Re: Beware of adding 0.0

• To: mathgroup at smc.vnet.net
• Subject: [mg50222] Re: Beware of adding 0.0
• From: "Mirek Gruszkiewicz" <gruszkiewicz at ornl.gov>
• Date: Sat, 21 Aug 2004 03:04:27 -0400 (EDT)
• Organization: Oak Ridge National Laboratory
• References: <cg4fcn\$cf5\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```"paul" <paul_tan at aoI.com> wrote in message news:cg4fcn\$cf5\$1 at smc.vnet.net...
> In Mathematica 5.0, I get a very strange result when I add 0.0 to a
number,
> why is this?  See below:
>
> p = SetPrecision[314159265358979323, 25]
> q = SetPrecision[314159265358979323., 25]
> r = SetPrecision[314159265358979323.00000000000000000000, 25]
> s = SetPrecision[p + 0.0, 25]
> {p == q, q == r, r == s, r == p}
> {Tan[s], N[Tan[p]], Tan[q], Tan[r]}
>
>
> \!\(3.14159265358979323`25.*^17\)
> Out[47]=
> \!\(3.14159265358979323`25.*^17\)
> Out[48]=
> \!\(3.14159265358979323`25.*^17\)
> Out[49]=
> \!\(3.14159265358979328`25.*^17\)   *****NOTICE the 28 instead of 23 at
the
> end, why does this happen? *******
> Out[50]=
> {True, True, False, True}
> Out[51]=
> {1.599808, -1.12979, -1.1297927, -1.1297927}
>

Also beware of multiplying by 1.0:

s1=SetPrecision[p*1.0, 25]
3.14159265358979328`25*^17

This is normal:

o=SetPrecision[1/9, 25]
oo=SetPrecision[1./9, 25]

0.1111111111111111111111111
0.1111111111111111049432054

Here is the magic:

ox = SetPrecision[o + 0.0, 25]
ooxx = SetPrecision[oo + 0.0, 25]

0.1111111111111111049432054
0.1111111111111111049432054

Generally, beware of most floating point operations.

MG

```

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