Modern Math CLog

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CLog

Returns the natural logarithm of a complex number, or its logarithm to a given base.

Syntax

CLog( byref z as Complex ) as Complex
CLog( byref z as Complex, byval baseValue as float64 ) as Complex

Notes

• Principal branch, cut along the negative real axis, with the cut below it: CLog( -1 + 0i ) is +πi and CLog( -1 - 0i ) is -πi. That is atan2's convention and C99's, and it is why the two zeros have to be distinguishable.
• Built on CLogAbs rather than on log( CAbs( z ) ), so it survives operands whose square would overflow.
• The two-argument form is CLog( z ) / log( baseValue ). A base of 1 gives NaN, as it must.
• CExp( CLog( z ) ) returns z; CLog( CExp( z ) ) returns z only while the imaginary part is inside (-π, π], because outside it a different branch is the principal one.

Examples

#import "std/numeric"
using numeric

print CToString( CLog( CSet( 3, 4 ) ) )       '' 1.6094379124341003+0.9272952180016122i
print CToString( CLog( CSet( -1, 0.0 ) ) )    '' 0+3.141592653589793i   -- above the cut
print CToString( CLog( CSet( -1, -0.0 ) ) )   '' 0-3.141592653589793i   -- below it
print CToString( CLog( CSet( 8, 0 ), 2.0 ) )  '' 3+0i   -- log base 2 of 8

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