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RE: st: Numbers with decimals and -float- command
From
Nick Cox <[email protected]>
To
"'[email protected]'" <[email protected]>
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
[email protected]
-----Original Message-----
From: [email protected] [mailto:[email protected]] On Behalf Of Joseph Monte
Sent: 08 November 2011 20:17
To: [email protected]
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 <[email protected]> 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 <[email protected]> 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.
>
> *
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>
*
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*
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