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;
15#[cfg(not(test))]
16use crate::intrinsics;
17use crate::mem;
18use crate::num::FpCategory;
19use crate::panic::const_assert;
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
136#[cfg(not(test))]
137impl f16 {
138    // FIXME(f16_f128): almost all methods in this `impl` are missing examples and a const
139    // implementation. Add these once we can run code on all platforms and have f16/f128 in CTFE.
140
141    /// The radix or base of the internal representation of `f16`.
142    #[unstable(feature = "f16", issue = "116909")]
143    pub const RADIX: u32 = 2;
144
145    /// Number of significant digits in base 2.
146    #[unstable(feature = "f16", issue = "116909")]
147    pub const MANTISSA_DIGITS: u32 = 11;
148
149    /// Approximate number of significant digits in base 10.
150    ///
151    /// This is the maximum <i>x</i> such that any decimal number with <i>x</i>
152    /// significant digits can be converted to `f16` and back without loss.
153    ///
154    /// Equal to floor(log<sub>10</sub>&nbsp;2<sup>[`MANTISSA_DIGITS`]&nbsp;&minus;&nbsp;1</sup>).
155    ///
156    /// [`MANTISSA_DIGITS`]: f16::MANTISSA_DIGITS
157    #[unstable(feature = "f16", issue = "116909")]
158    pub const DIGITS: u32 = 3;
159
160    /// [Machine epsilon] value for `f16`.
161    ///
162    /// This is the difference between `1.0` and the next larger representable number.
163    ///
164    /// Equal to 2<sup>1&nbsp;&minus;&nbsp;[`MANTISSA_DIGITS`]</sup>.
165    ///
166    /// [Machine epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon
167    /// [`MANTISSA_DIGITS`]: f16::MANTISSA_DIGITS
168    #[unstable(feature = "f16", issue = "116909")]
169    pub const EPSILON: f16 = 9.7656e-4_f16;
170
171    /// Smallest finite `f16` value.
172    ///
173    /// Equal to &minus;[`MAX`].
174    ///
175    /// [`MAX`]: f16::MAX
176    #[unstable(feature = "f16", issue = "116909")]
177    pub const MIN: f16 = -6.5504e+4_f16;
178    /// Smallest positive normal `f16` value.
179    ///
180    /// Equal to 2<sup>[`MIN_EXP`]&nbsp;&minus;&nbsp;1</sup>.
181    ///
182    /// [`MIN_EXP`]: f16::MIN_EXP
183    #[unstable(feature = "f16", issue = "116909")]
184    pub const MIN_POSITIVE: f16 = 6.1035e-5_f16;
185    /// Largest finite `f16` value.
186    ///
187    /// Equal to
188    /// (1&nbsp;&minus;&nbsp;2<sup>&minus;[`MANTISSA_DIGITS`]</sup>)&nbsp;2<sup>[`MAX_EXP`]</sup>.
189    ///
190    /// [`MANTISSA_DIGITS`]: f16::MANTISSA_DIGITS
191    /// [`MAX_EXP`]: f16::MAX_EXP
192    #[unstable(feature = "f16", issue = "116909")]
193    pub const MAX: f16 = 6.5504e+4_f16;
194
195    /// One greater than the minimum possible normal power of 2 exponent.
196    ///
197    /// If <i>x</i>&nbsp;=&nbsp;`MIN_EXP`, then normal numbers
198    /// ≥&nbsp;0.5&nbsp;×&nbsp;2<sup><i>x</i></sup>.
199    #[unstable(feature = "f16", issue = "116909")]
200    pub const MIN_EXP: i32 = -13;
201    /// Maximum possible power of 2 exponent.
202    ///
203    /// If <i>x</i>&nbsp;=&nbsp;`MAX_EXP`, then normal numbers
204    /// &lt;&nbsp;1&nbsp;×&nbsp;2<sup><i>x</i></sup>.
205    #[unstable(feature = "f16", issue = "116909")]
206    pub const MAX_EXP: i32 = 16;
207
208    /// Minimum <i>x</i> for which 10<sup><i>x</i></sup> is normal.
209    ///
210    /// Equal to ceil(log<sub>10</sub>&nbsp;[`MIN_POSITIVE`]).
211    ///
212    /// [`MIN_POSITIVE`]: f16::MIN_POSITIVE
213    #[unstable(feature = "f16", issue = "116909")]
214    pub const MIN_10_EXP: i32 = -4;
215    /// Maximum <i>x</i> for which 10<sup><i>x</i></sup> is normal.
216    ///
217    /// Equal to floor(log<sub>10</sub>&nbsp;[`MAX`]).
218    ///
219    /// [`MAX`]: f16::MAX
220    #[unstable(feature = "f16", issue = "116909")]
221    pub const MAX_10_EXP: i32 = 4;
222
223    /// Not a Number (NaN).
224    ///
225    /// Note that IEEE 754 doesn't define just a single NaN value;
226    /// a plethora of bit patterns are considered to be NaN.
227    /// Furthermore, the standard makes a difference
228    /// between a "signaling" and a "quiet" NaN,
229    /// and allows inspecting its "payload" (the unspecified bits in the bit pattern).
230    /// This constant isn't guaranteed to equal to any specific NaN bitpattern,
231    /// and the stability of its representation over Rust versions
232    /// and target platforms isn't guaranteed.
233    #[allow(clippy::eq_op)]
234    #[rustc_diagnostic_item = "f16_nan"]
235    #[unstable(feature = "f16", issue = "116909")]
236    pub const NAN: f16 = 0.0_f16 / 0.0_f16;
237
238    /// Infinity (∞).
239    #[unstable(feature = "f16", issue = "116909")]
240    pub const INFINITY: f16 = 1.0_f16 / 0.0_f16;
241
242    /// Negative infinity (−∞).
243    #[unstable(feature = "f16", issue = "116909")]
244    pub const NEG_INFINITY: f16 = -1.0_f16 / 0.0_f16;
245
246    /// Sign bit
247    pub(crate) const SIGN_MASK: u16 = 0x8000;
248
249    /// Exponent mask
250    pub(crate) const EXP_MASK: u16 = 0x7c00;
251
252    /// Mantissa mask
253    pub(crate) const MAN_MASK: u16 = 0x03ff;
254
255    /// Minimum representable positive value (min subnormal)
256    const TINY_BITS: u16 = 0x1;
257
258    /// Minimum representable negative value (min negative subnormal)
259    const NEG_TINY_BITS: u16 = Self::TINY_BITS | Self::SIGN_MASK;
260
261    /// Returns `true` if this value is NaN.
262    ///
263    /// ```
264    /// #![feature(f16)]
265    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
266    ///
267    /// let nan = f16::NAN;
268    /// let f = 7.0_f16;
269    ///
270    /// assert!(nan.is_nan());
271    /// assert!(!f.is_nan());
272    /// # }
273    /// ```
274    #[inline]
275    #[must_use]
276    #[unstable(feature = "f16", issue = "116909")]
277    #[allow(clippy::eq_op)] // > if you intended to check if the operand is NaN, use `.is_nan()` instead :)
278    pub const fn is_nan(self) -> bool {
279        self != self
280    }
281
282    /// Returns `true` if this value is positive infinity or negative infinity, and
283    /// `false` otherwise.
284    ///
285    /// ```
286    /// #![feature(f16)]
287    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
288    ///
289    /// let f = 7.0f16;
290    /// let inf = f16::INFINITY;
291    /// let neg_inf = f16::NEG_INFINITY;
292    /// let nan = f16::NAN;
293    ///
294    /// assert!(!f.is_infinite());
295    /// assert!(!nan.is_infinite());
296    ///
297    /// assert!(inf.is_infinite());
298    /// assert!(neg_inf.is_infinite());
299    /// # }
300    /// ```
301    #[inline]
302    #[must_use]
303    #[unstable(feature = "f16", issue = "116909")]
304    pub const fn is_infinite(self) -> bool {
305        (self == f16::INFINITY) | (self == f16::NEG_INFINITY)
306    }
307
308    /// Returns `true` if this number is neither infinite nor NaN.
309    ///
310    /// ```
311    /// #![feature(f16)]
312    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
313    ///
314    /// let f = 7.0f16;
315    /// let inf: f16 = f16::INFINITY;
316    /// let neg_inf: f16 = f16::NEG_INFINITY;
317    /// let nan: f16 = f16::NAN;
318    ///
319    /// assert!(f.is_finite());
320    ///
321    /// assert!(!nan.is_finite());
322    /// assert!(!inf.is_finite());
323    /// assert!(!neg_inf.is_finite());
324    /// # }
325    /// ```
326    #[inline]
327    #[must_use]
328    #[unstable(feature = "f16", issue = "116909")]
329    #[rustc_const_unstable(feature = "f16", issue = "116909")]
330    pub const fn is_finite(self) -> bool {
331        // There's no need to handle NaN separately: if self is NaN,
332        // the comparison is not true, exactly as desired.
333        self.abs() < Self::INFINITY
334    }
335
336    /// Returns `true` if the number is [subnormal].
337    ///
338    /// ```
339    /// #![feature(f16)]
340    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
341    ///
342    /// let min = f16::MIN_POSITIVE; // 6.1035e-5
343    /// let max = f16::MAX;
344    /// let lower_than_min = 1.0e-7_f16;
345    /// let zero = 0.0_f16;
346    ///
347    /// assert!(!min.is_subnormal());
348    /// assert!(!max.is_subnormal());
349    ///
350    /// assert!(!zero.is_subnormal());
351    /// assert!(!f16::NAN.is_subnormal());
352    /// assert!(!f16::INFINITY.is_subnormal());
353    /// // Values between `0` and `min` are Subnormal.
354    /// assert!(lower_than_min.is_subnormal());
355    /// # }
356    /// ```
357    /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
358    #[inline]
359    #[must_use]
360    #[unstable(feature = "f16", issue = "116909")]
361    pub const fn is_subnormal(self) -> bool {
362        matches!(self.classify(), FpCategory::Subnormal)
363    }
364
365    /// Returns `true` if the number is neither zero, infinite, [subnormal], or NaN.
366    ///
367    /// ```
368    /// #![feature(f16)]
369    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
370    ///
371    /// let min = f16::MIN_POSITIVE; // 6.1035e-5
372    /// let max = f16::MAX;
373    /// let lower_than_min = 1.0e-7_f16;
374    /// let zero = 0.0_f16;
375    ///
376    /// assert!(min.is_normal());
377    /// assert!(max.is_normal());
378    ///
379    /// assert!(!zero.is_normal());
380    /// assert!(!f16::NAN.is_normal());
381    /// assert!(!f16::INFINITY.is_normal());
382    /// // Values between `0` and `min` are Subnormal.
383    /// assert!(!lower_than_min.is_normal());
384    /// # }
385    /// ```
386    /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
387    #[inline]
388    #[must_use]
389    #[unstable(feature = "f16", issue = "116909")]
390    pub const fn is_normal(self) -> bool {
391        matches!(self.classify(), FpCategory::Normal)
392    }
393
394    /// Returns the floating point category of the number. If only one property
395    /// is going to be tested, it is generally faster to use the specific
396    /// predicate instead.
397    ///
398    /// ```
399    /// #![feature(f16)]
400    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
401    ///
402    /// use std::num::FpCategory;
403    ///
404    /// let num = 12.4_f16;
405    /// let inf = f16::INFINITY;
406    ///
407    /// assert_eq!(num.classify(), FpCategory::Normal);
408    /// assert_eq!(inf.classify(), FpCategory::Infinite);
409    /// # }
410    /// ```
411    #[inline]
412    #[unstable(feature = "f16", issue = "116909")]
413    pub const fn classify(self) -> FpCategory {
414        let b = self.to_bits();
415        match (b & Self::MAN_MASK, b & Self::EXP_MASK) {
416            (0, Self::EXP_MASK) => FpCategory::Infinite,
417            (_, Self::EXP_MASK) => FpCategory::Nan,
418            (0, 0) => FpCategory::Zero,
419            (_, 0) => FpCategory::Subnormal,
420            _ => FpCategory::Normal,
421        }
422    }
423
424    /// Returns `true` if `self` has a positive sign, including `+0.0`, NaNs with
425    /// positive sign bit and positive infinity.
426    ///
427    /// Note that IEEE 754 doesn't assign any meaning to the sign bit in case of
428    /// a NaN, and as Rust doesn't guarantee that the bit pattern of NaNs are
429    /// conserved over arithmetic operations, the result of `is_sign_positive` on
430    /// a NaN might produce an unexpected or non-portable result. See the [specification
431    /// of NaN bit patterns](f32#nan-bit-patterns) for more info. Use `self.signum() == 1.0`
432    /// if you need fully portable behavior (will return `false` for all NaNs).
433    ///
434    /// ```
435    /// #![feature(f16)]
436    /// # // FIXME(f16_f128): LLVM crashes on s390x, llvm/llvm-project#50374
437    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
438    ///
439    /// let f = 7.0_f16;
440    /// let g = -7.0_f16;
441    ///
442    /// assert!(f.is_sign_positive());
443    /// assert!(!g.is_sign_positive());
444    /// # }
445    /// ```
446    #[inline]
447    #[must_use]
448    #[unstable(feature = "f16", issue = "116909")]
449    pub const fn is_sign_positive(self) -> bool {
450        !self.is_sign_negative()
451    }
452
453    /// Returns `true` if `self` has a negative sign, including `-0.0`, NaNs with
454    /// negative sign bit and negative infinity.
455    ///
456    /// Note that IEEE 754 doesn't assign any meaning to the sign bit in case of
457    /// a NaN, and as Rust doesn't guarantee that the bit pattern of NaNs are
458    /// conserved over arithmetic operations, the result of `is_sign_negative` on
459    /// a NaN might produce an unexpected or non-portable result. See the [specification
460    /// of NaN bit patterns](f32#nan-bit-patterns) for more info. Use `self.signum() == -1.0`
461    /// if you need fully portable behavior (will return `false` for all NaNs).
462    ///
463    /// ```
464    /// #![feature(f16)]
465    /// # // FIXME(f16_f128): LLVM crashes on s390x, llvm/llvm-project#50374
466    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
467    ///
468    /// let f = 7.0_f16;
469    /// let g = -7.0_f16;
470    ///
471    /// assert!(!f.is_sign_negative());
472    /// assert!(g.is_sign_negative());
473    /// # }
474    /// ```
475    #[inline]
476    #[must_use]
477    #[unstable(feature = "f16", issue = "116909")]
478    pub const fn is_sign_negative(self) -> bool {
479        // IEEE754 says: isSignMinus(x) is true if and only if x has negative sign. isSignMinus
480        // applies to zeros and NaNs as well.
481        // SAFETY: This is just transmuting to get the sign bit, it's fine.
482        (self.to_bits() & (1 << 15)) != 0
483    }
484
485    /// Returns the least number greater than `self`.
486    ///
487    /// Let `TINY` be the smallest representable positive `f16`. Then,
488    ///  - if `self.is_nan()`, this returns `self`;
489    ///  - if `self` is [`NEG_INFINITY`], this returns [`MIN`];
490    ///  - if `self` is `-TINY`, this returns -0.0;
491    ///  - if `self` is -0.0 or +0.0, this returns `TINY`;
492    ///  - if `self` is [`MAX`] or [`INFINITY`], this returns [`INFINITY`];
493    ///  - otherwise the unique least value greater than `self` is returned.
494    ///
495    /// The identity `x.next_up() == -(-x).next_down()` holds for all non-NaN `x`. When `x`
496    /// is finite `x == x.next_up().next_down()` also holds.
497    ///
498    /// ```rust
499    /// #![feature(f16)]
500    /// # // FIXME(f16_f128): ABI issues on MSVC
501    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
502    ///
503    /// // f16::EPSILON is the difference between 1.0 and the next number up.
504    /// assert_eq!(1.0f16.next_up(), 1.0 + f16::EPSILON);
505    /// // But not for most numbers.
506    /// assert!(0.1f16.next_up() < 0.1 + f16::EPSILON);
507    /// assert_eq!(4356f16.next_up(), 4360.0);
508    /// # }
509    /// ```
510    ///
511    /// This operation corresponds to IEEE-754 `nextUp`.
512    ///
513    /// [`NEG_INFINITY`]: Self::NEG_INFINITY
514    /// [`INFINITY`]: Self::INFINITY
515    /// [`MIN`]: Self::MIN
516    /// [`MAX`]: Self::MAX
517    #[inline]
518    #[doc(alias = "nextUp")]
519    #[unstable(feature = "f16", issue = "116909")]
520    pub const fn next_up(self) -> Self {
521        // Some targets violate Rust's assumption of IEEE semantics, e.g. by flushing
522        // denormals to zero. This is in general unsound and unsupported, but here
523        // we do our best to still produce the correct result on such targets.
524        let bits = self.to_bits();
525        if self.is_nan() || bits == Self::INFINITY.to_bits() {
526            return self;
527        }
528
529        let abs = bits & !Self::SIGN_MASK;
530        let next_bits = if abs == 0 {
531            Self::TINY_BITS
532        } else if bits == abs {
533            bits + 1
534        } else {
535            bits - 1
536        };
537        Self::from_bits(next_bits)
538    }
539
540    /// Returns the greatest number less than `self`.
541    ///
542    /// Let `TINY` be the smallest representable positive `f16`. Then,
543    ///  - if `self.is_nan()`, this returns `self`;
544    ///  - if `self` is [`INFINITY`], this returns [`MAX`];
545    ///  - if `self` is `TINY`, this returns 0.0;
546    ///  - if `self` is -0.0 or +0.0, this returns `-TINY`;
547    ///  - if `self` is [`MIN`] or [`NEG_INFINITY`], this returns [`NEG_INFINITY`];
548    ///  - otherwise the unique greatest value less than `self` is returned.
549    ///
550    /// The identity `x.next_down() == -(-x).next_up()` holds for all non-NaN `x`. When `x`
551    /// is finite `x == x.next_down().next_up()` also holds.
552    ///
553    /// ```rust
554    /// #![feature(f16)]
555    /// # // FIXME(f16_f128): ABI issues on MSVC
556    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
557    ///
558    /// let x = 1.0f16;
559    /// // Clamp value into range [0, 1).
560    /// let clamped = x.clamp(0.0, 1.0f16.next_down());
561    /// assert!(clamped < 1.0);
562    /// assert_eq!(clamped.next_up(), 1.0);
563    /// # }
564    /// ```
565    ///
566    /// This operation corresponds to IEEE-754 `nextDown`.
567    ///
568    /// [`NEG_INFINITY`]: Self::NEG_INFINITY
569    /// [`INFINITY`]: Self::INFINITY
570    /// [`MIN`]: Self::MIN
571    /// [`MAX`]: Self::MAX
572    #[inline]
573    #[doc(alias = "nextDown")]
574    #[unstable(feature = "f16", issue = "116909")]
575    pub const fn next_down(self) -> Self {
576        // Some targets violate Rust's assumption of IEEE semantics, e.g. by flushing
577        // denormals to zero. This is in general unsound and unsupported, but here
578        // we do our best to still produce the correct result on such targets.
579        let bits = self.to_bits();
580        if self.is_nan() || bits == Self::NEG_INFINITY.to_bits() {
581            return self;
582        }
583
584        let abs = bits & !Self::SIGN_MASK;
585        let next_bits = if abs == 0 {
586            Self::NEG_TINY_BITS
587        } else if bits == abs {
588            bits - 1
589        } else {
590            bits + 1
591        };
592        Self::from_bits(next_bits)
593    }
594
595    /// Takes the reciprocal (inverse) of a number, `1/x`.
596    ///
597    /// ```
598    /// #![feature(f16)]
599    /// # // FIXME(f16_f128): extendhfsf2, truncsfhf2, __gnu_h2f_ieee, __gnu_f2h_ieee missing for many platforms
600    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
601    ///
602    /// let x = 2.0_f16;
603    /// let abs_difference = (x.recip() - (1.0 / x)).abs();
604    ///
605    /// assert!(abs_difference <= f16::EPSILON);
606    /// # }
607    /// ```
608    #[inline]
609    #[unstable(feature = "f16", issue = "116909")]
610    #[must_use = "this returns the result of the operation, without modifying the original"]
611    pub const fn recip(self) -> Self {
612        1.0 / self
613    }
614
615    /// Converts radians to degrees.
616    ///
617    /// ```
618    /// #![feature(f16)]
619    /// # // FIXME(f16_f128): extendhfsf2, truncsfhf2, __gnu_h2f_ieee, __gnu_f2h_ieee missing for many platforms
620    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
621    ///
622    /// let angle = std::f16::consts::PI;
623    ///
624    /// let abs_difference = (angle.to_degrees() - 180.0).abs();
625    /// assert!(abs_difference <= 0.5);
626    /// # }
627    /// ```
628    #[inline]
629    #[unstable(feature = "f16", issue = "116909")]
630    #[must_use = "this returns the result of the operation, without modifying the original"]
631    pub const fn to_degrees(self) -> Self {
632        // Use a literal for better precision.
633        const PIS_IN_180: f16 = 57.2957795130823208767981548141051703_f16;
634        self * PIS_IN_180
635    }
636
637    /// Converts degrees to radians.
638    ///
639    /// ```
640    /// #![feature(f16)]
641    /// # // FIXME(f16_f128): extendhfsf2, truncsfhf2, __gnu_h2f_ieee, __gnu_f2h_ieee missing for many platforms
642    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
643    ///
644    /// let angle = 180.0f16;
645    ///
646    /// let abs_difference = (angle.to_radians() - std::f16::consts::PI).abs();
647    ///
648    /// assert!(abs_difference <= 0.01);
649    /// # }
650    /// ```
651    #[inline]
652    #[unstable(feature = "f16", issue = "116909")]
653    #[must_use = "this returns the result of the operation, without modifying the original"]
654    pub const fn to_radians(self) -> f16 {
655        // Use a literal for better precision.
656        const RADS_PER_DEG: f16 = 0.017453292519943295769236907684886_f16;
657        self * RADS_PER_DEG
658    }
659
660    /// Returns the maximum of the two numbers, ignoring NaN.
661    ///
662    /// If one of the arguments is NaN, then the other argument is returned.
663    /// This follows the IEEE 754-2008 semantics for maxNum, except for handling of signaling NaNs;
664    /// this function handles all NaNs the same way and avoids maxNum's problems with associativity.
665    /// This also matches the behavior of libm’s fmax. In particular, if the inputs compare equal
666    /// (such as for the case of `+0.0` and `-0.0`), either input may be returned non-deterministically.
667    ///
668    /// ```
669    /// #![feature(f16)]
670    /// # #[cfg(target_arch = "aarch64")] { // FIXME(f16_F128): rust-lang/rust#123885
671    ///
672    /// let x = 1.0f16;
673    /// let y = 2.0f16;
674    ///
675    /// assert_eq!(x.max(y), y);
676    /// # }
677    /// ```
678    #[inline]
679    #[unstable(feature = "f16", issue = "116909")]
680    #[rustc_const_unstable(feature = "f16", issue = "116909")]
681    #[must_use = "this returns the result of the comparison, without modifying either input"]
682    pub const fn max(self, other: f16) -> f16 {
683        intrinsics::maxnumf16(self, other)
684    }
685
686    /// Returns the minimum of the two numbers, ignoring NaN.
687    ///
688    /// If one of the arguments is NaN, then the other argument is returned.
689    /// This follows the IEEE 754-2008 semantics for minNum, except for handling of signaling NaNs;
690    /// this function handles all NaNs the same way and avoids minNum's problems with associativity.
691    /// This also matches the behavior of libm’s fmin. In particular, if the inputs compare equal
692    /// (such as for the case of `+0.0` and `-0.0`), either input may be returned non-deterministically.
693    ///
694    /// ```
695    /// #![feature(f16)]
696    /// # #[cfg(target_arch = "aarch64")] { // FIXME(f16_F128): rust-lang/rust#123885
697    ///
698    /// let x = 1.0f16;
699    /// let y = 2.0f16;
700    ///
701    /// assert_eq!(x.min(y), x);
702    /// # }
703    /// ```
704    #[inline]
705    #[unstable(feature = "f16", issue = "116909")]
706    #[rustc_const_unstable(feature = "f16", issue = "116909")]
707    #[must_use = "this returns the result of the comparison, without modifying either input"]
708    pub const fn min(self, other: f16) -> f16 {
709        intrinsics::minnumf16(self, other)
710    }
711
712    /// Returns the maximum of the two numbers, propagating NaN.
713    ///
714    /// This returns NaN when *either* argument is NaN, as opposed to
715    /// [`f16::max`] which only returns NaN when *both* arguments are NaN.
716    ///
717    /// ```
718    /// #![feature(f16)]
719    /// #![feature(float_minimum_maximum)]
720    /// # #[cfg(target_arch = "aarch64")] { // FIXME(f16_F128): rust-lang/rust#123885
721    ///
722    /// let x = 1.0f16;
723    /// let y = 2.0f16;
724    ///
725    /// assert_eq!(x.maximum(y), y);
726    /// assert!(x.maximum(f16::NAN).is_nan());
727    /// # }
728    /// ```
729    ///
730    /// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the greater
731    /// of the two numbers. For this operation, -0.0 is considered to be less than +0.0.
732    /// Note that this follows the semantics specified in IEEE 754-2019.
733    ///
734    /// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN
735    /// operand is conserved; see the [specification of NaN bit patterns](f32#nan-bit-patterns) for more info.
736    #[inline]
737    #[unstable(feature = "f16", issue = "116909")]
738    // #[unstable(feature = "float_minimum_maximum", issue = "91079")]
739    #[must_use = "this returns the result of the comparison, without modifying either input"]
740    pub const fn maximum(self, other: f16) -> f16 {
741        if self > other {
742            self
743        } else if other > self {
744            other
745        } else if self == other {
746            if self.is_sign_positive() && other.is_sign_negative() { self } else { other }
747        } else {
748            self + other
749        }
750    }
751
752    /// Returns the minimum of the two numbers, propagating NaN.
753    ///
754    /// This returns NaN when *either* argument is NaN, as opposed to
755    /// [`f16::min`] which only returns NaN when *both* arguments are NaN.
756    ///
757    /// ```
758    /// #![feature(f16)]
759    /// #![feature(float_minimum_maximum)]
760    /// # #[cfg(target_arch = "aarch64")] { // FIXME(f16_F128): rust-lang/rust#123885
761    ///
762    /// let x = 1.0f16;
763    /// let y = 2.0f16;
764    ///
765    /// assert_eq!(x.minimum(y), x);
766    /// assert!(x.minimum(f16::NAN).is_nan());
767    /// # }
768    /// ```
769    ///
770    /// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the lesser
771    /// of the two numbers. For this operation, -0.0 is considered to be less than +0.0.
772    /// Note that this follows the semantics specified in IEEE 754-2019.
773    ///
774    /// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN
775    /// operand is conserved; see the [specification of NaN bit patterns](f32#nan-bit-patterns) for more info.
776    #[inline]
777    #[unstable(feature = "f16", issue = "116909")]
778    // #[unstable(feature = "float_minimum_maximum", issue = "91079")]
779    #[must_use = "this returns the result of the comparison, without modifying either input"]
780    pub const fn minimum(self, other: f16) -> f16 {
781        if self < other {
782            self
783        } else if other < self {
784            other
785        } else if self == other {
786            if self.is_sign_negative() && other.is_sign_positive() { self } else { other }
787        } else {
788            // At least one input is NaN. Use `+` to perform NaN propagation and quieting.
789            self + other
790        }
791    }
792
793    /// Calculates the middle point of `self` and `rhs`.
794    ///
795    /// This returns NaN when *either* argument is NaN or if a combination of
796    /// +inf and -inf is provided as arguments.
797    ///
798    /// # Examples
799    ///
800    /// ```
801    /// #![feature(f16)]
802    /// # #[cfg(target_arch = "aarch64")] { // FIXME(f16_F128): rust-lang/rust#123885
803    ///
804    /// assert_eq!(1f16.midpoint(4.0), 2.5);
805    /// assert_eq!((-5.5f16).midpoint(8.0), 1.25);
806    /// # }
807    /// ```
808    #[inline]
809    #[unstable(feature = "f16", issue = "116909")]
810    #[rustc_const_unstable(feature = "f16", issue = "116909")]
811    pub const fn midpoint(self, other: f16) -> f16 {
812        const LO: f16 = f16::MIN_POSITIVE * 2.;
813        const HI: f16 = f16::MAX / 2.;
814
815        let (a, b) = (self, other);
816        let abs_a = a.abs();
817        let abs_b = b.abs();
818
819        if abs_a <= HI && abs_b <= HI {
820            // Overflow is impossible
821            (a + b) / 2.
822        } else if abs_a < LO {
823            // Not safe to halve `a` (would underflow)
824            a + (b / 2.)
825        } else if abs_b < LO {
826            // Not safe to halve `b` (would underflow)
827            (a / 2.) + b
828        } else {
829            // Safe to halve `a` and `b`
830            (a / 2.) + (b / 2.)
831        }
832    }
833
834    /// Rounds toward zero and converts to any primitive integer type,
835    /// assuming that the value is finite and fits in that type.
836    ///
837    /// ```
838    /// #![feature(f16)]
839    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
840    ///
841    /// let value = 4.6_f16;
842    /// let rounded = unsafe { value.to_int_unchecked::<u16>() };
843    /// assert_eq!(rounded, 4);
844    ///
845    /// let value = -128.9_f16;
846    /// let rounded = unsafe { value.to_int_unchecked::<i8>() };
847    /// assert_eq!(rounded, i8::MIN);
848    /// # }
849    /// ```
850    ///
851    /// # Safety
852    ///
853    /// The value must:
854    ///
855    /// * Not be `NaN`
856    /// * Not be infinite
857    /// * Be representable in the return type `Int`, after truncating off its fractional part
858    #[inline]
859    #[unstable(feature = "f16", issue = "116909")]
860    #[must_use = "this returns the result of the operation, without modifying the original"]
861    pub unsafe fn to_int_unchecked<Int>(self) -> Int
862    where
863        Self: FloatToInt<Int>,
864    {
865        // SAFETY: the caller must uphold the safety contract for
866        // `FloatToInt::to_int_unchecked`.
867        unsafe { FloatToInt::<Int>::to_int_unchecked(self) }
868    }
869
870    /// Raw transmutation to `u16`.
871    ///
872    /// This is currently identical to `transmute::<f16, u16>(self)` on all platforms.
873    ///
874    /// See [`from_bits`](#method.from_bits) for some discussion of the
875    /// portability of this operation (there are almost no issues).
876    ///
877    /// Note that this function is distinct from `as` casting, which attempts to
878    /// preserve the *numeric* value, and not the bitwise value.
879    ///
880    /// ```
881    /// #![feature(f16)]
882    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
883    ///
884    /// # // FIXME(f16_f128): enable this once const casting works
885    /// # // assert_ne!((1f16).to_bits(), 1f16 as u128); // to_bits() is not casting!
886    /// assert_eq!((12.5f16).to_bits(), 0x4a40);
887    /// # }
888    /// ```
889    #[inline]
890    #[unstable(feature = "f16", issue = "116909")]
891    #[must_use = "this returns the result of the operation, without modifying the original"]
892    pub const fn to_bits(self) -> u16 {
893        // SAFETY: `u16` is a plain old datatype so we can always transmute to it.
894        unsafe { mem::transmute(self) }
895    }
896
897    /// Raw transmutation from `u16`.
898    ///
899    /// This is currently identical to `transmute::<u16, f16>(v)` on all platforms.
900    /// It turns out this is incredibly portable, for two reasons:
901    ///
902    /// * Floats and Ints have the same endianness on all supported platforms.
903    /// * IEEE 754 very precisely specifies the bit layout of floats.
904    ///
905    /// However there is one caveat: prior to the 2008 version of IEEE 754, how
906    /// to interpret the NaN signaling bit wasn't actually specified. Most platforms
907    /// (notably x86 and ARM) picked the interpretation that was ultimately
908    /// standardized in 2008, but some didn't (notably MIPS). As a result, all
909    /// signaling NaNs on MIPS are quiet NaNs on x86, and vice-versa.
910    ///
911    /// Rather than trying to preserve signaling-ness cross-platform, this
912    /// implementation favors preserving the exact bits. This means that
913    /// any payloads encoded in NaNs will be preserved even if the result of
914    /// this method is sent over the network from an x86 machine to a MIPS one.
915    ///
916    /// If the results of this method are only manipulated by the same
917    /// architecture that produced them, then there is no portability concern.
918    ///
919    /// If the input isn't NaN, then there is no portability concern.
920    ///
921    /// If you don't care about signalingness (very likely), then there is no
922    /// portability concern.
923    ///
924    /// Note that this function is distinct from `as` casting, which attempts to
925    /// preserve the *numeric* value, and not the bitwise value.
926    ///
927    /// ```
928    /// #![feature(f16)]
929    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
930    ///
931    /// let v = f16::from_bits(0x4a40);
932    /// assert_eq!(v, 12.5);
933    /// # }
934    /// ```
935    #[inline]
936    #[must_use]
937    #[unstable(feature = "f16", issue = "116909")]
938    pub const fn from_bits(v: u16) -> Self {
939        // It turns out the safety issues with sNaN were overblown! Hooray!
940        // SAFETY: `u16` is a plain old datatype so we can always transmute from it.
941        unsafe { mem::transmute(v) }
942    }
943
944    /// Returns the memory representation of this floating point number as a byte array in
945    /// big-endian (network) byte order.
946    ///
947    /// See [`from_bits`](Self::from_bits) for some discussion of the
948    /// portability of this operation (there are almost no issues).
949    ///
950    /// # Examples
951    ///
952    /// ```
953    /// #![feature(f16)]
954    /// # // FIXME(f16_f128): LLVM crashes on s390x, llvm/llvm-project#50374
955    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
956    ///
957    /// let bytes = 12.5f16.to_be_bytes();
958    /// assert_eq!(bytes, [0x4a, 0x40]);
959    /// # }
960    /// ```
961    #[inline]
962    #[unstable(feature = "f16", issue = "116909")]
963    #[must_use = "this returns the result of the operation, without modifying the original"]
964    pub const fn to_be_bytes(self) -> [u8; 2] {
965        self.to_bits().to_be_bytes()
966    }
967
968    /// Returns the memory representation of this floating point number as a byte array in
969    /// little-endian byte order.
970    ///
971    /// See [`from_bits`](Self::from_bits) for some discussion of the
972    /// portability of this operation (there are almost no issues).
973    ///
974    /// # Examples
975    ///
976    /// ```
977    /// #![feature(f16)]
978    /// # // FIXME(f16_f128): LLVM crashes on s390x, llvm/llvm-project#50374
979    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
980    ///
981    /// let bytes = 12.5f16.to_le_bytes();
982    /// assert_eq!(bytes, [0x40, 0x4a]);
983    /// # }
984    /// ```
985    #[inline]
986    #[unstable(feature = "f16", issue = "116909")]
987    #[must_use = "this returns the result of the operation, without modifying the original"]
988    pub const fn to_le_bytes(self) -> [u8; 2] {
989        self.to_bits().to_le_bytes()
990    }
991
992    /// Returns the memory representation of this floating point number as a byte array in
993    /// native byte order.
994    ///
995    /// As the target platform's native endianness is used, portable code
996    /// should use [`to_be_bytes`] or [`to_le_bytes`], as appropriate, instead.
997    ///
998    /// [`to_be_bytes`]: f16::to_be_bytes
999    /// [`to_le_bytes`]: f16::to_le_bytes
1000    ///
1001    /// See [`from_bits`](Self::from_bits) for some discussion of the
1002    /// portability of this operation (there are almost no issues).
1003    ///
1004    /// # Examples
1005    ///
1006    /// ```
1007    /// #![feature(f16)]
1008    /// # // FIXME(f16_f128): LLVM crashes on s390x, llvm/llvm-project#50374
1009    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1010    ///
1011    /// let bytes = 12.5f16.to_ne_bytes();
1012    /// assert_eq!(
1013    ///     bytes,
1014    ///     if cfg!(target_endian = "big") {
1015    ///         [0x4a, 0x40]
1016    ///     } else {
1017    ///         [0x40, 0x4a]
1018    ///     }
1019    /// );
1020    /// # }
1021    /// ```
1022    #[inline]
1023    #[unstable(feature = "f16", issue = "116909")]
1024    #[must_use = "this returns the result of the operation, without modifying the original"]
1025    pub const fn to_ne_bytes(self) -> [u8; 2] {
1026        self.to_bits().to_ne_bytes()
1027    }
1028
1029    /// Creates a floating point value from its representation as a byte array in big endian.
1030    ///
1031    /// See [`from_bits`](Self::from_bits) for some discussion of the
1032    /// portability of this operation (there are almost no issues).
1033    ///
1034    /// # Examples
1035    ///
1036    /// ```
1037    /// #![feature(f16)]
1038    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1039    ///
1040    /// let value = f16::from_be_bytes([0x4a, 0x40]);
1041    /// assert_eq!(value, 12.5);
1042    /// # }
1043    /// ```
1044    #[inline]
1045    #[must_use]
1046    #[unstable(feature = "f16", issue = "116909")]
1047    pub const fn from_be_bytes(bytes: [u8; 2]) -> Self {
1048        Self::from_bits(u16::from_be_bytes(bytes))
1049    }
1050
1051    /// Creates a floating point value from its representation as a byte array in little endian.
1052    ///
1053    /// See [`from_bits`](Self::from_bits) for some discussion of the
1054    /// portability of this operation (there are almost no issues).
1055    ///
1056    /// # Examples
1057    ///
1058    /// ```
1059    /// #![feature(f16)]
1060    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1061    ///
1062    /// let value = f16::from_le_bytes([0x40, 0x4a]);
1063    /// assert_eq!(value, 12.5);
1064    /// # }
1065    /// ```
1066    #[inline]
1067    #[must_use]
1068    #[unstable(feature = "f16", issue = "116909")]
1069    pub const fn from_le_bytes(bytes: [u8; 2]) -> Self {
1070        Self::from_bits(u16::from_le_bytes(bytes))
1071    }
1072
1073    /// Creates a floating point value from its representation as a byte array in native endian.
1074    ///
1075    /// As the target platform's native endianness is used, portable code
1076    /// likely wants to use [`from_be_bytes`] or [`from_le_bytes`], as
1077    /// appropriate instead.
1078    ///
1079    /// [`from_be_bytes`]: f16::from_be_bytes
1080    /// [`from_le_bytes`]: f16::from_le_bytes
1081    ///
1082    /// See [`from_bits`](Self::from_bits) for some discussion of the
1083    /// portability of this operation (there are almost no issues).
1084    ///
1085    /// # Examples
1086    ///
1087    /// ```
1088    /// #![feature(f16)]
1089    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1090    ///
1091    /// let value = f16::from_ne_bytes(if cfg!(target_endian = "big") {
1092    ///     [0x4a, 0x40]
1093    /// } else {
1094    ///     [0x40, 0x4a]
1095    /// });
1096    /// assert_eq!(value, 12.5);
1097    /// # }
1098    /// ```
1099    #[inline]
1100    #[must_use]
1101    #[unstable(feature = "f16", issue = "116909")]
1102    pub const fn from_ne_bytes(bytes: [u8; 2]) -> Self {
1103        Self::from_bits(u16::from_ne_bytes(bytes))
1104    }
1105
1106    /// Returns the ordering between `self` and `other`.
1107    ///
1108    /// Unlike the standard partial comparison between floating point numbers,
1109    /// this comparison always produces an ordering in accordance to
1110    /// the `totalOrder` predicate as defined in the IEEE 754 (2008 revision)
1111    /// floating point standard. The values are ordered in the following sequence:
1112    ///
1113    /// - negative quiet NaN
1114    /// - negative signaling NaN
1115    /// - negative infinity
1116    /// - negative numbers
1117    /// - negative subnormal numbers
1118    /// - negative zero
1119    /// - positive zero
1120    /// - positive subnormal numbers
1121    /// - positive numbers
1122    /// - positive infinity
1123    /// - positive signaling NaN
1124    /// - positive quiet NaN.
1125    ///
1126    /// The ordering established by this function does not always agree with the
1127    /// [`PartialOrd`] and [`PartialEq`] implementations of `f16`. For example,
1128    /// they consider negative and positive zero equal, while `total_cmp`
1129    /// doesn't.
1130    ///
1131    /// The interpretation of the signaling NaN bit follows the definition in
1132    /// the IEEE 754 standard, which may not match the interpretation by some of
1133    /// the older, non-conformant (e.g. MIPS) hardware implementations.
1134    ///
1135    /// # Example
1136    ///
1137    /// ```
1138    /// #![feature(f16)]
1139    /// # // FIXME(f16_f128): extendhfsf2, truncsfhf2, __gnu_h2f_ieee, __gnu_f2h_ieee missing for many platforms
1140    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1141    ///
1142    /// struct GoodBoy {
1143    ///     name: &'static str,
1144    ///     weight: f16,
1145    /// }
1146    ///
1147    /// let mut bois = vec![
1148    ///     GoodBoy { name: "Pucci", weight: 0.1 },
1149    ///     GoodBoy { name: "Woofer", weight: 99.0 },
1150    ///     GoodBoy { name: "Yapper", weight: 10.0 },
1151    ///     GoodBoy { name: "Chonk", weight: f16::INFINITY },
1152    ///     GoodBoy { name: "Abs. Unit", weight: f16::NAN },
1153    ///     GoodBoy { name: "Floaty", weight: -5.0 },
1154    /// ];
1155    ///
1156    /// bois.sort_by(|a, b| a.weight.total_cmp(&b.weight));
1157    ///
1158    /// // `f16::NAN` could be positive or negative, which will affect the sort order.
1159    /// if f16::NAN.is_sign_negative() {
1160    ///     bois.into_iter().map(|b| b.weight)
1161    ///         .zip([f16::NAN, -5.0, 0.1, 10.0, 99.0, f16::INFINITY].iter())
1162    ///         .for_each(|(a, b)| assert_eq!(a.to_bits(), b.to_bits()))
1163    /// } else {
1164    ///     bois.into_iter().map(|b| b.weight)
1165    ///         .zip([-5.0, 0.1, 10.0, 99.0, f16::INFINITY, f16::NAN].iter())
1166    ///         .for_each(|(a, b)| assert_eq!(a.to_bits(), b.to_bits()))
1167    /// }
1168    /// # }
1169    /// ```
1170    #[inline]
1171    #[must_use]
1172    #[unstable(feature = "f16", issue = "116909")]
1173    pub fn total_cmp(&self, other: &Self) -> crate::cmp::Ordering {
1174        let mut left = self.to_bits() as i16;
1175        let mut right = other.to_bits() as i16;
1176
1177        // In case of negatives, flip all the bits except the sign
1178        // to achieve a similar layout as two's complement integers
1179        //
1180        // Why does this work? IEEE 754 floats consist of three fields:
1181        // Sign bit, exponent and mantissa. The set of exponent and mantissa
1182        // fields as a whole have the property that their bitwise order is
1183        // equal to the numeric magnitude where the magnitude is defined.
1184        // The magnitude is not normally defined on NaN values, but
1185        // IEEE 754 totalOrder defines the NaN values also to follow the
1186        // bitwise order. This leads to order explained in the doc comment.
1187        // However, the representation of magnitude is the same for negative
1188        // and positive numbers – only the sign bit is different.
1189        // To easily compare the floats as signed integers, we need to
1190        // flip the exponent and mantissa bits in case of negative numbers.
1191        // We effectively convert the numbers to "two's complement" form.
1192        //
1193        // To do the flipping, we construct a mask and XOR against it.
1194        // We branchlessly calculate an "all-ones except for the sign bit"
1195        // mask from negative-signed values: right shifting sign-extends
1196        // the integer, so we "fill" the mask with sign bits, and then
1197        // convert to unsigned to push one more zero bit.
1198        // On positive values, the mask is all zeros, so it's a no-op.
1199        left ^= (((left >> 15) as u16) >> 1) as i16;
1200        right ^= (((right >> 15) as u16) >> 1) as i16;
1201
1202        left.cmp(&right)
1203    }
1204
1205    /// Restrict a value to a certain interval unless it is NaN.
1206    ///
1207    /// Returns `max` if `self` is greater than `max`, and `min` if `self` is
1208    /// less than `min`. Otherwise this returns `self`.
1209    ///
1210    /// Note that this function returns NaN if the initial value was NaN as
1211    /// well.
1212    ///
1213    /// # Panics
1214    ///
1215    /// Panics if `min > max`, `min` is NaN, or `max` is NaN.
1216    ///
1217    /// # Examples
1218    ///
1219    /// ```
1220    /// #![feature(f16)]
1221    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1222    ///
1223    /// assert!((-3.0f16).clamp(-2.0, 1.0) == -2.0);
1224    /// assert!((0.0f16).clamp(-2.0, 1.0) == 0.0);
1225    /// assert!((2.0f16).clamp(-2.0, 1.0) == 1.0);
1226    /// assert!((f16::NAN).clamp(-2.0, 1.0).is_nan());
1227    /// # }
1228    /// ```
1229    #[inline]
1230    #[unstable(feature = "f16", issue = "116909")]
1231    #[must_use = "method returns a new number and does not mutate the original value"]
1232    pub const fn clamp(mut self, min: f16, max: f16) -> f16 {
1233        const_assert!(
1234            min <= max,
1235            "min > max, or either was NaN",
1236            "min > max, or either was NaN. min = {min:?}, max = {max:?}",
1237            min: f16,
1238            max: f16,
1239        );
1240
1241        if self < min {
1242            self = min;
1243        }
1244        if self > max {
1245            self = max;
1246        }
1247        self
1248    }
1249
1250    /// Computes the absolute value of `self`.
1251    ///
1252    /// This function always returns the precise result.
1253    ///
1254    /// # Examples
1255    ///
1256    /// ```
1257    /// #![feature(f16)]
1258    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1259    ///
1260    /// let x = 3.5_f16;
1261    /// let y = -3.5_f16;
1262    ///
1263    /// assert_eq!(x.abs(), x);
1264    /// assert_eq!(y.abs(), -y);
1265    ///
1266    /// assert!(f16::NAN.abs().is_nan());
1267    /// # }
1268    /// ```
1269    #[inline]
1270    #[unstable(feature = "f16", issue = "116909")]
1271    #[rustc_const_unstable(feature = "f16", issue = "116909")]
1272    #[must_use = "method returns a new number and does not mutate the original value"]
1273    pub const fn abs(self) -> Self {
1274        // FIXME(f16_f128): replace with `intrinsics::fabsf16` when available
1275        Self::from_bits(self.to_bits() & !(1 << 15))
1276    }
1277
1278    /// Returns a number that represents the sign of `self`.
1279    ///
1280    /// - `1.0` if the number is positive, `+0.0` or `INFINITY`
1281    /// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
1282    /// - NaN if the number is NaN
1283    ///
1284    /// # Examples
1285    ///
1286    /// ```
1287    /// #![feature(f16)]
1288    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1289    ///
1290    /// let f = 3.5_f16;
1291    ///
1292    /// assert_eq!(f.signum(), 1.0);
1293    /// assert_eq!(f16::NEG_INFINITY.signum(), -1.0);
1294    ///
1295    /// assert!(f16::NAN.signum().is_nan());
1296    /// # }
1297    /// ```
1298    #[inline]
1299    #[unstable(feature = "f16", issue = "116909")]
1300    #[rustc_const_unstable(feature = "f16", issue = "116909")]
1301    #[must_use = "method returns a new number and does not mutate the original value"]
1302    pub const fn signum(self) -> f16 {
1303        if self.is_nan() { Self::NAN } else { 1.0_f16.copysign(self) }
1304    }
1305
1306    /// Returns a number composed of the magnitude of `self` and the sign of
1307    /// `sign`.
1308    ///
1309    /// Equal to `self` if the sign of `self` and `sign` are the same, otherwise equal to `-self`.
1310    /// If `self` is a NaN, then a NaN with the same payload as `self` and the sign bit of `sign` is
1311    /// returned.
1312    ///
1313    /// If `sign` is a NaN, then this operation will still carry over its sign into the result. Note
1314    /// that IEEE 754 doesn't assign any meaning to the sign bit in case of a NaN, and as Rust
1315    /// doesn't guarantee that the bit pattern of NaNs are conserved over arithmetic operations, the
1316    /// result of `copysign` with `sign` being a NaN might produce an unexpected or non-portable
1317    /// result. See the [specification of NaN bit patterns](primitive@f32#nan-bit-patterns) for more
1318    /// info.
1319    ///
1320    /// # Examples
1321    ///
1322    /// ```
1323    /// #![feature(f16)]
1324    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
1325    ///
1326    /// let f = 3.5_f16;
1327    ///
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    /// assert_eq!((-f).copysign(-0.42), -3.5_f16);
1332    ///
1333    /// assert!(f16::NAN.copysign(1.0).is_nan());
1334    /// # }
1335    /// ```
1336    #[inline]
1337    #[unstable(feature = "f16", issue = "116909")]
1338    #[rustc_const_unstable(feature = "f16", issue = "116909")]
1339    #[must_use = "method returns a new number and does not mutate the original value"]
1340    pub const fn copysign(self, sign: f16) -> f16 {
1341        // SAFETY: this is actually a safe intrinsic
1342        unsafe { intrinsics::copysignf16(self, sign) }
1343    }
1344}