::from_f32(2001.50f32).to_bits(), - f16::from_f32(2002.0).to_bits() - ); - assert_eq!( - f16::from_f32(2001.51f32).to_bits(), - f16::from_f32(2002.0).to_bits() - ); - assert_eq!( - f16::from_f32(2002.49f32).to_bits(), - f16::from_f32(2002.0).to_bits() - ); - assert_eq!( - f16::from_f32(2002.50f32).to_bits(), - f16::from_f32(2002.0).to_bits() - ); - assert_eq!( - f16::from_f32(2002.51f32).to_bits(), - f16::from_f32(2003.0).to_bits() - ); - } - - #[test] - #[allow(clippy::erasing_op, clippy::identity_op)] - fn round_to_even_f64() { - // smallest positive subnormal = 0b0.0000_0000_01 * 2^-14 = 2^-24 - let min_sub = f16::from_bits(1); - let min_sub_f = (-24f64).exp2(); - assert_eq!(f16::from_f64(min_sub_f).to_bits(), min_sub.to_bits()); - assert_eq!(f64::from(min_sub).to_bits(), min_sub_f.to_bits()); - - // 0.0000000000_011111 rounded to 0.0000000000 (< tie, no rounding) - // 0.0000000000_100000 rounded to 0.0000000000 (tie and even, remains at even) - // 0.0000000000_100001 rounded to 0.0000000001 (> tie, rounds up) - assert_eq!( - f16::from_f64(min_sub_f * 0.49).to_bits(), - min_sub.to_bits() * 0 - ); - assert_eq!( - f16::from_f64(min_sub_f * 0.50).to_bits(), - min_sub.to_bits() * 0 - ); - assert_eq!( - f16::from_f64(min_sub_f * 0.51).to_bits(), - min_sub.to_bits() * 1 - ); - - // 0.0000000001_011111 rounded to 0.0000000001 (< tie, no rounding) - // 0.0000000001_100000 rounded to 0.0000000010 (tie and odd, rounds up to even) - // 0.0000000001_100001 rounded to 0.0000000010 (> tie, rounds up) - assert_eq!( - f16::from_f64(min_sub_f * 1.49).to_bits(), - min_sub.to_bits() * 1 - ); - assert_eq!( - f16::from_f64(min_sub_f * 1.50).to_bits(), - min_sub.to_bits() * 2 - ); - assert_eq!( - f16::from_f64(min_sub_f * 1.51).to_bits(), - min_sub.to_bits() * 2 - ); - - // 0.0000000010_011111 rounded to 0.0000000010 (< tie, no rounding) - // 0.0000000010_100000 rounded to 0.0000000010 (tie and even, remains at even) - // 0.0000000010_100001 rounded to 0.0000000011 (> tie, rounds up) - assert_eq!( - f16::from_f64(min_sub_f * 2.49).to_bits(), - min_sub.to_bits() * 2 - ); - assert_eq!( - f16::from_f64(min_sub_f * 2.50).to_bits(), - min_sub.to_bits() * 2 - ); - assert_eq!( - f16::from_f64(min_sub_f * 2.51).to_bits(), - min_sub.to_bits() * 3 - ); - - assert_eq!( - f16::from_f64(2000.49f64).to_bits(), - f16::from_f64(2000.0).to_bits() - ); - assert_eq!( - f16::from_f64(2000.50f64).to_bits(), - f16::from_f64(2000.0).to_bits() - ); - assert_eq!( - f16::from_f64(2000.51f64).to_bits(), - f16::from_f64(2001.0).to_bits() - ); - assert_eq!( - f16::from_f64(2001.49f64).to_bits(), - f16::from_f64(2001.0).to_bits() - ); - assert_eq!( - f16::from_f64(2001.50f64).to_bits(), - f16::from_f64(2002.0).to_bits() - ); - assert_eq!( - f16::from_f64(2001.51f64).to_bits(), - f16::from_f64(2002.0).to_bits() - ); - assert_eq!( - f16::from_f64(2002.49f64).to_bits(), - f16::from_f64(2002.0).to_bits() - ); - assert_eq!( - f16::from_f64(2002.50f64).to_bits(), - f16::from_f64(2002.0).to_bits() - ); - assert_eq!( - f16::from_f64(2002.51f64).to_bits(), - f16::from_f64(2003.0).to_bits() - ); - } - - impl quickcheck::Arbitrary for f16 { - fn arbitrary(g: &mut quickcheck::Gen) -> Self { - f16(u16::arbitrary(g)) - } - } - - #[quickcheck] - fn qc_roundtrip_f16_f32_is_identity(f: f16) -> bool { - let roundtrip = f16::from_f32(f.to_f32()); - if f.is_nan() { - roundtrip.is_nan() && f.is_sign_negative() == roundtrip.is_sign_negative() - } else { - f.0 == roundtrip.0 - } - } - - #[quickcheck] - fn qc_roundtrip_f16_f64_is_identity(f: f16) -> bool { - let roundtrip = f16::from_f64(f.to_f64()); - if f.is_nan() { - roundtrip.is_nan() && f.is_sign_negative() == roundtrip.is_sign_negative() - } else { - f.0 == roundtrip.0 - } - } -} |