390 lines
11 KiB
Rust
390 lines
11 KiB
Rust
// Copyright 2012-2014 The Rust Project Developers. See the COPYRIGHT
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// file at the top-level directory of this distribution and at
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// http://rust-lang.org/COPYRIGHT.
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//
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// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
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// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
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// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
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// option. This file may not be copied, modified, or distributed
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// except according to those terms.
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//! Operations and constants for 64-bits floats (`f64` type)
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#![doc(primitive = "f64")]
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// FIXME: MIN_VALUE and MAX_VALUE literals are parsed as -inf and inf #14353
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#![allow(overflowing_literals)]
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#![stable]
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use intrinsics;
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use mem;
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use num::Float;
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use num::FpCategory as Fp;
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use option::Option;
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// FIXME(#5527): These constants should be deprecated once associated
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// constants are implemented in favour of referencing the respective
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// members of `Bounded` and `Float`.
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#[unstable = "pending integer conventions"]
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pub const RADIX: uint = 2u;
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pub const MANTISSA_DIGITS: uint = 53u;
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#[unstable = "pending integer conventions"]
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pub const DIGITS: uint = 15u;
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#[stable]
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pub const EPSILON: f64 = 2.2204460492503131e-16_f64;
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/// Smallest finite f64 value
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#[stable]
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pub const MIN_VALUE: f64 = -1.7976931348623157e+308_f64;
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/// Smallest positive, normalized f64 value
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#[stable]
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pub const MIN_POS_VALUE: f64 = 2.2250738585072014e-308_f64;
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/// Largest finite f64 value
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#[stable]
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pub const MAX_VALUE: f64 = 1.7976931348623157e+308_f64;
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#[unstable = "pending integer conventions"]
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pub const MIN_EXP: int = -1021;
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#[unstable = "pending integer conventions"]
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pub const MAX_EXP: int = 1024;
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#[unstable = "pending integer conventions"]
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pub const MIN_10_EXP: int = -307;
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#[unstable = "pending integer conventions"]
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pub const MAX_10_EXP: int = 308;
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#[stable]
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pub const NAN: f64 = 0.0_f64/0.0_f64;
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#[stable]
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pub const INFINITY: f64 = 1.0_f64/0.0_f64;
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#[stable]
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pub const NEG_INFINITY: f64 = -1.0_f64/0.0_f64;
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/// Various useful constants.
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#[unstable = "naming scheme needs to be revisited"]
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pub mod consts {
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// FIXME: replace with mathematical constants from cmath.
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// FIXME(#5527): These constants should be deprecated once associated
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// constants are implemented in favour of referencing the respective members
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// of `Float`.
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/// Archimedes' constant
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pub const PI: f64 = 3.14159265358979323846264338327950288_f64;
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/// pi * 2.0
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pub const PI_2: f64 = 6.28318530717958647692528676655900576_f64;
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/// pi/2.0
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pub const FRAC_PI_2: f64 = 1.57079632679489661923132169163975144_f64;
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/// pi/3.0
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pub const FRAC_PI_3: f64 = 1.04719755119659774615421446109316763_f64;
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/// pi/4.0
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pub const FRAC_PI_4: f64 = 0.785398163397448309615660845819875721_f64;
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/// pi/6.0
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pub const FRAC_PI_6: f64 = 0.52359877559829887307710723054658381_f64;
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/// pi/8.0
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pub const FRAC_PI_8: f64 = 0.39269908169872415480783042290993786_f64;
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/// 1.0/pi
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pub const FRAC_1_PI: f64 = 0.318309886183790671537767526745028724_f64;
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/// 2.0/pi
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pub const FRAC_2_PI: f64 = 0.636619772367581343075535053490057448_f64;
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/// 2.0/sqrt(pi)
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pub const FRAC_2_SQRTPI: f64 = 1.12837916709551257389615890312154517_f64;
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/// sqrt(2.0)
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pub const SQRT2: f64 = 1.41421356237309504880168872420969808_f64;
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/// 1.0/sqrt(2.0)
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pub const FRAC_1_SQRT2: f64 = 0.707106781186547524400844362104849039_f64;
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/// Euler's number
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pub const E: f64 = 2.71828182845904523536028747135266250_f64;
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/// log2(e)
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pub const LOG2_E: f64 = 1.44269504088896340735992468100189214_f64;
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/// log10(e)
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pub const LOG10_E: f64 = 0.434294481903251827651128918916605082_f64;
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/// ln(2.0)
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pub const LN_2: f64 = 0.693147180559945309417232121458176568_f64;
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/// ln(10.0)
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pub const LN_10: f64 = 2.30258509299404568401799145468436421_f64;
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}
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#[unstable = "trait is unstable"]
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impl Float for f64 {
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#[inline]
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fn nan() -> f64 { NAN }
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#[inline]
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fn infinity() -> f64 { INFINITY }
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#[inline]
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fn neg_infinity() -> f64 { NEG_INFINITY }
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#[inline]
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fn zero() -> f64 { 0.0 }
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#[inline]
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fn neg_zero() -> f64 { -0.0 }
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#[inline]
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fn one() -> f64 { 1.0 }
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/// Returns `true` if the number is NaN.
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#[inline]
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fn is_nan(self) -> bool { self != self }
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/// Returns `true` if the number is infinite.
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#[inline]
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fn is_infinite(self) -> bool {
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self == Float::infinity() || self == Float::neg_infinity()
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}
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/// Returns `true` if the number is neither infinite or NaN.
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#[inline]
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fn is_finite(self) -> bool {
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!(self.is_nan() || self.is_infinite())
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}
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/// Returns `true` if the number is neither zero, infinite, subnormal or NaN.
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#[inline]
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fn is_normal(self) -> bool {
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self.classify() == Fp::Normal
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}
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/// Returns the floating point category of the number. If only one property
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/// is going to be tested, it is generally faster to use the specific
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/// predicate instead.
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fn classify(self) -> Fp {
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const EXP_MASK: u64 = 0x7ff0000000000000;
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const MAN_MASK: u64 = 0x000fffffffffffff;
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let bits: u64 = unsafe { mem::transmute(self) };
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match (bits & MAN_MASK, bits & EXP_MASK) {
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(0, 0) => Fp::Zero,
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(_, 0) => Fp::Subnormal,
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(0, EXP_MASK) => Fp::Infinite,
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(_, EXP_MASK) => Fp::Nan,
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_ => Fp::Normal,
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}
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}
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#[inline]
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#[deprecated]
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fn mantissa_digits(_: Option<f64>) -> uint { MANTISSA_DIGITS }
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#[inline]
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#[deprecated]
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fn digits(_: Option<f64>) -> uint { DIGITS }
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#[inline]
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#[deprecated]
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fn epsilon() -> f64 { EPSILON }
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#[inline]
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#[deprecated]
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fn min_exp(_: Option<f64>) -> int { MIN_EXP }
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#[inline]
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#[deprecated]
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fn max_exp(_: Option<f64>) -> int { MAX_EXP }
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#[inline]
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#[deprecated]
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fn min_10_exp(_: Option<f64>) -> int { MIN_10_EXP }
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#[inline]
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#[deprecated]
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fn max_10_exp(_: Option<f64>) -> int { MAX_10_EXP }
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#[inline]
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#[deprecated]
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fn min_value() -> f64 { MIN_VALUE }
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#[inline]
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#[deprecated]
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fn min_pos_value(_: Option<f64>) -> f64 { MIN_POS_VALUE }
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#[inline]
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#[deprecated]
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fn max_value() -> f64 { MAX_VALUE }
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/// Returns the mantissa, exponent and sign as integers.
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fn integer_decode(self) -> (u64, i16, i8) {
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let bits: u64 = unsafe { mem::transmute(self) };
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let sign: i8 = if bits >> 63 == 0 { 1 } else { -1 };
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let mut exponent: i16 = ((bits >> 52) & 0x7ff) as i16;
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let mantissa = if exponent == 0 {
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(bits & 0xfffffffffffff) << 1
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} else {
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(bits & 0xfffffffffffff) | 0x10000000000000
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};
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// Exponent bias + mantissa shift
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exponent -= 1023 + 52;
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(mantissa, exponent, sign)
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}
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/// Rounds towards minus infinity.
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#[inline]
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fn floor(self) -> f64 {
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unsafe { intrinsics::floorf64(self) }
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}
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/// Rounds towards plus infinity.
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#[inline]
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fn ceil(self) -> f64 {
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unsafe { intrinsics::ceilf64(self) }
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}
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/// Rounds to nearest integer. Rounds half-way cases away from zero.
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#[inline]
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fn round(self) -> f64 {
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unsafe { intrinsics::roundf64(self) }
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}
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/// Returns the integer part of the number (rounds towards zero).
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#[inline]
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fn trunc(self) -> f64 {
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unsafe { intrinsics::truncf64(self) }
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}
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/// The fractional part of the number, satisfying:
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///
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/// ```rust
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/// use core::num::Float;
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///
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/// let x = 1.65f64;
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/// assert!(x == x.trunc() + x.fract())
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/// ```
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#[inline]
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fn fract(self) -> f64 { self - self.trunc() }
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/// Computes the absolute value of `self`. Returns `Float::nan()` if the
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/// number is `Float::nan()`.
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#[inline]
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fn abs(self) -> f64 {
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unsafe { intrinsics::fabsf64(self) }
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}
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/// Returns a number that represents the sign of `self`.
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///
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/// - `1.0` if the number is positive, `+0.0` or `Float::infinity()`
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/// - `-1.0` if the number is negative, `-0.0` or `Float::neg_infinity()`
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/// - `Float::nan()` if the number is `Float::nan()`
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#[inline]
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fn signum(self) -> f64 {
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if self.is_nan() {
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Float::nan()
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} else {
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unsafe { intrinsics::copysignf64(1.0, self) }
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}
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}
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/// Returns `true` if `self` is positive, including `+0.0` and
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/// `Float::infinity()`.
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#[inline]
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fn is_positive(self) -> bool {
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self > 0.0 || (1.0 / self) == Float::infinity()
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}
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/// Returns `true` if `self` is negative, including `-0.0` and
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/// `Float::neg_infinity()`.
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#[inline]
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fn is_negative(self) -> bool {
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self < 0.0 || (1.0 / self) == Float::neg_infinity()
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}
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/// Fused multiply-add. Computes `(self * a) + b` with only one rounding
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/// error. This produces a more accurate result with better performance than
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/// a separate multiplication operation followed by an add.
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#[inline]
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fn mul_add(self, a: f64, b: f64) -> f64 {
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unsafe { intrinsics::fmaf64(self, a, b) }
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}
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/// Returns the reciprocal (multiplicative inverse) of the number.
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#[inline]
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fn recip(self) -> f64 { 1.0 / self }
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#[inline]
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fn powf(self, n: f64) -> f64 {
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unsafe { intrinsics::powf64(self, n) }
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}
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#[inline]
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fn powi(self, n: i32) -> f64 {
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unsafe { intrinsics::powif64(self, n) }
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}
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#[inline]
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fn sqrt(self) -> f64 {
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if self < 0.0 {
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NAN
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} else {
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unsafe { intrinsics::sqrtf64(self) }
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}
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}
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#[inline]
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fn rsqrt(self) -> f64 { self.sqrt().recip() }
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/// Returns the exponential of the number.
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#[inline]
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fn exp(self) -> f64 {
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unsafe { intrinsics::expf64(self) }
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}
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/// Returns 2 raised to the power of the number.
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#[inline]
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fn exp2(self) -> f64 {
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unsafe { intrinsics::exp2f64(self) }
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}
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/// Returns the natural logarithm of the number.
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#[inline]
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fn ln(self) -> f64 {
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unsafe { intrinsics::logf64(self) }
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}
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/// Returns the logarithm of the number with respect to an arbitrary base.
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#[inline]
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fn log(self, base: f64) -> f64 { self.ln() / base.ln() }
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/// Returns the base 2 logarithm of the number.
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#[inline]
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fn log2(self) -> f64 {
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unsafe { intrinsics::log2f64(self) }
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}
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/// Returns the base 10 logarithm of the number.
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#[inline]
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fn log10(self) -> f64 {
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unsafe { intrinsics::log10f64(self) }
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}
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/// Converts to degrees, assuming the number is in radians.
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#[inline]
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fn to_degrees(self) -> f64 { self * (180.0f64 / consts::PI) }
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/// Converts to radians, assuming the number is in degrees.
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#[inline]
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fn to_radians(self) -> f64 {
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let value: f64 = consts::PI;
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self * (value / 180.0)
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}
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}
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