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]

Author: alexcrichton

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)
+    }
+}