why does realmax('single') display 8 digits?
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most texts agree that IEEE-754 sinlge persision has 7 signicant digits and double percision has 15
so why does realmax('single') display 8 digits and realmax('double') display 16 digits?
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Ameer Hamza
2020년 12월 17일
편집: Ameer Hamza
2020년 12월 17일
"most texts agree that IEEE-754 sinlge persision has 7 signicant digits and double percision has 15"
But they don't. More precisely, they have 24 and 53 significant binary digits, respectively. Both are capable of representing 2^24 and 2^53 consecutive integers without any loss of precision. MATLAB just returns these values.
Note that it is still possible to represent even bigger integers with full precision, but the only issue is that the number adjacent to them cannot be represented precisely.
Read here: https://en.wikipedia.org/wiki/IEEE_754#Basic_and_interchange_formats. They are capable of representing ~7.22 and ~15.96 decimal digits respectively.
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Bruno Luong
2020년 12월 17일
편집: Bruno Luong
2020년 12월 17일
"but there are others where 8 digits decimal is required."
Like
flintmax('single')
Other one need 17 digits in my example of 2^(-24) or even more (up to 20 digits).
Limiting about 7-8 digits is just like see only the emerging side of an ice-berg, and pretend digits after the 8th are not significant is just plain wrong, at least from my point of view.
Walter Roberson
2020년 12월 17일
Given N digits of a single precision number, is entering those N digits enough to exactly reproduce the same bit pattern?
fprintf('%1.20e\n', single(5.960464e-8))
fprintf('%1.20e\n', single(5.9604644e-8))
So 7 input digits is not enough to completely preproduce 2^-24 but 8 input digits is. Therefor, this particular number has 8 significant decimal digits in single precision. But there are other values that use "all" of the digits (no trailing 0 in decimal) that 7 copied digits is enough.
Walter Roberson
2020년 12월 17일
>> flintmax('single')
ans =
single
16777216
You get 7 full digits, up to 9999999 . And there is some spare room beyond that, but not enough for a full digit. It is about 7.22 digits.
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