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From |
wgould@stata.com (William Gould, Stata) |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Decimal precision, again |

Date |
Mon, 28 Jul 2003 08:03:11 -0500 |

Sylvain Friederich <S.Friederich@bristol.ac.uk> has solved the problem with float rounding and promoted his float variable to double using . gen double fixed = round(price*10,1)/10 About the data and the fix, Sylvain writes, > The variable I am considering is a share price. It will not take on very > large values, and can have no more than two-digit decimal precision. [...] > > . list price in 1/6 > > 417.8 > 418.68 > 418.9 > 419.28 > 425.35 > 426.55 The reason Sylvain wanted to promote price from float to double was > [...]although the Editor displays them as above, clicking on those cells > shows that Stata really holds them as: 417.7999 418.67999 418.89999 419.28 425.35001 426.54999 Sylvain asks, > For the sake of completeness, would my original intuition (coarse though it > may have been) of outsheeting and re-insheeting the dataset right away with > the "double" option have worked? Yes it would have worked. Displayed with the default %9.0g, the values were rounded in the desired way, so after -outfile-ing, -infile- would have seen 417.8, 418.68, 418.9, ... If Sylvain's desire to promote the variable was based solely on a desire to have the editor show the full values as 417.8, 418.68, 418.9, ..., rather than 417.7999, 418.67999, 418.89999, ..., then I have no qualm. The error, however, was never much. Taking the 418.68 case, the float value stored differed from the desired 418.68 by about 0.000007324219 (absolutely) and 0.000000017535 (relatively). Relative error is what matters in statistical calculations and there is not enough to matter. All that said, we here at Stata have written do-files to do accounting applications and, for those calculations, is is absolute error that matters. Moreover, accountants, the IRS, etc., prefer sums be accurate to the penny. When storing larger numbers, such as 418,680.02, the relative error remains the same, approximately, but the absolute error grows, in this case to .01125, which is too much for accountants. In financial datasets, the best way to store dollar amounts is in pennies as integers. This abolishes round-off error for addition and substraction and a -long- takes no more memory than a -float-. If amounts need to exceed $21 million, then use doubles (and still record pennies). -- Bill wgould@stata.com * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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