f32.rs

//! Constants specific to the `f32` single-precision floating point type.
//!
//! *[See also the `f32` primitive type][f32].*
//!
//! Mathematically significant numbers are provided in the `consts` sub-module.
//!
//! For the constants defined directly in this module
//! (as distinct from those defined in the `consts` sub-module),
//! new code should instead use the associated constants
//! defined directly on the `f32` type.

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

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`.
/// Use [`f32::RADIX`] instead.
///
/// # Examples
///
/// ```rust
/// // deprecated way
/// # #[allow(deprecated, deprecated_in_future)]
/// let r = std::f32::RADIX;
///
/// // intended way
/// let r = f32::RADIX;
/// ```
#[stable(feature = "rust1", since = "1.0.0")]
#[rustc_deprecated(since = "TBD", reason = "replaced by the `RADIX` associated constant on `f32`")]
pub const RADIX: u32 = f32::RADIX;

/// Number of significant digits in base 2.
/// Use [`f32::MANTISSA_DIGITS`] instead.
///
/// # Examples
///
/// ```rust
/// // deprecated way
/// # #[allow(deprecated, deprecated_in_future)]
/// let d = std::f32::MANTISSA_DIGITS;
///
/// // intended way
/// let d = f32::MANTISSA_DIGITS;
/// ```
#[stable(feature = "rust1", since = "1.0.0")]
#[rustc_deprecated(
    since = "TBD",
    reason = "replaced by the `MANTISSA_DIGITS` associated constant on `f32`"
)]
pub const MANTISSA_DIGITS: u32 = f32::MANTISSA_DIGITS;

/// Approximate number of significant digits in base 10.
/// Use [`f32::DIGITS`] instead.
///
/// # Examples
///
/// ```rust
/// // deprecated way
/// # #[allow(deprecated, deprecated_in_future)]
/// let d = std::f32::DIGITS;
///
/// // intended way
/// let d = f32::DIGITS;
/// ```
#[stable(feature = "rust1", since = "1.0.0")]
#[rustc_deprecated(since = "TBD", reason = "replaced by the `DIGITS` associated constant on `f32`")]
pub const DIGITS: u32 = f32::DIGITS;

/// [Machine epsilon] value for `f32`.
/// Use [`f32::EPSILON`] instead.
///
/// This is the difference between `1.0` and the next larger representable number.
///
/// [Machine epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon
///
/// # Examples
///
/// ```rust
/// // deprecated way
/// # #[allow(deprecated, deprecated_in_future)]
/// let e = std::f32::EPSILON;
///
/// // intended way
/// let e = f32::EPSILON;
/// ```
#[stable(feature = "rust1", since = "1.0.0")]
#[rustc_deprecated(
    since = "TBD",
    reason = "replaced by the `EPSILON` associated constant on `f32`"
)]
pub const EPSILON: f32 = f32::EPSILON;

/// Smallest finite `f32` value.
/// Use [`f32::MIN`] instead.
///
/// # Examples
///
/// ```rust
/// // deprecated way
/// # #[allow(deprecated, deprecated_in_future)]
/// let min = std::f32::MIN;
///
/// // intended way
/// let min = f32::MIN;
/// ```
#[stable(feature = "rust1", since = "1.0.0")]
#[rustc_deprecated(since = "TBD", reason = "replaced by the `MIN` associated constant on `f32`")]
pub const MIN: f32 = f32::MIN;

/// Smallest positive normal `f32` value.
/// Use [`f32::MIN_POSITIVE`] instead.
///
/// # Examples
///
/// ```rust
/// // deprecated way
/// # #[allow(deprecated, deprecated_in_future)]
/// let min = std::f32::MIN_POSITIVE;
///
/// // intended way
/// let min = f32::MIN_POSITIVE;
/// ```
#[stable(feature = "rust1", since = "1.0.0")]
#[rustc_deprecated(
    since = "TBD",
    reason = "replaced by the `MIN_POSITIVE` associated constant on `f32`"
)]
pub const MIN_POSITIVE: f32 = f32::MIN_POSITIVE;

/// Largest finite `f32` value.
/// Use [`f32::MAX`] instead.
///
/// # Examples
///
/// ```rust
/// // deprecated way
/// # #[allow(deprecated, deprecated_in_future)]
/// let max = std::f32::MAX;
///
/// // intended way
/// let max = f32::MAX;
/// ```
#[stable(feature = "rust1", since = "1.0.0")]
#[rustc_deprecated(since = "TBD", reason = "replaced by the `MAX` associated constant on `f32`")]
pub const MAX: f32 = f32::MAX;

/// One greater than the minimum possible normal power of 2 exponent.
/// Use [`f32::MIN_EXP`] instead.
///
/// # Examples
///
/// ```rust
/// // deprecated way
/// # #[allow(deprecated, deprecated_in_future)]
/// let min = std::f32::MIN_EXP;
///
/// // intended way
/// let min = f32::MIN_EXP;
/// ```
#[stable(feature = "rust1", since = "1.0.0")]
#[rustc_deprecated(
    since = "TBD",
    reason = "replaced by the `MIN_EXP` associated constant on `f32`"
)]
pub const MIN_EXP: i32 = f32::MIN_EXP;

/// Maximum possible power of 2 exponent.
/// Use [`f32::MAX_EXP`] instead.
///
/// # Examples
///
/// ```rust
/// // deprecated way
/// # #[allow(deprecated, deprecated_in_future)]
/// let max = std::f32::MAX_EXP;
///
/// // intended way
/// let max = f32::MAX_EXP;
/// ```
#[stable(feature = "rust1", since = "1.0.0")]
#[rustc_deprecated(
    since = "TBD",
    reason = "replaced by the `MAX_EXP` associated constant on `f32`"
)]
pub const MAX_EXP: i32 = f32::MAX_EXP;

/// Minimum possible normal power of 10 exponent.
/// Use [`f32::MIN_10_EXP`] instead.
///
/// # Examples
///
/// ```rust
/// // deprecated way
/// # #[allow(deprecated, deprecated_in_future)]
/// let min = std::f32::MIN_10_EXP;
///
/// // intended way
/// let min = f32::MIN_10_EXP;
/// ```
#[stable(feature = "rust1", since = "1.0.0")]
#[rustc_deprecated(
    since = "TBD",
    reason = "replaced by the `MIN_10_EXP` associated constant on `f32`"
)]
pub const MIN_10_EXP: i32 = f32::MIN_10_EXP;

/// Maximum possible power of 10 exponent.
/// Use [`f32::MAX_10_EXP`] instead.
///
/// # Examples
///
/// ```rust
/// // deprecated way
/// # #[allow(deprecated, deprecated_in_future)]
/// let max = std::f32::MAX_10_EXP;
///
/// // intended way
/// let max = f32::MAX_10_EXP;
/// ```
#[stable(feature = "rust1", since = "1.0.0")]
#[rustc_deprecated(
    since = "TBD",
    reason = "replaced by the `MAX_10_EXP` associated constant on `f32`"
)]
pub const MAX_10_EXP: i32 = f32::MAX_10_EXP;

/// Not a Number (NaN).
/// Use [`f32::NAN`] instead.
///
/// # Examples
///
/// ```rust
/// // deprecated way
/// # #[allow(deprecated, deprecated_in_future)]
/// let nan = std::f32::NAN;
///
/// // intended way
/// let nan = f32::NAN;
/// ```
#[stable(feature = "rust1", since = "1.0.0")]
#[rustc_deprecated(since = "TBD", reason = "replaced by the `NAN` associated constant on `f32`")]
pub const NAN: f32 = f32::NAN;

/// Infinity (∞).
/// Use [`f32::INFINITY`] instead.
///
/// # Examples
///
/// ```rust
/// // deprecated way
/// # #[allow(deprecated, deprecated_in_future)]
/// let inf = std::f32::INFINITY;
///
/// // intended way
/// let inf = f32::INFINITY;
/// ```
#[stable(feature = "rust1", since = "1.0.0")]
#[rustc_deprecated(
    since = "TBD",
    reason = "replaced by the `INFINITY` associated constant on `f32`"
)]
pub const INFINITY: f32 = f32::INFINITY;

/// Negative infinity (−∞).
/// Use [`f32::NEG_INFINITY`] instead.
///
/// # Examples
///
/// ```rust
/// // deprecated way
/// # #[allow(deprecated, deprecated_in_future)]
/// let ninf = std::f32::NEG_INFINITY;
///
/// // intended way
/// let ninf = f32::NEG_INFINITY;
/// ```
#[stable(feature = "rust1", since = "1.0.0")]
#[rustc_deprecated(
    since = "TBD",
    reason = "replaced by the `NEG_INFINITY` associated constant on `f32`"
)]
pub const NEG_INFINITY: f32 = f32::NEG_INFINITY;

/// 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.
    #[stable(feature = "tau_constant", since = "1.47.0")]
    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)
    #[stable(feature = "extra_log_consts", since = "1.43.0")]
    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)
    #[stable(feature = "extra_log_consts", since = "1.43.0")]
    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;
}

#[cfg(not(test))]
impl f32 {
    /// The radix or base of the internal representation of `f32`.
    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
    pub const RADIX: u32 = 2;

    /// Number of significant digits in base 2.
    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
    pub const MANTISSA_DIGITS: u32 = 24;

    /// Approximate number of significant digits in base 10.
    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
    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 = "assoc_int_consts", since = "1.43.0")]
    pub const EPSILON: f32 = 1.19209290e-07_f32;

    /// Smallest finite `f32` value.
    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
    pub const MIN: f32 = -3.40282347e+38_f32;
    /// Smallest positive normal `f32` value.
    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
    pub const MIN_POSITIVE: f32 = 1.17549435e-38_f32;
    /// Largest finite `f32` value.
    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
    pub const MAX: f32 = 3.40282347e+38_f32;

    /// One greater than the minimum possible normal power of 2 exponent.
    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
    pub const MIN_EXP: i32 = -125;
    /// Maximum possible power of 2 exponent.
    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
    pub const MAX_EXP: i32 = 128;

    /// Minimum possible normal power of 10 exponent.
    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
    pub const MIN_10_EXP: i32 = -37;
    /// Maximum possible power of 10 exponent.
    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
    pub const MAX_10_EXP: i32 = 38;

    /// Not a Number (NaN).
    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
    pub const NAN: f32 = 0.0_f32 / 0.0_f32;
    /// Infinity (∞).
    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
    pub const INFINITY: f32 = 1.0_f32 / 0.0_f32;
    /// Negative infinity (−∞).
    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
    pub const NEG_INFINITY: f32 = -1.0_f32 / 0.0_f32;

    /// Returns `true` if this value is `NaN`.
    ///
    /// ```
    /// let nan = f32::NAN;
    /// let f = 7.0_f32;
    ///
    /// assert!(nan.is_nan());
    /// assert!(!f.is_nan());
    /// ```
    #[must_use]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
    #[inline]
    pub const 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]
    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
    pub(crate) const fn abs_private(self) -> f32 {
        // SAFETY: This transmutation is fine. Probably. For the reasons std is using it.
        unsafe { mem::transmute::<u32, f32>(mem::transmute::<f32, u32>(self) & 0x7fff_ffff) }
    }

    /// Returns `true` if this value is positive infinity or negative infinity, and
    /// `false` otherwise.
    ///
    /// ```
    /// 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());
    /// ```
    #[must_use]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
    #[inline]
    pub const fn is_infinite(self) -> bool {
        // Getting clever with transmutation can result in incorrect answers on some FPUs
        // FIXME: alter the Rust <-> Rust calling convention to prevent this problem.
        // See https://github.com/rust-lang/rust/issues/72327
        (self == f32::INFINITY) | (self == f32::NEG_INFINITY)
    }

    /// Returns `true` if this number is neither infinite nor `NaN`.
    ///
    /// ```
    /// 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());
    /// ```
    #[must_use]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
    #[inline]
    pub const 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() < Self::INFINITY
    }

    /// Returns `true` if the number is [subnormal].
    ///
    /// ```
    /// 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_subnormal());
    /// assert!(!max.is_subnormal());
    ///
    /// assert!(!zero.is_subnormal());
    /// assert!(!f32::NAN.is_subnormal());
    /// assert!(!f32::INFINITY.is_subnormal());
    /// // Values between `0` and `min` are Subnormal.
    /// assert!(lower_than_min.is_subnormal());
    /// ```
    /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
    #[must_use]
    #[stable(feature = "is_subnormal", since = "1.53.0")]
    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
    #[inline]
    pub const fn is_subnormal(self) -> bool {
        matches!(self.classify(), FpCategory::Subnormal)
    }

    /// Returns `true` if the number is neither zero, infinite,
    /// [subnormal], or `NaN`.
    ///
    /// ```
    /// 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
    #[must_use]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
    #[inline]
    pub const fn is_normal(self) -> bool {
        matches!(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;
    ///
    /// 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")]
    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
    pub const fn classify(self) -> FpCategory {
        // A previous implementation tried to only use bitmask-based checks,
        // using f32::to_bits to transmute the float to its bit repr and match on that.
        // Unfortunately, floating point numbers can be much worse than that.
        // This also needs to not result in recursive evaluations of f64::to_bits.
        //
        // On some processors, in some cases, LLVM will "helpfully" lower floating point ops,
        // in spite of a request for them using f32 and f64, to things like x87 operations.
        // These have an f64's mantissa, but can have a larger than normal exponent.
        // FIXME(jubilee): Using x87 operations is never necessary in order to function
        // on x86 processors for Rust-to-Rust calls, so this issue should not happen.
        // Code generation should be adjusted to use non-C calling conventions, avoiding this.
        //
        if self.is_infinite() {
            // Thus, a value may compare unequal to infinity, despite having a "full" exponent mask.
            FpCategory::Infinite
        } else if self.is_nan() {
            // And it may not be NaN, as it can simply be an "overextended" finite value.
            FpCategory::Nan
        } else {
            // However, std can't simply compare to zero to check for zero, either,
            // as correctness requires avoiding equality tests that may be Subnormal == -0.0
            // because it may be wrong under "denormals are zero" and "flush to zero" modes.
            // Most of std's targets don't use those, but they are used for thumbv7neon.
            // So, this does use bitpattern matching for the rest.

            // SAFETY: f32 to u32 is fine. Usually.
            // If classify has gotten this far, the value is definitely in one of these categories.
            unsafe { f32::partial_classify(self) }
        }
    }

    // This doesn't actually return a right answer for NaN on purpose,
    // seeing as how it cannot correctly discern between a floating point NaN,
    // and some normal floating point numbers truncated from an x87 FPU.
    // FIXME(jubilee): This probably could at least answer things correctly for Infinity,
    // like the f64 version does, but I need to run more checks on how things go on x86.
    // I fear losing mantissa data that would have answered that differently.
    //
    // # Safety
    // This requires making sure you call this function for values it answers correctly on,
    // otherwise it returns a wrong answer. This is not important for memory safety per se,
    // but getting floats correct is important for not accidentally leaking const eval
    // runtime-deviating logic which may or may not be acceptable.
    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
    const unsafe fn partial_classify(self) -> FpCategory {
        const EXP_MASK: u32 = 0x7f800000;
        const MAN_MASK: u32 = 0x007fffff;

        // SAFETY: The caller is not asking questions for which this will tell lies.
        let b = unsafe { mem::transmute::<f32, u32>(self) };
        match (b & MAN_MASK, b & EXP_MASK) {
            (0, 0) => FpCategory::Zero,
            (_, 0) => FpCategory::Subnormal,
            _ => FpCategory::Normal,
        }
    }

    // This operates on bits, and only bits, so it can ignore concerns about weird FPUs.
    // FIXME(jubilee): In a just world, this would be the entire impl for classify,
    // plus a transmute. We do not live in a just world, but we can make it more so.
    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
    const fn classify_bits(b: u32) -> FpCategory {
        const EXP_MASK: u32 = 0x7f800000;
        const MAN_MASK: u32 = 0x007fffff;

        match (b & MAN_MASK, b & EXP_MASK) {
            (0, EXP_MASK) => FpCategory::Infinite,
            (_, EXP_MASK) => FpCategory::Nan,
            (0, 0) => FpCategory::Zero,
            (_, 0) => FpCategory::Subnormal,
            _ => 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());
    /// ```
    #[must_use]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
    #[inline]
    pub const 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());
    /// ```
    #[must_use]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
    #[inline]
    pub const 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.
        // SAFETY: This is just transmuting to get the sign bit, it's fine.
        unsafe { mem::transmute::<f32, u32>(self) & 0x8000_0000 != 0 }
    }

    /// Takes the reciprocal (inverse) of a number, `1/x`.
    ///
    /// ```
    /// let x = 2.0_f32;
    /// let abs_difference = (x.recip() - (1.0 / x)).abs();
    ///
    /// assert!(abs_difference <= f32::EPSILON);
    /// ```
    #[must_use = "this returns the result of the operation, without modifying the original"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn recip(self) -> f32 {
        1.0 / self
    }

    /// Converts radians to degrees.
    ///
    /// ```
    /// let angle = std::f32::consts::PI;
    ///
    /// let abs_difference = (angle.to_degrees() - 180.0).abs();
    ///
    /// assert!(abs_difference <= f32::EPSILON);
    /// ```
    #[must_use = "this returns the result of the operation, \
                  without modifying the original"]
    #[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.
    ///
    /// ```
    /// let angle = 180.0f32;
    ///
    /// let abs_difference = (angle.to_radians() - std::f32::consts::PI).abs();
    ///
    /// assert!(abs_difference <= f32::EPSILON);
    /// ```
    #[must_use = "this returns the result of the operation, \
                  without modifying the original"]
    #[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.
    ///
    /// Follows the IEEE-754 2008 semantics for maxNum, except for handling of signaling NaNs.
    /// This matches the behavior of libm’s fmax.
    ///
    /// ```
    /// 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.
    #[must_use = "this returns the result of the comparison, without modifying either input"]
    #[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.
    ///
    /// Follows the IEEE-754 2008 semantics for minNum, except for handling of signaling NaNs.
    /// This matches the behavior of libm’s fmin.
    ///
    /// ```
    /// 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.
    #[must_use = "this returns the result of the comparison, without modifying either input"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn min(self, other: f32) -> f32 {
        intrinsics::minnumf32(self, other)
    }

    /// Returns the maximum of the two numbers, propagating NaNs.
    ///
    /// This returns NaN when *either* argument is NaN, as opposed to
    /// [`f32::max`] which only returns NaN when *both* arguments are NaN.
    ///
    /// ```
    /// #![feature(float_minimum_maximum)]
    /// let x = 1.0f32;
    /// let y = 2.0f32;
    ///
    /// assert_eq!(x.maximum(y), y);
    /// assert!(x.maximum(f32::NAN).is_nan());
    /// ```
    ///
    /// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the greater
    /// of the two numbers. For this operation, -0.0 is considered to be less than +0.0.
    /// Note that this follows the semantics specified in IEEE 754-2019.
    #[must_use = "this returns the result of the comparison, without modifying either input"]
    #[unstable(feature = "float_minimum_maximum", issue = "91079")]
    #[inline]
    pub fn maximum(self, other: f32) -> f32 {
        if self > other {
            self
        } else if other > self {
            other
        } else if self == other {
            if self.is_sign_positive() && other.is_sign_negative() { self } else { other }
        } else {
            self + other
        }
    }

    /// Returns the minimum of the two numbers, propagating NaNs.
    ///
    /// This returns NaN when *either* argument is NaN, as opposed to
    /// [`f32::min`] which only returns NaN when *both* arguments are NaN.
    ///
    /// ```
    /// #![feature(float_minimum_maximum)]
    /// let x = 1.0f32;
    /// let y = 2.0f32;
    ///
    /// assert_eq!(x.minimum(y), x);
    /// assert!(x.minimum(f32::NAN).is_nan());
    /// ```
    ///
    /// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the lesser
    /// of the two numbers. For this operation, -0.0 is considered to be less than +0.0.
    /// Note that this follows the semantics specified in IEEE 754-2019.
    #[must_use = "this returns the result of the comparison, without modifying either input"]
    #[unstable(feature = "float_minimum_maximum", issue = "91079")]
    #[inline]
    pub fn minimum(self, other: f32) -> f32 {
        if self < other {
            self
        } else if other < self {
            other
        } else if self == other {
            if self.is_sign_negative() && other.is_sign_positive() { self } else { other }
        } else {
            self + other
        }
    }

    /// Rounds toward zero and converts to any primitive integer type,
    /// assuming that the value is finite and fits in that type.
    ///
    /// ```
    /// let value = 4.6_f32;
    /// let rounded = unsafe { value.to_int_unchecked::<u16>() };
    /// assert_eq!(rounded, 4);
    ///
    /// let value = -128.9_f32;
    /// let rounded = unsafe { value.to_int_unchecked::<i8>() };
    /// assert_eq!(rounded, 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
    #[must_use = "this returns the result of the operation, \
                  without modifying the original"]
    #[stable(feature = "float_approx_unchecked_to", since = "1.44.0")]
    #[inline]
    pub unsafe fn to_int_unchecked<Int>(self) -> Int
    where
        Self: FloatToInt<Int>,
    {
        // SAFETY: the caller must uphold the safety contract for
        // `FloatToInt::to_int_unchecked`.
        unsafe { FloatToInt::<Int>::to_int_unchecked(self) }
    }

    /// Raw transmutation to `u32`.
    ///
    /// This is currently identical to `transmute::<f32, u32>(self)` on all platforms.
    ///
    /// See [`from_bits`](Self::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);
    ///
    /// ```
    #[must_use = "this returns the result of the operation, \
                  without modifying the original"]
    #[stable(feature = "float_bits_conv", since = "1.20.0")]
    #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
    #[inline]
    pub const fn to_bits(self) -> u32 {
        // SAFETY: `u32` is a plain old datatype so we can always transmute to it.
        // ...sorta.
        //
        // It turns out that at runtime, it is possible for a floating point number
        // to be subject to a floating point mode that alters nonzero subnormal numbers
        // to zero on reads and writes, aka "denormals are zero" and "flush to zero".
        // This is not a problem per se, but at least one tier2 platform for Rust
        // actually exhibits this behavior by default.
        //
        // In addition, on x86 targets with SSE or SSE2 disabled and the x87 FPU enabled,
        // i.e. not soft-float, the way Rust does parameter passing can actually alter
        // a number that is "not infinity" to have the same exponent as infinity,
        // in a slightly unpredictable manner.
        //
        // And, of course evaluating to a NaN value is fairly nondeterministic.
        // More precisely: when NaN should be returned is knowable, but which NaN?
        // So far that's defined by a combination of LLVM and the CPU, not Rust.
        // This function, however, allows observing the bitstring of a NaN,
        // thus introspection on CTFE.
        //
        // In order to preserve, at least for the moment, const-to-runtime equivalence,
        // we reject any of these possible situations from happening.
        #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
        const fn ct_f32_to_u32(ct: f32) -> u32 {
            match ct.classify() {
                FpCategory::Nan => {
                    panic!("const-eval error: cannot use f32::to_bits on a NaN")
                }
                FpCategory::Subnormal => {
                    panic!("const-eval error: cannot use f32::to_bits on a subnormal number")
                }
                FpCategory::Infinite | FpCategory::Normal | FpCategory::Zero => {
                    // SAFETY: We have a normal floating point number. Now we transmute, i.e. do a bitcopy.
                    unsafe { mem::transmute::<f32, u32>(ct) }
                }
            }
        }
        // SAFETY: `u32` is a plain old datatype so we can always... uh...
        // ...look, just pretend you forgot what you just read.
        // Stability concerns.
        let rt_f32_to_u32 = |rt| unsafe { mem::transmute::<f32, u32>(rt) };
        // SAFETY: We use internal implementations that either always work or fail at compile time.
        unsafe { intrinsics::const_eval_select((self,), ct_f32_to_u32, rt_f32_to_u32) }
    }

    /// 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")]
    #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
    #[must_use]
    #[inline]
    pub const fn from_bits(v: u32) -> Self {
        // It turns out the safety issues with sNaN were overblown! Hooray!
        // SAFETY: `u32` is a plain old datatype so we can always transmute from it
        // ...sorta.
        //
        // It turns out that at runtime, it is possible for a floating point number
        // to be subject to floating point modes that alter nonzero subnormal numbers
        // to zero on reads and writes, aka "denormals are zero" and "flush to zero".
        // This is not a problem usually, but at least one tier2 platform for Rust
        // actually exhibits this behavior by default: thumbv7neon
        // aka "the Neon FPU in AArch32 state"
        //
        // In addition, on x86 targets with SSE or SSE2 disabled and the x87 FPU enabled,
        // i.e. not soft-float, the way Rust does parameter passing can actually alter
        // a number that is "not infinity" to have the same exponent as infinity,
        // in a slightly unpredictable manner.
        //
        // And, of course evaluating to a NaN value is fairly nondeterministic.
        // More precisely: when NaN should be returned is knowable, but which NaN?
        // So far that's defined by a combination of LLVM and the CPU, not Rust.
        // This function, however, allows observing the bitstring of a NaN,
        // thus introspection on CTFE.
        //
        // In order to preserve, at least for the moment, const-to-runtime equivalence,
        // reject any of these possible situations from happening.
        #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
        const fn ct_u32_to_f32(ct: u32) -> f32 {
            match f32::classify_bits(ct) {
                FpCategory::Subnormal => {
                    panic!("const-eval error: cannot use f32::from_bits on a subnormal number")
                }
                FpCategory::Nan => {
                    panic!("const-eval error: cannot use f32::from_bits on NaN")
                }
                FpCategory::Infinite | FpCategory::Normal | FpCategory::Zero => {
                    // SAFETY: It's not a frumious number
                    unsafe { mem::transmute::<u32, f32>(ct) }
                }
            }
        }
        // SAFETY: `u32` is a plain old datatype so we can always... uh...
        // ...look, just pretend you forgot what you just read.
        // Stability concerns.
        let rt_u32_to_f32 = |rt| unsafe { mem::transmute::<u32, f32>(rt) };
        // SAFETY: We use internal implementations that either always work or fail at compile time.
        unsafe { intrinsics::const_eval_select((v,), ct_u32_to_f32, rt_u32_to_f32) }
    }

    /// 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]);
    /// ```
    #[must_use = "this returns the result of the operation, \
                  without modifying the original"]
    #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
    #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
    #[inline]
    pub const 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]);
    /// ```
    #[must_use = "this returns the result of the operation, \
                  without modifying the original"]
    #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
    #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
    #[inline]
    pub const 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`]: f32::to_be_bytes
    /// [`to_le_bytes`]: f32::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]
    ///     }
    /// );
    /// ```
    #[must_use = "this returns the result of the operation, \
                  without modifying the original"]
    #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
    #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
    #[inline]
    pub const 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")]
    #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
    #[must_use]
    #[inline]
    pub const 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")]
    #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
    #[must_use]
    #[inline]
    pub const 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`]: f32::from_be_bytes
    /// [`from_le_bytes`]: f32::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")]
    #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
    #[must_use]
    #[inline]
    pub const fn from_ne_bytes(bytes: [u8; 4]) -> Self {
        Self::from_bits(u32::from_ne_bytes(bytes))
    }

    /// Return the ordering between `self` and `other`.
    ///
    /// Unlike the standard partial comparison between floating point numbers,
    /// this comparison always produces an ordering in accordance to
    /// the `totalOrder` predicate as defined in the IEEE 754 (2008 revision)
    /// floating point standard. The values are ordered in the following sequence:
    ///
    /// - negative quiet NaN
    /// - negative signaling NaN
    /// - negative infinity
    /// - negative numbers
    /// - negative subnormal numbers
    /// - negative zero
    /// - positive zero
    /// - positive subnormal numbers
    /// - positive numbers
    /// - positive infinity
    /// - positive signaling NaN
    /// - positive quiet NaN.
    ///
    /// The ordering established by this function does not always agree with the
    /// [`PartialOrd`] and [`PartialEq`] implementations of `f32`. For example,
    /// they consider negative and positive zero equal, while `total_cmp`
    /// doesn't.
    ///
    /// The interpretation of the signaling NaN bit follows the definition in
    /// the IEEE 754 standard, which may not match the interpretation by some of
    /// the older, non-conformant (e.g. MIPS) hardware implementations.
    ///
    /// # Example
    ///
    /// ```
    /// struct GoodBoy {
    ///     name: String,
    ///     weight: f32,
    /// }
    ///
    /// let mut bois = vec![
    ///     GoodBoy { name: "Pucci".to_owned(), weight: 0.1 },
    ///     GoodBoy { name: "Woofer".to_owned(), weight: 99.0 },
    ///     GoodBoy { name: "Yapper".to_owned(), weight: 10.0 },
    ///     GoodBoy { name: "Chonk".to_owned(), weight: f32::INFINITY },
    ///     GoodBoy { name: "Abs. Unit".to_owned(), weight: f32::NAN },
    ///     GoodBoy { name: "Floaty".to_owned(), weight: -5.0 },
    /// ];
    ///
    /// bois.sort_by(|a, b| a.weight.total_cmp(&b.weight));
    /// # assert!(bois.into_iter().map(|b| b.weight)
    /// #     .zip([-5.0, 0.1, 10.0, 99.0, f32::INFINITY, f32::NAN].iter())
    /// #     .all(|(a, b)| a.to_bits() == b.to_bits()))
    /// ```
    #[stable(feature = "total_cmp", since = "1.62.0")]
    #[must_use]
    #[inline]
    pub fn total_cmp(&self, other: &Self) -> crate::cmp::Ordering {
        let mut left = self.to_bits() as i32;
        let mut right = other.to_bits() as i32;

        // In case of negatives, flip all the bits except the sign
        // to achieve a similar layout as two's complement integers
        //
        // Why does this work? IEEE 754 floats consist of three fields:
        // Sign bit, exponent and mantissa. The set of exponent and mantissa
        // fields as a whole have the property that their bitwise order is
        // equal to the numeric magnitude where the magnitude is defined.
        // The magnitude is not normally defined on NaN values, but
        // IEEE 754 totalOrder defines the NaN values also to follow the
        // bitwise order. This leads to order explained in the doc comment.
        // However, the representation of magnitude is the same for negative
        // and positive numbers – only the sign bit is different.
        // To easily compare the floats as signed integers, we need to
        // flip the exponent and mantissa bits in case of negative numbers.
        // We effectively convert the numbers to "two's complement" form.
        //
        // To do the flipping, we construct a mask and XOR against it.
        // We branchlessly calculate an "all-ones except for the sign bit"
        // mask from negative-signed values: right shifting sign-extends
        // the integer, so we "fill" the mask with sign bits, and then
        // convert to unsigned to push one more zero bit.
        // On positive values, the mask is all zeros, so it's a no-op.
        left ^= (((left >> 31) as u32) >> 1) as i32;
        right ^= (((right >> 31) as u32) >> 1) as i32;

        left.cmp(&right)
    }

    /// Restrict a value to a certain interval unless it is NaN.
    ///
    /// Returns `max` if `self` is greater than `max`, and `min` if `self` is
    /// less than `min`. Otherwise this returns `self`.
    ///
    /// Note that this function returns NaN if the initial value was NaN as
    /// well.
    ///
    /// # Panics
    ///
    /// Panics if `min > max`, `min` is NaN, or `max` is NaN.
    ///
    /// # Examples
    ///
    /// ```
    /// assert!((-3.0f32).clamp(-2.0, 1.0) == -2.0);
    /// assert!((0.0f32).clamp(-2.0, 1.0) == 0.0);
    /// assert!((2.0f32).clamp(-2.0, 1.0) == 1.0);
    /// assert!((f32::NAN).clamp(-2.0, 1.0).is_nan());
    /// ```
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[stable(feature = "clamp", since = "1.50.0")]
    #[inline]
    pub fn clamp(self, min: f32, max: f32) -> f32 {
        assert!(min <= max);
        let mut x = self;
        if x < min {
            x = min;
        }
        if x > max {
            x = max;
        }
        x
    }
}