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v/vlib/math/factorial.v

69 lines
1.5 KiB
V

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
}
// factoriali returns 1 for n <= 0 and -1 if the result is too large for a 64 bit integer
pub fn factoriali(n int) i64 {
if n <= 0 {
return i64(1)
}
if n < 21 {
return i64(factorials_table[n])
}
return i64(-1)
}