Trait malachite_base::num::conversion::traits::RawMantissaAndExponent

pub trait RawMantissaAndExponent<M, E, T = Self>: Sized {
    // Required methods
    fn raw_mantissa_and_exponent(self) -> (M, E);
    fn from_raw_mantissa_and_exponent(raw_mantissa: M, raw_exponent: E) -> T;

    // Provided methods
    fn raw_mantissa(self) -> M { ... }
    fn raw_exponent(self) -> E { ... }
}

Converts a number to or from a raw mantissa and exponent.

See here for a definition of raw mantissa and exponent.

Required Methods

fn raw_mantissa_and_exponent(self) -> (M, E)

Extracts the raw mantissa and exponent from a number.

fn from_raw_mantissa_and_exponent(raw_mantissa: M, raw_exponent: E) -> T

Constructs a number from its raw mantissa and exponent.

Provided Methods

fn raw_mantissa(self) -> M

Extracts the raw mantissa from a number.

fn raw_exponent(self) -> E

Extracts the raw exponent from a number.

Object Safety

This trait is not object safe.

Implementations on Foreign Types

impl RawMantissaAndExponent<u64, u64> for f32

fn raw_mantissa_and_exponent(self) -> (u64, u64)

Returns the raw mantissa and exponent.

The raw exponent and raw mantissa are the actual bit patterns used to represent the components of self. When self is nonzero and finite, the raw exponent $e_r$ is an integer in $[0, 2^E-2]$ and the raw mantissa $m_r$ is an integer in $[0, 2^M-1]$.

When self is nonzero and finite, $f(x) = (m_r, e_r)$, where $$ m_r = \begin{cases} 2^{M+2^{E-1}-2}|x| & \text{if} \quad |x| < 2^{2-2^{E-1},} \\ 2^M \left ( \frac{|x|}{2^{\lfloor \log_2 |x| \rfloor}}-1\right ) & \textrm{otherwise}, \end{cases} $$ and $$ e_r = \begin{cases} 0 & \text{if} \quad |x| < 2^{2-2^{E-1}} \\ \lfloor \log_2 |x| \rfloor + 2^{E-1} - 1 & \textrm{otherwise}. \end{cases} $$ and $M$ and $E$ are the mantissa width and exponent width, respectively.

For zeros, infinities, or NaN, refer to IEEE 754 or look at the examples below.

The inverse operation is Self::from_raw_mantissa_and_exponent.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

fn raw_mantissa(self) -> u64

Returns the raw mantissa.

The raw mantissa is the actual bit pattern used to represent the mantissa of self. When self is nonzero and finite, it is an integer in $[0, 2^M-1]$.

When self is nonzero and finite, $$ f(x) = \begin{cases} 2^{M+2^{E-1}-2}|x| & \text{if} \quad |x| < 2^{2-2^{E-1}}, \\ 2^M \left ( \frac{|x|}{2^{\lfloor \log_2 |x| \rfloor}}-1\right ) & \textrm{otherwise}, \end{cases} $$ where $M$ and $E$ are the mantissa width and exponent width, respectively.

For zeros, infinities, or NaN, refer to IEEE 754 or look at the examples below.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

fn raw_exponent(self) -> u64

Returns the raw exponent.

The raw exponent is the actual bit pattern used to represent the exponent of self. When self is nonzero and finite, it is an integer in $[0, 2^E-2]$.

When self is nonzero and finite, $$ f(x) = \begin{cases} 0 & \text{if} \quad |x| < 2^{2-2^{E-1}}, \\ \lfloor \log_2 |x| \rfloor + 2^{E-1} - 1 & \textrm{otherwise}, \end{cases} $$ where $M$ and $E$ are the mantissa width and exponent width, respectively.

For zeros, infinities, or NaN, refer to IEEE 754 or look at the examples below.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

fn from_raw_mantissa_and_exponent(raw_mantissa: u64, raw_exponent: u64) -> f32

Constructs a float from its raw mantissa and exponent.

The raw exponent and raw mantissa are the actual bit patterns used to represent the components of a float. When the float is nonzero and finite, the raw exponent $e_r$ is an integer in $[0, 2^E-2]$ and the raw mantissa $m_r$ is an integer in $[0, 2^M-1]$.

When the exponent is not 2^E-1, $$ f(m_r, e_r) = \begin{cases} 2^{2-2^{E-1}-M}m_r & \text{if} \quad e_r = 0, \\ 2^{e_r-2^{E-1}+1}(2^{-M}m_r+1) & \textrm{otherwise}, \end{cases} $$ where $M$ and $E$ are the mantissa width and exponent width, respectively.

For zeros, infinities, or NaN, refer to IEEE 754 or look at the examples below.

This function only outputs a single, canonical, NaN.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

impl RawMantissaAndExponent<u64, u64> for f64

fn raw_mantissa_and_exponent(self) -> (u64, u64)

Returns the raw mantissa and exponent.

The raw exponent and raw mantissa are the actual bit patterns used to represent the components of self. When self is nonzero and finite, the raw exponent $e_r$ is an integer in $[0, 2^E-2]$ and the raw mantissa $m_r$ is an integer in $[0, 2^M-1]$.

When self is nonzero and finite, $f(x) = (m_r, e_r)$, where $$ m_r = \begin{cases} 2^{M+2^{E-1}-2}|x| & \text{if} \quad |x| < 2^{2-2^{E-1},} \\ 2^M \left ( \frac{|x|}{2^{\lfloor \log_2 |x| \rfloor}}-1\right ) & \textrm{otherwise}, \end{cases} $$ and $$ e_r = \begin{cases} 0 & \text{if} \quad |x| < 2^{2-2^{E-1}} \\ \lfloor \log_2 |x| \rfloor + 2^{E-1} - 1 & \textrm{otherwise}. \end{cases} $$ and $M$ and $E$ are the mantissa width and exponent width, respectively.

For zeros, infinities, or NaN, refer to IEEE 754 or look at the examples below.

The inverse operation is Self::from_raw_mantissa_and_exponent.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

fn raw_mantissa(self) -> u64

Returns the raw mantissa.

The raw mantissa is the actual bit pattern used to represent the mantissa of self. When self is nonzero and finite, it is an integer in $[0, 2^M-1]$.

When self is nonzero and finite, $$ f(x) = \begin{cases} 2^{M+2^{E-1}-2}|x| & \text{if} \quad |x| < 2^{2-2^{E-1}}, \\ 2^M \left ( \frac{|x|}{2^{\lfloor \log_2 |x| \rfloor}}-1\right ) & \textrm{otherwise}, \end{cases} $$ where $M$ and $E$ are the mantissa width and exponent width, respectively.

For zeros, infinities, or NaN, refer to IEEE 754 or look at the examples below.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

fn raw_exponent(self) -> u64

Returns the raw exponent.

The raw exponent is the actual bit pattern used to represent the exponent of self. When self is nonzero and finite, it is an integer in $[0, 2^E-2]$.

When self is nonzero and finite, $$ f(x) = \begin{cases} 0 & \text{if} \quad |x| < 2^{2-2^{E-1}}, \\ \lfloor \log_2 |x| \rfloor + 2^{E-1} - 1 & \textrm{otherwise}, \end{cases} $$ where $M$ and $E$ are the mantissa width and exponent width, respectively.

For zeros, infinities, or NaN, refer to IEEE 754 or look at the examples below.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

fn from_raw_mantissa_and_exponent(raw_mantissa: u64, raw_exponent: u64) -> f64

Constructs a float from its raw mantissa and exponent.

The raw exponent and raw mantissa are the actual bit patterns used to represent the components of a float. When the float is nonzero and finite, the raw exponent $e_r$ is an integer in $[0, 2^E-2]$ and the raw mantissa $m_r$ is an integer in $[0, 2^M-1]$.

When the exponent is not 2^E-1, $$ f(m_r, e_r) = \begin{cases} 2^{2-2^{E-1}-M}m_r & \text{if} \quad e_r = 0, \\ 2^{e_r-2^{E-1}+1}(2^{-M}m_r+1) & \textrm{otherwise}, \end{cases} $$ where $M$ and $E$ are the mantissa width and exponent width, respectively.

For zeros, infinities, or NaN, refer to IEEE 754 or look at the examples below.

This function only outputs a single, canonical, NaN.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

Implementors