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asinh — Areasinus Hyperbolikus
Berechnet den Areasinus Hyperbolikus von arg. Der Areasinus Hyperbolikus ist die Umkehrfunktion des Sinus Hyperbolikus, d.h. asinh(sinh(arg)) = arg.
Der zu verarbeitende Wert
Der Areasinus Hyperbolikus von arg
| Version | Beschreibung |
|---|---|
| 5.3.0 | Die Funktion ist nun auf allen Plattformen verfügbar. |
The correct implementation of asinh(x) for Windows plataform is:
-------------------------------------------------------
function asinh($x)
{
return ln($x + sqrt(1 + pow($x, 2)));
}
function ln($x)
{
return $x = log($x)/log(M_E);
}
--------------------------------------------------------
The worksheet above includes a comparation about the native asinh(x) and the implemented version using LN and LOG (like Snoyes posted on 27-Dec-2005 07:42)
http://www.mavadesign.com.br/allan/asinh(x).xls
This implementation using LN, give THE SAME results that function asinh(x) linux native.
Allan Patrick Engel
Curitiba - Paraná - Brasil
When using snoyes alternative bcasinh function, don't forget to check the precision of each single bcfunction or the default precision of ini setting bcmath.scale.
asinh for windows:
The definition for asinh is asinh(z) = log(z + sqrt(z^2 + 1))
The built-in math functions and operators give poor results for small values of z. The BCMath version produces closer results, but still quite distant if z < 1. A BCMath version of the log function might help.
if (!function_exists("asinh")) {
function asinh($z) {
return log($z + sqrt($z^2 +1));
}
}
if (!function_exists("bcasinh")) {
function bcasinh($z) {
return log(bcadd($z, bcsqrt(bcadd(bcpow($z, 2), 1))));
}
}
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