src/libstd/num/f32.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 //! Operations and constants for 32-bits floats (`f32` type)
  12
  13 #![stable(feature = "rust1", since = "1.0.0")]
  14 #![allow(missing_docs)]
  15 #![allow(unsigned_negation)]
  16 #![doc(primitive = "f32")]
  17
  18 use prelude::v1::*;
  19
  20 use core::num;
  21 use intrinsics;
  22 use libc::c_int;
  23 use num::{FpCategory, ParseFloatError};
  24
  25 pub use core::f32::{RADIX, MANTISSA_DIGITS, DIGITS, EPSILON};
  26 pub use core::f32::{MIN_EXP, MAX_EXP, MIN_10_EXP};
  27 pub use core::f32::{MAX_10_EXP, NAN, INFINITY, NEG_INFINITY};
  28 pub use core::f32::{MIN, MIN_POSITIVE, MAX};
  29 pub use core::f32::consts;
  30
  31 #[allow(dead_code)]
  32 mod cmath {
  33     use libc::{c_float, c_int};
  34
  35     extern {
  36         pub fn acosf(n: c_float) -> c_float;
  37         pub fn asinf(n: c_float) -> c_float;
  38         pub fn atanf(n: c_float) -> c_float;
  39         pub fn atan2f(a: c_float, b: c_float) -> c_float;
  40         pub fn cbrtf(n: c_float) -> c_float;
  41         pub fn coshf(n: c_float) -> c_float;
  42         pub fn erff(n: c_float) -> c_float;
  43         pub fn erfcf(n: c_float) -> c_float;
  44         pub fn expm1f(n: c_float) -> c_float;
  45         pub fn fdimf(a: c_float, b: c_float) -> c_float;
  46         pub fn fmaxf(a: c_float, b: c_float) -> c_float;
  47         pub fn fminf(a: c_float, b: c_float) -> c_float;
  48         pub fn fmodf(a: c_float, b: c_float) -> c_float;
  49         pub fn nextafterf(x: c_float, y: c_float) -> c_float;
  50         pub fn logbf(n: c_float) -> c_float;
  51         pub fn log1pf(n: c_float) -> c_float;
  52         pub fn ilogbf(n: c_float) -> c_int;
  53         pub fn modff(n: c_float, iptr: &mut c_float) -> c_float;
  54         pub fn sinhf(n: c_float) -> c_float;
  55         pub fn tanf(n: c_float) -> c_float;
  56         pub fn tanhf(n: c_float) -> c_float;
  57         pub fn tgammaf(n: c_float) -> c_float;
  58
  59         #[cfg_attr(all(windows, target_env = "msvc"), link_name = "__lgammaf_r")]
  60         pub fn lgammaf_r(n: c_float, sign: &mut c_int) -> c_float;
  61         #[cfg_attr(all(windows, target_env = "msvc"), link_name = "_hypotf")]
  62         pub fn hypotf(x: c_float, y: c_float) -> c_float;
  63
  64         #[cfg(any(unix, all(windows, not(target_env = "msvc"))))]
  65         pub fn frexpf(n: c_float, value: &mut c_int) -> c_float;
  66         #[cfg(any(unix, all(windows, not(target_env = "msvc"))))]
  67         pub fn ldexpf(x: c_float, n: c_int) -> c_float;
  68     }
  69
  70     #[cfg(all(windows, target_env = "msvc"))]
  71     pub unsafe fn ldexpf(x: c_float, n: c_int) -> c_float {
  72         f64::ldexp(x as f64, n as isize) as c_float
  73     }
  74
  75     #[cfg(all(windows, target_env = "msvc"))]
  76     pub unsafe fn frexpf(x: c_float, value: &mut c_int) -> c_float {
  77         let (a, b) = f64::frexp(x as f64);
  78         *value = b as c_int;
  79         a as c_float
  80     }
  81 }
  82
  83 #[cfg(not(test))]
  84 #[lang = "f32"]
  85 #[stable(feature = "rust1", since = "1.0.0")]
  86 impl f32 {
  87     /// Parses a float as with a given radix
  88     #[unstable(feature = "float_from_str_radix", reason = "recently moved API")]
  89     pub fn from_str_radix(s: &str, radix: u32) -> Result<f32, ParseFloatError> {
  90         num::Float::from_str_radix(s, radix)
  91     }
  92
  93     /// Returns `true` if this value is `NaN` and false otherwise.
  94     ///
  95     /// ```
  96     /// use std::f32;
  97     ///
  98     /// let nan = f32::NAN;
  99     /// let f = 7.0_f32;
 100     ///
 101     /// assert!(nan.is_nan());
 102     /// assert!(!f.is_nan());
 103     /// ```
 104     #[stable(feature = "rust1", since = "1.0.0")]
 105     #[inline]
 106     pub fn is_nan(self) -> bool { num::Float::is_nan(self) }
 107
 108     /// Returns `true` if this value is positive infinity or negative infinity and
 109     /// false otherwise.
 110     ///
 111     /// ```
 112     /// use std::f32;
 113     ///
 114     /// let f = 7.0f32;
 115     /// let inf = f32::INFINITY;
 116     /// let neg_inf = f32::NEG_INFINITY;
 117     /// let nan = f32::NAN;
 118     ///
 119     /// assert!(!f.is_infinite());
 120     /// assert!(!nan.is_infinite());
 121     ///
 122     /// assert!(inf.is_infinite());
 123     /// assert!(neg_inf.is_infinite());
 124     /// ```
 125     #[stable(feature = "rust1", since = "1.0.0")]
 126     #[inline]
 127     pub fn is_infinite(self) -> bool { num::Float::is_infinite(self) }
 128
 129     /// Returns `true` if this number is neither infinite nor `NaN`.
 130     ///
 131     /// ```
 132     /// use std::f32;
 133     ///
 134     /// let f = 7.0f32;
 135     /// let inf = f32::INFINITY;
 136     /// let neg_inf = f32::NEG_INFINITY;
 137     /// let nan = f32::NAN;
 138     ///
 139     /// assert!(f.is_finite());
 140     ///
 141     /// assert!(!nan.is_finite());
 142     /// assert!(!inf.is_finite());
 143     /// assert!(!neg_inf.is_finite());
 144     /// ```
 145     #[stable(feature = "rust1", since = "1.0.0")]
 146     #[inline]
 147     pub fn is_finite(self) -> bool { num::Float::is_finite(self) }
 148
 149     /// Returns `true` if the number is neither zero, infinite,
 150     /// [subnormal][subnormal], or `NaN`.
 151     ///
 152     /// ```
 153     /// use std::f32;
 154     ///
 155     /// let min = f32::MIN_POSITIVE; // 1.17549435e-38f32
 156     /// let max = f32::MAX;
 157     /// let lower_than_min = 1.0e-40_f32;
 158     /// let zero = 0.0_f32;
 159     ///
 160     /// assert!(min.is_normal());
 161     /// assert!(max.is_normal());
 162     ///
 163     /// assert!(!zero.is_normal());
 164     /// assert!(!f32::NAN.is_normal());
 165     /// assert!(!f32::INFINITY.is_normal());
 166     /// // Values between `0` and `min` are Subnormal.
 167     /// assert!(!lower_than_min.is_normal());
 168     /// ```
 169     /// [subnormal]: http://en.wikipedia.org/wiki/Denormal_number
 170     #[stable(feature = "rust1", since = "1.0.0")]
 171     #[inline]
 172     pub fn is_normal(self) -> bool { num::Float::is_normal(self) }
 173
 174     /// Returns the floating point category of the number. If only one property
 175     /// is going to be tested, it is generally faster to use the specific
 176     /// predicate instead.
 177     ///
 178     /// ```
 179     /// use std::num::FpCategory;
 180     /// use std::f32;
 181     ///
 182     /// let num = 12.4_f32;
 183     /// let inf = f32::INFINITY;
 184     ///
 185     /// assert_eq!(num.classify(), FpCategory::Normal);
 186     /// assert_eq!(inf.classify(), FpCategory::Infinite);
 187     /// ```
 188     #[stable(feature = "rust1", since = "1.0.0")]
 189     #[inline]
 190     pub fn classify(self) -> FpCategory { num::Float::classify(self) }
 191
 192     /// Returns the mantissa, base 2 exponent, and sign as integers, respectively.
 193     /// The original number can be recovered by `sign * mantissa * 2 ^ exponent`.
 194     /// The floating point encoding is documented in the [Reference][floating-point].
 195     ///
 196     /// ```
 197     /// # #![feature(float_extras)]
 198     /// use std::f32;
 199     ///
 200     /// let num = 2.0f32;
 201     ///
 202     /// // (8388608, -22, 1)
 203     /// let (mantissa, exponent, sign) = num.integer_decode();
 204     /// let sign_f = sign as f32;
 205     /// let mantissa_f = mantissa as f32;
 206     /// let exponent_f = num.powf(exponent as f32);
 207     ///
 208     /// // 1 * 8388608 * 2^(-22) == 2
 209     /// let abs_difference = (sign_f * mantissa_f * exponent_f - num).abs();
 210     ///
 211     /// assert!(abs_difference <= f32::EPSILON);
 212     /// ```
 213     /// [floating-point]: ../../../../../reference.html#machine-types
 214     #[unstable(feature = "float_extras", reason = "signature is undecided")]
 215     #[inline]
 216     pub fn integer_decode(self) -> (u64, i16, i8) {
 217         num::Float::integer_decode(self)
 218     }
 219
 220     /// Returns the largest integer less than or equal to a number.
 221     ///
 222     /// ```
 223     /// let f = 3.99_f32;
 224     /// let g = 3.0_f32;
 225     ///
 226     /// assert_eq!(f.floor(), 3.0);
 227     /// assert_eq!(g.floor(), 3.0);
 228     /// ```
 229     #[stable(feature = "rust1", since = "1.0.0")]
 230     #[inline]
 231     pub fn floor(self) -> f32 { num::Float::floor(self) }
 232
 233     /// Returns the smallest integer greater than or equal to a number.
 234     ///
 235     /// ```
 236     /// let f = 3.01_f32;
 237     /// let g = 4.0_f32;
 238     ///
 239     /// assert_eq!(f.ceil(), 4.0);
 240     /// assert_eq!(g.ceil(), 4.0);
 241     /// ```
 242     #[stable(feature = "rust1", since = "1.0.0")]
 243     #[inline]
 244     pub fn ceil(self) -> f32 { num::Float::ceil(self) }
 245
 246     /// Returns the nearest integer to a number. Round half-way cases away from
 247     /// `0.0`.
 248     ///
 249     /// ```
 250     /// let f = 3.3_f32;
 251     /// let g = -3.3_f32;
 252     ///
 253     /// assert_eq!(f.round(), 3.0);
 254     /// assert_eq!(g.round(), -3.0);
 255     /// ```
 256     #[stable(feature = "rust1", since = "1.0.0")]
 257     #[inline]
 258     pub fn round(self) -> f32 { num::Float::round(self) }
 259
 260     /// Returns the integer part of a number.
 261     ///
 262     /// ```
 263     /// let f = 3.3_f32;
 264     /// let g = -3.7_f32;
 265     ///
 266     /// assert_eq!(f.trunc(), 3.0);
 267     /// assert_eq!(g.trunc(), -3.0);
 268     /// ```
 269     #[stable(feature = "rust1", since = "1.0.0")]
 270     #[inline]
 271     pub fn trunc(self) -> f32 { num::Float::trunc(self) }
 272
 273     /// Returns the fractional part of a number.
 274     ///
 275     /// ```
 276     /// use std::f32;
 277     ///
 278     /// let x = 3.5_f32;
 279     /// let y = -3.5_f32;
 280     /// let abs_difference_x = (x.fract() - 0.5).abs();
 281     /// let abs_difference_y = (y.fract() - (-0.5)).abs();
 282     ///
 283     /// assert!(abs_difference_x <= f32::EPSILON);
 284     /// assert!(abs_difference_y <= f32::EPSILON);
 285     /// ```
 286     #[stable(feature = "rust1", since = "1.0.0")]
 287     #[inline]
 288     pub fn fract(self) -> f32 { num::Float::fract(self) }
 289
 290     /// Computes the absolute value of `self`. Returns `NAN` if the
 291     /// number is `NAN`.
 292     ///
 293     /// ```
 294     /// use std::f32;
 295     ///
 296     /// let x = 3.5_f32;
 297     /// let y = -3.5_f32;
 298     ///
 299     /// let abs_difference_x = (x.abs() - x).abs();
 300     /// let abs_difference_y = (y.abs() - (-y)).abs();
 301     ///
 302     /// assert!(abs_difference_x <= f32::EPSILON);
 303     /// assert!(abs_difference_y <= f32::EPSILON);
 304     ///
 305     /// assert!(f32::NAN.abs().is_nan());
 306     /// ```
 307     #[stable(feature = "rust1", since = "1.0.0")]
 308     #[inline]
 309     pub fn abs(self) -> f32 { num::Float::abs(self) }
 310
 311     /// Returns a number that represents the sign of `self`.
 312     ///
 313     /// - `1.0` if the number is positive, `+0.0` or `INFINITY`
 314     /// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
 315     /// - `NAN` if the number is `NAN`
 316     ///
 317     /// ```
 318     /// use std::f32;
 319     ///
 320     /// let f = 3.5_f32;
 321     ///
 322     /// assert_eq!(f.signum(), 1.0);
 323     /// assert_eq!(f32::NEG_INFINITY.signum(), -1.0);
 324     ///
 325     /// assert!(f32::NAN.signum().is_nan());
 326     /// ```
 327     #[stable(feature = "rust1", since = "1.0.0")]
 328     #[inline]
 329     pub fn signum(self) -> f32 { num::Float::signum(self) }
 330
 331     /// Returns `true` if `self`'s sign bit is positive, including
 332     /// `+0.0` and `INFINITY`.
 333     ///
 334     /// ```
 335     /// use std::f32;
 336     ///
 337     /// let nan = f32::NAN;
 338     /// let f = 7.0_f32;
 339     /// let g = -7.0_f32;
 340     ///
 341     /// assert!(f.is_sign_positive());
 342     /// assert!(!g.is_sign_positive());
 343     /// // Requires both tests to determine if is `NaN`
 344     /// assert!(!nan.is_sign_positive() && !nan.is_sign_negative());
 345     /// ```
 346     #[stable(feature = "rust1", since = "1.0.0")]
 347     #[inline]
 348     pub fn is_sign_positive(self) -> bool { num::Float::is_positive(self) }
 349
 350     /// Returns `true` if `self`'s sign is negative, including `-0.0`
 351     /// and `NEG_INFINITY`.
 352     ///
 353     /// ```
 354     /// use std::f32;
 355     ///
 356     /// let nan = f32::NAN;
 357     /// let f = 7.0f32;
 358     /// let g = -7.0f32;
 359     ///
 360     /// assert!(!f.is_sign_negative());
 361     /// assert!(g.is_sign_negative());
 362     /// // Requires both tests to determine if is `NaN`.
 363     /// assert!(!nan.is_sign_positive() && !nan.is_sign_negative());
 364     /// ```
 365     #[stable(feature = "rust1", since = "1.0.0")]
 366     #[inline]
 367     pub fn is_sign_negative(self) -> bool { num::Float::is_negative(self) }
 368
 369     /// Fused multiply-add. Computes `(self * a) + b` with only one rounding
 370     /// error. This produces a more accurate result with better performance than
 371     /// a separate multiplication operation followed by an add.
 372     ///
 373     /// ```
 374     /// use std::f32;
 375     ///
 376     /// let m = 10.0_f32;
 377     /// let x = 4.0_f32;
 378     /// let b = 60.0_f32;
 379     ///
 380     /// // 100.0
 381     /// let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs();
 382     ///
 383     /// assert!(abs_difference <= f32::EPSILON);
 384     /// ```
 385     #[stable(feature = "rust1", since = "1.0.0")]
 386     #[inline]
 387     pub fn mul_add(self, a: f32, b: f32) -> f32 { num::Float::mul_add(self, a, b) }
 388
 389     /// Takes the reciprocal (inverse) of a number, `1/x`.
 390     ///
 391     /// ```
 392     /// use std::f32;
 393     ///
 394     /// let x = 2.0_f32;
 395     /// let abs_difference = (x.recip() - (1.0/x)).abs();
 396     ///
 397     /// assert!(abs_difference <= f32::EPSILON);
 398     /// ```
 399     #[stable(feature = "rust1", since = "1.0.0")]
 400     #[inline]
 401     pub fn recip(self) -> f32 { num::Float::recip(self) }
 402
 403     /// Raises a number to an integer power.
 404     ///
 405     /// Using this function is generally faster than using `powf`
 406     ///
 407     /// ```
 408     /// use std::f32;
 409     ///
 410     /// let x = 2.0_f32;
 411     /// let abs_difference = (x.powi(2) - x*x).abs();
 412     ///
 413     /// assert!(abs_difference <= f32::EPSILON);
 414     /// ```
 415     #[stable(feature = "rust1", since = "1.0.0")]
 416     #[inline]
 417     pub fn powi(self, n: i32) -> f32 { num::Float::powi(self, n) }
 418
 419     /// Raises a number to a floating point power.
 420     ///
 421     /// ```
 422     /// use std::f32;
 423     ///
 424     /// let x = 2.0_f32;
 425     /// let abs_difference = (x.powf(2.0) - x*x).abs();
 426     ///
 427     /// assert!(abs_difference <= f32::EPSILON);
 428     /// ```
 429     #[stable(feature = "rust1", since = "1.0.0")]
 430     #[inline]
 431     pub fn powf(self, n: f32) -> f32 { num::Float::powf(self, n) }
 432
 433     /// Takes the square root of a number.
 434     ///
 435     /// Returns NaN if `self` is a negative number.
 436     ///
 437     /// ```
 438     /// use std::f32;
 439     ///
 440     /// let positive = 4.0_f32;
 441     /// let negative = -4.0_f32;
 442     ///
 443     /// let abs_difference = (positive.sqrt() - 2.0).abs();
 444     ///
 445     /// assert!(abs_difference <= f32::EPSILON);
 446     /// assert!(negative.sqrt().is_nan());
 447     /// ```
 448     #[stable(feature = "rust1", since = "1.0.0")]
 449     #[inline]
 450     pub fn sqrt(self) -> f32 { num::Float::sqrt(self) }
 451
 452     /// Returns `e^(self)`, (the exponential function).
 453     ///
 454     /// ```
 455     /// use std::f32;
 456     ///
 457     /// let one = 1.0f32;
 458     /// // e^1
 459     /// let e = one.exp();
 460     ///
 461     /// // ln(e) - 1 == 0
 462     /// let abs_difference = (e.ln() - 1.0).abs();
 463     ///
 464     /// assert!(abs_difference <= f32::EPSILON);
 465     /// ```
 466     #[stable(feature = "rust1", since = "1.0.0")]
 467     #[inline]
 468     pub fn exp(self) -> f32 { num::Float::exp(self) }
 469
 470     /// Returns `2^(self)`.
 471     ///
 472     /// ```
 473     /// use std::f32;
 474     ///
 475     /// let f = 2.0f32;
 476     ///
 477     /// // 2^2 - 4 == 0
 478     /// let abs_difference = (f.exp2() - 4.0).abs();
 479     ///
 480     /// assert!(abs_difference <= f32::EPSILON);
 481     /// ```
 482     #[stable(feature = "rust1", since = "1.0.0")]
 483     #[inline]
 484     pub fn exp2(self) -> f32 { num::Float::exp2(self) }
 485
 486     /// Returns the natural logarithm of the number.
 487     ///
 488     /// ```
 489     /// use std::f32;
 490     ///
 491     /// let one = 1.0f32;
 492     /// // e^1
 493     /// let e = one.exp();
 494     ///
 495     /// // ln(e) - 1 == 0
 496     /// let abs_difference = (e.ln() - 1.0).abs();
 497     ///
 498     /// assert!(abs_difference <= f32::EPSILON);
 499     /// ```
 500     #[stable(feature = "rust1", since = "1.0.0")]
 501     #[inline]
 502     pub fn ln(self) -> f32 { num::Float::ln(self) }
 503
 504     /// Returns the logarithm of the number with respect to an arbitrary base.
 505     ///
 506     /// ```
 507     /// use std::f32;
 508     ///
 509     /// let ten = 10.0f32;
 510     /// let two = 2.0f32;
 511     ///
 512     /// // log10(10) - 1 == 0
 513     /// let abs_difference_10 = (ten.log(10.0) - 1.0).abs();
 514     ///
 515     /// // log2(2) - 1 == 0
 516     /// let abs_difference_2 = (two.log(2.0) - 1.0).abs();
 517     ///
 518     /// assert!(abs_difference_10 <= f32::EPSILON);
 519     /// assert!(abs_difference_2 <= f32::EPSILON);
 520     /// ```
 521     #[stable(feature = "rust1", since = "1.0.0")]
 522     #[inline]
 523     pub fn log(self, base: f32) -> f32 { num::Float::log(self, base) }
 524
 525     /// Returns the base 2 logarithm of the number.
 526     ///
 527     /// ```
 528     /// use std::f32;
 529     ///
 530     /// let two = 2.0f32;
 531     ///
 532     /// // log2(2) - 1 == 0
 533     /// let abs_difference = (two.log2() - 1.0).abs();
 534     ///
 535     /// assert!(abs_difference <= f32::EPSILON);
 536     /// ```
 537     #[stable(feature = "rust1", since = "1.0.0")]
 538     #[inline]
 539     pub fn log2(self) -> f32 { num::Float::log2(self) }
 540
 541     /// Returns the base 10 logarithm of the number.
 542     ///
 543     /// ```
 544     /// use std::f32;
 545     ///
 546     /// let ten = 10.0f32;
 547     ///
 548     /// // log10(10) - 1 == 0
 549     /// let abs_difference = (ten.log10() - 1.0).abs();
 550     ///
 551     /// assert!(abs_difference <= f32::EPSILON);
 552     /// ```
 553     #[stable(feature = "rust1", since = "1.0.0")]
 554     #[inline]
 555     pub fn log10(self) -> f32 { num::Float::log10(self) }
 556
 557     /// Converts radians to degrees.
 558     ///
 559     /// ```
 560     /// # #![feature(float_extras)]
 561     /// use std::f32::{self, consts};
 562     ///
 563     /// let angle = consts::PI;
 564     ///
 565     /// let abs_difference = (angle.to_degrees() - 180.0).abs();
 566     ///
 567     /// assert!(abs_difference <= f32::EPSILON);
 568     /// ```
 569     #[unstable(feature = "float_extras", reason = "desirability is unclear")]
 570     #[inline]
 571     pub fn to_degrees(self) -> f32 { num::Float::to_degrees(self) }
 572
 573     /// Converts degrees to radians.
 574     ///
 575     /// ```
 576     /// # #![feature(float_extras)]
 577     /// use std::f32::{self, consts};
 578     ///
 579     /// let angle = 180.0f32;
 580     ///
 581     /// let abs_difference = (angle.to_radians() - consts::PI).abs();
 582     ///
 583     /// assert!(abs_difference <= f32::EPSILON);
 584     /// ```
 585     #[unstable(feature = "float_extras", reason = "desirability is unclear")]
 586     #[inline]
 587     pub fn to_radians(self) -> f32 { num::Float::to_radians(self) }
 588
 589     /// Constructs a floating point number of `x*2^exp`.
 590     ///
 591     /// ```
 592     /// # #![feature(float_extras)]
 593     /// use std::f32;
 594     /// // 3*2^2 - 12 == 0
 595     /// let abs_difference = (f32::ldexp(3.0, 2) - 12.0).abs();
 596     ///
 597     /// assert!(abs_difference <= f32::EPSILON);
 598     /// ```
 599     #[unstable(feature = "float_extras",
 600                reason = "pending integer conventions")]
 601     #[inline]
 602     pub fn ldexp(x: f32, exp: isize) -> f32 {
 603         unsafe { cmath::ldexpf(x, exp as c_int) }
 604     }
 605
 606     /// Breaks the number into a normalized fraction and a base-2 exponent,
 607     /// satisfying:
 608     ///
 609     ///  * `self = x * 2^exp`
 610     ///  * `0.5 <= abs(x) < 1.0`
 611     ///
 612     /// ```
 613     /// # #![feature(float_extras)]
 614     /// use std::f32;
 615     ///
 616     /// let x = 4.0f32;
 617     ///
 618     /// // (1/2)*2^3 -> 1 * 8/2 -> 4.0
 619     /// let f = x.frexp();
 620     /// let abs_difference_0 = (f.0 - 0.5).abs();
 621     /// let abs_difference_1 = (f.1 as f32 - 3.0).abs();
 622     ///
 623     /// assert!(abs_difference_0 <= f32::EPSILON);
 624     /// assert!(abs_difference_1 <= f32::EPSILON);
 625     /// ```
 626     #[unstable(feature = "float_extras",
 627                reason = "pending integer conventions")]
 628     #[inline]
 629     pub fn frexp(self) -> (f32, isize) {
 630         unsafe {
 631             let mut exp = 0;
 632             let x = cmath::frexpf(self, &mut exp);
 633             (x, exp as isize)
 634         }
 635     }
 636
 637     /// Returns the next representable floating-point value in the direction of
 638     /// `other`.
 639     ///
 640     /// ```
 641     /// # #![feature(float_extras)]
 642     /// use std::f32;
 643     ///
 644     /// let x = 1.0f32;
 645     ///
 646     /// let abs_diff = (x.next_after(2.0) - 1.00000011920928955078125_f32).abs();
 647     ///
 648     /// assert!(abs_diff <= f32::EPSILON);
 649     /// ```
 650     #[unstable(feature = "float_extras",
 651                reason = "unsure about its place in the world")]
 652     #[inline]
 653     pub fn next_after(self, other: f32) -> f32 {
 654         unsafe { cmath::nextafterf(self, other) }
 655     }
 656
 657     /// Returns the maximum of the two numbers.
 658     ///
 659     /// ```
 660     /// let x = 1.0f32;
 661     /// let y = 2.0f32;
 662     ///
 663     /// assert_eq!(x.max(y), y);
 664     /// ```
 665     ///
 666     /// If one of the arguments is NaN, then the other argument is returned.
 667     #[stable(feature = "rust1", since = "1.0.0")]
 668     #[inline]
 669     pub fn max(self, other: f32) -> f32 {
 670         unsafe { cmath::fmaxf(self, other) }
 671     }
 672
 673     /// Returns the minimum of the two numbers.
 674     ///
 675     /// ```
 676     /// let x = 1.0f32;
 677     /// let y = 2.0f32;
 678     ///
 679     /// assert_eq!(x.min(y), x);
 680     /// ```
 681     ///
 682     /// If one of the arguments is NaN, then the other argument is returned.
 683     #[stable(feature = "rust1", since = "1.0.0")]
 684     #[inline]
 685     pub fn min(self, other: f32) -> f32 {
 686         unsafe { cmath::fminf(self, other) }
 687     }
 688
 689     /// The positive difference of two numbers.
 690     ///
 691     /// * If `self <= other`: `0:0`
 692     /// * Else: `self - other`
 693     ///
 694     /// ```
 695     /// use std::f32;
 696     ///
 697     /// let x = 3.0f32;
 698     /// let y = -3.0f32;
 699     ///
 700     /// let abs_difference_x = (x.abs_sub(1.0) - 2.0).abs();
 701     /// let abs_difference_y = (y.abs_sub(1.0) - 0.0).abs();
 702     ///
 703     /// assert!(abs_difference_x <= f32::EPSILON);
 704     /// assert!(abs_difference_y <= f32::EPSILON);
 705     /// ```
 706     #[stable(feature = "rust1", since = "1.0.0")]
 707     #[inline]
 708     pub fn abs_sub(self, other: f32) -> f32 {
 709         unsafe { cmath::fdimf(self, other) }
 710     }
 711
 712     /// Takes the cubic root of a number.
 713     ///
 714     /// ```
 715     /// use std::f32;
 716     ///
 717     /// let x = 8.0f32;
 718     ///
 719     /// // x^(1/3) - 2 == 0
 720     /// let abs_difference = (x.cbrt() - 2.0).abs();
 721     ///
 722     /// assert!(abs_difference <= f32::EPSILON);
 723     /// ```
 724     #[stable(feature = "rust1", since = "1.0.0")]
 725     #[inline]
 726     pub fn cbrt(self) -> f32 {
 727         unsafe { cmath::cbrtf(self) }
 728     }
 729
 730     /// Calculates the length of the hypotenuse of a right-angle triangle given
 731     /// legs of length `x` and `y`.
 732     ///
 733     /// ```
 734     /// use std::f32;
 735     ///
 736     /// let x = 2.0f32;
 737     /// let y = 3.0f32;
 738     ///
 739     /// // sqrt(x^2 + y^2)
 740     /// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();
 741     ///
 742     /// assert!(abs_difference <= f32::EPSILON);
 743     /// ```
 744     #[stable(feature = "rust1", since = "1.0.0")]
 745     #[inline]
 746     pub fn hypot(self, other: f32) -> f32 {
 747         unsafe { cmath::hypotf(self, other) }
 748     }
 749
 750     /// Computes the sine of a number (in radians).
 751     ///
 752     /// ```
 753     /// use std::f32;
 754     ///
 755     /// let x = f32::consts::PI/2.0;
 756     ///
 757     /// let abs_difference = (x.sin() - 1.0).abs();
 758     ///
 759     /// assert!(abs_difference <= f32::EPSILON);
 760     /// ```
 761     #[stable(feature = "rust1", since = "1.0.0")]
 762     #[inline]
 763     pub fn sin(self) -> f32 {
 764         unsafe { intrinsics::sinf32(self) }
 765     }
 766
 767     /// Computes the cosine of a number (in radians).
 768     ///
 769     /// ```
 770     /// use std::f32;
 771     ///
 772     /// let x = 2.0*f32::consts::PI;
 773     ///
 774     /// let abs_difference = (x.cos() - 1.0).abs();
 775     ///
 776     /// assert!(abs_difference <= f32::EPSILON);
 777     /// ```
 778     #[stable(feature = "rust1", since = "1.0.0")]
 779     #[inline]
 780     pub fn cos(self) -> f32 {
 781         unsafe { intrinsics::cosf32(self) }
 782     }
 783
 784     /// Computes the tangent of a number (in radians).
 785     ///
 786     /// ```
 787     /// use std::f64;
 788     ///
 789     /// let x = f64::consts::PI/4.0;
 790     /// let abs_difference = (x.tan() - 1.0).abs();
 791     ///
 792     /// assert!(abs_difference < 1e-10);
 793     /// ```
 794     #[stable(feature = "rust1", since = "1.0.0")]
 795     #[inline]
 796     pub fn tan(self) -> f32 {
 797         unsafe { cmath::tanf(self) }
 798     }
 799
 800     /// Computes the arcsine of a number. Return value is in radians in
 801     /// the range [-pi/2, pi/2] or NaN if the number is outside the range
 802     /// [-1, 1].
 803     ///
 804     /// ```
 805     /// use std::f32;
 806     ///
 807     /// let f = f32::consts::PI / 2.0;
 808     ///
 809     /// // asin(sin(pi/2))
 810     /// let abs_difference = f.sin().asin().abs_sub(f32::consts::PI / 2.0);
 811     ///
 812     /// assert!(abs_difference <= f32::EPSILON);
 813     /// ```
 814     #[stable(feature = "rust1", since = "1.0.0")]
 815     #[inline]
 816     pub fn asin(self) -> f32 {
 817         unsafe { cmath::asinf(self) }
 818     }
 819
 820     /// Computes the arccosine of a number. Return value is in radians in
 821     /// the range [0, pi] or NaN if the number is outside the range
 822     /// [-1, 1].
 823     ///
 824     /// ```
 825     /// use std::f32;
 826     ///
 827     /// let f = f32::consts::PI / 4.0;
 828     ///
 829     /// // acos(cos(pi/4))
 830     /// let abs_difference = f.cos().acos().abs_sub(f32::consts::PI / 4.0);
 831     ///
 832     /// assert!(abs_difference <= f32::EPSILON);
 833     /// ```
 834     #[stable(feature = "rust1", since = "1.0.0")]
 835     #[inline]
 836     pub fn acos(self) -> f32 {
 837         unsafe { cmath::acosf(self) }
 838     }
 839
 840     /// Computes the arctangent of a number. Return value is in radians in the
 841     /// range [-pi/2, pi/2];
 842     ///
 843     /// ```
 844     /// use std::f32;
 845     ///
 846     /// let f = 1.0f32;
 847     ///
 848     /// // atan(tan(1))
 849     /// let abs_difference = f.tan().atan().abs_sub(1.0);
 850     ///
 851     /// assert!(abs_difference <= f32::EPSILON);
 852     /// ```
 853     #[stable(feature = "rust1", since = "1.0.0")]
 854     #[inline]
 855     pub fn atan(self) -> f32 {
 856         unsafe { cmath::atanf(self) }
 857     }
 858
 859     /// Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`).
 860     ///
 861     /// * `x = 0`, `y = 0`: `0`
 862     /// * `x >= 0`: `arctan(y/x)` -> `[-pi/2, pi/2]`
 863     /// * `y >= 0`: `arctan(y/x) + pi` -> `(pi/2, pi]`
 864     /// * `y < 0`: `arctan(y/x) - pi` -> `(-pi, -pi/2)`
 865     ///
 866     /// ```
 867     /// use std::f32;
 868     ///
 869     /// let pi = f32::consts::PI;
 870     /// // All angles from horizontal right (+x)
 871     /// // 45 deg counter-clockwise
 872     /// let x1 = 3.0f32;
 873     /// let y1 = -3.0f32;
 874     ///
 875     /// // 135 deg clockwise
 876     /// let x2 = -3.0f32;
 877     /// let y2 = 3.0f32;
 878     ///
 879     /// let abs_difference_1 = (y1.atan2(x1) - (-pi/4.0)).abs();
 880     /// let abs_difference_2 = (y2.atan2(x2) - 3.0*pi/4.0).abs();
 881     ///
 882     /// assert!(abs_difference_1 <= f32::EPSILON);
 883     /// assert!(abs_difference_2 <= f32::EPSILON);
 884     /// ```
 885     #[stable(feature = "rust1", since = "1.0.0")]
 886     #[inline]
 887     pub fn atan2(self, other: f32) -> f32 {
 888         unsafe { cmath::atan2f(self, other) }
 889     }
 890
 891     /// Simultaneously computes the sine and cosine of the number, `x`. Returns
 892     /// `(sin(x), cos(x))`.
 893     ///
 894     /// ```
 895     /// use std::f32;
 896     ///
 897     /// let x = f32::consts::PI/4.0;
 898     /// let f = x.sin_cos();
 899     ///
 900     /// let abs_difference_0 = (f.0 - x.sin()).abs();
 901     /// let abs_difference_1 = (f.1 - x.cos()).abs();
 902     ///
 903     /// assert!(abs_difference_0 <= f32::EPSILON);
 904     /// assert!(abs_difference_0 <= f32::EPSILON);
 905     /// ```
 906     #[stable(feature = "rust1", since = "1.0.0")]
 907     #[inline]
 908     pub fn sin_cos(self) -> (f32, f32) {
 909         (self.sin(), self.cos())
 910     }
 911
 912     /// Returns `e^(self) - 1` in a way that is accurate even if the
 913     /// number is close to zero.
 914     ///
 915     /// ```
 916     /// let x = 7.0f64;
 917     ///
 918     /// // e^(ln(7)) - 1
 919     /// let abs_difference = x.ln().exp_m1().abs_sub(6.0);
 920     ///
 921     /// assert!(abs_difference < 1e-10);
 922     /// ```
 923     #[stable(feature = "rust1", since = "1.0.0")]
 924     #[inline]
 925     pub fn exp_m1(self) -> f32 {
 926         unsafe { cmath::expm1f(self) }
 927     }
 928
 929     /// Returns `ln(1+n)` (natural logarithm) more accurately than if
 930     /// the operations were performed separately.
 931     ///
 932     /// ```
 933     /// use std::f32;
 934     ///
 935     /// let x = f32::consts::E - 1.0;
 936     ///
 937     /// // ln(1 + (e - 1)) == ln(e) == 1
 938     /// let abs_difference = (x.ln_1p() - 1.0).abs();
 939     ///
 940     /// assert!(abs_difference <= f32::EPSILON);
 941     /// ```
 942     #[stable(feature = "rust1", since = "1.0.0")]
 943     #[inline]
 944     pub fn ln_1p(self) -> f32 {
 945         unsafe { cmath::log1pf(self) }
 946     }
 947
 948     /// Hyperbolic sine function.
 949     ///
 950     /// ```
 951     /// use std::f32;
 952     ///
 953     /// let e = f32::consts::E;
 954     /// let x = 1.0f32;
 955     ///
 956     /// let f = x.sinh();
 957     /// // Solving sinh() at 1 gives `(e^2-1)/(2e)`
 958     /// let g = (e*e - 1.0)/(2.0*e);
 959     /// let abs_difference = (f - g).abs();
 960     ///
 961     /// assert!(abs_difference <= f32::EPSILON);
 962     /// ```
 963     #[stable(feature = "rust1", since = "1.0.0")]
 964     #[inline]
 965     pub fn sinh(self) -> f32 {
 966         unsafe { cmath::sinhf(self) }
 967     }
 968
 969     /// Hyperbolic cosine function.
 970     ///
 971     /// ```
 972     /// use std::f32;
 973     ///
 974     /// let e = f32::consts::E;
 975     /// let x = 1.0f32;
 976     /// let f = x.cosh();
 977     /// // Solving cosh() at 1 gives this result
 978     /// let g = (e*e + 1.0)/(2.0*e);
 979     /// let abs_difference = f.abs_sub(g);
 980     ///
 981     /// // Same result
 982     /// assert!(abs_difference <= f32::EPSILON);
 983     /// ```
 984     #[stable(feature = "rust1", since = "1.0.0")]
 985     #[inline]
 986     pub fn cosh(self) -> f32 {
 987         unsafe { cmath::coshf(self) }
 988     }
 989
 990     /// Hyperbolic tangent function.
 991     ///
 992     /// ```
 993     /// use std::f32;
 994     ///
 995     /// let e = f32::consts::E;
 996     /// let x = 1.0f32;
 997     ///
 998     /// let f = x.tanh();
 999     /// // Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))`
1000     /// let g = (1.0 - e.powi(-2))/(1.0 + e.powi(-2));
1001     /// let abs_difference = (f - g).abs();
1002     ///
1003     /// assert!(abs_difference <= f32::EPSILON);
1004     /// ```
1005     #[stable(feature = "rust1", since = "1.0.0")]
1006     #[inline]
1007     pub fn tanh(self) -> f32 {
1008         unsafe { cmath::tanhf(self) }
1009     }
1010
1011     /// Inverse hyperbolic sine function.
1012     ///
1013     /// ```
1014     /// use std::f32;
1015     ///
1016     /// let x = 1.0f32;
1017     /// let f = x.sinh().asinh();
1018     ///
1019     /// let abs_difference = (f - x).abs();
1020     ///
1021     /// assert!(abs_difference <= f32::EPSILON);
1022     /// ```
1023     #[stable(feature = "rust1", since = "1.0.0")]
1024     #[inline]
1025     pub fn asinh(self) -> f32 {
1026         match self {
1027             NEG_INFINITY => NEG_INFINITY,
1028             x => (x + ((x * x) + 1.0).sqrt()).ln(),
1029         }
1030     }
1031
1032     /// Inverse hyperbolic cosine function.
1033     ///
1034     /// ```
1035     /// use std::f32;
1036     ///
1037     /// let x = 1.0f32;
1038     /// let f = x.cosh().acosh();
1039     ///
1040     /// let abs_difference = (f - x).abs();
1041     ///
1042     /// assert!(abs_difference <= f32::EPSILON);
1043     /// ```
1044     #[stable(feature = "rust1", since = "1.0.0")]
1045     #[inline]
1046     pub fn acosh(self) -> f32 {
1047         match self {
1048             x if x < 1.0 => ::f32::NAN,
1049             x => (x + ((x * x) - 1.0).sqrt()).ln(),
1050         }
1051     }
1052
1053     /// Inverse hyperbolic tangent function.
1054     ///
1055     /// ```
1056     /// use std::f32;
1057     ///
1058     /// let e = f32::consts::E;
1059     /// let f = e.tanh().atanh();
1060     ///
1061     /// let abs_difference = f.abs_sub(e);
1062     ///
1063     /// assert!(abs_difference <= f32::EPSILON);
1064     /// ```
1065     #[stable(feature = "rust1", since = "1.0.0")]
1066     #[inline]
1067     pub fn atanh(self) -> f32 {
1068         0.5 * ((2.0 * self) / (1.0 - self)).ln_1p()
1069     }
1070 }
1071
1072 #[cfg(test)]
1073 mod tests {
1074     use f32;
1075     use f32::*;
1076     use num::*;
1077     use num::FpCategory as Fp;
1078
1079     #[test]
1080     fn test_num_f32() {
1081         test_num(10f32, 2f32);
1082     }
1083
1084     #[test]
1085     fn test_min_nan() {
1086         assert_eq!(NAN.min(2.0), 2.0);
1087         assert_eq!(2.0f32.min(NAN), 2.0);
1088     }
1089
1090     #[test]
1091     fn test_max_nan() {
1092         assert_eq!(NAN.max(2.0), 2.0);
1093         assert_eq!(2.0f32.max(NAN), 2.0);
1094     }
1095
1096     #[test]
1097     fn test_nan() {
1098         let nan: f32 = f32::NAN;
1099         assert!(nan.is_nan());
1100         assert!(!nan.is_infinite());
1101         assert!(!nan.is_finite());
1102         assert!(!nan.is_normal());
1103         assert!(!nan.is_sign_positive());
1104         assert!(!nan.is_sign_negative());
1105         assert_eq!(Fp::Nan, nan.classify());
1106     }
1107
1108     #[test]
1109     fn test_infinity() {
1110         let inf: f32 = f32::INFINITY;
1111         assert!(inf.is_infinite());
1112         assert!(!inf.is_finite());
1113         assert!(inf.is_sign_positive());
1114         assert!(!inf.is_sign_negative());
1115         assert!(!inf.is_nan());
1116         assert!(!inf.is_normal());
1117         assert_eq!(Fp::Infinite, inf.classify());
1118     }
1119
1120     #[test]
1121     fn test_neg_infinity() {
1122         let neg_inf: f32 = f32::NEG_INFINITY;
1123         assert!(neg_inf.is_infinite());
1124         assert!(!neg_inf.is_finite());
1125         assert!(!neg_inf.is_sign_positive());
1126         assert!(neg_inf.is_sign_negative());
1127         assert!(!neg_inf.is_nan());
1128         assert!(!neg_inf.is_normal());
1129         assert_eq!(Fp::Infinite, neg_inf.classify());
1130     }
1131
1132     #[test]
1133     fn test_zero() {
1134         let zero: f32 = 0.0f32;
1135         assert_eq!(0.0, zero);
1136         assert!(!zero.is_infinite());
1137         assert!(zero.is_finite());
1138         assert!(zero.is_sign_positive());
1139         assert!(!zero.is_sign_negative());
1140         assert!(!zero.is_nan());
1141         assert!(!zero.is_normal());
1142         assert_eq!(Fp::Zero, zero.classify());
1143     }
1144
1145     #[test]
1146     fn test_neg_zero() {
1147         let neg_zero: f32 = -0.0;
1148         assert_eq!(0.0, neg_zero);
1149         assert!(!neg_zero.is_infinite());
1150         assert!(neg_zero.is_finite());
1151         assert!(!neg_zero.is_sign_positive());
1152         assert!(neg_zero.is_sign_negative());
1153         assert!(!neg_zero.is_nan());
1154         assert!(!neg_zero.is_normal());
1155         assert_eq!(Fp::Zero, neg_zero.classify());
1156     }
1157
1158     #[test]
1159     fn test_one() {
1160         let one: f32 = 1.0f32;
1161         assert_eq!(1.0, one);
1162         assert!(!one.is_infinite());
1163         assert!(one.is_finite());
1164         assert!(one.is_sign_positive());
1165         assert!(!one.is_sign_negative());
1166         assert!(!one.is_nan());
1167         assert!(one.is_normal());
1168         assert_eq!(Fp::Normal, one.classify());
1169     }
1170
1171     #[test]
1172     fn test_is_nan() {
1173         let nan: f32 = f32::NAN;
1174         let inf: f32 = f32::INFINITY;
1175         let neg_inf: f32 = f32::NEG_INFINITY;
1176         assert!(nan.is_nan());
1177         assert!(!0.0f32.is_nan());
1178         assert!(!5.3f32.is_nan());
1179         assert!(!(-10.732f32).is_nan());
1180         assert!(!inf.is_nan());
1181         assert!(!neg_inf.is_nan());
1182     }
1183
1184     #[test]
1185     fn test_is_infinite() {
1186         let nan: f32 = f32::NAN;
1187         let inf: f32 = f32::INFINITY;
1188         let neg_inf: f32 = f32::NEG_INFINITY;
1189         assert!(!nan.is_infinite());
1190         assert!(inf.is_infinite());
1191         assert!(neg_inf.is_infinite());
1192         assert!(!0.0f32.is_infinite());
1193         assert!(!42.8f32.is_infinite());
1194         assert!(!(-109.2f32).is_infinite());
1195     }
1196
1197     #[test]
1198     fn test_is_finite() {
1199         let nan: f32 = f32::NAN;
1200         let inf: f32 = f32::INFINITY;
1201         let neg_inf: f32 = f32::NEG_INFINITY;
1202         assert!(!nan.is_finite());
1203         assert!(!inf.is_finite());
1204         assert!(!neg_inf.is_finite());
1205         assert!(0.0f32.is_finite());
1206         assert!(42.8f32.is_finite());
1207         assert!((-109.2f32).is_finite());
1208     }
1209
1210     #[test]
1211     fn test_is_normal() {
1212         let nan: f32 = f32::NAN;
1213         let inf: f32 = f32::INFINITY;
1214         let neg_inf: f32 = f32::NEG_INFINITY;
1215         let zero: f32 = 0.0f32;
1216         let neg_zero: f32 = -0.0;
1217         assert!(!nan.is_normal());
1218         assert!(!inf.is_normal());
1219         assert!(!neg_inf.is_normal());
1220         assert!(!zero.is_normal());
1221         assert!(!neg_zero.is_normal());
1222         assert!(1f32.is_normal());
1223         assert!(1e-37f32.is_normal());
1224         assert!(!1e-38f32.is_normal());
1225     }
1226
1227     #[test]
1228     fn test_classify() {
1229         let nan: f32 = f32::NAN;
1230         let inf: f32 = f32::INFINITY;
1231         let neg_inf: f32 = f32::NEG_INFINITY;
1232         let zero: f32 = 0.0f32;
1233         let neg_zero: f32 = -0.0;
1234         assert_eq!(nan.classify(), Fp::Nan);
1235         assert_eq!(inf.classify(), Fp::Infinite);
1236         assert_eq!(neg_inf.classify(), Fp::Infinite);
1237         assert_eq!(zero.classify(), Fp::Zero);
1238         assert_eq!(neg_zero.classify(), Fp::Zero);
1239         assert_eq!(1f32.classify(), Fp::Normal);
1240         assert_eq!(1e-37f32.classify(), Fp::Normal);
1241         assert_eq!(1e-38f32.classify(), Fp::Subnormal);
1242     }
1243
1244     #[test]
1245     fn test_integer_decode() {
1246         assert_eq!(3.14159265359f32.integer_decode(), (13176795, -22, 1));
1247         assert_eq!((-8573.5918555f32).integer_decode(), (8779358, -10, -1));
1248         assert_eq!(2f32.powf(100.0).integer_decode(), (8388608, 77, 1));
1249         assert_eq!(0f32.integer_decode(), (0, -150, 1));
1250         assert_eq!((-0f32).integer_decode(), (0, -150, -1));
1251         assert_eq!(INFINITY.integer_decode(), (8388608, 105, 1));
1252         assert_eq!(NEG_INFINITY.integer_decode(), (8388608, 105, -1));
1253         assert_eq!(NAN.integer_decode(), (12582912, 105, 1));
1254     }
1255
1256     #[test]
1257     fn test_floor() {
1258         assert_approx_eq!(1.0f32.floor(), 1.0f32);
1259         assert_approx_eq!(1.3f32.floor(), 1.0f32);
1260         assert_approx_eq!(1.5f32.floor(), 1.0f32);
1261         assert_approx_eq!(1.7f32.floor(), 1.0f32);
1262         assert_approx_eq!(0.0f32.floor(), 0.0f32);
1263         assert_approx_eq!((-0.0f32).floor(), -0.0f32);
1264         assert_approx_eq!((-1.0f32).floor(), -1.0f32);
1265         assert_approx_eq!((-1.3f32).floor(), -2.0f32);
1266         assert_approx_eq!((-1.5f32).floor(), -2.0f32);
1267         assert_approx_eq!((-1.7f32).floor(), -2.0f32);
1268     }
1269
1270     #[test]
1271     fn test_ceil() {
1272         assert_approx_eq!(1.0f32.ceil(), 1.0f32);
1273         assert_approx_eq!(1.3f32.ceil(), 2.0f32);
1274         assert_approx_eq!(1.5f32.ceil(), 2.0f32);
1275         assert_approx_eq!(1.7f32.ceil(), 2.0f32);
1276         assert_approx_eq!(0.0f32.ceil(), 0.0f32);
1277         assert_approx_eq!((-0.0f32).ceil(), -0.0f32);
1278         assert_approx_eq!((-1.0f32).ceil(), -1.0f32);
1279         assert_approx_eq!((-1.3f32).ceil(), -1.0f32);
1280         assert_approx_eq!((-1.5f32).ceil(), -1.0f32);
1281         assert_approx_eq!((-1.7f32).ceil(), -1.0f32);
1282     }
1283
1284     #[test]
1285     fn test_round() {
1286         assert_approx_eq!(1.0f32.round(), 1.0f32);
1287         assert_approx_eq!(1.3f32.round(), 1.0f32);
1288         assert_approx_eq!(1.5f32.round(), 2.0f32);
1289         assert_approx_eq!(1.7f32.round(), 2.0f32);
1290         assert_approx_eq!(0.0f32.round(), 0.0f32);
1291         assert_approx_eq!((-0.0f32).round(), -0.0f32);
1292         assert_approx_eq!((-1.0f32).round(), -1.0f32);
1293         assert_approx_eq!((-1.3f32).round(), -1.0f32);
1294         assert_approx_eq!((-1.5f32).round(), -2.0f32);
1295         assert_approx_eq!((-1.7f32).round(), -2.0f32);
1296     }
1297
1298     #[test]
1299     fn test_trunc() {
1300         assert_approx_eq!(1.0f32.trunc(), 1.0f32);
1301         assert_approx_eq!(1.3f32.trunc(), 1.0f32);
1302         assert_approx_eq!(1.5f32.trunc(), 1.0f32);
1303         assert_approx_eq!(1.7f32.trunc(), 1.0f32);
1304         assert_approx_eq!(0.0f32.trunc(), 0.0f32);
1305         assert_approx_eq!((-0.0f32).trunc(), -0.0f32);
1306         assert_approx_eq!((-1.0f32).trunc(), -1.0f32);
1307         assert_approx_eq!((-1.3f32).trunc(), -1.0f32);
1308         assert_approx_eq!((-1.5f32).trunc(), -1.0f32);
1309         assert_approx_eq!((-1.7f32).trunc(), -1.0f32);
1310     }
1311
1312     #[test]
1313     fn test_fract() {
1314         assert_approx_eq!(1.0f32.fract(), 0.0f32);
1315         assert_approx_eq!(1.3f32.fract(), 0.3f32);
1316         assert_approx_eq!(1.5f32.fract(), 0.5f32);
1317         assert_approx_eq!(1.7f32.fract(), 0.7f32);
1318         assert_approx_eq!(0.0f32.fract(), 0.0f32);
1319         assert_approx_eq!((-0.0f32).fract(), -0.0f32);
1320         assert_approx_eq!((-1.0f32).fract(), -0.0f32);
1321         assert_approx_eq!((-1.3f32).fract(), -0.3f32);
1322         assert_approx_eq!((-1.5f32).fract(), -0.5f32);
1323         assert_approx_eq!((-1.7f32).fract(), -0.7f32);
1324     }
1325
1326     #[test]
1327     fn test_abs() {
1328         assert_eq!(INFINITY.abs(), INFINITY);
1329         assert_eq!(1f32.abs(), 1f32);
1330         assert_eq!(0f32.abs(), 0f32);
1331         assert_eq!((-0f32).abs(), 0f32);
1332         assert_eq!((-1f32).abs(), 1f32);
1333         assert_eq!(NEG_INFINITY.abs(), INFINITY);
1334         assert_eq!((1f32/NEG_INFINITY).abs(), 0f32);
1335         assert!(NAN.abs().is_nan());
1336     }
1337
1338     #[test]
1339     fn test_signum() {
1340         assert_eq!(INFINITY.signum(), 1f32);
1341         assert_eq!(1f32.signum(), 1f32);
1342         assert_eq!(0f32.signum(), 1f32);
1343         assert_eq!((-0f32).signum(), -1f32);
1344         assert_eq!((-1f32).signum(), -1f32);
1345         assert_eq!(NEG_INFINITY.signum(), -1f32);
1346         assert_eq!((1f32/NEG_INFINITY).signum(), -1f32);
1347         assert!(NAN.signum().is_nan());
1348     }
1349
1350     #[test]
1351     fn test_is_sign_positive() {
1352         assert!(INFINITY.is_sign_positive());
1353         assert!(1f32.is_sign_positive());
1354         assert!(0f32.is_sign_positive());
1355         assert!(!(-0f32).is_sign_positive());
1356         assert!(!(-1f32).is_sign_positive());
1357         assert!(!NEG_INFINITY.is_sign_positive());
1358         assert!(!(1f32/NEG_INFINITY).is_sign_positive());
1359         assert!(!NAN.is_sign_positive());
1360     }
1361
1362     #[test]
1363     fn test_is_sign_negative() {
1364         assert!(!INFINITY.is_sign_negative());
1365         assert!(!1f32.is_sign_negative());
1366         assert!(!0f32.is_sign_negative());
1367         assert!((-0f32).is_sign_negative());
1368         assert!((-1f32).is_sign_negative());
1369         assert!(NEG_INFINITY.is_sign_negative());
1370         assert!((1f32/NEG_INFINITY).is_sign_negative());
1371         assert!(!NAN.is_sign_negative());
1372     }
1373
1374     #[test]
1375     fn test_mul_add() {
1376         let nan: f32 = f32::NAN;
1377         let inf: f32 = f32::INFINITY;
1378         let neg_inf: f32 = f32::NEG_INFINITY;
1379         assert_approx_eq!(12.3f32.mul_add(4.5, 6.7), 62.05);
1380         assert_approx_eq!((-12.3f32).mul_add(-4.5, -6.7), 48.65);
1381         assert_approx_eq!(0.0f32.mul_add(8.9, 1.2), 1.2);
1382         assert_approx_eq!(3.4f32.mul_add(-0.0, 5.6), 5.6);
1383         assert!(nan.mul_add(7.8, 9.0).is_nan());
1384         assert_eq!(inf.mul_add(7.8, 9.0), inf);
1385         assert_eq!(neg_inf.mul_add(7.8, 9.0), neg_inf);
1386         assert_eq!(8.9f32.mul_add(inf, 3.2), inf);
1387         assert_eq!((-3.2f32).mul_add(2.4, neg_inf), neg_inf);
1388     }
1389
1390     #[test]
1391     fn test_recip() {
1392         let nan: f32 = f32::NAN;
1393         let inf: f32 = f32::INFINITY;
1394         let neg_inf: f32 = f32::NEG_INFINITY;
1395         assert_eq!(1.0f32.recip(), 1.0);
1396         assert_eq!(2.0f32.recip(), 0.5);
1397         assert_eq!((-0.4f32).recip(), -2.5);
1398         assert_eq!(0.0f32.recip(), inf);
1399         assert!(nan.recip().is_nan());
1400         assert_eq!(inf.recip(), 0.0);
1401         assert_eq!(neg_inf.recip(), 0.0);
1402     }
1403
1404     #[test]
1405     fn test_powi() {
1406         let nan: f32 = f32::NAN;
1407         let inf: f32 = f32::INFINITY;
1408         let neg_inf: f32 = f32::NEG_INFINITY;
1409         assert_eq!(1.0f32.powi(1), 1.0);
1410         assert_approx_eq!((-3.1f32).powi(2), 9.61);
1411         assert_approx_eq!(5.9f32.powi(-2), 0.028727);
1412         assert_eq!(8.3f32.powi(0), 1.0);
1413         assert!(nan.powi(2).is_nan());
1414         assert_eq!(inf.powi(3), inf);
1415         assert_eq!(neg_inf.powi(2), inf);
1416     }
1417
1418     #[test]
1419     fn test_powf() {
1420         let nan: f32 = f32::NAN;
1421         let inf: f32 = f32::INFINITY;
1422         let neg_inf: f32 = f32::NEG_INFINITY;
1423         assert_eq!(1.0f32.powf(1.0), 1.0);
1424         assert_approx_eq!(3.4f32.powf(4.5), 246.408218);
1425         assert_approx_eq!(2.7f32.powf(-3.2), 0.041652);
1426         assert_approx_eq!((-3.1f32).powf(2.0), 9.61);
1427         assert_approx_eq!(5.9f32.powf(-2.0), 0.028727);
1428         assert_eq!(8.3f32.powf(0.0), 1.0);
1429         assert!(nan.powf(2.0).is_nan());
1430         assert_eq!(inf.powf(2.0), inf);
1431         assert_eq!(neg_inf.powf(3.0), neg_inf);
1432     }
1433
1434     #[test]
1435     fn test_sqrt_domain() {
1436         assert!(NAN.sqrt().is_nan());
1437         assert!(NEG_INFINITY.sqrt().is_nan());
1438         assert!((-1.0f32).sqrt().is_nan());
1439         assert_eq!((-0.0f32).sqrt(), -0.0);
1440         assert_eq!(0.0f32.sqrt(), 0.0);
1441         assert_eq!(1.0f32.sqrt(), 1.0);
1442         assert_eq!(INFINITY.sqrt(), INFINITY);
1443     }
1444
1445     #[test]
1446     fn test_exp() {
1447         assert_eq!(1.0, 0.0f32.exp());
1448         assert_approx_eq!(2.718282, 1.0f32.exp());
1449         assert_approx_eq!(148.413162, 5.0f32.exp());
1450
1451         let inf: f32 = f32::INFINITY;
1452         let neg_inf: f32 = f32::NEG_INFINITY;
1453         let nan: f32 = f32::NAN;
1454         assert_eq!(inf, inf.exp());
1455         assert_eq!(0.0, neg_inf.exp());
1456         assert!(nan.exp().is_nan());
1457     }
1458
1459     #[test]
1460     fn test_exp2() {
1461         assert_eq!(32.0, 5.0f32.exp2());
1462         assert_eq!(1.0, 0.0f32.exp2());
1463
1464         let inf: f32 = f32::INFINITY;
1465         let neg_inf: f32 = f32::NEG_INFINITY;
1466         let nan: f32 = f32::NAN;
1467         assert_eq!(inf, inf.exp2());
1468         assert_eq!(0.0, neg_inf.exp2());
1469         assert!(nan.exp2().is_nan());
1470     }
1471
1472     #[test]
1473     fn test_ln() {
1474         let nan: f32 = f32::NAN;
1475         let inf: f32 = f32::INFINITY;
1476         let neg_inf: f32 = f32::NEG_INFINITY;
1477         assert_approx_eq!(1.0f32.exp().ln(), 1.0);
1478         assert!(nan.ln().is_nan());
1479         assert_eq!(inf.ln(), inf);
1480         assert!(neg_inf.ln().is_nan());
1481         assert!((-2.3f32).ln().is_nan());
1482         assert_eq!((-0.0f32).ln(), neg_inf);
1483         assert_eq!(0.0f32.ln(), neg_inf);
1484         assert_approx_eq!(4.0f32.ln(), 1.386294);
1485     }
1486
1487     #[test]
1488     fn test_log() {
1489         let nan: f32 = f32::NAN;
1490         let inf: f32 = f32::INFINITY;
1491         let neg_inf: f32 = f32::NEG_INFINITY;
1492         assert_eq!(10.0f32.log(10.0), 1.0);
1493         assert_approx_eq!(2.3f32.log(3.5), 0.664858);
1494         assert_eq!(1.0f32.exp().log(1.0f32.exp()), 1.0);
1495         assert!(1.0f32.log(1.0).is_nan());
1496         assert!(1.0f32.log(-13.9).is_nan());
1497         assert!(nan.log(2.3).is_nan());
1498         assert_eq!(inf.log(10.0), inf);
1499         assert!(neg_inf.log(8.8).is_nan());
1500         assert!((-2.3f32).log(0.1).is_nan());
1501         assert_eq!((-0.0f32).log(2.0), neg_inf);
1502         assert_eq!(0.0f32.log(7.0), neg_inf);
1503     }
1504
1505     #[test]
1506     fn test_log2() {
1507         let nan: f32 = f32::NAN;
1508         let inf: f32 = f32::INFINITY;
1509         let neg_inf: f32 = f32::NEG_INFINITY;
1510         assert_approx_eq!(10.0f32.log2(), 3.321928);
1511         assert_approx_eq!(2.3f32.log2(), 1.201634);
1512         assert_approx_eq!(1.0f32.exp().log2(), 1.442695);
1513         assert!(nan.log2().is_nan());
1514         assert_eq!(inf.log2(), inf);
1515         assert!(neg_inf.log2().is_nan());
1516         assert!((-2.3f32).log2().is_nan());
1517         assert_eq!((-0.0f32).log2(), neg_inf);
1518         assert_eq!(0.0f32.log2(), neg_inf);
1519     }
1520
1521     #[test]
1522     fn test_log10() {
1523         let nan: f32 = f32::NAN;
1524         let inf: f32 = f32::INFINITY;
1525         let neg_inf: f32 = f32::NEG_INFINITY;
1526         assert_eq!(10.0f32.log10(), 1.0);
1527         assert_approx_eq!(2.3f32.log10(), 0.361728);
1528         assert_approx_eq!(1.0f32.exp().log10(), 0.434294);
1529         assert_eq!(1.0f32.log10(), 0.0);
1530         assert!(nan.log10().is_nan());
1531         assert_eq!(inf.log10(), inf);
1532         assert!(neg_inf.log10().is_nan());
1533         assert!((-2.3f32).log10().is_nan());
1534         assert_eq!((-0.0f32).log10(), neg_inf);
1535         assert_eq!(0.0f32.log10(), neg_inf);
1536     }
1537
1538     #[test]
1539     fn test_to_degrees() {
1540         let pi: f32 = consts::PI;
1541         let nan: f32 = f32::NAN;
1542         let inf: f32 = f32::INFINITY;
1543         let neg_inf: f32 = f32::NEG_INFINITY;
1544         assert_eq!(0.0f32.to_degrees(), 0.0);
1545         assert_approx_eq!((-5.8f32).to_degrees(), -332.315521);
1546         assert_eq!(pi.to_degrees(), 180.0);
1547         assert!(nan.to_degrees().is_nan());
1548         assert_eq!(inf.to_degrees(), inf);
1549         assert_eq!(neg_inf.to_degrees(), neg_inf);
1550     }
1551
1552     #[test]
1553     fn test_to_radians() {
1554         let pi: f32 = consts::PI;
1555         let nan: f32 = f32::NAN;
1556         let inf: f32 = f32::INFINITY;
1557         let neg_inf: f32 = f32::NEG_INFINITY;
1558         assert_eq!(0.0f32.to_radians(), 0.0);
1559         assert_approx_eq!(154.6f32.to_radians(), 2.698279);
1560         assert_approx_eq!((-332.31f32).to_radians(), -5.799903);
1561         assert_eq!(180.0f32.to_radians(), pi);
1562         assert!(nan.to_radians().is_nan());
1563         assert_eq!(inf.to_radians(), inf);
1564         assert_eq!(neg_inf.to_radians(), neg_inf);
1565     }
1566
1567     #[test]
1568     fn test_ldexp() {
1569         // We have to use from_str until base-2 exponents
1570         // are supported in floating-point literals
1571         let f1: f32 = f32::from_str_radix("1p-123", 16).unwrap();
1572         let f2: f32 = f32::from_str_radix("1p-111", 16).unwrap();
1573         let f3: f32 = f32::from_str_radix("1.Cp-12", 16).unwrap();
1574         assert_eq!(f32::ldexp(1f32, -123), f1);
1575         assert_eq!(f32::ldexp(1f32, -111), f2);
1576         assert_eq!(f32::ldexp(1.75f32, -12), f3);
1577
1578         assert_eq!(f32::ldexp(0f32, -123), 0f32);
1579         assert_eq!(f32::ldexp(-0f32, -123), -0f32);
1580
1581         let inf: f32 = f32::INFINITY;
1582         let neg_inf: f32 = f32::NEG_INFINITY;
1583         let nan: f32 = f32::NAN;
1584         assert_eq!(f32::ldexp(inf, -123), inf);
1585         assert_eq!(f32::ldexp(neg_inf, -123), neg_inf);
1586         assert!(f32::ldexp(nan, -123).is_nan());
1587     }
1588
1589     #[test]
1590     fn test_frexp() {
1591         // We have to use from_str until base-2 exponents
1592         // are supported in floating-point literals
1593         let f1: f32 = f32::from_str_radix("1p-123", 16).unwrap();
1594         let f2: f32 = f32::from_str_radix("1p-111", 16).unwrap();
1595         let f3: f32 = f32::from_str_radix("1.Cp-123", 16).unwrap();
1596         let (x1, exp1) = f1.frexp();
1597         let (x2, exp2) = f2.frexp();
1598         let (x3, exp3) = f3.frexp();
1599         assert_eq!((x1, exp1), (0.5f32, -122));
1600         assert_eq!((x2, exp2), (0.5f32, -110));
1601         assert_eq!((x3, exp3), (0.875f32, -122));
1602         assert_eq!(f32::ldexp(x1, exp1), f1);
1603         assert_eq!(f32::ldexp(x2, exp2), f2);
1604         assert_eq!(f32::ldexp(x3, exp3), f3);
1605
1606         assert_eq!(0f32.frexp(), (0f32, 0));
1607         assert_eq!((-0f32).frexp(), (-0f32, 0));
1608     }
1609
1610     #[test] #[cfg_attr(windows, ignore)] // FIXME #8755
1611     fn test_frexp_nowin() {
1612         let inf: f32 = f32::INFINITY;
1613         let neg_inf: f32 = f32::NEG_INFINITY;
1614         let nan: f32 = f32::NAN;
1615         assert_eq!(match inf.frexp() { (x, _) => x }, inf);
1616         assert_eq!(match neg_inf.frexp() { (x, _) => x }, neg_inf);
1617         assert!(match nan.frexp() { (x, _) => x.is_nan() })
1618     }
1619
1620     #[test]
1621     fn test_abs_sub() {
1622         assert_eq!((-1f32).abs_sub(1f32), 0f32);
1623         assert_eq!(1f32.abs_sub(1f32), 0f32);
1624         assert_eq!(1f32.abs_sub(0f32), 1f32);
1625         assert_eq!(1f32.abs_sub(-1f32), 2f32);
1626         assert_eq!(NEG_INFINITY.abs_sub(0f32), 0f32);
1627         assert_eq!(INFINITY.abs_sub(1f32), INFINITY);
1628         assert_eq!(0f32.abs_sub(NEG_INFINITY), INFINITY);
1629         assert_eq!(0f32.abs_sub(INFINITY), 0f32);
1630     }
1631
1632     #[test]
1633     fn test_abs_sub_nowin() {
1634         assert!(NAN.abs_sub(-1f32).is_nan());
1635         assert!(1f32.abs_sub(NAN).is_nan());
1636     }
1637
1638     #[test]
1639     fn test_asinh() {
1640         assert_eq!(0.0f32.asinh(), 0.0f32);
1641         assert_eq!((-0.0f32).asinh(), -0.0f32);
1642
1643         let inf: f32 = f32::INFINITY;
1644         let neg_inf: f32 = f32::NEG_INFINITY;
1645         let nan: f32 = f32::NAN;
1646         assert_eq!(inf.asinh(), inf);
1647         assert_eq!(neg_inf.asinh(), neg_inf);
1648         assert!(nan.asinh().is_nan());
1649         assert_approx_eq!(2.0f32.asinh(), 1.443635475178810342493276740273105f32);
1650         assert_approx_eq!((-2.0f32).asinh(), -1.443635475178810342493276740273105f32);
1651     }
1652
1653     #[test]
1654     fn test_acosh() {
1655         assert_eq!(1.0f32.acosh(), 0.0f32);
1656         assert!(0.999f32.acosh().is_nan());
1657
1658         let inf: f32 = f32::INFINITY;
1659         let neg_inf: f32 = f32::NEG_INFINITY;
1660         let nan: f32 = f32::NAN;
1661         assert_eq!(inf.acosh(), inf);
1662         assert!(neg_inf.acosh().is_nan());
1663         assert!(nan.acosh().is_nan());
1664         assert_approx_eq!(2.0f32.acosh(), 1.31695789692481670862504634730796844f32);
1665         assert_approx_eq!(3.0f32.acosh(), 1.76274717403908605046521864995958461f32);
1666     }
1667
1668     #[test]
1669     fn test_atanh() {
1670         assert_eq!(0.0f32.atanh(), 0.0f32);
1671         assert_eq!((-0.0f32).atanh(), -0.0f32);
1672
1673         let inf32: f32 = f32::INFINITY;
1674         let neg_inf32: f32 = f32::NEG_INFINITY;
1675         assert_eq!(1.0f32.atanh(), inf32);
1676         assert_eq!((-1.0f32).atanh(), neg_inf32);
1677
1678         assert!(2f64.atanh().atanh().is_nan());
1679         assert!((-2f64).atanh().atanh().is_nan());
1680
1681         let inf64: f32 = f32::INFINITY;
1682         let neg_inf64: f32 = f32::NEG_INFINITY;
1683         let nan32: f32 = f32::NAN;
1684         assert!(inf64.atanh().is_nan());
1685         assert!(neg_inf64.atanh().is_nan());
1686         assert!(nan32.atanh().is_nan());
1687
1688         assert_approx_eq!(0.5f32.atanh(), 0.54930614433405484569762261846126285f32);
1689         assert_approx_eq!((-0.5f32).atanh(), -0.54930614433405484569762261846126285f32);
1690     }
1691
1692     #[test]
1693     fn test_real_consts() {
1694         use super::consts;
1695
1696         let pi: f32 = consts::PI;
1697         let two_pi: f32 = consts::PI_2;
1698         let frac_pi_2: f32 = consts::FRAC_PI_2;
1699         let frac_pi_3: f32 = consts::FRAC_PI_3;
1700         let frac_pi_4: f32 = consts::FRAC_PI_4;
1701         let frac_pi_6: f32 = consts::FRAC_PI_6;
1702         let frac_pi_8: f32 = consts::FRAC_PI_8;
1703         let frac_1_pi: f32 = consts::FRAC_1_PI;
1704         let frac_2_pi: f32 = consts::FRAC_2_PI;
1705         let frac_2_sqrtpi: f32 = consts::FRAC_2_SQRT_PI;
1706         let sqrt2: f32 = consts::SQRT_2;
1707         let frac_1_sqrt2: f32 = consts::FRAC_1_SQRT_2;
1708         let e: f32 = consts::E;
1709         let log2_e: f32 = consts::LOG2_E;
1710         let log10_e: f32 = consts::LOG10_E;
1711         let ln_2: f32 = consts::LN_2;
1712         let ln_10: f32 = consts::LN_10;
1713
1714         assert_approx_eq!(two_pi, 2f32 * pi);
1715         assert_approx_eq!(frac_pi_2, pi / 2f32);
1716         assert_approx_eq!(frac_pi_3, pi / 3f32);
1717         assert_approx_eq!(frac_pi_4, pi / 4f32);
1718         assert_approx_eq!(frac_pi_6, pi / 6f32);
1719         assert_approx_eq!(frac_pi_8, pi / 8f32);
1720         assert_approx_eq!(frac_1_pi, 1f32 / pi);
1721         assert_approx_eq!(frac_2_pi, 2f32 / pi);
1722         assert_approx_eq!(frac_2_sqrtpi, 2f32 / pi.sqrt());
1723         assert_approx_eq!(sqrt2, 2f32.sqrt());
1724         assert_approx_eq!(frac_1_sqrt2, 1f32 / 2f32.sqrt());
1725         assert_approx_eq!(log2_e, e.log2());
1726         assert_approx_eq!(log10_e, e.log10());
1727         assert_approx_eq!(ln_2, 2f32.ln());
1728         assert_approx_eq!(ln_10, 10f32.ln());
1729     }
1730 }