Functions

Next: Mathematical Constants (pi.h) Up: Rational (rational.h) Previous: Input/Output

Functions

Arithmetical Operations:

Algorithm:      c := abs(a)

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

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

Algorithm:      c := sign(a)

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

Output:      $c\in\texttt{int}$ such that

     $\mbox{if }a = 0\mbox{ then }c = 0$

     else if $a \gt 0$ then c = 1

     else $c = -1\quad\Box$

Algorithm:      b := inv(a)

Input:      $a\in\textsf{Rational}\mbox{ where }a\geq0$ .

Output:      $b\in\textsf{Rational}$ such that $b = a^{-1}\quad\Box$

Algorithm:      c := pow(a, b)

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

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

Algorithm:      c := pow(a, b)

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

Output:      $c\in\textsf{Rational}$ such that $c = a^b\quad\Box$
Integer Functions:

Algorithm:      c := ceil(a)

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

Output:      $c\in\textsf{Integer}$ such that $c = \rceil a\lceil\quad\Box$

Algorithm:      c := floor(a)

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

Output:      $c\in\textsf{Integer}$ such that $c = \rfloor a\lfloor\quad\Box$

Algorithm:      c := round(a)

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

Output:      $c\in\textsf{Integer}$ such that $c = \rfloor a+\frac{1}{2}\lfloor\quad\Box$

Algorithm:      c := trunc(a)

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

Output:      $c\in\textsf{Integer}$ such that $c = \mathrm{sign}(a)\rfloor \vert a\vert\lfloor\quad\Box$
Basic Functions:

Algorithm:      swap(a, b)

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

Output:      $a,b\in\textsf{Rational}$ such that t := a, a := b, b := t

     where $t\in\textsf{Rational}\quad\Box$

Algorithm:      a.rand(n)

Input:      $n\in\texttt{size\_t}$ .

Output:      $a\in\textsf{Rational}$ such that $\vert a_1\vert < 2^n, a_2 \leq 2^n\mbox{ where }\frac{a_1}{a_2}=a\mbox{ (random number)}\quad\Box$

Algorithm:		`c := abs(a)`
Input:		$a\in\textsf{Rational}$ .
Output:		$c\in\textsf{Natural}$ such that $c = \vert a\vert\quad\Box$

Algorithm:		`c := sign(a)`
Input:		$a\in\textsf{Rational}$ .
Output:		$c\in\texttt{int}$ such that
		$\mbox{if }a = 0\mbox{ then }c = 0$
		else if $a \gt 0$ then c = 1
		else $c = -1\quad\Box$

Algorithm:		`b := inv(a)`
Input:		$a\in\textsf{Rational}\mbox{ where }a\geq0$ .
Output:		$b\in\textsf{Rational}$ such that $b = a^{-1}\quad\Box$

Algorithm:		`c := pow(a, b)`
Input:		$a\in\textsf{Rational}, b\in\textsf{Digit}$ .
Output:		$c\in\textsf{Rational}$ such that $c = a^b\quad\Box$

Algorithm:		`c := pow(a, b)`
Input:		$a\in\textsf{Rational}, b\in\textsf{Integer}$ .
Output:		$c\in\textsf{Rational}$ such that $c = a^b\quad\Box$

Algorithm:		`c := ceil(a)`
Input:		$a\in\textsf{Rational}$ .
Output:		$c\in\textsf{Integer}$ such that $c = \rceil a\lceil\quad\Box$

Algorithm:		`c := floor(a)`
Input:		$a\in\textsf{Rational}$ .
Output:		$c\in\textsf{Integer}$ such that $c = \rfloor a\lfloor\quad\Box$

Algorithm:		`c := round(a)`
Input:		$a\in\textsf{Rational}$ .
Output:		$c\in\textsf{Integer}$ such that $c = \rfloor a+\frac{1}{2}\lfloor\quad\Box$

Algorithm:		`c := trunc(a)`
Input:		$a\in\textsf{Rational}$ .
Output:		$c\in\textsf{Integer}$ such that $c = \mathrm{sign}(a)\rfloor \vert a\vert\lfloor\quad\Box$

Algorithm:		`swap(a, b)`
Input:		$a,b\in\textsf{Rational}$ .
Output:		$a,b\in\textsf{Rational}$ such that t := a, a := b, b := t
		where $t\in\textsf{Rational}\quad\Box$

Algorithm:		`a.rand(n)`
Input:		$n\in\texttt{size\_t}$ .
Output:		$a\in\textsf{Rational}$ such that $\vert a_1\vert < 2^n, a_2 \leq 2^n\mbox{ where }\frac{a_1}{a_2}=a\mbox{ (random number)}\quad\Box$

Next: Mathematical Constants (pi.h) Up: Rational (rational.h) Previous: Input/Output

Piologie Version 1.2
3/3/1998