| #[cfg(feature = "serde")] |
| use serde::{Deserialize, Serialize}; |
| |
| use core::{ |
| cmp::Ordering, |
| fmt::{Debug, Display, Error, Formatter, LowerExp, UpperExp}, |
| num::{FpCategory, ParseFloatError}, |
| str::FromStr, |
| }; |
| |
| 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. |
| /// |
| /// [`f16`]: struct.f16.html |
| /// [`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))] |
| pub struct f16(u16); |
| |
| #[deprecated( |
| since = "1.4.0", |
| note = "all constants moved to associated constants of [`f16`](../struct.f16.html)" |
| )] |
| pub mod consts { |
| //! Useful `f16` constants. |
| |
| use super::f16; |
| |
| /// Approximate number of [`f16`](../struct.f16.html) significant digits in base 10. |
| #[deprecated( |
| since = "1.4.0", |
| note = "moved to [`f16::DIGITS`](../struct.f16.html#associatedconstant.DIGITS)" |
| )] |
| pub const DIGITS: u32 = f16::DIGITS; |
| /// [`f16`](../struct.f16.html) |
| /// [machine epsilon](https://en.wikipedia.org/wiki/Machine_epsilon) value. |
| /// |
| /// This is the difference between 1.0 and the next largest representable number. |
| #[deprecated( |
| since = "1.4.0", |
| note = "moved to [`f16::EPSILON`](../struct.f16.html#associatedconstant.EPSILON)" |
| )] |
| pub const EPSILON: f16 = f16::EPSILON; |
| /// [`f16`](../struct.f16.html) positive Infinity (+∞). |
| #[deprecated( |
| since = "1.4.0", |
| note = "moved to [`f16::INFINITY`](../struct.f16.html#associatedconstant.INFINITY)" |
| )] |
| pub const INFINITY: f16 = f16::INFINITY; |
| /// Number of [`f16`](../struct.f16.html) significant digits in base 2. |
| #[deprecated( |
| since = "1.4.0", |
| note = "moved to [`f16::MANTISSA_DIGITS`](../struct.f16.html#associatedconstant.MANTISSA_DIGITS)" |
| )] |
| pub const MANTISSA_DIGITS: u32 = f16::MANTISSA_DIGITS; |
| /// Largest finite [`f16`](../struct.f16.html) value. |
| #[deprecated( |
| since = "1.4.0", |
| note = "moved to [`f16::MAX`](../struct.f16.html#associatedconstant.MAX)" |
| )] |
| pub const MAX: f16 = f16::MAX; |
| /// Maximum possible [`f16`](../struct.f16.html) power of 10 exponent. |
| #[deprecated( |
| since = "1.4.0", |
| note = "moved to [`f16::MAX_10_EXP`](../struct.f16.html#associatedconstant.MAX_10_EXP)" |
| )] |
| pub const MAX_10_EXP: i32 = f16::MAX_10_EXP; |
| /// Maximum possible [`f16`](../struct.f16.html) power of 2 exponent. |
| #[deprecated( |
| since = "1.4.0", |
| note = "moved to [`f16::MAX_EXP`](../struct.f16.html#associatedconstant.MAX_EXP)" |
| )] |
| pub const MAX_EXP: i32 = f16::MAX_EXP; |
| /// Smallest finite [`f16`](../struct.f16.html) value. |
| #[deprecated( |
| since = "1.4.0", |
| note = "moved to [`f16::MIN`](../struct.f16.html#associatedconstant.MIN)" |
| )] |
| pub const MIN: f16 = f16::MIN; |
| /// Minimum possible normal [`f16`](../struct.f16.html) power of 10 exponent. |
| #[deprecated( |
| since = "1.4.0", |
| note = "moved to [`f16::MIN_10_EXP`](../struct.f16.html#associatedconstant.MIN_10_EXP)" |
| )] |
| pub const MIN_10_EXP: i32 = f16::MIN_10_EXP; |
| /// One greater than the minimum possible normal [`f16`](../struct.f16.html) power of 2 exponent. |
| #[deprecated( |
| since = "1.4.0", |
| note = "moved to [`f16::MIN_EXP`](../struct.f16.html#associatedconstant.MIN_EXP)" |
| )] |
| pub const MIN_EXP: i32 = f16::MIN_EXP; |
| /// Smallest positive normal [`f16`](../struct.f16.html) value. |
| #[deprecated( |
| since = "1.4.0", |
| note = "moved to [`f16::MIN_POSITIVE`](../struct.f16.html#associatedconstant.MIN_POSITIVE)" |
| )] |
| pub const MIN_POSITIVE: f16 = f16::MIN_POSITIVE; |
| /// [`f16`](../struct.f16.html) Not a Number (NaN). |
| #[deprecated( |
| since = "1.4.0", |
| note = "moved to [`f16::NAN`](../struct.f16.html#associatedconstant.NAN)" |
| )] |
| pub const NAN: f16 = f16::NAN; |
| /// [`f16`](../struct.f16.html) negative infinity (-∞). |
| #[deprecated( |
| since = "1.4.0", |
| note = "moved to [`f16::NEG_INFINITY`](../struct.f16.html#associatedconstant.NEG_INFINITY)" |
| )] |
| pub const NEG_INFINITY: f16 = f16::NEG_INFINITY; |
| /// The radix or base of the internal representation of [`f16`](../struct.f16.html). |
| #[deprecated( |
| since = "1.4.0", |
| note = "moved to [`f16::RADIX`](../struct.f16.html#associatedconstant.RADIX)" |
| )] |
| pub const RADIX: u32 = f16::RADIX; |
| |
| /// Minimum positive subnormal [`f16`](../struct.f16.html) value. |
| #[deprecated( |
| since = "1.4.0", |
| note = "moved to [`f16::MIN_POSITIVE_SUBNORMAL`](../struct.f16.html#associatedconstant.MIN_POSITIVE_SUBNORMAL)" |
| )] |
| pub const MIN_POSITIVE_SUBNORMAL: f16 = f16::MIN_POSITIVE_SUBNORMAL; |
| /// Maximum subnormal [`f16`](../struct.f16.html) value. |
| #[deprecated( |
| since = "1.4.0", |
| note = "moved to [`f16::MAX_SUBNORMAL`](../struct.f16.html#associatedconstant.MAX_SUBNORMAL)" |
| )] |
| pub const MAX_SUBNORMAL: f16 = f16::MAX_SUBNORMAL; |
| |
| /// [`f16`](../struct.f16.html) 1 |
| #[deprecated( |
| since = "1.4.0", |
| note = "moved to [`f16::ONE`](../struct.f16.html#associatedconstant.ONE)" |
| )] |
| pub const ONE: f16 = f16::ONE; |
| /// [`f16`](../struct.f16.html) 0 |
| #[deprecated( |
| since = "1.4.0", |
| note = "moved to [`f16::ZERO`](../struct.f16.html#associatedconstant.ZERO)" |
| )] |
| pub const ZERO: f16 = f16::ZERO; |
| /// [`f16`](../struct.f16.html) -0 |
| #[deprecated( |
| since = "1.4.0", |
| note = "moved to [`f16::NEG_ZERO`](../struct.f16.html#associatedconstant.NEG_ZERO)" |
| )] |
| pub const NEG_ZERO: f16 = f16::NEG_ZERO; |
| |
| /// [`f16`](../struct.f16.html) Euler's number (ℯ). |
| #[deprecated( |
| since = "1.4.0", |
| note = "moved to [`f16::E`](../struct.f16.html#associatedconstant.E)" |
| )] |
| pub const E: f16 = f16::E; |
| /// [`f16`](../struct.f16.html) Archimedes' constant (π). |
| #[deprecated( |
| since = "1.4.0", |
| note = "moved to [`f16::PI`](../struct.f16.html#associatedconstant.PI)" |
| )] |
| pub const PI: f16 = f16::PI; |
| /// [`f16`](../struct.f16.html) 1/π |
| #[deprecated( |
| since = "1.4.0", |
| note = "moved to [`f16::FRAC_1_PI`](../struct.f16.html#associatedconstant.FRAC_1_PI)" |
| )] |
| pub const FRAC_1_PI: f16 = f16::FRAC_1_PI; |
| /// [`f16`](../struct.f16.html) 1/√2 |
| #[deprecated( |
| since = "1.4.0", |
| note = "moved to [`f16::FRAC_1_SQRT_2`](../struct.f16.html#associatedconstant.FRAC_1_SQRT_2)" |
| )] |
| pub const FRAC_1_SQRT_2: f16 = f16::FRAC_1_SQRT_2; |
| /// [`f16`](../struct.f16.html) 2/π |
| #[deprecated( |
| since = "1.4.0", |
| note = "moved to [`f16::FRAC_2_PI`](../struct.f16.html#associatedconstant.FRAC_2_PI)" |
| )] |
| pub const FRAC_2_PI: f16 = f16::FRAC_2_PI; |
| /// [`f16`](../struct.f16.html) 2/√π |
| #[deprecated( |
| since = "1.4.0", |
| note = "moved to [`f16::FRAC_2_SQRT_PI`](../struct.f16.html#associatedconstant.FRAC_2_SQRT_PI)" |
| )] |
| pub const FRAC_2_SQRT_PI: f16 = f16::FRAC_2_SQRT_PI; |
| /// [`f16`](../struct.f16.html) π/2 |
| #[deprecated( |
| since = "1.4.0", |
| note = "moved to [`f16::FRAC_PI_2`](../struct.f16.html#associatedconstant.FRAC_PI_2)" |
| )] |
| pub const FRAC_PI_2: f16 = f16::FRAC_PI_2; |
| /// [`f16`](../struct.f16.html) π/3 |
| #[deprecated( |
| since = "1.4.0", |
| note = "moved to [`f16::FRAC_PI_3`](../struct.f16.html#associatedconstant.FRAC_PI_3)" |
| )] |
| pub const FRAC_PI_3: f16 = f16::FRAC_PI_3; |
| /// [`f16`](../struct.f16.html) π/4 |
| #[deprecated( |
| since = "1.4.0", |
| note = "moved to [`f16::FRAC_PI_4`](../struct.f16.html#associatedconstant.FRAC_PI_4)" |
| )] |
| pub const FRAC_PI_4: f16 = f16::FRAC_PI_4; |
| /// [`f16`](../struct.f16.html) π/6 |
| #[deprecated( |
| since = "1.4.0", |
| note = "moved to [`f16::FRAC_PI_6`](../struct.f16.html#associatedconstant.FRAC_PI_6)" |
| )] |
| pub const FRAC_PI_6: f16 = f16::FRAC_PI_6; |
| /// [`f16`](../struct.f16.html) π/8 |
| #[deprecated( |
| since = "1.4.0", |
| note = "moved to [`f16::FRAC_PI_8`](../struct.f16.html#associatedconstant.FRAC_PI_8)" |
| )] |
| pub const FRAC_PI_8: f16 = f16::FRAC_PI_8; |
| /// [`f16`](../struct.f16.html) 𝗅𝗇 10 |
| #[deprecated( |
| since = "1.4.0", |
| note = "moved to [`f16::LN_10`](../struct.f16.html#associatedconstant.LN_10)" |
| )] |
| pub const LN_10: f16 = f16::LN_10; |
| /// [`f16`](../struct.f16.html) 𝗅𝗇 2 |
| #[deprecated( |
| since = "1.4.0", |
| note = "moved to [`f16::LN_2`](../struct.f16.html#associatedconstant.LN_2)" |
| )] |
| pub const LN_2: f16 = f16::LN_2; |
| /// [`f16`](../struct.f16.html) 𝗅𝗈𝗀₁₀ℯ |
| #[deprecated( |
| since = "1.4.0", |
| note = "moved to [`f16::LOG10_E`](../struct.f16.html#associatedconstant.LOG10_E)" |
| )] |
| pub const LOG10_E: f16 = f16::LOG10_E; |
| /// [`f16`](../struct.f16.html) 𝗅𝗈𝗀₂ℯ |
| #[deprecated( |
| since = "1.4.0", |
| note = "moved to [`f16::LOG2_E`](../struct.f16.html#associatedconstant.LOG2_E)" |
| )] |
| pub const LOG2_E: f16 = f16::LOG2_E; |
| /// [`f16`](../struct.f16.html) √2 |
| #[deprecated( |
| since = "1.4.0", |
| note = "moved to [`f16::SQRT_2`](../struct.f16.html#associatedconstant.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`](struct.f16.html) into the underlying bit representation. |
| #[inline] |
| pub const fn to_bits(self) -> u16 { |
| self.0 |
| } |
| |
| /// Return 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 fn to_le_bytes(self) -> [u8; 2] { |
| self.0.to_le_bytes() |
| } |
| |
| /// Return 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 fn to_be_bytes(self) -> [u8; 2] { |
| self.0.to_be_bytes() |
| } |
| |
| /// Return 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` |
| /// or `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 fn to_ne_bytes(self) -> [u8; 2] { |
| self.0.to_ne_bytes() |
| } |
| |
| /// Create 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 fn from_le_bytes(bytes: [u8; 2]) -> f16 { |
| f16::from_bits(u16::from_le_bytes(bytes)) |
| } |
| |
| /// Create 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 fn from_be_bytes(bytes: [u8; 2]) -> f16 { |
| f16::from_bits(u16::from_be_bytes(bytes)) |
| } |
| |
| /// Create 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` or `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 fn from_ne_bytes(bytes: [u8; 2]) -> f16 { |
| f16::from_bits(u16::from_ne_bytes(bytes)) |
| } |
| |
| /// Converts a [`f16`](struct.f16.html) into the underlying bit representation. |
| #[deprecated(since = "1.2.0", note = "renamed to [`to_bits`](#method.to_bits)")] |
| #[inline] |
| pub fn as_bits(self) -> u16 { |
| self.to_bits() |
| } |
| |
| /// Converts a [`f16`](struct.f16.html) 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`](struct.f16.html) 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 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 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` |
| /// * `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY` |
| /// * `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 fn signum(self) -> f16 { |
| if self.is_nan() { |
| self |
| } else if self.0 & 0x8000u16 != 0 { |
| f16::from_f32(-1.0) |
| } else { |
| f16::from_f32(1.0) |
| } |
| } |
| |
| /// 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 |
| } |
| |
| /// Approximate number of [`f16`](struct.f16.html) significant digits in base 10. |
| pub const DIGITS: u32 = 3; |
| /// [`f16`](struct.f16.html) |
| /// [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`](struct.f16.html) positive Infinity (+∞). |
| pub const INFINITY: f16 = f16(0x7C00u16); |
| /// Number of [`f16`](struct.f16.html) significant digits in base 2. |
| pub const MANTISSA_DIGITS: u32 = 11; |
| /// Largest finite [`f16`](struct.f16.html) value. |
| pub const MAX: f16 = f16(0x7BFF); |
| /// Maximum possible [`f16`](struct.f16.html) power of 10 exponent. |
| pub const MAX_10_EXP: i32 = 4; |
| /// Maximum possible [`f16`](struct.f16.html) power of 2 exponent. |
| pub const MAX_EXP: i32 = 16; |
| /// Smallest finite [`f16`](struct.f16.html) value. |
| pub const MIN: f16 = f16(0xFBFF); |
| /// Minimum possible normal [`f16`](struct.f16.html) power of 10 exponent. |
| pub const MIN_10_EXP: i32 = -4; |
| /// One greater than the minimum possible normal [`f16`](struct.f16.html) power of 2 exponent. |
| pub const MIN_EXP: i32 = -13; |
| /// Smallest positive normal [`f16`](struct.f16.html) value. |
| pub const MIN_POSITIVE: f16 = f16(0x0400u16); |
| /// [`f16`](struct.f16.html) Not a Number (NaN). |
| pub const NAN: f16 = f16(0x7E00u16); |
| /// [`f16`](struct.f16.html) negative infinity (-∞). |
| pub const NEG_INFINITY: f16 = f16(0xFC00u16); |
| /// The radix or base of the internal representation of [`f16`](struct.f16.html). |
| pub const RADIX: u32 = 2; |
| |
| /// Minimum positive subnormal [`f16`](struct.f16.html) value. |
| pub const MIN_POSITIVE_SUBNORMAL: f16 = f16(0x0001u16); |
| /// Maximum subnormal [`f16`](struct.f16.html) value. |
| pub const MAX_SUBNORMAL: f16 = f16(0x03FFu16); |
| |
| /// [`f16`](struct.f16.html) 1 |
| pub const ONE: f16 = f16(0x3C00u16); |
| /// [`f16`](struct.f16.html) 0 |
| pub const ZERO: f16 = f16(0x0000u16); |
| /// [`f16`](struct.f16.html) -0 |
| pub const NEG_ZERO: f16 = f16(0x8000u16); |
| |
| /// [`f16`](struct.f16.html) Euler's number (ℯ). |
| pub const E: f16 = f16(0x4170u16); |
| /// [`f16`](struct.f16.html) Archimedes' constant (π). |
| pub const PI: f16 = f16(0x4248u16); |
| /// [`f16`](struct.f16.html) 1/π |
| pub const FRAC_1_PI: f16 = f16(0x3518u16); |
| /// [`f16`](struct.f16.html) 1/√2 |
| pub const FRAC_1_SQRT_2: f16 = f16(0x39A8u16); |
| /// [`f16`](struct.f16.html) 2/π |
| pub const FRAC_2_PI: f16 = f16(0x3918u16); |
| /// [`f16`](struct.f16.html) 2/√π |
| pub const FRAC_2_SQRT_PI: f16 = f16(0x3C83u16); |
| /// [`f16`](struct.f16.html) π/2 |
| pub const FRAC_PI_2: f16 = f16(0x3E48u16); |
| /// [`f16`](struct.f16.html) π/3 |
| pub const FRAC_PI_3: f16 = f16(0x3C30u16); |
| /// [`f16`](struct.f16.html) π/4 |
| pub const FRAC_PI_4: f16 = f16(0x3A48u16); |
| /// [`f16`](struct.f16.html) π/6 |
| pub const FRAC_PI_6: f16 = f16(0x3830u16); |
| /// [`f16`](struct.f16.html) π/8 |
| pub const FRAC_PI_8: f16 = f16(0x3648u16); |
| /// [`f16`](struct.f16.html) 𝗅𝗇 10 |
| pub const LN_10: f16 = f16(0x409Bu16); |
| /// [`f16`](struct.f16.html) 𝗅𝗇 2 |
| pub const LN_2: f16 = f16(0x398Cu16); |
| /// [`f16`](struct.f16.html) 𝗅𝗈𝗀₁₀ℯ |
| pub const LOG10_E: f16 = f16(0x36F3u16); |
| /// [`f16`](struct.f16.html) 𝗅𝗈𝗀₁₀2 |
| pub const LOG10_2: f16 = f16(0x34D1u16); |
| /// [`f16`](struct.f16.html) 𝗅𝗈𝗀₂ℯ |
| pub const LOG2_E: f16 = f16(0x3DC5u16); |
| /// [`f16`](struct.f16.html) 𝗅𝗈𝗀₂10 |
| pub const LOG2_10: f16 = f16(0x42A5u16); |
| /// [`f16`](struct.f16.html) √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, "0x{:X}", self.0) |
| } |
| } |
| |
| 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()) |
| } |
| } |
| |
| #[allow( |
| clippy::cognitive_complexity, |
| clippy::float_cmp, |
| clippy::neg_cmp_op_on_partial_ord |
| )] |
| #[cfg(test)] |
| mod test { |
| use super::*; |
| use core; |
| use core::cmp::Ordering; |
| use quickcheck_macros::quickcheck; |
| |
| #[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 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::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: quickcheck::Gen>(g: &mut G) -> Self { |
| use rand::Rng; |
| f16(g.gen()) |
| } |
| } |
| |
| #[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 |
| } |
| } |
| } |
