Re: Looking for Ada Technique Name and References

[nahaj@u.cc.utah.edu (John Halleck)]

Diana Webster (dkweb@arlut.utexas.edu) wrote:
: This technique is called "composition" in mathematics, i.e., the composition
: of two functions,
: i.e, sum (average (xnum)).  Most programming languages support this.

  The trick posted is not a composition of functions.

  It keeps the notation of the composition of functions, but substitutes
  a special purpose routine faster than the composition of functions. 

  This trick is *** NOT *** supported by most languages.

: John Halleck <nahaj@u.cc.utah.edu> wrote in message
: news:88kh6q$j4j$1@coward.ks.cc.utah.edu...
: > > John Halleck (nahaj@u.cc.utah.edu) wrote:
: > > : I would appreciate it if someone could give me the name and a
: > > : print reference for the following technique.
: >
: > > Someone Replied:
: >
: > >  It is called overloading.
: >
: >   It uses overloading, but that was not the technique I was trying
: >   to get accross.
: >
: >   The technique in question is turning the what is normally written
: >   as two function calls  (More or less:)
: >       "*" (Transpose (A), B)
: >   into a type mark and a single function call to a special function
: >   that can handle it all more effeciently.
: >
: > >
: > > : Background:
: > >
: > > :    Many matrix methods are written in the form  A := Transpose(B)*C
: > > :    But, actually forming the transpose is expensive, and you are
: better
: > > :    off just writing a second matrix multiply routine that takes the
: > > :    two matrices and treats the one as a transpose without actually
: > > :    doing the transpose.
: > >
: > > :    Below is a technique that allows one to write it as one normally
: > > :    sees it written, but lets the Ada compiler do the selection of
: > > :    an appropriate routine.
: > >
: > > : Is there a name for this technique?   Does it appear already
: documented
: > > : somewhere?
: > >
: > >
: : --------------------------------------------------------------------------
: ----
: > >
: > > : --  ...
: > >
: > > : type Matrix is array (positive range <>, positive range <>) of Float;
: > > : type Transpose is new Matrix;
: > >
: > > : --  ...
: > >
: > > : -- This is just a matrix multiply routine.
: > > : function "*" (Left : Matrix; Right : Matrix) return Matrix;
: > >
: > > : -- This routine multiplies the transpose of Left by Right.
: > > : function "*" (Left : Transpose; Right : Matrix) return Matrix;
: > >
: > > : ----------
: > >
: > > : --  Examples:
: > > : A, B, C, D, E: Matrix;
: > >
: > > : --  ...
: > >
: > > : A := B * C;              --  Matrix multiply.
: > > : D := Transpose (E) * F;  --  D gets the result of multiplying E'F
: > > :                          --  (By selecting the appropriate routine.
: > >
: > > : ---------------------------------------------------------------------