1 //! Constants specific to the `f32` single-precision floating point type.
3 //! *[See also the `f32` primitive type](primitive@f32).*
5 //! Mathematically significant numbers are provided in the `consts` sub-module.
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.
12 #![stable(feature = "rust1", since = "1.0.0")]
13 #![allow(missing_docs)]
19 use crate::intrinsics;
21 use crate::sys::cmath;
23 #[stable(feature = "rust1", since = "1.0.0")]
24 #[allow(deprecated, deprecated_in_future)]
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,
31 #[lang = "f32_runtime"]
33 /// Returns the largest integer less than or equal to a number.
42 /// assert_eq!(f.floor(), 3.0);
43 /// assert_eq!(g.floor(), 3.0);
44 /// assert_eq!(h.floor(), -4.0);
46 #[must_use = "method returns a new number and does not mutate the original value"]
47 #[stable(feature = "rust1", since = "1.0.0")]
49 pub fn floor(self) -> f32 {
50 unsafe { intrinsics::floorf32(self) }
53 /// Returns the smallest integer greater than or equal to a number.
61 /// assert_eq!(f.ceil(), 4.0);
62 /// assert_eq!(g.ceil(), 4.0);
64 #[must_use = "method returns a new number and does not mutate the original value"]
65 #[stable(feature = "rust1", since = "1.0.0")]
67 pub fn ceil(self) -> f32 {
68 unsafe { intrinsics::ceilf32(self) }
71 /// Returns the nearest integer to a number. Round half-way cases away from
80 /// assert_eq!(f.round(), 3.0);
81 /// assert_eq!(g.round(), -3.0);
83 #[must_use = "method returns a new number and does not mutate the original value"]
84 #[stable(feature = "rust1", since = "1.0.0")]
86 pub fn round(self) -> f32 {
87 unsafe { intrinsics::roundf32(self) }
90 /// Returns the integer part of a number.
99 /// assert_eq!(f.trunc(), 3.0);
100 /// assert_eq!(g.trunc(), 3.0);
101 /// assert_eq!(h.trunc(), -3.0);
103 #[must_use = "method returns a new number and does not mutate the original value"]
104 #[stable(feature = "rust1", since = "1.0.0")]
106 pub fn trunc(self) -> f32 {
107 unsafe { intrinsics::truncf32(self) }
110 /// Returns the fractional part of a number.
116 /// let y = -3.6_f32;
117 /// let abs_difference_x = (x.fract() - 0.6).abs();
118 /// let abs_difference_y = (y.fract() - (-0.6)).abs();
120 /// assert!(abs_difference_x <= f32::EPSILON);
121 /// assert!(abs_difference_y <= f32::EPSILON);
123 #[must_use = "method returns a new number and does not mutate the original value"]
124 #[stable(feature = "rust1", since = "1.0.0")]
126 pub fn fract(self) -> f32 {
130 /// Computes the absolute value of `self`. Returns `NAN` if the
137 /// let y = -3.5_f32;
139 /// let abs_difference_x = (x.abs() - x).abs();
140 /// let abs_difference_y = (y.abs() - (-y)).abs();
142 /// assert!(abs_difference_x <= f32::EPSILON);
143 /// assert!(abs_difference_y <= f32::EPSILON);
145 /// assert!(f32::NAN.abs().is_nan());
147 #[must_use = "method returns a new number and does not mutate the original value"]
148 #[stable(feature = "rust1", since = "1.0.0")]
150 pub fn abs(self) -> f32 {
151 unsafe { intrinsics::fabsf32(self) }
154 /// Returns a number that represents the sign of `self`.
156 /// - `1.0` if the number is positive, `+0.0` or `INFINITY`
157 /// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
158 /// - `NAN` if the number is `NAN`
165 /// assert_eq!(f.signum(), 1.0);
166 /// assert_eq!(f32::NEG_INFINITY.signum(), -1.0);
168 /// assert!(f32::NAN.signum().is_nan());
170 #[must_use = "method returns a new number and does not mutate the original value"]
171 #[stable(feature = "rust1", since = "1.0.0")]
173 pub fn signum(self) -> f32 {
174 if self.is_nan() { Self::NAN } else { 1.0_f32.copysign(self) }
177 /// Returns a number composed of the magnitude of `self` and the sign of
180 /// Equal to `self` if the sign of `self` and `sign` are the same, otherwise
181 /// equal to `-self`. If `self` is a `NAN`, then a `NAN` with the sign of
182 /// `sign` is returned.
189 /// assert_eq!(f.copysign(0.42), 3.5_f32);
190 /// assert_eq!(f.copysign(-0.42), -3.5_f32);
191 /// assert_eq!((-f).copysign(0.42), 3.5_f32);
192 /// assert_eq!((-f).copysign(-0.42), -3.5_f32);
194 /// assert!(f32::NAN.copysign(1.0).is_nan());
196 #[must_use = "method returns a new number and does not mutate the original value"]
198 #[stable(feature = "copysign", since = "1.35.0")]
199 pub fn copysign(self, sign: f32) -> f32 {
200 unsafe { intrinsics::copysignf32(self, sign) }
203 /// Fused multiply-add. Computes `(self * a) + b` with only one rounding
204 /// error, yielding a more accurate result than an unfused multiply-add.
206 /// Using `mul_add` *may* be more performant than an unfused multiply-add if
207 /// the target architecture has a dedicated `fma` CPU instruction. However,
208 /// this is not always true, and will be heavily dependant on designing
209 /// algorithms with specific target hardware in mind.
214 /// let m = 10.0_f32;
216 /// let b = 60.0_f32;
219 /// let abs_difference = (m.mul_add(x, b) - ((m * x) + b)).abs();
221 /// assert!(abs_difference <= f32::EPSILON);
223 #[must_use = "method returns a new number and does not mutate the original value"]
224 #[stable(feature = "rust1", since = "1.0.0")]
226 pub fn mul_add(self, a: f32, b: f32) -> f32 {
227 unsafe { intrinsics::fmaf32(self, a, b) }
230 /// Calculates Euclidean division, the matching method for `rem_euclid`.
232 /// This computes the integer `n` such that
233 /// `self = n * rhs + self.rem_euclid(rhs)`.
234 /// In other words, the result is `self / rhs` rounded to the integer `n`
235 /// such that `self >= n * rhs`.
240 /// let a: f32 = 7.0;
242 /// assert_eq!(a.div_euclid(b), 1.0); // 7.0 > 4.0 * 1.0
243 /// assert_eq!((-a).div_euclid(b), -2.0); // -7.0 >= 4.0 * -2.0
244 /// assert_eq!(a.div_euclid(-b), -1.0); // 7.0 >= -4.0 * -1.0
245 /// assert_eq!((-a).div_euclid(-b), 2.0); // -7.0 >= -4.0 * 2.0
247 #[must_use = "method returns a new number and does not mutate the original value"]
249 #[stable(feature = "euclidean_division", since = "1.38.0")]
250 pub fn div_euclid(self, rhs: f32) -> f32 {
251 let q = (self / rhs).trunc();
252 if self % rhs < 0.0 {
253 return if rhs > 0.0 { q - 1.0 } else { q + 1.0 };
258 /// Calculates the least nonnegative remainder of `self (mod rhs)`.
260 /// In particular, the return value `r` satisfies `0.0 <= r < rhs.abs()` in
261 /// most cases. However, due to a floating point round-off error it can
262 /// result in `r == rhs.abs()`, violating the mathematical definition, if
263 /// `self` is much smaller than `rhs.abs()` in magnitude and `self < 0.0`.
264 /// This result is not an element of the function's codomain, but it is the
265 /// closest floating point number in the real numbers and thus fulfills the
266 /// property `self == self.div_euclid(rhs) * rhs + self.rem_euclid(rhs)`
272 /// let a: f32 = 7.0;
274 /// assert_eq!(a.rem_euclid(b), 3.0);
275 /// assert_eq!((-a).rem_euclid(b), 1.0);
276 /// assert_eq!(a.rem_euclid(-b), 3.0);
277 /// assert_eq!((-a).rem_euclid(-b), 1.0);
278 /// // limitation due to round-off error
279 /// assert!((-f32::EPSILON).rem_euclid(3.0) != 0.0);
281 #[must_use = "method returns a new number and does not mutate the original value"]
283 #[stable(feature = "euclidean_division", since = "1.38.0")]
284 pub fn rem_euclid(self, rhs: f32) -> f32 {
286 if r < 0.0 { r + rhs.abs() } else { r }
289 /// Raises a number to an integer power.
291 /// Using this function is generally faster than using `powf`
297 /// let abs_difference = (x.powi(2) - (x * x)).abs();
299 /// assert!(abs_difference <= f32::EPSILON);
301 #[must_use = "method returns a new number and does not mutate the original value"]
302 #[stable(feature = "rust1", since = "1.0.0")]
304 pub fn powi(self, n: i32) -> f32 {
305 unsafe { intrinsics::powif32(self, n) }
308 /// Raises a number to a floating point power.
314 /// let abs_difference = (x.powf(2.0) - (x * x)).abs();
316 /// assert!(abs_difference <= f32::EPSILON);
318 #[must_use = "method returns a new number and does not mutate the original value"]
319 #[stable(feature = "rust1", since = "1.0.0")]
321 pub fn powf(self, n: f32) -> f32 {
322 unsafe { intrinsics::powf32(self, n) }
325 /// Returns the square root of a number.
327 /// Returns NaN if `self` is a negative number.
332 /// let positive = 4.0_f32;
333 /// let negative = -4.0_f32;
335 /// let abs_difference = (positive.sqrt() - 2.0).abs();
337 /// assert!(abs_difference <= f32::EPSILON);
338 /// assert!(negative.sqrt().is_nan());
340 #[must_use = "method returns a new number and does not mutate the original value"]
341 #[stable(feature = "rust1", since = "1.0.0")]
343 pub fn sqrt(self) -> f32 {
344 unsafe { intrinsics::sqrtf32(self) }
347 /// Returns `e^(self)`, (the exponential function).
352 /// let one = 1.0f32;
354 /// let e = one.exp();
356 /// // ln(e) - 1 == 0
357 /// let abs_difference = (e.ln() - 1.0).abs();
359 /// assert!(abs_difference <= f32::EPSILON);
361 #[must_use = "method returns a new number and does not mutate the original value"]
362 #[stable(feature = "rust1", since = "1.0.0")]
364 pub fn exp(self) -> f32 {
365 unsafe { intrinsics::expf32(self) }
368 /// Returns `2^(self)`.
376 /// let abs_difference = (f.exp2() - 4.0).abs();
378 /// assert!(abs_difference <= f32::EPSILON);
380 #[must_use = "method returns a new number and does not mutate the original value"]
381 #[stable(feature = "rust1", since = "1.0.0")]
383 pub fn exp2(self) -> f32 {
384 unsafe { intrinsics::exp2f32(self) }
387 /// Returns the natural logarithm of the number.
392 /// let one = 1.0f32;
394 /// let e = one.exp();
396 /// // ln(e) - 1 == 0
397 /// let abs_difference = (e.ln() - 1.0).abs();
399 /// assert!(abs_difference <= f32::EPSILON);
401 #[must_use = "method returns a new number and does not mutate the original value"]
402 #[stable(feature = "rust1", since = "1.0.0")]
404 pub fn ln(self) -> f32 {
405 unsafe { intrinsics::logf32(self) }
408 /// Returns the logarithm of the number with respect to an arbitrary base.
410 /// The result may not be correctly rounded owing to implementation details;
411 /// `self.log2()` can produce more accurate results for base 2, and
412 /// `self.log10()` can produce more accurate results for base 10.
417 /// let five = 5.0f32;
419 /// // log5(5) - 1 == 0
420 /// let abs_difference = (five.log(5.0) - 1.0).abs();
422 /// assert!(abs_difference <= f32::EPSILON);
424 #[must_use = "method returns a new number and does not mutate the original value"]
425 #[stable(feature = "rust1", since = "1.0.0")]
427 pub fn log(self, base: f32) -> f32 {
428 self.ln() / base.ln()
431 /// Returns the base 2 logarithm of the number.
436 /// let two = 2.0f32;
438 /// // log2(2) - 1 == 0
439 /// let abs_difference = (two.log2() - 1.0).abs();
441 /// assert!(abs_difference <= f32::EPSILON);
443 #[must_use = "method returns a new number and does not mutate the original value"]
444 #[stable(feature = "rust1", since = "1.0.0")]
446 pub fn log2(self) -> f32 {
447 #[cfg(target_os = "android")]
448 return crate::sys::android::log2f32(self);
449 #[cfg(not(target_os = "android"))]
450 return unsafe { intrinsics::log2f32(self) };
453 /// Returns the base 10 logarithm of the number.
458 /// let ten = 10.0f32;
460 /// // log10(10) - 1 == 0
461 /// let abs_difference = (ten.log10() - 1.0).abs();
463 /// assert!(abs_difference <= f32::EPSILON);
465 #[must_use = "method returns a new number and does not mutate the original value"]
466 #[stable(feature = "rust1", since = "1.0.0")]
468 pub fn log10(self) -> f32 {
469 unsafe { intrinsics::log10f32(self) }
472 /// The positive difference of two numbers.
474 /// * If `self <= other`: `0:0`
475 /// * Else: `self - other`
483 /// let abs_difference_x = (x.abs_sub(1.0) - 2.0).abs();
484 /// let abs_difference_y = (y.abs_sub(1.0) - 0.0).abs();
486 /// assert!(abs_difference_x <= f32::EPSILON);
487 /// assert!(abs_difference_y <= f32::EPSILON);
489 #[must_use = "method returns a new number and does not mutate the original value"]
490 #[stable(feature = "rust1", since = "1.0.0")]
494 reason = "you probably meant `(self - other).abs()`: \
495 this operation is `(self - other).max(0.0)` \
496 except that `abs_sub` also propagates NaNs (also \
497 known as `fdimf` in C). If you truly need the positive \
498 difference, consider using that expression or the C function \
499 `fdimf`, depending on how you wish to handle NaN (please consider \
500 filing an issue describing your use-case too)."
502 pub fn abs_sub(self, other: f32) -> f32 {
503 unsafe { cmath::fdimf(self, other) }
506 /// Returns the cube root of a number.
513 /// // x^(1/3) - 2 == 0
514 /// let abs_difference = (x.cbrt() - 2.0).abs();
516 /// assert!(abs_difference <= f32::EPSILON);
518 #[must_use = "method returns a new number and does not mutate the original value"]
519 #[stable(feature = "rust1", since = "1.0.0")]
521 pub fn cbrt(self) -> f32 {
522 unsafe { cmath::cbrtf(self) }
525 /// Calculates the length of the hypotenuse of a right-angle triangle given
526 /// legs of length `x` and `y`.
534 /// // sqrt(x^2 + y^2)
535 /// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();
537 /// assert!(abs_difference <= f32::EPSILON);
539 #[must_use = "method returns a new number and does not mutate the original value"]
540 #[stable(feature = "rust1", since = "1.0.0")]
542 pub fn hypot(self, other: f32) -> f32 {
543 unsafe { cmath::hypotf(self, other) }
546 /// Computes the sine of a number (in radians).
551 /// let x = std::f32::consts::FRAC_PI_2;
553 /// let abs_difference = (x.sin() - 1.0).abs();
555 /// assert!(abs_difference <= f32::EPSILON);
557 #[must_use = "method returns a new number and does not mutate the original value"]
558 #[stable(feature = "rust1", since = "1.0.0")]
560 pub fn sin(self) -> f32 {
561 unsafe { intrinsics::sinf32(self) }
564 /// Computes the cosine of a number (in radians).
569 /// let x = 2.0 * std::f32::consts::PI;
571 /// let abs_difference = (x.cos() - 1.0).abs();
573 /// assert!(abs_difference <= f32::EPSILON);
575 #[must_use = "method returns a new number and does not mutate the original value"]
576 #[stable(feature = "rust1", since = "1.0.0")]
578 pub fn cos(self) -> f32 {
579 unsafe { intrinsics::cosf32(self) }
582 /// Computes the tangent of a number (in radians).
587 /// let x = std::f32::consts::FRAC_PI_4;
588 /// let abs_difference = (x.tan() - 1.0).abs();
590 /// assert!(abs_difference <= f32::EPSILON);
592 #[must_use = "method returns a new number and does not mutate the original value"]
593 #[stable(feature = "rust1", since = "1.0.0")]
595 pub fn tan(self) -> f32 {
596 unsafe { cmath::tanf(self) }
599 /// Computes the arcsine of a number. Return value is in radians in
600 /// the range [-pi/2, pi/2] or NaN if the number is outside the range
606 /// let f = std::f32::consts::FRAC_PI_2;
608 /// // asin(sin(pi/2))
609 /// let abs_difference = (f.sin().asin() - std::f32::consts::FRAC_PI_2).abs();
611 /// assert!(abs_difference <= f32::EPSILON);
613 #[must_use = "method returns a new number and does not mutate the original value"]
614 #[stable(feature = "rust1", since = "1.0.0")]
616 pub fn asin(self) -> f32 {
617 unsafe { cmath::asinf(self) }
620 /// Computes the arccosine of a number. Return value is in radians in
621 /// the range [0, pi] or NaN if the number is outside the range
627 /// let f = std::f32::consts::FRAC_PI_4;
629 /// // acos(cos(pi/4))
630 /// let abs_difference = (f.cos().acos() - std::f32::consts::FRAC_PI_4).abs();
632 /// assert!(abs_difference <= f32::EPSILON);
634 #[must_use = "method returns a new number and does not mutate the original value"]
635 #[stable(feature = "rust1", since = "1.0.0")]
637 pub fn acos(self) -> f32 {
638 unsafe { cmath::acosf(self) }
641 /// Computes the arctangent of a number. Return value is in radians in the
642 /// range [-pi/2, pi/2];
650 /// let abs_difference = (f.tan().atan() - 1.0).abs();
652 /// assert!(abs_difference <= f32::EPSILON);
654 #[must_use = "method returns a new number and does not mutate the original value"]
655 #[stable(feature = "rust1", since = "1.0.0")]
657 pub fn atan(self) -> f32 {
658 unsafe { cmath::atanf(self) }
661 /// Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`) in radians.
663 /// * `x = 0`, `y = 0`: `0`
664 /// * `x >= 0`: `arctan(y/x)` -> `[-pi/2, pi/2]`
665 /// * `y >= 0`: `arctan(y/x) + pi` -> `(pi/2, pi]`
666 /// * `y < 0`: `arctan(y/x) - pi` -> `(-pi, -pi/2)`
671 /// // Positive angles measured counter-clockwise
672 /// // from positive x axis
673 /// // -pi/4 radians (45 deg clockwise)
675 /// let y1 = -3.0f32;
677 /// // 3pi/4 radians (135 deg counter-clockwise)
678 /// let x2 = -3.0f32;
681 /// let abs_difference_1 = (y1.atan2(x1) - (-std::f32::consts::FRAC_PI_4)).abs();
682 /// let abs_difference_2 = (y2.atan2(x2) - (3.0 * std::f32::consts::FRAC_PI_4)).abs();
684 /// assert!(abs_difference_1 <= f32::EPSILON);
685 /// assert!(abs_difference_2 <= f32::EPSILON);
687 #[must_use = "method returns a new number and does not mutate the original value"]
688 #[stable(feature = "rust1", since = "1.0.0")]
690 pub fn atan2(self, other: f32) -> f32 {
691 unsafe { cmath::atan2f(self, other) }
694 /// Simultaneously computes the sine and cosine of the number, `x`. Returns
695 /// `(sin(x), cos(x))`.
700 /// let x = std::f32::consts::FRAC_PI_4;
701 /// let f = x.sin_cos();
703 /// let abs_difference_0 = (f.0 - x.sin()).abs();
704 /// let abs_difference_1 = (f.1 - x.cos()).abs();
706 /// assert!(abs_difference_0 <= f32::EPSILON);
707 /// assert!(abs_difference_1 <= f32::EPSILON);
709 #[stable(feature = "rust1", since = "1.0.0")]
711 pub fn sin_cos(self) -> (f32, f32) {
712 (self.sin(), self.cos())
715 /// Returns `e^(self) - 1` in a way that is accurate even if the
716 /// number is close to zero.
721 /// let x = 1e-8_f32;
723 /// // for very small x, e^x is approximately 1 + x + x^2 / 2
724 /// let approx = x + x * x / 2.0;
725 /// let abs_difference = (x.exp_m1() - approx).abs();
727 /// assert!(abs_difference < 1e-10);
729 #[must_use = "method returns a new number and does not mutate the original value"]
730 #[stable(feature = "rust1", since = "1.0.0")]
732 pub fn exp_m1(self) -> f32 {
733 unsafe { cmath::expm1f(self) }
736 /// Returns `ln(1+n)` (natural logarithm) more accurately than if
737 /// the operations were performed separately.
742 /// let x = 1e-8_f32;
744 /// // for very small x, ln(1 + x) is approximately x - x^2 / 2
745 /// let approx = x - x * x / 2.0;
746 /// let abs_difference = (x.ln_1p() - approx).abs();
748 /// assert!(abs_difference < 1e-10);
750 #[must_use = "method returns a new number and does not mutate the original value"]
751 #[stable(feature = "rust1", since = "1.0.0")]
753 pub fn ln_1p(self) -> f32 {
754 unsafe { cmath::log1pf(self) }
757 /// Hyperbolic sine function.
762 /// let e = std::f32::consts::E;
765 /// let f = x.sinh();
766 /// // Solving sinh() at 1 gives `(e^2-1)/(2e)`
767 /// let g = ((e * e) - 1.0) / (2.0 * e);
768 /// let abs_difference = (f - g).abs();
770 /// assert!(abs_difference <= f32::EPSILON);
772 #[must_use = "method returns a new number and does not mutate the original value"]
773 #[stable(feature = "rust1", since = "1.0.0")]
775 pub fn sinh(self) -> f32 {
776 unsafe { cmath::sinhf(self) }
779 /// Hyperbolic cosine function.
784 /// let e = std::f32::consts::E;
786 /// let f = x.cosh();
787 /// // Solving cosh() at 1 gives this result
788 /// let g = ((e * e) + 1.0) / (2.0 * e);
789 /// let abs_difference = (f - g).abs();
792 /// assert!(abs_difference <= f32::EPSILON);
794 #[must_use = "method returns a new number and does not mutate the original value"]
795 #[stable(feature = "rust1", since = "1.0.0")]
797 pub fn cosh(self) -> f32 {
798 unsafe { cmath::coshf(self) }
801 /// Hyperbolic tangent function.
806 /// let e = std::f32::consts::E;
809 /// let f = x.tanh();
810 /// // Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))`
811 /// let g = (1.0 - e.powi(-2)) / (1.0 + e.powi(-2));
812 /// let abs_difference = (f - g).abs();
814 /// assert!(abs_difference <= f32::EPSILON);
816 #[must_use = "method returns a new number and does not mutate the original value"]
817 #[stable(feature = "rust1", since = "1.0.0")]
819 pub fn tanh(self) -> f32 {
820 unsafe { cmath::tanhf(self) }
823 /// Inverse hyperbolic sine function.
829 /// let f = x.sinh().asinh();
831 /// let abs_difference = (f - x).abs();
833 /// assert!(abs_difference <= f32::EPSILON);
835 #[must_use = "method returns a new number and does not mutate the original value"]
836 #[stable(feature = "rust1", since = "1.0.0")]
838 pub fn asinh(self) -> f32 {
839 (self.abs() + ((self * self) + 1.0).sqrt()).ln().copysign(self)
842 /// Inverse hyperbolic cosine function.
848 /// let f = x.cosh().acosh();
850 /// let abs_difference = (f - x).abs();
852 /// assert!(abs_difference <= f32::EPSILON);
854 #[must_use = "method returns a new number and does not mutate the original value"]
855 #[stable(feature = "rust1", since = "1.0.0")]
857 pub fn acosh(self) -> f32 {
858 if self < 1.0 { Self::NAN } else { (self + ((self * self) - 1.0).sqrt()).ln() }
861 /// Inverse hyperbolic tangent function.
866 /// let e = std::f32::consts::E;
867 /// let f = e.tanh().atanh();
869 /// let abs_difference = (f - e).abs();
871 /// assert!(abs_difference <= 1e-5);
873 #[must_use = "method returns a new number and does not mutate the original value"]
874 #[stable(feature = "rust1", since = "1.0.0")]
876 pub fn atanh(self) -> f32 {
877 0.5 * ((2.0 * self) / (1.0 - self)).ln_1p()