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 //! Operations and constants for 64-bits floats (`f64` type)
13 // FIXME: MIN_VALUE and MAX_VALUE literals are parsed as -inf and inf #14353
14 #![allow(overflowing_literals)]
16 #![stable(feature = "rust1", since = "1.0.0")]
20 use num::FpCategory as Fp;
23 /// The radix or base of the internal representation of `f64`.
24 #[stable(feature = "rust1", since = "1.0.0")]
25 pub const RADIX: u32 = 2;
27 /// Number of significant digits in base 2.
28 #[stable(feature = "rust1", since = "1.0.0")]
29 pub const MANTISSA_DIGITS: u32 = 53;
30 /// Approximate number of significant digits in base 10.
31 #[stable(feature = "rust1", since = "1.0.0")]
32 pub const DIGITS: u32 = 15;
34 /// Difference between `1.0` and the next largest representable number.
35 #[stable(feature = "rust1", since = "1.0.0")]
36 pub const EPSILON: f64 = 2.2204460492503131e-16_f64;
38 /// Smallest finite `f64` value.
39 #[stable(feature = "rust1", since = "1.0.0")]
40 pub const MIN: f64 = -1.7976931348623157e+308_f64;
41 /// Smallest positive normal `f64` value.
42 #[stable(feature = "rust1", since = "1.0.0")]
43 pub const MIN_POSITIVE: f64 = 2.2250738585072014e-308_f64;
44 /// Largest finite `f64` value.
45 #[stable(feature = "rust1", since = "1.0.0")]
46 pub const MAX: f64 = 1.7976931348623157e+308_f64;
48 /// One greater than the minimum possible normal power of 2 exponent.
49 #[stable(feature = "rust1", since = "1.0.0")]
50 pub const MIN_EXP: i32 = -1021;
51 /// Maximum possible power of 2 exponent.
52 #[stable(feature = "rust1", since = "1.0.0")]
53 pub const MAX_EXP: i32 = 1024;
55 /// Minimum possible normal power of 10 exponent.
56 #[stable(feature = "rust1", since = "1.0.0")]
57 pub const MIN_10_EXP: i32 = -307;
58 /// Maximum possible power of 10 exponent.
59 #[stable(feature = "rust1", since = "1.0.0")]
60 pub const MAX_10_EXP: i32 = 308;
62 /// Not a Number (NaN).
63 #[stable(feature = "rust1", since = "1.0.0")]
64 pub const NAN: f64 = 0.0_f64 / 0.0_f64;
66 #[stable(feature = "rust1", since = "1.0.0")]
67 pub const INFINITY: f64 = 1.0_f64 / 0.0_f64;
68 /// Negative infinity (-∞).
69 #[stable(feature = "rust1", since = "1.0.0")]
70 pub const NEG_INFINITY: f64 = -1.0_f64 / 0.0_f64;
72 /// Basic mathematical constants.
73 #[stable(feature = "rust1", since = "1.0.0")]
75 // FIXME: replace with mathematical constants from cmath.
77 /// Archimedes' constant (π)
78 #[stable(feature = "rust1", since = "1.0.0")]
79 pub const PI: f64 = 3.14159265358979323846264338327950288_f64;
82 #[stable(feature = "rust1", since = "1.0.0")]
83 pub const FRAC_PI_2: f64 = 1.57079632679489661923132169163975144_f64;
86 #[stable(feature = "rust1", since = "1.0.0")]
87 pub const FRAC_PI_3: f64 = 1.04719755119659774615421446109316763_f64;
90 #[stable(feature = "rust1", since = "1.0.0")]
91 pub const FRAC_PI_4: f64 = 0.785398163397448309615660845819875721_f64;
94 #[stable(feature = "rust1", since = "1.0.0")]
95 pub const FRAC_PI_6: f64 = 0.52359877559829887307710723054658381_f64;
98 #[stable(feature = "rust1", since = "1.0.0")]
99 pub const FRAC_PI_8: f64 = 0.39269908169872415480783042290993786_f64;
102 #[stable(feature = "rust1", since = "1.0.0")]
103 pub const FRAC_1_PI: f64 = 0.318309886183790671537767526745028724_f64;
106 #[stable(feature = "rust1", since = "1.0.0")]
107 pub const FRAC_2_PI: f64 = 0.636619772367581343075535053490057448_f64;
110 #[stable(feature = "rust1", since = "1.0.0")]
111 pub const FRAC_2_SQRT_PI: f64 = 1.12837916709551257389615890312154517_f64;
114 #[stable(feature = "rust1", since = "1.0.0")]
115 pub const SQRT_2: f64 = 1.41421356237309504880168872420969808_f64;
118 #[stable(feature = "rust1", since = "1.0.0")]
119 pub const FRAC_1_SQRT_2: f64 = 0.707106781186547524400844362104849039_f64;
121 /// Euler's number (e)
122 #[stable(feature = "rust1", since = "1.0.0")]
123 pub const E: f64 = 2.71828182845904523536028747135266250_f64;
125 /// log<sub>2</sub>(e)
126 #[stable(feature = "rust1", since = "1.0.0")]
127 pub const LOG2_E: f64 = 1.44269504088896340735992468100189214_f64;
129 /// log<sub>10</sub>(e)
130 #[stable(feature = "rust1", since = "1.0.0")]
131 pub const LOG10_E: f64 = 0.434294481903251827651128918916605082_f64;
134 #[stable(feature = "rust1", since = "1.0.0")]
135 pub const LN_2: f64 = 0.693147180559945309417232121458176568_f64;
138 #[stable(feature = "rust1", since = "1.0.0")]
139 pub const LN_10: f64 = 2.30258509299404568401799145468436421_f64;
142 #[unstable(feature = "core_float",
143 reason = "stable interface is via `impl f{32,64}` in later crates",
146 /// Returns `true` if the number is NaN.
148 fn is_nan(self) -> bool {
152 /// Returns `true` if the number is infinite.
154 fn is_infinite(self) -> bool {
155 self == INFINITY || self == NEG_INFINITY
158 /// Returns `true` if the number is neither infinite or NaN.
160 fn is_finite(self) -> bool {
161 !(self.is_nan() || self.is_infinite())
164 /// Returns `true` if the number is neither zero, infinite, subnormal or NaN.
166 fn is_normal(self) -> bool {
167 self.classify() == Fp::Normal
170 /// Returns the floating point category of the number. If only one property
171 /// is going to be tested, it is generally faster to use the specific
172 /// predicate instead.
173 fn classify(self) -> Fp {
174 const EXP_MASK: u64 = 0x7ff0000000000000;
175 const MAN_MASK: u64 = 0x000fffffffffffff;
177 let bits: u64 = unsafe { mem::transmute(self) };
178 match (bits & MAN_MASK, bits & EXP_MASK) {
180 (_, 0) => Fp::Subnormal,
181 (0, EXP_MASK) => Fp::Infinite,
182 (_, EXP_MASK) => Fp::Nan,
187 /// Computes the absolute value of `self`. Returns `Float::nan()` if the
188 /// number is `Float::nan()`.
190 fn abs(self) -> f64 {
191 unsafe { intrinsics::fabsf64(self) }
194 /// Returns a number that represents the sign of `self`.
196 /// - `1.0` if the number is positive, `+0.0` or `Float::infinity()`
197 /// - `-1.0` if the number is negative, `-0.0` or `Float::neg_infinity()`
198 /// - `Float::nan()` if the number is `Float::nan()`
200 fn signum(self) -> f64 {
204 unsafe { intrinsics::copysignf64(1.0, self) }
208 /// Returns `true` if `self` is positive, including `+0.0` and
209 /// `Float::infinity()`.
211 fn is_sign_positive(self) -> bool {
212 self > 0.0 || (1.0 / self) == INFINITY
215 /// Returns `true` if `self` is negative, including `-0.0` and
216 /// `Float::neg_infinity()`.
218 fn is_sign_negative(self) -> bool {
219 self < 0.0 || (1.0 / self) == NEG_INFINITY
222 /// Returns the reciprocal (multiplicative inverse) of the number.
224 fn recip(self) -> f64 {
229 fn powi(self, n: i32) -> f64 {
230 unsafe { intrinsics::powif64(self, n) }
233 /// Converts to degrees, assuming the number is in radians.
235 fn to_degrees(self) -> f64 {
236 self * (180.0f64 / consts::PI)
239 /// Converts to radians, assuming the number is in degrees.
241 fn to_radians(self) -> f64 {
242 let value: f64 = consts::PI;
243 self * (value / 180.0)