```
fact(c(-1, 0, 1, NA, 171)) #=> NaN 1 1 NA Inf
fact(100) #=> 9.332621544394410e+157
factorial(100) #=> 9.332621544394225e+157
# correct value: 9.332621544394415e+157
# Stirling's approximation: 9.324847625269420e+157
# n! ~ sqrt(2*pi*n) * (n/e)^n
factorial2(8); factorial2(9); factorial2(10) # 384 945 3840
factorial(10) / factorial2(10) # => factorial2(9)
```

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