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")]
280#[rustc_diagnostic_item = "f64_consts_mod"]
281pub mod consts {
282 // FIXME: replace with mathematical constants from cmath.
283
284 /// Archimedes' constant (π)
285 #[stable(feature = "rust1", since = "1.0.0")]
286 pub const PI: f64 = 3.14159265358979323846264338327950288_f64;
287
288 /// The full circle constant (τ)
289 ///
290 /// Equal to 2π.
291 #[stable(feature = "tau_constant", since = "1.47.0")]
292 pub const TAU: f64 = 6.28318530717958647692528676655900577_f64;
293
294 /// The golden ratio (φ)
295 #[stable(feature = "euler_gamma_golden_ratio", since = "1.94.0")]
296 pub const GOLDEN_RATIO: f64 = 1.618033988749894848204586834365638118_f64;
297
298 /// The Euler-Mascheroni constant (γ)
299 #[stable(feature = "euler_gamma_golden_ratio", since = "1.94.0")]
300 pub const EULER_GAMMA: f64 = 0.577215664901532860606512090082402431_f64;
301
302 /// π/2
303 #[stable(feature = "rust1", since = "1.0.0")]
304 pub const FRAC_PI_2: f64 = 1.57079632679489661923132169163975144_f64;
305
306 /// π/3
307 #[stable(feature = "rust1", since = "1.0.0")]
308 pub const FRAC_PI_3: f64 = 1.04719755119659774615421446109316763_f64;
309
310 /// π/4
311 #[stable(feature = "rust1", since = "1.0.0")]
312 pub const FRAC_PI_4: f64 = 0.785398163397448309615660845819875721_f64;
313
314 /// π/6
315 #[stable(feature = "rust1", since = "1.0.0")]
316 pub const FRAC_PI_6: f64 = 0.52359877559829887307710723054658381_f64;
317
318 /// π/8
319 #[stable(feature = "rust1", since = "1.0.0")]
320 pub const FRAC_PI_8: f64 = 0.39269908169872415480783042290993786_f64;
321
322 /// 1/π
323 #[stable(feature = "rust1", since = "1.0.0")]
324 pub const FRAC_1_PI: f64 = 0.318309886183790671537767526745028724_f64;
325
326 /// 1/sqrt(π)
327 #[unstable(feature = "more_float_constants", issue = "146939")]
328 pub const FRAC_1_SQRT_PI: f64 = 0.564189583547756286948079451560772586_f64;
329
330 /// 1/sqrt(2π)
331 #[doc(alias = "FRAC_1_SQRT_TAU")]
332 #[unstable(feature = "more_float_constants", issue = "146939")]
333 pub const FRAC_1_SQRT_2PI: f64 = 0.398942280401432677939946059934381868_f64;
334
335 /// 2/π
336 #[stable(feature = "rust1", since = "1.0.0")]
337 pub const FRAC_2_PI: f64 = 0.636619772367581343075535053490057448_f64;
338
339 /// 2/sqrt(π)
340 #[stable(feature = "rust1", since = "1.0.0")]
341 pub const FRAC_2_SQRT_PI: f64 = 1.12837916709551257389615890312154517_f64;
342
343 /// sqrt(2)
344 #[stable(feature = "rust1", since = "1.0.0")]
345 pub const SQRT_2: f64 = 1.41421356237309504880168872420969808_f64;
346
347 /// 1/sqrt(2)
348 #[stable(feature = "rust1", since = "1.0.0")]
349 pub const FRAC_1_SQRT_2: f64 = 0.707106781186547524400844362104849039_f64;
350
351 /// sqrt(3)
352 #[unstable(feature = "more_float_constants", issue = "146939")]
353 pub const SQRT_3: f64 = 1.732050807568877293527446341505872367_f64;
354
355 /// 1/sqrt(3)
356 #[unstable(feature = "more_float_constants", issue = "146939")]
357 pub const FRAC_1_SQRT_3: f64 = 0.577350269189625764509148780501957456_f64;
358
359 /// sqrt(5)
360 #[unstable(feature = "more_float_constants", issue = "146939")]
361 pub const SQRT_5: f64 = 2.23606797749978969640917366873127623_f64;
362
363 /// 1/sqrt(5)
364 #[unstable(feature = "more_float_constants", issue = "146939")]
365 pub const FRAC_1_SQRT_5: f64 = 0.44721359549995793928183473374625524_f64;
366
367 /// Euler's number (e)
368 #[stable(feature = "rust1", since = "1.0.0")]
369 pub const E: f64 = 2.71828182845904523536028747135266250_f64;
370
371 /// log<sub>2</sub>(10)
372 #[stable(feature = "extra_log_consts", since = "1.43.0")]
373 pub const LOG2_10: f64 = 3.32192809488736234787031942948939018_f64;
374
375 /// log<sub>2</sub>(e)
376 #[stable(feature = "rust1", since = "1.0.0")]
377 pub const LOG2_E: f64 = 1.44269504088896340735992468100189214_f64;
378
379 /// log<sub>10</sub>(2)
380 #[stable(feature = "extra_log_consts", since = "1.43.0")]
381 pub const LOG10_2: f64 = 0.301029995663981195213738894724493027_f64;
382
383 /// log<sub>10</sub>(e)
384 #[stable(feature = "rust1", since = "1.0.0")]
385 pub const LOG10_E: f64 = 0.434294481903251827651128918916605082_f64;
386
387 /// ln(2)
388 #[stable(feature = "rust1", since = "1.0.0")]
389 pub const LN_2: f64 = 0.693147180559945309417232121458176568_f64;
390
391 /// ln(10)
392 #[stable(feature = "rust1", since = "1.0.0")]
393 pub const LN_10: f64 = 2.30258509299404568401799145468436421_f64;
394}
395
396impl f64 {
397 /// The radix or base of the internal representation of `f64`.
398 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
399 pub const RADIX: u32 = 2;
400
401 /// The size of this float type in bits.
402 #[unstable(feature = "float_bits_const", issue = "151073")]
403 pub const BITS: u32 = 64;
404
405 /// Number of significant digits in base 2.
406 ///
407 /// Note that the size of the mantissa in the bitwise representation is one
408 /// smaller than this since the leading 1 is not stored explicitly.
409 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
410 pub const MANTISSA_DIGITS: u32 = 53;
411 /// Approximate number of significant digits in base 10.
412 ///
413 /// This is the maximum <i>x</i> such that any decimal number with <i>x</i>
414 /// significant digits can be converted to `f64` and back without loss.
415 ///
416 /// Equal to floor(log<sub>10</sub>&nbsp;2<sup>[`MANTISSA_DIGITS`]&nbsp;&minus;&nbsp;1</sup>).
417 ///
418 /// [`MANTISSA_DIGITS`]: f64::MANTISSA_DIGITS
419 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
420 pub const DIGITS: u32 = 15;
421
422 /// [Machine epsilon] value for `f64`.
423 ///
424 /// This is the difference between `1.0` and the next larger representable number.
425 ///
426 /// Equal to 2<sup>1&nbsp;&minus;&nbsp;[`MANTISSA_DIGITS`]</sup>.
427 ///
428 /// [Machine epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon
429 /// [`MANTISSA_DIGITS`]: f64::MANTISSA_DIGITS
430 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
431 #[rustc_diagnostic_item = "f64_epsilon"]
432 pub const EPSILON: f64 = 2.2204460492503131e-16_f64;
433
434 /// Smallest finite `f64` value.
435 ///
436 /// Equal to &minus;[`MAX`].
437 ///
438 /// [`MAX`]: f64::MAX
439 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
440 pub const MIN: f64 = -1.7976931348623157e+308_f64;
441 /// Smallest positive normal `f64` value.
442 ///
443 /// Equal to 2<sup>[`MIN_EXP`]&nbsp;&minus;&nbsp;1</sup>.
444 ///
445 /// [`MIN_EXP`]: f64::MIN_EXP
446 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
447 pub const MIN_POSITIVE: f64 = 2.2250738585072014e-308_f64;
448 /// Largest finite `f64` value.
449 ///
450 /// Equal to
451 /// (1&nbsp;&minus;&nbsp;2<sup>&minus;[`MANTISSA_DIGITS`]</sup>)&nbsp;2<sup>[`MAX_EXP`]</sup>.
452 ///
453 /// [`MANTISSA_DIGITS`]: f64::MANTISSA_DIGITS
454 /// [`MAX_EXP`]: f64::MAX_EXP
455 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
456 pub const MAX: f64 = 1.7976931348623157e+308_f64;
457
458 /// One greater than the minimum possible *normal* power of 2 exponent
459 /// for a significand bounded by 1 ≤ x < 2 (i.e. the IEEE definition).
460 ///
461 /// This corresponds to the exact minimum possible *normal* power of 2 exponent
462 /// for a significand bounded by 0.5 ≤ x < 1 (i.e. the C definition).
463 /// In other words, all normal numbers representable by this type are
464 /// greater than or equal to 0.5&nbsp;×&nbsp;2<sup><i>MIN_EXP</i></sup>.
465 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
466 pub const MIN_EXP: i32 = -1021;
467 /// One greater than the maximum possible power of 2 exponent
468 /// for a significand bounded by 1 ≤ x < 2 (i.e. the IEEE definition).
469 ///
470 /// This corresponds to the exact maximum possible power of 2 exponent
471 /// for a significand bounded by 0.5 ≤ x < 1 (i.e. the C definition).
472 /// In other words, all numbers representable by this type are
473 /// strictly less than 2<sup><i>MAX_EXP</i></sup>.
474 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
475 pub const MAX_EXP: i32 = 1024;
476
477 /// Minimum <i>x</i> for which 10<sup><i>x</i></sup> is normal.
478 ///
479 /// Equal to ceil(log<sub>10</sub>&nbsp;[`MIN_POSITIVE`]).
480 ///
481 /// [`MIN_POSITIVE`]: f64::MIN_POSITIVE
482 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
483 pub const MIN_10_EXP: i32 = -307;
484 /// Maximum <i>x</i> for which 10<sup><i>x</i></sup> is normal.
485 ///
486 /// Equal to floor(log<sub>10</sub>&nbsp;[`MAX`]).
487 ///
488 /// [`MAX`]: f64::MAX
489 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
490 pub const MAX_10_EXP: i32 = 308;
491
492 /// Not a Number (NaN).
493 ///
494 /// Note that IEEE 754 doesn't define just a single NaN value; a plethora of bit patterns are
495 /// considered to be NaN. Furthermore, the standard makes a difference between a "signaling" and
496 /// a "quiet" NaN, and allows inspecting its "payload" (the unspecified bits in the bit pattern)
497 /// and its sign. See the [specification of NaN bit patterns](f32#nan-bit-patterns) for more
498 /// info.
499 ///
500 /// This constant is guaranteed to be a quiet NaN (on targets that follow the Rust assumptions
501 /// that the quiet/signaling bit being set to 1 indicates a quiet NaN). Beyond that, nothing is
502 /// guaranteed about the specific bit pattern chosen here: both payload and sign are arbitrary.
503 /// The concrete bit pattern may change across Rust versions and target platforms.
504 #[rustc_diagnostic_item = "f64_nan"]
505 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
506 #[allow(clippy::eq_op)]
507 pub const NAN: f64 = 0.0_f64 / 0.0_f64;
508 /// Infinity (∞).
509 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
510 pub const INFINITY: f64 = 1.0_f64 / 0.0_f64;
511 /// Negative infinity (−∞).
512 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
513 pub const NEG_INFINITY: f64 = -1.0_f64 / 0.0_f64;
514
515 /// Sign bit
516 pub(crate) const SIGN_MASK: u64 = 0x8000_0000_0000_0000;
517
518 /// Exponent mask
519 pub(crate) const EXP_MASK: u64 = 0x7ff0_0000_0000_0000;
520
521 /// Mantissa mask
522 pub(crate) const MAN_MASK: u64 = 0x000f_ffff_ffff_ffff;
523
524 /// Minimum representable positive value (min subnormal)
525 const TINY_BITS: u64 = 0x1;
526
527 /// Minimum representable negative value (min negative subnormal)
528 const NEG_TINY_BITS: u64 = Self::TINY_BITS | Self::SIGN_MASK;
529
530 /// Returns `true` if this value is NaN.
531 ///
532 /// ```
533 /// let nan = f64::NAN;
534 /// let f = 7.0_f64;
535 ///
536 /// assert!(nan.is_nan());
537 /// assert!(!f.is_nan());
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 #[allow(clippy::eq_op)] // > if you intended to check if the operand is NaN, use `.is_nan()` instead :)
544 pub const fn is_nan(self) -> bool {
545 self != self
546 }
547
548 /// Returns `true` if this value is positive infinity or negative infinity, and
549 /// `false` otherwise.
550 ///
551 /// ```
552 /// let f = 7.0f64;
553 /// let inf = f64::INFINITY;
554 /// let neg_inf = f64::NEG_INFINITY;
555 /// let nan = f64::NAN;
556 ///
557 /// assert!(!f.is_infinite());
558 /// assert!(!nan.is_infinite());
559 ///
560 /// assert!(inf.is_infinite());
561 /// assert!(neg_inf.is_infinite());
562 /// ```
563 #[must_use]
564 #[stable(feature = "rust1", since = "1.0.0")]
565 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
566 #[inline]
567 pub const fn is_infinite(self) -> bool {
568 // Getting clever with transmutation can result in incorrect answers on some FPUs
569 // FIXME: alter the Rust <-> Rust calling convention to prevent this problem.
570 // See https://github.com/rust-lang/rust/issues/72327
571 (self == f64::INFINITY) | (self == f64::NEG_INFINITY)
572 }
573
574 /// Returns `true` if this number is neither infinite nor NaN.
575 ///
576 /// ```
577 /// let f = 7.0f64;
578 /// let inf: f64 = f64::INFINITY;
579 /// let neg_inf: f64 = f64::NEG_INFINITY;
580 /// let nan: f64 = f64::NAN;
581 ///
582 /// assert!(f.is_finite());
583 ///
584 /// assert!(!nan.is_finite());
585 /// assert!(!inf.is_finite());
586 /// assert!(!neg_inf.is_finite());
587 /// ```
588 #[must_use]
589 #[stable(feature = "rust1", since = "1.0.0")]
590 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
591 #[inline]
592 pub const fn is_finite(self) -> bool {
593 // There's no need to handle NaN separately: if self is NaN,
594 // the comparison is not true, exactly as desired.
595 self.abs() < Self::INFINITY
596 }
597
598 /// Returns `true` if the number is [subnormal].
599 ///
600 /// ```
601 /// let min = f64::MIN_POSITIVE; // 2.2250738585072014e-308_f64
602 /// let max = f64::MAX;
603 /// let lower_than_min = 1.0e-308_f64;
604 /// let zero = 0.0_f64;
605 ///
606 /// assert!(!min.is_subnormal());
607 /// assert!(!max.is_subnormal());
608 ///
609 /// assert!(!zero.is_subnormal());
610 /// assert!(!f64::NAN.is_subnormal());
611 /// assert!(!f64::INFINITY.is_subnormal());
612 /// // Values between `0` and `min` are Subnormal.
613 /// assert!(lower_than_min.is_subnormal());
614 /// ```
615 /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
616 #[must_use]
617 #[stable(feature = "is_subnormal", since = "1.53.0")]
618 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
619 #[inline]
620 pub const fn is_subnormal(self) -> bool {
621 matches!(self.classify(), FpCategory::Subnormal)
622 }
623
624 /// Returns `true` if the number is neither zero, infinite,
625 /// [subnormal], or NaN.
626 ///
627 /// ```
628 /// let min = f64::MIN_POSITIVE; // 2.2250738585072014e-308f64
629 /// let max = f64::MAX;
630 /// let lower_than_min = 1.0e-308_f64;
631 /// let zero = 0.0f64;
632 ///
633 /// assert!(min.is_normal());
634 /// assert!(max.is_normal());
635 ///
636 /// assert!(!zero.is_normal());
637 /// assert!(!f64::NAN.is_normal());
638 /// assert!(!f64::INFINITY.is_normal());
639 /// // Values between `0` and `min` are Subnormal.
640 /// assert!(!lower_than_min.is_normal());
641 /// ```
642 /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
643 #[must_use]
644 #[stable(feature = "rust1", since = "1.0.0")]
645 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
646 #[inline]
647 pub const fn is_normal(self) -> bool {
648 matches!(self.classify(), FpCategory::Normal)
649 }
650
651 /// Returns the floating point category of the number. If only one property
652 /// is going to be tested, it is generally faster to use the specific
653 /// predicate instead.
654 ///
655 /// ```
656 /// use std::num::FpCategory;
657 ///
658 /// let num = 12.4_f64;
659 /// let inf = f64::INFINITY;
660 ///
661 /// assert_eq!(num.classify(), FpCategory::Normal);
662 /// assert_eq!(inf.classify(), FpCategory::Infinite);
663 /// ```
664 #[stable(feature = "rust1", since = "1.0.0")]
665 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
666 pub const fn classify(self) -> FpCategory {
667 // We used to have complicated logic here that avoids the simple bit-based tests to work
668 // around buggy codegen for x87 targets (see
669 // https://github.com/rust-lang/rust/issues/114479). However, some LLVM versions later, none
670 // of our tests is able to find any difference between the complicated and the naive
671 // version, so now we are back to the naive version.
672 let b = self.to_bits();
673 match (b & Self::MAN_MASK, b & Self::EXP_MASK) {
674 (0, Self::EXP_MASK) => FpCategory::Infinite,
675 (_, Self::EXP_MASK) => FpCategory::Nan,
676 (0, 0) => FpCategory::Zero,
677 (_, 0) => FpCategory::Subnormal,
678 _ => FpCategory::Normal,
679 }
680 }
681
682 /// Returns `true` if `self` has a positive sign, including `+0.0`, NaNs with
683 /// positive sign bit and positive infinity.
684 ///
685 /// Note that IEEE 754 doesn't assign any meaning to the sign bit in case of
686 /// a NaN, and as Rust doesn't guarantee that the bit pattern of NaNs are
687 /// conserved over arithmetic operations, the result of `is_sign_positive` on
688 /// a NaN might produce an unexpected or non-portable result. See the [specification
689 /// of NaN bit patterns](f32#nan-bit-patterns) for more info. Use `self.signum() == 1.0`
690 /// if you need fully portable behavior (will return `false` for all NaNs).
691 ///
692 /// ```
693 /// let f = 7.0_f64;
694 /// let g = -7.0_f64;
695 ///
696 /// assert!(f.is_sign_positive());
697 /// assert!(!g.is_sign_positive());
698 /// ```
699 #[must_use]
700 #[stable(feature = "rust1", since = "1.0.0")]
701 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
702 #[inline]
703 pub const fn is_sign_positive(self) -> bool {
704 !self.is_sign_negative()
705 }
706
707 #[must_use]
708 #[stable(feature = "rust1", since = "1.0.0")]
709 #[deprecated(since = "1.0.0", note = "renamed to is_sign_positive")]
710 #[inline]
711 #[doc(hidden)]
712 pub fn is_positive(self) -> bool {
713 self.is_sign_positive()
714 }
715
716 /// Returns `true` if `self` has a negative sign, including `-0.0`, NaNs with
717 /// negative sign bit and negative infinity.
718 ///
719 /// Note that IEEE 754 doesn't assign any meaning to the sign bit in case of
720 /// a NaN, and as Rust doesn't guarantee that the bit pattern of NaNs are
721 /// conserved over arithmetic operations, the result of `is_sign_negative` on
722 /// a NaN might produce an unexpected or non-portable result. See the [specification
723 /// of NaN bit patterns](f32#nan-bit-patterns) for more info. Use `self.signum() == -1.0`
724 /// if you need fully portable behavior (will return `false` for all NaNs).
725 ///
726 /// ```
727 /// let f = 7.0_f64;
728 /// let g = -7.0_f64;
729 ///
730 /// assert!(!f.is_sign_negative());
731 /// assert!(g.is_sign_negative());
732 /// ```
733 #[must_use]
734 #[stable(feature = "rust1", since = "1.0.0")]
735 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
736 #[inline]
737 pub const fn is_sign_negative(self) -> bool {
738 // IEEE754 says: isSignMinus(x) is true if and only if x has negative sign. isSignMinus
739 // applies to zeros and NaNs as well.
740 self.to_bits() & Self::SIGN_MASK != 0
741 }
742
743 #[must_use]
744 #[stable(feature = "rust1", since = "1.0.0")]
745 #[deprecated(since = "1.0.0", note = "renamed to is_sign_negative")]
746 #[inline]
747 #[doc(hidden)]
748 pub fn is_negative(self) -> bool {
749 self.is_sign_negative()
750 }
751
752 /// Returns the least number greater than `self`.
753 ///
754 /// Let `TINY` be the smallest representable positive `f64`. Then,
755 /// - if `self.is_nan()`, this returns `self`;
756 /// - if `self` is [`NEG_INFINITY`], this returns [`MIN`];
757 /// - if `self` is `-TINY`, this returns -0.0;
758 /// - if `self` is -0.0 or +0.0, this returns `TINY`;
759 /// - if `self` is [`MAX`] or [`INFINITY`], this returns [`INFINITY`];
760 /// - otherwise the unique least value greater than `self` is returned.
761 ///
762 /// The identity `x.next_up() == -(-x).next_down()` holds for all non-NaN `x`. When `x`
763 /// is finite `x == x.next_up().next_down()` also holds.
764 ///
765 /// ```rust
766 /// // f64::EPSILON is the difference between 1.0 and the next number up.
767 /// assert_eq!(1.0f64.next_up(), 1.0 + f64::EPSILON);
768 /// // But not for most numbers.
769 /// assert!(0.1f64.next_up() < 0.1 + f64::EPSILON);
770 /// assert_eq!(9007199254740992f64.next_up(), 9007199254740994.0);
771 /// ```
772 ///
773 /// This operation corresponds to IEEE-754 `nextUp`.
774 ///
775 /// [`NEG_INFINITY`]: Self::NEG_INFINITY
776 /// [`INFINITY`]: Self::INFINITY
777 /// [`MIN`]: Self::MIN
778 /// [`MAX`]: Self::MAX
779 #[inline]
780 #[doc(alias = "nextUp")]
781 #[stable(feature = "float_next_up_down", since = "1.86.0")]
782 #[rustc_const_stable(feature = "float_next_up_down", since = "1.86.0")]
783 pub const fn next_up(self) -> Self {
784 // Some targets violate Rust's assumption of IEEE semantics, e.g. by flushing
785 // denormals to zero. This is in general unsound and unsupported, but here
786 // we do our best to still produce the correct result on such targets.
787 let bits = self.to_bits();
788 if self.is_nan() || bits == Self::INFINITY.to_bits() {
789 return self;
790 }
791
792 let abs = bits & !Self::SIGN_MASK;
793 let next_bits = if abs == 0 {
794 Self::TINY_BITS
795 } else if bits == abs {
796 bits + 1
797 } else {
798 bits - 1
799 };
800 Self::from_bits(next_bits)
801 }
802
803 /// Returns the greatest number less than `self`.
804 ///
805 /// Let `TINY` be the smallest representable positive `f64`. Then,
806 /// - if `self.is_nan()`, this returns `self`;
807 /// - if `self` is [`INFINITY`], this returns [`MAX`];
808 /// - if `self` is `TINY`, this returns 0.0;
809 /// - if `self` is -0.0 or +0.0, this returns `-TINY`;
810 /// - if `self` is [`MIN`] or [`NEG_INFINITY`], this returns [`NEG_INFINITY`];
811 /// - otherwise the unique greatest value less than `self` is returned.
812 ///
813 /// The identity `x.next_down() == -(-x).next_up()` holds for all non-NaN `x`. When `x`
814 /// is finite `x == x.next_down().next_up()` also holds.
815 ///
816 /// ```rust
817 /// let x = 1.0f64;
818 /// // Clamp value into range [0, 1).
819 /// let clamped = x.clamp(0.0, 1.0f64.next_down());
820 /// assert!(clamped < 1.0);
821 /// assert_eq!(clamped.next_up(), 1.0);
822 /// ```
823 ///
824 /// This operation corresponds to IEEE-754 `nextDown`.
825 ///
826 /// [`NEG_INFINITY`]: Self::NEG_INFINITY
827 /// [`INFINITY`]: Self::INFINITY
828 /// [`MIN`]: Self::MIN
829 /// [`MAX`]: Self::MAX
830 #[inline]
831 #[doc(alias = "nextDown")]
832 #[stable(feature = "float_next_up_down", since = "1.86.0")]
833 #[rustc_const_stable(feature = "float_next_up_down", since = "1.86.0")]
834 pub const fn next_down(self) -> Self {
835 // Some targets violate Rust's assumption of IEEE semantics, e.g. by flushing
836 // denormals to zero. This is in general unsound and unsupported, but here
837 // we do our best to still produce the correct result on such targets.
838 let bits = self.to_bits();
839 if self.is_nan() || bits == Self::NEG_INFINITY.to_bits() {
840 return self;
841 }
842
843 let abs = bits & !Self::SIGN_MASK;
844 let next_bits = if abs == 0 {
845 Self::NEG_TINY_BITS
846 } else if bits == abs {
847 bits - 1
848 } else {
849 bits + 1
850 };
851 Self::from_bits(next_bits)
852 }
853
854 /// Takes the reciprocal (inverse) of a number, `1/x`.
855 ///
856 /// ```
857 /// let x = 2.0_f64;
858 /// let abs_difference = (x.recip() - (1.0 / x)).abs();
859 ///
860 /// assert!(abs_difference < 1e-10);
861 /// ```
862 #[must_use = "this returns the result of the operation, without modifying the original"]
863 #[stable(feature = "rust1", since = "1.0.0")]
864 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
865 #[inline]
866 pub const fn recip(self) -> f64 {
867 1.0 / self
868 }
869
870 /// Converts radians to degrees.
871 ///
872 /// # Unspecified precision
873 ///
874 /// The precision of this function is non-deterministic. This means it varies by platform,
875 /// Rust version, and can even differ within the same execution from one invocation to the next.
876 ///
877 /// # Examples
878 ///
879 /// ```
880 /// let angle = std::f64::consts::PI;
881 ///
882 /// let abs_difference = (angle.to_degrees() - 180.0).abs();
883 ///
884 /// assert!(abs_difference < 1e-10);
885 /// ```
886 #[must_use = "this returns the result of the operation, \
887 without modifying the original"]
888 #[stable(feature = "rust1", since = "1.0.0")]
889 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
890 #[inline]
891 pub const fn to_degrees(self) -> f64 {
892 // The division here is correctly rounded with respect to the true value of 180/π.
893 // Although π is irrational and already rounded, the double rounding happens
894 // to produce correct result for f64.
895 const PIS_IN_180: f64 = 180.0 / consts::PI;
896 self * PIS_IN_180
897 }
898
899 /// Converts degrees to radians.
900 ///
901 /// # Unspecified precision
902 ///
903 /// The precision of this function is non-deterministic. This means it varies by platform,
904 /// Rust version, and can even differ within the same execution from one invocation to the next.
905 ///
906 /// # Examples
907 ///
908 /// ```
909 /// let angle = 180.0_f64;
910 ///
911 /// let abs_difference = (angle.to_radians() - std::f64::consts::PI).abs();
912 ///
913 /// assert!(abs_difference < 1e-10);
914 /// ```
915 #[must_use = "this returns the result of the operation, \
916 without modifying the original"]
917 #[stable(feature = "rust1", since = "1.0.0")]
918 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
919 #[inline]
920 pub const fn to_radians(self) -> f64 {
921 // The division here is correctly rounded with respect to the true value of π/180.
922 // Although π is irrational and already rounded, the double rounding happens
923 // to produce correct result for f64.
924 const RADS_PER_DEG: f64 = consts::PI / 180.0;
925 self * RADS_PER_DEG
926 }
927
928 /// Returns the maximum of the two numbers, ignoring NaN.
929 ///
930 /// If exactly one of the arguments is NaN (quiet or signaling), then the other argument is
931 /// returned. If both arguments are NaN, the return value is NaN, with the bit pattern picked
932 /// using the usual [rules for arithmetic operations](f32#nan-bit-patterns). If the inputs
933 /// compare equal (such as for the case of `+0.0` and `-0.0`), either input may be returned
934 /// non-deterministically.
935 ///
936 /// The handling of NaNs follows the IEEE 754-2019 semantics for `maximumNumber`, treating all
937 /// NaNs the same way to ensure the operation is associative. The handling of signed zeros
938 /// follows the IEEE 754-2008 semantics for `maxNum`.
939 ///
940 /// ```
941 /// let x = 1.0_f64;
942 /// let y = 2.0_f64;
943 ///
944 /// assert_eq!(x.max(y), y);
945 /// assert_eq!(x.max(f64::NAN), x);
946 /// ```
947 #[must_use = "this returns the result of the comparison, without modifying either input"]
948 #[stable(feature = "rust1", since = "1.0.0")]
949 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
950 #[inline]
951 pub const fn max(self, other: f64) -> f64 {
952 intrinsics::maxnumf64(self, other)
953 }
954
955 /// Returns the minimum of the two numbers, ignoring NaN.
956 ///
957 /// If exactly one of the arguments is NaN (quiet or signaling), then the other argument is
958 /// returned. If both arguments are NaN, the return value is NaN, with the bit pattern picked
959 /// using the usual [rules for arithmetic operations](f32#nan-bit-patterns). If the inputs
960 /// compare equal (such as for the case of `+0.0` and `-0.0`), either input may be returned
961 /// non-deterministically.
962 ///
963 /// The handling of NaNs follows the IEEE 754-2019 semantics for `minimumNumber`, treating all
964 /// NaNs the same way to ensure the operation is associative. The handling of signed zeros
965 /// follows the IEEE 754-2008 semantics for `minNum`.
966 ///
967 /// ```
968 /// let x = 1.0_f64;
969 /// let y = 2.0_f64;
970 ///
971 /// assert_eq!(x.min(y), x);
972 /// assert_eq!(x.min(f64::NAN), x);
973 /// ```
974 #[must_use = "this returns the result of the comparison, without modifying either input"]
975 #[stable(feature = "rust1", since = "1.0.0")]
976 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
977 #[inline]
978 pub const fn min(self, other: f64) -> f64 {
979 intrinsics::minnumf64(self, other)
980 }
981
982 /// Returns the maximum of the two numbers, propagating NaN.
983 ///
984 /// If at least one of the arguments is NaN, the return value is NaN, with the bit pattern
985 /// picked using the usual [rules for arithmetic operations](f32#nan-bit-patterns). Furthermore,
986 /// `-0.0` is considered to be less than `+0.0`, making this function fully deterministic for
987 /// non-NaN inputs.
988 ///
989 /// This is in contrast to [`f64::max`] which only returns NaN when *both* arguments are NaN,
990 /// and which does not reliably order `-0.0` and `+0.0`.
991 ///
992 /// This follows the IEEE 754-2019 semantics for `maximum`.
993 ///
994 /// ```
995 /// #![feature(float_minimum_maximum)]
996 /// let x = 1.0_f64;
997 /// let y = 2.0_f64;
998 ///
999 /// assert_eq!(x.maximum(y), y);
1000 /// assert!(x.maximum(f64::NAN).is_nan());
1001 /// ```
1002 #[must_use = "this returns the result of the comparison, without modifying either input"]
1003 #[unstable(feature = "float_minimum_maximum", issue = "91079")]
1004 #[inline]
1005 pub const fn maximum(self, other: f64) -> f64 {
1006 intrinsics::maximumf64(self, other)
1007 }
1008
1009 /// Returns the minimum of the two numbers, propagating NaN.
1010 ///
1011 /// If at least one of the arguments is NaN, the return value is NaN, with the bit pattern
1012 /// picked using the usual [rules for arithmetic operations](f32#nan-bit-patterns). Furthermore,
1013 /// `-0.0` is considered to be less than `+0.0`, making this function fully deterministic for
1014 /// non-NaN inputs.
1015 ///
1016 /// This is in contrast to [`f64::min`] which only returns NaN when *both* arguments are NaN,
1017 /// and which does not reliably order `-0.0` and `+0.0`.
1018 ///
1019 /// This follows the IEEE 754-2019 semantics for `minimum`.
1020 ///
1021 /// ```
1022 /// #![feature(float_minimum_maximum)]
1023 /// let x = 1.0_f64;
1024 /// let y = 2.0_f64;
1025 ///
1026 /// assert_eq!(x.minimum(y), x);
1027 /// assert!(x.minimum(f64::NAN).is_nan());
1028 /// ```
1029 #[must_use = "this returns the result of the comparison, without modifying either input"]
1030 #[unstable(feature = "float_minimum_maximum", issue = "91079")]
1031 #[inline]
1032 pub const fn minimum(self, other: f64) -> f64 {
1033 intrinsics::minimumf64(self, other)
1034 }
1035
1036 /// Calculates the midpoint (average) between `self` and `rhs`.
1037 ///
1038 /// This returns NaN when *either* argument is NaN or if a combination of
1039 /// +inf and -inf is provided as arguments.
1040 ///
1041 /// # Examples
1042 ///
1043 /// ```
1044 /// assert_eq!(1f64.midpoint(4.0), 2.5);
1045 /// assert_eq!((-5.5f64).midpoint(8.0), 1.25);
1046 /// ```
1047 #[inline]
1048 #[doc(alias = "average")]
1049 #[stable(feature = "num_midpoint", since = "1.85.0")]
1050 #[rustc_const_stable(feature = "num_midpoint", since = "1.85.0")]
1051 pub const fn midpoint(self, other: f64) -> f64 {
1052 const HI: f64 = f64::MAX / 2.;
1053
1054 let (a, b) = (self, other);
1055 let abs_a = a.abs();
1056 let abs_b = b.abs();
1057
1058 if abs_a <= HI && abs_b <= HI {
1059 // Overflow is impossible
1060 (a + b) / 2.
1061 } else {
1062 (a / 2.) + (b / 2.)
1063 }
1064 }
1065
1066 /// Rounds toward zero and converts to any primitive integer type,
1067 /// assuming that the value is finite and fits in that type.
1068 ///
1069 /// ```
1070 /// let value = 4.6_f64;
1071 /// let rounded = unsafe { value.to_int_unchecked::<u16>() };
1072 /// assert_eq!(rounded, 4);
1073 ///
1074 /// let value = -128.9_f64;
1075 /// let rounded = unsafe { value.to_int_unchecked::<i8>() };
1076 /// assert_eq!(rounded, i8::MIN);
1077 /// ```
1078 ///
1079 /// # Safety
1080 ///
1081 /// The value must:
1082 ///
1083 /// * Not be `NaN`
1084 /// * Not be infinite
1085 /// * Be representable in the return type `Int`, after truncating off its fractional part
1086 #[must_use = "this returns the result of the operation, \
1087 without modifying the original"]
1088 #[stable(feature = "float_approx_unchecked_to", since = "1.44.0")]
1089 #[inline]
1090 pub unsafe fn to_int_unchecked<Int>(self) -> Int
1091 where
1092 Self: FloatToInt<Int>,
1093 {
1094 // SAFETY: the caller must uphold the safety contract for
1095 // `FloatToInt::to_int_unchecked`.
1096 unsafe { FloatToInt::<Int>::to_int_unchecked(self) }
1097 }
1098
1099 /// Raw transmutation to `u64`.
1100 ///
1101 /// This is currently identical to `transmute::<f64, u64>(self)` on all platforms.
1102 ///
1103 /// See [`from_bits`](Self::from_bits) for some discussion of the
1104 /// portability of this operation (there are almost no issues).
1105 ///
1106 /// Note that this function is distinct from `as` casting, which attempts to
1107 /// preserve the *numeric* value, and not the bitwise value.
1108 ///
1109 /// # Examples
1110 ///
1111 /// ```
1112 /// assert!((1f64).to_bits() != 1f64 as u64); // to_bits() is not casting!
1113 /// assert_eq!((12.5f64).to_bits(), 0x4029000000000000);
1114 /// ```
1115 #[must_use = "this returns the result of the operation, \
1116 without modifying the original"]
1117 #[stable(feature = "float_bits_conv", since = "1.20.0")]
1118 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1119 #[allow(unnecessary_transmutes)]
1120 #[inline]
1121 pub const fn to_bits(self) -> u64 {
1122 // SAFETY: `u64` is a plain old datatype so we can always transmute to it.
1123 unsafe { mem::transmute(self) }
1124 }
1125
1126 /// Raw transmutation from `u64`.
1127 ///
1128 /// This is currently identical to `transmute::<u64, f64>(v)` on all platforms.
1129 /// It turns out this is incredibly portable, for two reasons:
1130 ///
1131 /// * Floats and Ints have the same endianness on all supported platforms.
1132 /// * IEEE 754 very precisely specifies the bit layout of floats.
1133 ///
1134 /// However there is one caveat: prior to the 2008 version of IEEE 754, how
1135 /// to interpret the NaN signaling bit wasn't actually specified. Most platforms
1136 /// (notably x86 and ARM) picked the interpretation that was ultimately
1137 /// standardized in 2008, but some didn't (notably MIPS). As a result, all
1138 /// signaling NaNs on MIPS are quiet NaNs on x86, and vice-versa.
1139 ///
1140 /// Rather than trying to preserve signaling-ness cross-platform, this
1141 /// implementation favors preserving the exact bits. This means that
1142 /// any payloads encoded in NaNs will be preserved even if the result of
1143 /// this method is sent over the network from an x86 machine to a MIPS one.
1144 ///
1145 /// If the results of this method are only manipulated by the same
1146 /// architecture that produced them, then there is no portability concern.
1147 ///
1148 /// If the input isn't NaN, then there is no portability concern.
1149 ///
1150 /// If you don't care about signaling-ness (very likely), then there is no
1151 /// portability concern.
1152 ///
1153 /// Note that this function is distinct from `as` casting, which attempts to
1154 /// preserve the *numeric* value, and not the bitwise value.
1155 ///
1156 /// # Examples
1157 ///
1158 /// ```
1159 /// let v = f64::from_bits(0x4029000000000000);
1160 /// assert_eq!(v, 12.5);
1161 /// ```
1162 #[stable(feature = "float_bits_conv", since = "1.20.0")]
1163 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1164 #[must_use]
1165 #[inline]
1166 #[allow(unnecessary_transmutes)]
1167 pub const fn from_bits(v: u64) -> Self {
1168 // It turns out the safety issues with sNaN were overblown! Hooray!
1169 // SAFETY: `u64` is a plain old datatype so we can always transmute from it.
1170 unsafe { mem::transmute(v) }
1171 }
1172
1173 /// Returns the memory representation of this floating point number as a byte array in
1174 /// big-endian (network) byte order.
1175 ///
1176 /// See [`from_bits`](Self::from_bits) for some discussion of the
1177 /// portability of this operation (there are almost no issues).
1178 ///
1179 /// # Examples
1180 ///
1181 /// ```
1182 /// let bytes = 12.5f64.to_be_bytes();
1183 /// assert_eq!(bytes, [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]);
1184 /// ```
1185 #[must_use = "this returns the result of the operation, \
1186 without modifying the original"]
1187 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1188 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1189 #[inline]
1190 pub const fn to_be_bytes(self) -> [u8; 8] {
1191 self.to_bits().to_be_bytes()
1192 }
1193
1194 /// Returns the memory representation of this floating point number as a byte array in
1195 /// little-endian byte order.
1196 ///
1197 /// See [`from_bits`](Self::from_bits) for some discussion of the
1198 /// portability of this operation (there are almost no issues).
1199 ///
1200 /// # Examples
1201 ///
1202 /// ```
1203 /// let bytes = 12.5f64.to_le_bytes();
1204 /// assert_eq!(bytes, [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]);
1205 /// ```
1206 #[must_use = "this returns the result of the operation, \
1207 without modifying the original"]
1208 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1209 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1210 #[inline]
1211 pub const fn to_le_bytes(self) -> [u8; 8] {
1212 self.to_bits().to_le_bytes()
1213 }
1214
1215 /// Returns the memory representation of this floating point number as a byte array in
1216 /// native byte order.
1217 ///
1218 /// As the target platform's native endianness is used, portable code
1219 /// should use [`to_be_bytes`] or [`to_le_bytes`], as appropriate, instead.
1220 ///
1221 /// [`to_be_bytes`]: f64::to_be_bytes
1222 /// [`to_le_bytes`]: f64::to_le_bytes
1223 ///
1224 /// See [`from_bits`](Self::from_bits) for some discussion of the
1225 /// portability of this operation (there are almost no issues).
1226 ///
1227 /// # Examples
1228 ///
1229 /// ```
1230 /// let bytes = 12.5f64.to_ne_bytes();
1231 /// assert_eq!(
1232 /// bytes,
1233 /// if cfg!(target_endian = "big") {
1234 /// [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
1235 /// } else {
1236 /// [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]
1237 /// }
1238 /// );
1239 /// ```
1240 #[must_use = "this returns the result of the operation, \
1241 without modifying the original"]
1242 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1243 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1244 #[inline]
1245 pub const fn to_ne_bytes(self) -> [u8; 8] {
1246 self.to_bits().to_ne_bytes()
1247 }
1248
1249 /// Creates a floating point value from its representation as a byte array in big endian.
1250 ///
1251 /// See [`from_bits`](Self::from_bits) for some discussion of the
1252 /// portability of this operation (there are almost no issues).
1253 ///
1254 /// # Examples
1255 ///
1256 /// ```
1257 /// let value = f64::from_be_bytes([0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]);
1258 /// assert_eq!(value, 12.5);
1259 /// ```
1260 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1261 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1262 #[must_use]
1263 #[inline]
1264 pub const fn from_be_bytes(bytes: [u8; 8]) -> Self {
1265 Self::from_bits(u64::from_be_bytes(bytes))
1266 }
1267
1268 /// Creates a floating point value from its representation as a byte array in little endian.
1269 ///
1270 /// See [`from_bits`](Self::from_bits) for some discussion of the
1271 /// portability of this operation (there are almost no issues).
1272 ///
1273 /// # Examples
1274 ///
1275 /// ```
1276 /// let value = f64::from_le_bytes([0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]);
1277 /// assert_eq!(value, 12.5);
1278 /// ```
1279 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1280 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1281 #[must_use]
1282 #[inline]
1283 pub const fn from_le_bytes(bytes: [u8; 8]) -> Self {
1284 Self::from_bits(u64::from_le_bytes(bytes))
1285 }
1286
1287 /// Creates a floating point value from its representation as a byte array in native endian.
1288 ///
1289 /// As the target platform's native endianness is used, portable code
1290 /// likely wants to use [`from_be_bytes`] or [`from_le_bytes`], as
1291 /// appropriate instead.
1292 ///
1293 /// [`from_be_bytes`]: f64::from_be_bytes
1294 /// [`from_le_bytes`]: f64::from_le_bytes
1295 ///
1296 /// See [`from_bits`](Self::from_bits) for some discussion of the
1297 /// portability of this operation (there are almost no issues).
1298 ///
1299 /// # Examples
1300 ///
1301 /// ```
1302 /// let value = f64::from_ne_bytes(if cfg!(target_endian = "big") {
1303 /// [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
1304 /// } else {
1305 /// [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]
1306 /// });
1307 /// assert_eq!(value, 12.5);
1308 /// ```
1309 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1310 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1311 #[must_use]
1312 #[inline]
1313 pub const fn from_ne_bytes(bytes: [u8; 8]) -> Self {
1314 Self::from_bits(u64::from_ne_bytes(bytes))
1315 }
1316
1317 /// Returns the ordering between `self` and `other`.
1318 ///
1319 /// Unlike the standard partial comparison between floating point numbers,
1320 /// this comparison always produces an ordering in accordance to
1321 /// the `totalOrder` predicate as defined in the IEEE 754 (2008 revision)
1322 /// floating point standard. The values are ordered in the following sequence:
1323 ///
1324 /// - negative quiet NaN
1325 /// - negative signaling NaN
1326 /// - negative infinity
1327 /// - negative numbers
1328 /// - negative subnormal numbers
1329 /// - negative zero
1330 /// - positive zero
1331 /// - positive subnormal numbers
1332 /// - positive numbers
1333 /// - positive infinity
1334 /// - positive signaling NaN
1335 /// - positive quiet NaN.
1336 ///
1337 /// The ordering established by this function does not always agree with the
1338 /// [`PartialOrd`] and [`PartialEq`] implementations of `f64`. For example,
1339 /// they consider negative and positive zero equal, while `total_cmp`
1340 /// doesn't.
1341 ///
1342 /// The interpretation of the signaling NaN bit follows the definition in
1343 /// the IEEE 754 standard, which may not match the interpretation by some of
1344 /// the older, non-conformant (e.g. MIPS) hardware implementations.
1345 ///
1346 /// # Example
1347 ///
1348 /// ```
1349 /// struct GoodBoy {
1350 /// name: String,
1351 /// weight: f64,
1352 /// }
1353 ///
1354 /// let mut bois = vec![
1355 /// GoodBoy { name: "Pucci".to_owned(), weight: 0.1 },
1356 /// GoodBoy { name: "Woofer".to_owned(), weight: 99.0 },
1357 /// GoodBoy { name: "Yapper".to_owned(), weight: 10.0 },
1358 /// GoodBoy { name: "Chonk".to_owned(), weight: f64::INFINITY },
1359 /// GoodBoy { name: "Abs. Unit".to_owned(), weight: f64::NAN },
1360 /// GoodBoy { name: "Floaty".to_owned(), weight: -5.0 },
1361 /// ];
1362 ///
1363 /// bois.sort_by(|a, b| a.weight.total_cmp(&b.weight));
1364 ///
1365 /// // `f64::NAN` could be positive or negative, which will affect the sort order.
1366 /// if f64::NAN.is_sign_negative() {
1367 /// assert!(bois.into_iter().map(|b| b.weight)
1368 /// .zip([f64::NAN, -5.0, 0.1, 10.0, 99.0, f64::INFINITY].iter())
1369 /// .all(|(a, b)| a.to_bits() == b.to_bits()))
1370 /// } else {
1371 /// assert!(bois.into_iter().map(|b| b.weight)
1372 /// .zip([-5.0, 0.1, 10.0, 99.0, f64::INFINITY, f64::NAN].iter())
1373 /// .all(|(a, b)| a.to_bits() == b.to_bits()))
1374 /// }
1375 /// ```
1376 #[stable(feature = "total_cmp", since = "1.62.0")]
1377 #[rustc_const_unstable(feature = "const_cmp", issue = "143800")]
1378 #[must_use]
1379 #[inline]
1380 pub const fn total_cmp(&self, other: &Self) -> crate::cmp::Ordering {
1381 let mut left = self.to_bits() as i64;
1382 let mut right = other.to_bits() as i64;
1383
1384 // In case of negatives, flip all the bits except the sign
1385 // to achieve a similar layout as two's complement integers
1386 //
1387 // Why does this work? IEEE 754 floats consist of three fields:
1388 // Sign bit, exponent and mantissa. The set of exponent and mantissa
1389 // fields as a whole have the property that their bitwise order is
1390 // equal to the numeric magnitude where the magnitude is defined.
1391 // The magnitude is not normally defined on NaN values, but
1392 // IEEE 754 totalOrder defines the NaN values also to follow the
1393 // bitwise order. This leads to order explained in the doc comment.
1394 // However, the representation of magnitude is the same for negative
1395 // and positive numbers – only the sign bit is different.
1396 // To easily compare the floats as signed integers, we need to
1397 // flip the exponent and mantissa bits in case of negative numbers.
1398 // We effectively convert the numbers to "two's complement" form.
1399 //
1400 // To do the flipping, we construct a mask and XOR against it.
1401 // We branchlessly calculate an "all-ones except for the sign bit"
1402 // mask from negative-signed values: right shifting sign-extends
1403 // the integer, so we "fill" the mask with sign bits, and then
1404 // convert to unsigned to push one more zero bit.
1405 // On positive values, the mask is all zeros, so it's a no-op.
1406 left ^= (((left >> 63) as u64) >> 1) as i64;
1407 right ^= (((right >> 63) as u64) >> 1) as i64;
1408
1409 left.cmp(&right)
1410 }
1411
1412 /// Restrict a value to a certain interval unless it is NaN.
1413 ///
1414 /// Returns `max` if `self` is greater than `max`, and `min` if `self` is
1415 /// less than `min`. Otherwise this returns `self`.
1416 ///
1417 /// Note that this function returns NaN if the initial value was NaN as
1418 /// well. If the result is zero and among the three inputs `self`, `min`, and `max` there are
1419 /// zeros with different sign, either `0.0` or `-0.0` is returned non-deterministically.
1420 ///
1421 /// # Panics
1422 ///
1423 /// Panics if `min > max`, `min` is NaN, or `max` is NaN.
1424 ///
1425 /// # Examples
1426 ///
1427 /// ```
1428 /// assert!((-3.0f64).clamp(-2.0, 1.0) == -2.0);
1429 /// assert!((0.0f64).clamp(-2.0, 1.0) == 0.0);
1430 /// assert!((2.0f64).clamp(-2.0, 1.0) == 1.0);
1431 /// assert!((f64::NAN).clamp(-2.0, 1.0).is_nan());
1432 ///
1433 /// // These always returns zero, but the sign (which is ignored by `==`) is non-deterministic.
1434 /// assert!((0.0f64).clamp(-0.0, -0.0) == 0.0);
1435 /// assert!((1.0f64).clamp(-0.0, 0.0) == 0.0);
1436 /// // This is definitely a negative zero.
1437 /// assert!((-1.0f64).clamp(-0.0, 1.0).is_sign_negative());
1438 /// ```
1439 #[must_use = "method returns a new number and does not mutate the original value"]
1440 #[stable(feature = "clamp", since = "1.50.0")]
1441 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
1442 #[inline]
1443 pub const fn clamp(mut self, min: f64, max: f64) -> f64 {
1444 const_assert!(
1445 min <= max,
1446 "min > max, or either was NaN",
1447 "min > max, or either was NaN. min = {min:?}, max = {max:?}",
1448 min: f64,
1449 max: f64,
1450 );
1451
1452 if self < min {
1453 self = min;
1454 }
1455 if self > max {
1456 self = max;
1457 }
1458 self
1459 }
1460
1461 /// Clamps this number to a symmetric range centered around zero.
1462 ///
1463 /// The method clamps the number's magnitude (absolute value) to be at most `limit`.
1464 ///
1465 /// This is functionally equivalent to `self.clamp(-limit, limit)`, but is more
1466 /// explicit about the intent.
1467 ///
1468 /// # Panics
1469 ///
1470 /// Panics if `limit` is negative or NaN, as this indicates a logic error.
1471 ///
1472 /// # Examples
1473 ///
1474 /// ```
1475 /// #![feature(clamp_magnitude)]
1476 /// assert_eq!(5.0f64.clamp_magnitude(3.0), 3.0);
1477 /// assert_eq!((-5.0f64).clamp_magnitude(3.0), -3.0);
1478 /// assert_eq!(2.0f64.clamp_magnitude(3.0), 2.0);
1479 /// assert_eq!((-2.0f64).clamp_magnitude(3.0), -2.0);
1480 /// ```
1481 #[must_use = "this returns the clamped value and does not modify the original"]
1482 #[unstable(feature = "clamp_magnitude", issue = "148519")]
1483 #[inline]
1484 pub fn clamp_magnitude(self, limit: f64) -> f64 {
1485 assert!(limit >= 0.0, "limit must be non-negative");
1486 let limit = limit.abs(); // Canonicalises -0.0 to 0.0
1487 self.clamp(-limit, limit)
1488 }
1489
1490 /// Computes the absolute value of `self`.
1491 ///
1492 /// This function always returns the precise result.
1493 ///
1494 /// # Examples
1495 ///
1496 /// ```
1497 /// let x = 3.5_f64;
1498 /// let y = -3.5_f64;
1499 ///
1500 /// assert_eq!(x.abs(), x);
1501 /// assert_eq!(y.abs(), -y);
1502 ///
1503 /// assert!(f64::NAN.abs().is_nan());
1504 /// ```
1505 #[must_use = "method returns a new number and does not mutate the original value"]
1506 #[stable(feature = "rust1", since = "1.0.0")]
1507 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
1508 #[inline]
1509 pub const fn abs(self) -> f64 {
1510 intrinsics::fabsf64(self)
1511 }
1512
1513 /// Returns a number that represents the sign of `self`.
1514 ///
1515 /// - `1.0` if the number is positive, `+0.0` or `INFINITY`
1516 /// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
1517 /// - NaN if the number is NaN
1518 ///
1519 /// # Examples
1520 ///
1521 /// ```
1522 /// let f = 3.5_f64;
1523 ///
1524 /// assert_eq!(f.signum(), 1.0);
1525 /// assert_eq!(f64::NEG_INFINITY.signum(), -1.0);
1526 ///
1527 /// assert!(f64::NAN.signum().is_nan());
1528 /// ```
1529 #[must_use = "method returns a new number and does not mutate the original value"]
1530 #[stable(feature = "rust1", since = "1.0.0")]
1531 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
1532 #[inline]
1533 pub const fn signum(self) -> f64 {
1534 if self.is_nan() { Self::NAN } else { 1.0_f64.copysign(self) }
1535 }
1536
1537 /// Returns a number composed of the magnitude of `self` and the sign of
1538 /// `sign`.
1539 ///
1540 /// Equal to `self` if the sign of `self` and `sign` are the same, otherwise equal to `-self`.
1541 /// If `self` is a NaN, then a NaN with the same payload as `self` and the sign bit of `sign` is
1542 /// returned.
1543 ///
1544 /// If `sign` is a NaN, then this operation will still carry over its sign into the result. Note
1545 /// that IEEE 754 doesn't assign any meaning to the sign bit in case of a NaN, and as Rust
1546 /// doesn't guarantee that the bit pattern of NaNs are conserved over arithmetic operations, the
1547 /// result of `copysign` with `sign` being a NaN might produce an unexpected or non-portable
1548 /// result. See the [specification of NaN bit patterns](primitive@f32#nan-bit-patterns) for more
1549 /// info.
1550 ///
1551 /// # Examples
1552 ///
1553 /// ```
1554 /// let f = 3.5_f64;
1555 ///
1556 /// assert_eq!(f.copysign(0.42), 3.5_f64);
1557 /// assert_eq!(f.copysign(-0.42), -3.5_f64);
1558 /// assert_eq!((-f).copysign(0.42), 3.5_f64);
1559 /// assert_eq!((-f).copysign(-0.42), -3.5_f64);
1560 ///
1561 /// assert!(f64::NAN.copysign(1.0).is_nan());
1562 /// ```
1563 #[must_use = "method returns a new number and does not mutate the original value"]
1564 #[stable(feature = "copysign", since = "1.35.0")]
1565 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
1566 #[inline]
1567 pub const fn copysign(self, sign: f64) -> f64 {
1568 intrinsics::copysignf64(self, sign)
1569 }
1570
1571 /// Float addition that allows optimizations based on algebraic rules.
1572 ///
1573 /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1574 #[must_use = "method returns a new number and does not mutate the original value"]
1575 #[unstable(feature = "float_algebraic", issue = "136469")]
1576 #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1577 #[inline]
1578 pub const fn algebraic_add(self, rhs: f64) -> f64 {
1579 intrinsics::fadd_algebraic(self, rhs)
1580 }
1581
1582 /// Float subtraction that allows optimizations based on algebraic rules.
1583 ///
1584 /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1585 #[must_use = "method returns a new number and does not mutate the original value"]
1586 #[unstable(feature = "float_algebraic", issue = "136469")]
1587 #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1588 #[inline]
1589 pub const fn algebraic_sub(self, rhs: f64) -> f64 {
1590 intrinsics::fsub_algebraic(self, rhs)
1591 }
1592
1593 /// Float multiplication that allows optimizations based on algebraic rules.
1594 ///
1595 /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1596 #[must_use = "method returns a new number and does not mutate the original value"]
1597 #[unstable(feature = "float_algebraic", issue = "136469")]
1598 #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1599 #[inline]
1600 pub const fn algebraic_mul(self, rhs: f64) -> f64 {
1601 intrinsics::fmul_algebraic(self, rhs)
1602 }
1603
1604 /// Float division that allows optimizations based on algebraic rules.
1605 ///
1606 /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1607 #[must_use = "method returns a new number and does not mutate the original value"]
1608 #[unstable(feature = "float_algebraic", issue = "136469")]
1609 #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1610 #[inline]
1611 pub const fn algebraic_div(self, rhs: f64) -> f64 {
1612 intrinsics::fdiv_algebraic(self, rhs)
1613 }
1614
1615 /// Float remainder that allows optimizations based on algebraic rules.
1616 ///
1617 /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1618 #[must_use = "method returns a new number and does not mutate the original value"]
1619 #[unstable(feature = "float_algebraic", issue = "136469")]
1620 #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1621 #[inline]
1622 pub const fn algebraic_rem(self, rhs: f64) -> f64 {
1623 intrinsics::frem_algebraic(self, rhs)
1624 }
1625}
1626
1627#[unstable(feature = "core_float_math", issue = "137578")]
1628/// Experimental implementations of floating point functions in `core`.
1629///
1630/// _The standalone functions in this module are for testing only.
1631/// They will be stabilized as inherent methods._
1632pub mod math {
1633 use crate::intrinsics;
1634 use crate::num::libm;
1635
1636 /// Experimental version of `floor` in `core`. See [`f64::floor`] for details.
1637 ///
1638 /// # Examples
1639 ///
1640 /// ```
1641 /// #![feature(core_float_math)]
1642 ///
1643 /// use core::f64;
1644 ///
1645 /// let f = 3.7_f64;
1646 /// let g = 3.0_f64;
1647 /// let h = -3.7_f64;
1648 ///
1649 /// assert_eq!(f64::math::floor(f), 3.0);
1650 /// assert_eq!(f64::math::floor(g), 3.0);
1651 /// assert_eq!(f64::math::floor(h), -4.0);
1652 /// ```
1653 ///
1654 /// _This standalone function is for testing only.
1655 /// It will be stabilized as an inherent method._
1656 ///
1657 /// [`f64::floor`]: ../../../std/primitive.f64.html#method.floor
1658 #[inline]
1659 #[unstable(feature = "core_float_math", issue = "137578")]
1660 #[must_use = "method returns a new number and does not mutate the original value"]
1661 pub const fn floor(x: f64) -> f64 {
1662 intrinsics::floorf64(x)
1663 }
1664
1665 /// Experimental version of `ceil` in `core`. See [`f64::ceil`] for details.
1666 ///
1667 /// # Examples
1668 ///
1669 /// ```
1670 /// #![feature(core_float_math)]
1671 ///
1672 /// use core::f64;
1673 ///
1674 /// let f = 3.01_f64;
1675 /// let g = 4.0_f64;
1676 ///
1677 /// assert_eq!(f64::math::ceil(f), 4.0);
1678 /// assert_eq!(f64::math::ceil(g), 4.0);
1679 /// ```
1680 ///
1681 /// _This standalone function is for testing only.
1682 /// It will be stabilized as an inherent method._
1683 ///
1684 /// [`f64::ceil`]: ../../../std/primitive.f64.html#method.ceil
1685 #[inline]
1686 #[doc(alias = "ceiling")]
1687 #[unstable(feature = "core_float_math", issue = "137578")]
1688 #[must_use = "method returns a new number and does not mutate the original value"]
1689 pub const fn ceil(x: f64) -> f64 {
1690 intrinsics::ceilf64(x)
1691 }
1692
1693 /// Experimental version of `round` in `core`. See [`f64::round`] for details.
1694 ///
1695 /// # Examples
1696 ///
1697 /// ```
1698 /// #![feature(core_float_math)]
1699 ///
1700 /// use core::f64;
1701 ///
1702 /// let f = 3.3_f64;
1703 /// let g = -3.3_f64;
1704 /// let h = -3.7_f64;
1705 /// let i = 3.5_f64;
1706 /// let j = 4.5_f64;
1707 ///
1708 /// assert_eq!(f64::math::round(f), 3.0);
1709 /// assert_eq!(f64::math::round(g), -3.0);
1710 /// assert_eq!(f64::math::round(h), -4.0);
1711 /// assert_eq!(f64::math::round(i), 4.0);
1712 /// assert_eq!(f64::math::round(j), 5.0);
1713 /// ```
1714 ///
1715 /// _This standalone function is for testing only.
1716 /// It will be stabilized as an inherent method._
1717 ///
1718 /// [`f64::round`]: ../../../std/primitive.f64.html#method.round
1719 #[inline]
1720 #[unstable(feature = "core_float_math", issue = "137578")]
1721 #[must_use = "method returns a new number and does not mutate the original value"]
1722 pub const fn round(x: f64) -> f64 {
1723 intrinsics::roundf64(x)
1724 }
1725
1726 /// Experimental version of `round_ties_even` in `core`. See [`f64::round_ties_even`] for
1727 /// details.
1728 ///
1729 /// # Examples
1730 ///
1731 /// ```
1732 /// #![feature(core_float_math)]
1733 ///
1734 /// use core::f64;
1735 ///
1736 /// let f = 3.3_f64;
1737 /// let g = -3.3_f64;
1738 /// let h = 3.5_f64;
1739 /// let i = 4.5_f64;
1740 ///
1741 /// assert_eq!(f64::math::round_ties_even(f), 3.0);
1742 /// assert_eq!(f64::math::round_ties_even(g), -3.0);
1743 /// assert_eq!(f64::math::round_ties_even(h), 4.0);
1744 /// assert_eq!(f64::math::round_ties_even(i), 4.0);
1745 /// ```
1746 ///
1747 /// _This standalone function is for testing only.
1748 /// It will be stabilized as an inherent method._
1749 ///
1750 /// [`f64::round_ties_even`]: ../../../std/primitive.f64.html#method.round_ties_even
1751 #[inline]
1752 #[unstable(feature = "core_float_math", issue = "137578")]
1753 #[must_use = "method returns a new number and does not mutate the original value"]
1754 pub const fn round_ties_even(x: f64) -> f64 {
1755 intrinsics::round_ties_even_f64(x)
1756 }
1757
1758 /// Experimental version of `trunc` in `core`. See [`f64::trunc`] for details.
1759 ///
1760 /// # Examples
1761 ///
1762 /// ```
1763 /// #![feature(core_float_math)]
1764 ///
1765 /// use core::f64;
1766 ///
1767 /// let f = 3.7_f64;
1768 /// let g = 3.0_f64;
1769 /// let h = -3.7_f64;
1770 ///
1771 /// assert_eq!(f64::math::trunc(f), 3.0);
1772 /// assert_eq!(f64::math::trunc(g), 3.0);
1773 /// assert_eq!(f64::math::trunc(h), -3.0);
1774 /// ```
1775 ///
1776 /// _This standalone function is for testing only.
1777 /// It will be stabilized as an inherent method._
1778 ///
1779 /// [`f64::trunc`]: ../../../std/primitive.f64.html#method.trunc
1780 #[inline]
1781 #[doc(alias = "truncate")]
1782 #[unstable(feature = "core_float_math", issue = "137578")]
1783 #[must_use = "method returns a new number and does not mutate the original value"]
1784 pub const fn trunc(x: f64) -> f64 {
1785 intrinsics::truncf64(x)
1786 }
1787
1788 /// Experimental version of `fract` in `core`. See [`f64::fract`] for details.
1789 ///
1790 /// # Examples
1791 ///
1792 /// ```
1793 /// #![feature(core_float_math)]
1794 ///
1795 /// use core::f64;
1796 ///
1797 /// let x = 3.6_f64;
1798 /// let y = -3.6_f64;
1799 /// let abs_difference_x = (f64::math::fract(x) - 0.6).abs();
1800 /// let abs_difference_y = (f64::math::fract(y) - (-0.6)).abs();
1801 ///
1802 /// assert!(abs_difference_x < 1e-10);
1803 /// assert!(abs_difference_y < 1e-10);
1804 /// ```
1805 ///
1806 /// _This standalone function is for testing only.
1807 /// It will be stabilized as an inherent method._
1808 ///
1809 /// [`f64::fract`]: ../../../std/primitive.f64.html#method.fract
1810 #[inline]
1811 #[unstable(feature = "core_float_math", issue = "137578")]
1812 #[must_use = "method returns a new number and does not mutate the original value"]
1813 pub const fn fract(x: f64) -> f64 {
1814 x - trunc(x)
1815 }
1816
1817 /// Experimental version of `mul_add` in `core`. See [`f64::mul_add`] for details.
1818 ///
1819 /// # Examples
1820 ///
1821 /// ```
1822 /// #![feature(core_float_math)]
1823 ///
1824 /// # // FIXME(#140515): mingw has an incorrect fma
1825 /// # // https://sourceforge.net/p/mingw-w64/bugs/848/
1826 /// # #[cfg(all(target_os = "windows", target_env = "gnu", not(target_abi = "llvm")))] {
1827 /// use core::f64;
1828 ///
1829 /// let m = 10.0_f64;
1830 /// let x = 4.0_f64;
1831 /// let b = 60.0_f64;
1832 ///
1833 /// assert_eq!(f64::math::mul_add(m, x, b), 100.0);
1834 /// assert_eq!(m * x + b, 100.0);
1835 ///
1836 /// let one_plus_eps = 1.0_f64 + f64::EPSILON;
1837 /// let one_minus_eps = 1.0_f64 - f64::EPSILON;
1838 /// let minus_one = -1.0_f64;
1839 ///
1840 /// // The exact result (1 + eps) * (1 - eps) = 1 - eps * eps.
1841 /// assert_eq!(
1842 /// f64::math::mul_add(one_plus_eps, one_minus_eps, minus_one),
1843 /// -f64::EPSILON * f64::EPSILON
1844 /// );
1845 /// // Different rounding with the non-fused multiply and add.
1846 /// assert_eq!(one_plus_eps * one_minus_eps + minus_one, 0.0);
1847 /// # }
1848 /// ```
1849 ///
1850 /// _This standalone function is for testing only.
1851 /// It will be stabilized as an inherent method._
1852 ///
1853 /// [`f64::mul_add`]: ../../../std/primitive.f64.html#method.mul_add
1854 #[inline]
1855 #[doc(alias = "fma", alias = "fusedMultiplyAdd")]
1856 #[unstable(feature = "core_float_math", issue = "137578")]
1857 #[must_use = "method returns a new number and does not mutate the original value"]
1858 pub const fn mul_add(x: f64, a: f64, b: f64) -> f64 {
1859 intrinsics::fmaf64(x, a, b)
1860 }
1861
1862 /// Experimental version of `div_euclid` in `core`. See [`f64::div_euclid`] for details.
1863 ///
1864 /// # Examples
1865 ///
1866 /// ```
1867 /// #![feature(core_float_math)]
1868 ///
1869 /// use core::f64;
1870 ///
1871 /// let a: f64 = 7.0;
1872 /// let b = 4.0;
1873 /// assert_eq!(f64::math::div_euclid(a, b), 1.0); // 7.0 > 4.0 * 1.0
1874 /// assert_eq!(f64::math::div_euclid(-a, b), -2.0); // -7.0 >= 4.0 * -2.0
1875 /// assert_eq!(f64::math::div_euclid(a, -b), -1.0); // 7.0 >= -4.0 * -1.0
1876 /// assert_eq!(f64::math::div_euclid(-a, -b), 2.0); // -7.0 >= -4.0 * 2.0
1877 /// ```
1878 ///
1879 /// _This standalone function is for testing only.
1880 /// It will be stabilized as an inherent method._
1881 ///
1882 /// [`f64::div_euclid`]: ../../../std/primitive.f64.html#method.div_euclid
1883 #[inline]
1884 #[unstable(feature = "core_float_math", issue = "137578")]
1885 #[must_use = "method returns a new number and does not mutate the original value"]
1886 pub fn div_euclid(x: f64, rhs: f64) -> f64 {
1887 let q = trunc(x / rhs);
1888 if x % rhs < 0.0 {
1889 return if rhs > 0.0 { q - 1.0 } else { q + 1.0 };
1890 }
1891 q
1892 }
1893
1894 /// Experimental version of `rem_euclid` in `core`. See [`f64::rem_euclid`] for details.
1895 ///
1896 /// # Examples
1897 ///
1898 /// ```
1899 /// #![feature(core_float_math)]
1900 ///
1901 /// use core::f64;
1902 ///
1903 /// let a: f64 = 7.0;
1904 /// let b = 4.0;
1905 /// assert_eq!(f64::math::rem_euclid(a, b), 3.0);
1906 /// assert_eq!(f64::math::rem_euclid(-a, b), 1.0);
1907 /// assert_eq!(f64::math::rem_euclid(a, -b), 3.0);
1908 /// assert_eq!(f64::math::rem_euclid(-a, -b), 1.0);
1909 /// // limitation due to round-off error
1910 /// assert!(f64::math::rem_euclid(-f64::EPSILON, 3.0) != 0.0);
1911 /// ```
1912 ///
1913 /// _This standalone function is for testing only.
1914 /// It will be stabilized as an inherent method._
1915 ///
1916 /// [`f64::rem_euclid`]: ../../../std/primitive.f64.html#method.rem_euclid
1917 #[inline]
1918 #[doc(alias = "modulo", alias = "mod")]
1919 #[unstable(feature = "core_float_math", issue = "137578")]
1920 #[must_use = "method returns a new number and does not mutate the original value"]
1921 pub fn rem_euclid(x: f64, rhs: f64) -> f64 {
1922 let r = x % rhs;
1923 if r < 0.0 { r + rhs.abs() } else { r }
1924 }
1925
1926 /// Experimental version of `powi` in `core`. See [`f64::powi`] for details.
1927 ///
1928 /// # Examples
1929 ///
1930 /// ```
1931 /// #![feature(core_float_math)]
1932 ///
1933 /// use core::f64;
1934 ///
1935 /// let x = 2.0_f64;
1936 /// let abs_difference = (f64::math::powi(x, 2) - (x * x)).abs();
1937 /// assert!(abs_difference <= 1e-6);
1938 ///
1939 /// assert_eq!(f64::math::powi(f64::NAN, 0), 1.0);
1940 /// ```
1941 ///
1942 /// _This standalone function is for testing only.
1943 /// It will be stabilized as an inherent method._
1944 ///
1945 /// [`f64::powi`]: ../../../std/primitive.f64.html#method.powi
1946 #[inline]
1947 #[unstable(feature = "core_float_math", issue = "137578")]
1948 #[must_use = "method returns a new number and does not mutate the original value"]
1949 pub fn powi(x: f64, n: i32) -> f64 {
1950 intrinsics::powif64(x, n)
1951 }
1952
1953 /// Experimental version of `sqrt` in `core`. See [`f64::sqrt`] for details.
1954 ///
1955 /// # Examples
1956 ///
1957 /// ```
1958 /// #![feature(core_float_math)]
1959 ///
1960 /// use core::f64;
1961 ///
1962 /// let positive = 4.0_f64;
1963 /// let negative = -4.0_f64;
1964 /// let negative_zero = -0.0_f64;
1965 ///
1966 /// assert_eq!(f64::math::sqrt(positive), 2.0);
1967 /// assert!(f64::math::sqrt(negative).is_nan());
1968 /// assert_eq!(f64::math::sqrt(negative_zero), negative_zero);
1969 /// ```
1970 ///
1971 /// _This standalone function is for testing only.
1972 /// It will be stabilized as an inherent method._
1973 ///
1974 /// [`f64::sqrt`]: ../../../std/primitive.f64.html#method.sqrt
1975 #[inline]
1976 #[doc(alias = "squareRoot")]
1977 #[unstable(feature = "core_float_math", issue = "137578")]
1978 #[must_use = "method returns a new number and does not mutate the original value"]
1979 pub fn sqrt(x: f64) -> f64 {
1980 intrinsics::sqrtf64(x)
1981 }
1982
1983 /// Experimental version of `abs_sub` in `core`. See [`f64::abs_sub`] for details.
1984 ///
1985 /// # Examples
1986 ///
1987 /// ```
1988 /// #![feature(core_float_math)]
1989 ///
1990 /// use core::f64;
1991 ///
1992 /// let x = 3.0_f64;
1993 /// let y = -3.0_f64;
1994 ///
1995 /// let abs_difference_x = (f64::math::abs_sub(x, 1.0) - 2.0).abs();
1996 /// let abs_difference_y = (f64::math::abs_sub(y, 1.0) - 0.0).abs();
1997 ///
1998 /// assert!(abs_difference_x < 1e-10);
1999 /// assert!(abs_difference_y < 1e-10);
2000 /// ```
2001 ///
2002 /// _This standalone function is for testing only.
2003 /// It will be stabilized as an inherent method._
2004 ///
2005 /// [`f64::abs_sub`]: ../../../std/primitive.f64.html#method.abs_sub
2006 #[inline]
2007 #[unstable(feature = "core_float_math", issue = "137578")]
2008 #[deprecated(
2009 since = "1.10.0",
2010 note = "you probably meant `(self - other).abs()`: \
2011 this operation is `(self - other).max(0.0)` \
2012 except that `abs_sub` also propagates NaNs (also \
2013 known as `fdim` in C). If you truly need the positive \
2014 difference, consider using that expression or the C function \
2015 `fdim`, depending on how you wish to handle NaN (please consider \
2016 filing an issue describing your use-case too)."
2017 )]
2018 #[must_use = "method returns a new number and does not mutate the original value"]
2019 pub fn abs_sub(x: f64, other: f64) -> f64 {
2020 libm::fdim(x, other)
2021 }
2022
2023 /// Experimental version of `cbrt` in `core`. See [`f64::cbrt`] for details.
2024 ///
2025 /// # Examples
2026 ///
2027 /// ```
2028 /// #![feature(core_float_math)]
2029 ///
2030 /// use core::f64;
2031 ///
2032 /// let x = 8.0_f64;
2033 ///
2034 /// // x^(1/3) - 2 == 0
2035 /// let abs_difference = (f64::math::cbrt(x) - 2.0).abs();
2036 ///
2037 /// assert!(abs_difference < 1e-10);
2038 /// ```
2039 ///
2040 /// _This standalone function is for testing only.
2041 /// It will be stabilized as an inherent method._
2042 ///
2043 /// [`f64::cbrt`]: ../../../std/primitive.f64.html#method.cbrt
2044 #[inline]
2045 #[unstable(feature = "core_float_math", issue = "137578")]
2046 #[must_use = "method returns a new number and does not mutate the original value"]
2047 pub fn cbrt(x: f64) -> f64 {
2048 libm::cbrt(x)
2049 }
2050}
2051