Modern Math CAsinh

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CAsinh

Returns the inverse hyperbolic sine of a complex number.

Syntax

CAsinh( byref z as Complex ) as Complex

Notes

• Reached through the inverse trigonometric functions, so it inherits the Hull–Fairgrieve–Tang conditioning rather than carrying its own copy. asinh z = -i·asin( iz ).
• The real axis is answered directly, which is both more accurate and correct about the sign of a zero.
• asinh( ±0 ) is special-cased because mingw-w64's asinh( +0.0 ) returns -0.0. The function is odd and owes the sign of its argument back; that is a platform defect, not an inherited one.
• There is no float64 overload: the real asinh is defined everywhere, so there is nothing for one to fix. Use Asinh from math.tiko, in the same module.

Examples

#import "std/numeric"
using numeric

print CToString( CAsinh( CSet( 0.5, 0.25 ) ) )  '' 0.49267568342077056+0.22432845263466752i
print CToString( CAsinh( CSet( 0, 1 ) ) )       '' 0+1.5707963267948966i   -- PI/2 -- NaN before the fast path
print CToString( CAsinh( CSet( 1, 0 ) ) )       '' 0.8813735870195429+0i   -- the real asinh

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