f128.rs source code [crates/core/src/num/f128.rs]

1	//! Constants for the `f128` quadruple-precision floating point type.
2	//!
3	//! *[See also the `f128` primitive type][f128].*
4	//!
5	//! Mathematically significant numbers are provided in the `consts` sub-module.
6	//!
7	//! For the constants defined directly in this module
8	//! (as distinct from those defined in the `consts` sub-module),
9	//! new code should instead use the associated constants
10	//! defined directly on the `f128` type.
11
12	#![unstable(feature = "f128", issue = "116909")]
13
14	use crate::convert::FloatToInt;
15	use crate::num::FpCategory;
16	use crate::panic::const_assert;
17	use crate::{intrinsics, mem};
18
19	/// Basic mathematical constants.
20	#[unstable(feature = "f128", issue = "116909")]
21	pub mod consts {
22	// FIXME: replace with mathematical constants from cmath.
23
24	/// Archimedes' constant (π)
25	#[unstable(feature = "f128", issue = "116909")]
26	pub const PI: f128 = `3.14159265358979323846264338327950288419716939937510582097494_f128`;
27
28	/// The full circle constant (τ)
29	///
30	/// Equal to 2π.
31	#[unstable(feature = "f128", issue = "116909")]
32	pub const TAU: f128 = `6.28318530717958647692528676655900576839433879875021164194989_f128`;
33
34	/// The golden ratio (φ)
35	#[unstable(feature = "f128", issue = "116909")]
36	// Also, #[unstable(feature = "more_float_constants", issue = "103883")]
37	pub const PHI: f128 = `1.61803398874989484820458683436563811772030917980576286213545_f128`;
38
39	/// The Euler-Mascheroni constant (γ)
40	#[unstable(feature = "f128", issue = "116909")]
41	// Also, #[unstable(feature = "more_float_constants", issue = "103883")]
42	pub const EGAMMA: f128 = `0.577215664901532860606512090082402431042159335939923598805767_f128`;
43
44	/// π/2
45	#[unstable(feature = "f128", issue = "116909")]
46	pub const FRAC_PI_2: f128 = `1.57079632679489661923132169163975144209858469968755291048747_f128`;
47
48	/// π/3
49	#[unstable(feature = "f128", issue = "116909")]
50	pub const FRAC_PI_3: f128 = `1.04719755119659774615421446109316762806572313312503527365831_f128`;
51
52	/// π/4
53	#[unstable(feature = "f128", issue = "116909")]
54	pub const FRAC_PI_4: f128 = `0.785398163397448309615660845819875721049292349843776455243736_f128`;
55
56	/// π/6
57	#[unstable(feature = "f128", issue = "116909")]
58	pub const FRAC_PI_6: f128 = `0.523598775598298873077107230546583814032861566562517636829157_f128`;
59
60	/// π/8
61	#[unstable(feature = "f128", issue = "116909")]
62	pub const FRAC_PI_8: f128 = `0.392699081698724154807830422909937860524646174921888227621868_f128`;
63
64	/// 1/π
65	#[unstable(feature = "f128", issue = "116909")]
66	pub const FRAC_1_PI: f128 = `0.318309886183790671537767526745028724068919291480912897495335_f128`;
67
68	/// 1/sqrt(π)
69	#[unstable(feature = "f128", issue = "116909")]
70	// Also, #[unstable(feature = "more_float_constants", issue = "103883")]
71	pub const FRAC_1_SQRT_PI: f128 =
72	`0.564189583547756286948079451560772585844050629328998856844086_f128`;
73
74	/// 1/sqrt(2π)
75	#[doc(alias = "FRAC_1_SQRT_TAU")]
76	#[unstable(feature = "f128", issue = "116909")]
77	// Also, #[unstable(feature = "more_float_constants", issue = "103883")]
78	pub const FRAC_1_SQRT_2PI: f128 =
79	`0.398942280401432677939946059934381868475858631164934657665926_f128`;
80
81	/// 2/π
82	#[unstable(feature = "f128", issue = "116909")]
83	pub const FRAC_2_PI: f128 = `0.636619772367581343075535053490057448137838582961825794990669_f128`;
84
85	/// 2/sqrt(π)
86	#[unstable(feature = "f128", issue = "116909")]
87	pub const FRAC_2_SQRT_PI: f128 =
88	`1.12837916709551257389615890312154517168810125865799771368817_f128`;
89
90	/// sqrt(2)
91	#[unstable(feature = "f128", issue = "116909")]
92	pub const SQRT_2: f128 = `1.41421356237309504880168872420969807856967187537694807317668_f128`;
93
94	/// 1/sqrt(2)
95	#[unstable(feature = "f128", issue = "116909")]
96	pub const FRAC_1_SQRT_2: f128 =
97	`0.707106781186547524400844362104849039284835937688474036588340_f128`;
98
99	/// sqrt(3)
100	#[unstable(feature = "f128", issue = "116909")]
101	// Also, #[unstable(feature = "more_float_constants", issue = "103883")]
102	pub const SQRT_3: f128 = `1.73205080756887729352744634150587236694280525381038062805581_f128`;
103
104	/// 1/sqrt(3)
105	#[unstable(feature = "f128", issue = "116909")]
106	// Also, #[unstable(feature = "more_float_constants", issue = "103883")]
107	pub const FRAC_1_SQRT_3: f128 =
108	`0.577350269189625764509148780501957455647601751270126876018602_f128`;
109
110	/// Euler's number (e)
111	#[unstable(feature = "f128", issue = "116909")]
112	pub const E: f128 = `2.71828182845904523536028747135266249775724709369995957496697_f128`;
113
114	/// log<sub>2</sub>(10)
115	#[unstable(feature = "f128", issue = "116909")]
116	pub const LOG2_10: f128 = `3.32192809488736234787031942948939017586483139302458061205476_f128`;
117
118	/// log<sub>2</sub>(e)
119	#[unstable(feature = "f128", issue = "116909")]
120	pub const LOG2_E: f128 = `1.44269504088896340735992468100189213742664595415298593413545_f128`;
121
122	/// log<sub>10</sub>(2)
123	#[unstable(feature = "f128", issue = "116909")]
124	pub const LOG10_2: f128 = `0.301029995663981195213738894724493026768189881462108541310427_f128`;
125
126	/// log<sub>10</sub>(e)
127	#[unstable(feature = "f128", issue = "116909")]
128	pub const LOG10_E: f128 = `0.434294481903251827651128918916605082294397005803666566114454_f128`;
129
130	/// ln(2)
131	#[unstable(feature = "f128", issue = "116909")]
132	pub const LN_2: f128 = `0.693147180559945309417232121458176568075500134360255254120680_f128`;
133
134	/// ln(10)
135	#[unstable(feature = "f128", issue = "116909")]
136	pub const LN_10: f128 = `2.30258509299404568401799145468436420760110148862877297603333_f128`;
137	}
138
139	impl f128 {
140	// FIXME(f16_f128): almost all methods in this `impl` are missing examples and a const
141	// implementation. Add these once we can run code on all platforms and have f16/f128 in CTFE.
142
143	/// The radix or base of the internal representation of `f128`.
144	#[unstable(feature = "f128", issue = "116909")]
145	pub const RADIX: u32 = `2`;
146
147	/// Number of significant digits in base 2.
148	///
149	/// Note that the size of the mantissa in the bitwise representation is one
150	/// smaller than this since the leading 1 is not stored explicitly.
151	#[unstable(feature = "f128", issue = "116909")]
152	pub const MANTISSA_DIGITS: u32 = `113`;
153
154	/// Approximate number of significant digits in base 10.
155	///
156	/// This is the maximum <i>x</i> such that any decimal number with <i>x</i>
157	/// significant digits can be converted to `f128` and back without loss.
158	///
159	/// Equal to floor(log<sub>10</sub> 2<sup>[`MANTISSA_DIGITS`]* − 1</sup>).*
160	///
161	/// [`MANTISSA_DIGITS`]: f128::MANTISSA_DIGITS
162	#[unstable(feature = "f128", issue = "116909")]
163	pub const DIGITS: u32 = `33`;
164
165	/// [Machine epsilon] value for `f128`.
166	///
167	/// This is the difference between `1.0` and the next larger representable number.
168	///
169	/// Equal to 2<sup>1 − [`MANTISSA_DIGITS`]</sup>.
170	///
171	/// [Machine epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon
172	/// [`MANTISSA_DIGITS`]: f128::MANTISSA_DIGITS
173	#[unstable(feature = "f128", issue = "116909")]
174	#[rustc_diagnostic_item = "f128_epsilon"]
175	pub const EPSILON: f128 = `1.92592994438723585305597794258492732e-34_f128`;
176
177	/// Smallest finite `f128` value.
178	///
179	/// Equal to −[`MAX`].
180	///
181	/// [`MAX`]: f128::MAX
182	#[unstable(feature = "f128", issue = "116909")]
183	pub const MIN: f128 = `-1.18973149535723176508575932662800702e+4932_f128`;
184	/// Smallest positive normal `f128` value.
185	///
186	/// Equal to 2<sup>[`MIN_EXP`]* − 1</sup>.*
187	///
188	/// [`MIN_EXP`]: f128::MIN_EXP
189	#[unstable(feature = "f128", issue = "116909")]
190	pub const MIN_POSITIVE: f128 = `3.36210314311209350626267781732175260e-4932_f128`;
191	/// Largest finite `f128` value.
192	///
193	/// Equal to
194	/// (1 − 2<sup>−[`MANTISSA_DIGITS`]</sup>) 2<sup>[`MAX_EXP`]</sup>.
195	///
196	/// [`MANTISSA_DIGITS`]: f128::MANTISSA_DIGITS
197	/// [`MAX_EXP`]: f128::MAX_EXP
198	#[unstable(feature = "f128", issue = "116909")]
199	pub const MAX: f128 = `1.18973149535723176508575932662800702e+4932_f128`;
200
201	/// One greater than the minimum possible normal* power of 2 exponent*
202	/// for a significand bounded by 1 ≤ x < 2 (i.e. the IEEE definition).
203	///
204	/// This corresponds to the exact minimum possible normal* power of 2 exponent*
205	/// for a significand bounded by 0.5 ≤ x < 1 (i.e. the C definition).
206	/// In other words, all normal numbers representable by this type are
207	/// greater than or equal to 0.5 × 2<sup><i>MIN_EXP</i></sup>.
208	#[unstable(feature = "f128", issue = "116909")]
209	pub const MIN_EXP: i32 = `-16_381`;
210	/// One greater than the maximum possible power of 2 exponent
211	/// for a significand bounded by 1 ≤ x < 2 (i.e. the IEEE definition).
212	///
213	/// This corresponds to the exact maximum possible power of 2 exponent
214	/// for a significand bounded by 0.5 ≤ x < 1 (i.e. the C definition).
215	/// In other words, all numbers representable by this type are
216	/// strictly less than 2<sup><i>MAX_EXP</i></sup>.
217	#[unstable(feature = "f128", issue = "116909")]
218	pub const MAX_EXP: i32 = `16_384`;
219
220	/// Minimum <i>x</i> for which 10<sup><i>x</i></sup> is normal.
221	///
222	/// Equal to ceil(log<sub>10</sub> [`MIN_POSITIVE`]).
223	///
224	/// [`MIN_POSITIVE`]: f128::MIN_POSITIVE
225	#[unstable(feature = "f128", issue = "116909")]
226	pub const MIN_10_EXP: i32 = `-4_931`;
227	/// Maximum <i>x</i> for which 10<sup><i>x</i></sup> is normal.
228	///
229	/// Equal to floor(log<sub>10</sub> [`MAX`]).
230	///
231	/// [`MAX`]: f128::MAX
232	#[unstable(feature = "f128", issue = "116909")]
233	pub const MAX_10_EXP: i32 = `4_932`;
234
235	/// Not a Number (NaN).
236	///
237	/// Note that IEEE 754 doesn't define just a single NaN value; a plethora of bit patterns are
238	/// considered to be NaN. Furthermore, the standard makes a difference between a "signaling" and
239	/// a "quiet" NaN, and allows inspecting its "payload" (the unspecified bits in the bit pattern)
240	/// and its sign. See the [specification of NaN bit patterns](f32#nan-bit-patterns) for more
241	/// info.
242	///
243	/// This constant is guaranteed to be a quiet NaN (on targets that follow the Rust assumptions
244	/// that the quiet/signaling bit being set to 1 indicates a quiet NaN). Beyond that, nothing is
245	/// guaranteed about the specific bit pattern chosen here: both payload and sign are arbitrary.
246	/// The concrete bit pattern may change across Rust versions and target platforms.
247	#[allow(clippy::eq_op)]
248	#[rustc_diagnostic_item = "f128_nan"]
249	#[unstable(feature = "f128", issue = "116909")]
250	pub const NAN: f128 = `0.0_f128` / `0.0_f128`;
251
252	/// Infinity (∞).
253	#[unstable(feature = "f128", issue = "116909")]
254	pub const INFINITY: f128 = `1.0_f128` / `0.0_f128`;
255
256	/// Negative infinity (−∞).
257	#[unstable(feature = "f128", issue = "116909")]
258	pub const NEG_INFINITY: f128 = `-1.0_f128` / `0.0_f128`;
259
260	/// Sign bit
261	pub(crate) const SIGN_MASK: u128 = `0x8000_0000_0000_0000_0000_0000_0000_0000`;
262
263	/// Exponent mask
264	pub(crate) const EXP_MASK: u128 = `0x7fff_0000_0000_0000_0000_0000_0000_0000`;
265
266	/// Mantissa mask
267	pub(crate) const MAN_MASK: u128 = `0x0000_ffff_ffff_ffff_ffff_ffff_ffff_ffff`;
268
269	/// Minimum representable positive value (min subnormal)
270	const TINY_BITS: u128 = `0x1`;
271
272	/// Minimum representable negative value (min negative subnormal)
273	const NEG_TINY_BITS: u128 = Self::TINY_BITS \| Self::SIGN_MASK;
274
275	/// Returns `true` if this value is NaN.
276	///
277	/// ```
278	/// #![feature(f128)]
279	/// # // FIXME(f16_f128): remove when `unordtf2` is available
280	/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
281	///
282	/// let nan = f128::NAN;
283	/// let f = `7.0_f128`;
284	///
285	/// assert!(nan.is_nan());
286	/// assert!(!f.is_nan());
287	/// # }
288	/// ```
289	#[inline]
290	#[must_use]
291	#[unstable(feature = "f128", issue = "116909")]
292	#[allow(clippy::eq_op)] // > if you intended to check if the operand is NaN, use `.is_nan()` instead :)
293	pub const fn is_nan(self) -> bool {
294	self != self
295	}
296
297	/// Returns `true` if this value is positive infinity or negative infinity, and
298	/// `false` otherwise.
299	///
300	/// ```
301	/// #![feature(f128)]
302	/// # // FIXME(f16_f128): remove when `eqtf2` is available
303	/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
304	///
305	/// let f = `7.0f128`;
306	/// let inf = f128::INFINITY;
307	/// let neg_inf = f128::NEG_INFINITY;
308	/// let nan = f128::NAN;
309	///
310	/// assert!(!f.is_infinite());
311	/// assert!(!nan.is_infinite());
312	///
313	/// assert!(inf.is_infinite());
314	/// assert!(neg_inf.is_infinite());
315	/// # }
316	/// ```
317	#[inline]
318	#[must_use]
319	#[unstable(feature = "f128", issue = "116909")]
320	pub const fn is_infinite(self) -> bool {
321	(self == f128::INFINITY) \| (self == f128::NEG_INFINITY)
322	}
323
324	/// Returns `true` if this number is neither infinite nor NaN.
325	///
326	/// ```
327	/// #![feature(f128)]
328	/// # // FIXME(f16_f128): remove when `lttf2` is available
329	/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
330	///
331	/// let f = `7.0f128`;
332	/// let inf: f128 = f128::INFINITY;
333	/// let neg_inf: f128 = f128::NEG_INFINITY;
334	/// let nan: f128 = f128::NAN;
335	///
336	/// assert!(f.is_finite());
337	///
338	/// assert!(!nan.is_finite());
339	/// assert!(!inf.is_finite());
340	/// assert!(!neg_inf.is_finite());
341	/// # }
342	/// ```
343	#[inline]
344	#[must_use]
345	#[unstable(feature = "f128", issue = "116909")]
346	#[rustc_const_unstable(feature = "f128", issue = "116909")]
347	pub const fn is_finite(self) -> bool {
348	// There's no need to handle NaN separately: if self is NaN,
349	// the comparison is not true, exactly as desired.
350	self.abs() < Self::INFINITY
351	}
352
353	/// Returns `true` if the number is [subnormal].
354	///
355	/// ```
356	/// #![feature(f128)]
357	/// # // FIXME(f16_f128): remove when `eqtf2` is available
358	/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
359	///
360	/// let min = f128::MIN_POSITIVE; // 3.362103143e-4932f128
361	/// let max = f128::MAX;
362	/// let lower_than_min = `1.0e-4960_f128`;
363	/// let zero = `0.0_f128`;
364	///
365	/// assert!(!min.is_subnormal());
366	/// assert!(!max.is_subnormal());
367	///
368	/// assert!(!zero.is_subnormal());
369	/// assert!(!f128::NAN.is_subnormal());
370	/// assert!(!f128::INFINITY.is_subnormal());
371	/// // Values between `0` and `min` are Subnormal.
372	/// assert!(lower_than_min.is_subnormal());
373	/// # }
374	/// ```
375	///
376	/// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
377	#[inline]
378	#[must_use]
379	#[unstable(feature = "f128", issue = "116909")]
380	pub const fn is_subnormal(self) -> bool {
381	matches!(self.classify(), FpCategory::Subnormal)
382	}
383
384	/// Returns `true` if the number is neither zero, infinite, [subnormal], or NaN.
385	///
386	/// ```
387	/// #![feature(f128)]
388	/// # // FIXME(f16_f128): remove when `eqtf2` is available
389	/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
390	///
391	/// let min = f128::MIN_POSITIVE; // 3.362103143e-4932f128
392	/// let max = f128::MAX;
393	/// let lower_than_min = `1.0e-4960_f128`;
394	/// let zero = `0.0_f128`;
395	///
396	/// assert!(min.is_normal());
397	/// assert!(max.is_normal());
398	///
399	/// assert!(!zero.is_normal());
400	/// assert!(!f128::NAN.is_normal());
401	/// assert!(!f128::INFINITY.is_normal());
402	/// // Values between `0` and `min` are Subnormal.
403	/// assert!(!lower_than_min.is_normal());
404	/// # }
405	/// ```
406	///
407	/// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
408	#[inline]
409	#[must_use]
410	#[unstable(feature = "f128", issue = "116909")]
411	pub const fn is_normal(self) -> bool {
412	matches!(self.classify(), FpCategory::Normal)
413	}
414
415	/// Returns the floating point category of the number. If only one property
416	/// is going to be tested, it is generally faster to use the specific
417	/// predicate instead.
418	///
419	/// ```
420	/// #![feature(f128)]
421	/// # // FIXME(f16_f128): remove when `eqtf2` is available
422	/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
423	///
424	/// use std::num::FpCategory;
425	///
426	/// let num = `12.4_f128`;
427	/// let inf = f128::INFINITY;
428	///
429	/// assert_eq!(num.classify(), FpCategory::Normal);
430	/// assert_eq!(inf.classify(), FpCategory::Infinite);
431	/// # }
432	/// ```
433	#[inline]
434	#[unstable(feature = "f128", issue = "116909")]
435	pub const fn classify(self) -> FpCategory {
436	let bits = self.to_bits();
437	match (bits & Self::MAN_MASK, bits & Self::EXP_MASK) {
438	(`0`, Self::EXP_MASK) => FpCategory::Infinite,
439	(_, Self::EXP_MASK) => FpCategory::Nan,
440	(`0`, `0`) => FpCategory::Zero,
441	(_, `0`) => FpCategory::Subnormal,
442	_ => FpCategory::Normal,
443	}
444	}
445
446	/// Returns `true` if `self` has a positive sign, including `+0.0`, NaNs with
447	/// positive sign bit and positive infinity.
448	///
449	/// Note that IEEE 754 doesn't assign any meaning to the sign bit in case of
450	/// a NaN, and as Rust doesn't guarantee that the bit pattern of NaNs are
451	/// conserved over arithmetic operations, the result of `is_sign_positive` on
452	/// a NaN might produce an unexpected or non-portable result. See the [specification
453	/// of NaN bit patterns](f32#nan-bit-patterns) for more info. Use `self.signum() == 1.0`
454	/// if you need fully portable behavior (will return `false` for all NaNs).
455	///
456	/// ```
457	/// #![feature(f128)]
458	///
459	/// let f = `7.0_f128`;
460	/// let g = `-7.0_f128`;
461	///
462	/// assert!(f.is_sign_positive());
463	/// assert!(!g.is_sign_positive());
464	/// ```
465	#[inline]
466	#[must_use]
467	#[unstable(feature = "f128", issue = "116909")]
468	pub const fn is_sign_positive(self) -> bool {
469	!self.is_sign_negative()
470	}
471
472	/// Returns `true` if `self` has a negative sign, including `-0.0`, NaNs with
473	/// negative sign bit and negative infinity.
474	///
475	/// Note that IEEE 754 doesn't assign any meaning to the sign bit in case of
476	/// a NaN, and as Rust doesn't guarantee that the bit pattern of NaNs are
477	/// conserved over arithmetic operations, the result of `is_sign_negative` on
478	/// a NaN might produce an unexpected or non-portable result. See the [specification
479	/// of NaN bit patterns](f32#nan-bit-patterns) for more info. Use `self.signum() == -1.0`
480	/// if you need fully portable behavior (will return `false` for all NaNs).
481	///
482	/// ```
483	/// #![feature(f128)]
484	///
485	/// let f = `7.0_f128`;
486	/// let g = `-7.0_f128`;
487	///
488	/// assert!(!f.is_sign_negative());
489	/// assert!(g.is_sign_negative());
490	/// ```
491	#[inline]
492	#[must_use]
493	#[unstable(feature = "f128", issue = "116909")]
494	pub const fn is_sign_negative(self) -> bool {
495	// IEEE754 says: isSignMinus(x) is true if and only if x has negative sign. isSignMinus
496	// applies to zeros and NaNs as well.
497	// SAFETY: This is just transmuting to get the sign bit, it's fine.
498	(self.to_bits() & (`1` << `127`)) != `0`
499	}
500
501	/// Returns the least number greater than `self`.
502	///
503	/// Let `TINY` be the smallest representable positive `f128`. Then,
504	/// - if `self.is_nan()`, this returns `self`;
505	/// - if `self` is [`NEG_INFINITY`], this returns [`MIN`];
506	/// - if `self` is `-TINY`, this returns -0.0;
507	/// - if `self` is -0.0 or +0.0, this returns `TINY`;
508	/// - if `self` is [`MAX`] or [`INFINITY`], this returns [`INFINITY`];
509	/// - otherwise the unique least value greater than `self` is returned.
510	///
511	/// The identity `x.next_up() == -(-x).next_down()` holds for all non-NaN `x`. When `x`
512	/// is finite `x == x.next_up().next_down()` also holds.
513	///
514	/// ```rust
515	/// #![feature(f128)]
516	/// # // FIXME(f16_f128): remove when `eqtf2` is available
517	/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
518	///
519	/// // f128::EPSILON is the difference between 1.0 and the next number up.
520	/// assert_eq!(`1.0f128`.next_up(), `1.0` + f128::EPSILON);
521	/// // But not for most numbers.
522	/// assert!(`0.1f128`.next_up() < `0.1` + f128::EPSILON);
523	/// assert_eq!(`4611686018427387904f128`.next_up(), `4611686018427387904.000000000000001`);
524	/// # }
525	/// ```
526	///
527	/// This operation corresponds to IEEE-754 `nextUp`.
528	///
529	/// [`NEG_INFINITY`]: Self::NEG_INFINITY
530	/// [`INFINITY`]: Self::INFINITY
531	/// [`MIN`]: Self::MIN
532	/// [`MAX`]: Self::MAX
533	#[inline]
534	#[doc(alias = "nextUp")]
535	#[unstable(feature = "f128", issue = "116909")]
536	pub const fn next_up(self) -> Self {
537	// Some targets violate Rust's assumption of IEEE semantics, e.g. by flushing
538	// denormals to zero. This is in general unsound and unsupported, but here
539	// we do our best to still produce the correct result on such targets.
540	let bits = self.to_bits();
541	if self.is_nan() \|\| bits == Self::INFINITY.to_bits() {
542	return self;
543	}
544
545	let abs = bits & !Self::SIGN_MASK;
546	let next_bits = if abs == `0` {
547	Self::TINY_BITS
548	} else if bits == abs {
549	bits + `1`
550	} else {
551	bits - `1`
552	};
553	Self::from_bits(next_bits)
554	}
555
556	/// Returns the greatest number less than `self`.
557	///
558	/// Let `TINY` be the smallest representable positive `f128`. Then,
559	/// - if `self.is_nan()`, this returns `self`;
560	/// - if `self` is [`INFINITY`], this returns [`MAX`];
561	/// - if `self` is `TINY`, this returns 0.0;
562	/// - if `self` is -0.0 or +0.0, this returns `-TINY`;
563	/// - if `self` is [`MIN`] or [`NEG_INFINITY`], this returns [`NEG_INFINITY`];
564	/// - otherwise the unique greatest value less than `self` is returned.
565	///
566	/// The identity `x.next_down() == -(-x).next_up()` holds for all non-NaN `x`. When `x`
567	/// is finite `x == x.next_down().next_up()` also holds.
568	///
569	/// ```rust
570	/// #![feature(f128)]
571	/// # // FIXME(f16_f128): remove when `eqtf2` is available
572	/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
573	///
574	/// let x = `1.0f128`;
575	/// // Clamp value into range [0, 1).
576	/// let clamped = x.clamp(`0.0`, `1.0f128`.next_down());
577	/// assert!(clamped < `1.0`);
578	/// assert_eq!(clamped.next_up(), `1.0`);
579	/// # }
580	/// ```
581	///
582	/// This operation corresponds to IEEE-754 `nextDown`.
583	///
584	/// [`NEG_INFINITY`]: Self::NEG_INFINITY
585	/// [`INFINITY`]: Self::INFINITY
586	/// [`MIN`]: Self::MIN
587	/// [`MAX`]: Self::MAX
588	#[inline]
589	#[doc(alias = "nextDown")]
590	#[unstable(feature = "f128", issue = "116909")]
591	pub const fn next_down(self) -> Self {
592	// Some targets violate Rust's assumption of IEEE semantics, e.g. by flushing
593	// denormals to zero. This is in general unsound and unsupported, but here
594	// we do our best to still produce the correct result on such targets.
595	let bits = self.to_bits();
596	if self.is_nan() \|\| bits == Self::NEG_INFINITY.to_bits() {
597	return self;
598	}
599
600	let abs = bits & !Self::SIGN_MASK;
601	let next_bits = if abs == `0` {
602	Self::NEG_TINY_BITS
603	} else if bits == abs {
604	bits - `1`
605	} else {
606	bits + `1`
607	};
608	Self::from_bits(next_bits)
609	}
610
611	/// Takes the reciprocal (inverse) of a number, `1/x`.
612	///
613	/// ```
614	/// #![feature(f128)]
615	/// # // FIXME(f16_f128): remove when `eqtf2` is available
616	/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
617	///
618	/// let x = `2.0_f128`;
619	/// let abs_difference = (x.recip() - (`1.0` / x)).abs();
620	///
621	/// assert!(abs_difference <= f128::EPSILON);
622	/// # }
623	/// ```
624	#[inline]
625	#[unstable(feature = "f128", issue = "116909")]
626	#[must_use = "this returns the result of the operation, without modifying the original"]
627	pub const fn recip(self) -> Self {
628	`1.0` / self
629	}
630
631	/// Converts radians to degrees.
632	///
633	/// ```
634	/// #![feature(f128)]
635	/// # // FIXME(f16_f128): remove when `eqtf2` is available
636	/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
637	///
638	/// let angle = std::f128::consts::PI;
639	///
640	/// let abs_difference = (angle.to_degrees() - `180.0`).abs();
641	/// assert!(abs_difference <= f128::EPSILON);
642	/// # }
643	/// ```
644	#[inline]
645	#[unstable(feature = "f128", issue = "116909")]
646	#[must_use = "this returns the result of the operation, without modifying the original"]
647	pub const fn to_degrees(self) -> Self {
648	// Use a literal for better precision.
649	const PIS_IN_180: f128 = `57.2957795130823208767981548141051703324054724665643215491602_f128`;
650	self * PIS_IN_180
651	}
652
653	/// Converts degrees to radians.
654	///
655	/// ```
656	/// #![feature(f128)]
657	/// # // FIXME(f16_f128): remove when `eqtf2` is available
658	/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
659	///
660	/// let angle = `180.0f128`;
661	///
662	/// let abs_difference = (angle.to_radians() - std::f128::consts::PI).abs();
663	///
664	/// assert!(abs_difference <= `1e-30`);
665	/// # }
666	/// ```
667	#[inline]
668	#[unstable(feature = "f128", issue = "116909")]
669	#[must_use = "this returns the result of the operation, without modifying the original"]
670	pub const fn to_radians(self) -> f128 {
671	// Use a literal for better precision.
672	const RADS_PER_DEG: f128 =
673	`0.0174532925199432957692369076848861271344287188854172545609719_f128`;
674	self * RADS_PER_DEG
675	}
676
677	/// Returns the maximum of the two numbers, ignoring NaN.
678	///
679	/// If one of the arguments is NaN, then the other argument is returned.
680	/// This follows the IEEE 754-2008 semantics for maxNum, except for handling of signaling NaNs;
681	/// this function handles all NaNs the same way and avoids maxNum's problems with associativity.
682	/// This also matches the behavior of libm’s fmax. In particular, if the inputs compare equal
683	/// (such as for the case of `+0.0` and `-0.0`), either input may be returned non-deterministically.
684	///
685	/// ```
686	/// #![feature(f128)]
687	/// # // Using aarch64 because `reliable_f128_math` is needed
688	/// # #[cfg(all(target_arch = "aarch64", target_os = "linux"))] {
689	///
690	/// let x = `1.0f128`;
691	/// let y = `2.0f128`;
692	///
693	/// assert_eq!(x.max(y), y);
694	/// # }
695	/// ```
696	#[inline]
697	#[unstable(feature = "f128", issue = "116909")]
698	#[rustc_const_unstable(feature = "f128", issue = "116909")]
699	#[must_use = "this returns the result of the comparison, without modifying either input"]
700	pub const fn max(self, other: f128) -> f128 {
701	intrinsics::maxnumf128(self, other)
702	}
703
704	/// Returns the minimum of the two numbers, ignoring NaN.
705	///
706	/// If one of the arguments is NaN, then the other argument is returned.
707	/// This follows the IEEE 754-2008 semantics for minNum, except for handling of signaling NaNs;
708	/// this function handles all NaNs the same way and avoids minNum's problems with associativity.
709	/// This also matches the behavior of libm’s fmin. In particular, if the inputs compare equal
710	/// (such as for the case of `+0.0` and `-0.0`), either input may be returned non-deterministically.
711	///
712	/// ```
713	/// #![feature(f128)]
714	/// # // Using aarch64 because `reliable_f128_math` is needed
715	/// # #[cfg(all(target_arch = "aarch64", target_os = "linux"))] {
716	///
717	/// let x = `1.0f128`;
718	/// let y = `2.0f128`;
719	///
720	/// assert_eq!(x.min(y), x);
721	/// # }
722	/// ```
723	#[inline]
724	#[unstable(feature = "f128", issue = "116909")]
725	#[rustc_const_unstable(feature = "f128", issue = "116909")]
726	#[must_use = "this returns the result of the comparison, without modifying either input"]
727	pub const fn min(self, other: f128) -> f128 {
728	intrinsics::minnumf128(self, other)
729	}
730
731	/// Returns the maximum of the two numbers, propagating NaN.
732	///
733	/// This returns NaN when either* argument is NaN, as opposed to*
734	/// [`f128::max`] which only returns NaN when both* arguments are NaN.*
735	///
736	/// ```
737	/// #![feature(f128)]
738	/// #![feature(float_minimum_maximum)]
739	/// # // Using aarch64 because `reliable_f128_math` is needed
740	/// # #[cfg(all(target_arch = "aarch64", target_os = "linux"))] {
741	///
742	/// let x = `1.0f128`;
743	/// let y = `2.0f128`;
744	///
745	/// assert_eq!(x.maximum(y), y);
746	/// assert!(x.maximum(f128::NAN).is_nan());
747	/// # }
748	/// ```
749	///
750	/// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the greater
751	/// of the two numbers. For this operation, -0.0 is considered to be less than +0.0.
752	/// Note that this follows the semantics specified in IEEE 754-2019.
753	///
754	/// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN
755	/// operand is conserved; see the [specification of NaN bit patterns](f32#nan-bit-patterns) for more info.
756	#[inline]
757	#[unstable(feature = "f128", issue = "116909")]
758	// #[unstable(feature = "float_minimum_maximum", issue = "91079")]
759	#[must_use = "this returns the result of the comparison, without modifying either input"]
760	pub const fn maximum(self, other: f128) -> f128 {
761	intrinsics::maximumf128(self, other)
762	}
763
764	/// Returns the minimum of the two numbers, propagating NaN.
765	///
766	/// This returns NaN when either* argument is NaN, as opposed to*
767	/// [`f128::min`] which only returns NaN when both* arguments are NaN.*
768	///
769	/// ```
770	/// #![feature(f128)]
771	/// #![feature(float_minimum_maximum)]
772	/// # // Using aarch64 because `reliable_f128_math` is needed
773	/// # #[cfg(all(target_arch = "aarch64", target_os = "linux"))] {
774	///
775	/// let x = `1.0f128`;
776	/// let y = `2.0f128`;
777	///
778	/// assert_eq!(x.minimum(y), x);
779	/// assert!(x.minimum(f128::NAN).is_nan());
780	/// # }
781	/// ```
782	///
783	/// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the lesser
784	/// of the two numbers. For this operation, -0.0 is considered to be less than +0.0.
785	/// Note that this follows the semantics specified in IEEE 754-2019.
786	///
787	/// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN
788	/// operand is conserved; see the [specification of NaN bit patterns](f32#nan-bit-patterns) for more info.
789	#[inline]
790	#[unstable(feature = "f128", issue = "116909")]
791	// #[unstable(feature = "float_minimum_maximum", issue = "91079")]
792	#[must_use = "this returns the result of the comparison, without modifying either input"]
793	pub const fn minimum(self, other: f128) -> f128 {
794	intrinsics::minimumf128(self, other)
795	}
796
797	/// Calculates the midpoint (average) between `self` and `rhs`.
798	///
799	/// This returns NaN when either* argument is NaN or if a combination of*
800	/// +inf and -inf is provided as arguments.
801	///
802	/// # Examples
803	///
804	/// ```
805	/// #![feature(f128)]
806	/// # // Using aarch64 because `reliable_f128_math` is needed
807	/// # #[cfg(all(target_arch = "aarch64", target_os = "linux"))] {
808	///
809	/// assert_eq!(`1f128`.midpoint(`4.0`), `2.5`);
810	/// assert_eq!((-`5.5f128`).midpoint(`8.0`), `1.25`);
811	/// # }
812	/// ```
813	#[inline]
814	#[doc(alias = "average")]
815	#[unstable(feature = "f128", issue = "116909")]
816	#[rustc_const_unstable(feature = "f128", issue = "116909")]
817	pub const fn midpoint(self, other: f128) -> f128 {
818	const LO: f128 = f128::MIN_POSITIVE * `2.`;
819	const HI: f128 = f128::MAX / `2.`;
820
821	let (a, b) = (self, other);
822	let abs_a = a.abs();
823	let abs_b = b.abs();
824
825	if abs_a <= HI && abs_b <= HI {
826	// Overflow is impossible
827	(a + b) / `2.`
828	} else if abs_a < LO {
829	// Not safe to halve `a` (would underflow)
830	a + (b / `2.`)
831	} else if abs_b < LO {
832	// Not safe to halve `b` (would underflow)
833	(a / `2.`) + b
834	} else {
835	// Safe to halve `a` and `b`
836	(a / `2.`) + (b / `2.`)
837	}
838	}
839
840	/// Rounds toward zero and converts to any primitive integer type,
841	/// assuming that the value is finite and fits in that type.
842	///
843	/// ```
844	/// #![feature(f128)]
845	/// # // FIXME(f16_f128): remove when `floatitf` is available*
846	/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
847	///
848	/// let value = `4.6_f128`;
849	/// let rounded = unsafe { value.to_int_unchecked::<u16>() };
850	/// assert_eq!(rounded, `4`);
851	///
852	/// let value = `-128.9_f128`;
853	/// let rounded = unsafe { value.to_int_unchecked::<i8>() };
854	/// assert_eq!(rounded, i8::MIN);
855	/// # }
856	/// ```
857	///
858	/// # Safety
859	///
860	/// The value must:
861	///
862	/// Not be `NaN`*
863	/// Not be infinite*
864	/// Be representable in the return type `Int`, after truncating off its fractional part*
865	#[inline]
866	#[unstable(feature = "f128", issue = "116909")]
867	#[must_use = "this returns the result of the operation, without modifying the original"]
868	pub unsafe fn to_int_unchecked<Int>(self) -> Int
869	where
870	Self: FloatToInt<Int>,
871	{
872	// SAFETY: the caller must uphold the safety contract for
873	// `FloatToInt::to_int_unchecked`.
874	unsafe { FloatToInt::<Int>::to_int_unchecked(self) }
875	}
876
877	/// Raw transmutation to `u128`.
878	///
879	/// This is currently identical to `transmute::<f128, u128>(self)` on all platforms.
880	///
881	/// See [`from_bits`](#method.from_bits) for some discussion of the
882	/// portability of this operation (there are almost no issues).
883	///
884	/// Note that this function is distinct from `as` casting, which attempts to
885	/// preserve the numeric* value, and not the bitwise value.*
886	///
887	/// ```
888	/// #![feature(f128)]
889	///
890	/// # // FIXME(f16_f128): enable this once const casting works
891	/// # // assert_ne!((1f128).to_bits(), 1f128 as u128); // to_bits() is not casting!
892	/// assert_eq!((`12.5f128`).to_bits(), `0x40029000000000000000000000000000`);
893	/// ```
894	#[inline]
895	#[unstable(feature = "f128", issue = "116909")]
896	#[must_use = "this returns the result of the operation, without modifying the original"]
897	#[allow(unnecessary_transmutes)]
898	pub const fn to_bits(self) -> u128 {
899	// SAFETY: `u128` is a plain old datatype so we can always transmute to it.
900	unsafe { mem::transmute(self) }
901	}
902
903	/// Raw transmutation from `u128`.
904	///
905	/// This is currently identical to `transmute::<u128, f128>(v)` on all platforms.
906	/// It turns out this is incredibly portable, for two reasons:
907	///
908	/// Floats and Ints have the same endianness on all supported platforms.*
909	/// IEEE 754 very precisely specifies the bit layout of floats.*
910	///
911	/// However there is one caveat: prior to the 2008 version of IEEE 754, how
912	/// to interpret the NaN signaling bit wasn't actually specified. Most platforms
913	/// (notably x86 and ARM) picked the interpretation that was ultimately
914	/// standardized in 2008, but some didn't (notably MIPS). As a result, all
915	/// signaling NaNs on MIPS are quiet NaNs on x86, and vice-versa.
916	///
917	/// Rather than trying to preserve signaling-ness cross-platform, this
918	/// implementation favors preserving the exact bits. This means that
919	/// any payloads encoded in NaNs will be preserved even if the result of
920	/// this method is sent over the network from an x86 machine to a MIPS one.
921	///
922	/// If the results of this method are only manipulated by the same
923	/// architecture that produced them, then there is no portability concern.
924	///
925	/// If the input isn't NaN, then there is no portability concern.
926	///
927	/// If you don't care about signalingness (very likely), then there is no
928	/// portability concern.
929	///
930	/// Note that this function is distinct from `as` casting, which attempts to
931	/// preserve the numeric* value, and not the bitwise value.*
932	///
933	/// ```
934	/// #![feature(f128)]
935	/// # // FIXME(f16_f128): remove when `eqtf2` is available
936	/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
937	///
938	/// let v = f128::from_bits(`0x40029000000000000000000000000000`);
939	/// assert_eq!(v, `12.5`);
940	/// # }
941	/// ```
942	#[inline]
943	#[must_use]
944	#[unstable(feature = "f128", issue = "116909")]
945	#[allow(unnecessary_transmutes)]
946	pub const fn from_bits(v: u128) -> Self {
947	// It turns out the safety issues with sNaN were overblown! Hooray!
948	// SAFETY: `u128` is a plain old datatype so we can always transmute from it.
949	unsafe { mem::transmute(v) }
950	}
951
952	/// Returns the memory representation of this floating point number as a byte array in
953	/// big-endian (network) byte order.
954	///
955	/// See [`from_bits`](Self::from_bits) for some discussion of the
956	/// portability of this operation (there are almost no issues).
957	///
958	/// # Examples
959	///
960	/// ```
961	/// #![feature(f128)]
962	///
963	/// let bytes = `12.5f128`.to_be_bytes();
964	/// assert_eq!(
965	/// bytes,
966	/// [`0x40`, `0x02`, `0x90`, `0x00`, `0x00`, `0x00`, `0x00`, `0x00`,
967	/// `0x00`, `0x00`, `0x00`, `0x00`, `0x00`, `0x00`, `0x00`, `0x00`]
968	/// );
969	/// ```
970	#[inline]
971	#[unstable(feature = "f128", issue = "116909")]
972	#[must_use = "this returns the result of the operation, without modifying the original"]
973	pub const fn to_be_bytes(self) -> [u8; `16`] {
974	self.to_bits().to_be_bytes()
975	}
976
977	/// Returns the memory representation of this floating point number as a byte array in
978	/// little-endian byte order.
979	///
980	/// See [`from_bits`](Self::from_bits) for some discussion of the
981	/// portability of this operation (there are almost no issues).
982	///
983	/// # Examples
984	///
985	/// ```
986	/// #![feature(f128)]
987	///
988	/// let bytes = `12.5f128`.to_le_bytes();
989	/// assert_eq!(
990	/// bytes,
991	/// [`0x00`, `0x00`, `0x00`, `0x00`, `0x00`, `0x00`, `0x00`, `0x00`,
992	/// `0x00`, `0x00`, `0x00`, `0x00`, `0x00`, `0x90`, `0x02`, `0x40`]
993	/// );
994	/// ```
995	#[inline]
996	#[unstable(feature = "f128", issue = "116909")]
997	#[must_use = "this returns the result of the operation, without modifying the original"]
998	pub const fn to_le_bytes(self) -> [u8; `16`] {
999	self.to_bits().to_le_bytes()
1000	}
1001
1002	/// Returns the memory representation of this floating point number as a byte array in
1003	/// native byte order.
1004	///
1005	/// As the target platform's native endianness is used, portable code
1006	/// should use [`to_be_bytes`] or [`to_le_bytes`], as appropriate, instead.
1007	///
1008	/// [`to_be_bytes`]: f128::to_be_bytes
1009	/// [`to_le_bytes`]: f128::to_le_bytes
1010	///
1011	/// See [`from_bits`](Self::from_bits) for some discussion of the
1012	/// portability of this operation (there are almost no issues).
1013	///
1014	/// # Examples
1015	///
1016	/// ```
1017	/// #![feature(f128)]
1018	///
1019	/// let bytes = `12.5f128`.to_ne_bytes();
1020	/// assert_eq!(
1021	/// bytes,
1022	/// if cfg!(target_endian = "big") {
1023	/// [`0x40`, `0x02`, `0x90`, `0x00`, `0x00`, `0x00`, `0x00`, `0x00`,
1024	/// `0x00`, `0x00`, `0x00`, `0x00`, `0x00`, `0x00`, `0x00`, `0x00`]
1025	/// } else {
1026	/// [`0x00`, `0x00`, `0x00`, `0x00`, `0x00`, `0x00`, `0x00`, `0x00`,
1027	/// `0x00`, `0x00`, `0x00`, `0x00`, `0x00`, `0x90`, `0x02`, `0x40`]
1028	/// }
1029	/// );
1030	/// ```
1031	#[inline]
1032	#[unstable(feature = "f128", issue = "116909")]
1033	#[must_use = "this returns the result of the operation, without modifying the original"]
1034	pub const fn to_ne_bytes(self) -> [u8; `16`] {
1035	self.to_bits().to_ne_bytes()
1036	}
1037
1038	/// Creates a floating point value from its representation as a byte array in big endian.
1039	///
1040	/// See [`from_bits`](Self::from_bits) for some discussion of the
1041	/// portability of this operation (there are almost no issues).
1042	///
1043	/// # Examples
1044	///
1045	/// ```
1046	/// #![feature(f128)]
1047	/// # // FIXME(f16_f128): remove when `eqtf2` is available
1048	/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1049	///
1050	/// let value = f128::from_be_bytes(
1051	/// [`0x40`, `0x02`, `0x90`, `0x00`, `0x00`, `0x00`, `0x00`, `0x00`,
1052	/// `0x00`, `0x00`, `0x00`, `0x00`, `0x00`, `0x00`, `0x00`, `0x00`]
1053	/// );
1054	/// assert_eq!(value, `12.5`);
1055	/// # }
1056	/// ```
1057	#[inline]
1058	#[must_use]
1059	#[unstable(feature = "f128", issue = "116909")]
1060	pub const fn from_be_bytes(bytes: [u8; `16`]) -> Self {
1061	Self::from_bits(u128::from_be_bytes(bytes))
1062	}
1063
1064	/// Creates a floating point value from its representation as a byte array in little endian.
1065	///
1066	/// See [`from_bits`](Self::from_bits) for some discussion of the
1067	/// portability of this operation (there are almost no issues).
1068	///
1069	/// # Examples
1070	///
1071	/// ```
1072	/// #![feature(f128)]
1073	/// # // FIXME(f16_f128): remove when `eqtf2` is available
1074	/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1075	///
1076	/// let value = f128::from_le_bytes(
1077	/// [`0x00`, `0x00`, `0x00`, `0x00`, `0x00`, `0x00`, `0x00`, `0x00`,
1078	/// `0x00`, `0x00`, `0x00`, `0x00`, `0x00`, `0x90`, `0x02`, `0x40`]
1079	/// );
1080	/// assert_eq!(value, `12.5`);
1081	/// # }
1082	/// ```
1083	#[inline]
1084	#[must_use]
1085	#[unstable(feature = "f128", issue = "116909")]
1086	pub const fn from_le_bytes(bytes: [u8; `16`]) -> Self {
1087	Self::from_bits(u128::from_le_bytes(bytes))
1088	}
1089
1090	/// Creates a floating point value from its representation as a byte array in native endian.
1091	///
1092	/// As the target platform's native endianness is used, portable code
1093	/// likely wants to use [`from_be_bytes`] or [`from_le_bytes`], as
1094	/// appropriate instead.
1095	///
1096	/// [`from_be_bytes`]: f128::from_be_bytes
1097	/// [`from_le_bytes`]: f128::from_le_bytes
1098	///
1099	/// See [`from_bits`](Self::from_bits) for some discussion of the
1100	/// portability of this operation (there are almost no issues).
1101	///
1102	/// # Examples
1103	///
1104	/// ```
1105	/// #![feature(f128)]
1106	/// # // FIXME(f16_f128): remove when `eqtf2` is available
1107	/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1108	///
1109	/// let value = f128::from_ne_bytes(if cfg!(target_endian = "big") {
1110	/// [`0x40`, `0x02`, `0x90`, `0x00`, `0x00`, `0x00`, `0x00`, `0x00`,
1111	/// `0x00`, `0x00`, `0x00`, `0x00`, `0x00`, `0x00`, `0x00`, `0x00`]
1112	/// } else {
1113	/// [`0x00`, `0x00`, `0x00`, `0x00`, `0x00`, `0x00`, `0x00`, `0x00`,
1114	/// `0x00`, `0x00`, `0x00`, `0x00`, `0x00`, `0x90`, `0x02`, `0x40`]
1115	/// });
1116	/// assert_eq!(value, `12.5`);
1117	/// # }
1118	/// ```
1119	#[inline]
1120	#[must_use]
1121	#[unstable(feature = "f128", issue = "116909")]
1122	pub const fn from_ne_bytes(bytes: [u8; `16`]) -> Self {
1123	Self::from_bits(u128::from_ne_bytes(bytes))
1124	}
1125
1126	/// Returns the ordering between `self` and `other`.
1127	///
1128	/// Unlike the standard partial comparison between floating point numbers,
1129	/// this comparison always produces an ordering in accordance to
1130	/// the `totalOrder` predicate as defined in the IEEE 754 (2008 revision)
1131	/// floating point standard. The values are ordered in the following sequence:
1132	///
1133	/// - negative quiet NaN
1134	/// - negative signaling NaN
1135	/// - negative infinity
1136	/// - negative numbers
1137	/// - negative subnormal numbers
1138	/// - negative zero
1139	/// - positive zero
1140	/// - positive subnormal numbers
1141	/// - positive numbers
1142	/// - positive infinity
1143	/// - positive signaling NaN
1144	/// - positive quiet NaN.
1145	///
1146	/// The ordering established by this function does not always agree with the
1147	/// [`PartialOrd`] and [`PartialEq`] implementations of `f128`. For example,
1148	/// they consider negative and positive zero equal, while `total_cmp`
1149	/// doesn't.
1150	///
1151	/// The interpretation of the signaling NaN bit follows the definition in
1152	/// the IEEE 754 standard, which may not match the interpretation by some of
1153	/// the older, non-conformant (e.g. MIPS) hardware implementations.
1154	///
1155	/// # Example
1156	///
1157	/// ```
1158	/// #![feature(f128)]
1159	///
1160	/// struct GoodBoy {
1161	/// name: &'static str,
1162	/// weight: f128,
1163	/// }
1164	///
1165	/// let mut bois = vec![
1166	/// GoodBoy { name: "Pucci", weight: `0.1` },
1167	/// GoodBoy { name: "Woofer", weight: `99.0` },
1168	/// GoodBoy { name: "Yapper", weight: `10.0` },
1169	/// GoodBoy { name: "Chonk", weight: f128::INFINITY },
1170	/// GoodBoy { name: "Abs. Unit", weight: f128::NAN },
1171	/// GoodBoy { name: "Floaty", weight: -`5.0` },
1172	/// ];
1173	///
1174	/// bois.sort_by(\|a, b\| a.weight.total_cmp(&b.weight));
1175	///
1176	/// // `f128::NAN` could be positive or negative, which will affect the sort order.
1177	/// if f128::NAN.is_sign_negative() {
1178	/// bois.into_iter().map(\|b\| b.weight)
1179	/// .zip([f128::NAN, `-5.0`, `0.1`, `10.0`, `99.0`, f128::INFINITY].iter())
1180	/// .for_each(\|(a, b)\| assert_eq!(a.to_bits(), b.to_bits()))
1181	/// } else {
1182	/// bois.into_iter().map(\|b\| b.weight)
1183	/// .zip([`-5.0`, `0.1`, `10.0`, `99.0`, f128::INFINITY, f128::NAN].iter())
1184	/// .for_each(\|(a, b)\| assert_eq!(a.to_bits(), b.to_bits()))
1185	/// }
1186	/// ```
1187	#[inline]
1188	#[must_use]
1189	#[unstable(feature = "f128", issue = "116909")]
1190	pub fn total_cmp(&self, other: &Self) -> crate::cmp::Ordering {
1191	let mut left = self.to_bits() as i128;
1192	let mut right = other.to_bits() as i128;
1193
1194	// In case of negatives, flip all the bits except the sign
1195	// to achieve a similar layout as two's complement integers
1196	//
1197	// Why does this work? IEEE 754 floats consist of three fields:
1198	// Sign bit, exponent and mantissa. The set of exponent and mantissa
1199	// fields as a whole have the property that their bitwise order is
1200	// equal to the numeric magnitude where the magnitude is defined.
1201	// The magnitude is not normally defined on NaN values, but
1202	// IEEE 754 totalOrder defines the NaN values also to follow the
1203	// bitwise order. This leads to order explained in the doc comment.
1204	// However, the representation of magnitude is the same for negative
1205	// and positive numbers – only the sign bit is different.
1206	// To easily compare the floats as signed integers, we need to
1207	// flip the exponent and mantissa bits in case of negative numbers.
1208	// We effectively convert the numbers to "two's complement" form.
1209	//
1210	// To do the flipping, we construct a mask and XOR against it.
1211	// We branchlessly calculate an "all-ones except for the sign bit"
1212	// mask from negative-signed values: right shifting sign-extends
1213	// the integer, so we "fill" the mask with sign bits, and then
1214	// convert to unsigned to push one more zero bit.
1215	// On positive values, the mask is all zeros, so it's a no-op.
1216	left ^= (((left >> `127`) as u128) >> `1`) as i128;
1217	right ^= (((right >> `127`) as u128) >> `1`) as i128;
1218
1219	left.cmp(&right)
1220	}
1221
1222	/// Restrict a value to a certain interval unless it is NaN.
1223	///
1224	/// Returns `max` if `self` is greater than `max`, and `min` if `self` is
1225	/// less than `min`. Otherwise this returns `self`.
1226	///
1227	/// Note that this function returns NaN if the initial value was NaN as
1228	/// well.
1229	///
1230	/// # Panics
1231	///
1232	/// Panics if `min > max`, `min` is NaN, or `max` is NaN.
1233	///
1234	/// # Examples
1235	///
1236	/// ```
1237	/// #![feature(f128)]
1238	/// # // FIXME(f16_f128): remove when `{eq,gt,unord}tf` are available
1239	/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1240	///
1241	/// assert!((-`3.0f128`).clamp(-`2.0`, `1.0`) == -`2.0`);
1242	/// assert!((`0.0f128`).clamp(-`2.0`, `1.0`) == `0.0`);
1243	/// assert!((`2.0f128`).clamp(-`2.0`, `1.0`) == `1.0`);
1244	/// assert!((f128::NAN).clamp(-`2.0`, `1.0`).is_nan());
1245	/// # }
1246	/// ```
1247	#[inline]
1248	#[unstable(feature = "f128", issue = "116909")]
1249	#[must_use = "method returns a new number and does not mutate the original value"]
1250	pub const fn clamp(mut self, min: f128, max: f128) -> f128 {
1251	const_assert!(
1252	min <= max,
1253	"min > max, or either was NaN",
1254	"min > max, or either was NaN. min = {min:?}, max = {max:?}",
1255	min: f128,
1256	max: f128,
1257	);
1258
1259	if self < min {
1260	self = min;
1261	}
1262	if self > max {
1263	self = max;
1264	}
1265	self
1266	}
1267
1268	/// Computes the absolute value of `self`.
1269	///
1270	/// This function always returns the precise result.
1271	///
1272	/// # Examples
1273	///
1274	/// ```
1275	/// #![feature(f128)]
1276	/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1277	///
1278	/// let x = `3.5_f128`;
1279	/// let y = `-3.5_f128`;
1280	///
1281	/// assert_eq!(x.abs(), x);
1282	/// assert_eq!(y.abs(), -y);
1283	///
1284	/// assert!(f128::NAN.abs().is_nan());
1285	/// # }
1286	/// ```
1287	#[inline]
1288	#[unstable(feature = "f128", issue = "116909")]
1289	#[rustc_const_unstable(feature = "f128", issue = "116909")]
1290	#[must_use = "method returns a new number and does not mutate the original value"]
1291	pub const fn abs(self) -> Self {
1292	// FIXME(f16_f128): replace with `intrinsics::fabsf128` when available
1293	// We don't do this now because LLVM has lowering bugs for f128 math.
1294	Self::from_bits(self.to_bits() & !(`1` << `127`))
1295	}
1296
1297	/// Returns a number that represents the sign of `self`.
1298	///
1299	/// - `1.0` if the number is positive, `+0.0` or `INFINITY`
1300	/// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
1301	/// - NaN if the number is NaN
1302	///
1303	/// # Examples
1304	///
1305	/// ```
1306	/// #![feature(f128)]
1307	/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1308	///
1309	/// let f = `3.5_f128`;
1310	///
1311	/// assert_eq!(f.signum(), `1.0`);
1312	/// assert_eq!(f128::NEG_INFINITY.signum(), -`1.0`);
1313	///
1314	/// assert!(f128::NAN.signum().is_nan());
1315	/// # }
1316	/// ```
1317	#[inline]
1318	#[unstable(feature = "f128", issue = "116909")]
1319	#[rustc_const_unstable(feature = "f128", issue = "116909")]
1320	#[must_use = "method returns a new number and does not mutate the original value"]
1321	pub const fn signum(self) -> f128 {
1322	if self.is_nan() { Self::NAN } else { `1.0_f128`.copysign(self) }
1323	}
1324
1325	/// Returns a number composed of the magnitude of `self` and the sign of
1326	/// `sign`.
1327	///
1328	/// Equal to `self` if the sign of `self` and `sign` are the same, otherwise equal to `-self`.
1329	/// If `self` is a NaN, then a NaN with the same payload as `self` and the sign bit of `sign` is
1330	/// returned.
1331	///
1332	/// If `sign` is a NaN, then this operation will still carry over its sign into the result. Note
1333	/// that IEEE 754 doesn't assign any meaning to the sign bit in case of a NaN, and as Rust
1334	/// doesn't guarantee that the bit pattern of NaNs are conserved over arithmetic operations, the
1335	/// result of `copysign` with `sign` being a NaN might produce an unexpected or non-portable
1336	/// result. See the [specification of NaN bit patterns](primitive@f32#nan-bit-patterns) for more
1337	/// info.
1338	///
1339	/// # Examples
1340	///
1341	/// ```
1342	/// #![feature(f128)]
1343	/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1344	///
1345	/// let f = `3.5_f128`;
1346	///
1347	/// assert_eq!(f.copysign(`0.42`), `3.5_f128`);
1348	/// assert_eq!(f.copysign(-`0.42`), -`3.5_f128`);
1349	/// assert_eq!((-f).copysign(`0.42`), `3.5_f128`);
1350	/// assert_eq!((-f).copysign(-`0.42`), -`3.5_f128`);
1351	///
1352	/// assert!(f128::NAN.copysign(`1.0`).is_nan());
1353	/// # }
1354	/// ```
1355	#[inline]
1356	#[unstable(feature = "f128", issue = "116909")]
1357	#[rustc_const_unstable(feature = "f128", issue = "116909")]
1358	#[must_use = "method returns a new number and does not mutate the original value"]
1359	pub const fn copysign(self, sign: f128) -> f128 {
1360	// SAFETY: this is actually a safe intrinsic
1361	unsafe { intrinsics::copysignf128(self, sign) }
1362	}
1363
1364	/// Float addition that allows optimizations based on algebraic rules.
1365	///
1366	/// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1367	#[must_use = "method returns a new number and does not mutate the original value"]
1368	#[unstable(feature = "float_algebraic", issue = "136469")]
1369	#[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1370	#[inline]
1371	pub const fn algebraic_add(self, rhs: f128) -> f128 {
1372	intrinsics::fadd_algebraic(self, rhs)
1373	}
1374
1375	/// Float subtraction that allows optimizations based on algebraic rules.
1376	///
1377	/// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1378	#[must_use = "method returns a new number and does not mutate the original value"]
1379	#[unstable(feature = "float_algebraic", issue = "136469")]
1380	#[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1381	#[inline]
1382	pub const fn algebraic_sub(self, rhs: f128) -> f128 {
1383	intrinsics::fsub_algebraic(self, rhs)
1384	}
1385
1386	/// Float multiplication that allows optimizations based on algebraic rules.
1387	///
1388	/// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1389	#[must_use = "method returns a new number and does not mutate the original value"]
1390	#[unstable(feature = "float_algebraic", issue = "136469")]
1391	#[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1392	#[inline]
1393	pub const fn algebraic_mul(self, rhs: f128) -> f128 {
1394	intrinsics::fmul_algebraic(self, rhs)
1395	}
1396
1397	/// Float division that allows optimizations based on algebraic rules.
1398	///
1399	/// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1400	#[must_use = "method returns a new number and does not mutate the original value"]
1401	#[unstable(feature = "float_algebraic", issue = "136469")]
1402	#[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1403	#[inline]
1404	pub const fn algebraic_div(self, rhs: f128) -> f128 {
1405	intrinsics::fdiv_algebraic(self, rhs)
1406	}
1407
1408	/// Float remainder that allows optimizations based on algebraic rules.
1409	///
1410	/// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1411	#[must_use = "method returns a new number and does not mutate the original value"]
1412	#[unstable(feature = "float_algebraic", issue = "136469")]
1413	#[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1414	#[inline]
1415	pub const fn algebraic_rem(self, rhs: f128) -> f128 {
1416	intrinsics::frem_algebraic(self, rhs)
1417	}
1418	}
1419
1420	// Functions in this module fall into `core_float_math`
1421	// FIXME(f16_f128): all doctests must be gated to platforms that have `long double` === `_Float128`
1422	// due to https://github.com/llvm/llvm-project/issues/44744. aarch64 linux matches this.
1423	// #[unstable(feature = "core_float_math", issue = "137578")]
1424	#[cfg(not(test))]
1425	#[doc(test(attr(feature(cfg_target_has_reliable_f16_f128), expect(internal_features))))]
1426	impl f128 {
1427	/// Returns the largest integer less than or equal to `self`.
1428	///
1429	/// This function always returns the precise result.
1430	///
1431	/// # Examples
1432	///
1433	/// ```
1434	/// #![feature(f128)]
1435	/// # #[cfg(not(miri))]
1436	/// # #[cfg(target_has_reliable_f128_math)] {
1437	///
1438	/// let f = `3.7_f128`;
1439	/// let g = `3.0_f128`;
1440	/// let h = `-3.7_f128`;
1441	///
1442	/// assert_eq!(f.floor(), `3.0`);
1443	/// assert_eq!(g.floor(), `3.0`);
1444	/// assert_eq!(h.floor(), -`4.0`);
1445	/// # }
1446	/// ```
1447	#[inline]
1448	#[rustc_allow_incoherent_impl]
1449	#[unstable(feature = "f128", issue = "116909")]
1450	#[rustc_const_unstable(feature = "f128", issue = "116909")]
1451	// #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
1452	#[must_use = "method returns a new number and does not mutate the original value"]
1453	pub const fn floor(self) -> f128 {
1454	// SAFETY: intrinsic with no preconditions
1455	unsafe { intrinsics::floorf128(self) }
1456	}
1457
1458	/// Returns the smallest integer greater than or equal to `self`.
1459	///
1460	/// This function always returns the precise result.
1461	///
1462	/// # Examples
1463	///
1464	/// ```
1465	/// #![feature(f128)]
1466	/// # #[cfg(not(miri))]
1467	/// # #[cfg(target_has_reliable_f128_math)] {
1468	///
1469	/// let f = `3.01_f128`;
1470	/// let g = `4.0_f128`;
1471	///
1472	/// assert_eq!(f.ceil(), `4.0`);
1473	/// assert_eq!(g.ceil(), `4.0`);
1474	/// # }
1475	/// ```
1476	#[inline]
1477	#[doc(alias = "ceiling")]
1478	#[rustc_allow_incoherent_impl]
1479	#[unstable(feature = "f128", issue = "116909")]
1480	#[rustc_const_unstable(feature = "f128", issue = "116909")]
1481	// #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
1482	#[must_use = "method returns a new number and does not mutate the original value"]
1483	pub const fn ceil(self) -> f128 {
1484	// SAFETY: intrinsic with no preconditions
1485	unsafe { intrinsics::ceilf128(self) }
1486	}
1487
1488	/// Returns the nearest integer to `self`. If a value is half-way between two
1489	/// integers, round away from `0.0`.
1490	///
1491	/// This function always returns the precise result.
1492	///
1493	/// # Examples
1494	///
1495	/// ```
1496	/// #![feature(f128)]
1497	/// # #[cfg(not(miri))]
1498	/// # #[cfg(target_has_reliable_f128_math)] {
1499	///
1500	/// let f = `3.3_f128`;
1501	/// let g = `-3.3_f128`;
1502	/// let h = `-3.7_f128`;
1503	/// let i = `3.5_f128`;
1504	/// let j = `4.5_f128`;
1505	///
1506	/// assert_eq!(f.round(), `3.0`);
1507	/// assert_eq!(g.round(), -`3.0`);
1508	/// assert_eq!(h.round(), -`4.0`);
1509	/// assert_eq!(i.round(), `4.0`);
1510	/// assert_eq!(j.round(), `5.0`);
1511	/// # }
1512	/// ```
1513	#[inline]
1514	#[rustc_allow_incoherent_impl]
1515	#[unstable(feature = "f128", issue = "116909")]
1516	#[rustc_const_unstable(feature = "f128", issue = "116909")]
1517	// #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
1518	#[must_use = "method returns a new number and does not mutate the original value"]
1519	pub const fn round(self) -> f128 {
1520	// SAFETY: intrinsic with no preconditions
1521	unsafe { intrinsics::roundf128(self) }
1522	}
1523
1524	/// Returns the nearest integer to a number. Rounds half-way cases to the number
1525	/// with an even least significant digit.
1526	///
1527	/// This function always returns the precise result.
1528	///
1529	/// # Examples
1530	///
1531	/// ```
1532	/// #![feature(f128)]
1533	/// # #[cfg(not(miri))]
1534	/// # #[cfg(target_has_reliable_f128_math)] {
1535	///
1536	/// let f = `3.3_f128`;
1537	/// let g = `-3.3_f128`;
1538	/// let h = `3.5_f128`;
1539	/// let i = `4.5_f128`;
1540	///
1541	/// assert_eq!(f.round_ties_even(), `3.0`);
1542	/// assert_eq!(g.round_ties_even(), -`3.0`);
1543	/// assert_eq!(h.round_ties_even(), `4.0`);
1544	/// assert_eq!(i.round_ties_even(), `4.0`);
1545	/// # }
1546	/// ```
1547	#[inline]
1548	#[rustc_allow_incoherent_impl]
1549	#[unstable(feature = "f128", issue = "116909")]
1550	#[rustc_const_unstable(feature = "f128", issue = "116909")]
1551	// #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
1552	#[must_use = "method returns a new number and does not mutate the original value"]
1553	pub const fn round_ties_even(self) -> f128 {
1554	intrinsics::round_ties_even_f128(self)
1555	}
1556
1557	/// Returns the integer part of `self`.
1558	/// This means that non-integer numbers are always truncated towards zero.
1559	///
1560	/// This function always returns the precise result.
1561	///
1562	/// # Examples
1563	///
1564	/// ```
1565	/// #![feature(f128)]
1566	/// # #[cfg(not(miri))]
1567	/// # #[cfg(target_has_reliable_f128_math)] {
1568	///
1569	/// let f = `3.7_f128`;
1570	/// let g = `3.0_f128`;
1571	/// let h = `-3.7_f128`;
1572	///
1573	/// assert_eq!(f.trunc(), `3.0`);
1574	/// assert_eq!(g.trunc(), `3.0`);
1575	/// assert_eq!(h.trunc(), -`3.0`);
1576	/// # }
1577	/// ```
1578	#[inline]
1579	#[doc(alias = "truncate")]
1580	#[rustc_allow_incoherent_impl]
1581	#[unstable(feature = "f128", issue = "116909")]
1582	#[rustc_const_unstable(feature = "f128", issue = "116909")]
1583	// #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
1584	#[must_use = "method returns a new number and does not mutate the original value"]
1585	pub const fn trunc(self) -> f128 {
1586	// SAFETY: intrinsic with no preconditions
1587	unsafe { intrinsics::truncf128(self) }
1588	}
1589
1590	/// Returns the fractional part of `self`.
1591	///
1592	/// This function always returns the precise result.
1593	///
1594	/// # Examples
1595	///
1596	/// ```
1597	/// #![feature(f128)]
1598	/// # #[cfg(not(miri))]
1599	/// # #[cfg(target_has_reliable_f128_math)] {
1600	///
1601	/// let x = `3.6_f128`;
1602	/// let y = `-3.6_f128`;
1603	/// let abs_difference_x = (x.fract() - `0.6`).abs();
1604	/// let abs_difference_y = (y.fract() - (`-0.6`)).abs();
1605	///
1606	/// assert!(abs_difference_x <= f128::EPSILON);
1607	/// assert!(abs_difference_y <= f128::EPSILON);
1608	/// # }
1609	/// ```
1610	#[inline]
1611	#[rustc_allow_incoherent_impl]
1612	#[unstable(feature = "f128", issue = "116909")]
1613	#[rustc_const_unstable(feature = "f128", issue = "116909")]
1614	// #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
1615	#[must_use = "method returns a new number and does not mutate the original value"]
1616	pub const fn fract(self) -> f128 {
1617	self - self.trunc()
1618	}
1619
1620	/// Fused multiply-add. Computes `(self a) + b` with only one rounding*
1621	/// error, yielding a more accurate result than an unfused multiply-add.
1622	///
1623	/// Using `mul_add` may* be more performant than an unfused multiply-add if*
1624	/// the target architecture has a dedicated `fma` CPU instruction. However,
1625	/// this is not always true, and will be heavily dependant on designing
1626	/// algorithms with specific target hardware in mind.
1627	///
1628	/// # Precision
1629	///
1630	/// The result of this operation is guaranteed to be the rounded
1631	/// infinite-precision result. It is specified by IEEE 754 as
1632	/// `fusedMultiplyAdd` and guaranteed not to change.
1633	///
1634	/// # Examples
1635	///
1636	/// ```
1637	/// #![feature(f128)]
1638	/// # #[cfg(not(miri))]
1639	/// # #[cfg(target_has_reliable_f128_math)] {
1640	///
1641	/// let m = `10.0_f128`;
1642	/// let x = `4.0_f128`;
1643	/// let b = `60.0_f128`;
1644	///
1645	/// assert_eq!(m.mul_add(x, b), `100.0`);
1646	/// assert_eq!(m * x + b, `100.0`);
1647	///
1648	/// let one_plus_eps = `1.0_f128` + f128::EPSILON;
1649	/// let one_minus_eps = `1.0_f128` - f128::EPSILON;
1650	/// let minus_one = `-1.0_f128`;
1651	///
1652	/// // The exact result (1 + eps) (1 - eps) = 1 - eps * eps.*
1653	/// assert_eq!(one_plus_eps.mul_add(one_minus_eps, minus_one), -f128::EPSILON * f128::EPSILON);
1654	/// // Different rounding with the non-fused multiply and add.
1655	/// assert_eq!(one_plus_eps * one_minus_eps + minus_one, `0.0`);
1656	/// # }
1657	/// ```
1658	#[inline]
1659	#[rustc_allow_incoherent_impl]
1660	#[doc(alias = "fmaf128", alias = "fusedMultiplyAdd")]
1661	#[unstable(feature = "f128", issue = "116909")]
1662	#[must_use = "method returns a new number and does not mutate the original value"]
1663	pub fn mul_add(self, a: f128, b: f128) -> f128 {
1664	// SAFETY: intrinsic with no preconditions
1665	unsafe { intrinsics::fmaf128(self, a, b) }
1666	}
1667
1668	/// Calculates Euclidean division, the matching method for `rem_euclid`.
1669	///
1670	/// This computes the integer `n` such that
1671	/// `self = n rhs + self.rem_euclid(rhs)`.*
1672	/// In other words, the result is `self / rhs` rounded to the integer `n`
1673	/// such that `self >= n rhs`.*
1674	///
1675	/// # Precision
1676	///
1677	/// The result of this operation is guaranteed to be the rounded
1678	/// infinite-precision result.
1679	///
1680	/// # Examples
1681	///
1682	/// ```
1683	/// #![feature(f128)]
1684	/// # #[cfg(not(miri))]
1685	/// # #[cfg(target_has_reliable_f128_math)] {
1686	///
1687	/// let a: f128 = `7.0`;
1688	/// let b = `4.0`;
1689	/// assert_eq!(a.div_euclid(b), `1.0`); // 7.0 > 4.0 1.0*
1690	/// assert_eq!((-a).div_euclid(b), -`2.0`); // -7.0 >= 4.0 -2.0*
1691	/// assert_eq!(a.div_euclid(-b), -`1.0`); // 7.0 >= -4.0 -1.0*
1692	/// assert_eq!((-a).div_euclid(-b), `2.0`); // -7.0 >= -4.0 2.0*
1693	/// # }
1694	/// ```
1695	#[inline]
1696	#[rustc_allow_incoherent_impl]
1697	#[unstable(feature = "f128", issue = "116909")]
1698	#[must_use = "method returns a new number and does not mutate the original value"]
1699	pub fn div_euclid(self, rhs: f128) -> f128 {
1700	let q = (self / rhs).trunc();
1701	if self % rhs < `0.0` {
1702	return if rhs > `0.0` { q - `1.0` } else { q + `1.0` };
1703	}
1704	q
1705	}
1706
1707	/// Calculates the least nonnegative remainder of `self (mod rhs)`.
1708	///
1709	/// In particular, the return value `r` satisfies `0.0 <= r < rhs.abs()` in
1710	/// most cases. However, due to a floating point round-off error it can
1711	/// result in `r == rhs.abs()`, violating the mathematical definition, if
1712	/// `self` is much smaller than `rhs.abs()` in magnitude and `self < 0.0`.
1713	/// This result is not an element of the function's codomain, but it is the
1714	/// closest floating point number in the real numbers and thus fulfills the
1715	/// property `self == self.div_euclid(rhs) rhs + self.rem_euclid(rhs)`*
1716	/// approximately.
1717	///
1718	/// # Precision
1719	///
1720	/// The result of this operation is guaranteed to be the rounded
1721	/// infinite-precision result.
1722	///
1723	/// # Examples
1724	///
1725	/// ```
1726	/// #![feature(f128)]
1727	/// # #[cfg(not(miri))]
1728	/// # #[cfg(target_has_reliable_f128_math)] {
1729	///
1730	/// let a: f128 = `7.0`;
1731	/// let b = `4.0`;
1732	/// assert_eq!(a.rem_euclid(b), `3.0`);
1733	/// assert_eq!((-a).rem_euclid(b), `1.0`);
1734	/// assert_eq!(a.rem_euclid(-b), `3.0`);
1735	/// assert_eq!((-a).rem_euclid(-b), `1.0`);
1736	/// // limitation due to round-off error
1737	/// assert!((-f128::EPSILON).rem_euclid(`3.0`) != `0.0`);
1738	/// # }
1739	/// ```
1740	#[inline]
1741	#[rustc_allow_incoherent_impl]
1742	#[doc(alias = "modulo", alias = "mod")]
1743	#[unstable(feature = "f128", issue = "116909")]
1744	#[must_use = "method returns a new number and does not mutate the original value"]
1745	pub fn rem_euclid(self, rhs: f128) -> f128 {
1746	let r = self % rhs;
1747	if r < `0.0` { r + rhs.abs() } else { r }
1748	}
1749
1750	/// Raises a number to an integer power.
1751	///
1752	/// Using this function is generally faster than using `powf`.
1753	/// It might have a different sequence of rounding operations than `powf`,
1754	/// so the results are not guaranteed to agree.
1755	///
1756	/// # Unspecified precision
1757	///
1758	/// The precision of this function is non-deterministic. This means it varies by platform,
1759	/// Rust version, and can even differ within the same execution from one invocation to the next.
1760	///
1761	/// # Examples
1762	///
1763	/// ```
1764	/// #![feature(f128)]
1765	/// # #[cfg(not(miri))]
1766	/// # #[cfg(target_has_reliable_f128_math)] {
1767	///
1768	/// let x = `2.0_f128`;
1769	/// let abs_difference = (x.powi(`2`) - (x * x)).abs();
1770	/// assert!(abs_difference <= f128::EPSILON);
1771	///
1772	/// assert_eq!(f128::powi(f128::NAN, `0`), `1.0`);
1773	/// # }
1774	/// ```
1775	#[inline]
1776	#[rustc_allow_incoherent_impl]
1777	#[unstable(feature = "f128", issue = "116909")]
1778	#[must_use = "method returns a new number and does not mutate the original value"]
1779	pub fn powi(self, n: i32) -> f128 {
1780	// SAFETY: intrinsic with no preconditions
1781	unsafe { intrinsics::powif128(self, n) }
1782	}
1783
1784	/// Returns the square root of a number.
1785	///
1786	/// Returns NaN if `self` is a negative number other than `-0.0`.
1787	///
1788	/// # Precision
1789	///
1790	/// The result of this operation is guaranteed to be the rounded
1791	/// infinite-precision result. It is specified by IEEE 754 as `squareRoot`
1792	/// and guaranteed not to change.
1793	///
1794	/// # Examples
1795	///
1796	/// ```
1797	/// #![feature(f128)]
1798	/// # #[cfg(not(miri))]
1799	/// # #[cfg(target_has_reliable_f128_math)] {
1800	///
1801	/// let positive = `4.0_f128`;
1802	/// let negative = `-4.0_f128`;
1803	/// let negative_zero = `-0.0_f128`;
1804	///
1805	/// assert_eq!(positive.sqrt(), `2.0`);
1806	/// assert!(negative.sqrt().is_nan());
1807	/// assert!(negative_zero.sqrt() == negative_zero);
1808	/// # }
1809	/// ```
1810	#[inline]
1811	#[doc(alias = "squareRoot")]
1812	#[rustc_allow_incoherent_impl]
1813	#[unstable(feature = "f128", issue = "116909")]
1814	#[must_use = "method returns a new number and does not mutate the original value"]
1815	pub fn sqrt(self) -> f128 {
1816	// SAFETY: intrinsic with no preconditions
1817	unsafe { intrinsics::sqrtf128(self) }
1818	}
1819	}
1820