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

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

    #[cfg(not(bootstrap))]
    use crate::convert::FloatToInt;
    #[cfg(not(test))]
    use crate::intrinsics;
    use crate::mem;
    use crate::num::FpCategory;

    /// 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;

    /// [Machine epsilon] value for `f32`.
    ///
    /// This is the difference between `1.0` and the next larger representable number.
    ///
    /// [Machine epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon
    #[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;

        /// The full circle constant (τ)
        ///
        /// Equal to 2π.
        #[unstable(feature = "tau_constant", issue = "66770")]
        pub const TAU: f32 = 6.28318530717958647692528676655900577_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>2</sub>(10)
        #[unstable(feature = "extra_log_consts", issue = "50540")]
        pub const LOG2_10: f32 = 3.32192809488736234787031942948939018_f32;

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

        /// log<sub>10</sub>(2)
        #[unstable(feature = "extra_log_consts", issue = "50540")]
        pub const LOG10_2: f32 = 0.301029995663981195213738894724493027_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;
    }

    #[lang = "f32"]
    #[cfg(not(test))]
    impl f32 {
        /// Returns `true` if this value is `NaN`.
        ///
        /// ```
        /// use std::f32;
        ///
        /// let nan = f32::NAN;
        /// let f = 7.0_f32;
        ///
        /// assert!(nan.is_nan());
        /// assert!(!f.is_nan());
        /// ```
        #[stable(feature = "rust1", since = "1.0.0")]
        #[inline]
        pub fn is_nan(self) -> bool {
            self != self
        }

        // FIXME(#50145): `abs` is publicly unavailable in libcore due to
        // concerns about portability, so this implementation is for
        // private use internally.
        #[inline]
        fn abs_private(self) -> f32 {
            f32::from_bits(self.to_bits() & 0x7fff_ffff)
        }

        /// Returns `true` if this value is positive infinity or negative infinity, and
        /// `false` otherwise.
        ///
        /// ```
        /// use std::f32;
        ///
        /// let f = 7.0f32;
        /// let inf = f32::INFINITY;
        /// let neg_inf = f32::NEG_INFINITY;
        /// let nan = f32::NAN;
        ///
        /// assert!(!f.is_infinite());
        /// assert!(!nan.is_infinite());
        ///
        /// assert!(inf.is_infinite());
        /// assert!(neg_inf.is_infinite());
        /// ```
        #[stable(feature = "rust1", since = "1.0.0")]
        #[inline]
        pub fn is_infinite(self) -> bool {
            self.abs_private() == INFINITY
        }

        /// Returns `true` if this number is neither infinite nor `NaN`.
        ///
        /// ```
        /// use std::f32;
        ///
        /// let f = 7.0f32;
        /// let inf = f32::INFINITY;
        /// let neg_inf = f32::NEG_INFINITY;
        /// let nan = f32::NAN;
        ///
        /// assert!(f.is_finite());
        ///
        /// assert!(!nan.is_finite());
        /// assert!(!inf.is_finite());
        /// assert!(!neg_inf.is_finite());
        /// ```
        #[stable(feature = "rust1", since = "1.0.0")]
        #[inline]
        pub fn is_finite(self) -> bool {
            // There's no need to handle NaN separately: if self is NaN,
            // the comparison is not true, exactly as desired.
            self.abs_private() < INFINITY
        }

        /// Returns `true` if the number is neither zero, infinite,
        /// [subnormal][subnormal], or `NaN`.
        ///
        /// ```
        /// use std::f32;
        ///
        /// let min = f32::MIN_POSITIVE; // 1.17549435e-38f32
        /// let max = f32::MAX;
        /// let lower_than_min = 1.0e-40_f32;
        /// let zero = 0.0_f32;
        ///
        /// assert!(min.is_normal());
        /// assert!(max.is_normal());
        ///
        /// assert!(!zero.is_normal());
        /// assert!(!f32::NAN.is_normal());
        /// assert!(!f32::INFINITY.is_normal());
        /// // Values between `0` and `min` are Subnormal.
        /// assert!(!lower_than_min.is_normal());
        /// ```
        /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
        #[stable(feature = "rust1", since = "1.0.0")]
        #[inline]
        pub 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.
        ///
        /// ```
        /// use std::num::FpCategory;
        /// use std::f32;
        ///
        /// let num = 12.4_f32;
        /// let inf = f32::INFINITY;
        ///
        /// assert_eq!(num.classify(), FpCategory::Normal);
        /// assert_eq!(inf.classify(), FpCategory::Infinite);
        /// ```
        #[stable(feature = "rust1", since = "1.0.0")]
        pub fn classify(self) -> FpCategory {
            const EXP_MASK: u32 = 0x7f800000;
            const MAN_MASK: u32 = 0x007fffff;

            let bits = self.to_bits();
            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,
            }
        }

        /// Returns `true` if `self` has a positive sign, including `+0.0`, `NaN`s with
        /// positive sign bit and positive infinity.
        ///
        /// ```
        /// let f = 7.0_f32;
        /// let g = -7.0_f32;
        ///
        /// assert!(f.is_sign_positive());
        /// assert!(!g.is_sign_positive());
        /// ```
        #[stable(feature = "rust1", since = "1.0.0")]
        #[inline]
        pub fn is_sign_positive(self) -> bool {
            !self.is_sign_negative()
        }

        /// Returns `true` if `self` has a negative sign, including `-0.0`, `NaN`s with
        /// negative sign bit and negative infinity.
        ///
        /// ```
        /// let f = 7.0f32;
        /// let g = -7.0f32;
        ///
        /// assert!(!f.is_sign_negative());
        /// assert!(g.is_sign_negative());
        /// ```
        #[stable(feature = "rust1", since = "1.0.0")]
        #[inline]
        pub 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
        }

        /// Takes the reciprocal (inverse) of a number, `1/x`.
        ///
        /// ```
        /// use std::f32;
        ///
        /// let x = 2.0_f32;
        /// let abs_difference = (x.recip() - (1.0 / x)).abs();
        ///
        /// assert!(abs_difference <= f32::EPSILON);
        /// ```
        #[stable(feature = "rust1", since = "1.0.0")]
        #[inline]
        pub fn recip(self) -> f32 {
            1.0 / self
        }

        /// Converts radians to degrees.
        ///
        /// ```
        /// use std::f32::{self, consts};
        ///
        /// let angle = consts::PI;
        ///
        /// let abs_difference = (angle.to_degrees() - 180.0).abs();
        ///
        /// assert!(abs_difference <= f32::EPSILON);
        /// ```
        #[stable(feature = "f32_deg_rad_conversions", since="1.7.0")]
        #[inline]
        pub fn to_degrees(self) -> f32 {
            // Use a constant for better precision.
            const PIS_IN_180: f32 = 57.2957795130823208767981548141051703_f32;
            self * PIS_IN_180
        }

        /// Converts degrees to radians.
        ///
        /// ```
        /// use std::f32::{self, consts};
        ///
        /// let angle = 180.0f32;
        ///
        /// let abs_difference = (angle.to_radians() - consts::PI).abs();
        ///
        /// assert!(abs_difference <= f32::EPSILON);
        /// ```
        #[stable(feature = "f32_deg_rad_conversions", since="1.7.0")]
        #[inline]
        pub fn to_radians(self) -> f32 {
            let value: f32 = consts::PI;
            self * (value / 180.0f32)
        }

        /// Returns the maximum of the two numbers.
        ///
        /// ```
        /// let x = 1.0f32;
        /// let y = 2.0f32;
        ///
        /// assert_eq!(x.max(y), y);
        /// ```
        ///
        /// If one of the arguments is NaN, then the other argument is returned.
        #[stable(feature = "rust1", since = "1.0.0")]
        #[inline]
        pub fn max(self, other: f32) -> f32 {
            intrinsics::maxnumf32(self, other)
        }

        /// Returns the minimum of the two numbers.
        ///
        /// ```
        /// let x = 1.0f32;
        /// let y = 2.0f32;
        ///
        /// assert_eq!(x.min(y), x);
        /// ```
        ///
        /// If one of the arguments is NaN, then the other argument is returned.
        #[stable(feature = "rust1", since = "1.0.0")]
        #[inline]
        pub fn min(self, other: f32) -> f32 {
            intrinsics::minnumf32(self, other)
        }

        /// Rounds toward zero and converts to any primitive integer type,
        /// assuming that the value is finite and fits in that type.
        ///
        /// ```
        /// #![feature(float_approx_unchecked_to)]
        ///
        /// let value = 4.6_f32;
        /// let rounded = unsafe { value.approx_unchecked_to::<u16>() };
        /// assert_eq!(rounded, 4);
        ///
        /// let value = -128.9_f32;
        /// let rounded = unsafe { value.approx_unchecked_to::<i8>() };
        /// assert_eq!(rounded, std::i8::MIN);
        /// ```
        ///
        /// # Safety
        ///
        /// The value must:
        ///
        /// * Not be `NaN`
        /// * Not be infinite
        /// * Be representable in the return type `Int`, after truncating off its fractional part
        #[cfg(not(bootstrap))]
        #[unstable(feature = "float_approx_unchecked_to", issue = "67058")]
        #[inline]
        pub unsafe fn approx_unchecked_to<Int>(self) -> Int where Self: FloatToInt<Int> {
            FloatToInt::<Int>::approx_unchecked(self)
        }

        /// Raw transmutation to `u32`.
        ///
        /// This is currently identical to `transmute::<f32, u32>(self)` on all platforms.
        ///
        /// See `from_bits` for some discussion of the portability of this operation
        /// (there are almost no issues).
        ///
        /// Note that this function is distinct from `as` casting, which attempts to
        /// preserve the *numeric* value, and not the bitwise value.
        ///
        /// # Examples
        ///
        /// ```
        /// assert_ne!((1f32).to_bits(), 1f32 as u32); // to_bits() is not casting!
        /// assert_eq!((12.5f32).to_bits(), 0x41480000);
        ///
        /// ```
        #[stable(feature = "float_bits_conv", since = "1.20.0")]
        #[inline]
        pub fn to_bits(self) -> u32 {
            // SAFETY: `u32` is a plain old datatype so we can always transmute to it
            unsafe { mem::transmute(self) }
        }

        /// Raw transmutation from `u32`.
        ///
        /// This is currently identical to `transmute::<u32, f32>(v)` on all platforms.
        /// It turns out this is incredibly portable, for two reasons:
        ///
        /// * Floats and Ints have the same endianness on all supported platforms.
        /// * IEEE-754 very precisely specifies the bit layout of floats.
        ///
        /// However there is one caveat: prior to the 2008 version of IEEE-754, how
        /// to interpret the NaN signaling bit wasn't actually specified. Most platforms
        /// (notably x86 and ARM) picked the interpretation that was ultimately
        /// standardized in 2008, but some didn't (notably MIPS). As a result, all
        /// signaling NaNs on MIPS are quiet NaNs on x86, and vice-versa.
        ///
        /// Rather than trying to preserve signaling-ness cross-platform, this
        /// implementation favors preserving the exact bits. This means that
        /// any payloads encoded in NaNs will be preserved even if the result of
        /// this method is sent over the network from an x86 machine to a MIPS one.
        ///
        /// If the results of this method are only manipulated by the same
        /// architecture that produced them, then there is no portability concern.
        ///
        /// If the input isn't NaN, then there is no portability concern.
        ///
        /// If you don't care about signalingness (very likely), then there is no
        /// portability concern.
        ///
        /// Note that this function is distinct from `as` casting, which attempts to
        /// preserve the *numeric* value, and not the bitwise value.
        ///
        /// # Examples
        ///
        /// ```
        /// let v = f32::from_bits(0x41480000);
        /// assert_eq!(v, 12.5);
        /// ```
        #[stable(feature = "float_bits_conv", since = "1.20.0")]
        #[inline]
        pub fn from_bits(v: u32) -> Self {
            // SAFETY: `u32` is a plain old datatype so we can always transmute from it
            // It turns out the safety issues with sNaN were overblown! Hooray!
            unsafe { mem::transmute(v) }
        }

        /// Return the memory representation of this floating point number as a byte array in
        /// big-endian (network) byte order.
        ///
        /// # Examples
        ///
        /// ```
        /// let bytes = 12.5f32.to_be_bytes();
        /// assert_eq!(bytes, [0x41, 0x48, 0x00, 0x00]);
        /// ```
        #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
        #[inline]
        pub fn to_be_bytes(self) -> [u8; 4] {
            self.to_bits().to_be_bytes()
        }

        /// Return the memory representation of this floating point number as a byte array in
        /// little-endian byte order.
        ///
        /// # Examples
        ///
        /// ```
        /// let bytes = 12.5f32.to_le_bytes();
        /// assert_eq!(bytes, [0x00, 0x00, 0x48, 0x41]);
        /// ```
        #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
        #[inline]
        pub fn to_le_bytes(self) -> [u8; 4] {
            self.to_bits().to_le_bytes()
        }

        /// Return the memory representation of this floating point number as a byte array in
        /// native byte order.
        ///
        /// As the target platform's native endianness is used, portable code
        /// should use [`to_be_bytes`] or [`to_le_bytes`], as appropriate, instead.
        ///
        /// [`to_be_bytes`]: #method.to_be_bytes
        /// [`to_le_bytes`]: #method.to_le_bytes
        ///
        /// # Examples
        ///
        /// ```
        /// let bytes = 12.5f32.to_ne_bytes();
        /// assert_eq!(
        ///     bytes,
        ///     if cfg!(target_endian = "big") {
        ///         [0x41, 0x48, 0x00, 0x00]
        ///     } else {
        ///         [0x00, 0x00, 0x48, 0x41]
        ///     }
        /// );
        /// ```
        #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
        #[inline]
        pub fn to_ne_bytes(self) -> [u8; 4] {
            self.to_bits().to_ne_bytes()
        }

        /// Create a floating point value from its representation as a byte array in big endian.
        ///
        /// # Examples
        ///
        /// ```
        /// let value = f32::from_be_bytes([0x41, 0x48, 0x00, 0x00]);
        /// assert_eq!(value, 12.5);
        /// ```
        #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
        #[inline]
        pub fn from_be_bytes(bytes: [u8; 4]) -> Self {
            Self::from_bits(u32::from_be_bytes(bytes))
        }

        /// Create a floating point value from its representation as a byte array in little endian.
        ///
        /// # Examples
        ///
        /// ```
        /// let value = f32::from_le_bytes([0x00, 0x00, 0x48, 0x41]);
        /// assert_eq!(value, 12.5);
        /// ```
        #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
        #[inline]
        pub fn from_le_bytes(bytes: [u8; 4]) -> Self {
            Self::from_bits(u32::from_le_bytes(bytes))
        }

        /// Create a floating point value from its representation as a byte array in native endian.
        ///
        /// As the target platform's native endianness is used, portable code
        /// likely wants to use [`from_be_bytes`] or [`from_le_bytes`], as
        /// appropriate instead.
        ///
        /// [`from_be_bytes`]: #method.from_be_bytes
        /// [`from_le_bytes`]: #method.from_le_bytes
        ///
        /// # Examples
        ///
        /// ```
        /// let value = f32::from_ne_bytes(if cfg!(target_endian = "big") {
        ///     [0x41, 0x48, 0x00, 0x00]
        /// } else {
        ///     [0x00, 0x00, 0x48, 0x41]
        /// });
        /// assert_eq!(value, 12.5);
        /// ```
        #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
        #[inline]
        pub fn from_ne_bytes(bytes: [u8; 4]) -> Self {
            Self::from_bits(u32::from_ne_bytes(bytes))
        }
    }