2c64475069
doc: minus (U+2212) instead of dash (U+002D) for negative infinity The documentation for [`f32::NEG_INFINITY`](https://doc.rust-lang.org/std/f32/constant.NEG_INFINITY.html) contains “-∞” with a dash instead of a minus sign, “−∞” with a proper minus sign looks better with the used Source Serif Pro font. Similarly for [`f64::NEG_INFINITY`](https://doc.rust-lang.org/std/f64/constant.NEG_INFINITY.html).
612 lines
19 KiB
Rust
612 lines
19 KiB
Rust
//! This module provides constants which are specific to the implementation
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//! of the `f32` floating point data type.
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//!
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//! *[See also the `f32` primitive type](../../std/primitive.f32.html).*
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//!
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//! Mathematically significant numbers are provided in the `consts` sub-module.
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#![stable(feature = "rust1", since = "1.0.0")]
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use crate::convert::FloatToInt;
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#[cfg(not(test))]
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use crate::intrinsics;
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use crate::mem;
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use crate::num::FpCategory;
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/// The radix or base of the internal representation of `f32`.
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const RADIX: u32 = 2;
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/// Number of significant digits in base 2.
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const MANTISSA_DIGITS: u32 = 24;
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/// Approximate number of significant digits in base 10.
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const DIGITS: u32 = 6;
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/// [Machine epsilon] value for `f32`.
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///
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/// This is the difference between `1.0` and the next larger representable number.
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///
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/// [Machine epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const EPSILON: f32 = 1.1920929e-7_f32;
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/// Smallest finite `f32` value.
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const MIN: f32 = -3.40282347e+38_f32;
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/// Smallest positive normal `f32` value.
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const MIN_POSITIVE: f32 = 1.17549435e-38_f32;
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/// Largest finite `f32` value.
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const MAX: f32 = 3.40282347e+38_f32;
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/// One greater than the minimum possible normal power of 2 exponent.
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const MIN_EXP: i32 = -125;
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/// Maximum possible power of 2 exponent.
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const MAX_EXP: i32 = 128;
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/// Minimum possible normal power of 10 exponent.
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const MIN_10_EXP: i32 = -37;
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/// Maximum possible power of 10 exponent.
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const MAX_10_EXP: i32 = 38;
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/// Not a Number (NaN).
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const NAN: f32 = 0.0_f32 / 0.0_f32;
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/// Infinity (∞).
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const INFINITY: f32 = 1.0_f32 / 0.0_f32;
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/// Negative infinity (−∞).
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const NEG_INFINITY: f32 = -1.0_f32 / 0.0_f32;
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/// Basic mathematical constants.
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#[stable(feature = "rust1", since = "1.0.0")]
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pub mod consts {
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// FIXME: replace with mathematical constants from cmath.
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/// Archimedes' constant (π)
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const PI: f32 = 3.14159265358979323846264338327950288_f32;
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/// The full circle constant (τ)
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///
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/// Equal to 2π.
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#[unstable(feature = "tau_constant", issue = "66770")]
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pub const TAU: f32 = 6.28318530717958647692528676655900577_f32;
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/// π/2
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const FRAC_PI_2: f32 = 1.57079632679489661923132169163975144_f32;
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/// π/3
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const FRAC_PI_3: f32 = 1.04719755119659774615421446109316763_f32;
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/// π/4
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const FRAC_PI_4: f32 = 0.785398163397448309615660845819875721_f32;
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/// π/6
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const FRAC_PI_6: f32 = 0.52359877559829887307710723054658381_f32;
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/// π/8
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const FRAC_PI_8: f32 = 0.39269908169872415480783042290993786_f32;
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/// 1/π
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const FRAC_1_PI: f32 = 0.318309886183790671537767526745028724_f32;
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/// 2/π
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const FRAC_2_PI: f32 = 0.636619772367581343075535053490057448_f32;
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/// 2/sqrt(π)
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const FRAC_2_SQRT_PI: f32 = 1.12837916709551257389615890312154517_f32;
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/// sqrt(2)
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const SQRT_2: f32 = 1.41421356237309504880168872420969808_f32;
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/// 1/sqrt(2)
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const FRAC_1_SQRT_2: f32 = 0.707106781186547524400844362104849039_f32;
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/// Euler's number (e)
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const E: f32 = 2.71828182845904523536028747135266250_f32;
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/// log<sub>2</sub>(e)
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const LOG2_E: f32 = 1.44269504088896340735992468100189214_f32;
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/// log<sub>2</sub>(10)
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#[unstable(feature = "extra_log_consts", issue = "50540")]
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pub const LOG2_10: f32 = 3.32192809488736234787031942948939018_f32;
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/// log<sub>10</sub>(e)
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const LOG10_E: f32 = 0.434294481903251827651128918916605082_f32;
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/// log<sub>10</sub>(2)
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#[unstable(feature = "extra_log_consts", issue = "50540")]
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pub const LOG10_2: f32 = 0.301029995663981195213738894724493027_f32;
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/// ln(2)
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const LN_2: f32 = 0.693147180559945309417232121458176568_f32;
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/// ln(10)
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const LN_10: f32 = 2.30258509299404568401799145468436421_f32;
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}
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#[lang = "f32"]
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#[cfg(not(test))]
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impl f32 {
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/// Returns `true` if this value is `NaN`.
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///
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/// ```
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/// use std::f32;
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///
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/// let nan = f32::NAN;
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/// let f = 7.0_f32;
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///
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/// assert!(nan.is_nan());
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/// assert!(!f.is_nan());
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn is_nan(self) -> bool {
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self != self
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}
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// FIXME(#50145): `abs` is publicly unavailable in libcore due to
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// concerns about portability, so this implementation is for
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// private use internally.
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#[inline]
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fn abs_private(self) -> f32 {
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f32::from_bits(self.to_bits() & 0x7fff_ffff)
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}
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/// Returns `true` if this value is positive infinity or negative infinity, and
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/// `false` otherwise.
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///
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/// ```
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/// use std::f32;
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///
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/// let f = 7.0f32;
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/// let inf = f32::INFINITY;
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/// let neg_inf = f32::NEG_INFINITY;
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/// let nan = f32::NAN;
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///
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/// assert!(!f.is_infinite());
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/// assert!(!nan.is_infinite());
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///
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/// assert!(inf.is_infinite());
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/// assert!(neg_inf.is_infinite());
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn is_infinite(self) -> bool {
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self.abs_private() == INFINITY
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}
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/// Returns `true` if this number is neither infinite nor `NaN`.
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///
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/// ```
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/// use std::f32;
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///
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/// let f = 7.0f32;
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/// let inf = f32::INFINITY;
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/// let neg_inf = f32::NEG_INFINITY;
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/// let nan = f32::NAN;
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///
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/// assert!(f.is_finite());
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///
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/// assert!(!nan.is_finite());
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/// assert!(!inf.is_finite());
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/// assert!(!neg_inf.is_finite());
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn is_finite(self) -> bool {
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// There's no need to handle NaN separately: if self is NaN,
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// the comparison is not true, exactly as desired.
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self.abs_private() < INFINITY
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}
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/// Returns `true` if the number is neither zero, infinite,
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/// [subnormal], or `NaN`.
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///
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/// ```
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/// use std::f32;
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///
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/// let min = f32::MIN_POSITIVE; // 1.17549435e-38f32
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/// let max = f32::MAX;
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/// let lower_than_min = 1.0e-40_f32;
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/// let zero = 0.0_f32;
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///
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/// assert!(min.is_normal());
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/// assert!(max.is_normal());
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///
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/// assert!(!zero.is_normal());
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/// assert!(!f32::NAN.is_normal());
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/// assert!(!f32::INFINITY.is_normal());
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/// // Values between `0` and `min` are Subnormal.
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/// assert!(!lower_than_min.is_normal());
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/// ```
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/// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn is_normal(self) -> bool {
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self.classify() == FpCategory::Normal
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}
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/// Returns the floating point category of the number. If only one property
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/// is going to be tested, it is generally faster to use the specific
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/// predicate instead.
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///
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/// ```
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/// use std::num::FpCategory;
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/// use std::f32;
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///
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/// let num = 12.4_f32;
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/// let inf = f32::INFINITY;
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///
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/// assert_eq!(num.classify(), FpCategory::Normal);
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/// assert_eq!(inf.classify(), FpCategory::Infinite);
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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pub fn classify(self) -> FpCategory {
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const EXP_MASK: u32 = 0x7f800000;
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const MAN_MASK: u32 = 0x007fffff;
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let bits = self.to_bits();
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match (bits & MAN_MASK, bits & EXP_MASK) {
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(0, 0) => FpCategory::Zero,
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(_, 0) => FpCategory::Subnormal,
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(0, EXP_MASK) => FpCategory::Infinite,
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(_, EXP_MASK) => FpCategory::Nan,
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_ => FpCategory::Normal,
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}
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}
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/// Returns `true` if `self` has a positive sign, including `+0.0`, `NaN`s with
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/// positive sign bit and positive infinity.
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///
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/// ```
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/// let f = 7.0_f32;
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/// let g = -7.0_f32;
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///
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/// assert!(f.is_sign_positive());
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/// assert!(!g.is_sign_positive());
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn is_sign_positive(self) -> bool {
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!self.is_sign_negative()
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}
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/// Returns `true` if `self` has a negative sign, including `-0.0`, `NaN`s with
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/// negative sign bit and negative infinity.
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///
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/// ```
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/// let f = 7.0f32;
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/// let g = -7.0f32;
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///
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/// assert!(!f.is_sign_negative());
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/// assert!(g.is_sign_negative());
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn is_sign_negative(self) -> bool {
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// IEEE754 says: isSignMinus(x) is true if and only if x has negative sign. isSignMinus
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// applies to zeros and NaNs as well.
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self.to_bits() & 0x8000_0000 != 0
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}
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/// Takes the reciprocal (inverse) of a number, `1/x`.
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///
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/// ```
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/// use std::f32;
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///
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/// let x = 2.0_f32;
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/// let abs_difference = (x.recip() - (1.0 / x)).abs();
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///
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/// assert!(abs_difference <= f32::EPSILON);
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn recip(self) -> f32 {
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1.0 / self
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}
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/// Converts radians to degrees.
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///
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/// ```
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/// use std::f32::{self, consts};
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///
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/// let angle = consts::PI;
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///
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/// let abs_difference = (angle.to_degrees() - 180.0).abs();
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///
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/// assert!(abs_difference <= f32::EPSILON);
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/// ```
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#[stable(feature = "f32_deg_rad_conversions", since = "1.7.0")]
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#[inline]
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pub fn to_degrees(self) -> f32 {
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// Use a constant for better precision.
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const PIS_IN_180: f32 = 57.2957795130823208767981548141051703_f32;
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self * PIS_IN_180
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}
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/// Converts degrees to radians.
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///
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/// ```
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/// use std::f32::{self, consts};
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///
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/// let angle = 180.0f32;
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///
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/// let abs_difference = (angle.to_radians() - consts::PI).abs();
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///
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/// assert!(abs_difference <= f32::EPSILON);
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/// ```
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#[stable(feature = "f32_deg_rad_conversions", since = "1.7.0")]
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#[inline]
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pub fn to_radians(self) -> f32 {
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let value: f32 = consts::PI;
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self * (value / 180.0f32)
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}
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/// Returns the maximum of the two numbers.
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///
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/// ```
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/// let x = 1.0f32;
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/// let y = 2.0f32;
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///
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/// assert_eq!(x.max(y), y);
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/// ```
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///
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/// If one of the arguments is NaN, then the other argument is returned.
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn max(self, other: f32) -> f32 {
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intrinsics::maxnumf32(self, other)
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}
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/// Returns the minimum of the two numbers.
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///
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/// ```
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/// let x = 1.0f32;
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/// let y = 2.0f32;
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///
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/// assert_eq!(x.min(y), x);
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/// ```
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///
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/// If one of the arguments is NaN, then the other argument is returned.
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn min(self, other: f32) -> f32 {
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intrinsics::minnumf32(self, other)
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}
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/// Rounds toward zero and converts to any primitive integer type,
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/// assuming that the value is finite and fits in that type.
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///
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/// ```
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/// #![feature(float_approx_unchecked_to)]
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///
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/// let value = 4.6_f32;
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/// let rounded = unsafe { value.approx_unchecked_to::<u16>() };
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/// assert_eq!(rounded, 4);
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///
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/// let value = -128.9_f32;
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/// let rounded = unsafe { value.approx_unchecked_to::<i8>() };
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/// assert_eq!(rounded, std::i8::MIN);
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/// ```
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///
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/// # Safety
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///
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/// The value must:
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///
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/// * Not be `NaN`
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/// * Not be infinite
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/// * Be representable in the return type `Int`, after truncating off its fractional part
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#[unstable(feature = "float_approx_unchecked_to", issue = "67058")]
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#[inline]
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pub unsafe fn approx_unchecked_to<Int>(self) -> Int
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where
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Self: FloatToInt<Int>,
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{
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FloatToInt::<Int>::approx_unchecked(self)
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}
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/// Raw transmutation to `u32`.
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///
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/// This is currently identical to `transmute::<f32, u32>(self)` on all platforms.
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///
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/// See `from_bits` for some discussion of the portability of this operation
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/// (there are almost no issues).
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///
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/// Note that this function is distinct from `as` casting, which attempts to
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/// preserve the *numeric* value, and not the bitwise value.
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///
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/// # Examples
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///
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/// ```
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/// assert_ne!((1f32).to_bits(), 1f32 as u32); // to_bits() is not casting!
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/// assert_eq!((12.5f32).to_bits(), 0x41480000);
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///
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/// ```
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#[stable(feature = "float_bits_conv", since = "1.20.0")]
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#[inline]
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pub fn to_bits(self) -> u32 {
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// SAFETY: `u32` is a plain old datatype so we can always transmute to it
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|
unsafe { mem::transmute(self) }
|
|
}
|
|
|
|
/// Raw transmutation from `u32`.
|
|
///
|
|
/// This is currently identical to `transmute::<u32, f32>(v)` on all platforms.
|
|
/// It turns out this is incredibly portable, for two reasons:
|
|
///
|
|
/// * Floats and Ints have the same endianness on all supported platforms.
|
|
/// * IEEE-754 very precisely specifies the bit layout of floats.
|
|
///
|
|
/// However there is one caveat: prior to the 2008 version of IEEE-754, how
|
|
/// to interpret the NaN signaling bit wasn't actually specified. Most platforms
|
|
/// (notably x86 and ARM) picked the interpretation that was ultimately
|
|
/// standardized in 2008, but some didn't (notably MIPS). As a result, all
|
|
/// signaling NaNs on MIPS are quiet NaNs on x86, and vice-versa.
|
|
///
|
|
/// Rather than trying to preserve signaling-ness cross-platform, this
|
|
/// implementation favors preserving the exact bits. This means that
|
|
/// any payloads encoded in NaNs will be preserved even if the result of
|
|
/// this method is sent over the network from an x86 machine to a MIPS one.
|
|
///
|
|
/// If the results of this method are only manipulated by the same
|
|
/// architecture that produced them, then there is no portability concern.
|
|
///
|
|
/// If the input isn't NaN, then there is no portability concern.
|
|
///
|
|
/// If you don't care about signalingness (very likely), then there is no
|
|
/// portability concern.
|
|
///
|
|
/// Note that this function is distinct from `as` casting, which attempts to
|
|
/// preserve the *numeric* value, and not the bitwise value.
|
|
///
|
|
/// # Examples
|
|
///
|
|
/// ```
|
|
/// let v = f32::from_bits(0x41480000);
|
|
/// assert_eq!(v, 12.5);
|
|
/// ```
|
|
#[stable(feature = "float_bits_conv", since = "1.20.0")]
|
|
#[inline]
|
|
pub fn from_bits(v: u32) -> Self {
|
|
// SAFETY: `u32` 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 = 12.5f32.to_be_bytes();
|
|
/// assert_eq!(bytes, [0x41, 0x48, 0x00, 0x00]);
|
|
/// ```
|
|
#[stable(feature = "float_to_from_bytes", since = "1.40.0")]
|
|
#[inline]
|
|
pub fn to_be_bytes(self) -> [u8; 4] {
|
|
self.to_bits().to_be_bytes()
|
|
}
|
|
|
|
/// Return the memory representation of this floating point number as a byte array in
|
|
/// little-endian byte order.
|
|
///
|
|
/// # Examples
|
|
///
|
|
/// ```
|
|
/// let bytes = 12.5f32.to_le_bytes();
|
|
/// assert_eq!(bytes, [0x00, 0x00, 0x48, 0x41]);
|
|
/// ```
|
|
#[stable(feature = "float_to_from_bytes", since = "1.40.0")]
|
|
#[inline]
|
|
pub fn to_le_bytes(self) -> [u8; 4] {
|
|
self.to_bits().to_le_bytes()
|
|
}
|
|
|
|
/// Return the memory representation of this floating point number as a byte array in
|
|
/// native byte order.
|
|
///
|
|
/// As the target platform's native endianness is used, portable code
|
|
/// should use [`to_be_bytes`] or [`to_le_bytes`], as appropriate, instead.
|
|
///
|
|
/// [`to_be_bytes`]: #method.to_be_bytes
|
|
/// [`to_le_bytes`]: #method.to_le_bytes
|
|
///
|
|
/// # Examples
|
|
///
|
|
/// ```
|
|
/// let bytes = 12.5f32.to_ne_bytes();
|
|
/// assert_eq!(
|
|
/// bytes,
|
|
/// if cfg!(target_endian = "big") {
|
|
/// [0x41, 0x48, 0x00, 0x00]
|
|
/// } else {
|
|
/// [0x00, 0x00, 0x48, 0x41]
|
|
/// }
|
|
/// );
|
|
/// ```
|
|
#[stable(feature = "float_to_from_bytes", since = "1.40.0")]
|
|
#[inline]
|
|
pub fn to_ne_bytes(self) -> [u8; 4] {
|
|
self.to_bits().to_ne_bytes()
|
|
}
|
|
|
|
/// Create a floating point value from its representation as a byte array in big endian.
|
|
///
|
|
/// # Examples
|
|
///
|
|
/// ```
|
|
/// let value = f32::from_be_bytes([0x41, 0x48, 0x00, 0x00]);
|
|
/// assert_eq!(value, 12.5);
|
|
/// ```
|
|
#[stable(feature = "float_to_from_bytes", since = "1.40.0")]
|
|
#[inline]
|
|
pub fn from_be_bytes(bytes: [u8; 4]) -> Self {
|
|
Self::from_bits(u32::from_be_bytes(bytes))
|
|
}
|
|
|
|
/// Create a floating point value from its representation as a byte array in little endian.
|
|
///
|
|
/// # Examples
|
|
///
|
|
/// ```
|
|
/// let value = f32::from_le_bytes([0x00, 0x00, 0x48, 0x41]);
|
|
/// assert_eq!(value, 12.5);
|
|
/// ```
|
|
#[stable(feature = "float_to_from_bytes", since = "1.40.0")]
|
|
#[inline]
|
|
pub fn from_le_bytes(bytes: [u8; 4]) -> Self {
|
|
Self::from_bits(u32::from_le_bytes(bytes))
|
|
}
|
|
|
|
/// Create a floating point value from its representation as a byte array in native endian.
|
|
///
|
|
/// As the target platform's native endianness is used, portable code
|
|
/// likely wants to use [`from_be_bytes`] or [`from_le_bytes`], as
|
|
/// appropriate instead.
|
|
///
|
|
/// [`from_be_bytes`]: #method.from_be_bytes
|
|
/// [`from_le_bytes`]: #method.from_le_bytes
|
|
///
|
|
/// # Examples
|
|
///
|
|
/// ```
|
|
/// let value = f32::from_ne_bytes(if cfg!(target_endian = "big") {
|
|
/// [0x41, 0x48, 0x00, 0x00]
|
|
/// } else {
|
|
/// [0x00, 0x00, 0x48, 0x41]
|
|
/// });
|
|
/// assert_eq!(value, 12.5);
|
|
/// ```
|
|
#[stable(feature = "float_to_from_bytes", since = "1.40.0")]
|
|
#[inline]
|
|
pub fn from_ne_bytes(bytes: [u8; 4]) -> Self {
|
|
Self::from_bits(u32::from_ne_bytes(bytes))
|
|
}
|
|
}
|