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authorpravic <[email protected]>2016-04-12 17:47:49 +0300
committerpravic <[email protected]>2016-04-12 17:47:49 +0300
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parentadd native import libraries (diff)
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+// Copyright 2015 The Rust Project Developers. See the COPYRIGHT
+// file at the top-level directory of this distribution and at
+// http://rust-lang.org/COPYRIGHT.
+//
+// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
+// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
+// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
+// option. This file may not be copied, modified, or distributed
+// except according to those terms.
+
+//! 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 (`45`), 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, `Fp`). When all these fail, we bite the bullet and resort to a
+//! simple but very slow algorithm that involved computing `f * 10^e` fully and doing an iterative
+//! search for the best approximation.
+//!
+//! Primarily, this module and its children implement the algorithms described in:
+//! "How to Read Floating Point Numbers Accurately" by William D. Clinger,
+//! available online: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.45.4152
+//!
+//! In addition, there are numerous helper functions that are used in the paper but not available
+//! in Rust (or at least in core). Our version is additionally complicated by the need to handle
+//! overflow and underflow and the desire to handle subnormal numbers. Bellerophon and
+//! Algorithm R have trouble with overflow, subnormals, and underflow. We conservatively switch to
+//! Algorithm M (with the modifications described in section 8 of the paper) well before the
+//! inputs get into the critical region.
+//!
+//! 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.
+//!
+//! FIXME Although some code duplication is necessary, perhaps parts of the code could be shuffled
+//! around such that less code is duplicated. Large parts of the algorithms are independent of the
+//! float type to output, or only needs access to a few constants, which could be passed in as
+//! parameters.
+//!
+//! # 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 = "0")]
+
+use prelude::v1::*;
+use fmt;
+use str::FromStr;
+
+use self::parse::{parse_decimal, Decimal, Sign, ParseResult};
+use self::num::digits_to_big;
+use self::rawfp::RawFloat;
+
+mod algorithm;
+mod table;
+mod num;
+// These two have their own tests.
+pub mod rawfp;
+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'
+ /// * '.' (understood as 0)
+ /// * '5.'
+ /// * '.5', or, equivalently, '0.5'
+ /// * 'inf', '-inf', 'NaN'
+ ///
+ /// Leading and trailing whitespace represent an error.
+ ///
+ /// # 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`].
+///
+/// [`FromStr`]: ../str/trait.FromStr.html
+/// [`f32`]: ../../std/primitive.f32.html
+/// [`f64`]: ../../std/primitive.f64.html
+#[derive(Debug, Clone, PartialEq)]
+#[stable(feature = "rust1", since = "1.0.0")]
+pub struct ParseFloatError {
+ kind: FloatErrorKind
+}
+
+#[derive(Debug, Clone, PartialEq)]
+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 = "0")]
+ #[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)
+ }
+}
+
+fn pfe_empty() -> ParseFloatError {
+ ParseFloatError { kind: FloatErrorKind::Empty }
+}
+
+fn pfe_invalid() -> ParseFloatError {
+ ParseFloatError { kind: FloatErrorKind::Invalid }
+}
+
+/// Split decimal string into sign and the rest, without inspecting or validating the rest.
+fn extract_sign(s: &str) -> (Sign, &str) {
+ match s.as_bytes()[0] {
+ b'+' => (Sign::Positive, &s[1..]),
+ b'-' => (Sign::Negative, &s[1..]),
+ // If the string is invalid, we never use the sign, so we don't need to validate here.
+ _ => (Sign::Positive, s),
+ }
+}
+
+/// Convert a decimal string into a floating point number.
+fn dec2flt<T: RawFloat>(s: &str) -> Result<T, ParseFloatError> {
+ if s.is_empty() {
+ return Err(pfe_empty())
+ }
+ let (sign, s) = extract_sign(s);
+ let flt = match parse_decimal(s) {
+ ParseResult::Valid(decimal) => convert(decimal)?,
+ ParseResult::ShortcutToInf => T::infinity(),
+ ParseResult::ShortcutToZero => T::zero(),
+ ParseResult::Invalid => match s {
+ "inf" => T::infinity(),
+ "NaN" => T::nan(),
+ _ => { return Err(pfe_invalid()); }
+ }
+ };
+
+ match sign {
+ Sign::Positive => Ok(flt),
+ Sign::Negative => Ok(-flt),
+ }
+}
+
+/// The main workhorse for the decimal-to-float conversion: Orchestrate all the preprocessing
+/// and figure out which algorithm should do the actual conversion.
+fn convert<T: RawFloat>(mut decimal: Decimal) -> Result<T, ParseFloatError> {
+ simplify(&mut decimal);
+ if let Some(x) = trivial_cases(&decimal) {
+ return Ok(x);
+ }
+ // Remove/shift out the decimal point.
+ let e = decimal.exp - decimal.fractional.len() as i64;
+ if let Some(x) = algorithm::fast_path(decimal.integral, decimal.fractional, e) {
+ return Ok(x);
+ }
+ // Big32x40 is limited to 1280 bits, which translates to about 385 decimal digits.
+ // If we exceed this, we'll crash, so we error out before getting too close (within 10^10).
+ let upper_bound = bound_intermediate_digits(&decimal, e);
+ if upper_bound > 375 {
+ return Err(pfe_invalid());
+ }
+ let f = digits_to_big(decimal.integral, decimal.fractional);
+
+ // Now the exponent certainly fits in 16 bit, which is used throughout the main algorithms.
+ let e = e as i16;
+ // FIXME These bounds are rather conservative. A more careful analysis of the failure modes
+ // of Bellerophon could allow using it in more cases for a massive speed up.
+ let exponent_in_range = table::MIN_E <= e && e <= table::MAX_E;
+ let value_in_range = upper_bound <= T::max_normal_digits() as u64;
+ if exponent_in_range && value_in_range {
+ Ok(algorithm::bellerophon(&f, e))
+ } else {
+ Ok(algorithm::algorithm_m(&f, e))
+ }
+}
+
+// As written, this optimizes badly (see #27130, though it refers to an old version of the code).
+// `inline(always)` is a workaround for that. There are only two call sites overall and it doesn't
+// make code size worse.
+
+/// Strip zeros where possible, even when this requires changing the exponent
+#[inline(always)]
+fn simplify(decimal: &mut Decimal) {
+ let is_zero = &|&&d: &&u8| -> bool { d == b'0' };
+ // Trimming these zeros does not change anything but may enable the fast path (< 15 digits).
+ let leading_zeros = decimal.integral.iter().take_while(is_zero).count();
+ decimal.integral = &decimal.integral[leading_zeros..];
+ let trailing_zeros = decimal.fractional.iter().rev().take_while(is_zero).count();
+ let end = decimal.fractional.len() - trailing_zeros;
+ decimal.fractional = &decimal.fractional[..end];
+ // Simplify numbers of the form 0.0...x and x...0.0, adjusting the exponent accordingly.
+ // This may not always be a win (possibly pushes some numbers out of the fast path), but it
+ // simplifies other parts significantly (notably, approximating the magnitude of the value).
+ if decimal.integral.is_empty() {
+ let leading_zeros = decimal.fractional.iter().take_while(is_zero).count();
+ decimal.fractional = &decimal.fractional[leading_zeros..];
+ decimal.exp -= leading_zeros as i64;
+ } else if decimal.fractional.is_empty() {
+ let trailing_zeros = decimal.integral.iter().rev().take_while(is_zero).count();
+ let end = decimal.integral.len() - trailing_zeros;
+ decimal.integral = &decimal.integral[..end];
+ decimal.exp += trailing_zeros as i64;
+ }
+}
+
+/// Quick and dirty upper bound on the size (log10) of the largest value that Algorithm R and
+/// Algorithm M will compute while working on the given decimal.
+fn bound_intermediate_digits(decimal: &Decimal, e: i64) -> u64 {
+ // We don't need to worry too much about overflow here thanks to trivial_cases() and the
+ // parser, which filter out the most extreme inputs for us.
+ let f_len: u64 = decimal.integral.len() as u64 + decimal.fractional.len() as u64;
+ if e >= 0 {
+ // In the case e >= 0, both algorithms compute about `f * 10^e`. Algorithm R proceeds to
+ // do some complicated calculations with this but we can ignore that for the upper bound
+ // because it also reduces the fraction beforehand, so we have plenty of buffer there.
+ f_len + (e as u64)
+ } else {
+ // If e < 0, Algorithm R does roughly the same thing, but Algorithm M differs:
+ // It tries to find a positive number k such that `f << k / 10^e` is an in-range
+ // significand. This will result in about `2^53 * f * 10^e` < `10^17 * f * 10^e`.
+ // One input that triggers this is 0.33...33 (375 x 3).
+ f_len + (e.abs() as u64) + 17
+ }
+}
+
+/// Detect obvious overflows and underflows without even looking at the decimal digits.
+fn trivial_cases<T: RawFloat>(decimal: &Decimal) -> Option<T> {
+ // There were zeros but they were stripped by simplify()
+ if decimal.integral.is_empty() && decimal.fractional.is_empty() {
+ return Some(T::zero());
+ }
+ // This is a crude approximation of ceil(log10(the real value)). We don't need to worry too
+ // much about overflow here because the input length is tiny (at least compared to 2^64) and
+ // the parser already handles exponents whose absolute value is greater than 10^18
+ // (which is still 10^19 short of 2^64).
+ let max_place = decimal.exp + decimal.integral.len() as i64;
+ if max_place > T::inf_cutoff() {
+ return Some(T::infinity());
+ } else if max_place < T::zero_cutoff() {
+ return Some(T::zero());
+ }
+ None
+}