| //! This module provides constants which are specific to the implementation |
| //! of the `f64` floating point data type. |
| //! |
| //! *[See also the `f64` primitive type](../../std/primitive.f64.html).* |
| //! |
| //! Mathematically significant numbers are provided in the `consts` sub-module. |
| |
| #![stable(feature = "rust1", since = "1.0.0")] |
| |
| #[cfg(not(test))] |
| use crate::intrinsics; |
| |
| use crate::mem; |
| use crate::num::FpCategory; |
| |
| /// The radix or base of the internal representation of `f64`. |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub const RADIX: u32 = 2; |
| |
| /// Number of significant digits in base 2. |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub const MANTISSA_DIGITS: u32 = 53; |
| /// Approximate number of significant digits in base 10. |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub const DIGITS: u32 = 15; |
| |
| /// [Machine epsilon] value for `f64`. |
| /// |
| /// This is the difference between `1.0` and the next largest representable number. |
| /// |
| /// [Machine epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub const EPSILON: f64 = 2.2204460492503131e-16_f64; |
| |
| /// Smallest finite `f64` value. |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub const MIN: f64 = -1.7976931348623157e+308_f64; |
| /// Smallest positive normal `f64` value. |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub const MIN_POSITIVE: f64 = 2.2250738585072014e-308_f64; |
| /// Largest finite `f64` value. |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub const MAX: f64 = 1.7976931348623157e+308_f64; |
| |
| /// One greater than the minimum possible normal power of 2 exponent. |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub const MIN_EXP: i32 = -1021; |
| /// Maximum possible power of 2 exponent. |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub const MAX_EXP: i32 = 1024; |
| |
| /// Minimum possible normal power of 10 exponent. |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub const MIN_10_EXP: i32 = -307; |
| /// Maximum possible power of 10 exponent. |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub const MAX_10_EXP: i32 = 308; |
| |
| /// Not a Number (NaN). |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub const NAN: f64 = 0.0_f64 / 0.0_f64; |
| /// Infinity (∞). |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub const INFINITY: f64 = 1.0_f64 / 0.0_f64; |
| /// Negative infinity (-∞). |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub const NEG_INFINITY: f64 = -1.0_f64 / 0.0_f64; |
| |
| /// 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; |
| |
| /// 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) |
| #[unstable(feature = "extra_log_consts", issue = "50540")] |
| 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) |
| #[unstable(feature = "extra_log_consts", issue = "50540")] |
| 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; |
| } |
| |
| #[lang = "f64"] |
| #[cfg(not(test))] |
| impl f64 { |
| /// Returns `true` if this value is `NaN`. |
| /// |
| /// ``` |
| /// use std::f64; |
| /// |
| /// let nan = f64::NAN; |
| /// let f = 7.0_f64; |
| /// |
| /// assert!(nan.is_nan()); |
| /// assert!(!f.is_nan()); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn is_nan(self) -> bool { |
| self != self |
| } |
| |
| // FIXME(#50145): `abs` is publicly unavailable in libcore due to |
| // concerns about portability, so this implementation is for |
| // private use internally. |
| #[inline] |
| fn abs_private(self) -> f64 { |
| f64::from_bits(self.to_bits() & 0x7fff_ffff_ffff_ffff) |
| } |
| |
| /// Returns `true` if this value is positive infinity or negative infinity, and |
| /// `false` otherwise. |
| /// |
| /// ``` |
| /// use std::f64; |
| /// |
| /// 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()); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn is_infinite(self) -> bool { |
| self.abs_private() == INFINITY |
| } |
| |
| /// Returns `true` if this number is neither infinite nor `NaN`. |
| /// |
| /// ``` |
| /// use std::f64; |
| /// |
| /// 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()); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn is_finite(self) -> bool { |
| // There's no need to handle NaN separately: if self is NaN, |
| // the comparison is not true, exactly as desired. |
| self.abs_private() < INFINITY |
| } |
| |
| /// Returns `true` if the number is neither zero, infinite, |
| /// [subnormal][subnormal], or `NaN`. |
| /// |
| /// ``` |
| /// use std::f64; |
| /// |
| /// 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 |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn is_normal(self) -> bool { |
| self.classify() == FpCategory::Normal |
| } |
| |
| /// Returns the floating point category of the number. If only one property |
| /// is going to be tested, it is generally faster to use the specific |
| /// predicate instead. |
| /// |
| /// ``` |
| /// use std::num::FpCategory; |
| /// use std::f64; |
| /// |
| /// 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")] |
| pub fn classify(self) -> FpCategory { |
| const EXP_MASK: u64 = 0x7ff0000000000000; |
| const MAN_MASK: u64 = 0x000fffffffffffff; |
| |
| let bits = self.to_bits(); |
| match (bits & MAN_MASK, bits & EXP_MASK) { |
| (0, 0) => FpCategory::Zero, |
| (_, 0) => FpCategory::Subnormal, |
| (0, EXP_MASK) => FpCategory::Infinite, |
| (_, EXP_MASK) => FpCategory::Nan, |
| _ => FpCategory::Normal, |
| } |
| } |
| |
| /// Returns `true` if `self` has a positive sign, including `+0.0`, `NaN`s with |
| /// positive sign bit and positive infinity. |
| /// |
| /// ``` |
| /// let f = 7.0_f64; |
| /// let g = -7.0_f64; |
| /// |
| /// assert!(f.is_sign_positive()); |
| /// assert!(!g.is_sign_positive()); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn is_sign_positive(self) -> bool { |
| !self.is_sign_negative() |
| } |
| |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[rustc_deprecated(since = "1.0.0", reason = "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`, `NaN`s with |
| /// negative sign bit and negative infinity. |
| /// |
| /// ``` |
| /// let f = 7.0_f64; |
| /// let g = -7.0_f64; |
| /// |
| /// assert!(!f.is_sign_negative()); |
| /// assert!(g.is_sign_negative()); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn is_sign_negative(self) -> bool { |
| self.to_bits() & 0x8000_0000_0000_0000 != 0 |
| } |
| |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[rustc_deprecated(since = "1.0.0", reason = "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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn recip(self) -> f64 { |
| 1.0 / self |
| } |
| |
| /// Converts radians to degrees. |
| /// |
| /// ``` |
| /// use std::f64::consts; |
| /// |
| /// let angle = consts::PI; |
| /// |
| /// let abs_difference = (angle.to_degrees() - 180.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| #[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. |
| /// |
| /// ``` |
| /// use std::f64::consts; |
| /// |
| /// let angle = 180.0_f64; |
| /// |
| /// let abs_difference = (angle.to_radians() - consts::PI).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| #[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. |
| /// |
| /// ``` |
| /// let x = 1.0_f64; |
| /// let y = 2.0_f64; |
| /// |
| /// assert_eq!(x.max(y), y); |
| /// ``` |
| /// |
| /// If one of the arguments is NaN, then the other argument is returned. |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn max(self, other: f64) -> f64 { |
| intrinsics::maxnumf64(self, other) |
| } |
| |
| /// Returns the minimum of the two numbers. |
| /// |
| /// ``` |
| /// let x = 1.0_f64; |
| /// let y = 2.0_f64; |
| /// |
| /// assert_eq!(x.min(y), x); |
| /// ``` |
| /// |
| /// If one of the arguments is NaN, then the other argument is returned. |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn min(self, other: f64) -> f64 { |
| intrinsics::minnumf64(self, other) |
| } |
| |
| /// Raw transmutation to `u64`. |
| /// |
| /// This is currently identical to `transmute::<f64, u64>(self)` on all platforms. |
| /// |
| /// See `from_bits` for some discussion of the portability of this operation |
| /// (there are almost no issues). |
| /// |
| /// Note that this function is distinct from `as` casting, which attempts to |
| /// preserve the *numeric* value, and not the bitwise value. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// assert!((1f64).to_bits() != 1f64 as u64); // to_bits() is not casting! |
| /// assert_eq!((12.5f64).to_bits(), 0x4029000000000000); |
| /// |
| /// ``` |
| #[stable(feature = "float_bits_conv", since = "1.20.0")] |
| #[inline] |
| pub fn to_bits(self) -> u64 { |
| unsafe { mem::transmute(self) } |
| } |
| |
| /// 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 favours preserving the exact bits. This means that |
| /// any payloads encoded in NaNs will be preserved even if the result of |
| /// this method is sent over the network from an x86 machine to a MIPS one. |
| /// |
| /// If the results of this method are only manipulated by the same |
| /// architecture that produced them, then there is no portability concern. |
| /// |
| /// If the input isn't NaN, then there is no portability concern. |
| /// |
| /// If you don't care about signalingness (very likely), then there is no |
| /// portability concern. |
| /// |
| /// Note that this function is distinct from `as` casting, which attempts to |
| /// preserve the *numeric* value, and not the bitwise value. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// use std::f64; |
| /// let v = f64::from_bits(0x4029000000000000); |
| /// let difference = (v - 12.5).abs(); |
| /// assert!(difference <= 1e-5); |
| /// ``` |
| #[stable(feature = "float_bits_conv", since = "1.20.0")] |
| #[inline] |
| pub fn from_bits(v: u64) -> Self { |
| // It turns out the safety issues with sNaN were overblown! Hooray! |
| unsafe { mem::transmute(v) } |
| } |
| } |