sjthomas@cup.portal.com (Stephen J Thomas) (04/30/91)
MORE FRACTIONS ON THE HP 32SII
I have to agree with Joe Horn in his enthusiasm for the fraction
package in the 32SII. It is a substantial improvement over fraction
implementation on other calculators. However, there are a couple of
problems in the fraction system.
But first, for those who have not played with fractions on the 32SII,
here are a few basics:
As has been reported here several times, fraction entry is normally
done via the [.] key, which is used to separate any integer portion
from the numerator, and to separate the numerator from the
denominator. For instance, to enter 1 3/5, press 1.3.5. The display
shows normal fraction format, and automatically changes improper
fractions to an integer plus proper fraction display. To enter
fractions with no integer portion, such as 4/5, you can enter either
.4.5 or 4..5 .
The FDISP function toggles fraction display mode (and flag 7) with the
standard decimal display mode (FIX, SCI, ENG or ALL). If you are in a
decimal mode and execute FDISP, the current x-register value is
displayed as a fraction.
The display uses up [^] and down [v] arrow annunciators to indicate
if the actual x-register value is greater or less than the displayed
fraction.
You can enter any denominator with 4 or fewer digits. If your
denominator is greater than 4095 (which is the default denominator),
the fraction is changed to the closest fraction with a denominator
less than or equal to 4095. The integer portion and the numerator
together must comprise no more than 12 digits.
The /c function is used to establish the maximum desired denominator.
It's actual interpretation is subject to the current fraction format,
which is controlled by flags 8 and 9:
o MOST PRECISE FRACTION (CF 8): The default format. Fractions are
reduced as much as possible, with any denominator up to the /c value.
o FACTORS OF DENOMINATOR (SF 8, CF 9): Fractions are reduced as much
as possible, and the denominator is a factor of the /c value. So if
the /c value is 16, the possible denominators are 2, 4, 8 and 16.
o FIXED DENOMINATOR (SF 8, SF 9): Fractions are not reduced (except
to display improper fractions as proper fractions), and the
denominator is the /c value.
Now, some of the problems with the fraction package.
#1: The "Factors of Denominator" mode sometimes produces denominators
which are not factors. In these cases, the 32SII seems to
display the "Most Precise Mode" fraction, so this is a minor bug.
Example: SF 8
CF 9
8 /c
3 1/x See 0 1/3; but 3 isn't a factor of 8
#2: The "Fixed Denominator" mode (SF 8, SF 9) sometimes produces
denominators other than the specified one, along with incorrect
numerators. The amount of the error can be about +/- 1. HP is
now sending a manual addendum recommending that Flag 9 not be
used at all.
Example: SF 8
SF 9
1 ENTER ENTER ENTER
8 /c
32 1/x (which is 0.03125)
See v 0 7/8 (which is 0.875)
We should see ^ 0 0/8
(recall ^ and v are the up- and down-arrows.)
Now press + repeatedly. You'll see:
v 1 7/8
v 2 1/2
v 4
v 4 3/4
v 5 3/5
v 6 1/2
v 7 3/7
etc... all of which are WAY off, and very few of
which have a "fixed" denominator of 8.
#3: The "Most Precise" mode (CF 8, CF 9) and the "Factors of
Denominator" mode (SF 8, CF 9) sometimes violate the
commutativity of addition, and produce incorrect results. This
only occurs when the x value is close to 1/8 of the /c value, and
the last two digits of the LASTx register's exponent are nonzero.
The worst error this can produce is approximately +/- 0.125,
which makes this a substantial bug.
Example: CF 8
CF 9
8 /c
32 1/x See v 1/8; should be ^ 0 0/8
Pressing 0 + gives ^ 0, but
32 1/x 0 X<->Y + gives v 0 1/8
Addition should be commutative.
The LASTx value is causing the problems.
In late March, I called HP's Technical Support department about
problems with the fraction system (actually, at that time, I only knew
about bug #1). The HP employee stated that the 32SII can give
incorrect answers when using fractions (although she would not go into
any details about what problems were known), and that HP would likely
be instituting some type of exchange program this summer. She
suggested I call back after April 1 for details. I did call back,
left a message, and haven't heard back from them yet. I suppose I'll
try again after May 1.
Stephen J Thomas sjthomas@cup.portal.com
"I'll get by with a little help from my friends."
"Sir, I protest! I am NOT a merry man!" --Worf