Start basics of a quaternion library.

src/BBS-Numerical-quaternion.adb

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+with Ada.Numerics.Generic_Elementary_Functions;
+package body BBS.Numerical.quaternion is
+ package elem is new Ada.Numerics.Generic_Elementary_Functions(f);
+ --
+ -- Basic operations
+ --
+ function "+" (Left, Right : quaternion) return quaternion is
+ begin
+ return (r => Left.r + Right.r,
+ i => Left.i + Right.i,
+ j => Left.j + Right.j,
+ k => Left.k + Right.k);
+ end;
+ --
+ function "-" (Left, Right : quaternion) return quaternion is
+ begin
+ return (r => Left.r - Right.r,
+ i => Left.i - Right.i,
+ j => Left.j - Right.j,
+ k => Left.k - Right.k);
+ end;
+
+ function "*" (Left : f; Right : quaternion) return quaternion is
+ begin
+ return (r => Left * Right.r,
+ i => Left * Right.i,
+ j => Left * Right.j,
+ k => Left * Right.k);
+ end;
+ --
+ function "*" (Left : quaternion; Right : f) return quaternion is
+ begin
+ return (r => Left.r * Right,
+ i => Left.i * Right,
+ j => Left.j * Right,
+ k => Left.k * Right);
+ end;
+ --
+ function "/" (Left : quaternion; Right : f) return quaternion is
+ begin
+ return (r => Left.r / Right,
+ i => Left.i / Right,
+ j => Left.j / Right,
+ k => Left.k / Right);
+ end;
+ --
+ function magnitude(self : in quaternion) return f'Base is
+ begin
+ return elem.Sqrt(self.r * self.r + self.i * self.i +
+ self.j * self.j + self.k * self.k);
+ end;
+ --
+end BBS.Numerical.quaternion;

src/BBS-Numerical-quaternion.ads

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+--
+-- This is a simple package that supports basic functions on quaternions.
+--
+generic
+ type F is digits <>;
+package BBS.Numerical.quaternion is
+ type quaternion is tagged record
+ r : f'Base; -- Scalar part
+ i : f'Base; -- i, j, and k are the vector part
+ j : f'Base;
+ k : f'Base;
+ end record;
+ --
+ -- Basic arithmatic operations
+ --
+ function "+" (Left, Right : quaternion) return quaternion;
+ function "-" (Left, Right : quaternion) return quaternion;
+
+ function "*" (Left : f; Right : quaternion) return quaternion;
+ function "*" (Left : quaternion; Right : f) return quaternion;
+
+ function "/" (Left : quaternion; Right : f) return quaternion;
+
+ function magnitude(self : in quaternion) return f'Base;
+
+end BBS.Numerical.quaternion;