SIGNIF and GENFMT, SASe Macros for
Computing and Reporting Significant Digits
B. M. Horwedel, Oak Ridge National Laboratory'
J. E. Horwedel, Oak Ridge National Laboratory'
Abstract
excess digtts as a decimal fraction;
Reporting generalized statistics such as mean or standard
error with excessive significant digits can be misleading and
imply more precision than that fOlind in the original
measurements. Measurement data seldom warrant more
than two or three significant figures to represent values. An
appropriate number of digHs is determined by the precision
of the reported value.
(2) Kthe fraction is greater than 1/2, increment the
least significant digit;
(3) K the fraction is less than 1/2, do not
increment;
(4) If the fraction equals 1/2. increment the least
significant digH only ff H is odd.
This poster presents two SAS macros that are useful in
reporting values with a IimHed number of signfficant digHs.
SIGN IF is a macro that will return a value rounded to a
specffied number of digHs. GENFMT is a macro that will
generate a picture format to be used in printing numbers.
Examples using SIGNIF and GENFMT are shown.
The reason for rule (4) is that in many cases the fraction
equals etther 0 or 1/2 and conSistently incrementing the
least signfficant digH for a fraction of 1/2 would lead to a
systematiC error.
Discussion
The pseudocode for rounding a number to n significant
digHs is as follows:
Precision is communicated by the way in which a
measurement is reported.
MOVE selected number of significant digits to
Statistics reported with more
significant digits than the number of digHs found In the
original measurements are misleading.
I~
of decimal pOint.
The number of
significant figures refers to the number of numerical digits
used to express a value.
Set VALUE equal to truncated decimal.
If fractional part is GREATER than 0.5
increment VALUE
Computations on a computer can be so simple that the
final resu~ of a sequence of calculations will appear more
precise than tt really is. In most statistical work, H is best to
carry more figures into the final computation than seem
necessary and then to round the result to a meaningful
number of digits, relative to the precision of the original
measurements. An appropriate number of digHs is that
which is justified by the precision of the measurement. The
number of significant figures in a result is defined as:
Else, if fractional part EQUALS 0.5
then ff VALUE is ODD
Increment VALUE
SIGNIF is used like any other SAS macro.
Three
arguments must be specified. The first argument is the
variable to store- the result; the second argument is the
1. The leftmost nonzero digH is the most significant digH.
2. If there is no decimal pOint, the rightmost nonzero digit
is the least significant digtt.
3. If there is a decimal point, the rightmost digH is the least
signfficant digit, even ff H is O.
4. All digits between the least and most significant digHs
are counted as significant digits.
value to be rounded; and the third argument specifies the
Consider the following
number of signfficant digHs.
example:
x = 8.234;
&SIGNIF(y,X,2);
Y will be set to the value 8.2.
The rules for rounding numbers to a smaller number of
significant digits can be found in several references. [1]
The SAS function ROUND does provide some of the same
capabilities as SIGN IF; however, ROUND is more limited.
The ROUND function rounds a value to the nearest
(1) Truncate the number to n digits. and treat the
1306
picture format generated by GENFMT will provide this
control.
roundoff unn which must be supplied by the user. It is
difficutt to specify one roundoff unn for data wnh a large
range. SIGN IF is designed to work wnh a large range of
numbers.
Restrictions and Umitations
SIGNIF and GENFMT were implemented and tested on a
VAXNMS computer under SAS version 6.06. They should
be tranportable to any system that supports the MACRO
language.
GENFMT is a macro that will provide a picture format to be
used in reporting values with a specified number of digits.
GENFMT needs to be called once before using the format.
For example, to print numbers wnh two signnicant digns:
Condusion
&GENFMT(2);
SIGNIF is a macro callable from a SAS program to round
a value to a specnied number of digns. SIGN IF allows
reporting statistics on - measurement data limited to the
number of significant digits warranted by the precision of
the originaJ measurements without the limitations imposed
by the SAS ROUND function. GENFMT generates a picture
format to control the printing of values with a specnied
number of digtts.
GENFMT will generate a picture format, DIG2X. Use this
format as any other SAS format. See Reference 2.
An example of the use of SIGN IF and GENFMT in a SAS
program follows:
DATA TEST;
INPUT X;
&SIGNIF(y,X,2); '* y is x rounded to two digns*,
References
YY~Y;
RUN;
&GENFMT(2);
'* generate a picture formatO,
RUN;
PROC PRINT;
VAR X YYY;
FORMAT X Y BEST10. YY DIG2X.;
'* yy is printed wnh two significant figures *'
[11 BeVington, P.R., Data Reduction and Error Analysis for
the Physical SCiences. McGraw·HiII Book Company, 1969.
[21 SAS Instnute, Inc., SAS Language: Reference, Version
6, First Edition. Cary, NC: SAS Institute, Inc., 1990.
'Managed by Martin Marietta Energy Systems, Inc., under
contract DE·AC05·840R21400 wnh the U.S. Department of
Energy.
The variable Y is defined as X rounded to two significant
digits; YY is then set equal to Y. The variables X and Yare
printed wnh the BEST format; YY is printed wnh DIG2X.
The printout from the above program is shown:
x
y
0
51
1.75
1.85
99.5
1254
·51
·1.03
0.4451
0.0103
0.00185
0
51
1.8
1.8
100
1300
·51
·1
0.45
0.01
0.0018
"VMS is a trademark of Dignal Equipment Corporation,
Maynard, MA.
yy
0
51
1.8
1.8
100
1300
·51
·1.0
0.45
0.010
0.0018
Five picture formats are included in Appendix C. These
picture formats have been set up as separate files;
GENFMT will 'INCLUDE' the appropriate format. These
formats can be easily modnied to conform to your reporting
requirements (e.g., decimal alignment, ranges, etc.). In all
cases, the number 0 is printed as the dign 0 wnh no
decimal. Before using these picture formats, numbers must
be rounded; picture formats truncate. The SAS BEST
format will in most cases print a number with the proper
number of signnicant digns (after tt has been rounded);
however, there is no control in lining up the numbers. The
1307
Appendix A. Usting of SIGNIF.SAS.
%MACRO SIGNIF(value,inH_val,sig);
/*************************** •• ***.********.*
=
VALUEXX
&intt val;
- ~LVALUEXXNE-O)
then do;
~ &intt_val < 0
VALUEXX;
then VALUEXX
fACTORX 10**(&SIG.ceil( logI0LVALUEXX)));
VALUEXX
VALUEXX * FACTORX;
=INNALX
iriiLVALUEXX);
IFLVALUEXX - JNNALX > 0.5)
INNALX + 1;
THEN INNALX
ELSE
-
Macro: SIGNIF (value, Intt_val, sig)
Purpose: SIGNIF returns the first argument as the
second argument ·rounded~ to the number of
significant digtts specified by the third argument.
=
=
=
Authors: B. M. Horwedel, J. E. Horwedel
=
Computing and Telecommunications
Division
Martin Marietta Energy Systems
Oak Ridge National Laboratory
Building 6011, MS 6370
P.O. Box 2008
Oak Ridge, Tn. 3783t -6370
=
0.5)
IF LVALUEXX - JNNALX
THEN IF (modUNNALX,2)
1)
THEN INNALX
INNALX + 1;
&VALUE
INiVAlX/ FACTORX;
~ &inH_val 0 then &VALUE
-&VALUE;
end;
=
<"
=
Phone number: (615)-574-5413
(FTS)-624·5413
else
&value = 0;
DROP _FACTORX_INNALX;
%MEND;
Created: December 1, 1990
Arguments:
value:
intt_val:
sig:
=-
rounded result
value to be rounded
required number of significant
digits;
Notes: SIGN IF is a SAS macro that is used in a
SAS program to return a value wtth a spec~ied
number of significant digtts. The method is to
truncate the number to the spec~ied number of
digits. Treat the excess as a fraction. If the fraction
is greater than 0.5, increment the number. If the
fraction is equal to 0.5, increment the number only ~
it is odd. For further discussion see Reference 1.
Restrictions: Version 6 SAS must be available on
the Vf>J(NMS for implementation of
SIGN IF.
Pseudo code:
Determine factor to move sig digtts to left
of decimal.
Use factor to scale up (or down).
Get integral value and fractional part.
If fractional part is greater than 0.5
increment value;
else ~ fractional part equals .5
increment if value is
Odd.
Scale down (or up) with factor.
return value.
***************************************************/
1308
=
=
Appendix B. Usting of GENFMT.SAS.
*DIG4.SAS:
proc format:
picture DIG4X
%MACRO GENFMT(dig);
%include dig&dig;
%mend;
-0.9999--0.1
-9.999--1.0
-99.99--10.0
-999.9--100
-9999- -1 000
run;
o
Appendix C. Ustings of DIG1.SAS - DIG5.SAS.
0.1-0.9999
1.0-9.999
10.0-99.99
100-999.9
1000-99999
*DIG1.SASj
proc format:
picture DIG1X
,0.00099,,0.0001
'0.0099"0.001
-0.099--0.01
-0.99--0.1
-9999--1.0
= ,
='
9.9999'
9.999 I
9.99
9.9
.
=
I
o
I
0009
=
I
9
0.0001-0.00099
0.001-0.0099
0.01-0.099
0.1-0.99
1.0-99999
='
I
(prefix="')
(prefix='-')
(prefix='-')
(prefix='-')
o
=
0.001-0.0099
0.01-0.099
0.1-0.99
1.0-9.9
10.0-99999
I
0099
I
9
o
1.0-9.9
10.0-99.9
1000-9999
10000-99999
(prefix:'-')
(prefix='-')
(prefix='-')
9.9999'
9.999
9.99
9.9
'00099
*DIG3.SAS;
proc format:
picture DIG3X
-0.0999--0.01
-0.999--0.1
-9.99--1.0
-99.9--10
-9999--100
=
=
=
=
I
I
I
I
0999
o
1.0-9.99
10.0-99.9
100-99999
(prefix='-')
(prefix='-')
(prefix='-')
(prefix='-')
(prefix='- I)
9
9.9999'
0.01-0.0999
0.1-0.999
9.9999'
9.999 I
9.99 I
99.9
I
=
=
I
9.9999'
= ,
9.999
99.99
999.9
'09999
picture DIG5X
-9.9--1.0
-999--100
-9999- -1 000
(prefix;;'-')
I
(prefix='-')
(prefix=IMI)
(prefix='M')
proc format:
9.9999 1 (prefix='-')
9.999
9.99
9.9
(prefix="')
(prefix='o')
*DIG5.SAS;
9.9999'
9.999
9.99
= I
9.9
'00009
=,
=,
9.9999'
9.999
99.99
f
999.9
9999
9
(prefix='" )
*DIG2.SAS;
proc format;
picture DIG2X
-0.0099--0.001
-0.099--0.01
-0.99--0.1
-9.9--1.0
-9999--10.0
=,
=,
9.999
9.99
99.9
'00999
I
1309
9.9999' (prefix='_')
(prefix='-')
, 9999.9
(prefix=IMI)
=' 999.99
9
9.9999'
99.999'
I 9999.9
'99999