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    // Copyright 2012-2014 The Rust Project Developers. See the COPYRIGHT
    // file at the top-level directory of this distribution and at
    // http://rust-lang.org/COPYRIGHT.
    //
    // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
    // http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
    // <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
    // option. This file may not be copied, modified, or distributed
    // except according to those terms.

    //! This module provides constants which are specific to the implementation
    //! of the `f32` floating point data type.
    //!
    //! Mathematically significant numbers are provided in the `consts` sub-module.
    //!
    //! *[See also the `f32` primitive type](../../std/primitive.f32.html).*

    #![stable(feature = "rust1", since = "1.0.0")]

    use intrinsics;
    use mem;
    use num::Float;
    use num::FpCategory as Fp;

    /// The radix or base of the internal representation of `f32`.
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const RADIX: u32 = 2;

    /// Number of significant digits in base 2.
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const MANTISSA_DIGITS: u32 = 24;
    /// Approximate number of significant digits in base 10.
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const DIGITS: u32 = 6;

    /// Difference between `1.0` and the next largest representable number.
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const EPSILON: f32 = 1.19209290e-07_f32;

    /// Smallest finite `f32` value.
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const MIN: f32 = -3.40282347e+38_f32;
    /// Smallest positive normal `f32` value.
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const MIN_POSITIVE: f32 = 1.17549435e-38_f32;
    /// Largest finite `f32` value.
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const MAX: f32 = 3.40282347e+38_f32;

    /// One greater than the minimum possible normal power of 2 exponent.
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const MIN_EXP: i32 = -125;
    /// Maximum possible power of 2 exponent.
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const MAX_EXP: i32 = 128;

    /// Minimum possible normal power of 10 exponent.
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const MIN_10_EXP: i32 = -37;
    /// Maximum possible power of 10 exponent.
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const MAX_10_EXP: i32 = 38;

    /// Not a Number (NaN).
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const NAN: f32 = 0.0_f32 / 0.0_f32;
    /// Infinity (∞).
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const INFINITY: f32 = 1.0_f32 / 0.0_f32;
    /// Negative infinity (-∞).
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const NEG_INFINITY: f32 = -1.0_f32 / 0.0_f32;

    /// Basic mathematical constants.
    #[stable(feature = "rust1", since = "1.0.0")]
    pub mod consts {
        // FIXME: replace with mathematical constants from cmath.

        /// Archimedes' constant (π)
        #[stable(feature = "rust1", since = "1.0.0")]
        pub const PI: f32 = 3.14159265358979323846264338327950288_f32;

        /// π/2
        #[stable(feature = "rust1", since = "1.0.0")]
        pub const FRAC_PI_2: f32 = 1.57079632679489661923132169163975144_f32;

        /// π/3
        #[stable(feature = "rust1", since = "1.0.0")]
        pub const FRAC_PI_3: f32 = 1.04719755119659774615421446109316763_f32;

        /// π/4
        #[stable(feature = "rust1", since = "1.0.0")]
        pub const FRAC_PI_4: f32 = 0.785398163397448309615660845819875721_f32;

        /// π/6
        #[stable(feature = "rust1", since = "1.0.0")]
        pub const FRAC_PI_6: f32 = 0.52359877559829887307710723054658381_f32;

        /// π/8
        #[stable(feature = "rust1", since = "1.0.0")]
        pub const FRAC_PI_8: f32 = 0.39269908169872415480783042290993786_f32;

        /// 1/π
        #[stable(feature = "rust1", since = "1.0.0")]
        pub const FRAC_1_PI: f32 = 0.318309886183790671537767526745028724_f32;

        /// 2/π
        #[stable(feature = "rust1", since = "1.0.0")]
        pub const FRAC_2_PI: f32 = 0.636619772367581343075535053490057448_f32;

        /// 2/sqrt(π)
        #[stable(feature = "rust1", since = "1.0.0")]
        pub const FRAC_2_SQRT_PI: f32 = 1.12837916709551257389615890312154517_f32;

        /// sqrt(2)
        #[stable(feature = "rust1", since = "1.0.0")]
        pub const SQRT_2: f32 = 1.41421356237309504880168872420969808_f32;

        /// 1/sqrt(2)
        #[stable(feature = "rust1", since = "1.0.0")]
        pub const FRAC_1_SQRT_2: f32 = 0.707106781186547524400844362104849039_f32;

        /// Euler's number (e)
        #[stable(feature = "rust1", since = "1.0.0")]
        pub const E: f32 = 2.71828182845904523536028747135266250_f32;

        /// log<sub>2</sub>(e)
        #[stable(feature = "rust1", since = "1.0.0")]
        pub const LOG2_E: f32 = 1.44269504088896340735992468100189214_f32;

        /// log<sub>10</sub>(e)
        #[stable(feature = "rust1", since = "1.0.0")]
        pub const LOG10_E: f32 = 0.434294481903251827651128918916605082_f32;

        /// ln(2)
        #[stable(feature = "rust1", since = "1.0.0")]
        pub const LN_2: f32 = 0.693147180559945309417232121458176568_f32;

        /// ln(10)
        #[stable(feature = "rust1", since = "1.0.0")]
        pub const LN_10: f32 = 2.30258509299404568401799145468436421_f32;
    }

    #[unstable(feature = "core_float",
               reason = "stable interface is via `impl f{32,64}` in later crates",
               issue = "32110")]
    impl Float for f32 {
        type Bits = u32;

        /// 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 == INFINITY || 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() == Fp::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.
        fn classify(self) -> Fp {
            const EXP_MASK: u32 = 0x7f800000;
            const MAN_MASK: u32 = 0x007fffff;

            let bits = self.to_bits();
            match (bits & MAN_MASK, bits & EXP_MASK) {
                (0, 0) => Fp::Zero,
                (_, 0) => Fp::Subnormal,
                (0, EXP_MASK) => Fp::Infinite,
                (_, EXP_MASK) => Fp::Nan,
                _ => Fp::Normal,
            }
        }

        /// Computes the absolute value of `self`. Returns `Float::nan()` if the
        /// number is `Float::nan()`.
        #[inline]
        fn abs(self) -> f32 {
            unsafe { intrinsics::fabsf32(self) }
        }

        /// Returns a number that represents the sign of `self`.
        ///
        /// - `1.0` if the number is positive, `+0.0` or `Float::infinity()`
        /// - `-1.0` if the number is negative, `-0.0` or `Float::neg_infinity()`
        /// - `Float::nan()` if the number is `Float::nan()`
        #[inline]
        fn signum(self) -> f32 {
            if self.is_nan() {
                NAN
            } else {
                unsafe { intrinsics::copysignf32(1.0, self) }
            }
        }

        /// Returns `true` if and only if `self` has a positive sign, including `+0.0`, `NaN`s with
        /// positive sign bit and positive infinity.
        #[inline]
        fn is_sign_positive(self) -> bool {
            !self.is_sign_negative()
        }

        /// Returns `true` if and only if `self` has a negative sign, including `-0.0`, `NaN`s with
        /// negative sign bit and negative infinity.
        #[inline]
        fn is_sign_negative(self) -> bool {
            // IEEE754 says: isSignMinus(x) is true if and only if x has negative sign. isSignMinus
            // applies to zeros and NaNs as well.
            self.to_bits() & 0x8000_0000 != 0
        }

        /// Returns the reciprocal (multiplicative inverse) of the number.
        #[inline]
        fn recip(self) -> f32 {
            1.0 / self
        }

        #[inline]
        fn powi(self, n: i32) -> f32 {
            unsafe { intrinsics::powif32(self, n) }
        }

        /// Converts to degrees, assuming the number is in radians.
        #[inline]
        fn to_degrees(self) -> f32 {
            // Use a constant for better precision.
            const PIS_IN_180: f32 = 57.2957795130823208767981548141051703_f32;
            self * PIS_IN_180
        }

        /// Converts to radians, assuming the number is in degrees.
        #[inline]
        fn to_radians(self) -> f32 {
            let value: f32 = consts::PI;
            self * (value / 180.0f32)
        }

        /// Returns the maximum of the two numbers.
        #[inline]
        fn max(self, other: f32) -> f32 {
            // IEEE754 says: maxNum(x, y) is the canonicalized number y if x < y, x if y < x, the
            // canonicalized number if one operand is a number and the other a quiet NaN. Otherwise it
            // is either x or y, canonicalized (this means results might differ among implementations).
            // When either x or y is a signalingNaN, then the result is according to 6.2.
            //
            // Since we do not support sNaN in Rust yet, we do not need to handle them.
            // FIXME(nagisa): due to https://bugs.llvm.org/show_bug.cgi?id=33303 we canonicalize by
            // multiplying by 1.0. Should switch to the `canonicalize` when it works.
            (if self.is_nan() || self < other { other } else { self }) * 1.0
        }

        /// Returns the minimum of the two numbers.
        #[inline]
        fn min(self, other: f32) -> f32 {
            // IEEE754 says: minNum(x, y) is the canonicalized number x if x < y, y if y < x, the
            // canonicalized number if one operand is a number and the other a quiet NaN. Otherwise it
            // is either x or y, canonicalized (this means results might differ among implementations).
            // When either x or y is a signalingNaN, then the result is according to 6.2.
            //
            // Since we do not support sNaN in Rust yet, we do not need to handle them.
            // FIXME(nagisa): due to https://bugs.llvm.org/show_bug.cgi?id=33303 we canonicalize by
            // multiplying by 1.0. Should switch to the `canonicalize` when it works.
            (if other.is_nan() || self < other { self } else { other }) * 1.0
        }

        /// Raw transmutation to `u32`.
        #[inline]
        fn to_bits(self) -> u32 {
            unsafe { mem::transmute(self) }
        }

        /// Raw transmutation from `u32`.
        #[inline]
        fn from_bits(v: u32) -> Self {
            // It turns out the safety issues with sNaN were overblown! Hooray!
            unsafe { mem::transmute(v) }
        }
    }

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