1806 lines
57 KiB
Rust
1806 lines
57 KiB
Rust
#[cfg(feature = "bytemuck")]
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use bytemuck::{Pod, Zeroable};
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use core::{
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cmp::Ordering,
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iter::{Product, Sum},
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num::FpCategory,
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ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Rem, RemAssign, Sub, SubAssign},
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};
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#[cfg(not(target_arch = "spirv"))]
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use core::{
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fmt::{
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Binary, Debug, Display, Error, Formatter, LowerExp, LowerHex, Octal, UpperExp, UpperHex,
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},
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num::ParseFloatError,
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str::FromStr,
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};
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#[cfg(feature = "serde")]
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use serde::{Deserialize, Serialize};
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#[cfg(feature = "zerocopy")]
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use zerocopy::{AsBytes, FromBytes};
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pub(crate) mod convert;
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/// A 16-bit floating point type implementing the IEEE 754-2008 standard [`binary16`] a.k.a `half`
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/// format.
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///
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/// This 16-bit floating point type is intended for efficient storage where the full range and
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/// precision of a larger floating point value is not required. Because [`f16`] is primarily for
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/// efficient storage, floating point operations such as addition, multiplication, etc. are not
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/// implemented. Operations should be performed with [`f32`] or higher-precision types and converted
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/// to/from [`f16`] as necessary.
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///
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/// [`binary16`]: https://en.wikipedia.org/wiki/Half-precision_floating-point_format
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#[allow(non_camel_case_types)]
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#[derive(Clone, Copy, Default)]
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#[repr(transparent)]
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#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
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#[cfg_attr(feature = "bytemuck", derive(Zeroable, Pod))]
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#[cfg_attr(feature = "zerocopy", derive(AsBytes, FromBytes))]
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pub struct f16(u16);
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impl f16 {
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/// Constructs a 16-bit floating point value from the raw bits.
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#[inline]
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#[must_use]
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pub const fn from_bits(bits: u16) -> f16 {
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f16(bits)
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}
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/// Constructs a 16-bit floating point value from a 32-bit floating point value.
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///
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/// If the 32-bit value is to large to fit in 16-bits, ±∞ will result. NaN values are
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/// preserved. 32-bit subnormal values are too tiny to be represented in 16-bits and result in
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/// ±0. Exponents that underflow the minimum 16-bit exponent will result in 16-bit subnormals
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/// or ±0. All other values are truncated and rounded to the nearest representable 16-bit
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/// value.
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#[inline]
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#[must_use]
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pub fn from_f32(value: f32) -> f16 {
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f16(convert::f32_to_f16(value))
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}
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/// Constructs a 16-bit floating point value from a 32-bit floating point value.
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///
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/// This function is identical to [`from_f32`][Self::from_f32] except it never uses hardware
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/// intrinsics, which allows it to be `const`. [`from_f32`][Self::from_f32] should be preferred
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/// in any non-`const` context.
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///
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/// If the 32-bit value is to large to fit in 16-bits, ±∞ will result. NaN values are
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/// preserved. 32-bit subnormal values are too tiny to be represented in 16-bits and result in
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/// ±0. Exponents that underflow the minimum 16-bit exponent will result in 16-bit subnormals
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/// or ±0. All other values are truncated and rounded to the nearest representable 16-bit
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/// value.
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#[inline]
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#[must_use]
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pub const fn from_f32_const(value: f32) -> f16 {
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f16(convert::f32_to_f16_fallback(value))
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}
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/// Constructs a 16-bit floating point value from a 64-bit floating point value.
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///
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/// If the 64-bit value is to large to fit in 16-bits, ±∞ will result. NaN values are
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||
/// preserved. 64-bit subnormal values are too tiny to be represented in 16-bits and result in
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||
/// ±0. Exponents that underflow the minimum 16-bit exponent will result in 16-bit subnormals
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/// or ±0. All other values are truncated and rounded to the nearest representable 16-bit
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/// value.
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#[inline]
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#[must_use]
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pub fn from_f64(value: f64) -> f16 {
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f16(convert::f64_to_f16(value))
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}
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||
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/// Constructs a 16-bit floating point value from a 64-bit floating point value.
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///
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||
/// This function is identical to [`from_f64`][Self::from_f64] except it never uses hardware
|
||
/// intrinsics, which allows it to be `const`. [`from_f64`][Self::from_f64] should be preferred
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||
/// in any non-`const` context.
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||
///
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||
/// If the 64-bit value is to large to fit in 16-bits, ±∞ will result. NaN values are
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||
/// preserved. 64-bit subnormal values are too tiny to be represented in 16-bits and result in
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||
/// ±0. Exponents that underflow the minimum 16-bit exponent will result in 16-bit subnormals
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/// or ±0. All other values are truncated and rounded to the nearest representable 16-bit
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/// value.
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#[inline]
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#[must_use]
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pub const fn from_f64_const(value: f64) -> f16 {
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f16(convert::f64_to_f16_fallback(value))
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}
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/// Converts a [`f16`] into the underlying bit representation.
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#[inline]
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#[must_use]
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pub const fn to_bits(self) -> u16 {
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self.0
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}
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/// Returns the memory representation of the underlying bit representation as a byte array in
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/// little-endian byte order.
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///
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/// # Examples
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///
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/// ```rust
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/// # use half::prelude::*;
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/// let bytes = f16::from_f32(12.5).to_le_bytes();
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/// assert_eq!(bytes, [0x40, 0x4A]);
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/// ```
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#[inline]
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||
#[must_use]
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pub const fn to_le_bytes(self) -> [u8; 2] {
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self.0.to_le_bytes()
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}
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/// Returns the memory representation of the underlying bit representation as a byte array in
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/// big-endian (network) byte order.
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///
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/// # Examples
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///
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||
/// ```rust
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/// # use half::prelude::*;
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/// let bytes = f16::from_f32(12.5).to_be_bytes();
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/// assert_eq!(bytes, [0x4A, 0x40]);
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/// ```
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#[inline]
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#[must_use]
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pub const fn to_be_bytes(self) -> [u8; 2] {
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self.0.to_be_bytes()
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}
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/// Returns the memory representation of the underlying bit representation as a byte array in
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/// native byte order.
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///
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/// As the target platform's native endianness is used, portable code should use
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/// [`to_be_bytes`][Self::to_be_bytes] or [`to_le_bytes`][Self::to_le_bytes], as appropriate,
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/// instead.
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///
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/// # Examples
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///
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/// ```rust
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/// # use half::prelude::*;
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/// let bytes = f16::from_f32(12.5).to_ne_bytes();
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/// assert_eq!(bytes, if cfg!(target_endian = "big") {
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/// [0x4A, 0x40]
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/// } else {
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/// [0x40, 0x4A]
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/// });
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/// ```
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#[inline]
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#[must_use]
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pub const fn to_ne_bytes(self) -> [u8; 2] {
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self.0.to_ne_bytes()
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}
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/// Creates a floating point value from its representation as a byte array in little endian.
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///
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/// # Examples
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///
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/// ```rust
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/// # use half::prelude::*;
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/// let value = f16::from_le_bytes([0x40, 0x4A]);
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/// assert_eq!(value, f16::from_f32(12.5));
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/// ```
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#[inline]
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#[must_use]
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pub const fn from_le_bytes(bytes: [u8; 2]) -> f16 {
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f16::from_bits(u16::from_le_bytes(bytes))
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}
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/// Creates a floating point value from its representation as a byte array in big endian.
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///
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/// # Examples
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///
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/// ```rust
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/// # use half::prelude::*;
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/// let value = f16::from_be_bytes([0x4A, 0x40]);
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/// assert_eq!(value, f16::from_f32(12.5));
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/// ```
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#[inline]
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#[must_use]
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pub const fn from_be_bytes(bytes: [u8; 2]) -> f16 {
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f16::from_bits(u16::from_be_bytes(bytes))
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}
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/// Creates a floating point value from its representation as a byte array in native endian.
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///
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/// As the target platform's native endianness is used, portable code likely wants to use
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/// [`from_be_bytes`][Self::from_be_bytes] or [`from_le_bytes`][Self::from_le_bytes], as
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/// appropriate instead.
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///
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/// # Examples
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///
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/// ```rust
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/// # use half::prelude::*;
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/// let value = f16::from_ne_bytes(if cfg!(target_endian = "big") {
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/// [0x4A, 0x40]
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/// } else {
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/// [0x40, 0x4A]
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/// });
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/// assert_eq!(value, f16::from_f32(12.5));
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/// ```
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#[inline]
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#[must_use]
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pub const fn from_ne_bytes(bytes: [u8; 2]) -> f16 {
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f16::from_bits(u16::from_ne_bytes(bytes))
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}
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/// Converts a [`f16`] value into a `f32` value.
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///
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/// This conversion is lossless as all 16-bit floating point values can be represented exactly
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/// in 32-bit floating point.
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#[inline]
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||
#[must_use]
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pub fn to_f32(self) -> f32 {
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convert::f16_to_f32(self.0)
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}
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/// Converts a [`f16`] value into a `f32` value.
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///
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/// This function is identical to [`to_f32`][Self::to_f32] except it never uses hardware
|
||
/// intrinsics, which allows it to be `const`. [`to_f32`][Self::to_f32] should be preferred
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/// in any non-`const` context.
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///
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/// This conversion is lossless as all 16-bit floating point values can be represented exactly
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/// in 32-bit floating point.
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#[inline]
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#[must_use]
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pub const fn to_f32_const(self) -> f32 {
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convert::f16_to_f32_fallback(self.0)
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}
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/// Converts a [`f16`] value into a `f64` value.
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///
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/// This conversion is lossless as all 16-bit floating point values can be represented exactly
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/// in 64-bit floating point.
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#[inline]
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#[must_use]
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pub fn to_f64(self) -> f64 {
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convert::f16_to_f64(self.0)
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}
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/// Converts a [`f16`] value into a `f64` value.
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///
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||
/// This function is identical to [`to_f64`][Self::to_f64] except it never uses hardware
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||
/// intrinsics, which allows it to be `const`. [`to_f64`][Self::to_f64] should be preferred
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/// in any non-`const` context.
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///
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/// This conversion is lossless as all 16-bit floating point values can be represented exactly
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/// in 64-bit floating point.
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#[inline]
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#[must_use]
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pub const fn to_f64_const(self) -> f64 {
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convert::f16_to_f64_fallback(self.0)
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||
}
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||
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||
/// Returns `true` if this value is `NaN` and `false` otherwise.
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||
///
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||
/// # Examples
|
||
///
|
||
/// ```rust
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/// # use half::prelude::*;
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///
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/// let nan = f16::NAN;
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/// let f = f16::from_f32(7.0_f32);
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///
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/// assert!(nan.is_nan());
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/// assert!(!f.is_nan());
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||
/// ```
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#[inline]
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||
#[must_use]
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||
pub const fn is_nan(self) -> bool {
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self.0 & 0x7FFFu16 > 0x7C00u16
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||
}
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||
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||
/// Returns `true` if this value is ±∞ and `false`.
|
||
/// otherwise.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```rust
|
||
/// # use half::prelude::*;
|
||
///
|
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/// let f = f16::from_f32(7.0f32);
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/// let inf = f16::INFINITY;
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||
/// let neg_inf = f16::NEG_INFINITY;
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||
/// let nan = f16::NAN;
|
||
///
|
||
/// assert!(!f.is_infinite());
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||
/// assert!(!nan.is_infinite());
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///
|
||
/// assert!(inf.is_infinite());
|
||
/// assert!(neg_inf.is_infinite());
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||
/// ```
|
||
#[inline]
|
||
#[must_use]
|
||
pub const fn is_infinite(self) -> bool {
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self.0 & 0x7FFFu16 == 0x7C00u16
|
||
}
|
||
|
||
/// Returns `true` if this number is neither infinite nor `NaN`.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```rust
|
||
/// # use half::prelude::*;
|
||
///
|
||
/// let f = f16::from_f32(7.0f32);
|
||
/// let inf = f16::INFINITY;
|
||
/// let neg_inf = f16::NEG_INFINITY;
|
||
/// let nan = f16::NAN;
|
||
///
|
||
/// assert!(f.is_finite());
|
||
///
|
||
/// assert!(!nan.is_finite());
|
||
/// assert!(!inf.is_finite());
|
||
/// assert!(!neg_inf.is_finite());
|
||
/// ```
|
||
#[inline]
|
||
#[must_use]
|
||
pub const fn is_finite(self) -> bool {
|
||
self.0 & 0x7C00u16 != 0x7C00u16
|
||
}
|
||
|
||
/// Returns `true` if the number is neither zero, infinite, subnormal, or `NaN`.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```rust
|
||
/// # use half::prelude::*;
|
||
///
|
||
/// let min = f16::MIN_POSITIVE;
|
||
/// let max = f16::MAX;
|
||
/// let lower_than_min = f16::from_f32(1.0e-10_f32);
|
||
/// let zero = f16::from_f32(0.0_f32);
|
||
///
|
||
/// assert!(min.is_normal());
|
||
/// assert!(max.is_normal());
|
||
///
|
||
/// assert!(!zero.is_normal());
|
||
/// assert!(!f16::NAN.is_normal());
|
||
/// assert!(!f16::INFINITY.is_normal());
|
||
/// // Values between `0` and `min` are Subnormal.
|
||
/// assert!(!lower_than_min.is_normal());
|
||
/// ```
|
||
#[inline]
|
||
#[must_use]
|
||
pub const fn is_normal(self) -> bool {
|
||
let exp = self.0 & 0x7C00u16;
|
||
exp != 0x7C00u16 && exp != 0
|
||
}
|
||
|
||
/// Returns the floating point category of the number.
|
||
///
|
||
/// If only one property is going to be tested, it is generally faster to use the specific
|
||
/// predicate instead.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```rust
|
||
/// use std::num::FpCategory;
|
||
/// # use half::prelude::*;
|
||
///
|
||
/// let num = f16::from_f32(12.4_f32);
|
||
/// let inf = f16::INFINITY;
|
||
///
|
||
/// assert_eq!(num.classify(), FpCategory::Normal);
|
||
/// assert_eq!(inf.classify(), FpCategory::Infinite);
|
||
/// ```
|
||
#[must_use]
|
||
pub const fn classify(self) -> FpCategory {
|
||
let exp = self.0 & 0x7C00u16;
|
||
let man = self.0 & 0x03FFu16;
|
||
match (exp, man) {
|
||
(0, 0) => FpCategory::Zero,
|
||
(0, _) => FpCategory::Subnormal,
|
||
(0x7C00u16, 0) => FpCategory::Infinite,
|
||
(0x7C00u16, _) => FpCategory::Nan,
|
||
_ => FpCategory::Normal,
|
||
}
|
||
}
|
||
|
||
/// Returns a number that represents the sign of `self`.
|
||
///
|
||
/// * `1.0` if the number is positive, `+0.0` or [`INFINITY`][f16::INFINITY]
|
||
/// * `-1.0` if the number is negative, `-0.0` or [`NEG_INFINITY`][f16::NEG_INFINITY]
|
||
/// * [`NAN`][f16::NAN] if the number is `NaN`
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```rust
|
||
/// # use half::prelude::*;
|
||
///
|
||
/// let f = f16::from_f32(3.5_f32);
|
||
///
|
||
/// assert_eq!(f.signum(), f16::from_f32(1.0));
|
||
/// assert_eq!(f16::NEG_INFINITY.signum(), f16::from_f32(-1.0));
|
||
///
|
||
/// assert!(f16::NAN.signum().is_nan());
|
||
/// ```
|
||
#[must_use]
|
||
pub const fn signum(self) -> f16 {
|
||
if self.is_nan() {
|
||
self
|
||
} else if self.0 & 0x8000u16 != 0 {
|
||
Self::NEG_ONE
|
||
} else {
|
||
Self::ONE
|
||
}
|
||
}
|
||
|
||
/// Returns `true` if and only if `self` has a positive sign, including `+0.0`, `NaNs` with a
|
||
/// positive sign bit and +∞.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```rust
|
||
/// # use half::prelude::*;
|
||
///
|
||
/// let nan = f16::NAN;
|
||
/// let f = f16::from_f32(7.0_f32);
|
||
/// let g = f16::from_f32(-7.0_f32);
|
||
///
|
||
/// assert!(f.is_sign_positive());
|
||
/// assert!(!g.is_sign_positive());
|
||
/// // `NaN` can be either positive or negative
|
||
/// assert!(nan.is_sign_positive() != nan.is_sign_negative());
|
||
/// ```
|
||
#[inline]
|
||
#[must_use]
|
||
pub const fn is_sign_positive(self) -> bool {
|
||
self.0 & 0x8000u16 == 0
|
||
}
|
||
|
||
/// Returns `true` if and only if `self` has a negative sign, including `-0.0`, `NaNs` with a
|
||
/// negative sign bit and −∞.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```rust
|
||
/// # use half::prelude::*;
|
||
///
|
||
/// let nan = f16::NAN;
|
||
/// let f = f16::from_f32(7.0f32);
|
||
/// let g = f16::from_f32(-7.0f32);
|
||
///
|
||
/// assert!(!f.is_sign_negative());
|
||
/// assert!(g.is_sign_negative());
|
||
/// // `NaN` can be either positive or negative
|
||
/// assert!(nan.is_sign_positive() != nan.is_sign_negative());
|
||
/// ```
|
||
#[inline]
|
||
#[must_use]
|
||
pub const fn is_sign_negative(self) -> bool {
|
||
self.0 & 0x8000u16 != 0
|
||
}
|
||
|
||
/// Returns a number composed of the magnitude of `self` and the sign of `sign`.
|
||
///
|
||
/// Equal to `self` if the sign of `self` and `sign` are the same, otherwise equal to `-self`.
|
||
/// If `self` is NaN, then NaN with the sign of `sign` is returned.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// # use half::prelude::*;
|
||
/// let f = f16::from_f32(3.5);
|
||
///
|
||
/// assert_eq!(f.copysign(f16::from_f32(0.42)), f16::from_f32(3.5));
|
||
/// assert_eq!(f.copysign(f16::from_f32(-0.42)), f16::from_f32(-3.5));
|
||
/// assert_eq!((-f).copysign(f16::from_f32(0.42)), f16::from_f32(3.5));
|
||
/// assert_eq!((-f).copysign(f16::from_f32(-0.42)), f16::from_f32(-3.5));
|
||
///
|
||
/// assert!(f16::NAN.copysign(f16::from_f32(1.0)).is_nan());
|
||
/// ```
|
||
#[inline]
|
||
#[must_use]
|
||
pub const fn copysign(self, sign: f16) -> f16 {
|
||
f16((sign.0 & 0x8000u16) | (self.0 & 0x7FFFu16))
|
||
}
|
||
|
||
/// Returns the maximum of the two numbers.
|
||
///
|
||
/// If one of the arguments is NaN, then the other argument is returned.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// # use half::prelude::*;
|
||
/// let x = f16::from_f32(1.0);
|
||
/// let y = f16::from_f32(2.0);
|
||
///
|
||
/// assert_eq!(x.max(y), y);
|
||
/// ```
|
||
#[inline]
|
||
#[must_use]
|
||
pub fn max(self, other: f16) -> f16 {
|
||
if other > self && !other.is_nan() {
|
||
other
|
||
} else {
|
||
self
|
||
}
|
||
}
|
||
|
||
/// Returns the minimum of the two numbers.
|
||
///
|
||
/// If one of the arguments is NaN, then the other argument is returned.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// # use half::prelude::*;
|
||
/// let x = f16::from_f32(1.0);
|
||
/// let y = f16::from_f32(2.0);
|
||
///
|
||
/// assert_eq!(x.min(y), x);
|
||
/// ```
|
||
#[inline]
|
||
#[must_use]
|
||
pub fn min(self, other: f16) -> f16 {
|
||
if other < self && !other.is_nan() {
|
||
other
|
||
} else {
|
||
self
|
||
}
|
||
}
|
||
|
||
/// Restrict a value to a certain interval unless it is NaN.
|
||
///
|
||
/// Returns `max` if `self` is greater than `max`, and `min` if `self` is less than `min`.
|
||
/// Otherwise this returns `self`.
|
||
///
|
||
/// Note that this function returns NaN if the initial value was NaN as well.
|
||
///
|
||
/// # Panics
|
||
/// Panics if `min > max`, `min` is NaN, or `max` is NaN.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// # use half::prelude::*;
|
||
/// assert!(f16::from_f32(-3.0).clamp(f16::from_f32(-2.0), f16::from_f32(1.0)) == f16::from_f32(-2.0));
|
||
/// assert!(f16::from_f32(0.0).clamp(f16::from_f32(-2.0), f16::from_f32(1.0)) == f16::from_f32(0.0));
|
||
/// assert!(f16::from_f32(2.0).clamp(f16::from_f32(-2.0), f16::from_f32(1.0)) == f16::from_f32(1.0));
|
||
/// assert!(f16::NAN.clamp(f16::from_f32(-2.0), f16::from_f32(1.0)).is_nan());
|
||
/// ```
|
||
#[inline]
|
||
#[must_use]
|
||
pub fn clamp(self, min: f16, max: f16) -> f16 {
|
||
assert!(min <= max);
|
||
let mut x = self;
|
||
if x < min {
|
||
x = min;
|
||
}
|
||
if x > max {
|
||
x = max;
|
||
}
|
||
x
|
||
}
|
||
|
||
/// Returns the ordering between `self` and `other`.
|
||
///
|
||
/// Unlike the standard partial comparison between floating point numbers,
|
||
/// this comparison always produces an ordering in accordance to
|
||
/// the `totalOrder` predicate as defined in the IEEE 754 (2008 revision)
|
||
/// floating point standard. The values are ordered in the following sequence:
|
||
///
|
||
/// - negative quiet NaN
|
||
/// - negative signaling NaN
|
||
/// - negative infinity
|
||
/// - negative numbers
|
||
/// - negative subnormal numbers
|
||
/// - negative zero
|
||
/// - positive zero
|
||
/// - positive subnormal numbers
|
||
/// - positive numbers
|
||
/// - positive infinity
|
||
/// - positive signaling NaN
|
||
/// - positive quiet NaN.
|
||
///
|
||
/// The ordering established by this function does not always agree with the
|
||
/// [`PartialOrd`] and [`PartialEq`] implementations of `f16`. For example,
|
||
/// they consider negative and positive zero equal, while `total_cmp`
|
||
/// doesn't.
|
||
///
|
||
/// The interpretation of the signaling NaN bit follows the definition in
|
||
/// the IEEE 754 standard, which may not match the interpretation by some of
|
||
/// the older, non-conformant (e.g. MIPS) hardware implementations.
|
||
///
|
||
/// # Examples
|
||
/// ```
|
||
/// # use half::f16;
|
||
/// let mut v: Vec<f16> = vec![];
|
||
/// v.push(f16::ONE);
|
||
/// v.push(f16::INFINITY);
|
||
/// v.push(f16::NEG_INFINITY);
|
||
/// v.push(f16::NAN);
|
||
/// v.push(f16::MAX_SUBNORMAL);
|
||
/// v.push(-f16::MAX_SUBNORMAL);
|
||
/// v.push(f16::ZERO);
|
||
/// v.push(f16::NEG_ZERO);
|
||
/// v.push(f16::NEG_ONE);
|
||
/// v.push(f16::MIN_POSITIVE);
|
||
///
|
||
/// v.sort_by(|a, b| a.total_cmp(&b));
|
||
///
|
||
/// assert!(v
|
||
/// .into_iter()
|
||
/// .zip(
|
||
/// [
|
||
/// f16::NEG_INFINITY,
|
||
/// f16::NEG_ONE,
|
||
/// -f16::MAX_SUBNORMAL,
|
||
/// f16::NEG_ZERO,
|
||
/// f16::ZERO,
|
||
/// f16::MAX_SUBNORMAL,
|
||
/// f16::MIN_POSITIVE,
|
||
/// f16::ONE,
|
||
/// f16::INFINITY,
|
||
/// f16::NAN
|
||
/// ]
|
||
/// .iter()
|
||
/// )
|
||
/// .all(|(a, b)| a.to_bits() == b.to_bits()));
|
||
/// ```
|
||
// Implementation based on: https://doc.rust-lang.org/std/primitive.f32.html#method.total_cmp
|
||
#[inline]
|
||
#[must_use]
|
||
pub fn total_cmp(&self, other: &Self) -> Ordering {
|
||
let mut left = self.to_bits() as i16;
|
||
let mut right = other.to_bits() as i16;
|
||
left ^= (((left >> 15) as u16) >> 1) as i16;
|
||
right ^= (((right >> 15) as u16) >> 1) as i16;
|
||
left.cmp(&right)
|
||
}
|
||
|
||
/// Approximate number of [`f16`] significant digits in base 10
|
||
pub const DIGITS: u32 = 3;
|
||
/// [`f16`]
|
||
/// [machine epsilon](https://en.wikipedia.org/wiki/Machine_epsilon) value
|
||
///
|
||
/// This is the difference between 1.0 and the next largest representable number.
|
||
pub const EPSILON: f16 = f16(0x1400u16);
|
||
/// [`f16`] positive Infinity (+∞)
|
||
pub const INFINITY: f16 = f16(0x7C00u16);
|
||
/// Number of [`f16`] significant digits in base 2
|
||
pub const MANTISSA_DIGITS: u32 = 11;
|
||
/// Largest finite [`f16`] value
|
||
pub const MAX: f16 = f16(0x7BFF);
|
||
/// Maximum possible [`f16`] power of 10 exponent
|
||
pub const MAX_10_EXP: i32 = 4;
|
||
/// Maximum possible [`f16`] power of 2 exponent
|
||
pub const MAX_EXP: i32 = 16;
|
||
/// Smallest finite [`f16`] value
|
||
pub const MIN: f16 = f16(0xFBFF);
|
||
/// Minimum possible normal [`f16`] power of 10 exponent
|
||
pub const MIN_10_EXP: i32 = -4;
|
||
/// One greater than the minimum possible normal [`f16`] power of 2 exponent
|
||
pub const MIN_EXP: i32 = -13;
|
||
/// Smallest positive normal [`f16`] value
|
||
pub const MIN_POSITIVE: f16 = f16(0x0400u16);
|
||
/// [`f16`] Not a Number (NaN)
|
||
pub const NAN: f16 = f16(0x7E00u16);
|
||
/// [`f16`] negative infinity (-∞)
|
||
pub const NEG_INFINITY: f16 = f16(0xFC00u16);
|
||
/// The radix or base of the internal representation of [`f16`]
|
||
pub const RADIX: u32 = 2;
|
||
|
||
/// Minimum positive subnormal [`f16`] value
|
||
pub const MIN_POSITIVE_SUBNORMAL: f16 = f16(0x0001u16);
|
||
/// Maximum subnormal [`f16`] value
|
||
pub const MAX_SUBNORMAL: f16 = f16(0x03FFu16);
|
||
|
||
/// [`f16`] 1
|
||
pub const ONE: f16 = f16(0x3C00u16);
|
||
/// [`f16`] 0
|
||
pub const ZERO: f16 = f16(0x0000u16);
|
||
/// [`f16`] -0
|
||
pub const NEG_ZERO: f16 = f16(0x8000u16);
|
||
/// [`f16`] -1
|
||
pub const NEG_ONE: f16 = f16(0xBC00u16);
|
||
|
||
/// [`f16`] Euler's number (ℯ)
|
||
pub const E: f16 = f16(0x4170u16);
|
||
/// [`f16`] Archimedes' constant (π)
|
||
pub const PI: f16 = f16(0x4248u16);
|
||
/// [`f16`] 1/π
|
||
pub const FRAC_1_PI: f16 = f16(0x3518u16);
|
||
/// [`f16`] 1/√2
|
||
pub const FRAC_1_SQRT_2: f16 = f16(0x39A8u16);
|
||
/// [`f16`] 2/π
|
||
pub const FRAC_2_PI: f16 = f16(0x3918u16);
|
||
/// [`f16`] 2/√π
|
||
pub const FRAC_2_SQRT_PI: f16 = f16(0x3C83u16);
|
||
/// [`f16`] π/2
|
||
pub const FRAC_PI_2: f16 = f16(0x3E48u16);
|
||
/// [`f16`] π/3
|
||
pub const FRAC_PI_3: f16 = f16(0x3C30u16);
|
||
/// [`f16`] π/4
|
||
pub const FRAC_PI_4: f16 = f16(0x3A48u16);
|
||
/// [`f16`] π/6
|
||
pub const FRAC_PI_6: f16 = f16(0x3830u16);
|
||
/// [`f16`] π/8
|
||
pub const FRAC_PI_8: f16 = f16(0x3648u16);
|
||
/// [`f16`] 𝗅𝗇 10
|
||
pub const LN_10: f16 = f16(0x409Bu16);
|
||
/// [`f16`] 𝗅𝗇 2
|
||
pub const LN_2: f16 = f16(0x398Cu16);
|
||
/// [`f16`] 𝗅𝗈𝗀₁₀ℯ
|
||
pub const LOG10_E: f16 = f16(0x36F3u16);
|
||
/// [`f16`] 𝗅𝗈𝗀₁₀2
|
||
pub const LOG10_2: f16 = f16(0x34D1u16);
|
||
/// [`f16`] 𝗅𝗈𝗀₂ℯ
|
||
pub const LOG2_E: f16 = f16(0x3DC5u16);
|
||
/// [`f16`] 𝗅𝗈𝗀₂10
|
||
pub const LOG2_10: f16 = f16(0x42A5u16);
|
||
/// [`f16`] √2
|
||
pub const SQRT_2: f16 = f16(0x3DA8u16);
|
||
}
|
||
|
||
impl From<f16> for f32 {
|
||
#[inline]
|
||
fn from(x: f16) -> f32 {
|
||
x.to_f32()
|
||
}
|
||
}
|
||
|
||
impl From<f16> for f64 {
|
||
#[inline]
|
||
fn from(x: f16) -> f64 {
|
||
x.to_f64()
|
||
}
|
||
}
|
||
|
||
impl From<i8> for f16 {
|
||
#[inline]
|
||
fn from(x: i8) -> f16 {
|
||
// Convert to f32, then to f16
|
||
f16::from_f32(f32::from(x))
|
||
}
|
||
}
|
||
|
||
impl From<u8> for f16 {
|
||
#[inline]
|
||
fn from(x: u8) -> f16 {
|
||
// Convert to f32, then to f16
|
||
f16::from_f32(f32::from(x))
|
||
}
|
||
}
|
||
|
||
impl PartialEq for f16 {
|
||
fn eq(&self, other: &f16) -> bool {
|
||
if self.is_nan() || other.is_nan() {
|
||
false
|
||
} else {
|
||
(self.0 == other.0) || ((self.0 | other.0) & 0x7FFFu16 == 0)
|
||
}
|
||
}
|
||
}
|
||
|
||
impl PartialOrd for f16 {
|
||
fn partial_cmp(&self, other: &f16) -> Option<Ordering> {
|
||
if self.is_nan() || other.is_nan() {
|
||
None
|
||
} else {
|
||
let neg = self.0 & 0x8000u16 != 0;
|
||
let other_neg = other.0 & 0x8000u16 != 0;
|
||
match (neg, other_neg) {
|
||
(false, false) => Some(self.0.cmp(&other.0)),
|
||
(false, true) => {
|
||
if (self.0 | other.0) & 0x7FFFu16 == 0 {
|
||
Some(Ordering::Equal)
|
||
} else {
|
||
Some(Ordering::Greater)
|
||
}
|
||
}
|
||
(true, false) => {
|
||
if (self.0 | other.0) & 0x7FFFu16 == 0 {
|
||
Some(Ordering::Equal)
|
||
} else {
|
||
Some(Ordering::Less)
|
||
}
|
||
}
|
||
(true, true) => Some(other.0.cmp(&self.0)),
|
||
}
|
||
}
|
||
}
|
||
|
||
fn lt(&self, other: &f16) -> bool {
|
||
if self.is_nan() || other.is_nan() {
|
||
false
|
||
} else {
|
||
let neg = self.0 & 0x8000u16 != 0;
|
||
let other_neg = other.0 & 0x8000u16 != 0;
|
||
match (neg, other_neg) {
|
||
(false, false) => self.0 < other.0,
|
||
(false, true) => false,
|
||
(true, false) => (self.0 | other.0) & 0x7FFFu16 != 0,
|
||
(true, true) => self.0 > other.0,
|
||
}
|
||
}
|
||
}
|
||
|
||
fn le(&self, other: &f16) -> bool {
|
||
if self.is_nan() || other.is_nan() {
|
||
false
|
||
} else {
|
||
let neg = self.0 & 0x8000u16 != 0;
|
||
let other_neg = other.0 & 0x8000u16 != 0;
|
||
match (neg, other_neg) {
|
||
(false, false) => self.0 <= other.0,
|
||
(false, true) => (self.0 | other.0) & 0x7FFFu16 == 0,
|
||
(true, false) => true,
|
||
(true, true) => self.0 >= other.0,
|
||
}
|
||
}
|
||
}
|
||
|
||
fn gt(&self, other: &f16) -> bool {
|
||
if self.is_nan() || other.is_nan() {
|
||
false
|
||
} else {
|
||
let neg = self.0 & 0x8000u16 != 0;
|
||
let other_neg = other.0 & 0x8000u16 != 0;
|
||
match (neg, other_neg) {
|
||
(false, false) => self.0 > other.0,
|
||
(false, true) => (self.0 | other.0) & 0x7FFFu16 != 0,
|
||
(true, false) => false,
|
||
(true, true) => self.0 < other.0,
|
||
}
|
||
}
|
||
}
|
||
|
||
fn ge(&self, other: &f16) -> bool {
|
||
if self.is_nan() || other.is_nan() {
|
||
false
|
||
} else {
|
||
let neg = self.0 & 0x8000u16 != 0;
|
||
let other_neg = other.0 & 0x8000u16 != 0;
|
||
match (neg, other_neg) {
|
||
(false, false) => self.0 >= other.0,
|
||
(false, true) => true,
|
||
(true, false) => (self.0 | other.0) & 0x7FFFu16 == 0,
|
||
(true, true) => self.0 <= other.0,
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
#[cfg(not(target_arch = "spirv"))]
|
||
impl FromStr for f16 {
|
||
type Err = ParseFloatError;
|
||
fn from_str(src: &str) -> Result<f16, ParseFloatError> {
|
||
f32::from_str(src).map(f16::from_f32)
|
||
}
|
||
}
|
||
|
||
#[cfg(not(target_arch = "spirv"))]
|
||
impl Debug for f16 {
|
||
fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> {
|
||
write!(f, "{:?}", self.to_f32())
|
||
}
|
||
}
|
||
|
||
#[cfg(not(target_arch = "spirv"))]
|
||
impl Display for f16 {
|
||
fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> {
|
||
write!(f, "{}", self.to_f32())
|
||
}
|
||
}
|
||
|
||
#[cfg(not(target_arch = "spirv"))]
|
||
impl LowerExp for f16 {
|
||
fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> {
|
||
write!(f, "{:e}", self.to_f32())
|
||
}
|
||
}
|
||
|
||
#[cfg(not(target_arch = "spirv"))]
|
||
impl UpperExp for f16 {
|
||
fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> {
|
||
write!(f, "{:E}", self.to_f32())
|
||
}
|
||
}
|
||
|
||
#[cfg(not(target_arch = "spirv"))]
|
||
impl Binary for f16 {
|
||
fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> {
|
||
write!(f, "{:b}", self.0)
|
||
}
|
||
}
|
||
|
||
#[cfg(not(target_arch = "spirv"))]
|
||
impl Octal for f16 {
|
||
fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> {
|
||
write!(f, "{:o}", self.0)
|
||
}
|
||
}
|
||
|
||
#[cfg(not(target_arch = "spirv"))]
|
||
impl LowerHex for f16 {
|
||
fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> {
|
||
write!(f, "{:x}", self.0)
|
||
}
|
||
}
|
||
|
||
#[cfg(not(target_arch = "spirv"))]
|
||
impl UpperHex for f16 {
|
||
fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> {
|
||
write!(f, "{:X}", self.0)
|
||
}
|
||
}
|
||
|
||
impl Neg for f16 {
|
||
type Output = Self;
|
||
|
||
#[inline]
|
||
fn neg(self) -> Self::Output {
|
||
Self(self.0 ^ 0x8000)
|
||
}
|
||
}
|
||
|
||
impl Neg for &f16 {
|
||
type Output = <f16 as Neg>::Output;
|
||
|
||
#[inline]
|
||
fn neg(self) -> Self::Output {
|
||
Neg::neg(*self)
|
||
}
|
||
}
|
||
|
||
impl Add for f16 {
|
||
type Output = Self;
|
||
|
||
#[inline]
|
||
fn add(self, rhs: Self) -> Self::Output {
|
||
Self::from_f32(Self::to_f32(self) + Self::to_f32(rhs))
|
||
}
|
||
}
|
||
|
||
impl Add<&f16> for f16 {
|
||
type Output = <f16 as Add<f16>>::Output;
|
||
|
||
#[inline]
|
||
fn add(self, rhs: &f16) -> Self::Output {
|
||
self.add(*rhs)
|
||
}
|
||
}
|
||
|
||
impl Add<&f16> for &f16 {
|
||
type Output = <f16 as Add<f16>>::Output;
|
||
|
||
#[inline]
|
||
fn add(self, rhs: &f16) -> Self::Output {
|
||
(*self).add(*rhs)
|
||
}
|
||
}
|
||
|
||
impl Add<f16> for &f16 {
|
||
type Output = <f16 as Add<f16>>::Output;
|
||
|
||
#[inline]
|
||
fn add(self, rhs: f16) -> Self::Output {
|
||
(*self).add(rhs)
|
||
}
|
||
}
|
||
|
||
impl AddAssign for f16 {
|
||
#[inline]
|
||
fn add_assign(&mut self, rhs: Self) {
|
||
*self = (*self).add(rhs);
|
||
}
|
||
}
|
||
|
||
impl AddAssign<&f16> for f16 {
|
||
#[inline]
|
||
fn add_assign(&mut self, rhs: &f16) {
|
||
*self = (*self).add(rhs);
|
||
}
|
||
}
|
||
|
||
impl Sub for f16 {
|
||
type Output = Self;
|
||
|
||
#[inline]
|
||
fn sub(self, rhs: Self) -> Self::Output {
|
||
Self::from_f32(Self::to_f32(self) - Self::to_f32(rhs))
|
||
}
|
||
}
|
||
|
||
impl Sub<&f16> for f16 {
|
||
type Output = <f16 as Sub<f16>>::Output;
|
||
|
||
#[inline]
|
||
fn sub(self, rhs: &f16) -> Self::Output {
|
||
self.sub(*rhs)
|
||
}
|
||
}
|
||
|
||
impl Sub<&f16> for &f16 {
|
||
type Output = <f16 as Sub<f16>>::Output;
|
||
|
||
#[inline]
|
||
fn sub(self, rhs: &f16) -> Self::Output {
|
||
(*self).sub(*rhs)
|
||
}
|
||
}
|
||
|
||
impl Sub<f16> for &f16 {
|
||
type Output = <f16 as Sub<f16>>::Output;
|
||
|
||
#[inline]
|
||
fn sub(self, rhs: f16) -> Self::Output {
|
||
(*self).sub(rhs)
|
||
}
|
||
}
|
||
|
||
impl SubAssign for f16 {
|
||
#[inline]
|
||
fn sub_assign(&mut self, rhs: Self) {
|
||
*self = (*self).sub(rhs);
|
||
}
|
||
}
|
||
|
||
impl SubAssign<&f16> for f16 {
|
||
#[inline]
|
||
fn sub_assign(&mut self, rhs: &f16) {
|
||
*self = (*self).sub(rhs);
|
||
}
|
||
}
|
||
|
||
impl Mul for f16 {
|
||
type Output = Self;
|
||
|
||
#[inline]
|
||
fn mul(self, rhs: Self) -> Self::Output {
|
||
Self::from_f32(Self::to_f32(self) * Self::to_f32(rhs))
|
||
}
|
||
}
|
||
|
||
impl Mul<&f16> for f16 {
|
||
type Output = <f16 as Mul<f16>>::Output;
|
||
|
||
#[inline]
|
||
fn mul(self, rhs: &f16) -> Self::Output {
|
||
self.mul(*rhs)
|
||
}
|
||
}
|
||
|
||
impl Mul<&f16> for &f16 {
|
||
type Output = <f16 as Mul<f16>>::Output;
|
||
|
||
#[inline]
|
||
fn mul(self, rhs: &f16) -> Self::Output {
|
||
(*self).mul(*rhs)
|
||
}
|
||
}
|
||
|
||
impl Mul<f16> for &f16 {
|
||
type Output = <f16 as Mul<f16>>::Output;
|
||
|
||
#[inline]
|
||
fn mul(self, rhs: f16) -> Self::Output {
|
||
(*self).mul(rhs)
|
||
}
|
||
}
|
||
|
||
impl MulAssign for f16 {
|
||
#[inline]
|
||
fn mul_assign(&mut self, rhs: Self) {
|
||
*self = (*self).mul(rhs);
|
||
}
|
||
}
|
||
|
||
impl MulAssign<&f16> for f16 {
|
||
#[inline]
|
||
fn mul_assign(&mut self, rhs: &f16) {
|
||
*self = (*self).mul(rhs);
|
||
}
|
||
}
|
||
|
||
impl Div for f16 {
|
||
type Output = Self;
|
||
|
||
#[inline]
|
||
fn div(self, rhs: Self) -> Self::Output {
|
||
Self::from_f32(Self::to_f32(self) / Self::to_f32(rhs))
|
||
}
|
||
}
|
||
|
||
impl Div<&f16> for f16 {
|
||
type Output = <f16 as Div<f16>>::Output;
|
||
|
||
#[inline]
|
||
fn div(self, rhs: &f16) -> Self::Output {
|
||
self.div(*rhs)
|
||
}
|
||
}
|
||
|
||
impl Div<&f16> for &f16 {
|
||
type Output = <f16 as Div<f16>>::Output;
|
||
|
||
#[inline]
|
||
fn div(self, rhs: &f16) -> Self::Output {
|
||
(*self).div(*rhs)
|
||
}
|
||
}
|
||
|
||
impl Div<f16> for &f16 {
|
||
type Output = <f16 as Div<f16>>::Output;
|
||
|
||
#[inline]
|
||
fn div(self, rhs: f16) -> Self::Output {
|
||
(*self).div(rhs)
|
||
}
|
||
}
|
||
|
||
impl DivAssign for f16 {
|
||
#[inline]
|
||
fn div_assign(&mut self, rhs: Self) {
|
||
*self = (*self).div(rhs);
|
||
}
|
||
}
|
||
|
||
impl DivAssign<&f16> for f16 {
|
||
#[inline]
|
||
fn div_assign(&mut self, rhs: &f16) {
|
||
*self = (*self).div(rhs);
|
||
}
|
||
}
|
||
|
||
impl Rem for f16 {
|
||
type Output = Self;
|
||
|
||
#[inline]
|
||
fn rem(self, rhs: Self) -> Self::Output {
|
||
Self::from_f32(Self::to_f32(self) % Self::to_f32(rhs))
|
||
}
|
||
}
|
||
|
||
impl Rem<&f16> for f16 {
|
||
type Output = <f16 as Rem<f16>>::Output;
|
||
|
||
#[inline]
|
||
fn rem(self, rhs: &f16) -> Self::Output {
|
||
self.rem(*rhs)
|
||
}
|
||
}
|
||
|
||
impl Rem<&f16> for &f16 {
|
||
type Output = <f16 as Rem<f16>>::Output;
|
||
|
||
#[inline]
|
||
fn rem(self, rhs: &f16) -> Self::Output {
|
||
(*self).rem(*rhs)
|
||
}
|
||
}
|
||
|
||
impl Rem<f16> for &f16 {
|
||
type Output = <f16 as Rem<f16>>::Output;
|
||
|
||
#[inline]
|
||
fn rem(self, rhs: f16) -> Self::Output {
|
||
(*self).rem(rhs)
|
||
}
|
||
}
|
||
|
||
impl RemAssign for f16 {
|
||
#[inline]
|
||
fn rem_assign(&mut self, rhs: Self) {
|
||
*self = (*self).rem(rhs);
|
||
}
|
||
}
|
||
|
||
impl RemAssign<&f16> for f16 {
|
||
#[inline]
|
||
fn rem_assign(&mut self, rhs: &f16) {
|
||
*self = (*self).rem(rhs);
|
||
}
|
||
}
|
||
|
||
impl Product for f16 {
|
||
#[inline]
|
||
fn product<I: Iterator<Item = Self>>(iter: I) -> Self {
|
||
f16::from_f32(iter.map(|f| f.to_f32()).product())
|
||
}
|
||
}
|
||
|
||
impl<'a> Product<&'a f16> for f16 {
|
||
#[inline]
|
||
fn product<I: Iterator<Item = &'a f16>>(iter: I) -> Self {
|
||
f16::from_f32(iter.map(|f| f.to_f32()).product())
|
||
}
|
||
}
|
||
|
||
impl Sum for f16 {
|
||
#[inline]
|
||
fn sum<I: Iterator<Item = Self>>(iter: I) -> Self {
|
||
f16::from_f32(iter.map(|f| f.to_f32()).sum())
|
||
}
|
||
}
|
||
|
||
impl<'a> Sum<&'a f16> for f16 {
|
||
#[inline]
|
||
fn sum<I: Iterator<Item = &'a f16>>(iter: I) -> Self {
|
||
f16::from_f32(iter.map(|f| f.to_f32()).product())
|
||
}
|
||
}
|
||
|
||
#[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
|
||
}
|
||
}
|
||
}
|