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bpo-39648: Expand math.gcd() and math.lcm() to handle multiple arguments. (GH-18604)

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* 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@gmail.com>

Co-authored-by: Mark Dickinson <dickinsm@gmail.com>
This commit is contained in:
Serhiy Storchaka 2020-02-23 13:21:29 +02:00 committed by GitHub
parent fbe2e0bb8a
commit 559e7f165a
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GPG key ID: 4AEE18F83AFDEB23
6 changed files with 174 additions and 178 deletions
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33
Doc/library/math.rst
View file

@ -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

9
Doc/whatsnew/3.9.rst
View file

@ -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*.

56
Lib/test/test_math.py
View file

@ -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)

1
Misc/NEWS.d/next/Library/2020-02-22-12-49-04.bpo-39648.Y-9N7F.rst Normal file
View file

@ -0,0 +1 @@
Expanded :func:`math.gcd` and :func:`math.lcm` to handle multiple arguments.

62
Modules/clinic/mathmodule.c.h generated
View file

@ -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]*/

191
Modules/mathmodule.c
View file

@ -826,36 +826,124 @@ m_log10(double x)
}
/*[clinic input]
math.gcd
x as a: object
y as b: object
/
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]*/
math_gcd(PyObject *module, PyObject * const *args, Py_ssize_t nargs)
{
PyObject *g;
PyObject *res, *x;
Py_ssize_t i;
a = PyNumber_Index(a);
if (a == NULL)
return NULL;
b = PyNumber_Index(b);
if (b == NULL) {
Py_DECREF(a);
if (nargs == 0) {
return PyLong_FromLong(0);
}
res = PyNumber_Index(args[0]);
if (res == NULL) {
return NULL;
}
g = _PyLong_GCD(a, b);
Py_DECREF(a);
Py_DECREF(b);
return g;
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($module, *integers)\n"
"--\n"
"\n"
"Greatest Common Divisor.");
static PyObject *
long_lcm(PyObject *a, PyObject *b)
{
PyObject *g, *m, *f, *ab;
if (Py_SIZE(a) == 0 || Py_SIZE(b) == 0) {
return PyLong_FromLong(0);
}
g = _PyLong_GCD(a, b);
if (g == NULL) {
return NULL;
}
f = PyNumber_FloorDivide(a, g);
Py_DECREF(g);
if (f == NULL) {
return NULL;
}
m = PyNumber_Multiply(f, b);
Py_DECREF(f);
if (m == NULL) {
return NULL;
}
ab = PyNumber_Absolute(m);
Py_DECREF(m);
return ab;
}
static PyObject *
math_lcm(PyObject *module, PyObject * const *args, Py_ssize_t nargs)
{
PyObject *res, *x;
Py_ssize_t i;
if (nargs == 0) {
return PyLong_FromLong(1);
}
res = PyNumber_Index(args[0]);
if (res == NULL) {
return NULL;
}
if (nargs == 1) {
Py_SETREF(res, PyNumber_Absolute(res));
return res;
}
for (i = 1; i < nargs; i++) {
x = PyNumber_Index(args[i]);
if (x == NULL) {
Py_DECREF(res);
return NULL;
}
if (res == _PyLong_Zero) {
/* Fast path: just check arguments.
It is okay to use identity comparison here. */
Py_DECREF(x);
continue;
}
Py_SETREF(res, long_lcm(res, x));
Py_DECREF(x);
if (res == NULL) {
return NULL;
}
}
return res;
}
PyDoc_STRVAR(math_lcm_doc,
"lcm($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
@ -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