1//! Converting decimal strings into IEEE 754 binary floating point numbers.
2//!
3//! # Problem statement
4//!
5//! We are given a decimal string such as `12.34e56`. This string consists of integral (`12`),
6//! fractional (`34`), and exponent (`56`) parts. All parts are optional and interpreted as a
7//! default value (1 or 0) when missing.
8//!
9//! We seek the IEEE 754 floating point number that is closest to the exact value of the decimal
10//! string. It is well-known that many decimal strings do not have terminating representations in
11//! base two, so we round to 0.5 units in the last place (in other words, as well as possible).
12//! Ties, decimal values exactly half-way between two consecutive floats, are resolved with the
13//! half-to-even strategy, also known as banker's rounding.
14//!
15//! Needless to say, this is quite hard, both in terms of implementation complexity and in terms
16//! of CPU cycles taken.
17//!
18//! # Implementation
19//!
20//! First, we ignore signs. Or rather, we remove it at the very beginning of the conversion
21//! process and re-apply it at the very end. This is correct in all edge cases since IEEE
22//! floats are symmetric around zero, negating one simply flips the first bit.
23//!
24//! Then we remove the decimal point by adjusting the exponent: Conceptually, `12.34e56` turns
25//! into `1234e54`, which we describe with a positive integer `f = 1234` and an integer `e = 54`.
26//! The `(f, e)` representation is used by almost all code past the parsing stage.
27//!
28//! We then try a long chain of progressively more general and expensive special cases using
29//! machine-sized integers and small, fixed-sized floating point numbers (first `f32`/`f64`, then
30//! a type with 64 bit significand). The extended-precision algorithm
31//! uses the Eisel-Lemire algorithm, which uses a 128-bit (or 192-bit)
32//! representation that can accurately and quickly compute the vast majority
33//! of floats. When all these fail, we bite the bullet and resort to using
34//! a large-decimal representation, shifting the digits into range, calculating
35//! the upper significant bits and exactly round to the nearest representation.
36//!
37//! Another aspect that needs attention is the ``RawFloat`` trait by which almost all functions
38//! are parametrized. One might think that it's enough to parse to `f64` and cast the result to
39//! `f32`. Unfortunately this is not the world we live in, and this has nothing to do with using
40//! base two or half-to-even rounding.
41//!
42//! Consider for example two types `d2` and `d4` representing a decimal type with two decimal
43//! digits and four decimal digits each and take "0.01499" as input. Let's use half-up rounding.
44//! Going directly to two decimal digits gives `0.01`, but if we round to four digits first,
45//! we get `0.0150`, which is then rounded up to `0.02`. The same principle applies to other
46//! operations as well, if you want 0.5 ULP accuracy you need to do *everything* in full precision
47//! and round *exactly once, at the end*, by considering all truncated bits at once.
48//!
49//! Primarily, this module and its children implement the algorithms described in:
50//! "Number Parsing at a Gigabyte per Second", available online:
51//! <https://arxiv.org/abs/2101.11408>.
52//!
53//! # Other
54//!
55//! The conversion should *never* panic. There are assertions and explicit panics in the code,
56//! but they should never be triggered and only serve as internal sanity checks. Any panics should
57//! be considered a bug.
58//!
59//! There are unit tests but they are woefully inadequate at ensuring correctness, they only cover
60//! a small percentage of possible errors. Far more extensive tests are located in the directory
61//! `src/tools/test-float-parse` as a Rust program.
62//!
63//! A note on integer overflow: Many parts of this file perform arithmetic with the decimal
64//! exponent `e`. Primarily, we shift the decimal point around: Before the first decimal digit,
65//! after the last decimal digit, and so on. This could overflow if done carelessly. We rely on
66//! the parsing submodule to only hand out sufficiently small exponents, where "sufficient" means
67//! "such that the exponent +/- the number of decimal digits fits into a 64 bit integer".
68//! Larger exponents are accepted, but we don't do arithmetic with them, they are immediately
69//! turned into {positive,negative} {zero,infinity}.
70//!
71//! # Notation
72//!
73//! This module uses the same notation as the Lemire paper:
74//!
75//! - `m`: binary mantissa; always nonnegative
76//! - `p`: binary exponent; a signed integer
77//! - `w`: decimal significand; always nonnegative
78//! - `q`: decimal exponent; a signed integer
79//!
80//! This gives `m * 2^p` for the binary floating-point number, with `w * 10^q` as the decimal
81//! equivalent.
82
83#![doc(hidden)]
84#![unstable(
85 feature = "dec2flt",
86 reason = "internal routines only exposed for testing",
87 issue = "none"
88)]
89
90use self::common::BiasedFp;
91use self::float::RawFloat;
92use self::lemire::compute_float;
93use self::parse::{parse_inf_nan, parse_number};
94use self::slow::parse_long_mantissa;
95use crate::error::Error;
96use crate::fmt;
97use crate::str::FromStr;
98
99mod common;
100pub mod decimal;
101pub mod decimal_seq;
102mod fpu;
103mod slow;
104mod table;
105// float is used in flt2dec, and all are used in unit tests.
106pub mod float;
107pub mod lemire;
108pub mod parse;
109
110macro_rules! from_str_float_impl {
111 ($t:ty) => {
112 #[stable(feature = "rust1", since = "1.0.0")]
113 impl FromStr for $t {
114 type Err = ParseFloatError;
115
116 /// Converts a string in base 10 to a float.
117 /// Accepts an optional decimal exponent.
118 ///
119 /// This function accepts strings such as
120 ///
121 /// * '3.14'
122 /// * '-3.14'
123 /// * '2.5E10', or equivalently, '2.5e10'
124 /// * '2.5E-10'
125 /// * '5.'
126 /// * '.5', or, equivalently, '0.5'
127 /// * 'inf', '-inf', '+infinity', 'NaN'
128 ///
129 /// Note that alphabetical characters are not case-sensitive.
130 ///
131 /// Leading and trailing whitespace represent an error.
132 ///
133 /// # Grammar
134 ///
135 /// All strings that adhere to the following [EBNF] grammar when
136 /// lowercased will result in an [`Ok`] being returned:
137 ///
138 /// ```txt
139 /// Float ::= Sign? ( 'inf' | 'infinity' | 'nan' | Number )
140 /// Number ::= ( Digit+ |
141 /// Digit+ '.' Digit* |
142 /// Digit* '.' Digit+ ) Exp?
143 /// Exp ::= 'e' Sign? Digit+
144 /// Sign ::= [+-]
145 /// Digit ::= [0-9]
146 /// ```
147 ///
148 /// [EBNF]: https://www.w3.org/TR/REC-xml/#sec-notation
149 ///
150 /// # Arguments
151 ///
152 /// * src - A string
153 ///
154 /// # Return value
155 ///
156 /// `Err(ParseFloatError)` if the string did not represent a valid
157 /// number. Otherwise, `Ok(n)` where `n` is the closest
158 /// representable floating-point number to the number represented
159 /// by `src` (following the same rules for rounding as for the
160 /// results of primitive operations).
161 // We add the `#[inline(never)]` attribute, since its content will
162 // be filled with that of `dec2flt`, which has #[inline(always)].
163 // Since `dec2flt` is generic, a normal inline attribute on this function
164 // with `dec2flt` having no attributes results in heavily repeated
165 // generation of `dec2flt`, despite the fact only a maximum of 2
166 // possible instances can ever exist. Adding #[inline(never)] avoids this.
167 #[inline(never)]
168 fn from_str(src: &str) -> Result<Self, ParseFloatError> {
169 dec2flt(src)
170 }
171 }
172 };
173}
174
175#[cfg(target_has_reliable_f16)]
176from_str_float_impl!(f16);
177from_str_float_impl!(f32);
178from_str_float_impl!(f64);
179
180// FIXME(f16_f128): A fallback is used when the backend+target does not support f16 well, in order
181// to avoid ICEs.
182
183#[cfg(not(target_has_reliable_f16))]
184impl FromStr for f16 {
185 type Err = ParseFloatError;
186
187 #[inline]
188 fn from_str(_src: &str) -> Result<Self, ParseFloatError> {
189 unimplemented!("requires target_has_reliable_f16")
190 }
191}
192
193/// An error which can be returned when parsing a float.
194///
195/// This error is used as the error type for the [`FromStr`] implementation
196/// for [`f32`] and [`f64`].
197///
198/// # Example
199///
200/// ```
201/// use std::str::FromStr;
202///
203/// if let Err(e) = f64::from_str("a.12") {
204/// println!("Failed conversion to f64: {e}");
205/// }
206/// ```
207#[derive(Debug, Clone, PartialEq, Eq)]
208#[stable(feature = "rust1", since = "1.0.0")]
209pub struct ParseFloatError {
210 kind: FloatErrorKind,
211}
212
213#[derive(Debug, Clone, PartialEq, Eq)]
214enum FloatErrorKind {
215 Empty,
216 Invalid,
217}
218
219#[stable(feature = "rust1", since = "1.0.0")]
220impl Error for ParseFloatError {
221 #[allow(deprecated)]
222 fn description(&self) -> &str {
223 match self.kind {
224 FloatErrorKind::Empty => "cannot parse float from empty string",
225 FloatErrorKind::Invalid => "invalid float literal",
226 }
227 }
228}
229
230#[stable(feature = "rust1", since = "1.0.0")]
231impl fmt::Display for ParseFloatError {
232 fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
233 #[allow(deprecated)]
234 self.description().fmt(f)
235 }
236}
237
238#[inline]
239pub(super) fn pfe_empty() -> ParseFloatError {
240 ParseFloatError { kind: FloatErrorKind::Empty }
241}
242
243// Used in unit tests, keep public.
244// This is much better than making FloatErrorKind and ParseFloatError::kind public.
245#[inline]
246pub fn pfe_invalid() -> ParseFloatError {
247 ParseFloatError { kind: FloatErrorKind::Invalid }
248}
249
250/// Converts a `BiasedFp` to the closest machine float type.
251fn biased_fp_to_float<F: RawFloat>(x: BiasedFp) -> F {
252 let mut word: u64 = x.m;
253 word |= (x.p_biased as u64) << F::SIG_BITS;
254 F::from_u64_bits(word)
255}
256
257/// Converts a decimal string into a floating point number.
258#[inline(always)] // Will be inlined into a function with `#[inline(never)]`, see above
259pub fn dec2flt<F: RawFloat>(s: &str) -> Result<F, ParseFloatError> {
260 let mut s = s.as_bytes();
261 let c = if let Some(&c) = s.first() {
262 c
263 } else {
264 return Err(pfe_empty());
265 };
266 let negative = c == b'-';
267 if c == b'-' || c == b'+' {
268 s = &s[1..];
269 }
270 if s.is_empty() {
271 return Err(pfe_invalid());
272 }
273
274 let mut num = match parse_number(s) {
275 Some(r) => r,
276 None if let Some(value) = parse_inf_nan(s, negative) => return Ok(value),
277 None => return Err(pfe_invalid()),
278 };
279 num.negative = negative;
280 if !cfg!(feature = "optimize_for_size") {
281 if let Some(value) = num.try_fast_path::<F>() {
282 return Ok(value);
283 }
284 }
285
286 // If significant digits were truncated, then we can have rounding error
287 // only if `mantissa + 1` produces a different result. We also avoid
288 // redundantly using the Eisel-Lemire algorithm if it was unable to
289 // correctly round on the first pass.
290 let mut fp = compute_float::<F>(num.exponent, num.mantissa);
291 if num.many_digits
292 && fp.p_biased >= 0
293 && fp != compute_float::<F>(num.exponent, num.mantissa + 1)
294 {
295 fp.p_biased = -1;
296 }
297 // Unable to correctly round the float using the Eisel-Lemire algorithm.
298 // Fallback to a slower, but always correct algorithm.
299 if fp.p_biased < 0 {
300 fp = parse_long_mantissa::<F>(s);
301 }
302
303 let mut float = biased_fp_to_float::<F>(fp);
304 if num.negative {
305 float = -float;
306 }
307 Ok(float)
308}
309