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Diffstat (limited to 'vendor/half/src/binary16.rs')
| -rw-r--r-- | vendor/half/src/binary16.rs | 1711 |
1 files changed, 1711 insertions, 0 deletions
diff --git a/vendor/half/src/binary16.rs b/vendor/half/src/binary16.rs new file mode 100644 index 000000000..8d3fad75e --- /dev/null +++ b/vendor/half/src/binary16.rs @@ -0,0 +1,1711 @@ +#[cfg(feature = "bytemuck")] +use bytemuck::{Pod, Zeroable}; +use core::{ + cmp::Ordering, + fmt::{ + Binary, Debug, Display, Error, Formatter, LowerExp, LowerHex, Octal, UpperExp, UpperHex, + }, + iter::{Product, Sum}, + num::{FpCategory, ParseFloatError}, + ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Rem, RemAssign, Sub, SubAssign}, + str::FromStr, +}; +#[cfg(feature = "serde")] +use serde::{Deserialize, Serialize}; +#[cfg(feature = "zerocopy")] +use zerocopy::{AsBytes, FromBytes}; + +pub(crate) mod convert; + +/// A 16-bit floating point type implementing the IEEE 754-2008 standard [`binary16`] a.k.a `half` +/// format. +/// +/// This 16-bit floating point type is intended for efficient storage where the full range and +/// precision of a larger floating point value is not required. Because [`f16`] is primarily for +/// efficient storage, floating point operations such as addition, multiplication, etc. are not +/// implemented. Operations should be performed with [`f32`] or higher-precision types and converted +/// to/from [`f16`] as necessary. +/// +/// [`binary16`]: https://en.wikipedia.org/wiki/Half-precision_floating-point_format +#[allow(non_camel_case_types)] +#[derive(Clone, Copy, Default)] +#[repr(transparent)] +#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))] +#[cfg_attr(feature = "bytemuck", derive(Zeroable, Pod))] +#[cfg_attr(feature = "zerocopy", derive(AsBytes, FromBytes))] +pub struct f16(u16); + +#[doc(hidden)] +#[deprecated( + since = "1.4.0", + note = "all constants moved to associated constants of `f16`" +)] +pub mod consts { + use super::f16; + + #[deprecated(since = "1.4.0", note = "moved to `f16::DIGITS`")] + pub const DIGITS: u32 = f16::DIGITS; + #[deprecated(since = "1.4.0", note = "moved to `f16::EPSILON`")] + pub const EPSILON: f16 = f16::EPSILON; + #[deprecated(since = "1.4.0", note = "moved to `f16::INFINITY`")] + pub const INFINITY: f16 = f16::INFINITY; + #[deprecated(since = "1.4.0", note = "moved to `f16::MANTISSA_DIGITS`")] + pub const MANTISSA_DIGITS: u32 = f16::MANTISSA_DIGITS; + #[deprecated(since = "1.4.0", note = "moved to `f16::MAX`")] + pub const MAX: f16 = f16::MAX; + #[deprecated(since = "1.4.0", note = "moved to `f16::MAX_10_EXP`")] + pub const MAX_10_EXP: i32 = f16::MAX_10_EXP; + #[deprecated(since = "1.4.0", note = "moved to `f16::MAX_EXP`")] + pub const MAX_EXP: i32 = f16::MAX_EXP; + #[deprecated(since = "1.4.0", note = "moved to `f16::MIN`")] + pub const MIN: f16 = f16::MIN; + #[deprecated(since = "1.4.0", note = "moved to `f16::MIN_10_EXP`")] + pub const MIN_10_EXP: i32 = f16::MIN_10_EXP; + #[deprecated(since = "1.4.0", note = "moved to `f16::MIN_EXP`")] + pub const MIN_EXP: i32 = f16::MIN_EXP; + #[deprecated(since = "1.4.0", note = "moved to `f16::MIN_POSITIVE`")] + pub const MIN_POSITIVE: f16 = f16::MIN_POSITIVE; + #[deprecated(since = "1.4.0", note = "moved to `f16::NAN`")] + pub const NAN: f16 = f16::NAN; + #[deprecated(since = "1.4.0", note = "moved to `f16::NEG_INFINITY`")] + pub const NEG_INFINITY: f16 = f16::NEG_INFINITY; + #[deprecated(since = "1.4.0", note = "moved to `f16::RADIX`")] + pub const RADIX: u32 = f16::RADIX; + + #[deprecated(since = "1.4.0", note = "moved to `f16::MIN_POSITIVE_SUBNORMAL`")] + pub const MIN_POSITIVE_SUBNORMAL: f16 = f16::MIN_POSITIVE_SUBNORMAL; + #[deprecated(since = "1.4.0", note = "moved to `f16::MAX_SUBNORMAL`")] + pub const MAX_SUBNORMAL: f16 = f16::MAX_SUBNORMAL; + + #[deprecated(since = "1.4.0", note = "moved to `f16::ONE`")] + pub const ONE: f16 = f16::ONE; + #[deprecated(since = "1.4.0", note = "moved to `f16::ZERO`")] + pub const ZERO: f16 = f16::ZERO; + #[deprecated(since = "1.4.0", note = "moved to `f16::NEG_ZERO`")] + pub const NEG_ZERO: f16 = f16::NEG_ZERO; + + #[deprecated(since = "1.4.0", note = "moved to `f16::E`")] + pub const E: f16 = f16::E; + #[deprecated(since = "1.4.0", note = "moved to `f16::PI`")] + pub const PI: f16 = f16::PI; + #[deprecated(since = "1.4.0", note = "moved to `f16::FRAC_1_PI`")] + pub const FRAC_1_PI: f16 = f16::FRAC_1_PI; + #[deprecated(since = "1.4.0", note = "moved to `f16::FRAC_1_SQRT_2`")] + pub const FRAC_1_SQRT_2: f16 = f16::FRAC_1_SQRT_2; + #[deprecated(since = "1.4.0", note = "moved to `f16::FRAC_2_PI`")] + pub const FRAC_2_PI: f16 = f16::FRAC_2_PI; + #[deprecated(since = "1.4.0", note = "moved to `f16::FRAC_2_SQRT_PI`")] + pub const FRAC_2_SQRT_PI: f16 = f16::FRAC_2_SQRT_PI; + #[deprecated(since = "1.4.0", note = "moved to `f16::FRAC_PI_2`")] + pub const FRAC_PI_2: f16 = f16::FRAC_PI_2; + #[deprecated(since = "1.4.0", note = "moved to `f16::FRAC_PI_3`")] + pub const FRAC_PI_3: f16 = f16::FRAC_PI_3; + #[deprecated(since = "1.4.0", note = "moved to `f16::FRAC_PI_4`")] + pub const FRAC_PI_4: f16 = f16::FRAC_PI_4; + #[deprecated(since = "1.4.0", note = "moved to `f16::FRAC_PI_6`")] + pub const FRAC_PI_6: f16 = f16::FRAC_PI_6; + #[deprecated(since = "1.4.0", note = "moved to `f16::FRAC_PI_8`")] + pub const FRAC_PI_8: f16 = f16::FRAC_PI_8; + #[deprecated(since = "1.4.0", note = "moved to `f16::LN_10`")] + pub const LN_10: f16 = f16::LN_10; + #[deprecated(since = "1.4.0", note = "moved to `f16::LN_2`")] + pub const LN_2: f16 = f16::LN_2; + #[deprecated(since = "1.4.0", note = "moved to `f16::LOG10_E`")] + pub const LOG10_E: f16 = f16::LOG10_E; + #[deprecated(since = "1.4.0", note = "moved to `f16::LOG2_E`")] + pub const LOG2_E: f16 = f16::LOG2_E; + #[deprecated(since = "1.4.0", note = "moved to `f16::SQRT_2`")] + pub const SQRT_2: f16 = f16::SQRT_2; +} + +impl f16 { + /// Constructs a 16-bit floating point value from the raw bits. + #[inline] + pub const fn from_bits(bits: u16) -> f16 { + f16(bits) + } + + /// Constructs a 16-bit floating point value from a 32-bit floating point value. + /// + /// If the 32-bit value is to large to fit in 16-bits, ±∞ will result. NaN values are + /// preserved. 32-bit subnormal values are too tiny to be represented in 16-bits and result in + /// ±0. Exponents that underflow the minimum 16-bit exponent will result in 16-bit subnormals + /// or ±0. All other values are truncated and rounded to the nearest representable 16-bit + /// value. + #[inline] + pub fn from_f32(value: f32) -> f16 { + f16(convert::f32_to_f16(value)) + } + + /// Constructs a 16-bit floating point value from a 64-bit floating point value. + /// + /// If the 64-bit value is to large to fit in 16-bits, ±∞ will result. NaN values are + /// preserved. 64-bit subnormal values are too tiny to be represented in 16-bits and result in + /// ±0. Exponents that underflow the minimum 16-bit exponent will result in 16-bit subnormals + /// or ±0. All other values are truncated and rounded to the nearest representable 16-bit + /// value. + #[inline] + pub fn from_f64(value: f64) -> f16 { + f16(convert::f64_to_f16(value)) + } + + /// Converts a [`f16`] into the underlying bit representation. + #[inline] + pub const fn to_bits(self) -> u16 { + self.0 + } + + /// Returns the memory representation of the underlying bit representation as a byte array in + /// little-endian byte order. + /// + /// # Examples + /// + /// ```rust + /// # use half::prelude::*; + /// let bytes = f16::from_f32(12.5).to_le_bytes(); + /// assert_eq!(bytes, [0x40, 0x4A]); + /// ``` + #[inline] + pub const fn to_le_bytes(self) -> [u8; 2] { + self.0.to_le_bytes() + } + + /// Returns the memory representation of the underlying bit representation as a byte array in + /// big-endian (network) byte order. + /// + /// # Examples + /// + /// ```rust + /// # use half::prelude::*; + /// let bytes = f16::from_f32(12.5).to_be_bytes(); + /// assert_eq!(bytes, [0x4A, 0x40]); + /// ``` + #[inline] + pub const fn to_be_bytes(self) -> [u8; 2] { + self.0.to_be_bytes() + } + + /// Returns the memory representation of the underlying bit representation as a byte array in + /// native byte order. + /// + /// As the target platform's native endianness is used, portable code should use + /// [`to_be_bytes`][Self::to_be_bytes] or [`to_le_bytes`][Self::to_le_bytes], as appropriate, + /// instead. + /// + /// # Examples + /// + /// ```rust + /// # use half::prelude::*; + /// let bytes = f16::from_f32(12.5).to_ne_bytes(); + /// assert_eq!(bytes, if cfg!(target_endian = "big") { + /// [0x4A, 0x40] + /// } else { + /// [0x40, 0x4A] + /// }); + /// ``` + #[inline] + pub const fn to_ne_bytes(self) -> [u8; 2] { + self.0.to_ne_bytes() + } + + /// Creates a floating point value from its representation as a byte array in little endian. + /// + /// # Examples + /// + /// ```rust + /// # use half::prelude::*; + /// let value = f16::from_le_bytes([0x40, 0x4A]); + /// assert_eq!(value, f16::from_f32(12.5)); + /// ``` + #[inline] + pub const fn from_le_bytes(bytes: [u8; 2]) -> f16 { + f16::from_bits(u16::from_le_bytes(bytes)) + } + + /// Creates a floating point value from its representation as a byte array in big endian. + /// + /// # Examples + /// + /// ```rust + /// # use half::prelude::*; + /// let value = f16::from_be_bytes([0x4A, 0x40]); + /// assert_eq!(value, f16::from_f32(12.5)); + /// ``` + #[inline] + pub const fn from_be_bytes(bytes: [u8; 2]) -> f16 { + f16::from_bits(u16::from_be_bytes(bytes)) + } + + /// Creates a floating point value from its representation as a byte array in native endian. + /// + /// As the target platform's native endianness is used, portable code likely wants to use + /// [`from_be_bytes`][Self::from_be_bytes] or [`from_le_bytes`][Self::from_le_bytes], as + /// appropriate instead. + /// + /// # Examples + /// + /// ```rust + /// # use half::prelude::*; + /// let value = f16::from_ne_bytes(if cfg!(target_endian = "big") { + /// [0x4A, 0x40] + /// } else { + /// [0x40, 0x4A] + /// }); + /// assert_eq!(value, f16::from_f32(12.5)); + /// ``` + #[inline] + pub const fn from_ne_bytes(bytes: [u8; 2]) -> f16 { + f16::from_bits(u16::from_ne_bytes(bytes)) + } + + #[doc(hidden)] + #[deprecated(since = "1.2.0", note = "renamed to `to_bits`")] + #[inline] + pub fn as_bits(self) -> u16 { + self.to_bits() + } + + /// Converts a [`f16`] value into a `f32` value. + /// + /// This conversion is lossless as all 16-bit floating point values can be represented exactly + /// in 32-bit floating point. + #[inline] + pub fn to_f32(self) -> f32 { + convert::f16_to_f32(self.0) + } + + /// Converts a [`f16`] value into a `f64` value. + /// + /// This conversion is lossless as all 16-bit floating point values can be represented exactly + /// in 64-bit floating point. + #[inline] + pub fn to_f64(self) -> f64 { + convert::f16_to_f64(self.0) + } + + /// Returns `true` if this value is `NaN` and `false` otherwise. + /// + /// # Examples + /// + /// ```rust + /// # use half::prelude::*; + /// + /// let nan = f16::NAN; + /// let f = f16::from_f32(7.0_f32); + /// + /// assert!(nan.is_nan()); + /// assert!(!f.is_nan()); + /// ``` + #[inline] + pub const fn is_nan(self) -> bool { + self.0 & 0x7FFFu16 > 0x7C00u16 + } + + /// Returns `true` if this value is ±∞ and `false`. + /// otherwise. + /// + /// # Examples + /// + /// ```rust + /// # use half::prelude::*; + /// + /// let f = f16::from_f32(7.0f32); + /// let inf = f16::INFINITY; + /// let neg_inf = f16::NEG_INFINITY; + /// let nan = f16::NAN; + /// + /// assert!(!f.is_infinite()); + /// assert!(!nan.is_infinite()); + /// + /// assert!(inf.is_infinite()); + /// assert!(neg_inf.is_infinite()); + /// ``` + #[inline] + pub const fn is_infinite(self) -> bool { + self.0 & 0x7FFFu16 == 0x7C00u16 + } + + /// Returns `true` if this number is neither infinite nor `NaN`. + /// + /// # Examples + /// + /// ```rust + /// # use half::prelude::*; + /// + /// let f = f16::from_f32(7.0f32); + /// let inf = f16::INFINITY; + /// let neg_inf = f16::NEG_INFINITY; + /// let nan = f16::NAN; + /// + /// assert!(f.is_finite()); + /// + /// assert!(!nan.is_finite()); + /// assert!(!inf.is_finite()); + /// assert!(!neg_inf.is_finite()); + /// ``` + #[inline] + pub const fn is_finite(self) -> bool { + self.0 & 0x7C00u16 != 0x7C00u16 + } + + /// Returns `true` if the number is neither zero, infinite, subnormal, or `NaN`. + /// + /// # Examples + /// + /// ```rust + /// # use half::prelude::*; + /// + /// let min = f16::MIN_POSITIVE; + /// let max = f16::MAX; + /// let lower_than_min = f16::from_f32(1.0e-10_f32); + /// let zero = f16::from_f32(0.0_f32); + /// + /// assert!(min.is_normal()); + /// assert!(max.is_normal()); + /// + /// assert!(!zero.is_normal()); + /// assert!(!f16::NAN.is_normal()); + /// assert!(!f16::INFINITY.is_normal()); + /// // Values between `0` and `min` are Subnormal. + /// assert!(!lower_than_min.is_normal()); + /// ``` + #[inline] + pub const fn is_normal(self) -> bool { + let exp = self.0 & 0x7C00u16; + exp != 0x7C00u16 && exp != 0 + } + + /// Returns the floating point category of the number. + /// + /// If only one property is going to be tested, it is generally faster to use the specific + /// predicate instead. + /// + /// # Examples + /// + /// ```rust + /// use std::num::FpCategory; + /// # use half::prelude::*; + /// + /// let num = f16::from_f32(12.4_f32); + /// let inf = f16::INFINITY; + /// + /// assert_eq!(num.classify(), FpCategory::Normal); + /// assert_eq!(inf.classify(), FpCategory::Infinite); + /// ``` + pub const fn classify(self) -> FpCategory { + let exp = self.0 & 0x7C00u16; + let man = self.0 & 0x03FFu16; + match (exp, man) { + (0, 0) => FpCategory::Zero, + (0, _) => FpCategory::Subnormal, + (0x7C00u16, 0) => FpCategory::Infinite, + (0x7C00u16, _) => FpCategory::Nan, + _ => FpCategory::Normal, + } + } + + /// Returns a number that represents the sign of `self`. + /// + /// * `1.0` if the number is positive, `+0.0` or [`INFINITY`][f16::INFINITY] + /// * `-1.0` if the number is negative, `-0.0` or [`NEG_INFINITY`][f16::NEG_INFINITY] + /// * [`NAN`][f16::NAN] if the number is `NaN` + /// + /// # Examples + /// + /// ```rust + /// # use half::prelude::*; + /// + /// let f = f16::from_f32(3.5_f32); + /// + /// assert_eq!(f.signum(), f16::from_f32(1.0)); + /// assert_eq!(f16::NEG_INFINITY.signum(), f16::from_f32(-1.0)); + /// + /// assert!(f16::NAN.signum().is_nan()); + /// ``` + pub const fn signum(self) -> f16 { + if self.is_nan() { + self + } else if self.0 & 0x8000u16 != 0 { + Self::NEG_ONE + } else { + Self::ONE + } + } + + /// Returns `true` if and only if `self` has a positive sign, including `+0.0`, `NaNs` with a + /// positive sign bit and +∞. + /// + /// # Examples + /// + /// ```rust + /// # use half::prelude::*; + /// + /// let nan = f16::NAN; + /// let f = f16::from_f32(7.0_f32); + /// let g = f16::from_f32(-7.0_f32); + /// + /// assert!(f.is_sign_positive()); + /// assert!(!g.is_sign_positive()); + /// // `NaN` can be either positive or negative + /// assert!(nan.is_sign_positive() != nan.is_sign_negative()); + /// ``` + #[inline] + pub const fn is_sign_positive(self) -> bool { + self.0 & 0x8000u16 == 0 + } + + /// Returns `true` if and only if `self` has a negative sign, including `-0.0`, `NaNs` with a + /// negative sign bit and −∞. + /// + /// # Examples + /// + /// ```rust + /// # use half::prelude::*; + /// + /// let nan = f16::NAN; + /// let f = f16::from_f32(7.0f32); + /// let g = f16::from_f32(-7.0f32); + /// + /// assert!(!f.is_sign_negative()); + /// assert!(g.is_sign_negative()); + /// // `NaN` can be either positive or negative + /// assert!(nan.is_sign_positive() != nan.is_sign_negative()); + /// ``` + #[inline] + pub const fn is_sign_negative(self) -> bool { + self.0 & 0x8000u16 != 0 + } + + /// Returns a number composed of the magnitude of `self` and the sign of `sign`. + /// + /// Equal to `self` if the sign of `self` and `sign` are the same, otherwise equal to `-self`. + /// If `self` is NaN, then NaN with the sign of `sign` is returned. + /// + /// # Examples + /// + /// ``` + /// # use half::prelude::*; + /// let f = f16::from_f32(3.5); + /// + /// assert_eq!(f.copysign(f16::from_f32(0.42)), f16::from_f32(3.5)); + /// assert_eq!(f.copysign(f16::from_f32(-0.42)), f16::from_f32(-3.5)); + /// assert_eq!((-f).copysign(f16::from_f32(0.42)), f16::from_f32(3.5)); + /// assert_eq!((-f).copysign(f16::from_f32(-0.42)), f16::from_f32(-3.5)); + /// + /// assert!(f16::NAN.copysign(f16::from_f32(1.0)).is_nan()); + /// ``` + #[inline] + pub const fn copysign(self, sign: f16) -> f16 { + f16((sign.0 & 0x8000u16) | (self.0 & 0x7FFFu16)) + } + + /// Returns the maximum of the two numbers. + /// + /// If one of the arguments is NaN, then the other argument is returned. + /// + /// # Examples + /// + /// ``` + /// # use half::prelude::*; + /// let x = f16::from_f32(1.0); + /// let y = f16::from_f32(2.0); + /// + /// assert_eq!(x.max(y), y); + /// ``` + #[inline] + pub fn max(self, other: f16) -> f16 { + if other > self && !other.is_nan() { + other + } else { + self + } + } + + /// Returns the minimum of the two numbers. + /// + /// If one of the arguments is NaN, then the other argument is returned. + /// + /// # Examples + /// + /// ``` + /// # use half::prelude::*; + /// let x = f16::from_f32(1.0); + /// let y = f16::from_f32(2.0); + /// + /// assert_eq!(x.min(y), x); + /// ``` + #[inline] + pub fn min(self, other: f16) -> f16 { + if other < self && !other.is_nan() { + other + } else { + self + } + } + + /// Restrict a value to a certain interval unless it is NaN. + /// + /// Returns `max` if `self` is greater than `max`, and `min` if `self` is less than `min`. + /// Otherwise this returns `self`. + /// + /// Note that this function returns NaN if the initial value was NaN as well. + /// + /// # Panics + /// Panics if `min > max`, `min` is NaN, or `max` is NaN. + /// + /// # Examples + /// + /// ``` + /// # use half::prelude::*; + /// assert!(f16::from_f32(-3.0).clamp(f16::from_f32(-2.0), f16::from_f32(1.0)) == f16::from_f32(-2.0)); + /// assert!(f16::from_f32(0.0).clamp(f16::from_f32(-2.0), f16::from_f32(1.0)) == f16::from_f32(0.0)); + /// assert!(f16::from_f32(2.0).clamp(f16::from_f32(-2.0), f16::from_f32(1.0)) == f16::from_f32(1.0)); + /// assert!(f16::NAN.clamp(f16::from_f32(-2.0), f16::from_f32(1.0)).is_nan()); + /// ``` + #[inline] + pub fn clamp(self, min: f16, max: f16) -> f16 { + assert!(min <= max); + let mut x = self; + if x < min { + x = min; + } + if x > max { + x = max; + } + x + } + + /// Approximate number of [`f16`] significant digits in base 10 + pub const DIGITS: u32 = 3; + /// [`f16`] + /// [machine epsilon](https://en.wikipedia.org/wiki/Machine_epsilon) value + /// + /// This is the difference between 1.0 and the next largest representable number. + pub const EPSILON: f16 = f16(0x1400u16); + /// [`f16`] positive Infinity (+∞) + pub const INFINITY: f16 = f16(0x7C00u16); + /// Number of [`f16`] significant digits in base 2 + pub const MANTISSA_DIGITS: u32 = 11; + /// Largest finite [`f16`] value + pub const MAX: f16 = f16(0x7BFF); + /// Maximum possible [`f16`] power of 10 exponent + pub const MAX_10_EXP: i32 = 4; + /// Maximum possible [`f16`] power of 2 exponent + pub const MAX_EXP: i32 = 16; + /// Smallest finite [`f16`] value + pub const MIN: f16 = f16(0xFBFF); + /// Minimum possible normal [`f16`] power of 10 exponent + pub const MIN_10_EXP: i32 = -4; + /// One greater than the minimum possible normal [`f16`] power of 2 exponent + pub const MIN_EXP: i32 = -13; + /// Smallest positive normal [`f16`] value + pub const MIN_POSITIVE: f16 = f16(0x0400u16); + /// [`f16`] Not a Number (NaN) + pub const NAN: f16 = f16(0x7E00u16); + /// [`f16`] negative infinity (-∞) + pub const NEG_INFINITY: f16 = f16(0xFC00u16); + /// The radix or base of the internal representation of [`f16`] + pub const RADIX: u32 = 2; + + /// Minimum positive subnormal [`f16`] value + pub const MIN_POSITIVE_SUBNORMAL: f16 = f16(0x0001u16); + /// Maximum subnormal [`f16`] value + pub const MAX_SUBNORMAL: f16 = f16(0x03FFu16); + + /// [`f16`] 1 + pub const ONE: f16 = f16(0x3C00u16); + /// [`f16`] 0 + pub const ZERO: f16 = f16(0x0000u16); + /// [`f16`] -0 + pub const NEG_ZERO: f16 = f16(0x8000u16); + /// [`f16`] -1 + pub const NEG_ONE: f16 = f16(0xBC00u16); + + /// [`f16`] Euler's number (ℯ) + pub const E: f16 = f16(0x4170u16); + /// [`f16`] Archimedes' constant (π) + pub const PI: f16 = f16(0x4248u16); + /// [`f16`] 1/π + pub const FRAC_1_PI: f16 = f16(0x3518u16); + /// [`f16`] 1/√2 + pub const FRAC_1_SQRT_2: f16 = f16(0x39A8u16); + /// [`f16`] 2/π + pub const FRAC_2_PI: f16 = f16(0x3918u16); + /// [`f16`] 2/√π + pub const FRAC_2_SQRT_PI: f16 = f16(0x3C83u16); + /// [`f16`] π/2 + pub const FRAC_PI_2: f16 = f16(0x3E48u16); + /// [`f16`] π/3 + pub const FRAC_PI_3: f16 = f16(0x3C30u16); + /// [`f16`] π/4 + pub const FRAC_PI_4: f16 = f16(0x3A48u16); + /// [`f16`] π/6 + pub const FRAC_PI_6: f16 = f16(0x3830u16); + /// [`f16`] π/8 + pub const FRAC_PI_8: f16 = f16(0x3648u16); + /// [`f16`] 𝗅𝗇 10 + pub const LN_10: f16 = f16(0x409Bu16); + /// [`f16`] 𝗅𝗇 2 + pub const LN_2: f16 = f16(0x398Cu16); + /// [`f16`] 𝗅𝗈𝗀₁₀ℯ + pub const LOG10_E: f16 = f16(0x36F3u16); + /// [`f16`] 𝗅𝗈𝗀₁₀2 + pub const LOG10_2: f16 = f16(0x34D1u16); + /// [`f16`] 𝗅𝗈𝗀₂ℯ + pub const LOG2_E: f16 = f16(0x3DC5u16); + /// [`f16`] 𝗅𝗈𝗀₂10 + pub const LOG2_10: f16 = f16(0x42A5u16); + /// [`f16`] √2 + pub const SQRT_2: f16 = f16(0x3DA8u16); +} + +impl From<f16> for f32 { + #[inline] + fn from(x: f16) -> f32 { + x.to_f32() + } +} + +impl From<f16> for f64 { + #[inline] + fn from(x: f16) -> f64 { + x.to_f64() + } +} + +impl From<i8> for f16 { + #[inline] + fn from(x: i8) -> f16 { + // Convert to f32, then to f16 + f16::from_f32(f32::from(x)) + } +} + +impl From<u8> for f16 { + #[inline] + fn from(x: u8) -> f16 { + // Convert to f32, then to f16 + f16::from_f32(f32::from(x)) + } +} + +impl PartialEq for f16 { + fn eq(&self, other: &f16) -> bool { + if self.is_nan() || other.is_nan() { + false + } else { + (self.0 == other.0) || ((self.0 | other.0) & 0x7FFFu16 == 0) + } + } +} + +impl PartialOrd for f16 { + fn partial_cmp(&self, other: &f16) -> Option<Ordering> { + if self.is_nan() || other.is_nan() { + None + } else { + let neg = self.0 & 0x8000u16 != 0; + let other_neg = other.0 & 0x8000u16 != 0; + match (neg, other_neg) { + (false, false) => Some(self.0.cmp(&other.0)), + (false, true) => { + if (self.0 | other.0) & 0x7FFFu16 == 0 { + Some(Ordering::Equal) + } else { + Some(Ordering::Greater) + } + } + (true, false) => { + if (self.0 | other.0) & 0x7FFFu16 == 0 { + Some(Ordering::Equal) + } else { + Some(Ordering::Less) + } + } + (true, true) => Some(other.0.cmp(&self.0)), + } + } + } + + fn lt(&self, other: &f16) -> bool { + if self.is_nan() || other.is_nan() { + false + } else { + let neg = self.0 & 0x8000u16 != 0; + let other_neg = other.0 & 0x8000u16 != 0; + match (neg, other_neg) { + (false, false) => self.0 < other.0, + (false, true) => false, + (true, false) => (self.0 | other.0) & 0x7FFFu16 != 0, + (true, true) => self.0 > other.0, + } + } + } + + fn le(&self, other: &f16) -> bool { + if self.is_nan() || other.is_nan() { + false + } else { + let neg = self.0 & 0x8000u16 != 0; + let other_neg = other.0 & 0x8000u16 != 0; + match (neg, other_neg) { + (false, false) => self.0 <= other.0, + (false, true) => (self.0 | other.0) & 0x7FFFu16 == 0, + (true, false) => true, + (true, true) => self.0 >= other.0, + } + } + } + + fn gt(&self, other: &f16) -> bool { + if self.is_nan() || other.is_nan() { + false + } else { + let neg = self.0 & 0x8000u16 != 0; + let other_neg = other.0 & 0x8000u16 != 0; + match (neg, other_neg) { + (false, false) => self.0 > other.0, + (false, true) => (self.0 | other.0) & 0x7FFFu16 != 0, + (true, false) => false, + (true, true) => self.0 < other.0, + } + } + } + + fn ge(&self, other: &f16) -> bool { + if self.is_nan() || other.is_nan() { + false + } else { + let neg = self.0 & 0x8000u16 != 0; + let other_neg = other.0 & 0x8000u16 != 0; + match (neg, other_neg) { + (false, false) => self.0 >= other.0, + (false, true) => true, + (true, false) => (self.0 | other.0) & 0x7FFFu16 == 0, + (true, true) => self.0 <= other.0, + } + } + } +} + +impl FromStr for f16 { + type Err = ParseFloatError; + fn from_str(src: &str) -> Result<f16, ParseFloatError> { + f32::from_str(src).map(f16::from_f32) + } +} + +impl Debug for f16 { + fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> { + write!(f, "{:?}", self.to_f32()) + } +} + +impl Display for f16 { + fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> { + write!(f, "{}", self.to_f32()) + } +} + +impl LowerExp for f16 { + fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> { + write!(f, "{:e}", self.to_f32()) + } +} + +impl UpperExp for f16 { + fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> { + write!(f, "{:E}", self.to_f32()) + } +} + +impl Binary for f16 { + fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> { + write!(f, "{:b}", self.0) + } +} + +impl Octal for f16 { + fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> { + write!(f, "{:o}", self.0) + } +} + +impl LowerHex for f16 { + fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> { + write!(f, "{:x}", self.0) + } +} + +impl UpperHex for f16 { + fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> { + write!(f, "{:X}", self.0) + } +} + +impl Neg for f16 { + type Output = Self; + + #[inline] + fn neg(self) -> Self::Output { + Self(self.0 ^ 0x8000) + } +} + +impl Add for f16 { + type Output = Self; + + #[inline] + fn add(self, rhs: Self) -> Self::Output { + Self::from_f32(Self::to_f32(self) + Self::to_f32(rhs)) + } +} + +impl Add<&f16> for f16 { + type Output = <f16 as Add<f16>>::Output; + + #[inline] + fn add(self, rhs: &f16) -> Self::Output { + self.add(*rhs) + } +} + +impl Add<&f16> for &f16 { + type Output = <f16 as Add<f16>>::Output; + + #[inline] + fn add(self, rhs: &f16) -> Self::Output { + (*self).add(*rhs) + } +} + +impl Add<f16> for &f16 { + type Output = <f16 as Add<f16>>::Output; + + #[inline] + fn add(self, rhs: f16) -> Self::Output { + (*self).add(rhs) + } +} + +impl AddAssign for f16 { + #[inline] + fn add_assign(&mut self, rhs: Self) { + *self = (*self).add(rhs); + } +} + +impl AddAssign<&f16> for f16 { + #[inline] + fn add_assign(&mut self, rhs: &f16) { + *self = (*self).add(rhs); + } +} + +impl Sub for f16 { + type Output = Self; + + #[inline] + fn sub(self, rhs: Self) -> Self::Output { + Self::from_f32(Self::to_f32(self) - Self::to_f32(rhs)) + } +} + +impl Sub<&f16> for f16 { + type Output = <f16 as Sub<f16>>::Output; + + #[inline] + fn sub(self, rhs: &f16) -> Self::Output { + self.sub(*rhs) + } +} + +impl Sub<&f16> for &f16 { + type Output = <f16 as Sub<f16>>::Output; + + #[inline] + fn sub(self, rhs: &f16) -> Self::Output { + (*self).sub(*rhs) + } +} + +impl Sub<f16> for &f16 { + type Output = <f16 as Sub<f16>>::Output; + + #[inline] + fn sub(self, rhs: f16) -> Self::Output { + (*self).sub(rhs) + } +} + +impl SubAssign for f16 { + #[inline] + fn sub_assign(&mut self, rhs: Self) { + *self = (*self).sub(rhs); + } +} + +impl SubAssign<&f16> for f16 { + #[inline] + fn sub_assign(&mut self, rhs: &f16) { + *self = (*self).sub(rhs); + } +} + +impl Mul for f16 { + type Output = Self; + + #[inline] + fn mul(self, rhs: Self) -> Self::Output { + Self::from_f32(Self::to_f32(self) * Self::to_f32(rhs)) + } +} + +impl Mul<&f16> for f16 { + type Output = <f16 as Mul<f16>>::Output; + + #[inline] + fn mul(self, rhs: &f16) -> Self::Output { + self.mul(*rhs) + } +} + +impl Mul<&f16> for &f16 { + type Output = <f16 as Mul<f16>>::Output; + + #[inline] + fn mul(self, rhs: &f16) -> Self::Output { + (*self).mul(*rhs) + } +} + +impl Mul<f16> for &f16 { + type Output = <f16 as Mul<f16>>::Output; + + #[inline] + fn mul(self, rhs: f16) -> Self::Output { + (*self).mul(rhs) + } +} + +impl MulAssign for f16 { + #[inline] + fn mul_assign(&mut self, rhs: Self) { + *self = (*self).mul(rhs); + } +} + +impl MulAssign<&f16> for f16 { + #[inline] + fn mul_assign(&mut self, rhs: &f16) { + *self = (*self).mul(rhs); + } +} + +impl Div for f16 { + type Output = Self; + + #[inline] + fn div(self, rhs: Self) -> Self::Output { + Self::from_f32(Self::to_f32(self) / Self::to_f32(rhs)) + } +} + +impl Div<&f16> for f16 { + type Output = <f16 as Div<f16>>::Output; + + #[inline] + fn div(self, rhs: &f16) -> Self::Output { + self.div(*rhs) + } +} + +impl Div<&f16> for &f16 { + type Output = <f16 as Div<f16>>::Output; + + #[inline] + fn div(self, rhs: &f16) -> Self::Output { + (*self).div(*rhs) + } +} + +impl Div<f16> for &f16 { + type Output = <f16 as Div<f16>>::Output; + + #[inline] + fn div(self, rhs: f16) -> Self::Output { + (*self).div(rhs) + } +} + +impl DivAssign for f16 { + #[inline] + fn div_assign(&mut self, rhs: Self) { + *self = (*self).div(rhs); + } +} + +impl DivAssign<&f16> for f16 { + #[inline] + fn div_assign(&mut self, rhs: &f16) { + *self = (*self).div(rhs); + } +} + +impl Rem for f16 { + type Output = Self; + + #[inline] + fn rem(self, rhs: Self) -> Self::Output { + Self::from_f32(Self::to_f32(self) % Self::to_f32(rhs)) + } +} + +impl Rem<&f16> for f16 { + type Output = <f16 as Rem<f16>>::Output; + + #[inline] + fn rem(self, rhs: &f16) -> Self::Output { + self.rem(*rhs) + } +} + +impl Rem<&f16> for &f16 { + type Output = <f16 as Rem<f16>>::Output; + + #[inline] + fn rem(self, rhs: &f16) -> Self::Output { + (*self).rem(*rhs) + } +} + +impl Rem<f16> for &f16 { + type Output = <f16 as Rem<f16>>::Output; + + #[inline] + fn rem(self, rhs: f16) -> Self::Output { + (*self).rem(rhs) + } +} + +impl RemAssign for f16 { + #[inline] + fn rem_assign(&mut self, rhs: Self) { + *self = (*self).rem(rhs); + } +} + +impl RemAssign<&f16> for f16 { + #[inline] + fn rem_assign(&mut self, rhs: &f16) { + *self = (*self).rem(rhs); + } +} + +impl Product for f16 { + #[inline] + fn product<I: Iterator<Item = Self>>(iter: I) -> Self { + f16::from_f32(iter.map(|f| f.to_f32()).product()) + } +} + +impl<'a> Product<&'a f16> for f16 { + #[inline] + fn product<I: Iterator<Item = &'a f16>>(iter: I) -> Self { + f16::from_f32(iter.map(|f| f.to_f32()).product()) + } +} + +impl Sum for f16 { + #[inline] + fn sum<I: Iterator<Item = Self>>(iter: I) -> Self { + f16::from_f32(iter.map(|f| f.to_f32()).sum()) + } +} + +impl<'a> Sum<&'a f16> for f16 { + #[inline] + fn sum<I: Iterator<Item = &'a f16>>(iter: I) -> Self { + f16::from_f32(iter.map(|f| f.to_f32()).product()) + } +} + +#[allow( + clippy::cognitive_complexity, + clippy::float_cmp, + clippy::neg_cmp_op_on_partial_ord +)] +#[cfg(test)] +mod test { + use super::*; + use core::cmp::Ordering; + #[cfg(feature = "num-traits")] + use num_traits::{AsPrimitive, FromPrimitive, ToPrimitive}; + use quickcheck_macros::quickcheck; + + #[cfg(feature = "num-traits")] + #[test] + fn as_primitive() { + let two = f16::from_f32(2.0); + assert_eq!(<i32 as AsPrimitive<f16>>::as_(2), two); + assert_eq!(<f16 as AsPrimitive<i32>>::as_(two), 2); + + assert_eq!(<f32 as AsPrimitive<f16>>::as_(2.0), two); + assert_eq!(<f16 as AsPrimitive<f32>>::as_(two), 2.0); + + assert_eq!(<f64 as AsPrimitive<f16>>::as_(2.0), two); + assert_eq!(<f16 as AsPrimitive<f64>>::as_(two), 2.0); + } + + #[cfg(feature = "num-traits")] + #[test] + fn to_primitive() { + let two = f16::from_f32(2.0); + assert_eq!(ToPrimitive::to_i32(&two).unwrap(), 2i32); + assert_eq!(ToPrimitive::to_f32(&two).unwrap(), 2.0f32); + assert_eq!(ToPrimitive::to_f64(&two).unwrap(), 2.0f64); + } + + #[cfg(feature = "num-traits")] + #[test] + fn from_primitive() { + let two = f16::from_f32(2.0); + assert_eq!(<f16 as FromPrimitive>::from_i32(2).unwrap(), two); + assert_eq!(<f16 as FromPrimitive>::from_f32(2.0).unwrap(), two); + assert_eq!(<f16 as FromPrimitive>::from_f64(2.0).unwrap(), two); + } + + #[test] + fn test_f16_consts() { + // DIGITS + let digits = ((f16::MANTISSA_DIGITS as f32 - 1.0) * 2f32.log10()).floor() as u32; + assert_eq!(f16::DIGITS, digits); + // sanity check to show test is good + let digits32 = ((core::f32::MANTISSA_DIGITS as f32 - 1.0) * 2f32.log10()).floor() as u32; + assert_eq!(core::f32::DIGITS, digits32); + + // EPSILON + let one = f16::from_f32(1.0); + let one_plus_epsilon = f16::from_bits(one.to_bits() + 1); + let epsilon = f16::from_f32(one_plus_epsilon.to_f32() - 1.0); + assert_eq!(f16::EPSILON, epsilon); + // sanity check to show test is good + let one_plus_epsilon32 = f32::from_bits(1.0f32.to_bits() + 1); + let epsilon32 = one_plus_epsilon32 - 1f32; + assert_eq!(core::f32::EPSILON, epsilon32); + + // MAX, MIN and MIN_POSITIVE + let max = f16::from_bits(f16::INFINITY.to_bits() - 1); + let min = f16::from_bits(f16::NEG_INFINITY.to_bits() - 1); + let min_pos = f16::from_f32(2f32.powi(f16::MIN_EXP - 1)); + assert_eq!(f16::MAX, max); + assert_eq!(f16::MIN, min); + assert_eq!(f16::MIN_POSITIVE, min_pos); + // sanity check to show test is good + let max32 = f32::from_bits(core::f32::INFINITY.to_bits() - 1); + let min32 = f32::from_bits(core::f32::NEG_INFINITY.to_bits() - 1); + let min_pos32 = 2f32.powi(core::f32::MIN_EXP - 1); + assert_eq!(core::f32::MAX, max32); + assert_eq!(core::f32::MIN, min32); + assert_eq!(core::f32::MIN_POSITIVE, min_pos32); + + // MIN_10_EXP and MAX_10_EXP + let ten_to_min = 10f32.powi(f16::MIN_10_EXP); + assert!(ten_to_min / 10.0 < f16::MIN_POSITIVE.to_f32()); + assert!(ten_to_min > f16::MIN_POSITIVE.to_f32()); + let ten_to_max = 10f32.powi(f16::MAX_10_EXP); + assert!(ten_to_max < f16::MAX.to_f32()); + assert!(ten_to_max * 10.0 > f16::MAX.to_f32()); + // sanity check to show test is good + let ten_to_min32 = 10f64.powi(core::f32::MIN_10_EXP); + assert!(ten_to_min32 / 10.0 < f64::from(core::f32::MIN_POSITIVE)); + assert!(ten_to_min32 > f64::from(core::f32::MIN_POSITIVE)); + let ten_to_max32 = 10f64.powi(core::f32::MAX_10_EXP); + assert!(ten_to_max32 < f64::from(core::f32::MAX)); + assert!(ten_to_max32 * 10.0 > f64::from(core::f32::MAX)); + } + + #[test] + fn test_f16_consts_from_f32() { + let one = f16::from_f32(1.0); + let zero = f16::from_f32(0.0); + let neg_zero = f16::from_f32(-0.0); + let neg_one = f16::from_f32(-1.0); + let inf = f16::from_f32(core::f32::INFINITY); + let neg_inf = f16::from_f32(core::f32::NEG_INFINITY); + let nan = f16::from_f32(core::f32::NAN); + + assert_eq!(f16::ONE, one); + assert_eq!(f16::ZERO, zero); + assert!(zero.is_sign_positive()); + assert_eq!(f16::NEG_ZERO, neg_zero); + assert!(neg_zero.is_sign_negative()); + assert_eq!(f16::NEG_ONE, neg_one); + assert!(neg_one.is_sign_negative()); + assert_eq!(f16::INFINITY, inf); + assert_eq!(f16::NEG_INFINITY, neg_inf); + assert!(nan.is_nan()); + assert!(f16::NAN.is_nan()); + + let e = f16::from_f32(core::f32::consts::E); + let pi = f16::from_f32(core::f32::consts::PI); + let frac_1_pi = f16::from_f32(core::f32::consts::FRAC_1_PI); + let frac_1_sqrt_2 = f16::from_f32(core::f32::consts::FRAC_1_SQRT_2); + let frac_2_pi = f16::from_f32(core::f32::consts::FRAC_2_PI); + let frac_2_sqrt_pi = f16::from_f32(core::f32::consts::FRAC_2_SQRT_PI); + let frac_pi_2 = f16::from_f32(core::f32::consts::FRAC_PI_2); + let frac_pi_3 = f16::from_f32(core::f32::consts::FRAC_PI_3); + let frac_pi_4 = f16::from_f32(core::f32::consts::FRAC_PI_4); + let frac_pi_6 = f16::from_f32(core::f32::consts::FRAC_PI_6); + let frac_pi_8 = f16::from_f32(core::f32::consts::FRAC_PI_8); + let ln_10 = f16::from_f32(core::f32::consts::LN_10); + let ln_2 = f16::from_f32(core::f32::consts::LN_2); + let log10_e = f16::from_f32(core::f32::consts::LOG10_E); + // core::f32::consts::LOG10_2 requires rustc 1.43.0 + let log10_2 = f16::from_f32(2f32.log10()); + let log2_e = f16::from_f32(core::f32::consts::LOG2_E); + // core::f32::consts::LOG2_10 requires rustc 1.43.0 + let log2_10 = f16::from_f32(10f32.log2()); + let sqrt_2 = f16::from_f32(core::f32::consts::SQRT_2); + + assert_eq!(f16::E, e); + assert_eq!(f16::PI, pi); + assert_eq!(f16::FRAC_1_PI, frac_1_pi); + assert_eq!(f16::FRAC_1_SQRT_2, frac_1_sqrt_2); + assert_eq!(f16::FRAC_2_PI, frac_2_pi); + assert_eq!(f16::FRAC_2_SQRT_PI, frac_2_sqrt_pi); + assert_eq!(f16::FRAC_PI_2, frac_pi_2); + assert_eq!(f16::FRAC_PI_3, frac_pi_3); + assert_eq!(f16::FRAC_PI_4, frac_pi_4); + assert_eq!(f16::FRAC_PI_6, frac_pi_6); + assert_eq!(f16::FRAC_PI_8, frac_pi_8); + assert_eq!(f16::LN_10, ln_10); + assert_eq!(f16::LN_2, ln_2); + assert_eq!(f16::LOG10_E, log10_e); + assert_eq!(f16::LOG10_2, log10_2); + assert_eq!(f16::LOG2_E, log2_e); + assert_eq!(f16::LOG2_10, log2_10); + assert_eq!(f16::SQRT_2, sqrt_2); + } + + #[test] + fn test_f16_consts_from_f64() { + let one = f16::from_f64(1.0); + let zero = f16::from_f64(0.0); + let neg_zero = f16::from_f64(-0.0); + let inf = f16::from_f64(core::f64::INFINITY); + let neg_inf = f16::from_f64(core::f64::NEG_INFINITY); + let nan = f16::from_f64(core::f64::NAN); + + assert_eq!(f16::ONE, one); + assert_eq!(f16::ZERO, zero); + assert!(zero.is_sign_positive()); + assert_eq!(f16::NEG_ZERO, neg_zero); + assert!(neg_zero.is_sign_negative()); + assert_eq!(f16::INFINITY, inf); + assert_eq!(f16::NEG_INFINITY, neg_inf); + assert!(nan.is_nan()); + assert!(f16::NAN.is_nan()); + + let e = f16::from_f64(core::f64::consts::E); + let pi = f16::from_f64(core::f64::consts::PI); + let frac_1_pi = f16::from_f64(core::f64::consts::FRAC_1_PI); + let frac_1_sqrt_2 = f16::from_f64(core::f64::consts::FRAC_1_SQRT_2); + let frac_2_pi = f16::from_f64(core::f64::consts::FRAC_2_PI); + let frac_2_sqrt_pi = f16::from_f64(core::f64::consts::FRAC_2_SQRT_PI); + let frac_pi_2 = f16::from_f64(core::f64::consts::FRAC_PI_2); + let frac_pi_3 = f16::from_f64(core::f64::consts::FRAC_PI_3); + let frac_pi_4 = f16::from_f64(core::f64::consts::FRAC_PI_4); + let frac_pi_6 = f16::from_f64(core::f64::consts::FRAC_PI_6); + let frac_pi_8 = f16::from_f64(core::f64::consts::FRAC_PI_8); + let ln_10 = f16::from_f64(core::f64::consts::LN_10); + let ln_2 = f16::from_f64(core::f64::consts::LN_2); + let log10_e = f16::from_f64(core::f64::consts::LOG10_E); + // core::f64::consts::LOG10_2 requires rustc 1.43.0 + let log10_2 = f16::from_f64(2f64.log10()); + let log2_e = f16::from_f64(core::f64::consts::LOG2_E); + // core::f64::consts::LOG2_10 requires rustc 1.43.0 + let log2_10 = f16::from_f64(10f64.log2()); + let sqrt_2 = f16::from_f64(core::f64::consts::SQRT_2); + + assert_eq!(f16::E, e); + assert_eq!(f16::PI, pi); + assert_eq!(f16::FRAC_1_PI, frac_1_pi); + assert_eq!(f16::FRAC_1_SQRT_2, frac_1_sqrt_2); + assert_eq!(f16::FRAC_2_PI, frac_2_pi); + assert_eq!(f16::FRAC_2_SQRT_PI, frac_2_sqrt_pi); + assert_eq!(f16::FRAC_PI_2, frac_pi_2); + assert_eq!(f16::FRAC_PI_3, frac_pi_3); + assert_eq!(f16::FRAC_PI_4, frac_pi_4); + assert_eq!(f16::FRAC_PI_6, frac_pi_6); + assert_eq!(f16::FRAC_PI_8, frac_pi_8); + assert_eq!(f16::LN_10, ln_10); + assert_eq!(f16::LN_2, ln_2); + assert_eq!(f16::LOG10_E, log10_e); + assert_eq!(f16::LOG10_2, log10_2); + assert_eq!(f16::LOG2_E, log2_e); + assert_eq!(f16::LOG2_10, log2_10); + assert_eq!(f16::SQRT_2, sqrt_2); + } + + #[test] + fn test_nan_conversion_to_smaller() { + let nan64 = f64::from_bits(0x7FF0_0000_0000_0001u64); + let neg_nan64 = f64::from_bits(0xFFF0_0000_0000_0001u64); + let nan32 = f32::from_bits(0x7F80_0001u32); + let neg_nan32 = f32::from_bits(0xFF80_0001u32); + let nan32_from_64 = nan64 as f32; + let neg_nan32_from_64 = neg_nan64 as f32; + let nan16_from_64 = f16::from_f64(nan64); + let neg_nan16_from_64 = f16::from_f64(neg_nan64); + let nan16_from_32 = f16::from_f32(nan32); + let neg_nan16_from_32 = f16::from_f32(neg_nan32); + + assert!(nan64.is_nan() && nan64.is_sign_positive()); + assert!(neg_nan64.is_nan() && neg_nan64.is_sign_negative()); + assert!(nan32.is_nan() && nan32.is_sign_positive()); + assert!(neg_nan32.is_nan() && neg_nan32.is_sign_negative()); + assert!(nan32_from_64.is_nan() && nan32_from_64.is_sign_positive()); + assert!(neg_nan32_from_64.is_nan() && neg_nan32_from_64.is_sign_negative()); + assert!(nan16_from_64.is_nan() && nan16_from_64.is_sign_positive()); + assert!(neg_nan16_from_64.is_nan() && neg_nan16_from_64.is_sign_negative()); + assert!(nan16_from_32.is_nan() && nan16_from_32.is_sign_positive()); + assert!(neg_nan16_from_32.is_nan() && neg_nan16_from_32.is_sign_negative()); + } + + #[test] + fn test_nan_conversion_to_larger() { + let nan16 = f16::from_bits(0x7C01u16); + let neg_nan16 = f16::from_bits(0xFC01u16); + let nan32 = f32::from_bits(0x7F80_0001u32); + let neg_nan32 = f32::from_bits(0xFF80_0001u32); + let nan32_from_16 = f32::from(nan16); + let neg_nan32_from_16 = f32::from(neg_nan16); + let nan64_from_16 = f64::from(nan16); + let neg_nan64_from_16 = f64::from(neg_nan16); + let nan64_from_32 = f64::from(nan32); + let neg_nan64_from_32 = f64::from(neg_nan32); + + assert!(nan16.is_nan() && nan16.is_sign_positive()); + assert!(neg_nan16.is_nan() && neg_nan16.is_sign_negative()); + assert!(nan32.is_nan() && nan32.is_sign_positive()); + assert!(neg_nan32.is_nan() && neg_nan32.is_sign_negative()); + assert!(nan32_from_16.is_nan() && nan32_from_16.is_sign_positive()); + assert!(neg_nan32_from_16.is_nan() && neg_nan32_from_16.is_sign_negative()); + assert!(nan64_from_16.is_nan() && nan64_from_16.is_sign_positive()); + assert!(neg_nan64_from_16.is_nan() && neg_nan64_from_16.is_sign_negative()); + assert!(nan64_from_32.is_nan() && nan64_from_32.is_sign_positive()); + assert!(neg_nan64_from_32.is_nan() && neg_nan64_from_32.is_sign_negative()); + } + + #[test] + fn test_f16_to_f32() { + let f = f16::from_f32(7.0); + assert_eq!(f.to_f32(), 7.0f32); + + // 7.1 is NOT exactly representable in 16-bit, it's rounded + let f = f16::from_f32(7.1); + let diff = (f.to_f32() - 7.1f32).abs(); + // diff must be <= 4 * EPSILON, as 7 has two more significant bits than 1 + assert!(diff <= 4.0 * f16::EPSILON.to_f32()); + + assert_eq!(f16::from_bits(0x0000_0001).to_f32(), 2.0f32.powi(-24)); + assert_eq!(f16::from_bits(0x0000_0005).to_f32(), 5.0 * 2.0f32.powi(-24)); + + assert_eq!(f16::from_bits(0x0000_0001), f16::from_f32(2.0f32.powi(-24))); + assert_eq!( + f16::from_bits(0x0000_0005), + f16::from_f32(5.0 * 2.0f32.powi(-24)) + ); + } + + #[test] + fn test_f16_to_f64() { + let f = f16::from_f64(7.0); + assert_eq!(f.to_f64(), 7.0f64); + + // 7.1 is NOT exactly representable in 16-bit, it's rounded + let f = f16::from_f64(7.1); + let diff = (f.to_f64() - 7.1f64).abs(); + // diff must be <= 4 * EPSILON, as 7 has two more significant bits than 1 + assert!(diff <= 4.0 * f16::EPSILON.to_f64()); + + assert_eq!(f16::from_bits(0x0000_0001).to_f64(), 2.0f64.powi(-24)); + assert_eq!(f16::from_bits(0x0000_0005).to_f64(), 5.0 * 2.0f64.powi(-24)); + + assert_eq!(f16::from_bits(0x0000_0001), f16::from_f64(2.0f64.powi(-24))); + assert_eq!( + f16::from_bits(0x0000_0005), + f16::from_f64(5.0 * 2.0f64.powi(-24)) + ); + } + + #[test] + fn test_comparisons() { + let zero = f16::from_f64(0.0); + let one = f16::from_f64(1.0); + let neg_zero = f16::from_f64(-0.0); + let neg_one = f16::from_f64(-1.0); + + assert_eq!(zero.partial_cmp(&neg_zero), Some(Ordering::Equal)); + assert_eq!(neg_zero.partial_cmp(&zero), Some(Ordering::Equal)); + assert!(zero == neg_zero); + assert!(neg_zero == zero); + assert!(!(zero != neg_zero)); + assert!(!(neg_zero != zero)); + assert!(!(zero < neg_zero)); + assert!(!(neg_zero < zero)); + assert!(zero <= neg_zero); + assert!(neg_zero <= zero); + assert!(!(zero > neg_zero)); + assert!(!(neg_zero > zero)); + assert!(zero >= neg_zero); + assert!(neg_zero >= zero); + + assert_eq!(one.partial_cmp(&neg_zero), Some(Ordering::Greater)); + assert_eq!(neg_zero.partial_cmp(&one), Some(Ordering::Less)); + assert!(!(one == neg_zero)); + assert!(!(neg_zero == one)); + assert!(one != neg_zero); + assert!(neg_zero != one); + assert!(!(one < neg_zero)); + assert!(neg_zero < one); + assert!(!(one <= neg_zero)); + assert!(neg_zero <= one); + assert!(one > neg_zero); + assert!(!(neg_zero > one)); + assert!(one >= neg_zero); + assert!(!(neg_zero >= one)); + + assert_eq!(one.partial_cmp(&neg_one), Some(Ordering::Greater)); + assert_eq!(neg_one.partial_cmp(&one), Some(Ordering::Less)); + assert!(!(one == neg_one)); + assert!(!(neg_one == one)); + assert!(one != neg_one); + assert!(neg_one != one); + assert!(!(one < neg_one)); + assert!(neg_one < one); + assert!(!(one <= neg_one)); + assert!(neg_one <= one); + assert!(one > neg_one); + assert!(!(neg_one > one)); + assert!(one >= neg_one); + assert!(!(neg_one >= one)); + } + + #[test] + #[allow(clippy::erasing_op, clippy::identity_op)] + fn round_to_even_f32() { + // smallest positive subnormal = 0b0.0000_0000_01 * 2^-14 = 2^-24 + let min_sub = f16::from_bits(1); + let min_sub_f = (-24f32).exp2(); + assert_eq!(f16::from_f32(min_sub_f).to_bits(), min_sub.to_bits()); + assert_eq!(f32::from(min_sub).to_bits(), min_sub_f.to_bits()); + + // 0.0000000000_011111 rounded to 0.0000000000 (< tie, no rounding) + // 0.0000000000_100000 rounded to 0.0000000000 (tie and even, remains at even) + // 0.0000000000_100001 rounded to 0.0000000001 (> tie, rounds up) + assert_eq!( + f16::from_f32(min_sub_f * 0.49).to_bits(), + min_sub.to_bits() * 0 + ); + assert_eq!( + f16::from_f32(min_sub_f * 0.50).to_bits(), + min_sub.to_bits() * 0 + ); + assert_eq!( + f16::from_f32(min_sub_f * 0.51).to_bits(), + min_sub.to_bits() * 1 + ); + + // 0.0000000001_011111 rounded to 0.0000000001 (< tie, no rounding) + // 0.0000000001_100000 rounded to 0.0000000010 (tie and odd, rounds up to even) + // 0.0000000001_100001 rounded to 0.0000000010 (> tie, rounds up) + assert_eq!( + f16::from_f32(min_sub_f * 1.49).to_bits(), + min_sub.to_bits() * 1 + ); + assert_eq!( + f16::from_f32(min_sub_f * 1.50).to_bits(), + min_sub.to_bits() * 2 + ); + assert_eq!( + f16::from_f32(min_sub_f * 1.51).to_bits(), + min_sub.to_bits() * 2 + ); + + // 0.0000000010_011111 rounded to 0.0000000010 (< tie, no rounding) + // 0.0000000010_100000 rounded to 0.0000000010 (tie and even, remains at even) + // 0.0000000010_100001 rounded to 0.0000000011 (> tie, rounds up) + assert_eq!( + f16::from_f32(min_sub_f * 2.49).to_bits(), + min_sub.to_bits() * 2 + ); + assert_eq!( + f16::from_f32(min_sub_f * 2.50).to_bits(), + min_sub.to_bits() * 2 + ); + assert_eq!( + f16::from_f32(min_sub_f * 2.51).to_bits(), + min_sub.to_bits() * 3 + ); + + assert_eq!( + f16::from_f32(2000.49f32).to_bits(), + f16::from_f32(2000.0).to_bits() + ); + assert_eq!( + f16::from_f32(2000.50f32).to_bits(), + f16::from_f32(2000.0).to_bits() + ); + assert_eq!( + f16::from_f32(2000.51f32).to_bits(), + f16::from_f32(2001.0).to_bits() + ); + assert_eq!( + f16::from_f32(2001.49f32).to_bits(), + f16::from_f32(2001.0).to_bits() + ); + assert_eq!( + f16::from_f32(2001.50f32).to_bits(), + f16::from_f32(2002.0).to_bits() + ); + assert_eq!( + f16::from_f32(2001.51f32).to_bits(), + f16::from_f32(2002.0).to_bits() + ); + assert_eq!( + f16::from_f32(2002.49f32).to_bits(), + f16::from_f32(2002.0).to_bits() + ); + assert_eq!( + f16::from_f32(2002.50f32).to_bits(), + f16::from_f32(2002.0).to_bits() + ); + assert_eq!( + f16::from_f32(2002.51f32).to_bits(), + f16::from_f32(2003.0).to_bits() + ); + } + + #[test] + #[allow(clippy::erasing_op, clippy::identity_op)] + fn round_to_even_f64() { + // smallest positive subnormal = 0b0.0000_0000_01 * 2^-14 = 2^-24 + let min_sub = f16::from_bits(1); + let min_sub_f = (-24f64).exp2(); + assert_eq!(f16::from_f64(min_sub_f).to_bits(), min_sub.to_bits()); + assert_eq!(f64::from(min_sub).to_bits(), min_sub_f.to_bits()); + + // 0.0000000000_011111 rounded to 0.0000000000 (< tie, no rounding) + // 0.0000000000_100000 rounded to 0.0000000000 (tie and even, remains at even) + // 0.0000000000_100001 rounded to 0.0000000001 (> tie, rounds up) + assert_eq!( + f16::from_f64(min_sub_f * 0.49).to_bits(), + min_sub.to_bits() * 0 + ); + assert_eq!( + f16::from_f64(min_sub_f * 0.50).to_bits(), + min_sub.to_bits() * 0 + ); + assert_eq!( + f16::from_f64(min_sub_f * 0.51).to_bits(), + min_sub.to_bits() * 1 + ); + + // 0.0000000001_011111 rounded to 0.0000000001 (< tie, no rounding) + // 0.0000000001_100000 rounded to 0.0000000010 (tie and odd, rounds up to even) + // 0.0000000001_100001 rounded to 0.0000000010 (> tie, rounds up) + assert_eq!( + f16::from_f64(min_sub_f * 1.49).to_bits(), + min_sub.to_bits() * 1 + ); + assert_eq!( + f16::from_f64(min_sub_f * 1.50).to_bits(), + min_sub.to_bits() * 2 + ); + assert_eq!( + f16::from_f64(min_sub_f * 1.51).to_bits(), + min_sub.to_bits() * 2 + ); + + // 0.0000000010_011111 rounded to 0.0000000010 (< tie, no rounding) + // 0.0000000010_100000 rounded to 0.0000000010 (tie and even, remains at even) + // 0.0000000010_100001 rounded to 0.0000000011 (> tie, rounds up) + assert_eq!( + f16::from_f64(min_sub_f * 2.49).to_bits(), + min_sub.to_bits() * 2 + ); + assert_eq!( + f16::from_f64(min_sub_f * 2.50).to_bits(), + min_sub.to_bits() * 2 + ); + assert_eq!( + f16::from_f64(min_sub_f * 2.51).to_bits(), + min_sub.to_bits() * 3 + ); + + assert_eq!( + f16::from_f64(2000.49f64).to_bits(), + f16::from_f64(2000.0).to_bits() + ); + assert_eq!( + f16::from_f64(2000.50f64).to_bits(), + f16::from_f64(2000.0).to_bits() + ); + assert_eq!( + f16::from_f64(2000.51f64).to_bits(), + f16::from_f64(2001.0).to_bits() + ); + assert_eq!( + f16::from_f64(2001.49f64).to_bits(), + f16::from_f64(2001.0).to_bits() + ); + assert_eq!( + f16::from_f64(2001.50f64).to_bits(), + f16::from_f64(2002.0).to_bits() + ); + assert_eq!( + f16::from_f64(2001.51f64).to_bits(), + f16::from_f64(2002.0).to_bits() + ); + assert_eq!( + f16::from_f64(2002.49f64).to_bits(), + f16::from_f64(2002.0).to_bits() + ); + assert_eq!( + f16::from_f64(2002.50f64).to_bits(), + f16::from_f64(2002.0).to_bits() + ); + assert_eq!( + f16::from_f64(2002.51f64).to_bits(), + f16::from_f64(2003.0).to_bits() + ); + } + + impl quickcheck::Arbitrary for f16 { + fn arbitrary(g: &mut quickcheck::Gen) -> Self { + f16(u16::arbitrary(g)) + } + } + + #[quickcheck] + fn qc_roundtrip_f16_f32_is_identity(f: f16) -> bool { + let roundtrip = f16::from_f32(f.to_f32()); + if f.is_nan() { + roundtrip.is_nan() && f.is_sign_negative() == roundtrip.is_sign_negative() + } else { + f.0 == roundtrip.0 + } + } + + #[quickcheck] + fn qc_roundtrip_f16_f64_is_identity(f: f16) -> bool { + let roundtrip = f16::from_f64(f.to_f64()); + if f.is_nan() { + roundtrip.is_nan() && f.is_sign_negative() == roundtrip.is_sign_negative() + } else { + f.0 == roundtrip.0 + } + } +} |