Modern Math Complex Operators

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Complex operators

Adds, subtracts, multiplies, divides, raises and compares complex numbers.

Syntax

operator +  ( byref a as Complex, byref b as Complex ) as Complex
operator +  ( byref z as Complex, byval x as float64 ) as Complex
operator +  ( byval x as float64,  byref z as Complex ) as Complex
''  - * / ^ likewise, and unary -
operator =  ( byref a as Complex, byref b as Complex ) as boolean
operator =  ( byref z as Complex, byval x as float64 ) as boolean
operator =  ( byval x as float64,  byref z as Complex ) as boolean
''  <> likewise, in all three arrangements

Notes

• Every operator has all three arrangements — Complex with Complex, float64 with Complex, Complex with float64. That is why there is no CAddReal/CMulImag family: z + 3.0 and z * 2.0 already say it, and better.
• Division uses Smith's formula, in all three overloads. The naive (ac+bd)/(c²+d²) overflows its denominator once the components pass about 1.3e154, where the true quotient is an ordinary number.
• Multiplication is the plain four-multiply form, matching .NET. C99's infinity-recovery path is deliberately not implemented — it costs a branch on every multiply for a case that only arises in deliberate infinity arithmetic.
• ^ is CPow. z ^ 2.0, z ^ w and 2.0 ^ z all resolve to it.
• z = 3.0 means equal to the real number and on the real axis — the imaginary part must be exactly zero. Either sign of zero counts, because -0.0 = 0.0 as numbers.
• No < > <= >=. There is no ordering on ℂ. The same reasoning declined lexicographic ordering on tuples.

Examples

#import "std/numeric"
using numeric

dim as Complex a = CSet( 3, 4 ), b = CSet( -1, 2 )

print CToString( a + b )    '' 2+6i
print CToString( a * b )    '' -11+2i
print CToString( a / b )    '' 1-2i
print CToString( a + 2.0 )  '' 5+4i   -- the mixed form
print CToString( 2.0 - a )  '' -1-4i
print CToString( a ^ 2.0 )  '' -6.999999999999998+24.000000000000004i
print a = CSet( 3, 4 )      '' true
print a <> b                '' true
print CSet( 3, 0 ) = 3.0    '' true   -- on the real axis, and equal
print CSet( 3, 1 ) = 3.0    '' false   -- equal real part, but not on the axis

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