From f11c770329edf407de1e534e286ecbfd2a3495c9 Mon Sep 17 00:00:00 2001
From: Jed Barber <jjbarber@y7mail.com>
Date: Tue, 7 Feb 2017 00:21:59 +1100
Subject: Rationals package added

---
 src/rationals.adb | 380 ++++++++++++++++++++++++++++++++++++++++++++++++++++++
 src/rationals.ads | 218 +++++++++++++++++++++++++++++++
 2 files changed, 598 insertions(+)
 create mode 100644 src/rationals.adb
 create mode 100644 src/rationals.ads

diff --git a/src/rationals.adb b/src/rationals.adb
new file mode 100644
index 0000000..2255afe
--- /dev/null
+++ b/src/rationals.adb
@@ -0,0 +1,380 @@
+
+
+with Ada.Strings.Fixed;
+
+
+package body Rationals is
+
+
+    function Reduce
+           (Numerator, Denominator : in Integer)
+        return Fraction
+    is
+        A : Integer := Numerator;
+        B : Integer := Denominator;
+        Temp : Integer;
+    begin
+        --  Euclid's algorithm
+        loop
+            Temp := A;
+            A := B;
+            B := Temp mod B;
+            exit when B = 0;
+        end loop;
+        return (Num => Numerator / A, Den => Denominator / A);
+    end Reduce;
+
+
+
+
+    function "+"
+           (Left, Right : in Fraction)
+        return Fraction is
+    begin
+        return Reduce
+               (Left.Num * Right.Den + Left.Den * Right.Num,
+                Left.Den * Right.Den);
+    end "+";
+
+    function "+"
+           (Left  : in Fraction;
+            Right : in Integer)
+        return Fraction is
+    begin
+        return Reduce
+               (Left.Num + Left.Den * Right,
+                Left.Den);
+    end "+";
+
+    function "+"
+           (Left  : in Integer;
+            Right : in Fraction)
+        return Fraction is
+    begin
+        return Reduce
+               (Left * Right.Den + Right.Num,
+                Right.Den);
+    end "+";
+
+
+
+
+    function "-"
+           (Left, Right : in Fraction)
+        return Fraction is
+    begin
+        return Reduce
+               (Left.Num * Right.Den - Left.Den * Right.Num,
+                Left.Den * Right.Den);
+    end "-";
+
+    function "-"
+           (Left  : in Fraction;
+            Right : in Integer)
+        return Fraction is
+    begin
+        return Reduce
+               (Left.Num - Left.Den * Right,
+                Left.Den);
+    end "-";
+
+    function "-"
+           (Left  : in Integer;
+            Right : in Fraction)
+        return Fraction is
+    begin
+        return Reduce
+               (Left * Right.Den - Right.Num,
+                Right.Den);
+    end "-";
+
+
+
+
+    function "-"
+           (Right : in Fraction)
+        return Fraction is
+    begin
+        return (Num => - Right.Num, Den => Right.Den);
+    end "-";
+
+
+
+
+    function "*"
+           (Left, Right : in Fraction)
+        return Fraction is
+    begin
+        return Reduce
+               (Left.Num * Right.Num,
+                Left.Den * Right.Den);
+    end "*";
+
+    function "*"
+           (Left  : in Fraction;
+            Right : in Integer)
+        return Fraction is
+    begin
+        return Reduce
+               (Left.Num * Right,
+                Right);
+    end "*";
+
+    function "*"
+           (Left  : in Integer;
+            Right : in Fraction)
+        return Fraction is
+    begin
+        return Reduce
+               (Left * Right.Num,
+                Right.Den);
+    end "*";
+
+
+
+
+    function "/"
+           (Left, Right : in Fraction)
+        return Fraction is
+    begin
+        return Reduce
+               (Left.Num * Right.Den,
+                Left.Den * Right.Num);
+    end "/";
+
+    function "/"
+           (Left  : in Fraction;
+            Right : in Integer)
+        return Fraction is
+    begin
+        return Reduce
+               (Left.Num,
+                Left.Den * Right);
+    end "/";
+
+    function "/"
+           (Left  : in Integer;
+            Right : in Fraction)
+        return Fraction is
+    begin
+        return Reduce
+               (Right.Num,
+                Left * Right.Den);
+    end "/";
+
+    function "/"
+           (Left, Right : in Integer)
+        return Fraction is
+    begin
+        return Reduce (Left, Right);
+    end "/";
+
+
+
+
+    function "="
+           (Left, Right : in Fraction)
+        return Boolean is
+    begin
+        return  Left.Num = Right.Num and
+                Left.Den = Right.Den;
+    end "=";
+
+    function "="
+           (Left  : in Fraction;
+            Right : in Integer)
+        return Boolean is
+    begin
+        return Left.Num = Right and Left.Den = 1;
+    end "=";
+
+    function "="
+           (Left  : in Integer;
+            Right : in Fraction)
+        return Boolean is
+    begin
+        return Left = Right.Num and Right.Den = 1;
+    end "=";
+
+
+
+
+    function "<="
+           (Left, Right : in Fraction)
+        return Boolean is
+    begin
+        return Left.Num * Right.Den <= Left.Den * Right.Num;
+    end "<=";
+
+    function "<="
+           (Left  : in Fraction;
+            Right : in Integer)
+        return Boolean is
+    begin
+        return Left.Num <= Left.Den * Right;
+    end "<=";
+
+    function "<="
+           (Left  : in Integer;
+            Right : in Fraction)
+        return Boolean is
+    begin
+        return Left * Right.Den <= Right.Num;
+    end "<=";
+
+
+
+
+    function "<"
+           (Left, Right : in Fraction)
+        return Boolean is
+    begin
+        return Left.Num * Right.Den < Left.Den * Right.Num;
+    end "<";
+
+    function "<"
+           (Left  : in Fraction;
+            Right : in Integer)
+        return Boolean is
+    begin
+        return Left.Num < Left.Den * Right;
+    end "<";
+
+    function "<"
+           (Left  : in Integer;
+            Right : in Fraction)
+        return Boolean is
+    begin
+        return Left * Right.Den < Right.Num;
+    end "<";
+
+
+
+
+    function ">="
+           (Left, Right : in Fraction)
+        return Boolean is
+    begin
+        return Left.Num * Right.Den >= Left.Den * Right.Num;
+    end ">=";
+
+    function ">="
+           (Left  : in Fraction;
+            Right : in Integer)
+        return Boolean is
+    begin
+        return Left.Num >= Left.Den * Right;
+    end ">=";
+
+    function ">="
+           (Left  : in Integer;
+            Right : in Fraction)
+        return Boolean is
+    begin
+        return Left * Right.Den >= Right.Num;
+    end ">=";
+
+
+
+
+    function ">"
+           (Left, Right : in Fraction)
+        return Boolean is
+    begin
+        return Left.Num * Right.Den > Left.Den * Right.Num;
+    end ">";
+
+    function ">"
+           (Left  : in Fraction;
+            Right : in Integer)
+        return Boolean is
+    begin
+        return Left.Num > Left.Den * Right;
+    end ">";
+
+    function ">"
+           (Left  : in Integer;
+            Right : in Fraction)
+        return Boolean is
+    begin
+        return Left * Right.Den > Right.Num;
+    end ">";
+
+
+
+
+    function Numerator
+           (Item : in Fraction)
+        return Integer is
+    begin
+        return Item.Num;
+    end Numerator;
+
+    function Denominator
+           (Item : in Fraction)
+        return Integer is
+    begin
+        return Item.Den;
+    end Denominator;
+
+    function Floor
+           (Item : in Fraction)
+        return Integer is
+    begin
+        return Item.Num / Item.Den;
+    end Floor;
+
+    function Ceiling
+           (Item : in Fraction)
+        return Integer is
+    begin
+        if Item.Num mod Item.Den = 0 then
+            return Item.Num / Item.Den;
+        else
+            return 1 + Item.Num / Item.Den;
+        end if;
+    end Ceiling;
+
+    function Round
+           (Item : in Fraction)
+        return Integer is
+    begin
+        if Item.Num mod Item.Den > Standard."/" (Item.Den, 2) then
+            return 1 + Item.Num / Item.Den;
+        else
+            return Item.Num / Item.Den;
+        end if;
+    end Round;
+
+
+
+
+    function Image
+           (Item : in Fraction)
+        return String
+    is
+        use Ada.Strings;
+        use Ada.Strings.Fixed;
+    begin
+        return Trim (Integer'Image (Item.Num), Left) & '/' &
+                Trim (Integer'Image (Item.Den), Left);
+    end Image;
+
+    function Value
+           (Item : in String)
+        return Fraction
+    is
+        use Ada.Strings;
+        use Ada.Strings.Fixed;
+        A, B, S : Integer;
+    begin
+        S := Index (Item, "/");
+        A := Integer'Value (Item (Item'First .. S - 1));
+        B := Integer'Value (Item (S + 1 .. Item'Last));
+        return (Num => A, Den => B);
+    end Value;
+
+
+end Rationals;
+
+
diff --git a/src/rationals.ads b/src/rationals.ads
new file mode 100644
index 0000000..03ac95e
--- /dev/null
+++ b/src/rationals.ads
@@ -0,0 +1,218 @@
+
+
+package Rationals is
+
+
+    type Fraction is private;
+
+
+
+
+    function "+"
+           (Left, Right : in Fraction)
+        return Fraction;
+
+    function "+"
+           (Left  : in Fraction;
+            Right : in Integer)
+        return Fraction;
+
+    function "+"
+           (Left  : in Integer;
+            Right : in Fraction)
+        return Fraction;
+
+
+
+
+    function "-"
+           (Left, Right : in Fraction)
+        return Fraction;
+
+    function "-"
+           (Left  : in Fraction;
+            Right : in Integer)
+        return Fraction;
+
+    function "-"
+           (Left  : in Integer;
+            Right : in Fraction)
+        return Fraction;
+
+
+
+
+    function "-"
+           (Right : in Fraction)
+        return Fraction;
+
+
+
+
+    function "*"
+           (Left, Right : in Fraction)
+        return Fraction;
+
+    function "*"
+           (Left  : in Fraction;
+            Right : in Integer)
+        return Fraction;
+
+    function "*"
+           (Left  : in Integer;
+            Right : in Fraction)
+        return Fraction;
+
+
+
+
+    function "/"
+           (Left, Right : in Fraction)
+        return Fraction;
+
+    function "/"
+           (Left  : in Fraction;
+            Right : in Integer)
+        return Fraction;
+
+    function "/"
+           (Left  : in Integer;
+            Right : in Fraction)
+        return Fraction;
+
+    function "/"
+           (Left, Right : in Integer)
+        return Fraction;
+
+
+
+
+    function "="
+           (Left, Right : in Fraction)
+        return Boolean;
+
+    function "="
+           (Left  : in Fraction;
+            Right : in Integer)
+        return Boolean;
+
+    function "="
+           (Left  : in Integer;
+            Right : in Fraction)
+        return Boolean;
+
+
+
+
+    function "<="
+           (Left, Right : in Fraction)
+        return Boolean;
+
+    function "<="
+           (Left  : in Fraction;
+            Right : in Integer)
+        return Boolean;
+
+    function "<="
+           (Left  : in Integer;
+            Right : in Fraction)
+        return Boolean;
+
+
+
+
+    function "<"
+           (Left, Right : in Fraction)
+        return Boolean;
+
+    function "<"
+           (Left  : in Fraction;
+            Right : in Integer)
+        return Boolean;
+
+    function "<"
+           (Left  : in Integer;
+            Right : in Fraction)
+        return Boolean;
+
+
+
+
+    function ">="
+           (Left, Right : in Fraction)
+        return Boolean;
+
+    function ">="
+           (Left  : in Fraction;
+            Right : in Integer)
+        return Boolean;
+
+    function ">="
+           (Left  : in Integer;
+            Right : in Fraction)
+        return Boolean;
+
+
+
+
+    function ">"
+           (Left, Right : in Fraction)
+        return Boolean;
+
+    function ">"
+           (Left  : in Fraction;
+            Right : in Integer)
+        return Boolean;
+
+    function ">"
+           (Left  : in Integer;
+            Right : in Fraction)
+        return Boolean;
+
+
+
+
+    function Numerator
+           (Item : in Fraction)
+        return Integer;
+
+    function Denominator
+           (Item : in Fraction)
+        return Integer;
+
+    function Floor
+           (Item : in Fraction)
+        return Integer;
+
+    function Ceiling
+           (Item : in Fraction)
+        return Integer;
+
+    function Round
+           (Item : in Fraction)
+        return Integer;
+
+
+
+
+    function Image
+           (Item : in Fraction)
+        return String;
+
+    function Value
+           (Item : in String)
+        return Fraction;
+
+
+private
+
+
+    type Fraction is record
+        Num : Integer := 0;
+        Den : Integer := 1;
+    end record;
+
+
+end Rationals;
+
+
-- 
cgit