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Apr 29, 1991, 9:49:50 PM4/29/91

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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 sjth...@cup.portal.com

"I'll get by with a little help from my friends."

"Sir, I protest! I am NOT a merry man!" --Worf

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