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.
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.
11 //! Operations and constants for 64-bits floats (`f64` type)
13 #![doc(primitive = "f64")]
14 // FIXME: MIN_VALUE and MAX_VALUE literals are parsed as -inf and inf #14353
15 #![allow(overflowing_literals)]
22 use num::FpCategory as Fp;
23 use num::from_str_radix;
26 // FIXME(#5527): These constants should be deprecated once associated
27 // constants are implemented in favour of referencing the respective
28 // members of `Bounded` and `Float`.
31 pub const RADIX: uint = 2u;
34 pub const MANTISSA_DIGITS: uint = 53u;
36 pub const DIGITS: uint = 15u;
39 pub const EPSILON: f64 = 2.2204460492503131e-16_f64;
41 /// Smallest finite f64 value
43 pub const MIN_VALUE: f64 = -1.7976931348623157e+308_f64;
44 /// Smallest positive, normalized f64 value
46 pub const MIN_POS_VALUE: f64 = 2.2250738585072014e-308_f64;
47 /// Largest finite f64 value
49 pub const MAX_VALUE: f64 = 1.7976931348623157e+308_f64;
52 pub const MIN_EXP: int = -1021;
54 pub const MAX_EXP: int = 1024;
57 pub const MIN_10_EXP: int = -307;
59 pub const MAX_10_EXP: int = 308;
62 pub const NAN: f64 = 0.0_f64/0.0_f64;
64 pub const INFINITY: f64 = 1.0_f64/0.0_f64;
66 pub const NEG_INFINITY: f64 = -1.0_f64/0.0_f64;
68 /// Various useful constants.
69 #[unstable = "naming scheme needs to be revisited"]
71 // FIXME: replace with mathematical constants from cmath.
73 // FIXME(#5527): These constants should be deprecated once associated
74 // constants are implemented in favour of referencing the respective members
77 /// Archimedes' constant
78 pub const PI: f64 = 3.14159265358979323846264338327950288_f64;
81 pub const PI_2: f64 = 6.28318530717958647692528676655900576_f64;
84 pub const FRAC_PI_2: f64 = 1.57079632679489661923132169163975144_f64;
87 pub const FRAC_PI_3: f64 = 1.04719755119659774615421446109316763_f64;
90 pub const FRAC_PI_4: f64 = 0.785398163397448309615660845819875721_f64;
93 pub const FRAC_PI_6: f64 = 0.52359877559829887307710723054658381_f64;
96 pub const FRAC_PI_8: f64 = 0.39269908169872415480783042290993786_f64;
99 pub const FRAC_1_PI: f64 = 0.318309886183790671537767526745028724_f64;
102 pub const FRAC_2_PI: f64 = 0.636619772367581343075535053490057448_f64;
105 pub const FRAC_2_SQRTPI: f64 = 1.12837916709551257389615890312154517_f64;
108 pub const SQRT2: f64 = 1.41421356237309504880168872420969808_f64;
111 pub const FRAC_1_SQRT2: f64 = 0.707106781186547524400844362104849039_f64;
114 pub const E: f64 = 2.71828182845904523536028747135266250_f64;
117 pub const LOG2_E: f64 = 1.44269504088896340735992468100189214_f64;
120 pub const LOG10_E: f64 = 0.434294481903251827651128918916605082_f64;
123 pub const LN_2: f64 = 0.693147180559945309417232121458176568_f64;
126 pub const LN_10: f64 = 2.30258509299404568401799145468436421_f64;
129 #[unstable = "trait is unstable"]
132 fn nan() -> f64 { NAN }
135 fn infinity() -> f64 { INFINITY }
138 fn neg_infinity() -> f64 { NEG_INFINITY }
141 fn zero() -> f64 { 0.0 }
144 fn neg_zero() -> f64 { -0.0 }
147 fn one() -> f64 { 1.0 }
149 /// Returns `true` if the number is NaN.
151 fn is_nan(self) -> bool { self != self }
153 /// Returns `true` if the number is infinite.
155 fn is_infinite(self) -> bool {
156 self == Float::infinity() || self == Float::neg_infinity()
159 /// Returns `true` if the number is neither infinite or NaN.
161 fn is_finite(self) -> bool {
162 !(self.is_nan() || self.is_infinite())
165 /// Returns `true` if the number is neither zero, infinite, subnormal or NaN.
167 fn is_normal(self) -> bool {
168 self.classify() == Fp::Normal
171 /// Returns the floating point category of the number. If only one property
172 /// is going to be tested, it is generally faster to use the specific
173 /// predicate instead.
174 fn classify(self) -> Fp {
175 const EXP_MASK: u64 = 0x7ff0000000000000;
176 const MAN_MASK: u64 = 0x000fffffffffffff;
178 let bits: u64 = unsafe { mem::transmute(self) };
179 match (bits & MAN_MASK, bits & EXP_MASK) {
181 (_, 0) => Fp::Subnormal,
182 (0, EXP_MASK) => Fp::Infinite,
183 (_, EXP_MASK) => Fp::Nan,
189 fn mantissa_digits(_: Option<f64>) -> uint { MANTISSA_DIGITS }
192 fn digits(_: Option<f64>) -> uint { DIGITS }
195 fn epsilon() -> f64 { EPSILON }
198 fn min_exp(_: Option<f64>) -> int { MIN_EXP }
201 fn max_exp(_: Option<f64>) -> int { MAX_EXP }
204 fn min_10_exp(_: Option<f64>) -> int { MIN_10_EXP }
207 fn max_10_exp(_: Option<f64>) -> int { MAX_10_EXP }
210 fn min_value() -> f64 { MIN_VALUE }
213 fn min_pos_value(_: Option<f64>) -> f64 { MIN_POS_VALUE }
216 fn max_value() -> f64 { MAX_VALUE }
218 /// Returns the mantissa, exponent and sign as integers.
219 fn integer_decode(self) -> (u64, i16, i8) {
220 let bits: u64 = unsafe { mem::transmute(self) };
221 let sign: i8 = if bits >> 63 == 0 { 1 } else { -1 };
222 let mut exponent: i16 = ((bits >> 52) & 0x7ff) as i16;
223 let mantissa = if exponent == 0 {
224 (bits & 0xfffffffffffff) << 1
226 (bits & 0xfffffffffffff) | 0x10000000000000
228 // Exponent bias + mantissa shift
229 exponent -= 1023 + 52;
230 (mantissa, exponent, sign)
233 /// Rounds towards minus infinity.
235 fn floor(self) -> f64 {
236 unsafe { intrinsics::floorf64(self) }
239 /// Rounds towards plus infinity.
241 fn ceil(self) -> f64 {
242 unsafe { intrinsics::ceilf64(self) }
245 /// Rounds to nearest integer. Rounds half-way cases away from zero.
247 fn round(self) -> f64 {
248 unsafe { intrinsics::roundf64(self) }
251 /// Returns the integer part of the number (rounds towards zero).
253 fn trunc(self) -> f64 {
254 unsafe { intrinsics::truncf64(self) }
257 /// The fractional part of the number, satisfying:
260 /// use core::num::Float;
263 /// assert!(x == x.trunc() + x.fract())
266 fn fract(self) -> f64 { self - self.trunc() }
268 /// Computes the absolute value of `self`. Returns `Float::nan()` if the
269 /// number is `Float::nan()`.
271 fn abs(self) -> f64 {
272 unsafe { intrinsics::fabsf64(self) }
275 /// Returns a number that represents the sign of `self`.
277 /// - `1.0` if the number is positive, `+0.0` or `Float::infinity()`
278 /// - `-1.0` if the number is negative, `-0.0` or `Float::neg_infinity()`
279 /// - `Float::nan()` if the number is `Float::nan()`
281 fn signum(self) -> f64 {
285 unsafe { intrinsics::copysignf64(1.0, self) }
289 /// Returns `true` if `self` is positive, including `+0.0` and
290 /// `Float::infinity()`.
292 fn is_positive(self) -> bool {
293 self > 0.0 || (1.0 / self) == Float::infinity()
296 /// Returns `true` if `self` is negative, including `-0.0` and
297 /// `Float::neg_infinity()`.
299 fn is_negative(self) -> bool {
300 self < 0.0 || (1.0 / self) == Float::neg_infinity()
303 /// Fused multiply-add. Computes `(self * a) + b` with only one rounding
304 /// error. This produces a more accurate result with better performance than
305 /// a separate multiplication operation followed by an add.
307 fn mul_add(self, a: f64, b: f64) -> f64 {
308 unsafe { intrinsics::fmaf64(self, a, b) }
311 /// Returns the reciprocal (multiplicative inverse) of the number.
313 fn recip(self) -> f64 { 1.0 / self }
316 fn powf(self, n: f64) -> f64 {
317 unsafe { intrinsics::powf64(self, n) }
321 fn powi(self, n: i32) -> f64 {
322 unsafe { intrinsics::powif64(self, n) }
327 fn sqrt2() -> f64 { consts::SQRT2 }
331 fn frac_1_sqrt2() -> f64 { consts::FRAC_1_SQRT2 }
334 fn sqrt(self) -> f64 {
338 unsafe { intrinsics::sqrtf64(self) }
343 fn rsqrt(self) -> f64 { self.sqrt().recip() }
345 /// Archimedes' constant
347 fn pi() -> f64 { consts::PI }
351 fn two_pi() -> f64 { consts::PI_2 }
355 fn frac_pi_2() -> f64 { consts::FRAC_PI_2 }
359 fn frac_pi_3() -> f64 { consts::FRAC_PI_3 }
363 fn frac_pi_4() -> f64 { consts::FRAC_PI_4 }
367 fn frac_pi_6() -> f64 { consts::FRAC_PI_6 }
371 fn frac_pi_8() -> f64 { consts::FRAC_PI_8 }
375 fn frac_1_pi() -> f64 { consts::FRAC_1_PI }
379 fn frac_2_pi() -> f64 { consts::FRAC_2_PI }
383 fn frac_2_sqrtpi() -> f64 { consts::FRAC_2_SQRTPI }
387 fn e() -> f64 { consts::E }
391 fn log2_e() -> f64 { consts::LOG2_E }
395 fn log10_e() -> f64 { consts::LOG10_E }
399 fn ln_2() -> f64 { consts::LN_2 }
403 fn ln_10() -> f64 { consts::LN_10 }
405 /// Returns the exponential of the number.
407 fn exp(self) -> f64 {
408 unsafe { intrinsics::expf64(self) }
411 /// Returns 2 raised to the power of the number.
413 fn exp2(self) -> f64 {
414 unsafe { intrinsics::exp2f64(self) }
417 /// Returns the natural logarithm of the number.
420 unsafe { intrinsics::logf64(self) }
423 /// Returns the logarithm of the number with respect to an arbitrary base.
425 fn log(self, base: f64) -> f64 { self.ln() / base.ln() }
427 /// Returns the base 2 logarithm of the number.
429 fn log2(self) -> f64 {
430 unsafe { intrinsics::log2f64(self) }
433 /// Returns the base 10 logarithm of the number.
435 fn log10(self) -> f64 {
436 unsafe { intrinsics::log10f64(self) }
439 /// Converts to degrees, assuming the number is in radians.
441 fn to_degrees(self) -> f64 { self * (180.0f64 / consts::PI) }
443 /// Converts to radians, assuming the number is in degrees.
445 fn to_radians(self) -> f64 {
446 let value: f64 = consts::PI;
447 self * (value / 180.0)
452 #[allow(missing_docs)]
453 #[deprecated="Use `FromStrRadix::from_str_radix(src, 16)`"]
454 pub fn from_str_hex(src: &str) -> Option<f64> {
455 from_str_radix(src, 16)