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)
15 use num::{FPNormal, FPCategory, FPZero, FPSubnormal, FPInfinite, FPNaN};
19 // FIXME(#5527): These constants should be deprecated once associated
20 // constants are implemented in favour of referencing the respective
21 // members of `Bounded` and `Float`.
23 pub static RADIX: uint = 2u;
25 pub static MANTISSA_DIGITS: uint = 53u;
26 pub static DIGITS: uint = 15u;
28 pub static EPSILON: f64 = 2.2204460492503131e-16_f64;
30 /// Smallest finite f64 value
31 pub static MIN_VALUE: f64 = -1.7976931348623157e+308_f64;
32 /// Smallest positive, normalized f64 value
33 pub static MIN_POS_VALUE: f64 = 2.2250738585072014e-308_f64;
34 /// Largest finite f64 value
35 pub static MAX_VALUE: f64 = 1.7976931348623157e+308_f64;
37 pub static MIN_EXP: int = -1021;
38 pub static MAX_EXP: int = 1024;
40 pub static MIN_10_EXP: int = -307;
41 pub static MAX_10_EXP: int = 308;
43 pub static NAN: f64 = 0.0_f64/0.0_f64;
45 pub static INFINITY: f64 = 1.0_f64/0.0_f64;
47 pub static NEG_INFINITY: f64 = -1.0_f64/0.0_f64;
49 /// Various useful constants.
51 // FIXME: replace with mathematical constants from cmath.
53 // FIXME(#5527): These constants should be deprecated once associated
54 // constants are implemented in favour of referencing the respective members
57 /// Archimedes' constant
58 pub static PI: f64 = 3.14159265358979323846264338327950288_f64;
61 pub static PI_2: f64 = 6.28318530717958647692528676655900576_f64;
64 pub static FRAC_PI_2: f64 = 1.57079632679489661923132169163975144_f64;
67 pub static FRAC_PI_3: f64 = 1.04719755119659774615421446109316763_f64;
70 pub static FRAC_PI_4: f64 = 0.785398163397448309615660845819875721_f64;
73 pub static FRAC_PI_6: f64 = 0.52359877559829887307710723054658381_f64;
76 pub static FRAC_PI_8: f64 = 0.39269908169872415480783042290993786_f64;
79 pub static FRAC_1_PI: f64 = 0.318309886183790671537767526745028724_f64;
82 pub static FRAC_2_PI: f64 = 0.636619772367581343075535053490057448_f64;
85 pub static FRAC_2_SQRTPI: f64 = 1.12837916709551257389615890312154517_f64;
88 pub static SQRT2: f64 = 1.41421356237309504880168872420969808_f64;
91 pub static FRAC_1_SQRT2: f64 = 0.707106781186547524400844362104849039_f64;
94 pub static E: f64 = 2.71828182845904523536028747135266250_f64;
97 pub static LOG2_E: f64 = 1.44269504088896340735992468100189214_f64;
100 pub static LOG10_E: f64 = 0.434294481903251827651128918916605082_f64;
103 pub static LN_2: f64 = 0.693147180559945309417232121458176568_f64;
106 pub static LN_10: f64 = 2.30258509299404568401799145468436421_f64;
111 fn nan() -> f64 { NAN }
114 fn infinity() -> f64 { INFINITY }
117 fn neg_infinity() -> f64 { NEG_INFINITY }
120 fn neg_zero() -> f64 { -0.0 }
122 /// Returns `true` if the number is NaN
124 fn is_nan(self) -> bool { self != self }
126 /// Returns `true` if the number is infinite
128 fn is_infinite(self) -> bool {
129 self == Float::infinity() || self == Float::neg_infinity()
132 /// Returns `true` if the number is neither infinite or NaN
134 fn is_finite(self) -> bool {
135 !(self.is_nan() || self.is_infinite())
138 /// Returns `true` if the number is neither zero, infinite, subnormal or NaN
140 fn is_normal(self) -> bool {
141 self.classify() == FPNormal
144 /// Returns the floating point category of the number. If only one property
145 /// is going to be tested, it is generally faster to use the specific
146 /// predicate instead.
147 fn classify(self) -> FPCategory {
148 static EXP_MASK: u64 = 0x7ff0000000000000;
149 static MAN_MASK: u64 = 0x000fffffffffffff;
151 let bits: u64 = unsafe { mem::transmute(self) };
152 match (bits & MAN_MASK, bits & EXP_MASK) {
154 (_, 0) => FPSubnormal,
155 (0, EXP_MASK) => FPInfinite,
156 (_, EXP_MASK) => FPNaN,
162 fn mantissa_digits(_: Option<f64>) -> uint { MANTISSA_DIGITS }
165 fn digits(_: Option<f64>) -> uint { DIGITS }
168 fn epsilon() -> f64 { EPSILON }
171 fn min_exp(_: Option<f64>) -> int { MIN_EXP }
174 fn max_exp(_: Option<f64>) -> int { MAX_EXP }
177 fn min_10_exp(_: Option<f64>) -> int { MIN_10_EXP }
180 fn max_10_exp(_: Option<f64>) -> int { MAX_10_EXP }
183 fn min_pos_value(_: Option<f64>) -> f64 { MIN_POS_VALUE }
185 /// Returns the mantissa, exponent and sign as integers.
186 fn integer_decode(self) -> (u64, i16, i8) {
187 let bits: u64 = unsafe { mem::transmute(self) };
188 let sign: i8 = if bits >> 63 == 0 { 1 } else { -1 };
189 let mut exponent: i16 = ((bits >> 52) & 0x7ff) as i16;
190 let mantissa = if exponent == 0 {
191 (bits & 0xfffffffffffff) << 1
193 (bits & 0xfffffffffffff) | 0x10000000000000
195 // Exponent bias + mantissa shift
196 exponent -= 1023 + 52;
197 (mantissa, exponent, sign)
200 /// Round half-way cases toward `NEG_INFINITY`
202 fn floor(self) -> f64 {
203 unsafe { intrinsics::floorf64(self) }
206 /// Round half-way cases toward `INFINITY`
208 fn ceil(self) -> f64 {
209 unsafe { intrinsics::ceilf64(self) }
212 /// Round half-way cases away from `0.0`
214 fn round(self) -> f64 {
215 unsafe { intrinsics::roundf64(self) }
218 /// The integer part of the number (rounds towards `0.0`)
220 fn trunc(self) -> f64 {
221 unsafe { intrinsics::truncf64(self) }
224 /// The fractional part of the number, satisfying:
228 /// assert!(x == x.trunc() + x.fract())
231 fn fract(self) -> f64 { self - self.trunc() }
233 /// Fused multiply-add. Computes `(self * a) + b` with only one rounding
234 /// error. This produces a more accurate result with better performance than
235 /// a separate multiplication operation followed by an add.
237 fn mul_add(self, a: f64, b: f64) -> f64 {
238 unsafe { intrinsics::fmaf64(self, a, b) }
241 /// The reciprocal (multiplicative inverse) of the number
243 fn recip(self) -> f64 { 1.0 / self }
246 fn powf(self, n: f64) -> f64 {
247 unsafe { intrinsics::powf64(self, n) }
251 fn powi(self, n: i32) -> f64 {
252 unsafe { intrinsics::powif64(self, n) }
257 fn sqrt2() -> f64 { consts::SQRT2 }
261 fn frac_1_sqrt2() -> f64 { consts::FRAC_1_SQRT2 }
264 fn sqrt(self) -> f64 {
265 unsafe { intrinsics::sqrtf64(self) }
269 fn rsqrt(self) -> f64 { self.sqrt().recip() }
271 /// Archimedes' constant
273 fn pi() -> f64 { consts::PI }
277 fn two_pi() -> f64 { consts::PI_2 }
281 fn frac_pi_2() -> f64 { consts::FRAC_PI_2 }
285 fn frac_pi_3() -> f64 { consts::FRAC_PI_3 }
289 fn frac_pi_4() -> f64 { consts::FRAC_PI_4 }
293 fn frac_pi_6() -> f64 { consts::FRAC_PI_6 }
297 fn frac_pi_8() -> f64 { consts::FRAC_PI_8 }
301 fn frac_1_pi() -> f64 { consts::FRAC_1_PI }
305 fn frac_2_pi() -> f64 { consts::FRAC_2_PI }
309 fn frac_2_sqrtpi() -> f64 { consts::FRAC_2_SQRTPI }
313 fn e() -> f64 { consts::E }
317 fn log2_e() -> f64 { consts::LOG2_E }
321 fn log10_e() -> f64 { consts::LOG10_E }
325 fn ln_2() -> f64 { consts::LN_2 }
329 fn ln_10() -> f64 { consts::LN_10 }
331 /// Returns the exponential of the number
333 fn exp(self) -> f64 {
334 unsafe { intrinsics::expf64(self) }
337 /// Returns 2 raised to the power of the number
339 fn exp2(self) -> f64 {
340 unsafe { intrinsics::exp2f64(self) }
343 /// Returns the natural logarithm of the number
346 unsafe { intrinsics::logf64(self) }
349 /// Returns the logarithm of the number with respect to an arbitrary base
351 fn log(self, base: f64) -> f64 { self.ln() / base.ln() }
353 /// Returns the base 2 logarithm of the number
355 fn log2(self) -> f64 {
356 unsafe { intrinsics::log2f64(self) }
359 /// Returns the base 10 logarithm of the number
361 fn log10(self) -> f64 {
362 unsafe { intrinsics::log10f64(self) }
366 /// Converts to degrees, assuming the number is in radians
368 fn to_degrees(self) -> f64 { self * (180.0f64 / Float::pi()) }
370 /// Converts to radians, assuming the number is in degrees
372 fn to_radians(self) -> f64 {
373 let value: f64 = Float::pi();
374 self * (value / 180.0)