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