2038 lines
73 KiB
Rust
2038 lines
73 KiB
Rust
//! Constants for the `f64` double-precision floating point type.
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//!
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//! *[See also the `f64` primitive type][f64].*
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//!
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//! Mathematically significant numbers are provided in the `consts` sub-module.
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//!
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//! For the constants defined directly in this module
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//! (as distinct from those defined in the `consts` sub-module),
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//! new code should instead use the associated constants
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//! defined directly on the `f64` type.
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#![stable(feature = "rust1", since = "1.0.0")]
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use crate::convert::FloatToInt;
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use crate::num::FpCategory;
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use crate::panic::const_assert;
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use crate::{intrinsics, mem};
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/// The radix or base of the internal representation of `f64`.
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/// Use [`f64::RADIX`] instead.
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///
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/// # Examples
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///
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/// ```rust
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/// // deprecated way
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/// # #[allow(deprecated, deprecated_in_future)]
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/// let r = std::f64::RADIX;
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///
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/// // intended way
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/// let r = f64::RADIX;
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[deprecated(since = "TBD", note = "replaced by the `RADIX` associated constant on `f64`")]
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#[rustc_diagnostic_item = "f64_legacy_const_radix"]
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pub const RADIX: u32 = f64::RADIX;
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/// Number of significant digits in base 2.
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/// Use [`f64::MANTISSA_DIGITS`] instead.
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///
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/// # Examples
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///
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/// ```rust
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/// // deprecated way
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/// # #[allow(deprecated, deprecated_in_future)]
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/// let d = std::f64::MANTISSA_DIGITS;
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///
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/// // intended way
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/// let d = f64::MANTISSA_DIGITS;
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[deprecated(
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since = "TBD",
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note = "replaced by the `MANTISSA_DIGITS` associated constant on `f64`"
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)]
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#[rustc_diagnostic_item = "f64_legacy_const_mantissa_dig"]
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pub const MANTISSA_DIGITS: u32 = f64::MANTISSA_DIGITS;
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/// Approximate number of significant digits in base 10.
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/// Use [`f64::DIGITS`] instead.
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///
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/// # Examples
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///
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/// ```rust
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/// // deprecated way
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/// # #[allow(deprecated, deprecated_in_future)]
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/// let d = std::f64::DIGITS;
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///
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/// // intended way
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/// let d = f64::DIGITS;
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[deprecated(since = "TBD", note = "replaced by the `DIGITS` associated constant on `f64`")]
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#[rustc_diagnostic_item = "f64_legacy_const_digits"]
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pub const DIGITS: u32 = f64::DIGITS;
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/// [Machine epsilon] value for `f64`.
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/// Use [`f64::EPSILON`] instead.
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///
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/// This is the difference between `1.0` and the next larger representable number.
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///
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/// [Machine epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon
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///
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/// # Examples
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///
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/// ```rust
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/// // deprecated way
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/// # #[allow(deprecated, deprecated_in_future)]
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/// let e = std::f64::EPSILON;
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///
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/// // intended way
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/// let e = f64::EPSILON;
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[deprecated(since = "TBD", note = "replaced by the `EPSILON` associated constant on `f64`")]
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#[rustc_diagnostic_item = "f64_legacy_const_epsilon"]
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pub const EPSILON: f64 = f64::EPSILON;
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/// Smallest finite `f64` value.
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/// Use [`f64::MIN`] instead.
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///
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/// # Examples
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///
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/// ```rust
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/// // deprecated way
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/// # #[allow(deprecated, deprecated_in_future)]
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/// let min = std::f64::MIN;
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///
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/// // intended way
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/// let min = f64::MIN;
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[deprecated(since = "TBD", note = "replaced by the `MIN` associated constant on `f64`")]
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#[rustc_diagnostic_item = "f64_legacy_const_min"]
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pub const MIN: f64 = f64::MIN;
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/// Smallest positive normal `f64` value.
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/// Use [`f64::MIN_POSITIVE`] instead.
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///
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/// # Examples
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///
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/// ```rust
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/// // deprecated way
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/// # #[allow(deprecated, deprecated_in_future)]
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/// let min = std::f64::MIN_POSITIVE;
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///
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/// // intended way
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/// let min = f64::MIN_POSITIVE;
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[deprecated(since = "TBD", note = "replaced by the `MIN_POSITIVE` associated constant on `f64`")]
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#[rustc_diagnostic_item = "f64_legacy_const_min_positive"]
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pub const MIN_POSITIVE: f64 = f64::MIN_POSITIVE;
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/// Largest finite `f64` value.
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/// Use [`f64::MAX`] instead.
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///
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/// # Examples
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///
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/// ```rust
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/// // deprecated way
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/// # #[allow(deprecated, deprecated_in_future)]
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/// let max = std::f64::MAX;
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///
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/// // intended way
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/// let max = f64::MAX;
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[deprecated(since = "TBD", note = "replaced by the `MAX` associated constant on `f64`")]
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#[rustc_diagnostic_item = "f64_legacy_const_max"]
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pub const MAX: f64 = f64::MAX;
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/// One greater than the minimum possible normal power of 2 exponent.
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/// Use [`f64::MIN_EXP`] instead.
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///
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/// # Examples
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///
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/// ```rust
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/// // deprecated way
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/// # #[allow(deprecated, deprecated_in_future)]
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/// let min = std::f64::MIN_EXP;
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///
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/// // intended way
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/// let min = f64::MIN_EXP;
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[deprecated(since = "TBD", note = "replaced by the `MIN_EXP` associated constant on `f64`")]
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#[rustc_diagnostic_item = "f64_legacy_const_min_exp"]
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pub const MIN_EXP: i32 = f64::MIN_EXP;
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/// Maximum possible power of 2 exponent.
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/// Use [`f64::MAX_EXP`] instead.
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///
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/// # Examples
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///
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/// ```rust
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/// // deprecated way
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/// # #[allow(deprecated, deprecated_in_future)]
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/// let max = std::f64::MAX_EXP;
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///
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/// // intended way
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/// let max = f64::MAX_EXP;
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[deprecated(since = "TBD", note = "replaced by the `MAX_EXP` associated constant on `f64`")]
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#[rustc_diagnostic_item = "f64_legacy_const_max_exp"]
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pub const MAX_EXP: i32 = f64::MAX_EXP;
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/// Minimum possible normal power of 10 exponent.
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/// Use [`f64::MIN_10_EXP`] instead.
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///
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/// # Examples
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///
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/// ```rust
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/// // deprecated way
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/// # #[allow(deprecated, deprecated_in_future)]
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/// let min = std::f64::MIN_10_EXP;
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///
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/// // intended way
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/// let min = f64::MIN_10_EXP;
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[deprecated(since = "TBD", note = "replaced by the `MIN_10_EXP` associated constant on `f64`")]
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#[rustc_diagnostic_item = "f64_legacy_const_min_10_exp"]
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pub const MIN_10_EXP: i32 = f64::MIN_10_EXP;
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/// Maximum possible power of 10 exponent.
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/// Use [`f64::MAX_10_EXP`] instead.
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///
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/// # Examples
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///
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/// ```rust
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/// // deprecated way
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/// # #[allow(deprecated, deprecated_in_future)]
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/// let max = std::f64::MAX_10_EXP;
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///
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/// // intended way
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/// let max = f64::MAX_10_EXP;
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[deprecated(since = "TBD", note = "replaced by the `MAX_10_EXP` associated constant on `f64`")]
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#[rustc_diagnostic_item = "f64_legacy_const_max_10_exp"]
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pub const MAX_10_EXP: i32 = f64::MAX_10_EXP;
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/// Not a Number (NaN).
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/// Use [`f64::NAN`] instead.
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///
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/// # Examples
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///
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/// ```rust
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/// // deprecated way
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/// # #[allow(deprecated, deprecated_in_future)]
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/// let nan = std::f64::NAN;
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///
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/// // intended way
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/// let nan = f64::NAN;
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[deprecated(since = "TBD", note = "replaced by the `NAN` associated constant on `f64`")]
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#[rustc_diagnostic_item = "f64_legacy_const_nan"]
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pub const NAN: f64 = f64::NAN;
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/// Infinity (∞).
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/// Use [`f64::INFINITY`] instead.
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///
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/// # Examples
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///
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/// ```rust
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/// // deprecated way
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/// # #[allow(deprecated, deprecated_in_future)]
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/// let inf = std::f64::INFINITY;
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///
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/// // intended way
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/// let inf = f64::INFINITY;
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[deprecated(since = "TBD", note = "replaced by the `INFINITY` associated constant on `f64`")]
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#[rustc_diagnostic_item = "f64_legacy_const_infinity"]
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pub const INFINITY: f64 = f64::INFINITY;
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/// Negative infinity (−∞).
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/// Use [`f64::NEG_INFINITY`] instead.
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///
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/// # Examples
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///
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/// ```rust
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/// // deprecated way
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/// # #[allow(deprecated, deprecated_in_future)]
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/// let ninf = std::f64::NEG_INFINITY;
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///
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/// // intended way
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/// let ninf = f64::NEG_INFINITY;
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[deprecated(since = "TBD", note = "replaced by the `NEG_INFINITY` associated constant on `f64`")]
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#[rustc_diagnostic_item = "f64_legacy_const_neg_infinity"]
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pub const NEG_INFINITY: f64 = f64::NEG_INFINITY;
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/// Basic mathematical constants.
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#[stable(feature = "rust1", since = "1.0.0")]
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#[rustc_diagnostic_item = "f64_consts_mod"]
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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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/// The full circle constant (τ)
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///
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/// Equal to 2π.
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#[stable(feature = "tau_constant", since = "1.47.0")]
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pub const TAU: f64 = 6.28318530717958647692528676655900577_f64;
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/// The golden ratio (φ)
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#[stable(feature = "euler_gamma_golden_ratio", since = "1.94.0")]
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pub const GOLDEN_RATIO: f64 = 1.618033988749894848204586834365638118_f64;
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/// The Euler-Mascheroni constant (γ)
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#[stable(feature = "euler_gamma_golden_ratio", since = "1.94.0")]
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pub const EULER_GAMMA: f64 = 0.577215664901532860606512090082402431_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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/// 1/sqrt(π)
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#[unstable(feature = "more_float_constants", issue = "146939")]
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pub const FRAC_1_SQRT_PI: f64 = 0.564189583547756286948079451560772586_f64;
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/// 1/sqrt(2π)
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#[doc(alias = "FRAC_1_SQRT_TAU")]
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#[unstable(feature = "more_float_constants", issue = "146939")]
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pub const FRAC_1_SQRT_2PI: f64 = 0.398942280401432677939946059934381868_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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/// sqrt(3)
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#[unstable(feature = "more_float_constants", issue = "146939")]
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pub const SQRT_3: f64 = 1.732050807568877293527446341505872367_f64;
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|
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/// 1/sqrt(3)
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#[unstable(feature = "more_float_constants", issue = "146939")]
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pub const FRAC_1_SQRT_3: f64 = 0.577350269189625764509148780501957456_f64;
|
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|
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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;
|
||
|
||
/// log<sub>2</sub>(10)
|
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#[stable(feature = "extra_log_consts", since = "1.43.0")]
|
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pub const LOG2_10: f64 = 3.32192809488736234787031942948939018_f64;
|
||
|
||
/// 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;
|
||
|
||
/// log<sub>10</sub>(2)
|
||
#[stable(feature = "extra_log_consts", since = "1.43.0")]
|
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pub const LOG10_2: f64 = 0.301029995663981195213738894724493027_f64;
|
||
|
||
/// log<sub>10</sub>(e)
|
||
#[stable(feature = "rust1", since = "1.0.0")]
|
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pub const LOG10_E: f64 = 0.434294481903251827651128918916605082_f64;
|
||
|
||
/// ln(2)
|
||
#[stable(feature = "rust1", since = "1.0.0")]
|
||
pub const LN_2: f64 = 0.693147180559945309417232121458176568_f64;
|
||
|
||
/// ln(10)
|
||
#[stable(feature = "rust1", since = "1.0.0")]
|
||
pub const LN_10: f64 = 2.30258509299404568401799145468436421_f64;
|
||
}
|
||
|
||
impl f64 {
|
||
/// The radix or base of the internal representation of `f64`.
|
||
#[stable(feature = "assoc_int_consts", since = "1.43.0")]
|
||
pub const RADIX: u32 = 2;
|
||
|
||
/// Number of significant digits in base 2.
|
||
///
|
||
/// Note that the size of the mantissa in the bitwise representation is one
|
||
/// smaller than this since the leading 1 is not stored explicitly.
|
||
#[stable(feature = "assoc_int_consts", since = "1.43.0")]
|
||
pub const MANTISSA_DIGITS: u32 = 53;
|
||
/// Approximate number of significant digits in base 10.
|
||
///
|
||
/// This is the maximum <i>x</i> such that any decimal number with <i>x</i>
|
||
/// significant digits can be converted to `f64` and back without loss.
|
||
///
|
||
/// Equal to floor(log<sub>10</sub> 2<sup>[`MANTISSA_DIGITS`] − 1</sup>).
|
||
///
|
||
/// [`MANTISSA_DIGITS`]: f64::MANTISSA_DIGITS
|
||
#[stable(feature = "assoc_int_consts", since = "1.43.0")]
|
||
pub const DIGITS: u32 = 15;
|
||
|
||
/// [Machine epsilon] value for `f64`.
|
||
///
|
||
/// This is the difference between `1.0` and the next larger representable number.
|
||
///
|
||
/// Equal to 2<sup>1 − [`MANTISSA_DIGITS`]</sup>.
|
||
///
|
||
/// [Machine epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon
|
||
/// [`MANTISSA_DIGITS`]: f64::MANTISSA_DIGITS
|
||
#[stable(feature = "assoc_int_consts", since = "1.43.0")]
|
||
#[rustc_diagnostic_item = "f64_epsilon"]
|
||
pub const EPSILON: f64 = 2.2204460492503131e-16_f64;
|
||
|
||
/// Smallest finite `f64` value.
|
||
///
|
||
/// Equal to −[`MAX`].
|
||
///
|
||
/// [`MAX`]: f64::MAX
|
||
#[stable(feature = "assoc_int_consts", since = "1.43.0")]
|
||
pub const MIN: f64 = -1.7976931348623157e+308_f64;
|
||
/// Smallest positive normal `f64` value.
|
||
///
|
||
/// Equal to 2<sup>[`MIN_EXP`] − 1</sup>.
|
||
///
|
||
/// [`MIN_EXP`]: f64::MIN_EXP
|
||
#[stable(feature = "assoc_int_consts", since = "1.43.0")]
|
||
pub const MIN_POSITIVE: f64 = 2.2250738585072014e-308_f64;
|
||
/// Largest finite `f64` value.
|
||
///
|
||
/// Equal to
|
||
/// (1 − 2<sup>−[`MANTISSA_DIGITS`]</sup>) 2<sup>[`MAX_EXP`]</sup>.
|
||
///
|
||
/// [`MANTISSA_DIGITS`]: f64::MANTISSA_DIGITS
|
||
/// [`MAX_EXP`]: f64::MAX_EXP
|
||
#[stable(feature = "assoc_int_consts", since = "1.43.0")]
|
||
pub const MAX: f64 = 1.7976931348623157e+308_f64;
|
||
|
||
/// One greater than the minimum possible *normal* power of 2 exponent
|
||
/// for a significand bounded by 1 ≤ x < 2 (i.e. the IEEE definition).
|
||
///
|
||
/// This corresponds to the exact minimum possible *normal* power of 2 exponent
|
||
/// for a significand bounded by 0.5 ≤ x < 1 (i.e. the C definition).
|
||
/// In other words, all normal numbers representable by this type are
|
||
/// greater than or equal to 0.5 × 2<sup><i>MIN_EXP</i></sup>.
|
||
#[stable(feature = "assoc_int_consts", since = "1.43.0")]
|
||
pub const MIN_EXP: i32 = -1021;
|
||
/// One greater than the maximum possible power of 2 exponent
|
||
/// for a significand bounded by 1 ≤ x < 2 (i.e. the IEEE definition).
|
||
///
|
||
/// This corresponds to the exact maximum possible power of 2 exponent
|
||
/// for a significand bounded by 0.5 ≤ x < 1 (i.e. the C definition).
|
||
/// In other words, all numbers representable by this type are
|
||
/// strictly less than 2<sup><i>MAX_EXP</i></sup>.
|
||
#[stable(feature = "assoc_int_consts", since = "1.43.0")]
|
||
pub const MAX_EXP: i32 = 1024;
|
||
|
||
/// Minimum <i>x</i> for which 10<sup><i>x</i></sup> is normal.
|
||
///
|
||
/// Equal to ceil(log<sub>10</sub> [`MIN_POSITIVE`]).
|
||
///
|
||
/// [`MIN_POSITIVE`]: f64::MIN_POSITIVE
|
||
#[stable(feature = "assoc_int_consts", since = "1.43.0")]
|
||
pub const MIN_10_EXP: i32 = -307;
|
||
/// Maximum <i>x</i> for which 10<sup><i>x</i></sup> is normal.
|
||
///
|
||
/// Equal to floor(log<sub>10</sub> [`MAX`]).
|
||
///
|
||
/// [`MAX`]: f64::MAX
|
||
#[stable(feature = "assoc_int_consts", since = "1.43.0")]
|
||
pub const MAX_10_EXP: i32 = 308;
|
||
|
||
/// Not a Number (NaN).
|
||
///
|
||
/// Note that IEEE 754 doesn't define just a single NaN value; a plethora of bit patterns are
|
||
/// considered to be NaN. Furthermore, the standard makes a difference between a "signaling" and
|
||
/// a "quiet" NaN, and allows inspecting its "payload" (the unspecified bits in the bit pattern)
|
||
/// and its sign. See the [specification of NaN bit patterns](f32#nan-bit-patterns) for more
|
||
/// info.
|
||
///
|
||
/// This constant is guaranteed to be a quiet NaN (on targets that follow the Rust assumptions
|
||
/// that the quiet/signaling bit being set to 1 indicates a quiet NaN). Beyond that, nothing is
|
||
/// guaranteed about the specific bit pattern chosen here: both payload and sign are arbitrary.
|
||
/// The concrete bit pattern may change across Rust versions and target platforms.
|
||
#[rustc_diagnostic_item = "f64_nan"]
|
||
#[stable(feature = "assoc_int_consts", since = "1.43.0")]
|
||
#[allow(clippy::eq_op)]
|
||
pub const NAN: f64 = 0.0_f64 / 0.0_f64;
|
||
/// Infinity (∞).
|
||
#[stable(feature = "assoc_int_consts", since = "1.43.0")]
|
||
pub const INFINITY: f64 = 1.0_f64 / 0.0_f64;
|
||
/// Negative infinity (−∞).
|
||
#[stable(feature = "assoc_int_consts", since = "1.43.0")]
|
||
pub const NEG_INFINITY: f64 = -1.0_f64 / 0.0_f64;
|
||
|
||
/// Sign bit
|
||
pub(crate) const SIGN_MASK: u64 = 0x8000_0000_0000_0000;
|
||
|
||
/// Exponent mask
|
||
pub(crate) const EXP_MASK: u64 = 0x7ff0_0000_0000_0000;
|
||
|
||
/// Mantissa mask
|
||
pub(crate) const MAN_MASK: u64 = 0x000f_ffff_ffff_ffff;
|
||
|
||
/// Minimum representable positive value (min subnormal)
|
||
const TINY_BITS: u64 = 0x1;
|
||
|
||
/// Minimum representable negative value (min negative subnormal)
|
||
const NEG_TINY_BITS: u64 = Self::TINY_BITS | Self::SIGN_MASK;
|
||
|
||
/// Returns `true` if this value is NaN.
|
||
///
|
||
/// ```
|
||
/// let nan = f64::NAN;
|
||
/// let f = 7.0_f64;
|
||
///
|
||
/// assert!(nan.is_nan());
|
||
/// assert!(!f.is_nan());
|
||
/// ```
|
||
#[must_use]
|
||
#[stable(feature = "rust1", since = "1.0.0")]
|
||
#[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
|
||
#[inline]
|
||
#[allow(clippy::eq_op)] // > if you intended to check if the operand is NaN, use `.is_nan()` instead :)
|
||
pub const fn is_nan(self) -> bool {
|
||
self != self
|
||
}
|
||
|
||
/// Returns `true` if this value is positive infinity or negative infinity, and
|
||
/// `false` otherwise.
|
||
///
|
||
/// ```
|
||
/// let f = 7.0f64;
|
||
/// let inf = f64::INFINITY;
|
||
/// let neg_inf = f64::NEG_INFINITY;
|
||
/// let nan = f64::NAN;
|
||
///
|
||
/// assert!(!f.is_infinite());
|
||
/// assert!(!nan.is_infinite());
|
||
///
|
||
/// assert!(inf.is_infinite());
|
||
/// assert!(neg_inf.is_infinite());
|
||
/// ```
|
||
#[must_use]
|
||
#[stable(feature = "rust1", since = "1.0.0")]
|
||
#[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
|
||
#[inline]
|
||
pub const fn is_infinite(self) -> bool {
|
||
// Getting clever with transmutation can result in incorrect answers on some FPUs
|
||
// FIXME: alter the Rust <-> Rust calling convention to prevent this problem.
|
||
// See https://github.com/rust-lang/rust/issues/72327
|
||
(self == f64::INFINITY) | (self == f64::NEG_INFINITY)
|
||
}
|
||
|
||
/// Returns `true` if this number is neither infinite nor NaN.
|
||
///
|
||
/// ```
|
||
/// let f = 7.0f64;
|
||
/// let inf: f64 = f64::INFINITY;
|
||
/// let neg_inf: f64 = f64::NEG_INFINITY;
|
||
/// let nan: f64 = f64::NAN;
|
||
///
|
||
/// assert!(f.is_finite());
|
||
///
|
||
/// assert!(!nan.is_finite());
|
||
/// assert!(!inf.is_finite());
|
||
/// assert!(!neg_inf.is_finite());
|
||
/// ```
|
||
#[must_use]
|
||
#[stable(feature = "rust1", since = "1.0.0")]
|
||
#[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
|
||
#[inline]
|
||
pub const fn is_finite(self) -> bool {
|
||
// There's no need to handle NaN separately: if self is NaN,
|
||
// the comparison is not true, exactly as desired.
|
||
self.abs() < Self::INFINITY
|
||
}
|
||
|
||
/// Returns `true` if the number is [subnormal].
|
||
///
|
||
/// ```
|
||
/// let min = f64::MIN_POSITIVE; // 2.2250738585072014e-308_f64
|
||
/// let max = f64::MAX;
|
||
/// let lower_than_min = 1.0e-308_f64;
|
||
/// let zero = 0.0_f64;
|
||
///
|
||
/// assert!(!min.is_subnormal());
|
||
/// assert!(!max.is_subnormal());
|
||
///
|
||
/// assert!(!zero.is_subnormal());
|
||
/// assert!(!f64::NAN.is_subnormal());
|
||
/// assert!(!f64::INFINITY.is_subnormal());
|
||
/// // Values between `0` and `min` are Subnormal.
|
||
/// assert!(lower_than_min.is_subnormal());
|
||
/// ```
|
||
/// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
|
||
#[must_use]
|
||
#[stable(feature = "is_subnormal", since = "1.53.0")]
|
||
#[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
|
||
#[inline]
|
||
pub const fn is_subnormal(self) -> bool {
|
||
matches!(self.classify(), FpCategory::Subnormal)
|
||
}
|
||
|
||
/// Returns `true` if the number is neither zero, infinite,
|
||
/// [subnormal], or NaN.
|
||
///
|
||
/// ```
|
||
/// let min = f64::MIN_POSITIVE; // 2.2250738585072014e-308f64
|
||
/// let max = f64::MAX;
|
||
/// let lower_than_min = 1.0e-308_f64;
|
||
/// let zero = 0.0f64;
|
||
///
|
||
/// assert!(min.is_normal());
|
||
/// assert!(max.is_normal());
|
||
///
|
||
/// assert!(!zero.is_normal());
|
||
/// assert!(!f64::NAN.is_normal());
|
||
/// assert!(!f64::INFINITY.is_normal());
|
||
/// // Values between `0` and `min` are Subnormal.
|
||
/// assert!(!lower_than_min.is_normal());
|
||
/// ```
|
||
/// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
|
||
#[must_use]
|
||
#[stable(feature = "rust1", since = "1.0.0")]
|
||
#[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
|
||
#[inline]
|
||
pub const fn is_normal(self) -> bool {
|
||
matches!(self.classify(), FpCategory::Normal)
|
||
}
|
||
|
||
/// Returns the floating point category of the number. If only one property
|
||
/// is going to be tested, it is generally faster to use the specific
|
||
/// predicate instead.
|
||
///
|
||
/// ```
|
||
/// use std::num::FpCategory;
|
||
///
|
||
/// let num = 12.4_f64;
|
||
/// let inf = f64::INFINITY;
|
||
///
|
||
/// assert_eq!(num.classify(), FpCategory::Normal);
|
||
/// assert_eq!(inf.classify(), FpCategory::Infinite);
|
||
/// ```
|
||
#[stable(feature = "rust1", since = "1.0.0")]
|
||
#[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
|
||
pub const fn classify(self) -> FpCategory {
|
||
// We used to have complicated logic here that avoids the simple bit-based tests to work
|
||
// around buggy codegen for x87 targets (see
|
||
// https://github.com/rust-lang/rust/issues/114479). However, some LLVM versions later, none
|
||
// of our tests is able to find any difference between the complicated and the naive
|
||
// version, so now we are back to the naive version.
|
||
let b = self.to_bits();
|
||
match (b & Self::MAN_MASK, b & Self::EXP_MASK) {
|
||
(0, Self::EXP_MASK) => FpCategory::Infinite,
|
||
(_, Self::EXP_MASK) => FpCategory::Nan,
|
||
(0, 0) => FpCategory::Zero,
|
||
(_, 0) => FpCategory::Subnormal,
|
||
_ => FpCategory::Normal,
|
||
}
|
||
}
|
||
|
||
/// Returns `true` if `self` has a positive sign, including `+0.0`, NaNs with
|
||
/// positive sign bit and positive infinity.
|
||
///
|
||
/// Note that IEEE 754 doesn't assign any meaning to the sign bit in case of
|
||
/// a NaN, and as Rust doesn't guarantee that the bit pattern of NaNs are
|
||
/// conserved over arithmetic operations, the result of `is_sign_positive` on
|
||
/// a NaN might produce an unexpected or non-portable result. See the [specification
|
||
/// of NaN bit patterns](f32#nan-bit-patterns) for more info. Use `self.signum() == 1.0`
|
||
/// if you need fully portable behavior (will return `false` for all NaNs).
|
||
///
|
||
/// ```
|
||
/// let f = 7.0_f64;
|
||
/// let g = -7.0_f64;
|
||
///
|
||
/// assert!(f.is_sign_positive());
|
||
/// assert!(!g.is_sign_positive());
|
||
/// ```
|
||
#[must_use]
|
||
#[stable(feature = "rust1", since = "1.0.0")]
|
||
#[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
|
||
#[inline]
|
||
pub const fn is_sign_positive(self) -> bool {
|
||
!self.is_sign_negative()
|
||
}
|
||
|
||
#[must_use]
|
||
#[stable(feature = "rust1", since = "1.0.0")]
|
||
#[deprecated(since = "1.0.0", note = "renamed to is_sign_positive")]
|
||
#[inline]
|
||
#[doc(hidden)]
|
||
pub fn is_positive(self) -> bool {
|
||
self.is_sign_positive()
|
||
}
|
||
|
||
/// Returns `true` if `self` has a negative sign, including `-0.0`, NaNs with
|
||
/// negative sign bit and negative infinity.
|
||
///
|
||
/// Note that IEEE 754 doesn't assign any meaning to the sign bit in case of
|
||
/// a NaN, and as Rust doesn't guarantee that the bit pattern of NaNs are
|
||
/// conserved over arithmetic operations, the result of `is_sign_negative` on
|
||
/// a NaN might produce an unexpected or non-portable result. See the [specification
|
||
/// of NaN bit patterns](f32#nan-bit-patterns) for more info. Use `self.signum() == -1.0`
|
||
/// if you need fully portable behavior (will return `false` for all NaNs).
|
||
///
|
||
/// ```
|
||
/// let f = 7.0_f64;
|
||
/// let g = -7.0_f64;
|
||
///
|
||
/// assert!(!f.is_sign_negative());
|
||
/// assert!(g.is_sign_negative());
|
||
/// ```
|
||
#[must_use]
|
||
#[stable(feature = "rust1", since = "1.0.0")]
|
||
#[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
|
||
#[inline]
|
||
pub const fn is_sign_negative(self) -> bool {
|
||
// IEEE754 says: isSignMinus(x) is true if and only if x has negative sign. isSignMinus
|
||
// applies to zeros and NaNs as well.
|
||
self.to_bits() & Self::SIGN_MASK != 0
|
||
}
|
||
|
||
#[must_use]
|
||
#[stable(feature = "rust1", since = "1.0.0")]
|
||
#[deprecated(since = "1.0.0", note = "renamed to is_sign_negative")]
|
||
#[inline]
|
||
#[doc(hidden)]
|
||
pub fn is_negative(self) -> bool {
|
||
self.is_sign_negative()
|
||
}
|
||
|
||
/// Returns the least number greater than `self`.
|
||
///
|
||
/// Let `TINY` be the smallest representable positive `f64`. Then,
|
||
/// - if `self.is_nan()`, this returns `self`;
|
||
/// - if `self` is [`NEG_INFINITY`], this returns [`MIN`];
|
||
/// - if `self` is `-TINY`, this returns -0.0;
|
||
/// - if `self` is -0.0 or +0.0, this returns `TINY`;
|
||
/// - if `self` is [`MAX`] or [`INFINITY`], this returns [`INFINITY`];
|
||
/// - otherwise the unique least value greater than `self` is returned.
|
||
///
|
||
/// The identity `x.next_up() == -(-x).next_down()` holds for all non-NaN `x`. When `x`
|
||
/// is finite `x == x.next_up().next_down()` also holds.
|
||
///
|
||
/// ```rust
|
||
/// // f64::EPSILON is the difference between 1.0 and the next number up.
|
||
/// assert_eq!(1.0f64.next_up(), 1.0 + f64::EPSILON);
|
||
/// // But not for most numbers.
|
||
/// assert!(0.1f64.next_up() < 0.1 + f64::EPSILON);
|
||
/// assert_eq!(9007199254740992f64.next_up(), 9007199254740994.0);
|
||
/// ```
|
||
///
|
||
/// This operation corresponds to IEEE-754 `nextUp`.
|
||
///
|
||
/// [`NEG_INFINITY`]: Self::NEG_INFINITY
|
||
/// [`INFINITY`]: Self::INFINITY
|
||
/// [`MIN`]: Self::MIN
|
||
/// [`MAX`]: Self::MAX
|
||
#[inline]
|
||
#[doc(alias = "nextUp")]
|
||
#[stable(feature = "float_next_up_down", since = "1.86.0")]
|
||
#[rustc_const_stable(feature = "float_next_up_down", since = "1.86.0")]
|
||
pub const fn next_up(self) -> Self {
|
||
// Some targets violate Rust's assumption of IEEE semantics, e.g. by flushing
|
||
// denormals to zero. This is in general unsound and unsupported, but here
|
||
// we do our best to still produce the correct result on such targets.
|
||
let bits = self.to_bits();
|
||
if self.is_nan() || bits == Self::INFINITY.to_bits() {
|
||
return self;
|
||
}
|
||
|
||
let abs = bits & !Self::SIGN_MASK;
|
||
let next_bits = if abs == 0 {
|
||
Self::TINY_BITS
|
||
} else if bits == abs {
|
||
bits + 1
|
||
} else {
|
||
bits - 1
|
||
};
|
||
Self::from_bits(next_bits)
|
||
}
|
||
|
||
/// Returns the greatest number less than `self`.
|
||
///
|
||
/// Let `TINY` be the smallest representable positive `f64`. Then,
|
||
/// - if `self.is_nan()`, this returns `self`;
|
||
/// - if `self` is [`INFINITY`], this returns [`MAX`];
|
||
/// - if `self` is `TINY`, this returns 0.0;
|
||
/// - if `self` is -0.0 or +0.0, this returns `-TINY`;
|
||
/// - if `self` is [`MIN`] or [`NEG_INFINITY`], this returns [`NEG_INFINITY`];
|
||
/// - otherwise the unique greatest value less than `self` is returned.
|
||
///
|
||
/// The identity `x.next_down() == -(-x).next_up()` holds for all non-NaN `x`. When `x`
|
||
/// is finite `x == x.next_down().next_up()` also holds.
|
||
///
|
||
/// ```rust
|
||
/// let x = 1.0f64;
|
||
/// // Clamp value into range [0, 1).
|
||
/// let clamped = x.clamp(0.0, 1.0f64.next_down());
|
||
/// assert!(clamped < 1.0);
|
||
/// assert_eq!(clamped.next_up(), 1.0);
|
||
/// ```
|
||
///
|
||
/// This operation corresponds to IEEE-754 `nextDown`.
|
||
///
|
||
/// [`NEG_INFINITY`]: Self::NEG_INFINITY
|
||
/// [`INFINITY`]: Self::INFINITY
|
||
/// [`MIN`]: Self::MIN
|
||
/// [`MAX`]: Self::MAX
|
||
#[inline]
|
||
#[doc(alias = "nextDown")]
|
||
#[stable(feature = "float_next_up_down", since = "1.86.0")]
|
||
#[rustc_const_stable(feature = "float_next_up_down", since = "1.86.0")]
|
||
pub const fn next_down(self) -> Self {
|
||
// Some targets violate Rust's assumption of IEEE semantics, e.g. by flushing
|
||
// denormals to zero. This is in general unsound and unsupported, but here
|
||
// we do our best to still produce the correct result on such targets.
|
||
let bits = self.to_bits();
|
||
if self.is_nan() || bits == Self::NEG_INFINITY.to_bits() {
|
||
return self;
|
||
}
|
||
|
||
let abs = bits & !Self::SIGN_MASK;
|
||
let next_bits = if abs == 0 {
|
||
Self::NEG_TINY_BITS
|
||
} else if bits == abs {
|
||
bits - 1
|
||
} else {
|
||
bits + 1
|
||
};
|
||
Self::from_bits(next_bits)
|
||
}
|
||
|
||
/// Takes the reciprocal (inverse) of a number, `1/x`.
|
||
///
|
||
/// ```
|
||
/// let x = 2.0_f64;
|
||
/// let abs_difference = (x.recip() - (1.0 / x)).abs();
|
||
///
|
||
/// assert!(abs_difference < 1e-10);
|
||
/// ```
|
||
#[must_use = "this returns the result of the operation, without modifying the original"]
|
||
#[stable(feature = "rust1", since = "1.0.0")]
|
||
#[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
|
||
#[inline]
|
||
pub const fn recip(self) -> f64 {
|
||
1.0 / self
|
||
}
|
||
|
||
/// Converts radians to degrees.
|
||
///
|
||
/// # Unspecified precision
|
||
///
|
||
/// The precision of this function is non-deterministic. This means it varies by platform,
|
||
/// Rust version, and can even differ within the same execution from one invocation to the next.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// let angle = std::f64::consts::PI;
|
||
///
|
||
/// let abs_difference = (angle.to_degrees() - 180.0).abs();
|
||
///
|
||
/// assert!(abs_difference < 1e-10);
|
||
/// ```
|
||
#[must_use = "this returns the result of the operation, \
|
||
without modifying the original"]
|
||
#[stable(feature = "rust1", since = "1.0.0")]
|
||
#[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
|
||
#[inline]
|
||
pub const fn to_degrees(self) -> f64 {
|
||
// The division here is correctly rounded with respect to the true value of 180/π.
|
||
// Although π is irrational and already rounded, the double rounding happens
|
||
// to produce correct result for f64.
|
||
const PIS_IN_180: f64 = 180.0 / consts::PI;
|
||
self * PIS_IN_180
|
||
}
|
||
|
||
/// Converts degrees to radians.
|
||
///
|
||
/// # Unspecified precision
|
||
///
|
||
/// The precision of this function is non-deterministic. This means it varies by platform,
|
||
/// Rust version, and can even differ within the same execution from one invocation to the next.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// let angle = 180.0_f64;
|
||
///
|
||
/// let abs_difference = (angle.to_radians() - std::f64::consts::PI).abs();
|
||
///
|
||
/// assert!(abs_difference < 1e-10);
|
||
/// ```
|
||
#[must_use = "this returns the result of the operation, \
|
||
without modifying the original"]
|
||
#[stable(feature = "rust1", since = "1.0.0")]
|
||
#[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
|
||
#[inline]
|
||
pub const fn to_radians(self) -> f64 {
|
||
// The division here is correctly rounded with respect to the true value of π/180.
|
||
// Although π is irrational and already rounded, the double rounding happens
|
||
// to produce correct result for f64.
|
||
const RADS_PER_DEG: f64 = consts::PI / 180.0;
|
||
self * RADS_PER_DEG
|
||
}
|
||
|
||
/// Returns the maximum of the two numbers, ignoring NaN.
|
||
///
|
||
/// If exactly one of the arguments is NaN (quiet or signaling), then the other argument is
|
||
/// returned. If both arguments are NaN, the return value is NaN, with the bit pattern picked
|
||
/// using the usual [rules for arithmetic operations](f32#nan-bit-patterns). If the inputs
|
||
/// compare equal (such as for the case of `+0.0` and `-0.0`), either input may be returned
|
||
/// non-deterministically.
|
||
///
|
||
/// The handling of NaNs follows the IEEE 754-2019 semantics for `maximumNumber`, treating all
|
||
/// NaNs the same way to ensure the operation is associative. The handling of signed zeros
|
||
/// follows the IEEE 754-2008 semantics for `maxNum`.
|
||
///
|
||
/// ```
|
||
/// let x = 1.0_f64;
|
||
/// let y = 2.0_f64;
|
||
///
|
||
/// assert_eq!(x.max(y), y);
|
||
/// assert_eq!(x.max(f64::NAN), x);
|
||
/// ```
|
||
#[must_use = "this returns the result of the comparison, without modifying either input"]
|
||
#[stable(feature = "rust1", since = "1.0.0")]
|
||
#[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
|
||
#[inline]
|
||
pub const fn max(self, other: f64) -> f64 {
|
||
intrinsics::maxnumf64(self, other)
|
||
}
|
||
|
||
/// Returns the minimum of the two numbers, ignoring NaN.
|
||
///
|
||
/// If exactly one of the arguments is NaN (quiet or signaling), then the other argument is
|
||
/// returned. If both arguments are NaN, the return value is NaN, with the bit pattern picked
|
||
/// using the usual [rules for arithmetic operations](f32#nan-bit-patterns). If the inputs
|
||
/// compare equal (such as for the case of `+0.0` and `-0.0`), either input may be returned
|
||
/// non-deterministically.
|
||
///
|
||
/// The handling of NaNs follows the IEEE 754-2019 semantics for `minimumNumber`, treating all
|
||
/// NaNs the same way to ensure the operation is associative. The handling of signed zeros
|
||
/// follows the IEEE 754-2008 semantics for `minNum`.
|
||
///
|
||
/// ```
|
||
/// let x = 1.0_f64;
|
||
/// let y = 2.0_f64;
|
||
///
|
||
/// assert_eq!(x.min(y), x);
|
||
/// assert_eq!(x.min(f64::NAN), x);
|
||
/// ```
|
||
#[must_use = "this returns the result of the comparison, without modifying either input"]
|
||
#[stable(feature = "rust1", since = "1.0.0")]
|
||
#[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
|
||
#[inline]
|
||
pub const fn min(self, other: f64) -> f64 {
|
||
intrinsics::minnumf64(self, other)
|
||
}
|
||
|
||
/// Returns the maximum of the two numbers, propagating NaN.
|
||
///
|
||
/// If at least one of the arguments is NaN, the return value is NaN, with the bit pattern
|
||
/// picked using the usual [rules for arithmetic operations](f32#nan-bit-patterns). Furthermore,
|
||
/// `-0.0` is considered to be less than `+0.0`, making this function fully deterministic for
|
||
/// non-NaN inputs.
|
||
///
|
||
/// This is in contrast to [`f64::max`] which only returns NaN when *both* arguments are NaN,
|
||
/// and which does not reliably order `-0.0` and `+0.0`.
|
||
///
|
||
/// This follows the IEEE 754-2019 semantics for `maximum`.
|
||
///
|
||
/// ```
|
||
/// #![feature(float_minimum_maximum)]
|
||
/// let x = 1.0_f64;
|
||
/// let y = 2.0_f64;
|
||
///
|
||
/// assert_eq!(x.maximum(y), y);
|
||
/// assert!(x.maximum(f64::NAN).is_nan());
|
||
/// ```
|
||
#[must_use = "this returns the result of the comparison, without modifying either input"]
|
||
#[unstable(feature = "float_minimum_maximum", issue = "91079")]
|
||
#[inline]
|
||
pub const fn maximum(self, other: f64) -> f64 {
|
||
intrinsics::maximumf64(self, other)
|
||
}
|
||
|
||
/// Returns the minimum of the two numbers, propagating NaN.
|
||
///
|
||
/// If at least one of the arguments is NaN, the return value is NaN, with the bit pattern
|
||
/// picked using the usual [rules for arithmetic operations](f32#nan-bit-patterns). Furthermore,
|
||
/// `-0.0` is considered to be less than `+0.0`, making this function fully deterministic for
|
||
/// non-NaN inputs.
|
||
///
|
||
/// This is in contrast to [`f64::min`] which only returns NaN when *both* arguments are NaN,
|
||
/// and which does not reliably order `-0.0` and `+0.0`.
|
||
///
|
||
/// This follows the IEEE 754-2019 semantics for `minimum`.
|
||
///
|
||
/// ```
|
||
/// #![feature(float_minimum_maximum)]
|
||
/// let x = 1.0_f64;
|
||
/// let y = 2.0_f64;
|
||
///
|
||
/// assert_eq!(x.minimum(y), x);
|
||
/// assert!(x.minimum(f64::NAN).is_nan());
|
||
/// ```
|
||
#[must_use = "this returns the result of the comparison, without modifying either input"]
|
||
#[unstable(feature = "float_minimum_maximum", issue = "91079")]
|
||
#[inline]
|
||
pub const fn minimum(self, other: f64) -> f64 {
|
||
intrinsics::minimumf64(self, other)
|
||
}
|
||
|
||
/// Calculates the midpoint (average) between `self` and `rhs`.
|
||
///
|
||
/// This returns NaN when *either* argument is NaN or if a combination of
|
||
/// +inf and -inf is provided as arguments.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// assert_eq!(1f64.midpoint(4.0), 2.5);
|
||
/// assert_eq!((-5.5f64).midpoint(8.0), 1.25);
|
||
/// ```
|
||
#[inline]
|
||
#[doc(alias = "average")]
|
||
#[stable(feature = "num_midpoint", since = "1.85.0")]
|
||
#[rustc_const_stable(feature = "num_midpoint", since = "1.85.0")]
|
||
pub const fn midpoint(self, other: f64) -> f64 {
|
||
const HI: f64 = f64::MAX / 2.;
|
||
|
||
let (a, b) = (self, other);
|
||
let abs_a = a.abs();
|
||
let abs_b = b.abs();
|
||
|
||
if abs_a <= HI && abs_b <= HI {
|
||
// Overflow is impossible
|
||
(a + b) / 2.
|
||
} else {
|
||
(a / 2.) + (b / 2.)
|
||
}
|
||
}
|
||
|
||
/// Rounds toward zero and converts to any primitive integer type,
|
||
/// assuming that the value is finite and fits in that type.
|
||
///
|
||
/// ```
|
||
/// let value = 4.6_f64;
|
||
/// let rounded = unsafe { value.to_int_unchecked::<u16>() };
|
||
/// assert_eq!(rounded, 4);
|
||
///
|
||
/// let value = -128.9_f64;
|
||
/// let rounded = unsafe { value.to_int_unchecked::<i8>() };
|
||
/// assert_eq!(rounded, i8::MIN);
|
||
/// ```
|
||
///
|
||
/// # Safety
|
||
///
|
||
/// The value must:
|
||
///
|
||
/// * Not be `NaN`
|
||
/// * Not be infinite
|
||
/// * Be representable in the return type `Int`, after truncating off its fractional part
|
||
#[must_use = "this returns the result of the operation, \
|
||
without modifying the original"]
|
||
#[stable(feature = "float_approx_unchecked_to", since = "1.44.0")]
|
||
#[inline]
|
||
pub unsafe fn to_int_unchecked<Int>(self) -> Int
|
||
where
|
||
Self: FloatToInt<Int>,
|
||
{
|
||
// SAFETY: the caller must uphold the safety contract for
|
||
// `FloatToInt::to_int_unchecked`.
|
||
unsafe { FloatToInt::<Int>::to_int_unchecked(self) }
|
||
}
|
||
|
||
/// Raw transmutation to `u64`.
|
||
///
|
||
/// This is currently identical to `transmute::<f64, u64>(self)` on all platforms.
|
||
///
|
||
/// See [`from_bits`](Self::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);
|
||
/// ```
|
||
#[must_use = "this returns the result of the operation, \
|
||
without modifying the original"]
|
||
#[stable(feature = "float_bits_conv", since = "1.20.0")]
|
||
#[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
|
||
#[allow(unnecessary_transmutes)]
|
||
#[inline]
|
||
pub const fn to_bits(self) -> u64 {
|
||
// SAFETY: `u64` is a plain old datatype so we can always transmute to it.
|
||
unsafe { mem::transmute(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 favors 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 signaling-ness (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
|
||
///
|
||
/// ```
|
||
/// let v = f64::from_bits(0x4029000000000000);
|
||
/// assert_eq!(v, 12.5);
|
||
/// ```
|
||
#[stable(feature = "float_bits_conv", since = "1.20.0")]
|
||
#[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
|
||
#[must_use]
|
||
#[inline]
|
||
#[allow(unnecessary_transmutes)]
|
||
pub const fn from_bits(v: u64) -> Self {
|
||
// It turns out the safety issues with sNaN were overblown! Hooray!
|
||
// SAFETY: `u64` is a plain old datatype so we can always transmute from it.
|
||
unsafe { mem::transmute(v) }
|
||
}
|
||
|
||
/// Returns the memory representation of this floating point number as a byte array in
|
||
/// big-endian (network) byte order.
|
||
///
|
||
/// See [`from_bits`](Self::from_bits) for some discussion of the
|
||
/// portability of this operation (there are almost no issues).
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// let bytes = 12.5f64.to_be_bytes();
|
||
/// assert_eq!(bytes, [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]);
|
||
/// ```
|
||
#[must_use = "this returns the result of the operation, \
|
||
without modifying the original"]
|
||
#[stable(feature = "float_to_from_bytes", since = "1.40.0")]
|
||
#[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
|
||
#[inline]
|
||
pub const fn to_be_bytes(self) -> [u8; 8] {
|
||
self.to_bits().to_be_bytes()
|
||
}
|
||
|
||
/// Returns the memory representation of this floating point number as a byte array in
|
||
/// little-endian byte order.
|
||
///
|
||
/// See [`from_bits`](Self::from_bits) for some discussion of the
|
||
/// portability of this operation (there are almost no issues).
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// let bytes = 12.5f64.to_le_bytes();
|
||
/// assert_eq!(bytes, [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]);
|
||
/// ```
|
||
#[must_use = "this returns the result of the operation, \
|
||
without modifying the original"]
|
||
#[stable(feature = "float_to_from_bytes", since = "1.40.0")]
|
||
#[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
|
||
#[inline]
|
||
pub const fn to_le_bytes(self) -> [u8; 8] {
|
||
self.to_bits().to_le_bytes()
|
||
}
|
||
|
||
/// Returns the memory representation of this floating point number as a byte array in
|
||
/// native byte order.
|
||
///
|
||
/// As the target platform's native endianness is used, portable code
|
||
/// should use [`to_be_bytes`] or [`to_le_bytes`], as appropriate, instead.
|
||
///
|
||
/// [`to_be_bytes`]: f64::to_be_bytes
|
||
/// [`to_le_bytes`]: f64::to_le_bytes
|
||
///
|
||
/// See [`from_bits`](Self::from_bits) for some discussion of the
|
||
/// portability of this operation (there are almost no issues).
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// let bytes = 12.5f64.to_ne_bytes();
|
||
/// assert_eq!(
|
||
/// bytes,
|
||
/// if cfg!(target_endian = "big") {
|
||
/// [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
|
||
/// } else {
|
||
/// [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]
|
||
/// }
|
||
/// );
|
||
/// ```
|
||
#[must_use = "this returns the result of the operation, \
|
||
without modifying the original"]
|
||
#[stable(feature = "float_to_from_bytes", since = "1.40.0")]
|
||
#[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
|
||
#[inline]
|
||
pub const fn to_ne_bytes(self) -> [u8; 8] {
|
||
self.to_bits().to_ne_bytes()
|
||
}
|
||
|
||
/// Creates a floating point value from its representation as a byte array in big endian.
|
||
///
|
||
/// See [`from_bits`](Self::from_bits) for some discussion of the
|
||
/// portability of this operation (there are almost no issues).
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// let value = f64::from_be_bytes([0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]);
|
||
/// assert_eq!(value, 12.5);
|
||
/// ```
|
||
#[stable(feature = "float_to_from_bytes", since = "1.40.0")]
|
||
#[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
|
||
#[must_use]
|
||
#[inline]
|
||
pub const fn from_be_bytes(bytes: [u8; 8]) -> Self {
|
||
Self::from_bits(u64::from_be_bytes(bytes))
|
||
}
|
||
|
||
/// Creates a floating point value from its representation as a byte array in little endian.
|
||
///
|
||
/// See [`from_bits`](Self::from_bits) for some discussion of the
|
||
/// portability of this operation (there are almost no issues).
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// let value = f64::from_le_bytes([0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]);
|
||
/// assert_eq!(value, 12.5);
|
||
/// ```
|
||
#[stable(feature = "float_to_from_bytes", since = "1.40.0")]
|
||
#[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
|
||
#[must_use]
|
||
#[inline]
|
||
pub const fn from_le_bytes(bytes: [u8; 8]) -> Self {
|
||
Self::from_bits(u64::from_le_bytes(bytes))
|
||
}
|
||
|
||
/// Creates a floating point value from its representation as a byte array in native endian.
|
||
///
|
||
/// As the target platform's native endianness is used, portable code
|
||
/// likely wants to use [`from_be_bytes`] or [`from_le_bytes`], as
|
||
/// appropriate instead.
|
||
///
|
||
/// [`from_be_bytes`]: f64::from_be_bytes
|
||
/// [`from_le_bytes`]: f64::from_le_bytes
|
||
///
|
||
/// See [`from_bits`](Self::from_bits) for some discussion of the
|
||
/// portability of this operation (there are almost no issues).
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// let value = f64::from_ne_bytes(if cfg!(target_endian = "big") {
|
||
/// [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
|
||
/// } else {
|
||
/// [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]
|
||
/// });
|
||
/// assert_eq!(value, 12.5);
|
||
/// ```
|
||
#[stable(feature = "float_to_from_bytes", since = "1.40.0")]
|
||
#[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
|
||
#[must_use]
|
||
#[inline]
|
||
pub const fn from_ne_bytes(bytes: [u8; 8]) -> Self {
|
||
Self::from_bits(u64::from_ne_bytes(bytes))
|
||
}
|
||
|
||
/// Returns the ordering between `self` and `other`.
|
||
///
|
||
/// Unlike the standard partial comparison between floating point numbers,
|
||
/// this comparison always produces an ordering in accordance to
|
||
/// the `totalOrder` predicate as defined in the IEEE 754 (2008 revision)
|
||
/// floating point standard. The values are ordered in the following sequence:
|
||
///
|
||
/// - negative quiet NaN
|
||
/// - negative signaling NaN
|
||
/// - negative infinity
|
||
/// - negative numbers
|
||
/// - negative subnormal numbers
|
||
/// - negative zero
|
||
/// - positive zero
|
||
/// - positive subnormal numbers
|
||
/// - positive numbers
|
||
/// - positive infinity
|
||
/// - positive signaling NaN
|
||
/// - positive quiet NaN.
|
||
///
|
||
/// The ordering established by this function does not always agree with the
|
||
/// [`PartialOrd`] and [`PartialEq`] implementations of `f64`. For example,
|
||
/// they consider negative and positive zero equal, while `total_cmp`
|
||
/// doesn't.
|
||
///
|
||
/// The interpretation of the signaling NaN bit follows the definition in
|
||
/// the IEEE 754 standard, which may not match the interpretation by some of
|
||
/// the older, non-conformant (e.g. MIPS) hardware implementations.
|
||
///
|
||
/// # Example
|
||
///
|
||
/// ```
|
||
/// struct GoodBoy {
|
||
/// name: String,
|
||
/// weight: f64,
|
||
/// }
|
||
///
|
||
/// let mut bois = vec![
|
||
/// GoodBoy { name: "Pucci".to_owned(), weight: 0.1 },
|
||
/// GoodBoy { name: "Woofer".to_owned(), weight: 99.0 },
|
||
/// GoodBoy { name: "Yapper".to_owned(), weight: 10.0 },
|
||
/// GoodBoy { name: "Chonk".to_owned(), weight: f64::INFINITY },
|
||
/// GoodBoy { name: "Abs. Unit".to_owned(), weight: f64::NAN },
|
||
/// GoodBoy { name: "Floaty".to_owned(), weight: -5.0 },
|
||
/// ];
|
||
///
|
||
/// bois.sort_by(|a, b| a.weight.total_cmp(&b.weight));
|
||
///
|
||
/// // `f64::NAN` could be positive or negative, which will affect the sort order.
|
||
/// if f64::NAN.is_sign_negative() {
|
||
/// assert!(bois.into_iter().map(|b| b.weight)
|
||
/// .zip([f64::NAN, -5.0, 0.1, 10.0, 99.0, f64::INFINITY].iter())
|
||
/// .all(|(a, b)| a.to_bits() == b.to_bits()))
|
||
/// } else {
|
||
/// assert!(bois.into_iter().map(|b| b.weight)
|
||
/// .zip([-5.0, 0.1, 10.0, 99.0, f64::INFINITY, f64::NAN].iter())
|
||
/// .all(|(a, b)| a.to_bits() == b.to_bits()))
|
||
/// }
|
||
/// ```
|
||
#[stable(feature = "total_cmp", since = "1.62.0")]
|
||
#[rustc_const_unstable(feature = "const_cmp", issue = "143800")]
|
||
#[must_use]
|
||
#[inline]
|
||
pub const fn total_cmp(&self, other: &Self) -> crate::cmp::Ordering {
|
||
let mut left = self.to_bits() as i64;
|
||
let mut right = other.to_bits() as i64;
|
||
|
||
// In case of negatives, flip all the bits except the sign
|
||
// to achieve a similar layout as two's complement integers
|
||
//
|
||
// Why does this work? IEEE 754 floats consist of three fields:
|
||
// Sign bit, exponent and mantissa. The set of exponent and mantissa
|
||
// fields as a whole have the property that their bitwise order is
|
||
// equal to the numeric magnitude where the magnitude is defined.
|
||
// The magnitude is not normally defined on NaN values, but
|
||
// IEEE 754 totalOrder defines the NaN values also to follow the
|
||
// bitwise order. This leads to order explained in the doc comment.
|
||
// However, the representation of magnitude is the same for negative
|
||
// and positive numbers – only the sign bit is different.
|
||
// To easily compare the floats as signed integers, we need to
|
||
// flip the exponent and mantissa bits in case of negative numbers.
|
||
// We effectively convert the numbers to "two's complement" form.
|
||
//
|
||
// To do the flipping, we construct a mask and XOR against it.
|
||
// We branchlessly calculate an "all-ones except for the sign bit"
|
||
// mask from negative-signed values: right shifting sign-extends
|
||
// the integer, so we "fill" the mask with sign bits, and then
|
||
// convert to unsigned to push one more zero bit.
|
||
// On positive values, the mask is all zeros, so it's a no-op.
|
||
left ^= (((left >> 63) as u64) >> 1) as i64;
|
||
right ^= (((right >> 63) as u64) >> 1) as i64;
|
||
|
||
left.cmp(&right)
|
||
}
|
||
|
||
/// Restrict a value to a certain interval unless it is NaN.
|
||
///
|
||
/// Returns `max` if `self` is greater than `max`, and `min` if `self` is
|
||
/// less than `min`. Otherwise this returns `self`.
|
||
///
|
||
/// Note that this function returns NaN if the initial value was NaN as
|
||
/// well. If the result is zero and among the three inputs `self`, `min`, and `max` there are
|
||
/// zeros with different sign, either `0.0` or `-0.0` is returned non-deterministically.
|
||
///
|
||
/// # Panics
|
||
///
|
||
/// Panics if `min > max`, `min` is NaN, or `max` is NaN.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// assert!((-3.0f64).clamp(-2.0, 1.0) == -2.0);
|
||
/// assert!((0.0f64).clamp(-2.0, 1.0) == 0.0);
|
||
/// assert!((2.0f64).clamp(-2.0, 1.0) == 1.0);
|
||
/// assert!((f64::NAN).clamp(-2.0, 1.0).is_nan());
|
||
///
|
||
/// // These always returns zero, but the sign (which is ignored by `==`) is non-deterministic.
|
||
/// assert!((0.0f64).clamp(-0.0, -0.0) == 0.0);
|
||
/// assert!((1.0f64).clamp(-0.0, 0.0) == 0.0);
|
||
/// // This is definitely a negative zero.
|
||
/// assert!((-1.0f64).clamp(-0.0, 1.0).is_sign_negative());
|
||
/// ```
|
||
#[must_use = "method returns a new number and does not mutate the original value"]
|
||
#[stable(feature = "clamp", since = "1.50.0")]
|
||
#[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
|
||
#[inline]
|
||
pub const fn clamp(mut self, min: f64, max: f64) -> f64 {
|
||
const_assert!(
|
||
min <= max,
|
||
"min > max, or either was NaN",
|
||
"min > max, or either was NaN. min = {min:?}, max = {max:?}",
|
||
min: f64,
|
||
max: f64,
|
||
);
|
||
|
||
if self < min {
|
||
self = min;
|
||
}
|
||
if self > max {
|
||
self = max;
|
||
}
|
||
self
|
||
}
|
||
|
||
/// Clamps this number to a symmetric range centered around zero.
|
||
///
|
||
/// The method clamps the number's magnitude (absolute value) to be at most `limit`.
|
||
///
|
||
/// This is functionally equivalent to `self.clamp(-limit, limit)`, but is more
|
||
/// explicit about the intent.
|
||
///
|
||
/// # Panics
|
||
///
|
||
/// Panics if `limit` is negative or NaN, as this indicates a logic error.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// #![feature(clamp_magnitude)]
|
||
/// assert_eq!(5.0f64.clamp_magnitude(3.0), 3.0);
|
||
/// assert_eq!((-5.0f64).clamp_magnitude(3.0), -3.0);
|
||
/// assert_eq!(2.0f64.clamp_magnitude(3.0), 2.0);
|
||
/// assert_eq!((-2.0f64).clamp_magnitude(3.0), -2.0);
|
||
/// ```
|
||
#[must_use = "this returns the clamped value and does not modify the original"]
|
||
#[unstable(feature = "clamp_magnitude", issue = "148519")]
|
||
#[inline]
|
||
pub fn clamp_magnitude(self, limit: f64) -> f64 {
|
||
assert!(limit >= 0.0, "limit must be non-negative");
|
||
let limit = limit.abs(); // Canonicalises -0.0 to 0.0
|
||
self.clamp(-limit, limit)
|
||
}
|
||
|
||
/// Computes the absolute value of `self`.
|
||
///
|
||
/// This function always returns the precise result.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// let x = 3.5_f64;
|
||
/// let y = -3.5_f64;
|
||
///
|
||
/// assert_eq!(x.abs(), x);
|
||
/// assert_eq!(y.abs(), -y);
|
||
///
|
||
/// assert!(f64::NAN.abs().is_nan());
|
||
/// ```
|
||
#[must_use = "method returns a new number and does not mutate the original value"]
|
||
#[stable(feature = "rust1", since = "1.0.0")]
|
||
#[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
|
||
#[inline]
|
||
pub const fn abs(self) -> f64 {
|
||
intrinsics::fabsf64(self)
|
||
}
|
||
|
||
/// Returns a number that represents the sign of `self`.
|
||
///
|
||
/// - `1.0` if the number is positive, `+0.0` or `INFINITY`
|
||
/// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
|
||
/// - NaN if the number is NaN
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// let f = 3.5_f64;
|
||
///
|
||
/// assert_eq!(f.signum(), 1.0);
|
||
/// assert_eq!(f64::NEG_INFINITY.signum(), -1.0);
|
||
///
|
||
/// assert!(f64::NAN.signum().is_nan());
|
||
/// ```
|
||
#[must_use = "method returns a new number and does not mutate the original value"]
|
||
#[stable(feature = "rust1", since = "1.0.0")]
|
||
#[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
|
||
#[inline]
|
||
pub const fn signum(self) -> f64 {
|
||
if self.is_nan() { Self::NAN } else { 1.0_f64.copysign(self) }
|
||
}
|
||
|
||
/// Returns a number composed of the magnitude of `self` and the sign of
|
||
/// `sign`.
|
||
///
|
||
/// Equal to `self` if the sign of `self` and `sign` are the same, otherwise equal to `-self`.
|
||
/// If `self` is a NaN, then a NaN with the same payload as `self` and the sign bit of `sign` is
|
||
/// returned.
|
||
///
|
||
/// If `sign` is a NaN, then this operation will still carry over its sign into the result. Note
|
||
/// that IEEE 754 doesn't assign any meaning to the sign bit in case of a NaN, and as Rust
|
||
/// doesn't guarantee that the bit pattern of NaNs are conserved over arithmetic operations, the
|
||
/// result of `copysign` with `sign` being a NaN might produce an unexpected or non-portable
|
||
/// result. See the [specification of NaN bit patterns](primitive@f32#nan-bit-patterns) for more
|
||
/// info.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// let f = 3.5_f64;
|
||
///
|
||
/// assert_eq!(f.copysign(0.42), 3.5_f64);
|
||
/// assert_eq!(f.copysign(-0.42), -3.5_f64);
|
||
/// assert_eq!((-f).copysign(0.42), 3.5_f64);
|
||
/// assert_eq!((-f).copysign(-0.42), -3.5_f64);
|
||
///
|
||
/// assert!(f64::NAN.copysign(1.0).is_nan());
|
||
/// ```
|
||
#[must_use = "method returns a new number and does not mutate the original value"]
|
||
#[stable(feature = "copysign", since = "1.35.0")]
|
||
#[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
|
||
#[inline]
|
||
pub const fn copysign(self, sign: f64) -> f64 {
|
||
intrinsics::copysignf64(self, sign)
|
||
}
|
||
|
||
/// Float addition that allows optimizations based on algebraic rules.
|
||
///
|
||
/// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
|
||
#[must_use = "method returns a new number and does not mutate the original value"]
|
||
#[unstable(feature = "float_algebraic", issue = "136469")]
|
||
#[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
|
||
#[inline]
|
||
pub const fn algebraic_add(self, rhs: f64) -> f64 {
|
||
intrinsics::fadd_algebraic(self, rhs)
|
||
}
|
||
|
||
/// Float subtraction that allows optimizations based on algebraic rules.
|
||
///
|
||
/// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
|
||
#[must_use = "method returns a new number and does not mutate the original value"]
|
||
#[unstable(feature = "float_algebraic", issue = "136469")]
|
||
#[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
|
||
#[inline]
|
||
pub const fn algebraic_sub(self, rhs: f64) -> f64 {
|
||
intrinsics::fsub_algebraic(self, rhs)
|
||
}
|
||
|
||
/// Float multiplication that allows optimizations based on algebraic rules.
|
||
///
|
||
/// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
|
||
#[must_use = "method returns a new number and does not mutate the original value"]
|
||
#[unstable(feature = "float_algebraic", issue = "136469")]
|
||
#[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
|
||
#[inline]
|
||
pub const fn algebraic_mul(self, rhs: f64) -> f64 {
|
||
intrinsics::fmul_algebraic(self, rhs)
|
||
}
|
||
|
||
/// Float division that allows optimizations based on algebraic rules.
|
||
///
|
||
/// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
|
||
#[must_use = "method returns a new number and does not mutate the original value"]
|
||
#[unstable(feature = "float_algebraic", issue = "136469")]
|
||
#[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
|
||
#[inline]
|
||
pub const fn algebraic_div(self, rhs: f64) -> f64 {
|
||
intrinsics::fdiv_algebraic(self, rhs)
|
||
}
|
||
|
||
/// Float remainder that allows optimizations based on algebraic rules.
|
||
///
|
||
/// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
|
||
#[must_use = "method returns a new number and does not mutate the original value"]
|
||
#[unstable(feature = "float_algebraic", issue = "136469")]
|
||
#[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
|
||
#[inline]
|
||
pub const fn algebraic_rem(self, rhs: f64) -> f64 {
|
||
intrinsics::frem_algebraic(self, rhs)
|
||
}
|
||
}
|
||
|
||
#[unstable(feature = "core_float_math", issue = "137578")]
|
||
/// Experimental implementations of floating point functions in `core`.
|
||
///
|
||
/// _The standalone functions in this module are for testing only.
|
||
/// They will be stabilized as inherent methods._
|
||
pub mod math {
|
||
use crate::intrinsics;
|
||
use crate::num::libm;
|
||
|
||
/// Experimental version of `floor` in `core`. See [`f64::floor`] for details.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// #![feature(core_float_math)]
|
||
///
|
||
/// use core::f64;
|
||
///
|
||
/// let f = 3.7_f64;
|
||
/// let g = 3.0_f64;
|
||
/// let h = -3.7_f64;
|
||
///
|
||
/// assert_eq!(f64::math::floor(f), 3.0);
|
||
/// assert_eq!(f64::math::floor(g), 3.0);
|
||
/// assert_eq!(f64::math::floor(h), -4.0);
|
||
/// ```
|
||
///
|
||
/// _This standalone function is for testing only.
|
||
/// It will be stabilized as an inherent method._
|
||
///
|
||
/// [`f64::floor`]: ../../../std/primitive.f64.html#method.floor
|
||
#[inline]
|
||
#[unstable(feature = "core_float_math", issue = "137578")]
|
||
#[must_use = "method returns a new number and does not mutate the original value"]
|
||
pub const fn floor(x: f64) -> f64 {
|
||
intrinsics::floorf64(x)
|
||
}
|
||
|
||
/// Experimental version of `ceil` in `core`. See [`f64::ceil`] for details.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// #![feature(core_float_math)]
|
||
///
|
||
/// use core::f64;
|
||
///
|
||
/// let f = 3.01_f64;
|
||
/// let g = 4.0_f64;
|
||
///
|
||
/// assert_eq!(f64::math::ceil(f), 4.0);
|
||
/// assert_eq!(f64::math::ceil(g), 4.0);
|
||
/// ```
|
||
///
|
||
/// _This standalone function is for testing only.
|
||
/// It will be stabilized as an inherent method._
|
||
///
|
||
/// [`f64::ceil`]: ../../../std/primitive.f64.html#method.ceil
|
||
#[inline]
|
||
#[doc(alias = "ceiling")]
|
||
#[unstable(feature = "core_float_math", issue = "137578")]
|
||
#[must_use = "method returns a new number and does not mutate the original value"]
|
||
pub const fn ceil(x: f64) -> f64 {
|
||
intrinsics::ceilf64(x)
|
||
}
|
||
|
||
/// Experimental version of `round` in `core`. See [`f64::round`] for details.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// #![feature(core_float_math)]
|
||
///
|
||
/// use core::f64;
|
||
///
|
||
/// let f = 3.3_f64;
|
||
/// let g = -3.3_f64;
|
||
/// let h = -3.7_f64;
|
||
/// let i = 3.5_f64;
|
||
/// let j = 4.5_f64;
|
||
///
|
||
/// assert_eq!(f64::math::round(f), 3.0);
|
||
/// assert_eq!(f64::math::round(g), -3.0);
|
||
/// assert_eq!(f64::math::round(h), -4.0);
|
||
/// assert_eq!(f64::math::round(i), 4.0);
|
||
/// assert_eq!(f64::math::round(j), 5.0);
|
||
/// ```
|
||
///
|
||
/// _This standalone function is for testing only.
|
||
/// It will be stabilized as an inherent method._
|
||
///
|
||
/// [`f64::round`]: ../../../std/primitive.f64.html#method.round
|
||
#[inline]
|
||
#[unstable(feature = "core_float_math", issue = "137578")]
|
||
#[must_use = "method returns a new number and does not mutate the original value"]
|
||
pub const fn round(x: f64) -> f64 {
|
||
intrinsics::roundf64(x)
|
||
}
|
||
|
||
/// Experimental version of `round_ties_even` in `core`. See [`f64::round_ties_even`] for
|
||
/// details.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// #![feature(core_float_math)]
|
||
///
|
||
/// use core::f64;
|
||
///
|
||
/// let f = 3.3_f64;
|
||
/// let g = -3.3_f64;
|
||
/// let h = 3.5_f64;
|
||
/// let i = 4.5_f64;
|
||
///
|
||
/// assert_eq!(f64::math::round_ties_even(f), 3.0);
|
||
/// assert_eq!(f64::math::round_ties_even(g), -3.0);
|
||
/// assert_eq!(f64::math::round_ties_even(h), 4.0);
|
||
/// assert_eq!(f64::math::round_ties_even(i), 4.0);
|
||
/// ```
|
||
///
|
||
/// _This standalone function is for testing only.
|
||
/// It will be stabilized as an inherent method._
|
||
///
|
||
/// [`f64::round_ties_even`]: ../../../std/primitive.f64.html#method.round_ties_even
|
||
#[inline]
|
||
#[unstable(feature = "core_float_math", issue = "137578")]
|
||
#[must_use = "method returns a new number and does not mutate the original value"]
|
||
pub const fn round_ties_even(x: f64) -> f64 {
|
||
intrinsics::round_ties_even_f64(x)
|
||
}
|
||
|
||
/// Experimental version of `trunc` in `core`. See [`f64::trunc`] for details.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// #![feature(core_float_math)]
|
||
///
|
||
/// use core::f64;
|
||
///
|
||
/// let f = 3.7_f64;
|
||
/// let g = 3.0_f64;
|
||
/// let h = -3.7_f64;
|
||
///
|
||
/// assert_eq!(f64::math::trunc(f), 3.0);
|
||
/// assert_eq!(f64::math::trunc(g), 3.0);
|
||
/// assert_eq!(f64::math::trunc(h), -3.0);
|
||
/// ```
|
||
///
|
||
/// _This standalone function is for testing only.
|
||
/// It will be stabilized as an inherent method._
|
||
///
|
||
/// [`f64::trunc`]: ../../../std/primitive.f64.html#method.trunc
|
||
#[inline]
|
||
#[doc(alias = "truncate")]
|
||
#[unstable(feature = "core_float_math", issue = "137578")]
|
||
#[must_use = "method returns a new number and does not mutate the original value"]
|
||
pub const fn trunc(x: f64) -> f64 {
|
||
intrinsics::truncf64(x)
|
||
}
|
||
|
||
/// Experimental version of `fract` in `core`. See [`f64::fract`] for details.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// #![feature(core_float_math)]
|
||
///
|
||
/// use core::f64;
|
||
///
|
||
/// let x = 3.6_f64;
|
||
/// let y = -3.6_f64;
|
||
/// let abs_difference_x = (f64::math::fract(x) - 0.6).abs();
|
||
/// let abs_difference_y = (f64::math::fract(y) - (-0.6)).abs();
|
||
///
|
||
/// assert!(abs_difference_x < 1e-10);
|
||
/// assert!(abs_difference_y < 1e-10);
|
||
/// ```
|
||
///
|
||
/// _This standalone function is for testing only.
|
||
/// It will be stabilized as an inherent method._
|
||
///
|
||
/// [`f64::fract`]: ../../../std/primitive.f64.html#method.fract
|
||
#[inline]
|
||
#[unstable(feature = "core_float_math", issue = "137578")]
|
||
#[must_use = "method returns a new number and does not mutate the original value"]
|
||
pub const fn fract(x: f64) -> f64 {
|
||
x - trunc(x)
|
||
}
|
||
|
||
/// Experimental version of `mul_add` in `core`. See [`f64::mul_add`] for details.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// #![feature(core_float_math)]
|
||
///
|
||
/// # // FIXME(#140515): mingw has an incorrect fma
|
||
/// # // https://sourceforge.net/p/mingw-w64/bugs/848/
|
||
/// # #[cfg(all(target_os = "windows", target_env = "gnu", not(target_abi = "llvm")))] {
|
||
/// use core::f64;
|
||
///
|
||
/// let m = 10.0_f64;
|
||
/// let x = 4.0_f64;
|
||
/// let b = 60.0_f64;
|
||
///
|
||
/// assert_eq!(f64::math::mul_add(m, x, b), 100.0);
|
||
/// assert_eq!(m * x + b, 100.0);
|
||
///
|
||
/// let one_plus_eps = 1.0_f64 + f64::EPSILON;
|
||
/// let one_minus_eps = 1.0_f64 - f64::EPSILON;
|
||
/// let minus_one = -1.0_f64;
|
||
///
|
||
/// // The exact result (1 + eps) * (1 - eps) = 1 - eps * eps.
|
||
/// assert_eq!(
|
||
/// f64::math::mul_add(one_plus_eps, one_minus_eps, minus_one),
|
||
/// -f64::EPSILON * f64::EPSILON
|
||
/// );
|
||
/// // Different rounding with the non-fused multiply and add.
|
||
/// assert_eq!(one_plus_eps * one_minus_eps + minus_one, 0.0);
|
||
/// # }
|
||
/// ```
|
||
///
|
||
/// _This standalone function is for testing only.
|
||
/// It will be stabilized as an inherent method._
|
||
///
|
||
/// [`f64::mul_add`]: ../../../std/primitive.f64.html#method.mul_add
|
||
#[inline]
|
||
#[doc(alias = "fma", alias = "fusedMultiplyAdd")]
|
||
#[unstable(feature = "core_float_math", issue = "137578")]
|
||
#[must_use = "method returns a new number and does not mutate the original value"]
|
||
pub const fn mul_add(x: f64, a: f64, b: f64) -> f64 {
|
||
intrinsics::fmaf64(x, a, b)
|
||
}
|
||
|
||
/// Experimental version of `div_euclid` in `core`. See [`f64::div_euclid`] for details.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// #![feature(core_float_math)]
|
||
///
|
||
/// use core::f64;
|
||
///
|
||
/// let a: f64 = 7.0;
|
||
/// let b = 4.0;
|
||
/// assert_eq!(f64::math::div_euclid(a, b), 1.0); // 7.0 > 4.0 * 1.0
|
||
/// assert_eq!(f64::math::div_euclid(-a, b), -2.0); // -7.0 >= 4.0 * -2.0
|
||
/// assert_eq!(f64::math::div_euclid(a, -b), -1.0); // 7.0 >= -4.0 * -1.0
|
||
/// assert_eq!(f64::math::div_euclid(-a, -b), 2.0); // -7.0 >= -4.0 * 2.0
|
||
/// ```
|
||
///
|
||
/// _This standalone function is for testing only.
|
||
/// It will be stabilized as an inherent method._
|
||
///
|
||
/// [`f64::div_euclid`]: ../../../std/primitive.f64.html#method.div_euclid
|
||
#[inline]
|
||
#[unstable(feature = "core_float_math", issue = "137578")]
|
||
#[must_use = "method returns a new number and does not mutate the original value"]
|
||
pub fn div_euclid(x: f64, rhs: f64) -> f64 {
|
||
let q = trunc(x / rhs);
|
||
if x % rhs < 0.0 {
|
||
return if rhs > 0.0 { q - 1.0 } else { q + 1.0 };
|
||
}
|
||
q
|
||
}
|
||
|
||
/// Experimental version of `rem_euclid` in `core`. See [`f64::rem_euclid`] for details.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// #![feature(core_float_math)]
|
||
///
|
||
/// use core::f64;
|
||
///
|
||
/// let a: f64 = 7.0;
|
||
/// let b = 4.0;
|
||
/// assert_eq!(f64::math::rem_euclid(a, b), 3.0);
|
||
/// assert_eq!(f64::math::rem_euclid(-a, b), 1.0);
|
||
/// assert_eq!(f64::math::rem_euclid(a, -b), 3.0);
|
||
/// assert_eq!(f64::math::rem_euclid(-a, -b), 1.0);
|
||
/// // limitation due to round-off error
|
||
/// assert!(f64::math::rem_euclid(-f64::EPSILON, 3.0) != 0.0);
|
||
/// ```
|
||
///
|
||
/// _This standalone function is for testing only.
|
||
/// It will be stabilized as an inherent method._
|
||
///
|
||
/// [`f64::rem_euclid`]: ../../../std/primitive.f64.html#method.rem_euclid
|
||
#[inline]
|
||
#[doc(alias = "modulo", alias = "mod")]
|
||
#[unstable(feature = "core_float_math", issue = "137578")]
|
||
#[must_use = "method returns a new number and does not mutate the original value"]
|
||
pub fn rem_euclid(x: f64, rhs: f64) -> f64 {
|
||
let r = x % rhs;
|
||
if r < 0.0 { r + rhs.abs() } else { r }
|
||
}
|
||
|
||
/// Experimental version of `powi` in `core`. See [`f64::powi`] for details.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// #![feature(core_float_math)]
|
||
///
|
||
/// use core::f64;
|
||
///
|
||
/// let x = 2.0_f64;
|
||
/// let abs_difference = (f64::math::powi(x, 2) - (x * x)).abs();
|
||
/// assert!(abs_difference <= 1e-6);
|
||
///
|
||
/// assert_eq!(f64::math::powi(f64::NAN, 0), 1.0);
|
||
/// ```
|
||
///
|
||
/// _This standalone function is for testing only.
|
||
/// It will be stabilized as an inherent method._
|
||
///
|
||
/// [`f64::powi`]: ../../../std/primitive.f64.html#method.powi
|
||
#[inline]
|
||
#[unstable(feature = "core_float_math", issue = "137578")]
|
||
#[must_use = "method returns a new number and does not mutate the original value"]
|
||
pub fn powi(x: f64, n: i32) -> f64 {
|
||
intrinsics::powif64(x, n)
|
||
}
|
||
|
||
/// Experimental version of `sqrt` in `core`. See [`f64::sqrt`] for details.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// #![feature(core_float_math)]
|
||
///
|
||
/// use core::f64;
|
||
///
|
||
/// let positive = 4.0_f64;
|
||
/// let negative = -4.0_f64;
|
||
/// let negative_zero = -0.0_f64;
|
||
///
|
||
/// assert_eq!(f64::math::sqrt(positive), 2.0);
|
||
/// assert!(f64::math::sqrt(negative).is_nan());
|
||
/// assert_eq!(f64::math::sqrt(negative_zero), negative_zero);
|
||
/// ```
|
||
///
|
||
/// _This standalone function is for testing only.
|
||
/// It will be stabilized as an inherent method._
|
||
///
|
||
/// [`f64::sqrt`]: ../../../std/primitive.f64.html#method.sqrt
|
||
#[inline]
|
||
#[doc(alias = "squareRoot")]
|
||
#[unstable(feature = "core_float_math", issue = "137578")]
|
||
#[must_use = "method returns a new number and does not mutate the original value"]
|
||
pub fn sqrt(x: f64) -> f64 {
|
||
intrinsics::sqrtf64(x)
|
||
}
|
||
|
||
/// Experimental version of `abs_sub` in `core`. See [`f64::abs_sub`] for details.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// #![feature(core_float_math)]
|
||
///
|
||
/// use core::f64;
|
||
///
|
||
/// let x = 3.0_f64;
|
||
/// let y = -3.0_f64;
|
||
///
|
||
/// let abs_difference_x = (f64::math::abs_sub(x, 1.0) - 2.0).abs();
|
||
/// let abs_difference_y = (f64::math::abs_sub(y, 1.0) - 0.0).abs();
|
||
///
|
||
/// assert!(abs_difference_x < 1e-10);
|
||
/// assert!(abs_difference_y < 1e-10);
|
||
/// ```
|
||
///
|
||
/// _This standalone function is for testing only.
|
||
/// It will be stabilized as an inherent method._
|
||
///
|
||
/// [`f64::abs_sub`]: ../../../std/primitive.f64.html#method.abs_sub
|
||
#[inline]
|
||
#[unstable(feature = "core_float_math", issue = "137578")]
|
||
#[deprecated(
|
||
since = "1.10.0",
|
||
note = "you probably meant `(self - other).abs()`: \
|
||
this operation is `(self - other).max(0.0)` \
|
||
except that `abs_sub` also propagates NaNs (also \
|
||
known as `fdim` in C). If you truly need the positive \
|
||
difference, consider using that expression or the C function \
|
||
`fdim`, depending on how you wish to handle NaN (please consider \
|
||
filing an issue describing your use-case too)."
|
||
)]
|
||
#[must_use = "method returns a new number and does not mutate the original value"]
|
||
pub fn abs_sub(x: f64, other: f64) -> f64 {
|
||
libm::fdim(x, other)
|
||
}
|
||
|
||
/// Experimental version of `cbrt` in `core`. See [`f64::cbrt`] for details.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// #![feature(core_float_math)]
|
||
///
|
||
/// use core::f64;
|
||
///
|
||
/// let x = 8.0_f64;
|
||
///
|
||
/// // x^(1/3) - 2 == 0
|
||
/// let abs_difference = (f64::math::cbrt(x) - 2.0).abs();
|
||
///
|
||
/// assert!(abs_difference < 1e-10);
|
||
/// ```
|
||
///
|
||
/// _This standalone function is for testing only.
|
||
/// It will be stabilized as an inherent method._
|
||
///
|
||
/// [`f64::cbrt`]: ../../../std/primitive.f64.html#method.cbrt
|
||
#[inline]
|
||
#[unstable(feature = "core_float_math", issue = "137578")]
|
||
#[must_use = "method returns a new number and does not mutate the original value"]
|
||
pub fn cbrt(x: f64) -> f64 {
|
||
libm::cbrt(x)
|
||
}
|
||
}
|