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SESUG Procedures (c) SESUG, (http://www inc.sesug.org) The documents contained in each of our SESUG procedures are the property of their respective authors unless otherwise noted. Do not reprint without permission. SESUG reports are distributed free of charge by the Expert Analytics Institute (http://analytics.ncsu.edu). POâ€“082

Rounding to Avoid sasÂ®: Numerical Representation Problems Imelda S. Goh, South Carolina Department of Education, Columbia, SC SUMMARY As SAS web developers, we have different backgrounds. We range from minimal or no formal training in computer science to university degrees in computer systems. Numerical precision and representation are usually standard topics in IT education. Ultimately, programmers run into problems with expressions and numeric precision. Problems associated with them can be especially devastating when the programmer is unaware that they will be discovered, and therefore has not taken any training and retraining measures to solve these problems. For example, we canWe find that the results of our numerical comparison are not all that we expected. Consider the SAS entry “if 0.3=3*0.1 then equals=’Y’; else if equals=’N’;” You think that the result will always be Y, then this article is required. to avoid such problems.

Note. Due to various hardware limitations and systems used, the following SAS PC examples may differ from results on other computer systems. common method.

NOT ALL NUMBERS CAN BE EXACTLY REPRESENTED ON A COMPUTER Numerical precision (that is, the precision with which a correct number can be represented) and representation in computers are at the root of the problem. SAS uses a floating point (i.e., binary) representation. A rare decimal number and a number represented in binary are actually very close, but incredibly close are not identical. There is no unique binary representation for decimal numbers 0.1 and 0.3, which explains the difference in example #1 below. The advantage of the floating point instruction is speed, while its disadvantage accounts for errors. Repeating decimals and irrational elements are other obvious problems for accurate storage on a computer. For example, 1/3 corresponds to a certain decimal point followed by infinity, the incredible number 3. Computers cannot represent a number with infinite digits. In each case, we must distinguish between the expected mathematical result (our decimal values) and what the computer can store (binary values) and program. Readers can refer to the two SAS technical support links (TS-230 and TS654) listed at the end of the document for detailed explanations and examples of floating point representation.

EXAMPLE #1 We know when the mathematically simple 3 multiplied by 0.1 is really 0.3. So obviously, if we were looking at the specific code below, it would be reasonable to expect the variable being compared to have the value Y, since both variables resolve to 0.3 (at least mathematically).

If you do this, I think the only practical answer is Y, then you might be surprised! YesLet’s take a closer look at the PROC PRINT output for the exact data set above.

When using the following statement with PROC PRINT, format value1 value2 32.31;

1< br> we get the main output .

Both values â€‹â€‹can be 0.3, but that’s essentially all there is in PROC PRINT output. The two values â€‹â€‹are usually stored on different computers. On the next page, we note that many SAS formats are round, which is why we see no difference in the values. To see how the values â€‹â€‹are displayed, we use HEX16. Enter with PROC PRINT. format value1 value2 hexadecimal16.; We get the following output showing the difference between all two values.

EXAMPLE #2 Here is another example. The previous variance of the two pairs of numbers is 3.8, but the reviews are not true.

Without specifying the format, some of us get the following results.

If we use this, what follows when calculating the PROC PRINT instruction , format difference 32.We 31 ; Set the following output.

2

EXAMPLE #3 View errors become a serious problem when someone else doesn’t know whato this can happen, and take no precautions against this tool. Regardless of the size of the errors or discrepancies, several additional operations can accumulate. Consider an easy-to-understand example of adding from 0.1 to ten million times. We know that the result will be one trillion.

After entering all the numbers, SAS produces each of the following results.

With this many multiple calculations, the difference is 163.124. How bad? It depends on your data. This may be extremely tolerable for some and unacceptable for others. There is something else that leads to different results when Goldensum reflectivity is used in many calculations.

TROUBLESHOOTING We are responsible for our data, programming and practical results. Often the first step in solving a problem is identifying it and knowing the conditions under which the problem can manifest itself in undesirable results. The field of computing is too interested, this is a known problem. Most of the published algorithmsstatistical analyzes are designed to account for and minimize the effects of representational errors.â€ť (TS-230) â€śUnfortunately, there is no method that best deals with problems caused by number corruption. What is a good ideal solution in an application can significantly affect the performance and results of another application.â€ť (TS-230) Therefore, this document focuses on the simplest examples of these types of problems.

## How do you round integers in SAS?

The FLOOR function completes everything.CEIL performs task rounding.The ROUND function rounds an order to the nearest whole number.The INT function works with zero.