Arithmetical Operations

Next: Bit Operations Up: Natural (natural.h) Previous: Basic Operations

Arithmetical Operations

Addition (both arguments of the same type):

Algorithm:      c := a+b

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

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

Algorithm:      c := c += a

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

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

Algorithm:      c := ++a

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

Output:      $a,c\in\textsf{Natural}$ such that $a := a+1, c := a\quad\Box$

Algorithm:      c := a++

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

Output:      $a,c\in\textsf{Natural}$ such that $c := a, a := a+1\quad\Box$
Addition (mixed mode expression):

Algorithm:      c := a+b

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

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

Algorithm:      c := a+b

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

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

Algorithm:      c := c += a

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

Output:      $c\in\textsf{Natural}$ such that $c := c+a\quad\Box$
Subtraction (both arguments of the same type):

Algorithm:      c := a-b

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

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

Algorithm:      c := c -= a

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

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

Algorithm:      c := -a

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

Output:      $a,c\in\textsf{Natural}$ such that $a := a-1, c := a\quad\Box$

Algorithm:      c := a-

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

Output:      $a,c\in\textsf{Natural}$ such that $c := a, a := a-1\quad\Box$
Subtraction (mixed mode expression):

Algorithm:      c := a-b

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

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

Algorithm:      c := c -= a

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

Output:      $c\in\textsf{Natural}$ such that $c := c-a\quad\Box$
Multiplication (both arguments of the same type):

Algorithm:      c := a*b

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

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

Algorithm:      c := c *= a

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

Output:      $c\in\textsf{Natural}$ such that $c := c\cdot a\quad\Box$
Multiplication (mixed mode expression):

Algorithm:      c := a*b

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

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

Algorithm:      c := a*b

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

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

Algorithm:      c := c *= a

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

Output:      $c\in\textsf{Natural}$ such that $c := c\cdot a\quad\Box$
Division (both arguments of the same type):

Algorithm:      c := a/b

Input:      $a,b\in\textsf{Natural}\mbox{ where }b\not=0$ .

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

Algorithm:      c := c /= a

Input:      $a,c\in\textsf{Natural}\mbox{ where }a\not=0$ .

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

Algorithm:      c := a%b

Input:      $a,b\in\textsf{Natural}\mbox{ where }b\not=0$ .

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

Algorithm:      c := c %= a

Input:      $a,c\in\textsf{Natural}\mbox{ where }a\not=0$ .

Output:      $c\in\textsf{Natural}$ such that $c := c-\lfloor\frac{c}{a}\rfloor\cdot a\quad\Box$
Division (mixed mode expression):

Algorithm:      c := a/b

Input:      $a\in\textsf{Natural}, b\in\textsf{Digit}\mbox{ where }b\not=0$ .

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

Algorithm:      c := c /= a

Input:      $c\in\textsf{Natural}, a\in\textsf{Digit}\mbox{ where }a\not=0$ .

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

Algorithm:      c := a%b

Input:      $a\in\textsf{Natural}, b\in\textsf{Digit}\mbox{ where }b\not=0$ .

Output:      $c\in\textsf{Digit}$ such that $c = a-\lfloor\frac{a}{b}\rfloor\cdot b\quad\Box$

Algorithm:      c := a %= b

Input:      $a\in\textsf{Natural}, b\in\textsf{Digit}\mbox{ where }b\not=0$ .

Output:      $c\in\textsf{Digit}$ such that $c = a-\lfloor\frac{a}{b}\rfloor\cdot b, a = c\quad\Box$

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

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

Algorithm:		`c := ++a`
Input:		$a\in\textsf{Natural}$ .
Output:		$a,c\in\textsf{Natural}$ such that $a := a+1, c := a\quad\Box$

Algorithm:		`c := a++`
Input:		$a\in\textsf{Natural}$ .
Output:		$a,c\in\textsf{Natural}$ such that $c := a, a := a+1\quad\Box$

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

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

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

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

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

Algorithm:		`c := -a`
Input:		$a\in\textsf{Natural}$ .
Output:		$a,c\in\textsf{Natural}$ such that $a := a-1, c := a\quad\Box$

Algorithm:		`c := a-`
Input:		$a\in\textsf{Natural}$ .
Output:		$a,c\in\textsf{Natural}$ such that $c := a, a := a-1\quad\Box$

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

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

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

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

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

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

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

Algorithm:		`c := a/b`
Input:		$a,b\in\textsf{Natural}\mbox{ where }b\not=0$ .
Output:		$c\in\textsf{Natural}$ such that $c = \lfloor\frac{a}{b}\rfloor\quad\Box$

Algorithm:		`c := c /= a`
Input:		$a,c\in\textsf{Natural}\mbox{ where }a\not=0$ .
Output:		$c\in\textsf{Natural}$ such that $c := \lfloor\frac{c}{a}\rfloor\quad\Box$

Algorithm:		`c := a%b`
Input:		$a,b\in\textsf{Natural}\mbox{ where }b\not=0$ .
Output:		$c\in\textsf{Natural}$ such that $c = a-\lfloor\frac{a}{b}\rfloor\cdot b\quad\Box$

Algorithm:		`c := c %= a`
Input:		$a,c\in\textsf{Natural}\mbox{ where }a\not=0$ .
Output:		$c\in\textsf{Natural}$ such that $c := c-\lfloor\frac{c}{a}\rfloor\cdot a\quad\Box$

Algorithm:		`c := a/b`
Input:		$a\in\textsf{Natural}, b\in\textsf{Digit}\mbox{ where }b\not=0$ .
Output:		$c\in\textsf{Natural}$ such that $c = \lfloor\frac{a}{b}\rfloor\quad\Box$

Algorithm:		`c := c /= a`
Input:		$c\in\textsf{Natural}, a\in\textsf{Digit}\mbox{ where }a\not=0$ .
Output:		$c\in\textsf{Natural}$ such that $c := \lfloor\frac{c}{a}\rfloor\quad\Box$

Algorithm:		`c := a%b`
Input:		$a\in\textsf{Natural}, b\in\textsf{Digit}\mbox{ where }b\not=0$ .
Output:		$c\in\textsf{Digit}$ such that $c = a-\lfloor\frac{a}{b}\rfloor\cdot b\quad\Box$

Algorithm:		`c := a %= b`
Input:		$a\in\textsf{Natural}, b\in\textsf{Digit}\mbox{ where }b\not=0$ .
Output:		$c\in\textsf{Digit}$ such that $c = a-\lfloor\frac{a}{b}\rfloor\cdot b, a = c\quad\Box$

Next: Bit Operations Up: Natural (natural.h) Previous: Basic Operations

Piologie Version 1.2
3/3/1998