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")]
280#[rustc_diagnostic_item = "f32_consts_mod"]
281pub mod consts {
282 // FIXME: replace with mathematical constants from cmath.
283
284 /// Archimedes' constant (π)
285 #[stable(feature = "rust1", since = "1.0.0")]
286 pub const PI: f32 = 3.14159265358979323846264338327950288_f32;
287
288 /// The full circle constant (τ)
289 ///
290 /// Equal to 2π.
291 #[stable(feature = "tau_constant", since = "1.47.0")]
292 pub const TAU: f32 = 6.28318530717958647692528676655900577_f32;
293
294 /// The golden ratio (φ)
295 #[stable(feature = "euler_gamma_golden_ratio", since = "1.94.0")]
296 pub const GOLDEN_RATIO: f32 = 1.618033988749894848204586834365638118_f32;
297
298 /// The Euler-Mascheroni constant (γ)
299 #[stable(feature = "euler_gamma_golden_ratio", since = "1.94.0")]
300 pub const EULER_GAMMA: f32 = 0.577215664901532860606512090082402431_f32;
301
302 /// π/2
303 #[stable(feature = "rust1", since = "1.0.0")]
304 pub const FRAC_PI_2: f32 = 1.57079632679489661923132169163975144_f32;
305
306 /// π/3
307 #[stable(feature = "rust1", since = "1.0.0")]
308 pub const FRAC_PI_3: f32 = 1.04719755119659774615421446109316763_f32;
309
310 /// π/4
311 #[stable(feature = "rust1", since = "1.0.0")]
312 pub const FRAC_PI_4: f32 = 0.785398163397448309615660845819875721_f32;
313
314 /// π/6
315 #[stable(feature = "rust1", since = "1.0.0")]
316 pub const FRAC_PI_6: f32 = 0.52359877559829887307710723054658381_f32;
317
318 /// π/8
319 #[stable(feature = "rust1", since = "1.0.0")]
320 pub const FRAC_PI_8: f32 = 0.39269908169872415480783042290993786_f32;
321
322 /// 1/π
323 #[stable(feature = "rust1", since = "1.0.0")]
324 pub const FRAC_1_PI: f32 = 0.318309886183790671537767526745028724_f32;
325
326 /// 1/sqrt(π)
327 #[unstable(feature = "more_float_constants", issue = "146939")]
328 pub const FRAC_1_SQRT_PI: f32 = 0.564189583547756286948079451560772586_f32;
329
330 /// 1/sqrt(2π)
331 #[doc(alias = "FRAC_1_SQRT_TAU")]
332 #[unstable(feature = "more_float_constants", issue = "146939")]
333 pub const FRAC_1_SQRT_2PI: f32 = 0.398942280401432677939946059934381868_f32;
334
335 /// 2/π
336 #[stable(feature = "rust1", since = "1.0.0")]
337 pub const FRAC_2_PI: f32 = 0.636619772367581343075535053490057448_f32;
338
339 /// 2/sqrt(π)
340 #[stable(feature = "rust1", since = "1.0.0")]
341 pub const FRAC_2_SQRT_PI: f32 = 1.12837916709551257389615890312154517_f32;
342
343 /// sqrt(2)
344 #[stable(feature = "rust1", since = "1.0.0")]
345 pub const SQRT_2: f32 = 1.41421356237309504880168872420969808_f32;
346
347 /// 1/sqrt(2)
348 #[stable(feature = "rust1", since = "1.0.0")]
349 pub const FRAC_1_SQRT_2: f32 = 0.707106781186547524400844362104849039_f32;
350
351 /// sqrt(3)
352 #[unstable(feature = "more_float_constants", issue = "146939")]
353 pub const SQRT_3: f32 = 1.732050807568877293527446341505872367_f32;
354
355 /// 1/sqrt(3)
356 #[unstable(feature = "more_float_constants", issue = "146939")]
357 pub const FRAC_1_SQRT_3: f32 = 0.577350269189625764509148780501957456_f32;
358
359 /// sqrt(5)
360 #[unstable(feature = "more_float_constants", issue = "146939")]
361 pub const SQRT_5: f32 = 2.23606797749978969640917366873127623_f32;
362
363 /// 1/sqrt(5)
364 #[unstable(feature = "more_float_constants", issue = "146939")]
365 pub const FRAC_1_SQRT_5: f32 = 0.44721359549995793928183473374625524_f32;
366
367 /// Euler's number (e)
368 #[stable(feature = "rust1", since = "1.0.0")]
369 pub const E: f32 = 2.71828182845904523536028747135266250_f32;
370
371 /// log<sub>2</sub>(e)
372 #[stable(feature = "rust1", since = "1.0.0")]
373 pub const LOG2_E: f32 = 1.44269504088896340735992468100189214_f32;
374
375 /// log<sub>2</sub>(10)
376 #[stable(feature = "extra_log_consts", since = "1.43.0")]
377 pub const LOG2_10: f32 = 3.32192809488736234787031942948939018_f32;
378
379 /// log<sub>10</sub>(e)
380 #[stable(feature = "rust1", since = "1.0.0")]
381 pub const LOG10_E: f32 = 0.434294481903251827651128918916605082_f32;
382
383 /// log<sub>10</sub>(2)
384 #[stable(feature = "extra_log_consts", since = "1.43.0")]
385 pub const LOG10_2: f32 = 0.301029995663981195213738894724493027_f32;
386
387 /// ln(2)
388 #[stable(feature = "rust1", since = "1.0.0")]
389 pub const LN_2: f32 = 0.693147180559945309417232121458176568_f32;
390
391 /// ln(10)
392 #[stable(feature = "rust1", since = "1.0.0")]
393 pub const LN_10: f32 = 2.30258509299404568401799145468436421_f32;
394}
395
396impl f32 {
397 /// The radix or base of the internal representation of `f32`.
398 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
399 pub const RADIX: u32 = 2;
400
401 /// The size of this float type in bits.
402 #[unstable(feature = "float_bits_const", issue = "151073")]
403 pub const BITS: u32 = 32;
404
405 /// Number of significant digits in base 2.
406 ///
407 /// Note that the size of the mantissa in the bitwise representation is one
408 /// smaller than this since the leading 1 is not stored explicitly.
409 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
410 pub const MANTISSA_DIGITS: u32 = 24;
411
412 /// Approximate number of significant digits in base 10.
413 ///
414 /// This is the maximum <i>x</i> such that any decimal number with <i>x</i>
415 /// significant digits can be converted to `f32` and back without loss.
416 ///
417 /// Equal to floor(log<sub>10</sub>&nbsp;2<sup>[`MANTISSA_DIGITS`]&nbsp;&minus;&nbsp;1</sup>).
418 ///
419 /// [`MANTISSA_DIGITS`]: f32::MANTISSA_DIGITS
420 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
421 pub const DIGITS: u32 = 6;
422
423 /// [Machine epsilon] value for `f32`.
424 ///
425 /// This is the difference between `1.0` and the next larger representable number.
426 ///
427 /// Equal to 2<sup>1&nbsp;&minus;&nbsp;[`MANTISSA_DIGITS`]</sup>.
428 ///
429 /// [Machine epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon
430 /// [`MANTISSA_DIGITS`]: f32::MANTISSA_DIGITS
431 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
432 #[rustc_diagnostic_item = "f32_epsilon"]
433 pub const EPSILON: f32 = 1.19209290e-07_f32;
434
435 /// Smallest finite `f32` value.
436 ///
437 /// Equal to &minus;[`MAX`].
438 ///
439 /// [`MAX`]: f32::MAX
440 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
441 pub const MIN: f32 = -3.40282347e+38_f32;
442 /// Smallest positive normal `f32` value.
443 ///
444 /// Equal to 2<sup>[`MIN_EXP`]&nbsp;&minus;&nbsp;1</sup>.
445 ///
446 /// [`MIN_EXP`]: f32::MIN_EXP
447 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
448 pub const MIN_POSITIVE: f32 = 1.17549435e-38_f32;
449 /// Largest finite `f32` value.
450 ///
451 /// Equal to
452 /// (1&nbsp;&minus;&nbsp;2<sup>&minus;[`MANTISSA_DIGITS`]</sup>)&nbsp;2<sup>[`MAX_EXP`]</sup>.
453 ///
454 /// [`MANTISSA_DIGITS`]: f32::MANTISSA_DIGITS
455 /// [`MAX_EXP`]: f32::MAX_EXP
456 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
457 pub const MAX: f32 = 3.40282347e+38_f32;
458
459 /// One greater than the minimum possible *normal* power of 2 exponent
460 /// for a significand bounded by 1 ≤ x < 2 (i.e. the IEEE definition).
461 ///
462 /// This corresponds to the exact minimum possible *normal* power of 2 exponent
463 /// for a significand bounded by 0.5 ≤ x < 1 (i.e. the C definition).
464 /// In other words, all normal numbers representable by this type are
465 /// greater than or equal to 0.5&nbsp;×&nbsp;2<sup><i>MIN_EXP</i></sup>.
466 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
467 pub const MIN_EXP: i32 = -125;
468 /// One greater than the maximum possible power of 2 exponent
469 /// for a significand bounded by 1 ≤ x < 2 (i.e. the IEEE definition).
470 ///
471 /// This corresponds to the exact maximum possible power of 2 exponent
472 /// for a significand bounded by 0.5 ≤ x < 1 (i.e. the C definition).
473 /// In other words, all numbers representable by this type are
474 /// strictly less than 2<sup><i>MAX_EXP</i></sup>.
475 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
476 pub const MAX_EXP: i32 = 128;
477
478 /// Minimum <i>x</i> for which 10<sup><i>x</i></sup> is normal.
479 ///
480 /// Equal to ceil(log<sub>10</sub>&nbsp;[`MIN_POSITIVE`]).
481 ///
482 /// [`MIN_POSITIVE`]: f32::MIN_POSITIVE
483 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
484 pub const MIN_10_EXP: i32 = -37;
485 /// Maximum <i>x</i> for which 10<sup><i>x</i></sup> is normal.
486 ///
487 /// Equal to floor(log<sub>10</sub>&nbsp;[`MAX`]).
488 ///
489 /// [`MAX`]: f32::MAX
490 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
491 pub const MAX_10_EXP: i32 = 38;
492
493 /// Not a Number (NaN).
494 ///
495 /// Note that IEEE 754 doesn't define just a single NaN value; a plethora of bit patterns are
496 /// considered to be NaN. Furthermore, the standard makes a difference between a "signaling" and
497 /// a "quiet" NaN, and allows inspecting its "payload" (the unspecified bits in the bit pattern)
498 /// and its sign. See the [specification of NaN bit patterns](f32#nan-bit-patterns) for more
499 /// info.
500 ///
501 /// This constant is guaranteed to be a quiet NaN (on targets that follow the Rust assumptions
502 /// that the quiet/signaling bit being set to 1 indicates a quiet NaN). Beyond that, nothing is
503 /// guaranteed about the specific bit pattern chosen here: both payload and sign are arbitrary.
504 /// The concrete bit pattern may change across Rust versions and target platforms.
505 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
506 #[rustc_diagnostic_item = "f32_nan"]
507 #[allow(clippy::eq_op)]
508 pub const NAN: f32 = 0.0_f32 / 0.0_f32;
509 /// Infinity (∞).
510 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
511 pub const INFINITY: f32 = 1.0_f32 / 0.0_f32;
512 /// Negative infinity (−∞).
513 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
514 pub const NEG_INFINITY: f32 = -1.0_f32 / 0.0_f32;
515
516 /// Sign bit
517 pub(crate) const SIGN_MASK: u32 = 0x8000_0000;
518
519 /// Exponent mask
520 pub(crate) const EXP_MASK: u32 = 0x7f80_0000;
521
522 /// Mantissa mask
523 pub(crate) const MAN_MASK: u32 = 0x007f_ffff;
524
525 /// Minimum representable positive value (min subnormal)
526 const TINY_BITS: u32 = 0x1;
527
528 /// Minimum representable negative value (min negative subnormal)
529 const NEG_TINY_BITS: u32 = Self::TINY_BITS | Self::SIGN_MASK;
530
531 /// Returns `true` if this value is NaN.
532 ///
533 /// ```
534 /// let nan = f32::NAN;
535 /// let f = 7.0_f32;
536 ///
537 /// assert!(nan.is_nan());
538 /// assert!(!f.is_nan());
539 /// ```
540 #[must_use]
541 #[stable(feature = "rust1", since = "1.0.0")]
542 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
543 #[inline]
544 #[allow(clippy::eq_op)] // > if you intended to check if the operand is NaN, use `.is_nan()` instead :)
545 pub const fn is_nan(self) -> bool {
546 self != self
547 }
548
549 /// Returns `true` if this value is positive infinity or negative infinity, and
550 /// `false` otherwise.
551 ///
552 /// ```
553 /// let f = 7.0f32;
554 /// let inf = f32::INFINITY;
555 /// let neg_inf = f32::NEG_INFINITY;
556 /// let nan = f32::NAN;
557 ///
558 /// assert!(!f.is_infinite());
559 /// assert!(!nan.is_infinite());
560 ///
561 /// assert!(inf.is_infinite());
562 /// assert!(neg_inf.is_infinite());
563 /// ```
564 #[must_use]
565 #[stable(feature = "rust1", since = "1.0.0")]
566 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
567 #[inline]
568 pub const fn is_infinite(self) -> bool {
569 // Getting clever with transmutation can result in incorrect answers on some FPUs
570 // FIXME: alter the Rust <-> Rust calling convention to prevent this problem.
571 // See https://github.com/rust-lang/rust/issues/72327
572 (self == f32::INFINITY) | (self == f32::NEG_INFINITY)
573 }
574
575 /// Returns `true` if this number is neither infinite nor NaN.
576 ///
577 /// ```
578 /// let f = 7.0f32;
579 /// let inf = f32::INFINITY;
580 /// let neg_inf = f32::NEG_INFINITY;
581 /// let nan = f32::NAN;
582 ///
583 /// assert!(f.is_finite());
584 ///
585 /// assert!(!nan.is_finite());
586 /// assert!(!inf.is_finite());
587 /// assert!(!neg_inf.is_finite());
588 /// ```
589 #[must_use]
590 #[stable(feature = "rust1", since = "1.0.0")]
591 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
592 #[inline]
593 pub const fn is_finite(self) -> bool {
594 // There's no need to handle NaN separately: if self is NaN,
595 // the comparison is not true, exactly as desired.
596 self.abs() < Self::INFINITY
597 }
598
599 /// Returns `true` if the number is [subnormal].
600 ///
601 /// ```
602 /// let min = f32::MIN_POSITIVE; // 1.17549435e-38f32
603 /// let max = f32::MAX;
604 /// let lower_than_min = 1.0e-40_f32;
605 /// let zero = 0.0_f32;
606 ///
607 /// assert!(!min.is_subnormal());
608 /// assert!(!max.is_subnormal());
609 ///
610 /// assert!(!zero.is_subnormal());
611 /// assert!(!f32::NAN.is_subnormal());
612 /// assert!(!f32::INFINITY.is_subnormal());
613 /// // Values between `0` and `min` are Subnormal.
614 /// assert!(lower_than_min.is_subnormal());
615 /// ```
616 /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
617 #[must_use]
618 #[stable(feature = "is_subnormal", since = "1.53.0")]
619 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
620 #[inline]
621 pub const fn is_subnormal(self) -> bool {
622 matches!(self.classify(), FpCategory::Subnormal)
623 }
624
625 /// Returns `true` if the number is neither zero, infinite,
626 /// [subnormal], or NaN.
627 ///
628 /// ```
629 /// let min = f32::MIN_POSITIVE; // 1.17549435e-38f32
630 /// let max = f32::MAX;
631 /// let lower_than_min = 1.0e-40_f32;
632 /// let zero = 0.0_f32;
633 ///
634 /// assert!(min.is_normal());
635 /// assert!(max.is_normal());
636 ///
637 /// assert!(!zero.is_normal());
638 /// assert!(!f32::NAN.is_normal());
639 /// assert!(!f32::INFINITY.is_normal());
640 /// // Values between `0` and `min` are Subnormal.
641 /// assert!(!lower_than_min.is_normal());
642 /// ```
643 /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
644 #[must_use]
645 #[stable(feature = "rust1", since = "1.0.0")]
646 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
647 #[inline]
648 pub const fn is_normal(self) -> bool {
649 matches!(self.classify(), FpCategory::Normal)
650 }
651
652 /// Returns the floating point category of the number. If only one property
653 /// is going to be tested, it is generally faster to use the specific
654 /// predicate instead.
655 ///
656 /// ```
657 /// use std::num::FpCategory;
658 ///
659 /// let num = 12.4_f32;
660 /// let inf = f32::INFINITY;
661 ///
662 /// assert_eq!(num.classify(), FpCategory::Normal);
663 /// assert_eq!(inf.classify(), FpCategory::Infinite);
664 /// ```
665 #[stable(feature = "rust1", since = "1.0.0")]
666 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
667 pub const fn classify(self) -> FpCategory {
668 // We used to have complicated logic here that avoids the simple bit-based tests to work
669 // around buggy codegen for x87 targets (see
670 // https://github.com/rust-lang/rust/issues/114479). However, some LLVM versions later, none
671 // of our tests is able to find any difference between the complicated and the naive
672 // version, so now we are back to the naive version.
673 let b = self.to_bits();
674 match (b & Self::MAN_MASK, b & Self::EXP_MASK) {
675 (0, Self::EXP_MASK) => FpCategory::Infinite,
676 (_, Self::EXP_MASK) => FpCategory::Nan,
677 (0, 0) => FpCategory::Zero,
678 (_, 0) => FpCategory::Subnormal,
679 _ => FpCategory::Normal,
680 }
681 }
682
683 /// Returns `true` if `self` has a positive sign, including `+0.0`, NaNs with
684 /// positive sign bit and positive infinity.
685 ///
686 /// Note that IEEE 754 doesn't assign any meaning to the sign bit in case of
687 /// a NaN, and as Rust doesn't guarantee that the bit pattern of NaNs are
688 /// conserved over arithmetic operations, the result of `is_sign_positive` on
689 /// a NaN might produce an unexpected or non-portable result. See the [specification
690 /// of NaN bit patterns](f32#nan-bit-patterns) for more info. Use `self.signum() == 1.0`
691 /// if you need fully portable behavior (will return `false` for all NaNs).
692 ///
693 /// ```
694 /// let f = 7.0_f32;
695 /// let g = -7.0_f32;
696 ///
697 /// assert!(f.is_sign_positive());
698 /// assert!(!g.is_sign_positive());
699 /// ```
700 #[must_use]
701 #[stable(feature = "rust1", since = "1.0.0")]
702 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
703 #[inline]
704 pub const fn is_sign_positive(self) -> bool {
705 !self.is_sign_negative()
706 }
707
708 /// Returns `true` if `self` has a negative sign, including `-0.0`, NaNs with
709 /// negative sign bit and negative infinity.
710 ///
711 /// Note that IEEE 754 doesn't assign any meaning to the sign bit in case of
712 /// a NaN, and as Rust doesn't guarantee that the bit pattern of NaNs are
713 /// conserved over arithmetic operations, the result of `is_sign_negative` on
714 /// a NaN might produce an unexpected or non-portable result. See the [specification
715 /// of NaN bit patterns](f32#nan-bit-patterns) for more info. Use `self.signum() == -1.0`
716 /// if you need fully portable behavior (will return `false` for all NaNs).
717 ///
718 /// ```
719 /// let f = 7.0f32;
720 /// let g = -7.0f32;
721 ///
722 /// assert!(!f.is_sign_negative());
723 /// assert!(g.is_sign_negative());
724 /// ```
725 #[must_use]
726 #[stable(feature = "rust1", since = "1.0.0")]
727 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
728 #[inline]
729 pub const fn is_sign_negative(self) -> bool {
730 // IEEE754 says: isSignMinus(x) is true if and only if x has negative sign. isSignMinus
731 // applies to zeros and NaNs as well.
732 self.to_bits() & 0x8000_0000 != 0
733 }
734
735 /// Returns the least number greater than `self`.
736 ///
737 /// Let `TINY` be the smallest representable positive `f32`. Then,
738 /// - if `self.is_nan()`, this returns `self`;
739 /// - if `self` is [`NEG_INFINITY`], this returns [`MIN`];
740 /// - if `self` is `-TINY`, this returns -0.0;
741 /// - if `self` is -0.0 or +0.0, this returns `TINY`;
742 /// - if `self` is [`MAX`] or [`INFINITY`], this returns [`INFINITY`];
743 /// - otherwise the unique least value greater than `self` is returned.
744 ///
745 /// The identity `x.next_up() == -(-x).next_down()` holds for all non-NaN `x`. When `x`
746 /// is finite `x == x.next_up().next_down()` also holds.
747 ///
748 /// ```rust
749 /// // f32::EPSILON is the difference between 1.0 and the next number up.
750 /// assert_eq!(1.0f32.next_up(), 1.0 + f32::EPSILON);
751 /// // But not for most numbers.
752 /// assert!(0.1f32.next_up() < 0.1 + f32::EPSILON);
753 /// assert_eq!(16777216f32.next_up(), 16777218.0);
754 /// ```
755 ///
756 /// This operation corresponds to IEEE-754 `nextUp`.
757 ///
758 /// [`NEG_INFINITY`]: Self::NEG_INFINITY
759 /// [`INFINITY`]: Self::INFINITY
760 /// [`MIN`]: Self::MIN
761 /// [`MAX`]: Self::MAX
762 #[inline]
763 #[doc(alias = "nextUp")]
764 #[stable(feature = "float_next_up_down", since = "1.86.0")]
765 #[rustc_const_stable(feature = "float_next_up_down", since = "1.86.0")]
766 pub const fn next_up(self) -> Self {
767 // Some targets violate Rust's assumption of IEEE semantics, e.g. by flushing
768 // denormals to zero. This is in general unsound and unsupported, but here
769 // we do our best to still produce the correct result on such targets.
770 let bits = self.to_bits();
771 if self.is_nan() || bits == Self::INFINITY.to_bits() {
772 return self;
773 }
774
775 let abs = bits & !Self::SIGN_MASK;
776 let next_bits = if abs == 0 {
777 Self::TINY_BITS
778 } else if bits == abs {
779 bits + 1
780 } else {
781 bits - 1
782 };
783 Self::from_bits(next_bits)
784 }
785
786 /// Returns the greatest number less than `self`.
787 ///
788 /// Let `TINY` be the smallest representable positive `f32`. Then,
789 /// - if `self.is_nan()`, this returns `self`;
790 /// - if `self` is [`INFINITY`], this returns [`MAX`];
791 /// - if `self` is `TINY`, this returns 0.0;
792 /// - if `self` is -0.0 or +0.0, this returns `-TINY`;
793 /// - if `self` is [`MIN`] or [`NEG_INFINITY`], this returns [`NEG_INFINITY`];
794 /// - otherwise the unique greatest value less than `self` is returned.
795 ///
796 /// The identity `x.next_down() == -(-x).next_up()` holds for all non-NaN `x`. When `x`
797 /// is finite `x == x.next_down().next_up()` also holds.
798 ///
799 /// ```rust
800 /// let x = 1.0f32;
801 /// // Clamp value into range [0, 1).
802 /// let clamped = x.clamp(0.0, 1.0f32.next_down());
803 /// assert!(clamped < 1.0);
804 /// assert_eq!(clamped.next_up(), 1.0);
805 /// ```
806 ///
807 /// This operation corresponds to IEEE-754 `nextDown`.
808 ///
809 /// [`NEG_INFINITY`]: Self::NEG_INFINITY
810 /// [`INFINITY`]: Self::INFINITY
811 /// [`MIN`]: Self::MIN
812 /// [`MAX`]: Self::MAX
813 #[inline]
814 #[doc(alias = "nextDown")]
815 #[stable(feature = "float_next_up_down", since = "1.86.0")]
816 #[rustc_const_stable(feature = "float_next_up_down", since = "1.86.0")]
817 pub const fn next_down(self) -> Self {
818 // Some targets violate Rust's assumption of IEEE semantics, e.g. by flushing
819 // denormals to zero. This is in general unsound and unsupported, but here
820 // we do our best to still produce the correct result on such targets.
821 let bits = self.to_bits();
822 if self.is_nan() || bits == Self::NEG_INFINITY.to_bits() {
823 return self;
824 }
825
826 let abs = bits & !Self::SIGN_MASK;
827 let next_bits = if abs == 0 {
828 Self::NEG_TINY_BITS
829 } else if bits == abs {
830 bits - 1
831 } else {
832 bits + 1
833 };
834 Self::from_bits(next_bits)
835 }
836
837 /// Takes the reciprocal (inverse) of a number, `1/x`.
838 ///
839 /// ```
840 /// let x = 2.0_f32;
841 /// let abs_difference = (x.recip() - (1.0 / x)).abs();
842 ///
843 /// assert!(abs_difference <= f32::EPSILON);
844 /// ```
845 #[must_use = "this returns the result of the operation, without modifying the original"]
846 #[stable(feature = "rust1", since = "1.0.0")]
847 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
848 #[inline]
849 pub const fn recip(self) -> f32 {
850 1.0 / self
851 }
852
853 /// Converts radians to degrees.
854 ///
855 /// # Unspecified precision
856 ///
857 /// The precision of this function is non-deterministic. This means it varies by platform,
858 /// Rust version, and can even differ within the same execution from one invocation to the next.
859 ///
860 /// # Examples
861 ///
862 /// ```
863 /// let angle = std::f32::consts::PI;
864 ///
865 /// let abs_difference = (angle.to_degrees() - 180.0).abs();
866 /// # #[cfg(any(not(target_arch = "x86"), target_feature = "sse2"))]
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_degrees(self) -> f32 {
875 // Use a literal to avoid double rounding, consts::PI is already rounded,
876 // and dividing would round again.
877 const PIS_IN_180: f32 = 57.2957795130823208767981548141051703_f32;
878 self * PIS_IN_180
879 }
880
881 /// Converts degrees to radians.
882 ///
883 /// # Unspecified precision
884 ///
885 /// The precision of this function is non-deterministic. This means it varies by platform,
886 /// Rust version, and can even differ within the same execution from one invocation to the next.
887 ///
888 /// # Examples
889 ///
890 /// ```
891 /// let angle = 180.0f32;
892 ///
893 /// let abs_difference = (angle.to_radians() - std::f32::consts::PI).abs();
894 ///
895 /// assert!(abs_difference <= f32::EPSILON);
896 /// ```
897 #[must_use = "this returns the result of the operation, \
898 without modifying the original"]
899 #[stable(feature = "f32_deg_rad_conversions", since = "1.7.0")]
900 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
901 #[inline]
902 pub const fn to_radians(self) -> f32 {
903 // The division here is correctly rounded with respect to the true value of π/180.
904 // Although π is irrational and already rounded, the double rounding happens
905 // to produce correct result for f32.
906 const RADS_PER_DEG: f32 = consts::PI / 180.0;
907 self * RADS_PER_DEG
908 }
909
910 /// Returns the maximum of the two numbers, ignoring NaN.
911 ///
912 /// If exactly one of the arguments is NaN (quiet or signaling), then the other argument is
913 /// returned. If both arguments are NaN, the return value is NaN, with the bit pattern picked
914 /// using the usual [rules for arithmetic operations](f32#nan-bit-patterns). If the inputs
915 /// compare equal (such as for the case of `+0.0` and `-0.0`), either input may be returned
916 /// non-deterministically.
917 ///
918 /// The handling of NaNs follows the IEEE 754-2019 semantics for `maximumNumber`, treating all
919 /// NaNs the same way to ensure the operation is associative. The handling of signed zeros
920 /// follows the IEEE 754-2008 semantics for `maxNum`.
921 ///
922 /// ```
923 /// let x = 1.0f32;
924 /// let y = 2.0f32;
925 ///
926 /// assert_eq!(x.max(y), y);
927 /// assert_eq!(x.max(f32::NAN), x);
928 /// ```
929 #[must_use = "this returns the result of the comparison, without modifying either input"]
930 #[stable(feature = "rust1", since = "1.0.0")]
931 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
932 #[inline]
933 pub const fn max(self, other: f32) -> f32 {
934 intrinsics::maxnumf32(self, other)
935 }
936
937 /// Returns the minimum of the two numbers, ignoring NaN.
938 ///
939 /// If exactly one of the arguments is NaN (quiet or signaling), then the other argument is
940 /// returned. If both arguments are NaN, the return value is NaN, with the bit pattern picked
941 /// using the usual [rules for arithmetic operations](f32#nan-bit-patterns). If the inputs
942 /// compare equal (such as for the case of `+0.0` and `-0.0`), either input may be returned
943 /// non-deterministically.
944 ///
945 /// The handling of NaNs follows the IEEE 754-2019 semantics for `minimumNumber`, treating all
946 /// NaNs the same way to ensure the operation is associative. The handling of signed zeros
947 /// follows the IEEE 754-2008 semantics for `minNum`.
948 ///
949 /// ```
950 /// let x = 1.0f32;
951 /// let y = 2.0f32;
952 ///
953 /// assert_eq!(x.min(y), x);
954 /// assert_eq!(x.min(f32::NAN), x);
955 /// ```
956 #[must_use = "this returns the result of the comparison, without modifying either input"]
957 #[stable(feature = "rust1", since = "1.0.0")]
958 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
959 #[inline]
960 pub const fn min(self, other: f32) -> f32 {
961 intrinsics::minnumf32(self, other)
962 }
963
964 /// Returns the maximum of the two numbers, propagating NaN.
965 ///
966 /// If at least one of the arguments is NaN, the return value is NaN, with the bit pattern
967 /// picked using the usual [rules for arithmetic operations](f32#nan-bit-patterns). Furthermore,
968 /// `-0.0` is considered to be less than `+0.0`, making this function fully deterministic for
969 /// non-NaN inputs.
970 ///
971 /// This is in contrast to [`f32::max`] which only returns NaN when *both* arguments are NaN,
972 /// and which does not reliably order `-0.0` and `+0.0`.
973 ///
974 /// This follows the IEEE 754-2019 semantics for `maximum`.
975 ///
976 /// ```
977 /// #![feature(float_minimum_maximum)]
978 /// let x = 1.0f32;
979 /// let y = 2.0f32;
980 ///
981 /// assert_eq!(x.maximum(y), y);
982 /// assert!(x.maximum(f32::NAN).is_nan());
983 /// ```
984 #[must_use = "this returns the result of the comparison, without modifying either input"]
985 #[unstable(feature = "float_minimum_maximum", issue = "91079")]
986 #[inline]
987 pub const fn maximum(self, other: f32) -> f32 {
988 intrinsics::maximumf32(self, other)
989 }
990
991 /// Returns the minimum of the two numbers, propagating NaN.
992 ///
993 /// If at least one of the arguments is NaN, the return value is NaN, with the bit pattern
994 /// picked using the usual [rules for arithmetic operations](f32#nan-bit-patterns). Furthermore,
995 /// `-0.0` is considered to be less than `+0.0`, making this function fully deterministic for
996 /// non-NaN inputs.
997 ///
998 /// This is in contrast to [`f32::min`] which only returns NaN when *both* arguments are NaN,
999 /// and which does not reliably order `-0.0` and `+0.0`.
1000 ///
1001 /// This follows the IEEE 754-2019 semantics for `minimum`.
1002 ///
1003 /// ```
1004 /// #![feature(float_minimum_maximum)]
1005 /// let x = 1.0f32;
1006 /// let y = 2.0f32;
1007 ///
1008 /// assert_eq!(x.minimum(y), x);
1009 /// assert!(x.minimum(f32::NAN).is_nan());
1010 /// ```
1011 #[must_use = "this returns the result of the comparison, without modifying either input"]
1012 #[unstable(feature = "float_minimum_maximum", issue = "91079")]
1013 #[inline]
1014 pub const fn minimum(self, other: f32) -> f32 {
1015 intrinsics::minimumf32(self, other)
1016 }
1017
1018 /// Calculates the midpoint (average) between `self` and `rhs`.
1019 ///
1020 /// This returns NaN when *either* argument is NaN or if a combination of
1021 /// +inf and -inf is provided as arguments.
1022 ///
1023 /// # Examples
1024 ///
1025 /// ```
1026 /// assert_eq!(1f32.midpoint(4.0), 2.5);
1027 /// assert_eq!((-5.5f32).midpoint(8.0), 1.25);
1028 /// ```
1029 #[inline]
1030 #[doc(alias = "average")]
1031 #[stable(feature = "num_midpoint", since = "1.85.0")]
1032 #[rustc_const_stable(feature = "num_midpoint", since = "1.85.0")]
1033 pub const fn midpoint(self, other: f32) -> f32 {
1034 cfg_select! {
1035 // Allow faster implementation that have known good 64-bit float
1036 // implementations. Falling back to the branchy code on targets that don't
1037 // have 64-bit hardware floats or buggy implementations.
1038 // https://github.com/rust-lang/rust/pull/121062#issuecomment-2123408114
1039 any(
1040 target_arch = "x86_64",
1041 target_arch = "aarch64",
1042 all(any(target_arch = "riscv32", target_arch = "riscv64"), target_feature = "d"),
1043 all(target_arch = "loongarch64", target_feature = "d"),
1044 all(target_arch = "arm", target_feature = "vfp2"),
1045 target_arch = "wasm32",
1046 target_arch = "wasm64",
1047 ) => {
1048 ((self as f64 + other as f64) / 2.0) as f32
1049 }
1050 _ => {
1051 const HI: f32 = f32::MAX / 2.;
1052
1053 let (a, b) = (self, other);
1054 let abs_a = a.abs();
1055 let abs_b = b.abs();
1056
1057 if abs_a <= HI && abs_b <= HI {
1058 // Overflow is impossible
1059 (a + b) / 2.
1060 } else {
1061 (a / 2.) + (b / 2.)
1062 }
1063 }
1064 }
1065 }
1066
1067 /// Rounds toward zero and converts to any primitive integer type,
1068 /// assuming that the value is finite and fits in that type.
1069 ///
1070 /// ```
1071 /// let value = 4.6_f32;
1072 /// let rounded = unsafe { value.to_int_unchecked::<u16>() };
1073 /// assert_eq!(rounded, 4);
1074 ///
1075 /// let value = -128.9_f32;
1076 /// let rounded = unsafe { value.to_int_unchecked::<i8>() };
1077 /// assert_eq!(rounded, i8::MIN);
1078 /// ```
1079 ///
1080 /// # Safety
1081 ///
1082 /// The value must:
1083 ///
1084 /// * Not be `NaN`
1085 /// * Not be infinite
1086 /// * Be representable in the return type `Int`, after truncating off its fractional part
1087 #[must_use = "this returns the result of the operation, \
1088 without modifying the original"]
1089 #[stable(feature = "float_approx_unchecked_to", since = "1.44.0")]
1090 #[inline]
1091 pub unsafe fn to_int_unchecked<Int>(self) -> Int
1092 where
1093 Self: FloatToInt<Int>,
1094 {
1095 // SAFETY: the caller must uphold the safety contract for
1096 // `FloatToInt::to_int_unchecked`.
1097 unsafe { FloatToInt::<Int>::to_int_unchecked(self) }
1098 }
1099
1100 /// Raw transmutation to `u32`.
1101 ///
1102 /// This is currently identical to `transmute::<f32, u32>(self)` on all platforms.
1103 ///
1104 /// See [`from_bits`](Self::from_bits) for some discussion of the
1105 /// portability of this operation (there are almost no issues).
1106 ///
1107 /// Note that this function is distinct from `as` casting, which attempts to
1108 /// preserve the *numeric* value, and not the bitwise value.
1109 ///
1110 /// # Examples
1111 ///
1112 /// ```
1113 /// assert_ne!((1f32).to_bits(), 1f32 as u32); // to_bits() is not casting!
1114 /// assert_eq!((12.5f32).to_bits(), 0x41480000);
1115 ///
1116 /// ```
1117 #[must_use = "this returns the result of the operation, \
1118 without modifying the original"]
1119 #[stable(feature = "float_bits_conv", since = "1.20.0")]
1120 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1121 #[inline]
1122 #[allow(unnecessary_transmutes)]
1123 pub const fn to_bits(self) -> u32 {
1124 // SAFETY: `u32` is a plain old datatype so we can always transmute to it.
1125 unsafe { mem::transmute(self) }
1126 }
1127
1128 /// Raw transmutation from `u32`.
1129 ///
1130 /// This is currently identical to `transmute::<u32, f32>(v)` on all platforms.
1131 /// It turns out this is incredibly portable, for two reasons:
1132 ///
1133 /// * Floats and Ints have the same endianness on all supported platforms.
1134 /// * IEEE 754 very precisely specifies the bit layout of floats.
1135 ///
1136 /// However there is one caveat: prior to the 2008 version of IEEE 754, how
1137 /// to interpret the NaN signaling bit wasn't actually specified. Most platforms
1138 /// (notably x86 and ARM) picked the interpretation that was ultimately
1139 /// standardized in 2008, but some didn't (notably MIPS). As a result, all
1140 /// signaling NaNs on MIPS are quiet NaNs on x86, and vice-versa.
1141 ///
1142 /// Rather than trying to preserve signaling-ness cross-platform, this
1143 /// implementation favors preserving the exact bits. This means that
1144 /// any payloads encoded in NaNs will be preserved even if the result of
1145 /// this method is sent over the network from an x86 machine to a MIPS one.
1146 ///
1147 /// If the results of this method are only manipulated by the same
1148 /// architecture that produced them, then there is no portability concern.
1149 ///
1150 /// If the input isn't NaN, then there is no portability concern.
1151 ///
1152 /// If you don't care about signalingness (very likely), then there is no
1153 /// portability concern.
1154 ///
1155 /// Note that this function is distinct from `as` casting, which attempts to
1156 /// preserve the *numeric* value, and not the bitwise value.
1157 ///
1158 /// # Examples
1159 ///
1160 /// ```
1161 /// let v = f32::from_bits(0x41480000);
1162 /// assert_eq!(v, 12.5);
1163 /// ```
1164 #[stable(feature = "float_bits_conv", since = "1.20.0")]
1165 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1166 #[must_use]
1167 #[inline]
1168 #[allow(unnecessary_transmutes)]
1169 pub const fn from_bits(v: u32) -> Self {
1170 // It turns out the safety issues with sNaN were overblown! Hooray!
1171 // SAFETY: `u32` is a plain old datatype so we can always transmute from it.
1172 unsafe { mem::transmute(v) }
1173 }
1174
1175 /// Returns the memory representation of this floating point number as a byte array in
1176 /// big-endian (network) byte order.
1177 ///
1178 /// See [`from_bits`](Self::from_bits) for some discussion of the
1179 /// portability of this operation (there are almost no issues).
1180 ///
1181 /// # Examples
1182 ///
1183 /// ```
1184 /// let bytes = 12.5f32.to_be_bytes();
1185 /// assert_eq!(bytes, [0x41, 0x48, 0x00, 0x00]);
1186 /// ```
1187 #[must_use = "this returns the result of the operation, \
1188 without modifying the original"]
1189 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1190 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1191 #[inline]
1192 pub const fn to_be_bytes(self) -> [u8; 4] {
1193 self.to_bits().to_be_bytes()
1194 }
1195
1196 /// Returns the memory representation of this floating point number as a byte array in
1197 /// little-endian byte order.
1198 ///
1199 /// See [`from_bits`](Self::from_bits) for some discussion of the
1200 /// portability of this operation (there are almost no issues).
1201 ///
1202 /// # Examples
1203 ///
1204 /// ```
1205 /// let bytes = 12.5f32.to_le_bytes();
1206 /// assert_eq!(bytes, [0x00, 0x00, 0x48, 0x41]);
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_le_bytes(self) -> [u8; 4] {
1214 self.to_bits().to_le_bytes()
1215 }
1216
1217 /// Returns the memory representation of this floating point number as a byte array in
1218 /// native byte order.
1219 ///
1220 /// As the target platform's native endianness is used, portable code
1221 /// should use [`to_be_bytes`] or [`to_le_bytes`], as appropriate, instead.
1222 ///
1223 /// [`to_be_bytes`]: f32::to_be_bytes
1224 /// [`to_le_bytes`]: f32::to_le_bytes
1225 ///
1226 /// See [`from_bits`](Self::from_bits) for some discussion of the
1227 /// portability of this operation (there are almost no issues).
1228 ///
1229 /// # Examples
1230 ///
1231 /// ```
1232 /// let bytes = 12.5f32.to_ne_bytes();
1233 /// assert_eq!(
1234 /// bytes,
1235 /// if cfg!(target_endian = "big") {
1236 /// [0x41, 0x48, 0x00, 0x00]
1237 /// } else {
1238 /// [0x00, 0x00, 0x48, 0x41]
1239 /// }
1240 /// );
1241 /// ```
1242 #[must_use = "this returns the result of the operation, \
1243 without modifying the original"]
1244 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1245 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1246 #[inline]
1247 pub const fn to_ne_bytes(self) -> [u8; 4] {
1248 self.to_bits().to_ne_bytes()
1249 }
1250
1251 /// Creates a floating point value from its representation as a byte array in big endian.
1252 ///
1253 /// See [`from_bits`](Self::from_bits) for some discussion of the
1254 /// portability of this operation (there are almost no issues).
1255 ///
1256 /// # Examples
1257 ///
1258 /// ```
1259 /// let value = f32::from_be_bytes([0x41, 0x48, 0x00, 0x00]);
1260 /// assert_eq!(value, 12.5);
1261 /// ```
1262 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1263 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1264 #[must_use]
1265 #[inline]
1266 pub const fn from_be_bytes(bytes: [u8; 4]) -> Self {
1267 Self::from_bits(u32::from_be_bytes(bytes))
1268 }
1269
1270 /// Creates a floating point value from its representation as a byte array in little endian.
1271 ///
1272 /// See [`from_bits`](Self::from_bits) for some discussion of the
1273 /// portability of this operation (there are almost no issues).
1274 ///
1275 /// # Examples
1276 ///
1277 /// ```
1278 /// let value = f32::from_le_bytes([0x00, 0x00, 0x48, 0x41]);
1279 /// assert_eq!(value, 12.5);
1280 /// ```
1281 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1282 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1283 #[must_use]
1284 #[inline]
1285 pub const fn from_le_bytes(bytes: [u8; 4]) -> Self {
1286 Self::from_bits(u32::from_le_bytes(bytes))
1287 }
1288
1289 /// Creates a floating point value from its representation as a byte array in native endian.
1290 ///
1291 /// As the target platform's native endianness is used, portable code
1292 /// likely wants to use [`from_be_bytes`] or [`from_le_bytes`], as
1293 /// appropriate instead.
1294 ///
1295 /// [`from_be_bytes`]: f32::from_be_bytes
1296 /// [`from_le_bytes`]: f32::from_le_bytes
1297 ///
1298 /// See [`from_bits`](Self::from_bits) for some discussion of the
1299 /// portability of this operation (there are almost no issues).
1300 ///
1301 /// # Examples
1302 ///
1303 /// ```
1304 /// let value = f32::from_ne_bytes(if cfg!(target_endian = "big") {
1305 /// [0x41, 0x48, 0x00, 0x00]
1306 /// } else {
1307 /// [0x00, 0x00, 0x48, 0x41]
1308 /// });
1309 /// assert_eq!(value, 12.5);
1310 /// ```
1311 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1312 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1313 #[must_use]
1314 #[inline]
1315 pub const fn from_ne_bytes(bytes: [u8; 4]) -> Self {
1316 Self::from_bits(u32::from_ne_bytes(bytes))
1317 }
1318
1319 /// Returns the ordering between `self` and `other`.
1320 ///
1321 /// Unlike the standard partial comparison between floating point numbers,
1322 /// this comparison always produces an ordering in accordance to
1323 /// the `totalOrder` predicate as defined in the IEEE 754 (2008 revision)
1324 /// floating point standard. The values are ordered in the following sequence:
1325 ///
1326 /// - negative quiet NaN
1327 /// - negative signaling NaN
1328 /// - negative infinity
1329 /// - negative numbers
1330 /// - negative subnormal numbers
1331 /// - negative zero
1332 /// - positive zero
1333 /// - positive subnormal numbers
1334 /// - positive numbers
1335 /// - positive infinity
1336 /// - positive signaling NaN
1337 /// - positive quiet NaN.
1338 ///
1339 /// The ordering established by this function does not always agree with the
1340 /// [`PartialOrd`] and [`PartialEq`] implementations of `f32`. For example,
1341 /// they consider negative and positive zero equal, while `total_cmp`
1342 /// doesn't.
1343 ///
1344 /// The interpretation of the signaling NaN bit follows the definition in
1345 /// the IEEE 754 standard, which may not match the interpretation by some of
1346 /// the older, non-conformant (e.g. MIPS) hardware implementations.
1347 ///
1348 /// # Example
1349 ///
1350 /// ```
1351 /// struct GoodBoy {
1352 /// name: String,
1353 /// weight: f32,
1354 /// }
1355 ///
1356 /// let mut bois = vec![
1357 /// GoodBoy { name: "Pucci".to_owned(), weight: 0.1 },
1358 /// GoodBoy { name: "Woofer".to_owned(), weight: 99.0 },
1359 /// GoodBoy { name: "Yapper".to_owned(), weight: 10.0 },
1360 /// GoodBoy { name: "Chonk".to_owned(), weight: f32::INFINITY },
1361 /// GoodBoy { name: "Abs. Unit".to_owned(), weight: f32::NAN },
1362 /// GoodBoy { name: "Floaty".to_owned(), weight: -5.0 },
1363 /// ];
1364 ///
1365 /// bois.sort_by(|a, b| a.weight.total_cmp(&b.weight));
1366 ///
1367 /// // `f32::NAN` could be positive or negative, which will affect the sort order.
1368 /// if f32::NAN.is_sign_negative() {
1369 /// assert!(bois.into_iter().map(|b| b.weight)
1370 /// .zip([f32::NAN, -5.0, 0.1, 10.0, 99.0, f32::INFINITY].iter())
1371 /// .all(|(a, b)| a.to_bits() == b.to_bits()))
1372 /// } else {
1373 /// assert!(bois.into_iter().map(|b| b.weight)
1374 /// .zip([-5.0, 0.1, 10.0, 99.0, f32::INFINITY, f32::NAN].iter())
1375 /// .all(|(a, b)| a.to_bits() == b.to_bits()))
1376 /// }
1377 /// ```
1378 #[stable(feature = "total_cmp", since = "1.62.0")]
1379 #[rustc_const_unstable(feature = "const_cmp", issue = "143800")]
1380 #[must_use]
1381 #[inline]
1382 pub const fn total_cmp(&self, other: &Self) -> crate::cmp::Ordering {
1383 let mut left = self.to_bits() as i32;
1384 let mut right = other.to_bits() as i32;
1385
1386 // In case of negatives, flip all the bits except the sign
1387 // to achieve a similar layout as two's complement integers
1388 //
1389 // Why does this work? IEEE 754 floats consist of three fields:
1390 // Sign bit, exponent and mantissa. The set of exponent and mantissa
1391 // fields as a whole have the property that their bitwise order is
1392 // equal to the numeric magnitude where the magnitude is defined.
1393 // The magnitude is not normally defined on NaN values, but
1394 // IEEE 754 totalOrder defines the NaN values also to follow the
1395 // bitwise order. This leads to order explained in the doc comment.
1396 // However, the representation of magnitude is the same for negative
1397 // and positive numbers – only the sign bit is different.
1398 // To easily compare the floats as signed integers, we need to
1399 // flip the exponent and mantissa bits in case of negative numbers.
1400 // We effectively convert the numbers to "two's complement" form.
1401 //
1402 // To do the flipping, we construct a mask and XOR against it.
1403 // We branchlessly calculate an "all-ones except for the sign bit"
1404 // mask from negative-signed values: right shifting sign-extends
1405 // the integer, so we "fill" the mask with sign bits, and then
1406 // convert to unsigned to push one more zero bit.
1407 // On positive values, the mask is all zeros, so it's a no-op.
1408 left ^= (((left >> 31) as u32) >> 1) as i32;
1409 right ^= (((right >> 31) as u32) >> 1) as i32;
1410
1411 left.cmp(&right)
1412 }
1413
1414 /// Restrict a value to a certain interval unless it is NaN.
1415 ///
1416 /// Returns `max` if `self` is greater than `max`, and `min` if `self` is
1417 /// less than `min`. Otherwise this returns `self`.
1418 ///
1419 /// Note that this function returns NaN if the initial value was NaN as
1420 /// well. If the result is zero and among the three inputs `self`, `min`, and `max` there are
1421 /// zeros with different sign, either `0.0` or `-0.0` is returned non-deterministically.
1422 ///
1423 /// # Panics
1424 ///
1425 /// Panics if `min > max`, `min` is NaN, or `max` is NaN.
1426 ///
1427 /// # Examples
1428 ///
1429 /// ```
1430 /// assert!((-3.0f32).clamp(-2.0, 1.0) == -2.0);
1431 /// assert!((0.0f32).clamp(-2.0, 1.0) == 0.0);
1432 /// assert!((2.0f32).clamp(-2.0, 1.0) == 1.0);
1433 /// assert!((f32::NAN).clamp(-2.0, 1.0).is_nan());
1434 ///
1435 /// // These always returns zero, but the sign (which is ignored by `==`) is non-deterministic.
1436 /// assert!((0.0f32).clamp(-0.0, -0.0) == 0.0);
1437 /// assert!((1.0f32).clamp(-0.0, 0.0) == 0.0);
1438 /// // This is definitely a negative zero.
1439 /// assert!((-1.0f32).clamp(-0.0, 1.0).is_sign_negative());
1440 /// ```
1441 #[must_use = "method returns a new number and does not mutate the original value"]
1442 #[stable(feature = "clamp", since = "1.50.0")]
1443 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
1444 #[inline]
1445 pub const fn clamp(mut self, min: f32, max: f32) -> f32 {
1446 const_assert!(
1447 min <= max,
1448 "min > max, or either was NaN",
1449 "min > max, or either was NaN. min = {min:?}, max = {max:?}",
1450 min: f32,
1451 max: f32,
1452 );
1453
1454 if self < min {
1455 self = min;
1456 }
1457 if self > max {
1458 self = max;
1459 }
1460 self
1461 }
1462
1463 /// Clamps this number to a symmetric range centered around zero.
1464 ///
1465 /// The method clamps the number's magnitude (absolute value) to be at most `limit`.
1466 ///
1467 /// This is functionally equivalent to `self.clamp(-limit, limit)`, but is more
1468 /// explicit about the intent.
1469 ///
1470 /// # Panics
1471 ///
1472 /// Panics if `limit` is negative or NaN, as this indicates a logic error.
1473 ///
1474 /// # Examples
1475 ///
1476 /// ```
1477 /// #![feature(clamp_magnitude)]
1478 /// assert_eq!(5.0f32.clamp_magnitude(3.0), 3.0);
1479 /// assert_eq!((-5.0f32).clamp_magnitude(3.0), -3.0);
1480 /// assert_eq!(2.0f32.clamp_magnitude(3.0), 2.0);
1481 /// assert_eq!((-2.0f32).clamp_magnitude(3.0), -2.0);
1482 /// ```
1483 #[must_use = "this returns the clamped value and does not modify the original"]
1484 #[unstable(feature = "clamp_magnitude", issue = "148519")]
1485 #[inline]
1486 pub fn clamp_magnitude(self, limit: f32) -> f32 {
1487 assert!(limit >= 0.0, "limit must be non-negative");
1488 let limit = limit.abs(); // Canonicalises -0.0 to 0.0
1489 self.clamp(-limit, limit)
1490 }
1491
1492 /// Computes the absolute value of `self`.
1493 ///
1494 /// This function always returns the precise result.
1495 ///
1496 /// # Examples
1497 ///
1498 /// ```
1499 /// let x = 3.5_f32;
1500 /// let y = -3.5_f32;
1501 ///
1502 /// assert_eq!(x.abs(), x);
1503 /// assert_eq!(y.abs(), -y);
1504 ///
1505 /// assert!(f32::NAN.abs().is_nan());
1506 /// ```
1507 #[must_use = "method returns a new number and does not mutate the original value"]
1508 #[stable(feature = "rust1", since = "1.0.0")]
1509 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
1510 #[inline]
1511 pub const fn abs(self) -> f32 {
1512 intrinsics::fabsf32(self)
1513 }
1514
1515 /// Returns a number that represents the sign of `self`.
1516 ///
1517 /// - `1.0` if the number is positive, `+0.0` or `INFINITY`
1518 /// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
1519 /// - NaN if the number is NaN
1520 ///
1521 /// # Examples
1522 ///
1523 /// ```
1524 /// let f = 3.5_f32;
1525 ///
1526 /// assert_eq!(f.signum(), 1.0);
1527 /// assert_eq!(f32::NEG_INFINITY.signum(), -1.0);
1528 ///
1529 /// assert!(f32::NAN.signum().is_nan());
1530 /// ```
1531 #[must_use = "method returns a new number and does not mutate the original value"]
1532 #[stable(feature = "rust1", since = "1.0.0")]
1533 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
1534 #[inline]
1535 pub const fn signum(self) -> f32 {
1536 if self.is_nan() { Self::NAN } else { 1.0_f32.copysign(self) }
1537 }
1538
1539 /// Returns a number composed of the magnitude of `self` and the sign of
1540 /// `sign`.
1541 ///
1542 /// Equal to `self` if the sign of `self` and `sign` are the same, otherwise equal to `-self`.
1543 /// If `self` is a NaN, then a NaN with the same payload as `self` and the sign bit of `sign` is
1544 /// returned.
1545 ///
1546 /// If `sign` is a NaN, then this operation will still carry over its sign into the result. Note
1547 /// that IEEE 754 doesn't assign any meaning to the sign bit in case of a NaN, and as Rust
1548 /// doesn't guarantee that the bit pattern of NaNs are conserved over arithmetic operations, the
1549 /// result of `copysign` with `sign` being a NaN might produce an unexpected or non-portable
1550 /// result. See the [specification of NaN bit patterns](primitive@f32#nan-bit-patterns) for more
1551 /// info.
1552 ///
1553 /// # Examples
1554 ///
1555 /// ```
1556 /// let f = 3.5_f32;
1557 ///
1558 /// assert_eq!(f.copysign(0.42), 3.5_f32);
1559 /// assert_eq!(f.copysign(-0.42), -3.5_f32);
1560 /// assert_eq!((-f).copysign(0.42), 3.5_f32);
1561 /// assert_eq!((-f).copysign(-0.42), -3.5_f32);
1562 ///
1563 /// assert!(f32::NAN.copysign(1.0).is_nan());
1564 /// ```
1565 #[must_use = "method returns a new number and does not mutate the original value"]
1566 #[inline]
1567 #[stable(feature = "copysign", since = "1.35.0")]
1568 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
1569 pub const fn copysign(self, sign: f32) -> f32 {
1570 intrinsics::copysignf32(self, sign)
1571 }
1572
1573 /// Float addition that allows optimizations based on algebraic rules.
1574 ///
1575 /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1576 #[must_use = "method returns a new number and does not mutate the original value"]
1577 #[unstable(feature = "float_algebraic", issue = "136469")]
1578 #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1579 #[inline]
1580 pub const fn algebraic_add(self, rhs: f32) -> f32 {
1581 intrinsics::fadd_algebraic(self, rhs)
1582 }
1583
1584 /// Float subtraction that allows optimizations based on algebraic rules.
1585 ///
1586 /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1587 #[must_use = "method returns a new number and does not mutate the original value"]
1588 #[unstable(feature = "float_algebraic", issue = "136469")]
1589 #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1590 #[inline]
1591 pub const fn algebraic_sub(self, rhs: f32) -> f32 {
1592 intrinsics::fsub_algebraic(self, rhs)
1593 }
1594
1595 /// Float multiplication that allows optimizations based on algebraic rules.
1596 ///
1597 /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1598 #[must_use = "method returns a new number and does not mutate the original value"]
1599 #[unstable(feature = "float_algebraic", issue = "136469")]
1600 #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1601 #[inline]
1602 pub const fn algebraic_mul(self, rhs: f32) -> f32 {
1603 intrinsics::fmul_algebraic(self, rhs)
1604 }
1605
1606 /// Float division that allows optimizations based on algebraic rules.
1607 ///
1608 /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1609 #[must_use = "method returns a new number and does not mutate the original value"]
1610 #[unstable(feature = "float_algebraic", issue = "136469")]
1611 #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1612 #[inline]
1613 pub const fn algebraic_div(self, rhs: f32) -> f32 {
1614 intrinsics::fdiv_algebraic(self, rhs)
1615 }
1616
1617 /// Float remainder that allows optimizations based on algebraic rules.
1618 ///
1619 /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1620 #[must_use = "method returns a new number and does not mutate the original value"]
1621 #[unstable(feature = "float_algebraic", issue = "136469")]
1622 #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1623 #[inline]
1624 pub const fn algebraic_rem(self, rhs: f32) -> f32 {
1625 intrinsics::frem_algebraic(self, rhs)
1626 }
1627}
1628
1629/// Experimental implementations of floating point functions in `core`.
1630///
1631/// _The standalone functions in this module are for testing only.
1632/// They will be stabilized as inherent methods._
1633#[unstable(feature = "core_float_math", issue = "137578")]
1634pub mod math {
1635 use crate::intrinsics;
1636 use crate::num::libm;
1637
1638 /// Experimental version of `floor` in `core`. See [`f32::floor`] for details.
1639 ///
1640 /// # Examples
1641 ///
1642 /// ```
1643 /// #![feature(core_float_math)]
1644 ///
1645 /// use core::f32;
1646 ///
1647 /// let f = 3.7_f32;
1648 /// let g = 3.0_f32;
1649 /// let h = -3.7_f32;
1650 ///
1651 /// assert_eq!(f32::math::floor(f), 3.0);
1652 /// assert_eq!(f32::math::floor(g), 3.0);
1653 /// assert_eq!(f32::math::floor(h), -4.0);
1654 /// ```
1655 ///
1656 /// _This standalone function is for testing only.
1657 /// It will be stabilized as an inherent method._
1658 ///
1659 /// [`f32::floor`]: ../../../std/primitive.f32.html#method.floor
1660 #[inline]
1661 #[unstable(feature = "core_float_math", issue = "137578")]
1662 #[must_use = "method returns a new number and does not mutate the original value"]
1663 pub const fn floor(x: f32) -> f32 {
1664 intrinsics::floorf32(x)
1665 }
1666
1667 /// Experimental version of `ceil` in `core`. See [`f32::ceil`] for details.
1668 ///
1669 /// # Examples
1670 ///
1671 /// ```
1672 /// #![feature(core_float_math)]
1673 ///
1674 /// use core::f32;
1675 ///
1676 /// let f = 3.01_f32;
1677 /// let g = 4.0_f32;
1678 ///
1679 /// assert_eq!(f32::math::ceil(f), 4.0);
1680 /// assert_eq!(f32::math::ceil(g), 4.0);
1681 /// ```
1682 ///
1683 /// _This standalone function is for testing only.
1684 /// It will be stabilized as an inherent method._
1685 ///
1686 /// [`f32::ceil`]: ../../../std/primitive.f32.html#method.ceil
1687 #[inline]
1688 #[doc(alias = "ceiling")]
1689 #[must_use = "method returns a new number and does not mutate the original value"]
1690 #[unstable(feature = "core_float_math", issue = "137578")]
1691 pub const fn ceil(x: f32) -> f32 {
1692 intrinsics::ceilf32(x)
1693 }
1694
1695 /// Experimental version of `round` in `core`. See [`f32::round`] for details.
1696 ///
1697 /// # Examples
1698 ///
1699 /// ```
1700 /// #![feature(core_float_math)]
1701 ///
1702 /// use core::f32;
1703 ///
1704 /// let f = 3.3_f32;
1705 /// let g = -3.3_f32;
1706 /// let h = -3.7_f32;
1707 /// let i = 3.5_f32;
1708 /// let j = 4.5_f32;
1709 ///
1710 /// assert_eq!(f32::math::round(f), 3.0);
1711 /// assert_eq!(f32::math::round(g), -3.0);
1712 /// assert_eq!(f32::math::round(h), -4.0);
1713 /// assert_eq!(f32::math::round(i), 4.0);
1714 /// assert_eq!(f32::math::round(j), 5.0);
1715 /// ```
1716 ///
1717 /// _This standalone function is for testing only.
1718 /// It will be stabilized as an inherent method._
1719 ///
1720 /// [`f32::round`]: ../../../std/primitive.f32.html#method.round
1721 #[inline]
1722 #[unstable(feature = "core_float_math", issue = "137578")]
1723 #[must_use = "method returns a new number and does not mutate the original value"]
1724 pub const fn round(x: f32) -> f32 {
1725 intrinsics::roundf32(x)
1726 }
1727
1728 /// Experimental version of `round_ties_even` in `core`. See [`f32::round_ties_even`] for
1729 /// details.
1730 ///
1731 /// # Examples
1732 ///
1733 /// ```
1734 /// #![feature(core_float_math)]
1735 ///
1736 /// use core::f32;
1737 ///
1738 /// let f = 3.3_f32;
1739 /// let g = -3.3_f32;
1740 /// let h = 3.5_f32;
1741 /// let i = 4.5_f32;
1742 ///
1743 /// assert_eq!(f32::math::round_ties_even(f), 3.0);
1744 /// assert_eq!(f32::math::round_ties_even(g), -3.0);
1745 /// assert_eq!(f32::math::round_ties_even(h), 4.0);
1746 /// assert_eq!(f32::math::round_ties_even(i), 4.0);
1747 /// ```
1748 ///
1749 /// _This standalone function is for testing only.
1750 /// It will be stabilized as an inherent method._
1751 ///
1752 /// [`f32::round_ties_even`]: ../../../std/primitive.f32.html#method.round_ties_even
1753 #[inline]
1754 #[unstable(feature = "core_float_math", issue = "137578")]
1755 #[must_use = "method returns a new number and does not mutate the original value"]
1756 pub const fn round_ties_even(x: f32) -> f32 {
1757 intrinsics::round_ties_even_f32(x)
1758 }
1759
1760 /// Experimental version of `trunc` in `core`. See [`f32::trunc`] for details.
1761 ///
1762 /// # Examples
1763 ///
1764 /// ```
1765 /// #![feature(core_float_math)]
1766 ///
1767 /// use core::f32;
1768 ///
1769 /// let f = 3.7_f32;
1770 /// let g = 3.0_f32;
1771 /// let h = -3.7_f32;
1772 ///
1773 /// assert_eq!(f32::math::trunc(f), 3.0);
1774 /// assert_eq!(f32::math::trunc(g), 3.0);
1775 /// assert_eq!(f32::math::trunc(h), -3.0);
1776 /// ```
1777 ///
1778 /// _This standalone function is for testing only.
1779 /// It will be stabilized as an inherent method._
1780 ///
1781 /// [`f32::trunc`]: ../../../std/primitive.f32.html#method.trunc
1782 #[inline]
1783 #[doc(alias = "truncate")]
1784 #[must_use = "method returns a new number and does not mutate the original value"]
1785 #[unstable(feature = "core_float_math", issue = "137578")]
1786 pub const fn trunc(x: f32) -> f32 {
1787 intrinsics::truncf32(x)
1788 }
1789
1790 /// Experimental version of `fract` in `core`. See [`f32::fract`] for details.
1791 ///
1792 /// # Examples
1793 ///
1794 /// ```
1795 /// #![feature(core_float_math)]
1796 ///
1797 /// use core::f32;
1798 ///
1799 /// let x = 3.6_f32;
1800 /// let y = -3.6_f32;
1801 /// let abs_difference_x = (f32::math::fract(x) - 0.6).abs();
1802 /// let abs_difference_y = (f32::math::fract(y) - (-0.6)).abs();
1803 ///
1804 /// assert!(abs_difference_x <= f32::EPSILON);
1805 /// assert!(abs_difference_y <= f32::EPSILON);
1806 /// ```
1807 ///
1808 /// _This standalone function is for testing only.
1809 /// It will be stabilized as an inherent method._
1810 ///
1811 /// [`f32::fract`]: ../../../std/primitive.f32.html#method.fract
1812 #[inline]
1813 #[unstable(feature = "core_float_math", issue = "137578")]
1814 #[must_use = "method returns a new number and does not mutate the original value"]
1815 pub const fn fract(x: f32) -> f32 {
1816 x - trunc(x)
1817 }
1818
1819 /// Experimental version of `mul_add` in `core`. See [`f32::mul_add`] for details.
1820 ///
1821 /// # Examples
1822 ///
1823 /// ```
1824 /// #![feature(core_float_math)]
1825 ///
1826 /// # // FIXME(#140515): mingw has an incorrect fma
1827 /// # // https://sourceforge.net/p/mingw-w64/bugs/848/
1828 /// # #[cfg(all(target_os = "windows", target_env = "gnu", not(target_abi = "llvm")))] {
1829 /// use core::f32;
1830 ///
1831 /// let m = 10.0_f32;
1832 /// let x = 4.0_f32;
1833 /// let b = 60.0_f32;
1834 ///
1835 /// assert_eq!(f32::math::mul_add(m, x, b), 100.0);
1836 /// assert_eq!(m * x + b, 100.0);
1837 ///
1838 /// let one_plus_eps = 1.0_f32 + f32::EPSILON;
1839 /// let one_minus_eps = 1.0_f32 - f32::EPSILON;
1840 /// let minus_one = -1.0_f32;
1841 ///
1842 /// // The exact result (1 + eps) * (1 - eps) = 1 - eps * eps.
1843 /// assert_eq!(
1844 /// f32::math::mul_add(one_plus_eps, one_minus_eps, minus_one),
1845 /// -f32::EPSILON * f32::EPSILON
1846 /// );
1847 /// // Different rounding with the non-fused multiply and add.
1848 /// assert_eq!(one_plus_eps * one_minus_eps + minus_one, 0.0);
1849 /// # }
1850 /// ```
1851 ///
1852 /// _This standalone function is for testing only.
1853 /// It will be stabilized as an inherent method._
1854 ///
1855 /// [`f32::mul_add`]: ../../../std/primitive.f32.html#method.mul_add
1856 #[inline]
1857 #[doc(alias = "fmaf", alias = "fusedMultiplyAdd")]
1858 #[must_use = "method returns a new number and does not mutate the original value"]
1859 #[unstable(feature = "core_float_math", issue = "137578")]
1860 pub const fn mul_add(x: f32, y: f32, z: f32) -> f32 {
1861 intrinsics::fmaf32(x, y, z)
1862 }
1863
1864 /// Experimental version of `div_euclid` in `core`. See [`f32::div_euclid`] for details.
1865 ///
1866 /// # Examples
1867 ///
1868 /// ```
1869 /// #![feature(core_float_math)]
1870 ///
1871 /// use core::f32;
1872 ///
1873 /// let a: f32 = 7.0;
1874 /// let b = 4.0;
1875 /// assert_eq!(f32::math::div_euclid(a, b), 1.0); // 7.0 > 4.0 * 1.0
1876 /// assert_eq!(f32::math::div_euclid(-a, b), -2.0); // -7.0 >= 4.0 * -2.0
1877 /// assert_eq!(f32::math::div_euclid(a, -b), -1.0); // 7.0 >= -4.0 * -1.0
1878 /// assert_eq!(f32::math::div_euclid(-a, -b), 2.0); // -7.0 >= -4.0 * 2.0
1879 /// ```
1880 ///
1881 /// _This standalone function is for testing only.
1882 /// It will be stabilized as an inherent method._
1883 ///
1884 /// [`f32::div_euclid`]: ../../../std/primitive.f32.html#method.div_euclid
1885 #[inline]
1886 #[unstable(feature = "core_float_math", issue = "137578")]
1887 #[must_use = "method returns a new number and does not mutate the original value"]
1888 pub fn div_euclid(x: f32, rhs: f32) -> f32 {
1889 let q = trunc(x / rhs);
1890 if x % rhs < 0.0 {
1891 return if rhs > 0.0 { q - 1.0 } else { q + 1.0 };
1892 }
1893 q
1894 }
1895
1896 /// Experimental version of `rem_euclid` in `core`. See [`f32::rem_euclid`] for details.
1897 ///
1898 /// # Examples
1899 ///
1900 /// ```
1901 /// #![feature(core_float_math)]
1902 ///
1903 /// use core::f32;
1904 ///
1905 /// let a: f32 = 7.0;
1906 /// let b = 4.0;
1907 /// assert_eq!(f32::math::rem_euclid(a, b), 3.0);
1908 /// assert_eq!(f32::math::rem_euclid(-a, b), 1.0);
1909 /// assert_eq!(f32::math::rem_euclid(a, -b), 3.0);
1910 /// assert_eq!(f32::math::rem_euclid(-a, -b), 1.0);
1911 /// // limitation due to round-off error
1912 /// assert!(f32::math::rem_euclid(-f32::EPSILON, 3.0) != 0.0);
1913 /// ```
1914 ///
1915 /// _This standalone function is for testing only.
1916 /// It will be stabilized as an inherent method._
1917 ///
1918 /// [`f32::rem_euclid`]: ../../../std/primitive.f32.html#method.rem_euclid
1919 #[inline]
1920 #[doc(alias = "modulo", alias = "mod")]
1921 #[unstable(feature = "core_float_math", issue = "137578")]
1922 #[must_use = "method returns a new number and does not mutate the original value"]
1923 pub fn rem_euclid(x: f32, rhs: f32) -> f32 {
1924 let r = x % rhs;
1925 if r < 0.0 { r + rhs.abs() } else { r }
1926 }
1927
1928 /// Experimental version of `powi` in `core`. See [`f32::powi`] for details.
1929 ///
1930 /// # Examples
1931 ///
1932 /// ```
1933 /// #![feature(core_float_math)]
1934 ///
1935 /// use core::f32;
1936 ///
1937 /// let x = 2.0_f32;
1938 /// let abs_difference = (f32::math::powi(x, 2) - (x * x)).abs();
1939 /// assert!(abs_difference <= 1e-5);
1940 ///
1941 /// assert_eq!(f32::math::powi(f32::NAN, 0), 1.0);
1942 /// ```
1943 ///
1944 /// _This standalone function is for testing only.
1945 /// It will be stabilized as an inherent method._
1946 ///
1947 /// [`f32::powi`]: ../../../std/primitive.f32.html#method.powi
1948 #[inline]
1949 #[must_use = "method returns a new number and does not mutate the original value"]
1950 #[unstable(feature = "core_float_math", issue = "137578")]
1951 pub fn powi(x: f32, n: i32) -> f32 {
1952 intrinsics::powif32(x, n)
1953 }
1954
1955 /// Experimental version of `sqrt` in `core`. See [`f32::sqrt`] for details.
1956 ///
1957 /// # Examples
1958 ///
1959 /// ```
1960 /// #![feature(core_float_math)]
1961 ///
1962 /// use core::f32;
1963 ///
1964 /// let positive = 4.0_f32;
1965 /// let negative = -4.0_f32;
1966 /// let negative_zero = -0.0_f32;
1967 ///
1968 /// assert_eq!(f32::math::sqrt(positive), 2.0);
1969 /// assert!(f32::math::sqrt(negative).is_nan());
1970 /// assert_eq!(f32::math::sqrt(negative_zero), negative_zero);
1971 /// ```
1972 ///
1973 /// _This standalone function is for testing only.
1974 /// It will be stabilized as an inherent method._
1975 ///
1976 /// [`f32::sqrt`]: ../../../std/primitive.f32.html#method.sqrt
1977 #[inline]
1978 #[doc(alias = "squareRoot")]
1979 #[unstable(feature = "core_float_math", issue = "137578")]
1980 #[must_use = "method returns a new number and does not mutate the original value"]
1981 pub fn sqrt(x: f32) -> f32 {
1982 intrinsics::sqrtf32(x)
1983 }
1984
1985 /// Experimental version of `abs_sub` in `core`. See [`f32::abs_sub`] for details.
1986 ///
1987 /// # Examples
1988 ///
1989 /// ```
1990 /// #![feature(core_float_math)]
1991 ///
1992 /// use core::f32;
1993 ///
1994 /// let x = 3.0f32;
1995 /// let y = -3.0f32;
1996 ///
1997 /// let abs_difference_x = (f32::math::abs_sub(x, 1.0) - 2.0).abs();
1998 /// let abs_difference_y = (f32::math::abs_sub(y, 1.0) - 0.0).abs();
1999 ///
2000 /// assert!(abs_difference_x <= 1e-6);
2001 /// assert!(abs_difference_y <= 1e-6);
2002 /// ```
2003 ///
2004 /// _This standalone function is for testing only.
2005 /// It will be stabilized as an inherent method._
2006 ///
2007 /// [`f32::abs_sub`]: ../../../std/primitive.f32.html#method.abs_sub
2008 #[inline]
2009 #[stable(feature = "rust1", since = "1.0.0")]
2010 #[deprecated(
2011 since = "1.10.0",
2012 note = "you probably meant `(self - other).abs()`: \
2013 this operation is `(self - other).max(0.0)` \
2014 except that `abs_sub` also propagates NaNs (also \
2015 known as `fdimf` in C). If you truly need the positive \
2016 difference, consider using that expression or the C function \
2017 `fdimf`, depending on how you wish to handle NaN (please consider \
2018 filing an issue describing your use-case too)."
2019 )]
2020 #[must_use = "method returns a new number and does not mutate the original value"]
2021 pub fn abs_sub(x: f32, other: f32) -> f32 {
2022 libm::fdimf(x, other)
2023 }
2024
2025 /// Experimental version of `cbrt` in `core`. See [`f32::cbrt`] for details.
2026 ///
2027 /// # Unspecified precision
2028 ///
2029 /// The precision of this function is non-deterministic. This means it varies by platform, Rust version, and
2030 /// can even differ within the same execution from one invocation to the next.
2031 /// This function currently corresponds to the `cbrtf` from libc on Unix
2032 /// and Windows. Note that this might change in the future.
2033 ///
2034 /// # Examples
2035 ///
2036 /// ```
2037 /// #![feature(core_float_math)]
2038 ///
2039 /// use core::f32;
2040 ///
2041 /// let x = 8.0f32;
2042 ///
2043 /// // x^(1/3) - 2 == 0
2044 /// let abs_difference = (f32::math::cbrt(x) - 2.0).abs();
2045 ///
2046 /// assert!(abs_difference <= 1e-6);
2047 /// ```
2048 ///
2049 /// _This standalone function is for testing only.
2050 /// It will be stabilized as an inherent method._
2051 ///
2052 /// [`f32::cbrt`]: ../../../std/primitive.f32.html#method.cbrt
2053 #[inline]
2054 #[must_use = "method returns a new number and does not mutate the original value"]
2055 #[unstable(feature = "core_float_math", issue = "137578")]
2056 pub fn cbrt(x: f32) -> f32 {
2057 libm::cbrtf(x)
2058 }
2059}
2060