xref: /freebsd/lib/msun/man/hypot.3 (revision 195ebc7e9e4b129de810833791a19dfb4349d6a9)
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28.\"     from: @(#)hypot.3	6.7 (Berkeley) 5/6/91
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31.Dd March 30, 2008
32.Dt HYPOT 3
33.Os
34.Sh NAME
35.Nm hypot ,
36.Nm hypotf ,
37.Nm hypotl ,
38.Nm cabs ,
39.Nm cabsf ,
40.Nm cabsl
41.Nd Euclidean distance and complex absolute value functions
42.Sh LIBRARY
43.Lb libm
44.Sh SYNOPSIS
45.In math.h
46.Ft double
47.Fn hypot "double x" "double y"
48.Ft float
49.Fn hypotf "float x" "float y"
50.Ft "long double"
51.Fn hypotl "long double x" "long double y"
52.In complex.h
53.Ft double
54.Fn cabs "double complex z"
55.Ft float
56.Fn cabsf "float complex z"
57.Ft "long double"
58.Fn cabsl "long double complex z"
59.Sh DESCRIPTION
60The
61.Fn hypot ,
62.Fn hypotf
63and
64.Fn hypotl
65functions
66compute the
67sqrt(x*x+y*y)
68in such a way that underflow will not happen, and overflow
69occurs only if the final result deserves it.
70The
71.Fn cabs ,
72.Fn cabsf
73and
74.Fn cabsl
75functions compute the complex absolute value of
76.Fa z .
77.Pp
78.Fn hypot "\*(If" "v"
79=
80.Fn hypot "v" "\*(If"
81= +\*(If for all
82.Fa v ,
83including \*(Na.
84.Sh ERROR (due to Roundoff, etc.)
85Below 0.97
86.Em ulps .
87Consequently
88.Fn hypot "5.0" "12.0"
89= 13.0
90exactly;
91in general, hypot and cabs return an integer whenever an
92integer might be expected.
93.Sh NOTES
94As might be expected,
95.Fn hypot "v" "\*(Na"
96and
97.Fn hypot "\*(Na" "v"
98are \*(Na for all
99.Em finite
100.Fa v .
101But programmers
102might be surprised at first to discover that
103.Fn hypot "\(+-\*(If" "\*(Na"
104= +\*(If.
105This is intentional; it happens because
106.Fn hypot "\*(If" "v"
107= +\*(If
108for
109.Em all
110.Fa v ,
111finite or infinite.
112Hence
113.Fn hypot "\*(If" "v"
114is independent of
115.Fa v .
116Unlike the reserved operand fault on a
117.Tn VAX ,
118the
119.Tn IEEE
120\*(Na is designed to
121disappear when it turns out to be irrelevant, as it does in
122.Fn hypot "\*(If" "\*(Na" .
123.Sh SEE ALSO
124.Xr carg 3 ,
125.Xr math 3 ,
126.Xr sqrt 3
127.Sh HISTORY
128Both a
129.Fn hypot
130function and a
131.Fn cabs
132function
133appeared in
134.At v7 .
135.Sh STANDARDS
136The
137.Fn hypot ,
138.Fn hypotf ,
139.Fn hypotl ,
140.Fn cabs ,
141.Fn cabsf ,
142and
143.Fn cabsl
144functions conform to
145.St -isoC-99 .
146