HYPOT(3M)           RISC/os Reference Manual            HYPOT(3M)



NAME
     hypot, cabs - Euclidean distance, complex absolute value

SYNOPSIS
     #include <math.h>

     double hypot(x,y)
     double x,y;

     float fhypot(float x, float y)
     double x,y;

     double cabs(z)
     struct {double x,y;} z;

     float fcabs(z)
     struct {float x,y;} z;

DESCRIPTION
     Hypot(x,y), fhypot(x,y), cabs(x,y) and fcabs(x,y) return
     sqrt(x*x+y*y) computed in such a way that underflow will not
     happen, and overflow occurs only if the final result
     deserves it.

     Fhypot and fcabs are the same functions as hypot and cabs
     but for the float data type.

     hypot(infinity,v) = hypot(v,infinity) = +infinity for all v,
     including NaN.

DIAGNOSTICS
     When the correct value would overflow, hypot returns +infin-
     ity.

ERROR (due to Roundoff, etc.)
     Below 0.97 ulps.  Consequently hypot(5.0,12.0) = 13.0
     exactly; in general, hypot and cabs return an integer when-
     ever an integer might be expected.

     The same cannot be said for the shorter and faster version
     of hypot and cabs that is provided in the comments in
     cabs.c; its error can exceed 1.2 ulps.

NOTES
     As might be expected, hypot(v,NaN) and hypot(NaN,v) are NaN
     for all finite v.  Programmers might be surprised at first
     to discover that hypot(+infinity,NaN) = +infinity.  This is
     intentional; it happens because hypot(infinity,v) = +infin-
     ity for all v, finite or infinite.  Hence hypot(infinity,v)
     is independent of v.  The IEEE NaN is designed to disappear
     when it turns out to be irrelevant, as it does in
     hypot(infinity,NaN).



                        Printed 11/19/92                   Page 1

HYPOT(3M)           RISC/os Reference Manual            HYPOT(3M)



SEE ALSO
     math(3M), sqrt(3M)

AUTHOR
     W. Kahan


















































 Page 2                 Printed 11/19/92