src/libstd/num/f64.rs

   1 // Copyright 2012-2015 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 //! The 64-bit floating point type.
  12 //!
  13 //! *[See also the `f64` primitive type](../primitive.f64.html).*
  14
  15 #![stable(feature = "rust1", since = "1.0.0")]
  16 #![allow(missing_docs)]
  17
  18 #[cfg(not(test))]
  19 use core::num;
  20 #[cfg(not(test))]
  21 use intrinsics;
  22 #[cfg(not(test))]
  23 use libc::c_int;
  24 #[cfg(not(test))]
  25 use num::FpCategory;
  26
  27 #[stable(feature = "rust1", since = "1.0.0")]
  28 pub use core::f64::{RADIX, MANTISSA_DIGITS, DIGITS, EPSILON};
  29 #[stable(feature = "rust1", since = "1.0.0")]
  30 pub use core::f64::{MIN_EXP, MAX_EXP, MIN_10_EXP};
  31 #[stable(feature = "rust1", since = "1.0.0")]
  32 pub use core::f64::{MAX_10_EXP, NAN, INFINITY, NEG_INFINITY};
  33 #[stable(feature = "rust1", since = "1.0.0")]
  34 pub use core::f64::{MIN, MIN_POSITIVE, MAX};
  35 #[stable(feature = "rust1", since = "1.0.0")]
  36 pub use core::f64::consts;
  37
  38 #[allow(dead_code)]
  39 mod cmath {
  40     use libc::{c_double, c_int};
  41
  42     #[link_name = "m"]
  43     extern {
  44         pub fn acos(n: c_double) -> c_double;
  45         pub fn asin(n: c_double) -> c_double;
  46         pub fn atan(n: c_double) -> c_double;
  47         pub fn atan2(a: c_double, b: c_double) -> c_double;
  48         pub fn cbrt(n: c_double) -> c_double;
  49         pub fn cosh(n: c_double) -> c_double;
  50         pub fn erf(n: c_double) -> c_double;
  51         pub fn erfc(n: c_double) -> c_double;
  52         pub fn expm1(n: c_double) -> c_double;
  53         pub fn fdim(a: c_double, b: c_double) -> c_double;
  54         pub fn fmax(a: c_double, b: c_double) -> c_double;
  55         pub fn fmin(a: c_double, b: c_double) -> c_double;
  56         pub fn fmod(a: c_double, b: c_double) -> c_double;
  57         pub fn frexp(n: c_double, value: &mut c_int) -> c_double;
  58         pub fn ilogb(n: c_double) -> c_int;
  59         pub fn ldexp(x: c_double, n: c_int) -> c_double;
  60         pub fn logb(n: c_double) -> c_double;
  61         pub fn log1p(n: c_double) -> c_double;
  62         pub fn nextafter(x: c_double, y: c_double) -> c_double;
  63         pub fn modf(n: c_double, iptr: &mut c_double) -> c_double;
  64         pub fn sinh(n: c_double) -> c_double;
  65         pub fn tan(n: c_double) -> c_double;
  66         pub fn tanh(n: c_double) -> c_double;
  67         pub fn tgamma(n: c_double) -> c_double;
  68
  69         // These are commonly only available for doubles
  70
  71         pub fn j0(n: c_double) -> c_double;
  72         pub fn j1(n: c_double) -> c_double;
  73         pub fn jn(i: c_int, n: c_double) -> c_double;
  74
  75         pub fn y0(n: c_double) -> c_double;
  76         pub fn y1(n: c_double) -> c_double;
  77         pub fn yn(i: c_int, n: c_double) -> c_double;
  78
  79         #[cfg_attr(all(windows, target_env = "msvc"), link_name = "__lgamma_r")]
  80         pub fn lgamma_r(n: c_double, sign: &mut c_int) -> c_double;
  81
  82         #[cfg_attr(all(windows, target_env = "msvc"), link_name = "_hypot")]
  83         pub fn hypot(x: c_double, y: c_double) -> c_double;
  84     }
  85 }
  86
  87 #[cfg(not(test))]
  88 #[lang = "f64"]
  89 impl f64 {
  90     /// Returns `true` if this value is `NaN` and false otherwise.
  91     ///
  92     /// ```
  93     /// use std::f64;
  94     ///
  95     /// let nan = f64::NAN;
  96     /// let f = 7.0_f64;
  97     ///
  98     /// assert!(nan.is_nan());
  99     /// assert!(!f.is_nan());
 100     /// ```
 101     #[stable(feature = "rust1", since = "1.0.0")]
 102     #[inline]
 103     pub fn is_nan(self) -> bool { num::Float::is_nan(self) }
 104
 105     /// Returns `true` if this value is positive infinity or negative infinity and
 106     /// false otherwise.
 107     ///
 108     /// ```
 109     /// use std::f64;
 110     ///
 111     /// let f = 7.0f64;
 112     /// let inf = f64::INFINITY;
 113     /// let neg_inf = f64::NEG_INFINITY;
 114     /// let nan = f64::NAN;
 115     ///
 116     /// assert!(!f.is_infinite());
 117     /// assert!(!nan.is_infinite());
 118     ///
 119     /// assert!(inf.is_infinite());
 120     /// assert!(neg_inf.is_infinite());
 121     /// ```
 122     #[stable(feature = "rust1", since = "1.0.0")]
 123     #[inline]
 124     pub fn is_infinite(self) -> bool { num::Float::is_infinite(self) }
 125
 126     /// Returns `true` if this number is neither infinite nor `NaN`.
 127     ///
 128     /// ```
 129     /// use std::f64;
 130     ///
 131     /// let f = 7.0f64;
 132     /// let inf: f64 = f64::INFINITY;
 133     /// let neg_inf: f64 = f64::NEG_INFINITY;
 134     /// let nan: f64 = f64::NAN;
 135     ///
 136     /// assert!(f.is_finite());
 137     ///
 138     /// assert!(!nan.is_finite());
 139     /// assert!(!inf.is_finite());
 140     /// assert!(!neg_inf.is_finite());
 141     /// ```
 142     #[stable(feature = "rust1", since = "1.0.0")]
 143     #[inline]
 144     pub fn is_finite(self) -> bool { num::Float::is_finite(self) }
 145
 146     /// Returns `true` if the number is neither zero, infinite,
 147     /// [subnormal][subnormal], or `NaN`.
 148     ///
 149     /// ```
 150     /// use std::f32;
 151     ///
 152     /// let min = f32::MIN_POSITIVE; // 1.17549435e-38f64
 153     /// let max = f32::MAX;
 154     /// let lower_than_min = 1.0e-40_f32;
 155     /// let zero = 0.0f32;
 156     ///
 157     /// assert!(min.is_normal());
 158     /// assert!(max.is_normal());
 159     ///
 160     /// assert!(!zero.is_normal());
 161     /// assert!(!f32::NAN.is_normal());
 162     /// assert!(!f32::INFINITY.is_normal());
 163     /// // Values between `0` and `min` are Subnormal.
 164     /// assert!(!lower_than_min.is_normal());
 165     /// ```
 166     /// [subnormal]: http://en.wikipedia.org/wiki/Denormal_number
 167     #[stable(feature = "rust1", since = "1.0.0")]
 168     #[inline]
 169     pub fn is_normal(self) -> bool { num::Float::is_normal(self) }
 170
 171     /// Returns the floating point category of the number. If only one property
 172     /// is going to be tested, it is generally faster to use the specific
 173     /// predicate instead.
 174     ///
 175     /// ```
 176     /// use std::num::FpCategory;
 177     /// use std::f64;
 178     ///
 179     /// let num = 12.4_f64;
 180     /// let inf = f64::INFINITY;
 181     ///
 182     /// assert_eq!(num.classify(), FpCategory::Normal);
 183     /// assert_eq!(inf.classify(), FpCategory::Infinite);
 184     /// ```
 185     #[stable(feature = "rust1", since = "1.0.0")]
 186     #[inline]
 187     pub fn classify(self) -> FpCategory { num::Float::classify(self) }
 188
 189     /// Returns the mantissa, base 2 exponent, and sign as integers, respectively.
 190     /// The original number can be recovered by `sign * mantissa * 2 ^ exponent`.
 191     /// The floating point encoding is documented in the [Reference][floating-point].
 192     ///
 193     /// ```
 194     /// #![feature(float_extras)]
 195     ///
 196     /// let num = 2.0f64;
 197     ///
 198     /// // (8388608, -22, 1)
 199     /// let (mantissa, exponent, sign) = num.integer_decode();
 200     /// let sign_f = sign as f64;
 201     /// let mantissa_f = mantissa as f64;
 202     /// let exponent_f = num.powf(exponent as f64);
 203     ///
 204     /// // 1 * 8388608 * 2^(-22) == 2
 205     /// let abs_difference = (sign_f * mantissa_f * exponent_f - num).abs();
 206     ///
 207     /// assert!(abs_difference < 1e-10);
 208     /// ```
 209     /// [floating-point]: ../reference.html#machine-types
 210     #[unstable(feature = "float_extras", reason = "signature is undecided",
 211                issue = "27752")]
 212     #[inline]
 213     pub fn integer_decode(self) -> (u64, i16, i8) { num::Float::integer_decode(self) }
 214
 215     /// Returns the largest integer less than or equal to a number.
 216     ///
 217     /// ```
 218     /// let f = 3.99_f64;
 219     /// let g = 3.0_f64;
 220     ///
 221     /// assert_eq!(f.floor(), 3.0);
 222     /// assert_eq!(g.floor(), 3.0);
 223     /// ```
 224     #[stable(feature = "rust1", since = "1.0.0")]
 225     #[inline]
 226     pub fn floor(self) -> f64 {
 227         unsafe { intrinsics::floorf64(self) }
 228     }
 229
 230     /// Returns the smallest integer greater than or equal to a number.
 231     ///
 232     /// ```
 233     /// let f = 3.01_f64;
 234     /// let g = 4.0_f64;
 235     ///
 236     /// assert_eq!(f.ceil(), 4.0);
 237     /// assert_eq!(g.ceil(), 4.0);
 238     /// ```
 239     #[stable(feature = "rust1", since = "1.0.0")]
 240     #[inline]
 241     pub fn ceil(self) -> f64 {
 242         unsafe { intrinsics::ceilf64(self) }
 243     }
 244
 245     /// Returns the nearest integer to a number. Round half-way cases away from
 246     /// `0.0`.
 247     ///
 248     /// ```
 249     /// let f = 3.3_f64;
 250     /// let g = -3.3_f64;
 251     ///
 252     /// assert_eq!(f.round(), 3.0);
 253     /// assert_eq!(g.round(), -3.0);
 254     /// ```
 255     #[stable(feature = "rust1", since = "1.0.0")]
 256     #[inline]
 257     pub fn round(self) -> f64 {
 258         unsafe { intrinsics::roundf64(self) }
 259     }
 260
 261     /// Returns the integer part of a number.
 262     ///
 263     /// ```
 264     /// let f = 3.3_f64;
 265     /// let g = -3.7_f64;
 266     ///
 267     /// assert_eq!(f.trunc(), 3.0);
 268     /// assert_eq!(g.trunc(), -3.0);
 269     /// ```
 270     #[stable(feature = "rust1", since = "1.0.0")]
 271     #[inline]
 272     pub fn trunc(self) -> f64 {
 273         unsafe { intrinsics::truncf64(self) }
 274     }
 275
 276     /// Returns the fractional part of a number.
 277     ///
 278     /// ```
 279     /// let x = 3.5_f64;
 280     /// let y = -3.5_f64;
 281     /// let abs_difference_x = (x.fract() - 0.5).abs();
 282     /// let abs_difference_y = (y.fract() - (-0.5)).abs();
 283     ///
 284     /// assert!(abs_difference_x < 1e-10);
 285     /// assert!(abs_difference_y < 1e-10);
 286     /// ```
 287     #[stable(feature = "rust1", since = "1.0.0")]
 288     #[inline]
 289     pub fn fract(self) -> f64 { self - self.trunc() }
 290
 291     /// Computes the absolute value of `self`. Returns `NAN` if the
 292     /// number is `NAN`.
 293     ///
 294     /// ```
 295     /// use std::f64;
 296     ///
 297     /// let x = 3.5_f64;
 298     /// let y = -3.5_f64;
 299     ///
 300     /// let abs_difference_x = (x.abs() - x).abs();
 301     /// let abs_difference_y = (y.abs() - (-y)).abs();
 302     ///
 303     /// assert!(abs_difference_x < 1e-10);
 304     /// assert!(abs_difference_y < 1e-10);
 305     ///
 306     /// assert!(f64::NAN.abs().is_nan());
 307     /// ```
 308     #[stable(feature = "rust1", since = "1.0.0")]
 309     #[inline]
 310     pub fn abs(self) -> f64 { num::Float::abs(self) }
 311
 312     /// Returns a number that represents the sign of `self`.
 313     ///
 314     /// - `1.0` if the number is positive, `+0.0` or `INFINITY`
 315     /// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
 316     /// - `NAN` if the number is `NAN`
 317     ///
 318     /// ```
 319     /// use std::f64;
 320     ///
 321     /// let f = 3.5_f64;
 322     ///
 323     /// assert_eq!(f.signum(), 1.0);
 324     /// assert_eq!(f64::NEG_INFINITY.signum(), -1.0);
 325     ///
 326     /// assert!(f64::NAN.signum().is_nan());
 327     /// ```
 328     #[stable(feature = "rust1", since = "1.0.0")]
 329     #[inline]
 330     pub fn signum(self) -> f64 { num::Float::signum(self) }
 331
 332     /// Returns `true` if `self`'s sign bit is positive, including
 333     /// `+0.0` and `INFINITY`.
 334     ///
 335     /// ```
 336     /// use std::f64;
 337     ///
 338     /// let nan: f64 = f64::NAN;
 339     ///
 340     /// let f = 7.0_f64;
 341     /// let g = -7.0_f64;
 342     ///
 343     /// assert!(f.is_sign_positive());
 344     /// assert!(!g.is_sign_positive());
 345     /// // Requires both tests to determine if is `NaN`
 346     /// assert!(!nan.is_sign_positive() && !nan.is_sign_negative());
 347     /// ```
 348     #[stable(feature = "rust1", since = "1.0.0")]
 349     #[inline]
 350     pub fn is_sign_positive(self) -> bool { num::Float::is_sign_positive(self) }
 351
 352     #[stable(feature = "rust1", since = "1.0.0")]
 353     #[rustc_deprecated(since = "1.0.0", reason = "renamed to is_sign_positive")]
 354     #[inline]
 355     pub fn is_positive(self) -> bool { num::Float::is_sign_positive(self) }
 356
 357     /// Returns `true` if `self`'s sign is negative, including `-0.0`
 358     /// and `NEG_INFINITY`.
 359     ///
 360     /// ```
 361     /// use std::f64;
 362     ///
 363     /// let nan = f64::NAN;
 364     ///
 365     /// let f = 7.0_f64;
 366     /// let g = -7.0_f64;
 367     ///
 368     /// assert!(!f.is_sign_negative());
 369     /// assert!(g.is_sign_negative());
 370     /// // Requires both tests to determine if is `NaN`.
 371     /// assert!(!nan.is_sign_positive() && !nan.is_sign_negative());
 372     /// ```
 373     #[stable(feature = "rust1", since = "1.0.0")]
 374     #[inline]
 375     pub fn is_sign_negative(self) -> bool { num::Float::is_sign_negative(self) }
 376
 377     #[stable(feature = "rust1", since = "1.0.0")]
 378     #[rustc_deprecated(since = "1.0.0", reason = "renamed to is_sign_negative")]
 379     #[inline]
 380     pub fn is_negative(self) -> bool { num::Float::is_sign_negative(self) }
 381
 382     /// Fused multiply-add. Computes `(self * a) + b` with only one rounding
 383     /// error. This produces a more accurate result with better performance than
 384     /// a separate multiplication operation followed by an add.
 385     ///
 386     /// ```
 387     /// let m = 10.0_f64;
 388     /// let x = 4.0_f64;
 389     /// let b = 60.0_f64;
 390     ///
 391     /// // 100.0
 392     /// let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs();
 393     ///
 394     /// assert!(abs_difference < 1e-10);
 395     /// ```
 396     #[stable(feature = "rust1", since = "1.0.0")]
 397     #[inline]
 398     pub fn mul_add(self, a: f64, b: f64) -> f64 {
 399         unsafe { intrinsics::fmaf64(self, a, b) }
 400     }
 401
 402     /// Takes the reciprocal (inverse) of a number, `1/x`.
 403     ///
 404     /// ```
 405     /// let x = 2.0_f64;
 406     /// let abs_difference = (x.recip() - (1.0/x)).abs();
 407     ///
 408     /// assert!(abs_difference < 1e-10);
 409     /// ```
 410     #[stable(feature = "rust1", since = "1.0.0")]
 411     #[inline]
 412     pub fn recip(self) -> f64 { num::Float::recip(self) }
 413
 414     /// Raises a number to an integer power.
 415     ///
 416     /// Using this function is generally faster than using `powf`
 417     ///
 418     /// ```
 419     /// let x = 2.0_f64;
 420     /// let abs_difference = (x.powi(2) - x*x).abs();
 421     ///
 422     /// assert!(abs_difference < 1e-10);
 423     /// ```
 424     #[stable(feature = "rust1", since = "1.0.0")]
 425     #[inline]
 426     pub fn powi(self, n: i32) -> f64 { num::Float::powi(self, n) }
 427
 428     /// Raises a number to a floating point power.
 429     ///
 430     /// ```
 431     /// let x = 2.0_f64;
 432     /// let abs_difference = (x.powf(2.0) - x*x).abs();
 433     ///
 434     /// assert!(abs_difference < 1e-10);
 435     /// ```
 436     #[stable(feature = "rust1", since = "1.0.0")]
 437     #[inline]
 438     pub fn powf(self, n: f64) -> f64 {
 439         unsafe { intrinsics::powf64(self, n) }
 440     }
 441
 442     /// Takes the square root of a number.
 443     ///
 444     /// Returns NaN if `self` is a negative number.
 445     ///
 446     /// ```
 447     /// let positive = 4.0_f64;
 448     /// let negative = -4.0_f64;
 449     ///
 450     /// let abs_difference = (positive.sqrt() - 2.0).abs();
 451     ///
 452     /// assert!(abs_difference < 1e-10);
 453     /// assert!(negative.sqrt().is_nan());
 454     /// ```
 455     #[stable(feature = "rust1", since = "1.0.0")]
 456     #[inline]
 457     pub fn sqrt(self) -> f64 {
 458         if self < 0.0 {
 459             NAN
 460         } else {
 461             unsafe { intrinsics::sqrtf64(self) }
 462         }
 463     }
 464
 465     /// Returns `e^(self)`, (the exponential function).
 466     ///
 467     /// ```
 468     /// let one = 1.0_f64;
 469     /// // e^1
 470     /// let e = one.exp();
 471     ///
 472     /// // ln(e) - 1 == 0
 473     /// let abs_difference = (e.ln() - 1.0).abs();
 474     ///
 475     /// assert!(abs_difference < 1e-10);
 476     /// ```
 477     #[stable(feature = "rust1", since = "1.0.0")]
 478     #[inline]
 479     pub fn exp(self) -> f64 {
 480         unsafe { intrinsics::expf64(self) }
 481     }
 482
 483     /// Returns `2^(self)`.
 484     ///
 485     /// ```
 486     /// let f = 2.0_f64;
 487     ///
 488     /// // 2^2 - 4 == 0
 489     /// let abs_difference = (f.exp2() - 4.0).abs();
 490     ///
 491     /// assert!(abs_difference < 1e-10);
 492     /// ```
 493     #[stable(feature = "rust1", since = "1.0.0")]
 494     #[inline]
 495     pub fn exp2(self) -> f64 {
 496         unsafe { intrinsics::exp2f64(self) }
 497     }
 498
 499     /// Returns the natural logarithm of the number.
 500     ///
 501     /// ```
 502     /// let one = 1.0_f64;
 503     /// // e^1
 504     /// let e = one.exp();
 505     ///
 506     /// // ln(e) - 1 == 0
 507     /// let abs_difference = (e.ln() - 1.0).abs();
 508     ///
 509     /// assert!(abs_difference < 1e-10);
 510     /// ```
 511     #[stable(feature = "rust1", since = "1.0.0")]
 512     #[inline]
 513     pub fn ln(self) -> f64 {
 514         self.log_wrapper(|n| { unsafe { intrinsics::logf64(n) } })
 515     }
 516
 517     /// Returns the logarithm of the number with respect to an arbitrary base.
 518     ///
 519     /// ```
 520     /// let ten = 10.0_f64;
 521     /// let two = 2.0_f64;
 522     ///
 523     /// // log10(10) - 1 == 0
 524     /// let abs_difference_10 = (ten.log(10.0) - 1.0).abs();
 525     ///
 526     /// // log2(2) - 1 == 0
 527     /// let abs_difference_2 = (two.log(2.0) - 1.0).abs();
 528     ///
 529     /// assert!(abs_difference_10 < 1e-10);
 530     /// assert!(abs_difference_2 < 1e-10);
 531     /// ```
 532     #[stable(feature = "rust1", since = "1.0.0")]
 533     #[inline]
 534     pub fn log(self, base: f64) -> f64 { self.ln() / base.ln() }
 535
 536     /// Returns the base 2 logarithm of the number.
 537     ///
 538     /// ```
 539     /// let two = 2.0_f64;
 540     ///
 541     /// // log2(2) - 1 == 0
 542     /// let abs_difference = (two.log2() - 1.0).abs();
 543     ///
 544     /// assert!(abs_difference < 1e-10);
 545     /// ```
 546     #[stable(feature = "rust1", since = "1.0.0")]
 547     #[inline]
 548     pub fn log2(self) -> f64 {
 549         self.log_wrapper(|n| { unsafe { intrinsics::log2f64(n) } })
 550     }
 551
 552     /// Returns the base 10 logarithm of the number.
 553     ///
 554     /// ```
 555     /// let ten = 10.0_f64;
 556     ///
 557     /// // log10(10) - 1 == 0
 558     /// let abs_difference = (ten.log10() - 1.0).abs();
 559     ///
 560     /// assert!(abs_difference < 1e-10);
 561     /// ```
 562     #[stable(feature = "rust1", since = "1.0.0")]
 563     #[inline]
 564     pub fn log10(self) -> f64 {
 565         self.log_wrapper(|n| { unsafe { intrinsics::log10f64(n) } })
 566     }
 567
 568     /// Converts radians to degrees.
 569     ///
 570     /// ```
 571     /// use std::f64::consts;
 572     ///
 573     /// let angle = consts::PI;
 574     ///
 575     /// let abs_difference = (angle.to_degrees() - 180.0).abs();
 576     ///
 577     /// assert!(abs_difference < 1e-10);
 578     /// ```
 579     #[stable(feature = "rust1", since = "1.0.0")]
 580     #[inline]
 581     pub fn to_degrees(self) -> f64 { num::Float::to_degrees(self) }
 582
 583     /// Converts degrees to radians.
 584     ///
 585     /// ```
 586     /// use std::f64::consts;
 587     ///
 588     /// let angle = 180.0_f64;
 589     ///
 590     /// let abs_difference = (angle.to_radians() - consts::PI).abs();
 591     ///
 592     /// assert!(abs_difference < 1e-10);
 593     /// ```
 594     #[stable(feature = "rust1", since = "1.0.0")]
 595     #[inline]
 596     pub fn to_radians(self) -> f64 { num::Float::to_radians(self) }
 597
 598     /// Constructs a floating point number of `x*2^exp`.
 599     ///
 600     /// ```
 601     /// #![feature(float_extras)]
 602     ///
 603     /// // 3*2^2 - 12 == 0
 604     /// let abs_difference = (f64::ldexp(3.0, 2) - 12.0).abs();
 605     ///
 606     /// assert!(abs_difference < 1e-10);
 607     /// ```
 608     #[unstable(feature = "float_extras",
 609                reason = "pending integer conventions",
 610                issue = "27752")]
 611     #[inline]
 612     pub fn ldexp(x: f64, exp: isize) -> f64 {
 613         unsafe { cmath::ldexp(x, exp as c_int) }
 614     }
 615
 616     /// Breaks the number into a normalized fraction and a base-2 exponent,
 617     /// satisfying:
 618     ///
 619     ///  * `self = x * 2^exp`
 620     ///  * `0.5 <= abs(x) < 1.0`
 621     ///
 622     /// ```
 623     /// #![feature(float_extras)]
 624     ///
 625     /// let x = 4.0_f64;
 626     ///
 627     /// // (1/2)*2^3 -> 1 * 8/2 -> 4.0
 628     /// let f = x.frexp();
 629     /// let abs_difference_0 = (f.0 - 0.5).abs();
 630     /// let abs_difference_1 = (f.1 as f64 - 3.0).abs();
 631     ///
 632     /// assert!(abs_difference_0 < 1e-10);
 633     /// assert!(abs_difference_1 < 1e-10);
 634     /// ```
 635     #[unstable(feature = "float_extras",
 636                reason = "pending integer conventions",
 637                issue = "27752")]
 638     #[inline]
 639     pub fn frexp(self) -> (f64, isize) {
 640         unsafe {
 641             let mut exp = 0;
 642             let x = cmath::frexp(self, &mut exp);
 643             (x, exp as isize)
 644         }
 645     }
 646
 647     /// Returns the next representable floating-point value in the direction of
 648     /// `other`.
 649     ///
 650     /// ```
 651     /// #![feature(float_extras)]
 652     ///
 653     /// let x = 1.0f32;
 654     ///
 655     /// let abs_diff = (x.next_after(2.0) - 1.00000011920928955078125_f32).abs();
 656     ///
 657     /// assert!(abs_diff < 1e-10);
 658     /// ```
 659     #[unstable(feature = "float_extras",
 660                reason = "unsure about its place in the world",
 661                issue = "27752")]
 662     #[inline]
 663     pub fn next_after(self, other: f64) -> f64 {
 664         unsafe { cmath::nextafter(self, other) }
 665     }
 666
 667     /// Returns the maximum of the two numbers.
 668     ///
 669     /// ```
 670     /// let x = 1.0_f64;
 671     /// let y = 2.0_f64;
 672     ///
 673     /// assert_eq!(x.max(y), y);
 674     /// ```
 675     ///
 676     /// If one of the arguments is NaN, then the other argument is returned.
 677     #[stable(feature = "rust1", since = "1.0.0")]
 678     #[inline]
 679     pub fn max(self, other: f64) -> f64 {
 680         unsafe { cmath::fmax(self, other) }
 681     }
 682
 683     /// Returns the minimum of the two numbers.
 684     ///
 685     /// ```
 686     /// let x = 1.0_f64;
 687     /// let y = 2.0_f64;
 688     ///
 689     /// assert_eq!(x.min(y), x);
 690     /// ```
 691     ///
 692     /// If one of the arguments is NaN, then the other argument is returned.
 693     #[stable(feature = "rust1", since = "1.0.0")]
 694     #[inline]
 695     pub fn min(self, other: f64) -> f64 {
 696         unsafe { cmath::fmin(self, other) }
 697     }
 698
 699     /// The positive difference of two numbers.
 700     ///
 701     /// * If `self <= other`: `0:0`
 702     /// * Else: `self - other`
 703     ///
 704     /// ```
 705     /// let x = 3.0_f64;
 706     /// let y = -3.0_f64;
 707     ///
 708     /// let abs_difference_x = (x.abs_sub(1.0) - 2.0).abs();
 709     /// let abs_difference_y = (y.abs_sub(1.0) - 0.0).abs();
 710     ///
 711     /// assert!(abs_difference_x < 1e-10);
 712     /// assert!(abs_difference_y < 1e-10);
 713     /// ```
 714     #[stable(feature = "rust1", since = "1.0.0")]
 715     #[inline]
 716     pub fn abs_sub(self, other: f64) -> f64 {
 717         unsafe { cmath::fdim(self, other) }
 718     }
 719
 720     /// Takes the cubic root of a number.
 721     ///
 722     /// ```
 723     /// let x = 8.0_f64;
 724     ///
 725     /// // x^(1/3) - 2 == 0
 726     /// let abs_difference = (x.cbrt() - 2.0).abs();
 727     ///
 728     /// assert!(abs_difference < 1e-10);
 729     /// ```
 730     #[stable(feature = "rust1", since = "1.0.0")]
 731     #[inline]
 732     pub fn cbrt(self) -> f64 {
 733         unsafe { cmath::cbrt(self) }
 734     }
 735
 736     /// Calculates the length of the hypotenuse of a right-angle triangle given
 737     /// legs of length `x` and `y`.
 738     ///
 739     /// ```
 740     /// let x = 2.0_f64;
 741     /// let y = 3.0_f64;
 742     ///
 743     /// // sqrt(x^2 + y^2)
 744     /// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();
 745     ///
 746     /// assert!(abs_difference < 1e-10);
 747     /// ```
 748     #[stable(feature = "rust1", since = "1.0.0")]
 749     #[inline]
 750     pub fn hypot(self, other: f64) -> f64 {
 751         unsafe { cmath::hypot(self, other) }
 752     }
 753
 754     /// Computes the sine of a number (in radians).
 755     ///
 756     /// ```
 757     /// use std::f64;
 758     ///
 759     /// let x = f64::consts::PI/2.0;
 760     ///
 761     /// let abs_difference = (x.sin() - 1.0).abs();
 762     ///
 763     /// assert!(abs_difference < 1e-10);
 764     /// ```
 765     #[stable(feature = "rust1", since = "1.0.0")]
 766     #[inline]
 767     pub fn sin(self) -> f64 {
 768         unsafe { intrinsics::sinf64(self) }
 769     }
 770
 771     /// Computes the cosine of a number (in radians).
 772     ///
 773     /// ```
 774     /// use std::f64;
 775     ///
 776     /// let x = 2.0*f64::consts::PI;
 777     ///
 778     /// let abs_difference = (x.cos() - 1.0).abs();
 779     ///
 780     /// assert!(abs_difference < 1e-10);
 781     /// ```
 782     #[stable(feature = "rust1", since = "1.0.0")]
 783     #[inline]
 784     pub fn cos(self) -> f64 {
 785         unsafe { intrinsics::cosf64(self) }
 786     }
 787
 788     /// Computes the tangent of a number (in radians).
 789     ///
 790     /// ```
 791     /// use std::f64;
 792     ///
 793     /// let x = f64::consts::PI/4.0;
 794     /// let abs_difference = (x.tan() - 1.0).abs();
 795     ///
 796     /// assert!(abs_difference < 1e-14);
 797     /// ```
 798     #[stable(feature = "rust1", since = "1.0.0")]
 799     #[inline]
 800     pub fn tan(self) -> f64 {
 801         unsafe { cmath::tan(self) }
 802     }
 803
 804     /// Computes the arcsine of a number. Return value is in radians in
 805     /// the range [-pi/2, pi/2] or NaN if the number is outside the range
 806     /// [-1, 1].
 807     ///
 808     /// ```
 809     /// use std::f64;
 810     ///
 811     /// let f = f64::consts::PI / 2.0;
 812     ///
 813     /// // asin(sin(pi/2))
 814     /// let abs_difference = (f.sin().asin() - f64::consts::PI / 2.0).abs();
 815     ///
 816     /// assert!(abs_difference < 1e-10);
 817     /// ```
 818     #[stable(feature = "rust1", since = "1.0.0")]
 819     #[inline]
 820     pub fn asin(self) -> f64 {
 821         unsafe { cmath::asin(self) }
 822     }
 823
 824     /// Computes the arccosine of a number. Return value is in radians in
 825     /// the range [0, pi] or NaN if the number is outside the range
 826     /// [-1, 1].
 827     ///
 828     /// ```
 829     /// use std::f64;
 830     ///
 831     /// let f = f64::consts::PI / 4.0;
 832     ///
 833     /// // acos(cos(pi/4))
 834     /// let abs_difference = (f.cos().acos() - f64::consts::PI / 4.0).abs();
 835     ///
 836     /// assert!(abs_difference < 1e-10);
 837     /// ```
 838     #[stable(feature = "rust1", since = "1.0.0")]
 839     #[inline]
 840     pub fn acos(self) -> f64 {
 841         unsafe { cmath::acos(self) }
 842     }
 843
 844     /// Computes the arctangent of a number. Return value is in radians in the
 845     /// range [-pi/2, pi/2];
 846     ///
 847     /// ```
 848     /// let f = 1.0_f64;
 849     ///
 850     /// // atan(tan(1))
 851     /// let abs_difference = (f.tan().atan() - 1.0).abs();
 852     ///
 853     /// assert!(abs_difference < 1e-10);
 854     /// ```
 855     #[stable(feature = "rust1", since = "1.0.0")]
 856     #[inline]
 857     pub fn atan(self) -> f64 {
 858         unsafe { cmath::atan(self) }
 859     }
 860
 861     /// Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`).
 862     ///
 863     /// * `x = 0`, `y = 0`: `0`
 864     /// * `x >= 0`: `arctan(y/x)` -> `[-pi/2, pi/2]`
 865     /// * `y >= 0`: `arctan(y/x) + pi` -> `(pi/2, pi]`
 866     /// * `y < 0`: `arctan(y/x) - pi` -> `(-pi, -pi/2)`
 867     ///
 868     /// ```
 869     /// use std::f64;
 870     ///
 871     /// let pi = f64::consts::PI;
 872     /// // All angles from horizontal right (+x)
 873     /// // 45 deg counter-clockwise
 874     /// let x1 = 3.0_f64;
 875     /// let y1 = -3.0_f64;
 876     ///
 877     /// // 135 deg clockwise
 878     /// let x2 = -3.0_f64;
 879     /// let y2 = 3.0_f64;
 880     ///
 881     /// let abs_difference_1 = (y1.atan2(x1) - (-pi/4.0)).abs();
 882     /// let abs_difference_2 = (y2.atan2(x2) - 3.0*pi/4.0).abs();
 883     ///
 884     /// assert!(abs_difference_1 < 1e-10);
 885     /// assert!(abs_difference_2 < 1e-10);
 886     /// ```
 887     #[stable(feature = "rust1", since = "1.0.0")]
 888     #[inline]
 889     pub fn atan2(self, other: f64) -> f64 {
 890         unsafe { cmath::atan2(self, other) }
 891     }
 892
 893     /// Simultaneously computes the sine and cosine of the number, `x`. Returns
 894     /// `(sin(x), cos(x))`.
 895     ///
 896     /// ```
 897     /// use std::f64;
 898     ///
 899     /// let x = f64::consts::PI/4.0;
 900     /// let f = x.sin_cos();
 901     ///
 902     /// let abs_difference_0 = (f.0 - x.sin()).abs();
 903     /// let abs_difference_1 = (f.1 - x.cos()).abs();
 904     ///
 905     /// assert!(abs_difference_0 < 1e-10);
 906     /// assert!(abs_difference_0 < 1e-10);
 907     /// ```
 908     #[stable(feature = "rust1", since = "1.0.0")]
 909     #[inline]
 910     pub fn sin_cos(self) -> (f64, f64) {
 911         (self.sin(), self.cos())
 912     }
 913
 914     /// Returns `e^(self) - 1` in a way that is accurate even if the
 915     /// number is close to zero.
 916     ///
 917     /// ```
 918     /// let x = 7.0_f64;
 919     ///
 920     /// // e^(ln(7)) - 1
 921     /// let abs_difference = (x.ln().exp_m1() - 6.0).abs();
 922     ///
 923     /// assert!(abs_difference < 1e-10);
 924     /// ```
 925     #[stable(feature = "rust1", since = "1.0.0")]
 926     #[inline]
 927     pub fn exp_m1(self) -> f64 {
 928         unsafe { cmath::expm1(self) }
 929     }
 930
 931     /// Returns `ln(1+n)` (natural logarithm) more accurately than if
 932     /// the operations were performed separately.
 933     ///
 934     /// ```
 935     /// use std::f64;
 936     ///
 937     /// let x = f64::consts::E - 1.0;
 938     ///
 939     /// // ln(1 + (e - 1)) == ln(e) == 1
 940     /// let abs_difference = (x.ln_1p() - 1.0).abs();
 941     ///
 942     /// assert!(abs_difference < 1e-10);
 943     /// ```
 944     #[stable(feature = "rust1", since = "1.0.0")]
 945     #[inline]
 946     pub fn ln_1p(self) -> f64 {
 947         unsafe { cmath::log1p(self) }
 948     }
 949
 950     /// Hyperbolic sine function.
 951     ///
 952     /// ```
 953     /// use std::f64;
 954     ///
 955     /// let e = f64::consts::E;
 956     /// let x = 1.0_f64;
 957     ///
 958     /// let f = x.sinh();
 959     /// // Solving sinh() at 1 gives `(e^2-1)/(2e)`
 960     /// let g = (e*e - 1.0)/(2.0*e);
 961     /// let abs_difference = (f - g).abs();
 962     ///
 963     /// assert!(abs_difference < 1e-10);
 964     /// ```
 965     #[stable(feature = "rust1", since = "1.0.0")]
 966     #[inline]
 967     pub fn sinh(self) -> f64 {
 968         unsafe { cmath::sinh(self) }
 969     }
 970
 971     /// Hyperbolic cosine function.
 972     ///
 973     /// ```
 974     /// use std::f64;
 975     ///
 976     /// let e = f64::consts::E;
 977     /// let x = 1.0_f64;
 978     /// let f = x.cosh();
 979     /// // Solving cosh() at 1 gives this result
 980     /// let g = (e*e + 1.0)/(2.0*e);
 981     /// let abs_difference = (f - g).abs();
 982     ///
 983     /// // Same result
 984     /// assert!(abs_difference < 1.0e-10);
 985     /// ```
 986     #[stable(feature = "rust1", since = "1.0.0")]
 987     #[inline]
 988     pub fn cosh(self) -> f64 {
 989         unsafe { cmath::cosh(self) }
 990     }
 991
 992     /// Hyperbolic tangent function.
 993     ///
 994     /// ```
 995     /// use std::f64;
 996     ///
 997     /// let e = f64::consts::E;
 998     /// let x = 1.0_f64;
 999     ///
1000     /// let f = x.tanh();
1001     /// // Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))`
1002     /// let g = (1.0 - e.powi(-2))/(1.0 + e.powi(-2));
1003     /// let abs_difference = (f - g).abs();
1004     ///
1005     /// assert!(abs_difference < 1.0e-10);
1006     /// ```
1007     #[stable(feature = "rust1", since = "1.0.0")]
1008     #[inline]
1009     pub fn tanh(self) -> f64 {
1010         unsafe { cmath::tanh(self) }
1011     }
1012
1013     /// Inverse hyperbolic sine function.
1014     ///
1015     /// ```
1016     /// let x = 1.0_f64;
1017     /// let f = x.sinh().asinh();
1018     ///
1019     /// let abs_difference = (f - x).abs();
1020     ///
1021     /// assert!(abs_difference < 1.0e-10);
1022     /// ```
1023     #[stable(feature = "rust1", since = "1.0.0")]
1024     #[inline]
1025     pub fn asinh(self) -> f64 {
1026         if self == NEG_INFINITY {
1027             NEG_INFINITY
1028         } else {
1029             (self + ((self * self) + 1.0).sqrt()).ln()
1030         }
1031     }
1032
1033     /// Inverse hyperbolic cosine function.
1034     ///
1035     /// ```
1036     /// let x = 1.0_f64;
1037     /// let f = x.cosh().acosh();
1038     ///
1039     /// let abs_difference = (f - x).abs();
1040     ///
1041     /// assert!(abs_difference < 1.0e-10);
1042     /// ```
1043     #[stable(feature = "rust1", since = "1.0.0")]
1044     #[inline]
1045     pub fn acosh(self) -> f64 {
1046         match self {
1047             x if x < 1.0 => NAN,
1048             x => (x + ((x * x) - 1.0).sqrt()).ln(),
1049         }
1050     }
1051
1052     /// Inverse hyperbolic tangent function.
1053     ///
1054     /// ```
1055     /// use std::f64;
1056     ///
1057     /// let e = f64::consts::E;
1058     /// let f = e.tanh().atanh();
1059     ///
1060     /// let abs_difference = (f - e).abs();
1061     ///
1062     /// assert!(abs_difference < 1.0e-10);
1063     /// ```
1064     #[stable(feature = "rust1", since = "1.0.0")]
1065     #[inline]
1066     pub fn atanh(self) -> f64 {
1067         0.5 * ((2.0 * self) / (1.0 - self)).ln_1p()
1068     }
1069
1070     // Solaris/Illumos requires a wrapper around log, log2, and log10 functions
1071     // because of their non-standard behavior (e.g. log(-n) returns -Inf instead
1072     // of expected NaN).
1073     fn log_wrapper<F: Fn(f64) -> f64>(self, log_fn: F) -> f64 {
1074         if !cfg!(target_os = "solaris") {
1075             log_fn(self)
1076         } else {
1077             if self.is_finite() {
1078                 if self > 0.0 {
1079                     log_fn(self)
1080                 } else if self == 0.0 {
1081                     NEG_INFINITY // log(0) = -Inf
1082                 } else {
1083                     NAN // log(-n) = NaN
1084                 }
1085             } else if self.is_nan() {
1086                 self // log(NaN) = NaN
1087             } else if self > 0.0 {
1088                 self // log(Inf) = Inf
1089             } else {
1090                 NAN // log(-Inf) = NaN
1091             }
1092         }
1093     }
1094 }
1095
1096 #[cfg(test)]
1097 mod tests {
1098     use f64;
1099     use f64::*;
1100     use num::*;
1101     use num::FpCategory as Fp;
1102
1103     #[test]
1104     fn test_num_f64() {
1105         test_num(10f64, 2f64);
1106     }
1107
1108     #[test]
1109     fn test_min_nan() {
1110         assert_eq!(NAN.min(2.0), 2.0);
1111         assert_eq!(2.0f64.min(NAN), 2.0);
1112     }
1113
1114     #[test]
1115     fn test_max_nan() {
1116         assert_eq!(NAN.max(2.0), 2.0);
1117         assert_eq!(2.0f64.max(NAN), 2.0);
1118     }
1119
1120     #[test]
1121     fn test_nan() {
1122         let nan: f64 = NAN;
1123         assert!(nan.is_nan());
1124         assert!(!nan.is_infinite());
1125         assert!(!nan.is_finite());
1126         assert!(!nan.is_normal());
1127         assert!(!nan.is_sign_positive());
1128         assert!(!nan.is_sign_negative());
1129         assert_eq!(Fp::Nan, nan.classify());
1130     }
1131
1132     #[test]
1133     fn test_infinity() {
1134         let inf: f64 = INFINITY;
1135         assert!(inf.is_infinite());
1136         assert!(!inf.is_finite());
1137         assert!(inf.is_sign_positive());
1138         assert!(!inf.is_sign_negative());
1139         assert!(!inf.is_nan());
1140         assert!(!inf.is_normal());
1141         assert_eq!(Fp::Infinite, inf.classify());
1142     }
1143
1144     #[test]
1145     fn test_neg_infinity() {
1146         let neg_inf: f64 = NEG_INFINITY;
1147         assert!(neg_inf.is_infinite());
1148         assert!(!neg_inf.is_finite());
1149         assert!(!neg_inf.is_sign_positive());
1150         assert!(neg_inf.is_sign_negative());
1151         assert!(!neg_inf.is_nan());
1152         assert!(!neg_inf.is_normal());
1153         assert_eq!(Fp::Infinite, neg_inf.classify());
1154     }
1155
1156     #[test]
1157     fn test_zero() {
1158         let zero: f64 = 0.0f64;
1159         assert_eq!(0.0, zero);
1160         assert!(!zero.is_infinite());
1161         assert!(zero.is_finite());
1162         assert!(zero.is_sign_positive());
1163         assert!(!zero.is_sign_negative());
1164         assert!(!zero.is_nan());
1165         assert!(!zero.is_normal());
1166         assert_eq!(Fp::Zero, zero.classify());
1167     }
1168
1169     #[test]
1170     fn test_neg_zero() {
1171         let neg_zero: f64 = -0.0;
1172         assert_eq!(0.0, neg_zero);
1173         assert!(!neg_zero.is_infinite());
1174         assert!(neg_zero.is_finite());
1175         assert!(!neg_zero.is_sign_positive());
1176         assert!(neg_zero.is_sign_negative());
1177         assert!(!neg_zero.is_nan());
1178         assert!(!neg_zero.is_normal());
1179         assert_eq!(Fp::Zero, neg_zero.classify());
1180     }
1181
1182     #[test]
1183     fn test_one() {
1184         let one: f64 = 1.0f64;
1185         assert_eq!(1.0, one);
1186         assert!(!one.is_infinite());
1187         assert!(one.is_finite());
1188         assert!(one.is_sign_positive());
1189         assert!(!one.is_sign_negative());
1190         assert!(!one.is_nan());
1191         assert!(one.is_normal());
1192         assert_eq!(Fp::Normal, one.classify());
1193     }
1194
1195     #[test]
1196     fn test_is_nan() {
1197         let nan: f64 = NAN;
1198         let inf: f64 = INFINITY;
1199         let neg_inf: f64 = NEG_INFINITY;
1200         assert!(nan.is_nan());
1201         assert!(!0.0f64.is_nan());
1202         assert!(!5.3f64.is_nan());
1203         assert!(!(-10.732f64).is_nan());
1204         assert!(!inf.is_nan());
1205         assert!(!neg_inf.is_nan());
1206     }
1207
1208     #[test]
1209     fn test_is_infinite() {
1210         let nan: f64 = NAN;
1211         let inf: f64 = INFINITY;
1212         let neg_inf: f64 = NEG_INFINITY;
1213         assert!(!nan.is_infinite());
1214         assert!(inf.is_infinite());
1215         assert!(neg_inf.is_infinite());
1216         assert!(!0.0f64.is_infinite());
1217         assert!(!42.8f64.is_infinite());
1218         assert!(!(-109.2f64).is_infinite());
1219     }
1220
1221     #[test]
1222     fn test_is_finite() {
1223         let nan: f64 = NAN;
1224         let inf: f64 = INFINITY;
1225         let neg_inf: f64 = NEG_INFINITY;
1226         assert!(!nan.is_finite());
1227         assert!(!inf.is_finite());
1228         assert!(!neg_inf.is_finite());
1229         assert!(0.0f64.is_finite());
1230         assert!(42.8f64.is_finite());
1231         assert!((-109.2f64).is_finite());
1232     }
1233
1234     #[test]
1235     fn test_is_normal() {
1236         let nan: f64 = NAN;
1237         let inf: f64 = INFINITY;
1238         let neg_inf: f64 = NEG_INFINITY;
1239         let zero: f64 = 0.0f64;
1240         let neg_zero: f64 = -0.0;
1241         assert!(!nan.is_normal());
1242         assert!(!inf.is_normal());
1243         assert!(!neg_inf.is_normal());
1244         assert!(!zero.is_normal());
1245         assert!(!neg_zero.is_normal());
1246         assert!(1f64.is_normal());
1247         assert!(1e-307f64.is_normal());
1248         assert!(!1e-308f64.is_normal());
1249     }
1250
1251     #[test]
1252     fn test_classify() {
1253         let nan: f64 = NAN;
1254         let inf: f64 = INFINITY;
1255         let neg_inf: f64 = NEG_INFINITY;
1256         let zero: f64 = 0.0f64;
1257         let neg_zero: f64 = -0.0;
1258         assert_eq!(nan.classify(), Fp::Nan);
1259         assert_eq!(inf.classify(), Fp::Infinite);
1260         assert_eq!(neg_inf.classify(), Fp::Infinite);
1261         assert_eq!(zero.classify(), Fp::Zero);
1262         assert_eq!(neg_zero.classify(), Fp::Zero);
1263         assert_eq!(1e-307f64.classify(), Fp::Normal);
1264         assert_eq!(1e-308f64.classify(), Fp::Subnormal);
1265     }
1266
1267     #[test]
1268     #[rustc_no_mir] // FIXME #27840 MIR NAN ends up negative.
1269     fn test_integer_decode() {
1270         assert_eq!(3.14159265359f64.integer_decode(), (7074237752028906, -51, 1));
1271         assert_eq!((-8573.5918555f64).integer_decode(), (4713381968463931, -39, -1));
1272         assert_eq!(2f64.powf(100.0).integer_decode(), (4503599627370496, 48, 1));
1273         assert_eq!(0f64.integer_decode(), (0, -1075, 1));
1274         assert_eq!((-0f64).integer_decode(), (0, -1075, -1));
1275         assert_eq!(INFINITY.integer_decode(), (4503599627370496, 972, 1));
1276         assert_eq!(NEG_INFINITY.integer_decode(), (4503599627370496, 972, -1));
1277         assert_eq!(NAN.integer_decode(), (6755399441055744, 972, 1));
1278     }
1279
1280     #[test]
1281     fn test_floor() {
1282         assert_approx_eq!(1.0f64.floor(), 1.0f64);
1283         assert_approx_eq!(1.3f64.floor(), 1.0f64);
1284         assert_approx_eq!(1.5f64.floor(), 1.0f64);
1285         assert_approx_eq!(1.7f64.floor(), 1.0f64);
1286         assert_approx_eq!(0.0f64.floor(), 0.0f64);
1287         assert_approx_eq!((-0.0f64).floor(), -0.0f64);
1288         assert_approx_eq!((-1.0f64).floor(), -1.0f64);
1289         assert_approx_eq!((-1.3f64).floor(), -2.0f64);
1290         assert_approx_eq!((-1.5f64).floor(), -2.0f64);
1291         assert_approx_eq!((-1.7f64).floor(), -2.0f64);
1292     }
1293
1294     #[test]
1295     fn test_ceil() {
1296         assert_approx_eq!(1.0f64.ceil(), 1.0f64);
1297         assert_approx_eq!(1.3f64.ceil(), 2.0f64);
1298         assert_approx_eq!(1.5f64.ceil(), 2.0f64);
1299         assert_approx_eq!(1.7f64.ceil(), 2.0f64);
1300         assert_approx_eq!(0.0f64.ceil(), 0.0f64);
1301         assert_approx_eq!((-0.0f64).ceil(), -0.0f64);
1302         assert_approx_eq!((-1.0f64).ceil(), -1.0f64);
1303         assert_approx_eq!((-1.3f64).ceil(), -1.0f64);
1304         assert_approx_eq!((-1.5f64).ceil(), -1.0f64);
1305         assert_approx_eq!((-1.7f64).ceil(), -1.0f64);
1306     }
1307
1308     #[test]
1309     fn test_round() {
1310         assert_approx_eq!(1.0f64.round(), 1.0f64);
1311         assert_approx_eq!(1.3f64.round(), 1.0f64);
1312         assert_approx_eq!(1.5f64.round(), 2.0f64);
1313         assert_approx_eq!(1.7f64.round(), 2.0f64);
1314         assert_approx_eq!(0.0f64.round(), 0.0f64);
1315         assert_approx_eq!((-0.0f64).round(), -0.0f64);
1316         assert_approx_eq!((-1.0f64).round(), -1.0f64);
1317         assert_approx_eq!((-1.3f64).round(), -1.0f64);
1318         assert_approx_eq!((-1.5f64).round(), -2.0f64);
1319         assert_approx_eq!((-1.7f64).round(), -2.0f64);
1320     }
1321
1322     #[test]
1323     fn test_trunc() {
1324         assert_approx_eq!(1.0f64.trunc(), 1.0f64);
1325         assert_approx_eq!(1.3f64.trunc(), 1.0f64);
1326         assert_approx_eq!(1.5f64.trunc(), 1.0f64);
1327         assert_approx_eq!(1.7f64.trunc(), 1.0f64);
1328         assert_approx_eq!(0.0f64.trunc(), 0.0f64);
1329         assert_approx_eq!((-0.0f64).trunc(), -0.0f64);
1330         assert_approx_eq!((-1.0f64).trunc(), -1.0f64);
1331         assert_approx_eq!((-1.3f64).trunc(), -1.0f64);
1332         assert_approx_eq!((-1.5f64).trunc(), -1.0f64);
1333         assert_approx_eq!((-1.7f64).trunc(), -1.0f64);
1334     }
1335
1336     #[test]
1337     fn test_fract() {
1338         assert_approx_eq!(1.0f64.fract(), 0.0f64);
1339         assert_approx_eq!(1.3f64.fract(), 0.3f64);
1340         assert_approx_eq!(1.5f64.fract(), 0.5f64);
1341         assert_approx_eq!(1.7f64.fract(), 0.7f64);
1342         assert_approx_eq!(0.0f64.fract(), 0.0f64);
1343         assert_approx_eq!((-0.0f64).fract(), -0.0f64);
1344         assert_approx_eq!((-1.0f64).fract(), -0.0f64);
1345         assert_approx_eq!((-1.3f64).fract(), -0.3f64);
1346         assert_approx_eq!((-1.5f64).fract(), -0.5f64);
1347         assert_approx_eq!((-1.7f64).fract(), -0.7f64);
1348     }
1349
1350     #[test]
1351     fn test_abs() {
1352         assert_eq!(INFINITY.abs(), INFINITY);
1353         assert_eq!(1f64.abs(), 1f64);
1354         assert_eq!(0f64.abs(), 0f64);
1355         assert_eq!((-0f64).abs(), 0f64);
1356         assert_eq!((-1f64).abs(), 1f64);
1357         assert_eq!(NEG_INFINITY.abs(), INFINITY);
1358         assert_eq!((1f64/NEG_INFINITY).abs(), 0f64);
1359         assert!(NAN.abs().is_nan());
1360     }
1361
1362     #[test]
1363     fn test_signum() {
1364         assert_eq!(INFINITY.signum(), 1f64);
1365         assert_eq!(1f64.signum(), 1f64);
1366         assert_eq!(0f64.signum(), 1f64);
1367         assert_eq!((-0f64).signum(), -1f64);
1368         assert_eq!((-1f64).signum(), -1f64);
1369         assert_eq!(NEG_INFINITY.signum(), -1f64);
1370         assert_eq!((1f64/NEG_INFINITY).signum(), -1f64);
1371         assert!(NAN.signum().is_nan());
1372     }
1373
1374     #[test]
1375     fn test_is_sign_positive() {
1376         assert!(INFINITY.is_sign_positive());
1377         assert!(1f64.is_sign_positive());
1378         assert!(0f64.is_sign_positive());
1379         assert!(!(-0f64).is_sign_positive());
1380         assert!(!(-1f64).is_sign_positive());
1381         assert!(!NEG_INFINITY.is_sign_positive());
1382         assert!(!(1f64/NEG_INFINITY).is_sign_positive());
1383         assert!(!NAN.is_sign_positive());
1384     }
1385
1386     #[test]
1387     fn test_is_sign_negative() {
1388         assert!(!INFINITY.is_sign_negative());
1389         assert!(!1f64.is_sign_negative());
1390         assert!(!0f64.is_sign_negative());
1391         assert!((-0f64).is_sign_negative());
1392         assert!((-1f64).is_sign_negative());
1393         assert!(NEG_INFINITY.is_sign_negative());
1394         assert!((1f64/NEG_INFINITY).is_sign_negative());
1395         assert!(!NAN.is_sign_negative());
1396     }
1397
1398     #[test]
1399     fn test_mul_add() {
1400         let nan: f64 = NAN;
1401         let inf: f64 = INFINITY;
1402         let neg_inf: f64 = NEG_INFINITY;
1403         assert_approx_eq!(12.3f64.mul_add(4.5, 6.7), 62.05);
1404         assert_approx_eq!((-12.3f64).mul_add(-4.5, -6.7), 48.65);
1405         assert_approx_eq!(0.0f64.mul_add(8.9, 1.2), 1.2);
1406         assert_approx_eq!(3.4f64.mul_add(-0.0, 5.6), 5.6);
1407         assert!(nan.mul_add(7.8, 9.0).is_nan());
1408         assert_eq!(inf.mul_add(7.8, 9.0), inf);
1409         assert_eq!(neg_inf.mul_add(7.8, 9.0), neg_inf);
1410         assert_eq!(8.9f64.mul_add(inf, 3.2), inf);
1411         assert_eq!((-3.2f64).mul_add(2.4, neg_inf), neg_inf);
1412     }
1413
1414     #[test]
1415     fn test_recip() {
1416         let nan: f64 = NAN;
1417         let inf: f64 = INFINITY;
1418         let neg_inf: f64 = NEG_INFINITY;
1419         assert_eq!(1.0f64.recip(), 1.0);
1420         assert_eq!(2.0f64.recip(), 0.5);
1421         assert_eq!((-0.4f64).recip(), -2.5);
1422         assert_eq!(0.0f64.recip(), inf);
1423         assert!(nan.recip().is_nan());
1424         assert_eq!(inf.recip(), 0.0);
1425         assert_eq!(neg_inf.recip(), 0.0);
1426     }
1427
1428     #[test]
1429     fn test_powi() {
1430         let nan: f64 = NAN;
1431         let inf: f64 = INFINITY;
1432         let neg_inf: f64 = NEG_INFINITY;
1433         assert_eq!(1.0f64.powi(1), 1.0);
1434         assert_approx_eq!((-3.1f64).powi(2), 9.61);
1435         assert_approx_eq!(5.9f64.powi(-2), 0.028727);
1436         assert_eq!(8.3f64.powi(0), 1.0);
1437         assert!(nan.powi(2).is_nan());
1438         assert_eq!(inf.powi(3), inf);
1439         assert_eq!(neg_inf.powi(2), inf);
1440     }
1441
1442     #[test]
1443     fn test_powf() {
1444         let nan: f64 = NAN;
1445         let inf: f64 = INFINITY;
1446         let neg_inf: f64 = NEG_INFINITY;
1447         assert_eq!(1.0f64.powf(1.0), 1.0);
1448         assert_approx_eq!(3.4f64.powf(4.5), 246.408183);
1449         assert_approx_eq!(2.7f64.powf(-3.2), 0.041652);
1450         assert_approx_eq!((-3.1f64).powf(2.0), 9.61);
1451         assert_approx_eq!(5.9f64.powf(-2.0), 0.028727);
1452         assert_eq!(8.3f64.powf(0.0), 1.0);
1453         assert!(nan.powf(2.0).is_nan());
1454         assert_eq!(inf.powf(2.0), inf);
1455         assert_eq!(neg_inf.powf(3.0), neg_inf);
1456     }
1457
1458     #[test]
1459     fn test_sqrt_domain() {
1460         assert!(NAN.sqrt().is_nan());
1461         assert!(NEG_INFINITY.sqrt().is_nan());
1462         assert!((-1.0f64).sqrt().is_nan());
1463         assert_eq!((-0.0f64).sqrt(), -0.0);
1464         assert_eq!(0.0f64.sqrt(), 0.0);
1465         assert_eq!(1.0f64.sqrt(), 1.0);
1466         assert_eq!(INFINITY.sqrt(), INFINITY);
1467     }
1468
1469     #[test]
1470     fn test_exp() {
1471         assert_eq!(1.0, 0.0f64.exp());
1472         assert_approx_eq!(2.718282, 1.0f64.exp());
1473         assert_approx_eq!(148.413159, 5.0f64.exp());
1474
1475         let inf: f64 = INFINITY;
1476         let neg_inf: f64 = NEG_INFINITY;
1477         let nan: f64 = NAN;
1478         assert_eq!(inf, inf.exp());
1479         assert_eq!(0.0, neg_inf.exp());
1480         assert!(nan.exp().is_nan());
1481     }
1482
1483     #[test]
1484     fn test_exp2() {
1485         assert_eq!(32.0, 5.0f64.exp2());
1486         assert_eq!(1.0, 0.0f64.exp2());
1487
1488         let inf: f64 = INFINITY;
1489         let neg_inf: f64 = NEG_INFINITY;
1490         let nan: f64 = NAN;
1491         assert_eq!(inf, inf.exp2());
1492         assert_eq!(0.0, neg_inf.exp2());
1493         assert!(nan.exp2().is_nan());
1494     }
1495
1496     #[test]
1497     fn test_ln() {
1498         let nan: f64 = NAN;
1499         let inf: f64 = INFINITY;
1500         let neg_inf: f64 = NEG_INFINITY;
1501         assert_approx_eq!(1.0f64.exp().ln(), 1.0);
1502         assert!(nan.ln().is_nan());
1503         assert_eq!(inf.ln(), inf);
1504         assert!(neg_inf.ln().is_nan());
1505         assert!((-2.3f64).ln().is_nan());
1506         assert_eq!((-0.0f64).ln(), neg_inf);
1507         assert_eq!(0.0f64.ln(), neg_inf);
1508         assert_approx_eq!(4.0f64.ln(), 1.386294);
1509     }
1510
1511     #[test]
1512     fn test_log() {
1513         let nan: f64 = NAN;
1514         let inf: f64 = INFINITY;
1515         let neg_inf: f64 = NEG_INFINITY;
1516         assert_eq!(10.0f64.log(10.0), 1.0);
1517         assert_approx_eq!(2.3f64.log(3.5), 0.664858);
1518         assert_eq!(1.0f64.exp().log(1.0f64.exp()), 1.0);
1519         assert!(1.0f64.log(1.0).is_nan());
1520         assert!(1.0f64.log(-13.9).is_nan());
1521         assert!(nan.log(2.3).is_nan());
1522         assert_eq!(inf.log(10.0), inf);
1523         assert!(neg_inf.log(8.8).is_nan());
1524         assert!((-2.3f64).log(0.1).is_nan());
1525         assert_eq!((-0.0f64).log(2.0), neg_inf);
1526         assert_eq!(0.0f64.log(7.0), neg_inf);
1527     }
1528
1529     #[test]
1530     fn test_log2() {
1531         let nan: f64 = NAN;
1532         let inf: f64 = INFINITY;
1533         let neg_inf: f64 = NEG_INFINITY;
1534         assert_approx_eq!(10.0f64.log2(), 3.321928);
1535         assert_approx_eq!(2.3f64.log2(), 1.201634);
1536         assert_approx_eq!(1.0f64.exp().log2(), 1.442695);
1537         assert!(nan.log2().is_nan());
1538         assert_eq!(inf.log2(), inf);
1539         assert!(neg_inf.log2().is_nan());
1540         assert!((-2.3f64).log2().is_nan());
1541         assert_eq!((-0.0f64).log2(), neg_inf);
1542         assert_eq!(0.0f64.log2(), neg_inf);
1543     }
1544
1545     #[test]
1546     fn test_log10() {
1547         let nan: f64 = NAN;
1548         let inf: f64 = INFINITY;
1549         let neg_inf: f64 = NEG_INFINITY;
1550         assert_eq!(10.0f64.log10(), 1.0);
1551         assert_approx_eq!(2.3f64.log10(), 0.361728);
1552         assert_approx_eq!(1.0f64.exp().log10(), 0.434294);
1553         assert_eq!(1.0f64.log10(), 0.0);
1554         assert!(nan.log10().is_nan());
1555         assert_eq!(inf.log10(), inf);
1556         assert!(neg_inf.log10().is_nan());
1557         assert!((-2.3f64).log10().is_nan());
1558         assert_eq!((-0.0f64).log10(), neg_inf);
1559         assert_eq!(0.0f64.log10(), neg_inf);
1560     }
1561
1562     #[test]
1563     fn test_to_degrees() {
1564         let pi: f64 = consts::PI;
1565         let nan: f64 = NAN;
1566         let inf: f64 = INFINITY;
1567         let neg_inf: f64 = NEG_INFINITY;
1568         assert_eq!(0.0f64.to_degrees(), 0.0);
1569         assert_approx_eq!((-5.8f64).to_degrees(), -332.315521);
1570         assert_eq!(pi.to_degrees(), 180.0);
1571         assert!(nan.to_degrees().is_nan());
1572         assert_eq!(inf.to_degrees(), inf);
1573         assert_eq!(neg_inf.to_degrees(), neg_inf);
1574     }
1575
1576     #[test]
1577     fn test_to_radians() {
1578         let pi: f64 = consts::PI;
1579         let nan: f64 = NAN;
1580         let inf: f64 = INFINITY;
1581         let neg_inf: f64 = NEG_INFINITY;
1582         assert_eq!(0.0f64.to_radians(), 0.0);
1583         assert_approx_eq!(154.6f64.to_radians(), 2.698279);
1584         assert_approx_eq!((-332.31f64).to_radians(), -5.799903);
1585         assert_eq!(180.0f64.to_radians(), pi);
1586         assert!(nan.to_radians().is_nan());
1587         assert_eq!(inf.to_radians(), inf);
1588         assert_eq!(neg_inf.to_radians(), neg_inf);
1589     }
1590
1591     #[test]
1592     fn test_ldexp() {
1593         let f1 = 2.0f64.powi(-123);
1594         let f2 = 2.0f64.powi(-111);
1595         let f3 = 1.75 * 2.0f64.powi(-12);
1596         assert_eq!(f64::ldexp(1f64, -123), f1);
1597         assert_eq!(f64::ldexp(1f64, -111), f2);
1598         assert_eq!(f64::ldexp(1.75f64, -12), f3);
1599
1600         assert_eq!(f64::ldexp(0f64, -123), 0f64);
1601         assert_eq!(f64::ldexp(-0f64, -123), -0f64);
1602
1603         let inf: f64 = INFINITY;
1604         let neg_inf: f64 = NEG_INFINITY;
1605         let nan: f64 = NAN;
1606         assert_eq!(f64::ldexp(inf, -123), inf);
1607         assert_eq!(f64::ldexp(neg_inf, -123), neg_inf);
1608         assert!(f64::ldexp(nan, -123).is_nan());
1609     }
1610
1611     #[test]
1612     fn test_frexp() {
1613         let f1 = 2.0f64.powi(-123);
1614         let f2 = 2.0f64.powi(-111);
1615         let f3 = 1.75 * 2.0f64.powi(-123);
1616         let (x1, exp1) = f1.frexp();
1617         let (x2, exp2) = f2.frexp();
1618         let (x3, exp3) = f3.frexp();
1619         assert_eq!((x1, exp1), (0.5f64, -122));
1620         assert_eq!((x2, exp2), (0.5f64, -110));
1621         assert_eq!((x3, exp3), (0.875f64, -122));
1622         assert_eq!(f64::ldexp(x1, exp1), f1);
1623         assert_eq!(f64::ldexp(x2, exp2), f2);
1624         assert_eq!(f64::ldexp(x3, exp3), f3);
1625
1626         assert_eq!(0f64.frexp(), (0f64, 0));
1627         assert_eq!((-0f64).frexp(), (-0f64, 0));
1628     }
1629
1630     #[test] #[cfg_attr(windows, ignore)] // FIXME #8755
1631     fn test_frexp_nowin() {
1632         let inf: f64 = INFINITY;
1633         let neg_inf: f64 = NEG_INFINITY;
1634         let nan: f64 = NAN;
1635         assert_eq!(match inf.frexp() { (x, _) => x }, inf);
1636         assert_eq!(match neg_inf.frexp() { (x, _) => x }, neg_inf);
1637         assert!(match nan.frexp() { (x, _) => x.is_nan() })
1638     }
1639
1640     #[test]
1641     fn test_abs_sub() {
1642         assert_eq!((-1f64).abs_sub(1f64), 0f64);
1643         assert_eq!(1f64.abs_sub(1f64), 0f64);
1644         assert_eq!(1f64.abs_sub(0f64), 1f64);
1645         assert_eq!(1f64.abs_sub(-1f64), 2f64);
1646         assert_eq!(NEG_INFINITY.abs_sub(0f64), 0f64);
1647         assert_eq!(INFINITY.abs_sub(1f64), INFINITY);
1648         assert_eq!(0f64.abs_sub(NEG_INFINITY), INFINITY);
1649         assert_eq!(0f64.abs_sub(INFINITY), 0f64);
1650     }
1651
1652     #[test]
1653     fn test_abs_sub_nowin() {
1654         assert!(NAN.abs_sub(-1f64).is_nan());
1655         assert!(1f64.abs_sub(NAN).is_nan());
1656     }
1657
1658     #[test]
1659     fn test_asinh() {
1660         assert_eq!(0.0f64.asinh(), 0.0f64);
1661         assert_eq!((-0.0f64).asinh(), -0.0f64);
1662
1663         let inf: f64 = INFINITY;
1664         let neg_inf: f64 = NEG_INFINITY;
1665         let nan: f64 = NAN;
1666         assert_eq!(inf.asinh(), inf);
1667         assert_eq!(neg_inf.asinh(), neg_inf);
1668         assert!(nan.asinh().is_nan());
1669         assert_approx_eq!(2.0f64.asinh(), 1.443635475178810342493276740273105f64);
1670         assert_approx_eq!((-2.0f64).asinh(), -1.443635475178810342493276740273105f64);
1671     }
1672
1673     #[test]
1674     fn test_acosh() {
1675         assert_eq!(1.0f64.acosh(), 0.0f64);
1676         assert!(0.999f64.acosh().is_nan());
1677
1678         let inf: f64 = INFINITY;
1679         let neg_inf: f64 = NEG_INFINITY;
1680         let nan: f64 = NAN;
1681         assert_eq!(inf.acosh(), inf);
1682         assert!(neg_inf.acosh().is_nan());
1683         assert!(nan.acosh().is_nan());
1684         assert_approx_eq!(2.0f64.acosh(), 1.31695789692481670862504634730796844f64);
1685         assert_approx_eq!(3.0f64.acosh(), 1.76274717403908605046521864995958461f64);
1686     }
1687
1688     #[test]
1689     fn test_atanh() {
1690         assert_eq!(0.0f64.atanh(), 0.0f64);
1691         assert_eq!((-0.0f64).atanh(), -0.0f64);
1692
1693         let inf: f64 = INFINITY;
1694         let neg_inf: f64 = NEG_INFINITY;
1695         let nan: f64 = NAN;
1696         assert_eq!(1.0f64.atanh(), inf);
1697         assert_eq!((-1.0f64).atanh(), neg_inf);
1698         assert!(2f64.atanh().atanh().is_nan());
1699         assert!((-2f64).atanh().atanh().is_nan());
1700         assert!(inf.atanh().is_nan());
1701         assert!(neg_inf.atanh().is_nan());
1702         assert!(nan.atanh().is_nan());
1703         assert_approx_eq!(0.5f64.atanh(), 0.54930614433405484569762261846126285f64);
1704         assert_approx_eq!((-0.5f64).atanh(), -0.54930614433405484569762261846126285f64);
1705     }
1706
1707     #[test]
1708     fn test_real_consts() {
1709         use super::consts;
1710         let pi: f64 = consts::PI;
1711         let frac_pi_2: f64 = consts::FRAC_PI_2;
1712         let frac_pi_3: f64 = consts::FRAC_PI_3;
1713         let frac_pi_4: f64 = consts::FRAC_PI_4;
1714         let frac_pi_6: f64 = consts::FRAC_PI_6;
1715         let frac_pi_8: f64 = consts::FRAC_PI_8;
1716         let frac_1_pi: f64 = consts::FRAC_1_PI;
1717         let frac_2_pi: f64 = consts::FRAC_2_PI;
1718         let frac_2_sqrtpi: f64 = consts::FRAC_2_SQRT_PI;
1719         let sqrt2: f64 = consts::SQRT_2;
1720         let frac_1_sqrt2: f64 = consts::FRAC_1_SQRT_2;
1721         let e: f64 = consts::E;
1722         let log2_e: f64 = consts::LOG2_E;
1723         let log10_e: f64 = consts::LOG10_E;
1724         let ln_2: f64 = consts::LN_2;
1725         let ln_10: f64 = consts::LN_10;
1726
1727         assert_approx_eq!(frac_pi_2, pi / 2f64);
1728         assert_approx_eq!(frac_pi_3, pi / 3f64);
1729         assert_approx_eq!(frac_pi_4, pi / 4f64);
1730         assert_approx_eq!(frac_pi_6, pi / 6f64);
1731         assert_approx_eq!(frac_pi_8, pi / 8f64);
1732         assert_approx_eq!(frac_1_pi, 1f64 / pi);
1733         assert_approx_eq!(frac_2_pi, 2f64 / pi);
1734         assert_approx_eq!(frac_2_sqrtpi, 2f64 / pi.sqrt());
1735         assert_approx_eq!(sqrt2, 2f64.sqrt());
1736         assert_approx_eq!(frac_1_sqrt2, 1f64 / 2f64.sqrt());
1737         assert_approx_eq!(log2_e, e.log2());
1738         assert_approx_eq!(log10_e, e.log10());
1739         assert_approx_eq!(ln_2, 2f64.ln());
1740         assert_approx_eq!(ln_10, 10f64.ln());
1741     }
1742 }