The old round off problem?
David Treadwell
i.failed.turing.test at gmail.com
Sun Mar 5 05:01:36 CET 2006
I wish I knew!
So I asked Google. Here's what I learned:
Most implementations are based on, or similar to the implementation
in the fdlibm package.
sinh(x) and cosh(x) are both based on exp(x). See http://
www.netlib.org/cgi-bin/netlibfiles.pl?filename=/fdlibm/e_sinh.c
exp(x) is implemented by:
1. reducing x into the range |r| <= 0.5 * ln(2), such that x = k *
ln(2) + r
2. approximating exp(r) with a fifth-order polynomial,
3. re-scaling by multiplying by 2^k: exp(x) = 2^k * exp(r)
sinh(x) is mathematically ( exp(x) - exp(-x) )/2 but it's not
calculated directly that way.
My brain hurts at this point; it's late. I'll have another go at
hunting down the errors tomorrow. In the interim, does anybody out
there already know the answer?
:--David
On Mar 4, 2006, at 8:27 PM, sam wrote:
> David I beg I beg
> Can you answer the question?
>
> Also thanks for the information on using the Taylor series.
>
> Sam Schulenburg
>
> --
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