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//! Converting decimal strings into IEEE 754 binary floating point numbers. //! //! # Problem statement //! //! We are given a decimal string such as `12.34e56`. This string consists of integral (`12`), //! fractional (`34`), and exponent (`56`) parts. All parts are optional and interpreted as zero //! when missing. //! //! We seek the IEEE 754 floating point number that is closest to the exact value of the decimal //! string. It is well-known that many decimal strings do not have terminating representations in //! base two, so we round to 0.5 units in the last place (in other words, as well as possible). //! Ties, decimal values exactly half-way between two consecutive floats, are resolved with the //! half-to-even strategy, also known as banker's rounding. //! //! Needless to say, this is quite hard, both in terms of implementation complexity and in terms //! of CPU cycles taken. //! //! # Implementation //! //! First, we ignore signs. Or rather, we remove it at the very beginning of the conversion //! process and re-apply it at the very end. This is correct in all edge cases since IEEE //! floats are symmetric around zero, negating one simply flips the first bit. //! //! Then we remove the decimal point by adjusting the exponent: Conceptually, `12.34e56` turns //! into `1234e54`, which we describe with a positive integer `f = 1234` and an integer `e = 54`. //! The `(f, e)` representation is used by almost all code past the parsing stage. //! //! We then try a long chain of progressively more general and expensive special cases using //! machine-sized integers and small, fixed-sized floating point numbers (first `f32`/`f64`, then //! a type with 64 bit significand). The extended-precision algorithm //! uses the Eisel-Lemire algorithm, which uses a 128-bit (or 192-bit) //! representation that can accurately and quickly compute the vast majority //! of floats. When all these fail, we bite the bullet and resort to using //! a large-decimal representation, shifting the digits into range, calculating //! the upper significant bits and exactly round to the nearest representation. //! //! Another aspect that needs attention is the ``RawFloat`` trait by which almost all functions //! are parametrized. One might think that it's enough to parse to `f64` and cast the result to //! `f32`. Unfortunately this is not the world we live in, and this has nothing to do with using //! base two or half-to-even rounding. //! //! Consider for example two types `d2` and `d4` representing a decimal type with two decimal //! digits and four decimal digits each and take "0.01499" as input. Let's use half-up rounding. //! Going directly to two decimal digits gives `0.01`, but if we round to four digits first, //! we get `0.0150`, which is then rounded up to `0.02`. The same principle applies to other //! operations as well, if you want 0.5 ULP accuracy you need to do *everything* in full precision //! and round *exactly once, at the end*, by considering all truncated bits at once. //! //! Primarily, this module and its children implement the algorithms described in: //! "Number Parsing at a Gigabyte per Second", available online: //! <https://arxiv.org/abs/2101.11408>. //! //! # Other //! //! The conversion should *never* panic. There are assertions and explicit panics in the code, //! but they should never be triggered and only serve as internal sanity checks. Any panics should //! be considered a bug. //! //! There are unit tests but they are woefully inadequate at ensuring correctness, they only cover //! a small percentage of possible errors. Far more extensive tests are located in the directory //! `src/etc/test-float-parse` as a Python script. //! //! A note on integer overflow: Many parts of this file perform arithmetic with the decimal //! exponent `e`. Primarily, we shift the decimal point around: Before the first decimal digit, //! after the last decimal digit, and so on. This could overflow if done carelessly. We rely on //! the parsing submodule to only hand out sufficiently small exponents, where "sufficient" means //! "such that the exponent +/- the number of decimal digits fits into a 64 bit integer". //! Larger exponents are accepted, but we don't do arithmetic with them, they are immediately //! turned into {positive,negative} {zero,infinity}. #![doc(hidden)] #![unstable( feature = "dec2flt", reason = "internal routines only exposed for testing", issue = "none" )] use crate::fmt; use crate::str::FromStr; use self::common::{BiasedFp, ByteSlice}; use self::float::RawFloat; use self::lemire::compute_float; use self::parse::{parse_inf_nan, parse_number}; use self::slow::parse_long_mantissa; mod common; mod decimal; mod fpu; mod slow; mod table; // float is used in flt2dec, and all are used in unit tests. pub mod float; pub mod lemire; pub mod number; pub mod parse; macro_rules! from_str_float_impl { ($t:ty) => { #[stable(feature = "rust1", since = "1.0.0")] impl FromStr for $t { type Err = ParseFloatError; /// Converts a string in base 10 to a float. /// Accepts an optional decimal exponent. /// /// This function accepts strings such as /// /// * '3.14' /// * '-3.14' /// * '2.5E10', or equivalently, '2.5e10' /// * '2.5E-10' /// * '5.' /// * '.5', or, equivalently, '0.5' /// * 'inf', '-inf', 'NaN' /// /// Leading and trailing whitespace represent an error. /// /// # Grammar /// /// All strings that adhere to the following [EBNF] grammar /// will result in an [`Ok`] being returned: /// /// ```txt /// Float ::= Sign? ( 'inf' | 'NaN' | Number ) /// Number ::= ( Digit+ | /// Digit+ '.' Digit* | /// Digit* '.' Digit+ ) Exp? /// Exp ::= [eE] Sign? Digit+ /// Sign ::= [+-] /// Digit ::= [0-9] /// ``` /// /// [EBNF]: https://www.w3.org/TR/REC-xml/#sec-notation /// /// # Arguments /// /// * src - A string /// /// # Return value /// /// `Err(ParseFloatError)` if the string did not represent a valid /// number. Otherwise, `Ok(n)` where `n` is the floating-point /// number represented by `src`. #[inline] fn from_str(src: &str) -> Result<Self, ParseFloatError> { dec2flt(src) } } }; } from_str_float_impl!(f32); from_str_float_impl!(f64); /// An error which can be returned when parsing a float. /// /// This error is used as the error type for the [`FromStr`] implementation /// for [`f32`] and [`f64`]. /// /// # Example /// /// ``` /// use std::str::FromStr; /// /// if let Err(e) = f64::from_str("a.12") { /// println!("Failed conversion to f64: {}", e); /// } /// ``` #[derive(Debug, Clone, PartialEq, Eq)] #[stable(feature = "rust1", since = "1.0.0")] pub struct ParseFloatError { kind: FloatErrorKind, } #[derive(Debug, Clone, PartialEq, Eq)] enum FloatErrorKind { Empty, Invalid, } impl ParseFloatError { #[unstable( feature = "int_error_internals", reason = "available through Error trait and this method should \ not be exposed publicly", issue = "none" )] #[doc(hidden)] pub fn __description(&self) -> &str { match self.kind { FloatErrorKind::Empty => "cannot parse float from empty string", FloatErrorKind::Invalid => "invalid float literal", } } } #[stable(feature = "rust1", since = "1.0.0")] impl fmt::Display for ParseFloatError { fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { self.__description().fmt(f) } } pub(super) fn pfe_empty() -> ParseFloatError { ParseFloatError { kind: FloatErrorKind::Empty } } // Used in unit tests, keep public. // This is much better than making FloatErrorKind and ParseFloatError::kind public. pub fn pfe_invalid() -> ParseFloatError { ParseFloatError { kind: FloatErrorKind::Invalid } } /// Converts a `BiasedFp` to the closest machine float type. fn biased_fp_to_float<T: RawFloat>(x: BiasedFp) -> T { let mut word = x.f; word |= (x.e as u64) << T::MANTISSA_EXPLICIT_BITS; T::from_u64_bits(word) } /// Converts a decimal string into a floating point number. pub fn dec2flt<F: RawFloat>(s: &str) -> Result<F, ParseFloatError> { let mut s = s.as_bytes(); let c = if let Some(&c) = s.first() { c } else { return Err(pfe_empty()); }; let negative = c == b'-'; if c == b'-' || c == b'+' { s = s.advance(1); } if s.is_empty() { return Err(pfe_invalid()); } let num = match parse_number(s, negative) { Some(r) => r, None => { if let Some(value) = parse_inf_nan(s, negative) { return Ok(value); } else { return Err(pfe_invalid()); } } }; if let Some(value) = num.try_fast_path::<F>() { return Ok(value); } // If significant digits were truncated, then we can have rounding error // only if `mantissa + 1` produces a different result. We also avoid // redundantly using the Eisel-Lemire algorithm if it was unable to // correctly round on the first pass. let mut fp = compute_float::<F>(num.exponent, num.mantissa); if num.many_digits && fp.e >= 0 && fp != compute_float::<F>(num.exponent, num.mantissa + 1) { fp.e = -1; } // Unable to correctly round the float using the Eisel-Lemire algorithm. // Fallback to a slower, but always correct algorithm. if fp.e < 0 { fp = parse_long_mantissa::<F>(s); } let mut float = biased_fp_to_float::<F>(fp); if num.negative { float = -float; } Ok(float) }