Function‘round’. Numerical calculation question

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yang li
yang li 2018-11-17
评论： Walter Roberson 2018-11-17
Problem recurrence：
>> round(((6/40000)*10000))
ans =
1
but，
>> round(1.500000000000000)
ans =
2
Why is 1.5 such a value appearing when rounding off?The same value calculation results are different.

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回答（3 个）

Bruno Luong
Bruno Luong 2018-11-17
编辑：Bruno Luong 2018-11-17
Welcome to the work of floating point arithmetic
>> (6/40000)*10000-1.5
ans =
-2.2204e-16
>>
So actually the calculation of (6/40000)*10000 returns value stricly less than 1.5=3/2. Therefore what you have observed with round is explained.
  2 个评论
yang li
yang li 2018-11-17
Thank you for your answer, I need to look at the knowledge of floating point calculations.
Walter Roberson
Walter Roberson 2018-11-17
When you think of 1/10 in binary it can help to think about 1/7 in decimal, in that 1/7 decimal is an infinitely repeating multidigit pattern . If you truncate to any finite number of digits and then multiply back by 7 then you will not get exactly 1. Exactly the same mathematics reasons that lead 1/7 decimal to be infinite lead 1/10 to be infinite repeating multiple digits in binary. It is not a "quality of implementation" issue but rather a fundamental limitation of using any finite number of digits in a "base" numeric representation instead of using rational numbers as the representation .

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Walter Roberson
Walter Roberson 2018-11-17
1/10 is not exactly representable in binary floating point so you would need to calculate carefully to figure what is being computed.
But algebraically the first of those would be round(2/4) which would be round(0.5) which would round up to 1 and likewise round(1.5) rounds up to 2 so the results you see happen to agree with the algebraic results . Other combinations that are algebraically the same could come out differently because of 1/10 not being exactly representable.
  1 个评论
yang li
yang li 2018-11-17
I am sorry that my code part is wrong. The problem is as follows.
>> round((6/40000)*10000)
ans =
1
and
>> round(1.500000000000000)
ans =
2
I use matlab to calculate directly, but the same value gives different results.

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KSSV
KSSV 2018-11-17
if your number is less than 0.5.._round_ acts like floor function. For number greater than or equla to 0.5 it acts like ceil. YOu may check it yourself. Read about ceil and _floor_
x = 0:0.1:1
floor(x)
ceil(x)
round(x)
  1 个评论
yang li
yang li 2018-11-17
I am sorry that my code part is wrong. The problem is as follows.
>> round((6/40000)*10000)
ans =
1
and
>> round(1.500000000000000)
ans =
2
I use matlab to calculate directly, but the same value gives different results.

请先登录，再进行评论。

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