[Python-checkins] bpo-39648: Expand math.gcd() and math.lcm() to handle multiple arguments. (GH-18604)
Serhiy Storchaka
webhook-mailer at python.org
Sun Feb 23 06:21:43 EST 2020
https://github.com/python/cpython/commit/559e7f165ad03731e6bc2211c0e6d8d9c02fb549
commit: 559e7f165ad03731e6bc2211c0e6d8d9c02fb549
branch: master
author: Serhiy Storchaka <storchaka at gmail.com>
committer: GitHub <noreply at github.com>
date: 2020-02-23T11:21:29Z
summary:
bpo-39648: Expand math.gcd() and math.lcm() to handle multiple arguments. (GH-18604)
* bpo-39648: Expand math.gcd() and math.lcm() to handle multiple arguments.
* Simplify fast path.
* Difine lcm() without arguments returning 1.
* Apply suggestions from code review
Co-Authored-By: Mark Dickinson <dickinsm at gmail.com>
Co-authored-by: Mark Dickinson <dickinsm at gmail.com>
files:
A Misc/NEWS.d/next/Library/2020-02-22-12-49-04.bpo-39648.Y-9N7F.rst
M Doc/library/math.rst
M Doc/whatsnew/3.9.rst
M Lib/test/test_math.py
M Modules/clinic/mathmodule.c.h
M Modules/mathmodule.c
diff --git a/Doc/library/math.rst b/Doc/library/math.rst
index d8ac35256d1b4..6ec1feee35a6d 100644
--- a/Doc/library/math.rst
+++ b/Doc/library/math.rst
@@ -126,23 +126,19 @@ Number-theoretic and representation functions
<https://code.activestate.com/recipes/393090/>`_\.
-.. function:: gcd(a, b)
+.. function:: gcd(*integers)
- Return the greatest common divisor of the integers *a* and *b*. If either
- *a* or *b* is nonzero, then the value of ``gcd(a, b)`` is the largest
- positive integer that divides both *a* and *b*. ``gcd(0, 0)`` returns
- ``0``.
+ Return the greatest common divisor of the specified integer arguments.
+ If any of the arguments is nonzero, then the returned value is the largest
+ positive integer that is a divisor af all arguments. If all arguments
+ are zero, then the returned value is ``0``. ``gcd()`` without arguments
+ returns ``0``.
.. versionadded:: 3.5
-
-.. function:: lcm(a, b)
-
- Return the least common multiple of integers *a* and *b*. The value of
- ``lcm(a, b)`` is the smallest nonnegative integer that is a multiple of
- both *a* and *b*. If either *a* or *b* is zero then ``lcm(a, b)`` is zero.
-
- .. versionadded:: 3.9
+ .. versionchanged:: 3.9
+ Added support for an arbitrary number of arguments. Formerly, only two
+ arguments were supported.
.. function:: isclose(a, b, *, rel_tol=1e-09, abs_tol=0.0)
@@ -210,6 +206,17 @@ Number-theoretic and representation functions
.. versionadded:: 3.8
+.. function:: lcm(*integers)
+
+ Return the least common multiple of the specified integer arguments.
+ If all arguments are nonzero, then the returned value is the smallest
+ positive integer that is a multiple of all arguments. If any of the arguments
+ is zero, then the returned value is ``0``. ``lcm()`` without arguments
+ returns ``1``.
+
+ .. versionadded:: 3.9
+
+
.. function:: ldexp(x, i)
Return ``x * (2**i)``. This is essentially the inverse of function
diff --git a/Doc/whatsnew/3.9.rst b/Doc/whatsnew/3.9.rst
index 161675d32f670..a0ae4eb9b825a 100644
--- a/Doc/whatsnew/3.9.rst
+++ b/Doc/whatsnew/3.9.rst
@@ -216,8 +216,13 @@ import attempts.
math
----
-Add :func:`math.lcm`: return the least common multiple of *a* and *b*.
-(Contributed by Ananthakrishnan in :issue:`39479`.)
+Expanded the :func:`math.gcd` function to handle multiple arguments.
+Formerly, it only supported two arguments.
+(Contributed by Serhiy Storchaka in :issue:`39648`.)
+
+Add :func:`math.lcm`: return the least common multiple of specified arguments.
+(Contributed by Mark Dickinson, Ananthakrishnan and Serhiy Storchaka in
+:issue:`39479` and :issue:`39648`.)
Add :func:`math.nextafter`: return the next floating-point value after *x*
towards *y*.
diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py
index ad8273d50cc39..cc39402b3c60b 100644
--- a/Lib/test/test_math.py
+++ b/Lib/test/test_math.py
@@ -705,33 +705,32 @@ def testGcd(self):
self.assertEqual(gcd(84, -120), 12)
self.assertEqual(gcd(1216342683557601535506311712,
436522681849110124616458784), 32)
- c = 652560
+
x = 434610456570399902378880679233098819019853229470286994367836600566
y = 1064502245825115327754847244914921553977
- a = x * c
- b = y * c
- self.assertEqual(gcd(a, b), c)
- self.assertEqual(gcd(b, a), c)
- self.assertEqual(gcd(-a, b), c)
- self.assertEqual(gcd(b, -a), c)
- self.assertEqual(gcd(a, -b), c)
- self.assertEqual(gcd(-b, a), c)
- self.assertEqual(gcd(-a, -b), c)
- self.assertEqual(gcd(-b, -a), c)
- c = 576559230871654959816130551884856912003141446781646602790216406874
- a = x * c
- b = y * c
- self.assertEqual(gcd(a, b), c)
- self.assertEqual(gcd(b, a), c)
- self.assertEqual(gcd(-a, b), c)
- self.assertEqual(gcd(b, -a), c)
- self.assertEqual(gcd(a, -b), c)
- self.assertEqual(gcd(-b, a), c)
- self.assertEqual(gcd(-a, -b), c)
- self.assertEqual(gcd(-b, -a), c)
-
+ for c in (652560,
+ 576559230871654959816130551884856912003141446781646602790216406874):
+ a = x * c
+ b = y * c
+ self.assertEqual(gcd(a, b), c)
+ self.assertEqual(gcd(b, a), c)
+ self.assertEqual(gcd(-a, b), c)
+ self.assertEqual(gcd(b, -a), c)
+ self.assertEqual(gcd(a, -b), c)
+ self.assertEqual(gcd(-b, a), c)
+ self.assertEqual(gcd(-a, -b), c)
+ self.assertEqual(gcd(-b, -a), c)
+
+ self.assertEqual(gcd(), 0)
+ self.assertEqual(gcd(120), 120)
+ self.assertEqual(gcd(-120), 120)
+ self.assertEqual(gcd(120, 84, 102), 6)
+ self.assertEqual(gcd(120, 1, 84), 1)
+
+ self.assertRaises(TypeError, gcd, 120.0)
self.assertRaises(TypeError, gcd, 120.0, 84)
self.assertRaises(TypeError, gcd, 120, 84.0)
+ self.assertRaises(TypeError, gcd, 120, 1, 84.0)
self.assertEqual(gcd(MyIndexable(120), MyIndexable(84)), 12)
def testHypot(self):
@@ -989,9 +988,9 @@ def test_lcm(self):
self.assertEqual(lcm(1216342683557601535506311712,
436522681849110124616458784),
16592536571065866494401400422922201534178938447014944)
+
x = 43461045657039990237
y = 10645022458251153277
-
for c in (652560,
57655923087165495981):
a = x * c
@@ -1005,9 +1004,18 @@ def test_lcm(self):
self.assertEqual(lcm(-b, a), d)
self.assertEqual(lcm(-a, -b), d)
self.assertEqual(lcm(-b, -a), d)
- self.assertEqual(lcm(MyIndexable(120), MyIndexable(84)), 840)
+
+ self.assertEqual(lcm(), 1)
+ self.assertEqual(lcm(120), 120)
+ self.assertEqual(lcm(-120), 120)
+ self.assertEqual(lcm(120, 84, 102), 14280)
+ self.assertEqual(lcm(120, 0, 84), 0)
+
+ self.assertRaises(TypeError, lcm, 120.0)
self.assertRaises(TypeError, lcm, 120.0, 84)
self.assertRaises(TypeError, lcm, 120, 84.0)
+ self.assertRaises(TypeError, lcm, 120, 0, 84.0)
+ self.assertEqual(lcm(MyIndexable(120), MyIndexable(84)), 840)
def testLdexp(self):
self.assertRaises(TypeError, math.ldexp)
diff --git a/Misc/NEWS.d/next/Library/2020-02-22-12-49-04.bpo-39648.Y-9N7F.rst b/Misc/NEWS.d/next/Library/2020-02-22-12-49-04.bpo-39648.Y-9N7F.rst
new file mode 100644
index 0000000000000..f205911ad9bfd
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2020-02-22-12-49-04.bpo-39648.Y-9N7F.rst
@@ -0,0 +1 @@
+Expanded :func:`math.gcd` and :func:`math.lcm` to handle multiple arguments.
diff --git a/Modules/clinic/mathmodule.c.h b/Modules/clinic/mathmodule.c.h
index df45a1a0c5e85..65f3dd4f520ae 100644
--- a/Modules/clinic/mathmodule.c.h
+++ b/Modules/clinic/mathmodule.c.h
@@ -2,36 +2,6 @@
preserve
[clinic start generated code]*/
-PyDoc_STRVAR(math_gcd__doc__,
-"gcd($module, x, y, /)\n"
-"--\n"
-"\n"
-"greatest common divisor of x and y");
-
-#define MATH_GCD_METHODDEF \
- {"gcd", (PyCFunction)(void(*)(void))math_gcd, METH_FASTCALL, math_gcd__doc__},
-
-static PyObject *
-math_gcd_impl(PyObject *module, PyObject *a, PyObject *b);
-
-static PyObject *
-math_gcd(PyObject *module, PyObject *const *args, Py_ssize_t nargs)
-{
- PyObject *return_value = NULL;
- PyObject *a;
- PyObject *b;
-
- if (!_PyArg_CheckPositional("gcd", nargs, 2, 2)) {
- goto exit;
- }
- a = args[0];
- b = args[1];
- return_value = math_gcd_impl(module, a, b);
-
-exit:
- return return_value;
-}
-
PyDoc_STRVAR(math_ceil__doc__,
"ceil($module, x, /)\n"
"--\n"
@@ -85,36 +55,6 @@ PyDoc_STRVAR(math_factorial__doc__,
#define MATH_FACTORIAL_METHODDEF \
{"factorial", (PyCFunction)math_factorial, METH_O, math_factorial__doc__},
-PyDoc_STRVAR(math_lcm__doc__,
-"lcm($module, x, y, /)\n"
-"--\n"
-"\n"
-"least common multiple of x and y");
-
-#define MATH_LCM_METHODDEF \
- {"lcm", (PyCFunction)(void(*)(void))math_lcm, METH_FASTCALL, math_lcm__doc__},
-
-static PyObject *
-math_lcm_impl(PyObject *module, PyObject *a, PyObject *b);
-
-static PyObject *
-math_lcm(PyObject *module, PyObject *const *args, Py_ssize_t nargs)
-{
- PyObject *return_value = NULL;
- PyObject *a;
- PyObject *b;
-
- if (!_PyArg_CheckPositional("lcm", nargs, 2, 2)) {
- goto exit;
- }
- a = args[0];
- b = args[1];
- return_value = math_lcm_impl(module, a, b);
-
-exit:
- return return_value;
-}
-
PyDoc_STRVAR(math_trunc__doc__,
"trunc($module, x, /)\n"
"--\n"
@@ -925,4 +865,4 @@ math_ulp(PyObject *module, PyObject *arg)
exit:
return return_value;
}
-/*[clinic end generated code: output=f8daa185c043a7b7 input=a9049054013a1b77]*/
+/*[clinic end generated code: output=1eae2b3ef19568fa input=a9049054013a1b77]*/
diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index f74b7e1a34203..77e325cf0c63d 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -826,37 +826,125 @@ m_log10(double x)
}
-/*[clinic input]
-math.gcd
+static PyObject *
+math_gcd(PyObject *module, PyObject * const *args, Py_ssize_t nargs)
+{
+ PyObject *res, *x;
+ Py_ssize_t i;
- x as a: object
- y as b: object
- /
+ if (nargs == 0) {
+ return PyLong_FromLong(0);
+ }
+ res = PyNumber_Index(args[0]);
+ if (res == NULL) {
+ return NULL;
+ }
+ if (nargs == 1) {
+ Py_SETREF(res, PyNumber_Absolute(res));
+ return res;
+ }
+ for (i = 1; i < nargs; i++) {
+ x = PyNumber_Index(args[i]);
+ if (x == NULL) {
+ Py_DECREF(res);
+ return NULL;
+ }
+ if (res == _PyLong_One) {
+ /* Fast path: just check arguments.
+ It is okay to use identity comparison here. */
+ Py_DECREF(x);
+ continue;
+ }
+ Py_SETREF(res, _PyLong_GCD(res, x));
+ Py_DECREF(x);
+ if (res == NULL) {
+ return NULL;
+ }
+ }
+ return res;
+}
+
+PyDoc_STRVAR(math_gcd_doc,
+"gcd($module, *integers)\n"
+"--\n"
+"\n"
+"Greatest Common Divisor.");
-greatest common divisor of x and y
-[clinic start generated code]*/
static PyObject *
-math_gcd_impl(PyObject *module, PyObject *a, PyObject *b)
-/*[clinic end generated code: output=7b2e0c151bd7a5d8 input=c2691e57fb2a98fa]*/
+long_lcm(PyObject *a, PyObject *b)
{
- PyObject *g;
+ PyObject *g, *m, *f, *ab;
- a = PyNumber_Index(a);
- if (a == NULL)
+ if (Py_SIZE(a) == 0 || Py_SIZE(b) == 0) {
+ return PyLong_FromLong(0);
+ }
+ g = _PyLong_GCD(a, b);
+ if (g == NULL) {
return NULL;
- b = PyNumber_Index(b);
- if (b == NULL) {
- Py_DECREF(a);
+ }
+ f = PyNumber_FloorDivide(a, g);
+ Py_DECREF(g);
+ if (f == NULL) {
return NULL;
}
- g = _PyLong_GCD(a, b);
- Py_DECREF(a);
- Py_DECREF(b);
- return g;
+ m = PyNumber_Multiply(f, b);
+ Py_DECREF(f);
+ if (m == NULL) {
+ return NULL;
+ }
+ ab = PyNumber_Absolute(m);
+ Py_DECREF(m);
+ return ab;
}
+static PyObject *
+math_lcm(PyObject *module, PyObject * const *args, Py_ssize_t nargs)
+{
+ PyObject *res, *x;
+ Py_ssize_t i;
+
+ if (nargs == 0) {
+ return PyLong_FromLong(1);
+ }
+ res = PyNumber_Index(args[0]);
+ if (res == NULL) {
+ return NULL;
+ }
+ if (nargs == 1) {
+ Py_SETREF(res, PyNumber_Absolute(res));
+ return res;
+ }
+ for (i = 1; i < nargs; i++) {
+ x = PyNumber_Index(args[i]);
+ if (x == NULL) {
+ Py_DECREF(res);
+ return NULL;
+ }
+ if (res == _PyLong_Zero) {
+ /* Fast path: just check arguments.
+ It is okay to use identity comparison here. */
+ Py_DECREF(x);
+ continue;
+ }
+ Py_SETREF(res, long_lcm(res, x));
+ Py_DECREF(x);
+ if (res == NULL) {
+ return NULL;
+ }
+ }
+ return res;
+}
+
+
+PyDoc_STRVAR(math_lcm_doc,
+"lcm($module, *integers)\n"
+"--\n"
+"\n"
+"Least Common Multiple.");
+
+
/* Call is_error when errno != 0, and where x is the result libm
* returned. is_error will usually set up an exception and return
* true (1), but may return false (0) without setting up an exception.
@@ -2017,59 +2105,6 @@ math_factorial(PyObject *module, PyObject *arg)
}
-/*[clinic input]
-math.lcm
- x as a: object
- y as b: object
- /
-least common multiple of x and y
-[clinic start generated code]*/
-
-static PyObject *
-math_lcm_impl(PyObject *module, PyObject *a, PyObject *b)
-/*[clinic end generated code: output=6f83fb6d671074ba input=efb3d7b7334b7118]*/
-{
- PyObject *g, *m, *f, *ab;
-
- a = PyNumber_Index(a);
- if (a == NULL) {
- return NULL;
- }
- b = PyNumber_Index(b);
- if (b == NULL) {
- Py_DECREF(a);
- return NULL;
- }
- if (_PyLong_Sign(a) == 0 || _PyLong_Sign(b) == 0) {
- Py_DECREF(a);
- Py_DECREF(b);
- return PyLong_FromLong(0);
- }
- g = _PyLong_GCD(a, b);
- if (g == NULL) {
- Py_DECREF(a);
- Py_DECREF(b);
- return NULL;
- }
- f = PyNumber_FloorDivide(a, g);
- Py_DECREF(g);
- Py_DECREF(a);
- if (f == NULL) {
- Py_DECREF(b);
- return NULL;
- }
- m = PyNumber_Multiply(f, b);
- Py_DECREF(f);
- Py_DECREF(b);
- if (m == NULL) {
- return NULL;
- }
- ab = PyNumber_Absolute(m);
- Py_DECREF(m);
- return ab;
-}
-
-
/*[clinic input]
math.trunc
@@ -3408,14 +3443,14 @@ static PyMethodDef math_methods[] = {
MATH_FREXP_METHODDEF
MATH_FSUM_METHODDEF
{"gamma", math_gamma, METH_O, math_gamma_doc},
- MATH_GCD_METHODDEF
+ {"gcd", (PyCFunction)(void(*)(void))math_gcd, METH_FASTCALL, math_gcd_doc},
{"hypot", (PyCFunction)(void(*)(void))math_hypot, METH_FASTCALL, math_hypot_doc},
MATH_ISCLOSE_METHODDEF
MATH_ISFINITE_METHODDEF
MATH_ISINF_METHODDEF
MATH_ISNAN_METHODDEF
MATH_ISQRT_METHODDEF
- MATH_LCM_METHODDEF
+ {"lcm", (PyCFunction)(void(*)(void))math_lcm, METH_FASTCALL, math_lcm_doc},
MATH_LDEXP_METHODDEF
{"lgamma", math_lgamma, METH_O, math_lgamma_doc},
MATH_LOG_METHODDEF
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