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

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: programming error with -generate- |

Date |
Tue, 09 Mar 2010 09:17:45 -0600 |

Richard Williams writes, > At 04:31 PM 3/8/2010, Visintainer, Paul wrote: > >. gen y = 1.2x + 6 <----- why isn't there an error here? > > When I do this, y = 72 for all cases. So 1.2x must be getting > interpreted as 1.2 * 10 = 12. I don't know why, but just follow > Martin's advice and make it > > gen y = 1.2*x + 6 > > Maybe this is a "feature" but if so it doesn't seem like a good one, > since this could be an easy mistake to make. That is, one should type . gen y = 1.2*x + 6 but if one mistakenly omits the multiplication sign and types . gen y = 1.2x + 6 then 72 is stored in y! It has been noted that this odd behavior seemingly happens only when the variable is named -x-, but that's not true. Something similar is true of variables named -e-. You mean to type . gen y = 1.2*e + 6 but you mistakenly omit the multiplication sign and type . gen y = 1.2e + 6 Make that mistake and 1,200,000 will be stored in y! Well of course it will, you say. 1.2e+6 means 1.2*10^6. Well, I reply, 1.2x+6 means (1.2)-base-16 times 2^6, and that works out to (1+2/16)*2^6 = 72. That is, just as Stata has an e-notation for typing base-10 numbers, Stata has an x-notation for typing base-16 numbers. I have mentioned before that Stata has an output format %21x which will show you a floating-point number exactly as the computer stores it. I've used it in other posts, too, in explaining unexpected numeric results, usually caused by round-off error because some base-10 numbers such as 1.1 have no exact base-2 or base-16 representation. Let's see what %21x shows us for the number 72: . display %21x 72 +1.2000000000000X+006 It is documented that this x-notation is both an output and input format of Stata. Thus, Stata understands that 1.2x+6 is 72, just as it understands that 1e+2 is 100. By the way, it is a property of x-notation that the lead digit must be 1 unless the number is 0. That's because x-notation is really a binary format. Remember, the x+6 part means "multiply by 2^6. The first part is typed in hex, but that's just for convenience. What is out front is interpreted as a binary number. At StataCorp, we use x-notation to enter constants precisely and to ensure that the constant will be the same constant across computers. For instance, _pi is in fact defined as +1.921fb54442d18X+001. We also use x-notation in the certification process to ensure that Stata converts base-10 numbers to base-2 correctly. And sometimes we use it in certification to make sure that an answer is exactly, digit-by-digit, what we expected. -- Bill wgould@stata.com * * 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/

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