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st: Precision issues with double storage type (??)
Dear Stata users,
I am using Stata 9.2 (born July 20, 2007) for Windows. My Windows XP
Service Pack 2, too, is fully up to date.
I am puzzled by the discrepancies between what I expect Stata to do and
what it actually does, and I suspect storage/precision issues have
something to do with it. Before you castigate me for beating this dead
horse yet once again, please note that I have read relevant manual
entries ([U] 13.10 Precision and problems therein) and statalist
postings and that I encounter this problem even when numeric variables
with fractions are stored in -double- (it's entirely possible that my
feeble mind simply cannot comprehend the complexity of precision issues,
though).
Let me describe my problem with a concrete example. I am appending the
log file below.
I first create two observations, each of which has three variables of a
financial nature: DEPOSIT_A (amount of money deposited to procure a
service), PAYMENT_A (amount of money actually paid), and REFUND_A
(amount of money refunded). The mathematical relationship among them is:
DEPOSIT_A=PAYMENT_A+REFUND_A. Since I am in the U.S., the figures are in
U.S. dollars.
The data look like this:
ID DEPOSIT_A PAYMENT_A REFUND_A
1 61.42 21.30 40.12
2 69.00 68.49 .51
DEPOSIT_A, PAYMENT_A, and REFUND_A are stored in -float-.
When I type: count if DEPOSIT_A==61.42, Stata returns 0 as expected.
When I type: count if DEPOSIT_A==float(61.42), Stata returns 1 as expected.
***Here is my first problem:
But when I type:
gen CHECK_2=1 if float(DEPOSIT_A)==float(PAYMENT_A)+float(REFUND_A),
Stata fails to recognize this relationship in observation 2 (Please see
the log file below). I don't understand why Stata is not seeing this
relationship even when I use the -float- function in the equation.
Then I proceed to create another set of financial variables conveying
the same information in the -double- storage type.
Here is what I have done:
gen DEPOSIT_S=string(DEPOSIT_A, "%9.2f");
gen double DEPOSIT_B=real(DEPOSIT_S);
I have applied the same procedure to PAYMENT_A and REFUND_A to produce
PAYMENT_B and REFUND_B.
I have then used the Data Editor to conform the values of the new
variables are exactly what I want. The Data Editor shows that the value
of DEPOSIT_A for observation 1 to be 61.419998 while the value of
DEPOSIT_B to be 61.42.
When I type: gen CHECK_3=1 if DEPOSIT_B==PAYMENT_B+REFUND_B,
Stata recognizes this relationship in both observations (Please see the
log file below).
Then I computationally create REFUND_C by typing:
gen double REFUND_C=DEPOSIT_B-PAYMENT_B;
****Here is my second problem:
Then I type: gen FLAG_REFUND=1 if REFUND_C!=REFUND_B,
expecting Stata to produce two missing values. But Stata apparently
thinks that for both observations the values of REFUND_B and REFUND_C
are different (Please see the log file below).
I don't understand why this is happening because, after all, all the
variables involved in this operation are stored in -double- and
computations are conducted with -double- precision...
If anyone on this list could advise me on this matter, I would
appreciate it. Thank you.
Hiroshi Maeda
My demonstration begins here =======================================
. clear;
. set obs 2;
obs was 0, now 2
. gen ID=_n;
. gen float DEPOSIT_A=.;
(2 missing values generated)
. gen float PAYMENT_A=.;
(2 missing values generated)
. gen float REFUND_A=.;
(2 missing values generated)
. replace DEPOSIT_A=61.42 if ID==1;
(1 real change made)
. replace PAYMENT_A=21.30 if ID==1;
(1 real change made)
. replace REFUND_A =40.12 if ID==1;
(1 real change made)
. replace DEPOSIT_A=69.00 if ID==2;
(1 real change made)
. replace PAYMENT_A=68.49 if ID==2;
(1 real change made)
. replace REFUND_A = .51 if ID==2;
(1 real change made)
. format DEPOSIT_A %9.2f;
. format PAYMENT_A %9.2f;
. format REFUND_A %9.2f;
. desc;
Contains data
obs: 2
vars: 4
size: 48 (99.9% of memory free)
-------------------------------------------------------------------------------
storage display value
variable name type format label variable label
-------------------------------------------------------------------------------
ID double %10.0g
DEPOSIT_A float %9.2f
PAYMENT_A float %9.2f
REFUND_A float %9.2f
-------------------------------------------------------------------------------
Sorted by:
Note: dataset has changed since last saved
. list, nodisplay noobs compress sepby(ID);
+----------------------------+
| ID DEP~A PAY~A REF~A |
|----------------------------|
| 1 61.42 21.30 40.12 |
|----------------------------|
| 2 69.00 68.49 0.51 |
+----------------------------+
. count if DEPOSIT_A==61.42;
0
. count if DEPOSIT_A==float(61.42)
> /*=> This shows that I have read [U] 13.10 Precision and Problems
therein*/;
1
. count if PAYMENT_A==21.30;
0
. count if PAYMENT_A==float(21.30);
1
. count if REFUND_A==40.12;
0
. count if REFUND_A==float(40.12);
1
. count if DEPOSIT_A==69.00;
1
. count if DEPOSIT_A==float(69.00);
1
. count if PAYMENT_A==68.49;
0
. count if PAYMENT_A==float(68.49);
1
. count if REFUND_A==.51;
0
. count if REFUND_A==float(.51);
1
. gen CHECK_1=1 if DEPOSIT_A==PAYMENT_A+REFUND_A;
(1 missing value generated)
. gen CHECK_2=1 if float(DEPOSIT_A)==float(PAYMENT_A)+float(REFUND_A);
(1 missing value generated)
. list, nodisplay noobs compress sepby(ID)
> /*Problem 1: I don't understand why CHECK_2 is missing for
observation 2*/;
+--------------------------------------------+
| ID DEP~A PAY~A REF~A CHE~1 CHE~2 |
|--------------------------------------------|
| 1 61.42 21.30 40.12 1 1 |
|--------------------------------------------|
| 2 69.00 68.49 0.51 . . |
+--------------------------------------------+
. gen DEPOSIT_S=string(DEPOSIT_A, "%9.2f");
. gen PAYMENT_S=string(PAYMENT_A, "%9.2f");
. gen REFUND_S =string(REFUND_A, "%9.2f");
. gen double DEPOSIT_B=real(DEPOSIT_S);
. gen double PAYMENT_B=real(PAYMENT_S);
. gen double REFUND_B =real(REFUND_S);
. format DEPOSIT_B %9.2f;
. format PAYMENT_B %9.2f;
. format REFUND_B %9.2f;
. drop *_S;
. desc;
Contains data
obs: 2
vars: 9
size: 128 (99.9% of memory free)
-------------------------------------------------------------------------------
storage display value
variable name type format label variable label
-------------------------------------------------------------------------------
ID double %10.0g
DEPOSIT_A float %9.2f
PAYMENT_A float %9.2f
REFUND_A float %9.2f
CHECK_1 double %10.0g
CHECK_2 double %10.0g
DEPOSIT_B double %9.2f
PAYMENT_B double %9.2f
REFUND_B double %9.2f
-------------------------------------------------------------------------------
Sorted by:
Note: dataset has changed since last saved
. gen CHECK_3=1 if DEPOSIT_B==PAYMENT_B+REFUND_B;
. list DEPOSIT_A-REFUND_A DEPOSIT_B-REFUND_B CHECK_3, nodisplay noobs
compress sepby(ID);
+-------------------------------------------------------+
| DEP~A PAY~A REF~A DEP~B PAY~B REF~B CHE~3 |
|-------------------------------------------------------|
| 61.42 21.30 40.12 61.42 21.30 40.12 1 |
|-------------------------------------------------------|
| 69.00 68.49 0.51 69.00 68.49 0.51 1 |
+-------------------------------------------------------+
. gen REFUND_C=DEPOSIT_B-PAYMENT_B;
. format REFUND_C %9.2f;
. gen FLAG_REFUND=1 if REFUND_C!=REFUND_B;
. list DEPOSIT_A-REFUND_A DEPOSIT_B-REFUND_B FLAG_REFUND, nodisplay
noobs compress sepby(ID);
+-------------------------------------------------------+
| DEP~A PAY~A REF~A DEP~B PAY~B REF~B FLA~D |
|-------------------------------------------------------|
| 61.42 21.30 40.12 61.42 21.30 40.12 1 |
|-------------------------------------------------------|
| 69.00 68.49 0.51 69.00 68.49 0.51 1 |
+-------------------------------------------------------+
. /*Problem 2: I don't understand why FLAG_REFUND has flagged
observations 1 & 2*/;
--
Hiroshi Maeda
University of Illinois at Chicago
[email protected]
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