src/libcore/num/f64.rs

   1 // Copyright 2012-2014 The Rust Project Developers. See the COPYRIGHT
   2 // file at the top-level directory of this distribution and at
   3 // http://rust-lang.org/COPYRIGHT.
   4 //
   5 // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
   6 // http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
   7 // <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
   8 // option. This file may not be copied, modified, or distributed
   9 // except according to those terms.
  10
  11 //! Operations and constants for 64-bits floats (`f64` type)
  12
  13 // FIXME: MIN_VALUE and MAX_VALUE literals are parsed as -inf and inf #14353
  14 #![allow(overflowing_literals)]
  15
  16 #![stable(feature = "rust1", since = "1.0.0")]
  17
  18 use prelude::v1::*;
  19
  20 use intrinsics;
  21 use mem;
  22 use num::FpCategory as Fp;
  23 use num::{Float, ParseFloatError};
  24
  25 #[stable(feature = "rust1", since = "1.0.0")]
  26 #[allow(missing_docs)]
  27 pub const RADIX: u32 = 2;
  28
  29 #[stable(feature = "rust1", since = "1.0.0")]
  30 #[allow(missing_docs)]
  31 pub const MANTISSA_DIGITS: u32 = 53;
  32 #[stable(feature = "rust1", since = "1.0.0")]
  33 #[allow(missing_docs)]
  34 pub const DIGITS: u32 = 15;
  35
  36 #[stable(feature = "rust1", since = "1.0.0")]
  37 #[allow(missing_docs)]
  38 pub const EPSILON: f64 = 2.2204460492503131e-16_f64;
  39
  40 /// Smallest finite f64 value
  41 #[stable(feature = "rust1", since = "1.0.0")]
  42 pub const MIN: f64 = -1.7976931348623157e+308_f64;
  43 /// Smallest positive, normalized f64 value
  44 #[stable(feature = "rust1", since = "1.0.0")]
  45 pub const MIN_POSITIVE: f64 = 2.2250738585072014e-308_f64;
  46 /// Largest finite f64 value
  47 #[stable(feature = "rust1", since = "1.0.0")]
  48 pub const MAX: f64 = 1.7976931348623157e+308_f64;
  49
  50 #[stable(feature = "rust1", since = "1.0.0")]
  51 #[allow(missing_docs)]
  52 pub const MIN_EXP: i32 = -1021;
  53 #[stable(feature = "rust1", since = "1.0.0")]
  54 #[allow(missing_docs)]
  55 pub const MAX_EXP: i32 = 1024;
  56
  57 #[stable(feature = "rust1", since = "1.0.0")]
  58 #[allow(missing_docs)]
  59 pub const MIN_10_EXP: i32 = -307;
  60 #[stable(feature = "rust1", since = "1.0.0")]
  61 #[allow(missing_docs)]
  62 pub const MAX_10_EXP: i32 = 308;
  63
  64 #[stable(feature = "rust1", since = "1.0.0")]
  65 #[allow(missing_docs)]
  66 pub const NAN: f64 = 0.0_f64/0.0_f64;
  67 #[stable(feature = "rust1", since = "1.0.0")]
  68 #[allow(missing_docs)]
  69 pub const INFINITY: f64 = 1.0_f64/0.0_f64;
  70 #[stable(feature = "rust1", since = "1.0.0")]
  71 #[allow(missing_docs)]
  72 pub const NEG_INFINITY: f64 = -1.0_f64/0.0_f64;
  73
  74 /// Basic mathematial constants.
  75 #[stable(feature = "rust1", since = "1.0.0")]
  76 pub mod consts {
  77     // FIXME: replace with mathematical constants from cmath.
  78
  79     /// Archimedes' constant
  80     #[stable(feature = "rust1", since = "1.0.0")]
  81     pub const PI: f64 = 3.14159265358979323846264338327950288_f64;
  82
  83     /// pi/2.0
  84     #[stable(feature = "rust1", since = "1.0.0")]
  85     pub const FRAC_PI_2: f64 = 1.57079632679489661923132169163975144_f64;
  86
  87     /// pi/3.0
  88     #[stable(feature = "rust1", since = "1.0.0")]
  89     pub const FRAC_PI_3: f64 = 1.04719755119659774615421446109316763_f64;
  90
  91     /// pi/4.0
  92     #[stable(feature = "rust1", since = "1.0.0")]
  93     pub const FRAC_PI_4: f64 = 0.785398163397448309615660845819875721_f64;
  94
  95     /// pi/6.0
  96     #[stable(feature = "rust1", since = "1.0.0")]
  97     pub const FRAC_PI_6: f64 = 0.52359877559829887307710723054658381_f64;
  98
  99     /// pi/8.0
 100     #[stable(feature = "rust1", since = "1.0.0")]
 101     pub const FRAC_PI_8: f64 = 0.39269908169872415480783042290993786_f64;
 102
 103     /// 1.0/pi
 104     #[stable(feature = "rust1", since = "1.0.0")]
 105     pub const FRAC_1_PI: f64 = 0.318309886183790671537767526745028724_f64;
 106
 107     /// 2.0/pi
 108     #[stable(feature = "rust1", since = "1.0.0")]
 109     pub const FRAC_2_PI: f64 = 0.636619772367581343075535053490057448_f64;
 110
 111     /// 2.0/sqrt(pi)
 112     #[stable(feature = "rust1", since = "1.0.0")]
 113     pub const FRAC_2_SQRT_PI: f64 = 1.12837916709551257389615890312154517_f64;
 114
 115     /// sqrt(2.0)
 116     #[stable(feature = "rust1", since = "1.0.0")]
 117     pub const SQRT_2: f64 = 1.41421356237309504880168872420969808_f64;
 118
 119     /// 1.0/sqrt(2.0)
 120     #[stable(feature = "rust1", since = "1.0.0")]
 121     pub const FRAC_1_SQRT_2: f64 = 0.707106781186547524400844362104849039_f64;
 122
 123     /// Euler's number
 124     #[stable(feature = "rust1", since = "1.0.0")]
 125     pub const E: f64 = 2.71828182845904523536028747135266250_f64;
 126
 127     /// log2(e)
 128     #[stable(feature = "rust1", since = "1.0.0")]
 129     pub const LOG2_E: f64 = 1.44269504088896340735992468100189214_f64;
 130
 131     /// log10(e)
 132     #[stable(feature = "rust1", since = "1.0.0")]
 133     pub const LOG10_E: f64 = 0.434294481903251827651128918916605082_f64;
 134
 135     /// ln(2.0)
 136     #[stable(feature = "rust1", since = "1.0.0")]
 137     pub const LN_2: f64 = 0.693147180559945309417232121458176568_f64;
 138
 139     /// ln(10.0)
 140     #[stable(feature = "rust1", since = "1.0.0")]
 141     pub const LN_10: f64 = 2.30258509299404568401799145468436421_f64;
 142 }
 143
 144 impl Float for f64 {
 145     #[inline]
 146     fn nan() -> f64 { NAN }
 147
 148     #[inline]
 149     fn infinity() -> f64 { INFINITY }
 150
 151     #[inline]
 152     fn neg_infinity() -> f64 { NEG_INFINITY }
 153
 154     #[inline]
 155     fn zero() -> f64 { 0.0 }
 156
 157     #[inline]
 158     fn neg_zero() -> f64 { -0.0 }
 159
 160     #[inline]
 161     fn one() -> f64 { 1.0 }
 162
 163     from_str_radix_float_impl! { f64 }
 164
 165     /// Returns `true` if the number is NaN.
 166     #[inline]
 167     fn is_nan(self) -> bool { self != self }
 168
 169     /// Returns `true` if the number is infinite.
 170     #[inline]
 171     fn is_infinite(self) -> bool {
 172         self == Float::infinity() || self == Float::neg_infinity()
 173     }
 174
 175     /// Returns `true` if the number is neither infinite or NaN.
 176     #[inline]
 177     fn is_finite(self) -> bool {
 178         !(self.is_nan() || self.is_infinite())
 179     }
 180
 181     /// Returns `true` if the number is neither zero, infinite, subnormal or NaN.
 182     #[inline]
 183     fn is_normal(self) -> bool {
 184         self.classify() == Fp::Normal
 185     }
 186
 187     /// Returns the floating point category of the number. If only one property
 188     /// is going to be tested, it is generally faster to use the specific
 189     /// predicate instead.
 190     fn classify(self) -> Fp {
 191         const EXP_MASK: u64 = 0x7ff0000000000000;
 192         const MAN_MASK: u64 = 0x000fffffffffffff;
 193
 194         let bits: u64 = unsafe { mem::transmute(self) };
 195         match (bits & MAN_MASK, bits & EXP_MASK) {
 196             (0, 0)        => Fp::Zero,
 197             (_, 0)        => Fp::Subnormal,
 198             (0, EXP_MASK) => Fp::Infinite,
 199             (_, EXP_MASK) => Fp::Nan,
 200             _             => Fp::Normal,
 201         }
 202     }
 203
 204     /// Returns the mantissa, exponent and sign as integers.
 205     fn integer_decode(self) -> (u64, i16, i8) {
 206         let bits: u64 = unsafe { mem::transmute(self) };
 207         let sign: i8 = if bits >> 63 == 0 { 1 } else { -1 };
 208         let mut exponent: i16 = ((bits >> 52) & 0x7ff) as i16;
 209         let mantissa = if exponent == 0 {
 210             (bits & 0xfffffffffffff) << 1
 211         } else {
 212             (bits & 0xfffffffffffff) | 0x10000000000000
 213         };
 214         // Exponent bias + mantissa shift
 215         exponent -= 1023 + 52;
 216         (mantissa, exponent, sign)
 217     }
 218
 219     /// Computes the absolute value of `self`. Returns `Float::nan()` if the
 220     /// number is `Float::nan()`.
 221     #[inline]
 222     fn abs(self) -> f64 {
 223         unsafe { intrinsics::fabsf64(self) }
 224     }
 225
 226     /// Returns a number that represents the sign of `self`.
 227     ///
 228     /// - `1.0` if the number is positive, `+0.0` or `Float::infinity()`
 229     /// - `-1.0` if the number is negative, `-0.0` or `Float::neg_infinity()`
 230     /// - `Float::nan()` if the number is `Float::nan()`
 231     #[inline]
 232     fn signum(self) -> f64 {
 233         if self.is_nan() {
 234             Float::nan()
 235         } else {
 236             unsafe { intrinsics::copysignf64(1.0, self) }
 237         }
 238     }
 239
 240     /// Returns `true` if `self` is positive, including `+0.0` and
 241     /// `Float::infinity()`.
 242     #[inline]
 243     fn is_positive(self) -> bool {
 244         self > 0.0 || (1.0 / self) == Float::infinity()
 245     }
 246
 247     /// Returns `true` if `self` is negative, including `-0.0` and
 248     /// `Float::neg_infinity()`.
 249     #[inline]
 250     fn is_negative(self) -> bool {
 251         self < 0.0 || (1.0 / self) == Float::neg_infinity()
 252     }
 253
 254     /// Returns the reciprocal (multiplicative inverse) of the number.
 255     #[inline]
 256     fn recip(self) -> f64 { 1.0 / self }
 257
 258     #[inline]
 259     fn powi(self, n: i32) -> f64 {
 260         unsafe { intrinsics::powif64(self, n) }
 261     }
 262
 263     /// Converts to degrees, assuming the number is in radians.
 264     #[inline]
 265     fn to_degrees(self) -> f64 { self * (180.0f64 / consts::PI) }
 266
 267     /// Converts to radians, assuming the number is in degrees.
 268     #[inline]
 269     fn to_radians(self) -> f64 {
 270         let value: f64 = consts::PI;
 271         self * (value / 180.0)
 272     }
 273 }