Hi Waldek and all !
> Actually, now I am convinced that there is no simple "real" formula
> giving correct branch cuts. Official Lisp formula for asin is
> asin x == -%i*log(%i*x+sqrt(1-x^2))
> The Lisp formula stays away from branch cuts of logarithm, and only
> branch cut of sqrt matters (an
On Wed, 17 Jan 2007, Waldek Hebisch wrote:
| Gabriel Dos Reis wrote:
| > Waldek Hebisch <[EMAIL PROTECTED]> writes:
| > | However, the problem with asin is just one special case. We
| > | would like to support many multivalued special functions (which in
| > | numerical version require branch cut
Gabriel Dos Reis wrote:
> Waldek Hebisch <[EMAIL PROTECTED]> writes:
> | However, the problem with asin is just one special case. We
> | would like to support many multivalued special functions (which in
> | numerical version require branch cuts). Tracking that we get
> | "correct" values on cuts
I wrote:
> There is an easy workaround, put:
>
> asin x == -atan(-x/sqrt(1-x**2))
>
After further examination I have found that this does not work
(appearantly I was using different version for machine test, and
analysis shows that the formula above is wrong). Actually,
now I am convinced that
Waldek Hebisch <[EMAIL PROTECTED]> writes:
| The problem here is that sin asin(7.0::COMPLEX FLOAT) give something
| close to -7. This is due to wrong bunch cuts during evaliation.
| Namely in trigcat we have:
|
| asin x == atan(x/sqrt(1-x**2))
|
| this formula for asin has wrong branch cuts. Wh
The problem here is that sin asin(7.0::COMPLEX FLOAT) give something
close to -7. This is due to wrong bunch cuts during evaliation.
Namely in trigcat we have:
asin x == atan(x/sqrt(1-x**2))
this formula for asin has wrong branch cuts. When x is real and bigger
then 1 sqrt(1-x**2) is imaginary w
