568 lines
19 KiB
Rust
568 lines
19 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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//! This module provides constants which are specific to the implementation
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//! of the `f64` floating point data type.
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//!
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//! *[See also the `f64` primitive type](../../std/primitive.f64.html).*
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//!
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//! Mathematically significant numbers are provided in the `consts` sub-module.
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#![stable(feature = "rust1", since = "1.0.0")]
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use mem;
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use num::Float;
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#[cfg(not(stage0))] use num::FpCategory;
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use num::FpCategory as Fp;
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/// The radix or base of the internal representation of `f64`.
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const RADIX: u32 = 2;
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/// Number of significant digits in base 2.
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const MANTISSA_DIGITS: u32 = 53;
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/// Approximate number of significant digits in base 10.
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const DIGITS: u32 = 15;
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/// Difference between `1.0` and the next largest representable number.
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#[stable(feature = "rust1", since = "1.0.0")]
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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(feature = "rust1", since = "1.0.0")]
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pub const MIN: f64 = -1.7976931348623157e+308_f64;
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/// Smallest positive normal `f64` value.
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const MIN_POSITIVE: f64 = 2.2250738585072014e-308_f64;
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/// Largest finite `f64` value.
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const MAX: f64 = 1.7976931348623157e+308_f64;
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/// One greater than the minimum possible normal power of 2 exponent.
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const MIN_EXP: i32 = -1021;
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/// Maximum possible power of 2 exponent.
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const MAX_EXP: i32 = 1024;
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/// Minimum possible normal power of 10 exponent.
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const MIN_10_EXP: i32 = -307;
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/// Maximum possible power of 10 exponent.
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const MAX_10_EXP: i32 = 308;
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/// Not a Number (NaN).
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const NAN: f64 = 0.0_f64 / 0.0_f64;
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/// Infinity (∞).
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const INFINITY: f64 = 1.0_f64 / 0.0_f64;
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/// Negative infinity (-∞).
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const NEG_INFINITY: f64 = -1.0_f64 / 0.0_f64;
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/// Basic mathematical constants.
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#[stable(feature = "rust1", since = "1.0.0")]
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pub mod consts {
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// FIXME: replace with mathematical constants from cmath.
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/// Archimedes' constant (π)
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const PI: f64 = 3.14159265358979323846264338327950288_f64;
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/// π/2
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const FRAC_PI_2: f64 = 1.57079632679489661923132169163975144_f64;
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/// π/3
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const FRAC_PI_3: f64 = 1.04719755119659774615421446109316763_f64;
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/// π/4
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const FRAC_PI_4: f64 = 0.785398163397448309615660845819875721_f64;
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/// π/6
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const FRAC_PI_6: f64 = 0.52359877559829887307710723054658381_f64;
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/// π/8
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const FRAC_PI_8: f64 = 0.39269908169872415480783042290993786_f64;
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/// 1/π
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const FRAC_1_PI: f64 = 0.318309886183790671537767526745028724_f64;
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/// 2/π
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const FRAC_2_PI: f64 = 0.636619772367581343075535053490057448_f64;
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/// 2/sqrt(π)
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const FRAC_2_SQRT_PI: f64 = 1.12837916709551257389615890312154517_f64;
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/// sqrt(2)
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const SQRT_2: f64 = 1.41421356237309504880168872420969808_f64;
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/// 1/sqrt(2)
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const FRAC_1_SQRT_2: f64 = 0.707106781186547524400844362104849039_f64;
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/// Euler's number (e)
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const E: f64 = 2.71828182845904523536028747135266250_f64;
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/// log<sub>2</sub>(10)
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#[unstable(feature = "extra_log_consts", issue = "50540")]
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pub const LOG2_10: f64 = 3.32192809488736234787031942948939018_f64;
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/// log<sub>2</sub>(e)
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const LOG2_E: f64 = 1.44269504088896340735992468100189214_f64;
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/// log<sub>10</sub>(2)
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#[unstable(feature = "extra_log_consts", issue = "50540")]
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pub const LOG10_2: f64 = 0.301029995663981195213738894724493027_f64;
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/// log<sub>10</sub>(e)
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const LOG10_E: f64 = 0.434294481903251827651128918916605082_f64;
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/// ln(2)
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const LN_2: f64 = 0.693147180559945309417232121458176568_f64;
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/// ln(10)
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const LN_10: f64 = 2.30258509299404568401799145468436421_f64;
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}
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#[unstable(feature = "core_float",
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reason = "stable interface is via `impl f{32,64}` in later crates",
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issue = "32110")]
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impl Float for f64 {
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type Bits = u64;
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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 {
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self != self
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}
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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 == INFINITY || self == 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 = self.to_bits();
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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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/// Returns `true` if and only if `self` has a positive sign, including `+0.0`, `NaN`s with
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/// positive sign bit and positive infinity.
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#[inline]
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fn is_sign_positive(self) -> bool {
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!self.is_sign_negative()
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}
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/// Returns `true` if and only if `self` has a negative sign, including `-0.0`, `NaN`s with
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/// negative sign bit and negative infinity.
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#[inline]
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fn is_sign_negative(self) -> bool {
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self.to_bits() & 0x8000_0000_0000_0000 != 0
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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 {
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1.0 / 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 {
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// The division here is correctly rounded with respect to the true
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// value of 180/π. (This differs from f32, where a constant must be
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// used to ensure a correctly rounded result.)
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self * (180.0f64 / consts::PI)
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}
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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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/// Returns the maximum of the two numbers.
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#[inline]
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fn max(self, other: f64) -> f64 {
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// IEEE754 says: maxNum(x, y) is the canonicalized number y if x < y, x if y < x, the
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// canonicalized number if one operand is a number and the other a quiet NaN. Otherwise it
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// is either x or y, canonicalized (this means results might differ among implementations).
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// When either x or y is a signalingNaN, then the result is according to 6.2.
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//
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// Since we do not support sNaN in Rust yet, we do not need to handle them.
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// FIXME(nagisa): due to https://bugs.llvm.org/show_bug.cgi?id=33303 we canonicalize by
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// multiplying by 1.0. Should switch to the `canonicalize` when it works.
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(if self.is_nan() || self < other { other } else { self }) * 1.0
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}
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/// Returns the minimum of the two numbers.
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#[inline]
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fn min(self, other: f64) -> f64 {
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// IEEE754 says: minNum(x, y) is the canonicalized number x if x < y, y if y < x, the
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// canonicalized number if one operand is a number and the other a quiet NaN. Otherwise it
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// is either x or y, canonicalized (this means results might differ among implementations).
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// When either x or y is a signalingNaN, then the result is according to 6.2.
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//
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// Since we do not support sNaN in Rust yet, we do not need to handle them.
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// FIXME(nagisa): due to https://bugs.llvm.org/show_bug.cgi?id=33303 we canonicalize by
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// multiplying by 1.0. Should switch to the `canonicalize` when it works.
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(if other.is_nan() || self < other { self } else { other }) * 1.0
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}
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/// Raw transmutation to `u64`.
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#[inline]
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fn to_bits(self) -> u64 {
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unsafe { mem::transmute(self) }
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}
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/// Raw transmutation from `u64`.
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#[inline]
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fn from_bits(v: u64) -> Self {
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// It turns out the safety issues with sNaN were overblown! Hooray!
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unsafe { mem::transmute(v) }
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}
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}
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// FIXME: remove (inline) this macro and the Float trait
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// when updating to a bootstrap compiler that has the new lang items.
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#[cfg_attr(stage0, macro_export)]
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#[unstable(feature = "core_float", issue = "32110")]
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macro_rules! f64_core_methods { () => {
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/// Returns `true` if this value is `NaN` and false otherwise.
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///
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/// ```
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/// use std::f64;
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///
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/// let nan = f64::NAN;
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/// let f = 7.0_f64;
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///
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/// assert!(nan.is_nan());
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/// assert!(!f.is_nan());
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn is_nan(self) -> bool { Float::is_nan(self) }
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/// Returns `true` if this value is positive infinity or negative infinity and
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/// false otherwise.
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///
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/// ```
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/// use std::f64;
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///
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/// let f = 7.0f64;
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/// let inf = f64::INFINITY;
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/// let neg_inf = f64::NEG_INFINITY;
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/// let nan = f64::NAN;
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///
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/// assert!(!f.is_infinite());
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/// assert!(!nan.is_infinite());
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///
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/// assert!(inf.is_infinite());
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/// assert!(neg_inf.is_infinite());
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn is_infinite(self) -> bool { Float::is_infinite(self) }
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/// Returns `true` if this number is neither infinite nor `NaN`.
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///
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/// ```
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/// use std::f64;
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///
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/// let f = 7.0f64;
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/// let inf: f64 = f64::INFINITY;
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/// let neg_inf: f64 = f64::NEG_INFINITY;
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/// let nan: f64 = f64::NAN;
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///
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/// assert!(f.is_finite());
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///
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/// assert!(!nan.is_finite());
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/// assert!(!inf.is_finite());
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/// assert!(!neg_inf.is_finite());
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn is_finite(self) -> bool { Float::is_finite(self) }
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/// Returns `true` if the number is neither zero, infinite,
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/// [subnormal][subnormal], or `NaN`.
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///
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/// ```
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/// use std::f64;
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///
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/// let min = f64::MIN_POSITIVE; // 2.2250738585072014e-308f64
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/// let max = f64::MAX;
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/// let lower_than_min = 1.0e-308_f64;
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/// let zero = 0.0f64;
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///
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/// assert!(min.is_normal());
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/// assert!(max.is_normal());
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///
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/// assert!(!zero.is_normal());
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/// assert!(!f64::NAN.is_normal());
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/// assert!(!f64::INFINITY.is_normal());
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/// // Values between `0` and `min` are Subnormal.
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/// assert!(!lower_than_min.is_normal());
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/// ```
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/// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn is_normal(self) -> bool { Float::is_normal(self) }
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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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///
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/// ```
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/// use std::num::FpCategory;
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/// use std::f64;
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///
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/// let num = 12.4_f64;
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/// let inf = f64::INFINITY;
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///
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/// assert_eq!(num.classify(), FpCategory::Normal);
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/// assert_eq!(inf.classify(), FpCategory::Infinite);
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn classify(self) -> FpCategory { Float::classify(self) }
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/// Returns `true` if and only if `self` has a positive sign, including `+0.0`, `NaN`s with
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/// positive sign bit and positive infinity.
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///
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/// ```
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/// let f = 7.0_f64;
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/// let g = -7.0_f64;
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///
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/// assert!(f.is_sign_positive());
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/// assert!(!g.is_sign_positive());
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn is_sign_positive(self) -> bool { Float::is_sign_positive(self) }
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#[stable(feature = "rust1", since = "1.0.0")]
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#[rustc_deprecated(since = "1.0.0", reason = "renamed to is_sign_positive")]
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#[inline]
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#[doc(hidden)]
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pub fn is_positive(self) -> bool { Float::is_sign_positive(self) }
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/// Returns `true` if and only if `self` has a negative sign, including `-0.0`, `NaN`s with
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/// negative sign bit and negative infinity.
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///
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/// ```
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/// let f = 7.0_f64;
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/// let g = -7.0_f64;
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///
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/// assert!(!f.is_sign_negative());
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/// assert!(g.is_sign_negative());
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn is_sign_negative(self) -> bool { Float::is_sign_negative(self) }
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#[stable(feature = "rust1", since = "1.0.0")]
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#[rustc_deprecated(since = "1.0.0", reason = "renamed to is_sign_negative")]
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#[inline]
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#[doc(hidden)]
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pub fn is_negative(self) -> bool { Float::is_sign_negative(self) }
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/// Takes the reciprocal (inverse) of a number, `1/x`.
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///
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/// ```
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/// let x = 2.0_f64;
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/// let abs_difference = (x.recip() - (1.0/x)).abs();
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///
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/// assert!(abs_difference < 1e-10);
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn recip(self) -> f64 { Float::recip(self) }
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/// Converts radians to degrees.
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///
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/// ```
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/// use std::f64::consts;
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///
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/// let angle = consts::PI;
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///
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/// let abs_difference = (angle.to_degrees() - 180.0).abs();
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///
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/// assert!(abs_difference < 1e-10);
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn to_degrees(self) -> f64 { Float::to_degrees(self) }
|
|
|
|
/// Converts degrees to radians.
|
|
///
|
|
/// ```
|
|
/// use std::f64::consts;
|
|
///
|
|
/// let angle = 180.0_f64;
|
|
///
|
|
/// let abs_difference = (angle.to_radians() - consts::PI).abs();
|
|
///
|
|
/// assert!(abs_difference < 1e-10);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn to_radians(self) -> f64 { Float::to_radians(self) }
|
|
|
|
/// Returns the maximum of the two numbers.
|
|
///
|
|
/// ```
|
|
/// let x = 1.0_f64;
|
|
/// let y = 2.0_f64;
|
|
///
|
|
/// assert_eq!(x.max(y), y);
|
|
/// ```
|
|
///
|
|
/// If one of the arguments is NaN, then the other argument is returned.
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn max(self, other: f64) -> f64 {
|
|
Float::max(self, other)
|
|
}
|
|
|
|
/// Returns the minimum of the two numbers.
|
|
///
|
|
/// ```
|
|
/// let x = 1.0_f64;
|
|
/// let y = 2.0_f64;
|
|
///
|
|
/// assert_eq!(x.min(y), x);
|
|
/// ```
|
|
///
|
|
/// If one of the arguments is NaN, then the other argument is returned.
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn min(self, other: f64) -> f64 {
|
|
Float::min(self, other)
|
|
}
|
|
|
|
/// Raw transmutation to `u64`.
|
|
///
|
|
/// This is currently identical to `transmute::<f64, u64>(self)` on all platforms.
|
|
///
|
|
/// See `from_bits` for some discussion of the portability of this operation
|
|
/// (there are almost no issues).
|
|
///
|
|
/// Note that this function is distinct from `as` casting, which attempts to
|
|
/// preserve the *numeric* value, and not the bitwise value.
|
|
///
|
|
/// # Examples
|
|
///
|
|
/// ```
|
|
/// assert!((1f64).to_bits() != 1f64 as u64); // to_bits() is not casting!
|
|
/// assert_eq!((12.5f64).to_bits(), 0x4029000000000000);
|
|
///
|
|
/// ```
|
|
#[stable(feature = "float_bits_conv", since = "1.20.0")]
|
|
#[inline]
|
|
pub fn to_bits(self) -> u64 {
|
|
Float::to_bits(self)
|
|
}
|
|
|
|
/// Raw transmutation from `u64`.
|
|
///
|
|
/// This is currently identical to `transmute::<u64, f64>(v)` on all platforms.
|
|
/// It turns out this is incredibly portable, for two reasons:
|
|
///
|
|
/// * Floats and Ints have the same endianness on all supported platforms.
|
|
/// * IEEE-754 very precisely specifies the bit layout of floats.
|
|
///
|
|
/// However there is one caveat: prior to the 2008 version of IEEE-754, how
|
|
/// to interpret the NaN signaling bit wasn't actually specified. Most platforms
|
|
/// (notably x86 and ARM) picked the interpretation that was ultimately
|
|
/// standardized in 2008, but some didn't (notably MIPS). As a result, all
|
|
/// signaling NaNs on MIPS are quiet NaNs on x86, and vice-versa.
|
|
///
|
|
/// Rather than trying to preserve signaling-ness cross-platform, this
|
|
/// implementation favours preserving the exact bits. This means that
|
|
/// any payloads encoded in NaNs will be preserved even if the result of
|
|
/// this method is sent over the network from an x86 machine to a MIPS one.
|
|
///
|
|
/// If the results of this method are only manipulated by the same
|
|
/// architecture that produced them, then there is no portability concern.
|
|
///
|
|
/// If the input isn't NaN, then there is no portability concern.
|
|
///
|
|
/// If you don't care about signalingness (very likely), then there is no
|
|
/// portability concern.
|
|
///
|
|
/// Note that this function is distinct from `as` casting, which attempts to
|
|
/// preserve the *numeric* value, and not the bitwise value.
|
|
///
|
|
/// # Examples
|
|
///
|
|
/// ```
|
|
/// use std::f64;
|
|
/// let v = f64::from_bits(0x4029000000000000);
|
|
/// let difference = (v - 12.5).abs();
|
|
/// assert!(difference <= 1e-5);
|
|
/// ```
|
|
#[stable(feature = "float_bits_conv", since = "1.20.0")]
|
|
#[inline]
|
|
pub fn from_bits(v: u64) -> Self {
|
|
Float::from_bits(v)
|
|
}
|
|
}}
|
|
|
|
#[lang = "f64"]
|
|
#[cfg(not(test))]
|
|
#[cfg(not(stage0))]
|
|
impl f64 {
|
|
f64_core_methods!();
|
|
}
|