core: Implement f32/f64 formatting

This is a migration of the std::{f32, f64}::to_str* functionality to the core
library. This removes the growable `Vec` used in favor of a large stack buffer.
The maximum base 10 exponent for f64 is 308, so a stack buffer of 512 bytes
should be sufficient to store all floats.

src/libcore/fmt/float.rs

+// Copyright 2013-2014 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.
+
+#![allow(missing_doc)]
+
+use char;
+use container::Container;
+use fmt;
+use iter::{Iterator, range, DoubleEndedIterator};
+use num::{Float, FPNaN, FPInfinite, ToPrimitive, Primitive};
+use num::{Zero, One, cast};
+use option::{None, Some};
+use result::Ok;
+use slice::{ImmutableVector, MutableVector};
+use slice;
+use str::StrSlice;
+
+/// A flag that specifies whether to use exponential (scientific) notation.
+pub enum ExponentFormat {
+    /// Do not use exponential notation.
+    ExpNone,
+    /// Use exponential notation with the exponent having a base of 10 and the
+    /// exponent sign being `e` or `E`. For example, 1000 would be printed
+    /// 1e3.
+    ExpDec,
+    /// Use exponential notation with the exponent having a base of 2 and the
+    /// exponent sign being `p` or `P`. For example, 8 would be printed 1p3.
+    ExpBin,
+}
+
+/// The number of digits used for emitting the fractional part of a number, if
+/// any.
+pub enum SignificantDigits {
+    /// All calculable digits will be printed.
+    ///
+    /// Note that bignums or fractions may cause a surprisingly large number
+    /// of digits to be printed.
+    DigAll,
+
+    /// At most the given number of digits will be printed, truncating any
+    /// trailing zeroes.
+    DigMax(uint),
+
+    /// Precisely the given number of digits will be printed.
+    DigExact(uint)
+}
+
+/// How to emit the sign of a number.
+pub enum SignFormat {
+    /// No sign will be printed. The exponent sign will also be emitted.
+    SignNone,
+    /// `-` will be printed for negative values, but no sign will be emitted
+    /// for positive numbers.
+    SignNeg,
+    /// `+` will be printed for positive values, and `-` will be printed for
+    /// negative values.
+    SignAll,
+}
+
+static DIGIT_P_RADIX: uint = ('p' as uint) - ('a' as uint) + 11u;
+static DIGIT_E_RADIX: uint = ('e' as uint) - ('a' as uint) + 11u;
+
+/**
+ * Converts a number to its string representation as a byte vector.
+ * This is meant to be a common base implementation for all numeric string
+ * conversion functions like `to_str()` or `to_str_radix()`.
+ *
+ * # Arguments
+ * - `num`           - The number to convert. Accepts any number that
+ *                     implements the numeric traits.
+ * - `radix`         - Base to use. Accepts only the values 2-36. If the exponential notation
+ *                     is used, then this base is only used for the significand. The exponent
+ *                     itself always printed using a base of 10.
+ * - `negative_zero` - Whether to treat the special value `-0` as
+ *                     `-0` or as `+0`.
+ * - `sign`          - How to emit the sign. See `SignFormat`.
+ * - `digits`        - The amount of digits to use for emitting the fractional
+ *                     part, if any. See `SignificantDigits`.
+ * - `exp_format`   - Whether or not to use the exponential (scientific) notation.
+ *                    See `ExponentFormat`.
+ * - `exp_capital`   - Whether or not to use a capital letter for the exponent sign, if
+ *                     exponential notation is desired.
+ * - `f`             - A closure to invoke with the bytes representing the
+ *                     float.
+ *
+ * # Failure
+ * - Fails if `radix` < 2 or `radix` > 36.
+ * - Fails if `radix` > 14 and `exp_format` is `ExpDec` due to conflict
+ *   between digit and exponent sign `'e'`.
+ * - Fails if `radix` > 25 and `exp_format` is `ExpBin` due to conflict
+ *   between digit and exponent sign `'p'`.
+ */
+pub fn float_to_str_bytes_common<T: Primitive + Float, U>(
+    num: T,
+    radix: uint,
+    negative_zero: bool,
+    sign: SignFormat,
+    digits: SignificantDigits,
+    exp_format: ExponentFormat,
+    exp_upper: bool,
+    f: |&[u8]| -> U
+) -> U {
+    assert!(2 <= radix && radix <= 36);
+    match exp_format {
+        ExpDec if radix >= DIGIT_E_RADIX       // decimal exponent 'e'
+          => fail!("float_to_str_bytes_common: radix {} incompatible with \
+                    use of 'e' as decimal exponent", radix),
+        ExpBin if radix >= DIGIT_P_RADIX       // binary exponent 'p'
+          => fail!("float_to_str_bytes_common: radix {} incompatible with \
+                    use of 'p' as binary exponent", radix),
+        _ => ()
+    }
+
+    let _0: T = Zero::zero();
+    let _1: T = One::one();
+
+    match num.classify() {
+        FPNaN => return f("NaN".as_bytes()),
+        FPInfinite if num > _0 => {
+            return match sign {
+                SignAll => return f("+inf".as_bytes()),
+                _       => return f("inf".as_bytes()),
+            };
+        }
+        FPInfinite if num < _0 => {
+            return match sign {
+                SignNone => return f("inf".as_bytes()),
+                _        => return f("-inf".as_bytes()),
+            };
+        }
+        _ => {}
+    }
+
+    let neg = num < _0 || (negative_zero && _1 / num == Float::neg_infinity());
+    // For an f64 the exponent is in the range of [-1022, 1023] for base 2, so
+    // we may have up to that many digits. Give ourselves some extra wiggle room
+    // otherwise as well.
+    let mut buf = [0u8, ..1536];
+    let mut end = 0;
+    let radix_gen: T = cast(radix as int).unwrap();
+
+    let (num, exp) = match exp_format {
+        ExpNone => (num, 0i32),
+        ExpDec | ExpBin if num == _0 => (num, 0i32),
+        ExpDec | ExpBin => {
+            let (exp, exp_base) = match exp_format {
+                ExpDec => (num.abs().log10().floor(), cast::<f64, T>(10.0f64).unwrap()),
+                ExpBin => (num.abs().log2().floor(), cast::<f64, T>(2.0f64).unwrap()),
+                ExpNone => fail!("unreachable"),
+            };
+
+            (num / exp_base.powf(exp), cast::<T, i32>(exp).unwrap())
+        }
+    };
+
+    // First emit the non-fractional part, looping at least once to make
+    // sure at least a `0` gets emitted.
+    let mut deccum = num.trunc();
+    loop {
+        // Calculate the absolute value of each digit instead of only
+        // doing it once for the whole number because a
+        // representable negative number doesn't necessary have an
+        // representable additive inverse of the same type
+        // (See twos complement). But we assume that for the
+        // numbers [-35 .. 0] we always have [0 .. 35].
+        let current_digit = (deccum % radix_gen).abs();
+
+        // Decrease the deccumulator one digit at a time
+        deccum = deccum / radix_gen;
+        deccum = deccum.trunc();
+
+        let c = char::from_digit(current_digit.to_int().unwrap() as uint, radix);
+        buf[end] = c.unwrap() as u8;
+        end += 1;
+
+        // No more digits to calculate for the non-fractional part -> break
+        if deccum == _0 { break; }
+    }
+
+    // If limited digits, calculate one digit more for rounding.
+    let (limit_digits, digit_count, exact) = match digits {
+        DigAll          => (false, 0u,      false),
+        DigMax(count)   => (true,  count+1, false),
+        DigExact(count) => (true,  count+1, true)
+    };
+
+    // Decide what sign to put in front
+    match sign {
+        SignNeg | SignAll if neg => {
+            buf[end] = '-' as u8;
+            end += 1;
+        }
+        SignAll => {
+            buf[end] = '+' as u8;
+            end += 1;
+        }
+        _ => ()
+    }
+
+    buf.mut_slice_to(end).reverse();
+
+    // Remember start of the fractional digits.
+    // Points one beyond end of buf if none get generated,
+    // or at the '.' otherwise.
+    let start_fractional_digits = end;
+
+    // Now emit the fractional part, if any
+    deccum = num.fract();
+    if deccum != _0 || (limit_digits && exact && digit_count > 0) {
+        buf[end] = '.' as u8;
+        end += 1;
+        let mut dig = 0u;
+
+        // calculate new digits while
+        // - there is no limit and there are digits left
+        // - or there is a limit, it's not reached yet and
+        //   - it's exact
+        //   - or it's a maximum, and there are still digits left
+        while (!limit_digits && deccum != _0)
+           || (limit_digits && dig < digit_count && (
+                   exact
+                || (!exact && deccum != _0)
+              )
+        ) {
+            // Shift first fractional digit into the integer part
+            deccum = deccum * radix_gen;
+
+            // Calculate the absolute value of each digit.
+            // See note in first loop.
+            let current_digit = deccum.trunc().abs();
+
+            let c = char::from_digit(current_digit.to_int().unwrap() as uint,
+                                     radix);
+            buf[end] = c.unwrap() as u8;
+            end += 1;
+
+            // Decrease the deccumulator one fractional digit at a time
+            deccum = deccum.fract();
+            dig += 1u;
+        }
+
+        // If digits are limited, and that limit has been reached,
+        // cut off the one extra digit, and depending on its value
+        // round the remaining ones.
+        if limit_digits && dig == digit_count {
+            let ascii2value = |chr: u8| {
+                char::to_digit(chr as char, radix).unwrap()
+            };
+            let value2ascii = |val: uint| {
+                char::from_digit(val, radix).unwrap() as u8
+            };
+
+            let extra_digit = ascii2value(buf[end - 1]);
+            end -= 1;
+            if extra_digit >= radix / 2 { // -> need to round
+                let mut i: int = end as int - 1;
+                loop {
+                    // If reached left end of number, have to
+                    // insert additional digit:
+                    if i < 0
+                    || buf[i as uint] == '-' as u8
+                    || buf[i as uint] == '+' as u8 {
+                        for j in range(i as uint + 1, end).rev() {
+                            buf[j + 1] = buf[j];
+                        }
+                        buf[(i + 1) as uint] = value2ascii(1);
+                        end += 1;
+                        break;
+                    }
+
+                    // Skip the '.'
+                    if buf[i as uint] == '.' as u8 { i -= 1; continue; }
+
+                    // Either increment the digit,
+                    // or set to 0 if max and carry the 1.
+                    let current_digit = ascii2value(buf[i as uint]);
+                    if current_digit < (radix - 1) {
+                        buf[i as uint] = value2ascii(current_digit+1);
+                        break;
+                    } else {
+                        buf[i as uint] = value2ascii(0);
+                        i -= 1;
+                    }
+                }
+            }
+        }
+    }
+
+    // if number of digits is not exact, remove all trailing '0's up to
+    // and including the '.'
+    if !exact {
+        let buf_max_i = end - 1;
+
+        // index to truncate from
+        let mut i = buf_max_i;
+
+        // discover trailing zeros of fractional part
+        while i > start_fractional_digits && buf[i] == '0' as u8 {
+            i -= 1;
+        }
+
+        // Only attempt to truncate digits if buf has fractional digits
+        if i >= start_fractional_digits {
+            // If buf ends with '.', cut that too.
+            if buf[i] == '.' as u8 { i -= 1 }
+
+            // only resize buf if we actually remove digits
+            if i < buf_max_i {
+                end = i + 1;
+            }
+        }
+    } // If exact and trailing '.', just cut that
+    else {
+        let max_i = end - 1;
+        if buf[max_i] == '.' as u8 {
+            end = max_i;
+        }
+    }
+
+    match exp_format {
+        ExpNone => {},
+        _ => {
+            buf[end] = match exp_format {
+                ExpDec if exp_upper => 'E',
+                ExpDec if !exp_upper => 'e',
+                ExpBin if exp_upper => 'P',
+                ExpBin if !exp_upper => 'p',
+                _ => fail!("unreachable"),
+            } as u8;
+            end += 1;
+
+            struct Filler<'a> {
+                buf: &'a mut [u8],
+                end: &'a mut uint,
+            }
+
+            impl<'a> fmt::FormatWriter for Filler<'a> {
+                fn write(&mut self, bytes: &[u8]) -> fmt::Result {
+                    slice::bytes::copy_memory(self.buf.mut_slice_from(*self.end),
+                                              bytes);
+                    *self.end += bytes.len();
+                    Ok(())
+                }
+            }
+
+            let mut filler = Filler { buf: buf, end: &mut end };
+            match sign {
+                SignNeg => { let _ = write!(&mut filler, "{:-}", exp); }
+                SignNone | SignAll => { let _ = write!(&mut filler, "{}", exp); }
+            }
+        }
+    }
+
+    f(buf.slice_to(end))
+}