81 lines
1.9 KiB
V
81 lines
1.9 KiB
V
// Copyright (c) 2019-2020 Alexander Medvednikov. All rights reserved.
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// Use of this source code is governed by an MIT license
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// that can be found in the LICENSE file.
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// Module created by Ulises Jeremias Cornejo Fandos based on
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// the definitions provided in https://scientificc.github.io/cmathl/
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module factorial
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import math
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// factorial calculates the factorial of the provided value.
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pub fn factorial(n f64) f64 {
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// For a large postive argument (n >= FACTORIALS.len) return max_f64
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if n >= factorials_table.len {
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return math.max_f64
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}
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// Otherwise return n!.
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if n == f64(i64(n)) && n >= 0.0 {
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return factorials_table[i64(n)]
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}
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return math.gamma(n + 1.0)
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}
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// log_factorial calculates the log-factorial of the provided value.
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pub fn log_factorial(n f64) f64 {
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// For a large postive argument (n < 0) return max_f64
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if n < 0 {
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return -math.max_f64
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}
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// If n < N then return ln(n!).
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if n != f64(i64(n)) {
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return math.log_gamma(n+1)
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} else if n < log_factorials_table.len {
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return log_factorials_table[i64(n)]
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}
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// Otherwise return asymptotic expansion of ln(n!).
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return log_factorial_asymptotic_expansion(int(n))
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}
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fn log_factorial_asymptotic_expansion(n int) f64 {
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m := 6
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mut term := []f64{}
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xx := f64((n + 1) * (n + 1))
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mut xj := f64(n + 1)
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log_factorial := log_sqrt_2pi - xj + (xj - 0.5) * math.log(xj)
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mut i := 0
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for i = 0; i < m; i++ {
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term << b_numbers[i] / xj
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xj *= xx
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}
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mut sum := term[m-1]
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for i = m - 2; i >= 0; i-- {
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if math.abs(sum) <= math.abs(term[i]) {
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break
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}
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sum = term[i]
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}
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for i >= 0 {
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sum += term[i]
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i--
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}
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return log_factorial + sum
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}
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