886 lines
28 KiB
Rust
886 lines
28 KiB
Rust
//! This module provides constants which are specific to the implementation
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//! of the `f32` floating point data type.
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//!
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//! *[See also the `f32` primitive type](../../std/primitive.f32.html).*
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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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//! Although using these constants won’t cause compilation warnings,
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//! new code should use the associated constants directly on the primitive type.
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#![stable(feature = "rust1", since = "1.0.0")]
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use crate::convert::FloatToInt;
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#[cfg(not(test))]
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use crate::intrinsics;
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use crate::mem;
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use crate::num::FpCategory;
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/// The radix or base of the internal representation of `f32`.
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/// Use [`f32::RADIX`](../../std/primitive.f32.html#associatedconstant.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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/// let r = std::f32::RADIX;
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///
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/// // intended way
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/// let r = f32::RADIX;
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const RADIX: u32 = f32::RADIX;
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/// Number of significant digits in base 2.
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/// Use [`f32::MANTISSA_DIGITS`](../../std/primitive.f32.html#associatedconstant.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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/// let d = std::f32::MANTISSA_DIGITS;
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///
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/// // intended way
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/// let d = f32::MANTISSA_DIGITS;
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const MANTISSA_DIGITS: u32 = f32::MANTISSA_DIGITS;
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/// Approximate number of significant digits in base 10.
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/// Use [`f32::DIGITS`](../../std/primitive.f32.html#associatedconstant.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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/// let d = std::f32::DIGITS;
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///
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/// // intended way
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/// let d = f32::DIGITS;
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const DIGITS: u32 = f32::DIGITS;
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/// [Machine epsilon] value for `f32`.
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/// Use [`f32::EPSILON`](../../std/primitive.f32.html#associatedconstant.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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/// let e = std::f32::EPSILON;
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///
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/// // intended way
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/// let e = f32::EPSILON;
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const EPSILON: f32 = f32::EPSILON;
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/// Smallest finite `f32` value.
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/// Use [`f32::MIN`](../../std/primitive.f32.html#associatedconstant.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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/// let min = std::f32::MIN;
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///
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/// // intended way
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/// let min = f32::MIN;
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const MIN: f32 = f32::MIN;
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/// Smallest positive normal `f32` value.
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/// Use [`f32::MIN_POSITIVE`](../../std/primitive.f32.html#associatedconstant.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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/// let min = std::f32::MIN_POSITIVE;
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///
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/// // intended way
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/// let min = f32::MIN_POSITIVE;
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const MIN_POSITIVE: f32 = f32::MIN_POSITIVE;
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/// Largest finite `f32` value.
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/// Use [`f32::MAX`](../../std/primitive.f32.html#associatedconstant.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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/// let max = std::f32::MAX;
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///
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/// // intended way
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/// let max = f32::MAX;
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const MAX: f32 = f32::MAX;
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/// One greater than the minimum possible normal power of 2 exponent.
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/// Use [`f32::MIN_EXP`](../../std/primitive.f32.html#associatedconstant.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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/// let min = std::f32::MIN_EXP;
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///
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/// // intended way
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/// let min = f32::MIN_EXP;
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const MIN_EXP: i32 = f32::MIN_EXP;
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/// Maximum possible power of 2 exponent.
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/// Use [`f32::MAX_EXP`](../../std/primitive.f32.html#associatedconstant.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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/// let max = std::f32::MAX_EXP;
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///
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/// // intended way
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/// let max = f32::MAX_EXP;
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const MAX_EXP: i32 = f32::MAX_EXP;
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/// Minimum possible normal power of 10 exponent.
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/// Use [`f32::MIN_10_EXP`](../../std/primitive.f32.html#associatedconstant.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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/// let min = std::f32::MIN_10_EXP;
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///
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/// // intended way
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/// let min = f32::MIN_10_EXP;
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const MIN_10_EXP: i32 = f32::MIN_10_EXP;
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/// Maximum possible power of 10 exponent.
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/// Use [`f32::MAX_10_EXP`](../../std/primitive.f32.html#associatedconstant.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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/// let max = std::f32::MAX_10_EXP;
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///
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/// // intended way
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/// let max = f32::MAX_10_EXP;
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const MAX_10_EXP: i32 = f32::MAX_10_EXP;
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/// Not a Number (NaN).
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/// Use [`f32::NAN`](../../std/primitive.f32.html#associatedconstant.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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/// let nan = std::f32::NAN;
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///
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/// // intended way
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/// let nan = f32::NAN;
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const NAN: f32 = f32::NAN;
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/// Infinity (∞).
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/// Use [`f32::INFINITY`](../../std/primitive.f32.html#associatedconstant.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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/// let inf = std::f32::INFINITY;
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///
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/// // intended way
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/// let inf = f32::INFINITY;
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const INFINITY: f32 = f32::INFINITY;
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/// Negative infinity (−∞).
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/// Use [`f32::NEG_INFINITY`](../../std/primitive.f32.html#associatedconstant.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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/// let ninf = std::f32::NEG_INFINITY;
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///
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/// // intended way
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/// let ninf = f32::NEG_INFINITY;
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const NEG_INFINITY: f32 = f32::NEG_INFINITY;
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/// Basic mathematical constants.
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#[stable(feature = "rust1", since = "1.0.0")]
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pub mod consts {
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// FIXME: replace with mathematical constants from cmath.
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/// Archimedes' constant (π)
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const PI: f32 = 3.14159265358979323846264338327950288_f32;
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/// The full circle constant (τ)
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///
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/// Equal to 2π.
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#[unstable(feature = "tau_constant", issue = "66770")]
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pub const TAU: f32 = 6.28318530717958647692528676655900577_f32;
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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: f32 = 1.57079632679489661923132169163975144_f32;
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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: f32 = 1.04719755119659774615421446109316763_f32;
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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: f32 = 0.785398163397448309615660845819875721_f32;
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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: f32 = 0.52359877559829887307710723054658381_f32;
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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: f32 = 0.39269908169872415480783042290993786_f32;
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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: f32 = 0.318309886183790671537767526745028724_f32;
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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: f32 = 0.636619772367581343075535053490057448_f32;
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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: f32 = 1.12837916709551257389615890312154517_f32;
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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: f32 = 1.41421356237309504880168872420969808_f32;
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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: f32 = 0.707106781186547524400844362104849039_f32;
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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: f32 = 2.71828182845904523536028747135266250_f32;
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/// log<sub>2</sub>(e)
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const LOG2_E: f32 = 1.44269504088896340735992468100189214_f32;
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/// 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: f32 = 3.32192809488736234787031942948939018_f32;
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/// log<sub>10</sub>(e)
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const LOG10_E: f32 = 0.434294481903251827651128918916605082_f32;
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/// log<sub>10</sub>(2)
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#[stable(feature = "extra_log_consts", since = "1.43.0")]
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pub const LOG10_2: f32 = 0.301029995663981195213738894724493027_f32;
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/// ln(2)
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const LN_2: f32 = 0.693147180559945309417232121458176568_f32;
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/// ln(10)
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#[stable(feature = "rust1", since = "1.0.0")]
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pub const LN_10: f32 = 2.30258509299404568401799145468436421_f32;
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}
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#[lang = "f32"]
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#[cfg(not(test))]
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impl f32 {
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/// The radix or base of the internal representation of `f32`.
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#[stable(feature = "assoc_int_consts", since = "1.43.0")]
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pub const RADIX: u32 = 2;
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/// Number of significant digits in base 2.
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#[stable(feature = "assoc_int_consts", since = "1.43.0")]
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pub const MANTISSA_DIGITS: u32 = 24;
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/// Approximate number of significant digits in base 10.
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#[stable(feature = "assoc_int_consts", since = "1.43.0")]
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pub const DIGITS: u32 = 6;
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/// [Machine epsilon] value for `f32`.
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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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#[stable(feature = "assoc_int_consts", since = "1.43.0")]
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pub const EPSILON: f32 = 1.19209290e-07_f32;
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/// Smallest finite `f32` value.
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#[stable(feature = "assoc_int_consts", since = "1.43.0")]
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pub const MIN: f32 = -3.40282347e+38_f32;
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/// Smallest positive normal `f32` value.
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#[stable(feature = "assoc_int_consts", since = "1.43.0")]
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pub const MIN_POSITIVE: f32 = 1.17549435e-38_f32;
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/// Largest finite `f32` value.
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#[stable(feature = "assoc_int_consts", since = "1.43.0")]
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pub const MAX: f32 = 3.40282347e+38_f32;
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/// One greater than the minimum possible normal power of 2 exponent.
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#[stable(feature = "assoc_int_consts", since = "1.43.0")]
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pub const MIN_EXP: i32 = -125;
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/// Maximum possible power of 2 exponent.
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#[stable(feature = "assoc_int_consts", since = "1.43.0")]
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pub const MAX_EXP: i32 = 128;
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/// Minimum possible normal power of 10 exponent.
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#[stable(feature = "assoc_int_consts", since = "1.43.0")]
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pub const MIN_10_EXP: i32 = -37;
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/// Maximum possible power of 10 exponent.
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#[stable(feature = "assoc_int_consts", since = "1.43.0")]
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pub const MAX_10_EXP: i32 = 38;
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/// Not a Number (NaN).
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#[stable(feature = "assoc_int_consts", since = "1.43.0")]
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pub const NAN: f32 = 0.0_f32 / 0.0_f32;
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/// Infinity (∞).
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#[stable(feature = "assoc_int_consts", since = "1.43.0")]
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pub const INFINITY: f32 = 1.0_f32 / 0.0_f32;
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/// Negative infinity (−∞).
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#[stable(feature = "assoc_int_consts", since = "1.43.0")]
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pub const NEG_INFINITY: f32 = -1.0_f32 / 0.0_f32;
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/// Returns `true` if this value is `NaN`.
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///
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/// ```
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/// let nan = f32::NAN;
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/// let f = 7.0_f32;
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///
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/// assert!(nan.is_nan());
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/// assert!(!f.is_nan());
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn is_nan(self) -> bool {
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self != self
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}
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// FIXME(#50145): `abs` is publicly unavailable in libcore due to
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// concerns about portability, so this implementation is for
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// private use internally.
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#[inline]
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fn abs_private(self) -> f32 {
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f32::from_bits(self.to_bits() & 0x7fff_ffff)
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}
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/// Returns `true` if this value is positive infinity or negative infinity, and
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/// `false` otherwise.
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///
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/// ```
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/// let f = 7.0f32;
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/// let inf = f32::INFINITY;
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/// let neg_inf = f32::NEG_INFINITY;
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/// let nan = f32::NAN;
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///
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/// assert!(!f.is_infinite());
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/// assert!(!nan.is_infinite());
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///
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/// assert!(inf.is_infinite());
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/// assert!(neg_inf.is_infinite());
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn is_infinite(self) -> bool {
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self.abs_private() == Self::INFINITY
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}
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/// Returns `true` if this number is neither infinite nor `NaN`.
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///
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/// ```
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/// let f = 7.0f32;
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/// let inf = f32::INFINITY;
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/// let neg_inf = f32::NEG_INFINITY;
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/// let nan = f32::NAN;
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///
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/// assert!(f.is_finite());
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///
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/// assert!(!nan.is_finite());
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/// assert!(!inf.is_finite());
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/// assert!(!neg_inf.is_finite());
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn is_finite(self) -> bool {
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// There's no need to handle NaN separately: if self is NaN,
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// the comparison is not true, exactly as desired.
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self.abs_private() < Self::INFINITY
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}
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/// Returns `true` if the number is neither zero, infinite,
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/// [subnormal], or `NaN`.
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///
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/// ```
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/// let min = f32::MIN_POSITIVE; // 1.17549435e-38f32
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/// let max = f32::MAX;
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/// let lower_than_min = 1.0e-40_f32;
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/// let zero = 0.0_f32;
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///
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/// assert!(min.is_normal());
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/// assert!(max.is_normal());
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///
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/// assert!(!zero.is_normal());
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/// assert!(!f32::NAN.is_normal());
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/// assert!(!f32::INFINITY.is_normal());
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/// // Values between `0` and `min` are Subnormal.
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/// assert!(!lower_than_min.is_normal());
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/// ```
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/// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
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#[stable(feature = "rust1", since = "1.0.0")]
|
||
#[inline]
|
||
pub fn is_normal(self) -> bool {
|
||
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_f32;
|
||
/// let inf = f32::INFINITY;
|
||
///
|
||
/// assert_eq!(num.classify(), FpCategory::Normal);
|
||
/// assert_eq!(inf.classify(), FpCategory::Infinite);
|
||
/// ```
|
||
#[stable(feature = "rust1", since = "1.0.0")]
|
||
pub fn classify(self) -> FpCategory {
|
||
const EXP_MASK: u32 = 0x7f800000;
|
||
const MAN_MASK: u32 = 0x007fffff;
|
||
|
||
let bits = self.to_bits();
|
||
match (bits & MAN_MASK, bits & EXP_MASK) {
|
||
(0, 0) => FpCategory::Zero,
|
||
(_, 0) => FpCategory::Subnormal,
|
||
(0, EXP_MASK) => FpCategory::Infinite,
|
||
(_, EXP_MASK) => FpCategory::Nan,
|
||
_ => FpCategory::Normal,
|
||
}
|
||
}
|
||
|
||
/// Returns `true` if `self` has a positive sign, including `+0.0`, `NaN`s with
|
||
/// positive sign bit and positive infinity.
|
||
///
|
||
/// ```
|
||
/// let f = 7.0_f32;
|
||
/// let g = -7.0_f32;
|
||
///
|
||
/// assert!(f.is_sign_positive());
|
||
/// assert!(!g.is_sign_positive());
|
||
/// ```
|
||
#[stable(feature = "rust1", since = "1.0.0")]
|
||
#[inline]
|
||
pub fn is_sign_positive(self) -> bool {
|
||
!self.is_sign_negative()
|
||
}
|
||
|
||
/// Returns `true` if `self` has a negative sign, including `-0.0`, `NaN`s with
|
||
/// negative sign bit and negative infinity.
|
||
///
|
||
/// ```
|
||
/// let f = 7.0f32;
|
||
/// let g = -7.0f32;
|
||
///
|
||
/// assert!(!f.is_sign_negative());
|
||
/// assert!(g.is_sign_negative());
|
||
/// ```
|
||
#[stable(feature = "rust1", since = "1.0.0")]
|
||
#[inline]
|
||
pub 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() & 0x8000_0000 != 0
|
||
}
|
||
|
||
/// Takes the reciprocal (inverse) of a number, `1/x`.
|
||
///
|
||
/// ```
|
||
/// let x = 2.0_f32;
|
||
/// let abs_difference = (x.recip() - (1.0 / x)).abs();
|
||
///
|
||
/// assert!(abs_difference <= f32::EPSILON);
|
||
/// ```
|
||
#[stable(feature = "rust1", since = "1.0.0")]
|
||
#[inline]
|
||
pub fn recip(self) -> f32 {
|
||
1.0 / self
|
||
}
|
||
|
||
/// Converts radians to degrees.
|
||
///
|
||
/// ```
|
||
/// let angle = std::f32::consts::PI;
|
||
///
|
||
/// let abs_difference = (angle.to_degrees() - 180.0).abs();
|
||
///
|
||
/// assert!(abs_difference <= f32::EPSILON);
|
||
/// ```
|
||
#[stable(feature = "f32_deg_rad_conversions", since = "1.7.0")]
|
||
#[inline]
|
||
pub fn to_degrees(self) -> f32 {
|
||
// Use a constant for better precision.
|
||
const PIS_IN_180: f32 = 57.2957795130823208767981548141051703_f32;
|
||
self * PIS_IN_180
|
||
}
|
||
|
||
/// Converts degrees to radians.
|
||
///
|
||
/// ```
|
||
/// let angle = 180.0f32;
|
||
///
|
||
/// let abs_difference = (angle.to_radians() - std::f32::consts::PI).abs();
|
||
///
|
||
/// assert!(abs_difference <= f32::EPSILON);
|
||
/// ```
|
||
#[stable(feature = "f32_deg_rad_conversions", since = "1.7.0")]
|
||
#[inline]
|
||
pub fn to_radians(self) -> f32 {
|
||
let value: f32 = consts::PI;
|
||
self * (value / 180.0f32)
|
||
}
|
||
|
||
/// Returns the maximum of the two numbers.
|
||
///
|
||
/// ```
|
||
/// let x = 1.0f32;
|
||
/// let y = 2.0f32;
|
||
///
|
||
/// assert_eq!(x.max(y), y);
|
||
/// ```
|
||
///
|
||
/// If one of the arguments is NaN, then the other argument is returned.
|
||
#[stable(feature = "rust1", since = "1.0.0")]
|
||
#[inline]
|
||
pub fn max(self, other: f32) -> f32 {
|
||
intrinsics::maxnumf32(self, other)
|
||
}
|
||
|
||
/// Returns the minimum of the two numbers.
|
||
///
|
||
/// ```
|
||
/// let x = 1.0f32;
|
||
/// let y = 2.0f32;
|
||
///
|
||
/// assert_eq!(x.min(y), x);
|
||
/// ```
|
||
///
|
||
/// If one of the arguments is NaN, then the other argument is returned.
|
||
#[stable(feature = "rust1", since = "1.0.0")]
|
||
#[inline]
|
||
pub fn min(self, other: f32) -> f32 {
|
||
intrinsics::minnumf32(self, other)
|
||
}
|
||
|
||
/// 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_f32;
|
||
/// let rounded = unsafe { value.to_int_unchecked::<u16>() };
|
||
/// assert_eq!(rounded, 4);
|
||
///
|
||
/// let value = -128.9_f32;
|
||
/// 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
|
||
#[stable(feature = "float_approx_unchecked_to", since = "1.44.0")]
|
||
#[inline]
|
||
pub unsafe fn to_int_unchecked<Int>(self) -> Int
|
||
where
|
||
Self: FloatToInt<Int>,
|
||
{
|
||
FloatToInt::<Int>::to_int_unchecked(self)
|
||
}
|
||
|
||
/// Raw transmutation to `u32`.
|
||
///
|
||
/// This is currently identical to `transmute::<f32, u32>(self)` on all platforms.
|
||
///
|
||
/// See `from_bits` for some discussion of the portability of this operation
|
||
/// (there are almost no issues).
|
||
///
|
||
/// Note that this function is distinct from `as` casting, which attempts to
|
||
/// preserve the *numeric* value, and not the bitwise value.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// assert_ne!((1f32).to_bits(), 1f32 as u32); // to_bits() is not casting!
|
||
/// assert_eq!((12.5f32).to_bits(), 0x41480000);
|
||
///
|
||
/// ```
|
||
#[stable(feature = "float_bits_conv", since = "1.20.0")]
|
||
#[inline]
|
||
pub fn to_bits(self) -> u32 {
|
||
// SAFETY: `u32` is a plain old datatype so we can always transmute to it
|
||
unsafe { mem::transmute(self) }
|
||
}
|
||
|
||
/// Raw transmutation from `u32`.
|
||
///
|
||
/// This is currently identical to `transmute::<u32, f32>(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 signalingness (very likely), then there is no
|
||
/// portability concern.
|
||
///
|
||
/// Note that this function is distinct from `as` casting, which attempts to
|
||
/// preserve the *numeric* value, and not the bitwise value.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// let v = f32::from_bits(0x41480000);
|
||
/// assert_eq!(v, 12.5);
|
||
/// ```
|
||
#[stable(feature = "float_bits_conv", since = "1.20.0")]
|
||
#[inline]
|
||
pub fn from_bits(v: u32) -> Self {
|
||
// SAFETY: `u32` is a plain old datatype so we can always transmute from it
|
||
// It turns out the safety issues with sNaN were overblown! Hooray!
|
||
unsafe { mem::transmute(v) }
|
||
}
|
||
|
||
/// Return the memory representation of this floating point number as a byte array in
|
||
/// big-endian (network) byte order.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// let bytes = 12.5f32.to_be_bytes();
|
||
/// assert_eq!(bytes, [0x41, 0x48, 0x00, 0x00]);
|
||
/// ```
|
||
#[stable(feature = "float_to_from_bytes", since = "1.40.0")]
|
||
#[inline]
|
||
pub fn to_be_bytes(self) -> [u8; 4] {
|
||
self.to_bits().to_be_bytes()
|
||
}
|
||
|
||
/// Return the memory representation of this floating point number as a byte array in
|
||
/// little-endian byte order.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// let bytes = 12.5f32.to_le_bytes();
|
||
/// assert_eq!(bytes, [0x00, 0x00, 0x48, 0x41]);
|
||
/// ```
|
||
#[stable(feature = "float_to_from_bytes", since = "1.40.0")]
|
||
#[inline]
|
||
pub fn to_le_bytes(self) -> [u8; 4] {
|
||
self.to_bits().to_le_bytes()
|
||
}
|
||
|
||
/// Return 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`]: #method.to_be_bytes
|
||
/// [`to_le_bytes`]: #method.to_le_bytes
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// let bytes = 12.5f32.to_ne_bytes();
|
||
/// assert_eq!(
|
||
/// bytes,
|
||
/// if cfg!(target_endian = "big") {
|
||
/// [0x41, 0x48, 0x00, 0x00]
|
||
/// } else {
|
||
/// [0x00, 0x00, 0x48, 0x41]
|
||
/// }
|
||
/// );
|
||
/// ```
|
||
#[stable(feature = "float_to_from_bytes", since = "1.40.0")]
|
||
#[inline]
|
||
pub fn to_ne_bytes(self) -> [u8; 4] {
|
||
self.to_bits().to_ne_bytes()
|
||
}
|
||
|
||
/// Create a floating point value from its representation as a byte array in big endian.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// let value = f32::from_be_bytes([0x41, 0x48, 0x00, 0x00]);
|
||
/// assert_eq!(value, 12.5);
|
||
/// ```
|
||
#[stable(feature = "float_to_from_bytes", since = "1.40.0")]
|
||
#[inline]
|
||
pub fn from_be_bytes(bytes: [u8; 4]) -> Self {
|
||
Self::from_bits(u32::from_be_bytes(bytes))
|
||
}
|
||
|
||
/// Create a floating point value from its representation as a byte array in little endian.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// let value = f32::from_le_bytes([0x00, 0x00, 0x48, 0x41]);
|
||
/// assert_eq!(value, 12.5);
|
||
/// ```
|
||
#[stable(feature = "float_to_from_bytes", since = "1.40.0")]
|
||
#[inline]
|
||
pub fn from_le_bytes(bytes: [u8; 4]) -> Self {
|
||
Self::from_bits(u32::from_le_bytes(bytes))
|
||
}
|
||
|
||
/// Create 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`]: #method.from_be_bytes
|
||
/// [`from_le_bytes`]: #method.from_le_bytes
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// let value = f32::from_ne_bytes(if cfg!(target_endian = "big") {
|
||
/// [0x41, 0x48, 0x00, 0x00]
|
||
/// } else {
|
||
/// [0x00, 0x00, 0x48, 0x41]
|
||
/// });
|
||
/// assert_eq!(value, 12.5);
|
||
/// ```
|
||
#[stable(feature = "float_to_from_bytes", since = "1.40.0")]
|
||
#[inline]
|
||
pub fn from_ne_bytes(bytes: [u8; 4]) -> Self {
|
||
Self::from_bits(u32::from_ne_bytes(bytes))
|
||
}
|
||
|
||
/// Returns an ordering between self and other values.
|
||
/// Unlike the standard partial comparison between floating point numbers,
|
||
/// this comparison always produces an ordering in accordance to
|
||
/// the totalOrder predicate as defined in IEEE 754 (2008 revision)
|
||
/// floating point standard. The values are ordered in following order:
|
||
/// - 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
|
||
///
|
||
/// # Example
|
||
/// ```
|
||
/// #![feature(total_cmp)]
|
||
/// struct GoodBoy {
|
||
/// name: String,
|
||
/// weight: f32,
|
||
/// }
|
||
///
|
||
/// 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: f32::INFINITY },
|
||
/// GoodBoy { name: "Abs. Unit".to_owned(), weight: f32::NAN },
|
||
/// GoodBoy { name: "Floaty".to_owned(), weight: -5.0 },
|
||
/// ];
|
||
///
|
||
/// bois.sort_by(|a, b| a.weight.total_cmp(&b.weight));
|
||
/// # assert!(bois.into_iter().map(|b| b.weight)
|
||
/// # .zip([-5.0, 0.1, 10.0, 99.0, f32::INFINITY, f32::NAN].iter())
|
||
/// # .all(|(a, b)| a.to_bits() == b.to_bits()))
|
||
/// ```
|
||
#[must_use = "method returns a new number and does not mutate the original value"]
|
||
#[unstable(feature = "total_cmp", issue = "none")]
|
||
#[inline]
|
||
pub fn total_cmp(&self, other: &Self) -> crate::cmp::Ordering {
|
||
let mut left = self.to_bits() as i32;
|
||
let mut right = other.to_bits() as i32;
|
||
|
||
// 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.
|
||
if left < 0 {
|
||
// i32::MAX corresponds the bit pattern of "all ones except for the sign bit"
|
||
left ^= i32::MAX
|
||
};
|
||
if right < 0 {
|
||
right ^= i32::MAX
|
||
};
|
||
|
||
left.cmp(&right)
|
||
}
|
||
}
|