SAS why invalid data length

Question

data temp;
 length a 1 b 3 x;
 infile '';
 input a b x;
run;

The answer said "The data set TEMP is not created because variable A has an invalid length". Why it's invalid in this small program?

Answer 1

Length for numeric variables is not related to the display width (that is controlled solely by format); it is the storage used to hold the variable. In character variables it can be used in that manner, because characters take up 1 byte each, so $7 length is equivalent to $7. format directly. If you want to limit how a number is represented on the screen, use the format statement to control that (format a 1.;). If you want to tell SAS how many characters to input into a number, use informat (informat a 1.;).

However, for numeric variables, there is not the same relationship. Most numbers are 8 bytes, which stores the binary representation of the number as a double precision floating point number. So, a number with format 1. still typically takes up those 8 bytes, just as a number with format 16.3.

Now, you could limit the length somewhat if you wanted to, subject to some considerations. If you limit the length of a numeric variable, you risk losing some precision. In a 1. format number, the odds are that's not a concern; you can store up to 8192 (as an integer) precisely in a three byte numeric (3 digits of precision), so one digit is safe.

In general, unless dealing with very large amounts of data where storage is very costly, it is safer not to manipulate the length of numbers, as you may encounter problems with calculation accuracy (for example, division will very likely cause problems). The limit is not the integer size, but the precision; so for example, while 8192 is the maximum integer storable in a 3 byte number, 8191.5 is not storable in 3 bytes. In fact, 9/8 is, but 11/8 is not storable precisely - 8.192 is the maximum with 3 digits after the decimal, so 8.125 is storable but 8.375 is not.

You can read this article for more details on SAS numeric precision in Windows.

Numeric length can be 3 to 8. SAS uses nearly all of the first two bytes to store the sign and the exponent (the first bit is the sign and the next 11 bits are the exponent), so a 2 byte numeric would only have 5 bits of precision. While some languages have a type this small, SAS chooses not to.

Answer 2

It's invalid because SAS doesn't let you create numeric variables with a length of less then 3 or greater then 8.