library/std/src/f32.rs

   1 //! Constants specific to the `f32` single-precision floating point type.
   2 //!
   3 //! *[See also the `f32` primitive type](primitive@f32).*
   4 //!
   5 //! Mathematically significant numbers are provided in the `consts` sub-module.
   6 //!
   7 //! For the constants defined directly in this module
   8 //! (as distinct from those defined in the `consts` sub-module),
   9 //! new code should instead use the associated constants
  10 //! defined directly on the `f32` type.
  11
  12 #![stable(feature = "rust1", since = "1.0.0")]
  13 #![allow(missing_docs)]
  14
  15 #[cfg(test)]
  16 mod tests;
  17
  18 #[cfg(not(test))]
  19 use crate::intrinsics;
  20 #[cfg(not(test))]
  21 use crate::sys::cmath;
  22
  23 #[stable(feature = "rust1", since = "1.0.0")]
  24 #[allow(deprecated, deprecated_in_future)]
  25 pub use core::f32::{
  26     consts, DIGITS, EPSILON, INFINITY, MANTISSA_DIGITS, MAX, MAX_10_EXP, MAX_EXP, MIN, MIN_10_EXP,
  27     MIN_EXP, MIN_POSITIVE, NAN, NEG_INFINITY, RADIX,
  28 };
  29
  30 #[cfg(not(test))]
  31 impl f32 {
  32     /// Returns the largest integer less than or equal to `self`.
  33     ///
  34     /// # Examples
  35     ///
  36     /// ```
  37     /// let f = 3.7_f32;
  38     /// let g = 3.0_f32;
  39     /// let h = -3.7_f32;
  40     ///
  41     /// assert_eq!(f.floor(), 3.0);
  42     /// assert_eq!(g.floor(), 3.0);
  43     /// assert_eq!(h.floor(), -4.0);
  44     /// ```
  45     #[rustc_allow_incoherent_impl]
  46     #[must_use = "method returns a new number and does not mutate the original value"]
  47     #[stable(feature = "rust1", since = "1.0.0")]
  48     #[inline]
  49     pub fn floor(self) -> f32 {
  50         unsafe { intrinsics::floorf32(self) }
  51     }
  52
  53     /// Returns the smallest integer greater than or equal to `self`.
  54     ///
  55     /// # Examples
  56     ///
  57     /// ```
  58     /// let f = 3.01_f32;
  59     /// let g = 4.0_f32;
  60     ///
  61     /// assert_eq!(f.ceil(), 4.0);
  62     /// assert_eq!(g.ceil(), 4.0);
  63     /// ```
  64     #[rustc_allow_incoherent_impl]
  65     #[must_use = "method returns a new number and does not mutate the original value"]
  66     #[stable(feature = "rust1", since = "1.0.0")]
  67     #[inline]
  68     pub fn ceil(self) -> f32 {
  69         unsafe { intrinsics::ceilf32(self) }
  70     }
  71
  72     /// Returns the nearest integer to `self`. Round half-way cases away from
  73     /// `0.0`.
  74     ///
  75     /// # Examples
  76     ///
  77     /// ```
  78     /// let f = 3.3_f32;
  79     /// let g = -3.3_f32;
  80     ///
  81     /// assert_eq!(f.round(), 3.0);
  82     /// assert_eq!(g.round(), -3.0);
  83     /// ```
  84     #[rustc_allow_incoherent_impl]
  85     #[must_use = "method returns a new number and does not mutate the original value"]
  86     #[stable(feature = "rust1", since = "1.0.0")]
  87     #[inline]
  88     pub fn round(self) -> f32 {
  89         unsafe { intrinsics::roundf32(self) }
  90     }
  91
  92     /// Returns the integer part of `self`.
  93     /// This means that non-integer numbers are always truncated towards zero.
  94     ///
  95     /// # Examples
  96     ///
  97     /// ```
  98     /// let f = 3.7_f32;
  99     /// let g = 3.0_f32;
 100     /// let h = -3.7_f32;
 101     ///
 102     /// assert_eq!(f.trunc(), 3.0);
 103     /// assert_eq!(g.trunc(), 3.0);
 104     /// assert_eq!(h.trunc(), -3.0);
 105     /// ```
 106     #[rustc_allow_incoherent_impl]
 107     #[must_use = "method returns a new number and does not mutate the original value"]
 108     #[stable(feature = "rust1", since = "1.0.0")]
 109     #[inline]
 110     pub fn trunc(self) -> f32 {
 111         unsafe { intrinsics::truncf32(self) }
 112     }
 113
 114     /// Returns the fractional part of `self`.
 115     ///
 116     /// # Examples
 117     ///
 118     /// ```
 119     /// let x = 3.6_f32;
 120     /// let y = -3.6_f32;
 121     /// let abs_difference_x = (x.fract() - 0.6).abs();
 122     /// let abs_difference_y = (y.fract() - (-0.6)).abs();
 123     ///
 124     /// assert!(abs_difference_x <= f32::EPSILON);
 125     /// assert!(abs_difference_y <= f32::EPSILON);
 126     /// ```
 127     #[rustc_allow_incoherent_impl]
 128     #[must_use = "method returns a new number and does not mutate the original value"]
 129     #[stable(feature = "rust1", since = "1.0.0")]
 130     #[inline]
 131     pub fn fract(self) -> f32 {
 132         self - self.trunc()
 133     }
 134
 135     /// Computes the absolute value of `self`.
 136     ///
 137     /// # Examples
 138     ///
 139     /// ```
 140     /// let x = 3.5_f32;
 141     /// let y = -3.5_f32;
 142     ///
 143     /// let abs_difference_x = (x.abs() - x).abs();
 144     /// let abs_difference_y = (y.abs() - (-y)).abs();
 145     ///
 146     /// assert!(abs_difference_x <= f32::EPSILON);
 147     /// assert!(abs_difference_y <= f32::EPSILON);
 148     ///
 149     /// assert!(f32::NAN.abs().is_nan());
 150     /// ```
 151     #[rustc_allow_incoherent_impl]
 152     #[must_use = "method returns a new number and does not mutate the original value"]
 153     #[stable(feature = "rust1", since = "1.0.0")]
 154     #[inline]
 155     pub fn abs(self) -> f32 {
 156         unsafe { intrinsics::fabsf32(self) }
 157     }
 158
 159     /// Returns a number that represents the sign of `self`.
 160     ///
 161     /// - `1.0` if the number is positive, `+0.0` or `INFINITY`
 162     /// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
 163     /// - NaN if the number is NaN
 164     ///
 165     /// # Examples
 166     ///
 167     /// ```
 168     /// let f = 3.5_f32;
 169     ///
 170     /// assert_eq!(f.signum(), 1.0);
 171     /// assert_eq!(f32::NEG_INFINITY.signum(), -1.0);
 172     ///
 173     /// assert!(f32::NAN.signum().is_nan());
 174     /// ```
 175     #[rustc_allow_incoherent_impl]
 176     #[must_use = "method returns a new number and does not mutate the original value"]
 177     #[stable(feature = "rust1", since = "1.0.0")]
 178     #[inline]
 179     pub fn signum(self) -> f32 {
 180         if self.is_nan() { Self::NAN } else { 1.0_f32.copysign(self) }
 181     }
 182
 183     /// Returns a number composed of the magnitude of `self` and the sign of
 184     /// `sign`.
 185     ///
 186     /// Equal to `self` if the sign of `self` and `sign` are the same, otherwise
 187     /// equal to `-self`. If `self` is a NaN, then a NaN with the sign bit of
 188     /// `sign` is returned. Note, however, that conserving the sign bit on NaN
 189     /// across arithmetical operations is not generally guaranteed.
 190     /// See [explanation of NaN as a special value](primitive@f32) for more info.
 191     ///
 192     /// # Examples
 193     ///
 194     /// ```
 195     /// let f = 3.5_f32;
 196     ///
 197     /// assert_eq!(f.copysign(0.42), 3.5_f32);
 198     /// assert_eq!(f.copysign(-0.42), -3.5_f32);
 199     /// assert_eq!((-f).copysign(0.42), 3.5_f32);
 200     /// assert_eq!((-f).copysign(-0.42), -3.5_f32);
 201     ///
 202     /// assert!(f32::NAN.copysign(1.0).is_nan());
 203     /// ```
 204     #[rustc_allow_incoherent_impl]
 205     #[must_use = "method returns a new number and does not mutate the original value"]
 206     #[inline]
 207     #[stable(feature = "copysign", since = "1.35.0")]
 208     pub fn copysign(self, sign: f32) -> f32 {
 209         unsafe { intrinsics::copysignf32(self, sign) }
 210     }
 211
 212     /// Fused multiply-add. Computes `(self * a) + b` with only one rounding
 213     /// error, yielding a more accurate result than an unfused multiply-add.
 214     ///
 215     /// Using `mul_add` *may* be more performant than an unfused multiply-add if
 216     /// the target architecture has a dedicated `fma` CPU instruction. However,
 217     /// this is not always true, and will be heavily dependant on designing
 218     /// algorithms with specific target hardware in mind.
 219     ///
 220     /// # Examples
 221     ///
 222     /// ```
 223     /// let m = 10.0_f32;
 224     /// let x = 4.0_f32;
 225     /// let b = 60.0_f32;
 226     ///
 227     /// // 100.0
 228     /// let abs_difference = (m.mul_add(x, b) - ((m * x) + b)).abs();
 229     ///
 230     /// assert!(abs_difference <= f32::EPSILON);
 231     /// ```
 232     #[rustc_allow_incoherent_impl]
 233     #[must_use = "method returns a new number and does not mutate the original value"]
 234     #[stable(feature = "rust1", since = "1.0.0")]
 235     #[inline]
 236     pub fn mul_add(self, a: f32, b: f32) -> f32 {
 237         unsafe { intrinsics::fmaf32(self, a, b) }
 238     }
 239
 240     /// Calculates Euclidean division, the matching method for `rem_euclid`.
 241     ///
 242     /// This computes the integer `n` such that
 243     /// `self = n * rhs + self.rem_euclid(rhs)`.
 244     /// In other words, the result is `self / rhs` rounded to the integer `n`
 245     /// such that `self >= n * rhs`.
 246     ///
 247     /// # Examples
 248     ///
 249     /// ```
 250     /// let a: f32 = 7.0;
 251     /// let b = 4.0;
 252     /// assert_eq!(a.div_euclid(b), 1.0); // 7.0 > 4.0 * 1.0
 253     /// assert_eq!((-a).div_euclid(b), -2.0); // -7.0 >= 4.0 * -2.0
 254     /// assert_eq!(a.div_euclid(-b), -1.0); // 7.0 >= -4.0 * -1.0
 255     /// assert_eq!((-a).div_euclid(-b), 2.0); // -7.0 >= -4.0 * 2.0
 256     /// ```
 257     #[rustc_allow_incoherent_impl]
 258     #[must_use = "method returns a new number and does not mutate the original value"]
 259     #[inline]
 260     #[stable(feature = "euclidean_division", since = "1.38.0")]
 261     pub fn div_euclid(self, rhs: f32) -> f32 {
 262         let q = (self / rhs).trunc();
 263         if self % rhs < 0.0 {
 264             return if rhs > 0.0 { q - 1.0 } else { q + 1.0 };
 265         }
 266         q
 267     }
 268
 269     /// Calculates the least nonnegative remainder of `self (mod rhs)`.
 270     ///
 271     /// In particular, the return value `r` satisfies `0.0 <= r < rhs.abs()` in
 272     /// most cases. However, due to a floating point round-off error it can
 273     /// result in `r == rhs.abs()`, violating the mathematical definition, if
 274     /// `self` is much smaller than `rhs.abs()` in magnitude and `self < 0.0`.
 275     /// This result is not an element of the function's codomain, but it is the
 276     /// closest floating point number in the real numbers and thus fulfills the
 277     /// property `self == self.div_euclid(rhs) * rhs + self.rem_euclid(rhs)`
 278     /// approximatively.
 279     ///
 280     /// # Examples
 281     ///
 282     /// ```
 283     /// let a: f32 = 7.0;
 284     /// let b = 4.0;
 285     /// assert_eq!(a.rem_euclid(b), 3.0);
 286     /// assert_eq!((-a).rem_euclid(b), 1.0);
 287     /// assert_eq!(a.rem_euclid(-b), 3.0);
 288     /// assert_eq!((-a).rem_euclid(-b), 1.0);
 289     /// // limitation due to round-off error
 290     /// assert!((-f32::EPSILON).rem_euclid(3.0) != 0.0);
 291     /// ```
 292     #[rustc_allow_incoherent_impl]
 293     #[must_use = "method returns a new number and does not mutate the original value"]
 294     #[inline]
 295     #[stable(feature = "euclidean_division", since = "1.38.0")]
 296     pub fn rem_euclid(self, rhs: f32) -> f32 {
 297         let r = self % rhs;
 298         if r < 0.0 { r + rhs.abs() } else { r }
 299     }
 300
 301     /// Raises a number to an integer power.
 302     ///
 303     /// Using this function is generally faster than using `powf`.
 304     /// It might have a different sequence of rounding operations than `powf`,
 305     /// so the results are not guaranteed to agree.
 306     ///
 307     /// # Examples
 308     ///
 309     /// ```
 310     /// let x = 2.0_f32;
 311     /// let abs_difference = (x.powi(2) - (x * x)).abs();
 312     ///
 313     /// assert!(abs_difference <= f32::EPSILON);
 314     /// ```
 315     #[rustc_allow_incoherent_impl]
 316     #[must_use = "method returns a new number and does not mutate the original value"]
 317     #[stable(feature = "rust1", since = "1.0.0")]
 318     #[inline]
 319     pub fn powi(self, n: i32) -> f32 {
 320         unsafe { intrinsics::powif32(self, n) }
 321     }
 322
 323     /// Raises a number to a floating point power.
 324     ///
 325     /// # Examples
 326     ///
 327     /// ```
 328     /// let x = 2.0_f32;
 329     /// let abs_difference = (x.powf(2.0) - (x * x)).abs();
 330     ///
 331     /// assert!(abs_difference <= f32::EPSILON);
 332     /// ```
 333     #[rustc_allow_incoherent_impl]
 334     #[must_use = "method returns a new number and does not mutate the original value"]
 335     #[stable(feature = "rust1", since = "1.0.0")]
 336     #[inline]
 337     pub fn powf(self, n: f32) -> f32 {
 338         unsafe { intrinsics::powf32(self, n) }
 339     }
 340
 341     /// Returns the square root of a number.
 342     ///
 343     /// Returns NaN if `self` is a negative number other than `-0.0`.
 344     ///
 345     /// # Examples
 346     ///
 347     /// ```
 348     /// let positive = 4.0_f32;
 349     /// let negative = -4.0_f32;
 350     /// let negative_zero = -0.0_f32;
 351     ///
 352     /// let abs_difference = (positive.sqrt() - 2.0).abs();
 353     ///
 354     /// assert!(abs_difference <= f32::EPSILON);
 355     /// assert!(negative.sqrt().is_nan());
 356     /// assert!(negative_zero.sqrt() == negative_zero);
 357     /// ```
 358     #[rustc_allow_incoherent_impl]
 359     #[must_use = "method returns a new number and does not mutate the original value"]
 360     #[stable(feature = "rust1", since = "1.0.0")]
 361     #[inline]
 362     pub fn sqrt(self) -> f32 {
 363         unsafe { intrinsics::sqrtf32(self) }
 364     }
 365
 366     /// Returns `e^(self)`, (the exponential function).
 367     ///
 368     /// # Examples
 369     ///
 370     /// ```
 371     /// let one = 1.0f32;
 372     /// // e^1
 373     /// let e = one.exp();
 374     ///
 375     /// // ln(e) - 1 == 0
 376     /// let abs_difference = (e.ln() - 1.0).abs();
 377     ///
 378     /// assert!(abs_difference <= f32::EPSILON);
 379     /// ```
 380     #[rustc_allow_incoherent_impl]
 381     #[must_use = "method returns a new number and does not mutate the original value"]
 382     #[stable(feature = "rust1", since = "1.0.0")]
 383     #[inline]
 384     pub fn exp(self) -> f32 {
 385         unsafe { intrinsics::expf32(self) }
 386     }
 387
 388     /// Returns `2^(self)`.
 389     ///
 390     /// # Examples
 391     ///
 392     /// ```
 393     /// let f = 2.0f32;
 394     ///
 395     /// // 2^2 - 4 == 0
 396     /// let abs_difference = (f.exp2() - 4.0).abs();
 397     ///
 398     /// assert!(abs_difference <= f32::EPSILON);
 399     /// ```
 400     #[rustc_allow_incoherent_impl]
 401     #[must_use = "method returns a new number and does not mutate the original value"]
 402     #[stable(feature = "rust1", since = "1.0.0")]
 403     #[inline]
 404     pub fn exp2(self) -> f32 {
 405         unsafe { intrinsics::exp2f32(self) }
 406     }
 407
 408     /// Returns the natural logarithm of the number.
 409     ///
 410     /// # Examples
 411     ///
 412     /// ```
 413     /// let one = 1.0f32;
 414     /// // e^1
 415     /// let e = one.exp();
 416     ///
 417     /// // ln(e) - 1 == 0
 418     /// let abs_difference = (e.ln() - 1.0).abs();
 419     ///
 420     /// assert!(abs_difference <= f32::EPSILON);
 421     /// ```
 422     #[rustc_allow_incoherent_impl]
 423     #[must_use = "method returns a new number and does not mutate the original value"]
 424     #[stable(feature = "rust1", since = "1.0.0")]
 425     #[inline]
 426     pub fn ln(self) -> f32 {
 427         unsafe { intrinsics::logf32(self) }
 428     }
 429
 430     /// Returns the logarithm of the number with respect to an arbitrary base.
 431     ///
 432     /// The result might not be correctly rounded owing to implementation details;
 433     /// `self.log2()` can produce more accurate results for base 2, and
 434     /// `self.log10()` can produce more accurate results for base 10.
 435     ///
 436     /// # Examples
 437     ///
 438     /// ```
 439     /// let five = 5.0f32;
 440     ///
 441     /// // log5(5) - 1 == 0
 442     /// let abs_difference = (five.log(5.0) - 1.0).abs();
 443     ///
 444     /// assert!(abs_difference <= f32::EPSILON);
 445     /// ```
 446     #[rustc_allow_incoherent_impl]
 447     #[must_use = "method returns a new number and does not mutate the original value"]
 448     #[stable(feature = "rust1", since = "1.0.0")]
 449     #[inline]
 450     pub fn log(self, base: f32) -> f32 {
 451         self.ln() / base.ln()
 452     }
 453
 454     /// Returns the base 2 logarithm of the number.
 455     ///
 456     /// # Examples
 457     ///
 458     /// ```
 459     /// let two = 2.0f32;
 460     ///
 461     /// // log2(2) - 1 == 0
 462     /// let abs_difference = (two.log2() - 1.0).abs();
 463     ///
 464     /// assert!(abs_difference <= f32::EPSILON);
 465     /// ```
 466     #[rustc_allow_incoherent_impl]
 467     #[must_use = "method returns a new number and does not mutate the original value"]
 468     #[stable(feature = "rust1", since = "1.0.0")]
 469     #[inline]
 470     pub fn log2(self) -> f32 {
 471         #[cfg(target_os = "android")]
 472         return crate::sys::android::log2f32(self);
 473         #[cfg(not(target_os = "android"))]
 474         return unsafe { intrinsics::log2f32(self) };
 475     }
 476
 477     /// Returns the base 10 logarithm of the number.
 478     ///
 479     /// # Examples
 480     ///
 481     /// ```
 482     /// let ten = 10.0f32;
 483     ///
 484     /// // log10(10) - 1 == 0
 485     /// let abs_difference = (ten.log10() - 1.0).abs();
 486     ///
 487     /// assert!(abs_difference <= f32::EPSILON);
 488     /// ```
 489     #[rustc_allow_incoherent_impl]
 490     #[must_use = "method returns a new number and does not mutate the original value"]
 491     #[stable(feature = "rust1", since = "1.0.0")]
 492     #[inline]
 493     pub fn log10(self) -> f32 {
 494         unsafe { intrinsics::log10f32(self) }
 495     }
 496
 497     /// The positive difference of two numbers.
 498     ///
 499     /// * If `self <= other`: `0:0`
 500     /// * Else: `self - other`
 501     ///
 502     /// # Examples
 503     ///
 504     /// ```
 505     /// let x = 3.0f32;
 506     /// let y = -3.0f32;
 507     ///
 508     /// let abs_difference_x = (x.abs_sub(1.0) - 2.0).abs();
 509     /// let abs_difference_y = (y.abs_sub(1.0) - 0.0).abs();
 510     ///
 511     /// assert!(abs_difference_x <= f32::EPSILON);
 512     /// assert!(abs_difference_y <= f32::EPSILON);
 513     /// ```
 514     #[rustc_allow_incoherent_impl]
 515     #[must_use = "method returns a new number and does not mutate the original value"]
 516     #[stable(feature = "rust1", since = "1.0.0")]
 517     #[inline]
 518     #[deprecated(
 519         since = "1.10.0",
 520         note = "you probably meant `(self - other).abs()`: \
 521                 this operation is `(self - other).max(0.0)` \
 522                 except that `abs_sub` also propagates NaNs (also \
 523                 known as `fdimf` in C). If you truly need the positive \
 524                 difference, consider using that expression or the C function \
 525                 `fdimf`, depending on how you wish to handle NaN (please consider \
 526                 filing an issue describing your use-case too)."
 527     )]
 528     pub fn abs_sub(self, other: f32) -> f32 {
 529         unsafe { cmath::fdimf(self, other) }
 530     }
 531
 532     /// Returns the cube root of a number.
 533     ///
 534     /// # Examples
 535     ///
 536     /// ```
 537     /// let x = 8.0f32;
 538     ///
 539     /// // x^(1/3) - 2 == 0
 540     /// let abs_difference = (x.cbrt() - 2.0).abs();
 541     ///
 542     /// assert!(abs_difference <= f32::EPSILON);
 543     /// ```
 544     #[rustc_allow_incoherent_impl]
 545     #[must_use = "method returns a new number and does not mutate the original value"]
 546     #[stable(feature = "rust1", since = "1.0.0")]
 547     #[inline]
 548     pub fn cbrt(self) -> f32 {
 549         unsafe { cmath::cbrtf(self) }
 550     }
 551
 552     /// Calculates the length of the hypotenuse of a right-angle triangle given
 553     /// legs of length `x` and `y`.
 554     ///
 555     /// # Examples
 556     ///
 557     /// ```
 558     /// let x = 2.0f32;
 559     /// let y = 3.0f32;
 560     ///
 561     /// // sqrt(x^2 + y^2)
 562     /// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();
 563     ///
 564     /// assert!(abs_difference <= f32::EPSILON);
 565     /// ```
 566     #[rustc_allow_incoherent_impl]
 567     #[must_use = "method returns a new number and does not mutate the original value"]
 568     #[stable(feature = "rust1", since = "1.0.0")]
 569     #[inline]
 570     pub fn hypot(self, other: f32) -> f32 {
 571         unsafe { cmath::hypotf(self, other) }
 572     }
 573
 574     /// Computes the sine of a number (in radians).
 575     ///
 576     /// # Examples
 577     ///
 578     /// ```
 579     /// let x = std::f32::consts::FRAC_PI_2;
 580     ///
 581     /// let abs_difference = (x.sin() - 1.0).abs();
 582     ///
 583     /// assert!(abs_difference <= f32::EPSILON);
 584     /// ```
 585     #[rustc_allow_incoherent_impl]
 586     #[must_use = "method returns a new number and does not mutate the original value"]
 587     #[stable(feature = "rust1", since = "1.0.0")]
 588     #[inline]
 589     pub fn sin(self) -> f32 {
 590         unsafe { intrinsics::sinf32(self) }
 591     }
 592
 593     /// Computes the cosine of a number (in radians).
 594     ///
 595     /// # Examples
 596     ///
 597     /// ```
 598     /// let x = 2.0 * std::f32::consts::PI;
 599     ///
 600     /// let abs_difference = (x.cos() - 1.0).abs();
 601     ///
 602     /// assert!(abs_difference <= f32::EPSILON);
 603     /// ```
 604     #[rustc_allow_incoherent_impl]
 605     #[must_use = "method returns a new number and does not mutate the original value"]
 606     #[stable(feature = "rust1", since = "1.0.0")]
 607     #[inline]
 608     pub fn cos(self) -> f32 {
 609         unsafe { intrinsics::cosf32(self) }
 610     }
 611
 612     /// Computes the tangent of a number (in radians).
 613     ///
 614     /// # Examples
 615     ///
 616     /// ```
 617     /// let x = std::f32::consts::FRAC_PI_4;
 618     /// let abs_difference = (x.tan() - 1.0).abs();
 619     ///
 620     /// assert!(abs_difference <= f32::EPSILON);
 621     /// ```
 622     #[rustc_allow_incoherent_impl]
 623     #[must_use = "method returns a new number and does not mutate the original value"]
 624     #[stable(feature = "rust1", since = "1.0.0")]
 625     #[inline]
 626     pub fn tan(self) -> f32 {
 627         unsafe { cmath::tanf(self) }
 628     }
 629
 630     /// Computes the arcsine of a number. Return value is in radians in
 631     /// the range [-pi/2, pi/2] or NaN if the number is outside the range
 632     /// [-1, 1].
 633     ///
 634     /// # Examples
 635     ///
 636     /// ```
 637     /// let f = std::f32::consts::FRAC_PI_2;
 638     ///
 639     /// // asin(sin(pi/2))
 640     /// let abs_difference = (f.sin().asin() - std::f32::consts::FRAC_PI_2).abs();
 641     ///
 642     /// assert!(abs_difference <= f32::EPSILON);
 643     /// ```
 644     #[rustc_allow_incoherent_impl]
 645     #[must_use = "method returns a new number and does not mutate the original value"]
 646     #[stable(feature = "rust1", since = "1.0.0")]
 647     #[inline]
 648     pub fn asin(self) -> f32 {
 649         unsafe { cmath::asinf(self) }
 650     }
 651
 652     /// Computes the arccosine of a number. Return value is in radians in
 653     /// the range [0, pi] or NaN if the number is outside the range
 654     /// [-1, 1].
 655     ///
 656     /// # Examples
 657     ///
 658     /// ```
 659     /// let f = std::f32::consts::FRAC_PI_4;
 660     ///
 661     /// // acos(cos(pi/4))
 662     /// let abs_difference = (f.cos().acos() - std::f32::consts::FRAC_PI_4).abs();
 663     ///
 664     /// assert!(abs_difference <= f32::EPSILON);
 665     /// ```
 666     #[rustc_allow_incoherent_impl]
 667     #[must_use = "method returns a new number and does not mutate the original value"]
 668     #[stable(feature = "rust1", since = "1.0.0")]
 669     #[inline]
 670     pub fn acos(self) -> f32 {
 671         unsafe { cmath::acosf(self) }
 672     }
 673
 674     /// Computes the arctangent of a number. Return value is in radians in the
 675     /// range [-pi/2, pi/2];
 676     ///
 677     /// # Examples
 678     ///
 679     /// ```
 680     /// let f = 1.0f32;
 681     ///
 682     /// // atan(tan(1))
 683     /// let abs_difference = (f.tan().atan() - 1.0).abs();
 684     ///
 685     /// assert!(abs_difference <= f32::EPSILON);
 686     /// ```
 687     #[rustc_allow_incoherent_impl]
 688     #[must_use = "method returns a new number and does not mutate the original value"]
 689     #[stable(feature = "rust1", since = "1.0.0")]
 690     #[inline]
 691     pub fn atan(self) -> f32 {
 692         unsafe { cmath::atanf(self) }
 693     }
 694
 695     /// Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`) in radians.
 696     ///
 697     /// * `x = 0`, `y = 0`: `0`
 698     /// * `x >= 0`: `arctan(y/x)` -> `[-pi/2, pi/2]`
 699     /// * `y >= 0`: `arctan(y/x) + pi` -> `(pi/2, pi]`
 700     /// * `y < 0`: `arctan(y/x) - pi` -> `(-pi, -pi/2)`
 701     ///
 702     /// # Examples
 703     ///
 704     /// ```
 705     /// // Positive angles measured counter-clockwise
 706     /// // from positive x axis
 707     /// // -pi/4 radians (45 deg clockwise)
 708     /// let x1 = 3.0f32;
 709     /// let y1 = -3.0f32;
 710     ///
 711     /// // 3pi/4 radians (135 deg counter-clockwise)
 712     /// let x2 = -3.0f32;
 713     /// let y2 = 3.0f32;
 714     ///
 715     /// let abs_difference_1 = (y1.atan2(x1) - (-std::f32::consts::FRAC_PI_4)).abs();
 716     /// let abs_difference_2 = (y2.atan2(x2) - (3.0 * std::f32::consts::FRAC_PI_4)).abs();
 717     ///
 718     /// assert!(abs_difference_1 <= f32::EPSILON);
 719     /// assert!(abs_difference_2 <= f32::EPSILON);
 720     /// ```
 721     #[rustc_allow_incoherent_impl]
 722     #[must_use = "method returns a new number and does not mutate the original value"]
 723     #[stable(feature = "rust1", since = "1.0.0")]
 724     #[inline]
 725     pub fn atan2(self, other: f32) -> f32 {
 726         unsafe { cmath::atan2f(self, other) }
 727     }
 728
 729     /// Simultaneously computes the sine and cosine of the number, `x`. Returns
 730     /// `(sin(x), cos(x))`.
 731     ///
 732     /// # Examples
 733     ///
 734     /// ```
 735     /// let x = std::f32::consts::FRAC_PI_4;
 736     /// let f = x.sin_cos();
 737     ///
 738     /// let abs_difference_0 = (f.0 - x.sin()).abs();
 739     /// let abs_difference_1 = (f.1 - x.cos()).abs();
 740     ///
 741     /// assert!(abs_difference_0 <= f32::EPSILON);
 742     /// assert!(abs_difference_1 <= f32::EPSILON);
 743     /// ```
 744     #[rustc_allow_incoherent_impl]
 745     #[stable(feature = "rust1", since = "1.0.0")]
 746     #[inline]
 747     pub fn sin_cos(self) -> (f32, f32) {
 748         (self.sin(), self.cos())
 749     }
 750
 751     /// Returns `e^(self) - 1` in a way that is accurate even if the
 752     /// number is close to zero.
 753     ///
 754     /// # Examples
 755     ///
 756     /// ```
 757     /// let x = 1e-8_f32;
 758     ///
 759     /// // for very small x, e^x is approximately 1 + x + x^2 / 2
 760     /// let approx = x + x * x / 2.0;
 761     /// let abs_difference = (x.exp_m1() - approx).abs();
 762     ///
 763     /// assert!(abs_difference < 1e-10);
 764     /// ```
 765     #[rustc_allow_incoherent_impl]
 766     #[must_use = "method returns a new number and does not mutate the original value"]
 767     #[stable(feature = "rust1", since = "1.0.0")]
 768     #[inline]
 769     pub fn exp_m1(self) -> f32 {
 770         unsafe { cmath::expm1f(self) }
 771     }
 772
 773     /// Returns `ln(1+n)` (natural logarithm) more accurately than if
 774     /// the operations were performed separately.
 775     ///
 776     /// # Examples
 777     ///
 778     /// ```
 779     /// let x = 1e-8_f32;
 780     ///
 781     /// // for very small x, ln(1 + x) is approximately x - x^2 / 2
 782     /// let approx = x - x * x / 2.0;
 783     /// let abs_difference = (x.ln_1p() - approx).abs();
 784     ///
 785     /// assert!(abs_difference < 1e-10);
 786     /// ```
 787     #[rustc_allow_incoherent_impl]
 788     #[must_use = "method returns a new number and does not mutate the original value"]
 789     #[stable(feature = "rust1", since = "1.0.0")]
 790     #[inline]
 791     pub fn ln_1p(self) -> f32 {
 792         unsafe { cmath::log1pf(self) }
 793     }
 794
 795     /// Hyperbolic sine function.
 796     ///
 797     /// # Examples
 798     ///
 799     /// ```
 800     /// let e = std::f32::consts::E;
 801     /// let x = 1.0f32;
 802     ///
 803     /// let f = x.sinh();
 804     /// // Solving sinh() at 1 gives `(e^2-1)/(2e)`
 805     /// let g = ((e * e) - 1.0) / (2.0 * e);
 806     /// let abs_difference = (f - g).abs();
 807     ///
 808     /// assert!(abs_difference <= f32::EPSILON);
 809     /// ```
 810     #[rustc_allow_incoherent_impl]
 811     #[must_use = "method returns a new number and does not mutate the original value"]
 812     #[stable(feature = "rust1", since = "1.0.0")]
 813     #[inline]
 814     pub fn sinh(self) -> f32 {
 815         unsafe { cmath::sinhf(self) }
 816     }
 817
 818     /// Hyperbolic cosine function.
 819     ///
 820     /// # Examples
 821     ///
 822     /// ```
 823     /// let e = std::f32::consts::E;
 824     /// let x = 1.0f32;
 825     /// let f = x.cosh();
 826     /// // Solving cosh() at 1 gives this result
 827     /// let g = ((e * e) + 1.0) / (2.0 * e);
 828     /// let abs_difference = (f - g).abs();
 829     ///
 830     /// // Same result
 831     /// assert!(abs_difference <= f32::EPSILON);
 832     /// ```
 833     #[rustc_allow_incoherent_impl]
 834     #[must_use = "method returns a new number and does not mutate the original value"]
 835     #[stable(feature = "rust1", since = "1.0.0")]
 836     #[inline]
 837     pub fn cosh(self) -> f32 {
 838         unsafe { cmath::coshf(self) }
 839     }
 840
 841     /// Hyperbolic tangent function.
 842     ///
 843     /// # Examples
 844     ///
 845     /// ```
 846     /// let e = std::f32::consts::E;
 847     /// let x = 1.0f32;
 848     ///
 849     /// let f = x.tanh();
 850     /// // Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))`
 851     /// let g = (1.0 - e.powi(-2)) / (1.0 + e.powi(-2));
 852     /// let abs_difference = (f - g).abs();
 853     ///
 854     /// assert!(abs_difference <= f32::EPSILON);
 855     /// ```
 856     #[rustc_allow_incoherent_impl]
 857     #[must_use = "method returns a new number and does not mutate the original value"]
 858     #[stable(feature = "rust1", since = "1.0.0")]
 859     #[inline]
 860     pub fn tanh(self) -> f32 {
 861         unsafe { cmath::tanhf(self) }
 862     }
 863
 864     /// Inverse hyperbolic sine function.
 865     ///
 866     /// # Examples
 867     ///
 868     /// ```
 869     /// let x = 1.0f32;
 870     /// let f = x.sinh().asinh();
 871     ///
 872     /// let abs_difference = (f - x).abs();
 873     ///
 874     /// assert!(abs_difference <= f32::EPSILON);
 875     /// ```
 876     #[rustc_allow_incoherent_impl]
 877     #[must_use = "method returns a new number and does not mutate the original value"]
 878     #[stable(feature = "rust1", since = "1.0.0")]
 879     #[inline]
 880     pub fn asinh(self) -> f32 {
 881         (self.abs() + ((self * self) + 1.0).sqrt()).ln().copysign(self)
 882     }
 883
 884     /// Inverse hyperbolic cosine function.
 885     ///
 886     /// # Examples
 887     ///
 888     /// ```
 889     /// let x = 1.0f32;
 890     /// let f = x.cosh().acosh();
 891     ///
 892     /// let abs_difference = (f - x).abs();
 893     ///
 894     /// assert!(abs_difference <= f32::EPSILON);
 895     /// ```
 896     #[rustc_allow_incoherent_impl]
 897     #[must_use = "method returns a new number and does not mutate the original value"]
 898     #[stable(feature = "rust1", since = "1.0.0")]
 899     #[inline]
 900     pub fn acosh(self) -> f32 {
 901         if self < 1.0 { Self::NAN } else { (self + ((self * self) - 1.0).sqrt()).ln() }
 902     }
 903
 904     /// Inverse hyperbolic tangent function.
 905     ///
 906     /// # Examples
 907     ///
 908     /// ```
 909     /// let e = std::f32::consts::E;
 910     /// let f = e.tanh().atanh();
 911     ///
 912     /// let abs_difference = (f - e).abs();
 913     ///
 914     /// assert!(abs_difference <= 1e-5);
 915     /// ```
 916     #[rustc_allow_incoherent_impl]
 917     #[must_use = "method returns a new number and does not mutate the original value"]
 918     #[stable(feature = "rust1", since = "1.0.0")]
 919     #[inline]
 920     pub fn atanh(self) -> f32 {
 921         0.5 * ((2.0 * self) / (1.0 - self)).ln_1p()
 922     }
 923 }