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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', '+infinity', 'NaN'
///
/// Note that alphabetical characters are not case-sensitive.
///
/// Leading and trailing whitespace represent an error.
///
/// # Grammar
///
/// All strings that adhere to the following [EBNF] grammar when
/// lowercased will result in an [`Ok`] being returned:
///
/// ```txt
/// Float ::= Sign? ( 'inf' | 'infinity' | 'nan' | Number )
/// Number ::= ( Digit+ |
/// '.' Digit* |
/// Digit+ '.' Digit* |
/// Digit* '.' Digit+ ) Exp?
/// Exp ::= 'e' 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),
None => 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)
}
```