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RE: st: Numbers with decimals and -float- command


From   Nick Cox <n.j.cox@durham.ac.uk>
To   "'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Numbers with decimals and -float- command
Date   Tue, 8 Nov 2011 20:38:10 +0000

So they're different. One bit is enough! 

This is all about the fact that most decimal calculations do not have _exact_ binary equivalents. 

Forgetting about the 2, which is an integer, the difference is between 

.09 + .235 

and 

.325

and everyone on this list knows that away from a computer they are equivalent. But Stata can only do the first calculation by converting from decimal to binary first and converting back afterwards 

. di %21x  .325
+1.4cccccccccccdX-002

. di %21x  .09 + .235
+1.4ccccccccccccX-002

And there is the smallest possible difference other than zero. 

The main way to deal with this problem is just to ignore it. 

As you are aware of -float()- you are probably aware of discussions of this point, but here are some references. I'd start with Bill Gould's blog entries. 

FAQ     . . . . . . . . . . . . . . . . . . . Results of the mod(x,y) function
        . . . . . . . . . . . . . . . . . . . . . N. J. Cox and T. J. Steichen
        2/03    Why does the mod(x,y) function sometimes give
                puzzling results?
                Why is mod(0.3,0.1) not equal to 0?
                http://www.stata.com/support/faqs/data/mod.html

FAQ     . . . . . . . . . . . . . . . . .  The accuracy of the float data type
        . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . W. Gould
        5/01    How many significant digits are there in a float?
                http://www.stata.com/support/faqs/data/prec.html

FAQ     . . . . . . . . . Comparing floating-point values (the float function)
        . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  J. Wernow
        3/01    Why can't I compare two values that I know are equal?
                http://www.stata.com/support/faqs/data/float.html

Blog    . . . . . . . . . . . . . . . . .  How to read the %21x format, part 2
        . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . W. Gould
        2/11    http://blog.stata.com/2011/02/10/
                how-to-read-the-percent-21x-format-part-2/

FAQ     . . . . . . . . .  Why am I losing precision with large whole numbers?
        . . . . . . . . . . . . . . . . . .  UCLA Academic Technology Services
        7/08    http://www.ats.ucla.edu/stat/stata/faq/longid.htm

SJ-8-2  pr0038  Mata Matters: Overflow, underflow & IEEE floating-point format
        . . . . . . . . . . . . . . . . . . . . . . . . . . . .  J. M. Linhart
        Q2/08   SJ 8(2):255--268                                 (no commands)
        focuses on underflow and overflow and details of how
        floating-point numbers are stored in the IEEE 754
        floating-point standard

SJ-6-4  pr0025  . . . . . . . . . . . . . . . . . . .  Mata matters: Precision
        . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . W. Gould
        Q4/06   SJ 6(4):550--560                                 (no commands)
        looks at programming implications of the floating-point,
        base-2 encoding that modern computers use

SJ-6-2  dm0022  . Tip 33: Sweet sixteen: Hexadec. formats & precision problems
        . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  N. J. Cox
        Q2/06   SJ 6(2):282--283                                 (no commands)
        tip for using hexadecimal formats to understand precision
        problems in Stata

Nick 
n.j.cox@durham.ac.uk 


-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Joseph Monte
Sent: 08 November 2011 20:17
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: Numbers with decimals and -float- command

Nick,

Thanks for the suggestion and sorry for a) lack of clarity and b) the
misquote (Jeremy). I ran your suggested code and got the following.
Why is totsh1 not equal to totsh2?

. assert  totsh1 == totsh2 in 1870
assertion is false
r(9);

.
. di %21x (totsh1[1870] - totsh2[1870])
+1.0000000000000X-016


Note:- totsh1 = primsh1 + secsh1. Similarly, totsh2 = primsh2 + secsh2

. list primsh1 secsh1 totsh1 primsh2 secsh2 totsh2 in 1870

      +-------------------------------------------------------+
      | primsh1   secsh1   totsh1   primsh2   secsh2   totsh2 |
      |-------------------------------------------------------|
1870. |       2     .325    2.325      2.09     .235    2.325 |
      +-------------------------------------------------------+

As a further test, I recreated totsh1 & totsh2 naming them x and y
respectively. But, the results are the same.

. gen x=primsh1+secsh1
(4268 missing values generated)

. gen y=primsh2+secsh2
(4268 missing values generated)

. list x y in 1870

      +---------------+
      |     x       y |
      |---------------|
1870. | 2.325   2.325 |
      +---------------+

. assert  x == y in 1870
assertion is false
r(9);

.
.
.
. di %21x (x[1870] - y[1870])
+1.0000000000000X-016


Thanks,

Joe





On Tue, Nov 8, 2011 at 7:26 PM, Nick Cox <njcoxstata@gmail.com> wrote:
> I found this difficult to follow. It's not clear that we need to
> understand "upwards", "downwards" and "sideways", as the key question
> is whether or not certain values are equal.
>
> First note that the FAQ you cite is due to Jeremy Wernow.
>
> You are puzzled why your -if- condition ignores e.g. observation 1870
> in which you have
>
>  1870.     2.325      2.325      2.525          .        .      2.525
>
> and so on the face of should we be because (e.g.) the first and second
> values look identical. But that is just a matter of display format.
>
> As those variables are of the same type I would just look directly at
> those values
>
> assert  totsh1 == totsh2 in 1870
> di %21x (totsh1[1870] - totsh2[1870])
>
> I don't see that the -float()- function will be illuminating here.
>
> Nick
>
> On Mon, Nov 7, 2011 at 7:47 PM, Joseph Monte <hmjc66@gmail.com> wrote:
>
>> The output below should contain only observations where there are both
>> upwards and downwards (or vice versa) movements in "totsh" (from
>> "totsh1" through "totsho~r"). Sideways movements are allowed. As an
>> example, obs 1157 has a downward movement from "totsh1" to "totsh2"
>> then upward to "totsh3" and then sideways to "totsho~r", which is
>> fine. "obs" is the number of "totsh*" observations in each row.
>>
>> However, notice observations 1870 (where the path is upward and NOT
>> downward) & 3275 (where the path is downward and NOT upward). These
>> observations should not be in type 3 but in type 1 (which captures
>> upward (and sideways) movements) and type 2 (which captures downward
>> (and sideways) movements respectively) - these are not shown for
>> brevity. On further investigation, I expected the issue to be resolved
>> if I used the -float- command from Nick's FAQ.
>>
>> http://www.stata.com/support/faqs/data/float.html
>>
>> However, as shown below, the -float- command does not seem to solve
>> the problem. In obs 1870, totsh1 & totsh2 do not seem to be equal even
>> though both are 2.325. Same issue for obs 3275.
>>
>>
>> . list totsh1 totsh2 totsh3 totsh4 totsh5 totshoffer obs type if type==3
>>
>>      +----------------------------------------------------------------------------+
>>      |   totsh1     totsh2     totsh3     totsh4   totsh5   totsho~r
>>  obs   type |
>>      |----------------------------------------------------------------------------|
>> 1157. |      3.5   3.483289        3.5          .        .        3.5
>>   4      3 |
>> 1362. | 1.615159   1.588584          .          .        .          2
>>   3      3 |
>> 1543. |      1.5          2          .          .        .       1.75
>>   3      3 |
>> 1691. |       20         25         21         15        .         15
>>   5      3 |
>> 1762. |     1.75        1.9          .          .        .      1.865
>>   3      3 |
>>      |----------------------------------------------------------------------------|
>> 1764. | 1.785918    1.68277          .          .        .        2.4
>>   3      3 |
>> 1768. |     2.25          2          .          .        .   2.666667
>>   3      3 |
>> 1771. |      2.5        2.5          3          .        .        2.9
>>   4      3 |
>> 1774. |      5.5          4        4.7       4.65     4.65       4.65
>>   6      3 |
>> 1870. |    2.325      2.325      2.525          .        .      2.525
>>   4      3 |
>>      |----------------------------------------------------------------------------|
>> 2115. |    2.475       2.14        2.4          .        .        2.4
>>   4      3 |
>> 2256. |      2.1       1.85          .          .        .        2.1
>>   3      3 |
>> 2514. |      2.5       2.75          .          .        .        2.4
>>   3      3 |
>> 2524. |        4        2.7        2.2          2        .        2.2
>>   5      3 |
>> 2598. |      2.5          2       2.35          .        .        2.5
>>   4      3 |
>>      |----------------------------------------------------------------------------|
>> 2606. |      3.7       2.75          .          .        .       2.85
>>   3      3 |
>> 2645. |      3.4        2.3        3.3          .        .          3
>>   4      3 |
>> 2657. |      2.3        2.5        2.1       1.65        .       1.65
>>   5      3 |
>> 2719. |      2.5   2.949862          .          .        .        2.5
>>   3      3 |
>> 2737. |        2        1.5          .          .        .        1.7
>>   3      3 |
>>      |----------------------------------------------------------------------------|
>> 2760. |        1        1.2         .9          .        .         .9
>>   4      3 |
>> 2782. |     2.25          2          .          .        .        2.5
>>   3      3 |
>> 2838. |    5.883          4          .          .        .        4.8
>>   3      3 |
>> 2912. |        2      2.455        1.8          .        .        1.8
>>   4      3 |
>> 2962. |     1.15          1       1.05          .        .       1.05
>>   4      3 |
>>      |----------------------------------------------------------------------------|
>> 2980. |      2.7          2        2.3          .        .        2.3
>>   4      3 |
>> 2987. |        2        1.4        1.6          .        .       1.92
>>   4      3 |
>> 3027. |     5.45       5.55       5.65      5.553        .      5.553
>>   5      3 |
>> 3096. |      1.8       1.85       1.25       1.35        .       1.35
>>   5      3 |
>> 3132. |      1.5          1       1.25          .        .       1.25
>>   4      3 |
>>      |----------------------------------------------------------------------------|
>> 3188. |      2.3        2.7          .          .        .        2.3
>>   3      3 |
>> 3251. |     17.2          6          .          .        .          7
>>   3      3 |
>> 3275. |      6.8        6.8          5          .        .          5
>>   4      3 |
>> 3286. |      1.8        1.4        1.5          .        .        1.5
>>   4      3 |
>> 3306. |        6          4          5          .        .          5
>>   4      3 |
>>      |----------------------------------------------------------------------------|
>> 3488. |      2.5        2.2        2.5          .        .        2.5
>>   4      3 |
>> 3519. |    16.25      13.25       13.3       14.9        .       14.9
>>   5      3 |
>> 3566. |   12.575       10.5          5     4.0625        .      4.665
>>   5      3 |
>> 3667. |      3.5          4        3.6          .        .        3.6
>>   4      3 |
>> 3877. |     6.25        5.5        6.5          .        .        6.5
>>   4      3 |
>>      |----------------------------------------------------------------------------|
>> 3919. |        8       11.5        8.5          .        .        8.5
>>   4      3 |
>> 3944. |      7.5        4.7          .          .        .          5
>>   3      3 |
>> 3954. |        6          5          .          .        .       6.44
>>   3      3 |
>> 4002. |     10.3       14.6         10          .        .         10
>>   4      3 |
>> 4014. |        5       4.95   5.030305   5.045972        .   5.295972
>>   5      3 |
>>      +----------------------------------------------------------------------------+
>>
>> . list totsh1 totsh2 type if float(totsh1)==float(totsh2) & totsh1!=. & type==3
>>
>>      +------------------------+
>>      | totsh1   totsh2   type |
>>      |------------------------|
>> 1771. |    2.5      2.5      3 |
>>      +------------------------+
>>
>> . des totsh1 totsh2
>>
>>              storage  display     value
>> variable name   type   format      label      variable label
>> ---------------------------------------------------------------------------------------------------------------------------------------------
>> totsh1          float  %9.0g
>> totsh2          float  %9.0g
>>
>>
>> I would appreciate any help on the issue. I am using Stata 12.
>
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/
>

*
*   For searches and help try:
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