core: Move intrinsic float functionality from std

The Float trait in libstd is quite a large trait which has dependencies on cmath
(libm) and such, which libcore cannot satisfy. It also has many functions that
libcore can implement, however, as LLVM has intrinsics or they're just bit
twiddling.

This commit moves what it can of the Float trait from the standard library into
libcore to allow floats to be usable in the core library. The remaining
functions are now resident in a FloatMath trait in the standard library (in the
prelude now). Previous code which was generic over just the Float trait may now
need to be generic over the FloatMath trait.

[breaking-change]

3 files changed, 699 insertions, 2 deletions

diff --git a/src/libcore/num/f32.rs b/src/libcore/num/f32.rs
index c4cdc5a0a40..694f3e9fbd1 100644
--- a/src/libcore/num/f32.rs
+++ b/src/libcore/num/f32.rs
@@ -12,7 +12,10 @@
 
 use default::Default;
 use intrinsics;
-use num::{Zero, One, Bounded, Signed, Num, Primitive};
+use mem;
+use num::{FPNormal, FPCategory, FPZero, FPSubnormal, FPInfinite, FPNaN};
+use num::{Zero, One, Bounded, Signed, Num, Primitive, Float};
+use option::Option;
 
 #[cfg(not(test))] use cmp::{Eq, Ord};
 #[cfg(not(test))] use ops::{Add, Sub, Mul, Div, Rem, Neg};
@@ -225,3 +228,270 @@ impl Bounded for f32 {
     #[inline]
     fn max_value() -> f32 { MAX_VALUE }
 }
+
+impl Float for f32 {
+    #[inline]
+    fn nan() -> f32 { NAN }
+
+    #[inline]
+    fn infinity() -> f32 { INFINITY }
+
+    #[inline]
+    fn neg_infinity() -> f32 { NEG_INFINITY }
+
+    #[inline]
+    fn neg_zero() -> f32 { -0.0 }
+
+    /// 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 == Float::infinity() || self == Float::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() == FPNormal
+    }
+
+    /// 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.
+    fn classify(self) -> FPCategory {
+        static EXP_MASK: u32 = 0x7f800000;
+        static MAN_MASK: u32 = 0x007fffff;
+
+        let bits: u32 = unsafe { mem::transmute(self) };
+        match (bits & MAN_MASK, bits & EXP_MASK) {
+            (0, 0)        => FPZero,
+            (_, 0)        => FPSubnormal,
+            (0, EXP_MASK) => FPInfinite,
+            (_, EXP_MASK) => FPNaN,
+            _             => FPNormal,
+        }
+    }
+
+    #[inline]
+    fn mantissa_digits(_: Option<f32>) -> uint { MANTISSA_DIGITS }
+
+    #[inline]
+    fn digits(_: Option<f32>) -> uint { DIGITS }
+
+    #[inline]
+    fn epsilon() -> f32 { EPSILON }
+
+    #[inline]
+    fn min_exp(_: Option<f32>) -> int { MIN_EXP }
+
+    #[inline]
+    fn max_exp(_: Option<f32>) -> int { MAX_EXP }
+
+    #[inline]
+    fn min_10_exp(_: Option<f32>) -> int { MIN_10_EXP }
+
+    #[inline]
+    fn max_10_exp(_: Option<f32>) -> int { MAX_10_EXP }
+
+    #[inline]
+    fn min_pos_value(_: Option<f32>) -> f32 { MIN_POS_VALUE }
+
+    /// Returns the mantissa, exponent and sign as integers.
+    fn integer_decode(self) -> (u64, i16, i8) {
+        let bits: u32 = unsafe { mem::transmute(self) };
+        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
+        } else {
+            (bits & 0x7fffff) | 0x800000
+        };
+        // Exponent bias + mantissa shift
+        exponent -= 127 + 23;
+        (mantissa as u64, exponent, sign)
+    }
+
+    /// Round half-way cases toward `NEG_INFINITY`
+    #[inline]
+    fn floor(self) -> f32 {
+        unsafe { intrinsics::floorf32(self) }
+    }
+
+    /// Round half-way cases toward `INFINITY`
+    #[inline]
+    fn ceil(self) -> f32 {
+        unsafe { intrinsics::ceilf32(self) }
+    }
+
+    /// Round half-way cases away from `0.0`
+    #[inline]
+    fn round(self) -> f32 {
+        unsafe { intrinsics::roundf32(self) }
+    }
+
+    /// The integer part of the number (rounds towards `0.0`)
+    #[inline]
+    fn trunc(self) -> f32 {
+        unsafe { intrinsics::truncf32(self) }
+    }
+
+    /// The fractional part of the number, satisfying:
+    ///
+    /// ```rust
+    /// let x = 1.65f32;
+    /// assert!(x == x.trunc() + x.fract())
+    /// ```
+    #[inline]
+    fn fract(self) -> f32 { self - self.trunc() }
+
+    /// 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.
+    #[inline]
+    fn mul_add(self, a: f32, b: f32) -> f32 {
+        unsafe { intrinsics::fmaf32(self, a, b) }
+    }
+
+    /// The reciprocal (multiplicative inverse) of the number
+    #[inline]
+    fn recip(self) -> f32 { 1.0 / self }
+
+    fn powi(self, n: i32) -> f32 {
+        unsafe { intrinsics::powif32(self, n) }
+    }
+
+    #[inline]
+    fn powf(self, n: f32) -> f32 {
+        unsafe { intrinsics::powf32(self, n) }
+    }
+
+    /// sqrt(2.0)
+    #[inline]
+    fn sqrt2() -> f32 { consts::SQRT2 }
+
+    /// 1.0 / sqrt(2.0)
+    #[inline]
+    fn frac_1_sqrt2() -> f32 { consts::FRAC_1_SQRT2 }
+
+    #[inline]
+    fn sqrt(self) -> f32 {
+        unsafe { intrinsics::sqrtf32(self) }
+    }
+
+    #[inline]
+    fn rsqrt(self) -> f32 { self.sqrt().recip() }
+
+    /// Archimedes' constant
+    #[inline]
+    fn pi() -> f32 { consts::PI }
+
+    /// 2.0 * pi
+    #[inline]
+    fn two_pi() -> f32 { consts::PI_2 }
+
+    /// pi / 2.0
+    #[inline]
+    fn frac_pi_2() -> f32 { consts::FRAC_PI_2 }
+
+    /// pi / 3.0
+    #[inline]
+    fn frac_pi_3() -> f32 { consts::FRAC_PI_3 }
+
+    /// pi / 4.0
+    #[inline]
+    fn frac_pi_4() -> f32 { consts::FRAC_PI_4 }
+
+    /// pi / 6.0
+    #[inline]
+    fn frac_pi_6() -> f32 { consts::FRAC_PI_6 }
+
+    /// pi / 8.0
+    #[inline]
+    fn frac_pi_8() -> f32 { consts::FRAC_PI_8 }
+
+    /// 1 .0/ pi
+    #[inline]
+    fn frac_1_pi() -> f32 { consts::FRAC_1_PI }
+
+    /// 2.0 / pi
+    #[inline]
+    fn frac_2_pi() -> f32 { consts::FRAC_2_PI }
+
+    /// 2.0 / sqrt(pi)
+    #[inline]
+    fn frac_2_sqrtpi() -> f32 { consts::FRAC_2_SQRTPI }
+
+    /// Euler's number
+    #[inline]
+    fn e() -> f32 { consts::E }
+
+    /// log2(e)
+    #[inline]
+    fn log2_e() -> f32 { consts::LOG2_E }
+
+    /// log10(e)
+    #[inline]
+    fn log10_e() -> f32 { consts::LOG10_E }
+
+    /// ln(2.0)
+    #[inline]
+    fn ln_2() -> f32 { consts::LN_2 }
+
+    /// ln(10.0)
+    #[inline]
+    fn ln_10() -> f32 { consts::LN_10 }
+
+    /// Returns the exponential of the number
+    #[inline]
+    fn exp(self) -> f32 {
+        unsafe { intrinsics::expf32(self) }
+    }
+
+    /// Returns 2 raised to the power of the number
+    #[inline]
+    fn exp2(self) -> f32 {
+        unsafe { intrinsics::exp2f32(self) }
+    }
+
+    /// Returns the natural logarithm of the number
+    #[inline]
+    fn ln(self) -> f32 {
+        unsafe { intrinsics::logf32(self) }
+    }
+
+    /// Returns the logarithm of the number with respect to an arbitrary base
+    #[inline]
+    fn log(self, base: f32) -> f32 { self.ln() / base.ln() }
+
+    /// Returns the base 2 logarithm of the number
+    #[inline]
+    fn log2(self) -> f32 {
+        unsafe { intrinsics::log2f32(self) }
+    }
+
+    /// Returns the base 10 logarithm of the number
+    #[inline]
+    fn log10(self) -> f32 {
+        unsafe { intrinsics::log10f32(self) }
+    }
+
+    /// Converts to degrees, assuming the number is in radians
+    #[inline]
+    fn to_degrees(self) -> f32 { self * (180.0f32 / Float::pi()) }
+
+    /// Converts to radians, assuming the number is in degrees
+    #[inline]
+    fn to_radians(self) -> f32 {
+        let value: f32 = Float::pi();
+        self * (value / 180.0f32)
+    }
+}
diff --git a/src/libcore/num/f64.rs b/src/libcore/num/f64.rs
index b15b4566cdd..2c802f5d059 100644
--- a/src/libcore/num/f64.rs
+++ b/src/libcore/num/f64.rs
@@ -12,7 +12,10 @@
 
 use default::Default;
 use intrinsics;
-use num::{Zero, One, Bounded, Signed, Num, Primitive};
+use mem;
+use num::{FPNormal, FPCategory, FPZero, FPSubnormal, FPInfinite, FPNaN};
+use num::{Zero, One, Bounded, Signed, Num, Primitive, Float};
+use option::Option;
 
 #[cfg(not(test))] use cmp::{Eq, Ord};
 #[cfg(not(test))] use ops::{Add, Sub, Mul, Div, Rem, Neg};
@@ -225,3 +228,273 @@ impl Bounded for f64 {
     #[inline]
     fn max_value() -> f64 { MAX_VALUE }
 }
+
+impl Float for f64 {
+    #[inline]
+    fn nan() -> f64 { NAN }
+
+    #[inline]
+    fn infinity() -> f64 { INFINITY }
+
+    #[inline]
+    fn neg_infinity() -> f64 { NEG_INFINITY }
+
+    #[inline]
+    fn neg_zero() -> f64 { -0.0 }
+
+    /// 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 == Float::infinity() || self == Float::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() == FPNormal
+    }
+
+    /// 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.
+    fn classify(self) -> FPCategory {
+        static EXP_MASK: u64 = 0x7ff0000000000000;
+        static MAN_MASK: u64 = 0x000fffffffffffff;
+
+        let bits: u64 = unsafe { mem::transmute(self) };
+        match (bits & MAN_MASK, bits & EXP_MASK) {
+            (0, 0)        => FPZero,
+            (_, 0)        => FPSubnormal,
+            (0, EXP_MASK) => FPInfinite,
+            (_, EXP_MASK) => FPNaN,
+            _             => FPNormal,
+        }
+    }
+
+    #[inline]
+    fn mantissa_digits(_: Option<f64>) -> uint { MANTISSA_DIGITS }
+
+    #[inline]
+    fn digits(_: Option<f64>) -> uint { DIGITS }
+
+    #[inline]
+    fn epsilon() -> f64 { EPSILON }
+
+    #[inline]
+    fn min_exp(_: Option<f64>) -> int { MIN_EXP }
+
+    #[inline]
+    fn max_exp(_: Option<f64>) -> int { MAX_EXP }
+
+    #[inline]
+    fn min_10_exp(_: Option<f64>) -> int { MIN_10_EXP }
+
+    #[inline]
+    fn max_10_exp(_: Option<f64>) -> int { MAX_10_EXP }
+
+    #[inline]
+    fn min_pos_value(_: Option<f64>) -> f64 { MIN_POS_VALUE }
+
+    /// Returns the mantissa, exponent and sign as integers.
+    fn integer_decode(self) -> (u64, i16, i8) {
+        let bits: u64 = unsafe { mem::transmute(self) };
+        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
+        } else {
+            (bits & 0xfffffffffffff) | 0x10000000000000
+        };
+        // Exponent bias + mantissa shift
+        exponent -= 1023 + 52;
+        (mantissa, exponent, sign)
+    }
+
+    /// Round half-way cases toward `NEG_INFINITY`
+    #[inline]
+    fn floor(self) -> f64 {
+        unsafe { intrinsics::floorf64(self) }
+    }
+
+    /// Round half-way cases toward `INFINITY`
+    #[inline]
+    fn ceil(self) -> f64 {
+        unsafe { intrinsics::ceilf64(self) }
+    }
+
+    /// Round half-way cases away from `0.0`
+    #[inline]
+    fn round(self) -> f64 {
+        unsafe { intrinsics::roundf64(self) }
+    }
+
+    /// The integer part of the number (rounds towards `0.0`)
+    #[inline]
+    fn trunc(self) -> f64 {
+        unsafe { intrinsics::truncf64(self) }
+    }
+
+    /// The fractional part of the number, satisfying:
+    ///
+    /// ```rust
+    /// let x = 1.65f64;
+    /// assert!(x == x.trunc() + x.fract())
+    /// ```
+    #[inline]
+    fn fract(self) -> f64 { self - self.trunc() }
+
+    /// 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.
+    #[inline]
+    fn mul_add(self, a: f64, b: f64) -> f64 {
+        unsafe { intrinsics::fmaf64(self, a, b) }
+    }
+
+    /// The reciprocal (multiplicative inverse) of the number
+    #[inline]
+    fn recip(self) -> f64 { 1.0 / self }
+
+    #[inline]
+    fn powf(self, n: f64) -> f64 {
+        unsafe { intrinsics::powf64(self, n) }
+    }
+
+    #[inline]
+    fn powi(self, n: i32) -> f64 {
+        unsafe { intrinsics::powif64(self, n) }
+    }
+
+    /// sqrt(2.0)
+    #[inline]
+    fn sqrt2() -> f64 { consts::SQRT2 }
+
+    /// 1.0 / sqrt(2.0)
+    #[inline]
+    fn frac_1_sqrt2() -> f64 { consts::FRAC_1_SQRT2 }
+
+    #[inline]
+    fn sqrt(self) -> f64 {
+        unsafe { intrinsics::sqrtf64(self) }
+    }
+
+    #[inline]
+    fn rsqrt(self) -> f64 { self.sqrt().recip() }
+
+    /// Archimedes' constant
+    #[inline]
+    fn pi() -> f64 { consts::PI }
+
+    /// 2.0 * pi
+    #[inline]
+    fn two_pi() -> f64 { consts::PI_2 }
+
+    /// pi / 2.0
+    #[inline]
+    fn frac_pi_2() -> f64 { consts::FRAC_PI_2 }
+
+    /// pi / 3.0
+    #[inline]
+    fn frac_pi_3() -> f64 { consts::FRAC_PI_3 }
+
+    /// pi / 4.0
+    #[inline]
+    fn frac_pi_4() -> f64 { consts::FRAC_PI_4 }
+
+    /// pi / 6.0
+    #[inline]
+    fn frac_pi_6() -> f64 { consts::FRAC_PI_6 }
+
+    /// pi / 8.0
+    #[inline]
+    fn frac_pi_8() -> f64 { consts::FRAC_PI_8 }
+
+    /// 1.0 / pi
+    #[inline]
+    fn frac_1_pi() -> f64 { consts::FRAC_1_PI }
+
+    /// 2.0 / pi
+    #[inline]
+    fn frac_2_pi() -> f64 { consts::FRAC_2_PI }
+
+    /// 2.0 / sqrt(pi)
+    #[inline]
+    fn frac_2_sqrtpi() -> f64 { consts::FRAC_2_SQRTPI }
+
+    /// Euler's number
+    #[inline]
+    fn e() -> f64 { consts::E }
+
+    /// log2(e)
+    #[inline]
+    fn log2_e() -> f64 { consts::LOG2_E }
+
+    /// log10(e)
+    #[inline]
+    fn log10_e() -> f64 { consts::LOG10_E }
+
+    /// ln(2.0)
+    #[inline]
+    fn ln_2() -> f64 { consts::LN_2 }
+
+    /// ln(10.0)
+    #[inline]
+    fn ln_10() -> f64 { consts::LN_10 }
+
+    /// Returns the exponential of the number
+    #[inline]
+    fn exp(self) -> f64 {
+        unsafe { intrinsics::expf64(self) }
+    }
+
+    /// Returns 2 raised to the power of the number
+    #[inline]
+    fn exp2(self) -> f64 {
+        unsafe { intrinsics::exp2f64(self) }
+    }
+
+    /// Returns the natural logarithm of the number
+    #[inline]
+    fn ln(self) -> f64 {
+        unsafe { intrinsics::logf64(self) }
+    }
+
+    /// Returns the logarithm of the number with respect to an arbitrary base
+    #[inline]
+    fn log(self, base: f64) -> f64 { self.ln() / base.ln() }
+
+    /// Returns the base 2 logarithm of the number
+    #[inline]
+    fn log2(self) -> f64 {
+        unsafe { intrinsics::log2f64(self) }
+    }
+
+    /// Returns the base 10 logarithm of the number
+    #[inline]
+    fn log10(self) -> f64 {
+        unsafe { intrinsics::log10f64(self) }
+    }
+
+
+    /// Converts to degrees, assuming the number is in radians
+    #[inline]
+    fn to_degrees(self) -> f64 { self * (180.0f64 / Float::pi()) }
+
+    /// Converts to radians, assuming the number is in degrees
+    #[inline]
+    fn to_radians(self) -> f64 {
+        let value: f64 = Float::pi();
+        self * (value / 180.0)
+    }
+}
+
diff --git a/src/libcore/num/mod.rs b/src/libcore/num/mod.rs
index 22411fef3b2..47be5df67ea 100644
--- a/src/libcore/num/mod.rs
+++ b/src/libcore/num/mod.rs
@@ -874,3 +874,157 @@ pub fn test_num<T:Num + NumCast + ::std::fmt::Show>(ten: T, two: T) {
     assert_eq!(ten.div(&two),  ten / two);
     assert_eq!(ten.rem(&two),  ten % two);
 }
+
+/// Used for representing the classification of floating point numbers
+#[deriving(Eq, Show)]
+pub enum FPCategory {
+    /// "Not a Number", often obtained by dividing by zero
+    FPNaN,
+    /// Positive or negative infinity
+    FPInfinite ,
+    /// Positive or negative zero
+    FPZero,
+    /// De-normalized floating point representation (less precise than `FPNormal`)
+    FPSubnormal,
+    /// A regular floating point number
+    FPNormal,
+}
+
+/// Operations on primitive floating point numbers.
+// FIXME(#5527): In a future version of Rust, many of these functions will
+//               become constants.
+//
+// FIXME(#8888): Several of these functions have a parameter named
+//               `unused_self`. Removing it requires #8888 to be fixed.
+pub trait Float: Signed + Primitive {
+    /// Returns the NaN value.
+    fn nan() -> Self;
+    /// Returns the infinite value.
+    fn infinity() -> Self;
+    /// Returns the negative infinite value.
+    fn neg_infinity() -> Self;
+    /// Returns -0.0.
+    fn neg_zero() -> Self;
+
+    /// Returns true if this value is NaN and false otherwise.
+    fn is_nan(self) -> bool;
+    /// Returns true if this value is positive infinity or negative infinity and
+    /// false otherwise.
+    fn is_infinite(self) -> bool;
+    /// Returns true if this number is neither infinite nor NaN.
+    fn is_finite(self) -> bool;
+    /// Returns true if this number is neither zero, infinite, denormal, or NaN.
+    fn is_normal(self) -> bool;
+    /// Returns the category that this number falls into.
+    fn classify(self) -> FPCategory;
+
+    // FIXME (#5527): These should be associated constants
+
+    /// Returns the number of binary digits of mantissa that this type supports.
+    fn mantissa_digits(unused_self: Option<Self>) -> uint;
+    /// Returns the number of base-10 digits of precision that this type supports.
+    fn digits(unused_self: Option<Self>) -> uint;
+    /// Returns the difference between 1.0 and the smallest representable number larger than 1.0.
+    fn epsilon() -> Self;
+    /// Returns the minimum binary exponent that this type can represent.
+    fn min_exp(unused_self: Option<Self>) -> int;
+    /// Returns the maximum binary exponent that this type can represent.
+    fn max_exp(unused_self: Option<Self>) -> int;
+    /// Returns the minimum base-10 exponent that this type can represent.
+    fn min_10_exp(unused_self: Option<Self>) -> int;
+    /// Returns the maximum base-10 exponent that this type can represent.
+    fn max_10_exp(unused_self: Option<Self>) -> int;
+    /// Returns the smallest normalized positive number that this type can represent.
+    fn min_pos_value(unused_self: Option<Self>) -> Self;
+
+    /// Returns the mantissa, exponent and sign as integers, respectively.
+    fn integer_decode(self) -> (u64, i16, i8);
+
+    /// Return the largest integer less than or equal to a number.
+    fn floor(self) -> Self;
+    /// Return the smallest integer greater than or equal to a number.
+    fn ceil(self) -> Self;
+    /// Return the nearest integer to a number. Round half-way cases away from
+    /// `0.0`.
+    fn round(self) -> Self;
+    /// Return the integer part of a number.
+    fn trunc(self) -> Self;
+    /// Return the fractional part of a number.
+    fn fract(self) -> Self;
+
+    /// 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.
+    fn mul_add(self, a: Self, b: Self) -> Self;
+    /// Take the reciprocal (inverse) of a number, `1/x`.
+    fn recip(self) -> Self;
+
+    /// Raise a number to an integer power.
+    ///
+    /// Using this function is generally faster than using `powf`
+    fn powi(self, n: i32) -> Self;
+    /// Raise a number to a floating point power.
+    fn powf(self, n: Self) -> Self;
+
+    /// sqrt(2.0).
+    fn sqrt2() -> Self;
+    /// 1.0 / sqrt(2.0).
+    fn frac_1_sqrt2() -> Self;
+
+    /// Take the square root of a number.
+    fn sqrt(self) -> Self;
+    /// Take the reciprocal (inverse) square root of a number, `1/sqrt(x)`.
+    fn rsqrt(self) -> Self;
+
+    // FIXME (#5527): These should be associated constants
+
+    /// Archimedes' constant.
+    fn pi() -> Self;
+    /// 2.0 * pi.
+    fn two_pi() -> Self;
+    /// pi / 2.0.
+    fn frac_pi_2() -> Self;
+    /// pi / 3.0.
+    fn frac_pi_3() -> Self;
+    /// pi / 4.0.
+    fn frac_pi_4() -> Self;
+    /// pi / 6.0.
+    fn frac_pi_6() -> Self;
+    /// pi / 8.0.
+    fn frac_pi_8() -> Self;
+    /// 1.0 / pi.
+    fn frac_1_pi() -> Self;
+    /// 2.0 / pi.
+    fn frac_2_pi() -> Self;
+    /// 2.0 / sqrt(pi).
+    fn frac_2_sqrtpi() -> Self;
+
+    /// Euler's number.
+    fn e() -> Self;
+    /// log2(e).
+    fn log2_e() -> Self;
+    /// log10(e).
+    fn log10_e() -> Self;
+    /// ln(2.0).
+    fn ln_2() -> Self;
+    /// ln(10.0).
+    fn ln_10() -> Self;
+
+    /// Returns `e^(self)`, (the exponential function).
+    fn exp(self) -> Self;
+    /// Returns 2 raised to the power of the number, `2^(self)`.
+    fn exp2(self) -> Self;
+    /// Returns the natural logarithm of the number.
+    fn ln(self) -> Self;
+    /// Returns the logarithm of the number with respect to an arbitrary base.
+    fn log(self, base: Self) -> Self;
+    /// Returns the base 2 logarithm of the number.
+    fn log2(self) -> Self;
+    /// Returns the base 10 logarithm of the number.
+    fn log10(self) -> Self;
+
+    /// Convert radians to degrees.
+    fn to_degrees(self) -> Self;
+    /// Convert degrees to radians.
+    fn to_radians(self) -> Self;
+}