src/libcore/num/f32.rs

   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 #![cfg_attr(stage0, allow(overflowing_literals))]
  14
  15 #![stable(feature = "rust1", since = "1.0.0")]
  16
  17 use intrinsics;
  18 use mem;
  19 use num::Float;
  20 use num::FpCategory as Fp;
  21
  22 /// The radix or base of the internal representation of `f32`.
  23 #[stable(feature = "rust1", since = "1.0.0")]
  24 pub const RADIX: u32 = 2;
  25
  26 /// Number of significant digits in base 2.
  27 #[stable(feature = "rust1", since = "1.0.0")]
  28 pub const MANTISSA_DIGITS: u32 = 24;
  29 /// Approximate number of significant digits in base 10.
  30 #[stable(feature = "rust1", since = "1.0.0")]
  31 pub const DIGITS: u32 = 6;
  32
  33 /// Difference between `1.0` and the next largest representable number.
  34 #[stable(feature = "rust1", since = "1.0.0")]
  35 pub const EPSILON: f32 = 1.19209290e-07_f32;
  36
  37 /// Smallest finite `f32` value.
  38 #[stable(feature = "rust1", since = "1.0.0")]
  39 pub const MIN: f32 = -3.40282347e+38_f32;
  40 /// Smallest positive normal `f32` value.
  41 #[stable(feature = "rust1", since = "1.0.0")]
  42 pub const MIN_POSITIVE: f32 = 1.17549435e-38_f32;
  43 /// Largest finite `f32` value.
  44 #[stable(feature = "rust1", since = "1.0.0")]
  45 pub const MAX: f32 = 3.40282347e+38_f32;
  46
  47 /// One greater than the minimum possible normal power of 2 exponent.
  48 #[stable(feature = "rust1", since = "1.0.0")]
  49 pub const MIN_EXP: i32 = -125;
  50 /// Maximum possible power of 2 exponent.
  51 #[stable(feature = "rust1", since = "1.0.0")]
  52 pub const MAX_EXP: i32 = 128;
  53
  54 /// Minimum possible normal power of 10 exponent.
  55 #[stable(feature = "rust1", since = "1.0.0")]
  56 pub const MIN_10_EXP: i32 = -37;
  57 /// Maximum possible power of 10 exponent.
  58 #[stable(feature = "rust1", since = "1.0.0")]
  59 pub const MAX_10_EXP: i32 = 38;
  60
  61 /// Not a Number (NaN).
  62 #[stable(feature = "rust1", since = "1.0.0")]
  63 pub const NAN: f32 = 0.0_f32 / 0.0_f32;
  64 /// Infinity (∞).
  65 #[stable(feature = "rust1", since = "1.0.0")]
  66 pub const INFINITY: f32 = 1.0_f32 / 0.0_f32;
  67 /// Negative infinity (-∞).
  68 #[stable(feature = "rust1", since = "1.0.0")]
  69 pub const NEG_INFINITY: f32 = -1.0_f32 / 0.0_f32;
  70
  71 /// Basic mathematical constants.
  72 #[stable(feature = "rust1", since = "1.0.0")]
  73 pub mod consts {
  74     // FIXME: replace with mathematical constants from cmath.
  75
  76     /// Archimedes' constant (π)
  77     #[stable(feature = "rust1", since = "1.0.0")]
  78     pub const PI: f32 = 3.14159265358979323846264338327950288_f32;
  79
  80     /// π/2
  81     #[stable(feature = "rust1", since = "1.0.0")]
  82     pub const FRAC_PI_2: f32 = 1.57079632679489661923132169163975144_f32;
  83
  84     /// π/3
  85     #[stable(feature = "rust1", since = "1.0.0")]
  86     pub const FRAC_PI_3: f32 = 1.04719755119659774615421446109316763_f32;
  87
  88     /// π/4
  89     #[stable(feature = "rust1", since = "1.0.0")]
  90     pub const FRAC_PI_4: f32 = 0.785398163397448309615660845819875721_f32;
  91
  92     /// π/6
  93     #[stable(feature = "rust1", since = "1.0.0")]
  94     pub const FRAC_PI_6: f32 = 0.52359877559829887307710723054658381_f32;
  95
  96     /// π/8
  97     #[stable(feature = "rust1", since = "1.0.0")]
  98     pub const FRAC_PI_8: f32 = 0.39269908169872415480783042290993786_f32;
  99
 100     /// 1/π
 101     #[stable(feature = "rust1", since = "1.0.0")]
 102     pub const FRAC_1_PI: f32 = 0.318309886183790671537767526745028724_f32;
 103
 104     /// 2/π
 105     #[stable(feature = "rust1", since = "1.0.0")]
 106     pub const FRAC_2_PI: f32 = 0.636619772367581343075535053490057448_f32;
 107
 108     /// 2/sqrt(π)
 109     #[stable(feature = "rust1", since = "1.0.0")]
 110     pub const FRAC_2_SQRT_PI: f32 = 1.12837916709551257389615890312154517_f32;
 111
 112     /// sqrt(2)
 113     #[stable(feature = "rust1", since = "1.0.0")]
 114     pub const SQRT_2: f32 = 1.41421356237309504880168872420969808_f32;
 115
 116     /// 1/sqrt(2)
 117     #[stable(feature = "rust1", since = "1.0.0")]
 118     pub const FRAC_1_SQRT_2: f32 = 0.707106781186547524400844362104849039_f32;
 119
 120     /// Euler's number (e)
 121     #[stable(feature = "rust1", since = "1.0.0")]
 122     pub const E: f32 = 2.71828182845904523536028747135266250_f32;
 123
 124     /// log<sub>2</sub>(e)
 125     #[stable(feature = "rust1", since = "1.0.0")]
 126     pub const LOG2_E: f32 = 1.44269504088896340735992468100189214_f32;
 127
 128     /// log<sub>10</sub>(e)
 129     #[stable(feature = "rust1", since = "1.0.0")]
 130     pub const LOG10_E: f32 = 0.434294481903251827651128918916605082_f32;
 131
 132     /// ln(2)
 133     #[stable(feature = "rust1", since = "1.0.0")]
 134     pub const LN_2: f32 = 0.693147180559945309417232121458176568_f32;
 135
 136     /// ln(10)
 137     #[stable(feature = "rust1", since = "1.0.0")]
 138     pub const LN_10: f32 = 2.30258509299404568401799145468436421_f32;
 139 }
 140
 141 #[unstable(feature = "core_float",
 142            reason = "stable interface is via `impl f{32,64}` in later crates",
 143            issue = "32110")]
 144 impl Float for f32 {
 145     /// Returns `true` if the number is NaN.
 146     #[inline]
 147     fn is_nan(self) -> bool {
 148         self != self
 149     }
 150
 151     /// Returns `true` if the number is infinite.
 152     #[inline]
 153     fn is_infinite(self) -> bool {
 154         self == INFINITY || self == NEG_INFINITY
 155     }
 156
 157     /// Returns `true` if the number is neither infinite or NaN.
 158     #[inline]
 159     fn is_finite(self) -> bool {
 160         !(self.is_nan() || self.is_infinite())
 161     }
 162
 163     /// Returns `true` if the number is neither zero, infinite, subnormal or NaN.
 164     #[inline]
 165     fn is_normal(self) -> bool {
 166         self.classify() == Fp::Normal
 167     }
 168
 169     /// Returns the floating point category of the number. If only one property
 170     /// is going to be tested, it is generally faster to use the specific
 171     /// predicate instead.
 172     fn classify(self) -> Fp {
 173         const EXP_MASK: u32 = 0x7f800000;
 174         const MAN_MASK: u32 = 0x007fffff;
 175
 176         let bits: u32 = unsafe { mem::transmute(self) };
 177         match (bits & MAN_MASK, bits & EXP_MASK) {
 178             (0, 0) => Fp::Zero,
 179             (_, 0) => Fp::Subnormal,
 180             (0, EXP_MASK) => Fp::Infinite,
 181             (_, EXP_MASK) => Fp::Nan,
 182             _ => Fp::Normal,
 183         }
 184     }
 185
 186     /// Computes the absolute value of `self`. Returns `Float::nan()` if the
 187     /// number is `Float::nan()`.
 188     #[inline]
 189     fn abs(self) -> f32 {
 190         unsafe { intrinsics::fabsf32(self) }
 191     }
 192
 193     /// Returns a number that represents the sign of `self`.
 194     ///
 195     /// - `1.0` if the number is positive, `+0.0` or `Float::infinity()`
 196     /// - `-1.0` if the number is negative, `-0.0` or `Float::neg_infinity()`
 197     /// - `Float::nan()` if the number is `Float::nan()`
 198     #[inline]
 199     fn signum(self) -> f32 {
 200         if self.is_nan() {
 201             NAN
 202         } else {
 203             unsafe { intrinsics::copysignf32(1.0, self) }
 204         }
 205     }
 206
 207     /// Returns `true` if and only if `self` has a positive sign, including `+0.0`, `NaN`s with
 208     /// positive sign bit and positive infinity.
 209     #[inline]
 210     fn is_sign_positive(self) -> bool {
 211         !self.is_sign_negative()
 212     }
 213
 214     /// Returns `true` if and only if `self` has a negative sign, including `-0.0`, `NaN`s with
 215     /// negative sign bit and negative infinity.
 216     #[inline]
 217     fn is_sign_negative(self) -> bool {
 218         // IEEE754 says: isSignMinus(x) is true if and only if x has negative sign. isSignMinus
 219         // applies to zeros and NaNs as well.
 220         #[repr(C)]
 221         union F32Bytes {
 222             f: f32,
 223             b: u32
 224         }
 225         unsafe { F32Bytes { f: self }.b & 0x8000_0000 != 0 }
 226     }
 227
 228     /// Returns the reciprocal (multiplicative inverse) of the number.
 229     #[inline]
 230     fn recip(self) -> f32 {
 231         1.0 / self
 232     }
 233
 234     #[inline]
 235     fn powi(self, n: i32) -> f32 {
 236         unsafe { intrinsics::powif32(self, n) }
 237     }
 238
 239     /// Converts to degrees, assuming the number is in radians.
 240     #[inline]
 241     fn to_degrees(self) -> f32 {
 242         self * (180.0f32 / consts::PI)
 243     }
 244
 245     /// Converts to radians, assuming the number is in degrees.
 246     #[inline]
 247     fn to_radians(self) -> f32 {
 248         let value: f32 = consts::PI;
 249         self * (value / 180.0f32)
 250     }
 251
 252     /// Returns the maximum of the two numbers.
 253     #[inline]
 254     fn max(self, other: f32) -> f32 {
 255         // IEEE754 says: maxNum(x, y) is the canonicalized number y if x < y, x if y < x, the
 256         // canonicalized number if one operand is a number and the other a quiet NaN. Otherwise it
 257         // is either x or y, canonicalized (this means results might differ among implementations).
 258         // When either x or y is a signalingNaN, then the result is according to 6.2.
 259         //
 260         // Since we do not support sNaN in Rust yet, we do not need to handle them.
 261         // FIXME(nagisa): due to https://bugs.llvm.org/show_bug.cgi?id=33303 we canonicalize by
 262         // multiplying by 1.0. Should switch to the `canonicalize` when it works.
 263         (if self < other || self.is_nan() { other } else { self }) * 1.0
 264     }
 265
 266     /// Returns the minimum of the two numbers.
 267     #[inline]
 268     fn min(self, other: f32) -> f32 {
 269         // IEEE754 says: minNum(x, y) is the canonicalized number x if x < y, y if y < x, the
 270         // canonicalized number if one operand is a number and the other a quiet NaN. Otherwise it
 271         // is either x or y, canonicalized (this means results might differ among implementations).
 272         // When either x or y is a signalingNaN, then the result is according to 6.2.
 273         //
 274         // Since we do not support sNaN in Rust yet, we do not need to handle them.
 275         // FIXME(nagisa): due to https://bugs.llvm.org/show_bug.cgi?id=33303 we canonicalize by
 276         // multiplying by 1.0. Should switch to the `canonicalize` when it works.
 277         (if self < other || other.is_nan() { self } else { other }) * 1.0
 278     }
 279 }