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)
16 use num::{FPNormal, FPCategory, FPZero, FPSubnormal, FPInfinite, FPNaN};
17 use num::{Zero, One, Bounded, Signed, Num, Primitive, Float};
20 #[cfg(not(test))] use cmp::{Eq, Ord};
21 #[cfg(not(test))] use ops::{Add, Sub, Mul, Div, Rem, Neg};
23 // FIXME(#5527): These constants should be deprecated once associated
24 // constants are implemented in favour of referencing the respective
25 // members of `Bounded` and `Float`.
27 pub static RADIX: uint = 2u;
29 pub static MANTISSA_DIGITS: uint = 53u;
30 pub static DIGITS: uint = 15u;
32 pub static EPSILON: f64 = 2.2204460492503131e-16_f64;
34 /// Smallest finite f64 value
35 pub static MIN_VALUE: f64 = -1.7976931348623157e+308_f64;
36 /// Smallest positive, normalized f64 value
37 pub static MIN_POS_VALUE: f64 = 2.2250738585072014e-308_f64;
38 /// Largest finite f64 value
39 pub static MAX_VALUE: f64 = 1.7976931348623157e+308_f64;
41 pub static MIN_EXP: int = -1021;
42 pub static MAX_EXP: int = 1024;
44 pub static MIN_10_EXP: int = -307;
45 pub static MAX_10_EXP: int = 308;
47 pub static NAN: f64 = 0.0_f64/0.0_f64;
49 pub static INFINITY: f64 = 1.0_f64/0.0_f64;
51 pub static NEG_INFINITY: f64 = -1.0_f64/0.0_f64;
53 /// Various useful constants.
55 // FIXME: replace with mathematical constants from cmath.
57 // FIXME(#5527): These constants should be deprecated once associated
58 // constants are implemented in favour of referencing the respective members
61 /// Archimedes' constant
62 pub static PI: f64 = 3.14159265358979323846264338327950288_f64;
65 pub static PI_2: f64 = 6.28318530717958647692528676655900576_f64;
68 pub static FRAC_PI_2: f64 = 1.57079632679489661923132169163975144_f64;
71 pub static FRAC_PI_3: f64 = 1.04719755119659774615421446109316763_f64;
74 pub static FRAC_PI_4: f64 = 0.785398163397448309615660845819875721_f64;
77 pub static FRAC_PI_6: f64 = 0.52359877559829887307710723054658381_f64;
80 pub static FRAC_PI_8: f64 = 0.39269908169872415480783042290993786_f64;
83 pub static FRAC_1_PI: f64 = 0.318309886183790671537767526745028724_f64;
86 pub static FRAC_2_PI: f64 = 0.636619772367581343075535053490057448_f64;
89 pub static FRAC_2_SQRTPI: f64 = 1.12837916709551257389615890312154517_f64;
92 pub static SQRT2: f64 = 1.41421356237309504880168872420969808_f64;
95 pub static FRAC_1_SQRT2: f64 = 0.707106781186547524400844362104849039_f64;
98 pub static E: f64 = 2.71828182845904523536028747135266250_f64;
101 pub static LOG2_E: f64 = 1.44269504088896340735992468100189214_f64;
104 pub static LOG10_E: f64 = 0.434294481903251827651128918916605082_f64;
107 pub static LN_2: f64 = 0.693147180559945309417232121458176568_f64;
110 pub static LN_10: f64 = 2.30258509299404568401799145468436421_f64;
116 fn lt(&self, other: &f64) -> bool { (*self) < (*other) }
118 fn le(&self, other: &f64) -> bool { (*self) <= (*other) }
120 fn ge(&self, other: &f64) -> bool { (*self) >= (*other) }
122 fn gt(&self, other: &f64) -> bool { (*self) > (*other) }
127 fn eq(&self, other: &f64) -> bool { (*self) == (*other) }
130 impl Default for f64 {
132 fn default() -> f64 { 0.0 }
135 impl Primitive for f64 {}
141 fn zero() -> f64 { 0.0 }
143 /// Returns true if the number is equal to either `0.0` or `-0.0`
145 fn is_zero(&self) -> bool { *self == 0.0 || *self == -0.0 }
150 fn one() -> f64 { 1.0 }
154 impl Add<f64,f64> for f64 {
156 fn add(&self, other: &f64) -> f64 { *self + *other }
159 impl Sub<f64,f64> for f64 {
161 fn sub(&self, other: &f64) -> f64 { *self - *other }
164 impl Mul<f64,f64> for f64 {
166 fn mul(&self, other: &f64) -> f64 { *self * *other }
169 impl Div<f64,f64> for f64 {
171 fn div(&self, other: &f64) -> f64 { *self / *other }
174 impl Rem<f64,f64> for f64 {
176 fn rem(&self, other: &f64) -> f64 {
177 extern { fn fmod(a: f64, b: f64) -> f64; }
178 unsafe { fmod(*self, *other) }
182 impl Neg<f64> for f64 {
184 fn neg(&self) -> f64 { -*self }
187 impl Signed for f64 {
188 /// Computes the absolute value. Returns `NAN` if the number is `NAN`.
190 fn abs(&self) -> f64 {
191 unsafe { intrinsics::fabsf64(*self) }
194 /// The positive difference of two numbers. Returns `0.0` if the number is less than or
195 /// equal to `other`, otherwise the difference between`self` and `other` is returned.
197 fn abs_sub(&self, other: &f64) -> f64 {
198 extern { fn fdim(a: f64, b: f64) -> f64; }
199 unsafe { fdim(*self, *other) }
204 /// - `1.0` if the number is positive, `+0.0` or `INFINITY`
205 /// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
206 /// - `NAN` if the number is NaN
208 fn signum(&self) -> f64 {
209 if self != self { NAN } else {
210 unsafe { intrinsics::copysignf64(1.0, *self) }
214 /// Returns `true` if the number is positive, including `+0.0` and `INFINITY`
216 fn is_positive(&self) -> bool { *self > 0.0 || (1.0 / *self) == INFINITY }
218 /// Returns `true` if the number is negative, including `-0.0` and `NEG_INFINITY`
220 fn is_negative(&self) -> bool { *self < 0.0 || (1.0 / *self) == NEG_INFINITY }
223 impl Bounded for f64 {
224 // NOTE: this is the smallest non-infinite f32 value, *not* MIN_VALUE
226 fn min_value() -> f64 { -MAX_VALUE }
229 fn max_value() -> f64 { MAX_VALUE }
234 fn nan() -> f64 { NAN }
237 fn infinity() -> f64 { INFINITY }
240 fn neg_infinity() -> f64 { NEG_INFINITY }
243 fn neg_zero() -> f64 { -0.0 }
245 /// Returns `true` if the number is NaN
247 fn is_nan(self) -> bool { self != self }
249 /// Returns `true` if the number is infinite
251 fn is_infinite(self) -> bool {
252 self == Float::infinity() || self == Float::neg_infinity()
255 /// Returns `true` if the number is neither infinite or NaN
257 fn is_finite(self) -> bool {
258 !(self.is_nan() || self.is_infinite())
261 /// Returns `true` if the number is neither zero, infinite, subnormal or NaN
263 fn is_normal(self) -> bool {
264 self.classify() == FPNormal
267 /// Returns the floating point category of the number. If only one property
268 /// is going to be tested, it is generally faster to use the specific
269 /// predicate instead.
270 fn classify(self) -> FPCategory {
271 static EXP_MASK: u64 = 0x7ff0000000000000;
272 static MAN_MASK: u64 = 0x000fffffffffffff;
274 let bits: u64 = unsafe { mem::transmute(self) };
275 match (bits & MAN_MASK, bits & EXP_MASK) {
277 (_, 0) => FPSubnormal,
278 (0, EXP_MASK) => FPInfinite,
279 (_, EXP_MASK) => FPNaN,
285 fn mantissa_digits(_: Option<f64>) -> uint { MANTISSA_DIGITS }
288 fn digits(_: Option<f64>) -> uint { DIGITS }
291 fn epsilon() -> f64 { EPSILON }
294 fn min_exp(_: Option<f64>) -> int { MIN_EXP }
297 fn max_exp(_: Option<f64>) -> int { MAX_EXP }
300 fn min_10_exp(_: Option<f64>) -> int { MIN_10_EXP }
303 fn max_10_exp(_: Option<f64>) -> int { MAX_10_EXP }
306 fn min_pos_value(_: Option<f64>) -> f64 { MIN_POS_VALUE }
308 /// Returns the mantissa, exponent and sign as integers.
309 fn integer_decode(self) -> (u64, i16, i8) {
310 let bits: u64 = unsafe { mem::transmute(self) };
311 let sign: i8 = if bits >> 63 == 0 { 1 } else { -1 };
312 let mut exponent: i16 = ((bits >> 52) & 0x7ff) as i16;
313 let mantissa = if exponent == 0 {
314 (bits & 0xfffffffffffff) << 1
316 (bits & 0xfffffffffffff) | 0x10000000000000
318 // Exponent bias + mantissa shift
319 exponent -= 1023 + 52;
320 (mantissa, exponent, sign)
323 /// Round half-way cases toward `NEG_INFINITY`
325 fn floor(self) -> f64 {
326 unsafe { intrinsics::floorf64(self) }
329 /// Round half-way cases toward `INFINITY`
331 fn ceil(self) -> f64 {
332 unsafe { intrinsics::ceilf64(self) }
335 /// Round half-way cases away from `0.0`
337 fn round(self) -> f64 {
338 unsafe { intrinsics::roundf64(self) }
341 /// The integer part of the number (rounds towards `0.0`)
343 fn trunc(self) -> f64 {
344 unsafe { intrinsics::truncf64(self) }
347 /// The fractional part of the number, satisfying:
351 /// assert!(x == x.trunc() + x.fract())
354 fn fract(self) -> f64 { self - self.trunc() }
356 /// Fused multiply-add. Computes `(self * a) + b` with only one rounding
357 /// error. This produces a more accurate result with better performance than
358 /// a separate multiplication operation followed by an add.
360 fn mul_add(self, a: f64, b: f64) -> f64 {
361 unsafe { intrinsics::fmaf64(self, a, b) }
364 /// The reciprocal (multiplicative inverse) of the number
366 fn recip(self) -> f64 { 1.0 / self }
369 fn powf(self, n: f64) -> f64 {
370 unsafe { intrinsics::powf64(self, n) }
374 fn powi(self, n: i32) -> f64 {
375 unsafe { intrinsics::powif64(self, n) }
380 fn sqrt2() -> f64 { consts::SQRT2 }
384 fn frac_1_sqrt2() -> f64 { consts::FRAC_1_SQRT2 }
387 fn sqrt(self) -> f64 {
388 unsafe { intrinsics::sqrtf64(self) }
392 fn rsqrt(self) -> f64 { self.sqrt().recip() }
394 /// Archimedes' constant
396 fn pi() -> f64 { consts::PI }
400 fn two_pi() -> f64 { consts::PI_2 }
404 fn frac_pi_2() -> f64 { consts::FRAC_PI_2 }
408 fn frac_pi_3() -> f64 { consts::FRAC_PI_3 }
412 fn frac_pi_4() -> f64 { consts::FRAC_PI_4 }
416 fn frac_pi_6() -> f64 { consts::FRAC_PI_6 }
420 fn frac_pi_8() -> f64 { consts::FRAC_PI_8 }
424 fn frac_1_pi() -> f64 { consts::FRAC_1_PI }
428 fn frac_2_pi() -> f64 { consts::FRAC_2_PI }
432 fn frac_2_sqrtpi() -> f64 { consts::FRAC_2_SQRTPI }
436 fn e() -> f64 { consts::E }
440 fn log2_e() -> f64 { consts::LOG2_E }
444 fn log10_e() -> f64 { consts::LOG10_E }
448 fn ln_2() -> f64 { consts::LN_2 }
452 fn ln_10() -> f64 { consts::LN_10 }
454 /// Returns the exponential of the number
456 fn exp(self) -> f64 {
457 unsafe { intrinsics::expf64(self) }
460 /// Returns 2 raised to the power of the number
462 fn exp2(self) -> f64 {
463 unsafe { intrinsics::exp2f64(self) }
466 /// Returns the natural logarithm of the number
469 unsafe { intrinsics::logf64(self) }
472 /// Returns the logarithm of the number with respect to an arbitrary base
474 fn log(self, base: f64) -> f64 { self.ln() / base.ln() }
476 /// Returns the base 2 logarithm of the number
478 fn log2(self) -> f64 {
479 unsafe { intrinsics::log2f64(self) }
482 /// Returns the base 10 logarithm of the number
484 fn log10(self) -> f64 {
485 unsafe { intrinsics::log10f64(self) }
489 /// Converts to degrees, assuming the number is in radians
491 fn to_degrees(self) -> f64 { self * (180.0f64 / Float::pi()) }
493 /// Converts to radians, assuming the number is in degrees
495 fn to_radians(self) -> f64 {
496 let value: f64 = Float::pi();
497 self * (value / 180.0)