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Diffstat (limited to 'compiler/rustc_apfloat/src/lib.rs')
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1 files changed, 693 insertions, 0 deletions
diff --git a/compiler/rustc_apfloat/src/lib.rs b/compiler/rustc_apfloat/src/lib.rs new file mode 100644 index 000000000..cfc3d5b15 --- /dev/null +++ b/compiler/rustc_apfloat/src/lib.rs @@ -0,0 +1,693 @@ +//! Port of LLVM's APFloat software floating-point implementation from the +//! following C++ sources (please update commit hash when backporting): +//! <https://github.com/llvm-mirror/llvm/tree/23efab2bbd424ed13495a420ad8641cb2c6c28f9> +//! +//! * `include/llvm/ADT/APFloat.h` -> `Float` and `FloatConvert` traits +//! * `lib/Support/APFloat.cpp` -> `ieee` and `ppc` modules +//! * `unittests/ADT/APFloatTest.cpp` -> `tests` directory +//! +//! The port contains no unsafe code, global state, or side-effects in general, +//! and the only allocations are in the conversion to/from decimal strings. +//! +//! Most of the API and the testcases are intact in some form or another, +//! with some ergonomic changes, such as idiomatic short names, returning +//! new values instead of mutating the receiver, and having separate method +//! variants that take a non-default rounding mode (with the suffix `_r`). +//! Comments have been preserved where possible, only slightly adapted. +//! +//! Instead of keeping a pointer to a configuration struct and inspecting it +//! dynamically on every operation, types (e.g., `ieee::Double`), traits +//! (e.g., `ieee::Semantics`) and associated constants are employed for +//! increased type safety and performance. +//! +//! On-heap bigints are replaced everywhere (except in decimal conversion), +//! with short arrays of `type Limb = u128` elements (instead of `u64`), +//! This allows fitting the largest supported significands in one integer +//! (`ieee::Quad` and `ppc::Fallback` use slightly less than 128 bits). +//! All of the functions in the `ieee::sig` module operate on slices. +//! +//! # Note +//! +//! This API is completely unstable and subject to change. + +#![doc(html_root_url = "https://doc.rust-lang.org/nightly/nightly-rustc/")] +#![no_std] +#![forbid(unsafe_code)] + +#[macro_use] +extern crate alloc; + +use core::cmp::Ordering; +use core::fmt; +use core::ops::{Add, Div, Mul, Neg, Rem, Sub}; +use core::ops::{AddAssign, DivAssign, MulAssign, RemAssign, SubAssign}; +use core::str::FromStr; + +bitflags::bitflags! { + /// IEEE-754R 7: Default exception handling. + /// + /// UNDERFLOW or OVERFLOW are always returned or-ed with INEXACT. + #[must_use] + pub struct Status: u8 { + const OK = 0x00; + const INVALID_OP = 0x01; + const DIV_BY_ZERO = 0x02; + const OVERFLOW = 0x04; + const UNDERFLOW = 0x08; + const INEXACT = 0x10; + } +} + +#[must_use] +#[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Debug)] +pub struct StatusAnd<T> { + pub status: Status, + pub value: T, +} + +impl Status { + pub fn and<T>(self, value: T) -> StatusAnd<T> { + StatusAnd { status: self, value } + } +} + +impl<T> StatusAnd<T> { + pub fn map<F: FnOnce(T) -> U, U>(self, f: F) -> StatusAnd<U> { + StatusAnd { status: self.status, value: f(self.value) } + } +} + +#[macro_export] +macro_rules! unpack { + ($status:ident|=, $e:expr) => { + match $e { + $crate::StatusAnd { status, value } => { + $status |= status; + value + } + } + }; + ($status:ident=, $e:expr) => { + match $e { + $crate::StatusAnd { status, value } => { + $status = status; + value + } + } + }; +} + +/// Category of internally-represented number. +#[derive(Copy, Clone, PartialEq, Eq, Debug)] +pub enum Category { + Infinity, + NaN, + Normal, + Zero, +} + +/// IEEE-754R 4.3: Rounding-direction attributes. +#[derive(Copy, Clone, PartialEq, Eq, Debug)] +pub enum Round { + NearestTiesToEven, + TowardPositive, + TowardNegative, + TowardZero, + NearestTiesToAway, +} + +impl Neg for Round { + type Output = Round; + fn neg(self) -> Round { + match self { + Round::TowardPositive => Round::TowardNegative, + Round::TowardNegative => Round::TowardPositive, + Round::NearestTiesToEven | Round::TowardZero | Round::NearestTiesToAway => self, + } + } +} + +/// A signed type to represent a floating point number's unbiased exponent. +pub type ExpInt = i16; + +// \c ilogb error results. +pub const IEK_INF: ExpInt = ExpInt::MAX; +pub const IEK_NAN: ExpInt = ExpInt::MIN; +pub const IEK_ZERO: ExpInt = ExpInt::MIN + 1; + +#[derive(Copy, Clone, PartialEq, Eq, Debug)] +pub struct ParseError(pub &'static str); + +/// A self-contained host- and target-independent arbitrary-precision +/// floating-point software implementation. +/// +/// `apfloat` uses significand bignum integer arithmetic as provided by functions +/// in the `ieee::sig`. +/// +/// Written for clarity rather than speed, in particular with a view to use in +/// the front-end of a cross compiler so that target arithmetic can be correctly +/// performed on the host. Performance should nonetheless be reasonable, +/// particularly for its intended use. It may be useful as a base +/// implementation for a run-time library during development of a faster +/// target-specific one. +/// +/// All 5 rounding modes in the IEEE-754R draft are handled correctly for all +/// implemented operations. Currently implemented operations are add, subtract, +/// multiply, divide, fused-multiply-add, conversion-to-float, +/// conversion-to-integer and conversion-from-integer. New rounding modes +/// (e.g., away from zero) can be added with three or four lines of code. +/// +/// Four formats are built-in: IEEE single precision, double precision, +/// quadruple precision, and x87 80-bit extended double (when operating with +/// full extended precision). Adding a new format that obeys IEEE semantics +/// only requires adding two lines of code: a declaration and definition of the +/// format. +/// +/// All operations return the status of that operation as an exception bit-mask, +/// so multiple operations can be done consecutively with their results or-ed +/// together. The returned status can be useful for compiler diagnostics; e.g., +/// inexact, underflow and overflow can be easily diagnosed on constant folding, +/// and compiler optimizers can determine what exceptions would be raised by +/// folding operations and optimize, or perhaps not optimize, accordingly. +/// +/// At present, underflow tininess is detected after rounding; it should be +/// straight forward to add support for the before-rounding case too. +/// +/// The library reads hexadecimal floating point numbers as per C99, and +/// correctly rounds if necessary according to the specified rounding mode. +/// Syntax is required to have been validated by the caller. +/// +/// It also reads decimal floating point numbers and correctly rounds according +/// to the specified rounding mode. +/// +/// Non-zero finite numbers are represented internally as a sign bit, a 16-bit +/// signed exponent, and the significand as an array of integer limbs. After +/// normalization of a number of precision P the exponent is within the range of +/// the format, and if the number is not denormal the P-th bit of the +/// significand is set as an explicit integer bit. For denormals the most +/// significant bit is shifted right so that the exponent is maintained at the +/// format's minimum, so that the smallest denormal has just the least +/// significant bit of the significand set. The sign of zeros and infinities +/// is significant; the exponent and significand of such numbers is not stored, +/// but has a known implicit (deterministic) value: 0 for the significands, 0 +/// for zero exponent, all 1 bits for infinity exponent. For NaNs the sign and +/// significand are deterministic, although not really meaningful, and preserved +/// in non-conversion operations. The exponent is implicitly all 1 bits. +/// +/// `apfloat` does not provide any exception handling beyond default exception +/// handling. We represent Signaling NaNs via IEEE-754R 2008 6.2.1 should clause +/// by encoding Signaling NaNs with the first bit of its trailing significand +/// as 0. +/// +/// Future work +/// =========== +/// +/// Some features that may or may not be worth adding: +/// +/// Optional ability to detect underflow tininess before rounding. +/// +/// New formats: x87 in single and double precision mode (IEEE apart from +/// extended exponent range) (hard). +/// +/// New operations: sqrt, nexttoward. +/// +pub trait Float: + Copy + + Default + + FromStr<Err = ParseError> + + PartialOrd + + fmt::Display + + Neg<Output = Self> + + AddAssign + + SubAssign + + MulAssign + + DivAssign + + RemAssign + + Add<Output = StatusAnd<Self>> + + Sub<Output = StatusAnd<Self>> + + Mul<Output = StatusAnd<Self>> + + Div<Output = StatusAnd<Self>> + + Rem<Output = StatusAnd<Self>> +{ + /// Total number of bits in the in-memory format. + const BITS: usize; + + /// Number of bits in the significand. This includes the integer bit. + const PRECISION: usize; + + /// The largest E such that 2<sup>E</sup> is representable; this matches the + /// definition of IEEE 754. + const MAX_EXP: ExpInt; + + /// The smallest E such that 2<sup>E</sup> is a normalized number; this + /// matches the definition of IEEE 754. + const MIN_EXP: ExpInt; + + /// Positive Zero. + const ZERO: Self; + + /// Positive Infinity. + const INFINITY: Self; + + /// NaN (Not a Number). + // FIXME(eddyb) provide a default when qnan becomes const fn. + const NAN: Self; + + /// Factory for QNaN values. + // FIXME(eddyb) should be const fn. + fn qnan(payload: Option<u128>) -> Self; + + /// Factory for SNaN values. + // FIXME(eddyb) should be const fn. + fn snan(payload: Option<u128>) -> Self; + + /// Largest finite number. + // FIXME(eddyb) should be const (but FloatPair::largest is nontrivial). + fn largest() -> Self; + + /// Smallest (by magnitude) finite number. + /// Might be denormalized, which implies a relative loss of precision. + const SMALLEST: Self; + + /// Smallest (by magnitude) normalized finite number. + // FIXME(eddyb) should be const (but FloatPair::smallest_normalized is nontrivial). + fn smallest_normalized() -> Self; + + // Arithmetic + + fn add_r(self, rhs: Self, round: Round) -> StatusAnd<Self>; + fn sub_r(self, rhs: Self, round: Round) -> StatusAnd<Self> { + self.add_r(-rhs, round) + } + fn mul_r(self, rhs: Self, round: Round) -> StatusAnd<Self>; + fn mul_add_r(self, multiplicand: Self, addend: Self, round: Round) -> StatusAnd<Self>; + fn mul_add(self, multiplicand: Self, addend: Self) -> StatusAnd<Self> { + self.mul_add_r(multiplicand, addend, Round::NearestTiesToEven) + } + fn div_r(self, rhs: Self, round: Round) -> StatusAnd<Self>; + /// IEEE remainder. + // This is not currently correct in all cases. + fn ieee_rem(self, rhs: Self) -> StatusAnd<Self> { + let mut v = self; + + let status; + v = unpack!(status=, v / rhs); + if status == Status::DIV_BY_ZERO { + return status.and(self); + } + + assert!(Self::PRECISION < 128); + + let status; + let x = unpack!(status=, v.to_i128_r(128, Round::NearestTiesToEven, &mut false)); + if status == Status::INVALID_OP { + return status.and(self); + } + + let status; + let mut v = unpack!(status=, Self::from_i128(x)); + assert_eq!(status, Status::OK); // should always work + + let status; + v = unpack!(status=, v * rhs); + assert_eq!(status - Status::INEXACT, Status::OK); // should not overflow or underflow + + let status; + v = unpack!(status=, self - v); + assert_eq!(status - Status::INEXACT, Status::OK); // likewise + + if v.is_zero() { + status.and(v.copy_sign(self)) // IEEE754 requires this + } else { + status.and(v) + } + } + /// C fmod, or llvm frem. + fn c_fmod(self, rhs: Self) -> StatusAnd<Self>; + fn round_to_integral(self, round: Round) -> StatusAnd<Self>; + + /// IEEE-754R 2008 5.3.1: nextUp. + fn next_up(self) -> StatusAnd<Self>; + + /// IEEE-754R 2008 5.3.1: nextDown. + /// + /// *NOTE* since nextDown(x) = -nextUp(-x), we only implement nextUp with + /// appropriate sign switching before/after the computation. + fn next_down(self) -> StatusAnd<Self> { + (-self).next_up().map(|r| -r) + } + + fn abs(self) -> Self { + if self.is_negative() { -self } else { self } + } + fn copy_sign(self, rhs: Self) -> Self { + if self.is_negative() != rhs.is_negative() { -self } else { self } + } + + // Conversions + fn from_bits(input: u128) -> Self; + fn from_i128_r(input: i128, round: Round) -> StatusAnd<Self> { + if input < 0 { + Self::from_u128_r(input.wrapping_neg() as u128, -round).map(|r| -r) + } else { + Self::from_u128_r(input as u128, round) + } + } + fn from_i128(input: i128) -> StatusAnd<Self> { + Self::from_i128_r(input, Round::NearestTiesToEven) + } + fn from_u128_r(input: u128, round: Round) -> StatusAnd<Self>; + fn from_u128(input: u128) -> StatusAnd<Self> { + Self::from_u128_r(input, Round::NearestTiesToEven) + } + fn from_str_r(s: &str, round: Round) -> Result<StatusAnd<Self>, ParseError>; + fn to_bits(self) -> u128; + + /// Converts a floating point number to an integer according to the + /// rounding mode. In case of an invalid operation exception, + /// deterministic values are returned, namely zero for NaNs and the + /// minimal or maximal value respectively for underflow or overflow. + /// If the rounded value is in range but the floating point number is + /// not the exact integer, the C standard doesn't require an inexact + /// exception to be raised. IEEE-854 does require it so we do that. + /// + /// Note that for conversions to integer type the C standard requires + /// round-to-zero to always be used. + /// + /// The *is_exact output tells whether the result is exact, in the sense + /// that converting it back to the original floating point type produces + /// the original value. This is almost equivalent to `result == Status::OK`, + /// except for negative zeroes. + fn to_i128_r(self, width: usize, round: Round, is_exact: &mut bool) -> StatusAnd<i128> { + let status; + if self.is_negative() { + if self.is_zero() { + // Negative zero can't be represented as an int. + *is_exact = false; + } + let r = unpack!(status=, (-self).to_u128_r(width, -round, is_exact)); + + // Check for values that don't fit in the signed integer. + if r > (1 << (width - 1)) { + // Return the most negative integer for the given width. + *is_exact = false; + Status::INVALID_OP.and(-1 << (width - 1)) + } else { + status.and(r.wrapping_neg() as i128) + } + } else { + // Positive case is simpler, can pretend it's a smaller unsigned + // integer, and `to_u128` will take care of all the edge cases. + self.to_u128_r(width - 1, round, is_exact).map(|r| r as i128) + } + } + fn to_i128(self, width: usize) -> StatusAnd<i128> { + self.to_i128_r(width, Round::TowardZero, &mut true) + } + fn to_u128_r(self, width: usize, round: Round, is_exact: &mut bool) -> StatusAnd<u128>; + fn to_u128(self, width: usize) -> StatusAnd<u128> { + self.to_u128_r(width, Round::TowardZero, &mut true) + } + + fn cmp_abs_normal(self, rhs: Self) -> Ordering; + + /// Bitwise comparison for equality (QNaNs compare equal, 0!=-0). + fn bitwise_eq(self, rhs: Self) -> bool; + + // IEEE-754R 5.7.2 General operations. + + /// Implements IEEE minNum semantics. Returns the smaller of the 2 arguments if + /// both are not NaN. If either argument is a NaN, returns the other argument. + fn min(self, other: Self) -> Self { + if self.is_nan() { + other + } else if other.is_nan() { + self + } else if other.partial_cmp(&self) == Some(Ordering::Less) { + other + } else { + self + } + } + + /// Implements IEEE maxNum semantics. Returns the larger of the 2 arguments if + /// both are not NaN. If either argument is a NaN, returns the other argument. + fn max(self, other: Self) -> Self { + if self.is_nan() { + other + } else if other.is_nan() { + self + } else if self.partial_cmp(&other) == Some(Ordering::Less) { + other + } else { + self + } + } + + /// IEEE-754R isSignMinus: Returns whether the current value is + /// negative. + /// + /// This applies to zeros and NaNs as well. + fn is_negative(self) -> bool; + + /// IEEE-754R isNormal: Returns whether the current value is normal. + /// + /// This implies that the current value of the float is not zero, subnormal, + /// infinite, or NaN following the definition of normality from IEEE-754R. + fn is_normal(self) -> bool { + !self.is_denormal() && self.is_finite_non_zero() + } + + /// Returns `true` if the current value is zero, subnormal, or + /// normal. + /// + /// This means that the value is not infinite or NaN. + fn is_finite(self) -> bool { + !self.is_nan() && !self.is_infinite() + } + + /// Returns `true` if the float is plus or minus zero. + fn is_zero(self) -> bool { + self.category() == Category::Zero + } + + /// IEEE-754R isSubnormal(): Returns whether the float is a + /// denormal. + fn is_denormal(self) -> bool; + + /// IEEE-754R isInfinite(): Returns whether the float is infinity. + fn is_infinite(self) -> bool { + self.category() == Category::Infinity + } + + /// Returns `true` if the float is a quiet or signaling NaN. + fn is_nan(self) -> bool { + self.category() == Category::NaN + } + + /// Returns `true` if the float is a signaling NaN. + fn is_signaling(self) -> bool; + + // Simple Queries + + fn category(self) -> Category; + fn is_non_zero(self) -> bool { + !self.is_zero() + } + fn is_finite_non_zero(self) -> bool { + self.is_finite() && !self.is_zero() + } + fn is_pos_zero(self) -> bool { + self.is_zero() && !self.is_negative() + } + fn is_neg_zero(self) -> bool { + self.is_zero() && self.is_negative() + } + + /// Returns `true` if the number has the smallest possible non-zero + /// magnitude in the current semantics. + fn is_smallest(self) -> bool { + Self::SMALLEST.copy_sign(self).bitwise_eq(self) + } + + /// Returns `true` if the number has the largest possible finite + /// magnitude in the current semantics. + fn is_largest(self) -> bool { + Self::largest().copy_sign(self).bitwise_eq(self) + } + + /// Returns `true` if the number is an exact integer. + fn is_integer(self) -> bool { + // This could be made more efficient; I'm going for obviously correct. + if !self.is_finite() { + return false; + } + self.round_to_integral(Round::TowardZero).value.bitwise_eq(self) + } + + /// If this value has an exact multiplicative inverse, return it. + fn get_exact_inverse(self) -> Option<Self>; + + /// Returns the exponent of the internal representation of the Float. + /// + /// Because the radix of Float is 2, this is equivalent to floor(log2(x)). + /// For special Float values, this returns special error codes: + /// + /// NaN -> \c IEK_NAN + /// 0 -> \c IEK_ZERO + /// Inf -> \c IEK_INF + /// + fn ilogb(self) -> ExpInt; + + /// Returns: self * 2<sup>exp</sup> for integral exponents. + /// Equivalent to C standard library function `ldexp`. + fn scalbn_r(self, exp: ExpInt, round: Round) -> Self; + fn scalbn(self, exp: ExpInt) -> Self { + self.scalbn_r(exp, Round::NearestTiesToEven) + } + + /// Equivalent to C standard library function with the same name. + /// + /// While the C standard says exp is an unspecified value for infinity and nan, + /// this returns INT_MAX for infinities, and INT_MIN for NaNs (see `ilogb`). + fn frexp_r(self, exp: &mut ExpInt, round: Round) -> Self; + fn frexp(self, exp: &mut ExpInt) -> Self { + self.frexp_r(exp, Round::NearestTiesToEven) + } +} + +pub trait FloatConvert<T: Float>: Float { + /// Converts a value of one floating point type to another. + /// The return value corresponds to the IEEE754 exceptions. *loses_info + /// records whether the transformation lost information, i.e., whether + /// converting the result back to the original type will produce the + /// original value (this is almost the same as return `value == Status::OK`, + /// but there are edge cases where this is not so). + fn convert_r(self, round: Round, loses_info: &mut bool) -> StatusAnd<T>; + fn convert(self, loses_info: &mut bool) -> StatusAnd<T> { + self.convert_r(Round::NearestTiesToEven, loses_info) + } +} + +macro_rules! float_common_impls { + ($ty:ident<$t:tt>) => { + impl<$t> Default for $ty<$t> + where + Self: Float, + { + fn default() -> Self { + Self::ZERO + } + } + + impl<$t> ::core::str::FromStr for $ty<$t> + where + Self: Float, + { + type Err = ParseError; + fn from_str(s: &str) -> Result<Self, ParseError> { + Self::from_str_r(s, Round::NearestTiesToEven).map(|x| x.value) + } + } + + // Rounding ties to the nearest even, by default. + + impl<$t> ::core::ops::Add for $ty<$t> + where + Self: Float, + { + type Output = StatusAnd<Self>; + fn add(self, rhs: Self) -> StatusAnd<Self> { + self.add_r(rhs, Round::NearestTiesToEven) + } + } + + impl<$t> ::core::ops::Sub for $ty<$t> + where + Self: Float, + { + type Output = StatusAnd<Self>; + fn sub(self, rhs: Self) -> StatusAnd<Self> { + self.sub_r(rhs, Round::NearestTiesToEven) + } + } + + impl<$t> ::core::ops::Mul for $ty<$t> + where + Self: Float, + { + type Output = StatusAnd<Self>; + fn mul(self, rhs: Self) -> StatusAnd<Self> { + self.mul_r(rhs, Round::NearestTiesToEven) + } + } + + impl<$t> ::core::ops::Div for $ty<$t> + where + Self: Float, + { + type Output = StatusAnd<Self>; + fn div(self, rhs: Self) -> StatusAnd<Self> { + self.div_r(rhs, Round::NearestTiesToEven) + } + } + + impl<$t> ::core::ops::Rem for $ty<$t> + where + Self: Float, + { + type Output = StatusAnd<Self>; + fn rem(self, rhs: Self) -> StatusAnd<Self> { + self.c_fmod(rhs) + } + } + + impl<$t> ::core::ops::AddAssign for $ty<$t> + where + Self: Float, + { + fn add_assign(&mut self, rhs: Self) { + *self = (*self + rhs).value; + } + } + + impl<$t> ::core::ops::SubAssign for $ty<$t> + where + Self: Float, + { + fn sub_assign(&mut self, rhs: Self) { + *self = (*self - rhs).value; + } + } + + impl<$t> ::core::ops::MulAssign for $ty<$t> + where + Self: Float, + { + fn mul_assign(&mut self, rhs: Self) { + *self = (*self * rhs).value; + } + } + + impl<$t> ::core::ops::DivAssign for $ty<$t> + where + Self: Float, + { + fn div_assign(&mut self, rhs: Self) { + *self = (*self / rhs).value; + } + } + + impl<$t> ::core::ops::RemAssign for $ty<$t> + where + Self: Float, + { + fn rem_assign(&mut self, rhs: Self) { + *self = (*self % rhs).value; + } + } + }; +} + +pub mod ieee; +pub mod ppc; |