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Accuracy of Floating-Point Data
If the result of a floating-point arithmetic computation is not as precise as you had expected, it is
likely caused by the limitations of your computer's hardware. Probably, your result was a little less
exact because the hardware had insufficient bits to represent the result with perfect accuracy;
therefore, it truncated the resulting value.
Double-Precision Accuracy
Because there are only a finite number of double-precision numbers, you cannot represent all
numbers in double-precision storage. On any computer, there is a small gap between each doubleprecision number and the next larger double-precision number. You can determine the size of this
gap, which limits the precision of your results, using the eps function. For example, to find the
distance between 5 and the next larger double-precision number, enter
format long
eps(5)
ans =
8.881784197001252e-16
This tells you that there are no double-precision numbers between 5 and 5 + eps(5). If a doubleprecision computation returns the answer 5, the result is only accurate to within eps(5).
The value of eps(x) depends on x. This example shows that, as x gets larger, so does eps(x):
eps(50)
ans =
7.105427357601002e-15
If you enter eps with no input argument, MATLAB returns the value of eps(1), the distance from 1
to the next larger double-precision number.
Single-Precision Accuracy
Similarly, there are gaps between any two single-precision numbers. If x has type single, eps(x)
returns the distance between x and the next larger single-precision number. For example,
x = single(5);
eps(x)
returns
ans =
single
4.7684e-07
Note that this result is larger than eps(5). Because there are fewer single-precision numbers than
double-precision numbers, the gaps between the single-precision numbers are larger than the gaps
between double-precision numbers. This means that results in single-precision arithmetic are less
precise than in double-precision arithmetic.
4 Numeric Classes
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