1HYPOT(3M)                                                            HYPOT(3M)
2
3
4

NAME

6       hypot, cabs - Euclidean distance, complex absolute value
7

SYNOPSIS

9       #include <math.h>
10
11       double hypot(x,y)
12       double x,y;
13
14       double cabs(z)
15       struct {double x,y;} z;
16

DESCRIPTION

18       Hypot(x,y)  and  cabs(x,y)  return sqrt(x∗x+y∗y) computed in such a way
19       that underflow will not happen, and overflow occurs only if  the  final
20       result deserves it.
21
22       hypot(infinity,v)  = hypot(v,infinity) = +infinity for all v, including
23       NaN.
24

ERROR (due to Roundoff, etc.)

26       Below 0.97 ulps.  Consequently hypot(5.0,12.0) = 13.0 exactly; in  gen‐
27       eral,  hypot  and  cabs  return an integer whenever an integer might be
28       expected.
29
30       The same cannot be said for the shorter and faster version of hypot and
31       cabs  that  is provided in the comments in cabs.c; its error can exceed
32       1.2 ulps.
33

NOTES

35       As might be expected, hypot(v,NaN) and hypot(NaN,v)  are  NaN  for  all
36       finite  v;  with "reserved operand" in place of "NaN", the same is true
37       on a VAX.  But programmers on machines other than  a  VAX  (it  has  no
38       infinity)  might  be  surprised at first to discover that hypot(±infin‐
39       ity,NaN)  =  +infinity.   This  is  intentional;  it  happens   because
40       hypot(infinity,v)  =  +infinity  for  all v, finite or infinite.  Hence
41       hypot(infinity,v) is independent of v.  Unlike the reserved operand  on
42       a  VAX,  the  IEEE NaN is designed to disappear when it turns out to be
43       irrelevant, as it does in hypot(infinity,NaN).
44

SEE ALSO

46       math(3M), sqrt(3M)
47

AUTHOR

49       W. Kahan
50
51
52
534th Berkeley Distribution        May 12, 1986                        HYPOT(3M)