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//! This module provides constants which are specific to the implementation //! of the `f32` floating point data type. //! //! *[See also the `f32` primitive type](../../std/primitive.f32.html).* //! //! Mathematically significant numbers are provided in the `consts` sub-module. #![stable(feature = "rust1", since = "1.0.0")] use crate::mem; use crate::num::FpCategory; /// The radix or base of the internal representation of `f32`. #[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 = 24; /// Approximate number of significant digits in base 10. #[stable(feature = "rust1", since = "1.0.0")] pub const DIGITS: u32 = 6; /// [Machine epsilon] value for `f32`. /// /// 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: f32 = 1.19209290e-07_f32; /// Smallest finite `f32` value. #[stable(feature = "rust1", since = "1.0.0")] pub const MIN: f32 = -3.40282347e+38_f32; /// Smallest positive normal `f32` value. #[stable(feature = "rust1", since = "1.0.0")] pub const MIN_POSITIVE: f32 = 1.17549435e-38_f32; /// Largest finite `f32` value. #[stable(feature = "rust1", since = "1.0.0")] pub const MAX: f32 = 3.40282347e+38_f32; /// One greater than the minimum possible normal power of 2 exponent. #[stable(feature = "rust1", since = "1.0.0")] pub const MIN_EXP: i32 = -125; /// Maximum possible power of 2 exponent. #[stable(feature = "rust1", since = "1.0.0")] pub const MAX_EXP: i32 = 128; /// Minimum possible normal power of 10 exponent. #[stable(feature = "rust1", since = "1.0.0")] pub const MIN_10_EXP: i32 = -37; /// Maximum possible power of 10 exponent. #[stable(feature = "rust1", since = "1.0.0")] pub const MAX_10_EXP: i32 = 38; /// Not a Number (NaN). #[stable(feature = "rust1", since = "1.0.0")] pub const NAN: f32 = 0.0_f32 / 0.0_f32; /// Infinity (∞). #[stable(feature = "rust1", since = "1.0.0")] pub const INFINITY: f32 = 1.0_f32 / 0.0_f32; /// Negative infinity (-∞). #[stable(feature = "rust1", since = "1.0.0")] pub const NEG_INFINITY: f32 = -1.0_f32 / 0.0_f32; /// 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: f32 = 3.14159265358979323846264338327950288_f32; /// π/2 #[stable(feature = "rust1", since = "1.0.0")] pub const FRAC_PI_2: f32 = 1.57079632679489661923132169163975144_f32; /// π/3 #[stable(feature = "rust1", since = "1.0.0")] pub const FRAC_PI_3: f32 = 1.04719755119659774615421446109316763_f32; /// π/4 #[stable(feature = "rust1", since = "1.0.0")] pub const FRAC_PI_4: f32 = 0.785398163397448309615660845819875721_f32; /// π/6 #[stable(feature = "rust1", since = "1.0.0")] pub const FRAC_PI_6: f32 = 0.52359877559829887307710723054658381_f32; /// π/8 #[stable(feature = "rust1", since = "1.0.0")] pub const FRAC_PI_8: f32 = 0.39269908169872415480783042290993786_f32; /// 1/π #[stable(feature = "rust1", since = "1.0.0")] pub const FRAC_1_PI: f32 = 0.318309886183790671537767526745028724_f32; /// 2/π #[stable(feature = "rust1", since = "1.0.0")] pub const FRAC_2_PI: f32 = 0.636619772367581343075535053490057448_f32; /// 2/sqrt(π) #[stable(feature = "rust1", since = "1.0.0")] pub const FRAC_2_SQRT_PI: f32 = 1.12837916709551257389615890312154517_f32; /// sqrt(2) #[stable(feature = "rust1", since = "1.0.0")] pub const SQRT_2: f32 = 1.41421356237309504880168872420969808_f32; /// 1/sqrt(2) #[stable(feature = "rust1", since = "1.0.0")] pub const FRAC_1_SQRT_2: f32 = 0.707106781186547524400844362104849039_f32; /// Euler's number (e) #[stable(feature = "rust1", since = "1.0.0")] pub const E: f32 = 2.71828182845904523536028747135266250_f32; /// log<sub>2</sub>(e) #[stable(feature = "rust1", since = "1.0.0")] pub const LOG2_E: f32 = 1.44269504088896340735992468100189214_f32; /// log<sub>2</sub>(10) #[unstable(feature = "extra_log_consts", issue = "50540")] pub const LOG2_10: f32 = 3.32192809488736234787031942948939018_f32; /// log<sub>10</sub>(e) #[stable(feature = "rust1", since = "1.0.0")] pub const LOG10_E: f32 = 0.434294481903251827651128918916605082_f32; /// log<sub>10</sub>(2) #[unstable(feature = "extra_log_consts", issue = "50540")] pub const LOG10_2: f32 = 0.301029995663981195213738894724493027_f32; /// ln(2) #[stable(feature = "rust1", since = "1.0.0")] pub const LN_2: f32 = 0.693147180559945309417232121458176568_f32; /// ln(10) #[stable(feature = "rust1", since = "1.0.0")] pub const LN_10: f32 = 2.30258509299404568401799145468436421_f32; } #[lang = "f32"] #[cfg(not(test))] impl f32 { /// Returns `true` if this value is `NaN`. /// /// ``` /// use std::f32; /// /// let nan = f32::NAN; /// let f = 7.0_f32; /// /// 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) -> f32 { f32::from_bits(self.to_bits() & 0x7fff_ffff) } /// Returns `true` if this value is positive infinity or negative infinity, and /// `false` otherwise. /// /// ``` /// use std::f32; /// /// let f = 7.0f32; /// let inf = f32::INFINITY; /// let neg_inf = f32::NEG_INFINITY; /// let nan = f32::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::f32; /// /// let f = 7.0f32; /// let inf = f32::INFINITY; /// let neg_inf = f32::NEG_INFINITY; /// let nan = f32::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::f32; /// /// let min = f32::MIN_POSITIVE; // 1.17549435e-38f32 /// let max = f32::MAX; /// let lower_than_min = 1.0e-40_f32; /// let zero = 0.0_f32; /// /// assert!(min.is_normal()); /// assert!(max.is_normal()); /// /// assert!(!zero.is_normal()); /// assert!(!f32::NAN.is_normal()); /// assert!(!f32::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::f32; /// /// let num = 12.4_f32; /// let inf = f32::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: u32 = 0x7f800000; const MAN_MASK: u32 = 0x007fffff; 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_f32; /// let g = -7.0_f32; /// /// 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() } /// Returns `true` if `self` has a negative sign, including `-0.0`, `NaN`s with /// negative sign bit and negative infinity. /// /// ``` /// let f = 7.0f32; /// let g = -7.0f32; /// /// 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 { // IEEE754 says: isSignMinus(x) is true if and only if x has negative sign. isSignMinus // applies to zeros and NaNs as well. self.to_bits() & 0x8000_0000 != 0 } /// Takes the reciprocal (inverse) of a number, `1/x`. /// /// ``` /// use std::f32; /// /// let x = 2.0_f32; /// let abs_difference = (x.recip() - (1.0/x)).abs(); /// /// assert!(abs_difference <= f32::EPSILON); /// ``` #[stable(feature = "rust1", since = "1.0.0")] #[inline] pub fn recip(self) -> f32 { 1.0 / self } /// Converts radians to degrees. /// /// ``` /// use std::f32::{self, consts}; /// /// let angle = consts::PI; /// /// let abs_difference = (angle.to_degrees() - 180.0).abs(); /// /// assert!(abs_difference <= f32::EPSILON); /// ``` #[stable(feature = "f32_deg_rad_conversions", since="1.7.0")] #[inline] pub fn to_degrees(self) -> f32 { // Use a constant for better precision. const PIS_IN_180: f32 = 57.2957795130823208767981548141051703_f32; self * PIS_IN_180 } /// Converts degrees to radians. /// /// ``` /// use std::f32::{self, consts}; /// /// let angle = 180.0f32; /// /// let abs_difference = (angle.to_radians() - consts::PI).abs(); /// /// assert!(abs_difference <= f32::EPSILON); /// ``` #[stable(feature = "f32_deg_rad_conversions", since="1.7.0")] #[inline] pub fn to_radians(self) -> f32 { let value: f32 = consts::PI; self * (value / 180.0f32) } /// Returns the maximum of the two numbers. /// /// ``` /// let x = 1.0f32; /// let y = 2.0f32; /// /// 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: f32) -> f32 { // IEEE754 says: maxNum(x, y) is the canonicalized number y if x < y, x if y < x, the // canonicalized number if one operand is a number and the other a quiet NaN. Otherwise it // is either x or y, canonicalized (this means results might differ among implementations). // When either x or y is a signalingNaN, then the result is according to 6.2. // // Since we do not support sNaN in Rust yet, we do not need to handle them. // FIXME(nagisa): due to https://bugs.llvm.org/show_bug.cgi?id=33303 we canonicalize by // multiplying by 1.0. Should switch to the `canonicalize` when it works. (if self.is_nan() || self < other { other } else { self }) * 1.0 } /// Returns the minimum of the two numbers. /// /// ``` /// let x = 1.0f32; /// let y = 2.0f32; /// /// 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: f32) -> f32 { // IEEE754 says: minNum(x, y) is the canonicalized number x if x < y, y if y < x, the // canonicalized number if one operand is a number and the other a quiet NaN. Otherwise it // is either x or y, canonicalized (this means results might differ among implementations). // When either x or y is a signalingNaN, then the result is according to 6.2. // // Since we do not support sNaN in Rust yet, we do not need to handle them. // FIXME(nagisa): due to https://bugs.llvm.org/show_bug.cgi?id=33303 we canonicalize by // multiplying by 1.0. Should switch to the `canonicalize` when it works. (if other.is_nan() || self < other { self } else { other }) * 1.0 } /// Raw transmutation to `u32`. /// /// This is currently identical to `transmute::<f32, u32>(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_ne!((1f32).to_bits(), 1f32 as u32); // to_bits() is not casting! /// assert_eq!((12.5f32).to_bits(), 0x41480000); /// /// ``` #[stable(feature = "float_bits_conv", since = "1.20.0")] #[inline] pub fn to_bits(self) -> u32 { 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 /// /// ``` /// use std::f32; /// let v = f32::from_bits(0x41480000); /// 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: u32) -> Self { // It turns out the safety issues with sNaN were overblown! Hooray! unsafe { mem::transmute(v) } } }