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16
.multirust.sh Executable file
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#!/bin/sh
# Use multirust to locally run the same suite of tests as .travis.yml.
# (You should first install/update 1.0.0, beta, and nightly.)
set -ex
for toolchain in 1.0.0 beta nightly; do
run="multirust run $toolchain"
$run cargo build --verbose
$run cargo test --verbose
$run .travis/test_features.sh
if [ $toolchain = nightly ]; then
$run .travis/test_nightly.sh
fi
$run cargo doc
done

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.travis.yml
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@ -1,52 +1,22 @@
language: rust language: rust
sudo: false
rust: rust:
- 1.8.0 - 1.0.0
- 1.15.0
- 1.20.0
- 1.26.0 # has_i128
- 1.31.0 # 2018!
- stable
- beta - beta
- nightly - nightly
sudo: false
script: script:
- cargo build --verbose - cargo build --verbose
- ./ci/test_full.sh - cargo test --verbose
matrix: - .travis/test_features.sh
include: - |
# i586 presents floating point challenges for lack of SSE/SSE2 [ $TRAVIS_RUST_VERSION != nightly ] ||
- name: "i586" .travis/test_nightly.sh
rust: stable - cargo doc
env: TARGET=i586-unknown-linux-gnu after_success: |
addons: [ $TRAVIS_BRANCH = master ] &&
apt: [ $TRAVIS_PULL_REQUEST = false ] &&
packages: [ $TRAVIS_RUST_VERSION = nightly ] &&
- gcc-multilib ssh-agent .travis/deploy.sh
before_script:
- rustup target add $TARGET
script:
- cargo test --verbose --target $TARGET --all-features
# try a target that doesn't have std at all
- name: "no_std"
rust: stable
env: TARGET=thumbv6m-none-eabi
before_script:
- rustup target add $TARGET
script:
- cargo build --verbose --target $TARGET --no-default-features --features i128
- cargo build --verbose --target $TARGET --no-default-features --features libm
- name: "rustfmt"
rust: 1.31.0
before_script:
- rustup component add rustfmt
script:
- cargo fmt --all -- --check
notifications: notifications:
email: email:
on_success: never on_success: never
branches:
only:
- master
- next
- staging
- trying

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.travis/.gitignore vendored Normal file
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/deploy

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.travis/deploy.sh Executable file
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#!/bin/sh
set -ex
cp doc/* target/doc/
pip install ghp-import --user
$HOME/.local/bin/ghp-import -n target/doc
openssl aes-256-cbc -K $encrypted_9e86330b283d_key -iv $encrypted_9e86330b283d_iv -in .travis/deploy.enc -out .travis/deploy -d
chmod 600 .travis/deploy
ssh-add .travis/deploy
git push -qf ssh://git@github.com/${TRAVIS_REPO_SLUG}.git gh-pages

9
.travis/test_features.sh Executable file
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#!/bin/sh
set -ex
for feature in '' bigint rational complex; do
cargo build --verbose --no-default-features --features="$feature"
cargo test --verbose --no-default-features --features="$feature"
done

7
.travis/test_nightly.sh Executable file
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#!/bin/sh
set -ex
cargo bench --verbose
cargo test --verbose --manifest-path=num-macros/Cargo.toml

51
Cargo.toml
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@ -1,28 +1,37 @@
[package] [package]
authors = ["The Rust Project Developers"]
description = "Numeric traits for generic mathematics"
documentation = "https://docs.rs/num-traits"
homepage = "https://github.com/rust-num/num-traits"
keywords = ["mathematics", "numerics"]
categories = ["algorithms", "science", "no-std"]
license = "MIT/Apache-2.0"
repository = "https://github.com/rust-num/num-traits"
name = "num-traits"
version = "0.2.8"
readme = "README.md"
build = "build.rs"
exclude = ["/ci/*", "/.travis.yml", "/bors.toml"]
[package.metadata.docs.rs] name = "num"
features = ["std"] version = "0.1.31"
authors = ["The Rust Project Developers"]
license = "MIT/Apache-2.0"
homepage = "https://github.com/rust-num/num"
repository = "https://github.com/rust-num/num"
documentation = "http://rust-num.github.io/num"
keywords = ["mathematics", "numerics"]
description = """
A collection of numeric types and traits for Rust, including bigint,
complex, rational, range iterators, generic integers, and more!
"""
[dependencies] [dependencies]
libm = { version = "0.1.4", optional = true } rustc-serialize = { version = "0.3.13", optional = true }
rand = { version = "0.3.8", optional = true }
[dev-dependencies]
# Some tests of non-rand functionality still use rand because the tests
# themselves are randomized.
rand = { version = "0.3.8" }
[features] [features]
default = ["std"]
std = []
i128 = []
[build-dependencies] complex = []
autocfg = "0.1.3" rational = []
bigint = []
default = ["bigint", "complex", "rand", "rational", "rustc-serialize"]
[[bench]]
name = "bigint"
[[bench]]
name = "shootout-pidigits"
harness = false

48
README.md
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@ -1,11 +1,12 @@
# num-traits # num
[![crate](https://img.shields.io/crates/v/num-traits.svg)](https://crates.io/crates/num-traits) A collection of numeric types and traits for Rust.
[![documentation](https://docs.rs/num-traits/badge.svg)](https://docs.rs/num-traits)
![minimum rustc 1.8](https://img.shields.io/badge/rustc-1.8+-red.svg)
[![Travis status](https://travis-ci.org/rust-num/num-traits.svg?branch=master)](https://travis-ci.org/rust-num/num-traits)
Numeric traits for generic mathematics in Rust. This includes new types for big integers, rationals, and complex numbers,
new traits for generic programming on numeric properties like `Integer,
and generic range iterators.
[Documentation](http://rust-num.github.io/num)
## Usage ## Usage
@ -13,42 +14,11 @@ Add this to your `Cargo.toml`:
```toml ```toml
[dependencies] [dependencies]
num-traits = "0.2" num = "0.1"
``` ```
and this to your crate root: and this to your crate root:
```rust ```rust
extern crate num_traits; extern crate num;
``` ```
## Features
This crate can be used without the standard library (`#![no_std]`) by disabling
the default `std` feature. Use this in `Cargo.toml`:
```toml
[dependencies.num-traits]
version = "0.2"
default-features = false
# features = ["libm"] # <--- Uncomment if you wish to use `Float` and `Real` without `std`
```
The `Float` and `Real` traits are only available when either `std` or `libm` is enabled.
The `libm` feature is only available with Rust 1.31 and later ([see PR #99](https://github.com/rust-num/num-traits/pull/99)).
The `FloatCore` trait is always available. `MulAdd` and `MulAddAssign` for `f32`
and `f64` also require `std` or `libm`, as do implementations of signed and floating-
point exponents in `Pow`.
Implementations for `i128` and `u128` are only available with Rust 1.26 and
later. The build script automatically detects this, but you can make it
mandatory by enabling the `i128` crate feature.
## Releases
Release notes are available in [RELEASES.md](RELEASES.md).
## Compatibility
The `num-traits` crate is tested for rustc 1.8 and greater.

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RELEASES.md
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@ -1,154 +0,0 @@
# Release 0.2.8 (2019-05-21)
- [Fixed feature detection on `no_std` targets][116].
**Contributors**: @cuviper
[116]: https://github.com/rust-num/num-traits/pull/116
# Release 0.2.7 (2019-05-20)
- [Documented when `CheckedShl` and `CheckedShr` return `None`][90].
- [The new `Zero::set_zero` and `One::set_one`][104] will set values to their
identities in place, possibly optimized better than direct assignment.
- [Documented general features and intentions of `PrimInt`][108].
**Contributors**: @cuviper, @dvdhrm, @ignatenkobrain, @lcnr, @samueltardieu
[90]: https://github.com/rust-num/num-traits/pull/90
[104]: https://github.com/rust-num/num-traits/pull/104
[108]: https://github.com/rust-num/num-traits/pull/108
# Release 0.2.6 (2018-09-13)
- [Documented that `pow(0, 0)` returns `1`][79]. Mathematically, this is not
strictly defined, but the current behavior is a pragmatic choice that has
precedent in Rust `core` for the primitives and in many other languages.
- [The new `WrappingShl` and `WrappingShr` traits][81] will wrap the shift count
if it exceeds the bit size of the type.
**Contributors**: @cuviper, @edmccard, @meltinglava
[79]: https://github.com/rust-num/num-traits/pull/79
[81]: https://github.com/rust-num/num-traits/pull/81
# Release 0.2.5 (2018-06-20)
- [Documentation for `mul_add` now clarifies that it's not always faster.][70]
- [The default methods in `FromPrimitive` and `ToPrimitive` are more robust.][73]
**Contributors**: @cuviper, @frewsxcv
[70]: https://github.com/rust-num/num-traits/pull/70
[73]: https://github.com/rust-num/num-traits/pull/73
# Release 0.2.4 (2018-05-11)
- [Support for 128-bit integers is now automatically detected and enabled.][69]
Setting the `i128` crate feature now causes the build script to panic if such
support is not detected.
**Contributors**: @cuviper
[69]: https://github.com/rust-num/num-traits/pull/69
# Release 0.2.3 (2018-05-10)
- [The new `CheckedNeg` and `CheckedRem` traits][63] perform checked `Neg` and
`Rem`, returning `Some(output)` or `None` on overflow.
- [The `no_std` implementation of `FloatCore::to_degrees` for `f32`][61] now
uses a constant for greater accuracy, mirroring [rust#47919]. (With `std` it
just calls the inherent `f32::to_degrees` in the standard library.)
- [The new `MulAdd` and `MulAddAssign` traits][59] perform a fused multiply-
add. For integer types this is just a convenience, but for floating point
types this produces a more accurate result than the separate operations.
- [All applicable traits are now implemented for 128-bit integers][60] starting
with Rust 1.26, enabled by the new `i128` crate feature. The `FromPrimitive`
and `ToPrimitive` traits now also have corresponding 128-bit methods, which
default to converting via 64-bit integers for compatibility.
**Contributors**: @cuviper, @LEXUGE, @regexident, @vks
[59]: https://github.com/rust-num/num-traits/pull/59
[60]: https://github.com/rust-num/num-traits/pull/60
[61]: https://github.com/rust-num/num-traits/pull/61
[63]: https://github.com/rust-num/num-traits/pull/63
[rust#47919]: https://github.com/rust-lang/rust/pull/47919
# Release 0.2.2 (2018-03-18)
- [Casting from floating point to integers now returns `None` on overflow][52],
avoiding [rustc's undefined behavior][rust-10184]. This applies to the `cast`
function and the traits `NumCast`, `FromPrimitive`, and `ToPrimitive`.
**Contributors**: @apopiak, @cuviper, @dbarella
[52]: https://github.com/rust-num/num-traits/pull/52
[rust-10184]: https://github.com/rust-lang/rust/issues/10184
# Release 0.2.1 (2018-03-01)
- [The new `FloatCore` trait][32] offers a subset of `Float` for `#![no_std]` use.
[This includes everything][41] except the transcendental functions and FMA.
- [The new `Inv` trait][37] returns the multiplicative inverse, or reciprocal.
- [The new `Pow` trait][37] performs exponentiation, much like the existing `pow`
function, but with generic exponent types.
- [The new `One::is_one` method][39] tests if a value equals 1. Implementers
should override this method if there's a more efficient way to check for 1,
rather than comparing with a temporary `one()`.
**Contributors**: @clarcharr, @cuviper, @vks
[32]: https://github.com/rust-num/num-traits/pull/32
[37]: https://github.com/rust-num/num-traits/pull/37
[39]: https://github.com/rust-num/num-traits/pull/39
[41]: https://github.com/rust-num/num-traits/pull/41
# Release 0.2.0 (2018-02-06)
- **breaking change**: [There is now a `std` feature][30], enabled by default, along
with the implication that building *without* this feature makes this a
`#![no_std]` crate.
- The `Float` and `Real` traits are only available when `std` is enabled.
- Otherwise, the API is unchanged, and num-traits 0.1.43 now re-exports its
items from num-traits 0.2 for compatibility (the [semver-trick]).
**Contributors**: @cuviper, @termoshtt, @vks
[semver-trick]: https://github.com/dtolnay/semver-trick
[30]: https://github.com/rust-num/num-traits/pull/30
# Release 0.1.43 (2018-02-06)
- All items are now [re-exported from num-traits 0.2][31] for compatibility.
[31]: https://github.com/rust-num/num-traits/pull/31
# Release 0.1.42 (2018-01-22)
- [num-traits now has its own source repository][num-356] at [rust-num/num-traits][home].
- [`ParseFloatError` now implements `Display`][22].
- [The new `AsPrimitive` trait][17] implements generic casting with the `as` operator.
- [The new `CheckedShl` and `CheckedShr` traits][21] implement generic
support for the `checked_shl` and `checked_shr` methods on primitive integers.
- [The new `Real` trait][23] offers a subset of `Float` functionality that may be applicable to more
types, with a blanket implementation for all existing `T: Float` types.
Thanks to @cuviper, @Enet4, @fabianschuiki, @svartalf, and @yoanlcq for their contributions!
[home]: https://github.com/rust-num/num-traits
[num-356]: https://github.com/rust-num/num/pull/356
[17]: https://github.com/rust-num/num-traits/pull/17
[21]: https://github.com/rust-num/num-traits/pull/21
[22]: https://github.com/rust-num/num-traits/pull/22
[23]: https://github.com/rust-num/num-traits/pull/23
# Prior releases
No prior release notes were kept. Thanks all the same to the many
contributors that have made this crate what it is!

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benches/bigint.rs Normal file
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#![feature(test)]
extern crate test;
extern crate num;
extern crate rand;
use std::mem::replace;
use test::Bencher;
use num::{BigInt, BigUint, Zero, One, FromPrimitive};
use num::bigint::RandBigInt;
use rand::{SeedableRng, StdRng};
fn get_rng() -> StdRng {
let seed: &[_] = &[1, 2, 3, 4];
SeedableRng::from_seed(seed)
}
fn multiply_bench(b: &mut Bencher, xbits: usize, ybits: usize) {
let mut rng = get_rng();
let x = rng.gen_bigint(xbits);
let y = rng.gen_bigint(ybits);
b.iter(|| &x * &y);
}
fn divide_bench(b: &mut Bencher, xbits: usize, ybits: usize) {
let mut rng = get_rng();
let x = rng.gen_bigint(xbits);
let y = rng.gen_bigint(ybits);
b.iter(|| &x / &y);
}
fn factorial(n: usize) -> BigUint {
let mut f: BigUint = One::one();
for i in 1..(n+1) {
let bu: BigUint = FromPrimitive::from_usize(i).unwrap();
f = f * bu;
}
f
}
fn fib(n: usize) -> BigUint {
let mut f0: BigUint = Zero::zero();
let mut f1: BigUint = One::one();
for _ in 0..n {
let f2 = f0 + &f1;
f0 = replace(&mut f1, f2);
}
f0
}
#[bench]
fn multiply_0(b: &mut Bencher) {
multiply_bench(b, 1 << 8, 1 << 8);
}
#[bench]
fn multiply_1(b: &mut Bencher) {
multiply_bench(b, 1 << 8, 1 << 16);
}
#[bench]
fn multiply_2(b: &mut Bencher) {
multiply_bench(b, 1 << 16, 1 << 16);
}
#[bench]
fn divide_0(b: &mut Bencher) {
divide_bench(b, 1 << 8, 1 << 6);
}
#[bench]
fn divide_1(b: &mut Bencher) {
divide_bench(b, 1 << 12, 1 << 8);
}
#[bench]
fn divide_2(b: &mut Bencher) {
divide_bench(b, 1 << 16, 1 << 12);
}
#[bench]
fn factorial_100(b: &mut Bencher) {
b.iter(|| factorial(100));
}
#[bench]
fn fib_100(b: &mut Bencher) {
b.iter(|| fib(100));
}
#[bench]
fn fac_to_string(b: &mut Bencher) {
let fac = factorial(100);
b.iter(|| fac.to_string());
}
#[bench]
fn fib_to_string(b: &mut Bencher) {
let fib = fib(100);
b.iter(|| fib.to_string());
}
fn to_str_radix_bench(b: &mut Bencher, radix: u32) {
let mut rng = get_rng();
let x = rng.gen_bigint(1009);
b.iter(|| x.to_str_radix(radix));
}
#[bench]
fn to_str_radix_02(b: &mut Bencher) {
to_str_radix_bench(b, 2);
}
#[bench]
fn to_str_radix_08(b: &mut Bencher) {
to_str_radix_bench(b, 8);
}
#[bench]
fn to_str_radix_10(b: &mut Bencher) {
to_str_radix_bench(b, 10);
}
#[bench]
fn to_str_radix_16(b: &mut Bencher) {
to_str_radix_bench(b, 16);
}
#[bench]
fn to_str_radix_36(b: &mut Bencher) {
to_str_radix_bench(b, 36);
}
fn from_str_radix_bench(b: &mut Bencher, radix: u32) {
use num::Num;
let mut rng = get_rng();
let x = rng.gen_bigint(1009);
let s = x.to_str_radix(radix);
assert_eq!(x, BigInt::from_str_radix(&s, radix).unwrap());
b.iter(|| BigInt::from_str_radix(&s, radix));
}
#[bench]
fn from_str_radix_02(b: &mut Bencher) {
from_str_radix_bench(b, 2);
}
#[bench]
fn from_str_radix_08(b: &mut Bencher) {
from_str_radix_bench(b, 8);
}
#[bench]
fn from_str_radix_10(b: &mut Bencher) {
from_str_radix_bench(b, 10);
}
#[bench]
fn from_str_radix_16(b: &mut Bencher) {
from_str_radix_bench(b, 16);
}
#[bench]
fn from_str_radix_36(b: &mut Bencher) {
from_str_radix_bench(b, 36);
}
#[bench]
fn shl(b: &mut Bencher) {
let n = BigUint::one() << 1000;
b.iter(|| {
let mut m = n.clone();
for i in 0..50 {
m = m << i;
}
})
}
#[bench]
fn shr(b: &mut Bencher) {
let n = BigUint::one() << 2000;
b.iter(|| {
let mut m = n.clone();
for i in 0..50 {
m = m >> i;
}
})
}
#[bench]
fn hash(b: &mut Bencher) {
use std::collections::HashSet;
let mut rng = get_rng();
let v: Vec<BigInt> = (1000..2000).map(|bits| rng.gen_bigint(bits)).collect();
b.iter(|| {
let h: HashSet<&BigInt> = v.iter().collect();
assert_eq!(h.len(), v.len());
});
}
#[bench]
fn pow_bench(b: &mut Bencher) {
b.iter(|| {
let upper = 100_usize;
for i in 2..upper + 1 {
for j in 2..upper + 1 {
let i_big = BigUint::from_usize(i).unwrap();
num::pow(i_big, j);
}
}
});
}

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benches/shootout-pidigits.rs Normal file
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// The Computer Language Benchmarks Game
// http://benchmarksgame.alioth.debian.org/
//
// contributed by the Rust Project Developers
// Copyright (c) 2013-2014 The Rust Project Developers
//
// All rights reserved.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions
// are met:
//
// - Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
//
// - Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in
// the documentation and/or other materials provided with the
// distribution.
//
// - Neither the name of "The Computer Language Benchmarks Game" nor
// the name of "The Computer Language Shootout Benchmarks" nor the
// names of its contributors may be used to endorse or promote
// products derived from this software without specific prior
// written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
// FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
// COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
// INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
// (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
// SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
// HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
// STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
// OF THE POSSIBILITY OF SUCH DAMAGE.
extern crate num;
use std::str::FromStr;
use std::io;
use num::traits::{FromPrimitive, ToPrimitive};
use num::{BigInt, Integer, One, Zero};
struct Context {
numer: BigInt,
accum: BigInt,
denom: BigInt,
}
impl Context {
fn new() -> Context {
Context {
numer: One::one(),
accum: Zero::zero(),
denom: One::one(),
}
}
fn from_i32(i: i32) -> BigInt {
FromPrimitive::from_i32(i).unwrap()
}
fn extract_digit(&self) -> i32 {
if self.numer > self.accum {return -1;}
let (q, r) =
(&self.numer * Context::from_i32(3) + &self.accum)
.div_rem(&self.denom);
if r + &self.numer >= self.denom {return -1;}
q.to_i32().unwrap()
}
fn next_term(&mut self, k: i32) {
let y2 = Context::from_i32(k * 2 + 1);
self.accum = (&self.accum + (&self.numer << 1)) * &y2;
self.numer = &self.numer * Context::from_i32(k);
self.denom = &self.denom * y2;
}
fn eliminate_digit(&mut self, d: i32) {
let d = Context::from_i32(d);
let ten = Context::from_i32(10);
self.accum = (&self.accum - &self.denom * d) * &ten;
self.numer = &self.numer * ten;
}
}
fn pidigits(n: isize, out: &mut io::Write) -> io::Result<()> {
let mut k = 0;
let mut context = Context::new();
for i in 1..(n+1) {
let mut d;
loop {
k += 1;
context.next_term(k);
d = context.extract_digit();
if d != -1 {break;}
}
try!(write!(out, "{}", d));
if i % 10 == 0 { try!(write!(out, "\t:{}\n", i)); }
context.eliminate_digit(d);
}
let m = n % 10;
if m != 0 {
for _ in m..10 { try!(write!(out, " ")); }
try!(write!(out, "\t:{}\n", n));
}
Ok(())
}
const DEFAULT_DIGITS: isize = 512;
fn main() {
let args = std::env::args().collect::<Vec<_>>();
let n = if args.len() < 2 {
DEFAULT_DIGITS
} else if args[1] == "--bench" {
return pidigits(DEFAULT_DIGITS, &mut std::io::sink()).unwrap()
} else {
FromStr::from_str(&args[1]).unwrap()
};
pidigits(n, &mut std::io::stdout()).unwrap();
}

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status = [
"continuous-integration/travis-ci/push",
]

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extern crate autocfg;
use std::env;
fn main() {
let ac = autocfg::new();
if ac.probe_type("i128") {
println!("cargo:rustc-cfg=has_i128");
} else if env::var_os("CARGO_FEATURE_I128").is_some() {
panic!("i128 support was not detected!");
}
autocfg::rerun_path(file!());
}

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#!/bin/sh
# Use rustup to locally run the same suite of tests as .travis.yml.
# (You should first install/update 1.8.0, stable, beta, and nightly.)
set -ex
export TRAVIS_RUST_VERSION
for TRAVIS_RUST_VERSION in 1.8.0 1.15.0 1.20.0 stable beta nightly; do
run="rustup run $TRAVIS_RUST_VERSION"
$run $PWD/ci/test_full.sh
done

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ci/test_full.sh
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#!/bin/bash
set -ex
echo Testing num-traits on rustc ${TRAVIS_RUST_VERSION}
# num-traits should build and test everywhere.
cargo build --verbose
cargo test --verbose
# test `no_std`
cargo build --verbose --no-default-features
cargo test --verbose --no-default-features
if [[ "$TRAVIS_RUST_VERSION" =~ ^(nightly|beta|stable)$ ]]; then
# test `i128`
cargo build --verbose --features=i128
cargo test --verbose --features=i128
# test with std and libm (libm build fails on Rust 1.26 and earlier)
cargo build --verbose --features "libm"
cargo test --verbose --features "libm"
# test `no_std` with libm (libm build fails on Rust 1.26 and earlier)
cargo build --verbose --no-default-features --features "libm"
cargo test --verbose --no-default-features --features "libm"
fi

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[package]
name = "num-macros"
version = "0.1.31"
authors = ["The Rust Project Developers"]
license = "MIT/Apache-2.0"
homepage = "https://github.com/rust-num/num"
repository = "https://github.com/rust-num/num"
documentation = "http://rust-num.github.io/num"
keywords = ["mathematics", "numerics"]
description = """
Numeric syntax extensions.
"""
[lib]
name = "num_macros"
plugin = true
[dev-dependencies]
num = { path = "..", version = "0.1" }

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// Copyright 2012-2015 The Rust Project Developers. See the COPYRIGHT
// file at the top-level directory of this distribution and at
// http://rust-lang.org/COPYRIGHT.
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
// option. This file may not be copied, modified, or distributed
// except according to those terms.
#![feature(plugin_registrar, rustc_private)]
extern crate syntax;
extern crate syntax_ext;
extern crate rustc_plugin;
use syntax::ast::{MetaItem, Expr, BinOpKind};
use syntax::ast;
use syntax::codemap::Span;
use syntax::ext::base::{ExtCtxt, Annotatable};
use syntax::ext::build::AstBuilder;
use syntax_ext::deriving::generic::*;
use syntax_ext::deriving::generic::ty::*;
use syntax::parse::token::InternedString;
use syntax::ptr::P;
use syntax::ext::base::MultiDecorator;
use syntax::parse::token;
use rustc_plugin::Registry;
macro_rules! pathvec {
($($x:ident)::+) => (
vec![ $( stringify!($x) ),+ ]
)
}
macro_rules! path {
($($x:tt)*) => (
::syntax_ext::deriving::generic::ty::Path::new( pathvec!( $($x)* ) )
)
}
macro_rules! path_local {
($x:ident) => (
::syntax_ext::deriving::generic::ty::Path::new_local(stringify!($x))
)
}
macro_rules! pathvec_std {
($cx:expr, $first:ident :: $($rest:ident)::+) => ({
let mut v = pathvec!($($rest)::+);
if let Some(s) = $cx.crate_root {
v.insert(0, s);
}
v
})
}
pub fn expand_deriving_from_primitive(cx: &mut ExtCtxt,
span: Span,
mitem: &MetaItem,
item: &Annotatable,
push: &mut FnMut(Annotatable))
{
let inline = cx.meta_word(span, InternedString::new("inline"));
let attrs = vec!(cx.attribute(span, inline));
let trait_def = TraitDef {
is_unsafe: false,
span: span,
attributes: Vec::new(),
path: path!(num::FromPrimitive),
additional_bounds: Vec::new(),
generics: LifetimeBounds::empty(),
methods: vec!(
MethodDef {
name: "from_i64",
is_unsafe: false,
generics: LifetimeBounds::empty(),
explicit_self: None,
args: vec!(Literal(path_local!(i64))),
ret_ty: Literal(Path::new_(pathvec_std!(cx, core::option::Option),
None,
vec!(Box::new(Self_)),
true)),
// #[inline] liable to cause code-bloat
attributes: attrs.clone(),
combine_substructure: combine_substructure(Box::new(|c, s, sub| {
cs_from("i64", c, s, sub)
})),
},
MethodDef {
name: "from_u64",
is_unsafe: false,
generics: LifetimeBounds::empty(),
explicit_self: None,
args: vec!(Literal(path_local!(u64))),
ret_ty: Literal(Path::new_(pathvec_std!(cx, core::option::Option),
None,
vec!(Box::new(Self_)),
true)),
// #[inline] liable to cause code-bloat
attributes: attrs,
combine_substructure: combine_substructure(Box::new(|c, s, sub| {
cs_from("u64", c, s, sub)
})),
}
),
associated_types: Vec::new(),
};
trait_def.expand(cx, mitem, &item, push)
}
fn cs_from(name: &str, cx: &mut ExtCtxt, trait_span: Span, substr: &Substructure) -> P<Expr> {
if substr.nonself_args.len() != 1 {
cx.span_bug(trait_span, "incorrect number of arguments in `derive(FromPrimitive)`")
}
let n = &substr.nonself_args[0];
match *substr.fields {
StaticStruct(..) => {
cx.span_err(trait_span, "`FromPrimitive` cannot be derived for structs");
return cx.expr_fail(trait_span, InternedString::new(""));
}
StaticEnum(enum_def, _) => {
if enum_def.variants.is_empty() {
cx.span_err(trait_span,
"`FromPrimitive` cannot be derived for enums with no variants");
return cx.expr_fail(trait_span, InternedString::new(""));
}
let mut arms = Vec::new();
for variant in &enum_def.variants {
match variant.node.data {
ast::VariantData::Unit(..) => {
let span = variant.span;
// expr for `$n == $variant as $name`
let path = cx.path(span, vec![substr.type_ident, variant.node.name]);
let variant = cx.expr_path(path);
let ty = cx.ty_ident(span, cx.ident_of(name));
let cast = cx.expr_cast(span, variant.clone(), ty);
let guard = cx.expr_binary(span, BinOpKind::Eq, n.clone(), cast);
// expr for `Some($variant)`
let body = cx.expr_some(span, variant);
// arm for `_ if $guard => $body`
let arm = ast::Arm {
attrs: vec!(),
pats: vec!(cx.pat_wild(span)),
guard: Some(guard),
body: body,
};
arms.push(arm);
}
ast::VariantData::Tuple(..) => {
cx.span_err(trait_span,
"`FromPrimitive` cannot be derived for \
enum variants with arguments");
return cx.expr_fail(trait_span,
InternedString::new(""));
}
ast::VariantData::Struct(..) => {
cx.span_err(trait_span,
"`FromPrimitive` cannot be derived for enums \
with struct variants");
return cx.expr_fail(trait_span,
InternedString::new(""));
}
}
}
// arm for `_ => None`
let arm = ast::Arm {
attrs: vec!(),
pats: vec!(cx.pat_wild(trait_span)),
guard: None,
body: cx.expr_none(trait_span),
};
arms.push(arm);
cx.expr_match(trait_span, n.clone(), arms)
}
_ => cx.span_bug(trait_span, "expected StaticEnum in derive(FromPrimitive)")
}
}
#[plugin_registrar]
#[doc(hidden)]
pub fn plugin_registrar(reg: &mut Registry) {
reg.register_syntax_extension(
token::intern("derive_NumFromPrimitive"),
MultiDecorator(Box::new(expand_deriving_from_primitive)));
}

36
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// Copyright 2013-2015 The Rust Project Developers. See the COPYRIGHT
// file at the top-level directory of this distribution and at
// http://rust-lang.org/COPYRIGHT.
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
// option. This file may not be copied, modified, or distributed
// except according to those terms.
#![feature(custom_derive, plugin)]
#![plugin(num_macros)]
extern crate num;
#[derive(Debug, PartialEq, NumFromPrimitive)]
enum Color {
Red,
Blue,
Green,
}
#[test]
fn test_from_primitive() {
let v: Vec<Option<Color>> = vec![
num::FromPrimitive::from_u64(0),
num::FromPrimitive::from_u64(1),
num::FromPrimitive::from_u64(2),
num::FromPrimitive::from_u64(3),
];
assert_eq!(
v,
vec![Some(Color::Red), Some(Color::Blue), Some(Color::Green), None]
);
}

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use core::num::Wrapping;
use core::{f32, f64};
#[cfg(has_i128)]
use core::{i128, u128};
use core::{i16, i32, i64, i8, isize};
use core::{u16, u32, u64, u8, usize};
/// Numbers which have upper and lower bounds
pub trait Bounded {
// FIXME (#5527): These should be associated constants
/// returns the smallest finite number this type can represent
fn min_value() -> Self;
/// returns the largest finite number this type can represent
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!(usize, usize::MIN, usize::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);
#[cfg(has_i128)]
bounded_impl!(u128, u128::MIN, u128::MAX);
bounded_impl!(isize, isize::MIN, isize::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);
#[cfg(has_i128)]
bounded_impl!(i128, i128::MIN, i128::MAX);
impl<T: Bounded> Bounded for Wrapping<T> {
fn min_value() -> Self {
Wrapping(T::min_value())
}
fn max_value() -> Self {
Wrapping(T::max_value())
}
}
bounded_impl!(f32, f32::MIN, f32::MAX);
macro_rules! for_each_tuple_ {
( $m:ident !! ) => (
$m! { }
);
( $m:ident !! $h:ident, $($t:ident,)* ) => (
$m! { $h $($t)* }
for_each_tuple_! { $m !! $($t,)* }
);
}
macro_rules! for_each_tuple {
($m:ident) => {
for_each_tuple_! { $m !! A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, }
};
}
macro_rules! bounded_tuple {
( $($name:ident)* ) => (
impl<$($name: Bounded,)*> Bounded for ($($name,)*) {
#[inline]
fn min_value() -> Self {
($($name::min_value(),)*)
}
#[inline]
fn max_value() -> Self {
($($name::max_value(),)*)
}
}
);
}
for_each_tuple!(bounded_tuple);
bounded_impl!(f64, f64::MIN, f64::MAX);
#[test]
fn wrapping_bounded() {
macro_rules! test_wrapping_bounded {
($($t:ty)+) => {
$(
assert_eq!(<Wrapping<$t> as Bounded>::min_value().0, <$t>::min_value());
assert_eq!(<Wrapping<$t> as Bounded>::max_value().0, <$t>::max_value());
)+
};
}
test_wrapping_bounded!(usize u8 u16 u32 u64 isize i8 i16 i32 i64);
}
#[cfg(has_i128)]
#[test]
fn wrapping_bounded_i128() {
macro_rules! test_wrapping_bounded {
($($t:ty)+) => {
$(
assert_eq!(<Wrapping<$t> as Bounded>::min_value().0, <$t>::min_value());
assert_eq!(<Wrapping<$t> as Bounded>::max_value().0, <$t>::max_value());
)+
};
}
test_wrapping_bounded!(u128 i128);
}
#[test]
fn wrapping_is_bounded() {
fn require_bounded<T: Bounded>(_: &T) {}
require_bounded(&Wrapping(42_u32));
require_bounded(&Wrapping(-42));
}

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use core::mem::size_of;
use core::num::Wrapping;
use core::{f32, f64};
#[cfg(has_i128)]
use core::{i128, u128};
use core::{i16, i32, i64, i8, isize};
use core::{u16, u32, u64, u8, usize};
use float::FloatCore;
/// A generic trait for converting a value to a number.
pub trait ToPrimitive {
/// Converts the value of `self` to an `isize`.
#[inline]
fn to_isize(&self) -> Option<isize> {
self.to_i64().as_ref().and_then(ToPrimitive::to_isize)
}
/// Converts the value of `self` to an `i8`.
#[inline]
fn to_i8(&self) -> Option<i8> {
self.to_i64().as_ref().and_then(ToPrimitive::to_i8)
}
/// Converts the value of `self` to an `i16`.
#[inline]
fn to_i16(&self) -> Option<i16> {
self.to_i64().as_ref().and_then(ToPrimitive::to_i16)
}
/// Converts the value of `self` to an `i32`.
#[inline]
fn to_i32(&self) -> Option<i32> {
self.to_i64().as_ref().and_then(ToPrimitive::to_i32)
}
/// Converts the value of `self` to an `i64`.
fn to_i64(&self) -> Option<i64>;
/// Converts the value of `self` to an `i128`.
///
/// This method is only available with feature `i128` enabled on Rust >= 1.26.
///
/// The default implementation converts through `to_i64()`. Types implementing
/// this trait should override this method if they can represent a greater range.
#[inline]
#[cfg(has_i128)]
fn to_i128(&self) -> Option<i128> {
self.to_i64().map(From::from)
}
/// Converts the value of `self` to a `usize`.
#[inline]
fn to_usize(&self) -> Option<usize> {
self.to_u64().as_ref().and_then(ToPrimitive::to_usize)
}
/// Converts the value of `self` to an `u8`.
#[inline]
fn to_u8(&self) -> Option<u8> {
self.to_u64().as_ref().and_then(ToPrimitive::to_u8)
}
/// Converts the value of `self` to an `u16`.
#[inline]
fn to_u16(&self) -> Option<u16> {
self.to_u64().as_ref().and_then(ToPrimitive::to_u16)
}
/// Converts the value of `self` to an `u32`.
#[inline]
fn to_u32(&self) -> Option<u32> {
self.to_u64().as_ref().and_then(ToPrimitive::to_u32)
}
/// Converts the value of `self` to an `u64`.
#[inline]
fn to_u64(&self) -> Option<u64>;
/// Converts the value of `self` to an `u128`.
///
/// This method is only available with feature `i128` enabled on Rust >= 1.26.
///
/// The default implementation converts through `to_u64()`. Types implementing
/// this trait should override this method if they can represent a greater range.
#[inline]
#[cfg(has_i128)]
fn to_u128(&self) -> Option<u128> {
self.to_u64().map(From::from)
}
/// Converts the value of `self` to an `f32`.
#[inline]
fn to_f32(&self) -> Option<f32> {
self.to_f64().as_ref().and_then(ToPrimitive::to_f32)
}
/// Converts the value of `self` to an `f64`.
#[inline]
fn to_f64(&self) -> Option<f64> {
match self.to_i64() {
Some(i) => i.to_f64(),
None => self.to_u64().as_ref().and_then(ToPrimitive::to_f64),
}
}
}
macro_rules! impl_to_primitive_int_to_int {
($SrcT:ident : $( $(#[$cfg:meta])* fn $method:ident -> $DstT:ident ; )*) => {$(
#[inline]
$(#[$cfg])*
fn $method(&self) -> Option<$DstT> {
let min = $DstT::MIN as $SrcT;
let max = $DstT::MAX as $SrcT;
if size_of::<$SrcT>() <= size_of::<$DstT>() || (min <= *self && *self <= max) {
Some(*self as $DstT)
} else {
None
}
}
)*}
}
macro_rules! impl_to_primitive_int_to_uint {
($SrcT:ident : $( $(#[$cfg:meta])* fn $method:ident -> $DstT:ident ; )*) => {$(
#[inline]
$(#[$cfg])*
fn $method(&self) -> Option<$DstT> {
let max = $DstT::MAX as $SrcT;
if 0 <= *self && (size_of::<$SrcT>() <= size_of::<$DstT>() || *self <= max) {
Some(*self as $DstT)
} else {
None
}
}
)*}
}
macro_rules! impl_to_primitive_int {
($T:ident) => {
impl ToPrimitive for $T {
impl_to_primitive_int_to_int! { $T:
fn to_isize -> isize;
fn to_i8 -> i8;
fn to_i16 -> i16;
fn to_i32 -> i32;
fn to_i64 -> i64;
#[cfg(has_i128)]
fn to_i128 -> i128;
}
impl_to_primitive_int_to_uint! { $T:
fn to_usize -> usize;
fn to_u8 -> u8;
fn to_u16 -> u16;
fn to_u32 -> u32;
fn to_u64 -> u64;
#[cfg(has_i128)]
fn to_u128 -> u128;
}
#[inline]
fn to_f32(&self) -> Option<f32> {
Some(*self as f32)
}
#[inline]
fn to_f64(&self) -> Option<f64> {
Some(*self as f64)
}
}
};
}
impl_to_primitive_int!(isize);
impl_to_primitive_int!(i8);
impl_to_primitive_int!(i16);
impl_to_primitive_int!(i32);
impl_to_primitive_int!(i64);
#[cfg(has_i128)]
impl_to_primitive_int!(i128);
macro_rules! impl_to_primitive_uint_to_int {
($SrcT:ident : $( $(#[$cfg:meta])* fn $method:ident -> $DstT:ident ; )*) => {$(
#[inline]
$(#[$cfg])*
fn $method(&self) -> Option<$DstT> {
let max = $DstT::MAX as $SrcT;
if size_of::<$SrcT>() < size_of::<$DstT>() || *self <= max {
Some(*self as $DstT)
} else {
None
}
}
)*}
}
macro_rules! impl_to_primitive_uint_to_uint {
($SrcT:ident : $( $(#[$cfg:meta])* fn $method:ident -> $DstT:ident ; )*) => {$(
#[inline]
$(#[$cfg])*
fn $method(&self) -> Option<$DstT> {
let max = $DstT::MAX as $SrcT;
if size_of::<$SrcT>() <= size_of::<$DstT>() || *self <= max {
Some(*self as $DstT)
} else {
None
}
}
)*}
}
macro_rules! impl_to_primitive_uint {
($T:ident) => {
impl ToPrimitive for $T {
impl_to_primitive_uint_to_int! { $T:
fn to_isize -> isize;
fn to_i8 -> i8;
fn to_i16 -> i16;
fn to_i32 -> i32;
fn to_i64 -> i64;
#[cfg(has_i128)]
fn to_i128 -> i128;
}
impl_to_primitive_uint_to_uint! { $T:
fn to_usize -> usize;
fn to_u8 -> u8;
fn to_u16 -> u16;
fn to_u32 -> u32;
fn to_u64 -> u64;
#[cfg(has_i128)]
fn to_u128 -> u128;
}
#[inline]
fn to_f32(&self) -> Option<f32> {
Some(*self as f32)
}
#[inline]
fn to_f64(&self) -> Option<f64> {
Some(*self as f64)
}
}
};
}
impl_to_primitive_uint!(usize);
impl_to_primitive_uint!(u8);
impl_to_primitive_uint!(u16);
impl_to_primitive_uint!(u32);
impl_to_primitive_uint!(u64);
#[cfg(has_i128)]
impl_to_primitive_uint!(u128);
macro_rules! impl_to_primitive_float_to_float {
($SrcT:ident : $( fn $method:ident -> $DstT:ident ; )*) => {$(
#[inline]
fn $method(&self) -> Option<$DstT> {
// Only finite values that are reducing size need to worry about overflow.
if size_of::<$SrcT>() > size_of::<$DstT>() && FloatCore::is_finite(*self) {
let n = *self as f64;
if n < $DstT::MIN as f64 || n > $DstT::MAX as f64 {
return None;
}
}
// We can safely cast NaN, +-inf, and finite values in range.
Some(*self as $DstT)
}
)*}
}
macro_rules! impl_to_primitive_float_to_signed_int {
($f:ident : $( $(#[$cfg:meta])* fn $method:ident -> $i:ident ; )*) => {$(
#[inline]
$(#[$cfg])*
fn $method(&self) -> Option<$i> {
// Float as int truncates toward zero, so we want to allow values
// in the exclusive range `(MIN-1, MAX+1)`.
if size_of::<$f>() > size_of::<$i>() {
// With a larger size, we can represent the range exactly.
const MIN_M1: $f = $i::MIN as $f - 1.0;
const MAX_P1: $f = $i::MAX as $f + 1.0;
if *self > MIN_M1 && *self < MAX_P1 {
return Some(*self as $i);
}
} else {
// We can't represent `MIN-1` exactly, but there's no fractional part
// at this magnitude, so we can just use a `MIN` inclusive boundary.
const MIN: $f = $i::MIN as $f;
// We can't represent `MAX` exactly, but it will round up to exactly
// `MAX+1` (a power of two) when we cast it.
const MAX_P1: $f = $i::MAX as $f;
if *self >= MIN && *self < MAX_P1 {
return Some(*self as $i);
}
}
None
}
)*}
}
macro_rules! impl_to_primitive_float_to_unsigned_int {
($f:ident : $( $(#[$cfg:meta])* fn $method:ident -> $u:ident ; )*) => {$(
#[inline]
$(#[$cfg])*
fn $method(&self) -> Option<$u> {
// Float as int truncates toward zero, so we want to allow values
// in the exclusive range `(-1, MAX+1)`.
if size_of::<$f>() > size_of::<$u>() {
// With a larger size, we can represent the range exactly.
const MAX_P1: $f = $u::MAX as $f + 1.0;
if *self > -1.0 && *self < MAX_P1 {
return Some(*self as $u);
}
} else {
// We can't represent `MAX` exactly, but it will round up to exactly
// `MAX+1` (a power of two) when we cast it.
// (`u128::MAX as f32` is infinity, but this is still ok.)
const MAX_P1: $f = $u::MAX as $f;
if *self > -1.0 && *self < MAX_P1 {
return Some(*self as $u);
}
}
None
}
)*}
}
macro_rules! impl_to_primitive_float {
($T:ident) => {
impl ToPrimitive for $T {
impl_to_primitive_float_to_signed_int! { $T:
fn to_isize -> isize;
fn to_i8 -> i8;
fn to_i16 -> i16;
fn to_i32 -> i32;
fn to_i64 -> i64;
#[cfg(has_i128)]
fn to_i128 -> i128;
}
impl_to_primitive_float_to_unsigned_int! { $T:
fn to_usize -> usize;
fn to_u8 -> u8;
fn to_u16 -> u16;
fn to_u32 -> u32;
fn to_u64 -> u64;
#[cfg(has_i128)]
fn to_u128 -> u128;
}
impl_to_primitive_float_to_float! { $T:
fn to_f32 -> f32;
fn to_f64 -> f64;
}
}
};
}
impl_to_primitive_float!(f32);
impl_to_primitive_float!(f64);
/// A generic trait for converting a number to a value.
pub trait FromPrimitive: Sized {
/// Convert an `isize` to return an optional value of this type. If the
/// value cannot be represented by this value, then `None` is returned.
#[inline]
fn from_isize(n: isize) -> Option<Self> {
n.to_i64().and_then(FromPrimitive::from_i64)
}
/// Convert an `i8` to return an optional value of this type. If the
/// type cannot be represented by this value, then `None` is returned.
#[inline]
fn from_i8(n: i8) -> Option<Self> {
FromPrimitive::from_i64(From::from(n))
}
/// Convert an `i16` to return an optional value of this type. If the
/// type cannot be represented by this value, then `None` is returned.
#[inline]
fn from_i16(n: i16) -> Option<Self> {
FromPrimitive::from_i64(From::from(n))
}
/// Convert an `i32` to return an optional value of this type. If the
/// type cannot be represented by this value, then `None` is returned.
#[inline]
fn from_i32(n: i32) -> Option<Self> {
FromPrimitive::from_i64(From::from(n))
}
/// Convert an `i64` to return an optional value of this type. If the
/// type cannot be represented by this value, then `None` is returned.
fn from_i64(n: i64) -> Option<Self>;
/// Convert an `i128` to return an optional value of this type. If the
/// type cannot be represented by this value, then `None` is returned.
///
/// This method is only available with feature `i128` enabled on Rust >= 1.26.
///
/// The default implementation converts through `from_i64()`. Types implementing
/// this trait should override this method if they can represent a greater range.
#[inline]
#[cfg(has_i128)]
fn from_i128(n: i128) -> Option<Self> {
n.to_i64().and_then(FromPrimitive::from_i64)
}
/// Convert a `usize` to return an optional value of this type. If the
/// type cannot be represented by this value, then `None` is returned.
#[inline]
fn from_usize(n: usize) -> Option<Self> {
n.to_u64().and_then(FromPrimitive::from_u64)
}
/// Convert an `u8` to return an optional value of this type. If the
/// type cannot be represented by this value, then `None` is returned.
#[inline]
fn from_u8(n: u8) -> Option<Self> {
FromPrimitive::from_u64(From::from(n))
}
/// Convert an `u16` to return an optional value of this type. If the
/// type cannot be represented by this value, then `None` is returned.
#[inline]
fn from_u16(n: u16) -> Option<Self> {
FromPrimitive::from_u64(From::from(n))
}
/// Convert an `u32` to return an optional value of this type. If the
/// type cannot be represented by this value, then `None` is returned.
#[inline]
fn from_u32(n: u32) -> Option<Self> {
FromPrimitive::from_u64(From::from(n))
}
/// Convert an `u64` to return an optional value of this type. If the
/// type cannot be represented by this value, then `None` is returned.
fn from_u64(n: u64) -> Option<Self>;
/// Convert an `u128` to return an optional value of this type. If the
/// type cannot be represented by this value, then `None` is returned.
///
/// This method is only available with feature `i128` enabled on Rust >= 1.26.
///
/// The default implementation converts through `from_u64()`. Types implementing
/// this trait should override this method if they can represent a greater range.
#[inline]
#[cfg(has_i128)]
fn from_u128(n: u128) -> Option<Self> {
n.to_u64().and_then(FromPrimitive::from_u64)
}
/// Convert a `f32` to return an optional value of this type. If the
/// type cannot be represented by this value, then `None` is returned.
#[inline]
fn from_f32(n: f32) -> Option<Self> {
FromPrimitive::from_f64(From::from(n))
}
/// Convert a `f64` to return an optional value of this type. If the
/// type cannot be represented by this value, then `None` is returned.
#[inline]
fn from_f64(n: f64) -> Option<Self> {
match n.to_i64() {
Some(i) => FromPrimitive::from_i64(i),
None => n.to_u64().and_then(FromPrimitive::from_u64),
}
}
}
macro_rules! impl_from_primitive {
($T:ty, $to_ty:ident) => {
#[allow(deprecated)]
impl FromPrimitive for $T {
#[inline]
fn from_isize(n: isize) -> Option<$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.$to_ty()
}
#[cfg(has_i128)]
#[inline]
fn from_i128(n: i128) -> Option<$T> {
n.$to_ty()
}
#[inline]
fn from_usize(n: usize) -> Option<$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.$to_ty()
}
#[cfg(has_i128)]
#[inline]
fn from_u128(n: u128) -> Option<$T> {
n.$to_ty()
}
#[inline]
fn from_f32(n: f32) -> Option<$T> {
n.$to_ty()
}
#[inline]
fn from_f64(n: f64) -> Option<$T> {
n.$to_ty()
}
}
};
}
impl_from_primitive!(isize, to_isize);
impl_from_primitive!(i8, to_i8);
impl_from_primitive!(i16, to_i16);
impl_from_primitive!(i32, to_i32);
impl_from_primitive!(i64, to_i64);
#[cfg(has_i128)]
impl_from_primitive!(i128, to_i128);
impl_from_primitive!(usize, to_usize);
impl_from_primitive!(u8, to_u8);
impl_from_primitive!(u16, to_u16);
impl_from_primitive!(u32, to_u32);
impl_from_primitive!(u64, to_u64);
#[cfg(has_i128)]
impl_from_primitive!(u128, to_u128);
impl_from_primitive!(f32, to_f32);
impl_from_primitive!(f64, to_f64);
macro_rules! impl_to_primitive_wrapping {
($( $(#[$cfg:meta])* fn $method:ident -> $i:ident ; )*) => {$(
#[inline]
$(#[$cfg])*
fn $method(&self) -> Option<$i> {
(self.0).$method()
}
)*}
}
impl<T: ToPrimitive> ToPrimitive for Wrapping<T> {
impl_to_primitive_wrapping! {
fn to_isize -> isize;
fn to_i8 -> i8;
fn to_i16 -> i16;
fn to_i32 -> i32;
fn to_i64 -> i64;
#[cfg(has_i128)]
fn to_i128 -> i128;
fn to_usize -> usize;
fn to_u8 -> u8;
fn to_u16 -> u16;
fn to_u32 -> u32;
fn to_u64 -> u64;
#[cfg(has_i128)]
fn to_u128 -> u128;
fn to_f32 -> f32;
fn to_f64 -> f64;
}
}
macro_rules! impl_from_primitive_wrapping {
($( $(#[$cfg:meta])* fn $method:ident ( $i:ident ); )*) => {$(
#[inline]
$(#[$cfg])*
fn $method(n: $i) -> Option<Self> {
T::$method(n).map(Wrapping)
}
)*}
}
impl<T: FromPrimitive> FromPrimitive for Wrapping<T> {
impl_from_primitive_wrapping! {
fn from_isize(isize);
fn from_i8(i8);
fn from_i16(i16);
fn from_i32(i32);
fn from_i64(i64);
#[cfg(has_i128)]
fn from_i128(i128);
fn from_usize(usize);
fn from_u8(u8);
fn from_u16(u16);
fn from_u32(u32);
fn from_u64(u64);
#[cfg(has_i128)]
fn from_u128(u128);
fn from_f32(f32);
fn from_f64(f64);
}
}
/// Cast from one machine scalar to another.
///
/// # Examples
///
/// ```
/// # use num_traits as num;
/// let twenty: f32 = num::cast(0x14).unwrap();
/// assert_eq!(twenty, 20f32);
/// ```
///
#[inline]
pub fn cast<T: NumCast, U: NumCast>(n: T) -> Option<U> {
NumCast::from(n)
}
/// An interface for casting between machine scalars.
pub trait NumCast: Sized + 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 $T {
#[inline]
#[allow(deprecated)]
fn from<N: ToPrimitive>(n: N) -> Option<$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);
#[cfg(has_i128)]
impl_num_cast!(u128, to_u128);
impl_num_cast!(usize, to_usize);
impl_num_cast!(i8, to_i8);
impl_num_cast!(i16, to_i16);
impl_num_cast!(i32, to_i32);
impl_num_cast!(i64, to_i64);
#[cfg(has_i128)]
impl_num_cast!(i128, to_i128);
impl_num_cast!(isize, to_isize);
impl_num_cast!(f32, to_f32);
impl_num_cast!(f64, to_f64);
impl<T: NumCast> NumCast for Wrapping<T> {
fn from<U: ToPrimitive>(n: U) -> Option<Self> {
T::from(n).map(Wrapping)
}
}
/// A generic interface for casting between machine scalars with the
/// `as` operator, which admits narrowing and precision loss.
/// Implementers of this trait `AsPrimitive` should behave like a primitive
/// numeric type (e.g. a newtype around another primitive), and the
/// intended conversion must never fail.
///
/// # Examples
///
/// ```
/// # use num_traits::AsPrimitive;
/// let three: i32 = (3.14159265f32).as_();
/// assert_eq!(three, 3);
/// ```
///
/// # Safety
///
/// Currently, some uses of the `as` operator are not entirely safe.
/// In particular, it is undefined behavior if:
///
/// - A truncated floating point value cannot fit in the target integer
/// type ([#10184](https://github.com/rust-lang/rust/issues/10184));
///
/// ```ignore
/// # use num_traits::AsPrimitive;
/// let x: u8 = (1.04E+17).as_(); // UB
/// ```
///
/// - Or a floating point value does not fit in another floating
/// point type ([#15536](https://github.com/rust-lang/rust/issues/15536)).
///
/// ```ignore
/// # use num_traits::AsPrimitive;
/// let x: f32 = (1e300f64).as_(); // UB
/// ```
///
pub trait AsPrimitive<T>: 'static + Copy
where
T: 'static + Copy,
{
/// Convert a value to another, using the `as` operator.
fn as_(self) -> T;
}
macro_rules! impl_as_primitive {
(@ $T: ty => $(#[$cfg:meta])* impl $U: ty ) => {
$(#[$cfg])*
impl AsPrimitive<$U> for $T {
#[inline] fn as_(self) -> $U { self as $U }
}
};
(@ $T: ty => { $( $U: ty ),* } ) => {$(
impl_as_primitive!(@ $T => impl $U);
)*};
($T: ty => { $( $U: ty ),* } ) => {
impl_as_primitive!(@ $T => { $( $U ),* });
impl_as_primitive!(@ $T => { u8, u16, u32, u64, usize });
impl_as_primitive!(@ $T => #[cfg(has_i128)] impl u128);
impl_as_primitive!(@ $T => { i8, i16, i32, i64, isize });
impl_as_primitive!(@ $T => #[cfg(has_i128)] impl i128);
};
}
impl_as_primitive!(u8 => { char, f32, f64 });
impl_as_primitive!(i8 => { f32, f64 });
impl_as_primitive!(u16 => { f32, f64 });
impl_as_primitive!(i16 => { f32, f64 });
impl_as_primitive!(u32 => { f32, f64 });
impl_as_primitive!(i32 => { f32, f64 });
impl_as_primitive!(u64 => { f32, f64 });
impl_as_primitive!(i64 => { f32, f64 });
#[cfg(has_i128)]
impl_as_primitive!(u128 => { f32, f64 });
#[cfg(has_i128)]
impl_as_primitive!(i128 => { f32, f64 });
impl_as_primitive!(usize => { f32, f64 });
impl_as_primitive!(isize => { f32, f64 });
impl_as_primitive!(f32 => { f32, f64 });
impl_as_primitive!(f64 => { f32, f64 });
impl_as_primitive!(char => { char });
impl_as_primitive!(bool => {});

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src/float.rs
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207
src/identities.rs
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use core::num::Wrapping;
use core::ops::{Add, Mul};
/// Defines an additive identity element for `Self`.
///
/// # Laws
///
/// ```{.text}
/// a + 0 = a ∀ a ∈ Self
/// 0 + a = a ∀ a ∈ Self
/// ```
pub trait Zero: Sized + Add<Self, Output = Self> {
/// Returns the additive identity element of `Self`, `0`.
/// # Purity
///
/// This function should return the same result at all times regardless of
/// external mutable state, for example values stored in TLS or in
/// `static mut`s.
// This cannot be an associated constant, because of bignums.
fn zero() -> Self;
/// Sets `self` to the additive identity element of `Self`, `0`.
fn set_zero(&mut self) {
*self = Zero::zero();
}
/// Returns `true` if `self` is equal to the additive identity.
#[inline]
fn is_zero(&self) -> bool;
}
macro_rules! zero_impl {
($t:ty, $v:expr) => {
impl Zero for $t {
#[inline]
fn zero() -> $t {
$v
}
#[inline]
fn is_zero(&self) -> bool {
*self == $v
}
}
};
}
zero_impl!(usize, 0);
zero_impl!(u8, 0);
zero_impl!(u16, 0);
zero_impl!(u32, 0);
zero_impl!(u64, 0);
#[cfg(has_i128)]
zero_impl!(u128, 0);
zero_impl!(isize, 0);
zero_impl!(i8, 0);
zero_impl!(i16, 0);
zero_impl!(i32, 0);
zero_impl!(i64, 0);
#[cfg(has_i128)]
zero_impl!(i128, 0);
zero_impl!(f32, 0.0);
zero_impl!(f64, 0.0);
impl<T: Zero> Zero for Wrapping<T>
where
Wrapping<T>: Add<Output = Wrapping<T>>,
{
fn is_zero(&self) -> bool {
self.0.is_zero()
}
fn set_zero(&mut self) {
self.0.set_zero();
}
fn zero() -> Self {
Wrapping(T::zero())
}
}
/// Defines a multiplicative identity element for `Self`.
///
/// # Laws
///
/// ```{.text}
/// a * 1 = a ∀ a ∈ Self
/// 1 * a = a ∀ a ∈ Self
/// ```
pub trait One: Sized + Mul<Self, Output = Self> {
/// Returns the multiplicative identity element of `Self`, `1`.
///
/// # Purity
///
/// This function should return the same result at all times regardless of
/// external mutable state, for example values stored in TLS or in
/// `static mut`s.
// This cannot be an associated constant, because of bignums.
fn one() -> Self;
/// Sets `self` to the multiplicative identity element of `Self`, `1`.
fn set_one(&mut self) {
*self = One::one();
}
/// Returns `true` if `self` is equal to the multiplicative identity.
///
/// For performance reasons, it's best to implement this manually.
/// After a semver bump, this method will be required, and the
/// `where Self: PartialEq` bound will be removed.
#[inline]
fn is_one(&self) -> bool
where
Self: PartialEq,
{
*self == Self::one()
}
}
macro_rules! one_impl {
($t:ty, $v:expr) => {
impl One for $t {
#[inline]
fn one() -> $t {
$v
}
#[inline]
fn is_one(&self) -> bool {
*self == $v
}
}
};
}
one_impl!(usize, 1);
one_impl!(u8, 1);
one_impl!(u16, 1);
one_impl!(u32, 1);
one_impl!(u64, 1);
#[cfg(has_i128)]
one_impl!(u128, 1);
one_impl!(isize, 1);
one_impl!(i8, 1);
one_impl!(i16, 1);
one_impl!(i32, 1);
one_impl!(i64, 1);
#[cfg(has_i128)]
one_impl!(i128, 1);
one_impl!(f32, 1.0);
one_impl!(f64, 1.0);
impl<T: One> One for Wrapping<T>
where
Wrapping<T>: Mul<Output = Wrapping<T>>,
{
fn set_one(&mut self) {
self.0.set_one();
}
fn one() -> Self {
Wrapping(T::one())
}
}
// Some helper functions provided for backwards compatibility.
/// Returns the additive identity, `0`.
#[inline(always)]
pub fn zero<T: Zero>() -> T {
Zero::zero()
}
/// Returns the multiplicative identity, `1`.
#[inline(always)]
pub fn one<T: One>() -> T {
One::one()
}
#[test]
fn wrapping_identities() {
macro_rules! test_wrapping_identities {
($($t:ty)+) => {
$(
assert_eq!(zero::<$t>(), zero::<Wrapping<$t>>().0);
assert_eq!(one::<$t>(), one::<Wrapping<$t>>().0);
assert_eq!((0 as $t).is_zero(), Wrapping(0 as $t).is_zero());
assert_eq!((1 as $t).is_zero(), Wrapping(1 as $t).is_zero());
)+
};
}
test_wrapping_identities!(isize i8 i16 i32 i64 usize u8 u16 u32 u64);
}
#[test]
fn wrapping_is_zero() {
fn require_zero<T: Zero>(_: &T) {}
require_zero(&Wrapping(42));
}
#[test]
fn wrapping_is_one() {
fn require_one<T: One>(_: &T) {}
require_one(&Wrapping(42));
}

409
src/int.rs
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@ -1,409 +0,0 @@
use core::ops::{BitAnd, BitOr, BitXor, Not, Shl, Shr};
use bounds::Bounded;
use ops::checked::*;
use ops::saturating::Saturating;
use {Num, NumCast};
/// Generic trait for primitive integers.
///
/// The `PrimInt` trait is an abstraction over the builtin primitive integer types (e.g., `u8`,
/// `u32`, `isize`, `i128`, ...). It inherits the basic numeric traits and extends them with
/// bitwise operators and non-wrapping arithmetic.
///
/// The trait explicitly inherits `Copy`, `Eq`, `Ord`, and `Sized`. The intention is that all
/// types implementing this trait behave like primitive types that are passed by value by default
/// and behave like builtin integers. Furthermore, the types are expected to expose the integer
/// value in binary representation and support bitwise operators. The standard bitwise operations
/// (e.g., bitwise-and, bitwise-or, right-shift, left-shift) are inherited and the trait extends
/// these with introspective queries (e.g., `PrimInt::count_ones()`, `PrimInt::leading_zeros()`),
/// bitwise combinators (e.g., `PrimInt::rotate_left()`), and endianness converters (e.g.,
/// `PrimInt::to_be()`).
///
/// All `PrimInt` types are expected to be fixed-width binary integers. The width can be queried
/// via `T::zero().count_zeros()`. The trait currently lacks a way to query the width at
/// compile-time.
///
/// While a default implementation for all builtin primitive integers is provided, the trait is in
/// no way restricted to these. Other integer types that fulfil the requirements are free to
/// implement the trait was well.
///
/// This trait and many of the method names originate in the unstable `core::num::Int` trait from
/// the rust standard library. The original trait was never stabilized and thus removed from the
/// standard library.
pub trait PrimInt:
Sized
+ Copy
+ Num
+ NumCast
+ Bounded
+ PartialOrd
+ Ord
+ Eq
+ Not<Output = Self>
+ BitAnd<Output = Self>
+ BitOr<Output = Self>
+ BitXor<Output = Self>
+ Shl<usize, Output = Self>
+ Shr<usize, Output = Self>
+ CheckedAdd<Output = Self>
+ CheckedSub<Output = Self>
+ CheckedMul<Output = Self>
+ CheckedDiv<Output = Self>
+ Saturating
{
/// Returns the number of ones in the binary representation of `self`.
///
/// # Examples
///
/// ```
/// use num_traits::PrimInt;
///
/// let n = 0b01001100u8;
///
/// assert_eq!(n.count_ones(), 3);
/// ```
fn count_ones(self) -> u32;
/// Returns the number of zeros in the binary representation of `self`.
///
/// # Examples
///
/// ```
/// use num_traits::PrimInt;
///
/// let n = 0b01001100u8;
///
/// assert_eq!(n.count_zeros(), 5);
/// ```
fn count_zeros(self) -> u32;
/// Returns the number of leading zeros in the binary representation
/// of `self`.
///
/// # Examples
///
/// ```
/// use num_traits::PrimInt;
///
/// let n = 0b0101000u16;
///
/// assert_eq!(n.leading_zeros(), 10);
/// ```
fn leading_zeros(self) -> u32;
/// Returns the number of trailing zeros in the binary representation
/// of `self`.
///
/// # Examples
///
/// ```
/// use num_traits::PrimInt;
///
/// let n = 0b0101000u16;
///
/// assert_eq!(n.trailing_zeros(), 3);
/// ```
fn trailing_zeros(self) -> u32;
/// Shifts the bits to the left by a specified amount amount, `n`, wrapping
/// the truncated bits to the end of the resulting integer.
///
/// # Examples
///
/// ```
/// use num_traits::PrimInt;
///
/// let n = 0x0123456789ABCDEFu64;
/// let m = 0x3456789ABCDEF012u64;
///
/// assert_eq!(n.rotate_left(12), m);
/// ```
fn rotate_left(self, n: u32) -> Self;
/// Shifts the bits to the right by a specified amount amount, `n`, wrapping
/// the truncated bits to the beginning of the resulting integer.
///
/// # Examples
///
/// ```
/// use num_traits::PrimInt;
///
/// let n = 0x0123456789ABCDEFu64;
/// let m = 0xDEF0123456789ABCu64;
///
/// assert_eq!(n.rotate_right(12), m);
/// ```
fn rotate_right(self, n: u32) -> Self;
/// Shifts the bits to the left by a specified amount amount, `n`, filling
/// zeros in the least significant bits.
///
/// This is bitwise equivalent to signed `Shl`.
///
/// # Examples
///
/// ```
/// use num_traits::PrimInt;
///
/// let n = 0x0123456789ABCDEFu64;
/// let m = 0x3456789ABCDEF000u64;
///
/// assert_eq!(n.signed_shl(12), m);
/// ```
fn signed_shl(self, n: u32) -> Self;
/// Shifts the bits to the right by a specified amount amount, `n`, copying
/// the "sign bit" in the most significant bits even for unsigned types.
///
/// This is bitwise equivalent to signed `Shr`.
///
/// # Examples
///
/// ```
/// use num_traits::PrimInt;
///
/// let n = 0xFEDCBA9876543210u64;
/// let m = 0xFFFFEDCBA9876543u64;
///
/// assert_eq!(n.signed_shr(12), m);
/// ```
fn signed_shr(self, n: u32) -> Self;
/// Shifts the bits to the left by a specified amount amount, `n`, filling
/// zeros in the least significant bits.
///
/// This is bitwise equivalent to unsigned `Shl`.
///
/// # Examples
///
/// ```
/// use num_traits::PrimInt;
///
/// let n = 0x0123456789ABCDEFi64;
/// let m = 0x3456789ABCDEF000i64;
///
/// assert_eq!(n.unsigned_shl(12), m);
/// ```
fn unsigned_shl(self, n: u32) -> Self;
/// Shifts the bits to the right by a specified amount amount, `n`, filling
/// zeros in the most significant bits.
///
/// This is bitwise equivalent to unsigned `Shr`.
///
/// # Examples
///
/// ```
/// use num_traits::PrimInt;
///
/// let n = -8i8; // 0b11111000
/// let m = 62i8; // 0b00111110
///
/// assert_eq!(n.unsigned_shr(2), m);
/// ```
fn unsigned_shr(self, n: u32) -> Self;
/// Reverses the byte order of the integer.
///
/// # Examples
///
/// ```
/// use num_traits::PrimInt;
///
/// let n = 0x0123456789ABCDEFu64;
/// let m = 0xEFCDAB8967452301u64;
///
/// assert_eq!(n.swap_bytes(), m);
/// ```
fn swap_bytes(self) -> Self;
/// Convert an integer from big endian to the target's endianness.
///
/// On big endian this is a no-op. On little endian the bytes are swapped.
///
/// # Examples
///
/// ```
/// use num_traits::PrimInt;
///
/// let n = 0x0123456789ABCDEFu64;
///
/// if cfg!(target_endian = "big") {
/// assert_eq!(u64::from_be(n), n)
/// } else {
/// assert_eq!(u64::from_be(n), n.swap_bytes())
/// }
/// ```
fn from_be(x: Self) -> Self;
/// Convert an integer from little endian to the target's endianness.
///
/// On little endian this is a no-op. On big endian the bytes are swapped.
///
/// # Examples
///
/// ```
/// use num_traits::PrimInt;
///
/// let n = 0x0123456789ABCDEFu64;
///
/// if cfg!(target_endian = "little") {
/// assert_eq!(u64::from_le(n), n)
/// } else {
/// assert_eq!(u64::from_le(n), n.swap_bytes())
/// }
/// ```
fn from_le(x: Self) -> Self;
/// Convert `self` to big endian from the target's endianness.
///
/// On big endian this is a no-op. On little endian the bytes are swapped.
///
/// # Examples
///
/// ```
/// use num_traits::PrimInt;
///
/// let n = 0x0123456789ABCDEFu64;
///
/// if cfg!(target_endian = "big") {
/// assert_eq!(n.to_be(), n)
/// } else {
/// assert_eq!(n.to_be(), n.swap_bytes())
/// }
/// ```
fn to_be(self) -> Self;
/// Convert `self` to little endian from the target's endianness.
///
/// On little endian this is a no-op. On big endian the bytes are swapped.
///
/// # Examples
///
/// ```
/// use num_traits::PrimInt;
///
/// let n = 0x0123456789ABCDEFu64;
///
/// if cfg!(target_endian = "little") {
/// assert_eq!(n.to_le(), n)
/// } else {
/// assert_eq!(n.to_le(), n.swap_bytes())
/// }
/// ```
fn to_le(self) -> Self;
/// Raises self to the power of `exp`, using exponentiation by squaring.
///
/// # Examples
///
/// ```
/// use num_traits::PrimInt;
///
/// assert_eq!(2i32.pow(4), 16);
/// ```
fn pow(self, exp: u32) -> Self;
}
macro_rules! prim_int_impl {
($T:ty, $S:ty, $U:ty) => {
impl PrimInt for $T {
#[inline]
fn count_ones(self) -> u32 {
<$T>::count_ones(self)
}
#[inline]
fn count_zeros(self) -> u32 {
<$T>::count_zeros(self)
}
#[inline]
fn leading_zeros(self) -> u32 {
<$T>::leading_zeros(self)
}
#[inline]
fn trailing_zeros(self) -> u32 {
<$T>::trailing_zeros(self)
}
#[inline]
fn rotate_left(self, n: u32) -> Self {
<$T>::rotate_left(self, n)
}
#[inline]
fn rotate_right(self, n: u32) -> Self {
<$T>::rotate_right(self, n)
}
#[inline]
fn signed_shl(self, n: u32) -> Self {
((self as $S) << n) as $T
}
#[inline]
fn signed_shr(self, n: u32) -> Self {
((self as $S) >> n) as $T
}
#[inline]
fn unsigned_shl(self, n: u32) -> Self {
((self as $U) << n) as $T
}
#[inline]
fn unsigned_shr(self, n: u32) -> Self {
((self as $U) >> n) as $T
}
#[inline]
fn swap_bytes(self) -> Self {
<$T>::swap_bytes(self)
}
#[inline]
fn from_be(x: Self) -> Self {
<$T>::from_be(x)
}
#[inline]
fn from_le(x: Self) -> Self {
<$T>::from_le(x)
}
#[inline]
fn to_be(self) -> Self {
<$T>::to_be(self)
}
#[inline]
fn to_le(self) -> Self {
<$T>::to_le(self)
}
#[inline]
fn pow(self, exp: u32) -> Self {
<$T>::pow(self, exp)
}
}
};
}
// prim_int_impl!(type, signed, unsigned);
prim_int_impl!(u8, i8, u8);
prim_int_impl!(u16, i16, u16);
prim_int_impl!(u32, i32, u32);
prim_int_impl!(u64, i64, u64);
#[cfg(has_i128)]
prim_int_impl!(u128, i128, u128);
prim_int_impl!(usize, isize, usize);
prim_int_impl!(i8, i8, u8);
prim_int_impl!(i16, i16, u16);
prim_int_impl!(i32, i32, u32);
prim_int_impl!(i64, i64, u64);
#[cfg(has_i128)]
prim_int_impl!(i128, i128, u128);
prim_int_impl!(isize, isize, usize);

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// Copyright 2013-2014 The Rust Project Developers. See the COPYRIGHT
// file at the top-level directory of this distribution and at
// http://rust-lang.org/COPYRIGHT.
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
// option. This file may not be copied, modified, or distributed
// except according to those terms.
//! Integer trait and functions.
use {Num, Signed};
pub trait Integer
: Sized
+ Num
+ PartialOrd + Ord + Eq
{
/// Floored integer division.
///
/// # Examples
///
/// ~~~
/// # use num::Integer;
/// assert!(( 8).div_floor(& 3) == 2);
/// assert!(( 8).div_floor(&-3) == -3);
/// assert!((-8).div_floor(& 3) == -3);
/// assert!((-8).div_floor(&-3) == 2);
///
/// assert!(( 1).div_floor(& 2) == 0);
/// assert!(( 1).div_floor(&-2) == -1);
/// assert!((-1).div_floor(& 2) == -1);
/// assert!((-1).div_floor(&-2) == 0);
/// ~~~
fn div_floor(&self, other: &Self) -> Self;
/// Floored integer modulo, satisfying:
///
/// ~~~
/// # use num::Integer;
/// # let n = 1; let d = 1;
/// assert!(n.div_floor(&d) * d + n.mod_floor(&d) == n)
/// ~~~
///
/// # Examples
///
/// ~~~
/// # use num::Integer;
/// assert!(( 8).mod_floor(& 3) == 2);
/// assert!(( 8).mod_floor(&-3) == -1);
/// assert!((-8).mod_floor(& 3) == 1);
/// assert!((-8).mod_floor(&-3) == -2);
///
/// assert!(( 1).mod_floor(& 2) == 1);
/// assert!(( 1).mod_floor(&-2) == -1);
/// assert!((-1).mod_floor(& 2) == 1);
/// assert!((-1).mod_floor(&-2) == -1);
/// ~~~
fn mod_floor(&self, other: &Self) -> Self;
/// Greatest Common Divisor (GCD).
///
/// # Examples
///
/// ~~~
/// # use num::Integer;
/// assert_eq!(6.gcd(&8), 2);
/// assert_eq!(7.gcd(&3), 1);
/// ~~~
fn gcd(&self, other: &Self) -> Self;
/// Lowest Common Multiple (LCM).
///
/// # Examples
///
/// ~~~
/// # use num::Integer;
/// assert_eq!(7.lcm(&3), 21);
/// assert_eq!(2.lcm(&4), 4);
/// ~~~
fn lcm(&self, other: &Self) -> Self;
/// Deprecated, use `is_multiple_of` instead.
fn divides(&self, other: &Self) -> bool;
/// Returns `true` if `other` is a multiple of `self`.
///
/// # Examples
///
/// ~~~
/// # use num::Integer;
/// assert_eq!(9.is_multiple_of(&3), true);
/// assert_eq!(3.is_multiple_of(&9), false);
/// ~~~
fn is_multiple_of(&self, other: &Self) -> bool;
/// Returns `true` if the number is even.
///
/// # Examples
///
/// ~~~
/// # use num::Integer;
/// assert_eq!(3.is_even(), false);
/// assert_eq!(4.is_even(), true);
/// ~~~
fn is_even(&self) -> bool;
/// Returns `true` if the number is odd.
///
/// # Examples
///
/// ~~~
/// # use num::Integer;
/// assert_eq!(3.is_odd(), true);
/// assert_eq!(4.is_odd(), false);
/// ~~~
fn is_odd(&self) -> bool;
/// Simultaneous truncated integer division and modulus.
/// Returns `(quotient, remainder)`.
///
/// # Examples
///
/// ~~~
/// # use num::Integer;
/// assert_eq!(( 8).div_rem( &3), ( 2, 2));
/// assert_eq!(( 8).div_rem(&-3), (-2, 2));
/// assert_eq!((-8).div_rem( &3), (-2, -2));
/// assert_eq!((-8).div_rem(&-3), ( 2, -2));
///
/// assert_eq!(( 1).div_rem( &2), ( 0, 1));
/// assert_eq!(( 1).div_rem(&-2), ( 0, 1));
/// assert_eq!((-1).div_rem( &2), ( 0, -1));
/// assert_eq!((-1).div_rem(&-2), ( 0, -1));
/// ~~~
#[inline]
fn div_rem(&self, other: &Self) -> (Self, Self);
/// Simultaneous floored integer division and modulus.
/// Returns `(quotient, remainder)`.
///
/// # Examples
///
/// ~~~
/// # use num::Integer;
/// assert_eq!(( 8).div_mod_floor( &3), ( 2, 2));
/// assert_eq!(( 8).div_mod_floor(&-3), (-3, -1));
/// assert_eq!((-8).div_mod_floor( &3), (-3, 1));
/// assert_eq!((-8).div_mod_floor(&-3), ( 2, -2));
///
/// assert_eq!(( 1).div_mod_floor( &2), ( 0, 1));
/// assert_eq!(( 1).div_mod_floor(&-2), (-1, -1));
/// assert_eq!((-1).div_mod_floor( &2), (-1, 1));
/// assert_eq!((-1).div_mod_floor(&-2), ( 0, -1));
/// ~~~
fn div_mod_floor(&self, other: &Self) -> (Self, Self) {
(self.div_floor(other), self.mod_floor(other))
}
}
/// Simultaneous integer division and modulus
#[inline] pub fn div_rem<T: Integer>(x: T, y: T) -> (T, T) { x.div_rem(&y) }
/// Floored integer division
#[inline] pub fn div_floor<T: Integer>(x: T, y: T) -> T { x.div_floor(&y) }
/// Floored integer modulus
#[inline] pub fn mod_floor<T: Integer>(x: T, y: T) -> T { x.mod_floor(&y) }
/// Simultaneous floored integer division and modulus
#[inline] pub fn div_mod_floor<T: Integer>(x: T, y: T) -> (T, T) { x.div_mod_floor(&y) }
/// Calculates the Greatest Common Divisor (GCD) of the number and `other`. The
/// result is always positive.
#[inline(always)] pub fn gcd<T: Integer>(x: T, y: T) -> T { x.gcd(&y) }
/// Calculates the Lowest Common Multiple (LCM) of the number and `other`.
#[inline(always)] pub fn lcm<T: Integer>(x: T, y: T) -> T { x.lcm(&y) }
macro_rules! impl_integer_for_isize {
($T:ty, $test_mod:ident) => (
impl Integer for $T {
/// Floored integer division
#[inline]
fn div_floor(&self, other: &$T) -> $T {
// Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_,
// December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf)
match self.div_rem(other) {
(d, r) if (r > 0 && *other < 0)
|| (r < 0 && *other > 0) => d - 1,
(d, _) => d,
}
}
/// Floored integer modulo
#[inline]
fn mod_floor(&self, other: &$T) -> $T {
// Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_,
// December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf)
match *self % *other {
r if (r > 0 && *other < 0)
|| (r < 0 && *other > 0) => r + *other,
r => r,
}
}
/// Calculates `div_floor` and `mod_floor` simultaneously
#[inline]
fn div_mod_floor(&self, other: &$T) -> ($T,$T) {
// Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_,
// December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf)
match self.div_rem(other) {
(d, r) if (r > 0 && *other < 0)
|| (r < 0 && *other > 0) => (d - 1, r + *other),
(d, r) => (d, r),
}
}
/// Calculates the Greatest Common Divisor (GCD) of the number and
/// `other`. The result is always positive.
#[inline]
fn gcd(&self, other: &$T) -> $T {
// Use Stein's algorithm
let mut m = *self;
let mut n = *other;
if m == 0 || n == 0 { return (m | n).abs() }
// find common factors of 2
let shift = (m | n).trailing_zeros();
// The algorithm needs positive numbers, but the minimum value
// can't be represented as a positive one.
// It's also a power of two, so the gcd can be
// calculated by bitshifting in that case
// Assuming two's complement, the number created by the shift
// is positive for all numbers except gcd = abs(min value)
// The call to .abs() causes a panic in debug mode
if m == <$T>::min_value() || n == <$T>::min_value() {
return (1 << shift).abs()
}
// guaranteed to be positive now, rest like unsigned algorithm
m = m.abs();
n = n.abs();
// divide n and m by 2 until odd
// m inside loop
n >>= n.trailing_zeros();
while m != 0 {
m >>= m.trailing_zeros();
if n > m { ::std::mem::swap(&mut n, &mut m) }
m -= n;
}
n << shift
}
/// Calculates the Lowest Common Multiple (LCM) of the number and
/// `other`.
#[inline]
fn lcm(&self, other: &$T) -> $T {
// should not have to recalculate abs
((*self * *other) / self.gcd(other)).abs()
}
/// Deprecated, use `is_multiple_of` instead.
#[inline]
fn divides(&self, other: &$T) -> bool { return self.is_multiple_of(other); }
/// Returns `true` if the number is a multiple of `other`.
#[inline]
fn is_multiple_of(&self, other: &$T) -> bool { *self % *other == 0 }
/// Returns `true` if the number is divisible by `2`
#[inline]
fn is_even(&self) -> bool { (*self) & 1 == 0 }
/// Returns `true` if the number is not divisible by `2`
#[inline]
fn is_odd(&self) -> bool { !self.is_even() }
/// Simultaneous truncated integer division and modulus.
#[inline]
fn div_rem(&self, other: &$T) -> ($T, $T) {
(*self / *other, *self % *other)
}
}
#[cfg(test)]
mod $test_mod {
use Integer;
/// Checks that the division rule holds for:
///
/// - `n`: numerator (dividend)
/// - `d`: denominator (divisor)
/// - `qr`: quotient and remainder
#[cfg(test)]
fn test_division_rule((n,d): ($T,$T), (q,r): ($T,$T)) {
assert_eq!(d * q + r, n);
}
#[test]
fn test_div_rem() {
fn test_nd_dr(nd: ($T,$T), qr: ($T,$T)) {
let (n,d) = nd;
let separate_div_rem = (n / d, n % d);
let combined_div_rem = n.div_rem(&d);
assert_eq!(separate_div_rem, qr);
assert_eq!(combined_div_rem, qr);
test_division_rule(nd, separate_div_rem);
test_division_rule(nd, combined_div_rem);
}
test_nd_dr(( 8, 3), ( 2, 2));
test_nd_dr(( 8, -3), (-2, 2));
test_nd_dr((-8, 3), (-2, -2));
test_nd_dr((-8, -3), ( 2, -2));
test_nd_dr(( 1, 2), ( 0, 1));
test_nd_dr(( 1, -2), ( 0, 1));
test_nd_dr((-1, 2), ( 0, -1));
test_nd_dr((-1, -2), ( 0, -1));
}
#[test]
fn test_div_mod_floor() {
fn test_nd_dm(nd: ($T,$T), dm: ($T,$T)) {
let (n,d) = nd;
let separate_div_mod_floor = (n.div_floor(&d), n.mod_floor(&d));
let combined_div_mod_floor = n.div_mod_floor(&d);
assert_eq!(separate_div_mod_floor, dm);
assert_eq!(combined_div_mod_floor, dm);
test_division_rule(nd, separate_div_mod_floor);
test_division_rule(nd, combined_div_mod_floor);
}
test_nd_dm(( 8, 3), ( 2, 2));
test_nd_dm(( 8, -3), (-3, -1));
test_nd_dm((-8, 3), (-3, 1));
test_nd_dm((-8, -3), ( 2, -2));
test_nd_dm(( 1, 2), ( 0, 1));
test_nd_dm(( 1, -2), (-1, -1));
test_nd_dm((-1, 2), (-1, 1));
test_nd_dm((-1, -2), ( 0, -1));
}
#[test]
fn test_gcd() {
assert_eq!((10 as $T).gcd(&2), 2 as $T);
assert_eq!((10 as $T).gcd(&3), 1 as $T);
assert_eq!((0 as $T).gcd(&3), 3 as $T);
assert_eq!((3 as $T).gcd(&3), 3 as $T);
assert_eq!((56 as $T).gcd(&42), 14 as $T);
assert_eq!((3 as $T).gcd(&-3), 3 as $T);
assert_eq!((-6 as $T).gcd(&3), 3 as $T);
assert_eq!((-4 as $T).gcd(&-2), 2 as $T);
}
#[test]
fn test_gcd_cmp_with_euclidean() {
fn euclidean_gcd(mut m: $T, mut n: $T) -> $T {
while m != 0 {
::std::mem::swap(&mut m, &mut n);
m %= n;
}
n.abs()
}
// gcd(-128, b) = 128 is not representable as positive value
// for i8
for i in -127..127 {
for j in -127..127 {
assert_eq!(euclidean_gcd(i,j), i.gcd(&j));
}
}
// last value
// FIXME: Use inclusive ranges for above loop when implemented
let i = 127;
for j in -127..127 {
assert_eq!(euclidean_gcd(i,j), i.gcd(&j));
}
assert_eq!(127.gcd(&127), 127);
}
#[test]
fn test_gcd_min_val() {
let min = <$T>::min_value();
let max = <$T>::max_value();
let max_pow2 = max / 2 + 1;
assert_eq!(min.gcd(&max), 1 as $T);
assert_eq!(max.gcd(&min), 1 as $T);
assert_eq!(min.gcd(&max_pow2), max_pow2);
assert_eq!(max_pow2.gcd(&min), max_pow2);
assert_eq!(min.gcd(&42), 2 as $T);
assert_eq!((42 as $T).gcd(&min), 2 as $T);
}
#[test]
#[should_panic]
fn test_gcd_min_val_min_val() {
let min = <$T>::min_value();
assert!(min.gcd(&min) >= 0);
}
#[test]
#[should_panic]
fn test_gcd_min_val_0() {
let min = <$T>::min_value();
assert!(min.gcd(&0) >= 0);
}
#[test]
#[should_panic]
fn test_gcd_0_min_val() {
let min = <$T>::min_value();
assert!((0 as $T).gcd(&min) >= 0);
}
#[test]
fn test_lcm() {
assert_eq!((1 as $T).lcm(&0), 0 as $T);
assert_eq!((0 as $T).lcm(&1), 0 as $T);
assert_eq!((1 as $T).lcm(&1), 1 as $T);
assert_eq!((-1 as $T).lcm(&1), 1 as $T);
assert_eq!((1 as $T).lcm(&-1), 1 as $T);
assert_eq!((-1 as $T).lcm(&-1), 1 as $T);
assert_eq!((8 as $T).lcm(&9), 72 as $T);
assert_eq!((11 as $T).lcm(&5), 55 as $T);
}
#[test]
fn test_even() {
assert_eq!((-4 as $T).is_even(), true);
assert_eq!((-3 as $T).is_even(), false);
assert_eq!((-2 as $T).is_even(), true);
assert_eq!((-1 as $T).is_even(), false);
assert_eq!((0 as $T).is_even(), true);
assert_eq!((1 as $T).is_even(), false);
assert_eq!((2 as $T).is_even(), true);
assert_eq!((3 as $T).is_even(), false);
assert_eq!((4 as $T).is_even(), true);
}
#[test]
fn test_odd() {
assert_eq!((-4 as $T).is_odd(), false);
assert_eq!((-3 as $T).is_odd(), true);
assert_eq!((-2 as $T).is_odd(), false);
assert_eq!((-1 as $T).is_odd(), true);
assert_eq!((0 as $T).is_odd(), false);
assert_eq!((1 as $T).is_odd(), true);
assert_eq!((2 as $T).is_odd(), false);
assert_eq!((3 as $T).is_odd(), true);
assert_eq!((4 as $T).is_odd(), false);
}
}
)
}
impl_integer_for_isize!(i8, test_integer_i8);
impl_integer_for_isize!(i16, test_integer_i16);
impl_integer_for_isize!(i32, test_integer_i32);
impl_integer_for_isize!(i64, test_integer_i64);
impl_integer_for_isize!(isize, test_integer_isize);
macro_rules! impl_integer_for_usize {
($T:ty, $test_mod:ident) => (
impl Integer for $T {
/// Unsigned integer division. Returns the same result as `div` (`/`).
#[inline]
fn div_floor(&self, other: &$T) -> $T { *self / *other }
/// Unsigned integer modulo operation. Returns the same result as `rem` (`%`).
#[inline]
fn mod_floor(&self, other: &$T) -> $T { *self % *other }
/// Calculates the Greatest Common Divisor (GCD) of the number and `other`
#[inline]
fn gcd(&self, other: &$T) -> $T {
// Use Stein's algorithm
let mut m = *self;
let mut n = *other;
if m == 0 || n == 0 { return m | n }
// find common factors of 2
let shift = (m | n).trailing_zeros();
// divide n and m by 2 until odd
// m inside loop
n >>= n.trailing_zeros();
while m != 0 {
m >>= m.trailing_zeros();
if n > m { ::std::mem::swap(&mut n, &mut m) }
m -= n;
}
n << shift
}
/// Calculates the Lowest Common Multiple (LCM) of the number and `other`.
#[inline]
fn lcm(&self, other: &$T) -> $T {
(*self * *other) / self.gcd(other)
}
/// Deprecated, use `is_multiple_of` instead.
#[inline]
fn divides(&self, other: &$T) -> bool { return self.is_multiple_of(other); }
/// Returns `true` if the number is a multiple of `other`.
#[inline]
fn is_multiple_of(&self, other: &$T) -> bool { *self % *other == 0 }
/// Returns `true` if the number is divisible by `2`.
#[inline]
fn is_even(&self) -> bool { (*self) & 1 == 0 }
/// Returns `true` if the number is not divisible by `2`.
#[inline]
fn is_odd(&self) -> bool { !(*self).is_even() }
/// Simultaneous truncated integer division and modulus.
#[inline]
fn div_rem(&self, other: &$T) -> ($T, $T) {
(*self / *other, *self % *other)
}
}
#[cfg(test)]
mod $test_mod {
use Integer;
#[test]
fn test_div_mod_floor() {
assert_eq!((10 as $T).div_floor(&(3 as $T)), 3 as $T);
assert_eq!((10 as $T).mod_floor(&(3 as $T)), 1 as $T);
assert_eq!((10 as $T).div_mod_floor(&(3 as $T)), (3 as $T, 1 as $T));
assert_eq!((5 as $T).div_floor(&(5 as $T)), 1 as $T);
assert_eq!((5 as $T).mod_floor(&(5 as $T)), 0 as $T);
assert_eq!((5 as $T).div_mod_floor(&(5 as $T)), (1 as $T, 0 as $T));
assert_eq!((3 as $T).div_floor(&(7 as $T)), 0 as $T);
assert_eq!((3 as $T).mod_floor(&(7 as $T)), 3 as $T);
assert_eq!((3 as $T).div_mod_floor(&(7 as $T)), (0 as $T, 3 as $T));
}
#[test]
fn test_gcd() {
assert_eq!((10 as $T).gcd(&2), 2 as $T);
assert_eq!((10 as $T).gcd(&3), 1 as $T);
assert_eq!((0 as $T).gcd(&3), 3 as $T);
assert_eq!((3 as $T).gcd(&3), 3 as $T);
assert_eq!((56 as $T).gcd(&42), 14 as $T);
}
#[test]
fn test_gcd_cmp_with_euclidean() {
fn euclidean_gcd(mut m: $T, mut n: $T) -> $T {
while m != 0 {
::std::mem::swap(&mut m, &mut n);
m %= n;
}
n
}
for i in 0..255 {
for j in 0..255 {
assert_eq!(euclidean_gcd(i,j), i.gcd(&j));
}
}
// last value
// FIXME: Use inclusive ranges for above loop when implemented
let i = 255;
for j in 0..255 {
assert_eq!(euclidean_gcd(i,j), i.gcd(&j));
}
assert_eq!(255.gcd(&255), 255);
}
#[test]
fn test_lcm() {
assert_eq!((1 as $T).lcm(&0), 0 as $T);
assert_eq!((0 as $T).lcm(&1), 0 as $T);
assert_eq!((1 as $T).lcm(&1), 1 as $T);
assert_eq!((8 as $T).lcm(&9), 72 as $T);
assert_eq!((11 as $T).lcm(&5), 55 as $T);
assert_eq!((15 as $T).lcm(&17), 255 as $T);
}
#[test]
fn test_is_multiple_of() {
assert!((6 as $T).is_multiple_of(&(6 as $T)));
assert!((6 as $T).is_multiple_of(&(3 as $T)));
assert!((6 as $T).is_multiple_of(&(1 as $T)));
}
#[test]
fn test_even() {
assert_eq!((0 as $T).is_even(), true);
assert_eq!((1 as $T).is_even(), false);
assert_eq!((2 as $T).is_even(), true);
assert_eq!((3 as $T).is_even(), false);
assert_eq!((4 as $T).is_even(), true);
}
#[test]
fn test_odd() {
assert_eq!((0 as $T).is_odd(), false);
assert_eq!((1 as $T).is_odd(), true);
assert_eq!((2 as $T).is_odd(), false);
assert_eq!((3 as $T).is_odd(), true);
assert_eq!((4 as $T).is_odd(), false);
}
}
)
}
impl_integer_for_usize!(u8, test_integer_u8);
impl_integer_for_usize!(u16, test_integer_u16);
impl_integer_for_usize!(u32, test_integer_u32);
impl_integer_for_usize!(u64, test_integer_u64);
impl_integer_for_usize!(usize, test_integer_usize);

372
src/iter.rs Normal file
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@ -0,0 +1,372 @@
// Copyright 2013-2014 The Rust Project Developers. See the COPYRIGHT
// file at the top-level directory of this distribution and at
// http://rust-lang.org/COPYRIGHT.
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
// option. This file may not be copied, modified, or distributed
// except according to those terms.
//! External iterators for generic mathematics
use {Integer, Zero, One, CheckedAdd, ToPrimitive};
use std::ops::{Add, Sub};
/// An iterator over the range [start, stop)
#[derive(Clone)]
pub struct Range<A> {
state: A,
stop: A,
one: A
}
/// Returns an iterator over the given range [start, stop) (that is, starting
/// at start (inclusive), and ending at stop (exclusive)).
///
/// # Example
///
/// ```rust
/// use num::iter;
///
/// let array = [0, 1, 2, 3, 4];
///
/// for i in iter::range(0, 5) {
/// println!("{}", i);
/// assert_eq!(i, array[i]);
/// }
/// ```
#[inline]
pub fn range<A>(start: A, stop: A) -> Range<A>
where A: Add<A, Output = A> + PartialOrd + Clone + One
{
Range{state: start, stop: stop, one: One::one()}
}
// FIXME: rust-lang/rust#10414: Unfortunate type bound
impl<A> Iterator for Range<A>
where A: Add<A, Output = A> + PartialOrd + Clone + ToPrimitive
{
type Item = A;
#[inline]
fn next(&mut self) -> Option<A> {
if self.state < self.stop {
let result = self.state.clone();
self.state = self.state.clone() + self.one.clone();
Some(result)
} else {
None
}
}
#[inline]
fn size_hint(&self) -> (usize, Option<usize>) {
// This first checks if the elements are representable as i64. If they aren't, try u64 (to
// handle cases like range(huge, huger)). We don't use usize/int because the difference of
// the i64/u64 might lie within their range.
let bound = match self.state.to_i64() {
Some(a) => {
let sz = self.stop.to_i64().map(|b| b.checked_sub(a));
match sz {
Some(Some(bound)) => bound.to_usize(),
_ => None,
}
},
None => match self.state.to_u64() {
Some(a) => {
let sz = self.stop.to_u64().map(|b| b.checked_sub(a));
match sz {
Some(Some(bound)) => bound.to_usize(),
_ => None
}
},
None => None
}
};
match bound {
Some(b) => (b, Some(b)),
// Standard fallback for unbounded/unrepresentable bounds
None => (0, None)
}
}
}
/// `Integer` is required to ensure the range will be the same regardless of
/// the direction it is consumed.
impl<A> DoubleEndedIterator for Range<A>
where A: Integer + PartialOrd + Clone + ToPrimitive
{
#[inline]
fn next_back(&mut self) -> Option<A> {
if self.stop > self.state {
self.stop = self.stop.clone() - self.one.clone();
Some(self.stop.clone())
} else {
None
}
}
}
/// An iterator over the range [start, stop]
#[derive(Clone)]
pub struct RangeInclusive<A> {
range: Range<A>,
done: bool,
}
/// Return an iterator over the range [start, stop]
#[inline]
pub fn range_inclusive<A>(start: A, stop: A) -> RangeInclusive<A>
where A: Add<A, Output = A> + PartialOrd + Clone + One
{
RangeInclusive{range: range(start, stop), done: false}
}
impl<A> Iterator for RangeInclusive<A>
where A: Add<A, Output = A> + PartialOrd + Clone + ToPrimitive
{
type Item = A;
#[inline]
fn next(&mut self) -> Option<A> {
match self.range.next() {
Some(x) => Some(x),
None => {
if !self.done && self.range.state == self.range.stop {
self.done = true;
Some(self.range.stop.clone())
} else {
None
}
}
}
}
#[inline]
fn size_hint(&self) -> (usize, Option<usize>) {
let (lo, hi) = self.range.size_hint();
if self.done {
(lo, hi)
} else {
let lo = lo.saturating_add(1);
let hi = match hi {
Some(x) => x.checked_add(1),
None => None
};
(lo, hi)
}
}
}
impl<A> DoubleEndedIterator for RangeInclusive<A>
where A: Sub<A, Output = A> + Integer + PartialOrd + Clone + ToPrimitive
{
#[inline]
fn next_back(&mut self) -> Option<A> {
if self.range.stop > self.range.state {
let result = self.range.stop.clone();
self.range.stop = self.range.stop.clone() - self.range.one.clone();
Some(result)
} else if !self.done && self.range.state == self.range.stop {
self.done = true;
Some(self.range.stop.clone())
} else {
None
}
}
}
/// An iterator over the range [start, stop) by `step`. It handles overflow by stopping.
#[derive(Clone)]
pub struct RangeStep<A> {
state: A,
stop: A,
step: A,
rev: bool,
}
/// Return an iterator over the range [start, stop) by `step`. It handles overflow by stopping.
#[inline]
pub fn range_step<A>(start: A, stop: A, step: A) -> RangeStep<A>
where A: CheckedAdd + PartialOrd + Clone + Zero
{
let rev = step < Zero::zero();
RangeStep{state: start, stop: stop, step: step, rev: rev}
}
impl<A> Iterator for RangeStep<A>
where A: CheckedAdd + PartialOrd + Clone
{
type Item = A;
#[inline]
fn next(&mut self) -> Option<A> {
if (self.rev && self.state > self.stop) || (!self.rev && self.state < self.stop) {
let result = self.state.clone();
match self.state.checked_add(&self.step) {
Some(x) => self.state = x,
None => self.state = self.stop.clone()
}
Some(result)
} else {
None
}
}
}
/// An iterator over the range [start, stop] by `step`. It handles overflow by stopping.
#[derive(Clone)]
pub struct RangeStepInclusive<A> {
state: A,
stop: A,
step: A,
rev: bool,
done: bool,
}
/// Return an iterator over the range [start, stop] by `step`. It handles overflow by stopping.
#[inline]
pub fn range_step_inclusive<A>(start: A, stop: A, step: A) -> RangeStepInclusive<A>
where A: CheckedAdd + PartialOrd + Clone + Zero
{
let rev = step < Zero::zero();
RangeStepInclusive{state: start, stop: stop, step: step, rev: rev, done: false}
}
impl<A> Iterator for RangeStepInclusive<A>
where A: CheckedAdd + PartialOrd + Clone + PartialEq
{
type Item = A;
#[inline]
fn next(&mut self) -> Option<A> {
if !self.done && ((self.rev && self.state >= self.stop) ||
(!self.rev && self.state <= self.stop)) {
let result = self.state.clone();
match self.state.checked_add(&self.step) {
Some(x) => self.state = x,
None => self.done = true
}
Some(result)
} else {
None
}
}
}
#[cfg(test)]
mod tests {
use std::usize;
use std::ops::{Add, Mul};
use std::cmp::Ordering;
use {One, ToPrimitive};
#[test]
fn test_range() {
/// A mock type to check Range when ToPrimitive returns None
struct Foo;
impl ToPrimitive for Foo {
fn to_i64(&self) -> Option<i64> { None }
fn to_u64(&self) -> Option<u64> { None }
}
impl Add<Foo> for Foo {
type Output = Foo;
fn add(self, _: Foo) -> Foo {
Foo
}
}
impl PartialEq for Foo {
fn eq(&self, _: &Foo) -> bool {
true
}
}
impl PartialOrd for Foo {
fn partial_cmp(&self, _: &Foo) -> Option<Ordering> {
None
}
}
impl Clone for Foo {
fn clone(&self) -> Foo {
Foo
}
}
impl Mul<Foo> for Foo {
type Output = Foo;
fn mul(self, _: Foo) -> Foo {
Foo
}
}
impl One for Foo {
fn one() -> Foo {
Foo
}
}
assert!(super::range(0, 5).collect::<Vec<isize>>() == vec![0, 1, 2, 3, 4]);
assert!(super::range(-10, -1).collect::<Vec<isize>>() ==
vec![-10, -9, -8, -7, -6, -5, -4, -3, -2]);
assert!(super::range(0, 5).rev().collect::<Vec<isize>>() == vec![4, 3, 2, 1, 0]);
assert_eq!(super::range(200, -5).count(), 0);
assert_eq!(super::range(200, -5).rev().count(), 0);
assert_eq!(super::range(200, 200).count(), 0);
assert_eq!(super::range(200, 200).rev().count(), 0);
assert_eq!(super::range(0, 100).size_hint(), (100, Some(100)));
// this test is only meaningful when sizeof usize < sizeof u64
assert_eq!(super::range(usize::MAX - 1, usize::MAX).size_hint(), (1, Some(1)));
assert_eq!(super::range(-10, -1).size_hint(), (9, Some(9)));
}
#[test]
fn test_range_inclusive() {
assert!(super::range_inclusive(0, 5).collect::<Vec<isize>>() ==
vec![0, 1, 2, 3, 4, 5]);
assert!(super::range_inclusive(0, 5).rev().collect::<Vec<isize>>() ==
vec![5, 4, 3, 2, 1, 0]);
assert_eq!(super::range_inclusive(200, -5).count(), 0);
assert_eq!(super::range_inclusive(200, -5).rev().count(), 0);
assert!(super::range_inclusive(200, 200).collect::<Vec<isize>>() == vec![200]);
assert!(super::range_inclusive(200, 200).rev().collect::<Vec<isize>>() == vec![200]);
}
#[test]
fn test_range_step() {
assert!(super::range_step(0, 20, 5).collect::<Vec<isize>>() ==
vec![0, 5, 10, 15]);
assert!(super::range_step(20, 0, -5).collect::<Vec<isize>>() ==
vec![20, 15, 10, 5]);
assert!(super::range_step(20, 0, -6).collect::<Vec<isize>>() ==
vec![20, 14, 8, 2]);
assert!(super::range_step(200u8, 255, 50).collect::<Vec<u8>>() ==
vec![200u8, 250]);
assert!(super::range_step(200, -5, 1).collect::<Vec<isize>>() == vec![]);
assert!(super::range_step(200, 200, 1).collect::<Vec<isize>>() == vec![]);
}
#[test]
fn test_range_step_inclusive() {
assert!(super::range_step_inclusive(0, 20, 5).collect::<Vec<isize>>() ==
vec![0, 5, 10, 15, 20]);
assert!(super::range_step_inclusive(20, 0, -5).collect::<Vec<isize>>() ==
vec![20, 15, 10, 5, 0]);
assert!(super::range_step_inclusive(20, 0, -6).collect::<Vec<isize>>() ==
vec![20, 14, 8, 2]);
assert!(super::range_step_inclusive(200u8, 255, 50).collect::<Vec<u8>>() ==
vec![200u8, 250]);
assert!(super::range_step_inclusive(200, -5, 1).collect::<Vec<isize>>() ==
vec![]);
assert!(super::range_step_inclusive(200, 200, 1).collect::<Vec<isize>>() ==
vec![200]);
}
}

695
src/lib.rs
View File

@ -1,4 +1,4 @@
// Copyright 2013-2014 The Rust Project Developers. See the COPYRIGHT // Copyright 2014-2016 The Rust Project Developers. See the COPYRIGHT
// file at the top-level directory of this distribution and at // file at the top-level directory of this distribution and at
// http://rust-lang.org/COPYRIGHT. // http://rust-lang.org/COPYRIGHT.
// //
@ -8,565 +8,206 @@
// option. This file may not be copied, modified, or distributed // option. This file may not be copied, modified, or distributed
// except according to those terms. // except according to those terms.
//! Numeric traits for generic mathematics //! A collection of numeric types and traits for Rust.
//! //!
//! ## Compatibility //! This includes new types for big integers, rationals, and complex numbers,
//! new traits for generic programming on numeric properties like `Integer`,
//! and generic range iterators.
//! //!
//! The `num-traits` crate is tested for rustc 1.8 and greater. //! ## Example
//!
//! This example uses the BigRational type and [Newton's method][newt] to
//! approximate a square root to arbitrary precision:
//!
//! ```
//! extern crate num;
//! # #[cfg(all(feature = "bigint", feature="rational"))]
//! # mod test {
//!
//! use num::FromPrimitive;
//! use num::bigint::BigInt;
//! use num::rational::{Ratio, BigRational};
//!
//! # pub
//! fn approx_sqrt(number: u64, iterations: usize) -> BigRational {
//! let start: Ratio<BigInt> = Ratio::from_integer(FromPrimitive::from_u64(number).unwrap());
//! let mut approx = start.clone();
//!
//! for _ in 0..iterations {
//! approx = (&approx + (&start / &approx)) /
//! Ratio::from_integer(FromPrimitive::from_u64(2).unwrap());
//! }
//!
//! approx
//! }
//! # }
//! # #[cfg(not(all(feature = "bigint", feature="rational")))]
//! # mod test { pub fn approx_sqrt(n: u64, _: usize) -> u64 { n } }
//! # use test::approx_sqrt;
//!
//! fn main() {
//! println!("{}", approx_sqrt(10, 4)); // prints 4057691201/1283082416
//! }
//!
//! ```
//!
//! [newt]: https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method
#![doc(html_logo_url = "http://rust-num.github.io/num/rust-logo-128x128-blk-v2.png",
html_favicon_url = "http://rust-num.github.io/num/favicon.ico",
html_root_url = "http://rust-num.github.io/num/",
html_playground_url = "http://play.rust-lang.org/")]
#![doc(html_root_url = "https://docs.rs/num-traits/0.2")] #[cfg(feature = "rustc-serialize")]
#![deny(unconditional_recursion)] extern crate rustc_serialize;
#![no_std]
#[cfg(feature = "std")]
extern crate std;
// Only `no_std` builds actually use `libm`. // Some of the tests of non-RNG-based functionality are randomized using the
#[cfg(all(not(feature = "std"), feature = "libm"))] // RNG-based functionality, so the RNG-based functionality needs to be enabled
extern crate libm; // for tests.
#[cfg(any(feature = "rand", all(feature = "bigint", test)))]
extern crate rand;
use core::fmt; #[cfg(feature = "bigint")]
use core::num::Wrapping; pub use bigint::{BigInt, BigUint};
use core::ops::{Add, Div, Mul, Rem, Sub}; #[cfg(feature = "rational")]
use core::ops::{AddAssign, DivAssign, MulAssign, RemAssign, SubAssign}; pub use rational::Rational;
#[cfg(all(feature = "rational", feature="bigint"))]
pub use rational::BigRational;
#[cfg(feature = "complex")]
pub use complex::Complex;
pub use integer::Integer;
pub use iter::{range, range_inclusive, range_step, range_step_inclusive};
pub use traits::{Num, Zero, One, Signed, Unsigned, Bounded,
Saturating, CheckedAdd, CheckedSub, CheckedMul, CheckedDiv,
PrimInt, Float, ToPrimitive, FromPrimitive, NumCast, cast};
pub use bounds::Bounded; #[cfg(test)] use std::hash;
#[cfg(any(feature = "std", feature = "libm"))]
pub use float::Float;
pub use float::FloatConst;
// pub use real::{FloatCore, Real}; // NOTE: Don't do this, it breaks `use num_traits::*;`.
pub use cast::{cast, AsPrimitive, FromPrimitive, NumCast, ToPrimitive};
pub use identities::{one, zero, One, Zero};
pub use int::PrimInt;
pub use ops::checked::{
CheckedAdd, CheckedDiv, CheckedMul, CheckedNeg, CheckedRem, CheckedShl, CheckedShr, CheckedSub,
};
pub use ops::inv::Inv;
pub use ops::mul_add::{MulAdd, MulAddAssign};
pub use ops::saturating::Saturating;
pub use ops::wrapping::{WrappingAdd, WrappingMul, WrappingShl, WrappingShr, WrappingSub};
pub use pow::{checked_pow, pow, Pow};
pub use sign::{abs, abs_sub, signum, Signed, Unsigned};
#[macro_use] use std::ops::{Mul};
mod macros;
pub mod bounds; #[cfg(feature = "bigint")]
pub mod cast; pub mod bigint;
pub mod float; pub mod complex;
pub mod identities; pub mod integer;
pub mod int; pub mod iter;
pub mod ops; pub mod traits;
pub mod pow; #[cfg(feature = "rational")]
pub mod real; pub mod rational;
pub mod sign;
/// The base trait for numeric types, covering `0` and `1` values, /// Returns the additive identity, `0`.
/// comparisons, basic numeric operations, and string conversion. #[inline(always)] pub fn zero<T: Zero>() -> T { Zero::zero() }
pub trait Num: PartialEq + Zero + One + NumOps {
type FromStrRadixErr;
/// Convert from a string and radix <= 36. /// Returns the multiplicative identity, `1`.
/// #[inline(always)] pub fn one<T: One>() -> T { One::one() }
/// # Examples
/// /// Computes the absolute value.
/// ```rust ///
/// use num_traits::Num; /// For `f32` and `f64`, `NaN` will be returned if the number is `NaN`
/// ///
/// let result = <i32 as Num>::from_str_radix("27", 10); /// For signed integers, `::MIN` will be returned if the number is `::MIN`.
/// assert_eq!(result, Ok(27)); #[inline(always)]
/// pub fn abs<T: Signed>(value: T) -> T {
/// let result = <i32 as Num>::from_str_radix("foo", 10); value.abs()
/// assert!(result.is_err());
/// ```
fn from_str_radix(str: &str, radix: u32) -> Result<Self, Self::FromStrRadixErr>;
} }
/// The trait for types implementing basic numeric operations /// The positive difference of two numbers.
/// ///
/// This is automatically implemented for types which implement the operators. /// Returns zero if `x` is less than or equal to `y`, otherwise the difference
pub trait NumOps<Rhs = Self, Output = Self>: /// between `x` and `y` is returned.
Add<Rhs, Output = Output> #[inline(always)]
+ Sub<Rhs, Output = Output> pub fn abs_sub<T: Signed>(x: T, y: T) -> T {
+ Mul<Rhs, Output = Output> x.abs_sub(&y)
+ Div<Rhs, Output = Output>
+ Rem<Rhs, Output = Output>
{
} }
impl<T, Rhs, Output> NumOps<Rhs, Output> for T where /// Returns the sign of the number.
T: Add<Rhs, Output = Output>
+ Sub<Rhs, Output = Output>
+ Mul<Rhs, Output = Output>
+ Div<Rhs, Output = Output>
+ Rem<Rhs, Output = Output>
{
}
/// The trait for `Num` types which also implement numeric operations taking
/// the second operand by reference.
/// ///
/// This is automatically implemented for types which implement the operators. /// For `f32` and `f64`:
pub trait NumRef: Num + for<'r> NumOps<&'r Self> {}
impl<T> NumRef for T where T: Num + for<'r> NumOps<&'r T> {}
/// The trait for references which implement numeric operations, taking the
/// second operand either by value or by reference.
/// ///
/// This is automatically implemented for types which implement the operators. /// * `1.0` if the number is positive, `+0.0` or `INFINITY`
pub trait RefNum<Base>: NumOps<Base, Base> + for<'r> NumOps<&'r Base, Base> {} /// * `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
impl<T, Base> RefNum<Base> for T where T: NumOps<Base, Base> + for<'r> NumOps<&'r Base, Base> {} /// * `NaN` if the number is `NaN`
/// The trait for types implementing numeric assignment operators (like `+=`).
/// ///
/// This is automatically implemented for types which implement the operators. /// For signed integers:
pub trait NumAssignOps<Rhs = Self>:
AddAssign<Rhs> + SubAssign<Rhs> + MulAssign<Rhs> + DivAssign<Rhs> + RemAssign<Rhs>
{
}
impl<T, Rhs> NumAssignOps<Rhs> for T where
T: AddAssign<Rhs> + SubAssign<Rhs> + MulAssign<Rhs> + DivAssign<Rhs> + RemAssign<Rhs>
{
}
/// The trait for `Num` types which also implement assignment operators.
/// ///
/// This is automatically implemented for types which implement the operators. /// * `0` if the number is zero
pub trait NumAssign: Num + NumAssignOps {} /// * `1` if the number is positive
impl<T> NumAssign for T where T: Num + NumAssignOps {} /// * `-1` if the number is negative
#[inline(always)] pub fn signum<T: Signed>(value: T) -> T { value.signum() }
/// The trait for `NumAssign` types which also implement assignment operations /// Raises a value to the power of exp, using exponentiation by squaring.
/// taking the second operand by reference.
/// ///
/// This is automatically implemented for types which implement the operators. /// # Example
pub trait NumAssignRef: NumAssign + for<'r> NumAssignOps<&'r Self> {} ///
impl<T> NumAssignRef for T where T: NumAssign + for<'r> NumAssignOps<&'r T> {} /// ```rust
/// use num;
///
/// assert_eq!(num::pow(2i8, 4), 16);
/// assert_eq!(num::pow(6u8, 3), 216);
/// ```
#[inline]
pub fn pow<T: Clone + One + Mul<T, Output = T>>(mut base: T, mut exp: usize) -> T {
if exp == 0 { return T::one() }
macro_rules! int_trait_impl { while exp & 1 == 0 {
($name:ident for $($t:ty)*) => ($( base = base.clone() * base;
impl $name for $t { exp >>= 1;
type FromStrRadixErr = ::core::num::ParseIntError; }
#[inline] if exp == 1 { return base }
fn from_str_radix(s: &str, radix: u32)
-> Result<Self, ::core::num::ParseIntError> let mut acc = base.clone();
{ while exp > 1 {
<$t>::from_str_radix(s, radix) exp >>= 1;
} base = base.clone() * base;
if exp & 1 == 1 {
acc = acc * base.clone();
} }
)*)
}
int_trait_impl!(Num for usize u8 u16 u32 u64 isize i8 i16 i32 i64);
#[cfg(has_i128)]
int_trait_impl!(Num for u128 i128);
impl<T: Num> Num for Wrapping<T>
where
Wrapping<T>: Add<Output = Wrapping<T>>
+ Sub<Output = Wrapping<T>>
+ Mul<Output = Wrapping<T>>
+ Div<Output = Wrapping<T>>
+ Rem<Output = Wrapping<T>>,
{
type FromStrRadixErr = T::FromStrRadixErr;
fn from_str_radix(str: &str, radix: u32) -> Result<Self, Self::FromStrRadixErr> {
T::from_str_radix(str, radix).map(Wrapping)
} }
acc
} }
#[derive(Debug)] /// Raises a value to the power of exp, returning `None` if an overflow occurred.
pub enum FloatErrorKind { ///
Empty, /// Otherwise same as the `pow` function.
Invalid, ///
} /// # Example
// FIXME: core::num::ParseFloatError is stable in 1.0, but opaque to us, ///
// so there's not really any way for us to reuse it. /// ```rust
#[derive(Debug)] /// use num;
pub struct ParseFloatError { ///
pub kind: FloatErrorKind, /// assert_eq!(num::checked_pow(2i8, 4), Some(16));
} /// assert_eq!(num::checked_pow(7i8, 8), None);
/// assert_eq!(num::checked_pow(7u32, 8), Some(5_764_801));
/// ```
#[inline]
pub fn checked_pow<T: Clone + One + CheckedMul>(mut base: T, mut exp: usize) -> Option<T> {
if exp == 0 { return Some(T::one()) }
impl fmt::Display for ParseFloatError { macro_rules! optry {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { ( $ expr : expr ) => {
let description = match self.kind { if let Some(val) = $expr { val } else { return None }
FloatErrorKind::Empty => "cannot parse float from empty string",
FloatErrorKind::Invalid => "invalid float literal",
};
description.fmt(f)
}
}
// FIXME: The standard library from_str_radix on floats was deprecated, so we're stuck
// with this implementation ourselves until we want to make a breaking change.
// (would have to drop it from `Num` though)
macro_rules! float_trait_impl {
($name:ident for $($t:ident)*) => ($(
impl $name for $t {
type FromStrRadixErr = ParseFloatError;
fn from_str_radix(src: &str, radix: u32)
-> Result<Self, Self::FromStrRadixErr>
{
use self::FloatErrorKind::*;
use self::ParseFloatError as PFE;
// Special values
match src {
"inf" => return Ok(core::$t::INFINITY),
"-inf" => return Ok(core::$t::NEG_INFINITY),
"NaN" => return Ok(core::$t::NAN),
_ => {},
}
fn slice_shift_char(src: &str) -> Option<(char, &str)> {
let mut chars = src.chars();
if let Some(ch) = chars.next() {
Some((ch, chars.as_str()))
} else {
None
}
}
let (is_positive, src) = match slice_shift_char(src) {
None => return Err(PFE { kind: Empty }),
Some(('-', "")) => return Err(PFE { kind: Empty }),
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, usize)>;
// Parse the integer part of the significand
for (i, c) in cs.by_ref() {
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 isize) as $t);
} else {
sig = sig - ((digit as isize) as $t);
}
// Detect overflow by comparing to last value, except
// if we've not seen any non-zero digits.
if prev_sig != 0.0 {
if is_positive && sig <= prev_sig
{ return Ok(core::$t::INFINITY); }
if !is_positive && sig >= prev_sig
{ return Ok(core::$t::NEG_INFINITY); }
// Detect overflow by reversing the shift-and-add process
if is_positive && (prev_sig != (sig - digit as $t) / radix as $t)
{ return Ok(core::$t::INFINITY); }
if !is_positive && (prev_sig != (sig + digit as $t) / radix as $t)
{ return Ok(core::$t::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 Err(PFE { kind: Invalid });
},
},
}
}
// 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.by_ref() {
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 $t) * power
};
// Detect overflow by comparing to last value
if is_positive && sig < prev_sig
{ return Ok(core::$t::INFINITY); }
if !is_positive && sig > prev_sig
{ return Ok(core::$t::NEG_INFINITY); }
prev_sig = sig;
},
None => match c {
'e' | 'E' | 'p' | 'P' => {
exp_info = Some((c, i + 1));
break; // start of exponent
},
_ => {
return Err(PFE { kind: Invalid });
},
},
}
}
}
// Parse and calculate the exponent
let exp = match exp_info {
Some((c, offset)) => {
let base = match c {
'E' | 'e' if radix == 10 => 10.0,
'P' | 'p' if radix == 16 => 2.0,
_ => return Err(PFE { kind: Invalid }),
};
// Parse the exponent as decimal integer
let src = &src[offset..];
let (is_positive, exp) = match slice_shift_char(src) {
Some(('-', src)) => (false, src.parse::<usize>()),
Some(('+', src)) => (true, src.parse::<usize>()),
Some((_, _)) => (true, src.parse::<usize>()),
None => return Err(PFE { kind: Invalid }),
};
#[cfg(feature = "std")]
fn pow(base: $t, exp: usize) -> $t {
Float::powi(base, exp as i32)
}
// otherwise uses the generic `pow` from the root
match (is_positive, exp) {
(true, Ok(exp)) => pow(base, exp),
(false, Ok(exp)) => 1.0 / pow(base, exp),
(_, Err(_)) => return Err(PFE { kind: Invalid }),
}
},
None => 1.0, // no exponent
};
Ok(sig * exp)
}
} }
)*)
}
float_trait_impl!(Num for f32 f64);
/// A value bounded by a minimum and a maximum
///
/// If input is less than min then this returns min.
/// If input is greater than max then this returns max.
/// Otherwise this returns input.
///
/// **Panics** in debug mode if `!(min <= max)`.
#[inline]
pub fn clamp<T: PartialOrd>(input: T, min: T, max: T) -> T {
debug_assert!(min <= max, "min must be less than or equal to max");
if input < min {
min
} else if input > max {
max
} else {
input
}
}
/// A value bounded by a minimum value
///
/// If input is less than min then this returns min.
/// Otherwise this returns input.
/// `clamp_min(std::f32::NAN, 1.0)` preserves `NAN` different from `f32::min(std::f32::NAN, 1.0)`.
///
/// **Panics** in debug mode if `!(min == min)`. (This occurs if `min` is `NAN`.)
#[inline]
pub fn clamp_min<T: PartialOrd>(input: T, min: T) -> T {
debug_assert!(min == min, "min must not be NAN");
if input < min {
min
} else {
input
}
}
/// A value bounded by a maximum value
///
/// If input is greater than max then this returns max.
/// Otherwise this returns input.
/// `clamp_max(std::f32::NAN, 1.0)` preserves `NAN` different from `f32::max(std::f32::NAN, 1.0)`.
///
/// **Panics** in debug mode if `!(max == max)`. (This occurs if `max` is `NAN`.)
#[inline]
pub fn clamp_max<T: PartialOrd>(input: T, max: T) -> T {
debug_assert!(max == max, "max must not be NAN");
if input > max {
max
} else {
input
}
}
#[test]
fn clamp_test() {
// Int test
assert_eq!(1, clamp(1, -1, 2));
assert_eq!(-1, clamp(-2, -1, 2));
assert_eq!(2, clamp(3, -1, 2));
assert_eq!(1, clamp_min(1, -1));
assert_eq!(-1, clamp_min(-2, -1));
assert_eq!(-1, clamp_max(1, -1));
assert_eq!(-2, clamp_max(-2, -1));
// Float test
assert_eq!(1.0, clamp(1.0, -1.0, 2.0));
assert_eq!(-1.0, clamp(-2.0, -1.0, 2.0));
assert_eq!(2.0, clamp(3.0, -1.0, 2.0));
assert_eq!(1.0, clamp_min(1.0, -1.0));
assert_eq!(-1.0, clamp_min(-2.0, -1.0));
assert_eq!(-1.0, clamp_max(1.0, -1.0));
assert_eq!(-2.0, clamp_max(-2.0, -1.0));
assert!(clamp(::core::f32::NAN, -1.0, 1.0).is_nan());
assert!(clamp_min(::core::f32::NAN, 1.0).is_nan());
assert!(clamp_max(::core::f32::NAN, 1.0).is_nan());
}
#[test]
#[should_panic]
#[cfg(debug_assertions)]
fn clamp_nan_min() {
clamp(0., ::core::f32::NAN, 1.);
}
#[test]
#[should_panic]
#[cfg(debug_assertions)]
fn clamp_nan_max() {
clamp(0., -1., ::core::f32::NAN);
}
#[test]
#[should_panic]
#[cfg(debug_assertions)]
fn clamp_nan_min_max() {
clamp(0., ::core::f32::NAN, ::core::f32::NAN);
}
#[test]
#[should_panic]
#[cfg(debug_assertions)]
fn clamp_min_nan_min() {
clamp_min(0., ::core::f32::NAN);
}
#[test]
#[should_panic]
#[cfg(debug_assertions)]
fn clamp_max_nan_max() {
clamp_max(0., ::core::f32::NAN);
}
#[test]
fn from_str_radix_unwrap() {
// The Result error must impl Debug to allow unwrap()
let i: i32 = Num::from_str_radix("0", 10).unwrap();
assert_eq!(i, 0);
let f: f32 = Num::from_str_radix("0.0", 10).unwrap();
assert_eq!(f, 0.0);
}
#[test]
fn from_str_radix_multi_byte_fail() {
// Ensure parsing doesn't panic, even on invalid sign characters
assert!(f32::from_str_radix("™0.2", 10).is_err());
// Even when parsing the exponent sign
assert!(f32::from_str_radix("0.2E™1", 10).is_err());
}
#[test]
fn wrapping_is_num() {
fn require_num<T: Num>(_: &T) {}
require_num(&Wrapping(42_u32));
require_num(&Wrapping(-42));
}
#[test]
fn wrapping_from_str_radix() {
macro_rules! test_wrapping_from_str_radix {
($($t:ty)+) => {
$(
for &(s, r) in &[("42", 10), ("42", 2), ("-13.0", 10), ("foo", 10)] {
let w = Wrapping::<$t>::from_str_radix(s, r).map(|w| w.0);
assert_eq!(w, <$t as Num>::from_str_radix(s, r));
}
)+
};
} }
test_wrapping_from_str_radix!(usize u8 u16 u32 u64 isize i8 i16 i32 i64); while exp & 1 == 0 {
} base = optry!(base.checked_mul(&base));
exp >>= 1;
#[test]
fn check_num_ops() {
fn compute<T: Num + Copy>(x: T, y: T) -> T {
x * y / y % y + y - y
} }
assert_eq!(compute(1, 2), 1) if exp == 1 { return Some(base) }
}
#[test] let mut acc = base.clone();
fn check_numref_ops() { while exp > 1 {
fn compute<T: NumRef>(x: T, y: &T) -> T { exp >>= 1;
x * y / y % y + y - y base = optry!(base.checked_mul(&base));
if exp & 1 == 1 {
acc = optry!(acc.checked_mul(&base));
}
} }
assert_eq!(compute(1, &2), 1) Some(acc)
} }
#[test] #[cfg(test)]
fn check_refnum_ops() { fn hash<T: hash::Hash>(x: &T) -> u64 {
fn compute<T: Copy>(x: &T, y: T) -> T use std::hash::Hasher;
where let mut hasher = hash::SipHasher::new();
for<'a> &'a T: RefNum<T>, x.hash(&mut hasher);
{ hasher.finish()
&(&(&(&(x * y) / y) % y) + y) - y
}
assert_eq!(compute(&1, 2), 1)
} }
#[test]
fn check_refref_ops() {
fn compute<T>(x: &T, y: &T) -> T
where
for<'a> &'a T: RefNum<T>,
{
&(&(&(&(x * y) / y) % y) + y) - y
}
assert_eq!(compute(&1, &2), 1)
}
#[test]
fn check_numassign_ops() {
fn compute<T: NumAssign + Copy>(mut x: T, y: T) -> T {
x *= y;
x /= y;
x %= y;
x += y;
x -= y;
x
}
assert_eq!(compute(1, 2), 1)
}
// TODO test `NumAssignRef`, but even the standard numeric types don't
// implement this yet. (see rust pr41336)

37
src/macros.rs
View File

@ -1,37 +0,0 @@
// not all are used in all features configurations
#![allow(unused)]
/// Forward a method to an inherent method or a base trait method.
macro_rules! forward {
($( Self :: $method:ident ( self $( , $arg:ident : $ty:ty )* ) -> $ret:ty ; )*)
=> {$(
#[inline]
fn $method(self $( , $arg : $ty )* ) -> $ret {
Self::$method(self $( , $arg )* )
}
)*};
($( $base:ident :: $method:ident ( self $( , $arg:ident : $ty:ty )* ) -> $ret:ty ; )*)
=> {$(
#[inline]
fn $method(self $( , $arg : $ty )* ) -> $ret {
<Self as $base>::$method(self $( , $arg )* )
}
)*};
($( $base:ident :: $method:ident ( $( $arg:ident : $ty:ty ),* ) -> $ret:ty ; )*)
=> {$(
#[inline]
fn $method( $( $arg : $ty ),* ) -> $ret {
<Self as $base>::$method( $( $arg ),* )
}
)*}
}
macro_rules! constant {
($( $method:ident () -> $ret:expr ; )*)
=> {$(
#[inline]
fn $method() -> Self {
$ret
}
)*};
}

277
src/ops/checked.rs
View File

@ -1,277 +0,0 @@
use core::ops::{Add, Div, Mul, Rem, Shl, Shr, Sub};
/// Performs addition that returns `None` instead of wrapping around on
/// overflow.
pub trait CheckedAdd: Sized + Add<Self, Output = Self> {
/// Adds two numbers, checking for overflow. If overflow happens, `None` is
/// returned.
fn checked_add(&self, v: &Self) -> Option<Self>;
}
macro_rules! checked_impl {
($trait_name:ident, $method:ident, $t:ty) => {
impl $trait_name for $t {
#[inline]
fn $method(&self, v: &$t) -> Option<$t> {
<$t>::$method(*self, *v)
}
}
};
}
checked_impl!(CheckedAdd, checked_add, u8);
checked_impl!(CheckedAdd, checked_add, u16);
checked_impl!(CheckedAdd, checked_add, u32);
checked_impl!(CheckedAdd, checked_add, u64);
checked_impl!(CheckedAdd, checked_add, usize);
#[cfg(has_i128)]
checked_impl!(CheckedAdd, checked_add, u128);
checked_impl!(CheckedAdd, checked_add, i8);
checked_impl!(CheckedAdd, checked_add, i16);
checked_impl!(CheckedAdd, checked_add, i32);
checked_impl!(CheckedAdd, checked_add, i64);
checked_impl!(CheckedAdd, checked_add, isize);
#[cfg(has_i128)]
checked_impl!(CheckedAdd, checked_add, i128);
/// Performs subtraction that returns `None` instead of wrapping around on underflow.
pub trait CheckedSub: Sized + Sub<Self, Output = Self> {
/// Subtracts two numbers, checking for underflow. If underflow happens,
/// `None` is returned.
fn checked_sub(&self, v: &Self) -> Option<Self>;
}
checked_impl!(CheckedSub, checked_sub, u8);
checked_impl!(CheckedSub, checked_sub, u16);
checked_impl!(CheckedSub, checked_sub, u32);
checked_impl!(CheckedSub, checked_sub, u64);
checked_impl!(CheckedSub, checked_sub, usize);
#[cfg(has_i128)]
checked_impl!(CheckedSub, checked_sub, u128);
checked_impl!(CheckedSub, checked_sub, i8);
checked_impl!(CheckedSub, checked_sub, i16);
checked_impl!(CheckedSub, checked_sub, i32);
checked_impl!(CheckedSub, checked_sub, i64);
checked_impl!(CheckedSub, checked_sub, isize);
#[cfg(has_i128)]
checked_impl!(CheckedSub, checked_sub, i128);
/// Performs multiplication that returns `None` instead of wrapping around on underflow or
/// overflow.
pub trait CheckedMul: Sized + Mul<Self, Output = Self> {
/// Multiplies two numbers, checking for underflow or overflow. If underflow
/// or overflow happens, `None` is returned.
fn checked_mul(&self, v: &Self) -> Option<Self>;
}
checked_impl!(CheckedMul, checked_mul, u8);
checked_impl!(CheckedMul, checked_mul, u16);
checked_impl!(CheckedMul, checked_mul, u32);
checked_impl!(CheckedMul, checked_mul, u64);
checked_impl!(CheckedMul, checked_mul, usize);
#[cfg(has_i128)]
checked_impl!(CheckedMul, checked_mul, u128);
checked_impl!(CheckedMul, checked_mul, i8);
checked_impl!(CheckedMul, checked_mul, i16);
checked_impl!(CheckedMul, checked_mul, i32);
checked_impl!(CheckedMul, checked_mul, i64);
checked_impl!(CheckedMul, checked_mul, isize);
#[cfg(has_i128)]
checked_impl!(CheckedMul, checked_mul, i128);
/// Performs division that returns `None` instead of panicking on division by zero and instead of
/// wrapping around on underflow and overflow.
pub trait CheckedDiv: Sized + Div<Self, Output = Self> {
/// Divides two numbers, checking for underflow, overflow and division by
/// zero. If any of that happens, `None` is returned.
fn checked_div(&self, v: &Self) -> Option<Self>;
}
checked_impl!(CheckedDiv, checked_div, u8);
checked_impl!(CheckedDiv, checked_div, u16);
checked_impl!(CheckedDiv, checked_div, u32);
checked_impl!(CheckedDiv, checked_div, u64);
checked_impl!(CheckedDiv, checked_div, usize);
#[cfg(has_i128)]
checked_impl!(CheckedDiv, checked_div, u128);
checked_impl!(CheckedDiv, checked_div, i8);
checked_impl!(CheckedDiv, checked_div, i16);
checked_impl!(CheckedDiv, checked_div, i32);
checked_impl!(CheckedDiv, checked_div, i64);
checked_impl!(CheckedDiv, checked_div, isize);
#[cfg(has_i128)]
checked_impl!(CheckedDiv, checked_div, i128);
/// Performs an integral remainder that returns `None` instead of panicking on division by zero and
/// instead of wrapping around on underflow and overflow.
pub trait CheckedRem: Sized + Rem<Self, Output = Self> {
/// Finds the remainder of dividing two numbers, checking for underflow, overflow and division
/// by zero. If any of that happens, `None` is returned.
///
/// # Examples
///
/// ```
/// use num_traits::CheckedRem;
/// use std::i32::MIN;
///
/// assert_eq!(CheckedRem::checked_rem(&10, &7), Some(3));
/// assert_eq!(CheckedRem::checked_rem(&10, &-7), Some(3));
/// assert_eq!(CheckedRem::checked_rem(&-10, &7), Some(-3));
/// assert_eq!(CheckedRem::checked_rem(&-10, &-7), Some(-3));
///
/// assert_eq!(CheckedRem::checked_rem(&10, &0), None);
///
/// assert_eq!(CheckedRem::checked_rem(&MIN, &1), Some(0));
/// assert_eq!(CheckedRem::checked_rem(&MIN, &-1), None);
/// ```
fn checked_rem(&self, v: &Self) -> Option<Self>;
}
checked_impl!(CheckedRem, checked_rem, u8);
checked_impl!(CheckedRem, checked_rem, u16);
checked_impl!(CheckedRem, checked_rem, u32);
checked_impl!(CheckedRem, checked_rem, u64);
checked_impl!(CheckedRem, checked_rem, usize);
#[cfg(has_i128)]
checked_impl!(CheckedRem, checked_rem, u128);
checked_impl!(CheckedRem, checked_rem, i8);
checked_impl!(CheckedRem, checked_rem, i16);
checked_impl!(CheckedRem, checked_rem, i32);
checked_impl!(CheckedRem, checked_rem, i64);
checked_impl!(CheckedRem, checked_rem, isize);
#[cfg(has_i128)]
checked_impl!(CheckedRem, checked_rem, i128);
macro_rules! checked_impl_unary {
($trait_name:ident, $method:ident, $t:ty) => {
impl $trait_name for $t {
#[inline]
fn $method(&self) -> Option<$t> {
<$t>::$method(*self)
}
}
};
}
/// Performs negation that returns `None` if the result can't be represented.
pub trait CheckedNeg: Sized {
/// Negates a number, returning `None` for results that can't be represented, like signed `MIN`
/// values that can't be positive, or non-zero unsigned values that can't be negative.
///
/// # Examples
///
/// ```
/// use num_traits::CheckedNeg;
/// use std::i32::MIN;
///
/// assert_eq!(CheckedNeg::checked_neg(&1_i32), Some(-1));
/// assert_eq!(CheckedNeg::checked_neg(&-1_i32), Some(1));
/// assert_eq!(CheckedNeg::checked_neg(&MIN), None);
///
/// assert_eq!(CheckedNeg::checked_neg(&0_u32), Some(0));
/// assert_eq!(CheckedNeg::checked_neg(&1_u32), None);
/// ```
fn checked_neg(&self) -> Option<Self>;
}
checked_impl_unary!(CheckedNeg, checked_neg, u8);
checked_impl_unary!(CheckedNeg, checked_neg, u16);
checked_impl_unary!(CheckedNeg, checked_neg, u32);
checked_impl_unary!(CheckedNeg, checked_neg, u64);
checked_impl_unary!(CheckedNeg, checked_neg, usize);
#[cfg(has_i128)]
checked_impl_unary!(CheckedNeg, checked_neg, u128);
checked_impl_unary!(CheckedNeg, checked_neg, i8);
checked_impl_unary!(CheckedNeg, checked_neg, i16);
checked_impl_unary!(CheckedNeg, checked_neg, i32);
checked_impl_unary!(CheckedNeg, checked_neg, i64);
checked_impl_unary!(CheckedNeg, checked_neg, isize);
#[cfg(has_i128)]
checked_impl_unary!(CheckedNeg, checked_neg, i128);
/// Performs a left shift that returns `None` on shifts larger than
/// the type width.
pub trait CheckedShl: Sized + Shl<u32, Output = Self> {
/// Checked shift left. Computes `self << rhs`, returning `None`
/// if `rhs` is larger than or equal to the number of bits in `self`.
///
/// ```
/// use num_traits::CheckedShl;
///
/// let x: u16 = 0x0001;
///
/// assert_eq!(CheckedShl::checked_shl(&x, 0), Some(0x0001));
/// assert_eq!(CheckedShl::checked_shl(&x, 1), Some(0x0002));
/// assert_eq!(CheckedShl::checked_shl(&x, 15), Some(0x8000));
/// assert_eq!(CheckedShl::checked_shl(&x, 16), None);
/// ```
fn checked_shl(&self, rhs: u32) -> Option<Self>;
}
macro_rules! checked_shift_impl {
($trait_name:ident, $method:ident, $t:ty) => {
impl $trait_name for $t {
#[inline]
fn $method(&self, rhs: u32) -> Option<$t> {
<$t>::$method(*self, rhs)
}
}
};
}
checked_shift_impl!(CheckedShl, checked_shl, u8);
checked_shift_impl!(CheckedShl, checked_shl, u16);
checked_shift_impl!(CheckedShl, checked_shl, u32);
checked_shift_impl!(CheckedShl, checked_shl, u64);
checked_shift_impl!(CheckedShl, checked_shl, usize);
#[cfg(has_i128)]
checked_shift_impl!(CheckedShl, checked_shl, u128);
checked_shift_impl!(CheckedShl, checked_shl, i8);
checked_shift_impl!(CheckedShl, checked_shl, i16);
checked_shift_impl!(CheckedShl, checked_shl, i32);
checked_shift_impl!(CheckedShl, checked_shl, i64);
checked_shift_impl!(CheckedShl, checked_shl, isize);
#[cfg(has_i128)]
checked_shift_impl!(CheckedShl, checked_shl, i128);
/// Performs a right shift that returns `None` on shifts larger than
/// the type width.
pub trait CheckedShr: Sized + Shr<u32, Output = Self> {
/// Checked shift right. Computes `self >> rhs`, returning `None`
/// if `rhs` is larger than or equal to the number of bits in `self`.
///
/// ```
/// use num_traits::CheckedShr;
///
/// let x: u16 = 0x8000;
///
/// assert_eq!(CheckedShr::checked_shr(&x, 0), Some(0x8000));
/// assert_eq!(CheckedShr::checked_shr(&x, 1), Some(0x4000));
/// assert_eq!(CheckedShr::checked_shr(&x, 15), Some(0x0001));
/// assert_eq!(CheckedShr::checked_shr(&x, 16), None);
/// ```
fn checked_shr(&self, rhs: u32) -> Option<Self>;
}
checked_shift_impl!(CheckedShr, checked_shr, u8);
checked_shift_impl!(CheckedShr, checked_shr, u16);
checked_shift_impl!(CheckedShr, checked_shr, u32);
checked_shift_impl!(CheckedShr, checked_shr, u64);
checked_shift_impl!(CheckedShr, checked_shr, usize);
#[cfg(has_i128)]
checked_shift_impl!(CheckedShr, checked_shr, u128);
checked_shift_impl!(CheckedShr, checked_shr, i8);
checked_shift_impl!(CheckedShr, checked_shr, i16);
checked_shift_impl!(CheckedShr, checked_shr, i32);
checked_shift_impl!(CheckedShr, checked_shr, i64);
checked_shift_impl!(CheckedShr, checked_shr, isize);
#[cfg(has_i128)]
checked_shift_impl!(CheckedShr, checked_shr, i128);

47
src/ops/inv.rs
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@ -1,47 +0,0 @@
/// Unary operator for retrieving the multiplicative inverse, or reciprocal, of a value.
pub trait Inv {
/// The result after applying the operator.
type Output;
/// Returns the multiplicative inverse of `self`.
///
/// # Examples
///
/// ```
/// use std::f64::INFINITY;
/// use num_traits::Inv;
///
/// assert_eq!(7.0.inv() * 7.0, 1.0);
/// assert_eq!((-0.0).inv(), -INFINITY);
/// ```
fn inv(self) -> Self::Output;
}
impl Inv for f32 {
type Output = f32;
#[inline]
fn inv(self) -> f32 {
1.0 / self
}
}
impl Inv for f64 {
type Output = f64;
#[inline]
fn inv(self) -> f64 {
1.0 / self
}
}
impl<'a> Inv for &'a f32 {
type Output = f32;
#[inline]
fn inv(self) -> f32 {
1.0 / *self
}
}
impl<'a> Inv for &'a f64 {
type Output = f64;
#[inline]
fn inv(self) -> f64 {
1.0 / *self
}
}

5
src/ops/mod.rs
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@ -1,5 +0,0 @@
pub mod checked;
pub mod inv;
pub mod mul_add;
pub mod saturating;
pub mod wrapping;

151
src/ops/mul_add.rs
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@ -1,151 +0,0 @@
/// Fused multiply-add. Computes `(self * a) + b` with only one rounding
/// error, yielding a more accurate result than an unfused multiply-add.
///
/// Using `mul_add` can be more performant than an unfused multiply-add if
/// the target architecture has a dedicated `fma` CPU instruction.
///
/// Note that `A` and `B` are `Self` by default, but this is not mandatory.
///
/// # Example
///
/// ```
/// use std::f32;
///
/// let m = 10.0_f32;
/// let x = 4.0_f32;
/// let b = 60.0_f32;
///
/// // 100.0
/// let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs();
///
/// assert!(abs_difference <= 100.0 * f32::EPSILON);
/// ```
pub trait MulAdd<A = Self, B = Self> {
/// The resulting type after applying the fused multiply-add.
type Output;
/// Performs the fused multiply-add operation.
fn mul_add(self, a: A, b: B) -> Self::Output;
}
/// The fused multiply-add assignment operation.
pub trait MulAddAssign<A = Self, B = Self> {
/// Performs the fused multiply-add operation.
fn mul_add_assign(&mut self, a: A, b: B);
}
#[cfg(any(feature = "std", feature = "libm"))]
impl MulAdd<f32, f32> for f32 {
type Output = Self;
#[inline]
fn mul_add(self, a: Self, b: Self) -> Self::Output {
<Self as ::Float>::mul_add(self, a, b)
}
}
#[cfg(any(feature = "std", feature = "libm"))]
impl MulAdd<f64, f64> for f64 {
type Output = Self;
#[inline]
fn mul_add(self, a: Self, b: Self) -> Self::Output {
<Self as ::Float>::mul_add(self, a, b)
}
}
macro_rules! mul_add_impl {
($trait_name:ident for $($t:ty)*) => {$(
impl $trait_name for $t {
type Output = Self;
#[inline]
fn mul_add(self, a: Self, b: Self) -> Self::Output {
(self * a) + b
}
}
)*}
}
mul_add_impl!(MulAdd for isize usize i8 u8 i16 u16 i32 u32 i64 u64);
#[cfg(has_i128)]
mul_add_impl!(MulAdd for i128 u128);
#[cfg(any(feature = "std", feature = "libm"))]
impl MulAddAssign<f32, f32> for f32 {
#[inline]
fn mul_add_assign(&mut self, a: Self, b: Self) {
*self = <Self as ::Float>::mul_add(*self, a, b)
}
}
#[cfg(any(feature = "std", feature = "libm"))]
impl MulAddAssign<f64, f64> for f64 {
#[inline]
fn mul_add_assign(&mut self, a: Self, b: Self) {
*self = <Self as ::Float>::mul_add(*self, a, b)
}
}
macro_rules! mul_add_assign_impl {
($trait_name:ident for $($t:ty)*) => {$(
impl $trait_name for $t {
#[inline]
fn mul_add_assign(&mut self, a: Self, b: Self) {
*self = (*self * a) + b
}
}
)*}
}
mul_add_assign_impl!(MulAddAssign for isize usize i8 u8 i16 u16 i32 u32 i64 u64);
#[cfg(has_i128)]
mul_add_assign_impl!(MulAddAssign for i128 u128);
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn mul_add_integer() {
macro_rules! test_mul_add {
($($t:ident)+) => {
$(
{
let m: $t = 2;
let x: $t = 3;
let b: $t = 4;
assert_eq!(MulAdd::mul_add(m, x, b), (m*x + b));
}
)+
};
}
test_mul_add!(usize u8 u16 u32 u64 isize i8 i16 i32 i64);
}
#[test]
#[cfg(feature = "std")]
fn mul_add_float() {
macro_rules! test_mul_add {
($($t:ident)+) => {
$(
{
use core::$t;
let m: $t = 12.0;
let x: $t = 3.4;
let b: $t = 5.6;
let abs_difference = (MulAdd::mul_add(m, x, b) - (m*x + b)).abs();
assert!(abs_difference <= 46.4 * $t::EPSILON);
}
)+
};
}
test_mul_add!(f32 f64);
}
}

30
src/ops/saturating.rs
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@ -1,30 +0,0 @@
/// Saturating math operations
pub trait Saturating {
/// Saturating addition operator.
/// Returns a+b, saturating at the numeric bounds instead of overflowing.
fn saturating_add(self, v: Self) -> Self;
/// Saturating subtraction operator.
/// Returns a-b, saturating at the numeric bounds instead of overflowing.
fn saturating_sub(self, v: Self) -> Self;
}
macro_rules! saturating_impl {
($trait_name:ident for $($t:ty)*) => {$(
impl $trait_name for $t {
#[inline]
fn saturating_add(self, v: Self) -> Self {
Self::saturating_add(self, v)
}
#[inline]
fn saturating_sub(self, v: Self) -> Self {
Self::saturating_sub(self, v)
}
}
)*}
}
saturating_impl!(Saturating for isize usize i8 u8 i16 u16 i32 u32 i64 u64);
#[cfg(has_i128)]
saturating_impl!(Saturating for i128 u128);

272
src/ops/wrapping.rs
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@ -1,272 +0,0 @@
use core::num::Wrapping;
use core::ops::{Add, Mul, Shl, Shr, Sub};
macro_rules! wrapping_impl {
($trait_name:ident, $method:ident, $t:ty) => {
impl $trait_name for $t {
#[inline]
fn $method(&self, v: &Self) -> Self {
<$t>::$method(*self, *v)
}
}
};
($trait_name:ident, $method:ident, $t:ty, $rhs:ty) => {
impl $trait_name<$rhs> for $t {
#[inline]
fn $method(&self, v: &$rhs) -> Self {
<$t>::$method(*self, *v)
}
}
};
}
/// Performs addition that wraps around on overflow.
pub trait WrappingAdd: Sized + Add<Self, Output = Self> {
/// Wrapping (modular) addition. Computes `self + other`, wrapping around at the boundary of
/// the type.
fn wrapping_add(&self, v: &Self) -> Self;
}
wrapping_impl!(WrappingAdd, wrapping_add, u8);
wrapping_impl!(WrappingAdd, wrapping_add, u16);
wrapping_impl!(WrappingAdd, wrapping_add, u32);
wrapping_impl!(WrappingAdd, wrapping_add, u64);
wrapping_impl!(WrappingAdd, wrapping_add, usize);
#[cfg(has_i128)]
wrapping_impl!(WrappingAdd, wrapping_add, u128);
wrapping_impl!(WrappingAdd, wrapping_add, i8);
wrapping_impl!(WrappingAdd, wrapping_add, i16);
wrapping_impl!(WrappingAdd, wrapping_add, i32);
wrapping_impl!(WrappingAdd, wrapping_add, i64);
wrapping_impl!(WrappingAdd, wrapping_add, isize);
#[cfg(has_i128)]
wrapping_impl!(WrappingAdd, wrapping_add, i128);
/// Performs subtraction that wraps around on overflow.
pub trait WrappingSub: Sized + Sub<Self, Output = Self> {
/// Wrapping (modular) subtraction. Computes `self - other`, wrapping around at the boundary
/// of the type.
fn wrapping_sub(&self, v: &Self) -> Self;
}
wrapping_impl!(WrappingSub, wrapping_sub, u8);
wrapping_impl!(WrappingSub, wrapping_sub, u16);
wrapping_impl!(WrappingSub, wrapping_sub, u32);
wrapping_impl!(WrappingSub, wrapping_sub, u64);
wrapping_impl!(WrappingSub, wrapping_sub, usize);
#[cfg(has_i128)]
wrapping_impl!(WrappingSub, wrapping_sub, u128);
wrapping_impl!(WrappingSub, wrapping_sub, i8);
wrapping_impl!(WrappingSub, wrapping_sub, i16);
wrapping_impl!(WrappingSub, wrapping_sub, i32);
wrapping_impl!(WrappingSub, wrapping_sub, i64);
wrapping_impl!(WrappingSub, wrapping_sub, isize);
#[cfg(has_i128)]
wrapping_impl!(WrappingSub, wrapping_sub, i128);
/// Performs multiplication that wraps around on overflow.
pub trait WrappingMul: Sized + Mul<Self, Output = Self> {
/// Wrapping (modular) multiplication. Computes `self * other`, wrapping around at the boundary
/// of the type.
fn wrapping_mul(&self, v: &Self) -> Self;
}
wrapping_impl!(WrappingMul, wrapping_mul, u8);
wrapping_impl!(WrappingMul, wrapping_mul, u16);
wrapping_impl!(WrappingMul, wrapping_mul, u32);
wrapping_impl!(WrappingMul, wrapping_mul, u64);
wrapping_impl!(WrappingMul, wrapping_mul, usize);
#[cfg(has_i128)]
wrapping_impl!(WrappingMul, wrapping_mul, u128);
wrapping_impl!(WrappingMul, wrapping_mul, i8);
wrapping_impl!(WrappingMul, wrapping_mul, i16);
wrapping_impl!(WrappingMul, wrapping_mul, i32);
wrapping_impl!(WrappingMul, wrapping_mul, i64);
wrapping_impl!(WrappingMul, wrapping_mul, isize);
#[cfg(has_i128)]
wrapping_impl!(WrappingMul, wrapping_mul, i128);
macro_rules! wrapping_shift_impl {
($trait_name:ident, $method:ident, $t:ty) => {
impl $trait_name for $t {
#[inline]
fn $method(&self, rhs: u32) -> $t {
<$t>::$method(*self, rhs)
}
}
};
}
/// Performs a left shift that does not panic.
pub trait WrappingShl: Sized + Shl<usize, Output = Self> {
/// Panic-free bitwise shift-left; yields `self << mask(rhs)`,
/// where `mask` removes any high order bits of `rhs` that would
/// cause the shift to exceed the bitwidth of the type.
///
/// ```
/// use num_traits::WrappingShl;
///
/// let x: u16 = 0x0001;
///
/// assert_eq!(WrappingShl::wrapping_shl(&x, 0), 0x0001);
/// assert_eq!(WrappingShl::wrapping_shl(&x, 1), 0x0002);
/// assert_eq!(WrappingShl::wrapping_shl(&x, 15), 0x8000);
/// assert_eq!(WrappingShl::wrapping_shl(&x, 16), 0x0001);
/// ```
fn wrapping_shl(&self, rhs: u32) -> Self;
}
wrapping_shift_impl!(WrappingShl, wrapping_shl, u8);
wrapping_shift_impl!(WrappingShl, wrapping_shl, u16);
wrapping_shift_impl!(WrappingShl, wrapping_shl, u32);
wrapping_shift_impl!(WrappingShl, wrapping_shl, u64);
wrapping_shift_impl!(WrappingShl, wrapping_shl, usize);
#[cfg(has_i128)]
wrapping_shift_impl!(WrappingShl, wrapping_shl, u128);
wrapping_shift_impl!(WrappingShl, wrapping_shl, i8);
wrapping_shift_impl!(WrappingShl, wrapping_shl, i16);
wrapping_shift_impl!(WrappingShl, wrapping_shl, i32);
wrapping_shift_impl!(WrappingShl, wrapping_shl, i64);
wrapping_shift_impl!(WrappingShl, wrapping_shl, isize);
#[cfg(has_i128)]
wrapping_shift_impl!(WrappingShl, wrapping_shl, i128);
/// Performs a right shift that does not panic.
pub trait WrappingShr: Sized + Shr<usize, Output = Self> {
/// Panic-free bitwise shift-right; yields `self >> mask(rhs)`,
/// where `mask` removes any high order bits of `rhs` that would
/// cause the shift to exceed the bitwidth of the type.
///
/// ```
/// use num_traits::WrappingShr;
///
/// let x: u16 = 0x8000;
///
/// assert_eq!(WrappingShr::wrapping_shr(&x, 0), 0x8000);
/// assert_eq!(WrappingShr::wrapping_shr(&x, 1), 0x4000);
/// assert_eq!(WrappingShr::wrapping_shr(&x, 15), 0x0001);
/// assert_eq!(WrappingShr::wrapping_shr(&x, 16), 0x8000);
/// ```
fn wrapping_shr(&self, rhs: u32) -> Self;
}
wrapping_shift_impl!(WrappingShr, wrapping_shr, u8);
wrapping_shift_impl!(WrappingShr, wrapping_shr, u16);
wrapping_shift_impl!(WrappingShr, wrapping_shr, u32);
wrapping_shift_impl!(WrappingShr, wrapping_shr, u64);
wrapping_shift_impl!(WrappingShr, wrapping_shr, usize);
#[cfg(has_i128)]
wrapping_shift_impl!(WrappingShr, wrapping_shr, u128);
wrapping_shift_impl!(WrappingShr, wrapping_shr, i8);
wrapping_shift_impl!(WrappingShr, wrapping_shr, i16);
wrapping_shift_impl!(WrappingShr, wrapping_shr, i32);
wrapping_shift_impl!(WrappingShr, wrapping_shr, i64);
wrapping_shift_impl!(WrappingShr, wrapping_shr, isize);
#[cfg(has_i128)]
wrapping_shift_impl!(WrappingShr, wrapping_shr, i128);
// Well this is a bit funny, but all the more appropriate.
impl<T: WrappingAdd> WrappingAdd for Wrapping<T>
where
Wrapping<T>: Add<Output = Wrapping<T>>,
{
fn wrapping_add(&self, v: &Self) -> Self {
Wrapping(self.0.wrapping_add(&v.0))
}
}
impl<T: WrappingSub> WrappingSub for Wrapping<T>
where
Wrapping<T>: Sub<Output = Wrapping<T>>,
{
fn wrapping_sub(&self, v: &Self) -> Self {
Wrapping(self.0.wrapping_sub(&v.0))
}
}
impl<T: WrappingMul> WrappingMul for Wrapping<T>
where
Wrapping<T>: Mul<Output = Wrapping<T>>,
{
fn wrapping_mul(&self, v: &Self) -> Self {
Wrapping(self.0.wrapping_mul(&v.0))
}
}
impl<T: WrappingShl> WrappingShl for Wrapping<T>
where
Wrapping<T>: Shl<usize, Output = Wrapping<T>>,
{
fn wrapping_shl(&self, rhs: u32) -> Self {
Wrapping(self.0.wrapping_shl(rhs))
}
}
impl<T: WrappingShr> WrappingShr for Wrapping<T>
where
Wrapping<T>: Shr<usize, Output = Wrapping<T>>,
{
fn wrapping_shr(&self, rhs: u32) -> Self {
Wrapping(self.0.wrapping_shr(rhs))
}
}
#[test]
fn test_wrapping_traits() {
fn wrapping_add<T: WrappingAdd>(a: T, b: T) -> T {
a.wrapping_add(&b)
}
fn wrapping_sub<T: WrappingSub>(a: T, b: T) -> T {
a.wrapping_sub(&b)
}
fn wrapping_mul<T: WrappingMul>(a: T, b: T) -> T {
a.wrapping_mul(&b)
}
fn wrapping_shl<T: WrappingShl>(a: T, b: u32) -> T {
a.wrapping_shl(b)
}
fn wrapping_shr<T: WrappingShr>(a: T, b: u32) -> T {
a.wrapping_shr(b)
}
assert_eq!(wrapping_add(255, 1), 0u8);
assert_eq!(wrapping_sub(0, 1), 255u8);
assert_eq!(wrapping_mul(255, 2), 254u8);
assert_eq!(wrapping_shl(255, 8), 255u8);
assert_eq!(wrapping_shr(255, 8), 255u8);
assert_eq!(wrapping_add(255, 1), (Wrapping(255u8) + Wrapping(1u8)).0);
assert_eq!(wrapping_sub(0, 1), (Wrapping(0u8) - Wrapping(1u8)).0);
assert_eq!(wrapping_mul(255, 2), (Wrapping(255u8) * Wrapping(2u8)).0);
assert_eq!(wrapping_shl(255, 8), (Wrapping(255u8) << 8).0);
assert_eq!(wrapping_shr(255, 8), (Wrapping(255u8) >> 8).0);
}
#[test]
fn wrapping_is_wrappingadd() {
fn require_wrappingadd<T: WrappingAdd>(_: &T) {}
require_wrappingadd(&Wrapping(42));
}
#[test]
fn wrapping_is_wrappingsub() {
fn require_wrappingsub<T: WrappingSub>(_: &T) {}
require_wrappingsub(&Wrapping(42));
}
#[test]
fn wrapping_is_wrappingmul() {
fn require_wrappingmul<T: WrappingMul>(_: &T) {}
require_wrappingmul(&Wrapping(42));
}
#[test]
fn wrapping_is_wrappingshl() {
fn require_wrappingshl<T: WrappingShl>(_: &T) {}
require_wrappingshl(&Wrapping(42));
}
#[test]
fn wrapping_is_wrappingshr() {
fn require_wrappingshr<T: WrappingShr>(_: &T) {}
require_wrappingshr(&Wrapping(42));
}

262
src/pow.rs
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@ -1,262 +0,0 @@
use core::num::Wrapping;
use core::ops::Mul;
use {CheckedMul, One};
/// Binary operator for raising a value to a power.
pub trait Pow<RHS> {
/// The result after applying the operator.
type Output;
/// Returns `self` to the power `rhs`.
///
/// # Examples
///
/// ```
/// use num_traits::Pow;
/// assert_eq!(Pow::pow(10u32, 2u32), 100);
/// ```
fn pow(self, rhs: RHS) -> Self::Output;
}
macro_rules! pow_impl {
($t:ty) => {
pow_impl!($t, u8);
pow_impl!($t, usize);
// FIXME: these should be possible
// pow_impl!($t, u16);
// pow_impl!($t, u32);
// pow_impl!($t, u64);
};
($t:ty, $rhs:ty) => {
pow_impl!($t, $rhs, usize, pow);
};
($t:ty, $rhs:ty, $desired_rhs:ty, $method:expr) => {
impl Pow<$rhs> for $t {
type Output = $t;
#[inline]
fn pow(self, rhs: $rhs) -> $t {
($method)(self, <$desired_rhs>::from(rhs))
}
}
impl<'a> Pow<&'a $rhs> for $t {
type Output = $t;
#[inline]
fn pow(self, rhs: &'a $rhs) -> $t {
($method)(self, <$desired_rhs>::from(*rhs))
}
}
impl<'a> Pow<$rhs> for &'a $t {
type Output = $t;
#[inline]
fn pow(self, rhs: $rhs) -> $t {
($method)(*self, <$desired_rhs>::from(rhs))
}
}
impl<'a, 'b> Pow<&'a $rhs> for &'b $t {
type Output = $t;
#[inline]
fn pow(self, rhs: &'a $rhs) -> $t {
($method)(*self, <$desired_rhs>::from(*rhs))
}
}
};
}
pow_impl!(u8, u8, u32, u8::pow);
pow_impl!(u8, u16, u32, u8::pow);
pow_impl!(u8, u32, u32, u8::pow);
pow_impl!(u8, usize);
pow_impl!(i8, u8, u32, i8::pow);
pow_impl!(i8, u16, u32, i8::pow);
pow_impl!(i8, u32, u32, i8::pow);
pow_impl!(i8, usize);
pow_impl!(u16, u8, u32, u16::pow);
pow_impl!(u16, u16, u32, u16::pow);
pow_impl!(u16, u32, u32, u16::pow);
pow_impl!(u16, usize);
pow_impl!(i16, u8, u32, i16::pow);
pow_impl!(i16, u16, u32, i16::pow);
pow_impl!(i16, u32, u32, i16::pow);
pow_impl!(i16, usize);
pow_impl!(u32, u8, u32, u32::pow);
pow_impl!(u32, u16, u32, u32::pow);
pow_impl!(u32, u32, u32, u32::pow);
pow_impl!(u32, usize);
pow_impl!(i32, u8, u32, i32::pow);
pow_impl!(i32, u16, u32, i32::pow);
pow_impl!(i32, u32, u32, i32::pow);
pow_impl!(i32, usize);
pow_impl!(u64, u8, u32, u64::pow);
pow_impl!(u64, u16, u32, u64::pow);
pow_impl!(u64, u32, u32, u64::pow);
pow_impl!(u64, usize);
pow_impl!(i64, u8, u32, i64::pow);
pow_impl!(i64, u16, u32, i64::pow);
pow_impl!(i64, u32, u32, i64::pow);
pow_impl!(i64, usize);
#[cfg(has_i128)]
pow_impl!(u128, u8, u32, u128::pow);
#[cfg(has_i128)]
pow_impl!(u128, u16, u32, u128::pow);
#[cfg(has_i128)]
pow_impl!(u128, u32, u32, u128::pow);
#[cfg(has_i128)]
pow_impl!(u128, usize);
#[cfg(has_i128)]
pow_impl!(i128, u8, u32, i128::pow);
#[cfg(has_i128)]
pow_impl!(i128, u16, u32, i128::pow);
#[cfg(has_i128)]
pow_impl!(i128, u32, u32, i128::pow);
#[cfg(has_i128)]
pow_impl!(i128, usize);
pow_impl!(usize, u8, u32, usize::pow);
pow_impl!(usize, u16, u32, usize::pow);
pow_impl!(usize, u32, u32, usize::pow);
pow_impl!(usize, usize);
pow_impl!(isize, u8, u32, isize::pow);
pow_impl!(isize, u16, u32, isize::pow);
pow_impl!(isize, u32, u32, isize::pow);
pow_impl!(isize, usize);
pow_impl!(Wrapping<u8>);
pow_impl!(Wrapping<i8>);
pow_impl!(Wrapping<u16>);
pow_impl!(Wrapping<i16>);
pow_impl!(Wrapping<u32>);
pow_impl!(Wrapping<i32>);
pow_impl!(Wrapping<u64>);
pow_impl!(Wrapping<i64>);
#[cfg(has_i128)]
pow_impl!(Wrapping<u128>);
#[cfg(has_i128)]
pow_impl!(Wrapping<i128>);
pow_impl!(Wrapping<usize>);
pow_impl!(Wrapping<isize>);
// FIXME: these should be possible
// pow_impl!(u8, u64);
// pow_impl!(i16, u64);
// pow_impl!(i8, u64);
// pow_impl!(u16, u64);
// pow_impl!(u32, u64);
// pow_impl!(i32, u64);
// pow_impl!(u64, u64);
// pow_impl!(i64, u64);
// pow_impl!(usize, u64);
// pow_impl!(isize, u64);
#[cfg(any(feature = "std", feature = "libm"))]
mod float_impls {
use super::Pow;
use Float;
pow_impl!(f32, i8, i32, <f32 as Float>::powi);
pow_impl!(f32, u8, i32, <f32 as Float>::powi);
pow_impl!(f32, i16, i32, <f32 as Float>::powi);
pow_impl!(f32, u16, i32, <f32 as Float>::powi);
pow_impl!(f32, i32, i32, <f32 as Float>::powi);
pow_impl!(f64, i8, i32, <f64 as Float>::powi);
pow_impl!(f64, u8, i32, <f64 as Float>::powi);
pow_impl!(f64, i16, i32, <f64 as Float>::powi);
pow_impl!(f64, u16, i32, <f64 as Float>::powi);
pow_impl!(f64, i32, i32, <f64 as Float>::powi);
pow_impl!(f32, f32, f32, <f32 as Float>::powf);
pow_impl!(f64, f32, f64, <f64 as Float>::powf);
pow_impl!(f64, f64, f64, <f64 as Float>::powf);
}
/// Raises a value to the power of exp, using exponentiation by squaring.
///
/// Note that `0⁰` (`pow(0, 0)`) returns `1`. Mathematically this is undefined.
///
/// # Example
///
/// ```rust
/// use num_traits::pow;
///
/// assert_eq!(pow(2i8, 4), 16);
/// assert_eq!(pow(6u8, 3), 216);
/// assert_eq!(pow(0u8, 0), 1); // Be aware if this case affects you
/// ```
#[inline]
pub fn pow<T: Clone + One + Mul<T, Output = T>>(mut base: T, mut exp: usize) -> T {
if exp == 0 {
return T::one();
}
while exp & 1 == 0 {
base = base.clone() * base;
exp >>= 1;
}
if exp == 1 {
return base;
}
let mut acc = base.clone();
while exp > 1 {
exp >>= 1;
base = base.clone() * base;
if exp & 1 == 1 {
acc = acc * base.clone();
}
}
acc
}
/// Raises a value to the power of exp, returning `None` if an overflow occurred.
///
/// Note that `0⁰` (`checked_pow(0, 0)`) returns `Some(1)`. Mathematically this is undefined.
///
/// Otherwise same as the `pow` function.
///
/// # Example
///
/// ```rust
/// use num_traits::checked_pow;
///
/// assert_eq!(checked_pow(2i8, 4), Some(16));
/// assert_eq!(checked_pow(7i8, 8), None);
/// assert_eq!(checked_pow(7u32, 8), Some(5_764_801));
/// assert_eq!(checked_pow(0u32, 0), Some(1)); // Be aware if this case affect you
/// ```
#[inline]
pub fn checked_pow<T: Clone + One + CheckedMul>(mut base: T, mut exp: usize) -> Option<T> {
if exp == 0 {
return Some(T::one());
}
macro_rules! optry {
($expr:expr) => {
if let Some(val) = $expr {
val
} else {
return None;
}
};
}
while exp & 1 == 0 {
base = optry!(base.checked_mul(&base));
exp >>= 1;
}
if exp == 1 {
return Some(base);
}
let mut acc = base.clone();
while exp > 1 {
exp >>= 1;
base = optry!(base.checked_mul(&base));
if exp & 1 == 1 {
acc = optry!(acc.checked_mul(&base));
}
}
Some(acc)
}

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// Copyright 2013-2014 The Rust Project Developers. See the COPYRIGHT
// file at the top-level directory of this distribution and at
// http://rust-lang.org/COPYRIGHT.
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
// option. This file may not be copied, modified, or distributed
// except according to those terms.
//! Rational numbers
use Integer;
use std::cmp;
use std::error::Error;
use std::fmt;
use std::ops::{Add, Div, Mul, Neg, Rem, Sub};
use std::str::FromStr;
#[cfg(feature = "bigint")]
use bigint::{BigInt, BigUint, Sign};
use traits::{FromPrimitive, Float, PrimInt};
use {Num, Signed, Zero, One};
/// Represents the ratio between 2 numbers.
#[derive(Copy, Clone, Hash, Debug)]
#[cfg_attr(feature = "rustc-serialize", derive(RustcEncodable, RustcDecodable))]
#[allow(missing_docs)]
pub struct Ratio<T> {
numer: T,
denom: T
}
/// Alias for a `Ratio` of machine-sized integers.
pub type Rational = Ratio<isize>;
pub type Rational32 = Ratio<i32>;
pub type Rational64 = Ratio<i64>;
#[cfg(feature = "bigint")]
/// Alias for arbitrary precision rationals.
pub type BigRational = Ratio<BigInt>;
impl<T: Clone + Integer + PartialOrd> Ratio<T> {
/// Creates a ratio representing the integer `t`.
#[inline]
pub fn from_integer(t: T) -> Ratio<T> {
Ratio::new_raw(t, One::one())
}
/// Creates a ratio without checking for `denom == 0` or reducing.
#[inline]
pub fn new_raw(numer: T, denom: T) -> Ratio<T> {
Ratio { numer: numer, denom: denom }
}
/// Create a new Ratio. Fails if `denom == 0`.
#[inline]
pub fn new(numer: T, denom: T) -> Ratio<T> {
if denom == Zero::zero() {
panic!("denominator == 0");
}
let mut ret = Ratio::new_raw(numer, denom);
ret.reduce();
ret
}
/// Converts to an integer.
#[inline]
pub fn to_integer(&self) -> T {
self.trunc().numer
}
/// Gets an immutable reference to the numerator.
#[inline]
pub fn numer<'a>(&'a self) -> &'a T {
&self.numer
}
/// Gets an immutable reference to the denominator.
#[inline]
pub fn denom<'a>(&'a self) -> &'a T {
&self.denom
}
/// Returns true if the rational number is an integer (denominator is 1).
#[inline]
pub fn is_integer(&self) -> bool {
self.denom == One::one()
}
/// Put self into lowest terms, with denom > 0.
fn reduce(&mut self) {
let g : T = self.numer.gcd(&self.denom);
// FIXME(#5992): assignment operator overloads
// self.numer /= g;
self.numer = self.numer.clone() / g.clone();
// FIXME(#5992): assignment operator overloads
// self.denom /= g;
self.denom = self.denom.clone() / g;
// keep denom positive!
if self.denom < T::zero() {
self.numer = T::zero() - self.numer.clone();
self.denom = T::zero() - self.denom.clone();
}
}
/// Returns a `reduce`d copy of self.
pub fn reduced(&self) -> Ratio<T> {
let mut ret = self.clone();
ret.reduce();
ret
}
/// Returns the reciprocal.
#[inline]
pub fn recip(&self) -> Ratio<T> {
Ratio::new_raw(self.denom.clone(), self.numer.clone())
}
/// Rounds towards minus infinity.
#[inline]
pub fn floor(&self) -> Ratio<T> {
if *self < Zero::zero() {
let one: T = One::one();
Ratio::from_integer((self.numer.clone() - self.denom.clone() + one) / self.denom.clone())
} else {
Ratio::from_integer(self.numer.clone() / self.denom.clone())
}
}
/// Rounds towards plus infinity.
#[inline]
pub fn ceil(&self) -> Ratio<T> {
if *self < Zero::zero() {
Ratio::from_integer(self.numer.clone() / self.denom.clone())
} else {
let one: T = One::one();
Ratio::from_integer((self.numer.clone() + self.denom.clone() - one) / self.denom.clone())
}
}
/// Rounds to the nearest integer. Rounds half-way cases away from zero.
#[inline]
pub fn round(&self) -> Ratio<T> {
let zero: Ratio<T> = Zero::zero();
let one: T = One::one();
let two: T = one.clone() + one.clone();
// Find unsigned fractional part of rational number
let mut fractional = self.fract();
if fractional < zero { fractional = zero - fractional };
// The algorithm compares the unsigned fractional part with 1/2, that
// is, a/b >= 1/2, or a >= b/2. For odd denominators, we use
// a >= (b/2)+1. This avoids overflow issues.
let half_or_larger = if fractional.denom().is_even() {
*fractional.numer() >= fractional.denom().clone() / two.clone()
} else {
*fractional.numer() >= (fractional.denom().clone() / two.clone()) + one.clone()
};
if half_or_larger {
let one: Ratio<T> = One::one();
if *self >= Zero::zero() {
self.trunc() + one
} else {
self.trunc() - one
}
} else {
self.trunc()
}
}
/// Rounds towards zero.
#[inline]
pub fn trunc(&self) -> Ratio<T> {
Ratio::from_integer(self.numer.clone() / self.denom.clone())
}
/// Returns the fractional part of a number.
#[inline]
pub fn fract(&self) -> Ratio<T> {
Ratio::new_raw(self.numer.clone() % self.denom.clone(), self.denom.clone())
}
}
impl<T: Clone + Integer + PartialOrd + PrimInt> Ratio<T> {
/// Raises the ratio to the power of an exponent
#[inline]
pub fn pow(&self, expon: i32) -> Ratio<T> {
match expon.cmp(&0) {
cmp::Ordering::Equal => One::one(),
cmp::Ordering::Less => self.recip().pow(-expon),
cmp::Ordering::Greater => Ratio::new_raw(self.numer.pow(expon as u32),
self.denom.pow(expon as u32)),
}
}
}
#[cfg(feature = "bigint")]
impl Ratio<BigInt> {
/// Converts a float into a rational number.
pub fn from_float<T: Float>(f: T) -> Option<BigRational> {
if !f.is_finite() {
return None;
}
let (mantissa, exponent, sign) = f.integer_decode();
let bigint_sign = if sign == 1 { Sign::Plus } else { Sign::Minus };
if exponent < 0 {
let one: BigInt = One::one();
let denom: BigInt = one << ((-exponent) as usize);
let numer: BigUint = FromPrimitive::from_u64(mantissa).unwrap();
Some(Ratio::new(BigInt::from_biguint(bigint_sign, numer), denom))
} else {
let mut numer: BigUint = FromPrimitive::from_u64(mantissa).unwrap();
numer = numer << (exponent as usize);
Some(Ratio::from_integer(BigInt::from_biguint(bigint_sign, numer)))
}
}
}
/* Comparisons */
// comparing a/b and c/d is the same as comparing a*d and b*c, so we
// abstract that pattern. The following macro takes a trait and either
// a comma-separated list of "method name -> return value" or just
// "method name" (return value is bool in that case)
macro_rules! cmp_impl {
(impl $imp:ident, $($method:ident),+) => {
cmp_impl!(impl $imp, $($method -> bool),+);
};
// return something other than a Ratio<T>
(impl $imp:ident, $($method:ident -> $res:ty),*) => {
impl<T> $imp for Ratio<T> where
T: Clone + Mul<T, Output = T> + $imp
{
$(
#[inline]
fn $method(&self, other: &Ratio<T>) -> $res {
(self.numer.clone() * other.denom.clone()). $method (&(self.denom.clone()*other.numer.clone()))
}
)*
}
};
}
cmp_impl!(impl PartialEq, eq, ne);
cmp_impl!(impl PartialOrd, lt -> bool, gt -> bool, le -> bool, ge -> bool,
partial_cmp -> Option<cmp::Ordering>);
cmp_impl!(impl Eq, );
cmp_impl!(impl Ord, cmp -> cmp::Ordering);
macro_rules! forward_val_val_binop {
(impl $imp:ident, $method:ident) => {
impl<T: Clone + Integer + PartialOrd> $imp<Ratio<T>> for Ratio<T> {
type Output = Ratio<T>;
#[inline]
fn $method(self, other: Ratio<T>) -> Ratio<T> {
(&self).$method(&other)
}
}
}
}
macro_rules! forward_ref_val_binop {
(impl $imp:ident, $method:ident) => {
impl<'a, T> $imp<Ratio<T>> for &'a Ratio<T> where
T: Clone + Integer + PartialOrd
{
type Output = Ratio<T>;
#[inline]
fn $method(self, other: Ratio<T>) -> Ratio<T> {
self.$method(&other)
}
}
}
}
macro_rules! forward_val_ref_binop {
(impl $imp:ident, $method:ident) => {
impl<'a, T> $imp<&'a Ratio<T>> for Ratio<T> where
T: Clone + Integer + PartialOrd
{
type Output = Ratio<T>;
#[inline]
fn $method(self, other: &Ratio<T>) -> Ratio<T> {
(&self).$method(other)
}
}
}
}
macro_rules! forward_all_binop {
(impl $imp:ident, $method:ident) => {
forward_val_val_binop!(impl $imp, $method);
forward_ref_val_binop!(impl $imp, $method);
forward_val_ref_binop!(impl $imp, $method);
};
}
/* Arithmetic */
forward_all_binop!(impl Mul, mul);
// a/b * c/d = (a*c)/(b*d)
impl<'a, 'b, T> Mul<&'b Ratio<T>> for &'a Ratio<T>
where T: Clone + Integer + PartialOrd
{
type Output = Ratio<T>;
#[inline]
fn mul(self, rhs: &Ratio<T>) -> Ratio<T> {
Ratio::new(self.numer.clone() * rhs.numer.clone(), self.denom.clone() * rhs.denom.clone())
}
}
forward_all_binop!(impl Div, div);
// (a/b) / (c/d) = (a*d)/(b*c)
impl<'a, 'b, T> Div<&'b Ratio<T>> for &'a Ratio<T>
where T: Clone + Integer + PartialOrd
{
type Output = Ratio<T>;
#[inline]
fn div(self, rhs: &Ratio<T>) -> Ratio<T> {
Ratio::new(self.numer.clone() * rhs.denom.clone(), self.denom.clone() * rhs.numer.clone())
}
}
// Abstracts the a/b `op` c/d = (a*d `op` b*d) / (b*d) pattern
macro_rules! arith_impl {
(impl $imp:ident, $method:ident) => {
forward_all_binop!(impl $imp, $method);
impl<'a, 'b, T: Clone + Integer + PartialOrd>
$imp<&'b Ratio<T>> for &'a Ratio<T> {
type Output = Ratio<T>;
#[inline]
fn $method(self, rhs: &Ratio<T>) -> Ratio<T> {
Ratio::new((self.numer.clone() * rhs.denom.clone()).$method(self.denom.clone() * rhs.numer.clone()),
self.denom.clone() * rhs.denom.clone())
}
}
}
}
// a/b + c/d = (a*d + b*c)/(b*d)
arith_impl!(impl Add, add);
// a/b - c/d = (a*d - b*c)/(b*d)
arith_impl!(impl Sub, sub);
// a/b % c/d = (a*d % b*c)/(b*d)
arith_impl!(impl Rem, rem);
impl<T> Neg for Ratio<T>
where T: Clone + Integer + PartialOrd + Neg<Output = T>
{
type Output = Ratio<T>;
#[inline]
fn neg(self) -> Ratio<T> { -&self }
}
impl<'a, T> Neg for &'a Ratio<T>
where T: Clone + Integer + PartialOrd + Neg<Output = T>
{
type Output = Ratio<T>;
#[inline]
fn neg(self) -> Ratio<T> {
Ratio::new_raw(-self.numer.clone(), self.denom.clone())
}
}
/* Constants */
impl<T: Clone + Integer + PartialOrd>
Zero for Ratio<T> {
#[inline]
fn zero() -> Ratio<T> {
Ratio::new_raw(Zero::zero(), One::one())
}
#[inline]
fn is_zero(&self) -> bool {
*self == Zero::zero()
}
}
impl<T: Clone + Integer + PartialOrd>
One for Ratio<T> {
#[inline]
fn one() -> Ratio<T> {
Ratio::new_raw(One::one(), One::one())
}
}
impl<T: Clone + Integer + PartialOrd> Num for Ratio<T> {
type FromStrRadixErr = ParseRatioError;
/// Parses `numer/denom` where the numbers are in base `radix`.
fn from_str_radix(s: &str, radix: u32) -> Result<Ratio<T>, ParseRatioError> {
let split: Vec<&str> = s.splitn(2, '/').collect();
if split.len() < 2 {
Err(ParseRatioError{kind: RatioErrorKind::ParseError})
} else {
let a_result: Result<T, _> = T::from_str_radix(
split[0],
radix).map_err(|_| ParseRatioError{kind: RatioErrorKind::ParseError});
a_result.and_then(|a| {
let b_result: Result<T, _> =
T::from_str_radix(split[1], radix).map_err(
|_| ParseRatioError{kind: RatioErrorKind::ParseError});
b_result.and_then(|b| if b.is_zero() {
Err(ParseRatioError{kind: RatioErrorKind::ZeroDenominator})
} else {
Ok(Ratio::new(a.clone(), b.clone()))
})
})
}
}
}
impl<T: Clone + Integer + PartialOrd + Signed> Signed for Ratio<T> {
#[inline]
fn abs(&self) -> Ratio<T> {
if self.is_negative() { -self.clone() } else { self.clone() }
}
#[inline]
fn abs_sub(&self, other: &Ratio<T>) -> Ratio<T> {
if *self <= *other { Zero::zero() } else { self - other }
}
#[inline]
fn signum(&self) -> Ratio<T> {
if *self > Zero::zero() {
One::one()
} else if self.is_zero() {
Zero::zero()
} else {
- ::one::<Ratio<T>>()
}
}
#[inline]
fn is_positive(&self) -> bool { *self > Zero::zero() }
#[inline]
fn is_negative(&self) -> bool { *self < Zero::zero() }
}
/* String conversions */
impl<T> fmt::Display for Ratio<T> where
T: fmt::Display + Eq + One
{
/// Renders as `numer/denom`. If denom=1, renders as numer.
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
if self.denom == One::one() {
write!(f, "{}", self.numer)
} else {
write!(f, "{}/{}", self.numer, self.denom)
}
}
}
impl<T: FromStr + Clone + Integer + PartialOrd> FromStr for Ratio<T> {
type Err = ParseRatioError;
/// Parses `numer/denom` or just `numer`.
fn from_str(s: &str) -> Result<Ratio<T>, ParseRatioError> {
let mut split = s.splitn(2, '/');
let n = try!(split.next().ok_or(
ParseRatioError{kind: RatioErrorKind::ParseError}));
let num = try!(FromStr::from_str(n).map_err(
|_| ParseRatioError{kind: RatioErrorKind::ParseError}));
let d = split.next().unwrap_or("1");
let den = try!(FromStr::from_str(d).map_err(
|_| ParseRatioError{kind: RatioErrorKind::ParseError}));
if Zero::is_zero(&den) {
Err(ParseRatioError{kind: RatioErrorKind::ZeroDenominator})
} else {
Ok(Ratio::new(num, den))
}
}
}
// FIXME: Bubble up specific errors
#[derive(Copy, Clone, Debug, PartialEq)]
pub struct ParseRatioError { kind: RatioErrorKind }
#[derive(Copy, Clone, Debug, PartialEq)]
enum RatioErrorKind {
ParseError,
ZeroDenominator,
}
impl fmt::Display for ParseRatioError {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
self.description().fmt(f)
}
}
impl Error for ParseRatioError {
fn description(&self) -> &str { self.kind.description() }
}
impl RatioErrorKind {
fn description(&self) -> &'static str {
match *self {
RatioErrorKind::ParseError => "failed to parse integer",
RatioErrorKind::ZeroDenominator => "zero value denominator",
}
}
}
#[cfg(test)]
mod test {
use super::{Ratio, Rational};
#[cfg(feature = "bigint")]
use super::BigRational;
use std::str::FromStr;
use std::i32;
use {Zero, One, Signed, FromPrimitive, Float};
pub const _0 : Rational = Ratio { numer: 0, denom: 1};
pub const _1 : Rational = Ratio { numer: 1, denom: 1};
pub const _2: Rational = Ratio { numer: 2, denom: 1};
pub const _1_2: Rational = Ratio { numer: 1, denom: 2};
pub const _3_2: Rational = Ratio { numer: 3, denom: 2};
pub const _NEG1_2: Rational = Ratio { numer: -1, denom: 2};
pub const _1_3: Rational = Ratio { numer: 1, denom: 3};
pub const _NEG1_3: Rational = Ratio { numer: -1, denom: 3};
pub const _2_3: Rational = Ratio { numer: 2, denom: 3};
pub const _NEG2_3: Rational = Ratio { numer: -2, denom: 3};
#[cfg(feature = "bigint")]
pub fn to_big(n: Rational) -> BigRational {
Ratio::new(
FromPrimitive::from_isize(n.numer).unwrap(),
FromPrimitive::from_isize(n.denom).unwrap()
)
}
#[cfg(not(feature = "bigint"))]
pub fn to_big(n: Rational) -> Rational {
Ratio::new(
FromPrimitive::from_isize(n.numer).unwrap(),
FromPrimitive::from_isize(n.denom).unwrap()
)
}
#[test]
fn test_test_constants() {
// check our constants are what Ratio::new etc. would make.
assert_eq!(_0, Zero::zero());
assert_eq!(_1, One::one());
assert_eq!(_2, Ratio::from_integer(2));
assert_eq!(_1_2, Ratio::new(1,2));
assert_eq!(_3_2, Ratio::new(3,2));
assert_eq!(_NEG1_2, Ratio::new(-1,2));
}
#[test]
fn test_new_reduce() {
let one22 = Ratio::new(2,2);
assert_eq!(one22, One::one());
}
#[test]
#[should_panic]
fn test_new_zero() {
let _a = Ratio::new(1,0);
}
#[test]
fn test_cmp() {
assert!(_0 == _0 && _1 == _1);
assert!(_0 != _1 && _1 != _0);
assert!(_0 < _1 && !(_1 < _0));
assert!(_1 > _0 && !(_0 > _1));
assert!(_0 <= _0 && _1 <= _1);
assert!(_0 <= _1 && !(_1 <= _0));
assert!(_0 >= _0 && _1 >= _1);
assert!(_1 >= _0 && !(_0 >= _1));
}
#[test]
fn test_to_integer() {
assert_eq!(_0.to_integer(), 0);
assert_eq!(_1.to_integer(), 1);
assert_eq!(_2.to_integer(), 2);
assert_eq!(_1_2.to_integer(), 0);
assert_eq!(_3_2.to_integer(), 1);
assert_eq!(_NEG1_2.to_integer(), 0);
}
#[test]
fn test_numer() {
assert_eq!(_0.numer(), &0);
assert_eq!(_1.numer(), &1);
assert_eq!(_2.numer(), &2);
assert_eq!(_1_2.numer(), &1);
assert_eq!(_3_2.numer(), &3);
assert_eq!(_NEG1_2.numer(), &(-1));
}
#[test]
fn test_denom() {
assert_eq!(_0.denom(), &1);
assert_eq!(_1.denom(), &1);
assert_eq!(_2.denom(), &1);
assert_eq!(_1_2.denom(), &2);
assert_eq!(_3_2.denom(), &2);
assert_eq!(_NEG1_2.denom(), &2);
}
#[test]
fn test_is_integer() {
assert!(_0.is_integer());
assert!(_1.is_integer());
assert!(_2.is_integer());
assert!(!_1_2.is_integer());
assert!(!_3_2.is_integer());
assert!(!_NEG1_2.is_integer());
}
#[test]
fn test_show() {
assert_eq!(format!("{}", _2), "2".to_string());
assert_eq!(format!("{}", _1_2), "1/2".to_string());
assert_eq!(format!("{}", _0), "0".to_string());
assert_eq!(format!("{}", Ratio::from_integer(-2)), "-2".to_string());
}
mod arith {
use super::{_0, _1, _2, _1_2, _3_2, _NEG1_2, to_big};
use super::super::{Ratio, Rational};
#[test]
fn test_add() {
fn test(a: Rational, b: Rational, c: Rational) {
assert_eq!(a + b, c);
assert_eq!(to_big(a) + to_big(b), to_big(c));
}
test(_1, _1_2, _3_2);
test(_1, _1, _2);
test(_1_2, _3_2, _2);
test(_1_2, _NEG1_2, _0);
}
#[test]
fn test_sub() {
fn test(a: Rational, b: Rational, c: Rational) {
assert_eq!(a - b, c);
assert_eq!(to_big(a) - to_big(b), to_big(c))
}
test(_1, _1_2, _1_2);
test(_3_2, _1_2, _1);
test(_1, _NEG1_2, _3_2);
}
#[test]
fn test_mul() {
fn test(a: Rational, b: Rational, c: Rational) {
assert_eq!(a * b, c);
assert_eq!(to_big(a) * to_big(b), to_big(c))
}
test(_1, _1_2, _1_2);
test(_1_2, _3_2, Ratio::new(3,4));
test(_1_2, _NEG1_2, Ratio::new(-1, 4));
}
#[test]
fn test_div() {
fn test(a: Rational, b: Rational, c: Rational) {
assert_eq!(a / b, c);
assert_eq!(to_big(a) / to_big(b), to_big(c))
}
test(_1, _1_2, _2);
test(_3_2, _1_2, _1 + _2);
test(_1, _NEG1_2, _NEG1_2 + _NEG1_2 + _NEG1_2 + _NEG1_2);
}
#[test]
fn test_rem() {
fn test(a: Rational, b: Rational, c: Rational) {
assert_eq!(a % b, c);
assert_eq!(to_big(a) % to_big(b), to_big(c))
}
test(_3_2, _1, _1_2);
test(_2, _NEG1_2, _0);
test(_1_2, _2, _1_2);
}
#[test]
fn test_neg() {
fn test(a: Rational, b: Rational) {
assert_eq!(-a, b);
assert_eq!(-to_big(a), to_big(b))
}
test(_0, _0);
test(_1_2, _NEG1_2);
test(-_1, _1);
}
#[test]
fn test_zero() {
assert_eq!(_0 + _0, _0);
assert_eq!(_0 * _0, _0);
assert_eq!(_0 * _1, _0);
assert_eq!(_0 / _NEG1_2, _0);
assert_eq!(_0 - _0, _0);
}
#[test]
#[should_panic]
fn test_div_0() {
let _a = _1 / _0;
}
}
#[test]
fn test_round() {
assert_eq!(_1_3.ceil(), _1);
assert_eq!(_1_3.floor(), _0);
assert_eq!(_1_3.round(), _0);
assert_eq!(_1_3.trunc(), _0);
assert_eq!(_NEG1_3.ceil(), _0);
assert_eq!(_NEG1_3.floor(), -_1);
assert_eq!(_NEG1_3.round(), _0);
assert_eq!(_NEG1_3.trunc(), _0);
assert_eq!(_2_3.ceil(), _1);
assert_eq!(_2_3.floor(), _0);
assert_eq!(_2_3.round(), _1);
assert_eq!(_2_3.trunc(), _0);
assert_eq!(_NEG2_3.ceil(), _0);
assert_eq!(_NEG2_3.floor(), -_1);
assert_eq!(_NEG2_3.round(), -_1);
assert_eq!(_NEG2_3.trunc(), _0);
assert_eq!(_1_2.ceil(), _1);
assert_eq!(_1_2.floor(), _0);
assert_eq!(_1_2.round(), _1);
assert_eq!(_1_2.trunc(), _0);
assert_eq!(_NEG1_2.ceil(), _0);
assert_eq!(_NEG1_2.floor(), -_1);
assert_eq!(_NEG1_2.round(), -_1);
assert_eq!(_NEG1_2.trunc(), _0);
assert_eq!(_1.ceil(), _1);
assert_eq!(_1.floor(), _1);
assert_eq!(_1.round(), _1);
assert_eq!(_1.trunc(), _1);
// Overflow checks
let _neg1 = Ratio::from_integer(-1);
let _large_rat1 = Ratio::new(i32::MAX, i32::MAX-1);
let _large_rat2 = Ratio::new(i32::MAX-1, i32::MAX);
let _large_rat3 = Ratio::new(i32::MIN+2, i32::MIN+1);
let _large_rat4 = Ratio::new(i32::MIN+1, i32::MIN+2);
let _large_rat5 = Ratio::new(i32::MIN+2, i32::MAX);
let _large_rat6 = Ratio::new(i32::MAX, i32::MIN+2);
let _large_rat7 = Ratio::new(1, i32::MIN+1);
let _large_rat8 = Ratio::new(1, i32::MAX);
assert_eq!(_large_rat1.round(), One::one());
assert_eq!(_large_rat2.round(), One::one());
assert_eq!(_large_rat3.round(), One::one());
assert_eq!(_large_rat4.round(), One::one());
assert_eq!(_large_rat5.round(), _neg1);
assert_eq!(_large_rat6.round(), _neg1);
assert_eq!(_large_rat7.round(), Zero::zero());
assert_eq!(_large_rat8.round(), Zero::zero());
}
#[test]
fn test_fract() {
assert_eq!(_1.fract(), _0);
assert_eq!(_NEG1_2.fract(), _NEG1_2);
assert_eq!(_1_2.fract(), _1_2);
assert_eq!(_3_2.fract(), _1_2);
}
#[test]
fn test_recip() {
assert_eq!(_1 * _1.recip(), _1);
assert_eq!(_2 * _2.recip(), _1);
assert_eq!(_1_2 * _1_2.recip(), _1);
assert_eq!(_3_2 * _3_2.recip(), _1);
assert_eq!(_NEG1_2 * _NEG1_2.recip(), _1);
}
#[test]
fn test_pow() {
assert_eq!(_1_2.pow(2), Ratio::new(1, 4));
assert_eq!(_1_2.pow(-2), Ratio::new(4, 1));
assert_eq!(_1.pow(1), _1);
assert_eq!(_NEG1_2.pow(2), _1_2.pow(2));
assert_eq!(_NEG1_2.pow(3), -_1_2.pow(3));
assert_eq!(_3_2.pow(0), _1);
assert_eq!(_3_2.pow(-1), _3_2.recip());
assert_eq!(_3_2.pow(3), Ratio::new(27, 8));
}
#[test]
fn test_to_from_str() {
fn test(r: Rational, s: String) {
assert_eq!(FromStr::from_str(&s), Ok(r));
assert_eq!(r.to_string(), s);
}
test(_1, "1".to_string());
test(_0, "0".to_string());
test(_1_2, "1/2".to_string());
test(_3_2, "3/2".to_string());
test(_2, "2".to_string());
test(_NEG1_2, "-1/2".to_string());
}
#[test]
fn test_from_str_fail() {
fn test(s: &str) {
let rational: Result<Rational, _> = FromStr::from_str(s);
assert!(rational.is_err());
}
let xs = ["0 /1", "abc", "", "1/", "--1/2","3/2/1", "1/0"];
for &s in xs.iter() {
test(s);
}
}
#[cfg(feature = "bigint")]
#[test]
fn test_from_float() {
fn test<T: Float>(given: T, (numer, denom): (&str, &str)) {
let ratio: BigRational = Ratio::from_float(given).unwrap();
assert_eq!(ratio, Ratio::new(
FromStr::from_str(numer).unwrap(),
FromStr::from_str(denom).unwrap()));
}
// f32
test(3.14159265359f32, ("13176795", "4194304"));
test(2f32.powf(100.), ("1267650600228229401496703205376", "1"));
test(-2f32.powf(100.), ("-1267650600228229401496703205376", "1"));
test(1.0 / 2f32.powf(100.), ("1", "1267650600228229401496703205376"));
test(684729.48391f32, ("1369459", "2"));
test(-8573.5918555f32, ("-4389679", "512"));
// f64
test(3.14159265359f64, ("3537118876014453", "1125899906842624"));
test(2f64.powf(100.), ("1267650600228229401496703205376", "1"));
test(-2f64.powf(100.), ("-1267650600228229401496703205376", "1"));
test(684729.48391f64, ("367611342500051", "536870912"));
test(-8573.5918555f64, ("-4713381968463931", "549755813888"));
test(1.0 / 2f64.powf(100.), ("1", "1267650600228229401496703205376"));
}
#[cfg(feature = "bigint")]
#[test]
fn test_from_float_fail() {
use std::{f32, f64};
assert_eq!(Ratio::from_float(f32::NAN), None);
assert_eq!(Ratio::from_float(f32::INFINITY), None);
assert_eq!(Ratio::from_float(f32::NEG_INFINITY), None);
assert_eq!(Ratio::from_float(f64::NAN), None);
assert_eq!(Ratio::from_float(f64::INFINITY), None);
assert_eq!(Ratio::from_float(f64::NEG_INFINITY), None);
}
#[test]
fn test_signed() {
assert_eq!(_NEG1_2.abs(), _1_2);
assert_eq!(_3_2.abs_sub(&_1_2), _1);
assert_eq!(_1_2.abs_sub(&_3_2), Zero::zero());
assert_eq!(_1_2.signum(), One::one());
assert_eq!(_NEG1_2.signum(), - ::one::<Ratio<isize>>());
assert!(_NEG1_2.is_negative());
assert!(! _NEG1_2.is_positive());
assert!(! _1_2.is_negative());
}
#[test]
fn test_hash() {
assert!(::hash(&_0) != ::hash(&_1));
assert!(::hash(&_0) != ::hash(&_3_2));
}
}

834
src/real.rs
View File

@ -1,834 +0,0 @@
#![cfg(any(feature = "std", feature = "libm"))]
use core::ops::Neg;
use {Float, Num, NumCast};
// NOTE: These doctests have the same issue as those in src/float.rs.
// They're testing the inherent methods directly, and not those of `Real`.
/// A trait for real number types that do not necessarily have
/// floating-point-specific characteristics such as NaN and infinity.
///
/// See [this Wikipedia article](https://en.wikipedia.org/wiki/Real_data_type)
/// for a list of data types that could meaningfully implement this trait.
///
/// This trait is only available with the `std` feature, or with the `libm` feature otherwise.
pub trait Real: Num + Copy + NumCast + PartialOrd + Neg<Output = Self> {
/// Returns the smallest finite value that this type can represent.
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let x: f64 = Real::min_value();
///
/// assert_eq!(x, f64::MIN);
/// ```
fn min_value() -> Self;
/// Returns the smallest positive, normalized value that this type can represent.
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let x: f64 = Real::min_positive_value();
///
/// assert_eq!(x, f64::MIN_POSITIVE);
/// ```
fn min_positive_value() -> Self;
/// Returns epsilon, a small positive value.
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let x: f64 = Real::epsilon();
///
/// assert_eq!(x, f64::EPSILON);
/// ```
///
/// # Panics
///
/// The default implementation will panic if `f32::EPSILON` cannot
/// be cast to `Self`.
fn epsilon() -> Self;
/// Returns the largest finite value that this type can represent.
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let x: f64 = Real::max_value();
/// assert_eq!(x, f64::MAX);
/// ```
fn max_value() -> Self;
/// Returns the largest integer less than or equal to a number.
///
/// ```
/// use num_traits::real::Real;
///
/// let f = 3.99;
/// let g = 3.0;
///
/// assert_eq!(f.floor(), 3.0);
/// assert_eq!(g.floor(), 3.0);
/// ```
fn floor(self) -> Self;
/// Returns the smallest integer greater than or equal to a number.
///
/// ```
/// use num_traits::real::Real;
///
/// let f = 3.01;
/// let g = 4.0;
///
/// assert_eq!(f.ceil(), 4.0);
/// assert_eq!(g.ceil(), 4.0);
/// ```
fn ceil(self) -> Self;
/// Returns the nearest integer to a number. Round half-way cases away from
/// `0.0`.
///
/// ```
/// use num_traits::real::Real;
///
/// let f = 3.3;
/// let g = -3.3;
///
/// assert_eq!(f.round(), 3.0);
/// assert_eq!(g.round(), -3.0);
/// ```
fn round(self) -> Self;
/// Return the integer part of a number.
///
/// ```
/// use num_traits::real::Real;
///
/// let f = 3.3;
/// let g = -3.7;
///
/// assert_eq!(f.trunc(), 3.0);
/// assert_eq!(g.trunc(), -3.0);
/// ```
fn trunc(self) -> Self;
/// Returns the fractional part of a number.
///
/// ```
/// use num_traits::real::Real;
///
/// let x = 3.5;
/// let y = -3.5;
/// let abs_difference_x = (x.fract() - 0.5).abs();
/// let abs_difference_y = (y.fract() - (-0.5)).abs();
///
/// assert!(abs_difference_x < 1e-10);
/// assert!(abs_difference_y < 1e-10);
/// ```
fn fract(self) -> Self;
/// Computes the absolute value of `self`. Returns `Float::nan()` if the
/// number is `Float::nan()`.
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let x = 3.5;
/// let y = -3.5;
///
/// let abs_difference_x = (x.abs() - x).abs();
/// let abs_difference_y = (y.abs() - (-y)).abs();
///
/// assert!(abs_difference_x < 1e-10);
/// assert!(abs_difference_y < 1e-10);
///
/// assert!(::num_traits::Float::is_nan(f64::NAN.abs()));
/// ```
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()`
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let f = 3.5;
///
/// assert_eq!(f.signum(), 1.0);
/// assert_eq!(f64::NEG_INFINITY.signum(), -1.0);
///
/// assert!(f64::NAN.signum().is_nan());
/// ```
fn signum(self) -> Self;
/// Returns `true` if `self` is positive, including `+0.0`,
/// `Float::infinity()`, and with newer versions of Rust `f64::NAN`.
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let neg_nan: f64 = -f64::NAN;
///
/// let f = 7.0;
/// let g = -7.0;
///
/// assert!(f.is_sign_positive());
/// assert!(!g.is_sign_positive());
/// assert!(!neg_nan.is_sign_positive());
/// ```
fn is_sign_positive(self) -> bool;
/// Returns `true` if `self` is negative, including `-0.0`,
/// `Float::neg_infinity()`, and with newer versions of Rust `-f64::NAN`.
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let nan: f64 = f64::NAN;
///
/// let f = 7.0;
/// let g = -7.0;
///
/// assert!(!f.is_sign_negative());
/// assert!(g.is_sign_negative());
/// assert!(!nan.is_sign_negative());
/// ```
fn is_sign_negative(self) -> bool;
/// Fused multiply-add. Computes `(self * a) + b` with only one rounding
/// error, yielding a more accurate result than an unfused multiply-add.
///
/// Using `mul_add` can be more performant than an unfused multiply-add if
/// the target architecture has a dedicated `fma` CPU instruction.
///
/// ```
/// use num_traits::real::Real;
///
/// let m = 10.0;
/// let x = 4.0;
/// let b = 60.0;
///
/// // 100.0
/// let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn mul_add(self, a: Self, b: Self) -> Self;
/// Take the reciprocal (inverse) of a number, `1/x`.
///
/// ```
/// use num_traits::real::Real;
///
/// let x = 2.0;
/// let abs_difference = (x.recip() - (1.0/x)).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn recip(self) -> Self;
/// Raise a number to an integer power.
///
/// Using this function is generally faster than using `powf`
///
/// ```
/// use num_traits::real::Real;
///
/// let x = 2.0;
/// let abs_difference = (x.powi(2) - x*x).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn powi(self, n: i32) -> Self;
/// Raise a number to a real number power.
///
/// ```
/// use num_traits::real::Real;
///
/// let x = 2.0;
/// let abs_difference = (x.powf(2.0) - x*x).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn powf(self, n: Self) -> Self;
/// Take the square root of a number.
///
/// Returns NaN if `self` is a negative floating-point number.
///
/// # Panics
///
/// If the implementing type doesn't support NaN, this method should panic if `self < 0`.
///
/// ```
/// use num_traits::real::Real;
///
/// let positive = 4.0;
/// let negative = -4.0;
///
/// let abs_difference = (positive.sqrt() - 2.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// assert!(::num_traits::Float::is_nan(negative.sqrt()));
/// ```
fn sqrt(self) -> Self;
/// Returns `e^(self)`, (the exponential function).
///
/// ```
/// use num_traits::real::Real;
///
/// let one = 1.0;
/// // e^1
/// let e = one.exp();
///
/// // ln(e) - 1 == 0
/// let abs_difference = (e.ln() - 1.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn exp(self) -> Self;
/// Returns `2^(self)`.
///
/// ```
/// use num_traits::real::Real;
///
/// let f = 2.0;
///
/// // 2^2 - 4 == 0
/// let abs_difference = (f.exp2() - 4.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn exp2(self) -> Self;
/// Returns the natural logarithm of the number.
///
/// # Panics
///
/// If `self <= 0` and this type does not support a NaN representation, this function should panic.
///
/// ```
/// use num_traits::real::Real;
///
/// let one = 1.0;
/// // e^1
/// let e = one.exp();
///
/// // ln(e) - 1 == 0
/// let abs_difference = (e.ln() - 1.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn ln(self) -> Self;
/// Returns the logarithm of the number with respect to an arbitrary base.
///
/// # Panics
///
/// If `self <= 0` and this type does not support a NaN representation, this function should panic.
///
/// ```
/// use num_traits::real::Real;
///
/// let ten = 10.0;
/// let two = 2.0;
///
/// // log10(10) - 1 == 0
/// let abs_difference_10 = (ten.log(10.0) - 1.0).abs();
///
/// // log2(2) - 1 == 0
/// let abs_difference_2 = (two.log(2.0) - 1.0).abs();
///
/// assert!(abs_difference_10 < 1e-10);
/// assert!(abs_difference_2 < 1e-10);
/// ```
fn log(self, base: Self) -> Self;
/// Returns the base 2 logarithm of the number.
///
/// # Panics
///
/// If `self <= 0` and this type does not support a NaN representation, this function should panic.
///
/// ```
/// use num_traits::real::Real;
///
/// let two = 2.0;
///
/// // log2(2) - 1 == 0
/// let abs_difference = (two.log2() - 1.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn log2(self) -> Self;
/// Returns the base 10 logarithm of the number.
///
/// # Panics
///
/// If `self <= 0` and this type does not support a NaN representation, this function should panic.
///
///
/// ```
/// use num_traits::real::Real;
///
/// let ten = 10.0;
///
/// // log10(10) - 1 == 0
/// let abs_difference = (ten.log10() - 1.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn log10(self) -> Self;
/// Converts radians to degrees.
///
/// ```
/// use std::f64::consts;
///
/// let angle = consts::PI;
///
/// let abs_difference = (angle.to_degrees() - 180.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn to_degrees(self) -> Self;
/// Converts degrees to radians.
///
/// ```
/// use std::f64::consts;
///
/// let angle = 180.0_f64;
///
/// let abs_difference = (angle.to_radians() - consts::PI).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn to_radians(self) -> Self;
/// Returns the maximum of the two numbers.
///
/// ```
/// use num_traits::real::Real;
///
/// let x = 1.0;
/// let y = 2.0;
///
/// assert_eq!(x.max(y), y);
/// ```
fn max(self, other: Self) -> Self;
/// Returns the minimum of the two numbers.
///
/// ```
/// use num_traits::real::Real;
///
/// let x = 1.0;
/// let y = 2.0;
///
/// assert_eq!(x.min(y), x);
/// ```
fn min(self, other: Self) -> Self;
/// The positive difference of two numbers.
///
/// * If `self <= other`: `0:0`
/// * Else: `self - other`
///
/// ```
/// use num_traits::real::Real;
///
/// let x = 3.0;
/// let y = -3.0;
///
/// let abs_difference_x = (x.abs_sub(1.0) - 2.0).abs();
/// let abs_difference_y = (y.abs_sub(1.0) - 0.0).abs();
///
/// assert!(abs_difference_x < 1e-10);
/// assert!(abs_difference_y < 1e-10);
/// ```
fn abs_sub(self, other: Self) -> Self;
/// Take the cubic root of a number.
///
/// ```
/// use num_traits::real::Real;
///
/// let x = 8.0;
///
/// // x^(1/3) - 2 == 0
/// let abs_difference = (x.cbrt() - 2.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn cbrt(self) -> Self;
/// Calculate the length of the hypotenuse of a right-angle triangle given
/// legs of length `x` and `y`.
///
/// ```
/// use num_traits::real::Real;
///
/// let x = 2.0;
/// let y = 3.0;
///
/// // sqrt(x^2 + y^2)
/// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn hypot(self, other: Self) -> Self;
/// Computes the sine of a number (in radians).
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let x = f64::consts::PI/2.0;
///
/// let abs_difference = (x.sin() - 1.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn sin(self) -> Self;
/// Computes the cosine of a number (in radians).
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let x = 2.0*f64::consts::PI;
///
/// let abs_difference = (x.cos() - 1.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn cos(self) -> Self;
/// Computes the tangent of a number (in radians).
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let x = f64::consts::PI/4.0;
/// let abs_difference = (x.tan() - 1.0).abs();
///
/// assert!(abs_difference < 1e-14);
/// ```
fn tan(self) -> Self;
/// Computes the arcsine of a number. Return value is in radians in
/// the range [-pi/2, pi/2] or NaN if the number is outside the range
/// [-1, 1].
///
/// # Panics
///
/// If this type does not support a NaN representation, this function should panic
/// if the number is outside the range [-1, 1].
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let f = f64::consts::PI / 2.0;
///
/// // asin(sin(pi/2))
/// let abs_difference = (f.sin().asin() - f64::consts::PI / 2.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn asin(self) -> Self;
/// Computes the arccosine of a number. Return value is in radians in
/// the range [0, pi] or NaN if the number is outside the range
/// [-1, 1].
///
/// # Panics
///
/// If this type does not support a NaN representation, this function should panic
/// if the number is outside the range [-1, 1].
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let f = f64::consts::PI / 4.0;
///
/// // acos(cos(pi/4))
/// let abs_difference = (f.cos().acos() - f64::consts::PI / 4.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn acos(self) -> Self;
/// Computes the arctangent of a number. Return value is in radians in the
/// range [-pi/2, pi/2];
///
/// ```
/// use num_traits::real::Real;
///
/// let f = 1.0;
///
/// // atan(tan(1))
/// let abs_difference = (f.tan().atan() - 1.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn atan(self) -> Self;
/// Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`).
///
/// * `x = 0`, `y = 0`: `0`
/// * `x >= 0`: `arctan(y/x)` -> `[-pi/2, pi/2]`
/// * `y >= 0`: `arctan(y/x) + pi` -> `(pi/2, pi]`
/// * `y < 0`: `arctan(y/x) - pi` -> `(-pi, -pi/2)`
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let pi = f64::consts::PI;
/// // All angles from horizontal right (+x)
/// // 45 deg counter-clockwise
/// let x1 = 3.0;
/// let y1 = -3.0;
///
/// // 135 deg clockwise
/// let x2 = -3.0;
/// let y2 = 3.0;
///
/// let abs_difference_1 = (y1.atan2(x1) - (-pi/4.0)).abs();
/// let abs_difference_2 = (y2.atan2(x2) - 3.0*pi/4.0).abs();
///
/// assert!(abs_difference_1 < 1e-10);
/// assert!(abs_difference_2 < 1e-10);
/// ```
fn atan2(self, other: Self) -> Self;
/// Simultaneously computes the sine and cosine of the number, `x`. Returns
/// `(sin(x), cos(x))`.
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let x = f64::consts::PI/4.0;
/// let f = x.sin_cos();
///
/// let abs_difference_0 = (f.0 - x.sin()).abs();
/// let abs_difference_1 = (f.1 - x.cos()).abs();
///
/// assert!(abs_difference_0 < 1e-10);
/// assert!(abs_difference_0 < 1e-10);
/// ```
fn sin_cos(self) -> (Self, Self);
/// Returns `e^(self) - 1` in a way that is accurate even if the
/// number is close to zero.
///
/// ```
/// use num_traits::real::Real;
///
/// let x = 7.0;
///
/// // e^(ln(7)) - 1
/// let abs_difference = (x.ln().exp_m1() - 6.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn exp_m1(self) -> Self;
/// Returns `ln(1+n)` (natural logarithm) more accurately than if
/// the operations were performed separately.
///
/// # Panics
///
/// If this type does not support a NaN representation, this function should panic
/// if `self-1 <= 0`.
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let x = f64::consts::E - 1.0;
///
/// // ln(1 + (e - 1)) == ln(e) == 1
/// let abs_difference = (x.ln_1p() - 1.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn ln_1p(self) -> Self;
/// Hyperbolic sine function.
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let e = f64::consts::E;
/// let x = 1.0;
///
/// let f = x.sinh();
/// // Solving sinh() at 1 gives `(e^2-1)/(2e)`
/// let g = (e*e - 1.0)/(2.0*e);
/// let abs_difference = (f - g).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn sinh(self) -> Self;
/// Hyperbolic cosine function.
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let e = f64::consts::E;
/// let x = 1.0;
/// let f = x.cosh();
/// // Solving cosh() at 1 gives this result
/// let g = (e*e + 1.0)/(2.0*e);
/// let abs_difference = (f - g).abs();
///
/// // Same result
/// assert!(abs_difference < 1.0e-10);
/// ```
fn cosh(self) -> Self;
/// Hyperbolic tangent function.
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let e = f64::consts::E;
/// let x = 1.0;
///
/// let f = x.tanh();
/// // Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))`
/// let g = (1.0 - e.powi(-2))/(1.0 + e.powi(-2));
/// let abs_difference = (f - g).abs();
///
/// assert!(abs_difference < 1.0e-10);
/// ```
fn tanh(self) -> Self;
/// Inverse hyperbolic sine function.
///
/// ```
/// use num_traits::real::Real;
///
/// let x = 1.0;
/// let f = x.sinh().asinh();
///
/// let abs_difference = (f - x).abs();
///
/// assert!(abs_difference < 1.0e-10);
/// ```
fn asinh(self) -> Self;
/// Inverse hyperbolic cosine function.
///
/// ```
/// use num_traits::real::Real;
///
/// let x = 1.0;
/// let f = x.cosh().acosh();
///
/// let abs_difference = (f - x).abs();
///
/// assert!(abs_difference < 1.0e-10);
/// ```
fn acosh(self) -> Self;
/// Inverse hyperbolic tangent function.
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let e = f64::consts::E;
/// let f = e.tanh().atanh();
///
/// let abs_difference = (f - e).abs();
///
/// assert!(abs_difference < 1.0e-10);
/// ```
fn atanh(self) -> Self;
}
impl<T: Float> Real for T {
forward! {
Float::min_value() -> Self;
Float::min_positive_value() -> Self;
Float::epsilon() -> Self;
Float::max_value() -> Self;
}
forward! {
Float::floor(self) -> Self;
Float::ceil(self) -> Self;
Float::round(self) -> Self;
Float::trunc(self) -> Self;
Float::fract(self) -> Self;
Float::abs(self) -> Self;
Float::signum(self) -> Self;
Float::is_sign_positive(self) -> bool;
Float::is_sign_negative(self) -> bool;
Float::mul_add(self, a: Self, b: Self) -> Self;
Float::recip(self) -> Self;
Float::powi(self, n: i32) -> Self;
Float::powf(self, n: Self) -> Self;
Float::sqrt(self) -> Self;
Float::exp(self) -> Self;
Float::exp2(self) -> Self;
Float::ln(self) -> Self;
Float::log(self, base: Self) -> Self;
Float::log2(self) -> Self;
Float::log10(self) -> Self;
Float::to_degrees(self) -> Self;
Float::to_radians(self) -> Self;
Float::max(self, other: Self) -> Self;
Float::min(self, other: Self) -> Self;
Float::abs_sub(self, other: Self) -> Self;
Float::cbrt(self) -> Self;
Float::hypot(self, other: Self) -> Self;
Float::sin(self) -> Self;
Float::cos(self) -> Self;
Float::tan(self) -> Self;
Float::asin(self) -> Self;
Float::acos(self) -> Self;
Float::atan(self) -> Self;
Float::atan2(self, other: Self) -> Self;
Float::sin_cos(self) -> (Self, Self);
Float::exp_m1(self) -> Self;
Float::ln_1p(self) -> Self;
Float::sinh(self) -> Self;
Float::cosh(self) -> Self;
Float::tanh(self) -> Self;
Float::asinh(self) -> Self;
Float::acosh(self) -> Self;
Float::atanh(self) -> Self;
}
}

225
src/sign.rs
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use core::num::Wrapping;
use core::ops::Neg;
use float::FloatCore;
use Num;
/// Useful functions for signed numbers (i.e. numbers that can be negative).
pub trait Signed: Sized + Num + Neg<Output = Self> {
/// Computes the absolute value.
///
/// For `f32` and `f64`, `NaN` will be returned if the number is `NaN`.
///
/// For signed integers, `::MIN` will be returned if the number is `::MIN`.
fn abs(&self) -> Self;
/// The positive difference of two numbers.
///
/// Returns `zero` if the number is less than or equal to `other`, otherwise the difference
/// between `self` and `other` is returned.
fn abs_sub(&self, other: &Self) -> Self;
/// Returns the sign of the number.
///
/// For `f32` and `f64`:
///
/// * `1.0` if the number is positive, `+0.0` or `INFINITY`
/// * `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
/// * `NaN` if the number is `NaN`
///
/// For signed integers:
///
/// * `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 the number is positive and false if the number is zero or negative.
fn is_positive(&self) -> bool;
/// Returns true if the number is negative and false if the number is zero or positive.
fn is_negative(&self) -> bool;
}
macro_rules! signed_impl {
($($t:ty)*) => ($(
impl Signed for $t {
#[inline]
fn abs(&self) -> $t {
if self.is_negative() { -*self } else { *self }
}
#[inline]
fn abs_sub(&self, other: &$t) -> $t {
if *self <= *other { 0 } else { *self - *other }
}
#[inline]
fn signum(&self) -> $t {
match *self {
n if n > 0 => 1,
0 => 0,
_ => -1,
}
}
#[inline]
fn is_positive(&self) -> bool { *self > 0 }
#[inline]
fn is_negative(&self) -> bool { *self < 0 }
}
)*)
}
signed_impl!(isize i8 i16 i32 i64);
#[cfg(has_i128)]
signed_impl!(i128);
impl<T: Signed> Signed for Wrapping<T>
where
Wrapping<T>: Num + Neg<Output = Wrapping<T>>,
{
#[inline]
fn abs(&self) -> Self {
Wrapping(self.0.abs())
}
#[inline]
fn abs_sub(&self, other: &Self) -> Self {
Wrapping(self.0.abs_sub(&other.0))
}
#[inline]
fn signum(&self) -> Self {
Wrapping(self.0.signum())
}
#[inline]
fn is_positive(&self) -> bool {
self.0.is_positive()
}
#[inline]
fn is_negative(&self) -> bool {
self.0.is_negative()
}
}
macro_rules! signed_float_impl {
($t:ty) => {
impl Signed for $t {
/// Computes the absolute value. Returns `NAN` if the number is `NAN`.
#[inline]
fn abs(&self) -> $t {
FloatCore::abs(*self)
}
/// The positive difference of two numbers. Returns `0.0` if the number is
/// less than or equal to `other`, otherwise the difference between`self`
/// and `other` is returned.
#[inline]
fn abs_sub(&self, other: &$t) -> $t {
if *self <= *other {
0.
} else {
*self - *other
}
}
/// # Returns
///
/// - `1.0` if the number is positive, `+0.0` or `INFINITY`
/// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
/// - `NAN` if the number is NaN
#[inline]
fn signum(&self) -> $t {
FloatCore::signum(*self)
}
/// Returns `true` if the number is positive, including `+0.0` and `INFINITY`
#[inline]
fn is_positive(&self) -> bool {
FloatCore::is_sign_positive(*self)
}
/// Returns `true` if the number is negative, including `-0.0` and `NEG_INFINITY`
#[inline]
fn is_negative(&self) -> bool {
FloatCore::is_sign_negative(*self)
}
}
};
}
signed_float_impl!(f32);
signed_float_impl!(f64);
/// Computes the absolute value.
///
/// For `f32` and `f64`, `NaN` will be returned if the number is `NaN`
///
/// For signed integers, `::MIN` will be returned if the number is `::MIN`.
#[inline(always)]
pub fn abs<T: Signed>(value: T) -> T {
value.abs()
}
/// The positive difference of two numbers.
///
/// Returns zero if `x` is less than or equal to `y`, otherwise the difference
/// between `x` and `y` is returned.
#[inline(always)]
pub fn abs_sub<T: Signed>(x: T, y: T) -> T {
x.abs_sub(&y)
}
/// Returns the sign of the number.
///
/// For `f32` and `f64`:
///
/// * `1.0` if the number is positive, `+0.0` or `INFINITY`
/// * `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
/// * `NaN` if the number is `NaN`
///
/// For signed integers:
///
/// * `0` if the number is zero
/// * `1` if the number is positive
/// * `-1` if the number is negative
#[inline(always)]
pub fn signum<T: Signed>(value: T) -> T {
value.signum()
}
/// A trait for values which cannot be negative
pub trait Unsigned: Num {}
macro_rules! empty_trait_impl {
($name:ident for $($t:ty)*) => ($(
impl $name for $t {}
)*)
}
empty_trait_impl!(Unsigned for usize u8 u16 u32 u64);
#[cfg(has_i128)]
empty_trait_impl!(Unsigned for u128);
impl<T: Unsigned> Unsigned for Wrapping<T> where Wrapping<T>: Num {}
#[test]
fn unsigned_wrapping_is_unsigned() {
fn require_unsigned<T: Unsigned>(_: &T) {}
require_unsigned(&Wrapping(42_u32));
}
/*
// Commenting this out since it doesn't compile on Rust 1.8,
// because on this version Wrapping doesn't implement Neg and therefore can't
// implement Signed.
#[test]
fn signed_wrapping_is_signed() {
fn require_signed<T: Signed>(_: &T) {}
require_signed(&Wrapping(-42));
}
*/

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//! Tests of `num_traits::cast`.
#![no_std]
#[cfg(feature = "std")]
#[macro_use]
extern crate std;
extern crate num_traits;
use num_traits::cast::*;
use num_traits::Bounded;
use core::{f32, f64};
#[cfg(has_i128)]
use core::{i128, u128};
use core::{i16, i32, i64, i8, isize};
use core::{u16, u32, u64, u8, usize};
use core::fmt::Debug;
use core::mem;
use core::num::Wrapping;
#[test]
fn to_primitive_float() {
let f32_toolarge = 1e39f64;
assert_eq!(f32_toolarge.to_f32(), None);
assert_eq!((f32::MAX as f64).to_f32(), Some(f32::MAX));
assert_eq!((-f32::MAX as f64).to_f32(), Some(-f32::MAX));
assert_eq!(f64::INFINITY.to_f32(), Some(f32::INFINITY));
assert_eq!((f64::NEG_INFINITY).to_f32(), Some(f32::NEG_INFINITY));
assert!((f64::NAN).to_f32().map_or(false, |f| f.is_nan()));
}
#[test]
fn wrapping_to_primitive() {
macro_rules! test_wrapping_to_primitive {
($($t:ty)+) => {
$({
let i: $t = 0;
let w = Wrapping(i);
assert_eq!(i.to_u8(), w.to_u8());
assert_eq!(i.to_u16(), w.to_u16());
assert_eq!(i.to_u32(), w.to_u32());
assert_eq!(i.to_u64(), w.to_u64());
assert_eq!(i.to_usize(), w.to_usize());
assert_eq!(i.to_i8(), w.to_i8());
assert_eq!(i.to_i16(), w.to_i16());
assert_eq!(i.to_i32(), w.to_i32());
assert_eq!(i.to_i64(), w.to_i64());
assert_eq!(i.to_isize(), w.to_isize());
assert_eq!(i.to_f32(), w.to_f32());
assert_eq!(i.to_f64(), w.to_f64());
})+
};
}
test_wrapping_to_primitive!(usize u8 u16 u32 u64 isize i8 i16 i32 i64);
}
#[test]
fn wrapping_is_toprimitive() {
fn require_toprimitive<T: ToPrimitive>(_: &T) {}
require_toprimitive(&Wrapping(42));
}
#[test]
fn wrapping_is_fromprimitive() {
fn require_fromprimitive<T: FromPrimitive>(_: &T) {}
require_fromprimitive(&Wrapping(42));
}
#[test]
fn wrapping_is_numcast() {
fn require_numcast<T: NumCast>(_: &T) {}
require_numcast(&Wrapping(42));
}
#[test]
fn as_primitive() {
let x: f32 = (1.625f64).as_();
assert_eq!(x, 1.625f32);
let x: f32 = (3.14159265358979323846f64).as_();
assert_eq!(x, 3.1415927f32);
let x: u8 = (768i16).as_();
assert_eq!(x, 0);
}
#[test]
fn float_to_integer_checks_overflow() {
// This will overflow an i32
let source: f64 = 1.0e+123f64;
// Expect the overflow to be caught
assert_eq!(cast::<f64, i32>(source), None);
}
#[test]
fn cast_to_int_checks_overflow() {
let big_f: f64 = 1.0e123;
let normal_f: f64 = 1.0;
let small_f: f64 = -1.0e123;
assert_eq!(None, cast::<f64, isize>(big_f));
assert_eq!(None, cast::<f64, i8>(big_f));
assert_eq!(None, cast::<f64, i16>(big_f));
assert_eq!(None, cast::<f64, i32>(big_f));
assert_eq!(None, cast::<f64, i64>(big_f));
assert_eq!(Some(normal_f as isize), cast::<f64, isize>(normal_f));
assert_eq!(Some(normal_f as i8), cast::<f64, i8>(normal_f));
assert_eq!(Some(normal_f as i16), cast::<f64, i16>(normal_f));
assert_eq!(Some(normal_f as i32), cast::<f64, i32>(normal_f));
assert_eq!(Some(normal_f as i64), cast::<f64, i64>(normal_f));
assert_eq!(None, cast::<f64, isize>(small_f));
assert_eq!(None, cast::<f64, i8>(small_f));
assert_eq!(None, cast::<f64, i16>(small_f));
assert_eq!(None, cast::<f64, i32>(small_f));
assert_eq!(None, cast::<f64, i64>(small_f));
}
#[test]
fn cast_to_unsigned_int_checks_overflow() {
let big_f: f64 = 1.0e123;
let normal_f: f64 = 1.0;
let small_f: f64 = -1.0e123;
assert_eq!(None, cast::<f64, usize>(big_f));
assert_eq!(None, cast::<f64, u8>(big_f));
assert_eq!(None, cast::<f64, u16>(big_f));
assert_eq!(None, cast::<f64, u32>(big_f));
assert_eq!(None, cast::<f64, u64>(big_f));
assert_eq!(Some(normal_f as usize), cast::<f64, usize>(normal_f));
assert_eq!(Some(normal_f as u8), cast::<f64, u8>(normal_f));
assert_eq!(Some(normal_f as u16), cast::<f64, u16>(normal_f));
assert_eq!(Some(normal_f as u32), cast::<f64, u32>(normal_f));
assert_eq!(Some(normal_f as u64), cast::<f64, u64>(normal_f));
assert_eq!(None, cast::<f64, usize>(small_f));
assert_eq!(None, cast::<f64, u8>(small_f));
assert_eq!(None, cast::<f64, u16>(small_f));
assert_eq!(None, cast::<f64, u32>(small_f));
assert_eq!(None, cast::<f64, u64>(small_f));
}
#[test]
#[cfg(has_i128)]
fn cast_to_i128_checks_overflow() {
let big_f: f64 = 1.0e123;
let normal_f: f64 = 1.0;
let small_f: f64 = -1.0e123;
assert_eq!(None, cast::<f64, i128>(big_f));
assert_eq!(None, cast::<f64, u128>(big_f));
assert_eq!(Some(normal_f as i128), cast::<f64, i128>(normal_f));
assert_eq!(Some(normal_f as u128), cast::<f64, u128>(normal_f));
assert_eq!(None, cast::<f64, i128>(small_f));
assert_eq!(None, cast::<f64, u128>(small_f));
}
#[cfg(feature = "std")]
fn dbg(args: ::core::fmt::Arguments) {
println!("{}", args);
}
#[cfg(not(feature = "std"))]
fn dbg(_: ::core::fmt::Arguments) {}
// Rust 1.8 doesn't handle cfg on macros correctly
macro_rules! dbg { ($($tok:tt)*) => { dbg(format_args!($($tok)*)) } }
macro_rules! float_test_edge {
($f:ident -> $($t:ident)+) => { $({
dbg!("testing cast edge cases for {} -> {}", stringify!($f), stringify!($t));
let small = if $t::MIN == 0 || mem::size_of::<$t>() < mem::size_of::<$f>() {
$t::MIN as $f - 1.0
} else {
($t::MIN as $f).raw_offset(1).floor()
};
let fmin = small.raw_offset(-1);
dbg!(" testing min {}\n\tvs. {:.0}\n\tand {:.0}", $t::MIN, fmin, small);
assert_eq!(Some($t::MIN), cast::<$f, $t>($t::MIN as $f));
assert_eq!(Some($t::MIN), cast::<$f, $t>(fmin));
assert_eq!(None, cast::<$f, $t>(small));
let (max, large) = if mem::size_of::<$t>() < mem::size_of::<$f>() {
($t::MAX, $t::MAX as $f + 1.0)
} else {
let large = $t::MAX as $f; // rounds up!
let max = large.raw_offset(-1) as $t; // the next smallest possible
assert_eq!(max.count_ones(), $f::MANTISSA_DIGITS);
(max, large)
};
let fmax = large.raw_offset(-1);
dbg!(" testing max {}\n\tvs. {:.0}\n\tand {:.0}", max, fmax, large);
assert_eq!(Some(max), cast::<$f, $t>(max as $f));
assert_eq!(Some(max), cast::<$f, $t>(fmax));
assert_eq!(None, cast::<$f, $t>(large));
dbg!(" testing non-finite values");
assert_eq!(None, cast::<$f, $t>($f::NAN));
assert_eq!(None, cast::<$f, $t>($f::INFINITY));
assert_eq!(None, cast::<$f, $t>($f::NEG_INFINITY));
})+}
}
trait RawOffset: Sized {
type Raw;
fn raw_offset(self, offset: Self::Raw) -> Self;
}
impl RawOffset for f32 {
type Raw = i32;
fn raw_offset(self, offset: Self::Raw) -> Self {
unsafe {
let raw: Self::Raw = mem::transmute(self);
mem::transmute(raw + offset)
}
}
}
impl RawOffset for f64 {
type Raw = i64;
fn raw_offset(self, offset: Self::Raw) -> Self {
unsafe {
let raw: Self::Raw = mem::transmute(self);
mem::transmute(raw + offset)
}
}
}
#[test]
fn cast_float_to_int_edge_cases() {
float_test_edge!(f32 -> isize i8 i16 i32 i64);
float_test_edge!(f32 -> usize u8 u16 u32 u64);
float_test_edge!(f64 -> isize i8 i16 i32 i64);
float_test_edge!(f64 -> usize u8 u16 u32 u64);
}
#[test]
#[cfg(has_i128)]
fn cast_float_to_i128_edge_cases() {
float_test_edge!(f32 -> i128 u128);
float_test_edge!(f64 -> i128 u128);
}
macro_rules! int_test_edge {
($f:ident -> { $($t:ident)+ } with $BigS:ident $BigU:ident ) => { $({
fn test_edge() {
dbg!("testing cast edge cases for {} -> {}", stringify!($f), stringify!($t));
match ($f::MIN as $BigS).cmp(&($t::MIN as $BigS)) {
Greater => {
assert_eq!(Some($f::MIN as $t), cast::<$f, $t>($f::MIN));
}
Equal => {
assert_eq!(Some($t::MIN), cast::<$f, $t>($f::MIN));
}
Less => {
let min = $t::MIN as $f;
assert_eq!(Some($t::MIN), cast::<$f, $t>(min));
assert_eq!(None, cast::<$f, $t>(min - 1));
}
}
match ($f::MAX as $BigU).cmp(&($t::MAX as $BigU)) {
Greater => {
let max = $t::MAX as $f;
assert_eq!(Some($t::MAX), cast::<$f, $t>(max));
assert_eq!(None, cast::<$f, $t>(max + 1));
}
Equal => {
assert_eq!(Some($t::MAX), cast::<$f, $t>($f::MAX));
}
Less => {
assert_eq!(Some($f::MAX as $t), cast::<$f, $t>($f::MAX));
}
}
}
test_edge();
})+}
}
#[test]
fn cast_int_to_int_edge_cases() {
use core::cmp::Ordering::*;
macro_rules! test_edge {
($( $from:ident )+) => { $({
int_test_edge!($from -> { isize i8 i16 i32 i64 } with i64 u64);
int_test_edge!($from -> { usize u8 u16 u32 u64 } with i64 u64);
})+}
}
test_edge!(isize i8 i16 i32 i64);
test_edge!(usize u8 u16 u32 u64);
}
#[test]
#[cfg(has_i128)]
fn cast_int_to_128_edge_cases() {
use core::cmp::Ordering::*;
macro_rules! test_edge {
($( $t:ident )+) => {
$(
int_test_edge!($t -> { i128 u128 } with i128 u128);
)+
int_test_edge!(i128 -> { $( $t )+ } with i128 u128);
int_test_edge!(u128 -> { $( $t )+ } with i128 u128);
}
}
test_edge!(isize i8 i16 i32 i64 i128);
test_edge!(usize u8 u16 u32 u64 u128);
}
#[test]
fn newtype_from_primitive() {
#[derive(PartialEq, Debug)]
struct New<T>(T);
// minimal impl
impl<T: FromPrimitive> FromPrimitive for New<T> {
fn from_i64(n: i64) -> Option<Self> {
T::from_i64(n).map(New)
}
fn from_u64(n: u64) -> Option<Self> {
T::from_u64(n).map(New)
}
}
macro_rules! assert_eq_from {
($( $from:ident )+) => {$(
assert_eq!(T::$from(Bounded::min_value()).map(New),
New::<T>::$from(Bounded::min_value()));
assert_eq!(T::$from(Bounded::max_value()).map(New),
New::<T>::$from(Bounded::max_value()));
)+}
}
fn check<T: PartialEq + Debug + FromPrimitive>() {
assert_eq_from!(from_i8 from_i16 from_i32 from_i64 from_isize);
assert_eq_from!(from_u8 from_u16 from_u32 from_u64 from_usize);
assert_eq_from!(from_f32 from_f64);
}
macro_rules! check {
($( $ty:ty )+) => {$( check::<$ty>(); )+}
}
check!(i8 i16 i32 i64 isize);
check!(u8 u16 u32 u64 usize);
}
#[test]
fn newtype_to_primitive() {
#[derive(PartialEq, Debug)]
struct New<T>(T);
// minimal impl
impl<T: ToPrimitive> ToPrimitive for New<T> {
fn to_i64(&self) -> Option<i64> {
self.0.to_i64()
}
fn to_u64(&self) -> Option<u64> {
self.0.to_u64()
}
}
macro_rules! assert_eq_to {
($( $to:ident )+) => {$(
assert_eq!(T::$to(&Bounded::min_value()),
New::<T>::$to(&New(Bounded::min_value())));
assert_eq!(T::$to(&Bounded::max_value()),
New::<T>::$to(&New(Bounded::max_value())));
)+}
}
fn check<T: PartialEq + Debug + Bounded + ToPrimitive>() {
assert_eq_to!(to_i8 to_i16 to_i32 to_i64 to_isize);
assert_eq_to!(to_u8 to_u16 to_u32 to_u64 to_usize);
assert_eq_to!(to_f32 to_f64);
}
macro_rules! check {
($( $ty:ty )+) => {$( check::<$ty>(); )+}
}
check!(i8 i16 i32 i64 isize);
check!(u8 u16 u32 u64 usize);
}