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 intrinsics::round_ties_even_f128(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 /// 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(f128)]
482 /// # #[cfg(reliable_f128_math)] {
483 ///
484 /// let one = 1.0f128;
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 <= f128::EPSILON);
492 /// # }
493 /// ```
494 ///
495 /// Non-positive values:
496 /// ```
497 /// #![feature(f128)]
498 /// # #[cfg(reliable_f128_math)] {
499 ///
500 /// assert_eq!(0_f128.ln(), f128::NEG_INFINITY);
501 /// assert!((-42_f128).ln().is_nan());
502 /// # }
503 /// ```
504 #[inline]
505 #[rustc_allow_incoherent_impl]
506 #[unstable(feature = "f128", issue = "116909")]
507 #[must_use = "method returns a new number and does not mutate the original value"]
508 pub fn ln(self) -> f128 {
509 unsafe { intrinsics::logf128(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(f128)]
529 /// # #[cfg(reliable_f128_math)] {
530 ///
531 /// let five = 5.0f128;
532 ///
533 /// // log5(5) - 1 == 0
534 /// let abs_difference = (five.log(5.0) - 1.0).abs();
535 ///
536 /// assert!(abs_difference <= f128::EPSILON);
537 /// # }
538 /// ```
539 ///
540 /// Non-positive values:
541 /// ```
542 /// #![feature(f128)]
543 /// # #[cfg(reliable_f128_math)] {
544 ///
545 /// assert_eq!(0_f128.log(10.0), f128::NEG_INFINITY);
546 /// assert!((-42_f128).log(10.0).is_nan());
547 /// # }
548 /// ```
549 #[inline]
550 #[rustc_allow_incoherent_impl]
551 #[unstable(feature = "f128", issue = "116909")]
552 #[must_use = "method returns a new number and does not mutate the original value"]
553 pub fn log(self, base: f128) -> f128 {
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(f128)]
570 /// # #[cfg(reliable_f128_math)] {
571 ///
572 /// let two = 2.0f128;
573 ///
574 /// // log2(2) - 1 == 0
575 /// let abs_difference = (two.log2() - 1.0).abs();
576 ///
577 /// assert!(abs_difference <= f128::EPSILON);
578 /// # }
579 /// ```
580 ///
581 /// Non-positive values:
582 /// ```
583 /// #![feature(f128)]
584 /// # #[cfg(reliable_f128_math)] {
585 ///
586 /// assert_eq!(0_f128.log2(), f128::NEG_INFINITY);
587 /// assert!((-42_f128).log2().is_nan());
588 /// # }
589 /// ```
590 #[inline]
591 #[rustc_allow_incoherent_impl]
592 #[unstable(feature = "f128", issue = "116909")]
593 #[must_use = "method returns a new number and does not mutate the original value"]
594 pub fn log2(self) -> f128 {
595 unsafe { intrinsics::log2f128(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(f128)]
611 /// # #[cfg(reliable_f128_math)] {
612 ///
613 /// let ten = 10.0f128;
614 ///
615 /// // log10(10) - 1 == 0
616 /// let abs_difference = (ten.log10() - 1.0).abs();
617 ///
618 /// assert!(abs_difference <= f128::EPSILON);
619 /// # }
620 /// ```
621 ///
622 /// Non-positive values:
623 /// ```
624 /// #![feature(f128)]
625 /// # #[cfg(reliable_f128_math)] {
626 ///
627 /// assert_eq!(0_f128.log10(), f128::NEG_INFINITY);
628 /// assert!((-42_f128).log10().is_nan());
629 /// # }
630 /// ```
631 #[inline]
632 #[rustc_allow_incoherent_impl]
633 #[unstable(feature = "f128", issue = "116909")]
634 #[must_use = "method returns a new number and does not mutate the original value"]
635 pub fn log10(self) -> f128 {
636 unsafe { intrinsics::log10f128(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 ///
647 /// This function currently corresponds to the `cbrtf128` from libc on Unix
648 /// and Windows. Note that this might change in the future.
649 ///
650 /// # Examples
651 ///
652 /// ```
653 /// #![feature(f128)]
654 /// # #[cfg(reliable_f128_math)] {
655 ///
656 /// let x = 8.0f128;
657 ///
658 /// // x^(1/3) - 2 == 0
659 /// let abs_difference = (x.cbrt() - 2.0).abs();
660 ///
661 /// assert!(abs_difference <= f128::EPSILON);
662 /// # }
663 /// ```
664 #[inline]
665 #[rustc_allow_incoherent_impl]
666 #[unstable(feature = "f128", issue = "116909")]
667 #[must_use = "method returns a new number and does not mutate the original value"]
668 pub fn cbrt(self) -> f128 {
669 unsafe { cmath::cbrtf128(self) }
670 }
671
672 /// Compute the distance between the origin and a point (`x`, `y`) on the
673 /// Euclidean plane. Equivalently, compute the length of the hypotenuse of a
674 /// right-angle triangle with other sides having length `x.abs()` and
675 /// `y.abs()`.
676 ///
677 /// # Unspecified precision
678 ///
679 /// The precision of this function is non-deterministic. This means it varies by platform,
680 /// Rust version, and can even differ within the same execution from one invocation to the next.
681 ///
682 ///
683 /// This function currently corresponds to the `hypotf128` from libc on Unix
684 /// and Windows. Note that this might change in the future.
685 ///
686 /// # Examples
687 ///
688 /// ```
689 /// #![feature(f128)]
690 /// # #[cfg(reliable_f128_math)] {
691 ///
692 /// let x = 2.0f128;
693 /// let y = 3.0f128;
694 ///
695 /// // sqrt(x^2 + y^2)
696 /// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();
697 ///
698 /// assert!(abs_difference <= f128::EPSILON);
699 /// # }
700 /// ```
701 #[inline]
702 #[rustc_allow_incoherent_impl]
703 #[unstable(feature = "f128", issue = "116909")]
704 #[must_use = "method returns a new number and does not mutate the original value"]
705 pub fn hypot(self, other: f128) -> f128 {
706 unsafe { cmath::hypotf128(self, other) }
707 }
708
709 /// Computes the sine of a number (in radians).
710 ///
711 /// # Unspecified precision
712 ///
713 /// The precision of this function is non-deterministic. This means it varies by platform,
714 /// Rust version, and can even differ within the same execution from one invocation to the next.
715 ///
716 /// # Examples
717 ///
718 /// ```
719 /// #![feature(f128)]
720 /// # #[cfg(reliable_f128_math)] {
721 ///
722 /// let x = std::f128::consts::FRAC_PI_2;
723 ///
724 /// let abs_difference = (x.sin() - 1.0).abs();
725 ///
726 /// assert!(abs_difference <= f128::EPSILON);
727 /// # }
728 /// ```
729 #[inline]
730 #[rustc_allow_incoherent_impl]
731 #[unstable(feature = "f128", issue = "116909")]
732 #[must_use = "method returns a new number and does not mutate the original value"]
733 pub fn sin(self) -> f128 {
734 unsafe { intrinsics::sinf128(self) }
735 }
736
737 /// Computes the cosine of a number (in radians).
738 ///
739 /// # Unspecified precision
740 ///
741 /// The precision of this function is non-deterministic. This means it varies by platform,
742 /// Rust version, and can even differ within the same execution from one invocation to the next.
743 ///
744 /// # Examples
745 ///
746 /// ```
747 /// #![feature(f128)]
748 /// # #[cfg(reliable_f128_math)] {
749 ///
750 /// let x = 2.0 * std::f128::consts::PI;
751 ///
752 /// let abs_difference = (x.cos() - 1.0).abs();
753 ///
754 /// assert!(abs_difference <= f128::EPSILON);
755 /// # }
756 /// ```
757 #[inline]
758 #[rustc_allow_incoherent_impl]
759 #[unstable(feature = "f128", issue = "116909")]
760 #[must_use = "method returns a new number and does not mutate the original value"]
761 pub fn cos(self) -> f128 {
762 unsafe { intrinsics::cosf128(self) }
763 }
764
765 /// Computes the tangent of a number (in radians).
766 ///
767 /// # Unspecified precision
768 ///
769 /// The precision of this function is non-deterministic. This means it varies by platform,
770 /// Rust version, and can even differ within the same execution from one invocation to the next.
771 ///
772 /// This function currently corresponds to the `tanf128` from libc on Unix and
773 /// Windows. Note that this might change in the future.
774 ///
775 /// # Examples
776 ///
777 /// ```
778 /// #![feature(f128)]
779 /// # #[cfg(reliable_f128_math)] {
780 ///
781 /// let x = std::f128::consts::FRAC_PI_4;
782 /// let abs_difference = (x.tan() - 1.0).abs();
783 ///
784 /// assert!(abs_difference <= f128::EPSILON);
785 /// # }
786 /// ```
787 #[inline]
788 #[rustc_allow_incoherent_impl]
789 #[unstable(feature = "f128", issue = "116909")]
790 #[must_use = "method returns a new number and does not mutate the original value"]
791 pub fn tan(self) -> f128 {
792 unsafe { cmath::tanf128(self) }
793 }
794
795 /// Computes the arcsine of a number. Return value is in radians in
796 /// the range [-pi/2, pi/2] or NaN if the number is outside the range
797 /// [-1, 1].
798 ///
799 /// # Unspecified precision
800 ///
801 /// The precision of this function is non-deterministic. This means it varies by platform,
802 /// Rust version, and can even differ within the same execution from one invocation to the next.
803 ///
804 /// This function currently corresponds to the `asinf128` from libc on Unix
805 /// and Windows. Note that this might change in the future.
806 ///
807 /// # Examples
808 ///
809 /// ```
810 /// #![feature(f128)]
811 /// # #[cfg(reliable_f128_math)] {
812 ///
813 /// let f = std::f128::consts::FRAC_PI_2;
814 ///
815 /// // asin(sin(pi/2))
816 /// let abs_difference = (f.sin().asin() - std::f128::consts::FRAC_PI_2).abs();
817 ///
818 /// assert!(abs_difference <= f128::EPSILON);
819 /// # }
820 /// ```
821 #[inline]
822 #[doc(alias = "arcsin")]
823 #[rustc_allow_incoherent_impl]
824 #[unstable(feature = "f128", issue = "116909")]
825 #[must_use = "method returns a new number and does not mutate the original value"]
826 pub fn asin(self) -> f128 {
827 unsafe { cmath::asinf128(self) }
828 }
829
830 /// Computes the arccosine of a number. Return value is in radians in
831 /// the range [0, pi] or NaN if the number is outside the range
832 /// [-1, 1].
833 ///
834 /// # Unspecified precision
835 ///
836 /// The precision of this function is non-deterministic. This means it varies by platform,
837 /// Rust version, and can even differ within the same execution from one invocation to the next.
838 ///
839 /// This function currently corresponds to the `acosf128` from libc on Unix
840 /// and Windows. Note that this might change in the future.
841 ///
842 /// # Examples
843 ///
844 /// ```
845 /// #![feature(f128)]
846 /// # #[cfg(reliable_f128_math)] {
847 ///
848 /// let f = std::f128::consts::FRAC_PI_4;
849 ///
850 /// // acos(cos(pi/4))
851 /// let abs_difference = (f.cos().acos() - std::f128::consts::FRAC_PI_4).abs();
852 ///
853 /// assert!(abs_difference <= f128::EPSILON);
854 /// # }
855 /// ```
856 #[inline]
857 #[doc(alias = "arccos")]
858 #[rustc_allow_incoherent_impl]
859 #[unstable(feature = "f128", issue = "116909")]
860 #[must_use = "method returns a new number and does not mutate the original value"]
861 pub fn acos(self) -> f128 {
862 unsafe { cmath::acosf128(self) }
863 }
864
865 /// Computes the arctangent of a number. Return value is in radians in the
866 /// range [-pi/2, pi/2];
867 ///
868 /// # Unspecified precision
869 ///
870 /// The precision of this function is non-deterministic. This means it varies by platform,
871 /// Rust version, and can even differ within the same execution from one invocation to the next.
872 ///
873 /// This function currently corresponds to the `atanf128` from libc on Unix
874 /// and Windows. Note that this might change in the future.
875 ///
876 /// # Examples
877 ///
878 /// ```
879 /// #![feature(f128)]
880 /// # #[cfg(reliable_f128_math)] {
881 ///
882 /// let f = 1.0f128;
883 ///
884 /// // atan(tan(1))
885 /// let abs_difference = (f.tan().atan() - 1.0).abs();
886 ///
887 /// assert!(abs_difference <= f128::EPSILON);
888 /// # }
889 /// ```
890 #[inline]
891 #[doc(alias = "arctan")]
892 #[rustc_allow_incoherent_impl]
893 #[unstable(feature = "f128", issue = "116909")]
894 #[must_use = "method returns a new number and does not mutate the original value"]
895 pub fn atan(self) -> f128 {
896 unsafe { cmath::atanf128(self) }
897 }
898
899 /// Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`) in radians.
900 ///
901 /// * `x = 0`, `y = 0`: `0`
902 /// * `x >= 0`: `arctan(y/x)` -> `[-pi/2, pi/2]`
903 /// * `y >= 0`: `arctan(y/x) + pi` -> `(pi/2, pi]`
904 /// * `y < 0`: `arctan(y/x) - pi` -> `(-pi, -pi/2)`
905 ///
906 /// # Unspecified precision
907 ///
908 /// The precision of this function is non-deterministic. This means it varies by platform,
909 /// Rust version, and can even differ within the same execution from one invocation to the next.
910 ///
911 /// This function currently corresponds to the `atan2f128` from libc on Unix
912 /// and Windows. Note that this might change in the future.
913 ///
914 /// # Examples
915 ///
916 /// ```
917 /// #![feature(f128)]
918 /// # #[cfg(reliable_f128_math)] {
919 ///
920 /// // Positive angles measured counter-clockwise
921 /// // from positive x axis
922 /// // -pi/4 radians (45 deg clockwise)
923 /// let x1 = 3.0f128;
924 /// let y1 = -3.0f128;
925 ///
926 /// // 3pi/4 radians (135 deg counter-clockwise)
927 /// let x2 = -3.0f128;
928 /// let y2 = 3.0f128;
929 ///
930 /// let abs_difference_1 = (y1.atan2(x1) - (-std::f128::consts::FRAC_PI_4)).abs();
931 /// let abs_difference_2 = (y2.atan2(x2) - (3.0 * std::f128::consts::FRAC_PI_4)).abs();
932 ///
933 /// assert!(abs_difference_1 <= f128::EPSILON);
934 /// assert!(abs_difference_2 <= f128::EPSILON);
935 /// # }
936 /// ```
937 #[inline]
938 #[rustc_allow_incoherent_impl]
939 #[unstable(feature = "f128", issue = "116909")]
940 #[must_use = "method returns a new number and does not mutate the original value"]
941 pub fn atan2(self, other: f128) -> f128 {
942 unsafe { cmath::atan2f128(self, other) }
943 }
944
945 /// Simultaneously computes the sine and cosine of the number, `x`. Returns
946 /// `(sin(x), cos(x))`.
947 ///
948 /// # Unspecified precision
949 ///
950 /// The precision of this function is non-deterministic. This means it varies by platform,
951 /// Rust version, and can even differ within the same execution from one invocation to the next.
952 ///
953 /// This function currently corresponds to the `(f128::sin(x),
954 /// f128::cos(x))`. Note that this might change in the future.
955 ///
956 /// # Examples
957 ///
958 /// ```
959 /// #![feature(f128)]
960 /// # #[cfg(reliable_f128_math)] {
961 ///
962 /// let x = std::f128::consts::FRAC_PI_4;
963 /// let f = x.sin_cos();
964 ///
965 /// let abs_difference_0 = (f.0 - x.sin()).abs();
966 /// let abs_difference_1 = (f.1 - x.cos()).abs();
967 ///
968 /// assert!(abs_difference_0 <= f128::EPSILON);
969 /// assert!(abs_difference_1 <= f128::EPSILON);
970 /// # }
971 /// ```
972 #[inline]
973 #[doc(alias = "sincos")]
974 #[rustc_allow_incoherent_impl]
975 #[unstable(feature = "f128", issue = "116909")]
976 pub fn sin_cos(self) -> (f128, f128) {
977 (self.sin(), self.cos())
978 }
979
980 /// Returns `e^(self) - 1` in a way that is accurate even if the
981 /// number is close to zero.
982 ///
983 /// # Unspecified precision
984 ///
985 /// The precision of this function is non-deterministic. This means it varies by platform,
986 /// Rust version, and can even differ within the same execution from one invocation to the next.
987 ///
988 /// This function currently corresponds to the `expm1f128` from libc on Unix
989 /// and Windows. Note that this might change in the future.
990 ///
991 /// # Examples
992 ///
993 /// ```
994 /// #![feature(f128)]
995 /// # #[cfg(reliable_f128_math)] {
996 ///
997 /// let x = 1e-8_f128;
998 ///
999 /// // for very small x, e^x is approximately 1 + x + x^2 / 2
1000 /// let approx = x + x * x / 2.0;
1001 /// let abs_difference = (x.exp_m1() - approx).abs();
1002 ///
1003 /// assert!(abs_difference < 1e-10);
1004 /// # }
1005 /// ```
1006 #[inline]
1007 #[rustc_allow_incoherent_impl]
1008 #[unstable(feature = "f128", issue = "116909")]
1009 #[must_use = "method returns a new number and does not mutate the original value"]
1010 pub fn exp_m1(self) -> f128 {
1011 unsafe { cmath::expm1f128(self) }
1012 }
1013
1014 /// Returns `ln(1+n)` (natural logarithm) more accurately than if
1015 /// the operations were performed separately.
1016 ///
1017 /// This returns NaN when `n < -1.0`, and negative infinity when `n == -1.0`.
1018 ///
1019 /// # Unspecified precision
1020 ///
1021 /// The precision of this function is non-deterministic. This means it varies by platform,
1022 /// Rust version, and can even differ within the same execution from one invocation to the next.
1023 ///
1024 /// This function currently corresponds to the `log1pf128` from libc on Unix
1025 /// and Windows. Note that this might change in the future.
1026 ///
1027 /// # Examples
1028 ///
1029 /// ```
1030 /// #![feature(f128)]
1031 /// # #[cfg(reliable_f128_math)] {
1032 ///
1033 /// let x = 1e-8_f128;
1034 ///
1035 /// // for very small x, ln(1 + x) is approximately x - x^2 / 2
1036 /// let approx = x - x * x / 2.0;
1037 /// let abs_difference = (x.ln_1p() - approx).abs();
1038 ///
1039 /// assert!(abs_difference < 1e-10);
1040 /// # }
1041 /// ```
1042 ///
1043 /// Out-of-range values:
1044 /// ```
1045 /// #![feature(f128)]
1046 /// # #[cfg(reliable_f128_math)] {
1047 ///
1048 /// assert_eq!((-1.0_f128).ln_1p(), f128::NEG_INFINITY);
1049 /// assert!((-2.0_f128).ln_1p().is_nan());
1050 /// # }
1051 /// ```
1052 #[inline]
1053 #[doc(alias = "log1p")]
1054 #[must_use = "method returns a new number and does not mutate the original value"]
1055 #[rustc_allow_incoherent_impl]
1056 #[unstable(feature = "f128", issue = "116909")]
1057 pub fn ln_1p(self) -> f128 {
1058 unsafe { cmath::log1pf128(self) }
1059 }
1060
1061 /// Hyperbolic sine function.
1062 ///
1063 /// # Unspecified precision
1064 ///
1065 /// The precision of this function is non-deterministic. This means it varies by platform,
1066 /// Rust version, and can even differ within the same execution from one invocation to the next.
1067 ///
1068 /// This function currently corresponds to the `sinhf128` from libc on Unix
1069 /// and Windows. Note that this might change in the future.
1070 ///
1071 /// # Examples
1072 ///
1073 /// ```
1074 /// #![feature(f128)]
1075 /// # #[cfg(reliable_f128_math)] {
1076 ///
1077 /// let e = std::f128::consts::E;
1078 /// let x = 1.0f128;
1079 ///
1080 /// let f = x.sinh();
1081 /// // Solving sinh() at 1 gives `(e^2-1)/(2e)`
1082 /// let g = ((e * e) - 1.0) / (2.0 * e);
1083 /// let abs_difference = (f - g).abs();
1084 ///
1085 /// assert!(abs_difference <= f128::EPSILON);
1086 /// # }
1087 /// ```
1088 #[inline]
1089 #[rustc_allow_incoherent_impl]
1090 #[unstable(feature = "f128", issue = "116909")]
1091 #[must_use = "method returns a new number and does not mutate the original value"]
1092 pub fn sinh(self) -> f128 {
1093 unsafe { cmath::sinhf128(self) }
1094 }
1095
1096 /// Hyperbolic cosine function.
1097 ///
1098 /// # Unspecified precision
1099 ///
1100 /// The precision of this function is non-deterministic. This means it varies by platform,
1101 /// Rust version, and can even differ within the same execution from one invocation to the next.
1102 ///
1103 /// This function currently corresponds to the `coshf128` from libc on Unix
1104 /// and Windows. Note that this might change in the future.
1105 ///
1106 /// # Examples
1107 ///
1108 /// ```
1109 /// #![feature(f128)]
1110 /// # #[cfg(reliable_f128_math)] {
1111 ///
1112 /// let e = std::f128::consts::E;
1113 /// let x = 1.0f128;
1114 /// let f = x.cosh();
1115 /// // Solving cosh() at 1 gives this result
1116 /// let g = ((e * e) + 1.0) / (2.0 * e);
1117 /// let abs_difference = (f - g).abs();
1118 ///
1119 /// // Same result
1120 /// assert!(abs_difference <= f128::EPSILON);
1121 /// # }
1122 /// ```
1123 #[inline]
1124 #[rustc_allow_incoherent_impl]
1125 #[unstable(feature = "f128", issue = "116909")]
1126 #[must_use = "method returns a new number and does not mutate the original value"]
1127 pub fn cosh(self) -> f128 {
1128 unsafe { cmath::coshf128(self) }
1129 }
1130
1131 /// Hyperbolic tangent function.
1132 ///
1133 /// # Unspecified precision
1134 ///
1135 /// The precision of this function is non-deterministic. This means it varies by platform,
1136 /// Rust version, and can even differ within the same execution from one invocation to the next.
1137 ///
1138 /// This function currently corresponds to the `tanhf128` from libc on Unix
1139 /// and Windows. Note that this might change in the future.
1140 ///
1141 /// # Examples
1142 ///
1143 /// ```
1144 /// #![feature(f128)]
1145 /// # #[cfg(reliable_f128_math)] {
1146 ///
1147 /// let e = std::f128::consts::E;
1148 /// let x = 1.0f128;
1149 ///
1150 /// let f = x.tanh();
1151 /// // Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))`
1152 /// let g = (1.0 - e.powi(-2)) / (1.0 + e.powi(-2));
1153 /// let abs_difference = (f - g).abs();
1154 ///
1155 /// assert!(abs_difference <= f128::EPSILON);
1156 /// # }
1157 /// ```
1158 #[inline]
1159 #[rustc_allow_incoherent_impl]
1160 #[unstable(feature = "f128", issue = "116909")]
1161 #[must_use = "method returns a new number and does not mutate the original value"]
1162 pub fn tanh(self) -> f128 {
1163 unsafe { cmath::tanhf128(self) }
1164 }
1165
1166 /// Inverse hyperbolic sine function.
1167 ///
1168 /// # Unspecified precision
1169 ///
1170 /// The precision of this function is non-deterministic. This means it varies by platform,
1171 /// Rust version, and can even differ within the same execution from one invocation to the next.
1172 ///
1173 /// # Examples
1174 ///
1175 /// ```
1176 /// #![feature(f128)]
1177 /// # #[cfg(reliable_f128_math)] {
1178 ///
1179 /// let x = 1.0f128;
1180 /// let f = x.sinh().asinh();
1181 ///
1182 /// let abs_difference = (f - x).abs();
1183 ///
1184 /// assert!(abs_difference <= f128::EPSILON);
1185 /// # }
1186 /// ```
1187 #[inline]
1188 #[doc(alias = "arcsinh")]
1189 #[rustc_allow_incoherent_impl]
1190 #[unstable(feature = "f128", issue = "116909")]
1191 #[must_use = "method returns a new number and does not mutate the original value"]
1192 pub fn asinh(self) -> f128 {
1193 let ax = self.abs();
1194 let ix = 1.0 / ax;
1195 (ax + (ax / (Self::hypot(1.0, ix) + ix))).ln_1p().copysign(self)
1196 }
1197
1198 /// Inverse hyperbolic cosine function.
1199 ///
1200 /// # Unspecified precision
1201 ///
1202 /// The precision of this function is non-deterministic. This means it varies by platform,
1203 /// Rust version, and can even differ within the same execution from one invocation to the next.
1204 ///
1205 /// # Examples
1206 ///
1207 /// ```
1208 /// #![feature(f128)]
1209 /// # #[cfg(reliable_f128_math)] {
1210 ///
1211 /// let x = 1.0f128;
1212 /// let f = x.cosh().acosh();
1213 ///
1214 /// let abs_difference = (f - x).abs();
1215 ///
1216 /// assert!(abs_difference <= f128::EPSILON);
1217 /// # }
1218 /// ```
1219 #[inline]
1220 #[doc(alias = "arccosh")]
1221 #[rustc_allow_incoherent_impl]
1222 #[unstable(feature = "f128", issue = "116909")]
1223 #[must_use = "method returns a new number and does not mutate the original value"]
1224 pub fn acosh(self) -> f128 {
1225 if self < 1.0 {
1226 Self::NAN
1227 } else {
1228 (self + ((self - 1.0).sqrt() * (self + 1.0).sqrt())).ln()
1229 }
1230 }
1231
1232 /// Inverse hyperbolic tangent function.
1233 ///
1234 /// # Unspecified precision
1235 ///
1236 /// The precision of this function is non-deterministic. This means it varies by platform,
1237 /// Rust version, and can even differ within the same execution from one invocation to the next.
1238 ///
1239 /// # Examples
1240 ///
1241 /// ```
1242 /// #![feature(f128)]
1243 /// # #[cfg(reliable_f128_math)] {
1244 ///
1245 /// let e = std::f128::consts::E;
1246 /// let f = e.tanh().atanh();
1247 ///
1248 /// let abs_difference = (f - e).abs();
1249 ///
1250 /// assert!(abs_difference <= 1e-5);
1251 /// # }
1252 /// ```
1253 #[inline]
1254 #[doc(alias = "arctanh")]
1255 #[rustc_allow_incoherent_impl]
1256 #[unstable(feature = "f128", issue = "116909")]
1257 #[must_use = "method returns a new number and does not mutate the original value"]
1258 pub fn atanh(self) -> f128 {
1259 0.5 * ((2.0 * self) / (1.0 - self)).ln_1p()
1260 }
1261
1262 /// Gamma function.
1263 ///
1264 /// # Unspecified precision
1265 ///
1266 /// The precision of this function is non-deterministic. This means it varies by platform,
1267 /// Rust version, and can even differ within the same execution from one invocation to the next.
1268 ///
1269 /// This function currently corresponds to the `tgammaf128` from libc on Unix
1270 /// and Windows. Note that this might change in the future.
1271 ///
1272 /// # Examples
1273 ///
1274 /// ```
1275 /// #![feature(f128)]
1276 /// #![feature(float_gamma)]
1277 /// # #[cfg(reliable_f128_math)] {
1278 ///
1279 /// let x = 5.0f128;
1280 ///
1281 /// let abs_difference = (x.gamma() - 24.0).abs();
1282 ///
1283 /// assert!(abs_difference <= f128::EPSILON);
1284 /// # }
1285 /// ```
1286 #[inline]
1287 #[rustc_allow_incoherent_impl]
1288 #[unstable(feature = "f128", issue = "116909")]
1289 // #[unstable(feature = "float_gamma", issue = "99842")]
1290 #[must_use = "method returns a new number and does not mutate the original value"]
1291 pub fn gamma(self) -> f128 {
1292 unsafe { cmath::tgammaf128(self) }
1293 }
1294
1295 /// Natural logarithm of the absolute value of the gamma function
1296 ///
1297 /// The integer part of the tuple indicates the sign of the gamma function.
1298 ///
1299 /// # Unspecified precision
1300 ///
1301 /// The precision of this function is non-deterministic. This means it varies by platform,
1302 /// Rust version, and can even differ within the same execution from one invocation to the next.
1303 ///
1304 /// This function currently corresponds to the `lgammaf128_r` from libc on Unix
1305 /// and Windows. Note that this might change in the future.
1306 ///
1307 /// # Examples
1308 ///
1309 /// ```
1310 /// #![feature(f128)]
1311 /// #![feature(float_gamma)]
1312 /// # #[cfg(reliable_f128_math)] {
1313 ///
1314 /// let x = 2.0f128;
1315 ///
1316 /// let abs_difference = (x.ln_gamma().0 - 0.0).abs();
1317 ///
1318 /// assert!(abs_difference <= f128::EPSILON);
1319 /// # }
1320 /// ```
1321 #[inline]
1322 #[rustc_allow_incoherent_impl]
1323 #[unstable(feature = "f128", issue = "116909")]
1324 // #[unstable(feature = "float_gamma", issue = "99842")]
1325 #[must_use = "method returns a new number and does not mutate the original value"]
1326 pub fn ln_gamma(self) -> (f128, i32) {
1327 let mut signgamp: i32 = 0;
1328 let x = unsafe { cmath::lgammaf128_r(self, &mut signgamp) };
1329 (x, signgamp)
1330 }
1331
1332 /// Error function.
1333 ///
1334 /// # Unspecified precision
1335 ///
1336 /// The precision of this function is non-deterministic. This means it varies by platform,
1337 /// Rust version, and can even differ within the same execution from one invocation to the next.
1338 ///
1339 /// This function currently corresponds to the `erff128` from libc on Unix
1340 /// and Windows. Note that this might change in the future.
1341 ///
1342 /// # Examples
1343 ///
1344 /// ```
1345 /// #![feature(f128)]
1346 /// #![feature(float_erf)]
1347 /// # #[cfg(reliable_f128_math)] {
1348 /// /// The error function relates what percent of a normal distribution lies
1349 /// /// within `x` standard deviations (scaled by `1/sqrt(2)`).
1350 /// fn within_standard_deviations(x: f128) -> f128 {
1351 /// (x * std::f128::consts::FRAC_1_SQRT_2).erf() * 100.0
1352 /// }
1353 ///
1354 /// // 68% of a normal distribution is within one standard deviation
1355 /// assert!((within_standard_deviations(1.0) - 68.269).abs() < 0.01);
1356 /// // 95% of a normal distribution is within two standard deviations
1357 /// assert!((within_standard_deviations(2.0) - 95.450).abs() < 0.01);
1358 /// // 99.7% of a normal distribution is within three standard deviations
1359 /// assert!((within_standard_deviations(3.0) - 99.730).abs() < 0.01);
1360 /// # }
1361 /// ```
1362 #[rustc_allow_incoherent_impl]
1363 #[must_use = "method returns a new number and does not mutate the original value"]
1364 #[unstable(feature = "f128", issue = "116909")]
1365 // #[unstable(feature = "float_erf", issue = "136321")]
1366 #[inline]
1367 pub fn erf(self) -> f128 {
1368 unsafe { cmath::erff128(self) }
1369 }
1370
1371 /// Complementary error function.
1372 ///
1373 /// # Unspecified precision
1374 ///
1375 /// The precision of this function is non-deterministic. This means it varies by platform,
1376 /// Rust version, and can even differ within the same execution from one invocation to the next.
1377 ///
1378 /// This function currently corresponds to the `erfcf128` from libc on Unix
1379 /// and Windows. Note that this might change in the future.
1380 ///
1381 /// # Examples
1382 ///
1383 /// ```
1384 /// #![feature(f128)]
1385 /// #![feature(float_erf)]
1386 /// # #[cfg(reliable_f128_math)] {
1387 /// let x: f128 = 0.123;
1388 ///
1389 /// let one = x.erf() + x.erfc();
1390 /// let abs_difference = (one - 1.0).abs();
1391 ///
1392 /// assert!(abs_difference <= f128::EPSILON);
1393 /// # }
1394 /// ```
1395 #[rustc_allow_incoherent_impl]
1396 #[must_use = "method returns a new number and does not mutate the original value"]
1397 #[unstable(feature = "f128", issue = "116909")]
1398 // #[unstable(feature = "float_erf", issue = "136321")]
1399 #[inline]
1400 pub fn erfc(self) -> f128 {
1401 unsafe { cmath::erfcf128(self) }
1402 }
1403}
1404