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From: daver@hpsgpa.HP.COM (Dave Rabinowitz)
Newsgroups: comp.sys.hp
Subject: Re: HP28C
Message-ID: <2790006@hpsgpa.HP.COM>
Date: Tue, 27-Oct-87 04:31:07 EST
Article-I.D.: hpsgpa.2790006
Posted: Tue Oct 27 04:31:07 1987
Date-Received: Fri, 30-Oct-87 02:20:53 EST
References: <3969@watdcsu.waterloo.edu>
Organization: HP Singapore IC Design Ctr
Lines: 19

>  When I compare the results of 253! from the programs below, I get
>  accuracy differences.  What is the reason for this?  

> Results:   5.17346 09926 9 E 499  	FACT function
>            5.17346 09926 4 E 499	Program 2	
>            5.17346 09928 2 E 499	Program 1	

The exact result for 253! will have 500 digits, so there will be rounding
errors whenever it is calculated with fewer than 500 digits.  The FACT 
function, and all other built-in functions, carry extra significant digits to
reduce the rounding errors in the final result, and the result is usually
accurate to the last digit.  When you run a program, each time a built-in
function is completed the result is rounded to 12 digits and this rounded
result is used in further calculations, so the result will not be as accurate
as the built-in function, which uses at least 14 digits in all its
calculations.  The reason the two programs give different answers is that they
do the multiplications in a different order, the first doing 253*252*251...*1
while the second does 1*2*3*...*253, which will lead to different rounding
errors.