Re: erroneous result when adding reals

• To: mathgroup at smc.vnet.net
• Subject: [mg100877] Re: erroneous result when adding reals
• From: dh <dh at metrohm.com>
• Date: Wed, 17 Jun 2009 04:36:15 -0400 (EDT)
• References: <h19i46\$p29\$1@smc.vnet.net>

```

real numbers. You will see that machine binary real numbers cover only a

(unevenly spaced )grid in the domain of real numbers.

Your problem is that 1/100 can not be exactly represented as a machine

binary real number. Try e.g.:

FromDigits@RealDigits[1/100, 2]

Further, the sum can also not exact.

Therefore, the error you get by subsequent summation depends on h and

the current sum.

Daniel

> Hi all,

>

> I'm fairly new to Mathematica and today I ran into an issue that

> confuses me endlessly. It has to do with simple addition of real

> numbers. It seems like adding x (anything) to 0. (the real) produces a

> result different from x, within something close to machine precision.

> The problem becomes more serious when I do the addition in a Do loop,

> like below:

>

> Module[{tnew, tcur = 0., h = 1/100},

>   Clear[ts]; ts = {tcur};     (* ts is a list *)

>   Do[tcur = ts[[-1]];

>    tnew = tcur + h;          (* add h to the last element of the list

> *)

>    AppendTo[ts, tnew],   (* and then push it at the end of the list *)

>    {step, 1, 300}             (* repead 300 times *)

>    ]

> ];

> ListLinePlot[Table[h, {h, 0, 3, 1/100}] - ts, InterpolationOrder ->

> 0]

>

> The plot I get is NOT constant, and the error introduced through the

> "real addition" done in the Do loop is systematic and adds up to

> something relatively large. Notice that if I substitute 0. (the real)

> with 0 (the integer or rational), then the result is exactly like

> expected.

>

> Do any of you know why this happens and how I could avoid it, other

> than working with *only* rational numbers? Thank you!

>

```

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