Calculating e^x-1 on classic HPs

[Paul Dale]

A nice identity using hyperbolics is: e^x-1 = tanh(x/2) (e^x+1)

The 34S uses:

Code:


    u = e^x
    v = u - 1
    if v = 0, return x
    if v = -1, return -1
    return v * x / ln(u)

As William Kahan said of this: nearly full working relative accuracy despite cancellation no matter how tiny x may be.

Dieter's method avoids the conditionals which is a plus for some machines.


- Pauli