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 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 /// Computes the absolute value of `self`. Returns `Float::nan()` if the
192 /// number is `Float::nan()`.
194 fn abs(self) -> f64 {
195 unsafe { intrinsics::fabsf64(self) }
198 /// Returns a number that represents the sign of `self`.
200 /// - `1.0` if the number is positive, `+0.0` or `Float::infinity()`
201 /// - `-1.0` if the number is negative, `-0.0` or `Float::neg_infinity()`
202 /// - `Float::nan()` if the number is `Float::nan()`
204 fn signum(self) -> f64 {
208 unsafe { intrinsics::copysignf64(1.0, self) }
212 /// Returns `true` if and only if `self` has a positive sign, including `+0.0`, `NaN`s with
213 /// positive sign bit and positive infinity.
215 fn is_sign_positive(self) -> bool {
216 !self.is_sign_negative()
219 /// Returns `true` if and only if `self` has a negative sign, including `-0.0`, `NaN`s with
220 /// negative sign bit and negative infinity.
222 fn is_sign_negative(self) -> bool {
223 self.to_bits() & 0x8000_0000_0000_0000 != 0
226 /// Returns the reciprocal (multiplicative inverse) of the number.
228 fn recip(self) -> f64 {
233 fn powi(self, n: i32) -> f64 {
234 unsafe { intrinsics::powif64(self, n) }
237 /// Converts to degrees, assuming the number is in radians.
239 fn to_degrees(self) -> f64 {
240 self * (180.0f64 / consts::PI)
243 /// Converts to radians, assuming the number is in degrees.
245 fn to_radians(self) -> f64 {
246 let value: f64 = consts::PI;
247 self * (value / 180.0)
250 /// Returns the maximum of the two numbers.
252 fn max(self, other: f64) -> f64 {
253 // IEEE754 says: maxNum(x, y) is the canonicalized number y if x < y, x if y < x, the
254 // canonicalized number if one operand is a number and the other a quiet NaN. Otherwise it
255 // is either x or y, canonicalized (this means results might differ among implementations).
256 // When either x or y is a signalingNaN, then the result is according to 6.2.
258 // Since we do not support sNaN in Rust yet, we do not need to handle them.
259 // FIXME(nagisa): due to https://bugs.llvm.org/show_bug.cgi?id=33303 we canonicalize by
260 // multiplying by 1.0. Should switch to the `canonicalize` when it works.
261 (if self.is_nan() || self < other { other } else { self }) * 1.0
264 /// Returns the minimum of the two numbers.
266 fn min(self, other: f64) -> f64 {
267 // IEEE754 says: minNum(x, y) is the canonicalized number x if x < y, y if y < x, the
268 // canonicalized number if one operand is a number and the other a quiet NaN. Otherwise it
269 // is either x or y, canonicalized (this means results might differ among implementations).
270 // When either x or y is a signalingNaN, then the result is according to 6.2.
272 // Since we do not support sNaN in Rust yet, we do not need to handle them.
273 // FIXME(nagisa): due to https://bugs.llvm.org/show_bug.cgi?id=33303 we canonicalize by
274 // multiplying by 1.0. Should switch to the `canonicalize` when it works.
275 (if other.is_nan() || self < other { self } else { other }) * 1.0
278 /// Raw transmutation to `u64`.
280 fn to_bits(self) -> u64 {
281 unsafe { mem::transmute(self) }
284 /// Raw transmutation from `u64`.
286 fn from_bits(v: u64) -> Self {
287 // It turns out the safety issues with sNaN were overblown! Hooray!
288 unsafe { mem::transmute(v) }