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
14use crate::convert::FloatToInt;
15use crate::num::FpCategory;
16use crate::panic::const_assert;
17use crate::{intrinsics, mem};
18
19/// Basic mathematical constants.
20#[unstable(feature = "f128", issue = "116909")]
21pub 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
139impl 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 #[unstable(feature = "f128", issue = "116909")]
149 pub const MANTISSA_DIGITS: u32 = 113;
150
151 /// Approximate number of significant digits in base 10.
152 ///
153 /// This is the maximum <i>x</i> such that any decimal number with <i>x</i>
154 /// significant digits can be converted to `f128` and back without loss.
155 ///
156 /// Equal to floor(log<sub>10</sub>&nbsp;2<sup>[`MANTISSA_DIGITS`]&nbsp;&minus;&nbsp;1</sup>).
157 ///
158 /// [`MANTISSA_DIGITS`]: f128::MANTISSA_DIGITS
159 #[unstable(feature = "f128", issue = "116909")]
160 pub const DIGITS: u32 = 33;
161
162 /// [Machine epsilon] value for `f128`.
163 ///
164 /// This is the difference between `1.0` and the next larger representable number.
165 ///
166 /// Equal to 2<sup>1&nbsp;&minus;&nbsp;[`MANTISSA_DIGITS`]</sup>.
167 ///
168 /// [Machine epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon
169 /// [`MANTISSA_DIGITS`]: f128::MANTISSA_DIGITS
170 #[unstable(feature = "f128", issue = "116909")]
171 pub const EPSILON: f128 = 1.92592994438723585305597794258492732e-34_f128;
172
173 /// Smallest finite `f128` value.
174 ///
175 /// Equal to &minus;[`MAX`].
176 ///
177 /// [`MAX`]: f128::MAX
178 #[unstable(feature = "f128", issue = "116909")]
179 pub const MIN: f128 = -1.18973149535723176508575932662800702e+4932_f128;
180 /// Smallest positive normal `f128` value.
181 ///
182 /// Equal to 2<sup>[`MIN_EXP`]&nbsp;&minus;&nbsp;1</sup>.
183 ///
184 /// [`MIN_EXP`]: f128::MIN_EXP
185 #[unstable(feature = "f128", issue = "116909")]
186 pub const MIN_POSITIVE: f128 = 3.36210314311209350626267781732175260e-4932_f128;
187 /// Largest finite `f128` value.
188 ///
189 /// Equal to
190 /// (1&nbsp;&minus;&nbsp;2<sup>&minus;[`MANTISSA_DIGITS`]</sup>)&nbsp;2<sup>[`MAX_EXP`]</sup>.
191 ///
192 /// [`MANTISSA_DIGITS`]: f128::MANTISSA_DIGITS
193 /// [`MAX_EXP`]: f128::MAX_EXP
194 #[unstable(feature = "f128", issue = "116909")]
195 pub const MAX: f128 = 1.18973149535723176508575932662800702e+4932_f128;
196
197 /// One greater than the minimum possible normal power of 2 exponent.
198 ///
199 /// If <i>x</i>&nbsp;=&nbsp;`MIN_EXP`, then normal numbers
200 /// ≥&nbsp;0.5&nbsp;×&nbsp;2<sup><i>x</i></sup>.
201 #[unstable(feature = "f128", issue = "116909")]
202 pub const MIN_EXP: i32 = -16_381;
203 /// Maximum possible power of 2 exponent.
204 ///
205 /// If <i>x</i>&nbsp;=&nbsp;`MAX_EXP`, then normal numbers
206 /// &lt;&nbsp;1&nbsp;×&nbsp;2<sup><i>x</i></sup>.
207 #[unstable(feature = "f128", issue = "116909")]
208 pub const MAX_EXP: i32 = 16_384;
209
210 /// Minimum <i>x</i> for which 10<sup><i>x</i></sup> is normal.
211 ///
212 /// Equal to ceil(log<sub>10</sub>&nbsp;[`MIN_POSITIVE`]).
213 ///
214 /// [`MIN_POSITIVE`]: f128::MIN_POSITIVE
215 #[unstable(feature = "f128", issue = "116909")]
216 pub const MIN_10_EXP: i32 = -4_931;
217 /// Maximum <i>x</i> for which 10<sup><i>x</i></sup> is normal.
218 ///
219 /// Equal to floor(log<sub>10</sub>&nbsp;[`MAX`]).
220 ///
221 /// [`MAX`]: f128::MAX
222 #[unstable(feature = "f128", issue = "116909")]
223 pub const MAX_10_EXP: i32 = 4_932;
224
225 /// Not a Number (NaN).
226 ///
227 /// Note that IEEE 754 doesn't define just a single NaN value;
228 /// a plethora of bit patterns are considered to be NaN.
229 /// Furthermore, the standard makes a difference
230 /// between a "signaling" and a "quiet" NaN,
231 /// and allows inspecting its "payload" (the unspecified bits in the bit pattern).
232 /// This constant isn't guaranteed to equal to any specific NaN bitpattern,
233 /// and the stability of its representation over Rust versions
234 /// and target platforms isn't guaranteed.
235 #[allow(clippy::eq_op)]
236 #[rustc_diagnostic_item = "f128_nan"]
237 #[unstable(feature = "f128", issue = "116909")]
238 pub const NAN: f128 = 0.0_f128 / 0.0_f128;
239
240 /// Infinity (∞).
241 #[unstable(feature = "f128", issue = "116909")]
242 pub const INFINITY: f128 = 1.0_f128 / 0.0_f128;
243
244 /// Negative infinity (−∞).
245 #[unstable(feature = "f128", issue = "116909")]
246 pub const NEG_INFINITY: f128 = -1.0_f128 / 0.0_f128;
247
248 /// Sign bit
249 pub(crate) const SIGN_MASK: u128 = 0x8000_0000_0000_0000_0000_0000_0000_0000;
250
251 /// Exponent mask
252 pub(crate) const EXP_MASK: u128 = 0x7fff_0000_0000_0000_0000_0000_0000_0000;
253
254 /// Mantissa mask
255 pub(crate) const MAN_MASK: u128 = 0x0000_ffff_ffff_ffff_ffff_ffff_ffff_ffff;
256
257 /// Minimum representable positive value (min subnormal)
258 const TINY_BITS: u128 = 0x1;
259
260 /// Minimum representable negative value (min negative subnormal)
261 const NEG_TINY_BITS: u128 = Self::TINY_BITS | Self::SIGN_MASK;
262
263 /// Returns `true` if this value is NaN.
264 ///
265 /// ```
266 /// #![feature(f128)]
267 /// # // FIXME(f16_f128): remove when `unordtf2` is available
268 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
269 ///
270 /// let nan = f128::NAN;
271 /// let f = 7.0_f128;
272 ///
273 /// assert!(nan.is_nan());
274 /// assert!(!f.is_nan());
275 /// # }
276 /// ```
277 #[inline]
278 #[must_use]
279 #[unstable(feature = "f128", issue = "116909")]
280 #[allow(clippy::eq_op)] // > if you intended to check if the operand is NaN, use `.is_nan()` instead :)
281 pub const fn is_nan(self) -> bool {
282 self != self
283 }
284
285 /// Returns `true` if this value is positive infinity or negative infinity, and
286 /// `false` otherwise.
287 ///
288 /// ```
289 /// #![feature(f128)]
290 /// # // FIXME(f16_f128): remove when `eqtf2` is available
291 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
292 ///
293 /// let f = 7.0f128;
294 /// let inf = f128::INFINITY;
295 /// let neg_inf = f128::NEG_INFINITY;
296 /// let nan = f128::NAN;
297 ///
298 /// assert!(!f.is_infinite());
299 /// assert!(!nan.is_infinite());
300 ///
301 /// assert!(inf.is_infinite());
302 /// assert!(neg_inf.is_infinite());
303 /// # }
304 /// ```
305 #[inline]
306 #[must_use]
307 #[unstable(feature = "f128", issue = "116909")]
308 pub const fn is_infinite(self) -> bool {
309 (self == f128::INFINITY) | (self == f128::NEG_INFINITY)
310 }
311
312 /// Returns `true` if this number is neither infinite nor NaN.
313 ///
314 /// ```
315 /// #![feature(f128)]
316 /// # // FIXME(f16_f128): remove when `lttf2` is available
317 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
318 ///
319 /// let f = 7.0f128;
320 /// let inf: f128 = f128::INFINITY;
321 /// let neg_inf: f128 = f128::NEG_INFINITY;
322 /// let nan: f128 = f128::NAN;
323 ///
324 /// assert!(f.is_finite());
325 ///
326 /// assert!(!nan.is_finite());
327 /// assert!(!inf.is_finite());
328 /// assert!(!neg_inf.is_finite());
329 /// # }
330 /// ```
331 #[inline]
332 #[must_use]
333 #[unstable(feature = "f128", issue = "116909")]
334 #[rustc_const_unstable(feature = "f128", issue = "116909")]
335 pub const fn is_finite(self) -> bool {
336 // There's no need to handle NaN separately: if self is NaN,
337 // the comparison is not true, exactly as desired.
338 self.abs() < Self::INFINITY
339 }
340
341 /// Returns `true` if the number is [subnormal].
342 ///
343 /// ```
344 /// #![feature(f128)]
345 /// # // FIXME(f16_f128): remove when `eqtf2` is available
346 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
347 ///
348 /// let min = f128::MIN_POSITIVE; // 3.362103143e-4932f128
349 /// let max = f128::MAX;
350 /// let lower_than_min = 1.0e-4960_f128;
351 /// let zero = 0.0_f128;
352 ///
353 /// assert!(!min.is_subnormal());
354 /// assert!(!max.is_subnormal());
355 ///
356 /// assert!(!zero.is_subnormal());
357 /// assert!(!f128::NAN.is_subnormal());
358 /// assert!(!f128::INFINITY.is_subnormal());
359 /// // Values between `0` and `min` are Subnormal.
360 /// assert!(lower_than_min.is_subnormal());
361 /// # }
362 /// ```
363 ///
364 /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
365 #[inline]
366 #[must_use]
367 #[unstable(feature = "f128", issue = "116909")]
368 pub const fn is_subnormal(self) -> bool {
369 matches!(self.classify(), FpCategory::Subnormal)
370 }
371
372 /// Returns `true` if the number is neither zero, infinite, [subnormal], or NaN.
373 ///
374 /// ```
375 /// #![feature(f128)]
376 /// # // FIXME(f16_f128): remove when `eqtf2` is available
377 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
378 ///
379 /// let min = f128::MIN_POSITIVE; // 3.362103143e-4932f128
380 /// let max = f128::MAX;
381 /// let lower_than_min = 1.0e-4960_f128;
382 /// let zero = 0.0_f128;
383 ///
384 /// assert!(min.is_normal());
385 /// assert!(max.is_normal());
386 ///
387 /// assert!(!zero.is_normal());
388 /// assert!(!f128::NAN.is_normal());
389 /// assert!(!f128::INFINITY.is_normal());
390 /// // Values between `0` and `min` are Subnormal.
391 /// assert!(!lower_than_min.is_normal());
392 /// # }
393 /// ```
394 ///
395 /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
396 #[inline]
397 #[must_use]
398 #[unstable(feature = "f128", issue = "116909")]
399 pub const fn is_normal(self) -> bool {
400 matches!(self.classify(), FpCategory::Normal)
401 }
402
403 /// Returns the floating point category of the number. If only one property
404 /// is going to be tested, it is generally faster to use the specific
405 /// predicate instead.
406 ///
407 /// ```
408 /// #![feature(f128)]
409 /// # // FIXME(f16_f128): remove when `eqtf2` is available
410 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
411 ///
412 /// use std::num::FpCategory;
413 ///
414 /// let num = 12.4_f128;
415 /// let inf = f128::INFINITY;
416 ///
417 /// assert_eq!(num.classify(), FpCategory::Normal);
418 /// assert_eq!(inf.classify(), FpCategory::Infinite);
419 /// # }
420 /// ```
421 #[inline]
422 #[unstable(feature = "f128", issue = "116909")]
423 pub const fn classify(self) -> FpCategory {
424 let bits = self.to_bits();
425 match (bits & Self::MAN_MASK, bits & Self::EXP_MASK) {
426 (0, Self::EXP_MASK) => FpCategory::Infinite,
427 (_, Self::EXP_MASK) => FpCategory::Nan,
428 (0, 0) => FpCategory::Zero,
429 (_, 0) => FpCategory::Subnormal,
430 _ => FpCategory::Normal,
431 }
432 }
433
434 /// Returns `true` if `self` has a positive sign, including `+0.0`, NaNs with
435 /// positive sign bit and positive infinity.
436 ///
437 /// Note that IEEE 754 doesn't assign any meaning to the sign bit in case of
438 /// a NaN, and as Rust doesn't guarantee that the bit pattern of NaNs are
439 /// conserved over arithmetic operations, the result of `is_sign_positive` on
440 /// a NaN might produce an unexpected or non-portable result. See the [specification
441 /// of NaN bit patterns](f32#nan-bit-patterns) for more info. Use `self.signum() == 1.0`
442 /// if you need fully portable behavior (will return `false` for all NaNs).
443 ///
444 /// ```
445 /// #![feature(f128)]
446 ///
447 /// let f = 7.0_f128;
448 /// let g = -7.0_f128;
449 ///
450 /// assert!(f.is_sign_positive());
451 /// assert!(!g.is_sign_positive());
452 /// ```
453 #[inline]
454 #[must_use]
455 #[unstable(feature = "f128", issue = "116909")]
456 pub const fn is_sign_positive(self) -> bool {
457 !self.is_sign_negative()
458 }
459
460 /// Returns `true` if `self` has a negative sign, including `-0.0`, NaNs with
461 /// negative sign bit and negative infinity.
462 ///
463 /// Note that IEEE 754 doesn't assign any meaning to the sign bit in case of
464 /// a NaN, and as Rust doesn't guarantee that the bit pattern of NaNs are
465 /// conserved over arithmetic operations, the result of `is_sign_negative` on
466 /// a NaN might produce an unexpected or non-portable result. See the [specification
467 /// of NaN bit patterns](f32#nan-bit-patterns) for more info. Use `self.signum() == -1.0`
468 /// if you need fully portable behavior (will return `false` for all NaNs).
469 ///
470 /// ```
471 /// #![feature(f128)]
472 ///
473 /// let f = 7.0_f128;
474 /// let g = -7.0_f128;
475 ///
476 /// assert!(!f.is_sign_negative());
477 /// assert!(g.is_sign_negative());
478 /// ```
479 #[inline]
480 #[must_use]
481 #[unstable(feature = "f128", issue = "116909")]
482 pub const fn is_sign_negative(self) -> bool {
483 // IEEE754 says: isSignMinus(x) is true if and only if x has negative sign. isSignMinus
484 // applies to zeros and NaNs as well.
485 // SAFETY: This is just transmuting to get the sign bit, it's fine.
486 (self.to_bits() & (1 << 127)) != 0
487 }
488
489 /// Returns the least number greater than `self`.
490 ///
491 /// Let `TINY` be the smallest representable positive `f128`. Then,
492 /// - if `self.is_nan()`, this returns `self`;
493 /// - if `self` is [`NEG_INFINITY`], this returns [`MIN`];
494 /// - if `self` is `-TINY`, this returns -0.0;
495 /// - if `self` is -0.0 or +0.0, this returns `TINY`;
496 /// - if `self` is [`MAX`] or [`INFINITY`], this returns [`INFINITY`];
497 /// - otherwise the unique least value greater than `self` is returned.
498 ///
499 /// The identity `x.next_up() == -(-x).next_down()` holds for all non-NaN `x`. When `x`
500 /// is finite `x == x.next_up().next_down()` also holds.
501 ///
502 /// ```rust
503 /// #![feature(f128)]
504 /// # // FIXME(f16_f128): remove when `eqtf2` is available
505 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
506 ///
507 /// // f128::EPSILON is the difference between 1.0 and the next number up.
508 /// assert_eq!(1.0f128.next_up(), 1.0 + f128::EPSILON);
509 /// // But not for most numbers.
510 /// assert!(0.1f128.next_up() < 0.1 + f128::EPSILON);
511 /// assert_eq!(4611686018427387904f128.next_up(), 4611686018427387904.000000000000001);
512 /// # }
513 /// ```
514 ///
515 /// This operation corresponds to IEEE-754 `nextUp`.
516 ///
517 /// [`NEG_INFINITY`]: Self::NEG_INFINITY
518 /// [`INFINITY`]: Self::INFINITY
519 /// [`MIN`]: Self::MIN
520 /// [`MAX`]: Self::MAX
521 #[inline]
522 #[doc(alias = "nextUp")]
523 #[unstable(feature = "f128", issue = "116909")]
524 pub const fn next_up(self) -> Self {
525 // Some targets violate Rust's assumption of IEEE semantics, e.g. by flushing
526 // denormals to zero. This is in general unsound and unsupported, but here
527 // we do our best to still produce the correct result on such targets.
528 let bits = self.to_bits();
529 if self.is_nan() || bits == Self::INFINITY.to_bits() {
530 return self;
531 }
532
533 let abs = bits & !Self::SIGN_MASK;
534 let next_bits = if abs == 0 {
535 Self::TINY_BITS
536 } else if bits == abs {
537 bits + 1
538 } else {
539 bits - 1
540 };
541 Self::from_bits(next_bits)
542 }
543
544 /// Returns the greatest number less than `self`.
545 ///
546 /// Let `TINY` be the smallest representable positive `f128`. Then,
547 /// - if `self.is_nan()`, this returns `self`;
548 /// - if `self` is [`INFINITY`], this returns [`MAX`];
549 /// - if `self` is `TINY`, this returns 0.0;
550 /// - if `self` is -0.0 or +0.0, this returns `-TINY`;
551 /// - if `self` is [`MIN`] or [`NEG_INFINITY`], this returns [`NEG_INFINITY`];
552 /// - otherwise the unique greatest value less than `self` is returned.
553 ///
554 /// The identity `x.next_down() == -(-x).next_up()` holds for all non-NaN `x`. When `x`
555 /// is finite `x == x.next_down().next_up()` also holds.
556 ///
557 /// ```rust
558 /// #![feature(f128)]
559 /// # // FIXME(f16_f128): remove when `eqtf2` is available
560 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
561 ///
562 /// let x = 1.0f128;
563 /// // Clamp value into range [0, 1).
564 /// let clamped = x.clamp(0.0, 1.0f128.next_down());
565 /// assert!(clamped < 1.0);
566 /// assert_eq!(clamped.next_up(), 1.0);
567 /// # }
568 /// ```
569 ///
570 /// This operation corresponds to IEEE-754 `nextDown`.
571 ///
572 /// [`NEG_INFINITY`]: Self::NEG_INFINITY
573 /// [`INFINITY`]: Self::INFINITY
574 /// [`MIN`]: Self::MIN
575 /// [`MAX`]: Self::MAX
576 #[inline]
577 #[doc(alias = "nextDown")]
578 #[unstable(feature = "f128", issue = "116909")]
579 pub const fn next_down(self) -> Self {
580 // Some targets violate Rust's assumption of IEEE semantics, e.g. by flushing
581 // denormals to zero. This is in general unsound and unsupported, but here
582 // we do our best to still produce the correct result on such targets.
583 let bits = self.to_bits();
584 if self.is_nan() || bits == Self::NEG_INFINITY.to_bits() {
585 return self;
586 }
587
588 let abs = bits & !Self::SIGN_MASK;
589 let next_bits = if abs == 0 {
590 Self::NEG_TINY_BITS
591 } else if bits == abs {
592 bits - 1
593 } else {
594 bits + 1
595 };
596 Self::from_bits(next_bits)
597 }
598
599 /// Takes the reciprocal (inverse) of a number, `1/x`.
600 ///
601 /// ```
602 /// #![feature(f128)]
603 /// # // FIXME(f16_f128): remove when `eqtf2` is available
604 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
605 ///
606 /// let x = 2.0_f128;
607 /// let abs_difference = (x.recip() - (1.0 / x)).abs();
608 ///
609 /// assert!(abs_difference <= f128::EPSILON);
610 /// # }
611 /// ```
612 #[inline]
613 #[unstable(feature = "f128", issue = "116909")]
614 #[must_use = "this returns the result of the operation, without modifying the original"]
615 pub const fn recip(self) -> Self {
616 1.0 / self
617 }
618
619 /// Converts radians to degrees.
620 ///
621 /// ```
622 /// #![feature(f128)]
623 /// # // FIXME(f16_f128): remove when `eqtf2` is available
624 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
625 ///
626 /// let angle = std::f128::consts::PI;
627 ///
628 /// let abs_difference = (angle.to_degrees() - 180.0).abs();
629 /// assert!(abs_difference <= f128::EPSILON);
630 /// # }
631 /// ```
632 #[inline]
633 #[unstable(feature = "f128", issue = "116909")]
634 #[must_use = "this returns the result of the operation, without modifying the original"]
635 pub const fn to_degrees(self) -> Self {
636 // Use a literal for better precision.
637 const PIS_IN_180: f128 = 57.2957795130823208767981548141051703324054724665643215491602_f128;
638 self * PIS_IN_180
639 }
640
641 /// Converts degrees to radians.
642 ///
643 /// ```
644 /// #![feature(f128)]
645 /// # // FIXME(f16_f128): remove when `eqtf2` is available
646 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
647 ///
648 /// let angle = 180.0f128;
649 ///
650 /// let abs_difference = (angle.to_radians() - std::f128::consts::PI).abs();
651 ///
652 /// assert!(abs_difference <= 1e-30);
653 /// # }
654 /// ```
655 #[inline]
656 #[unstable(feature = "f128", issue = "116909")]
657 #[must_use = "this returns the result of the operation, without modifying the original"]
658 pub const fn to_radians(self) -> f128 {
659 // Use a literal for better precision.
660 const RADS_PER_DEG: f128 =
661 0.0174532925199432957692369076848861271344287188854172545609719_f128;
662 self * RADS_PER_DEG
663 }
664
665 /// Returns the maximum of the two numbers, ignoring NaN.
666 ///
667 /// If one of the arguments is NaN, then the other argument is returned.
668 /// This follows the IEEE 754-2008 semantics for maxNum, except for handling of signaling NaNs;
669 /// this function handles all NaNs the same way and avoids maxNum's problems with associativity.
670 /// This also matches the behavior of libm’s fmax. In particular, if the inputs compare equal
671 /// (such as for the case of `+0.0` and `-0.0`), either input may be returned non-deterministically.
672 ///
673 /// ```
674 /// #![feature(f128)]
675 /// # // Using aarch64 because `reliable_f128_math` is needed
676 /// # #[cfg(all(target_arch = "aarch64", target_os = "linux"))] {
677 ///
678 /// let x = 1.0f128;
679 /// let y = 2.0f128;
680 ///
681 /// assert_eq!(x.max(y), y);
682 /// # }
683 /// ```
684 #[inline]
685 #[unstable(feature = "f128", issue = "116909")]
686 #[rustc_const_unstable(feature = "f128", issue = "116909")]
687 #[must_use = "this returns the result of the comparison, without modifying either input"]
688 pub const fn max(self, other: f128) -> f128 {
689 intrinsics::maxnumf128(self, other)
690 }
691
692 /// Returns the minimum of the two numbers, ignoring NaN.
693 ///
694 /// If one of the arguments is NaN, then the other argument is returned.
695 /// This follows the IEEE 754-2008 semantics for minNum, except for handling of signaling NaNs;
696 /// this function handles all NaNs the same way and avoids minNum's problems with associativity.
697 /// This also matches the behavior of libm’s fmin. In particular, if the inputs compare equal
698 /// (such as for the case of `+0.0` and `-0.0`), either input may be returned non-deterministically.
699 ///
700 /// ```
701 /// #![feature(f128)]
702 /// # // Using aarch64 because `reliable_f128_math` is needed
703 /// # #[cfg(all(target_arch = "aarch64", target_os = "linux"))] {
704 ///
705 /// let x = 1.0f128;
706 /// let y = 2.0f128;
707 ///
708 /// assert_eq!(x.min(y), x);
709 /// # }
710 /// ```
711 #[inline]
712 #[unstable(feature = "f128", issue = "116909")]
713 #[rustc_const_unstable(feature = "f128", issue = "116909")]
714 #[must_use = "this returns the result of the comparison, without modifying either input"]
715 pub const fn min(self, other: f128) -> f128 {
716 intrinsics::minnumf128(self, other)
717 }
718
719 /// Returns the maximum of the two numbers, propagating NaN.
720 ///
721 /// This returns NaN when *either* argument is NaN, as opposed to
722 /// [`f128::max`] which only returns NaN when *both* arguments are NaN.
723 ///
724 /// ```
725 /// #![feature(f128)]
726 /// #![feature(float_minimum_maximum)]
727 /// # // Using aarch64 because `reliable_f128_math` is needed
728 /// # #[cfg(all(target_arch = "aarch64", target_os = "linux"))] {
729 ///
730 /// let x = 1.0f128;
731 /// let y = 2.0f128;
732 ///
733 /// assert_eq!(x.maximum(y), y);
734 /// assert!(x.maximum(f128::NAN).is_nan());
735 /// # }
736 /// ```
737 ///
738 /// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the greater
739 /// of the two numbers. For this operation, -0.0 is considered to be less than +0.0.
740 /// Note that this follows the semantics specified in IEEE 754-2019.
741 ///
742 /// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN
743 /// operand is conserved; see the [specification of NaN bit patterns](f32#nan-bit-patterns) for more info.
744 #[inline]
745 #[unstable(feature = "f128", issue = "116909")]
746 // #[unstable(feature = "float_minimum_maximum", issue = "91079")]
747 #[must_use = "this returns the result of the comparison, without modifying either input"]
748 pub const fn maximum(self, other: f128) -> f128 {
749 if self > other {
750 self
751 } else if other > self {
752 other
753 } else if self == other {
754 if self.is_sign_positive() && other.is_sign_negative() { self } else { other }
755 } else {
756 self + other
757 }
758 }
759
760 /// Returns the minimum of the two numbers, propagating NaN.
761 ///
762 /// This returns NaN when *either* argument is NaN, as opposed to
763 /// [`f128::min`] which only returns NaN when *both* arguments are NaN.
764 ///
765 /// ```
766 /// #![feature(f128)]
767 /// #![feature(float_minimum_maximum)]
768 /// # // Using aarch64 because `reliable_f128_math` is needed
769 /// # #[cfg(all(target_arch = "aarch64", target_os = "linux"))] {
770 ///
771 /// let x = 1.0f128;
772 /// let y = 2.0f128;
773 ///
774 /// assert_eq!(x.minimum(y), x);
775 /// assert!(x.minimum(f128::NAN).is_nan());
776 /// # }
777 /// ```
778 ///
779 /// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the lesser
780 /// of the two numbers. For this operation, -0.0 is considered to be less than +0.0.
781 /// Note that this follows the semantics specified in IEEE 754-2019.
782 ///
783 /// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN
784 /// operand is conserved; see the [specification of NaN bit patterns](f32#nan-bit-patterns) for more info.
785 #[inline]
786 #[unstable(feature = "f128", issue = "116909")]
787 // #[unstable(feature = "float_minimum_maximum", issue = "91079")]
788 #[must_use = "this returns the result of the comparison, without modifying either input"]
789 pub const fn minimum(self, other: f128) -> f128 {
790 if self < other {
791 self
792 } else if other < self {
793 other
794 } else if self == other {
795 if self.is_sign_negative() && other.is_sign_positive() { self } else { other }
796 } else {
797 // At least one input is NaN. Use `+` to perform NaN propagation and quieting.
798 self + other
799 }
800 }
801
802 /// Calculates the middle point of `self` and `rhs`.
803 ///
804 /// This returns NaN when *either* argument is NaN or if a combination of
805 /// +inf and -inf is provided as arguments.
806 ///
807 /// # Examples
808 ///
809 /// ```
810 /// #![feature(f128)]
811 /// # // Using aarch64 because `reliable_f128_math` is needed
812 /// # #[cfg(all(target_arch = "aarch64", target_os = "linux"))] {
813 ///
814 /// assert_eq!(1f128.midpoint(4.0), 2.5);
815 /// assert_eq!((-5.5f128).midpoint(8.0), 1.25);
816 /// # }
817 /// ```
818 #[inline]
819 #[unstable(feature = "f128", issue = "116909")]
820 #[rustc_const_unstable(feature = "f128", issue = "116909")]
821 pub const fn midpoint(self, other: f128) -> f128 {
822 const LO: f128 = f128::MIN_POSITIVE * 2.;
823 const HI: f128 = f128::MAX / 2.;
824
825 let (a, b) = (self, other);
826 let abs_a = a.abs();
827 let abs_b = b.abs();
828
829 if abs_a <= HI && abs_b <= HI {
830 // Overflow is impossible
831 (a + b) / 2.
832 } else if abs_a < LO {
833 // Not safe to halve `a` (would underflow)
834 a + (b / 2.)
835 } else if abs_b < LO {
836 // Not safe to halve `b` (would underflow)
837 (a / 2.) + b
838 } else {
839 // Safe to halve `a` and `b`
840 (a / 2.) + (b / 2.)
841 }
842 }
843
844 /// Rounds toward zero and converts to any primitive integer type,
845 /// assuming that the value is finite and fits in that type.
846 ///
847 /// ```
848 /// #![feature(f128)]
849 /// # // FIXME(f16_f128): remove when `float*itf` is available
850 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
851 ///
852 /// let value = 4.6_f128;
853 /// let rounded = unsafe { value.to_int_unchecked::<u16>() };
854 /// assert_eq!(rounded, 4);
855 ///
856 /// let value = -128.9_f128;
857 /// let rounded = unsafe { value.to_int_unchecked::<i8>() };
858 /// assert_eq!(rounded, i8::MIN);
859 /// # }
860 /// ```
861 ///
862 /// # Safety
863 ///
864 /// The value must:
865 ///
866 /// * Not be `NaN`
867 /// * Not be infinite
868 /// * Be representable in the return type `Int`, after truncating off its fractional part
869 #[inline]
870 #[unstable(feature = "f128", issue = "116909")]
871 #[must_use = "this returns the result of the operation, without modifying the original"]
872 pub unsafe fn to_int_unchecked<Int>(self) -> Int
873 where
874 Self: FloatToInt<Int>,
875 {
876 // SAFETY: the caller must uphold the safety contract for
877 // `FloatToInt::to_int_unchecked`.
878 unsafe { FloatToInt::<Int>::to_int_unchecked(self) }
879 }
880
881 /// Raw transmutation to `u128`.
882 ///
883 /// This is currently identical to `transmute::<f128, u128>(self)` on all platforms.
884 ///
885 /// See [`from_bits`](#method.from_bits) for some discussion of the
886 /// portability of this operation (there are almost no issues).
887 ///
888 /// Note that this function is distinct from `as` casting, which attempts to
889 /// preserve the *numeric* value, and not the bitwise value.
890 ///
891 /// ```
892 /// #![feature(f128)]
893 ///
894 /// # // FIXME(f16_f128): enable this once const casting works
895 /// # // assert_ne!((1f128).to_bits(), 1f128 as u128); // to_bits() is not casting!
896 /// assert_eq!((12.5f128).to_bits(), 0x40029000000000000000000000000000);
897 /// ```
898 #[inline]
899 #[unstable(feature = "f128", issue = "116909")]
900 #[must_use = "this returns the result of the operation, without modifying the original"]
901 pub const fn to_bits(self) -> u128 {
902 // SAFETY: `u128` is a plain old datatype so we can always transmute to it.
903 unsafe { mem::transmute(self) }
904 }
905
906 /// Raw transmutation from `u128`.
907 ///
908 /// This is currently identical to `transmute::<u128, f128>(v)` on all platforms.
909 /// It turns out this is incredibly portable, for two reasons:
910 ///
911 /// * Floats and Ints have the same endianness on all supported platforms.
912 /// * IEEE 754 very precisely specifies the bit layout of floats.
913 ///
914 /// However there is one caveat: prior to the 2008 version of IEEE 754, how
915 /// to interpret the NaN signaling bit wasn't actually specified. Most platforms
916 /// (notably x86 and ARM) picked the interpretation that was ultimately
917 /// standardized in 2008, but some didn't (notably MIPS). As a result, all
918 /// signaling NaNs on MIPS are quiet NaNs on x86, and vice-versa.
919 ///
920 /// Rather than trying to preserve signaling-ness cross-platform, this
921 /// implementation favors preserving the exact bits. This means that
922 /// any payloads encoded in NaNs will be preserved even if the result of
923 /// this method is sent over the network from an x86 machine to a MIPS one.
924 ///
925 /// If the results of this method are only manipulated by the same
926 /// architecture that produced them, then there is no portability concern.
927 ///
928 /// If the input isn't NaN, then there is no portability concern.
929 ///
930 /// If you don't care about signalingness (very likely), then there is no
931 /// portability concern.
932 ///
933 /// Note that this function is distinct from `as` casting, which attempts to
934 /// preserve the *numeric* value, and not the bitwise value.
935 ///
936 /// ```
937 /// #![feature(f128)]
938 /// # // FIXME(f16_f128): remove when `eqtf2` is available
939 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
940 ///
941 /// let v = f128::from_bits(0x40029000000000000000000000000000);
942 /// assert_eq!(v, 12.5);
943 /// # }
944 /// ```
945 #[inline]
946 #[must_use]
947 #[unstable(feature = "f128", issue = "116909")]
948 pub const fn from_bits(v: u128) -> Self {
949 // It turns out the safety issues with sNaN were overblown! Hooray!
950 // SAFETY: `u128` is a plain old datatype so we can always transmute from it.
951 unsafe { mem::transmute(v) }
952 }
953
954 /// Returns the memory representation of this floating point number as a byte array in
955 /// big-endian (network) byte order.
956 ///
957 /// See [`from_bits`](Self::from_bits) for some discussion of the
958 /// portability of this operation (there are almost no issues).
959 ///
960 /// # Examples
961 ///
962 /// ```
963 /// #![feature(f128)]
964 ///
965 /// let bytes = 12.5f128.to_be_bytes();
966 /// assert_eq!(
967 /// bytes,
968 /// [0x40, 0x02, 0x90, 0x00, 0x00, 0x00, 0x00, 0x00,
969 /// 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
970 /// );
971 /// ```
972 #[inline]
973 #[unstable(feature = "f128", issue = "116909")]
974 #[must_use = "this returns the result of the operation, without modifying the original"]
975 pub const fn to_be_bytes(self) -> [u8; 16] {
976 self.to_bits().to_be_bytes()
977 }
978
979 /// Returns the memory representation of this floating point number as a byte array in
980 /// little-endian byte order.
981 ///
982 /// See [`from_bits`](Self::from_bits) for some discussion of the
983 /// portability of this operation (there are almost no issues).
984 ///
985 /// # Examples
986 ///
987 /// ```
988 /// #![feature(f128)]
989 ///
990 /// let bytes = 12.5f128.to_le_bytes();
991 /// assert_eq!(
992 /// bytes,
993 /// [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
994 /// 0x00, 0x00, 0x00, 0x00, 0x00, 0x90, 0x02, 0x40]
995 /// );
996 /// ```
997 #[inline]
998 #[unstable(feature = "f128", issue = "116909")]
999 #[must_use = "this returns the result of the operation, without modifying the original"]
1000 pub const fn to_le_bytes(self) -> [u8; 16] {
1001 self.to_bits().to_le_bytes()
1002 }
1003
1004 /// Returns the memory representation of this floating point number as a byte array in
1005 /// native byte order.
1006 ///
1007 /// As the target platform's native endianness is used, portable code
1008 /// should use [`to_be_bytes`] or [`to_le_bytes`], as appropriate, instead.
1009 ///
1010 /// [`to_be_bytes`]: f128::to_be_bytes
1011 /// [`to_le_bytes`]: f128::to_le_bytes
1012 ///
1013 /// See [`from_bits`](Self::from_bits) for some discussion of the
1014 /// portability of this operation (there are almost no issues).
1015 ///
1016 /// # Examples
1017 ///
1018 /// ```
1019 /// #![feature(f128)]
1020 ///
1021 /// let bytes = 12.5f128.to_ne_bytes();
1022 /// assert_eq!(
1023 /// bytes,
1024 /// if cfg!(target_endian = "big") {
1025 /// [0x40, 0x02, 0x90, 0x00, 0x00, 0x00, 0x00, 0x00,
1026 /// 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
1027 /// } else {
1028 /// [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
1029 /// 0x00, 0x00, 0x00, 0x00, 0x00, 0x90, 0x02, 0x40]
1030 /// }
1031 /// );
1032 /// ```
1033 #[inline]
1034 #[unstable(feature = "f128", issue = "116909")]
1035 #[must_use = "this returns the result of the operation, without modifying the original"]
1036 pub const fn to_ne_bytes(self) -> [u8; 16] {
1037 self.to_bits().to_ne_bytes()
1038 }
1039
1040 /// Creates a floating point value from its representation as a byte array in big endian.
1041 ///
1042 /// See [`from_bits`](Self::from_bits) for some discussion of the
1043 /// portability of this operation (there are almost no issues).
1044 ///
1045 /// # Examples
1046 ///
1047 /// ```
1048 /// #![feature(f128)]
1049 /// # // FIXME(f16_f128): remove when `eqtf2` is available
1050 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1051 ///
1052 /// let value = f128::from_be_bytes(
1053 /// [0x40, 0x02, 0x90, 0x00, 0x00, 0x00, 0x00, 0x00,
1054 /// 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
1055 /// );
1056 /// assert_eq!(value, 12.5);
1057 /// # }
1058 /// ```
1059 #[inline]
1060 #[must_use]
1061 #[unstable(feature = "f128", issue = "116909")]
1062 pub const fn from_be_bytes(bytes: [u8; 16]) -> Self {
1063 Self::from_bits(u128::from_be_bytes(bytes))
1064 }
1065
1066 /// Creates a floating point value from its representation as a byte array in little endian.
1067 ///
1068 /// See [`from_bits`](Self::from_bits) for some discussion of the
1069 /// portability of this operation (there are almost no issues).
1070 ///
1071 /// # Examples
1072 ///
1073 /// ```
1074 /// #![feature(f128)]
1075 /// # // FIXME(f16_f128): remove when `eqtf2` is available
1076 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1077 ///
1078 /// let value = f128::from_le_bytes(
1079 /// [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
1080 /// 0x00, 0x00, 0x00, 0x00, 0x00, 0x90, 0x02, 0x40]
1081 /// );
1082 /// assert_eq!(value, 12.5);
1083 /// # }
1084 /// ```
1085 #[inline]
1086 #[must_use]
1087 #[unstable(feature = "f128", issue = "116909")]
1088 pub const fn from_le_bytes(bytes: [u8; 16]) -> Self {
1089 Self::from_bits(u128::from_le_bytes(bytes))
1090 }
1091
1092 /// Creates a floating point value from its representation as a byte array in native endian.
1093 ///
1094 /// As the target platform's native endianness is used, portable code
1095 /// likely wants to use [`from_be_bytes`] or [`from_le_bytes`], as
1096 /// appropriate instead.
1097 ///
1098 /// [`from_be_bytes`]: f128::from_be_bytes
1099 /// [`from_le_bytes`]: f128::from_le_bytes
1100 ///
1101 /// See [`from_bits`](Self::from_bits) for some discussion of the
1102 /// portability of this operation (there are almost no issues).
1103 ///
1104 /// # Examples
1105 ///
1106 /// ```
1107 /// #![feature(f128)]
1108 /// # // FIXME(f16_f128): remove when `eqtf2` is available
1109 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1110 ///
1111 /// let value = f128::from_ne_bytes(if cfg!(target_endian = "big") {
1112 /// [0x40, 0x02, 0x90, 0x00, 0x00, 0x00, 0x00, 0x00,
1113 /// 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
1114 /// } else {
1115 /// [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
1116 /// 0x00, 0x00, 0x00, 0x00, 0x00, 0x90, 0x02, 0x40]
1117 /// });
1118 /// assert_eq!(value, 12.5);
1119 /// # }
1120 /// ```
1121 #[inline]
1122 #[must_use]
1123 #[unstable(feature = "f128", issue = "116909")]
1124 pub const fn from_ne_bytes(bytes: [u8; 16]) -> Self {
1125 Self::from_bits(u128::from_ne_bytes(bytes))
1126 }
1127
1128 /// Returns the ordering between `self` and `other`.
1129 ///
1130 /// Unlike the standard partial comparison between floating point numbers,
1131 /// this comparison always produces an ordering in accordance to
1132 /// the `totalOrder` predicate as defined in the IEEE 754 (2008 revision)
1133 /// floating point standard. The values are ordered in the following sequence:
1134 ///
1135 /// - negative quiet NaN
1136 /// - negative signaling NaN
1137 /// - negative infinity
1138 /// - negative numbers
1139 /// - negative subnormal numbers
1140 /// - negative zero
1141 /// - positive zero
1142 /// - positive subnormal numbers
1143 /// - positive numbers
1144 /// - positive infinity
1145 /// - positive signaling NaN
1146 /// - positive quiet NaN.
1147 ///
1148 /// The ordering established by this function does not always agree with the
1149 /// [`PartialOrd`] and [`PartialEq`] implementations of `f128`. For example,
1150 /// they consider negative and positive zero equal, while `total_cmp`
1151 /// doesn't.
1152 ///
1153 /// The interpretation of the signaling NaN bit follows the definition in
1154 /// the IEEE 754 standard, which may not match the interpretation by some of
1155 /// the older, non-conformant (e.g. MIPS) hardware implementations.
1156 ///
1157 /// # Example
1158 ///
1159 /// ```
1160 /// #![feature(f128)]
1161 ///
1162 /// struct GoodBoy {
1163 /// name: &'static str,
1164 /// weight: f128,
1165 /// }
1166 ///
1167 /// let mut bois = vec![
1168 /// GoodBoy { name: "Pucci", weight: 0.1 },
1169 /// GoodBoy { name: "Woofer", weight: 99.0 },
1170 /// GoodBoy { name: "Yapper", weight: 10.0 },
1171 /// GoodBoy { name: "Chonk", weight: f128::INFINITY },
1172 /// GoodBoy { name: "Abs. Unit", weight: f128::NAN },
1173 /// GoodBoy { name: "Floaty", weight: -5.0 },
1174 /// ];
1175 ///
1176 /// bois.sort_by(|a, b| a.weight.total_cmp(&b.weight));
1177 ///
1178 /// // `f128::NAN` could be positive or negative, which will affect the sort order.
1179 /// if f128::NAN.is_sign_negative() {
1180 /// bois.into_iter().map(|b| b.weight)
1181 /// .zip([f128::NAN, -5.0, 0.1, 10.0, 99.0, f128::INFINITY].iter())
1182 /// .for_each(|(a, b)| assert_eq!(a.to_bits(), b.to_bits()))
1183 /// } else {
1184 /// bois.into_iter().map(|b| b.weight)
1185 /// .zip([-5.0, 0.1, 10.0, 99.0, f128::INFINITY, f128::NAN].iter())
1186 /// .for_each(|(a, b)| assert_eq!(a.to_bits(), b.to_bits()))
1187 /// }
1188 /// ```
1189 #[inline]
1190 #[must_use]
1191 #[unstable(feature = "f128", issue = "116909")]
1192 pub fn total_cmp(&self, other: &Self) -> crate::cmp::Ordering {
1193 let mut left = self.to_bits() as i128;
1194 let mut right = other.to_bits() as i128;
1195
1196 // In case of negatives, flip all the bits except the sign
1197 // to achieve a similar layout as two's complement integers
1198 //
1199 // Why does this work? IEEE 754 floats consist of three fields:
1200 // Sign bit, exponent and mantissa. The set of exponent and mantissa
1201 // fields as a whole have the property that their bitwise order is
1202 // equal to the numeric magnitude where the magnitude is defined.
1203 // The magnitude is not normally defined on NaN values, but
1204 // IEEE 754 totalOrder defines the NaN values also to follow the
1205 // bitwise order. This leads to order explained in the doc comment.
1206 // However, the representation of magnitude is the same for negative
1207 // and positive numbers – only the sign bit is different.
1208 // To easily compare the floats as signed integers, we need to
1209 // flip the exponent and mantissa bits in case of negative numbers.
1210 // We effectively convert the numbers to "two's complement" form.
1211 //
1212 // To do the flipping, we construct a mask and XOR against it.
1213 // We branchlessly calculate an "all-ones except for the sign bit"
1214 // mask from negative-signed values: right shifting sign-extends
1215 // the integer, so we "fill" the mask with sign bits, and then
1216 // convert to unsigned to push one more zero bit.
1217 // On positive values, the mask is all zeros, so it's a no-op.
1218 left ^= (((left >> 127) as u128) >> 1) as i128;
1219 right ^= (((right >> 127) as u128) >> 1) as i128;
1220
1221 left.cmp(&right)
1222 }
1223
1224 /// Restrict a value to a certain interval unless it is NaN.
1225 ///
1226 /// Returns `max` if `self` is greater than `max`, and `min` if `self` is
1227 /// less than `min`. Otherwise this returns `self`.
1228 ///
1229 /// Note that this function returns NaN if the initial value was NaN as
1230 /// well.
1231 ///
1232 /// # Panics
1233 ///
1234 /// Panics if `min > max`, `min` is NaN, or `max` is NaN.
1235 ///
1236 /// # Examples
1237 ///
1238 /// ```
1239 /// #![feature(f128)]
1240 /// # // FIXME(f16_f128): remove when `{eq,gt,unord}tf` are available
1241 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1242 ///
1243 /// assert!((-3.0f128).clamp(-2.0, 1.0) == -2.0);
1244 /// assert!((0.0f128).clamp(-2.0, 1.0) == 0.0);
1245 /// assert!((2.0f128).clamp(-2.0, 1.0) == 1.0);
1246 /// assert!((f128::NAN).clamp(-2.0, 1.0).is_nan());
1247 /// # }
1248 /// ```
1249 #[inline]
1250 #[unstable(feature = "f128", issue = "116909")]
1251 #[must_use = "method returns a new number and does not mutate the original value"]
1252 pub const fn clamp(mut self, min: f128, max: f128) -> f128 {
1253 const_assert!(
1254 min <= max,
1255 "min > max, or either was NaN",
1256 "min > max, or either was NaN. min = {min:?}, max = {max:?}",
1257 min: f128,
1258 max: f128,
1259 );
1260
1261 if self < min {
1262 self = min;
1263 }
1264 if self > max {
1265 self = max;
1266 }
1267 self
1268 }
1269
1270 /// Computes the absolute value of `self`.
1271 ///
1272 /// This function always returns the precise result.
1273 ///
1274 /// # Examples
1275 ///
1276 /// ```
1277 /// #![feature(f128)]
1278 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1279 ///
1280 /// let x = 3.5_f128;
1281 /// let y = -3.5_f128;
1282 ///
1283 /// assert_eq!(x.abs(), x);
1284 /// assert_eq!(y.abs(), -y);
1285 ///
1286 /// assert!(f128::NAN.abs().is_nan());
1287 /// # }
1288 /// ```
1289 #[inline]
1290 #[unstable(feature = "f128", issue = "116909")]
1291 #[rustc_const_unstable(feature = "f128", issue = "116909")]
1292 #[must_use = "method returns a new number and does not mutate the original value"]
1293 pub const fn abs(self) -> Self {
1294 // FIXME(f16_f128): replace with `intrinsics::fabsf128` when available
1295 // We don't do this now because LLVM has lowering bugs for f128 math.
1296 Self::from_bits(self.to_bits() & !(1 << 127))
1297 }
1298
1299 /// Returns a number that represents the sign of `self`.
1300 ///
1301 /// - `1.0` if the number is positive, `+0.0` or `INFINITY`
1302 /// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
1303 /// - NaN if the number is NaN
1304 ///
1305 /// # Examples
1306 ///
1307 /// ```
1308 /// #![feature(f128)]
1309 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1310 ///
1311 /// let f = 3.5_f128;
1312 ///
1313 /// assert_eq!(f.signum(), 1.0);
1314 /// assert_eq!(f128::NEG_INFINITY.signum(), -1.0);
1315 ///
1316 /// assert!(f128::NAN.signum().is_nan());
1317 /// # }
1318 /// ```
1319 #[inline]
1320 #[unstable(feature = "f128", issue = "116909")]
1321 #[rustc_const_unstable(feature = "f128", issue = "116909")]
1322 #[must_use = "method returns a new number and does not mutate the original value"]
1323 pub const fn signum(self) -> f128 {
1324 if self.is_nan() { Self::NAN } else { 1.0_f128.copysign(self) }
1325 }
1326
1327 /// Returns a number composed of the magnitude of `self` and the sign of
1328 /// `sign`.
1329 ///
1330 /// Equal to `self` if the sign of `self` and `sign` are the same, otherwise equal to `-self`.
1331 /// If `self` is a NaN, then a NaN with the same payload as `self` and the sign bit of `sign` is
1332 /// returned.
1333 ///
1334 /// If `sign` is a NaN, then this operation will still carry over its sign into the result. Note
1335 /// that IEEE 754 doesn't assign any meaning to the sign bit in case of a NaN, and as Rust
1336 /// doesn't guarantee that the bit pattern of NaNs are conserved over arithmetic operations, the
1337 /// result of `copysign` with `sign` being a NaN might produce an unexpected or non-portable
1338 /// result. See the [specification of NaN bit patterns](primitive@f32#nan-bit-patterns) for more
1339 /// info.
1340 ///
1341 /// # Examples
1342 ///
1343 /// ```
1344 /// #![feature(f128)]
1345 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1346 ///
1347 /// let f = 3.5_f128;
1348 ///
1349 /// assert_eq!(f.copysign(0.42), 3.5_f128);
1350 /// assert_eq!(f.copysign(-0.42), -3.5_f128);
1351 /// assert_eq!((-f).copysign(0.42), 3.5_f128);
1352 /// assert_eq!((-f).copysign(-0.42), -3.5_f128);
1353 ///
1354 /// assert!(f128::NAN.copysign(1.0).is_nan());
1355 /// # }
1356 /// ```
1357 #[inline]
1358 #[unstable(feature = "f128", issue = "116909")]
1359 #[rustc_const_unstable(feature = "f128", issue = "116909")]
1360 #[must_use = "method returns a new number and does not mutate the original value"]
1361 pub const fn copysign(self, sign: f128) -> f128 {
1362 // SAFETY: this is actually a safe intrinsic
1363 unsafe { intrinsics::copysignf128(self, sign) }
1364 }
1365}
1366