| // 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 <LICENSE-APACHE or |
| // http://www.apache.org/licenses/LICENSE-2.0> or the MIT license |
| // <LICENSE-MIT or http://opensource.org/licenses/MIT>, 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; |
| |
| /// 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; |
| |
| /// Difference between `1.0` and the next largest representable number. |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub const EPSILON: f64 = 2.2204460492503131e-16_f64; |
| |
| /// Smallest finite `f64` value. |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub const MIN: f64 = -1.7976931348623157e+308_f64; |
| /// Smallest positive normal `f64` value. |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub const MIN_POSITIVE: f64 = 2.2250738585072014e-308_f64; |
| /// Largest finite `f64` value. |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub const MAX: f64 = 1.7976931348623157e+308_f64; |
| |
| /// One greater than the minimum possible normal power of 2 exponent. |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub const MIN_EXP: i32 = -1021; |
| /// Maximum possible power of 2 exponent. |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub const MAX_EXP: i32 = 1024; |
| |
| /// Minimum possible normal power of 10 exponent. |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub const MIN_10_EXP: i32 = -307; |
| /// Maximum possible power of 10 exponent. |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub const MAX_10_EXP: i32 = 308; |
| |
| /// Not a Number (NaN). |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub const NAN: f64 = 0.0_f64/0.0_f64; |
| /// Infinity (∞). |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub const INFINITY: f64 = 1.0_f64/0.0_f64; |
| /// Negative infinity (-∞). |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub const NEG_INFINITY: f64 = -1.0_f64/0.0_f64; |
| |
| /// Basic mathematical constants. |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub mod consts { |
| // FIXME: replace with mathematical constants from cmath. |
| |
| /// Archimedes' constant (π) |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub const PI: f64 = 3.14159265358979323846264338327950288_f64; |
| |
| /// π/2 |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub const FRAC_PI_2: f64 = 1.57079632679489661923132169163975144_f64; |
| |
| /// π/3 |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub const FRAC_PI_3: f64 = 1.04719755119659774615421446109316763_f64; |
| |
| /// π/4 |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub const FRAC_PI_4: f64 = 0.785398163397448309615660845819875721_f64; |
| |
| /// π/6 |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub const FRAC_PI_6: f64 = 0.52359877559829887307710723054658381_f64; |
| |
| /// π/8 |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub const FRAC_PI_8: f64 = 0.39269908169872415480783042290993786_f64; |
| |
| /// 1/π |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub const FRAC_1_PI: f64 = 0.318309886183790671537767526745028724_f64; |
| |
| /// 2/π |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub const FRAC_2_PI: f64 = 0.636619772367581343075535053490057448_f64; |
| |
| /// 2/sqrt(π) |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub const FRAC_2_SQRT_PI: f64 = 1.12837916709551257389615890312154517_f64; |
| |
| /// sqrt(2) |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub const SQRT_2: f64 = 1.41421356237309504880168872420969808_f64; |
| |
| /// 1/sqrt(2) |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub const FRAC_1_SQRT_2: f64 = 0.707106781186547524400844362104849039_f64; |
| |
| /// Euler's number (e) |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub const E: f64 = 2.71828182845904523536028747135266250_f64; |
| |
| /// log<sub>2</sub>(e) |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub const LOG2_E: f64 = 1.44269504088896340735992468100189214_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; |
| } |
| |
| #[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 == INFINITY || self == 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() { |
| 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) == 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) == 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) |
| } |
| } |