blob: 116e08398ec8f4e0f14514163ec8505c45bf327d (
plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
|
module math
// factorial calculates the factorial of the provided value.
pub fn factorial(n f64) f64 {
// For a large postive argument (n >= factorials_table.len) return max_f64
if n >= factorials_table.len {
return max_f64
}
// Otherwise return n!.
if n == f64(i64(n)) && n >= 0.0 {
return factorials_table[i64(n)]
}
return gamma(n + 1.0)
}
// log_factorial calculates the log-factorial of the provided value.
pub fn log_factorial(n f64) f64 {
// For a large postive argument (n < 0) return max_f64
if n < 0 {
return -max_f64
}
// If n < N then return ln(n!).
if n != f64(i64(n)) {
return log_gamma(n + 1)
} else if n < log_factorials_table.len {
return log_factorials_table[i64(n)]
}
// Otherwise return asymptotic expansion of ln(n!).
return log_factorial_asymptotic_expansion(int(n))
}
fn log_factorial_asymptotic_expansion(n int) f64 {
m := 6
mut term := []f64{}
xx := f64((n + 1) * (n + 1))
mut xj := f64(n + 1)
log_factorial := log_sqrt_2pi - xj + (xj - 0.5) * log(xj)
mut i := 0
for i = 0; i < m; i++ {
term << bernoulli[i] / xj
xj *= xx
}
mut sum := term[m - 1]
for i = m - 2; i >= 0; i-- {
if abs(sum) <= abs(term[i]) {
break
}
sum = term[i]
}
for i >= 0 {
sum += term[i]
i--
}
return log_factorial + sum
}
|
