      1
      2
      3
      4
      5
      6
      7
      8
      9
     10
     11
     12
     13
     14
     15
     16
     17
     18
     19
     20
     21
     22
     23
     24
     25
     26
     27
     28
     29
     30
     31
     32
     33
     34
     35
     36
     37
     38
     39
     40
     41
     42
     43
     44
     45
     46
     47
     48
     49
     50
     51
     52
     53
     54
     55
     56
     57
     58
     59
     60
     61
     62
     63
     64
     65
     66
     67
     68
     69
     70
     71
     72
     73
     74
     75
     76
     77
     78
     79
     80
     81
     82
     83
     84
     85
     86
     87
     88
     89
     90
     91
     92
     93
     94
     95
     96
     97
     98
     99
    100
    101
    102
    103
    104
    105
    106
    107
    108
    109
    110
    111
    112
    113
    114
    115
    116
    117
    118
    119
    120
    121
    122
    123
    124
    125
    126
    127
    128
    129
    130
    131
    132
    133
    134
    135
    136
    137
    138
    139
    140
    141
    142
    143
    144
    145
    146
    147
    148
    149
    150
    151
    152
    153
    154
    155
    156
    157
    158
    159
    160
    161
    162
    163
    164
    165
    166
    167
    168
    169
    170
    171
    172
    173
    174
    175
    176
    177
    178
    179
    180
    181
    182
    183
    184
    185
    186
    187
    188
    189
    190
    191
    192
    193
    194
    195
    196
    197
    198
    199
    200
    201
    202
    203
    204
    205
    206
    207
    208
    209
    210
    211
    212
    213
    214
    215
    216
    217
    218
    219
    220
    221
    222
    223
    224
    225
    226
    227
    228
    229
    230
    231
    232
    233
    234
    235
    236
    237
    238
    239
    240
    241
    242
    243
    244
    245
    246
    247
    248
    249
    250
    251
    252
    253
    254
    255
    256
    257
    258
    259
    260
    261
    262
    263
    264
    265
    266
    267
    268
    269
    270
    271
    272
    273
    274
    275

    // Copyright 2012-2014 The Rust Project Developers. See the COPYRIGHT
    // file at the top-level directory of this distribution and at
    // http://rust-lang.org/COPYRIGHT.
    //
    // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
    // http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
    // <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
    // option. This file may not be copied, modified, or distributed
    // except according to those terms.

    //! Operations and constants for 64-bits floats (`f64` type)

    #![stable(feature = "rust1", since = "1.0.0")]

    use intrinsics;
    use mem;
    use num::FpCategory as Fp;
    use num::Float;

    /// The radix or base of the internal representation of `f64`.
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const RADIX: u32 = 2;

    /// Number of significant digits in base 2.
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const MANTISSA_DIGITS: u32 = 53;
    /// Approximate number of significant digits in base 10.
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const DIGITS: u32 = 15;

    /// Difference between `1.0` and the next largest representable number.
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const EPSILON: f64 = 2.2204460492503131e-16_f64;

    /// Smallest finite `f64` value.
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const MIN: f64 = -1.7976931348623157e+308_f64;
    /// Smallest positive normal `f64` value.
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const MIN_POSITIVE: f64 = 2.2250738585072014e-308_f64;
    /// Largest finite `f64` value.
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const MAX: f64 = 1.7976931348623157e+308_f64;

    /// One greater than the minimum possible normal power of 2 exponent.
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const MIN_EXP: i32 = -1021;
    /// Maximum possible power of 2 exponent.
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const MAX_EXP: i32 = 1024;

    /// Minimum possible normal power of 10 exponent.
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const MIN_10_EXP: i32 = -307;
    /// Maximum possible power of 10 exponent.
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const MAX_10_EXP: i32 = 308;

    /// Not a Number (NaN).
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const NAN: f64 = 0.0_f64 / 0.0_f64;
    /// Infinity (∞).
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const INFINITY: f64 = 1.0_f64 / 0.0_f64;
    /// Negative infinity (-∞).
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const NEG_INFINITY: f64 = -1.0_f64 / 0.0_f64;

    /// Basic mathematical constants.
    #[stable(feature = "rust1", since = "1.0.0")]
    pub mod consts {
        // FIXME: replace with mathematical constants from cmath.

        /// Archimedes' constant (π)
        #[stable(feature = "rust1", since = "1.0.0")]
        pub const PI: f64 = 3.14159265358979323846264338327950288_f64;

        /// π/2
        #[stable(feature = "rust1", since = "1.0.0")]
        pub const FRAC_PI_2: f64 = 1.57079632679489661923132169163975144_f64;

        /// π/3
        #[stable(feature = "rust1", since = "1.0.0")]
        pub const FRAC_PI_3: f64 = 1.04719755119659774615421446109316763_f64;

        /// π/4
        #[stable(feature = "rust1", since = "1.0.0")]
        pub const FRAC_PI_4: f64 = 0.785398163397448309615660845819875721_f64;

        /// π/6
        #[stable(feature = "rust1", since = "1.0.0")]
        pub const FRAC_PI_6: f64 = 0.52359877559829887307710723054658381_f64;

        /// π/8
        #[stable(feature = "rust1", since = "1.0.0")]
        pub const FRAC_PI_8: f64 = 0.39269908169872415480783042290993786_f64;

        /// 1/π
        #[stable(feature = "rust1", since = "1.0.0")]
        pub const FRAC_1_PI: f64 = 0.318309886183790671537767526745028724_f64;

        /// 2/π
        #[stable(feature = "rust1", since = "1.0.0")]
        pub const FRAC_2_PI: f64 = 0.636619772367581343075535053490057448_f64;

        /// 2/sqrt(π)
        #[stable(feature = "rust1", since = "1.0.0")]
        pub const FRAC_2_SQRT_PI: f64 = 1.12837916709551257389615890312154517_f64;

        /// sqrt(2)
        #[stable(feature = "rust1", since = "1.0.0")]
        pub const SQRT_2: f64 = 1.41421356237309504880168872420969808_f64;

        /// 1/sqrt(2)
        #[stable(feature = "rust1", since = "1.0.0")]
        pub const FRAC_1_SQRT_2: f64 = 0.707106781186547524400844362104849039_f64;

        /// Euler's number (e)
        #[stable(feature = "rust1", since = "1.0.0")]
        pub const E: f64 = 2.71828182845904523536028747135266250_f64;

        /// log<sub>2</sub>(e)
        #[stable(feature = "rust1", since = "1.0.0")]
        pub const LOG2_E: f64 = 1.44269504088896340735992468100189214_f64;

        /// log<sub>10</sub>(e)
        #[stable(feature = "rust1", since = "1.0.0")]
        pub const LOG10_E: f64 = 0.434294481903251827651128918916605082_f64;

        /// ln(2)
        #[stable(feature = "rust1", since = "1.0.0")]
        pub const LN_2: f64 = 0.693147180559945309417232121458176568_f64;

        /// ln(10)
        #[stable(feature = "rust1", since = "1.0.0")]
        pub const LN_10: f64 = 2.30258509299404568401799145468436421_f64;
    }

    #[unstable(feature = "core_float",
               reason = "stable interface is via `impl f{32,64}` in later crates",
               issue = "32110")]
    impl Float for f64 {
        /// Returns `true` if the number is NaN.
        #[inline]
        fn is_nan(self) -> bool {
            self != self
        }

        /// Returns `true` if the number is infinite.
        #[inline]
        fn is_infinite(self) -> bool {
            self == INFINITY || self == NEG_INFINITY
        }

        /// Returns `true` if the number is neither infinite or NaN.
        #[inline]
        fn is_finite(self) -> bool {
            !(self.is_nan() || self.is_infinite())
        }

        /// Returns `true` if the number is neither zero, infinite, subnormal or NaN.
        #[inline]
        fn is_normal(self) -> bool {
            self.classify() == Fp::Normal
        }

        /// Returns the floating point category of the number. If only one property
        /// is going to be tested, it is generally faster to use the specific
        /// predicate instead.
        fn classify(self) -> Fp {
            const EXP_MASK: u64 = 0x7ff0000000000000;
            const MAN_MASK: u64 = 0x000fffffffffffff;

            let bits: u64 = unsafe { mem::transmute(self) };
            match (bits & MAN_MASK, bits & EXP_MASK) {
                (0, 0) => Fp::Zero,
                (_, 0) => Fp::Subnormal,
                (0, EXP_MASK) => Fp::Infinite,
                (_, EXP_MASK) => Fp::Nan,
                _ => Fp::Normal,
            }
        }

        /// Computes the absolute value of `self`. Returns `Float::nan()` if the
        /// number is `Float::nan()`.
        #[inline]
        fn abs(self) -> f64 {
            unsafe { intrinsics::fabsf64(self) }
        }

        /// Returns a number that represents the sign of `self`.
        ///
        /// - `1.0` if the number is positive, `+0.0` or `Float::infinity()`
        /// - `-1.0` if the number is negative, `-0.0` or `Float::neg_infinity()`
        /// - `Float::nan()` if the number is `Float::nan()`
        #[inline]
        fn signum(self) -> f64 {
            if self.is_nan() {
                NAN
            } else {
                unsafe { intrinsics::copysignf64(1.0, self) }
            }
        }

        /// Returns `true` if and only if `self` has a positive sign, including `+0.0`, `NaN`s with
        /// positive sign bit and positive infinity.
        #[inline]
        fn is_sign_positive(self) -> bool {
            !self.is_sign_negative()
        }

        /// Returns `true` if and only if `self` has a negative sign, including `-0.0`, `NaN`s with
        /// negative sign bit and negative infinity.
        #[inline]
        fn is_sign_negative(self) -> bool {
            #[repr(C)]
            union F64Bytes {
                f: f64,
                b: u64
            }
            unsafe { F64Bytes { f: self }.b & 0x8000_0000_0000_0000 != 0 }
        }

        /// Returns the reciprocal (multiplicative inverse) of the number.
        #[inline]
        fn recip(self) -> f64 {
            1.0 / self
        }

        #[inline]
        fn powi(self, n: i32) -> f64 {
            unsafe { intrinsics::powif64(self, n) }
        }

        /// Converts to degrees, assuming the number is in radians.
        #[inline]
        fn to_degrees(self) -> f64 {
            self * (180.0f64 / consts::PI)
        }

        /// Converts to radians, assuming the number is in degrees.
        #[inline]
        fn to_radians(self) -> f64 {
            let value: f64 = consts::PI;
            self * (value / 180.0)
        }

        /// Returns the maximum of the two numbers.
        #[inline]
        fn max(self, other: f64) -> f64 {
            // IEEE754 says: maxNum(x, y) is the canonicalized number y if x < y, x if y < x, the
            // canonicalized number if one operand is a number and the other a quiet NaN. Otherwise it
            // is either x or y, canonicalized (this means results might differ among implementations).
            // When either x or y is a signalingNaN, then the result is according to 6.2.
            //
            // Since we do not support sNaN in Rust yet, we do not need to handle them.
            // FIXME(nagisa): due to https://bugs.llvm.org/show_bug.cgi?id=33303 we canonicalize by
            // multiplying by 1.0. Should switch to the `canonicalize` when it works.
            (if self < other || self.is_nan() { other } else { self }) * 1.0
        }

        /// Returns the minimum of the two numbers.
        #[inline]
        fn min(self, other: f64) -> f64 {
            // IEEE754 says: minNum(x, y) is the canonicalized number x if x < y, y if y < x, the
            // canonicalized number if one operand is a number and the other a quiet NaN. Otherwise it
            // is either x or y, canonicalized (this means results might differ among implementations).
            // When either x or y is a signalingNaN, then the result is according to 6.2.
            //
            // Since we do not support sNaN in Rust yet, we do not need to handle them.
            // FIXME(nagisa): due to https://bugs.llvm.org/show_bug.cgi?id=33303 we canonicalize by
            // multiplying by 1.0. Should switch to the `canonicalize` when it works.
            (if self < other || other.is_nan() { self } else { other }) * 1.0
        }
    }

# Help

## Keyboard Shortcuts

?
  Show this help dialog
S
  Focus the search field
⇤
  Move up in search results
⇥
  Move down in search results
⏎
  Go to active search result
+
  Collapse/expand all sections

## Search Tricks

Prefix searches with a type followed by a colon (e.g. `fn:`) to restrict the search to a given type.

Accepted types are: `fn`, `mod`, `struct`, `enum`, `trait`, `type`, `macro`, and `const`.

Search functions by type signature (e.g. `vec -> usize` or `* -> vec`)