library/core/src/num/f64.rs

   1 //! This module provides constants which are specific to the implementation
   2 //! of the `f64` floating point data type.
   3 //!
   4 //! *[See also the `f64` primitive type](../../std/primitive.f64.html).*
   5 //!
   6 //! Mathematically significant numbers are provided in the `consts` sub-module.
   7 //!
   8 //! Although using these constants won’t cause compilation warnings,
   9 //! new code should use the associated constants directly on the primitive type.
  10
  11 #![stable(feature = "rust1", since = "1.0.0")]
  12
  13 use crate::convert::FloatToInt;
  14 #[cfg(not(test))]
  15 use crate::intrinsics;
  16 use crate::mem;
  17 use crate::num::FpCategory;
  18
  19 /// The radix or base of the internal representation of `f64`.
  20 /// Use [`f64::RADIX`](../../std/primitive.f64.html#associatedconstant.RADIX) instead.
  21 ///
  22 /// # Examples
  23 ///
  24 /// ```rust
  25 /// // deprecated way
  26 /// let r = std::f64::RADIX;
  27 ///
  28 /// // intended way
  29 /// let r = f64::RADIX;
  30 /// ```
  31 #[stable(feature = "rust1", since = "1.0.0")]
  32 pub const RADIX: u32 = f64::RADIX;
  33
  34 /// Number of significant digits in base 2.
  35 /// Use [`f64::MANTISSA_DIGITS`](../../std/primitive.f64.html#associatedconstant.MANTISSA_DIGITS) instead.
  36 ///
  37 /// # Examples
  38 ///
  39 /// ```rust
  40 /// // deprecated way
  41 /// let d = std::f64::MANTISSA_DIGITS;
  42 ///
  43 /// // intended way
  44 /// let d = f64::MANTISSA_DIGITS;
  45 /// ```
  46 #[stable(feature = "rust1", since = "1.0.0")]
  47 pub const MANTISSA_DIGITS: u32 = f64::MANTISSA_DIGITS;
  48
  49 /// Approximate number of significant digits in base 10.
  50 /// Use [`f64::DIGITS`](../../std/primitive.f64.html#associatedconstant.DIGITS) instead.
  51 ///
  52 /// # Examples
  53 ///
  54 /// ```rust
  55 /// // deprecated way
  56 /// let d = std::f64::DIGITS;
  57 ///
  58 /// // intended way
  59 /// let d = f64::DIGITS;
  60 /// ```
  61 #[stable(feature = "rust1", since = "1.0.0")]
  62 pub const DIGITS: u32 = f64::DIGITS;
  63
  64 /// [Machine epsilon] value for `f64`.
  65 /// Use [`f64::EPSILON`](../../std/primitive.f64.html#associatedconstant.EPSILON) instead.
  66 ///
  67 /// This is the difference between `1.0` and the next larger representable number.
  68 ///
  69 /// [Machine epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon
  70 ///
  71 /// # Examples
  72 ///
  73 /// ```rust
  74 /// // deprecated way
  75 /// let e = std::f64::EPSILON;
  76 ///
  77 /// // intended way
  78 /// let e = f64::EPSILON;
  79 /// ```
  80 #[stable(feature = "rust1", since = "1.0.0")]
  81 pub const EPSILON: f64 = f64::EPSILON;
  82
  83 /// Smallest finite `f64` value.
  84 /// Use [`f64::MIN`](../../std/primitive.f64.html#associatedconstant.MIN) instead.
  85 ///
  86 /// # Examples
  87 ///
  88 /// ```rust
  89 /// // deprecated way
  90 /// let min = std::f64::MIN;
  91 ///
  92 /// // intended way
  93 /// let min = f64::MIN;
  94 /// ```
  95 #[stable(feature = "rust1", since = "1.0.0")]
  96 pub const MIN: f64 = f64::MIN;
  97
  98 /// Smallest positive normal `f64` value.
  99 /// Use [`f64::MIN_POSITIVE`](../../std/primitive.f64.html#associatedconstant.MIN_POSITIVE) instead.
 100 ///
 101 /// # Examples
 102 ///
 103 /// ```rust
 104 /// // deprecated way
 105 /// let min = std::f64::MIN_POSITIVE;
 106 ///
 107 /// // intended way
 108 /// let min = f64::MIN_POSITIVE;
 109 /// ```
 110 #[stable(feature = "rust1", since = "1.0.0")]
 111 pub const MIN_POSITIVE: f64 = f64::MIN_POSITIVE;
 112
 113 /// Largest finite `f64` value.
 114 /// Use [`f64::MAX`](../../std/primitive.f64.html#associatedconstant.MAX) instead.
 115 ///
 116 /// # Examples
 117 ///
 118 /// ```rust
 119 /// // deprecated way
 120 /// let max = std::f64::MAX;
 121 ///
 122 /// // intended way
 123 /// let max = f64::MAX;
 124 /// ```
 125 #[stable(feature = "rust1", since = "1.0.0")]
 126 pub const MAX: f64 = f64::MAX;
 127
 128 /// One greater than the minimum possible normal power of 2 exponent.
 129 /// Use [`f64::MIN_EXP`](../../std/primitive.f64.html#associatedconstant.MIN_EXP) instead.
 130 ///
 131 /// # Examples
 132 ///
 133 /// ```rust
 134 /// // deprecated way
 135 /// let min = std::f64::MIN_EXP;
 136 ///
 137 /// // intended way
 138 /// let min = f64::MIN_EXP;
 139 /// ```
 140 #[stable(feature = "rust1", since = "1.0.0")]
 141 pub const MIN_EXP: i32 = f64::MIN_EXP;
 142
 143 /// Maximum possible power of 2 exponent.
 144 /// Use [`f64::MAX_EXP`](../../std/primitive.f64.html#associatedconstant.MAX_EXP) instead.
 145 ///
 146 /// # Examples
 147 ///
 148 /// ```rust
 149 /// // deprecated way
 150 /// let max = std::f64::MAX_EXP;
 151 ///
 152 /// // intended way
 153 /// let max = f64::MAX_EXP;
 154 /// ```
 155 #[stable(feature = "rust1", since = "1.0.0")]
 156 pub const MAX_EXP: i32 = f64::MAX_EXP;
 157
 158 /// Minimum possible normal power of 10 exponent.
 159 /// Use [`f64::MIN_10_EXP`](../../std/primitive.f64.html#associatedconstant.MIN_10_EXP) instead.
 160 ///
 161 /// # Examples
 162 ///
 163 /// ```rust
 164 /// // deprecated way
 165 /// let min = std::f64::MIN_10_EXP;
 166 ///
 167 /// // intended way
 168 /// let min = f64::MIN_10_EXP;
 169 /// ```
 170 #[stable(feature = "rust1", since = "1.0.0")]
 171 pub const MIN_10_EXP: i32 = f64::MIN_10_EXP;
 172
 173 /// Maximum possible power of 10 exponent.
 174 /// Use [`f64::MAX_10_EXP`](../../std/primitive.f64.html#associatedconstant.MAX_10_EXP) instead.
 175 ///
 176 /// # Examples
 177 ///
 178 /// ```rust
 179 /// // deprecated way
 180 /// let max = std::f64::MAX_10_EXP;
 181 ///
 182 /// // intended way
 183 /// let max = f64::MAX_10_EXP;
 184 /// ```
 185 #[stable(feature = "rust1", since = "1.0.0")]
 186 pub const MAX_10_EXP: i32 = f64::MAX_10_EXP;
 187
 188 /// Not a Number (NaN).
 189 /// Use [`f64::NAN`](../../std/primitive.f64.html#associatedconstant.NAN) instead.
 190 ///
 191 /// # Examples
 192 ///
 193 /// ```rust
 194 /// // deprecated way
 195 /// let nan = std::f64::NAN;
 196 ///
 197 /// // intended way
 198 /// let nan = f64::NAN;
 199 /// ```
 200 #[stable(feature = "rust1", since = "1.0.0")]
 201 pub const NAN: f64 = f64::NAN;
 202
 203 /// Infinity (∞).
 204 /// Use [`f64::INFINITY`](../../std/primitive.f64.html#associatedconstant.INFINITY) instead.
 205 ///
 206 /// # Examples
 207 ///
 208 /// ```rust
 209 /// // deprecated way
 210 /// let inf = std::f64::INFINITY;
 211 ///
 212 /// // intended way
 213 /// let inf = f64::INFINITY;
 214 /// ```
 215 #[stable(feature = "rust1", since = "1.0.0")]
 216 pub const INFINITY: f64 = f64::INFINITY;
 217
 218 /// Negative infinity (−∞).
 219 /// Use [`f64::NEG_INFINITY`](../../std/primitive.f64.html#associatedconstant.NEG_INFINITY) instead.
 220 ///
 221 /// # Examples
 222 ///
 223 /// ```rust
 224 /// // deprecated way
 225 /// let ninf = std::f64::NEG_INFINITY;
 226 ///
 227 /// // intended way
 228 /// let ninf = f64::NEG_INFINITY;
 229 /// ```
 230 #[stable(feature = "rust1", since = "1.0.0")]
 231 pub const NEG_INFINITY: f64 = f64::NEG_INFINITY;
 232
 233 /// Basic mathematical constants.
 234 #[stable(feature = "rust1", since = "1.0.0")]
 235 pub mod consts {
 236     // FIXME: replace with mathematical constants from cmath.
 237
 238     /// Archimedes' constant (π)
 239     #[stable(feature = "rust1", since = "1.0.0")]
 240     pub const PI: f64 = 3.14159265358979323846264338327950288_f64;
 241
 242     /// The full circle constant (τ)
 243     ///
 244     /// Equal to 2π.
 245     #[stable(feature = "tau_constant", since = "1.47.0")]
 246     pub const TAU: f64 = 6.28318530717958647692528676655900577_f64;
 247
 248     /// π/2
 249     #[stable(feature = "rust1", since = "1.0.0")]
 250     pub const FRAC_PI_2: f64 = 1.57079632679489661923132169163975144_f64;
 251
 252     /// π/3
 253     #[stable(feature = "rust1", since = "1.0.0")]
 254     pub const FRAC_PI_3: f64 = 1.04719755119659774615421446109316763_f64;
 255
 256     /// π/4
 257     #[stable(feature = "rust1", since = "1.0.0")]
 258     pub const FRAC_PI_4: f64 = 0.785398163397448309615660845819875721_f64;
 259
 260     /// π/6
 261     #[stable(feature = "rust1", since = "1.0.0")]
 262     pub const FRAC_PI_6: f64 = 0.52359877559829887307710723054658381_f64;
 263
 264     /// π/8
 265     #[stable(feature = "rust1", since = "1.0.0")]
 266     pub const FRAC_PI_8: f64 = 0.39269908169872415480783042290993786_f64;
 267
 268     /// 1/π
 269     #[stable(feature = "rust1", since = "1.0.0")]
 270     pub const FRAC_1_PI: f64 = 0.318309886183790671537767526745028724_f64;
 271
 272     /// 2/π
 273     #[stable(feature = "rust1", since = "1.0.0")]
 274     pub const FRAC_2_PI: f64 = 0.636619772367581343075535053490057448_f64;
 275
 276     /// 2/sqrt(π)
 277     #[stable(feature = "rust1", since = "1.0.0")]
 278     pub const FRAC_2_SQRT_PI: f64 = 1.12837916709551257389615890312154517_f64;
 279
 280     /// sqrt(2)
 281     #[stable(feature = "rust1", since = "1.0.0")]
 282     pub const SQRT_2: f64 = 1.41421356237309504880168872420969808_f64;
 283
 284     /// 1/sqrt(2)
 285     #[stable(feature = "rust1", since = "1.0.0")]
 286     pub const FRAC_1_SQRT_2: f64 = 0.707106781186547524400844362104849039_f64;
 287
 288     /// Euler's number (e)
 289     #[stable(feature = "rust1", since = "1.0.0")]
 290     pub const E: f64 = 2.71828182845904523536028747135266250_f64;
 291
 292     /// log<sub>2</sub>(10)
 293     #[stable(feature = "extra_log_consts", since = "1.43.0")]
 294     pub const LOG2_10: f64 = 3.32192809488736234787031942948939018_f64;
 295
 296     /// log<sub>2</sub>(e)
 297     #[stable(feature = "rust1", since = "1.0.0")]
 298     pub const LOG2_E: f64 = 1.44269504088896340735992468100189214_f64;
 299
 300     /// log<sub>10</sub>(2)
 301     #[stable(feature = "extra_log_consts", since = "1.43.0")]
 302     pub const LOG10_2: f64 = 0.301029995663981195213738894724493027_f64;
 303
 304     /// log<sub>10</sub>(e)
 305     #[stable(feature = "rust1", since = "1.0.0")]
 306     pub const LOG10_E: f64 = 0.434294481903251827651128918916605082_f64;
 307
 308     /// ln(2)
 309     #[stable(feature = "rust1", since = "1.0.0")]
 310     pub const LN_2: f64 = 0.693147180559945309417232121458176568_f64;
 311
 312     /// ln(10)
 313     #[stable(feature = "rust1", since = "1.0.0")]
 314     pub const LN_10: f64 = 2.30258509299404568401799145468436421_f64;
 315 }
 316
 317 #[lang = "f64"]
 318 #[cfg(not(test))]
 319 impl f64 {
 320     /// The radix or base of the internal representation of `f64`.
 321     #[stable(feature = "assoc_int_consts", since = "1.43.0")]
 322     pub const RADIX: u32 = 2;
 323
 324     /// Number of significant digits in base 2.
 325     #[stable(feature = "assoc_int_consts", since = "1.43.0")]
 326     pub const MANTISSA_DIGITS: u32 = 53;
 327     /// Approximate number of significant digits in base 10.
 328     #[stable(feature = "assoc_int_consts", since = "1.43.0")]
 329     pub const DIGITS: u32 = 15;
 330
 331     /// [Machine epsilon] value for `f64`.
 332     ///
 333     /// This is the difference between `1.0` and the next larger representable number.
 334     ///
 335     /// [Machine epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon
 336     #[stable(feature = "assoc_int_consts", since = "1.43.0")]
 337     pub const EPSILON: f64 = 2.2204460492503131e-16_f64;
 338
 339     /// Smallest finite `f64` value.
 340     #[stable(feature = "assoc_int_consts", since = "1.43.0")]
 341     pub const MIN: f64 = -1.7976931348623157e+308_f64;
 342     /// Smallest positive normal `f64` value.
 343     #[stable(feature = "assoc_int_consts", since = "1.43.0")]
 344     pub const MIN_POSITIVE: f64 = 2.2250738585072014e-308_f64;
 345     /// Largest finite `f64` value.
 346     #[stable(feature = "assoc_int_consts", since = "1.43.0")]
 347     pub const MAX: f64 = 1.7976931348623157e+308_f64;
 348
 349     /// One greater than the minimum possible normal power of 2 exponent.
 350     #[stable(feature = "assoc_int_consts", since = "1.43.0")]
 351     pub const MIN_EXP: i32 = -1021;
 352     /// Maximum possible power of 2 exponent.
 353     #[stable(feature = "assoc_int_consts", since = "1.43.0")]
 354     pub const MAX_EXP: i32 = 1024;
 355
 356     /// Minimum possible normal power of 10 exponent.
 357     #[stable(feature = "assoc_int_consts", since = "1.43.0")]
 358     pub const MIN_10_EXP: i32 = -307;
 359     /// Maximum possible power of 10 exponent.
 360     #[stable(feature = "assoc_int_consts", since = "1.43.0")]
 361     pub const MAX_10_EXP: i32 = 308;
 362
 363     /// Not a Number (NaN).
 364     #[stable(feature = "assoc_int_consts", since = "1.43.0")]
 365     pub const NAN: f64 = 0.0_f64 / 0.0_f64;
 366     /// Infinity (∞).
 367     #[stable(feature = "assoc_int_consts", since = "1.43.0")]
 368     pub const INFINITY: f64 = 1.0_f64 / 0.0_f64;
 369     /// Negative infinity (−∞).
 370     #[stable(feature = "assoc_int_consts", since = "1.43.0")]
 371     pub const NEG_INFINITY: f64 = -1.0_f64 / 0.0_f64;
 372
 373     /// Returns `true` if this value is `NaN`.
 374     ///
 375     /// ```
 376     /// let nan = f64::NAN;
 377     /// let f = 7.0_f64;
 378     ///
 379     /// assert!(nan.is_nan());
 380     /// assert!(!f.is_nan());
 381     /// ```
 382     #[stable(feature = "rust1", since = "1.0.0")]
 383     #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
 384     #[inline]
 385     pub const fn is_nan(self) -> bool {
 386         self != self
 387     }
 388
 389     // FIXME(#50145): `abs` is publicly unavailable in libcore due to
 390     // concerns about portability, so this implementation is for
 391     // private use internally.
 392     #[inline]
 393     #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
 394     const fn abs_private(self) -> f64 {
 395         f64::from_bits(self.to_bits() & 0x7fff_ffff_ffff_ffff)
 396     }
 397
 398     /// Returns `true` if this value is positive infinity or negative infinity, and
 399     /// `false` otherwise.
 400     ///
 401     /// ```
 402     /// let f = 7.0f64;
 403     /// let inf = f64::INFINITY;
 404     /// let neg_inf = f64::NEG_INFINITY;
 405     /// let nan = f64::NAN;
 406     ///
 407     /// assert!(!f.is_infinite());
 408     /// assert!(!nan.is_infinite());
 409     ///
 410     /// assert!(inf.is_infinite());
 411     /// assert!(neg_inf.is_infinite());
 412     /// ```
 413     #[stable(feature = "rust1", since = "1.0.0")]
 414     #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
 415     #[inline]
 416     pub const fn is_infinite(self) -> bool {
 417         self.abs_private() == Self::INFINITY
 418     }
 419
 420     /// Returns `true` if this number is neither infinite nor `NaN`.
 421     ///
 422     /// ```
 423     /// let f = 7.0f64;
 424     /// let inf: f64 = f64::INFINITY;
 425     /// let neg_inf: f64 = f64::NEG_INFINITY;
 426     /// let nan: f64 = f64::NAN;
 427     ///
 428     /// assert!(f.is_finite());
 429     ///
 430     /// assert!(!nan.is_finite());
 431     /// assert!(!inf.is_finite());
 432     /// assert!(!neg_inf.is_finite());
 433     /// ```
 434     #[stable(feature = "rust1", since = "1.0.0")]
 435     #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
 436     #[inline]
 437     pub const fn is_finite(self) -> bool {
 438         // There's no need to handle NaN separately: if self is NaN,
 439         // the comparison is not true, exactly as desired.
 440         self.abs_private() < Self::INFINITY
 441     }
 442
 443     /// Returns `true` if the number is neither zero, infinite,
 444     /// [subnormal], or `NaN`.
 445     ///
 446     /// ```
 447     /// let min = f64::MIN_POSITIVE; // 2.2250738585072014e-308f64
 448     /// let max = f64::MAX;
 449     /// let lower_than_min = 1.0e-308_f64;
 450     /// let zero = 0.0f64;
 451     ///
 452     /// assert!(min.is_normal());
 453     /// assert!(max.is_normal());
 454     ///
 455     /// assert!(!zero.is_normal());
 456     /// assert!(!f64::NAN.is_normal());
 457     /// assert!(!f64::INFINITY.is_normal());
 458     /// // Values between `0` and `min` are Subnormal.
 459     /// assert!(!lower_than_min.is_normal());
 460     /// ```
 461     /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
 462     #[stable(feature = "rust1", since = "1.0.0")]
 463     #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
 464     #[inline]
 465     pub const fn is_normal(self) -> bool {
 466         matches!(self.classify(), FpCategory::Normal)
 467     }
 468
 469     /// Returns the floating point category of the number. If only one property
 470     /// is going to be tested, it is generally faster to use the specific
 471     /// predicate instead.
 472     ///
 473     /// ```
 474     /// use std::num::FpCategory;
 475     ///
 476     /// let num = 12.4_f64;
 477     /// let inf = f64::INFINITY;
 478     ///
 479     /// assert_eq!(num.classify(), FpCategory::Normal);
 480     /// assert_eq!(inf.classify(), FpCategory::Infinite);
 481     /// ```
 482     #[stable(feature = "rust1", since = "1.0.0")]
 483     #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
 484     pub const fn classify(self) -> FpCategory {
 485         const EXP_MASK: u64 = 0x7ff0000000000000;
 486         const MAN_MASK: u64 = 0x000fffffffffffff;
 487
 488         let bits = self.to_bits();
 489         match (bits & MAN_MASK, bits & EXP_MASK) {
 490             (0, 0) => FpCategory::Zero,
 491             (_, 0) => FpCategory::Subnormal,
 492             (0, EXP_MASK) => FpCategory::Infinite,
 493             (_, EXP_MASK) => FpCategory::Nan,
 494             _ => FpCategory::Normal,
 495         }
 496     }
 497
 498     /// Returns `true` if `self` has a positive sign, including `+0.0`, `NaN`s with
 499     /// positive sign bit and positive infinity.
 500     ///
 501     /// ```
 502     /// let f = 7.0_f64;
 503     /// let g = -7.0_f64;
 504     ///
 505     /// assert!(f.is_sign_positive());
 506     /// assert!(!g.is_sign_positive());
 507     /// ```
 508     #[stable(feature = "rust1", since = "1.0.0")]
 509     #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
 510     #[inline]
 511     pub const fn is_sign_positive(self) -> bool {
 512         !self.is_sign_negative()
 513     }
 514
 515     #[stable(feature = "rust1", since = "1.0.0")]
 516     #[rustc_deprecated(since = "1.0.0", reason = "renamed to is_sign_positive")]
 517     #[inline]
 518     #[doc(hidden)]
 519     pub fn is_positive(self) -> bool {
 520         self.is_sign_positive()
 521     }
 522
 523     /// Returns `true` if `self` has a negative sign, including `-0.0`, `NaN`s with
 524     /// negative sign bit and negative infinity.
 525     ///
 526     /// ```
 527     /// let f = 7.0_f64;
 528     /// let g = -7.0_f64;
 529     ///
 530     /// assert!(!f.is_sign_negative());
 531     /// assert!(g.is_sign_negative());
 532     /// ```
 533     #[stable(feature = "rust1", since = "1.0.0")]
 534     #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
 535     #[inline]
 536     pub const fn is_sign_negative(self) -> bool {
 537         self.to_bits() & 0x8000_0000_0000_0000 != 0
 538     }
 539
 540     #[stable(feature = "rust1", since = "1.0.0")]
 541     #[rustc_deprecated(since = "1.0.0", reason = "renamed to is_sign_negative")]
 542     #[inline]
 543     #[doc(hidden)]
 544     pub fn is_negative(self) -> bool {
 545         self.is_sign_negative()
 546     }
 547
 548     /// Takes the reciprocal (inverse) of a number, `1/x`.
 549     ///
 550     /// ```
 551     /// let x = 2.0_f64;
 552     /// let abs_difference = (x.recip() - (1.0 / x)).abs();
 553     ///
 554     /// assert!(abs_difference < 1e-10);
 555     /// ```
 556     #[stable(feature = "rust1", since = "1.0.0")]
 557     #[inline]
 558     pub fn recip(self) -> f64 {
 559         1.0 / self
 560     }
 561
 562     /// Converts radians to degrees.
 563     ///
 564     /// ```
 565     /// let angle = std::f64::consts::PI;
 566     ///
 567     /// let abs_difference = (angle.to_degrees() - 180.0).abs();
 568     ///
 569     /// assert!(abs_difference < 1e-10);
 570     /// ```
 571     #[stable(feature = "rust1", since = "1.0.0")]
 572     #[inline]
 573     pub fn to_degrees(self) -> f64 {
 574         // The division here is correctly rounded with respect to the true
 575         // value of 180/π. (This differs from f32, where a constant must be
 576         // used to ensure a correctly rounded result.)
 577         self * (180.0f64 / consts::PI)
 578     }
 579
 580     /// Converts degrees to radians.
 581     ///
 582     /// ```
 583     /// let angle = 180.0_f64;
 584     ///
 585     /// let abs_difference = (angle.to_radians() - std::f64::consts::PI).abs();
 586     ///
 587     /// assert!(abs_difference < 1e-10);
 588     /// ```
 589     #[stable(feature = "rust1", since = "1.0.0")]
 590     #[inline]
 591     pub fn to_radians(self) -> f64 {
 592         let value: f64 = consts::PI;
 593         self * (value / 180.0)
 594     }
 595
 596     /// Returns the maximum of the two numbers.
 597     ///
 598     /// ```
 599     /// let x = 1.0_f64;
 600     /// let y = 2.0_f64;
 601     ///
 602     /// assert_eq!(x.max(y), y);
 603     /// ```
 604     ///
 605     /// If one of the arguments is NaN, then the other argument is returned.
 606     #[stable(feature = "rust1", since = "1.0.0")]
 607     #[inline]
 608     pub fn max(self, other: f64) -> f64 {
 609         intrinsics::maxnumf64(self, other)
 610     }
 611
 612     /// Returns the minimum of the two numbers.
 613     ///
 614     /// ```
 615     /// let x = 1.0_f64;
 616     /// let y = 2.0_f64;
 617     ///
 618     /// assert_eq!(x.min(y), x);
 619     /// ```
 620     ///
 621     /// If one of the arguments is NaN, then the other argument is returned.
 622     #[stable(feature = "rust1", since = "1.0.0")]
 623     #[inline]
 624     pub fn min(self, other: f64) -> f64 {
 625         intrinsics::minnumf64(self, other)
 626     }
 627
 628     /// Rounds toward zero and converts to any primitive integer type,
 629     /// assuming that the value is finite and fits in that type.
 630     ///
 631     /// ```
 632     /// let value = 4.6_f64;
 633     /// let rounded = unsafe { value.to_int_unchecked::<u16>() };
 634     /// assert_eq!(rounded, 4);
 635     ///
 636     /// let value = -128.9_f64;
 637     /// let rounded = unsafe { value.to_int_unchecked::<i8>() };
 638     /// assert_eq!(rounded, i8::MIN);
 639     /// ```
 640     ///
 641     /// # Safety
 642     ///
 643     /// The value must:
 644     ///
 645     /// * Not be `NaN`
 646     /// * Not be infinite
 647     /// * Be representable in the return type `Int`, after truncating off its fractional part
 648     #[stable(feature = "float_approx_unchecked_to", since = "1.44.0")]
 649     #[inline]
 650     pub unsafe fn to_int_unchecked<Int>(self) -> Int
 651     where
 652         Self: FloatToInt<Int>,
 653     {
 654         // SAFETY: the caller must uphold the safety contract for
 655         // `FloatToInt::to_int_unchecked`.
 656         unsafe { FloatToInt::<Int>::to_int_unchecked(self) }
 657     }
 658
 659     /// Raw transmutation to `u64`.
 660     ///
 661     /// This is currently identical to `transmute::<f64, u64>(self)` on all platforms.
 662     ///
 663     /// See `from_bits` for some discussion of the portability of this operation
 664     /// (there are almost no issues).
 665     ///
 666     /// Note that this function is distinct from `as` casting, which attempts to
 667     /// preserve the *numeric* value, and not the bitwise value.
 668     ///
 669     /// # Examples
 670     ///
 671     /// ```
 672     /// assert!((1f64).to_bits() != 1f64 as u64); // to_bits() is not casting!
 673     /// assert_eq!((12.5f64).to_bits(), 0x4029000000000000);
 674     ///
 675     /// ```
 676     #[stable(feature = "float_bits_conv", since = "1.20.0")]
 677     #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
 678     #[inline]
 679     pub const fn to_bits(self) -> u64 {
 680         // SAFETY: `u64` is a plain old datatype so we can always transmute to it
 681         unsafe { mem::transmute(self) }
 682     }
 683
 684     /// Raw transmutation from `u64`.
 685     ///
 686     /// This is currently identical to `transmute::<u64, f64>(v)` on all platforms.
 687     /// It turns out this is incredibly portable, for two reasons:
 688     ///
 689     /// * Floats and Ints have the same endianness on all supported platforms.
 690     /// * IEEE-754 very precisely specifies the bit layout of floats.
 691     ///
 692     /// However there is one caveat: prior to the 2008 version of IEEE-754, how
 693     /// to interpret the NaN signaling bit wasn't actually specified. Most platforms
 694     /// (notably x86 and ARM) picked the interpretation that was ultimately
 695     /// standardized in 2008, but some didn't (notably MIPS). As a result, all
 696     /// signaling NaNs on MIPS are quiet NaNs on x86, and vice-versa.
 697     ///
 698     /// Rather than trying to preserve signaling-ness cross-platform, this
 699     /// implementation favors preserving the exact bits. This means that
 700     /// any payloads encoded in NaNs will be preserved even if the result of
 701     /// this method is sent over the network from an x86 machine to a MIPS one.
 702     ///
 703     /// If the results of this method are only manipulated by the same
 704     /// architecture that produced them, then there is no portability concern.
 705     ///
 706     /// If the input isn't NaN, then there is no portability concern.
 707     ///
 708     /// If you don't care about signaling-ness (very likely), then there is no
 709     /// portability concern.
 710     ///
 711     /// Note that this function is distinct from `as` casting, which attempts to
 712     /// preserve the *numeric* value, and not the bitwise value.
 713     ///
 714     /// # Examples
 715     ///
 716     /// ```
 717     /// let v = f64::from_bits(0x4029000000000000);
 718     /// assert_eq!(v, 12.5);
 719     /// ```
 720     #[stable(feature = "float_bits_conv", since = "1.20.0")]
 721     #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
 722     #[inline]
 723     pub const fn from_bits(v: u64) -> Self {
 724         // SAFETY: `u64` is a plain old datatype so we can always transmute from it
 725         // It turns out the safety issues with sNaN were overblown! Hooray!
 726         unsafe { mem::transmute(v) }
 727     }
 728
 729     /// Return the memory representation of this floating point number as a byte array in
 730     /// big-endian (network) byte order.
 731     ///
 732     /// # Examples
 733     ///
 734     /// ```
 735     /// let bytes = 12.5f64.to_be_bytes();
 736     /// assert_eq!(bytes, [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]);
 737     /// ```
 738     #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
 739     #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
 740     #[inline]
 741     pub const fn to_be_bytes(self) -> [u8; 8] {
 742         self.to_bits().to_be_bytes()
 743     }
 744
 745     /// Return the memory representation of this floating point number as a byte array in
 746     /// little-endian byte order.
 747     ///
 748     /// # Examples
 749     ///
 750     /// ```
 751     /// let bytes = 12.5f64.to_le_bytes();
 752     /// assert_eq!(bytes, [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]);
 753     /// ```
 754     #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
 755     #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
 756     #[inline]
 757     pub const fn to_le_bytes(self) -> [u8; 8] {
 758         self.to_bits().to_le_bytes()
 759     }
 760
 761     /// Return the memory representation of this floating point number as a byte array in
 762     /// native byte order.
 763     ///
 764     /// As the target platform's native endianness is used, portable code
 765     /// should use [`to_be_bytes`] or [`to_le_bytes`], as appropriate, instead.
 766     ///
 767     /// [`to_be_bytes`]: #method.to_be_bytes
 768     /// [`to_le_bytes`]: #method.to_le_bytes
 769     ///
 770     /// # Examples
 771     ///
 772     /// ```
 773     /// let bytes = 12.5f64.to_ne_bytes();
 774     /// assert_eq!(
 775     ///     bytes,
 776     ///     if cfg!(target_endian = "big") {
 777     ///         [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
 778     ///     } else {
 779     ///         [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]
 780     ///     }
 781     /// );
 782     /// ```
 783     #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
 784     #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
 785     #[inline]
 786     pub const fn to_ne_bytes(self) -> [u8; 8] {
 787         self.to_bits().to_ne_bytes()
 788     }
 789
 790     /// Create a floating point value from its representation as a byte array in big endian.
 791     ///
 792     /// # Examples
 793     ///
 794     /// ```
 795     /// let value = f64::from_be_bytes([0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]);
 796     /// assert_eq!(value, 12.5);
 797     /// ```
 798     #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
 799     #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
 800     #[inline]
 801     pub const fn from_be_bytes(bytes: [u8; 8]) -> Self {
 802         Self::from_bits(u64::from_be_bytes(bytes))
 803     }
 804
 805     /// Create a floating point value from its representation as a byte array in little endian.
 806     ///
 807     /// # Examples
 808     ///
 809     /// ```
 810     /// let value = f64::from_le_bytes([0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]);
 811     /// assert_eq!(value, 12.5);
 812     /// ```
 813     #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
 814     #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
 815     #[inline]
 816     pub const fn from_le_bytes(bytes: [u8; 8]) -> Self {
 817         Self::from_bits(u64::from_le_bytes(bytes))
 818     }
 819
 820     /// Create a floating point value from its representation as a byte array in native endian.
 821     ///
 822     /// As the target platform's native endianness is used, portable code
 823     /// likely wants to use [`from_be_bytes`] or [`from_le_bytes`], as
 824     /// appropriate instead.
 825     ///
 826     /// [`from_be_bytes`]: #method.from_be_bytes
 827     /// [`from_le_bytes`]: #method.from_le_bytes
 828     ///
 829     /// # Examples
 830     ///
 831     /// ```
 832     /// let value = f64::from_ne_bytes(if cfg!(target_endian = "big") {
 833     ///     [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
 834     /// } else {
 835     ///     [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]
 836     /// });
 837     /// assert_eq!(value, 12.5);
 838     /// ```
 839     #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
 840     #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
 841     #[inline]
 842     pub const fn from_ne_bytes(bytes: [u8; 8]) -> Self {
 843         Self::from_bits(u64::from_ne_bytes(bytes))
 844     }
 845
 846     /// Returns an ordering between self and other values.
 847     /// Unlike the standard partial comparison between floating point numbers,
 848     /// this comparison always produces an ordering in accordance to
 849     /// the totalOrder predicate as defined in IEEE 754 (2008 revision)
 850     /// floating point standard. The values are ordered in following order:
 851     /// - Negative quiet NaN
 852     /// - Negative signaling NaN
 853     /// - Negative infinity
 854     /// - Negative numbers
 855     /// - Negative subnormal numbers
 856     /// - Negative zero
 857     /// - Positive zero
 858     /// - Positive subnormal numbers
 859     /// - Positive numbers
 860     /// - Positive infinity
 861     /// - Positive signaling NaN
 862     /// - Positive quiet NaN
 863     ///
 864     /// # Example
 865     /// ```
 866     /// #![feature(total_cmp)]
 867     /// struct GoodBoy {
 868     ///     name: String,
 869     ///     weight: f64,
 870     /// }
 871     ///
 872     /// let mut bois = vec![
 873     ///     GoodBoy { name: "Pucci".to_owned(), weight: 0.1 },
 874     ///     GoodBoy { name: "Woofer".to_owned(), weight: 99.0 },
 875     ///     GoodBoy { name: "Yapper".to_owned(), weight: 10.0 },
 876     ///     GoodBoy { name: "Chonk".to_owned(), weight: f64::INFINITY },
 877     ///     GoodBoy { name: "Abs. Unit".to_owned(), weight: f64::NAN },
 878     ///     GoodBoy { name: "Floaty".to_owned(), weight: -5.0 },
 879     /// ];
 880     ///
 881     /// bois.sort_by(|a, b| a.weight.total_cmp(&b.weight));
 882     /// # assert!(bois.into_iter().map(|b| b.weight)
 883     /// #     .zip([-5.0, 0.1, 10.0, 99.0, f64::INFINITY, f64::NAN].iter())
 884     /// #     .all(|(a, b)| a.to_bits() == b.to_bits()))
 885     /// ```
 886     #[unstable(feature = "total_cmp", issue = "72599")]
 887     #[inline]
 888     pub fn total_cmp(&self, other: &Self) -> crate::cmp::Ordering {
 889         let mut left = self.to_bits() as i64;
 890         let mut right = other.to_bits() as i64;
 891
 892         // In case of negatives, flip all the bits except the sign
 893         // to achieve a similar layout as two's complement integers
 894         //
 895         // Why does this work? IEEE 754 floats consist of three fields:
 896         // Sign bit, exponent and mantissa. The set of exponent and mantissa
 897         // fields as a whole have the property that their bitwise order is
 898         // equal to the numeric magnitude where the magnitude is defined.
 899         // The magnitude is not normally defined on NaN values, but
 900         // IEEE 754 totalOrder defines the NaN values also to follow the
 901         // bitwise order. This leads to order explained in the doc comment.
 902         // However, the representation of magnitude is the same for negative
 903         // and positive numbers – only the sign bit is different.
 904         // To easily compare the floats as signed integers, we need to
 905         // flip the exponent and mantissa bits in case of negative numbers.
 906         // We effectively convert the numbers to "two's complement" form.
 907         //
 908         // To do the flipping, we construct a mask and XOR against it.
 909         // We branchlessly calculate an "all-ones except for the sign bit"
 910         // mask from negative-signed values: right shifting sign-extends
 911         // the integer, so we "fill" the mask with sign bits, and then
 912         // convert to unsigned to push one more zero bit.
 913         // On positive values, the mask is all zeros, so it's a no-op.
 914         left ^= (((left >> 63) as u64) >> 1) as i64;
 915         right ^= (((right >> 63) as u64) >> 1) as i64;
 916
 917         left.cmp(&right)
 918     }
 919 }