math: factorial submodule

vlib/math/factorial/factorial.v

@@ -0,0 +1,80 @@
+// Copyright (c) 2019 Alexander Medvednikov. All rights reserved.
+// Use of this source code is governed by an MIT license
+// that can be found in the LICENSE file.
+
+// Module created by Ulises Jeremias Cornejo Fandos based on
+// the definitions provided in https://scientificc.github.io/cmathl/
+
+module factorial
+
+import math
+
+// factorial calculates the factorial of the provided value.
+pub fn factorial(n f64) f64 {
+	// For a large postive argument (n >= FACTORIALS.len) return max_f64
+
+	if n >= FACTORIALS.len {
+			return math.max_f64
+	}
+
+	// Otherwise return n!.
+	if n == f64(i64(n)) && n >= 0.0 {
+		return FACTORIALS[i64(n)]
+	}
+
+	return math.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 -math.max_f64
+	}
+
+	// If n < N then return ln(n!).
+
+	if n != f64(i64(n)) {
+		return math.log_gamma(n+1)
+	} else if n < LOG_FACTORIALS.len {
+                return LOG_FACTORIALS[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) * math.log(xj)
+        
+        mut i := 0
+
+        for i = 0; i < m; i++ {
+                term << B[i] / xj
+                xj *= xx
+        }
+
+        mut sum := term[m-1]
+
+        for i = m - 2; i >= 0; i-- {
+                if math.abs(sum) <= math.abs(term[i]) {
+                        break
+                }
+
+                sum = term[i]
+        }
+
+        for i >= 0 {
+                sum += term[i]
+                i--
+        }
+
+        return log_factorial + sum
+}