// Copyright 2012-2014 The Rust Project Developers. See the COPYRIGHT // file at the top-level directory of this distribution and at // http://rust-lang.org/COPYRIGHT. // // Licensed under the Apache License, Version 2.0 or the MIT license // , at your // option. This file may not be copied, modified, or distributed // except according to those terms. //! Operations and constants for 64-bits floats (`f64` type) // FIXME: MIN_VALUE and MAX_VALUE literals are parsed as -inf and inf #14353 #![allow(overflowing_literals)] #![stable(feature = "rust1", since = "1.0.0")] use intrinsics; use mem; use num::FpCategory as Fp; use num::Float; #[stable(feature = "rust1", since = "1.0.0")] #[allow(missing_docs)] pub const RADIX: u32 = 2; #[stable(feature = "rust1", since = "1.0.0")] #[allow(missing_docs)] pub const MANTISSA_DIGITS: u32 = 53; #[stable(feature = "rust1", since = "1.0.0")] #[allow(missing_docs)] pub const DIGITS: u32 = 15; #[stable(feature = "rust1", since = "1.0.0")] #[allow(missing_docs)] 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, normalized 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; #[stable(feature = "rust1", since = "1.0.0")] #[allow(missing_docs)] pub const MIN_EXP: i32 = -1021; #[stable(feature = "rust1", since = "1.0.0")] #[allow(missing_docs)] pub const MAX_EXP: i32 = 1024; #[stable(feature = "rust1", since = "1.0.0")] #[allow(missing_docs)] pub const MIN_10_EXP: i32 = -307; #[stable(feature = "rust1", since = "1.0.0")] #[allow(missing_docs)] pub const MAX_10_EXP: i32 = 308; #[stable(feature = "rust1", since = "1.0.0")] #[allow(missing_docs)] pub const NAN: f64 = 0.0_f64/0.0_f64; #[stable(feature = "rust1", since = "1.0.0")] #[allow(missing_docs)] pub const INFINITY: f64 = 1.0_f64/0.0_f64; #[stable(feature = "rust1", since = "1.0.0")] #[allow(missing_docs)] 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 #[stable(feature = "rust1", since = "1.0.0")] pub const PI: f64 = 3.14159265358979323846264338327950288_f64; /// pi/2.0 #[stable(feature = "rust1", since = "1.0.0")] pub const FRAC_PI_2: f64 = 1.57079632679489661923132169163975144_f64; /// pi/3.0 #[stable(feature = "rust1", since = "1.0.0")] pub const FRAC_PI_3: f64 = 1.04719755119659774615421446109316763_f64; /// pi/4.0 #[stable(feature = "rust1", since = "1.0.0")] pub const FRAC_PI_4: f64 = 0.785398163397448309615660845819875721_f64; /// pi/6.0 #[stable(feature = "rust1", since = "1.0.0")] pub const FRAC_PI_6: f64 = 0.52359877559829887307710723054658381_f64; /// pi/8.0 #[stable(feature = "rust1", since = "1.0.0")] pub const FRAC_PI_8: f64 = 0.39269908169872415480783042290993786_f64; /// 1.0/pi #[stable(feature = "rust1", since = "1.0.0")] pub const FRAC_1_PI: f64 = 0.318309886183790671537767526745028724_f64; /// 2.0/pi #[stable(feature = "rust1", since = "1.0.0")] pub const FRAC_2_PI: f64 = 0.636619772367581343075535053490057448_f64; /// 2.0/sqrt(pi) #[stable(feature = "rust1", since = "1.0.0")] pub const FRAC_2_SQRT_PI: f64 = 1.12837916709551257389615890312154517_f64; /// sqrt(2.0) #[stable(feature = "rust1", since = "1.0.0")] pub const SQRT_2: f64 = 1.41421356237309504880168872420969808_f64; /// 1.0/sqrt(2.0) #[stable(feature = "rust1", since = "1.0.0")] pub const FRAC_1_SQRT_2: f64 = 0.707106781186547524400844362104849039_f64; /// Euler's number #[stable(feature = "rust1", since = "1.0.0")] pub const E: f64 = 2.71828182845904523536028747135266250_f64; /// log2(e) #[stable(feature = "rust1", since = "1.0.0")] pub const LOG2_E: f64 = 1.44269504088896340735992468100189214_f64; /// log10(e) #[stable(feature = "rust1", since = "1.0.0")] pub const LOG10_E: f64 = 0.434294481903251827651128918916605082_f64; /// ln(2.0) #[stable(feature = "rust1", since = "1.0.0")] pub const LN_2: f64 = 0.693147180559945309417232121458176568_f64; /// ln(10.0) #[stable(feature = "rust1", since = "1.0.0")] pub const LN_10: f64 = 2.30258509299404568401799145468436421_f64; } #[unstable(feature = "core_float", reason = "stable interface is via `impl f{32,64}` in later crates", issue = "32110")] impl Float for f64 { #[inline] fn nan() -> f64 { NAN } #[inline] fn infinity() -> f64 { INFINITY } #[inline] fn neg_infinity() -> f64 { NEG_INFINITY } #[inline] fn zero() -> f64 { 0.0 } #[inline] fn neg_zero() -> f64 { -0.0 } #[inline] fn one() -> f64 { 1.0 } /// Returns `true` if the number is NaN. #[inline] fn is_nan(self) -> bool { self != self } /// Returns `true` if the number is infinite. #[inline] fn is_infinite(self) -> bool { self == Float::infinity() || self == Float::neg_infinity() } /// Returns `true` if the number is neither infinite or NaN. #[inline] fn is_finite(self) -> bool { !(self.is_nan() || self.is_infinite()) } /// Returns `true` if the number is neither zero, infinite, subnormal or NaN. #[inline] fn is_normal(self) -> bool { self.classify() == Fp::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. fn classify(self) -> Fp { const EXP_MASK: u64 = 0x7ff0000000000000; const MAN_MASK: u64 = 0x000fffffffffffff; let bits: u64 = unsafe { mem::transmute(self) }; match (bits & MAN_MASK, bits & EXP_MASK) { (0, 0) => Fp::Zero, (_, 0) => Fp::Subnormal, (0, EXP_MASK) => Fp::Infinite, (_, EXP_MASK) => Fp::Nan, _ => Fp::Normal, } } /// Returns the mantissa, exponent and sign as integers. fn integer_decode(self) -> (u64, i16, i8) { let bits: u64 = unsafe { mem::transmute(self) }; let sign: i8 = if bits >> 63 == 0 { 1 } else { -1 }; let mut exponent: i16 = ((bits >> 52) & 0x7ff) as i16; let mantissa = if exponent == 0 { (bits & 0xfffffffffffff) << 1 } else { (bits & 0xfffffffffffff) | 0x10000000000000 }; // Exponent bias + mantissa shift exponent -= 1023 + 52; (mantissa, exponent, sign) } /// Computes the absolute value of `self`. Returns `Float::nan()` if the /// number is `Float::nan()`. #[inline] fn abs(self) -> f64 { unsafe { intrinsics::fabsf64(self) } } /// Returns a number that represents the sign of `self`. /// /// - `1.0` if the number is positive, `+0.0` or `Float::infinity()` /// - `-1.0` if the number is negative, `-0.0` or `Float::neg_infinity()` /// - `Float::nan()` if the number is `Float::nan()` #[inline] fn signum(self) -> f64 { if self.is_nan() { Float::nan() } else { unsafe { intrinsics::copysignf64(1.0, self) } } } /// Returns `true` if `self` is positive, including `+0.0` and /// `Float::infinity()`. #[inline] fn is_sign_positive(self) -> bool { self > 0.0 || (1.0 / self) == Float::infinity() } /// Returns `true` if `self` is negative, including `-0.0` and /// `Float::neg_infinity()`. #[inline] fn is_sign_negative(self) -> bool { self < 0.0 || (1.0 / self) == Float::neg_infinity() } /// Returns the reciprocal (multiplicative inverse) of the number. #[inline] fn recip(self) -> f64 { 1.0 / self } #[inline] fn powi(self, n: i32) -> f64 { unsafe { intrinsics::powif64(self, n) } } /// Converts to degrees, assuming the number is in radians. #[inline] fn to_degrees(self) -> f64 { self * (180.0f64 / consts::PI) } /// Converts to radians, assuming the number is in degrees. #[inline] fn to_radians(self) -> f64 { let value: f64 = consts::PI; self * (value / 180.0) } }