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 `f32` floating point data type.
14 //! Mathematically significant numbers are provided in the `consts` sub-module.
16 //! *[See also the `f32` primitive type](../../std/primitive.f32.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 `f32`.
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 = 24;
32 /// Approximate number of significant digits in base 10.
33 #[stable(feature = "rust1", since = "1.0.0")]
34 pub const DIGITS: u32 = 6;
36 /// Difference between `1.0` and the next largest representable number.
37 #[stable(feature = "rust1", since = "1.0.0")]
38 pub const EPSILON: f32 = 1.19209290e-07_f32;
40 /// Smallest finite `f32` value.
41 #[stable(feature = "rust1", since = "1.0.0")]
42 pub const MIN: f32 = -3.40282347e+38_f32;
43 /// Smallest positive normal `f32` value.
44 #[stable(feature = "rust1", since = "1.0.0")]
45 pub const MIN_POSITIVE: f32 = 1.17549435e-38_f32;
46 /// Largest finite `f32` value.
47 #[stable(feature = "rust1", since = "1.0.0")]
48 pub const MAX: f32 = 3.40282347e+38_f32;
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 = -125;
53 /// Maximum possible power of 2 exponent.
54 #[stable(feature = "rust1", since = "1.0.0")]
55 pub const MAX_EXP: i32 = 128;
57 /// Minimum possible normal power of 10 exponent.
58 #[stable(feature = "rust1", since = "1.0.0")]
59 pub const MIN_10_EXP: i32 = -37;
60 /// Maximum possible power of 10 exponent.
61 #[stable(feature = "rust1", since = "1.0.0")]
62 pub const MAX_10_EXP: i32 = 38;
64 /// Not a Number (NaN).
65 #[stable(feature = "rust1", since = "1.0.0")]
66 pub const NAN: f32 = 0.0_f32 / 0.0_f32;
68 #[stable(feature = "rust1", since = "1.0.0")]
69 pub const INFINITY: f32 = 1.0_f32 / 0.0_f32;
70 /// Negative infinity (-∞).
71 #[stable(feature = "rust1", since = "1.0.0")]
72 pub const NEG_INFINITY: f32 = -1.0_f32 / 0.0_f32;
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: f32 = 3.14159265358979323846264338327950288_f32;
84 #[stable(feature = "rust1", since = "1.0.0")]
85 pub const FRAC_PI_2: f32 = 1.57079632679489661923132169163975144_f32;
88 #[stable(feature = "rust1", since = "1.0.0")]
89 pub const FRAC_PI_3: f32 = 1.04719755119659774615421446109316763_f32;
92 #[stable(feature = "rust1", since = "1.0.0")]
93 pub const FRAC_PI_4: f32 = 0.785398163397448309615660845819875721_f32;
96 #[stable(feature = "rust1", since = "1.0.0")]
97 pub const FRAC_PI_6: f32 = 0.52359877559829887307710723054658381_f32;
100 #[stable(feature = "rust1", since = "1.0.0")]
101 pub const FRAC_PI_8: f32 = 0.39269908169872415480783042290993786_f32;
104 #[stable(feature = "rust1", since = "1.0.0")]
105 pub const FRAC_1_PI: f32 = 0.318309886183790671537767526745028724_f32;
108 #[stable(feature = "rust1", since = "1.0.0")]
109 pub const FRAC_2_PI: f32 = 0.636619772367581343075535053490057448_f32;
112 #[stable(feature = "rust1", since = "1.0.0")]
113 pub const FRAC_2_SQRT_PI: f32 = 1.12837916709551257389615890312154517_f32;
116 #[stable(feature = "rust1", since = "1.0.0")]
117 pub const SQRT_2: f32 = 1.41421356237309504880168872420969808_f32;
120 #[stable(feature = "rust1", since = "1.0.0")]
121 pub const FRAC_1_SQRT_2: f32 = 0.707106781186547524400844362104849039_f32;
123 /// Euler's number (e)
124 #[stable(feature = "rust1", since = "1.0.0")]
125 pub const E: f32 = 2.71828182845904523536028747135266250_f32;
127 /// log<sub>2</sub>(e)
128 #[stable(feature = "rust1", since = "1.0.0")]
129 pub const LOG2_E: f32 = 1.44269504088896340735992468100189214_f32;
131 /// log<sub>2</sub>(10)
132 #[unstable(feature = "extra_log_consts", issue = "50540")]
133 pub const LOG2_10: f32 = 3.32192809488736234787031942948939018_f32;
135 /// log<sub>10</sub>(e)
136 #[stable(feature = "rust1", since = "1.0.0")]
137 pub const LOG10_E: f32 = 0.434294481903251827651128918916605082_f32;
139 /// log<sub>10</sub>(2)
140 #[unstable(feature = "extra_log_consts", issue = "50540")]
141 pub const LOG10_2: f32 = 0.301029995663981195213738894724493027_f32;
144 #[stable(feature = "rust1", since = "1.0.0")]
145 pub const LN_2: f32 = 0.693147180559945309417232121458176568_f32;
148 #[stable(feature = "rust1", since = "1.0.0")]
149 pub const LN_10: f32 = 2.30258509299404568401799145468436421_f32;
152 #[unstable(feature = "core_float",
153 reason = "stable interface is via `impl f{32,64}` in later crates",
158 /// Returns `true` if the number is NaN.
160 fn is_nan(self) -> bool {
164 /// Returns `true` if the number is infinite.
166 fn is_infinite(self) -> bool {
167 self == INFINITY || self == NEG_INFINITY
170 /// Returns `true` if the number is neither infinite or NaN.
172 fn is_finite(self) -> bool {
173 !(self.is_nan() || self.is_infinite())
176 /// Returns `true` if the number is neither zero, infinite, subnormal or NaN.
178 fn is_normal(self) -> bool {
179 self.classify() == Fp::Normal
182 /// Returns the floating point category of the number. If only one property
183 /// is going to be tested, it is generally faster to use the specific
184 /// predicate instead.
185 fn classify(self) -> Fp {
186 const EXP_MASK: u32 = 0x7f800000;
187 const MAN_MASK: u32 = 0x007fffff;
189 let bits = self.to_bits();
190 match (bits & MAN_MASK, bits & EXP_MASK) {
192 (_, 0) => Fp::Subnormal,
193 (0, EXP_MASK) => Fp::Infinite,
194 (_, EXP_MASK) => Fp::Nan,
199 /// Returns `true` if and only if `self` has a positive sign, including `+0.0`, `NaN`s with
200 /// positive sign bit and positive infinity.
202 fn is_sign_positive(self) -> bool {
203 !self.is_sign_negative()
206 /// Returns `true` if and only if `self` has a negative sign, including `-0.0`, `NaN`s with
207 /// negative sign bit and negative infinity.
209 fn is_sign_negative(self) -> bool {
210 // IEEE754 says: isSignMinus(x) is true if and only if x has negative sign. isSignMinus
211 // applies to zeros and NaNs as well.
212 self.to_bits() & 0x8000_0000 != 0
215 /// Returns the reciprocal (multiplicative inverse) of the number.
217 fn recip(self) -> f32 {
221 /// Converts to degrees, assuming the number is in radians.
223 fn to_degrees(self) -> f32 {
224 // Use a constant for better precision.
225 const PIS_IN_180: f32 = 57.2957795130823208767981548141051703_f32;
229 /// Converts to radians, assuming the number is in degrees.
231 fn to_radians(self) -> f32 {
232 let value: f32 = consts::PI;
233 self * (value / 180.0f32)
236 /// Returns the maximum of the two numbers.
238 fn max(self, other: f32) -> f32 {
239 // IEEE754 says: maxNum(x, y) is the canonicalized number y if x < y, x if y < x, the
240 // canonicalized number if one operand is a number and the other a quiet NaN. Otherwise it
241 // is either x or y, canonicalized (this means results might differ among implementations).
242 // When either x or y is a signalingNaN, then the result is according to 6.2.
244 // Since we do not support sNaN in Rust yet, we do not need to handle them.
245 // FIXME(nagisa): due to https://bugs.llvm.org/show_bug.cgi?id=33303 we canonicalize by
246 // multiplying by 1.0. Should switch to the `canonicalize` when it works.
247 (if self.is_nan() || self < other { other } else { self }) * 1.0
250 /// Returns the minimum of the two numbers.
252 fn min(self, other: f32) -> f32 {
253 // IEEE754 says: minNum(x, y) is the canonicalized number x if x < y, y 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 other.is_nan() || self < other { self } else { other }) * 1.0
264 /// Raw transmutation to `u32`.
266 fn to_bits(self) -> u32 {
267 unsafe { mem::transmute(self) }
270 /// Raw transmutation from `u32`.
272 fn from_bits(v: u32) -> Self {
273 // It turns out the safety issues with sNaN were overblown! Hooray!
274 unsafe { mem::transmute(v) }
278 // FIXME: remove (inline) this macro and the Float trait
279 // when updating to a bootstrap compiler that has the new lang items.
280 #[cfg_attr(stage0, macro_export)]
281 #[unstable(feature = "core_float", issue = "32110")]
282 macro_rules! f32_core_methods { () => {
283 /// Returns `true` if this value is `NaN` and false otherwise.
288 /// let nan = f32::NAN;
291 /// assert!(nan.is_nan());
292 /// assert!(!f.is_nan());
294 #[stable(feature = "rust1", since = "1.0.0")]
296 pub fn is_nan(self) -> bool { Float::is_nan(self) }
298 /// Returns `true` if this value is positive infinity or negative infinity and
305 /// let inf = f32::INFINITY;
306 /// let neg_inf = f32::NEG_INFINITY;
307 /// let nan = f32::NAN;
309 /// assert!(!f.is_infinite());
310 /// assert!(!nan.is_infinite());
312 /// assert!(inf.is_infinite());
313 /// assert!(neg_inf.is_infinite());
315 #[stable(feature = "rust1", since = "1.0.0")]
317 pub fn is_infinite(self) -> bool { Float::is_infinite(self) }
319 /// Returns `true` if this number is neither infinite nor `NaN`.
325 /// let inf = f32::INFINITY;
326 /// let neg_inf = f32::NEG_INFINITY;
327 /// let nan = f32::NAN;
329 /// assert!(f.is_finite());
331 /// assert!(!nan.is_finite());
332 /// assert!(!inf.is_finite());
333 /// assert!(!neg_inf.is_finite());
335 #[stable(feature = "rust1", since = "1.0.0")]
337 pub fn is_finite(self) -> bool { Float::is_finite(self) }
339 /// Returns `true` if the number is neither zero, infinite,
340 /// [subnormal][subnormal], or `NaN`.
345 /// let min = f32::MIN_POSITIVE; // 1.17549435e-38f32
346 /// let max = f32::MAX;
347 /// let lower_than_min = 1.0e-40_f32;
348 /// let zero = 0.0_f32;
350 /// assert!(min.is_normal());
351 /// assert!(max.is_normal());
353 /// assert!(!zero.is_normal());
354 /// assert!(!f32::NAN.is_normal());
355 /// assert!(!f32::INFINITY.is_normal());
356 /// // Values between `0` and `min` are Subnormal.
357 /// assert!(!lower_than_min.is_normal());
359 /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
360 #[stable(feature = "rust1", since = "1.0.0")]
362 pub fn is_normal(self) -> bool { Float::is_normal(self) }
364 /// Returns the floating point category of the number. If only one property
365 /// is going to be tested, it is generally faster to use the specific
366 /// predicate instead.
369 /// use std::num::FpCategory;
372 /// let num = 12.4_f32;
373 /// let inf = f32::INFINITY;
375 /// assert_eq!(num.classify(), FpCategory::Normal);
376 /// assert_eq!(inf.classify(), FpCategory::Infinite);
378 #[stable(feature = "rust1", since = "1.0.0")]
380 pub fn classify(self) -> FpCategory { Float::classify(self) }
382 /// Returns `true` if and only if `self` has a positive sign, including `+0.0`, `NaN`s with
383 /// positive sign bit and positive infinity.
387 /// let g = -7.0_f32;
389 /// assert!(f.is_sign_positive());
390 /// assert!(!g.is_sign_positive());
392 #[stable(feature = "rust1", since = "1.0.0")]
394 pub fn is_sign_positive(self) -> bool { Float::is_sign_positive(self) }
396 /// Returns `true` if and only if `self` has a negative sign, including `-0.0`, `NaN`s with
397 /// negative sign bit and negative infinity.
403 /// assert!(!f.is_sign_negative());
404 /// assert!(g.is_sign_negative());
406 #[stable(feature = "rust1", since = "1.0.0")]
408 pub fn is_sign_negative(self) -> bool { Float::is_sign_negative(self) }
410 /// Takes the reciprocal (inverse) of a number, `1/x`.
416 /// let abs_difference = (x.recip() - (1.0/x)).abs();
418 /// assert!(abs_difference <= f32::EPSILON);
420 #[stable(feature = "rust1", since = "1.0.0")]
422 pub fn recip(self) -> f32 { Float::recip(self) }
424 /// Converts radians to degrees.
427 /// use std::f32::{self, consts};
429 /// let angle = consts::PI;
431 /// let abs_difference = (angle.to_degrees() - 180.0).abs();
433 /// assert!(abs_difference <= f32::EPSILON);
435 #[stable(feature = "f32_deg_rad_conversions", since="1.7.0")]
437 pub fn to_degrees(self) -> f32 { Float::to_degrees(self) }
439 /// Converts degrees to radians.
442 /// use std::f32::{self, consts};
444 /// let angle = 180.0f32;
446 /// let abs_difference = (angle.to_radians() - consts::PI).abs();
448 /// assert!(abs_difference <= f32::EPSILON);
450 #[stable(feature = "f32_deg_rad_conversions", since="1.7.0")]
452 pub fn to_radians(self) -> f32 { Float::to_radians(self) }
454 /// Returns the maximum of the two numbers.
460 /// assert_eq!(x.max(y), y);
463 /// If one of the arguments is NaN, then the other argument is returned.
464 #[stable(feature = "rust1", since = "1.0.0")]
466 pub fn max(self, other: f32) -> f32 {
467 Float::max(self, other)
470 /// Returns the minimum of the two numbers.
476 /// assert_eq!(x.min(y), x);
479 /// If one of the arguments is NaN, then the other argument is returned.
480 #[stable(feature = "rust1", since = "1.0.0")]
482 pub fn min(self, other: f32) -> f32 {
483 Float::min(self, other)
486 /// Raw transmutation to `u32`.
488 /// This is currently identical to `transmute::<f32, u32>(self)` on all platforms.
490 /// See `from_bits` for some discussion of the portability of this operation
491 /// (there are almost no issues).
493 /// Note that this function is distinct from `as` casting, which attempts to
494 /// preserve the *numeric* value, and not the bitwise value.
499 /// assert_ne!((1f32).to_bits(), 1f32 as u32); // to_bits() is not casting!
500 /// assert_eq!((12.5f32).to_bits(), 0x41480000);
503 #[stable(feature = "float_bits_conv", since = "1.20.0")]
505 pub fn to_bits(self) -> u32 {
509 /// Raw transmutation from `u32`.
511 /// This is currently identical to `transmute::<u32, f32>(v)` on all platforms.
512 /// It turns out this is incredibly portable, for two reasons:
514 /// * Floats and Ints have the same endianness on all supported platforms.
515 /// * IEEE-754 very precisely specifies the bit layout of floats.
517 /// However there is one caveat: prior to the 2008 version of IEEE-754, how
518 /// to interpret the NaN signaling bit wasn't actually specified. Most platforms
519 /// (notably x86 and ARM) picked the interpretation that was ultimately
520 /// standardized in 2008, but some didn't (notably MIPS). As a result, all
521 /// signaling NaNs on MIPS are quiet NaNs on x86, and vice-versa.
523 /// Rather than trying to preserve signaling-ness cross-platform, this
524 /// implementation favours preserving the exact bits. This means that
525 /// any payloads encoded in NaNs will be preserved even if the result of
526 /// this method is sent over the network from an x86 machine to a MIPS one.
528 /// If the results of this method are only manipulated by the same
529 /// architecture that produced them, then there is no portability concern.
531 /// If the input isn't NaN, then there is no portability concern.
533 /// If you don't care about signalingness (very likely), then there is no
534 /// portability concern.
536 /// Note that this function is distinct from `as` casting, which attempts to
537 /// preserve the *numeric* value, and not the bitwise value.
543 /// let v = f32::from_bits(0x41480000);
544 /// let difference = (v - 12.5).abs();
545 /// assert!(difference <= 1e-5);
547 #[stable(feature = "float_bits_conv", since = "1.20.0")]
549 pub fn from_bits(v: u32) -> Self {