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Move num-traits to its own repo 

All the prior `num` history is kept, so old `num-traits` tags are still
valid, but future development here will be just for `num-traits`.
This commit is contained in:
Josh Stone 2017-12-18 17:35:41 -08:00
parent f172ef3a6b
commit 42a610d323
68 changed files with 437 additions and 16108 deletions
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16
.travis.yml
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@ -1,25 +1,13 @@
language: rust
rust:
- 1.15.0
- 1.8.0
- stable
- beta
- nightly
matrix:
include:
- rust: 1.8.0
before_script:
# libc 0.2.34 started using #[deprecated]
- cargo generate-lockfile
- cargo update --package libc --precise 0.2.33
sudo: false
script:
- cargo build --verbose
- ./ci/test_full.sh
- cargo doc
after_success: |
[ $TRAVIS_BRANCH = master ] &&
[ $TRAVIS_PULL_REQUEST = false ] &&
[ $TRAVIS_RUST_VERSION = nightly ] &&
ssh-agent ./ci/deploy.sh
notifications:
email:
on_success: never

75
Cargo.toml
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@ -1,73 +1,14 @@
[package]
authors = ["The Rust Project Developers"]
description = "A collection of numeric types and traits for Rust, including bigint,\ncomplex, rational, range iterators, generic integers, and more!\n"
documentation = "http://rust-num.github.io/num"
homepage = "https://github.com/rust-num/num"
keywords = ["mathematics", "numerics", "bignum"]
categories = [ "algorithms", "data-structures", "science" ]
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" ]
license = "MIT/Apache-2.0"
repository = "https://github.com/rust-num/num"
name = "num"
repository = "https://github.com/rust-num/num-traits"
name = "num-traits"
version = "0.1.41"
[badges]
travis-ci = { repository = "rust-num/num" }
[[bench]]
name = "bigint"
[[bench]]
harness = false
name = "shootout-pidigits"
readme = "README.md"
[dependencies]
[dependencies.num-bigint]
optional = true
path = "bigint"
version = "0.1.41"
[dependencies.num-complex]
optional = true
path = "complex"
version = "0.1.41"
[dependencies.num-integer]
path = "./integer"
version = "0.1.35"
[dependencies.num-iter]
optional = false
path = "iter"
version = "0.1.34"
[dependencies.num-rational]
optional = true
path = "rational"
version = "0.1.40"
[dependencies.num-traits]
path = "./traits"
version = "0.1.41"
[dev-dependencies]
[dev-dependencies.rand]
version = "0.3.8"
[features]
bigint = ["num-bigint"]
complex = ["num-complex"]
rational = ["num-rational"]
default = ["bigint", "complex", "rational", "rustc-serialize"]
serde = [
"num-bigint/serde",
"num-complex/serde",
"num-rational/serde"
]
rustc-serialize = [
"num-bigint/rustc-serialize",
"num-complex/rustc-serialize",
"num-rational/rustc-serialize"
]

21
README.md
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@ -1,14 +1,10 @@
# num
# num-traits
[![](https://travis-ci.org/rust-num/num.svg)](https://travis-ci.org/rust-num/num)
[![crate](https://img.shields.io/crates/v/num-traits.svg)](https://crates.io/crates/num-traits)
[![documentation](https://docs.rs/num-traits/badge.svg)](https://docs.rs/num-traits)
[![Travis status](https://travis-ci.org/rust-num/num-traits.svg?branch=master)](https://travis-ci.org/rust-num/num-traits)
A collection of numeric types and traits for 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)
Numeric traits for generic mathematics in Rust.
## Usage
@ -16,16 +12,15 @@ Add this to your `Cargo.toml`:
```toml
[dependencies]
num = "0.1"
num-traits = "0.1"
```
and this to your crate root:
```rust
extern crate num;
extern crate num_traits;
```
## Compatibility
Most of the `num` crates are tested for rustc 1.8 and greater.
The exception is `num-derive` which requires at least rustc 1.15.
The `num-traits` crate is tested for rustc 1.8 and greater.

294
benches/bigint.rs
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@ -1,294 +0,0 @@
#![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, Num};
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
}
/// Compute Fibonacci numbers
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
}
/// Compute Fibonacci numbers with two ops per iteration
/// (add and subtract, like issue #200)
fn fib2(n: usize) -> BigUint {
let mut f0: BigUint = Zero::zero();
let mut f1: BigUint = One::one();
for _ in 0..n {
f1 = f1 + &f0;
f0 = &f1 - f0;
}
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 multiply_3(b: &mut Bencher) {
multiply_bench(b, 1 << 16, 1 << 17);
}
#[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 fib_1000(b: &mut Bencher) {
b.iter(|| fib(1000));
}
#[bench]
fn fib_10000(b: &mut Bencher) {
b.iter(|| fib(10000));
}
#[bench]
fn fib2_100(b: &mut Bencher) {
b.iter(|| fib2(100));
}
#[bench]
fn fib2_1000(b: &mut Bencher) {
b.iter(|| fib2(1000));
}
#[bench]
fn fib2_10000(b: &mut Bencher) {
b.iter(|| fib2(10000));
}
#[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);
}
}
});
}
/// This modulus is the prime from the 2048-bit MODP DH group:
/// https://tools.ietf.org/html/rfc3526#section-3
const RFC3526_2048BIT_MODP_GROUP: &'static str = "\
FFFFFFFF_FFFFFFFF_C90FDAA2_2168C234_C4C6628B_80DC1CD1\
29024E08_8A67CC74_020BBEA6_3B139B22_514A0879_8E3404DD\
EF9519B3_CD3A431B_302B0A6D_F25F1437_4FE1356D_6D51C245\
E485B576_625E7EC6_F44C42E9_A637ED6B_0BFF5CB6_F406B7ED\
EE386BFB_5A899FA5_AE9F2411_7C4B1FE6_49286651_ECE45B3D\
C2007CB8_A163BF05_98DA4836_1C55D39A_69163FA8_FD24CF5F\
83655D23_DCA3AD96_1C62F356_208552BB_9ED52907_7096966D\
670C354E_4ABC9804_F1746C08_CA18217C_32905E46_2E36CE3B\
E39E772C_180E8603_9B2783A2_EC07A28F_B5C55DF0_6F4C52C9\
DE2BCBF6_95581718_3995497C_EA956AE5_15D22618_98FA0510\
15728E5A_8AACAA68_FFFFFFFF_FFFFFFFF";
#[bench]
fn modpow(b: &mut Bencher) {
let mut rng = get_rng();
let base = rng.gen_biguint(2048);
let e = rng.gen_biguint(2048);
let m = BigUint::from_str_radix(RFC3526_2048BIT_MODP_GROUP, 16).unwrap();
b.iter(|| base.modpow(&e, &m));
}
#[bench]
fn modpow_even(b: &mut Bencher) {
let mut rng = get_rng();
let base = rng.gen_biguint(2048);
let e = rng.gen_biguint(2048);
// Make the modulus even, so monty (base-2^32) doesn't apply.
let m = BigUint::from_str_radix(RFC3526_2048BIT_MODP_GROUP, 16).unwrap() - 1u32;
b.iter(|| base.modpow(&e, &m));
}

131
benches/shootout-pidigits.rs
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@ -1,131 +0,0 @@
// 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();
}

39
bigint/Cargo.toml
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@ -1,39 +0,0 @@
[package]
authors = ["The Rust Project Developers"]
description = "Big integer implementation for Rust"
documentation = "http://rust-num.github.io/num"
homepage = "https://github.com/rust-num/num"
keywords = ["mathematics", "numerics", "bignum"]
categories = [ "algorithms", "data-structures", "science" ]
license = "MIT/Apache-2.0"
name = "num-bigint"
repository = "https://github.com/rust-num/num"
version = "0.1.41"
[dependencies]
[dependencies.num-integer]
path = "../integer"
version = "0.1.32"
[dependencies.num-traits]
path = "../traits"
version = "0.1.32"
[dependencies.rand]
optional = true
version = "0.3.14"
[dependencies.rustc-serialize]
optional = true
version = "0.3.19"
[dependencies.serde]
optional = true
version = ">= 0.7.0, < 0.9.0"
[dev-dependencies.rand]
version = "0.3.14"
[features]
default = ["rand", "rustc-serialize"]

201
bigint/LICENSE-APACHE
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@ -1,201 +0,0 @@
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25
bigint/LICENSE-MIT
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@ -1,25 +0,0 @@
Copyright (c) 2014 The Rust Project Developers
Permission is hereby granted, free of charge, to any
person obtaining a copy of this software and associated
documentation files (the "Software"), to deal in the
Software without restriction, including without
limitation the rights to use, copy, modify, merge,
publish, distribute, sublicense, and/or sell copies of
the Software, and to permit persons to whom the Software
is furnished to do so, subject to the following
conditions:
The above copyright notice and this permission notice
shall be included in all copies or substantial portions
of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF
ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED
TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A
PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT
SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR
IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
DEALINGS IN THE SOFTWARE.

658
bigint/src/algorithms.rs
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use std::borrow::Cow;
use std::cmp;
use std::cmp::Ordering::{self, Less, Greater, Equal};
use std::iter::repeat;
use std::mem;
use traits;
use traits::{Zero, One};
use biguint::BigUint;
use bigint::BigInt;
use bigint::Sign;
use bigint::Sign::{Minus, NoSign, Plus};
#[allow(non_snake_case)]
pub mod big_digit {
/// A `BigDigit` is a `BigUint`'s composing element.
pub type BigDigit = u32;
/// A `DoubleBigDigit` is the internal type used to do the computations. Its
/// size is the double of the size of `BigDigit`.
pub type DoubleBigDigit = u64;
pub const ZERO_BIG_DIGIT: BigDigit = 0;
// `DoubleBigDigit` size dependent
pub const BITS: usize = 32;
pub const BASE: DoubleBigDigit = 1 << BITS;
const LO_MASK: DoubleBigDigit = (-1i32 as DoubleBigDigit) >> BITS;
#[inline]
fn get_hi(n: DoubleBigDigit) -> BigDigit {
(n >> BITS) as BigDigit
}
#[inline]
fn get_lo(n: DoubleBigDigit) -> BigDigit {
(n & LO_MASK) as BigDigit
}
/// Split one `DoubleBigDigit` into two `BigDigit`s.
#[inline]
pub fn from_doublebigdigit(n: DoubleBigDigit) -> (BigDigit, BigDigit) {
(get_hi(n), get_lo(n))
}
/// Join two `BigDigit`s into one `DoubleBigDigit`
#[inline]
pub fn to_doublebigdigit(hi: BigDigit, lo: BigDigit) -> DoubleBigDigit {
(lo as DoubleBigDigit) | ((hi as DoubleBigDigit) << BITS)
}
}
use big_digit::{BigDigit, DoubleBigDigit};
// Generic functions for add/subtract/multiply with carry/borrow:
// Add with carry:
#[inline]
fn adc(a: BigDigit, b: BigDigit, carry: &mut BigDigit) -> BigDigit {
let (hi, lo) = big_digit::from_doublebigdigit((a as DoubleBigDigit) + (b as DoubleBigDigit) +
(*carry as DoubleBigDigit));
*carry = hi;
lo
}
// Subtract with borrow:
#[inline]
fn sbb(a: BigDigit, b: BigDigit, borrow: &mut BigDigit) -> BigDigit {
let (hi, lo) = big_digit::from_doublebigdigit(big_digit::BASE + (a as DoubleBigDigit) -
(b as DoubleBigDigit) -
(*borrow as DoubleBigDigit));
// hi * (base) + lo == 1*(base) + ai - bi - borrow
// => ai - bi - borrow < 0 <=> hi == 0
*borrow = (hi == 0) as BigDigit;
lo
}
#[inline]
pub fn mac_with_carry(a: BigDigit, b: BigDigit, c: BigDigit, carry: &mut BigDigit) -> BigDigit {
let (hi, lo) = big_digit::from_doublebigdigit((a as DoubleBigDigit) +
(b as DoubleBigDigit) * (c as DoubleBigDigit) +
(*carry as DoubleBigDigit));
*carry = hi;
lo
}
#[inline]
pub fn mul_with_carry(a: BigDigit, b: BigDigit, carry: &mut BigDigit) -> BigDigit {
let (hi, lo) = big_digit::from_doublebigdigit((a as DoubleBigDigit) * (b as DoubleBigDigit) +
(*carry as DoubleBigDigit));
*carry = hi;
lo
}
/// Divide a two digit numerator by a one digit divisor, returns quotient and remainder:
///
/// Note: the caller must ensure that both the quotient and remainder will fit into a single digit.
/// This is _not_ true for an arbitrary numerator/denominator.
///
/// (This function also matches what the x86 divide instruction does).
#[inline]
fn div_wide(hi: BigDigit, lo: BigDigit, divisor: BigDigit) -> (BigDigit, BigDigit) {
debug_assert!(hi < divisor);
let lhs = big_digit::to_doublebigdigit(hi, lo);
let rhs = divisor as DoubleBigDigit;
((lhs / rhs) as BigDigit, (lhs % rhs) as BigDigit)
}
pub fn div_rem_digit(mut a: BigUint, b: BigDigit) -> (BigUint, BigDigit) {
let mut rem = 0;
for d in a.data.iter_mut().rev() {
let (q, r) = div_wide(rem, *d, b);
*d = q;
rem = r;
}
(a.normalized(), rem)
}
// Only for the Add impl:
#[inline]
pub fn __add2(a: &mut [BigDigit], b: &[BigDigit]) -> BigDigit {
debug_assert!(a.len() >= b.len());
let mut carry = 0;
let (a_lo, a_hi) = a.split_at_mut(b.len());
for (a, b) in a_lo.iter_mut().zip(b) {
*a = adc(*a, *b, &mut carry);
}
if carry != 0 {
for a in a_hi {
*a = adc(*a, 0, &mut carry);
if carry == 0 { break }
}
}
carry
}
/// /Two argument addition of raw slices:
/// a += b
///
/// The caller _must_ ensure that a is big enough to store the result - typically this means
/// resizing a to max(a.len(), b.len()) + 1, to fit a possible carry.
pub fn add2(a: &mut [BigDigit], b: &[BigDigit]) {
let carry = __add2(a, b);
debug_assert!(carry == 0);
}
pub fn sub2(a: &mut [BigDigit], b: &[BigDigit]) {
let mut borrow = 0;
let len = cmp::min(a.len(), b.len());
let (a_lo, a_hi) = a.split_at_mut(len);
let (b_lo, b_hi) = b.split_at(len);
for (a, b) in a_lo.iter_mut().zip(b_lo) {
*a = sbb(*a, *b, &mut borrow);
}
if borrow != 0 {
for a in a_hi {
*a = sbb(*a, 0, &mut borrow);
if borrow == 0 { break }
}
}
// note: we're _required_ to fail on underflow
assert!(borrow == 0 && b_hi.iter().all(|x| *x == 0),
"Cannot subtract b from a because b is larger than a.");
}
pub fn sub2rev(a: &[BigDigit], b: &mut [BigDigit]) {
debug_assert!(b.len() >= a.len());
let mut borrow = 0;
let len = cmp::min(a.len(), b.len());
let (a_lo, a_hi) = a.split_at(len);
let (b_lo, b_hi) = b.split_at_mut(len);
for (a, b) in a_lo.iter().zip(b_lo) {
*b = sbb(*a, *b, &mut borrow);
}
assert!(a_hi.is_empty());
// note: we're _required_ to fail on underflow
assert!(borrow == 0 && b_hi.iter().all(|x| *x == 0),
"Cannot subtract b from a because b is larger than a.");
}
pub fn sub_sign(a: &[BigDigit], b: &[BigDigit]) -> (Sign, BigUint) {
// Normalize:
let a = &a[..a.iter().rposition(|&x| x != 0).map_or(0, |i| i + 1)];
let b = &b[..b.iter().rposition(|&x| x != 0).map_or(0, |i| i + 1)];
match cmp_slice(a, b) {
Greater => {
let mut a = a.to_vec();
sub2(&mut a, b);
(Plus, BigUint::new(a))
}
Less => {
let mut b = b.to_vec();
sub2(&mut b, a);
(Minus, BigUint::new(b))
}
_ => (NoSign, Zero::zero()),
}
}
/// Three argument multiply accumulate:
/// acc += b * c
pub fn mac_digit(acc: &mut [BigDigit], b: &[BigDigit], c: BigDigit) {
if c == 0 {
return;
}
let mut carry = 0;
let (a_lo, a_hi) = acc.split_at_mut(b.len());
for (a, &b) in a_lo.iter_mut().zip(b) {
*a = mac_with_carry(*a, b, c, &mut carry);
}
let mut a = a_hi.iter_mut();
while carry != 0 {
let a = a.next().expect("carry overflow during multiplication!");
*a = adc(*a, 0, &mut carry);
}
}
/// Three argument multiply accumulate:
/// acc += b * c
fn mac3(acc: &mut [BigDigit], b: &[BigDigit], c: &[BigDigit]) {
let (x, y) = if b.len() < c.len() {
(b, c)
} else {
(c, b)
};
// We use three algorithms for different input sizes.
//
// - For small inputs, long multiplication is fastest.
// - Next we use Karatsuba multiplication (Toom-2), which we have optimized
// to avoid unnecessary allocations for intermediate values.
// - For the largest inputs we use Toom-3, which better optimizes the
// number of operations, but uses more temporary allocations.
//
// The thresholds are somewhat arbitrary, chosen by evaluating the results
// of `cargo bench --bench bigint multiply`.
if x.len() <= 32 {
// Long multiplication:
for (i, xi) in x.iter().enumerate() {
mac_digit(&mut acc[i..], y, *xi);
}
} else if x.len() <= 256 {
/*
* Karatsuba multiplication:
*
* The idea is that we break x and y up into two smaller numbers that each have about half
* as many digits, like so (note that multiplying by b is just a shift):
*
* x = x0 + x1 * b
* y = y0 + y1 * b
*
* With some algebra, we can compute x * y with three smaller products, where the inputs to
* each of the smaller products have only about half as many digits as x and y:
*
* x * y = (x0 + x1 * b) * (y0 + y1 * b)
*
* x * y = x0 * y0
* + x0 * y1 * b
* + x1 * y0 * b
* + x1 * y1 * b^2
*
* Let p0 = x0 * y0 and p2 = x1 * y1:
*
* x * y = p0
* + (x0 * y1 + x1 * y0) * b
* + p2 * b^2
*
* The real trick is that middle term:
*
* x0 * y1 + x1 * y0
*
* = x0 * y1 + x1 * y0 - p0 + p0 - p2 + p2
*
* = x0 * y1 + x1 * y0 - x0 * y0 - x1 * y1 + p0 + p2
*
* Now we complete the square:
*
* = -(x0 * y0 - x0 * y1 - x1 * y0 + x1 * y1) + p0 + p2
*
* = -((x1 - x0) * (y1 - y0)) + p0 + p2
*
* Let p1 = (x1 - x0) * (y1 - y0), and substitute back into our original formula:
*
* x * y = p0
* + (p0 + p2 - p1) * b
* + p2 * b^2
*
* Where the three intermediate products are:
*
* p0 = x0 * y0
* p1 = (x1 - x0) * (y1 - y0)
* p2 = x1 * y1
*
* In doing the computation, we take great care to avoid unnecessary temporary variables
* (since creating a BigUint requires a heap allocation): thus, we rearrange the formula a
* bit so we can use the same temporary variable for all the intermediate products:
*
* x * y = p2 * b^2 + p2 * b
* + p0 * b + p0
* - p1 * b
*
* The other trick we use is instead of doing explicit shifts, we slice acc at the
* appropriate offset when doing the add.
*/
/*
* When x is smaller than y, it's significantly faster to pick b such that x is split in
* half, not y:
*/
let b = x.len() / 2;
let (x0, x1) = x.split_at(b);
let (y0, y1) = y.split_at(b);
/*
* We reuse the same BigUint for all the intermediate multiplies and have to size p
* appropriately here: x1.len() >= x0.len and y1.len() >= y0.len():
*/
let len = x1.len() + y1.len() + 1;
let mut p = BigUint { data: vec![0; len] };
// p2 = x1 * y1
mac3(&mut p.data[..], x1, y1);
// Not required, but the adds go faster if we drop any unneeded 0s from the end:
p.normalize();
add2(&mut acc[b..], &p.data[..]);
add2(&mut acc[b * 2..], &p.data[..]);
// Zero out p before the next multiply:
p.data.truncate(0);
p.data.extend(repeat(0).take(len));
// p0 = x0 * y0
mac3(&mut p.data[..], x0, y0);
p.normalize();
add2(&mut acc[..], &p.data[..]);
add2(&mut acc[b..], &p.data[..]);
// p1 = (x1 - x0) * (y1 - y0)
// We do this one last, since it may be negative and acc can't ever be negative:
let (j0_sign, j0) = sub_sign(x1, x0);
let (j1_sign, j1) = sub_sign(y1, y0);
match j0_sign * j1_sign {
Plus => {
p.data.truncate(0);
p.data.extend(repeat(0).take(len));
mac3(&mut p.data[..], &j0.data[..], &j1.data[..]);
p.normalize();
sub2(&mut acc[b..], &p.data[..]);
},
Minus => {
mac3(&mut acc[b..], &j0.data[..], &j1.data[..]);
},
NoSign => (),
}
} else {
// Toom-3 multiplication:
//
// Toom-3 is like Karatsuba above, but dividing the inputs into three parts.
// Both are instances of Toom-Cook, using `k=3` and `k=2` respectively.
//
// FIXME: It would be nice to have comments breaking down the operations below.
let i = y.len()/3 + 1;
let x0_len = cmp::min(x.len(), i);
let x1_len = cmp::min(x.len() - x0_len, i);
let y0_len = i;
let y1_len = cmp::min(y.len() - y0_len, i);
let x0 = BigInt::from_slice(Plus, &x[..x0_len]);
let x1 = BigInt::from_slice(Plus, &x[x0_len..x0_len + x1_len]);
let x2 = BigInt::from_slice(Plus, &x[x0_len + x1_len..]);
let y0 = BigInt::from_slice(Plus, &y[..y0_len]);
let y1 = BigInt::from_slice(Plus, &y[y0_len..y0_len + y1_len]);
let y2 = BigInt::from_slice(Plus, &y[y0_len + y1_len..]);
let p = &x0 + &x2;
let q = &y0 + &y2;
let p2 = &p - &x1;
let q2 = &q - &y1;
let r0 = &x0 * &y0;
let r4 = &x2 * &y2;
let r1 = (p + x1) * (q + y1);
let r2 = &p2 * &q2;
let r3 = ((p2 + x2)*2 - x0) * ((q2 + y2)*2 - y0);
let mut comp3: BigInt = (r3 - &r1) / 3;
let mut comp1: BigInt = (r1 - &r2) / 2;
let mut comp2: BigInt = r2 - &r0;
comp3 = (&comp2 - comp3)/2 + &r4*2;
comp2 = comp2 + &comp1 - &r4;
comp1 = comp1 - &comp3;
let result = r0 + (comp1 << 32*i) + (comp2 << 2*32*i) + (comp3 << 3*32*i) + (r4 << 4*32*i);
let result_pos = result.to_biguint().unwrap();
add2(&mut acc[..], &result_pos.data);
}
}
pub fn mul3(x: &[BigDigit], y: &[BigDigit]) -> BigUint {
let len = x.len() + y.len() + 1;
let mut prod = BigUint { data: vec![0; len] };
mac3(&mut prod.data[..], x, y);
prod.normalized()
}
pub fn scalar_mul(a: &mut [BigDigit], b: BigDigit) -> BigDigit {
let mut carry = 0;
for a in a.iter_mut() {
*a = mul_with_carry(*a, b, &mut carry);
}
carry
}
pub fn div_rem(u: &BigUint, d: &BigUint) -> (BigUint, BigUint) {
if d.is_zero() {
panic!()
}
if u.is_zero() {
return (Zero::zero(), Zero::zero());
}
if *d == One::one() {
return (u.clone(), Zero::zero());
}
// Required or the q_len calculation below can underflow:
match u.cmp(d) {
Less => return (Zero::zero(), u.clone()),
Equal => return (One::one(), Zero::zero()),
Greater => {} // Do nothing
}
// This algorithm is from Knuth, TAOCP vol 2 section 4.3, algorithm D:
//
// First, normalize the arguments so the highest bit in the highest digit of the divisor is
// set: the main loop uses the highest digit of the divisor for generating guesses, so we
// want it to be the largest number we can efficiently divide by.
//
let shift = d.data.last().unwrap().leading_zeros() as usize;
let mut a = u << shift;
let b = d << shift;
// The algorithm works by incrementally calculating "guesses", q0, for part of the
// remainder. Once we have any number q0 such that q0 * b <= a, we can set
//
// q += q0
// a -= q0 * b
//
// and then iterate until a < b. Then, (q, a) will be our desired quotient and remainder.
//
// q0, our guess, is calculated by dividing the last few digits of a by the last digit of b
// - this should give us a guess that is "close" to the actual quotient, but is possibly
// greater than the actual quotient. If q0 * b > a, we simply use iterated subtraction
// until we have a guess such that q0 * b <= a.
//
let bn = *b.data.last().unwrap();
let q_len = a.data.len() - b.data.len() + 1;
let mut q = BigUint { data: vec![0; q_len] };
// We reuse the same temporary to avoid hitting the allocator in our inner loop - this is
// sized to hold a0 (in the common case; if a particular digit of the quotient is zero a0
// can be bigger).
//
let mut tmp = BigUint { data: Vec::with_capacity(2) };
for j in (0..q_len).rev() {
/*
* When calculating our next guess q0, we don't need to consider the digits below j
* + b.data.len() - 1: we're guessing digit j of the quotient (i.e. q0 << j) from
* digit bn of the divisor (i.e. bn << (b.data.len() - 1) - so the product of those
* two numbers will be zero in all digits up to (j + b.data.len() - 1).
*/
let offset = j + b.data.len() - 1;
if offset >= a.data.len() {
continue;
}
/* just avoiding a heap allocation: */
let mut a0 = tmp;
a0.data.truncate(0);
a0.data.extend(a.data[offset..].iter().cloned());
/*
* q0 << j * big_digit::BITS is our actual quotient estimate - we do the shifts
* implicitly at the end, when adding and subtracting to a and q. Not only do we
* save the cost of the shifts, the rest of the arithmetic gets to work with
* smaller numbers.
*/
let (mut q0, _) = div_rem_digit(a0, bn);
let mut prod = &b * &q0;
while cmp_slice(&prod.data[..], &a.data[j..]) == Greater {
let one: BigUint = One::one();
q0 = q0 - one;
prod = prod - &b;
}
add2(&mut q.data[j..], &q0.data[..]);
sub2(&mut a.data[j..], &prod.data[..]);
a.normalize();
tmp = q0;
}
debug_assert!(a < b);
(q.normalized(), a >> shift)
}
/// Find last set bit
/// fls(0) == 0, fls(u32::MAX) == 32
pub fn fls<T: traits::PrimInt>(v: T) -> usize {
mem::size_of::<T>() * 8 - v.leading_zeros() as usize
}
pub fn ilog2<T: traits::PrimInt>(v: T) -> usize {
fls(v) - 1
}
#[inline]
pub fn biguint_shl(n: Cow<BigUint>, bits: usize) -> BigUint {
let n_unit = bits / big_digit::BITS;
let mut data = match n_unit {
0 => n.into_owned().data,
_ => {
let len = n_unit + n.data.len() + 1;
let mut data = Vec::with_capacity(len);
data.extend(repeat(0).take(n_unit));
data.extend(n.data.iter().cloned());
data
}
};
let n_bits = bits % big_digit::BITS;
if n_bits > 0 {
let mut carry = 0;
for elem in data[n_unit..].iter_mut() {
let new_carry = *elem >> (big_digit::BITS - n_bits);
*elem = (*elem << n_bits) | carry;
carry = new_carry;
}
if carry != 0 {
data.push(carry);
}
}
BigUint::new(data)
}
#[inline]
pub fn biguint_shr(n: Cow<BigUint>, bits: usize) -> BigUint {
let n_unit = bits / big_digit::BITS;
if n_unit >= n.data.len() {
return Zero::zero();
}
let mut data = match n_unit {
0 => n.into_owned().data,
_ => n.data[n_unit..].to_vec(),
};
let n_bits = bits % big_digit::BITS;
if n_bits > 0 {
let mut borrow = 0;
for elem in data.iter_mut().rev() {
let new_borrow = *elem << (big_digit::BITS - n_bits);
*elem = (*elem >> n_bits) | borrow;
borrow = new_borrow;
}
}
BigUint::new(data)
}
pub fn cmp_slice(a: &[BigDigit], b: &[BigDigit]) -> Ordering {
debug_assert!(a.last() != Some(&0));
debug_assert!(b.last() != Some(&0));
let (a_len, b_len) = (a.len(), b.len());
if a_len < b_len {
return Less;
}
if a_len > b_len {
return Greater;
}
for (&ai, &bi) in a.iter().rev().zip(b.iter().rev()) {
if ai < bi {
return Less;
}
if ai > bi {
return Greater;
}
}
return Equal;
}
#[cfg(test)]
mod algorithm_tests {
use {BigDigit, BigUint, BigInt};
use Sign::Plus;
use traits::Num;
#[test]
fn test_sub_sign() {
use super::sub_sign;
fn sub_sign_i(a: &[BigDigit], b: &[BigDigit]) -> BigInt {
let (sign, val) = sub_sign(a, b);
BigInt::from_biguint(sign, val)
}
let a = BigUint::from_str_radix("265252859812191058636308480000000", 10).unwrap();
let b = BigUint::from_str_radix("26525285981219105863630848000000", 10).unwrap();
let a_i = BigInt::from_biguint(Plus, a.clone());
let b_i = BigInt::from_biguint(Plus, b.clone());
assert_eq!(sub_sign_i(&a.data[..], &b.data[..]), &a_i - &b_i);
assert_eq!(sub_sign_i(&b.data[..], &a.data[..]), &b_i - &a_i);
}
}

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bigint/src/lib.rs
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@ -1,154 +0,0 @@
// 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.
//! A Big integer (signed version: `BigInt`, unsigned version: `BigUint`).
//!
//! A `BigUint` is represented as a vector of `BigDigit`s.
//! A `BigInt` is a combination of `BigUint` and `Sign`.
//!
//! Common numerical operations are overloaded, so we can treat them
//! the same way we treat other numbers.
//!
//! ## Example
//!
//! ```rust
//! extern crate num_bigint;
//! extern crate num_traits;
//!
//! # fn main() {
//! use num_bigint::BigUint;
//! use num_traits::{Zero, One};
//! use std::mem::replace;
//!
//! // Calculate large fibonacci numbers.
//! 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;
//! // This is a low cost way of swapping f0 with f1 and f1 with f2.
//! f0 = replace(&mut f1, f2);
//! }
//! f0
//! }
//!
//! // This is a very large number.
//! println!("fib(1000) = {}", fib(1000));
//! # }
//! ```
//!
//! It's easy to generate large random numbers:
//!
//! ```rust
//! extern crate rand;
//! extern crate num_bigint as bigint;
//!
//! # #[cfg(feature = "rand")]
//! # fn main() {
//! use bigint::{ToBigInt, RandBigInt};
//!
//! let mut rng = rand::thread_rng();
//! let a = rng.gen_bigint(1000);
//!
//! let low = -10000.to_bigint().unwrap();
//! let high = 10000.to_bigint().unwrap();
//! let b = rng.gen_bigint_range(&low, &high);
//!
//! // Probably an even larger number.
//! println!("{}", a * b);
//! # }
//!
//! # #[cfg(not(feature = "rand"))]
//! # fn main() {
//! # }
//! ```
#![doc(html_logo_url = "https://rust-num.github.io/num/rust-logo-128x128-blk-v2.png",
html_favicon_url = "https://rust-num.github.io/num/favicon.ico",
html_root_url = "https://rust-num.github.io/num/",
html_playground_url = "http://play.integer32.com/")]
#[cfg(any(feature = "rand", test))]
extern crate rand;
#[cfg(feature = "rustc-serialize")]
extern crate rustc_serialize;
#[cfg(feature = "serde")]
extern crate serde;
extern crate num_integer as integer;
extern crate num_traits as traits;
use std::error::Error;
use std::num::ParseIntError;
use std::fmt;
#[cfg(target_pointer_width = "32")]
type UsizePromotion = u32;
#[cfg(target_pointer_width = "64")]
type UsizePromotion = u64;
#[cfg(target_pointer_width = "32")]
type IsizePromotion = i32;
#[cfg(target_pointer_width = "64")]
type IsizePromotion = i64;
#[derive(Debug, PartialEq)]
pub enum ParseBigIntError {
ParseInt(ParseIntError),
Other,
}
impl fmt::Display for ParseBigIntError {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
match self {
&ParseBigIntError::ParseInt(ref e) => e.fmt(f),
&ParseBigIntError::Other => "failed to parse provided string".fmt(f),
}
}
}
impl Error for ParseBigIntError {
fn description(&self) -> &str {
"failed to parse bigint/biguint"
}
}
impl From<ParseIntError> for ParseBigIntError {
fn from(err: ParseIntError) -> ParseBigIntError {
ParseBigIntError::ParseInt(err)
}
}
#[cfg(test)]
use std::hash;
#[cfg(test)]
fn hash<T: hash::Hash>(x: &T) -> u64 {
use std::hash::{BuildHasher, Hasher};
use std::collections::hash_map::RandomState;
let mut hasher = <RandomState as BuildHasher>::Hasher::new();
x.hash(&mut hasher);
hasher.finish()
}
#[macro_use]
mod macros;
mod biguint;
mod bigint;
pub use biguint::BigUint;
pub use biguint::ToBigUint;
pub use biguint::big_digit;
pub use biguint::big_digit::{BigDigit, DoubleBigDigit, ZERO_BIG_DIGIT};
pub use bigint::Sign;
pub use bigint::BigInt;
pub use bigint::ToBigInt;
pub use bigint::RandBigInt;

316
bigint/src/macros.rs
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@ -1,316 +0,0 @@
#![allow(unknown_lints)] // older rustc doesn't know `unused_macros`
#![allow(unused_macros)]
macro_rules! forward_val_val_binop {
(impl $imp:ident for $res:ty, $method:ident) => {
impl $imp<$res> for $res {
type Output = $res;
#[inline]
fn $method(self, other: $res) -> $res {
// forward to val-ref
$imp::$method(self, &other)
}
}
}
}
macro_rules! forward_val_val_binop_commutative {
(impl $imp:ident for $res:ty, $method:ident) => {
impl $imp<$res> for $res {
type Output = $res;
#[inline]
fn $method(self, other: $res) -> $res {
// forward to val-ref, with the larger capacity as val
if self.data.capacity() >= other.data.capacity() {
$imp::$method(self, &other)
} else {
$imp::$method(other, &self)
}
}
}
}
}
macro_rules! forward_ref_val_binop {
(impl $imp:ident for $res:ty, $method:ident) => {
impl<'a> $imp<$res> for &'a $res {
type Output = $res;
#[inline]
fn $method(self, other: $res) -> $res {
// forward to ref-ref
$imp::$method(self, &other)
}
}
}
}
macro_rules! forward_ref_val_binop_commutative {
(impl $imp:ident for $res:ty, $method:ident) => {
impl<'a> $imp<$res> for &'a $res {
type Output = $res;
#[inline]
fn $method(self, other: $res) -> $res {
// reverse, forward to val-ref
$imp::$method(other, self)
}
}
}
}
macro_rules! forward_val_ref_binop {
(impl $imp:ident for $res:ty, $method:ident) => {
impl<'a> $imp<&'a $res> for $res {
type Output = $res;
#[inline]
fn $method(self, other: &$res) -> $res {
// forward to ref-ref
$imp::$method(&self, other)
}
}
}
}
macro_rules! forward_ref_ref_binop {
(impl $imp:ident for $res:ty, $method:ident) => {
impl<'a, 'b> $imp<&'b $res> for &'a $res {
type Output = $res;
#[inline]
fn $method(self, other: &$res) -> $res {
// forward to val-ref
$imp::$method(self.clone(), other)
}
}
}
}
macro_rules! forward_ref_ref_binop_commutative {
(impl $imp:ident for $res:ty, $method:ident) => {
impl<'a, 'b> $imp<&'b $res> for &'a $res {
type Output = $res;
#[inline]
fn $method(self, other: &$res) -> $res {
// forward to val-ref, choosing the larger to clone
if self.data.len() >= other.data.len() {
$imp::$method(self.clone(), other)
} else {
$imp::$method(other.clone(), self)
}
}
}
}
}
macro_rules! forward_val_assign {
(impl $imp:ident for $res:ty, $method:ident) => {
impl $imp<$res> for $res {
#[inline]
fn $method(&mut self, other: $res) {
self.$method(&other);
}
}
}
}
macro_rules! forward_val_assign_scalar {
(impl $imp:ident for $res:ty, $scalar:ty, $method:ident) => {
impl $imp<$res> for $scalar {
#[inline]
fn $method(&mut self, other: $res) {
self.$method(&other);
}
}
}
}
macro_rules! forward_scalar_val_val_binop_commutative {
(impl $imp:ident<$scalar:ty> for $res:ty, $method: ident) => {
impl $imp<$res> for $scalar {
type Output = $res;
#[inline]
fn $method(self, other: $res) -> $res {
$imp::$method(other, self)
}
}
}
}
macro_rules! forward_scalar_val_ref_binop {
(impl $imp:ident<$scalar:ty> for $res:ty, $method:ident) => {
impl<'a> $imp<&'a $scalar> for $res {
type Output = $res;
#[inline]
fn $method(self, other: &$scalar) -> $res {
$imp::$method(self, *other)
}
}
impl<'a> $imp<$res> for &'a $scalar {
type Output = $res;
#[inline]
fn $method(self, other: $res) -> $res {
$imp::$method(*self, other)
}
}
}
}
macro_rules! forward_scalar_ref_val_binop {
(impl $imp:ident<$scalar:ty> for $res:ty, $method:ident) => {
impl<'a> $imp<$scalar> for &'a $res {
type Output = $res;
#[inline]
fn $method(self, other: $scalar) -> $res {
$imp::$method(self.clone(), other)
}
}
impl<'a> $imp<&'a $res> for $scalar {
type Output = $res;
#[inline]
fn $method(self, other: &$res) -> $res {
$imp::$method(self, other.clone())
}
}
}
}
macro_rules! forward_scalar_ref_ref_binop {
(impl $imp:ident<$scalar:ty> for $res:ty, $method:ident) => {
impl<'a, 'b> $imp<&'b $scalar> for &'a $res {
type Output = $res;
#[inline]
fn $method(self, other: &$scalar) -> $res {
$imp::$method(self.clone(), *other)
}
}
impl<'a, 'b> $imp<&'a $res> for &'b $scalar {
type Output = $res;
#[inline]
fn $method(self, other: &$res) -> $res {
$imp::$method(*self, other.clone())
}
}
}
}
macro_rules! promote_scalars {
(impl $imp:ident<$promo:ty> for $res:ty, $method:ident, $( $scalar:ty ),*) => {
$(
forward_all_scalar_binop_to_val_val!(impl $imp<$scalar> for $res, $method);
impl $imp<$scalar> for $res {
type Output = $res;
#[inline]
fn $method(self, other: $scalar) -> $res {
$imp::$method(self, other as $promo)
}
}
impl $imp<$res> for $scalar {
type Output = $res;
#[inline]
fn $method(self, other: $res) -> $res {
$imp::$method(self as $promo, other)
}
}
)*
}
}
macro_rules! promote_scalars_assign {
(impl $imp:ident<$promo:ty> for $res:ty, $method:ident, $( $scalar:ty ),*) => {
$(
impl $imp<$scalar> for $res {
#[inline]
fn $method(&mut self, other: $scalar) {
self.$method(other as $promo);
}
}
)*
}
}
macro_rules! promote_unsigned_scalars {
(impl $imp:ident for $res:ty, $method:ident) => {
promote_scalars!(impl $imp<u32> for $res, $method, u8, u16);
promote_scalars!(impl $imp<UsizePromotion> for $res, $method, usize);
}
}
macro_rules! promote_unsigned_scalars_assign {
(impl $imp:ident for $res:ty, $method:ident) => {
promote_scalars_assign!(impl $imp<u32> for $res, $method, u8, u16);
promote_scalars_assign!(impl $imp<UsizePromotion> for $res, $method, usize);
}
}
macro_rules! promote_signed_scalars {
(impl $imp:ident for $res:ty, $method:ident) => {
promote_scalars!(impl $imp<i32> for $res, $method, i8, i16);
promote_scalars!(impl $imp<IsizePromotion> for $res, $method, isize);
}
}
// Forward everything to ref-ref, when reusing storage is not helpful
macro_rules! forward_all_binop_to_ref_ref {
(impl $imp:ident for $res:ty, $method:ident) => {
forward_val_val_binop!(impl $imp for $res, $method);
forward_val_ref_binop!(impl $imp for $res, $method);
forward_ref_val_binop!(impl $imp for $res, $method);
};
}
// Forward everything to val-ref, so LHS storage can be reused
macro_rules! forward_all_binop_to_val_ref {
(impl $imp:ident for $res:ty, $method:ident) => {
forward_val_val_binop!(impl $imp for $res, $method);
forward_ref_val_binop!(impl $imp for $res, $method);
forward_ref_ref_binop!(impl $imp for $res, $method);
};
}
// Forward everything to val-ref, commutatively, so either LHS or RHS storage can be reused
macro_rules! forward_all_binop_to_val_ref_commutative {
(impl $imp:ident for $res:ty, $method:ident) => {
forward_val_val_binop_commutative!(impl $imp for $res, $method);
forward_ref_val_binop_commutative!(impl $imp for $res, $method);
forward_ref_ref_binop_commutative!(impl $imp for $res, $method);
};
}
macro_rules! forward_all_scalar_binop_to_val_val {
(impl $imp:ident<$scalar:ty> for $res:ty, $method:ident) => {
forward_scalar_val_ref_binop!(impl $imp<$scalar> for $res, $method);
forward_scalar_ref_val_binop!(impl $imp<$scalar> for $res, $method);
forward_scalar_ref_ref_binop!(impl $imp<$scalar> for $res, $method);
}
}
macro_rules! forward_all_scalar_binop_to_val_val_commutative {
(impl $imp:ident<$scalar:ty> for $res:ty, $method:ident) => {
forward_scalar_val_val_binop_commutative!(impl $imp<$scalar> for $res, $method);
forward_all_scalar_binop_to_val_val!(impl $imp<$scalar> for $res, $method);
}
}
macro_rules! promote_all_scalars {
(impl $imp:ident for $res:ty, $method:ident) => {
promote_unsigned_scalars!(impl $imp for $res, $method);
promote_signed_scalars!(impl $imp for $res, $method);
}
}

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bigint/src/monty.rs
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@ -1,127 +0,0 @@
use integer::Integer;
use traits::Zero;
use biguint::BigUint;
struct MontyReducer<'a> {
n: &'a BigUint,
n0inv: u32
}
// Calculate the modular inverse of `num`, using Extended GCD.
//
// Reference:
// Brent & Zimmermann, Modern Computer Arithmetic, v0.5.9, Algorithm 1.20
fn inv_mod_u32(num: u32) -> u32 {
// num needs to be relatively prime to 2**32 -- i.e. it must be odd.
assert!(num % 2 != 0);
let mut a: i64 = num as i64;
let mut b: i64 = (u32::max_value() as i64) + 1;
// ExtendedGcd
// Input: positive integers a and b
// Output: integers (g, u, v) such that g = gcd(a, b) = ua + vb
// As we don't need v for modular inverse, we don't calculate it.
// 1: (u, w) <- (1, 0)
let mut u = 1;
let mut w = 0;
// 3: while b != 0
while b != 0 {
// 4: (q, r) <- DivRem(a, b)
let q = a / b;
let r = a % b;
// 5: (a, b) <- (b, r)
a = b; b = r;
// 6: (u, w) <- (w, u - qw)
let m = u - w*q;
u = w; w = m;
}
assert!(a == 1);
// Downcasting acts like a mod 2^32 too.
u as u32
}
impl<'a> MontyReducer<'a> {
fn new(n: &'a BigUint) -> Self {
let n0inv = inv_mod_u32(n.data[0]);
MontyReducer { n: n, n0inv: n0inv }
}
}
// Montgomery Reduction
//
// Reference:
// Brent & Zimmermann, Modern Computer Arithmetic, v0.5.9, Algorithm 2.6
fn monty_redc(a: BigUint, mr: &MontyReducer) -> BigUint {
let mut c = a.data;
let n = &mr.n.data;
let n_size = n.len();
// Allocate sufficient work space
c.resize(2 * n_size + 2, 0);
// β is the size of a word, in this case 32 bits. So "a mod β" is
// equivalent to masking a to 32 bits.
// mu <- -N^(-1) mod β
let mu = 0u32.wrapping_sub(mr.n0inv);
// 1: for i = 0 to (n-1)
for i in 0..n_size {
// 2: q_i <- mu*c_i mod β
let q_i = c[i].wrapping_mul(mu);
// 3: C <- C + q_i * N * β^i
super::algorithms::mac_digit(&mut c[i..], n, q_i);
}
// 4: R <- C * β^(-n)
// This is an n-word bitshift, equivalent to skipping n words.
let ret = BigUint::new(c[n_size..].to_vec());
// 5: if R >= β^n then return R-N else return R.
if &ret < mr.n {
ret
} else {
ret - mr.n
}
}
// Montgomery Multiplication
fn monty_mult(a: BigUint, b: &BigUint, mr: &MontyReducer) -> BigUint {
monty_redc(a * b, mr)
}
// Montgomery Squaring
fn monty_sqr(a: BigUint, mr: &MontyReducer) -> BigUint {
// TODO: Replace with an optimised squaring function
monty_redc(&a * &a, mr)
}
pub fn monty_modpow(a: &BigUint, exp: &BigUint, modulus: &BigUint) -> BigUint{
let mr = MontyReducer::new(modulus);
// Calculate the Montgomery parameter
let mut v = vec![0; modulus.data.len()];
v.push(1);
let r = BigUint::new(v);
// Map the base to the Montgomery domain
let mut apri = a * &r % modulus;
// Binary exponentiation
let mut ans = &r % modulus;
let mut e = exp.clone();
while !e.is_zero() {
if e.is_odd() {
ans = monty_mult(ans, &apri, &mr);
}
apri = monty_sqr(apri, &mr);
e = e >> 1;
}
// Map the result back to the residues domain
monty_redc(ans, &mr)
}

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1
ci/.gitignore vendored
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@ -1 +0,0 @@
/deploy

BIN
ci/deploy.enc
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12
ci/deploy.sh
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@ -1,12 +0,0 @@
#!/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 $encrypted_9e86330b283d_iv -in ./ci/deploy.enc -out ./ci/deploy -d
chmod 600 ./ci/deploy
ssh-add ./ci/deploy
git push -qf ssh://git@github.com/${TRAVIS_REPO_SLUG}.git gh-pages

10
ci/rustup.sh
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@ -1,18 +1,12 @@
#!/bin/sh
# Use rustup to locally run the same suite of tests as .travis.yml.
# (You should first install/update 1.8.0, 1.15.0, beta, and nightly.)
# (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 beta nightly; do
for TRAVIS_RUST_VERSION in 1.8.0 stable beta nightly; do
run="rustup run $TRAVIS_RUST_VERSION"
if [ "$TRAVIS_RUST_VERSION" = 1.8.0 ]; then
# libc 0.2.34 started using #[deprecated]
$run cargo generate-lockfile
$run cargo update --package libc --precise 0.2.33 || :
fi
$run cargo build --verbose
$run $PWD/ci/test_full.sh
$run cargo doc
done

49
ci/test_full.sh
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@ -2,49 +2,10 @@
set -ex
echo Testing num on rustc ${TRAVIS_RUST_VERSION}
echo Testing num-traits on rustc ${TRAVIS_RUST_VERSION}
# All of these packages should build and test everywhere.
for package in bigint complex integer iter rational traits; do
if [ "$TRAVIS_RUST_VERSION" = 1.8.0 ]; then
# libc 0.2.34 started using #[deprecated]
cargo generate-lockfile --manifest-path $package/Cargo.toml
cargo update --manifest-path $package/Cargo.toml --package libc --precise 0.2.33 || :
fi
cargo build --manifest-path $package/Cargo.toml
cargo test --manifest-path $package/Cargo.toml
done
# num-integer should build and test everywhere.
cargo build --verbose
cargo test --verbose
# They all should build with minimal features too
for package in bigint complex integer iter rational traits; do
cargo build --manifest-path $package/Cargo.toml --no-default-features
cargo test --manifest-path $package/Cargo.toml --no-default-features
done
# Each isolated feature should also work everywhere.
for feature in '' bigint rational complex; do
cargo build --verbose --no-default-features --features="$feature"
cargo test --verbose --no-default-features --features="$feature"
done
# Build test for the serde feature
cargo build --verbose --features "serde"
# Downgrade serde and build test the 0.7.0 channel as well
cargo update -p serde --precise 0.7.0
cargo build --verbose --features "serde"
if [ "$TRAVIS_RUST_VERSION" = 1.8.0 ]; then exit; fi
# num-derive should build on 1.15.0+
cargo build --verbose --manifest-path=derive/Cargo.toml
if [ "$TRAVIS_RUST_VERSION" != nightly ]; then exit; fi
# num-derive testing requires compiletest_rs, which requires nightly
cargo test --verbose --manifest-path=derive/Cargo.toml
# benchmarks only work on nightly
cargo bench --verbose
# We have no features to test...

30
complex/Cargo.toml
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@ -1,30 +0,0 @@
[package]
authors = ["The Rust Project Developers"]
description = "Complex numbers implementation for Rust"
documentation = "http://rust-num.github.io/num"
homepage = "https://github.com/rust-num/num"
keywords = ["mathematics", "numerics"]
categories = [ "algorithms", "data-structures", "science" ]
license = "MIT/Apache-2.0"
name = "num-complex"
repository = "https://github.com/rust-num/num"
version = "0.1.41"
[dependencies]
[dependencies.num-traits]
optional = false
path = "../traits"
version = "0.1.39"
[dependencies.rustc-serialize]
optional = true
version = "0.3.19"
[dependencies.serde]
optional = true
version = ">= 0.7.0, < 0.9.0"
[features]
default = ["rustc-serialize"]
unstable = []

201
complex/LICENSE-APACHE
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@ -1,201 +0,0 @@
Apache License
Version 2.0, January 2004
http://www.apache.org/licenses/
TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
1. Definitions.
"License" shall mean the terms and conditions for use, reproduction,
and distribution as defined by Sections 1 through 9 of this document.
"Licensor" shall mean the copyright owner or entity authorized by
the copyright owner that is granting the License.
"Legal Entity" shall mean the union of the acting entity and all
other entities that control, are controlled by, or are under common
control with that entity. For the purposes of this definition,
"control" means (i) the power, direct or indirect, to cause the
direction or management of such entity, whether by contract or
otherwise, or (ii) ownership of fifty percent (50%) or more of the
outstanding shares, or (iii) beneficial ownership of such entity.
"You" (or "Your") shall mean an individual or Legal Entity
exercising permissions granted by this License.
"Source" form shall mean the preferred form for making modifications,
including but not limited to software source code, documentation
source, and configuration files.
"Object" form shall mean any form resulting from mechanical
transformation or translation of a Source form, including but
not limited to compiled object code, generated documentation,
and conversions to other media types.
"Work" shall mean the work of authorship, whether in Source or
Object form, made available under the License, as indicated by a
copyright notice that is included in or attached to the work
(an example is provided in the Appendix below).
"Derivative Works" shall mean any work, whether in Source or Object
form, that is based on (or derived from) the Work and for which the
editorial revisions, annotations, elaborations, or other modifications
represent, as a whole, an original work of authorship. For the purposes
of this License, Derivative Works shall not include works that remain
separable from, or merely link (or bind by name) to the interfaces of,
the Work and Derivative Works thereof.
"Contribution" shall mean any work of authorship, including
the original version of the Work and any modifications or additions
to that Work or Derivative Works thereof, that is intentionally
submitted to Licensor for inclusion in the Work by the copyright owner
or by an individual or Legal Entity authorized to submit on behalf of
the copyright owner. For the purposes of this definition, "submitted"
means any form of electronic, verbal, or written communication sent
to the Licensor or its representatives, including but not limited to
communication on electronic mailing lists, source code control systems,
and issue tracking systems that are managed by, or on behalf of, the
Licensor for the purpose of discussing and improving the Work, but
excluding communication that is conspicuously marked or otherwise
designated in writing by the copyright owner as "Not a Contribution."
"Contributor" shall mean Licensor and any individual or Legal Entity
on behalf of whom a Contribution has been received by Licensor and
subsequently incorporated within the Work.
2. Grant of Copyright License. Subject to the terms and conditions of
this License, each Contributor hereby grants to You a perpetual,
worldwide, non-exclusive, no-charge, royalty-free, irrevocable
copyright license to reproduce, prepare Derivative Works of,
publicly display, publicly perform, sublicense, and distribute the
Work and such Derivative Works in Source or Object form.
3. Grant of Patent License. Subject to the terms and conditions of
this License, each Contributor hereby grants to You a perpetual,
worldwide, non-exclusive, no-charge, royalty-free, irrevocable
(except as stated in this section) patent license to make, have made,
use, offer to sell, sell, import, and otherwise transfer the Work,
where such license applies only to those patent claims licensable
by such Contributor that are necessarily infringed by their
Contribution(s) alone or by combination of their Contribution(s)
with the Work to which such Contribution(s) was submitted. If You
institute patent litigation against any entity (including a
cross-claim or counterclaim in a lawsuit) alleging that the Work
or a Contribution incorporated within the Work constitutes direct
or contributory patent infringement, then any patent licenses
granted to You under this License for that Work shall terminate
as of the date such litigation is filed.
4. Redistribution. You may reproduce and distribute copies of the
Work or Derivative Works thereof in any medium, with or without
modifications, and in Source or Object form, provided that You
meet the following conditions:
(a) You must give any other recipients of the Work or
Derivative Works a copy of this License; and
(b) You must cause any modified files to carry prominent notices
stating that You changed the files; and
(c) You must retain, in the Source form of any Derivative Works
that You distribute, all copyright, patent, trademark, and
attribution notices from the Source form of the Work,
excluding those notices that do not pertain to any part of
the Derivative Works; and
(d) If the Work includes a "NOTICE" text file as part of its
distribution, then any Derivative Works that You distribute must
include a readable copy of the attribution notices contained
within such NOTICE file, excluding those notices that do not
pertain to any part of the Derivative Works, in at least one
of the following places: within a NOTICE text file distributed
as part of the Derivative Works; within the Source form or
documentation, if provided along with the Derivative Works; or,
within a display generated by the Derivative Works, if and
wherever such third-party notices normally appear. The contents
of the NOTICE file are for informational purposes only and
do not modify the License. You may add Your own attribution
notices within Derivative Works that You distribute, alongside
or as an addendum to the NOTICE text from the Work, provided
that such additional attribution notices cannot be construed
as modifying the License.
You may add Your own copyright statement to Your modifications and
may provide additional or different license terms and conditions
for use, reproduction, or distribution of Your modifications, or
for any such Derivative Works as a whole, provided Your use,
reproduction, and distribution of the Work otherwise complies with
the conditions stated in this License.
5. Submission of Contributions. Unless You explicitly state otherwise,
any Contribution intentionally submitted for inclusion in the Work
by You to the Licensor shall be under the terms and conditions of
this License, without any additional terms or conditions.
Notwithstanding the above, nothing herein shall supersede or modify
the terms of any separate license agreement you may have executed
with Licensor regarding such Contributions.
6. Trademarks. This License does not grant permission to use the trade
names, trademarks, service marks, or product names of the Licensor,
except as required for reasonable and customary use in describing the
origin of the Work and reproducing the content of the NOTICE file.
7. Disclaimer of Warranty. Unless required by applicable law or
agreed to in writing, Licensor provides the Work (and each
Contributor provides its Contributions) on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or
implied, including, without limitation, any warranties or conditions
of TITLE, NON-INFRINGEMENT, MERCHANTABILITY, or FITNESS FOR A
PARTICULAR PURPOSE. You are solely responsible for determining the
appropriateness of using or redistributing the Work and assume any
risks associated with Your exercise of permissions under this License.
8. Limitation of Liability. In no event and under no legal theory,
whether in tort (including negligence), contract, or otherwise,
unless required by applicable law (such as deliberate and grossly
negligent acts) or agreed to in writing, shall any Contributor be
liable to You for damages, including any direct, indirect, special,
incidental, or consequential damages of any character arising as a
result of this License or out of the use or inability to use the
Work (including but not limited to damages for loss of goodwill,
work stoppage, computer failure or malfunction, or any and all
other commercial damages or losses), even if such Contributor
has been advised of the possibility of such damages.
9. Accepting Warranty or Additional Liability. While redistributing
the Work or Derivative Works thereof, You may choose to offer,
and charge a fee for, acceptance of support, warranty, indemnity,
or other liability obligations and/or rights consistent with this
License. However, in accepting such obligations, You may act only
on Your own behalf and on Your sole responsibility, not on behalf
of any other Contributor, and only if You agree to indemnify,
defend, and hold each Contributor harmless for any liability
incurred by, or claims asserted against, such Contributor by reason
of your accepting any such warranty or additional liability.
END OF TERMS AND CONDITIONS
APPENDIX: How to apply the Apache License to your work.
To apply the Apache License to your work, attach the following
boilerplate notice, with the fields enclosed by brackets "[]"
replaced with your own identifying information. (Don't include
the brackets!) The text should be enclosed in the appropriate
comment syntax for the file format. We also recommend that a
file or class name and description of purpose be included on the
same "printed page" as the copyright notice for easier
identification within third-party archives.
Copyright [yyyy] [name of copyright owner]
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.

25
complex/LICENSE-MIT
View File

@ -1,25 +0,0 @@
Copyright (c) 2014 The Rust Project Developers
Permission is hereby granted, free of charge, to any
person obtaining a copy of this software and associated
documentation files (the "Software"), to deal in the
Software without restriction, including without
limitation the rights to use, copy, modify, merge,
publish, distribute, sublicense, and/or sell copies of
the Software, and to permit persons to whom the Software
is furnished to do so, subject to the following
conditions:
The above copyright notice and this permission notice
shall be included in all copies or substantial portions
of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF
ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED
TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A
PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT
SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR
IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
DEALINGS IN THE SOFTWARE.

1899
complex/src/lib.rs
View File

File diff suppressed because it is too large Load Diff

27
derive/Cargo.toml
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@ -1,27 +0,0 @@
[package]
authors = ["The Rust Project Developers"]
description = "Numeric syntax extensions"
documentation = "http://rust-num.github.io/num"
homepage = "https://github.com/rust-num/num"
keywords = ["mathematics", "numerics"]
categories = [ "science" ]
license = "MIT/Apache-2.0"
name = "num-derive"
repository = "https://github.com/rust-num/num"
version = "0.1.41"
[dependencies]
quote = "0.1.3"
syn = "0.7.0"
[dev-dependencies]
compiletest_rs = "0.2.5"
[dev-dependencies.num]
path = ".."
version = "0.1"
[lib]
name = "num_derive"
proc-macro = true
test = false

201
derive/LICENSE-APACHE
View File

@ -1,201 +0,0 @@
Apache License
Version 2.0, January 2004
http://www.apache.org/licenses/
TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
1. Definitions.
"License" shall mean the terms and conditions for use, reproduction,
and distribution as defined by Sections 1 through 9 of this document.
"Licensor" shall mean the copyright owner or entity authorized by
the copyright owner that is granting the License.
"Legal Entity" shall mean the union of the acting entity and all
other entities that control, are controlled by, or are under common
control with that entity. For the purposes of this definition,
"control" means (i) the power, direct or indirect, to cause the
direction or management of such entity, whether by contract or
otherwise, or (ii) ownership of fifty percent (50%) or more of the
outstanding shares, or (iii) beneficial ownership of such entity.
"You" (or "Your") shall mean an individual or Legal Entity
exercising permissions granted by this License.
"Source" form shall mean the preferred form for making modifications,
including but not limited to software source code, documentation
source, and configuration files.
"Object" form shall mean any form resulting from mechanical
transformation or translation of a Source form, including but
not limited to compiled object code, generated documentation,
and conversions to other media types.
"Work" shall mean the work of authorship, whether in Source or
Object form, made available under the License, as indicated by a
copyright notice that is included in or attached to the work
(an example is provided in the Appendix below).
"Derivative Works" shall mean any work, whether in Source or Object
form, that is based on (or derived from) the Work and for which the
editorial revisions, annotations, elaborations, or other modifications
represent, as a whole, an original work of authorship. For the purposes
of this License, Derivative Works shall not include works that remain
separable from, or merely link (or bind by name) to the interfaces of,
the Work and Derivative Works thereof.
"Contribution" shall mean any work of authorship, including
the original version of the Work and any modifications or additions
to that Work or Derivative Works thereof, that is intentionally
submitted to Licensor for inclusion in the Work by the copyright owner
or by an individual or Legal Entity authorized to submit on behalf of
the copyright owner. For the purposes of this definition, "submitted"
means any form of electronic, verbal, or written communication sent
to the Licensor or its representatives, including but not limited to
communication on electronic mailing lists, source code control systems,
and issue tracking systems that are managed by, or on behalf of, the
Licensor for the purpose of discussing and improving the Work, but
excluding communication that is conspicuously marked or otherwise
designated in writing by the copyright owner as "Not a Contribution."
"Contributor" shall mean Licensor and any individual or Legal Entity
on behalf of whom a Contribution has been received by Licensor and
subsequently incorporated within the Work.
2. Grant of Copyright License. Subject to the terms and conditions of
this License, each Contributor hereby grants to You a perpetual,
worldwide, non-exclusive, no-charge, royalty-free, irrevocable
copyright license to reproduce, prepare Derivative Works of,
publicly display, publicly perform, sublicense, and distribute the
Work and such Derivative Works in Source or Object form.
3. Grant of Patent License. Subject to the terms and conditions of
this License, each Contributor hereby grants to You a perpetual,
worldwide, non-exclusive, no-charge, royalty-free, irrevocable
(except as stated in this section) patent license to make, have made,
use, offer to sell, sell, import, and otherwise transfer the Work,
where such license applies only to those patent claims licensable
by such Contributor that are necessarily infringed by their
Contribution(s) alone or by combination of their Contribution(s)
with the Work to which such Contribution(s) was submitted. If You
institute patent litigation against any entity (including a
cross-claim or counterclaim in a lawsuit) alleging that the Work
or a Contribution incorporated within the Work constitutes direct
or contributory patent infringement, then any patent licenses
granted to You under this License for that Work shall terminate
as of the date such litigation is filed.
4. Redistribution. You may reproduce and distribute copies of the
Work or Derivative Works thereof in any medium, with or without
modifications, and in Source or Object form, provided that You
meet the following conditions:
(a) You must give any other recipients of the Work or
Derivative Works a copy of this License; and
(b) You must cause any modified files to carry prominent notices
stating that You changed the files; and
(c) You must retain, in the Source form of any Derivative Works
that You distribute, all copyright, patent, trademark, and
attribution notices from the Source form of the Work,
excluding those notices that do not pertain to any part of
the Derivative Works; and
(d) If the Work includes a "NOTICE" text file as part of its
distribution, then any Derivative Works that You distribute must
include a readable copy of the attribution notices contained
within such NOTICE file, excluding those notices that do not
pertain to any part of the Derivative Works, in at least one
of the following places: within a NOTICE text file distributed
as part of the Derivative Works; within the Source form or
documentation, if provided along with the Derivative Works; or,
within a display generated by the Derivative Works, if and
wherever such third-party notices normally appear. The contents
of the NOTICE file are for informational purposes only and
do not modify the License. You may add Your own attribution
notices within Derivative Works that You distribute, alongside
or as an addendum to the NOTICE text from the Work, provided
that such additional attribution notices cannot be construed
as modifying the License.
You may add Your own copyright statement to Your modifications and
may provide additional or different license terms and conditions
for use, reproduction, or distribution of Your modifications, or
for any such Derivative Works as a whole, provided Your use,
reproduction, and distribution of the Work otherwise complies with
the conditions stated in this License.
5. Submission of Contributions. Unless You explicitly state otherwise,
any Contribution intentionally submitted for inclusion in the Work
by You to the Licensor shall be under the terms and conditions of
this License, without any additional terms or conditions.
Notwithstanding the above, nothing herein shall supersede or modify
the terms of any separate license agreement you may have executed
with Licensor regarding such Contributions.
6. Trademarks. This License does not grant permission to use the trade
names, trademarks, service marks, or product names of the Licensor,
except as required for reasonable and customary use in describing the
origin of the Work and reproducing the content of the NOTICE file.
7. Disclaimer of Warranty. Unless required by applicable law or
agreed to in writing, Licensor provides the Work (and each
Contributor provides its Contributions) on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or
implied, including, without limitation, any warranties or conditions
of TITLE, NON-INFRINGEMENT, MERCHANTABILITY, or FITNESS FOR A
PARTICULAR PURPOSE. You are solely responsible for determining the
appropriateness of using or redistributing the Work and assume any
risks associated with Your exercise of permissions under this License.
8. Limitation of Liability. In no event and under no legal theory,
whether in tort (including negligence), contract, or otherwise,
unless required by applicable law (such as deliberate and grossly
negligent acts) or agreed to in writing, shall any Contributor be
liable to You for damages, including any direct, indirect, special,
incidental, or consequential damages of any character arising as a
result of this License or out of the use or inability to use the
Work (including but not limited to damages for loss of goodwill,
work stoppage, computer failure or malfunction, or any and all
other commercial damages or losses), even if such Contributor
has been advised of the possibility of such damages.
9. Accepting Warranty or Additional Liability. While redistributing
the Work or Derivative Works thereof, You may choose to offer,
and charge a fee for, acceptance of support, warranty, indemnity,
or other liability obligations and/or rights consistent with this
License. However, in accepting such obligations, You may act only
on Your own behalf and on Your sole responsibility, not on behalf
of any other Contributor, and only if You agree to indemnify,
defend, and hold each Contributor harmless for any liability
incurred by, or claims asserted against, such Contributor by reason
of your accepting any such warranty or additional liability.
END OF TERMS AND CONDITIONS
APPENDIX: How to apply the Apache License to your work.
To apply the Apache License to your work, attach the following
boilerplate notice, with the fields enclosed by brackets "[]"
replaced with your own identifying information. (Don't include
the brackets!) The text should be enclosed in the appropriate
comment syntax for the file format. We also recommend that a
file or class name and description of purpose be included on the
same "printed page" as the copyright notice for easier
identification within third-party archives.
Copyright [yyyy] [name of copyright owner]
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.

25
derive/LICENSE-MIT
View File

@ -1,25 +0,0 @@
Copyright (c) 2014 The Rust Project Developers
Permission is hereby granted, free of charge, to any
person obtaining a copy of this software and associated
documentation files (the "Software"), to deal in the
Software without restriction, including without
limitation the rights to use, copy, modify, merge,
publish, distribute, sublicense, and/or sell copies of
the Software, and to permit persons to whom the Software
is furnished to do so, subject to the following
conditions:
The above copyright notice and this permission notice
shall be included in all copies or substantial portions
of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF
ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED
TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A
PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT
SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR
IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
DEALINGS IN THE SOFTWARE.

118
derive/src/lib.rs
View File

@ -1,118 +0,0 @@
// 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.
#![crate_type = "proc-macro"]
extern crate syn;
#[macro_use]
extern crate quote;
extern crate proc_macro;
use proc_macro::TokenStream;
use syn::Body::Enum;
use syn::VariantData::Unit;
#[proc_macro_derive(FromPrimitive)]
pub fn from_primitive(input: TokenStream) -> TokenStream {
let source = input.to_string();
let ast = syn::parse_macro_input(&source).unwrap();
let name = &ast.ident;
let variants = match ast.body {
Enum(ref variants) => variants,
_ => panic!("`FromPrimitive` can be applied only to the enums, {} is not an enum", name)
};
let mut idx = 0;
let variants: Vec<_> = variants.iter()
.map(|variant| {
let ident = &variant.ident;
match variant.data {
Unit => (),
_ => {
panic!("`FromPrimitive` can be applied only to unitary enums, {}::{} is either struct or tuple", name, ident)
},
}
if let Some(val) = variant.discriminant {
idx = val.value;
}
let tt = quote!(#idx => Some(#name::#ident));
idx += 1;
tt
})
.collect();
let res = quote! {
impl ::num::traits::FromPrimitive for #name {
fn from_i64(n: i64) -> Option<Self> {
Self::from_u64(n as u64)
}
fn from_u64(n: u64) -> Option<Self> {
match n {
#(variants,)*
_ => None,
}
}
}
};
res.to_string().parse().unwrap()
}
#[proc_macro_derive(ToPrimitive)]
pub fn to_primitive(input: TokenStream) -> TokenStream {
let source = input.to_string();
let ast = syn::parse_macro_input(&source).unwrap();
let name = &ast.ident;
let variants = match ast.body {
Enum(ref variants) => variants,
_ => panic!("`ToPrimitive` can be applied only to the enums, {} is not an enum", name)
};
let mut idx = 0;
let variants: Vec<_> = variants.iter()
.map(|variant| {
let ident = &variant.ident;
match variant.data {
Unit => (),
_ => {
panic!("`ToPrimitive` can be applied only to unitary enums, {}::{} is either struct or tuple", name, ident)
},
}
if let Some(val) = variant.discriminant {
idx = val.value;
}
let tt = quote!(#name::#ident => #idx);
idx += 1;
tt
})
.collect();
let res = quote! {
impl ::num::traits::ToPrimitive for #name {
fn to_i64(&self) -> Option<i64> {
self.to_u64().map(|x| x as i64)
}
fn to_u64(&self) -> Option<u64> {
Some(match *self {
#(variants,)*
})
}
}
};
res.to_string().parse().unwrap()
}

22
derive/tests/compile-fail/from-primitive/derive_on_struct.rs
View File

@ -1,22 +0,0 @@
// 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.
extern crate num;
#[macro_use]
extern crate num_derive;
#[derive(Debug, PartialEq, FromPrimitive)] //~ ERROR
struct Color {
r: u8,
g: u8,
b: u8,
}
fn main() {}

21
derive/tests/compile-fail/from-primitive/enum_with_associated_data.rs
View File

@ -1,21 +0,0 @@
// 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.
extern crate num;
#[macro_use]
extern crate num_derive;
#[derive(Debug, PartialEq, FromPrimitive)] //~ ERROR
enum Color {
Rgb(u8, u8, u8),
Hsv(u8, u8, u8),
}
fn main() {}

22
derive/tests/compile-fail/to-primitive/derive_on_struct.rs
View File

@ -1,22 +0,0 @@
// 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.
extern crate num;
#[macro_use]
extern crate num_derive;
#[derive(Debug, PartialEq, ToPrimitive)] //~ ERROR
struct Color {
r: u8,
g: u8,
b: u8,
}
fn main() {}

21
derive/tests/compile-fail/to-primitive/enum_with_associated_data.rs
View File

@ -1,21 +0,0 @@
// 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.
extern crate num;
#[macro_use]
extern crate num_derive;
#[derive(Debug, PartialEq, ToPrimitive)] //~ ERROR
enum Color {
Rgb(u8, u8, u8),
Hsv(u8, u8, u8),
}
fn main() {}

25
derive/tests/compiletest.rs
View File

@ -1,25 +0,0 @@
extern crate compiletest_rs as compiletest;
use std::path::PathBuf;
use std::env::var;
fn run_mode(mode: &'static str) {
let mut config = compiletest::default_config();
let cfg_mode = mode.parse().ok().expect("Invalid mode");
config.target_rustcflags = Some("-L target/debug/ -L target/debug/deps/".to_owned());
if let Ok(name) = var::<&str>("TESTNAME") {
let s : String = name.to_owned();
config.filter = Some(s)
}
config.mode = cfg_mode;
config.src_base = PathBuf::from(format!("tests/{}", mode));
compiletest::run_tests(&config);
}
#[test]
fn compile_test() {
run_mode("compile-fail");
}

23
derive/tests/empty_enum.rs
View File

@ -1,23 +0,0 @@
// 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.
extern crate num;
#[macro_use]
extern crate num_derive;
#[derive(Debug, PartialEq, FromPrimitive, ToPrimitive)]
enum Color {}
#[test]
fn test_empty_enum() {
let v: [Option<Color>; 1] = [num::FromPrimitive::from_u64(0)];
assert_eq!(v, [None]);
}

52
derive/tests/trivial.rs
View File

@ -1,52 +0,0 @@
// 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.
extern crate num;
#[macro_use]
extern crate num_derive;
#[derive(Debug, PartialEq, FromPrimitive, ToPrimitive)]
enum Color {
Red,
Blue,
Green,
}
#[test]
fn test_from_primitive_for_trivial_case() {
let v: [Option<Color>; 4] = [num::FromPrimitive::from_u64(0),
num::FromPrimitive::from_u64(1),
num::FromPrimitive::from_u64(2),
num::FromPrimitive::from_u64(3)];
assert_eq!(v,
[Some(Color::Red), Some(Color::Blue), Some(Color::Green), None]);
}
#[test]
fn test_to_primitive_for_trivial_case() {
let v: [Option<u64>; 3] = [num::ToPrimitive::to_u64(&Color::Red),
num::ToPrimitive::to_u64(&Color::Blue),
num::ToPrimitive::to_u64(&Color::Green)];
assert_eq!(v, [Some(0), Some(1), Some(2)]);
}
#[test]
fn test_reflexive_for_trivial_case() {
let before: [u64; 3] = [0, 1, 2];
let after: Vec<Option<u64>> = before.iter()
.map(|&x| -> Option<Color> { num::FromPrimitive::from_u64(x) })
.map(|x| x.and_then(|x| num::ToPrimitive::to_u64(&x)))
.collect();
let before = before.into_iter().cloned().map(Some).collect::<Vec<_>>();
assert_eq!(before, after);
}

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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.
extern crate num;
#[macro_use]
extern crate num_derive;
#[derive(Debug, PartialEq, FromPrimitive)]
enum Color {
Red,
Blue = 5,
Green,
}
#[test]
fn test_from_primitive_for_enum_with_custom_value() {
let v: [Option<Color>; 4] = [num::FromPrimitive::from_u64(0),
num::FromPrimitive::from_u64(5),
num::FromPrimitive::from_u64(6),
num::FromPrimitive::from_u64(3)];
assert_eq!(v,
[Some(Color::Red), Some(Color::Blue), Some(Color::Green), None]);
}

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integer/Cargo.toml
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[package]
authors = ["The Rust Project Developers"]
description = "Integer traits and functions"
documentation = "http://rust-num.github.io/num"
homepage = "https://github.com/rust-num/num"
keywords = ["mathematics", "numerics"]
categories = [ "algorithms", "science" ]
license = "MIT/Apache-2.0"
repository = "https://github.com/rust-num/num"
name = "num-integer"
version = "0.1.35"
[dependencies.num-traits]
path = "../traits"
version = "0.1.32"

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25
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Copyright (c) 2014 The Rust Project Developers
Permission is hereby granted, free of charge, to any
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF
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988
integer/src/lib.rs
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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.
#![doc(html_logo_url = "https://rust-num.github.io/num/rust-logo-128x128-blk-v2.png",
html_favicon_url = "https://rust-num.github.io/num/favicon.ico",
html_root_url = "https://rust-num.github.io/num/",
html_playground_url = "http://play.integer32.com/")]
extern crate num_traits as traits;
use std::ops::Add;
use traits::{Num, Signed};
pub trait Integer: Sized + Num + PartialOrd + Ord + Eq {
/// Floored integer division.
///
/// # Examples
///
/// ~~~
/// # use num_integer::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::Integer;
/// # let n = 1; let d = 1;
/// assert!(n.div_floor(&d) * d + n.mod_floor(&d) == n)
/// ~~~
///
/// # Examples
///
/// ~~~
/// # use num_integer::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::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::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::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::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::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::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::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: &Self) -> Self {
// 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: &Self) -> Self {
// 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: &Self) -> (Self, Self) {
// 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: &Self) -> Self {
// 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 == Self::min_value() || n == Self::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: &Self) -> Self {
// should not have to recalculate abs
(*self * (*other / self.gcd(other))).abs()
}
/// Deprecated, use `is_multiple_of` instead.
#[inline]
fn divides(&self, other: &Self) -> bool {
self.is_multiple_of(other)
}
/// Returns `true` if the number is a multiple of `other`.
#[inline]
fn is_multiple_of(&self, other: &Self) -> 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: &Self) -> (Self, Self) {
(*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: &Self) -> Self {
*self / *other
}
/// Unsigned integer modulo operation. Returns the same result as `rem` (`%`).
#[inline]
fn mod_floor(&self, other: &Self) -> Self {
*self % *other
}
/// Calculates the Greatest Common Divisor (GCD) of the number and `other`
#[inline]
fn gcd(&self, other: &Self) -> Self {
// 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: &Self) -> Self {
*self * (*other / self.gcd(other))
}
/// Deprecated, use `is_multiple_of` instead.
#[inline]
fn divides(&self, other: &Self) -> bool {
self.is_multiple_of(other)
}
/// Returns `true` if the number is a multiple of `other`.
#[inline]
fn is_multiple_of(&self, other: &Self) -> bool {
*self % *other == 0
}
/// Returns `true` if the number is divisible by `2`.
#[inline]
fn is_even(&self) -> bool {
*self % 2 == 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: &Self) -> (Self, Self) {
(*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);
/// An iterator over binomial coefficients.
pub struct IterBinomial<T> {
a: T,
n: T,
k: T,
}
impl<T> IterBinomial<T>
where T: Integer,
{
/// For a given n, iterate over all binomial coefficients binomial(n, k), for k=0...n.
///
/// Note that this might overflow, depending on `T`. For the primitive
/// integer types, the following n are the largest ones for which there will
/// be no overflow:
///
/// type | n
/// -----|---
/// u8 | 10
/// i8 | 9
/// u16 | 18
/// i16 | 17
/// u32 | 34
/// i32 | 33
/// u64 | 67
/// i64 | 66
///
/// For larger n, `T` should be a bigint type.
pub fn new(n: T) -> IterBinomial<T> {
IterBinomial {
k: T::zero(), a: T::one(), n: n
}
}
}
impl<T> Iterator for IterBinomial<T>
where T: Integer + Clone
{
type Item = T;
fn next(&mut self) -> Option<T> {
if self.k > self.n {
return None;
}
self.a = if !self.k.is_zero() {
multiply_and_divide(
self.a.clone(),
self.n.clone() - self.k.clone() + T::one(),
self.k.clone()
)
} else {
T::one()
};
self.k = self.k.clone() + T::one();
Some(self.a.clone())
}
}
/// Calculate r * a / b, avoiding overflows and fractions.
///
/// Assumes that b divides r * a evenly.
fn multiply_and_divide<T: Integer + Clone>(r: T, a: T, b: T) -> T {
// See http://blog.plover.com/math/choose-2.html for the idea.
let g = gcd(r.clone(), b.clone());
r/g.clone() * (a / (b/g))
}
/// Calculate the binomial coefficient.
///
/// Note that this might overflow, depending on `T`. For the primitive integer
/// types, the following n are the largest ones possible such that there will
/// be no overflow for any k:
///
/// type | n
/// -----|---
/// u8 | 10
/// i8 | 9
/// u16 | 18
/// i16 | 17
/// u32 | 34
/// i32 | 33
/// u64 | 67
/// i64 | 66
///
/// For larger n, consider using a bigint type for `T`.
pub fn binomial<T: Integer + Clone>(mut n: T, k: T) -> T {
// See http://blog.plover.com/math/choose.html for the idea.
if k > n {
return T::zero();
}
if k > n.clone() - k.clone() {
return binomial(n.clone(), n - k);
}
let mut r = T::one();
let mut d = T::one();
loop {
if d > k {
break;
}
r = multiply_and_divide(r, n.clone(), d.clone());
n = n - T::one();
d = d + T::one();
}
r
}
/// Calculate the multinomial coefficient.
pub fn multinomial<T: Integer + Clone>(k: &[T]) -> T
where for<'a> T: Add<&'a T, Output = T>
{
let mut r = T::one();
let mut p = T::zero();
for i in k {
p = p + i;
r = r * binomial(p.clone(), i.clone());
}
r
}
#[test]
fn test_lcm_overflow() {
macro_rules! check {
($t:ty, $x:expr, $y:expr, $r:expr) => { {
let x: $t = $x;
let y: $t = $y;
let o = x.checked_mul(y);
assert!(o.is_none(),
"sanity checking that {} input {} * {} overflows",
stringify!($t), x, y);
assert_eq!(x.lcm(&y), $r);
assert_eq!(y.lcm(&x), $r);
} }
}
// Original bug (Issue #166)
check!(i64, 46656000000000000, 600, 46656000000000000);
check!(i8, 0x40, 0x04, 0x40);
check!(u8, 0x80, 0x02, 0x80);
check!(i16, 0x40_00, 0x04, 0x40_00);
check!(u16, 0x80_00, 0x02, 0x80_00);
check!(i32, 0x4000_0000, 0x04, 0x4000_0000);
check!(u32, 0x8000_0000, 0x02, 0x8000_0000);
check!(i64, 0x4000_0000_0000_0000, 0x04, 0x4000_0000_0000_0000);
check!(u64, 0x8000_0000_0000_0000, 0x02, 0x8000_0000_0000_0000);
}
#[test]
fn test_iter_binomial() {
macro_rules! check_simple {
($t:ty) => { {
let n: $t = 3;
let c: Vec<_> = IterBinomial::new(n).collect();
let expected = vec![1, 3, 3, 1];
assert_eq!(c, expected);
} }
}
check_simple!(u8);
check_simple!(i8);
check_simple!(u16);
check_simple!(i16);
check_simple!(u32);
check_simple!(i32);
check_simple!(u64);
check_simple!(i64);
macro_rules! check_binomial {
($t:ty, $n:expr) => { {
let n: $t = $n;
let c: Vec<_> = IterBinomial::new(n).collect();
let mut k: $t = 0;
for b in c {
assert_eq!(b, binomial(n, k));
k += 1;
}
} }
}
// Check the largest n for which there is no overflow.
check_binomial!(u8, 10);
check_binomial!(i8, 9);
check_binomial!(u16, 18);
check_binomial!(i16, 17);
check_binomial!(u32, 34);
check_binomial!(i32, 33);
check_binomial!(u64, 67);
check_binomial!(i64, 66);
}
#[test]
fn test_binomial() {
macro_rules! check {
($t:ty, $x:expr, $y:expr, $r:expr) => { {
let x: $t = $x;
let y: $t = $y;
let expected: $t = $r;
assert_eq!(binomial(x, y), expected);
if y <= x {
assert_eq!(binomial(x, x - y), expected);
}
} }
}
check!(u8, 9, 4, 126);
check!(u8, 0, 0, 1);
check!(u8, 2, 3, 0);
check!(i8, 9, 4, 126);
check!(i8, 0, 0, 1);
check!(i8, 2, 3, 0);
check!(u16, 100, 2, 4950);
check!(u16, 14, 4, 1001);
check!(u16, 0, 0, 1);
check!(u16, 2, 3, 0);
check!(i16, 100, 2, 4950);
check!(i16, 14, 4, 1001);
check!(i16, 0, 0, 1);
check!(i16, 2, 3, 0);
check!(u32, 100, 2, 4950);
check!(u32, 35, 11, 417225900);
check!(u32, 14, 4, 1001);
check!(u32, 0, 0, 1);
check!(u32, 2, 3, 0);
check!(i32, 100, 2, 4950);
check!(i32, 35, 11, 417225900);
check!(i32, 14, 4, 1001);
check!(i32, 0, 0, 1);
check!(i32, 2, 3, 0);
check!(u64, 100, 2, 4950);
check!(u64, 35, 11, 417225900);
check!(u64, 14, 4, 1001);
check!(u64, 0, 0, 1);
check!(u64, 2, 3, 0);
check!(i64, 100, 2, 4950);
check!(i64, 35, 11, 417225900);
check!(i64, 14, 4, 1001);
check!(i64, 0, 0, 1);
check!(i64, 2, 3, 0);
}
#[test]
fn test_multinomial() {
macro_rules! check_binomial {
($t:ty, $k:expr) => { {
let n: $t = $k.iter().fold(0, |acc, &x| acc + x);
let k: &[$t] = $k;
assert_eq!(k.len(), 2);
assert_eq!(multinomial(k), binomial(n, k[0]));
} }
}
check_binomial!(u8, &[4, 5]);
check_binomial!(i8, &[4, 5]);
check_binomial!(u16, &[2, 98]);
check_binomial!(u16, &[4, 10]);
check_binomial!(i16, &[2, 98]);
check_binomial!(i16, &[4, 10]);
check_binomial!(u32, &[2, 98]);
check_binomial!(u32, &[11, 24]);
check_binomial!(u32, &[4, 10]);
check_binomial!(i32, &[2, 98]);
check_binomial!(i32, &[11, 24]);
check_binomial!(i32, &[4, 10]);
check_binomial!(u64, &[2, 98]);
check_binomial!(u64, &[11, 24]);
check_binomial!(u64, &[4, 10]);
check_binomial!(i64, &[2, 98]);
check_binomial!(i64, &[11, 24]);
check_binomial!(i64, &[4, 10]);
macro_rules! check_multinomial {
($t:ty, $k:expr, $r:expr) => { {
let k: &[$t] = $k;
let expected: $t = $r;
assert_eq!(multinomial(k), expected);
} }
}
check_multinomial!(u8, &[2, 1, 2], 30);
check_multinomial!(u8, &[2, 3, 0], 10);
check_multinomial!(i8, &[2, 1, 2], 30);
check_multinomial!(i8, &[2, 3, 0], 10);
check_multinomial!(u16, &[2, 1, 2], 30);
check_multinomial!(u16, &[2, 3, 0], 10);
check_multinomial!(i16, &[2, 1, 2], 30);
check_multinomial!(i16, &[2, 3, 0], 10);
check_multinomial!(u32, &[2, 1, 2], 30);
check_multinomial!(u32, &[2, 3, 0], 10);
check_multinomial!(i32, &[2, 1, 2], 30);
check_multinomial!(i32, &[2, 3, 0], 10);
check_multinomial!(u64, &[2, 1, 2], 30);
check_multinomial!(u64, &[2, 3, 0], 10);
check_multinomial!(i64, &[2, 1, 2], 30);
check_multinomial!(i64, &[2, 3, 0], 10);
check_multinomial!(u64, &[], 1);
check_multinomial!(u64, &[0], 1);
check_multinomial!(u64, &[12345], 1);
}

23
iter/Cargo.toml
View File

@ -1,23 +0,0 @@
[package]
authors = ["The Rust Project Developers"]
description = "External iterators for generic mathematics"
documentation = "http://rust-num.github.io/num"
homepage = "https://github.com/rust-num/num"
keywords = ["mathematics", "numerics"]
categories = [ "algorithms", "science" ]
license = "MIT/Apache-2.0"
repository = "https://github.com/rust-num/num"
name = "num-iter"
version = "0.1.34"
[dependencies]
[dependencies.num-integer]
optional = false
path = "../integer"
version = "0.1.32"
[dependencies.num-traits]
optional = false
path = "../traits"
version = "0.1.32"

201
iter/LICENSE-APACHE
View File

@ -1,201 +0,0 @@
Apache License
Version 2.0, January 2004
http://www.apache.org/licenses/
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25
iter/LICENSE-MIT
View File

@ -1,25 +0,0 @@
Copyright (c) 2014 The Rust Project Developers
Permission is hereby granted, free of charge, to any
person obtaining a copy of this software and associated
documentation files (the "Software"), to deal in the
Software without restriction, including without
limitation the rights to use, copy, modify, merge,
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The above copyright notice and this permission notice
shall be included in all copies or substantial portions
of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF
ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED
TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A
PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT
SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR
IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
DEALINGS IN THE SOFTWARE.

378
iter/src/lib.rs
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@ -1,378 +0,0 @@
// 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
#![doc(html_logo_url = "https://rust-num.github.io/num/rust-logo-128x128-blk-v2.png",
html_favicon_url = "https://rust-num.github.io/num/favicon.ico",
html_root_url = "https://rust-num.github.io/num/",
html_playground_url = "http://play.integer32.com/")]
extern crate num_traits as traits;
extern crate num_integer as integer;
use integer::Integer;
use traits::{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
/// let array = [0, 1, 2, 3, 4];
///
/// for i in num_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 + 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 + 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 traits::{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]);
}
}

38
rational/Cargo.toml
View File

@ -1,38 +0,0 @@
[package]
authors = ["The Rust Project Developers"]
description = "Rational numbers implementation for Rust"
documentation = "http://rust-num.github.io/num"
homepage = "https://github.com/rust-num/num"
keywords = ["mathematics", "numerics"]
categories = [ "algorithms", "data-structures", "science" ]
license = "MIT/Apache-2.0"
name = "num-rational"
repository = "https://github.com/rust-num/num"
version = "0.1.40"
[dependencies]
[dependencies.num-bigint]
optional = true
path = "../bigint"
version = "0.1.32"
[dependencies.num-integer]
path = "../integer"
version = "0.1.32"
[dependencies.num-traits]
path = "../traits"
version = "0.1.32"
[dependencies.rustc-serialize]
optional = true
version = "0.3.19"
[dependencies.serde]
optional = true
version = ">= 0.7.0, < 0.9.0"
[features]
default = ["bigint", "rustc-serialize"]
bigint = ["num-bigint"]

201
rational/LICENSE-APACHE
View File

@ -1,201 +0,0 @@
Apache License
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http://www.apache.org/licenses/
TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
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of your accepting any such warranty or additional liability.
END OF TERMS AND CONDITIONS
APPENDIX: How to apply the Apache License to your work.
To apply the Apache License to your work, attach the following
boilerplate notice, with the fields enclosed by brackets "[]"
replaced with your own identifying information. (Don't include
the brackets!) The text should be enclosed in the appropriate
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25
rational/LICENSE-MIT
View File

@ -1,25 +0,0 @@
Copyright (c) 2014 The Rust Project Developers
Permission is hereby granted, free of charge, to any
person obtaining a copy of this software and associated
documentation files (the "Software"), to deal in the
Software without restriction, including without
limitation the rights to use, copy, modify, merge,
publish, distribute, sublicense, and/or sell copies of
the Software, and to permit persons to whom the Software
is furnished to do so, subject to the following
conditions:
The above copyright notice and this permission notice
shall be included in all copies or substantial portions
of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF
ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED
TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A
PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT
SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR
IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
DEALINGS IN THE SOFTWARE.

1413
rational/src/lib.rs
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0
traits/src/bounds.rs → src/bounds.rs
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0
traits/src/cast.rs → src/cast.rs
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0
traits/src/float.rs → src/float.rs
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0
traits/src/identities.rs → src/identities.rs
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0
traits/src/int.rs → src/int.rs
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500
src/lib.rs
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@ -1,4 +1,4 @@
// Copyright 2014-2016 The Rust Project Developers. See the COPYRIGHT
// 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.
//
@ -8,104 +8,428 @@
// option. This file may not be copied, modified, or distributed
// except according to those terms.
//! A collection of numeric types and traits for 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.
//!
//! ## 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 = "https://rust-num.github.io/num/rust-logo-128x128-blk-v2.png",
html_favicon_url = "https://rust-num.github.io/num/favicon.ico",
html_root_url = "https://rust-num.github.io/num/",
html_playground_url = "http://play.integer32.com/")]
//! Numeric traits for generic mathematics
extern crate num_traits;
extern crate num_integer;
extern crate num_iter;
#[cfg(feature = "num-complex")]
extern crate num_complex;
#[cfg(feature = "num-bigint")]
extern crate num_bigint;
#[cfg(feature = "num-rational")]
extern crate num_rational;
#![doc(html_root_url = "https://docs.rs/num-traits/0.1")]
#[cfg(feature = "num-bigint")]
pub use num_bigint::{BigInt, BigUint};
#[cfg(feature = "num-rational")]
pub use num_rational::Rational;
#[cfg(all(feature = "num-rational", feature="num-bigint"))]
pub use num_rational::BigRational;
#[cfg(feature = "num-complex")]
pub use num_complex::Complex;
pub use num_integer::Integer;
pub use num_iter::{range, range_inclusive, range_step, range_step_inclusive};
pub use num_traits::{Num, Zero, One, Signed, Unsigned, Bounded,
one, zero, abs, abs_sub, signum,
Saturating, CheckedAdd, CheckedSub, CheckedMul, CheckedDiv,
PrimInt, Float, ToPrimitive, FromPrimitive, NumCast, cast,
pow, checked_pow, clamp};
use std::ops::{Add, Sub, Mul, Div, Rem};
use std::ops::{AddAssign, SubAssign, MulAssign, DivAssign, RemAssign};
use std::num::Wrapping;
#[cfg(feature = "num-bigint")]
pub mod bigint {
pub use num_bigint::*;
pub use bounds::Bounded;
pub use float::{Float, FloatConst};
pub use identities::{Zero, One, zero, one};
pub use ops::checked::*;
pub use ops::wrapping::*;
pub use ops::saturating::Saturating;
pub use sign::{Signed, Unsigned, abs, abs_sub, signum};
pub use cast::*;
pub use int::PrimInt;
pub use pow::{pow, checked_pow};
pub mod identities;
pub mod sign;
pub mod ops;
pub mod bounds;
pub mod float;
pub mod cast;
pub mod int;
pub mod pow;
/// The base trait for numeric types, covering `0` and `1` values,
/// comparisons, basic numeric operations, and string conversion.
pub trait Num: PartialEq + Zero + One + NumOps
{
type FromStrRadixErr;
/// Convert from a string and radix <= 36.
///
/// # Examples
///
/// ```rust
/// use num_traits::Num;
///
/// let result = <i32 as Num>::from_str_radix("27", 10);
/// assert_eq!(result, Ok(27));
///
/// let result = <i32 as Num>::from_str_radix("foo", 10);
/// assert!(result.is_err());
/// ```
fn from_str_radix(str: &str, radix: u32) -> Result<Self, Self::FromStrRadixErr>;
}
#[cfg(feature = "num-complex")]
pub mod complex {
pub use num_complex::*;
/// The trait for types implementing basic numeric operations
///
/// This is automatically implemented for types which implement the operators.
pub trait NumOps<Rhs = Self, Output = Self>
: Add<Rhs, Output = Output>
+ Sub<Rhs, Output = Output>
+ Mul<Rhs, Output = Output>
+ Div<Rhs, Output = Output>
+ Rem<Rhs, Output = Output>
{}
impl<T, Rhs, Output> NumOps<Rhs, Output> for T
where 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.
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.
pub trait RefNum<Base>: NumOps<Base, Base> + for<'r> NumOps<&'r Base, Base> {}
impl<T, Base> RefNum<Base> for T where T: NumOps<Base, Base> + for<'r> NumOps<&'r Base, Base> {}
/// The trait for types implementing numeric assignment operators (like `+=`).
///
/// This is automatically implemented for types which implement the operators.
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.
pub trait NumAssign: Num + NumAssignOps {}
impl<T> NumAssign for T where T: Num + NumAssignOps {}
/// The trait for `NumAssign` types which also implement assignment operations
/// taking the second operand by reference.
///
/// This is automatically implemented for types which implement the operators.
pub trait NumAssignRef: NumAssign + for<'r> NumAssignOps<&'r Self> {}
impl<T> NumAssignRef for T where T: NumAssign + for<'r> NumAssignOps<&'r T> {}
macro_rules! int_trait_impl {
($name:ident for $($t:ty)*) => ($(
impl $name for $t {
type FromStrRadixErr = ::std::num::ParseIntError;
#[inline]
fn from_str_radix(s: &str, radix: u32)
-> Result<Self, ::std::num::ParseIntError>
{
<$t>::from_str_radix(s, radix)
}
}
)*)
}
int_trait_impl!(Num for usize u8 u16 u32 u64 isize i8 i16 i32 i64);
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)
}
}
pub mod integer {
pub use num_integer::*;
#[derive(Debug)]
pub enum FloatErrorKind {
Empty,
Invalid,
}
// FIXME: std::num::ParseFloatError is stable in 1.0, but opaque to us,
// so there's not really any way for us to reuse it.
#[derive(Debug)]
pub struct ParseFloatError {
pub kind: FloatErrorKind,
}
pub mod iter {
pub use num_iter::*;
// 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:ty)*) => ($(
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(Float::infinity()),
"-inf" => return Ok(Float::neg_infinity()),
"NaN" => return Ok(Float::nan()),
_ => {},
}
fn slice_shift_char(src: &str) -> Option<(char, &str)> {
src.chars().nth(0).map(|ch| (ch, &src[1..]))
}
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(Float::infinity()); }
if !is_positive && sig >= prev_sig
{ return Ok(Float::neg_infinity()); }
// Detect overflow by reversing the shift-and-add process
if is_positive && (prev_sig != (sig - digit as $t) / radix as $t)
{ return Ok(Float::infinity()); }
if !is_positive && (prev_sig != (sig + digit as $t) / radix as $t)
{ return Ok(Float::neg_infinity()); }
}
prev_sig = sig;
},
None => match c {
'e' | 'E' | 'p' | 'P' => {
exp_info = Some((c, i + 1));
break; // start of exponent
},
'.' => {
break; // start of fractional part
},
_ => {
return 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(Float::infinity()); }
if !is_positive && sig > prev_sig
{ return Ok(Float::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 }),
};
match (is_positive, exp) {
(true, Ok(exp)) => base.powi(exp as i32),
(false, Ok(exp)) => 1.0 / base.powi(exp as i32),
(_, 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.
#[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
}
}
pub mod traits {
pub use num_traits::*;
#[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));
// 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));
}
#[cfg(feature = "num-rational")]
pub mod rational {
pub use num_rational::*;
#[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 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);
}
#[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)
}
#[test]
fn check_numref_ops() {
fn compute<T: NumRef>(x: T, y: &T) -> T {
x * y / y % y + y - y
}
assert_eq!(compute(1, &2), 1)
}
#[test]
fn check_refnum_ops() {
fn compute<T: Copy>(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_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)

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traits/Cargo.toml
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@ -1,13 +0,0 @@
[package]
authors = ["The Rust Project Developers"]
description = "Numeric traits for generic mathematics"
documentation = "http://rust-num.github.io/num"
homepage = "https://github.com/rust-num/num"
keywords = ["mathematics", "numerics"]
categories = [ "algorithms", "science" ]
license = "MIT/Apache-2.0"
repository = "https://github.com/rust-num/num"
name = "num-traits"
version = "0.1.41"
[dependencies]

201
traits/LICENSE-APACHE
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@ -1,201 +0,0 @@
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traits/LICENSE-MIT
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Copyright (c) 2014 The Rust Project Developers
Permission is hereby granted, free of charge, to any
person obtaining a copy of this software and associated
documentation files (the "Software"), to deal in the
Software without restriction, including without
limitation the rights to use, copy, modify, merge,
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conditions:
The above copyright notice and this permission notice
shall be included in all copies or substantial portions
of the Software.
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TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A
PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT
SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
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traits/src/lib.rs
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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.
//! Numeric traits for generic mathematics
#![doc(html_logo_url = "https://rust-num.github.io/num/rust-logo-128x128-blk-v2.png",
html_favicon_url = "https://rust-num.github.io/num/favicon.ico",
html_root_url = "https://rust-num.github.io/num/",
html_playground_url = "http://play.integer32.com/")]
use std::ops::{Add, Sub, Mul, Div, Rem};
use std::ops::{AddAssign, SubAssign, MulAssign, DivAssign, RemAssign};
use std::num::Wrapping;
pub use bounds::Bounded;
pub use float::{Float, FloatConst};
pub use identities::{Zero, One, zero, one};
pub use ops::checked::*;
pub use ops::wrapping::*;
pub use ops::saturating::Saturating;
pub use sign::{Signed, Unsigned, abs, abs_sub, signum};
pub use cast::*;
pub use int::PrimInt;
pub use pow::{pow, checked_pow};
pub mod identities;
pub mod sign;
pub mod ops;
pub mod bounds;
pub mod float;
pub mod cast;
pub mod int;
pub mod pow;
/// The base trait for numeric types, covering `0` and `1` values,
/// comparisons, basic numeric operations, and string conversion.
pub trait Num: PartialEq + Zero + One + NumOps
{
type FromStrRadixErr;
/// Convert from a string and radix <= 36.
///
/// # Examples
///
/// ```rust
/// use num_traits::Num;
///
/// let result = <i32 as Num>::from_str_radix("27", 10);
/// assert_eq!(result, Ok(27));
///
/// let result = <i32 as Num>::from_str_radix("foo", 10);
/// assert!(result.is_err());
/// ```
fn from_str_radix(str: &str, radix: u32) -> Result<Self, Self::FromStrRadixErr>;
}
/// The trait for types implementing basic numeric operations
///
/// This is automatically implemented for types which implement the operators.
pub trait NumOps<Rhs = Self, Output = Self>
: Add<Rhs, Output = Output>
+ Sub<Rhs, Output = Output>
+ Mul<Rhs, Output = Output>
+ Div<Rhs, Output = Output>
+ Rem<Rhs, Output = Output>
{}
impl<T, Rhs, Output> NumOps<Rhs, Output> for T
where 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.
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.
pub trait RefNum<Base>: NumOps<Base, Base> + for<'r> NumOps<&'r Base, Base> {}
impl<T, Base> RefNum<Base> for T where T: NumOps<Base, Base> + for<'r> NumOps<&'r Base, Base> {}
/// The trait for types implementing numeric assignment operators (like `+=`).
///
/// This is automatically implemented for types which implement the operators.
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.
pub trait NumAssign: Num + NumAssignOps {}
impl<T> NumAssign for T where T: Num + NumAssignOps {}
/// The trait for `NumAssign` types which also implement assignment operations
/// taking the second operand by reference.
///
/// This is automatically implemented for types which implement the operators.
pub trait NumAssignRef: NumAssign + for<'r> NumAssignOps<&'r Self> {}
impl<T> NumAssignRef for T where T: NumAssign + for<'r> NumAssignOps<&'r T> {}
macro_rules! int_trait_impl {
($name:ident for $($t:ty)*) => ($(
impl $name for $t {
type FromStrRadixErr = ::std::num::ParseIntError;
#[inline]
fn from_str_radix(s: &str, radix: u32)
-> Result<Self, ::std::num::ParseIntError>
{
<$t>::from_str_radix(s, radix)
}
}
)*)
}
int_trait_impl!(Num for usize u8 u16 u32 u64 isize i8 i16 i32 i64);
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)
}
}
#[derive(Debug)]
pub enum FloatErrorKind {
Empty,
Invalid,
}
// FIXME: std::num::ParseFloatError is stable in 1.0, but opaque to us,
// so there's not really any way for us to reuse it.
#[derive(Debug)]
pub struct ParseFloatError {
pub kind: FloatErrorKind,
}
// 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:ty)*) => ($(
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(Float::infinity()),
"-inf" => return Ok(Float::neg_infinity()),
"NaN" => return Ok(Float::nan()),
_ => {},
}
fn slice_shift_char(src: &str) -> Option<(char, &str)> {
src.chars().nth(0).map(|ch| (ch, &src[1..]))
}
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(Float::infinity()); }
if !is_positive && sig >= prev_sig
{ return Ok(Float::neg_infinity()); }
// Detect overflow by reversing the shift-and-add process
if is_positive && (prev_sig != (sig - digit as $t) / radix as $t)
{ return Ok(Float::infinity()); }
if !is_positive && (prev_sig != (sig + digit as $t) / radix as $t)
{ return Ok(Float::neg_infinity()); }
}
prev_sig = sig;
},
None => match c {
'e' | 'E' | 'p' | 'P' => {
exp_info = Some((c, i + 1));
break; // start of exponent
},
'.' => {
break; // start of fractional part
},
_ => {
return 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(Float::infinity()); }
if !is_positive && sig > prev_sig
{ return Ok(Float::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 }),
};
match (is_positive, exp) {
(true, Ok(exp)) => base.powi(exp as i32),
(false, Ok(exp)) => 1.0 / base.powi(exp as i32),
(_, 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.
#[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
}
}
#[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));
// 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));
}
#[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 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);
}
#[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)
}
#[test]
fn check_numref_ops() {
fn compute<T: NumRef>(x: T, y: &T) -> T {
x * y / y % y + y - y
}
assert_eq!(compute(1, &2), 1)
}
#[test]
fn check_refnum_ops() {
fn compute<T: Copy>(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_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)