86 changed files with 18956 additions and 6344 deletions
--- a/.travis.yml
+++ b/.travis.yml
@ -1,46 +1,25 @@
 language: rust
 sudo: false
 rust:
  - 1.8.0
  - 1.15.0
  - 1.20.0
  - 1.26.0 # has_i128
  - 1.31.0 # 2018!
  - 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
-matrix:
+  - cargo doc
-  include:
+after_success: |
-    # i586 presents floating point challenges for lack of SSE/SSE2
+  [ $TRAVIS_BRANCH = master ] &&
-    - name: "i586"
+  [ $TRAVIS_PULL_REQUEST = false ] &&
-      rust: stable
+  [ $TRAVIS_RUST_VERSION = nightly ] &&
-      env: TARGET=i586-unknown-linux-gnu
+  ssh-agent ./ci/deploy.sh
      addons:
        apt:
          packages:
            - gcc-multilib
      before_script:
        - rustup target add $TARGET
      script:
        - cargo test --verbose --target $TARGET --all-features
    # try a target that doesn't have std at all
    - name: "no_std"
      rust: stable
      env: TARGET=thumbv6m-none-eabi
      before_script:
        - rustup target add $TARGET
      script:
        - cargo build --verbose --target $TARGET --no-default-features --features i128
        - cargo build --verbose --target $TARGET --no-default-features --features libm
    - name: "rustfmt"
      rust: 1.31.0
      before_script:
        - rustup component add rustfmt
      script:
        - cargo fmt --all -- --check
 notifications:
  email:
    on_success: never
--- a/Cargo.toml
+++ b/Cargo.toml
@ -1,28 +1,73 @@
 [package]
 authors = ["The Rust Project Developers"]
-description = "Numeric traits for generic mathematics"
+description = "A collection of numeric types and traits for Rust, including bigint,\ncomplex, rational, range iterators, generic integers, and more!\n"
-documentation = "https://docs.rs/num-traits"
+documentation = "http://rust-num.github.io/num"
-homepage = "https://github.com/rust-num/num-traits"
+homepage = "https://github.com/rust-num/num"
-keywords = ["mathematics", "numerics"]
+keywords = ["mathematics", "numerics", "bignum"]
-categories = ["algorithms", "science", "no-std"]
+categories = [ "algorithms", "data-structures", "science" ]
 license = "MIT/Apache-2.0"
-repository = "https://github.com/rust-num/num-traits"
+repository = "https://github.com/rust-num/num"
-name = "num-traits"
+name = "num"
-version = "0.2.8"
+version = "0.1.40"
 readme = "README.md"
 build = "build.rs"
 exclude = ["/ci/*", "/.travis.yml", "/bors.toml"]
-[package.metadata.docs.rs]
+[badges]
-features = ["std"]
+travis-ci = { repository = "rust-num/num" }
 [[bench]]
 name = "bigint"
 [[bench]]
 harness = false
 name = "shootout-pidigits"
 [dependencies]
-libm = { version = "0.1.4", optional = true }
+
 [dependencies.num-bigint]
 optional = true
 path = "bigint"
 version = "0.1.40"
 [dependencies.num-complex]
 optional = true
 path = "complex"
 version = "0.1.39"
 [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 = "0.1.39"
 [dependencies.num-traits]
 path = "./traits"
 version = "0.1.40"
 [dev-dependencies]
 [dev-dependencies.rand]
 version = "0.3.8"
 [features]
-default = ["std"]
+bigint = ["num-bigint"]
-std = []
+complex = ["num-complex"]
-i128 = []
+rational = ["num-rational"]
 default = ["bigint", "complex", "rational", "rustc-serialize"]
-[build-dependencies]
+serde = [
-autocfg = "0.1.3"
+  "num-bigint/serde",
  "num-complex/serde",
  "num-rational/serde"
 ]
 rustc-serialize = [
  "num-bigint/rustc-serialize",
  "num-complex/rustc-serialize",
  "num-rational/rustc-serialize"
 ]
--- a/README.md
+++ b/README.md
@ -1,11 +1,14 @@
-# num-traits
+# num
-[![crate](https://img.shields.io/crates/v/num-traits.svg)](https://crates.io/crates/num-traits)
+[![](https://travis-ci.org/rust-num/num.svg)](https://travis-ci.org/rust-num/num)
 [![documentation](https://docs.rs/num-traits/badge.svg)](https://docs.rs/num-traits)
 ![minimum rustc 1.8](https://img.shields.io/badge/rustc-1.8+-red.svg)
 [![Travis status](https://travis-ci.org/rust-num/num-traits.svg?branch=master)](https://travis-ci.org/rust-num/num-traits)
-Numeric traits for generic mathematics in Rust.
+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)
 ## Usage
@ -13,42 +16,17 @@ Add this to your `Cargo.toml`:
 ```toml
 [dependencies]
-num-traits = "0.2"
+num = "0.1"
 ```
 and this to your crate root:
 ```rust
-extern crate num_traits;
+extern crate num;
 ```
 ## Features
 This crate can be used without the standard library (`#![no_std]`) by disabling
 the default `std` feature. Use this in `Cargo.toml`:
 ```toml
 [dependencies.num-traits]
 version = "0.2"
 default-features = false
 # features = ["libm"]    # <--- Uncomment if you wish to use `Float` and `Real` without `std`
 ```
 The `Float` and `Real` traits are only available when either `std` or `libm` is enabled.  
 The `libm` feature is only available with Rust 1.31 and later ([see PR #99](https://github.com/rust-num/num-traits/pull/99)).
 The `FloatCore` trait is always available.  `MulAdd` and `MulAddAssign` for `f32`
 and `f64` also require `std` or `libm`, as do implementations of signed and floating-
 point exponents in `Pow`.
 Implementations for `i128` and `u128` are only available with Rust 1.26 and
 later.  The build script automatically detects this, but you can make it
 mandatory by enabling the `i128` crate feature.
 ## Releases
 Release notes are available in [RELEASES.md](RELEASES.md).
 ## Compatibility
-The `num-traits` crate is tested for rustc 1.8 and greater.
+Most of the `num` crates are tested for rustc 1.8 and greater.
 The exceptions are `num-derive` which requires at least rustc 1.15,
 and the deprecated `num-macros` which requires nightly rustc.
--- a/RELEASES.md
+++ b/RELEASES.md
@ -1,154 +0,0 @@
 # Release 0.2.8 (2019-05-21)
 - [Fixed feature detection on `no_std` targets][116].
 **Contributors**: @cuviper
 [116]: https://github.com/rust-num/num-traits/pull/116
 # Release 0.2.7 (2019-05-20)
 - [Documented when `CheckedShl` and `CheckedShr` return `None`][90].
 - [The new `Zero::set_zero` and `One::set_one`][104] will set values to their
  identities in place, possibly optimized better than direct assignment.
 - [Documented general features and intentions of `PrimInt`][108].
 **Contributors**: @cuviper, @dvdhrm, @ignatenkobrain, @lcnr, @samueltardieu
 [90]: https://github.com/rust-num/num-traits/pull/90
 [104]: https://github.com/rust-num/num-traits/pull/104
 [108]: https://github.com/rust-num/num-traits/pull/108
 # Release 0.2.6 (2018-09-13)
 - [Documented that `pow(0, 0)` returns `1`][79].  Mathematically, this is not
  strictly defined, but the current behavior is a pragmatic choice that has
  precedent in Rust `core` for the primitives and in many other languages.
 - [The new `WrappingShl` and `WrappingShr` traits][81] will wrap the shift count
  if it exceeds the bit size of the type.
 **Contributors**: @cuviper, @edmccard, @meltinglava
 [79]: https://github.com/rust-num/num-traits/pull/79
 [81]: https://github.com/rust-num/num-traits/pull/81
 # Release 0.2.5 (2018-06-20)
 - [Documentation for `mul_add` now clarifies that it's not always faster.][70]
 - [The default methods in `FromPrimitive` and `ToPrimitive` are more robust.][73]
 **Contributors**: @cuviper, @frewsxcv
 [70]: https://github.com/rust-num/num-traits/pull/70
 [73]: https://github.com/rust-num/num-traits/pull/73
 # Release 0.2.4 (2018-05-11)
 - [Support for 128-bit integers is now automatically detected and enabled.][69]
  Setting the `i128` crate feature now causes the build script to panic if such
  support is not detected.
 **Contributors**: @cuviper
 [69]: https://github.com/rust-num/num-traits/pull/69
 # Release 0.2.3 (2018-05-10)
 - [The new `CheckedNeg` and `CheckedRem` traits][63] perform checked `Neg` and
  `Rem`, returning `Some(output)` or `None` on overflow.
 - [The `no_std` implementation of `FloatCore::to_degrees` for `f32`][61] now
  uses a constant for greater accuracy, mirroring [rust#47919].  (With `std` it
  just calls the inherent `f32::to_degrees` in the standard library.)
 - [The new `MulAdd` and `MulAddAssign` traits][59] perform a fused multiply-
  add.  For integer types this is just a convenience, but for floating point
  types this produces a more accurate result than the separate operations.
 - [All applicable traits are now implemented for 128-bit integers][60] starting
  with Rust 1.26, enabled by the new `i128` crate feature.  The `FromPrimitive`
  and `ToPrimitive` traits now also have corresponding 128-bit methods, which
  default to converting via 64-bit integers for compatibility.
 **Contributors**: @cuviper, @LEXUGE, @regexident, @vks
 [59]: https://github.com/rust-num/num-traits/pull/59
 [60]: https://github.com/rust-num/num-traits/pull/60
 [61]: https://github.com/rust-num/num-traits/pull/61
 [63]: https://github.com/rust-num/num-traits/pull/63
 [rust#47919]: https://github.com/rust-lang/rust/pull/47919
 # Release 0.2.2 (2018-03-18)
 - [Casting from floating point to integers now returns `None` on overflow][52],
  avoiding [rustc's undefined behavior][rust-10184]. This applies to the `cast`
  function and the traits `NumCast`, `FromPrimitive`, and `ToPrimitive`.
 **Contributors**: @apopiak, @cuviper, @dbarella
 [52]: https://github.com/rust-num/num-traits/pull/52
 [rust-10184]: https://github.com/rust-lang/rust/issues/10184
 # Release 0.2.1 (2018-03-01)
 - [The new `FloatCore` trait][32] offers a subset of `Float` for `#![no_std]` use.
  [This includes everything][41] except the transcendental functions and FMA.
 - [The new `Inv` trait][37] returns the multiplicative inverse, or reciprocal.
 - [The new `Pow` trait][37] performs exponentiation, much like the existing `pow`
  function, but with generic exponent types.
 - [The new `One::is_one` method][39] tests if a value equals 1.  Implementers
  should override this method if there's a more efficient way to check for 1,
  rather than comparing with a temporary `one()`.
 **Contributors**: @clarcharr, @cuviper, @vks
 [32]: https://github.com/rust-num/num-traits/pull/32
 [37]: https://github.com/rust-num/num-traits/pull/37
 [39]: https://github.com/rust-num/num-traits/pull/39
 [41]: https://github.com/rust-num/num-traits/pull/41
 # Release 0.2.0 (2018-02-06)
 - **breaking change**: [There is now a `std` feature][30], enabled by default, along
  with the implication that building *without* this feature makes this a
  `#![no_std]` crate.
  - The `Float` and `Real` traits are only available when `std` is enabled.
  - Otherwise, the API is unchanged, and num-traits 0.1.43 now re-exports its
    items from num-traits 0.2 for compatibility (the [semver-trick]).
 **Contributors**: @cuviper, @termoshtt, @vks
 [semver-trick]: https://github.com/dtolnay/semver-trick
 [30]: https://github.com/rust-num/num-traits/pull/30
 # Release 0.1.43 (2018-02-06)
 - All items are now [re-exported from num-traits 0.2][31] for compatibility.
 [31]: https://github.com/rust-num/num-traits/pull/31
 # Release 0.1.42 (2018-01-22)
 - [num-traits now has its own source repository][num-356] at [rust-num/num-traits][home].
 - [`ParseFloatError` now implements `Display`][22].
 - [The new `AsPrimitive` trait][17] implements generic casting with the `as` operator.
 - [The new `CheckedShl` and `CheckedShr` traits][21] implement generic
  support for the `checked_shl` and `checked_shr` methods on primitive integers.
 - [The new `Real` trait][23] offers a subset of `Float` functionality that may be applicable to more
  types, with a blanket implementation for all existing `T: Float` types.
 Thanks to @cuviper, @Enet4, @fabianschuiki, @svartalf, and @yoanlcq for their contributions!
 [home]: https://github.com/rust-num/num-traits
 [num-356]: https://github.com/rust-num/num/pull/356
 [17]: https://github.com/rust-num/num-traits/pull/17
 [21]: https://github.com/rust-num/num-traits/pull/21
 [22]: https://github.com/rust-num/num-traits/pull/22
 [23]: https://github.com/rust-num/num-traits/pull/23
 # Prior releases
 No prior release notes were kept.  Thanks all the same to the many
 contributors that have made this crate what it is!
--- a/benches/bigint.rs
+++ b/benches/bigint.rs
@ -0,0 +1,294 @@
 #![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));
 }
--- a/benches/shootout-pidigits.rs
+++ b/benches/shootout-pidigits.rs
@ -0,0 +1,131 @@
 // 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();
 }
--- a/bigint/Cargo.toml
+++ b/bigint/Cargo.toml
@ -0,0 +1,39 @@
 [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 = "0.1.40"
 [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"]
--- a/bigint/LICENSE-APACHE
+++ b/bigint/LICENSE-APACHE
@ -0,0 +1,201 @@
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--- a/bigint/LICENSE-MIT
+++ b/bigint/LICENSE-MIT
@ -0,0 +1,25 @@
 Copyright (c) 2014 The Rust Project Developers
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 DEALINGS IN THE SOFTWARE.
--- a/bigint/src/algorithms.rs
+++ b/bigint/src/algorithms.rs
@ -0,0 +1,658 @@
 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);
    }
 }
--- a/bigint/src/bigint.rs
+++ b/bigint/src/bigint.rs
--- a/bigint/src/biguint.rs
+++ b/bigint/src/biguint.rs
--- a/bigint/src/lib.rs
+++ b/bigint/src/lib.rs
@ -0,0 +1,154 @@
 // 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;
--- a/bigint/src/macros.rs
+++ b/bigint/src/macros.rs
@ -0,0 +1,316 @@
 #![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);
    }
 }
--- a/bigint/src/monty.rs
+++ b/bigint/src/monty.rs
@ -0,0 +1,127 @@
 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)
 }
--- a/bigint/src/tests/bigint.rs
+++ b/bigint/src/tests/bigint.rs
--- a/bigint/src/tests/biguint.rs
+++ b/bigint/src/tests/biguint.rs
--- a/build.rs
+++ b/build.rs
@ -1,14 +0,0 @@
 extern crate autocfg;
 use std::env;
 fn main() {
    let ac = autocfg::new();
    if ac.probe_type("i128") {
        println!("cargo:rustc-cfg=has_i128");
    } else if env::var_os("CARGO_FEATURE_I128").is_some() {
        panic!("i128 support was not detected!");
    }
    autocfg::rerun_path(file!());
 }
--- a/ci/.gitignore
+++ b/ci/.gitignore
@ -0,0 +1 @@
 /deploy
--- a/ci/deploy.enc
+++ b/ci/deploy.enc
--- a/ci/deploy.sh
+++ b/ci/deploy.sh
@ -0,0 +1,12 @@
 #!/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
--- a/ci/rustup.sh
+++ b/ci/rustup.sh
@ -1,11 +1,18 @@
 #!/bin/sh
 # Use rustup to locally run the same suite of tests as .travis.yml.
-# (You should first install/update 1.8.0, stable, beta, and nightly.)
+# (You should first install/update 1.8.0, 1.15.0, beta, and nightly.)
 set -ex
 export TRAVIS_RUST_VERSION
-for TRAVIS_RUST_VERSION in 1.8.0 1.15.0 1.20.0 stable beta nightly; do
+for TRAVIS_RUST_VERSION in 1.8.0 1.15.0 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
--- a/ci/test_full.sh
+++ b/ci/test_full.sh
@ -2,26 +2,53 @@
 set -ex
-echo Testing num-traits on rustc ${TRAVIS_RUST_VERSION}
+echo Testing num on rustc ${TRAVIS_RUST_VERSION}
-# num-traits should build and test everywhere.
+# All of these packages should build and test everywhere.
-cargo build --verbose
+for package in bigint complex integer iter rational traits; do
-cargo test --verbose
+  if [ "$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
-# test `no_std`
+# They all should build with minimal features too
-cargo build --verbose --no-default-features
+for package in bigint complex integer iter rational traits; do
-cargo test --verbose --no-default-features
+  cargo build --manifest-path $package/Cargo.toml --no-default-features
  cargo test --manifest-path $package/Cargo.toml --no-default-features
 done
-if [[ "$TRAVIS_RUST_VERSION" =~ ^(nightly|beta|stable)$ ]]; then
+# Each isolated feature should also work everywhere.
-    # test `i128`
+for feature in '' bigint rational complex; do
-    cargo build --verbose --features=i128
+  cargo build --verbose --no-default-features --features="$feature"
-    cargo test --verbose --features=i128
+  cargo test --verbose --no-default-features --features="$feature"
 done
-    # test with std and libm (libm build fails on Rust 1.26 and earlier)
+# Build test for the serde feature
-    cargo build --verbose --features "libm"
+cargo build --verbose --features "serde"
    cargo test --verbose --features "libm"
-    # test `no_std` with libm (libm build fails on Rust 1.26 and earlier)
+# Downgrade serde and build test the 0.7.0 channel as well
-    cargo build --verbose --no-default-features --features "libm"
+cargo update -p serde --precise 0.7.0
-    cargo test --verbose --no-default-features --features "libm"
+cargo build --verbose --features "serde"
-fi
+
 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
 # num-macros only works on nightly, soon to be deprecated
 cargo build --verbose --manifest-path=macros/Cargo.toml
 cargo test --verbose --manifest-path=macros/Cargo.toml
 # benchmarks only work on nightly
 cargo bench --verbose
--- a/complex/Cargo.toml
+++ b/complex/Cargo.toml
@ -0,0 +1,30 @@
 [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 = "0.1.40"
 [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 = []
--- a/complex/LICENSE-APACHE
+++ b/complex/LICENSE-APACHE
@ -0,0 +1,201 @@
                              Apache License
                        Version 2.0, January 2004
                     http://www.apache.org/licenses/
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--- a/complex/LICENSE-MIT
+++ b/complex/LICENSE-MIT
@ -0,0 +1,25 @@
 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
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 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.
--- a/complex/src/lib.rs
+++ b/complex/src/lib.rs
--- a/derive/Cargo.toml
+++ b/derive/Cargo.toml
@ -0,0 +1,27 @@
 [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
--- a/derive/LICENSE-APACHE
+++ b/derive/LICENSE-APACHE
@ -0,0 +1,201 @@
                              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,
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   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.
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   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).
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   form, that is based on (or derived from) the Work and for which the
   editorial revisions, annotations, elaborations, or other modifications
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 APPENDIX: How to apply the Apache License to your work.
   To apply the Apache License to your work, attach the following
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 Licensed under the Apache License, Version 2.0 (the "License");
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--- a/derive/LICENSE-MIT
+++ b/derive/LICENSE-MIT
@ -0,0 +1,25 @@
 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.
--- a/derive/src/lib.rs
+++ b/derive/src/lib.rs
@ -0,0 +1,118 @@
 // 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()
 }
--- a/derive/tests/compile-fail/from-primitive/derive_on_struct.rs
+++ b/derive/tests/compile-fail/from-primitive/derive_on_struct.rs
@ -0,0 +1,22 @@
 // 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() {}
--- a/derive/tests/compile-fail/from-primitive/enum_with_associated_data.rs
+++ b/derive/tests/compile-fail/from-primitive/enum_with_associated_data.rs
@ -0,0 +1,21 @@
 // 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() {}
--- a/derive/tests/compile-fail/to-primitive/derive_on_struct.rs
+++ b/derive/tests/compile-fail/to-primitive/derive_on_struct.rs
@ -0,0 +1,22 @@
 // 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() {}
--- a/derive/tests/compile-fail/to-primitive/enum_with_associated_data.rs
+++ b/derive/tests/compile-fail/to-primitive/enum_with_associated_data.rs
@ -0,0 +1,21 @@
 // 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() {}
--- a/derive/tests/compiletest.rs
+++ b/derive/tests/compiletest.rs
@ -0,0 +1,25 @@
 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");
 }
--- a/derive/tests/empty_enum.rs
+++ b/derive/tests/empty_enum.rs
@ -0,0 +1,23 @@
 // 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]);
 }
--- a/derive/tests/trivial.rs
+++ b/derive/tests/trivial.rs
@ -0,0 +1,52 @@
 // 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);
 }
--- a/derive/tests/with_custom_values.rs
+++ b/derive/tests/with_custom_values.rs
@ -0,0 +1,31 @@
 // 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]);
 }
--- a/doc/favicon.ico
+++ b/doc/favicon.ico
--- a/doc/index.html
+++ b/doc/index.html
@ -0,0 +1 @@
 <meta http-equiv=refresh content=0;url=num/index.html>
--- a/doc/rust-logo-128x128-blk-v2.png
+++ b/doc/rust-logo-128x128-blk-v2.png
--- a/integer/Cargo.toml
+++ b/integer/Cargo.toml
@ -0,0 +1,15 @@
 [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"
--- a/integer/LICENSE-APACHE
+++ b/integer/LICENSE-APACHE
@ -0,0 +1,201 @@
                              Apache License
                        Version 2.0, January 2004
                     http://www.apache.org/licenses/
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   meet the following conditions:
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   (b) You must cause any modified files to carry prominent notices
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   by You to the Licensor shall be under the terms and conditions of
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--- a/integer/LICENSE-MIT
+++ b/integer/LICENSE-MIT
@ -0,0 +1,25 @@
 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.
--- a/integer/src/lib.rs
+++ b/integer/src/lib.rs
@ -0,0 +1,988 @@
 // 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);
 }
--- a/iter/Cargo.toml
+++ b/iter/Cargo.toml
@ -0,0 +1,23 @@
 [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"
--- a/iter/LICENSE-APACHE
+++ b/iter/LICENSE-APACHE
@ -0,0 +1,201 @@
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--- a/iter/LICENSE-MIT
+++ b/iter/LICENSE-MIT
@ -0,0 +1,25 @@
 Copyright (c) 2014 The Rust Project Developers
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--- a/iter/src/lib.rs
+++ b/iter/src/lib.rs
@ -0,0 +1,378 @@
 // 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]);
    }
 }
--- a/macros/Cargo.toml
+++ b/macros/Cargo.toml
@ -0,0 +1,18 @@
 [package]
 name = "num-macros"
 version = "0.1.39"
 authors = ["The Rust Project Developers"]
 license = "MIT/Apache-2.0"
 homepage = "https://github.com/rust-num/num"
 repository = "https://github.com/rust-num/num"
 documentation = "http://rust-num.github.io/num"
 keywords = ["mathematics", "numerics"]
 categories = [ "science" ]
 description = "Numeric syntax extensions"
 [lib]
 name = "num_macros"
 plugin = true
 [dev-dependencies]
 num = { path = "..", version = "0.1" }
--- a/macros/LICENSE-APACHE
+++ b/macros/LICENSE-APACHE
@ -0,0 +1,201 @@
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--- a/macros/LICENSE-MIT
+++ b/macros/LICENSE-MIT
@ -0,0 +1,25 @@
 Copyright (c) 2014 The Rust Project Developers
 Permission is hereby granted, free of charge, to any
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 The above copyright notice and this permission notice
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 TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A
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 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.
--- a/macros/src/lib.rs
+++ b/macros/src/lib.rs
@ -0,0 +1,206 @@
 // Copyright 2012-2015 The Rust Project Developers. See the COPYRIGHT
 // file at the top-level directory of this distribution and at
 // http://rust-lang.org/COPYRIGHT.
 //
 // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
 // http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
 // <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
 // option. This file may not be copied, modified, or distributed
 // except according to those terms.
 #![feature(plugin_registrar, rustc_private)]
 #![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 syntax;
 extern crate syntax_ext;
 extern crate rustc_plugin;
 use syntax::ast::{MetaItem, Expr, BinOpKind};
 use syntax::ast;
 use syntax::codemap::Span;
 use syntax::ext::base::{ExtCtxt, Annotatable};
 use syntax::ext::build::AstBuilder;
 use syntax_ext::deriving::generic::*;
 use syntax_ext::deriving::generic::ty::*;
 use syntax::symbol::Symbol;
 use syntax::ptr::P;
 use syntax::ext::base::MultiDecorator;
 use rustc_plugin::Registry;
 macro_rules! pathvec {
    ($($x:ident)::+) => (
        vec![ $( stringify!($x) ),+ ]
    )
 }
 macro_rules! path {
    ($($x:tt)*) => (
        ::syntax_ext::deriving::generic::ty::Path::new( pathvec!( $($x)* ) )
    )
 }
 macro_rules! path_local {
    ($x:ident) => (
        ::syntax_ext::deriving::generic::ty::Path::new_local(stringify!($x))
    )
 }
 macro_rules! pathvec_std {
    ($cx:expr, $first:ident :: $($rest:ident)::+) => ({
        let mut v = pathvec!($($rest)::+);
        if let Some(s) = $cx.crate_root {
            v.insert(0, s);
        }
        v
    })
 }
 pub fn expand_deriving_from_primitive(cx: &mut ExtCtxt,
                                      span: Span,
                                      mitem: &MetaItem,
                                      item: &Annotatable,
                                      push: &mut FnMut(Annotatable))
 {
    let inline = cx.meta_word(span, Symbol::intern("inline"));
    let attrs = vec!(cx.attribute(span, inline));
    let trait_def = TraitDef {
        is_unsafe: false,
        span: span,
        attributes: Vec::new(),
        path: path!(num::FromPrimitive),
        additional_bounds: Vec::new(),
        generics: LifetimeBounds::empty(),
        methods: vec!(
            MethodDef {
                name: "from_i64",
                is_unsafe: false,
                unify_fieldless_variants: false,
                generics: LifetimeBounds::empty(),
                explicit_self: None,
                args: vec!(Literal(path_local!(i64))),
                ret_ty: Literal(Path::new_(pathvec_std!(cx, core::option::Option),
                                           None,
                                           vec!(Box::new(Self_)),
                                           true)),
                // #[inline] liable to cause code-bloat
                attributes: attrs.clone(),
                combine_substructure: combine_substructure(Box::new(|c, s, sub| {
                    cs_from("i64", c, s, sub)
                })),
            },
            MethodDef {
                name: "from_u64",
                is_unsafe: false,
                unify_fieldless_variants: false,
                generics: LifetimeBounds::empty(),
                explicit_self: None,
                args: vec!(Literal(path_local!(u64))),
                ret_ty: Literal(Path::new_(pathvec_std!(cx, core::option::Option),
                                           None,
                                           vec!(Box::new(Self_)),
                                           true)),
                // #[inline] liable to cause code-bloat
                attributes: attrs,
                combine_substructure: combine_substructure(Box::new(|c, s, sub| {
                    cs_from("u64", c, s, sub)
                })),
            }
        ),
        associated_types: Vec::new(),
        supports_unions: false,
    };
    trait_def.expand(cx, mitem, &item, push)
 }
 fn cs_from(name: &str, cx: &mut ExtCtxt, trait_span: Span, substr: &Substructure) -> P<Expr> {
    if substr.nonself_args.len() != 1 {
        cx.span_bug(trait_span, "incorrect number of arguments in `derive(FromPrimitive)`")
    }
    let n = &substr.nonself_args[0];
    match *substr.fields {
        StaticStruct(..) => {
            cx.span_err(trait_span, "`FromPrimitive` cannot be derived for structs");
            return cx.expr_fail(trait_span, Symbol::intern(""));
        }
        StaticEnum(enum_def, _) => {
            if enum_def.variants.is_empty() {
                cx.span_err(trait_span,
                            "`FromPrimitive` cannot be derived for enums with no variants");
                return cx.expr_fail(trait_span, Symbol::intern(""));
            }
            let mut arms = Vec::new();
            for variant in &enum_def.variants {
                match variant.node.data {
                    ast::VariantData::Unit(..) => {
                        let span = variant.span;
                        // expr for `$n == $variant as $name`
                        let path = cx.path(span, vec![substr.type_ident, variant.node.name]);
                        let variant = cx.expr_path(path);
                        let ty = cx.ty_ident(span, cx.ident_of(name));
                        let cast = cx.expr_cast(span, variant.clone(), ty);
                        let guard = cx.expr_binary(span, BinOpKind::Eq, n.clone(), cast);
                        // expr for `Some($variant)`
                        let body = cx.expr_some(span, variant);
                        // arm for `_ if $guard => $body`
                        let arm = ast::Arm {
                            attrs: vec!(),
                            pats: vec!(cx.pat_wild(span)),
                            guard: Some(guard),
                            body: body,
                            beginning_vert: None,
                        };
                        arms.push(arm);
                    }
                    ast::VariantData::Tuple(..) => {
                        cx.span_err(trait_span,
                                    "`FromPrimitive` cannot be derived for \
                                    enum variants with arguments");
                        return cx.expr_fail(trait_span,
                                            Symbol::intern(""));
                    }
                    ast::VariantData::Struct(..) => {
                        cx.span_err(trait_span,
                                    "`FromPrimitive` cannot be derived for enums \
                                    with struct variants");
                        return cx.expr_fail(trait_span,
                                            Symbol::intern(""));
                    }
                }
            }
            // arm for `_ => None`
            let arm = ast::Arm {
                attrs: vec!(),
                pats: vec!(cx.pat_wild(trait_span)),
                guard: None,
                body: cx.expr_none(trait_span),
                beginning_vert: None,
            };
            arms.push(arm);
            cx.expr_match(trait_span, n.clone(), arms)
        }
        _ => cx.span_bug(trait_span, "expected StaticEnum in derive(FromPrimitive)")
    }
 }
 #[plugin_registrar]
 #[doc(hidden)]
 pub fn plugin_registrar(reg: &mut Registry) {
    reg.register_syntax_extension(
        Symbol::intern("derive_NumFromPrimitive"),
        MultiDecorator(Box::new(expand_deriving_from_primitive)));
 }
--- a/macros/tests/test_macro.rs
+++ b/macros/tests/test_macro.rs
@ -0,0 +1,36 @@
 // Copyright 2013-2015 The Rust Project Developers. See the COPYRIGHT
 // file at the top-level directory of this distribution and at
 // http://rust-lang.org/COPYRIGHT.
 //
 // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
 // http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
 // <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
 // option. This file may not be copied, modified, or distributed
 // except according to those terms.
 #![feature(custom_derive, plugin)]
 #![plugin(num_macros)]
 extern crate num;
 #[derive(Debug, PartialEq, NumFromPrimitive)]
 enum Color {
    Red,
    Blue,
    Green,
 }
 #[test]
 fn test_from_primitive() {
    let v: Vec<Option<Color>> = vec![
        num::FromPrimitive::from_u64(0),
        num::FromPrimitive::from_u64(1),
        num::FromPrimitive::from_u64(2),
        num::FromPrimitive::from_u64(3),
    ];
    assert_eq!(
        v,
        vec![Some(Color::Red), Some(Color::Blue), Some(Color::Green), None]
    );
 }
--- a/rational/Cargo.toml
+++ b/rational/Cargo.toml
@ -0,0 +1,38 @@
 [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"]
--- a/rational/LICENSE-APACHE
+++ b/rational/LICENSE-APACHE
@ -0,0 +1,201 @@
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--- a/rational/LICENSE-MIT
+++ b/rational/LICENSE-MIT
@ -0,0 +1,25 @@
 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
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 conditions:
 The above copyright notice and this permission notice
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 of the Software.
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 TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A
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 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.
--- a/rational/src/lib.rs
+++ b/rational/src/lib.rs
--- a/src/cast.rs
+++ b/src/cast.rs
@ -1,762 +0,0 @@
 use core::mem::size_of;
 use core::num::Wrapping;
 use core::{f32, f64};
 #[cfg(has_i128)]
 use core::{i128, u128};
 use core::{i16, i32, i64, i8, isize};
 use core::{u16, u32, u64, u8, usize};
 use float::FloatCore;
 /// A generic trait for converting a value to a number.
 pub trait ToPrimitive {
    /// Converts the value of `self` to an `isize`.
    #[inline]
    fn to_isize(&self) -> Option<isize> {
        self.to_i64().as_ref().and_then(ToPrimitive::to_isize)
    }
    /// Converts the value of `self` to an `i8`.
    #[inline]
    fn to_i8(&self) -> Option<i8> {
        self.to_i64().as_ref().and_then(ToPrimitive::to_i8)
    }
    /// Converts the value of `self` to an `i16`.
    #[inline]
    fn to_i16(&self) -> Option<i16> {
        self.to_i64().as_ref().and_then(ToPrimitive::to_i16)
    }
    /// Converts the value of `self` to an `i32`.
    #[inline]
    fn to_i32(&self) -> Option<i32> {
        self.to_i64().as_ref().and_then(ToPrimitive::to_i32)
    }
    /// Converts the value of `self` to an `i64`.
    fn to_i64(&self) -> Option<i64>;
    /// Converts the value of `self` to an `i128`.
    ///
    /// This method is only available with feature `i128` enabled on Rust >= 1.26.
    ///
    /// The default implementation converts through `to_i64()`.  Types implementing
    /// this trait should override this method if they can represent a greater range.
    #[inline]
    #[cfg(has_i128)]
    fn to_i128(&self) -> Option<i128> {
        self.to_i64().map(From::from)
    }
    /// Converts the value of `self` to a `usize`.
    #[inline]
    fn to_usize(&self) -> Option<usize> {
        self.to_u64().as_ref().and_then(ToPrimitive::to_usize)
    }
    /// Converts the value of `self` to an `u8`.
    #[inline]
    fn to_u8(&self) -> Option<u8> {
        self.to_u64().as_ref().and_then(ToPrimitive::to_u8)
    }
    /// Converts the value of `self` to an `u16`.
    #[inline]
    fn to_u16(&self) -> Option<u16> {
        self.to_u64().as_ref().and_then(ToPrimitive::to_u16)
    }
    /// Converts the value of `self` to an `u32`.
    #[inline]
    fn to_u32(&self) -> Option<u32> {
        self.to_u64().as_ref().and_then(ToPrimitive::to_u32)
    }
    /// Converts the value of `self` to an `u64`.
    #[inline]
    fn to_u64(&self) -> Option<u64>;
    /// Converts the value of `self` to an `u128`.
    ///
    /// This method is only available with feature `i128` enabled on Rust >= 1.26.
    ///
    /// The default implementation converts through `to_u64()`.  Types implementing
    /// this trait should override this method if they can represent a greater range.
    #[inline]
    #[cfg(has_i128)]
    fn to_u128(&self) -> Option<u128> {
        self.to_u64().map(From::from)
    }
    /// Converts the value of `self` to an `f32`.
    #[inline]
    fn to_f32(&self) -> Option<f32> {
        self.to_f64().as_ref().and_then(ToPrimitive::to_f32)
    }
    /// Converts the value of `self` to an `f64`.
    #[inline]
    fn to_f64(&self) -> Option<f64> {
        match self.to_i64() {
            Some(i) => i.to_f64(),
            None => self.to_u64().as_ref().and_then(ToPrimitive::to_f64),
        }
    }
 }
 macro_rules! impl_to_primitive_int_to_int {
    ($SrcT:ident : $( $(#[$cfg:meta])* fn $method:ident -> $DstT:ident ; )*) => {$(
        #[inline]
        $(#[$cfg])*
        fn $method(&self) -> Option<$DstT> {
            let min = $DstT::MIN as $SrcT;
            let max = $DstT::MAX as $SrcT;
            if size_of::<$SrcT>() <= size_of::<$DstT>() || (min <= *self && *self <= max) {
                Some(*self as $DstT)
            } else {
                None
            }
        }
    )*}
 }
 macro_rules! impl_to_primitive_int_to_uint {
    ($SrcT:ident : $( $(#[$cfg:meta])* fn $method:ident -> $DstT:ident ; )*) => {$(
        #[inline]
        $(#[$cfg])*
        fn $method(&self) -> Option<$DstT> {
            let max = $DstT::MAX as $SrcT;
            if 0 <= *self && (size_of::<$SrcT>() <= size_of::<$DstT>() || *self <= max) {
                Some(*self as $DstT)
            } else {
                None
            }
        }
    )*}
 }
 macro_rules! impl_to_primitive_int {
    ($T:ident) => {
        impl ToPrimitive for $T {
            impl_to_primitive_int_to_int! { $T:
                fn to_isize -> isize;
                fn to_i8 -> i8;
                fn to_i16 -> i16;
                fn to_i32 -> i32;
                fn to_i64 -> i64;
                #[cfg(has_i128)]
                fn to_i128 -> i128;
            }
            impl_to_primitive_int_to_uint! { $T:
                fn to_usize -> usize;
                fn to_u8 -> u8;
                fn to_u16 -> u16;
                fn to_u32 -> u32;
                fn to_u64 -> u64;
                #[cfg(has_i128)]
                fn to_u128 -> u128;
            }
            #[inline]
            fn to_f32(&self) -> Option<f32> {
                Some(*self as f32)
            }
            #[inline]
            fn to_f64(&self) -> Option<f64> {
                Some(*self as f64)
            }
        }
    };
 }
 impl_to_primitive_int!(isize);
 impl_to_primitive_int!(i8);
 impl_to_primitive_int!(i16);
 impl_to_primitive_int!(i32);
 impl_to_primitive_int!(i64);
 #[cfg(has_i128)]
 impl_to_primitive_int!(i128);
 macro_rules! impl_to_primitive_uint_to_int {
    ($SrcT:ident : $( $(#[$cfg:meta])* fn $method:ident -> $DstT:ident ; )*) => {$(
        #[inline]
        $(#[$cfg])*
        fn $method(&self) -> Option<$DstT> {
            let max = $DstT::MAX as $SrcT;
            if size_of::<$SrcT>() < size_of::<$DstT>() || *self <= max {
                Some(*self as $DstT)
            } else {
                None
            }
        }
    )*}
 }
 macro_rules! impl_to_primitive_uint_to_uint {
    ($SrcT:ident : $( $(#[$cfg:meta])* fn $method:ident -> $DstT:ident ; )*) => {$(
        #[inline]
        $(#[$cfg])*
        fn $method(&self) -> Option<$DstT> {
            let max = $DstT::MAX as $SrcT;
            if size_of::<$SrcT>() <= size_of::<$DstT>() || *self <= max {
                Some(*self as $DstT)
            } else {
                None
            }
        }
    )*}
 }
 macro_rules! impl_to_primitive_uint {
    ($T:ident) => {
        impl ToPrimitive for $T {
            impl_to_primitive_uint_to_int! { $T:
                fn to_isize -> isize;
                fn to_i8 -> i8;
                fn to_i16 -> i16;
                fn to_i32 -> i32;
                fn to_i64 -> i64;
                #[cfg(has_i128)]
                fn to_i128 -> i128;
            }
            impl_to_primitive_uint_to_uint! { $T:
                fn to_usize -> usize;
                fn to_u8 -> u8;
                fn to_u16 -> u16;
                fn to_u32 -> u32;
                fn to_u64 -> u64;
                #[cfg(has_i128)]
                fn to_u128 -> u128;
            }
            #[inline]
            fn to_f32(&self) -> Option<f32> {
                Some(*self as f32)
            }
            #[inline]
            fn to_f64(&self) -> Option<f64> {
                Some(*self as f64)
            }
        }
    };
 }
 impl_to_primitive_uint!(usize);
 impl_to_primitive_uint!(u8);
 impl_to_primitive_uint!(u16);
 impl_to_primitive_uint!(u32);
 impl_to_primitive_uint!(u64);
 #[cfg(has_i128)]
 impl_to_primitive_uint!(u128);
 macro_rules! impl_to_primitive_float_to_float {
    ($SrcT:ident : $( fn $method:ident -> $DstT:ident ; )*) => {$(
        #[inline]
        fn $method(&self) -> Option<$DstT> {
            // Only finite values that are reducing size need to worry about overflow.
            if size_of::<$SrcT>() > size_of::<$DstT>() && FloatCore::is_finite(*self) {
                let n = *self as f64;
                if n < $DstT::MIN as f64 || n > $DstT::MAX as f64 {
                    return None;
                }
            }
            // We can safely cast NaN, +-inf, and finite values in range.
            Some(*self as $DstT)
        }
    )*}
 }
 macro_rules! impl_to_primitive_float_to_signed_int {
    ($f:ident : $( $(#[$cfg:meta])* fn $method:ident -> $i:ident ; )*) => {$(
        #[inline]
        $(#[$cfg])*
        fn $method(&self) -> Option<$i> {
            // Float as int truncates toward zero, so we want to allow values
            // in the exclusive range `(MIN-1, MAX+1)`.
            if size_of::<$f>() > size_of::<$i>() {
                // With a larger size, we can represent the range exactly.
                const MIN_M1: $f = $i::MIN as $f - 1.0;
                const MAX_P1: $f = $i::MAX as $f + 1.0;
                if *self > MIN_M1 && *self < MAX_P1 {
                    return Some(*self as $i);
                }
            } else {
                // We can't represent `MIN-1` exactly, but there's no fractional part
                // at this magnitude, so we can just use a `MIN` inclusive boundary.
                const MIN: $f = $i::MIN as $f;
                // We can't represent `MAX` exactly, but it will round up to exactly
                // `MAX+1` (a power of two) when we cast it.
                const MAX_P1: $f = $i::MAX as $f;
                if *self >= MIN && *self < MAX_P1 {
                    return Some(*self as $i);
                }
            }
            None
        }
    )*}
 }
 macro_rules! impl_to_primitive_float_to_unsigned_int {
    ($f:ident : $( $(#[$cfg:meta])* fn $method:ident -> $u:ident ; )*) => {$(
        #[inline]
        $(#[$cfg])*
        fn $method(&self) -> Option<$u> {
            // Float as int truncates toward zero, so we want to allow values
            // in the exclusive range `(-1, MAX+1)`.
            if size_of::<$f>() > size_of::<$u>() {
                // With a larger size, we can represent the range exactly.
                const MAX_P1: $f = $u::MAX as $f + 1.0;
                if *self > -1.0 && *self < MAX_P1 {
                    return Some(*self as $u);
                }
            } else {
                // We can't represent `MAX` exactly, but it will round up to exactly
                // `MAX+1` (a power of two) when we cast it.
                // (`u128::MAX as f32` is infinity, but this is still ok.)
                const MAX_P1: $f = $u::MAX as $f;
                if *self > -1.0 && *self < MAX_P1 {
                    return Some(*self as $u);
                }
            }
            None
        }
    )*}
 }
 macro_rules! impl_to_primitive_float {
    ($T:ident) => {
        impl ToPrimitive for $T {
            impl_to_primitive_float_to_signed_int! { $T:
                fn to_isize -> isize;
                fn to_i8 -> i8;
                fn to_i16 -> i16;
                fn to_i32 -> i32;
                fn to_i64 -> i64;
                #[cfg(has_i128)]
                fn to_i128 -> i128;
            }
            impl_to_primitive_float_to_unsigned_int! { $T:
                fn to_usize -> usize;
                fn to_u8 -> u8;
                fn to_u16 -> u16;
                fn to_u32 -> u32;
                fn to_u64 -> u64;
                #[cfg(has_i128)]
                fn to_u128 -> u128;
            }
            impl_to_primitive_float_to_float! { $T:
                fn to_f32 -> f32;
                fn to_f64 -> f64;
            }
        }
    };
 }
 impl_to_primitive_float!(f32);
 impl_to_primitive_float!(f64);
 /// A generic trait for converting a number to a value.
 pub trait FromPrimitive: Sized {
    /// Convert an `isize` to return an optional value of this type. If the
    /// value cannot be represented by this value, then `None` is returned.
    #[inline]
    fn from_isize(n: isize) -> Option<Self> {
        n.to_i64().and_then(FromPrimitive::from_i64)
    }
    /// Convert an `i8` to return an optional value of this type. If the
    /// type cannot be represented by this value, then `None` is returned.
    #[inline]
    fn from_i8(n: i8) -> Option<Self> {
        FromPrimitive::from_i64(From::from(n))
    }
    /// Convert an `i16` to return an optional value of this type. If the
    /// type cannot be represented by this value, then `None` is returned.
    #[inline]
    fn from_i16(n: i16) -> Option<Self> {
        FromPrimitive::from_i64(From::from(n))
    }
    /// Convert an `i32` to return an optional value of this type. If the
    /// type cannot be represented by this value, then `None` is returned.
    #[inline]
    fn from_i32(n: i32) -> Option<Self> {
        FromPrimitive::from_i64(From::from(n))
    }
    /// Convert an `i64` to return an optional value of this type. If the
    /// type cannot be represented by this value, then `None` is returned.
    fn from_i64(n: i64) -> Option<Self>;
    /// Convert an `i128` to return an optional value of this type. If the
    /// type cannot be represented by this value, then `None` is returned.
    ///
    /// This method is only available with feature `i128` enabled on Rust >= 1.26.
    ///
    /// The default implementation converts through `from_i64()`.  Types implementing
    /// this trait should override this method if they can represent a greater range.
    #[inline]
    #[cfg(has_i128)]
    fn from_i128(n: i128) -> Option<Self> {
        n.to_i64().and_then(FromPrimitive::from_i64)
    }
    /// Convert a `usize` to return an optional value of this type. If the
    /// type cannot be represented by this value, then `None` is returned.
    #[inline]
    fn from_usize(n: usize) -> Option<Self> {
        n.to_u64().and_then(FromPrimitive::from_u64)
    }
    /// Convert an `u8` to return an optional value of this type. If the
    /// type cannot be represented by this value, then `None` is returned.
    #[inline]
    fn from_u8(n: u8) -> Option<Self> {
        FromPrimitive::from_u64(From::from(n))
    }
    /// Convert an `u16` to return an optional value of this type. If the
    /// type cannot be represented by this value, then `None` is returned.
    #[inline]
    fn from_u16(n: u16) -> Option<Self> {
        FromPrimitive::from_u64(From::from(n))
    }
    /// Convert an `u32` to return an optional value of this type. If the
    /// type cannot be represented by this value, then `None` is returned.
    #[inline]
    fn from_u32(n: u32) -> Option<Self> {
        FromPrimitive::from_u64(From::from(n))
    }
    /// Convert an `u64` to return an optional value of this type. If the
    /// type cannot be represented by this value, then `None` is returned.
    fn from_u64(n: u64) -> Option<Self>;
    /// Convert an `u128` to return an optional value of this type. If the
    /// type cannot be represented by this value, then `None` is returned.
    ///
    /// This method is only available with feature `i128` enabled on Rust >= 1.26.
    ///
    /// The default implementation converts through `from_u64()`.  Types implementing
    /// this trait should override this method if they can represent a greater range.
    #[inline]
    #[cfg(has_i128)]
    fn from_u128(n: u128) -> Option<Self> {
        n.to_u64().and_then(FromPrimitive::from_u64)
    }
    /// Convert a `f32` to return an optional value of this type. If the
    /// type cannot be represented by this value, then `None` is returned.
    #[inline]
    fn from_f32(n: f32) -> Option<Self> {
        FromPrimitive::from_f64(From::from(n))
    }
    /// Convert a `f64` to return an optional value of this type. If the
    /// type cannot be represented by this value, then `None` is returned.
    #[inline]
    fn from_f64(n: f64) -> Option<Self> {
        match n.to_i64() {
            Some(i) => FromPrimitive::from_i64(i),
            None => n.to_u64().and_then(FromPrimitive::from_u64),
        }
    }
 }
 macro_rules! impl_from_primitive {
    ($T:ty, $to_ty:ident) => {
        #[allow(deprecated)]
        impl FromPrimitive for $T {
            #[inline]
            fn from_isize(n: isize) -> Option<$T> {
                n.$to_ty()
            }
            #[inline]
            fn from_i8(n: i8) -> Option<$T> {
                n.$to_ty()
            }
            #[inline]
            fn from_i16(n: i16) -> Option<$T> {
                n.$to_ty()
            }
            #[inline]
            fn from_i32(n: i32) -> Option<$T> {
                n.$to_ty()
            }
            #[inline]
            fn from_i64(n: i64) -> Option<$T> {
                n.$to_ty()
            }
            #[cfg(has_i128)]
            #[inline]
            fn from_i128(n: i128) -> Option<$T> {
                n.$to_ty()
            }
            #[inline]
            fn from_usize(n: usize) -> Option<$T> {
                n.$to_ty()
            }
            #[inline]
            fn from_u8(n: u8) -> Option<$T> {
                n.$to_ty()
            }
            #[inline]
            fn from_u16(n: u16) -> Option<$T> {
                n.$to_ty()
            }
            #[inline]
            fn from_u32(n: u32) -> Option<$T> {
                n.$to_ty()
            }
            #[inline]
            fn from_u64(n: u64) -> Option<$T> {
                n.$to_ty()
            }
            #[cfg(has_i128)]
            #[inline]
            fn from_u128(n: u128) -> Option<$T> {
                n.$to_ty()
            }
            #[inline]
            fn from_f32(n: f32) -> Option<$T> {
                n.$to_ty()
            }
            #[inline]
            fn from_f64(n: f64) -> Option<$T> {
                n.$to_ty()
            }
        }
    };
 }
 impl_from_primitive!(isize, to_isize);
 impl_from_primitive!(i8, to_i8);
 impl_from_primitive!(i16, to_i16);
 impl_from_primitive!(i32, to_i32);
 impl_from_primitive!(i64, to_i64);
 #[cfg(has_i128)]
 impl_from_primitive!(i128, to_i128);
 impl_from_primitive!(usize, to_usize);
 impl_from_primitive!(u8, to_u8);
 impl_from_primitive!(u16, to_u16);
 impl_from_primitive!(u32, to_u32);
 impl_from_primitive!(u64, to_u64);
 #[cfg(has_i128)]
 impl_from_primitive!(u128, to_u128);
 impl_from_primitive!(f32, to_f32);
 impl_from_primitive!(f64, to_f64);
 macro_rules! impl_to_primitive_wrapping {
    ($( $(#[$cfg:meta])* fn $method:ident -> $i:ident ; )*) => {$(
        #[inline]
        $(#[$cfg])*
        fn $method(&self) -> Option<$i> {
            (self.0).$method()
        }
    )*}
 }
 impl<T: ToPrimitive> ToPrimitive for Wrapping<T> {
    impl_to_primitive_wrapping! {
        fn to_isize -> isize;
        fn to_i8 -> i8;
        fn to_i16 -> i16;
        fn to_i32 -> i32;
        fn to_i64 -> i64;
        #[cfg(has_i128)]
        fn to_i128 -> i128;
        fn to_usize -> usize;
        fn to_u8 -> u8;
        fn to_u16 -> u16;
        fn to_u32 -> u32;
        fn to_u64 -> u64;
        #[cfg(has_i128)]
        fn to_u128 -> u128;
        fn to_f32 -> f32;
        fn to_f64 -> f64;
    }
 }
 macro_rules! impl_from_primitive_wrapping {
    ($( $(#[$cfg:meta])* fn $method:ident ( $i:ident ); )*) => {$(
        #[inline]
        $(#[$cfg])*
        fn $method(n: $i) -> Option<Self> {
            T::$method(n).map(Wrapping)
        }
    )*}
 }
 impl<T: FromPrimitive> FromPrimitive for Wrapping<T> {
    impl_from_primitive_wrapping! {
        fn from_isize(isize);
        fn from_i8(i8);
        fn from_i16(i16);
        fn from_i32(i32);
        fn from_i64(i64);
        #[cfg(has_i128)]
        fn from_i128(i128);
        fn from_usize(usize);
        fn from_u8(u8);
        fn from_u16(u16);
        fn from_u32(u32);
        fn from_u64(u64);
        #[cfg(has_i128)]
        fn from_u128(u128);
        fn from_f32(f32);
        fn from_f64(f64);
    }
 }
 /// Cast from one machine scalar to another.
 ///
 /// # Examples
 ///
 /// ```
 /// # use num_traits as num;
 /// let twenty: f32 = num::cast(0x14).unwrap();
 /// assert_eq!(twenty, 20f32);
 /// ```
 ///
 #[inline]
 pub fn cast<T: NumCast, U: NumCast>(n: T) -> Option<U> {
    NumCast::from(n)
 }
 /// An interface for casting between machine scalars.
 pub trait NumCast: Sized + ToPrimitive {
    /// Creates a number from another value that can be converted into
    /// a primitive via the `ToPrimitive` trait.
    fn from<T: ToPrimitive>(n: T) -> Option<Self>;
 }
 macro_rules! impl_num_cast {
    ($T:ty, $conv:ident) => {
        impl NumCast for $T {
            #[inline]
            #[allow(deprecated)]
            fn from<N: ToPrimitive>(n: N) -> Option<$T> {
                // `$conv` could be generated using `concat_idents!`, but that
                // macro seems to be broken at the moment
                n.$conv()
            }
        }
    };
 }
 impl_num_cast!(u8, to_u8);
 impl_num_cast!(u16, to_u16);
 impl_num_cast!(u32, to_u32);
 impl_num_cast!(u64, to_u64);
 #[cfg(has_i128)]
 impl_num_cast!(u128, to_u128);
 impl_num_cast!(usize, to_usize);
 impl_num_cast!(i8, to_i8);
 impl_num_cast!(i16, to_i16);
 impl_num_cast!(i32, to_i32);
 impl_num_cast!(i64, to_i64);
 #[cfg(has_i128)]
 impl_num_cast!(i128, to_i128);
 impl_num_cast!(isize, to_isize);
 impl_num_cast!(f32, to_f32);
 impl_num_cast!(f64, to_f64);
 impl<T: NumCast> NumCast for Wrapping<T> {
    fn from<U: ToPrimitive>(n: U) -> Option<Self> {
        T::from(n).map(Wrapping)
    }
 }
 /// A generic interface for casting between machine scalars with the
 /// `as` operator, which admits narrowing and precision loss.
 /// Implementers of this trait `AsPrimitive` should behave like a primitive
 /// numeric type (e.g. a newtype around another primitive), and the
 /// intended conversion must never fail.
 ///
 /// # Examples
 ///
 /// ```
 /// # use num_traits::AsPrimitive;
 /// let three: i32 = (3.14159265f32).as_();
 /// assert_eq!(three, 3);
 /// ```
 ///
 /// # Safety
 ///
 /// Currently, some uses of the `as` operator are not entirely safe.
 /// In particular, it is undefined behavior if:
 ///
 /// - A truncated floating point value cannot fit in the target integer
 ///   type ([#10184](https://github.com/rust-lang/rust/issues/10184));
 ///
 /// ```ignore
 /// # use num_traits::AsPrimitive;
 /// let x: u8 = (1.04E+17).as_(); // UB
 /// ```
 ///
 /// - Or a floating point value does not fit in another floating
 ///   point type ([#15536](https://github.com/rust-lang/rust/issues/15536)).
 ///
 /// ```ignore
 /// # use num_traits::AsPrimitive;
 /// let x: f32 = (1e300f64).as_(); // UB
 /// ```
 ///
 pub trait AsPrimitive<T>: 'static + Copy
 where
    T: 'static + Copy,
 {
    /// Convert a value to another, using the `as` operator.
    fn as_(self) -> T;
 }
 macro_rules! impl_as_primitive {
    (@ $T: ty => $(#[$cfg:meta])* impl $U: ty ) => {
        $(#[$cfg])*
        impl AsPrimitive<$U> for $T {
            #[inline] fn as_(self) -> $U { self as $U }
        }
    };
    (@ $T: ty => { $( $U: ty ),* } ) => {$(
        impl_as_primitive!(@ $T => impl $U);
    )*};
    ($T: ty => { $( $U: ty ),* } ) => {
        impl_as_primitive!(@ $T => { $( $U ),* });
        impl_as_primitive!(@ $T => { u8, u16, u32, u64, usize });
        impl_as_primitive!(@ $T => #[cfg(has_i128)] impl u128);
        impl_as_primitive!(@ $T => { i8, i16, i32, i64, isize });
        impl_as_primitive!(@ $T => #[cfg(has_i128)] impl i128);
    };
 }
 impl_as_primitive!(u8 => { char, f32, f64 });
 impl_as_primitive!(i8 => { f32, f64 });
 impl_as_primitive!(u16 => { f32, f64 });
 impl_as_primitive!(i16 => { f32, f64 });
 impl_as_primitive!(u32 => { f32, f64 });
 impl_as_primitive!(i32 => { f32, f64 });
 impl_as_primitive!(u64 => { f32, f64 });
 impl_as_primitive!(i64 => { f32, f64 });
 #[cfg(has_i128)]
 impl_as_primitive!(u128 => { f32, f64 });
 #[cfg(has_i128)]
 impl_as_primitive!(i128 => { f32, f64 });
 impl_as_primitive!(usize => { f32, f64 });
 impl_as_primitive!(isize => { f32, f64 });
 impl_as_primitive!(f32 => { f32, f64 });
 impl_as_primitive!(f64 => { f32, f64 });
 impl_as_primitive!(char => { char });
 impl_as_primitive!(bool => {});
--- a/src/float.rs
+++ b/src/float.rs
--- a/src/identities.rs
+++ b/src/identities.rs
@ -1,207 +0,0 @@
 use core::num::Wrapping;
 use core::ops::{Add, Mul};
 /// Defines an additive identity element for `Self`.
 ///
 /// # Laws
 ///
 /// ```{.text}
 /// a + 0 = a       ∀ a ∈ Self
 /// 0 + a = a       ∀ a ∈ Self
 /// ```
 pub trait Zero: Sized + Add<Self, Output = Self> {
    /// Returns the additive identity element of `Self`, `0`.
    /// # Purity
    ///
    /// This function should return the same result at all times regardless of
    /// external mutable state, for example values stored in TLS or in
    /// `static mut`s.
    // This cannot be an associated constant, because of bignums.
    fn zero() -> Self;
    /// Sets `self` to the additive identity element of `Self`, `0`.
    fn set_zero(&mut self) {
        *self = Zero::zero();
    }
    /// Returns `true` if `self` is equal to the additive identity.
    #[inline]
    fn is_zero(&self) -> bool;
 }
 macro_rules! zero_impl {
    ($t:ty, $v:expr) => {
        impl Zero for $t {
            #[inline]
            fn zero() -> $t {
                $v
            }
            #[inline]
            fn is_zero(&self) -> bool {
                *self == $v
            }
        }
    };
 }
 zero_impl!(usize, 0);
 zero_impl!(u8, 0);
 zero_impl!(u16, 0);
 zero_impl!(u32, 0);
 zero_impl!(u64, 0);
 #[cfg(has_i128)]
 zero_impl!(u128, 0);
 zero_impl!(isize, 0);
 zero_impl!(i8, 0);
 zero_impl!(i16, 0);
 zero_impl!(i32, 0);
 zero_impl!(i64, 0);
 #[cfg(has_i128)]
 zero_impl!(i128, 0);
 zero_impl!(f32, 0.0);
 zero_impl!(f64, 0.0);
 impl<T: Zero> Zero for Wrapping<T>
 where
    Wrapping<T>: Add<Output = Wrapping<T>>,
 {
    fn is_zero(&self) -> bool {
        self.0.is_zero()
    }
    fn set_zero(&mut self) {
        self.0.set_zero();
    }
    fn zero() -> Self {
        Wrapping(T::zero())
    }
 }
 /// Defines a multiplicative identity element for `Self`.
 ///
 /// # Laws
 ///
 /// ```{.text}
 /// a * 1 = a       ∀ a ∈ Self
 /// 1 * a = a       ∀ a ∈ Self
 /// ```
 pub trait One: Sized + Mul<Self, Output = Self> {
    /// Returns the multiplicative identity element of `Self`, `1`.
    ///
    /// # Purity
    ///
    /// This function should return the same result at all times regardless of
    /// external mutable state, for example values stored in TLS or in
    /// `static mut`s.
    // This cannot be an associated constant, because of bignums.
    fn one() -> Self;
    /// Sets `self` to the multiplicative identity element of `Self`, `1`.
    fn set_one(&mut self) {
        *self = One::one();
    }
    /// Returns `true` if `self` is equal to the multiplicative identity.
    ///
    /// For performance reasons, it's best to implement this manually.
    /// After a semver bump, this method will be required, and the
    /// `where Self: PartialEq` bound will be removed.
    #[inline]
    fn is_one(&self) -> bool
    where
        Self: PartialEq,
    {
        *self == Self::one()
    }
 }
 macro_rules! one_impl {
    ($t:ty, $v:expr) => {
        impl One for $t {
            #[inline]
            fn one() -> $t {
                $v
            }
            #[inline]
            fn is_one(&self) -> bool {
                *self == $v
            }
        }
    };
 }
 one_impl!(usize, 1);
 one_impl!(u8, 1);
 one_impl!(u16, 1);
 one_impl!(u32, 1);
 one_impl!(u64, 1);
 #[cfg(has_i128)]
 one_impl!(u128, 1);
 one_impl!(isize, 1);
 one_impl!(i8, 1);
 one_impl!(i16, 1);
 one_impl!(i32, 1);
 one_impl!(i64, 1);
 #[cfg(has_i128)]
 one_impl!(i128, 1);
 one_impl!(f32, 1.0);
 one_impl!(f64, 1.0);
 impl<T: One> One for Wrapping<T>
 where
    Wrapping<T>: Mul<Output = Wrapping<T>>,
 {
    fn set_one(&mut self) {
        self.0.set_one();
    }
    fn one() -> Self {
        Wrapping(T::one())
    }
 }
 // Some helper functions provided for backwards compatibility.
 /// Returns the additive identity, `0`.
 #[inline(always)]
 pub fn zero<T: Zero>() -> T {
    Zero::zero()
 }
 /// Returns the multiplicative identity, `1`.
 #[inline(always)]
 pub fn one<T: One>() -> T {
    One::one()
 }
 #[test]
 fn wrapping_identities() {
    macro_rules! test_wrapping_identities {
        ($($t:ty)+) => {
            $(
                assert_eq!(zero::<$t>(), zero::<Wrapping<$t>>().0);
                assert_eq!(one::<$t>(), one::<Wrapping<$t>>().0);
                assert_eq!((0 as $t).is_zero(), Wrapping(0 as $t).is_zero());
                assert_eq!((1 as $t).is_zero(), Wrapping(1 as $t).is_zero());
            )+
        };
    }
    test_wrapping_identities!(isize i8 i16 i32 i64 usize u8 u16 u32 u64);
 }
 #[test]
 fn wrapping_is_zero() {
    fn require_zero<T: Zero>(_: &T) {}
    require_zero(&Wrapping(42));
 }
 #[test]
 fn wrapping_is_one() {
    fn require_one<T: One>(_: &T) {}
    require_one(&Wrapping(42));
 }
--- a/src/lib.rs
+++ b/src/lib.rs
@ -1,4 +1,4 @@
-// Copyright 2013-2014 The Rust Project Developers. See the COPYRIGHT
+// Copyright 2014-2016 The Rust Project Developers. See the COPYRIGHT
 // file at the top-level directory of this distribution and at
 // http://rust-lang.org/COPYRIGHT.
 //
@ -8,565 +8,104 @@
 // option. This file may not be copied, modified, or distributed
 // except according to those terms.
-//! Numeric traits for generic mathematics
+//! A collection of numeric types and traits for Rust.
 //!
-//! ## Compatibility
+//! This includes new types for big integers, rationals, and complex numbers,
 //! new traits for generic programming on numeric properties like `Integer`,
 //! and generic range iterators.
 //!
-//! The `num-traits` crate is tested for rustc 1.8 and greater.
+//! ## Example
 //!
 //! This example uses the BigRational type and [Newton's method][newt] to
 //! approximate a square root to arbitrary precision:
 //!
 //! ```
 //! extern crate num;
 //! # #[cfg(all(feature = "bigint", feature="rational"))]
 //! # mod test {
 //!
 //! use num::FromPrimitive;
 //! use num::bigint::BigInt;
 //! use num::rational::{Ratio, BigRational};
 //!
 //! # pub
 //! fn approx_sqrt(number: u64, iterations: usize) -> BigRational {
 //!     let start: Ratio<BigInt> = Ratio::from_integer(FromPrimitive::from_u64(number).unwrap());
 //!     let mut approx = start.clone();
 //!
 //!     for _ in 0..iterations {
 //!         approx = (&approx + (&start / &approx)) /
 //!             Ratio::from_integer(FromPrimitive::from_u64(2).unwrap());
 //!     }
 //!
 //!     approx
 //! }
 //! # }
 //! # #[cfg(not(all(feature = "bigint", feature="rational")))]
 //! # mod test { pub fn approx_sqrt(n: u64, _: usize) -> u64 { n } }
 //! # use test::approx_sqrt;
 //!
 //! fn main() {
 //!     println!("{}", approx_sqrt(10, 4)); // prints 4057691201/1283082416
 //! }
 //!
 //! ```
 //!
 //! [newt]: https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method
 #![doc(html_logo_url = "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/")]
-#![doc(html_root_url = "https://docs.rs/num-traits/0.2")]
+extern crate num_traits;
-#![deny(unconditional_recursion)]
+extern crate num_integer;
-#![no_std]
+extern crate num_iter;
-#[cfg(feature = "std")]
+#[cfg(feature = "num-complex")]
-extern crate std;
+extern crate num_complex;
 #[cfg(feature = "num-bigint")]
 extern crate num_bigint;
 #[cfg(feature = "num-rational")]
 extern crate num_rational;
-// Only `no_std` builds actually use `libm`.
+#[cfg(feature = "num-bigint")]
-#[cfg(all(not(feature = "std"), feature = "libm"))]
+pub use num_bigint::{BigInt, BigUint};
-extern crate libm;
+#[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 core::fmt;
+#[cfg(feature = "num-bigint")]
-use core::num::Wrapping;
+pub mod bigint {
-use core::ops::{Add, Div, Mul, Rem, Sub};
+    pub use num_bigint::*;
 use core::ops::{AddAssign, DivAssign, MulAssign, RemAssign, SubAssign};
 pub use bounds::Bounded;
 #[cfg(any(feature = "std", feature = "libm"))]
 pub use float::Float;
 pub use float::FloatConst;
 // pub use real::{FloatCore, Real}; // NOTE: Don't do this, it breaks `use num_traits::*;`.
 pub use cast::{cast, AsPrimitive, FromPrimitive, NumCast, ToPrimitive};
 pub use identities::{one, zero, One, Zero};
 pub use int::PrimInt;
 pub use ops::checked::{
    CheckedAdd, CheckedDiv, CheckedMul, CheckedNeg, CheckedRem, CheckedShl, CheckedShr, CheckedSub,
 };
 pub use ops::inv::Inv;
 pub use ops::mul_add::{MulAdd, MulAddAssign};
 pub use ops::saturating::Saturating;
 pub use ops::wrapping::{WrappingAdd, WrappingMul, WrappingShl, WrappingShr, WrappingSub};
 pub use pow::{checked_pow, pow, Pow};
 pub use sign::{abs, abs_sub, signum, Signed, Unsigned};
 #[macro_use]
 mod macros;
 pub mod bounds;
 pub mod cast;
 pub mod float;
 pub mod identities;
 pub mod int;
 pub mod ops;
 pub mod pow;
 pub mod real;
 pub mod sign;
 /// 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
+#[cfg(feature = "num-complex")]
-///
+pub mod complex {
-/// This is automatically implemented for types which implement the operators.
+    pub use num_complex::*;
 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
+pub mod integer {
-    T: Add<Rhs, Output = Output>
+    pub use num_integer::*;
        + 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
+pub mod iter {
-/// the second operand by reference.
+    pub use num_iter::*;
 ///
 /// 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
+pub mod traits {
-    T: AddAssign<Rhs> + SubAssign<Rhs> + MulAssign<Rhs> + DivAssign<Rhs> + RemAssign<Rhs>
+    pub use num_traits::*;
 {
 }
-/// The trait for `Num` types which also implement assignment operators.
+#[cfg(feature = "num-rational")]
-///
+pub mod rational {
-/// This is automatically implemented for types which implement the operators.
+    pub use num_rational::*;
 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 $t {
            type FromStrRadixErr = ::core::num::ParseIntError;
            #[inline]
            fn from_str_radix(s: &str, radix: u32)
                              -> Result<Self, ::core::num::ParseIntError>
            {
                <$t>::from_str_radix(s, radix)
            }
        }
    )*)
 }
 int_trait_impl!(Num for usize u8 u16 u32 u64 isize i8 i16 i32 i64);
 #[cfg(has_i128)]
 int_trait_impl!(Num for u128 i128);
 impl<T: Num> Num for Wrapping<T>
 where
    Wrapping<T>: Add<Output = Wrapping<T>>
        + Sub<Output = Wrapping<T>>
        + Mul<Output = Wrapping<T>>
        + Div<Output = Wrapping<T>>
        + Rem<Output = Wrapping<T>>,
 {
    type FromStrRadixErr = T::FromStrRadixErr;
    fn from_str_radix(str: &str, radix: u32) -> Result<Self, Self::FromStrRadixErr> {
        T::from_str_radix(str, radix).map(Wrapping)
    }
 }
 #[derive(Debug)]
 pub enum FloatErrorKind {
    Empty,
    Invalid,
 }
 // FIXME: core::num::ParseFloatError is stable in 1.0, but opaque to us,
 // so there's not really any way for us to reuse it.
 #[derive(Debug)]
 pub struct ParseFloatError {
    pub kind: FloatErrorKind,
 }
 impl fmt::Display for ParseFloatError {
    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
        let description = match self.kind {
            FloatErrorKind::Empty => "cannot parse float from empty string",
            FloatErrorKind::Invalid => "invalid float literal",
        };
        description.fmt(f)
    }
 }
 // FIXME: The standard library from_str_radix on floats was deprecated, so we're stuck
 // with this implementation ourselves until we want to make a breaking change.
 // (would have to drop it from `Num` though)
 macro_rules! float_trait_impl {
    ($name:ident for $($t:ident)*) => ($(
        impl $name for $t {
            type FromStrRadixErr = ParseFloatError;
            fn from_str_radix(src: &str, radix: u32)
                              -> Result<Self, Self::FromStrRadixErr>
            {
                use self::FloatErrorKind::*;
                use self::ParseFloatError as PFE;
                // Special values
                match src {
                    "inf"   => return Ok(core::$t::INFINITY),
                    "-inf"  => return Ok(core::$t::NEG_INFINITY),
                    "NaN"   => return Ok(core::$t::NAN),
                    _       => {},
                }
                fn slice_shift_char(src: &str) -> Option<(char, &str)> {
                    let mut chars = src.chars();
                    if let Some(ch) = chars.next() {
                        Some((ch, chars.as_str()))
                    } else {
                        None
                    }
                }
                let (is_positive, src) =  match slice_shift_char(src) {
                    None             => return Err(PFE { kind: Empty }),
                    Some(('-', ""))  => return Err(PFE { kind: Empty }),
                    Some(('-', src)) => (false, src),
                    Some((_, _))     => (true,  src),
                };
                // The significand to accumulate
                let mut sig = if is_positive { 0.0 } else { -0.0 };
                // Necessary to detect overflow
                let mut prev_sig = sig;
                let mut cs = src.chars().enumerate();
                // Exponent prefix and exponent index offset
                let mut exp_info = None::<(char, usize)>;
                // Parse the integer part of the significand
                for (i, c) in cs.by_ref() {
                    match c.to_digit(radix) {
                        Some(digit) => {
                            // shift significand one digit left
                            sig = sig * (radix as $t);
                            // add/subtract current digit depending on sign
                            if is_positive {
                                sig = sig + ((digit as isize) as $t);
                            } else {
                                sig = sig - ((digit as isize) as $t);
                            }
                            // Detect overflow by comparing to last value, except
                            // if we've not seen any non-zero digits.
                            if prev_sig != 0.0 {
                                if is_positive && sig <= prev_sig
                                    { return Ok(core::$t::INFINITY); }
                                if !is_positive && sig >= prev_sig
                                    { return Ok(core::$t::NEG_INFINITY); }
                                // Detect overflow by reversing the shift-and-add process
                                if is_positive && (prev_sig != (sig - digit as $t) / radix as $t)
                                    { return Ok(core::$t::INFINITY); }
                                if !is_positive && (prev_sig != (sig + digit as $t) / radix as $t)
                                    { return Ok(core::$t::NEG_INFINITY); }
                            }
                            prev_sig = sig;
                        },
                        None => match c {
                            'e' | 'E' | 'p' | 'P' => {
                                exp_info = Some((c, i + 1));
                                break;  // start of exponent
                            },
                            '.' => {
                                break;  // start of fractional part
                            },
                            _ => {
                                return Err(PFE { kind: Invalid });
                            },
                        },
                    }
                }
                // If we are not yet at the exponent parse the fractional
                // part of the significand
                if exp_info.is_none() {
                    let mut power = 1.0;
                    for (i, c) in cs.by_ref() {
                        match c.to_digit(radix) {
                            Some(digit) => {
                                // Decrease power one order of magnitude
                                power = power / (radix as $t);
                                // add/subtract current digit depending on sign
                                sig = if is_positive {
                                    sig + (digit as $t) * power
                                } else {
                                    sig - (digit as $t) * power
                                };
                                // Detect overflow by comparing to last value
                                if is_positive && sig < prev_sig
                                    { return Ok(core::$t::INFINITY); }
                                if !is_positive && sig > prev_sig
                                    { return Ok(core::$t::NEG_INFINITY); }
                                prev_sig = sig;
                            },
                            None => match c {
                                'e' | 'E' | 'p' | 'P' => {
                                    exp_info = Some((c, i + 1));
                                    break; // start of exponent
                                },
                                _ => {
                                    return Err(PFE { kind: Invalid });
                                },
                            },
                        }
                    }
                }
                // Parse and calculate the exponent
                let exp = match exp_info {
                    Some((c, offset)) => {
                        let base = match c {
                            'E' | 'e' if radix == 10 => 10.0,
                            'P' | 'p' if radix == 16 => 2.0,
                            _ => return Err(PFE { kind: Invalid }),
                        };
                        // Parse the exponent as decimal integer
                        let src = &src[offset..];
                        let (is_positive, exp) = match slice_shift_char(src) {
                            Some(('-', src)) => (false, src.parse::<usize>()),
                            Some(('+', src)) => (true,  src.parse::<usize>()),
                            Some((_, _))     => (true,  src.parse::<usize>()),
                            None             => return Err(PFE { kind: Invalid }),
                        };
                        #[cfg(feature = "std")]
                        fn pow(base: $t, exp: usize) -> $t {
                            Float::powi(base, exp as i32)
                        }
                        // otherwise uses the generic `pow` from the root
                        match (is_positive, exp) {
                            (true,  Ok(exp)) => pow(base, exp),
                            (false, Ok(exp)) => 1.0 / pow(base, exp),
                            (_, Err(_))      => return Err(PFE { kind: Invalid }),
                        }
                    },
                    None => 1.0, // no exponent
                };
                Ok(sig * exp)
            }
        }
    )*)
 }
 float_trait_impl!(Num for f32 f64);
 /// A value bounded by a minimum and a maximum
 ///
 ///  If input is less than min then this returns min.
 ///  If input is greater than max then this returns max.
 ///  Otherwise this returns input.
 ///
 /// **Panics** in debug mode if `!(min <= max)`.
 #[inline]
 pub fn clamp<T: PartialOrd>(input: T, min: T, max: T) -> T {
    debug_assert!(min <= max, "min must be less than or equal to max");
    if input < min {
        min
    } else if input > max {
        max
    } else {
        input
    }
 }
 /// A value bounded by a minimum value
 ///
 ///  If input is less than min then this returns min.
 ///  Otherwise this returns input.
 ///  `clamp_min(std::f32::NAN, 1.0)` preserves `NAN` different from `f32::min(std::f32::NAN, 1.0)`.
 ///
 /// **Panics** in debug mode if `!(min == min)`. (This occurs if `min` is `NAN`.)
 #[inline]
 pub fn clamp_min<T: PartialOrd>(input: T, min: T) -> T {
    debug_assert!(min == min, "min must not be NAN");
    if input < min {
        min
    } else {
        input
    }
 }
 /// A value bounded by a maximum value
 ///
 ///  If input is greater than max then this returns max.
 ///  Otherwise this returns input.
 ///  `clamp_max(std::f32::NAN, 1.0)` preserves `NAN` different from `f32::max(std::f32::NAN, 1.0)`.
 ///
 /// **Panics** in debug mode if `!(max == max)`. (This occurs if `max` is `NAN`.)
 #[inline]
 pub fn clamp_max<T: PartialOrd>(input: T, max: T) -> T {
    debug_assert!(max == max, "max must not be NAN");
    if input > max {
        max
    } else {
        input
    }
 }
 #[test]
 fn clamp_test() {
    // Int test
    assert_eq!(1, clamp(1, -1, 2));
    assert_eq!(-1, clamp(-2, -1, 2));
    assert_eq!(2, clamp(3, -1, 2));
    assert_eq!(1, clamp_min(1, -1));
    assert_eq!(-1, clamp_min(-2, -1));
    assert_eq!(-1, clamp_max(1, -1));
    assert_eq!(-2, clamp_max(-2, -1));
    // Float test
    assert_eq!(1.0, clamp(1.0, -1.0, 2.0));
    assert_eq!(-1.0, clamp(-2.0, -1.0, 2.0));
    assert_eq!(2.0, clamp(3.0, -1.0, 2.0));
    assert_eq!(1.0, clamp_min(1.0, -1.0));
    assert_eq!(-1.0, clamp_min(-2.0, -1.0));
    assert_eq!(-1.0, clamp_max(1.0, -1.0));
    assert_eq!(-2.0, clamp_max(-2.0, -1.0));
    assert!(clamp(::core::f32::NAN, -1.0, 1.0).is_nan());
    assert!(clamp_min(::core::f32::NAN, 1.0).is_nan());
    assert!(clamp_max(::core::f32::NAN, 1.0).is_nan());
 }
 #[test]
 #[should_panic]
 #[cfg(debug_assertions)]
 fn clamp_nan_min() {
    clamp(0., ::core::f32::NAN, 1.);
 }
 #[test]
 #[should_panic]
 #[cfg(debug_assertions)]
 fn clamp_nan_max() {
    clamp(0., -1., ::core::f32::NAN);
 }
 #[test]
 #[should_panic]
 #[cfg(debug_assertions)]
 fn clamp_nan_min_max() {
    clamp(0., ::core::f32::NAN, ::core::f32::NAN);
 }
 #[test]
 #[should_panic]
 #[cfg(debug_assertions)]
 fn clamp_min_nan_min() {
    clamp_min(0., ::core::f32::NAN);
 }
 #[test]
 #[should_panic]
 #[cfg(debug_assertions)]
 fn clamp_max_nan_max() {
    clamp_max(0., ::core::f32::NAN);
 }
 #[test]
 fn from_str_radix_unwrap() {
    // The Result error must impl Debug to allow unwrap()
    let i: i32 = Num::from_str_radix("0", 10).unwrap();
    assert_eq!(i, 0);
    let f: f32 = Num::from_str_radix("0.0", 10).unwrap();
    assert_eq!(f, 0.0);
 }
 #[test]
 fn from_str_radix_multi_byte_fail() {
    // Ensure parsing doesn't panic, even on invalid sign characters
    assert!(f32::from_str_radix("™0.2", 10).is_err());
    // Even when parsing the exponent sign
    assert!(f32::from_str_radix("0.2E™1", 10).is_err());
 }
 #[test]
 fn wrapping_is_num() {
    fn require_num<T: Num>(_: &T) {}
    require_num(&Wrapping(42_u32));
    require_num(&Wrapping(-42));
 }
 #[test]
 fn wrapping_from_str_radix() {
    macro_rules! test_wrapping_from_str_radix {
        ($($t:ty)+) => {
            $(
                for &(s, r) in &[("42", 10), ("42", 2), ("-13.0", 10), ("foo", 10)] {
                    let w = Wrapping::<$t>::from_str_radix(s, r).map(|w| w.0);
                    assert_eq!(w, <$t as Num>::from_str_radix(s, r));
                }
            )+
        };
    }
    test_wrapping_from_str_radix!(usize u8 u16 u32 u64 isize i8 i16 i32 i64);
 }
 #[test]
 fn check_num_ops() {
    fn compute<T: Num + Copy>(x: T, y: T) -> T {
        x * y / y % y + y - y
    }
    assert_eq!(compute(1, 2), 1)
 }
 #[test]
 fn check_numref_ops() {
    fn compute<T: NumRef>(x: T, y: &T) -> T {
        x * y / y % y + y - y
    }
    assert_eq!(compute(1, &2), 1)
 }
 #[test]
 fn check_refnum_ops() {
    fn compute<T: Copy>(x: &T, y: T) -> T
    where
        for<'a> &'a T: RefNum<T>,
    {
        &(&(&(&(x * y) / y) % y) + y) - y
    }
    assert_eq!(compute(&1, 2), 1)
 }
 #[test]
 fn check_refref_ops() {
    fn compute<T>(x: &T, y: &T) -> T
    where
        for<'a> &'a T: RefNum<T>,
    {
        &(&(&(&(x * y) / y) % y) + y) - y
    }
    assert_eq!(compute(&1, &2), 1)
 }
 #[test]
 fn check_numassign_ops() {
    fn compute<T: NumAssign + Copy>(mut x: T, y: T) -> T {
        x *= y;
        x /= y;
        x %= y;
        x += y;
        x -= y;
        x
    }
    assert_eq!(compute(1, 2), 1)
 }
 // TODO test `NumAssignRef`, but even the standard numeric types don't
 // implement this yet. (see rust pr41336)
--- a/src/macros.rs
+++ b/src/macros.rs
@ -1,37 +0,0 @@
 // not all are used in all features configurations
 #![allow(unused)]
 /// Forward a method to an inherent method or a base trait method.
 macro_rules! forward {
    ($( Self :: $method:ident ( self $( , $arg:ident : $ty:ty )* ) -> $ret:ty ; )*)
        => {$(
            #[inline]
            fn $method(self $( , $arg : $ty )* ) -> $ret {
                Self::$method(self $( , $arg )* )
            }
        )*};
    ($( $base:ident :: $method:ident ( self $( , $arg:ident : $ty:ty )* ) -> $ret:ty ; )*)
        => {$(
            #[inline]
            fn $method(self $( , $arg : $ty )* ) -> $ret {
                <Self as $base>::$method(self $( , $arg )* )
            }
        )*};
    ($( $base:ident :: $method:ident ( $( $arg:ident : $ty:ty ),* ) -> $ret:ty ; )*)
        => {$(
            #[inline]
            fn $method( $( $arg : $ty ),* ) -> $ret {
                <Self as $base>::$method( $( $arg ),* )
            }
        )*}
 }
 macro_rules! constant {
    ($( $method:ident () -> $ret:expr ; )*)
        => {$(
            #[inline]
            fn $method() -> Self {
                $ret
            }
        )*};
 }
--- a/src/ops/checked.rs
+++ b/src/ops/checked.rs
@ -1,277 +0,0 @@
 use core::ops::{Add, Div, Mul, Rem, Shl, Shr, Sub};
 /// Performs addition that returns `None` instead of wrapping around on
 /// overflow.
 pub trait CheckedAdd: Sized + Add<Self, Output = Self> {
    /// Adds two numbers, checking for overflow. If overflow happens, `None` is
    /// returned.
    fn checked_add(&self, v: &Self) -> Option<Self>;
 }
 macro_rules! checked_impl {
    ($trait_name:ident, $method:ident, $t:ty) => {
        impl $trait_name for $t {
            #[inline]
            fn $method(&self, v: &$t) -> Option<$t> {
                <$t>::$method(*self, *v)
            }
        }
    };
 }
 checked_impl!(CheckedAdd, checked_add, u8);
 checked_impl!(CheckedAdd, checked_add, u16);
 checked_impl!(CheckedAdd, checked_add, u32);
 checked_impl!(CheckedAdd, checked_add, u64);
 checked_impl!(CheckedAdd, checked_add, usize);
 #[cfg(has_i128)]
 checked_impl!(CheckedAdd, checked_add, u128);
 checked_impl!(CheckedAdd, checked_add, i8);
 checked_impl!(CheckedAdd, checked_add, i16);
 checked_impl!(CheckedAdd, checked_add, i32);
 checked_impl!(CheckedAdd, checked_add, i64);
 checked_impl!(CheckedAdd, checked_add, isize);
 #[cfg(has_i128)]
 checked_impl!(CheckedAdd, checked_add, i128);
 /// Performs subtraction that returns `None` instead of wrapping around on underflow.
 pub trait CheckedSub: Sized + Sub<Self, Output = Self> {
    /// Subtracts two numbers, checking for underflow. If underflow happens,
    /// `None` is returned.
    fn checked_sub(&self, v: &Self) -> Option<Self>;
 }
 checked_impl!(CheckedSub, checked_sub, u8);
 checked_impl!(CheckedSub, checked_sub, u16);
 checked_impl!(CheckedSub, checked_sub, u32);
 checked_impl!(CheckedSub, checked_sub, u64);
 checked_impl!(CheckedSub, checked_sub, usize);
 #[cfg(has_i128)]
 checked_impl!(CheckedSub, checked_sub, u128);
 checked_impl!(CheckedSub, checked_sub, i8);
 checked_impl!(CheckedSub, checked_sub, i16);
 checked_impl!(CheckedSub, checked_sub, i32);
 checked_impl!(CheckedSub, checked_sub, i64);
 checked_impl!(CheckedSub, checked_sub, isize);
 #[cfg(has_i128)]
 checked_impl!(CheckedSub, checked_sub, i128);
 /// Performs multiplication that returns `None` instead of wrapping around on underflow or
 /// overflow.
 pub trait CheckedMul: Sized + Mul<Self, Output = Self> {
    /// Multiplies two numbers, checking for underflow or overflow. If underflow
    /// or overflow happens, `None` is returned.
    fn checked_mul(&self, v: &Self) -> Option<Self>;
 }
 checked_impl!(CheckedMul, checked_mul, u8);
 checked_impl!(CheckedMul, checked_mul, u16);
 checked_impl!(CheckedMul, checked_mul, u32);
 checked_impl!(CheckedMul, checked_mul, u64);
 checked_impl!(CheckedMul, checked_mul, usize);
 #[cfg(has_i128)]
 checked_impl!(CheckedMul, checked_mul, u128);
 checked_impl!(CheckedMul, checked_mul, i8);
 checked_impl!(CheckedMul, checked_mul, i16);
 checked_impl!(CheckedMul, checked_mul, i32);
 checked_impl!(CheckedMul, checked_mul, i64);
 checked_impl!(CheckedMul, checked_mul, isize);
 #[cfg(has_i128)]
 checked_impl!(CheckedMul, checked_mul, i128);
 /// Performs division that returns `None` instead of panicking on division by zero and instead of
 /// wrapping around on underflow and overflow.
 pub trait CheckedDiv: Sized + Div<Self, Output = Self> {
    /// Divides two numbers, checking for underflow, overflow and division by
    /// zero. If any of that happens, `None` is returned.
    fn checked_div(&self, v: &Self) -> Option<Self>;
 }
 checked_impl!(CheckedDiv, checked_div, u8);
 checked_impl!(CheckedDiv, checked_div, u16);
 checked_impl!(CheckedDiv, checked_div, u32);
 checked_impl!(CheckedDiv, checked_div, u64);
 checked_impl!(CheckedDiv, checked_div, usize);
 #[cfg(has_i128)]
 checked_impl!(CheckedDiv, checked_div, u128);
 checked_impl!(CheckedDiv, checked_div, i8);
 checked_impl!(CheckedDiv, checked_div, i16);
 checked_impl!(CheckedDiv, checked_div, i32);
 checked_impl!(CheckedDiv, checked_div, i64);
 checked_impl!(CheckedDiv, checked_div, isize);
 #[cfg(has_i128)]
 checked_impl!(CheckedDiv, checked_div, i128);
 /// Performs an integral remainder that returns `None` instead of panicking on division by zero and
 /// instead of wrapping around on underflow and overflow.
 pub trait CheckedRem: Sized + Rem<Self, Output = Self> {
    /// Finds the remainder of dividing two numbers, checking for underflow, overflow and division
    /// by zero. If any of that happens, `None` is returned.
    ///
    /// # Examples
    ///
    /// ```
    /// use num_traits::CheckedRem;
    /// use std::i32::MIN;
    ///
    /// assert_eq!(CheckedRem::checked_rem(&10, &7), Some(3));
    /// assert_eq!(CheckedRem::checked_rem(&10, &-7), Some(3));
    /// assert_eq!(CheckedRem::checked_rem(&-10, &7), Some(-3));
    /// assert_eq!(CheckedRem::checked_rem(&-10, &-7), Some(-3));
    ///
    /// assert_eq!(CheckedRem::checked_rem(&10, &0), None);
    ///
    /// assert_eq!(CheckedRem::checked_rem(&MIN, &1), Some(0));
    /// assert_eq!(CheckedRem::checked_rem(&MIN, &-1), None);
    /// ```
    fn checked_rem(&self, v: &Self) -> Option<Self>;
 }
 checked_impl!(CheckedRem, checked_rem, u8);
 checked_impl!(CheckedRem, checked_rem, u16);
 checked_impl!(CheckedRem, checked_rem, u32);
 checked_impl!(CheckedRem, checked_rem, u64);
 checked_impl!(CheckedRem, checked_rem, usize);
 #[cfg(has_i128)]
 checked_impl!(CheckedRem, checked_rem, u128);
 checked_impl!(CheckedRem, checked_rem, i8);
 checked_impl!(CheckedRem, checked_rem, i16);
 checked_impl!(CheckedRem, checked_rem, i32);
 checked_impl!(CheckedRem, checked_rem, i64);
 checked_impl!(CheckedRem, checked_rem, isize);
 #[cfg(has_i128)]
 checked_impl!(CheckedRem, checked_rem, i128);
 macro_rules! checked_impl_unary {
    ($trait_name:ident, $method:ident, $t:ty) => {
        impl $trait_name for $t {
            #[inline]
            fn $method(&self) -> Option<$t> {
                <$t>::$method(*self)
            }
        }
    };
 }
 /// Performs negation that returns `None` if the result can't be represented.
 pub trait CheckedNeg: Sized {
    /// Negates a number, returning `None` for results that can't be represented, like signed `MIN`
    /// values that can't be positive, or non-zero unsigned values that can't be negative.
    ///
    /// # Examples
    ///
    /// ```
    /// use num_traits::CheckedNeg;
    /// use std::i32::MIN;
    ///
    /// assert_eq!(CheckedNeg::checked_neg(&1_i32), Some(-1));
    /// assert_eq!(CheckedNeg::checked_neg(&-1_i32), Some(1));
    /// assert_eq!(CheckedNeg::checked_neg(&MIN), None);
    ///
    /// assert_eq!(CheckedNeg::checked_neg(&0_u32), Some(0));
    /// assert_eq!(CheckedNeg::checked_neg(&1_u32), None);
    /// ```
    fn checked_neg(&self) -> Option<Self>;
 }
 checked_impl_unary!(CheckedNeg, checked_neg, u8);
 checked_impl_unary!(CheckedNeg, checked_neg, u16);
 checked_impl_unary!(CheckedNeg, checked_neg, u32);
 checked_impl_unary!(CheckedNeg, checked_neg, u64);
 checked_impl_unary!(CheckedNeg, checked_neg, usize);
 #[cfg(has_i128)]
 checked_impl_unary!(CheckedNeg, checked_neg, u128);
 checked_impl_unary!(CheckedNeg, checked_neg, i8);
 checked_impl_unary!(CheckedNeg, checked_neg, i16);
 checked_impl_unary!(CheckedNeg, checked_neg, i32);
 checked_impl_unary!(CheckedNeg, checked_neg, i64);
 checked_impl_unary!(CheckedNeg, checked_neg, isize);
 #[cfg(has_i128)]
 checked_impl_unary!(CheckedNeg, checked_neg, i128);
 /// Performs a left shift that returns `None` on shifts larger than
 /// the type width.
 pub trait CheckedShl: Sized + Shl<u32, Output = Self> {
    /// Checked shift left. Computes `self << rhs`, returning `None`
    /// if `rhs` is larger than or equal to the number of bits in `self`.
    ///
    /// ```
    /// use num_traits::CheckedShl;
    ///
    /// let x: u16 = 0x0001;
    ///
    /// assert_eq!(CheckedShl::checked_shl(&x, 0),  Some(0x0001));
    /// assert_eq!(CheckedShl::checked_shl(&x, 1),  Some(0x0002));
    /// assert_eq!(CheckedShl::checked_shl(&x, 15), Some(0x8000));
    /// assert_eq!(CheckedShl::checked_shl(&x, 16), None);
    /// ```
    fn checked_shl(&self, rhs: u32) -> Option<Self>;
 }
 macro_rules! checked_shift_impl {
    ($trait_name:ident, $method:ident, $t:ty) => {
        impl $trait_name for $t {
            #[inline]
            fn $method(&self, rhs: u32) -> Option<$t> {
                <$t>::$method(*self, rhs)
            }
        }
    };
 }
 checked_shift_impl!(CheckedShl, checked_shl, u8);
 checked_shift_impl!(CheckedShl, checked_shl, u16);
 checked_shift_impl!(CheckedShl, checked_shl, u32);
 checked_shift_impl!(CheckedShl, checked_shl, u64);
 checked_shift_impl!(CheckedShl, checked_shl, usize);
 #[cfg(has_i128)]
 checked_shift_impl!(CheckedShl, checked_shl, u128);
 checked_shift_impl!(CheckedShl, checked_shl, i8);
 checked_shift_impl!(CheckedShl, checked_shl, i16);
 checked_shift_impl!(CheckedShl, checked_shl, i32);
 checked_shift_impl!(CheckedShl, checked_shl, i64);
 checked_shift_impl!(CheckedShl, checked_shl, isize);
 #[cfg(has_i128)]
 checked_shift_impl!(CheckedShl, checked_shl, i128);
 /// Performs a right shift that returns `None` on shifts larger than
 /// the type width.
 pub trait CheckedShr: Sized + Shr<u32, Output = Self> {
    /// Checked shift right. Computes `self >> rhs`, returning `None`
    /// if `rhs` is larger than or equal to the number of bits in `self`.
    ///
    /// ```
    /// use num_traits::CheckedShr;
    ///
    /// let x: u16 = 0x8000;
    ///
    /// assert_eq!(CheckedShr::checked_shr(&x, 0),  Some(0x8000));
    /// assert_eq!(CheckedShr::checked_shr(&x, 1),  Some(0x4000));
    /// assert_eq!(CheckedShr::checked_shr(&x, 15), Some(0x0001));
    /// assert_eq!(CheckedShr::checked_shr(&x, 16), None);
    /// ```
    fn checked_shr(&self, rhs: u32) -> Option<Self>;
 }
 checked_shift_impl!(CheckedShr, checked_shr, u8);
 checked_shift_impl!(CheckedShr, checked_shr, u16);
 checked_shift_impl!(CheckedShr, checked_shr, u32);
 checked_shift_impl!(CheckedShr, checked_shr, u64);
 checked_shift_impl!(CheckedShr, checked_shr, usize);
 #[cfg(has_i128)]
 checked_shift_impl!(CheckedShr, checked_shr, u128);
 checked_shift_impl!(CheckedShr, checked_shr, i8);
 checked_shift_impl!(CheckedShr, checked_shr, i16);
 checked_shift_impl!(CheckedShr, checked_shr, i32);
 checked_shift_impl!(CheckedShr, checked_shr, i64);
 checked_shift_impl!(CheckedShr, checked_shr, isize);
 #[cfg(has_i128)]
 checked_shift_impl!(CheckedShr, checked_shr, i128);
--- a/src/ops/inv.rs
+++ b/src/ops/inv.rs
@ -1,47 +0,0 @@
 /// Unary operator for retrieving the multiplicative inverse, or reciprocal, of a value.
 pub trait Inv {
    /// The result after applying the operator.
    type Output;
    /// Returns the multiplicative inverse of `self`.
    ///
    /// # Examples
    ///
    /// ```
    /// use std::f64::INFINITY;
    /// use num_traits::Inv;
    ///
    /// assert_eq!(7.0.inv() * 7.0, 1.0);
    /// assert_eq!((-0.0).inv(), -INFINITY);
    /// ```
    fn inv(self) -> Self::Output;
 }
 impl Inv for f32 {
    type Output = f32;
    #[inline]
    fn inv(self) -> f32 {
        1.0 / self
    }
 }
 impl Inv for f64 {
    type Output = f64;
    #[inline]
    fn inv(self) -> f64 {
        1.0 / self
    }
 }
 impl<'a> Inv for &'a f32 {
    type Output = f32;
    #[inline]
    fn inv(self) -> f32 {
        1.0 / *self
    }
 }
 impl<'a> Inv for &'a f64 {
    type Output = f64;
    #[inline]
    fn inv(self) -> f64 {
        1.0 / *self
    }
 }
--- a/src/ops/mul_add.rs
+++ b/src/ops/mul_add.rs
@ -1,151 +0,0 @@
 /// Fused multiply-add. Computes `(self * a) + b` with only one rounding
 /// error, yielding a more accurate result than an unfused multiply-add.
 ///
 /// Using `mul_add` can be more performant than an unfused multiply-add if
 /// the target architecture has a dedicated `fma` CPU instruction.
 ///
 /// Note that `A` and `B` are `Self` by default, but this is not mandatory.
 ///
 /// # Example
 ///
 /// ```
 /// use std::f32;
 ///
 /// let m = 10.0_f32;
 /// let x = 4.0_f32;
 /// let b = 60.0_f32;
 ///
 /// // 100.0
 /// let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs();
 ///
 /// assert!(abs_difference <= 100.0 * f32::EPSILON);
 /// ```
 pub trait MulAdd<A = Self, B = Self> {
    /// The resulting type after applying the fused multiply-add.
    type Output;
    /// Performs the fused multiply-add operation.
    fn mul_add(self, a: A, b: B) -> Self::Output;
 }
 /// The fused multiply-add assignment operation.
 pub trait MulAddAssign<A = Self, B = Self> {
    /// Performs the fused multiply-add operation.
    fn mul_add_assign(&mut self, a: A, b: B);
 }
 #[cfg(any(feature = "std", feature = "libm"))]
 impl MulAdd<f32, f32> for f32 {
    type Output = Self;
    #[inline]
    fn mul_add(self, a: Self, b: Self) -> Self::Output {
        <Self as ::Float>::mul_add(self, a, b)
    }
 }
 #[cfg(any(feature = "std", feature = "libm"))]
 impl MulAdd<f64, f64> for f64 {
    type Output = Self;
    #[inline]
    fn mul_add(self, a: Self, b: Self) -> Self::Output {
        <Self as ::Float>::mul_add(self, a, b)
    }
 }
 macro_rules! mul_add_impl {
    ($trait_name:ident for $($t:ty)*) => {$(
        impl $trait_name for $t {
            type Output = Self;
            #[inline]
            fn mul_add(self, a: Self, b: Self) -> Self::Output {
                (self * a) + b
            }
        }
    )*}
 }
 mul_add_impl!(MulAdd for isize usize i8 u8 i16 u16 i32 u32 i64 u64);
 #[cfg(has_i128)]
 mul_add_impl!(MulAdd for i128 u128);
 #[cfg(any(feature = "std", feature = "libm"))]
 impl MulAddAssign<f32, f32> for f32 {
    #[inline]
    fn mul_add_assign(&mut self, a: Self, b: Self) {
        *self = <Self as ::Float>::mul_add(*self, a, b)
    }
 }
 #[cfg(any(feature = "std", feature = "libm"))]
 impl MulAddAssign<f64, f64> for f64 {
    #[inline]
    fn mul_add_assign(&mut self, a: Self, b: Self) {
        *self = <Self as ::Float>::mul_add(*self, a, b)
    }
 }
 macro_rules! mul_add_assign_impl {
    ($trait_name:ident for $($t:ty)*) => {$(
        impl $trait_name for $t {
            #[inline]
            fn mul_add_assign(&mut self, a: Self, b: Self) {
                *self = (*self * a) + b
            }
        }
    )*}
 }
 mul_add_assign_impl!(MulAddAssign for isize usize i8 u8 i16 u16 i32 u32 i64 u64);
 #[cfg(has_i128)]
 mul_add_assign_impl!(MulAddAssign for i128 u128);
 #[cfg(test)]
 mod tests {
    use super::*;
    #[test]
    fn mul_add_integer() {
        macro_rules! test_mul_add {
            ($($t:ident)+) => {
                $(
                    {
                        let m: $t = 2;
                        let x: $t = 3;
                        let b: $t = 4;
                        assert_eq!(MulAdd::mul_add(m, x, b), (m*x + b));
                    }
                )+
            };
        }
        test_mul_add!(usize u8 u16 u32 u64 isize i8 i16 i32 i64);
    }
    #[test]
    #[cfg(feature = "std")]
    fn mul_add_float() {
        macro_rules! test_mul_add {
            ($($t:ident)+) => {
                $(
                    {
                        use core::$t;
                        let m: $t = 12.0;
                        let x: $t = 3.4;
                        let b: $t = 5.6;
                        let abs_difference = (MulAdd::mul_add(m, x, b) - (m*x + b)).abs();
                        assert!(abs_difference <= 46.4 * $t::EPSILON);
                    }
                )+
            };
        }
        test_mul_add!(f32 f64);
    }
 }
--- a/src/ops/wrapping.rs
+++ b/src/ops/wrapping.rs
@ -1,272 +0,0 @@
 use core::num::Wrapping;
 use core::ops::{Add, Mul, Shl, Shr, Sub};
 macro_rules! wrapping_impl {
    ($trait_name:ident, $method:ident, $t:ty) => {
        impl $trait_name for $t {
            #[inline]
            fn $method(&self, v: &Self) -> Self {
                <$t>::$method(*self, *v)
            }
        }
    };
    ($trait_name:ident, $method:ident, $t:ty, $rhs:ty) => {
        impl $trait_name<$rhs> for $t {
            #[inline]
            fn $method(&self, v: &$rhs) -> Self {
                <$t>::$method(*self, *v)
            }
        }
    };
 }
 /// Performs addition that wraps around on overflow.
 pub trait WrappingAdd: Sized + Add<Self, Output = Self> {
    /// Wrapping (modular) addition. Computes `self + other`, wrapping around at the boundary of
    /// the type.
    fn wrapping_add(&self, v: &Self) -> Self;
 }
 wrapping_impl!(WrappingAdd, wrapping_add, u8);
 wrapping_impl!(WrappingAdd, wrapping_add, u16);
 wrapping_impl!(WrappingAdd, wrapping_add, u32);
 wrapping_impl!(WrappingAdd, wrapping_add, u64);
 wrapping_impl!(WrappingAdd, wrapping_add, usize);
 #[cfg(has_i128)]
 wrapping_impl!(WrappingAdd, wrapping_add, u128);
 wrapping_impl!(WrappingAdd, wrapping_add, i8);
 wrapping_impl!(WrappingAdd, wrapping_add, i16);
 wrapping_impl!(WrappingAdd, wrapping_add, i32);
 wrapping_impl!(WrappingAdd, wrapping_add, i64);
 wrapping_impl!(WrappingAdd, wrapping_add, isize);
 #[cfg(has_i128)]
 wrapping_impl!(WrappingAdd, wrapping_add, i128);
 /// Performs subtraction that wraps around on overflow.
 pub trait WrappingSub: Sized + Sub<Self, Output = Self> {
    /// Wrapping (modular) subtraction. Computes `self - other`, wrapping around at the boundary
    /// of the type.
    fn wrapping_sub(&self, v: &Self) -> Self;
 }
 wrapping_impl!(WrappingSub, wrapping_sub, u8);
 wrapping_impl!(WrappingSub, wrapping_sub, u16);
 wrapping_impl!(WrappingSub, wrapping_sub, u32);
 wrapping_impl!(WrappingSub, wrapping_sub, u64);
 wrapping_impl!(WrappingSub, wrapping_sub, usize);
 #[cfg(has_i128)]
 wrapping_impl!(WrappingSub, wrapping_sub, u128);
 wrapping_impl!(WrappingSub, wrapping_sub, i8);
 wrapping_impl!(WrappingSub, wrapping_sub, i16);
 wrapping_impl!(WrappingSub, wrapping_sub, i32);
 wrapping_impl!(WrappingSub, wrapping_sub, i64);
 wrapping_impl!(WrappingSub, wrapping_sub, isize);
 #[cfg(has_i128)]
 wrapping_impl!(WrappingSub, wrapping_sub, i128);
 /// Performs multiplication that wraps around on overflow.
 pub trait WrappingMul: Sized + Mul<Self, Output = Self> {
    /// Wrapping (modular) multiplication. Computes `self * other`, wrapping around at the boundary
    /// of the type.
    fn wrapping_mul(&self, v: &Self) -> Self;
 }
 wrapping_impl!(WrappingMul, wrapping_mul, u8);
 wrapping_impl!(WrappingMul, wrapping_mul, u16);
 wrapping_impl!(WrappingMul, wrapping_mul, u32);
 wrapping_impl!(WrappingMul, wrapping_mul, u64);
 wrapping_impl!(WrappingMul, wrapping_mul, usize);
 #[cfg(has_i128)]
 wrapping_impl!(WrappingMul, wrapping_mul, u128);
 wrapping_impl!(WrappingMul, wrapping_mul, i8);
 wrapping_impl!(WrappingMul, wrapping_mul, i16);
 wrapping_impl!(WrappingMul, wrapping_mul, i32);
 wrapping_impl!(WrappingMul, wrapping_mul, i64);
 wrapping_impl!(WrappingMul, wrapping_mul, isize);
 #[cfg(has_i128)]
 wrapping_impl!(WrappingMul, wrapping_mul, i128);
 macro_rules! wrapping_shift_impl {
    ($trait_name:ident, $method:ident, $t:ty) => {
        impl $trait_name for $t {
            #[inline]
            fn $method(&self, rhs: u32) -> $t {
                <$t>::$method(*self, rhs)
            }
        }
    };
 }
 /// Performs a left shift that does not panic.
 pub trait WrappingShl: Sized + Shl<usize, Output = Self> {
    /// Panic-free bitwise shift-left; yields `self << mask(rhs)`,
    /// where `mask` removes any high order bits of `rhs` that would
    /// cause the shift to exceed the bitwidth of the type.
    ///
    /// ```
    /// use num_traits::WrappingShl;
    ///
    /// let x: u16 = 0x0001;
    ///
    /// assert_eq!(WrappingShl::wrapping_shl(&x, 0),  0x0001);
    /// assert_eq!(WrappingShl::wrapping_shl(&x, 1),  0x0002);
    /// assert_eq!(WrappingShl::wrapping_shl(&x, 15), 0x8000);
    /// assert_eq!(WrappingShl::wrapping_shl(&x, 16), 0x0001);
    /// ```
    fn wrapping_shl(&self, rhs: u32) -> Self;
 }
 wrapping_shift_impl!(WrappingShl, wrapping_shl, u8);
 wrapping_shift_impl!(WrappingShl, wrapping_shl, u16);
 wrapping_shift_impl!(WrappingShl, wrapping_shl, u32);
 wrapping_shift_impl!(WrappingShl, wrapping_shl, u64);
 wrapping_shift_impl!(WrappingShl, wrapping_shl, usize);
 #[cfg(has_i128)]
 wrapping_shift_impl!(WrappingShl, wrapping_shl, u128);
 wrapping_shift_impl!(WrappingShl, wrapping_shl, i8);
 wrapping_shift_impl!(WrappingShl, wrapping_shl, i16);
 wrapping_shift_impl!(WrappingShl, wrapping_shl, i32);
 wrapping_shift_impl!(WrappingShl, wrapping_shl, i64);
 wrapping_shift_impl!(WrappingShl, wrapping_shl, isize);
 #[cfg(has_i128)]
 wrapping_shift_impl!(WrappingShl, wrapping_shl, i128);
 /// Performs a right shift that does not panic.
 pub trait WrappingShr: Sized + Shr<usize, Output = Self> {
    /// Panic-free bitwise shift-right; yields `self >> mask(rhs)`,
    /// where `mask` removes any high order bits of `rhs` that would
    /// cause the shift to exceed the bitwidth of the type.
    ///
    /// ```
    /// use num_traits::WrappingShr;
    ///
    /// let x: u16 = 0x8000;
    ///
    /// assert_eq!(WrappingShr::wrapping_shr(&x, 0),  0x8000);
    /// assert_eq!(WrappingShr::wrapping_shr(&x, 1),  0x4000);
    /// assert_eq!(WrappingShr::wrapping_shr(&x, 15), 0x0001);
    /// assert_eq!(WrappingShr::wrapping_shr(&x, 16), 0x8000);
    /// ```
    fn wrapping_shr(&self, rhs: u32) -> Self;
 }
 wrapping_shift_impl!(WrappingShr, wrapping_shr, u8);
 wrapping_shift_impl!(WrappingShr, wrapping_shr, u16);
 wrapping_shift_impl!(WrappingShr, wrapping_shr, u32);
 wrapping_shift_impl!(WrappingShr, wrapping_shr, u64);
 wrapping_shift_impl!(WrappingShr, wrapping_shr, usize);
 #[cfg(has_i128)]
 wrapping_shift_impl!(WrappingShr, wrapping_shr, u128);
 wrapping_shift_impl!(WrappingShr, wrapping_shr, i8);
 wrapping_shift_impl!(WrappingShr, wrapping_shr, i16);
 wrapping_shift_impl!(WrappingShr, wrapping_shr, i32);
 wrapping_shift_impl!(WrappingShr, wrapping_shr, i64);
 wrapping_shift_impl!(WrappingShr, wrapping_shr, isize);
 #[cfg(has_i128)]
 wrapping_shift_impl!(WrappingShr, wrapping_shr, i128);
 // Well this is a bit funny, but all the more appropriate.
 impl<T: WrappingAdd> WrappingAdd for Wrapping<T>
 where
    Wrapping<T>: Add<Output = Wrapping<T>>,
 {
    fn wrapping_add(&self, v: &Self) -> Self {
        Wrapping(self.0.wrapping_add(&v.0))
    }
 }
 impl<T: WrappingSub> WrappingSub for Wrapping<T>
 where
    Wrapping<T>: Sub<Output = Wrapping<T>>,
 {
    fn wrapping_sub(&self, v: &Self) -> Self {
        Wrapping(self.0.wrapping_sub(&v.0))
    }
 }
 impl<T: WrappingMul> WrappingMul for Wrapping<T>
 where
    Wrapping<T>: Mul<Output = Wrapping<T>>,
 {
    fn wrapping_mul(&self, v: &Self) -> Self {
        Wrapping(self.0.wrapping_mul(&v.0))
    }
 }
 impl<T: WrappingShl> WrappingShl for Wrapping<T>
 where
    Wrapping<T>: Shl<usize, Output = Wrapping<T>>,
 {
    fn wrapping_shl(&self, rhs: u32) -> Self {
        Wrapping(self.0.wrapping_shl(rhs))
    }
 }
 impl<T: WrappingShr> WrappingShr for Wrapping<T>
 where
    Wrapping<T>: Shr<usize, Output = Wrapping<T>>,
 {
    fn wrapping_shr(&self, rhs: u32) -> Self {
        Wrapping(self.0.wrapping_shr(rhs))
    }
 }
 #[test]
 fn test_wrapping_traits() {
    fn wrapping_add<T: WrappingAdd>(a: T, b: T) -> T {
        a.wrapping_add(&b)
    }
    fn wrapping_sub<T: WrappingSub>(a: T, b: T) -> T {
        a.wrapping_sub(&b)
    }
    fn wrapping_mul<T: WrappingMul>(a: T, b: T) -> T {
        a.wrapping_mul(&b)
    }
    fn wrapping_shl<T: WrappingShl>(a: T, b: u32) -> T {
        a.wrapping_shl(b)
    }
    fn wrapping_shr<T: WrappingShr>(a: T, b: u32) -> T {
        a.wrapping_shr(b)
    }
    assert_eq!(wrapping_add(255, 1), 0u8);
    assert_eq!(wrapping_sub(0, 1), 255u8);
    assert_eq!(wrapping_mul(255, 2), 254u8);
    assert_eq!(wrapping_shl(255, 8), 255u8);
    assert_eq!(wrapping_shr(255, 8), 255u8);
    assert_eq!(wrapping_add(255, 1), (Wrapping(255u8) + Wrapping(1u8)).0);
    assert_eq!(wrapping_sub(0, 1), (Wrapping(0u8) - Wrapping(1u8)).0);
    assert_eq!(wrapping_mul(255, 2), (Wrapping(255u8) * Wrapping(2u8)).0);
    assert_eq!(wrapping_shl(255, 8), (Wrapping(255u8) << 8).0);
    assert_eq!(wrapping_shr(255, 8), (Wrapping(255u8) >> 8).0);
 }
 #[test]
 fn wrapping_is_wrappingadd() {
    fn require_wrappingadd<T: WrappingAdd>(_: &T) {}
    require_wrappingadd(&Wrapping(42));
 }
 #[test]
 fn wrapping_is_wrappingsub() {
    fn require_wrappingsub<T: WrappingSub>(_: &T) {}
    require_wrappingsub(&Wrapping(42));
 }
 #[test]
 fn wrapping_is_wrappingmul() {
    fn require_wrappingmul<T: WrappingMul>(_: &T) {}
    require_wrappingmul(&Wrapping(42));
 }
 #[test]
 fn wrapping_is_wrappingshl() {
    fn require_wrappingshl<T: WrappingShl>(_: &T) {}
    require_wrappingshl(&Wrapping(42));
 }
 #[test]
 fn wrapping_is_wrappingshr() {
    fn require_wrappingshr<T: WrappingShr>(_: &T) {}
    require_wrappingshr(&Wrapping(42));
 }
--- a/src/pow.rs
+++ b/src/pow.rs
@ -1,262 +0,0 @@
 use core::num::Wrapping;
 use core::ops::Mul;
 use {CheckedMul, One};
 /// Binary operator for raising a value to a power.
 pub trait Pow<RHS> {
    /// The result after applying the operator.
    type Output;
    /// Returns `self` to the power `rhs`.
    ///
    /// # Examples
    ///
    /// ```
    /// use num_traits::Pow;
    /// assert_eq!(Pow::pow(10u32, 2u32), 100);
    /// ```
    fn pow(self, rhs: RHS) -> Self::Output;
 }
 macro_rules! pow_impl {
    ($t:ty) => {
        pow_impl!($t, u8);
        pow_impl!($t, usize);
        // FIXME: these should be possible
        // pow_impl!($t, u16);
        // pow_impl!($t, u32);
        // pow_impl!($t, u64);
    };
    ($t:ty, $rhs:ty) => {
        pow_impl!($t, $rhs, usize, pow);
    };
    ($t:ty, $rhs:ty, $desired_rhs:ty, $method:expr) => {
        impl Pow<$rhs> for $t {
            type Output = $t;
            #[inline]
            fn pow(self, rhs: $rhs) -> $t {
                ($method)(self, <$desired_rhs>::from(rhs))
            }
        }
        impl<'a> Pow<&'a $rhs> for $t {
            type Output = $t;
            #[inline]
            fn pow(self, rhs: &'a $rhs) -> $t {
                ($method)(self, <$desired_rhs>::from(*rhs))
            }
        }
        impl<'a> Pow<$rhs> for &'a $t {
            type Output = $t;
            #[inline]
            fn pow(self, rhs: $rhs) -> $t {
                ($method)(*self, <$desired_rhs>::from(rhs))
            }
        }
        impl<'a, 'b> Pow<&'a $rhs> for &'b $t {
            type Output = $t;
            #[inline]
            fn pow(self, rhs: &'a $rhs) -> $t {
                ($method)(*self, <$desired_rhs>::from(*rhs))
            }
        }
    };
 }
 pow_impl!(u8, u8, u32, u8::pow);
 pow_impl!(u8, u16, u32, u8::pow);
 pow_impl!(u8, u32, u32, u8::pow);
 pow_impl!(u8, usize);
 pow_impl!(i8, u8, u32, i8::pow);
 pow_impl!(i8, u16, u32, i8::pow);
 pow_impl!(i8, u32, u32, i8::pow);
 pow_impl!(i8, usize);
 pow_impl!(u16, u8, u32, u16::pow);
 pow_impl!(u16, u16, u32, u16::pow);
 pow_impl!(u16, u32, u32, u16::pow);
 pow_impl!(u16, usize);
 pow_impl!(i16, u8, u32, i16::pow);
 pow_impl!(i16, u16, u32, i16::pow);
 pow_impl!(i16, u32, u32, i16::pow);
 pow_impl!(i16, usize);
 pow_impl!(u32, u8, u32, u32::pow);
 pow_impl!(u32, u16, u32, u32::pow);
 pow_impl!(u32, u32, u32, u32::pow);
 pow_impl!(u32, usize);
 pow_impl!(i32, u8, u32, i32::pow);
 pow_impl!(i32, u16, u32, i32::pow);
 pow_impl!(i32, u32, u32, i32::pow);
 pow_impl!(i32, usize);
 pow_impl!(u64, u8, u32, u64::pow);
 pow_impl!(u64, u16, u32, u64::pow);
 pow_impl!(u64, u32, u32, u64::pow);
 pow_impl!(u64, usize);
 pow_impl!(i64, u8, u32, i64::pow);
 pow_impl!(i64, u16, u32, i64::pow);
 pow_impl!(i64, u32, u32, i64::pow);
 pow_impl!(i64, usize);
 #[cfg(has_i128)]
 pow_impl!(u128, u8, u32, u128::pow);
 #[cfg(has_i128)]
 pow_impl!(u128, u16, u32, u128::pow);
 #[cfg(has_i128)]
 pow_impl!(u128, u32, u32, u128::pow);
 #[cfg(has_i128)]
 pow_impl!(u128, usize);
 #[cfg(has_i128)]
 pow_impl!(i128, u8, u32, i128::pow);
 #[cfg(has_i128)]
 pow_impl!(i128, u16, u32, i128::pow);
 #[cfg(has_i128)]
 pow_impl!(i128, u32, u32, i128::pow);
 #[cfg(has_i128)]
 pow_impl!(i128, usize);
 pow_impl!(usize, u8, u32, usize::pow);
 pow_impl!(usize, u16, u32, usize::pow);
 pow_impl!(usize, u32, u32, usize::pow);
 pow_impl!(usize, usize);
 pow_impl!(isize, u8, u32, isize::pow);
 pow_impl!(isize, u16, u32, isize::pow);
 pow_impl!(isize, u32, u32, isize::pow);
 pow_impl!(isize, usize);
 pow_impl!(Wrapping<u8>);
 pow_impl!(Wrapping<i8>);
 pow_impl!(Wrapping<u16>);
 pow_impl!(Wrapping<i16>);
 pow_impl!(Wrapping<u32>);
 pow_impl!(Wrapping<i32>);
 pow_impl!(Wrapping<u64>);
 pow_impl!(Wrapping<i64>);
 #[cfg(has_i128)]
 pow_impl!(Wrapping<u128>);
 #[cfg(has_i128)]
 pow_impl!(Wrapping<i128>);
 pow_impl!(Wrapping<usize>);
 pow_impl!(Wrapping<isize>);
 // FIXME: these should be possible
 // pow_impl!(u8, u64);
 // pow_impl!(i16, u64);
 // pow_impl!(i8, u64);
 // pow_impl!(u16, u64);
 // pow_impl!(u32, u64);
 // pow_impl!(i32, u64);
 // pow_impl!(u64, u64);
 // pow_impl!(i64, u64);
 // pow_impl!(usize, u64);
 // pow_impl!(isize, u64);
 #[cfg(any(feature = "std", feature = "libm"))]
 mod float_impls {
    use super::Pow;
    use Float;
    pow_impl!(f32, i8, i32, <f32 as Float>::powi);
    pow_impl!(f32, u8, i32, <f32 as Float>::powi);
    pow_impl!(f32, i16, i32, <f32 as Float>::powi);
    pow_impl!(f32, u16, i32, <f32 as Float>::powi);
    pow_impl!(f32, i32, i32, <f32 as Float>::powi);
    pow_impl!(f64, i8, i32, <f64 as Float>::powi);
    pow_impl!(f64, u8, i32, <f64 as Float>::powi);
    pow_impl!(f64, i16, i32, <f64 as Float>::powi);
    pow_impl!(f64, u16, i32, <f64 as Float>::powi);
    pow_impl!(f64, i32, i32, <f64 as Float>::powi);
    pow_impl!(f32, f32, f32, <f32 as Float>::powf);
    pow_impl!(f64, f32, f64, <f64 as Float>::powf);
    pow_impl!(f64, f64, f64, <f64 as Float>::powf);
 }
 /// Raises a value to the power of exp, using exponentiation by squaring.
 ///
 /// Note that `0⁰` (`pow(0, 0)`) returns `1`. Mathematically this is undefined.
 ///
 /// # Example
 ///
 /// ```rust
 /// use num_traits::pow;
 ///
 /// assert_eq!(pow(2i8, 4), 16);
 /// assert_eq!(pow(6u8, 3), 216);
 /// assert_eq!(pow(0u8, 0), 1); // Be aware if this case affects you
 /// ```
 #[inline]
 pub fn pow<T: Clone + One + Mul<T, Output = T>>(mut base: T, mut exp: usize) -> T {
    if exp == 0 {
        return T::one();
    }
    while exp & 1 == 0 {
        base = base.clone() * base;
        exp >>= 1;
    }
    if exp == 1 {
        return base;
    }
    let mut acc = base.clone();
    while exp > 1 {
        exp >>= 1;
        base = base.clone() * base;
        if exp & 1 == 1 {
            acc = acc * base.clone();
        }
    }
    acc
 }
 /// Raises a value to the power of exp, returning `None` if an overflow occurred.
 ///
 /// Note that `0⁰` (`checked_pow(0, 0)`) returns `Some(1)`. Mathematically this is undefined.
 ///
 /// Otherwise same as the `pow` function.
 ///
 /// # Example
 ///
 /// ```rust
 /// use num_traits::checked_pow;
 ///
 /// assert_eq!(checked_pow(2i8, 4), Some(16));
 /// assert_eq!(checked_pow(7i8, 8), None);
 /// assert_eq!(checked_pow(7u32, 8), Some(5_764_801));
 /// assert_eq!(checked_pow(0u32, 0), Some(1)); // Be aware if this case affect you
 /// ```
 #[inline]
 pub fn checked_pow<T: Clone + One + CheckedMul>(mut base: T, mut exp: usize) -> Option<T> {
    if exp == 0 {
        return Some(T::one());
    }
    macro_rules! optry {
        ($expr:expr) => {
            if let Some(val) = $expr {
                val
            } else {
                return None;
            }
        };
    }
    while exp & 1 == 0 {
        base = optry!(base.checked_mul(&base));
        exp >>= 1;
    }
    if exp == 1 {
        return Some(base);
    }
    let mut acc = base.clone();
    while exp > 1 {
        exp >>= 1;
        base = optry!(base.checked_mul(&base));
        if exp & 1 == 1 {
            acc = optry!(acc.checked_mul(&base));
        }
    }
    Some(acc)
 }
--- a/src/real.rs
+++ b/src/real.rs
@ -1,834 +0,0 @@
 #![cfg(any(feature = "std", feature = "libm"))]
 use core::ops::Neg;
 use {Float, Num, NumCast};
 // NOTE: These doctests have the same issue as those in src/float.rs.
 // They're testing the inherent methods directly, and not those of `Real`.
 /// A trait for real number types that do not necessarily have
 /// floating-point-specific characteristics such as NaN and infinity.
 ///
 /// See [this Wikipedia article](https://en.wikipedia.org/wiki/Real_data_type)
 /// for a list of data types that could meaningfully implement this trait.
 ///
 /// This trait is only available with the `std` feature, or with the `libm` feature otherwise.
 pub trait Real: Num + Copy + NumCast + PartialOrd + Neg<Output = Self> {
    /// Returns the smallest finite value that this type can represent.
    ///
    /// ```
    /// use num_traits::real::Real;
    /// use std::f64;
    ///
    /// let x: f64 = Real::min_value();
    ///
    /// assert_eq!(x, f64::MIN);
    /// ```
    fn min_value() -> Self;
    /// Returns the smallest positive, normalized value that this type can represent.
    ///
    /// ```
    /// use num_traits::real::Real;
    /// use std::f64;
    ///
    /// let x: f64 = Real::min_positive_value();
    ///
    /// assert_eq!(x, f64::MIN_POSITIVE);
    /// ```
    fn min_positive_value() -> Self;
    /// Returns epsilon, a small positive value.
    ///
    /// ```
    /// use num_traits::real::Real;
    /// use std::f64;
    ///
    /// let x: f64 = Real::epsilon();
    ///
    /// assert_eq!(x, f64::EPSILON);
    /// ```
    ///
    /// # Panics
    ///
    /// The default implementation will panic if `f32::EPSILON` cannot
    /// be cast to `Self`.
    fn epsilon() -> Self;
    /// Returns the largest finite value that this type can represent.
    ///
    /// ```
    /// use num_traits::real::Real;
    /// use std::f64;
    ///
    /// let x: f64 = Real::max_value();
    /// assert_eq!(x, f64::MAX);
    /// ```
    fn max_value() -> Self;
    /// Returns the largest integer less than or equal to a number.
    ///
    /// ```
    /// use num_traits::real::Real;
    ///
    /// let f = 3.99;
    /// let g = 3.0;
    ///
    /// assert_eq!(f.floor(), 3.0);
    /// assert_eq!(g.floor(), 3.0);
    /// ```
    fn floor(self) -> Self;
    /// Returns the smallest integer greater than or equal to a number.
    ///
    /// ```
    /// use num_traits::real::Real;
    ///
    /// let f = 3.01;
    /// let g = 4.0;
    ///
    /// assert_eq!(f.ceil(), 4.0);
    /// assert_eq!(g.ceil(), 4.0);
    /// ```
    fn ceil(self) -> Self;
    /// Returns the nearest integer to a number. Round half-way cases away from
    /// `0.0`.
    ///
    /// ```
    /// use num_traits::real::Real;
    ///
    /// let f = 3.3;
    /// let g = -3.3;
    ///
    /// assert_eq!(f.round(), 3.0);
    /// assert_eq!(g.round(), -3.0);
    /// ```
    fn round(self) -> Self;
    /// Return the integer part of a number.
    ///
    /// ```
    /// use num_traits::real::Real;
    ///
    /// let f = 3.3;
    /// let g = -3.7;
    ///
    /// assert_eq!(f.trunc(), 3.0);
    /// assert_eq!(g.trunc(), -3.0);
    /// ```
    fn trunc(self) -> Self;
    /// Returns the fractional part of a number.
    ///
    /// ```
    /// use num_traits::real::Real;
    ///
    /// let x = 3.5;
    /// let y = -3.5;
    /// let abs_difference_x = (x.fract() - 0.5).abs();
    /// let abs_difference_y = (y.fract() - (-0.5)).abs();
    ///
    /// assert!(abs_difference_x < 1e-10);
    /// assert!(abs_difference_y < 1e-10);
    /// ```
    fn fract(self) -> Self;
    /// Computes the absolute value of `self`. Returns `Float::nan()` if the
    /// number is `Float::nan()`.
    ///
    /// ```
    /// use num_traits::real::Real;
    /// use std::f64;
    ///
    /// let x = 3.5;
    /// let y = -3.5;
    ///
    /// let abs_difference_x = (x.abs() - x).abs();
    /// let abs_difference_y = (y.abs() - (-y)).abs();
    ///
    /// assert!(abs_difference_x < 1e-10);
    /// assert!(abs_difference_y < 1e-10);
    ///
    /// assert!(::num_traits::Float::is_nan(f64::NAN.abs()));
    /// ```
    fn abs(self) -> Self;
    /// Returns a number that represents the sign of `self`.
    ///
    /// - `1.0` if the number is positive, `+0.0` or `Float::infinity()`
    /// - `-1.0` if the number is negative, `-0.0` or `Float::neg_infinity()`
    /// - `Float::nan()` if the number is `Float::nan()`
    ///
    /// ```
    /// use num_traits::real::Real;
    /// use std::f64;
    ///
    /// let f = 3.5;
    ///
    /// assert_eq!(f.signum(), 1.0);
    /// assert_eq!(f64::NEG_INFINITY.signum(), -1.0);
    ///
    /// assert!(f64::NAN.signum().is_nan());
    /// ```
    fn signum(self) -> Self;
    /// Returns `true` if `self` is positive, including `+0.0`,
    /// `Float::infinity()`, and with newer versions of Rust `f64::NAN`.
    ///
    /// ```
    /// use num_traits::real::Real;
    /// use std::f64;
    ///
    /// let neg_nan: f64 = -f64::NAN;
    ///
    /// let f = 7.0;
    /// let g = -7.0;
    ///
    /// assert!(f.is_sign_positive());
    /// assert!(!g.is_sign_positive());
    /// assert!(!neg_nan.is_sign_positive());
    /// ```
    fn is_sign_positive(self) -> bool;
    /// Returns `true` if `self` is negative, including `-0.0`,
    /// `Float::neg_infinity()`, and with newer versions of Rust `-f64::NAN`.
    ///
    /// ```
    /// use num_traits::real::Real;
    /// use std::f64;
    ///
    /// let nan: f64 = f64::NAN;
    ///
    /// let f = 7.0;
    /// let g = -7.0;
    ///
    /// assert!(!f.is_sign_negative());
    /// assert!(g.is_sign_negative());
    /// assert!(!nan.is_sign_negative());
    /// ```
    fn is_sign_negative(self) -> bool;
    /// Fused multiply-add. Computes `(self * a) + b` with only one rounding
    /// error, yielding a more accurate result than an unfused multiply-add.
    ///
    /// Using `mul_add` can be more performant than an unfused multiply-add if
    /// the target architecture has a dedicated `fma` CPU instruction.
    ///
    /// ```
    /// use num_traits::real::Real;
    ///
    /// let m = 10.0;
    /// let x = 4.0;
    /// let b = 60.0;
    ///
    /// // 100.0
    /// let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs();
    ///
    /// assert!(abs_difference < 1e-10);
    /// ```
    fn mul_add(self, a: Self, b: Self) -> Self;
    /// Take the reciprocal (inverse) of a number, `1/x`.
    ///
    /// ```
    /// use num_traits::real::Real;
    ///
    /// let x = 2.0;
    /// let abs_difference = (x.recip() - (1.0/x)).abs();
    ///
    /// assert!(abs_difference < 1e-10);
    /// ```
    fn recip(self) -> Self;
    /// Raise a number to an integer power.
    ///
    /// Using this function is generally faster than using `powf`
    ///
    /// ```
    /// use num_traits::real::Real;
    ///
    /// let x = 2.0;
    /// let abs_difference = (x.powi(2) - x*x).abs();
    ///
    /// assert!(abs_difference < 1e-10);
    /// ```
    fn powi(self, n: i32) -> Self;
    /// Raise a number to a real number power.
    ///
    /// ```
    /// use num_traits::real::Real;
    ///
    /// let x = 2.0;
    /// let abs_difference = (x.powf(2.0) - x*x).abs();
    ///
    /// assert!(abs_difference < 1e-10);
    /// ```
    fn powf(self, n: Self) -> Self;
    /// Take the square root of a number.
    ///
    /// Returns NaN if `self` is a negative floating-point number.  
    ///
    /// # Panics
    ///
    /// If the implementing type doesn't support NaN, this method should panic if `self < 0`.
    ///
    /// ```
    /// use num_traits::real::Real;
    ///
    /// let positive = 4.0;
    /// let negative = -4.0;
    ///
    /// let abs_difference = (positive.sqrt() - 2.0).abs();
    ///
    /// assert!(abs_difference < 1e-10);
    /// assert!(::num_traits::Float::is_nan(negative.sqrt()));
    /// ```
    fn sqrt(self) -> Self;
    /// Returns `e^(self)`, (the exponential function).
    ///
    /// ```
    /// use num_traits::real::Real;
    ///
    /// let one = 1.0;
    /// // e^1
    /// let e = one.exp();
    ///
    /// // ln(e) - 1 == 0
    /// let abs_difference = (e.ln() - 1.0).abs();
    ///
    /// assert!(abs_difference < 1e-10);
    /// ```
    fn exp(self) -> Self;
    /// Returns `2^(self)`.
    ///
    /// ```
    /// use num_traits::real::Real;
    ///
    /// let f = 2.0;
    ///
    /// // 2^2 - 4 == 0
    /// let abs_difference = (f.exp2() - 4.0).abs();
    ///
    /// assert!(abs_difference < 1e-10);
    /// ```
    fn exp2(self) -> Self;
    /// Returns the natural logarithm of the number.
    ///
    /// # Panics
    ///
    /// If `self <= 0` and this type does not support a NaN representation, this function should panic.
    ///
    /// ```
    /// use num_traits::real::Real;
    ///
    /// let one = 1.0;
    /// // e^1
    /// let e = one.exp();
    ///
    /// // ln(e) - 1 == 0
    /// let abs_difference = (e.ln() - 1.0).abs();
    ///
    /// assert!(abs_difference < 1e-10);
    /// ```
    fn ln(self) -> Self;
    /// Returns the logarithm of the number with respect to an arbitrary base.
    ///
    /// # Panics
    ///
    /// If `self <= 0` and this type does not support a NaN representation, this function should panic.
    ///
    /// ```
    /// use num_traits::real::Real;
    ///
    /// let ten = 10.0;
    /// let two = 2.0;
    ///
    /// // log10(10) - 1 == 0
    /// let abs_difference_10 = (ten.log(10.0) - 1.0).abs();
    ///
    /// // log2(2) - 1 == 0
    /// let abs_difference_2 = (two.log(2.0) - 1.0).abs();
    ///
    /// assert!(abs_difference_10 < 1e-10);
    /// assert!(abs_difference_2 < 1e-10);
    /// ```
    fn log(self, base: Self) -> Self;
    /// Returns the base 2 logarithm of the number.
    ///
    /// # Panics
    ///
    /// If `self <= 0` and this type does not support a NaN representation, this function should panic.
    ///
    /// ```
    /// use num_traits::real::Real;
    ///
    /// let two = 2.0;
    ///
    /// // log2(2) - 1 == 0
    /// let abs_difference = (two.log2() - 1.0).abs();
    ///
    /// assert!(abs_difference < 1e-10);
    /// ```
    fn log2(self) -> Self;
    /// Returns the base 10 logarithm of the number.
    ///
    /// # Panics
    ///
    /// If `self <= 0` and this type does not support a NaN representation, this function should panic.
    ///
    ///
    /// ```
    /// use num_traits::real::Real;
    ///
    /// let ten = 10.0;
    ///
    /// // log10(10) - 1 == 0
    /// let abs_difference = (ten.log10() - 1.0).abs();
    ///
    /// assert!(abs_difference < 1e-10);
    /// ```
    fn log10(self) -> Self;
    /// Converts radians to degrees.
    ///
    /// ```
    /// use std::f64::consts;
    ///
    /// let angle = consts::PI;
    ///
    /// let abs_difference = (angle.to_degrees() - 180.0).abs();
    ///
    /// assert!(abs_difference < 1e-10);
    /// ```
    fn to_degrees(self) -> Self;
    /// Converts degrees to radians.
    ///
    /// ```
    /// use std::f64::consts;
    ///
    /// let angle = 180.0_f64;
    ///
    /// let abs_difference = (angle.to_radians() - consts::PI).abs();
    ///
    /// assert!(abs_difference < 1e-10);
    /// ```
    fn to_radians(self) -> Self;
    /// Returns the maximum of the two numbers.
    ///
    /// ```
    /// use num_traits::real::Real;
    ///
    /// let x = 1.0;
    /// let y = 2.0;
    ///
    /// assert_eq!(x.max(y), y);
    /// ```
    fn max(self, other: Self) -> Self;
    /// Returns the minimum of the two numbers.
    ///
    /// ```
    /// use num_traits::real::Real;
    ///
    /// let x = 1.0;
    /// let y = 2.0;
    ///
    /// assert_eq!(x.min(y), x);
    /// ```
    fn min(self, other: Self) -> Self;
    /// The positive difference of two numbers.
    ///
    /// * If `self <= other`: `0:0`
    /// * Else: `self - other`
    ///
    /// ```
    /// use num_traits::real::Real;
    ///
    /// let x = 3.0;
    /// let y = -3.0;
    ///
    /// let abs_difference_x = (x.abs_sub(1.0) - 2.0).abs();
    /// let abs_difference_y = (y.abs_sub(1.0) - 0.0).abs();
    ///
    /// assert!(abs_difference_x < 1e-10);
    /// assert!(abs_difference_y < 1e-10);
    /// ```
    fn abs_sub(self, other: Self) -> Self;
    /// Take the cubic root of a number.
    ///
    /// ```
    /// use num_traits::real::Real;
    ///
    /// let x = 8.0;
    ///
    /// // x^(1/3) - 2 == 0
    /// let abs_difference = (x.cbrt() - 2.0).abs();
    ///
    /// assert!(abs_difference < 1e-10);
    /// ```
    fn cbrt(self) -> Self;
    /// Calculate the length of the hypotenuse of a right-angle triangle given
    /// legs of length `x` and `y`.
    ///
    /// ```
    /// use num_traits::real::Real;
    ///
    /// let x = 2.0;
    /// let y = 3.0;
    ///
    /// // sqrt(x^2 + y^2)
    /// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();
    ///
    /// assert!(abs_difference < 1e-10);
    /// ```
    fn hypot(self, other: Self) -> Self;
    /// Computes the sine of a number (in radians).
    ///
    /// ```
    /// use num_traits::real::Real;
    /// use std::f64;
    ///
    /// let x = f64::consts::PI/2.0;
    ///
    /// let abs_difference = (x.sin() - 1.0).abs();
    ///
    /// assert!(abs_difference < 1e-10);
    /// ```
    fn sin(self) -> Self;
    /// Computes the cosine of a number (in radians).
    ///
    /// ```
    /// use num_traits::real::Real;
    /// use std::f64;
    ///
    /// let x = 2.0*f64::consts::PI;
    ///
    /// let abs_difference = (x.cos() - 1.0).abs();
    ///
    /// assert!(abs_difference < 1e-10);
    /// ```
    fn cos(self) -> Self;
    /// Computes the tangent of a number (in radians).
    ///
    /// ```
    /// use num_traits::real::Real;
    /// use std::f64;
    ///
    /// let x = f64::consts::PI/4.0;
    /// let abs_difference = (x.tan() - 1.0).abs();
    ///
    /// assert!(abs_difference < 1e-14);
    /// ```
    fn tan(self) -> Self;
    /// Computes the arcsine of a number. Return value is in radians in
    /// the range [-pi/2, pi/2] or NaN if the number is outside the range
    /// [-1, 1].
    ///
    /// # Panics
    ///
    /// If this type does not support a NaN representation, this function should panic
    /// if the number is outside the range [-1, 1].
    ///
    /// ```
    /// use num_traits::real::Real;
    /// use std::f64;
    ///
    /// let f = f64::consts::PI / 2.0;
    ///
    /// // asin(sin(pi/2))
    /// let abs_difference = (f.sin().asin() - f64::consts::PI / 2.0).abs();
    ///
    /// assert!(abs_difference < 1e-10);
    /// ```
    fn asin(self) -> Self;
    /// Computes the arccosine of a number. Return value is in radians in
    /// the range [0, pi] or NaN if the number is outside the range
    /// [-1, 1].
    ///
    /// # Panics
    ///
    /// If this type does not support a NaN representation, this function should panic
    /// if the number is outside the range [-1, 1].
    ///
    /// ```
    /// use num_traits::real::Real;
    /// use std::f64;
    ///
    /// let f = f64::consts::PI / 4.0;
    ///
    /// // acos(cos(pi/4))
    /// let abs_difference = (f.cos().acos() - f64::consts::PI / 4.0).abs();
    ///
    /// assert!(abs_difference < 1e-10);
    /// ```
    fn acos(self) -> Self;
    /// Computes the arctangent of a number. Return value is in radians in the
    /// range [-pi/2, pi/2];
    ///
    /// ```
    /// use num_traits::real::Real;
    ///
    /// let f = 1.0;
    ///
    /// // atan(tan(1))
    /// let abs_difference = (f.tan().atan() - 1.0).abs();
    ///
    /// assert!(abs_difference < 1e-10);
    /// ```
    fn atan(self) -> Self;
    /// Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`).
    ///
    /// * `x = 0`, `y = 0`: `0`
    /// * `x >= 0`: `arctan(y/x)` -> `[-pi/2, pi/2]`
    /// * `y >= 0`: `arctan(y/x) + pi` -> `(pi/2, pi]`
    /// * `y < 0`: `arctan(y/x) - pi` -> `(-pi, -pi/2)`
    ///
    /// ```
    /// use num_traits::real::Real;
    /// use std::f64;
    ///
    /// let pi = f64::consts::PI;
    /// // All angles from horizontal right (+x)
    /// // 45 deg counter-clockwise
    /// let x1 = 3.0;
    /// let y1 = -3.0;
    ///
    /// // 135 deg clockwise
    /// let x2 = -3.0;
    /// let y2 = 3.0;
    ///
    /// let abs_difference_1 = (y1.atan2(x1) - (-pi/4.0)).abs();
    /// let abs_difference_2 = (y2.atan2(x2) - 3.0*pi/4.0).abs();
    ///
    /// assert!(abs_difference_1 < 1e-10);
    /// assert!(abs_difference_2 < 1e-10);
    /// ```
    fn atan2(self, other: Self) -> Self;
    /// Simultaneously computes the sine and cosine of the number, `x`. Returns
    /// `(sin(x), cos(x))`.
    ///
    /// ```
    /// use num_traits::real::Real;
    /// use std::f64;
    ///
    /// let x = f64::consts::PI/4.0;
    /// let f = x.sin_cos();
    ///
    /// let abs_difference_0 = (f.0 - x.sin()).abs();
    /// let abs_difference_1 = (f.1 - x.cos()).abs();
    ///
    /// assert!(abs_difference_0 < 1e-10);
    /// assert!(abs_difference_0 < 1e-10);
    /// ```
    fn sin_cos(self) -> (Self, Self);
    /// Returns `e^(self) - 1` in a way that is accurate even if the
    /// number is close to zero.
    ///
    /// ```
    /// use num_traits::real::Real;
    ///
    /// let x = 7.0;
    ///
    /// // e^(ln(7)) - 1
    /// let abs_difference = (x.ln().exp_m1() - 6.0).abs();
    ///
    /// assert!(abs_difference < 1e-10);
    /// ```
    fn exp_m1(self) -> Self;
    /// Returns `ln(1+n)` (natural logarithm) more accurately than if
    /// the operations were performed separately.
    ///
    /// # Panics
    ///
    /// If this type does not support a NaN representation, this function should panic
    /// if `self-1 <= 0`.
    ///
    /// ```
    /// use num_traits::real::Real;
    /// use std::f64;
    ///
    /// let x = f64::consts::E - 1.0;
    ///
    /// // ln(1 + (e - 1)) == ln(e) == 1
    /// let abs_difference = (x.ln_1p() - 1.0).abs();
    ///
    /// assert!(abs_difference < 1e-10);
    /// ```
    fn ln_1p(self) -> Self;
    /// Hyperbolic sine function.
    ///
    /// ```
    /// use num_traits::real::Real;
    /// use std::f64;
    ///
    /// let e = f64::consts::E;
    /// let x = 1.0;
    ///
    /// let f = x.sinh();
    /// // Solving sinh() at 1 gives `(e^2-1)/(2e)`
    /// let g = (e*e - 1.0)/(2.0*e);
    /// let abs_difference = (f - g).abs();
    ///
    /// assert!(abs_difference < 1e-10);
    /// ```
    fn sinh(self) -> Self;
    /// Hyperbolic cosine function.
    ///
    /// ```
    /// use num_traits::real::Real;
    /// use std::f64;
    ///
    /// let e = f64::consts::E;
    /// let x = 1.0;
    /// let f = x.cosh();
    /// // Solving cosh() at 1 gives this result
    /// let g = (e*e + 1.0)/(2.0*e);
    /// let abs_difference = (f - g).abs();
    ///
    /// // Same result
    /// assert!(abs_difference < 1.0e-10);
    /// ```
    fn cosh(self) -> Self;
    /// Hyperbolic tangent function.
    ///
    /// ```
    /// use num_traits::real::Real;
    /// use std::f64;
    ///
    /// let e = f64::consts::E;
    /// let x = 1.0;
    ///
    /// let f = x.tanh();
    /// // Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))`
    /// let g = (1.0 - e.powi(-2))/(1.0 + e.powi(-2));
    /// let abs_difference = (f - g).abs();
    ///
    /// assert!(abs_difference < 1.0e-10);
    /// ```
    fn tanh(self) -> Self;
    /// Inverse hyperbolic sine function.
    ///
    /// ```
    /// use num_traits::real::Real;
    ///
    /// let x = 1.0;
    /// let f = x.sinh().asinh();
    ///
    /// let abs_difference = (f - x).abs();
    ///
    /// assert!(abs_difference < 1.0e-10);
    /// ```
    fn asinh(self) -> Self;
    /// Inverse hyperbolic cosine function.
    ///
    /// ```
    /// use num_traits::real::Real;
    ///
    /// let x = 1.0;
    /// let f = x.cosh().acosh();
    ///
    /// let abs_difference = (f - x).abs();
    ///
    /// assert!(abs_difference < 1.0e-10);
    /// ```
    fn acosh(self) -> Self;
    /// Inverse hyperbolic tangent function.
    ///
    /// ```
    /// use num_traits::real::Real;
    /// use std::f64;
    ///
    /// let e = f64::consts::E;
    /// let f = e.tanh().atanh();
    ///
    /// let abs_difference = (f - e).abs();
    ///
    /// assert!(abs_difference < 1.0e-10);
    /// ```
    fn atanh(self) -> Self;
 }
 impl<T: Float> Real for T {
    forward! {
        Float::min_value() -> Self;
        Float::min_positive_value() -> Self;
        Float::epsilon() -> Self;
        Float::max_value() -> Self;
    }
    forward! {
        Float::floor(self) -> Self;
        Float::ceil(self) -> Self;
        Float::round(self) -> Self;
        Float::trunc(self) -> Self;
        Float::fract(self) -> Self;
        Float::abs(self) -> Self;
        Float::signum(self) -> Self;
        Float::is_sign_positive(self) -> bool;
        Float::is_sign_negative(self) -> bool;
        Float::mul_add(self, a: Self, b: Self) -> Self;
        Float::recip(self) -> Self;
        Float::powi(self, n: i32) -> Self;
        Float::powf(self, n: Self) -> Self;
        Float::sqrt(self) -> Self;
        Float::exp(self) -> Self;
        Float::exp2(self) -> Self;
        Float::ln(self) -> Self;
        Float::log(self, base: Self) -> Self;
        Float::log2(self) -> Self;
        Float::log10(self) -> Self;
        Float::to_degrees(self) -> Self;
        Float::to_radians(self) -> Self;
        Float::max(self, other: Self) -> Self;
        Float::min(self, other: Self) -> Self;
        Float::abs_sub(self, other: Self) -> Self;
        Float::cbrt(self) -> Self;
        Float::hypot(self, other: Self) -> Self;
        Float::sin(self) -> Self;
        Float::cos(self) -> Self;
        Float::tan(self) -> Self;
        Float::asin(self) -> Self;
        Float::acos(self) -> Self;
        Float::atan(self) -> Self;
        Float::atan2(self, other: Self) -> Self;
        Float::sin_cos(self) -> (Self, Self);
        Float::exp_m1(self) -> Self;
        Float::ln_1p(self) -> Self;
        Float::sinh(self) -> Self;
        Float::cosh(self) -> Self;
        Float::tanh(self) -> Self;
        Float::asinh(self) -> Self;
        Float::acosh(self) -> Self;
        Float::atanh(self) -> Self;
    }
 }
--- a/tests/cast.rs
+++ b/tests/cast.rs
@ -1,396 +0,0 @@
 //! Tests of `num_traits::cast`.
 #![no_std]
 #[cfg(feature = "std")]
 #[macro_use]
 extern crate std;
 extern crate num_traits;
 use num_traits::cast::*;
 use num_traits::Bounded;
 use core::{f32, f64};
 #[cfg(has_i128)]
 use core::{i128, u128};
 use core::{i16, i32, i64, i8, isize};
 use core::{u16, u32, u64, u8, usize};
 use core::fmt::Debug;
 use core::mem;
 use core::num::Wrapping;
 #[test]
 fn to_primitive_float() {
    let f32_toolarge = 1e39f64;
    assert_eq!(f32_toolarge.to_f32(), None);
    assert_eq!((f32::MAX as f64).to_f32(), Some(f32::MAX));
    assert_eq!((-f32::MAX as f64).to_f32(), Some(-f32::MAX));
    assert_eq!(f64::INFINITY.to_f32(), Some(f32::INFINITY));
    assert_eq!((f64::NEG_INFINITY).to_f32(), Some(f32::NEG_INFINITY));
    assert!((f64::NAN).to_f32().map_or(false, |f| f.is_nan()));
 }
 #[test]
 fn wrapping_to_primitive() {
    macro_rules! test_wrapping_to_primitive {
        ($($t:ty)+) => {
            $({
                let i: $t = 0;
                let w = Wrapping(i);
                assert_eq!(i.to_u8(),    w.to_u8());
                assert_eq!(i.to_u16(),   w.to_u16());
                assert_eq!(i.to_u32(),   w.to_u32());
                assert_eq!(i.to_u64(),   w.to_u64());
                assert_eq!(i.to_usize(), w.to_usize());
                assert_eq!(i.to_i8(),    w.to_i8());
                assert_eq!(i.to_i16(),   w.to_i16());
                assert_eq!(i.to_i32(),   w.to_i32());
                assert_eq!(i.to_i64(),   w.to_i64());
                assert_eq!(i.to_isize(), w.to_isize());
                assert_eq!(i.to_f32(),   w.to_f32());
                assert_eq!(i.to_f64(),   w.to_f64());
            })+
        };
    }
    test_wrapping_to_primitive!(usize u8 u16 u32 u64 isize i8 i16 i32 i64);
 }
 #[test]
 fn wrapping_is_toprimitive() {
    fn require_toprimitive<T: ToPrimitive>(_: &T) {}
    require_toprimitive(&Wrapping(42));
 }
 #[test]
 fn wrapping_is_fromprimitive() {
    fn require_fromprimitive<T: FromPrimitive>(_: &T) {}
    require_fromprimitive(&Wrapping(42));
 }
 #[test]
 fn wrapping_is_numcast() {
    fn require_numcast<T: NumCast>(_: &T) {}
    require_numcast(&Wrapping(42));
 }
 #[test]
 fn as_primitive() {
    let x: f32 = (1.625f64).as_();
    assert_eq!(x, 1.625f32);
    let x: f32 = (3.14159265358979323846f64).as_();
    assert_eq!(x, 3.1415927f32);
    let x: u8 = (768i16).as_();
    assert_eq!(x, 0);
 }
 #[test]
 fn float_to_integer_checks_overflow() {
    // This will overflow an i32
    let source: f64 = 1.0e+123f64;
    // Expect the overflow to be caught
    assert_eq!(cast::<f64, i32>(source), None);
 }
 #[test]
 fn cast_to_int_checks_overflow() {
    let big_f: f64 = 1.0e123;
    let normal_f: f64 = 1.0;
    let small_f: f64 = -1.0e123;
    assert_eq!(None, cast::<f64, isize>(big_f));
    assert_eq!(None, cast::<f64, i8>(big_f));
    assert_eq!(None, cast::<f64, i16>(big_f));
    assert_eq!(None, cast::<f64, i32>(big_f));
    assert_eq!(None, cast::<f64, i64>(big_f));
    assert_eq!(Some(normal_f as isize), cast::<f64, isize>(normal_f));
    assert_eq!(Some(normal_f as i8), cast::<f64, i8>(normal_f));
    assert_eq!(Some(normal_f as i16), cast::<f64, i16>(normal_f));
    assert_eq!(Some(normal_f as i32), cast::<f64, i32>(normal_f));
    assert_eq!(Some(normal_f as i64), cast::<f64, i64>(normal_f));
    assert_eq!(None, cast::<f64, isize>(small_f));
    assert_eq!(None, cast::<f64, i8>(small_f));
    assert_eq!(None, cast::<f64, i16>(small_f));
    assert_eq!(None, cast::<f64, i32>(small_f));
    assert_eq!(None, cast::<f64, i64>(small_f));
 }
 #[test]
 fn cast_to_unsigned_int_checks_overflow() {
    let big_f: f64 = 1.0e123;
    let normal_f: f64 = 1.0;
    let small_f: f64 = -1.0e123;
    assert_eq!(None, cast::<f64, usize>(big_f));
    assert_eq!(None, cast::<f64, u8>(big_f));
    assert_eq!(None, cast::<f64, u16>(big_f));
    assert_eq!(None, cast::<f64, u32>(big_f));
    assert_eq!(None, cast::<f64, u64>(big_f));
    assert_eq!(Some(normal_f as usize), cast::<f64, usize>(normal_f));
    assert_eq!(Some(normal_f as u8), cast::<f64, u8>(normal_f));
    assert_eq!(Some(normal_f as u16), cast::<f64, u16>(normal_f));
    assert_eq!(Some(normal_f as u32), cast::<f64, u32>(normal_f));
    assert_eq!(Some(normal_f as u64), cast::<f64, u64>(normal_f));
    assert_eq!(None, cast::<f64, usize>(small_f));
    assert_eq!(None, cast::<f64, u8>(small_f));
    assert_eq!(None, cast::<f64, u16>(small_f));
    assert_eq!(None, cast::<f64, u32>(small_f));
    assert_eq!(None, cast::<f64, u64>(small_f));
 }
 #[test]
 #[cfg(has_i128)]
 fn cast_to_i128_checks_overflow() {
    let big_f: f64 = 1.0e123;
    let normal_f: f64 = 1.0;
    let small_f: f64 = -1.0e123;
    assert_eq!(None, cast::<f64, i128>(big_f));
    assert_eq!(None, cast::<f64, u128>(big_f));
    assert_eq!(Some(normal_f as i128), cast::<f64, i128>(normal_f));
    assert_eq!(Some(normal_f as u128), cast::<f64, u128>(normal_f));
    assert_eq!(None, cast::<f64, i128>(small_f));
    assert_eq!(None, cast::<f64, u128>(small_f));
 }
 #[cfg(feature = "std")]
 fn dbg(args: ::core::fmt::Arguments) {
    println!("{}", args);
 }
 #[cfg(not(feature = "std"))]
 fn dbg(_: ::core::fmt::Arguments) {}
 // Rust 1.8 doesn't handle cfg on macros correctly
 macro_rules! dbg { ($($tok:tt)*) => { dbg(format_args!($($tok)*)) } }
 macro_rules! float_test_edge {
    ($f:ident -> $($t:ident)+) => { $({
        dbg!("testing cast edge cases for {} -> {}", stringify!($f), stringify!($t));
        let small = if $t::MIN == 0 || mem::size_of::<$t>() < mem::size_of::<$f>() {
            $t::MIN as $f - 1.0
        } else {
            ($t::MIN as $f).raw_offset(1).floor()
        };
        let fmin = small.raw_offset(-1);
        dbg!("  testing min {}\n\tvs. {:.0}\n\tand {:.0}", $t::MIN, fmin, small);
        assert_eq!(Some($t::MIN), cast::<$f, $t>($t::MIN as $f));
        assert_eq!(Some($t::MIN), cast::<$f, $t>(fmin));
        assert_eq!(None, cast::<$f, $t>(small));
        let (max, large) = if mem::size_of::<$t>() < mem::size_of::<$f>() {
            ($t::MAX, $t::MAX as $f + 1.0)
        } else {
            let large = $t::MAX as $f; // rounds up!
            let max = large.raw_offset(-1) as $t; // the next smallest possible
            assert_eq!(max.count_ones(), $f::MANTISSA_DIGITS);
            (max, large)
        };
        let fmax = large.raw_offset(-1);
        dbg!("  testing max {}\n\tvs. {:.0}\n\tand {:.0}", max, fmax, large);
        assert_eq!(Some(max), cast::<$f, $t>(max as $f));
        assert_eq!(Some(max), cast::<$f, $t>(fmax));
        assert_eq!(None, cast::<$f, $t>(large));
        dbg!("  testing non-finite values");
        assert_eq!(None, cast::<$f, $t>($f::NAN));
        assert_eq!(None, cast::<$f, $t>($f::INFINITY));
        assert_eq!(None, cast::<$f, $t>($f::NEG_INFINITY));
    })+}
 }
 trait RawOffset: Sized {
    type Raw;
    fn raw_offset(self, offset: Self::Raw) -> Self;
 }
 impl RawOffset for f32 {
    type Raw = i32;
    fn raw_offset(self, offset: Self::Raw) -> Self {
        unsafe {
            let raw: Self::Raw = mem::transmute(self);
            mem::transmute(raw + offset)
        }
    }
 }
 impl RawOffset for f64 {
    type Raw = i64;
    fn raw_offset(self, offset: Self::Raw) -> Self {
        unsafe {
            let raw: Self::Raw = mem::transmute(self);
            mem::transmute(raw + offset)
        }
    }
 }
 #[test]
 fn cast_float_to_int_edge_cases() {
    float_test_edge!(f32 -> isize i8 i16 i32 i64);
    float_test_edge!(f32 -> usize u8 u16 u32 u64);
    float_test_edge!(f64 -> isize i8 i16 i32 i64);
    float_test_edge!(f64 -> usize u8 u16 u32 u64);
 }
 #[test]
 #[cfg(has_i128)]
 fn cast_float_to_i128_edge_cases() {
    float_test_edge!(f32 -> i128 u128);
    float_test_edge!(f64 -> i128 u128);
 }
 macro_rules! int_test_edge {
    ($f:ident -> { $($t:ident)+ } with $BigS:ident $BigU:ident ) => { $({
        fn test_edge() {
            dbg!("testing cast edge cases for {} -> {}", stringify!($f), stringify!($t));
            match ($f::MIN as $BigS).cmp(&($t::MIN as $BigS)) {
                Greater => {
                    assert_eq!(Some($f::MIN as $t), cast::<$f, $t>($f::MIN));
                }
                Equal => {
                    assert_eq!(Some($t::MIN), cast::<$f, $t>($f::MIN));
                }
                Less => {
                    let min = $t::MIN as $f;
                    assert_eq!(Some($t::MIN), cast::<$f, $t>(min));
                    assert_eq!(None, cast::<$f, $t>(min - 1));
                }
            }
            match ($f::MAX as $BigU).cmp(&($t::MAX as $BigU)) {
                Greater => {
                    let max = $t::MAX as $f;
                    assert_eq!(Some($t::MAX), cast::<$f, $t>(max));
                    assert_eq!(None, cast::<$f, $t>(max + 1));
                }
                Equal => {
                    assert_eq!(Some($t::MAX), cast::<$f, $t>($f::MAX));
                }
                Less => {
                    assert_eq!(Some($f::MAX as $t), cast::<$f, $t>($f::MAX));
                }
            }
        }
        test_edge();
    })+}
 }
 #[test]
 fn cast_int_to_int_edge_cases() {
    use core::cmp::Ordering::*;
    macro_rules! test_edge {
        ($( $from:ident )+) => { $({
            int_test_edge!($from -> { isize i8 i16 i32 i64 } with i64 u64);
            int_test_edge!($from -> { usize u8 u16 u32 u64 } with i64 u64);
        })+}
    }
    test_edge!(isize i8 i16 i32 i64);
    test_edge!(usize u8 u16 u32 u64);
 }
 #[test]
 #[cfg(has_i128)]
 fn cast_int_to_128_edge_cases() {
    use core::cmp::Ordering::*;
    macro_rules! test_edge {
        ($( $t:ident )+) => {
            $(
                int_test_edge!($t -> { i128 u128 } with i128 u128);
            )+
            int_test_edge!(i128 -> { $( $t )+ } with i128 u128);
            int_test_edge!(u128 -> { $( $t )+ } with i128 u128);
        }
    }
    test_edge!(isize i8 i16 i32 i64 i128);
    test_edge!(usize u8 u16 u32 u64 u128);
 }
 #[test]
 fn newtype_from_primitive() {
    #[derive(PartialEq, Debug)]
    struct New<T>(T);
    // minimal impl
    impl<T: FromPrimitive> FromPrimitive for New<T> {
        fn from_i64(n: i64) -> Option<Self> {
            T::from_i64(n).map(New)
        }
        fn from_u64(n: u64) -> Option<Self> {
            T::from_u64(n).map(New)
        }
    }
    macro_rules! assert_eq_from {
        ($( $from:ident )+) => {$(
            assert_eq!(T::$from(Bounded::min_value()).map(New),
                       New::<T>::$from(Bounded::min_value()));
            assert_eq!(T::$from(Bounded::max_value()).map(New),
                       New::<T>::$from(Bounded::max_value()));
        )+}
    }
    fn check<T: PartialEq + Debug + FromPrimitive>() {
        assert_eq_from!(from_i8 from_i16 from_i32 from_i64 from_isize);
        assert_eq_from!(from_u8 from_u16 from_u32 from_u64 from_usize);
        assert_eq_from!(from_f32 from_f64);
    }
    macro_rules! check {
        ($( $ty:ty )+) => {$( check::<$ty>(); )+}
    }
    check!(i8 i16 i32 i64 isize);
    check!(u8 u16 u32 u64 usize);
 }
 #[test]
 fn newtype_to_primitive() {
    #[derive(PartialEq, Debug)]
    struct New<T>(T);
    // minimal impl
    impl<T: ToPrimitive> ToPrimitive for New<T> {
        fn to_i64(&self) -> Option<i64> {
            self.0.to_i64()
        }
        fn to_u64(&self) -> Option<u64> {
            self.0.to_u64()
        }
    }
    macro_rules! assert_eq_to {
        ($( $to:ident )+) => {$(
            assert_eq!(T::$to(&Bounded::min_value()),
                       New::<T>::$to(&New(Bounded::min_value())));
            assert_eq!(T::$to(&Bounded::max_value()),
                       New::<T>::$to(&New(Bounded::max_value())));
        )+}
    }
    fn check<T: PartialEq + Debug + Bounded + ToPrimitive>() {
        assert_eq_to!(to_i8 to_i16 to_i32 to_i64 to_isize);
        assert_eq_to!(to_u8 to_u16 to_u32 to_u64 to_usize);
        assert_eq_to!(to_f32 to_f64);
    }
    macro_rules! check {
        ($( $ty:ty )+) => {$( check::<$ty>(); )+}
    }
    check!(i8 i16 i32 i64 isize);
    check!(u8 u16 u32 u64 usize);
 }
--- a/traits/Cargo.toml
+++ b/traits/Cargo.toml
@ -0,0 +1,13 @@
 [package]
 authors = ["The Rust Project Developers"]
 description = "Numeric traits for generic mathematics"
 documentation = "http://rust-num.github.io/num"
 homepage = "https://github.com/rust-num/num"
 keywords = ["mathematics", "numerics"]
 categories = [ "algorithms", "science" ]
 license = "MIT/Apache-2.0"
 repository = "https://github.com/rust-num/num"
 name = "num-traits"
 version = "0.1.41"
 [dependencies]
--- a/traits/LICENSE-APACHE
+++ b/traits/LICENSE-APACHE
@ -0,0 +1,201 @@
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--- a/traits/LICENSE-MIT
+++ b/traits/LICENSE-MIT
@ -0,0 +1,25 @@
 Copyright (c) 2014 The Rust Project Developers
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 IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
 DEALINGS IN THE SOFTWARE.
--- a/traits/src/bounds.rs
+++ b/traits/src/bounds.rs
@ -1,9 +1,7 @@
-use core::num::Wrapping;
+use std::{usize, u8, u16, u32, u64};
-use core::{f32, f64};
+use std::{isize, i8, i16, i32, i64};
-#[cfg(has_i128)]
+use std::{f32, f64};
-use core::{i128, u128};
+use std::num::Wrapping;
 use core::{i16, i32, i64, i8, isize};
 use core::{u16, u32, u64, u8, usize};
 /// Numbers which have upper and lower bounds
 pub trait Bounded {
@ -18,16 +16,12 @@ macro_rules! bounded_impl {
    ($t:ty, $min:expr, $max:expr) => {
        impl Bounded for $t {
            #[inline]
-            fn min_value() -> $t {
+            fn min_value() -> $t { $min }
                $min
            }
            #[inline]
-            fn max_value() -> $t {
+            fn max_value() -> $t { $max }
                $max
        }
    }
    };
 }
 bounded_impl!(usize, usize::MIN, usize::MAX);
@ -35,24 +29,16 @@ bounded_impl!(u8, u8::MIN, u8::MAX);
 bounded_impl!(u16,   u16::MIN,   u16::MAX);
 bounded_impl!(u32,   u32::MIN,   u32::MAX);
 bounded_impl!(u64,   u64::MIN,   u64::MAX);
 #[cfg(has_i128)]
 bounded_impl!(u128, u128::MIN, u128::MAX);
 bounded_impl!(isize, isize::MIN, isize::MAX);
 bounded_impl!(i8,    i8::MIN,    i8::MAX);
 bounded_impl!(i16,   i16::MIN,   i16::MAX);
 bounded_impl!(i32,   i32::MIN,   i32::MAX);
 bounded_impl!(i64,   i64::MIN,   i64::MAX);
 #[cfg(has_i128)]
 bounded_impl!(i128, i128::MIN, i128::MAX);
 impl<T: Bounded> Bounded for Wrapping<T> {
-    fn min_value() -> Self {
+    fn min_value() -> Self { Wrapping(T::min_value()) }
-        Wrapping(T::min_value())
+    fn max_value() -> Self { Wrapping(T::max_value()) }
    }
    fn max_value() -> Self {
        Wrapping(T::max_value())
    }
 }
 bounded_impl!(f32, f32::MIN, f32::MAX);
@ -67,9 +53,9 @@ macro_rules! for_each_tuple_ {
    );
 }
 macro_rules! for_each_tuple {
-    ($m:ident) => {
+    ( $m:ident ) => (
        for_each_tuple_! { $m !! A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, }
-    };
+    );
 }
 macro_rules! bounded_tuple {
@ -90,13 +76,14 @@ macro_rules! bounded_tuple {
 for_each_tuple!(bounded_tuple);
 bounded_impl!(f64, f64::MIN, f64::MAX);
 #[test]
 fn wrapping_bounded() {
    macro_rules! test_wrapping_bounded {
        ($($t:ty)+) => {
            $(
-                assert_eq!(<Wrapping<$t> as Bounded>::min_value().0, <$t>::min_value());
+                assert_eq!(Wrapping::<$t>::min_value().0, <$t>::min_value());
-                assert_eq!(<Wrapping<$t> as Bounded>::max_value().0, <$t>::max_value());
+                assert_eq!(Wrapping::<$t>::max_value().0, <$t>::max_value());
            )+
        };
    }
@ -104,21 +91,6 @@ fn wrapping_bounded() {
    test_wrapping_bounded!(usize u8 u16 u32 u64 isize i8 i16 i32 i64);
 }
 #[cfg(has_i128)]
 #[test]
 fn wrapping_bounded_i128() {
    macro_rules! test_wrapping_bounded {
        ($($t:ty)+) => {
            $(
                assert_eq!(<Wrapping<$t> as Bounded>::min_value().0, <$t>::min_value());
                assert_eq!(<Wrapping<$t> as Bounded>::max_value().0, <$t>::max_value());
            )+
        };
    }
    test_wrapping_bounded!(u128 i128);
 }
 #[test]
 fn wrapping_is_bounded() {
    fn require_bounded<T: Bounded>(_: &T) {}
--- a/traits/src/cast.rs
+++ b/traits/src/cast.rs
@ -0,0 +1,511 @@
 use std::mem::size_of;
 use std::num::Wrapping;
 use identities::Zero;
 use bounds::Bounded;
 /// A generic trait for converting a value to a number.
 pub trait ToPrimitive {
    /// Converts the value of `self` to an `isize`.
    #[inline]
    fn to_isize(&self) -> Option<isize> {
        self.to_i64().and_then(|x| x.to_isize())
    }
    /// Converts the value of `self` to an `i8`.
    #[inline]
    fn to_i8(&self) -> Option<i8> {
        self.to_i64().and_then(|x| x.to_i8())
    }
    /// Converts the value of `self` to an `i16`.
    #[inline]
    fn to_i16(&self) -> Option<i16> {
        self.to_i64().and_then(|x| x.to_i16())
    }
    /// Converts the value of `self` to an `i32`.
    #[inline]
    fn to_i32(&self) -> Option<i32> {
        self.to_i64().and_then(|x| x.to_i32())
    }
    /// Converts the value of `self` to an `i64`.
    fn to_i64(&self) -> Option<i64>;
    /// Converts the value of `self` to a `usize`.
    #[inline]
    fn to_usize(&self) -> Option<usize> {
        self.to_u64().and_then(|x| x.to_usize())
    }
    /// Converts the value of `self` to an `u8`.
    #[inline]
    fn to_u8(&self) -> Option<u8> {
        self.to_u64().and_then(|x| x.to_u8())
    }
    /// Converts the value of `self` to an `u16`.
    #[inline]
    fn to_u16(&self) -> Option<u16> {
        self.to_u64().and_then(|x| x.to_u16())
    }
    /// Converts the value of `self` to an `u32`.
    #[inline]
    fn to_u32(&self) -> Option<u32> {
        self.to_u64().and_then(|x| x.to_u32())
    }
    /// Converts the value of `self` to an `u64`.
    #[inline]
    fn to_u64(&self) -> Option<u64>;
    /// Converts the value of `self` to an `f32`.
    #[inline]
    fn to_f32(&self) -> Option<f32> {
        self.to_f64().and_then(|x| x.to_f32())
    }
    /// Converts the value of `self` to an `f64`.
    #[inline]
    fn to_f64(&self) -> Option<f64> {
        self.to_i64().and_then(|x| x.to_f64())
    }
 }
 macro_rules! impl_to_primitive_int_to_int {
    ($SrcT:ty, $DstT:ty, $slf:expr) => (
        {
            if size_of::<$SrcT>() <= size_of::<$DstT>() {
                Some($slf as $DstT)
            } else {
                let n = $slf as i64;
                let min_value: $DstT = Bounded::min_value();
                let max_value: $DstT = Bounded::max_value();
                if min_value as i64 <= n && n <= max_value as i64 {
                    Some($slf as $DstT)
                } else {
                    None
                }
            }
        }
    )
 }
 macro_rules! impl_to_primitive_int_to_uint {
    ($SrcT:ty, $DstT:ty, $slf:expr) => (
        {
            let zero: $SrcT = Zero::zero();
            let max_value: $DstT = Bounded::max_value();
            if zero <= $slf && $slf as u64 <= max_value as u64 {
                Some($slf as $DstT)
            } else {
                None
            }
        }
    )
 }
 macro_rules! impl_to_primitive_int {
    ($T:ty) => (
        impl ToPrimitive for $T {
            #[inline]
            fn to_isize(&self) -> Option<isize> { impl_to_primitive_int_to_int!($T, isize, *self) }
            #[inline]
            fn to_i8(&self) -> Option<i8> { impl_to_primitive_int_to_int!($T, i8, *self) }
            #[inline]
            fn to_i16(&self) -> Option<i16> { impl_to_primitive_int_to_int!($T, i16, *self) }
            #[inline]
            fn to_i32(&self) -> Option<i32> { impl_to_primitive_int_to_int!($T, i32, *self) }
            #[inline]
            fn to_i64(&self) -> Option<i64> { impl_to_primitive_int_to_int!($T, i64, *self) }
            #[inline]
            fn to_usize(&self) -> Option<usize> { impl_to_primitive_int_to_uint!($T, usize, *self) }
            #[inline]
            fn to_u8(&self) -> Option<u8> { impl_to_primitive_int_to_uint!($T, u8, *self) }
            #[inline]
            fn to_u16(&self) -> Option<u16> { impl_to_primitive_int_to_uint!($T, u16, *self) }
            #[inline]
            fn to_u32(&self) -> Option<u32> { impl_to_primitive_int_to_uint!($T, u32, *self) }
            #[inline]
            fn to_u64(&self) -> Option<u64> { impl_to_primitive_int_to_uint!($T, u64, *self) }
            #[inline]
            fn to_f32(&self) -> Option<f32> { Some(*self as f32) }
            #[inline]
            fn to_f64(&self) -> Option<f64> { Some(*self as f64) }
        }
    )
 }
 impl_to_primitive_int!(isize);
 impl_to_primitive_int!(i8);
 impl_to_primitive_int!(i16);
 impl_to_primitive_int!(i32);
 impl_to_primitive_int!(i64);
 macro_rules! impl_to_primitive_uint_to_int {
    ($DstT:ty, $slf:expr) => (
        {
            let max_value: $DstT = Bounded::max_value();
            if $slf as u64 <= max_value as u64 {
                Some($slf as $DstT)
            } else {
                None
            }
        }
    )
 }
 macro_rules! impl_to_primitive_uint_to_uint {
    ($SrcT:ty, $DstT:ty, $slf:expr) => (
        {
            if size_of::<$SrcT>() <= size_of::<$DstT>() {
                Some($slf as $DstT)
            } else {
                let zero: $SrcT = Zero::zero();
                let max_value: $DstT = Bounded::max_value();
                if zero <= $slf && $slf as u64 <= max_value as u64 {
                    Some($slf as $DstT)
                } else {
                    None
                }
            }
        }
    )
 }
 macro_rules! impl_to_primitive_uint {
    ($T:ty) => (
        impl ToPrimitive for $T {
            #[inline]
            fn to_isize(&self) -> Option<isize> { impl_to_primitive_uint_to_int!(isize, *self) }
            #[inline]
            fn to_i8(&self) -> Option<i8> { impl_to_primitive_uint_to_int!(i8, *self) }
            #[inline]
            fn to_i16(&self) -> Option<i16> { impl_to_primitive_uint_to_int!(i16, *self) }
            #[inline]
            fn to_i32(&self) -> Option<i32> { impl_to_primitive_uint_to_int!(i32, *self) }
            #[inline]
            fn to_i64(&self) -> Option<i64> { impl_to_primitive_uint_to_int!(i64, *self) }
            #[inline]
            fn to_usize(&self) -> Option<usize> {
                impl_to_primitive_uint_to_uint!($T, usize, *self)
            }
            #[inline]
            fn to_u8(&self) -> Option<u8> { impl_to_primitive_uint_to_uint!($T, u8, *self) }
            #[inline]
            fn to_u16(&self) -> Option<u16> { impl_to_primitive_uint_to_uint!($T, u16, *self) }
            #[inline]
            fn to_u32(&self) -> Option<u32> { impl_to_primitive_uint_to_uint!($T, u32, *self) }
            #[inline]
            fn to_u64(&self) -> Option<u64> { impl_to_primitive_uint_to_uint!($T, u64, *self) }
            #[inline]
            fn to_f32(&self) -> Option<f32> { Some(*self as f32) }
            #[inline]
            fn to_f64(&self) -> Option<f64> { Some(*self as f64) }
        }
    )
 }
 impl_to_primitive_uint!(usize);
 impl_to_primitive_uint!(u8);
 impl_to_primitive_uint!(u16);
 impl_to_primitive_uint!(u32);
 impl_to_primitive_uint!(u64);
 macro_rules! impl_to_primitive_float_to_float {
    ($SrcT:ident, $DstT:ident, $slf:expr) => (
        if size_of::<$SrcT>() <= size_of::<$DstT>() {
            Some($slf as $DstT)
        } else {
            // Make sure the value is in range for the cast.
            // NaN and +-inf are cast as they are.
            let n = $slf as f64;
            let max_value: $DstT = ::std::$DstT::MAX;
            if !n.is_finite() || (-max_value as f64 <= n && n <= max_value as f64) {
                Some($slf as $DstT)
            } else {
                None
            }
        }
    )
 }
 macro_rules! impl_to_primitive_float {
    ($T:ident) => (
        impl ToPrimitive for $T {
            #[inline]
            fn to_isize(&self) -> Option<isize> { Some(*self as isize) }
            #[inline]
            fn to_i8(&self) -> Option<i8> { Some(*self as i8) }
            #[inline]
            fn to_i16(&self) -> Option<i16> { Some(*self as i16) }
            #[inline]
            fn to_i32(&self) -> Option<i32> { Some(*self as i32) }
            #[inline]
            fn to_i64(&self) -> Option<i64> { Some(*self as i64) }
            #[inline]
            fn to_usize(&self) -> Option<usize> { Some(*self as usize) }
            #[inline]
            fn to_u8(&self) -> Option<u8> { Some(*self as u8) }
            #[inline]
            fn to_u16(&self) -> Option<u16> { Some(*self as u16) }
            #[inline]
            fn to_u32(&self) -> Option<u32> { Some(*self as u32) }
            #[inline]
            fn to_u64(&self) -> Option<u64> { Some(*self as u64) }
            #[inline]
            fn to_f32(&self) -> Option<f32> { impl_to_primitive_float_to_float!($T, f32, *self) }
            #[inline]
            fn to_f64(&self) -> Option<f64> { impl_to_primitive_float_to_float!($T, f64, *self) }
        }
    )
 }
 impl_to_primitive_float!(f32);
 impl_to_primitive_float!(f64);
 /// A generic trait for converting a number to a value.
 pub trait FromPrimitive: Sized {
    /// Convert an `isize` to return an optional value of this type. If the
    /// value cannot be represented by this value, the `None` is returned.
    #[inline]
    fn from_isize(n: isize) -> Option<Self> {
        FromPrimitive::from_i64(n as i64)
    }
    /// Convert an `i8` to return an optional value of this type. If the
    /// type cannot be represented by this value, the `None` is returned.
    #[inline]
    fn from_i8(n: i8) -> Option<Self> {
        FromPrimitive::from_i64(n as i64)
    }
    /// Convert an `i16` to return an optional value of this type. If the
    /// type cannot be represented by this value, the `None` is returned.
    #[inline]
    fn from_i16(n: i16) -> Option<Self> {
        FromPrimitive::from_i64(n as i64)
    }
    /// Convert an `i32` to return an optional value of this type. If the
    /// type cannot be represented by this value, the `None` is returned.
    #[inline]
    fn from_i32(n: i32) -> Option<Self> {
        FromPrimitive::from_i64(n as i64)
    }
    /// Convert an `i64` to return an optional value of this type. If the
    /// type cannot be represented by this value, the `None` is returned.
    fn from_i64(n: i64) -> Option<Self>;
    /// Convert a `usize` to return an optional value of this type. If the
    /// type cannot be represented by this value, the `None` is returned.
    #[inline]
    fn from_usize(n: usize) -> Option<Self> {
        FromPrimitive::from_u64(n as u64)
    }
    /// Convert an `u8` to return an optional value of this type. If the
    /// type cannot be represented by this value, the `None` is returned.
    #[inline]
    fn from_u8(n: u8) -> Option<Self> {
        FromPrimitive::from_u64(n as u64)
    }
    /// Convert an `u16` to return an optional value of this type. If the
    /// type cannot be represented by this value, the `None` is returned.
    #[inline]
    fn from_u16(n: u16) -> Option<Self> {
        FromPrimitive::from_u64(n as u64)
    }
    /// Convert an `u32` to return an optional value of this type. If the
    /// type cannot be represented by this value, the `None` is returned.
    #[inline]
    fn from_u32(n: u32) -> Option<Self> {
        FromPrimitive::from_u64(n as u64)
    }
    /// Convert an `u64` to return an optional value of this type. If the
    /// type cannot be represented by this value, the `None` is returned.
    fn from_u64(n: u64) -> Option<Self>;
    /// Convert a `f32` to return an optional value of this type. If the
    /// type cannot be represented by this value, the `None` is returned.
    #[inline]
    fn from_f32(n: f32) -> Option<Self> {
        FromPrimitive::from_f64(n as f64)
    }
    /// Convert a `f64` to return an optional value of this type. If the
    /// type cannot be represented by this value, the `None` is returned.
    #[inline]
    fn from_f64(n: f64) -> Option<Self> {
        FromPrimitive::from_i64(n as i64)
    }
 }
 macro_rules! impl_from_primitive {
    ($T:ty, $to_ty:ident) => (
        #[allow(deprecated)]
        impl FromPrimitive for $T {
            #[inline] fn from_i8(n: i8) -> Option<$T> { n.$to_ty() }
            #[inline] fn from_i16(n: i16) -> Option<$T> { n.$to_ty() }
            #[inline] fn from_i32(n: i32) -> Option<$T> { n.$to_ty() }
            #[inline] fn from_i64(n: i64) -> Option<$T> { n.$to_ty() }
            #[inline] fn from_u8(n: u8) -> Option<$T> { n.$to_ty() }
            #[inline] fn from_u16(n: u16) -> Option<$T> { n.$to_ty() }
            #[inline] fn from_u32(n: u32) -> Option<$T> { n.$to_ty() }
            #[inline] fn from_u64(n: u64) -> Option<$T> { n.$to_ty() }
            #[inline] fn from_f32(n: f32) -> Option<$T> { n.$to_ty() }
            #[inline] fn from_f64(n: f64) -> Option<$T> { n.$to_ty() }
        }
    )
 }
 impl_from_primitive!(isize, to_isize);
 impl_from_primitive!(i8,    to_i8);
 impl_from_primitive!(i16,   to_i16);
 impl_from_primitive!(i32,   to_i32);
 impl_from_primitive!(i64,   to_i64);
 impl_from_primitive!(usize, to_usize);
 impl_from_primitive!(u8,    to_u8);
 impl_from_primitive!(u16,   to_u16);
 impl_from_primitive!(u32,   to_u32);
 impl_from_primitive!(u64,   to_u64);
 impl_from_primitive!(f32,   to_f32);
 impl_from_primitive!(f64,   to_f64);
 impl<T: ToPrimitive> ToPrimitive for Wrapping<T> {
    fn to_i64(&self) -> Option<i64> { self.0.to_i64() }
    fn to_u64(&self) -> Option<u64> { self.0.to_u64() }
 }
 impl<T: FromPrimitive> FromPrimitive for Wrapping<T> {
    fn from_u64(n: u64) -> Option<Self> { T::from_u64(n).map(Wrapping) }
    fn from_i64(n: i64) -> Option<Self> { T::from_i64(n).map(Wrapping) }
 }
 /// Cast from one machine scalar to another.
 ///
 /// # Examples
 ///
 /// ```
 /// # use num_traits as num;
 /// let twenty: f32 = num::cast(0x14).unwrap();
 /// assert_eq!(twenty, 20f32);
 /// ```
 ///
 #[inline]
 pub fn cast<T: NumCast, U: NumCast>(n: T) -> Option<U> {
    NumCast::from(n)
 }
 /// An interface for casting between machine scalars.
 pub trait NumCast: Sized + ToPrimitive {
    /// Creates a number from another value that can be converted into
    /// a primitive via the `ToPrimitive` trait.
    fn from<T: ToPrimitive>(n: T) -> Option<Self>;
 }
 macro_rules! impl_num_cast {
    ($T:ty, $conv:ident) => (
        impl NumCast for $T {
            #[inline]
            #[allow(deprecated)]
            fn from<N: ToPrimitive>(n: N) -> Option<$T> {
                // `$conv` could be generated using `concat_idents!`, but that
                // macro seems to be broken at the moment
                n.$conv()
            }
        }
    )
 }
 impl_num_cast!(u8,    to_u8);
 impl_num_cast!(u16,   to_u16);
 impl_num_cast!(u32,   to_u32);
 impl_num_cast!(u64,   to_u64);
 impl_num_cast!(usize, to_usize);
 impl_num_cast!(i8,    to_i8);
 impl_num_cast!(i16,   to_i16);
 impl_num_cast!(i32,   to_i32);
 impl_num_cast!(i64,   to_i64);
 impl_num_cast!(isize, to_isize);
 impl_num_cast!(f32,   to_f32);
 impl_num_cast!(f64,   to_f64);
 impl<T: NumCast> NumCast for Wrapping<T> {
    fn from<U: ToPrimitive>(n: U) -> Option<Self> {
        T::from(n).map(Wrapping)
    }
 }
 #[test]
 fn to_primitive_float() {
    use std::f32;
    use std::f64;
    let f32_toolarge = 1e39f64;
    assert_eq!(f32_toolarge.to_f32(), None);
    assert_eq!((f32::MAX as f64).to_f32(), Some(f32::MAX));
    assert_eq!((-f32::MAX as f64).to_f32(), Some(-f32::MAX));
    assert_eq!(f64::INFINITY.to_f32(), Some(f32::INFINITY));
    assert_eq!((f64::NEG_INFINITY).to_f32(), Some(f32::NEG_INFINITY));
    assert!((f64::NAN).to_f32().map_or(false, |f| f.is_nan()));
 }
 #[test]
 fn wrapping_to_primitive() {
    macro_rules! test_wrapping_to_primitive {
        ($($t:ty)+) => {
            $({
                let i: $t = 0;
                let w = Wrapping(i);
                assert_eq!(i.to_u8(),    w.to_u8());
                assert_eq!(i.to_u16(),   w.to_u16());
                assert_eq!(i.to_u32(),   w.to_u32());
                assert_eq!(i.to_u64(),   w.to_u64());
                assert_eq!(i.to_usize(), w.to_usize());
                assert_eq!(i.to_i8(),    w.to_i8());
                assert_eq!(i.to_i16(),   w.to_i16());
                assert_eq!(i.to_i32(),   w.to_i32());
                assert_eq!(i.to_i64(),   w.to_i64());
                assert_eq!(i.to_isize(), w.to_isize());
                assert_eq!(i.to_f32(),   w.to_f32());
                assert_eq!(i.to_f64(),   w.to_f64());
            })+
        };
    }
    test_wrapping_to_primitive!(usize u8 u16 u32 u64 isize i8 i16 i32 i64);
 }
 #[test]
 fn wrapping_is_toprimitive() {
    fn require_toprimitive<T: ToPrimitive>(_: &T) {}
    require_toprimitive(&Wrapping(42));
 }
 #[test]
 fn wrapping_is_fromprimitive() {
    fn require_fromprimitive<T: FromPrimitive>(_: &T) {}
    require_fromprimitive(&Wrapping(42));
 }
 #[test]
 fn wrapping_is_numcast() {
    fn require_numcast<T: NumCast>(_: &T) {}
    require_numcast(&Wrapping(42));
 }
--- a/traits/src/float.rs
+++ b/traits/src/float.rs
--- a/traits/src/identities.rs
+++ b/traits/src/identities.rs
@ -0,0 +1,148 @@
 use std::ops::{Add, Mul};
 use std::num::Wrapping;
 /// Defines an additive identity element for `Self`.
 pub trait Zero: Sized + Add<Self, Output = Self> {
    /// Returns the additive identity element of `Self`, `0`.
    ///
    /// # Laws
    ///
    /// ```{.text}
    /// a + 0 = a       ∀ a ∈ Self
    /// 0 + a = a       ∀ a ∈ Self
    /// ```
    ///
    /// # Purity
    ///
    /// This function should return the same result at all times regardless of
    /// external mutable state, for example values stored in TLS or in
    /// `static mut`s.
    // FIXME (#5527): This should be an associated constant
    fn zero() -> Self;
    /// Returns `true` if `self` is equal to the additive identity.
    #[inline]
    fn is_zero(&self) -> bool;
 }
 macro_rules! zero_impl {
    ($t:ty, $v:expr) => {
        impl Zero for $t {
            #[inline]
            fn zero() -> $t { $v }
            #[inline]
            fn is_zero(&self) -> bool { *self == $v }
        }
    }
 }
 zero_impl!(usize, 0usize);
 zero_impl!(u8,    0u8);
 zero_impl!(u16,   0u16);
 zero_impl!(u32,   0u32);
 zero_impl!(u64,   0u64);
 zero_impl!(isize, 0isize);
 zero_impl!(i8,    0i8);
 zero_impl!(i16,   0i16);
 zero_impl!(i32,   0i32);
 zero_impl!(i64,   0i64);
 zero_impl!(f32, 0.0f32);
 zero_impl!(f64, 0.0f64);
 impl<T: Zero> Zero for Wrapping<T> where Wrapping<T>: Add<Output=Wrapping<T>> {
    fn is_zero(&self) -> bool {
        self.0.is_zero()
    }
    fn zero() -> Self {
        Wrapping(T::zero())
    }
 }
 /// Defines a multiplicative identity element for `Self`.
 pub trait One: Sized + Mul<Self, Output = Self> {
    /// Returns the multiplicative identity element of `Self`, `1`.
    ///
    /// # Laws
    ///
    /// ```{.text}
    /// a * 1 = a       ∀ a ∈ Self
    /// 1 * a = a       ∀ a ∈ Self
    /// ```
    ///
    /// # Purity
    ///
    /// This function should return the same result at all times regardless of
    /// external mutable state, for example values stored in TLS or in
    /// `static mut`s.
    // FIXME (#5527): This should be an associated constant
    fn one() -> Self;
 }
 macro_rules! one_impl {
    ($t:ty, $v:expr) => {
        impl One for $t {
            #[inline]
            fn one() -> $t { $v }
        }
    }
 }
 one_impl!(usize, 1usize);
 one_impl!(u8,    1u8);
 one_impl!(u16,   1u16);
 one_impl!(u32,   1u32);
 one_impl!(u64,   1u64);
 one_impl!(isize, 1isize);
 one_impl!(i8,    1i8);
 one_impl!(i16,   1i16);
 one_impl!(i32,   1i32);
 one_impl!(i64,   1i64);
 one_impl!(f32, 1.0f32);
 one_impl!(f64, 1.0f64);
 impl<T: One> One for Wrapping<T> where Wrapping<T>: Mul<Output=Wrapping<T>> {
    fn one() -> Self {
        Wrapping(T::one())
    }
 }
 // Some helper functions provided for backwards compatibility.
 /// Returns the additive identity, `0`.
 #[inline(always)] pub fn zero<T: Zero>() -> T { Zero::zero() }
 /// Returns the multiplicative identity, `1`.
 #[inline(always)] pub fn one<T: One>() -> T { One::one() }
 #[test]
 fn wrapping_identities() {
    macro_rules! test_wrapping_identities {
        ($($t:ty)+) => {
            $(
                assert_eq!(zero::<$t>(), zero::<Wrapping<$t>>().0);
                assert_eq!(one::<$t>(), one::<Wrapping<$t>>().0);
                assert_eq!((0 as $t).is_zero(), Wrapping(0 as $t).is_zero());
                assert_eq!((1 as $t).is_zero(), Wrapping(1 as $t).is_zero());
            )+
        };
    }
    test_wrapping_identities!(isize i8 i16 i32 i64 usize u8 u16 u32 u64);
 }
 #[test]
 fn wrapping_is_zero() {
    fn require_zero<T: Zero>(_: &T) {}
    require_zero(&Wrapping(42));
 }
 #[test]
 fn wrapping_is_one() {
    fn require_one<T: One>(_: &T) {}
    require_one(&Wrapping(42));
 }
--- a/traits/src/int.rs
+++ b/traits/src/int.rs
@ -1,55 +1,26 @@
-use core::ops::{BitAnd, BitOr, BitXor, Not, Shl, Shr};
+use std::ops::{Not, BitAnd, BitOr, BitXor, Shl, Shr};
 use {Num, NumCast};
 use bounds::Bounded;
 use ops::checked::*;
 use ops::saturating::Saturating;
 use {Num, NumCast};
-/// Generic trait for primitive integers.
+pub trait PrimInt
-///
+    : Sized
 /// The `PrimInt` trait is an abstraction over the builtin primitive integer types (e.g., `u8`,
 /// `u32`, `isize`, `i128`, ...). It inherits the basic numeric traits and extends them with
 /// bitwise operators and non-wrapping arithmetic.
 ///
 /// The trait explicitly inherits `Copy`, `Eq`, `Ord`, and `Sized`. The intention is that all
 /// types implementing this trait behave like primitive types that are passed by value by default
 /// and behave like builtin integers. Furthermore, the types are expected to expose the integer
 /// value in binary representation and support bitwise operators. The standard bitwise operations
 /// (e.g., bitwise-and, bitwise-or, right-shift, left-shift) are inherited and the trait extends
 /// these with introspective queries (e.g., `PrimInt::count_ones()`, `PrimInt::leading_zeros()`),
 /// bitwise combinators (e.g., `PrimInt::rotate_left()`), and endianness converters (e.g.,
 /// `PrimInt::to_be()`).
 ///
 /// All `PrimInt` types are expected to be fixed-width binary integers. The width can be queried
 /// via `T::zero().count_zeros()`. The trait currently lacks a way to query the width at
 /// compile-time.
 ///
 /// While a default implementation for all builtin primitive integers is provided, the trait is in
 /// no way restricted to these. Other integer types that fulfil the requirements are free to
 /// implement the trait was well.
 ///
 /// This trait and many of the method names originate in the unstable `core::num::Int` trait from
 /// the rust standard library. The original trait was never stabilized and thus removed from the
 /// standard library.
 pub trait PrimInt:
    Sized
    + Copy
-    + Num
+    + Num + NumCast
    + NumCast
    + Bounded
-    + PartialOrd
+    + PartialOrd + Ord + Eq
-    + Ord
+    + Not<Output=Self>
-    + Eq
+    + BitAnd<Output=Self>
-    + Not<Output = Self>
+    + BitOr<Output=Self>
-    + BitAnd<Output = Self>
+    + BitXor<Output=Self>
-    + BitOr<Output = Self>
+    + Shl<usize, Output=Self>
-    + BitXor<Output = Self>
+    + Shr<usize, Output=Self>
-    + Shl<usize, Output = Self>
+    + CheckedAdd<Output=Self>
-    + Shr<usize, Output = Self>
+    + CheckedSub<Output=Self>
-    + CheckedAdd<Output = Self>
+    + CheckedMul<Output=Self>
-    + CheckedSub<Output = Self>
+    + CheckedDiv<Output=Self>
    + CheckedMul<Output = Self>
    + CheckedDiv<Output = Self>
    + Saturating
 {
    /// Returns the number of ones in the binary representation of `self`.
@ -197,10 +168,10 @@ pub trait PrimInt:
    /// ```
    /// use num_traits::PrimInt;
    ///
-    /// let n = -8i8; // 0b11111000
+    /// let n = 0xFEDCBA9876543210i64;
-    /// let m = 62i8; // 0b00111110
+    /// let m = 0x000FEDCBA9876543i64;
    ///
-    /// assert_eq!(n.unsigned_shr(2), m);
+    /// assert_eq!(n.unsigned_shr(12), m);
    /// ```
    fn unsigned_shr(self, n: u32) -> Self;
@ -307,7 +278,7 @@ pub trait PrimInt:
 }
 macro_rules! prim_int_impl {
-    ($T:ty, $S:ty, $U:ty) => {
+    ($T:ty, $S:ty, $U:ty) => (
        impl PrimInt for $T {
            #[inline]
            fn count_ones(self) -> u32 {
@ -389,7 +360,7 @@ macro_rules! prim_int_impl {
                <$T>::pow(self, exp)
            }
        }
-    };
+    )
 }
 // prim_int_impl!(type, signed, unsigned);
@ -397,13 +368,9 @@ prim_int_impl!(u8, i8, u8);
 prim_int_impl!(u16,   i16,   u16);
 prim_int_impl!(u32,   i32,   u32);
 prim_int_impl!(u64,   i64,   u64);
 #[cfg(has_i128)]
 prim_int_impl!(u128, i128, u128);
 prim_int_impl!(usize, isize, usize);
 prim_int_impl!(i8,    i8,    u8);
 prim_int_impl!(i16,   i16,   u16);
 prim_int_impl!(i32,   i32,   u32);
 prim_int_impl!(i64,   i64,   u64);
 #[cfg(has_i128)]
 prim_int_impl!(i128, i128, u128);
 prim_int_impl!(isize, isize, usize);
--- a/traits/src/lib.rs
+++ b/traits/src/lib.rs
@ -0,0 +1,437 @@
 // 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, <$t as Num>::from_str_radix(s, r));
                }
            )+
        };
    }
    test_wrapping_from_str_radix!(usize u8 u16 u32 u64 isize i8 i16 i32 i64);
 }
 #[test]
 fn check_num_ops() {
    fn compute<T: Num + Copy>(x: T, y: T) -> T {
        x * y / y % y + y - y
    }
    assert_eq!(compute(1, 2), 1)
 }
 #[test]
 fn check_numref_ops() {
    fn compute<T: NumRef>(x: T, y: &T) -> T {
        x * y / y % y + y - y
    }
    assert_eq!(compute(1, &2), 1)
 }
 #[test]
 fn check_refnum_ops() {
    fn compute<T: Copy>(x: &T, y: T) -> T
        where for<'a> &'a T: RefNum<T>
    {
        &(&(&(&(x * y) / y) % y) + y) - y
    }
    assert_eq!(compute(&1, 2), 1)
 }
 #[test]
 fn check_refref_ops() {
    fn compute<T>(x: &T, y: &T) -> T
        where for<'a> &'a T: RefNum<T>
    {
        &(&(&(&(x * y) / y) % y) + y) - y
    }
    assert_eq!(compute(&1, &2), 1)
 }
 #[test]
 fn check_numassign_ops() {
    fn compute<T: NumAssign + Copy>(mut x: T, y: T) -> T {
        x *= y;
        x /= y;
        x %= y;
        x += y;
        x -= y;
        x
    }
    assert_eq!(compute(1, 2), 1)
 }
 // TODO test `NumAssignRef`, but even the standard numeric types don't
 // implement this yet. (see rust pr41336)
--- a/traits/src/ops/checked.rs
+++ b/traits/src/ops/checked.rs
@ -0,0 +1,92 @@
 use std::ops::{Add, Sub, Mul, Div};
 /// Performs addition that returns `None` instead of wrapping around on
 /// overflow.
 pub trait CheckedAdd: Sized + Add<Self, Output=Self> {
    /// Adds two numbers, checking for overflow. If overflow happens, `None` is
    /// returned.
    fn checked_add(&self, v: &Self) -> Option<Self>;
 }
 macro_rules! checked_impl {
    ($trait_name:ident, $method:ident, $t:ty) => {
        impl $trait_name for $t {
            #[inline]
            fn $method(&self, v: &$t) -> Option<$t> {
                <$t>::$method(*self, *v)
            }
        }
    }
 }
 checked_impl!(CheckedAdd, checked_add, u8);
 checked_impl!(CheckedAdd, checked_add, u16);
 checked_impl!(CheckedAdd, checked_add, u32);
 checked_impl!(CheckedAdd, checked_add, u64);
 checked_impl!(CheckedAdd, checked_add, usize);
 checked_impl!(CheckedAdd, checked_add, i8);
 checked_impl!(CheckedAdd, checked_add, i16);
 checked_impl!(CheckedAdd, checked_add, i32);
 checked_impl!(CheckedAdd, checked_add, i64);
 checked_impl!(CheckedAdd, checked_add, isize);
 /// Performs subtraction that returns `None` instead of wrapping around on underflow.
 pub trait CheckedSub: Sized + Sub<Self, Output=Self> {
    /// Subtracts two numbers, checking for underflow. If underflow happens,
    /// `None` is returned.
    fn checked_sub(&self, v: &Self) -> Option<Self>;
 }
 checked_impl!(CheckedSub, checked_sub, u8);
 checked_impl!(CheckedSub, checked_sub, u16);
 checked_impl!(CheckedSub, checked_sub, u32);
 checked_impl!(CheckedSub, checked_sub, u64);
 checked_impl!(CheckedSub, checked_sub, usize);
 checked_impl!(CheckedSub, checked_sub, i8);
 checked_impl!(CheckedSub, checked_sub, i16);
 checked_impl!(CheckedSub, checked_sub, i32);
 checked_impl!(CheckedSub, checked_sub, i64);
 checked_impl!(CheckedSub, checked_sub, isize);
 /// Performs multiplication that returns `None` instead of wrapping around on underflow or
 /// overflow.
 pub trait CheckedMul: Sized + Mul<Self, Output=Self> {
    /// Multiplies two numbers, checking for underflow or overflow. If underflow
    /// or overflow happens, `None` is returned.
    fn checked_mul(&self, v: &Self) -> Option<Self>;
 }
 checked_impl!(CheckedMul, checked_mul, u8);
 checked_impl!(CheckedMul, checked_mul, u16);
 checked_impl!(CheckedMul, checked_mul, u32);
 checked_impl!(CheckedMul, checked_mul, u64);
 checked_impl!(CheckedMul, checked_mul, usize);
 checked_impl!(CheckedMul, checked_mul, i8);
 checked_impl!(CheckedMul, checked_mul, i16);
 checked_impl!(CheckedMul, checked_mul, i32);
 checked_impl!(CheckedMul, checked_mul, i64);
 checked_impl!(CheckedMul, checked_mul, isize);
 /// Performs division that returns `None` instead of panicking on division by zero and instead of
 /// wrapping around on underflow and overflow.
 pub trait CheckedDiv: Sized + Div<Self, Output=Self> {
    /// Divides two numbers, checking for underflow, overflow and division by
    /// zero. If any of that happens, `None` is returned.
    fn checked_div(&self, v: &Self) -> Option<Self>;
 }
 checked_impl!(CheckedDiv, checked_div, u8);
 checked_impl!(CheckedDiv, checked_div, u16);
 checked_impl!(CheckedDiv, checked_div, u32);
 checked_impl!(CheckedDiv, checked_div, u64);
 checked_impl!(CheckedDiv, checked_div, usize);
 checked_impl!(CheckedDiv, checked_div, i8);
 checked_impl!(CheckedDiv, checked_div, i16);
 checked_impl!(CheckedDiv, checked_div, i32);
 checked_impl!(CheckedDiv, checked_div, i64);
 checked_impl!(CheckedDiv, checked_div, isize);
--- a/traits/src/ops/mod.rs
+++ b/traits/src/ops/mod.rs
@ -1,5 +1,3 @@
 pub mod checked;
 pub mod inv;
 pub mod mul_add;
 pub mod saturating;
 pub mod checked;
 pub mod wrapping;
--- a/traits/src/ops/saturating.rs
+++ b/traits/src/ops/saturating.rs
@ -26,5 +26,3 @@ macro_rules! saturating_impl {
 }
 saturating_impl!(Saturating for isize usize i8 u8 i16 u16 i32 u32 i64 u64);
 #[cfg(has_i128)]
 saturating_impl!(Saturating for i128 u128);
--- a/traits/src/ops/wrapping.rs
+++ b/traits/src/ops/wrapping.rs
@ -0,0 +1,127 @@
 use std::ops::{Add, Sub, Mul};
 use std::num::Wrapping;
 macro_rules! wrapping_impl {
    ($trait_name:ident, $method:ident, $t:ty) => {
        impl $trait_name for $t {
            #[inline]
            fn $method(&self, v: &Self) -> Self {
                <$t>::$method(*self, *v)
            }
        }
    };
    ($trait_name:ident, $method:ident, $t:ty, $rhs:ty) => {
        impl $trait_name<$rhs> for $t {
            #[inline]
            fn $method(&self, v: &$rhs) -> Self {
                <$t>::$method(*self, *v)
            }
        }
    }
 }
 /// Performs addition that wraps around on overflow.
 pub trait WrappingAdd: Sized + Add<Self, Output=Self> {
    /// Wrapping (modular) addition. Computes `self + other`, wrapping around at the boundary of
    /// the type.
    fn wrapping_add(&self, v: &Self) -> Self;
 }
 wrapping_impl!(WrappingAdd, wrapping_add, u8);
 wrapping_impl!(WrappingAdd, wrapping_add, u16);
 wrapping_impl!(WrappingAdd, wrapping_add, u32);
 wrapping_impl!(WrappingAdd, wrapping_add, u64);
 wrapping_impl!(WrappingAdd, wrapping_add, usize);
 wrapping_impl!(WrappingAdd, wrapping_add, i8);
 wrapping_impl!(WrappingAdd, wrapping_add, i16);
 wrapping_impl!(WrappingAdd, wrapping_add, i32);
 wrapping_impl!(WrappingAdd, wrapping_add, i64);
 wrapping_impl!(WrappingAdd, wrapping_add, isize);
 /// Performs subtraction that wraps around on overflow.
 pub trait WrappingSub: Sized + Sub<Self, Output=Self> {
    /// Wrapping (modular) subtraction. Computes `self - other`, wrapping around at the boundary
    /// of the type.
    fn wrapping_sub(&self, v: &Self) -> Self;
 }
 wrapping_impl!(WrappingSub, wrapping_sub, u8);
 wrapping_impl!(WrappingSub, wrapping_sub, u16);
 wrapping_impl!(WrappingSub, wrapping_sub, u32);
 wrapping_impl!(WrappingSub, wrapping_sub, u64);
 wrapping_impl!(WrappingSub, wrapping_sub, usize);
 wrapping_impl!(WrappingSub, wrapping_sub, i8);
 wrapping_impl!(WrappingSub, wrapping_sub, i16);
 wrapping_impl!(WrappingSub, wrapping_sub, i32);
 wrapping_impl!(WrappingSub, wrapping_sub, i64);
 wrapping_impl!(WrappingSub, wrapping_sub, isize);
 /// Performs multiplication that wraps around on overflow.
 pub trait WrappingMul: Sized + Mul<Self, Output=Self> {
    /// Wrapping (modular) multiplication. Computes `self * other`, wrapping around at the boundary
    /// of the type.
    fn wrapping_mul(&self, v: &Self) -> Self;
 }
 wrapping_impl!(WrappingMul, wrapping_mul, u8);
 wrapping_impl!(WrappingMul, wrapping_mul, u16);
 wrapping_impl!(WrappingMul, wrapping_mul, u32);
 wrapping_impl!(WrappingMul, wrapping_mul, u64);
 wrapping_impl!(WrappingMul, wrapping_mul, usize);
 wrapping_impl!(WrappingMul, wrapping_mul, i8);
 wrapping_impl!(WrappingMul, wrapping_mul, i16);
 wrapping_impl!(WrappingMul, wrapping_mul, i32);
 wrapping_impl!(WrappingMul, wrapping_mul, i64);
 wrapping_impl!(WrappingMul, wrapping_mul, isize);
 // Well this is a bit funny, but all the more appropriate.
 impl<T: WrappingAdd> WrappingAdd for Wrapping<T> where Wrapping<T>: Add<Output = Wrapping<T>> {
    fn wrapping_add(&self, v: &Self) -> Self {
        Wrapping(self.0.wrapping_add(&v.0))
    }
 }
 impl<T: WrappingSub> WrappingSub for Wrapping<T> where Wrapping<T>: Sub<Output = Wrapping<T>> {
    fn wrapping_sub(&self, v: &Self) -> Self {
        Wrapping(self.0.wrapping_sub(&v.0))
    }
 }
 impl<T: WrappingMul> WrappingMul for Wrapping<T> where Wrapping<T>: Mul<Output = Wrapping<T>> {
    fn wrapping_mul(&self, v: &Self) -> Self {
        Wrapping(self.0.wrapping_mul(&v.0))
    }
 }
 #[test]
 fn test_wrapping_traits() {
    fn wrapping_add<T: WrappingAdd>(a: T, b: T) -> T { a.wrapping_add(&b) }
    fn wrapping_sub<T: WrappingSub>(a: T, b: T) -> T { a.wrapping_sub(&b) }
    fn wrapping_mul<T: WrappingMul>(a: T, b: T) -> T { a.wrapping_mul(&b) }
    assert_eq!(wrapping_add(255, 1), 0u8);
    assert_eq!(wrapping_sub(0, 1), 255u8);
    assert_eq!(wrapping_mul(255, 2), 254u8);
    assert_eq!(wrapping_add(255, 1), (Wrapping(255u8) + Wrapping(1u8)).0);
    assert_eq!(wrapping_sub(0, 1), (Wrapping(0u8) - Wrapping(1u8)).0);
    assert_eq!(wrapping_mul(255, 2), (Wrapping(255u8) * Wrapping(2u8)).0);
 }
 #[test]
 fn wrapping_is_wrappingadd() {
    fn require_wrappingadd<T: WrappingAdd>(_: &T) {}
    require_wrappingadd(&Wrapping(42));
 }
 #[test]
 fn wrapping_is_wrappingsub() {
    fn require_wrappingsub<T: WrappingSub>(_: &T) {}
    require_wrappingsub(&Wrapping(42));
 }
 #[test]
 fn wrapping_is_wrappingmul() {
    fn require_wrappingmul<T: WrappingMul>(_: &T) {}
    require_wrappingmul(&Wrapping(42));
 }
--- a/traits/src/pow.rs
+++ b/traits/src/pow.rs
@ -0,0 +1,73 @@
 use std::ops::Mul;
 use {One, CheckedMul};
 /// Raises a value to the power of exp, using exponentiation by squaring.
 ///
 /// # Example
 ///
 /// ```rust
 /// use num_traits::pow;
 ///
 /// assert_eq!(pow(2i8, 4), 16);
 /// assert_eq!(pow(6u8, 3), 216);
 /// ```
 #[inline]
 pub fn pow<T: Clone + One + Mul<T, Output = T>>(mut base: T, mut exp: usize) -> T {
    if exp == 0 { return T::one() }
    while exp & 1 == 0 {
        base = base.clone() * base;
        exp >>= 1;
    }
    if exp == 1 { return base }
    let mut acc = base.clone();
    while exp > 1 {
        exp >>= 1;
        base = base.clone() * base;
        if exp & 1 == 1 {
            acc = acc * base.clone();
        }
    }
    acc
 }
 /// Raises a value to the power of exp, returning `None` if an overflow occurred.
 ///
 /// Otherwise same as the `pow` function.
 ///
 /// # Example
 ///
 /// ```rust
 /// use num_traits::checked_pow;
 ///
 /// assert_eq!(checked_pow(2i8, 4), Some(16));
 /// assert_eq!(checked_pow(7i8, 8), None);
 /// assert_eq!(checked_pow(7u32, 8), Some(5_764_801));
 /// ```
 #[inline]
 pub fn checked_pow<T: Clone + One + CheckedMul>(mut base: T, mut exp: usize) -> Option<T> {
    if exp == 0 { return Some(T::one()) }
    macro_rules! optry {
        ( $ expr : expr ) => {
            if let Some(val) = $expr { val } else { return None }
        }
    }
    while exp & 1 == 0 {
        base = optry!(base.checked_mul(&base));
        exp >>= 1;
    }
    if exp == 1 { return Some(base) }
    let mut acc = base.clone();
    while exp > 1 {
        exp >>= 1;
        base = optry!(base.checked_mul(&base));
        if exp & 1 == 1 {
            acc = optry!(acc.checked_mul(&base));
        }
    }
    Some(acc)
 }
--- a/traits/src/sign.rs
+++ b/traits/src/sign.rs
@ -1,7 +1,7 @@
-use core::num::Wrapping;
+use std::ops::Neg;
-use core::ops::Neg;
+use std::{f32, f64};
 use std::num::Wrapping;
 use float::FloatCore;
 use Num;
 /// Useful functions for signed numbers (i.e. numbers that can be negative).
@ -74,12 +74,7 @@ macro_rules! signed_impl {
 signed_impl!(isize i8 i16 i32 i64);
-#[cfg(has_i128)]
+impl<T: Signed> Signed for Wrapping<T> where Wrapping<T>: Num + Neg<Output=Wrapping<T>>
 signed_impl!(i128);
 impl<T: Signed> Signed for Wrapping<T>
 where
    Wrapping<T>: Num + Neg<Output = Wrapping<T>>,
 {
    #[inline]
    fn abs(&self) -> Self {
@ -97,35 +92,28 @@ where
    }
    #[inline]
-    fn is_positive(&self) -> bool {
+    fn is_positive(&self) -> bool { self.0.is_positive() }
        self.0.is_positive()
    }
    #[inline]
-    fn is_negative(&self) -> bool {
+    fn is_negative(&self) -> bool { self.0.is_negative() }
        self.0.is_negative()
    }
 }
 macro_rules! signed_float_impl {
-    ($t:ty) => {
+    ($t:ty, $nan:expr, $inf:expr, $neg_inf:expr) => {
        impl Signed for $t {
            /// Computes the absolute value. Returns `NAN` if the number is `NAN`.
            #[inline]
            fn abs(&self) -> $t {
-                FloatCore::abs(*self)
+                <$t>::abs(*self)
            }
            /// The positive difference of two numbers. Returns `0.0` if the number is
            /// less than or equal to `other`, otherwise the difference between`self`
            /// and `other` is returned.
            #[inline]
            #[allow(deprecated)]
            fn abs_sub(&self, other: &$t) -> $t {
-                if *self <= *other {
+                <$t>::abs_sub(*self, *other)
                    0.
                } else {
                    *self - *other
                }
            }
            /// # Returns
@ -135,26 +123,22 @@ macro_rules! signed_float_impl {
            /// - `NAN` if the number is NaN
            #[inline]
            fn signum(&self) -> $t {
-                FloatCore::signum(*self)
+                <$t>::signum(*self)
            }
            /// Returns `true` if the number is positive, including `+0.0` and `INFINITY`
            #[inline]
-            fn is_positive(&self) -> bool {
+            fn is_positive(&self) -> bool { *self > 0.0 || (1.0 / *self) == $inf }
                FloatCore::is_sign_positive(*self)
            }
            /// Returns `true` if the number is negative, including `-0.0` and `NEG_INFINITY`
            #[inline]
-            fn is_negative(&self) -> bool {
+            fn is_negative(&self) -> bool { *self < 0.0 || (1.0 / *self) == $neg_inf }
                FloatCore::is_sign_negative(*self)
        }
    }
    };
 }
-signed_float_impl!(f32);
+signed_float_impl!(f32, f32::NAN, f32::INFINITY, f32::NEG_INFINITY);
-signed_float_impl!(f64);
+signed_float_impl!(f64, f64::NAN, f64::INFINITY, f64::NEG_INFINITY);
 /// Computes the absolute value.
 ///
@ -188,10 +172,7 @@ pub fn abs_sub<T: Signed>(x: T, y: T) -> T {
 /// * `0` if the number is zero
 /// * `1` if the number is positive
 /// * `-1` if the number is negative
-#[inline(always)]
+#[inline(always)] pub fn signum<T: Signed>(value: T) -> T { value.signum() }
 pub fn signum<T: Signed>(value: T) -> T {
    value.signum()
 }
 /// A trait for values which cannot be negative
 pub trait Unsigned: Num {}
@ -203,8 +184,6 @@ macro_rules! empty_trait_impl {
 }
 empty_trait_impl!(Unsigned for usize u8 u16 u32 u64);
 #[cfg(has_i128)]
 empty_trait_impl!(Unsigned for u128);
 impl<T: Unsigned> Unsigned for Wrapping<T> where Wrapping<T>: Num {}
		`@ -0,0 +1 @@`
							`<meta http-equiv=refresh content=0;url=num/index.html>`