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RE: bug in IntegerPart ?

• To: mathgroup at smc.vnet.net
• Subject: [mg47787] RE: [mg47736] bug in IntegerPart ?
• From: "Wolf, Hartmut" <Hartmut.Wolf at t-systems.com>
• Date: Tue, 27 Apr 2004 04:46:26 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

>-----Original Message-----
>From: Dennis de Lang [mailto:lang.NO at science.uva.nl]
To: mathgroup at smc.vnet.net
>Sent: Saturday, April 24, 2004 10:16 AM
>To: mathgroup at smc.vnet.net
>Subject: [mg47787] [mg47736] bug in IntegerPart ?
>
>
>Why does the following happen?
>
>In[1]:= (1.65 - 1.3)/0.007
>Out[1]:= 50.
>In[2]:= IntegerPart[%]
>Out[2]:= 49
>
>but:
>
>In[1]:= 0.35/0.007
>Out[1]:= 50.
>In[2]:= IntegerPart[%]
>Out[2]:= 50
>
>I'm puzzled....
>- Dennis
>
>

To answer the why: simply because this is not the same! 
This is a basic fact of finite machine arithmetic.
 
In[1]:= (1.65 - 1.3)/0.007
Out[1]= 50.
In[2]:= {IntegerPart[%], FractionalPart[%]}
Out[2]=  {49, 1.}
In[3]:= %% // FullForm
Out[3]//FullForm= 49.999999999999986`
 
In[4]:= 0.35/0.007
Out[4]= 50.
In[5]:= {IntegerPart[%], FractionalPart[%]}
Out[5]= {50, 0.}
In[6]:= %% // FullForm
Out[6]//FullForm= 50.`
 

You see the minute difference of the numerators in the binary digits:

In[7]:= RealDigits[.35, 2]
Out[7]=
{{1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0,

  0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0,
  1, 1, 0}, -1}


In[8]:= RealDigits[(1.65 - 1.3), 2]
Out[8]=
{{1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0,

  0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0,
  1, 0, 0}, -1}


(Details may be different on your machine.)

--
Hartmut Wolf