std/
f128.rs

1//! Constants for the `f128` quadruple-precision floating point type.
2//!
3//! *[See also the `f128` primitive type](primitive@f128).*
4//!
5//! Mathematically significant numbers are provided in the `consts` sub-module.
6
7#[unstable(feature = "f128", issue = "116909")]
8pub use core::f128::consts;
9
10#[cfg(not(test))]
11use crate::intrinsics;
12#[cfg(not(test))]
13use crate::sys::cmath;
14
15#[cfg(not(test))]
16impl f128 {
17    /// Returns the largest integer less than or equal to `self`.
18    ///
19    /// This function always returns the precise result.
20    ///
21    /// # Examples
22    ///
23    /// ```
24    /// #![feature(f128)]
25    /// # #[cfg(reliable_f128_math)] {
26    ///
27    /// let f = 3.7_f128;
28    /// let g = 3.0_f128;
29    /// let h = -3.7_f128;
30    ///
31    /// assert_eq!(f.floor(), 3.0);
32    /// assert_eq!(g.floor(), 3.0);
33    /// assert_eq!(h.floor(), -4.0);
34    /// # }
35    /// ```
36    #[inline]
37    #[rustc_allow_incoherent_impl]
38    #[unstable(feature = "f128", issue = "116909")]
39    #[must_use = "method returns a new number and does not mutate the original value"]
40    pub fn floor(self) -> f128 {
41        unsafe { intrinsics::floorf128(self) }
42    }
43
44    /// Returns the smallest integer greater than or equal to `self`.
45    ///
46    /// This function always returns the precise result.
47    ///
48    /// # Examples
49    ///
50    /// ```
51    /// #![feature(f128)]
52    /// # #[cfg(reliable_f128_math)] {
53    ///
54    /// let f = 3.01_f128;
55    /// let g = 4.0_f128;
56    ///
57    /// assert_eq!(f.ceil(), 4.0);
58    /// assert_eq!(g.ceil(), 4.0);
59    /// # }
60    /// ```
61    #[inline]
62    #[doc(alias = "ceiling")]
63    #[rustc_allow_incoherent_impl]
64    #[unstable(feature = "f128", issue = "116909")]
65    #[must_use = "method returns a new number and does not mutate the original value"]
66    pub fn ceil(self) -> f128 {
67        unsafe { intrinsics::ceilf128(self) }
68    }
69
70    /// Returns the nearest integer to `self`. If a value is half-way between two
71    /// integers, round away from `0.0`.
72    ///
73    /// This function always returns the precise result.
74    ///
75    /// # Examples
76    ///
77    /// ```
78    /// #![feature(f128)]
79    /// # #[cfg(reliable_f128_math)] {
80    ///
81    /// let f = 3.3_f128;
82    /// let g = -3.3_f128;
83    /// let h = -3.7_f128;
84    /// let i = 3.5_f128;
85    /// let j = 4.5_f128;
86    ///
87    /// assert_eq!(f.round(), 3.0);
88    /// assert_eq!(g.round(), -3.0);
89    /// assert_eq!(h.round(), -4.0);
90    /// assert_eq!(i.round(), 4.0);
91    /// assert_eq!(j.round(), 5.0);
92    /// # }
93    /// ```
94    #[inline]
95    #[rustc_allow_incoherent_impl]
96    #[unstable(feature = "f128", issue = "116909")]
97    #[must_use = "method returns a new number and does not mutate the original value"]
98    pub fn round(self) -> f128 {
99        unsafe { intrinsics::roundf128(self) }
100    }
101
102    /// Returns the nearest integer to a number. Rounds half-way cases to the number
103    /// with an even least significant digit.
104    ///
105    /// This function always returns the precise result.
106    ///
107    /// # Examples
108    ///
109    /// ```
110    /// #![feature(f128)]
111    /// # #[cfg(reliable_f128_math)] {
112    ///
113    /// let f = 3.3_f128;
114    /// let g = -3.3_f128;
115    /// let h = 3.5_f128;
116    /// let i = 4.5_f128;
117    ///
118    /// assert_eq!(f.round_ties_even(), 3.0);
119    /// assert_eq!(g.round_ties_even(), -3.0);
120    /// assert_eq!(h.round_ties_even(), 4.0);
121    /// assert_eq!(i.round_ties_even(), 4.0);
122    /// # }
123    /// ```
124    #[inline]
125    #[rustc_allow_incoherent_impl]
126    #[unstable(feature = "f128", issue = "116909")]
127    #[must_use = "method returns a new number and does not mutate the original value"]
128    pub fn round_ties_even(self) -> f128 {
129        unsafe { intrinsics::rintf128(self) }
130    }
131
132    /// Returns the integer part of `self`.
133    /// This means that non-integer numbers are always truncated towards zero.
134    ///
135    /// This function always returns the precise result.
136    ///
137    /// # Examples
138    ///
139    /// ```
140    /// #![feature(f128)]
141    /// # #[cfg(reliable_f128_math)] {
142    ///
143    /// let f = 3.7_f128;
144    /// let g = 3.0_f128;
145    /// let h = -3.7_f128;
146    ///
147    /// assert_eq!(f.trunc(), 3.0);
148    /// assert_eq!(g.trunc(), 3.0);
149    /// assert_eq!(h.trunc(), -3.0);
150    /// # }
151    /// ```
152    #[inline]
153    #[doc(alias = "truncate")]
154    #[rustc_allow_incoherent_impl]
155    #[unstable(feature = "f128", issue = "116909")]
156    #[must_use = "method returns a new number and does not mutate the original value"]
157    pub fn trunc(self) -> f128 {
158        unsafe { intrinsics::truncf128(self) }
159    }
160
161    /// Returns the fractional part of `self`.
162    ///
163    /// This function always returns the precise result.
164    ///
165    /// # Examples
166    ///
167    /// ```
168    /// #![feature(f128)]
169    /// # #[cfg(reliable_f128_math)] {
170    ///
171    /// let x = 3.6_f128;
172    /// let y = -3.6_f128;
173    /// let abs_difference_x = (x.fract() - 0.6).abs();
174    /// let abs_difference_y = (y.fract() - (-0.6)).abs();
175    ///
176    /// assert!(abs_difference_x <= f128::EPSILON);
177    /// assert!(abs_difference_y <= f128::EPSILON);
178    /// # }
179    /// ```
180    #[inline]
181    #[rustc_allow_incoherent_impl]
182    #[unstable(feature = "f128", issue = "116909")]
183    #[must_use = "method returns a new number and does not mutate the original value"]
184    pub fn fract(self) -> f128 {
185        self - self.trunc()
186    }
187
188    /// Fused multiply-add. Computes `(self * a) + b` with only one rounding
189    /// error, yielding a more accurate result than an unfused multiply-add.
190    ///
191    /// Using `mul_add` *may* be more performant than an unfused multiply-add if
192    /// the target architecture has a dedicated `fma` CPU instruction. However,
193    /// this is not always true, and will be heavily dependant on designing
194    /// algorithms with specific target hardware in mind.
195    ///
196    /// # Precision
197    ///
198    /// The result of this operation is guaranteed to be the rounded
199    /// infinite-precision result. It is specified by IEEE 754 as
200    /// `fusedMultiplyAdd` and guaranteed not to change.
201    ///
202    /// # Examples
203    ///
204    /// ```
205    /// #![feature(f128)]
206    /// # #[cfg(reliable_f128_math)] {
207    ///
208    /// let m = 10.0_f128;
209    /// let x = 4.0_f128;
210    /// let b = 60.0_f128;
211    ///
212    /// assert_eq!(m.mul_add(x, b), 100.0);
213    /// assert_eq!(m * x + b, 100.0);
214    ///
215    /// let one_plus_eps = 1.0_f128 + f128::EPSILON;
216    /// let one_minus_eps = 1.0_f128 - f128::EPSILON;
217    /// let minus_one = -1.0_f128;
218    ///
219    /// // The exact result (1 + eps) * (1 - eps) = 1 - eps * eps.
220    /// assert_eq!(one_plus_eps.mul_add(one_minus_eps, minus_one), -f128::EPSILON * f128::EPSILON);
221    /// // Different rounding with the non-fused multiply and add.
222    /// assert_eq!(one_plus_eps * one_minus_eps + minus_one, 0.0);
223    /// # }
224    /// ```
225    #[inline]
226    #[rustc_allow_incoherent_impl]
227    #[doc(alias = "fmaf128", alias = "fusedMultiplyAdd")]
228    #[unstable(feature = "f128", issue = "116909")]
229    #[must_use = "method returns a new number and does not mutate the original value"]
230    pub fn mul_add(self, a: f128, b: f128) -> f128 {
231        unsafe { intrinsics::fmaf128(self, a, b) }
232    }
233
234    /// Calculates Euclidean division, the matching method for `rem_euclid`.
235    ///
236    /// This computes the integer `n` such that
237    /// `self = n * rhs + self.rem_euclid(rhs)`.
238    /// In other words, the result is `self / rhs` rounded to the integer `n`
239    /// such that `self >= n * rhs`.
240    ///
241    /// # Precision
242    ///
243    /// The result of this operation is guaranteed to be the rounded
244    /// infinite-precision result.
245    ///
246    /// # Examples
247    ///
248    /// ```
249    /// #![feature(f128)]
250    /// # #[cfg(reliable_f128_math)] {
251    ///
252    /// let a: f128 = 7.0;
253    /// let b = 4.0;
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    /// assert_eq!(a.div_euclid(-b), -1.0); // 7.0 >= -4.0 * -1.0
257    /// assert_eq!((-a).div_euclid(-b), 2.0); // -7.0 >= -4.0 * 2.0
258    /// # }
259    /// ```
260    #[inline]
261    #[rustc_allow_incoherent_impl]
262    #[unstable(feature = "f128", issue = "116909")]
263    #[must_use = "method returns a new number and does not mutate the original value"]
264    pub fn div_euclid(self, rhs: f128) -> f128 {
265        let q = (self / rhs).trunc();
266        if self % rhs < 0.0 {
267            return if rhs > 0.0 { q - 1.0 } else { q + 1.0 };
268        }
269        q
270    }
271
272    /// Calculates the least nonnegative remainder of `self (mod rhs)`.
273    ///
274    /// In particular, the return value `r` satisfies `0.0 <= r < rhs.abs()` in
275    /// most cases. However, due to a floating point round-off error it can
276    /// result in `r == rhs.abs()`, violating the mathematical definition, if
277    /// `self` is much smaller than `rhs.abs()` in magnitude and `self < 0.0`.
278    /// This result is not an element of the function's codomain, but it is the
279    /// closest floating point number in the real numbers and thus fulfills the
280    /// property `self == self.div_euclid(rhs) * rhs + self.rem_euclid(rhs)`
281    /// approximately.
282    ///
283    /// # Precision
284    ///
285    /// The result of this operation is guaranteed to be the rounded
286    /// infinite-precision result.
287    ///
288    /// # Examples
289    ///
290    /// ```
291    /// #![feature(f128)]
292    /// # #[cfg(reliable_f128_math)] {
293    ///
294    /// let a: f128 = 7.0;
295    /// let b = 4.0;
296    /// assert_eq!(a.rem_euclid(b), 3.0);
297    /// assert_eq!((-a).rem_euclid(b), 1.0);
298    /// assert_eq!(a.rem_euclid(-b), 3.0);
299    /// assert_eq!((-a).rem_euclid(-b), 1.0);
300    /// // limitation due to round-off error
301    /// assert!((-f128::EPSILON).rem_euclid(3.0) != 0.0);
302    /// # }
303    /// ```
304    #[inline]
305    #[rustc_allow_incoherent_impl]
306    #[doc(alias = "modulo", alias = "mod")]
307    #[unstable(feature = "f128", issue = "116909")]
308    #[must_use = "method returns a new number and does not mutate the original value"]
309    pub fn rem_euclid(self, rhs: f128) -> f128 {
310        let r = self % rhs;
311        if r < 0.0 { r + rhs.abs() } else { r }
312    }
313
314    /// Raises a number to an integer power.
315    ///
316    /// Using this function is generally faster than using `powf`.
317    /// It might have a different sequence of rounding operations than `powf`,
318    /// so the results are not guaranteed to agree.
319    ///
320    /// # Unspecified precision
321    ///
322    /// The precision of this function is non-deterministic. This means it varies by platform,
323    /// Rust version, and can even differ within the same execution from one invocation to the next.
324    ///
325    /// # Examples
326    ///
327    /// ```
328    /// #![feature(f128)]
329    /// # #[cfg(reliable_f128_math)] {
330    ///
331    /// let x = 2.0_f128;
332    /// let abs_difference = (x.powi(2) - (x * x)).abs();
333    /// assert!(abs_difference <= f128::EPSILON);
334    ///
335    /// assert_eq!(f128::powi(f128::NAN, 0), 1.0);
336    /// # }
337    /// ```
338    #[inline]
339    #[rustc_allow_incoherent_impl]
340    #[unstable(feature = "f128", issue = "116909")]
341    #[must_use = "method returns a new number and does not mutate the original value"]
342    pub fn powi(self, n: i32) -> f128 {
343        unsafe { intrinsics::powif128(self, n) }
344    }
345
346    /// Raises a number to a floating point power.
347    ///
348    /// # Unspecified precision
349    ///
350    /// The precision of this function is non-deterministic. This means it varies by platform,
351    /// Rust version, and can even differ within the same execution from one invocation to the next.
352    ///
353    /// # Examples
354    ///
355    /// ```
356    /// #![feature(f128)]
357    /// # #[cfg(reliable_f128_math)] {
358    ///
359    /// let x = 2.0_f128;
360    /// let abs_difference = (x.powf(2.0) - (x * x)).abs();
361    /// assert!(abs_difference <= f128::EPSILON);
362    ///
363    /// assert_eq!(f128::powf(1.0, f128::NAN), 1.0);
364    /// assert_eq!(f128::powf(f128::NAN, 0.0), 1.0);
365    /// # }
366    /// ```
367    #[inline]
368    #[rustc_allow_incoherent_impl]
369    #[unstable(feature = "f128", issue = "116909")]
370    #[must_use = "method returns a new number and does not mutate the original value"]
371    pub fn powf(self, n: f128) -> f128 {
372        unsafe { intrinsics::powf128(self, n) }
373    }
374
375    /// Returns the square root of a number.
376    ///
377    /// Returns NaN if `self` is a negative number other than `-0.0`.
378    ///
379    /// # Precision
380    ///
381    /// The result of this operation is guaranteed to be the rounded
382    /// infinite-precision result. It is specified by IEEE 754 as `squareRoot`
383    /// and guaranteed not to change.
384    ///
385    /// # Examples
386    ///
387    /// ```
388    /// #![feature(f128)]
389    /// # #[cfg(reliable_f128_math)] {
390    ///
391    /// let positive = 4.0_f128;
392    /// let negative = -4.0_f128;
393    /// let negative_zero = -0.0_f128;
394    ///
395    /// assert_eq!(positive.sqrt(), 2.0);
396    /// assert!(negative.sqrt().is_nan());
397    /// assert!(negative_zero.sqrt() == negative_zero);
398    /// # }
399    /// ```
400    #[inline]
401    #[doc(alias = "squareRoot")]
402    #[rustc_allow_incoherent_impl]
403    #[unstable(feature = "f128", issue = "116909")]
404    #[must_use = "method returns a new number and does not mutate the original value"]
405    pub fn sqrt(self) -> f128 {
406        unsafe { intrinsics::sqrtf128(self) }
407    }
408
409    /// Returns `e^(self)`, (the exponential function).
410    ///
411    /// # Unspecified precision
412    ///
413    /// The precision of this function is non-deterministic. This means it varies by platform,
414    /// Rust version, and can even differ within the same execution from one invocation to the next.
415    ///
416    /// # Examples
417    ///
418    /// ```
419    /// #![feature(f128)]
420    /// # #[cfg(reliable_f128_math)] {
421    ///
422    /// let one = 1.0f128;
423    /// // e^1
424    /// let e = one.exp();
425    ///
426    /// // ln(e) - 1 == 0
427    /// let abs_difference = (e.ln() - 1.0).abs();
428    ///
429    /// assert!(abs_difference <= f128::EPSILON);
430    /// # }
431    /// ```
432    #[inline]
433    #[rustc_allow_incoherent_impl]
434    #[unstable(feature = "f128", issue = "116909")]
435    #[must_use = "method returns a new number and does not mutate the original value"]
436    pub fn exp(self) -> f128 {
437        unsafe { intrinsics::expf128(self) }
438    }
439
440    /// Returns `2^(self)`.
441    ///
442    /// # Unspecified precision
443    ///
444    /// The precision of this function is non-deterministic. This means it varies by platform,
445    /// Rust version, and can even differ within the same execution from one invocation to the next.
446    ///
447    /// # Examples
448    ///
449    /// ```
450    /// #![feature(f128)]
451    /// # #[cfg(reliable_f128_math)] {
452    ///
453    /// let f = 2.0f128;
454    ///
455    /// // 2^2 - 4 == 0
456    /// let abs_difference = (f.exp2() - 4.0).abs();
457    ///
458    /// assert!(abs_difference <= f128::EPSILON);
459    /// # }
460    /// ```
461    #[inline]
462    #[rustc_allow_incoherent_impl]
463    #[unstable(feature = "f128", issue = "116909")]
464    #[must_use = "method returns a new number and does not mutate the original value"]
465    pub fn exp2(self) -> f128 {
466        unsafe { intrinsics::exp2f128(self) }
467    }
468
469    /// Returns the natural logarithm of the number.
470    ///
471    /// # Unspecified precision
472    ///
473    /// The precision of this function is non-deterministic. This means it varies by platform,
474    /// Rust version, and can even differ within the same execution from one invocation to the next.
475    ///
476    /// # Examples
477    ///
478    /// ```
479    /// #![feature(f128)]
480    /// # #[cfg(reliable_f128_math)] {
481    ///
482    /// let one = 1.0f128;
483    /// // e^1
484    /// let e = one.exp();
485    ///
486    /// // ln(e) - 1 == 0
487    /// let abs_difference = (e.ln() - 1.0).abs();
488    ///
489    /// assert!(abs_difference <= f128::EPSILON);
490    /// # }
491    /// ```
492    #[inline]
493    #[rustc_allow_incoherent_impl]
494    #[unstable(feature = "f128", issue = "116909")]
495    #[must_use = "method returns a new number and does not mutate the original value"]
496    pub fn ln(self) -> f128 {
497        unsafe { intrinsics::logf128(self) }
498    }
499
500    /// Returns the logarithm of the number with respect to an arbitrary base.
501    ///
502    /// The result might not be correctly rounded owing to implementation details;
503    /// `self.log2()` can produce more accurate results for base 2, and
504    /// `self.log10()` can produce more accurate results for base 10.
505    ///
506    /// # Unspecified precision
507    ///
508    /// The precision of this function is non-deterministic. This means it varies by platform,
509    /// Rust version, and can even differ within the same execution from one invocation to the next.
510    ///
511    /// # Examples
512    ///
513    /// ```
514    /// #![feature(f128)]
515    /// # #[cfg(reliable_f128_math)] {
516    ///
517    /// let five = 5.0f128;
518    ///
519    /// // log5(5) - 1 == 0
520    /// let abs_difference = (five.log(5.0) - 1.0).abs();
521    ///
522    /// assert!(abs_difference <= f128::EPSILON);
523    /// # }
524    /// ```
525    #[inline]
526    #[rustc_allow_incoherent_impl]
527    #[unstable(feature = "f128", issue = "116909")]
528    #[must_use = "method returns a new number and does not mutate the original value"]
529    pub fn log(self, base: f128) -> f128 {
530        self.ln() / base.ln()
531    }
532
533    /// Returns the base 2 logarithm of the number.
534    ///
535    /// # Unspecified precision
536    ///
537    /// The precision of this function is non-deterministic. This means it varies by platform,
538    /// Rust version, and can even differ within the same execution from one invocation to the next.
539    ///
540    /// # Examples
541    ///
542    /// ```
543    /// #![feature(f128)]
544    /// # #[cfg(reliable_f128_math)] {
545    ///
546    /// let two = 2.0f128;
547    ///
548    /// // log2(2) - 1 == 0
549    /// let abs_difference = (two.log2() - 1.0).abs();
550    ///
551    /// assert!(abs_difference <= f128::EPSILON);
552    /// # }
553    /// ```
554    #[inline]
555    #[rustc_allow_incoherent_impl]
556    #[unstable(feature = "f128", issue = "116909")]
557    #[must_use = "method returns a new number and does not mutate the original value"]
558    pub fn log2(self) -> f128 {
559        unsafe { intrinsics::log2f128(self) }
560    }
561
562    /// Returns the base 10 logarithm of the number.
563    ///
564    /// # Unspecified precision
565    ///
566    /// The precision of this function is non-deterministic. This means it varies by platform,
567    /// Rust version, and can even differ within the same execution from one invocation to the next.
568    ///
569    /// # Examples
570    ///
571    /// ```
572    /// #![feature(f128)]
573    /// # #[cfg(reliable_f128_math)] {
574    ///
575    /// let ten = 10.0f128;
576    ///
577    /// // log10(10) - 1 == 0
578    /// let abs_difference = (ten.log10() - 1.0).abs();
579    ///
580    /// assert!(abs_difference <= f128::EPSILON);
581    /// # }
582    /// ```
583    #[inline]
584    #[rustc_allow_incoherent_impl]
585    #[unstable(feature = "f128", issue = "116909")]
586    #[must_use = "method returns a new number and does not mutate the original value"]
587    pub fn log10(self) -> f128 {
588        unsafe { intrinsics::log10f128(self) }
589    }
590
591    /// Returns the cube root of a number.
592    ///
593    /// # Unspecified precision
594    ///
595    /// The precision of this function is non-deterministic. This means it varies by platform,
596    /// Rust version, and can even differ within the same execution from one invocation to the next.
597    ///
598    ///
599    /// This function currently corresponds to the `cbrtf128` from libc on Unix
600    /// and Windows. Note that this might change in the future.
601    ///
602    /// # Examples
603    ///
604    /// ```
605    /// #![feature(f128)]
606    /// # #[cfg(reliable_f128_math)] {
607    ///
608    /// let x = 8.0f128;
609    ///
610    /// // x^(1/3) - 2 == 0
611    /// let abs_difference = (x.cbrt() - 2.0).abs();
612    ///
613    /// assert!(abs_difference <= f128::EPSILON);
614    /// # }
615    /// ```
616    #[inline]
617    #[rustc_allow_incoherent_impl]
618    #[unstable(feature = "f128", issue = "116909")]
619    #[must_use = "method returns a new number and does not mutate the original value"]
620    pub fn cbrt(self) -> f128 {
621        unsafe { cmath::cbrtf128(self) }
622    }
623
624    /// Compute the distance between the origin and a point (`x`, `y`) on the
625    /// Euclidean plane. Equivalently, compute the length of the hypotenuse of a
626    /// right-angle triangle with other sides having length `x.abs()` and
627    /// `y.abs()`.
628    ///
629    /// # Unspecified precision
630    ///
631    /// The precision of this function is non-deterministic. This means it varies by platform,
632    /// Rust version, and can even differ within the same execution from one invocation to the next.
633    ///
634    ///
635    /// This function currently corresponds to the `hypotf128` from libc on Unix
636    /// and Windows. Note that this might change in the future.
637    ///
638    /// # Examples
639    ///
640    /// ```
641    /// #![feature(f128)]
642    /// # #[cfg(reliable_f128_math)] {
643    ///
644    /// let x = 2.0f128;
645    /// let y = 3.0f128;
646    ///
647    /// // sqrt(x^2 + y^2)
648    /// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();
649    ///
650    /// assert!(abs_difference <= f128::EPSILON);
651    /// # }
652    /// ```
653    #[inline]
654    #[rustc_allow_incoherent_impl]
655    #[unstable(feature = "f128", issue = "116909")]
656    #[must_use = "method returns a new number and does not mutate the original value"]
657    pub fn hypot(self, other: f128) -> f128 {
658        unsafe { cmath::hypotf128(self, other) }
659    }
660
661    /// Computes the sine of a number (in radians).
662    ///
663    /// # Unspecified precision
664    ///
665    /// The precision of this function is non-deterministic. This means it varies by platform,
666    /// Rust version, and can even differ within the same execution from one invocation to the next.
667    ///
668    /// # Examples
669    ///
670    /// ```
671    /// #![feature(f128)]
672    /// # #[cfg(reliable_f128_math)] {
673    ///
674    /// let x = std::f128::consts::FRAC_PI_2;
675    ///
676    /// let abs_difference = (x.sin() - 1.0).abs();
677    ///
678    /// assert!(abs_difference <= f128::EPSILON);
679    /// # }
680    /// ```
681    #[inline]
682    #[rustc_allow_incoherent_impl]
683    #[unstable(feature = "f128", issue = "116909")]
684    #[must_use = "method returns a new number and does not mutate the original value"]
685    pub fn sin(self) -> f128 {
686        unsafe { intrinsics::sinf128(self) }
687    }
688
689    /// Computes the cosine of a number (in radians).
690    ///
691    /// # Unspecified precision
692    ///
693    /// The precision of this function is non-deterministic. This means it varies by platform,
694    /// Rust version, and can even differ within the same execution from one invocation to the next.
695    ///
696    /// # Examples
697    ///
698    /// ```
699    /// #![feature(f128)]
700    /// # #[cfg(reliable_f128_math)] {
701    ///
702    /// let x = 2.0 * std::f128::consts::PI;
703    ///
704    /// let abs_difference = (x.cos() - 1.0).abs();
705    ///
706    /// assert!(abs_difference <= f128::EPSILON);
707    /// # }
708    /// ```
709    #[inline]
710    #[rustc_allow_incoherent_impl]
711    #[unstable(feature = "f128", issue = "116909")]
712    #[must_use = "method returns a new number and does not mutate the original value"]
713    pub fn cos(self) -> f128 {
714        unsafe { intrinsics::cosf128(self) }
715    }
716
717    /// Computes the tangent of a number (in radians).
718    ///
719    /// # Unspecified precision
720    ///
721    /// The precision of this function is non-deterministic. This means it varies by platform,
722    /// Rust version, and can even differ within the same execution from one invocation to the next.
723    ///
724    /// This function currently corresponds to the `tanf128` from libc on Unix and
725    /// Windows. Note that this might change in the future.
726    ///
727    /// # Examples
728    ///
729    /// ```
730    /// #![feature(f128)]
731    /// # #[cfg(reliable_f128_math)] {
732    ///
733    /// let x = std::f128::consts::FRAC_PI_4;
734    /// let abs_difference = (x.tan() - 1.0).abs();
735    ///
736    /// assert!(abs_difference <= f128::EPSILON);
737    /// # }
738    /// ```
739    #[inline]
740    #[rustc_allow_incoherent_impl]
741    #[unstable(feature = "f128", issue = "116909")]
742    #[must_use = "method returns a new number and does not mutate the original value"]
743    pub fn tan(self) -> f128 {
744        unsafe { cmath::tanf128(self) }
745    }
746
747    /// Computes the arcsine of a number. Return value is in radians in
748    /// the range [-pi/2, pi/2] or NaN if the number is outside the range
749    /// [-1, 1].
750    ///
751    /// # Unspecified precision
752    ///
753    /// The precision of this function is non-deterministic. This means it varies by platform,
754    /// Rust version, and can even differ within the same execution from one invocation to the next.
755    ///
756    /// This function currently corresponds to the `asinf128` from libc on Unix
757    /// and Windows. Note that this might change in the future.
758    ///
759    /// # Examples
760    ///
761    /// ```
762    /// #![feature(f128)]
763    /// # #[cfg(reliable_f128_math)] {
764    ///
765    /// let f = std::f128::consts::FRAC_PI_2;
766    ///
767    /// // asin(sin(pi/2))
768    /// let abs_difference = (f.sin().asin() - std::f128::consts::FRAC_PI_2).abs();
769    ///
770    /// assert!(abs_difference <= f128::EPSILON);
771    /// # }
772    /// ```
773    #[inline]
774    #[doc(alias = "arcsin")]
775    #[rustc_allow_incoherent_impl]
776    #[unstable(feature = "f128", issue = "116909")]
777    #[must_use = "method returns a new number and does not mutate the original value"]
778    pub fn asin(self) -> f128 {
779        unsafe { cmath::asinf128(self) }
780    }
781
782    /// Computes the arccosine of a number. Return value is in radians in
783    /// the range [0, pi] or NaN if the number is outside the range
784    /// [-1, 1].
785    ///
786    /// # Unspecified precision
787    ///
788    /// The precision of this function is non-deterministic. This means it varies by platform,
789    /// Rust version, and can even differ within the same execution from one invocation to the next.
790    ///
791    /// This function currently corresponds to the `acosf128` from libc on Unix
792    /// and Windows. Note that this might change in the future.
793    ///
794    /// # Examples
795    ///
796    /// ```
797    /// #![feature(f128)]
798    /// # #[cfg(reliable_f128_math)] {
799    ///
800    /// let f = std::f128::consts::FRAC_PI_4;
801    ///
802    /// // acos(cos(pi/4))
803    /// let abs_difference = (f.cos().acos() - std::f128::consts::FRAC_PI_4).abs();
804    ///
805    /// assert!(abs_difference <= f128::EPSILON);
806    /// # }
807    /// ```
808    #[inline]
809    #[doc(alias = "arccos")]
810    #[rustc_allow_incoherent_impl]
811    #[unstable(feature = "f128", issue = "116909")]
812    #[must_use = "method returns a new number and does not mutate the original value"]
813    pub fn acos(self) -> f128 {
814        unsafe { cmath::acosf128(self) }
815    }
816
817    /// Computes the arctangent of a number. Return value is in radians in the
818    /// range [-pi/2, pi/2];
819    ///
820    /// # Unspecified precision
821    ///
822    /// The precision of this function is non-deterministic. This means it varies by platform,
823    /// Rust version, and can even differ within the same execution from one invocation to the next.
824    ///
825    /// This function currently corresponds to the `atanf128` from libc on Unix
826    /// and Windows. Note that this might change in the future.
827    ///
828    /// # Examples
829    ///
830    /// ```
831    /// #![feature(f128)]
832    /// # #[cfg(reliable_f128_math)] {
833    ///
834    /// let f = 1.0f128;
835    ///
836    /// // atan(tan(1))
837    /// let abs_difference = (f.tan().atan() - 1.0).abs();
838    ///
839    /// assert!(abs_difference <= f128::EPSILON);
840    /// # }
841    /// ```
842    #[inline]
843    #[doc(alias = "arctan")]
844    #[rustc_allow_incoherent_impl]
845    #[unstable(feature = "f128", issue = "116909")]
846    #[must_use = "method returns a new number and does not mutate the original value"]
847    pub fn atan(self) -> f128 {
848        unsafe { cmath::atanf128(self) }
849    }
850
851    /// Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`) in radians.
852    ///
853    /// * `x = 0`, `y = 0`: `0`
854    /// * `x >= 0`: `arctan(y/x)` -> `[-pi/2, pi/2]`
855    /// * `y >= 0`: `arctan(y/x) + pi` -> `(pi/2, pi]`
856    /// * `y < 0`: `arctan(y/x) - pi` -> `(-pi, -pi/2)`
857    ///
858    /// # Unspecified precision
859    ///
860    /// The precision of this function is non-deterministic. This means it varies by platform,
861    /// Rust version, and can even differ within the same execution from one invocation to the next.
862    ///
863    /// This function currently corresponds to the `atan2f128` from libc on Unix
864    /// and Windows. Note that this might change in the future.
865    ///
866    /// # Examples
867    ///
868    /// ```
869    /// #![feature(f128)]
870    /// # #[cfg(reliable_f128_math)] {
871    ///
872    /// // Positive angles measured counter-clockwise
873    /// // from positive x axis
874    /// // -pi/4 radians (45 deg clockwise)
875    /// let x1 = 3.0f128;
876    /// let y1 = -3.0f128;
877    ///
878    /// // 3pi/4 radians (135 deg counter-clockwise)
879    /// let x2 = -3.0f128;
880    /// let y2 = 3.0f128;
881    ///
882    /// let abs_difference_1 = (y1.atan2(x1) - (-std::f128::consts::FRAC_PI_4)).abs();
883    /// let abs_difference_2 = (y2.atan2(x2) - (3.0 * std::f128::consts::FRAC_PI_4)).abs();
884    ///
885    /// assert!(abs_difference_1 <= f128::EPSILON);
886    /// assert!(abs_difference_2 <= f128::EPSILON);
887    /// # }
888    /// ```
889    #[inline]
890    #[rustc_allow_incoherent_impl]
891    #[unstable(feature = "f128", issue = "116909")]
892    #[must_use = "method returns a new number and does not mutate the original value"]
893    pub fn atan2(self, other: f128) -> f128 {
894        unsafe { cmath::atan2f128(self, other) }
895    }
896
897    /// Simultaneously computes the sine and cosine of the number, `x`. Returns
898    /// `(sin(x), cos(x))`.
899    ///
900    /// # Unspecified precision
901    ///
902    /// The precision of this function is non-deterministic. This means it varies by platform,
903    /// Rust version, and can even differ within the same execution from one invocation to the next.
904    ///
905    /// This function currently corresponds to the `(f128::sin(x),
906    /// f128::cos(x))`. Note that this might change in the future.
907    ///
908    /// # Examples
909    ///
910    /// ```
911    /// #![feature(f128)]
912    /// # #[cfg(reliable_f128_math)] {
913    ///
914    /// let x = std::f128::consts::FRAC_PI_4;
915    /// let f = x.sin_cos();
916    ///
917    /// let abs_difference_0 = (f.0 - x.sin()).abs();
918    /// let abs_difference_1 = (f.1 - x.cos()).abs();
919    ///
920    /// assert!(abs_difference_0 <= f128::EPSILON);
921    /// assert!(abs_difference_1 <= f128::EPSILON);
922    /// # }
923    /// ```
924    #[inline]
925    #[doc(alias = "sincos")]
926    #[rustc_allow_incoherent_impl]
927    #[unstable(feature = "f128", issue = "116909")]
928    pub fn sin_cos(self) -> (f128, f128) {
929        (self.sin(), self.cos())
930    }
931
932    /// Returns `e^(self) - 1` in a way that is accurate even if the
933    /// number is close to zero.
934    ///
935    /// # Unspecified precision
936    ///
937    /// The precision of this function is non-deterministic. This means it varies by platform,
938    /// Rust version, and can even differ within the same execution from one invocation to the next.
939    ///
940    /// This function currently corresponds to the `expm1f128` from libc on Unix
941    /// and Windows. Note that this might change in the future.
942    ///
943    /// # Examples
944    ///
945    /// ```
946    /// #![feature(f128)]
947    /// # #[cfg(reliable_f128_math)] {
948    ///
949    /// let x = 1e-8_f128;
950    ///
951    /// // for very small x, e^x is approximately 1 + x + x^2 / 2
952    /// let approx = x + x * x / 2.0;
953    /// let abs_difference = (x.exp_m1() - approx).abs();
954    ///
955    /// assert!(abs_difference < 1e-10);
956    /// # }
957    /// ```
958    #[inline]
959    #[rustc_allow_incoherent_impl]
960    #[unstable(feature = "f128", issue = "116909")]
961    #[must_use = "method returns a new number and does not mutate the original value"]
962    pub fn exp_m1(self) -> f128 {
963        unsafe { cmath::expm1f128(self) }
964    }
965
966    /// Returns `ln(1+n)` (natural logarithm) more accurately than if
967    /// the operations were performed separately.
968    ///
969    /// # Unspecified precision
970    ///
971    /// The precision of this function is non-deterministic. This means it varies by platform,
972    /// Rust version, and can even differ within the same execution from one invocation to the next.
973    ///
974    /// This function currently corresponds to the `log1pf128` from libc on Unix
975    /// and Windows. Note that this might change in the future.
976    ///
977    /// # Examples
978    ///
979    /// ```
980    /// #![feature(f128)]
981    /// # #[cfg(reliable_f128_math)] {
982    ///
983    /// let x = 1e-8_f128;
984    ///
985    /// // for very small x, ln(1 + x) is approximately x - x^2 / 2
986    /// let approx = x - x * x / 2.0;
987    /// let abs_difference = (x.ln_1p() - approx).abs();
988    ///
989    /// assert!(abs_difference < 1e-10);
990    /// # }
991    /// ```
992    #[inline]
993    #[doc(alias = "log1p")]
994    #[must_use = "method returns a new number and does not mutate the original value"]
995    #[rustc_allow_incoherent_impl]
996    #[unstable(feature = "f128", issue = "116909")]
997    pub fn ln_1p(self) -> f128 {
998        unsafe { cmath::log1pf128(self) }
999    }
1000
1001    /// Hyperbolic sine function.
1002    ///
1003    /// # Unspecified precision
1004    ///
1005    /// The precision of this function is non-deterministic. This means it varies by platform,
1006    /// Rust version, and can even differ within the same execution from one invocation to the next.
1007    ///
1008    /// This function currently corresponds to the `sinhf128` from libc on Unix
1009    /// and Windows. Note that this might change in the future.
1010    ///
1011    /// # Examples
1012    ///
1013    /// ```
1014    /// #![feature(f128)]
1015    /// # #[cfg(reliable_f128_math)] {
1016    ///
1017    /// let e = std::f128::consts::E;
1018    /// let x = 1.0f128;
1019    ///
1020    /// let f = x.sinh();
1021    /// // Solving sinh() at 1 gives `(e^2-1)/(2e)`
1022    /// let g = ((e * e) - 1.0) / (2.0 * e);
1023    /// let abs_difference = (f - g).abs();
1024    ///
1025    /// assert!(abs_difference <= f128::EPSILON);
1026    /// # }
1027    /// ```
1028    #[inline]
1029    #[rustc_allow_incoherent_impl]
1030    #[unstable(feature = "f128", issue = "116909")]
1031    #[must_use = "method returns a new number and does not mutate the original value"]
1032    pub fn sinh(self) -> f128 {
1033        unsafe { cmath::sinhf128(self) }
1034    }
1035
1036    /// Hyperbolic cosine function.
1037    ///
1038    /// # Unspecified precision
1039    ///
1040    /// The precision of this function is non-deterministic. This means it varies by platform,
1041    /// Rust version, and can even differ within the same execution from one invocation to the next.
1042    ///
1043    /// This function currently corresponds to the `coshf128` from libc on Unix
1044    /// and Windows. Note that this might change in the future.
1045    ///
1046    /// # Examples
1047    ///
1048    /// ```
1049    /// #![feature(f128)]
1050    /// # #[cfg(reliable_f128_math)] {
1051    ///
1052    /// let e = std::f128::consts::E;
1053    /// let x = 1.0f128;
1054    /// let f = x.cosh();
1055    /// // Solving cosh() at 1 gives this result
1056    /// let g = ((e * e) + 1.0) / (2.0 * e);
1057    /// let abs_difference = (f - g).abs();
1058    ///
1059    /// // Same result
1060    /// assert!(abs_difference <= f128::EPSILON);
1061    /// # }
1062    /// ```
1063    #[inline]
1064    #[rustc_allow_incoherent_impl]
1065    #[unstable(feature = "f128", issue = "116909")]
1066    #[must_use = "method returns a new number and does not mutate the original value"]
1067    pub fn cosh(self) -> f128 {
1068        unsafe { cmath::coshf128(self) }
1069    }
1070
1071    /// Hyperbolic tangent function.
1072    ///
1073    /// # Unspecified precision
1074    ///
1075    /// The precision of this function is non-deterministic. This means it varies by platform,
1076    /// Rust version, and can even differ within the same execution from one invocation to the next.
1077    ///
1078    /// This function currently corresponds to the `tanhf128` from libc on Unix
1079    /// and Windows. Note that this might change in the future.
1080    ///
1081    /// # Examples
1082    ///
1083    /// ```
1084    /// #![feature(f128)]
1085    /// # #[cfg(reliable_f128_math)] {
1086    ///
1087    /// let e = std::f128::consts::E;
1088    /// let x = 1.0f128;
1089    ///
1090    /// let f = x.tanh();
1091    /// // Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))`
1092    /// let g = (1.0 - e.powi(-2)) / (1.0 + e.powi(-2));
1093    /// let abs_difference = (f - g).abs();
1094    ///
1095    /// assert!(abs_difference <= f128::EPSILON);
1096    /// # }
1097    /// ```
1098    #[inline]
1099    #[rustc_allow_incoherent_impl]
1100    #[unstable(feature = "f128", issue = "116909")]
1101    #[must_use = "method returns a new number and does not mutate the original value"]
1102    pub fn tanh(self) -> f128 {
1103        unsafe { cmath::tanhf128(self) }
1104    }
1105
1106    /// Inverse hyperbolic sine function.
1107    ///
1108    /// # Unspecified precision
1109    ///
1110    /// The precision of this function is non-deterministic. This means it varies by platform,
1111    /// Rust version, and can even differ within the same execution from one invocation to the next.
1112    ///
1113    /// # Examples
1114    ///
1115    /// ```
1116    /// #![feature(f128)]
1117    /// # #[cfg(reliable_f128_math)] {
1118    ///
1119    /// let x = 1.0f128;
1120    /// let f = x.sinh().asinh();
1121    ///
1122    /// let abs_difference = (f - x).abs();
1123    ///
1124    /// assert!(abs_difference <= f128::EPSILON);
1125    /// # }
1126    /// ```
1127    #[inline]
1128    #[doc(alias = "arcsinh")]
1129    #[rustc_allow_incoherent_impl]
1130    #[unstable(feature = "f128", issue = "116909")]
1131    #[must_use = "method returns a new number and does not mutate the original value"]
1132    pub fn asinh(self) -> f128 {
1133        let ax = self.abs();
1134        let ix = 1.0 / ax;
1135        (ax + (ax / (Self::hypot(1.0, ix) + ix))).ln_1p().copysign(self)
1136    }
1137
1138    /// Inverse hyperbolic cosine function.
1139    ///
1140    /// # Unspecified precision
1141    ///
1142    /// The precision of this function is non-deterministic. This means it varies by platform,
1143    /// Rust version, and can even differ within the same execution from one invocation to the next.
1144    ///
1145    /// # Examples
1146    ///
1147    /// ```
1148    /// #![feature(f128)]
1149    /// # #[cfg(reliable_f128_math)] {
1150    ///
1151    /// let x = 1.0f128;
1152    /// let f = x.cosh().acosh();
1153    ///
1154    /// let abs_difference = (f - x).abs();
1155    ///
1156    /// assert!(abs_difference <= f128::EPSILON);
1157    /// # }
1158    /// ```
1159    #[inline]
1160    #[doc(alias = "arccosh")]
1161    #[rustc_allow_incoherent_impl]
1162    #[unstable(feature = "f128", issue = "116909")]
1163    #[must_use = "method returns a new number and does not mutate the original value"]
1164    pub fn acosh(self) -> f128 {
1165        if self < 1.0 {
1166            Self::NAN
1167        } else {
1168            (self + ((self - 1.0).sqrt() * (self + 1.0).sqrt())).ln()
1169        }
1170    }
1171
1172    /// Inverse hyperbolic tangent function.
1173    ///
1174    /// # Unspecified precision
1175    ///
1176    /// The precision of this function is non-deterministic. This means it varies by platform,
1177    /// Rust version, and can even differ within the same execution from one invocation to the next.
1178    ///
1179    /// # Examples
1180    ///
1181    /// ```
1182    /// #![feature(f128)]
1183    /// # #[cfg(reliable_f128_math)] {
1184    ///
1185    /// let e = std::f128::consts::E;
1186    /// let f = e.tanh().atanh();
1187    ///
1188    /// let abs_difference = (f - e).abs();
1189    ///
1190    /// assert!(abs_difference <= 1e-5);
1191    /// # }
1192    /// ```
1193    #[inline]
1194    #[doc(alias = "arctanh")]
1195    #[rustc_allow_incoherent_impl]
1196    #[unstable(feature = "f128", issue = "116909")]
1197    #[must_use = "method returns a new number and does not mutate the original value"]
1198    pub fn atanh(self) -> f128 {
1199        0.5 * ((2.0 * self) / (1.0 - self)).ln_1p()
1200    }
1201
1202    /// Gamma function.
1203    ///
1204    /// # Unspecified precision
1205    ///
1206    /// The precision of this function is non-deterministic. This means it varies by platform,
1207    /// Rust version, and can even differ within the same execution from one invocation to the next.
1208    ///
1209    /// This function currently corresponds to the `tgammaf128` from libc on Unix
1210    /// and Windows. Note that this might change in the future.
1211    ///
1212    /// # Examples
1213    ///
1214    /// ```
1215    /// #![feature(f128)]
1216    /// #![feature(float_gamma)]
1217    /// # #[cfg(reliable_f128_math)] {
1218    ///
1219    /// let x = 5.0f128;
1220    ///
1221    /// let abs_difference = (x.gamma() - 24.0).abs();
1222    ///
1223    /// assert!(abs_difference <= f128::EPSILON);
1224    /// # }
1225    /// ```
1226    #[inline]
1227    #[rustc_allow_incoherent_impl]
1228    #[unstable(feature = "f128", issue = "116909")]
1229    // #[unstable(feature = "float_gamma", issue = "99842")]
1230    #[must_use = "method returns a new number and does not mutate the original value"]
1231    pub fn gamma(self) -> f128 {
1232        unsafe { cmath::tgammaf128(self) }
1233    }
1234
1235    /// Natural logarithm of the absolute value of the gamma function
1236    ///
1237    /// The integer part of the tuple indicates the sign of the gamma function.
1238    ///
1239    /// # Unspecified precision
1240    ///
1241    /// The precision of this function is non-deterministic. This means it varies by platform,
1242    /// Rust version, and can even differ within the same execution from one invocation to the next.
1243    ///
1244    /// This function currently corresponds to the `lgammaf128_r` from libc on Unix
1245    /// and Windows. Note that this might change in the future.
1246    ///
1247    /// # Examples
1248    ///
1249    /// ```
1250    /// #![feature(f128)]
1251    /// #![feature(float_gamma)]
1252    /// # #[cfg(reliable_f128_math)] {
1253    ///
1254    /// let x = 2.0f128;
1255    ///
1256    /// let abs_difference = (x.ln_gamma().0 - 0.0).abs();
1257    ///
1258    /// assert!(abs_difference <= f128::EPSILON);
1259    /// # }
1260    /// ```
1261    #[inline]
1262    #[rustc_allow_incoherent_impl]
1263    #[unstable(feature = "f128", issue = "116909")]
1264    // #[unstable(feature = "float_gamma", issue = "99842")]
1265    #[must_use = "method returns a new number and does not mutate the original value"]
1266    pub fn ln_gamma(self) -> (f128, i32) {
1267        let mut signgamp: i32 = 0;
1268        let x = unsafe { cmath::lgammaf128_r(self, &mut signgamp) };
1269        (x, signgamp)
1270    }
1271
1272    /// Error function.
1273    ///
1274    /// # Unspecified precision
1275    ///
1276    /// The precision of this function is non-deterministic. This means it varies by platform,
1277    /// Rust version, and can even differ within the same execution from one invocation to the next.
1278    ///
1279    /// This function currently corresponds to the `erff128` from libc on Unix
1280    /// and Windows. Note that this might change in the future.
1281    ///
1282    /// # Examples
1283    ///
1284    /// ```
1285    /// #![feature(f128)]
1286    /// #![feature(float_erf)]
1287    /// # #[cfg(reliable_f128_math)] {
1288    /// /// The error function relates what percent of a normal distribution lies
1289    /// /// within `x` standard deviations (scaled by `1/sqrt(2)`).
1290    /// fn within_standard_deviations(x: f128) -> f128 {
1291    ///     (x * std::f128::consts::FRAC_1_SQRT_2).erf() * 100.0
1292    /// }
1293    ///
1294    /// // 68% of a normal distribution is within one standard deviation
1295    /// assert!((within_standard_deviations(1.0) - 68.269).abs() < 0.01);
1296    /// // 95% of a normal distribution is within two standard deviations
1297    /// assert!((within_standard_deviations(2.0) - 95.450).abs() < 0.01);
1298    /// // 99.7% of a normal distribution is within three standard deviations
1299    /// assert!((within_standard_deviations(3.0) - 99.730).abs() < 0.01);
1300    /// # }
1301    /// ```
1302    #[rustc_allow_incoherent_impl]
1303    #[must_use = "method returns a new number and does not mutate the original value"]
1304    #[unstable(feature = "f128", issue = "116909")]
1305    // #[unstable(feature = "float_erf", issue = "136321")]
1306    #[inline]
1307    pub fn erf(self) -> f128 {
1308        unsafe { cmath::erff128(self) }
1309    }
1310
1311    /// Complementary error function.
1312    ///
1313    /// # Unspecified precision
1314    ///
1315    /// The precision of this function is non-deterministic. This means it varies by platform,
1316    /// Rust version, and can even differ within the same execution from one invocation to the next.
1317    ///
1318    /// This function currently corresponds to the `erfcf128` from libc on Unix
1319    /// and Windows. Note that this might change in the future.
1320    ///
1321    /// # Examples
1322    ///
1323    /// ```
1324    /// #![feature(f128)]
1325    /// #![feature(float_erf)]
1326    /// # #[cfg(reliable_f128_math)] {
1327    /// let x: f128 = 0.123;
1328    ///
1329    /// let one = x.erf() + x.erfc();
1330    /// let abs_difference = (one - 1.0).abs();
1331    ///
1332    /// assert!(abs_difference <= f128::EPSILON);
1333    /// # }
1334    /// ```
1335    #[rustc_allow_incoherent_impl]
1336    #[must_use = "method returns a new number and does not mutate the original value"]
1337    #[unstable(feature = "f128", issue = "116909")]
1338    // #[unstable(feature = "float_erf", issue = "136321")]
1339    #[inline]
1340    pub fn erfc(self) -> f128 {
1341        unsafe { cmath::erfcf128(self) }
1342    }
1343}