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 #![doc(primitive = "f32")]
  14 // FIXME: MIN_VALUE and MAX_VALUE literals are parsed as -inf and inf #14353
  15 #![allow(overflowing_literals)]
  16
  17 #![stable(feature = "rust1", since = "1.0.0")]
  18
  19 use prelude::*;
  20
  21 use intrinsics;
  22 use mem;
  23 use num::{Float, ParseFloatError};
  24 use num::FpCategory as Fp;
  25
  26 #[stable(feature = "rust1", since = "1.0.0")]
  27 pub const RADIX: u32 = 2;
  28
  29 #[stable(feature = "rust1", since = "1.0.0")]
  30 pub const MANTISSA_DIGITS: u32 = 24;
  31 #[stable(feature = "rust1", since = "1.0.0")]
  32 pub const DIGITS: u32 = 6;
  33
  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, normalized 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 #[stable(feature = "rust1", since = "1.0.0")]
  48 pub const MIN_EXP: i32 = -125;
  49 #[stable(feature = "rust1", since = "1.0.0")]
  50 pub const MAX_EXP: i32 = 128;
  51
  52 #[stable(feature = "rust1", since = "1.0.0")]
  53 pub const MIN_10_EXP: i32 = -37;
  54 #[stable(feature = "rust1", since = "1.0.0")]
  55 pub const MAX_10_EXP: i32 = 38;
  56
  57 #[stable(feature = "rust1", since = "1.0.0")]
  58 pub const NAN: f32 = 0.0_f32/0.0_f32;
  59 #[stable(feature = "rust1", since = "1.0.0")]
  60 pub const INFINITY: f32 = 1.0_f32/0.0_f32;
  61 #[stable(feature = "rust1", since = "1.0.0")]
  62 pub const NEG_INFINITY: f32 = -1.0_f32/0.0_f32;
  63
  64 /// Basic mathematial constants.
  65 #[stable(feature = "rust1", since = "1.0.0")]
  66 pub mod consts {
  67     // FIXME: replace with mathematical constants from cmath.
  68
  69     /// Archimedes' constant
  70     #[stable(feature = "rust1", since = "1.0.0")]
  71     pub const PI: f32 = 3.14159265358979323846264338327950288_f32;
  72
  73     /// pi * 2.0
  74     #[unstable(feature = "float_consts",
  75                reason = "unclear naming convention/usefulness")]
  76     #[deprecated(since = "1.2.0", reason = "unclear on usefulness")]
  77     pub const PI_2: f32 = 6.28318530717958647692528676655900576_f32;
  78
  79     /// pi/2.0
  80     #[stable(feature = "rust1", since = "1.0.0")]
  81     pub const FRAC_PI_2: f32 = 1.57079632679489661923132169163975144_f32;
  82
  83     /// pi/3.0
  84     #[stable(feature = "rust1", since = "1.0.0")]
  85     pub const FRAC_PI_3: f32 = 1.04719755119659774615421446109316763_f32;
  86
  87     /// pi/4.0
  88     #[stable(feature = "rust1", since = "1.0.0")]
  89     pub const FRAC_PI_4: f32 = 0.785398163397448309615660845819875721_f32;
  90
  91     /// pi/6.0
  92     #[stable(feature = "rust1", since = "1.0.0")]
  93     pub const FRAC_PI_6: f32 = 0.52359877559829887307710723054658381_f32;
  94
  95     /// pi/8.0
  96     #[stable(feature = "rust1", since = "1.0.0")]
  97     pub const FRAC_PI_8: f32 = 0.39269908169872415480783042290993786_f32;
  98
  99     /// 1.0/pi
 100     #[stable(feature = "rust1", since = "1.0.0")]
 101     pub const FRAC_1_PI: f32 = 0.318309886183790671537767526745028724_f32;
 102
 103     /// 2.0/pi
 104     #[stable(feature = "rust1", since = "1.0.0")]
 105     pub const FRAC_2_PI: f32 = 0.636619772367581343075535053490057448_f32;
 106
 107     /// 2.0/sqrt(pi)
 108     #[stable(feature = "rust1", since = "1.0.0")]
 109     pub const FRAC_2_SQRT_PI: f32 = 1.12837916709551257389615890312154517_f32;
 110
 111     /// sqrt(2.0)
 112     #[stable(feature = "rust1", since = "1.0.0")]
 113     pub const SQRT_2: f32 = 1.41421356237309504880168872420969808_f32;
 114
 115     /// 1.0/sqrt(2.0)
 116     #[stable(feature = "rust1", since = "1.0.0")]
 117     pub const FRAC_1_SQRT_2: f32 = 0.707106781186547524400844362104849039_f32;
 118
 119     /// Euler's number
 120     #[stable(feature = "rust1", since = "1.0.0")]
 121     pub const E: f32 = 2.71828182845904523536028747135266250_f32;
 122
 123     /// log2(e)
 124     #[stable(feature = "rust1", since = "1.0.0")]
 125     pub const LOG2_E: f32 = 1.44269504088896340735992468100189214_f32;
 126
 127     /// log10(e)
 128     #[stable(feature = "rust1", since = "1.0.0")]
 129     pub const LOG10_E: f32 = 0.434294481903251827651128918916605082_f32;
 130
 131     /// ln(2.0)
 132     #[stable(feature = "rust1", since = "1.0.0")]
 133     pub const LN_2: f32 = 0.693147180559945309417232121458176568_f32;
 134
 135     /// ln(10.0)
 136     #[stable(feature = "rust1", since = "1.0.0")]
 137     pub const LN_10: f32 = 2.30258509299404568401799145468436421_f32;
 138 }
 139
 140 impl Float for f32 {
 141     #[inline]
 142     fn nan() -> f32 { NAN }
 143
 144     #[inline]
 145     fn infinity() -> f32 { INFINITY }
 146
 147     #[inline]
 148     fn neg_infinity() -> f32 { NEG_INFINITY }
 149
 150     #[inline]
 151     fn zero() -> f32 { 0.0 }
 152
 153     #[inline]
 154     fn neg_zero() -> f32 { -0.0 }
 155
 156     #[inline]
 157     fn one() -> f32 { 1.0 }
 158
 159     from_str_radix_float_impl! { f32 }
 160
 161     /// Returns `true` if the number is NaN.
 162     #[inline]
 163     fn is_nan(self) -> bool { self != self }
 164
 165     /// Returns `true` if the number is infinite.
 166     #[inline]
 167     fn is_infinite(self) -> bool {
 168         self == Float::infinity() || self == Float::neg_infinity()
 169     }
 170
 171     /// Returns `true` if the number is neither infinite or NaN.
 172     #[inline]
 173     fn is_finite(self) -> bool {
 174         !(self.is_nan() || self.is_infinite())
 175     }
 176
 177     /// Returns `true` if the number is neither zero, infinite, subnormal or NaN.
 178     #[inline]
 179     fn is_normal(self) -> bool {
 180         self.classify() == Fp::Normal
 181     }
 182
 183     /// Returns the floating point category of the number. If only one property
 184     /// is going to be tested, it is generally faster to use the specific
 185     /// predicate instead.
 186     fn classify(self) -> Fp {
 187         const EXP_MASK: u32 = 0x7f800000;
 188         const MAN_MASK: u32 = 0x007fffff;
 189
 190         let bits: u32 = unsafe { mem::transmute(self) };
 191         match (bits & MAN_MASK, bits & EXP_MASK) {
 192             (0, 0)        => Fp::Zero,
 193             (_, 0)        => Fp::Subnormal,
 194             (0, EXP_MASK) => Fp::Infinite,
 195             (_, EXP_MASK) => Fp::Nan,
 196             _             => Fp::Normal,
 197         }
 198     }
 199
 200     /// Returns the mantissa, exponent and sign as integers.
 201     fn integer_decode(self) -> (u64, i16, i8) {
 202         let bits: u32 = unsafe { mem::transmute(self) };
 203         let sign: i8 = if bits >> 31 == 0 { 1 } else { -1 };
 204         let mut exponent: i16 = ((bits >> 23) & 0xff) as i16;
 205         let mantissa = if exponent == 0 {
 206             (bits & 0x7fffff) << 1
 207         } else {
 208             (bits & 0x7fffff) | 0x800000
 209         };
 210         // Exponent bias + mantissa shift
 211         exponent -= 127 + 23;
 212         (mantissa as u64, exponent, sign)
 213     }
 214
 215     /// Rounds towards minus infinity.
 216     #[inline]
 217     fn floor(self) -> f32 {
 218         unsafe { intrinsics::floorf32(self) }
 219     }
 220
 221     /// Rounds towards plus infinity.
 222     #[inline]
 223     fn ceil(self) -> f32 {
 224         unsafe { intrinsics::ceilf32(self) }
 225     }
 226
 227     /// Rounds to nearest integer. Rounds half-way cases away from zero.
 228     #[inline]
 229     fn round(self) -> f32 {
 230         unsafe { intrinsics::roundf32(self) }
 231     }
 232
 233     /// Returns the integer part of the number (rounds towards zero).
 234     #[inline]
 235     fn trunc(self) -> f32 {
 236         unsafe { intrinsics::truncf32(self) }
 237     }
 238
 239     /// The fractional part of the number, satisfying:
 240     ///
 241     /// ```
 242     /// let x = 1.65f32;
 243     /// assert!(x == x.trunc() + x.fract())
 244     /// ```
 245     #[inline]
 246     fn fract(self) -> f32 { self - self.trunc() }
 247
 248     /// Computes the absolute value of `self`. Returns `Float::nan()` if the
 249     /// number is `Float::nan()`.
 250     #[inline]
 251     fn abs(self) -> f32 {
 252         unsafe { intrinsics::fabsf32(self) }
 253     }
 254
 255     /// Returns a number that represents the sign of `self`.
 256     ///
 257     /// - `1.0` if the number is positive, `+0.0` or `Float::infinity()`
 258     /// - `-1.0` if the number is negative, `-0.0` or `Float::neg_infinity()`
 259     /// - `Float::nan()` if the number is `Float::nan()`
 260     #[inline]
 261     fn signum(self) -> f32 {
 262         if self.is_nan() {
 263             Float::nan()
 264         } else {
 265             unsafe { intrinsics::copysignf32(1.0, self) }
 266         }
 267     }
 268
 269     /// Returns `true` if `self` is positive, including `+0.0` and
 270     /// `Float::infinity()`.
 271     #[inline]
 272     fn is_positive(self) -> bool {
 273         self > 0.0 || (1.0 / self) == Float::infinity()
 274     }
 275
 276     /// Returns `true` if `self` is negative, including `-0.0` and
 277     /// `Float::neg_infinity()`.
 278     #[inline]
 279     fn is_negative(self) -> bool {
 280         self < 0.0 || (1.0 / self) == Float::neg_infinity()
 281     }
 282
 283     /// Fused multiply-add. Computes `(self * a) + b` with only one rounding
 284     /// error. This produces a more accurate result with better performance than
 285     /// a separate multiplication operation followed by an add.
 286     #[inline]
 287     fn mul_add(self, a: f32, b: f32) -> f32 {
 288         unsafe { intrinsics::fmaf32(self, a, b) }
 289     }
 290
 291     /// Returns the reciprocal (multiplicative inverse) of the number.
 292     #[inline]
 293     fn recip(self) -> f32 { 1.0 / self }
 294
 295     #[inline]
 296     fn powi(self, n: i32) -> f32 {
 297         unsafe { intrinsics::powif32(self, n) }
 298     }
 299
 300     #[inline]
 301     fn powf(self, n: f32) -> f32 {
 302         unsafe { intrinsics::powf32(self, n) }
 303     }
 304
 305     #[inline]
 306     fn sqrt(self) -> f32 {
 307         if self < 0.0 {
 308             NAN
 309         } else {
 310             unsafe { intrinsics::sqrtf32(self) }
 311         }
 312     }
 313
 314     #[inline]
 315     fn rsqrt(self) -> f32 { self.sqrt().recip() }
 316
 317     /// Returns the exponential of the number.
 318     #[inline]
 319     fn exp(self) -> f32 {
 320         unsafe { intrinsics::expf32(self) }
 321     }
 322
 323     /// Returns 2 raised to the power of the number.
 324     #[inline]
 325     fn exp2(self) -> f32 {
 326         unsafe { intrinsics::exp2f32(self) }
 327     }
 328
 329     /// Returns the natural logarithm of the number.
 330     #[inline]
 331     fn ln(self) -> f32 {
 332         unsafe { intrinsics::logf32(self) }
 333     }
 334
 335     /// Returns the logarithm of the number with respect to an arbitrary base.
 336     #[inline]
 337     fn log(self, base: f32) -> f32 { self.ln() / base.ln() }
 338
 339     /// Returns the base 2 logarithm of the number.
 340     #[inline]
 341     fn log2(self) -> f32 {
 342         unsafe { intrinsics::log2f32(self) }
 343     }
 344
 345     /// Returns the base 10 logarithm of the number.
 346     #[inline]
 347     fn log10(self) -> f32 {
 348         unsafe { intrinsics::log10f32(self) }
 349     }
 350
 351     /// Converts to degrees, assuming the number is in radians.
 352     #[inline]
 353     fn to_degrees(self) -> f32 { self * (180.0f32 / consts::PI) }
 354
 355     /// Converts to radians, assuming the number is in degrees.
 356     #[inline]
 357     fn to_radians(self) -> f32 {
 358         let value: f32 = consts::PI;
 359         self * (value / 180.0f32)
 360     }
 361 }