//! Constants for the `f16` half-precision floating point type. //! //! *[See also the `f16` primitive type][f16].* //! //! Mathematically significant numbers are provided in the `consts` sub-module. //! //! For the constants defined directly in this module //! (as distinct from those defined in the `consts` sub-module), //! new code should instead use the associated constants //! defined directly on the `f16` type. #![unstable(feature = "f16", issue = "116909")] use crate::convert::FloatToInt; use crate::num::FpCategory; use crate::panic::const_assert; use crate::{intrinsics, mem}; /// Basic mathematical constants. #[unstable(feature = "f16", issue = "116909")] pub mod consts { // FIXME: replace with mathematical constants from cmath. /// Archimedes' constant (π) #[unstable(feature = "f16", issue = "116909")] pub const PI: f16 = 3.14159265358979323846264338327950288_f16; /// The full circle constant (τ) /// /// Equal to 2π. #[unstable(feature = "f16", issue = "116909")] pub const TAU: f16 = 6.28318530717958647692528676655900577_f16; /// The golden ratio (φ) #[unstable(feature = "f16", issue = "116909")] // Also, #[unstable(feature = "more_float_constants", issue = "103883")] pub const PHI: f16 = 1.618033988749894848204586834365638118_f16; /// The Euler-Mascheroni constant (γ) #[unstable(feature = "f16", issue = "116909")] // Also, #[unstable(feature = "more_float_constants", issue = "103883")] pub const EGAMMA: f16 = 0.577215664901532860606512090082402431_f16; /// π/2 #[unstable(feature = "f16", issue = "116909")] pub const FRAC_PI_2: f16 = 1.57079632679489661923132169163975144_f16; /// π/3 #[unstable(feature = "f16", issue = "116909")] pub const FRAC_PI_3: f16 = 1.04719755119659774615421446109316763_f16; /// π/4 #[unstable(feature = "f16", issue = "116909")] pub const FRAC_PI_4: f16 = 0.785398163397448309615660845819875721_f16; /// π/6 #[unstable(feature = "f16", issue = "116909")] pub const FRAC_PI_6: f16 = 0.52359877559829887307710723054658381_f16; /// π/8 #[unstable(feature = "f16", issue = "116909")] pub const FRAC_PI_8: f16 = 0.39269908169872415480783042290993786_f16; /// 1/π #[unstable(feature = "f16", issue = "116909")] pub const FRAC_1_PI: f16 = 0.318309886183790671537767526745028724_f16; /// 1/sqrt(π) #[unstable(feature = "f16", issue = "116909")] // Also, #[unstable(feature = "more_float_constants", issue = "103883")] pub const FRAC_1_SQRT_PI: f16 = 0.564189583547756286948079451560772586_f16; /// 1/sqrt(2π) #[doc(alias = "FRAC_1_SQRT_TAU")] #[unstable(feature = "f16", issue = "116909")] // Also, #[unstable(feature = "more_float_constants", issue = "103883")] pub const FRAC_1_SQRT_2PI: f16 = 0.398942280401432677939946059934381868_f16; /// 2/π #[unstable(feature = "f16", issue = "116909")] pub const FRAC_2_PI: f16 = 0.636619772367581343075535053490057448_f16; /// 2/sqrt(π) #[unstable(feature = "f16", issue = "116909")] pub const FRAC_2_SQRT_PI: f16 = 1.12837916709551257389615890312154517_f16; /// sqrt(2) #[unstable(feature = "f16", issue = "116909")] pub const SQRT_2: f16 = 1.41421356237309504880168872420969808_f16; /// 1/sqrt(2) #[unstable(feature = "f16", issue = "116909")] pub const FRAC_1_SQRT_2: f16 = 0.707106781186547524400844362104849039_f16; /// sqrt(3) #[unstable(feature = "f16", issue = "116909")] // Also, #[unstable(feature = "more_float_constants", issue = "103883")] pub const SQRT_3: f16 = 1.732050807568877293527446341505872367_f16; /// 1/sqrt(3) #[unstable(feature = "f16", issue = "116909")] // Also, #[unstable(feature = "more_float_constants", issue = "103883")] pub const FRAC_1_SQRT_3: f16 = 0.577350269189625764509148780501957456_f16; /// Euler's number (e) #[unstable(feature = "f16", issue = "116909")] pub const E: f16 = 2.71828182845904523536028747135266250_f16; /// log₂(10) #[unstable(feature = "f16", issue = "116909")] pub const LOG2_10: f16 = 3.32192809488736234787031942948939018_f16; /// log₂(e) #[unstable(feature = "f16", issue = "116909")] pub const LOG2_E: f16 = 1.44269504088896340735992468100189214_f16; /// log₁₀(2) #[unstable(feature = "f16", issue = "116909")] pub const LOG10_2: f16 = 0.301029995663981195213738894724493027_f16; /// log₁₀(e) #[unstable(feature = "f16", issue = "116909")] pub const LOG10_E: f16 = 0.434294481903251827651128918916605082_f16; /// ln(2) #[unstable(feature = "f16", issue = "116909")] pub const LN_2: f16 = 0.693147180559945309417232121458176568_f16; /// ln(10) #[unstable(feature = "f16", issue = "116909")] pub const LN_10: f16 = 2.30258509299404568401799145468436421_f16; } impl f16 { // FIXME(f16_f128): almost all methods in this `impl` are missing examples and a const // implementation. Add these once we can run code on all platforms and have f16/f128 in CTFE. /// The radix or base of the internal representation of `f16`. #[unstable(feature = "f16", issue = "116909")] pub const RADIX: u32 = 2; /// Number of significant digits in base 2. #[unstable(feature = "f16", issue = "116909")] pub const MANTISSA_DIGITS: u32 = 11; /// Approximate number of significant digits in base 10. /// /// This is the maximum x such that any decimal number with x /// significant digits can be converted to `f16` and back without loss. /// /// Equal to floor(log₁₀ 2^{[`MANTISSA_DIGITS`] − 1}). /// /// [`MANTISSA_DIGITS`]: f16::MANTISSA_DIGITS #[unstable(feature = "f16", issue = "116909")] pub const DIGITS: u32 = 3; /// [Machine epsilon] value for `f16`. /// /// This is the difference between `1.0` and the next larger representable number. /// /// Equal to 2^{1 − [`MANTISSA_DIGITS`]}. /// /// [Machine epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon /// [`MANTISSA_DIGITS`]: f16::MANTISSA_DIGITS #[unstable(feature = "f16", issue = "116909")] pub const EPSILON: f16 = 9.7656e-4_f16; /// Smallest finite `f16` value. /// /// Equal to −[`MAX`]. /// /// [`MAX`]: f16::MAX #[unstable(feature = "f16", issue = "116909")] pub const MIN: f16 = -6.5504e+4_f16; /// Smallest positive normal `f16` value. /// /// Equal to 2^{[`MIN_EXP`] − 1}. /// /// [`MIN_EXP`]: f16::MIN_EXP #[unstable(feature = "f16", issue = "116909")] pub const MIN_POSITIVE: f16 = 6.1035e-5_f16; /// Largest finite `f16` value. /// /// Equal to /// (1 − 2^{−[`MANTISSA_DIGITS`]}) 2^[`MAX_EXP`]. /// /// [`MANTISSA_DIGITS`]: f16::MANTISSA_DIGITS /// [`MAX_EXP`]: f16::MAX_EXP #[unstable(feature = "f16", issue = "116909")] pub const MAX: f16 = 6.5504e+4_f16; /// One greater than the minimum possible normal power of 2 exponent. /// /// If x = `MIN_EXP`, then normal numbers /// ≥ 0.5 × 2^x. #[unstable(feature = "f16", issue = "116909")] pub const MIN_EXP: i32 = -13; /// Maximum possible power of 2 exponent. /// /// If x = `MAX_EXP`, then normal numbers /// < 1 × 2^x. #[unstable(feature = "f16", issue = "116909")] pub const MAX_EXP: i32 = 16; /// Minimum x for which 10^x is normal. /// /// Equal to ceil(log₁₀ [`MIN_POSITIVE`]). /// /// [`MIN_POSITIVE`]: f16::MIN_POSITIVE #[unstable(feature = "f16", issue = "116909")] pub const MIN_10_EXP: i32 = -4; /// Maximum x for which 10^x is normal. /// /// Equal to floor(log₁₀ [`MAX`]). /// /// [`MAX`]: f16::MAX #[unstable(feature = "f16", issue = "116909")] pub const MAX_10_EXP: i32 = 4; /// Not a Number (NaN). /// /// Note that IEEE 754 doesn't define just a single NaN value; /// a plethora of bit patterns are considered to be NaN. /// Furthermore, the standard makes a difference /// between a "signaling" and a "quiet" NaN, /// and allows inspecting its "payload" (the unspecified bits in the bit pattern). /// This constant isn't guaranteed to equal to any specific NaN bitpattern, /// and the stability of its representation over Rust versions /// and target platforms isn't guaranteed. #[allow(clippy::eq_op)] #[rustc_diagnostic_item = "f16_nan"] #[unstable(feature = "f16", issue = "116909")] pub const NAN: f16 = 0.0_f16 / 0.0_f16; /// Infinity (∞). #[unstable(feature = "f16", issue = "116909")] pub const INFINITY: f16 = 1.0_f16 / 0.0_f16; /// Negative infinity (−∞). #[unstable(feature = "f16", issue = "116909")] pub const NEG_INFINITY: f16 = -1.0_f16 / 0.0_f16; /// Sign bit pub(crate) const SIGN_MASK: u16 = 0x8000; /// Exponent mask pub(crate) const EXP_MASK: u16 = 0x7c00; /// Mantissa mask pub(crate) const MAN_MASK: u16 = 0x03ff; /// Minimum representable positive value (min subnormal) const TINY_BITS: u16 = 0x1; /// Minimum representable negative value (min negative subnormal) const NEG_TINY_BITS: u16 = Self::TINY_BITS | Self::SIGN_MASK; /// Returns `true` if this value is NaN. /// /// ``` /// #![feature(f16)] /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { /// /// let nan = f16::NAN; /// let f = 7.0_f16; /// /// assert!(nan.is_nan()); /// assert!(!f.is_nan()); /// # } /// ``` #[inline] #[must_use] #[unstable(feature = "f16", issue = "116909")] #[allow(clippy::eq_op)] // > if you intended to check if the operand is NaN, use `.is_nan()` instead :) pub const fn is_nan(self) -> bool { self != self } /// Returns `true` if this value is positive infinity or negative infinity, and /// `false` otherwise. /// /// ``` /// #![feature(f16)] /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { /// /// let f = 7.0f16; /// let inf = f16::INFINITY; /// let neg_inf = f16::NEG_INFINITY; /// let nan = f16::NAN; /// /// assert!(!f.is_infinite()); /// assert!(!nan.is_infinite()); /// /// assert!(inf.is_infinite()); /// assert!(neg_inf.is_infinite()); /// # } /// ``` #[inline] #[must_use] #[unstable(feature = "f16", issue = "116909")] pub const fn is_infinite(self) -> bool { (self == f16::INFINITY) | (self == f16::NEG_INFINITY) } /// Returns `true` if this number is neither infinite nor NaN. /// /// ``` /// #![feature(f16)] /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { /// /// let f = 7.0f16; /// let inf: f16 = f16::INFINITY; /// let neg_inf: f16 = f16::NEG_INFINITY; /// let nan: f16 = f16::NAN; /// /// assert!(f.is_finite()); /// /// assert!(!nan.is_finite()); /// assert!(!inf.is_finite()); /// assert!(!neg_inf.is_finite()); /// # } /// ``` #[inline] #[must_use] #[unstable(feature = "f16", issue = "116909")] #[rustc_const_unstable(feature = "f16", issue = "116909")] pub const fn is_finite(self) -> bool { // There's no need to handle NaN separately: if self is NaN, // the comparison is not true, exactly as desired. self.abs() < Self::INFINITY } /// Returns `true` if the number is [subnormal]. /// /// ``` /// #![feature(f16)] /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { /// /// let min = f16::MIN_POSITIVE; // 6.1035e-5 /// let max = f16::MAX; /// let lower_than_min = 1.0e-7_f16; /// let zero = 0.0_f16; /// /// assert!(!min.is_subnormal()); /// assert!(!max.is_subnormal()); /// /// assert!(!zero.is_subnormal()); /// assert!(!f16::NAN.is_subnormal()); /// assert!(!f16::INFINITY.is_subnormal()); /// // Values between `0` and `min` are Subnormal. /// assert!(lower_than_min.is_subnormal()); /// # } /// ``` /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number #[inline] #[must_use] #[unstable(feature = "f16", issue = "116909")] pub const fn is_subnormal(self) -> bool { matches!(self.classify(), FpCategory::Subnormal) } /// Returns `true` if the number is neither zero, infinite, [subnormal], or NaN. /// /// ``` /// #![feature(f16)] /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { /// /// let min = f16::MIN_POSITIVE; // 6.1035e-5 /// let max = f16::MAX; /// let lower_than_min = 1.0e-7_f16; /// let zero = 0.0_f16; /// /// 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()); /// # } /// ``` /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number #[inline] #[must_use] #[unstable(feature = "f16", issue = "116909")] pub const fn is_normal(self) -> bool { matches!(self.classify(), FpCategory::Normal) } /// 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. /// /// ``` /// #![feature(f16)] /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { /// /// use std::num::FpCategory; /// /// let num = 12.4_f16; /// let inf = f16::INFINITY; /// /// assert_eq!(num.classify(), FpCategory::Normal); /// assert_eq!(inf.classify(), FpCategory::Infinite); /// # } /// ``` #[inline] #[unstable(feature = "f16", issue = "116909")] pub const fn classify(self) -> FpCategory { let b = self.to_bits(); match (b & Self::MAN_MASK, b & Self::EXP_MASK) { (0, Self::EXP_MASK) => FpCategory::Infinite, (_, Self::EXP_MASK) => FpCategory::Nan, (0, 0) => FpCategory::Zero, (_, 0) => FpCategory::Subnormal, _ => FpCategory::Normal, } } /// Returns `true` if `self` has a positive sign, including `+0.0`, NaNs with /// positive sign bit and positive infinity. /// /// Note that IEEE 754 doesn't assign any meaning to the sign bit in case of /// a NaN, and as Rust doesn't guarantee that the bit pattern of NaNs are /// conserved over arithmetic operations, the result of `is_sign_positive` on /// a NaN might produce an unexpected or non-portable result. See the [specification /// of NaN bit patterns](f32#nan-bit-patterns) for more info. Use `self.signum() == 1.0` /// if you need fully portable behavior (will return `false` for all NaNs). /// /// ``` /// #![feature(f16)] /// # // FIXME(f16_f128): LLVM crashes on s390x, llvm/llvm-project#50374 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { /// /// let f = 7.0_f16; /// let g = -7.0_f16; /// /// assert!(f.is_sign_positive()); /// assert!(!g.is_sign_positive()); /// # } /// ``` #[inline] #[must_use] #[unstable(feature = "f16", issue = "116909")] pub const fn is_sign_positive(self) -> bool { !self.is_sign_negative() } /// Returns `true` if `self` has a negative sign, including `-0.0`, NaNs with /// negative sign bit and negative infinity. /// /// Note that IEEE 754 doesn't assign any meaning to the sign bit in case of /// a NaN, and as Rust doesn't guarantee that the bit pattern of NaNs are /// conserved over arithmetic operations, the result of `is_sign_negative` on /// a NaN might produce an unexpected or non-portable result. See the [specification /// of NaN bit patterns](f32#nan-bit-patterns) for more info. Use `self.signum() == -1.0` /// if you need fully portable behavior (will return `false` for all NaNs). /// /// ``` /// #![feature(f16)] /// # // FIXME(f16_f128): LLVM crashes on s390x, llvm/llvm-project#50374 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { /// /// let f = 7.0_f16; /// let g = -7.0_f16; /// /// assert!(!f.is_sign_negative()); /// assert!(g.is_sign_negative()); /// # } /// ``` #[inline] #[must_use] #[unstable(feature = "f16", issue = "116909")] pub const fn is_sign_negative(self) -> bool { // IEEE754 says: isSignMinus(x) is true if and only if x has negative sign. isSignMinus // applies to zeros and NaNs as well. // SAFETY: This is just transmuting to get the sign bit, it's fine. (self.to_bits() & (1 << 15)) != 0 } /// Returns the least number greater than `self`. /// /// Let `TINY` be the smallest representable positive `f16`. Then, /// - if `self.is_nan()`, this returns `self`; /// - if `self` is [`NEG_INFINITY`], this returns [`MIN`]; /// - if `self` is `-TINY`, this returns -0.0; /// - if `self` is -0.0 or +0.0, this returns `TINY`; /// - if `self` is [`MAX`] or [`INFINITY`], this returns [`INFINITY`]; /// - otherwise the unique least value greater than `self` is returned. /// /// The identity `x.next_up() == -(-x).next_down()` holds for all non-NaN `x`. When `x` /// is finite `x == x.next_up().next_down()` also holds. /// /// ```rust /// #![feature(f16)] /// # // FIXME(f16_f128): ABI issues on MSVC /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { /// /// // f16::EPSILON is the difference between 1.0 and the next number up. /// assert_eq!(1.0f16.next_up(), 1.0 + f16::EPSILON); /// // But not for most numbers. /// assert!(0.1f16.next_up() < 0.1 + f16::EPSILON); /// assert_eq!(4356f16.next_up(), 4360.0); /// # } /// ``` /// /// This operation corresponds to IEEE-754 `nextUp`. /// /// [`NEG_INFINITY`]: Self::NEG_INFINITY /// [`INFINITY`]: Self::INFINITY /// [`MIN`]: Self::MIN /// [`MAX`]: Self::MAX #[inline] #[doc(alias = "nextUp")] #[unstable(feature = "f16", issue = "116909")] pub const fn next_up(self) -> Self { // Some targets violate Rust's assumption of IEEE semantics, e.g. by flushing // denormals to zero. This is in general unsound and unsupported, but here // we do our best to still produce the correct result on such targets. let bits = self.to_bits(); if self.is_nan() || bits == Self::INFINITY.to_bits() { return self; } let abs = bits & !Self::SIGN_MASK; let next_bits = if abs == 0 { Self::TINY_BITS } else if bits == abs { bits + 1 } else { bits - 1 }; Self::from_bits(next_bits) } /// Returns the greatest number less than `self`. /// /// Let `TINY` be the smallest representable positive `f16`. Then, /// - if `self.is_nan()`, this returns `self`; /// - if `self` is [`INFINITY`], this returns [`MAX`]; /// - if `self` is `TINY`, this returns 0.0; /// - if `self` is -0.0 or +0.0, this returns `-TINY`; /// - if `self` is [`MIN`] or [`NEG_INFINITY`], this returns [`NEG_INFINITY`]; /// - otherwise the unique greatest value less than `self` is returned. /// /// The identity `x.next_down() == -(-x).next_up()` holds for all non-NaN `x`. When `x` /// is finite `x == x.next_down().next_up()` also holds. /// /// ```rust /// #![feature(f16)] /// # // FIXME(f16_f128): ABI issues on MSVC /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { /// /// let x = 1.0f16; /// // Clamp value into range [0, 1). /// let clamped = x.clamp(0.0, 1.0f16.next_down()); /// assert!(clamped < 1.0); /// assert_eq!(clamped.next_up(), 1.0); /// # } /// ``` /// /// This operation corresponds to IEEE-754 `nextDown`. /// /// [`NEG_INFINITY`]: Self::NEG_INFINITY /// [`INFINITY`]: Self::INFINITY /// [`MIN`]: Self::MIN /// [`MAX`]: Self::MAX #[inline] #[doc(alias = "nextDown")] #[unstable(feature = "f16", issue = "116909")] pub const fn next_down(self) -> Self { // Some targets violate Rust's assumption of IEEE semantics, e.g. by flushing // denormals to zero. This is in general unsound and unsupported, but here // we do our best to still produce the correct result on such targets. let bits = self.to_bits(); if self.is_nan() || bits == Self::NEG_INFINITY.to_bits() { return self; } let abs = bits & !Self::SIGN_MASK; let next_bits = if abs == 0 { Self::NEG_TINY_BITS } else if bits == abs { bits - 1 } else { bits + 1 }; Self::from_bits(next_bits) } /// Takes the reciprocal (inverse) of a number, `1/x`. /// /// ``` /// #![feature(f16)] /// # // FIXME(f16_f128): extendhfsf2, truncsfhf2, __gnu_h2f_ieee, __gnu_f2h_ieee missing for many platforms /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { /// /// let x = 2.0_f16; /// let abs_difference = (x.recip() - (1.0 / x)).abs(); /// /// assert!(abs_difference <= f16::EPSILON); /// # } /// ``` #[inline] #[unstable(feature = "f16", issue = "116909")] #[must_use = "this returns the result of the operation, without modifying the original"] pub const fn recip(self) -> Self { 1.0 / self } /// Converts radians to degrees. /// /// ``` /// #![feature(f16)] /// # // FIXME(f16_f128): extendhfsf2, truncsfhf2, __gnu_h2f_ieee, __gnu_f2h_ieee missing for many platforms /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { /// /// let angle = std::f16::consts::PI; /// /// let abs_difference = (angle.to_degrees() - 180.0).abs(); /// assert!(abs_difference <= 0.5); /// # } /// ``` #[inline] #[unstable(feature = "f16", issue = "116909")] #[must_use = "this returns the result of the operation, without modifying the original"] pub const fn to_degrees(self) -> Self { // Use a literal for better precision. const PIS_IN_180: f16 = 57.2957795130823208767981548141051703_f16; self * PIS_IN_180 } /// Converts degrees to radians. /// /// ``` /// #![feature(f16)] /// # // FIXME(f16_f128): extendhfsf2, truncsfhf2, __gnu_h2f_ieee, __gnu_f2h_ieee missing for many platforms /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { /// /// let angle = 180.0f16; /// /// let abs_difference = (angle.to_radians() - std::f16::consts::PI).abs(); /// /// assert!(abs_difference <= 0.01); /// # } /// ``` #[inline] #[unstable(feature = "f16", issue = "116909")] #[must_use = "this returns the result of the operation, without modifying the original"] pub const fn to_radians(self) -> f16 { // Use a literal for better precision. const RADS_PER_DEG: f16 = 0.017453292519943295769236907684886_f16; self * RADS_PER_DEG } /// Returns the maximum of the two numbers, ignoring NaN. /// /// If one of the arguments is NaN, then the other argument is returned. /// This follows the IEEE 754-2008 semantics for maxNum, except for handling of signaling NaNs; /// this function handles all NaNs the same way and avoids maxNum's problems with associativity. /// This also matches the behavior of libm’s fmax. In particular, if the inputs compare equal /// (such as for the case of `+0.0` and `-0.0`), either input may be returned non-deterministically. /// /// ``` /// #![feature(f16)] /// # #[cfg(target_arch = "aarch64")] { // FIXME(f16_F128): rust-lang/rust#123885 /// /// let x = 1.0f16; /// let y = 2.0f16; /// /// assert_eq!(x.max(y), y); /// # } /// ``` #[inline] #[unstable(feature = "f16", issue = "116909")] #[rustc_const_unstable(feature = "f16", issue = "116909")] #[must_use = "this returns the result of the comparison, without modifying either input"] pub const fn max(self, other: f16) -> f16 { intrinsics::maxnumf16(self, other) } /// Returns the minimum of the two numbers, ignoring NaN. /// /// If one of the arguments is NaN, then the other argument is returned. /// This follows the IEEE 754-2008 semantics for minNum, except for handling of signaling NaNs; /// this function handles all NaNs the same way and avoids minNum's problems with associativity. /// This also matches the behavior of libm’s fmin. In particular, if the inputs compare equal /// (such as for the case of `+0.0` and `-0.0`), either input may be returned non-deterministically. /// /// ``` /// #![feature(f16)] /// # #[cfg(target_arch = "aarch64")] { // FIXME(f16_F128): rust-lang/rust#123885 /// /// let x = 1.0f16; /// let y = 2.0f16; /// /// assert_eq!(x.min(y), x); /// # } /// ``` #[inline] #[unstable(feature = "f16", issue = "116909")] #[rustc_const_unstable(feature = "f16", issue = "116909")] #[must_use = "this returns the result of the comparison, without modifying either input"] pub const fn min(self, other: f16) -> f16 { intrinsics::minnumf16(self, other) } /// Returns the maximum of the two numbers, propagating NaN. /// /// This returns NaN when *either* argument is NaN, as opposed to /// [`f16::max`] which only returns NaN when *both* arguments are NaN. /// /// ``` /// #![feature(f16)] /// #![feature(float_minimum_maximum)] /// # #[cfg(target_arch = "aarch64")] { // FIXME(f16_F128): rust-lang/rust#123885 /// /// let x = 1.0f16; /// let y = 2.0f16; /// /// assert_eq!(x.maximum(y), y); /// assert!(x.maximum(f16::NAN).is_nan()); /// # } /// ``` /// /// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the greater /// of the two numbers. For this operation, -0.0 is considered to be less than +0.0. /// Note that this follows the semantics specified in IEEE 754-2019. /// /// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN /// operand is conserved; see the [specification of NaN bit patterns](f32#nan-bit-patterns) for more info. #[inline] #[unstable(feature = "f16", issue = "116909")] // #[unstable(feature = "float_minimum_maximum", issue = "91079")] #[must_use = "this returns the result of the comparison, without modifying either input"] pub const fn maximum(self, other: f16) -> f16 { if self > other { self } else if other > self { other } else if self == other { if self.is_sign_positive() && other.is_sign_negative() { self } else { other } } else { self + other } } /// Returns the minimum of the two numbers, propagating NaN. /// /// This returns NaN when *either* argument is NaN, as opposed to /// [`f16::min`] which only returns NaN when *both* arguments are NaN. /// /// ``` /// #![feature(f16)] /// #![feature(float_minimum_maximum)] /// # #[cfg(target_arch = "aarch64")] { // FIXME(f16_F128): rust-lang/rust#123885 /// /// let x = 1.0f16; /// let y = 2.0f16; /// /// assert_eq!(x.minimum(y), x); /// assert!(x.minimum(f16::NAN).is_nan()); /// # } /// ``` /// /// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the lesser /// of the two numbers. For this operation, -0.0 is considered to be less than +0.0. /// Note that this follows the semantics specified in IEEE 754-2019. /// /// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN /// operand is conserved; see the [specification of NaN bit patterns](f32#nan-bit-patterns) for more info. #[inline] #[unstable(feature = "f16", issue = "116909")] // #[unstable(feature = "float_minimum_maximum", issue = "91079")] #[must_use = "this returns the result of the comparison, without modifying either input"] pub const fn minimum(self, other: f16) -> f16 { if self < other { self } else if other < self { other } else if self == other { if self.is_sign_negative() && other.is_sign_positive() { self } else { other } } else { // At least one input is NaN. Use `+` to perform NaN propagation and quieting. self + other } } /// Calculates the middle point of `self` and `rhs`. /// /// This returns NaN when *either* argument is NaN or if a combination of /// +inf and -inf is provided as arguments. /// /// # Examples /// /// ``` /// #![feature(f16)] /// # #[cfg(target_arch = "aarch64")] { // FIXME(f16_F128): rust-lang/rust#123885 /// /// assert_eq!(1f16.midpoint(4.0), 2.5); /// assert_eq!((-5.5f16).midpoint(8.0), 1.25); /// # } /// ``` #[inline] #[unstable(feature = "f16", issue = "116909")] #[rustc_const_unstable(feature = "f16", issue = "116909")] pub const fn midpoint(self, other: f16) -> f16 { const LO: f16 = f16::MIN_POSITIVE * 2.; const HI: f16 = f16::MAX / 2.; let (a, b) = (self, other); let abs_a = a.abs(); let abs_b = b.abs(); if abs_a <= HI && abs_b <= HI { // Overflow is impossible (a + b) / 2. } else if abs_a < LO { // Not safe to halve `a` (would underflow) a + (b / 2.) } else if abs_b < LO { // Not safe to halve `b` (would underflow) (a / 2.) + b } else { // Safe to halve `a` and `b` (a / 2.) + (b / 2.) } } /// Rounds toward zero and converts to any primitive integer type, /// assuming that the value is finite and fits in that type. /// /// ``` /// #![feature(f16)] /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { /// /// let value = 4.6_f16; /// let rounded = unsafe { value.to_int_unchecked::() }; /// assert_eq!(rounded, 4); /// /// let value = -128.9_f16; /// let rounded = unsafe { value.to_int_unchecked::() }; /// assert_eq!(rounded, i8::MIN); /// # } /// ``` /// /// # Safety /// /// The value must: /// /// * Not be `NaN` /// * Not be infinite /// * Be representable in the return type `Int`, after truncating off its fractional part #[inline] #[unstable(feature = "f16", issue = "116909")] #[must_use = "this returns the result of the operation, without modifying the original"] pub unsafe fn to_int_unchecked(self) -> Int where Self: FloatToInt, { // SAFETY: the caller must uphold the safety contract for // `FloatToInt::to_int_unchecked`. unsafe { FloatToInt::::to_int_unchecked(self) } } /// Raw transmutation to `u16`. /// /// This is currently identical to `transmute::(self)` on all platforms. /// /// See [`from_bits`](#method.from_bits) for some discussion of the /// portability of this operation (there are almost no issues). /// /// Note that this function is distinct from `as` casting, which attempts to /// preserve the *numeric* value, and not the bitwise value. /// /// ``` /// #![feature(f16)] /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { /// /// # // FIXME(f16_f128): enable this once const casting works /// # // assert_ne!((1f16).to_bits(), 1f16 as u128); // to_bits() is not casting! /// assert_eq!((12.5f16).to_bits(), 0x4a40); /// # } /// ``` #[inline] #[unstable(feature = "f16", issue = "116909")] #[must_use = "this returns the result of the operation, without modifying the original"] pub const fn to_bits(self) -> u16 { // SAFETY: `u16` is a plain old datatype so we can always transmute to it. unsafe { mem::transmute(self) } } /// Raw transmutation from `u16`. /// /// This is currently identical to `transmute::(v)` on all platforms. /// It turns out this is incredibly portable, for two reasons: /// /// * Floats and Ints have the same endianness on all supported platforms. /// * IEEE 754 very precisely specifies the bit layout of floats. /// /// However there is one caveat: prior to the 2008 version of IEEE 754, how /// to interpret the NaN signaling bit wasn't actually specified. Most platforms /// (notably x86 and ARM) picked the interpretation that was ultimately /// standardized in 2008, but some didn't (notably MIPS). As a result, all /// signaling NaNs on MIPS are quiet NaNs on x86, and vice-versa. /// /// Rather than trying to preserve signaling-ness cross-platform, this /// implementation favors preserving the exact bits. This means that /// any payloads encoded in NaNs will be preserved even if the result of /// this method is sent over the network from an x86 machine to a MIPS one. /// /// If the results of this method are only manipulated by the same /// architecture that produced them, then there is no portability concern. /// /// If the input isn't NaN, then there is no portability concern. /// /// If you don't care about signalingness (very likely), then there is no /// portability concern. /// /// Note that this function is distinct from `as` casting, which attempts to /// preserve the *numeric* value, and not the bitwise value. /// /// ``` /// #![feature(f16)] /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { /// /// let v = f16::from_bits(0x4a40); /// assert_eq!(v, 12.5); /// # } /// ``` #[inline] #[must_use] #[unstable(feature = "f16", issue = "116909")] pub const fn from_bits(v: u16) -> Self { // It turns out the safety issues with sNaN were overblown! Hooray! // SAFETY: `u16` is a plain old datatype so we can always transmute from it. unsafe { mem::transmute(v) } } /// Returns the memory representation of this floating point number as a byte array in /// big-endian (network) byte order. /// /// See [`from_bits`](Self::from_bits) for some discussion of the /// portability of this operation (there are almost no issues). /// /// # Examples /// /// ``` /// #![feature(f16)] /// # // FIXME(f16_f128): LLVM crashes on s390x, llvm/llvm-project#50374 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { /// /// let bytes = 12.5f16.to_be_bytes(); /// assert_eq!(bytes, [0x4a, 0x40]); /// # } /// ``` #[inline] #[unstable(feature = "f16", issue = "116909")] #[must_use = "this returns the result of the operation, without modifying the original"] pub const fn to_be_bytes(self) -> [u8; 2] { self.to_bits().to_be_bytes() } /// Returns the memory representation of this floating point number as a byte array in /// little-endian byte order. /// /// See [`from_bits`](Self::from_bits) for some discussion of the /// portability of this operation (there are almost no issues). /// /// # Examples /// /// ``` /// #![feature(f16)] /// # // FIXME(f16_f128): LLVM crashes on s390x, llvm/llvm-project#50374 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { /// /// let bytes = 12.5f16.to_le_bytes(); /// assert_eq!(bytes, [0x40, 0x4a]); /// # } /// ``` #[inline] #[unstable(feature = "f16", issue = "116909")] #[must_use = "this returns the result of the operation, without modifying the original"] pub const fn to_le_bytes(self) -> [u8; 2] { self.to_bits().to_le_bytes() } /// Returns the memory representation of this floating point number 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. /// /// [`to_be_bytes`]: f16::to_be_bytes /// [`to_le_bytes`]: f16::to_le_bytes /// /// See [`from_bits`](Self::from_bits) for some discussion of the /// portability of this operation (there are almost no issues). /// /// # Examples /// /// ``` /// #![feature(f16)] /// # // FIXME(f16_f128): LLVM crashes on s390x, llvm/llvm-project#50374 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { /// /// let bytes = 12.5f16.to_ne_bytes(); /// assert_eq!( /// bytes, /// if cfg!(target_endian = "big") { /// [0x4a, 0x40] /// } else { /// [0x40, 0x4a] /// } /// ); /// # } /// ``` #[inline] #[unstable(feature = "f16", issue = "116909")] #[must_use = "this returns the result of the operation, without modifying the original"] pub const fn to_ne_bytes(self) -> [u8; 2] { self.to_bits().to_ne_bytes() } /// Creates a floating point value from its representation as a byte array in big endian. /// /// See [`from_bits`](Self::from_bits) for some discussion of the /// portability of this operation (there are almost no issues). /// /// # Examples /// /// ``` /// #![feature(f16)] /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { /// /// let value = f16::from_be_bytes([0x4a, 0x40]); /// assert_eq!(value, 12.5); /// # } /// ``` #[inline] #[must_use] #[unstable(feature = "f16", issue = "116909")] pub const fn from_be_bytes(bytes: [u8; 2]) -> Self { Self::from_bits(u16::from_be_bytes(bytes)) } /// Creates a floating point value from its representation as a byte array in little endian. /// /// See [`from_bits`](Self::from_bits) for some discussion of the /// portability of this operation (there are almost no issues). /// /// # Examples /// /// ``` /// #![feature(f16)] /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { /// /// let value = f16::from_le_bytes([0x40, 0x4a]); /// assert_eq!(value, 12.5); /// # } /// ``` #[inline] #[must_use] #[unstable(feature = "f16", issue = "116909")] pub const fn from_le_bytes(bytes: [u8; 2]) -> Self { Self::from_bits(u16::from_le_bytes(bytes)) } /// Creates a floating point value from its representation as a byte array in native endian. /// /// As the target platform's native endianness is used, portable code /// likely wants to use [`from_be_bytes`] or [`from_le_bytes`], as /// appropriate instead. /// /// [`from_be_bytes`]: f16::from_be_bytes /// [`from_le_bytes`]: f16::from_le_bytes /// /// See [`from_bits`](Self::from_bits) for some discussion of the /// portability of this operation (there are almost no issues). /// /// # Examples /// /// ``` /// #![feature(f16)] /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { /// /// let value = f16::from_ne_bytes(if cfg!(target_endian = "big") { /// [0x4a, 0x40] /// } else { /// [0x40, 0x4a] /// }); /// assert_eq!(value, 12.5); /// # } /// ``` #[inline] #[must_use] #[unstable(feature = "f16", issue = "116909")] pub const fn from_ne_bytes(bytes: [u8; 2]) -> Self { Self::from_bits(u16::from_ne_bytes(bytes)) } /// 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. /// /// # Example /// /// ``` /// #![feature(f16)] /// # // FIXME(f16_f128): extendhfsf2, truncsfhf2, __gnu_h2f_ieee, __gnu_f2h_ieee missing for many platforms /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { /// /// struct GoodBoy { /// name: &'static str, /// weight: f16, /// } /// /// let mut bois = vec![ /// GoodBoy { name: "Pucci", weight: 0.1 }, /// GoodBoy { name: "Woofer", weight: 99.0 }, /// GoodBoy { name: "Yapper", weight: 10.0 }, /// GoodBoy { name: "Chonk", weight: f16::INFINITY }, /// GoodBoy { name: "Abs. Unit", weight: f16::NAN }, /// GoodBoy { name: "Floaty", weight: -5.0 }, /// ]; /// /// bois.sort_by(|a, b| a.weight.total_cmp(&b.weight)); /// /// // `f16::NAN` could be positive or negative, which will affect the sort order. /// if f16::NAN.is_sign_negative() { /// bois.into_iter().map(|b| b.weight) /// .zip([f16::NAN, -5.0, 0.1, 10.0, 99.0, f16::INFINITY].iter()) /// .for_each(|(a, b)| assert_eq!(a.to_bits(), b.to_bits())) /// } else { /// bois.into_iter().map(|b| b.weight) /// .zip([-5.0, 0.1, 10.0, 99.0, f16::INFINITY, f16::NAN].iter()) /// .for_each(|(a, b)| assert_eq!(a.to_bits(), b.to_bits())) /// } /// # } /// ``` #[inline] #[must_use] #[unstable(feature = "f16", issue = "116909")] pub fn total_cmp(&self, other: &Self) -> crate::cmp::Ordering { let mut left = self.to_bits() as i16; let mut right = other.to_bits() as i16; // In case of negatives, flip all the bits except the sign // to achieve a similar layout as two's complement integers // // Why does this work? IEEE 754 floats consist of three fields: // Sign bit, exponent and mantissa. The set of exponent and mantissa // fields as a whole have the property that their bitwise order is // equal to the numeric magnitude where the magnitude is defined. // The magnitude is not normally defined on NaN values, but // IEEE 754 totalOrder defines the NaN values also to follow the // bitwise order. This leads to order explained in the doc comment. // However, the representation of magnitude is the same for negative // and positive numbers – only the sign bit is different. // To easily compare the floats as signed integers, we need to // flip the exponent and mantissa bits in case of negative numbers. // We effectively convert the numbers to "two's complement" form. // // To do the flipping, we construct a mask and XOR against it. // We branchlessly calculate an "all-ones except for the sign bit" // mask from negative-signed values: right shifting sign-extends // the integer, so we "fill" the mask with sign bits, and then // convert to unsigned to push one more zero bit. // On positive values, the mask is all zeros, so it's a no-op. left ^= (((left >> 15) as u16) >> 1) as i16; right ^= (((right >> 15) as u16) >> 1) as i16; left.cmp(&right) } /// 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 /// /// ``` /// #![feature(f16)] /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { /// /// assert!((-3.0f16).clamp(-2.0, 1.0) == -2.0); /// assert!((0.0f16).clamp(-2.0, 1.0) == 0.0); /// assert!((2.0f16).clamp(-2.0, 1.0) == 1.0); /// assert!((f16::NAN).clamp(-2.0, 1.0).is_nan()); /// # } /// ``` #[inline] #[unstable(feature = "f16", issue = "116909")] #[must_use = "method returns a new number and does not mutate the original value"] pub const fn clamp(mut self, min: f16, max: f16) -> f16 { const_assert!( min <= max, "min > max, or either was NaN", "min > max, or either was NaN. min = {min:?}, max = {max:?}", min: f16, max: f16, ); if self < min { self = min; } if self > max { self = max; } self } /// Computes the absolute value of `self`. /// /// This function always returns the precise result. /// /// # Examples /// /// ``` /// #![feature(f16)] /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { /// /// let x = 3.5_f16; /// let y = -3.5_f16; /// /// assert_eq!(x.abs(), x); /// assert_eq!(y.abs(), -y); /// /// assert!(f16::NAN.abs().is_nan()); /// # } /// ``` #[inline] #[unstable(feature = "f16", issue = "116909")] #[rustc_const_unstable(feature = "f16", issue = "116909")] #[must_use = "method returns a new number and does not mutate the original value"] pub const fn abs(self) -> Self { // FIXME(f16_f128): replace with `intrinsics::fabsf16` when available Self::from_bits(self.to_bits() & !(1 << 15)) } /// 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 /// /// ``` /// #![feature(f16)] /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { /// /// let f = 3.5_f16; /// /// assert_eq!(f.signum(), 1.0); /// assert_eq!(f16::NEG_INFINITY.signum(), -1.0); /// /// assert!(f16::NAN.signum().is_nan()); /// # } /// ``` #[inline] #[unstable(feature = "f16", issue = "116909")] #[rustc_const_unstable(feature = "f16", issue = "116909")] #[must_use = "method returns a new number and does not mutate the original value"] pub const fn signum(self) -> f16 { if self.is_nan() { Self::NAN } else { 1.0_f16.copysign(self) } } /// 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 a NaN, then a NaN with the same payload as `self` and the sign bit of `sign` is /// returned. /// /// If `sign` is a NaN, then this operation will still carry over its sign into the result. Note /// that IEEE 754 doesn't assign any meaning to the sign bit in case of a NaN, and as Rust /// doesn't guarantee that the bit pattern of NaNs are conserved over arithmetic operations, the /// result of `copysign` with `sign` being a NaN might produce an unexpected or non-portable /// result. See the [specification of NaN bit patterns](primitive@f32#nan-bit-patterns) for more /// info. /// /// # Examples /// /// ``` /// #![feature(f16)] /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { /// /// let f = 3.5_f16; /// /// assert_eq!(f.copysign(0.42), 3.5_f16); /// assert_eq!(f.copysign(-0.42), -3.5_f16); /// assert_eq!((-f).copysign(0.42), 3.5_f16); /// assert_eq!((-f).copysign(-0.42), -3.5_f16); /// /// assert!(f16::NAN.copysign(1.0).is_nan()); /// # } /// ``` #[inline] #[unstable(feature = "f16", issue = "116909")] #[rustc_const_unstable(feature = "f16", issue = "116909")] #[must_use = "method returns a new number and does not mutate the original value"] pub const fn copysign(self, sign: f16) -> f16 { // SAFETY: this is actually a safe intrinsic unsafe { intrinsics::copysignf16(self, sign) } } /// Float addition that allows optimizations based on algebraic rules. /// /// See [algebraic operators](primitive@f32#algebraic-operators) for more info. #[must_use = "method returns a new number and does not mutate the original value"] #[unstable(feature = "float_algebraic", issue = "136469")] #[inline] pub fn algebraic_add(self, rhs: f16) -> f16 { intrinsics::fadd_algebraic(self, rhs) } /// Float subtraction that allows optimizations based on algebraic rules. /// /// See [algebraic operators](primitive@f32#algebraic-operators) for more info. #[must_use = "method returns a new number and does not mutate the original value"] #[unstable(feature = "float_algebraic", issue = "136469")] #[inline] pub fn algebraic_sub(self, rhs: f16) -> f16 { intrinsics::fsub_algebraic(self, rhs) } /// Float multiplication that allows optimizations based on algebraic rules. /// /// See [algebraic operators](primitive@f32#algebraic-operators) for more info. #[must_use = "method returns a new number and does not mutate the original value"] #[unstable(feature = "float_algebraic", issue = "136469")] #[inline] pub fn algebraic_mul(self, rhs: f16) -> f16 { intrinsics::fmul_algebraic(self, rhs) } /// Float division that allows optimizations based on algebraic rules. /// /// See [algebraic operators](primitive@f32#algebraic-operators) for more info. #[must_use = "method returns a new number and does not mutate the original value"] #[unstable(feature = "float_algebraic", issue = "136469")] #[inline] pub fn algebraic_div(self, rhs: f16) -> f16 { intrinsics::fdiv_algebraic(self, rhs) } /// Float remainder that allows optimizations based on algebraic rules. /// /// See [algebraic operators](primitive@f32#algebraic-operators) for more info. #[must_use = "method returns a new number and does not mutate the original value"] #[unstable(feature = "float_algebraic", issue = "136469")] #[inline] pub fn algebraic_rem(self, rhs: f16) -> f16 { intrinsics::frem_algebraic(self, rhs) } }