src/libcore/num/f64.rs - third_party/rust - Git at Google

 //! 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(bootstrap))]
 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`.
 #[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 larger 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;

     /// The full circle constant (τ)
     ///
     /// Equal to 2π.
     #[unstable(feature = "tau_constant", issue = "66770")]
     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)
     #[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)
     }

     /// Rounds toward zero and converts to any primitive integer type,
     /// assuming that the value is finite and fits in that type.
     ///
     /// ```
     /// #![feature(float_approx_unchecked_to)]
     ///
     /// let value = 4.6_f32;
     /// let rounded = unsafe { value.approx_unchecked_to::<u16>() };
     /// assert_eq!(rounded, 4);
     ///
     /// let value = -128.9_f32;
     /// let rounded = unsafe { value.approx_unchecked_to::<i8>() };
     /// assert_eq!(rounded, std::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
     #[cfg(not(bootstrap))]
     #[unstable(feature = "float_approx_unchecked_to", issue = "67058")]
     #[inline]
     pub unsafe fn approx_unchecked_to<Int>(self) -> Int where Self: FloatToInt<Int> {
         FloatToInt::<Int>::approx_unchecked(self)
     }

     /// 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 {
         // SAFETY: `u64` is a plain old datatype so we can always transmute to it
         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
     ///
     /// ```
     /// let v = f64::from_bits(0x4029000000000000);
     /// assert_eq!(v, 12.5);
     /// ```
     #[stable(feature = "float_bits_conv", since = "1.20.0")]
     #[inline]
     pub fn from_bits(v: u64) -> Self {
         // SAFETY: `u64` is a plain old datatype so we can always transmute from it
         // It turns out the safety issues with sNaN were overblown! Hooray!
         unsafe { mem::transmute(v) }
     }

     /// Return the memory representation of this floating point number as a byte array in
     /// big-endian (network) byte order.
     ///
     /// # Examples
     ///
     /// ```
     /// let bytes = 12.5f64.to_be_bytes();
     /// assert_eq!(bytes, [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]);
     /// ```
     #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
     #[inline]
     pub 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.
     ///
     /// # Examples
     ///
     /// ```
     /// let bytes = 12.5f64.to_le_bytes();
     /// assert_eq!(bytes, [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]);
     /// ```
     #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
     #[inline]
     pub 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`]: #method.to_be_bytes
     /// [`to_le_bytes`]: #method.to_le_bytes
     ///
     /// # 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]
     ///     }
     /// );
     /// ```
     #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
     #[inline]
     pub 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.
     ///
     /// # 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")]
     #[inline]
     pub 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.
     ///
     /// # 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")]
     #[inline]
     pub 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`]: #method.from_be_bytes
     /// [`from_le_bytes`]: #method.from_le_bytes
     ///
     /// # 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")]
     #[inline]
     pub fn from_ne_bytes(bytes: [u8; 8]) -> Self {
         Self::from_bits(u64::from_ne_bytes(bytes))
     }
 }
	//! 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(bootstrap))]
	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`.
	#[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 larger 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;

	/// The full circle constant (τ)
	///
	/// Equal to 2π.
	#[unstable(feature = "tau_constant", issue = "66770")]
	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)
	#[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)
	}

	/// Rounds toward zero and converts to any primitive integer type,
	/// assuming that the value is finite and fits in that type.
	///
	/// ```
	/// #![feature(float_approx_unchecked_to)]
	///
	/// let value = 4.6_f32;
	/// let rounded = unsafe { value.approx_unchecked_to::<u16>() };
	/// assert_eq!(rounded, 4);
	///
	/// let value = -128.9_f32;
	/// let rounded = unsafe { value.approx_unchecked_to::<i8>() };
	/// assert_eq!(rounded, std::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
	#[cfg(not(bootstrap))]
	#[unstable(feature = "float_approx_unchecked_to", issue = "67058")]
	#[inline]
	pub unsafe fn approx_unchecked_to<Int>(self) -> Int where Self: FloatToInt<Int> {
	FloatToInt::<Int>::approx_unchecked(self)
	}

	/// 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 {
	// SAFETY: `u64` is a plain old datatype so we can always transmute to it
	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
	///
	/// ```
	/// let v = f64::from_bits(0x4029000000000000);
	/// assert_eq!(v, 12.5);
	/// ```
	#[stable(feature = "float_bits_conv", since = "1.20.0")]
	#[inline]
	pub fn from_bits(v: u64) -> Self {
	// SAFETY: `u64` is a plain old datatype so we can always transmute from it
	// It turns out the safety issues with sNaN were overblown! Hooray!
	unsafe { mem::transmute(v) }
	}

	/// Return the memory representation of this floating point number as a byte array in
	/// big-endian (network) byte order.
	///
	/// # Examples
	///
	/// ```
	/// let bytes = 12.5f64.to_be_bytes();
	/// assert_eq!(bytes, [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]);
	/// ```
	#[stable(feature = "float_to_from_bytes", since = "1.40.0")]
	#[inline]
	pub 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.
	///
	/// # Examples
	///
	/// ```
	/// let bytes = 12.5f64.to_le_bytes();
	/// assert_eq!(bytes, [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]);
	/// ```
	#[stable(feature = "float_to_from_bytes", since = "1.40.0")]
	#[inline]
	pub 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`]: #method.to_be_bytes
	/// [`to_le_bytes`]: #method.to_le_bytes
	///
	/// # 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]
	/// }
	/// );
	/// ```
	#[stable(feature = "float_to_from_bytes", since = "1.40.0")]
	#[inline]
	pub 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.
	///
	/// # 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")]
	#[inline]
	pub 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.
	///
	/// # 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")]
	#[inline]
	pub 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`]: #method.from_be_bytes
	/// [`from_le_bytes`]: #method.from_le_bytes
	///
	/// # 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")]
	#[inline]
	pub fn from_ne_bytes(bytes: [u8; 8]) -> Self {
	Self::from_bits(u64::from_ne_bytes(bytes))
	}
	}