Factorial of input
f = factorial( returns
the product of all positive integers less than or equal to n)n,
where n is a nonnegative integer value. If n is
an array, then f contains the factorial of each
value of n. The data type and size of f is
the same as that of n.
The factorial of n is commonly written in
math notation using the exclamation point character as n!.
Note that n! is not a valid MATLAB® syntax
for calculating the factorial of n.
Limitations
For double-precision inputs, the result is exact when n is
less than or equal to 21. Larger values of n produce
a result that has the correct order of magnitude and is accurate for
the first 15 digits. This is because double-precision numbers are
only accurate up to 15 digits.
For single-precision inputs, the result is exact when n is
less than or equal to 13. Larger values of n produce
a result that has the correct order of magnitude and is accurate for
the first 8 digits. This is because single-precision numbers are only
accurate up to 8 digits.
Saturation
The table below describes the saturation behavior
of each data type when used with the factorial function.
The values in the last column indicate the saturation point; that
is, the first positive integer whose actual factorial is larger than
the maximum representable value in the middle column. For single and double,
all values larger than the maximum value are returned as Inf.
For the integer data types, the saturation value is equal to the maximum
value in the middle column.
| Data type | Maximum Value | Factorial Saturation Threshold |
|---|---|---|
double | realmax | factorial(171) |
single | realmax('single') | factorial(single(35)) |
uint64 | 264-1 | factorial(uint64(21)) |
int64 | 263-1 | factorial(int64(21)) |
uint32 | 232-1 | factorial(uint32(13)) |
int32 | 231-1 | factorial(int32(13)) |
uint16 | 216-1 | factorial(uint16(9)) |
int16 | 215-1 | factorial(int16(8)) |
uint8 | 28-1 | factorial(uint8(6)) |
int8 | 27-1 | factorial(int8(6)) |