rounding floating point variables

[Paul Purvis]

i woiuld like to revist the rounding issues in powerbasic.
i am using another basic for finance problems.
but i need to use powerbasic now.
i don't want to use integers or binary coded decimal variables for math.
i read where the floating point variables use an IEEE STANDARD.
i also read that rounding is not done correctly using these IEEE STANDARD.

if i want to round a floating point variable of 2.5 to a whole number
i want the answer of 3.
i understand it will round to the nearest even number of 2 instead.

also is there a built in function that will truncate a floating point
to a whole number(chop off the numbers to the right of the decimal point)

thanks paul




[This message has been edited by paul d purvis (edited April 21, 2005).]

[Eric Pearson]

Paul --

> i also read that rounding is not done correctly
> using these IEEE STANDARD.

That depends on what you mean by "correctly". PB does round numbers in the way that is specified by the IEEE standards. In other words it implements the IEEE standard correctly. But the IEEE standard may not be "correct" if you need another type of rounding.

Check out the CEIL and INT functions in the documentation. If they are not exactly what you need, links in the Help File will point you toward additional functions.

-- Eric


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[This message has been edited by Eric Pearson (edited April 20, 2005).]

[Michael Mattias]

>i don't want to use integers or binary coded decimal variables for math.

Why the heck not? BCD (PB/DOS type FIX) is ideal for money calculations when rounding is undesireable.

[Paul Purvis]

thanks for the posting and ideas
my programming experience in basic (non powerbasic) has had on two types of
numeric variables integers and real(floating), where there were only one type of each
i am of some belief that if i can stick with just those two types of numeric variables, it
might make my programming easier, and only use other types of numeric variables where i am
force too.

yes it will make my programs slower and bigger, but after converting some code to powerbasic lastnight.
powerbasic was so much faster in math ability, it really did blow my socks off.
that was really impressive, i guess it was using the math coprocessor.

there is my code below
i want to use extended floating point numbers
integers are used just for flags and looping concerns for the most part

in order to get values correct, rounding, etc,
it seams i have to make sure i put the "##" behind all my values
is that correct.


and on the subject of ceil, int, fix
do those return an integer and will those integers only be
between -36768 to 36767
or will they return larger values
in the reference book it talks about those routines returning an integer or does
it meant to mean those routines return a whole number.


thanks for responses once again
paul


start of code

rem program to compute the annual percentage rate on a loan( or rate of return)
rem the term must be larger than 1 right now, that part is to be worked on
rem odddays=represents the number of days odd days where there is more than a month until the firstpayment
rem for example from january 1, 2000 to january 1,2000 there is a whole month and 0(zero) odd days
rem for example from january 1, 2000 to january 2,2000 there is a whole month and 1 odd days
rem for example from january 29, 2000 to february 29,2000 there is a whole month and 0 odd days
rem for example from january 30, 2000 to february 29,2000 there is a whole month and 0 odd days
rem for example from january 31, 2000 to february 29,2000 there is a whole month and 0 odd days
rem for example from december 31, 1999 to february 29,2000 there is a whole month and 30 odd days
rem odd days are worked from the first payment day back in equal months and a equal month is 30 days

rem the payment schedule may have a first odd payment amount to the remaining regular payments


rem ton##=top of note
rem charges##=finance charges plus any other charges classified as interest for computing the annual percentage rate(apr)
rem as defined by regulation z in usa by the federal reserve board.
rem term%=the total payments on a loan
rem firstpayment##= the first payment amount, amount maybe not equal to the remaining payments
rem regpayment##= the remaining payment amounts
rem

rem start of program
rem warning this program is not yet ready to do a calculation on the term being equal to 1
rem and it is not complete, a term of 1 will return a value of -1

TON##=1209.96##
TERM%=36
ODDDAYS%=0
CHARGES##=209.96##
FIRSTPAYMENT##=33.61##
REGPAYMENT##=33.61##

TEST%=0
RATE##=0.0##
COMPUTEBAL##=0.0##
IF TERM%=1 THEN _
IF ODDDAYS%=0 THEN RATE##=-1.0##:GOTO 1002


ODDDAYS##=ODDDAYS%

PRINCIPAL##=TON##-CHARGES##
PRINCIPALTEMP##=INT(PRINCIPAL##*1000##)

HIGHRATE##=20.0##
LOWRATE##=0.0##

99
HIGHRATE##=HIGHRATE##+(HIGHRATE##*2.0##)
COMPUTEBAL##=0.0##
TEMP##=(HIGHRATE##/12.0)*.01##
TEMP1##=1##+((ODDDAYS##/30.0##)*TEMP##)
TEMP2##=1##+TEMP##
COMPUTEBAL##=COMPUTEBAL##+(FIRSTPAYMENT##/(TEMP1##*(TEMP2##)^1))
FOR J%=2 TO TERM%
COMPUTEBAL##=COMPUTEBAL##+(REGPAYMENT##/ (TEMP1##*((TEMP2##)^J%)))
NEXT J%
IF COMPUTEBAL##<PRINCIPAL## THEN GOTO 999
LOWRATE##=HIGHRATE##
GOTO 99

999
100
RATE##=((HIGHRATE##-LOWRATE##)/2.0##)+LOWRATE##

101
COMPUTEBAL##=0.0##

TEMP##=(RATE##/12.0##)*.01##
REM CALCULATING FOR A SINGLE ADVANCE AND SINGLE PAYMENT LESS THAN ONE YEAR
IF TERM%=1 THEN _
ODDDAYSINT##=0.0:_
TEMP##=(RATE##*.01):_
ODDDAYSINT##=((ODDDAYS##*TEMP##)/365)*PRINCIPAL##:_
COMPUTEBAL##=TON##-ODDDAYSINT##:_
GOTO 900

TEMP1##=1##+((ODDDAYS##/30.0##)*TEMP##)
TEMP2##=1##+TEMP##
COMPUTEBAL##=COMPUTEBAL##+(FIRSTPAYMENT##/(TEMP1##*(TEMP2##)^1))
FOR J##=2 TO TERM%
COMPUTEBAL##=COMPUTEBAL##+(REGPAYMENT##/ (TEMP1##*((TEMP2##)^J##)))
NEXT J##

900
IF TEST%>0 THEN _
IF TEST%=4 THEN GOTO 1001 ELSE _
IF TEST%=3 THEN GOTO 1000 ELSE _
IF TEST%=2 THEN TEST%=3:GOTO 1000 ELSE _
IF TEST%=1 THEN GOTO 997

IF (HIGHRATE##-LOWRATE##)<.0001## THEN TEST%=1:GOTO 997
IF PRINCIPALTEMP##=INT(COMPUTEBAL##*1000##) THEN _
TEST%=1:GOTO 997
IF PRINCIPAL##<COMPUTEBAL## THEN LOWRATE##=RATE##:GOTO 100
IF PRINCIPAL##>COMPUTEBAL## THEN HIGHRATE##=RATE##:GOTO 100
GOTO 100
997
TEST%=2
GOTO 101
1000
IF COMPUTEBAL##<(PRINCIPAL##+.005##) THEN RATE##=RATE##-.0001##:GOTO 101
LOWRATE##=RATE##+.0001##
TEST%=4
1001
IF COMPUTEBAL##>(PRINCIPAL##-.005##) THEN RATE##=RATE##+.0001##:GOTO 101
HIGHRATE##=RATE##-.0001##
RATE##=LOWRATE##+((HIGHRATE##-LOWRATE##)/2##)
1002
PRINT LOWRATE##
PRINT HIGHRATE##
PRINT RATE##
RATECALC##=ROUND(RATE##,4)
PRINT RATECALC##
STOP
END

end of code

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[This message has been edited by paul d purvis (edited April 21, 2005).]

[Paul Dixon]

Paul,

in order to get values correct, rounding, etc,
it seams i have to make sure i put the "##" behind all my values
is that correct.

You can add ## after each variable or, if most of your variables are to be that type, you can add "DEFEXT A-Z" to the start of your code so all variables which aren't given a type will default to extended.

But using extended precision variables doesn't solve the problem it just reduces the rounding error by 11bits (about 1/2000th) compared to double precision.

<<do those return an integer and will those integers only be between -36768 to 36767>>

They'll return any integer type, check the help file to see what types are available.

Paul.

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[Michael Mattias]

>so all variables which aren't given a type will default to extended.

While the variables may use either the "DEFxxx" default or the "LOCAL|STATIC|SHARED xxx AS TYPE" syntax to insure the specified precision, numeric literals must include a type specifier (as was done here).

Still doesn't eliminate the rounding inherent in floating point operations; BCD is still IMO a better choice for all this 'money' stuff.




[This message has been edited by Michael Mattias (edited April 21, 2005).]