BSD 4_3_Net_2 release

[unix-history] / usr / src / lib / libm / common_source / hypot.3

diff --git a/usr/src/lib/libm/common_source/hypot.3 b/usr/src/lib/libm/common_source/hypot.3
index 9c23ab8..01250c4 100644 (file)
--- a/usr/src/lib/libm/common_source/hypot.3
+++ b/usr/src/lib/libm/common_source/hypot.3
@@ -1,29 +1,124 @@
-.\"    @(#)hypot.3     6.1 (Berkeley) %G%
+.\" Copyright (c) 1985, 1991 Regents of the University of California.
+.\" All rights reserved.

 .\"
 .\"

-.TH HYPOT 3M  ""
-.AT 3
-.SH NAME
-hypot, cabs \- Euclidean distance
-.SH SYNOPSIS
-.nf
-.B #include <math.h>
-.PP
-.B double hypot(x, y)
-.B double x, y;
-.PP
-.B double cabs(z)
-.B struct { double x, y;} z;
-.fi
-.SH DESCRIPTION
-.I Hypot
+.\" Redistribution and use in source and binary forms, with or without
+.\" modification, are permitted provided that the following conditions
+.\" are met:
+.\" 1. Redistributions of source code must retain the above copyright
+.\"    notice, this list of conditions and the following disclaimer.
+.\" 2. Redistributions in binary form must reproduce the above copyright
+.\"    notice, this list of conditions and the following disclaimer in the
+.\"    documentation and/or other materials provided with the distribution.
+.\" 3. All advertising materials mentioning features or use of this software
+.\"    must display the following acknowledgement:
+.\"    This product includes software developed by the University of
+.\"    California, Berkeley and its contributors.
+.\" 4. Neither the name of the University nor the names of its contributors
+.\"    may be used to endorse or promote products derived from this software
+.\"    without specific prior written permission.
+.\"
+.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
+.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+.\" ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
+.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+.\" SUCH DAMAGE.
+.\"
+.\"     @(#)hypot.3    6.7 (Berkeley) 5/6/91
+.\"
+.Dd May 6, 1991
+.Dt HYPOT 3
+.Os BSD 4
+.Sh NAME
+.Nm hypot ,
+.Nm cabs
+.Nd euclidean distance and complex absolute value functions
+.Sh SYNOPSIS
+.Fd #include <math.h>
+.Ft double
+.Fn hypot "double x" "double y"
+.Fd struct {double x, y;} z;
+.Ft double
+.Fn cabs z
+.Sh DESCRIPTION
+The
+.Fn hypot
+and
+.Fn cabs
+functions
+computes 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.
+.Pp
+.Fn hypot "\*(If" "v"
+=
+.Fn hypot "v" "\*(If"
+= +\*(If for all
+.Ar 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.
+.Pp
+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
 and

-.I cabs
-return
-.PP
-.IP
-sqrt(x*x + y*y),
-.LP
-taking precautions against unwarranted overflows.
-.SH SEE ALSO
-exp(3M) for
-.I sqrt
+.Fn hypot "\*(Na" "v"
+are \*(Na for all
+.Em finite
+.Ar v ;
+with "reserved operand" in place of "\*(Na", the
+same is true on a
+.Tn VAX .
+But programmers on machines other than a
+.Tn VAX
+(if has no \*(If)
+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
+.Ar v ,
+finite or infinite.
+Hence
+.Fn hypot "\*(If" "v"
+is independent of
+.Ar 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 .