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 ///
394 /// Note that the size of the mantissa in the bitwise representation is one
395 /// smaller than this since the leading 1 is not stored explicitly.
396 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
397 pub const MANTISSA_DIGITS: u32 = 53;
398 /// Approximate number of significant digits in base 10.
399 ///
400 /// This is the maximum <i>x</i> such that any decimal number with <i>x</i>
401 /// significant digits can be converted to `f64` and back without loss.
402 ///
403 /// Equal to floor(log<sub>10</sub>&nbsp;2<sup>[`MANTISSA_DIGITS`]&nbsp;&minus;&nbsp;1</sup>).
404 ///
405 /// [`MANTISSA_DIGITS`]: f64::MANTISSA_DIGITS
406 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
407 pub const DIGITS: u32 = 15;
408
409 /// [Machine epsilon] value for `f64`.
410 ///
411 /// This is the difference between `1.0` and the next larger representable number.
412 ///
413 /// Equal to 2<sup>1&nbsp;&minus;&nbsp;[`MANTISSA_DIGITS`]</sup>.
414 ///
415 /// [Machine epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon
416 /// [`MANTISSA_DIGITS`]: f64::MANTISSA_DIGITS
417 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
418 #[rustc_diagnostic_item = "f64_epsilon"]
419 pub const EPSILON: f64 = 2.2204460492503131e-16_f64;
420
421 /// Smallest finite `f64` value.
422 ///
423 /// Equal to &minus;[`MAX`].
424 ///
425 /// [`MAX`]: f64::MAX
426 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
427 pub const MIN: f64 = -1.7976931348623157e+308_f64;
428 /// Smallest positive normal `f64` value.
429 ///
430 /// Equal to 2<sup>[`MIN_EXP`]&nbsp;&minus;&nbsp;1</sup>.
431 ///
432 /// [`MIN_EXP`]: f64::MIN_EXP
433 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
434 pub const MIN_POSITIVE: f64 = 2.2250738585072014e-308_f64;
435 /// Largest finite `f64` value.
436 ///
437 /// Equal to
438 /// (1&nbsp;&minus;&nbsp;2<sup>&minus;[`MANTISSA_DIGITS`]</sup>)&nbsp;2<sup>[`MAX_EXP`]</sup>.
439 ///
440 /// [`MANTISSA_DIGITS`]: f64::MANTISSA_DIGITS
441 /// [`MAX_EXP`]: f64::MAX_EXP
442 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
443 pub const MAX: f64 = 1.7976931348623157e+308_f64;
444
445 /// One greater than the minimum possible *normal* power of 2 exponent
446 /// for a significand bounded by 1 ≤ x < 2 (i.e. the IEEE definition).
447 ///
448 /// This corresponds to the exact minimum possible *normal* power of 2 exponent
449 /// for a significand bounded by 0.5 ≤ x < 1 (i.e. the C definition).
450 /// In other words, all normal numbers representable by this type are
451 /// greater than or equal to 0.5&nbsp;×&nbsp;2<sup><i>MIN_EXP</i></sup>.
452 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
453 pub const MIN_EXP: i32 = -1021;
454 /// One greater than the maximum possible power of 2 exponent
455 /// for a significand bounded by 1 ≤ x < 2 (i.e. the IEEE definition).
456 ///
457 /// This corresponds to the exact maximum possible power of 2 exponent
458 /// for a significand bounded by 0.5 ≤ x < 1 (i.e. the C definition).
459 /// In other words, all numbers representable by this type are
460 /// strictly less than 2<sup><i>MAX_EXP</i></sup>.
461 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
462 pub const MAX_EXP: i32 = 1024;
463
464 /// Minimum <i>x</i> for which 10<sup><i>x</i></sup> is normal.
465 ///
466 /// Equal to ceil(log<sub>10</sub>&nbsp;[`MIN_POSITIVE`]).
467 ///
468 /// [`MIN_POSITIVE`]: f64::MIN_POSITIVE
469 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
470 pub const MIN_10_EXP: i32 = -307;
471 /// Maximum <i>x</i> for which 10<sup><i>x</i></sup> is normal.
472 ///
473 /// Equal to floor(log<sub>10</sub>&nbsp;[`MAX`]).
474 ///
475 /// [`MAX`]: f64::MAX
476 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
477 pub const MAX_10_EXP: i32 = 308;
478
479 /// Not a Number (NaN).
480 ///
481 /// Note that IEEE 754 doesn't define just a single NaN value; a plethora of bit patterns are
482 /// considered to be NaN. Furthermore, the standard makes a difference between a "signaling" and
483 /// a "quiet" NaN, and allows inspecting its "payload" (the unspecified bits in the bit pattern)
484 /// and its sign. See the [specification of NaN bit patterns](f32#nan-bit-patterns) for more
485 /// info.
486 ///
487 /// This constant is guaranteed to be a quiet NaN (on targets that follow the Rust assumptions
488 /// that the quiet/signaling bit being set to 1 indicates a quiet NaN). Beyond that, nothing is
489 /// guaranteed about the specific bit pattern chosen here: both payload and sign are arbitrary.
490 /// The concrete bit pattern may change across Rust versions and target platforms.
491 #[rustc_diagnostic_item = "f64_nan"]
492 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
493 #[allow(clippy::eq_op)]
494 pub const NAN: f64 = 0.0_f64 / 0.0_f64;
495 /// Infinity (∞).
496 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
497 pub const INFINITY: f64 = 1.0_f64 / 0.0_f64;
498 /// Negative infinity (−∞).
499 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
500 pub const NEG_INFINITY: f64 = -1.0_f64 / 0.0_f64;
501
502 /// Sign bit
503 pub(crate) const SIGN_MASK: u64 = 0x8000_0000_0000_0000;
504
505 /// Exponent mask
506 pub(crate) const EXP_MASK: u64 = 0x7ff0_0000_0000_0000;
507
508 /// Mantissa mask
509 pub(crate) const MAN_MASK: u64 = 0x000f_ffff_ffff_ffff;
510
511 /// Minimum representable positive value (min subnormal)
512 const TINY_BITS: u64 = 0x1;
513
514 /// Minimum representable negative value (min negative subnormal)
515 const NEG_TINY_BITS: u64 = Self::TINY_BITS | Self::SIGN_MASK;
516
517 /// Returns `true` if this value is NaN.
518 ///
519 /// ```
520 /// let nan = f64::NAN;
521 /// let f = 7.0_f64;
522 ///
523 /// assert!(nan.is_nan());
524 /// assert!(!f.is_nan());
525 /// ```
526 #[must_use]
527 #[stable(feature = "rust1", since = "1.0.0")]
528 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
529 #[inline]
530 #[allow(clippy::eq_op)] // > if you intended to check if the operand is NaN, use `.is_nan()` instead :)
531 pub const fn is_nan(self) -> bool {
532 self != self
533 }
534
535 /// Returns `true` if this value is positive infinity or negative infinity, and
536 /// `false` otherwise.
537 ///
538 /// ```
539 /// let f = 7.0f64;
540 /// let inf = f64::INFINITY;
541 /// let neg_inf = f64::NEG_INFINITY;
542 /// let nan = f64::NAN;
543 ///
544 /// assert!(!f.is_infinite());
545 /// assert!(!nan.is_infinite());
546 ///
547 /// assert!(inf.is_infinite());
548 /// assert!(neg_inf.is_infinite());
549 /// ```
550 #[must_use]
551 #[stable(feature = "rust1", since = "1.0.0")]
552 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
553 #[inline]
554 pub const fn is_infinite(self) -> bool {
555 // Getting clever with transmutation can result in incorrect answers on some FPUs
556 // FIXME: alter the Rust <-> Rust calling convention to prevent this problem.
557 // See https://github.com/rust-lang/rust/issues/72327
558 (self == f64::INFINITY) | (self == f64::NEG_INFINITY)
559 }
560
561 /// Returns `true` if this number is neither infinite nor NaN.
562 ///
563 /// ```
564 /// let f = 7.0f64;
565 /// let inf: f64 = f64::INFINITY;
566 /// let neg_inf: f64 = f64::NEG_INFINITY;
567 /// let nan: f64 = f64::NAN;
568 ///
569 /// assert!(f.is_finite());
570 ///
571 /// assert!(!nan.is_finite());
572 /// assert!(!inf.is_finite());
573 /// assert!(!neg_inf.is_finite());
574 /// ```
575 #[must_use]
576 #[stable(feature = "rust1", since = "1.0.0")]
577 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
578 #[inline]
579 pub const fn is_finite(self) -> bool {
580 // There's no need to handle NaN separately: if self is NaN,
581 // the comparison is not true, exactly as desired.
582 self.abs() < Self::INFINITY
583 }
584
585 /// Returns `true` if the number is [subnormal].
586 ///
587 /// ```
588 /// let min = f64::MIN_POSITIVE; // 2.2250738585072014e-308_f64
589 /// let max = f64::MAX;
590 /// let lower_than_min = 1.0e-308_f64;
591 /// let zero = 0.0_f64;
592 ///
593 /// assert!(!min.is_subnormal());
594 /// assert!(!max.is_subnormal());
595 ///
596 /// assert!(!zero.is_subnormal());
597 /// assert!(!f64::NAN.is_subnormal());
598 /// assert!(!f64::INFINITY.is_subnormal());
599 /// // Values between `0` and `min` are Subnormal.
600 /// assert!(lower_than_min.is_subnormal());
601 /// ```
602 /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
603 #[must_use]
604 #[stable(feature = "is_subnormal", since = "1.53.0")]
605 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
606 #[inline]
607 pub const fn is_subnormal(self) -> bool {
608 matches!(self.classify(), FpCategory::Subnormal)
609 }
610
611 /// Returns `true` if the number is neither zero, infinite,
612 /// [subnormal], or NaN.
613 ///
614 /// ```
615 /// let min = f64::MIN_POSITIVE; // 2.2250738585072014e-308f64
616 /// let max = f64::MAX;
617 /// let lower_than_min = 1.0e-308_f64;
618 /// let zero = 0.0f64;
619 ///
620 /// assert!(min.is_normal());
621 /// assert!(max.is_normal());
622 ///
623 /// assert!(!zero.is_normal());
624 /// assert!(!f64::NAN.is_normal());
625 /// assert!(!f64::INFINITY.is_normal());
626 /// // Values between `0` and `min` are Subnormal.
627 /// assert!(!lower_than_min.is_normal());
628 /// ```
629 /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
630 #[must_use]
631 #[stable(feature = "rust1", since = "1.0.0")]
632 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
633 #[inline]
634 pub const fn is_normal(self) -> bool {
635 matches!(self.classify(), FpCategory::Normal)
636 }
637
638 /// Returns the floating point category of the number. If only one property
639 /// is going to be tested, it is generally faster to use the specific
640 /// predicate instead.
641 ///
642 /// ```
643 /// use std::num::FpCategory;
644 ///
645 /// let num = 12.4_f64;
646 /// let inf = f64::INFINITY;
647 ///
648 /// assert_eq!(num.classify(), FpCategory::Normal);
649 /// assert_eq!(inf.classify(), FpCategory::Infinite);
650 /// ```
651 #[stable(feature = "rust1", since = "1.0.0")]
652 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
653 pub const fn classify(self) -> FpCategory {
654 // We used to have complicated logic here that avoids the simple bit-based tests to work
655 // around buggy codegen for x87 targets (see
656 // https://github.com/rust-lang/rust/issues/114479). However, some LLVM versions later, none
657 // of our tests is able to find any difference between the complicated and the naive
658 // version, so now we are back to the naive version.
659 let b = self.to_bits();
660 match (b & Self::MAN_MASK, b & Self::EXP_MASK) {
661 (0, Self::EXP_MASK) => FpCategory::Infinite,
662 (_, Self::EXP_MASK) => FpCategory::Nan,
663 (0, 0) => FpCategory::Zero,
664 (_, 0) => FpCategory::Subnormal,
665 _ => FpCategory::Normal,
666 }
667 }
668
669 /// Returns `true` if `self` has a positive sign, including `+0.0`, NaNs with
670 /// positive sign bit and positive infinity.
671 ///
672 /// Note that IEEE 754 doesn't assign any meaning to the sign bit in case of
673 /// a NaN, and as Rust doesn't guarantee that the bit pattern of NaNs are
674 /// conserved over arithmetic operations, the result of `is_sign_positive` on
675 /// a NaN might produce an unexpected or non-portable result. See the [specification
676 /// of NaN bit patterns](f32#nan-bit-patterns) for more info. Use `self.signum() == 1.0`
677 /// if you need fully portable behavior (will return `false` for all NaNs).
678 ///
679 /// ```
680 /// let f = 7.0_f64;
681 /// let g = -7.0_f64;
682 ///
683 /// assert!(f.is_sign_positive());
684 /// assert!(!g.is_sign_positive());
685 /// ```
686 #[must_use]
687 #[stable(feature = "rust1", since = "1.0.0")]
688 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
689 #[inline]
690 pub const fn is_sign_positive(self) -> bool {
691 !self.is_sign_negative()
692 }
693
694 #[must_use]
695 #[stable(feature = "rust1", since = "1.0.0")]
696 #[deprecated(since = "1.0.0", note = "renamed to is_sign_positive")]
697 #[inline]
698 #[doc(hidden)]
699 pub fn is_positive(self) -> bool {
700 self.is_sign_positive()
701 }
702
703 /// Returns `true` if `self` has a negative sign, including `-0.0`, NaNs with
704 /// negative sign bit and negative infinity.
705 ///
706 /// Note that IEEE 754 doesn't assign any meaning to the sign bit in case of
707 /// a NaN, and as Rust doesn't guarantee that the bit pattern of NaNs are
708 /// conserved over arithmetic operations, the result of `is_sign_negative` on
709 /// a NaN might produce an unexpected or non-portable result. See the [specification
710 /// of NaN bit patterns](f32#nan-bit-patterns) for more info. Use `self.signum() == -1.0`
711 /// if you need fully portable behavior (will return `false` for all NaNs).
712 ///
713 /// ```
714 /// let f = 7.0_f64;
715 /// let g = -7.0_f64;
716 ///
717 /// assert!(!f.is_sign_negative());
718 /// assert!(g.is_sign_negative());
719 /// ```
720 #[must_use]
721 #[stable(feature = "rust1", since = "1.0.0")]
722 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
723 #[inline]
724 pub const fn is_sign_negative(self) -> bool {
725 // IEEE754 says: isSignMinus(x) is true if and only if x has negative sign. isSignMinus
726 // applies to zeros and NaNs as well.
727 self.to_bits() & Self::SIGN_MASK != 0
728 }
729
730 #[must_use]
731 #[stable(feature = "rust1", since = "1.0.0")]
732 #[deprecated(since = "1.0.0", note = "renamed to is_sign_negative")]
733 #[inline]
734 #[doc(hidden)]
735 pub fn is_negative(self) -> bool {
736 self.is_sign_negative()
737 }
738
739 /// Returns the least number greater than `self`.
740 ///
741 /// Let `TINY` be the smallest representable positive `f64`. Then,
742 /// - if `self.is_nan()`, this returns `self`;
743 /// - if `self` is [`NEG_INFINITY`], this returns [`MIN`];
744 /// - if `self` is `-TINY`, this returns -0.0;
745 /// - if `self` is -0.0 or +0.0, this returns `TINY`;
746 /// - if `self` is [`MAX`] or [`INFINITY`], this returns [`INFINITY`];
747 /// - otherwise the unique least value greater than `self` is returned.
748 ///
749 /// The identity `x.next_up() == -(-x).next_down()` holds for all non-NaN `x`. When `x`
750 /// is finite `x == x.next_up().next_down()` also holds.
751 ///
752 /// ```rust
753 /// // f64::EPSILON is the difference between 1.0 and the next number up.
754 /// assert_eq!(1.0f64.next_up(), 1.0 + f64::EPSILON);
755 /// // But not for most numbers.
756 /// assert!(0.1f64.next_up() < 0.1 + f64::EPSILON);
757 /// assert_eq!(9007199254740992f64.next_up(), 9007199254740994.0);
758 /// ```
759 ///
760 /// This operation corresponds to IEEE-754 `nextUp`.
761 ///
762 /// [`NEG_INFINITY`]: Self::NEG_INFINITY
763 /// [`INFINITY`]: Self::INFINITY
764 /// [`MIN`]: Self::MIN
765 /// [`MAX`]: Self::MAX
766 #[inline]
767 #[doc(alias = "nextUp")]
768 #[stable(feature = "float_next_up_down", since = "1.86.0")]
769 #[rustc_const_stable(feature = "float_next_up_down", since = "1.86.0")]
770 pub const fn next_up(self) -> Self {
771 // Some targets violate Rust's assumption of IEEE semantics, e.g. by flushing
772 // denormals to zero. This is in general unsound and unsupported, but here
773 // we do our best to still produce the correct result on such targets.
774 let bits = self.to_bits();
775 if self.is_nan() || bits == Self::INFINITY.to_bits() {
776 return self;
777 }
778
779 let abs = bits & !Self::SIGN_MASK;
780 let next_bits = if abs == 0 {
781 Self::TINY_BITS
782 } else if bits == abs {
783 bits + 1
784 } else {
785 bits - 1
786 };
787 Self::from_bits(next_bits)
788 }
789
790 /// Returns the greatest number less than `self`.
791 ///
792 /// Let `TINY` be the smallest representable positive `f64`. Then,
793 /// - if `self.is_nan()`, this returns `self`;
794 /// - if `self` is [`INFINITY`], this returns [`MAX`];
795 /// - if `self` is `TINY`, this returns 0.0;
796 /// - if `self` is -0.0 or +0.0, this returns `-TINY`;
797 /// - if `self` is [`MIN`] or [`NEG_INFINITY`], this returns [`NEG_INFINITY`];
798 /// - otherwise the unique greatest value less than `self` is returned.
799 ///
800 /// The identity `x.next_down() == -(-x).next_up()` holds for all non-NaN `x`. When `x`
801 /// is finite `x == x.next_down().next_up()` also holds.
802 ///
803 /// ```rust
804 /// let x = 1.0f64;
805 /// // Clamp value into range [0, 1).
806 /// let clamped = x.clamp(0.0, 1.0f64.next_down());
807 /// assert!(clamped < 1.0);
808 /// assert_eq!(clamped.next_up(), 1.0);
809 /// ```
810 ///
811 /// This operation corresponds to IEEE-754 `nextDown`.
812 ///
813 /// [`NEG_INFINITY`]: Self::NEG_INFINITY
814 /// [`INFINITY`]: Self::INFINITY
815 /// [`MIN`]: Self::MIN
816 /// [`MAX`]: Self::MAX
817 #[inline]
818 #[doc(alias = "nextDown")]
819 #[stable(feature = "float_next_up_down", since = "1.86.0")]
820 #[rustc_const_stable(feature = "float_next_up_down", since = "1.86.0")]
821 pub const fn next_down(self) -> Self {
822 // Some targets violate Rust's assumption of IEEE semantics, e.g. by flushing
823 // denormals to zero. This is in general unsound and unsupported, but here
824 // we do our best to still produce the correct result on such targets.
825 let bits = self.to_bits();
826 if self.is_nan() || bits == Self::NEG_INFINITY.to_bits() {
827 return self;
828 }
829
830 let abs = bits & !Self::SIGN_MASK;
831 let next_bits = if abs == 0 {
832 Self::NEG_TINY_BITS
833 } else if bits == abs {
834 bits - 1
835 } else {
836 bits + 1
837 };
838 Self::from_bits(next_bits)
839 }
840
841 /// Takes the reciprocal (inverse) of a number, `1/x`.
842 ///
843 /// ```
844 /// let x = 2.0_f64;
845 /// let abs_difference = (x.recip() - (1.0 / x)).abs();
846 ///
847 /// assert!(abs_difference < 1e-10);
848 /// ```
849 #[must_use = "this returns the result of the operation, without modifying the original"]
850 #[stable(feature = "rust1", since = "1.0.0")]
851 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
852 #[inline]
853 pub const fn recip(self) -> f64 {
854 1.0 / self
855 }
856
857 /// Converts radians to degrees.
858 ///
859 /// ```
860 /// let angle = std::f64::consts::PI;
861 ///
862 /// let abs_difference = (angle.to_degrees() - 180.0).abs();
863 ///
864 /// assert!(abs_difference < 1e-10);
865 /// ```
866 #[must_use = "this returns the result of the operation, \
867 without modifying the original"]
868 #[stable(feature = "rust1", since = "1.0.0")]
869 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
870 #[inline]
871 pub const fn to_degrees(self) -> f64 {
872 // The division here is correctly rounded with respect to the true
873 // value of 180/π. (This differs from f32, where a constant must be
874 // used to ensure a correctly rounded result.)
875 self * (180.0f64 / consts::PI)
876 }
877
878 /// Converts degrees to radians.
879 ///
880 /// ```
881 /// let angle = 180.0_f64;
882 ///
883 /// let abs_difference = (angle.to_radians() - std::f64::consts::PI).abs();
884 ///
885 /// assert!(abs_difference < 1e-10);
886 /// ```
887 #[must_use = "this returns the result of the operation, \
888 without modifying the original"]
889 #[stable(feature = "rust1", since = "1.0.0")]
890 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
891 #[inline]
892 pub const fn to_radians(self) -> f64 {
893 const RADS_PER_DEG: f64 = consts::PI / 180.0;
894 self * RADS_PER_DEG
895 }
896
897 /// Returns the maximum of the two numbers, ignoring NaN.
898 ///
899 /// If one of the arguments is NaN, then the other argument is returned.
900 /// This follows the IEEE 754-2008 semantics for maxNum, except for handling of signaling NaNs;
901 /// this function handles all NaNs the same way and avoids maxNum's problems with associativity.
902 /// This also matches the behavior of libm’s fmax. In particular, if the inputs compare equal
903 /// (such as for the case of `+0.0` and `-0.0`), either input may be returned non-deterministically.
904 ///
905 /// ```
906 /// let x = 1.0_f64;
907 /// let y = 2.0_f64;
908 ///
909 /// assert_eq!(x.max(y), y);
910 /// ```
911 #[must_use = "this returns the result of the comparison, without modifying either input"]
912 #[stable(feature = "rust1", since = "1.0.0")]
913 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
914 #[inline]
915 pub const fn max(self, other: f64) -> f64 {
916 intrinsics::maxnumf64(self, other)
917 }
918
919 /// Returns the minimum of the two numbers, ignoring NaN.
920 ///
921 /// If one of the arguments is NaN, then the other argument is returned.
922 /// This follows the IEEE 754-2008 semantics for minNum, except for handling of signaling NaNs;
923 /// this function handles all NaNs the same way and avoids minNum's problems with associativity.
924 /// This also matches the behavior of libm’s fmin. In particular, if the inputs compare equal
925 /// (such as for the case of `+0.0` and `-0.0`), either input may be returned non-deterministically.
926 ///
927 /// ```
928 /// let x = 1.0_f64;
929 /// let y = 2.0_f64;
930 ///
931 /// assert_eq!(x.min(y), x);
932 /// ```
933 #[must_use = "this returns the result of the comparison, without modifying either input"]
934 #[stable(feature = "rust1", since = "1.0.0")]
935 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
936 #[inline]
937 pub const fn min(self, other: f64) -> f64 {
938 intrinsics::minnumf64(self, other)
939 }
940
941 /// Returns the maximum of the two numbers, propagating NaN.
942 ///
943 /// This returns NaN when *either* argument is NaN, as opposed to
944 /// [`f64::max`] which only returns NaN when *both* arguments are NaN.
945 ///
946 /// ```ignore-arm-unknown-linux-gnueabihf (see https://github.com/rust-lang/rust/issues/141087)
947 /// #![feature(float_minimum_maximum)]
948 /// let x = 1.0_f64;
949 /// let y = 2.0_f64;
950 ///
951 /// assert_eq!(x.maximum(y), y);
952 /// assert!(x.maximum(f64::NAN).is_nan());
953 /// ```
954 ///
955 /// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the greater
956 /// of the two numbers. For this operation, -0.0 is considered to be less than +0.0.
957 /// Note that this follows the semantics specified in IEEE 754-2019.
958 ///
959 /// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN
960 /// operand is conserved; see the [specification of NaN bit patterns](f32#nan-bit-patterns) for more info.
961 #[must_use = "this returns the result of the comparison, without modifying either input"]
962 #[unstable(feature = "float_minimum_maximum", issue = "91079")]
963 #[inline]
964 pub const fn maximum(self, other: f64) -> f64 {
965 intrinsics::maximumf64(self, other)
966 }
967
968 /// Returns the minimum of the two numbers, propagating NaN.
969 ///
970 /// This returns NaN when *either* argument is NaN, as opposed to
971 /// [`f64::min`] which only returns NaN when *both* arguments are NaN.
972 ///
973 /// ```ignore-arm-unknown-linux-gnueabihf (see https://github.com/rust-lang/rust/issues/141087)
974 /// #![feature(float_minimum_maximum)]
975 /// let x = 1.0_f64;
976 /// let y = 2.0_f64;
977 ///
978 /// assert_eq!(x.minimum(y), x);
979 /// assert!(x.minimum(f64::NAN).is_nan());
980 /// ```
981 ///
982 /// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the lesser
983 /// of the two numbers. For this operation, -0.0 is considered to be less than +0.0.
984 /// Note that this follows the semantics specified in IEEE 754-2019.
985 ///
986 /// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN
987 /// operand is conserved; see the [specification of NaN bit patterns](f32#nan-bit-patterns) for more info.
988 #[must_use = "this returns the result of the comparison, without modifying either input"]
989 #[unstable(feature = "float_minimum_maximum", issue = "91079")]
990 #[inline]
991 pub const fn minimum(self, other: f64) -> f64 {
992 intrinsics::minimumf64(self, other)
993 }
994
995 /// Calculates the midpoint (average) between `self` and `rhs`.
996 ///
997 /// This returns NaN when *either* argument is NaN or if a combination of
998 /// +inf and -inf is provided as arguments.
999 ///
1000 /// # Examples
1001 ///
1002 /// ```
1003 /// assert_eq!(1f64.midpoint(4.0), 2.5);
1004 /// assert_eq!((-5.5f64).midpoint(8.0), 1.25);
1005 /// ```
1006 #[inline]
1007 #[doc(alias = "average")]
1008 #[stable(feature = "num_midpoint", since = "1.85.0")]
1009 #[rustc_const_stable(feature = "num_midpoint", since = "1.85.0")]
1010 pub const fn midpoint(self, other: f64) -> f64 {
1011 const LO: f64 = f64::MIN_POSITIVE * 2.;
1012 const HI: f64 = f64::MAX / 2.;
1013
1014 let (a, b) = (self, other);
1015 let abs_a = a.abs();
1016 let abs_b = b.abs();
1017
1018 if abs_a <= HI && abs_b <= HI {
1019 // Overflow is impossible
1020 (a + b) / 2.
1021 } else if abs_a < LO {
1022 // Not safe to halve `a` (would underflow)
1023 a + (b / 2.)
1024 } else if abs_b < LO {
1025 // Not safe to halve `b` (would underflow)
1026 (a / 2.) + b
1027 } else {
1028 // Safe to halve `a` and `b`
1029 (a / 2.) + (b / 2.)
1030 }
1031 }
1032
1033 /// Rounds toward zero and converts to any primitive integer type,
1034 /// assuming that the value is finite and fits in that type.
1035 ///
1036 /// ```
1037 /// let value = 4.6_f64;
1038 /// let rounded = unsafe { value.to_int_unchecked::<u16>() };
1039 /// assert_eq!(rounded, 4);
1040 ///
1041 /// let value = -128.9_f64;
1042 /// let rounded = unsafe { value.to_int_unchecked::<i8>() };
1043 /// assert_eq!(rounded, i8::MIN);
1044 /// ```
1045 ///
1046 /// # Safety
1047 ///
1048 /// The value must:
1049 ///
1050 /// * Not be `NaN`
1051 /// * Not be infinite
1052 /// * Be representable in the return type `Int`, after truncating off its fractional part
1053 #[must_use = "this returns the result of the operation, \
1054 without modifying the original"]
1055 #[stable(feature = "float_approx_unchecked_to", since = "1.44.0")]
1056 #[inline]
1057 pub unsafe fn to_int_unchecked<Int>(self) -> Int
1058 where
1059 Self: FloatToInt<Int>,
1060 {
1061 // SAFETY: the caller must uphold the safety contract for
1062 // `FloatToInt::to_int_unchecked`.
1063 unsafe { FloatToInt::<Int>::to_int_unchecked(self) }
1064 }
1065
1066 /// Raw transmutation to `u64`.
1067 ///
1068 /// This is currently identical to `transmute::<f64, u64>(self)` on all platforms.
1069 ///
1070 /// See [`from_bits`](Self::from_bits) for some discussion of the
1071 /// portability of this operation (there are almost no issues).
1072 ///
1073 /// Note that this function is distinct from `as` casting, which attempts to
1074 /// preserve the *numeric* value, and not the bitwise value.
1075 ///
1076 /// # Examples
1077 ///
1078 /// ```
1079 /// assert!((1f64).to_bits() != 1f64 as u64); // to_bits() is not casting!
1080 /// assert_eq!((12.5f64).to_bits(), 0x4029000000000000);
1081 /// ```
1082 #[must_use = "this returns the result of the operation, \
1083 without modifying the original"]
1084 #[stable(feature = "float_bits_conv", since = "1.20.0")]
1085 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1086 #[allow(unnecessary_transmutes)]
1087 #[inline]
1088 pub const fn to_bits(self) -> u64 {
1089 // SAFETY: `u64` is a plain old datatype so we can always transmute to it.
1090 unsafe { mem::transmute(self) }
1091 }
1092
1093 /// Raw transmutation from `u64`.
1094 ///
1095 /// This is currently identical to `transmute::<u64, f64>(v)` on all platforms.
1096 /// It turns out this is incredibly portable, for two reasons:
1097 ///
1098 /// * Floats and Ints have the same endianness on all supported platforms.
1099 /// * IEEE 754 very precisely specifies the bit layout of floats.
1100 ///
1101 /// However there is one caveat: prior to the 2008 version of IEEE 754, how
1102 /// to interpret the NaN signaling bit wasn't actually specified. Most platforms
1103 /// (notably x86 and ARM) picked the interpretation that was ultimately
1104 /// standardized in 2008, but some didn't (notably MIPS). As a result, all
1105 /// signaling NaNs on MIPS are quiet NaNs on x86, and vice-versa.
1106 ///
1107 /// Rather than trying to preserve signaling-ness cross-platform, this
1108 /// implementation favors preserving the exact bits. This means that
1109 /// any payloads encoded in NaNs will be preserved even if the result of
1110 /// this method is sent over the network from an x86 machine to a MIPS one.
1111 ///
1112 /// If the results of this method are only manipulated by the same
1113 /// architecture that produced them, then there is no portability concern.
1114 ///
1115 /// If the input isn't NaN, then there is no portability concern.
1116 ///
1117 /// If you don't care about signaling-ness (very likely), then there is no
1118 /// portability concern.
1119 ///
1120 /// Note that this function is distinct from `as` casting, which attempts to
1121 /// preserve the *numeric* value, and not the bitwise value.
1122 ///
1123 /// # Examples
1124 ///
1125 /// ```
1126 /// let v = f64::from_bits(0x4029000000000000);
1127 /// assert_eq!(v, 12.5);
1128 /// ```
1129 #[stable(feature = "float_bits_conv", since = "1.20.0")]
1130 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1131 #[must_use]
1132 #[inline]
1133 #[allow(unnecessary_transmutes)]
1134 pub const fn from_bits(v: u64) -> Self {
1135 // It turns out the safety issues with sNaN were overblown! Hooray!
1136 // SAFETY: `u64` is a plain old datatype so we can always transmute from it.
1137 unsafe { mem::transmute(v) }
1138 }
1139
1140 /// Returns the memory representation of this floating point number as a byte array in
1141 /// big-endian (network) byte order.
1142 ///
1143 /// See [`from_bits`](Self::from_bits) for some discussion of the
1144 /// portability of this operation (there are almost no issues).
1145 ///
1146 /// # Examples
1147 ///
1148 /// ```
1149 /// let bytes = 12.5f64.to_be_bytes();
1150 /// assert_eq!(bytes, [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]);
1151 /// ```
1152 #[must_use = "this returns the result of the operation, \
1153 without modifying the original"]
1154 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1155 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1156 #[inline]
1157 pub const fn to_be_bytes(self) -> [u8; 8] {
1158 self.to_bits().to_be_bytes()
1159 }
1160
1161 /// Returns the memory representation of this floating point number as a byte array in
1162 /// little-endian byte order.
1163 ///
1164 /// See [`from_bits`](Self::from_bits) for some discussion of the
1165 /// portability of this operation (there are almost no issues).
1166 ///
1167 /// # Examples
1168 ///
1169 /// ```
1170 /// let bytes = 12.5f64.to_le_bytes();
1171 /// assert_eq!(bytes, [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]);
1172 /// ```
1173 #[must_use = "this returns the result of the operation, \
1174 without modifying the original"]
1175 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1176 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1177 #[inline]
1178 pub const fn to_le_bytes(self) -> [u8; 8] {
1179 self.to_bits().to_le_bytes()
1180 }
1181
1182 /// Returns the memory representation of this floating point number as a byte array in
1183 /// native byte order.
1184 ///
1185 /// As the target platform's native endianness is used, portable code
1186 /// should use [`to_be_bytes`] or [`to_le_bytes`], as appropriate, instead.
1187 ///
1188 /// [`to_be_bytes`]: f64::to_be_bytes
1189 /// [`to_le_bytes`]: f64::to_le_bytes
1190 ///
1191 /// See [`from_bits`](Self::from_bits) for some discussion of the
1192 /// portability of this operation (there are almost no issues).
1193 ///
1194 /// # Examples
1195 ///
1196 /// ```
1197 /// let bytes = 12.5f64.to_ne_bytes();
1198 /// assert_eq!(
1199 /// bytes,
1200 /// if cfg!(target_endian = "big") {
1201 /// [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
1202 /// } else {
1203 /// [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]
1204 /// }
1205 /// );
1206 /// ```
1207 #[must_use = "this returns the result of the operation, \
1208 without modifying the original"]
1209 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1210 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1211 #[inline]
1212 pub const fn to_ne_bytes(self) -> [u8; 8] {
1213 self.to_bits().to_ne_bytes()
1214 }
1215
1216 /// Creates a floating point value from its representation as a byte array in big endian.
1217 ///
1218 /// See [`from_bits`](Self::from_bits) for some discussion of the
1219 /// portability of this operation (there are almost no issues).
1220 ///
1221 /// # Examples
1222 ///
1223 /// ```
1224 /// let value = f64::from_be_bytes([0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]);
1225 /// assert_eq!(value, 12.5);
1226 /// ```
1227 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1228 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1229 #[must_use]
1230 #[inline]
1231 pub const fn from_be_bytes(bytes: [u8; 8]) -> Self {
1232 Self::from_bits(u64::from_be_bytes(bytes))
1233 }
1234
1235 /// Creates a floating point value from its representation as a byte array in little endian.
1236 ///
1237 /// See [`from_bits`](Self::from_bits) for some discussion of the
1238 /// portability of this operation (there are almost no issues).
1239 ///
1240 /// # Examples
1241 ///
1242 /// ```
1243 /// let value = f64::from_le_bytes([0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]);
1244 /// assert_eq!(value, 12.5);
1245 /// ```
1246 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1247 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1248 #[must_use]
1249 #[inline]
1250 pub const fn from_le_bytes(bytes: [u8; 8]) -> Self {
1251 Self::from_bits(u64::from_le_bytes(bytes))
1252 }
1253
1254 /// Creates a floating point value from its representation as a byte array in native endian.
1255 ///
1256 /// As the target platform's native endianness is used, portable code
1257 /// likely wants to use [`from_be_bytes`] or [`from_le_bytes`], as
1258 /// appropriate instead.
1259 ///
1260 /// [`from_be_bytes`]: f64::from_be_bytes
1261 /// [`from_le_bytes`]: f64::from_le_bytes
1262 ///
1263 /// See [`from_bits`](Self::from_bits) for some discussion of the
1264 /// portability of this operation (there are almost no issues).
1265 ///
1266 /// # Examples
1267 ///
1268 /// ```
1269 /// let value = f64::from_ne_bytes(if cfg!(target_endian = "big") {
1270 /// [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
1271 /// } else {
1272 /// [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]
1273 /// });
1274 /// assert_eq!(value, 12.5);
1275 /// ```
1276 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1277 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1278 #[must_use]
1279 #[inline]
1280 pub const fn from_ne_bytes(bytes: [u8; 8]) -> Self {
1281 Self::from_bits(u64::from_ne_bytes(bytes))
1282 }
1283
1284 /// Returns the ordering between `self` and `other`.
1285 ///
1286 /// Unlike the standard partial comparison between floating point numbers,
1287 /// this comparison always produces an ordering in accordance to
1288 /// the `totalOrder` predicate as defined in the IEEE 754 (2008 revision)
1289 /// floating point standard. The values are ordered in the following sequence:
1290 ///
1291 /// - negative quiet NaN
1292 /// - negative signaling NaN
1293 /// - negative infinity
1294 /// - negative numbers
1295 /// - negative subnormal numbers
1296 /// - negative zero
1297 /// - positive zero
1298 /// - positive subnormal numbers
1299 /// - positive numbers
1300 /// - positive infinity
1301 /// - positive signaling NaN
1302 /// - positive quiet NaN.
1303 ///
1304 /// The ordering established by this function does not always agree with the
1305 /// [`PartialOrd`] and [`PartialEq`] implementations of `f64`. For example,
1306 /// they consider negative and positive zero equal, while `total_cmp`
1307 /// doesn't.
1308 ///
1309 /// The interpretation of the signaling NaN bit follows the definition in
1310 /// the IEEE 754 standard, which may not match the interpretation by some of
1311 /// the older, non-conformant (e.g. MIPS) hardware implementations.
1312 ///
1313 /// # Example
1314 ///
1315 /// ```
1316 /// struct GoodBoy {
1317 /// name: String,
1318 /// weight: f64,
1319 /// }
1320 ///
1321 /// let mut bois = vec![
1322 /// GoodBoy { name: "Pucci".to_owned(), weight: 0.1 },
1323 /// GoodBoy { name: "Woofer".to_owned(), weight: 99.0 },
1324 /// GoodBoy { name: "Yapper".to_owned(), weight: 10.0 },
1325 /// GoodBoy { name: "Chonk".to_owned(), weight: f64::INFINITY },
1326 /// GoodBoy { name: "Abs. Unit".to_owned(), weight: f64::NAN },
1327 /// GoodBoy { name: "Floaty".to_owned(), weight: -5.0 },
1328 /// ];
1329 ///
1330 /// bois.sort_by(|a, b| a.weight.total_cmp(&b.weight));
1331 ///
1332 /// // `f64::NAN` could be positive or negative, which will affect the sort order.
1333 /// if f64::NAN.is_sign_negative() {
1334 /// assert!(bois.into_iter().map(|b| b.weight)
1335 /// .zip([f64::NAN, -5.0, 0.1, 10.0, 99.0, f64::INFINITY].iter())
1336 /// .all(|(a, b)| a.to_bits() == b.to_bits()))
1337 /// } else {
1338 /// assert!(bois.into_iter().map(|b| b.weight)
1339 /// .zip([-5.0, 0.1, 10.0, 99.0, f64::INFINITY, f64::NAN].iter())
1340 /// .all(|(a, b)| a.to_bits() == b.to_bits()))
1341 /// }
1342 /// ```
1343 #[stable(feature = "total_cmp", since = "1.62.0")]
1344 #[must_use]
1345 #[inline]
1346 pub fn total_cmp(&self, other: &Self) -> crate::cmp::Ordering {
1347 let mut left = self.to_bits() as i64;
1348 let mut right = other.to_bits() as i64;
1349
1350 // In case of negatives, flip all the bits except the sign
1351 // to achieve a similar layout as two's complement integers
1352 //
1353 // Why does this work? IEEE 754 floats consist of three fields:
1354 // Sign bit, exponent and mantissa. The set of exponent and mantissa
1355 // fields as a whole have the property that their bitwise order is
1356 // equal to the numeric magnitude where the magnitude is defined.
1357 // The magnitude is not normally defined on NaN values, but
1358 // IEEE 754 totalOrder defines the NaN values also to follow the
1359 // bitwise order. This leads to order explained in the doc comment.
1360 // However, the representation of magnitude is the same for negative
1361 // and positive numbers – only the sign bit is different.
1362 // To easily compare the floats as signed integers, we need to
1363 // flip the exponent and mantissa bits in case of negative numbers.
1364 // We effectively convert the numbers to "two's complement" form.
1365 //
1366 // To do the flipping, we construct a mask and XOR against it.
1367 // We branchlessly calculate an "all-ones except for the sign bit"
1368 // mask from negative-signed values: right shifting sign-extends
1369 // the integer, so we "fill" the mask with sign bits, and then
1370 // convert to unsigned to push one more zero bit.
1371 // On positive values, the mask is all zeros, so it's a no-op.
1372 left ^= (((left >> 63) as u64) >> 1) as i64;
1373 right ^= (((right >> 63) as u64) >> 1) as i64;
1374
1375 left.cmp(&right)
1376 }
1377
1378 /// Restrict a value to a certain interval unless it is NaN.
1379 ///
1380 /// Returns `max` if `self` is greater than `max`, and `min` if `self` is
1381 /// less than `min`. Otherwise this returns `self`.
1382 ///
1383 /// Note that this function returns NaN if the initial value was NaN as
1384 /// well.
1385 ///
1386 /// # Panics
1387 ///
1388 /// Panics if `min > max`, `min` is NaN, or `max` is NaN.
1389 ///
1390 /// # Examples
1391 ///
1392 /// ```
1393 /// assert!((-3.0f64).clamp(-2.0, 1.0) == -2.0);
1394 /// assert!((0.0f64).clamp(-2.0, 1.0) == 0.0);
1395 /// assert!((2.0f64).clamp(-2.0, 1.0) == 1.0);
1396 /// assert!((f64::NAN).clamp(-2.0, 1.0).is_nan());
1397 /// ```
1398 #[must_use = "method returns a new number and does not mutate the original value"]
1399 #[stable(feature = "clamp", since = "1.50.0")]
1400 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
1401 #[inline]
1402 pub const fn clamp(mut self, min: f64, max: f64) -> f64 {
1403 const_assert!(
1404 min <= max,
1405 "min > max, or either was NaN",
1406 "min > max, or either was NaN. min = {min:?}, max = {max:?}",
1407 min: f64,
1408 max: f64,
1409 );
1410
1411 if self < min {
1412 self = min;
1413 }
1414 if self > max {
1415 self = max;
1416 }
1417 self
1418 }
1419
1420 /// Computes the absolute value of `self`.
1421 ///
1422 /// This function always returns the precise result.
1423 ///
1424 /// # Examples
1425 ///
1426 /// ```
1427 /// let x = 3.5_f64;
1428 /// let y = -3.5_f64;
1429 ///
1430 /// assert_eq!(x.abs(), x);
1431 /// assert_eq!(y.abs(), -y);
1432 ///
1433 /// assert!(f64::NAN.abs().is_nan());
1434 /// ```
1435 #[must_use = "method returns a new number and does not mutate the original value"]
1436 #[stable(feature = "rust1", since = "1.0.0")]
1437 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
1438 #[inline]
1439 pub const fn abs(self) -> f64 {
1440 // SAFETY: this is actually a safe intrinsic
1441 unsafe { intrinsics::fabsf64(self) }
1442 }
1443
1444 /// Returns a number that represents the sign of `self`.
1445 ///
1446 /// - `1.0` if the number is positive, `+0.0` or `INFINITY`
1447 /// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
1448 /// - NaN if the number is NaN
1449 ///
1450 /// # Examples
1451 ///
1452 /// ```
1453 /// let f = 3.5_f64;
1454 ///
1455 /// assert_eq!(f.signum(), 1.0);
1456 /// assert_eq!(f64::NEG_INFINITY.signum(), -1.0);
1457 ///
1458 /// assert!(f64::NAN.signum().is_nan());
1459 /// ```
1460 #[must_use = "method returns a new number and does not mutate the original value"]
1461 #[stable(feature = "rust1", since = "1.0.0")]
1462 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
1463 #[inline]
1464 pub const fn signum(self) -> f64 {
1465 if self.is_nan() { Self::NAN } else { 1.0_f64.copysign(self) }
1466 }
1467
1468 /// Returns a number composed of the magnitude of `self` and the sign of
1469 /// `sign`.
1470 ///
1471 /// Equal to `self` if the sign of `self` and `sign` are the same, otherwise equal to `-self`.
1472 /// If `self` is a NaN, then a NaN with the same payload as `self` and the sign bit of `sign` is
1473 /// returned.
1474 ///
1475 /// If `sign` is a NaN, then this operation will still carry over its sign into the result. Note
1476 /// that IEEE 754 doesn't assign any meaning to the sign bit in case of a NaN, and as Rust
1477 /// doesn't guarantee that the bit pattern of NaNs are conserved over arithmetic operations, the
1478 /// result of `copysign` with `sign` being a NaN might produce an unexpected or non-portable
1479 /// result. See the [specification of NaN bit patterns](primitive@f32#nan-bit-patterns) for more
1480 /// info.
1481 ///
1482 /// # Examples
1483 ///
1484 /// ```
1485 /// let f = 3.5_f64;
1486 ///
1487 /// assert_eq!(f.copysign(0.42), 3.5_f64);
1488 /// assert_eq!(f.copysign(-0.42), -3.5_f64);
1489 /// assert_eq!((-f).copysign(0.42), 3.5_f64);
1490 /// assert_eq!((-f).copysign(-0.42), -3.5_f64);
1491 ///
1492 /// assert!(f64::NAN.copysign(1.0).is_nan());
1493 /// ```
1494 #[must_use = "method returns a new number and does not mutate the original value"]
1495 #[stable(feature = "copysign", since = "1.35.0")]
1496 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
1497 #[inline]
1498 pub const fn copysign(self, sign: f64) -> f64 {
1499 // SAFETY: this is actually a safe intrinsic
1500 unsafe { intrinsics::copysignf64(self, sign) }
1501 }
1502
1503 /// Float addition that allows optimizations based on algebraic rules.
1504 ///
1505 /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1506 #[must_use = "method returns a new number and does not mutate the original value"]
1507 #[unstable(feature = "float_algebraic", issue = "136469")]
1508 #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1509 #[inline]
1510 pub const fn algebraic_add(self, rhs: f64) -> f64 {
1511 intrinsics::fadd_algebraic(self, rhs)
1512 }
1513
1514 /// Float subtraction that allows optimizations based on algebraic rules.
1515 ///
1516 /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1517 #[must_use = "method returns a new number and does not mutate the original value"]
1518 #[unstable(feature = "float_algebraic", issue = "136469")]
1519 #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1520 #[inline]
1521 pub const fn algebraic_sub(self, rhs: f64) -> f64 {
1522 intrinsics::fsub_algebraic(self, rhs)
1523 }
1524
1525 /// Float multiplication that allows optimizations based on algebraic rules.
1526 ///
1527 /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1528 #[must_use = "method returns a new number and does not mutate the original value"]
1529 #[unstable(feature = "float_algebraic", issue = "136469")]
1530 #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1531 #[inline]
1532 pub const fn algebraic_mul(self, rhs: f64) -> f64 {
1533 intrinsics::fmul_algebraic(self, rhs)
1534 }
1535
1536 /// Float division that allows optimizations based on algebraic rules.
1537 ///
1538 /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1539 #[must_use = "method returns a new number and does not mutate the original value"]
1540 #[unstable(feature = "float_algebraic", issue = "136469")]
1541 #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1542 #[inline]
1543 pub const fn algebraic_div(self, rhs: f64) -> f64 {
1544 intrinsics::fdiv_algebraic(self, rhs)
1545 }
1546
1547 /// Float remainder that allows optimizations based on algebraic rules.
1548 ///
1549 /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1550 #[must_use = "method returns a new number and does not mutate the original value"]
1551 #[unstable(feature = "float_algebraic", issue = "136469")]
1552 #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1553 #[inline]
1554 pub const fn algebraic_rem(self, rhs: f64) -> f64 {
1555 intrinsics::frem_algebraic(self, rhs)
1556 }
1557}
1558
1559#[unstable(feature = "core_float_math", issue = "137578")]
1560/// Experimental implementations of floating point functions in `core`.
1561///
1562/// _The standalone functions in this module are for testing only.
1563/// They will be stabilized as inherent methods._
1564pub mod math {
1565 use crate::intrinsics;
1566 use crate::num::libm;
1567
1568 /// Experimental version of `floor` in `core`. See [`f64::floor`] for details.
1569 ///
1570 /// # Examples
1571 ///
1572 /// ```
1573 /// #![feature(core_float_math)]
1574 ///
1575 /// use core::f64;
1576 ///
1577 /// let f = 3.7_f64;
1578 /// let g = 3.0_f64;
1579 /// let h = -3.7_f64;
1580 ///
1581 /// assert_eq!(f64::math::floor(f), 3.0);
1582 /// assert_eq!(f64::math::floor(g), 3.0);
1583 /// assert_eq!(f64::math::floor(h), -4.0);
1584 /// ```
1585 ///
1586 /// _This standalone function is for testing only.
1587 /// It will be stabilized as an inherent method._
1588 ///
1589 /// [`f64::floor`]: ../../../std/primitive.f64.html#method.floor
1590 #[inline]
1591 #[unstable(feature = "core_float_math", issue = "137578")]
1592 #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
1593 #[must_use = "method returns a new number and does not mutate the original value"]
1594 pub const fn floor(x: f64) -> f64 {
1595 // SAFETY: intrinsic with no preconditions
1596 unsafe { intrinsics::floorf64(x) }
1597 }
1598
1599 /// Experimental version of `ceil` in `core`. See [`f64::ceil`] for details.
1600 ///
1601 /// # Examples
1602 ///
1603 /// ```
1604 /// #![feature(core_float_math)]
1605 ///
1606 /// use core::f64;
1607 ///
1608 /// let f = 3.01_f64;
1609 /// let g = 4.0_f64;
1610 ///
1611 /// assert_eq!(f64::math::ceil(f), 4.0);
1612 /// assert_eq!(f64::math::ceil(g), 4.0);
1613 /// ```
1614 ///
1615 /// _This standalone function is for testing only.
1616 /// It will be stabilized as an inherent method._
1617 ///
1618 /// [`f64::ceil`]: ../../../std/primitive.f64.html#method.ceil
1619 #[inline]
1620 #[doc(alias = "ceiling")]
1621 #[unstable(feature = "core_float_math", issue = "137578")]
1622 #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
1623 #[must_use = "method returns a new number and does not mutate the original value"]
1624 pub const fn ceil(x: f64) -> f64 {
1625 // SAFETY: intrinsic with no preconditions
1626 unsafe { intrinsics::ceilf64(x) }
1627 }
1628
1629 /// Experimental version of `round` in `core`. See [`f64::round`] for details.
1630 ///
1631 /// # Examples
1632 ///
1633 /// ```
1634 /// #![feature(core_float_math)]
1635 ///
1636 /// use core::f64;
1637 ///
1638 /// let f = 3.3_f64;
1639 /// let g = -3.3_f64;
1640 /// let h = -3.7_f64;
1641 /// let i = 3.5_f64;
1642 /// let j = 4.5_f64;
1643 ///
1644 /// assert_eq!(f64::math::round(f), 3.0);
1645 /// assert_eq!(f64::math::round(g), -3.0);
1646 /// assert_eq!(f64::math::round(h), -4.0);
1647 /// assert_eq!(f64::math::round(i), 4.0);
1648 /// assert_eq!(f64::math::round(j), 5.0);
1649 /// ```
1650 ///
1651 /// _This standalone function is for testing only.
1652 /// It will be stabilized as an inherent method._
1653 ///
1654 /// [`f64::round`]: ../../../std/primitive.f64.html#method.round
1655 #[inline]
1656 #[unstable(feature = "core_float_math", issue = "137578")]
1657 #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
1658 #[must_use = "method returns a new number and does not mutate the original value"]
1659 pub const fn round(x: f64) -> f64 {
1660 // SAFETY: intrinsic with no preconditions
1661 unsafe { intrinsics::roundf64(x) }
1662 }
1663
1664 /// Experimental version of `round_ties_even` in `core`. See [`f64::round_ties_even`] for
1665 /// details.
1666 ///
1667 /// # Examples
1668 ///
1669 /// ```
1670 /// #![feature(core_float_math)]
1671 ///
1672 /// use core::f64;
1673 ///
1674 /// let f = 3.3_f64;
1675 /// let g = -3.3_f64;
1676 /// let h = 3.5_f64;
1677 /// let i = 4.5_f64;
1678 ///
1679 /// assert_eq!(f64::math::round_ties_even(f), 3.0);
1680 /// assert_eq!(f64::math::round_ties_even(g), -3.0);
1681 /// assert_eq!(f64::math::round_ties_even(h), 4.0);
1682 /// assert_eq!(f64::math::round_ties_even(i), 4.0);
1683 /// ```
1684 ///
1685 /// _This standalone function is for testing only.
1686 /// It will be stabilized as an inherent method._
1687 ///
1688 /// [`f64::round_ties_even`]: ../../../std/primitive.f64.html#method.round_ties_even
1689 #[inline]
1690 #[unstable(feature = "core_float_math", issue = "137578")]
1691 #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
1692 #[must_use = "method returns a new number and does not mutate the original value"]
1693 pub const fn round_ties_even(x: f64) -> f64 {
1694 intrinsics::round_ties_even_f64(x)
1695 }
1696
1697 /// Experimental version of `trunc` in `core`. See [`f64::trunc`] for details.
1698 ///
1699 /// # Examples
1700 ///
1701 /// ```
1702 /// #![feature(core_float_math)]
1703 ///
1704 /// use core::f64;
1705 ///
1706 /// let f = 3.7_f64;
1707 /// let g = 3.0_f64;
1708 /// let h = -3.7_f64;
1709 ///
1710 /// assert_eq!(f64::math::trunc(f), 3.0);
1711 /// assert_eq!(f64::math::trunc(g), 3.0);
1712 /// assert_eq!(f64::math::trunc(h), -3.0);
1713 /// ```
1714 ///
1715 /// _This standalone function is for testing only.
1716 /// It will be stabilized as an inherent method._
1717 ///
1718 /// [`f64::trunc`]: ../../../std/primitive.f64.html#method.trunc
1719 #[inline]
1720 #[doc(alias = "truncate")]
1721 #[unstable(feature = "core_float_math", issue = "137578")]
1722 #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
1723 #[must_use = "method returns a new number and does not mutate the original value"]
1724 pub const fn trunc(x: f64) -> f64 {
1725 // SAFETY: intrinsic with no preconditions
1726 unsafe { intrinsics::truncf64(x) }
1727 }
1728
1729 /// Experimental version of `fract` in `core`. See [`f64::fract`] for details.
1730 ///
1731 /// # Examples
1732 ///
1733 /// ```
1734 /// #![feature(core_float_math)]
1735 ///
1736 /// use core::f64;
1737 ///
1738 /// let x = 3.6_f64;
1739 /// let y = -3.6_f64;
1740 /// let abs_difference_x = (f64::math::fract(x) - 0.6).abs();
1741 /// let abs_difference_y = (f64::math::fract(y) - (-0.6)).abs();
1742 ///
1743 /// assert!(abs_difference_x < 1e-10);
1744 /// assert!(abs_difference_y < 1e-10);
1745 /// ```
1746 ///
1747 /// _This standalone function is for testing only.
1748 /// It will be stabilized as an inherent method._
1749 ///
1750 /// [`f64::fract`]: ../../../std/primitive.f64.html#method.fract
1751 #[inline]
1752 #[unstable(feature = "core_float_math", issue = "137578")]
1753 #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
1754 #[must_use = "method returns a new number and does not mutate the original value"]
1755 pub const fn fract(x: f64) -> f64 {
1756 x - trunc(x)
1757 }
1758
1759 /// Experimental version of `mul_add` in `core`. See [`f64::mul_add`] for details.
1760 ///
1761 /// # Examples
1762 ///
1763 /// ```
1764 /// #![feature(core_float_math)]
1765 ///
1766 /// # // FIXME(#140515): mingw has an incorrect fma
1767 /// # // https://sourceforge.net/p/mingw-w64/bugs/848/
1768 /// # #[cfg(all(target_os = "windows", target_env = "gnu", not(target_abi = "llvm")))] {
1769 /// use core::f64;
1770 ///
1771 /// let m = 10.0_f64;
1772 /// let x = 4.0_f64;
1773 /// let b = 60.0_f64;
1774 ///
1775 /// assert_eq!(f64::math::mul_add(m, x, b), 100.0);
1776 /// assert_eq!(m * x + b, 100.0);
1777 ///
1778 /// let one_plus_eps = 1.0_f64 + f64::EPSILON;
1779 /// let one_minus_eps = 1.0_f64 - f64::EPSILON;
1780 /// let minus_one = -1.0_f64;
1781 ///
1782 /// // The exact result (1 + eps) * (1 - eps) = 1 - eps * eps.
1783 /// assert_eq!(
1784 /// f64::math::mul_add(one_plus_eps, one_minus_eps, minus_one),
1785 /// -f64::EPSILON * f64::EPSILON
1786 /// );
1787 /// // Different rounding with the non-fused multiply and add.
1788 /// assert_eq!(one_plus_eps * one_minus_eps + minus_one, 0.0);
1789 /// # }
1790 /// ```
1791 ///
1792 /// _This standalone function is for testing only.
1793 /// It will be stabilized as an inherent method._
1794 ///
1795 /// [`f64::mul_add`]: ../../../std/primitive.f64.html#method.mul_add
1796 #[inline]
1797 #[doc(alias = "fma", alias = "fusedMultiplyAdd")]
1798 #[unstable(feature = "core_float_math", issue = "137578")]
1799 #[must_use = "method returns a new number and does not mutate the original value"]
1800 pub fn mul_add(x: f64, a: f64, b: f64) -> f64 {
1801 // SAFETY: intrinsic with no preconditions
1802 unsafe { intrinsics::fmaf64(x, a, b) }
1803 }
1804
1805 /// Experimental version of `div_euclid` in `core`. See [`f64::div_euclid`] for details.
1806 ///
1807 /// # Examples
1808 ///
1809 /// ```
1810 /// #![feature(core_float_math)]
1811 ///
1812 /// use core::f64;
1813 ///
1814 /// let a: f64 = 7.0;
1815 /// let b = 4.0;
1816 /// assert_eq!(f64::math::div_euclid(a, b), 1.0); // 7.0 > 4.0 * 1.0
1817 /// assert_eq!(f64::math::div_euclid(-a, b), -2.0); // -7.0 >= 4.0 * -2.0
1818 /// assert_eq!(f64::math::div_euclid(a, -b), -1.0); // 7.0 >= -4.0 * -1.0
1819 /// assert_eq!(f64::math::div_euclid(-a, -b), 2.0); // -7.0 >= -4.0 * 2.0
1820 /// ```
1821 ///
1822 /// _This standalone function is for testing only.
1823 /// It will be stabilized as an inherent method._
1824 ///
1825 /// [`f64::div_euclid`]: ../../../std/primitive.f64.html#method.div_euclid
1826 #[inline]
1827 #[unstable(feature = "core_float_math", issue = "137578")]
1828 #[must_use = "method returns a new number and does not mutate the original value"]
1829 pub fn div_euclid(x: f64, rhs: f64) -> f64 {
1830 let q = trunc(x / rhs);
1831 if x % rhs < 0.0 {
1832 return if rhs > 0.0 { q - 1.0 } else { q + 1.0 };
1833 }
1834 q
1835 }
1836
1837 /// Experimental version of `rem_euclid` in `core`. See [`f64::rem_euclid`] for details.
1838 ///
1839 /// # Examples
1840 ///
1841 /// ```
1842 /// #![feature(core_float_math)]
1843 ///
1844 /// use core::f64;
1845 ///
1846 /// let a: f64 = 7.0;
1847 /// let b = 4.0;
1848 /// assert_eq!(f64::math::rem_euclid(a, b), 3.0);
1849 /// assert_eq!(f64::math::rem_euclid(-a, b), 1.0);
1850 /// assert_eq!(f64::math::rem_euclid(a, -b), 3.0);
1851 /// assert_eq!(f64::math::rem_euclid(-a, -b), 1.0);
1852 /// // limitation due to round-off error
1853 /// assert!(f64::math::rem_euclid(-f64::EPSILON, 3.0) != 0.0);
1854 /// ```
1855 ///
1856 /// _This standalone function is for testing only.
1857 /// It will be stabilized as an inherent method._
1858 ///
1859 /// [`f64::rem_euclid`]: ../../../std/primitive.f64.html#method.rem_euclid
1860 #[inline]
1861 #[doc(alias = "modulo", alias = "mod")]
1862 #[unstable(feature = "core_float_math", issue = "137578")]
1863 #[must_use = "method returns a new number and does not mutate the original value"]
1864 pub fn rem_euclid(x: f64, rhs: f64) -> f64 {
1865 let r = x % rhs;
1866 if r < 0.0 { r + rhs.abs() } else { r }
1867 }
1868
1869 /// Experimental version of `powi` in `core`. See [`f64::powi`] for details.
1870 ///
1871 /// # Examples
1872 ///
1873 /// ```
1874 /// #![feature(core_float_math)]
1875 ///
1876 /// use core::f64;
1877 ///
1878 /// let x = 2.0_f64;
1879 /// let abs_difference = (f64::math::powi(x, 2) - (x * x)).abs();
1880 /// assert!(abs_difference <= 1e-6);
1881 ///
1882 /// assert_eq!(f64::math::powi(f64::NAN, 0), 1.0);
1883 /// ```
1884 ///
1885 /// _This standalone function is for testing only.
1886 /// It will be stabilized as an inherent method._
1887 ///
1888 /// [`f64::powi`]: ../../../std/primitive.f64.html#method.powi
1889 #[inline]
1890 #[unstable(feature = "core_float_math", issue = "137578")]
1891 #[must_use = "method returns a new number and does not mutate the original value"]
1892 pub fn powi(x: f64, n: i32) -> f64 {
1893 // SAFETY: intrinsic with no preconditions
1894 unsafe { intrinsics::powif64(x, n) }
1895 }
1896
1897 /// Experimental version of `sqrt` in `core`. See [`f64::sqrt`] for details.
1898 ///
1899 /// # Examples
1900 ///
1901 /// ```
1902 /// #![feature(core_float_math)]
1903 ///
1904 /// use core::f64;
1905 ///
1906 /// let positive = 4.0_f64;
1907 /// let negative = -4.0_f64;
1908 /// let negative_zero = -0.0_f64;
1909 ///
1910 /// assert_eq!(f64::math::sqrt(positive), 2.0);
1911 /// assert!(f64::math::sqrt(negative).is_nan());
1912 /// assert_eq!(f64::math::sqrt(negative_zero), negative_zero);
1913 /// ```
1914 ///
1915 /// _This standalone function is for testing only.
1916 /// It will be stabilized as an inherent method._
1917 ///
1918 /// [`f64::sqrt`]: ../../../std/primitive.f64.html#method.sqrt
1919 #[inline]
1920 #[doc(alias = "squareRoot")]
1921 #[unstable(feature = "core_float_math", issue = "137578")]
1922 #[must_use = "method returns a new number and does not mutate the original value"]
1923 pub fn sqrt(x: f64) -> f64 {
1924 // SAFETY: intrinsic with no preconditions
1925 unsafe { intrinsics::sqrtf64(x) }
1926 }
1927
1928 /// Experimental version of `abs_sub` in `core`. See [`f64::abs_sub`] for details.
1929 ///
1930 /// # Examples
1931 ///
1932 /// ```
1933 /// #![feature(core_float_math)]
1934 ///
1935 /// use core::f64;
1936 ///
1937 /// let x = 3.0_f64;
1938 /// let y = -3.0_f64;
1939 ///
1940 /// let abs_difference_x = (f64::math::abs_sub(x, 1.0) - 2.0).abs();
1941 /// let abs_difference_y = (f64::math::abs_sub(y, 1.0) - 0.0).abs();
1942 ///
1943 /// assert!(abs_difference_x < 1e-10);
1944 /// assert!(abs_difference_y < 1e-10);
1945 /// ```
1946 ///
1947 /// _This standalone function is for testing only.
1948 /// It will be stabilized as an inherent method._
1949 ///
1950 /// [`f64::abs_sub`]: ../../../std/primitive.f64.html#method.abs_sub
1951 #[inline]
1952 #[unstable(feature = "core_float_math", issue = "137578")]
1953 #[deprecated(
1954 since = "1.10.0",
1955 note = "you probably meant `(self - other).abs()`: \
1956 this operation is `(self - other).max(0.0)` \
1957 except that `abs_sub` also propagates NaNs (also \
1958 known as `fdim` in C). If you truly need the positive \
1959 difference, consider using that expression or the C function \
1960 `fdim`, depending on how you wish to handle NaN (please consider \
1961 filing an issue describing your use-case too)."
1962 )]
1963 #[must_use = "method returns a new number and does not mutate the original value"]
1964 pub fn abs_sub(x: f64, other: f64) -> f64 {
1965 libm::fdim(x, other)
1966 }
1967
1968 /// Experimental version of `cbrt` in `core`. See [`f64::cbrt`] for details.
1969 ///
1970 /// # Examples
1971 ///
1972 /// ```
1973 /// #![feature(core_float_math)]
1974 ///
1975 /// use core::f64;
1976 ///
1977 /// let x = 8.0_f64;
1978 ///
1979 /// // x^(1/3) - 2 == 0
1980 /// let abs_difference = (f64::math::cbrt(x) - 2.0).abs();
1981 ///
1982 /// assert!(abs_difference < 1e-10);
1983 /// ```
1984 ///
1985 /// _This standalone function is for testing only.
1986 /// It will be stabilized as an inherent method._
1987 ///
1988 /// [`f64::cbrt`]: ../../../std/primitive.f64.html#method.cbrt
1989 #[inline]
1990 #[unstable(feature = "core_float_math", issue = "137578")]
1991 #[must_use = "method returns a new number and does not mutate the original value"]
1992 pub fn cbrt(x: f64) -> f64 {
1993 libm::cbrt(x)
1994 }
1995}
1996