```Date: Tue, 22 Dec 1998 10:35:41 -0500 Reply-To: Emil Hrivnak Sender: "SPSSX(r) Discussion" From: Emil Hrivnak Subject: Re: greater than a negative number In-Reply-To: <000301be2d47\$d2865720\$8a23400c@worldnet.worldnet.att.net> Content-Type: text/plain; charset="us-ascii" You can have one of two things going on here, or most likely, both. First, since you're displaying the numbers to an F8.2 format, the number stored internally in the computer isn't exactly what you are seeing when it's displayed to 2 decimal places. You are rounding it to display it. Internally the values are such that x is not exactly equal to 0.64 and y is not exactly equal to -1.01. Try displaying the numbers with 16 or 17 decimal places showing. You should see the differences then. (Double precision binary numbers have about 15, 16, 17 digits of decimal precision. There are only enough bits in the internal representation to store the number this accurately.) The second item is that computers generally store numbers in binary. Unless the decimal number you are using is exactly a combination of numbers that can be represented as powers of 2, such as: 2 ^ 0 (2 to the zero power) = 1 2 ^ 1 = 2 2 ^ 2 = 4 2 ^ 3 = 8 2 ^ 4 = 16 . . . 2 ^ 10 = 1024 and so on or numbers that are 1 over a power of 2, such as: 1 / (2 ^ 1) = 1/2 1 / (2 ^ 2) = 1/4 1 / (2 ^ 3) = 1/8 1 / (2 ^ 4) = 1/16 and so on, you cannot exactly represent the number in binary. 0.75 can exactly be represented because it is a summation of 1/2 and 1/4. 0.33 cannot be exactly represented in the computer. Just ask yourself what is 1/3? Is it 0.3 or 0.33 or 0.3333 . . . 3333 with a thousand 3's. That's still not the exact value. Computations done with real numbers that are not summations of 2 to a power and 1 over 2 to a power will not be exact. They'll be correctly rounded to 15 or 16 decimal digits of precision, but not exact. You have to work around it by deciding how many digits of precision you want, multiply the number by a power of ten, truncated it, and then compare those results. By the way, if you try some of these on a calculator, or a Lotus or Excel spreadsheet, you'll see different answers. Calculators and those spreadsheets generally do their internal calculations in decimal, rather than binary. It's slower and more wasteful, but the general population and accountants don't like roundoff when working with decimal numbers. We don't either. But for speed, computers generally work in binary. E Hrivnak eeh@vicon.net At 03:09 PM 12/21/98 -1000, you wrote: >Aloha everybody: > >Looking for an explanation for the following: > >I have two numeric variables (F8.2), say x=.64; y=1.65. > >I have the following syntax: > > If ((x-y) > -1.01) z=1. > >When I execute this command, I get z=1. Why ? > >Mark Scott Verschell >1427 A Dominis Street >Honolulu, Hawaii 96822 >mverschell@worldnet.att.net > > ```

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