An oddity Round function:- Can somebody who has used both R and SAS provide some insights

[novinosrin]

Can somebody who has used both R and SAS provide some insights

Scully, Jim 

Feb 4 at 10:34 AM

Hey Nav,

# In R, the round function rounds floats.

# A first example rounds 1234.15 to the 1st decimal place, and returns 1234.2

round(1234.15, 1)

# A second example rounds 12345.15 to the 1st decimal place, and returns 12345.1

round(12345.15, 1)

# Why does the first example round up, and the second example round down?

# I suspect round-off error in the second example

# 12345.15 is not actually stored as 12345.15

# Rather, it is stored as 12345.15 plus or minus 0.00000000000001 (large finite number of zeros)

# So, 12345.15 is actually stored as 12345.149999999999999, which does round to 12345.1

Can you do a comparative reasoning with SAS?

[mkeintz]

SAS numeric are 8-bytes floats.  On my windows machine, the largest consecutive integer in SAS is

9,007,199,254,740,992.   (=   constant('exactint',8).

Call it  X.

Then, given that data are stored as binary mantissa and binary exponent.

1.  The only numbers available from X to 2X  are the even numbers
2.  The only number from 2X to 4X  are 0mod4.
3.  etc.

Similarly:

1.  Only integers are available from  X down to X/2
2.  Only integers and halves from X/2  to X/4
3.  etc.

You can work your way down to any base-2 level of precision to show this asymmetry of precision surrounding X times some power of 2.

But back to your problem as stated - rounding to the tenth does not produced expected value:

filename values temp;

data _null_; /* Write out starting and expected round */
  file values;
  put 'datalines;';
  length value  expect  $15;
  do ndigits=1 to 10;
    value=cats(repeat('9',ndigits),.15);
	expect=cats(repeat('9',ndigits),.2);
	put value= expect=;
  end;
  put 'run;';
run;

data oops; /* Read starting and expected value, calculate round and check */
  input value= expect=;
  check=round(value,.1);
  format value expect check comma22.2;
  if check^=expect then flag='OOPS';
  %include values;
run;
proc print;
run;

Notice OOPS flag  is on for a couple numbers generated above.

[Rick_SAS]

I think your friend's assumption about representable numbers is incorrect.

I think you are seeing that R (and more recently, Python) adopted the engineering convention of “round to even” when rounding off a 5.  See the documentation for the round function in r: ?round

SAS rounds 5 away from 0. See Rounding up, rounding down

[mkeintz]

I suspect the "round to even"  approach is a  way to eliminate bias in rounding for samples with well-behaved distributions at the larger order of magnitude.  Ceteris paribus, it would round up and down about the same number of times.

But over here in the academic financial analysis world, our users would be mighty surprised, and often annoyed, if 5 were not rounded up.

I suppose you could work around each of these behaviors to produce the other,

[Patrick]

@Rick_SAS 

I can't find "round half to even" in the blog you've posted. I guess it would need some formula along the line of below.

data test;
  input have expected;
  even=mod(int(have)+1,2);
  dot5=abs(mod(have,1))=0.5;
  calculated=round(have) - (even * dot5);
  calculated2= round(have) - mod(int(have)+1,2) * (abs(mod(have,1))=0.5);
  correct= expected=calculated;
  datalines;
23.49 23
23.50 24
23.51 24
23.99 24
24.00 24
24.01 24
24.49 24
24.50 24
24.51 25
-23.49 -23
-23.50 -24
-23.51 -24
-23.99 -24
-24.00 -24
-24.01 -24
-24.49 -24
-24.50 -24
-24.51 -25
;

proc print;
run;

[Rick_SAS]

No, it's much easier. Just use the ROUNDE function. The 'E' in the name is for "round to Even".

For more information about the round-to-even method, including examples of using the ROUNDE function in SAS, see the article "Round to even."

[ballardw]

Does R support rounding to values like 0.7?

Such as:

data example;
 do i= 1 to 2 by 0.01;
   y= round(i,0.7);
   output;
 end;
run;

[Rick_SAS]

Not via the standard round() function. It rounds to powers of 10.

Here is the round() doc in R.

[novinosrin]

Thank you gentlemen @Rick_SAS . @mkeintz  and @ballardw  for your responses. I am basically writing to acknowledge and value your time. I am yet to sit with my friend, dig in on the very subject. I will honor the help and will come back with some substance soon as I can. Cheers!

[cminard]

http://theobligatescientist.blogspot.com/2010/02/r-i-still-love-you-but-i-hate-your.html