Auto merge of #24612 - lifthrasiir:flt2dec, r=pnkfelix

This is a direct port of my prior work on the float formatting. The detailed description is available [here](https://github.com/lifthrasiir/rust-strconv#flt2dec). In brief,

* This adds a new hidden module `core::num::flt2dec` for testing from `libcoretest`. Why is it in `core::num` instead of `core::fmt`? Because I envision that the table used by `flt2dec` is directly applicable to `dec2flt` (cf. #24557) as well, which exceeds the realm of "formatting".
* This contains both Dragon4 algorithm (exact, complete but slow) and Grisu3 algorithm (exact, fast but incomplete).
* The code is accompanied with a large amount of self-tests and some exhaustive tests. In particular, `libcoretest` gets a new dependency on `librand`. For the external interface it relies on the existing test suite.
* It is known that, in the best case, the entire formatting code has about 30 KBs of binary overhead (judged from strconv experiments). Not too bad but there might be a potential room for improvements.

This is rather large code. I did my best to comment and annotate the code, but you have been warned.

For the maximal availability the original code was licensed in CC0, but I've also dual-licensed it in MIT/Apache as well so there should be no licensing concern.

This is [breaking-change] as it changes the float output slightly (and it also affects the casing of `inf` and `nan`). I hope this is not a big deal though :)

Fixes #7030, #18038 and #24556. Also related to #6220 and #20870.

## Known Issues

- [x] I've yet to finish `make check-stage1`. It does pass main test suites including `run-pass` but there might be some unknown edges on the doctests.
- [ ] Figure out how this PR affects rustc.
- [ ] Determine which internal routine is mapped to the formatting specifier. Depending on the decision, some internal routine can be safely removed (for instance, currently `to_shortest_str` is unused).

1 files changed, 105 insertions, 0 deletions

diff --git a/src/libcore/num/flt2dec/decoder.rs b/src/libcore/num/flt2dec/decoder.rs
new file mode 100644
index 00000000000..f98bc11a315
--- /dev/null
+++ b/src/libcore/num/flt2dec/decoder.rs
@@ -0,0 +1,105 @@
+// 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.
+
+//! Decodes a floating-point value into individual parts and error ranges.
+
+use prelude::*;
+
+use {f32, f64};
+use num::{Float, FpCategory};
+
+/// Decoded unsigned finite value, such that:
+///
+/// - The original value equals to `mant * 2^exp`.
+///
+/// - Any number from `(mant - minus) * 2^exp` to `(mant + plus) * 2^exp` will
+///   round to the original value. The range is inclusive only when
+///   `inclusive` is true.
+#[derive(Copy, Clone, Debug, PartialEq)]
+pub struct Decoded {
+    /// The scaled mantissa.
+    pub mant: u64,
+    /// The lower error range.
+    pub minus: u64,
+    /// The upper error range.
+    pub plus: u64,
+    /// The shared exponent in base 2.
+    pub exp: i16,
+    /// True when the error range is inclusive.
+    ///
+    /// In IEEE 754, this is true when the original mantissa was even.
+    pub inclusive: bool,
+}
+
+/// Decoded unsigned value.
+#[derive(Copy, Clone, Debug, PartialEq)]
+pub enum FullDecoded {
+    /// Not-a-number.
+    Nan,
+    /// Infinities, either positive or negative.
+    Infinite,
+    /// Zero, either positive or negative.
+    Zero,
+    /// Finite numbers with further decoded fields.
+    Finite(Decoded),
+}
+
+/// A floating point type which can be `decode`d.
+pub trait DecodableFloat: Float + Copy {
+    /// Returns `x * 2^exp`. Almost same to `std::{f32,f64}::ldexp`.
+    /// This is used for testing.
+    fn ldexpi(f: i64, exp: isize) -> Self;
+    /// The minimum positive normalized value.
+    fn min_pos_norm_value() -> Self;
+}
+
+impl DecodableFloat for f32 {
+    fn ldexpi(f: i64, exp: isize) -> Self { f as Self * (exp as Self).exp2() }
+    fn min_pos_norm_value() -> Self { f32::MIN_POSITIVE }
+}
+
+impl DecodableFloat for f64 {
+    fn ldexpi(f: i64, exp: isize) -> Self { f as Self * (exp as Self).exp2() }
+    fn min_pos_norm_value() -> Self { f64::MIN_POSITIVE }
+}
+
+/// Returns a sign (true when negative) and `FullDecoded` value
+/// from given floating point number.
+pub fn decode<T: DecodableFloat>(v: T) -> (/*negative?*/ bool, FullDecoded) {
+    let (mant, exp, sign) = v.integer_decode();
+    let even = (mant & 1) == 0;
+    let decoded = match v.classify() {
+        FpCategory::Nan => FullDecoded::Nan,
+        FpCategory::Infinite => FullDecoded::Infinite,
+        FpCategory::Zero => FullDecoded::Zero,
+        FpCategory::Subnormal => {
+            // neighbors: (mant - 2, exp) -- (mant, exp) -- (mant + 2, exp)
+            // Float::integer_decode always preserves the exponent,
+            // so the mantissa is scaled for subnormals.
+            FullDecoded::Finite(Decoded { mant: mant, minus: 1, plus: 1,
+                                          exp: exp, inclusive: even })
+        }
+        FpCategory::Normal => {
+            let minnorm = <T as DecodableFloat>::min_pos_norm_value().integer_decode();
+            if mant == minnorm.0 {
+                // neighbors: (maxmant, exp - 1) -- (minnormmant, exp) -- (minnormmant + 1, exp)
+                // where maxmant = minnormmant * 2 - 1
+                FullDecoded::Finite(Decoded { mant: mant << 2, minus: 1, plus: 2,
+                                              exp: exp - 2, inclusive: even })
+            } else {
+                // neighbors: (mant - 1, exp) -- (mant, exp) -- (mant + 1, exp)
+                FullDecoded::Finite(Decoded { mant: mant << 1, minus: 1, plus: 1,
+                                              exp: exp - 1, inclusive: even })
+            }
+        }
+    };
+    (sign < 0, decoded)
+}
+