Modern Math CAcos

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CAcos

Returns the inverse cosine of a complex number, or of any real number.

Syntax

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

Notes

• The Hull–Fairgrieve–Tang method, transcribed from .NET's Asin_Internal. The textbook -i·Log( iz + CSqrt( 1 - z² ) ) cancels catastrophically near the branch points at ±1, which is exactly where an inverse sine is most often evaluated. This does not.
• Same NaN at exactly ±1 as CAsin, and the same fix — that segment is answered directly.
• Same cuts as CAsin, and the same sign-bit correction against .NET.
• The float64 overload is AfxNova's CArcCosReal.
• The imaginary part is the negation of CAsin's: CAcos( 1 + 0i ) is 0 - 0i.

Examples

#import "std/numeric"
using numeric

print CToString( CAcos( CSet( 0.5, 0.25 ) ) )  '' 1.0691874735193958-0.2813960562452928i
print CToString( CAcos( CSet( 1, 0 ) ) )       '' 0-0i
print CToString( CAcos( 2.0 ) )                '' 0-1.3169578969248166i
print CToString( CAcos( CSet( -2, 0.0 ) ) )    '' 3.141592653589793-1.3169578969248166i

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