Re: st: Precision issues with double storage type (??)

[Keith Dear <keith.dear@anu.edu.au>]

Double precision is not infinite precision.  Here are the two numbers 
you are comparing:

. di %24.18f .51
    0.510000000000000010

. di %24.18f 69-68.49
    0.510000000000005120

. di .51==(69-68.49)
0

As you can see, and as "==" is reporting, they are not quite the 
same. One answer, as Maarten says, is to count cents not dollars so 
that you can use integer variables.

. di %24.18f 51
   51.000000000000000000

. di %24.18f 6900-6849
   51.000000000000000000

. di 51==(6900-6849)
1

kd

At 08:36 AM 7/08/2007, you wrote:

<snip>


> ****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
> hmaeda1@uic.edu
>
> *
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*
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