515 lines
16 KiB
Rust
515 lines
16 KiB
Rust
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// Copyright 2013-2014 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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//! Numeric traits for generic mathematics
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use std::intrinsics;
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use std::{uint, u8, u16, u32, u64};
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use std::{int, i8, i16, i32, i64};
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use std::{f32, f64};
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/// The base trait for numeric types
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pub trait Num: PartialEq + Zero + One
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+ Neg<Self>
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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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macro_rules! trait_impl(
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($name:ident for $($t:ty)*) => ($(
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impl $name for $t {}
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)*)
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)
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trait_impl!(Num for uint u8 u16 u32 u64 int i8 i16 i32 i64 f32 f64)
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/// Defines an additive identity element for `Self`.
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///
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/// # Deriving
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///
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/// This trait can be automatically be derived using `#[deriving(Zero)]`
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/// attribute. If you choose to use this, make sure that the laws outlined in
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/// the documentation for `Zero::zero` still hold.
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pub trait Zero: Add<Self, Self> {
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/// Returns the additive identity element of `Self`, `0`.
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///
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/// # Laws
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///
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/// ```{.text}
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/// a + 0 = a ∀ a ∈ Self
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/// 0 + a = a ∀ a ∈ Self
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/// ```
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///
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/// # Purity
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///
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/// This function should return the same result at all times regardless of
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/// external mutable state, for example values stored in TLS or in
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/// `static mut`s.
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// FIXME (#5527): This should be an associated constant
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fn zero() -> Self;
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/// Returns `true` if `self` is equal to the additive identity.
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#[inline]
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fn is_zero(&self) -> bool;
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}
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macro_rules! zero_impl(
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($t:ty, $v:expr) => {
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impl Zero for $t {
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#[inline]
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fn zero() -> $t { $v }
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#[inline]
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fn is_zero(&self) -> bool { *self == $v }
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}
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}
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)
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zero_impl!(uint, 0u)
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zero_impl!(u8, 0u8)
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zero_impl!(u16, 0u16)
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zero_impl!(u32, 0u32)
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zero_impl!(u64, 0u64)
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zero_impl!(int, 0i)
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zero_impl!(i8, 0i8)
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zero_impl!(i16, 0i16)
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zero_impl!(i32, 0i32)
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zero_impl!(i64, 0i64)
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zero_impl!(f32, 0.0f32)
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zero_impl!(f64, 0.0f64)
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/// Defines a multiplicative identity element for `Self`.
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pub trait One: Mul<Self, Self> {
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/// Returns the multiplicative identity element of `Self`, `1`.
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///
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/// # Laws
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///
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/// ```{.text}
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/// a * 1 = a ∀ a ∈ Self
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/// 1 * a = a ∀ a ∈ Self
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/// ```
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///
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/// # Purity
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///
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/// This function should return the same result at all times regardless of
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/// external mutable state, for example values stored in TLS or in
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/// `static mut`s.
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// FIXME (#5527): This should be an associated constant
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fn one() -> Self;
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}
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macro_rules! one_impl(
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($t:ty, $v:expr) => {
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impl One for $t {
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#[inline]
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fn one() -> $t { $v }
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}
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}
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)
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one_impl!(uint, 1u)
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one_impl!(u8, 1u8)
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one_impl!(u16, 1u16)
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one_impl!(u32, 1u32)
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one_impl!(u64, 1u64)
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one_impl!(int, 1i)
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one_impl!(i8, 1i8)
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one_impl!(i16, 1i16)
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one_impl!(i32, 1i32)
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one_impl!(i64, 1i64)
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one_impl!(f32, 1.0f32)
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one_impl!(f64, 1.0f64)
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/// Useful functions for signed numbers (i.e. numbers that can be negative).
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pub trait Signed: Num + Neg<Self> {
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/// Computes the absolute value.
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///
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/// For `f32` and `f64`, `NaN` will be returned if the number is `NaN`.
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///
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/// For signed integers, `::MIN` will be returned if the number is `::MIN`.
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fn abs(&self) -> Self;
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/// The positive difference of two numbers.
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///
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/// Returns `zero` if the number is less than or equal to `other`, otherwise the difference
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/// between `self` and `other` is returned.
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fn abs_sub(&self, other: &Self) -> Self;
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/// Returns the sign of the number.
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///
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/// For `f32` and `f64`:
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///
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/// * `1.0` if the number is positive, `+0.0` or `INFINITY`
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/// * `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
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/// * `NaN` if the number is `NaN`
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///
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/// For signed integers:
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///
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/// * `0` if the number is zero
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/// * `1` if the number is positive
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/// * `-1` if the number is negative
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fn signum(&self) -> Self;
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/// Returns true if the number is positive and false if the number is zero or negative.
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fn is_positive(&self) -> bool;
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/// Returns true if the number is negative and false if the number is zero or positive.
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fn is_negative(&self) -> bool;
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}
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macro_rules! signed_impl(
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($($t:ty)*) => ($(
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impl Signed for $t {
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#[inline]
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fn abs(&self) -> $t {
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if self.is_negative() { -*self } else { *self }
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}
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#[inline]
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fn abs_sub(&self, other: &$t) -> $t {
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if *self <= *other { 0 } else { *self - *other }
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}
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#[inline]
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fn signum(&self) -> $t {
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match *self {
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n if n > 0 => 1,
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0 => 0,
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_ => -1,
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}
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}
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#[inline]
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fn is_positive(&self) -> bool { *self > 0 }
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#[inline]
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fn is_negative(&self) -> bool { *self < 0 }
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}
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)*)
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)
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signed_impl!(int i8 i16 i32 i64)
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macro_rules! signed_float_impl(
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($t:ty, $nan:expr, $inf:expr, $neg_inf:expr, $fabs:path, $fcopysign:path, $fdim:ident) => {
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impl Signed for $t {
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/// Computes the absolute value. Returns `NAN` if the number is `NAN`.
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#[inline]
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fn abs(&self) -> $t {
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unsafe { $fabs(*self) }
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}
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/// The positive difference of two numbers. Returns `0.0` if the number is
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/// less than or equal to `other`, otherwise the difference between`self`
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/// and `other` is returned.
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#[inline]
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fn abs_sub(&self, other: &$t) -> $t {
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extern { fn $fdim(a: $t, b: $t) -> $t; }
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unsafe { $fdim(*self, *other) }
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}
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/// # Returns
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///
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/// - `1.0` if the number is positive, `+0.0` or `INFINITY`
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/// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
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/// - `NAN` if the number is NaN
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#[inline]
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fn signum(&self) -> $t {
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if self != self { $nan } else {
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unsafe { $fcopysign(1.0, *self) }
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}
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}
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/// Returns `true` if the number is positive, including `+0.0` and `INFINITY`
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#[inline]
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fn is_positive(&self) -> bool { *self > 0.0 || (1.0 / *self) == $inf }
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/// Returns `true` if the number is negative, including `-0.0` and `NEG_INFINITY`
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#[inline]
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fn is_negative(&self) -> bool { *self < 0.0 || (1.0 / *self) == $neg_inf }
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}
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}
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)
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signed_float_impl!(f32, f32::NAN, f32::INFINITY, f32::NEG_INFINITY,
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intrinsics::fabsf32, intrinsics::copysignf32, fdimf)
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signed_float_impl!(f64, f64::NAN, f64::INFINITY, f64::NEG_INFINITY,
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intrinsics::fabsf64, intrinsics::copysignf64, fdim)
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/// A trait for values which cannot be negative
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pub trait Unsigned: Num {}
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trait_impl!(Unsigned for uint u8 u16 u32 u64)
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/// Numbers which have upper and lower bounds
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pub trait Bounded {
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// FIXME (#5527): These should be associated constants
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/// returns the smallest finite number this type can represent
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fn min_value() -> Self;
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/// returns the largest finite number this type can represent
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fn max_value() -> Self;
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}
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macro_rules! bounded_impl(
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($t:ty, $min:expr, $max:expr) => {
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impl Bounded for $t {
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#[inline]
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fn min_value() -> $t { $min }
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#[inline]
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fn max_value() -> $t { $max }
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}
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}
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)
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bounded_impl!(uint, uint::MIN, uint::MAX)
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bounded_impl!(u8, u8::MIN, u8::MAX)
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bounded_impl!(u16, u16::MIN, u16::MAX)
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bounded_impl!(u32, u32::MIN, u32::MAX)
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bounded_impl!(u64, u64::MIN, u64::MAX)
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bounded_impl!(int, int::MIN, int::MAX)
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bounded_impl!(i8, i8::MIN, i8::MAX)
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bounded_impl!(i16, i16::MIN, i16::MAX)
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bounded_impl!(i32, i32::MIN, i32::MAX)
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bounded_impl!(i64, i64::MIN, i64::MAX)
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bounded_impl!(f32, f32::MIN_VALUE, f32::MAX_VALUE)
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bounded_impl!(f64, f64::MIN_VALUE, f64::MAX_VALUE)
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/// Saturating math operations
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pub trait Saturating {
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/// Saturating addition operator.
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/// Returns a+b, saturating at the numeric bounds instead of overflowing.
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fn saturating_add(self, v: Self) -> Self;
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/// Saturating subtraction operator.
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/// Returns a-b, saturating at the numeric bounds instead of overflowing.
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fn saturating_sub(self, v: Self) -> Self;
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}
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impl<T: CheckedAdd + CheckedSub + Zero + PartialOrd + Bounded> Saturating for T {
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#[inline]
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fn saturating_add(self, v: T) -> T {
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match self.checked_add(&v) {
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Some(x) => x,
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None => if v >= Zero::zero() {
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Bounded::max_value()
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} else {
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Bounded::min_value()
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}
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}
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}
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#[inline]
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fn saturating_sub(self, v: T) -> T {
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match self.checked_sub(&v) {
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Some(x) => x,
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None => if v >= Zero::zero() {
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Bounded::min_value()
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} else {
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Bounded::max_value()
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}
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}
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}
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}
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/// Performs addition that returns `None` instead of wrapping around on overflow.
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pub trait CheckedAdd: Add<Self, Self> {
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/// Adds two numbers, checking for overflow. If overflow happens, `None` is returned.
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///
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/// # Example
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///
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/// ```rust
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/// use num::CheckedAdd;
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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, v: &Self) -> Option<Self>;
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}
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macro_rules! checked_impl(
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($trait_name:ident, $method:ident, $t:ty, $op:path) => {
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impl $trait_name for $t {
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#[inline]
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fn $method(&self, v: &$t) -> Option<$t> {
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unsafe {
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let (x, y) = $op(*self, *v);
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if y { None } else { Some(x) }
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}
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}
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}
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}
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)
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macro_rules! checked_cast_impl(
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($trait_name:ident, $method:ident, $t:ty, $cast:ty, $op:path) => {
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impl $trait_name for $t {
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#[inline]
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fn $method(&self, v: &$t) -> Option<$t> {
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unsafe {
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let (x, y) = $op(*self as $cast, *v as $cast);
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if y { None } else { Some(x as $t) }
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}
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}
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}
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}
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)
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#[cfg(target_word_size = "32")]
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checked_cast_impl!(CheckedAdd, checked_add, uint, u32, intrinsics::u32_add_with_overflow)
|
||
|
|
#[cfg(target_word_size = "64")]
|
||
|
|
checked_cast_impl!(CheckedAdd, checked_add, uint, u64, intrinsics::u64_add_with_overflow)
|
||
|
|
|
||
|
|
checked_impl!(CheckedAdd, checked_add, u8, intrinsics::u8_add_with_overflow)
|
||
|
|
checked_impl!(CheckedAdd, checked_add, u16, intrinsics::u16_add_with_overflow)
|
||
|
|
checked_impl!(CheckedAdd, checked_add, u32, intrinsics::u32_add_with_overflow)
|
||
|
|
checked_impl!(CheckedAdd, checked_add, u64, intrinsics::u64_add_with_overflow)
|
||
|
|
|
||
|
|
#[cfg(target_word_size = "32")]
|
||
|
|
checked_cast_impl!(CheckedAdd, checked_add, int, i32, intrinsics::i32_add_with_overflow)
|
||
|
|
#[cfg(target_word_size = "64")]
|
||
|
|
checked_cast_impl!(CheckedAdd, checked_add, int, i64, intrinsics::i64_add_with_overflow)
|
||
|
|
|
||
|
|
checked_impl!(CheckedAdd, checked_add, i8, intrinsics::i8_add_with_overflow)
|
||
|
|
checked_impl!(CheckedAdd, checked_add, i16, intrinsics::i16_add_with_overflow)
|
||
|
|
checked_impl!(CheckedAdd, checked_add, i32, intrinsics::i32_add_with_overflow)
|
||
|
|
checked_impl!(CheckedAdd, checked_add, i64, intrinsics::i64_add_with_overflow)
|
||
|
|
|
||
|
|
/// Performs subtraction that returns `None` instead of wrapping around on underflow.
|
||
|
|
pub trait CheckedSub: Sub<Self, Self> {
|
||
|
|
/// Subtracts two numbers, checking for underflow. If underflow happens, `None` is returned.
|
||
|
|
///
|
||
|
|
/// # Example
|
||
|
|
///
|
||
|
|
/// ```rust
|
||
|
|
/// use num::CheckedSub;
|
||
|
|
/// assert_eq!((-127i8).checked_sub(&1), Some(-128));
|
||
|
|
/// assert_eq!((-128i8).checked_sub(&1), None);
|
||
|
|
/// ```
|
||
|
|
fn checked_sub(&self, v: &Self) -> Option<Self>;
|
||
|
|
}
|
||
|
|
|
||
|
|
#[cfg(target_word_size = "32")]
|
||
|
|
checked_cast_impl!(CheckedSub, checked_sub, uint, u32, intrinsics::u32_sub_with_overflow)
|
||
|
|
#[cfg(target_word_size = "64")]
|
||
|
|
checked_cast_impl!(CheckedSub, checked_sub, uint, u64, intrinsics::u64_sub_with_overflow)
|
||
|
|
|
||
|
|
checked_impl!(CheckedSub, checked_sub, u8, intrinsics::u8_sub_with_overflow)
|
||
|
|
checked_impl!(CheckedSub, checked_sub, u16, intrinsics::u16_sub_with_overflow)
|
||
|
|
checked_impl!(CheckedSub, checked_sub, u32, intrinsics::u32_sub_with_overflow)
|
||
|
|
checked_impl!(CheckedSub, checked_sub, u64, intrinsics::u64_sub_with_overflow)
|
||
|
|
|
||
|
|
#[cfg(target_word_size = "32")]
|
||
|
|
checked_cast_impl!(CheckedSub, checked_sub, int, i32, intrinsics::i32_sub_with_overflow)
|
||
|
|
#[cfg(target_word_size = "64")]
|
||
|
|
checked_cast_impl!(CheckedSub, checked_sub, int, i64, intrinsics::i64_sub_with_overflow)
|
||
|
|
|
||
|
|
checked_impl!(CheckedSub, checked_sub, i8, intrinsics::i8_sub_with_overflow)
|
||
|
|
checked_impl!(CheckedSub, checked_sub, i16, intrinsics::i16_sub_with_overflow)
|
||
|
|
checked_impl!(CheckedSub, checked_sub, i32, intrinsics::i32_sub_with_overflow)
|
||
|
|
checked_impl!(CheckedSub, checked_sub, i64, intrinsics::i64_sub_with_overflow)
|
||
|
|
|
||
|
|
/// Performs multiplication that returns `None` instead of wrapping around on underflow or
|
||
|
|
/// overflow.
|
||
|
|
pub trait CheckedMul: Mul<Self, Self> {
|
||
|
|
/// Multiplies two numbers, checking for underflow or overflow. If underflow or overflow
|
||
|
|
/// happens, `None` is returned.
|
||
|
|
///
|
||
|
|
/// # Example
|
||
|
|
///
|
||
|
|
/// ```rust
|
||
|
|
/// use num::CheckedMul;
|
||
|
|
/// assert_eq!(5u8.checked_mul(&51), Some(255));
|
||
|
|
/// assert_eq!(5u8.checked_mul(&52), None);
|
||
|
|
/// ```
|
||
|
|
fn checked_mul(&self, v: &Self) -> Option<Self>;
|
||
|
|
}
|
||
|
|
|
||
|
|
#[cfg(target_word_size = "32")]
|
||
|
|
checked_cast_impl!(CheckedMul, checked_mul, uint, u32, intrinsics::u32_mul_with_overflow)
|
||
|
|
#[cfg(target_word_size = "64")]
|
||
|
|
checked_cast_impl!(CheckedMul, checked_mul, uint, u64, intrinsics::u64_mul_with_overflow)
|
||
|
|
|
||
|
|
checked_impl!(CheckedMul, checked_mul, u8, intrinsics::u8_mul_with_overflow)
|
||
|
|
checked_impl!(CheckedMul, checked_mul, u16, intrinsics::u16_mul_with_overflow)
|
||
|
|
checked_impl!(CheckedMul, checked_mul, u32, intrinsics::u32_mul_with_overflow)
|
||
|
|
checked_impl!(CheckedMul, checked_mul, u64, intrinsics::u64_mul_with_overflow)
|
||
|
|
|
||
|
|
#[cfg(target_word_size = "32")]
|
||
|
|
checked_cast_impl!(CheckedMul, checked_mul, int, i32, intrinsics::i32_mul_with_overflow)
|
||
|
|
#[cfg(target_word_size = "64")]
|
||
|
|
checked_cast_impl!(CheckedMul, checked_mul, int, i64, intrinsics::i64_mul_with_overflow)
|
||
|
|
|
||
|
|
checked_impl!(CheckedMul, checked_mul, i8, intrinsics::i8_mul_with_overflow)
|
||
|
|
checked_impl!(CheckedMul, checked_mul, i16, intrinsics::i16_mul_with_overflow)
|
||
|
|
checked_impl!(CheckedMul, checked_mul, i32, intrinsics::i32_mul_with_overflow)
|
||
|
|
checked_impl!(CheckedMul, checked_mul, i64, intrinsics::i64_mul_with_overflow)
|
||
|
|
|
||
|
|
/// Performs division that returns `None` instead of panicking on division by zero and instead of
|
||
|
|
/// wrapping around on underflow and overflow.
|
||
|
|
pub trait CheckedDiv: Div<Self, Self> {
|
||
|
|
/// Divides two numbers, checking for underflow, overflow and division by zero. If any of that
|
||
|
|
/// happens, `None` is returned.
|
||
|
|
///
|
||
|
|
/// # Example
|
||
|
|
///
|
||
|
|
/// ```rust
|
||
|
|
/// use num::CheckedDiv;
|
||
|
|
/// assert_eq!((-127i8).checked_div(&-1), Some(127));
|
||
|
|
/// assert_eq!((-128i8).checked_div(&-1), None);
|
||
|
|
/// assert_eq!((1i8).checked_div(&0), None);
|
||
|
|
/// ```
|
||
|
|
fn checked_div(&self, v: &Self) -> Option<Self>;
|
||
|
|
}
|
||
|
|
|
||
|
|
macro_rules! checkeddiv_int_impl(
|
||
|
|
($t:ty, $min:expr) => {
|
||
|
|
impl CheckedDiv for $t {
|
||
|
|
#[inline]
|
||
|
|
fn checked_div(&self, v: &$t) -> Option<$t> {
|
||
|
|
if *v == 0 || (*self == $min && *v == -1) {
|
||
|
|
None
|
||
|
|
} else {
|
||
|
|
Some(*self / *v)
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
)
|
||
|
|
|
||
|
|
checkeddiv_int_impl!(int, int::MIN)
|
||
|
|
checkeddiv_int_impl!(i8, i8::MIN)
|
||
|
|
checkeddiv_int_impl!(i16, i16::MIN)
|
||
|
|
checkeddiv_int_impl!(i32, i32::MIN)
|
||
|
|
checkeddiv_int_impl!(i64, i64::MIN)
|
||
|
|
|
||
|
|
macro_rules! checkeddiv_uint_impl(
|
||
|
|
($($t:ty)*) => ($(
|
||
|
|
impl CheckedDiv for $t {
|
||
|
|
#[inline]
|
||
|
|
fn checked_div(&self, v: &$t) -> Option<$t> {
|
||
|
|
if *v == 0 {
|
||
|
|
None
|
||
|
|
} else {
|
||
|
|
Some(*self / *v)
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
)*)
|
||
|
|
)
|
||
|
|
|
||
|
|
checkeddiv_uint_impl!(uint u8 u16 u32 u64)
|
||
|
|
|