Comparisons

Next: Input/Output Up: Rational (rational.h) Previous: Bit Operations

Comparisons

Both arguments of the same type:

Algorithm:      c := a == b

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

Output:      $c\in\texttt{bool}$ such that $\mbox{if }a = b\mbox{ then }c = \texttt{true}\mbox{ else }c = \texttt{false}\quad\Box$

Algorithm:      c := a != b

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

Output:      $c\in\texttt{bool}$ such that $\mbox{if }a \not= b\mbox{ then }c = \texttt{true}\mbox{ else }c = \texttt{false}\quad\Box$

Algorithm:      c := a < b

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

Output:      $c\in\texttt{bool}$ such that $\mbox{if }a < b\mbox{ then }c = \texttt{true}\mbox{ else }c = \texttt{false}\quad\Box$

Algorithm:      c := a <= b

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

Output:      $c\in\texttt{bool}$ such that $\mbox{if }a \leq b\mbox{ then }c = \texttt{true}\mbox{ else }c = \texttt{false}\quad\Box$

Algorithm:      c := a > b

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

Output:      $c\in\texttt{bool}$ such that $\mbox{if }a \gt b\mbox{ then }c = \texttt{true}\mbox{ else }c = \texttt{false}\quad\Box$

Algorithm:      c := a >= b

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

Output:      $c\in\texttt{bool}$ such that $\mbox{if }a \geq b\mbox{ then }c = \texttt{true}\mbox{ else }c = \texttt{false}\quad\Box$
Mixed mode expression:

Algorithm:      c := a == b

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

Output:      $c\in\texttt{bool}$ such that $\mbox{if }a = b\mbox{ then }c = \texttt{true}\mbox{ else }c = \texttt{false}\quad\Box$

Algorithm:      c := a != b

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

Output:      $c\in\texttt{bool}$ such that $\mbox{if }a \not= b\mbox{ then }c = \texttt{true}\mbox{ else }c = \texttt{false}\quad\Box$

Algorithm:      c := a < b

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

Output:      $c\in\texttt{bool}$ such that $\mbox{if }a < b\mbox{ then }c = \texttt{true}\mbox{ else }c = \texttt{false}\quad\Box$

Algorithm:      c := a <= b

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

Output:      $c\in\texttt{bool}$ such that $\mbox{if }a \leq b\mbox{ then }c = \texttt{true}\mbox{ else }c = \texttt{false}\quad\Box$

Algorithm:      c := a > b

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

Output:      $c\in\texttt{bool}$ such that $\mbox{if }a \gt b\mbox{ then }c = \texttt{true}\mbox{ else }c = \texttt{false}\quad\Box$

Algorithm:      c := a >= b

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

Output:      $c\in\texttt{bool}$ such that $\mbox{if }a \geq b\mbox{ then }c = \texttt{true}\mbox{ else }c = \texttt{false}\quad\Box$

Algorithm:		`c := a == b`
Input:		$a,b\in\textsf{Rational}$ .
Output:		$c\in\texttt{bool}$ such that $\mbox{if }a = b\mbox{ then }c = \texttt{true}\mbox{ else }c = \texttt{false}\quad\Box$

Algorithm:		`c := a != b`
Input:		$a,b\in\textsf{Rational}$ .
Output:		$c\in\texttt{bool}$ such that $\mbox{if }a \not= b\mbox{ then }c = \texttt{true}\mbox{ else }c = \texttt{false}\quad\Box$

Algorithm:		`c := a < b`
Input:		$a,b\in\textsf{Rational}$ .
Output:		$c\in\texttt{bool}$ such that $\mbox{if }a < b\mbox{ then }c = \texttt{true}\mbox{ else }c = \texttt{false}\quad\Box$

Algorithm:		`c := a <= b`
Input:		$a,b\in\textsf{Rational}$ .
Output:		$c\in\texttt{bool}$ such that $\mbox{if }a \leq b\mbox{ then }c = \texttt{true}\mbox{ else }c = \texttt{false}\quad\Box$

Algorithm:		`c := a > b`
Input:		$a,b\in\textsf{Rational}$ .
Output:		$c\in\texttt{bool}$ such that $\mbox{if }a \gt b\mbox{ then }c = \texttt{true}\mbox{ else }c = \texttt{false}\quad\Box$

Algorithm:		`c := a >= b`
Input:		$a,b\in\textsf{Rational}$ .
Output:		$c\in\texttt{bool}$ such that $\mbox{if }a \geq b\mbox{ then }c = \texttt{true}\mbox{ else }c = \texttt{false}\quad\Box$

Algorithm:		`c := a == b`
Input:		$a\in\textsf{Rational}, b\in\textsf{Digit}$ .
Output:		$c\in\texttt{bool}$ such that $\mbox{if }a = b\mbox{ then }c = \texttt{true}\mbox{ else }c = \texttt{false}\quad\Box$

Algorithm:		`c := a != b`
Input:		$a\in\textsf{Rational}, b\in\textsf{Digit}$ .
Output:		$c\in\texttt{bool}$ such that $\mbox{if }a \not= b\mbox{ then }c = \texttt{true}\mbox{ else }c = \texttt{false}\quad\Box$

Algorithm:		`c := a < b`
Input:		$a\in\textsf{Rational}, b\in\textsf{Digit}$ .
Output:		$c\in\texttt{bool}$ such that $\mbox{if }a < b\mbox{ then }c = \texttt{true}\mbox{ else }c = \texttt{false}\quad\Box$

Algorithm:		`c := a <= b`
Input:		$a\in\textsf{Rational}, b\in\textsf{Digit}$ .
Output:		$c\in\texttt{bool}$ such that $\mbox{if }a \leq b\mbox{ then }c = \texttt{true}\mbox{ else }c = \texttt{false}\quad\Box$

Algorithm:		`c := a > b`
Input:		$a\in\textsf{Rational}, b\in\textsf{Digit}$ .
Output:		$c\in\texttt{bool}$ such that $\mbox{if }a \gt b\mbox{ then }c = \texttt{true}\mbox{ else }c = \texttt{false}\quad\Box$

Algorithm:		`c := a >= b`
Input:		$a\in\textsf{Rational}, b\in\textsf{Digit}$ .
Output:		$c\in\texttt{bool}$ such that $\mbox{if }a \geq b\mbox{ then }c = \texttt{true}\mbox{ else }c = \texttt{false}\quad\Box$

Next: Input/Output Up: Rational (rational.h) Previous: Bit Operations

Piologie Version 1.2
3/3/1998