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csqrt
Complex square root.SYNOPSIS:
void csqrt();
cmplx z, w;
csqrt(&z, &w);
DESCRIPTION:
If z = x + iy, r = |z|, then
1/2
Im w = [ (r - x)/2 ] ,
Re w = y / 2 Im w.
Note that -w is also a square root of z. The root chosen is always in the upper half plane.
Because of the potential for a cancellation error in r - x, the result is sharpened by doing a Heron iteration (see sqrt) in complex arithmetic.
ACCURACY:
Relative error:
arithmetic domain # trials peak rms
DEC -10,+10 25000 3.2e-17 9.6e-18
IEEE -10,+10 100000 3.2e-16 7.7e-17
JavaScript:
var x = {"r":4.5,"i":3.14} ;
var a = cephes.csqrt(x);
returns a, complex object of schema
{
"r" : double,
"i": double
}