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# Re: st: Numbers with decimals and -float- command

 From Joseph Monte To statalist@hsphsun2.harvard.edu Subject Re: st: Numbers with decimals and -float- command Date Mon, 21 Nov 2011 08:48:15 +0000

```Thanks, Nick. Hopefully, this will solve my problem based on the
reference you sent me below.

gen double totsh1a = round(totsh1*1000000)
gen double totsh2a = round(totsh2*1000000)
gen x=1 if totsh2a>=totsh1a

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

Joe

On Thu, Nov 17, 2011 at 11:40 PM, Nick Cox <njcoxstata@gmail.com> wrote:
> -round()- is a function, not a command.
>
> It would be nice if you had solved your problem but you are still
> playing with fire. -round()- is defined generally, but its use with
> non-integers is fraught with dangers.
>
> Nick
>
> On Thu, Nov 17, 2011 at 9:49 PM, Joseph Monte <hmjc66@gmail.com> wrote:
>> 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 <n.j.cox@durham.ac.uk> 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/
>>>
>>> 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.
>>>>
>
> *
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>

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```