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nest-open-source / manifest_repos / toolchain / 6143c57c644e0da7c4a10d1b4af322f92e74e6f7 / . / armv7a / usr / lib / rustlib / src / rust / library / core / src / num / f32.rs
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//! Constants for 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")]
#[deprecated(since = "TBD", note = "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")]
#[deprecated(
since = "TBD",
note = "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")]
#[deprecated(since = "TBD", note = "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")]
#[deprecated(since = "TBD", note = "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")]
#[deprecated(since = "TBD", note = "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")]
#[deprecated(since = "TBD", note = "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")]
#[deprecated(since = "TBD", note = "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")]
#[deprecated(since = "TBD", note = "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")]
#[deprecated(since = "TBD", note = "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")]
#[deprecated(since = "TBD", note = "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")]
#[deprecated(since = "TBD", note = "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")]
#[deprecated(since = "TBD", note = "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")]
#[deprecated(since = "TBD", note = "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")]
#[deprecated(since = "TBD", note = "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).
///
/// Note that IEEE 754 doesn't define just a single NaN value;
/// a plethora of bit patterns are considered to be NaN.
/// Furthermore, the standard makes a difference
/// between a "signaling" and a "quiet" NaN,
/// and allows inspecting its "payload" (the unspecified bits in the bit pattern).
/// This constant isn't guaranteed to equal to any specific NaN bitpattern,
/// and the stability of its representation over Rust versions
/// and target platforms isn't guaranteed.
#[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`, NaNs with
/// positive sign bit and positive infinity. Note that IEEE 754 doesn't assign any
/// meaning to the sign bit in case of a NaN, and as Rust doesn't guarantee that
/// the bit pattern of NaNs are conserved over arithmetic operations, the result of
/// `is_sign_positive` on a NaN might produce an unexpected result in some cases.
/// See [explanation of NaN as a special value](f32) for more info.
///
/// ```
/// 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`, NaNs with
/// negative sign bit and negative infinity. Note that IEEE 754 doesn't assign any
/// meaning to the sign bit in case of a NaN, and as Rust doesn't guarantee that
/// the bit pattern of NaNs are conserved over arithmetic operations, the result of
/// `is_sign_negative` on a NaN might produce an unexpected result in some cases.
/// See [explanation of NaN as a special value](f32) for more info.
///
/// ```
/// 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 }
}
/// Returns the least number greater than `self`.
///
/// Let `TINY` be the smallest representable positive `f32`. Then,
/// - if `self.is_nan()`, this returns `self`;
/// - if `self` is [`NEG_INFINITY`], this returns [`MIN`];
/// - if `self` is `-TINY`, this returns -0.0;
/// - if `self` is -0.0 or +0.0, this returns `TINY`;
/// - if `self` is [`MAX`] or [`INFINITY`], this returns [`INFINITY`];
/// - otherwise the unique least value greater than `self` is returned.
///
/// The identity `x.next_up() == -(-x).next_down()` holds for all non-NaN `x`. When `x`
/// is finite `x == x.next_up().next_down()` also holds.
///
/// ```rust
/// #![feature(float_next_up_down)]
/// // f32::EPSILON is the difference between 1.0 and the next number up.
/// assert_eq!(1.0f32.next_up(), 1.0 + f32::EPSILON);
/// // But not for most numbers.
/// assert!(0.1f32.next_up() < 0.1 + f32::EPSILON);
/// assert_eq!(16777216f32.next_up(), 16777218.0);
/// ```
///
/// [`NEG_INFINITY`]: Self::NEG_INFINITY
/// [`INFINITY`]: Self::INFINITY
/// [`MIN`]: Self::MIN
/// [`MAX`]: Self::MAX
#[unstable(feature = "float_next_up_down", issue = "91399")]
#[rustc_const_unstable(feature = "float_next_up_down", issue = "91399")]
pub const fn next_up(self) -> Self {
// We must use strictly integer arithmetic to prevent denormals from
// flushing to zero after an arithmetic operation on some platforms.
const TINY_BITS: u32 = 0x1; // Smallest positive f32.
const CLEAR_SIGN_MASK: u32 = 0x7fff_ffff;
let bits = self.to_bits();
if self.is_nan() || bits == Self::INFINITY.to_bits() {
return self;
}
let abs = bits & CLEAR_SIGN_MASK;
let next_bits = if abs == 0 {
TINY_BITS
} else if bits == abs {
bits + 1
} else {
bits - 1
};
Self::from_bits(next_bits)
}
/// Returns the greatest number less than `self`.
///
/// Let `TINY` be the smallest representable positive `f32`. Then,
/// - if `self.is_nan()`, this returns `self`;
/// - if `self` is [`INFINITY`], this returns [`MAX`];
/// - if `self` is `TINY`, this returns 0.0;
/// - if `self` is -0.0 or +0.0, this returns `-TINY`;
/// - if `self` is [`MIN`] or [`NEG_INFINITY`], this returns [`NEG_INFINITY`];
/// - otherwise the unique greatest value less than `self` is returned.
///
/// The identity `x.next_down() == -(-x).next_up()` holds for all non-NaN `x`. When `x`
/// is finite `x == x.next_down().next_up()` also holds.
///
/// ```rust
/// #![feature(float_next_up_down)]
/// let x = 1.0f32;
/// // Clamp value into range [0, 1).
/// let clamped = x.clamp(0.0, 1.0f32.next_down());
/// assert!(clamped < 1.0);
/// assert_eq!(clamped.next_up(), 1.0);
/// ```
///
/// [`NEG_INFINITY`]: Self::NEG_INFINITY
/// [`INFINITY`]: Self::INFINITY
/// [`MIN`]: Self::MIN
/// [`MAX`]: Self::MAX
#[unstable(feature = "float_next_up_down", issue = "91399")]
#[rustc_const_unstable(feature = "float_next_up_down", issue = "91399")]
pub const fn next_down(self) -> Self {
// We must use strictly integer arithmetic to prevent denormals from
// flushing to zero after an arithmetic operation on some platforms.
const NEG_TINY_BITS: u32 = 0x8000_0001; // Smallest (in magnitude) negative f32.
const CLEAR_SIGN_MASK: u32 = 0x7fff_ffff;
let bits = self.to_bits();
if self.is_nan() || bits == Self::NEG_INFINITY.to_bits() {
return self;
}
let abs = bits & CLEAR_SIGN_MASK;
let next_bits = if abs == 0 {
NEG_TINY_BITS
} else if bits == abs {
bits - 1
} else {
bits + 1
};
Self::from_bits(next_bits)
}
/// 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, ignoring NaN.
///
/// If one of the arguments is NaN, then the other argument is returned.
/// This follows the IEEE 754-2008 semantics for maxNum, except for handling of signaling NaNs;
/// this function handles all NaNs the same way and avoids maxNum's problems with associativity.
/// This also matches the behavior of libm’s fmax.
///
/// ```
/// let x = 1.0f32;
/// let y = 2.0f32;
///
/// assert_eq!(x.max(y), y);
/// ```
#[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, ignoring NaN.
///
/// If one of the arguments is NaN, then the other argument is returned.
/// This follows the IEEE 754-2008 semantics for minNum, except for handling of signaling NaNs;
/// this function handles all NaNs the same way and avoids minNum's problems with associativity.
/// This also matches the behavior of libm’s fmin.
///
/// ```
/// let x = 1.0f32;
/// let y = 2.0f32;
///
/// assert_eq!(x.min(y), x);
/// ```
#[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 NaN.
///
/// 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.
///
/// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN
/// operand is conserved; see [explanation of NaN as a special value](f32) for more info.
#[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 NaN.
///
/// 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.
///
/// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN
/// operand is conserved; see [explanation of NaN as a special value](f32) for more info.
#[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) }
}
}
}
#[inline(always)] // See https://github.com/rust-lang/compiler-builtins/issues/491
fn rt_f32_to_u32(x: f32) -> u32 {
// SAFETY: `u32` is a plain old datatype so we can always... uh...
// ...look, just pretend you forgot what you just read.
// Stability concerns.
unsafe { mem::transmute(x) }
}
// 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) }
}
}
}
#[inline(always)] // See https://github.com/rust-lang/compiler-builtins/issues/491
fn rt_u32_to_f32(x: u32) -> f32 {
// SAFETY: `u32` is a plain old datatype so we can always... uh...
// ...look, just pretend you forgot what you just read.
// Stability concerns.
unsafe { mem::transmute(x) }
}
// 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.
///
/// See [`from_bits`](Self::from_bits) for some discussion of the
/// portability of this operation (there are almost no issues).
///
/// # 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.
///
/// See [`from_bits`](Self::from_bits) for some discussion of the
/// portability of this operation (there are almost no issues).
///
/// # 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
///
/// See [`from_bits`](Self::from_bits) for some discussion of the
/// portability of this operation (there are almost no issues).
///
/// # 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.
///
/// See [`from_bits`](Self::from_bits) for some discussion of the
/// portability of this operation (there are almost no issues).
///
/// # 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.
///
/// See [`from_bits`](Self::from_bits) for some discussion of the
/// portability of this operation (there are almost no issues).
///
/// # 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
///
/// See [`from_bits`](Self::from_bits) for some discussion of the
/// portability of this operation (there are almost no issues).
///
/// # 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(mut self, min: f32, max: f32) -> f32 {
assert!(min <= max);
if self < min {
self = min;
}
if self > max {
self = max;
}
self
}
}