1 // Copyright 2015 The Rust Project Developers. See the COPYRIGHT
2 // file at the top-level directory of this distribution and at
3 // http://rust-lang.org/COPYRIGHT.
5 // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
6 // http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
7 // <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
8 // option. This file may not be copied, modified, or distributed
9 // except according to those terms.
11 //! Converting decimal strings into IEEE 754 binary floating point numbers.
13 //! # Problem statement
15 //! We are given a decimal string such as `12.34e56`. This string consists of integral (`12`),
16 //! fractional (`45`), and exponent (`56`) parts. All parts are optional and interpreted as zero
19 //! We seek the IEEE 754 floating point number that is closest to the exact value of the decimal
20 //! string. It is well-known that many decimal strings do not have terminating representations in
21 //! base two, so we round to 0.5 units in the last place (in other words, as well as possible).
22 //! Ties, decimal values exactly half-way between two consecutive floats, are resolved with the
23 //! half-to-even strategy, also known as banker's rounding.
25 //! Needless to say, this is quite hard, both in terms of implementation complexity and in terms
26 //! of CPU cycles taken.
30 //! First, we ignore signs. Or rather, we remove it at the very beginning of the conversion
31 //! process and re-apply it at the very end. This is correct in all edge cases since IEEE
32 //! floats are symmetric around zero, negating one simply flips the first bit.
34 //! Then we remove the decimal point by adjusting the exponent: Conceptually, `12.34e56` turns
35 //! into `1234e54`, which we describe with a positive integer `f = 1234` and an integer `e = 54`.
36 //! The `(f, e)` representation is used by almost all code past the parsing stage.
38 //! We then try a long chain of progressively more general and expensive special cases using
39 //! machine-sized integers and small, fixed-sized floating point numbers (first `f32`/`f64`, then
40 //! a type with 64 bit significand, `Fp`). When all these fail, we bite the bullet and resort to a
41 //! simple but very slow algorithm that involved computing `f * 10^e` fully and doing an iterative
42 //! search for the best approximation.
44 //! Primarily, this module and its children implement the algorithms described in:
45 //! "How to Read Floating Point Numbers Accurately" by William D. Clinger,
46 //! available online: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.45.4152
48 //! In addition, there are numerous helper functions that are used in the paper but not available
49 //! in Rust (or at least in core). Our version is additionally complicated by the need to handle
50 //! overflow and underflow and the desire to handle subnormal numbers. Bellerophon and
51 //! Algorithm R have trouble with overflow, subnormals, and underflow. We conservatively switch to
52 //! Algorithm M (with the modifications described in section 8 of the paper) well before the
53 //! inputs get into the critical region.
55 //! Another aspect that needs attention is the ``RawFloat`` trait by which almost all functions
56 //! are parametrized. One might think that it's enough to parse to `f64` and cast the result to
57 //! `f32`. Unfortunately this is not the world we live in, and this has nothing to do with using
58 //! base two or half-to-even rounding.
60 //! Consider for example two types `d2` and `d4` representing a decimal type with two decimal
61 //! digits and four decimal digits each and take "0.01499" as input. Let's use half-up rounding.
62 //! Going directly to two decimal digits gives `0.01`, but if we round to four digits first,
63 //! we get `0.0150`, which is then rounded up to `0.02`. The same principle applies to other
64 //! operations as well, if you want 0.5 ULP accuracy you need to do *everything* in full precision
65 //! and round *exactly once, at the end*, by considering all truncated bits at once.
67 //! FIXME Although some code duplication is necessary, perhaps parts of the code could be shuffled
68 //! around such that less code is duplicated. Large parts of the algorithms are independent of the
69 //! float type to output, or only needs access to a few constants, which could be passed in as
74 //! The conversion should *never* panic. There are assertions and explicit panics in the code,
75 //! but they should never be triggered and only serve as internal sanity checks. Any panics should
76 //! be considered a bug.
78 //! There are unit tests but they are woefully inadequate at ensuring correctness, they only cover
79 //! a small percentage of possible errors. Far more extensive tests are located in the directory
80 //! `src/etc/test-float-parse` as a Python script.
82 //! A note on integer overflow: Many parts of this file perform arithmetic with the decimal
83 //! exponent `e`. Primarily, we shift the decimal point around: Before the first decimal digit,
84 //! after the last decimal digit, and so on. This could overflow if done carelessly. We rely on
85 //! the parsing submodule to only hand out sufficiently small exponents, where "sufficient" means
86 //! "such that the exponent +/- the number of decimal digits fits into a 64 bit integer".
87 //! Larger exponents are accepted, but we don't do arithmetic with them, they are immediately
88 //! turned into {positive,negative} {zero,infinity}.
90 //! FIXME: this uses several things from core::num::flt2dec, which is nonsense. Those things
91 //! should be moved into core::num::<something else>.
94 #![unstable(feature = "dec2flt",
95 reason
= "internal routines only exposed for testing",
102 use self::parse
::{parse_decimal, Decimal, Sign}
;
103 use self::parse
::ParseResult
::{self, Valid, ShortcutToInf, ShortcutToZero}
;
104 use self::num
::digits_to_big
;
105 use self::rawfp
::RawFloat
;
110 // These two have their own tests.
114 macro_rules
! from_str_float_impl
{
115 ($t
:ty
, $func
:ident
) => {
116 #[stable(feature = "rust1", since = "1.0.0")]
117 impl FromStr
for $t
{
118 type Err
= ParseFloatError
;
120 /// Converts a string in base 10 to a float.
121 /// Accepts an optional decimal exponent.
123 /// This function accepts strings such as
127 /// * '2.5E10', or equivalently, '2.5e10'
129 /// * '.' (understood as 0)
131 /// * '.5', or, equivalently, '0.5'
132 /// * 'inf', '-inf', 'NaN'
134 /// Leading and trailing whitespace represent an error.
142 /// `Err(ParseFloatError)` if the string did not represent a valid
143 /// number. Otherwise, `Ok(n)` where `n` is the floating-point
144 /// number represented by `src`.
146 fn from_str(src
: &str) -> Result
<Self, ParseFloatError
> {
152 from_str_float_impl
!(f32, to_f32
);
153 from_str_float_impl
!(f64, to_f64
);
155 /// An error which can be returned when parsing a float.
156 #[derive(Debug, Clone, PartialEq)]
157 #[stable(feature = "rust1", since = "1.0.0")]
158 pub struct ParseFloatError
{
162 #[derive(Debug, Clone, PartialEq)]
163 enum FloatErrorKind
{
168 impl ParseFloatError
{
169 #[unstable(feature = "int_error_internals",
170 reason
= "available through Error trait and this method should \
171 not be exposed publicly",
174 pub fn __description(&self) -> &str {
176 FloatErrorKind
::Empty
=> "cannot parse float from empty string",
177 FloatErrorKind
::Invalid
=> "invalid float literal",
182 #[stable(feature = "rust1", since = "1.0.0")]
183 impl fmt
::Display
for ParseFloatError
{
184 fn fmt(&self, f
: &mut fmt
::Formatter
) -> fmt
::Result
{
185 self.__description().fmt(f
)
189 pub fn pfe_empty() -> ParseFloatError
{
190 ParseFloatError { kind: FloatErrorKind::Empty }
193 pub fn pfe_invalid() -> ParseFloatError
{
194 ParseFloatError { kind: FloatErrorKind::Invalid }
197 /// Split decimal string into sign and the rest, without inspecting or validating the rest.
198 fn extract_sign(s
: &str) -> (Sign
, &str) {
199 match s
.as_bytes()[0] {
200 b'
+'
=> (Sign
::Positive
, &s
[1..]),
201 b'
-'
=> (Sign
::Negative
, &s
[1..]),
202 // If the string is invalid, we never use the sign, so we don't need to validate here.
203 _
=> (Sign
::Positive
, s
),
207 /// Convert a decimal string into a floating point number.
208 fn dec2flt
<T
: RawFloat
>(s
: &str) -> Result
<T
, ParseFloatError
> {
210 return Err(pfe_empty())
212 let (sign
, s
) = extract_sign(s
);
213 let flt
= match parse_decimal(s
) {
214 Valid(decimal
) => try
!(convert(decimal
)),
215 ShortcutToInf
=> T
::infinity(),
216 ShortcutToZero
=> T
::zero(),
217 ParseResult
::Invalid
=> match s
{
218 "inf" => T
::infinity(),
220 _
=> { return Err(pfe_invalid()); }
225 Sign
::Positive
=> Ok(flt
),
226 Sign
::Negative
=> Ok(-flt
),
230 /// The main workhorse for the decimal-to-float conversion: Orchestrate all the preprocessing
231 /// and figure out which algorithm should do the actual conversion.
232 fn convert
<T
: RawFloat
>(mut decimal
: Decimal
) -> Result
<T
, ParseFloatError
> {
233 simplify(&mut decimal
);
234 if let Some(x
) = trivial_cases(&decimal
) {
237 // AlgorithmM and AlgorithmR both compute approximately `f * 10^e`.
238 let max_digits
= decimal
.integral
.len() + decimal
.fractional
.len() +
239 decimal
.exp
.abs() as usize;
240 // Remove/shift out the decimal point.
241 let e
= decimal
.exp
- decimal
.fractional
.len() as i64;
242 if let Some(x
) = algorithm
::fast_path(decimal
.integral
, decimal
.fractional
, e
) {
245 // Big32x40 is limited to 1280 bits, which translates to about 385 decimal digits.
246 // If we exceed this, perhaps while calculating `f * 10^e` in Algorithm R or Algorithm M,
247 // we'll crash. So we error out before getting too close, with a generous safety margin.
248 if max_digits
> 375 {
249 return Err(pfe_invalid());
251 let f
= digits_to_big(decimal
.integral
, decimal
.fractional
);
253 // Now the exponent certainly fits in 16 bit, which is used throughout the main algorithms.
255 // FIXME These bounds are rather conservative. A more careful analysis of the failure modes
256 // of Bellerophon could allow using it in more cases for a massive speed up.
257 let exponent_in_range
= table
::MIN_E
<= e
&& e
<= table
::MAX_E
;
258 let value_in_range
= max_digits
<= T
::max_normal_digits();
259 if exponent_in_range
&& value_in_range
{
260 Ok(algorithm
::bellerophon(&f
, e
))
262 Ok(algorithm
::algorithm_m(&f
, e
))
266 // As written, this optimizes badly (see #27130, though it refers to an old version of the code).
267 // `inline(always)` is a workaround for that. There are only two call sites overall and it doesn't
268 // make code size worse.
270 /// Strip zeros where possible, even when this requires changing the exponent
272 fn simplify(decimal
: &mut Decimal
) {
273 let is_zero
= &|&&d
: &&u8| -> bool { d == b'0' }
;
274 // Trimming these zeros does not change anything but may enable the fast path (< 15 digits).
275 let leading_zeros
= decimal
.integral
.iter().take_while(is_zero
).count();
276 decimal
.integral
= &decimal
.integral
[leading_zeros
..];
277 let trailing_zeros
= decimal
.fractional
.iter().rev().take_while(is_zero
).count();
278 let end
= decimal
.fractional
.len() - trailing_zeros
;
279 decimal
.fractional
= &decimal
.fractional
[..end
];
280 // Simplify numbers of the form 0.0...x and x...0.0, adjusting the exponent accordingly.
281 // This may not always be a win (possibly pushes some numbers out of the fast path), but it
282 // simplifies other parts significantly (notably, approximating the magnitude of the value).
283 if decimal
.integral
.is_empty() {
284 let leading_zeros
= decimal
.fractional
.iter().take_while(is_zero
).count();
285 decimal
.fractional
= &decimal
.fractional
[leading_zeros
..];
286 decimal
.exp
-= leading_zeros
as i64;
287 } else if decimal
.fractional
.is_empty() {
288 let trailing_zeros
= decimal
.integral
.iter().rev().take_while(is_zero
).count();
289 let end
= decimal
.integral
.len() - trailing_zeros
;
290 decimal
.integral
= &decimal
.integral
[..end
];
291 decimal
.exp
+= trailing_zeros
as i64;
295 /// Detect obvious overflows and underflows without even looking at the decimal digits.
296 fn trivial_cases
<T
: RawFloat
>(decimal
: &Decimal
) -> Option
<T
> {
297 // There were zeros but they were stripped by simplify()
298 if decimal
.integral
.is_empty() && decimal
.fractional
.is_empty() {
299 return Some(T
::zero());
301 // This is a crude approximation of ceil(log10(the real value)).
302 let max_place
= decimal
.exp
+ decimal
.integral
.len() as i64;
303 if max_place
> T
::inf_cutoff() {
304 return Some(T
::infinity());
305 } else if max_place
< T
::zero_cutoff() {
306 return Some(T
::zero());