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    /// ```
843    /// let angle = std::f32::consts::PI;
844    ///
845    /// let abs_difference = (angle.to_degrees() - 180.0).abs();
846    /// # #[cfg(any(not(target_arch = "x86"), target_feature = "sse2"))]
847    /// assert!(abs_difference <= f32::EPSILON);
848    /// ```
849    #[must_use = "this returns the result of the operation, \
850                  without modifying the original"]
851    #[stable(feature = "f32_deg_rad_conversions", since = "1.7.0")]
852    #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
853    #[inline]
854    pub const fn to_degrees(self) -> f32 {
855        // Use a constant for better precision.
856        const PIS_IN_180: f32 = 57.2957795130823208767981548141051703_f32;
857        self * PIS_IN_180
858    }
859
860    /// Converts degrees to radians.
861    ///
862    /// ```
863    /// let angle = 180.0f32;
864    ///
865    /// let abs_difference = (angle.to_radians() - std::f32::consts::PI).abs();
866    ///
867    /// assert!(abs_difference <= f32::EPSILON);
868    /// ```
869    #[must_use = "this returns the result of the operation, \
870                  without modifying the original"]
871    #[stable(feature = "f32_deg_rad_conversions", since = "1.7.0")]
872    #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
873    #[inline]
874    pub const fn to_radians(self) -> f32 {
875        const RADS_PER_DEG: f32 = consts::PI / 180.0;
876        self * RADS_PER_DEG
877    }
878
879    /// Returns the maximum of the two numbers, ignoring NaN.
880    ///
881    /// If one of the arguments is NaN, then the other argument is returned.
882    /// This follows the IEEE 754-2008 semantics for maxNum, except for handling of signaling NaNs;
883    /// this function handles all NaNs the same way and avoids maxNum's problems with associativity.
884    /// This also matches the behavior of libm’s fmax. In particular, if the inputs compare equal
885    /// (such as for the case of `+0.0` and `-0.0`), either input may be returned non-deterministically.
886    ///
887    /// ```
888    /// let x = 1.0f32;
889    /// let y = 2.0f32;
890    ///
891    /// assert_eq!(x.max(y), y);
892    /// ```
893    #[must_use = "this returns the result of the comparison, without modifying either input"]
894    #[stable(feature = "rust1", since = "1.0.0")]
895    #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
896    #[inline]
897    pub const fn max(self, other: f32) -> f32 {
898        intrinsics::maxnumf32(self, other)
899    }
900
901    /// Returns the minimum of the two numbers, ignoring NaN.
902    ///
903    /// If one of the arguments is NaN, then the other argument is returned.
904    /// This follows the IEEE 754-2008 semantics for minNum, except for handling of signaling NaNs;
905    /// this function handles all NaNs the same way and avoids minNum's problems with associativity.
906    /// This also matches the behavior of libm’s fmin. In particular, if the inputs compare equal
907    /// (such as for the case of `+0.0` and `-0.0`), either input may be returned non-deterministically.
908    ///
909    /// ```
910    /// let x = 1.0f32;
911    /// let y = 2.0f32;
912    ///
913    /// assert_eq!(x.min(y), x);
914    /// ```
915    #[must_use = "this returns the result of the comparison, without modifying either input"]
916    #[stable(feature = "rust1", since = "1.0.0")]
917    #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
918    #[inline]
919    pub const fn min(self, other: f32) -> f32 {
920        intrinsics::minnumf32(self, other)
921    }
922
923    /// Returns the maximum of the two numbers, propagating NaN.
924    ///
925    /// This returns NaN when *either* argument is NaN, as opposed to
926    /// [`f32::max`] which only returns NaN when *both* arguments are NaN.
927    ///
928    /// ```
929    /// #![feature(float_minimum_maximum)]
930    /// let x = 1.0f32;
931    /// let y = 2.0f32;
932    ///
933    /// assert_eq!(x.maximum(y), y);
934    /// assert!(x.maximum(f32::NAN).is_nan());
935    /// ```
936    ///
937    /// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the greater
938    /// of the two numbers. For this operation, -0.0 is considered to be less than +0.0.
939    /// Note that this follows the semantics specified in IEEE 754-2019.
940    ///
941    /// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN
942    /// operand is conserved; see the [specification of NaN bit patterns](f32#nan-bit-patterns) for more info.
943    #[must_use = "this returns the result of the comparison, without modifying either input"]
944    #[unstable(feature = "float_minimum_maximum", issue = "91079")]
945    #[inline]
946    pub const fn maximum(self, other: f32) -> f32 {
947        intrinsics::maximumf32(self, other)
948    }
949
950    /// Returns the minimum of the two numbers, propagating NaN.
951    ///
952    /// This returns NaN when *either* argument is NaN, as opposed to
953    /// [`f32::min`] which only returns NaN when *both* arguments are NaN.
954    ///
955    /// ```
956    /// #![feature(float_minimum_maximum)]
957    /// let x = 1.0f32;
958    /// let y = 2.0f32;
959    ///
960    /// assert_eq!(x.minimum(y), x);
961    /// assert!(x.minimum(f32::NAN).is_nan());
962    /// ```
963    ///
964    /// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the lesser
965    /// of the two numbers. For this operation, -0.0 is considered to be less than +0.0.
966    /// Note that this follows the semantics specified in IEEE 754-2019.
967    ///
968    /// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN
969    /// operand is conserved; see the [specification of NaN bit patterns](f32#nan-bit-patterns) for more info.
970    #[must_use = "this returns the result of the comparison, without modifying either input"]
971    #[unstable(feature = "float_minimum_maximum", issue = "91079")]
972    #[inline]
973    pub const fn minimum(self, other: f32) -> f32 {
974        intrinsics::minimumf32(self, other)
975    }
976
977    /// Calculates the midpoint (average) between `self` and `rhs`.
978    ///
979    /// This returns NaN when *either* argument is NaN or if a combination of
980    /// +inf and -inf is provided as arguments.
981    ///
982    /// # Examples
983    ///
984    /// ```
985    /// assert_eq!(1f32.midpoint(4.0), 2.5);
986    /// assert_eq!((-5.5f32).midpoint(8.0), 1.25);
987    /// ```
988    #[inline]
989    #[doc(alias = "average")]
990    #[stable(feature = "num_midpoint", since = "1.85.0")]
991    #[rustc_const_stable(feature = "num_midpoint", since = "1.85.0")]
992    pub const fn midpoint(self, other: f32) -> f32 {
993        cfg_select! {
994            // Allow faster implementation that have known good 64-bit float
995            // implementations. Falling back to the branchy code on targets that don't
996            // have 64-bit hardware floats or buggy implementations.
997            // https://github.com/rust-lang/rust/pull/121062#issuecomment-2123408114
998            any(
999                target_arch = "x86_64",
1000                target_arch = "aarch64",
1001                all(any(target_arch = "riscv32", target_arch = "riscv64"), target_feature = "d"),
1002                all(target_arch = "loongarch64", target_feature = "d"),
1003                all(target_arch = "arm", target_feature = "vfp2"),
1004                target_arch = "wasm32",
1005                target_arch = "wasm64",
1006            ) => {
1007                ((self as f64 + other as f64) / 2.0) as f32
1008            }
1009            _ => {
1010                const LO: f32 = f32::MIN_POSITIVE * 2.;
1011                const HI: f32 = f32::MAX / 2.;
1012
1013                let (a, b) = (self, other);
1014                let abs_a = a.abs();
1015                let abs_b = b.abs();
1016
1017                if abs_a <= HI && abs_b <= HI {
1018                    // Overflow is impossible
1019                    (a + b) / 2.
1020                } else if abs_a < LO {
1021                    // Not safe to halve `a` (would underflow)
1022                    a + (b / 2.)
1023                } else if abs_b < LO {
1024                    // Not safe to halve `b` (would underflow)
1025                    (a / 2.) + b
1026                } else {
1027                    // Safe to halve `a` and `b`
1028                    (a / 2.) + (b / 2.)
1029                }
1030            }
1031        }
1032    }
1033
1034    /// Rounds toward zero and converts to any primitive integer type,
1035    /// assuming that the value is finite and fits in that type.
1036    ///
1037    /// ```
1038    /// let value = 4.6_f32;
1039    /// let rounded = unsafe { value.to_int_unchecked::<u16>() };
1040    /// assert_eq!(rounded, 4);
1041    ///
1042    /// let value = -128.9_f32;
1043    /// let rounded = unsafe { value.to_int_unchecked::<i8>() };
1044    /// assert_eq!(rounded, i8::MIN);
1045    /// ```
1046    ///
1047    /// # Safety
1048    ///
1049    /// The value must:
1050    ///
1051    /// * Not be `NaN`
1052    /// * Not be infinite
1053    /// * Be representable in the return type `Int`, after truncating off its fractional part
1054    #[must_use = "this returns the result of the operation, \
1055                  without modifying the original"]
1056    #[stable(feature = "float_approx_unchecked_to", since = "1.44.0")]
1057    #[inline]
1058    pub unsafe fn to_int_unchecked<Int>(self) -> Int
1059    where
1060        Self: FloatToInt<Int>,
1061    {
1062        // SAFETY: the caller must uphold the safety contract for
1063        // `FloatToInt::to_int_unchecked`.
1064        unsafe { FloatToInt::<Int>::to_int_unchecked(self) }
1065    }
1066
1067    /// Raw transmutation to `u32`.
1068    ///
1069    /// This is currently identical to `transmute::<f32, u32>(self)` on all platforms.
1070    ///
1071    /// See [`from_bits`](Self::from_bits) for some discussion of the
1072    /// portability of this operation (there are almost no issues).
1073    ///
1074    /// Note that this function is distinct from `as` casting, which attempts to
1075    /// preserve the *numeric* value, and not the bitwise value.
1076    ///
1077    /// # Examples
1078    ///
1079    /// ```
1080    /// assert_ne!((1f32).to_bits(), 1f32 as u32); // to_bits() is not casting!
1081    /// assert_eq!((12.5f32).to_bits(), 0x41480000);
1082    ///
1083    /// ```
1084    #[must_use = "this returns the result of the operation, \
1085                  without modifying the original"]
1086    #[stable(feature = "float_bits_conv", since = "1.20.0")]
1087    #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1088    #[inline]
1089    #[allow(unnecessary_transmutes)]
1090    pub const fn to_bits(self) -> u32 {
1091        // SAFETY: `u32` is a plain old datatype so we can always transmute to it.
1092        unsafe { mem::transmute(self) }
1093    }
1094
1095    /// Raw transmutation from `u32`.
1096    ///
1097    /// This is currently identical to `transmute::<u32, f32>(v)` on all platforms.
1098    /// It turns out this is incredibly portable, for two reasons:
1099    ///
1100    /// * Floats and Ints have the same endianness on all supported platforms.
1101    /// * IEEE 754 very precisely specifies the bit layout of floats.
1102    ///
1103    /// However there is one caveat: prior to the 2008 version of IEEE 754, how
1104    /// to interpret the NaN signaling bit wasn't actually specified. Most platforms
1105    /// (notably x86 and ARM) picked the interpretation that was ultimately
1106    /// standardized in 2008, but some didn't (notably MIPS). As a result, all
1107    /// signaling NaNs on MIPS are quiet NaNs on x86, and vice-versa.
1108    ///
1109    /// Rather than trying to preserve signaling-ness cross-platform, this
1110    /// implementation favors preserving the exact bits. This means that
1111    /// any payloads encoded in NaNs will be preserved even if the result of
1112    /// this method is sent over the network from an x86 machine to a MIPS one.
1113    ///
1114    /// If the results of this method are only manipulated by the same
1115    /// architecture that produced them, then there is no portability concern.
1116    ///
1117    /// If the input isn't NaN, then there is no portability concern.
1118    ///
1119    /// If you don't care about signalingness (very likely), then there is no
1120    /// portability concern.
1121    ///
1122    /// Note that this function is distinct from `as` casting, which attempts to
1123    /// preserve the *numeric* value, and not the bitwise value.
1124    ///
1125    /// # Examples
1126    ///
1127    /// ```
1128    /// let v = f32::from_bits(0x41480000);
1129    /// assert_eq!(v, 12.5);
1130    /// ```
1131    #[stable(feature = "float_bits_conv", since = "1.20.0")]
1132    #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1133    #[must_use]
1134    #[inline]
1135    #[allow(unnecessary_transmutes)]
1136    pub const fn from_bits(v: u32) -> Self {
1137        // It turns out the safety issues with sNaN were overblown! Hooray!
1138        // SAFETY: `u32` is a plain old datatype so we can always transmute from it.
1139        unsafe { mem::transmute(v) }
1140    }
1141
1142    /// Returns the memory representation of this floating point number as a byte array in
1143    /// big-endian (network) byte order.
1144    ///
1145    /// See [`from_bits`](Self::from_bits) for some discussion of the
1146    /// portability of this operation (there are almost no issues).
1147    ///
1148    /// # Examples
1149    ///
1150    /// ```
1151    /// let bytes = 12.5f32.to_be_bytes();
1152    /// assert_eq!(bytes, [0x41, 0x48, 0x00, 0x00]);
1153    /// ```
1154    #[must_use = "this returns the result of the operation, \
1155                  without modifying the original"]
1156    #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1157    #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1158    #[inline]
1159    pub const fn to_be_bytes(self) -> [u8; 4] {
1160        self.to_bits().to_be_bytes()
1161    }
1162
1163    /// Returns the memory representation of this floating point number as a byte array in
1164    /// little-endian byte order.
1165    ///
1166    /// See [`from_bits`](Self::from_bits) for some discussion of the
1167    /// portability of this operation (there are almost no issues).
1168    ///
1169    /// # Examples
1170    ///
1171    /// ```
1172    /// let bytes = 12.5f32.to_le_bytes();
1173    /// assert_eq!(bytes, [0x00, 0x00, 0x48, 0x41]);
1174    /// ```
1175    #[must_use = "this returns the result of the operation, \
1176                  without modifying the original"]
1177    #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1178    #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1179    #[inline]
1180    pub const fn to_le_bytes(self) -> [u8; 4] {
1181        self.to_bits().to_le_bytes()
1182    }
1183
1184    /// Returns the memory representation of this floating point number as a byte array in
1185    /// native byte order.
1186    ///
1187    /// As the target platform's native endianness is used, portable code
1188    /// should use [`to_be_bytes`] or [`to_le_bytes`], as appropriate, instead.
1189    ///
1190    /// [`to_be_bytes`]: f32::to_be_bytes
1191    /// [`to_le_bytes`]: f32::to_le_bytes
1192    ///
1193    /// See [`from_bits`](Self::from_bits) for some discussion of the
1194    /// portability of this operation (there are almost no issues).
1195    ///
1196    /// # Examples
1197    ///
1198    /// ```
1199    /// let bytes = 12.5f32.to_ne_bytes();
1200    /// assert_eq!(
1201    ///     bytes,
1202    ///     if cfg!(target_endian = "big") {
1203    ///         [0x41, 0x48, 0x00, 0x00]
1204    ///     } else {
1205    ///         [0x00, 0x00, 0x48, 0x41]
1206    ///     }
1207    /// );
1208    /// ```
1209    #[must_use = "this returns the result of the operation, \
1210                  without modifying the original"]
1211    #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1212    #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1213    #[inline]
1214    pub const fn to_ne_bytes(self) -> [u8; 4] {
1215        self.to_bits().to_ne_bytes()
1216    }
1217
1218    /// Creates a floating point value from its representation as a byte array in big endian.
1219    ///
1220    /// See [`from_bits`](Self::from_bits) for some discussion of the
1221    /// portability of this operation (there are almost no issues).
1222    ///
1223    /// # Examples
1224    ///
1225    /// ```
1226    /// let value = f32::from_be_bytes([0x41, 0x48, 0x00, 0x00]);
1227    /// assert_eq!(value, 12.5);
1228    /// ```
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    #[must_use]
1232    #[inline]
1233    pub const fn from_be_bytes(bytes: [u8; 4]) -> Self {
1234        Self::from_bits(u32::from_be_bytes(bytes))
1235    }
1236
1237    /// Creates a floating point value from its representation as a byte array in little endian.
1238    ///
1239    /// See [`from_bits`](Self::from_bits) for some discussion of the
1240    /// portability of this operation (there are almost no issues).
1241    ///
1242    /// # Examples
1243    ///
1244    /// ```
1245    /// let value = f32::from_le_bytes([0x00, 0x00, 0x48, 0x41]);
1246    /// assert_eq!(value, 12.5);
1247    /// ```
1248    #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1249    #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1250    #[must_use]
1251    #[inline]
1252    pub const fn from_le_bytes(bytes: [u8; 4]) -> Self {
1253        Self::from_bits(u32::from_le_bytes(bytes))
1254    }
1255
1256    /// Creates a floating point value from its representation as a byte array in native endian.
1257    ///
1258    /// As the target platform's native endianness is used, portable code
1259    /// likely wants to use [`from_be_bytes`] or [`from_le_bytes`], as
1260    /// appropriate instead.
1261    ///
1262    /// [`from_be_bytes`]: f32::from_be_bytes
1263    /// [`from_le_bytes`]: f32::from_le_bytes
1264    ///
1265    /// See [`from_bits`](Self::from_bits) for some discussion of the
1266    /// portability of this operation (there are almost no issues).
1267    ///
1268    /// # Examples
1269    ///
1270    /// ```
1271    /// let value = f32::from_ne_bytes(if cfg!(target_endian = "big") {
1272    ///     [0x41, 0x48, 0x00, 0x00]
1273    /// } else {
1274    ///     [0x00, 0x00, 0x48, 0x41]
1275    /// });
1276    /// assert_eq!(value, 12.5);
1277    /// ```
1278    #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1279    #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1280    #[must_use]
1281    #[inline]
1282    pub const fn from_ne_bytes(bytes: [u8; 4]) -> Self {
1283        Self::from_bits(u32::from_ne_bytes(bytes))
1284    }
1285
1286    /// Returns the ordering between `self` and `other`.
1287    ///
1288    /// Unlike the standard partial comparison between floating point numbers,
1289    /// this comparison always produces an ordering in accordance to
1290    /// the `totalOrder` predicate as defined in the IEEE 754 (2008 revision)
1291    /// floating point standard. The values are ordered in the following sequence:
1292    ///
1293    /// - negative quiet NaN
1294    /// - negative signaling NaN
1295    /// - negative infinity
1296    /// - negative numbers
1297    /// - negative subnormal numbers
1298    /// - negative zero
1299    /// - positive zero
1300    /// - positive subnormal numbers
1301    /// - positive numbers
1302    /// - positive infinity
1303    /// - positive signaling NaN
1304    /// - positive quiet NaN.
1305    ///
1306    /// The ordering established by this function does not always agree with the
1307    /// [`PartialOrd`] and [`PartialEq`] implementations of `f32`. For example,
1308    /// they consider negative and positive zero equal, while `total_cmp`
1309    /// doesn't.
1310    ///
1311    /// The interpretation of the signaling NaN bit follows the definition in
1312    /// the IEEE 754 standard, which may not match the interpretation by some of
1313    /// the older, non-conformant (e.g. MIPS) hardware implementations.
1314    ///
1315    /// # Example
1316    ///
1317    /// ```
1318    /// struct GoodBoy {
1319    ///     name: String,
1320    ///     weight: f32,
1321    /// }
1322    ///
1323    /// let mut bois = vec![
1324    ///     GoodBoy { name: "Pucci".to_owned(), weight: 0.1 },
1325    ///     GoodBoy { name: "Woofer".to_owned(), weight: 99.0 },
1326    ///     GoodBoy { name: "Yapper".to_owned(), weight: 10.0 },
1327    ///     GoodBoy { name: "Chonk".to_owned(), weight: f32::INFINITY },
1328    ///     GoodBoy { name: "Abs. Unit".to_owned(), weight: f32::NAN },
1329    ///     GoodBoy { name: "Floaty".to_owned(), weight: -5.0 },
1330    /// ];
1331    ///
1332    /// bois.sort_by(|a, b| a.weight.total_cmp(&b.weight));
1333    ///
1334    /// // `f32::NAN` could be positive or negative, which will affect the sort order.
1335    /// if f32::NAN.is_sign_negative() {
1336    ///     assert!(bois.into_iter().map(|b| b.weight)
1337    ///         .zip([f32::NAN, -5.0, 0.1, 10.0, 99.0, f32::INFINITY].iter())
1338    ///         .all(|(a, b)| a.to_bits() == b.to_bits()))
1339    /// } else {
1340    ///     assert!(bois.into_iter().map(|b| b.weight)
1341    ///         .zip([-5.0, 0.1, 10.0, 99.0, f32::INFINITY, f32::NAN].iter())
1342    ///         .all(|(a, b)| a.to_bits() == b.to_bits()))
1343    /// }
1344    /// ```
1345    #[stable(feature = "total_cmp", since = "1.62.0")]
1346    #[must_use]
1347    #[inline]
1348    pub fn total_cmp(&self, other: &Self) -> crate::cmp::Ordering {
1349        let mut left = self.to_bits() as i32;
1350        let mut right = other.to_bits() as i32;
1351
1352        // In case of negatives, flip all the bits except the sign
1353        // to achieve a similar layout as two's complement integers
1354        //
1355        // Why does this work? IEEE 754 floats consist of three fields:
1356        // Sign bit, exponent and mantissa. The set of exponent and mantissa
1357        // fields as a whole have the property that their bitwise order is
1358        // equal to the numeric magnitude where the magnitude is defined.
1359        // The magnitude is not normally defined on NaN values, but
1360        // IEEE 754 totalOrder defines the NaN values also to follow the
1361        // bitwise order. This leads to order explained in the doc comment.
1362        // However, the representation of magnitude is the same for negative
1363        // and positive numbers – only the sign bit is different.
1364        // To easily compare the floats as signed integers, we need to
1365        // flip the exponent and mantissa bits in case of negative numbers.
1366        // We effectively convert the numbers to "two's complement" form.
1367        //
1368        // To do the flipping, we construct a mask and XOR against it.
1369        // We branchlessly calculate an "all-ones except for the sign bit"
1370        // mask from negative-signed values: right shifting sign-extends
1371        // the integer, so we "fill" the mask with sign bits, and then
1372        // convert to unsigned to push one more zero bit.
1373        // On positive values, the mask is all zeros, so it's a no-op.
1374        left ^= (((left >> 31) as u32) >> 1) as i32;
1375        right ^= (((right >> 31) as u32) >> 1) as i32;
1376
1377        left.cmp(&right)
1378    }
1379
1380    /// Restrict a value to a certain interval unless it is NaN.
1381    ///
1382    /// Returns `max` if `self` is greater than `max`, and `min` if `self` is
1383    /// less than `min`. Otherwise this returns `self`.
1384    ///
1385    /// Note that this function returns NaN if the initial value was NaN as
1386    /// well.
1387    ///
1388    /// # Panics
1389    ///
1390    /// Panics if `min > max`, `min` is NaN, or `max` is NaN.
1391    ///
1392    /// # Examples
1393    ///
1394    /// ```
1395    /// assert!((-3.0f32).clamp(-2.0, 1.0) == -2.0);
1396    /// assert!((0.0f32).clamp(-2.0, 1.0) == 0.0);
1397    /// assert!((2.0f32).clamp(-2.0, 1.0) == 1.0);
1398    /// assert!((f32::NAN).clamp(-2.0, 1.0).is_nan());
1399    /// ```
1400    #[must_use = "method returns a new number and does not mutate the original value"]
1401    #[stable(feature = "clamp", since = "1.50.0")]
1402    #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
1403    #[inline]
1404    pub const fn clamp(mut self, min: f32, max: f32) -> f32 {
1405        const_assert!(
1406            min <= max,
1407            "min > max, or either was NaN",
1408            "min > max, or either was NaN. min = {min:?}, max = {max:?}",
1409            min: f32,
1410            max: f32,
1411        );
1412
1413        if self < min {
1414            self = min;
1415        }
1416        if self > max {
1417            self = max;
1418        }
1419        self
1420    }
1421
1422    /// Computes the absolute value of `self`.
1423    ///
1424    /// This function always returns the precise result.
1425    ///
1426    /// # Examples
1427    ///
1428    /// ```
1429    /// let x = 3.5_f32;
1430    /// let y = -3.5_f32;
1431    ///
1432    /// assert_eq!(x.abs(), x);
1433    /// assert_eq!(y.abs(), -y);
1434    ///
1435    /// assert!(f32::NAN.abs().is_nan());
1436    /// ```
1437    #[must_use = "method returns a new number and does not mutate the original value"]
1438    #[stable(feature = "rust1", since = "1.0.0")]
1439    #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
1440    #[inline]
1441    pub const fn abs(self) -> f32 {
1442        // SAFETY: this is actually a safe intrinsic
1443        unsafe { intrinsics::fabsf32(self) }
1444    }
1445
1446    /// Returns a number that represents the sign of `self`.
1447    ///
1448    /// - `1.0` if the number is positive, `+0.0` or `INFINITY`
1449    /// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
1450    /// - NaN if the number is NaN
1451    ///
1452    /// # Examples
1453    ///
1454    /// ```
1455    /// let f = 3.5_f32;
1456    ///
1457    /// assert_eq!(f.signum(), 1.0);
1458    /// assert_eq!(f32::NEG_INFINITY.signum(), -1.0);
1459    ///
1460    /// assert!(f32::NAN.signum().is_nan());
1461    /// ```
1462    #[must_use = "method returns a new number and does not mutate the original value"]
1463    #[stable(feature = "rust1", since = "1.0.0")]
1464    #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
1465    #[inline]
1466    pub const fn signum(self) -> f32 {
1467        if self.is_nan() { Self::NAN } else { 1.0_f32.copysign(self) }
1468    }
1469
1470    /// Returns a number composed of the magnitude of `self` and the sign of
1471    /// `sign`.
1472    ///
1473    /// Equal to `self` if the sign of `self` and `sign` are the same, otherwise equal to `-self`.
1474    /// If `self` is a NaN, then a NaN with the same payload as `self` and the sign bit of `sign` is
1475    /// returned.
1476    ///
1477    /// If `sign` is a NaN, then this operation will still carry over its sign into the result. Note
1478    /// that IEEE 754 doesn't assign any meaning to the sign bit in case of a NaN, and as Rust
1479    /// doesn't guarantee that the bit pattern of NaNs are conserved over arithmetic operations, the
1480    /// result of `copysign` with `sign` being a NaN might produce an unexpected or non-portable
1481    /// result. See the [specification of NaN bit patterns](primitive@f32#nan-bit-patterns) for more
1482    /// info.
1483    ///
1484    /// # Examples
1485    ///
1486    /// ```
1487    /// let f = 3.5_f32;
1488    ///
1489    /// assert_eq!(f.copysign(0.42), 3.5_f32);
1490    /// assert_eq!(f.copysign(-0.42), -3.5_f32);
1491    /// assert_eq!((-f).copysign(0.42), 3.5_f32);
1492    /// assert_eq!((-f).copysign(-0.42), -3.5_f32);
1493    ///
1494    /// assert!(f32::NAN.copysign(1.0).is_nan());
1495    /// ```
1496    #[must_use = "method returns a new number and does not mutate the original value"]
1497    #[inline]
1498    #[stable(feature = "copysign", since = "1.35.0")]
1499    #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
1500    pub const fn copysign(self, sign: f32) -> f32 {
1501        // SAFETY: this is actually a safe intrinsic
1502        unsafe { intrinsics::copysignf32(self, sign) }
1503    }
1504
1505    /// Float addition that allows optimizations based on algebraic rules.
1506    ///
1507    /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1508    #[must_use = "method returns a new number and does not mutate the original value"]
1509    #[unstable(feature = "float_algebraic", issue = "136469")]
1510    #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1511    #[inline]
1512    pub const fn algebraic_add(self, rhs: f32) -> f32 {
1513        intrinsics::fadd_algebraic(self, rhs)
1514    }
1515
1516    /// Float subtraction that allows optimizations based on algebraic rules.
1517    ///
1518    /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1519    #[must_use = "method returns a new number and does not mutate the original value"]
1520    #[unstable(feature = "float_algebraic", issue = "136469")]
1521    #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1522    #[inline]
1523    pub const fn algebraic_sub(self, rhs: f32) -> f32 {
1524        intrinsics::fsub_algebraic(self, rhs)
1525    }
1526
1527    /// Float multiplication that allows optimizations based on algebraic rules.
1528    ///
1529    /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1530    #[must_use = "method returns a new number and does not mutate the original value"]
1531    #[unstable(feature = "float_algebraic", issue = "136469")]
1532    #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1533    #[inline]
1534    pub const fn algebraic_mul(self, rhs: f32) -> f32 {
1535        intrinsics::fmul_algebraic(self, rhs)
1536    }
1537
1538    /// Float division that allows optimizations based on algebraic rules.
1539    ///
1540    /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1541    #[must_use = "method returns a new number and does not mutate the original value"]
1542    #[unstable(feature = "float_algebraic", issue = "136469")]
1543    #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1544    #[inline]
1545    pub const fn algebraic_div(self, rhs: f32) -> f32 {
1546        intrinsics::fdiv_algebraic(self, rhs)
1547    }
1548
1549    /// Float remainder that allows optimizations based on algebraic rules.
1550    ///
1551    /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1552    #[must_use = "method returns a new number and does not mutate the original value"]
1553    #[unstable(feature = "float_algebraic", issue = "136469")]
1554    #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1555    #[inline]
1556    pub const fn algebraic_rem(self, rhs: f32) -> f32 {
1557        intrinsics::frem_algebraic(self, rhs)
1558    }
1559}
1560
1561/// Experimental implementations of floating point functions in `core`.
1562///
1563/// _The standalone functions in this module are for testing only.
1564/// They will be stabilized as inherent methods._
1565#[unstable(feature = "core_float_math", issue = "137578")]
1566pub mod math {
1567    use crate::intrinsics;
1568    use crate::num::libm;
1569
1570    /// Experimental version of `floor` in `core`. See [`f32::floor`] for details.
1571    ///
1572    /// # Examples
1573    ///
1574    /// ```
1575    /// #![feature(core_float_math)]
1576    ///
1577    /// use core::f32;
1578    ///
1579    /// let f = 3.7_f32;
1580    /// let g = 3.0_f32;
1581    /// let h = -3.7_f32;
1582    ///
1583    /// assert_eq!(f32::math::floor(f), 3.0);
1584    /// assert_eq!(f32::math::floor(g), 3.0);
1585    /// assert_eq!(f32::math::floor(h), -4.0);
1586    /// ```
1587    ///
1588    /// _This standalone function is for testing only.
1589    /// It will be stabilized as an inherent method._
1590    ///
1591    /// [`f32::floor`]: ../../../std/primitive.f32.html#method.floor
1592    #[inline]
1593    #[unstable(feature = "core_float_math", issue = "137578")]
1594    #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
1595    #[must_use = "method returns a new number and does not mutate the original value"]
1596    pub const fn floor(x: f32) -> f32 {
1597        // SAFETY: intrinsic with no preconditions
1598        unsafe { intrinsics::floorf32(x) }
1599    }
1600
1601    /// Experimental version of `ceil` in `core`. See [`f32::ceil`] for details.
1602    ///
1603    /// # Examples
1604    ///
1605    /// ```
1606    /// #![feature(core_float_math)]
1607    ///
1608    /// use core::f32;
1609    ///
1610    /// let f = 3.01_f32;
1611    /// let g = 4.0_f32;
1612    ///
1613    /// assert_eq!(f32::math::ceil(f), 4.0);
1614    /// assert_eq!(f32::math::ceil(g), 4.0);
1615    /// ```
1616    ///
1617    /// _This standalone function is for testing only.
1618    /// It will be stabilized as an inherent method._
1619    ///
1620    /// [`f32::ceil`]: ../../../std/primitive.f32.html#method.ceil
1621    #[inline]
1622    #[doc(alias = "ceiling")]
1623    #[must_use = "method returns a new number and does not mutate the original value"]
1624    #[unstable(feature = "core_float_math", issue = "137578")]
1625    #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
1626    pub const fn ceil(x: f32) -> f32 {
1627        // SAFETY: intrinsic with no preconditions
1628        unsafe { intrinsics::ceilf32(x) }
1629    }
1630
1631    /// Experimental version of `round` in `core`. See [`f32::round`] for details.
1632    ///
1633    /// # Examples
1634    ///
1635    /// ```
1636    /// #![feature(core_float_math)]
1637    ///
1638    /// use core::f32;
1639    ///
1640    /// let f = 3.3_f32;
1641    /// let g = -3.3_f32;
1642    /// let h = -3.7_f32;
1643    /// let i = 3.5_f32;
1644    /// let j = 4.5_f32;
1645    ///
1646    /// assert_eq!(f32::math::round(f), 3.0);
1647    /// assert_eq!(f32::math::round(g), -3.0);
1648    /// assert_eq!(f32::math::round(h), -4.0);
1649    /// assert_eq!(f32::math::round(i), 4.0);
1650    /// assert_eq!(f32::math::round(j), 5.0);
1651    /// ```
1652    ///
1653    /// _This standalone function is for testing only.
1654    /// It will be stabilized as an inherent method._
1655    ///
1656    /// [`f32::round`]: ../../../std/primitive.f32.html#method.round
1657    #[inline]
1658    #[unstable(feature = "core_float_math", issue = "137578")]
1659    #[must_use = "method returns a new number and does not mutate the original value"]
1660    #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
1661    pub const fn round(x: f32) -> f32 {
1662        // SAFETY: intrinsic with no preconditions
1663        unsafe { intrinsics::roundf32(x) }
1664    }
1665
1666    /// Experimental version of `round_ties_even` in `core`. See [`f32::round_ties_even`] for
1667    /// details.
1668    ///
1669    /// # Examples
1670    ///
1671    /// ```
1672    /// #![feature(core_float_math)]
1673    ///
1674    /// use core::f32;
1675    ///
1676    /// let f = 3.3_f32;
1677    /// let g = -3.3_f32;
1678    /// let h = 3.5_f32;
1679    /// let i = 4.5_f32;
1680    ///
1681    /// assert_eq!(f32::math::round_ties_even(f), 3.0);
1682    /// assert_eq!(f32::math::round_ties_even(g), -3.0);
1683    /// assert_eq!(f32::math::round_ties_even(h), 4.0);
1684    /// assert_eq!(f32::math::round_ties_even(i), 4.0);
1685    /// ```
1686    ///
1687    /// _This standalone function is for testing only.
1688    /// It will be stabilized as an inherent method._
1689    ///
1690    /// [`f32::round_ties_even`]: ../../../std/primitive.f32.html#method.round_ties_even
1691    #[inline]
1692    #[unstable(feature = "core_float_math", issue = "137578")]
1693    #[must_use = "method returns a new number and does not mutate the original value"]
1694    #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
1695    pub const fn round_ties_even(x: f32) -> f32 {
1696        intrinsics::round_ties_even_f32(x)
1697    }
1698
1699    /// Experimental version of `trunc` in `core`. See [`f32::trunc`] for details.
1700    ///
1701    /// # Examples
1702    ///
1703    /// ```
1704    /// #![feature(core_float_math)]
1705    ///
1706    /// use core::f32;
1707    ///
1708    /// let f = 3.7_f32;
1709    /// let g = 3.0_f32;
1710    /// let h = -3.7_f32;
1711    ///
1712    /// assert_eq!(f32::math::trunc(f), 3.0);
1713    /// assert_eq!(f32::math::trunc(g), 3.0);
1714    /// assert_eq!(f32::math::trunc(h), -3.0);
1715    /// ```
1716    ///
1717    /// _This standalone function is for testing only.
1718    /// It will be stabilized as an inherent method._
1719    ///
1720    /// [`f32::trunc`]: ../../../std/primitive.f32.html#method.trunc
1721    #[inline]
1722    #[doc(alias = "truncate")]
1723    #[must_use = "method returns a new number and does not mutate the original value"]
1724    #[unstable(feature = "core_float_math", issue = "137578")]
1725    #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
1726    pub const fn trunc(x: f32) -> f32 {
1727        // SAFETY: intrinsic with no preconditions
1728        unsafe { intrinsics::truncf32(x) }
1729    }
1730
1731    /// Experimental version of `fract` in `core`. See [`f32::fract`] for details.
1732    ///
1733    /// # Examples
1734    ///
1735    /// ```
1736    /// #![feature(core_float_math)]
1737    ///
1738    /// use core::f32;
1739    ///
1740    /// let x = 3.6_f32;
1741    /// let y = -3.6_f32;
1742    /// let abs_difference_x = (f32::math::fract(x) - 0.6).abs();
1743    /// let abs_difference_y = (f32::math::fract(y) - (-0.6)).abs();
1744    ///
1745    /// assert!(abs_difference_x <= f32::EPSILON);
1746    /// assert!(abs_difference_y <= f32::EPSILON);
1747    /// ```
1748    ///
1749    /// _This standalone function is for testing only.
1750    /// It will be stabilized as an inherent method._
1751    ///
1752    /// [`f32::fract`]: ../../../std/primitive.f32.html#method.fract
1753    #[inline]
1754    #[unstable(feature = "core_float_math", issue = "137578")]
1755    #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
1756    #[must_use = "method returns a new number and does not mutate the original value"]
1757    pub const fn fract(x: f32) -> f32 {
1758        x - trunc(x)
1759    }
1760
1761    /// Experimental version of `mul_add` in `core`. See [`f32::mul_add`] for details.
1762    ///
1763    /// # Examples
1764    ///
1765    /// ```
1766    /// #![feature(core_float_math)]
1767    ///
1768    /// # // FIXME(#140515): mingw has an incorrect fma
1769    /// # // https://sourceforge.net/p/mingw-w64/bugs/848/
1770    /// # #[cfg(all(target_os = "windows", target_env = "gnu", not(target_abi = "llvm")))] {
1771    /// use core::f32;
1772    ///
1773    /// let m = 10.0_f32;
1774    /// let x = 4.0_f32;
1775    /// let b = 60.0_f32;
1776    ///
1777    /// assert_eq!(f32::math::mul_add(m, x, b), 100.0);
1778    /// assert_eq!(m * x + b, 100.0);
1779    ///
1780    /// let one_plus_eps = 1.0_f32 + f32::EPSILON;
1781    /// let one_minus_eps = 1.0_f32 - f32::EPSILON;
1782    /// let minus_one = -1.0_f32;
1783    ///
1784    /// // The exact result (1 + eps) * (1 - eps) = 1 - eps * eps.
1785    /// assert_eq!(
1786    ///     f32::math::mul_add(one_plus_eps, one_minus_eps, minus_one),
1787    ///     -f32::EPSILON * f32::EPSILON
1788    /// );
1789    /// // Different rounding with the non-fused multiply and add.
1790    /// assert_eq!(one_plus_eps * one_minus_eps + minus_one, 0.0);
1791    /// # }
1792    /// ```
1793    ///
1794    /// _This standalone function is for testing only.
1795    /// It will be stabilized as an inherent method._
1796    ///
1797    /// [`f32::mul_add`]: ../../../std/primitive.f32.html#method.mul_add
1798    #[inline]
1799    #[doc(alias = "fmaf", alias = "fusedMultiplyAdd")]
1800    #[must_use = "method returns a new number and does not mutate the original value"]
1801    #[unstable(feature = "core_float_math", issue = "137578")]
1802    pub fn mul_add(x: f32, y: f32, z: f32) -> f32 {
1803        // SAFETY: intrinsic with no preconditions
1804        unsafe { intrinsics::fmaf32(x, y, z) }
1805    }
1806
1807    /// Experimental version of `div_euclid` in `core`. See [`f32::div_euclid`] for details.
1808    ///
1809    /// # Examples
1810    ///
1811    /// ```
1812    /// #![feature(core_float_math)]
1813    ///
1814    /// use core::f32;
1815    ///
1816    /// let a: f32 = 7.0;
1817    /// let b = 4.0;
1818    /// assert_eq!(f32::math::div_euclid(a, b), 1.0); // 7.0 > 4.0 * 1.0
1819    /// assert_eq!(f32::math::div_euclid(-a, b), -2.0); // -7.0 >= 4.0 * -2.0
1820    /// assert_eq!(f32::math::div_euclid(a, -b), -1.0); // 7.0 >= -4.0 * -1.0
1821    /// assert_eq!(f32::math::div_euclid(-a, -b), 2.0); // -7.0 >= -4.0 * 2.0
1822    /// ```
1823    ///
1824    /// _This standalone function is for testing only.
1825    /// It will be stabilized as an inherent method._
1826    ///
1827    /// [`f32::div_euclid`]: ../../../std/primitive.f32.html#method.div_euclid
1828    #[inline]
1829    #[unstable(feature = "core_float_math", issue = "137578")]
1830    #[must_use = "method returns a new number and does not mutate the original value"]
1831    pub fn div_euclid(x: f32, rhs: f32) -> f32 {
1832        let q = trunc(x / rhs);
1833        if x % rhs < 0.0 {
1834            return if rhs > 0.0 { q - 1.0 } else { q + 1.0 };
1835        }
1836        q
1837    }
1838
1839    /// Experimental version of `rem_euclid` in `core`. See [`f32::rem_euclid`] for details.
1840    ///
1841    /// # Examples
1842    ///
1843    /// ```
1844    /// #![feature(core_float_math)]
1845    ///
1846    /// use core::f32;
1847    ///
1848    /// let a: f32 = 7.0;
1849    /// let b = 4.0;
1850    /// assert_eq!(f32::math::rem_euclid(a, b), 3.0);
1851    /// assert_eq!(f32::math::rem_euclid(-a, b), 1.0);
1852    /// assert_eq!(f32::math::rem_euclid(a, -b), 3.0);
1853    /// assert_eq!(f32::math::rem_euclid(-a, -b), 1.0);
1854    /// // limitation due to round-off error
1855    /// assert!(f32::math::rem_euclid(-f32::EPSILON, 3.0) != 0.0);
1856    /// ```
1857    ///
1858    /// _This standalone function is for testing only.
1859    /// It will be stabilized as an inherent method._
1860    ///
1861    /// [`f32::rem_euclid`]: ../../../std/primitive.f32.html#method.rem_euclid
1862    #[inline]
1863    #[doc(alias = "modulo", alias = "mod")]
1864    #[unstable(feature = "core_float_math", issue = "137578")]
1865    #[must_use = "method returns a new number and does not mutate the original value"]
1866    pub fn rem_euclid(x: f32, rhs: f32) -> f32 {
1867        let r = x % rhs;
1868        if r < 0.0 { r + rhs.abs() } else { r }
1869    }
1870
1871    /// Experimental version of `powi` in `core`. See [`f32::powi`] for details.
1872    ///
1873    /// # Examples
1874    ///
1875    /// ```
1876    /// #![feature(core_float_math)]
1877    ///
1878    /// use core::f32;
1879    ///
1880    /// let x = 2.0_f32;
1881    /// let abs_difference = (f32::math::powi(x, 2) - (x * x)).abs();
1882    /// assert!(abs_difference <= 1e-5);
1883    ///
1884    /// assert_eq!(f32::math::powi(f32::NAN, 0), 1.0);
1885    /// ```
1886    ///
1887    /// _This standalone function is for testing only.
1888    /// It will be stabilized as an inherent method._
1889    ///
1890    /// [`f32::powi`]: ../../../std/primitive.f32.html#method.powi
1891    #[inline]
1892    #[must_use = "method returns a new number and does not mutate the original value"]
1893    #[unstable(feature = "core_float_math", issue = "137578")]
1894    pub fn powi(x: f32, n: i32) -> f32 {
1895        // SAFETY: intrinsic with no preconditions
1896        unsafe { intrinsics::powif32(x, n) }
1897    }
1898
1899    /// Experimental version of `sqrt` in `core`. See [`f32::sqrt`] for details.
1900    ///
1901    /// # Examples
1902    ///
1903    /// ```
1904    /// #![feature(core_float_math)]
1905    ///
1906    /// use core::f32;
1907    ///
1908    /// let positive = 4.0_f32;
1909    /// let negative = -4.0_f32;
1910    /// let negative_zero = -0.0_f32;
1911    ///
1912    /// assert_eq!(f32::math::sqrt(positive), 2.0);
1913    /// assert!(f32::math::sqrt(negative).is_nan());
1914    /// assert_eq!(f32::math::sqrt(negative_zero), negative_zero);
1915    /// ```
1916    ///
1917    /// _This standalone function is for testing only.
1918    /// It will be stabilized as an inherent method._
1919    ///
1920    /// [`f32::sqrt`]: ../../../std/primitive.f32.html#method.sqrt
1921    #[inline]
1922    #[doc(alias = "squareRoot")]
1923    #[unstable(feature = "core_float_math", issue = "137578")]
1924    #[must_use = "method returns a new number and does not mutate the original value"]
1925    pub fn sqrt(x: f32) -> f32 {
1926        // SAFETY: intrinsic with no preconditions
1927        unsafe { intrinsics::sqrtf32(x) }
1928    }
1929
1930    /// Experimental version of `abs_sub` in `core`. See [`f32::abs_sub`] for details.
1931    ///
1932    /// # Examples
1933    ///
1934    /// ```
1935    /// #![feature(core_float_math)]
1936    ///
1937    /// use core::f32;
1938    ///
1939    /// let x = 3.0f32;
1940    /// let y = -3.0f32;
1941    ///
1942    /// let abs_difference_x = (f32::math::abs_sub(x, 1.0) - 2.0).abs();
1943    /// let abs_difference_y = (f32::math::abs_sub(y, 1.0) - 0.0).abs();
1944    ///
1945    /// assert!(abs_difference_x <= f32::EPSILON);
1946    /// assert!(abs_difference_y <= f32::EPSILON);
1947    /// ```
1948    ///
1949    /// _This standalone function is for testing only.
1950    /// It will be stabilized as an inherent method._
1951    ///
1952    /// [`f32::abs_sub`]: ../../../std/primitive.f32.html#method.abs_sub
1953    #[inline]
1954    #[stable(feature = "rust1", since = "1.0.0")]
1955    #[deprecated(
1956        since = "1.10.0",
1957        note = "you probably meant `(self - other).abs()`: \
1958            this operation is `(self - other).max(0.0)` \
1959            except that `abs_sub` also propagates NaNs (also \
1960            known as `fdimf` in C). If you truly need the positive \
1961            difference, consider using that expression or the C function \
1962            `fdimf`, depending on how you wish to handle NaN (please consider \
1963            filing an issue describing your use-case too)."
1964    )]
1965    #[must_use = "method returns a new number and does not mutate the original value"]
1966    pub fn abs_sub(x: f32, other: f32) -> f32 {
1967        libm::fdimf(x, other)
1968    }
1969
1970    /// Experimental version of `cbrt` in `core`. See [`f32::cbrt`] for details.
1971    ///
1972    /// # Unspecified precision
1973    ///
1974    /// The precision of this function is non-deterministic. This means it varies by platform, Rust version, and
1975    /// can even differ within the same execution from one invocation to the next.
1976    /// This function currently corresponds to the `cbrtf` from libc on Unix
1977    /// and Windows. Note that this might change in the future.
1978    ///
1979    /// # Examples
1980    ///
1981    /// ```
1982    /// #![feature(core_float_math)]
1983    ///
1984    /// use core::f32;
1985    ///
1986    /// let x = 8.0f32;
1987    ///
1988    /// // x^(1/3) - 2 == 0
1989    /// let abs_difference = (f32::math::cbrt(x) - 2.0).abs();
1990    ///
1991    /// assert!(abs_difference <= f32::EPSILON);
1992    /// ```
1993    ///
1994    /// _This standalone function is for testing only.
1995    /// It will be stabilized as an inherent method._
1996    ///
1997    /// [`f32::cbrt`]: ../../../std/primitive.f32.html#method.cbrt
1998    #[inline]
1999    #[must_use = "method returns a new number and does not mutate the original value"]
2000    #[unstable(feature = "core_float_math", issue = "137578")]
2001    pub fn cbrt(x: f32) -> f32 {
2002        libm::cbrtf(x)
2003    }
2004}