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
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
// 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.

//! This module provides constants which are specific to the implementation
//! of the `f64` floating point data type.
//!
//! *[See also the `f64` primitive type](../../std/primitive.f64.html).*
//!
//! Mathematically significant numbers are provided in the `consts` sub-module.

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

use mem;
use num::FpCategory;

/// 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;

/// [Machine epsilon] value for `f64`.
///
/// This is the difference between `1.0` and the next largest representable number.
///
/// [Machine epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon
#[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>(10)
    #[unstable(feature = "extra_log_consts", issue = "50540")]
    pub const LOG2_10: f64 = 3.32192809488736234787031942948939018_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>(2)
    #[unstable(feature = "extra_log_consts", issue = "50540")]
    pub const LOG10_2: f64 = 0.301029995663981195213738894724493027_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;
}

#[lang = "f64"]
#[cfg(not(test))]
impl f64 {
    /// Returns `true` if this value is `NaN` and false otherwise.
    ///
    /// ```
    /// use std::f64;
    ///
    /// let nan = f64::NAN;
    /// let f = 7.0_f64;
    ///
    /// assert!(nan.is_nan());
    /// assert!(!f.is_nan());
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn is_nan(self) -> bool {
        self != self
    }

    /// Returns `true` if this value is positive infinity or negative infinity and
    /// false otherwise.
    ///
    /// ```
    /// use std::f64;
    ///
    /// let f = 7.0f64;
    /// let inf = f64::INFINITY;
    /// let neg_inf = f64::NEG_INFINITY;
    /// let nan = f64::NAN;
    ///
    /// assert!(!f.is_infinite());
    /// assert!(!nan.is_infinite());
    ///
    /// assert!(inf.is_infinite());
    /// assert!(neg_inf.is_infinite());
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn is_infinite(self) -> bool {
        self == INFINITY || self == NEG_INFINITY
    }

    /// Returns `true` if this number is neither infinite nor `NaN`.
    ///
    /// ```
    /// use std::f64;
    ///
    /// let f = 7.0f64;
    /// let inf: f64 = f64::INFINITY;
    /// let neg_inf: f64 = f64::NEG_INFINITY;
    /// let nan: f64 = f64::NAN;
    ///
    /// assert!(f.is_finite());
    ///
    /// assert!(!nan.is_finite());
    /// assert!(!inf.is_finite());
    /// assert!(!neg_inf.is_finite());
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn is_finite(self) -> bool {
        !(self.is_nan() || self.is_infinite())
    }

    /// Returns `true` if the number is neither zero, infinite,
    /// [subnormal][subnormal], or `NaN`.
    ///
    /// ```
    /// use std::f64;
    ///
    /// let min = f64::MIN_POSITIVE; // 2.2250738585072014e-308f64
    /// let max = f64::MAX;
    /// let lower_than_min = 1.0e-308_f64;
    /// let zero = 0.0f64;
    ///
    /// assert!(min.is_normal());
    /// assert!(max.is_normal());
    ///
    /// assert!(!zero.is_normal());
    /// assert!(!f64::NAN.is_normal());
    /// assert!(!f64::INFINITY.is_normal());
    /// // Values between `0` and `min` are Subnormal.
    /// assert!(!lower_than_min.is_normal());
    /// ```
    /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn is_normal(self) -> bool {
        self.classify() == FpCategory::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.
    ///
    /// ```
    /// use std::num::FpCategory;
    /// use std::f64;
    ///
    /// let num = 12.4_f64;
    /// let inf = f64::INFINITY;
    ///
    /// assert_eq!(num.classify(), FpCategory::Normal);
    /// assert_eq!(inf.classify(), FpCategory::Infinite);
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    pub fn classify(self) -> FpCategory {
        const EXP_MASK: u64 = 0x7ff0000000000000;
        const MAN_MASK: u64 = 0x000fffffffffffff;

        let bits = self.to_bits();
        match (bits & MAN_MASK, bits & EXP_MASK) {
            (0, 0) => FpCategory::Zero,
            (_, 0) => FpCategory::Subnormal,
            (0, EXP_MASK) => FpCategory::Infinite,
            (_, EXP_MASK) => FpCategory::Nan,
            _ => FpCategory::Normal,
        }
    }

    /// Returns `true` if and only if `self` has a positive sign, including `+0.0`, `NaN`s with
    /// positive sign bit and positive infinity.
    ///
    /// ```
    /// let f = 7.0_f64;
    /// let g = -7.0_f64;
    ///
    /// assert!(f.is_sign_positive());
    /// assert!(!g.is_sign_positive());
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn is_sign_positive(self) -> bool {
        !self.is_sign_negative()
    }

    #[stable(feature = "rust1", since = "1.0.0")]
    #[rustc_deprecated(since = "1.0.0", reason = "renamed to is_sign_positive")]
    #[inline]
    #[doc(hidden)]
    pub fn is_positive(self) -> bool {
        self.is_sign_positive()
    }

    /// Returns `true` if and only if `self` has a negative sign, including `-0.0`, `NaN`s with
    /// negative sign bit and negative infinity.
    ///
    /// ```
    /// let f = 7.0_f64;
    /// let g = -7.0_f64;
    ///
    /// assert!(!f.is_sign_negative());
    /// assert!(g.is_sign_negative());
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn is_sign_negative(self) -> bool {
        self.to_bits() & 0x8000_0000_0000_0000 != 0
    }

    #[stable(feature = "rust1", since = "1.0.0")]
    #[rustc_deprecated(since = "1.0.0", reason = "renamed to is_sign_negative")]
    #[inline]
    #[doc(hidden)]
    pub fn is_negative(self) -> bool {
        self.is_sign_negative()
    }

    /// Takes the reciprocal (inverse) of a number, `1/x`.
    ///
    /// ```
    /// let x = 2.0_f64;
    /// let abs_difference = (x.recip() - (1.0/x)).abs();
    ///
    /// assert!(abs_difference < 1e-10);
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn recip(self) -> f64 {
        1.0 / self
    }

    /// Converts radians to degrees.
    ///
    /// ```
    /// use std::f64::consts;
    ///
    /// let angle = consts::PI;
    ///
    /// let abs_difference = (angle.to_degrees() - 180.0).abs();
    ///
    /// assert!(abs_difference < 1e-10);
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn to_degrees(self) -> f64 {
        // The division here is correctly rounded with respect to the true
        // value of 180/π. (This differs from f32, where a constant must be
        // used to ensure a correctly rounded result.)
        self * (180.0f64 / consts::PI)
    }

    /// Converts degrees to radians.
    ///
    /// ```
    /// use std::f64::consts;
    ///
    /// let angle = 180.0_f64;
    ///
    /// let abs_difference = (angle.to_radians() - consts::PI).abs();
    ///
    /// assert!(abs_difference < 1e-10);
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn to_radians(self) -> f64 {
        let value: f64 = consts::PI;
        self * (value / 180.0)
    }

    /// Returns the maximum of the two numbers.
    ///
    /// ```
    /// let x = 1.0_f64;
    /// let y = 2.0_f64;
    ///
    /// assert_eq!(x.max(y), y);
    /// ```
    ///
    /// If one of the arguments is NaN, then the other argument is returned.
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub 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.is_nan() || self < other { other } else { self }) * 1.0
    }

    /// Returns the minimum of the two numbers.
    ///
    /// ```
    /// let x = 1.0_f64;
    /// let y = 2.0_f64;
    ///
    /// assert_eq!(x.min(y), x);
    /// ```
    ///
    /// If one of the arguments is NaN, then the other argument is returned.
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub 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 other.is_nan() || self < other { self } else { other }) * 1.0
    }

    /// Raw transmutation to `u64`.
    ///
    /// This is currently identical to `transmute::<f64, u64>(self)` on all platforms.
    ///
    /// See `from_bits` for some discussion of the portability of this operation
    /// (there are almost no issues).
    ///
    /// Note that this function is distinct from `as` casting, which attempts to
    /// preserve the *numeric* value, and not the bitwise value.
    ///
    /// # Examples
    ///
    /// ```
    /// assert!((1f64).to_bits() != 1f64 as u64); // to_bits() is not casting!
    /// assert_eq!((12.5f64).to_bits(), 0x4029000000000000);
    ///
    /// ```
    #[stable(feature = "float_bits_conv", since = "1.20.0")]
    #[inline]
    pub fn to_bits(self) -> u64 {
        unsafe { mem::transmute(self) }
    }

    /// Raw transmutation from `u64`.
    ///
    /// This is currently identical to `transmute::<u64, f64>(v)` on all platforms.
    /// It turns out this is incredibly portable, for two reasons:
    ///
    /// * Floats and Ints have the same endianness on all supported platforms.
    /// * IEEE-754 very precisely specifies the bit layout of floats.
    ///
    /// However there is one caveat: prior to the 2008 version of IEEE-754, how
    /// to interpret the NaN signaling bit wasn't actually specified. Most platforms
    /// (notably x86 and ARM) picked the interpretation that was ultimately
    /// standardized in 2008, but some didn't (notably MIPS). As a result, all
    /// signaling NaNs on MIPS are quiet NaNs on x86, and vice-versa.
    ///
    /// Rather than trying to preserve signaling-ness cross-platform, this
    /// implementation favours preserving the exact bits. This means that
    /// any payloads encoded in NaNs will be preserved even if the result of
    /// this method is sent over the network from an x86 machine to a MIPS one.
    ///
    /// If the results of this method are only manipulated by the same
    /// architecture that produced them, then there is no portability concern.
    ///
    /// If the input isn't NaN, then there is no portability concern.
    ///
    /// If you don't care about signalingness (very likely), then there is no
    /// portability concern.
    ///
    /// Note that this function is distinct from `as` casting, which attempts to
    /// preserve the *numeric* value, and not the bitwise value.
    ///
    /// # Examples
    ///
    /// ```
    /// use std::f64;
    /// let v = f64::from_bits(0x4029000000000000);
    /// let difference = (v - 12.5).abs();
    /// assert!(difference <= 1e-5);
    /// ```
    #[stable(feature = "float_bits_conv", since = "1.20.0")]
    #[inline]
    pub fn from_bits(v: u64) -> Self {
        // It turns out the safety issues with sNaN were overblown! Hooray!
        unsafe { mem::transmute(v) }
    }
}