GCD, LCM, SIGNUM.

diff --git a/src/numbers.lisp b/src/numbers.lisp
index 18d679c..66c2db8 100644 (file)
--- a/src/numbers.lisp
+++ b/src/numbers.lisp
@@ -59,6 +59,9 @@
 (defun zerop (x) (= x 0))
 (defun plusp (x) (< 0 x))
 
+(defun signum (x)
+  (if (zerop x) x (/ x (abs x))))
+
 ;; TODO: Use MACROLET when it exists
 (defmacro defcomparison (operator)
   `(defun ,operator (x &rest args)
@@ -91,3 +94,33 @@
 
 (defun expt (base power) (expt base              power))
 (defun exp  (power)      (expt 2.718281828459045 power))
+
+(defun gcd-2 (a b)
+  (if (zerop b)
+      (abs a)
+    (gcd-2 b (mod a b))))
+
+(defun gcd (&rest integers)
+  (cond ((null integers)
+        0)
+       ((null (cdr integers))
+        (abs (first integers)))
+       ((null (cddr integers))
+        (gcd-2 (first integers) (second integers)))
+       (t
+        (apply #'gcd (gcd (first integers) (second integers)) (nthcdr 2 integers)))))
+
+(defun lcm-2 (a b)
+  (if (or (zerop a) (zerop b))
+      0
+    (/ (abs (* a b)) (gcd a b))))
+
+(defun lcm (&rest integers)
+  (cond ((null integers)
+        1)
+       ((null (cdr integers))
+        (abs (first integers)))
+       ((null (cddr integers))
+        (lcm-2 (first integers) (second integers)))
+       (t
+        (apply #'lcm (lcm (first integers) (second integers)) (nthcdr 2 integers)))))

diff --git a/tests/numbers.lisp b/tests/numbers.lisp
index 2d44def..811d423 100644 (file)
--- a/tests/numbers.lisp
+++ b/tests/numbers.lisp
@@ -66,3 +66,21 @@
 (test             (floatp    pi))
 (test             (floatp (- pi)))
 (test        (not (floatp    1)))
+
+;;; GCD
+(test (= 0 (gcd)))
+(test (= 6 (gcd 60 42)))
+(test (= 1 (gcd 3333 -33 101)))
+(test (= 11 (gcd 3333 -33 1002001)))
+(test (= 7 (gcd 91 -49)))
+(test (= 7 (gcd 63 -42 35)))
+(test (= 5 (gcd 5)))
+(test (= 4 (gcd -4)))
+
+;;; LCM
+(test (= 10 (lcm 10)))
+(test (= 150 (lcm 25 30)))
+(test (= 360 (lcm -24 18 10)))
+(test (= 70 (lcm 14 35)))
+(test (= 0 (lcm 0 5)))
+(test (= 60 (lcm 1 2 3 4 5 6)))