Le 17/09/2019 à 15:33, Stéphane Mottelet a écrit :
Le 17/09/2019 à 15:20, Federico Miyara a écrit :
Dear all,
I think that saying that
1.70000000000000018
should be represented as
1.7000000
and that representing it as
1.7
instead is dishonest seems a bit too much for me.
What about
1.71234564999999999?
With the available decimal places you would represent it as
1.7123456
Wouldn't you?
However, there is no clue that the number is inaccurate by the next
(8th) decimal digit, whereas 1.7 is inaccurate by the 16th decimal
digit. So the clue would be given only if there are any places
available after the last non-zero digit. If the trailing zeros serve
the purpose of calling attention to the fact that the result is
inaccurate then the same opportunity should be given to numbers such
as 1.71234564999999999, which is clearly impossible with the
available decimal places.
I think no trailing zeros should be added except in rare cases when
formatting for a table (outside Scilab), or when, as in experimental
physics, the number of exact digits is important, but in such case
1.7000000 would be as dishonest as 1.7, being 1.700000000000000 the
only "honest" choice, again, impossible with 7 decimal places. At
best, this could be acceptable as a non-default formatting option.
For me, the only change should be to prevent that 1.60000000000000009
be represented as 1.6 while 1.70000000000000018 is represented as
1.7000000.
Let me give the following rationale. When parsing with msscanf we get
--> msscanf("1.60000000000000009","%lf")==1.6
ans =
T
but
--> msscanf("1.70000000000000018","%lf")==1.7
ans =
F
The actual display algorithm does not use msscanf but a cross-platform
code (msscanf give different results on Windows and Linux/OSX), but
this was just a way to explain why the display of 1.7
I meant x(8) when x=1:0.1:2, i.e. 1.70000000000000018
could (not should) be different.
S.
Regards,
Federico Miyara
On 13/09/2019 10:21, Stéphane Mottelet wrote:
Le 13/09/2019 à 15:13, Dang Ngoc Chan, Christophe a écrit :
Hello,
De : Stéphane Mottelet
Envoyé : vendredi 13 septembre 2019 14:23
I think that we do agree about the fact that the actual Scilab
display
[...]
--> x(8)
ans =
1.7
--> x(8)-1.7
ans =
2.220D-16
is pretty but not correct/homogeneous/honest
Maybe I was not clear enough.
1.7 cannot be stored exactly in IEEE754 encoding so it should always
be displayed with trailing zeros.
So
--> x(8)-1.7
ans =
2.220D-16
is OK and should always be displayed like this, but the previous
display
--> x(8)
ans =
1.7
is not OK. What is not correct/homogeneous/honest is the fact that
we have this both displays in the current version of Scilab.
I don't agree about this.
The decimal number can only rarely be represented exactly in binary
according to IEEE 754.
This means that there should always be trailing zeros to highlight
the fact that there is a 10^-16 discrepancy between the stored
value and the displayed value?
I don't find this convenient.
The fact that some people are not aware of this discrepancy can be
a problem but it is the general problem of underflow or subtractive
cancellation or round-off error etc.
The problem is not less important than ignoring a number is complex
with a zero imaginary part, but I'm not sure it can be handled in
the same way.
-- Christophe Dang Ngoc Chan
Mechanical calculation engineer
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Stéphane Mottelet
Ingénieur de recherche
EA 4297 Transformations Intégrées de la Matière Renouvelable
Département Génie des Procédés Industriels
Sorbonne Universités - Université de Technologie de Compiègne
CS 60319, 60203 Compiègne cedex
Tel : +33(0)344234688
http://www.utc.fr/~mottelet
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