Re: Unexpected behavior of Floor and IntegerPart

• To: mathgroup at smc.vnet.net
• Subject: [mg97962] Re: Unexpected behavior of Floor and IntegerPart
• From: dh <dh at metrohm.com>
• Date: Thu, 26 Mar 2009 05:25:25 -0500 (EST)
• References: <gqacr4\$jbm\$1@smc.vnet.net>

```
Hi Curtis,

look at:

Table[{i, i 100 - Round[100 i]}, {i, 0, 1, 0.01}]

and you will see that 0.29 (and 0.58 as well)  is a little bit smaller

in the binary machine representation than in the decimal input

representation.

Daniel

Curtis Osterhoudt wrote:

> Dear List,

>

>    I'm sure this is a result of non-infinite-precision arithmetic, but it would be nice to have a more consistent behavior:

>

> In[26]:= IntegerPart[0.29*100]

>

> Out[26]= 28

>

> In[25]:= Floor[0.29*100]

>

> Out[25]= 28

>

> In[27]:= Floor[(29/100)*100]

>

> Out[27]= 29

>

> In[32]:= (Floor[#1*100] & ) /@ Range[0, 1, 0.01]

>

> Out[32]= {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, \

> 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 28, 30, 31, 32, 33, \

> 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, \

> 51, 52, 53, 54, 55, 56, 57, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67,

> 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, \

> 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100}

>

> In[33]:= Differences[%]

>

> Out[33]= {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, \

> 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, \

> 1,

>    1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 1, 1, 1, 1, 1, 1, \

> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,

>    1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

>

>

>

> An interesting hint as to what may be happening is obtained by:

>

> ListPlot[Differences[(Floor[#1*100] & ) /@ Range[0, 100, 0.01]]]

>

>                      Regards,

>                                     C.O.

>

>

>

```

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