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mdickinson merged 4 commits into from
Feb 23, 2020
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bpo-39648: Expand math.gcd() and math.lcm() to handle multiple arguments. #18604

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bd7e068
bpo-39648: Expand math.gcd() and math.lcm() to handle multiple argume…
serhiy-storchaka Feb 22, 2020
469819b
Simplify fast path.
serhiy-storchaka Feb 22, 2020
ba9f44a
Difine lcm() without arguments returning 1.
serhiy-storchaka Feb 22, 2020
88998f7
Apply suggestions from code review
serhiy-storchaka Feb 23, 2020
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33 changes: 20 additions & 13 deletions Doc/library/math.rst
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Original file line number Diff line number Diff line change
Expand Up @@ -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)
Expand Down Expand Up @@ -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
Expand Down
9 changes: 7 additions & 2 deletions Doc/whatsnew/3.9.rst
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Expand Up @@ -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*.
Expand Down
58 changes: 33 additions & 25 deletions Lib/test/test_math.py
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Expand Up @@ -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):
Expand Down Expand Up @@ -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
Expand All @@ -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)
Expand Down
1 change: 1 addition & 0 deletions Misc/NEWS.d/next/Library/2020-02-22-12-49-04.bpo-39648.Y-9N7F.rst
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@@ -0,0 +1 @@
Expanded :func:`math.gcd` and :func:`math.lcm` to handle multiple arguments.
62 changes: 1 addition & 61 deletions Modules/clinic/mathmodule.c.h
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