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 intrinsics::round_ties_even_f16(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 /// This returns NaN when the number is negative, and negative infinity when number is zero.
472 ///
473 /// # Unspecified precision
474 ///
475 /// The precision of this function is non-deterministic. This means it varies by platform,
476 /// Rust version, and can even differ within the same execution from one invocation to the next.
477 ///
478 /// # Examples
479 ///
480 /// ```
481 /// #![feature(f16)]
482 /// # #[cfg(reliable_f16_math)] {
483 ///
484 /// let one = 1.0f16;
485 /// // e^1
486 /// let e = one.exp();
487 ///
488 /// // ln(e) - 1 == 0
489 /// let abs_difference = (e.ln() - 1.0).abs();
490 ///
491 /// assert!(abs_difference <= f16::EPSILON);
492 /// # }
493 /// ```
494 ///
495 /// Non-positive values:
496 /// ```
497 /// #![feature(f16)]
498 /// # #[cfg(reliable_f16_math)] {
499 ///
500 /// assert_eq!(0_f16.ln(), f16::NEG_INFINITY);
501 /// assert!((-42_f16).ln().is_nan());
502 /// # }
503 /// ```
504 #[inline]
505 #[rustc_allow_incoherent_impl]
506 #[unstable(feature = "f16", issue = "116909")]
507 #[must_use = "method returns a new number and does not mutate the original value"]
508 pub fn ln(self) -> f16 {
509 unsafe { intrinsics::logf16(self) }
510 }
511
512 /// Returns the logarithm of the number with respect to an arbitrary base.
513 ///
514 /// This returns NaN when the number is negative, and negative infinity when number is zero.
515 ///
516 /// The result might not be correctly rounded owing to implementation details;
517 /// `self.log2()` can produce more accurate results for base 2, and
518 /// `self.log10()` can produce more accurate results for base 10.
519 ///
520 /// # Unspecified precision
521 ///
522 /// The precision of this function is non-deterministic. This means it varies by platform,
523 /// Rust version, and can even differ within the same execution from one invocation to the next.
524 ///
525 /// # Examples
526 ///
527 /// ```
528 /// #![feature(f16)]
529 /// # #[cfg(reliable_f16_math)] {
530 ///
531 /// let five = 5.0f16;
532 ///
533 /// // log5(5) - 1 == 0
534 /// let abs_difference = (five.log(5.0) - 1.0).abs();
535 ///
536 /// assert!(abs_difference <= f16::EPSILON);
537 /// # }
538 /// ```
539 ///
540 /// Non-positive values:
541 /// ```
542 /// #![feature(f16)]
543 /// # #[cfg(reliable_f16_math)] {
544 ///
545 /// assert_eq!(0_f16.log(10.0), f16::NEG_INFINITY);
546 /// assert!((-42_f16).log(10.0).is_nan());
547 /// # }
548 /// ```
549 #[inline]
550 #[rustc_allow_incoherent_impl]
551 #[unstable(feature = "f16", issue = "116909")]
552 #[must_use = "method returns a new number and does not mutate the original value"]
553 pub fn log(self, base: f16) -> f16 {
554 self.ln() / base.ln()
555 }
556
557 /// Returns the base 2 logarithm of the number.
558 ///
559 /// This returns NaN when the number is negative, and negative infinity when number is zero.
560 ///
561 /// # Unspecified precision
562 ///
563 /// The precision of this function is non-deterministic. This means it varies by platform,
564 /// Rust version, and can even differ within the same execution from one invocation to the next.
565 ///
566 /// # Examples
567 ///
568 /// ```
569 /// #![feature(f16)]
570 /// # #[cfg(reliable_f16_math)] {
571 ///
572 /// let two = 2.0f16;
573 ///
574 /// // log2(2) - 1 == 0
575 /// let abs_difference = (two.log2() - 1.0).abs();
576 ///
577 /// assert!(abs_difference <= f16::EPSILON);
578 /// # }
579 /// ```
580 ///
581 /// Non-positive values:
582 /// ```
583 /// #![feature(f16)]
584 /// # #[cfg(reliable_f16_math)] {
585 ///
586 /// assert_eq!(0_f16.log2(), f16::NEG_INFINITY);
587 /// assert!((-42_f16).log2().is_nan());
588 /// # }
589 /// ```
590 #[inline]
591 #[rustc_allow_incoherent_impl]
592 #[unstable(feature = "f16", issue = "116909")]
593 #[must_use = "method returns a new number and does not mutate the original value"]
594 pub fn log2(self) -> f16 {
595 unsafe { intrinsics::log2f16(self) }
596 }
597
598 /// Returns the base 10 logarithm of the number.
599 ///
600 /// This returns NaN when the number is negative, and negative infinity when number is zero.
601 ///
602 /// # Unspecified precision
603 ///
604 /// The precision of this function is non-deterministic. This means it varies by platform,
605 /// Rust version, and can even differ within the same execution from one invocation to the next.
606 ///
607 /// # Examples
608 ///
609 /// ```
610 /// #![feature(f16)]
611 /// # #[cfg(reliable_f16_math)] {
612 ///
613 /// let ten = 10.0f16;
614 ///
615 /// // log10(10) - 1 == 0
616 /// let abs_difference = (ten.log10() - 1.0).abs();
617 ///
618 /// assert!(abs_difference <= f16::EPSILON);
619 /// # }
620 /// ```
621 ///
622 /// Non-positive values:
623 /// ```
624 /// #![feature(f16)]
625 /// # #[cfg(reliable_f16_math)] {
626 ///
627 /// assert_eq!(0_f16.log10(), f16::NEG_INFINITY);
628 /// assert!((-42_f16).log10().is_nan());
629 /// # }
630 /// ```
631 #[inline]
632 #[rustc_allow_incoherent_impl]
633 #[unstable(feature = "f16", issue = "116909")]
634 #[must_use = "method returns a new number and does not mutate the original value"]
635 pub fn log10(self) -> f16 {
636 unsafe { intrinsics::log10f16(self) }
637 }
638
639 /// Returns the cube root of a number.
640 ///
641 /// # Unspecified precision
642 ///
643 /// The precision of this function is non-deterministic. This means it varies by platform,
644 /// Rust version, and can even differ within the same execution from one invocation to the next.
645 ///
646 /// This function currently corresponds to the `cbrtf` from libc on Unix
647 /// and Windows. Note that this might change in the future.
648 ///
649 /// # Examples
650 ///
651 /// ```
652 /// #![feature(f16)]
653 /// # #[cfg(reliable_f16_math)] {
654 ///
655 /// let x = 8.0f16;
656 ///
657 /// // x^(1/3) - 2 == 0
658 /// let abs_difference = (x.cbrt() - 2.0).abs();
659 ///
660 /// assert!(abs_difference <= f16::EPSILON);
661 /// # }
662 /// ```
663 #[inline]
664 #[rustc_allow_incoherent_impl]
665 #[unstable(feature = "f16", issue = "116909")]
666 #[must_use = "method returns a new number and does not mutate the original value"]
667 pub fn cbrt(self) -> f16 {
668 (unsafe { cmath::cbrtf(self as f32) }) as f16
669 }
670
671 /// Compute the distance between the origin and a point (`x`, `y`) on the
672 /// Euclidean plane. Equivalently, compute the length of the hypotenuse of a
673 /// right-angle triangle with other sides having length `x.abs()` and
674 /// `y.abs()`.
675 ///
676 /// # Unspecified precision
677 ///
678 /// The precision of this function is non-deterministic. This means it varies by platform,
679 /// Rust version, and can even differ within the same execution from one invocation to the next.
680 ///
681 /// This function currently corresponds to the `hypotf` from libc on Unix
682 /// and Windows. Note that this might change in the future.
683 ///
684 /// # Examples
685 ///
686 /// ```
687 /// #![feature(f16)]
688 /// # #[cfg(reliable_f16_math)] {
689 ///
690 /// let x = 2.0f16;
691 /// let y = 3.0f16;
692 ///
693 /// // sqrt(x^2 + y^2)
694 /// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();
695 ///
696 /// assert!(abs_difference <= f16::EPSILON);
697 /// # }
698 /// ```
699 #[inline]
700 #[rustc_allow_incoherent_impl]
701 #[unstable(feature = "f16", issue = "116909")]
702 #[must_use = "method returns a new number and does not mutate the original value"]
703 pub fn hypot(self, other: f16) -> f16 {
704 (unsafe { cmath::hypotf(self as f32, other as f32) }) as f16
705 }
706
707 /// Computes the sine of a number (in radians).
708 ///
709 /// # Unspecified precision
710 ///
711 /// The precision of this function is non-deterministic. This means it varies by platform,
712 /// Rust version, and can even differ within the same execution from one invocation to the next.
713 ///
714 /// # Examples
715 ///
716 /// ```
717 /// #![feature(f16)]
718 /// # #[cfg(reliable_f16_math)] {
719 ///
720 /// let x = std::f16::consts::FRAC_PI_2;
721 ///
722 /// let abs_difference = (x.sin() - 1.0).abs();
723 ///
724 /// assert!(abs_difference <= f16::EPSILON);
725 /// # }
726 /// ```
727 #[inline]
728 #[rustc_allow_incoherent_impl]
729 #[unstable(feature = "f16", issue = "116909")]
730 #[must_use = "method returns a new number and does not mutate the original value"]
731 pub fn sin(self) -> f16 {
732 unsafe { intrinsics::sinf16(self) }
733 }
734
735 /// Computes the cosine of a number (in radians).
736 ///
737 /// # Unspecified precision
738 ///
739 /// The precision of this function is non-deterministic. This means it varies by platform,
740 /// Rust version, and can even differ within the same execution from one invocation to the next.
741 ///
742 /// # Examples
743 ///
744 /// ```
745 /// #![feature(f16)]
746 /// # #[cfg(reliable_f16_math)] {
747 ///
748 /// let x = 2.0 * std::f16::consts::PI;
749 ///
750 /// let abs_difference = (x.cos() - 1.0).abs();
751 ///
752 /// assert!(abs_difference <= f16::EPSILON);
753 /// # }
754 /// ```
755 #[inline]
756 #[rustc_allow_incoherent_impl]
757 #[unstable(feature = "f16", issue = "116909")]
758 #[must_use = "method returns a new number and does not mutate the original value"]
759 pub fn cos(self) -> f16 {
760 unsafe { intrinsics::cosf16(self) }
761 }
762
763 /// Computes the tangent of a number (in radians).
764 ///
765 /// # Unspecified precision
766 ///
767 /// The precision of this function is non-deterministic. This means it varies by platform,
768 /// Rust version, and can even differ within the same execution from one invocation to the next.
769 ///
770 /// This function currently corresponds to the `tanf` from libc on Unix and
771 /// Windows. Note that this might change in the future.
772 ///
773 /// # Examples
774 ///
775 /// ```
776 /// #![feature(f16)]
777 /// # #[cfg(reliable_f16_math)] {
778 ///
779 /// let x = std::f16::consts::FRAC_PI_4;
780 /// let abs_difference = (x.tan() - 1.0).abs();
781 ///
782 /// assert!(abs_difference <= f16::EPSILON);
783 /// # }
784 /// ```
785 #[inline]
786 #[rustc_allow_incoherent_impl]
787 #[unstable(feature = "f16", issue = "116909")]
788 #[must_use = "method returns a new number and does not mutate the original value"]
789 pub fn tan(self) -> f16 {
790 (unsafe { cmath::tanf(self as f32) }) as f16
791 }
792
793 /// Computes the arcsine of a number. Return value is in radians in
794 /// the range [-pi/2, pi/2] or NaN if the number is outside the range
795 /// [-1, 1].
796 ///
797 /// # Unspecified precision
798 ///
799 /// The precision of this function is non-deterministic. This means it varies by platform,
800 /// Rust version, and can even differ within the same execution from one invocation to the next.
801 ///
802 /// This function currently corresponds to the `asinf` from libc on Unix
803 /// and Windows. Note that this might change in the future.
804 ///
805 /// # Examples
806 ///
807 /// ```
808 /// #![feature(f16)]
809 /// # #[cfg(reliable_f16_math)] {
810 ///
811 /// let f = std::f16::consts::FRAC_PI_2;
812 ///
813 /// // asin(sin(pi/2))
814 /// let abs_difference = (f.sin().asin() - std::f16::consts::FRAC_PI_2).abs();
815 ///
816 /// assert!(abs_difference <= f16::EPSILON);
817 /// # }
818 /// ```
819 #[inline]
820 #[doc(alias = "arcsin")]
821 #[rustc_allow_incoherent_impl]
822 #[unstable(feature = "f16", issue = "116909")]
823 #[must_use = "method returns a new number and does not mutate the original value"]
824 pub fn asin(self) -> f16 {
825 (unsafe { cmath::asinf(self as f32) }) as f16
826 }
827
828 /// Computes the arccosine of a number. Return value is in radians in
829 /// the range [0, pi] or NaN if the number is outside the range
830 /// [-1, 1].
831 ///
832 /// # Unspecified precision
833 ///
834 /// The precision of this function is non-deterministic. This means it varies by platform,
835 /// Rust version, and can even differ within the same execution from one invocation to the next.
836 ///
837 /// This function currently corresponds to the `acosf` from libc on Unix
838 /// and Windows. Note that this might change in the future.
839 ///
840 /// # Examples
841 ///
842 /// ```
843 /// #![feature(f16)]
844 /// # #[cfg(reliable_f16_math)] {
845 ///
846 /// let f = std::f16::consts::FRAC_PI_4;
847 ///
848 /// // acos(cos(pi/4))
849 /// let abs_difference = (f.cos().acos() - std::f16::consts::FRAC_PI_4).abs();
850 ///
851 /// assert!(abs_difference <= f16::EPSILON);
852 /// # }
853 /// ```
854 #[inline]
855 #[doc(alias = "arccos")]
856 #[rustc_allow_incoherent_impl]
857 #[unstable(feature = "f16", issue = "116909")]
858 #[must_use = "method returns a new number and does not mutate the original value"]
859 pub fn acos(self) -> f16 {
860 (unsafe { cmath::acosf(self as f32) }) as f16
861 }
862
863 /// Computes the arctangent of a number. Return value is in radians in the
864 /// range [-pi/2, pi/2];
865 ///
866 /// # Unspecified precision
867 ///
868 /// The precision of this function is non-deterministic. This means it varies by platform,
869 /// Rust version, and can even differ within the same execution from one invocation to the next.
870 ///
871 /// This function currently corresponds to the `atanf` from libc on Unix
872 /// and Windows. Note that this might change in the future.
873 ///
874 /// # Examples
875 ///
876 /// ```
877 /// #![feature(f16)]
878 /// # #[cfg(reliable_f16_math)] {
879 ///
880 /// let f = 1.0f16;
881 ///
882 /// // atan(tan(1))
883 /// let abs_difference = (f.tan().atan() - 1.0).abs();
884 ///
885 /// assert!(abs_difference <= f16::EPSILON);
886 /// # }
887 /// ```
888 #[inline]
889 #[doc(alias = "arctan")]
890 #[rustc_allow_incoherent_impl]
891 #[unstable(feature = "f16", issue = "116909")]
892 #[must_use = "method returns a new number and does not mutate the original value"]
893 pub fn atan(self) -> f16 {
894 (unsafe { cmath::atanf(self as f32) }) as f16
895 }
896
897 /// Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`) in radians.
898 ///
899 /// * `x = 0`, `y = 0`: `0`
900 /// * `x >= 0`: `arctan(y/x)` -> `[-pi/2, pi/2]`
901 /// * `y >= 0`: `arctan(y/x) + pi` -> `(pi/2, pi]`
902 /// * `y < 0`: `arctan(y/x) - pi` -> `(-pi, -pi/2)`
903 ///
904 /// # Unspecified precision
905 ///
906 /// The precision of this function is non-deterministic. This means it varies by platform,
907 /// Rust version, and can even differ within the same execution from one invocation to the next.
908 ///
909 /// This function currently corresponds to the `atan2f` from libc on Unix
910 /// and Windows. Note that this might change in the future.
911 ///
912 /// # Examples
913 ///
914 /// ```
915 /// #![feature(f16)]
916 /// # #[cfg(reliable_f16_math)] {
917 ///
918 /// // Positive angles measured counter-clockwise
919 /// // from positive x axis
920 /// // -pi/4 radians (45 deg clockwise)
921 /// let x1 = 3.0f16;
922 /// let y1 = -3.0f16;
923 ///
924 /// // 3pi/4 radians (135 deg counter-clockwise)
925 /// let x2 = -3.0f16;
926 /// let y2 = 3.0f16;
927 ///
928 /// let abs_difference_1 = (y1.atan2(x1) - (-std::f16::consts::FRAC_PI_4)).abs();
929 /// let abs_difference_2 = (y2.atan2(x2) - (3.0 * std::f16::consts::FRAC_PI_4)).abs();
930 ///
931 /// assert!(abs_difference_1 <= f16::EPSILON);
932 /// assert!(abs_difference_2 <= f16::EPSILON);
933 /// # }
934 /// ```
935 #[inline]
936 #[rustc_allow_incoherent_impl]
937 #[unstable(feature = "f16", issue = "116909")]
938 #[must_use = "method returns a new number and does not mutate the original value"]
939 pub fn atan2(self, other: f16) -> f16 {
940 (unsafe { cmath::atan2f(self as f32, other as f32) }) as f16
941 }
942
943 /// Simultaneously computes the sine and cosine of the number, `x`. Returns
944 /// `(sin(x), cos(x))`.
945 ///
946 /// # Unspecified precision
947 ///
948 /// The precision of this function is non-deterministic. This means it varies by platform,
949 /// Rust version, and can even differ within the same execution from one invocation to the next.
950 ///
951 /// This function currently corresponds to the `(f16::sin(x),
952 /// f16::cos(x))`. Note that this might change in the future.
953 ///
954 /// # Examples
955 ///
956 /// ```
957 /// #![feature(f16)]
958 /// # #[cfg(reliable_f16_math)] {
959 ///
960 /// let x = std::f16::consts::FRAC_PI_4;
961 /// let f = x.sin_cos();
962 ///
963 /// let abs_difference_0 = (f.0 - x.sin()).abs();
964 /// let abs_difference_1 = (f.1 - x.cos()).abs();
965 ///
966 /// assert!(abs_difference_0 <= f16::EPSILON);
967 /// assert!(abs_difference_1 <= f16::EPSILON);
968 /// # }
969 /// ```
970 #[inline]
971 #[doc(alias = "sincos")]
972 #[rustc_allow_incoherent_impl]
973 #[unstable(feature = "f16", issue = "116909")]
974 pub fn sin_cos(self) -> (f16, f16) {
975 (self.sin(), self.cos())
976 }
977
978 /// Returns `e^(self) - 1` in a way that is accurate even if the
979 /// number is close to zero.
980 ///
981 /// # Unspecified precision
982 ///
983 /// The precision of this function is non-deterministic. This means it varies by platform,
984 /// Rust version, and can even differ within the same execution from one invocation to the next.
985 ///
986 /// This function currently corresponds to the `expm1f` from libc on Unix
987 /// and Windows. Note that this might change in the future.
988 ///
989 /// # Examples
990 ///
991 /// ```
992 /// #![feature(f16)]
993 /// # #[cfg(reliable_f16_math)] {
994 ///
995 /// let x = 1e-4_f16;
996 ///
997 /// // for very small x, e^x is approximately 1 + x + x^2 / 2
998 /// let approx = x + x * x / 2.0;
999 /// let abs_difference = (x.exp_m1() - approx).abs();
1000 ///
1001 /// assert!(abs_difference < 1e-4);
1002 /// # }
1003 /// ```
1004 #[inline]
1005 #[rustc_allow_incoherent_impl]
1006 #[unstable(feature = "f16", issue = "116909")]
1007 #[must_use = "method returns a new number and does not mutate the original value"]
1008 pub fn exp_m1(self) -> f16 {
1009 (unsafe { cmath::expm1f(self as f32) }) as f16
1010 }
1011
1012 /// Returns `ln(1+n)` (natural logarithm) more accurately than if
1013 /// the operations were performed separately.
1014 ///
1015 /// This returns NaN when `n < -1.0`, and negative infinity when `n == -1.0`.
1016 ///
1017 /// # Unspecified precision
1018 ///
1019 /// The precision of this function is non-deterministic. This means it varies by platform,
1020 /// Rust version, and can even differ within the same execution from one invocation to the next.
1021 ///
1022 /// This function currently corresponds to the `log1pf` from libc on Unix
1023 /// and Windows. Note that this might change in the future.
1024 ///
1025 /// # Examples
1026 ///
1027 /// ```
1028 /// #![feature(f16)]
1029 /// # #[cfg(reliable_f16_math)] {
1030 ///
1031 /// let x = 1e-4_f16;
1032 ///
1033 /// // for very small x, ln(1 + x) is approximately x - x^2 / 2
1034 /// let approx = x - x * x / 2.0;
1035 /// let abs_difference = (x.ln_1p() - approx).abs();
1036 ///
1037 /// assert!(abs_difference < 1e-4);
1038 /// # }
1039 /// ```
1040 ///
1041 /// Out-of-range values:
1042 /// ```
1043 /// #![feature(f16)]
1044 /// # #[cfg(reliable_f16_math)] {
1045 ///
1046 /// assert_eq!((-1.0_f16).ln_1p(), f16::NEG_INFINITY);
1047 /// assert!((-2.0_f16).ln_1p().is_nan());
1048 /// # }
1049 /// ```
1050 #[inline]
1051 #[doc(alias = "log1p")]
1052 #[rustc_allow_incoherent_impl]
1053 #[unstable(feature = "f16", issue = "116909")]
1054 #[must_use = "method returns a new number and does not mutate the original value"]
1055 pub fn ln_1p(self) -> f16 {
1056 (unsafe { cmath::log1pf(self as f32) }) as f16
1057 }
1058
1059 /// Hyperbolic sine function.
1060 ///
1061 /// # Unspecified precision
1062 ///
1063 /// The precision of this function is non-deterministic. This means it varies by platform,
1064 /// Rust version, and can even differ within the same execution from one invocation to the next.
1065 ///
1066 /// This function currently corresponds to the `sinhf` from libc on Unix
1067 /// and Windows. Note that this might change in the future.
1068 ///
1069 /// # Examples
1070 ///
1071 /// ```
1072 /// #![feature(f16)]
1073 /// # #[cfg(reliable_f16_math)] {
1074 ///
1075 /// let e = std::f16::consts::E;
1076 /// let x = 1.0f16;
1077 ///
1078 /// let f = x.sinh();
1079 /// // Solving sinh() at 1 gives `(e^2-1)/(2e)`
1080 /// let g = ((e * e) - 1.0) / (2.0 * e);
1081 /// let abs_difference = (f - g).abs();
1082 ///
1083 /// assert!(abs_difference <= f16::EPSILON);
1084 /// # }
1085 /// ```
1086 #[inline]
1087 #[rustc_allow_incoherent_impl]
1088 #[unstable(feature = "f16", issue = "116909")]
1089 #[must_use = "method returns a new number and does not mutate the original value"]
1090 pub fn sinh(self) -> f16 {
1091 (unsafe { cmath::sinhf(self as f32) }) as f16
1092 }
1093
1094 /// Hyperbolic cosine function.
1095 ///
1096 /// # Unspecified precision
1097 ///
1098 /// The precision of this function is non-deterministic. This means it varies by platform,
1099 /// Rust version, and can even differ within the same execution from one invocation to the next.
1100 ///
1101 /// This function currently corresponds to the `coshf` from libc on Unix
1102 /// and Windows. Note that this might change in the future.
1103 ///
1104 /// # Examples
1105 ///
1106 /// ```
1107 /// #![feature(f16)]
1108 /// # #[cfg(reliable_f16_math)] {
1109 ///
1110 /// let e = std::f16::consts::E;
1111 /// let x = 1.0f16;
1112 /// let f = x.cosh();
1113 /// // Solving cosh() at 1 gives this result
1114 /// let g = ((e * e) + 1.0) / (2.0 * e);
1115 /// let abs_difference = (f - g).abs();
1116 ///
1117 /// // Same result
1118 /// assert!(abs_difference <= f16::EPSILON);
1119 /// # }
1120 /// ```
1121 #[inline]
1122 #[rustc_allow_incoherent_impl]
1123 #[unstable(feature = "f16", issue = "116909")]
1124 #[must_use = "method returns a new number and does not mutate the original value"]
1125 pub fn cosh(self) -> f16 {
1126 (unsafe { cmath::coshf(self as f32) }) as f16
1127 }
1128
1129 /// Hyperbolic tangent function.
1130 ///
1131 /// # Unspecified precision
1132 ///
1133 /// The precision of this function is non-deterministic. This means it varies by platform,
1134 /// Rust version, and can even differ within the same execution from one invocation to the next.
1135 ///
1136 /// This function currently corresponds to the `tanhf` from libc on Unix
1137 /// and Windows. Note that this might change in the future.
1138 ///
1139 /// # Examples
1140 ///
1141 /// ```
1142 /// #![feature(f16)]
1143 /// # #[cfg(reliable_f16_math)] {
1144 ///
1145 /// let e = std::f16::consts::E;
1146 /// let x = 1.0f16;
1147 ///
1148 /// let f = x.tanh();
1149 /// // Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))`
1150 /// let g = (1.0 - e.powi(-2)) / (1.0 + e.powi(-2));
1151 /// let abs_difference = (f - g).abs();
1152 ///
1153 /// assert!(abs_difference <= f16::EPSILON);
1154 /// # }
1155 /// ```
1156 #[inline]
1157 #[rustc_allow_incoherent_impl]
1158 #[unstable(feature = "f16", issue = "116909")]
1159 #[must_use = "method returns a new number and does not mutate the original value"]
1160 pub fn tanh(self) -> f16 {
1161 (unsafe { cmath::tanhf(self as f32) }) as f16
1162 }
1163
1164 /// Inverse hyperbolic sine function.
1165 ///
1166 /// # Unspecified precision
1167 ///
1168 /// The precision of this function is non-deterministic. This means it varies by platform,
1169 /// Rust version, and can even differ within the same execution from one invocation to the next.
1170 ///
1171 /// # Examples
1172 ///
1173 /// ```
1174 /// #![feature(f16)]
1175 /// # #[cfg(reliable_f16_math)] {
1176 ///
1177 /// let x = 1.0f16;
1178 /// let f = x.sinh().asinh();
1179 ///
1180 /// let abs_difference = (f - x).abs();
1181 ///
1182 /// assert!(abs_difference <= f16::EPSILON);
1183 /// # }
1184 /// ```
1185 #[inline]
1186 #[doc(alias = "arcsinh")]
1187 #[rustc_allow_incoherent_impl]
1188 #[unstable(feature = "f16", issue = "116909")]
1189 #[must_use = "method returns a new number and does not mutate the original value"]
1190 pub fn asinh(self) -> f16 {
1191 let ax = self.abs();
1192 let ix = 1.0 / ax;
1193 (ax + (ax / (Self::hypot(1.0, ix) + ix))).ln_1p().copysign(self)
1194 }
1195
1196 /// Inverse hyperbolic cosine function.
1197 ///
1198 /// # Unspecified precision
1199 ///
1200 /// The precision of this function is non-deterministic. This means it varies by platform,
1201 /// Rust version, and can even differ within the same execution from one invocation to the next.
1202 ///
1203 /// # Examples
1204 ///
1205 /// ```
1206 /// #![feature(f16)]
1207 /// # #[cfg(reliable_f16_math)] {
1208 ///
1209 /// let x = 1.0f16;
1210 /// let f = x.cosh().acosh();
1211 ///
1212 /// let abs_difference = (f - x).abs();
1213 ///
1214 /// assert!(abs_difference <= f16::EPSILON);
1215 /// # }
1216 /// ```
1217 #[inline]
1218 #[doc(alias = "arccosh")]
1219 #[rustc_allow_incoherent_impl]
1220 #[unstable(feature = "f16", issue = "116909")]
1221 #[must_use = "method returns a new number and does not mutate the original value"]
1222 pub fn acosh(self) -> f16 {
1223 if self < 1.0 {
1224 Self::NAN
1225 } else {
1226 (self + ((self - 1.0).sqrt() * (self + 1.0).sqrt())).ln()
1227 }
1228 }
1229
1230 /// Inverse hyperbolic tangent function.
1231 ///
1232 /// # Unspecified precision
1233 ///
1234 /// The precision of this function is non-deterministic. This means it varies by platform,
1235 /// Rust version, and can even differ within the same execution from one invocation to the next.
1236 ///
1237 /// # Examples
1238 ///
1239 /// ```
1240 /// #![feature(f16)]
1241 /// # #[cfg(reliable_f16_math)] {
1242 ///
1243 /// let e = std::f16::consts::E;
1244 /// let f = e.tanh().atanh();
1245 ///
1246 /// let abs_difference = (f - e).abs();
1247 ///
1248 /// assert!(abs_difference <= 0.01);
1249 /// # }
1250 /// ```
1251 #[inline]
1252 #[doc(alias = "arctanh")]
1253 #[rustc_allow_incoherent_impl]
1254 #[unstable(feature = "f16", issue = "116909")]
1255 #[must_use = "method returns a new number and does not mutate the original value"]
1256 pub fn atanh(self) -> f16 {
1257 0.5 * ((2.0 * self) / (1.0 - self)).ln_1p()
1258 }
1259
1260 /// Gamma function.
1261 ///
1262 /// # Unspecified precision
1263 ///
1264 /// The precision of this function is non-deterministic. This means it varies by platform,
1265 /// Rust version, and can even differ within the same execution from one invocation to the next.
1266 ///
1267 /// This function currently corresponds to the `tgammaf` from libc on Unix
1268 /// and Windows. Note that this might change in the future.
1269 ///
1270 /// # Examples
1271 ///
1272 /// ```
1273 /// #![feature(f16)]
1274 /// #![feature(float_gamma)]
1275 /// # #[cfg(reliable_f16_math)] {
1276 ///
1277 /// let x = 5.0f16;
1278 ///
1279 /// let abs_difference = (x.gamma() - 24.0).abs();
1280 ///
1281 /// assert!(abs_difference <= f16::EPSILON);
1282 /// # }
1283 /// ```
1284 #[inline]
1285 #[rustc_allow_incoherent_impl]
1286 #[unstable(feature = "f16", issue = "116909")]
1287 // #[unstable(feature = "float_gamma", issue = "99842")]
1288 #[must_use = "method returns a new number and does not mutate the original value"]
1289 pub fn gamma(self) -> f16 {
1290 (unsafe { cmath::tgammaf(self as f32) }) as f16
1291 }
1292
1293 /// Natural logarithm of the absolute value of the gamma function
1294 ///
1295 /// The integer part of the tuple indicates the sign of the gamma function.
1296 ///
1297 /// # Unspecified precision
1298 ///
1299 /// The precision of this function is non-deterministic. This means it varies by platform,
1300 /// Rust version, and can even differ within the same execution from one invocation to the next.
1301 ///
1302 /// This function currently corresponds to the `lgamma_r` from libc on Unix
1303 /// and Windows. Note that this might change in the future.
1304 ///
1305 /// # Examples
1306 ///
1307 /// ```
1308 /// #![feature(f16)]
1309 /// #![feature(float_gamma)]
1310 /// # #[cfg(reliable_f16_math)] {
1311 ///
1312 /// let x = 2.0f16;
1313 ///
1314 /// let abs_difference = (x.ln_gamma().0 - 0.0).abs();
1315 ///
1316 /// assert!(abs_difference <= f16::EPSILON);
1317 /// # }
1318 /// ```
1319 #[inline]
1320 #[rustc_allow_incoherent_impl]
1321 #[unstable(feature = "f16", issue = "116909")]
1322 // #[unstable(feature = "float_gamma", issue = "99842")]
1323 #[must_use = "method returns a new number and does not mutate the original value"]
1324 pub fn ln_gamma(self) -> (f16, i32) {
1325 let mut signgamp: i32 = 0;
1326 let x = (unsafe { cmath::lgammaf_r(self as f32, &mut signgamp) }) as f16;
1327 (x, signgamp)
1328 }
1329
1330 /// Error function.
1331 ///
1332 /// # Unspecified precision
1333 ///
1334 /// The precision of this function is non-deterministic. This means it varies by platform,
1335 /// Rust version, and can even differ within the same execution from one invocation to the next.
1336 ///
1337 /// This function currently corresponds to the `erff` from libc on Unix
1338 /// and Windows. Note that this might change in the future.
1339 ///
1340 /// # Examples
1341 ///
1342 /// ```
1343 /// #![feature(f16)]
1344 /// #![feature(float_erf)]
1345 /// # #[cfg(reliable_f16_math)] {
1346 /// /// The error function relates what percent of a normal distribution lies
1347 /// /// within `x` standard deviations (scaled by `1/sqrt(2)`).
1348 /// fn within_standard_deviations(x: f16) -> f16 {
1349 /// (x * std::f16::consts::FRAC_1_SQRT_2).erf() * 100.0
1350 /// }
1351 ///
1352 /// // 68% of a normal distribution is within one standard deviation
1353 /// assert!((within_standard_deviations(1.0) - 68.269).abs() < 0.1);
1354 /// // 95% of a normal distribution is within two standard deviations
1355 /// assert!((within_standard_deviations(2.0) - 95.450).abs() < 0.1);
1356 /// // 99.7% of a normal distribution is within three standard deviations
1357 /// assert!((within_standard_deviations(3.0) - 99.730).abs() < 0.1);
1358 /// # }
1359 /// ```
1360 #[rustc_allow_incoherent_impl]
1361 #[must_use = "method returns a new number and does not mutate the original value"]
1362 #[unstable(feature = "f16", issue = "116909")]
1363 // #[unstable(feature = "float_erf", issue = "136321")]
1364 #[inline]
1365 pub fn erf(self) -> f16 {
1366 (unsafe { cmath::erff(self as f32) }) as f16
1367 }
1368
1369 /// Complementary error function.
1370 ///
1371 /// # Unspecified precision
1372 ///
1373 /// The precision of this function is non-deterministic. This means it varies by platform,
1374 /// Rust version, and can even differ within the same execution from one invocation to the next.
1375 ///
1376 /// This function currently corresponds to the `erfcf` from libc on Unix
1377 /// and Windows. Note that this might change in the future.
1378 ///
1379 /// # Examples
1380 ///
1381 /// ```
1382 /// #![feature(f16)]
1383 /// #![feature(float_erf)]
1384 /// # #[cfg(reliable_f16_math)] {
1385 /// let x: f16 = 0.123;
1386 ///
1387 /// let one = x.erf() + x.erfc();
1388 /// let abs_difference = (one - 1.0).abs();
1389 ///
1390 /// assert!(abs_difference <= f16::EPSILON);
1391 /// # }
1392 /// ```
1393 #[rustc_allow_incoherent_impl]
1394 #[must_use = "method returns a new number and does not mutate the original value"]
1395 #[unstable(feature = "f16", issue = "116909")]
1396 // #[unstable(feature = "float_erf", issue = "136321")]
1397 #[inline]
1398 pub fn erfc(self) -> f16 {
1399 (unsafe { cmath::erfcf(self as f32) }) as f16
1400 }
1401}
1402