std/f16.rs
1//! Constants for the `f16` half-precision floating point type.
2//!
3//! *[See also the `f16` primitive type](primitive@f16).*
4//!
5//! Mathematically significant numbers are provided in the `consts` sub-module.
6
7#[unstable(feature = "f16", issue = "116909")]
8pub use core::f16::consts;
9
10#[cfg(not(test))]
11use crate::intrinsics;
12#[cfg(not(test))]
13use crate::sys::cmath;
14
15#[cfg(not(test))]
16impl f16 {
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(f16)]
25 /// # #[cfg(reliable_f16_math)] {
26 ///
27 /// let f = 3.7_f16;
28 /// let g = 3.0_f16;
29 /// let h = -3.7_f16;
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 = "f16", issue = "116909")]
39 #[must_use = "method returns a new number and does not mutate the original value"]
40 pub fn floor(self) -> f16 {
41 unsafe { intrinsics::floorf16(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(f16)]
52 /// # #[cfg(reliable_f16_math)] {
53 ///
54 /// let f = 3.01_f16;
55 /// let g = 4.0_f16;
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 = "f16", issue = "116909")]
65 #[must_use = "method returns a new number and does not mutate the original value"]
66 pub fn ceil(self) -> f16 {
67 unsafe { intrinsics::ceilf16(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(f16)]
79 /// # #[cfg(reliable_f16_math)] {
80 ///
81 /// let f = 3.3_f16;
82 /// let g = -3.3_f16;
83 /// let h = -3.7_f16;
84 /// let i = 3.5_f16;
85 /// let j = 4.5_f16;
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 = "f16", issue = "116909")]
97 #[must_use = "method returns a new number and does not mutate the original value"]
98 pub fn round(self) -> f16 {
99 unsafe { intrinsics::roundf16(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(f16)]
111 /// # #[cfg(reliable_f16_math)] {
112 ///
113 /// let f = 3.3_f16;
114 /// let g = -3.3_f16;
115 /// let h = 3.5_f16;
116 /// let i = 4.5_f16;
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 = "f16", issue = "116909")]
127 #[must_use = "method returns a new number and does not mutate the original value"]
128 pub fn round_ties_even(self) -> f16 {
129 unsafe { intrinsics::rintf16(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(f16)]
141 /// # #[cfg(reliable_f16_math)] {
142 ///
143 /// let f = 3.7_f16;
144 /// let g = 3.0_f16;
145 /// let h = -3.7_f16;
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 = "f16", issue = "116909")]
156 #[must_use = "method returns a new number and does not mutate the original value"]
157 pub fn trunc(self) -> f16 {
158 unsafe { intrinsics::truncf16(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(f16)]
169 /// # #[cfg(reliable_f16_math)] {
170 ///
171 /// let x = 3.6_f16;
172 /// let y = -3.6_f16;
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 <= f16::EPSILON);
177 /// assert!(abs_difference_y <= f16::EPSILON);
178 /// # }
179 /// ```
180 #[inline]
181 #[rustc_allow_incoherent_impl]
182 #[unstable(feature = "f16", issue = "116909")]
183 #[must_use = "method returns a new number and does not mutate the original value"]
184 pub fn fract(self) -> f16 {
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(f16)]
206 /// # #[cfg(reliable_f16_math)] {
207 ///
208 /// let m = 10.0_f16;
209 /// let x = 4.0_f16;
210 /// let b = 60.0_f16;
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_f16 + f16::EPSILON;
216 /// let one_minus_eps = 1.0_f16 - f16::EPSILON;
217 /// let minus_one = -1.0_f16;
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), -f16::EPSILON * f16::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 #[unstable(feature = "f16", issue = "116909")]
228 #[doc(alias = "fmaf16", alias = "fusedMultiplyAdd")]
229 #[must_use = "method returns a new number and does not mutate the original value"]
230 pub fn mul_add(self, a: f16, b: f16) -> f16 {
231 unsafe { intrinsics::fmaf16(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(f16)]
250 /// # #[cfg(reliable_f16_math)] {
251 ///
252 /// let a: f16 = 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 = "f16", issue = "116909")]
263 #[must_use = "method returns a new number and does not mutate the original value"]
264 pub fn div_euclid(self, rhs: f16) -> f16 {
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(f16)]
292 /// # #[cfg(reliable_f16_math)] {
293 ///
294 /// let a: f16 = 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!((-f16::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 = "f16", issue = "116909")]
308 #[must_use = "method returns a new number and does not mutate the original value"]
309 pub fn rem_euclid(self, rhs: f16) -> f16 {
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(f16)]
329 /// # #[cfg(reliable_f16_math)] {
330 ///
331 /// let x = 2.0_f16;
332 /// let abs_difference = (x.powi(2) - (x * x)).abs();
333 /// assert!(abs_difference <= f16::EPSILON);
334 ///
335 /// assert_eq!(f16::powi(f16::NAN, 0), 1.0);
336 /// # }
337 /// ```
338 #[inline]
339 #[rustc_allow_incoherent_impl]
340 #[unstable(feature = "f16", issue = "116909")]
341 #[must_use = "method returns a new number and does not mutate the original value"]
342 pub fn powi(self, n: i32) -> f16 {
343 unsafe { intrinsics::powif16(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(f16)]
357 /// # #[cfg(reliable_f16_math)] {
358 ///
359 /// let x = 2.0_f16;
360 /// let abs_difference = (x.powf(2.0) - (x * x)).abs();
361 /// assert!(abs_difference <= f16::EPSILON);
362 ///
363 /// assert_eq!(f16::powf(1.0, f16::NAN), 1.0);
364 /// assert_eq!(f16::powf(f16::NAN, 0.0), 1.0);
365 /// # }
366 /// ```
367 #[inline]
368 #[rustc_allow_incoherent_impl]
369 #[unstable(feature = "f16", issue = "116909")]
370 #[must_use = "method returns a new number and does not mutate the original value"]
371 pub fn powf(self, n: f16) -> f16 {
372 unsafe { intrinsics::powf16(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(f16)]
389 /// # #[cfg(reliable_f16_math)] {
390 ///
391 /// let positive = 4.0_f16;
392 /// let negative = -4.0_f16;
393 /// let negative_zero = -0.0_f16;
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 = "f16", issue = "116909")]
404 #[must_use = "method returns a new number and does not mutate the original value"]
405 pub fn sqrt(self) -> f16 {
406 unsafe { intrinsics::sqrtf16(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(f16)]
420 /// # #[cfg(reliable_f16_math)] {
421 ///
422 /// let one = 1.0f16;
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 <= f16::EPSILON);
430 /// # }
431 /// ```
432 #[inline]
433 #[rustc_allow_incoherent_impl]
434 #[unstable(feature = "f16", issue = "116909")]
435 #[must_use = "method returns a new number and does not mutate the original value"]
436 pub fn exp(self) -> f16 {
437 unsafe { intrinsics::expf16(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(f16)]
451 /// # #[cfg(reliable_f16_math)] {
452 ///
453 /// let f = 2.0f16;
454 ///
455 /// // 2^2 - 4 == 0
456 /// let abs_difference = (f.exp2() - 4.0).abs();
457 ///
458 /// assert!(abs_difference <= f16::EPSILON);
459 /// # }
460 /// ```
461 #[inline]
462 #[rustc_allow_incoherent_impl]
463 #[unstable(feature = "f16", issue = "116909")]
464 #[must_use = "method returns a new number and does not mutate the original value"]
465 pub fn exp2(self) -> f16 {
466 unsafe { intrinsics::exp2f16(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(f16)]
480 /// # #[cfg(reliable_f16_math)] {
481 ///
482 /// let one = 1.0f16;
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 <= f16::EPSILON);
490 /// # }
491 /// ```
492 #[inline]
493 #[rustc_allow_incoherent_impl]
494 #[unstable(feature = "f16", issue = "116909")]
495 #[must_use = "method returns a new number and does not mutate the original value"]
496 pub fn ln(self) -> f16 {
497 unsafe { intrinsics::logf16(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(f16)]
515 /// # #[cfg(reliable_f16_math)] {
516 ///
517 /// let five = 5.0f16;
518 ///
519 /// // log5(5) - 1 == 0
520 /// let abs_difference = (five.log(5.0) - 1.0).abs();
521 ///
522 /// assert!(abs_difference <= f16::EPSILON);
523 /// # }
524 /// ```
525 #[inline]
526 #[rustc_allow_incoherent_impl]
527 #[unstable(feature = "f16", issue = "116909")]
528 #[must_use = "method returns a new number and does not mutate the original value"]
529 pub fn log(self, base: f16) -> f16 {
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(f16)]
544 /// # #[cfg(reliable_f16_math)] {
545 ///
546 /// let two = 2.0f16;
547 ///
548 /// // log2(2) - 1 == 0
549 /// let abs_difference = (two.log2() - 1.0).abs();
550 ///
551 /// assert!(abs_difference <= f16::EPSILON);
552 /// # }
553 /// ```
554 #[inline]
555 #[rustc_allow_incoherent_impl]
556 #[unstable(feature = "f16", issue = "116909")]
557 #[must_use = "method returns a new number and does not mutate the original value"]
558 pub fn log2(self) -> f16 {
559 unsafe { intrinsics::log2f16(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(f16)]
573 /// # #[cfg(reliable_f16_math)] {
574 ///
575 /// let ten = 10.0f16;
576 ///
577 /// // log10(10) - 1 == 0
578 /// let abs_difference = (ten.log10() - 1.0).abs();
579 ///
580 /// assert!(abs_difference <= f16::EPSILON);
581 /// # }
582 /// ```
583 #[inline]
584 #[rustc_allow_incoherent_impl]
585 #[unstable(feature = "f16", issue = "116909")]
586 #[must_use = "method returns a new number and does not mutate the original value"]
587 pub fn log10(self) -> f16 {
588 unsafe { intrinsics::log10f16(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 /// This function currently corresponds to the `cbrtf` from libc on Unix
599 /// and Windows. Note that this might change in the future.
600 ///
601 /// # Examples
602 ///
603 /// ```
604 /// #![feature(f16)]
605 /// # #[cfg(reliable_f16_math)] {
606 ///
607 /// let x = 8.0f16;
608 ///
609 /// // x^(1/3) - 2 == 0
610 /// let abs_difference = (x.cbrt() - 2.0).abs();
611 ///
612 /// assert!(abs_difference <= f16::EPSILON);
613 /// # }
614 /// ```
615 #[inline]
616 #[rustc_allow_incoherent_impl]
617 #[unstable(feature = "f16", issue = "116909")]
618 #[must_use = "method returns a new number and does not mutate the original value"]
619 pub fn cbrt(self) -> f16 {
620 (unsafe { cmath::cbrtf(self as f32) }) as f16
621 }
622
623 /// Compute the distance between the origin and a point (`x`, `y`) on the
624 /// Euclidean plane. Equivalently, compute the length of the hypotenuse of a
625 /// right-angle triangle with other sides having length `x.abs()` and
626 /// `y.abs()`.
627 ///
628 /// # Unspecified precision
629 ///
630 /// The precision of this function is non-deterministic. This means it varies by platform,
631 /// Rust version, and can even differ within the same execution from one invocation to the next.
632 ///
633 /// This function currently corresponds to the `hypotf` from libc on Unix
634 /// and Windows. Note that this might change in the future.
635 ///
636 /// # Examples
637 ///
638 /// ```
639 /// #![feature(f16)]
640 /// # #[cfg(reliable_f16_math)] {
641 ///
642 /// let x = 2.0f16;
643 /// let y = 3.0f16;
644 ///
645 /// // sqrt(x^2 + y^2)
646 /// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();
647 ///
648 /// assert!(abs_difference <= f16::EPSILON);
649 /// # }
650 /// ```
651 #[inline]
652 #[rustc_allow_incoherent_impl]
653 #[unstable(feature = "f16", issue = "116909")]
654 #[must_use = "method returns a new number and does not mutate the original value"]
655 pub fn hypot(self, other: f16) -> f16 {
656 (unsafe { cmath::hypotf(self as f32, other as f32) }) as f16
657 }
658
659 /// Computes the sine of a number (in radians).
660 ///
661 /// # Unspecified precision
662 ///
663 /// The precision of this function is non-deterministic. This means it varies by platform,
664 /// Rust version, and can even differ within the same execution from one invocation to the next.
665 ///
666 /// # Examples
667 ///
668 /// ```
669 /// #![feature(f16)]
670 /// # #[cfg(reliable_f16_math)] {
671 ///
672 /// let x = std::f16::consts::FRAC_PI_2;
673 ///
674 /// let abs_difference = (x.sin() - 1.0).abs();
675 ///
676 /// assert!(abs_difference <= f16::EPSILON);
677 /// # }
678 /// ```
679 #[inline]
680 #[rustc_allow_incoherent_impl]
681 #[unstable(feature = "f16", issue = "116909")]
682 #[must_use = "method returns a new number and does not mutate the original value"]
683 pub fn sin(self) -> f16 {
684 unsafe { intrinsics::sinf16(self) }
685 }
686
687 /// Computes the cosine of a number (in radians).
688 ///
689 /// # Unspecified precision
690 ///
691 /// The precision of this function is non-deterministic. This means it varies by platform,
692 /// Rust version, and can even differ within the same execution from one invocation to the next.
693 ///
694 /// # Examples
695 ///
696 /// ```
697 /// #![feature(f16)]
698 /// # #[cfg(reliable_f16_math)] {
699 ///
700 /// let x = 2.0 * std::f16::consts::PI;
701 ///
702 /// let abs_difference = (x.cos() - 1.0).abs();
703 ///
704 /// assert!(abs_difference <= f16::EPSILON);
705 /// # }
706 /// ```
707 #[inline]
708 #[rustc_allow_incoherent_impl]
709 #[unstable(feature = "f16", issue = "116909")]
710 #[must_use = "method returns a new number and does not mutate the original value"]
711 pub fn cos(self) -> f16 {
712 unsafe { intrinsics::cosf16(self) }
713 }
714
715 /// Computes the tangent of a number (in radians).
716 ///
717 /// # Unspecified precision
718 ///
719 /// The precision of this function is non-deterministic. This means it varies by platform,
720 /// Rust version, and can even differ within the same execution from one invocation to the next.
721 ///
722 /// This function currently corresponds to the `tanf` from libc on Unix and
723 /// Windows. Note that this might change in the future.
724 ///
725 /// # Examples
726 ///
727 /// ```
728 /// #![feature(f16)]
729 /// # #[cfg(reliable_f16_math)] {
730 ///
731 /// let x = std::f16::consts::FRAC_PI_4;
732 /// let abs_difference = (x.tan() - 1.0).abs();
733 ///
734 /// assert!(abs_difference <= f16::EPSILON);
735 /// # }
736 /// ```
737 #[inline]
738 #[rustc_allow_incoherent_impl]
739 #[unstable(feature = "f16", issue = "116909")]
740 #[must_use = "method returns a new number and does not mutate the original value"]
741 pub fn tan(self) -> f16 {
742 (unsafe { cmath::tanf(self as f32) }) as f16
743 }
744
745 /// Computes the arcsine of a number. Return value is in radians in
746 /// the range [-pi/2, pi/2] or NaN if the number is outside the range
747 /// [-1, 1].
748 ///
749 /// # Unspecified precision
750 ///
751 /// The precision of this function is non-deterministic. This means it varies by platform,
752 /// Rust version, and can even differ within the same execution from one invocation to the next.
753 ///
754 /// This function currently corresponds to the `asinf` from libc on Unix
755 /// and Windows. Note that this might change in the future.
756 ///
757 /// # Examples
758 ///
759 /// ```
760 /// #![feature(f16)]
761 /// # #[cfg(reliable_f16_math)] {
762 ///
763 /// let f = std::f16::consts::FRAC_PI_2;
764 ///
765 /// // asin(sin(pi/2))
766 /// let abs_difference = (f.sin().asin() - std::f16::consts::FRAC_PI_2).abs();
767 ///
768 /// assert!(abs_difference <= f16::EPSILON);
769 /// # }
770 /// ```
771 #[inline]
772 #[doc(alias = "arcsin")]
773 #[rustc_allow_incoherent_impl]
774 #[unstable(feature = "f16", issue = "116909")]
775 #[must_use = "method returns a new number and does not mutate the original value"]
776 pub fn asin(self) -> f16 {
777 (unsafe { cmath::asinf(self as f32) }) as f16
778 }
779
780 /// Computes the arccosine of a number. Return value is in radians in
781 /// the range [0, pi] or NaN if the number is outside the range
782 /// [-1, 1].
783 ///
784 /// # Unspecified precision
785 ///
786 /// The precision of this function is non-deterministic. This means it varies by platform,
787 /// Rust version, and can even differ within the same execution from one invocation to the next.
788 ///
789 /// This function currently corresponds to the `acosf` from libc on Unix
790 /// and Windows. Note that this might change in the future.
791 ///
792 /// # Examples
793 ///
794 /// ```
795 /// #![feature(f16)]
796 /// # #[cfg(reliable_f16_math)] {
797 ///
798 /// let f = std::f16::consts::FRAC_PI_4;
799 ///
800 /// // acos(cos(pi/4))
801 /// let abs_difference = (f.cos().acos() - std::f16::consts::FRAC_PI_4).abs();
802 ///
803 /// assert!(abs_difference <= f16::EPSILON);
804 /// # }
805 /// ```
806 #[inline]
807 #[doc(alias = "arccos")]
808 #[rustc_allow_incoherent_impl]
809 #[unstable(feature = "f16", issue = "116909")]
810 #[must_use = "method returns a new number and does not mutate the original value"]
811 pub fn acos(self) -> f16 {
812 (unsafe { cmath::acosf(self as f32) }) as f16
813 }
814
815 /// Computes the arctangent of a number. Return value is in radians in the
816 /// range [-pi/2, pi/2];
817 ///
818 /// # Unspecified precision
819 ///
820 /// The precision of this function is non-deterministic. This means it varies by platform,
821 /// Rust version, and can even differ within the same execution from one invocation to the next.
822 ///
823 /// This function currently corresponds to the `atanf` from libc on Unix
824 /// and Windows. Note that this might change in the future.
825 ///
826 /// # Examples
827 ///
828 /// ```
829 /// #![feature(f16)]
830 /// # #[cfg(reliable_f16_math)] {
831 ///
832 /// let f = 1.0f16;
833 ///
834 /// // atan(tan(1))
835 /// let abs_difference = (f.tan().atan() - 1.0).abs();
836 ///
837 /// assert!(abs_difference <= f16::EPSILON);
838 /// # }
839 /// ```
840 #[inline]
841 #[doc(alias = "arctan")]
842 #[rustc_allow_incoherent_impl]
843 #[unstable(feature = "f16", issue = "116909")]
844 #[must_use = "method returns a new number and does not mutate the original value"]
845 pub fn atan(self) -> f16 {
846 (unsafe { cmath::atanf(self as f32) }) as f16
847 }
848
849 /// Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`) in radians.
850 ///
851 /// * `x = 0`, `y = 0`: `0`
852 /// * `x >= 0`: `arctan(y/x)` -> `[-pi/2, pi/2]`
853 /// * `y >= 0`: `arctan(y/x) + pi` -> `(pi/2, pi]`
854 /// * `y < 0`: `arctan(y/x) - pi` -> `(-pi, -pi/2)`
855 ///
856 /// # Unspecified precision
857 ///
858 /// The precision of this function is non-deterministic. This means it varies by platform,
859 /// Rust version, and can even differ within the same execution from one invocation to the next.
860 ///
861 /// This function currently corresponds to the `atan2f` from libc on Unix
862 /// and Windows. Note that this might change in the future.
863 ///
864 /// # Examples
865 ///
866 /// ```
867 /// #![feature(f16)]
868 /// # #[cfg(reliable_f16_math)] {
869 ///
870 /// // Positive angles measured counter-clockwise
871 /// // from positive x axis
872 /// // -pi/4 radians (45 deg clockwise)
873 /// let x1 = 3.0f16;
874 /// let y1 = -3.0f16;
875 ///
876 /// // 3pi/4 radians (135 deg counter-clockwise)
877 /// let x2 = -3.0f16;
878 /// let y2 = 3.0f16;
879 ///
880 /// let abs_difference_1 = (y1.atan2(x1) - (-std::f16::consts::FRAC_PI_4)).abs();
881 /// let abs_difference_2 = (y2.atan2(x2) - (3.0 * std::f16::consts::FRAC_PI_4)).abs();
882 ///
883 /// assert!(abs_difference_1 <= f16::EPSILON);
884 /// assert!(abs_difference_2 <= f16::EPSILON);
885 /// # }
886 /// ```
887 #[inline]
888 #[rustc_allow_incoherent_impl]
889 #[unstable(feature = "f16", issue = "116909")]
890 #[must_use = "method returns a new number and does not mutate the original value"]
891 pub fn atan2(self, other: f16) -> f16 {
892 (unsafe { cmath::atan2f(self as f32, other as f32) }) as f16
893 }
894
895 /// Simultaneously computes the sine and cosine of the number, `x`. Returns
896 /// `(sin(x), cos(x))`.
897 ///
898 /// # Unspecified precision
899 ///
900 /// The precision of this function is non-deterministic. This means it varies by platform,
901 /// Rust version, and can even differ within the same execution from one invocation to the next.
902 ///
903 /// This function currently corresponds to the `(f16::sin(x),
904 /// f16::cos(x))`. Note that this might change in the future.
905 ///
906 /// # Examples
907 ///
908 /// ```
909 /// #![feature(f16)]
910 /// # #[cfg(reliable_f16_math)] {
911 ///
912 /// let x = std::f16::consts::FRAC_PI_4;
913 /// let f = x.sin_cos();
914 ///
915 /// let abs_difference_0 = (f.0 - x.sin()).abs();
916 /// let abs_difference_1 = (f.1 - x.cos()).abs();
917 ///
918 /// assert!(abs_difference_0 <= f16::EPSILON);
919 /// assert!(abs_difference_1 <= f16::EPSILON);
920 /// # }
921 /// ```
922 #[inline]
923 #[doc(alias = "sincos")]
924 #[rustc_allow_incoherent_impl]
925 #[unstable(feature = "f16", issue = "116909")]
926 pub fn sin_cos(self) -> (f16, f16) {
927 (self.sin(), self.cos())
928 }
929
930 /// Returns `e^(self) - 1` in a way that is accurate even if the
931 /// number is close to zero.
932 ///
933 /// # Unspecified precision
934 ///
935 /// The precision of this function is non-deterministic. This means it varies by platform,
936 /// Rust version, and can even differ within the same execution from one invocation to the next.
937 ///
938 /// This function currently corresponds to the `expm1f` from libc on Unix
939 /// and Windows. Note that this might change in the future.
940 ///
941 /// # Examples
942 ///
943 /// ```
944 /// #![feature(f16)]
945 /// # #[cfg(reliable_f16_math)] {
946 ///
947 /// let x = 1e-4_f16;
948 ///
949 /// // for very small x, e^x is approximately 1 + x + x^2 / 2
950 /// let approx = x + x * x / 2.0;
951 /// let abs_difference = (x.exp_m1() - approx).abs();
952 ///
953 /// assert!(abs_difference < 1e-4);
954 /// # }
955 /// ```
956 #[inline]
957 #[rustc_allow_incoherent_impl]
958 #[unstable(feature = "f16", issue = "116909")]
959 #[must_use = "method returns a new number and does not mutate the original value"]
960 pub fn exp_m1(self) -> f16 {
961 (unsafe { cmath::expm1f(self as f32) }) as f16
962 }
963
964 /// Returns `ln(1+n)` (natural logarithm) more accurately than if
965 /// the operations were performed separately.
966 ///
967 /// # Unspecified precision
968 ///
969 /// The precision of this function is non-deterministic. This means it varies by platform,
970 /// Rust version, and can even differ within the same execution from one invocation to the next.
971 ///
972 /// This function currently corresponds to the `log1pf` from libc on Unix
973 /// and Windows. Note that this might change in the future.
974 ///
975 /// # Examples
976 ///
977 /// ```
978 /// #![feature(f16)]
979 /// # #[cfg(reliable_f16_math)] {
980 ///
981 /// let x = 1e-4_f16;
982 ///
983 /// // for very small x, ln(1 + x) is approximately x - x^2 / 2
984 /// let approx = x - x * x / 2.0;
985 /// let abs_difference = (x.ln_1p() - approx).abs();
986 ///
987 /// assert!(abs_difference < 1e-4);
988 /// # }
989 /// ```
990 #[inline]
991 #[doc(alias = "log1p")]
992 #[rustc_allow_incoherent_impl]
993 #[unstable(feature = "f16", issue = "116909")]
994 #[must_use = "method returns a new number and does not mutate the original value"]
995 pub fn ln_1p(self) -> f16 {
996 (unsafe { cmath::log1pf(self as f32) }) as f16
997 }
998
999 /// Hyperbolic sine function.
1000 ///
1001 /// # Unspecified precision
1002 ///
1003 /// The precision of this function is non-deterministic. This means it varies by platform,
1004 /// Rust version, and can even differ within the same execution from one invocation to the next.
1005 ///
1006 /// This function currently corresponds to the `sinhf` from libc on Unix
1007 /// and Windows. Note that this might change in the future.
1008 ///
1009 /// # Examples
1010 ///
1011 /// ```
1012 /// #![feature(f16)]
1013 /// # #[cfg(reliable_f16_math)] {
1014 ///
1015 /// let e = std::f16::consts::E;
1016 /// let x = 1.0f16;
1017 ///
1018 /// let f = x.sinh();
1019 /// // Solving sinh() at 1 gives `(e^2-1)/(2e)`
1020 /// let g = ((e * e) - 1.0) / (2.0 * e);
1021 /// let abs_difference = (f - g).abs();
1022 ///
1023 /// assert!(abs_difference <= f16::EPSILON);
1024 /// # }
1025 /// ```
1026 #[inline]
1027 #[rustc_allow_incoherent_impl]
1028 #[unstable(feature = "f16", issue = "116909")]
1029 #[must_use = "method returns a new number and does not mutate the original value"]
1030 pub fn sinh(self) -> f16 {
1031 (unsafe { cmath::sinhf(self as f32) }) as f16
1032 }
1033
1034 /// Hyperbolic cosine function.
1035 ///
1036 /// # Unspecified precision
1037 ///
1038 /// The precision of this function is non-deterministic. This means it varies by platform,
1039 /// Rust version, and can even differ within the same execution from one invocation to the next.
1040 ///
1041 /// This function currently corresponds to the `coshf` from libc on Unix
1042 /// and Windows. Note that this might change in the future.
1043 ///
1044 /// # Examples
1045 ///
1046 /// ```
1047 /// #![feature(f16)]
1048 /// # #[cfg(reliable_f16_math)] {
1049 ///
1050 /// let e = std::f16::consts::E;
1051 /// let x = 1.0f16;
1052 /// let f = x.cosh();
1053 /// // Solving cosh() at 1 gives this result
1054 /// let g = ((e * e) + 1.0) / (2.0 * e);
1055 /// let abs_difference = (f - g).abs();
1056 ///
1057 /// // Same result
1058 /// assert!(abs_difference <= f16::EPSILON);
1059 /// # }
1060 /// ```
1061 #[inline]
1062 #[rustc_allow_incoherent_impl]
1063 #[unstable(feature = "f16", issue = "116909")]
1064 #[must_use = "method returns a new number and does not mutate the original value"]
1065 pub fn cosh(self) -> f16 {
1066 (unsafe { cmath::coshf(self as f32) }) as f16
1067 }
1068
1069 /// Hyperbolic tangent function.
1070 ///
1071 /// # Unspecified precision
1072 ///
1073 /// The precision of this function is non-deterministic. This means it varies by platform,
1074 /// Rust version, and can even differ within the same execution from one invocation to the next.
1075 ///
1076 /// This function currently corresponds to the `tanhf` from libc on Unix
1077 /// and Windows. Note that this might change in the future.
1078 ///
1079 /// # Examples
1080 ///
1081 /// ```
1082 /// #![feature(f16)]
1083 /// # #[cfg(reliable_f16_math)] {
1084 ///
1085 /// let e = std::f16::consts::E;
1086 /// let x = 1.0f16;
1087 ///
1088 /// let f = x.tanh();
1089 /// // Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))`
1090 /// let g = (1.0 - e.powi(-2)) / (1.0 + e.powi(-2));
1091 /// let abs_difference = (f - g).abs();
1092 ///
1093 /// assert!(abs_difference <= f16::EPSILON);
1094 /// # }
1095 /// ```
1096 #[inline]
1097 #[rustc_allow_incoherent_impl]
1098 #[unstable(feature = "f16", issue = "116909")]
1099 #[must_use = "method returns a new number and does not mutate the original value"]
1100 pub fn tanh(self) -> f16 {
1101 (unsafe { cmath::tanhf(self as f32) }) as f16
1102 }
1103
1104 /// Inverse hyperbolic sine function.
1105 ///
1106 /// # Unspecified precision
1107 ///
1108 /// The precision of this function is non-deterministic. This means it varies by platform,
1109 /// Rust version, and can even differ within the same execution from one invocation to the next.
1110 ///
1111 /// # Examples
1112 ///
1113 /// ```
1114 /// #![feature(f16)]
1115 /// # #[cfg(reliable_f16_math)] {
1116 ///
1117 /// let x = 1.0f16;
1118 /// let f = x.sinh().asinh();
1119 ///
1120 /// let abs_difference = (f - x).abs();
1121 ///
1122 /// assert!(abs_difference <= f16::EPSILON);
1123 /// # }
1124 /// ```
1125 #[inline]
1126 #[doc(alias = "arcsinh")]
1127 #[rustc_allow_incoherent_impl]
1128 #[unstable(feature = "f16", issue = "116909")]
1129 #[must_use = "method returns a new number and does not mutate the original value"]
1130 pub fn asinh(self) -> f16 {
1131 let ax = self.abs();
1132 let ix = 1.0 / ax;
1133 (ax + (ax / (Self::hypot(1.0, ix) + ix))).ln_1p().copysign(self)
1134 }
1135
1136 /// Inverse hyperbolic cosine function.
1137 ///
1138 /// # Unspecified precision
1139 ///
1140 /// The precision of this function is non-deterministic. This means it varies by platform,
1141 /// Rust version, and can even differ within the same execution from one invocation to the next.
1142 ///
1143 /// # Examples
1144 ///
1145 /// ```
1146 /// #![feature(f16)]
1147 /// # #[cfg(reliable_f16_math)] {
1148 ///
1149 /// let x = 1.0f16;
1150 /// let f = x.cosh().acosh();
1151 ///
1152 /// let abs_difference = (f - x).abs();
1153 ///
1154 /// assert!(abs_difference <= f16::EPSILON);
1155 /// # }
1156 /// ```
1157 #[inline]
1158 #[doc(alias = "arccosh")]
1159 #[rustc_allow_incoherent_impl]
1160 #[unstable(feature = "f16", issue = "116909")]
1161 #[must_use = "method returns a new number and does not mutate the original value"]
1162 pub fn acosh(self) -> f16 {
1163 if self < 1.0 {
1164 Self::NAN
1165 } else {
1166 (self + ((self - 1.0).sqrt() * (self + 1.0).sqrt())).ln()
1167 }
1168 }
1169
1170 /// Inverse hyperbolic tangent function.
1171 ///
1172 /// # Unspecified precision
1173 ///
1174 /// The precision of this function is non-deterministic. This means it varies by platform,
1175 /// Rust version, and can even differ within the same execution from one invocation to the next.
1176 ///
1177 /// # Examples
1178 ///
1179 /// ```
1180 /// #![feature(f16)]
1181 /// # #[cfg(reliable_f16_math)] {
1182 ///
1183 /// let e = std::f16::consts::E;
1184 /// let f = e.tanh().atanh();
1185 ///
1186 /// let abs_difference = (f - e).abs();
1187 ///
1188 /// assert!(abs_difference <= 0.01);
1189 /// # }
1190 /// ```
1191 #[inline]
1192 #[doc(alias = "arctanh")]
1193 #[rustc_allow_incoherent_impl]
1194 #[unstable(feature = "f16", issue = "116909")]
1195 #[must_use = "method returns a new number and does not mutate the original value"]
1196 pub fn atanh(self) -> f16 {
1197 0.5 * ((2.0 * self) / (1.0 - self)).ln_1p()
1198 }
1199
1200 /// Gamma function.
1201 ///
1202 /// # Unspecified precision
1203 ///
1204 /// The precision of this function is non-deterministic. This means it varies by platform,
1205 /// Rust version, and can even differ within the same execution from one invocation to the next.
1206 ///
1207 /// This function currently corresponds to the `tgammaf` from libc on Unix
1208 /// and Windows. Note that this might change in the future.
1209 ///
1210 /// # Examples
1211 ///
1212 /// ```
1213 /// #![feature(f16)]
1214 /// #![feature(float_gamma)]
1215 /// # #[cfg(reliable_f16_math)] {
1216 ///
1217 /// let x = 5.0f16;
1218 ///
1219 /// let abs_difference = (x.gamma() - 24.0).abs();
1220 ///
1221 /// assert!(abs_difference <= f16::EPSILON);
1222 /// # }
1223 /// ```
1224 #[inline]
1225 #[rustc_allow_incoherent_impl]
1226 #[unstable(feature = "f16", issue = "116909")]
1227 // #[unstable(feature = "float_gamma", issue = "99842")]
1228 #[must_use = "method returns a new number and does not mutate the original value"]
1229 pub fn gamma(self) -> f16 {
1230 (unsafe { cmath::tgammaf(self as f32) }) as f16
1231 }
1232
1233 /// Natural logarithm of the absolute value of the gamma function
1234 ///
1235 /// The integer part of the tuple indicates the sign of the gamma function.
1236 ///
1237 /// # Unspecified precision
1238 ///
1239 /// The precision of this function is non-deterministic. This means it varies by platform,
1240 /// Rust version, and can even differ within the same execution from one invocation to the next.
1241 ///
1242 /// This function currently corresponds to the `lgamma_r` from libc on Unix
1243 /// and Windows. Note that this might change in the future.
1244 ///
1245 /// # Examples
1246 ///
1247 /// ```
1248 /// #![feature(f16)]
1249 /// #![feature(float_gamma)]
1250 /// # #[cfg(reliable_f16_math)] {
1251 ///
1252 /// let x = 2.0f16;
1253 ///
1254 /// let abs_difference = (x.ln_gamma().0 - 0.0).abs();
1255 ///
1256 /// assert!(abs_difference <= f16::EPSILON);
1257 /// # }
1258 /// ```
1259 #[inline]
1260 #[rustc_allow_incoherent_impl]
1261 #[unstable(feature = "f16", issue = "116909")]
1262 // #[unstable(feature = "float_gamma", issue = "99842")]
1263 #[must_use = "method returns a new number and does not mutate the original value"]
1264 pub fn ln_gamma(self) -> (f16, i32) {
1265 let mut signgamp: i32 = 0;
1266 let x = (unsafe { cmath::lgammaf_r(self as f32, &mut signgamp) }) as f16;
1267 (x, signgamp)
1268 }
1269
1270 /// Error function.
1271 ///
1272 /// # Unspecified precision
1273 ///
1274 /// The precision of this function is non-deterministic. This means it varies by platform,
1275 /// Rust version, and can even differ within the same execution from one invocation to the next.
1276 ///
1277 /// This function currently corresponds to the `erff` from libc on Unix
1278 /// and Windows. Note that this might change in the future.
1279 ///
1280 /// # Examples
1281 ///
1282 /// ```
1283 /// #![feature(f16)]
1284 /// #![feature(float_erf)]
1285 /// # #[cfg(reliable_f16_math)] {
1286 /// /// The error function relates what percent of a normal distribution lies
1287 /// /// within `x` standard deviations (scaled by `1/sqrt(2)`).
1288 /// fn within_standard_deviations(x: f16) -> f16 {
1289 /// (x * std::f16::consts::FRAC_1_SQRT_2).erf() * 100.0
1290 /// }
1291 ///
1292 /// // 68% of a normal distribution is within one standard deviation
1293 /// assert!((within_standard_deviations(1.0) - 68.269).abs() < 0.1);
1294 /// // 95% of a normal distribution is within two standard deviations
1295 /// assert!((within_standard_deviations(2.0) - 95.450).abs() < 0.1);
1296 /// // 99.7% of a normal distribution is within three standard deviations
1297 /// assert!((within_standard_deviations(3.0) - 99.730).abs() < 0.1);
1298 /// # }
1299 /// ```
1300 #[rustc_allow_incoherent_impl]
1301 #[must_use = "method returns a new number and does not mutate the original value"]
1302 #[unstable(feature = "f16", issue = "116909")]
1303 // #[unstable(feature = "float_erf", issue = "136321")]
1304 #[inline]
1305 pub fn erf(self) -> f16 {
1306 (unsafe { cmath::erff(self as f32) }) as f16
1307 }
1308
1309 /// Complementary error function.
1310 ///
1311 /// # Unspecified precision
1312 ///
1313 /// The precision of this function is non-deterministic. This means it varies by platform,
1314 /// Rust version, and can even differ within the same execution from one invocation to the next.
1315 ///
1316 /// This function currently corresponds to the `erfcf` from libc on Unix
1317 /// and Windows. Note that this might change in the future.
1318 ///
1319 /// # Examples
1320 ///
1321 /// ```
1322 /// #![feature(f16)]
1323 /// #![feature(float_erf)]
1324 /// let x: f16 = 0.123;
1325 ///
1326 /// let one = x.erf() + x.erfc();
1327 /// let abs_difference = (one - 1.0).abs();
1328 ///
1329 /// assert!(abs_difference <= f16::EPSILON);
1330 /// ```
1331 #[rustc_allow_incoherent_impl]
1332 #[must_use = "method returns a new number and does not mutate the original value"]
1333 #[unstable(feature = "f16", issue = "116909")]
1334 // #[unstable(feature = "float_erf", issue = "136321")]
1335 #[inline]
1336 pub fn erfc(self) -> f16 {
1337 (unsafe { cmath::erfcf(self as f32) }) as f16
1338 }
1339}