INTERFACE PZProc;

(* Miscellaneous functions and procedures *)

TYPE
  LONG = LONGREAL;

PROCEDURE Squeeze(x: LONG; epsilon, delta: LONG): LONG;
  (*
    Returns the "significant" value of "x" assuming it is contaminated
    by noise of absolute magnitude "epsilon" and relative magnitude "delta".
    I.e. the result is approximately "x/epsilon" when "ABS(x)" is small,
    and approximately "SGN(x)*log(ABS(x))/delta" when "ABS(x)" is large *)
    
PROCEDURE Interpolate(t: LONG; t0, p0: LONG; t1, p1: LONG): LONG;
  (*
    Interpolates linearly the value at time "t" between 
    values "p0" and "p1", assuming they have times "t0" and "t1".
  *)
  
PROCEDURE CubicInterpolate(
    t: LONG; 
    t0, p0: LONG; 
    t1, p1: LONG;
    t2, p2: LONG;
    t3, p3: LONG;
  ): LONG;
  (*
    Interpolates cubically some function at time
    "t", assuming it has values "p0,..p3" at times "t0,..t3".
  *)
  
PROCEDURE Mismatch(
    intgDiffSqr: LONG;  (* Square difference, integrated over length *) 
    length: LONG;       (* Length of match *)
    maxDiffSqr: LONG;   (* Maximum difference square *)
  ): LONG;  

<* UNUSED *> PROCEDURE OldMismatch(
    intgDiffSqr: LONG;  (* Square difference, integrated over length *) 
    length: LONG;       (* Length of match *)
    fractality: LONG;   (* Fractality exponent *)
  ): LONG;
  (*
    Computes a `mismatch measure' for the match between two segments
    (taken from two curves, two curvature graphs, or two symbolic
    curvature chains).  The parameter "intgDiffSqr" must be the 
    integral of some `difference' squared, over some measure of the
    extent of the match; and "length" must be that measure.  
    
    The result is "sqrt(intgDiffSqr/length**fractality)".
    If "fractality = 1", this formula reduces to the
    root mean square difference bethween the matched values.
    If fractality is greater than 1, this formula favors
    longer matches over shorter ones, even if they have the
    same root mean square difference.
  *)


PROCEDURE IntersectIntervals(
    aini, afin: CARDINAL;
    bini, bfin: CARDINAL;
    (*OUT*)
    VAR ini, fin: CARDINAL;
  ): BOOLEAN;
  (*
    Computes the intersection "[ini..fin]" of two index ranges "[aini..afin]"
    and "[bini..bfin]", taking into account that they have been 
    reduced modulo some integer "m", and hence they may wrap around
    (i.e. "afin" may be less than "aini", and similarly for "bfin"/"bini".)
    Returns TRUE iff the intersection is non-empty. *)
    

PROCEDURE JoinIntervals(
    aini, afin: CARDINAL;
    bini, bfin: CARDINAL;
    (*OUT*)
    VAR ini, fin: CARDINAL;
  );
  (*
    Computes the join "[ini..fin]" of two simply overlapping 
    index ranges "[aini..afin]" and "[bini..bfin]", 
    taking into account that they have been 
    reduced modulo some integer "m", and hence they may wrap around
    (i.e. "afin" may be less than "aini", and similarly for "bfin"/"bini".) *)

END PZProc.