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Re: st: Numbers with decimals and -float- command
From
Joseph Monte <[email protected]>
To
[email protected]
Subject
Re: st: Numbers with decimals and -float- command
Date
Thu, 17 Nov 2011 21:49:03 +0000
Thanks, Nick. I think I may have solved my problem by using the
-round()- command since totsh1, totsh2, etc. have six legitimate
decimal places (the numbers represent millions).
Specifically,
gen x=1 if round(totsh2,0.000001)>=round(totsh1,0.000001)
Joe
On Tue, Nov 8, 2011 at 8:38 PM, Nick Cox <[email protected]> wrote:
> 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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>
*
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