From f33f672956ef0084da7b6f8e6a9c260e460d4b60 Mon Sep 17 00:00:00 2001 From: Trevor Gross Date: Mon, 7 Aug 2023 23:34:06 -0400 Subject: [PATCH] Compiler checks correctly --- .../rustc_codegen_ssa/src/traits/type_.rs | 2 + compiler/rustc_lint/src/types.rs | 4 + compiler/rustc_mir_build/src/build/mod.rs | 72 +- library/core/src/num/f128.rs | 1198 +++++++++++++++++ library/core/src/num/f16.rs | 1198 +++++++++++++++++ 5 files changed, 2473 insertions(+), 1 deletion(-) create mode 100644 library/core/src/num/f128.rs create mode 100644 library/core/src/num/f16.rs diff --git a/compiler/rustc_codegen_ssa/src/traits/type_.rs b/compiler/rustc_codegen_ssa/src/traits/type_.rs index dc3dbd9d81949..a84c801ef20ef 100644 --- a/compiler/rustc_codegen_ssa/src/traits/type_.rs +++ b/compiler/rustc_codegen_ssa/src/traits/type_.rs @@ -19,8 +19,10 @@ pub trait BaseTypeMethods<'tcx>: Backend<'tcx> { fn type_i128(&self) -> Self::Type; fn type_isize(&self) -> Self::Type; + fn type_f16(&self) -> Self::Type; fn type_f32(&self) -> Self::Type; fn type_f64(&self) -> Self::Type; + fn type_f128(&self) -> Self::Type; fn type_array(&self, ty: Self::Type, len: u64) -> Self::Type; fn type_func(&self, args: &[Self::Type], ret: Self::Type) -> Self::Type; diff --git a/compiler/rustc_lint/src/types.rs b/compiler/rustc_lint/src/types.rs index 226d01b79a89a..950ed3f177d70 100644 --- a/compiler/rustc_lint/src/types.rs +++ b/compiler/rustc_lint/src/types.rs @@ -525,8 +525,12 @@ fn lint_literal<'tcx>( ty::Float(t) => { let is_infinite = match lit.node { ast::LitKind::Float(v, _) => match t { + // v.as_str().parse().map(f16::is_infinite) + ty::FloatTy::F16 => todo!("f16::is_infinite"), ty::FloatTy::F32 => v.as_str().parse().map(f32::is_infinite), ty::FloatTy::F64 => v.as_str().parse().map(f64::is_infinite), + // v.as_str().parse().map(f128::is_infinite), + ty::FloatTy::F128 => todo!("f128::is_infinite"), }, _ => bug!(), }; diff --git a/compiler/rustc_mir_build/src/build/mod.rs b/compiler/rustc_mir_build/src/build/mod.rs index c66eba5520e1c..db77ec675ca3a 100644 --- a/compiler/rustc_mir_build/src/build/mod.rs +++ b/compiler/rustc_mir_build/src/build/mod.rs @@ -1,6 +1,6 @@ use crate::build::expr::as_place::PlaceBuilder; use crate::build::scope::DropKind; -use rustc_apfloat::ieee::{Double, Single}; +use rustc_apfloat::ieee::{Double, Half, Quad, Single}; use rustc_apfloat::Float; use rustc_ast::attr; use rustc_data_structures::fx::FxHashMap; @@ -967,13 +967,60 @@ fn parse_float_into_constval<'tcx>( parse_float_into_scalar(num, float_ty, neg).map(ConstValue::Scalar) } +// #[cfg(not(bootstrap))] +// fn parse_f16(num: &str) -> Option { +// num.parse().ok() +// } + +// FIXME: bootstrap `f16` parsing via `f32` +// #[cfg(bootstrap)] +fn parse_f16(num: &str) -> Option { + num.parse().ok() +} + +// #[cfg(not(bootstrap))] +// fn parse_f128(num: &str) -> Option { +// num.parse().ok() +// } + +// FIXME: bootstrap `f16` parsing via `f32` +// #[cfg(bootstrap)] +fn parse_f128(num: &str) -> Option { + num.parse().ok() +} + pub(crate) fn parse_float_into_scalar( num: Symbol, float_ty: ty::FloatTy, neg: bool, ) -> Option { let num = num.as_str(); + match float_ty { + ty::FloatTy::F16 => { + let rust_f = parse_f16(num)?; + + let mut f = num + .parse::() + .unwrap_or_else(|e| panic!("apfloat::ieee::Half failed to parse `{num}`: {e:?}")); + + assert!( + u128::from(rust_f.to_bits()) == f.to_bits(), + "apfloat::ieee::Half gave different result for `{}`: \ + {}({:#x}) vs Rust's {}({:#x})", + rust_f, + f, + f.to_bits(), + Half::from_bits(rust_f.to_bits().into()), + rust_f.to_bits() + ); + + if neg { + f = -f; + } + + Some(Scalar::from_f16(f)) + } ty::FloatTy::F32 => { let Ok(rust_f) = num.parse::() else { return None }; let mut f = num @@ -1020,6 +1067,29 @@ pub(crate) fn parse_float_into_scalar( Some(Scalar::from_f64(f)) } + ty::FloatTy::F128 => { + let rust_f = parse_f128(num)?; + let mut f = num + .parse::() + .unwrap_or_else(|e| panic!("apfloat::ieee::Quad failed to parse `{num}`: {e:?}")); + + assert!( + u128::from(rust_f.to_bits()) == f.to_bits(), + "apfloat::ieee::Quad gave different result for `{}`: \ + {}({:#x}) vs Rust's {}({:#x})", + rust_f, + f, + f.to_bits(), + Quad::from_bits(rust_f.to_bits().into()), + rust_f.to_bits() + ); + + if neg { + f = -f; + } + + Some(Scalar::from_f128(f)) + } } } diff --git a/library/core/src/num/f128.rs b/library/core/src/num/f128.rs new file mode 100644 index 0000000000000..0a80b8ba5d156 --- /dev/null +++ b/library/core/src/num/f128.rs @@ -0,0 +1,1198 @@ +//! Constants for the `f128` double-precision floating point type. +//! +//! *[See also the `f128` primitive type][f128].* +//! +//! 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 `f128` type. + +#![unstable(feature = "f128", issue = "00000")] + +use crate::convert::FloatToInt; +#[cfg(not(test))] +use crate::intrinsics; +use crate::mem; +use crate::num::FpCategory; + +/// Basic mathematical constants. +#[unstable(feature = "f128", issue = "00000")] +pub mod consts { + // FIXME: replace with mathematical constants from cmath. + + /// Archimedes' constant (π) + #[unstable(feature = "f128", issue = "00000")] + pub const PI: f128 = 3.14159265358979323846264338327950288_f128; + + /// The full circle constant (τ) + /// + /// Equal to 2π. + #[unstable(feature = "f128", issue = "00000")] + pub const TAU: f128 = 6.28318530717958647692528676655900577_f128; + + /// π/2 + #[unstable(feature = "f128", issue = "00000")] + pub const FRAC_PI_2: f128 = 1.57079632679489661923132169163975144_f128; + + /// π/3 + #[unstable(feature = "f128", issue = "00000")] + pub const FRAC_PI_3: f128 = 1.04719755119659774615421446109316763_f128; + + /// π/4 + #[unstable(feature = "f128", issue = "00000")] + pub const FRAC_PI_4: f128 = 0.785398163397448309615660845819875721_f128; + + /// π/6 + #[unstable(feature = "f128", issue = "00000")] + pub const FRAC_PI_6: f128 = 0.52359877559829887307710723054658381_f128; + + /// π/8 + #[unstable(feature = "f128", issue = "00000")] + pub const FRAC_PI_8: f128 = 0.39269908169872415480783042290993786_f128; + + /// 1/π + #[unstable(feature = "f128", issue = "00000")] + pub const FRAC_1_PI: f128 = 0.318309886183790671537767526745028724_f128; + + /// 2/π + #[unstable(feature = "f128", issue = "00000")] + pub const FRAC_2_PI: f128 = 0.636619772367581343075535053490057448_f128; + + /// 2/sqrt(π) + #[unstable(feature = "f128", issue = "00000")] + pub const FRAC_2_SQRT_PI: f128 = 1.12837916709551257389615890312154517_f128; + + /// sqrt(2) + #[unstable(feature = "f128", issue = "00000")] + pub const SQRT_2: f128 = 1.41421356237309504880168872420969808_f128; + + /// 1/sqrt(2) + #[unstable(feature = "f128", issue = "00000")] + pub const FRAC_1_SQRT_2: f128 = 0.707106781186547524400844362104849039_f128; + + /// Euler's number (e) + #[unstable(feature = "f128", issue = "00000")] + pub const E: f128 = 2.71828182845904523536028747135266250_f128; + + /// log2(10) + #[unstable(feature = "f128", issue = "00000")] + pub const LOG2_10: f128 = 3.32192809488736234787031942948939018_f128; + + /// log2(e) + #[unstable(feature = "f128", issue = "00000")] + pub const LOG2_E: f128 = 1.44269504088896340735992468100189214_f128; + + /// log10(2) + #[unstable(feature = "f128", issue = "00000")] + pub const LOG10_2: f128 = 0.301029995663981195213738894724493027_f128; + + /// log10(e) + #[unstable(feature = "f128", issue = "00000")] + pub const LOG10_E: f128 = 0.434294481903251827651128918916605082_f128; + + /// ln(2) + #[unstable(feature = "f128", issue = "00000")] + pub const LN_2: f128 = 0.693147180559945309417232121458176568_f128; + + /// ln(10) + #[unstable(feature = "f128", issue = "00000")] + pub const LN_10: f128 = 2.30258509299404568401799145468436421_f128; +} + +// TODO: this is probably all wrong +#[cfg(not(test))] +impl f128 { + /// The radix or base of the internal representation of `f128`. + #[unstable(feature = "f128", issue = "00000")] + pub const RADIX: u32 = 2; + + /// Number of significant digits in base 2. + #[unstable(feature = "f128", issue = "00000")] + pub const MANTISSA_DIGITS: u32 = 53; + + /// Approximate number of significant digits in base 10. + #[unstable(feature = "f128", issue = "00000")] + pub const DIGITS: u32 = 15; + + /// [Machine epsilon] value for `f128`. + /// + /// This is the difference between `1.0` and the next larger representable number. + /// + /// [Machine epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon + #[unstable(feature = "f128", issue = "00000")] + pub const EPSILON: f128 = 0.00097656_f128; + + /// Smallest finite `f128` value. + #[unstable(feature = "f128", issue = "00000")] + pub const MIN: f128 = -1.7976931348623157e+308_f128; + + /// Smallest positive normal `f128` value. + #[unstable(feature = "f128", issue = "00000")] + pub const MIN_POSITIVE: f128 = 0.000000059604645_f128; + + /// Largest finite `f128` value. + #[unstable(feature = "f128", issue = "00000")] + pub const MAX: f128 = 65504_f128; + + /// One greater than the minimum possible normal power of 2 exponent. + #[unstable(feature = "f128", issue = "00000")] + pub const MIN_EXP: i32 = -1021; + + /// Maximum possible power of 2 exponent. + #[unstable(feature = "f128", issue = "00000")] + pub const MAX_EXP: i32 = 1024; + + /// Minimum possible normal power of 10 exponent. + #[unstable(feature = "f128", issue = "00000")] + pub const MIN_10_EXP: i32 = -307; + /// Maximum possible power of 10 exponent. + #[unstable(feature = "f128", issue = "00000")] + pub const MAX_10_EXP: i32 = 308; + + /// 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. + #[rustc_diagnostic_item = "f128_nan"] + #[unstable(feature = "f128", issue = "00000")] + pub const NAN: f128 = 0.0_f128 / 0.0_f128; + /// Infinity (∞). + #[unstable(feature = "f128", issue = "00000")] + pub const INFINITY: f128 = 1.0_f128 / 0.0_f128; + /// Negative infinity (−∞). + #[unstable(feature = "f128", issue = "00000")] + pub const NEG_INFINITY: f128 = -1.0_f128 / 0.0_f128; + + /// Returns `true` if this value is NaN. + /// + /// ``` + /// let nan = f128::NAN; + /// let f = 7.0_f128; + /// + /// assert!(nan.is_nan()); + /// assert!(!f.is_nan()); + /// ``` + #[must_use] + #[unstable(feature = "f128", issue = "00000")] + #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")] + #[inline] + pub const fn is_nan(self) -> bool { + self != self + } + + // FIXME(#50145): `abs` is publicly unavailable in core due to + // concerns about portability, so this implementation is for + // private use internally. + #[inline] + #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")] + pub(crate) const fn abs_private(self) -> f128 { + // SAFETY: This transmutation is fine. Probably. For the reasons std is using it. + unsafe { + mem::transmute::(mem::transmute::(self) & 0x7fff_ffff_ffff_ffff) + } + } + + /// Returns `true` if this value is positive infinity or negative infinity, and + /// `false` otherwise. + /// + /// ``` + /// let f = 7.0f128; + /// let inf = f128::INFINITY; + /// let neg_inf = f128::NEG_INFINITY; + /// let nan = f128::NAN; + /// + /// assert!(!f.is_infinite()); + /// assert!(!nan.is_infinite()); + /// + /// assert!(inf.is_infinite()); + /// assert!(neg_inf.is_infinite()); + /// ``` + #[must_use] + #[unstable(feature = "f128", issue = "00000")] + #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")] + #[inline] + pub const fn is_infinite(self) -> bool { + // Getting clever with transmutation can result in incorrect answers on some FPUs + // FIXME: alter the Rust <-> Rust calling convention to prevent this problem. + // See https://github.com/rust-lang/rust/issues/72327 + (self == f128::INFINITY) | (self == f128::NEG_INFINITY) + } + + /// Returns `true` if this number is neither infinite nor NaN. + /// + /// ``` + /// let f = 7.0f128; + /// let inf: f128 = f128::INFINITY; + /// let neg_inf: f128 = f128::NEG_INFINITY; + /// let nan: f128 = f128::NAN; + /// + /// assert!(f.is_finite()); + /// + /// assert!(!nan.is_finite()); + /// assert!(!inf.is_finite()); + /// assert!(!neg_inf.is_finite()); + /// ``` + #[must_use] + #[unstable(feature = "f128", issue = "00000")] + #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")] + #[inline] + 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_private() < Self::INFINITY + } + + /// Returns `true` if the number is [subnormal]. + /// + /// ``` + /// let min = f128::MIN_POSITIVE; // 2.2250738585072014e-308_f128 + /// let max = f128::MAX; + /// let lower_than_min = 1.0e-308_f128; + /// let zero = 0.0_f128; + /// + /// assert!(!min.is_subnormal()); + /// assert!(!max.is_subnormal()); + /// + /// assert!(!zero.is_subnormal()); + /// assert!(!f128::NAN.is_subnormal()); + /// assert!(!f128::INFINITY.is_subnormal()); + /// // Values between `0` and `min` are Subnormal. + /// assert!(lower_than_min.is_subnormal()); + /// ``` + /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number + #[must_use] + #[unstable(feature = "f128", issue = "00000")] + #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")] + #[inline] + pub const fn is_subnormal(self) -> bool { + matches!(self.classify(), FpCategory::Subnormal) + } + + /// Returns `true` if the number is neither zero, infinite, + /// [subnormal], or NaN. + /// + /// ``` + /// let min = f128::MIN_POSITIVE; // 2.2250738585072014e-308f128 + /// let max = f128::MAX; + /// let lower_than_min = 1.0e-308_f128; + /// let zero = 0.0f128; + /// + /// assert!(min.is_normal()); + /// assert!(max.is_normal()); + /// + /// assert!(!zero.is_normal()); + /// assert!(!f128::NAN.is_normal()); + /// assert!(!f128::INFINITY.is_normal()); + /// // Values between `0` and `min` are Subnormal. + /// assert!(!lower_than_min.is_normal()); + /// ``` + /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number + #[must_use] + #[unstable(feature = "f128", issue = "00000")] + #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")] + #[inline] + 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. + /// + /// ``` + /// use std::num::FpCategory; + /// + /// let num = 12.4_f128; + /// let inf = f128::INFINITY; + /// + /// assert_eq!(num.classify(), FpCategory::Normal); + /// assert_eq!(inf.classify(), FpCategory::Infinite); + /// ``` + #[unstable(feature = "f128", issue = "00000")] + #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")] + pub const fn classify(self) -> FpCategory { + // A previous implementation tried to only use bitmask-based checks, + // using f128::to_bits to transmute the float to its bit repr and match on that. + // Unfortunately, floating point numbers can be much worse than that. + // This also needs to not result in recursive evaluations of f128::to_bits. + // + // On some processors, in some cases, LLVM will "helpfully" lower floating point ops, + // in spite of a request for them using f32 and f128, to things like x87 operations. + // These have an f128's mantissa, but can have a larger than normal exponent. + // FIXME(jubilee): Using x87 operations is never necessary in order to function + // on x86 processors for Rust-to-Rust calls, so this issue should not happen. + // Code generation should be adjusted to use non-C calling conventions, avoiding this. + // + // Thus, a value may compare unequal to infinity, despite having a "full" exponent mask. + // And it may not be NaN, as it can simply be an "overextended" finite value. + if self.is_nan() { + FpCategory::Nan + } else { + // However, std can't simply compare to zero to check for zero, either, + // as correctness requires avoiding equality tests that may be Subnormal == -0.0 + // because it may be wrong under "denormals are zero" and "flush to zero" modes. + // Most of std's targets don't use those, but they are used for thumbv7neon. + // So, this does use bitpattern matching for the rest. + + // SAFETY: f128 to u64 is fine. Usually. + // If control flow has gotten this far, the value is definitely in one of the categories + // that f128::partial_classify can correctly analyze. + unsafe { f128::partial_classify(self) } + } + } + + // This doesn't actually return a right answer for NaN on purpose, + // seeing as how it cannot correctly discern between a floating point NaN, + // and some normal floating point numbers truncated from an x87 FPU. + #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")] + const unsafe fn partial_classify(self) -> FpCategory { + const EXP_MASK: u64 = 0x7ff0000000000000; + const MAN_MASK: u64 = 0x000fffffffffffff; + + // SAFETY: The caller is not asking questions for which this will tell lies. + let b = unsafe { mem::transmute::(self) }; + match (b & MAN_MASK, b & EXP_MASK) { + (0, EXP_MASK) => FpCategory::Infinite, + (0, 0) => FpCategory::Zero, + (_, 0) => FpCategory::Subnormal, + _ => FpCategory::Normal, + } + } + + // This operates on bits, and only bits, so it can ignore concerns about weird FPUs. + // FIXME(jubilee): In a just world, this would be the entire impl for classify, + // plus a transmute. We do not live in a just world, but we can make it more so. + #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")] + const fn classify_bits(b: u64) -> FpCategory { + const EXP_MASK: u64 = 0x7ff0000000000000; + const MAN_MASK: u64 = 0x000fffffffffffff; + + match (b & MAN_MASK, b & EXP_MASK) { + (0, EXP_MASK) => FpCategory::Infinite, + (_, 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 result in some cases. + /// See [explanation of NaN as a special value](f32) for more info. + /// + /// ``` + /// let f = 7.0_f128; + /// let g = -7.0_f128; + /// + /// assert!(f.is_sign_positive()); + /// assert!(!g.is_sign_positive()); + /// ``` + #[must_use] + #[unstable(feature = "f128", issue = "00000")] + #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")] + #[inline] + pub const fn is_sign_positive(self) -> bool { + !self.is_sign_negative() + } + + #[must_use] + #[unstable(feature = "f128", issue = "00000")] + #[deprecated(since = "1.0.0", note = "renamed to is_sign_positive")] + #[inline] + #[doc(hidden)] + pub fn is_positive(self) -> bool { + self.is_sign_positive() + } + + /// 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 result in some cases. + /// See [explanation of NaN as a special value](f32) for more info. + /// + /// ``` + /// let f = 7.0_f128; + /// let g = -7.0_f128; + /// + /// assert!(!f.is_sign_negative()); + /// assert!(g.is_sign_negative()); + /// ``` + #[must_use] + #[unstable(feature = "f128", issue = "00000")] + #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")] + #[inline] + 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. + unsafe { mem::transmute::(self) & 0x8000_0000_0000_0000 != 0 } + } + + #[must_use] + #[unstable(feature = "f128", issue = "00000")] + #[deprecated(since = "1.0.0", note = "renamed to is_sign_negative")] + #[inline] + #[doc(hidden)] + pub fn is_negative(self) -> bool { + self.is_sign_negative() + } + + /// Returns the least number greater than `self`. + /// + /// Let `TINY` be the smallest representable positive `f128`. 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(float_next_up_down)] + /// // f128::EPSILON is the difference between 1.0 and the next number up. + /// assert_eq!(1.0f128.next_up(), 1.0 + f128::EPSILON); + /// // But not for most numbers. + /// assert!(0.1f128.next_up() < 0.1 + f128::EPSILON); + /// assert_eq!(9007199254740992f128.next_up(), 9007199254740994.0); + /// ``` + /// + /// [`NEG_INFINITY`]: Self::NEG_INFINITY + /// [`INFINITY`]: Self::INFINITY + /// [`MIN`]: Self::MIN + /// [`MAX`]: Self::MAX + #[unstable(feature = "float_next_up_down", issue = "91399")] + #[rustc_const_unstable(feature = "float_next_up_down", issue = "91399")] + pub const fn next_up(self) -> Self { + // We must use strictly integer arithmetic to prevent denormals from + // flushing to zero after an arithmetic operation on some platforms. + const TINY_BITS: u64 = 0x1; // Smallest positive f128. + const CLEAR_SIGN_MASK: u64 = 0x7fff_ffff_ffff_ffff; + + let bits = self.to_bits(); + if self.is_nan() || bits == Self::INFINITY.to_bits() { + return self; + } + + let abs = bits & CLEAR_SIGN_MASK; + let next_bits = if abs == 0 { + 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 `f128`. 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(float_next_up_down)] + /// let x = 1.0f128; + /// // Clamp value into range [0, 1). + /// let clamped = x.clamp(0.0, 1.0f128.next_down()); + /// assert!(clamped < 1.0); + /// assert_eq!(clamped.next_up(), 1.0); + /// ``` + /// + /// [`NEG_INFINITY`]: Self::NEG_INFINITY + /// [`INFINITY`]: Self::INFINITY + /// [`MIN`]: Self::MIN + /// [`MAX`]: Self::MAX + #[unstable(feature = "float_next_up_down", issue = "91399")] + #[rustc_const_unstable(feature = "float_next_up_down", issue = "91399")] + pub const fn next_down(self) -> Self { + // We must use strictly integer arithmetic to prevent denormals from + // flushing to zero after an arithmetic operation on some platforms. + const NEG_TINY_BITS: u64 = 0x8000_0000_0000_0001; // Smallest (in magnitude) negative f128. + const CLEAR_SIGN_MASK: u64 = 0x7fff_ffff_ffff_ffff; + + let bits = self.to_bits(); + if self.is_nan() || bits == Self::NEG_INFINITY.to_bits() { + return self; + } + + let abs = bits & CLEAR_SIGN_MASK; + let next_bits = if abs == 0 { + 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`. + /// + /// ``` + /// let x = 2.0_f128; + /// let abs_difference = (x.recip() - (1.0 / x)).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` + #[must_use = "this returns the result of the operation, without modifying the original"] + #[unstable(feature = "f128", issue = "00000")] + #[inline] + pub fn recip(self) -> f128 { + 1.0 / self + } + + /// Converts radians to degrees. + /// + /// ``` + /// let angle = std::f128::consts::PI; + /// + /// let abs_difference = (angle.to_degrees() - 180.0).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` + #[must_use = "this returns the result of the operation, \ + without modifying the original"] + #[unstable(feature = "f128", issue = "00000")] + #[inline] + pub fn to_degrees(self) -> f128 { + // The division here is correctly rounded with respect to the true + // value of 180/π. (This differs from f32, where a constant must be + // used to ensure a correctly rounded result.) + self * (180.0f128 / consts::PI) + } + + /// Converts degrees to radians. + /// + /// ``` + /// let angle = 180.0_f128; + /// + /// let abs_difference = (angle.to_radians() - std::f128::consts::PI).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` + #[must_use = "this returns the result of the operation, \ + without modifying the original"] + #[unstable(feature = "f128", issue = "00000")] + #[inline] + pub fn to_radians(self) -> f128 { + let value: f128 = consts::PI; + self * (value / 180.0) + } + + /// 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. + /// + /// ``` + /// let x = 1.0_f128; + /// let y = 2.0_f128; + /// + /// assert_eq!(x.max(y), y); + /// ``` + #[must_use = "this returns the result of the comparison, without modifying either input"] + #[unstable(feature = "f128", issue = "00000")] + #[inline] + pub fn max(self, other: f128) -> f128 { + intrinsics::maxnumf128(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. + /// + /// ``` + /// let x = 1.0_f128; + /// let y = 2.0_f128; + /// + /// assert_eq!(x.min(y), x); + /// ``` + #[must_use = "this returns the result of the comparison, without modifying either input"] + #[unstable(feature = "f128", issue = "00000")] + #[inline] + pub fn min(self, other: f128) -> f128 { + intrinsics::minnumf128(self, other) + } + + /// Returns the maximum of the two numbers, propagating NaN. + /// + /// This returns NaN when *either* argument is NaN, as opposed to + /// [`f128::max`] which only returns NaN when *both* arguments are NaN. + /// + /// ``` + /// #![feature(float_minimum_maximum)] + /// let x = 1.0_f128; + /// let y = 2.0_f128; + /// + /// assert_eq!(x.maximum(y), y); + /// assert!(x.maximum(f128::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 [explanation of NaN as a special value](f32) for more info. + #[must_use = "this returns the result of the comparison, without modifying either input"] + #[unstable(feature = "float_minimum_maximum", issue = "91079")] + #[inline] + pub fn maximum(self, other: f128) -> f128 { + 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 + /// [`f128::min`] which only returns NaN when *both* arguments are NaN. + /// + /// ``` + /// #![feature(float_minimum_maximum)] + /// let x = 1.0_f128; + /// let y = 2.0_f128; + /// + /// assert_eq!(x.minimum(y), x); + /// assert!(x.minimum(f128::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 [explanation of NaN as a special value](f32) for more info. + #[must_use = "this returns the result of the comparison, without modifying either input"] + #[unstable(feature = "float_minimum_maximum", issue = "91079")] + #[inline] + pub fn minimum(self, other: f128) -> f128 { + 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 { + 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(num_midpoint)] + /// assert_eq!(1f128.midpoint(4.0), 2.5); + /// assert_eq!((-5.5f128).midpoint(8.0), 1.25); + /// ``` + #[unstable(feature = "num_midpoint", issue = "110840")] + pub fn midpoint(self, other: f128) -> f128 { + const LO: f128 = f128::MIN_POSITIVE * 2.; + const HI: f128 = f128::MAX / 2.; + + let (a, b) = (self, other); + let abs_a = a.abs_private(); + let abs_b = b.abs_private(); + + if abs_a <= HI && abs_b <= HI { + // Overflow is impossible + (a + b) / 2. + } else if abs_a < LO { + // Not safe to halve a + a + (b / 2.) + } else if abs_b < LO { + // Not safe to halve b + (a / 2.) + b + } else { + // Not 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. + /// + /// ``` + /// let value = 4.6_f128; + /// let rounded = unsafe { value.to_int_unchecked::() }; + /// assert_eq!(rounded, 4); + /// + /// let value = -128.9_f128; + /// 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 + #[must_use = "this returns the result of the operation, \ + without modifying the original"] + #[unstable(feature = "f128", issue = "00000")] + #[inline] + 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 `u64`. + /// + /// This is currently identical to `transmute::(self)` on all platforms. + /// + /// See [`from_bits`](Self::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. + /// + /// # Examples + /// + /// ``` + /// assert!((1f128).to_bits() != 1f128 as u64); // to_bits() is not casting! + /// assert_eq!((12.5f128).to_bits(), 0x4029000000000000); + /// + /// ``` + #[must_use = "this returns the result of the operation, \ + without modifying the original"] + #[unstable(feature = "f128", issue = "00000")] + #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")] + #[inline] + pub const fn to_bits(self) -> u64 { + // SAFETY: `u64` is a plain old datatype so we can always transmute to it. + // ...sorta. + // + // See the SAFETY comment in f128::from_bits for more. + #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")] + const fn ct_f128_to_u64(ct: f128) -> u64 { + match ct.classify() { + FpCategory::Nan => { + panic!("const-eval error: cannot use f128::to_bits on a NaN") + } + FpCategory::Subnormal => { + panic!("const-eval error: cannot use f128::to_bits on a subnormal number") + } + FpCategory::Infinite | FpCategory::Normal | FpCategory::Zero => { + // SAFETY: We have a normal floating point number. Now we transmute, i.e. do a bitcopy. + unsafe { mem::transmute::(ct) } + } + } + } + + #[inline(always)] // See https://github.com/rust-lang/compiler-builtins/issues/491 + fn rt_f128_to_u64(rt: f128) -> u64 { + // SAFETY: `u64` is a plain old datatype so we can always... uh... + // ...look, just pretend you forgot what you just read. + // Stability concerns. + unsafe { mem::transmute::(rt) } + } + // SAFETY: We use internal implementations that either always work or fail at compile time. + unsafe { intrinsics::const_eval_select((self,), ct_f128_to_u64, rt_f128_to_u64) } + } + + /// Raw transmutation from `u64`. + /// + /// 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 signaling-ness (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. + /// + /// # Examples + /// + /// ``` + /// let v = f128::from_bits(0x4029000000000000); + /// assert_eq!(v, 12.5); + /// ``` + #[unstable(feature = "f128", issue = "00000")] + #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")] + #[must_use] + #[inline] + pub const fn from_bits(v: u64) -> Self { + // It turns out the safety issues with sNaN were overblown! Hooray! + // SAFETY: `u64` is a plain old datatype so we can always transmute from it + // ...sorta. + // + // It turns out that at runtime, it is possible for a floating point number + // to be subject to floating point modes that alter nonzero subnormal numbers + // to zero on reads and writes, aka "denormals are zero" and "flush to zero". + // This is not a problem usually, but at least one tier2 platform for Rust + // actually exhibits an FTZ behavior by default: thumbv7neon + // aka "the Neon FPU in AArch32 state" + // + // Even with this, not all instructions exhibit the FTZ behaviors on thumbv7neon, + // so this should load the same bits if LLVM emits the "correct" instructions, + // but LLVM sometimes makes interesting choices about float optimization, + // and other FPUs may do similar. Thus, it is wise to indulge luxuriously in caution. + // + // In addition, on x86 targets with SSE or SSE2 disabled and the x87 FPU enabled, + // i.e. not soft-float, the way Rust does parameter passing can actually alter + // a number that is "not infinity" to have the same exponent as infinity, + // in a slightly unpredictable manner. + // + // And, of course evaluating to a NaN value is fairly nondeterministic. + // More precisely: when NaN should be returned is knowable, but which NaN? + // So far that's defined by a combination of LLVM and the CPU, not Rust. + // This function, however, allows observing the bitstring of a NaN, + // thus introspection on CTFE. + // + // In order to preserve, at least for the moment, const-to-runtime equivalence, + // reject any of these possible situations from happening. + #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")] + const fn ct_u64_to_f128(ct: u64) -> f128 { + match f128::classify_bits(ct) { + FpCategory::Subnormal => { + panic!("const-eval error: cannot use f128::from_bits on a subnormal number") + } + FpCategory::Nan => { + panic!("const-eval error: cannot use f128::from_bits on NaN") + } + FpCategory::Infinite | FpCategory::Normal | FpCategory::Zero => { + // SAFETY: It's not a frumious number + unsafe { mem::transmute::(ct) } + } + } + } + + #[inline(always)] // See https://github.com/rust-lang/compiler-builtins/issues/491 + fn rt_u64_to_f128(rt: u64) -> f128 { + // SAFETY: `u64` is a plain old datatype so we can always... uh... + // ...look, just pretend you forgot what you just read. + // Stability concerns. + unsafe { mem::transmute::(rt) } + } + // SAFETY: We use internal implementations that either always work or fail at compile time. + unsafe { intrinsics::const_eval_select((v,), ct_u64_to_f128, rt_u64_to_f128) } + } + + /// Return 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 + /// + /// ``` + /// let bytes = 12.5f128.to_be_bytes(); + /// assert_eq!(bytes, [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]); + /// ``` + #[must_use = "this returns the result of the operation, \ + without modifying the original"] + #[unstable(feature = "f128", issue = "00000")] + #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")] + #[inline] + pub const fn to_be_bytes(self) -> [u8; 8] { + self.to_bits().to_be_bytes() + } + + /// Return 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 + /// + /// ``` + /// let bytes = 12.5f128.to_le_bytes(); + /// assert_eq!(bytes, [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]); + /// ``` + #[must_use = "this returns the result of the operation, \ + without modifying the original"] + #[unstable(feature = "f128", issue = "00000")] + #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")] + #[inline] + pub const fn to_le_bytes(self) -> [u8; 8] { + self.to_bits().to_le_bytes() + } + + /// Return 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`]: f128::to_be_bytes + /// [`to_le_bytes`]: f128::to_le_bytes + /// + /// See [`from_bits`](Self::from_bits) for some discussion of the + /// portability of this operation (there are almost no issues). + /// + /// # Examples + /// + /// ``` + /// let bytes = 12.5f128.to_ne_bytes(); + /// assert_eq!( + /// bytes, + /// if cfg!(target_endian = "big") { + /// [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00] + /// } else { + /// [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40] + /// } + /// ); + /// ``` + #[must_use = "this returns the result of the operation, \ + without modifying the original"] + #[unstable(feature = "f128", issue = "00000")] + #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")] + #[inline] + pub const fn to_ne_bytes(self) -> [u8; 8] { + self.to_bits().to_ne_bytes() + } + + /// Create 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 + /// + /// ``` + /// let value = f128::from_be_bytes([0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]); + /// assert_eq!(value, 12.5); + /// ``` + #[unstable(feature = "f128", issue = "00000")] + #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")] + #[must_use] + #[inline] + pub const fn from_be_bytes(bytes: [u8; 8]) -> Self { + Self::from_bits(u64::from_be_bytes(bytes)) + } + + /// Create 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 + /// + /// ``` + /// let value = f128::from_le_bytes([0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]); + /// assert_eq!(value, 12.5); + /// ``` + #[unstable(feature = "f128", issue = "00000")] + #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")] + #[must_use] + #[inline] + pub const fn from_le_bytes(bytes: [u8; 8]) -> Self { + Self::from_bits(u64::from_le_bytes(bytes)) + } + + /// Create a floating point value from its representation as a byte array in native endian. + /// + /// As the target platform's native endianness is used, portable code + /// likely wants to use [`from_be_bytes`] or [`from_le_bytes`], as + /// appropriate instead. + /// + /// [`from_be_bytes`]: f128::from_be_bytes + /// [`from_le_bytes`]: f128::from_le_bytes + /// + /// See [`from_bits`](Self::from_bits) for some discussion of the + /// portability of this operation (there are almost no issues). + /// + /// # Examples + /// + /// ``` + /// let value = f128::from_ne_bytes(if cfg!(target_endian = "big") { + /// [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00] + /// } else { + /// [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40] + /// }); + /// assert_eq!(value, 12.5); + /// ``` + #[unstable(feature = "f128", issue = "00000")] + #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")] + #[must_use] + #[inline] + pub const fn from_ne_bytes(bytes: [u8; 8]) -> Self { + Self::from_bits(u64::from_ne_bytes(bytes)) + } + + /// Return 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 `f128`. 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 + /// + /// ``` + /// struct GoodBoy { + /// name: String, + /// weight: f128, + /// } + /// + /// let mut bois = vec![ + /// GoodBoy { name: "Pucci".to_owned(), weight: 0.1 }, + /// GoodBoy { name: "Woofer".to_owned(), weight: 99.0 }, + /// GoodBoy { name: "Yapper".to_owned(), weight: 10.0 }, + /// GoodBoy { name: "Chonk".to_owned(), weight: f128::INFINITY }, + /// GoodBoy { name: "Abs. Unit".to_owned(), weight: f128::NAN }, + /// GoodBoy { name: "Floaty".to_owned(), weight: -5.0 }, + /// ]; + /// + /// bois.sort_by(|a, b| a.weight.total_cmp(&b.weight)); + /// # assert!(bois.into_iter().map(|b| b.weight) + /// # .zip([-5.0, 0.1, 10.0, 99.0, f128::INFINITY, f128::NAN].iter()) + /// # .all(|(a, b)| a.to_bits() == b.to_bits())) + /// ``` + #[unstable(feature = "f128", issue = "00000")] + #[must_use] + #[inline] + pub fn total_cmp(&self, other: &Self) -> crate::cmp::Ordering { + let mut left = self.to_bits() as i64; + let mut right = other.to_bits() as i64; + + // 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 >> 63) as u64) >> 1) as i64; + right ^= (((right >> 63) as u64) >> 1) as i64; + + 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 + /// + /// ``` + /// assert!((-3.0f128).clamp(-2.0, 1.0) == -2.0); + /// assert!((0.0f128).clamp(-2.0, 1.0) == 0.0); + /// assert!((2.0f128).clamp(-2.0, 1.0) == 1.0); + /// assert!((f128::NAN).clamp(-2.0, 1.0).is_nan()); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[unstable(feature = "f128", issue = "00000")] + #[inline] + pub fn clamp(mut self, min: f128, max: f128) -> f128 { + assert!(min <= max, "min > max, or either was NaN. min = {min:?}, max = {max:?}"); + if self < min { + self = min; + } + if self > max { + self = max; + } + self + } +} diff --git a/library/core/src/num/f16.rs b/library/core/src/num/f16.rs new file mode 100644 index 0000000000000..d6d4ec1160647 --- /dev/null +++ b/library/core/src/num/f16.rs @@ -0,0 +1,1198 @@ +//! Constants for the `f16` double-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 = "00000")] + +use crate::convert::FloatToInt; +#[cfg(not(test))] +use crate::intrinsics; +use crate::mem; +use crate::num::FpCategory; + +/// Basic mathematical constants. +#[unstable(feature = "f16", issue = "00000")] +pub mod consts { + // FIXME: replace with mathematical constants from cmath. + + /// Archimedes' constant (π) + #[unstable(feature = "f16", issue = "00000")] + pub const PI: f16 = 3.14159265358979323846264338327950288_f16; + + /// The full circle constant (τ) + /// + /// Equal to 2π. + #[unstable(feature = "f16", issue = "00000")] + pub const TAU: f16 = 6.28318530717958647692528676655900577_f16; + + /// π/2 + #[unstable(feature = "f16", issue = "00000")] + pub const FRAC_PI_2: f16 = 1.57079632679489661923132169163975144_f16; + + /// π/3 + #[unstable(feature = "f16", issue = "00000")] + pub const FRAC_PI_3: f16 = 1.04719755119659774615421446109316763_f16; + + /// π/4 + #[unstable(feature = "f16", issue = "00000")] + pub const FRAC_PI_4: f16 = 0.785398163397448309615660845819875721_f16; + + /// π/6 + #[unstable(feature = "f16", issue = "00000")] + pub const FRAC_PI_6: f16 = 0.52359877559829887307710723054658381_f16; + + /// π/8 + #[unstable(feature = "f16", issue = "00000")] + pub const FRAC_PI_8: f16 = 0.39269908169872415480783042290993786_f16; + + /// 1/π + #[unstable(feature = "f16", issue = "00000")] + pub const FRAC_1_PI: f16 = 0.318309886183790671537767526745028724_f16; + + /// 2/π + #[unstable(feature = "f16", issue = "00000")] + pub const FRAC_2_PI: f16 = 0.636619772367581343075535053490057448_f16; + + /// 2/sqrt(π) + #[unstable(feature = "f16", issue = "00000")] + pub const FRAC_2_SQRT_PI: f16 = 1.12837916709551257389615890312154517_f16; + + /// sqrt(2) + #[unstable(feature = "f16", issue = "00000")] + pub const SQRT_2: f16 = 1.41421356237309504880168872420969808_f16; + + /// 1/sqrt(2) + #[unstable(feature = "f16", issue = "00000")] + pub const FRAC_1_SQRT_2: f16 = 0.707106781186547524400844362104849039_f16; + + /// Euler's number (e) + #[unstable(feature = "f16", issue = "00000")] + pub const E: f16 = 2.71828182845904523536028747135266250_f16; + + /// log2(10) + #[unstable(feature = "f16", issue = "00000")] + pub const LOG2_10: f16 = 3.32192809488736234787031942948939018_f16; + + /// log2(e) + #[unstable(feature = "f16", issue = "00000")] + pub const LOG2_E: f16 = 1.44269504088896340735992468100189214_f16; + + /// log10(2) + #[unstable(feature = "f16", issue = "00000")] + pub const LOG10_2: f16 = 0.301029995663981195213738894724493027_f16; + + /// log10(e) + #[unstable(feature = "f16", issue = "00000")] + pub const LOG10_E: f16 = 0.434294481903251827651128918916605082_f16; + + /// ln(2) + #[unstable(feature = "f16", issue = "00000")] + pub const LN_2: f16 = 0.693147180559945309417232121458176568_f16; + + /// ln(10) + #[unstable(feature = "f16", issue = "00000")] + pub const LN_10: f16 = 2.30258509299404568401799145468436421_f16; +} + +// TODO: this is probably all wrong +#[cfg(not(test))] +impl f16 { + /// The radix or base of the internal representation of `f16`. + #[unstable(feature = "f16", issue = "00000")] + pub const RADIX: u32 = 2; + + /// Number of significant digits in base 2. + #[unstable(feature = "f16", issue = "00000")] + pub const MANTISSA_DIGITS: u32 = 53; + + /// Approximate number of significant digits in base 10. + #[unstable(feature = "f16", issue = "00000")] + pub const DIGITS: u32 = 15; + + /// [Machine epsilon] value for `f16`. + /// + /// This is the difference between `1.0` and the next larger representable number. + /// + /// [Machine epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon + #[unstable(feature = "f16", issue = "00000")] + pub const EPSILON: f16 = 0.00097656_f16; + + /// Smallest finite `f16` value. + #[unstable(feature = "f16", issue = "00000")] + pub const MIN: f16 = -1.7976931348623157e+308_f16; + + /// Smallest positive normal `f16` value. + #[unstable(feature = "f16", issue = "00000")] + pub const MIN_POSITIVE: f16 = 0.000000059604645_f16; + + /// Largest finite `f16` value. + #[unstable(feature = "f16", issue = "00000")] + pub const MAX: f16 = 65504_f16; + + /// One greater than the minimum possible normal power of 2 exponent. + #[unstable(feature = "f16", issue = "00000")] + pub const MIN_EXP: i32 = -1021; + + /// Maximum possible power of 2 exponent. + #[unstable(feature = "f16", issue = "00000")] + pub const MAX_EXP: i32 = 1024; + + /// Minimum possible normal power of 10 exponent. + #[unstable(feature = "f16", issue = "00000")] + pub const MIN_10_EXP: i32 = -307; + /// Maximum possible power of 10 exponent. + #[unstable(feature = "f16", issue = "00000")] + pub const MAX_10_EXP: i32 = 308; + + /// 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. + #[rustc_diagnostic_item = "f16_nan"] + #[unstable(feature = "f16", issue = "00000")] + pub const NAN: f16 = 0.0_f16 / 0.0_f16; + /// Infinity (∞). + #[unstable(feature = "f16", issue = "00000")] + pub const INFINITY: f16 = 1.0_f16 / 0.0_f16; + /// Negative infinity (−∞). + #[unstable(feature = "f16", issue = "00000")] + pub const NEG_INFINITY: f16 = -1.0_f16 / 0.0_f16; + + /// Returns `true` if this value is NaN. + /// + /// ``` + /// let nan = f16::NAN; + /// let f = 7.0_f16; + /// + /// assert!(nan.is_nan()); + /// assert!(!f.is_nan()); + /// ``` + #[must_use] + #[unstable(feature = "f16", issue = "00000")] + #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")] + #[inline] + pub const fn is_nan(self) -> bool { + self != self + } + + // FIXME(#50145): `abs` is publicly unavailable in core due to + // concerns about portability, so this implementation is for + // private use internally. + #[inline] + #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")] + pub(crate) const fn abs_private(self) -> f16 { + // SAFETY: This transmutation is fine. Probably. For the reasons std is using it. + unsafe { + mem::transmute::(mem::transmute::(self) & 0x7fff_ffff_ffff_ffff) + } + } + + /// Returns `true` if this value is positive infinity or negative infinity, and + /// `false` otherwise. + /// + /// ``` + /// 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()); + /// ``` + #[must_use] + #[unstable(feature = "f16", issue = "00000")] + #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")] + #[inline] + pub const fn is_infinite(self) -> bool { + // Getting clever with transmutation can result in incorrect answers on some FPUs + // FIXME: alter the Rust <-> Rust calling convention to prevent this problem. + // See https://github.com/rust-lang/rust/issues/72327 + (self == f16::INFINITY) | (self == f16::NEG_INFINITY) + } + + /// Returns `true` if this number is neither infinite nor NaN. + /// + /// ``` + /// 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()); + /// ``` + #[must_use] + #[unstable(feature = "f16", issue = "00000")] + #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")] + #[inline] + 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_private() < Self::INFINITY + } + + /// Returns `true` if the number is [subnormal]. + /// + /// ``` + /// let min = f16::MIN_POSITIVE; // 2.2250738585072014e-308_f16 + /// let max = f16::MAX; + /// let lower_than_min = 1.0e-308_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 + #[must_use] + #[unstable(feature = "f16", issue = "00000")] + #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")] + #[inline] + pub const fn is_subnormal(self) -> bool { + matches!(self.classify(), FpCategory::Subnormal) + } + + /// Returns `true` if the number is neither zero, infinite, + /// [subnormal], or NaN. + /// + /// ``` + /// let min = f16::MIN_POSITIVE; // 2.2250738585072014e-308f16 + /// let max = f16::MAX; + /// let lower_than_min = 1.0e-308_f16; + /// let zero = 0.0f16; + /// + /// 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 + #[must_use] + #[unstable(feature = "f16", issue = "00000")] + #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")] + #[inline] + 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. + /// + /// ``` + /// 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); + /// ``` + #[unstable(feature = "f16", issue = "00000")] + #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")] + pub const fn classify(self) -> FpCategory { + // A previous implementation tried to only use bitmask-based checks, + // using f16::to_bits to transmute the float to its bit repr and match on that. + // Unfortunately, floating point numbers can be much worse than that. + // This also needs to not result in recursive evaluations of f16::to_bits. + // + // On some processors, in some cases, LLVM will "helpfully" lower floating point ops, + // in spite of a request for them using f32 and f16, to things like x87 operations. + // These have an f16's mantissa, but can have a larger than normal exponent. + // FIXME(jubilee): Using x87 operations is never necessary in order to function + // on x86 processors for Rust-to-Rust calls, so this issue should not happen. + // Code generation should be adjusted to use non-C calling conventions, avoiding this. + // + // Thus, a value may compare unequal to infinity, despite having a "full" exponent mask. + // And it may not be NaN, as it can simply be an "overextended" finite value. + if self.is_nan() { + FpCategory::Nan + } else { + // However, std can't simply compare to zero to check for zero, either, + // as correctness requires avoiding equality tests that may be Subnormal == -0.0 + // because it may be wrong under "denormals are zero" and "flush to zero" modes. + // Most of std's targets don't use those, but they are used for thumbv7neon. + // So, this does use bitpattern matching for the rest. + + // SAFETY: f16 to u64 is fine. Usually. + // If control flow has gotten this far, the value is definitely in one of the categories + // that f16::partial_classify can correctly analyze. + unsafe { f16::partial_classify(self) } + } + } + + // This doesn't actually return a right answer for NaN on purpose, + // seeing as how it cannot correctly discern between a floating point NaN, + // and some normal floating point numbers truncated from an x87 FPU. + #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")] + const unsafe fn partial_classify(self) -> FpCategory { + const EXP_MASK: u64 = 0x7ff0000000000000; + const MAN_MASK: u64 = 0x000fffffffffffff; + + // SAFETY: The caller is not asking questions for which this will tell lies. + let b = unsafe { mem::transmute::(self) }; + match (b & MAN_MASK, b & EXP_MASK) { + (0, EXP_MASK) => FpCategory::Infinite, + (0, 0) => FpCategory::Zero, + (_, 0) => FpCategory::Subnormal, + _ => FpCategory::Normal, + } + } + + // This operates on bits, and only bits, so it can ignore concerns about weird FPUs. + // FIXME(jubilee): In a just world, this would be the entire impl for classify, + // plus a transmute. We do not live in a just world, but we can make it more so. + #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")] + const fn classify_bits(b: u64) -> FpCategory { + const EXP_MASK: u64 = 0x7ff0000000000000; + const MAN_MASK: u64 = 0x000fffffffffffff; + + match (b & MAN_MASK, b & EXP_MASK) { + (0, EXP_MASK) => FpCategory::Infinite, + (_, 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 result in some cases. + /// See [explanation of NaN as a special value](f32) for more info. + /// + /// ``` + /// let f = 7.0_f16; + /// let g = -7.0_f16; + /// + /// assert!(f.is_sign_positive()); + /// assert!(!g.is_sign_positive()); + /// ``` + #[must_use] + #[unstable(feature = "f16", issue = "00000")] + #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")] + #[inline] + pub const fn is_sign_positive(self) -> bool { + !self.is_sign_negative() + } + + #[must_use] + #[unstable(feature = "f16", issue = "00000")] + #[deprecated(since = "1.0.0", note = "renamed to is_sign_positive")] + #[inline] + #[doc(hidden)] + pub fn is_positive(self) -> bool { + self.is_sign_positive() + } + + /// 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 result in some cases. + /// See [explanation of NaN as a special value](f32) for more info. + /// + /// ``` + /// let f = 7.0_f16; + /// let g = -7.0_f16; + /// + /// assert!(!f.is_sign_negative()); + /// assert!(g.is_sign_negative()); + /// ``` + #[must_use] + #[unstable(feature = "f16", issue = "00000")] + #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")] + #[inline] + 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. + unsafe { mem::transmute::(self) & 0x8000_0000_0000_0000 != 0 } + } + + #[must_use] + #[unstable(feature = "f16", issue = "00000")] + #[deprecated(since = "1.0.0", note = "renamed to is_sign_negative")] + #[inline] + #[doc(hidden)] + pub fn is_negative(self) -> bool { + self.is_sign_negative() + } + + /// 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(float_next_up_down)] + /// // 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!(9007199254740992f16.next_up(), 9007199254740994.0); + /// ``` + /// + /// [`NEG_INFINITY`]: Self::NEG_INFINITY + /// [`INFINITY`]: Self::INFINITY + /// [`MIN`]: Self::MIN + /// [`MAX`]: Self::MAX + #[unstable(feature = "float_next_up_down", issue = "91399")] + #[rustc_const_unstable(feature = "float_next_up_down", issue = "91399")] + pub const fn next_up(self) -> Self { + // We must use strictly integer arithmetic to prevent denormals from + // flushing to zero after an arithmetic operation on some platforms. + const TINY_BITS: u64 = 0x1; // Smallest positive f16. + const CLEAR_SIGN_MASK: u64 = 0x7fff_ffff_ffff_ffff; + + let bits = self.to_bits(); + if self.is_nan() || bits == Self::INFINITY.to_bits() { + return self; + } + + let abs = bits & CLEAR_SIGN_MASK; + let next_bits = if abs == 0 { + 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(float_next_up_down)] + /// 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); + /// ``` + /// + /// [`NEG_INFINITY`]: Self::NEG_INFINITY + /// [`INFINITY`]: Self::INFINITY + /// [`MIN`]: Self::MIN + /// [`MAX`]: Self::MAX + #[unstable(feature = "float_next_up_down", issue = "91399")] + #[rustc_const_unstable(feature = "float_next_up_down", issue = "91399")] + pub const fn next_down(self) -> Self { + // We must use strictly integer arithmetic to prevent denormals from + // flushing to zero after an arithmetic operation on some platforms. + const NEG_TINY_BITS: u64 = 0x8000_0000_0000_0001; // Smallest (in magnitude) negative f16. + const CLEAR_SIGN_MASK: u64 = 0x7fff_ffff_ffff_ffff; + + let bits = self.to_bits(); + if self.is_nan() || bits == Self::NEG_INFINITY.to_bits() { + return self; + } + + let abs = bits & CLEAR_SIGN_MASK; + let next_bits = if abs == 0 { + 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`. + /// + /// ``` + /// let x = 2.0_f16; + /// let abs_difference = (x.recip() - (1.0 / x)).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` + #[must_use = "this returns the result of the operation, without modifying the original"] + #[unstable(feature = "f16", issue = "00000")] + #[inline] + pub fn recip(self) -> f16 { + 1.0 / self + } + + /// Converts radians to degrees. + /// + /// ``` + /// let angle = std::f16::consts::PI; + /// + /// let abs_difference = (angle.to_degrees() - 180.0).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` + #[must_use = "this returns the result of the operation, \ + without modifying the original"] + #[unstable(feature = "f16", issue = "00000")] + #[inline] + pub fn to_degrees(self) -> f16 { + // The division here is correctly rounded with respect to the true + // value of 180/π. (This differs from f32, where a constant must be + // used to ensure a correctly rounded result.) + self * (180.0f16 / consts::PI) + } + + /// Converts degrees to radians. + /// + /// ``` + /// let angle = 180.0_f16; + /// + /// let abs_difference = (angle.to_radians() - std::f16::consts::PI).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` + #[must_use = "this returns the result of the operation, \ + without modifying the original"] + #[unstable(feature = "f16", issue = "00000")] + #[inline] + pub fn to_radians(self) -> f16 { + let value: f16 = consts::PI; + self * (value / 180.0) + } + + /// 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. + /// + /// ``` + /// let x = 1.0_f16; + /// let y = 2.0_f16; + /// + /// assert_eq!(x.max(y), y); + /// ``` + #[must_use = "this returns the result of the comparison, without modifying either input"] + #[unstable(feature = "f16", issue = "00000")] + #[inline] + pub 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. + /// + /// ``` + /// let x = 1.0_f16; + /// let y = 2.0_f16; + /// + /// assert_eq!(x.min(y), x); + /// ``` + #[must_use = "this returns the result of the comparison, without modifying either input"] + #[unstable(feature = "f16", issue = "00000")] + #[inline] + pub 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(float_minimum_maximum)] + /// let x = 1.0_f16; + /// let y = 2.0_f16; + /// + /// 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 [explanation of NaN as a special value](f32) for more info. + #[must_use = "this returns the result of the comparison, without modifying either input"] + #[unstable(feature = "float_minimum_maximum", issue = "91079")] + #[inline] + pub 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(float_minimum_maximum)] + /// let x = 1.0_f16; + /// let y = 2.0_f16; + /// + /// 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 [explanation of NaN as a special value](f32) for more info. + #[must_use = "this returns the result of the comparison, without modifying either input"] + #[unstable(feature = "float_minimum_maximum", issue = "91079")] + #[inline] + pub 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 { + 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(num_midpoint)] + /// assert_eq!(1f16.midpoint(4.0), 2.5); + /// assert_eq!((-5.5f16).midpoint(8.0), 1.25); + /// ``` + #[unstable(feature = "num_midpoint", issue = "110840")] + pub 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_private(); + let abs_b = b.abs_private(); + + if abs_a <= HI && abs_b <= HI { + // Overflow is impossible + (a + b) / 2. + } else if abs_a < LO { + // Not safe to halve a + a + (b / 2.) + } else if abs_b < LO { + // Not safe to halve b + (a / 2.) + b + } else { + // Not 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. + /// + /// ``` + /// 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 + #[must_use = "this returns the result of the operation, \ + without modifying the original"] + #[unstable(feature = "f16", issue = "00000")] + #[inline] + 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 `u64`. + /// + /// This is currently identical to `transmute::(self)` on all platforms. + /// + /// See [`from_bits`](Self::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. + /// + /// # Examples + /// + /// ``` + /// assert!((1f16).to_bits() != 1f16 as u64); // to_bits() is not casting! + /// assert_eq!((12.5f16).to_bits(), 0x4029000000000000); + /// + /// ``` + #[must_use = "this returns the result of the operation, \ + without modifying the original"] + #[unstable(feature = "f16", issue = "00000")] + #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")] + #[inline] + pub const fn to_bits(self) -> u64 { + // SAFETY: `u64` is a plain old datatype so we can always transmute to it. + // ...sorta. + // + // See the SAFETY comment in f16::from_bits for more. + #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")] + const fn ct_f16_to_u64(ct: f16) -> u64 { + match ct.classify() { + FpCategory::Nan => { + panic!("const-eval error: cannot use f16::to_bits on a NaN") + } + FpCategory::Subnormal => { + panic!("const-eval error: cannot use f16::to_bits on a subnormal number") + } + FpCategory::Infinite | FpCategory::Normal | FpCategory::Zero => { + // SAFETY: We have a normal floating point number. Now we transmute, i.e. do a bitcopy. + unsafe { mem::transmute::(ct) } + } + } + } + + #[inline(always)] // See https://github.com/rust-lang/compiler-builtins/issues/491 + fn rt_f16_to_u64(rt: f16) -> u64 { + // SAFETY: `u64` is a plain old datatype so we can always... uh... + // ...look, just pretend you forgot what you just read. + // Stability concerns. + unsafe { mem::transmute::(rt) } + } + // SAFETY: We use internal implementations that either always work or fail at compile time. + unsafe { intrinsics::const_eval_select((self,), ct_f16_to_u64, rt_f16_to_u64) } + } + + /// Raw transmutation from `u64`. + /// + /// 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 signaling-ness (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. + /// + /// # Examples + /// + /// ``` + /// let v = f16::from_bits(0x4029000000000000); + /// assert_eq!(v, 12.5); + /// ``` + #[unstable(feature = "f16", issue = "00000")] + #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")] + #[must_use] + #[inline] + pub const fn from_bits(v: u64) -> Self { + // It turns out the safety issues with sNaN were overblown! Hooray! + // SAFETY: `u64` is a plain old datatype so we can always transmute from it + // ...sorta. + // + // It turns out that at runtime, it is possible for a floating point number + // to be subject to floating point modes that alter nonzero subnormal numbers + // to zero on reads and writes, aka "denormals are zero" and "flush to zero". + // This is not a problem usually, but at least one tier2 platform for Rust + // actually exhibits an FTZ behavior by default: thumbv7neon + // aka "the Neon FPU in AArch32 state" + // + // Even with this, not all instructions exhibit the FTZ behaviors on thumbv7neon, + // so this should load the same bits if LLVM emits the "correct" instructions, + // but LLVM sometimes makes interesting choices about float optimization, + // and other FPUs may do similar. Thus, it is wise to indulge luxuriously in caution. + // + // In addition, on x86 targets with SSE or SSE2 disabled and the x87 FPU enabled, + // i.e. not soft-float, the way Rust does parameter passing can actually alter + // a number that is "not infinity" to have the same exponent as infinity, + // in a slightly unpredictable manner. + // + // And, of course evaluating to a NaN value is fairly nondeterministic. + // More precisely: when NaN should be returned is knowable, but which NaN? + // So far that's defined by a combination of LLVM and the CPU, not Rust. + // This function, however, allows observing the bitstring of a NaN, + // thus introspection on CTFE. + // + // In order to preserve, at least for the moment, const-to-runtime equivalence, + // reject any of these possible situations from happening. + #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")] + const fn ct_u64_to_f16(ct: u64) -> f16 { + match f16::classify_bits(ct) { + FpCategory::Subnormal => { + panic!("const-eval error: cannot use f16::from_bits on a subnormal number") + } + FpCategory::Nan => { + panic!("const-eval error: cannot use f16::from_bits on NaN") + } + FpCategory::Infinite | FpCategory::Normal | FpCategory::Zero => { + // SAFETY: It's not a frumious number + unsafe { mem::transmute::(ct) } + } + } + } + + #[inline(always)] // See https://github.com/rust-lang/compiler-builtins/issues/491 + fn rt_u64_to_f16(rt: u64) -> f16 { + // SAFETY: `u64` is a plain old datatype so we can always... uh... + // ...look, just pretend you forgot what you just read. + // Stability concerns. + unsafe { mem::transmute::(rt) } + } + // SAFETY: We use internal implementations that either always work or fail at compile time. + unsafe { intrinsics::const_eval_select((v,), ct_u64_to_f16, rt_u64_to_f16) } + } + + /// Return 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 + /// + /// ``` + /// let bytes = 12.5f16.to_be_bytes(); + /// assert_eq!(bytes, [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]); + /// ``` + #[must_use = "this returns the result of the operation, \ + without modifying the original"] + #[unstable(feature = "f16", issue = "00000")] + #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")] + #[inline] + pub const fn to_be_bytes(self) -> [u8; 8] { + self.to_bits().to_be_bytes() + } + + /// Return 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 + /// + /// ``` + /// let bytes = 12.5f16.to_le_bytes(); + /// assert_eq!(bytes, [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]); + /// ``` + #[must_use = "this returns the result of the operation, \ + without modifying the original"] + #[unstable(feature = "f16", issue = "00000")] + #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")] + #[inline] + pub const fn to_le_bytes(self) -> [u8; 8] { + self.to_bits().to_le_bytes() + } + + /// Return 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 + /// + /// ``` + /// let bytes = 12.5f16.to_ne_bytes(); + /// assert_eq!( + /// bytes, + /// if cfg!(target_endian = "big") { + /// [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00] + /// } else { + /// [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40] + /// } + /// ); + /// ``` + #[must_use = "this returns the result of the operation, \ + without modifying the original"] + #[unstable(feature = "f16", issue = "00000")] + #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")] + #[inline] + pub const fn to_ne_bytes(self) -> [u8; 8] { + self.to_bits().to_ne_bytes() + } + + /// Create 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 + /// + /// ``` + /// let value = f16::from_be_bytes([0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]); + /// assert_eq!(value, 12.5); + /// ``` + #[unstable(feature = "f16", issue = "00000")] + #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")] + #[must_use] + #[inline] + pub const fn from_be_bytes(bytes: [u8; 8]) -> Self { + Self::from_bits(u64::from_be_bytes(bytes)) + } + + /// Create 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 + /// + /// ``` + /// let value = f16::from_le_bytes([0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]); + /// assert_eq!(value, 12.5); + /// ``` + #[unstable(feature = "f16", issue = "00000")] + #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")] + #[must_use] + #[inline] + pub const fn from_le_bytes(bytes: [u8; 8]) -> Self { + Self::from_bits(u64::from_le_bytes(bytes)) + } + + /// Create a floating point value from its representation as a byte array in native endian. + /// + /// As the target platform's native endianness is used, portable code + /// likely wants to use [`from_be_bytes`] or [`from_le_bytes`], as + /// appropriate instead. + /// + /// [`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 + /// + /// ``` + /// let value = f16::from_ne_bytes(if cfg!(target_endian = "big") { + /// [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00] + /// } else { + /// [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40] + /// }); + /// assert_eq!(value, 12.5); + /// ``` + #[unstable(feature = "f16", issue = "00000")] + #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")] + #[must_use] + #[inline] + pub const fn from_ne_bytes(bytes: [u8; 8]) -> Self { + Self::from_bits(u64::from_ne_bytes(bytes)) + } + + /// Return 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 + /// + /// ``` + /// struct GoodBoy { + /// name: String, + /// weight: f16, + /// } + /// + /// let mut bois = vec![ + /// GoodBoy { name: "Pucci".to_owned(), weight: 0.1 }, + /// GoodBoy { name: "Woofer".to_owned(), weight: 99.0 }, + /// GoodBoy { name: "Yapper".to_owned(), weight: 10.0 }, + /// GoodBoy { name: "Chonk".to_owned(), weight: f16::INFINITY }, + /// GoodBoy { name: "Abs. Unit".to_owned(), weight: f16::NAN }, + /// GoodBoy { name: "Floaty".to_owned(), weight: -5.0 }, + /// ]; + /// + /// bois.sort_by(|a, b| a.weight.total_cmp(&b.weight)); + /// # assert!(bois.into_iter().map(|b| b.weight) + /// # .zip([-5.0, 0.1, 10.0, 99.0, f16::INFINITY, f16::NAN].iter()) + /// # .all(|(a, b)| a.to_bits() == b.to_bits())) + /// ``` + #[unstable(feature = "f16", issue = "00000")] + #[must_use] + #[inline] + pub fn total_cmp(&self, other: &Self) -> crate::cmp::Ordering { + let mut left = self.to_bits() as i64; + let mut right = other.to_bits() as i64; + + // 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 >> 63) as u64) >> 1) as i64; + right ^= (((right >> 63) as u64) >> 1) as i64; + + 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 + /// + /// ``` + /// 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()); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[unstable(feature = "f16", issue = "00000")] + #[inline] + pub fn clamp(mut self, min: f16, max: f16) -> f16 { + assert!(min <= max, "min > max, or either was NaN. min = {min:?}, max = {max:?}"); + if self < min { + self = min; + } + if self > max { + self = max; + } + self + } +}