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 #![doc(primitive = "f64")]
  14 // FIXME: MIN_VALUE and MAX_VALUE literals are parsed as -inf and inf #14353
  15 #![allow(overflowing_literals)]
  16
  17 #![stable(feature = "rust1", since = "1.0.0")]
  18
  19 use intrinsics;
  20 use mem;
  21 use num::Float;
  22 use num::FpCategory as Fp;
  23 use option::Option;
  24
  25 // FIXME(#5527): These constants should be deprecated once associated
  26 // constants are implemented in favour of referencing the respective
  27 // members of `Bounded` and `Float`.
  28
  29 #[unstable(feature = "core", reason = "pending integer conventions")]
  30 pub const RADIX: uint = 2;
  31
  32 pub const MANTISSA_DIGITS: uint = 53;
  33 #[unstable(feature = "core", reason = "pending integer conventions")]
  34 pub const DIGITS: uint = 15;
  35
  36 #[stable(feature = "rust1", since = "1.0.0")]
  37 pub const EPSILON: f64 = 2.2204460492503131e-16_f64;
  38
  39 /// Smallest finite f64 value
  40 #[stable(feature = "rust1", since = "1.0.0")]
  41 #[deprecated(since = "1.0.0", reason = "use `std::f64::MIN`")]
  42 pub const MIN_VALUE: f64 = -1.7976931348623157e+308_f64;
  43 /// Smallest positive, normalized f64 value
  44 #[stable(feature = "rust1", since = "1.0.0")]
  45 #[deprecated(since = "1.0.0", reason = "use `std::f64::MIN_POSITIVE`")]
  46 pub const MIN_POS_VALUE: f64 = 2.2250738585072014e-308_f64;
  47 /// Largest finite f64 value
  48 #[stable(feature = "rust1", since = "1.0.0")]
  49 #[deprecated(since = "1.0.0", reason = "use `std::f64::MAX`")]
  50 pub const MAX_VALUE: f64 = 1.7976931348623157e+308_f64;
  51
  52 /// Smallest finite f64 value
  53 #[stable(feature = "rust1", since = "1.0.0")]
  54 pub const MIN: f64 = -1.7976931348623157e+308_f64;
  55 /// Smallest positive, normalized f64 value
  56 #[stable(feature = "rust1", since = "1.0.0")]
  57 pub const MIN_POSITIVE: f64 = 2.2250738585072014e-308_f64;
  58 /// Largest finite f64 value
  59 #[stable(feature = "rust1", since = "1.0.0")]
  60 pub const MAX: f64 = 1.7976931348623157e+308_f64;
  61
  62 #[unstable(feature = "core", reason = "pending integer conventions")]
  63 pub const MIN_EXP: int = -1021;
  64 #[unstable(feature = "core", reason = "pending integer conventions")]
  65 pub const MAX_EXP: int = 1024;
  66
  67 #[unstable(feature = "core", reason = "pending integer conventions")]
  68 pub const MIN_10_EXP: int = -307;
  69 #[unstable(feature = "core", reason = "pending integer conventions")]
  70 pub const MAX_10_EXP: int = 308;
  71
  72 #[stable(feature = "rust1", since = "1.0.0")]
  73 pub const NAN: f64 = 0.0_f64/0.0_f64;
  74 #[stable(feature = "rust1", since = "1.0.0")]
  75 pub const INFINITY: f64 = 1.0_f64/0.0_f64;
  76 #[stable(feature = "rust1", since = "1.0.0")]
  77 pub const NEG_INFINITY: f64 = -1.0_f64/0.0_f64;
  78
  79 /// Various useful constants.
  80 #[unstable(feature = "core",
  81            reason = "naming scheme needs to be revisited")]
  82 pub mod consts {
  83     // FIXME: replace with mathematical constants from cmath.
  84
  85     // FIXME(#5527): These constants should be deprecated once associated
  86     // constants are implemented in favour of referencing the respective members
  87     // of `Float`.
  88
  89     /// Archimedes' constant
  90     pub const PI: f64 = 3.14159265358979323846264338327950288_f64;
  91
  92     /// pi * 2.0
  93     pub const PI_2: f64 = 6.28318530717958647692528676655900576_f64;
  94
  95     /// pi/2.0
  96     pub const FRAC_PI_2: f64 = 1.57079632679489661923132169163975144_f64;
  97
  98     /// pi/3.0
  99     pub const FRAC_PI_3: f64 = 1.04719755119659774615421446109316763_f64;
 100
 101     /// pi/4.0
 102     pub const FRAC_PI_4: f64 = 0.785398163397448309615660845819875721_f64;
 103
 104     /// pi/6.0
 105     pub const FRAC_PI_6: f64 = 0.52359877559829887307710723054658381_f64;
 106
 107     /// pi/8.0
 108     pub const FRAC_PI_8: f64 = 0.39269908169872415480783042290993786_f64;
 109
 110     /// 1.0/pi
 111     pub const FRAC_1_PI: f64 = 0.318309886183790671537767526745028724_f64;
 112
 113     /// 2.0/pi
 114     pub const FRAC_2_PI: f64 = 0.636619772367581343075535053490057448_f64;
 115
 116     /// 2.0/sqrt(pi)
 117     pub const FRAC_2_SQRTPI: f64 = 1.12837916709551257389615890312154517_f64;
 118
 119     /// sqrt(2.0)
 120     pub const SQRT2: f64 = 1.41421356237309504880168872420969808_f64;
 121
 122     /// 1.0/sqrt(2.0)
 123     pub const FRAC_1_SQRT2: f64 = 0.707106781186547524400844362104849039_f64;
 124
 125     /// Euler's number
 126     pub const E: f64 = 2.71828182845904523536028747135266250_f64;
 127
 128     /// log2(e)
 129     pub const LOG2_E: f64 = 1.44269504088896340735992468100189214_f64;
 130
 131     /// log10(e)
 132     pub const LOG10_E: f64 = 0.434294481903251827651128918916605082_f64;
 133
 134     /// ln(2.0)
 135     pub const LN_2: f64 = 0.693147180559945309417232121458176568_f64;
 136
 137     /// ln(10.0)
 138     pub const LN_10: f64 = 2.30258509299404568401799145468436421_f64;
 139 }
 140
 141 #[unstable(feature = "core", reason = "trait is unstable")]
 142 impl Float for f64 {
 143     #[inline]
 144     fn nan() -> f64 { NAN }
 145
 146     #[inline]
 147     fn infinity() -> f64 { INFINITY }
 148
 149     #[inline]
 150     fn neg_infinity() -> f64 { NEG_INFINITY }
 151
 152     #[inline]
 153     fn zero() -> f64 { 0.0 }
 154
 155     #[inline]
 156     fn neg_zero() -> f64 { -0.0 }
 157
 158     #[inline]
 159     fn one() -> f64 { 1.0 }
 160
 161     /// Returns `true` if the number is NaN.
 162     #[inline]
 163     fn is_nan(self) -> bool { self != self }
 164
 165     /// Returns `true` if the number is infinite.
 166     #[inline]
 167     fn is_infinite(self) -> bool {
 168         self == Float::infinity() || self == Float::neg_infinity()
 169     }
 170
 171     /// Returns `true` if the number is neither infinite or NaN.
 172     #[inline]
 173     fn is_finite(self) -> bool {
 174         !(self.is_nan() || self.is_infinite())
 175     }
 176
 177     /// Returns `true` if the number is neither zero, infinite, subnormal or NaN.
 178     #[inline]
 179     fn is_normal(self) -> bool {
 180         self.classify() == Fp::Normal
 181     }
 182
 183     /// Returns the floating point category of the number. If only one property
 184     /// is going to be tested, it is generally faster to use the specific
 185     /// predicate instead.
 186     fn classify(self) -> Fp {
 187         const EXP_MASK: u64 = 0x7ff0000000000000;
 188         const MAN_MASK: u64 = 0x000fffffffffffff;
 189
 190         let bits: u64 = unsafe { mem::transmute(self) };
 191         match (bits & MAN_MASK, bits & EXP_MASK) {
 192             (0, 0)        => Fp::Zero,
 193             (_, 0)        => Fp::Subnormal,
 194             (0, EXP_MASK) => Fp::Infinite,
 195             (_, EXP_MASK) => Fp::Nan,
 196             _             => Fp::Normal,
 197         }
 198     }
 199
 200     #[inline]
 201     #[unstable(feature = "core")]
 202     #[deprecated(since = "1.0.0")]
 203     fn mantissa_digits(_: Option<f64>) -> uint { MANTISSA_DIGITS }
 204
 205     #[inline]
 206     #[unstable(feature = "core")]
 207     #[deprecated(since = "1.0.0")]
 208     fn digits(_: Option<f64>) -> uint { DIGITS }
 209
 210     #[inline]
 211     #[unstable(feature = "core")]
 212     #[deprecated(since = "1.0.0")]
 213     fn epsilon() -> f64 { EPSILON }
 214
 215     #[inline]
 216     #[unstable(feature = "core")]
 217     #[deprecated(since = "1.0.0")]
 218     fn min_exp(_: Option<f64>) -> int { MIN_EXP }
 219
 220     #[inline]
 221     #[unstable(feature = "core")]
 222     #[deprecated(since = "1.0.0")]
 223     fn max_exp(_: Option<f64>) -> int { MAX_EXP }
 224
 225     #[inline]
 226     #[unstable(feature = "core")]
 227     #[deprecated(since = "1.0.0")]
 228     fn min_10_exp(_: Option<f64>) -> int { MIN_10_EXP }
 229
 230     #[inline]
 231     #[unstable(feature = "core")]
 232     #[deprecated(since = "1.0.0")]
 233     fn max_10_exp(_: Option<f64>) -> int { MAX_10_EXP }
 234
 235     #[inline]
 236     #[unstable(feature = "core")]
 237     #[deprecated(since = "1.0.0")]
 238     fn min_value() -> f64 { MIN }
 239
 240     #[inline]
 241     #[unstable(feature = "core")]
 242     #[deprecated(since = "1.0.0")]
 243     fn min_pos_value(_: Option<f64>) -> f64 { MIN_POSITIVE }
 244
 245     #[inline]
 246     #[unstable(feature = "core")]
 247     #[deprecated(since = "1.0.0")]
 248     fn max_value() -> f64 { MAX }
 249
 250     /// Returns the mantissa, exponent and sign as integers.
 251     fn integer_decode(self) -> (u64, i16, i8) {
 252         let bits: u64 = unsafe { mem::transmute(self) };
 253         let sign: i8 = if bits >> 63 == 0 { 1 } else { -1 };
 254         let mut exponent: i16 = ((bits >> 52) & 0x7ff) as i16;
 255         let mantissa = if exponent == 0 {
 256             (bits & 0xfffffffffffff) << 1
 257         } else {
 258             (bits & 0xfffffffffffff) | 0x10000000000000
 259         };
 260         // Exponent bias + mantissa shift
 261         exponent -= 1023 + 52;
 262         (mantissa, exponent, sign)
 263     }
 264
 265     /// Rounds towards minus infinity.
 266     #[inline]
 267     fn floor(self) -> f64 {
 268         unsafe { intrinsics::floorf64(self) }
 269     }
 270
 271     /// Rounds towards plus infinity.
 272     #[inline]
 273     fn ceil(self) -> f64 {
 274         unsafe { intrinsics::ceilf64(self) }
 275     }
 276
 277     /// Rounds to nearest integer. Rounds half-way cases away from zero.
 278     #[inline]
 279     fn round(self) -> f64 {
 280         unsafe { intrinsics::roundf64(self) }
 281     }
 282
 283     /// Returns the integer part of the number (rounds towards zero).
 284     #[inline]
 285     fn trunc(self) -> f64 {
 286         unsafe { intrinsics::truncf64(self) }
 287     }
 288
 289     /// The fractional part of the number, satisfying:
 290     ///
 291     /// ```rust
 292     /// use core::num::Float;
 293     ///
 294     /// let x = 1.65f64;
 295     /// assert!(x == x.trunc() + x.fract())
 296     /// ```
 297     #[inline]
 298     fn fract(self) -> f64 { self - self.trunc() }
 299
 300     /// Computes the absolute value of `self`. Returns `Float::nan()` if the
 301     /// number is `Float::nan()`.
 302     #[inline]
 303     fn abs(self) -> f64 {
 304         unsafe { intrinsics::fabsf64(self) }
 305     }
 306
 307     /// Returns a number that represents the sign of `self`.
 308     ///
 309     /// - `1.0` if the number is positive, `+0.0` or `Float::infinity()`
 310     /// - `-1.0` if the number is negative, `-0.0` or `Float::neg_infinity()`
 311     /// - `Float::nan()` if the number is `Float::nan()`
 312     #[inline]
 313     fn signum(self) -> f64 {
 314         if self.is_nan() {
 315             Float::nan()
 316         } else {
 317             unsafe { intrinsics::copysignf64(1.0, self) }
 318         }
 319     }
 320
 321     /// Returns `true` if `self` is positive, including `+0.0` and
 322     /// `Float::infinity()`.
 323     #[inline]
 324     fn is_positive(self) -> bool {
 325         self > 0.0 || (1.0 / self) == Float::infinity()
 326     }
 327
 328     /// Returns `true` if `self` is negative, including `-0.0` and
 329     /// `Float::neg_infinity()`.
 330     #[inline]
 331     fn is_negative(self) -> bool {
 332         self < 0.0 || (1.0 / self) == Float::neg_infinity()
 333     }
 334
 335     /// Fused multiply-add. Computes `(self * a) + b` with only one rounding
 336     /// error. This produces a more accurate result with better performance than
 337     /// a separate multiplication operation followed by an add.
 338     #[inline]
 339     fn mul_add(self, a: f64, b: f64) -> f64 {
 340         unsafe { intrinsics::fmaf64(self, a, b) }
 341     }
 342
 343     /// Returns the reciprocal (multiplicative inverse) of the number.
 344     #[inline]
 345     fn recip(self) -> f64 { 1.0 / self }
 346
 347     #[inline]
 348     fn powf(self, n: f64) -> f64 {
 349         unsafe { intrinsics::powf64(self, n) }
 350     }
 351
 352     #[inline]
 353     fn powi(self, n: i32) -> f64 {
 354         unsafe { intrinsics::powif64(self, n) }
 355     }
 356
 357     #[inline]
 358     fn sqrt(self) -> f64 {
 359         if self < 0.0 {
 360             NAN
 361         } else {
 362             unsafe { intrinsics::sqrtf64(self) }
 363         }
 364     }
 365
 366     #[inline]
 367     fn rsqrt(self) -> f64 { self.sqrt().recip() }
 368
 369     /// Returns the exponential of the number.
 370     #[inline]
 371     fn exp(self) -> f64 {
 372         unsafe { intrinsics::expf64(self) }
 373     }
 374
 375     /// Returns 2 raised to the power of the number.
 376     #[inline]
 377     fn exp2(self) -> f64 {
 378         unsafe { intrinsics::exp2f64(self) }
 379     }
 380
 381     /// Returns the natural logarithm of the number.
 382     #[inline]
 383     fn ln(self) -> f64 {
 384         unsafe { intrinsics::logf64(self) }
 385     }
 386
 387     /// Returns the logarithm of the number with respect to an arbitrary base.
 388     #[inline]
 389     fn log(self, base: f64) -> f64 { self.ln() / base.ln() }
 390
 391     /// Returns the base 2 logarithm of the number.
 392     #[inline]
 393     fn log2(self) -> f64 {
 394         unsafe { intrinsics::log2f64(self) }
 395     }
 396
 397     /// Returns the base 10 logarithm of the number.
 398     #[inline]
 399     fn log10(self) -> f64 {
 400         unsafe { intrinsics::log10f64(self) }
 401     }
 402
 403     /// Converts to degrees, assuming the number is in radians.
 404     #[inline]
 405     fn to_degrees(self) -> f64 { self * (180.0f64 / consts::PI) }
 406
 407     /// Converts to radians, assuming the number is in degrees.
 408     #[inline]
 409     fn to_radians(self) -> f64 {
 410         let value: f64 = consts::PI;
 411         self * (value / 180.0)
 412     }
 413 }