core/num/f16.rs
1//! Constants for the `f16` half-precision floating point type.
2//!
3//! *[See also the `f16` primitive type][f16].*
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 `f16` type.
11
12#![unstable(feature = "f16", 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 = "f16", issue = "116909")]
21pub mod consts {
22 // FIXME: replace with mathematical constants from cmath.
23
24 /// Archimedes' constant (π)
25 #[unstable(feature = "f16", issue = "116909")]
26 pub const PI: f16 = 3.14159265358979323846264338327950288_f16;
27
28 /// The full circle constant (τ)
29 ///
30 /// Equal to 2π.
31 #[unstable(feature = "f16", issue = "116909")]
32 pub const TAU: f16 = 6.28318530717958647692528676655900577_f16;
33
34 /// The golden ratio (φ)
35 #[unstable(feature = "f16", issue = "116909")]
36 // Also, #[unstable(feature = "more_float_constants", issue = "103883")]
37 pub const PHI: f16 = 1.618033988749894848204586834365638118_f16;
38
39 /// The Euler-Mascheroni constant (γ)
40 #[unstable(feature = "f16", issue = "116909")]
41 // Also, #[unstable(feature = "more_float_constants", issue = "103883")]
42 pub const EGAMMA: f16 = 0.577215664901532860606512090082402431_f16;
43
44 /// π/2
45 #[unstable(feature = "f16", issue = "116909")]
46 pub const FRAC_PI_2: f16 = 1.57079632679489661923132169163975144_f16;
47
48 /// π/3
49 #[unstable(feature = "f16", issue = "116909")]
50 pub const FRAC_PI_3: f16 = 1.04719755119659774615421446109316763_f16;
51
52 /// π/4
53 #[unstable(feature = "f16", issue = "116909")]
54 pub const FRAC_PI_4: f16 = 0.785398163397448309615660845819875721_f16;
55
56 /// π/6
57 #[unstable(feature = "f16", issue = "116909")]
58 pub const FRAC_PI_6: f16 = 0.52359877559829887307710723054658381_f16;
59
60 /// π/8
61 #[unstable(feature = "f16", issue = "116909")]
62 pub const FRAC_PI_8: f16 = 0.39269908169872415480783042290993786_f16;
63
64 /// 1/π
65 #[unstable(feature = "f16", issue = "116909")]
66 pub const FRAC_1_PI: f16 = 0.318309886183790671537767526745028724_f16;
67
68 /// 1/sqrt(π)
69 #[unstable(feature = "f16", issue = "116909")]
70 // Also, #[unstable(feature = "more_float_constants", issue = "103883")]
71 pub const FRAC_1_SQRT_PI: f16 = 0.564189583547756286948079451560772586_f16;
72
73 /// 1/sqrt(2π)
74 #[doc(alias = "FRAC_1_SQRT_TAU")]
75 #[unstable(feature = "f16", issue = "116909")]
76 // Also, #[unstable(feature = "more_float_constants", issue = "103883")]
77 pub const FRAC_1_SQRT_2PI: f16 = 0.398942280401432677939946059934381868_f16;
78
79 /// 2/π
80 #[unstable(feature = "f16", issue = "116909")]
81 pub const FRAC_2_PI: f16 = 0.636619772367581343075535053490057448_f16;
82
83 /// 2/sqrt(π)
84 #[unstable(feature = "f16", issue = "116909")]
85 pub const FRAC_2_SQRT_PI: f16 = 1.12837916709551257389615890312154517_f16;
86
87 /// sqrt(2)
88 #[unstable(feature = "f16", issue = "116909")]
89 pub const SQRT_2: f16 = 1.41421356237309504880168872420969808_f16;
90
91 /// 1/sqrt(2)
92 #[unstable(feature = "f16", issue = "116909")]
93 pub const FRAC_1_SQRT_2: f16 = 0.707106781186547524400844362104849039_f16;
94
95 /// sqrt(3)
96 #[unstable(feature = "f16", issue = "116909")]
97 // Also, #[unstable(feature = "more_float_constants", issue = "103883")]
98 pub const SQRT_3: f16 = 1.732050807568877293527446341505872367_f16;
99
100 /// 1/sqrt(3)
101 #[unstable(feature = "f16", issue = "116909")]
102 // Also, #[unstable(feature = "more_float_constants", issue = "103883")]
103 pub const FRAC_1_SQRT_3: f16 = 0.577350269189625764509148780501957456_f16;
104
105 /// Euler's number (e)
106 #[unstable(feature = "f16", issue = "116909")]
107 pub const E: f16 = 2.71828182845904523536028747135266250_f16;
108
109 /// log<sub>2</sub>(10)
110 #[unstable(feature = "f16", issue = "116909")]
111 pub const LOG2_10: f16 = 3.32192809488736234787031942948939018_f16;
112
113 /// log<sub>2</sub>(e)
114 #[unstable(feature = "f16", issue = "116909")]
115 pub const LOG2_E: f16 = 1.44269504088896340735992468100189214_f16;
116
117 /// log<sub>10</sub>(2)
118 #[unstable(feature = "f16", issue = "116909")]
119 pub const LOG10_2: f16 = 0.301029995663981195213738894724493027_f16;
120
121 /// log<sub>10</sub>(e)
122 #[unstable(feature = "f16", issue = "116909")]
123 pub const LOG10_E: f16 = 0.434294481903251827651128918916605082_f16;
124
125 /// ln(2)
126 #[unstable(feature = "f16", issue = "116909")]
127 pub const LN_2: f16 = 0.693147180559945309417232121458176568_f16;
128
129 /// ln(10)
130 #[unstable(feature = "f16", issue = "116909")]
131 pub const LN_10: f16 = 2.30258509299404568401799145468436421_f16;
132}
133
134impl f16 {
135 // FIXME(f16_f128): almost all methods in this `impl` are missing examples and a const
136 // implementation. Add these once we can run code on all platforms and have f16/f128 in CTFE.
137
138 /// The radix or base of the internal representation of `f16`.
139 #[unstable(feature = "f16", issue = "116909")]
140 pub const RADIX: u32 = 2;
141
142 /// Number of significant digits in base 2.
143 #[unstable(feature = "f16", issue = "116909")]
144 pub const MANTISSA_DIGITS: u32 = 11;
145
146 /// Approximate number of significant digits in base 10.
147 ///
148 /// This is the maximum <i>x</i> such that any decimal number with <i>x</i>
149 /// significant digits can be converted to `f16` and back without loss.
150 ///
151 /// Equal to floor(log<sub>10</sub> 2<sup>[`MANTISSA_DIGITS`] − 1</sup>).
152 ///
153 /// [`MANTISSA_DIGITS`]: f16::MANTISSA_DIGITS
154 #[unstable(feature = "f16", issue = "116909")]
155 pub const DIGITS: u32 = 3;
156
157 /// [Machine epsilon] value for `f16`.
158 ///
159 /// This is the difference between `1.0` and the next larger representable number.
160 ///
161 /// Equal to 2<sup>1 − [`MANTISSA_DIGITS`]</sup>.
162 ///
163 /// [Machine epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon
164 /// [`MANTISSA_DIGITS`]: f16::MANTISSA_DIGITS
165 #[unstable(feature = "f16", issue = "116909")]
166 pub const EPSILON: f16 = 9.7656e-4_f16;
167
168 /// Smallest finite `f16` value.
169 ///
170 /// Equal to −[`MAX`].
171 ///
172 /// [`MAX`]: f16::MAX
173 #[unstable(feature = "f16", issue = "116909")]
174 pub const MIN: f16 = -6.5504e+4_f16;
175 /// Smallest positive normal `f16` value.
176 ///
177 /// Equal to 2<sup>[`MIN_EXP`] − 1</sup>.
178 ///
179 /// [`MIN_EXP`]: f16::MIN_EXP
180 #[unstable(feature = "f16", issue = "116909")]
181 pub const MIN_POSITIVE: f16 = 6.1035e-5_f16;
182 /// Largest finite `f16` value.
183 ///
184 /// Equal to
185 /// (1 − 2<sup>−[`MANTISSA_DIGITS`]</sup>) 2<sup>[`MAX_EXP`]</sup>.
186 ///
187 /// [`MANTISSA_DIGITS`]: f16::MANTISSA_DIGITS
188 /// [`MAX_EXP`]: f16::MAX_EXP
189 #[unstable(feature = "f16", issue = "116909")]
190 pub const MAX: f16 = 6.5504e+4_f16;
191
192 /// One greater than the minimum possible normal power of 2 exponent.
193 ///
194 /// If <i>x</i> = `MIN_EXP`, then normal numbers
195 /// ≥ 0.5 × 2<sup><i>x</i></sup>.
196 #[unstable(feature = "f16", issue = "116909")]
197 pub const MIN_EXP: i32 = -13;
198 /// Maximum possible power of 2 exponent.
199 ///
200 /// If <i>x</i> = `MAX_EXP`, then normal numbers
201 /// < 1 × 2<sup><i>x</i></sup>.
202 #[unstable(feature = "f16", issue = "116909")]
203 pub const MAX_EXP: i32 = 16;
204
205 /// Minimum <i>x</i> for which 10<sup><i>x</i></sup> is normal.
206 ///
207 /// Equal to ceil(log<sub>10</sub> [`MIN_POSITIVE`]).
208 ///
209 /// [`MIN_POSITIVE`]: f16::MIN_POSITIVE
210 #[unstable(feature = "f16", issue = "116909")]
211 pub const MIN_10_EXP: i32 = -4;
212 /// Maximum <i>x</i> for which 10<sup><i>x</i></sup> is normal.
213 ///
214 /// Equal to floor(log<sub>10</sub> [`MAX`]).
215 ///
216 /// [`MAX`]: f16::MAX
217 #[unstable(feature = "f16", issue = "116909")]
218 pub const MAX_10_EXP: i32 = 4;
219
220 /// Not a Number (NaN).
221 ///
222 /// Note that IEEE 754 doesn't define just a single NaN value; a plethora of bit patterns are
223 /// considered to be NaN. Furthermore, the standard makes a difference between a "signaling" and
224 /// a "quiet" NaN, and allows inspecting its "payload" (the unspecified bits in the bit pattern)
225 /// and its sign. See the [specification of NaN bit patterns](f32#nan-bit-patterns) for more
226 /// info.
227 ///
228 /// This constant is guaranteed to be a quiet NaN (on targets that follow the Rust assumptions
229 /// that the quiet/signaling bit being set to 1 indicates a quiet NaN). Beyond that, nothing is
230 /// guaranteed about the specific bit pattern chosen here: both payload and sign are arbitrary.
231 /// The concrete bit pattern may change across Rust versions and target platforms.
232 #[allow(clippy::eq_op)]
233 #[rustc_diagnostic_item = "f16_nan"]
234 #[unstable(feature = "f16", issue = "116909")]
235 pub const NAN: f16 = 0.0_f16 / 0.0_f16;
236
237 /// Infinity (∞).
238 #[unstable(feature = "f16", issue = "116909")]
239 pub const INFINITY: f16 = 1.0_f16 / 0.0_f16;
240
241 /// Negative infinity (−∞).
242 #[unstable(feature = "f16", issue = "116909")]
243 pub const NEG_INFINITY: f16 = -1.0_f16 / 0.0_f16;
244
245 /// Sign bit
246 pub(crate) const SIGN_MASK: u16 = 0x8000;
247
248 /// Exponent mask
249 pub(crate) const EXP_MASK: u16 = 0x7c00;
250
251 /// Mantissa mask
252 pub(crate) const MAN_MASK: u16 = 0x03ff;
253
254 /// Minimum representable positive value (min subnormal)
255 const TINY_BITS: u16 = 0x1;
256
257 /// Minimum representable negative value (min negative subnormal)
258 const NEG_TINY_BITS: u16 = Self::TINY_BITS | Self::SIGN_MASK;
259
260 /// Returns `true` if this value is NaN.
261 ///
262 /// ```
263 /// #![feature(f16)]
264 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
265 ///
266 /// let nan = f16::NAN;
267 /// let f = 7.0_f16;
268 ///
269 /// assert!(nan.is_nan());
270 /// assert!(!f.is_nan());
271 /// # }
272 /// ```
273 #[inline]
274 #[must_use]
275 #[unstable(feature = "f16", issue = "116909")]
276 #[allow(clippy::eq_op)] // > if you intended to check if the operand is NaN, use `.is_nan()` instead :)
277 pub const fn is_nan(self) -> bool {
278 self != self
279 }
280
281 /// Returns `true` if this value is positive infinity or negative infinity, and
282 /// `false` otherwise.
283 ///
284 /// ```
285 /// #![feature(f16)]
286 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
287 ///
288 /// let f = 7.0f16;
289 /// let inf = f16::INFINITY;
290 /// let neg_inf = f16::NEG_INFINITY;
291 /// let nan = f16::NAN;
292 ///
293 /// assert!(!f.is_infinite());
294 /// assert!(!nan.is_infinite());
295 ///
296 /// assert!(inf.is_infinite());
297 /// assert!(neg_inf.is_infinite());
298 /// # }
299 /// ```
300 #[inline]
301 #[must_use]
302 #[unstable(feature = "f16", issue = "116909")]
303 pub const fn is_infinite(self) -> bool {
304 (self == f16::INFINITY) | (self == f16::NEG_INFINITY)
305 }
306
307 /// Returns `true` if this number is neither infinite nor NaN.
308 ///
309 /// ```
310 /// #![feature(f16)]
311 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
312 ///
313 /// let f = 7.0f16;
314 /// let inf: f16 = f16::INFINITY;
315 /// let neg_inf: f16 = f16::NEG_INFINITY;
316 /// let nan: f16 = f16::NAN;
317 ///
318 /// assert!(f.is_finite());
319 ///
320 /// assert!(!nan.is_finite());
321 /// assert!(!inf.is_finite());
322 /// assert!(!neg_inf.is_finite());
323 /// # }
324 /// ```
325 #[inline]
326 #[must_use]
327 #[unstable(feature = "f16", issue = "116909")]
328 #[rustc_const_unstable(feature = "f16", issue = "116909")]
329 pub const fn is_finite(self) -> bool {
330 // There's no need to handle NaN separately: if self is NaN,
331 // the comparison is not true, exactly as desired.
332 self.abs() < Self::INFINITY
333 }
334
335 /// Returns `true` if the number is [subnormal].
336 ///
337 /// ```
338 /// #![feature(f16)]
339 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
340 ///
341 /// let min = f16::MIN_POSITIVE; // 6.1035e-5
342 /// let max = f16::MAX;
343 /// let lower_than_min = 1.0e-7_f16;
344 /// let zero = 0.0_f16;
345 ///
346 /// assert!(!min.is_subnormal());
347 /// assert!(!max.is_subnormal());
348 ///
349 /// assert!(!zero.is_subnormal());
350 /// assert!(!f16::NAN.is_subnormal());
351 /// assert!(!f16::INFINITY.is_subnormal());
352 /// // Values between `0` and `min` are Subnormal.
353 /// assert!(lower_than_min.is_subnormal());
354 /// # }
355 /// ```
356 /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
357 #[inline]
358 #[must_use]
359 #[unstable(feature = "f16", issue = "116909")]
360 pub const fn is_subnormal(self) -> bool {
361 matches!(self.classify(), FpCategory::Subnormal)
362 }
363
364 /// Returns `true` if the number is neither zero, infinite, [subnormal], or NaN.
365 ///
366 /// ```
367 /// #![feature(f16)]
368 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
369 ///
370 /// let min = f16::MIN_POSITIVE; // 6.1035e-5
371 /// let max = f16::MAX;
372 /// let lower_than_min = 1.0e-7_f16;
373 /// let zero = 0.0_f16;
374 ///
375 /// assert!(min.is_normal());
376 /// assert!(max.is_normal());
377 ///
378 /// assert!(!zero.is_normal());
379 /// assert!(!f16::NAN.is_normal());
380 /// assert!(!f16::INFINITY.is_normal());
381 /// // Values between `0` and `min` are Subnormal.
382 /// assert!(!lower_than_min.is_normal());
383 /// # }
384 /// ```
385 /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
386 #[inline]
387 #[must_use]
388 #[unstable(feature = "f16", issue = "116909")]
389 pub const fn is_normal(self) -> bool {
390 matches!(self.classify(), FpCategory::Normal)
391 }
392
393 /// Returns the floating point category of the number. If only one property
394 /// is going to be tested, it is generally faster to use the specific
395 /// predicate instead.
396 ///
397 /// ```
398 /// #![feature(f16)]
399 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
400 ///
401 /// use std::num::FpCategory;
402 ///
403 /// let num = 12.4_f16;
404 /// let inf = f16::INFINITY;
405 ///
406 /// assert_eq!(num.classify(), FpCategory::Normal);
407 /// assert_eq!(inf.classify(), FpCategory::Infinite);
408 /// # }
409 /// ```
410 #[inline]
411 #[unstable(feature = "f16", issue = "116909")]
412 pub const fn classify(self) -> FpCategory {
413 let b = self.to_bits();
414 match (b & Self::MAN_MASK, b & Self::EXP_MASK) {
415 (0, Self::EXP_MASK) => FpCategory::Infinite,
416 (_, Self::EXP_MASK) => FpCategory::Nan,
417 (0, 0) => FpCategory::Zero,
418 (_, 0) => FpCategory::Subnormal,
419 _ => FpCategory::Normal,
420 }
421 }
422
423 /// Returns `true` if `self` has a positive sign, including `+0.0`, NaNs with
424 /// positive sign bit and positive infinity.
425 ///
426 /// Note that IEEE 754 doesn't assign any meaning to the sign bit in case of
427 /// a NaN, and as Rust doesn't guarantee that the bit pattern of NaNs are
428 /// conserved over arithmetic operations, the result of `is_sign_positive` on
429 /// a NaN might produce an unexpected or non-portable result. See the [specification
430 /// of NaN bit patterns](f32#nan-bit-patterns) for more info. Use `self.signum() == 1.0`
431 /// if you need fully portable behavior (will return `false` for all NaNs).
432 ///
433 /// ```
434 /// #![feature(f16)]
435 /// # // FIXME(f16_f128): LLVM crashes on s390x, llvm/llvm-project#50374
436 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
437 ///
438 /// let f = 7.0_f16;
439 /// let g = -7.0_f16;
440 ///
441 /// assert!(f.is_sign_positive());
442 /// assert!(!g.is_sign_positive());
443 /// # }
444 /// ```
445 #[inline]
446 #[must_use]
447 #[unstable(feature = "f16", issue = "116909")]
448 pub const fn is_sign_positive(self) -> bool {
449 !self.is_sign_negative()
450 }
451
452 /// Returns `true` if `self` has a negative sign, including `-0.0`, NaNs with
453 /// negative sign bit and negative infinity.
454 ///
455 /// Note that IEEE 754 doesn't assign any meaning to the sign bit in case of
456 /// a NaN, and as Rust doesn't guarantee that the bit pattern of NaNs are
457 /// conserved over arithmetic operations, the result of `is_sign_negative` on
458 /// a NaN might produce an unexpected or non-portable result. See the [specification
459 /// of NaN bit patterns](f32#nan-bit-patterns) for more info. Use `self.signum() == -1.0`
460 /// if you need fully portable behavior (will return `false` for all NaNs).
461 ///
462 /// ```
463 /// #![feature(f16)]
464 /// # // FIXME(f16_f128): LLVM crashes on s390x, llvm/llvm-project#50374
465 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
466 ///
467 /// let f = 7.0_f16;
468 /// let g = -7.0_f16;
469 ///
470 /// assert!(!f.is_sign_negative());
471 /// assert!(g.is_sign_negative());
472 /// # }
473 /// ```
474 #[inline]
475 #[must_use]
476 #[unstable(feature = "f16", issue = "116909")]
477 pub const fn is_sign_negative(self) -> bool {
478 // IEEE754 says: isSignMinus(x) is true if and only if x has negative sign. isSignMinus
479 // applies to zeros and NaNs as well.
480 // SAFETY: This is just transmuting to get the sign bit, it's fine.
481 (self.to_bits() & (1 << 15)) != 0
482 }
483
484 /// Returns the least number greater than `self`.
485 ///
486 /// Let `TINY` be the smallest representable positive `f16`. Then,
487 /// - if `self.is_nan()`, this returns `self`;
488 /// - if `self` is [`NEG_INFINITY`], this returns [`MIN`];
489 /// - if `self` is `-TINY`, this returns -0.0;
490 /// - if `self` is -0.0 or +0.0, this returns `TINY`;
491 /// - if `self` is [`MAX`] or [`INFINITY`], this returns [`INFINITY`];
492 /// - otherwise the unique least value greater than `self` is returned.
493 ///
494 /// The identity `x.next_up() == -(-x).next_down()` holds for all non-NaN `x`. When `x`
495 /// is finite `x == x.next_up().next_down()` also holds.
496 ///
497 /// ```rust
498 /// #![feature(f16)]
499 /// # // FIXME(f16_f128): ABI issues on MSVC
500 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
501 ///
502 /// // f16::EPSILON is the difference between 1.0 and the next number up.
503 /// assert_eq!(1.0f16.next_up(), 1.0 + f16::EPSILON);
504 /// // But not for most numbers.
505 /// assert!(0.1f16.next_up() < 0.1 + f16::EPSILON);
506 /// assert_eq!(4356f16.next_up(), 4360.0);
507 /// # }
508 /// ```
509 ///
510 /// This operation corresponds to IEEE-754 `nextUp`.
511 ///
512 /// [`NEG_INFINITY`]: Self::NEG_INFINITY
513 /// [`INFINITY`]: Self::INFINITY
514 /// [`MIN`]: Self::MIN
515 /// [`MAX`]: Self::MAX
516 #[inline]
517 #[doc(alias = "nextUp")]
518 #[unstable(feature = "f16", issue = "116909")]
519 pub const fn next_up(self) -> Self {
520 // Some targets violate Rust's assumption of IEEE semantics, e.g. by flushing
521 // denormals to zero. This is in general unsound and unsupported, but here
522 // we do our best to still produce the correct result on such targets.
523 let bits = self.to_bits();
524 if self.is_nan() || bits == Self::INFINITY.to_bits() {
525 return self;
526 }
527
528 let abs = bits & !Self::SIGN_MASK;
529 let next_bits = if abs == 0 {
530 Self::TINY_BITS
531 } else if bits == abs {
532 bits + 1
533 } else {
534 bits - 1
535 };
536 Self::from_bits(next_bits)
537 }
538
539 /// Returns the greatest number less than `self`.
540 ///
541 /// Let `TINY` be the smallest representable positive `f16`. Then,
542 /// - if `self.is_nan()`, this returns `self`;
543 /// - if `self` is [`INFINITY`], this returns [`MAX`];
544 /// - if `self` is `TINY`, this returns 0.0;
545 /// - if `self` is -0.0 or +0.0, this returns `-TINY`;
546 /// - if `self` is [`MIN`] or [`NEG_INFINITY`], this returns [`NEG_INFINITY`];
547 /// - otherwise the unique greatest value less than `self` is returned.
548 ///
549 /// The identity `x.next_down() == -(-x).next_up()` holds for all non-NaN `x`. When `x`
550 /// is finite `x == x.next_down().next_up()` also holds.
551 ///
552 /// ```rust
553 /// #![feature(f16)]
554 /// # // FIXME(f16_f128): ABI issues on MSVC
555 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
556 ///
557 /// let x = 1.0f16;
558 /// // Clamp value into range [0, 1).
559 /// let clamped = x.clamp(0.0, 1.0f16.next_down());
560 /// assert!(clamped < 1.0);
561 /// assert_eq!(clamped.next_up(), 1.0);
562 /// # }
563 /// ```
564 ///
565 /// This operation corresponds to IEEE-754 `nextDown`.
566 ///
567 /// [`NEG_INFINITY`]: Self::NEG_INFINITY
568 /// [`INFINITY`]: Self::INFINITY
569 /// [`MIN`]: Self::MIN
570 /// [`MAX`]: Self::MAX
571 #[inline]
572 #[doc(alias = "nextDown")]
573 #[unstable(feature = "f16", issue = "116909")]
574 pub const fn next_down(self) -> Self {
575 // Some targets violate Rust's assumption of IEEE semantics, e.g. by flushing
576 // denormals to zero. This is in general unsound and unsupported, but here
577 // we do our best to still produce the correct result on such targets.
578 let bits = self.to_bits();
579 if self.is_nan() || bits == Self::NEG_INFINITY.to_bits() {
580 return self;
581 }
582
583 let abs = bits & !Self::SIGN_MASK;
584 let next_bits = if abs == 0 {
585 Self::NEG_TINY_BITS
586 } else if bits == abs {
587 bits - 1
588 } else {
589 bits + 1
590 };
591 Self::from_bits(next_bits)
592 }
593
594 /// Takes the reciprocal (inverse) of a number, `1/x`.
595 ///
596 /// ```
597 /// #![feature(f16)]
598 /// # // FIXME(f16_f128): extendhfsf2, truncsfhf2, __gnu_h2f_ieee, __gnu_f2h_ieee missing for many platforms
599 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
600 ///
601 /// let x = 2.0_f16;
602 /// let abs_difference = (x.recip() - (1.0 / x)).abs();
603 ///
604 /// assert!(abs_difference <= f16::EPSILON);
605 /// # }
606 /// ```
607 #[inline]
608 #[unstable(feature = "f16", issue = "116909")]
609 #[must_use = "this returns the result of the operation, without modifying the original"]
610 pub const fn recip(self) -> Self {
611 1.0 / self
612 }
613
614 /// Converts radians to degrees.
615 ///
616 /// ```
617 /// #![feature(f16)]
618 /// # // FIXME(f16_f128): extendhfsf2, truncsfhf2, __gnu_h2f_ieee, __gnu_f2h_ieee missing for many platforms
619 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
620 ///
621 /// let angle = std::f16::consts::PI;
622 ///
623 /// let abs_difference = (angle.to_degrees() - 180.0).abs();
624 /// assert!(abs_difference <= 0.5);
625 /// # }
626 /// ```
627 #[inline]
628 #[unstable(feature = "f16", issue = "116909")]
629 #[must_use = "this returns the result of the operation, without modifying the original"]
630 pub const fn to_degrees(self) -> Self {
631 // Use a literal for better precision.
632 const PIS_IN_180: f16 = 57.2957795130823208767981548141051703_f16;
633 self * PIS_IN_180
634 }
635
636 /// Converts degrees to radians.
637 ///
638 /// ```
639 /// #![feature(f16)]
640 /// # // FIXME(f16_f128): extendhfsf2, truncsfhf2, __gnu_h2f_ieee, __gnu_f2h_ieee missing for many platforms
641 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
642 ///
643 /// let angle = 180.0f16;
644 ///
645 /// let abs_difference = (angle.to_radians() - std::f16::consts::PI).abs();
646 ///
647 /// assert!(abs_difference <= 0.01);
648 /// # }
649 /// ```
650 #[inline]
651 #[unstable(feature = "f16", issue = "116909")]
652 #[must_use = "this returns the result of the operation, without modifying the original"]
653 pub const fn to_radians(self) -> f16 {
654 // Use a literal for better precision.
655 const RADS_PER_DEG: f16 = 0.017453292519943295769236907684886_f16;
656 self * RADS_PER_DEG
657 }
658
659 /// Returns the maximum of the two numbers, ignoring NaN.
660 ///
661 /// If one of the arguments is NaN, then the other argument is returned.
662 /// This follows the IEEE 754-2008 semantics for maxNum, except for handling of signaling NaNs;
663 /// this function handles all NaNs the same way and avoids maxNum's problems with associativity.
664 /// This also matches the behavior of libm’s fmax. In particular, if the inputs compare equal
665 /// (such as for the case of `+0.0` and `-0.0`), either input may be returned non-deterministically.
666 ///
667 /// ```
668 /// #![feature(f16)]
669 /// # #[cfg(target_arch = "aarch64")] { // FIXME(f16_F128): rust-lang/rust#123885
670 ///
671 /// let x = 1.0f16;
672 /// let y = 2.0f16;
673 ///
674 /// assert_eq!(x.max(y), y);
675 /// # }
676 /// ```
677 #[inline]
678 #[unstable(feature = "f16", issue = "116909")]
679 #[rustc_const_unstable(feature = "f16", issue = "116909")]
680 #[must_use = "this returns the result of the comparison, without modifying either input"]
681 pub const fn max(self, other: f16) -> f16 {
682 intrinsics::maxnumf16(self, other)
683 }
684
685 /// Returns the minimum of the two numbers, ignoring NaN.
686 ///
687 /// If one of the arguments is NaN, then the other argument is returned.
688 /// This follows the IEEE 754-2008 semantics for minNum, except for handling of signaling NaNs;
689 /// this function handles all NaNs the same way and avoids minNum's problems with associativity.
690 /// This also matches the behavior of libm’s fmin. In particular, if the inputs compare equal
691 /// (such as for the case of `+0.0` and `-0.0`), either input may be returned non-deterministically.
692 ///
693 /// ```
694 /// #![feature(f16)]
695 /// # #[cfg(target_arch = "aarch64")] { // FIXME(f16_F128): rust-lang/rust#123885
696 ///
697 /// let x = 1.0f16;
698 /// let y = 2.0f16;
699 ///
700 /// assert_eq!(x.min(y), x);
701 /// # }
702 /// ```
703 #[inline]
704 #[unstable(feature = "f16", issue = "116909")]
705 #[rustc_const_unstable(feature = "f16", issue = "116909")]
706 #[must_use = "this returns the result of the comparison, without modifying either input"]
707 pub const fn min(self, other: f16) -> f16 {
708 intrinsics::minnumf16(self, other)
709 }
710
711 /// Returns the maximum of the two numbers, propagating NaN.
712 ///
713 /// This returns NaN when *either* argument is NaN, as opposed to
714 /// [`f16::max`] which only returns NaN when *both* arguments are NaN.
715 ///
716 /// ```
717 /// #![feature(f16)]
718 /// #![feature(float_minimum_maximum)]
719 /// # #[cfg(target_arch = "aarch64")] { // FIXME(f16_F128): rust-lang/rust#123885
720 ///
721 /// let x = 1.0f16;
722 /// let y = 2.0f16;
723 ///
724 /// assert_eq!(x.maximum(y), y);
725 /// assert!(x.maximum(f16::NAN).is_nan());
726 /// # }
727 /// ```
728 ///
729 /// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the greater
730 /// of the two numbers. For this operation, -0.0 is considered to be less than +0.0.
731 /// Note that this follows the semantics specified in IEEE 754-2019.
732 ///
733 /// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN
734 /// operand is conserved; see the [specification of NaN bit patterns](f32#nan-bit-patterns) for more info.
735 #[inline]
736 #[unstable(feature = "f16", issue = "116909")]
737 // #[unstable(feature = "float_minimum_maximum", issue = "91079")]
738 #[must_use = "this returns the result of the comparison, without modifying either input"]
739 pub const fn maximum(self, other: f16) -> f16 {
740 if self > other {
741 self
742 } else if other > self {
743 other
744 } else if self == other {
745 if self.is_sign_positive() && other.is_sign_negative() { self } else { other }
746 } else {
747 self + other
748 }
749 }
750
751 /// Returns the minimum of the two numbers, propagating NaN.
752 ///
753 /// This returns NaN when *either* argument is NaN, as opposed to
754 /// [`f16::min`] which only returns NaN when *both* arguments are NaN.
755 ///
756 /// ```
757 /// #![feature(f16)]
758 /// #![feature(float_minimum_maximum)]
759 /// # #[cfg(target_arch = "aarch64")] { // FIXME(f16_F128): rust-lang/rust#123885
760 ///
761 /// let x = 1.0f16;
762 /// let y = 2.0f16;
763 ///
764 /// assert_eq!(x.minimum(y), x);
765 /// assert!(x.minimum(f16::NAN).is_nan());
766 /// # }
767 /// ```
768 ///
769 /// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the lesser
770 /// of the two numbers. For this operation, -0.0 is considered to be less than +0.0.
771 /// Note that this follows the semantics specified in IEEE 754-2019.
772 ///
773 /// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN
774 /// operand is conserved; see the [specification of NaN bit patterns](f32#nan-bit-patterns) for more info.
775 #[inline]
776 #[unstable(feature = "f16", issue = "116909")]
777 // #[unstable(feature = "float_minimum_maximum", issue = "91079")]
778 #[must_use = "this returns the result of the comparison, without modifying either input"]
779 pub const fn minimum(self, other: f16) -> f16 {
780 if self < other {
781 self
782 } else if other < self {
783 other
784 } else if self == other {
785 if self.is_sign_negative() && other.is_sign_positive() { self } else { other }
786 } else {
787 // At least one input is NaN. Use `+` to perform NaN propagation and quieting.
788 self + other
789 }
790 }
791
792 /// Calculates the middle point of `self` and `rhs`.
793 ///
794 /// This returns NaN when *either* argument is NaN or if a combination of
795 /// +inf and -inf is provided as arguments.
796 ///
797 /// # Examples
798 ///
799 /// ```
800 /// #![feature(f16)]
801 /// # #[cfg(target_arch = "aarch64")] { // FIXME(f16_F128): rust-lang/rust#123885
802 ///
803 /// assert_eq!(1f16.midpoint(4.0), 2.5);
804 /// assert_eq!((-5.5f16).midpoint(8.0), 1.25);
805 /// # }
806 /// ```
807 #[inline]
808 #[unstable(feature = "f16", issue = "116909")]
809 #[rustc_const_unstable(feature = "f16", issue = "116909")]
810 pub const fn midpoint(self, other: f16) -> f16 {
811 const LO: f16 = f16::MIN_POSITIVE * 2.;
812 const HI: f16 = f16::MAX / 2.;
813
814 let (a, b) = (self, other);
815 let abs_a = a.abs();
816 let abs_b = b.abs();
817
818 if abs_a <= HI && abs_b <= HI {
819 // Overflow is impossible
820 (a + b) / 2.
821 } else if abs_a < LO {
822 // Not safe to halve `a` (would underflow)
823 a + (b / 2.)
824 } else if abs_b < LO {
825 // Not safe to halve `b` (would underflow)
826 (a / 2.) + b
827 } else {
828 // Safe to halve `a` and `b`
829 (a / 2.) + (b / 2.)
830 }
831 }
832
833 /// Rounds toward zero and converts to any primitive integer type,
834 /// assuming that the value is finite and fits in that type.
835 ///
836 /// ```
837 /// #![feature(f16)]
838 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
839 ///
840 /// let value = 4.6_f16;
841 /// let rounded = unsafe { value.to_int_unchecked::<u16>() };
842 /// assert_eq!(rounded, 4);
843 ///
844 /// let value = -128.9_f16;
845 /// let rounded = unsafe { value.to_int_unchecked::<i8>() };
846 /// assert_eq!(rounded, i8::MIN);
847 /// # }
848 /// ```
849 ///
850 /// # Safety
851 ///
852 /// The value must:
853 ///
854 /// * Not be `NaN`
855 /// * Not be infinite
856 /// * Be representable in the return type `Int`, after truncating off its fractional part
857 #[inline]
858 #[unstable(feature = "f16", issue = "116909")]
859 #[must_use = "this returns the result of the operation, without modifying the original"]
860 pub unsafe fn to_int_unchecked<Int>(self) -> Int
861 where
862 Self: FloatToInt<Int>,
863 {
864 // SAFETY: the caller must uphold the safety contract for
865 // `FloatToInt::to_int_unchecked`.
866 unsafe { FloatToInt::<Int>::to_int_unchecked(self) }
867 }
868
869 /// Raw transmutation to `u16`.
870 ///
871 /// This is currently identical to `transmute::<f16, u16>(self)` on all platforms.
872 ///
873 /// See [`from_bits`](#method.from_bits) for some discussion of the
874 /// portability of this operation (there are almost no issues).
875 ///
876 /// Note that this function is distinct from `as` casting, which attempts to
877 /// preserve the *numeric* value, and not the bitwise value.
878 ///
879 /// ```
880 /// #![feature(f16)]
881 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
882 ///
883 /// # // FIXME(f16_f128): enable this once const casting works
884 /// # // assert_ne!((1f16).to_bits(), 1f16 as u128); // to_bits() is not casting!
885 /// assert_eq!((12.5f16).to_bits(), 0x4a40);
886 /// # }
887 /// ```
888 #[inline]
889 #[unstable(feature = "f16", issue = "116909")]
890 #[must_use = "this returns the result of the operation, without modifying the original"]
891 pub const fn to_bits(self) -> u16 {
892 // SAFETY: `u16` is a plain old datatype so we can always transmute to it.
893 unsafe { mem::transmute(self) }
894 }
895
896 /// Raw transmutation from `u16`.
897 ///
898 /// This is currently identical to `transmute::<u16, f16>(v)` on all platforms.
899 /// It turns out this is incredibly portable, for two reasons:
900 ///
901 /// * Floats and Ints have the same endianness on all supported platforms.
902 /// * IEEE 754 very precisely specifies the bit layout of floats.
903 ///
904 /// However there is one caveat: prior to the 2008 version of IEEE 754, how
905 /// to interpret the NaN signaling bit wasn't actually specified. Most platforms
906 /// (notably x86 and ARM) picked the interpretation that was ultimately
907 /// standardized in 2008, but some didn't (notably MIPS). As a result, all
908 /// signaling NaNs on MIPS are quiet NaNs on x86, and vice-versa.
909 ///
910 /// Rather than trying to preserve signaling-ness cross-platform, this
911 /// implementation favors preserving the exact bits. This means that
912 /// any payloads encoded in NaNs will be preserved even if the result of
913 /// this method is sent over the network from an x86 machine to a MIPS one.
914 ///
915 /// If the results of this method are only manipulated by the same
916 /// architecture that produced them, then there is no portability concern.
917 ///
918 /// If the input isn't NaN, then there is no portability concern.
919 ///
920 /// If you don't care about signalingness (very likely), then there is no
921 /// portability concern.
922 ///
923 /// Note that this function is distinct from `as` casting, which attempts to
924 /// preserve the *numeric* value, and not the bitwise value.
925 ///
926 /// ```
927 /// #![feature(f16)]
928 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
929 ///
930 /// let v = f16::from_bits(0x4a40);
931 /// assert_eq!(v, 12.5);
932 /// # }
933 /// ```
934 #[inline]
935 #[must_use]
936 #[unstable(feature = "f16", issue = "116909")]
937 pub const fn from_bits(v: u16) -> Self {
938 // It turns out the safety issues with sNaN were overblown! Hooray!
939 // SAFETY: `u16` is a plain old datatype so we can always transmute from it.
940 unsafe { mem::transmute(v) }
941 }
942
943 /// Returns the memory representation of this floating point number as a byte array in
944 /// big-endian (network) byte order.
945 ///
946 /// See [`from_bits`](Self::from_bits) for some discussion of the
947 /// portability of this operation (there are almost no issues).
948 ///
949 /// # Examples
950 ///
951 /// ```
952 /// #![feature(f16)]
953 /// # // FIXME(f16_f128): LLVM crashes on s390x, llvm/llvm-project#50374
954 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
955 ///
956 /// let bytes = 12.5f16.to_be_bytes();
957 /// assert_eq!(bytes, [0x4a, 0x40]);
958 /// # }
959 /// ```
960 #[inline]
961 #[unstable(feature = "f16", issue = "116909")]
962 #[must_use = "this returns the result of the operation, without modifying the original"]
963 pub const fn to_be_bytes(self) -> [u8; 2] {
964 self.to_bits().to_be_bytes()
965 }
966
967 /// Returns the memory representation of this floating point number as a byte array in
968 /// little-endian byte order.
969 ///
970 /// See [`from_bits`](Self::from_bits) for some discussion of the
971 /// portability of this operation (there are almost no issues).
972 ///
973 /// # Examples
974 ///
975 /// ```
976 /// #![feature(f16)]
977 /// # // FIXME(f16_f128): LLVM crashes on s390x, llvm/llvm-project#50374
978 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
979 ///
980 /// let bytes = 12.5f16.to_le_bytes();
981 /// assert_eq!(bytes, [0x40, 0x4a]);
982 /// # }
983 /// ```
984 #[inline]
985 #[unstable(feature = "f16", issue = "116909")]
986 #[must_use = "this returns the result of the operation, without modifying the original"]
987 pub const fn to_le_bytes(self) -> [u8; 2] {
988 self.to_bits().to_le_bytes()
989 }
990
991 /// Returns the memory representation of this floating point number as a byte array in
992 /// native byte order.
993 ///
994 /// As the target platform's native endianness is used, portable code
995 /// should use [`to_be_bytes`] or [`to_le_bytes`], as appropriate, instead.
996 ///
997 /// [`to_be_bytes`]: f16::to_be_bytes
998 /// [`to_le_bytes`]: f16::to_le_bytes
999 ///
1000 /// See [`from_bits`](Self::from_bits) for some discussion of the
1001 /// portability of this operation (there are almost no issues).
1002 ///
1003 /// # Examples
1004 ///
1005 /// ```
1006 /// #![feature(f16)]
1007 /// # // FIXME(f16_f128): LLVM crashes on s390x, llvm/llvm-project#50374
1008 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1009 ///
1010 /// let bytes = 12.5f16.to_ne_bytes();
1011 /// assert_eq!(
1012 /// bytes,
1013 /// if cfg!(target_endian = "big") {
1014 /// [0x4a, 0x40]
1015 /// } else {
1016 /// [0x40, 0x4a]
1017 /// }
1018 /// );
1019 /// # }
1020 /// ```
1021 #[inline]
1022 #[unstable(feature = "f16", issue = "116909")]
1023 #[must_use = "this returns the result of the operation, without modifying the original"]
1024 pub const fn to_ne_bytes(self) -> [u8; 2] {
1025 self.to_bits().to_ne_bytes()
1026 }
1027
1028 /// Creates a floating point value from its representation as a byte array in big endian.
1029 ///
1030 /// See [`from_bits`](Self::from_bits) for some discussion of the
1031 /// portability of this operation (there are almost no issues).
1032 ///
1033 /// # Examples
1034 ///
1035 /// ```
1036 /// #![feature(f16)]
1037 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1038 ///
1039 /// let value = f16::from_be_bytes([0x4a, 0x40]);
1040 /// assert_eq!(value, 12.5);
1041 /// # }
1042 /// ```
1043 #[inline]
1044 #[must_use]
1045 #[unstable(feature = "f16", issue = "116909")]
1046 pub const fn from_be_bytes(bytes: [u8; 2]) -> Self {
1047 Self::from_bits(u16::from_be_bytes(bytes))
1048 }
1049
1050 /// Creates a floating point value from its representation as a byte array in little endian.
1051 ///
1052 /// See [`from_bits`](Self::from_bits) for some discussion of the
1053 /// portability of this operation (there are almost no issues).
1054 ///
1055 /// # Examples
1056 ///
1057 /// ```
1058 /// #![feature(f16)]
1059 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1060 ///
1061 /// let value = f16::from_le_bytes([0x40, 0x4a]);
1062 /// assert_eq!(value, 12.5);
1063 /// # }
1064 /// ```
1065 #[inline]
1066 #[must_use]
1067 #[unstable(feature = "f16", issue = "116909")]
1068 pub const fn from_le_bytes(bytes: [u8; 2]) -> Self {
1069 Self::from_bits(u16::from_le_bytes(bytes))
1070 }
1071
1072 /// Creates a floating point value from its representation as a byte array in native endian.
1073 ///
1074 /// As the target platform's native endianness is used, portable code
1075 /// likely wants to use [`from_be_bytes`] or [`from_le_bytes`], as
1076 /// appropriate instead.
1077 ///
1078 /// [`from_be_bytes`]: f16::from_be_bytes
1079 /// [`from_le_bytes`]: f16::from_le_bytes
1080 ///
1081 /// See [`from_bits`](Self::from_bits) for some discussion of the
1082 /// portability of this operation (there are almost no issues).
1083 ///
1084 /// # Examples
1085 ///
1086 /// ```
1087 /// #![feature(f16)]
1088 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1089 ///
1090 /// let value = f16::from_ne_bytes(if cfg!(target_endian = "big") {
1091 /// [0x4a, 0x40]
1092 /// } else {
1093 /// [0x40, 0x4a]
1094 /// });
1095 /// assert_eq!(value, 12.5);
1096 /// # }
1097 /// ```
1098 #[inline]
1099 #[must_use]
1100 #[unstable(feature = "f16", issue = "116909")]
1101 pub const fn from_ne_bytes(bytes: [u8; 2]) -> Self {
1102 Self::from_bits(u16::from_ne_bytes(bytes))
1103 }
1104
1105 /// Returns the ordering between `self` and `other`.
1106 ///
1107 /// Unlike the standard partial comparison between floating point numbers,
1108 /// this comparison always produces an ordering in accordance to
1109 /// the `totalOrder` predicate as defined in the IEEE 754 (2008 revision)
1110 /// floating point standard. The values are ordered in the following sequence:
1111 ///
1112 /// - negative quiet NaN
1113 /// - negative signaling NaN
1114 /// - negative infinity
1115 /// - negative numbers
1116 /// - negative subnormal numbers
1117 /// - negative zero
1118 /// - positive zero
1119 /// - positive subnormal numbers
1120 /// - positive numbers
1121 /// - positive infinity
1122 /// - positive signaling NaN
1123 /// - positive quiet NaN.
1124 ///
1125 /// The ordering established by this function does not always agree with the
1126 /// [`PartialOrd`] and [`PartialEq`] implementations of `f16`. For example,
1127 /// they consider negative and positive zero equal, while `total_cmp`
1128 /// doesn't.
1129 ///
1130 /// The interpretation of the signaling NaN bit follows the definition in
1131 /// the IEEE 754 standard, which may not match the interpretation by some of
1132 /// the older, non-conformant (e.g. MIPS) hardware implementations.
1133 ///
1134 /// # Example
1135 ///
1136 /// ```
1137 /// #![feature(f16)]
1138 /// # // FIXME(f16_f128): extendhfsf2, truncsfhf2, __gnu_h2f_ieee, __gnu_f2h_ieee missing for many platforms
1139 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1140 ///
1141 /// struct GoodBoy {
1142 /// name: &'static str,
1143 /// weight: f16,
1144 /// }
1145 ///
1146 /// let mut bois = vec![
1147 /// GoodBoy { name: "Pucci", weight: 0.1 },
1148 /// GoodBoy { name: "Woofer", weight: 99.0 },
1149 /// GoodBoy { name: "Yapper", weight: 10.0 },
1150 /// GoodBoy { name: "Chonk", weight: f16::INFINITY },
1151 /// GoodBoy { name: "Abs. Unit", weight: f16::NAN },
1152 /// GoodBoy { name: "Floaty", weight: -5.0 },
1153 /// ];
1154 ///
1155 /// bois.sort_by(|a, b| a.weight.total_cmp(&b.weight));
1156 ///
1157 /// // `f16::NAN` could be positive or negative, which will affect the sort order.
1158 /// if f16::NAN.is_sign_negative() {
1159 /// bois.into_iter().map(|b| b.weight)
1160 /// .zip([f16::NAN, -5.0, 0.1, 10.0, 99.0, f16::INFINITY].iter())
1161 /// .for_each(|(a, b)| assert_eq!(a.to_bits(), b.to_bits()))
1162 /// } else {
1163 /// bois.into_iter().map(|b| b.weight)
1164 /// .zip([-5.0, 0.1, 10.0, 99.0, f16::INFINITY, f16::NAN].iter())
1165 /// .for_each(|(a, b)| assert_eq!(a.to_bits(), b.to_bits()))
1166 /// }
1167 /// # }
1168 /// ```
1169 #[inline]
1170 #[must_use]
1171 #[unstable(feature = "f16", issue = "116909")]
1172 pub fn total_cmp(&self, other: &Self) -> crate::cmp::Ordering {
1173 let mut left = self.to_bits() as i16;
1174 let mut right = other.to_bits() as i16;
1175
1176 // In case of negatives, flip all the bits except the sign
1177 // to achieve a similar layout as two's complement integers
1178 //
1179 // Why does this work? IEEE 754 floats consist of three fields:
1180 // Sign bit, exponent and mantissa. The set of exponent and mantissa
1181 // fields as a whole have the property that their bitwise order is
1182 // equal to the numeric magnitude where the magnitude is defined.
1183 // The magnitude is not normally defined on NaN values, but
1184 // IEEE 754 totalOrder defines the NaN values also to follow the
1185 // bitwise order. This leads to order explained in the doc comment.
1186 // However, the representation of magnitude is the same for negative
1187 // and positive numbers – only the sign bit is different.
1188 // To easily compare the floats as signed integers, we need to
1189 // flip the exponent and mantissa bits in case of negative numbers.
1190 // We effectively convert the numbers to "two's complement" form.
1191 //
1192 // To do the flipping, we construct a mask and XOR against it.
1193 // We branchlessly calculate an "all-ones except for the sign bit"
1194 // mask from negative-signed values: right shifting sign-extends
1195 // the integer, so we "fill" the mask with sign bits, and then
1196 // convert to unsigned to push one more zero bit.
1197 // On positive values, the mask is all zeros, so it's a no-op.
1198 left ^= (((left >> 15) as u16) >> 1) as i16;
1199 right ^= (((right >> 15) as u16) >> 1) as i16;
1200
1201 left.cmp(&right)
1202 }
1203
1204 /// Restrict a value to a certain interval unless it is NaN.
1205 ///
1206 /// Returns `max` if `self` is greater than `max`, and `min` if `self` is
1207 /// less than `min`. Otherwise this returns `self`.
1208 ///
1209 /// Note that this function returns NaN if the initial value was NaN as
1210 /// well.
1211 ///
1212 /// # Panics
1213 ///
1214 /// Panics if `min > max`, `min` is NaN, or `max` is NaN.
1215 ///
1216 /// # Examples
1217 ///
1218 /// ```
1219 /// #![feature(f16)]
1220 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1221 ///
1222 /// assert!((-3.0f16).clamp(-2.0, 1.0) == -2.0);
1223 /// assert!((0.0f16).clamp(-2.0, 1.0) == 0.0);
1224 /// assert!((2.0f16).clamp(-2.0, 1.0) == 1.0);
1225 /// assert!((f16::NAN).clamp(-2.0, 1.0).is_nan());
1226 /// # }
1227 /// ```
1228 #[inline]
1229 #[unstable(feature = "f16", issue = "116909")]
1230 #[must_use = "method returns a new number and does not mutate the original value"]
1231 pub const fn clamp(mut self, min: f16, max: f16) -> f16 {
1232 const_assert!(
1233 min <= max,
1234 "min > max, or either was NaN",
1235 "min > max, or either was NaN. min = {min:?}, max = {max:?}",
1236 min: f16,
1237 max: f16,
1238 );
1239
1240 if self < min {
1241 self = min;
1242 }
1243 if self > max {
1244 self = max;
1245 }
1246 self
1247 }
1248
1249 /// Computes the absolute value of `self`.
1250 ///
1251 /// This function always returns the precise result.
1252 ///
1253 /// # Examples
1254 ///
1255 /// ```
1256 /// #![feature(f16)]
1257 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1258 ///
1259 /// let x = 3.5_f16;
1260 /// let y = -3.5_f16;
1261 ///
1262 /// assert_eq!(x.abs(), x);
1263 /// assert_eq!(y.abs(), -y);
1264 ///
1265 /// assert!(f16::NAN.abs().is_nan());
1266 /// # }
1267 /// ```
1268 #[inline]
1269 #[unstable(feature = "f16", issue = "116909")]
1270 #[rustc_const_unstable(feature = "f16", issue = "116909")]
1271 #[must_use = "method returns a new number and does not mutate the original value"]
1272 pub const fn abs(self) -> Self {
1273 // FIXME(f16_f128): replace with `intrinsics::fabsf16` when available
1274 Self::from_bits(self.to_bits() & !(1 << 15))
1275 }
1276
1277 /// Returns a number that represents the sign of `self`.
1278 ///
1279 /// - `1.0` if the number is positive, `+0.0` or `INFINITY`
1280 /// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
1281 /// - NaN if the number is NaN
1282 ///
1283 /// # Examples
1284 ///
1285 /// ```
1286 /// #![feature(f16)]
1287 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1288 ///
1289 /// let f = 3.5_f16;
1290 ///
1291 /// assert_eq!(f.signum(), 1.0);
1292 /// assert_eq!(f16::NEG_INFINITY.signum(), -1.0);
1293 ///
1294 /// assert!(f16::NAN.signum().is_nan());
1295 /// # }
1296 /// ```
1297 #[inline]
1298 #[unstable(feature = "f16", issue = "116909")]
1299 #[rustc_const_unstable(feature = "f16", issue = "116909")]
1300 #[must_use = "method returns a new number and does not mutate the original value"]
1301 pub const fn signum(self) -> f16 {
1302 if self.is_nan() { Self::NAN } else { 1.0_f16.copysign(self) }
1303 }
1304
1305 /// Returns a number composed of the magnitude of `self` and the sign of
1306 /// `sign`.
1307 ///
1308 /// Equal to `self` if the sign of `self` and `sign` are the same, otherwise equal to `-self`.
1309 /// If `self` is a NaN, then a NaN with the same payload as `self` and the sign bit of `sign` is
1310 /// returned.
1311 ///
1312 /// If `sign` is a NaN, then this operation will still carry over its sign into the result. Note
1313 /// that IEEE 754 doesn't assign any meaning to the sign bit in case of a NaN, and as Rust
1314 /// doesn't guarantee that the bit pattern of NaNs are conserved over arithmetic operations, the
1315 /// result of `copysign` with `sign` being a NaN might produce an unexpected or non-portable
1316 /// result. See the [specification of NaN bit patterns](primitive@f32#nan-bit-patterns) for more
1317 /// info.
1318 ///
1319 /// # Examples
1320 ///
1321 /// ```
1322 /// #![feature(f16)]
1323 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1324 ///
1325 /// let f = 3.5_f16;
1326 ///
1327 /// assert_eq!(f.copysign(0.42), 3.5_f16);
1328 /// assert_eq!(f.copysign(-0.42), -3.5_f16);
1329 /// assert_eq!((-f).copysign(0.42), 3.5_f16);
1330 /// assert_eq!((-f).copysign(-0.42), -3.5_f16);
1331 ///
1332 /// assert!(f16::NAN.copysign(1.0).is_nan());
1333 /// # }
1334 /// ```
1335 #[inline]
1336 #[unstable(feature = "f16", issue = "116909")]
1337 #[rustc_const_unstable(feature = "f16", issue = "116909")]
1338 #[must_use = "method returns a new number and does not mutate the original value"]
1339 pub const fn copysign(self, sign: f16) -> f16 {
1340 // SAFETY: this is actually a safe intrinsic
1341 unsafe { intrinsics::copysignf16(self, sign) }
1342 }
1343
1344 /// Float addition that allows optimizations based on algebraic rules.
1345 ///
1346 /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1347 #[must_use = "method returns a new number and does not mutate the original value"]
1348 #[unstable(feature = "float_algebraic", issue = "136469")]
1349 #[inline]
1350 pub fn algebraic_add(self, rhs: f16) -> f16 {
1351 intrinsics::fadd_algebraic(self, rhs)
1352 }
1353
1354 /// Float subtraction that allows optimizations based on algebraic rules.
1355 ///
1356 /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1357 #[must_use = "method returns a new number and does not mutate the original value"]
1358 #[unstable(feature = "float_algebraic", issue = "136469")]
1359 #[inline]
1360 pub fn algebraic_sub(self, rhs: f16) -> f16 {
1361 intrinsics::fsub_algebraic(self, rhs)
1362 }
1363
1364 /// Float multiplication 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 #[inline]
1370 pub fn algebraic_mul(self, rhs: f16) -> f16 {
1371 intrinsics::fmul_algebraic(self, rhs)
1372 }
1373
1374 /// Float division that allows optimizations based on algebraic rules.
1375 ///
1376 /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1377 #[must_use = "method returns a new number and does not mutate the original value"]
1378 #[unstable(feature = "float_algebraic", issue = "136469")]
1379 #[inline]
1380 pub fn algebraic_div(self, rhs: f16) -> f16 {
1381 intrinsics::fdiv_algebraic(self, rhs)
1382 }
1383
1384 /// Float remainder that allows optimizations based on algebraic rules.
1385 ///
1386 /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1387 #[must_use = "method returns a new number and does not mutate the original value"]
1388 #[unstable(feature = "float_algebraic", issue = "136469")]
1389 #[inline]
1390 pub fn algebraic_rem(self, rhs: f16) -> f16 {
1391 intrinsics::frem_algebraic(self, rhs)
1392 }
1393}