1 // Copyright 2012-2014 The Rust Project Developers. See the COPYRIGHT
2 // file at the top-level directory of this distribution and at
3 // http://rust-lang.org/COPYRIGHT.
5 // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
6 // http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
7 // <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
8 // option. This file may not be copied, modified, or distributed
9 // except according to those terms.
11 //! This module provides constants which are specific to the implementation
12 //! of the `f64` floating point data type.
14 //! Mathematically significant numbers are provided in the `consts` sub-module.
16 //! *[See also the `f64` primitive type](../../std/primitive.f64.html).*
18 #![stable(feature = "rust1", since = "1.0.0")]
22 #[cfg(not(stage0))] use num::FpCategory;
23 use num::FpCategory as Fp;
25 /// The radix or base of the internal representation of `f64`.
26 #[stable(feature = "rust1", since = "1.0.0")]
27 pub const RADIX: u32 = 2;
29 /// Number of significant digits in base 2.
30 #[stable(feature = "rust1", since = "1.0.0")]
31 pub const MANTISSA_DIGITS: u32 = 53;
32 /// Approximate number of significant digits in base 10.
33 #[stable(feature = "rust1", since = "1.0.0")]
34 pub const DIGITS: u32 = 15;
36 /// Difference between `1.0` and the next largest representable number.
37 #[stable(feature = "rust1", since = "1.0.0")]
38 pub const EPSILON: f64 = 2.2204460492503131e-16_f64;
40 /// Smallest finite `f64` value.
41 #[stable(feature = "rust1", since = "1.0.0")]
42 pub const MIN: f64 = -1.7976931348623157e+308_f64;
43 /// Smallest positive normal `f64` value.
44 #[stable(feature = "rust1", since = "1.0.0")]
45 pub const MIN_POSITIVE: f64 = 2.2250738585072014e-308_f64;
46 /// Largest finite `f64` value.
47 #[stable(feature = "rust1", since = "1.0.0")]
48 pub const MAX: f64 = 1.7976931348623157e+308_f64;
50 /// One greater than the minimum possible normal power of 2 exponent.
51 #[stable(feature = "rust1", since = "1.0.0")]
52 pub const MIN_EXP: i32 = -1021;
53 /// Maximum possible power of 2 exponent.
54 #[stable(feature = "rust1", since = "1.0.0")]
55 pub const MAX_EXP: i32 = 1024;
57 /// Minimum possible normal power of 10 exponent.
58 #[stable(feature = "rust1", since = "1.0.0")]
59 pub const MIN_10_EXP: i32 = -307;
60 /// Maximum possible power of 10 exponent.
61 #[stable(feature = "rust1", since = "1.0.0")]
62 pub const MAX_10_EXP: i32 = 308;
64 /// Not a Number (NaN).
65 #[stable(feature = "rust1", since = "1.0.0")]
66 pub const NAN: f64 = 0.0_f64 / 0.0_f64;
68 #[stable(feature = "rust1", since = "1.0.0")]
69 pub const INFINITY: f64 = 1.0_f64 / 0.0_f64;
70 /// Negative infinity (-∞).
71 #[stable(feature = "rust1", since = "1.0.0")]
72 pub const NEG_INFINITY: f64 = -1.0_f64 / 0.0_f64;
74 /// Basic mathematical constants.
75 #[stable(feature = "rust1", since = "1.0.0")]
77 // FIXME: replace with mathematical constants from cmath.
79 /// Archimedes' constant (π)
80 #[stable(feature = "rust1", since = "1.0.0")]
81 pub const PI: f64 = 3.14159265358979323846264338327950288_f64;
84 #[stable(feature = "rust1", since = "1.0.0")]
85 pub const FRAC_PI_2: f64 = 1.57079632679489661923132169163975144_f64;
88 #[stable(feature = "rust1", since = "1.0.0")]
89 pub const FRAC_PI_3: f64 = 1.04719755119659774615421446109316763_f64;
92 #[stable(feature = "rust1", since = "1.0.0")]
93 pub const FRAC_PI_4: f64 = 0.785398163397448309615660845819875721_f64;
96 #[stable(feature = "rust1", since = "1.0.0")]
97 pub const FRAC_PI_6: f64 = 0.52359877559829887307710723054658381_f64;
100 #[stable(feature = "rust1", since = "1.0.0")]
101 pub const FRAC_PI_8: f64 = 0.39269908169872415480783042290993786_f64;
104 #[stable(feature = "rust1", since = "1.0.0")]
105 pub const FRAC_1_PI: f64 = 0.318309886183790671537767526745028724_f64;
108 #[stable(feature = "rust1", since = "1.0.0")]
109 pub const FRAC_2_PI: f64 = 0.636619772367581343075535053490057448_f64;
112 #[stable(feature = "rust1", since = "1.0.0")]
113 pub const FRAC_2_SQRT_PI: f64 = 1.12837916709551257389615890312154517_f64;
116 #[stable(feature = "rust1", since = "1.0.0")]
117 pub const SQRT_2: f64 = 1.41421356237309504880168872420969808_f64;
120 #[stable(feature = "rust1", since = "1.0.0")]
121 pub const FRAC_1_SQRT_2: f64 = 0.707106781186547524400844362104849039_f64;
123 /// Euler's number (e)
124 #[stable(feature = "rust1", since = "1.0.0")]
125 pub const E: f64 = 2.71828182845904523536028747135266250_f64;
127 /// log<sub>2</sub>(e)
128 #[stable(feature = "rust1", since = "1.0.0")]
129 pub const LOG2_E: f64 = 1.44269504088896340735992468100189214_f64;
131 /// log<sub>10</sub>(e)
132 #[stable(feature = "rust1", since = "1.0.0")]
133 pub const LOG10_E: f64 = 0.434294481903251827651128918916605082_f64;
136 #[stable(feature = "rust1", since = "1.0.0")]
137 pub const LN_2: f64 = 0.693147180559945309417232121458176568_f64;
140 #[stable(feature = "rust1", since = "1.0.0")]
141 pub const LN_10: f64 = 2.30258509299404568401799145468436421_f64;
144 #[unstable(feature = "core_float",
145 reason = "stable interface is via `impl f{32,64}` in later crates",
150 /// Returns `true` if the number is NaN.
152 fn is_nan(self) -> bool {
156 /// Returns `true` if the number is infinite.
158 fn is_infinite(self) -> bool {
159 self == INFINITY || self == NEG_INFINITY
162 /// Returns `true` if the number is neither infinite or NaN.
164 fn is_finite(self) -> bool {
165 !(self.is_nan() || self.is_infinite())
168 /// Returns `true` if the number is neither zero, infinite, subnormal or NaN.
170 fn is_normal(self) -> bool {
171 self.classify() == Fp::Normal
174 /// Returns the floating point category of the number. If only one property
175 /// is going to be tested, it is generally faster to use the specific
176 /// predicate instead.
177 fn classify(self) -> Fp {
178 const EXP_MASK: u64 = 0x7ff0000000000000;
179 const MAN_MASK: u64 = 0x000fffffffffffff;
181 let bits = self.to_bits();
182 match (bits & MAN_MASK, bits & EXP_MASK) {
184 (_, 0) => Fp::Subnormal,
185 (0, EXP_MASK) => Fp::Infinite,
186 (_, EXP_MASK) => Fp::Nan,
191 /// Returns `true` if and only if `self` has a positive sign, including `+0.0`, `NaN`s with
192 /// positive sign bit and positive infinity.
194 fn is_sign_positive(self) -> bool {
195 !self.is_sign_negative()
198 /// Returns `true` if and only if `self` has a negative sign, including `-0.0`, `NaN`s with
199 /// negative sign bit and negative infinity.
201 fn is_sign_negative(self) -> bool {
202 self.to_bits() & 0x8000_0000_0000_0000 != 0
205 /// Returns the reciprocal (multiplicative inverse) of the number.
207 fn recip(self) -> f64 {
211 /// Converts to degrees, assuming the number is in radians.
213 fn to_degrees(self) -> f64 {
214 // The division here is correctly rounded with respect to the true
215 // value of 180/π. (This differs from f32, where a constant must be
216 // used to ensure a correctly rounded result.)
217 self * (180.0f64 / consts::PI)
220 /// Converts to radians, assuming the number is in degrees.
222 fn to_radians(self) -> f64 {
223 let value: f64 = consts::PI;
224 self * (value / 180.0)
227 /// Returns the maximum of the two numbers.
229 fn max(self, other: f64) -> f64 {
230 // IEEE754 says: maxNum(x, y) is the canonicalized number y if x < y, x if y < x, the
231 // canonicalized number if one operand is a number and the other a quiet NaN. Otherwise it
232 // is either x or y, canonicalized (this means results might differ among implementations).
233 // When either x or y is a signalingNaN, then the result is according to 6.2.
235 // Since we do not support sNaN in Rust yet, we do not need to handle them.
236 // FIXME(nagisa): due to https://bugs.llvm.org/show_bug.cgi?id=33303 we canonicalize by
237 // multiplying by 1.0. Should switch to the `canonicalize` when it works.
238 (if self.is_nan() || self < other { other } else { self }) * 1.0
241 /// Returns the minimum of the two numbers.
243 fn min(self, other: f64) -> f64 {
244 // IEEE754 says: minNum(x, y) is the canonicalized number x if x < y, y if y < x, the
245 // canonicalized number if one operand is a number and the other a quiet NaN. Otherwise it
246 // is either x or y, canonicalized (this means results might differ among implementations).
247 // When either x or y is a signalingNaN, then the result is according to 6.2.
249 // Since we do not support sNaN in Rust yet, we do not need to handle them.
250 // FIXME(nagisa): due to https://bugs.llvm.org/show_bug.cgi?id=33303 we canonicalize by
251 // multiplying by 1.0. Should switch to the `canonicalize` when it works.
252 (if other.is_nan() || self < other { self } else { other }) * 1.0
255 /// Raw transmutation to `u64`.
257 fn to_bits(self) -> u64 {
258 unsafe { mem::transmute(self) }
261 /// Raw transmutation from `u64`.
263 fn from_bits(v: u64) -> Self {
264 // It turns out the safety issues with sNaN were overblown! Hooray!
265 unsafe { mem::transmute(v) }
269 // FIXME: remove (inline) this macro and the Float trait
270 // when updating to a bootstrap compiler that has the new lang items.
271 #[cfg_attr(stage0, macro_export)]
272 #[unstable(feature = "core_float", issue = "32110")]
273 macro_rules! f64_core_methods { () => {
274 /// Returns `true` if this value is `NaN` and false otherwise.
279 /// let nan = f64::NAN;
282 /// assert!(nan.is_nan());
283 /// assert!(!f.is_nan());
285 #[stable(feature = "rust1", since = "1.0.0")]
287 pub fn is_nan(self) -> bool { Float::is_nan(self) }
289 /// Returns `true` if this value is positive infinity or negative infinity and
296 /// let inf = f64::INFINITY;
297 /// let neg_inf = f64::NEG_INFINITY;
298 /// let nan = f64::NAN;
300 /// assert!(!f.is_infinite());
301 /// assert!(!nan.is_infinite());
303 /// assert!(inf.is_infinite());
304 /// assert!(neg_inf.is_infinite());
306 #[stable(feature = "rust1", since = "1.0.0")]
308 pub fn is_infinite(self) -> bool { Float::is_infinite(self) }
310 /// Returns `true` if this number is neither infinite nor `NaN`.
316 /// let inf: f64 = f64::INFINITY;
317 /// let neg_inf: f64 = f64::NEG_INFINITY;
318 /// let nan: f64 = f64::NAN;
320 /// assert!(f.is_finite());
322 /// assert!(!nan.is_finite());
323 /// assert!(!inf.is_finite());
324 /// assert!(!neg_inf.is_finite());
326 #[stable(feature = "rust1", since = "1.0.0")]
328 pub fn is_finite(self) -> bool { Float::is_finite(self) }
330 /// Returns `true` if the number is neither zero, infinite,
331 /// [subnormal][subnormal], or `NaN`.
336 /// let min = f64::MIN_POSITIVE; // 2.2250738585072014e-308f64
337 /// let max = f64::MAX;
338 /// let lower_than_min = 1.0e-308_f64;
339 /// let zero = 0.0f64;
341 /// assert!(min.is_normal());
342 /// assert!(max.is_normal());
344 /// assert!(!zero.is_normal());
345 /// assert!(!f64::NAN.is_normal());
346 /// assert!(!f64::INFINITY.is_normal());
347 /// // Values between `0` and `min` are Subnormal.
348 /// assert!(!lower_than_min.is_normal());
350 /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
351 #[stable(feature = "rust1", since = "1.0.0")]
353 pub fn is_normal(self) -> bool { Float::is_normal(self) }
355 /// Returns the floating point category of the number. If only one property
356 /// is going to be tested, it is generally faster to use the specific
357 /// predicate instead.
360 /// use std::num::FpCategory;
363 /// let num = 12.4_f64;
364 /// let inf = f64::INFINITY;
366 /// assert_eq!(num.classify(), FpCategory::Normal);
367 /// assert_eq!(inf.classify(), FpCategory::Infinite);
369 #[stable(feature = "rust1", since = "1.0.0")]
371 pub fn classify(self) -> FpCategory { Float::classify(self) }
373 /// Returns `true` if and only if `self` has a positive sign, including `+0.0`, `NaN`s with
374 /// positive sign bit and positive infinity.
378 /// let g = -7.0_f64;
380 /// assert!(f.is_sign_positive());
381 /// assert!(!g.is_sign_positive());
383 #[stable(feature = "rust1", since = "1.0.0")]
385 pub fn is_sign_positive(self) -> bool { Float::is_sign_positive(self) }
387 #[stable(feature = "rust1", since = "1.0.0")]
388 #[rustc_deprecated(since = "1.0.0", reason = "renamed to is_sign_positive")]
391 pub fn is_positive(self) -> bool { Float::is_sign_positive(self) }
393 /// Returns `true` if and only if `self` has a negative sign, including `-0.0`, `NaN`s with
394 /// negative sign bit and negative infinity.
398 /// let g = -7.0_f64;
400 /// assert!(!f.is_sign_negative());
401 /// assert!(g.is_sign_negative());
403 #[stable(feature = "rust1", since = "1.0.0")]
405 pub fn is_sign_negative(self) -> bool { Float::is_sign_negative(self) }
407 #[stable(feature = "rust1", since = "1.0.0")]
408 #[rustc_deprecated(since = "1.0.0", reason = "renamed to is_sign_negative")]
411 pub fn is_negative(self) -> bool { Float::is_sign_negative(self) }
413 /// Takes the reciprocal (inverse) of a number, `1/x`.
417 /// let abs_difference = (x.recip() - (1.0/x)).abs();
419 /// assert!(abs_difference < 1e-10);
421 #[stable(feature = "rust1", since = "1.0.0")]
423 pub fn recip(self) -> f64 { Float::recip(self) }
425 /// Converts radians to degrees.
428 /// use std::f64::consts;
430 /// let angle = consts::PI;
432 /// let abs_difference = (angle.to_degrees() - 180.0).abs();
434 /// assert!(abs_difference < 1e-10);
436 #[stable(feature = "rust1", since = "1.0.0")]
438 pub fn to_degrees(self) -> f64 { Float::to_degrees(self) }
440 /// Converts degrees to radians.
443 /// use std::f64::consts;
445 /// let angle = 180.0_f64;
447 /// let abs_difference = (angle.to_radians() - consts::PI).abs();
449 /// assert!(abs_difference < 1e-10);
451 #[stable(feature = "rust1", since = "1.0.0")]
453 pub fn to_radians(self) -> f64 { Float::to_radians(self) }
455 /// Returns the maximum of the two numbers.
461 /// assert_eq!(x.max(y), y);
464 /// If one of the arguments is NaN, then the other argument is returned.
465 #[stable(feature = "rust1", since = "1.0.0")]
467 pub fn max(self, other: f64) -> f64 {
468 Float::max(self, other)
471 /// Returns the minimum of the two numbers.
477 /// assert_eq!(x.min(y), x);
480 /// If one of the arguments is NaN, then the other argument is returned.
481 #[stable(feature = "rust1", since = "1.0.0")]
483 pub fn min(self, other: f64) -> f64 {
484 Float::min(self, other)
487 /// Raw transmutation to `u64`.
489 /// This is currently identical to `transmute::<f64, u64>(self)` on all platforms.
491 /// See `from_bits` for some discussion of the portability of this operation
492 /// (there are almost no issues).
494 /// Note that this function is distinct from `as` casting, which attempts to
495 /// preserve the *numeric* value, and not the bitwise value.
500 /// assert!((1f64).to_bits() != 1f64 as u64); // to_bits() is not casting!
501 /// assert_eq!((12.5f64).to_bits(), 0x4029000000000000);
504 #[stable(feature = "float_bits_conv", since = "1.20.0")]
506 pub fn to_bits(self) -> u64 {
510 /// Raw transmutation from `u64`.
512 /// This is currently identical to `transmute::<u64, f64>(v)` on all platforms.
513 /// It turns out this is incredibly portable, for two reasons:
515 /// * Floats and Ints have the same endianness on all supported platforms.
516 /// * IEEE-754 very precisely specifies the bit layout of floats.
518 /// However there is one caveat: prior to the 2008 version of IEEE-754, how
519 /// to interpret the NaN signaling bit wasn't actually specified. Most platforms
520 /// (notably x86 and ARM) picked the interpretation that was ultimately
521 /// standardized in 2008, but some didn't (notably MIPS). As a result, all
522 /// signaling NaNs on MIPS are quiet NaNs on x86, and vice-versa.
524 /// Rather than trying to preserve signaling-ness cross-platform, this
525 /// implementation favours preserving the exact bits. This means that
526 /// any payloads encoded in NaNs will be preserved even if the result of
527 /// this method is sent over the network from an x86 machine to a MIPS one.
529 /// If the results of this method are only manipulated by the same
530 /// architecture that produced them, then there is no portability concern.
532 /// If the input isn't NaN, then there is no portability concern.
534 /// If you don't care about signalingness (very likely), then there is no
535 /// portability concern.
537 /// Note that this function is distinct from `as` casting, which attempts to
538 /// preserve the *numeric* value, and not the bitwise value.
544 /// let v = f64::from_bits(0x4029000000000000);
545 /// let difference = (v - 12.5).abs();
546 /// assert!(difference <= 1e-5);
548 #[stable(feature = "float_bits_conv", since = "1.20.0")]
550 pub fn from_bits(v: u64) -> Self {