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Initial vendor packages

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Signed-off-by: Valentin Popov <valentin@popov.link>
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Valentin Popov
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{"files":{"Cargo.toml":"01a1f6e6771981ddeaf682be79918c45a88d032d887f188fdcb1ee7eedcf63a6","LICENSE-APACHE":"a60eea817514531668d7e00765731449fe14d059d3249e0bc93b36de45f759f2","LICENSE-MIT":"6485b8ed310d3f0340bf1ad1f47645069ce4069dcc6bb46c7d5c6faf41de1fdb","README.md":"68f533703554b9130ea902776bd9eb20d1a2d32b213ebadebcd49ed0f1ef9728","RELEASES.md":"21252a72a308b4dfff190bc4b67d95f2be968fab5d7ddb58cd5cfbcdab8c5adf","benches/average.rs":"94ceeb7423bcd18ab0476bc3499505ce12d9552e53fa959e50975d71300f8404","benches/gcd.rs":"9b5c0ae8ccd6c7fc8f8384fb351d10cfdd0be5fbea9365f9ea925d8915b015bf","benches/roots.rs":"79b4ab2d8fe7bbf43fe65314d2e1bc206165bc4cb34b3ceaa899f9ea7af31c09","build.rs":"575b157527243fe355a7c8d7d874a1f790c3fb0177beba9032076a7803c5b9dd","src/average.rs":"a66cf6a49f893e60697c17b2540258e69daa15ab97d8d444c6f2e8cac2f01ae9","src/lib.rs":"b77bd1a04555b180da9661d98d69fb28eb59a02f02abbaaa332c2b27c4e753c9","src/roots.rs":"2a9b908bd3666b5cffc58c1b37d329e46ed02f71ad6d5deea1e8440c10660e1a","tests/average.rs":"5f26a31be042626e9af66f7b751798621561fa090da48b1ec5ab63e388288a91","tests/roots.rs":"a0caa4142899ec8cb806a7a0d3410c39d50de97cceadc4c2ceca707be91b1ddd"},"package":"225d3389fb3509a24c93f5c29eb6bde2586b98d9f016636dff58d7c6f7569cd9"}

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# THIS FILE IS AUTOMATICALLY GENERATED BY CARGO
#
# When uploading crates to the registry Cargo will automatically
# "normalize" Cargo.toml files for maximal compatibility
# with all versions of Cargo and also rewrite `path` dependencies
# to registry (e.g., crates.io) dependencies.
#
# If you are reading this file be aware that the original Cargo.toml
# will likely look very different (and much more reasonable).
# See Cargo.toml.orig for the original contents.
[package]
name = "num-integer"
version = "0.1.45"
authors = ["The Rust Project Developers"]
build = "build.rs"
exclude = [
"/bors.toml",
"/ci/*",
"/.github/*",
]
description = "Integer traits and functions"
homepage = "https://github.com/rust-num/num-integer"
documentation = "https://docs.rs/num-integer"
readme = "README.md"
keywords = [
"mathematics",
"numerics",
]
categories = [
"algorithms",
"science",
"no-std",
]
license = "MIT OR Apache-2.0"
repository = "https://github.com/rust-num/num-integer"
[package.metadata.docs.rs]
features = ["std"]
[dependencies.num-traits]
version = "0.2.11"
default-features = false
[build-dependencies.autocfg]
version = "1"
[features]
default = ["std"]
i128 = ["num-traits/i128"]
std = ["num-traits/std"]

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Copyright (c) 2014 The Rust Project Developers
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# num-integer
[![crate](https://img.shields.io/crates/v/num-integer.svg)](https://crates.io/crates/num-integer)
[![documentation](https://docs.rs/num-integer/badge.svg)](https://docs.rs/num-integer)
[![minimum rustc 1.8](https://img.shields.io/badge/rustc-1.8+-red.svg)](https://rust-lang.github.io/rfcs/2495-min-rust-version.html)
[![build status](https://github.com/rust-num/num-integer/workflows/master/badge.svg)](https://github.com/rust-num/num-integer/actions)
`Integer` trait and functions for Rust.
## Usage
Add this to your `Cargo.toml`:
```toml
[dependencies]
num-integer = "0.1"
```
and this to your crate root:
```rust
extern crate num_integer;
```
## Features
This crate can be used without the standard library (`#![no_std]`) by disabling
the default `std` feature. Use this in `Cargo.toml`:
```toml
[dependencies.num-integer]
version = "0.1.36"
default-features = false
```
There is no functional difference with and without `std` at this time, but
there may be in the future.
Implementations for `i128` and `u128` are only available with Rust 1.26 and
later. The build script automatically detects this, but you can make it
mandatory by enabling the `i128` crate feature.
## Releases
Release notes are available in [RELEASES.md](RELEASES.md).
## Compatibility
The `num-integer` crate is tested for rustc 1.8 and greater.
## License
Licensed under either of
* [Apache License, Version 2.0](http://www.apache.org/licenses/LICENSE-2.0)
* [MIT license](http://opensource.org/licenses/MIT)
at your option.
### Contribution
Unless you explicitly state otherwise, any contribution intentionally submitted
for inclusion in the work by you, as defined in the Apache-2.0 license, shall be
dual licensed as above, without any additional terms or conditions.

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# Release 0.1.45 (2022-04-29)
- [`Integer::next_multiple_of` and `prev_multiple_of` no longer overflow -1][45].
- [`Integer::is_multiple_of` now handles a 0 argument without panicking][47]
for primitive integers.
- [`ExtendedGcd` no longer has any private fields][46], making it possible for
external implementations to customize `Integer::extended_gcd`.
**Contributors**: @ciphergoth, @cuviper, @tspiteri, @WizardOfMenlo
[45]: https://github.com/rust-num/num-integer/pull/45
[46]: https://github.com/rust-num/num-integer/pull/46
[47]: https://github.com/rust-num/num-integer/pull/47
# Release 0.1.44 (2020-10-29)
- [The "i128" feature now bypasses compiler probing][35]. The build script
used to probe anyway and panic if requested support wasn't found, but
sometimes this ran into bad corner cases with `autocfg`.
**Contributors**: @cuviper
[35]: https://github.com/rust-num/num-integer/pull/35
# Release 0.1.43 (2020-06-11)
- [The new `Average` trait][31] computes fast integer averages, rounded up or
down, without any risk of overflow.
**Contributors**: @althonos, @cuviper
[31]: https://github.com/rust-num/num-integer/pull/31
# Release 0.1.42 (2020-01-09)
- [Updated the `autocfg` build dependency to 1.0][29].
**Contributors**: @cuviper, @dingelish
[29]: https://github.com/rust-num/num-integer/pull/29
# Release 0.1.41 (2019-05-21)
- [Fixed feature detection on `no_std` targets][25].
**Contributors**: @cuviper
[25]: https://github.com/rust-num/num-integer/pull/25
# Release 0.1.40 (2019-05-20)
- [Optimized primitive `gcd` by avoiding memory swaps][11].
- [Fixed `lcm(0, 0)` to return `0`, rather than panicking][18].
- [Added `Integer::div_ceil`, `next_multiple_of`, and `prev_multiple_of`][16].
- [Added `Integer::gcd_lcm`, `extended_gcd`, and `extended_gcd_lcm`][19].
**Contributors**: @cuviper, @ignatenkobrain, @smarnach, @strake
[11]: https://github.com/rust-num/num-integer/pull/11
[16]: https://github.com/rust-num/num-integer/pull/16
[18]: https://github.com/rust-num/num-integer/pull/18
[19]: https://github.com/rust-num/num-integer/pull/19
# Release 0.1.39 (2018-06-20)
- [The new `Roots` trait provides `sqrt`, `cbrt`, and `nth_root` methods][9],
calculating an `Integer`'s principal roots rounded toward zero.
**Contributors**: @cuviper
[9]: https://github.com/rust-num/num-integer/pull/9
# Release 0.1.38 (2018-05-11)
- [Support for 128-bit integers is now automatically detected and enabled.][8]
Setting the `i128` crate feature now causes the build script to panic if such
support is not detected.
**Contributors**: @cuviper
[8]: https://github.com/rust-num/num-integer/pull/8
# Release 0.1.37 (2018-05-10)
- [`Integer` is now implemented for `i128` and `u128`][7] starting with Rust
1.26, enabled by the new `i128` crate feature.
**Contributors**: @cuviper
[7]: https://github.com/rust-num/num-integer/pull/7
# Release 0.1.36 (2018-02-06)
- [num-integer now has its own source repository][num-356] at [rust-num/num-integer][home].
- [Corrected the argument order documented in `Integer::is_multiple_of`][1]
- [There is now a `std` feature][5], enabled by default, along with the implication
that building *without* this feature makes this a `#[no_std]` crate.
- There is no difference in the API at this time.
**Contributors**: @cuviper, @jaystrictor
[home]: https://github.com/rust-num/num-integer
[num-356]: https://github.com/rust-num/num/pull/356
[1]: https://github.com/rust-num/num-integer/pull/1
[5]: https://github.com/rust-num/num-integer/pull/5
# Prior releases
No prior release notes were kept. Thanks all the same to the many
contributors that have made this crate what it is!

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//! Benchmark sqrt and cbrt
#![feature(test)]
extern crate num_integer;
extern crate num_traits;
extern crate test;
use num_integer::Integer;
use num_traits::{AsPrimitive, PrimInt, WrappingAdd, WrappingMul};
use std::cmp::{max, min};
use std::fmt::Debug;
use test::{black_box, Bencher};
// --- Utilities for RNG ----------------------------------------------------
trait BenchInteger: Integer + PrimInt + WrappingAdd + WrappingMul + 'static {}
impl<T> BenchInteger for T where T: Integer + PrimInt + WrappingAdd + WrappingMul + 'static {}
// Simple PRNG so we don't have to worry about rand compatibility
fn lcg<T>(x: T) -> T
where
u32: AsPrimitive<T>,
T: BenchInteger,
{
// LCG parameters from Numerical Recipes
// (but we're applying it to arbitrary sizes)
const LCG_A: u32 = 1664525;
const LCG_C: u32 = 1013904223;
x.wrapping_mul(&LCG_A.as_()).wrapping_add(&LCG_C.as_())
}
// --- Alt. Implementations -------------------------------------------------
trait NaiveAverage {
fn naive_average_ceil(&self, other: &Self) -> Self;
fn naive_average_floor(&self, other: &Self) -> Self;
}
trait UncheckedAverage {
fn unchecked_average_ceil(&self, other: &Self) -> Self;
fn unchecked_average_floor(&self, other: &Self) -> Self;
}
trait ModuloAverage {
fn modulo_average_ceil(&self, other: &Self) -> Self;
fn modulo_average_floor(&self, other: &Self) -> Self;
}
macro_rules! naive_average {
($T:ident) => {
impl super::NaiveAverage for $T {
fn naive_average_floor(&self, other: &$T) -> $T {
match self.checked_add(*other) {
Some(z) => Integer::div_floor(&z, &2),
None => {
if self > other {
let diff = self - other;
other + Integer::div_floor(&diff, &2)
} else {
let diff = other - self;
self + Integer::div_floor(&diff, &2)
}
}
}
}
fn naive_average_ceil(&self, other: &$T) -> $T {
match self.checked_add(*other) {
Some(z) => Integer::div_ceil(&z, &2),
None => {
if self > other {
let diff = self - other;
self - Integer::div_floor(&diff, &2)
} else {
let diff = other - self;
other - Integer::div_floor(&diff, &2)
}
}
}
}
}
};
}
macro_rules! unchecked_average {
($T:ident) => {
impl super::UncheckedAverage for $T {
fn unchecked_average_floor(&self, other: &$T) -> $T {
self.wrapping_add(*other) / 2
}
fn unchecked_average_ceil(&self, other: &$T) -> $T {
(self.wrapping_add(*other) / 2).wrapping_add(1)
}
}
};
}
macro_rules! modulo_average {
($T:ident) => {
impl super::ModuloAverage for $T {
fn modulo_average_ceil(&self, other: &$T) -> $T {
let (q1, r1) = self.div_mod_floor(&2);
let (q2, r2) = other.div_mod_floor(&2);
q1 + q2 + (r1 | r2)
}
fn modulo_average_floor(&self, other: &$T) -> $T {
let (q1, r1) = self.div_mod_floor(&2);
let (q2, r2) = other.div_mod_floor(&2);
q1 + q2 + (r1 * r2)
}
}
};
}
// --- Bench functions ------------------------------------------------------
fn bench_unchecked<T, F>(b: &mut Bencher, v: &[(T, T)], f: F)
where
T: Integer + Debug + Copy,
F: Fn(&T, &T) -> T,
{
b.iter(|| {
for (x, y) in v {
black_box(f(x, y));
}
});
}
fn bench_ceil<T, F>(b: &mut Bencher, v: &[(T, T)], f: F)
where
T: Integer + Debug + Copy,
F: Fn(&T, &T) -> T,
{
for &(i, j) in v {
let rt = f(&i, &j);
let (a, b) = (min(i, j), max(i, j));
// if both number are the same sign, check rt is in the middle
if (a < T::zero()) == (b < T::zero()) {
if (b - a).is_even() {
assert_eq!(rt - a, b - rt);
} else {
assert_eq!(rt - a, b - rt + T::one());
}
// if both number have a different sign,
} else {
if (a + b).is_even() {
assert_eq!(rt, (a + b) / (T::one() + T::one()))
} else {
assert_eq!(rt, (a + b + T::one()) / (T::one() + T::one()))
}
}
}
bench_unchecked(b, v, f);
}
fn bench_floor<T, F>(b: &mut Bencher, v: &[(T, T)], f: F)
where
T: Integer + Debug + Copy,
F: Fn(&T, &T) -> T,
{
for &(i, j) in v {
let rt = f(&i, &j);
let (a, b) = (min(i, j), max(i, j));
// if both number are the same sign, check rt is in the middle
if (a < T::zero()) == (b < T::zero()) {
if (b - a).is_even() {
assert_eq!(rt - a, b - rt);
} else {
assert_eq!(rt - a + T::one(), b - rt);
}
// if both number have a different sign,
} else {
if (a + b).is_even() {
assert_eq!(rt, (a + b) / (T::one() + T::one()))
} else {
assert_eq!(rt, (a + b - T::one()) / (T::one() + T::one()))
}
}
}
bench_unchecked(b, v, f);
}
// --- Bench implementation -------------------------------------------------
macro_rules! bench_average {
($($T:ident),*) => {$(
mod $T {
use test::Bencher;
use num_integer::{Average, Integer};
use super::{UncheckedAverage, NaiveAverage, ModuloAverage};
use super::{bench_ceil, bench_floor, bench_unchecked};
naive_average!($T);
unchecked_average!($T);
modulo_average!($T);
const SIZE: $T = 30;
fn overflowing() -> Vec<($T, $T)> {
(($T::max_value()-SIZE)..$T::max_value())
.flat_map(|x| -> Vec<_> {
(($T::max_value()-100)..($T::max_value()-100+SIZE))
.map(|y| (x, y))
.collect()
})
.collect()
}
fn small() -> Vec<($T, $T)> {
(0..SIZE)
.flat_map(|x| -> Vec<_> {(0..SIZE).map(|y| (x, y)).collect()})
.collect()
}
fn rand() -> Vec<($T, $T)> {
small()
.into_iter()
.map(|(x, y)| (super::lcg(x), super::lcg(y)))
.collect()
}
mod ceil {
use super::*;
mod small {
use super::*;
#[bench]
fn optimized(b: &mut Bencher) {
let v = small();
bench_ceil(b, &v, |x: &$T, y: &$T| x.average_ceil(y));
}
#[bench]
fn naive(b: &mut Bencher) {
let v = small();
bench_ceil(b, &v, |x: &$T, y: &$T| x.naive_average_ceil(y));
}
#[bench]
fn unchecked(b: &mut Bencher) {
let v = small();
bench_unchecked(b, &v, |x: &$T, y: &$T| x.unchecked_average_ceil(y));
}
#[bench]
fn modulo(b: &mut Bencher) {
let v = small();
bench_ceil(b, &v, |x: &$T, y: &$T| x.modulo_average_ceil(y));
}
}
mod overflowing {
use super::*;
#[bench]
fn optimized(b: &mut Bencher) {
let v = overflowing();
bench_ceil(b, &v, |x: &$T, y: &$T| x.average_ceil(y));
}
#[bench]
fn naive(b: &mut Bencher) {
let v = overflowing();
bench_ceil(b, &v, |x: &$T, y: &$T| x.naive_average_ceil(y));
}
#[bench]
fn unchecked(b: &mut Bencher) {
let v = overflowing();
bench_unchecked(b, &v, |x: &$T, y: &$T| x.unchecked_average_ceil(y));
}
#[bench]
fn modulo(b: &mut Bencher) {
let v = overflowing();
bench_ceil(b, &v, |x: &$T, y: &$T| x.modulo_average_ceil(y));
}
}
mod rand {
use super::*;
#[bench]
fn optimized(b: &mut Bencher) {
let v = rand();
bench_ceil(b, &v, |x: &$T, y: &$T| x.average_ceil(y));
}
#[bench]
fn naive(b: &mut Bencher) {
let v = rand();
bench_ceil(b, &v, |x: &$T, y: &$T| x.naive_average_ceil(y));
}
#[bench]
fn unchecked(b: &mut Bencher) {
let v = rand();
bench_unchecked(b, &v, |x: &$T, y: &$T| x.unchecked_average_ceil(y));
}
#[bench]
fn modulo(b: &mut Bencher) {
let v = rand();
bench_ceil(b, &v, |x: &$T, y: &$T| x.modulo_average_ceil(y));
}
}
}
mod floor {
use super::*;
mod small {
use super::*;
#[bench]
fn optimized(b: &mut Bencher) {
let v = small();
bench_floor(b, &v, |x: &$T, y: &$T| x.average_floor(y));
}
#[bench]
fn naive(b: &mut Bencher) {
let v = small();
bench_floor(b, &v, |x: &$T, y: &$T| x.naive_average_floor(y));
}
#[bench]
fn unchecked(b: &mut Bencher) {
let v = small();
bench_unchecked(b, &v, |x: &$T, y: &$T| x.unchecked_average_floor(y));
}
#[bench]
fn modulo(b: &mut Bencher) {
let v = small();
bench_floor(b, &v, |x: &$T, y: &$T| x.modulo_average_floor(y));
}
}
mod overflowing {
use super::*;
#[bench]
fn optimized(b: &mut Bencher) {
let v = overflowing();
bench_floor(b, &v, |x: &$T, y: &$T| x.average_floor(y));
}
#[bench]
fn naive(b: &mut Bencher) {
let v = overflowing();
bench_floor(b, &v, |x: &$T, y: &$T| x.naive_average_floor(y));
}
#[bench]
fn unchecked(b: &mut Bencher) {
let v = overflowing();
bench_unchecked(b, &v, |x: &$T, y: &$T| x.unchecked_average_floor(y));
}
#[bench]
fn modulo(b: &mut Bencher) {
let v = overflowing();
bench_floor(b, &v, |x: &$T, y: &$T| x.modulo_average_floor(y));
}
}
mod rand {
use super::*;
#[bench]
fn optimized(b: &mut Bencher) {
let v = rand();
bench_floor(b, &v, |x: &$T, y: &$T| x.average_floor(y));
}
#[bench]
fn naive(b: &mut Bencher) {
let v = rand();
bench_floor(b, &v, |x: &$T, y: &$T| x.naive_average_floor(y));
}
#[bench]
fn unchecked(b: &mut Bencher) {
let v = rand();
bench_unchecked(b, &v, |x: &$T, y: &$T| x.unchecked_average_floor(y));
}
#[bench]
fn modulo(b: &mut Bencher) {
let v = rand();
bench_floor(b, &v, |x: &$T, y: &$T| x.modulo_average_floor(y));
}
}
}
}
)*}
}
bench_average!(i8, i16, i32, i64, i128, isize);
bench_average!(u8, u16, u32, u64, u128, usize);

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//! Benchmark comparing the current GCD implemtation against an older one.
#![feature(test)]
extern crate num_integer;
extern crate num_traits;
extern crate test;
use num_integer::Integer;
use num_traits::{AsPrimitive, Bounded, Signed};
use test::{black_box, Bencher};
trait GcdOld: Integer {
fn gcd_old(&self, other: &Self) -> Self;
}
macro_rules! impl_gcd_old_for_isize {
($T:ty) => {
impl GcdOld for $T {
/// Calculates the Greatest Common Divisor (GCD) of the number and
/// `other`. The result is always positive.
#[inline]
fn gcd_old(&self, other: &Self) -> Self {
// Use Stein's algorithm
let mut m = *self;
let mut n = *other;
if m == 0 || n == 0 {
return (m | n).abs();
}
// find common factors of 2
let shift = (m | n).trailing_zeros();
// The algorithm needs positive numbers, but the minimum value
// can't be represented as a positive one.
// It's also a power of two, so the gcd can be
// calculated by bitshifting in that case
// Assuming two's complement, the number created by the shift
// is positive for all numbers except gcd = abs(min value)
// The call to .abs() causes a panic in debug mode
if m == Self::min_value() || n == Self::min_value() {
return (1 << shift).abs();
}
// guaranteed to be positive now, rest like unsigned algorithm
m = m.abs();
n = n.abs();
// divide n and m by 2 until odd
// m inside loop
n >>= n.trailing_zeros();
while m != 0 {
m >>= m.trailing_zeros();
if n > m {
std::mem::swap(&mut n, &mut m)
}
m -= n;
}
n << shift
}
}
};
}
impl_gcd_old_for_isize!(i8);
impl_gcd_old_for_isize!(i16);
impl_gcd_old_for_isize!(i32);
impl_gcd_old_for_isize!(i64);
impl_gcd_old_for_isize!(isize);
impl_gcd_old_for_isize!(i128);
macro_rules! impl_gcd_old_for_usize {
($T:ty) => {
impl GcdOld for $T {
/// Calculates the Greatest Common Divisor (GCD) of the number and
/// `other`. The result is always positive.
#[inline]
fn gcd_old(&self, other: &Self) -> Self {
// Use Stein's algorithm
let mut m = *self;
let mut n = *other;
if m == 0 || n == 0 {
return m | n;
}
// find common factors of 2
let shift = (m | n).trailing_zeros();
// divide n and m by 2 until odd
// m inside loop
n >>= n.trailing_zeros();
while m != 0 {
m >>= m.trailing_zeros();
if n > m {
std::mem::swap(&mut n, &mut m)
}
m -= n;
}
n << shift
}
}
};
}
impl_gcd_old_for_usize!(u8);
impl_gcd_old_for_usize!(u16);
impl_gcd_old_for_usize!(u32);
impl_gcd_old_for_usize!(u64);
impl_gcd_old_for_usize!(usize);
impl_gcd_old_for_usize!(u128);
/// Return an iterator that yields all Fibonacci numbers fitting into a u128.
fn fibonacci() -> impl Iterator<Item = u128> {
(0..185).scan((0, 1), |&mut (ref mut a, ref mut b), _| {
let tmp = *a;
*a = *b;
*b += tmp;
Some(*b)
})
}
fn run_bench<T: Integer + Bounded + Copy + 'static>(b: &mut Bencher, gcd: fn(&T, &T) -> T)
where
T: AsPrimitive<u128>,
u128: AsPrimitive<T>,
{
let max_value: u128 = T::max_value().as_();
let pairs: Vec<(T, T)> = fibonacci()
.collect::<Vec<_>>()
.windows(2)
.filter(|&pair| pair[0] <= max_value && pair[1] <= max_value)
.map(|pair| (pair[0].as_(), pair[1].as_()))
.collect();
b.iter(|| {
for &(ref m, ref n) in &pairs {
black_box(gcd(m, n));
}
});
}
macro_rules! bench_gcd {
($T:ident) => {
mod $T {
use crate::{run_bench, GcdOld};
use num_integer::Integer;
use test::Bencher;
#[bench]
fn bench_gcd(b: &mut Bencher) {
run_bench(b, $T::gcd);
}
#[bench]
fn bench_gcd_old(b: &mut Bencher) {
run_bench(b, $T::gcd_old);
}
}
};
}
bench_gcd!(u8);
bench_gcd!(u16);
bench_gcd!(u32);
bench_gcd!(u64);
bench_gcd!(u128);
bench_gcd!(i8);
bench_gcd!(i16);
bench_gcd!(i32);
bench_gcd!(i64);
bench_gcd!(i128);

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//! Benchmark sqrt and cbrt
#![feature(test)]
extern crate num_integer;
extern crate num_traits;
extern crate test;
use num_integer::Integer;
use num_traits::checked_pow;
use num_traits::{AsPrimitive, PrimInt, WrappingAdd, WrappingMul};
use test::{black_box, Bencher};
trait BenchInteger: Integer + PrimInt + WrappingAdd + WrappingMul + 'static {}
impl<T> BenchInteger for T where T: Integer + PrimInt + WrappingAdd + WrappingMul + 'static {}
fn bench<T, F>(b: &mut Bencher, v: &[T], f: F, n: u32)
where
T: BenchInteger,
F: Fn(&T) -> T,
{
// Pre-validate the results...
for i in v {
let rt = f(i);
if *i >= T::zero() {
let rt1 = rt + T::one();
assert!(rt.pow(n) <= *i);
if let Some(x) = checked_pow(rt1, n as usize) {
assert!(*i < x);
}
} else {
let rt1 = rt - T::one();
assert!(rt < T::zero());
assert!(*i <= rt.pow(n));
if let Some(x) = checked_pow(rt1, n as usize) {
assert!(x < *i);
}
};
}
// Now just run as fast as we can!
b.iter(|| {
for i in v {
black_box(f(i));
}
});
}
// Simple PRNG so we don't have to worry about rand compatibility
fn lcg<T>(x: T) -> T
where
u32: AsPrimitive<T>,
T: BenchInteger,
{
// LCG parameters from Numerical Recipes
// (but we're applying it to arbitrary sizes)
const LCG_A: u32 = 1664525;
const LCG_C: u32 = 1013904223;
x.wrapping_mul(&LCG_A.as_()).wrapping_add(&LCG_C.as_())
}
fn bench_rand<T, F>(b: &mut Bencher, f: F, n: u32)
where
u32: AsPrimitive<T>,
T: BenchInteger,
F: Fn(&T) -> T,
{
let mut x: T = 3u32.as_();
let v: Vec<T> = (0..1000)
.map(|_| {
x = lcg(x);
x
})
.collect();
bench(b, &v, f, n);
}
fn bench_rand_pos<T, F>(b: &mut Bencher, f: F, n: u32)
where
u32: AsPrimitive<T>,
T: BenchInteger,
F: Fn(&T) -> T,
{
let mut x: T = 3u32.as_();
let v: Vec<T> = (0..1000)
.map(|_| {
x = lcg(x);
while x < T::zero() {
x = lcg(x);
}
x
})
.collect();
bench(b, &v, f, n);
}
fn bench_small<T, F>(b: &mut Bencher, f: F, n: u32)
where
u32: AsPrimitive<T>,
T: BenchInteger,
F: Fn(&T) -> T,
{
let v: Vec<T> = (0..1000).map(|i| i.as_()).collect();
bench(b, &v, f, n);
}
fn bench_small_pos<T, F>(b: &mut Bencher, f: F, n: u32)
where
u32: AsPrimitive<T>,
T: BenchInteger,
F: Fn(&T) -> T,
{
let v: Vec<T> = (0..1000)
.map(|i| i.as_().mod_floor(&T::max_value()))
.collect();
bench(b, &v, f, n);
}
macro_rules! bench_roots {
($($T:ident),*) => {$(
mod $T {
use test::Bencher;
use num_integer::Roots;
#[bench]
fn sqrt_rand(b: &mut Bencher) {
::bench_rand_pos(b, $T::sqrt, 2);
}
#[bench]
fn sqrt_small(b: &mut Bencher) {
::bench_small_pos(b, $T::sqrt, 2);
}
#[bench]
fn cbrt_rand(b: &mut Bencher) {
::bench_rand(b, $T::cbrt, 3);
}
#[bench]
fn cbrt_small(b: &mut Bencher) {
::bench_small(b, $T::cbrt, 3);
}
#[bench]
fn fourth_root_rand(b: &mut Bencher) {
::bench_rand_pos(b, |x: &$T| x.nth_root(4), 4);
}
#[bench]
fn fourth_root_small(b: &mut Bencher) {
::bench_small_pos(b, |x: &$T| x.nth_root(4), 4);
}
#[bench]
fn fifth_root_rand(b: &mut Bencher) {
::bench_rand(b, |x: &$T| x.nth_root(5), 5);
}
#[bench]
fn fifth_root_small(b: &mut Bencher) {
::bench_small(b, |x: &$T| x.nth_root(5), 5);
}
}
)*}
}
bench_roots!(i8, i16, i32, i64, i128);
bench_roots!(u8, u16, u32, u64, u128);

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extern crate autocfg;
use std::env;
fn main() {
// If the "i128" feature is explicity requested, don't bother probing for it.
// It will still cause a build error if that was set improperly.
if env::var_os("CARGO_FEATURE_I128").is_some() || autocfg::new().probe_type("i128") {
autocfg::emit("has_i128");
}
autocfg::rerun_path("build.rs");
}

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use core::ops::{BitAnd, BitOr, BitXor, Shr};
use Integer;
/// Provides methods to compute the average of two integers, without overflows.
pub trait Average: Integer {
/// Returns the ceiling value of the average of `self` and `other`.
/// -- `⌈(self + other)/2⌉`
///
/// # Examples
///
/// ```
/// use num_integer::Average;
///
/// assert_eq!(( 3).average_ceil(&10), 7);
/// assert_eq!((-2).average_ceil(&-5), -3);
/// assert_eq!(( 4).average_ceil(& 4), 4);
///
/// assert_eq!(u8::max_value().average_ceil(&2), 129);
/// assert_eq!(i8::min_value().average_ceil(&-1), -64);
/// assert_eq!(i8::min_value().average_ceil(&i8::max_value()), 0);
/// ```
///
fn average_ceil(&self, other: &Self) -> Self;
/// Returns the floor value of the average of `self` and `other`.
/// -- `⌊(self + other)/2⌋`
///
/// # Examples
///
/// ```
/// use num_integer::Average;
///
/// assert_eq!(( 3).average_floor(&10), 6);
/// assert_eq!((-2).average_floor(&-5), -4);
/// assert_eq!(( 4).average_floor(& 4), 4);
///
/// assert_eq!(u8::max_value().average_floor(&2), 128);
/// assert_eq!(i8::min_value().average_floor(&-1), -65);
/// assert_eq!(i8::min_value().average_floor(&i8::max_value()), -1);
/// ```
///
fn average_floor(&self, other: &Self) -> Self;
}
impl<I> Average for I
where
I: Integer + Shr<usize, Output = I>,
for<'a, 'b> &'a I:
BitAnd<&'b I, Output = I> + BitOr<&'b I, Output = I> + BitXor<&'b I, Output = I>,
{
// The Henry Gordon Dietz implementation as shown in the Hacker's Delight,
// see http://aggregate.org/MAGIC/#Average%20of%20Integers
/// Returns the floor value of the average of `self` and `other`.
#[inline]
fn average_floor(&self, other: &I) -> I {
(self & other) + ((self ^ other) >> 1)
}
/// Returns the ceil value of the average of `self` and `other`.
#[inline]
fn average_ceil(&self, other: &I) -> I {
(self | other) - ((self ^ other) >> 1)
}
}
/// Returns the floor value of the average of `x` and `y` --
/// see [Average::average_floor](trait.Average.html#tymethod.average_floor).
#[inline]
pub fn average_floor<T: Average>(x: T, y: T) -> T {
x.average_floor(&y)
}
/// Returns the ceiling value of the average of `x` and `y` --
/// see [Average::average_ceil](trait.Average.html#tymethod.average_ceil).
#[inline]
pub fn average_ceil<T: Average>(x: T, y: T) -> T {
x.average_ceil(&y)
}

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use core;
use core::mem;
use traits::checked_pow;
use traits::PrimInt;
use Integer;
/// Provides methods to compute an integer's square root, cube root,
/// and arbitrary `n`th root.
pub trait Roots: Integer {
/// Returns the truncated principal `n`th root of an integer
/// -- `if x >= 0 { ⌊ⁿ√x⌋ } else { ⌈ⁿ√x⌉ }`
///
/// This is solving for `r` in `rⁿ = x`, rounding toward zero.
/// If `x` is positive, the result will satisfy `rⁿ ≤ x < (r+1)ⁿ`.
/// If `x` is negative and `n` is odd, then `(r-1)ⁿ < x ≤ rⁿ`.
///
/// # Panics
///
/// Panics if `n` is zero:
///
/// ```should_panic
/// # use num_integer::Roots;
/// println!("can't compute ⁰√x : {}", 123.nth_root(0));
/// ```
///
/// or if `n` is even and `self` is negative:
///
/// ```should_panic
/// # use num_integer::Roots;
/// println!("no imaginary numbers... {}", (-1).nth_root(10));
/// ```
///
/// # Examples
///
/// ```
/// use num_integer::Roots;
///
/// let x: i32 = 12345;
/// assert_eq!(x.nth_root(1), x);
/// assert_eq!(x.nth_root(2), x.sqrt());
/// assert_eq!(x.nth_root(3), x.cbrt());
/// assert_eq!(x.nth_root(4), 10);
/// assert_eq!(x.nth_root(13), 2);
/// assert_eq!(x.nth_root(14), 1);
/// assert_eq!(x.nth_root(std::u32::MAX), 1);
///
/// assert_eq!(std::i32::MAX.nth_root(30), 2);
/// assert_eq!(std::i32::MAX.nth_root(31), 1);
/// assert_eq!(std::i32::MIN.nth_root(31), -2);
/// assert_eq!((std::i32::MIN + 1).nth_root(31), -1);
///
/// assert_eq!(std::u32::MAX.nth_root(31), 2);
/// assert_eq!(std::u32::MAX.nth_root(32), 1);
/// ```
fn nth_root(&self, n: u32) -> Self;
/// Returns the truncated principal square root of an integer -- `⌊√x⌋`
///
/// This is solving for `r` in `r² = x`, rounding toward zero.
/// The result will satisfy `r² ≤ x < (r+1)²`.
///
/// # Panics
///
/// Panics if `self` is less than zero:
///
/// ```should_panic
/// # use num_integer::Roots;
/// println!("no imaginary numbers... {}", (-1).sqrt());
/// ```
///
/// # Examples
///
/// ```
/// use num_integer::Roots;
///
/// let x: i32 = 12345;
/// assert_eq!((x * x).sqrt(), x);
/// assert_eq!((x * x + 1).sqrt(), x);
/// assert_eq!((x * x - 1).sqrt(), x - 1);
/// ```
#[inline]
fn sqrt(&self) -> Self {
self.nth_root(2)
}
/// Returns the truncated principal cube root of an integer --
/// `if x >= 0 { ⌊∛x⌋ } else { ⌈∛x⌉ }`
///
/// This is solving for `r` in `r³ = x`, rounding toward zero.
/// If `x` is positive, the result will satisfy `r³ ≤ x < (r+1)³`.
/// If `x` is negative, then `(r-1)³ < x ≤ r³`.
///
/// # Examples
///
/// ```
/// use num_integer::Roots;
///
/// let x: i32 = 1234;
/// assert_eq!((x * x * x).cbrt(), x);
/// assert_eq!((x * x * x + 1).cbrt(), x);
/// assert_eq!((x * x * x - 1).cbrt(), x - 1);
///
/// assert_eq!((-(x * x * x)).cbrt(), -x);
/// assert_eq!((-(x * x * x + 1)).cbrt(), -x);
/// assert_eq!((-(x * x * x - 1)).cbrt(), -(x - 1));
/// ```
#[inline]
fn cbrt(&self) -> Self {
self.nth_root(3)
}
}
/// Returns the truncated principal square root of an integer --
/// see [Roots::sqrt](trait.Roots.html#method.sqrt).
#[inline]
pub fn sqrt<T: Roots>(x: T) -> T {
x.sqrt()
}
/// Returns the truncated principal cube root of an integer --
/// see [Roots::cbrt](trait.Roots.html#method.cbrt).
#[inline]
pub fn cbrt<T: Roots>(x: T) -> T {
x.cbrt()
}
/// Returns the truncated principal `n`th root of an integer --
/// see [Roots::nth_root](trait.Roots.html#tymethod.nth_root).
#[inline]
pub fn nth_root<T: Roots>(x: T, n: u32) -> T {
x.nth_root(n)
}
macro_rules! signed_roots {
($T:ty, $U:ty) => {
impl Roots for $T {
#[inline]
fn nth_root(&self, n: u32) -> Self {
if *self >= 0 {
(*self as $U).nth_root(n) as Self
} else {
assert!(n.is_odd(), "even roots of a negative are imaginary");
-((self.wrapping_neg() as $U).nth_root(n) as Self)
}
}
#[inline]
fn sqrt(&self) -> Self {
assert!(*self >= 0, "the square root of a negative is imaginary");
(*self as $U).sqrt() as Self
}
#[inline]
fn cbrt(&self) -> Self {
if *self >= 0 {
(*self as $U).cbrt() as Self
} else {
-((self.wrapping_neg() as $U).cbrt() as Self)
}
}
}
};
}
signed_roots!(i8, u8);
signed_roots!(i16, u16);
signed_roots!(i32, u32);
signed_roots!(i64, u64);
#[cfg(has_i128)]
signed_roots!(i128, u128);
signed_roots!(isize, usize);
#[inline]
fn fixpoint<T, F>(mut x: T, f: F) -> T
where
T: Integer + Copy,
F: Fn(T) -> T,
{
let mut xn = f(x);
while x < xn {
x = xn;
xn = f(x);
}
while x > xn {
x = xn;
xn = f(x);
}
x
}
#[inline]
fn bits<T>() -> u32 {
8 * mem::size_of::<T>() as u32
}
#[inline]
fn log2<T: PrimInt>(x: T) -> u32 {
debug_assert!(x > T::zero());
bits::<T>() - 1 - x.leading_zeros()
}
macro_rules! unsigned_roots {
($T:ident) => {
impl Roots for $T {
#[inline]
fn nth_root(&self, n: u32) -> Self {
fn go(a: $T, n: u32) -> $T {
// Specialize small roots
match n {
0 => panic!("can't find a root of degree 0!"),
1 => return a,
2 => return a.sqrt(),
3 => return a.cbrt(),
_ => (),
}
// The root of values less than 2ⁿ can only be 0 or 1.
if bits::<$T>() <= n || a < (1 << n) {
return (a > 0) as $T;
}
if bits::<$T>() > 64 {
// 128-bit division is slow, so do a bitwise `nth_root` until it's small enough.
return if a <= core::u64::MAX as $T {
(a as u64).nth_root(n) as $T
} else {
let lo = (a >> n).nth_root(n) << 1;
let hi = lo + 1;
// 128-bit `checked_mul` also involves division, but we can't always
// compute `hiⁿ` without risking overflow. Try to avoid it though...
if hi.next_power_of_two().trailing_zeros() * n >= bits::<$T>() {
match checked_pow(hi, n as usize) {
Some(x) if x <= a => hi,
_ => lo,
}
} else {
if hi.pow(n) <= a {
hi
} else {
lo
}
}
};
}
#[cfg(feature = "std")]
#[inline]
fn guess(x: $T, n: u32) -> $T {
// for smaller inputs, `f64` doesn't justify its cost.
if bits::<$T>() <= 32 || x <= core::u32::MAX as $T {
1 << ((log2(x) + n - 1) / n)
} else {
((x as f64).ln() / f64::from(n)).exp() as $T
}
}
#[cfg(not(feature = "std"))]
#[inline]
fn guess(x: $T, n: u32) -> $T {
1 << ((log2(x) + n - 1) / n)
}
// https://en.wikipedia.org/wiki/Nth_root_algorithm
let n1 = n - 1;
let next = |x: $T| {
let y = match checked_pow(x, n1 as usize) {
Some(ax) => a / ax,
None => 0,
};
(y + x * n1 as $T) / n as $T
};
fixpoint(guess(a, n), next)
}
go(*self, n)
}
#[inline]
fn sqrt(&self) -> Self {
fn go(a: $T) -> $T {
if bits::<$T>() > 64 {
// 128-bit division is slow, so do a bitwise `sqrt` until it's small enough.
return if a <= core::u64::MAX as $T {
(a as u64).sqrt() as $T
} else {
let lo = (a >> 2u32).sqrt() << 1;
let hi = lo + 1;
if hi * hi <= a {
hi
} else {
lo
}
};
}
if a < 4 {
return (a > 0) as $T;
}
#[cfg(feature = "std")]
#[inline]
fn guess(x: $T) -> $T {
(x as f64).sqrt() as $T
}
#[cfg(not(feature = "std"))]
#[inline]
fn guess(x: $T) -> $T {
1 << ((log2(x) + 1) / 2)
}
// https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method
let next = |x: $T| (a / x + x) >> 1;
fixpoint(guess(a), next)
}
go(*self)
}
#[inline]
fn cbrt(&self) -> Self {
fn go(a: $T) -> $T {
if bits::<$T>() > 64 {
// 128-bit division is slow, so do a bitwise `cbrt` until it's small enough.
return if a <= core::u64::MAX as $T {
(a as u64).cbrt() as $T
} else {
let lo = (a >> 3u32).cbrt() << 1;
let hi = lo + 1;
if hi * hi * hi <= a {
hi
} else {
lo
}
};
}
if bits::<$T>() <= 32 {
// Implementation based on Hacker's Delight `icbrt2`
let mut x = a;
let mut y2 = 0;
let mut y = 0;
let smax = bits::<$T>() / 3;
for s in (0..smax + 1).rev() {
let s = s * 3;
y2 *= 4;
y *= 2;
let b = 3 * (y2 + y) + 1;
if x >> s >= b {
x -= b << s;
y2 += 2 * y + 1;
y += 1;
}
}
return y;
}
if a < 8 {
return (a > 0) as $T;
}
if a <= core::u32::MAX as $T {
return (a as u32).cbrt() as $T;
}
#[cfg(feature = "std")]
#[inline]
fn guess(x: $T) -> $T {
(x as f64).cbrt() as $T
}
#[cfg(not(feature = "std"))]
#[inline]
fn guess(x: $T) -> $T {
1 << ((log2(x) + 2) / 3)
}
// https://en.wikipedia.org/wiki/Cube_root#Numerical_methods
let next = |x: $T| (a / (x * x) + x * 2) / 3;
fixpoint(guess(a), next)
}
go(*self)
}
}
};
}
unsigned_roots!(u8);
unsigned_roots!(u16);
unsigned_roots!(u32);
unsigned_roots!(u64);
#[cfg(has_i128)]
unsigned_roots!(u128);
unsigned_roots!(usize);

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extern crate num_integer;
extern crate num_traits;
macro_rules! test_average {
($I:ident, $U:ident) => {
mod $I {
mod ceil {
use num_integer::Average;
#[test]
fn same_sign() {
assert_eq!((14 as $I).average_ceil(&16), 15 as $I);
assert_eq!((14 as $I).average_ceil(&17), 16 as $I);
let max = $crate::std::$I::MAX;
assert_eq!((max - 3).average_ceil(&(max - 1)), max - 2);
assert_eq!((max - 3).average_ceil(&(max - 2)), max - 2);
}
#[test]
fn different_sign() {
assert_eq!((14 as $I).average_ceil(&-4), 5 as $I);
assert_eq!((14 as $I).average_ceil(&-5), 5 as $I);
let min = $crate::std::$I::MIN;
let max = $crate::std::$I::MAX;
assert_eq!(min.average_ceil(&max), 0 as $I);
}
}
mod floor {
use num_integer::Average;
#[test]
fn same_sign() {
assert_eq!((14 as $I).average_floor(&16), 15 as $I);
assert_eq!((14 as $I).average_floor(&17), 15 as $I);
let max = $crate::std::$I::MAX;
assert_eq!((max - 3).average_floor(&(max - 1)), max - 2);
assert_eq!((max - 3).average_floor(&(max - 2)), max - 3);
}
#[test]
fn different_sign() {
assert_eq!((14 as $I).average_floor(&-4), 5 as $I);
assert_eq!((14 as $I).average_floor(&-5), 4 as $I);
let min = $crate::std::$I::MIN;
let max = $crate::std::$I::MAX;
assert_eq!(min.average_floor(&max), -1 as $I);
}
}
}
mod $U {
mod ceil {
use num_integer::Average;
#[test]
fn bounded() {
assert_eq!((14 as $U).average_ceil(&16), 15 as $U);
assert_eq!((14 as $U).average_ceil(&17), 16 as $U);
}
#[test]
fn overflow() {
let max = $crate::std::$U::MAX;
assert_eq!((max - 3).average_ceil(&(max - 1)), max - 2);
assert_eq!((max - 3).average_ceil(&(max - 2)), max - 2);
}
}
mod floor {
use num_integer::Average;
#[test]
fn bounded() {
assert_eq!((14 as $U).average_floor(&16), 15 as $U);
assert_eq!((14 as $U).average_floor(&17), 15 as $U);
}
#[test]
fn overflow() {
let max = $crate::std::$U::MAX;
assert_eq!((max - 3).average_floor(&(max - 1)), max - 2);
assert_eq!((max - 3).average_floor(&(max - 2)), max - 3);
}
}
}
};
}
test_average!(i8, u8);
test_average!(i16, u16);
test_average!(i32, u32);
test_average!(i64, u64);
#[cfg(has_i128)]
test_average!(i128, u128);
test_average!(isize, usize);

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extern crate num_integer;
extern crate num_traits;
use num_integer::Roots;
use num_traits::checked_pow;
use num_traits::{AsPrimitive, PrimInt, Signed};
use std::f64::MANTISSA_DIGITS;
use std::fmt::Debug;
use std::mem;
trait TestInteger: Roots + PrimInt + Debug + AsPrimitive<f64> + 'static {}
impl<T> TestInteger for T where T: Roots + PrimInt + Debug + AsPrimitive<f64> + 'static {}
/// Check that each root is correct
///
/// If `x` is positive, check `rⁿ ≤ x < (r+1)ⁿ`.
/// If `x` is negative, check `(r-1)ⁿ < x ≤ rⁿ`.
fn check<T>(v: &[T], n: u32)
where
T: TestInteger,
{
for i in v {
let rt = i.nth_root(n);
// println!("nth_root({:?}, {}) = {:?}", i, n, rt);
if n == 2 {
assert_eq!(rt, i.sqrt());
} else if n == 3 {
assert_eq!(rt, i.cbrt());
}
if *i >= T::zero() {
let rt1 = rt + T::one();
assert!(rt.pow(n) <= *i);
if let Some(x) = checked_pow(rt1, n as usize) {
assert!(*i < x);
}
} else {
let rt1 = rt - T::one();
assert!(rt < T::zero());
assert!(*i <= rt.pow(n));
if let Some(x) = checked_pow(rt1, n as usize) {
assert!(x < *i);
}
};
}
}
/// Get the maximum value that will round down as `f64` (if any),
/// and its successor that will round up.
///
/// Important because the `std` implementations cast to `f64` to
/// get a close approximation of the roots.
fn mantissa_max<T>() -> Option<(T, T)>
where
T: TestInteger,
{
let bits = if T::min_value().is_zero() {
8 * mem::size_of::<T>()
} else {
8 * mem::size_of::<T>() - 1
};
if bits > MANTISSA_DIGITS as usize {
let rounding_bit = T::one() << (bits - MANTISSA_DIGITS as usize - 1);
let x = T::max_value() - rounding_bit;
let x1 = x + T::one();
let x2 = x1 + T::one();
assert!(x.as_() < x1.as_());
assert_eq!(x1.as_(), x2.as_());
Some((x, x1))
} else {
None
}
}
fn extend<T>(v: &mut Vec<T>, start: T, end: T)
where
T: TestInteger,
{
let mut i = start;
while i < end {
v.push(i);
i = i + T::one();
}
v.push(i);
}
fn extend_shl<T>(v: &mut Vec<T>, start: T, end: T, mask: T)
where
T: TestInteger,
{
let mut i = start;
while i != end {
v.push(i);
i = (i << 1) & mask;
}
}
fn extend_shr<T>(v: &mut Vec<T>, start: T, end: T)
where
T: TestInteger,
{
let mut i = start;
while i != end {
v.push(i);
i = i >> 1;
}
}
fn pos<T>() -> Vec<T>
where
T: TestInteger,
i8: AsPrimitive<T>,
{
let mut v: Vec<T> = vec![];
if mem::size_of::<T>() == 1 {
extend(&mut v, T::zero(), T::max_value());
} else {
extend(&mut v, T::zero(), i8::max_value().as_());
extend(
&mut v,
T::max_value() - i8::max_value().as_(),
T::max_value(),
);
if let Some((i, j)) = mantissa_max::<T>() {
v.push(i);
v.push(j);
}
extend_shl(&mut v, T::max_value(), T::zero(), !T::min_value());
extend_shr(&mut v, T::max_value(), T::zero());
}
v
}
fn neg<T>() -> Vec<T>
where
T: TestInteger + Signed,
i8: AsPrimitive<T>,
{
let mut v: Vec<T> = vec![];
if mem::size_of::<T>() <= 1 {
extend(&mut v, T::min_value(), T::zero());
} else {
extend(&mut v, i8::min_value().as_(), T::zero());
extend(
&mut v,
T::min_value(),
T::min_value() - i8::min_value().as_(),
);
if let Some((i, j)) = mantissa_max::<T>() {
v.push(-i);
v.push(-j);
}
extend_shl(&mut v, -T::one(), T::min_value(), !T::zero());
extend_shr(&mut v, T::min_value(), -T::one());
}
v
}
macro_rules! test_roots {
($I:ident, $U:ident) => {
mod $I {
use check;
use neg;
use num_integer::Roots;
use pos;
use std::mem;
#[test]
#[should_panic]
fn zeroth_root() {
(123 as $I).nth_root(0);
}
#[test]
fn sqrt() {
check(&pos::<$I>(), 2);
}
#[test]
#[should_panic]
fn sqrt_neg() {
(-123 as $I).sqrt();
}
#[test]
fn cbrt() {
check(&pos::<$I>(), 3);
}
#[test]
fn cbrt_neg() {
check(&neg::<$I>(), 3);
}
#[test]
fn nth_root() {
let bits = 8 * mem::size_of::<$I>() as u32 - 1;
let pos = pos::<$I>();
for n in 4..bits {
check(&pos, n);
}
}
#[test]
fn nth_root_neg() {
let bits = 8 * mem::size_of::<$I>() as u32 - 1;
let neg = neg::<$I>();
for n in 2..bits / 2 {
check(&neg, 2 * n + 1);
}
}
#[test]
fn bit_size() {
let bits = 8 * mem::size_of::<$I>() as u32 - 1;
assert_eq!($I::max_value().nth_root(bits - 1), 2);
assert_eq!($I::max_value().nth_root(bits), 1);
assert_eq!($I::min_value().nth_root(bits), -2);
assert_eq!(($I::min_value() + 1).nth_root(bits), -1);
}
}
mod $U {
use check;
use num_integer::Roots;
use pos;
use std::mem;
#[test]
#[should_panic]
fn zeroth_root() {
(123 as $U).nth_root(0);
}
#[test]
fn sqrt() {
check(&pos::<$U>(), 2);
}
#[test]
fn cbrt() {
check(&pos::<$U>(), 3);
}
#[test]
fn nth_root() {
let bits = 8 * mem::size_of::<$I>() as u32 - 1;
let pos = pos::<$I>();
for n in 4..bits {
check(&pos, n);
}
}
#[test]
fn bit_size() {
let bits = 8 * mem::size_of::<$U>() as u32;
assert_eq!($U::max_value().nth_root(bits - 1), 2);
assert_eq!($U::max_value().nth_root(bits), 1);
}
}
};
}
test_roots!(i8, u8);
test_roots!(i16, u16);
test_roots!(i32, u32);
test_roots!(i64, u64);
#[cfg(has_i128)]
test_roots!(i128, u128);
test_roots!(isize, usize);