Copyright (c) 2007-2008 David Schultz <das@FreeBSD.org>
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THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
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$FreeBSD$
.Dd March 30, 2008 .Dt CSQRT 3 .Os .Sh NAME .Nm csqrt , .Nm csqrtf , .Nm csqrtl .Nd complex square root functions .Sh LIBRARY .Lb libm .Sh SYNOPSIS n complex.h .Ft double complex .Fn csqrt "double complex z" .Ft float complex .Fn csqrtf "float complex z" .Ft long double complex .Fn csqrtl "long double complex z" .Sh DESCRIPTION The .Fn csqrt , .Fn csqrtf , and .Fn csqrtl functions compute the square root of .Fa z in the complex plane, with a branch cut along the negative real axis. In other words, .Fn csqrt , .Fn csqrtf , and .Fn csqrtl always return the square root whose real part is non-negative. .Sh RETURN VALUES These functions return the requested square root. The square root of 0 is .Li +0 \*(Pm 0 , where the imaginary parts of the input and respective result have the same sign. For infinities and \*(Nas, the following rules apply, with the earlier rules having precedence: l -column -offset indent "-\*(If + \*(Na*I" "\*(If \*(Pm \*(If*I " "(for all k)" .Em "Input" Ta Em "Result" Ta \& k + \*(If*I \*(If + \*(If*I (for all k) -\*(If + \*(Na*I \*(Na \*(Pm \*(If*I \& \*(If + \*(Na*I \*(If + \*(Na*I \& k + \*(Na*I \*(Na + \*(Na*I \& \*(Na + k*I \*(Na + \*(Na*I \& -\*(If + k*I +0 + \*(If*I \& \*(If + k*I \*(If + 0*I \& .El
All rights reserved.
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.
THIS SOFTWARE IS PROVIDED BY THE AUTHOR 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 AUTHOR 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.
$FreeBSD$
.Dd March 30, 2008 .Dt CSQRT 3 .Os .Sh NAME .Nm csqrt , .Nm csqrtf , .Nm csqrtl .Nd complex square root functions .Sh LIBRARY .Lb libm .Sh SYNOPSIS n complex.h .Ft double complex .Fn csqrt "double complex z" .Ft float complex .Fn csqrtf "float complex z" .Ft long double complex .Fn csqrtl "long double complex z" .Sh DESCRIPTION The .Fn csqrt , .Fn csqrtf , and .Fn csqrtl functions compute the square root of .Fa z in the complex plane, with a branch cut along the negative real axis. In other words, .Fn csqrt , .Fn csqrtf , and .Fn csqrtl always return the square root whose real part is non-negative. .Sh RETURN VALUES These functions return the requested square root. The square root of 0 is .Li +0 \*(Pm 0 , where the imaginary parts of the input and respective result have the same sign. For infinities and \*(Nas, the following rules apply, with the earlier rules having precedence: l -column -offset indent "-\*(If + \*(Na*I" "\*(If \*(Pm \*(If*I " "(for all k)" .Em "Input" Ta Em "Result" Ta \& k + \*(If*I \*(If + \*(If*I (for all k) -\*(If + \*(Na*I \*(Na \*(Pm \*(If*I \& \*(If + \*(Na*I \*(If + \*(Na*I \& k + \*(Na*I \*(Na + \*(Na*I \& \*(Na + k*I \*(Na + \*(Na*I \& -\*(If + k*I +0 + \*(If*I \& \*(If + k*I \*(If + 0*I \& .El
p For numbers with negative imaginary parts, the above special cases apply given the identity: .Dl csqrt(conj(z) = conj(sqrt(z)) Note that the sign of \*(Na is indeterminate. Also, if the real or imaginary part of the input is finite and an \*(Na is generated, an invalid exception will be thrown. .Sh SEE ALSO .Xr cabs 3 , .Xr fenv 3 , .Xr math 3 , .Sh STANDARDS The .Fn csqrt , .Fn csqrtf , and .Fn csqrtl functions conform to .St -isoC-99 . .Sh BUGS For .Fn csqrt and .Fn csqrtl , inexact results are not always correctly rounded.