with PRECISE_TYPES ; use PRECISE_TYPES ;

package RATIONAL_TYPES is

-- This package defines the type RATIONAL for automatically sized fractions.
-- Rational numbers can be much more accurate than even the longest
-- floating point numbers. The RATIONAL objects are maintained in reduced form
-- There is no limit on the size of integers except when memory runs out.
--
-- The operations  +  -  *  /  ** abs    +(unary) -(unary) are defined
--
-- Comparison operators  >  >=  <  <=  are defined
--          =  and  /=  are predefined
--
-- The constants RATIONAL_ZERO and RATIONAL_ONE are defined
--
-- The function FRACTION is defined to create a RATIONAL object from a pair
-- of integers over the available range of integer.
--
-- The functions INTEGER_TO_RATIONAL and RATIONAL_TO_INTEGER are defined for
-- the available range of single and pairs of INTEGER.
--
-- The functions STRING_TO_RATIONAL and RATIONAL_TO_STRING are defined for
-- a pair of strings of decimal digits.
--
-- The functions FLOAT_TO_RATIONAL and RATIONAL_TO_FLOAT are approximate
-- conversions for the available range of FLOAT.
--
-- The function REDUCE is defined to minimize the size of numerator and
-- denominator and thus the space needed by a RATIONAL object
-- 
-- The function GCD computes the Greatest Common Divisor of two PRECISE numbers
--
-- The function LCM computes the Least Common Multiple of two PRECISE numbers
--
-- This package is used by RATIONAL_ARRAYS... that provides the
-- so called "infinite precision" matrix arithmetic.
--
-- Written 3/16/87 by Jon Squire
-- Copyright 1987 Westinghouse Electric Corporation
--
--
  type RATIONAL is
    record
      P : PRECISE ;
      Q : PRECISE ;
    end record ;

  RATIONAL_ZERO : constant RATIONAL := ( PRECISE_ZERO , PRECISE_ONE ) ;
  RATIONAL_ONE : constant RATIONAL := ( PRECISE_ONE , PRECISE_ONE ) ;

  function "+" ( LEFT , RIGHT : RATIONAL ) return RATIONAL ;

  function "-" ( LEFT , RIGHT : RATIONAL ) return RATIONAL ;

  function "*" ( LEFT , RIGHT : RATIONAL ) return RATIONAL ;

  function "/" ( LEFT , RIGHT : RATIONAL ) return RATIONAL ;

  function "**" ( LEFT : RATIONAL ;
                  RIGHT : INTEGER ) return RATIONAL ;

  function "+" ( RIGHT : RATIONAL ) return RATIONAL ;

  function "-" ( RIGHT : RATIONAL ) return RATIONAL ;

  function "abs" ( RIGHT : RATIONAL ) return RATIONAL ;

  function ">" ( LEFT , RIGHT : RATIONAL ) return BOOLEAN ;

  function ">=" ( LEFT , RIGHT : RATIONAL ) return BOOLEAN ;

  function "<" ( LEFT , RIGHT : RATIONAL ) return BOOLEAN ;

  function "<=" ( LEFT , RIGHT : RATIONAL ) return BOOLEAN ;

  function RATIONAL_TO_INTEGER ( ITEM : RATIONAL ) return INTEGER ;

  function INTEGER_TO_RATIONAL ( ITEM : INTEGER ) return RATIONAL ;

  procedure RATIONAL_TO_STRING ( ITEM   : in RATIONAL;
                                 RESULT : out STRING;
                                 LAST   : out NATURAL );

  function STRING_TO_RATIONAL ( ITEM : STRING ) return RATIONAL ;

  function RATIONAL_TO_FLOAT ( ITEM : RATIONAL ) return FLOAT ;

  function FLOAT_TO_RATIONAL ( ITEM : FLOAT ) return RATIONAL ;

  function FRACTION ( LEFT , RIGHT : INTEGER ) return RATIONAL ;

  function GCD ( LEFT , RIGHT : PRECISE ) return PRECISE ;

  function LCM ( LEFT , RIGHT : PRECISE ) return PRECISE ;

  function REDUCE ( RIGHT : RATIONAL ) return RATIONAL ;

end RATIONAL_TYPES ;