Modern Math CSqrt

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CSqrt

Returns the principal square root of a complex number or of a negative real.

Syntax

CSqrt( byref z as Complex ) as Complex
CSqrt( byval x as float64 ) as Complex

Notes

• The principal root, always in the right half plane — the real part is never negative.
• This is the .NET Core 3.0 algorithm, not the polar form. The old vector header and AfxNova both shipped FromPolar( sqr(|z|), Arg(z)/2 ), which is .NET Framework 4.7's and loses most of its significant digits near the negative real axis, where Arg is the difference of two nearly-equal quantities.
• The cut is the negative real axis and the sign of a zero imaginary part decides the side: CSqrt( -4 + 0i ) is +2i and CSqrt( -4 - 0i ) is -2i. Both source libraries test imaginary == 0 and return the positive root for both, which puts half the axis on the wrong branch.
• The float64 overload is the square root of a real that may be negative — AfxNova's CSqrReal, expressed as an overload because it is the same concept with a different argument type.
• Operands near the type maximum take a rescale-by-¼ path, so CSqrt of 1e308 + 1e308i is finite.

Examples

#import "std/numeric"
using numeric

print CToString( CSqrt( CSet( 3, 4 ) ) )          '' 2+1i   -- exact: (2+i)^2 = 3+4i
print CToString( CSqrt( -1.0 ) )                  '' 0+1i   -- the double overload
print CToString( CSqrt( CSet( -4, 0.0 ) ) )       '' 0+2i   -- above the cut
print CToString( CSqrt( CSet( -4, -0.0 ) ) )      '' 0-2i   -- below it
print CIsFinite( CSqrt( CSet( 1e308, 1e308 ) ) )  '' true   -- the rescale path

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Library: Math Library
Category: Math Library
Documented under: Members