103 lines
3.1 KiB
Groff
103 lines
3.1 KiB
Groff
.\" Copyright (c) 2007-2008 David Schultz <das@FreeBSD.org>
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.\" All rights reserved.
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.\"
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.\" Redistribution and use in source and binary forms, with or without
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.\" modification, are permitted provided that the following conditions
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.\" are met:
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.\" 1. Redistributions of source code must retain the above copyright
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.\" notice, this list of conditions and the following disclaimer.
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.\" 2. Redistributions in binary form must reproduce the above copyright
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.\" notice, this list of conditions and the following disclaimer in the
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.\" documentation and/or other materials provided with the distribution.
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.\"
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.\" THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
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.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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.\" ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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.\" SUCH DAMAGE.
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.\"
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.\" $FreeBSD$
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.\"
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.Dd March 30, 2008
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.Dt CSQRT 3
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.Os
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.Sh NAME
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.Nm csqrt ,
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.Nm csqrtf ,
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.Nm csqrtl
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.Nd complex square root functions
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.Sh LIBRARY
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.Lb libm
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.Sh SYNOPSIS
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.In complex.h
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.Ft double complex
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.Fn csqrt "double complex z"
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.Ft float complex
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.Fn csqrtf "float complex z"
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.Ft long double complex
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.Fn csqrtl "long double complex z"
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.Sh DESCRIPTION
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The
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.Fn csqrt ,
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.Fn csqrtf ,
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and
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.Fn csqrtl
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functions compute the square root of
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.Fa z
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in the complex plane, with a branch cut along the negative real axis.
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In other words,
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.Fn csqrt ,
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.Fn csqrtf ,
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and
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.Fn csqrtl
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always return the square root whose real part is non-negative.
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.Sh RETURN VALUES
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These functions return the requested square root.
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The square root of 0 is
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.Li +0 \*(Pm 0 ,
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where the imaginary parts of the input and respective result have
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the same sign.
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For infinities and \*(Nas, the following rules apply, with the
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earlier rules having precedence:
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.Bl -column -offset indent "-\*(If + \*(Na*I" "\*(If \*(Pm \*(If*I " "(for all k)"
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.Em Input Result
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k + \*(If*I \*(If + \*(If*I (for all k)
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-\*(If + \*(Na*I \*(Na \*(Pm \*(If*I
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\*(If + \*(Na*I \*(If + \*(Na*I
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k + \*(Na*I \*(Na + \*(Na*I
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\*(Na + k*I \*(Na + \*(Na*I
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-\*(If + k*I +0 + \*(If*I
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\*(If + k*I \*(If + 0*I
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.El
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.Pp
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For numbers with negative imaginary parts, the above special cases
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apply given the identity:
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.Dl csqrt(conj(z) = conj(sqrt(z))
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Note that the sign of \*(Na is indeterminate.
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Also, if the real or imaginary part of the input is finite and
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an \*(Na is generated, an invalid exception will be thrown.
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.Sh SEE ALSO
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.Xr cabs 3 ,
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.Xr fenv 3 ,
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.Xr math 3 ,
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.Sh STANDARDS
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The
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.Fn csqrt ,
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.Fn csqrtf ,
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and
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.Fn csqrtl
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functions conform to
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.St -isoC-99 .
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.Sh BUGS
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For
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.Fn csqrt
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and
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.Fn csqrtl ,
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inexact results are not always correctly rounded.
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