26 Nov
2005
26 Nov
'05
6:37 p.m.
Jerome H. Fine wrote:
Hi All,
...
Background: I want to calculate the reciprocal
(inverse) of a
number between 1 and 65535 to an accuracy of 256 bits after
the binary (or decimal) point. This result will then be used to
calculate the logarithm of that value which in turn will be used
to calculate li(x) for values of x up to 10**38. The code is in
FORTRAN 77 (could also be in FORTRAN IV) which calls
MACRO-11 code to do the really low level stuff such as
repeated addition of many words with MANY Adc instructions
following each addition (99.9% of the time the Adc instructions
are never used).
Jerome, I didn't read all of this, but I have to ask: why do you need to compute
the reciprocal at all?
log(x^y) = y*log(x)
in this case, y=-1, so
log(1/x) = -log(x)
accuracy is limited to your log computation, rather than being limited by your
reciprocal and your log approximations.