[Rd] hypot(x,y) instead of pythag(a,b) ?!

[Martin Maechler]

>>>>> "KH" == Kurt Hornik <Kurt.Hornik@ci.tuwien.ac.at> writes:

>>>>> Martin Maechler writes:
    >> Some of you may have seen the  pythag() part in the R API definition in 
    >> "Writing R Extensions" (source = doc/manual/R-exts.texinfo).

    >> or followed the report and Prof. Brian Ripley's answer about pythag()'s
    >> availability from R's binary.

    >> As we say in above manual

    >>>> `pythag(A, B)' computes `sqrt(A^2 + B^2)' without overflow or
    >>>> destructive underflow: for example it still works when both A and
    >>>> B are between `1e200' and `1e300' (in IEEE double precision).

    >> --
    >> "Problem" is : 
    >> The GNU C library (and other C libraries ??)
    >> defines a function	 
    >> double hypot(double x, double y)

    >> with identical semantics to our pythag() from above
    >> The Info (e.g. in Linux Emacs C-h i "m libc") about "Libc" contains
    >> (in the section "Exponentiation and Logarithms"):

    >> =============================
    >>>> - Function: double hypot (double X, double Y)
    >>>> - Function: float hypotf (float X, float Y)
    >>>> - Function: long double hypotl (long double X, long double Y)
    >>>> These functions return `sqrt (X*X + Y*Y)'.  This is the length of
    >>>> the hypotenuse of a right triangle with sides of length X and Y,
    >>>> or the distance of the point (X, Y) from the origin.  Using this
    >>>> function instead of the direct formula is wise, since the error is
    >>>> much smaller.  See also the function `cabs' in *Note Absolute
    >>>> Value::.

    >> Further "problem": In R, we are already partially relying on the
    >> availability of the hypot() function :

    >> At the toplevel of R-1.0.1's source
    >> grep -rwn hypot . 
    >> ~~~~~~~~~~~~~~~~~ (with a newer GNU grep that has "-r" for "recursive"):
    >> gives

    >> ./src/appl/cpoly.c:145:	shr[i] = hypot(pr[i], pi[i]);
    >> ./src/appl/fortran.c:111:    return hypot(z->r, z->i);
    >> ./src/main/complex.c:122:    logr = log(hypot(a->r, a->i) );
    >> ./src/main/complex.c:279:  REAL(y)[i] = hypot(COMPLEX(x)[i].r, COMPLEX(x)[i].i);
    >> ./src/main/complex.c:285:  REAL(y)[i] = hypot(COMPLEX(x)[i].r, COMPLEX(x)[i].i);
    >> ./src/main/complex.c:388:    r->r = log(hypot( z->r, z->i ));
    >> ./src/main/complex.c:411:    if( (mag = hypot(z->r, z->i)) == 0.0)
    >> ./src/main/plot.c:1201:		if ((f = d/hypot(xx-xold, yy-yold)) < 0.5) {
    >> ./src/main/plot.c:2455:double hypot(double x, double y)
    >> ./src/main/plot.c:2559:		d = hypot(xp-xi, yp-yi);
    >> ./src/gnuwin32/math/protos.h:43:extern double hypot ( double x, double y );

    >> ---------

    >> My "theses"
   
    >> o when hypot() is available, it should be used since it will be 
    >> efficient, precise, etc.
    >> o when it's not available, our "configure" should find out, and set
    >> corresponding "HAVE_HYPOT" to `false'.
    >> o in that case, we should provide a hypot()  {for the above code to
    >> work!}, and we probably should use (an improvement?) of the current
    >> pythag() function [src/appl/pythag.c in R versions <= 1.0.1].
   
    >> o Hence, we should drop pythag() from the R API and rather say that we
    >> provide hypot() whenever the system's C library 
    >> (or its "math.h", aka libm.*, aka "-m" part, respectively) does *not* 
    >> provide it.

    >> o I think an R function  hypot() would also make sense.

    >> We'll be glad to hear feedback about this!

    KH> I have no strong opinions about this, but the above seems to make
    KH> sense.

    KH> If I should make changes to configure, then pls let me know.

Yes, please. 
We should check for it's presence with configure and
then use

#ifndef HAVE_HYPOT
double hypot(double x, double y) {

  ...
  ...

}
#endif


In the mean time I've seen that it exists in 
   - GNU lib"c" (libm infact)
   - Solaris
   - HP-UX
   - DEC Alpha Unix

and it is part of the X/Open "XPG4" standard,
but not POSIX (as of Don Lewine) nor ANSI C.

Martin
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