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, libm};
16use crate::panic::const_assert;
17use crate::{cfg_match, 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> 2<sup>[`MANTISSA_DIGITS`] − 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 − [`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 −[`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`] − 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 − 2<sup>−[`MANTISSA_DIGITS`]</sup>) 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 × 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> [`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> [`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_match! {
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 = "arm", target_feature = "vfp2"),
1003 target_arch = "wasm32",
1004 target_arch = "wasm64",
1005 ) => {
1006 ((self as f64 + other as f64) / 2.0) as f32
1007 }
1008 _ => {
1009 const LO: f32 = f32::MIN_POSITIVE * 2.;
1010 const HI: f32 = f32::MAX / 2.;
1011
1012 let (a, b) = (self, other);
1013 let abs_a = a.abs();
1014 let abs_b = b.abs();
1015
1016 if abs_a <= HI && abs_b <= HI {
1017 // Overflow is impossible
1018 (a + b) / 2.
1019 } else if abs_a < LO {
1020 // Not safe to halve `a` (would underflow)
1021 a + (b / 2.)
1022 } else if abs_b < LO {
1023 // Not safe to halve `b` (would underflow)
1024 (a / 2.) + b
1025 } else {
1026 // Safe to halve `a` and `b`
1027 (a / 2.) + (b / 2.)
1028 }
1029 }
1030 }
1031 }
1032
1033 /// Rounds toward zero and converts to any primitive integer type,
1034 /// assuming that the value is finite and fits in that type.
1035 ///
1036 /// ```
1037 /// let value = 4.6_f32;
1038 /// let rounded = unsafe { value.to_int_unchecked::<u16>() };
1039 /// assert_eq!(rounded, 4);
1040 ///
1041 /// let value = -128.9_f32;
1042 /// let rounded = unsafe { value.to_int_unchecked::<i8>() };
1043 /// assert_eq!(rounded, i8::MIN);
1044 /// ```
1045 ///
1046 /// # Safety
1047 ///
1048 /// The value must:
1049 ///
1050 /// * Not be `NaN`
1051 /// * Not be infinite
1052 /// * Be representable in the return type `Int`, after truncating off its fractional part
1053 #[must_use = "this returns the result of the operation, \
1054 without modifying the original"]
1055 #[stable(feature = "float_approx_unchecked_to", since = "1.44.0")]
1056 #[inline]
1057 pub unsafe fn to_int_unchecked<Int>(self) -> Int
1058 where
1059 Self: FloatToInt<Int>,
1060 {
1061 // SAFETY: the caller must uphold the safety contract for
1062 // `FloatToInt::to_int_unchecked`.
1063 unsafe { FloatToInt::<Int>::to_int_unchecked(self) }
1064 }
1065
1066 /// Raw transmutation to `u32`.
1067 ///
1068 /// This is currently identical to `transmute::<f32, u32>(self)` on all platforms.
1069 ///
1070 /// See [`from_bits`](Self::from_bits) for some discussion of the
1071 /// portability of this operation (there are almost no issues).
1072 ///
1073 /// Note that this function is distinct from `as` casting, which attempts to
1074 /// preserve the *numeric* value, and not the bitwise value.
1075 ///
1076 /// # Examples
1077 ///
1078 /// ```
1079 /// assert_ne!((1f32).to_bits(), 1f32 as u32); // to_bits() is not casting!
1080 /// assert_eq!((12.5f32).to_bits(), 0x41480000);
1081 ///
1082 /// ```
1083 #[must_use = "this returns the result of the operation, \
1084 without modifying the original"]
1085 #[stable(feature = "float_bits_conv", since = "1.20.0")]
1086 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1087 #[inline]
1088 #[allow(unnecessary_transmutes)]
1089 pub const fn to_bits(self) -> u32 {
1090 // SAFETY: `u32` is a plain old datatype so we can always transmute to it.
1091 unsafe { mem::transmute(self) }
1092 }
1093
1094 /// Raw transmutation from `u32`.
1095 ///
1096 /// This is currently identical to `transmute::<u32, f32>(v)` on all platforms.
1097 /// It turns out this is incredibly portable, for two reasons:
1098 ///
1099 /// * Floats and Ints have the same endianness on all supported platforms.
1100 /// * IEEE 754 very precisely specifies the bit layout of floats.
1101 ///
1102 /// However there is one caveat: prior to the 2008 version of IEEE 754, how
1103 /// to interpret the NaN signaling bit wasn't actually specified. Most platforms
1104 /// (notably x86 and ARM) picked the interpretation that was ultimately
1105 /// standardized in 2008, but some didn't (notably MIPS). As a result, all
1106 /// signaling NaNs on MIPS are quiet NaNs on x86, and vice-versa.
1107 ///
1108 /// Rather than trying to preserve signaling-ness cross-platform, this
1109 /// implementation favors preserving the exact bits. This means that
1110 /// any payloads encoded in NaNs will be preserved even if the result of
1111 /// this method is sent over the network from an x86 machine to a MIPS one.
1112 ///
1113 /// If the results of this method are only manipulated by the same
1114 /// architecture that produced them, then there is no portability concern.
1115 ///
1116 /// If the input isn't NaN, then there is no portability concern.
1117 ///
1118 /// If you don't care about signalingness (very likely), then there is no
1119 /// portability concern.
1120 ///
1121 /// Note that this function is distinct from `as` casting, which attempts to
1122 /// preserve the *numeric* value, and not the bitwise value.
1123 ///
1124 /// # Examples
1125 ///
1126 /// ```
1127 /// let v = f32::from_bits(0x41480000);
1128 /// assert_eq!(v, 12.5);
1129 /// ```
1130 #[stable(feature = "float_bits_conv", since = "1.20.0")]
1131 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1132 #[must_use]
1133 #[inline]
1134 #[allow(unnecessary_transmutes)]
1135 pub const fn from_bits(v: u32) -> Self {
1136 // It turns out the safety issues with sNaN were overblown! Hooray!
1137 // SAFETY: `u32` is a plain old datatype so we can always transmute from it.
1138 unsafe { mem::transmute(v) }
1139 }
1140
1141 /// Returns the memory representation of this floating point number as a byte array in
1142 /// big-endian (network) byte order.
1143 ///
1144 /// See [`from_bits`](Self::from_bits) for some discussion of the
1145 /// portability of this operation (there are almost no issues).
1146 ///
1147 /// # Examples
1148 ///
1149 /// ```
1150 /// let bytes = 12.5f32.to_be_bytes();
1151 /// assert_eq!(bytes, [0x41, 0x48, 0x00, 0x00]);
1152 /// ```
1153 #[must_use = "this returns the result of the operation, \
1154 without modifying the original"]
1155 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1156 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1157 #[inline]
1158 pub const fn to_be_bytes(self) -> [u8; 4] {
1159 self.to_bits().to_be_bytes()
1160 }
1161
1162 /// Returns the memory representation of this floating point number as a byte array in
1163 /// little-endian byte order.
1164 ///
1165 /// See [`from_bits`](Self::from_bits) for some discussion of the
1166 /// portability of this operation (there are almost no issues).
1167 ///
1168 /// # Examples
1169 ///
1170 /// ```
1171 /// let bytes = 12.5f32.to_le_bytes();
1172 /// assert_eq!(bytes, [0x00, 0x00, 0x48, 0x41]);
1173 /// ```
1174 #[must_use = "this returns the result of the operation, \
1175 without modifying the original"]
1176 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1177 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1178 #[inline]
1179 pub const fn to_le_bytes(self) -> [u8; 4] {
1180 self.to_bits().to_le_bytes()
1181 }
1182
1183 /// Returns the memory representation of this floating point number as a byte array in
1184 /// native byte order.
1185 ///
1186 /// As the target platform's native endianness is used, portable code
1187 /// should use [`to_be_bytes`] or [`to_le_bytes`], as appropriate, instead.
1188 ///
1189 /// [`to_be_bytes`]: f32::to_be_bytes
1190 /// [`to_le_bytes`]: f32::to_le_bytes
1191 ///
1192 /// See [`from_bits`](Self::from_bits) for some discussion of the
1193 /// portability of this operation (there are almost no issues).
1194 ///
1195 /// # Examples
1196 ///
1197 /// ```
1198 /// let bytes = 12.5f32.to_ne_bytes();
1199 /// assert_eq!(
1200 /// bytes,
1201 /// if cfg!(target_endian = "big") {
1202 /// [0x41, 0x48, 0x00, 0x00]
1203 /// } else {
1204 /// [0x00, 0x00, 0x48, 0x41]
1205 /// }
1206 /// );
1207 /// ```
1208 #[must_use = "this returns the result of the operation, \
1209 without modifying the original"]
1210 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1211 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1212 #[inline]
1213 pub const fn to_ne_bytes(self) -> [u8; 4] {
1214 self.to_bits().to_ne_bytes()
1215 }
1216
1217 /// Creates a floating point value from its representation as a byte array in big endian.
1218 ///
1219 /// See [`from_bits`](Self::from_bits) for some discussion of the
1220 /// portability of this operation (there are almost no issues).
1221 ///
1222 /// # Examples
1223 ///
1224 /// ```
1225 /// let value = f32::from_be_bytes([0x41, 0x48, 0x00, 0x00]);
1226 /// assert_eq!(value, 12.5);
1227 /// ```
1228 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1229 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1230 #[must_use]
1231 #[inline]
1232 pub const fn from_be_bytes(bytes: [u8; 4]) -> Self {
1233 Self::from_bits(u32::from_be_bytes(bytes))
1234 }
1235
1236 /// Creates a floating point value from its representation as a byte array in little 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_le_bytes([0x00, 0x00, 0x48, 0x41]);
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_le_bytes(bytes: [u8; 4]) -> Self {
1252 Self::from_bits(u32::from_le_bytes(bytes))
1253 }
1254
1255 /// Creates a floating point value from its representation as a byte array in native endian.
1256 ///
1257 /// As the target platform's native endianness is used, portable code
1258 /// likely wants to use [`from_be_bytes`] or [`from_le_bytes`], as
1259 /// appropriate instead.
1260 ///
1261 /// [`from_be_bytes`]: f32::from_be_bytes
1262 /// [`from_le_bytes`]: f32::from_le_bytes
1263 ///
1264 /// See [`from_bits`](Self::from_bits) for some discussion of the
1265 /// portability of this operation (there are almost no issues).
1266 ///
1267 /// # Examples
1268 ///
1269 /// ```
1270 /// let value = f32::from_ne_bytes(if cfg!(target_endian = "big") {
1271 /// [0x41, 0x48, 0x00, 0x00]
1272 /// } else {
1273 /// [0x00, 0x00, 0x48, 0x41]
1274 /// });
1275 /// assert_eq!(value, 12.5);
1276 /// ```
1277 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1278 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1279 #[must_use]
1280 #[inline]
1281 pub const fn from_ne_bytes(bytes: [u8; 4]) -> Self {
1282 Self::from_bits(u32::from_ne_bytes(bytes))
1283 }
1284
1285 /// Returns the ordering between `self` and `other`.
1286 ///
1287 /// Unlike the standard partial comparison between floating point numbers,
1288 /// this comparison always produces an ordering in accordance to
1289 /// the `totalOrder` predicate as defined in the IEEE 754 (2008 revision)
1290 /// floating point standard. The values are ordered in the following sequence:
1291 ///
1292 /// - negative quiet NaN
1293 /// - negative signaling NaN
1294 /// - negative infinity
1295 /// - negative numbers
1296 /// - negative subnormal numbers
1297 /// - negative zero
1298 /// - positive zero
1299 /// - positive subnormal numbers
1300 /// - positive numbers
1301 /// - positive infinity
1302 /// - positive signaling NaN
1303 /// - positive quiet NaN.
1304 ///
1305 /// The ordering established by this function does not always agree with the
1306 /// [`PartialOrd`] and [`PartialEq`] implementations of `f32`. For example,
1307 /// they consider negative and positive zero equal, while `total_cmp`
1308 /// doesn't.
1309 ///
1310 /// The interpretation of the signaling NaN bit follows the definition in
1311 /// the IEEE 754 standard, which may not match the interpretation by some of
1312 /// the older, non-conformant (e.g. MIPS) hardware implementations.
1313 ///
1314 /// # Example
1315 ///
1316 /// ```
1317 /// struct GoodBoy {
1318 /// name: String,
1319 /// weight: f32,
1320 /// }
1321 ///
1322 /// let mut bois = vec![
1323 /// GoodBoy { name: "Pucci".to_owned(), weight: 0.1 },
1324 /// GoodBoy { name: "Woofer".to_owned(), weight: 99.0 },
1325 /// GoodBoy { name: "Yapper".to_owned(), weight: 10.0 },
1326 /// GoodBoy { name: "Chonk".to_owned(), weight: f32::INFINITY },
1327 /// GoodBoy { name: "Abs. Unit".to_owned(), weight: f32::NAN },
1328 /// GoodBoy { name: "Floaty".to_owned(), weight: -5.0 },
1329 /// ];
1330 ///
1331 /// bois.sort_by(|a, b| a.weight.total_cmp(&b.weight));
1332 ///
1333 /// // `f32::NAN` could be positive or negative, which will affect the sort order.
1334 /// if f32::NAN.is_sign_negative() {
1335 /// assert!(bois.into_iter().map(|b| b.weight)
1336 /// .zip([f32::NAN, -5.0, 0.1, 10.0, 99.0, f32::INFINITY].iter())
1337 /// .all(|(a, b)| a.to_bits() == b.to_bits()))
1338 /// } else {
1339 /// assert!(bois.into_iter().map(|b| b.weight)
1340 /// .zip([-5.0, 0.1, 10.0, 99.0, f32::INFINITY, f32::NAN].iter())
1341 /// .all(|(a, b)| a.to_bits() == b.to_bits()))
1342 /// }
1343 /// ```
1344 #[stable(feature = "total_cmp", since = "1.62.0")]
1345 #[must_use]
1346 #[inline]
1347 pub fn total_cmp(&self, other: &Self) -> crate::cmp::Ordering {
1348 let mut left = self.to_bits() as i32;
1349 let mut right = other.to_bits() as i32;
1350
1351 // In case of negatives, flip all the bits except the sign
1352 // to achieve a similar layout as two's complement integers
1353 //
1354 // Why does this work? IEEE 754 floats consist of three fields:
1355 // Sign bit, exponent and mantissa. The set of exponent and mantissa
1356 // fields as a whole have the property that their bitwise order is
1357 // equal to the numeric magnitude where the magnitude is defined.
1358 // The magnitude is not normally defined on NaN values, but
1359 // IEEE 754 totalOrder defines the NaN values also to follow the
1360 // bitwise order. This leads to order explained in the doc comment.
1361 // However, the representation of magnitude is the same for negative
1362 // and positive numbers – only the sign bit is different.
1363 // To easily compare the floats as signed integers, we need to
1364 // flip the exponent and mantissa bits in case of negative numbers.
1365 // We effectively convert the numbers to "two's complement" form.
1366 //
1367 // To do the flipping, we construct a mask and XOR against it.
1368 // We branchlessly calculate an "all-ones except for the sign bit"
1369 // mask from negative-signed values: right shifting sign-extends
1370 // the integer, so we "fill" the mask with sign bits, and then
1371 // convert to unsigned to push one more zero bit.
1372 // On positive values, the mask is all zeros, so it's a no-op.
1373 left ^= (((left >> 31) as u32) >> 1) as i32;
1374 right ^= (((right >> 31) as u32) >> 1) as i32;
1375
1376 left.cmp(&right)
1377 }
1378
1379 /// Restrict a value to a certain interval unless it is NaN.
1380 ///
1381 /// Returns `max` if `self` is greater than `max`, and `min` if `self` is
1382 /// less than `min`. Otherwise this returns `self`.
1383 ///
1384 /// Note that this function returns NaN if the initial value was NaN as
1385 /// well.
1386 ///
1387 /// # Panics
1388 ///
1389 /// Panics if `min > max`, `min` is NaN, or `max` is NaN.
1390 ///
1391 /// # Examples
1392 ///
1393 /// ```
1394 /// assert!((-3.0f32).clamp(-2.0, 1.0) == -2.0);
1395 /// assert!((0.0f32).clamp(-2.0, 1.0) == 0.0);
1396 /// assert!((2.0f32).clamp(-2.0, 1.0) == 1.0);
1397 /// assert!((f32::NAN).clamp(-2.0, 1.0).is_nan());
1398 /// ```
1399 #[must_use = "method returns a new number and does not mutate the original value"]
1400 #[stable(feature = "clamp", since = "1.50.0")]
1401 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
1402 #[inline]
1403 pub const fn clamp(mut self, min: f32, max: f32) -> f32 {
1404 const_assert!(
1405 min <= max,
1406 "min > max, or either was NaN",
1407 "min > max, or either was NaN. min = {min:?}, max = {max:?}",
1408 min: f32,
1409 max: f32,
1410 );
1411
1412 if self < min {
1413 self = min;
1414 }
1415 if self > max {
1416 self = max;
1417 }
1418 self
1419 }
1420
1421 /// Computes the absolute value of `self`.
1422 ///
1423 /// This function always returns the precise result.
1424 ///
1425 /// # Examples
1426 ///
1427 /// ```
1428 /// let x = 3.5_f32;
1429 /// let y = -3.5_f32;
1430 ///
1431 /// assert_eq!(x.abs(), x);
1432 /// assert_eq!(y.abs(), -y);
1433 ///
1434 /// assert!(f32::NAN.abs().is_nan());
1435 /// ```
1436 #[must_use = "method returns a new number and does not mutate the original value"]
1437 #[stable(feature = "rust1", since = "1.0.0")]
1438 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
1439 #[inline]
1440 pub const fn abs(self) -> f32 {
1441 // SAFETY: this is actually a safe intrinsic
1442 unsafe { intrinsics::fabsf32(self) }
1443 }
1444
1445 /// Returns a number that represents the sign of `self`.
1446 ///
1447 /// - `1.0` if the number is positive, `+0.0` or `INFINITY`
1448 /// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
1449 /// - NaN if the number is NaN
1450 ///
1451 /// # Examples
1452 ///
1453 /// ```
1454 /// let f = 3.5_f32;
1455 ///
1456 /// assert_eq!(f.signum(), 1.0);
1457 /// assert_eq!(f32::NEG_INFINITY.signum(), -1.0);
1458 ///
1459 /// assert!(f32::NAN.signum().is_nan());
1460 /// ```
1461 #[must_use = "method returns a new number and does not mutate the original value"]
1462 #[stable(feature = "rust1", since = "1.0.0")]
1463 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
1464 #[inline]
1465 pub const fn signum(self) -> f32 {
1466 if self.is_nan() { Self::NAN } else { 1.0_f32.copysign(self) }
1467 }
1468
1469 /// Returns a number composed of the magnitude of `self` and the sign of
1470 /// `sign`.
1471 ///
1472 /// Equal to `self` if the sign of `self` and `sign` are the same, otherwise equal to `-self`.
1473 /// If `self` is a NaN, then a NaN with the same payload as `self` and the sign bit of `sign` is
1474 /// returned.
1475 ///
1476 /// If `sign` is a NaN, then this operation will still carry over its sign into the result. Note
1477 /// that IEEE 754 doesn't assign any meaning to the sign bit in case of a NaN, and as Rust
1478 /// doesn't guarantee that the bit pattern of NaNs are conserved over arithmetic operations, the
1479 /// result of `copysign` with `sign` being a NaN might produce an unexpected or non-portable
1480 /// result. See the [specification of NaN bit patterns](primitive@f32#nan-bit-patterns) for more
1481 /// info.
1482 ///
1483 /// # Examples
1484 ///
1485 /// ```
1486 /// let f = 3.5_f32;
1487 ///
1488 /// assert_eq!(f.copysign(0.42), 3.5_f32);
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 ///
1493 /// assert!(f32::NAN.copysign(1.0).is_nan());
1494 /// ```
1495 #[must_use = "method returns a new number and does not mutate the original value"]
1496 #[inline]
1497 #[stable(feature = "copysign", since = "1.35.0")]
1498 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
1499 pub const fn copysign(self, sign: f32) -> f32 {
1500 // SAFETY: this is actually a safe intrinsic
1501 unsafe { intrinsics::copysignf32(self, sign) }
1502 }
1503
1504 /// Float addition that allows optimizations based on algebraic rules.
1505 ///
1506 /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1507 #[must_use = "method returns a new number and does not mutate the original value"]
1508 #[unstable(feature = "float_algebraic", issue = "136469")]
1509 #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1510 #[inline]
1511 pub const fn algebraic_add(self, rhs: f32) -> f32 {
1512 intrinsics::fadd_algebraic(self, rhs)
1513 }
1514
1515 /// Float subtraction that allows optimizations based on algebraic rules.
1516 ///
1517 /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1518 #[must_use = "method returns a new number and does not mutate the original value"]
1519 #[unstable(feature = "float_algebraic", issue = "136469")]
1520 #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1521 #[inline]
1522 pub const fn algebraic_sub(self, rhs: f32) -> f32 {
1523 intrinsics::fsub_algebraic(self, rhs)
1524 }
1525
1526 /// Float multiplication that allows optimizations based on algebraic rules.
1527 ///
1528 /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1529 #[must_use = "method returns a new number and does not mutate the original value"]
1530 #[unstable(feature = "float_algebraic", issue = "136469")]
1531 #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1532 #[inline]
1533 pub const fn algebraic_mul(self, rhs: f32) -> f32 {
1534 intrinsics::fmul_algebraic(self, rhs)
1535 }
1536
1537 /// Float division that allows optimizations based on algebraic rules.
1538 ///
1539 /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1540 #[must_use = "method returns a new number and does not mutate the original value"]
1541 #[unstable(feature = "float_algebraic", issue = "136469")]
1542 #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1543 #[inline]
1544 pub const fn algebraic_div(self, rhs: f32) -> f32 {
1545 intrinsics::fdiv_algebraic(self, rhs)
1546 }
1547
1548 /// Float remainder that allows optimizations based on algebraic rules.
1549 ///
1550 /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1551 #[must_use = "method returns a new number and does not mutate the original value"]
1552 #[unstable(feature = "float_algebraic", issue = "136469")]
1553 #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1554 #[inline]
1555 pub const fn algebraic_rem(self, rhs: f32) -> f32 {
1556 intrinsics::frem_algebraic(self, rhs)
1557 }
1558}
1559
1560/// Experimental version of `floor` in `core`. See [`f32::floor`] for details.
1561///
1562/// # Examples
1563///
1564/// ```
1565/// #![feature(core_float_math)]
1566///
1567/// use core::f32;
1568///
1569/// let f = 3.7_f32;
1570/// let g = 3.0_f32;
1571/// let h = -3.7_f32;
1572///
1573/// assert_eq!(f32::floor(f), 3.0);
1574/// assert_eq!(f32::floor(g), 3.0);
1575/// assert_eq!(f32::floor(h), -4.0);
1576/// ```
1577///
1578/// _This standalone function is for testing only. It will be stabilized as an inherent method._
1579///
1580/// [`f32::floor`]: ../../std/primitive.f32.html#method.floor
1581#[inline]
1582#[unstable(feature = "core_float_math", issue = "137578")]
1583#[must_use = "method returns a new number and does not mutate the original value"]
1584pub fn floor(x: f32) -> f32 {
1585 // SAFETY: intrinsic with no preconditions
1586 unsafe { intrinsics::floorf32(x) }
1587}
1588
1589/// Experimental version of `ceil` in `core`. See [`f32::ceil`] for details.
1590///
1591/// # Examples
1592///
1593/// ```
1594/// #![feature(core_float_math)]
1595///
1596/// use core::f32;
1597///
1598/// let f = 3.01_f32;
1599/// let g = 4.0_f32;
1600///
1601/// assert_eq!(f32::ceil(f), 4.0);
1602/// assert_eq!(f32::ceil(g), 4.0);
1603/// ```
1604///
1605/// _This standalone function is for testing only. It will be stabilized as an inherent method._
1606///
1607/// [`f32::ceil`]: ../../std/primitive.f32.html#method.ceil
1608#[inline]
1609#[doc(alias = "ceiling")]
1610#[must_use = "method returns a new number and does not mutate the original value"]
1611#[unstable(feature = "core_float_math", issue = "137578")]
1612pub fn ceil(x: f32) -> f32 {
1613 // SAFETY: intrinsic with no preconditions
1614 unsafe { intrinsics::ceilf32(x) }
1615}
1616
1617/// Experimental version of `round` in `core`. See [`f32::round`] for details.
1618///
1619/// # Examples
1620///
1621/// ```
1622/// #![feature(core_float_math)]
1623///
1624/// use core::f32;
1625///
1626/// let f = 3.3_f32;
1627/// let g = -3.3_f32;
1628/// let h = -3.7_f32;
1629/// let i = 3.5_f32;
1630/// let j = 4.5_f32;
1631///
1632/// assert_eq!(f32::round(f), 3.0);
1633/// assert_eq!(f32::round(g), -3.0);
1634/// assert_eq!(f32::round(h), -4.0);
1635/// assert_eq!(f32::round(i), 4.0);
1636/// assert_eq!(f32::round(j), 5.0);
1637/// ```
1638///
1639/// _This standalone function is for testing only. It will be stabilized as an inherent method._
1640///
1641/// [`f32::round`]: ../../std/primitive.f32.html#method.round
1642#[inline]
1643#[unstable(feature = "core_float_math", issue = "137578")]
1644#[must_use = "method returns a new number and does not mutate the original value"]
1645pub fn round(x: f32) -> f32 {
1646 // SAFETY: intrinsic with no preconditions
1647 unsafe { intrinsics::roundf32(x) }
1648}
1649
1650/// Experimental version of `round_ties_even` in `core`. See [`f32::round_ties_even`] for details.
1651///
1652/// # Examples
1653///
1654/// ```
1655/// #![feature(core_float_math)]
1656///
1657/// use core::f32;
1658///
1659/// let f = 3.3_f32;
1660/// let g = -3.3_f32;
1661/// let h = 3.5_f32;
1662/// let i = 4.5_f32;
1663///
1664/// assert_eq!(f32::round_ties_even(f), 3.0);
1665/// assert_eq!(f32::round_ties_even(g), -3.0);
1666/// assert_eq!(f32::round_ties_even(h), 4.0);
1667/// assert_eq!(f32::round_ties_even(i), 4.0);
1668/// ```
1669///
1670/// _This standalone function is for testing only. It will be stabilized as an inherent method._
1671///
1672/// [`f32::round_ties_even`]: ../../std/primitive.f32.html#method.round_ties_even
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"]
1676pub fn round_ties_even(x: f32) -> f32 {
1677 intrinsics::round_ties_even_f32(x)
1678}
1679
1680/// Experimental version of `trunc` in `core`. See [`f32::trunc`] for details.
1681///
1682/// # Examples
1683///
1684/// ```
1685/// #![feature(core_float_math)]
1686///
1687/// use core::f32;
1688///
1689/// let f = 3.7_f32;
1690/// let g = 3.0_f32;
1691/// let h = -3.7_f32;
1692///
1693/// assert_eq!(f32::trunc(f), 3.0);
1694/// assert_eq!(f32::trunc(g), 3.0);
1695/// assert_eq!(f32::trunc(h), -3.0);
1696/// ```
1697///
1698/// _This standalone function is for testing only. It will be stabilized as an inherent method._
1699///
1700/// [`f32::trunc`]: ../../std/primitive.f32.html#method.trunc
1701#[inline]
1702#[doc(alias = "truncate")]
1703#[must_use = "method returns a new number and does not mutate the original value"]
1704#[unstable(feature = "core_float_math", issue = "137578")]
1705pub fn trunc(x: f32) -> f32 {
1706 // SAFETY: intrinsic with no preconditions
1707 unsafe { intrinsics::truncf32(x) }
1708}
1709
1710/// Experimental version of `fract` in `core`. See [`f32::fract`] for details.
1711///
1712/// # Examples
1713///
1714/// ```
1715/// #![feature(core_float_math)]
1716///
1717/// use core::f32;
1718///
1719/// let x = 3.6_f32;
1720/// let y = -3.6_f32;
1721/// let abs_difference_x = (f32::fract(x) - 0.6).abs();
1722/// let abs_difference_y = (f32::fract(y) - (-0.6)).abs();
1723///
1724/// assert!(abs_difference_x <= f32::EPSILON);
1725/// assert!(abs_difference_y <= f32::EPSILON);
1726/// ```
1727///
1728/// _This standalone function is for testing only. It will be stabilized as an inherent method._
1729///
1730/// [`f32::fract`]: ../../std/primitive.f32.html#method.fract
1731#[inline]
1732#[unstable(feature = "core_float_math", issue = "137578")]
1733#[must_use = "method returns a new number and does not mutate the original value"]
1734pub fn fract(x: f32) -> f32 {
1735 x - trunc(x)
1736}
1737
1738/// Experimental version of `mul_add` in `core`. See [`f32::mul_add`] for details.
1739///
1740/// # Examples
1741///
1742/// ```
1743/// #![feature(core_float_math)]
1744///
1745/// # // FIXME(#140515): mingw has an incorrect fma https://sourceforge.net/p/mingw-w64/bugs/848/
1746/// # #[cfg(all(target_os = "windows", target_env = "gnu", not(target_abi = "llvm")))] {
1747/// use core::f32;
1748///
1749/// let m = 10.0_f32;
1750/// let x = 4.0_f32;
1751/// let b = 60.0_f32;
1752///
1753/// assert_eq!(f32::mul_add(m, x, b), 100.0);
1754/// assert_eq!(m * x + b, 100.0);
1755///
1756/// let one_plus_eps = 1.0_f32 + f32::EPSILON;
1757/// let one_minus_eps = 1.0_f32 - f32::EPSILON;
1758/// let minus_one = -1.0_f32;
1759///
1760/// // The exact result (1 + eps) * (1 - eps) = 1 - eps * eps.
1761/// assert_eq!(f32::mul_add(one_plus_eps, one_minus_eps, minus_one), -f32::EPSILON * f32::EPSILON);
1762/// // Different rounding with the non-fused multiply and add.
1763/// assert_eq!(one_plus_eps * one_minus_eps + minus_one, 0.0);
1764/// # }
1765/// ```
1766///
1767/// _This standalone function is for testing only. It will be stabilized as an inherent method._
1768///
1769/// [`f32::mul_add`]: ../../std/primitive.f32.html#method.mul_add
1770#[inline]
1771#[doc(alias = "fmaf", alias = "fusedMultiplyAdd")]
1772#[must_use = "method returns a new number and does not mutate the original value"]
1773#[unstable(feature = "core_float_math", issue = "137578")]
1774pub fn mul_add(x: f32, y: f32, z: f32) -> f32 {
1775 // SAFETY: intrinsic with no preconditions
1776 unsafe { intrinsics::fmaf32(x, y, z) }
1777}
1778
1779/// Experimental version of `div_euclid` in `core`. See [`f32::div_euclid`] for details.
1780///
1781/// # Examples
1782///
1783/// ```
1784/// #![feature(core_float_math)]
1785///
1786/// use core::f32;
1787///
1788/// let a: f32 = 7.0;
1789/// let b = 4.0;
1790/// assert_eq!(f32::div_euclid(a, b), 1.0); // 7.0 > 4.0 * 1.0
1791/// assert_eq!(f32::div_euclid(-a, b), -2.0); // -7.0 >= 4.0 * -2.0
1792/// assert_eq!(f32::div_euclid(a, -b), -1.0); // 7.0 >= -4.0 * -1.0
1793/// assert_eq!(f32::div_euclid(-a, -b), 2.0); // -7.0 >= -4.0 * 2.0
1794/// ```
1795///
1796/// _This standalone function is for testing only. It will be stabilized as an inherent method._
1797///
1798/// [`f32::div_euclid`]: ../../std/primitive.f32.html#method.div_euclid
1799#[inline]
1800#[unstable(feature = "core_float_math", issue = "137578")]
1801#[must_use = "method returns a new number and does not mutate the original value"]
1802pub fn div_euclid(x: f32, rhs: f32) -> f32 {
1803 let q = trunc(x / rhs);
1804 if x % rhs < 0.0 {
1805 return if rhs > 0.0 { q - 1.0 } else { q + 1.0 };
1806 }
1807 q
1808}
1809
1810/// Experimental version of `rem_euclid` in `core`. See [`f32::rem_euclid`] for details.
1811///
1812/// # Examples
1813///
1814/// ```
1815/// #![feature(core_float_math)]
1816///
1817/// use core::f32;
1818///
1819/// let a: f32 = 7.0;
1820/// let b = 4.0;
1821/// assert_eq!(f32::rem_euclid(a, b), 3.0);
1822/// assert_eq!(f32::rem_euclid(-a, b), 1.0);
1823/// assert_eq!(f32::rem_euclid(a, -b), 3.0);
1824/// assert_eq!(f32::rem_euclid(-a, -b), 1.0);
1825/// // limitation due to round-off error
1826/// assert!(f32::rem_euclid(-f32::EPSILON, 3.0) != 0.0);
1827/// ```
1828///
1829/// _This standalone function is for testing only. It will be stabilized as an inherent method._
1830///
1831/// [`f32::rem_euclid`]: ../../std/primitive.f32.html#method.rem_euclid
1832#[inline]
1833#[doc(alias = "modulo", alias = "mod")]
1834#[unstable(feature = "core_float_math", issue = "137578")]
1835#[must_use = "method returns a new number and does not mutate the original value"]
1836pub fn rem_euclid(x: f32, rhs: f32) -> f32 {
1837 let r = x % rhs;
1838 if r < 0.0 { r + rhs.abs() } else { r }
1839}
1840
1841/// Experimental version of `powi` in `core`. See [`f32::powi`] for details.
1842///
1843/// # Examples
1844///
1845/// ```
1846/// #![feature(core_float_math)]
1847///
1848/// use core::f32;
1849///
1850/// let x = 2.0_f32;
1851/// let abs_difference = (f32::powi(x, 2) - (x * x)).abs();
1852/// assert!(abs_difference <= f32::EPSILON);
1853///
1854/// assert_eq!(f32::powi(f32::NAN, 0), 1.0);
1855/// ```
1856///
1857/// _This standalone function is for testing only. It will be stabilized as an inherent method._
1858///
1859/// [`f32::powi`]: ../../std/primitive.f32.html#method.powi
1860#[inline]
1861#[must_use = "method returns a new number and does not mutate the original value"]
1862#[unstable(feature = "core_float_math", issue = "137578")]
1863pub fn powi(x: f32, n: i32) -> f32 {
1864 // SAFETY: intrinsic with no preconditions
1865 unsafe { intrinsics::powif32(x, n) }
1866}
1867
1868/// Experimental version of `sqrt` in `core`. See [`f32::sqrt`] for details.
1869///
1870/// # Examples
1871///
1872/// ```
1873/// #![feature(core_float_math)]
1874///
1875/// use core::f32;
1876///
1877/// let positive = 4.0_f32;
1878/// let negative = -4.0_f32;
1879/// let negative_zero = -0.0_f32;
1880///
1881/// assert_eq!(f32::sqrt(positive), 2.0);
1882/// assert!(f32::sqrt(negative).is_nan());
1883/// assert_eq!(f32::sqrt(negative_zero), negative_zero);
1884/// ```
1885///
1886/// _This standalone function is for testing only. It will be stabilized as an inherent method._
1887///
1888/// [`f32::sqrt`]: ../../std/primitive.f32.html#method.sqrt
1889#[inline]
1890#[doc(alias = "squareRoot")]
1891#[unstable(feature = "core_float_math", issue = "137578")]
1892#[must_use = "method returns a new number and does not mutate the original value"]
1893pub fn sqrt(x: f32) -> f32 {
1894 // SAFETY: intrinsic with no preconditions
1895 unsafe { intrinsics::sqrtf32(x) }
1896}
1897
1898/// Experimental version of `abs_sub` in `core`. See [`f32::abs_sub`] for details.
1899///
1900/// # Examples
1901///
1902/// ```
1903/// #![feature(core_float_math)]
1904///
1905/// use core::f32;
1906///
1907/// let x = 3.0f32;
1908/// let y = -3.0f32;
1909///
1910/// let abs_difference_x = (f32::abs_sub(x, 1.0) - 2.0).abs();
1911/// let abs_difference_y = (f32::abs_sub(y, 1.0) - 0.0).abs();
1912///
1913/// assert!(abs_difference_x <= f32::EPSILON);
1914/// assert!(abs_difference_y <= f32::EPSILON);
1915/// ```
1916///
1917/// _This standalone function is for testing only. It will be stabilized as an inherent method._
1918///
1919/// [`f32::abs_sub`]: ../../std/primitive.f32.html#method.abs_sub
1920#[inline]
1921#[stable(feature = "rust1", since = "1.0.0")]
1922#[deprecated(
1923 since = "1.10.0",
1924 note = "you probably meant `(self - other).abs()`: \
1925 this operation is `(self - other).max(0.0)` \
1926 except that `abs_sub` also propagates NaNs (also \
1927 known as `fdimf` in C). If you truly need the positive \
1928 difference, consider using that expression or the C function \
1929 `fdimf`, depending on how you wish to handle NaN (please consider \
1930 filing an issue describing your use-case too)."
1931)]
1932#[must_use = "method returns a new number and does not mutate the original value"]
1933pub fn abs_sub(x: f32, other: f32) -> f32 {
1934 libm::fdimf(x, other)
1935}
1936
1937/// Experimental version of `cbrt` in `core`. See [`f32::cbrt`] for details.
1938///
1939/// # Unspecified precision
1940///
1941/// The precision of this function is non-deterministic. This means it varies by platform, Rust version, and
1942/// can even differ within the same execution from one invocation to the next.
1943/// This function currently corresponds to the `cbrtf` from libc on Unix
1944/// and Windows. Note that this might change in the future.
1945///
1946/// # Examples
1947///
1948/// ```
1949/// #![feature(core_float_math)]
1950///
1951/// use core::f32;
1952///
1953/// let x = 8.0f32;
1954///
1955/// // x^(1/3) - 2 == 0
1956/// let abs_difference = (f32::cbrt(x) - 2.0).abs();
1957///
1958/// assert!(abs_difference <= f32::EPSILON);
1959/// ```
1960///
1961/// _This standalone function is for testing only. It will be stabilized as an inherent method._
1962///
1963/// [`f32::cbrt`]: ../../std/primitive.f32.html#method.cbrt
1964#[inline]
1965#[must_use = "method returns a new number and does not mutate the original value"]
1966#[unstable(feature = "core_float_math", issue = "137578")]
1967pub fn cbrt(x: f32) -> f32 {
1968 libm::cbrtf(x)
1969}