Trait malachite_base::num::conversion::traits::RawMantissaAndExponent
source · [−]pub trait RawMantissaAndExponent<M, E, T = Self>: Sized {
fn raw_mantissa_and_exponent(self) -> (M, E);
fn from_raw_mantissa_and_exponent(raw_mantissa: M, raw_exponent: E) -> T;
fn raw_mantissa(self) -> M { ... }
fn raw_exponent(self) -> E { ... }
}Expand description
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)
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
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
fn raw_mantissa(self) -> M
Extracts the raw mantissa from a number.
fn raw_exponent(self) -> E
fn raw_exponent(self) -> E
Extracts the raw exponent from a number.
Implementations on Foreign Types
sourceimpl RawMantissaAndExponent<u64, u64, f32> for f32
impl RawMantissaAndExponent<u64, u64, f32> for f32
sourcefn raw_mantissa_and_exponent(self) -> (u64, u64)
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.
sourcefn raw_mantissa(self) -> u64
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.
sourcefn raw_exponent(self) -> u64
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.
sourcefn from_raw_mantissa_and_exponent(raw_mantissa: u64, raw_exponent: u64) -> f32
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.
sourceimpl RawMantissaAndExponent<u64, u64, f64> for f64
impl RawMantissaAndExponent<u64, u64, f64> for f64
sourcefn raw_mantissa_and_exponent(self) -> (u64, u64)
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.
sourcefn raw_mantissa(self) -> u64
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.
sourcefn raw_exponent(self) -> u64
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.
sourcefn from_raw_mantissa_and_exponent(raw_mantissa: u64, raw_exponent: u64) -> f64
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.