bdbc09ad48
This commit adds stability markers for the APIs that have recently been aligned with [numerics reform](https://github.com/rust-lang/rfcs/pull/369). For APIs that were changed as part of that reform, `#[unstable]` is used to reflect the recency, but the APIs will become `#[stable]` in a follow-up pass. In addition, a few aspects of the APIs not explicitly covered by the RFC are marked here -- in particular, constants for floats. This commit does not mark the `uint` or `int` modules as `#[stable]`, given the ongoing debate out the names and roles of these types. Due to some deprecation (see the RFC for details), this is a: [breaking-change]
1847 lines
59 KiB
Rust
1847 lines
59 KiB
Rust
// Copyright 2012-2014 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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//
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// ignore-lexer-test FIXME #15679
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//! Numeric traits and functions for the built-in numeric types.
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#![stable]
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#![allow(missing_docs)]
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pub use self::FPCategory::*;
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use {int, i8, i16, i32, i64};
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use {uint, u8, u16, u32, u64};
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use {f32, f64};
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use char::Char;
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use clone::Clone;
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use cmp::{PartialEq, Eq};
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use cmp::{PartialOrd, Ord};
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use intrinsics;
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use iter::Iterator;
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use kinds::Copy;
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use mem::size_of;
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use ops::{Add, Sub, Mul, Div, Rem, Neg};
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use ops::{Not, BitAnd, BitOr, BitXor, Shl, Shr};
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use option::{Option, Some, None};
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use str::{FromStr, from_str, StrPrelude};
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/// Simultaneous division and remainder
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#[inline]
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#[deprecated = "use division and remainder directly"]
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pub fn div_rem<T: Div<T, T> + Rem<T, T>>(x: T, y: T) -> (T, T) {
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(x / y, x % y)
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}
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/// Raises a `base` to the power of `exp`, using exponentiation by squaring.
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#[inline]
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#[deprecated = "Use Int::pow() instead, as in 2i.pow(4)"]
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pub fn pow<T: Int>(base: T, exp: uint) -> T {
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base.pow(exp)
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}
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/// A built-in signed or unsigned integer.
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#[unstable = "recently settled as part of numerics reform"]
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pub trait Int
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: Copy + Clone
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+ NumCast
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+ PartialOrd + Ord
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+ PartialEq + Eq
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+ Add<Self,Self>
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+ Sub<Self,Self>
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+ Mul<Self,Self>
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+ Div<Self,Self>
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+ Rem<Self,Self>
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+ Not<Self>
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+ BitAnd<Self,Self>
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+ BitOr<Self,Self>
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+ BitXor<Self,Self>
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+ Shl<uint,Self>
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+ Shr<uint,Self>
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{
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/// Returns the `0` value of this integer type.
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// FIXME (#5527): Should be an associated constant
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fn zero() -> Self;
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/// Returns the `1` value of this integer type.
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// FIXME (#5527): Should be an associated constant
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fn one() -> Self;
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/// Returns the smallest value that can be represented by this integer type.
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// FIXME (#5527): Should be and associated constant
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fn min_value() -> Self;
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/// Returns the largest value that can be represented by this integer type.
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// FIXME (#5527): Should be and associated constant
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fn max_value() -> Self;
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/// Returns the number of ones in the binary representation of `self`.
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///
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/// # Example
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///
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/// ```rust
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/// use std::num::Int;
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///
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/// let n = 0b01001100u8;
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///
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/// assert_eq!(n.count_ones(), 3);
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/// ```
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fn count_ones(self) -> uint;
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/// Returns the number of zeros in the binary representation of `self`.
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///
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/// # Example
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///
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/// ```rust
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/// use std::num::Int;
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///
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/// let n = 0b01001100u8;
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///
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/// assert_eq!(n.count_zeros(), 5);
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/// ```
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#[inline]
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fn count_zeros(self) -> uint {
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(!self).count_ones()
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}
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/// Returns the number of leading zeros in the binary representation
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/// of `self`.
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///
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/// # Example
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///
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/// ```rust
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/// use std::num::Int;
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///
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/// let n = 0b0101000u16;
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///
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/// assert_eq!(n.leading_zeros(), 10);
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/// ```
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fn leading_zeros(self) -> uint;
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/// Returns the number of trailing zeros in the binary representation
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/// of `self`.
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///
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/// # Example
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///
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/// ```rust
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/// use std::num::Int;
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///
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/// let n = 0b0101000u16;
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///
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/// assert_eq!(n.trailing_zeros(), 3);
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/// ```
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fn trailing_zeros(self) -> uint;
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/// Shifts the bits to the left by a specified amount amount, `n`, wrapping
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/// the truncated bits to the end of the resulting integer.
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///
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/// # Example
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///
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/// ```rust
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/// use std::num::Int;
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///
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/// let n = 0x0123456789ABCDEFu64;
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/// let m = 0x3456789ABCDEF012u64;
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///
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/// assert_eq!(n.rotate_left(12), m);
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/// ```
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fn rotate_left(self, n: uint) -> Self;
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/// Shifts the bits to the right by a specified amount amount, `n`, wrapping
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/// the truncated bits to the beginning of the resulting integer.
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///
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/// # Example
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///
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/// ```rust
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/// use std::num::Int;
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///
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/// let n = 0x0123456789ABCDEFu64;
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/// let m = 0xDEF0123456789ABCu64;
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///
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/// assert_eq!(n.rotate_right(12), m);
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/// ```
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fn rotate_right(self, n: uint) -> Self;
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/// Reverses the byte order of the integer.
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///
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/// # Example
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///
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/// ```rust
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/// use std::num::Int;
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///
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/// let n = 0x0123456789ABCDEFu64;
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/// let m = 0xEFCDAB8967452301u64;
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///
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/// assert_eq!(n.swap_bytes(), m);
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/// ```
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fn swap_bytes(self) -> Self;
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/// Convert an integer from big endian to the target's endianness.
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///
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/// On big endian this is a no-op. On little endian the bytes are swapped.
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///
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/// # Example
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///
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/// ```rust
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/// use std::num::Int;
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///
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/// let n = 0x0123456789ABCDEFu64;
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///
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/// if cfg!(target_endian = "big") {
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/// assert_eq!(Int::from_be(n), n)
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/// } else {
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/// assert_eq!(Int::from_be(n), n.swap_bytes())
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/// }
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/// ```
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#[inline]
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fn from_be(x: Self) -> Self {
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if cfg!(target_endian = "big") { x } else { x.swap_bytes() }
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}
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/// Convert an integer from little endian to the target's endianness.
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///
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/// On little endian this is a no-op. On big endian the bytes are swapped.
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///
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/// # Example
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///
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/// ```rust
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/// use std::num::Int;
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///
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/// let n = 0x0123456789ABCDEFu64;
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///
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/// if cfg!(target_endian = "little") {
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/// assert_eq!(Int::from_le(n), n)
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/// } else {
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/// assert_eq!(Int::from_le(n), n.swap_bytes())
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/// }
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/// ```
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#[inline]
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fn from_le(x: Self) -> Self {
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if cfg!(target_endian = "little") { x } else { x.swap_bytes() }
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}
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/// Convert `self` to big endian from the target's endianness.
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///
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/// On big endian this is a no-op. On little endian the bytes are swapped.
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///
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/// # Example
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///
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/// ```rust
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/// use std::num::Int;
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///
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/// let n = 0x0123456789ABCDEFu64;
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///
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/// if cfg!(target_endian = "big") {
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/// assert_eq!(n.to_be(), n)
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/// } else {
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/// assert_eq!(n.to_be(), n.swap_bytes())
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/// }
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/// ```
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#[inline]
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fn to_be(self) -> Self { // or not to be?
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if cfg!(target_endian = "big") { self } else { self.swap_bytes() }
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}
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/// Convert `self` to little endian from the target's endianness.
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///
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/// On little endian this is a no-op. On big endian the bytes are swapped.
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///
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/// # Example
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///
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/// ```rust
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/// use std::num::Int;
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///
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/// let n = 0x0123456789ABCDEFu64;
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///
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/// if cfg!(target_endian = "little") {
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/// assert_eq!(n.to_le(), n)
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/// } else {
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/// assert_eq!(n.to_le(), n.swap_bytes())
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/// }
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/// ```
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#[inline]
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fn to_le(self) -> Self {
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if cfg!(target_endian = "little") { self } else { self.swap_bytes() }
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}
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/// Checked integer addition. Computes `self + other`, returning `None` if
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/// overflow occurred.
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///
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/// # Example
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///
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/// ```rust
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/// use std::num::Int;
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///
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/// assert_eq!(5u16.checked_add(65530), Some(65535));
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/// assert_eq!(6u16.checked_add(65530), None);
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/// ```
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fn checked_add(self, other: Self) -> Option<Self>;
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/// Checked integer subtraction. Computes `self + other`, returning `None`
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/// if underflow occurred.
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///
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/// # Example
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///
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/// ```rust
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/// use std::num::Int;
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///
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/// assert_eq!((-127i8).checked_sub(1), Some(-128));
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/// assert_eq!((-128i8).checked_sub(1), None);
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/// ```
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fn checked_sub(self, other: Self) -> Option<Self>;
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/// Checked integer multiplication. Computes `self + other`, returning
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/// `None` if underflow or overflow occurred.
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///
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/// # Example
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///
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/// ```rust
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/// use std::num::Int;
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///
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/// assert_eq!(5u8.checked_mul(51), Some(255));
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/// assert_eq!(5u8.checked_mul(52), None);
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/// ```
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fn checked_mul(self, other: Self) -> Option<Self>;
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/// Checked integer division. Computes `self + other` returning `None` if
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/// `self == 0` or the operation results in underflow or overflow.
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///
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/// # Example
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///
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/// ```rust
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/// use std::num::Int;
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///
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/// assert_eq!((-127i8).checked_div(-1), Some(127));
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/// assert_eq!((-128i8).checked_div(-1), None);
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/// assert_eq!((1i8).checked_div(0), None);
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/// ```
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#[inline]
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fn checked_div(self, other: Self) -> Option<Self>;
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/// Saturating integer addition. Computes `self + other`, saturating at
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/// the numeric bounds instead of overflowing.
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#[inline]
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fn saturating_add(self, other: Self) -> Self {
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match self.checked_add(other) {
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Some(x) => x,
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None if other >= Int::zero() => Int::max_value(),
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None => Int::min_value(),
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}
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}
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/// Saturating integer subtraction. Computes `self - other`, saturating at
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/// the numeric bounds instead of overflowing.
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#[inline]
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fn saturating_sub(self, other: Self) -> Self {
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match self.checked_sub(other) {
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Some(x) => x,
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None if other >= Int::zero() => Int::min_value(),
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None => Int::max_value(),
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}
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}
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/// Raises self to the power of `exp`, using exponentiation by squaring.
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///
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/// # Example
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///
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/// ```rust
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/// use std::num::Int;
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///
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/// assert_eq!(2i.pow(4), 16);
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/// ```
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#[inline]
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fn pow(self, mut exp: uint) -> Self {
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let mut base = self;
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let mut acc: Self = Int::one();
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while exp > 0 {
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if (exp & 1) == 1 {
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acc = acc * base;
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}
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base = base * base;
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exp /= 2;
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}
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acc
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}
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}
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macro_rules! checked_op {
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($T:ty, $U:ty, $op:path, $x:expr, $y:expr) => {{
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let (result, overflowed) = unsafe { $op($x as $U, $y as $U) };
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if overflowed { None } else { Some(result as $T) }
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}}
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}
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macro_rules! uint_impl {
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($T:ty = $ActualT:ty, $BITS:expr,
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$ctpop:path,
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$ctlz:path,
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$cttz:path,
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$bswap:path,
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$add_with_overflow:path,
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$sub_with_overflow:path,
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$mul_with_overflow:path) => {
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#[unstable = "trait is unstable"]
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impl Int for $T {
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#[inline]
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fn zero() -> $T { 0 }
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#[inline]
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fn one() -> $T { 1 }
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#[inline]
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fn min_value() -> $T { 0 }
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#[inline]
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fn max_value() -> $T { -1 }
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#[inline]
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fn count_ones(self) -> uint { unsafe { $ctpop(self as $ActualT) as uint } }
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#[inline]
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fn leading_zeros(self) -> uint { unsafe { $ctlz(self as $ActualT) as uint } }
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#[inline]
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fn trailing_zeros(self) -> uint { unsafe { $cttz(self as $ActualT) as uint } }
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#[inline]
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fn rotate_left(self, n: uint) -> $T {
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// Protect against undefined behaviour for over-long bit shifts
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let n = n % $BITS;
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(self << n) | (self >> (($BITS - n) % $BITS))
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}
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#[inline]
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fn rotate_right(self, n: uint) -> $T {
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// Protect against undefined behaviour for over-long bit shifts
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let n = n % $BITS;
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(self >> n) | (self << (($BITS - n) % $BITS))
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}
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#[inline]
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fn swap_bytes(self) -> $T { unsafe { $bswap(self as $ActualT) as $T } }
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#[inline]
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fn checked_add(self, other: $T) -> Option<$T> {
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checked_op!($T, $ActualT, $add_with_overflow, self, other)
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}
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#[inline]
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fn checked_sub(self, other: $T) -> Option<$T> {
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checked_op!($T, $ActualT, $sub_with_overflow, self, other)
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}
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#[inline]
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fn checked_mul(self, other: $T) -> Option<$T> {
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checked_op!($T, $ActualT, $mul_with_overflow, self, other)
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}
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#[inline]
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fn checked_div(self, v: $T) -> Option<$T> {
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match v {
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0 => None,
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v => Some(self / v),
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}
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}
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}
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}
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}
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/// Swapping a single byte is a no-op. This is marked as `unsafe` for
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/// consistency with the other `bswap` intrinsics.
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unsafe fn bswap8(x: u8) -> u8 { x }
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uint_impl!(u8 = u8, 8,
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intrinsics::ctpop8,
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intrinsics::ctlz8,
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intrinsics::cttz8,
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bswap8,
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intrinsics::u8_add_with_overflow,
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intrinsics::u8_sub_with_overflow,
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intrinsics::u8_mul_with_overflow)
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uint_impl!(u16 = u16, 16,
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intrinsics::ctpop16,
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intrinsics::ctlz16,
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intrinsics::cttz16,
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intrinsics::bswap16,
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intrinsics::u16_add_with_overflow,
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intrinsics::u16_sub_with_overflow,
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intrinsics::u16_mul_with_overflow)
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uint_impl!(u32 = u32, 32,
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intrinsics::ctpop32,
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intrinsics::ctlz32,
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intrinsics::cttz32,
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intrinsics::bswap32,
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intrinsics::u32_add_with_overflow,
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intrinsics::u32_sub_with_overflow,
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intrinsics::u32_mul_with_overflow)
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uint_impl!(u64 = u64, 64,
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intrinsics::ctpop64,
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intrinsics::ctlz64,
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intrinsics::cttz64,
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intrinsics::bswap64,
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intrinsics::u64_add_with_overflow,
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intrinsics::u64_sub_with_overflow,
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intrinsics::u64_mul_with_overflow)
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#[cfg(target_word_size = "32")]
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uint_impl!(uint = u32, 32,
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intrinsics::ctpop32,
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intrinsics::ctlz32,
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intrinsics::cttz32,
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intrinsics::bswap32,
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intrinsics::u32_add_with_overflow,
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intrinsics::u32_sub_with_overflow,
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intrinsics::u32_mul_with_overflow)
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#[cfg(target_word_size = "64")]
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uint_impl!(uint = u64, 64,
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intrinsics::ctpop64,
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intrinsics::ctlz64,
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intrinsics::cttz64,
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intrinsics::bswap64,
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intrinsics::u64_add_with_overflow,
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intrinsics::u64_sub_with_overflow,
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intrinsics::u64_mul_with_overflow)
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macro_rules! int_impl {
|
|
($T:ty = $ActualT:ty, $UnsignedT:ty, $BITS:expr,
|
|
$add_with_overflow:path,
|
|
$sub_with_overflow:path,
|
|
$mul_with_overflow:path) => {
|
|
#[unstable = "trait is unstable"]
|
|
impl Int for $T {
|
|
#[inline]
|
|
fn zero() -> $T { 0 }
|
|
|
|
#[inline]
|
|
fn one() -> $T { 1 }
|
|
|
|
#[inline]
|
|
fn min_value() -> $T { (-1 as $T) << ($BITS - 1) }
|
|
|
|
#[inline]
|
|
fn max_value() -> $T { let min: $T = Int::min_value(); !min }
|
|
|
|
#[inline]
|
|
fn count_ones(self) -> uint { (self as $UnsignedT).count_ones() }
|
|
|
|
#[inline]
|
|
fn leading_zeros(self) -> uint { (self as $UnsignedT).leading_zeros() }
|
|
|
|
#[inline]
|
|
fn trailing_zeros(self) -> uint { (self as $UnsignedT).trailing_zeros() }
|
|
|
|
#[inline]
|
|
fn rotate_left(self, n: uint) -> $T { (self as $UnsignedT).rotate_left(n) as $T }
|
|
|
|
#[inline]
|
|
fn rotate_right(self, n: uint) -> $T { (self as $UnsignedT).rotate_right(n) as $T }
|
|
|
|
#[inline]
|
|
fn swap_bytes(self) -> $T { (self as $UnsignedT).swap_bytes() as $T }
|
|
|
|
#[inline]
|
|
fn checked_add(self, other: $T) -> Option<$T> {
|
|
checked_op!($T, $ActualT, $add_with_overflow, self, other)
|
|
}
|
|
|
|
#[inline]
|
|
fn checked_sub(self, other: $T) -> Option<$T> {
|
|
checked_op!($T, $ActualT, $sub_with_overflow, self, other)
|
|
}
|
|
|
|
#[inline]
|
|
fn checked_mul(self, other: $T) -> Option<$T> {
|
|
checked_op!($T, $ActualT, $mul_with_overflow, self, other)
|
|
}
|
|
|
|
#[inline]
|
|
fn checked_div(self, v: $T) -> Option<$T> {
|
|
match v {
|
|
0 => None,
|
|
-1 if self == Int::min_value()
|
|
=> None,
|
|
v => Some(self / v),
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
int_impl!(i8 = i8, u8, 8,
|
|
intrinsics::i8_add_with_overflow,
|
|
intrinsics::i8_sub_with_overflow,
|
|
intrinsics::i8_mul_with_overflow)
|
|
|
|
int_impl!(i16 = i16, u16, 16,
|
|
intrinsics::i16_add_with_overflow,
|
|
intrinsics::i16_sub_with_overflow,
|
|
intrinsics::i16_mul_with_overflow)
|
|
|
|
int_impl!(i32 = i32, u32, 32,
|
|
intrinsics::i32_add_with_overflow,
|
|
intrinsics::i32_sub_with_overflow,
|
|
intrinsics::i32_mul_with_overflow)
|
|
|
|
int_impl!(i64 = i64, u64, 64,
|
|
intrinsics::i64_add_with_overflow,
|
|
intrinsics::i64_sub_with_overflow,
|
|
intrinsics::i64_mul_with_overflow)
|
|
|
|
#[cfg(target_word_size = "32")]
|
|
int_impl!(int = i32, u32, 32,
|
|
intrinsics::i32_add_with_overflow,
|
|
intrinsics::i32_sub_with_overflow,
|
|
intrinsics::i32_mul_with_overflow)
|
|
|
|
#[cfg(target_word_size = "64")]
|
|
int_impl!(int = i64, u64, 64,
|
|
intrinsics::i64_add_with_overflow,
|
|
intrinsics::i64_sub_with_overflow,
|
|
intrinsics::i64_mul_with_overflow)
|
|
|
|
/// A built-in two's complement integer.
|
|
#[unstable = "recently settled as part of numerics reform"]
|
|
pub trait SignedInt
|
|
: Int
|
|
+ Neg<Self>
|
|
{
|
|
/// Computes the absolute value of `self`. `Int::min_value()` will be
|
|
/// returned if the number is `Int::min_value()`.
|
|
fn abs(self) -> Self;
|
|
|
|
/// Returns a number representing sign of `self`.
|
|
///
|
|
/// - `0` if the number is zero
|
|
/// - `1` if the number is positive
|
|
/// - `-1` if the number is negative
|
|
fn signum(self) -> Self;
|
|
|
|
/// Returns `true` if `self` is positive and `false` if the number
|
|
/// is zero or negative.
|
|
fn is_positive(self) -> bool;
|
|
|
|
/// Returns `true` if `self` is negative and `false` if the number
|
|
/// is zero or positive.
|
|
fn is_negative(self) -> bool;
|
|
}
|
|
|
|
macro_rules! signed_int_impl {
|
|
($T:ty) => {
|
|
impl SignedInt for $T {
|
|
#[inline]
|
|
fn abs(self) -> $T {
|
|
if self.is_negative() { -self } else { self }
|
|
}
|
|
|
|
#[inline]
|
|
fn signum(self) -> $T {
|
|
match self {
|
|
n if n > 0 => 1,
|
|
0 => 0,
|
|
_ => -1,
|
|
}
|
|
}
|
|
|
|
#[inline]
|
|
fn is_positive(self) -> bool { self > 0 }
|
|
|
|
#[inline]
|
|
fn is_negative(self) -> bool { self < 0 }
|
|
}
|
|
}
|
|
}
|
|
|
|
signed_int_impl!(i8)
|
|
signed_int_impl!(i16)
|
|
signed_int_impl!(i32)
|
|
signed_int_impl!(i64)
|
|
signed_int_impl!(int)
|
|
|
|
/// A built-in unsigned integer.
|
|
#[unstable = "recently settled as part of numerics reform"]
|
|
pub trait UnsignedInt: Int {
|
|
/// Returns `true` iff `self == 2^k` for some `k`.
|
|
fn is_power_of_two(self) -> bool {
|
|
(self - Int::one()) & self == Int::zero()
|
|
}
|
|
|
|
/// Returns the smallest power of two greater than or equal to `self`.
|
|
#[inline]
|
|
fn next_power_of_two(self) -> Self {
|
|
let halfbits = size_of::<Self>() * 4;
|
|
let mut tmp = self - Int::one();
|
|
let mut shift = 1u;
|
|
while shift <= halfbits {
|
|
tmp = tmp | (tmp >> shift);
|
|
shift = shift << 1u;
|
|
}
|
|
tmp + Int::one()
|
|
}
|
|
|
|
/// Returns the smallest power of two greater than or equal to `n`. If the
|
|
/// next power of two is greater than the type's maximum value, `None` is
|
|
/// returned, otherwise the power of two is wrapped in `Some`.
|
|
fn checked_next_power_of_two(self) -> Option<Self> {
|
|
let halfbits = size_of::<Self>() * 4;
|
|
let mut tmp = self - Int::one();
|
|
let mut shift = 1u;
|
|
while shift <= halfbits {
|
|
tmp = tmp | (tmp >> shift);
|
|
shift = shift << 1u;
|
|
}
|
|
tmp.checked_add(Int::one())
|
|
}
|
|
}
|
|
|
|
#[unstable = "trait is unstable"]
|
|
impl UnsignedInt for uint {}
|
|
|
|
#[unstable = "trait is unstable"]
|
|
impl UnsignedInt for u8 {}
|
|
|
|
#[unstable = "trait is unstable"]
|
|
impl UnsignedInt for u16 {}
|
|
|
|
#[unstable = "trait is unstable"]
|
|
impl UnsignedInt for u32 {}
|
|
|
|
#[unstable = "trait is unstable"]
|
|
impl UnsignedInt for u64 {}
|
|
|
|
/// A generic trait for converting a value to a number.
|
|
#[experimental = "trait is likely to be removed"]
|
|
pub trait ToPrimitive {
|
|
/// Converts the value of `self` to an `int`.
|
|
#[inline]
|
|
fn to_int(&self) -> Option<int> {
|
|
self.to_i64().and_then(|x| x.to_int())
|
|
}
|
|
|
|
/// Converts the value of `self` to an `i8`.
|
|
#[inline]
|
|
fn to_i8(&self) -> Option<i8> {
|
|
self.to_i64().and_then(|x| x.to_i8())
|
|
}
|
|
|
|
/// Converts the value of `self` to an `i16`.
|
|
#[inline]
|
|
fn to_i16(&self) -> Option<i16> {
|
|
self.to_i64().and_then(|x| x.to_i16())
|
|
}
|
|
|
|
/// Converts the value of `self` to an `i32`.
|
|
#[inline]
|
|
fn to_i32(&self) -> Option<i32> {
|
|
self.to_i64().and_then(|x| x.to_i32())
|
|
}
|
|
|
|
/// Converts the value of `self` to an `i64`.
|
|
fn to_i64(&self) -> Option<i64>;
|
|
|
|
/// Converts the value of `self` to an `uint`.
|
|
#[inline]
|
|
fn to_uint(&self) -> Option<uint> {
|
|
self.to_u64().and_then(|x| x.to_uint())
|
|
}
|
|
|
|
/// Converts the value of `self` to an `u8`.
|
|
#[inline]
|
|
fn to_u8(&self) -> Option<u8> {
|
|
self.to_u64().and_then(|x| x.to_u8())
|
|
}
|
|
|
|
/// Converts the value of `self` to an `u16`.
|
|
#[inline]
|
|
fn to_u16(&self) -> Option<u16> {
|
|
self.to_u64().and_then(|x| x.to_u16())
|
|
}
|
|
|
|
/// Converts the value of `self` to an `u32`.
|
|
#[inline]
|
|
fn to_u32(&self) -> Option<u32> {
|
|
self.to_u64().and_then(|x| x.to_u32())
|
|
}
|
|
|
|
/// Converts the value of `self` to an `u64`.
|
|
#[inline]
|
|
fn to_u64(&self) -> Option<u64>;
|
|
|
|
/// Converts the value of `self` to an `f32`.
|
|
#[inline]
|
|
fn to_f32(&self) -> Option<f32> {
|
|
self.to_f64().and_then(|x| x.to_f32())
|
|
}
|
|
|
|
/// Converts the value of `self` to an `f64`.
|
|
#[inline]
|
|
fn to_f64(&self) -> Option<f64> {
|
|
self.to_i64().and_then(|x| x.to_f64())
|
|
}
|
|
}
|
|
|
|
macro_rules! impl_to_primitive_int_to_int(
|
|
($SrcT:ty, $DstT:ty, $slf:expr) => (
|
|
{
|
|
if size_of::<$SrcT>() <= size_of::<$DstT>() {
|
|
Some($slf as $DstT)
|
|
} else {
|
|
let n = $slf as i64;
|
|
let min_value: $DstT = Int::min_value();
|
|
let max_value: $DstT = Int::max_value();
|
|
if min_value as i64 <= n && n <= max_value as i64 {
|
|
Some($slf as $DstT)
|
|
} else {
|
|
None
|
|
}
|
|
}
|
|
}
|
|
)
|
|
)
|
|
|
|
macro_rules! impl_to_primitive_int_to_uint(
|
|
($SrcT:ty, $DstT:ty, $slf:expr) => (
|
|
{
|
|
let zero: $SrcT = Int::zero();
|
|
let max_value: $DstT = Int::max_value();
|
|
if zero <= $slf && $slf as u64 <= max_value as u64 {
|
|
Some($slf as $DstT)
|
|
} else {
|
|
None
|
|
}
|
|
}
|
|
)
|
|
)
|
|
|
|
macro_rules! impl_to_primitive_int(
|
|
($T:ty) => (
|
|
impl ToPrimitive for $T {
|
|
#[inline]
|
|
fn to_int(&self) -> Option<int> { impl_to_primitive_int_to_int!($T, int, *self) }
|
|
#[inline]
|
|
fn to_i8(&self) -> Option<i8> { impl_to_primitive_int_to_int!($T, i8, *self) }
|
|
#[inline]
|
|
fn to_i16(&self) -> Option<i16> { impl_to_primitive_int_to_int!($T, i16, *self) }
|
|
#[inline]
|
|
fn to_i32(&self) -> Option<i32> { impl_to_primitive_int_to_int!($T, i32, *self) }
|
|
#[inline]
|
|
fn to_i64(&self) -> Option<i64> { impl_to_primitive_int_to_int!($T, i64, *self) }
|
|
|
|
#[inline]
|
|
fn to_uint(&self) -> Option<uint> { impl_to_primitive_int_to_uint!($T, uint, *self) }
|
|
#[inline]
|
|
fn to_u8(&self) -> Option<u8> { impl_to_primitive_int_to_uint!($T, u8, *self) }
|
|
#[inline]
|
|
fn to_u16(&self) -> Option<u16> { impl_to_primitive_int_to_uint!($T, u16, *self) }
|
|
#[inline]
|
|
fn to_u32(&self) -> Option<u32> { impl_to_primitive_int_to_uint!($T, u32, *self) }
|
|
#[inline]
|
|
fn to_u64(&self) -> Option<u64> { impl_to_primitive_int_to_uint!($T, u64, *self) }
|
|
|
|
#[inline]
|
|
fn to_f32(&self) -> Option<f32> { Some(*self as f32) }
|
|
#[inline]
|
|
fn to_f64(&self) -> Option<f64> { Some(*self as f64) }
|
|
}
|
|
)
|
|
)
|
|
|
|
impl_to_primitive_int!(int)
|
|
impl_to_primitive_int!(i8)
|
|
impl_to_primitive_int!(i16)
|
|
impl_to_primitive_int!(i32)
|
|
impl_to_primitive_int!(i64)
|
|
|
|
macro_rules! impl_to_primitive_uint_to_int(
|
|
($DstT:ty, $slf:expr) => (
|
|
{
|
|
let max_value: $DstT = Int::max_value();
|
|
if $slf as u64 <= max_value as u64 {
|
|
Some($slf as $DstT)
|
|
} else {
|
|
None
|
|
}
|
|
}
|
|
)
|
|
)
|
|
|
|
macro_rules! impl_to_primitive_uint_to_uint(
|
|
($SrcT:ty, $DstT:ty, $slf:expr) => (
|
|
{
|
|
if size_of::<$SrcT>() <= size_of::<$DstT>() {
|
|
Some($slf as $DstT)
|
|
} else {
|
|
let zero: $SrcT = Int::zero();
|
|
let max_value: $DstT = Int::max_value();
|
|
if zero <= $slf && $slf as u64 <= max_value as u64 {
|
|
Some($slf as $DstT)
|
|
} else {
|
|
None
|
|
}
|
|
}
|
|
}
|
|
)
|
|
)
|
|
|
|
macro_rules! impl_to_primitive_uint(
|
|
($T:ty) => (
|
|
impl ToPrimitive for $T {
|
|
#[inline]
|
|
fn to_int(&self) -> Option<int> { impl_to_primitive_uint_to_int!(int, *self) }
|
|
#[inline]
|
|
fn to_i8(&self) -> Option<i8> { impl_to_primitive_uint_to_int!(i8, *self) }
|
|
#[inline]
|
|
fn to_i16(&self) -> Option<i16> { impl_to_primitive_uint_to_int!(i16, *self) }
|
|
#[inline]
|
|
fn to_i32(&self) -> Option<i32> { impl_to_primitive_uint_to_int!(i32, *self) }
|
|
#[inline]
|
|
fn to_i64(&self) -> Option<i64> { impl_to_primitive_uint_to_int!(i64, *self) }
|
|
|
|
#[inline]
|
|
fn to_uint(&self) -> Option<uint> { impl_to_primitive_uint_to_uint!($T, uint, *self) }
|
|
#[inline]
|
|
fn to_u8(&self) -> Option<u8> { impl_to_primitive_uint_to_uint!($T, u8, *self) }
|
|
#[inline]
|
|
fn to_u16(&self) -> Option<u16> { impl_to_primitive_uint_to_uint!($T, u16, *self) }
|
|
#[inline]
|
|
fn to_u32(&self) -> Option<u32> { impl_to_primitive_uint_to_uint!($T, u32, *self) }
|
|
#[inline]
|
|
fn to_u64(&self) -> Option<u64> { impl_to_primitive_uint_to_uint!($T, u64, *self) }
|
|
|
|
#[inline]
|
|
fn to_f32(&self) -> Option<f32> { Some(*self as f32) }
|
|
#[inline]
|
|
fn to_f64(&self) -> Option<f64> { Some(*self as f64) }
|
|
}
|
|
)
|
|
)
|
|
|
|
impl_to_primitive_uint!(uint)
|
|
impl_to_primitive_uint!(u8)
|
|
impl_to_primitive_uint!(u16)
|
|
impl_to_primitive_uint!(u32)
|
|
impl_to_primitive_uint!(u64)
|
|
|
|
macro_rules! impl_to_primitive_float_to_float(
|
|
($SrcT:ty, $DstT:ty, $slf:expr) => (
|
|
if size_of::<$SrcT>() <= size_of::<$DstT>() {
|
|
Some($slf as $DstT)
|
|
} else {
|
|
let n = $slf as f64;
|
|
let max_value: $SrcT = Float::max_value();
|
|
if -max_value as f64 <= n && n <= max_value as f64 {
|
|
Some($slf as $DstT)
|
|
} else {
|
|
None
|
|
}
|
|
}
|
|
)
|
|
)
|
|
|
|
macro_rules! impl_to_primitive_float(
|
|
($T:ty) => (
|
|
impl ToPrimitive for $T {
|
|
#[inline]
|
|
fn to_int(&self) -> Option<int> { Some(*self as int) }
|
|
#[inline]
|
|
fn to_i8(&self) -> Option<i8> { Some(*self as i8) }
|
|
#[inline]
|
|
fn to_i16(&self) -> Option<i16> { Some(*self as i16) }
|
|
#[inline]
|
|
fn to_i32(&self) -> Option<i32> { Some(*self as i32) }
|
|
#[inline]
|
|
fn to_i64(&self) -> Option<i64> { Some(*self as i64) }
|
|
|
|
#[inline]
|
|
fn to_uint(&self) -> Option<uint> { Some(*self as uint) }
|
|
#[inline]
|
|
fn to_u8(&self) -> Option<u8> { Some(*self as u8) }
|
|
#[inline]
|
|
fn to_u16(&self) -> Option<u16> { Some(*self as u16) }
|
|
#[inline]
|
|
fn to_u32(&self) -> Option<u32> { Some(*self as u32) }
|
|
#[inline]
|
|
fn to_u64(&self) -> Option<u64> { Some(*self as u64) }
|
|
|
|
#[inline]
|
|
fn to_f32(&self) -> Option<f32> { impl_to_primitive_float_to_float!($T, f32, *self) }
|
|
#[inline]
|
|
fn to_f64(&self) -> Option<f64> { impl_to_primitive_float_to_float!($T, f64, *self) }
|
|
}
|
|
)
|
|
)
|
|
|
|
impl_to_primitive_float!(f32)
|
|
impl_to_primitive_float!(f64)
|
|
|
|
/// A generic trait for converting a number to a value.
|
|
#[experimental = "trait is likely to be removed"]
|
|
pub trait FromPrimitive {
|
|
/// Convert an `int` to return an optional value of this type. If the
|
|
/// value cannot be represented by this value, the `None` is returned.
|
|
#[inline]
|
|
fn from_int(n: int) -> Option<Self> {
|
|
FromPrimitive::from_i64(n as i64)
|
|
}
|
|
|
|
/// Convert an `i8` to return an optional value of this type. If the
|
|
/// type cannot be represented by this value, the `None` is returned.
|
|
#[inline]
|
|
fn from_i8(n: i8) -> Option<Self> {
|
|
FromPrimitive::from_i64(n as i64)
|
|
}
|
|
|
|
/// Convert an `i16` to return an optional value of this type. If the
|
|
/// type cannot be represented by this value, the `None` is returned.
|
|
#[inline]
|
|
fn from_i16(n: i16) -> Option<Self> {
|
|
FromPrimitive::from_i64(n as i64)
|
|
}
|
|
|
|
/// Convert an `i32` to return an optional value of this type. If the
|
|
/// type cannot be represented by this value, the `None` is returned.
|
|
#[inline]
|
|
fn from_i32(n: i32) -> Option<Self> {
|
|
FromPrimitive::from_i64(n as i64)
|
|
}
|
|
|
|
/// Convert an `i64` to return an optional value of this type. If the
|
|
/// type cannot be represented by this value, the `None` is returned.
|
|
fn from_i64(n: i64) -> Option<Self>;
|
|
|
|
/// Convert an `uint` to return an optional value of this type. If the
|
|
/// type cannot be represented by this value, the `None` is returned.
|
|
#[inline]
|
|
fn from_uint(n: uint) -> Option<Self> {
|
|
FromPrimitive::from_u64(n as u64)
|
|
}
|
|
|
|
/// Convert an `u8` to return an optional value of this type. If the
|
|
/// type cannot be represented by this value, the `None` is returned.
|
|
#[inline]
|
|
fn from_u8(n: u8) -> Option<Self> {
|
|
FromPrimitive::from_u64(n as u64)
|
|
}
|
|
|
|
/// Convert an `u16` to return an optional value of this type. If the
|
|
/// type cannot be represented by this value, the `None` is returned.
|
|
#[inline]
|
|
fn from_u16(n: u16) -> Option<Self> {
|
|
FromPrimitive::from_u64(n as u64)
|
|
}
|
|
|
|
/// Convert an `u32` to return an optional value of this type. If the
|
|
/// type cannot be represented by this value, the `None` is returned.
|
|
#[inline]
|
|
fn from_u32(n: u32) -> Option<Self> {
|
|
FromPrimitive::from_u64(n as u64)
|
|
}
|
|
|
|
/// Convert an `u64` to return an optional value of this type. If the
|
|
/// type cannot be represented by this value, the `None` is returned.
|
|
fn from_u64(n: u64) -> Option<Self>;
|
|
|
|
/// Convert a `f32` to return an optional value of this type. If the
|
|
/// type cannot be represented by this value, the `None` is returned.
|
|
#[inline]
|
|
fn from_f32(n: f32) -> Option<Self> {
|
|
FromPrimitive::from_f64(n as f64)
|
|
}
|
|
|
|
/// Convert a `f64` to return an optional value of this type. If the
|
|
/// type cannot be represented by this value, the `None` is returned.
|
|
#[inline]
|
|
fn from_f64(n: f64) -> Option<Self> {
|
|
FromPrimitive::from_i64(n as i64)
|
|
}
|
|
}
|
|
|
|
/// A utility function that just calls `FromPrimitive::from_int`.
|
|
#[experimental = "likely to be removed"]
|
|
pub fn from_int<A: FromPrimitive>(n: int) -> Option<A> {
|
|
FromPrimitive::from_int(n)
|
|
}
|
|
|
|
/// A utility function that just calls `FromPrimitive::from_i8`.
|
|
#[experimental = "likely to be removed"]
|
|
pub fn from_i8<A: FromPrimitive>(n: i8) -> Option<A> {
|
|
FromPrimitive::from_i8(n)
|
|
}
|
|
|
|
/// A utility function that just calls `FromPrimitive::from_i16`.
|
|
#[experimental = "likely to be removed"]
|
|
pub fn from_i16<A: FromPrimitive>(n: i16) -> Option<A> {
|
|
FromPrimitive::from_i16(n)
|
|
}
|
|
|
|
/// A utility function that just calls `FromPrimitive::from_i32`.
|
|
#[experimental = "likely to be removed"]
|
|
pub fn from_i32<A: FromPrimitive>(n: i32) -> Option<A> {
|
|
FromPrimitive::from_i32(n)
|
|
}
|
|
|
|
/// A utility function that just calls `FromPrimitive::from_i64`.
|
|
#[experimental = "likely to be removed"]
|
|
pub fn from_i64<A: FromPrimitive>(n: i64) -> Option<A> {
|
|
FromPrimitive::from_i64(n)
|
|
}
|
|
|
|
/// A utility function that just calls `FromPrimitive::from_uint`.
|
|
#[experimental = "likely to be removed"]
|
|
pub fn from_uint<A: FromPrimitive>(n: uint) -> Option<A> {
|
|
FromPrimitive::from_uint(n)
|
|
}
|
|
|
|
/// A utility function that just calls `FromPrimitive::from_u8`.
|
|
#[experimental = "likely to be removed"]
|
|
pub fn from_u8<A: FromPrimitive>(n: u8) -> Option<A> {
|
|
FromPrimitive::from_u8(n)
|
|
}
|
|
|
|
/// A utility function that just calls `FromPrimitive::from_u16`.
|
|
#[experimental = "likely to be removed"]
|
|
pub fn from_u16<A: FromPrimitive>(n: u16) -> Option<A> {
|
|
FromPrimitive::from_u16(n)
|
|
}
|
|
|
|
/// A utility function that just calls `FromPrimitive::from_u32`.
|
|
#[experimental = "likely to be removed"]
|
|
pub fn from_u32<A: FromPrimitive>(n: u32) -> Option<A> {
|
|
FromPrimitive::from_u32(n)
|
|
}
|
|
|
|
/// A utility function that just calls `FromPrimitive::from_u64`.
|
|
#[experimental = "likely to be removed"]
|
|
pub fn from_u64<A: FromPrimitive>(n: u64) -> Option<A> {
|
|
FromPrimitive::from_u64(n)
|
|
}
|
|
|
|
/// A utility function that just calls `FromPrimitive::from_f32`.
|
|
#[experimental = "likely to be removed"]
|
|
pub fn from_f32<A: FromPrimitive>(n: f32) -> Option<A> {
|
|
FromPrimitive::from_f32(n)
|
|
}
|
|
|
|
/// A utility function that just calls `FromPrimitive::from_f64`.
|
|
#[experimental = "likely to be removed"]
|
|
pub fn from_f64<A: FromPrimitive>(n: f64) -> Option<A> {
|
|
FromPrimitive::from_f64(n)
|
|
}
|
|
|
|
macro_rules! impl_from_primitive(
|
|
($T:ty, $to_ty:ident) => (
|
|
impl FromPrimitive for $T {
|
|
#[inline] fn from_int(n: int) -> Option<$T> { n.$to_ty() }
|
|
#[inline] fn from_i8(n: i8) -> Option<$T> { n.$to_ty() }
|
|
#[inline] fn from_i16(n: i16) -> Option<$T> { n.$to_ty() }
|
|
#[inline] fn from_i32(n: i32) -> Option<$T> { n.$to_ty() }
|
|
#[inline] fn from_i64(n: i64) -> Option<$T> { n.$to_ty() }
|
|
|
|
#[inline] fn from_uint(n: uint) -> Option<$T> { n.$to_ty() }
|
|
#[inline] fn from_u8(n: u8) -> Option<$T> { n.$to_ty() }
|
|
#[inline] fn from_u16(n: u16) -> Option<$T> { n.$to_ty() }
|
|
#[inline] fn from_u32(n: u32) -> Option<$T> { n.$to_ty() }
|
|
#[inline] fn from_u64(n: u64) -> Option<$T> { n.$to_ty() }
|
|
|
|
#[inline] fn from_f32(n: f32) -> Option<$T> { n.$to_ty() }
|
|
#[inline] fn from_f64(n: f64) -> Option<$T> { n.$to_ty() }
|
|
}
|
|
)
|
|
)
|
|
|
|
impl_from_primitive!(int, to_int)
|
|
impl_from_primitive!(i8, to_i8)
|
|
impl_from_primitive!(i16, to_i16)
|
|
impl_from_primitive!(i32, to_i32)
|
|
impl_from_primitive!(i64, to_i64)
|
|
impl_from_primitive!(uint, to_uint)
|
|
impl_from_primitive!(u8, to_u8)
|
|
impl_from_primitive!(u16, to_u16)
|
|
impl_from_primitive!(u32, to_u32)
|
|
impl_from_primitive!(u64, to_u64)
|
|
impl_from_primitive!(f32, to_f32)
|
|
impl_from_primitive!(f64, to_f64)
|
|
|
|
/// Cast from one machine scalar to another.
|
|
///
|
|
/// # Example
|
|
///
|
|
/// ```
|
|
/// use std::num;
|
|
///
|
|
/// let twenty: f32 = num::cast(0x14i).unwrap();
|
|
/// assert_eq!(twenty, 20f32);
|
|
/// ```
|
|
///
|
|
#[inline]
|
|
#[experimental = "likely to be removed"]
|
|
pub fn cast<T: NumCast,U: NumCast>(n: T) -> Option<U> {
|
|
NumCast::from(n)
|
|
}
|
|
|
|
/// An interface for casting between machine scalars.
|
|
#[experimental = "trait is likely to be removed"]
|
|
pub trait NumCast: ToPrimitive {
|
|
/// Creates a number from another value that can be converted into a primitive via the
|
|
/// `ToPrimitive` trait.
|
|
fn from<T: ToPrimitive>(n: T) -> Option<Self>;
|
|
}
|
|
|
|
macro_rules! impl_num_cast(
|
|
($T:ty, $conv:ident) => (
|
|
impl NumCast for $T {
|
|
#[inline]
|
|
fn from<N: ToPrimitive>(n: N) -> Option<$T> {
|
|
// `$conv` could be generated using `concat_idents!`, but that
|
|
// macro seems to be broken at the moment
|
|
n.$conv()
|
|
}
|
|
}
|
|
)
|
|
)
|
|
|
|
impl_num_cast!(u8, to_u8)
|
|
impl_num_cast!(u16, to_u16)
|
|
impl_num_cast!(u32, to_u32)
|
|
impl_num_cast!(u64, to_u64)
|
|
impl_num_cast!(uint, to_uint)
|
|
impl_num_cast!(i8, to_i8)
|
|
impl_num_cast!(i16, to_i16)
|
|
impl_num_cast!(i32, to_i32)
|
|
impl_num_cast!(i64, to_i64)
|
|
impl_num_cast!(int, to_int)
|
|
impl_num_cast!(f32, to_f32)
|
|
impl_num_cast!(f64, to_f64)
|
|
|
|
/// Used for representing the classification of floating point numbers
|
|
#[deriving(PartialEq, Show)]
|
|
#[unstable = "may be renamed"]
|
|
pub enum FPCategory {
|
|
/// "Not a Number", often obtained by dividing by zero
|
|
FPNaN,
|
|
/// Positive or negative infinity
|
|
FPInfinite ,
|
|
/// Positive or negative zero
|
|
FPZero,
|
|
/// De-normalized floating point representation (less precise than `FPNormal`)
|
|
FPSubnormal,
|
|
/// A regular floating point number
|
|
FPNormal,
|
|
}
|
|
|
|
/// A built-in floating point number.
|
|
// FIXME(#5527): In a future version of Rust, many of these functions will
|
|
// become constants.
|
|
//
|
|
// FIXME(#8888): Several of these functions have a parameter named
|
|
// `unused_self`. Removing it requires #8888 to be fixed.
|
|
#[unstable = "recently settled as part of numerics reform"]
|
|
pub trait Float
|
|
: Copy + Clone
|
|
+ NumCast
|
|
+ PartialOrd
|
|
+ PartialEq
|
|
+ Neg<Self>
|
|
+ Add<Self,Self>
|
|
+ Sub<Self,Self>
|
|
+ Mul<Self,Self>
|
|
+ Div<Self,Self>
|
|
+ Rem<Self,Self>
|
|
{
|
|
/// Returns the NaN value.
|
|
fn nan() -> Self;
|
|
/// Returns the infinite value.
|
|
fn infinity() -> Self;
|
|
/// Returns the negative infinite value.
|
|
fn neg_infinity() -> Self;
|
|
/// Returns the `0` value.
|
|
fn zero() -> Self;
|
|
/// Returns -0.0.
|
|
fn neg_zero() -> Self;
|
|
/// Returns the `1` value.
|
|
fn one() -> Self;
|
|
|
|
/// Returns true if this value is NaN and false otherwise.
|
|
fn is_nan(self) -> bool;
|
|
/// Returns true if this value is positive infinity or negative infinity and
|
|
/// false otherwise.
|
|
fn is_infinite(self) -> bool;
|
|
/// Returns true if this number is neither infinite nor NaN.
|
|
fn is_finite(self) -> bool;
|
|
/// Returns true if this number is neither zero, infinite, denormal, or NaN.
|
|
fn is_normal(self) -> bool;
|
|
/// Returns the category that this number falls into.
|
|
fn classify(self) -> FPCategory;
|
|
|
|
// FIXME (#5527): These should be associated constants
|
|
|
|
/// Returns the number of binary digits of mantissa that this type supports.
|
|
fn mantissa_digits(unused_self: Option<Self>) -> uint;
|
|
/// Returns the number of base-10 digits of precision that this type supports.
|
|
fn digits(unused_self: Option<Self>) -> uint;
|
|
/// Returns the difference between 1.0 and the smallest representable number larger than 1.0.
|
|
fn epsilon() -> Self;
|
|
/// Returns the minimum binary exponent that this type can represent.
|
|
fn min_exp(unused_self: Option<Self>) -> int;
|
|
/// Returns the maximum binary exponent that this type can represent.
|
|
fn max_exp(unused_self: Option<Self>) -> int;
|
|
/// Returns the minimum base-10 exponent that this type can represent.
|
|
fn min_10_exp(unused_self: Option<Self>) -> int;
|
|
/// Returns the maximum base-10 exponent that this type can represent.
|
|
fn max_10_exp(unused_self: Option<Self>) -> int;
|
|
/// Returns the smallest finite value that this type can represent.
|
|
fn min_value() -> Self;
|
|
/// Returns the smallest normalized positive number that this type can represent.
|
|
fn min_pos_value(unused_self: Option<Self>) -> Self;
|
|
/// Returns the largest finite value that this type can represent.
|
|
fn max_value() -> Self;
|
|
|
|
/// Returns the mantissa, exponent and sign as integers, respectively.
|
|
fn integer_decode(self) -> (u64, i16, i8);
|
|
|
|
/// Return the largest integer less than or equal to a number.
|
|
fn floor(self) -> Self;
|
|
/// Return the smallest integer greater than or equal to a number.
|
|
fn ceil(self) -> Self;
|
|
/// Return the nearest integer to a number. Round half-way cases away from
|
|
/// `0.0`.
|
|
fn round(self) -> Self;
|
|
/// Return the integer part of a number.
|
|
fn trunc(self) -> Self;
|
|
/// Return the fractional part of a number.
|
|
fn fract(self) -> Self;
|
|
|
|
/// Computes the absolute value of `self`. Returns `Float::nan()` if the
|
|
/// number is `Float::nan()`.
|
|
fn abs(self) -> Self;
|
|
/// Returns a number that represents the sign of `self`.
|
|
///
|
|
/// - `1.0` if the number is positive, `+0.0` or `Float::infinity()`
|
|
/// - `-1.0` if the number is negative, `-0.0` or `Float::neg_infinity()`
|
|
/// - `Float::nan()` if the number is `Float::nan()`
|
|
fn signum(self) -> Self;
|
|
/// Returns `true` if `self` is positive, including `+0.0` and
|
|
/// `Float::infinity()`.
|
|
fn is_positive(self) -> bool;
|
|
/// Returns `true` if `self` is negative, including `-0.0` and
|
|
/// `Float::neg_infinity()`.
|
|
fn is_negative(self) -> bool;
|
|
|
|
/// Fused multiply-add. Computes `(self * a) + b` with only one rounding
|
|
/// error. This produces a more accurate result with better performance than
|
|
/// a separate multiplication operation followed by an add.
|
|
fn mul_add(self, a: Self, b: Self) -> Self;
|
|
/// Take the reciprocal (inverse) of a number, `1/x`.
|
|
fn recip(self) -> Self;
|
|
|
|
/// Raise a number to an integer power.
|
|
///
|
|
/// Using this function is generally faster than using `powf`
|
|
fn powi(self, n: i32) -> Self;
|
|
/// Raise a number to a floating point power.
|
|
fn powf(self, n: Self) -> Self;
|
|
|
|
/// sqrt(2.0).
|
|
fn sqrt2() -> Self;
|
|
/// 1.0 / sqrt(2.0).
|
|
fn frac_1_sqrt2() -> Self;
|
|
|
|
/// Take the square root of a number.
|
|
///
|
|
/// Returns NaN if `self` is a negative number.
|
|
fn sqrt(self) -> Self;
|
|
/// Take the reciprocal (inverse) square root of a number, `1/sqrt(x)`.
|
|
fn rsqrt(self) -> Self;
|
|
|
|
/// Archimedes' constant.
|
|
#[deprecated = "use f32::consts or f64::consts instead"]
|
|
fn pi() -> Self;
|
|
/// 2.0 * pi.
|
|
#[deprecated = "use f32::consts or f64::consts instead"]
|
|
fn two_pi() -> Self;
|
|
/// pi / 2.0.
|
|
#[deprecated = "use f32::consts or f64::consts instead"]
|
|
fn frac_pi_2() -> Self;
|
|
/// pi / 3.0.
|
|
#[deprecated = "use f32::consts or f64::consts instead"]
|
|
fn frac_pi_3() -> Self;
|
|
/// pi / 4.0.
|
|
#[deprecated = "use f32::consts or f64::consts instead"]
|
|
fn frac_pi_4() -> Self;
|
|
/// pi / 6.0.
|
|
#[deprecated = "use f32::consts or f64::consts instead"]
|
|
fn frac_pi_6() -> Self;
|
|
/// pi / 8.0.
|
|
#[deprecated = "use f32::consts or f64::consts instead"]
|
|
fn frac_pi_8() -> Self;
|
|
/// 1.0 / pi.
|
|
#[deprecated = "use f32::consts or f64::consts instead"]
|
|
fn frac_1_pi() -> Self;
|
|
/// 2.0 / pi.
|
|
#[deprecated = "use f32::consts or f64::consts instead"]
|
|
fn frac_2_pi() -> Self;
|
|
/// 2.0 / sqrt(pi).
|
|
#[deprecated = "use f32::consts or f64::consts instead"]
|
|
fn frac_2_sqrtpi() -> Self;
|
|
|
|
/// Euler's number.
|
|
#[deprecated = "use f32::consts or f64::consts instead"]
|
|
fn e() -> Self;
|
|
/// log2(e).
|
|
#[deprecated = "use f32::consts or f64::consts instead"]
|
|
fn log2_e() -> Self;
|
|
/// log10(e).
|
|
#[deprecated = "use f32::consts or f64::consts instead"]
|
|
fn log10_e() -> Self;
|
|
/// ln(2.0).
|
|
#[deprecated = "use f32::consts or f64::consts instead"]
|
|
fn ln_2() -> Self;
|
|
/// ln(10.0).
|
|
#[deprecated = "use f32::consts or f64::consts instead"]
|
|
fn ln_10() -> Self;
|
|
|
|
/// Returns `e^(self)`, (the exponential function).
|
|
fn exp(self) -> Self;
|
|
/// Returns 2 raised to the power of the number, `2^(self)`.
|
|
fn exp2(self) -> Self;
|
|
/// Returns the natural logarithm of the number.
|
|
fn ln(self) -> Self;
|
|
/// Returns the logarithm of the number with respect to an arbitrary base.
|
|
fn log(self, base: Self) -> Self;
|
|
/// Returns the base 2 logarithm of the number.
|
|
fn log2(self) -> Self;
|
|
/// Returns the base 10 logarithm of the number.
|
|
fn log10(self) -> Self;
|
|
|
|
/// Convert radians to degrees.
|
|
fn to_degrees(self) -> Self;
|
|
/// Convert degrees to radians.
|
|
fn to_radians(self) -> Self;
|
|
}
|
|
|
|
/// A generic trait for converting a string with a radix (base) to a value
|
|
#[experimental = "might need to return Result"]
|
|
pub trait FromStrRadix {
|
|
fn from_str_radix(str: &str, radix: uint) -> Option<Self>;
|
|
}
|
|
|
|
/// A utility function that just calls FromStrRadix::from_str_radix.
|
|
#[experimental = "might need to return Result"]
|
|
pub fn from_str_radix<T: FromStrRadix>(str: &str, radix: uint) -> Option<T> {
|
|
FromStrRadix::from_str_radix(str, radix)
|
|
}
|
|
|
|
macro_rules! from_str_radix_float_impl {
|
|
($T:ty) => {
|
|
#[experimental = "might need to return Result"]
|
|
impl FromStr for $T {
|
|
/// Convert a string in base 10 to a float.
|
|
/// Accepts an optional decimal exponent.
|
|
///
|
|
/// This function accepts strings such as
|
|
///
|
|
/// * '3.14'
|
|
/// * '+3.14', equivalent to '3.14'
|
|
/// * '-3.14'
|
|
/// * '2.5E10', or equivalently, '2.5e10'
|
|
/// * '2.5E-10'
|
|
/// * '.' (understood as 0)
|
|
/// * '5.'
|
|
/// * '.5', or, equivalently, '0.5'
|
|
/// * '+inf', 'inf', '-inf', 'NaN'
|
|
///
|
|
/// Leading and trailing whitespace represent an error.
|
|
///
|
|
/// # Arguments
|
|
///
|
|
/// * src - A string
|
|
///
|
|
/// # Return value
|
|
///
|
|
/// `None` if the string did not represent a valid number. Otherwise,
|
|
/// `Some(n)` where `n` is the floating-point number represented by `src`.
|
|
#[inline]
|
|
fn from_str(src: &str) -> Option<$T> {
|
|
from_str_radix(src, 10)
|
|
}
|
|
}
|
|
|
|
#[experimental = "might need to return Result"]
|
|
impl FromStrRadix for $T {
|
|
/// Convert a string in a given base to a float.
|
|
///
|
|
/// Due to possible conflicts, this function does **not** accept
|
|
/// the special values `inf`, `-inf`, `+inf` and `NaN`, **nor**
|
|
/// does it recognize exponents of any kind.
|
|
///
|
|
/// Leading and trailing whitespace represent an error.
|
|
///
|
|
/// # Arguments
|
|
///
|
|
/// * src - A string
|
|
/// * radix - The base to use. Must lie in the range [2 .. 36]
|
|
///
|
|
/// # Return value
|
|
///
|
|
/// `None` if the string did not represent a valid number. Otherwise,
|
|
/// `Some(n)` where `n` is the floating-point number represented by `src`.
|
|
fn from_str_radix(src: &str, radix: uint) -> Option<$T> {
|
|
assert!(radix >= 2 && radix <= 36,
|
|
"from_str_radix_float: must lie in the range `[2, 36]` - found {}",
|
|
radix);
|
|
|
|
// Special values
|
|
match src {
|
|
"inf" => return Some(Float::infinity()),
|
|
"-inf" => return Some(Float::neg_infinity()),
|
|
"NaN" => return Some(Float::nan()),
|
|
_ => {},
|
|
}
|
|
|
|
let (is_positive, src) = match src.slice_shift_char() {
|
|
None => return None,
|
|
Some(('-', "")) => return None,
|
|
Some(('-', src)) => (false, src),
|
|
Some((_, _)) => (true, src),
|
|
};
|
|
|
|
// The significand to accumulate
|
|
let mut sig = if is_positive { 0.0 } else { -0.0 };
|
|
// Necessary to detect overflow
|
|
let mut prev_sig = sig;
|
|
let mut cs = src.chars().enumerate();
|
|
// Exponent prefix and exponent index offset
|
|
let mut exp_info = None::<(char, uint)>;
|
|
|
|
// Parse the integer part of the significand
|
|
for (i, c) in cs {
|
|
match c.to_digit(radix) {
|
|
Some(digit) => {
|
|
// shift significand one digit left
|
|
sig = sig * (radix as $T);
|
|
|
|
// add/subtract current digit depending on sign
|
|
if is_positive {
|
|
sig = sig + ((digit as int) as $T);
|
|
} else {
|
|
sig = sig - ((digit as int) as $T);
|
|
}
|
|
|
|
// Detect overflow by comparing to last value, except
|
|
// if we've not seen any non-zero digits.
|
|
if prev_sig != 0.0 {
|
|
if is_positive && sig <= prev_sig
|
|
{ return Some(Float::infinity()); }
|
|
if !is_positive && sig >= prev_sig
|
|
{ return Some(Float::neg_infinity()); }
|
|
|
|
// Detect overflow by reversing the shift-and-add process
|
|
if is_positive && (prev_sig != (sig - digit as $T) / radix as $T)
|
|
{ return Some(Float::infinity()); }
|
|
if !is_positive && (prev_sig != (sig + digit as $T) / radix as $T)
|
|
{ return Some(Float::neg_infinity()); }
|
|
}
|
|
prev_sig = sig;
|
|
},
|
|
None => match c {
|
|
'e' | 'E' | 'p' | 'P' => {
|
|
exp_info = Some((c, i + 1));
|
|
break; // start of exponent
|
|
},
|
|
'.' => {
|
|
break; // start of fractional part
|
|
},
|
|
_ => {
|
|
return None;
|
|
},
|
|
},
|
|
}
|
|
}
|
|
|
|
// If we are not yet at the exponent parse the fractional
|
|
// part of the significand
|
|
if exp_info.is_none() {
|
|
let mut power = 1.0;
|
|
for (i, c) in cs {
|
|
match c.to_digit(radix) {
|
|
Some(digit) => {
|
|
// Decrease power one order of magnitude
|
|
power = power / (radix as $T);
|
|
// add/subtract current digit depending on sign
|
|
sig = if is_positive {
|
|
sig + (digit as $T) * power
|
|
} else {
|
|
sig - (digit as $T) * power
|
|
};
|
|
// Detect overflow by comparing to last value
|
|
if is_positive && sig < prev_sig
|
|
{ return Some(Float::infinity()); }
|
|
if !is_positive && sig > prev_sig
|
|
{ return Some(Float::neg_infinity()); }
|
|
prev_sig = sig;
|
|
},
|
|
None => match c {
|
|
'e' | 'E' | 'p' | 'P' => {
|
|
exp_info = Some((c, i + 1));
|
|
break; // start of exponent
|
|
},
|
|
_ => {
|
|
return None; // invalid number
|
|
},
|
|
},
|
|
}
|
|
}
|
|
}
|
|
|
|
// Parse and calculate the exponent
|
|
let exp = match exp_info {
|
|
Some((c, offset)) => {
|
|
let base = match c {
|
|
'E' | 'e' if radix == 10 => 10u as $T,
|
|
'P' | 'p' if radix == 16 => 2u as $T,
|
|
_ => return None,
|
|
};
|
|
|
|
// Parse the exponent as decimal integer
|
|
let src = src[offset..];
|
|
let (is_positive, exp) = match src.slice_shift_char() {
|
|
Some(('-', src)) => (false, from_str::<uint>(src)),
|
|
Some(('+', src)) => (true, from_str::<uint>(src)),
|
|
Some((_, _)) => (true, from_str::<uint>(src)),
|
|
None => return None,
|
|
};
|
|
|
|
match (is_positive, exp) {
|
|
(true, Some(exp)) => base.powi(exp as i32),
|
|
(false, Some(exp)) => 1.0 / base.powi(exp as i32),
|
|
(_, None) => return None,
|
|
}
|
|
},
|
|
None => 1.0, // no exponent
|
|
};
|
|
|
|
Some(sig * exp)
|
|
}
|
|
}
|
|
}
|
|
}
|
|
from_str_radix_float_impl!(f32)
|
|
from_str_radix_float_impl!(f64)
|
|
|
|
macro_rules! from_str_radix_int_impl {
|
|
($T:ty) => {
|
|
#[experimental = "might need to return Result"]
|
|
impl FromStr for $T {
|
|
#[inline]
|
|
fn from_str(src: &str) -> Option<$T> {
|
|
from_str_radix(src, 10)
|
|
}
|
|
}
|
|
|
|
#[experimental = "might need to return Result"]
|
|
impl FromStrRadix for $T {
|
|
fn from_str_radix(src: &str, radix: uint) -> Option<$T> {
|
|
assert!(radix >= 2 && radix <= 36,
|
|
"from_str_radix_int: must lie in the range `[2, 36]` - found {}",
|
|
radix);
|
|
|
|
let is_signed_ty = (0 as $T) > Int::min_value();
|
|
|
|
match src.slice_shift_char() {
|
|
Some(('-', src)) if is_signed_ty => {
|
|
// The number is negative
|
|
let mut result = 0;
|
|
for c in src.chars() {
|
|
let x = match c.to_digit(radix) {
|
|
Some(x) => x,
|
|
None => return None,
|
|
};
|
|
result = match result.checked_mul(radix as $T) {
|
|
Some(result) => result,
|
|
None => return None,
|
|
};
|
|
result = match result.checked_sub(x as $T) {
|
|
Some(result) => result,
|
|
None => return None,
|
|
};
|
|
}
|
|
Some(result)
|
|
},
|
|
Some((_, _)) => {
|
|
// The number is signed
|
|
let mut result = 0;
|
|
for c in src.chars() {
|
|
let x = match c.to_digit(radix) {
|
|
Some(x) => x,
|
|
None => return None,
|
|
};
|
|
result = match result.checked_mul(radix as $T) {
|
|
Some(result) => result,
|
|
None => return None,
|
|
};
|
|
result = match result.checked_add(x as $T) {
|
|
Some(result) => result,
|
|
None => return None,
|
|
};
|
|
}
|
|
Some(result)
|
|
},
|
|
None => None,
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
from_str_radix_int_impl!(int)
|
|
from_str_radix_int_impl!(i8)
|
|
from_str_radix_int_impl!(i16)
|
|
from_str_radix_int_impl!(i32)
|
|
from_str_radix_int_impl!(i64)
|
|
from_str_radix_int_impl!(uint)
|
|
from_str_radix_int_impl!(u8)
|
|
from_str_radix_int_impl!(u16)
|
|
from_str_radix_int_impl!(u32)
|
|
from_str_radix_int_impl!(u64)
|
|
|
|
// DEPRECATED
|
|
|
|
macro_rules! trait_impl {
|
|
($name:ident for $($t:ty)*) => {
|
|
$(#[allow(deprecated)] impl $name for $t {})*
|
|
};
|
|
}
|
|
|
|
#[deprecated = "Generalised numbers are no longer supported"]
|
|
#[allow(deprecated)]
|
|
pub trait Num: PartialEq + Zero + One
|
|
+ Neg<Self>
|
|
+ Add<Self,Self>
|
|
+ Sub<Self,Self>
|
|
+ Mul<Self,Self>
|
|
+ Div<Self,Self>
|
|
+ Rem<Self,Self> {}
|
|
trait_impl!(Num for uint u8 u16 u32 u64 int i8 i16 i32 i64 f32 f64)
|
|
|
|
#[deprecated = "Generalised unsigned numbers are no longer supported"]
|
|
#[allow(deprecated)]
|
|
pub trait Unsigned: Num {}
|
|
trait_impl!(Unsigned for uint u8 u16 u32 u64)
|
|
|
|
#[deprecated = "Use `Float` or `Int`"]
|
|
#[allow(deprecated)]
|
|
pub trait Primitive: Copy + Clone + Num + NumCast + PartialOrd {}
|
|
trait_impl!(Primitive for uint u8 u16 u32 u64 int i8 i16 i32 i64 f32 f64)
|
|
|
|
#[deprecated = "The generic `Zero` trait will be removed soon."]
|
|
pub trait Zero: Add<Self, Self> {
|
|
#[deprecated = "Use `Int::zero()` or `Float::zero()`."]
|
|
fn zero() -> Self;
|
|
#[deprecated = "Use `x == Int::zero()` or `x == Float::zero()`."]
|
|
fn is_zero(&self) -> bool;
|
|
}
|
|
#[deprecated = "Use `Int::zero()` or `Float::zero()`."]
|
|
#[allow(deprecated)]
|
|
pub fn zero<T: Zero>() -> T { Zero::zero() }
|
|
macro_rules! zero_impl {
|
|
($t:ty, $v:expr) => {
|
|
impl Zero for $t {
|
|
fn zero() -> $t { $v }
|
|
fn is_zero(&self) -> bool { *self == $v }
|
|
}
|
|
}
|
|
}
|
|
zero_impl!(uint, 0u)
|
|
zero_impl!(u8, 0u8)
|
|
zero_impl!(u16, 0u16)
|
|
zero_impl!(u32, 0u32)
|
|
zero_impl!(u64, 0u64)
|
|
zero_impl!(int, 0i)
|
|
zero_impl!(i8, 0i8)
|
|
zero_impl!(i16, 0i16)
|
|
zero_impl!(i32, 0i32)
|
|
zero_impl!(i64, 0i64)
|
|
zero_impl!(f32, 0.0f32)
|
|
zero_impl!(f64, 0.0f64)
|
|
|
|
#[deprecated = "The generic `One` trait will be removed soon."]
|
|
pub trait One: Mul<Self, Self> {
|
|
#[deprecated = "Use `Int::one()` or `Float::one()`."]
|
|
fn one() -> Self;
|
|
}
|
|
#[deprecated = "Use `Int::one()` or `Float::one()`."]
|
|
#[allow(deprecated)]
|
|
pub fn one<T: One>() -> T { One::one() }
|
|
macro_rules! one_impl {
|
|
($t:ty, $v:expr) => {
|
|
impl One for $t {
|
|
fn one() -> $t { $v }
|
|
}
|
|
}
|
|
}
|
|
one_impl!(uint, 1u)
|
|
one_impl!(u8, 1u8)
|
|
one_impl!(u16, 1u16)
|
|
one_impl!(u32, 1u32)
|
|
one_impl!(u64, 1u64)
|
|
one_impl!(int, 1i)
|
|
one_impl!(i8, 1i8)
|
|
one_impl!(i16, 1i16)
|
|
one_impl!(i32, 1i32)
|
|
one_impl!(i64, 1i64)
|
|
one_impl!(f32, 1.0f32)
|
|
one_impl!(f64, 1.0f64)
|
|
|
|
#[deprecated = "Use `UnsignedInt::next_power_of_two`"]
|
|
pub fn next_power_of_two<T: UnsignedInt>(n: T) -> T {
|
|
n.next_power_of_two()
|
|
}
|
|
#[deprecated = "Use `UnsignedInt::is_power_of_two`"]
|
|
pub fn is_power_of_two<T: UnsignedInt>(n: T) -> bool {
|
|
n.is_power_of_two()
|
|
}
|
|
#[deprecated = "Use `UnsignedInt::checked_next_power_of_two`"]
|
|
pub fn checked_next_power_of_two<T: UnsignedInt>(n: T) -> Option<T> {
|
|
n.checked_next_power_of_two()
|
|
}
|
|
|
|
#[deprecated = "Generalised bounded values are no longer supported"]
|
|
pub trait Bounded {
|
|
#[deprecated = "Use `Int::min_value` or `Float::min_value`"]
|
|
fn min_value() -> Self;
|
|
#[deprecated = "Use `Int::max_value` or `Float::max_value`"]
|
|
fn max_value() -> Self;
|
|
}
|
|
macro_rules! bounded_impl {
|
|
($T:ty, $min:expr, $max:expr) => {
|
|
impl Bounded for $T {
|
|
#[inline]
|
|
fn min_value() -> $T { $min }
|
|
|
|
#[inline]
|
|
fn max_value() -> $T { $max }
|
|
}
|
|
};
|
|
}
|
|
bounded_impl!(uint, uint::MIN, uint::MAX)
|
|
bounded_impl!(u8, u8::MIN, u8::MAX)
|
|
bounded_impl!(u16, u16::MIN, u16::MAX)
|
|
bounded_impl!(u32, u32::MIN, u32::MAX)
|
|
bounded_impl!(u64, u64::MIN, u64::MAX)
|
|
bounded_impl!(int, int::MIN, int::MAX)
|
|
bounded_impl!(i8, i8::MIN, i8::MAX)
|
|
bounded_impl!(i16, i16::MIN, i16::MAX)
|
|
bounded_impl!(i32, i32::MIN, i32::MAX)
|
|
bounded_impl!(i64, i64::MIN, i64::MAX)
|
|
bounded_impl!(f32, f32::MIN_VALUE, f32::MAX_VALUE)
|
|
bounded_impl!(f64, f64::MIN_VALUE, f64::MAX_VALUE)
|