// Use of this source code is governed by a BSD-style

package cmplx

import

// The original C code, the long comment, and the constants
// below are from http://netlib.sandia.gov/cephes/c9x-complex/clog.c.
// The go code is a simplified version of the original C.
//
// Cephes Math Library Release 2.8:  June, 2000
// Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
//
// The readme file at http://netlib.sandia.gov/cephes/ says:
//    Some software in this archive may be from the book _Methods and
// Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster
// International, 1989) or from the Cephes Mathematical Library, a
// commercial product. In either event, it is copyrighted by the author.
// What you see here may be used freely but it comes with no support or
// guarantee.
//
//   The two known misprints in the book are repaired here in the
// source listings for the gamma function and the incomplete beta
// integral.
//
//   Stephen L. Moshier
//   moshier@na-net.ornl.gov

// Complex square root
//
// DESCRIPTION:
//
// If z = x + iy,  r = |z|, then
//
//                       1/2
// Re w  =  [ (r + x)/2 ]   ,
//
//                       1/2
// Im w  =  [ (r - x)/2 ]   .
//
// Cancellation error in r-x or r+x is avoided by using the
// identity  2 Re w Im w  =  y.
//
// Note that -w is also a square root of z. The root chosen
// is always in the right half plane and Im w has the same sign as y.
//
// ACCURACY:
//
//                      Relative error:
// arithmetic   domain     # trials      peak         rms
//    DEC       -10,+10     25000       3.2e-17     9.6e-18
//    IEEE      -10,+10   1,000,000     2.9e-16     6.1e-17

// Sqrt returns the square root of x.
// The result r is chosen so that real(r) ≥ 0 and imag(r) has the same sign as imag(x).
func ( complex128) complex128 {
if imag() == 0 {
// Ensure that imag(r) has the same sign as imag(x) for imag(x) == signed zero.
if real() == 0 {
return complex(0, imag())
}
if real() < 0 {
return complex(0, math.Copysign(math.Sqrt(-real()), imag()))
}
return complex(math.Sqrt(real()), imag())
} else if math.IsInf(imag(), 0) {
return complex(math.Inf(1.0), imag())
}
if real() == 0 {
if imag() < 0 {
:= math.Sqrt(-0.5 * imag())
return complex(, -)
}
:= math.Sqrt(0.5 * imag())
return complex(, )
}
:= real()
:= imag()
var  float64
// Rescale to avoid internal overflow or underflow.
if math.Abs() > 4 || math.Abs() > 4 {
*= 0.25
*= 0.25
= 2
} else {
*= 1.8014398509481984e16 // 2**54
*= 1.8014398509481984e16
= 7.450580596923828125e-9 // 2**-27
}
:= math.Hypot(, )
var  float64
if  > 0 {
= math.Sqrt(0.5* + 0.5*)
=  * math.Abs((0.5*)/)
*=
} else {
= math.Sqrt(0.5* - 0.5*)
=  * math.Abs((0.5*)/)
*=
}
if  < 0 {
return complex(, -)
}
return complex(, )
}