1//! Constants for the `f64` double-precision floating point type.
2//!
3//! *[See also the `f64` primitive type][f64].*
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 `f64` type.
11
12#![stable(feature = "rust1", since = "1.0.0")]
13
14use crate::convert::FloatToInt;
15#[cfg(not(test))]
16use crate::intrinsics;
17use crate::mem;
18use crate::num::FpCategory;
19
20/// The radix or base of the internal representation of `f64`.
21/// Use [`f64::RADIX`] instead.
22///
23/// # Examples
24///
25/// ```rust
26/// // deprecated way
27/// # #[allow(deprecated, deprecated_in_future)]
28/// let r = std::f64::RADIX;
29///
30/// // intended way
31/// let r = f64::RADIX;
32/// ```
33#[stable(feature = "rust1", since = "1.0.0")]
34#[deprecated(since = "TBD", note = "replaced by the `RADIX` associated constant on `f64`")]
35#[rustc_diagnostic_item = "f64_legacy_const_radix"]
36pub const RADIX: u32 = f64::RADIX;
37
38/// Number of significant digits in base 2.
39/// Use [`f64::MANTISSA_DIGITS`] instead.
40///
41/// # Examples
42///
43/// ```rust
44/// // deprecated way
45/// # #[allow(deprecated, deprecated_in_future)]
46/// let d = std::f64::MANTISSA_DIGITS;
47///
48/// // intended way
49/// let d = f64::MANTISSA_DIGITS;
50/// ```
51#[stable(feature = "rust1", since = "1.0.0")]
52#[deprecated(
53 since = "TBD",
54 note = "replaced by the `MANTISSA_DIGITS` associated constant on `f64`"
55)]
56#[rustc_diagnostic_item = "f64_legacy_const_mantissa_dig"]
57pub const MANTISSA_DIGITS: u32 = f64::MANTISSA_DIGITS;
58
59/// Approximate number of significant digits in base 10.
60/// Use [`f64::DIGITS`] instead.
61///
62/// # Examples
63///
64/// ```rust
65/// // deprecated way
66/// # #[allow(deprecated, deprecated_in_future)]
67/// let d = std::f64::DIGITS;
68///
69/// // intended way
70/// let d = f64::DIGITS;
71/// ```
72#[stable(feature = "rust1", since = "1.0.0")]
73#[deprecated(since = "TBD", note = "replaced by the `DIGITS` associated constant on `f64`")]
74#[rustc_diagnostic_item = "f64_legacy_const_digits"]
75pub const DIGITS: u32 = f64::DIGITS;
76
77/// [Machine epsilon] value for `f64`.
78/// Use [`f64::EPSILON`] instead.
79///
80/// This is the difference between `1.0` and the next larger representable number.
81///
82/// [Machine epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon
83///
84/// # Examples
85///
86/// ```rust
87/// // deprecated way
88/// # #[allow(deprecated, deprecated_in_future)]
89/// let e = std::f64::EPSILON;
90///
91/// // intended way
92/// let e = f64::EPSILON;
93/// ```
94#[stable(feature = "rust1", since = "1.0.0")]
95#[deprecated(since = "TBD", note = "replaced by the `EPSILON` associated constant on `f64`")]
96#[rustc_diagnostic_item = "f64_legacy_const_epsilon"]
97pub const EPSILON: f64 = f64::EPSILON;
98
99/// Smallest finite `f64` value.
100/// Use [`f64::MIN`] instead.
101///
102/// # Examples
103///
104/// ```rust
105/// // deprecated way
106/// # #[allow(deprecated, deprecated_in_future)]
107/// let min = std::f64::MIN;
108///
109/// // intended way
110/// let min = f64::MIN;
111/// ```
112#[stable(feature = "rust1", since = "1.0.0")]
113#[deprecated(since = "TBD", note = "replaced by the `MIN` associated constant on `f64`")]
114#[rustc_diagnostic_item = "f64_legacy_const_min"]
115pub const MIN: f64 = f64::MIN;
116
117/// Smallest positive normal `f64` value.
118/// Use [`f64::MIN_POSITIVE`] instead.
119///
120/// # Examples
121///
122/// ```rust
123/// // deprecated way
124/// # #[allow(deprecated, deprecated_in_future)]
125/// let min = std::f64::MIN_POSITIVE;
126///
127/// // intended way
128/// let min = f64::MIN_POSITIVE;
129/// ```
130#[stable(feature = "rust1", since = "1.0.0")]
131#[deprecated(since = "TBD", note = "replaced by the `MIN_POSITIVE` associated constant on `f64`")]
132#[rustc_diagnostic_item = "f64_legacy_const_min_positive"]
133pub const MIN_POSITIVE: f64 = f64::MIN_POSITIVE;
134
135/// Largest finite `f64` value.
136/// Use [`f64::MAX`] instead.
137///
138/// # Examples
139///
140/// ```rust
141/// // deprecated way
142/// # #[allow(deprecated, deprecated_in_future)]
143/// let max = std::f64::MAX;
144///
145/// // intended way
146/// let max = f64::MAX;
147/// ```
148#[stable(feature = "rust1", since = "1.0.0")]
149#[deprecated(since = "TBD", note = "replaced by the `MAX` associated constant on `f64`")]
150#[rustc_diagnostic_item = "f64_legacy_const_max"]
151pub const MAX: f64 = f64::MAX;
152
153/// One greater than the minimum possible normal power of 2 exponent.
154/// Use [`f64::MIN_EXP`] instead.
155///
156/// # Examples
157///
158/// ```rust
159/// // deprecated way
160/// # #[allow(deprecated, deprecated_in_future)]
161/// let min = std::f64::MIN_EXP;
162///
163/// // intended way
164/// let min = f64::MIN_EXP;
165/// ```
166#[stable(feature = "rust1", since = "1.0.0")]
167#[deprecated(since = "TBD", note = "replaced by the `MIN_EXP` associated constant on `f64`")]
168#[rustc_diagnostic_item = "f64_legacy_const_min_exp"]
169pub const MIN_EXP: i32 = f64::MIN_EXP;
170
171/// Maximum possible power of 2 exponent.
172/// Use [`f64::MAX_EXP`] instead.
173///
174/// # Examples
175///
176/// ```rust
177/// // deprecated way
178/// # #[allow(deprecated, deprecated_in_future)]
179/// let max = std::f64::MAX_EXP;
180///
181/// // intended way
182/// let max = f64::MAX_EXP;
183/// ```
184#[stable(feature = "rust1", since = "1.0.0")]
185#[deprecated(since = "TBD", note = "replaced by the `MAX_EXP` associated constant on `f64`")]
186#[rustc_diagnostic_item = "f64_legacy_const_max_exp"]
187pub const MAX_EXP: i32 = f64::MAX_EXP;
188
189/// Minimum possible normal power of 10 exponent.
190/// Use [`f64::MIN_10_EXP`] instead.
191///
192/// # Examples
193///
194/// ```rust
195/// // deprecated way
196/// # #[allow(deprecated, deprecated_in_future)]
197/// let min = std::f64::MIN_10_EXP;
198///
199/// // intended way
200/// let min = f64::MIN_10_EXP;
201/// ```
202#[stable(feature = "rust1", since = "1.0.0")]
203#[deprecated(since = "TBD", note = "replaced by the `MIN_10_EXP` associated constant on `f64`")]
204#[rustc_diagnostic_item = "f64_legacy_const_min_10_exp"]
205pub const MIN_10_EXP: i32 = f64::MIN_10_EXP;
206
207/// Maximum possible power of 10 exponent.
208/// Use [`f64::MAX_10_EXP`] instead.
209///
210/// # Examples
211///
212/// ```rust
213/// // deprecated way
214/// # #[allow(deprecated, deprecated_in_future)]
215/// let max = std::f64::MAX_10_EXP;
216///
217/// // intended way
218/// let max = f64::MAX_10_EXP;
219/// ```
220#[stable(feature = "rust1", since = "1.0.0")]
221#[deprecated(since = "TBD", note = "replaced by the `MAX_10_EXP` associated constant on `f64`")]
222#[rustc_diagnostic_item = "f64_legacy_const_max_10_exp"]
223pub const MAX_10_EXP: i32 = f64::MAX_10_EXP;
224
225/// Not a Number (NaN).
226/// Use [`f64::NAN`] instead.
227///
228/// # Examples
229///
230/// ```rust
231/// // deprecated way
232/// # #[allow(deprecated, deprecated_in_future)]
233/// let nan = std::f64::NAN;
234///
235/// // intended way
236/// let nan = f64::NAN;
237/// ```
238#[stable(feature = "rust1", since = "1.0.0")]
239#[deprecated(since = "TBD", note = "replaced by the `NAN` associated constant on `f64`")]
240#[rustc_diagnostic_item = "f64_legacy_const_nan"]
241pub const NAN: f64 = f64::NAN;
242
243/// Infinity (∞).
244/// Use [`f64::INFINITY`] instead.
245///
246/// # Examples
247///
248/// ```rust
249/// // deprecated way
250/// # #[allow(deprecated, deprecated_in_future)]
251/// let inf = std::f64::INFINITY;
252///
253/// // intended way
254/// let inf = f64::INFINITY;
255/// ```
256#[stable(feature = "rust1", since = "1.0.0")]
257#[deprecated(since = "TBD", note = "replaced by the `INFINITY` associated constant on `f64`")]
258#[rustc_diagnostic_item = "f64_legacy_const_infinity"]
259pub const INFINITY: f64 = f64::INFINITY;
260
261/// Negative infinity (−∞).
262/// Use [`f64::NEG_INFINITY`] instead.
263///
264/// # Examples
265///
266/// ```rust
267/// // deprecated way
268/// # #[allow(deprecated, deprecated_in_future)]
269/// let ninf = std::f64::NEG_INFINITY;
270///
271/// // intended way
272/// let ninf = f64::NEG_INFINITY;
273/// ```
274#[stable(feature = "rust1", since = "1.0.0")]
275#[deprecated(since = "TBD", note = "replaced by the `NEG_INFINITY` associated constant on `f64`")]
276#[rustc_diagnostic_item = "f64_legacy_const_neg_infinity"]
277pub const NEG_INFINITY: f64 = f64::NEG_INFINITY;
278
279/// Basic mathematical constants.
280#[stable(feature = "rust1", since = "1.0.0")]
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: f64 = 3.14159265358979323846264338327950288_f64;
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: f64 = 6.28318530717958647692528676655900577_f64;
293
294 /// The golden ratio (φ)
295 #[unstable(feature = "more_float_constants", issue = "103883")]
296 pub const PHI: f64 = 1.618033988749894848204586834365638118_f64;
297
298 /// The Euler-Mascheroni constant (γ)
299 #[unstable(feature = "more_float_constants", issue = "103883")]
300 pub const EGAMMA: f64 = 0.577215664901532860606512090082402431_f64;
301
302 /// π/2
303 #[stable(feature = "rust1", since = "1.0.0")]
304 pub const FRAC_PI_2: f64 = 1.57079632679489661923132169163975144_f64;
305
306 /// π/3
307 #[stable(feature = "rust1", since = "1.0.0")]
308 pub const FRAC_PI_3: f64 = 1.04719755119659774615421446109316763_f64;
309
310 /// π/4
311 #[stable(feature = "rust1", since = "1.0.0")]
312 pub const FRAC_PI_4: f64 = 0.785398163397448309615660845819875721_f64;
313
314 /// π/6
315 #[stable(feature = "rust1", since = "1.0.0")]
316 pub const FRAC_PI_6: f64 = 0.52359877559829887307710723054658381_f64;
317
318 /// π/8
319 #[stable(feature = "rust1", since = "1.0.0")]
320 pub const FRAC_PI_8: f64 = 0.39269908169872415480783042290993786_f64;
321
322 /// 1/π
323 #[stable(feature = "rust1", since = "1.0.0")]
324 pub const FRAC_1_PI: f64 = 0.318309886183790671537767526745028724_f64;
325
326 /// 1/sqrt(π)
327 #[unstable(feature = "more_float_constants", issue = "103883")]
328 pub const FRAC_1_SQRT_PI: f64 = 0.564189583547756286948079451560772586_f64;
329
330 /// 2/π
331 #[stable(feature = "rust1", since = "1.0.0")]
332 pub const FRAC_2_PI: f64 = 0.636619772367581343075535053490057448_f64;
333
334 /// 2/sqrt(π)
335 #[stable(feature = "rust1", since = "1.0.0")]
336 pub const FRAC_2_SQRT_PI: f64 = 1.12837916709551257389615890312154517_f64;
337
338 /// sqrt(2)
339 #[stable(feature = "rust1", since = "1.0.0")]
340 pub const SQRT_2: f64 = 1.41421356237309504880168872420969808_f64;
341
342 /// 1/sqrt(2)
343 #[stable(feature = "rust1", since = "1.0.0")]
344 pub const FRAC_1_SQRT_2: f64 = 0.707106781186547524400844362104849039_f64;
345
346 /// sqrt(3)
347 #[unstable(feature = "more_float_constants", issue = "103883")]
348 pub const SQRT_3: f64 = 1.732050807568877293527446341505872367_f64;
349
350 /// 1/sqrt(3)
351 #[unstable(feature = "more_float_constants", issue = "103883")]
352 pub const FRAC_1_SQRT_3: f64 = 0.577350269189625764509148780501957456_f64;
353
354 /// Euler's number (e)
355 #[stable(feature = "rust1", since = "1.0.0")]
356 pub const E: f64 = 2.71828182845904523536028747135266250_f64;
357
358 /// log<sub>2</sub>(10)
359 #[stable(feature = "extra_log_consts", since = "1.43.0")]
360 pub const LOG2_10: f64 = 3.32192809488736234787031942948939018_f64;
361
362 /// log<sub>2</sub>(e)
363 #[stable(feature = "rust1", since = "1.0.0")]
364 pub const LOG2_E: f64 = 1.44269504088896340735992468100189214_f64;
365
366 /// log<sub>10</sub>(2)
367 #[stable(feature = "extra_log_consts", since = "1.43.0")]
368 pub const LOG10_2: f64 = 0.301029995663981195213738894724493027_f64;
369
370 /// log<sub>10</sub>(e)
371 #[stable(feature = "rust1", since = "1.0.0")]
372 pub const LOG10_E: f64 = 0.434294481903251827651128918916605082_f64;
373
374 /// ln(2)
375 #[stable(feature = "rust1", since = "1.0.0")]
376 pub const LN_2: f64 = 0.693147180559945309417232121458176568_f64;
377
378 /// ln(10)
379 #[stable(feature = "rust1", since = "1.0.0")]
380 pub const LN_10: f64 = 2.30258509299404568401799145468436421_f64;
381}
382
383#[cfg(not(test))]
384impl f64 {
385 /// The radix or base of the internal representation of `f64`.
386 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
387 pub const RADIX: u32 = 2;
388
389 /// Number of significant digits in base 2.
390 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
391 pub const MANTISSA_DIGITS: u32 = 53;
392 /// Approximate number of significant digits in base 10.
393 ///
394 /// This is the maximum <i>x</i> such that any decimal number with <i>x</i>
395 /// significant digits can be converted to `f64` and back without loss.
396 ///
397 /// Equal to floor(log<sub>10</sub>&nbsp;2<sup>[`MANTISSA_DIGITS`]&nbsp;&minus;&nbsp;1</sup>).
398 ///
399 /// [`MANTISSA_DIGITS`]: f64::MANTISSA_DIGITS
400 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
401 pub const DIGITS: u32 = 15;
402
403 /// [Machine epsilon] value for `f64`.
404 ///
405 /// This is the difference between `1.0` and the next larger representable number.
406 ///
407 /// Equal to 2<sup>1&nbsp;&minus;&nbsp;[`MANTISSA_DIGITS`]</sup>.
408 ///
409 /// [Machine epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon
410 /// [`MANTISSA_DIGITS`]: f64::MANTISSA_DIGITS
411 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
412 pub const EPSILON: f64 = 2.2204460492503131e-16_f64;
413
414 /// Smallest finite `f64` value.
415 ///
416 /// Equal to &minus;[`MAX`].
417 ///
418 /// [`MAX`]: f64::MAX
419 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
420 pub const MIN: f64 = -1.7976931348623157e+308_f64;
421 /// Smallest positive normal `f64` value.
422 ///
423 /// Equal to 2<sup>[`MIN_EXP`]&nbsp;&minus;&nbsp;1</sup>.
424 ///
425 /// [`MIN_EXP`]: f64::MIN_EXP
426 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
427 pub const MIN_POSITIVE: f64 = 2.2250738585072014e-308_f64;
428 /// Largest finite `f64` value.
429 ///
430 /// Equal to
431 /// (1&nbsp;&minus;&nbsp;2<sup>&minus;[`MANTISSA_DIGITS`]</sup>)&nbsp;2<sup>[`MAX_EXP`]</sup>.
432 ///
433 /// [`MANTISSA_DIGITS`]: f64::MANTISSA_DIGITS
434 /// [`MAX_EXP`]: f64::MAX_EXP
435 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
436 pub const MAX: f64 = 1.7976931348623157e+308_f64;
437
438 /// One greater than the minimum possible normal power of 2 exponent.
439 ///
440 /// If <i>x</i>&nbsp;=&nbsp;`MIN_EXP`, then normal numbers
441 /// ≥&nbsp;0.5&nbsp;×&nbsp;2<sup><i>x</i></sup>.
442 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
443 pub const MIN_EXP: i32 = -1021;
444 /// Maximum possible power of 2 exponent.
445 ///
446 /// If <i>x</i>&nbsp;=&nbsp;`MAX_EXP`, then normal numbers
447 /// &lt;&nbsp;1&nbsp;×&nbsp;2<sup><i>x</i></sup>.
448 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
449 pub const MAX_EXP: i32 = 1024;
450
451 /// Minimum <i>x</i> for which 10<sup><i>x</i></sup> is normal.
452 ///
453 /// Equal to ceil(log<sub>10</sub>&nbsp;[`MIN_POSITIVE`]).
454 ///
455 /// [`MIN_POSITIVE`]: f64::MIN_POSITIVE
456 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
457 pub const MIN_10_EXP: i32 = -307;
458 /// Maximum <i>x</i> for which 10<sup><i>x</i></sup> is normal.
459 ///
460 /// Equal to floor(log<sub>10</sub>&nbsp;[`MAX`]).
461 ///
462 /// [`MAX`]: f64::MAX
463 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
464 pub const MAX_10_EXP: i32 = 308;
465
466 /// Not a Number (NaN).
467 ///
468 /// Note that IEEE 754 doesn't define just a single NaN value;
469 /// a plethora of bit patterns are considered to be NaN.
470 /// Furthermore, the standard makes a difference
471 /// between a "signaling" and a "quiet" NaN,
472 /// and allows inspecting its "payload" (the unspecified bits in the bit pattern).
473 /// This constant isn't guaranteed to equal to any specific NaN bitpattern,
474 /// and the stability of its representation over Rust versions
475 /// and target platforms isn't guaranteed.
476 #[rustc_diagnostic_item = "f64_nan"]
477 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
478 #[allow(clippy::eq_op)]
479 pub const NAN: f64 = 0.0_f64 / 0.0_f64;
480 /// Infinity (∞).
481 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
482 pub const INFINITY: f64 = 1.0_f64 / 0.0_f64;
483 /// Negative infinity (−∞).
484 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
485 pub const NEG_INFINITY: f64 = -1.0_f64 / 0.0_f64;
486
487 /// Returns `true` if this value is NaN.
488 ///
489 /// ```
490 /// let nan = f64::NAN;
491 /// let f = 7.0_f64;
492 ///
493 /// assert!(nan.is_nan());
494 /// assert!(!f.is_nan());
495 /// ```
496 #[must_use]
497 #[stable(feature = "rust1", since = "1.0.0")]
498 #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
499 #[inline]
500 #[allow(clippy::eq_op)] // > if you intended to check if the operand is NaN, use `.is_nan()` instead :)
501 pub const fn is_nan(self) -> bool {
502 self != self
503 }
504
505 // FIXME(#50145): `abs` is publicly unavailable in core due to
506 // concerns about portability, so this implementation is for
507 // private use internally.
508 #[inline]
509 #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
510 pub(crate) const fn abs_private(self) -> f64 {
511 // SAFETY: This transmutation is fine. Probably. For the reasons std is using it.
512 unsafe {
513 mem::transmute::<u64, f64>(mem::transmute::<f64, u64>(self) & 0x7fff_ffff_ffff_ffff)
514 }
515 }
516
517 /// Returns `true` if this value is positive infinity or negative infinity, and
518 /// `false` otherwise.
519 ///
520 /// ```
521 /// let f = 7.0f64;
522 /// let inf = f64::INFINITY;
523 /// let neg_inf = f64::NEG_INFINITY;
524 /// let nan = f64::NAN;
525 ///
526 /// assert!(!f.is_infinite());
527 /// assert!(!nan.is_infinite());
528 ///
529 /// assert!(inf.is_infinite());
530 /// assert!(neg_inf.is_infinite());
531 /// ```
532 #[must_use]
533 #[stable(feature = "rust1", since = "1.0.0")]
534 #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
535 #[inline]
536 pub const fn is_infinite(self) -> bool {
537 // Getting clever with transmutation can result in incorrect answers on some FPUs
538 // FIXME: alter the Rust <-> Rust calling convention to prevent this problem.
539 // See https://github.com/rust-lang/rust/issues/72327
540 (self == f64::INFINITY) | (self == f64::NEG_INFINITY)
541 }
542
543 /// Returns `true` if this number is neither infinite nor NaN.
544 ///
545 /// ```
546 /// let f = 7.0f64;
547 /// let inf: f64 = f64::INFINITY;
548 /// let neg_inf: f64 = f64::NEG_INFINITY;
549 /// let nan: f64 = f64::NAN;
550 ///
551 /// assert!(f.is_finite());
552 ///
553 /// assert!(!nan.is_finite());
554 /// assert!(!inf.is_finite());
555 /// assert!(!neg_inf.is_finite());
556 /// ```
557 #[must_use]
558 #[stable(feature = "rust1", since = "1.0.0")]
559 #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
560 #[inline]
561 pub const fn is_finite(self) -> bool {
562 // There's no need to handle NaN separately: if self is NaN,
563 // the comparison is not true, exactly as desired.
564 self.abs_private() < Self::INFINITY
565 }
566
567 /// Returns `true` if the number is [subnormal].
568 ///
569 /// ```
570 /// let min = f64::MIN_POSITIVE; // 2.2250738585072014e-308_f64
571 /// let max = f64::MAX;
572 /// let lower_than_min = 1.0e-308_f64;
573 /// let zero = 0.0_f64;
574 ///
575 /// assert!(!min.is_subnormal());
576 /// assert!(!max.is_subnormal());
577 ///
578 /// assert!(!zero.is_subnormal());
579 /// assert!(!f64::NAN.is_subnormal());
580 /// assert!(!f64::INFINITY.is_subnormal());
581 /// // Values between `0` and `min` are Subnormal.
582 /// assert!(lower_than_min.is_subnormal());
583 /// ```
584 /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
585 #[must_use]
586 #[stable(feature = "is_subnormal", since = "1.53.0")]
587 #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
588 #[inline]
589 pub const fn is_subnormal(self) -> bool {
590 matches!(self.classify(), FpCategory::Subnormal)
591 }
592
593 /// Returns `true` if the number is neither zero, infinite,
594 /// [subnormal], or NaN.
595 ///
596 /// ```
597 /// let min = f64::MIN_POSITIVE; // 2.2250738585072014e-308f64
598 /// let max = f64::MAX;
599 /// let lower_than_min = 1.0e-308_f64;
600 /// let zero = 0.0f64;
601 ///
602 /// assert!(min.is_normal());
603 /// assert!(max.is_normal());
604 ///
605 /// assert!(!zero.is_normal());
606 /// assert!(!f64::NAN.is_normal());
607 /// assert!(!f64::INFINITY.is_normal());
608 /// // Values between `0` and `min` are Subnormal.
609 /// assert!(!lower_than_min.is_normal());
610 /// ```
611 /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
612 #[must_use]
613 #[stable(feature = "rust1", since = "1.0.0")]
614 #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
615 #[inline]
616 pub const fn is_normal(self) -> bool {
617 matches!(self.classify(), FpCategory::Normal)
618 }
619
620 /// Returns the floating point category of the number. If only one property
621 /// is going to be tested, it is generally faster to use the specific
622 /// predicate instead.
623 ///
624 /// ```
625 /// use std::num::FpCategory;
626 ///
627 /// let num = 12.4_f64;
628 /// let inf = f64::INFINITY;
629 ///
630 /// assert_eq!(num.classify(), FpCategory::Normal);
631 /// assert_eq!(inf.classify(), FpCategory::Infinite);
632 /// ```
633 #[stable(feature = "rust1", since = "1.0.0")]
634 #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
635 pub const fn classify(self) -> FpCategory {
636 // A previous implementation tried to only use bitmask-based checks,
637 // using f64::to_bits to transmute the float to its bit repr and match on that.
638 // Unfortunately, floating point numbers can be much worse than that.
639 // This also needs to not result in recursive evaluations of f64::to_bits.
640 //
641 // On some processors, in some cases, LLVM will "helpfully" lower floating point ops,
642 // in spite of a request for them using f32 and f64, to things like x87 operations.
643 // These have an f64's mantissa, but can have a larger than normal exponent.
644 // FIXME(jubilee): Using x87 operations is never necessary in order to function
645 // on x86 processors for Rust-to-Rust calls, so this issue should not happen.
646 // Code generation should be adjusted to use non-C calling conventions, avoiding this.
647 //
648 // Thus, a value may compare unequal to infinity, despite having a "full" exponent mask.
649 // And it may not be NaN, as it can simply be an "overextended" finite value.
650 if self.is_nan() {
651 FpCategory::Nan
652 } else {
653 // However, std can't simply compare to zero to check for zero, either,
654 // as correctness requires avoiding equality tests that may be Subnormal == -0.0
655 // because it may be wrong under "denormals are zero" and "flush to zero" modes.
656 // Most of std's targets don't use those, but they are used for thumbv7neon.
657 // So, this does use bitpattern matching for the rest.
658
659 // SAFETY: f64 to u64 is fine. Usually.
660 // If control flow has gotten this far, the value is definitely in one of the categories
661 // that f64::partial_classify can correctly analyze.
662 unsafe { f64::partial_classify(self) }
663 }
664 }
665
666 // This doesn't actually return a right answer for NaN on purpose,
667 // seeing as how it cannot correctly discern between a floating point NaN,
668 // and some normal floating point numbers truncated from an x87 FPU.
669 #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
670 const unsafe fn partial_classify(self) -> FpCategory {
671 const EXP_MASK: u64 = 0x7ff0000000000000;
672 const MAN_MASK: u64 = 0x000fffffffffffff;
673
674 // SAFETY: The caller is not asking questions for which this will tell lies.
675 let b = unsafe { mem::transmute::<f64, u64>(self) };
676 match (b & MAN_MASK, b & EXP_MASK) {
677 (0, EXP_MASK) => FpCategory::Infinite,
678 (0, 0) => FpCategory::Zero,
679 (_, 0) => FpCategory::Subnormal,
680 _ => FpCategory::Normal,
681 }
682 }
683
684 // This operates on bits, and only bits, so it can ignore concerns about weird FPUs.
685 // FIXME(jubilee): In a just world, this would be the entire impl for classify,
686 // plus a transmute. We do not live in a just world, but we can make it more so.
687 #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
688 const fn classify_bits(b: u64) -> FpCategory {
689 const EXP_MASK: u64 = 0x7ff0000000000000;
690 const MAN_MASK: u64 = 0x000fffffffffffff;
691
692 match (b & MAN_MASK, b & EXP_MASK) {
693 (0, EXP_MASK) => FpCategory::Infinite,
694 (_, EXP_MASK) => FpCategory::Nan,
695 (0, 0) => FpCategory::Zero,
696 (_, 0) => FpCategory::Subnormal,
697 _ => FpCategory::Normal,
698 }
699 }
700
701 /// Returns `true` if `self` has a positive sign, including `+0.0`, NaNs with
702 /// positive sign bit and positive infinity. Note that IEEE 754 doesn't assign any
703 /// meaning to the sign bit in case of a NaN, and as Rust doesn't guarantee that
704 /// the bit pattern of NaNs are conserved over arithmetic operations, the result of
705 /// `is_sign_positive` on a NaN might produce an unexpected result in some cases.
706 /// See [explanation of NaN as a special value](f32) for more info.
707 ///
708 /// ```
709 /// let f = 7.0_f64;
710 /// let g = -7.0_f64;
711 ///
712 /// assert!(f.is_sign_positive());
713 /// assert!(!g.is_sign_positive());
714 /// ```
715 #[must_use]
716 #[stable(feature = "rust1", since = "1.0.0")]
717 #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
718 #[inline]
719 pub const fn is_sign_positive(self) -> bool {
720 !self.is_sign_negative()
721 }
722
723 #[must_use]
724 #[stable(feature = "rust1", since = "1.0.0")]
725 #[deprecated(since = "1.0.0", note = "renamed to is_sign_positive")]
726 #[inline]
727 #[doc(hidden)]
728 pub fn is_positive(self) -> bool {
729 self.is_sign_positive()
730 }
731
732 /// Returns `true` if `self` has a negative sign, including `-0.0`, NaNs with
733 /// negative sign bit and negative infinity. Note that IEEE 754 doesn't assign any
734 /// meaning to the sign bit in case of a NaN, and as Rust doesn't guarantee that
735 /// the bit pattern of NaNs are conserved over arithmetic operations, the result of
736 /// `is_sign_negative` on a NaN might produce an unexpected result in some cases.
737 /// See [explanation of NaN as a special value](f32) for more info.
738 ///
739 /// ```
740 /// let f = 7.0_f64;
741 /// let g = -7.0_f64;
742 ///
743 /// assert!(!f.is_sign_negative());
744 /// assert!(g.is_sign_negative());
745 /// ```
746 #[must_use]
747 #[stable(feature = "rust1", since = "1.0.0")]
748 #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
749 #[inline]
750 pub const fn is_sign_negative(self) -> bool {
751 // IEEE754 says: isSignMinus(x) is true if and only if x has negative sign. isSignMinus
752 // applies to zeros and NaNs as well.
753 // SAFETY: This is just transmuting to get the sign bit, it's fine.
754 unsafe { mem::transmute::<f64, u64>(self) & 0x8000_0000_0000_0000 != 0 }
755 }
756
757 #[must_use]
758 #[stable(feature = "rust1", since = "1.0.0")]
759 #[deprecated(since = "1.0.0", note = "renamed to is_sign_negative")]
760 #[inline]
761 #[doc(hidden)]
762 pub fn is_negative(self) -> bool {
763 self.is_sign_negative()
764 }
765
766 /// Returns the least number greater than `self`.
767 ///
768 /// Let `TINY` be the smallest representable positive `f64`. Then,
769 /// - if `self.is_nan()`, this returns `self`;
770 /// - if `self` is [`NEG_INFINITY`], this returns [`MIN`];
771 /// - if `self` is `-TINY`, this returns -0.0;
772 /// - if `self` is -0.0 or +0.0, this returns `TINY`;
773 /// - if `self` is [`MAX`] or [`INFINITY`], this returns [`INFINITY`];
774 /// - otherwise the unique least value greater than `self` is returned.
775 ///
776 /// The identity `x.next_up() == -(-x).next_down()` holds for all non-NaN `x`. When `x`
777 /// is finite `x == x.next_up().next_down()` also holds.
778 ///
779 /// ```rust
780 /// #![feature(float_next_up_down)]
781 /// // f64::EPSILON is the difference between 1.0 and the next number up.
782 /// assert_eq!(1.0f64.next_up(), 1.0 + f64::EPSILON);
783 /// // But not for most numbers.
784 /// assert!(0.1f64.next_up() < 0.1 + f64::EPSILON);
785 /// assert_eq!(9007199254740992f64.next_up(), 9007199254740994.0);
786 /// ```
787 ///
788 /// [`NEG_INFINITY`]: Self::NEG_INFINITY
789 /// [`INFINITY`]: Self::INFINITY
790 /// [`MIN`]: Self::MIN
791 /// [`MAX`]: Self::MAX
792 #[unstable(feature = "float_next_up_down", issue = "91399")]
793 #[rustc_const_unstable(feature = "float_next_up_down", issue = "91399")]
794 pub const fn next_up(self) -> Self {
795 // We must use strictly integer arithmetic to prevent denormals from
796 // flushing to zero after an arithmetic operation on some platforms.
797 const TINY_BITS: u64 = 0x1; // Smallest positive f64.
798 const CLEAR_SIGN_MASK: u64 = 0x7fff_ffff_ffff_ffff;
799
800 let bits = self.to_bits();
801 if self.is_nan() || bits == Self::INFINITY.to_bits() {
802 return self;
803 }
804
805 let abs = bits & CLEAR_SIGN_MASK;
806 let next_bits = if abs == 0 {
807 TINY_BITS
808 } else if bits == abs {
809 bits + 1
810 } else {
811 bits - 1
812 };
813 Self::from_bits(next_bits)
814 }
815
816 /// Returns the greatest number less than `self`.
817 ///
818 /// Let `TINY` be the smallest representable positive `f64`. Then,
819 /// - if `self.is_nan()`, this returns `self`;
820 /// - if `self` is [`INFINITY`], this returns [`MAX`];
821 /// - if `self` is `TINY`, this returns 0.0;
822 /// - if `self` is -0.0 or +0.0, this returns `-TINY`;
823 /// - if `self` is [`MIN`] or [`NEG_INFINITY`], this returns [`NEG_INFINITY`];
824 /// - otherwise the unique greatest value less than `self` is returned.
825 ///
826 /// The identity `x.next_down() == -(-x).next_up()` holds for all non-NaN `x`. When `x`
827 /// is finite `x == x.next_down().next_up()` also holds.
828 ///
829 /// ```rust
830 /// #![feature(float_next_up_down)]
831 /// let x = 1.0f64;
832 /// // Clamp value into range [0, 1).
833 /// let clamped = x.clamp(0.0, 1.0f64.next_down());
834 /// assert!(clamped < 1.0);
835 /// assert_eq!(clamped.next_up(), 1.0);
836 /// ```
837 ///
838 /// [`NEG_INFINITY`]: Self::NEG_INFINITY
839 /// [`INFINITY`]: Self::INFINITY
840 /// [`MIN`]: Self::MIN
841 /// [`MAX`]: Self::MAX
842 #[unstable(feature = "float_next_up_down", issue = "91399")]
843 #[rustc_const_unstable(feature = "float_next_up_down", issue = "91399")]
844 pub const fn next_down(self) -> Self {
845 // We must use strictly integer arithmetic to prevent denormals from
846 // flushing to zero after an arithmetic operation on some platforms.
847 const NEG_TINY_BITS: u64 = 0x8000_0000_0000_0001; // Smallest (in magnitude) negative f64.
848 const CLEAR_SIGN_MASK: u64 = 0x7fff_ffff_ffff_ffff;
849
850 let bits = self.to_bits();
851 if self.is_nan() || bits == Self::NEG_INFINITY.to_bits() {
852 return self;
853 }
854
855 let abs = bits & CLEAR_SIGN_MASK;
856 let next_bits = if abs == 0 {
857 NEG_TINY_BITS
858 } else if bits == abs {
859 bits - 1
860 } else {
861 bits + 1
862 };
863 Self::from_bits(next_bits)
864 }
865
866 /// Takes the reciprocal (inverse) of a number, `1/x`.
867 ///
868 /// ```
869 /// let x = 2.0_f64;
870 /// let abs_difference = (x.recip() - (1.0 / x)).abs();
871 ///
872 /// assert!(abs_difference < 1e-10);
873 /// ```
874 #[must_use = "this returns the result of the operation, without modifying the original"]
875 #[stable(feature = "rust1", since = "1.0.0")]
876 #[inline]
877 pub fn recip(self) -> f64 {
878 1.0 / self
879 }
880
881 /// Converts radians to degrees.
882 ///
883 /// ```
884 /// let angle = std::f64::consts::PI;
885 ///
886 /// let abs_difference = (angle.to_degrees() - 180.0).abs();
887 ///
888 /// assert!(abs_difference < 1e-10);
889 /// ```
890 #[must_use = "this returns the result of the operation, \
891 without modifying the original"]
892 #[stable(feature = "rust1", since = "1.0.0")]
893 #[inline]
894 pub fn to_degrees(self) -> f64 {
895 // The division here is correctly rounded with respect to the true
896 // value of 180/π. (This differs from f32, where a constant must be
897 // used to ensure a correctly rounded result.)
898 self * (180.0f64 / consts::PI)
899 }
900
901 /// Converts degrees to radians.
902 ///
903 /// ```
904 /// let angle = 180.0_f64;
905 ///
906 /// let abs_difference = (angle.to_radians() - std::f64::consts::PI).abs();
907 ///
908 /// assert!(abs_difference < 1e-10);
909 /// ```
910 #[must_use = "this returns the result of the operation, \
911 without modifying the original"]
912 #[stable(feature = "rust1", since = "1.0.0")]
913 #[inline]
914 pub fn to_radians(self) -> f64 {
915 let value: f64 = consts::PI;
916 self * (value / 180.0)
917 }
918
919 /// Returns the maximum 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 maxNum, except for handling of signaling NaNs;
923 /// this function handles all NaNs the same way and avoids maxNum's problems with associativity.
924 /// This also matches the behavior of libm’s fmax.
925 ///
926 /// ```
927 /// let x = 1.0_f64;
928 /// let y = 2.0_f64;
929 ///
930 /// assert_eq!(x.max(y), y);
931 /// ```
932 #[must_use = "this returns the result of the comparison, without modifying either input"]
933 #[stable(feature = "rust1", since = "1.0.0")]
934 #[inline]
935 pub fn max(self, other: f64) -> f64 {
936 intrinsics::maxnumf64(self, other)
937 }
938
939 /// Returns the minimum of the two numbers, ignoring NaN.
940 ///
941 /// If one of the arguments is NaN, then the other argument is returned.
942 /// This follows the IEEE 754-2008 semantics for minNum, except for handling of signaling NaNs;
943 /// this function handles all NaNs the same way and avoids minNum's problems with associativity.
944 /// This also matches the behavior of libm’s fmin.
945 ///
946 /// ```
947 /// let x = 1.0_f64;
948 /// let y = 2.0_f64;
949 ///
950 /// assert_eq!(x.min(y), x);
951 /// ```
952 #[must_use = "this returns the result of the comparison, without modifying either input"]
953 #[stable(feature = "rust1", since = "1.0.0")]
954 #[inline]
955 pub fn min(self, other: f64) -> f64 {
956 intrinsics::minnumf64(self, other)
957 }
958
959 /// Returns the maximum of the two numbers, propagating NaN.
960 ///
961 /// This returns NaN when *either* argument is NaN, as opposed to
962 /// [`f64::max`] which only returns NaN when *both* arguments are NaN.
963 ///
964 /// ```
965 /// #![feature(float_minimum_maximum)]
966 /// let x = 1.0_f64;
967 /// let y = 2.0_f64;
968 ///
969 /// assert_eq!(x.maximum(y), y);
970 /// assert!(x.maximum(f64::NAN).is_nan());
971 /// ```
972 ///
973 /// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the greater
974 /// of the two numbers. For this operation, -0.0 is considered to be less than +0.0.
975 /// Note that this follows the semantics specified in IEEE 754-2019.
976 ///
977 /// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN
978 /// operand is conserved; see [explanation of NaN as a special value](f32) for more info.
979 #[must_use = "this returns the result of the comparison, without modifying either input"]
980 #[unstable(feature = "float_minimum_maximum", issue = "91079")]
981 #[inline]
982 pub fn maximum(self, other: f64) -> f64 {
983 if self > other {
984 self
985 } else if other > self {
986 other
987 } else if self == other {
988 if self.is_sign_positive() && other.is_sign_negative() { self } else { other }
989 } else {
990 self + other
991 }
992 }
993
994 /// Returns the minimum of the two numbers, propagating NaN.
995 ///
996 /// This returns NaN when *either* argument is NaN, as opposed to
997 /// [`f64::min`] which only returns NaN when *both* arguments are NaN.
998 ///
999 /// ```
1000 /// #![feature(float_minimum_maximum)]
1001 /// let x = 1.0_f64;
1002 /// let y = 2.0_f64;
1003 ///
1004 /// assert_eq!(x.minimum(y), x);
1005 /// assert!(x.minimum(f64::NAN).is_nan());
1006 /// ```
1007 ///
1008 /// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the lesser
1009 /// of the two numbers. For this operation, -0.0 is considered to be less than +0.0.
1010 /// Note that this follows the semantics specified in IEEE 754-2019.
1011 ///
1012 /// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN
1013 /// operand is conserved; see [explanation of NaN as a special value](f32) for more info.
1014 #[must_use = "this returns the result of the comparison, without modifying either input"]
1015 #[unstable(feature = "float_minimum_maximum", issue = "91079")]
1016 #[inline]
1017 pub fn minimum(self, other: f64) -> f64 {
1018 if self < other {
1019 self
1020 } else if other < self {
1021 other
1022 } else if self == other {
1023 if self.is_sign_negative() && other.is_sign_positive() { self } else { other }
1024 } else {
1025 // At least one input is NaN. Use `+` to perform NaN propagation and quieting.
1026 self + other
1027 }
1028 }
1029
1030 /// Calculates the middle point of `self` and `rhs`.
1031 ///
1032 /// This returns NaN when *either* argument is NaN or if a combination of
1033 /// +inf and -inf is provided as arguments.
1034 ///
1035 /// # Examples
1036 ///
1037 /// ```
1038 /// #![feature(num_midpoint)]
1039 /// assert_eq!(1f64.midpoint(4.0), 2.5);
1040 /// assert_eq!((-5.5f64).midpoint(8.0), 1.25);
1041 /// ```
1042 #[unstable(feature = "num_midpoint", issue = "110840")]
1043 pub fn midpoint(self, other: f64) -> f64 {
1044 const LO: f64 = f64::MIN_POSITIVE * 2.;
1045 const HI: f64 = f64::MAX / 2.;
1046
1047 let (a, b) = (self, other);
1048 let abs_a = a.abs_private();
1049 let abs_b = b.abs_private();
1050
1051 if abs_a <= HI && abs_b <= HI {
1052 // Overflow is impossible
1053 (a + b) / 2.
1054 } else if abs_a < LO {
1055 // Not safe to halve a
1056 a + (b / 2.)
1057 } else if abs_b < LO {
1058 // Not safe to halve b
1059 (a / 2.) + b
1060 } else {
1061 // Not safe to halve a and b
1062 (a / 2.) + (b / 2.)
1063 }
1064 }
1065
1066 /// Rounds toward zero and converts to any primitive integer type,
1067 /// assuming that the value is finite and fits in that type.
1068 ///
1069 /// ```
1070 /// let value = 4.6_f64;
1071 /// let rounded = unsafe { value.to_int_unchecked::<u16>() };
1072 /// assert_eq!(rounded, 4);
1073 ///
1074 /// let value = -128.9_f64;
1075 /// let rounded = unsafe { value.to_int_unchecked::<i8>() };
1076 /// assert_eq!(rounded, i8::MIN);
1077 /// ```
1078 ///
1079 /// # Safety
1080 ///
1081 /// The value must:
1082 ///
1083 /// * Not be `NaN`
1084 /// * Not be infinite
1085 /// * Be representable in the return type `Int`, after truncating off its fractional part
1086 #[must_use = "this returns the result of the operation, \
1087 without modifying the original"]
1088 #[stable(feature = "float_approx_unchecked_to", since = "1.44.0")]
1089 #[inline]
1090 pub unsafe fn to_int_unchecked<Int>(self) -> Int
1091 where
1092 Self: FloatToInt<Int>,
1093 {
1094 // SAFETY: the caller must uphold the safety contract for
1095 // `FloatToInt::to_int_unchecked`.
1096 unsafe { FloatToInt::<Int>::to_int_unchecked(self) }
1097 }
1098
1099 /// Raw transmutation to `u64`.
1100 ///
1101 /// This is currently identical to `transmute::<f64, u64>(self)` on all platforms.
1102 ///
1103 /// See [`from_bits`](Self::from_bits) for some discussion of the
1104 /// portability of this operation (there are almost no issues).
1105 ///
1106 /// Note that this function is distinct from `as` casting, which attempts to
1107 /// preserve the *numeric* value, and not the bitwise value.
1108 ///
1109 /// # Examples
1110 ///
1111 /// ```
1112 /// assert!((1f64).to_bits() != 1f64 as u64); // to_bits() is not casting!
1113 /// assert_eq!((12.5f64).to_bits(), 0x4029000000000000);
1114 ///
1115 /// ```
1116 #[must_use = "this returns the result of the operation, \
1117 without modifying the original"]
1118 #[stable(feature = "float_bits_conv", since = "1.20.0")]
1119 #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
1120 #[inline]
1121 pub const fn to_bits(self) -> u64 {
1122 // SAFETY: `u64` is a plain old datatype so we can always transmute to it.
1123 // ...sorta.
1124 //
1125 // See the SAFETY comment in f64::from_bits for more.
1126 #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
1127 const fn ct_f64_to_u64(ct: f64) -> u64 {
1128 match ct.classify() {
1129 FpCategory::Nan => {
1130 panic!("const-eval error: cannot use f64::to_bits on a NaN")
1131 }
1132 FpCategory::Subnormal => {
1133 panic!("const-eval error: cannot use f64::to_bits on a subnormal number")
1134 }
1135 FpCategory::Infinite | FpCategory::Normal | FpCategory::Zero => {
1136 // SAFETY: We have a normal floating point number. Now we transmute, i.e. do a bitcopy.
1137 unsafe { mem::transmute::<f64, u64>(ct) }
1138 }
1139 }
1140 }
1141
1142 #[inline(always)] // See https://github.com/rust-lang/compiler-builtins/issues/491
1143 fn rt_f64_to_u64(rt: f64) -> u64 {
1144 // SAFETY: `u64` is a plain old datatype so we can always... uh...
1145 // ...look, just pretend you forgot what you just read.
1146 // Stability concerns.
1147 unsafe { mem::transmute::<f64, u64>(rt) }
1148 }
1149 intrinsics::const_eval_select((self,), ct_f64_to_u64, rt_f64_to_u64)
1150 }
1151
1152 /// Raw transmutation from `u64`.
1153 ///
1154 /// This is currently identical to `transmute::<u64, f64>(v)` on all platforms.
1155 /// It turns out this is incredibly portable, for two reasons:
1156 ///
1157 /// * Floats and Ints have the same endianness on all supported platforms.
1158 /// * IEEE 754 very precisely specifies the bit layout of floats.
1159 ///
1160 /// However there is one caveat: prior to the 2008 version of IEEE 754, how
1161 /// to interpret the NaN signaling bit wasn't actually specified. Most platforms
1162 /// (notably x86 and ARM) picked the interpretation that was ultimately
1163 /// standardized in 2008, but some didn't (notably MIPS). As a result, all
1164 /// signaling NaNs on MIPS are quiet NaNs on x86, and vice-versa.
1165 ///
1166 /// Rather than trying to preserve signaling-ness cross-platform, this
1167 /// implementation favors preserving the exact bits. This means that
1168 /// any payloads encoded in NaNs will be preserved even if the result of
1169 /// this method is sent over the network from an x86 machine to a MIPS one.
1170 ///
1171 /// If the results of this method are only manipulated by the same
1172 /// architecture that produced them, then there is no portability concern.
1173 ///
1174 /// If the input isn't NaN, then there is no portability concern.
1175 ///
1176 /// If you don't care about signaling-ness (very likely), then there is no
1177 /// portability concern.
1178 ///
1179 /// Note that this function is distinct from `as` casting, which attempts to
1180 /// preserve the *numeric* value, and not the bitwise value.
1181 ///
1182 /// # Examples
1183 ///
1184 /// ```
1185 /// let v = f64::from_bits(0x4029000000000000);
1186 /// assert_eq!(v, 12.5);
1187 /// ```
1188 #[stable(feature = "float_bits_conv", since = "1.20.0")]
1189 #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
1190 #[must_use]
1191 #[inline]
1192 pub const fn from_bits(v: u64) -> Self {
1193 // It turns out the safety issues with sNaN were overblown! Hooray!
1194 // SAFETY: `u64` is a plain old datatype so we can always transmute from it
1195 // ...sorta.
1196 //
1197 // It turns out that at runtime, it is possible for a floating point number
1198 // to be subject to floating point modes that alter nonzero subnormal numbers
1199 // to zero on reads and writes, aka "denormals are zero" and "flush to zero".
1200 // This is not a problem usually, but at least one tier2 platform for Rust
1201 // actually exhibits an FTZ behavior by default: thumbv7neon
1202 // aka "the Neon FPU in AArch32 state"
1203 //
1204 // Even with this, not all instructions exhibit the FTZ behaviors on thumbv7neon,
1205 // so this should load the same bits if LLVM emits the "correct" instructions,
1206 // but LLVM sometimes makes interesting choices about float optimization,
1207 // and other FPUs may do similar. Thus, it is wise to indulge luxuriously in caution.
1208 //
1209 // In addition, on x86 targets with SSE or SSE2 disabled and the x87 FPU enabled,
1210 // i.e. not soft-float, the way Rust does parameter passing can actually alter
1211 // a number that is "not infinity" to have the same exponent as infinity,
1212 // in a slightly unpredictable manner.
1213 //
1214 // And, of course evaluating to a NaN value is fairly nondeterministic.
1215 // More precisely: when NaN should be returned is knowable, but which NaN?
1216 // So far that's defined by a combination of LLVM and the CPU, not Rust.
1217 // This function, however, allows observing the bitstring of a NaN,
1218 // thus introspection on CTFE.
1219 //
1220 // In order to preserve, at least for the moment, const-to-runtime equivalence,
1221 // reject any of these possible situations from happening.
1222 #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
1223 const fn ct_u64_to_f64(ct: u64) -> f64 {
1224 match f64::classify_bits(ct) {
1225 FpCategory::Subnormal => {
1226 panic!("const-eval error: cannot use f64::from_bits on a subnormal number")
1227 }
1228 FpCategory::Nan => {
1229 panic!("const-eval error: cannot use f64::from_bits on NaN")
1230 }
1231 FpCategory::Infinite | FpCategory::Normal | FpCategory::Zero => {
1232 // SAFETY: It's not a frumious number
1233 unsafe { mem::transmute::<u64, f64>(ct) }
1234 }
1235 }
1236 }
1237
1238 #[inline(always)] // See https://github.com/rust-lang/compiler-builtins/issues/491
1239 fn rt_u64_to_f64(rt: u64) -> f64 {
1240 // SAFETY: `u64` is a plain old datatype so we can always... uh...
1241 // ...look, just pretend you forgot what you just read.
1242 // Stability concerns.
1243 unsafe { mem::transmute::<u64, f64>(rt) }
1244 }
1245 intrinsics::const_eval_select((v,), ct_u64_to_f64, rt_u64_to_f64)
1246 }
1247
1248 /// Return the memory representation of this floating point number as a byte array in
1249 /// big-endian (network) byte order.
1250 ///
1251 /// See [`from_bits`](Self::from_bits) for some discussion of the
1252 /// portability of this operation (there are almost no issues).
1253 ///
1254 /// # Examples
1255 ///
1256 /// ```
1257 /// let bytes = 12.5f64.to_be_bytes();
1258 /// assert_eq!(bytes, [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]);
1259 /// ```
1260 #[must_use = "this returns the result of the operation, \
1261 without modifying the original"]
1262 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1263 #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
1264 #[inline]
1265 pub const fn to_be_bytes(self) -> [u8; 8] {
1266 self.to_bits().to_be_bytes()
1267 }
1268
1269 /// Return the memory representation of this floating point number as a byte array in
1270 /// little-endian byte order.
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 bytes = 12.5f64.to_le_bytes();
1279 /// assert_eq!(bytes, [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]);
1280 /// ```
1281 #[must_use = "this returns the result of the operation, \
1282 without modifying the original"]
1283 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1284 #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
1285 #[inline]
1286 pub const fn to_le_bytes(self) -> [u8; 8] {
1287 self.to_bits().to_le_bytes()
1288 }
1289
1290 /// Return the memory representation of this floating point number as a byte array in
1291 /// native byte order.
1292 ///
1293 /// As the target platform's native endianness is used, portable code
1294 /// should use [`to_be_bytes`] or [`to_le_bytes`], as appropriate, instead.
1295 ///
1296 /// [`to_be_bytes`]: f64::to_be_bytes
1297 /// [`to_le_bytes`]: f64::to_le_bytes
1298 ///
1299 /// See [`from_bits`](Self::from_bits) for some discussion of the
1300 /// portability of this operation (there are almost no issues).
1301 ///
1302 /// # Examples
1303 ///
1304 /// ```
1305 /// let bytes = 12.5f64.to_ne_bytes();
1306 /// assert_eq!(
1307 /// bytes,
1308 /// if cfg!(target_endian = "big") {
1309 /// [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
1310 /// } else {
1311 /// [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]
1312 /// }
1313 /// );
1314 /// ```
1315 #[must_use = "this returns the result of the operation, \
1316 without modifying the original"]
1317 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1318 #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
1319 #[inline]
1320 pub const fn to_ne_bytes(self) -> [u8; 8] {
1321 self.to_bits().to_ne_bytes()
1322 }
1323
1324 /// Create a floating point value from its representation as a byte array in big endian.
1325 ///
1326 /// See [`from_bits`](Self::from_bits) for some discussion of the
1327 /// portability of this operation (there are almost no issues).
1328 ///
1329 /// # Examples
1330 ///
1331 /// ```
1332 /// let value = f64::from_be_bytes([0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]);
1333 /// assert_eq!(value, 12.5);
1334 /// ```
1335 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1336 #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
1337 #[must_use]
1338 #[inline]
1339 pub const fn from_be_bytes(bytes: [u8; 8]) -> Self {
1340 Self::from_bits(u64::from_be_bytes(bytes))
1341 }
1342
1343 /// Create a floating point value from its representation as a byte array in little endian.
1344 ///
1345 /// See [`from_bits`](Self::from_bits) for some discussion of the
1346 /// portability of this operation (there are almost no issues).
1347 ///
1348 /// # Examples
1349 ///
1350 /// ```
1351 /// let value = f64::from_le_bytes([0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]);
1352 /// assert_eq!(value, 12.5);
1353 /// ```
1354 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1355 #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
1356 #[must_use]
1357 #[inline]
1358 pub const fn from_le_bytes(bytes: [u8; 8]) -> Self {
1359 Self::from_bits(u64::from_le_bytes(bytes))
1360 }
1361
1362 /// Create a floating point value from its representation as a byte array in native endian.
1363 ///
1364 /// As the target platform's native endianness is used, portable code
1365 /// likely wants to use [`from_be_bytes`] or [`from_le_bytes`], as
1366 /// appropriate instead.
1367 ///
1368 /// [`from_be_bytes`]: f64::from_be_bytes
1369 /// [`from_le_bytes`]: f64::from_le_bytes
1370 ///
1371 /// See [`from_bits`](Self::from_bits) for some discussion of the
1372 /// portability of this operation (there are almost no issues).
1373 ///
1374 /// # Examples
1375 ///
1376 /// ```
1377 /// let value = f64::from_ne_bytes(if cfg!(target_endian = "big") {
1378 /// [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
1379 /// } else {
1380 /// [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]
1381 /// });
1382 /// assert_eq!(value, 12.5);
1383 /// ```
1384 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1385 #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
1386 #[must_use]
1387 #[inline]
1388 pub const fn from_ne_bytes(bytes: [u8; 8]) -> Self {
1389 Self::from_bits(u64::from_ne_bytes(bytes))
1390 }
1391
1392 /// Return the ordering between `self` and `other`.
1393 ///
1394 /// Unlike the standard partial comparison between floating point numbers,
1395 /// this comparison always produces an ordering in accordance to
1396 /// the `totalOrder` predicate as defined in the IEEE 754 (2008 revision)
1397 /// floating point standard. The values are ordered in the following sequence:
1398 ///
1399 /// - negative quiet NaN
1400 /// - negative signaling NaN
1401 /// - negative infinity
1402 /// - negative numbers
1403 /// - negative subnormal numbers
1404 /// - negative zero
1405 /// - positive zero
1406 /// - positive subnormal numbers
1407 /// - positive numbers
1408 /// - positive infinity
1409 /// - positive signaling NaN
1410 /// - positive quiet NaN.
1411 ///
1412 /// The ordering established by this function does not always agree with the
1413 /// [`PartialOrd`] and [`PartialEq`] implementations of `f64`. For example,
1414 /// they consider negative and positive zero equal, while `total_cmp`
1415 /// doesn't.
1416 ///
1417 /// The interpretation of the signaling NaN bit follows the definition in
1418 /// the IEEE 754 standard, which may not match the interpretation by some of
1419 /// the older, non-conformant (e.g. MIPS) hardware implementations.
1420 ///
1421 /// # Example
1422 ///
1423 /// ```
1424 /// struct GoodBoy {
1425 /// name: String,
1426 /// weight: f64,
1427 /// }
1428 ///
1429 /// let mut bois = vec![
1430 /// GoodBoy { name: "Pucci".to_owned(), weight: 0.1 },
1431 /// GoodBoy { name: "Woofer".to_owned(), weight: 99.0 },
1432 /// GoodBoy { name: "Yapper".to_owned(), weight: 10.0 },
1433 /// GoodBoy { name: "Chonk".to_owned(), weight: f64::INFINITY },
1434 /// GoodBoy { name: "Abs. Unit".to_owned(), weight: f64::NAN },
1435 /// GoodBoy { name: "Floaty".to_owned(), weight: -5.0 },
1436 /// ];
1437 ///
1438 /// bois.sort_by(|a, b| a.weight.total_cmp(&b.weight));
1439 ///
1440 /// // `f64::NAN` could be positive or negative, which will affect the sort order.
1441 /// if f64::NAN.is_sign_negative() {
1442 /// assert!(bois.into_iter().map(|b| b.weight)
1443 /// .zip([f64::NAN, -5.0, 0.1, 10.0, 99.0, f64::INFINITY].iter())
1444 /// .all(|(a, b)| a.to_bits() == b.to_bits()))
1445 /// } else {
1446 /// assert!(bois.into_iter().map(|b| b.weight)
1447 /// .zip([-5.0, 0.1, 10.0, 99.0, f64::INFINITY, f64::NAN].iter())
1448 /// .all(|(a, b)| a.to_bits() == b.to_bits()))
1449 /// }
1450 /// ```
1451 #[stable(feature = "total_cmp", since = "1.62.0")]
1452 #[must_use]
1453 #[inline]
1454 pub fn total_cmp(&self, other: &Self) -> crate::cmp::Ordering {
1455 let mut left = self.to_bits() as i64;
1456 let mut right = other.to_bits() as i64;
1457
1458 // In case of negatives, flip all the bits except the sign
1459 // to achieve a similar layout as two's complement integers
1460 //
1461 // Why does this work? IEEE 754 floats consist of three fields:
1462 // Sign bit, exponent and mantissa. The set of exponent and mantissa
1463 // fields as a whole have the property that their bitwise order is
1464 // equal to the numeric magnitude where the magnitude is defined.
1465 // The magnitude is not normally defined on NaN values, but
1466 // IEEE 754 totalOrder defines the NaN values also to follow the
1467 // bitwise order. This leads to order explained in the doc comment.
1468 // However, the representation of magnitude is the same for negative
1469 // and positive numbers – only the sign bit is different.
1470 // To easily compare the floats as signed integers, we need to
1471 // flip the exponent and mantissa bits in case of negative numbers.
1472 // We effectively convert the numbers to "two's complement" form.
1473 //
1474 // To do the flipping, we construct a mask and XOR against it.
1475 // We branchlessly calculate an "all-ones except for the sign bit"
1476 // mask from negative-signed values: right shifting sign-extends
1477 // the integer, so we "fill" the mask with sign bits, and then
1478 // convert to unsigned to push one more zero bit.
1479 // On positive values, the mask is all zeros, so it's a no-op.
1480 left ^= (((left >> 63) as u64) >> 1) as i64;
1481 right ^= (((right >> 63) as u64) >> 1) as i64;
1482
1483 left.cmp(&right)
1484 }
1485
1486 /// Restrict a value to a certain interval unless it is NaN.
1487 ///
1488 /// Returns `max` if `self` is greater than `max`, and `min` if `self` is
1489 /// less than `min`. Otherwise this returns `self`.
1490 ///
1491 /// Note that this function returns NaN if the initial value was NaN as
1492 /// well.
1493 ///
1494 /// # Panics
1495 ///
1496 /// Panics if `min > max`, `min` is NaN, or `max` is NaN.
1497 ///
1498 /// # Examples
1499 ///
1500 /// ```
1501 /// assert!((-3.0f64).clamp(-2.0, 1.0) == -2.0);
1502 /// assert!((0.0f64).clamp(-2.0, 1.0) == 0.0);
1503 /// assert!((2.0f64).clamp(-2.0, 1.0) == 1.0);
1504 /// assert!((f64::NAN).clamp(-2.0, 1.0).is_nan());
1505 /// ```
1506 #[must_use = "method returns a new number and does not mutate the original value"]
1507 #[stable(feature = "clamp", since = "1.50.0")]
1508 #[inline]
1509 pub fn clamp(mut self, min: f64, max: f64) -> f64 {
1510 assert!(min <= max, "min > max, or either was NaN. min = {min:?}, max = {max:?}");
1511 if self < min {
1512 self = min;
1513 }
1514 if self > max {
1515 self = max;
1516 }
1517 self
1518 }
1519}
1520