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;
16#[cfg(not(test))]
17use crate::num::libm;
18use crate::panic::const_assert;
19use crate::{intrinsics, mem};
20
21/// Basic mathematical constants.
22#[unstable(feature = "f16", issue = "116909")]
23pub mod consts {
24 // FIXME: replace with mathematical constants from cmath.
25
26 /// Archimedes' constant (π)
27 #[unstable(feature = "f16", issue = "116909")]
28 pub const PI: f16 = 3.14159265358979323846264338327950288_f16;
29
30 /// The full circle constant (τ)
31 ///
32 /// Equal to 2π.
33 #[unstable(feature = "f16", issue = "116909")]
34 pub const TAU: f16 = 6.28318530717958647692528676655900577_f16;
35
36 /// The golden ratio (φ)
37 #[unstable(feature = "f16", issue = "116909")]
38 // Also, #[unstable(feature = "more_float_constants", issue = "103883")]
39 pub const PHI: f16 = 1.618033988749894848204586834365638118_f16;
40
41 /// The Euler-Mascheroni constant (γ)
42 #[unstable(feature = "f16", issue = "116909")]
43 // Also, #[unstable(feature = "more_float_constants", issue = "103883")]
44 pub const EGAMMA: f16 = 0.577215664901532860606512090082402431_f16;
45
46 /// π/2
47 #[unstable(feature = "f16", issue = "116909")]
48 pub const FRAC_PI_2: f16 = 1.57079632679489661923132169163975144_f16;
49
50 /// π/3
51 #[unstable(feature = "f16", issue = "116909")]
52 pub const FRAC_PI_3: f16 = 1.04719755119659774615421446109316763_f16;
53
54 /// π/4
55 #[unstable(feature = "f16", issue = "116909")]
56 pub const FRAC_PI_4: f16 = 0.785398163397448309615660845819875721_f16;
57
58 /// π/6
59 #[unstable(feature = "f16", issue = "116909")]
60 pub const FRAC_PI_6: f16 = 0.52359877559829887307710723054658381_f16;
61
62 /// π/8
63 #[unstable(feature = "f16", issue = "116909")]
64 pub const FRAC_PI_8: f16 = 0.39269908169872415480783042290993786_f16;
65
66 /// 1/π
67 #[unstable(feature = "f16", issue = "116909")]
68 pub const FRAC_1_PI: f16 = 0.318309886183790671537767526745028724_f16;
69
70 /// 1/sqrt(π)
71 #[unstable(feature = "f16", issue = "116909")]
72 // Also, #[unstable(feature = "more_float_constants", issue = "103883")]
73 pub const FRAC_1_SQRT_PI: f16 = 0.564189583547756286948079451560772586_f16;
74
75 /// 1/sqrt(2π)
76 #[doc(alias = "FRAC_1_SQRT_TAU")]
77 #[unstable(feature = "f16", issue = "116909")]
78 // Also, #[unstable(feature = "more_float_constants", issue = "103883")]
79 pub const FRAC_1_SQRT_2PI: f16 = 0.398942280401432677939946059934381868_f16;
80
81 /// 2/π
82 #[unstable(feature = "f16", issue = "116909")]
83 pub const FRAC_2_PI: f16 = 0.636619772367581343075535053490057448_f16;
84
85 /// 2/sqrt(π)
86 #[unstable(feature = "f16", issue = "116909")]
87 pub const FRAC_2_SQRT_PI: f16 = 1.12837916709551257389615890312154517_f16;
88
89 /// sqrt(2)
90 #[unstable(feature = "f16", issue = "116909")]
91 pub const SQRT_2: f16 = 1.41421356237309504880168872420969808_f16;
92
93 /// 1/sqrt(2)
94 #[unstable(feature = "f16", issue = "116909")]
95 pub const FRAC_1_SQRT_2: f16 = 0.707106781186547524400844362104849039_f16;
96
97 /// sqrt(3)
98 #[unstable(feature = "f16", issue = "116909")]
99 // Also, #[unstable(feature = "more_float_constants", issue = "103883")]
100 pub const SQRT_3: f16 = 1.732050807568877293527446341505872367_f16;
101
102 /// 1/sqrt(3)
103 #[unstable(feature = "f16", issue = "116909")]
104 // Also, #[unstable(feature = "more_float_constants", issue = "103883")]
105 pub const FRAC_1_SQRT_3: f16 = 0.577350269189625764509148780501957456_f16;
106
107 /// Euler's number (e)
108 #[unstable(feature = "f16", issue = "116909")]
109 pub const E: f16 = 2.71828182845904523536028747135266250_f16;
110
111 /// log<sub>2</sub>(10)
112 #[unstable(feature = "f16", issue = "116909")]
113 pub const LOG2_10: f16 = 3.32192809488736234787031942948939018_f16;
114
115 /// log<sub>2</sub>(e)
116 #[unstable(feature = "f16", issue = "116909")]
117 pub const LOG2_E: f16 = 1.44269504088896340735992468100189214_f16;
118
119 /// log<sub>10</sub>(2)
120 #[unstable(feature = "f16", issue = "116909")]
121 pub const LOG10_2: f16 = 0.301029995663981195213738894724493027_f16;
122
123 /// log<sub>10</sub>(e)
124 #[unstable(feature = "f16", issue = "116909")]
125 pub const LOG10_E: f16 = 0.434294481903251827651128918916605082_f16;
126
127 /// ln(2)
128 #[unstable(feature = "f16", issue = "116909")]
129 pub const LN_2: f16 = 0.693147180559945309417232121458176568_f16;
130
131 /// ln(10)
132 #[unstable(feature = "f16", issue = "116909")]
133 pub const LN_10: f16 = 2.30258509299404568401799145468436421_f16;
134}
135
136impl f16 {
137 // FIXME(f16_f128): almost all methods in this `impl` are missing examples and a const
138 // implementation. Add these once we can run code on all platforms and have f16/f128 in CTFE.
139
140 /// The radix or base of the internal representation of `f16`.
141 #[unstable(feature = "f16", issue = "116909")]
142 pub const RADIX: u32 = 2;
143
144 /// Number of significant digits in base 2.
145 ///
146 /// Note that the size of the mantissa in the bitwise representation is one
147 /// smaller than this since the leading 1 is not stored explicitly.
148 #[unstable(feature = "f16", issue = "116909")]
149 pub const MANTISSA_DIGITS: u32 = 11;
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 `f16` 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`]: f16::MANTISSA_DIGITS
159 #[unstable(feature = "f16", issue = "116909")]
160 pub const DIGITS: u32 = 3;
161
162 /// [Machine epsilon] value for `f16`.
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`]: f16::MANTISSA_DIGITS
170 #[unstable(feature = "f16", issue = "116909")]
171 #[rustc_diagnostic_item = "f16_epsilon"]
172 pub const EPSILON: f16 = 9.7656e-4_f16;
173
174 /// Smallest finite `f16` value.
175 ///
176 /// Equal to &minus;[`MAX`].
177 ///
178 /// [`MAX`]: f16::MAX
179 #[unstable(feature = "f16", issue = "116909")]
180 pub const MIN: f16 = -6.5504e+4_f16;
181 /// Smallest positive normal `f16` value.
182 ///
183 /// Equal to 2<sup>[`MIN_EXP`]&nbsp;&minus;&nbsp;1</sup>.
184 ///
185 /// [`MIN_EXP`]: f16::MIN_EXP
186 #[unstable(feature = "f16", issue = "116909")]
187 pub const MIN_POSITIVE: f16 = 6.1035e-5_f16;
188 /// Largest finite `f16` value.
189 ///
190 /// Equal to
191 /// (1&nbsp;&minus;&nbsp;2<sup>&minus;[`MANTISSA_DIGITS`]</sup>)&nbsp;2<sup>[`MAX_EXP`]</sup>.
192 ///
193 /// [`MANTISSA_DIGITS`]: f16::MANTISSA_DIGITS
194 /// [`MAX_EXP`]: f16::MAX_EXP
195 #[unstable(feature = "f16", issue = "116909")]
196 pub const MAX: f16 = 6.5504e+4_f16;
197
198 /// One greater than the minimum possible *normal* power of 2 exponent
199 /// for a significand bounded by 1 ≤ x < 2 (i.e. the IEEE definition).
200 ///
201 /// This corresponds to the exact minimum possible *normal* power of 2 exponent
202 /// for a significand bounded by 0.5 ≤ x < 1 (i.e. the C definition).
203 /// In other words, all normal numbers representable by this type are
204 /// greater than or equal to 0.5&nbsp;×&nbsp;2<sup><i>MIN_EXP</i></sup>.
205 #[unstable(feature = "f16", issue = "116909")]
206 pub const MIN_EXP: i32 = -13;
207 /// One greater than the maximum possible power of 2 exponent
208 /// for a significand bounded by 1 ≤ x < 2 (i.e. the IEEE definition).
209 ///
210 /// This corresponds to the exact maximum possible power of 2 exponent
211 /// for a significand bounded by 0.5 ≤ x < 1 (i.e. the C definition).
212 /// In other words, all numbers representable by this type are
213 /// strictly less than 2<sup><i>MAX_EXP</i></sup>.
214 #[unstable(feature = "f16", issue = "116909")]
215 pub const MAX_EXP: i32 = 16;
216
217 /// Minimum <i>x</i> for which 10<sup><i>x</i></sup> is normal.
218 ///
219 /// Equal to ceil(log<sub>10</sub>&nbsp;[`MIN_POSITIVE`]).
220 ///
221 /// [`MIN_POSITIVE`]: f16::MIN_POSITIVE
222 #[unstable(feature = "f16", issue = "116909")]
223 pub const MIN_10_EXP: i32 = -4;
224 /// Maximum <i>x</i> for which 10<sup><i>x</i></sup> is normal.
225 ///
226 /// Equal to floor(log<sub>10</sub>&nbsp;[`MAX`]).
227 ///
228 /// [`MAX`]: f16::MAX
229 #[unstable(feature = "f16", issue = "116909")]
230 pub const MAX_10_EXP: i32 = 4;
231
232 /// Not a Number (NaN).
233 ///
234 /// Note that IEEE 754 doesn't define just a single NaN value; a plethora of bit patterns are
235 /// considered to be NaN. Furthermore, the standard makes a difference between a "signaling" and
236 /// a "quiet" NaN, and allows inspecting its "payload" (the unspecified bits in the bit pattern)
237 /// and its sign. See the [specification of NaN bit patterns](f32#nan-bit-patterns) for more
238 /// info.
239 ///
240 /// This constant is guaranteed to be a quiet NaN (on targets that follow the Rust assumptions
241 /// that the quiet/signaling bit being set to 1 indicates a quiet NaN). Beyond that, nothing is
242 /// guaranteed about the specific bit pattern chosen here: both payload and sign are arbitrary.
243 /// The concrete bit pattern may change across Rust versions and target platforms.
244 #[allow(clippy::eq_op)]
245 #[rustc_diagnostic_item = "f16_nan"]
246 #[unstable(feature = "f16", issue = "116909")]
247 pub const NAN: f16 = 0.0_f16 / 0.0_f16;
248
249 /// Infinity (∞).
250 #[unstable(feature = "f16", issue = "116909")]
251 pub const INFINITY: f16 = 1.0_f16 / 0.0_f16;
252
253 /// Negative infinity (−∞).
254 #[unstable(feature = "f16", issue = "116909")]
255 pub const NEG_INFINITY: f16 = -1.0_f16 / 0.0_f16;
256
257 /// Sign bit
258 pub(crate) const SIGN_MASK: u16 = 0x8000;
259
260 /// Exponent mask
261 pub(crate) const EXP_MASK: u16 = 0x7c00;
262
263 /// Mantissa mask
264 pub(crate) const MAN_MASK: u16 = 0x03ff;
265
266 /// Minimum representable positive value (min subnormal)
267 const TINY_BITS: u16 = 0x1;
268
269 /// Minimum representable negative value (min negative subnormal)
270 const NEG_TINY_BITS: u16 = Self::TINY_BITS | Self::SIGN_MASK;
271
272 /// Returns `true` if this value is NaN.
273 ///
274 /// ```
275 /// #![feature(f16)]
276 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
277 ///
278 /// let nan = f16::NAN;
279 /// let f = 7.0_f16;
280 ///
281 /// assert!(nan.is_nan());
282 /// assert!(!f.is_nan());
283 /// # }
284 /// ```
285 #[inline]
286 #[must_use]
287 #[unstable(feature = "f16", issue = "116909")]
288 #[allow(clippy::eq_op)] // > if you intended to check if the operand is NaN, use `.is_nan()` instead :)
289 pub const fn is_nan(self) -> bool {
290 self != self
291 }
292
293 /// Returns `true` if this value is positive infinity or negative infinity, and
294 /// `false` otherwise.
295 ///
296 /// ```
297 /// #![feature(f16)]
298 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
299 ///
300 /// let f = 7.0f16;
301 /// let inf = f16::INFINITY;
302 /// let neg_inf = f16::NEG_INFINITY;
303 /// let nan = f16::NAN;
304 ///
305 /// assert!(!f.is_infinite());
306 /// assert!(!nan.is_infinite());
307 ///
308 /// assert!(inf.is_infinite());
309 /// assert!(neg_inf.is_infinite());
310 /// # }
311 /// ```
312 #[inline]
313 #[must_use]
314 #[unstable(feature = "f16", issue = "116909")]
315 pub const fn is_infinite(self) -> bool {
316 (self == f16::INFINITY) | (self == f16::NEG_INFINITY)
317 }
318
319 /// Returns `true` if this number is neither infinite nor NaN.
320 ///
321 /// ```
322 /// #![feature(f16)]
323 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
324 ///
325 /// let f = 7.0f16;
326 /// let inf: f16 = f16::INFINITY;
327 /// let neg_inf: f16 = f16::NEG_INFINITY;
328 /// let nan: f16 = f16::NAN;
329 ///
330 /// assert!(f.is_finite());
331 ///
332 /// assert!(!nan.is_finite());
333 /// assert!(!inf.is_finite());
334 /// assert!(!neg_inf.is_finite());
335 /// # }
336 /// ```
337 #[inline]
338 #[must_use]
339 #[unstable(feature = "f16", issue = "116909")]
340 #[rustc_const_unstable(feature = "f16", issue = "116909")]
341 pub const fn is_finite(self) -> bool {
342 // There's no need to handle NaN separately: if self is NaN,
343 // the comparison is not true, exactly as desired.
344 self.abs() < Self::INFINITY
345 }
346
347 /// Returns `true` if the number is [subnormal].
348 ///
349 /// ```
350 /// #![feature(f16)]
351 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
352 ///
353 /// let min = f16::MIN_POSITIVE; // 6.1035e-5
354 /// let max = f16::MAX;
355 /// let lower_than_min = 1.0e-7_f16;
356 /// let zero = 0.0_f16;
357 ///
358 /// assert!(!min.is_subnormal());
359 /// assert!(!max.is_subnormal());
360 ///
361 /// assert!(!zero.is_subnormal());
362 /// assert!(!f16::NAN.is_subnormal());
363 /// assert!(!f16::INFINITY.is_subnormal());
364 /// // Values between `0` and `min` are Subnormal.
365 /// assert!(lower_than_min.is_subnormal());
366 /// # }
367 /// ```
368 /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
369 #[inline]
370 #[must_use]
371 #[unstable(feature = "f16", issue = "116909")]
372 pub const fn is_subnormal(self) -> bool {
373 matches!(self.classify(), FpCategory::Subnormal)
374 }
375
376 /// Returns `true` if the number is neither zero, infinite, [subnormal], or NaN.
377 ///
378 /// ```
379 /// #![feature(f16)]
380 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
381 ///
382 /// let min = f16::MIN_POSITIVE; // 6.1035e-5
383 /// let max = f16::MAX;
384 /// let lower_than_min = 1.0e-7_f16;
385 /// let zero = 0.0_f16;
386 ///
387 /// assert!(min.is_normal());
388 /// assert!(max.is_normal());
389 ///
390 /// assert!(!zero.is_normal());
391 /// assert!(!f16::NAN.is_normal());
392 /// assert!(!f16::INFINITY.is_normal());
393 /// // Values between `0` and `min` are Subnormal.
394 /// assert!(!lower_than_min.is_normal());
395 /// # }
396 /// ```
397 /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
398 #[inline]
399 #[must_use]
400 #[unstable(feature = "f16", issue = "116909")]
401 pub const fn is_normal(self) -> bool {
402 matches!(self.classify(), FpCategory::Normal)
403 }
404
405 /// Returns the floating point category of the number. If only one property
406 /// is going to be tested, it is generally faster to use the specific
407 /// predicate instead.
408 ///
409 /// ```
410 /// #![feature(f16)]
411 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
412 ///
413 /// use std::num::FpCategory;
414 ///
415 /// let num = 12.4_f16;
416 /// let inf = f16::INFINITY;
417 ///
418 /// assert_eq!(num.classify(), FpCategory::Normal);
419 /// assert_eq!(inf.classify(), FpCategory::Infinite);
420 /// # }
421 /// ```
422 #[inline]
423 #[unstable(feature = "f16", issue = "116909")]
424 pub const fn classify(self) -> FpCategory {
425 let b = self.to_bits();
426 match (b & Self::MAN_MASK, b & Self::EXP_MASK) {
427 (0, Self::EXP_MASK) => FpCategory::Infinite,
428 (_, Self::EXP_MASK) => FpCategory::Nan,
429 (0, 0) => FpCategory::Zero,
430 (_, 0) => FpCategory::Subnormal,
431 _ => FpCategory::Normal,
432 }
433 }
434
435 /// Returns `true` if `self` has a positive sign, including `+0.0`, NaNs with
436 /// positive sign bit and positive infinity.
437 ///
438 /// Note that IEEE 754 doesn't assign any meaning to the sign bit in case of
439 /// a NaN, and as Rust doesn't guarantee that the bit pattern of NaNs are
440 /// conserved over arithmetic operations, the result of `is_sign_positive` on
441 /// a NaN might produce an unexpected or non-portable result. See the [specification
442 /// of NaN bit patterns](f32#nan-bit-patterns) for more info. Use `self.signum() == 1.0`
443 /// if you need fully portable behavior (will return `false` for all NaNs).
444 ///
445 /// ```
446 /// #![feature(f16)]
447 /// # // FIXME(f16_f128): LLVM crashes on s390x, llvm/llvm-project#50374
448 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
449 ///
450 /// let f = 7.0_f16;
451 /// let g = -7.0_f16;
452 ///
453 /// assert!(f.is_sign_positive());
454 /// assert!(!g.is_sign_positive());
455 /// # }
456 /// ```
457 #[inline]
458 #[must_use]
459 #[unstable(feature = "f16", issue = "116909")]
460 pub const fn is_sign_positive(self) -> bool {
461 !self.is_sign_negative()
462 }
463
464 /// Returns `true` if `self` has a negative sign, including `-0.0`, NaNs with
465 /// negative sign bit and negative infinity.
466 ///
467 /// Note that IEEE 754 doesn't assign any meaning to the sign bit in case of
468 /// a NaN, and as Rust doesn't guarantee that the bit pattern of NaNs are
469 /// conserved over arithmetic operations, the result of `is_sign_negative` on
470 /// a NaN might produce an unexpected or non-portable result. See the [specification
471 /// of NaN bit patterns](f32#nan-bit-patterns) for more info. Use `self.signum() == -1.0`
472 /// if you need fully portable behavior (will return `false` for all NaNs).
473 ///
474 /// ```
475 /// #![feature(f16)]
476 /// # // FIXME(f16_f128): LLVM crashes on s390x, llvm/llvm-project#50374
477 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
478 ///
479 /// let f = 7.0_f16;
480 /// let g = -7.0_f16;
481 ///
482 /// assert!(!f.is_sign_negative());
483 /// assert!(g.is_sign_negative());
484 /// # }
485 /// ```
486 #[inline]
487 #[must_use]
488 #[unstable(feature = "f16", issue = "116909")]
489 pub const fn is_sign_negative(self) -> bool {
490 // IEEE754 says: isSignMinus(x) is true if and only if x has negative sign. isSignMinus
491 // applies to zeros and NaNs as well.
492 // SAFETY: This is just transmuting to get the sign bit, it's fine.
493 (self.to_bits() & (1 << 15)) != 0
494 }
495
496 /// Returns the least number greater than `self`.
497 ///
498 /// Let `TINY` be the smallest representable positive `f16`. Then,
499 /// - if `self.is_nan()`, this returns `self`;
500 /// - if `self` is [`NEG_INFINITY`], this returns [`MIN`];
501 /// - if `self` is `-TINY`, this returns -0.0;
502 /// - if `self` is -0.0 or +0.0, this returns `TINY`;
503 /// - if `self` is [`MAX`] or [`INFINITY`], this returns [`INFINITY`];
504 /// - otherwise the unique least value greater than `self` is returned.
505 ///
506 /// The identity `x.next_up() == -(-x).next_down()` holds for all non-NaN `x`. When `x`
507 /// is finite `x == x.next_up().next_down()` also holds.
508 ///
509 /// ```rust
510 /// #![feature(f16)]
511 /// # // FIXME(f16_f128): ABI issues on MSVC
512 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
513 ///
514 /// // f16::EPSILON is the difference between 1.0 and the next number up.
515 /// assert_eq!(1.0f16.next_up(), 1.0 + f16::EPSILON);
516 /// // But not for most numbers.
517 /// assert!(0.1f16.next_up() < 0.1 + f16::EPSILON);
518 /// assert_eq!(4356f16.next_up(), 4360.0);
519 /// # }
520 /// ```
521 ///
522 /// This operation corresponds to IEEE-754 `nextUp`.
523 ///
524 /// [`NEG_INFINITY`]: Self::NEG_INFINITY
525 /// [`INFINITY`]: Self::INFINITY
526 /// [`MIN`]: Self::MIN
527 /// [`MAX`]: Self::MAX
528 #[inline]
529 #[doc(alias = "nextUp")]
530 #[unstable(feature = "f16", issue = "116909")]
531 pub const fn next_up(self) -> Self {
532 // Some targets violate Rust's assumption of IEEE semantics, e.g. by flushing
533 // denormals to zero. This is in general unsound and unsupported, but here
534 // we do our best to still produce the correct result on such targets.
535 let bits = self.to_bits();
536 if self.is_nan() || bits == Self::INFINITY.to_bits() {
537 return self;
538 }
539
540 let abs = bits & !Self::SIGN_MASK;
541 let next_bits = if abs == 0 {
542 Self::TINY_BITS
543 } else if bits == abs {
544 bits + 1
545 } else {
546 bits - 1
547 };
548 Self::from_bits(next_bits)
549 }
550
551 /// Returns the greatest number less than `self`.
552 ///
553 /// Let `TINY` be the smallest representable positive `f16`. Then,
554 /// - if `self.is_nan()`, this returns `self`;
555 /// - if `self` is [`INFINITY`], this returns [`MAX`];
556 /// - if `self` is `TINY`, this returns 0.0;
557 /// - if `self` is -0.0 or +0.0, this returns `-TINY`;
558 /// - if `self` is [`MIN`] or [`NEG_INFINITY`], this returns [`NEG_INFINITY`];
559 /// - otherwise the unique greatest value less than `self` is returned.
560 ///
561 /// The identity `x.next_down() == -(-x).next_up()` holds for all non-NaN `x`. When `x`
562 /// is finite `x == x.next_down().next_up()` also holds.
563 ///
564 /// ```rust
565 /// #![feature(f16)]
566 /// # // FIXME(f16_f128): ABI issues on MSVC
567 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
568 ///
569 /// let x = 1.0f16;
570 /// // Clamp value into range [0, 1).
571 /// let clamped = x.clamp(0.0, 1.0f16.next_down());
572 /// assert!(clamped < 1.0);
573 /// assert_eq!(clamped.next_up(), 1.0);
574 /// # }
575 /// ```
576 ///
577 /// This operation corresponds to IEEE-754 `nextDown`.
578 ///
579 /// [`NEG_INFINITY`]: Self::NEG_INFINITY
580 /// [`INFINITY`]: Self::INFINITY
581 /// [`MIN`]: Self::MIN
582 /// [`MAX`]: Self::MAX
583 #[inline]
584 #[doc(alias = "nextDown")]
585 #[unstable(feature = "f16", issue = "116909")]
586 pub const fn next_down(self) -> Self {
587 // Some targets violate Rust's assumption of IEEE semantics, e.g. by flushing
588 // denormals to zero. This is in general unsound and unsupported, but here
589 // we do our best to still produce the correct result on such targets.
590 let bits = self.to_bits();
591 if self.is_nan() || bits == Self::NEG_INFINITY.to_bits() {
592 return self;
593 }
594
595 let abs = bits & !Self::SIGN_MASK;
596 let next_bits = if abs == 0 {
597 Self::NEG_TINY_BITS
598 } else if bits == abs {
599 bits - 1
600 } else {
601 bits + 1
602 };
603 Self::from_bits(next_bits)
604 }
605
606 /// Takes the reciprocal (inverse) of a number, `1/x`.
607 ///
608 /// ```
609 /// #![feature(f16)]
610 /// # // FIXME(f16_f128): extendhfsf2, truncsfhf2, __gnu_h2f_ieee, __gnu_f2h_ieee missing for many platforms
611 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
612 ///
613 /// let x = 2.0_f16;
614 /// let abs_difference = (x.recip() - (1.0 / x)).abs();
615 ///
616 /// assert!(abs_difference <= f16::EPSILON);
617 /// # }
618 /// ```
619 #[inline]
620 #[unstable(feature = "f16", issue = "116909")]
621 #[must_use = "this returns the result of the operation, without modifying the original"]
622 pub const fn recip(self) -> Self {
623 1.0 / self
624 }
625
626 /// Converts radians to degrees.
627 ///
628 /// ```
629 /// #![feature(f16)]
630 /// # // FIXME(f16_f128): extendhfsf2, truncsfhf2, __gnu_h2f_ieee, __gnu_f2h_ieee missing for many platforms
631 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
632 ///
633 /// let angle = std::f16::consts::PI;
634 ///
635 /// let abs_difference = (angle.to_degrees() - 180.0).abs();
636 /// assert!(abs_difference <= 0.5);
637 /// # }
638 /// ```
639 #[inline]
640 #[unstable(feature = "f16", issue = "116909")]
641 #[must_use = "this returns the result of the operation, without modifying the original"]
642 pub const fn to_degrees(self) -> Self {
643 // Use a literal for better precision.
644 const PIS_IN_180: f16 = 57.2957795130823208767981548141051703_f16;
645 self * PIS_IN_180
646 }
647
648 /// Converts degrees to radians.
649 ///
650 /// ```
651 /// #![feature(f16)]
652 /// # // FIXME(f16_f128): extendhfsf2, truncsfhf2, __gnu_h2f_ieee, __gnu_f2h_ieee missing for many platforms
653 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
654 ///
655 /// let angle = 180.0f16;
656 ///
657 /// let abs_difference = (angle.to_radians() - std::f16::consts::PI).abs();
658 ///
659 /// assert!(abs_difference <= 0.01);
660 /// # }
661 /// ```
662 #[inline]
663 #[unstable(feature = "f16", issue = "116909")]
664 #[must_use = "this returns the result of the operation, without modifying the original"]
665 pub const fn to_radians(self) -> f16 {
666 // Use a literal for better precision.
667 const RADS_PER_DEG: f16 = 0.017453292519943295769236907684886_f16;
668 self * RADS_PER_DEG
669 }
670
671 /// Returns the maximum of the two numbers, ignoring NaN.
672 ///
673 /// If one of the arguments is NaN, then the other argument is returned.
674 /// This follows the IEEE 754-2008 semantics for maxNum, except for handling of signaling NaNs;
675 /// this function handles all NaNs the same way and avoids maxNum's problems with associativity.
676 /// This also matches the behavior of libm’s fmax. In particular, if the inputs compare equal
677 /// (such as for the case of `+0.0` and `-0.0`), either input may be returned non-deterministically.
678 ///
679 /// ```
680 /// #![feature(f16)]
681 /// # #[cfg(target_arch = "aarch64")] { // FIXME(f16_F128): rust-lang/rust#123885
682 ///
683 /// let x = 1.0f16;
684 /// let y = 2.0f16;
685 ///
686 /// assert_eq!(x.max(y), y);
687 /// # }
688 /// ```
689 #[inline]
690 #[unstable(feature = "f16", issue = "116909")]
691 #[rustc_const_unstable(feature = "f16", issue = "116909")]
692 #[must_use = "this returns the result of the comparison, without modifying either input"]
693 pub const fn max(self, other: f16) -> f16 {
694 intrinsics::maxnumf16(self, other)
695 }
696
697 /// Returns the minimum of the two numbers, ignoring NaN.
698 ///
699 /// If one of the arguments is NaN, then the other argument is returned.
700 /// This follows the IEEE 754-2008 semantics for minNum, except for handling of signaling NaNs;
701 /// this function handles all NaNs the same way and avoids minNum's problems with associativity.
702 /// This also matches the behavior of libm’s fmin. In particular, if the inputs compare equal
703 /// (such as for the case of `+0.0` and `-0.0`), either input may be returned non-deterministically.
704 ///
705 /// ```
706 /// #![feature(f16)]
707 /// # #[cfg(target_arch = "aarch64")] { // FIXME(f16_F128): rust-lang/rust#123885
708 ///
709 /// let x = 1.0f16;
710 /// let y = 2.0f16;
711 ///
712 /// assert_eq!(x.min(y), x);
713 /// # }
714 /// ```
715 #[inline]
716 #[unstable(feature = "f16", issue = "116909")]
717 #[rustc_const_unstable(feature = "f16", issue = "116909")]
718 #[must_use = "this returns the result of the comparison, without modifying either input"]
719 pub const fn min(self, other: f16) -> f16 {
720 intrinsics::minnumf16(self, other)
721 }
722
723 /// Returns the maximum of the two numbers, propagating NaN.
724 ///
725 /// This returns NaN when *either* argument is NaN, as opposed to
726 /// [`f16::max`] which only returns NaN when *both* arguments are NaN.
727 ///
728 /// ```
729 /// #![feature(f16)]
730 /// #![feature(float_minimum_maximum)]
731 /// # #[cfg(target_arch = "aarch64")] { // FIXME(f16_F128): rust-lang/rust#123885
732 ///
733 /// let x = 1.0f16;
734 /// let y = 2.0f16;
735 ///
736 /// assert_eq!(x.maximum(y), y);
737 /// assert!(x.maximum(f16::NAN).is_nan());
738 /// # }
739 /// ```
740 ///
741 /// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the greater
742 /// of the two numbers. For this operation, -0.0 is considered to be less than +0.0.
743 /// Note that this follows the semantics specified in IEEE 754-2019.
744 ///
745 /// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN
746 /// operand is conserved; see the [specification of NaN bit patterns](f32#nan-bit-patterns) for more info.
747 #[inline]
748 #[unstable(feature = "f16", issue = "116909")]
749 // #[unstable(feature = "float_minimum_maximum", issue = "91079")]
750 #[must_use = "this returns the result of the comparison, without modifying either input"]
751 pub const fn maximum(self, other: f16) -> f16 {
752 intrinsics::maximumf16(self, other)
753 }
754
755 /// Returns the minimum of the two numbers, propagating NaN.
756 ///
757 /// This returns NaN when *either* argument is NaN, as opposed to
758 /// [`f16::min`] which only returns NaN when *both* arguments are NaN.
759 ///
760 /// ```
761 /// #![feature(f16)]
762 /// #![feature(float_minimum_maximum)]
763 /// # #[cfg(target_arch = "aarch64")] { // FIXME(f16_F128): rust-lang/rust#123885
764 ///
765 /// let x = 1.0f16;
766 /// let y = 2.0f16;
767 ///
768 /// assert_eq!(x.minimum(y), x);
769 /// assert!(x.minimum(f16::NAN).is_nan());
770 /// # }
771 /// ```
772 ///
773 /// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the lesser
774 /// of the two numbers. For this operation, -0.0 is considered to be less than +0.0.
775 /// Note that this follows the semantics specified in IEEE 754-2019.
776 ///
777 /// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN
778 /// operand is conserved; see the [specification of NaN bit patterns](f32#nan-bit-patterns) for more info.
779 #[inline]
780 #[unstable(feature = "f16", issue = "116909")]
781 // #[unstable(feature = "float_minimum_maximum", issue = "91079")]
782 #[must_use = "this returns the result of the comparison, without modifying either input"]
783 pub const fn minimum(self, other: f16) -> f16 {
784 intrinsics::minimumf16(self, other)
785 }
786
787 /// Calculates the midpoint (average) between `self` and `rhs`.
788 ///
789 /// This returns NaN when *either* argument is NaN or if a combination of
790 /// +inf and -inf is provided as arguments.
791 ///
792 /// # Examples
793 ///
794 /// ```
795 /// #![feature(f16)]
796 /// # #[cfg(target_arch = "aarch64")] { // FIXME(f16_F128): rust-lang/rust#123885
797 ///
798 /// assert_eq!(1f16.midpoint(4.0), 2.5);
799 /// assert_eq!((-5.5f16).midpoint(8.0), 1.25);
800 /// # }
801 /// ```
802 #[inline]
803 #[doc(alias = "average")]
804 #[unstable(feature = "f16", issue = "116909")]
805 #[rustc_const_unstable(feature = "f16", issue = "116909")]
806 pub const fn midpoint(self, other: f16) -> f16 {
807 const LO: f16 = f16::MIN_POSITIVE * 2.;
808 const HI: f16 = f16::MAX / 2.;
809
810 let (a, b) = (self, other);
811 let abs_a = a.abs();
812 let abs_b = b.abs();
813
814 if abs_a <= HI && abs_b <= HI {
815 // Overflow is impossible
816 (a + b) / 2.
817 } else if abs_a < LO {
818 // Not safe to halve `a` (would underflow)
819 a + (b / 2.)
820 } else if abs_b < LO {
821 // Not safe to halve `b` (would underflow)
822 (a / 2.) + b
823 } else {
824 // Safe to halve `a` and `b`
825 (a / 2.) + (b / 2.)
826 }
827 }
828
829 /// Rounds toward zero and converts to any primitive integer type,
830 /// assuming that the value is finite and fits in that type.
831 ///
832 /// ```
833 /// #![feature(f16)]
834 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
835 ///
836 /// let value = 4.6_f16;
837 /// let rounded = unsafe { value.to_int_unchecked::<u16>() };
838 /// assert_eq!(rounded, 4);
839 ///
840 /// let value = -128.9_f16;
841 /// let rounded = unsafe { value.to_int_unchecked::<i8>() };
842 /// assert_eq!(rounded, i8::MIN);
843 /// # }
844 /// ```
845 ///
846 /// # Safety
847 ///
848 /// The value must:
849 ///
850 /// * Not be `NaN`
851 /// * Not be infinite
852 /// * Be representable in the return type `Int`, after truncating off its fractional part
853 #[inline]
854 #[unstable(feature = "f16", issue = "116909")]
855 #[must_use = "this returns the result of the operation, without modifying the original"]
856 pub unsafe fn to_int_unchecked<Int>(self) -> Int
857 where
858 Self: FloatToInt<Int>,
859 {
860 // SAFETY: the caller must uphold the safety contract for
861 // `FloatToInt::to_int_unchecked`.
862 unsafe { FloatToInt::<Int>::to_int_unchecked(self) }
863 }
864
865 /// Raw transmutation to `u16`.
866 ///
867 /// This is currently identical to `transmute::<f16, u16>(self)` on all platforms.
868 ///
869 /// See [`from_bits`](#method.from_bits) for some discussion of the
870 /// portability of this operation (there are almost no issues).
871 ///
872 /// Note that this function is distinct from `as` casting, which attempts to
873 /// preserve the *numeric* value, and not the bitwise value.
874 ///
875 /// ```
876 /// #![feature(f16)]
877 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
878 ///
879 /// # // FIXME(f16_f128): enable this once const casting works
880 /// # // assert_ne!((1f16).to_bits(), 1f16 as u128); // to_bits() is not casting!
881 /// assert_eq!((12.5f16).to_bits(), 0x4a40);
882 /// # }
883 /// ```
884 #[inline]
885 #[unstable(feature = "f16", issue = "116909")]
886 #[must_use = "this returns the result of the operation, without modifying the original"]
887 #[allow(unnecessary_transmutes)]
888 pub const fn to_bits(self) -> u16 {
889 // SAFETY: `u16` is a plain old datatype so we can always transmute to it.
890 unsafe { mem::transmute(self) }
891 }
892
893 /// Raw transmutation from `u16`.
894 ///
895 /// This is currently identical to `transmute::<u16, f16>(v)` on all platforms.
896 /// It turns out this is incredibly portable, for two reasons:
897 ///
898 /// * Floats and Ints have the same endianness on all supported platforms.
899 /// * IEEE 754 very precisely specifies the bit layout of floats.
900 ///
901 /// However there is one caveat: prior to the 2008 version of IEEE 754, how
902 /// to interpret the NaN signaling bit wasn't actually specified. Most platforms
903 /// (notably x86 and ARM) picked the interpretation that was ultimately
904 /// standardized in 2008, but some didn't (notably MIPS). As a result, all
905 /// signaling NaNs on MIPS are quiet NaNs on x86, and vice-versa.
906 ///
907 /// Rather than trying to preserve signaling-ness cross-platform, this
908 /// implementation favors preserving the exact bits. This means that
909 /// any payloads encoded in NaNs will be preserved even if the result of
910 /// this method is sent over the network from an x86 machine to a MIPS one.
911 ///
912 /// If the results of this method are only manipulated by the same
913 /// architecture that produced them, then there is no portability concern.
914 ///
915 /// If the input isn't NaN, then there is no portability concern.
916 ///
917 /// If you don't care about signalingness (very likely), then there is no
918 /// portability concern.
919 ///
920 /// Note that this function is distinct from `as` casting, which attempts to
921 /// preserve the *numeric* value, and not the bitwise value.
922 ///
923 /// ```
924 /// #![feature(f16)]
925 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
926 ///
927 /// let v = f16::from_bits(0x4a40);
928 /// assert_eq!(v, 12.5);
929 /// # }
930 /// ```
931 #[inline]
932 #[must_use]
933 #[unstable(feature = "f16", issue = "116909")]
934 #[allow(unnecessary_transmutes)]
935 pub const fn from_bits(v: u16) -> Self {
936 // It turns out the safety issues with sNaN were overblown! Hooray!
937 // SAFETY: `u16` is a plain old datatype so we can always transmute from it.
938 unsafe { mem::transmute(v) }
939 }
940
941 /// Returns the memory representation of this floating point number as a byte array in
942 /// big-endian (network) byte order.
943 ///
944 /// See [`from_bits`](Self::from_bits) for some discussion of the
945 /// portability of this operation (there are almost no issues).
946 ///
947 /// # Examples
948 ///
949 /// ```
950 /// #![feature(f16)]
951 /// # // FIXME(f16_f128): LLVM crashes on s390x, llvm/llvm-project#50374
952 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
953 ///
954 /// let bytes = 12.5f16.to_be_bytes();
955 /// assert_eq!(bytes, [0x4a, 0x40]);
956 /// # }
957 /// ```
958 #[inline]
959 #[unstable(feature = "f16", issue = "116909")]
960 #[must_use = "this returns the result of the operation, without modifying the original"]
961 pub const fn to_be_bytes(self) -> [u8; 2] {
962 self.to_bits().to_be_bytes()
963 }
964
965 /// Returns the memory representation of this floating point number as a byte array in
966 /// little-endian byte order.
967 ///
968 /// See [`from_bits`](Self::from_bits) for some discussion of the
969 /// portability of this operation (there are almost no issues).
970 ///
971 /// # Examples
972 ///
973 /// ```
974 /// #![feature(f16)]
975 /// # // FIXME(f16_f128): LLVM crashes on s390x, llvm/llvm-project#50374
976 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
977 ///
978 /// let bytes = 12.5f16.to_le_bytes();
979 /// assert_eq!(bytes, [0x40, 0x4a]);
980 /// # }
981 /// ```
982 #[inline]
983 #[unstable(feature = "f16", issue = "116909")]
984 #[must_use = "this returns the result of the operation, without modifying the original"]
985 pub const fn to_le_bytes(self) -> [u8; 2] {
986 self.to_bits().to_le_bytes()
987 }
988
989 /// Returns the memory representation of this floating point number as a byte array in
990 /// native byte order.
991 ///
992 /// As the target platform's native endianness is used, portable code
993 /// should use [`to_be_bytes`] or [`to_le_bytes`], as appropriate, instead.
994 ///
995 /// [`to_be_bytes`]: f16::to_be_bytes
996 /// [`to_le_bytes`]: f16::to_le_bytes
997 ///
998 /// See [`from_bits`](Self::from_bits) for some discussion of the
999 /// portability of this operation (there are almost no issues).
1000 ///
1001 /// # Examples
1002 ///
1003 /// ```
1004 /// #![feature(f16)]
1005 /// # // FIXME(f16_f128): LLVM crashes on s390x, llvm/llvm-project#50374
1006 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1007 ///
1008 /// let bytes = 12.5f16.to_ne_bytes();
1009 /// assert_eq!(
1010 /// bytes,
1011 /// if cfg!(target_endian = "big") {
1012 /// [0x4a, 0x40]
1013 /// } else {
1014 /// [0x40, 0x4a]
1015 /// }
1016 /// );
1017 /// # }
1018 /// ```
1019 #[inline]
1020 #[unstable(feature = "f16", issue = "116909")]
1021 #[must_use = "this returns the result of the operation, without modifying the original"]
1022 pub const fn to_ne_bytes(self) -> [u8; 2] {
1023 self.to_bits().to_ne_bytes()
1024 }
1025
1026 /// Creates a floating point value from its representation as a byte array in big endian.
1027 ///
1028 /// See [`from_bits`](Self::from_bits) for some discussion of the
1029 /// portability of this operation (there are almost no issues).
1030 ///
1031 /// # Examples
1032 ///
1033 /// ```
1034 /// #![feature(f16)]
1035 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1036 ///
1037 /// let value = f16::from_be_bytes([0x4a, 0x40]);
1038 /// assert_eq!(value, 12.5);
1039 /// # }
1040 /// ```
1041 #[inline]
1042 #[must_use]
1043 #[unstable(feature = "f16", issue = "116909")]
1044 pub const fn from_be_bytes(bytes: [u8; 2]) -> Self {
1045 Self::from_bits(u16::from_be_bytes(bytes))
1046 }
1047
1048 /// Creates a floating point value from its representation as a byte array in little endian.
1049 ///
1050 /// See [`from_bits`](Self::from_bits) for some discussion of the
1051 /// portability of this operation (there are almost no issues).
1052 ///
1053 /// # Examples
1054 ///
1055 /// ```
1056 /// #![feature(f16)]
1057 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1058 ///
1059 /// let value = f16::from_le_bytes([0x40, 0x4a]);
1060 /// assert_eq!(value, 12.5);
1061 /// # }
1062 /// ```
1063 #[inline]
1064 #[must_use]
1065 #[unstable(feature = "f16", issue = "116909")]
1066 pub const fn from_le_bytes(bytes: [u8; 2]) -> Self {
1067 Self::from_bits(u16::from_le_bytes(bytes))
1068 }
1069
1070 /// Creates a floating point value from its representation as a byte array in native endian.
1071 ///
1072 /// As the target platform's native endianness is used, portable code
1073 /// likely wants to use [`from_be_bytes`] or [`from_le_bytes`], as
1074 /// appropriate instead.
1075 ///
1076 /// [`from_be_bytes`]: f16::from_be_bytes
1077 /// [`from_le_bytes`]: f16::from_le_bytes
1078 ///
1079 /// See [`from_bits`](Self::from_bits) for some discussion of the
1080 /// portability of this operation (there are almost no issues).
1081 ///
1082 /// # Examples
1083 ///
1084 /// ```
1085 /// #![feature(f16)]
1086 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1087 ///
1088 /// let value = f16::from_ne_bytes(if cfg!(target_endian = "big") {
1089 /// [0x4a, 0x40]
1090 /// } else {
1091 /// [0x40, 0x4a]
1092 /// });
1093 /// assert_eq!(value, 12.5);
1094 /// # }
1095 /// ```
1096 #[inline]
1097 #[must_use]
1098 #[unstable(feature = "f16", issue = "116909")]
1099 pub const fn from_ne_bytes(bytes: [u8; 2]) -> Self {
1100 Self::from_bits(u16::from_ne_bytes(bytes))
1101 }
1102
1103 /// Returns the ordering between `self` and `other`.
1104 ///
1105 /// Unlike the standard partial comparison between floating point numbers,
1106 /// this comparison always produces an ordering in accordance to
1107 /// the `totalOrder` predicate as defined in the IEEE 754 (2008 revision)
1108 /// floating point standard. The values are ordered in the following sequence:
1109 ///
1110 /// - negative quiet NaN
1111 /// - negative signaling NaN
1112 /// - negative infinity
1113 /// - negative numbers
1114 /// - negative subnormal numbers
1115 /// - negative zero
1116 /// - positive zero
1117 /// - positive subnormal numbers
1118 /// - positive numbers
1119 /// - positive infinity
1120 /// - positive signaling NaN
1121 /// - positive quiet NaN.
1122 ///
1123 /// The ordering established by this function does not always agree with the
1124 /// [`PartialOrd`] and [`PartialEq`] implementations of `f16`. For example,
1125 /// they consider negative and positive zero equal, while `total_cmp`
1126 /// doesn't.
1127 ///
1128 /// The interpretation of the signaling NaN bit follows the definition in
1129 /// the IEEE 754 standard, which may not match the interpretation by some of
1130 /// the older, non-conformant (e.g. MIPS) hardware implementations.
1131 ///
1132 /// # Example
1133 ///
1134 /// ```
1135 /// #![feature(f16)]
1136 /// # // FIXME(f16_f128): extendhfsf2, truncsfhf2, __gnu_h2f_ieee, __gnu_f2h_ieee missing for many platforms
1137 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1138 ///
1139 /// struct GoodBoy {
1140 /// name: &'static str,
1141 /// weight: f16,
1142 /// }
1143 ///
1144 /// let mut bois = vec![
1145 /// GoodBoy { name: "Pucci", weight: 0.1 },
1146 /// GoodBoy { name: "Woofer", weight: 99.0 },
1147 /// GoodBoy { name: "Yapper", weight: 10.0 },
1148 /// GoodBoy { name: "Chonk", weight: f16::INFINITY },
1149 /// GoodBoy { name: "Abs. Unit", weight: f16::NAN },
1150 /// GoodBoy { name: "Floaty", weight: -5.0 },
1151 /// ];
1152 ///
1153 /// bois.sort_by(|a, b| a.weight.total_cmp(&b.weight));
1154 ///
1155 /// // `f16::NAN` could be positive or negative, which will affect the sort order.
1156 /// if f16::NAN.is_sign_negative() {
1157 /// bois.into_iter().map(|b| b.weight)
1158 /// .zip([f16::NAN, -5.0, 0.1, 10.0, 99.0, f16::INFINITY].iter())
1159 /// .for_each(|(a, b)| assert_eq!(a.to_bits(), b.to_bits()))
1160 /// } else {
1161 /// bois.into_iter().map(|b| b.weight)
1162 /// .zip([-5.0, 0.1, 10.0, 99.0, f16::INFINITY, f16::NAN].iter())
1163 /// .for_each(|(a, b)| assert_eq!(a.to_bits(), b.to_bits()))
1164 /// }
1165 /// # }
1166 /// ```
1167 #[inline]
1168 #[must_use]
1169 #[unstable(feature = "f16", issue = "116909")]
1170 pub fn total_cmp(&self, other: &Self) -> crate::cmp::Ordering {
1171 let mut left = self.to_bits() as i16;
1172 let mut right = other.to_bits() as i16;
1173
1174 // In case of negatives, flip all the bits except the sign
1175 // to achieve a similar layout as two's complement integers
1176 //
1177 // Why does this work? IEEE 754 floats consist of three fields:
1178 // Sign bit, exponent and mantissa. The set of exponent and mantissa
1179 // fields as a whole have the property that their bitwise order is
1180 // equal to the numeric magnitude where the magnitude is defined.
1181 // The magnitude is not normally defined on NaN values, but
1182 // IEEE 754 totalOrder defines the NaN values also to follow the
1183 // bitwise order. This leads to order explained in the doc comment.
1184 // However, the representation of magnitude is the same for negative
1185 // and positive numbers – only the sign bit is different.
1186 // To easily compare the floats as signed integers, we need to
1187 // flip the exponent and mantissa bits in case of negative numbers.
1188 // We effectively convert the numbers to "two's complement" form.
1189 //
1190 // To do the flipping, we construct a mask and XOR against it.
1191 // We branchlessly calculate an "all-ones except for the sign bit"
1192 // mask from negative-signed values: right shifting sign-extends
1193 // the integer, so we "fill" the mask with sign bits, and then
1194 // convert to unsigned to push one more zero bit.
1195 // On positive values, the mask is all zeros, so it's a no-op.
1196 left ^= (((left >> 15) as u16) >> 1) as i16;
1197 right ^= (((right >> 15) as u16) >> 1) as i16;
1198
1199 left.cmp(&right)
1200 }
1201
1202 /// Restrict a value to a certain interval unless it is NaN.
1203 ///
1204 /// Returns `max` if `self` is greater than `max`, and `min` if `self` is
1205 /// less than `min`. Otherwise this returns `self`.
1206 ///
1207 /// Note that this function returns NaN if the initial value was NaN as
1208 /// well.
1209 ///
1210 /// # Panics
1211 ///
1212 /// Panics if `min > max`, `min` is NaN, or `max` is NaN.
1213 ///
1214 /// # Examples
1215 ///
1216 /// ```
1217 /// #![feature(f16)]
1218 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1219 ///
1220 /// assert!((-3.0f16).clamp(-2.0, 1.0) == -2.0);
1221 /// assert!((0.0f16).clamp(-2.0, 1.0) == 0.0);
1222 /// assert!((2.0f16).clamp(-2.0, 1.0) == 1.0);
1223 /// assert!((f16::NAN).clamp(-2.0, 1.0).is_nan());
1224 /// # }
1225 /// ```
1226 #[inline]
1227 #[unstable(feature = "f16", issue = "116909")]
1228 #[must_use = "method returns a new number and does not mutate the original value"]
1229 pub const fn clamp(mut self, min: f16, max: f16) -> f16 {
1230 const_assert!(
1231 min <= max,
1232 "min > max, or either was NaN",
1233 "min > max, or either was NaN. min = {min:?}, max = {max:?}",
1234 min: f16,
1235 max: f16,
1236 );
1237
1238 if self < min {
1239 self = min;
1240 }
1241 if self > max {
1242 self = max;
1243 }
1244 self
1245 }
1246
1247 /// Computes the absolute value of `self`.
1248 ///
1249 /// This function always returns the precise result.
1250 ///
1251 /// # Examples
1252 ///
1253 /// ```
1254 /// #![feature(f16)]
1255 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1256 ///
1257 /// let x = 3.5_f16;
1258 /// let y = -3.5_f16;
1259 ///
1260 /// assert_eq!(x.abs(), x);
1261 /// assert_eq!(y.abs(), -y);
1262 ///
1263 /// assert!(f16::NAN.abs().is_nan());
1264 /// # }
1265 /// ```
1266 #[inline]
1267 #[unstable(feature = "f16", issue = "116909")]
1268 #[rustc_const_unstable(feature = "f16", issue = "116909")]
1269 #[must_use = "method returns a new number and does not mutate the original value"]
1270 pub const fn abs(self) -> Self {
1271 // FIXME(f16_f128): replace with `intrinsics::fabsf16` when available
1272 Self::from_bits(self.to_bits() & !(1 << 15))
1273 }
1274
1275 /// Returns a number that represents the sign of `self`.
1276 ///
1277 /// - `1.0` if the number is positive, `+0.0` or `INFINITY`
1278 /// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
1279 /// - NaN if the number is NaN
1280 ///
1281 /// # Examples
1282 ///
1283 /// ```
1284 /// #![feature(f16)]
1285 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1286 ///
1287 /// let f = 3.5_f16;
1288 ///
1289 /// assert_eq!(f.signum(), 1.0);
1290 /// assert_eq!(f16::NEG_INFINITY.signum(), -1.0);
1291 ///
1292 /// assert!(f16::NAN.signum().is_nan());
1293 /// # }
1294 /// ```
1295 #[inline]
1296 #[unstable(feature = "f16", issue = "116909")]
1297 #[rustc_const_unstable(feature = "f16", issue = "116909")]
1298 #[must_use = "method returns a new number and does not mutate the original value"]
1299 pub const fn signum(self) -> f16 {
1300 if self.is_nan() { Self::NAN } else { 1.0_f16.copysign(self) }
1301 }
1302
1303 /// Returns a number composed of the magnitude of `self` and the sign of
1304 /// `sign`.
1305 ///
1306 /// Equal to `self` if the sign of `self` and `sign` are the same, otherwise equal to `-self`.
1307 /// If `self` is a NaN, then a NaN with the same payload as `self` and the sign bit of `sign` is
1308 /// returned.
1309 ///
1310 /// If `sign` is a NaN, then this operation will still carry over its sign into the result. Note
1311 /// that IEEE 754 doesn't assign any meaning to the sign bit in case of a NaN, and as Rust
1312 /// doesn't guarantee that the bit pattern of NaNs are conserved over arithmetic operations, the
1313 /// result of `copysign` with `sign` being a NaN might produce an unexpected or non-portable
1314 /// result. See the [specification of NaN bit patterns](primitive@f32#nan-bit-patterns) for more
1315 /// info.
1316 ///
1317 /// # Examples
1318 ///
1319 /// ```
1320 /// #![feature(f16)]
1321 /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1322 ///
1323 /// let f = 3.5_f16;
1324 ///
1325 /// assert_eq!(f.copysign(0.42), 3.5_f16);
1326 /// assert_eq!(f.copysign(-0.42), -3.5_f16);
1327 /// assert_eq!((-f).copysign(0.42), 3.5_f16);
1328 /// assert_eq!((-f).copysign(-0.42), -3.5_f16);
1329 ///
1330 /// assert!(f16::NAN.copysign(1.0).is_nan());
1331 /// # }
1332 /// ```
1333 #[inline]
1334 #[unstable(feature = "f16", issue = "116909")]
1335 #[rustc_const_unstable(feature = "f16", issue = "116909")]
1336 #[must_use = "method returns a new number and does not mutate the original value"]
1337 pub const fn copysign(self, sign: f16) -> f16 {
1338 // SAFETY: this is actually a safe intrinsic
1339 unsafe { intrinsics::copysignf16(self, sign) }
1340 }
1341
1342 /// Float addition that allows optimizations based on algebraic rules.
1343 ///
1344 /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1345 #[must_use = "method returns a new number and does not mutate the original value"]
1346 #[unstable(feature = "float_algebraic", issue = "136469")]
1347 #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1348 #[inline]
1349 pub const fn algebraic_add(self, rhs: f16) -> f16 {
1350 intrinsics::fadd_algebraic(self, rhs)
1351 }
1352
1353 /// Float subtraction that allows optimizations based on algebraic rules.
1354 ///
1355 /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1356 #[must_use = "method returns a new number and does not mutate the original value"]
1357 #[unstable(feature = "float_algebraic", issue = "136469")]
1358 #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1359 #[inline]
1360 pub const 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 #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1370 #[inline]
1371 pub const fn algebraic_mul(self, rhs: f16) -> f16 {
1372 intrinsics::fmul_algebraic(self, rhs)
1373 }
1374
1375 /// Float division that allows optimizations based on algebraic rules.
1376 ///
1377 /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1378 #[must_use = "method returns a new number and does not mutate the original value"]
1379 #[unstable(feature = "float_algebraic", issue = "136469")]
1380 #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1381 #[inline]
1382 pub const fn algebraic_div(self, rhs: f16) -> f16 {
1383 intrinsics::fdiv_algebraic(self, rhs)
1384 }
1385
1386 /// Float remainder that allows optimizations based on algebraic rules.
1387 ///
1388 /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1389 #[must_use = "method returns a new number and does not mutate the original value"]
1390 #[unstable(feature = "float_algebraic", issue = "136469")]
1391 #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1392 #[inline]
1393 pub const fn algebraic_rem(self, rhs: f16) -> f16 {
1394 intrinsics::frem_algebraic(self, rhs)
1395 }
1396}
1397
1398// Functions in this module fall into `core_float_math`
1399// #[unstable(feature = "core_float_math", issue = "137578")]
1400#[cfg(not(test))]
1401#[doc(test(attr(feature(cfg_target_has_reliable_f16_f128), expect(internal_features))))]
1402impl f16 {
1403 /// Returns the largest integer less than or equal to `self`.
1404 ///
1405 /// This function always returns the precise result.
1406 ///
1407 /// # Examples
1408 ///
1409 /// ```
1410 /// #![feature(f16)]
1411 /// # #[cfg(not(miri))]
1412 /// # #[cfg(target_has_reliable_f16_math)] {
1413 ///
1414 /// let f = 3.7_f16;
1415 /// let g = 3.0_f16;
1416 /// let h = -3.7_f16;
1417 ///
1418 /// assert_eq!(f.floor(), 3.0);
1419 /// assert_eq!(g.floor(), 3.0);
1420 /// assert_eq!(h.floor(), -4.0);
1421 /// # }
1422 /// ```
1423 #[inline]
1424 #[rustc_allow_incoherent_impl]
1425 #[unstable(feature = "f16", issue = "116909")]
1426 #[rustc_const_unstable(feature = "f16", issue = "116909")]
1427 // #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
1428 #[must_use = "method returns a new number and does not mutate the original value"]
1429 pub const fn floor(self) -> f16 {
1430 // SAFETY: intrinsic with no preconditions
1431 unsafe { intrinsics::floorf16(self) }
1432 }
1433
1434 /// Returns the smallest integer greater than or equal to `self`.
1435 ///
1436 /// This function always returns the precise result.
1437 ///
1438 /// # Examples
1439 ///
1440 /// ```
1441 /// #![feature(f16)]
1442 /// # #[cfg(not(miri))]
1443 /// # #[cfg(target_has_reliable_f16_math)] {
1444 ///
1445 /// let f = 3.01_f16;
1446 /// let g = 4.0_f16;
1447 ///
1448 /// assert_eq!(f.ceil(), 4.0);
1449 /// assert_eq!(g.ceil(), 4.0);
1450 /// # }
1451 /// ```
1452 #[inline]
1453 #[doc(alias = "ceiling")]
1454 #[rustc_allow_incoherent_impl]
1455 #[unstable(feature = "f16", issue = "116909")]
1456 #[rustc_const_unstable(feature = "f16", issue = "116909")]
1457 // #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
1458 #[must_use = "method returns a new number and does not mutate the original value"]
1459 pub const fn ceil(self) -> f16 {
1460 // SAFETY: intrinsic with no preconditions
1461 unsafe { intrinsics::ceilf16(self) }
1462 }
1463
1464 /// Returns the nearest integer to `self`. If a value is half-way between two
1465 /// integers, round away from `0.0`.
1466 ///
1467 /// This function always returns the precise result.
1468 ///
1469 /// # Examples
1470 ///
1471 /// ```
1472 /// #![feature(f16)]
1473 /// # #[cfg(not(miri))]
1474 /// # #[cfg(target_has_reliable_f16_math)] {
1475 ///
1476 /// let f = 3.3_f16;
1477 /// let g = -3.3_f16;
1478 /// let h = -3.7_f16;
1479 /// let i = 3.5_f16;
1480 /// let j = 4.5_f16;
1481 ///
1482 /// assert_eq!(f.round(), 3.0);
1483 /// assert_eq!(g.round(), -3.0);
1484 /// assert_eq!(h.round(), -4.0);
1485 /// assert_eq!(i.round(), 4.0);
1486 /// assert_eq!(j.round(), 5.0);
1487 /// # }
1488 /// ```
1489 #[inline]
1490 #[rustc_allow_incoherent_impl]
1491 #[unstable(feature = "f16", issue = "116909")]
1492 #[rustc_const_unstable(feature = "f16", issue = "116909")]
1493 // #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
1494 #[must_use = "method returns a new number and does not mutate the original value"]
1495 pub const fn round(self) -> f16 {
1496 // SAFETY: intrinsic with no preconditions
1497 unsafe { intrinsics::roundf16(self) }
1498 }
1499
1500 /// Returns the nearest integer to a number. Rounds half-way cases to the number
1501 /// with an even least significant digit.
1502 ///
1503 /// This function always returns the precise result.
1504 ///
1505 /// # Examples
1506 ///
1507 /// ```
1508 /// #![feature(f16)]
1509 /// # #[cfg(not(miri))]
1510 /// # #[cfg(target_has_reliable_f16_math)] {
1511 ///
1512 /// let f = 3.3_f16;
1513 /// let g = -3.3_f16;
1514 /// let h = 3.5_f16;
1515 /// let i = 4.5_f16;
1516 ///
1517 /// assert_eq!(f.round_ties_even(), 3.0);
1518 /// assert_eq!(g.round_ties_even(), -3.0);
1519 /// assert_eq!(h.round_ties_even(), 4.0);
1520 /// assert_eq!(i.round_ties_even(), 4.0);
1521 /// # }
1522 /// ```
1523 #[inline]
1524 #[rustc_allow_incoherent_impl]
1525 #[unstable(feature = "f16", issue = "116909")]
1526 #[rustc_const_unstable(feature = "f16", issue = "116909")]
1527 // #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
1528 #[must_use = "method returns a new number and does not mutate the original value"]
1529 pub const fn round_ties_even(self) -> f16 {
1530 intrinsics::round_ties_even_f16(self)
1531 }
1532
1533 /// Returns the integer part of `self`.
1534 /// This means that non-integer numbers are always truncated towards zero.
1535 ///
1536 /// This function always returns the precise result.
1537 ///
1538 /// # Examples
1539 ///
1540 /// ```
1541 /// #![feature(f16)]
1542 /// # #[cfg(not(miri))]
1543 /// # #[cfg(target_has_reliable_f16_math)] {
1544 ///
1545 /// let f = 3.7_f16;
1546 /// let g = 3.0_f16;
1547 /// let h = -3.7_f16;
1548 ///
1549 /// assert_eq!(f.trunc(), 3.0);
1550 /// assert_eq!(g.trunc(), 3.0);
1551 /// assert_eq!(h.trunc(), -3.0);
1552 /// # }
1553 /// ```
1554 #[inline]
1555 #[doc(alias = "truncate")]
1556 #[rustc_allow_incoherent_impl]
1557 #[unstable(feature = "f16", issue = "116909")]
1558 #[rustc_const_unstable(feature = "f16", issue = "116909")]
1559 // #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
1560 #[must_use = "method returns a new number and does not mutate the original value"]
1561 pub const fn trunc(self) -> f16 {
1562 // SAFETY: intrinsic with no preconditions
1563 unsafe { intrinsics::truncf16(self) }
1564 }
1565
1566 /// Returns the fractional part of `self`.
1567 ///
1568 /// This function always returns the precise result.
1569 ///
1570 /// # Examples
1571 ///
1572 /// ```
1573 /// #![feature(f16)]
1574 /// # #[cfg(not(miri))]
1575 /// # #[cfg(target_has_reliable_f16_math)] {
1576 ///
1577 /// let x = 3.6_f16;
1578 /// let y = -3.6_f16;
1579 /// let abs_difference_x = (x.fract() - 0.6).abs();
1580 /// let abs_difference_y = (y.fract() - (-0.6)).abs();
1581 ///
1582 /// assert!(abs_difference_x <= f16::EPSILON);
1583 /// assert!(abs_difference_y <= f16::EPSILON);
1584 /// # }
1585 /// ```
1586 #[inline]
1587 #[rustc_allow_incoherent_impl]
1588 #[unstable(feature = "f16", issue = "116909")]
1589 #[rustc_const_unstable(feature = "f16", issue = "116909")]
1590 // #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
1591 #[must_use = "method returns a new number and does not mutate the original value"]
1592 pub const fn fract(self) -> f16 {
1593 self - self.trunc()
1594 }
1595
1596 /// Fused multiply-add. Computes `(self * a) + b` with only one rounding
1597 /// error, yielding a more accurate result than an unfused multiply-add.
1598 ///
1599 /// Using `mul_add` *may* be more performant than an unfused multiply-add if
1600 /// the target architecture has a dedicated `fma` CPU instruction. However,
1601 /// this is not always true, and will be heavily dependant on designing
1602 /// algorithms with specific target hardware in mind.
1603 ///
1604 /// # Precision
1605 ///
1606 /// The result of this operation is guaranteed to be the rounded
1607 /// infinite-precision result. It is specified by IEEE 754 as
1608 /// `fusedMultiplyAdd` and guaranteed not to change.
1609 ///
1610 /// # Examples
1611 ///
1612 /// ```
1613 /// #![feature(f16)]
1614 /// # #[cfg(not(miri))]
1615 /// # #[cfg(target_has_reliable_f16_math)] {
1616 ///
1617 /// let m = 10.0_f16;
1618 /// let x = 4.0_f16;
1619 /// let b = 60.0_f16;
1620 ///
1621 /// assert_eq!(m.mul_add(x, b), 100.0);
1622 /// assert_eq!(m * x + b, 100.0);
1623 ///
1624 /// let one_plus_eps = 1.0_f16 + f16::EPSILON;
1625 /// let one_minus_eps = 1.0_f16 - f16::EPSILON;
1626 /// let minus_one = -1.0_f16;
1627 ///
1628 /// // The exact result (1 + eps) * (1 - eps) = 1 - eps * eps.
1629 /// assert_eq!(one_plus_eps.mul_add(one_minus_eps, minus_one), -f16::EPSILON * f16::EPSILON);
1630 /// // Different rounding with the non-fused multiply and add.
1631 /// assert_eq!(one_plus_eps * one_minus_eps + minus_one, 0.0);
1632 /// # }
1633 /// ```
1634 #[inline]
1635 #[rustc_allow_incoherent_impl]
1636 #[unstable(feature = "f16", issue = "116909")]
1637 #[doc(alias = "fmaf16", alias = "fusedMultiplyAdd")]
1638 #[must_use = "method returns a new number and does not mutate the original value"]
1639 pub fn mul_add(self, a: f16, b: f16) -> f16 {
1640 // SAFETY: intrinsic with no preconditions
1641 unsafe { intrinsics::fmaf16(self, a, b) }
1642 }
1643
1644 /// Calculates Euclidean division, the matching method for `rem_euclid`.
1645 ///
1646 /// This computes the integer `n` such that
1647 /// `self = n * rhs + self.rem_euclid(rhs)`.
1648 /// In other words, the result is `self / rhs` rounded to the integer `n`
1649 /// such that `self >= n * rhs`.
1650 ///
1651 /// # Precision
1652 ///
1653 /// The result of this operation is guaranteed to be the rounded
1654 /// infinite-precision result.
1655 ///
1656 /// # Examples
1657 ///
1658 /// ```
1659 /// #![feature(f16)]
1660 /// # #[cfg(not(miri))]
1661 /// # #[cfg(target_has_reliable_f16_math)] {
1662 ///
1663 /// let a: f16 = 7.0;
1664 /// let b = 4.0;
1665 /// assert_eq!(a.div_euclid(b), 1.0); // 7.0 > 4.0 * 1.0
1666 /// assert_eq!((-a).div_euclid(b), -2.0); // -7.0 >= 4.0 * -2.0
1667 /// assert_eq!(a.div_euclid(-b), -1.0); // 7.0 >= -4.0 * -1.0
1668 /// assert_eq!((-a).div_euclid(-b), 2.0); // -7.0 >= -4.0 * 2.0
1669 /// # }
1670 /// ```
1671 #[inline]
1672 #[rustc_allow_incoherent_impl]
1673 #[unstable(feature = "f16", issue = "116909")]
1674 #[must_use = "method returns a new number and does not mutate the original value"]
1675 pub fn div_euclid(self, rhs: f16) -> f16 {
1676 let q = (self / rhs).trunc();
1677 if self % rhs < 0.0 {
1678 return if rhs > 0.0 { q - 1.0 } else { q + 1.0 };
1679 }
1680 q
1681 }
1682
1683 /// Calculates the least nonnegative remainder of `self (mod rhs)`.
1684 ///
1685 /// In particular, the return value `r` satisfies `0.0 <= r < rhs.abs()` in
1686 /// most cases. However, due to a floating point round-off error it can
1687 /// result in `r == rhs.abs()`, violating the mathematical definition, if
1688 /// `self` is much smaller than `rhs.abs()` in magnitude and `self < 0.0`.
1689 /// This result is not an element of the function's codomain, but it is the
1690 /// closest floating point number in the real numbers and thus fulfills the
1691 /// property `self == self.div_euclid(rhs) * rhs + self.rem_euclid(rhs)`
1692 /// approximately.
1693 ///
1694 /// # Precision
1695 ///
1696 /// The result of this operation is guaranteed to be the rounded
1697 /// infinite-precision result.
1698 ///
1699 /// # Examples
1700 ///
1701 /// ```
1702 /// #![feature(f16)]
1703 /// # #[cfg(not(miri))]
1704 /// # #[cfg(target_has_reliable_f16_math)] {
1705 ///
1706 /// let a: f16 = 7.0;
1707 /// let b = 4.0;
1708 /// assert_eq!(a.rem_euclid(b), 3.0);
1709 /// assert_eq!((-a).rem_euclid(b), 1.0);
1710 /// assert_eq!(a.rem_euclid(-b), 3.0);
1711 /// assert_eq!((-a).rem_euclid(-b), 1.0);
1712 /// // limitation due to round-off error
1713 /// assert!((-f16::EPSILON).rem_euclid(3.0) != 0.0);
1714 /// # }
1715 /// ```
1716 #[inline]
1717 #[rustc_allow_incoherent_impl]
1718 #[doc(alias = "modulo", alias = "mod")]
1719 #[unstable(feature = "f16", issue = "116909")]
1720 #[must_use = "method returns a new number and does not mutate the original value"]
1721 pub fn rem_euclid(self, rhs: f16) -> f16 {
1722 let r = self % rhs;
1723 if r < 0.0 { r + rhs.abs() } else { r }
1724 }
1725
1726 /// Raises a number to an integer power.
1727 ///
1728 /// Using this function is generally faster than using `powf`.
1729 /// It might have a different sequence of rounding operations than `powf`,
1730 /// so the results are not guaranteed to agree.
1731 ///
1732 /// # Unspecified precision
1733 ///
1734 /// The precision of this function is non-deterministic. This means it varies by platform,
1735 /// Rust version, and can even differ within the same execution from one invocation to the next.
1736 ///
1737 /// # Examples
1738 ///
1739 /// ```
1740 /// #![feature(f16)]
1741 /// # #[cfg(not(miri))]
1742 /// # #[cfg(target_has_reliable_f16_math)] {
1743 ///
1744 /// let x = 2.0_f16;
1745 /// let abs_difference = (x.powi(2) - (x * x)).abs();
1746 /// assert!(abs_difference <= f16::EPSILON);
1747 ///
1748 /// assert_eq!(f16::powi(f16::NAN, 0), 1.0);
1749 /// # }
1750 /// ```
1751 #[inline]
1752 #[rustc_allow_incoherent_impl]
1753 #[unstable(feature = "f16", issue = "116909")]
1754 #[must_use = "method returns a new number and does not mutate the original value"]
1755 pub fn powi(self, n: i32) -> f16 {
1756 // SAFETY: intrinsic with no preconditions
1757 unsafe { intrinsics::powif16(self, n) }
1758 }
1759
1760 /// Returns the square root of a number.
1761 ///
1762 /// Returns NaN if `self` is a negative number other than `-0.0`.
1763 ///
1764 /// # Precision
1765 ///
1766 /// The result of this operation is guaranteed to be the rounded
1767 /// infinite-precision result. It is specified by IEEE 754 as `squareRoot`
1768 /// and guaranteed not to change.
1769 ///
1770 /// # Examples
1771 ///
1772 /// ```
1773 /// #![feature(f16)]
1774 /// # #[cfg(not(miri))]
1775 /// # #[cfg(target_has_reliable_f16_math)] {
1776 ///
1777 /// let positive = 4.0_f16;
1778 /// let negative = -4.0_f16;
1779 /// let negative_zero = -0.0_f16;
1780 ///
1781 /// assert_eq!(positive.sqrt(), 2.0);
1782 /// assert!(negative.sqrt().is_nan());
1783 /// assert!(negative_zero.sqrt() == negative_zero);
1784 /// # }
1785 /// ```
1786 #[inline]
1787 #[doc(alias = "squareRoot")]
1788 #[rustc_allow_incoherent_impl]
1789 #[unstable(feature = "f16", issue = "116909")]
1790 #[must_use = "method returns a new number and does not mutate the original value"]
1791 pub fn sqrt(self) -> f16 {
1792 // SAFETY: intrinsic with no preconditions
1793 unsafe { intrinsics::sqrtf16(self) }
1794 }
1795
1796 /// Returns the cube root of a number.
1797 ///
1798 /// # Unspecified precision
1799 ///
1800 /// The precision of this function is non-deterministic. This means it varies by platform,
1801 /// Rust version, and can even differ within the same execution from one invocation to the next.
1802 ///
1803 /// This function currently corresponds to the `cbrtf` from libc on Unix
1804 /// and Windows. Note that this might change in the future.
1805 ///
1806 /// # Examples
1807 ///
1808 /// ```
1809 /// #![feature(f16)]
1810 /// # #[cfg(not(miri))]
1811 /// # #[cfg(target_has_reliable_f16_math)] {
1812 ///
1813 /// let x = 8.0f16;
1814 ///
1815 /// // x^(1/3) - 2 == 0
1816 /// let abs_difference = (x.cbrt() - 2.0).abs();
1817 ///
1818 /// assert!(abs_difference <= f16::EPSILON);
1819 /// # }
1820 /// ```
1821 #[inline]
1822 #[rustc_allow_incoherent_impl]
1823 #[unstable(feature = "f16", issue = "116909")]
1824 #[must_use = "method returns a new number and does not mutate the original value"]
1825 pub fn cbrt(self) -> f16 {
1826 libm::cbrtf(self as f32) as f16
1827 }
1828}
1829