648 lines
22 KiB
Rust
648 lines
22 KiB
Rust
// Copyright 2013 The Rust Project Developers. See the COPYRIGHT
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// file at the top-level directory of this distribution and at
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// http://rust-lang.org/COPYRIGHT.
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//
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// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
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// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
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// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
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// option. This file may not be copied, modified, or distributed
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// except according to those terms.
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use core::cmp::{Ord, Eq};
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use ops::{Add, Div, Modulo, Mul, Neg, Sub};
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use option::{None, Option, Some};
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use char;
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use str;
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use kinds::Copy;
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use vec;
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use num::{NumCast, Zero, One, cast, pow_with_uint};
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use f64;
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pub enum ExponentFormat {
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ExpNone,
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ExpDec,
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ExpBin
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}
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pub enum SignificantDigits {
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DigAll,
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DigMax(uint),
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DigExact(uint)
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}
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pub enum SignFormat {
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SignNone,
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SignNeg,
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SignAll
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}
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#[inline(always)]
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fn is_NaN<T:Eq>(num: &T) -> bool {
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*num != *num
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}
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#[inline(always)]
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fn is_inf<T:Eq+NumStrConv>(num: &T) -> bool {
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match NumStrConv::inf() {
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None => false,
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Some(n) => *num == n
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}
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}
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#[inline(always)]
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fn is_neg_inf<T:Eq+NumStrConv>(num: &T) -> bool {
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match NumStrConv::neg_inf() {
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None => false,
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Some(n) => *num == n
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}
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}
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#[inline(always)]
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fn is_neg_zero<T:Eq+One+Zero+NumStrConv+Div<T,T>>(num: &T) -> bool {
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let _0: T = Zero::zero();
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let _1: T = One::one();
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*num == _0 && is_neg_inf(&(_1 / *num))
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}
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pub trait NumStrConv {
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fn NaN() -> Option<Self>;
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fn inf() -> Option<Self>;
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fn neg_inf() -> Option<Self>;
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fn neg_zero() -> Option<Self>;
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fn round_to_zero(&self) -> Self;
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fn fractional_part(&self) -> Self;
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}
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macro_rules! impl_NumStrConv_Floating (($t:ty) => (
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impl NumStrConv for $t {
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#[inline(always)]
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fn NaN() -> Option<$t> { Some( 0.0 / 0.0) }
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#[inline(always)]
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fn inf() -> Option<$t> { Some( 1.0 / 0.0) }
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#[inline(always)]
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fn neg_inf() -> Option<$t> { Some(-1.0 / 0.0) }
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#[inline(always)]
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fn neg_zero() -> Option<$t> { Some(-0.0 ) }
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#[inline(always)]
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fn round_to_zero(&self) -> $t {
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( if *self < 0.0 { f64::ceil(*self as f64) }
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else { f64::floor(*self as f64) }
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) as $t
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}
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#[inline(always)]
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fn fractional_part(&self) -> $t {
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*self - self.round_to_zero()
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}
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}
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))
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macro_rules! impl_NumStrConv_Integer (($t:ty) => (
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impl NumStrConv for $t {
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#[inline(always)] fn NaN() -> Option<$t> { None }
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#[inline(always)] fn inf() -> Option<$t> { None }
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#[inline(always)] fn neg_inf() -> Option<$t> { None }
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#[inline(always)] fn neg_zero() -> Option<$t> { None }
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#[inline(always)] fn round_to_zero(&self) -> $t { *self }
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#[inline(always)] fn fractional_part(&self) -> $t { 0 }
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}
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))
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// FIXME: #4955
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// Replace by two generic impls for traits 'Integral' and 'Floating'
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impl_NumStrConv_Floating!(float)
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impl_NumStrConv_Floating!(f32)
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impl_NumStrConv_Floating!(f64)
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impl_NumStrConv_Integer!(int)
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impl_NumStrConv_Integer!(i8)
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impl_NumStrConv_Integer!(i16)
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impl_NumStrConv_Integer!(i32)
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impl_NumStrConv_Integer!(i64)
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impl_NumStrConv_Integer!(uint)
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impl_NumStrConv_Integer!(u8)
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impl_NumStrConv_Integer!(u16)
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impl_NumStrConv_Integer!(u32)
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impl_NumStrConv_Integer!(u64)
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// Special value strings as [u8] consts.
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static inf_buf: [u8, ..3] = ['i' as u8, 'n' as u8, 'f' as u8];
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static positive_inf_buf: [u8, ..4] = ['+' as u8, 'i' as u8, 'n' as u8,
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'f' as u8];
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static negative_inf_buf: [u8, ..4] = ['-' as u8, 'i' as u8, 'n' as u8,
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'f' as u8];
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static nan_buf: [u8, ..3] = ['N' as u8, 'a' as u8, 'N' as u8];
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/**
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* Converts a number to its string representation as a byte vector.
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* This is meant to be a common base implementation for all numeric string
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* conversion functions like `to_str()` or `to_str_radix()`.
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*
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* # Arguments
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* - `num` - The number to convert. Accepts any number that
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* implements the numeric traits.
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* - `radix` - Base to use. Accepts only the values 2-36.
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* - `negative_zero` - Whether to treat the special value `-0` as
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* `-0` or as `+0`.
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* - `sign` - How to emit the sign. Options are:
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* - `SignNone`: No sign at all. Basically emits `abs(num)`.
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* - `SignNeg`: Only `-` on negative values.
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* - `SignAll`: Both `+` on positive, and `-` on negative numbers.
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* - `digits` - The amount of digits to use for emitting the
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* fractional part, if any. Options are:
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* - `DigAll`: All calculatable digits. Beware of bignums or
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* fractions!
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* - `DigMax(uint)`: Maximum N digits, truncating any trailing zeros.
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* - `DigExact(uint)`: Exactly N digits.
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*
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* # Return value
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* A tuple containing the byte vector, and a boolean flag indicating
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* whether it represents a special value like `inf`, `-inf`, `NaN` or not.
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* It returns a tuple because there can be ambiguity between a special value
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* and a number representation at higher bases.
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*
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* # Failure
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* - Fails if `radix` < 2 or `radix` > 36.
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*/
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pub fn to_str_bytes_common<T:NumCast+Zero+One+Eq+Ord+NumStrConv+Copy+
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Div<T,T>+Neg<T>+Modulo<T,T>+Mul<T,T>>(
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num: &T, radix: uint, negative_zero: bool,
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sign: SignFormat, digits: SignificantDigits) -> (~[u8], bool) {
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if (radix as int) < 2 {
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fail!(fmt!("to_str_bytes_common: radix %? to low, \
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must lie in the range [2, 36]", radix));
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} else if radix as int > 36 {
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fail!(fmt!("to_str_bytes_common: radix %? to high, \
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must lie in the range [2, 36]", radix));
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}
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let _0: T = Zero::zero();
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let _1: T = One::one();
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if is_NaN(num) {
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return (str::to_bytes("NaN"), true);
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}
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else if is_inf(num){
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return match sign {
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SignAll => (str::to_bytes("+inf"), true),
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_ => (str::to_bytes("inf"), true)
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}
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}
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else if is_neg_inf(num) {
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return match sign {
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SignNone => (str::to_bytes("inf"), true),
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_ => (str::to_bytes("-inf"), true),
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}
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}
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let neg = *num < _0 || (negative_zero && is_neg_zero(num));
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let mut buf: ~[u8] = ~[];
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let radix_gen: T = cast(radix as int);
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let mut deccum;
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// First emit the non-fractional part, looping at least once to make
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// sure at least a `0` gets emitted.
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deccum = num.round_to_zero();
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loop {
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// Calculate the absolute value of each digit instead of only
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// doing it once for the whole number because a
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// representable negative number doesn't necessary have an
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// representable additive inverse of the same type
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// (See twos complement). But we assume that for the
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// numbers [-35 .. 0] we always have [0 .. 35].
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let current_digit_signed = deccum % radix_gen;
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let current_digit = if current_digit_signed < _0 {
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-current_digit_signed
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} else {
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current_digit_signed
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};
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// Decrease the deccumulator one digit at a time
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deccum /= radix_gen;
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deccum = deccum.round_to_zero();
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unsafe { // FIXME: Pureness workaround (#4568)
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buf.push(char::from_digit(current_digit.to_int() as uint, radix)
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.unwrap() as u8);
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}
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// No more digits to calculate for the non-fractional part -> break
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if deccum == _0 { break; }
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}
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// If limited digits, calculate one digit more for rounding.
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let (limit_digits, digit_count, exact) = match digits {
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DigAll => (false, 0u, false),
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DigMax(count) => (true, count+1, false),
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DigExact(count) => (true, count+1, true)
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};
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// Decide what sign to put in front
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match sign {
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SignNeg | SignAll if neg => {
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unsafe { // FIXME: Pureness workaround (#4568)
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buf.push('-' as u8);
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}
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}
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SignAll => {
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unsafe { // FIXME: Pureness workaround (#4568)
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buf.push('+' as u8);
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}
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}
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_ => ()
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}
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unsafe { // FIXME: Pureness workaround (#4568)
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vec::reverse(buf);
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}
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// Remember start of the fractional digits.
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// Points one beyond end of buf if none get generated,
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// or at the '.' otherwise.
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let start_fractional_digits = buf.len();
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// Now emit the fractional part, if any
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deccum = num.fractional_part();
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if deccum != _0 || (limit_digits && exact && digit_count > 0) {
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unsafe { // FIXME: Pureness workaround (#4568)
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buf.push('.' as u8);
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}
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let mut dig = 0u;
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// calculate new digits while
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// - there is no limit and there are digits left
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// - or there is a limit, it's not reached yet and
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// - it's exact
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// - or it's a maximum, and there are still digits left
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while (!limit_digits && deccum != _0)
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|| (limit_digits && dig < digit_count && (
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exact
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|| (!exact && deccum != _0)
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)
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) {
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// Shift first fractional digit into the integer part
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deccum *= radix_gen;
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// Calculate the absolute value of each digit.
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// See note in first loop.
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let current_digit_signed = deccum.round_to_zero();
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let current_digit = if current_digit_signed < _0 {
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-current_digit_signed
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} else {
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current_digit_signed
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};
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unsafe { // FIXME: Pureness workaround (#4568)
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buf.push(char::from_digit(
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current_digit.to_int() as uint, radix).unwrap() as u8);
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}
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// Decrease the deccumulator one fractional digit at a time
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deccum = deccum.fractional_part();
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dig += 1u;
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}
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// If digits are limited, and that limit has been reached,
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// cut off the one extra digit, and depending on its value
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// round the remaining ones.
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if limit_digits && dig == digit_count {
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let ascii2value = |chr: u8| {
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char::to_digit(chr as char, radix).unwrap() as uint
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};
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let value2ascii = |val: uint| {
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char::from_digit(val, radix).unwrap() as u8
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};
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unsafe { // FIXME: Pureness workaround (#4568)
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let extra_digit = ascii2value(buf.pop());
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if extra_digit >= radix / 2 { // -> need to round
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let mut i: int = buf.len() as int - 1;
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loop {
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// If reached left end of number, have to
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// insert additional digit:
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if i < 0
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|| buf[i] == '-' as u8
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|| buf[i] == '+' as u8 {
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buf.insert((i + 1) as uint, value2ascii(1));
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break;
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}
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// Skip the '.'
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if buf[i] == '.' as u8 { i -= 1; loop; }
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// Either increment the digit,
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// or set to 0 if max and carry the 1.
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let current_digit = ascii2value(buf[i]);
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if current_digit < (radix - 1) {
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buf[i] = value2ascii(current_digit+1);
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break;
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} else {
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buf[i] = value2ascii(0);
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i -= 1;
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}
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}
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}
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}
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}
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}
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// if number of digits is not exact, remove all trailing '0's up to
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// and including the '.'
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if !exact {
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let buf_max_i = buf.len() - 1;
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// index to truncate from
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let mut i = buf_max_i;
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// discover trailing zeros of fractional part
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while i > start_fractional_digits && buf[i] == '0' as u8 {
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i -= 1;
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}
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// Only attempt to truncate digits if buf has fractional digits
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if i >= start_fractional_digits {
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// If buf ends with '.', cut that too.
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if buf[i] == '.' as u8 { i -= 1 }
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// only resize buf if we actually remove digits
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if i < buf_max_i {
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buf = buf.slice(0, i + 1).to_owned();
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}
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}
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} // If exact and trailing '.', just cut that
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else {
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let max_i = buf.len() - 1;
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if buf[max_i] == '.' as u8 {
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buf = buf.slice(0, max_i).to_owned();
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}
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}
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(buf, false)
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}
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/**
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* Converts a number to its string representation. This is a wrapper for
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* `to_str_bytes_common()`, for details see there.
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*/
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#[inline(always)]
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pub fn to_str_common<T:NumCast+Zero+One+Eq+Ord+NumStrConv+Copy+
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Div<T,T>+Neg<T>+Modulo<T,T>+Mul<T,T>>(
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num: &T, radix: uint, negative_zero: bool,
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sign: SignFormat, digits: SignificantDigits) -> (~str, bool) {
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let (bytes, special) = to_str_bytes_common(num, radix,
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negative_zero, sign, digits);
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(str::from_bytes(bytes), special)
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}
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// Some constants for from_str_bytes_common's input validation,
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// they define minimum radix values for which the character is a valid digit.
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priv static DIGIT_P_RADIX: uint = ('p' as uint) - ('a' as uint) + 11u;
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priv static DIGIT_I_RADIX: uint = ('i' as uint) - ('a' as uint) + 11u;
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priv static DIGIT_E_RADIX: uint = ('e' as uint) - ('a' as uint) + 11u;
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/**
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* Parses a byte slice as a number. This is meant to
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* be a common base implementation for all numeric string conversion
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* functions like `from_str()` or `from_str_radix()`.
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*
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* # Arguments
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* - `buf` - The byte slice to parse.
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* - `radix` - Which base to parse the number as. Accepts 2-36.
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* - `negative` - Whether to accept negative numbers.
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* - `fractional` - Whether to accept numbers with fractional parts.
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* - `special` - Whether to accept special values like `inf`
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* and `NaN`. Can conflict with `radix`, see Failure.
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* - `exponent` - Which exponent format to accept. Options are:
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* - `ExpNone`: No Exponent, accepts just plain numbers like `42` or
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* `-8.2`.
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* - `ExpDec`: Accepts numbers with a decimal exponent like `42e5` or
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* `8.2E-2`. The exponent string itself is always base 10.
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* Can conflict with `radix`, see Failure.
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* - `ExpBin`: Accepts numbers with a binary exponent like `42P-8` or
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* `FFp128`. The exponent string itself is always base 10.
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* Can conflict with `radix`, see Failure.
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* - `empty_zero` - Whether to accept a empty `buf` as a 0 or not.
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*
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* # Return value
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* Returns `Some(n)` if `buf` parses to a number n without overflowing, and
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* `None` otherwise, depending on the constraints set by the remaining
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* arguments.
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*
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* # Failure
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* - Fails if `radix` < 2 or `radix` > 36.
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* - Fails if `radix` > 14 and `exponent` is `ExpDec` due to conflict
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* between digit and exponent sign `'e'`.
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* - Fails if `radix` > 25 and `exponent` is `ExpBin` due to conflict
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* between digit and exponent sign `'p'`.
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* - Fails if `radix` > 18 and `special == true` due to conflict
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* between digit and lowest first character in `inf` and `NaN`, the `'i'`.
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*
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* # Possible improvements
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* - Could accept option to allow ignoring underscores, allowing for numbers
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* formated like `FF_AE_FF_FF`.
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*/
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pub fn from_str_bytes_common<T:NumCast+Zero+One+Ord+Copy+Div<T,T>+
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Mul<T,T>+Sub<T,T>+Neg<T>+Add<T,T>+
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NumStrConv>(
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buf: &[u8], radix: uint, negative: bool, fractional: bool,
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special: bool, exponent: ExponentFormat, empty_zero: bool
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) -> Option<T> {
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match exponent {
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ExpDec if radix >= DIGIT_E_RADIX // decimal exponent 'e'
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=> fail!(fmt!("from_str_bytes_common: radix %? incompatible with \
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use of 'e' as decimal exponent", radix)),
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ExpBin if radix >= DIGIT_P_RADIX // binary exponent 'p'
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=> fail!(fmt!("from_str_bytes_common: radix %? incompatible with \
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use of 'p' as binary exponent", radix)),
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_ if special && radix >= DIGIT_I_RADIX // first digit of 'inf'
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=> fail!(fmt!("from_str_bytes_common: radix %? incompatible with \
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special values 'inf' and 'NaN'", radix)),
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_ if (radix as int) < 2
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=> fail!(fmt!("from_str_bytes_common: radix %? to low, \
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must lie in the range [2, 36]", radix)),
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_ if (radix as int) > 36
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=> fail!(fmt!("from_str_bytes_common: radix %? to high, \
|
|
must lie in the range [2, 36]", radix)),
|
|
_ => ()
|
|
}
|
|
|
|
let _0: T = Zero::zero();
|
|
let _1: T = One::one();
|
|
let radix_gen: T = cast(radix as int);
|
|
|
|
let len = buf.len();
|
|
|
|
if len == 0 {
|
|
if empty_zero {
|
|
return Some(_0);
|
|
} else {
|
|
return None;
|
|
}
|
|
}
|
|
|
|
if special {
|
|
if buf == inf_buf || buf == positive_inf_buf {
|
|
return NumStrConv::inf();
|
|
} else if buf == negative_inf_buf {
|
|
if negative {
|
|
return NumStrConv::neg_inf();
|
|
} else {
|
|
return None;
|
|
}
|
|
} else if buf == nan_buf {
|
|
return NumStrConv::NaN();
|
|
}
|
|
}
|
|
|
|
let (start, accum_positive) = match buf[0] {
|
|
'-' as u8 if !negative => return None,
|
|
'-' as u8 => (1u, false),
|
|
'+' as u8 => (1u, true),
|
|
_ => (0u, true)
|
|
};
|
|
|
|
// Initialize accumulator with signed zero for floating point parsing to
|
|
// work
|
|
let mut accum = if accum_positive { _0 } else { -_1 * _0};
|
|
let mut last_accum = accum; // Necessary to detect overflow
|
|
let mut i = start;
|
|
let mut exp_found = false;
|
|
|
|
// Parse integer part of number
|
|
while i < len {
|
|
let c = buf[i] as char;
|
|
|
|
match char::to_digit(c, radix) {
|
|
Some(digit) => {
|
|
// shift accum one digit left
|
|
accum *= radix_gen;
|
|
|
|
// add/subtract current digit depending on sign
|
|
if accum_positive {
|
|
accum += cast(digit as int);
|
|
} else {
|
|
accum -= cast(digit as int);
|
|
}
|
|
|
|
// Detect overflow by comparing to last value
|
|
if accum_positive && accum < last_accum { return None; }
|
|
if !accum_positive && accum > last_accum { return None; }
|
|
last_accum = accum;
|
|
}
|
|
None => match c {
|
|
'e' | 'E' | 'p' | 'P' => {
|
|
exp_found = true;
|
|
break; // start of exponent
|
|
}
|
|
'.' if fractional => {
|
|
i += 1u; // skip the '.'
|
|
break; // start of fractional part
|
|
}
|
|
_ => return None // invalid number
|
|
}
|
|
}
|
|
|
|
i += 1u;
|
|
}
|
|
|
|
// Parse fractional part of number
|
|
// Skip if already reached start of exponent
|
|
if !exp_found {
|
|
let mut power = _1;
|
|
|
|
while i < len {
|
|
let c = buf[i] as char;
|
|
|
|
match char::to_digit(c, radix) {
|
|
Some(digit) => {
|
|
// Decrease power one order of magnitude
|
|
power /= radix_gen;
|
|
|
|
let digit_t: T = cast(digit);
|
|
|
|
// add/subtract current digit depending on sign
|
|
if accum_positive {
|
|
accum += digit_t * power;
|
|
} else {
|
|
accum -= digit_t * power;
|
|
}
|
|
|
|
// Detect overflow by comparing to last value
|
|
if accum_positive && accum < last_accum { return None; }
|
|
if !accum_positive && accum > last_accum { return None; }
|
|
last_accum = accum;
|
|
}
|
|
None => match c {
|
|
'e' | 'E' | 'p' | 'P' => {
|
|
exp_found = true;
|
|
break; // start of exponent
|
|
}
|
|
_ => return None // invalid number
|
|
}
|
|
}
|
|
|
|
i += 1u;
|
|
}
|
|
}
|
|
|
|
// Special case: buf not empty, but does not contain any digit in front
|
|
// of the exponent sign -> number is empty string
|
|
if i == start {
|
|
if empty_zero {
|
|
return Some(_0);
|
|
} else {
|
|
return None;
|
|
}
|
|
}
|
|
|
|
let mut multiplier = _1;
|
|
|
|
if exp_found {
|
|
let c = buf[i] as char;
|
|
let base = match (c, exponent) {
|
|
('e', ExpDec) | ('E', ExpDec) => 10u,
|
|
('p', ExpBin) | ('P', ExpBin) => 2u,
|
|
_ => return None // char doesn't fit given exponent format
|
|
};
|
|
|
|
// parse remaining bytes as decimal integer,
|
|
// skipping the exponent char
|
|
let exp: Option<int> = from_str_bytes_common(
|
|
buf.slice(i+1, len), 10, true, false, false, ExpNone, false);
|
|
|
|
match exp {
|
|
Some(exp_pow) => {
|
|
multiplier = if exp_pow < 0 {
|
|
_1 / pow_with_uint::<T>(base, (-exp_pow.to_int()) as uint)
|
|
} else {
|
|
pow_with_uint::<T>(base, exp_pow.to_int() as uint)
|
|
}
|
|
}
|
|
None => return None // invalid exponent -> invalid number
|
|
}
|
|
}
|
|
|
|
Some(accum * multiplier)
|
|
}
|
|
|
|
/**
|
|
* Parses a string as a number. This is a wrapper for
|
|
* `from_str_bytes_common()`, for details see there.
|
|
*/
|
|
#[inline(always)]
|
|
pub fn from_str_common<T:NumCast+Zero+One+Ord+Copy+Div<T,T>+Mul<T,T>+
|
|
Sub<T,T>+Neg<T>+Add<T,T>+NumStrConv>(
|
|
buf: &str, radix: uint, negative: bool, fractional: bool,
|
|
special: bool, exponent: ExponentFormat, empty_zero: bool
|
|
) -> Option<T> {
|
|
from_str_bytes_common(str::to_bytes(buf), radix, negative,
|
|
fractional, special, exponent, empty_zero)
|
|
}
|