Re: Cannot summate small float values

[Niklas Holsti <niklas.holsti@tidorum.invalid>]

tolkamp wrote:
> On 20 nov, 14:49, Niklas Holsti <niklas.hol...@tidorum.invalid> wrote:
>> tolkamp wrote:
>>> When I summate Float values smaller then 1.0E-6 then the summation is
>>> not done.
>>> Code Example:
>>> X, Dx : Float;
>>> X := 0.0;
>>> Dx := 1.0E-7;
>>> lwhile X <  1.0 loop
>>>     X = X + Dx;
>>>     Float_Io.Put(X, 3,9,0); New_Line;
>>> end loop;
>> Certainly the addition is done. Your program (after some small syntactic
>> corrections) prints:
>>
>>    0.000000100
>>    0.000000200
>>    0.000000300
>>    0.000000400
>>    0.000000500
>>    0.000000600
>>    0.000000700
>>
>> and so on. If your program prints out something else, please show the
>> source code of your whole program, exactly as you compile and run it.
>> Don't re-type it into your message.
>>
>> However, when X approaches 1.0, at some point the addition of 1.0E-7 may
>> be lost in round-off, since it is close to the precision limit of the
>> Float type, relative to 1.0. On my system (Debian, Gnat) the X variable
>> does reach 1.0 and the program stops.
>>
>> What are you really trying to do? There are probably safer and more
>> accurate ways of doing it.
>>
>> Here is the program that I used:
>>
>> with Ada.Text_IO;
>> with Ada.Float_Text_IO;
>>
>> procedure Sums
>> is
>>     use Ada.Text_IO, Ada.Float_Text_IO;
>>     X, Dx : Float;
>> begin
>>     X := 0.0;
>>     Dx := 1.0E-7;
>>     while X <  1.0 loop
>>         X := X + Dx;
>>         Put(X, 3,9,0); New_Line;
>>     end loop;
>> end Sums;
>>
> 
> Thank you your reaction.
> Using your procedure Sums I found out that when the start value of X <
> 0.24 the summation works correct with Dx = 1.0E-8
> When start X > 0.25 the summation remains 0.250000000.

That is still correct behaviour, because floating point addition can 
behave like that when the two addends have very different magnitudes. If 
you need to compute the sum of a large set of floating-point numbers, 
you should use a floating-point type with more digits or use a smart 
summation algorithm like the one by Kahan,
http://en.wikipedia.org/wiki/Kahan_summation_algorithm

-- 
Niklas Holsti
Tidorum Ltd
niklas holsti tidorum fi
       .      @       .