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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.
4 //
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.
10
11 //! Operations and constants for 32-bits floats (`f32` type)
12
13 // FIXME: MIN_VALUE and MAX_VALUE literals are parsed as -inf and inf #14353
14 #![allow(overflowing_literals)]
15
16 #![stable(feature = "rust1", since = "1.0.0")]
17
18 use prelude::v1::*;
19
20 use intrinsics;
21 use mem;
22 use num::{Float, ParseFloatError};
23 use num::FpCategory as Fp;
24
25 #[stable(feature = "rust1", since = "1.0.0")]
26 #[allow(missing_docs)]
27 pub const RADIX: u32 = 2;
28
29 #[stable(feature = "rust1", since = "1.0.0")]
30 #[allow(missing_docs)]
31 pub const MANTISSA_DIGITS: u32 = 24;
32 #[stable(feature = "rust1", since = "1.0.0")]
33 #[allow(missing_docs)]
34 pub const DIGITS: u32 = 6;
35
36 #[stable(feature = "rust1", since = "1.0.0")]
37 #[allow(missing_docs)]
38 pub const EPSILON: f32 = 1.19209290e-07_f32;
39
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, normalized 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;
49
50 #[stable(feature = "rust1", since = "1.0.0")]
51 #[allow(missing_docs)]
52 pub const MIN_EXP: i32 = -125;
53 #[stable(feature = "rust1", since = "1.0.0")]
54 #[allow(missing_docs)]
55 pub const MAX_EXP: i32 = 128;
56
57 #[stable(feature = "rust1", since = "1.0.0")]
58 #[allow(missing_docs)]
59 pub const MIN_10_EXP: i32 = -37;
60 #[stable(feature = "rust1", since = "1.0.0")]
61 #[allow(missing_docs)]
62 pub const MAX_10_EXP: i32 = 38;
63
64 #[stable(feature = "rust1", since = "1.0.0")]
65 #[allow(missing_docs)]
66 pub const NAN: f32 = 0.0_f32/0.0_f32;
67 #[stable(feature = "rust1", since = "1.0.0")]
68 #[allow(missing_docs)]
69 pub const INFINITY: f32 = 1.0_f32/0.0_f32;
70 #[stable(feature = "rust1", since = "1.0.0")]
71 #[allow(missing_docs)]
72 pub const NEG_INFINITY: f32 = -1.0_f32/0.0_f32;
73
74 /// Basic mathematical constants.
75 #[stable(feature = "rust1", since = "1.0.0")]
76 pub mod consts {
77 // FIXME: replace with mathematical constants from cmath.
78
79 /// Archimedes' constant
80 #[stable(feature = "rust1", since = "1.0.0")]
81 pub const PI: f32 = 3.14159265358979323846264338327950288_f32;
82
83 /// pi/2.0
84 #[stable(feature = "rust1", since = "1.0.0")]
85 pub const FRAC_PI_2: f32 = 1.57079632679489661923132169163975144_f32;
86
87 /// pi/3.0
88 #[stable(feature = "rust1", since = "1.0.0")]
89 pub const FRAC_PI_3: f32 = 1.04719755119659774615421446109316763_f32;
90
91 /// pi/4.0
92 #[stable(feature = "rust1", since = "1.0.0")]
93 pub const FRAC_PI_4: f32 = 0.785398163397448309615660845819875721_f32;
94
95 /// pi/6.0
96 #[stable(feature = "rust1", since = "1.0.0")]
97 pub const FRAC_PI_6: f32 = 0.52359877559829887307710723054658381_f32;
98
99 /// pi/8.0
100 #[stable(feature = "rust1", since = "1.0.0")]
101 pub const FRAC_PI_8: f32 = 0.39269908169872415480783042290993786_f32;
102
103 /// 1.0/pi
104 #[stable(feature = "rust1", since = "1.0.0")]
105 pub const FRAC_1_PI: f32 = 0.318309886183790671537767526745028724_f32;
106
107 /// 2.0/pi
108 #[stable(feature = "rust1", since = "1.0.0")]
109 pub const FRAC_2_PI: f32 = 0.636619772367581343075535053490057448_f32;
110
111 /// 2.0/sqrt(pi)
112 #[stable(feature = "rust1", since = "1.0.0")]
113 pub const FRAC_2_SQRT_PI: f32 = 1.12837916709551257389615890312154517_f32;
114
115 /// sqrt(2.0)
116 #[stable(feature = "rust1", since = "1.0.0")]
117 pub const SQRT_2: f32 = 1.41421356237309504880168872420969808_f32;
118
119 /// 1.0/sqrt(2.0)
120 #[stable(feature = "rust1", since = "1.0.0")]
121 pub const FRAC_1_SQRT_2: f32 = 0.707106781186547524400844362104849039_f32;
122
123 /// Euler's number
124 #[stable(feature = "rust1", since = "1.0.0")]
125 pub const E: f32 = 2.71828182845904523536028747135266250_f32;
126
127 /// log2(e)
128 #[stable(feature = "rust1", since = "1.0.0")]
129 pub const LOG2_E: f32 = 1.44269504088896340735992468100189214_f32;
130
131 /// log10(e)
132 #[stable(feature = "rust1", since = "1.0.0")]
133 pub const LOG10_E: f32 = 0.434294481903251827651128918916605082_f32;
134
135 /// ln(2.0)
136 #[stable(feature = "rust1", since = "1.0.0")]
137 pub const LN_2: f32 = 0.693147180559945309417232121458176568_f32;
138
139 /// ln(10.0)
140 #[stable(feature = "rust1", since = "1.0.0")]
141 pub const LN_10: f32 = 2.30258509299404568401799145468436421_f32;
142 }
143
144 #[unstable(feature = "core_float",
145 reason = "stable interface is via `impl f{32,64}` in later crates",
146 issue = "27702")]
147 impl Float for f32 {
148 #[inline]
149 fn nan() -> f32 { NAN }
150
151 #[inline]
152 fn infinity() -> f32 { INFINITY }
153
154 #[inline]
155 fn neg_infinity() -> f32 { NEG_INFINITY }
156
157 #[inline]
158 fn zero() -> f32 { 0.0 }
159
160 #[inline]
161 fn neg_zero() -> f32 { -0.0 }
162
163 #[inline]
164 fn one() -> f32 { 1.0 }
165
166 from_str_radix_float_impl! { f32 }
167
168 /// Returns `true` if the number is NaN.
169 #[inline]
170 fn is_nan(self) -> bool { self != self }
171
172 /// Returns `true` if the number is infinite.
173 #[inline]
174 fn is_infinite(self) -> bool {
175 self == Float::infinity() || self == Float::neg_infinity()
176 }
177
178 /// Returns `true` if the number is neither infinite or NaN.
179 #[inline]
180 fn is_finite(self) -> bool {
181 !(self.is_nan() || self.is_infinite())
182 }
183
184 /// Returns `true` if the number is neither zero, infinite, subnormal or NaN.
185 #[inline]
186 fn is_normal(self) -> bool {
187 self.classify() == Fp::Normal
188 }
189
190 /// Returns the floating point category of the number. If only one property
191 /// is going to be tested, it is generally faster to use the specific
192 /// predicate instead.
193 fn classify(self) -> Fp {
194 const EXP_MASK: u32 = 0x7f800000;
195 const MAN_MASK: u32 = 0x007fffff;
196
197 let bits: u32 = unsafe { mem::transmute(self) };
198 match (bits & MAN_MASK, bits & EXP_MASK) {
199 (0, 0) => Fp::Zero,
200 (_, 0) => Fp::Subnormal,
201 (0, EXP_MASK) => Fp::Infinite,
202 (_, EXP_MASK) => Fp::Nan,
203 _ => Fp::Normal,
204 }
205 }
206
207 /// Returns the mantissa, exponent and sign as integers.
208 fn integer_decode(self) -> (u64, i16, i8) {
209 let bits: u32 = unsafe { mem::transmute(self) };
210 let sign: i8 = if bits >> 31 == 0 { 1 } else { -1 };
211 let mut exponent: i16 = ((bits >> 23) & 0xff) as i16;
212 let mantissa = if exponent == 0 {
213 (bits & 0x7fffff) << 1
214 } else {
215 (bits & 0x7fffff) | 0x800000
216 };
217 // Exponent bias + mantissa shift
218 exponent -= 127 + 23;
219 (mantissa as u64, exponent, sign)
220 }
221
222 /// Computes the absolute value of `self`. Returns `Float::nan()` if the
223 /// number is `Float::nan()`.
224 #[inline]
225 fn abs(self) -> f32 {
226 unsafe { intrinsics::fabsf32(self) }
227 }
228
229 /// Returns a number that represents the sign of `self`.
230 ///
231 /// - `1.0` if the number is positive, `+0.0` or `Float::infinity()`
232 /// - `-1.0` if the number is negative, `-0.0` or `Float::neg_infinity()`
233 /// - `Float::nan()` if the number is `Float::nan()`
234 #[inline]
235 fn signum(self) -> f32 {
236 if self.is_nan() {
237 Float::nan()
238 } else {
239 unsafe { intrinsics::copysignf32(1.0, self) }
240 }
241 }
242
243 /// Returns `true` if `self` is positive, including `+0.0` and
244 /// `Float::infinity()`.
245 #[inline]
246 fn is_sign_positive(self) -> bool {
247 self > 0.0 || (1.0 / self) == Float::infinity()
248 }
249
250 /// Returns `true` if `self` is negative, including `-0.0` and
251 /// `Float::neg_infinity()`.
252 #[inline]
253 fn is_sign_negative(self) -> bool {
254 self < 0.0 || (1.0 / self) == Float::neg_infinity()
255 }
256
257 /// Returns the reciprocal (multiplicative inverse) of the number.
258 #[inline]
259 fn recip(self) -> f32 { 1.0 / self }
260
261 #[inline]
262 fn powi(self, n: i32) -> f32 {
263 unsafe { intrinsics::powif32(self, n) }
264 }
265
266 /// Converts to degrees, assuming the number is in radians.
267 #[inline]
268 fn to_degrees(self) -> f32 { self * (180.0f32 / consts::PI) }
269
270 /// Converts to radians, assuming the number is in degrees.
271 #[inline]
272 fn to_radians(self) -> f32 {
273 let value: f32 = consts::PI;
274 self * (value / 180.0f32)
275 }
276 }