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Diffstat (limited to 'library/core/src/num/f64.rs')
| -rw-r--r-- | library/core/src/num/f64.rs | 1294 |
1 files changed, 1294 insertions, 0 deletions
diff --git a/library/core/src/num/f64.rs b/library/core/src/num/f64.rs new file mode 100644 index 000000000..75c92c2f8 --- /dev/null +++ b/library/core/src/num/f64.rs @@ -0,0 +1,1294 @@ +//! Constants specific to the `f64` double-precision floating point type. +//! +//! *[See also the `f64` primitive type][f64].* +//! +//! 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 `f64` 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 `f64`. +/// Use [`f64::RADIX`] instead. +/// +/// # Examples +/// +/// ```rust +/// // deprecated way +/// # #[allow(deprecated, deprecated_in_future)] +/// let r = std::f64::RADIX; +/// +/// // intended way +/// let r = f64::RADIX; +/// ``` +#[stable(feature = "rust1", since = "1.0.0")] +#[deprecated(since = "TBD", note = "replaced by the `RADIX` associated constant on `f64`")] +pub const RADIX: u32 = f64::RADIX; + +/// Number of significant digits in base 2. +/// Use [`f64::MANTISSA_DIGITS`] instead. +/// +/// # Examples +/// +/// ```rust +/// // deprecated way +/// # #[allow(deprecated, deprecated_in_future)] +/// let d = std::f64::MANTISSA_DIGITS; +/// +/// // intended way +/// let d = f64::MANTISSA_DIGITS; +/// ``` +#[stable(feature = "rust1", since = "1.0.0")] +#[deprecated( + since = "TBD", + note = "replaced by the `MANTISSA_DIGITS` associated constant on `f64`" +)] +pub const MANTISSA_DIGITS: u32 = f64::MANTISSA_DIGITS; + +/// Approximate number of significant digits in base 10. +/// Use [`f64::DIGITS`] instead. +/// +/// # Examples +/// +/// ```rust +/// // deprecated way +/// # #[allow(deprecated, deprecated_in_future)] +/// let d = std::f64::DIGITS; +/// +/// // intended way +/// let d = f64::DIGITS; +/// ``` +#[stable(feature = "rust1", since = "1.0.0")] +#[deprecated(since = "TBD", note = "replaced by the `DIGITS` associated constant on `f64`")] +pub const DIGITS: u32 = f64::DIGITS; + +/// [Machine epsilon] value for `f64`. +/// Use [`f64::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::f64::EPSILON; +/// +/// // intended way +/// let e = f64::EPSILON; +/// ``` +#[stable(feature = "rust1", since = "1.0.0")] +#[deprecated(since = "TBD", note = "replaced by the `EPSILON` associated constant on `f64`")] +pub const EPSILON: f64 = f64::EPSILON; + +/// Smallest finite `f64` value. +/// Use [`f64::MIN`] instead. +/// +/// # Examples +/// +/// ```rust +/// // deprecated way +/// # #[allow(deprecated, deprecated_in_future)] +/// let min = std::f64::MIN; +/// +/// // intended way +/// let min = f64::MIN; +/// ``` +#[stable(feature = "rust1", since = "1.0.0")] +#[deprecated(since = "TBD", note = "replaced by the `MIN` associated constant on `f64`")] +pub const MIN: f64 = f64::MIN; + +/// Smallest positive normal `f64` value. +/// Use [`f64::MIN_POSITIVE`] instead. +/// +/// # Examples +/// +/// ```rust +/// // deprecated way +/// # #[allow(deprecated, deprecated_in_future)] +/// let min = std::f64::MIN_POSITIVE; +/// +/// // intended way +/// let min = f64::MIN_POSITIVE; +/// ``` +#[stable(feature = "rust1", since = "1.0.0")] +#[deprecated(since = "TBD", note = "replaced by the `MIN_POSITIVE` associated constant on `f64`")] +pub const MIN_POSITIVE: f64 = f64::MIN_POSITIVE; + +/// Largest finite `f64` value. +/// Use [`f64::MAX`] instead. +/// +/// # Examples +/// +/// ```rust +/// // deprecated way +/// # #[allow(deprecated, deprecated_in_future)] +/// let max = std::f64::MAX; +/// +/// // intended way +/// let max = f64::MAX; +/// ``` +#[stable(feature = "rust1", since = "1.0.0")] +#[deprecated(since = "TBD", note = "replaced by the `MAX` associated constant on `f64`")] +pub const MAX: f64 = f64::MAX; + +/// One greater than the minimum possible normal power of 2 exponent. +/// Use [`f64::MIN_EXP`] instead. +/// +/// # Examples +/// +/// ```rust +/// // deprecated way +/// # #[allow(deprecated, deprecated_in_future)] +/// let min = std::f64::MIN_EXP; +/// +/// // intended way +/// let min = f64::MIN_EXP; +/// ``` +#[stable(feature = "rust1", since = "1.0.0")] +#[deprecated(since = "TBD", note = "replaced by the `MIN_EXP` associated constant on `f64`")] +pub const MIN_EXP: i32 = f64::MIN_EXP; + +/// Maximum possible power of 2 exponent. +/// Use [`f64::MAX_EXP`] instead. +/// +/// # Examples +/// +/// ```rust +/// // deprecated way +/// # #[allow(deprecated, deprecated_in_future)] +/// let max = std::f64::MAX_EXP; +/// +/// // intended way +/// let max = f64::MAX_EXP; +/// ``` +#[stable(feature = "rust1", since = "1.0.0")] +#[deprecated(since = "TBD", note = "replaced by the `MAX_EXP` associated constant on `f64`")] +pub const MAX_EXP: i32 = f64::MAX_EXP; + +/// Minimum possible normal power of 10 exponent. +/// Use [`f64::MIN_10_EXP`] instead. +/// +/// # Examples +/// +/// ```rust +/// // deprecated way +/// # #[allow(deprecated, deprecated_in_future)] +/// let min = std::f64::MIN_10_EXP; +/// +/// // intended way +/// let min = f64::MIN_10_EXP; +/// ``` +#[stable(feature = "rust1", since = "1.0.0")] +#[deprecated(since = "TBD", note = "replaced by the `MIN_10_EXP` associated constant on `f64`")] +pub const MIN_10_EXP: i32 = f64::MIN_10_EXP; + +/// Maximum possible power of 10 exponent. +/// Use [`f64::MAX_10_EXP`] instead. +/// +/// # Examples +/// +/// ```rust +/// // deprecated way +/// # #[allow(deprecated, deprecated_in_future)] +/// let max = std::f64::MAX_10_EXP; +/// +/// // intended way +/// let max = f64::MAX_10_EXP; +/// ``` +#[stable(feature = "rust1", since = "1.0.0")] +#[deprecated(since = "TBD", note = "replaced by the `MAX_10_EXP` associated constant on `f64`")] +pub const MAX_10_EXP: i32 = f64::MAX_10_EXP; + +/// Not a Number (NaN). +/// Use [`f64::NAN`] instead. +/// +/// # Examples +/// +/// ```rust +/// // deprecated way +/// # #[allow(deprecated, deprecated_in_future)] +/// let nan = std::f64::NAN; +/// +/// // intended way +/// let nan = f64::NAN; +/// ``` +#[stable(feature = "rust1", since = "1.0.0")] +#[deprecated(since = "TBD", note = "replaced by the `NAN` associated constant on `f64`")] +pub const NAN: f64 = f64::NAN; + +/// Infinity (∞). +/// Use [`f64::INFINITY`] instead. +/// +/// # Examples +/// +/// ```rust +/// // deprecated way +/// # #[allow(deprecated, deprecated_in_future)] +/// let inf = std::f64::INFINITY; +/// +/// // intended way +/// let inf = f64::INFINITY; +/// ``` +#[stable(feature = "rust1", since = "1.0.0")] +#[deprecated(since = "TBD", note = "replaced by the `INFINITY` associated constant on `f64`")] +pub const INFINITY: f64 = f64::INFINITY; + +/// Negative infinity (−∞). +/// Use [`f64::NEG_INFINITY`] instead. +/// +/// # Examples +/// +/// ```rust +/// // deprecated way +/// # #[allow(deprecated, deprecated_in_future)] +/// let ninf = std::f64::NEG_INFINITY; +/// +/// // intended way +/// let ninf = f64::NEG_INFINITY; +/// ``` +#[stable(feature = "rust1", since = "1.0.0")] +#[deprecated(since = "TBD", note = "replaced by the `NEG_INFINITY` associated constant on `f64`")] +pub const NEG_INFINITY: f64 = f64::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: f64 = 3.14159265358979323846264338327950288_f64; + + /// The full circle constant (τ) + /// + /// Equal to 2π. + #[stable(feature = "tau_constant", since = "1.47.0")] + pub const TAU: f64 = 6.28318530717958647692528676655900577_f64; + + /// π/2 + #[stable(feature = "rust1", since = "1.0.0")] + pub const FRAC_PI_2: f64 = 1.57079632679489661923132169163975144_f64; + + /// π/3 + #[stable(feature = "rust1", since = "1.0.0")] + pub const FRAC_PI_3: f64 = 1.04719755119659774615421446109316763_f64; + + /// π/4 + #[stable(feature = "rust1", since = "1.0.0")] + pub const FRAC_PI_4: f64 = 0.785398163397448309615660845819875721_f64; + + /// π/6 + #[stable(feature = "rust1", since = "1.0.0")] + pub const FRAC_PI_6: f64 = 0.52359877559829887307710723054658381_f64; + + /// π/8 + #[stable(feature = "rust1", since = "1.0.0")] + pub const FRAC_PI_8: f64 = 0.39269908169872415480783042290993786_f64; + + /// 1/π + #[stable(feature = "rust1", since = "1.0.0")] + pub const FRAC_1_PI: f64 = 0.318309886183790671537767526745028724_f64; + + /// 2/π + #[stable(feature = "rust1", since = "1.0.0")] + pub const FRAC_2_PI: f64 = 0.636619772367581343075535053490057448_f64; + + /// 2/sqrt(π) + #[stable(feature = "rust1", since = "1.0.0")] + pub const FRAC_2_SQRT_PI: f64 = 1.12837916709551257389615890312154517_f64; + + /// sqrt(2) + #[stable(feature = "rust1", since = "1.0.0")] + pub const SQRT_2: f64 = 1.41421356237309504880168872420969808_f64; + + /// 1/sqrt(2) + #[stable(feature = "rust1", since = "1.0.0")] + pub const FRAC_1_SQRT_2: f64 = 0.707106781186547524400844362104849039_f64; + + /// Euler's number (e) + #[stable(feature = "rust1", since = "1.0.0")] + pub const E: f64 = 2.71828182845904523536028747135266250_f64; + + /// log<sub>2</sub>(10) + #[stable(feature = "extra_log_consts", since = "1.43.0")] + pub const LOG2_10: f64 = 3.32192809488736234787031942948939018_f64; + + /// log<sub>2</sub>(e) + #[stable(feature = "rust1", since = "1.0.0")] + pub const LOG2_E: f64 = 1.44269504088896340735992468100189214_f64; + + /// log<sub>10</sub>(2) + #[stable(feature = "extra_log_consts", since = "1.43.0")] + pub const LOG10_2: f64 = 0.301029995663981195213738894724493027_f64; + + /// log<sub>10</sub>(e) + #[stable(feature = "rust1", since = "1.0.0")] + pub const LOG10_E: f64 = 0.434294481903251827651128918916605082_f64; + + /// ln(2) + #[stable(feature = "rust1", since = "1.0.0")] + pub const LN_2: f64 = 0.693147180559945309417232121458176568_f64; + + /// ln(10) + #[stable(feature = "rust1", since = "1.0.0")] + pub const LN_10: f64 = 2.30258509299404568401799145468436421_f64; +} + +#[cfg(not(test))] +impl f64 { + /// The radix or base of the internal representation of `f64`. + #[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 = 53; + /// Approximate number of significant digits in base 10. + #[stable(feature = "assoc_int_consts", since = "1.43.0")] + pub const DIGITS: u32 = 15; + + /// [Machine epsilon] value for `f64`. + /// + /// 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: f64 = 2.2204460492503131e-16_f64; + + /// Smallest finite `f64` value. + #[stable(feature = "assoc_int_consts", since = "1.43.0")] + pub const MIN: f64 = -1.7976931348623157e+308_f64; + /// Smallest positive normal `f64` value. + #[stable(feature = "assoc_int_consts", since = "1.43.0")] + pub const MIN_POSITIVE: f64 = 2.2250738585072014e-308_f64; + /// Largest finite `f64` value. + #[stable(feature = "assoc_int_consts", since = "1.43.0")] + pub const MAX: f64 = 1.7976931348623157e+308_f64; + + /// 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 = -1021; + /// Maximum possible power of 2 exponent. + #[stable(feature = "assoc_int_consts", since = "1.43.0")] + pub const MAX_EXP: i32 = 1024; + + /// Minimum possible normal power of 10 exponent. + #[stable(feature = "assoc_int_consts", since = "1.43.0")] + pub const MIN_10_EXP: i32 = -307; + /// Maximum possible power of 10 exponent. + #[stable(feature = "assoc_int_consts", since = "1.43.0")] + pub const MAX_10_EXP: i32 = 308; + + /// Not a Number (NaN). + /// + /// Note that IEEE-745 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: f64 = 0.0_f64 / 0.0_f64; + /// Infinity (∞). + #[stable(feature = "assoc_int_consts", since = "1.43.0")] + pub const INFINITY: f64 = 1.0_f64 / 0.0_f64; + /// Negative infinity (−∞). + #[stable(feature = "assoc_int_consts", since = "1.43.0")] + pub const NEG_INFINITY: f64 = -1.0_f64 / 0.0_f64; + + /// Returns `true` if this value is NaN. + /// + /// ``` + /// let nan = f64::NAN; + /// let f = 7.0_f64; + /// + /// 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) -> f64 { + // SAFETY: This transmutation is fine. Probably. For the reasons std is using it. + unsafe { + mem::transmute::<u64, f64>(mem::transmute::<f64, u64>(self) & 0x7fff_ffff_ffff_ffff) + } + } + + /// Returns `true` if this value is positive infinity or negative infinity, and + /// `false` otherwise. + /// + /// ``` + /// let f = 7.0f64; + /// let inf = f64::INFINITY; + /// let neg_inf = f64::NEG_INFINITY; + /// let nan = f64::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 == f64::INFINITY) | (self == f64::NEG_INFINITY) + } + + /// Returns `true` if this number is neither infinite nor NaN. + /// + /// ``` + /// let f = 7.0f64; + /// let inf: f64 = f64::INFINITY; + /// let neg_inf: f64 = f64::NEG_INFINITY; + /// let nan: f64 = f64::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 = f64::MIN_POSITIVE; // 2.2250738585072014e-308_f64 + /// let max = f64::MAX; + /// let lower_than_min = 1.0e-308_f64; + /// let zero = 0.0_f64; + /// + /// assert!(!min.is_subnormal()); + /// assert!(!max.is_subnormal()); + /// + /// assert!(!zero.is_subnormal()); + /// assert!(!f64::NAN.is_subnormal()); + /// assert!(!f64::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 = f64::MIN_POSITIVE; // 2.2250738585072014e-308f64 + /// let max = f64::MAX; + /// let lower_than_min = 1.0e-308_f64; + /// let zero = 0.0f64; + /// + /// assert!(min.is_normal()); + /// assert!(max.is_normal()); + /// + /// assert!(!zero.is_normal()); + /// assert!(!f64::NAN.is_normal()); + /// assert!(!f64::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_f64; + /// let inf = f64::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 f64::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. + // + // Thus, a value may compare unequal to infinity, despite having a "full" exponent mask. + // And it may not be NaN, as it can simply be an "overextended" finite value. + if self.is_nan() { + 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: f64 to u64 is fine. Usually. + // If control flow has gotten this far, the value is definitely in one of the categories + // that f64::partial_classify can correctly analyze. + unsafe { f64::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. + #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")] + const unsafe fn partial_classify(self) -> FpCategory { + const EXP_MASK: u64 = 0x7ff0000000000000; + const MAN_MASK: u64 = 0x000fffffffffffff; + + // SAFETY: The caller is not asking questions for which this will tell lies. + let b = unsafe { mem::transmute::<f64, u64>(self) }; + match (b & MAN_MASK, b & EXP_MASK) { + (0, EXP_MASK) => FpCategory::Infinite, + (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: u64) -> FpCategory { + const EXP_MASK: u64 = 0x7ff0000000000000; + const MAN_MASK: u64 = 0x000fffffffffffff; + + 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-745 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_f64; + /// let g = -7.0_f64; + /// + /// 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() + } + + #[must_use] + #[stable(feature = "rust1", since = "1.0.0")] + #[deprecated(since = "1.0.0", note = "renamed to is_sign_positive")] + #[inline] + #[doc(hidden)] + pub fn is_positive(self) -> bool { + self.is_sign_positive() + } + + /// Returns `true` if `self` has a negative sign, including `-0.0`, NaNs with + /// negative sign bit and negative infinity. Note that IEEE-745 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 = 7.0_f64; + /// let g = -7.0_f64; + /// + /// 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::<f64, u64>(self) & 0x8000_0000_0000_0000 != 0 } + } + + #[must_use] + #[stable(feature = "rust1", since = "1.0.0")] + #[deprecated(since = "1.0.0", note = "renamed to is_sign_negative")] + #[inline] + #[doc(hidden)] + pub fn is_negative(self) -> bool { + self.is_sign_negative() + } + + /// Takes the reciprocal (inverse) of a number, `1/x`. + /// + /// ``` + /// let x = 2.0_f64; + /// let abs_difference = (x.recip() - (1.0 / x)).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` + #[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) -> f64 { + 1.0 / self + } + + /// Converts radians to degrees. + /// + /// ``` + /// let angle = std::f64::consts::PI; + /// + /// let abs_difference = (angle.to_degrees() - 180.0).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` + #[must_use = "this returns the result of the operation, \ + without modifying the original"] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + pub fn to_degrees(self) -> f64 { + // The division here is correctly rounded with respect to the true + // value of 180/π. (This differs from f32, where a constant must be + // used to ensure a correctly rounded result.) + self * (180.0f64 / consts::PI) + } + + /// Converts degrees to radians. + /// + /// ``` + /// let angle = 180.0_f64; + /// + /// let abs_difference = (angle.to_radians() - std::f64::consts::PI).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` + #[must_use = "this returns the result of the operation, \ + without modifying the original"] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + pub fn to_radians(self) -> f64 { + let value: f64 = consts::PI; + self * (value / 180.0) + } + + /// 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 = 1.0_f64; + /// let y = 2.0_f64; + /// + /// 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: f64) -> f64 { + intrinsics::maxnumf64(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 = 1.0_f64; + /// let y = 2.0_f64; + /// + /// 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: f64) -> f64 { + intrinsics::minnumf64(self, other) + } + + /// Returns the maximum of the two numbers, propagating NaN. + /// + /// This returns NaN when *either* argument is NaN, as opposed to + /// [`f64::max`] which only returns NaN when *both* arguments are NaN. + /// + /// ``` + /// #![feature(float_minimum_maximum)] + /// let x = 1.0_f64; + /// let y = 2.0_f64; + /// + /// assert_eq!(x.maximum(y), y); + /// assert!(x.maximum(f64::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: f64) -> f64 { + 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 + /// [`f64::min`] which only returns NaN when *both* arguments are NaN. + /// + /// ``` + /// #![feature(float_minimum_maximum)] + /// let x = 1.0_f64; + /// let y = 2.0_f64; + /// + /// assert_eq!(x.minimum(y), x); + /// assert!(x.minimum(f64::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: f64) -> f64 { + 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_f64; + /// let rounded = unsafe { value.to_int_unchecked::<u16>() }; + /// assert_eq!(rounded, 4); + /// + /// let value = -128.9_f64; + /// 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 `u64`. + /// + /// This is currently identical to `transmute::<f64, u64>(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!((1f64).to_bits() != 1f64 as u64); // to_bits() is not casting! + /// assert_eq!((12.5f64).to_bits(), 0x4029000000000000); + /// + /// ``` + #[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) -> u64 { + // SAFETY: `u64` is a plain old datatype so we can always transmute to it. + // ...sorta. + // + // See the SAFETY comment in f64::from_bits for more. + #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")] + const fn ct_f64_to_u64(ct: f64) -> u64 { + match ct.classify() { + FpCategory::Nan => { + panic!("const-eval error: cannot use f64::to_bits on a NaN") + } + FpCategory::Subnormal => { + panic!("const-eval error: cannot use f64::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::<f64, u64>(ct) } + } + } + } + // SAFETY: `u64` is a plain old datatype so we can always... uh... + // ...look, just pretend you forgot what you just read. + // Stability concerns. + let rt_f64_to_u64 = |rt| unsafe { mem::transmute::<f64, u64>(rt) }; + // SAFETY: We use internal implementations that either always work or fail at compile time. + unsafe { intrinsics::const_eval_select((self,), ct_f64_to_u64, rt_f64_to_u64) } + } + + /// Raw transmutation from `u64`. + /// + /// This is currently identical to `transmute::<u64, f64>(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 signaling-ness (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 = f64::from_bits(0x4029000000000000); + /// 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: u64) -> Self { + // It turns out the safety issues with sNaN were overblown! Hooray! + // SAFETY: `u64` 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 an FTZ behavior by default: thumbv7neon + // aka "the Neon FPU in AArch32 state" + // + // Even with this, not all instructions exhibit the FTZ behaviors on thumbv7neon, + // so this should load the same bits if LLVM emits the "correct" instructions, + // but LLVM sometimes makes interesting choices about float optimization, + // and other FPUs may do similar. Thus, it is wise to indulge luxuriously in caution. + // + // 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_u64_to_f64(ct: u64) -> f64 { + match f64::classify_bits(ct) { + FpCategory::Subnormal => { + panic!("const-eval error: cannot use f64::from_bits on a subnormal number") + } + FpCategory::Nan => { + panic!("const-eval error: cannot use f64::from_bits on NaN") + } + FpCategory::Infinite | FpCategory::Normal | FpCategory::Zero => { + // SAFETY: It's not a frumious number + unsafe { mem::transmute::<u64, f64>(ct) } + } + } + } + // SAFETY: `u64` is a plain old datatype so we can always... uh... + // ...look, just pretend you forgot what you just read. + // Stability concerns. + let rt_u64_to_f64 = |rt| unsafe { mem::transmute::<u64, f64>(rt) }; + // SAFETY: We use internal implementations that either always work or fail at compile time. + unsafe { intrinsics::const_eval_select((v,), ct_u64_to_f64, rt_u64_to_f64) } + } + + /// 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 = 12.5f64.to_be_bytes(); + /// assert_eq!(bytes, [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 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; 8] { + 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 = 12.5f64.to_le_bytes(); + /// assert_eq!(bytes, [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]); + /// ``` + #[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; 8] { + 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`]: f64::to_be_bytes + /// [`to_le_bytes`]: f64::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 = 12.5f64.to_ne_bytes(); + /// assert_eq!( + /// bytes, + /// if cfg!(target_endian = "big") { + /// [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00] + /// } else { + /// [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40] + /// } + /// ); + /// ``` + #[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; 8] { + 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 = f64::from_be_bytes([0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 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; 8]) -> Self { + Self::from_bits(u64::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 = f64::from_le_bytes([0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]); + /// 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; 8]) -> Self { + Self::from_bits(u64::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`]: f64::from_be_bytes + /// [`from_le_bytes`]: f64::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 = f64::from_ne_bytes(if cfg!(target_endian = "big") { + /// [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00] + /// } else { + /// [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40] + /// }); + /// 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; 8]) -> Self { + Self::from_bits(u64::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 `f64`. 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: f64, + /// } + /// + /// 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: f64::INFINITY }, + /// GoodBoy { name: "Abs. Unit".to_owned(), weight: f64::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, f64::INFINITY, f64::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 i64; + let mut right = other.to_bits() as i64; + + // 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 >> 63) as u64) >> 1) as i64; + right ^= (((right >> 63) as u64) >> 1) as i64; + + 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!((-3.0f64).clamp(-2.0, 1.0) == -2.0); + /// assert!((0.0f64).clamp(-2.0, 1.0) == 0.0); + /// assert!((2.0f64).clamp(-2.0, 1.0) == 1.0); + /// assert!((f64::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: f64, max: f64) -> f64 { + assert!(min <= max); + let mut x = self; + if x < min { + x = min; + } + if x > max { + x = max; + } + x + } +} |