casio fx10
here is the casio fx10, released in may 1974, their first pocket scientific
calculator and what a splendid machine it is. the machine is quite chunky
and takes 4 AA cells.
notice the use of the small zero found on early casio models. for some
reason this was standard until they decided to use the outer segments that
we now recognise. the small zero looks quirky and weird by comparison.
being a scientific model, i immediately put it through its paces in
terms of accuracy and calculation domain. it has an interesting set of
functions. sin, cos and tan but no inverses. arctan would have been nice.
natural log and e^x are here, also common log. the machine works in
degrees and rather helpfully has a deg/min/second button for such entry.
this does not however, show the number in the (later) casio style with the
time sexagesimal separated by an upper zero. instead it just divides by 60
in the right way as you enter numbers.
integer powering is on offer with a^n. n can only be an integer from 0
to 9 and a is whatever is on display. it computes the result as soon as
the first digit is pressed after the a^n button and clearly calculates it
by repeated multiply. this is not so daft. the two reasons are time and
accuracy. time because arbitrary powering can be performed manually using
the logs available, which takes much longer incidentally and accuracy
because some accuracy is lost powering by logs. this is exactly the
approach taken by the casio fx1 (here sold as remington).
the functional domain for sin, cos and tan is not +/360 degrees as
claimed by the manual, but in fact the magic 1440 degrees of many later
casios (eg fx39) 

log operates on any input, yes even negative ones. the manual admits that the
sign is ignored for both logs and square roots. e^x only accepts arguments
within +/10. this must be down to the internal algorithm because e^x of bigger
numbers could be displayed. notice that there is no Exp button. there is no way to
supply an exponent and no exponential values are displayed. anything bigger than
the 8 digits is overflow.
i discovered a fascinating secret fact with the tan function for values near
90 degrees. this was during my attempt at tan 355/226 radians as part of the torture
test. interestingly values near enough to 90 degrees that cause the result
to exceed 1000 are rejected as overflow (ie reported as an error). this means
the closest value to 90 that tan accepts is arctan(1000) = 89.9427 and
tan(89.9427) is reported as 999.93. the range exclusion around 90 is not
documented but what is interesting is that the engineers knew that the results
were somewhat wrong near 90 and decided to exclude this range rather than
display the wrong answer. this is commendable because giving out bogus answers
is bad form. it must work by performing the internal algorithm then testing
against 1000 and rejecting afterwards.
something else i didnt mention that you cant see here, is the most splendid
way the display flickers and dances whilst the calculations are in progress.
some take a few seconds (none as long as the fx1 which takes 16 seconds for
cube root, then again this model does not have that one). 