| //! Constants for the `f128` quadruple-precision floating point type. |
| //! |
| //! *[See also the `f128` primitive type][f128].* |
| //! |
| //! 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 `f128` type. |
| |
| #![unstable(feature = "f128", issue = "116909")] |
| |
| use crate::convert::FloatToInt; |
| #[cfg(not(test))] |
| use crate::intrinsics; |
| use crate::mem; |
| use crate::num::FpCategory; |
| |
| /// Basic mathematical constants. |
| #[unstable(feature = "f128", issue = "116909")] |
| pub mod consts { |
| // FIXME: replace with mathematical constants from cmath. |
| |
| /// Archimedes' constant (π) |
| #[unstable(feature = "f128", issue = "116909")] |
| pub const PI: f128 = 3.14159265358979323846264338327950288419716939937510582097494_f128; |
| |
| /// The full circle constant (τ) |
| /// |
| /// Equal to 2π. |
| #[unstable(feature = "f128", issue = "116909")] |
| pub const TAU: f128 = 6.28318530717958647692528676655900576839433879875021164194989_f128; |
| |
| /// The golden ratio (φ) |
| #[unstable(feature = "f128", issue = "116909")] |
| // Also, #[unstable(feature = "more_float_constants", issue = "103883")] |
| pub const PHI: f128 = 1.61803398874989484820458683436563811772030917980576286213545_f128; |
| |
| /// The Euler-Mascheroni constant (γ) |
| #[unstable(feature = "f128", issue = "116909")] |
| // Also, #[unstable(feature = "more_float_constants", issue = "103883")] |
| pub const EGAMMA: f128 = 0.577215664901532860606512090082402431042159335939923598805767_f128; |
| |
| /// π/2 |
| #[unstable(feature = "f128", issue = "116909")] |
| pub const FRAC_PI_2: f128 = 1.57079632679489661923132169163975144209858469968755291048747_f128; |
| |
| /// π/3 |
| #[unstable(feature = "f128", issue = "116909")] |
| pub const FRAC_PI_3: f128 = 1.04719755119659774615421446109316762806572313312503527365831_f128; |
| |
| /// π/4 |
| #[unstable(feature = "f128", issue = "116909")] |
| pub const FRAC_PI_4: f128 = 0.785398163397448309615660845819875721049292349843776455243736_f128; |
| |
| /// π/6 |
| #[unstable(feature = "f128", issue = "116909")] |
| pub const FRAC_PI_6: f128 = 0.523598775598298873077107230546583814032861566562517636829157_f128; |
| |
| /// π/8 |
| #[unstable(feature = "f128", issue = "116909")] |
| pub const FRAC_PI_8: f128 = 0.392699081698724154807830422909937860524646174921888227621868_f128; |
| |
| /// 1/π |
| #[unstable(feature = "f128", issue = "116909")] |
| pub const FRAC_1_PI: f128 = 0.318309886183790671537767526745028724068919291480912897495335_f128; |
| |
| /// 1/sqrt(π) |
| #[unstable(feature = "f128", issue = "116909")] |
| // Also, #[unstable(feature = "more_float_constants", issue = "103883")] |
| pub const FRAC_1_SQRT_PI: f128 = |
| 0.564189583547756286948079451560772585844050629328998856844086_f128; |
| |
| /// 1/sqrt(2π) |
| #[doc(alias = "FRAC_1_SQRT_TAU")] |
| #[unstable(feature = "f128", issue = "116909")] |
| // Also, #[unstable(feature = "more_float_constants", issue = "103883")] |
| pub const FRAC_1_SQRT_2PI: f128 = |
| 0.398942280401432677939946059934381868475858631164934657665926_f128; |
| |
| /// 2/π |
| #[unstable(feature = "f128", issue = "116909")] |
| pub const FRAC_2_PI: f128 = 0.636619772367581343075535053490057448137838582961825794990669_f128; |
| |
| /// 2/sqrt(π) |
| #[unstable(feature = "f128", issue = "116909")] |
| pub const FRAC_2_SQRT_PI: f128 = |
| 1.12837916709551257389615890312154517168810125865799771368817_f128; |
| |
| /// sqrt(2) |
| #[unstable(feature = "f128", issue = "116909")] |
| pub const SQRT_2: f128 = 1.41421356237309504880168872420969807856967187537694807317668_f128; |
| |
| /// 1/sqrt(2) |
| #[unstable(feature = "f128", issue = "116909")] |
| pub const FRAC_1_SQRT_2: f128 = |
| 0.707106781186547524400844362104849039284835937688474036588340_f128; |
| |
| /// sqrt(3) |
| #[unstable(feature = "f128", issue = "116909")] |
| // Also, #[unstable(feature = "more_float_constants", issue = "103883")] |
| pub const SQRT_3: f128 = 1.73205080756887729352744634150587236694280525381038062805581_f128; |
| |
| /// 1/sqrt(3) |
| #[unstable(feature = "f128", issue = "116909")] |
| // Also, #[unstable(feature = "more_float_constants", issue = "103883")] |
| pub const FRAC_1_SQRT_3: f128 = |
| 0.577350269189625764509148780501957455647601751270126876018602_f128; |
| |
| /// Euler's number (e) |
| #[unstable(feature = "f128", issue = "116909")] |
| pub const E: f128 = 2.71828182845904523536028747135266249775724709369995957496697_f128; |
| |
| /// log<sub>2</sub>(10) |
| #[unstable(feature = "f128", issue = "116909")] |
| pub const LOG2_10: f128 = 3.32192809488736234787031942948939017586483139302458061205476_f128; |
| |
| /// log<sub>2</sub>(e) |
| #[unstable(feature = "f128", issue = "116909")] |
| pub const LOG2_E: f128 = 1.44269504088896340735992468100189213742664595415298593413545_f128; |
| |
| /// log<sub>10</sub>(2) |
| #[unstable(feature = "f128", issue = "116909")] |
| pub const LOG10_2: f128 = 0.301029995663981195213738894724493026768189881462108541310427_f128; |
| |
| /// log<sub>10</sub>(e) |
| #[unstable(feature = "f128", issue = "116909")] |
| pub const LOG10_E: f128 = 0.434294481903251827651128918916605082294397005803666566114454_f128; |
| |
| /// ln(2) |
| #[unstable(feature = "f128", issue = "116909")] |
| pub const LN_2: f128 = 0.693147180559945309417232121458176568075500134360255254120680_f128; |
| |
| /// ln(10) |
| #[unstable(feature = "f128", issue = "116909")] |
| pub const LN_10: f128 = 2.30258509299404568401799145468436420760110148862877297603333_f128; |
| } |
| |
| #[cfg(not(test))] |
| impl f128 { |
| // FIXME(f16_f128): almost all methods in this `impl` are missing examples and a const |
| // implementation. Add these once we can run code on all platforms and have f16/f128 in CTFE. |
| |
| /// The radix or base of the internal representation of `f128`. |
| #[unstable(feature = "f128", issue = "116909")] |
| pub const RADIX: u32 = 2; |
| |
| /// Number of significant digits in base 2. |
| #[unstable(feature = "f128", issue = "116909")] |
| pub const MANTISSA_DIGITS: u32 = 113; |
| |
| /// Approximate number of significant digits in base 10. |
| /// |
| /// This is the maximum <i>x</i> such that any decimal number with <i>x</i> |
| /// significant digits can be converted to `f128` and back without loss. |
| /// |
| /// Equal to floor(log<sub>10</sub> 2<sup>[`MANTISSA_DIGITS`] − 1</sup>). |
| /// |
| /// [`MANTISSA_DIGITS`]: f128::MANTISSA_DIGITS |
| #[unstable(feature = "f128", issue = "116909")] |
| pub const DIGITS: u32 = 33; |
| |
| /// [Machine epsilon] value for `f128`. |
| /// |
| /// This is the difference between `1.0` and the next larger representable number. |
| /// |
| /// Equal to 2<sup>1 − [`MANTISSA_DIGITS`]</sup>. |
| /// |
| /// [Machine epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon |
| /// [`MANTISSA_DIGITS`]: f128::MANTISSA_DIGITS |
| #[unstable(feature = "f128", issue = "116909")] |
| pub const EPSILON: f128 = 1.92592994438723585305597794258492732e-34_f128; |
| |
| /// Smallest finite `f128` value. |
| /// |
| /// Equal to −[`MAX`]. |
| /// |
| /// [`MAX`]: f128::MAX |
| #[unstable(feature = "f128", issue = "116909")] |
| pub const MIN: f128 = -1.18973149535723176508575932662800702e+4932_f128; |
| /// Smallest positive normal `f128` value. |
| /// |
| /// Equal to 2<sup>[`MIN_EXP`] − 1</sup>. |
| /// |
| /// [`MIN_EXP`]: f128::MIN_EXP |
| #[unstable(feature = "f128", issue = "116909")] |
| pub const MIN_POSITIVE: f128 = 3.36210314311209350626267781732175260e-4932_f128; |
| /// Largest finite `f128` value. |
| /// |
| /// Equal to |
| /// (1 − 2<sup>−[`MANTISSA_DIGITS`]</sup>) 2<sup>[`MAX_EXP`]</sup>. |
| /// |
| /// [`MANTISSA_DIGITS`]: f128::MANTISSA_DIGITS |
| /// [`MAX_EXP`]: f128::MAX_EXP |
| #[unstable(feature = "f128", issue = "116909")] |
| pub const MAX: f128 = 1.18973149535723176508575932662800702e+4932_f128; |
| |
| /// One greater than the minimum possible normal power of 2 exponent. |
| /// |
| /// If <i>x</i> = `MIN_EXP`, then normal numbers |
| /// ≥ 0.5 × 2<sup><i>x</i></sup>. |
| #[unstable(feature = "f128", issue = "116909")] |
| pub const MIN_EXP: i32 = -16_381; |
| /// Maximum possible power of 2 exponent. |
| /// |
| /// If <i>x</i> = `MAX_EXP`, then normal numbers |
| /// < 1 × 2<sup><i>x</i></sup>. |
| #[unstable(feature = "f128", issue = "116909")] |
| pub const MAX_EXP: i32 = 16_384; |
| |
| /// Minimum <i>x</i> for which 10<sup><i>x</i></sup> is normal. |
| /// |
| /// Equal to ceil(log<sub>10</sub> [`MIN_POSITIVE`]). |
| /// |
| /// [`MIN_POSITIVE`]: f128::MIN_POSITIVE |
| #[unstable(feature = "f128", issue = "116909")] |
| pub const MIN_10_EXP: i32 = -4_931; |
| /// Maximum <i>x</i> for which 10<sup><i>x</i></sup> is normal. |
| /// |
| /// Equal to floor(log<sub>10</sub> [`MAX`]). |
| /// |
| /// [`MAX`]: f128::MAX |
| #[unstable(feature = "f128", issue = "116909")] |
| pub const MAX_10_EXP: i32 = 4_932; |
| |
| /// 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. |
| #[allow(clippy::eq_op)] |
| #[rustc_diagnostic_item = "f128_nan"] |
| #[unstable(feature = "f128", issue = "116909")] |
| pub const NAN: f128 = 0.0_f128 / 0.0_f128; |
| |
| /// Infinity (∞). |
| #[unstable(feature = "f128", issue = "116909")] |
| pub const INFINITY: f128 = 1.0_f128 / 0.0_f128; |
| |
| /// Negative infinity (−∞). |
| #[unstable(feature = "f128", issue = "116909")] |
| pub const NEG_INFINITY: f128 = -1.0_f128 / 0.0_f128; |
| |
| /// Sign bit |
| pub(crate) const SIGN_MASK: u128 = 0x8000_0000_0000_0000_0000_0000_0000_0000; |
| |
| /// Exponent mask |
| pub(crate) const EXP_MASK: u128 = 0x7fff_0000_0000_0000_0000_0000_0000_0000; |
| |
| /// Mantissa mask |
| pub(crate) const MAN_MASK: u128 = 0x0000_ffff_ffff_ffff_ffff_ffff_ffff_ffff; |
| |
| /// Minimum representable positive value (min subnormal) |
| const TINY_BITS: u128 = 0x1; |
| |
| /// Minimum representable negative value (min negative subnormal) |
| const NEG_TINY_BITS: u128 = Self::TINY_BITS | Self::SIGN_MASK; |
| |
| /// Returns `true` if this value is NaN. |
| /// |
| /// ``` |
| /// #![feature(f128)] |
| /// # // FIXME(f16_f128): remove when `unordtf2` is available |
| /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { |
| /// |
| /// let nan = f128::NAN; |
| /// let f = 7.0_f128; |
| /// |
| /// assert!(nan.is_nan()); |
| /// assert!(!f.is_nan()); |
| /// # } |
| /// ``` |
| #[inline] |
| #[must_use] |
| #[unstable(feature = "f128", issue = "116909")] |
| #[allow(clippy::eq_op)] // > if you intended to check if the operand is NaN, use `.is_nan()` instead :) |
| pub const fn is_nan(self) -> bool { |
| self != self |
| } |
| |
| // FIXME(#50145): `abs` is publicly unavailable in core 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) -> f128 { |
| // SAFETY: This transmutation is fine just like in `to_bits`/`from_bits`. |
| unsafe { |
| mem::transmute::<u128, f128>(mem::transmute::<f128, u128>(self) & !Self::SIGN_MASK) |
| } |
| } |
| |
| /// Returns `true` if this value is positive infinity or negative infinity, and |
| /// `false` otherwise. |
| /// |
| /// ``` |
| /// #![feature(f128)] |
| /// # // FIXME(f16_f128): remove when `eqtf2` is available |
| /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { |
| /// |
| /// let f = 7.0f128; |
| /// let inf = f128::INFINITY; |
| /// let neg_inf = f128::NEG_INFINITY; |
| /// let nan = f128::NAN; |
| /// |
| /// assert!(!f.is_infinite()); |
| /// assert!(!nan.is_infinite()); |
| /// |
| /// assert!(inf.is_infinite()); |
| /// assert!(neg_inf.is_infinite()); |
| /// # } |
| /// ``` |
| #[inline] |
| #[must_use] |
| #[unstable(feature = "f128", issue = "116909")] |
| #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")] |
| pub const fn is_infinite(self) -> bool { |
| (self == f128::INFINITY) | (self == f128::NEG_INFINITY) |
| } |
| |
| /// Returns `true` if this number is neither infinite nor NaN. |
| /// |
| /// ``` |
| /// #![feature(f128)] |
| /// # // FIXME(f16_f128): remove when `lttf2` is available |
| /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { |
| /// |
| /// let f = 7.0f128; |
| /// let inf: f128 = f128::INFINITY; |
| /// let neg_inf: f128 = f128::NEG_INFINITY; |
| /// let nan: f128 = f128::NAN; |
| /// |
| /// assert!(f.is_finite()); |
| /// |
| /// assert!(!nan.is_finite()); |
| /// assert!(!inf.is_finite()); |
| /// assert!(!neg_inf.is_finite()); |
| /// # } |
| /// ``` |
| #[inline] |
| #[must_use] |
| #[unstable(feature = "f128", issue = "116909")] |
| #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")] |
| 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]. |
| /// |
| /// ``` |
| /// #![feature(f128)] |
| /// # // FIXME(f16_f128): remove when `eqtf2` is available |
| /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { |
| /// |
| /// let min = f128::MIN_POSITIVE; // 3.362103143e-4932f128 |
| /// let max = f128::MAX; |
| /// let lower_than_min = 1.0e-4960_f128; |
| /// let zero = 0.0_f128; |
| /// |
| /// assert!(!min.is_subnormal()); |
| /// assert!(!max.is_subnormal()); |
| /// |
| /// assert!(!zero.is_subnormal()); |
| /// assert!(!f128::NAN.is_subnormal()); |
| /// assert!(!f128::INFINITY.is_subnormal()); |
| /// // Values between `0` and `min` are Subnormal. |
| /// assert!(lower_than_min.is_subnormal()); |
| /// # } |
| /// ``` |
| /// |
| /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number |
| #[inline] |
| #[must_use] |
| #[unstable(feature = "f128", issue = "116909")] |
| #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")] |
| pub const fn is_subnormal(self) -> bool { |
| matches!(self.classify(), FpCategory::Subnormal) |
| } |
| |
| /// Returns `true` if the number is neither zero, infinite, [subnormal], or NaN. |
| /// |
| /// ``` |
| /// #![feature(f128)] |
| /// # // FIXME(f16_f128): remove when `eqtf2` is available |
| /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { |
| /// |
| /// let min = f128::MIN_POSITIVE; // 3.362103143e-4932f128 |
| /// let max = f128::MAX; |
| /// let lower_than_min = 1.0e-4960_f128; |
| /// let zero = 0.0_f128; |
| /// |
| /// assert!(min.is_normal()); |
| /// assert!(max.is_normal()); |
| /// |
| /// assert!(!zero.is_normal()); |
| /// assert!(!f128::NAN.is_normal()); |
| /// assert!(!f128::INFINITY.is_normal()); |
| /// // Values between `0` and `min` are Subnormal. |
| /// assert!(!lower_than_min.is_normal()); |
| /// # } |
| /// ``` |
| /// |
| /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number |
| #[inline] |
| #[must_use] |
| #[unstable(feature = "f128", issue = "116909")] |
| #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")] |
| 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. |
| /// |
| /// ``` |
| /// #![feature(f128)] |
| /// # // FIXME(f16_f128): remove when `eqtf2` is available |
| /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { |
| /// |
| /// use std::num::FpCategory; |
| /// |
| /// let num = 12.4_f128; |
| /// let inf = f128::INFINITY; |
| /// |
| /// assert_eq!(num.classify(), FpCategory::Normal); |
| /// assert_eq!(inf.classify(), FpCategory::Infinite); |
| /// # } |
| /// ``` |
| #[inline] |
| #[unstable(feature = "f128", issue = "116909")] |
| #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")] |
| pub const fn classify(self) -> FpCategory { |
| // Other float types suffer from various platform bugs that violate the usual IEEE semantics |
| // and also make bitwise classification not always work reliably. However, `f128` cannot fit |
| // into any other float types so this is not a concern, and we can rely on bit patterns. |
| |
| let bits = self.to_bits(); |
| match (bits & Self::MAN_MASK, bits & Self::EXP_MASK) { |
| (0, Self::EXP_MASK) => FpCategory::Infinite, |
| (_, Self::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](f128) for more info. |
| /// |
| /// ``` |
| /// #![feature(f128)] |
| /// |
| /// let f = 7.0_f128; |
| /// let g = -7.0_f128; |
| /// |
| /// assert!(f.is_sign_positive()); |
| /// assert!(!g.is_sign_positive()); |
| /// ``` |
| #[inline] |
| #[must_use] |
| #[unstable(feature = "f128", issue = "116909")] |
| pub 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](f128) for more info. |
| /// |
| /// ``` |
| /// #![feature(f128)] |
| /// |
| /// let f = 7.0_f128; |
| /// let g = -7.0_f128; |
| /// |
| /// assert!(!f.is_sign_negative()); |
| /// assert!(g.is_sign_negative()); |
| /// ``` |
| #[inline] |
| #[must_use] |
| #[unstable(feature = "f128", issue = "116909")] |
| pub fn is_sign_negative(self) -> bool { |
| // IEEE754 says: isSignMinus(x) is true if and only if x has negative sign. isSignMinus |
| // applies to zeros and NaNs as well. |
| // SAFETY: This is just transmuting to get the sign bit, it's fine. |
| (self.to_bits() & (1 << 127)) != 0 |
| } |
| |
| /// Returns the least number greater than `self`. |
| /// |
| /// Let `TINY` be the smallest representable positive `f128`. 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(f128)] |
| /// #![feature(float_next_up_down)] |
| /// # // FIXME(f16_f128): remove when `eqtf2` is available |
| /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { |
| /// |
| /// // f128::EPSILON is the difference between 1.0 and the next number up. |
| /// assert_eq!(1.0f128.next_up(), 1.0 + f128::EPSILON); |
| /// // But not for most numbers. |
| /// assert!(0.1f128.next_up() < 0.1 + f128::EPSILON); |
| /// assert_eq!(4611686018427387904f128.next_up(), 4611686018427387904.000000000000001); |
| /// # } |
| /// ``` |
| /// |
| /// [`NEG_INFINITY`]: Self::NEG_INFINITY |
| /// [`INFINITY`]: Self::INFINITY |
| /// [`MIN`]: Self::MIN |
| /// [`MAX`]: Self::MAX |
| #[inline] |
| #[unstable(feature = "f128", issue = "116909")] |
| // #[unstable(feature = "float_next_up_down", issue = "91399")] |
| pub fn next_up(self) -> Self { |
| // Some targets violate Rust's assumption of IEEE semantics, e.g. by flushing |
| // denormals to zero. This is in general unsound and unsupported, but here |
| // we do our best to still produce the correct result on such targets. |
| let bits = self.to_bits(); |
| if self.is_nan() || bits == Self::INFINITY.to_bits() { |
| return self; |
| } |
| |
| let abs = bits & !Self::SIGN_MASK; |
| let next_bits = if abs == 0 { |
| Self::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 `f128`. 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(f128)] |
| /// #![feature(float_next_up_down)] |
| /// # // FIXME(f16_f128): remove when `eqtf2` is available |
| /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { |
| /// |
| /// let x = 1.0f128; |
| /// // Clamp value into range [0, 1). |
| /// let clamped = x.clamp(0.0, 1.0f128.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 |
| #[inline] |
| #[unstable(feature = "f128", issue = "116909")] |
| // #[unstable(feature = "float_next_up_down", issue = "91399")] |
| pub fn next_down(self) -> Self { |
| // Some targets violate Rust's assumption of IEEE semantics, e.g. by flushing |
| // denormals to zero. This is in general unsound and unsupported, but here |
| // we do our best to still produce the correct result on such targets. |
| let bits = self.to_bits(); |
| if self.is_nan() || bits == Self::NEG_INFINITY.to_bits() { |
| return self; |
| } |
| |
| let abs = bits & !Self::SIGN_MASK; |
| let next_bits = if abs == 0 { |
| Self::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`. |
| /// |
| /// ``` |
| /// #![feature(f128)] |
| /// # // FIXME(f16_f128): remove when `eqtf2` is available |
| /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { |
| /// |
| /// let x = 2.0_f128; |
| /// let abs_difference = (x.recip() - (1.0 / x)).abs(); |
| /// |
| /// assert!(abs_difference <= f128::EPSILON); |
| /// # } |
| /// ``` |
| #[inline] |
| #[unstable(feature = "f128", issue = "116909")] |
| #[must_use = "this returns the result of the operation, without modifying the original"] |
| pub fn recip(self) -> Self { |
| 1.0 / self |
| } |
| |
| /// Converts radians to degrees. |
| /// |
| /// ``` |
| /// #![feature(f128)] |
| /// # // FIXME(f16_f128): remove when `eqtf2` is available |
| /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { |
| /// |
| /// let angle = std::f128::consts::PI; |
| /// |
| /// let abs_difference = (angle.to_degrees() - 180.0).abs(); |
| /// assert!(abs_difference <= f128::EPSILON); |
| /// # } |
| /// ``` |
| #[inline] |
| #[unstable(feature = "f128", issue = "116909")] |
| #[must_use = "this returns the result of the operation, without modifying the original"] |
| pub fn to_degrees(self) -> Self { |
| // Use a literal for better precision. |
| const PIS_IN_180: f128 = 57.2957795130823208767981548141051703324054724665643215491602_f128; |
| self * PIS_IN_180 |
| } |
| |
| /// Converts degrees to radians. |
| /// |
| /// ``` |
| /// #![feature(f128)] |
| /// # // FIXME(f16_f128): remove when `eqtf2` is available |
| /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { |
| /// |
| /// let angle = 180.0f128; |
| /// |
| /// let abs_difference = (angle.to_radians() - std::f128::consts::PI).abs(); |
| /// |
| /// assert!(abs_difference <= 1e-30); |
| /// # } |
| /// ``` |
| #[inline] |
| #[unstable(feature = "f128", issue = "116909")] |
| #[must_use = "this returns the result of the operation, without modifying the original"] |
| pub fn to_radians(self) -> f128 { |
| // Use a literal for better precision. |
| const RADS_PER_DEG: f128 = |
| 0.0174532925199432957692369076848861271344287188854172545609719_f128; |
| self * RADS_PER_DEG |
| } |
| |
| /// 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. |
| /// |
| /// ``` |
| /// #![feature(f128)] |
| /// # // Using aarch64 because `reliable_f128_math` is needed |
| /// # #[cfg(all(target_arch = "aarch64", target_os = "linux"))] { |
| /// |
| /// let x = 1.0f128; |
| /// let y = 2.0f128; |
| /// |
| /// assert_eq!(x.max(y), y); |
| /// # } |
| /// ``` |
| #[inline] |
| #[unstable(feature = "f128", issue = "116909")] |
| #[must_use = "this returns the result of the comparison, without modifying either input"] |
| pub fn max(self, other: f128) -> f128 { |
| intrinsics::maxnumf128(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. |
| /// |
| /// ``` |
| /// #![feature(f128)] |
| /// # // Using aarch64 because `reliable_f128_math` is needed |
| /// # #[cfg(all(target_arch = "aarch64", target_os = "linux"))] { |
| /// |
| /// let x = 1.0f128; |
| /// let y = 2.0f128; |
| /// |
| /// assert_eq!(x.min(y), x); |
| /// # } |
| /// ``` |
| #[inline] |
| #[unstable(feature = "f128", issue = "116909")] |
| #[must_use = "this returns the result of the comparison, without modifying either input"] |
| pub fn min(self, other: f128) -> f128 { |
| intrinsics::minnumf128(self, other) |
| } |
| |
| /// Returns the maximum of the two numbers, propagating NaN. |
| /// |
| /// This returns NaN when *either* argument is NaN, as opposed to |
| /// [`f128::max`] which only returns NaN when *both* arguments are NaN. |
| /// |
| /// ``` |
| /// #![feature(f128)] |
| /// #![feature(float_minimum_maximum)] |
| /// # // Using aarch64 because `reliable_f128_math` is needed |
| /// # #[cfg(all(target_arch = "aarch64", target_os = "linux"))] { |
| /// |
| /// let x = 1.0f128; |
| /// let y = 2.0f128; |
| /// |
| /// assert_eq!(x.maximum(y), y); |
| /// assert!(x.maximum(f128::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](f128) for more info. |
| #[inline] |
| #[unstable(feature = "f128", issue = "116909")] |
| // #[unstable(feature = "float_minimum_maximum", issue = "91079")] |
| #[must_use = "this returns the result of the comparison, without modifying either input"] |
| pub fn maximum(self, other: f128) -> f128 { |
| 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 |
| /// [`f128::min`] which only returns NaN when *both* arguments are NaN. |
| /// |
| /// ``` |
| /// #![feature(f128)] |
| /// #![feature(float_minimum_maximum)] |
| /// # // Using aarch64 because `reliable_f128_math` is needed |
| /// # #[cfg(all(target_arch = "aarch64", target_os = "linux"))] { |
| /// |
| /// let x = 1.0f128; |
| /// let y = 2.0f128; |
| /// |
| /// assert_eq!(x.minimum(y), x); |
| /// assert!(x.minimum(f128::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](f128) for more info. |
| #[inline] |
| #[unstable(feature = "f128", issue = "116909")] |
| // #[unstable(feature = "float_minimum_maximum", issue = "91079")] |
| #[must_use = "this returns the result of the comparison, without modifying either input"] |
| pub fn minimum(self, other: f128) -> f128 { |
| 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 { |
| // At least one input is NaN. Use `+` to perform NaN propagation and quieting. |
| self + other |
| } |
| } |
| |
| /// Calculates the middle point of `self` and `rhs`. |
| /// |
| /// This returns NaN when *either* argument is NaN or if a combination of |
| /// +inf and -inf is provided as arguments. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// #![feature(f128)] |
| /// #![feature(num_midpoint)] |
| /// # // Using aarch64 because `reliable_f128_math` is needed |
| /// # #[cfg(all(target_arch = "aarch64", target_os = "linux"))] { |
| /// |
| /// assert_eq!(1f128.midpoint(4.0), 2.5); |
| /// assert_eq!((-5.5f128).midpoint(8.0), 1.25); |
| /// # } |
| /// ``` |
| #[inline] |
| #[unstable(feature = "f128", issue = "116909")] |
| // #[unstable(feature = "num_midpoint", issue = "110840")] |
| pub fn midpoint(self, other: f128) -> f128 { |
| const LO: f128 = f128::MIN_POSITIVE * 2.; |
| const HI: f128 = f128::MAX / 2.; |
| |
| let (a, b) = (self, other); |
| let abs_a = a.abs_private(); |
| let abs_b = b.abs_private(); |
| |
| if abs_a <= HI && abs_b <= HI { |
| // Overflow is impossible |
| (a + b) / 2. |
| } else if abs_a < LO { |
| // Not safe to halve `a` (would underflow) |
| a + (b / 2.) |
| } else if abs_b < LO { |
| // Not safe to halve `b` (would underflow) |
| (a / 2.) + b |
| } else { |
| // Safe to halve `a` and `b` |
| (a / 2.) + (b / 2.) |
| } |
| } |
| |
| /// Rounds toward zero and converts to any primitive integer type, |
| /// assuming that the value is finite and fits in that type. |
| /// |
| /// ``` |
| /// #![feature(f128)] |
| /// # // FIXME(f16_f128): remove when `float*itf` is available |
| /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { |
| /// |
| /// let value = 4.6_f128; |
| /// let rounded = unsafe { value.to_int_unchecked::<u16>() }; |
| /// assert_eq!(rounded, 4); |
| /// |
| /// let value = -128.9_f128; |
| /// 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 |
| #[inline] |
| #[unstable(feature = "f128", issue = "116909")] |
| #[must_use = "this returns the result of the operation, without modifying the original"] |
| 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 `u128`. |
| /// |
| /// This is currently identical to `transmute::<f128, u128>(self)` on all platforms. |
| /// |
| /// See [`from_bits`](#method.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. |
| /// |
| /// ``` |
| /// #![feature(f128)] |
| /// |
| /// # // FIXME(f16_f128): enable this once const casting works |
| /// # // assert_ne!((1f128).to_bits(), 1f128 as u128); // to_bits() is not casting! |
| /// assert_eq!((12.5f128).to_bits(), 0x40029000000000000000000000000000); |
| /// ``` |
| #[inline] |
| #[unstable(feature = "f128", issue = "116909")] |
| #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")] |
| #[must_use = "this returns the result of the operation, without modifying the original"] |
| pub const fn to_bits(self) -> u128 { |
| // SAFETY: `u128` is a plain old datatype so we can always transmute to it. |
| unsafe { mem::transmute(self) } |
| } |
| |
| /// Raw transmutation from `u128`. |
| /// |
| /// This is currently identical to `transmute::<u128, f128>(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. |
| /// |
| /// ``` |
| /// #![feature(f128)] |
| /// # // FIXME(f16_f128): remove when `eqtf2` is available |
| /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { |
| /// |
| /// let v = f128::from_bits(0x40029000000000000000000000000000); |
| /// assert_eq!(v, 12.5); |
| /// # } |
| /// ``` |
| #[inline] |
| #[must_use] |
| #[unstable(feature = "f128", issue = "116909")] |
| #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")] |
| pub const fn from_bits(v: u128) -> Self { |
| // It turns out the safety issues with sNaN were overblown! Hooray! |
| // SAFETY: `u128` is a plain old datatype so we can always transmute from it. |
| unsafe { mem::transmute(v) } |
| } |
| |
| /// Returns 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 |
| /// |
| /// ``` |
| /// #![feature(f128)] |
| /// |
| /// let bytes = 12.5f128.to_be_bytes(); |
| /// assert_eq!( |
| /// bytes, |
| /// [0x40, 0x02, 0x90, 0x00, 0x00, 0x00, 0x00, 0x00, |
| /// 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00] |
| /// ); |
| /// ``` |
| #[inline] |
| #[unstable(feature = "f128", issue = "116909")] |
| #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")] |
| #[must_use = "this returns the result of the operation, without modifying the original"] |
| pub const fn to_be_bytes(self) -> [u8; 16] { |
| self.to_bits().to_be_bytes() |
| } |
| |
| /// Returns 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 |
| /// |
| /// ``` |
| /// #![feature(f128)] |
| /// |
| /// let bytes = 12.5f128.to_le_bytes(); |
| /// assert_eq!( |
| /// bytes, |
| /// [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, |
| /// 0x00, 0x00, 0x00, 0x00, 0x00, 0x90, 0x02, 0x40] |
| /// ); |
| /// ``` |
| #[inline] |
| #[unstable(feature = "f128", issue = "116909")] |
| #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")] |
| #[must_use = "this returns the result of the operation, without modifying the original"] |
| pub const fn to_le_bytes(self) -> [u8; 16] { |
| self.to_bits().to_le_bytes() |
| } |
| |
| /// Returns 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`]: f128::to_be_bytes |
| /// [`to_le_bytes`]: f128::to_le_bytes |
| /// |
| /// See [`from_bits`](Self::from_bits) for some discussion of the |
| /// portability of this operation (there are almost no issues). |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// #![feature(f128)] |
| /// |
| /// let bytes = 12.5f128.to_ne_bytes(); |
| /// assert_eq!( |
| /// bytes, |
| /// if cfg!(target_endian = "big") { |
| /// [0x40, 0x02, 0x90, 0x00, 0x00, 0x00, 0x00, 0x00, |
| /// 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00] |
| /// } else { |
| /// [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, |
| /// 0x00, 0x00, 0x00, 0x00, 0x00, 0x90, 0x02, 0x40] |
| /// } |
| /// ); |
| /// ``` |
| #[inline] |
| #[unstable(feature = "f128", issue = "116909")] |
| #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")] |
| #[must_use = "this returns the result of the operation, without modifying the original"] |
| pub const fn to_ne_bytes(self) -> [u8; 16] { |
| self.to_bits().to_ne_bytes() |
| } |
| |
| /// Creates 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 |
| /// |
| /// ``` |
| /// #![feature(f128)] |
| /// # // FIXME(f16_f128): remove when `eqtf2` is available |
| /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { |
| /// |
| /// let value = f128::from_be_bytes( |
| /// [0x40, 0x02, 0x90, 0x00, 0x00, 0x00, 0x00, 0x00, |
| /// 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00] |
| /// ); |
| /// assert_eq!(value, 12.5); |
| /// # } |
| /// ``` |
| #[inline] |
| #[must_use] |
| #[unstable(feature = "f128", issue = "116909")] |
| #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")] |
| pub const fn from_be_bytes(bytes: [u8; 16]) -> Self { |
| Self::from_bits(u128::from_be_bytes(bytes)) |
| } |
| |
| /// Creates 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 |
| /// |
| /// ``` |
| /// #![feature(f128)] |
| /// # // FIXME(f16_f128): remove when `eqtf2` is available |
| /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { |
| /// |
| /// let value = f128::from_le_bytes( |
| /// [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, |
| /// 0x00, 0x00, 0x00, 0x00, 0x00, 0x90, 0x02, 0x40] |
| /// ); |
| /// assert_eq!(value, 12.5); |
| /// # } |
| /// ``` |
| #[inline] |
| #[must_use] |
| #[unstable(feature = "f128", issue = "116909")] |
| #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")] |
| pub const fn from_le_bytes(bytes: [u8; 16]) -> Self { |
| Self::from_bits(u128::from_le_bytes(bytes)) |
| } |
| |
| /// Creates 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`]: f128::from_be_bytes |
| /// [`from_le_bytes`]: f128::from_le_bytes |
| /// |
| /// See [`from_bits`](Self::from_bits) for some discussion of the |
| /// portability of this operation (there are almost no issues). |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// #![feature(f128)] |
| /// # // FIXME(f16_f128): remove when `eqtf2` is available |
| /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { |
| /// |
| /// let value = f128::from_ne_bytes(if cfg!(target_endian = "big") { |
| /// [0x40, 0x02, 0x90, 0x00, 0x00, 0x00, 0x00, 0x00, |
| /// 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00] |
| /// } else { |
| /// [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, |
| /// 0x00, 0x00, 0x00, 0x00, 0x00, 0x90, 0x02, 0x40] |
| /// }); |
| /// assert_eq!(value, 12.5); |
| /// # } |
| /// ``` |
| #[inline] |
| #[must_use] |
| #[unstable(feature = "f128", issue = "116909")] |
| #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")] |
| pub const fn from_ne_bytes(bytes: [u8; 16]) -> Self { |
| Self::from_bits(u128::from_ne_bytes(bytes)) |
| } |
| |
| /// Returns 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 `f128`. 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 |
| /// |
| /// ``` |
| /// #![feature(f128)] |
| /// |
| /// struct GoodBoy { |
| /// name: &'static str, |
| /// weight: f128, |
| /// } |
| /// |
| /// let mut bois = vec![ |
| /// GoodBoy { name: "Pucci", weight: 0.1 }, |
| /// GoodBoy { name: "Woofer", weight: 99.0 }, |
| /// GoodBoy { name: "Yapper", weight: 10.0 }, |
| /// GoodBoy { name: "Chonk", weight: f128::INFINITY }, |
| /// GoodBoy { name: "Abs. Unit", weight: f128::NAN }, |
| /// GoodBoy { name: "Floaty", weight: -5.0 }, |
| /// ]; |
| /// |
| /// bois.sort_by(|a, b| a.weight.total_cmp(&b.weight)); |
| /// |
| /// // `f128::NAN` could be positive or negative, which will affect the sort order. |
| /// if f128::NAN.is_sign_negative() { |
| /// bois.into_iter().map(|b| b.weight) |
| /// .zip([f128::NAN, -5.0, 0.1, 10.0, 99.0, f128::INFINITY].iter()) |
| /// .for_each(|(a, b)| assert_eq!(a.to_bits(), b.to_bits())) |
| /// } else { |
| /// bois.into_iter().map(|b| b.weight) |
| /// .zip([-5.0, 0.1, 10.0, 99.0, f128::INFINITY, f128::NAN].iter()) |
| /// .for_each(|(a, b)| assert_eq!(a.to_bits(), b.to_bits())) |
| /// } |
| /// ``` |
| #[inline] |
| #[must_use] |
| #[unstable(feature = "f128", issue = "116909")] |
| pub fn total_cmp(&self, other: &Self) -> crate::cmp::Ordering { |
| let mut left = self.to_bits() as i128; |
| let mut right = other.to_bits() as i128; |
| |
| // 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 >> 127) as u128) >> 1) as i128; |
| right ^= (((right >> 127) as u128) >> 1) as i128; |
| |
| 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 |
| /// |
| /// ``` |
| /// #![feature(f128)] |
| /// # // FIXME(f16_f128): remove when `{eq,gt,unord}tf` are available |
| /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] { |
| /// |
| /// assert!((-3.0f128).clamp(-2.0, 1.0) == -2.0); |
| /// assert!((0.0f128).clamp(-2.0, 1.0) == 0.0); |
| /// assert!((2.0f128).clamp(-2.0, 1.0) == 1.0); |
| /// assert!((f128::NAN).clamp(-2.0, 1.0).is_nan()); |
| /// # } |
| /// ``` |
| #[inline] |
| #[unstable(feature = "f128", issue = "116909")] |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| pub fn clamp(mut self, min: f128, max: f128) -> f128 { |
| assert!(min <= max, "min > max, or either was NaN. min = {min:?}, max = {max:?}"); |
| if self < min { |
| self = min; |
| } |
| if self > max { |
| self = max; |
| } |
| self |
| } |
| } |
