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rationals

## NAME

rationals - rational number library

## SYNOPSIS

#include rationals.f83

rationals

## DESCRIPTION

The tile forth rational number library. Allows definition and manipulation of rational numbers. Defines a recognition function so that standard rational notation may be used, i.e., <num>/<denom>, where <num> and <denom> are integer values. The rational number system also includes the numbers "undefined" and "infinity". All rational number functions normalize their results to maintain as small numbers as possible. Overflow conditions are not checked. Rational numbers are maintained on the stack as an integer number pair. No extra memory is required for arithmetic operations. Double number stack words may be used to mainipulate the rational number.

rational -infinity ( -- num denom)
The rational number constant for minus infinity.
: 1/r ( num1 denom1 -- num2 denom2)
Returns the result of dividing one by the rational number, "num1"/"denom1".
: ?r< ( num1 denom1 num2 denom2 -- bool)
Returns "true" if the rational number, "num1"/"denom1", is arithmetic less than the rational number, "num2"/"denom2" else "false".
: ?r= ( num1 denom1 num2 denom2 -- bool)
Returns "true" if the rational number, "num1"/"denom1", is arithmetic equal than the rational number, "num2"/"denom2" else "false".
: ?r> ( num1 denom1 num2 denom2 -- bool)
Returns "true" if the rational number, "num1"/"denom1", is arithmetic greater than the rational number, "num2"/"denom2" else "false".
: ?rational ( str -- [num denom true] or [str false]) recognizer
The rational number vocabulary literal recognizer function. Will determinate if the string is a rational number using the syntax "<num>/<denom>", where <num> is an integer and <denom> a positive number. The rational number is normalized using the function, "rnormalize", and the value return with the flag "true". If the string is not a rational number the string is returned with the flag "false"
struct.type RATIONAL ( -- )
Used in the following form:

RATIONAL <name> ( -- rational)
to create a rational variable. The variable should be accessed with the double number memory access functions, "2@" and "2!". The structure type "RATIONAL" contains two private fields; "+num" and "+denom".

: i>r ( x -- num denom)
Converts the integer value to a rational number.
rational infinity ( -- num denom)
Returns the value for the rational number for infinity.
: r* ( num1 denom1 num2 denom2 -- num3 denom3)
Returns the product of the two rational numbers, "num1"/"denom1" and "num2"/"denom2". The result is always normalized.
: r+ ( num1 denom1 num2 denom2 -- num3 denom3)
Returns the sum of the two rational numbers, "num1"/"denom1" and "num2"/"denom2". The result is always normalized.
: r- ( num1 denom1 num2 denom2 -- num3 denom3)
Returns the difference of the two rational numbers, "num1"/"denom1" and "num2"/"denom2". The result is always normalized.
: r. ( num denom -- )
Displays the rational number in the standard format, "num"/"denom". If the value is zero or infinity these strings are displayed.
: r/ ( num1 denom1 num2 denom2 -- num3 denom3)
Returns the quotient of the two rational numbers, "num1"/"denom1" and "num2"/"denom2". The result is always normalized.
: r>i ( num denom -- x)
Converts the rational number to an integer. The result is truncated.
: rational ( num denom -- )
Used in the following form:

<num> <denom> rational <name> ( -- num denom)
to create a rational number constant. The rational number is restored when the entry is used.

vocabulary rationals ( -- )
The rational number extension vocabulary. Include into the vocabulary search set, "context", to allow access of this library.
: rnegate ( num1 denom1 -- num2 denom2)
Returns the result of negating the rational number, "num1"/"denom1".
: rnormalize ( num1 denom1 -- num2 denom2)
Normalizes the rational number, "num1"/"denom1", towards zero using greatest common divisor.
rational undefined ( -- num denom)
The rational number constant for undefined.
rational zero ( -- num denom)
The rational number constant for zero. The value "0/0" may also be used for zero.

## INTERNALS

Private definitions in the rationals vocabulary;

long +denom ( rational -- addr) private
Access field within a "RATIONAL" structure instance, variable, to the denominate number.
long +num ( rational -- addr) private
Access field within a "RATIONAL" structure instance, variable, to the numerate number.

tile(1), forth(3X), structures(3X).

## NOTE

The function list is sorted in ASCII order. The type and mode of the entries are indicated together with their parameter stack effect.

## COPYING

Copyright (C) 1990 Mikael R.K. Patel

Permission is granted to make and distribute verbatim copies of this manual provided the copyright notice and this permission notice are preserved on all copies.

Permission is granted to copy and distribute modified versions of this manual under the conditions for verbatim copying, provided also that the section entitled "GNU General Public License" is included exactly as in the original, and provided that the entire resulting derived work is distributed under the terms of a permission notice identical to this one.

Permission is granted to copy and distribute translations of this manual into another language, under the above conditions for modified versions, except that the section entitled "GNU General Public License" may be included in a translation approved by the author instead of in the original English.

## AUTHOR

```Mikael R.K. Patel
Computer Aided Design Laboratory (CADLAB)
Department of Computer and Information Science