traits: Introduce std feature

This makes it possible to build `traits` without `std`. For this a new
trait `BasicFloat` was introduced, implementing some basic functionality
that works with `core`. Most notably this is lacking functions like
`cos`, `sin`, etc.

`Float` is not available without `std`.

Refs #216.

traits/Cargo.toml

@@ -10,3 +10,7 @@ name = "num-traits"
 version = "0.1.37"
 
 [dependencies]
+
+[features]
+default = ["std"]
+std = []

traits/src/bounds.rs

@@ -1,7 +1,7 @@
-use std::{usize, u8, u16, u32, u64};
-use std::{isize, i8, i16, i32, i64};
-use std::{f32, f64};
-use std::num::Wrapping;
+use core::{usize, u8, u16, u32, u64};
+use core::{isize, i8, i16, i32, i64};
+use core::{f32, f64};
+use core::num::Wrapping;
 
 /// Numbers which have upper and lower bounds
 pub trait Bounded {

traits/src/cast.rs

@@ -1,8 +1,9 @@
-use std::mem::size_of;
-use std::num::Wrapping;
+use core::mem::size_of;
+use core::num::Wrapping;
 
 use identities::Zero;
 use bounds::Bounded;
+use float::BasicFloat;
 
 /// A generic trait for converting a value to a number.
 pub trait ToPrimitive {
@@ -226,8 +227,8 @@ macro_rules! impl_to_primitive_float_to_float {
             // Make sure the value is in range for the cast.
             // NaN and +-inf are cast as they are.
             let n = $slf as f64;
-            let max_value: $DstT = ::std::$DstT::MAX;
-            if !n.is_finite() || (-max_value as f64 <= n && n <= max_value as f64) {
+            let max_value: $DstT = ::core::$DstT::MAX;
+            if !BasicFloat::is_finite(n) || (-max_value as f64 <= n && n <= max_value as f64) {
                 Some($slf as $DstT)
             } else {
                 None
@@ -454,8 +455,8 @@ impl<T: NumCast> NumCast for Wrapping<T> {
 
 #[test]
 fn to_primitive_float() {
-    use std::f32;
-    use std::f64;
+    use core::f32;
+    use core::f64;
 
     let f32_toolarge = 1e39f64;
     assert_eq!(f32_toolarge.to_f32(), None);

traits/src/float.rs

@@ -1,15 +1,209 @@
-use std::mem;
-use std::ops::Neg;
-use std::num::FpCategory;
+use core::mem;
+use core::ops::Neg;
+use core::num::FpCategory;
 
 // Used for default implementation of `epsilon`
-use std::f32;
+use core::f32;
 
 use {Num, NumCast};
 
+/// Basic floating point operations that work with `core`.
+pub trait BasicFloat: Num + Neg<Output = Self> + PartialOrd + Copy {
+    /// Returns positive infinity.
+    #[inline]
+    fn infinity() -> Self;
+
+    /// Returns negative infinity.
+    #[inline]
+    fn neg_infinity() -> Self;
+
+    /// Returns NaN.
+    #[inline]
+    fn nan() -> Self;
+
+    /// Returns `true` if the number is NaN.
+    #[inline]
+    fn is_nan(self) -> bool {
+        self != self
+    }
+
+    /// Returns `true` if the number is infinite.
+    #[inline]
+    fn is_infinite(self) -> bool {
+        self == Self::infinity() || self == Self::neg_infinity()
+    }
+
+    /// Returns `true` if the number is neither infinite or NaN.
+    #[inline]
+    fn is_finite(self) -> bool {
+        !(self.is_nan() || self.is_infinite())
+    }
+
+    /// Returns `true` if the number is neither zero, infinite, subnormal or NaN.
+    #[inline]
+    fn is_normal(self) -> bool {
+        self.classify() == FpCategory::Normal
+    }
+
+    /// Returns the floating point category of the number. If only one property
+    /// is going to be tested, it is generally faster to use the specific
+    /// predicate instead.
+    #[inline]
+    fn classify(self) -> FpCategory;
+
+    /// Computes the absolute value of `self`. Returns `BasicFloat::nan()` if the
+    /// number is `BasicFloat::nan()`.
+    #[inline]
+    fn abs(self) -> Self {
+        if self.is_sign_positive() {
+            return self;
+        }
+        if self.is_sign_negative() {
+            return -self;
+        }
+        Self::nan()
+    }
+
+    /// Returns a number that represents the sign of `self`.
+    ///
+    /// - `1.0` if the number is positive, `+0.0` or `BasicFloat::infinity()`
+    /// - `-1.0` if the number is negative, `-0.0` or `BasicFloat::neg_infinity()`
+    /// - `BasicFloat::nan()` if the number is `BasicFloat::nan()`
+    #[inline]
+    fn signum(self) -> Self {
+        if self.is_sign_positive() {
+            return Self::one();
+        }
+        if self.is_sign_negative() {
+            return -Self::one();
+        }
+        Self::nan()
+    }
+
+    /// Returns `true` if `self` is positive, including `+0.0` and
+    /// `BasicFloat::infinity()`.
+    #[inline]
+    fn is_sign_positive(self) -> bool {
+        self > Self::zero() || (Self::one() / self) == Self::infinity()
+    }
+
+    /// Returns `true` if `self` is negative, including `-0.0` and
+    /// `BasicFloat::neg_infinity()`.
+    #[inline]
+    fn is_sign_negative(self) -> bool {
+        self < Self::zero() || (Self::one() / self) == Self::neg_infinity()
+    }
+
+    /// Returns the reciprocal (multiplicative inverse) of the number.
+    #[inline]
+    fn recip(self) -> Self {
+        Self::one() / self
+    }
+
+    #[inline]
+    fn powi(self, mut exp: i32) -> Self {
+        if exp == 0 { return Self::one() }
+
+        let mut base;
+        if exp < 0 {
+            exp = -exp;
+            base = self.recip();
+        } else {
+            base = self;
+        }
+
+        while exp & 1 == 0 {
+            base = base * base;
+            exp >>= 1;
+        }
+        if exp == 1 { return base }
+
+        let mut acc = base;
+        while exp > 1 {
+            exp >>= 1;
+            base = base * base;
+            if exp & 1 == 1 {
+                acc = acc * base;
+            }
+        }
+        acc
+    }
+
+    /// Converts to degrees, assuming the number is in radians.
+    #[inline]
+    fn to_degrees(self) -> Self;
+
+    /// Converts to radians, assuming the number is in degrees.
+    #[inline]
+    fn to_radians(self) -> Self;
+}
+
+impl BasicFloat for f32 {
+    fn infinity() -> Self {
+        ::core::f32::INFINITY
+    }
+    fn neg_infinity() -> Self {
+        ::core::f32::INFINITY
+    }
+    fn nan() -> Self {
+        ::core::f32::NAN
+    }
+    fn classify(self) -> FpCategory {
+        const EXP_MASK: u32 = 0x7f800000;
+        const MAN_MASK: u32 = 0x007fffff;
+
+        let bits: u32 = unsafe { mem::transmute(self) };
+        match (bits & MAN_MASK, bits & EXP_MASK) {
+            (0, 0) => FpCategory::Zero,
+            (_, 0) => FpCategory::Subnormal,
+            (0, EXP_MASK) => FpCategory::Infinite,
+            (_, EXP_MASK) => FpCategory::Nan,
+            _ => FpCategory::Normal,
+        }
+    }
+    fn to_degrees(self) -> Self {
+        self * (180.0 / ::core::f32::consts::PI)
+    }
+    fn to_radians(self) -> Self {
+        self * (::core::f32::consts::PI / 180.0)
+    }
+}
+
+impl BasicFloat for f64 {
+    fn infinity() -> Self {
+        ::core::f64::INFINITY
+    }
+    fn neg_infinity() -> Self {
+        ::core::f64::INFINITY
+    }
+    fn nan() -> Self {
+        ::core::f64::NAN
+    }
+    fn classify(self) -> FpCategory {
+        const EXP_MASK: u64 = 0x7ff0000000000000;
+        const MAN_MASK: u64 = 0x000fffffffffffff;
+
+        let bits: u64 = unsafe { mem::transmute(self) };
+        match (bits & MAN_MASK, bits & EXP_MASK) {
+            (0, 0) => FpCategory::Zero,
+            (_, 0) => FpCategory::Subnormal,
+            (0, EXP_MASK) => FpCategory::Infinite,
+            (_, EXP_MASK) => FpCategory::Nan,
+            _ => FpCategory::Normal,
+        }
+    }
+    fn to_degrees(self) -> Self {
+        self * (180.0 / ::core::f64::consts::PI)
+    }
+    fn to_radians(self) -> Self {
+        self * (::core::f64::consts::PI / 180.0)
+    }
+}
+
 // FIXME: these doctests aren't actually helpful, because they're using and
 // testing the inherent methods directly, not going through `Float`.
 
+/// Floating point operations that work with `std`.
 pub trait Float
     : Num
     + Copy
@@ -930,17 +1124,17 @@ macro_rules! float_impl {
         impl Float for $T {
             #[inline]
             fn nan() -> Self {
-                ::std::$T::NAN
+                ::core::$T::NAN
             }
 
             #[inline]
             fn infinity() -> Self {
-                ::std::$T::INFINITY
+                ::core::$T::INFINITY
             }
 
             #[inline]
             fn neg_infinity() -> Self {
-                ::std::$T::NEG_INFINITY
+                ::core::$T::NEG_INFINITY
             }
 
             #[inline]
@@ -950,22 +1144,22 @@ macro_rules! float_impl {
 
             #[inline]
             fn min_value() -> Self {
-                ::std::$T::MIN
+                ::core::$T::MIN
             }
 
             #[inline]
             fn min_positive_value() -> Self {
-                ::std::$T::MIN_POSITIVE
+                ::core::$T::MIN_POSITIVE
             }
 
             #[inline]
             fn epsilon() -> Self {
-                ::std::$T::EPSILON
+                ::core::$T::EPSILON
             }
 
             #[inline]
             fn max_value() -> Self {
-                ::std::$T::MAX
+                ::core::$T::MAX
             }
 
             #[inline]
@@ -1097,14 +1291,14 @@ macro_rules! float_impl {
             fn to_degrees(self) -> Self {
                 // NB: `f32` didn't stabilize this until 1.7
                 // <$T>::to_degrees(self)
-                self * (180. / ::std::$T::consts::PI)
+                self * (180. / ::core::$T::consts::PI)
             }
 
             #[inline]
             fn to_radians(self) -> Self {
                 // NB: `f32` didn't stabilize this until 1.7
                 // <$T>::to_radians(self)
-                self * (::std::$T::consts::PI / 180.)
+                self * (::core::$T::consts::PI / 180.)
             }
 
             #[inline]
@@ -1257,7 +1451,9 @@ fn integer_decode_f64(f: f64) -> (u64, i16, i8) {
     (mantissa, exponent, sign)
 }
 
+#[cfg(feature = "std")]
 float_impl!(f32 integer_decode_f32);
+#[cfg(feature = "std")]
 float_impl!(f64 integer_decode_f64);
 
 macro_rules! float_const_impl {
@@ -1274,7 +1470,7 @@ macro_rules! float_const_impl {
             $(
                 #[inline]
                 fn $constant() -> Self {
-                    ::std::$T::consts::$constant
+                    ::core::$T::consts::$constant
                 }
             )+
         }
@@ -1318,21 +1514,35 @@ float_const_impl! {
 
 #[cfg(test)]
 mod tests {
-    use Float;
+    use BasicFloat;
+    use core::f64::consts;
+
+    const DEG_RAD_PAIRS: [(f64, f64); 7] = [
+        (0.0, 0.),
+        (22.5, consts::FRAC_PI_8),
+        (30.0, consts::FRAC_PI_6),
+        (45.0, consts::FRAC_PI_4),
+        (60.0, consts::FRAC_PI_3),
+        (90.0, consts::FRAC_PI_2),
+        (180.0, consts::PI),
+    ];
+
+    #[test]
+    fn convert_deg_rad_core() {
+        for &(deg, rad) in &DEG_RAD_PAIRS {
+            assert!((BasicFloat::to_degrees(rad) - deg).abs() < 1e-6);
+            assert!((BasicFloat::to_radians(deg) - rad).abs() < 1e-6);
+
+            let (deg, rad) = (deg as f32, rad as f32);
+            assert!((BasicFloat::to_degrees(rad) - deg).abs() < 1e-6);
+            assert!((BasicFloat::to_radians(deg) - rad).abs() < 1e-6);
+        }
+    }
 
+    #[cfg(std)]
     #[test]
-    fn convert_deg_rad() {
-        use std::f64::consts;
-
-        const DEG_RAD_PAIRS: [(f64, f64); 7] = [
-            (0.0, 0.),
-            (22.5, consts::FRAC_PI_8),
-            (30.0, consts::FRAC_PI_6),
-            (45.0, consts::FRAC_PI_4),
-            (60.0, consts::FRAC_PI_3),
-            (90.0, consts::FRAC_PI_2),
-            (180.0, consts::PI),
-        ];
+    fn convert_deg_rad_std() {
+        use Float;
 
         for &(deg, rad) in &DEG_RAD_PAIRS {
             assert!((Float::to_degrees(rad) - deg).abs() < 1e-6);

traits/src/identities.rs

@@ -1,5 +1,5 @@
-use std::ops::{Add, Mul};
-use std::num::Wrapping;
+use core::ops::{Add, Mul};
+use core::num::Wrapping;
 
 /// Defines an additive identity element for `Self`.
 pub trait Zero: Sized + Add<Self, Output = Self> {

traits/src/int.rs

@@ -1,4 +1,4 @@
-use std::ops::{Not, BitAnd, BitOr, BitXor, Shl, Shr};
+use core::ops::{Not, BitAnd, BitOr, BitXor, Shl, Shr};
 
 use {Num, NumCast};
 use bounds::Bounded;

traits/src/lib.rs

@@ -14,12 +14,16 @@
        html_root_url = "https://rust-num.github.io/num/",
        html_playground_url = "http://play.integer32.com/")]
 
-use std::ops::{Add, Sub, Mul, Div, Rem};
-use std::ops::{AddAssign, SubAssign, MulAssign, DivAssign, RemAssign};
-use std::num::Wrapping;
+#![cfg_attr(not(feature = "std"), no_std)]
+#[cfg(feature = "std")]
+extern crate core;
+
+use core::ops::{Add, Sub, Mul, Div, Rem};
+use core::ops::{AddAssign, SubAssign, MulAssign, DivAssign, RemAssign};
+use core::num::Wrapping;
 
 pub use bounds::Bounded;
-pub use float::{Float, FloatConst};
+pub use float::{BasicFloat, Float, FloatConst};
 pub use identities::{Zero, One, zero, one};
 pub use ops::checked::*;
 pub use ops::wrapping::*;
@@ -129,10 +133,10 @@ impl<T> NumAssignRef for T where T: NumAssign + for<'r> NumAssignOps<&'r T> {}
 macro_rules! int_trait_impl {
     ($name:ident for $($t:ty)*) => ($(
         impl $name for $t {
-            type FromStrRadixErr = ::std::num::ParseIntError;
+            type FromStrRadixErr = ::core::num::ParseIntError;
             #[inline]
             fn from_str_radix(s: &str, radix: u32)
-                              -> Result<Self, ::std::num::ParseIntError>
+                              -> Result<Self, ::core::num::ParseIntError>
             {
                 <$t>::from_str_radix(s, radix)
             }
@@ -158,7 +162,7 @@ pub enum FloatErrorKind {
     Empty,
     Invalid,
 }
-// FIXME: std::num::ParseFloatError is stable in 1.0, but opaque to us,
+// 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 {
@@ -181,9 +185,9 @@ macro_rules! float_trait_impl {
 
                 // Special values
                 match src {
-                    "inf"   => return Ok(Float::infinity()),
-                    "-inf"  => return Ok(Float::neg_infinity()),
-                    "NaN"   => return Ok(Float::nan()),
+                    "inf"   => return Ok(BasicFloat::infinity()),
+                    "-inf"  => return Ok(BasicFloat::neg_infinity()),
+                    "NaN"   => return Ok(BasicFloat::nan()),
                     _       => {},
                 }
 
@@ -224,15 +228,15 @@ macro_rules! float_trait_impl {
                             // if we've not seen any non-zero digits.
                             if prev_sig != 0.0 {
                                 if is_positive && sig <= prev_sig
-                                    { return Ok(Float::infinity()); }
+                                    { return Ok(BasicFloat::infinity()); }
                                 if !is_positive && sig >= prev_sig
-                                    { return Ok(Float::neg_infinity()); }
+                                    { return Ok(BasicFloat::neg_infinity()); }
 
                                 // Detect overflow by reversing the shift-and-add process
                                 if is_positive && (prev_sig != (sig - digit as $t) / radix as $t)
-                                    { return Ok(Float::infinity()); }
+                                    { return Ok(BasicFloat::infinity()); }
                                 if !is_positive && (prev_sig != (sig + digit as $t) / radix as $t)
-                                    { return Ok(Float::neg_infinity()); }
+                                    { return Ok(BasicFloat::neg_infinity()); }
                             }
                             prev_sig = sig;
                         },
@@ -268,9 +272,9 @@ macro_rules! float_trait_impl {
                                 };
                                 // Detect overflow by comparing to last value
                                 if is_positive && sig < prev_sig
-                                    { return Ok(Float::infinity()); }
+                                    { return Ok(BasicFloat::infinity()); }
                                 if !is_positive && sig > prev_sig
-                                    { return Ok(Float::neg_infinity()); }
+                                    { return Ok(BasicFloat::neg_infinity()); }
                                 prev_sig = sig;
                             },
                             None => match c {
@@ -305,8 +309,8 @@ macro_rules! float_trait_impl {
                         };
 
                         match (is_positive, exp) {
-                            (true,  Ok(exp)) => base.powi(exp as i32),
-                            (false, Ok(exp)) => 1.0 / base.powi(exp as i32),
+                            (true,  Ok(exp)) => BasicFloat::powi(base, exp as i32),
+                            (false, Ok(exp)) => 1.0 / BasicFloat::powi(base, exp as i32),
                             (_, Err(_))      => return Err(PFE { kind: Invalid }),
                         }
                     },

traits/src/ops/checked.rs

@@ -1,4 +1,4 @@
-use std::ops::{Add, Sub, Mul, Div};
+use core::ops::{Add, Sub, Mul, Div};
 
 /// Performs addition that returns `None` instead of wrapping around on
 /// overflow.

traits/src/ops/wrapping.rs

@@ -1,5 +1,5 @@
-use std::ops::{Add, Sub, Mul};
-use std::num::Wrapping;
+use core::ops::{Add, Sub, Mul};
+use core::num::Wrapping;
 
 macro_rules! wrapping_impl {
     ($trait_name:ident, $method:ident, $t:ty) => {

traits/src/pow.rs

@@ -1,4 +1,4 @@
-use std::ops::Mul;
+use core::ops::Mul;
 use {One, CheckedMul};
 
 /// Raises a value to the power of exp, using exponentiation by squaring.

traits/src/sign.rs

@@ -1,6 +1,6 @@
-use std::ops::Neg;
-use std::{f32, f64};
-use std::num::Wrapping;
+use core::ops::Neg;
+use core::{f32, f64};
+use core::num::Wrapping;
 
 use Num;
 
@@ -104,16 +104,15 @@ macro_rules! signed_float_impl {
             /// Computes the absolute value. Returns `NAN` if the number is `NAN`.
             #[inline]
             fn abs(&self) -> $t {
-                <$t>::abs(*self)
+                (*self).abs()
             }
 
             /// The positive difference of two numbers. Returns `0.0` if the number is
             /// less than or equal to `other`, otherwise the difference between`self`
             /// and `other` is returned.
             #[inline]
-            #[allow(deprecated)]
             fn abs_sub(&self, other: &$t) -> $t {
-                <$t>::abs_sub(*self, *other)
+                if *self <= *other { 0. } else { *self - *other }
             }
 
             /// # Returns
@@ -123,7 +122,7 @@ macro_rules! signed_float_impl {
             /// - `NAN` if the number is NaN
             #[inline]
             fn signum(&self) -> $t {
-                <$t>::signum(*self)
+                (*self).signum()
             }
 
             /// Returns `true` if the number is positive, including `+0.0` and `INFINITY`