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

@@ -1,13 +1,46 @@
 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

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 = "0.2.2"
+version = "0.2.8"
 readme = "README.md"
+build = "build.rs"
+exclude = ["/ci/*", "/.travis.yml", "/bors.toml"]
+
+[package.metadata.docs.rs]
+features = ["std"]
 
 [dependencies]
+libm = { version = "0.1.4", optional = true }
 
 [features]
 default = ["std"]
 std = []
+i128 = []
+
+[build-dependencies]
+autocfg = "0.1.3"

README.md

@@ -25,16 +25,25 @@ 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`:
+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 `std` is enabled. The
-`FloatCore` trait is always available.
+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
 

RELEASES.md

@@ -1,4 +1,81 @@
-# Release 0.2.2
+# Release 0.2.8 (2019-05-21)
+
+- [Fixed feature detection on `no_std` targets][116].
+
+**Contributors**: @cuviper
+
+[116]: https://github.com/rust-num/num-traits/pull/116
+
+# Release 0.2.7 (2019-05-20)
+
+- [Documented when `CheckedShl` and `CheckedShr` return `None`][90].
+- [The new `Zero::set_zero` and `One::set_one`][104] will set values to their
+  identities in place, possibly optimized better than direct assignment.
+- [Documented general features and intentions of `PrimInt`][108].
+
+**Contributors**: @cuviper, @dvdhrm, @ignatenkobrain, @lcnr, @samueltardieu
+
+[90]: https://github.com/rust-num/num-traits/pull/90
+[104]: https://github.com/rust-num/num-traits/pull/104
+[108]: https://github.com/rust-num/num-traits/pull/108
+
+# Release 0.2.6 (2018-09-13)
+
+- [Documented that `pow(0, 0)` returns `1`][79].  Mathematically, this is not
+  strictly defined, but the current behavior is a pragmatic choice that has
+  precedent in Rust `core` for the primitives and in many other languages.
+- [The new `WrappingShl` and `WrappingShr` traits][81] will wrap the shift count
+  if it exceeds the bit size of the type.
+
+**Contributors**: @cuviper, @edmccard, @meltinglava
+
+[79]: https://github.com/rust-num/num-traits/pull/79
+[81]: https://github.com/rust-num/num-traits/pull/81
+
+# Release 0.2.5 (2018-06-20)
+
+- [Documentation for `mul_add` now clarifies that it's not always faster.][70]
+- [The default methods in `FromPrimitive` and `ToPrimitive` are more robust.][73]
+
+**Contributors**: @cuviper, @frewsxcv
+
+[70]: https://github.com/rust-num/num-traits/pull/70
+[73]: https://github.com/rust-num/num-traits/pull/73
+
+# Release 0.2.4 (2018-05-11)
+
+- [Support for 128-bit integers is now automatically detected and enabled.][69]
+  Setting the `i128` crate feature now causes the build script to panic if such
+  support is not detected.
+
+**Contributors**: @cuviper
+
+[69]: https://github.com/rust-num/num-traits/pull/69
+
+# Release 0.2.3 (2018-05-10)
+
+- [The new `CheckedNeg` and `CheckedRem` traits][63] perform checked `Neg` and
+  `Rem`, returning `Some(output)` or `None` on overflow.
+- [The `no_std` implementation of `FloatCore::to_degrees` for `f32`][61] now
+  uses a constant for greater accuracy, mirroring [rust#47919].  (With `std` it
+  just calls the inherent `f32::to_degrees` in the standard library.)
+- [The new `MulAdd` and `MulAddAssign` traits][59] perform a fused multiply-
+  add.  For integer types this is just a convenience, but for floating point
+  types this produces a more accurate result than the separate operations.
+- [All applicable traits are now implemented for 128-bit integers][60] starting
+  with Rust 1.26, enabled by the new `i128` crate feature.  The `FromPrimitive`
+  and `ToPrimitive` traits now also have corresponding 128-bit methods, which
+  default to converting via 64-bit integers for compatibility.
+
+**Contributors**: @cuviper, @LEXUGE, @regexident, @vks
+
+[59]: https://github.com/rust-num/num-traits/pull/59
+[60]: https://github.com/rust-num/num-traits/pull/60
+[61]: https://github.com/rust-num/num-traits/pull/61
+[63]: https://github.com/rust-num/num-traits/pull/63
+[rust#47919]: https://github.com/rust-lang/rust/pull/47919
+
+# Release 0.2.2 (2018-03-18)
 
 - [Casting from floating point to integers now returns `None` on overflow][52],
   avoiding [rustc's undefined behavior][rust-10184]. This applies to the `cast`
@@ -10,7 +87,7 @@
 [rust-10184]: https://github.com/rust-lang/rust/issues/10184
 
 
-# Release 0.2.1
+# 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.
@@ -29,7 +106,7 @@
 [41]: https://github.com/rust-num/num-traits/pull/41
 
 
-# Release 0.2.0
+# 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
@@ -44,14 +121,14 @@
 [30]: https://github.com/rust-num/num-traits/pull/30
 
 
-# Release 0.1.43
+# Release 0.1.43 (2018-02-06)
 
 - All items are now [re-exported from num-traits 0.2][31] for compatibility.
 
 [31]: https://github.com/rust-num/num-traits/pull/31
 
 
-# Release 0.1.42
+# 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

@@ -11,3 +11,17 @@ cargo test --verbose
 # test `no_std`
 cargo build --verbose --no-default-features
 cargo test --verbose --no-default-features
+
+if [[ "$TRAVIS_RUST_VERSION" =~ ^(nightly|beta|stable)$ ]]; then
+    # test `i128`
+    cargo build --verbose --features=i128
+    cargo test --verbose --features=i128
+
+    # test with std and libm (libm build fails on Rust 1.26 and earlier)
+    cargo build --verbose --features "libm"
+    cargo test --verbose --features "libm"
+
+    # test `no_std` with libm (libm build fails on Rust 1.26 and earlier)
+    cargo build --verbose --no-default-features --features "libm"
+    cargo test --verbose --no-default-features --features "libm"
+fi

src/bounds.rs

@@ -1,7 +1,9 @@
-use core::{usize, u8, u16, u32, u64};
-use core::{isize, i8, i16, i32, i64};
-use core::{f32, f64};
 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 {
@@ -16,29 +18,41 @@ macro_rules! bounded_impl {
     ($t:ty, $min:expr, $max:expr) => {
         impl Bounded for $t {
             #[inline]
-            fn min_value() -> $t { $min }
+            fn min_value() -> $t {
+                $min
+            }
 
             #[inline]
-            fn max_value() -> $t { $max }
+            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);
+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);
+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()) }
+    fn min_value() -> Self {
+        Wrapping(T::min_value())
+    }
+    fn max_value() -> Self {
+        Wrapping(T::max_value())
+    }
 }
 
 bounded_impl!(f32, f32::MIN, f32::MAX);
@@ -53,9 +67,9 @@ macro_rules! for_each_tuple_ {
     );
 }
 macro_rules! for_each_tuple {
-    ( $m:ident ) => (
+    ($m:ident) => {
         for_each_tuple_! { $m !! A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, }
-    );
+    };
 }
 
 macro_rules! bounded_tuple {
@@ -76,14 +90,13 @@ macro_rules! bounded_tuple {
 for_each_tuple!(bounded_tuple);
 bounded_impl!(f64, f64::MIN, f64::MAX);
 
-
 #[test]
 fn wrapping_bounded() {
     macro_rules! test_wrapping_bounded {
         ($($t:ty)+) => {
             $(
-                assert_eq!(Wrapping::<$t>::min_value().0, <$t>::min_value());
-                assert_eq!(Wrapping::<$t>::max_value().0, <$t>::max_value());
+                assert_eq!(<Wrapping<$t> as Bounded>::min_value().0, <$t>::min_value());
+                assert_eq!(<Wrapping<$t> as Bounded>::max_value().0, <$t>::max_value());
             )+
         };
     }
@@ -91,6 +104,21 @@ fn wrapping_bounded() {
     test_wrapping_bounded!(usize u8 u16 u32 u64 isize i8 i16 i32 i64);
 }
 
+#[cfg(has_i128)]
+#[test]
+fn wrapping_bounded_i128() {
+    macro_rules! test_wrapping_bounded {
+        ($($t:ty)+) => {
+            $(
+                assert_eq!(<Wrapping<$t> as Bounded>::min_value().0, <$t>::min_value());
+                assert_eq!(<Wrapping<$t> as Bounded>::max_value().0, <$t>::max_value());
+            )+
+        };
+    }
+
+    test_wrapping_bounded!(u128 i128);
+}
+
 #[test]
 fn wrapping_is_bounded() {
     fn require_bounded<T: Bounded>(_: &T) {}

src/float.rs

@@ -1,12 +1,15 @@
 use core::mem;
-use core::ops::Neg;
 use core::num::FpCategory;
+use core::ops::Neg;
 
 use core::f32;
 use core::f64;
 
 use {Num, NumCast, ToPrimitive};
 
+#[cfg(all(not(feature = "std"), feature = "libm"))]
+use libm::{F32Ext, F64Ext};
+
 /// Generic trait for floating point numbers that works with `no_std`.
 ///
 /// This trait implements a subset of the `Float` trait.
@@ -586,7 +589,11 @@ pub trait FloatCore: Num + NumCast + Neg<Output = Self> + PartialOrd + Copy {
         if other.is_nan() {
             return self;
         }
-        if self < other { self } else { other }
+        if self < other {
+            self
+        } else {
+            other
+        }
     }
 
     /// Returns the maximum of the two numbers.
@@ -616,7 +623,11 @@ pub trait FloatCore: Num + NumCast + Neg<Output = Self> + PartialOrd + Copy {
         if other.is_nan() {
             return self;
         }
-        if self > other { self } else { other }
+        if self > other {
+            self
+        } else {
+            other
+        }
     }
 
     /// Returns the reciprocal (multiplicative inverse) of the number.
@@ -758,6 +769,8 @@ impl FloatCore for f32 {
         const EXP_MASK: u32 = 0x7f800000;
         const MAN_MASK: u32 = 0x007fffff;
 
+        // Safety: this identical to the implementation of f32::to_bits(),
+        // which is only available starting at Rust 1.20
         let bits: u32 = unsafe { mem::transmute(self) };
         match (bits & MAN_MASK, bits & EXP_MASK) {
             (0, 0) => FpCategory::Zero,
@@ -771,7 +784,9 @@ impl FloatCore for f32 {
     #[inline]
     #[cfg(not(feature = "std"))]
     fn to_degrees(self) -> Self {
-        self * (180.0 / f32::consts::PI)
+        // Use a constant for better precision.
+        const PIS_IN_180: f32 = 57.2957795130823208767981548141051703_f32;
+        self * PIS_IN_180
     }
 
     #[inline]
@@ -828,6 +843,8 @@ impl FloatCore for f64 {
         const EXP_MASK: u64 = 0x7ff0000000000000;
         const MAN_MASK: u64 = 0x000fffffffffffff;
 
+        // Safety: this identical to the implementation of f64::to_bits(),
+        // which is only available starting at Rust 1.20
         let bits: u64 = unsafe { mem::transmute(self) };
         match (bits & MAN_MASK, bits & EXP_MASK) {
             (0, 0) => FpCategory::Zero,
@@ -841,6 +858,9 @@ impl FloatCore for f64 {
     #[inline]
     #[cfg(not(feature = "std"))]
     fn to_degrees(self) -> Self {
+        // The division here is correctly rounded with respect to the true
+        // value of 180/π. (This differs from f32, where a constant must be
+        // used to ensure a correctly rounded result.)
         self * (180.0 / f64::consts::PI)
     }
 
@@ -880,15 +900,9 @@ impl FloatCore for f64 {
 
 /// Generic trait for floating point numbers
 ///
-/// This trait is only available with the `std` feature.
-#[cfg(feature = "std")]
-pub trait Float
-    : Num
-    + Copy
-    + NumCast
-    + PartialOrd
-    + Neg<Output = Self>
-{
+/// This trait is only available with the `std` feature, or with the `libm` feature otherwise.
+#[cfg(any(feature = "std", feature = "libm"))]
+pub trait Float: Num + Copy + NumCast + PartialOrd + Neg<Output = Self> {
     /// Returns the `NaN` value.
     ///
     /// ```
@@ -1232,8 +1246,10 @@ pub trait Float
     fn is_sign_negative(self) -> bool;
 
     /// Fused multiply-add. Computes `(self * a) + b` with only one rounding
-    /// error. This produces a more accurate result with better performance than
-    /// a separate multiplication operation followed by an add.
+    /// 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::Float;
@@ -1770,7 +1786,6 @@ pub trait Float
     /// ```
     fn atanh(self) -> Self;
 
-
     /// Returns the mantissa, base 2 exponent, and sign as integers, respectively.
     /// The original number can be recovered by `sign * mantissa * 2 ^ exponent`.
     ///
@@ -1794,8 +1809,8 @@ pub trait Float
 }
 
 #[cfg(feature = "std")]
-macro_rules! float_impl {
-    ($T:ident $decode:ident) => (
+macro_rules! float_impl_std {
+    ($T:ident $decode:ident) => {
         impl Float for $T {
             constant! {
                 nan() -> $T::NAN;
@@ -1869,16 +1884,93 @@ macro_rules! float_impl {
                 Self::atanh(self) -> Self;
             }
         }
-    )
+    };
+}
+
+#[cfg(all(not(feature = "std"), feature = "libm"))]
+macro_rules! float_impl_libm {
+    ($T:ident $decode:ident $LibmImpl:ident) => {
+        impl Float for $T {
+            constant! {
+                nan() -> $T::NAN;
+                infinity() -> $T::INFINITY;
+                neg_infinity() -> $T::NEG_INFINITY;
+                neg_zero() -> -0.0;
+                min_value() -> $T::MIN;
+                min_positive_value() -> $T::MIN_POSITIVE;
+                epsilon() -> $T::EPSILON;
+                max_value() -> $T::MAX;
+            }
+
+            #[inline]
+            #[allow(deprecated)]
+            fn abs_sub(self, other: Self) -> Self {
+                <$T as $LibmImpl>::fdim(self, other)
+            }
+
+            #[inline]
+            fn integer_decode(self) -> (u64, i16, i8) {
+                $decode(self)
+            }
+
+            forward! {
+                FloatCore::is_nan(self) -> bool;
+                FloatCore::is_infinite(self) -> bool;
+                FloatCore::is_finite(self) -> bool;
+                FloatCore::is_normal(self) -> bool;
+                FloatCore::classify(self) -> FpCategory;
+                $LibmImpl::floor(self) -> Self;
+                $LibmImpl::ceil(self) -> Self;
+                $LibmImpl::round(self) -> Self;
+                $LibmImpl::trunc(self) -> Self;
+                $LibmImpl::fract(self) -> Self;
+                $LibmImpl::abs(self) -> Self;
+                FloatCore::signum(self) -> Self;
+                FloatCore::is_sign_positive(self) -> bool;
+                FloatCore::is_sign_negative(self) -> bool;
+                $LibmImpl::mul_add(self, a: Self, b: Self) -> Self;
+                FloatCore::recip(self) -> Self;
+                FloatCore::powi(self, n: i32) -> Self;
+                $LibmImpl::powf(self, n: Self) -> Self;
+                $LibmImpl::sqrt(self) -> Self;
+                $LibmImpl::exp(self) -> Self;
+                $LibmImpl::exp2(self) -> Self;
+                $LibmImpl::ln(self) -> Self;
+                $LibmImpl::log(self, base: Self) -> Self;
+                $LibmImpl::log2(self) -> Self;
+                $LibmImpl::log10(self) -> Self;
+                FloatCore::to_degrees(self) -> Self;
+                FloatCore::to_radians(self) -> Self;
+                FloatCore::max(self, other: Self) -> Self;
+                FloatCore::min(self, other: Self) -> Self;
+                $LibmImpl::cbrt(self) -> Self;
+                $LibmImpl::hypot(self, other: Self) -> Self;
+                $LibmImpl::sin(self) -> Self;
+                $LibmImpl::cos(self) -> Self;
+                $LibmImpl::tan(self) -> Self;
+                $LibmImpl::asin(self) -> Self;
+                $LibmImpl::acos(self) -> Self;
+                $LibmImpl::atan(self) -> Self;
+                $LibmImpl::atan2(self, other: Self) -> Self;
+                $LibmImpl::sin_cos(self) -> (Self, Self);
+                $LibmImpl::exp_m1(self) -> Self;
+                $LibmImpl::ln_1p(self) -> Self;
+                $LibmImpl::sinh(self) -> Self;
+                $LibmImpl::cosh(self) -> Self;
+                $LibmImpl::tanh(self) -> Self;
+                $LibmImpl::asinh(self) -> Self;
+                $LibmImpl::acosh(self) -> Self;
+                $LibmImpl::atanh(self) -> Self;
+            }
+        }
+    };
 }
 
 fn integer_decode_f32(f: f32) -> (u64, i16, i8) {
+    // Safety: this identical to the implementation of f32::to_bits(),
+    // which is only available starting at Rust 1.20
     let bits: u32 = unsafe { mem::transmute(f) };
-    let sign: i8 = if bits >> 31 == 0 {
-        1
-    } else {
-        -1
-    };
+    let sign: i8 = if bits >> 31 == 0 { 1 } else { -1 };
     let mut exponent: i16 = ((bits >> 23) & 0xff) as i16;
     let mantissa = if exponent == 0 {
         (bits & 0x7fffff) << 1
@@ -1891,12 +1983,10 @@ fn integer_decode_f32(f: f32) -> (u64, i16, i8) {
 }
 
 fn integer_decode_f64(f: f64) -> (u64, i16, i8) {
+    // Safety: this identical to the implementation of f64::to_bits(),
+    // which is only available starting at Rust 1.20
     let bits: u64 = unsafe { mem::transmute(f) };
-    let sign: i8 = if bits >> 63 == 0 {
-        1
-    } else {
-        -1
-    };
+    let sign: i8 = if bits >> 63 == 0 { 1 } else { -1 };
     let mut exponent: i16 = ((bits >> 52) & 0x7ff) as i16;
     let mantissa = if exponent == 0 {
         (bits & 0xfffffffffffff) << 1
@@ -1909,9 +1999,14 @@ fn integer_decode_f64(f: f64) -> (u64, i16, i8) {
 }
 
 #[cfg(feature = "std")]
-float_impl!(f32 integer_decode_f32);
+float_impl_std!(f32 integer_decode_f32);
 #[cfg(feature = "std")]
-float_impl!(f64 integer_decode_f64);
+float_impl_std!(f64 integer_decode_f64);
+
+#[cfg(all(not(feature = "std"), feature = "libm"))]
+float_impl_libm!(f32 integer_decode_f32 F32Ext);
+#[cfg(all(not(feature = "std"), feature = "libm"))]
+float_impl_libm!(f64 integer_decode_f64 F64Ext);
 
 macro_rules! float_const_impl {
     ($(#[$doc:meta] $constant:ident,)+) => (
@@ -1994,7 +2089,7 @@ mod tests {
         }
     }
 
-    #[cfg(feature = "std")]
+    #[cfg(any(feature = "std", feature = "libm"))]
     #[test]
     fn convert_deg_rad_std() {
         for &(deg, rad) in &DEG_RAD_PAIRS {
@@ -2008,4 +2103,17 @@ mod tests {
             assert!((Float::to_radians(deg) - rad).abs() < 1e-5);
         }
     }
+
+    #[test]
+    // This fails with the forwarded `std` implementation in Rust 1.8.
+    // To avoid the failure, the test is limited to `no_std` builds.
+    #[cfg(not(feature = "std"))]
+    fn to_degrees_rounding() {
+        use float::FloatCore;
+
+        assert_eq!(
+            FloatCore::to_degrees(1_f32),
+            57.2957795130823208767981548141051703
+        );
+    }
 }

src/identities.rs

@@ -1,25 +1,29 @@
-use core::ops::{Add, Mul};
 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`.
-    ///
-    /// # Laws
-    ///
-    /// ```{.text}
-    /// a + 0 = a       ∀ a ∈ Self
-    /// 0 + a = a       ∀ a ∈ Self
-    /// ```
-    ///
     /// # Purity
     ///
     /// This function should return the same result at all times regardless of
     /// external mutable state, for example values stored in TLS or in
     /// `static mut`s.
-    // FIXME (#5527): This should be an associated constant
+    // 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;
@@ -29,64 +33,87 @@ macro_rules! zero_impl {
     ($t:ty, $v:expr) => {
         impl Zero for $t {
             #[inline]
-            fn zero() -> $t { $v }
+            fn zero() -> $t {
+                $v
+            }
             #[inline]
-            fn is_zero(&self) -> bool { *self == $v }
+            fn is_zero(&self) -> bool {
+                *self == $v
+            }
         }
-    }
+    };
 }
 
-zero_impl!(usize, 0usize);
-zero_impl!(u8,    0u8);
-zero_impl!(u16,   0u16);
-zero_impl!(u32,   0u32);
-zero_impl!(u64,   0u64);
+zero_impl!(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, 0isize);
-zero_impl!(i8,    0i8);
-zero_impl!(i16,   0i16);
-zero_impl!(i32,   0i32);
-zero_impl!(i64,   0i64);
+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, 0.0f32);
-zero_impl!(f64, 0.0f64);
+zero_impl!(f32, 0.0);
+zero_impl!(f64, 0.0);
 
-impl<T: Zero> Zero for Wrapping<T> where Wrapping<T>: Add<Output=Wrapping<T>> {
+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`.
     ///
-    /// # Laws
-    ///
-    /// ```{.text}
-    /// a * 1 = a       ∀ a ∈ Self
-    /// 1 * a = a       ∀ a ∈ Self
-    /// ```
-    ///
     /// # Purity
     ///
     /// This function should return the same result at all times regardless of
     /// external mutable state, for example values stored in TLS or in
     /// `static mut`s.
-    // FIXME (#5527): This should be an associated constant
+    // 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 {
+    fn is_one(&self) -> bool
+    where
+        Self: PartialEq,
+    {
         *self == Self::one()
     }
 }
@@ -95,27 +122,44 @@ macro_rules! one_impl {
     ($t:ty, $v:expr) => {
         impl One for $t {
             #[inline]
-            fn one() -> $t { $v }
+            fn one() -> $t {
+                $v
+            }
+            #[inline]
+            fn is_one(&self) -> bool {
+                *self == $v
+            }
         }
-    }
+    };
 }
 
-one_impl!(usize, 1usize);
-one_impl!(u8,    1u8);
-one_impl!(u16,   1u16);
-one_impl!(u32,   1u32);
-one_impl!(u64,   1u64);
+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, 1isize);
-one_impl!(i8,    1i8);
-one_impl!(i16,   1i16);
-one_impl!(i32,   1i32);
-one_impl!(i64,   1i64);
+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, 1.0f32);
-one_impl!(f64, 1.0f64);
+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();
+    }
 
-impl<T: One> One for Wrapping<T> where Wrapping<T>: Mul<Output=Wrapping<T>> {
     fn one() -> Self {
         Wrapping(T::one())
     }
@@ -124,11 +168,16 @@ impl<T: One> One for Wrapping<T> where Wrapping<T>: Mul<Output=Wrapping<T>> {
 // Some helper functions provided for backwards compatibility.
 
 /// Returns the additive identity, `0`.
-#[inline(always)] pub fn zero<T: Zero>() -> T { Zero::zero() }
+#[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() }
-
+#[inline(always)]
+pub fn one<T: One>() -> T {
+    One::one()
+}
 
 #[test]
 fn wrapping_identities() {

src/int.rs

@@ -1,26 +1,55 @@
-use core::ops::{Not, BitAnd, BitOr, BitXor, Shl, Shr};
+use core::ops::{BitAnd, BitOr, BitXor, Not, Shl, Shr};
 
-use {Num, NumCast};
 use bounds::Bounded;
 use ops::checked::*;
 use ops::saturating::Saturating;
+use {Num, NumCast};
 
-pub trait PrimInt
-    : Sized
+/// 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
+    + 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>
+    + 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`.
@@ -168,10 +197,10 @@ pub trait PrimInt
     /// ```
     /// use num_traits::PrimInt;
     ///
-    /// let n = 0xFEDCBA9876543210i64;
-    /// let m = 0x000FEDCBA9876543i64;
+    /// let n = -8i8; // 0b11111000
+    /// let m = 62i8; // 0b00111110
     ///
-    /// assert_eq!(n.unsigned_shr(12), m);
+    /// assert_eq!(n.unsigned_shr(2), m);
     /// ```
     fn unsigned_shr(self, n: u32) -> Self;
 
@@ -278,7 +307,7 @@ pub trait PrimInt
 }
 
 macro_rules! prim_int_impl {
-    ($T:ty, $S:ty, $U:ty) => (
+    ($T:ty, $S:ty, $U:ty) => {
         impl PrimInt for $T {
             #[inline]
             fn count_ones(self) -> u32 {
@@ -360,17 +389,21 @@ macro_rules! prim_int_impl {
                 <$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);
+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);
+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

@@ -15,51 +15,54 @@
 //! The `num-traits` crate is tested for rustc 1.8 and greater.
 
 #![doc(html_root_url = "https://docs.rs/num-traits/0.2")]
-
 #![deny(unconditional_recursion)]
-
-#![cfg_attr(not(feature = "std"), no_std)]
+#![no_std]
 #[cfg(feature = "std")]
-extern crate core;
+extern crate std;
+
+// Only `no_std` builds actually use `libm`.
+#[cfg(all(not(feature = "std"), feature = "libm"))]
+extern crate libm;
 
-use core::ops::{Add, Sub, Mul, Div, Rem};
-use core::ops::{AddAssign, SubAssign, MulAssign, DivAssign, RemAssign};
-use core::num::Wrapping;
 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;
-#[cfg(feature = "std")]
+#[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 identities::{Zero, One, zero, one};
-pub use ops::inv::Inv;
-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};
+pub use cast::{cast, AsPrimitive, FromPrimitive, NumCast, ToPrimitive};
+pub use identities::{one, zero, One, Zero};
 pub use int::PrimInt;
-pub use pow::{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;
 
-pub mod identities;
-pub mod sign;
-pub mod ops;
 pub mod bounds;
-pub mod float;
-#[cfg(feature = "std")]
-pub mod real;
 pub mod cast;
+pub mod float;
+pub mod identities;
 pub mod int;
+pub mod ops;
 pub mod pow;
+pub mod real;
+pub mod sign;
 
 /// The base trait for numeric types, covering `0` and `1` values,
 /// comparisons, basic numeric operations, and string conversion.
-pub trait Num: PartialEq + Zero + One + NumOps
-{
+pub trait Num: PartialEq + Zero + One + NumOps {
     type FromStrRadixErr;
 
     /// Convert from a string and radix <= 36.
@@ -81,21 +84,23 @@ pub trait Num: PartialEq + Zero + One + NumOps
 /// 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>
+pub trait NumOps<Rhs = Self, Output = Self>:
+    Add<Rhs, Output = Output>
     + Sub<Rhs, Output = Output>
     + Mul<Rhs, Output = Output>
     + Div<Rhs, Output = Output>
     + Rem<Rhs, Output = Output>
-{}
+{
+}
 
-impl<T, Rhs, Output> NumOps<Rhs, Output> for T
-where T: Add<Rhs, Output = Output>
-       + Sub<Rhs, Output = Output>
-       + Mul<Rhs, Output = Output>
-       + Div<Rhs, Output = Output>
-       + Rem<Rhs, Output = Output>
-{}
+impl<T, Rhs, Output> NumOps<Rhs, Output> for T where
+    T: Add<Rhs, Output = Output>
+        + Sub<Rhs, Output = Output>
+        + Mul<Rhs, Output = Output>
+        + Div<Rhs, Output = Output>
+        + Rem<Rhs, Output = Output>
+{
+}
 
 /// The trait for `Num` types which also implement numeric operations taking
 /// the second operand by reference.
@@ -114,21 +119,15 @@ impl<T, Base> RefNum<Base> for T where T: NumOps<Base, Base> + for<'r> NumOps<&'
 /// 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>
-{}
+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>
-{}
+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.
 ///
@@ -143,7 +142,6 @@ impl<T> NumAssign for T where T: Num + NumAssignOps {}
 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 {
@@ -158,11 +156,16 @@ macro_rules! int_trait_impl {
     )*)
 }
 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>>
+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> {
@@ -170,7 +173,6 @@ impl<T: Num> Num for Wrapping<T>
     }
 }
 
-
 #[derive(Debug)]
 pub enum FloatErrorKind {
     Empty,
@@ -217,7 +219,12 @@ macro_rules! float_trait_impl {
                 }
 
                 fn slice_shift_char(src: &str) -> Option<(char, &str)> {
-                    src.chars().nth(0).map(|ch| (ch, &src[1..]))
+                    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) {
@@ -360,6 +367,8 @@ float_trait_impl!(Num for f32 f64);
 ///  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");
@@ -372,17 +381,97 @@ pub fn clamp<T: PartialOrd>(input: T, min: T, max: T) -> T {
     }
 }
 
+/// A value bounded by a minimum value
+///
+///  If input is less than min then this returns min.
+///  Otherwise this returns input.
+///  `clamp_min(std::f32::NAN, 1.0)` preserves `NAN` different from `f32::min(std::f32::NAN, 1.0)`.
+///
+/// **Panics** in debug mode if `!(min == min)`. (This occurs if `min` is `NAN`.)
+#[inline]
+pub fn clamp_min<T: PartialOrd>(input: T, min: T) -> T {
+    debug_assert!(min == min, "min must not be NAN");
+    if input < min {
+        min
+    } else {
+        input
+    }
+}
+
+/// A value bounded by a maximum value
+///
+///  If input is greater than max then this returns max.
+///  Otherwise this returns input.
+///  `clamp_max(std::f32::NAN, 1.0)` preserves `NAN` different from `f32::max(std::f32::NAN, 1.0)`.
+///
+/// **Panics** in debug mode if `!(max == max)`. (This occurs if `max` is `NAN`.)
+#[inline]
+pub fn clamp_max<T: PartialOrd>(input: T, max: T) -> T {
+    debug_assert!(max == max, "max must not be NAN");
+    if input > max {
+        max
+    } else {
+        input
+    }
+}
+
 #[test]
 fn clamp_test() {
     // Int test
     assert_eq!(1, clamp(1, -1, 2));
     assert_eq!(-1, clamp(-2, -1, 2));
     assert_eq!(2, clamp(3, -1, 2));
+    assert_eq!(1, clamp_min(1, -1));
+    assert_eq!(-1, clamp_min(-2, -1));
+    assert_eq!(-1, clamp_max(1, -1));
+    assert_eq!(-2, clamp_max(-2, -1));
 
     // Float test
     assert_eq!(1.0, clamp(1.0, -1.0, 2.0));
     assert_eq!(-1.0, clamp(-2.0, -1.0, 2.0));
     assert_eq!(2.0, clamp(3.0, -1.0, 2.0));
+    assert_eq!(1.0, clamp_min(1.0, -1.0));
+    assert_eq!(-1.0, clamp_min(-2.0, -1.0));
+    assert_eq!(-1.0, clamp_max(1.0, -1.0));
+    assert_eq!(-2.0, clamp_max(-2.0, -1.0));
+    assert!(clamp(::core::f32::NAN, -1.0, 1.0).is_nan());
+    assert!(clamp_min(::core::f32::NAN, 1.0).is_nan());
+    assert!(clamp_max(::core::f32::NAN, 1.0).is_nan());
+}
+
+#[test]
+#[should_panic]
+#[cfg(debug_assertions)]
+fn clamp_nan_min() {
+    clamp(0., ::core::f32::NAN, 1.);
+}
+
+#[test]
+#[should_panic]
+#[cfg(debug_assertions)]
+fn clamp_nan_max() {
+    clamp(0., -1., ::core::f32::NAN);
+}
+
+#[test]
+#[should_panic]
+#[cfg(debug_assertions)]
+fn clamp_nan_min_max() {
+    clamp(0., ::core::f32::NAN, ::core::f32::NAN);
+}
+
+#[test]
+#[should_panic]
+#[cfg(debug_assertions)]
+fn clamp_min_nan_min() {
+    clamp_min(0., ::core::f32::NAN);
+}
+
+#[test]
+#[should_panic]
+#[cfg(debug_assertions)]
+fn clamp_max_nan_max() {
+    clamp_max(0., ::core::f32::NAN);
 }
 
 #[test]
@@ -396,6 +485,15 @@ fn from_str_radix_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) {}
@@ -438,7 +536,8 @@ fn check_numref_ops() {
 #[test]
 fn check_refnum_ops() {
     fn compute<T: Copy>(x: &T, y: T) -> T
-        where for<'a> &'a T: RefNum<T>
+    where
+        for<'a> &'a T: RefNum<T>,
     {
         &(&(&(&(x * y) / y) % y) + y) - y
     }
@@ -448,7 +547,8 @@ fn check_refnum_ops() {
 #[test]
 fn check_refref_ops() {
     fn compute<T>(x: &T, y: &T) -> T
-        where for<'a> &'a T: RefNum<T>
+    where
+        for<'a> &'a T: RefNum<T>,
     {
         &(&(&(&(x * y) / y) % y) + y) - y
     }

src/ops/checked.rs

@@ -1,8 +1,8 @@
-use core::ops::{Add, Sub, Mul, Div, Shl, Shr};
+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> {
+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>;
@@ -16,7 +16,7 @@ macro_rules! checked_impl {
                 <$t>::$method(*self, *v)
             }
         }
-    }
+    };
 }
 
 checked_impl!(CheckedAdd, checked_add, u8);
@@ -24,15 +24,19 @@ 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> {
+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>;
@@ -43,16 +47,20 @@ 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> {
+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>;
@@ -63,16 +71,20 @@ 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> {
+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>;
@@ -83,17 +95,111 @@ 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 a left shift that returns `None` on overflow.
-pub trait CheckedShl: Sized + Shl<u32, Output=Self> {
-    /// Shifts a number to the left, checking for overflow. If overflow happens,
-    /// `None` is returned.
+/// 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;
@@ -116,7 +222,7 @@ macro_rules! checked_shift_impl {
                 <$t>::$method(*self, rhs)
             }
         }
-    }
+    };
 }
 
 checked_shift_impl!(CheckedShl, checked_shl, u8);
@@ -124,17 +230,22 @@ 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 overflow.
-pub trait CheckedShr: Sized + Shr<u32, Output=Self> {
-    /// Shifts a number to the left, checking for overflow. If overflow happens,
-    /// `None` is returned.
+/// 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;
@@ -154,9 +265,13 @@ 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

@@ -20,20 +20,28 @@ pub trait Inv {
 impl Inv for f32 {
     type Output = f32;
     #[inline]
-    fn inv(self) -> f32 { 1.0 / self }
+    fn inv(self) -> f32 {
+        1.0 / self
+    }
 }
 impl Inv for f64 {
     type Output = f64;
     #[inline]
-    fn inv(self) -> f64 { 1.0 / self }
+    fn inv(self) -> f64 {
+        1.0 / self
+    }
 }
 impl<'a> Inv for &'a f32 {
     type Output = f32;
     #[inline]
-    fn inv(self) -> f32 { 1.0 / *self }
+    fn inv(self) -> f32 {
+        1.0 / *self
+    }
 }
 impl<'a> Inv for &'a f64 {
     type Output = f64;
     #[inline]
-    fn inv(self) -> f64 { 1.0 / *self }
+    fn inv(self) -> f64 {
+        1.0 / *self
+    }
 }

src/ops/mod.rs

@@ -1,4 +1,5 @@
-pub mod saturating;
 pub mod checked;
-pub mod wrapping;
 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

@@ -26,3 +26,5 @@ macro_rules! saturating_impl {
 }
 
 saturating_impl!(Saturating for isize usize i8 u8 i16 u16 i32 u32 i64 u64);
+#[cfg(has_i128)]
+saturating_impl!(Saturating for i128 u128);

src/ops/wrapping.rs

@@ -1,5 +1,5 @@
-use core::ops::{Add, Sub, Mul};
 use core::num::Wrapping;
+use core::ops::{Add, Mul, Shl, Shr, Sub};
 
 macro_rules! wrapping_impl {
     ($trait_name:ident, $method:ident, $t:ty) => {
@@ -17,11 +17,11 @@ macro_rules! wrapping_impl {
                 <$t>::$method(*self, *v)
             }
         }
-    }
+    };
 }
 
 /// Performs addition that wraps around on overflow.
-pub trait WrappingAdd: Sized + Add<Self, Output=Self> {
+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;
@@ -32,15 +32,19 @@ 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> {
+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;
@@ -51,15 +55,19 @@ 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> {
+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;
@@ -70,42 +78,167 @@ 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>> {
+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>> {
+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>> {
+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_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]
@@ -125,3 +258,15 @@ 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

@@ -1,6 +1,6 @@
-use core::ops::Mul;
 use core::num::Wrapping;
-use {One, CheckedMul};
+use core::ops::Mul;
+use {CheckedMul, One};
 
 /// Binary operator for raising a value to a power.
 pub trait Pow<RHS> {
@@ -98,6 +98,25 @@ 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);
@@ -114,6 +133,10 @@ 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>);
 
@@ -129,27 +152,30 @@ pow_impl!(Wrapping<isize>);
 // pow_impl!(usize, u64);
 // pow_impl!(isize, u64);
 
-#[cfg(feature = "std")]
+#[cfg(any(feature = "std", feature = "libm"))]
 mod float_impls {
     use super::Pow;
+    use Float;
 
-    pow_impl!(f32, i8, i32, f32::powi);
-    pow_impl!(f32, u8, i32, f32::powi);
-    pow_impl!(f32, i16, i32, f32::powi);
-    pow_impl!(f32, u16, i32, f32::powi);
-    pow_impl!(f32, i32, i32, f32::powi);
-    pow_impl!(f64, i8, i32, f64::powi);
-    pow_impl!(f64, u8, i32, f64::powi);
-    pow_impl!(f64, i16, i32, f64::powi);
-    pow_impl!(f64, u16, i32, f64::powi);
-    pow_impl!(f64, i32, i32, f64::powi);
-    pow_impl!(f32, f32, f32, f32::powf);
-    pow_impl!(f64, f32, f64, f64::powf);
-    pow_impl!(f64, f64, f64, f64::powf);
+    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
@@ -157,16 +183,21 @@ mod float_impls {
 ///
 /// 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() }
+    if exp == 0 {
+        return T::one();
+    }
 
     while exp & 1 == 0 {
         base = base.clone() * base;
         exp >>= 1;
     }
-    if exp == 1 { return base }
+    if exp == 1 {
+        return base;
+    }
 
     let mut acc = base.clone();
     while exp > 1 {
@@ -181,6 +212,8 @@ pub fn pow<T: Clone + One + Mul<T, Output = T>>(mut base: T, mut exp: usize) ->
 
 /// 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
@@ -191,22 +224,31 @@ pub fn pow<T: Clone + One + Mul<T, Output = T>>(mut base: T, mut exp: usize) ->
 /// 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()) }
+    if exp == 0 {
+        return Some(T::one());
+    }
 
     macro_rules! optry {
-        ( $ expr : expr ) => {
-            if let Some(val) = $expr { val } else { return None }
-        }
+        ($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) }
+    if exp == 1 {
+        return Some(base);
+    }
 
     let mut acc = base.clone();
     while exp > 1 {

src/real.rs

@@ -1,6 +1,8 @@
-use std::ops::Neg;
+#![cfg(any(feature = "std", feature = "libm"))]
 
-use {Num, NumCast, Float};
+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`.
@@ -11,14 +13,8 @@ use {Num, NumCast, Float};
 /// 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.
-pub trait Real
-    : Num
-    + Copy
-    + NumCast
-    + PartialOrd
-    + Neg<Output = Self>
-{
+/// 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.
     ///
     /// ```
@@ -215,8 +211,10 @@ pub trait Real
     fn is_sign_negative(self) -> bool;
 
     /// Fused multiply-add. Computes `(self * a) + b` with only one rounding
-    /// error. This produces a more accurate result with better performance than
-    /// a separate multiplication operation followed by an add.
+    /// 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;

src/sign.rs

@@ -1,8 +1,8 @@
-use core::ops::Neg;
 use core::num::Wrapping;
+use core::ops::Neg;
 
-use Num;
 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> {
@@ -74,7 +74,12 @@ macro_rules! signed_impl {
 
 signed_impl!(isize i8 i16 i32 i64);
 
-impl<T: Signed> Signed for Wrapping<T> where Wrapping<T>: Num + Neg<Output=Wrapping<T>>
+#[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 {
@@ -92,10 +97,14 @@ impl<T: Signed> Signed for Wrapping<T> where Wrapping<T>: Num + Neg<Output=Wrapp
     }
 
     #[inline]
-    fn is_positive(&self) -> bool { self.0.is_positive() }
+    fn is_positive(&self) -> bool {
+        self.0.is_positive()
+    }
 
     #[inline]
-    fn is_negative(&self) -> bool { self.0.is_negative() }
+    fn is_negative(&self) -> bool {
+        self.0.is_negative()
+    }
 }
 
 macro_rules! signed_float_impl {
@@ -112,7 +121,11 @@ macro_rules! signed_float_impl {
             /// and `other` is returned.
             #[inline]
             fn abs_sub(&self, other: &$t) -> $t {
-                if *self <= *other { 0. } else { *self - *other }
+                if *self <= *other {
+                    0.
+                } else {
+                    *self - *other
+                }
             }
 
             /// # Returns
@@ -127,13 +140,17 @@ macro_rules! signed_float_impl {
 
             /// Returns `true` if the number is positive, including `+0.0` and `INFINITY`
             #[inline]
-            fn is_positive(&self) -> bool { FloatCore::is_sign_positive(*self) }
+            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) }
+            fn is_negative(&self) -> bool {
+                FloatCore::is_sign_negative(*self)
+            }
         }
-    }
+    };
 }
 
 signed_float_impl!(f32);
@@ -171,7 +188,10 @@ pub fn abs_sub<T: Signed>(x: T, y: T) -> T {
 /// * `0` if the number is zero
 /// * `1` if the number is positive
 /// * `-1` if the number is negative
-#[inline(always)] pub fn signum<T: Signed>(value: T) -> T { value.signum() }
+#[inline(always)]
+pub fn signum<T: Signed>(value: T) -> T {
+    value.signum()
+}
 
 /// A trait for values which cannot be negative
 pub trait Unsigned: Num {}
@@ -183,6 +203,8 @@ macro_rules! empty_trait_impl {
 }
 
 empty_trait_impl!(Unsigned for usize u8 u16 u32 u64);
+#[cfg(has_i128)]
+empty_trait_impl!(Unsigned for u128);
 
 impl<T: Unsigned> Unsigned for Wrapping<T> where Wrapping<T>: Num {}
 

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);
+}