Fix GCD; add LCM (#396)

stdlib/math.codon

@@ -516,18 +516,60 @@ def remainder(x: float, y: float) -> float:
     """
     return _check2(x, y, _C.remainder(x, y))
 
-def gcd(a: float, b: float) -> float:
-    """
-    gcd(float, float) -> float
-
-    returns greatest common divisor of x and y.
-    """
+def _gcd2(a, b):
     a = abs(a)
     b = abs(b)
     while a:
         a, b = b % a, a
     return b
 
+def gcd(*args):
+    """
+    gcd(*args)
+
+    returns greatest common divisor of arguments.
+    """
+    if staticlen(args) == 0:
+        return 0
+
+    res = args[0]
+    T = type(res)
+
+    if staticlen(args) == 1:
+        return abs(res)
+
+    for i in range(1, len(args)):
+        if res == T(1):
+            break
+        res = _gcd2(res, args[i])
+
+    return res
+
+def lcm(*args):
+    """
+    lcm(*args)
+
+    returns least common multiple of arguments.
+    """
+    def lcm2(a, b):
+        return abs((a // _gcd2(a, b)) * b)
+
+    if staticlen(args) == 0:
+        return 1
+
+    res = args[0]
+    T = type(res)
+
+    if staticlen(args) == 1:
+        return abs(res)
+
+    for i in range(1, len(args)):
+        if not res:
+            break
+        res = lcm2(res, args[i])
+
+    return res
+
 @pure
 def frexp(x: float) -> Tuple[float, int]:
     """
@@ -1195,19 +1237,6 @@ def remainder(x: float32, y: float32) -> float32:
     """
     return _C.remainderf(x, y)
 
-@overload
-def gcd(a: float32, b: float32) -> float32:
-    """
-    gcd(float32, float32) -> float32
-
-    returns greatest common divisor of x and y.
-    """
-    a = abs(a)
-    b = abs(b)
-    while a:
-        a, b = b % a, a
-    return b
-
 @overload
 @pure
 def frexp(x: float32) -> Tuple[float32, int]:

test/stdlib/math_test.codon

@@ -411,16 +411,73 @@ def test_remainder():
 
 @test
 def test_gcd():
-    assert math.gcd(0.0, 0.0) == 0
-    assert math.gcd(1.0, 0.0) == 1
-    assert math.gcd(-1.0, 0.0) == 1
-    assert math.gcd(0.0, -1.0) == 1
-    assert math.gcd(0.0, 1.0) == 1
-    assert math.gcd(7.0, 1.0) == 1
-    assert math.gcd(7.0, -1.0) == 1
-    assert math.gcd(-23.0, 15.0) == 1
-    assert math.gcd(120.0, 84.0) == 12
-    assert math.gcd(84.0, -120.0) == 12
+    assert math.gcd(0, 0) == 0
+    assert math.gcd(1, 0) == 1
+    assert math.gcd(-1, 0) == 1
+    assert math.gcd(0, 1) == 1
+    assert math.gcd(0, -1) == 1
+    assert math.gcd(7, 1) == 1
+    assert math.gcd(7, -1) == 1
+    assert math.gcd(-23, 15) == 1
+    assert math.gcd(120, 84) == 12
+    assert math.gcd(84, -120) == 12
+    assert math.gcd(Int[128]('1216342683557601535506311712'), Int[128]('436522681849110124616458784')) == Int[128](32)
+
+    x = 43461
+    y = 1064
+    for c in (652560, 576559230):
+        a = x * c
+        b = y * c
+        assert math.gcd(a, b) == c
+        assert math.gcd(b, a) == c
+        assert math.gcd(-a, b) == c
+        assert math.gcd(b, -a) == c
+        assert math.gcd(a, -b) == c
+        assert math.gcd(-b, a) == c
+        assert math.gcd(-a, -b) == c
+        assert math.gcd(-b, -a) == c
+
+    assert math.gcd() == 0
+    assert math.gcd(120) == 120
+    assert math.gcd(-120) == 120
+    assert math.gcd(120, 84, 102) == 6
+    assert math.gcd(120, 1, 84) == 1
+
+
+@test
+def test_lcm():
+    assert math.lcm(0, 0) == 0
+    assert math.lcm(1, 0) == 0
+    assert math.lcm(-1, 0) == 0
+    assert math.lcm(0, 1) == 0
+    assert math.lcm(0, -1) == 0
+    assert math.lcm(7, 1) == 7
+    assert math.lcm(7, -1) == 7
+    assert math.lcm(-23, 15) == 345
+    assert math.lcm(120, 84) == 840
+    assert math.lcm(84, -120) == 840
+    #assert math.lcm(1216342683557601535506311712, 436522681849110124616458784) == 16592536571065866494401400422922201534178938447014944
+
+    x = 4346103
+    y = 1064501
+    for c in (8171, 58657):
+        a = x * c
+        b = y * c
+        d = x * y * c
+        assert math.lcm(a, b) == d
+        assert math.lcm(b, a) == d
+        assert math.lcm(-a, b) == d
+        assert math.lcm(b, -a) == d
+        assert math.lcm(a, -b) == d
+        assert math.lcm(-b, a) == d
+        assert math.lcm(-a, -b) == d
+        assert math.lcm(-b, -a) == d
+
+    assert math.lcm() == 1
+    assert math.lcm(120) == 120
+    assert math.lcm(-120) == 120
+    assert math.lcm(120, 84, 102) == 14280
+    assert math.lcm(120, 0, 84) == 0
 
 
 @test
@@ -714,6 +771,7 @@ test_gamma()
 test_lgamma()
 test_remainder()
 test_gcd()
+test_lcm()
 test_frexp()
 test_modf()
 test_isclose()
@@ -1131,20 +1189,6 @@ def test_float32_remainder():
     assert math.isnan(math.remainder(NAN32, 1.0f32)) == True
 
 
-@test
-def test_float32_gcd():
-    assert math.gcd(0.0f32, 0.0f32) == 0.0f32
-    assert math.gcd(1.0f32, 0.0f32) == 1.0f32
-    assert math.gcd(-1.0f32, 0.0f32) == 1.0f32
-    assert math.gcd(0.0f32, -1.0f32) == 1.0f32
-    assert math.gcd(0.0f32, 1.0f32) == 1.0f32
-    assert math.gcd(7.0f32, 1.0f32) == 1.0f32
-    assert math.gcd(7.0f32, -1.0f32) == 1.0f32
-    assert math.gcd(-23.0f32, 15.0f32) == 1.0f32
-    assert math.gcd(120.0f32, 84.0f32) == 12.0f32
-    assert math.gcd(84.0f32, -120.0f32) == 12.0f32
-
-
 @test
 def test_float32_frexp():
     assert math.frexp(-2.0f32) == (-0.5f32, 2)
@@ -1222,7 +1266,6 @@ test_float32_erfc()
 test_float32_gamma()
 test_float32_lgamma()
 test_float32_remainder()
-test_float32_gcd()
 test_float32_frexp()
 test_float32_modf()
 test_float32_isclose()