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;
15use crate::num::FpCategory;
16use crate::panic::const_assert;
17use crate::{intrinsics, mem};
18
19/// The radix or base of the internal representation of `f64`.
20/// Use [`f64::RADIX`] instead.
21///
22/// # Examples
23///
24/// ```rust
25/// // deprecated way
26/// # #[allow(deprecated, deprecated_in_future)]
27/// let r = std::f64::RADIX;
28///
29/// // intended way
30/// let r = f64::RADIX;
31/// ```
32#[stable(feature = "rust1", since = "1.0.0")]
33#[deprecated(since = "TBD", note = "replaced by the `RADIX` associated constant on `f64`")]
34#[rustc_diagnostic_item = "f64_legacy_const_radix"]
35pub const RADIX: u32 = f64::RADIX;
36
37/// Number of significant digits in base 2.
38/// Use [`f64::MANTISSA_DIGITS`] instead.
39///
40/// # Examples
41///
42/// ```rust
43/// // deprecated way
44/// # #[allow(deprecated, deprecated_in_future)]
45/// let d = std::f64::MANTISSA_DIGITS;
46///
47/// // intended way
48/// let d = f64::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 `f64`"
54)]
55#[rustc_diagnostic_item = "f64_legacy_const_mantissa_dig"]
56pub const MANTISSA_DIGITS: u32 = f64::MANTISSA_DIGITS;
57
58/// Approximate number of significant digits in base 10.
59/// Use [`f64::DIGITS`] instead.
60///
61/// # Examples
62///
63/// ```rust
64/// // deprecated way
65/// # #[allow(deprecated, deprecated_in_future)]
66/// let d = std::f64::DIGITS;
67///
68/// // intended way
69/// let d = f64::DIGITS;
70/// ```
71#[stable(feature = "rust1", since = "1.0.0")]
72#[deprecated(since = "TBD", note = "replaced by the `DIGITS` associated constant on `f64`")]
73#[rustc_diagnostic_item = "f64_legacy_const_digits"]
74pub const DIGITS: u32 = f64::DIGITS;
75
76/// [Machine epsilon] value for `f64`.
77/// Use [`f64::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::f64::EPSILON;
89///
90/// // intended way
91/// let e = f64::EPSILON;
92/// ```
93#[stable(feature = "rust1", since = "1.0.0")]
94#[deprecated(since = "TBD", note = "replaced by the `EPSILON` associated constant on `f64`")]
95#[rustc_diagnostic_item = "f64_legacy_const_epsilon"]
96pub const EPSILON: f64 = f64::EPSILON;
97
98/// Smallest finite `f64` value.
99/// Use [`f64::MIN`] instead.
100///
101/// # Examples
102///
103/// ```rust
104/// // deprecated way
105/// # #[allow(deprecated, deprecated_in_future)]
106/// let min = std::f64::MIN;
107///
108/// // intended way
109/// let min = f64::MIN;
110/// ```
111#[stable(feature = "rust1", since = "1.0.0")]
112#[deprecated(since = "TBD", note = "replaced by the `MIN` associated constant on `f64`")]
113#[rustc_diagnostic_item = "f64_legacy_const_min"]
114pub const MIN: f64 = f64::MIN;
115
116/// Smallest positive normal `f64` value.
117/// Use [`f64::MIN_POSITIVE`] instead.
118///
119/// # Examples
120///
121/// ```rust
122/// // deprecated way
123/// # #[allow(deprecated, deprecated_in_future)]
124/// let min = std::f64::MIN_POSITIVE;
125///
126/// // intended way
127/// let min = f64::MIN_POSITIVE;
128/// ```
129#[stable(feature = "rust1", since = "1.0.0")]
130#[deprecated(since = "TBD", note = "replaced by the `MIN_POSITIVE` associated constant on `f64`")]
131#[rustc_diagnostic_item = "f64_legacy_const_min_positive"]
132pub const MIN_POSITIVE: f64 = f64::MIN_POSITIVE;
133
134/// Largest finite `f64` value.
135/// Use [`f64::MAX`] instead.
136///
137/// # Examples
138///
139/// ```rust
140/// // deprecated way
141/// # #[allow(deprecated, deprecated_in_future)]
142/// let max = std::f64::MAX;
143///
144/// // intended way
145/// let max = f64::MAX;
146/// ```
147#[stable(feature = "rust1", since = "1.0.0")]
148#[deprecated(since = "TBD", note = "replaced by the `MAX` associated constant on `f64`")]
149#[rustc_diagnostic_item = "f64_legacy_const_max"]
150pub const MAX: f64 = f64::MAX;
151
152/// One greater than the minimum possible normal power of 2 exponent.
153/// Use [`f64::MIN_EXP`] instead.
154///
155/// # Examples
156///
157/// ```rust
158/// // deprecated way
159/// # #[allow(deprecated, deprecated_in_future)]
160/// let min = std::f64::MIN_EXP;
161///
162/// // intended way
163/// let min = f64::MIN_EXP;
164/// ```
165#[stable(feature = "rust1", since = "1.0.0")]
166#[deprecated(since = "TBD", note = "replaced by the `MIN_EXP` associated constant on `f64`")]
167#[rustc_diagnostic_item = "f64_legacy_const_min_exp"]
168pub const MIN_EXP: i32 = f64::MIN_EXP;
169
170/// Maximum possible power of 2 exponent.
171/// Use [`f64::MAX_EXP`] instead.
172///
173/// # Examples
174///
175/// ```rust
176/// // deprecated way
177/// # #[allow(deprecated, deprecated_in_future)]
178/// let max = std::f64::MAX_EXP;
179///
180/// // intended way
181/// let max = f64::MAX_EXP;
182/// ```
183#[stable(feature = "rust1", since = "1.0.0")]
184#[deprecated(since = "TBD", note = "replaced by the `MAX_EXP` associated constant on `f64`")]
185#[rustc_diagnostic_item = "f64_legacy_const_max_exp"]
186pub const MAX_EXP: i32 = f64::MAX_EXP;
187
188/// Minimum possible normal power of 10 exponent.
189/// Use [`f64::MIN_10_EXP`] instead.
190///
191/// # Examples
192///
193/// ```rust
194/// // deprecated way
195/// # #[allow(deprecated, deprecated_in_future)]
196/// let min = std::f64::MIN_10_EXP;
197///
198/// // intended way
199/// let min = f64::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 `f64`")]
203#[rustc_diagnostic_item = "f64_legacy_const_min_10_exp"]
204pub const MIN_10_EXP: i32 = f64::MIN_10_EXP;
205
206/// Maximum possible power of 10 exponent.
207/// Use [`f64::MAX_10_EXP`] instead.
208///
209/// # Examples
210///
211/// ```rust
212/// // deprecated way
213/// # #[allow(deprecated, deprecated_in_future)]
214/// let max = std::f64::MAX_10_EXP;
215///
216/// // intended way
217/// let max = f64::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 `f64`")]
221#[rustc_diagnostic_item = "f64_legacy_const_max_10_exp"]
222pub const MAX_10_EXP: i32 = f64::MAX_10_EXP;
223
224/// Not a Number (NaN).
225/// Use [`f64::NAN`] instead.
226///
227/// # Examples
228///
229/// ```rust
230/// // deprecated way
231/// # #[allow(deprecated, deprecated_in_future)]
232/// let nan = std::f64::NAN;
233///
234/// // intended way
235/// let nan = f64::NAN;
236/// ```
237#[stable(feature = "rust1", since = "1.0.0")]
238#[deprecated(since = "TBD", note = "replaced by the `NAN` associated constant on `f64`")]
239#[rustc_diagnostic_item = "f64_legacy_const_nan"]
240pub const NAN: f64 = f64::NAN;
241
242/// Infinity (∞).
243/// Use [`f64::INFINITY`] instead.
244///
245/// # Examples
246///
247/// ```rust
248/// // deprecated way
249/// # #[allow(deprecated, deprecated_in_future)]
250/// let inf = std::f64::INFINITY;
251///
252/// // intended way
253/// let inf = f64::INFINITY;
254/// ```
255#[stable(feature = "rust1", since = "1.0.0")]
256#[deprecated(since = "TBD", note = "replaced by the `INFINITY` associated constant on `f64`")]
257#[rustc_diagnostic_item = "f64_legacy_const_infinity"]
258pub const INFINITY: f64 = f64::INFINITY;
259
260/// Negative infinity (−∞).
261/// Use [`f64::NEG_INFINITY`] instead.
262///
263/// # Examples
264///
265/// ```rust
266/// // deprecated way
267/// # #[allow(deprecated, deprecated_in_future)]
268/// let ninf = std::f64::NEG_INFINITY;
269///
270/// // intended way
271/// let ninf = f64::NEG_INFINITY;
272/// ```
273#[stable(feature = "rust1", since = "1.0.0")]
274#[deprecated(since = "TBD", note = "replaced by the `NEG_INFINITY` associated constant on `f64`")]
275#[rustc_diagnostic_item = "f64_legacy_const_neg_infinity"]
276pub const NEG_INFINITY: f64 = f64::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: f64 = 3.14159265358979323846264338327950288_f64;
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: f64 = 6.28318530717958647692528676655900577_f64;
292
293 /// The golden ratio (φ)
294 #[unstable(feature = "more_float_constants", issue = "103883")]
295 pub const PHI: f64 = 1.618033988749894848204586834365638118_f64;
296
297 /// The Euler-Mascheroni constant (γ)
298 #[unstable(feature = "more_float_constants", issue = "103883")]
299 pub const EGAMMA: f64 = 0.577215664901532860606512090082402431_f64;
300
301 /// π/2
302 #[stable(feature = "rust1", since = "1.0.0")]
303 pub const FRAC_PI_2: f64 = 1.57079632679489661923132169163975144_f64;
304
305 /// π/3
306 #[stable(feature = "rust1", since = "1.0.0")]
307 pub const FRAC_PI_3: f64 = 1.04719755119659774615421446109316763_f64;
308
309 /// π/4
310 #[stable(feature = "rust1", since = "1.0.0")]
311 pub const FRAC_PI_4: f64 = 0.785398163397448309615660845819875721_f64;
312
313 /// π/6
314 #[stable(feature = "rust1", since = "1.0.0")]
315 pub const FRAC_PI_6: f64 = 0.52359877559829887307710723054658381_f64;
316
317 /// π/8
318 #[stable(feature = "rust1", since = "1.0.0")]
319 pub const FRAC_PI_8: f64 = 0.39269908169872415480783042290993786_f64;
320
321 /// 1/π
322 #[stable(feature = "rust1", since = "1.0.0")]
323 pub const FRAC_1_PI: f64 = 0.318309886183790671537767526745028724_f64;
324
325 /// 1/sqrt(π)
326 #[unstable(feature = "more_float_constants", issue = "103883")]
327 pub const FRAC_1_SQRT_PI: f64 = 0.564189583547756286948079451560772586_f64;
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: f64 = 0.398942280401432677939946059934381868_f64;
333
334 /// 2/π
335 #[stable(feature = "rust1", since = "1.0.0")]
336 pub const FRAC_2_PI: f64 = 0.636619772367581343075535053490057448_f64;
337
338 /// 2/sqrt(π)
339 #[stable(feature = "rust1", since = "1.0.0")]
340 pub const FRAC_2_SQRT_PI: f64 = 1.12837916709551257389615890312154517_f64;
341
342 /// sqrt(2)
343 #[stable(feature = "rust1", since = "1.0.0")]
344 pub const SQRT_2: f64 = 1.41421356237309504880168872420969808_f64;
345
346 /// 1/sqrt(2)
347 #[stable(feature = "rust1", since = "1.0.0")]
348 pub const FRAC_1_SQRT_2: f64 = 0.707106781186547524400844362104849039_f64;
349
350 /// sqrt(3)
351 #[unstable(feature = "more_float_constants", issue = "103883")]
352 pub const SQRT_3: f64 = 1.732050807568877293527446341505872367_f64;
353
354 /// 1/sqrt(3)
355 #[unstable(feature = "more_float_constants", issue = "103883")]
356 pub const FRAC_1_SQRT_3: f64 = 0.577350269189625764509148780501957456_f64;
357
358 /// Euler's number (e)
359 #[stable(feature = "rust1", since = "1.0.0")]
360 pub const E: f64 = 2.71828182845904523536028747135266250_f64;
361
362 /// log<sub>2</sub>(10)
363 #[stable(feature = "extra_log_consts", since = "1.43.0")]
364 pub const LOG2_10: f64 = 3.32192809488736234787031942948939018_f64;
365
366 /// log<sub>2</sub>(e)
367 #[stable(feature = "rust1", since = "1.0.0")]
368 pub const LOG2_E: f64 = 1.44269504088896340735992468100189214_f64;
369
370 /// log<sub>10</sub>(2)
371 #[stable(feature = "extra_log_consts", since = "1.43.0")]
372 pub const LOG10_2: f64 = 0.301029995663981195213738894724493027_f64;
373
374 /// log<sub>10</sub>(e)
375 #[stable(feature = "rust1", since = "1.0.0")]
376 pub const LOG10_E: f64 = 0.434294481903251827651128918916605082_f64;
377
378 /// ln(2)
379 #[stable(feature = "rust1", since = "1.0.0")]
380 pub const LN_2: f64 = 0.693147180559945309417232121458176568_f64;
381
382 /// ln(10)
383 #[stable(feature = "rust1", since = "1.0.0")]
384 pub const LN_10: f64 = 2.30258509299404568401799145468436421_f64;
385}
386
387impl f64 {
388 /// The radix or base of the internal representation of `f64`.
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 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
394 pub const MANTISSA_DIGITS: u32 = 53;
395 /// Approximate number of significant digits in base 10.
396 ///
397 /// This is the maximum <i>x</i> such that any decimal number with <i>x</i>
398 /// significant digits can be converted to `f64` and back without loss.
399 ///
400 /// Equal to floor(log<sub>10</sub>&nbsp;2<sup>[`MANTISSA_DIGITS`]&nbsp;&minus;&nbsp;1</sup>).
401 ///
402 /// [`MANTISSA_DIGITS`]: f64::MANTISSA_DIGITS
403 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
404 pub const DIGITS: u32 = 15;
405
406 /// [Machine epsilon] value for `f64`.
407 ///
408 /// This is the difference between `1.0` and the next larger representable number.
409 ///
410 /// Equal to 2<sup>1&nbsp;&minus;&nbsp;[`MANTISSA_DIGITS`]</sup>.
411 ///
412 /// [Machine epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon
413 /// [`MANTISSA_DIGITS`]: f64::MANTISSA_DIGITS
414 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
415 #[rustc_diagnostic_item = "f64_epsilon"]
416 pub const EPSILON: f64 = 2.2204460492503131e-16_f64;
417
418 /// Smallest finite `f64` value.
419 ///
420 /// Equal to &minus;[`MAX`].
421 ///
422 /// [`MAX`]: f64::MAX
423 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
424 pub const MIN: f64 = -1.7976931348623157e+308_f64;
425 /// Smallest positive normal `f64` value.
426 ///
427 /// Equal to 2<sup>[`MIN_EXP`]&nbsp;&minus;&nbsp;1</sup>.
428 ///
429 /// [`MIN_EXP`]: f64::MIN_EXP
430 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
431 pub const MIN_POSITIVE: f64 = 2.2250738585072014e-308_f64;
432 /// Largest finite `f64` value.
433 ///
434 /// Equal to
435 /// (1&nbsp;&minus;&nbsp;2<sup>&minus;[`MANTISSA_DIGITS`]</sup>)&nbsp;2<sup>[`MAX_EXP`]</sup>.
436 ///
437 /// [`MANTISSA_DIGITS`]: f64::MANTISSA_DIGITS
438 /// [`MAX_EXP`]: f64::MAX_EXP
439 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
440 pub const MAX: f64 = 1.7976931348623157e+308_f64;
441
442 /// One greater than the minimum possible normal power of 2 exponent.
443 ///
444 /// If <i>x</i>&nbsp;=&nbsp;`MIN_EXP`, then normal numbers
445 /// ≥&nbsp;0.5&nbsp;×&nbsp;2<sup><i>x</i></sup>.
446 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
447 pub const MIN_EXP: i32 = -1021;
448 /// Maximum possible power of 2 exponent.
449 ///
450 /// If <i>x</i>&nbsp;=&nbsp;`MAX_EXP`, then normal numbers
451 /// &lt;&nbsp;1&nbsp;×&nbsp;2<sup><i>x</i></sup>.
452 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
453 pub const MAX_EXP: i32 = 1024;
454
455 /// Minimum <i>x</i> for which 10<sup><i>x</i></sup> is normal.
456 ///
457 /// Equal to ceil(log<sub>10</sub>&nbsp;[`MIN_POSITIVE`]).
458 ///
459 /// [`MIN_POSITIVE`]: f64::MIN_POSITIVE
460 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
461 pub const MIN_10_EXP: i32 = -307;
462 /// Maximum <i>x</i> for which 10<sup><i>x</i></sup> is normal.
463 ///
464 /// Equal to floor(log<sub>10</sub>&nbsp;[`MAX`]).
465 ///
466 /// [`MAX`]: f64::MAX
467 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
468 pub const MAX_10_EXP: i32 = 308;
469
470 /// Not a Number (NaN).
471 ///
472 /// Note that IEEE 754 doesn't define just a single NaN value;
473 /// a plethora of bit patterns are considered to be NaN.
474 /// Furthermore, the standard makes a difference
475 /// between a "signaling" and a "quiet" NaN,
476 /// and allows inspecting its "payload" (the unspecified bits in the bit pattern).
477 /// This constant isn't guaranteed to equal to any specific NaN bitpattern,
478 /// and the stability of its representation over Rust versions
479 /// and target platforms isn't guaranteed.
480 #[rustc_diagnostic_item = "f64_nan"]
481 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
482 #[allow(clippy::eq_op)]
483 pub const NAN: f64 = 0.0_f64 / 0.0_f64;
484 /// Infinity (∞).
485 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
486 pub const INFINITY: f64 = 1.0_f64 / 0.0_f64;
487 /// Negative infinity (−∞).
488 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
489 pub const NEG_INFINITY: f64 = -1.0_f64 / 0.0_f64;
490
491 /// Sign bit
492 pub(crate) const SIGN_MASK: u64 = 0x8000_0000_0000_0000;
493
494 /// Exponent mask
495 pub(crate) const EXP_MASK: u64 = 0x7ff0_0000_0000_0000;
496
497 /// Mantissa mask
498 pub(crate) const MAN_MASK: u64 = 0x000f_ffff_ffff_ffff;
499
500 /// Minimum representable positive value (min subnormal)
501 const TINY_BITS: u64 = 0x1;
502
503 /// Minimum representable negative value (min negative subnormal)
504 const NEG_TINY_BITS: u64 = Self::TINY_BITS | Self::SIGN_MASK;
505
506 /// Returns `true` if this value is NaN.
507 ///
508 /// ```
509 /// let nan = f64::NAN;
510 /// let f = 7.0_f64;
511 ///
512 /// assert!(nan.is_nan());
513 /// assert!(!f.is_nan());
514 /// ```
515 #[must_use]
516 #[stable(feature = "rust1", since = "1.0.0")]
517 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
518 #[inline]
519 #[allow(clippy::eq_op)] // > if you intended to check if the operand is NaN, use `.is_nan()` instead :)
520 pub const fn is_nan(self) -> bool {
521 self != self
522 }
523
524 /// Returns `true` if this value is positive infinity or negative infinity, and
525 /// `false` otherwise.
526 ///
527 /// ```
528 /// let f = 7.0f64;
529 /// let inf = f64::INFINITY;
530 /// let neg_inf = f64::NEG_INFINITY;
531 /// let nan = f64::NAN;
532 ///
533 /// assert!(!f.is_infinite());
534 /// assert!(!nan.is_infinite());
535 ///
536 /// assert!(inf.is_infinite());
537 /// assert!(neg_inf.is_infinite());
538 /// ```
539 #[must_use]
540 #[stable(feature = "rust1", since = "1.0.0")]
541 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
542 #[inline]
543 pub const fn is_infinite(self) -> bool {
544 // Getting clever with transmutation can result in incorrect answers on some FPUs
545 // FIXME: alter the Rust <-> Rust calling convention to prevent this problem.
546 // See https://github.com/rust-lang/rust/issues/72327
547 (self == f64::INFINITY) | (self == f64::NEG_INFINITY)
548 }
549
550 /// Returns `true` if this number is neither infinite nor NaN.
551 ///
552 /// ```
553 /// let f = 7.0f64;
554 /// let inf: f64 = f64::INFINITY;
555 /// let neg_inf: f64 = f64::NEG_INFINITY;
556 /// let nan: f64 = f64::NAN;
557 ///
558 /// assert!(f.is_finite());
559 ///
560 /// assert!(!nan.is_finite());
561 /// assert!(!inf.is_finite());
562 /// assert!(!neg_inf.is_finite());
563 /// ```
564 #[must_use]
565 #[stable(feature = "rust1", since = "1.0.0")]
566 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
567 #[inline]
568 pub const fn is_finite(self) -> bool {
569 // There's no need to handle NaN separately: if self is NaN,
570 // the comparison is not true, exactly as desired.
571 self.abs() < Self::INFINITY
572 }
573
574 /// Returns `true` if the number is [subnormal].
575 ///
576 /// ```
577 /// let min = f64::MIN_POSITIVE; // 2.2250738585072014e-308_f64
578 /// let max = f64::MAX;
579 /// let lower_than_min = 1.0e-308_f64;
580 /// let zero = 0.0_f64;
581 ///
582 /// assert!(!min.is_subnormal());
583 /// assert!(!max.is_subnormal());
584 ///
585 /// assert!(!zero.is_subnormal());
586 /// assert!(!f64::NAN.is_subnormal());
587 /// assert!(!f64::INFINITY.is_subnormal());
588 /// // Values between `0` and `min` are Subnormal.
589 /// assert!(lower_than_min.is_subnormal());
590 /// ```
591 /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
592 #[must_use]
593 #[stable(feature = "is_subnormal", since = "1.53.0")]
594 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
595 #[inline]
596 pub const fn is_subnormal(self) -> bool {
597 matches!(self.classify(), FpCategory::Subnormal)
598 }
599
600 /// Returns `true` if the number is neither zero, infinite,
601 /// [subnormal], or NaN.
602 ///
603 /// ```
604 /// let min = f64::MIN_POSITIVE; // 2.2250738585072014e-308f64
605 /// let max = f64::MAX;
606 /// let lower_than_min = 1.0e-308_f64;
607 /// let zero = 0.0f64;
608 ///
609 /// assert!(min.is_normal());
610 /// assert!(max.is_normal());
611 ///
612 /// assert!(!zero.is_normal());
613 /// assert!(!f64::NAN.is_normal());
614 /// assert!(!f64::INFINITY.is_normal());
615 /// // Values between `0` and `min` are Subnormal.
616 /// assert!(!lower_than_min.is_normal());
617 /// ```
618 /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
619 #[must_use]
620 #[stable(feature = "rust1", since = "1.0.0")]
621 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
622 #[inline]
623 pub const fn is_normal(self) -> bool {
624 matches!(self.classify(), FpCategory::Normal)
625 }
626
627 /// Returns the floating point category of the number. If only one property
628 /// is going to be tested, it is generally faster to use the specific
629 /// predicate instead.
630 ///
631 /// ```
632 /// use std::num::FpCategory;
633 ///
634 /// let num = 12.4_f64;
635 /// let inf = f64::INFINITY;
636 ///
637 /// assert_eq!(num.classify(), FpCategory::Normal);
638 /// assert_eq!(inf.classify(), FpCategory::Infinite);
639 /// ```
640 #[stable(feature = "rust1", since = "1.0.0")]
641 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
642 pub const fn classify(self) -> FpCategory {
643 // We used to have complicated logic here that avoids the simple bit-based tests to work
644 // around buggy codegen for x87 targets (see
645 // https://github.com/rust-lang/rust/issues/114479). However, some LLVM versions later, none
646 // of our tests is able to find any difference between the complicated and the naive
647 // version, so now we are back to the naive version.
648 let b = self.to_bits();
649 match (b & Self::MAN_MASK, b & Self::EXP_MASK) {
650 (0, Self::EXP_MASK) => FpCategory::Infinite,
651 (_, Self::EXP_MASK) => FpCategory::Nan,
652 (0, 0) => FpCategory::Zero,
653 (_, 0) => FpCategory::Subnormal,
654 _ => FpCategory::Normal,
655 }
656 }
657
658 /// Returns `true` if `self` has a positive sign, including `+0.0`, NaNs with
659 /// positive sign bit and positive infinity.
660 ///
661 /// Note that IEEE 754 doesn't assign any meaning to the sign bit in case of
662 /// a NaN, and as Rust doesn't guarantee that the bit pattern of NaNs are
663 /// conserved over arithmetic operations, the result of `is_sign_positive` on
664 /// a NaN might produce an unexpected or non-portable result. See the [specification
665 /// of NaN bit patterns](f32#nan-bit-patterns) for more info. Use `self.signum() == 1.0`
666 /// if you need fully portable behavior (will return `false` for all NaNs).
667 ///
668 /// ```
669 /// let f = 7.0_f64;
670 /// let g = -7.0_f64;
671 ///
672 /// assert!(f.is_sign_positive());
673 /// assert!(!g.is_sign_positive());
674 /// ```
675 #[must_use]
676 #[stable(feature = "rust1", since = "1.0.0")]
677 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
678 #[inline]
679 pub const fn is_sign_positive(self) -> bool {
680 !self.is_sign_negative()
681 }
682
683 #[must_use]
684 #[stable(feature = "rust1", since = "1.0.0")]
685 #[deprecated(since = "1.0.0", note = "renamed to is_sign_positive")]
686 #[inline]
687 #[doc(hidden)]
688 pub fn is_positive(self) -> bool {
689 self.is_sign_positive()
690 }
691
692 /// Returns `true` if `self` has a negative sign, including `-0.0`, NaNs with
693 /// negative sign bit and negative infinity.
694 ///
695 /// Note that IEEE 754 doesn't assign any meaning to the sign bit in case of
696 /// a NaN, and as Rust doesn't guarantee that the bit pattern of NaNs are
697 /// conserved over arithmetic operations, the result of `is_sign_negative` on
698 /// a NaN might produce an unexpected or non-portable result. See the [specification
699 /// of NaN bit patterns](f32#nan-bit-patterns) for more info. Use `self.signum() == -1.0`
700 /// if you need fully portable behavior (will return `false` for all NaNs).
701 ///
702 /// ```
703 /// let f = 7.0_f64;
704 /// let g = -7.0_f64;
705 ///
706 /// assert!(!f.is_sign_negative());
707 /// assert!(g.is_sign_negative());
708 /// ```
709 #[must_use]
710 #[stable(feature = "rust1", since = "1.0.0")]
711 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
712 #[inline]
713 pub const fn is_sign_negative(self) -> bool {
714 // IEEE754 says: isSignMinus(x) is true if and only if x has negative sign. isSignMinus
715 // applies to zeros and NaNs as well.
716 // SAFETY: This is just transmuting to get the sign bit, it's fine.
717 unsafe { mem::transmute::<f64, u64>(self) & Self::SIGN_MASK != 0 }
718 }
719
720 #[must_use]
721 #[stable(feature = "rust1", since = "1.0.0")]
722 #[deprecated(since = "1.0.0", note = "renamed to is_sign_negative")]
723 #[inline]
724 #[doc(hidden)]
725 pub fn is_negative(self) -> bool {
726 self.is_sign_negative()
727 }
728
729 /// Returns the least number greater than `self`.
730 ///
731 /// Let `TINY` be the smallest representable positive `f64`. Then,
732 /// - if `self.is_nan()`, this returns `self`;
733 /// - if `self` is [`NEG_INFINITY`], this returns [`MIN`];
734 /// - if `self` is `-TINY`, this returns -0.0;
735 /// - if `self` is -0.0 or +0.0, this returns `TINY`;
736 /// - if `self` is [`MAX`] or [`INFINITY`], this returns [`INFINITY`];
737 /// - otherwise the unique least value greater than `self` is returned.
738 ///
739 /// The identity `x.next_up() == -(-x).next_down()` holds for all non-NaN `x`. When `x`
740 /// is finite `x == x.next_up().next_down()` also holds.
741 ///
742 /// ```rust
743 /// // f64::EPSILON is the difference between 1.0 and the next number up.
744 /// assert_eq!(1.0f64.next_up(), 1.0 + f64::EPSILON);
745 /// // But not for most numbers.
746 /// assert!(0.1f64.next_up() < 0.1 + f64::EPSILON);
747 /// assert_eq!(9007199254740992f64.next_up(), 9007199254740994.0);
748 /// ```
749 ///
750 /// This operation corresponds to IEEE-754 `nextUp`.
751 ///
752 /// [`NEG_INFINITY`]: Self::NEG_INFINITY
753 /// [`INFINITY`]: Self::INFINITY
754 /// [`MIN`]: Self::MIN
755 /// [`MAX`]: Self::MAX
756 #[inline]
757 #[doc(alias = "nextUp")]
758 #[stable(feature = "float_next_up_down", since = "1.86.0")]
759 #[rustc_const_stable(feature = "float_next_up_down", since = "1.86.0")]
760 pub const fn next_up(self) -> Self {
761 // Some targets violate Rust's assumption of IEEE semantics, e.g. by flushing
762 // denormals to zero. This is in general unsound and unsupported, but here
763 // we do our best to still produce the correct result on such targets.
764 let bits = self.to_bits();
765 if self.is_nan() || bits == Self::INFINITY.to_bits() {
766 return self;
767 }
768
769 let abs = bits & !Self::SIGN_MASK;
770 let next_bits = if abs == 0 {
771 Self::TINY_BITS
772 } else if bits == abs {
773 bits + 1
774 } else {
775 bits - 1
776 };
777 Self::from_bits(next_bits)
778 }
779
780 /// Returns the greatest number less than `self`.
781 ///
782 /// Let `TINY` be the smallest representable positive `f64`. Then,
783 /// - if `self.is_nan()`, this returns `self`;
784 /// - if `self` is [`INFINITY`], this returns [`MAX`];
785 /// - if `self` is `TINY`, this returns 0.0;
786 /// - if `self` is -0.0 or +0.0, this returns `-TINY`;
787 /// - if `self` is [`MIN`] or [`NEG_INFINITY`], this returns [`NEG_INFINITY`];
788 /// - otherwise the unique greatest value less than `self` is returned.
789 ///
790 /// The identity `x.next_down() == -(-x).next_up()` holds for all non-NaN `x`. When `x`
791 /// is finite `x == x.next_down().next_up()` also holds.
792 ///
793 /// ```rust
794 /// let x = 1.0f64;
795 /// // Clamp value into range [0, 1).
796 /// let clamped = x.clamp(0.0, 1.0f64.next_down());
797 /// assert!(clamped < 1.0);
798 /// assert_eq!(clamped.next_up(), 1.0);
799 /// ```
800 ///
801 /// This operation corresponds to IEEE-754 `nextDown`.
802 ///
803 /// [`NEG_INFINITY`]: Self::NEG_INFINITY
804 /// [`INFINITY`]: Self::INFINITY
805 /// [`MIN`]: Self::MIN
806 /// [`MAX`]: Self::MAX
807 #[inline]
808 #[doc(alias = "nextDown")]
809 #[stable(feature = "float_next_up_down", since = "1.86.0")]
810 #[rustc_const_stable(feature = "float_next_up_down", since = "1.86.0")]
811 pub const fn next_down(self) -> Self {
812 // Some targets violate Rust's assumption of IEEE semantics, e.g. by flushing
813 // denormals to zero. This is in general unsound and unsupported, but here
814 // we do our best to still produce the correct result on such targets.
815 let bits = self.to_bits();
816 if self.is_nan() || bits == Self::NEG_INFINITY.to_bits() {
817 return self;
818 }
819
820 let abs = bits & !Self::SIGN_MASK;
821 let next_bits = if abs == 0 {
822 Self::NEG_TINY_BITS
823 } else if bits == abs {
824 bits - 1
825 } else {
826 bits + 1
827 };
828 Self::from_bits(next_bits)
829 }
830
831 /// Takes the reciprocal (inverse) of a number, `1/x`.
832 ///
833 /// ```
834 /// let x = 2.0_f64;
835 /// let abs_difference = (x.recip() - (1.0 / x)).abs();
836 ///
837 /// assert!(abs_difference < 1e-10);
838 /// ```
839 #[must_use = "this returns the result of the operation, without modifying the original"]
840 #[stable(feature = "rust1", since = "1.0.0")]
841 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
842 #[inline]
843 pub const fn recip(self) -> f64 {
844 1.0 / self
845 }
846
847 /// Converts radians to degrees.
848 ///
849 /// ```
850 /// let angle = std::f64::consts::PI;
851 ///
852 /// let abs_difference = (angle.to_degrees() - 180.0).abs();
853 ///
854 /// assert!(abs_difference < 1e-10);
855 /// ```
856 #[must_use = "this returns the result of the operation, \
857 without modifying the original"]
858 #[stable(feature = "rust1", since = "1.0.0")]
859 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
860 #[inline]
861 pub const fn to_degrees(self) -> f64 {
862 // The division here is correctly rounded with respect to the true
863 // value of 180/π. (This differs from f32, where a constant must be
864 // used to ensure a correctly rounded result.)
865 self * (180.0f64 / consts::PI)
866 }
867
868 /// Converts degrees to radians.
869 ///
870 /// ```
871 /// let angle = 180.0_f64;
872 ///
873 /// let abs_difference = (angle.to_radians() - std::f64::consts::PI).abs();
874 ///
875 /// assert!(abs_difference < 1e-10);
876 /// ```
877 #[must_use = "this returns the result of the operation, \
878 without modifying the original"]
879 #[stable(feature = "rust1", since = "1.0.0")]
880 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
881 #[inline]
882 pub const fn to_radians(self) -> f64 {
883 const RADS_PER_DEG: f64 = consts::PI / 180.0;
884 self * RADS_PER_DEG
885 }
886
887 /// Returns the maximum of the two numbers, ignoring NaN.
888 ///
889 /// If one of the arguments is NaN, then the other argument is returned.
890 /// This follows the IEEE 754-2008 semantics for maxNum, except for handling of signaling NaNs;
891 /// this function handles all NaNs the same way and avoids maxNum's problems with associativity.
892 /// This also matches the behavior of libm’s fmax. In particular, if the inputs compare equal
893 /// (such as for the case of `+0.0` and `-0.0`), either input may be returned non-deterministically.
894 ///
895 /// ```
896 /// let x = 1.0_f64;
897 /// let y = 2.0_f64;
898 ///
899 /// assert_eq!(x.max(y), y);
900 /// ```
901 #[must_use = "this returns the result of the comparison, without modifying either input"]
902 #[stable(feature = "rust1", since = "1.0.0")]
903 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
904 #[inline]
905 pub const fn max(self, other: f64) -> f64 {
906 intrinsics::maxnumf64(self, other)
907 }
908
909 /// Returns the minimum of the two numbers, ignoring NaN.
910 ///
911 /// If one of the arguments is NaN, then the other argument is returned.
912 /// This follows the IEEE 754-2008 semantics for minNum, except for handling of signaling NaNs;
913 /// this function handles all NaNs the same way and avoids minNum's problems with associativity.
914 /// This also matches the behavior of libm’s fmin. In particular, if the inputs compare equal
915 /// (such as for the case of `+0.0` and `-0.0`), either input may be returned non-deterministically.
916 ///
917 /// ```
918 /// let x = 1.0_f64;
919 /// let y = 2.0_f64;
920 ///
921 /// assert_eq!(x.min(y), x);
922 /// ```
923 #[must_use = "this returns the result of the comparison, without modifying either input"]
924 #[stable(feature = "rust1", since = "1.0.0")]
925 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
926 #[inline]
927 pub const fn min(self, other: f64) -> f64 {
928 intrinsics::minnumf64(self, other)
929 }
930
931 /// Returns the maximum of the two numbers, propagating NaN.
932 ///
933 /// This returns NaN when *either* argument is NaN, as opposed to
934 /// [`f64::max`] which only returns NaN when *both* arguments are NaN.
935 ///
936 /// ```
937 /// #![feature(float_minimum_maximum)]
938 /// let x = 1.0_f64;
939 /// let y = 2.0_f64;
940 ///
941 /// assert_eq!(x.maximum(y), y);
942 /// assert!(x.maximum(f64::NAN).is_nan());
943 /// ```
944 ///
945 /// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the greater
946 /// of the two numbers. For this operation, -0.0 is considered to be less than +0.0.
947 /// Note that this follows the semantics specified in IEEE 754-2019.
948 ///
949 /// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN
950 /// operand is conserved; see the [specification of NaN bit patterns](f32#nan-bit-patterns) for more info.
951 #[must_use = "this returns the result of the comparison, without modifying either input"]
952 #[unstable(feature = "float_minimum_maximum", issue = "91079")]
953 #[inline]
954 pub const fn maximum(self, other: f64) -> f64 {
955 if self > other {
956 self
957 } else if other > self {
958 other
959 } else if self == other {
960 if self.is_sign_positive() && other.is_sign_negative() { self } else { other }
961 } else {
962 self + other
963 }
964 }
965
966 /// Returns the minimum of the two numbers, propagating NaN.
967 ///
968 /// This returns NaN when *either* argument is NaN, as opposed to
969 /// [`f64::min`] which only returns NaN when *both* arguments are NaN.
970 ///
971 /// ```
972 /// #![feature(float_minimum_maximum)]
973 /// let x = 1.0_f64;
974 /// let y = 2.0_f64;
975 ///
976 /// assert_eq!(x.minimum(y), x);
977 /// assert!(x.minimum(f64::NAN).is_nan());
978 /// ```
979 ///
980 /// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the lesser
981 /// of the two numbers. For this operation, -0.0 is considered to be less than +0.0.
982 /// Note that this follows the semantics specified in IEEE 754-2019.
983 ///
984 /// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN
985 /// operand is conserved; see the [specification of NaN bit patterns](f32#nan-bit-patterns) for more info.
986 #[must_use = "this returns the result of the comparison, without modifying either input"]
987 #[unstable(feature = "float_minimum_maximum", issue = "91079")]
988 #[inline]
989 pub const fn minimum(self, other: f64) -> f64 {
990 if self < other {
991 self
992 } else if other < self {
993 other
994 } else if self == other {
995 if self.is_sign_negative() && other.is_sign_positive() { self } else { other }
996 } else {
997 // At least one input is NaN. Use `+` to perform NaN propagation and quieting.
998 self + other
999 }
1000 }
1001
1002 /// Calculates the middle point of `self` and `rhs`.
1003 ///
1004 /// This returns NaN when *either* argument is NaN or if a combination of
1005 /// +inf and -inf is provided as arguments.
1006 ///
1007 /// # Examples
1008 ///
1009 /// ```
1010 /// assert_eq!(1f64.midpoint(4.0), 2.5);
1011 /// assert_eq!((-5.5f64).midpoint(8.0), 1.25);
1012 /// ```
1013 #[inline]
1014 #[stable(feature = "num_midpoint", since = "1.85.0")]
1015 #[rustc_const_stable(feature = "num_midpoint", since = "1.85.0")]
1016 pub const fn midpoint(self, other: f64) -> f64 {
1017 const LO: f64 = f64::MIN_POSITIVE * 2.;
1018 const HI: f64 = f64::MAX / 2.;
1019
1020 let (a, b) = (self, other);
1021 let abs_a = a.abs();
1022 let abs_b = b.abs();
1023
1024 if abs_a <= HI && abs_b <= HI {
1025 // Overflow is impossible
1026 (a + b) / 2.
1027 } else if abs_a < LO {
1028 // Not safe to halve `a` (would underflow)
1029 a + (b / 2.)
1030 } else if abs_b < LO {
1031 // Not safe to halve `b` (would underflow)
1032 (a / 2.) + b
1033 } else {
1034 // Safe to halve `a` and `b`
1035 (a / 2.) + (b / 2.)
1036 }
1037 }
1038
1039 /// Rounds toward zero and converts to any primitive integer type,
1040 /// assuming that the value is finite and fits in that type.
1041 ///
1042 /// ```
1043 /// let value = 4.6_f64;
1044 /// let rounded = unsafe { value.to_int_unchecked::<u16>() };
1045 /// assert_eq!(rounded, 4);
1046 ///
1047 /// let value = -128.9_f64;
1048 /// let rounded = unsafe { value.to_int_unchecked::<i8>() };
1049 /// assert_eq!(rounded, i8::MIN);
1050 /// ```
1051 ///
1052 /// # Safety
1053 ///
1054 /// The value must:
1055 ///
1056 /// * Not be `NaN`
1057 /// * Not be infinite
1058 /// * Be representable in the return type `Int`, after truncating off its fractional part
1059 #[must_use = "this returns the result of the operation, \
1060 without modifying the original"]
1061 #[stable(feature = "float_approx_unchecked_to", since = "1.44.0")]
1062 #[inline]
1063 pub unsafe fn to_int_unchecked<Int>(self) -> Int
1064 where
1065 Self: FloatToInt<Int>,
1066 {
1067 // SAFETY: the caller must uphold the safety contract for
1068 // `FloatToInt::to_int_unchecked`.
1069 unsafe { FloatToInt::<Int>::to_int_unchecked(self) }
1070 }
1071
1072 /// Raw transmutation to `u64`.
1073 ///
1074 /// This is currently identical to `transmute::<f64, u64>(self)` on all platforms.
1075 ///
1076 /// See [`from_bits`](Self::from_bits) for some discussion of the
1077 /// portability of this operation (there are almost no issues).
1078 ///
1079 /// Note that this function is distinct from `as` casting, which attempts to
1080 /// preserve the *numeric* value, and not the bitwise value.
1081 ///
1082 /// # Examples
1083 ///
1084 /// ```
1085 /// assert!((1f64).to_bits() != 1f64 as u64); // to_bits() is not casting!
1086 /// assert_eq!((12.5f64).to_bits(), 0x4029000000000000);
1087 /// ```
1088 #[must_use = "this returns the result of the operation, \
1089 without modifying the original"]
1090 #[stable(feature = "float_bits_conv", since = "1.20.0")]
1091 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1092 #[inline]
1093 pub const fn to_bits(self) -> u64 {
1094 // SAFETY: `u64` is a plain old datatype so we can always transmute to it.
1095 unsafe { mem::transmute(self) }
1096 }
1097
1098 /// Raw transmutation from `u64`.
1099 ///
1100 /// This is currently identical to `transmute::<u64, f64>(v)` on all platforms.
1101 /// It turns out this is incredibly portable, for two reasons:
1102 ///
1103 /// * Floats and Ints have the same endianness on all supported platforms.
1104 /// * IEEE 754 very precisely specifies the bit layout of floats.
1105 ///
1106 /// However there is one caveat: prior to the 2008 version of IEEE 754, how
1107 /// to interpret the NaN signaling bit wasn't actually specified. Most platforms
1108 /// (notably x86 and ARM) picked the interpretation that was ultimately
1109 /// standardized in 2008, but some didn't (notably MIPS). As a result, all
1110 /// signaling NaNs on MIPS are quiet NaNs on x86, and vice-versa.
1111 ///
1112 /// Rather than trying to preserve signaling-ness cross-platform, this
1113 /// implementation favors preserving the exact bits. This means that
1114 /// any payloads encoded in NaNs will be preserved even if the result of
1115 /// this method is sent over the network from an x86 machine to a MIPS one.
1116 ///
1117 /// If the results of this method are only manipulated by the same
1118 /// architecture that produced them, then there is no portability concern.
1119 ///
1120 /// If the input isn't NaN, then there is no portability concern.
1121 ///
1122 /// If you don't care about signaling-ness (very likely), then there is no
1123 /// portability concern.
1124 ///
1125 /// Note that this function is distinct from `as` casting, which attempts to
1126 /// preserve the *numeric* value, and not the bitwise value.
1127 ///
1128 /// # Examples
1129 ///
1130 /// ```
1131 /// let v = f64::from_bits(0x4029000000000000);
1132 /// assert_eq!(v, 12.5);
1133 /// ```
1134 #[stable(feature = "float_bits_conv", since = "1.20.0")]
1135 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1136 #[must_use]
1137 #[inline]
1138 pub const fn from_bits(v: u64) -> Self {
1139 // It turns out the safety issues with sNaN were overblown! Hooray!
1140 // SAFETY: `u64` is a plain old datatype so we can always transmute from it.
1141 unsafe { mem::transmute(v) }
1142 }
1143
1144 /// Returns the memory representation of this floating point number as a byte array in
1145 /// big-endian (network) byte order.
1146 ///
1147 /// See [`from_bits`](Self::from_bits) for some discussion of the
1148 /// portability of this operation (there are almost no issues).
1149 ///
1150 /// # Examples
1151 ///
1152 /// ```
1153 /// let bytes = 12.5f64.to_be_bytes();
1154 /// assert_eq!(bytes, [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]);
1155 /// ```
1156 #[must_use = "this returns the result of the operation, \
1157 without modifying the original"]
1158 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1159 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1160 #[inline]
1161 pub const fn to_be_bytes(self) -> [u8; 8] {
1162 self.to_bits().to_be_bytes()
1163 }
1164
1165 /// Returns the memory representation of this floating point number as a byte array in
1166 /// little-endian byte order.
1167 ///
1168 /// See [`from_bits`](Self::from_bits) for some discussion of the
1169 /// portability of this operation (there are almost no issues).
1170 ///
1171 /// # Examples
1172 ///
1173 /// ```
1174 /// let bytes = 12.5f64.to_le_bytes();
1175 /// assert_eq!(bytes, [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]);
1176 /// ```
1177 #[must_use = "this returns the result of the operation, \
1178 without modifying the original"]
1179 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1180 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1181 #[inline]
1182 pub const fn to_le_bytes(self) -> [u8; 8] {
1183 self.to_bits().to_le_bytes()
1184 }
1185
1186 /// Returns the memory representation of this floating point number as a byte array in
1187 /// native byte order.
1188 ///
1189 /// As the target platform's native endianness is used, portable code
1190 /// should use [`to_be_bytes`] or [`to_le_bytes`], as appropriate, instead.
1191 ///
1192 /// [`to_be_bytes`]: f64::to_be_bytes
1193 /// [`to_le_bytes`]: f64::to_le_bytes
1194 ///
1195 /// See [`from_bits`](Self::from_bits) for some discussion of the
1196 /// portability of this operation (there are almost no issues).
1197 ///
1198 /// # Examples
1199 ///
1200 /// ```
1201 /// let bytes = 12.5f64.to_ne_bytes();
1202 /// assert_eq!(
1203 /// bytes,
1204 /// if cfg!(target_endian = "big") {
1205 /// [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
1206 /// } else {
1207 /// [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]
1208 /// }
1209 /// );
1210 /// ```
1211 #[must_use = "this returns the result of the operation, \
1212 without modifying the original"]
1213 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1214 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1215 #[inline]
1216 pub const fn to_ne_bytes(self) -> [u8; 8] {
1217 self.to_bits().to_ne_bytes()
1218 }
1219
1220 /// Creates a floating point value from its representation as a byte array in big endian.
1221 ///
1222 /// See [`from_bits`](Self::from_bits) for some discussion of the
1223 /// portability of this operation (there are almost no issues).
1224 ///
1225 /// # Examples
1226 ///
1227 /// ```
1228 /// let value = f64::from_be_bytes([0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]);
1229 /// assert_eq!(value, 12.5);
1230 /// ```
1231 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1232 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1233 #[must_use]
1234 #[inline]
1235 pub const fn from_be_bytes(bytes: [u8; 8]) -> Self {
1236 Self::from_bits(u64::from_be_bytes(bytes))
1237 }
1238
1239 /// Creates a floating point value from its representation as a byte array in little endian.
1240 ///
1241 /// See [`from_bits`](Self::from_bits) for some discussion of the
1242 /// portability of this operation (there are almost no issues).
1243 ///
1244 /// # Examples
1245 ///
1246 /// ```
1247 /// let value = f64::from_le_bytes([0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]);
1248 /// assert_eq!(value, 12.5);
1249 /// ```
1250 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1251 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1252 #[must_use]
1253 #[inline]
1254 pub const fn from_le_bytes(bytes: [u8; 8]) -> Self {
1255 Self::from_bits(u64::from_le_bytes(bytes))
1256 }
1257
1258 /// Creates a floating point value from its representation as a byte array in native endian.
1259 ///
1260 /// As the target platform's native endianness is used, portable code
1261 /// likely wants to use [`from_be_bytes`] or [`from_le_bytes`], as
1262 /// appropriate instead.
1263 ///
1264 /// [`from_be_bytes`]: f64::from_be_bytes
1265 /// [`from_le_bytes`]: f64::from_le_bytes
1266 ///
1267 /// See [`from_bits`](Self::from_bits) for some discussion of the
1268 /// portability of this operation (there are almost no issues).
1269 ///
1270 /// # Examples
1271 ///
1272 /// ```
1273 /// let value = f64::from_ne_bytes(if cfg!(target_endian = "big") {
1274 /// [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
1275 /// } else {
1276 /// [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]
1277 /// });
1278 /// assert_eq!(value, 12.5);
1279 /// ```
1280 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1281 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1282 #[must_use]
1283 #[inline]
1284 pub const fn from_ne_bytes(bytes: [u8; 8]) -> Self {
1285 Self::from_bits(u64::from_ne_bytes(bytes))
1286 }
1287
1288 /// Returns the ordering between `self` and `other`.
1289 ///
1290 /// Unlike the standard partial comparison between floating point numbers,
1291 /// this comparison always produces an ordering in accordance to
1292 /// the `totalOrder` predicate as defined in the IEEE 754 (2008 revision)
1293 /// floating point standard. The values are ordered in the following sequence:
1294 ///
1295 /// - negative quiet NaN
1296 /// - negative signaling NaN
1297 /// - negative infinity
1298 /// - negative numbers
1299 /// - negative subnormal numbers
1300 /// - negative zero
1301 /// - positive zero
1302 /// - positive subnormal numbers
1303 /// - positive numbers
1304 /// - positive infinity
1305 /// - positive signaling NaN
1306 /// - positive quiet NaN.
1307 ///
1308 /// The ordering established by this function does not always agree with the
1309 /// [`PartialOrd`] and [`PartialEq`] implementations of `f64`. For example,
1310 /// they consider negative and positive zero equal, while `total_cmp`
1311 /// doesn't.
1312 ///
1313 /// The interpretation of the signaling NaN bit follows the definition in
1314 /// the IEEE 754 standard, which may not match the interpretation by some of
1315 /// the older, non-conformant (e.g. MIPS) hardware implementations.
1316 ///
1317 /// # Example
1318 ///
1319 /// ```
1320 /// struct GoodBoy {
1321 /// name: String,
1322 /// weight: f64,
1323 /// }
1324 ///
1325 /// let mut bois = vec![
1326 /// GoodBoy { name: "Pucci".to_owned(), weight: 0.1 },
1327 /// GoodBoy { name: "Woofer".to_owned(), weight: 99.0 },
1328 /// GoodBoy { name: "Yapper".to_owned(), weight: 10.0 },
1329 /// GoodBoy { name: "Chonk".to_owned(), weight: f64::INFINITY },
1330 /// GoodBoy { name: "Abs. Unit".to_owned(), weight: f64::NAN },
1331 /// GoodBoy { name: "Floaty".to_owned(), weight: -5.0 },
1332 /// ];
1333 ///
1334 /// bois.sort_by(|a, b| a.weight.total_cmp(&b.weight));
1335 ///
1336 /// // `f64::NAN` could be positive or negative, which will affect the sort order.
1337 /// if f64::NAN.is_sign_negative() {
1338 /// assert!(bois.into_iter().map(|b| b.weight)
1339 /// .zip([f64::NAN, -5.0, 0.1, 10.0, 99.0, f64::INFINITY].iter())
1340 /// .all(|(a, b)| a.to_bits() == b.to_bits()))
1341 /// } else {
1342 /// assert!(bois.into_iter().map(|b| b.weight)
1343 /// .zip([-5.0, 0.1, 10.0, 99.0, f64::INFINITY, f64::NAN].iter())
1344 /// .all(|(a, b)| a.to_bits() == b.to_bits()))
1345 /// }
1346 /// ```
1347 #[stable(feature = "total_cmp", since = "1.62.0")]
1348 #[must_use]
1349 #[inline]
1350 pub fn total_cmp(&self, other: &Self) -> crate::cmp::Ordering {
1351 let mut left = self.to_bits() as i64;
1352 let mut right = other.to_bits() as i64;
1353
1354 // In case of negatives, flip all the bits except the sign
1355 // to achieve a similar layout as two's complement integers
1356 //
1357 // Why does this work? IEEE 754 floats consist of three fields:
1358 // Sign bit, exponent and mantissa. The set of exponent and mantissa
1359 // fields as a whole have the property that their bitwise order is
1360 // equal to the numeric magnitude where the magnitude is defined.
1361 // The magnitude is not normally defined on NaN values, but
1362 // IEEE 754 totalOrder defines the NaN values also to follow the
1363 // bitwise order. This leads to order explained in the doc comment.
1364 // However, the representation of magnitude is the same for negative
1365 // and positive numbers – only the sign bit is different.
1366 // To easily compare the floats as signed integers, we need to
1367 // flip the exponent and mantissa bits in case of negative numbers.
1368 // We effectively convert the numbers to "two's complement" form.
1369 //
1370 // To do the flipping, we construct a mask and XOR against it.
1371 // We branchlessly calculate an "all-ones except for the sign bit"
1372 // mask from negative-signed values: right shifting sign-extends
1373 // the integer, so we "fill" the mask with sign bits, and then
1374 // convert to unsigned to push one more zero bit.
1375 // On positive values, the mask is all zeros, so it's a no-op.
1376 left ^= (((left >> 63) as u64) >> 1) as i64;
1377 right ^= (((right >> 63) as u64) >> 1) as i64;
1378
1379 left.cmp(&right)
1380 }
1381
1382 /// Restrict a value to a certain interval unless it is NaN.
1383 ///
1384 /// Returns `max` if `self` is greater than `max`, and `min` if `self` is
1385 /// less than `min`. Otherwise this returns `self`.
1386 ///
1387 /// Note that this function returns NaN if the initial value was NaN as
1388 /// well.
1389 ///
1390 /// # Panics
1391 ///
1392 /// Panics if `min > max`, `min` is NaN, or `max` is NaN.
1393 ///
1394 /// # Examples
1395 ///
1396 /// ```
1397 /// assert!((-3.0f64).clamp(-2.0, 1.0) == -2.0);
1398 /// assert!((0.0f64).clamp(-2.0, 1.0) == 0.0);
1399 /// assert!((2.0f64).clamp(-2.0, 1.0) == 1.0);
1400 /// assert!((f64::NAN).clamp(-2.0, 1.0).is_nan());
1401 /// ```
1402 #[must_use = "method returns a new number and does not mutate the original value"]
1403 #[stable(feature = "clamp", since = "1.50.0")]
1404 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
1405 #[inline]
1406 pub const fn clamp(mut self, min: f64, max: f64) -> f64 {
1407 const_assert!(
1408 min <= max,
1409 "min > max, or either was NaN",
1410 "min > max, or either was NaN. min = {min:?}, max = {max:?}",
1411 min: f64,
1412 max: f64,
1413 );
1414
1415 if self < min {
1416 self = min;
1417 }
1418 if self > max {
1419 self = max;
1420 }
1421 self
1422 }
1423
1424 /// Computes the absolute value of `self`.
1425 ///
1426 /// This function always returns the precise result.
1427 ///
1428 /// # Examples
1429 ///
1430 /// ```
1431 /// let x = 3.5_f64;
1432 /// let y = -3.5_f64;
1433 ///
1434 /// assert_eq!(x.abs(), x);
1435 /// assert_eq!(y.abs(), -y);
1436 ///
1437 /// assert!(f64::NAN.abs().is_nan());
1438 /// ```
1439 #[must_use = "method returns a new number and does not mutate the original value"]
1440 #[stable(feature = "rust1", since = "1.0.0")]
1441 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
1442 #[inline]
1443 pub const fn abs(self) -> f64 {
1444 // SAFETY: this is actually a safe intrinsic
1445 unsafe { intrinsics::fabsf64(self) }
1446 }
1447
1448 /// Returns a number that represents the sign of `self`.
1449 ///
1450 /// - `1.0` if the number is positive, `+0.0` or `INFINITY`
1451 /// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
1452 /// - NaN if the number is NaN
1453 ///
1454 /// # Examples
1455 ///
1456 /// ```
1457 /// let f = 3.5_f64;
1458 ///
1459 /// assert_eq!(f.signum(), 1.0);
1460 /// assert_eq!(f64::NEG_INFINITY.signum(), -1.0);
1461 ///
1462 /// assert!(f64::NAN.signum().is_nan());
1463 /// ```
1464 #[must_use = "method returns a new number and does not mutate the original value"]
1465 #[stable(feature = "rust1", since = "1.0.0")]
1466 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
1467 #[inline]
1468 pub const fn signum(self) -> f64 {
1469 if self.is_nan() { Self::NAN } else { 1.0_f64.copysign(self) }
1470 }
1471
1472 /// Returns a number composed of the magnitude of `self` and the sign of
1473 /// `sign`.
1474 ///
1475 /// Equal to `self` if the sign of `self` and `sign` are the same, otherwise equal to `-self`.
1476 /// If `self` is a NaN, then a NaN with the same payload as `self` and the sign bit of `sign` is
1477 /// returned.
1478 ///
1479 /// If `sign` is a NaN, then this operation will still carry over its sign into the result. Note
1480 /// that IEEE 754 doesn't assign any meaning to the sign bit in case of a NaN, and as Rust
1481 /// doesn't guarantee that the bit pattern of NaNs are conserved over arithmetic operations, the
1482 /// result of `copysign` with `sign` being a NaN might produce an unexpected or non-portable
1483 /// result. See the [specification of NaN bit patterns](primitive@f32#nan-bit-patterns) for more
1484 /// info.
1485 ///
1486 /// # Examples
1487 ///
1488 /// ```
1489 /// let f = 3.5_f64;
1490 ///
1491 /// assert_eq!(f.copysign(0.42), 3.5_f64);
1492 /// assert_eq!(f.copysign(-0.42), -3.5_f64);
1493 /// assert_eq!((-f).copysign(0.42), 3.5_f64);
1494 /// assert_eq!((-f).copysign(-0.42), -3.5_f64);
1495 ///
1496 /// assert!(f64::NAN.copysign(1.0).is_nan());
1497 /// ```
1498 #[must_use = "method returns a new number and does not mutate the original value"]
1499 #[stable(feature = "copysign", since = "1.35.0")]
1500 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
1501 #[inline]
1502 pub const fn copysign(self, sign: f64) -> f64 {
1503 // SAFETY: this is actually a safe intrinsic
1504 unsafe { intrinsics::copysignf64(self, sign) }
1505 }
1506}
1507

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