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 // 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 intrinsics;
  19 use mem;
  20 use num::Float;
  21 use num::FpCategory as Fp;
  22
  23 /// The radix or base of the internal representation of `f32`.
  24 #[stable(feature = "rust1", since = "1.0.0")]
  25 pub const RADIX: u32 = 2;
  26
  27 /// Number of significant digits in base 2.
  28 #[stable(feature = "rust1", since = "1.0.0")]
  29 pub const MANTISSA_DIGITS: u32 = 24;
  30 /// Approximate number of significant digits in base 10.
  31 #[stable(feature = "rust1", since = "1.0.0")]
  32 pub const DIGITS: u32 = 6;
  33
  34 /// Difference between `1.0` and the next largest representable number.
  35 #[stable(feature = "rust1", since = "1.0.0")]
  36 pub const EPSILON: f32 = 1.19209290e-07_f32;
  37
  38 /// Smallest finite `f32` value.
  39 #[stable(feature = "rust1", since = "1.0.0")]
  40 pub const MIN: f32 = -3.40282347e+38_f32;
  41 /// Smallest positive normal `f32` value.
  42 #[stable(feature = "rust1", since = "1.0.0")]
  43 pub const MIN_POSITIVE: f32 = 1.17549435e-38_f32;
  44 /// Largest finite `f32` value.
  45 #[stable(feature = "rust1", since = "1.0.0")]
  46 pub const MAX: f32 = 3.40282347e+38_f32;
  47
  48 /// One greater than the minimum possible normal power of 2 exponent.
  49 #[stable(feature = "rust1", since = "1.0.0")]
  50 pub const MIN_EXP: i32 = -125;
  51 /// Maximum possible power of 2 exponent.
  52 #[stable(feature = "rust1", since = "1.0.0")]
  53 pub const MAX_EXP: i32 = 128;
  54
  55 /// Minimum possible normal power of 10 exponent.
  56 #[stable(feature = "rust1", since = "1.0.0")]
  57 pub const MIN_10_EXP: i32 = -37;
  58 /// Maximum possible power of 10 exponent.
  59 #[stable(feature = "rust1", since = "1.0.0")]
  60 pub const MAX_10_EXP: i32 = 38;
  61
  62 /// Not a Number (NaN).
  63 #[stable(feature = "rust1", since = "1.0.0")]
  64 pub const NAN: f32 = 0.0_f32/0.0_f32;
  65 /// Infinity (∞).
  66 #[stable(feature = "rust1", since = "1.0.0")]
  67 pub const INFINITY: f32 = 1.0_f32/0.0_f32;
  68 /// Negative infinity (-∞).
  69 #[stable(feature = "rust1", since = "1.0.0")]
  70 pub const NEG_INFINITY: f32 = -1.0_f32/0.0_f32;
  71
  72 /// Basic mathematical constants.
  73 #[stable(feature = "rust1", since = "1.0.0")]
  74 pub mod consts {
  75     // FIXME: replace with mathematical constants from cmath.
  76
  77     /// Archimedes' constant (π)
  78     #[stable(feature = "rust1", since = "1.0.0")]
  79     pub const PI: f32 = 3.14159265358979323846264338327950288_f32;
  80
  81     /// π/2
  82     #[stable(feature = "rust1", since = "1.0.0")]
  83     pub const FRAC_PI_2: f32 = 1.57079632679489661923132169163975144_f32;
  84
  85     /// π/3
  86     #[stable(feature = "rust1", since = "1.0.0")]
  87     pub const FRAC_PI_3: f32 = 1.04719755119659774615421446109316763_f32;
  88
  89     /// π/4
  90     #[stable(feature = "rust1", since = "1.0.0")]
  91     pub const FRAC_PI_4: f32 = 0.785398163397448309615660845819875721_f32;
  92
  93     /// π/6
  94     #[stable(feature = "rust1", since = "1.0.0")]
  95     pub const FRAC_PI_6: f32 = 0.52359877559829887307710723054658381_f32;
  96
  97     /// π/8
  98     #[stable(feature = "rust1", since = "1.0.0")]
  99     pub const FRAC_PI_8: f32 = 0.39269908169872415480783042290993786_f32;
 100
 101     /// 1/π
 102     #[stable(feature = "rust1", since = "1.0.0")]
 103     pub const FRAC_1_PI: f32 = 0.318309886183790671537767526745028724_f32;
 104
 105     /// 2/π
 106     #[stable(feature = "rust1", since = "1.0.0")]
 107     pub const FRAC_2_PI: f32 = 0.636619772367581343075535053490057448_f32;
 108
 109     /// 2/sqrt(π)
 110     #[stable(feature = "rust1", since = "1.0.0")]
 111     pub const FRAC_2_SQRT_PI: f32 = 1.12837916709551257389615890312154517_f32;
 112
 113     /// sqrt(2)
 114     #[stable(feature = "rust1", since = "1.0.0")]
 115     pub const SQRT_2: f32 = 1.41421356237309504880168872420969808_f32;
 116
 117     /// 1/sqrt(2)
 118     #[stable(feature = "rust1", since = "1.0.0")]
 119     pub const FRAC_1_SQRT_2: f32 = 0.707106781186547524400844362104849039_f32;
 120
 121     /// Euler's number (e)
 122     #[stable(feature = "rust1", since = "1.0.0")]
 123     pub const E: f32 = 2.71828182845904523536028747135266250_f32;
 124
 125     /// log<sub>2</sub>(e)
 126     #[stable(feature = "rust1", since = "1.0.0")]
 127     pub const LOG2_E: f32 = 1.44269504088896340735992468100189214_f32;
 128
 129     /// log<sub>10</sub>(e)
 130     #[stable(feature = "rust1", since = "1.0.0")]
 131     pub const LOG10_E: f32 = 0.434294481903251827651128918916605082_f32;
 132
 133     /// ln(2)
 134     #[stable(feature = "rust1", since = "1.0.0")]
 135     pub const LN_2: f32 = 0.693147180559945309417232121458176568_f32;
 136
 137     /// ln(10)
 138     #[stable(feature = "rust1", since = "1.0.0")]
 139     pub const LN_10: f32 = 2.30258509299404568401799145468436421_f32;
 140 }
 141
 142 #[unstable(feature = "core_float",
 143            reason = "stable interface is via `impl f{32,64}` in later crates",
 144            issue = "32110")]
 145 impl Float for f32 {
 146     #[inline]
 147     fn nan() -> f32 { NAN }
 148
 149     #[inline]
 150     fn infinity() -> f32 { INFINITY }
 151
 152     #[inline]
 153     fn neg_infinity() -> f32 { NEG_INFINITY }
 154
 155     #[inline]
 156     fn zero() -> f32 { 0.0 }
 157
 158     #[inline]
 159     fn neg_zero() -> f32 { -0.0 }
 160
 161     #[inline]
 162     fn one() -> f32 { 1.0 }
 163
 164     /// Returns `true` if the number is NaN.
 165     #[inline]
 166     fn is_nan(self) -> bool { self != self }
 167
 168     /// Returns `true` if the number is infinite.
 169     #[inline]
 170     fn is_infinite(self) -> bool {
 171         self == INFINITY || self == NEG_INFINITY
 172     }
 173
 174     /// Returns `true` if the number is neither infinite or NaN.
 175     #[inline]
 176     fn is_finite(self) -> bool {
 177         !(self.is_nan() || self.is_infinite())
 178     }
 179
 180     /// Returns `true` if the number is neither zero, infinite, subnormal or NaN.
 181     #[inline]
 182     fn is_normal(self) -> bool {
 183         self.classify() == Fp::Normal
 184     }
 185
 186     /// Returns the floating point category of the number. If only one property
 187     /// is going to be tested, it is generally faster to use the specific
 188     /// predicate instead.
 189     fn classify(self) -> Fp {
 190         const EXP_MASK: u32 = 0x7f800000;
 191         const MAN_MASK: u32 = 0x007fffff;
 192
 193         let bits: u32 = unsafe { mem::transmute(self) };
 194         match (bits & MAN_MASK, bits & EXP_MASK) {
 195             (0, 0)        => Fp::Zero,
 196             (_, 0)        => Fp::Subnormal,
 197             (0, EXP_MASK) => Fp::Infinite,
 198             (_, EXP_MASK) => Fp::Nan,
 199             _             => Fp::Normal,
 200         }
 201     }
 202
 203     /// Returns the mantissa, exponent and sign as integers.
 204     fn integer_decode(self) -> (u64, i16, i8) {
 205         let bits: u32 = unsafe { mem::transmute(self) };
 206         let sign: i8 = if bits >> 31 == 0 { 1 } else { -1 };
 207         let mut exponent: i16 = ((bits >> 23) & 0xff) as i16;
 208         let mantissa = if exponent == 0 {
 209             (bits & 0x7fffff) << 1
 210         } else {
 211             (bits & 0x7fffff) | 0x800000
 212         };
 213         // Exponent bias + mantissa shift
 214         exponent -= 127 + 23;
 215         (mantissa as u64, exponent, sign)
 216     }
 217
 218     /// Computes the absolute value of `self`. Returns `Float::nan()` if the
 219     /// number is `Float::nan()`.
 220     #[inline]
 221     fn abs(self) -> f32 {
 222         unsafe { intrinsics::fabsf32(self) }
 223     }
 224
 225     /// Returns a number that represents the sign of `self`.
 226     ///
 227     /// - `1.0` if the number is positive, `+0.0` or `Float::infinity()`
 228     /// - `-1.0` if the number is negative, `-0.0` or `Float::neg_infinity()`
 229     /// - `Float::nan()` if the number is `Float::nan()`
 230     #[inline]
 231     fn signum(self) -> f32 {
 232         if self.is_nan() {
 233             NAN
 234         } else {
 235             unsafe { intrinsics::copysignf32(1.0, self) }
 236         }
 237     }
 238
 239     /// Returns `true` if `self` is positive, including `+0.0` and
 240     /// `Float::infinity()`.
 241     #[inline]
 242     fn is_sign_positive(self) -> bool {
 243         self > 0.0 || (1.0 / self) == INFINITY
 244     }
 245
 246     /// Returns `true` if `self` is negative, including `-0.0` and
 247     /// `Float::neg_infinity()`.
 248     #[inline]
 249     fn is_sign_negative(self) -> bool {
 250         self < 0.0 || (1.0 / self) == NEG_INFINITY
 251     }
 252
 253     /// Returns the reciprocal (multiplicative inverse) of the number.
 254     #[inline]
 255     fn recip(self) -> f32 { 1.0 / self }
 256
 257     #[inline]
 258     fn powi(self, n: i32) -> f32 {
 259         unsafe { intrinsics::powif32(self, n) }
 260     }
 261
 262     /// Converts to degrees, assuming the number is in radians.
 263     #[inline]
 264     fn to_degrees(self) -> f32 { self * (180.0f32 / consts::PI) }
 265
 266     /// Converts to radians, assuming the number is in degrees.
 267     #[inline]
 268     fn to_radians(self) -> f32 {
 269         let value: f32 = consts::PI;
 270         self * (value / 180.0f32)
 271     }
 272 }