RATIONALS
Section: Miscellaneous Library Functions (3X)
Updated: August 6, 1990
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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.
SEE ALSO
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
Linkoping University
S-581 83 LINKOPING
SWEDEN
Email: mip@ida.liu.se
Index
- NAME
-
- SYNOPSIS
-
- DESCRIPTION
-
- INTERNALS
-
- SEE ALSO
-
- NOTE
-
- COPYING
-
- AUTHOR
-
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