RE: floor problems

*To*: mathgroup at smc.vnet.net*Subject*: [mg8131] RE: [mg8113] floor problems*From*: Ersek_Ted%PAX1A at mr.nawcad.navy.mil*Date*: Fri, 15 Aug 1997 23:41:43 -0400*Sender*: owner-wri-mathgroup at wolfram.com

Tom De Vires wrote: |I had a very frustrating time trying to debug some work I was doing in |Mathematica. | |Floor[(.7 67 10)] | |469 | |Floor[(67 10 .7)] | |468 | Consider the following: In[1]:= b=67*10*0.7 Out[1]= 469. 0.7 is a machine precision number rather than an exact number such as an Integer or Rational. Arithmetic involving machine precision numbers gives machine precision (imprecise) results. Now lets see how far the result is from 469. In[2]:= error=469-b Out[2]= 5.68434x10^-14 It turns out the result (b) is a tiny bit less than 469. Hence the Floor of this value is 468. It turns out we do have an idea how much error there can be in such a result. You should always find the magnatude of the error from any machine precision calculation is less than the value times $MachineEpsilon. $MachineEpsilon is explained below. In[3]:= error<469 * $MachineEpsilon Out[3]= True Sure enough the error is less than (469)*$MacineEpsilon. In[4]:= ?$MachineEpsilon Out[4] $MachineEpsilon gives the smallest machine-precision number which can be added to 1.0 to give a result that is distinguishable from 1.0. Now when the machine precision (imprecise) multiplication is computed in a different order, the result is as close as you can get to 469. It should be no surprise that the Floor of this result is 469. In[5]:= a=0.7*67*10; 469-a Out[5]= 0. However, I wouldn't read to much into the result above. You will only have things work out this good in special situations. To read more about machine precision calculations in Mathematica goto: http://www.wolfram.com/support/Math/Numerics/NumericalError.html Ted Ersek

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**Re: floor problems**

**Re: floor problems**