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