core/num/
f32.rs

1//! Constants for the `f32` single-precision floating point type.
2//!
3//! *[See also the `f32` primitive type][f32].*
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 `f32` type.
11
12#![stable(feature = "rust1", since = "1.0.0")]
13
14use crate::convert::FloatToInt;
15use crate::num::FpCategory;
16use crate::panic::const_assert;
17use crate::{cfg_select, intrinsics, mem};
18
19/// The radix or base of the internal representation of `f32`.
20/// Use [`f32::RADIX`] instead.
21///
22/// # Examples
23///
24/// ```rust
25/// // deprecated way
26/// # #[allow(deprecated, deprecated_in_future)]
27/// let r = std::f32::RADIX;
28///
29/// // intended way
30/// let r = f32::RADIX;
31/// ```
32#[stable(feature = "rust1", since = "1.0.0")]
33#[deprecated(since = "TBD", note = "replaced by the `RADIX` associated constant on `f32`")]
34#[rustc_diagnostic_item = "f32_legacy_const_radix"]
35pub const RADIX: u32 = f32::RADIX;
36
37/// Number of significant digits in base 2.
38/// Use [`f32::MANTISSA_DIGITS`] instead.
39///
40/// # Examples
41///
42/// ```rust
43/// // deprecated way
44/// # #[allow(deprecated, deprecated_in_future)]
45/// let d = std::f32::MANTISSA_DIGITS;
46///
47/// // intended way
48/// let d = f32::MANTISSA_DIGITS;
49/// ```
50#[stable(feature = "rust1", since = "1.0.0")]
51#[deprecated(
52    since = "TBD",
53    note = "replaced by the `MANTISSA_DIGITS` associated constant on `f32`"
54)]
55#[rustc_diagnostic_item = "f32_legacy_const_mantissa_dig"]
56pub const MANTISSA_DIGITS: u32 = f32::MANTISSA_DIGITS;
57
58/// Approximate number of significant digits in base 10.
59/// Use [`f32::DIGITS`] instead.
60///
61/// # Examples
62///
63/// ```rust
64/// // deprecated way
65/// # #[allow(deprecated, deprecated_in_future)]
66/// let d = std::f32::DIGITS;
67///
68/// // intended way
69/// let d = f32::DIGITS;
70/// ```
71#[stable(feature = "rust1", since = "1.0.0")]
72#[deprecated(since = "TBD", note = "replaced by the `DIGITS` associated constant on `f32`")]
73#[rustc_diagnostic_item = "f32_legacy_const_digits"]
74pub const DIGITS: u32 = f32::DIGITS;
75
76/// [Machine epsilon] value for `f32`.
77/// Use [`f32::EPSILON`] instead.
78///
79/// This is the difference between `1.0` and the next larger representable number.
80///
81/// [Machine epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon
82///
83/// # Examples
84///
85/// ```rust
86/// // deprecated way
87/// # #[allow(deprecated, deprecated_in_future)]
88/// let e = std::f32::EPSILON;
89///
90/// // intended way
91/// let e = f32::EPSILON;
92/// ```
93#[stable(feature = "rust1", since = "1.0.0")]
94#[deprecated(since = "TBD", note = "replaced by the `EPSILON` associated constant on `f32`")]
95#[rustc_diagnostic_item = "f32_legacy_const_epsilon"]
96pub const EPSILON: f32 = f32::EPSILON;
97
98/// Smallest finite `f32` value.
99/// Use [`f32::MIN`] instead.
100///
101/// # Examples
102///
103/// ```rust
104/// // deprecated way
105/// # #[allow(deprecated, deprecated_in_future)]
106/// let min = std::f32::MIN;
107///
108/// // intended way
109/// let min = f32::MIN;
110/// ```
111#[stable(feature = "rust1", since = "1.0.0")]
112#[deprecated(since = "TBD", note = "replaced by the `MIN` associated constant on `f32`")]
113#[rustc_diagnostic_item = "f32_legacy_const_min"]
114pub const MIN: f32 = f32::MIN;
115
116/// Smallest positive normal `f32` value.
117/// Use [`f32::MIN_POSITIVE`] instead.
118///
119/// # Examples
120///
121/// ```rust
122/// // deprecated way
123/// # #[allow(deprecated, deprecated_in_future)]
124/// let min = std::f32::MIN_POSITIVE;
125///
126/// // intended way
127/// let min = f32::MIN_POSITIVE;
128/// ```
129#[stable(feature = "rust1", since = "1.0.0")]
130#[deprecated(since = "TBD", note = "replaced by the `MIN_POSITIVE` associated constant on `f32`")]
131#[rustc_diagnostic_item = "f32_legacy_const_min_positive"]
132pub const MIN_POSITIVE: f32 = f32::MIN_POSITIVE;
133
134/// Largest finite `f32` value.
135/// Use [`f32::MAX`] instead.
136///
137/// # Examples
138///
139/// ```rust
140/// // deprecated way
141/// # #[allow(deprecated, deprecated_in_future)]
142/// let max = std::f32::MAX;
143///
144/// // intended way
145/// let max = f32::MAX;
146/// ```
147#[stable(feature = "rust1", since = "1.0.0")]
148#[deprecated(since = "TBD", note = "replaced by the `MAX` associated constant on `f32`")]
149#[rustc_diagnostic_item = "f32_legacy_const_max"]
150pub const MAX: f32 = f32::MAX;
151
152/// One greater than the minimum possible normal power of 2 exponent.
153/// Use [`f32::MIN_EXP`] instead.
154///
155/// # Examples
156///
157/// ```rust
158/// // deprecated way
159/// # #[allow(deprecated, deprecated_in_future)]
160/// let min = std::f32::MIN_EXP;
161///
162/// // intended way
163/// let min = f32::MIN_EXP;
164/// ```
165#[stable(feature = "rust1", since = "1.0.0")]
166#[deprecated(since = "TBD", note = "replaced by the `MIN_EXP` associated constant on `f32`")]
167#[rustc_diagnostic_item = "f32_legacy_const_min_exp"]
168pub const MIN_EXP: i32 = f32::MIN_EXP;
169
170/// Maximum possible power of 2 exponent.
171/// Use [`f32::MAX_EXP`] instead.
172///
173/// # Examples
174///
175/// ```rust
176/// // deprecated way
177/// # #[allow(deprecated, deprecated_in_future)]
178/// let max = std::f32::MAX_EXP;
179///
180/// // intended way
181/// let max = f32::MAX_EXP;
182/// ```
183#[stable(feature = "rust1", since = "1.0.0")]
184#[deprecated(since = "TBD", note = "replaced by the `MAX_EXP` associated constant on `f32`")]
185#[rustc_diagnostic_item = "f32_legacy_const_max_exp"]
186pub const MAX_EXP: i32 = f32::MAX_EXP;
187
188/// Minimum possible normal power of 10 exponent.
189/// Use [`f32::MIN_10_EXP`] instead.
190///
191/// # Examples
192///
193/// ```rust
194/// // deprecated way
195/// # #[allow(deprecated, deprecated_in_future)]
196/// let min = std::f32::MIN_10_EXP;
197///
198/// // intended way
199/// let min = f32::MIN_10_EXP;
200/// ```
201#[stable(feature = "rust1", since = "1.0.0")]
202#[deprecated(since = "TBD", note = "replaced by the `MIN_10_EXP` associated constant on `f32`")]
203#[rustc_diagnostic_item = "f32_legacy_const_min_10_exp"]
204pub const MIN_10_EXP: i32 = f32::MIN_10_EXP;
205
206/// Maximum possible power of 10 exponent.
207/// Use [`f32::MAX_10_EXP`] instead.
208///
209/// # Examples
210///
211/// ```rust
212/// // deprecated way
213/// # #[allow(deprecated, deprecated_in_future)]
214/// let max = std::f32::MAX_10_EXP;
215///
216/// // intended way
217/// let max = f32::MAX_10_EXP;
218/// ```
219#[stable(feature = "rust1", since = "1.0.0")]
220#[deprecated(since = "TBD", note = "replaced by the `MAX_10_EXP` associated constant on `f32`")]
221#[rustc_diagnostic_item = "f32_legacy_const_max_10_exp"]
222pub const MAX_10_EXP: i32 = f32::MAX_10_EXP;
223
224/// Not a Number (NaN).
225/// Use [`f32::NAN`] instead.
226///
227/// # Examples
228///
229/// ```rust
230/// // deprecated way
231/// # #[allow(deprecated, deprecated_in_future)]
232/// let nan = std::f32::NAN;
233///
234/// // intended way
235/// let nan = f32::NAN;
236/// ```
237#[stable(feature = "rust1", since = "1.0.0")]
238#[deprecated(since = "TBD", note = "replaced by the `NAN` associated constant on `f32`")]
239#[rustc_diagnostic_item = "f32_legacy_const_nan"]
240pub const NAN: f32 = f32::NAN;
241
242/// Infinity (∞).
243/// Use [`f32::INFINITY`] instead.
244///
245/// # Examples
246///
247/// ```rust
248/// // deprecated way
249/// # #[allow(deprecated, deprecated_in_future)]
250/// let inf = std::f32::INFINITY;
251///
252/// // intended way
253/// let inf = f32::INFINITY;
254/// ```
255#[stable(feature = "rust1", since = "1.0.0")]
256#[deprecated(since = "TBD", note = "replaced by the `INFINITY` associated constant on `f32`")]
257#[rustc_diagnostic_item = "f32_legacy_const_infinity"]
258pub const INFINITY: f32 = f32::INFINITY;
259
260/// Negative infinity (−∞).
261/// Use [`f32::NEG_INFINITY`] instead.
262///
263/// # Examples
264///
265/// ```rust
266/// // deprecated way
267/// # #[allow(deprecated, deprecated_in_future)]
268/// let ninf = std::f32::NEG_INFINITY;
269///
270/// // intended way
271/// let ninf = f32::NEG_INFINITY;
272/// ```
273#[stable(feature = "rust1", since = "1.0.0")]
274#[deprecated(since = "TBD", note = "replaced by the `NEG_INFINITY` associated constant on `f32`")]
275#[rustc_diagnostic_item = "f32_legacy_const_neg_infinity"]
276pub const NEG_INFINITY: f32 = f32::NEG_INFINITY;
277
278/// Basic mathematical constants.
279#[stable(feature = "rust1", since = "1.0.0")]
280pub mod consts {
281    // FIXME: replace with mathematical constants from cmath.
282
283    /// Archimedes' constant (π)
284    #[stable(feature = "rust1", since = "1.0.0")]
285    pub const PI: f32 = 3.14159265358979323846264338327950288_f32;
286
287    /// The full circle constant (τ)
288    ///
289    /// Equal to 2π.
290    #[stable(feature = "tau_constant", since = "1.47.0")]
291    pub const TAU: f32 = 6.28318530717958647692528676655900577_f32;
292
293    /// The golden ratio (φ)
294    #[unstable(feature = "more_float_constants", issue = "103883")]
295    pub const PHI: f32 = 1.618033988749894848204586834365638118_f32;
296
297    /// The Euler-Mascheroni constant (γ)
298    #[unstable(feature = "more_float_constants", issue = "103883")]
299    pub const EGAMMA: f32 = 0.577215664901532860606512090082402431_f32;
300
301    /// π/2
302    #[stable(feature = "rust1", since = "1.0.0")]
303    pub const FRAC_PI_2: f32 = 1.57079632679489661923132169163975144_f32;
304
305    /// π/3
306    #[stable(feature = "rust1", since = "1.0.0")]
307    pub const FRAC_PI_3: f32 = 1.04719755119659774615421446109316763_f32;
308
309    /// π/4
310    #[stable(feature = "rust1", since = "1.0.0")]
311    pub const FRAC_PI_4: f32 = 0.785398163397448309615660845819875721_f32;
312
313    /// π/6
314    #[stable(feature = "rust1", since = "1.0.0")]
315    pub const FRAC_PI_6: f32 = 0.52359877559829887307710723054658381_f32;
316
317    /// π/8
318    #[stable(feature = "rust1", since = "1.0.0")]
319    pub const FRAC_PI_8: f32 = 0.39269908169872415480783042290993786_f32;
320
321    /// 1/π
322    #[stable(feature = "rust1", since = "1.0.0")]
323    pub const FRAC_1_PI: f32 = 0.318309886183790671537767526745028724_f32;
324
325    /// 1/sqrt(π)
326    #[unstable(feature = "more_float_constants", issue = "103883")]
327    pub const FRAC_1_SQRT_PI: f32 = 0.564189583547756286948079451560772586_f32;
328
329    /// 1/sqrt(2π)
330    #[doc(alias = "FRAC_1_SQRT_TAU")]
331    #[unstable(feature = "more_float_constants", issue = "103883")]
332    pub const FRAC_1_SQRT_2PI: f32 = 0.398942280401432677939946059934381868_f32;
333
334    /// 2/π
335    #[stable(feature = "rust1", since = "1.0.0")]
336    pub const FRAC_2_PI: f32 = 0.636619772367581343075535053490057448_f32;
337
338    /// 2/sqrt(π)
339    #[stable(feature = "rust1", since = "1.0.0")]
340    pub const FRAC_2_SQRT_PI: f32 = 1.12837916709551257389615890312154517_f32;
341
342    /// sqrt(2)
343    #[stable(feature = "rust1", since = "1.0.0")]
344    pub const SQRT_2: f32 = 1.41421356237309504880168872420969808_f32;
345
346    /// 1/sqrt(2)
347    #[stable(feature = "rust1", since = "1.0.0")]
348    pub const FRAC_1_SQRT_2: f32 = 0.707106781186547524400844362104849039_f32;
349
350    /// sqrt(3)
351    #[unstable(feature = "more_float_constants", issue = "103883")]
352    pub const SQRT_3: f32 = 1.732050807568877293527446341505872367_f32;
353
354    /// 1/sqrt(3)
355    #[unstable(feature = "more_float_constants", issue = "103883")]
356    pub const FRAC_1_SQRT_3: f32 = 0.577350269189625764509148780501957456_f32;
357
358    /// Euler's number (e)
359    #[stable(feature = "rust1", since = "1.0.0")]
360    pub const E: f32 = 2.71828182845904523536028747135266250_f32;
361
362    /// log<sub>2</sub>(e)
363    #[stable(feature = "rust1", since = "1.0.0")]
364    pub const LOG2_E: f32 = 1.44269504088896340735992468100189214_f32;
365
366    /// log<sub>2</sub>(10)
367    #[stable(feature = "extra_log_consts", since = "1.43.0")]
368    pub const LOG2_10: f32 = 3.32192809488736234787031942948939018_f32;
369
370    /// log<sub>10</sub>(e)
371    #[stable(feature = "rust1", since = "1.0.0")]
372    pub const LOG10_E: f32 = 0.434294481903251827651128918916605082_f32;
373
374    /// log<sub>10</sub>(2)
375    #[stable(feature = "extra_log_consts", since = "1.43.0")]
376    pub const LOG10_2: f32 = 0.301029995663981195213738894724493027_f32;
377
378    /// ln(2)
379    #[stable(feature = "rust1", since = "1.0.0")]
380    pub const LN_2: f32 = 0.693147180559945309417232121458176568_f32;
381
382    /// ln(10)
383    #[stable(feature = "rust1", since = "1.0.0")]
384    pub const LN_10: f32 = 2.30258509299404568401799145468436421_f32;
385}
386
387impl f32 {
388    /// The radix or base of the internal representation of `f32`.
389    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
390    pub const RADIX: u32 = 2;
391
392    /// Number of significant digits in base 2.
393    ///
394    /// Note that the size of the mantissa in the bitwise representation is one
395    /// smaller than this since the leading 1 is not stored explicitly.
396    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
397    pub const MANTISSA_DIGITS: u32 = 24;
398
399    /// Approximate number of significant digits in base 10.
400    ///
401    /// This is the maximum <i>x</i> such that any decimal number with <i>x</i>
402    /// significant digits can be converted to `f32` and back without loss.
403    ///
404    /// Equal to floor(log<sub>10</sub>&nbsp;2<sup>[`MANTISSA_DIGITS`]&nbsp;&minus;&nbsp;1</sup>).
405    ///
406    /// [`MANTISSA_DIGITS`]: f32::MANTISSA_DIGITS
407    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
408    pub const DIGITS: u32 = 6;
409
410    /// [Machine epsilon] value for `f32`.
411    ///
412    /// This is the difference between `1.0` and the next larger representable number.
413    ///
414    /// Equal to 2<sup>1&nbsp;&minus;&nbsp;[`MANTISSA_DIGITS`]</sup>.
415    ///
416    /// [Machine epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon
417    /// [`MANTISSA_DIGITS`]: f32::MANTISSA_DIGITS
418    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
419    #[rustc_diagnostic_item = "f32_epsilon"]
420    pub const EPSILON: f32 = 1.19209290e-07_f32;
421
422    /// Smallest finite `f32` value.
423    ///
424    /// Equal to &minus;[`MAX`].
425    ///
426    /// [`MAX`]: f32::MAX
427    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
428    pub const MIN: f32 = -3.40282347e+38_f32;
429    /// Smallest positive normal `f32` value.
430    ///
431    /// Equal to 2<sup>[`MIN_EXP`]&nbsp;&minus;&nbsp;1</sup>.
432    ///
433    /// [`MIN_EXP`]: f32::MIN_EXP
434    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
435    pub const MIN_POSITIVE: f32 = 1.17549435e-38_f32;
436    /// Largest finite `f32` value.
437    ///
438    /// Equal to
439    /// (1&nbsp;&minus;&nbsp;2<sup>&minus;[`MANTISSA_DIGITS`]</sup>)&nbsp;2<sup>[`MAX_EXP`]</sup>.
440    ///
441    /// [`MANTISSA_DIGITS`]: f32::MANTISSA_DIGITS
442    /// [`MAX_EXP`]: f32::MAX_EXP
443    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
444    pub const MAX: f32 = 3.40282347e+38_f32;
445
446    /// One greater than the minimum possible *normal* power of 2 exponent
447    /// for a significand bounded by 1 ≤ x < 2 (i.e. the IEEE definition).
448    ///
449    /// This corresponds to the exact minimum possible *normal* power of 2 exponent
450    /// for a significand bounded by 0.5 ≤ x < 1 (i.e. the C definition).
451    /// In other words, all normal numbers representable by this type are
452    /// greater than or equal to 0.5&nbsp;×&nbsp;2<sup><i>MIN_EXP</i></sup>.
453    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
454    pub const MIN_EXP: i32 = -125;
455    /// One greater than the maximum possible power of 2 exponent
456    /// for a significand bounded by 1 ≤ x < 2 (i.e. the IEEE definition).
457    ///
458    /// This corresponds to the exact maximum possible power of 2 exponent
459    /// for a significand bounded by 0.5 ≤ x < 1 (i.e. the C definition).
460    /// In other words, all numbers representable by this type are
461    /// strictly less than 2<sup><i>MAX_EXP</i></sup>.
462    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
463    pub const MAX_EXP: i32 = 128;
464
465    /// Minimum <i>x</i> for which 10<sup><i>x</i></sup> is normal.
466    ///
467    /// Equal to ceil(log<sub>10</sub>&nbsp;[`MIN_POSITIVE`]).
468    ///
469    /// [`MIN_POSITIVE`]: f32::MIN_POSITIVE
470    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
471    pub const MIN_10_EXP: i32 = -37;
472    /// Maximum <i>x</i> for which 10<sup><i>x</i></sup> is normal.
473    ///
474    /// Equal to floor(log<sub>10</sub>&nbsp;[`MAX`]).
475    ///
476    /// [`MAX`]: f32::MAX
477    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
478    pub const MAX_10_EXP: i32 = 38;
479
480    /// Not a Number (NaN).
481    ///
482    /// Note that IEEE 754 doesn't define just a single NaN value; a plethora of bit patterns are
483    /// considered to be NaN. Furthermore, the standard makes a difference between a "signaling" and
484    /// a "quiet" NaN, and allows inspecting its "payload" (the unspecified bits in the bit pattern)
485    /// and its sign. See the [specification of NaN bit patterns](f32#nan-bit-patterns) for more
486    /// info.
487    ///
488    /// This constant is guaranteed to be a quiet NaN (on targets that follow the Rust assumptions
489    /// that the quiet/signaling bit being set to 1 indicates a quiet NaN). Beyond that, nothing is
490    /// guaranteed about the specific bit pattern chosen here: both payload and sign are arbitrary.
491    /// The concrete bit pattern may change across Rust versions and target platforms.
492    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
493    #[rustc_diagnostic_item = "f32_nan"]
494    #[allow(clippy::eq_op)]
495    pub const NAN: f32 = 0.0_f32 / 0.0_f32;
496    /// Infinity (∞).
497    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
498    pub const INFINITY: f32 = 1.0_f32 / 0.0_f32;
499    /// Negative infinity (−∞).
500    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
501    pub const NEG_INFINITY: f32 = -1.0_f32 / 0.0_f32;
502
503    /// Sign bit
504    pub(crate) const SIGN_MASK: u32 = 0x8000_0000;
505
506    /// Exponent mask
507    pub(crate) const EXP_MASK: u32 = 0x7f80_0000;
508
509    /// Mantissa mask
510    pub(crate) const MAN_MASK: u32 = 0x007f_ffff;
511
512    /// Minimum representable positive value (min subnormal)
513    const TINY_BITS: u32 = 0x1;
514
515    /// Minimum representable negative value (min negative subnormal)
516    const NEG_TINY_BITS: u32 = Self::TINY_BITS | Self::SIGN_MASK;
517
518    /// Returns `true` if this value is NaN.
519    ///
520    /// ```
521    /// let nan = f32::NAN;
522    /// let f = 7.0_f32;
523    ///
524    /// assert!(nan.is_nan());
525    /// assert!(!f.is_nan());
526    /// ```
527    #[must_use]
528    #[stable(feature = "rust1", since = "1.0.0")]
529    #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
530    #[inline]
531    #[allow(clippy::eq_op)] // > if you intended to check if the operand is NaN, use `.is_nan()` instead :)
532    pub const fn is_nan(self) -> bool {
533        self != self
534    }
535
536    /// Returns `true` if this value is positive infinity or negative infinity, and
537    /// `false` otherwise.
538    ///
539    /// ```
540    /// let f = 7.0f32;
541    /// let inf = f32::INFINITY;
542    /// let neg_inf = f32::NEG_INFINITY;
543    /// let nan = f32::NAN;
544    ///
545    /// assert!(!f.is_infinite());
546    /// assert!(!nan.is_infinite());
547    ///
548    /// assert!(inf.is_infinite());
549    /// assert!(neg_inf.is_infinite());
550    /// ```
551    #[must_use]
552    #[stable(feature = "rust1", since = "1.0.0")]
553    #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
554    #[inline]
555    pub const fn is_infinite(self) -> bool {
556        // Getting clever with transmutation can result in incorrect answers on some FPUs
557        // FIXME: alter the Rust <-> Rust calling convention to prevent this problem.
558        // See https://github.com/rust-lang/rust/issues/72327
559        (self == f32::INFINITY) | (self == f32::NEG_INFINITY)
560    }
561
562    /// Returns `true` if this number is neither infinite nor NaN.
563    ///
564    /// ```
565    /// let f = 7.0f32;
566    /// let inf = f32::INFINITY;
567    /// let neg_inf = f32::NEG_INFINITY;
568    /// let nan = f32::NAN;
569    ///
570    /// assert!(f.is_finite());
571    ///
572    /// assert!(!nan.is_finite());
573    /// assert!(!inf.is_finite());
574    /// assert!(!neg_inf.is_finite());
575    /// ```
576    #[must_use]
577    #[stable(feature = "rust1", since = "1.0.0")]
578    #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
579    #[inline]
580    pub const fn is_finite(self) -> bool {
581        // There's no need to handle NaN separately: if self is NaN,
582        // the comparison is not true, exactly as desired.
583        self.abs() < Self::INFINITY
584    }
585
586    /// Returns `true` if the number is [subnormal].
587    ///
588    /// ```
589    /// let min = f32::MIN_POSITIVE; // 1.17549435e-38f32
590    /// let max = f32::MAX;
591    /// let lower_than_min = 1.0e-40_f32;
592    /// let zero = 0.0_f32;
593    ///
594    /// assert!(!min.is_subnormal());
595    /// assert!(!max.is_subnormal());
596    ///
597    /// assert!(!zero.is_subnormal());
598    /// assert!(!f32::NAN.is_subnormal());
599    /// assert!(!f32::INFINITY.is_subnormal());
600    /// // Values between `0` and `min` are Subnormal.
601    /// assert!(lower_than_min.is_subnormal());
602    /// ```
603    /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
604    #[must_use]
605    #[stable(feature = "is_subnormal", since = "1.53.0")]
606    #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
607    #[inline]
608    pub const fn is_subnormal(self) -> bool {
609        matches!(self.classify(), FpCategory::Subnormal)
610    }
611
612    /// Returns `true` if the number is neither zero, infinite,
613    /// [subnormal], or NaN.
614    ///
615    /// ```
616    /// let min = f32::MIN_POSITIVE; // 1.17549435e-38f32
617    /// let max = f32::MAX;
618    /// let lower_than_min = 1.0e-40_f32;
619    /// let zero = 0.0_f32;
620    ///
621    /// assert!(min.is_normal());
622    /// assert!(max.is_normal());
623    ///
624    /// assert!(!zero.is_normal());
625    /// assert!(!f32::NAN.is_normal());
626    /// assert!(!f32::INFINITY.is_normal());
627    /// // Values between `0` and `min` are Subnormal.
628    /// assert!(!lower_than_min.is_normal());
629    /// ```
630    /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
631    #[must_use]
632    #[stable(feature = "rust1", since = "1.0.0")]
633    #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
634    #[inline]
635    pub const fn is_normal(self) -> bool {
636        matches!(self.classify(), FpCategory::Normal)
637    }
638
639    /// Returns the floating point category of the number. If only one property
640    /// is going to be tested, it is generally faster to use the specific
641    /// predicate instead.
642    ///
643    /// ```
644    /// use std::num::FpCategory;
645    ///
646    /// let num = 12.4_f32;
647    /// let inf = f32::INFINITY;
648    ///
649    /// assert_eq!(num.classify(), FpCategory::Normal);
650    /// assert_eq!(inf.classify(), FpCategory::Infinite);
651    /// ```
652    #[stable(feature = "rust1", since = "1.0.0")]
653    #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
654    pub const fn classify(self) -> FpCategory {
655        // We used to have complicated logic here that avoids the simple bit-based tests to work
656        // around buggy codegen for x87 targets (see
657        // https://github.com/rust-lang/rust/issues/114479). However, some LLVM versions later, none
658        // of our tests is able to find any difference between the complicated and the naive
659        // version, so now we are back to the naive version.
660        let b = self.to_bits();
661        match (b & Self::MAN_MASK, b & Self::EXP_MASK) {
662            (0, Self::EXP_MASK) => FpCategory::Infinite,
663            (_, Self::EXP_MASK) => FpCategory::Nan,
664            (0, 0) => FpCategory::Zero,
665            (_, 0) => FpCategory::Subnormal,
666            _ => FpCategory::Normal,
667        }
668    }
669
670    /// Returns `true` if `self` has a positive sign, including `+0.0`, NaNs with
671    /// positive sign bit and positive infinity.
672    ///
673    /// Note that IEEE 754 doesn't assign any meaning to the sign bit in case of
674    /// a NaN, and as Rust doesn't guarantee that the bit pattern of NaNs are
675    /// conserved over arithmetic operations, the result of `is_sign_positive` on
676    /// a NaN might produce an unexpected or non-portable result. See the [specification
677    /// of NaN bit patterns](f32#nan-bit-patterns) for more info. Use `self.signum() == 1.0`
678    /// if you need fully portable behavior (will return `false` for all NaNs).
679    ///
680    /// ```
681    /// let f = 7.0_f32;
682    /// let g = -7.0_f32;
683    ///
684    /// assert!(f.is_sign_positive());
685    /// assert!(!g.is_sign_positive());
686    /// ```
687    #[must_use]
688    #[stable(feature = "rust1", since = "1.0.0")]
689    #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
690    #[inline]
691    pub const fn is_sign_positive(self) -> bool {
692        !self.is_sign_negative()
693    }
694
695    /// Returns `true` if `self` has a negative sign, including `-0.0`, NaNs with
696    /// negative sign bit and negative infinity.
697    ///
698    /// Note that IEEE 754 doesn't assign any meaning to the sign bit in case of
699    /// a NaN, and as Rust doesn't guarantee that the bit pattern of NaNs are
700    /// conserved over arithmetic operations, the result of `is_sign_negative` on
701    /// a NaN might produce an unexpected or non-portable result. See the [specification
702    /// of NaN bit patterns](f32#nan-bit-patterns) for more info. Use `self.signum() == -1.0`
703    /// if you need fully portable behavior (will return `false` for all NaNs).
704    ///
705    /// ```
706    /// let f = 7.0f32;
707    /// let g = -7.0f32;
708    ///
709    /// assert!(!f.is_sign_negative());
710    /// assert!(g.is_sign_negative());
711    /// ```
712    #[must_use]
713    #[stable(feature = "rust1", since = "1.0.0")]
714    #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
715    #[inline]
716    pub const fn is_sign_negative(self) -> bool {
717        // IEEE754 says: isSignMinus(x) is true if and only if x has negative sign. isSignMinus
718        // applies to zeros and NaNs as well.
719        self.to_bits() & 0x8000_0000 != 0
720    }
721
722    /// Returns the least number greater than `self`.
723    ///
724    /// Let `TINY` be the smallest representable positive `f32`. Then,
725    ///  - if `self.is_nan()`, this returns `self`;
726    ///  - if `self` is [`NEG_INFINITY`], this returns [`MIN`];
727    ///  - if `self` is `-TINY`, this returns -0.0;
728    ///  - if `self` is -0.0 or +0.0, this returns `TINY`;
729    ///  - if `self` is [`MAX`] or [`INFINITY`], this returns [`INFINITY`];
730    ///  - otherwise the unique least value greater than `self` is returned.
731    ///
732    /// The identity `x.next_up() == -(-x).next_down()` holds for all non-NaN `x`. When `x`
733    /// is finite `x == x.next_up().next_down()` also holds.
734    ///
735    /// ```rust
736    /// // f32::EPSILON is the difference between 1.0 and the next number up.
737    /// assert_eq!(1.0f32.next_up(), 1.0 + f32::EPSILON);
738    /// // But not for most numbers.
739    /// assert!(0.1f32.next_up() < 0.1 + f32::EPSILON);
740    /// assert_eq!(16777216f32.next_up(), 16777218.0);
741    /// ```
742    ///
743    /// This operation corresponds to IEEE-754 `nextUp`.
744    ///
745    /// [`NEG_INFINITY`]: Self::NEG_INFINITY
746    /// [`INFINITY`]: Self::INFINITY
747    /// [`MIN`]: Self::MIN
748    /// [`MAX`]: Self::MAX
749    #[inline]
750    #[doc(alias = "nextUp")]
751    #[stable(feature = "float_next_up_down", since = "1.86.0")]
752    #[rustc_const_stable(feature = "float_next_up_down", since = "1.86.0")]
753    pub const fn next_up(self) -> Self {
754        // Some targets violate Rust's assumption of IEEE semantics, e.g. by flushing
755        // denormals to zero. This is in general unsound and unsupported, but here
756        // we do our best to still produce the correct result on such targets.
757        let bits = self.to_bits();
758        if self.is_nan() || bits == Self::INFINITY.to_bits() {
759            return self;
760        }
761
762        let abs = bits & !Self::SIGN_MASK;
763        let next_bits = if abs == 0 {
764            Self::TINY_BITS
765        } else if bits == abs {
766            bits + 1
767        } else {
768            bits - 1
769        };
770        Self::from_bits(next_bits)
771    }
772
773    /// Returns the greatest number less than `self`.
774    ///
775    /// Let `TINY` be the smallest representable positive `f32`. Then,
776    ///  - if `self.is_nan()`, this returns `self`;
777    ///  - if `self` is [`INFINITY`], this returns [`MAX`];
778    ///  - if `self` is `TINY`, this returns 0.0;
779    ///  - if `self` is -0.0 or +0.0, this returns `-TINY`;
780    ///  - if `self` is [`MIN`] or [`NEG_INFINITY`], this returns [`NEG_INFINITY`];
781    ///  - otherwise the unique greatest value less than `self` is returned.
782    ///
783    /// The identity `x.next_down() == -(-x).next_up()` holds for all non-NaN `x`. When `x`
784    /// is finite `x == x.next_down().next_up()` also holds.
785    ///
786    /// ```rust
787    /// let x = 1.0f32;
788    /// // Clamp value into range [0, 1).
789    /// let clamped = x.clamp(0.0, 1.0f32.next_down());
790    /// assert!(clamped < 1.0);
791    /// assert_eq!(clamped.next_up(), 1.0);
792    /// ```
793    ///
794    /// This operation corresponds to IEEE-754 `nextDown`.
795    ///
796    /// [`NEG_INFINITY`]: Self::NEG_INFINITY
797    /// [`INFINITY`]: Self::INFINITY
798    /// [`MIN`]: Self::MIN
799    /// [`MAX`]: Self::MAX
800    #[inline]
801    #[doc(alias = "nextDown")]
802    #[stable(feature = "float_next_up_down", since = "1.86.0")]
803    #[rustc_const_stable(feature = "float_next_up_down", since = "1.86.0")]
804    pub const fn next_down(self) -> Self {
805        // Some targets violate Rust's assumption of IEEE semantics, e.g. by flushing
806        // denormals to zero. This is in general unsound and unsupported, but here
807        // we do our best to still produce the correct result on such targets.
808        let bits = self.to_bits();
809        if self.is_nan() || bits == Self::NEG_INFINITY.to_bits() {
810            return self;
811        }
812
813        let abs = bits & !Self::SIGN_MASK;
814        let next_bits = if abs == 0 {
815            Self::NEG_TINY_BITS
816        } else if bits == abs {
817            bits - 1
818        } else {
819            bits + 1
820        };
821        Self::from_bits(next_bits)
822    }
823
824    /// Takes the reciprocal (inverse) of a number, `1/x`.
825    ///
826    /// ```
827    /// let x = 2.0_f32;
828    /// let abs_difference = (x.recip() - (1.0 / x)).abs();
829    ///
830    /// assert!(abs_difference <= f32::EPSILON);
831    /// ```
832    #[must_use = "this returns the result of the operation, without modifying the original"]
833    #[stable(feature = "rust1", since = "1.0.0")]
834    #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
835    #[inline]
836    pub const fn recip(self) -> f32 {
837        1.0 / self
838    }
839
840    /// Converts radians to degrees.
841    ///
842    /// # Unspecified precision
843    ///
844    /// The precision of this function is non-deterministic. This means it varies by platform,
845    /// Rust version, and can even differ within the same execution from one invocation to the next.
846    ///
847    /// # Examples
848    ///
849    /// ```
850    /// let angle = std::f32::consts::PI;
851    ///
852    /// let abs_difference = (angle.to_degrees() - 180.0).abs();
853    /// # #[cfg(any(not(target_arch = "x86"), target_feature = "sse2"))]
854    /// assert!(abs_difference <= f32::EPSILON);
855    /// ```
856    #[must_use = "this returns the result of the operation, \
857                  without modifying the original"]
858    #[stable(feature = "f32_deg_rad_conversions", since = "1.7.0")]
859    #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
860    #[inline]
861    pub const fn to_degrees(self) -> f32 {
862        // Use a literal to avoid double rounding, consts::PI is already rounded,
863        // and dividing would round again.
864        const PIS_IN_180: f32 = 57.2957795130823208767981548141051703_f32;
865        self * PIS_IN_180
866    }
867
868    /// Converts degrees to radians.
869    ///
870    /// # Unspecified precision
871    ///
872    /// The precision of this function is non-deterministic. This means it varies by platform,
873    /// Rust version, and can even differ within the same execution from one invocation to the next.
874    ///
875    /// # Examples
876    ///
877    /// ```
878    /// let angle = 180.0f32;
879    ///
880    /// let abs_difference = (angle.to_radians() - std::f32::consts::PI).abs();
881    ///
882    /// assert!(abs_difference <= f32::EPSILON);
883    /// ```
884    #[must_use = "this returns the result of the operation, \
885                  without modifying the original"]
886    #[stable(feature = "f32_deg_rad_conversions", since = "1.7.0")]
887    #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
888    #[inline]
889    pub const fn to_radians(self) -> f32 {
890        // The division here is correctly rounded with respect to the true value of π/180.
891        // Although π is irrational and already rounded, the double rounding happens
892        // to produce correct result for f32.
893        const RADS_PER_DEG: f32 = consts::PI / 180.0;
894        self * RADS_PER_DEG
895    }
896
897    /// Returns the maximum of the two numbers, ignoring NaN.
898    ///
899    /// If one of the arguments is NaN, then the other argument is returned.
900    /// This follows the IEEE 754-2008 semantics for maxNum, except for handling of signaling NaNs;
901    /// this function handles all NaNs the same way and avoids maxNum's problems with associativity.
902    /// This also matches the behavior of libm’s fmax. In particular, if the inputs compare equal
903    /// (such as for the case of `+0.0` and `-0.0`), either input may be returned non-deterministically.
904    ///
905    /// ```
906    /// let x = 1.0f32;
907    /// let y = 2.0f32;
908    ///
909    /// assert_eq!(x.max(y), y);
910    /// ```
911    #[must_use = "this returns the result of the comparison, without modifying either input"]
912    #[stable(feature = "rust1", since = "1.0.0")]
913    #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
914    #[inline]
915    pub const fn max(self, other: f32) -> f32 {
916        intrinsics::maxnumf32(self, other)
917    }
918
919    /// Returns the minimum of the two numbers, ignoring NaN.
920    ///
921    /// If one of the arguments is NaN, then the other argument is returned.
922    /// This follows the IEEE 754-2008 semantics for minNum, except for handling of signaling NaNs;
923    /// this function handles all NaNs the same way and avoids minNum's problems with associativity.
924    /// This also matches the behavior of libm’s fmin. In particular, if the inputs compare equal
925    /// (such as for the case of `+0.0` and `-0.0`), either input may be returned non-deterministically.
926    ///
927    /// ```
928    /// let x = 1.0f32;
929    /// let y = 2.0f32;
930    ///
931    /// assert_eq!(x.min(y), x);
932    /// ```
933    #[must_use = "this returns the result of the comparison, without modifying either input"]
934    #[stable(feature = "rust1", since = "1.0.0")]
935    #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
936    #[inline]
937    pub const fn min(self, other: f32) -> f32 {
938        intrinsics::minnumf32(self, other)
939    }
940
941    /// Returns the maximum of the two numbers, propagating NaN.
942    ///
943    /// This returns NaN when *either* argument is NaN, as opposed to
944    /// [`f32::max`] which only returns NaN when *both* arguments are NaN.
945    ///
946    /// ```
947    /// #![feature(float_minimum_maximum)]
948    /// let x = 1.0f32;
949    /// let y = 2.0f32;
950    ///
951    /// assert_eq!(x.maximum(y), y);
952    /// assert!(x.maximum(f32::NAN).is_nan());
953    /// ```
954    ///
955    /// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the greater
956    /// of the two numbers. For this operation, -0.0 is considered to be less than +0.0.
957    /// Note that this follows the semantics specified in IEEE 754-2019.
958    ///
959    /// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN
960    /// operand is conserved; see the [specification of NaN bit patterns](f32#nan-bit-patterns) for more info.
961    #[must_use = "this returns the result of the comparison, without modifying either input"]
962    #[unstable(feature = "float_minimum_maximum", issue = "91079")]
963    #[inline]
964    pub const fn maximum(self, other: f32) -> f32 {
965        intrinsics::maximumf32(self, other)
966    }
967
968    /// Returns the minimum of the two numbers, propagating NaN.
969    ///
970    /// This returns NaN when *either* argument is NaN, as opposed to
971    /// [`f32::min`] which only returns NaN when *both* arguments are NaN.
972    ///
973    /// ```
974    /// #![feature(float_minimum_maximum)]
975    /// let x = 1.0f32;
976    /// let y = 2.0f32;
977    ///
978    /// assert_eq!(x.minimum(y), x);
979    /// assert!(x.minimum(f32::NAN).is_nan());
980    /// ```
981    ///
982    /// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the lesser
983    /// of the two numbers. For this operation, -0.0 is considered to be less than +0.0.
984    /// Note that this follows the semantics specified in IEEE 754-2019.
985    ///
986    /// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN
987    /// operand is conserved; see the [specification of NaN bit patterns](f32#nan-bit-patterns) for more info.
988    #[must_use = "this returns the result of the comparison, without modifying either input"]
989    #[unstable(feature = "float_minimum_maximum", issue = "91079")]
990    #[inline]
991    pub const fn minimum(self, other: f32) -> f32 {
992        intrinsics::minimumf32(self, other)
993    }
994
995    /// Calculates the midpoint (average) between `self` and `rhs`.
996    ///
997    /// This returns NaN when *either* argument is NaN or if a combination of
998    /// +inf and -inf is provided as arguments.
999    ///
1000    /// # Examples
1001    ///
1002    /// ```
1003    /// assert_eq!(1f32.midpoint(4.0), 2.5);
1004    /// assert_eq!((-5.5f32).midpoint(8.0), 1.25);
1005    /// ```
1006    #[inline]
1007    #[doc(alias = "average")]
1008    #[stable(feature = "num_midpoint", since = "1.85.0")]
1009    #[rustc_const_stable(feature = "num_midpoint", since = "1.85.0")]
1010    pub const fn midpoint(self, other: f32) -> f32 {
1011        cfg_select! {
1012            // Allow faster implementation that have known good 64-bit float
1013            // implementations. Falling back to the branchy code on targets that don't
1014            // have 64-bit hardware floats or buggy implementations.
1015            // https://github.com/rust-lang/rust/pull/121062#issuecomment-2123408114
1016            any(
1017                target_arch = "x86_64",
1018                target_arch = "aarch64",
1019                all(any(target_arch = "riscv32", target_arch = "riscv64"), target_feature = "d"),
1020                all(target_arch = "loongarch64", target_feature = "d"),
1021                all(target_arch = "arm", target_feature = "vfp2"),
1022                target_arch = "wasm32",
1023                target_arch = "wasm64",
1024            ) => {
1025                ((self as f64 + other as f64) / 2.0) as f32
1026            }
1027            _ => {
1028                const LO: f32 = f32::MIN_POSITIVE * 2.;
1029                const HI: f32 = f32::MAX / 2.;
1030
1031                let (a, b) = (self, other);
1032                let abs_a = a.abs();
1033                let abs_b = b.abs();
1034
1035                if abs_a <= HI && abs_b <= HI {
1036                    // Overflow is impossible
1037                    (a + b) / 2.
1038                } else if abs_a < LO {
1039                    // Not safe to halve `a` (would underflow)
1040                    a + (b / 2.)
1041                } else if abs_b < LO {
1042                    // Not safe to halve `b` (would underflow)
1043                    (a / 2.) + b
1044                } else {
1045                    // Safe to halve `a` and `b`
1046                    (a / 2.) + (b / 2.)
1047                }
1048            }
1049        }
1050    }
1051
1052    /// Rounds toward zero and converts to any primitive integer type,
1053    /// assuming that the value is finite and fits in that type.
1054    ///
1055    /// ```
1056    /// let value = 4.6_f32;
1057    /// let rounded = unsafe { value.to_int_unchecked::<u16>() };
1058    /// assert_eq!(rounded, 4);
1059    ///
1060    /// let value = -128.9_f32;
1061    /// let rounded = unsafe { value.to_int_unchecked::<i8>() };
1062    /// assert_eq!(rounded, i8::MIN);
1063    /// ```
1064    ///
1065    /// # Safety
1066    ///
1067    /// The value must:
1068    ///
1069    /// * Not be `NaN`
1070    /// * Not be infinite
1071    /// * Be representable in the return type `Int`, after truncating off its fractional part
1072    #[must_use = "this returns the result of the operation, \
1073                  without modifying the original"]
1074    #[stable(feature = "float_approx_unchecked_to", since = "1.44.0")]
1075    #[inline]
1076    pub unsafe fn to_int_unchecked<Int>(self) -> Int
1077    where
1078        Self: FloatToInt<Int>,
1079    {
1080        // SAFETY: the caller must uphold the safety contract for
1081        // `FloatToInt::to_int_unchecked`.
1082        unsafe { FloatToInt::<Int>::to_int_unchecked(self) }
1083    }
1084
1085    /// Raw transmutation to `u32`.
1086    ///
1087    /// This is currently identical to `transmute::<f32, u32>(self)` on all platforms.
1088    ///
1089    /// See [`from_bits`](Self::from_bits) for some discussion of the
1090    /// portability of this operation (there are almost no issues).
1091    ///
1092    /// Note that this function is distinct from `as` casting, which attempts to
1093    /// preserve the *numeric* value, and not the bitwise value.
1094    ///
1095    /// # Examples
1096    ///
1097    /// ```
1098    /// assert_ne!((1f32).to_bits(), 1f32 as u32); // to_bits() is not casting!
1099    /// assert_eq!((12.5f32).to_bits(), 0x41480000);
1100    ///
1101    /// ```
1102    #[must_use = "this returns the result of the operation, \
1103                  without modifying the original"]
1104    #[stable(feature = "float_bits_conv", since = "1.20.0")]
1105    #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1106    #[inline]
1107    #[allow(unnecessary_transmutes)]
1108    pub const fn to_bits(self) -> u32 {
1109        // SAFETY: `u32` is a plain old datatype so we can always transmute to it.
1110        unsafe { mem::transmute(self) }
1111    }
1112
1113    /// Raw transmutation from `u32`.
1114    ///
1115    /// This is currently identical to `transmute::<u32, f32>(v)` on all platforms.
1116    /// It turns out this is incredibly portable, for two reasons:
1117    ///
1118    /// * Floats and Ints have the same endianness on all supported platforms.
1119    /// * IEEE 754 very precisely specifies the bit layout of floats.
1120    ///
1121    /// However there is one caveat: prior to the 2008 version of IEEE 754, how
1122    /// to interpret the NaN signaling bit wasn't actually specified. Most platforms
1123    /// (notably x86 and ARM) picked the interpretation that was ultimately
1124    /// standardized in 2008, but some didn't (notably MIPS). As a result, all
1125    /// signaling NaNs on MIPS are quiet NaNs on x86, and vice-versa.
1126    ///
1127    /// Rather than trying to preserve signaling-ness cross-platform, this
1128    /// implementation favors preserving the exact bits. This means that
1129    /// any payloads encoded in NaNs will be preserved even if the result of
1130    /// this method is sent over the network from an x86 machine to a MIPS one.
1131    ///
1132    /// If the results of this method are only manipulated by the same
1133    /// architecture that produced them, then there is no portability concern.
1134    ///
1135    /// If the input isn't NaN, then there is no portability concern.
1136    ///
1137    /// If you don't care about signalingness (very likely), then there is no
1138    /// portability concern.
1139    ///
1140    /// Note that this function is distinct from `as` casting, which attempts to
1141    /// preserve the *numeric* value, and not the bitwise value.
1142    ///
1143    /// # Examples
1144    ///
1145    /// ```
1146    /// let v = f32::from_bits(0x41480000);
1147    /// assert_eq!(v, 12.5);
1148    /// ```
1149    #[stable(feature = "float_bits_conv", since = "1.20.0")]
1150    #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1151    #[must_use]
1152    #[inline]
1153    #[allow(unnecessary_transmutes)]
1154    pub const fn from_bits(v: u32) -> Self {
1155        // It turns out the safety issues with sNaN were overblown! Hooray!
1156        // SAFETY: `u32` is a plain old datatype so we can always transmute from it.
1157        unsafe { mem::transmute(v) }
1158    }
1159
1160    /// Returns the memory representation of this floating point number as a byte array in
1161    /// big-endian (network) byte order.
1162    ///
1163    /// See [`from_bits`](Self::from_bits) for some discussion of the
1164    /// portability of this operation (there are almost no issues).
1165    ///
1166    /// # Examples
1167    ///
1168    /// ```
1169    /// let bytes = 12.5f32.to_be_bytes();
1170    /// assert_eq!(bytes, [0x41, 0x48, 0x00, 0x00]);
1171    /// ```
1172    #[must_use = "this returns the result of the operation, \
1173                  without modifying the original"]
1174    #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1175    #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1176    #[inline]
1177    pub const fn to_be_bytes(self) -> [u8; 4] {
1178        self.to_bits().to_be_bytes()
1179    }
1180
1181    /// Returns the memory representation of this floating point number as a byte array in
1182    /// little-endian byte order.
1183    ///
1184    /// See [`from_bits`](Self::from_bits) for some discussion of the
1185    /// portability of this operation (there are almost no issues).
1186    ///
1187    /// # Examples
1188    ///
1189    /// ```
1190    /// let bytes = 12.5f32.to_le_bytes();
1191    /// assert_eq!(bytes, [0x00, 0x00, 0x48, 0x41]);
1192    /// ```
1193    #[must_use = "this returns the result of the operation, \
1194                  without modifying the original"]
1195    #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1196    #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1197    #[inline]
1198    pub const fn to_le_bytes(self) -> [u8; 4] {
1199        self.to_bits().to_le_bytes()
1200    }
1201
1202    /// Returns the memory representation of this floating point number as a byte array in
1203    /// native byte order.
1204    ///
1205    /// As the target platform's native endianness is used, portable code
1206    /// should use [`to_be_bytes`] or [`to_le_bytes`], as appropriate, instead.
1207    ///
1208    /// [`to_be_bytes`]: f32::to_be_bytes
1209    /// [`to_le_bytes`]: f32::to_le_bytes
1210    ///
1211    /// See [`from_bits`](Self::from_bits) for some discussion of the
1212    /// portability of this operation (there are almost no issues).
1213    ///
1214    /// # Examples
1215    ///
1216    /// ```
1217    /// let bytes = 12.5f32.to_ne_bytes();
1218    /// assert_eq!(
1219    ///     bytes,
1220    ///     if cfg!(target_endian = "big") {
1221    ///         [0x41, 0x48, 0x00, 0x00]
1222    ///     } else {
1223    ///         [0x00, 0x00, 0x48, 0x41]
1224    ///     }
1225    /// );
1226    /// ```
1227    #[must_use = "this returns the result of the operation, \
1228                  without modifying the original"]
1229    #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1230    #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1231    #[inline]
1232    pub const fn to_ne_bytes(self) -> [u8; 4] {
1233        self.to_bits().to_ne_bytes()
1234    }
1235
1236    /// Creates a floating point value from its representation as a byte array in big endian.
1237    ///
1238    /// See [`from_bits`](Self::from_bits) for some discussion of the
1239    /// portability of this operation (there are almost no issues).
1240    ///
1241    /// # Examples
1242    ///
1243    /// ```
1244    /// let value = f32::from_be_bytes([0x41, 0x48, 0x00, 0x00]);
1245    /// assert_eq!(value, 12.5);
1246    /// ```
1247    #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1248    #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1249    #[must_use]
1250    #[inline]
1251    pub const fn from_be_bytes(bytes: [u8; 4]) -> Self {
1252        Self::from_bits(u32::from_be_bytes(bytes))
1253    }
1254
1255    /// Creates a floating point value from its representation as a byte array in little endian.
1256    ///
1257    /// See [`from_bits`](Self::from_bits) for some discussion of the
1258    /// portability of this operation (there are almost no issues).
1259    ///
1260    /// # Examples
1261    ///
1262    /// ```
1263    /// let value = f32::from_le_bytes([0x00, 0x00, 0x48, 0x41]);
1264    /// assert_eq!(value, 12.5);
1265    /// ```
1266    #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1267    #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1268    #[must_use]
1269    #[inline]
1270    pub const fn from_le_bytes(bytes: [u8; 4]) -> Self {
1271        Self::from_bits(u32::from_le_bytes(bytes))
1272    }
1273
1274    /// Creates a floating point value from its representation as a byte array in native endian.
1275    ///
1276    /// As the target platform's native endianness is used, portable code
1277    /// likely wants to use [`from_be_bytes`] or [`from_le_bytes`], as
1278    /// appropriate instead.
1279    ///
1280    /// [`from_be_bytes`]: f32::from_be_bytes
1281    /// [`from_le_bytes`]: f32::from_le_bytes
1282    ///
1283    /// See [`from_bits`](Self::from_bits) for some discussion of the
1284    /// portability of this operation (there are almost no issues).
1285    ///
1286    /// # Examples
1287    ///
1288    /// ```
1289    /// let value = f32::from_ne_bytes(if cfg!(target_endian = "big") {
1290    ///     [0x41, 0x48, 0x00, 0x00]
1291    /// } else {
1292    ///     [0x00, 0x00, 0x48, 0x41]
1293    /// });
1294    /// assert_eq!(value, 12.5);
1295    /// ```
1296    #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1297    #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1298    #[must_use]
1299    #[inline]
1300    pub const fn from_ne_bytes(bytes: [u8; 4]) -> Self {
1301        Self::from_bits(u32::from_ne_bytes(bytes))
1302    }
1303
1304    /// Returns the ordering between `self` and `other`.
1305    ///
1306    /// Unlike the standard partial comparison between floating point numbers,
1307    /// this comparison always produces an ordering in accordance to
1308    /// the `totalOrder` predicate as defined in the IEEE 754 (2008 revision)
1309    /// floating point standard. The values are ordered in the following sequence:
1310    ///
1311    /// - negative quiet NaN
1312    /// - negative signaling NaN
1313    /// - negative infinity
1314    /// - negative numbers
1315    /// - negative subnormal numbers
1316    /// - negative zero
1317    /// - positive zero
1318    /// - positive subnormal numbers
1319    /// - positive numbers
1320    /// - positive infinity
1321    /// - positive signaling NaN
1322    /// - positive quiet NaN.
1323    ///
1324    /// The ordering established by this function does not always agree with the
1325    /// [`PartialOrd`] and [`PartialEq`] implementations of `f32`. For example,
1326    /// they consider negative and positive zero equal, while `total_cmp`
1327    /// doesn't.
1328    ///
1329    /// The interpretation of the signaling NaN bit follows the definition in
1330    /// the IEEE 754 standard, which may not match the interpretation by some of
1331    /// the older, non-conformant (e.g. MIPS) hardware implementations.
1332    ///
1333    /// # Example
1334    ///
1335    /// ```
1336    /// struct GoodBoy {
1337    ///     name: String,
1338    ///     weight: f32,
1339    /// }
1340    ///
1341    /// let mut bois = vec![
1342    ///     GoodBoy { name: "Pucci".to_owned(), weight: 0.1 },
1343    ///     GoodBoy { name: "Woofer".to_owned(), weight: 99.0 },
1344    ///     GoodBoy { name: "Yapper".to_owned(), weight: 10.0 },
1345    ///     GoodBoy { name: "Chonk".to_owned(), weight: f32::INFINITY },
1346    ///     GoodBoy { name: "Abs. Unit".to_owned(), weight: f32::NAN },
1347    ///     GoodBoy { name: "Floaty".to_owned(), weight: -5.0 },
1348    /// ];
1349    ///
1350    /// bois.sort_by(|a, b| a.weight.total_cmp(&b.weight));
1351    ///
1352    /// // `f32::NAN` could be positive or negative, which will affect the sort order.
1353    /// if f32::NAN.is_sign_negative() {
1354    ///     assert!(bois.into_iter().map(|b| b.weight)
1355    ///         .zip([f32::NAN, -5.0, 0.1, 10.0, 99.0, f32::INFINITY].iter())
1356    ///         .all(|(a, b)| a.to_bits() == b.to_bits()))
1357    /// } else {
1358    ///     assert!(bois.into_iter().map(|b| b.weight)
1359    ///         .zip([-5.0, 0.1, 10.0, 99.0, f32::INFINITY, f32::NAN].iter())
1360    ///         .all(|(a, b)| a.to_bits() == b.to_bits()))
1361    /// }
1362    /// ```
1363    #[stable(feature = "total_cmp", since = "1.62.0")]
1364    #[must_use]
1365    #[inline]
1366    pub fn total_cmp(&self, other: &Self) -> crate::cmp::Ordering {
1367        let mut left = self.to_bits() as i32;
1368        let mut right = other.to_bits() as i32;
1369
1370        // In case of negatives, flip all the bits except the sign
1371        // to achieve a similar layout as two's complement integers
1372        //
1373        // Why does this work? IEEE 754 floats consist of three fields:
1374        // Sign bit, exponent and mantissa. The set of exponent and mantissa
1375        // fields as a whole have the property that their bitwise order is
1376        // equal to the numeric magnitude where the magnitude is defined.
1377        // The magnitude is not normally defined on NaN values, but
1378        // IEEE 754 totalOrder defines the NaN values also to follow the
1379        // bitwise order. This leads to order explained in the doc comment.
1380        // However, the representation of magnitude is the same for negative
1381        // and positive numbers – only the sign bit is different.
1382        // To easily compare the floats as signed integers, we need to
1383        // flip the exponent and mantissa bits in case of negative numbers.
1384        // We effectively convert the numbers to "two's complement" form.
1385        //
1386        // To do the flipping, we construct a mask and XOR against it.
1387        // We branchlessly calculate an "all-ones except for the sign bit"
1388        // mask from negative-signed values: right shifting sign-extends
1389        // the integer, so we "fill" the mask with sign bits, and then
1390        // convert to unsigned to push one more zero bit.
1391        // On positive values, the mask is all zeros, so it's a no-op.
1392        left ^= (((left >> 31) as u32) >> 1) as i32;
1393        right ^= (((right >> 31) as u32) >> 1) as i32;
1394
1395        left.cmp(&right)
1396    }
1397
1398    /// Restrict a value to a certain interval unless it is NaN.
1399    ///
1400    /// Returns `max` if `self` is greater than `max`, and `min` if `self` is
1401    /// less than `min`. Otherwise this returns `self`.
1402    ///
1403    /// Note that this function returns NaN if the initial value was NaN as
1404    /// well.
1405    ///
1406    /// # Panics
1407    ///
1408    /// Panics if `min > max`, `min` is NaN, or `max` is NaN.
1409    ///
1410    /// # Examples
1411    ///
1412    /// ```
1413    /// assert!((-3.0f32).clamp(-2.0, 1.0) == -2.0);
1414    /// assert!((0.0f32).clamp(-2.0, 1.0) == 0.0);
1415    /// assert!((2.0f32).clamp(-2.0, 1.0) == 1.0);
1416    /// assert!((f32::NAN).clamp(-2.0, 1.0).is_nan());
1417    /// ```
1418    #[must_use = "method returns a new number and does not mutate the original value"]
1419    #[stable(feature = "clamp", since = "1.50.0")]
1420    #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
1421    #[inline]
1422    pub const fn clamp(mut self, min: f32, max: f32) -> f32 {
1423        const_assert!(
1424            min <= max,
1425            "min > max, or either was NaN",
1426            "min > max, or either was NaN. min = {min:?}, max = {max:?}",
1427            min: f32,
1428            max: f32,
1429        );
1430
1431        if self < min {
1432            self = min;
1433        }
1434        if self > max {
1435            self = max;
1436        }
1437        self
1438    }
1439
1440    /// Computes the absolute value of `self`.
1441    ///
1442    /// This function always returns the precise result.
1443    ///
1444    /// # Examples
1445    ///
1446    /// ```
1447    /// let x = 3.5_f32;
1448    /// let y = -3.5_f32;
1449    ///
1450    /// assert_eq!(x.abs(), x);
1451    /// assert_eq!(y.abs(), -y);
1452    ///
1453    /// assert!(f32::NAN.abs().is_nan());
1454    /// ```
1455    #[must_use = "method returns a new number and does not mutate the original value"]
1456    #[stable(feature = "rust1", since = "1.0.0")]
1457    #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
1458    #[inline]
1459    pub const fn abs(self) -> f32 {
1460        // SAFETY: this is actually a safe intrinsic
1461        unsafe { intrinsics::fabsf32(self) }
1462    }
1463
1464    /// Returns a number that represents the sign of `self`.
1465    ///
1466    /// - `1.0` if the number is positive, `+0.0` or `INFINITY`
1467    /// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
1468    /// - NaN if the number is NaN
1469    ///
1470    /// # Examples
1471    ///
1472    /// ```
1473    /// let f = 3.5_f32;
1474    ///
1475    /// assert_eq!(f.signum(), 1.0);
1476    /// assert_eq!(f32::NEG_INFINITY.signum(), -1.0);
1477    ///
1478    /// assert!(f32::NAN.signum().is_nan());
1479    /// ```
1480    #[must_use = "method returns a new number and does not mutate the original value"]
1481    #[stable(feature = "rust1", since = "1.0.0")]
1482    #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
1483    #[inline]
1484    pub const fn signum(self) -> f32 {
1485        if self.is_nan() { Self::NAN } else { 1.0_f32.copysign(self) }
1486    }
1487
1488    /// Returns a number composed of the magnitude of `self` and the sign of
1489    /// `sign`.
1490    ///
1491    /// Equal to `self` if the sign of `self` and `sign` are the same, otherwise equal to `-self`.
1492    /// If `self` is a NaN, then a NaN with the same payload as `self` and the sign bit of `sign` is
1493    /// returned.
1494    ///
1495    /// If `sign` is a NaN, then this operation will still carry over its sign into the result. Note
1496    /// that IEEE 754 doesn't assign any meaning to the sign bit in case of a NaN, and as Rust
1497    /// doesn't guarantee that the bit pattern of NaNs are conserved over arithmetic operations, the
1498    /// result of `copysign` with `sign` being a NaN might produce an unexpected or non-portable
1499    /// result. See the [specification of NaN bit patterns](primitive@f32#nan-bit-patterns) for more
1500    /// info.
1501    ///
1502    /// # Examples
1503    ///
1504    /// ```
1505    /// let f = 3.5_f32;
1506    ///
1507    /// assert_eq!(f.copysign(0.42), 3.5_f32);
1508    /// assert_eq!(f.copysign(-0.42), -3.5_f32);
1509    /// assert_eq!((-f).copysign(0.42), 3.5_f32);
1510    /// assert_eq!((-f).copysign(-0.42), -3.5_f32);
1511    ///
1512    /// assert!(f32::NAN.copysign(1.0).is_nan());
1513    /// ```
1514    #[must_use = "method returns a new number and does not mutate the original value"]
1515    #[inline]
1516    #[stable(feature = "copysign", since = "1.35.0")]
1517    #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
1518    pub const fn copysign(self, sign: f32) -> f32 {
1519        // SAFETY: this is actually a safe intrinsic
1520        unsafe { intrinsics::copysignf32(self, sign) }
1521    }
1522
1523    /// Float addition that allows optimizations based on algebraic rules.
1524    ///
1525    /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1526    #[must_use = "method returns a new number and does not mutate the original value"]
1527    #[unstable(feature = "float_algebraic", issue = "136469")]
1528    #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1529    #[inline]
1530    pub const fn algebraic_add(self, rhs: f32) -> f32 {
1531        intrinsics::fadd_algebraic(self, rhs)
1532    }
1533
1534    /// Float subtraction that allows optimizations based on algebraic rules.
1535    ///
1536    /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1537    #[must_use = "method returns a new number and does not mutate the original value"]
1538    #[unstable(feature = "float_algebraic", issue = "136469")]
1539    #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1540    #[inline]
1541    pub const fn algebraic_sub(self, rhs: f32) -> f32 {
1542        intrinsics::fsub_algebraic(self, rhs)
1543    }
1544
1545    /// Float multiplication that allows optimizations based on algebraic rules.
1546    ///
1547    /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1548    #[must_use = "method returns a new number and does not mutate the original value"]
1549    #[unstable(feature = "float_algebraic", issue = "136469")]
1550    #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1551    #[inline]
1552    pub const fn algebraic_mul(self, rhs: f32) -> f32 {
1553        intrinsics::fmul_algebraic(self, rhs)
1554    }
1555
1556    /// Float division that allows optimizations based on algebraic rules.
1557    ///
1558    /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1559    #[must_use = "method returns a new number and does not mutate the original value"]
1560    #[unstable(feature = "float_algebraic", issue = "136469")]
1561    #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1562    #[inline]
1563    pub const fn algebraic_div(self, rhs: f32) -> f32 {
1564        intrinsics::fdiv_algebraic(self, rhs)
1565    }
1566
1567    /// Float remainder that allows optimizations based on algebraic rules.
1568    ///
1569    /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1570    #[must_use = "method returns a new number and does not mutate the original value"]
1571    #[unstable(feature = "float_algebraic", issue = "136469")]
1572    #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1573    #[inline]
1574    pub const fn algebraic_rem(self, rhs: f32) -> f32 {
1575        intrinsics::frem_algebraic(self, rhs)
1576    }
1577}
1578
1579/// Experimental implementations of floating point functions in `core`.
1580///
1581/// _The standalone functions in this module are for testing only.
1582/// They will be stabilized as inherent methods._
1583#[unstable(feature = "core_float_math", issue = "137578")]
1584pub mod math {
1585    use crate::intrinsics;
1586    use crate::num::libm;
1587
1588    /// Experimental version of `floor` in `core`. See [`f32::floor`] for details.
1589    ///
1590    /// # Examples
1591    ///
1592    /// ```
1593    /// #![feature(core_float_math)]
1594    ///
1595    /// use core::f32;
1596    ///
1597    /// let f = 3.7_f32;
1598    /// let g = 3.0_f32;
1599    /// let h = -3.7_f32;
1600    ///
1601    /// assert_eq!(f32::math::floor(f), 3.0);
1602    /// assert_eq!(f32::math::floor(g), 3.0);
1603    /// assert_eq!(f32::math::floor(h), -4.0);
1604    /// ```
1605    ///
1606    /// _This standalone function is for testing only.
1607    /// It will be stabilized as an inherent method._
1608    ///
1609    /// [`f32::floor`]: ../../../std/primitive.f32.html#method.floor
1610    #[inline]
1611    #[unstable(feature = "core_float_math", issue = "137578")]
1612    #[must_use = "method returns a new number and does not mutate the original value"]
1613    pub const fn floor(x: f32) -> f32 {
1614        // SAFETY: intrinsic with no preconditions
1615        unsafe { intrinsics::floorf32(x) }
1616    }
1617
1618    /// Experimental version of `ceil` in `core`. See [`f32::ceil`] for details.
1619    ///
1620    /// # Examples
1621    ///
1622    /// ```
1623    /// #![feature(core_float_math)]
1624    ///
1625    /// use core::f32;
1626    ///
1627    /// let f = 3.01_f32;
1628    /// let g = 4.0_f32;
1629    ///
1630    /// assert_eq!(f32::math::ceil(f), 4.0);
1631    /// assert_eq!(f32::math::ceil(g), 4.0);
1632    /// ```
1633    ///
1634    /// _This standalone function is for testing only.
1635    /// It will be stabilized as an inherent method._
1636    ///
1637    /// [`f32::ceil`]: ../../../std/primitive.f32.html#method.ceil
1638    #[inline]
1639    #[doc(alias = "ceiling")]
1640    #[must_use = "method returns a new number and does not mutate the original value"]
1641    #[unstable(feature = "core_float_math", issue = "137578")]
1642    pub const fn ceil(x: f32) -> f32 {
1643        // SAFETY: intrinsic with no preconditions
1644        unsafe { intrinsics::ceilf32(x) }
1645    }
1646
1647    /// Experimental version of `round` in `core`. See [`f32::round`] for details.
1648    ///
1649    /// # Examples
1650    ///
1651    /// ```
1652    /// #![feature(core_float_math)]
1653    ///
1654    /// use core::f32;
1655    ///
1656    /// let f = 3.3_f32;
1657    /// let g = -3.3_f32;
1658    /// let h = -3.7_f32;
1659    /// let i = 3.5_f32;
1660    /// let j = 4.5_f32;
1661    ///
1662    /// assert_eq!(f32::math::round(f), 3.0);
1663    /// assert_eq!(f32::math::round(g), -3.0);
1664    /// assert_eq!(f32::math::round(h), -4.0);
1665    /// assert_eq!(f32::math::round(i), 4.0);
1666    /// assert_eq!(f32::math::round(j), 5.0);
1667    /// ```
1668    ///
1669    /// _This standalone function is for testing only.
1670    /// It will be stabilized as an inherent method._
1671    ///
1672    /// [`f32::round`]: ../../../std/primitive.f32.html#method.round
1673    #[inline]
1674    #[unstable(feature = "core_float_math", issue = "137578")]
1675    #[must_use = "method returns a new number and does not mutate the original value"]
1676    pub const fn round(x: f32) -> f32 {
1677        // SAFETY: intrinsic with no preconditions
1678        unsafe { intrinsics::roundf32(x) }
1679    }
1680
1681    /// Experimental version of `round_ties_even` in `core`. See [`f32::round_ties_even`] for
1682    /// details.
1683    ///
1684    /// # Examples
1685    ///
1686    /// ```
1687    /// #![feature(core_float_math)]
1688    ///
1689    /// use core::f32;
1690    ///
1691    /// let f = 3.3_f32;
1692    /// let g = -3.3_f32;
1693    /// let h = 3.5_f32;
1694    /// let i = 4.5_f32;
1695    ///
1696    /// assert_eq!(f32::math::round_ties_even(f), 3.0);
1697    /// assert_eq!(f32::math::round_ties_even(g), -3.0);
1698    /// assert_eq!(f32::math::round_ties_even(h), 4.0);
1699    /// assert_eq!(f32::math::round_ties_even(i), 4.0);
1700    /// ```
1701    ///
1702    /// _This standalone function is for testing only.
1703    /// It will be stabilized as an inherent method._
1704    ///
1705    /// [`f32::round_ties_even`]: ../../../std/primitive.f32.html#method.round_ties_even
1706    #[inline]
1707    #[unstable(feature = "core_float_math", issue = "137578")]
1708    #[must_use = "method returns a new number and does not mutate the original value"]
1709    pub const fn round_ties_even(x: f32) -> f32 {
1710        intrinsics::round_ties_even_f32(x)
1711    }
1712
1713    /// Experimental version of `trunc` in `core`. See [`f32::trunc`] for details.
1714    ///
1715    /// # Examples
1716    ///
1717    /// ```
1718    /// #![feature(core_float_math)]
1719    ///
1720    /// use core::f32;
1721    ///
1722    /// let f = 3.7_f32;
1723    /// let g = 3.0_f32;
1724    /// let h = -3.7_f32;
1725    ///
1726    /// assert_eq!(f32::math::trunc(f), 3.0);
1727    /// assert_eq!(f32::math::trunc(g), 3.0);
1728    /// assert_eq!(f32::math::trunc(h), -3.0);
1729    /// ```
1730    ///
1731    /// _This standalone function is for testing only.
1732    /// It will be stabilized as an inherent method._
1733    ///
1734    /// [`f32::trunc`]: ../../../std/primitive.f32.html#method.trunc
1735    #[inline]
1736    #[doc(alias = "truncate")]
1737    #[must_use = "method returns a new number and does not mutate the original value"]
1738    #[unstable(feature = "core_float_math", issue = "137578")]
1739    pub const fn trunc(x: f32) -> f32 {
1740        // SAFETY: intrinsic with no preconditions
1741        unsafe { intrinsics::truncf32(x) }
1742    }
1743
1744    /// Experimental version of `fract` in `core`. See [`f32::fract`] for details.
1745    ///
1746    /// # Examples
1747    ///
1748    /// ```
1749    /// #![feature(core_float_math)]
1750    ///
1751    /// use core::f32;
1752    ///
1753    /// let x = 3.6_f32;
1754    /// let y = -3.6_f32;
1755    /// let abs_difference_x = (f32::math::fract(x) - 0.6).abs();
1756    /// let abs_difference_y = (f32::math::fract(y) - (-0.6)).abs();
1757    ///
1758    /// assert!(abs_difference_x <= f32::EPSILON);
1759    /// assert!(abs_difference_y <= f32::EPSILON);
1760    /// ```
1761    ///
1762    /// _This standalone function is for testing only.
1763    /// It will be stabilized as an inherent method._
1764    ///
1765    /// [`f32::fract`]: ../../../std/primitive.f32.html#method.fract
1766    #[inline]
1767    #[unstable(feature = "core_float_math", issue = "137578")]
1768    #[must_use = "method returns a new number and does not mutate the original value"]
1769    pub const fn fract(x: f32) -> f32 {
1770        x - trunc(x)
1771    }
1772
1773    /// Experimental version of `mul_add` in `core`. See [`f32::mul_add`] for details.
1774    ///
1775    /// # Examples
1776    ///
1777    /// ```
1778    /// #![feature(core_float_math)]
1779    ///
1780    /// # // FIXME(#140515): mingw has an incorrect fma
1781    /// # // https://sourceforge.net/p/mingw-w64/bugs/848/
1782    /// # #[cfg(all(target_os = "windows", target_env = "gnu", not(target_abi = "llvm")))] {
1783    /// use core::f32;
1784    ///
1785    /// let m = 10.0_f32;
1786    /// let x = 4.0_f32;
1787    /// let b = 60.0_f32;
1788    ///
1789    /// assert_eq!(f32::math::mul_add(m, x, b), 100.0);
1790    /// assert_eq!(m * x + b, 100.0);
1791    ///
1792    /// let one_plus_eps = 1.0_f32 + f32::EPSILON;
1793    /// let one_minus_eps = 1.0_f32 - f32::EPSILON;
1794    /// let minus_one = -1.0_f32;
1795    ///
1796    /// // The exact result (1 + eps) * (1 - eps) = 1 - eps * eps.
1797    /// assert_eq!(
1798    ///     f32::math::mul_add(one_plus_eps, one_minus_eps, minus_one),
1799    ///     -f32::EPSILON * f32::EPSILON
1800    /// );
1801    /// // Different rounding with the non-fused multiply and add.
1802    /// assert_eq!(one_plus_eps * one_minus_eps + minus_one, 0.0);
1803    /// # }
1804    /// ```
1805    ///
1806    /// _This standalone function is for testing only.
1807    /// It will be stabilized as an inherent method._
1808    ///
1809    /// [`f32::mul_add`]: ../../../std/primitive.f32.html#method.mul_add
1810    #[inline]
1811    #[doc(alias = "fmaf", alias = "fusedMultiplyAdd")]
1812    #[must_use = "method returns a new number and does not mutate the original value"]
1813    #[unstable(feature = "core_float_math", issue = "137578")]
1814    pub fn mul_add(x: f32, y: f32, z: f32) -> f32 {
1815        // SAFETY: intrinsic with no preconditions
1816        unsafe { intrinsics::fmaf32(x, y, z) }
1817    }
1818
1819    /// Experimental version of `div_euclid` in `core`. See [`f32::div_euclid`] for details.
1820    ///
1821    /// # Examples
1822    ///
1823    /// ```
1824    /// #![feature(core_float_math)]
1825    ///
1826    /// use core::f32;
1827    ///
1828    /// let a: f32 = 7.0;
1829    /// let b = 4.0;
1830    /// assert_eq!(f32::math::div_euclid(a, b), 1.0); // 7.0 > 4.0 * 1.0
1831    /// assert_eq!(f32::math::div_euclid(-a, b), -2.0); // -7.0 >= 4.0 * -2.0
1832    /// assert_eq!(f32::math::div_euclid(a, -b), -1.0); // 7.0 >= -4.0 * -1.0
1833    /// assert_eq!(f32::math::div_euclid(-a, -b), 2.0); // -7.0 >= -4.0 * 2.0
1834    /// ```
1835    ///
1836    /// _This standalone function is for testing only.
1837    /// It will be stabilized as an inherent method._
1838    ///
1839    /// [`f32::div_euclid`]: ../../../std/primitive.f32.html#method.div_euclid
1840    #[inline]
1841    #[unstable(feature = "core_float_math", issue = "137578")]
1842    #[must_use = "method returns a new number and does not mutate the original value"]
1843    pub fn div_euclid(x: f32, rhs: f32) -> f32 {
1844        let q = trunc(x / rhs);
1845        if x % rhs < 0.0 {
1846            return if rhs > 0.0 { q - 1.0 } else { q + 1.0 };
1847        }
1848        q
1849    }
1850
1851    /// Experimental version of `rem_euclid` in `core`. See [`f32::rem_euclid`] for details.
1852    ///
1853    /// # Examples
1854    ///
1855    /// ```
1856    /// #![feature(core_float_math)]
1857    ///
1858    /// use core::f32;
1859    ///
1860    /// let a: f32 = 7.0;
1861    /// let b = 4.0;
1862    /// assert_eq!(f32::math::rem_euclid(a, b), 3.0);
1863    /// assert_eq!(f32::math::rem_euclid(-a, b), 1.0);
1864    /// assert_eq!(f32::math::rem_euclid(a, -b), 3.0);
1865    /// assert_eq!(f32::math::rem_euclid(-a, -b), 1.0);
1866    /// // limitation due to round-off error
1867    /// assert!(f32::math::rem_euclid(-f32::EPSILON, 3.0) != 0.0);
1868    /// ```
1869    ///
1870    /// _This standalone function is for testing only.
1871    /// It will be stabilized as an inherent method._
1872    ///
1873    /// [`f32::rem_euclid`]: ../../../std/primitive.f32.html#method.rem_euclid
1874    #[inline]
1875    #[doc(alias = "modulo", alias = "mod")]
1876    #[unstable(feature = "core_float_math", issue = "137578")]
1877    #[must_use = "method returns a new number and does not mutate the original value"]
1878    pub fn rem_euclid(x: f32, rhs: f32) -> f32 {
1879        let r = x % rhs;
1880        if r < 0.0 { r + rhs.abs() } else { r }
1881    }
1882
1883    /// Experimental version of `powi` in `core`. See [`f32::powi`] for details.
1884    ///
1885    /// # Examples
1886    ///
1887    /// ```
1888    /// #![feature(core_float_math)]
1889    ///
1890    /// use core::f32;
1891    ///
1892    /// let x = 2.0_f32;
1893    /// let abs_difference = (f32::math::powi(x, 2) - (x * x)).abs();
1894    /// assert!(abs_difference <= 1e-5);
1895    ///
1896    /// assert_eq!(f32::math::powi(f32::NAN, 0), 1.0);
1897    /// ```
1898    ///
1899    /// _This standalone function is for testing only.
1900    /// It will be stabilized as an inherent method._
1901    ///
1902    /// [`f32::powi`]: ../../../std/primitive.f32.html#method.powi
1903    #[inline]
1904    #[must_use = "method returns a new number and does not mutate the original value"]
1905    #[unstable(feature = "core_float_math", issue = "137578")]
1906    pub fn powi(x: f32, n: i32) -> f32 {
1907        // SAFETY: intrinsic with no preconditions
1908        unsafe { intrinsics::powif32(x, n) }
1909    }
1910
1911    /// Experimental version of `sqrt` in `core`. See [`f32::sqrt`] for details.
1912    ///
1913    /// # Examples
1914    ///
1915    /// ```
1916    /// #![feature(core_float_math)]
1917    ///
1918    /// use core::f32;
1919    ///
1920    /// let positive = 4.0_f32;
1921    /// let negative = -4.0_f32;
1922    /// let negative_zero = -0.0_f32;
1923    ///
1924    /// assert_eq!(f32::math::sqrt(positive), 2.0);
1925    /// assert!(f32::math::sqrt(negative).is_nan());
1926    /// assert_eq!(f32::math::sqrt(negative_zero), negative_zero);
1927    /// ```
1928    ///
1929    /// _This standalone function is for testing only.
1930    /// It will be stabilized as an inherent method._
1931    ///
1932    /// [`f32::sqrt`]: ../../../std/primitive.f32.html#method.sqrt
1933    #[inline]
1934    #[doc(alias = "squareRoot")]
1935    #[unstable(feature = "core_float_math", issue = "137578")]
1936    #[must_use = "method returns a new number and does not mutate the original value"]
1937    pub fn sqrt(x: f32) -> f32 {
1938        // SAFETY: intrinsic with no preconditions
1939        unsafe { intrinsics::sqrtf32(x) }
1940    }
1941
1942    /// Experimental version of `abs_sub` in `core`. See [`f32::abs_sub`] for details.
1943    ///
1944    /// # Examples
1945    ///
1946    /// ```
1947    /// #![feature(core_float_math)]
1948    ///
1949    /// use core::f32;
1950    ///
1951    /// let x = 3.0f32;
1952    /// let y = -3.0f32;
1953    ///
1954    /// let abs_difference_x = (f32::math::abs_sub(x, 1.0) - 2.0).abs();
1955    /// let abs_difference_y = (f32::math::abs_sub(y, 1.0) - 0.0).abs();
1956    ///
1957    /// assert!(abs_difference_x <= f32::EPSILON);
1958    /// assert!(abs_difference_y <= f32::EPSILON);
1959    /// ```
1960    ///
1961    /// _This standalone function is for testing only.
1962    /// It will be stabilized as an inherent method._
1963    ///
1964    /// [`f32::abs_sub`]: ../../../std/primitive.f32.html#method.abs_sub
1965    #[inline]
1966    #[stable(feature = "rust1", since = "1.0.0")]
1967    #[deprecated(
1968        since = "1.10.0",
1969        note = "you probably meant `(self - other).abs()`: \
1970            this operation is `(self - other).max(0.0)` \
1971            except that `abs_sub` also propagates NaNs (also \
1972            known as `fdimf` in C). If you truly need the positive \
1973            difference, consider using that expression or the C function \
1974            `fdimf`, depending on how you wish to handle NaN (please consider \
1975            filing an issue describing your use-case too)."
1976    )]
1977    #[must_use = "method returns a new number and does not mutate the original value"]
1978    pub fn abs_sub(x: f32, other: f32) -> f32 {
1979        libm::fdimf(x, other)
1980    }
1981
1982    /// Experimental version of `cbrt` in `core`. See [`f32::cbrt`] for details.
1983    ///
1984    /// # Unspecified precision
1985    ///
1986    /// The precision of this function is non-deterministic. This means it varies by platform, Rust version, and
1987    /// can even differ within the same execution from one invocation to the next.
1988    /// This function currently corresponds to the `cbrtf` from libc on Unix
1989    /// and Windows. Note that this might change in the future.
1990    ///
1991    /// # Examples
1992    ///
1993    /// ```
1994    /// #![feature(core_float_math)]
1995    ///
1996    /// use core::f32;
1997    ///
1998    /// let x = 8.0f32;
1999    ///
2000    /// // x^(1/3) - 2 == 0
2001    /// let abs_difference = (f32::math::cbrt(x) - 2.0).abs();
2002    ///
2003    /// assert!(abs_difference <= f32::EPSILON);
2004    /// ```
2005    ///
2006    /// _This standalone function is for testing only.
2007    /// It will be stabilized as an inherent method._
2008    ///
2009    /// [`f32::cbrt`]: ../../../std/primitive.f32.html#method.cbrt
2010    #[inline]
2011    #[must_use = "method returns a new number and does not mutate the original value"]
2012    #[unstable(feature = "core_float_math", issue = "137578")]
2013    pub fn cbrt(x: f32) -> f32 {
2014        libm::cbrtf(x)
2015    }
2016}