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

Martin Maechler Martin Maechler <maechler@stat.math.ethz.ch>
Wed, 24 May 2000 14:30:24 +0200 (CEST)

```>>>>> "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
>>>> 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.

KH> sense.

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

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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