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from: @(#)hypot.3 6.7 (Berkeley) 5/6/91
$FreeBSD: src/lib/msun/man/hypot.3,v 1.13 2005/01/14 23:28:28 das Exp $
.Dd January 14, 2005 .Dt HYPOT 3 .Os .Sh NAME .Nm hypot , .Nm hypotf , .Nm cabs , .Nm cabsf .Nd Euclidean distance and complex absolute value functions .Sh LIBRARY .Lb libm .Sh SYNOPSIS n math.h .Ft double .Fn hypot "double x" "double y" .Ft float .Fn hypotf "float x" "float y" n complex.h .Ft double .Fn cabs "double complex z" .Ft float .Fn cabsf "float complex z" .Sh DESCRIPTION The .Fn hypot and .Fn hypotf functions compute the sqrt(x*x+y*y) in such a way that underflow will not happen, and overflow occurs only if the final result deserves it. The .Fn cabs and .Fn cabsf functions compute the complex absolute value of .Fa z .
p .Fn hypot "\*(If" "v" = .Fn hypot "v" "\*(If" = +\*(If for all .Fa v , including \*(Na. .Sh ERROR (due to Roundoff, etc.) Below 0.97 .Em ulps . Consequently .Fn hypot "5.0" "12.0" = 13.0 exactly; in general, hypot and cabs return an integer whenever an integer might be expected.
p 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 .Em ulps . .Sh NOTES As might be expected, .Fn hypot "v" "\*(Na" and .Fn hypot "\*(Na" "v" are \*(Na for all .Em finite .Fa v . But programmers might be surprised at first to discover that .Fn hypot "\(+-\*(If" "\*(Na" = +\*(If. This is intentional; it happens because .Fn hypot "\*(If" "v" = +\*(If for .Em all .Fa v , finite or infinite. Hence .Fn hypot "\*(If" "v" is independent of .Fa v . Unlike the reserved operand fault on a .Tn VAX , the .Tn IEEE \*(Na is designed to disappear when it turns out to be irrelevant, as it does in .Fn hypot "\*(If" "\*(Na" . .Sh SEE ALSO .Xr math 3 , .Xr sqrt 3 .Sh HISTORY Both a .Fn hypot function and a .Fn cabs function appeared in .At v7 .
