Improper negative number representation

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Vittorio Picco
Vittorio Picco 2020-11-11
评论： James Tursa 2020-11-11
I have encountered a very strange issue. I was having trouble with an if statement that was comparing two numbers. Although the numbers were apparently identical, the equality was seen as false. I dug a little deeper and I found this extremely simple minimal working example. Why is this happening? This doesn't make any sense!
>> format long
>> A = -6*1e-9
A =
-6.000000000000001e-09
  2 个评论
Vittorio Picco
Vittorio Picco 2020-11-11
Interesting discovery, this only happens with some numbers but not others. I am even more confused:
>> -1*1e-9
ans =
-1.000000000000000e-09
>> -2*1e-9
ans =
-2.000000000000000e-09
>> -3*1e-9
ans =
-3.000000000000000e-09
>> -4*1e-9
ans =
-4.000000000000000e-09
>> -5*1e-9
ans =
-5.000000000000000e-09
>> -6*1e-9
ans =
-6.000000000000001e-09
>> -7*1e-9
ans =
-7.000000000000001e-09
>> -8*1e-9
ans =
-8.000000000000000e-09
>> -9*1e-9
ans =
-9.000000000000001e-09
David Hill
David Hill 2020-11-11
Floating point numbers! There is lots of matlab documentation on floating point numbers, you just need to search for it.

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采纳的回答

James Tursa
James Tursa 2020-11-11
编辑：James Tursa 2020-11-11
IEEE double precision floating point cannot represent the number -6e-9 exactly. What you are seeing is the decimal representation of the closest binary floating point bit pattern that IEEE double can represent. This is normal behavior for binary floating point systems. See this link for more discussion:
https://www.mathworks.com/matlabcentral/answers/57444-faq-why-is-0-3-0-2-0-1-not-equal-to-zero?s_tid=ta_ans_results
The "exact" decimal conversion of the binary floating point numbers stored for the numbers in your examples:
>> num2strexact(-1*1e-9)
ans =
'-1.0000000000000000622815914577798564188970686927859787829220294952392578125e-9'
>> num2strexact(-2*1e-9)
ans =
'-2.000000000000000124563182915559712837794137385571957565844058990478515625e-9'
>> num2strexact(-3*1e-9)
ans =
'-3.0000000000000003936399275115964879745433790958486497402191162109375e-9'
>> num2strexact(-4*1e-9)
ans =
'-4.00000000000000024912636583111942567558827477114391513168811798095703125e-9'
>> num2strexact(-5*1e-9)
ans =
'-5.0000000000000001046128041506423633766331704464391805231571197509765625e-9'
>> num2strexact(-6*1e-9)
ans =
'-6.000000000000000787279855023192975949086758191697299480438232421875e-9'
>> num2strexact(-7*1e-9)
ans =
'-7.00000000000000064276629334271591365013165386699256487190723419189453125e-9'
>> num2strexact(-8*1e-9)
ans =
'-8.0000000000000004982527316622388513511765495422878302633762359619140625e-9'
>> num2strexact(-9*1e-9)
ans =
'-9.0000000000000011809197825347894639236301372875459492206573486328125e-9'
  2 个评论
Vittorio Picco
Vittorio Picco 2020-11-11
Thank you very much, makes sense! I'll modify my IF statement from a == b to an abs(a-b)<tolerance
James Tursa
James Tursa 2020-11-11
Good choice. When working with floating point comparisons it is best to use tolerances unless you know for sure that the numbers being compared are exact integers.

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