Bit Operations

Next: Comparisons Up: Natural (natural.h) Previous: Arithmetical Operations

Bit Operations

Shifting

Algorithm:      c := a << b

Input:      $a\in\textsf{Natural}, b\in\texttt{size\_t}$ .

Output:      $c\in\textsf{Natural}$ such that $c = a\cdot 2^b\quad\Box$

Algorithm:      c := c <<= a

Input:      $a\in\texttt{size\_t}, c\in\textsf{Natural}$ .

Output:      $c\in\textsf{Natural}$ such that $c := c\cdot 2^a\quad\Box$

Algorithm:      c := a >> b

Input:      $a\in\textsf{Natural}, b\in\texttt{size\_t}$ .

Output:      $c\in\textsf{Natural}$ such that $c = \lfloor\frac{a}{2^b}\rfloor\quad\Box$

Algorithm:      c := c >>= a

Input:      $a\in\texttt{size\_t}, c\in\textsf{Natural}$ .

Output:      $c\in\textsf{Natural}$ such that $c := \lfloor\frac{c}{2^a}\rfloor\quad\Box$
Both arguments of the same type:

Algorithm:      c := a & b

Input:      $a,b\in\textsf{Natural}$ .

Output:      $c\in\textsf{Natural}$ such that $c = a\wedge b\quad\Box$

Algorithm:      c := c &= a

Input:      $a,c\in\textsf{Natural}$ .

Output:      $c\in\textsf{Natural}$ such that $c := c\wedge a\quad\Box$

Algorithm:      c := a | b

Input:      $a,b\in\textsf{Natural}$ .

Output:      $c\in\textsf{Natural}$ such that $c = a\vee b\quad\Box$

Algorithm:      c := c |= a

Input:      $a,c\in\textsf{Natural}$ .

Output:      $c\in\textsf{Natural}$ such that $c := c\vee a\quad\Box$

Algorithm:      c := a ^ b

Input:      $a,b\in\textsf{Natural}$ .

Output:      $c\in\textsf{Natural}$ such that $c = \neg a\wedge b\vee a\wedge\neg b\quad\Box$

Algorithm:      c := c ^= a

Input:      $a,c\in\textsf{Natural}$ .

Output:      $c\in\textsf{Natural}$ such that $c := \neg c\wedge a\vee c\wedge\neg a\quad\Box$

Algorithm:      c := ~a

Input:      $a\in\textsf{Natural}$ .

Output:      $c\in\textsf{Natural}$ such that $c = \neg a\quad\Box$
Mixed mode expression:

Algorithm:      c := a & b

Input:      $a\in\textsf{Natural}, b\in\textsf{Digit}$ .

Output:      $c\in\textsf{Digit}$ such that $c = a\wedge b\quad\Box$

Algorithm:      c := a &= b

Input:      $a\in\textsf{Natural}, b\in\textsf{Digit}$ .

Output:      $a\in\textsf{Natural}, c\in\textsf{Digit}$ such that $a := a \wedge b, c = a\quad\Box$

Algorithm:      c := a | b

Input:      $a\in\textsf{Natural}, b\in\textsf{Digit}$ .

Output:      $c\in\textsf{Natural}$ such that $c = a\vee b\quad\Box$

Algorithm:      c := c |= a

Input:      $c\in\textsf{Natural}, a\in\textsf{Digit}$ .

Output:      $c\in\textsf{Natural}$ such that $c := c\vee a\quad\Box$

Algorithm:      c := c ^= a

Input:      $c\in\textsf{Natural}, a\in\textsf{Digit}$ .

Output:      $c\in\textsf{Natural}$ such that $c := \neg c\wedge a\vee c\wedge\neg a\quad\Box$

Algorithm:		`c := a << b`
Input:		$a\in\textsf{Natural}, b\in\texttt{size\_t}$ .
Output:		$c\in\textsf{Natural}$ such that $c = a\cdot 2^b\quad\Box$

Algorithm:		`c := c <<= a`
Input:		$a\in\texttt{size\_t}, c\in\textsf{Natural}$ .
Output:		$c\in\textsf{Natural}$ such that $c := c\cdot 2^a\quad\Box$

Algorithm:		`c := a >> b`
Input:		$a\in\textsf{Natural}, b\in\texttt{size\_t}$ .
Output:		$c\in\textsf{Natural}$ such that $c = \lfloor\frac{a}{2^b}\rfloor\quad\Box$

Algorithm:		`c := c >>= a`
Input:		$a\in\texttt{size\_t}, c\in\textsf{Natural}$ .
Output:		$c\in\textsf{Natural}$ such that $c := \lfloor\frac{c}{2^a}\rfloor\quad\Box$

Algorithm:		`c := a & b`
Input:		$a,b\in\textsf{Natural}$ .
Output:		$c\in\textsf{Natural}$ such that $c = a\wedge b\quad\Box$

Algorithm:		`c := c &= a`
Input:		$a,c\in\textsf{Natural}$ .
Output:		$c\in\textsf{Natural}$ such that $c := c\wedge a\quad\Box$

Algorithm:		`c := a \| b`
Input:		$a,b\in\textsf{Natural}$ .
Output:		$c\in\textsf{Natural}$ such that $c = a\vee b\quad\Box$

Algorithm:		`c := c \|= a`
Input:		$a,c\in\textsf{Natural}$ .
Output:		$c\in\textsf{Natural}$ such that $c := c\vee a\quad\Box$

Algorithm:		`c := a ^ b`
Input:		$a,b\in\textsf{Natural}$ .
Output:		$c\in\textsf{Natural}$ such that $c = \neg a\wedge b\vee a\wedge\neg b\quad\Box$

Algorithm:		`c := c ^= a`
Input:		$a,c\in\textsf{Natural}$ .
Output:		$c\in\textsf{Natural}$ such that $c := \neg c\wedge a\vee c\wedge\neg a\quad\Box$

Algorithm:		`c := ~a`
Input:		$a\in\textsf{Natural}$ .
Output:		$c\in\textsf{Natural}$ such that $c = \neg a\quad\Box$

Algorithm:		`c := a & b`
Input:		$a\in\textsf{Natural}, b\in\textsf{Digit}$ .
Output:		$c\in\textsf{Digit}$ such that $c = a\wedge b\quad\Box$

Algorithm:		`c := a &= b`
Input:		$a\in\textsf{Natural}, b\in\textsf{Digit}$ .
Output:		$a\in\textsf{Natural}, c\in\textsf{Digit}$ such that $a := a \wedge b, c = a\quad\Box$

Algorithm:		`c := a \| b`
Input:		$a\in\textsf{Natural}, b\in\textsf{Digit}$ .
Output:		$c\in\textsf{Natural}$ such that $c = a\vee b\quad\Box$

Algorithm:		`c := c \|= a`
Input:		$c\in\textsf{Natural}, a\in\textsf{Digit}$ .
Output:		$c\in\textsf{Natural}$ such that $c := c\vee a\quad\Box$

Algorithm:		`c := c ^= a`
Input:		$c\in\textsf{Natural}, a\in\textsf{Digit}$ .
Output:		$c\in\textsf{Natural}$ such that $c := \neg c\wedge a\vee c\wedge\neg a\quad\Box$

Next: Comparisons Up: Natural (natural.h) Previous: Arithmetical Operations

Piologie Version 1.2
3/3/1998