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From: John H Meyers on 4 Jun 2010 19:28
On 6/4/2010 6:42 AM, Giovanni wrote:

> From what I understood, you can occasionally make more precise
> calculations than the calculator would normally let you do?
> How can you do that?

"User" functions operate upon (and return)
floating-point "real" values with 12 mantissa digits
and exponent (of ten) in the range -499 to +499.

Some internal functions that may be
employed by "user" functions operate upon (and return)
floating-point "long real" values with 15 mantissa digits
and exponent (of ten) in the range -49999 to +49999.

After performing 256.04 MENU
you should see a function LR~R above the "D" key;
this function converts "long real" <-> "real" data types.

Although the HP49/50 series calculators can display "long real"
values on the stack, no "user" functions accept or return "long reals."

Rather, various "user" functions may first
convert their "real" inputs to "long real,"
then calculate internally with "long real" intermediate values,
then round final results to "real" final output,
which provides improved overall accuracy for "real input" -> "real output"
(carefully designed and deeply analyzed algorithms
are also an ingredient of the calculators' excellent overall accuracy).

To gain direct access to the internal "long real" (and "long complex") functions
requires programming in SysRPL, which has thousands of available functions,
but at the same time doesn't spend time protecting itself against invalid input,
hence can end up crashing or wiping out memory (and even all stored objects)
if mistakes are made.

Additional external software also exists for extended precision calculation
of various sorts, e.g. http://www.hpcalc.org/search.php?query=long+real
(some of these are for older HP48 series only).

The following system (double-precision reals,
preserving 24-digit correctly rounded results
for all provided basic functions) employs only "user" functions,
and its "source" should work on HP49/50 series as well,
after adjusting each instance of one variable name
(e.g. DIV2 -> Div2, because DIV2 is now "reserved" as a command name):
http://www.hpcalc.org/search.php?query=digi24

Come to think of it, has anyone seen "The Phantom" since last Halloween?

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