Re: bug in IntegerPart ?
- To: mathgroup at smc.vnet.net
- Subject: [mg47871] Re: bug in IntegerPart ?
- From: "Peltio" <peltio at twilight.zone>
- Date: Thu, 29 Apr 2004 03:05:44 -0400 (EDT)
- References: <firstname.lastname@example.org> <email@example.com>
- Reply-to: "Peltio" <peltioNOSP at Mdespammed.com.invalid>
- Sender: owner-wri-mathgroup at wolfram.com
"AC" wrote: (incidentally my first reply in this thread never made it to the group, hope this one will be luckier : ) ) >The decimal numbers (1.65 - 1.3) and .35 are identical. The way >Mathematica performs subtraction makes them different. I think this is a correct statement, but is a little bit too specific. I'd rather say: the way _digital computers_ perform subtractions makes them different. The subtraction of machine precision numbers is done with machine arithmetics, and that requires the terms to be translated into binary. We can experience the same loss of precision with decimal arithmetic, by adding two rational numbers. We know that 1/6+2/3=5/6 Now suppose we have a 'decimal computer' with a machine precision of three digits. Additions and subtractions have to be carried out in this machine precision. What do we get? 1/6 becomes 0.167 2/3 becomes 0.667 theis sum, accordind to our Decimal ALU (that operates only on the truncated decimal expansions of our rational numbers). is: 0.167+0.667 = 0.834 Which is different from the decimal representation of the correct result 5/6 is 0.833 Hence, in machine precision, 1/6+2/3 is different from 5/6, depsite the fact that every children know they are the same. This is the world of machine precision arithmetic. It's a harsh world : ] cheers, Peltio PS In my previous (lost) post I pointed out that in this world things are different according to the order of the computation. Evaluate the following to see what I mean: (1.65/0.007 - 1.3/0.007) - 0.35/0.007 (1.65 - 1.3)/0.007 - 0.35/0.007 (1.65 - 1.3 - 0.35)/0.007 (1.65 - (1.3 + 0.35))/0.007 Repeat the same calculations in a C program with double precision and see what you get.