Merge #99

99: Revive Float+Real in no_std thanks to libm r=cuviper a=yoanlcq

Greetings,

This is a hopeful fix for #75.  
Basically: Add `libm` as an optional dependency, and handle three possible cases depending on which features are enabled:
- std and libm: std is used;
- std and not libm: std is used;
- libm and not std: libm and FloatCore are used.

It was briefly mentioned that `libm` wasn't ready yet, but this was months ago, and I believe it is better not to wait for too long.  
If anything, bugs in `libm` should be fixed in `libm`; `num-traits` is only delegating its implementations to it; not to mention that the more `libm` is used, the likelier issues are to be found and hopefully fixed.

Thanks in advance!

Co-authored-by: Yoan Lecoq <yoanlecoq.io@gmail.com>
Co-authored-by: Josh Stone <cuviper@gmail.com>

.travis.yml

@@ -1,20 +1,52 @@
 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
-sudo: false
 script:
   - cargo build --verbose
   - ./ci/test_full.sh
+matrix:
+  include:
+    # i586 presents floating point challenges for lack of SSE/SSE2
+    - name: "i586"
+      rust: stable
+      env: TARGET=i586-unknown-linux-gnu
+      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
 branches:
   only:
     - master
-    - num-traits-0.1.x
     - next
     - staging
     - trying

Cargo.toml

@@ -4,15 +4,25 @@ description = "Numeric traits for generic mathematics"
 documentation = "https://docs.rs/num-traits"
 homepage = "https://github.com/rust-num/num-traits"
 keywords = ["mathematics", "numerics"]
-categories = [ "algorithms", "science" ]
+categories = ["algorithms", "science", "no-std"]
 license = "MIT/Apache-2.0"
 repository = "https://github.com/rust-num/num-traits"
 name = "num-traits"
-version = "0.1.43"
+version = "0.2.8"
 readme = "README.md"
+build = "build.rs"
+exclude = ["/ci/*", "/.travis.yml", "/bors.toml"]
 
-[lib]
-doctest = false # multiple rlib candidates for `num_traits` found
+[package.metadata.docs.rs]
+features = ["std"]
 
-[dependencies.num-traits]
-version = "0.2.0"
+[dependencies]
+libm = { version = "0.1.4", optional = true }
+
+[features]
+default = ["std"]
+std = []
+i128 = []
+
+[build-dependencies]
+autocfg = "0.1.3"

README.md

@@ -2,20 +2,18 @@
 
 [![crate](https://img.shields.io/crates/v/num-traits.svg)](https://crates.io/crates/num-traits)
 [![documentation](https://docs.rs/num-traits/badge.svg)](https://docs.rs/num-traits)
+![minimum rustc 1.8](https://img.shields.io/badge/rustc-1.8+-red.svg)
 [![Travis status](https://travis-ci.org/rust-num/num-traits.svg?branch=master)](https://travis-ci.org/rust-num/num-traits)
 
 Numeric traits for generic mathematics in Rust.
 
-This version of the crate only exists to re-export compatible
-items from `num-traits` 0.2.  Please consider updating!
-
 ## Usage
 
 Add this to your `Cargo.toml`:
 
 ```toml
 [dependencies]
-num-traits = "0.1"
+num-traits = "0.2"
 ```
 
 and this to your crate root:
@@ -24,6 +22,29 @@ and this to your crate root:
 extern crate num_traits;
 ```
 
+## 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).

RELEASES.md

@@ -1,8 +1,116 @@
-# Release 0.2.0
+# Release 0.2.8 (2019-05-21)
 
-- **breaking change**: There is now a `std` feature, enabled by default, along
+- [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.
+  `#![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]).
@@ -10,12 +118,17 @@
 **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
 
-- All items are now re-exported from num-traits 0.2 for compatibility.
+# Release 0.1.43 (2018-02-06)
 
-# Release 0.1.42
+- 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].

build.rs

@@ -0,0 +1,14 @@
+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!());
+}

ci/rustup.sh

@@ -5,8 +5,7 @@
 set -ex
 
 export TRAVIS_RUST_VERSION
-for TRAVIS_RUST_VERSION in 1.8.0 stable beta nightly; do
+for TRAVIS_RUST_VERSION in 1.8.0 1.15.0 1.20.0 stable beta nightly; do
     run="rustup run $TRAVIS_RUST_VERSION"
-    $run cargo build --verbose
     $run $PWD/ci/test_full.sh
 done

ci/test_full.sh

@@ -4,8 +4,24 @@ set -ex
 
 echo Testing num-traits on rustc ${TRAVIS_RUST_VERSION}
 
-# num-integer should build and test everywhere.
+# num-traits should build and test everywhere.
 cargo build --verbose
 cargo test --verbose
 
-# We have no features to test...
+# test `no_std`
+cargo build --verbose --no-default-features
+cargo test --verbose --no-default-features
+
+if [[ "$TRAVIS_RUST_VERSION" =~ ^(nightly|beta|stable)$ ]]; then
+    # test `i128`
+    cargo build --verbose --features=i128
+    cargo test --verbose --features=i128
+
+    # test with std and libm (libm build fails on Rust 1.26 and earlier)
+    cargo build --verbose --features "libm"
+    cargo test --verbose --features "libm"
+
+    # test `no_std` with libm (libm build fails on Rust 1.26 and earlier)
+    cargo build --verbose --no-default-features --features "libm"
+    cargo test --verbose --no-default-features --features "libm"
+fi

src/bounds.rs

@@ -0,0 +1,127 @@
+use core::num::Wrapping;
+use core::{f32, f64};
+#[cfg(has_i128)]
+use core::{i128, u128};
+use core::{i16, i32, i64, i8, isize};
+use core::{u16, u32, u64, u8, usize};
+
+/// Numbers which have upper and lower bounds
+pub trait Bounded {
+    // FIXME (#5527): These should be associated constants
+    /// returns the smallest finite number this type can represent
+    fn min_value() -> Self;
+    /// returns the largest finite number this type can represent
+    fn max_value() -> Self;
+}
+
+macro_rules! bounded_impl {
+    ($t:ty, $min:expr, $max:expr) => {
+        impl Bounded for $t {
+            #[inline]
+            fn min_value() -> $t {
+                $min
+            }
+
+            #[inline]
+            fn max_value() -> $t {
+                $max
+            }
+        }
+    };
+}
+
+bounded_impl!(usize, usize::MIN, usize::MAX);
+bounded_impl!(u8, u8::MIN, u8::MAX);
+bounded_impl!(u16, u16::MIN, u16::MAX);
+bounded_impl!(u32, u32::MIN, u32::MAX);
+bounded_impl!(u64, u64::MIN, u64::MAX);
+#[cfg(has_i128)]
+bounded_impl!(u128, u128::MIN, u128::MAX);
+
+bounded_impl!(isize, isize::MIN, isize::MAX);
+bounded_impl!(i8, i8::MIN, i8::MAX);
+bounded_impl!(i16, i16::MIN, i16::MAX);
+bounded_impl!(i32, i32::MIN, i32::MAX);
+bounded_impl!(i64, i64::MIN, i64::MAX);
+#[cfg(has_i128)]
+bounded_impl!(i128, i128::MIN, i128::MAX);
+
+impl<T: Bounded> Bounded for Wrapping<T> {
+    fn min_value() -> Self {
+        Wrapping(T::min_value())
+    }
+    fn max_value() -> Self {
+        Wrapping(T::max_value())
+    }
+}
+
+bounded_impl!(f32, f32::MIN, f32::MAX);
+
+macro_rules! for_each_tuple_ {
+    ( $m:ident !! ) => (
+        $m! { }
+    );
+    ( $m:ident !! $h:ident, $($t:ident,)* ) => (
+        $m! { $h $($t)* }
+        for_each_tuple_! { $m !! $($t,)* }
+    );
+}
+macro_rules! for_each_tuple {
+    ($m:ident) => {
+        for_each_tuple_! { $m !! A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, }
+    };
+}
+
+macro_rules! bounded_tuple {
+    ( $($name:ident)* ) => (
+        impl<$($name: Bounded,)*> Bounded for ($($name,)*) {
+            #[inline]
+            fn min_value() -> Self {
+                ($($name::min_value(),)*)
+            }
+            #[inline]
+            fn max_value() -> Self {
+                ($($name::max_value(),)*)
+            }
+        }
+    );
+}
+
+for_each_tuple!(bounded_tuple);
+bounded_impl!(f64, f64::MIN, f64::MAX);
+
+#[test]
+fn wrapping_bounded() {
+    macro_rules! test_wrapping_bounded {
+        ($($t:ty)+) => {
+            $(
+                assert_eq!(<Wrapping<$t> as Bounded>::min_value().0, <$t>::min_value());
+                assert_eq!(<Wrapping<$t> as Bounded>::max_value().0, <$t>::max_value());
+            )+
+        };
+    }
+
+    test_wrapping_bounded!(usize u8 u16 u32 u64 isize i8 i16 i32 i64);
+}
+
+#[cfg(has_i128)]
+#[test]
+fn wrapping_bounded_i128() {
+    macro_rules! test_wrapping_bounded {
+        ($($t:ty)+) => {
+            $(
+                assert_eq!(<Wrapping<$t> as Bounded>::min_value().0, <$t>::min_value());
+                assert_eq!(<Wrapping<$t> as Bounded>::max_value().0, <$t>::max_value());
+            )+
+        };
+    }
+
+    test_wrapping_bounded!(u128 i128);
+}
+
+#[test]
+fn wrapping_is_bounded() {
+    fn require_bounded<T: Bounded>(_: &T) {}
+    require_bounded(&Wrapping(42_u32));
+    require_bounded(&Wrapping(-42));
+}

src/cast.rs

@@ -0,0 +1,762 @@
+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 => {});

src/identities.rs

@@ -0,0 +1,207 @@
+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));
+}

src/int.rs

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

src/lib.rs

@@ -10,79 +10,563 @@
 
 //! Numeric traits for generic mathematics
 //!
-//! This version of the crate only exists to re-export compatible
-//! items from num-traits 0.2.  Please consider updating!
+//! ## Compatibility
+//!
+//! The `num-traits` crate is tested for rustc 1.8 and greater.
 
-#![doc(html_root_url = "https://docs.rs/num-traits/0.1")]
+#![doc(html_root_url = "https://docs.rs/num-traits/0.2")]
+#![deny(unconditional_recursion)]
+#![no_std]
+#[cfg(feature = "std")]
+extern crate std;
 
-extern crate num_traits;
+// Only `no_std` builds actually use `libm`.
+#[cfg(all(not(feature = "std"), feature = "libm"))]
+extern crate libm;
+
+use core::fmt;
+use core::num::Wrapping;
+use core::ops::{Add, Div, Mul, Rem, Sub};
+use core::ops::{AddAssign, DivAssign, MulAssign, RemAssign, SubAssign};
 
 pub use bounds::Bounded;
-pub use float::{Float, FloatConst};
-// pub use real::Real; // NOTE: Don't do this, it breaks `use num_traits::*;`.
-pub use identities::{Zero, One, zero, one};
-pub use ops::checked::{CheckedAdd, CheckedSub, CheckedMul, CheckedDiv, CheckedShl, CheckedShr};
-pub use ops::wrapping::{WrappingAdd, WrappingMul, WrappingSub};
-pub use ops::saturating::Saturating;
-pub use sign::{Signed, Unsigned, abs, abs_sub, signum};
-pub use cast::{AsPrimitive, FromPrimitive, ToPrimitive, NumCast, cast};
+#[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 pow::{pow, checked_pow};
+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;
 
-// Re-exports from num-traits 0.2!
+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;
 
-pub use num_traits::{Num, NumOps, NumRef, RefNum};
-pub use num_traits::{NumAssignOps, NumAssign, NumAssignRef};
-pub use num_traits::{FloatErrorKind, ParseFloatError};
-pub use num_traits::clamp;
+/// 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;
 
-// Note: the module structure is explicitly re-created, rather than re-exporting en masse,
-// so we won't expose any items that may be added later in the new version.
-
-pub mod identities {
-    pub use num_traits::identities::{Zero, One, zero, one};
+    /// 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>;
 }
 
-pub mod sign {
-    pub use num_traits::sign::{Signed, Unsigned, abs, abs_sub, signum};
+/// 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>
+{
 }
 
-pub mod ops {
-    pub mod saturating {
-        pub use num_traits::ops::saturating::Saturating;
-    }
+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>
+{
+}
 
-    pub mod checked {
-        pub use num_traits::ops::checked::{CheckedAdd, CheckedSub, CheckedMul, CheckedDiv,
-                                           CheckedShl, CheckedShr};
-    }
+/// 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> {}
 
-    pub mod wrapping {
-        pub use num_traits::ops::wrapping::{WrappingAdd, WrappingMul, WrappingSub};
+/// 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 $t {
+            type FromStrRadixErr = ::core::num::ParseIntError;
+            #[inline]
+            fn from_str_radix(s: &str, radix: u32)
+                              -> Result<Self, ::core::num::ParseIntError>
+            {
+                <$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)
     }
 }
 
-pub mod bounds {
-    pub use num_traits::bounds::Bounded;
+#[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,
 }
 
-pub mod float {
-    pub use num_traits::float::{Float, FloatConst};
+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)
+    }
 }
 
-pub mod real {
-    pub use num_traits::real::Real;
+// 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
+    }
 }
 
-pub mod cast {
-    pub use num_traits::cast::{AsPrimitive, FromPrimitive, ToPrimitive, NumCast, cast};
+/// 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
+    }
 }
 
-pub mod int {
-    pub use num_traits::int::PrimInt;
+/// 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
+    }
 }
 
-pub mod pow {
-    pub use num_traits::pow::{pow, checked_pow};
+#[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)

src/macros.rs

@@ -0,0 +1,37 @@
+// 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
+            }
+        )*};
+}

src/ops/checked.rs

@@ -0,0 +1,277 @@
+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);

src/ops/inv.rs

@@ -0,0 +1,47 @@
+/// 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
+    }
+}

src/ops/mod.rs

@@ -0,0 +1,5 @@
+pub mod checked;
+pub mod inv;
+pub mod mul_add;
+pub mod saturating;
+pub mod wrapping;

src/ops/mul_add.rs

@@ -0,0 +1,151 @@
+/// 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);
+    }
+}

src/ops/saturating.rs

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

src/ops/wrapping.rs

@@ -0,0 +1,272 @@
+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));
+}

src/pow.rs

@@ -0,0 +1,262 @@
+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)
+}

src/real.rs

@@ -0,0 +1,834 @@
+#![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;
+    }
+}

src/sign.rs

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

tests/cast.rs

@@ -0,0 +1,396 @@
+//! 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);
+}