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Merged
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Dec 13, 2017
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ENH: Add gcd and lcm ufuncs #8774

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7ab0f15
ENH: Add gcd and lcm ufuncs
eric-wieser Mar 12, 2017
1da646c
ENH: Add support for object arrays
eric-wieser Mar 12, 2017
bf35ddc
TST: Add additional tests of lcm and gcd
eric-wieser Dec 13, 2017
58998a8
DOC: Add release notes for lcm and gcd
eric-wieser Dec 13, 2017
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9 changes: 9 additions & 0 deletions doc/release/1.15.0-notes.rst
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Expand Up @@ -10,6 +10,9 @@ Highlights
New functions
=============

* `np.gcd` and `np.lcm`, to compute the greatest common divisor and least
common multiple.


Deprecations
============
Expand Down Expand Up @@ -40,6 +43,12 @@ C API changes
New Features
============

``np.gcd`` and ``np.lcm`` ufuncs added for integer and objects types
--------------------------------------------------------------------
These compute the greatest common divisor, and lowest common multiple,
respectively. These work on all the numpy integer types, as well as the
builtin arbitrary-precision `Decimal` and `long` types.


Improvements
============
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8 changes: 8 additions & 0 deletions doc/source/reference/routines.math.rst
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Expand Up @@ -101,6 +101,14 @@ Floating point routines
nextafter
spacing

Rational routines
-----------------
.. autosummary::
:toctree: generated/

lcm
gcd

Arithmetic operations
---------------------
.. autosummary::
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2 changes: 2 additions & 0 deletions doc/source/reference/ufuncs.rst
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Expand Up @@ -550,6 +550,8 @@ Math operations
square
cbrt
reciprocal
gcd
lcm

.. tip::

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14 changes: 14 additions & 0 deletions numpy/core/code_generators/generate_umath.py
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Expand Up @@ -875,6 +875,20 @@ def english_upper(s):
TypeDescription('d', None, 'd', 'di'),
TypeDescription('g', None, 'g', 'gi'),
],
),
'gcd' :
Ufunc(2, 1, Zero,
docstrings.get('numpy.core.umath.gcd'),
"PyUFunc_SimpleBinaryOperationTypeResolver",
TD(ints),
TD('O', f='npy_ObjectGCD'),
),
'lcm' :
Ufunc(2, 1, None,
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@eric-wieser eric-wieser May 6, 2017 •
edited
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Got this wrong until now. The identity of gcd is 0 since by definition, gcd(a, 0) == a.

The identity for lcm is some kind of epsilon. For the integers, that epsilon is simply 1 (lcm(a, 1) = a). However, for the rationals, (ie decimal.Decimal), this is incorrect (lcm(0.2, 1) != 0.2), nor is such an epsilon really representable anyway.

docstrings.get('numpy.core.umath.lcm'),
"PyUFunc_SimpleBinaryOperationTypeResolver",
TD(ints),
TD('O', f='npy_ObjectLCM'),
)
}

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60 changes: 60 additions & 0 deletions numpy/core/code_generators/ufunc_docstrings.py
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Expand Up @@ -3679,3 +3679,63 @@ def add_newdoc(place, name, doc):
array([ 0., 1., 2., 3., 4., 5.])

""")

add_newdoc('numpy.core.umath', 'gcd',
"""
Returns the greatest common divisor of |x1| and |x2|

Parameters
----------
x1, x2 : array_like, int
Arrays of values

Returns
-------
y : ndarray or scalar
The greatest common divisor of the absolute value of the inputs

See Also
--------
lcm : The lowest common multiple

Examples
--------
>>> np.gcd(12, 20)
4
>>> np.gcd.reduce([15, 25, 35])
5
>>> np.gcd(np.arange(6), 20)
array([20, 1, 2, 1, 4, 5])

""")

add_newdoc('numpy.core.umath', 'lcm',
"""
Returns the lowest common multiple of |x1| and |x2|

Parameters
----------
x1, x2 : array_like, int
Arrays of values

Returns
-------
y : ndarray or scalar
The lowest common multiple of the absolute value of the inputs

See Also
--------
gcd : The greatest common divisor

Examples
--------
>>> np.lcm(12, 20)
60
>>> np.lcm.reduce([3, 12, 20])
60
>>> np.lcm.reduce([40, 12, 20])
120
>>> np.lcm(np.arange(6), 20)
array([ 0, 20, 20, 60, 20, 20])

""")
38 changes: 38 additions & 0 deletions numpy/core/src/npymath/npy_math_internal.h.src
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Expand Up @@ -678,3 +678,41 @@ npy_divmod@c@(@type@ a, @type@ b, @type@ *modulus)
#undef DEG2RAD

/**end repeat**/

/**begin repeat
*
* #type = npy_uint, npy_ulong, npy_ulonglong#
* #c = u,ul,ull#
*/
NPY_INPLACE @type@
npy_gcd@c@(@type@ a, @type@ b)
{
@type@ c;
while (a != 0) {
c = a;
a = b%a;
b = c;
}
return b;
}

NPY_INPLACE @type@
npy_lcm@c@(@type@ a, @type@ b)
{
@type@ gcd = npy_gcd@c@(a, b);
return gcd == 0 ? 0 : a / gcd * b;
}
/**end repeat**/

/**begin repeat
*
* #type = (npy_int, npy_long, npy_longlong)*2#
* #c = (,l,ll)*2#
* #func=gcd*3,lcm*3#
*/
NPY_INPLACE @type@
npy_@func@@c@(@type@ a, @type@ b)
{
return npy_@func@u@c@(a < 0 ? -a : a, b < 0 ? -b : b);
}
/**end repeat**/
68 changes: 68 additions & 0 deletions numpy/core/src/umath/funcs.inc.src
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Expand Up @@ -8,6 +8,7 @@

#define NPY_NO_DEPRECATED_API NPY_API_VERSION
#include "npy_pycompat.h"
#include "npy_import.h"


/*
Expand Down Expand Up @@ -158,6 +159,73 @@ npy_ObjectLogicalNot(PyObject *i1)
}
}

static PyObject *
npy_ObjectGCD(PyObject *i1, PyObject *i2)
{
PyObject *gcd = NULL;

/* use math.gcd if available, and valid on the provided types */
#if PY_VERSION_HEX >= 0x03050000
{
static PyObject *math_gcd_func = NULL;

npy_cache_import("math", "gcd", &math_gcd_func);
if (math_gcd_func == NULL) {
return NULL;
}
gcd = PyObject_CallFunction(math_gcd_func, "OO", i1, i2);
if (gcd != NULL) {
return gcd;
}
/* silence errors, and fall back on pure-python gcd */
PyErr_Clear();
}
#endif

/* otherwise, use our internal one, written in python */
{
static PyObject *internal_gcd_func = NULL;

npy_cache_import("numpy.core._internal", "_gcd", &internal_gcd_func);
if (internal_gcd_func == NULL) {
return NULL;
}
gcd = PyObject_CallFunction(internal_gcd_func, "OO", i1, i2);
if (gcd == NULL) {
return NULL;
}
/* _gcd has some unusual behaviour regarding sign */
return PyNumber_Absolute(gcd);
}
}

static PyObject *
npy_ObjectLCM(PyObject *i1, PyObject *i2)
{
/* lcm(a, b) = abs(a // gcd(a, b) * b) */

PyObject *gcd = npy_ObjectGCD(i1, i2);
PyObject *tmp;
if(gcd == NULL) {
return NULL;
}
/* Floor divide preserves integer types - we know the division will have
* no remainder
*/
tmp = PyNumber_FloorDivide(i1, gcd);
if(tmp == NULL) {
return NULL;
}

tmp = PyNumber_Multiply(tmp, i2);
if(tmp == NULL) {
return NULL;
}

/* even though we fix gcd to be positive, we need to do it again here */
return PyNumber_Absolute(tmp);
}

/*
*****************************************************************************
** COMPLEX FUNCTIONS **
Expand Down
30 changes: 30 additions & 0 deletions numpy/core/src/umath/loops.c.src
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Expand Up @@ -1041,6 +1041,7 @@ NPY_NO_EXPORT void
/**begin repeat
* #TYPE = BYTE, SHORT, INT, LONG, LONGLONG#
* #type = npy_byte, npy_short, npy_int, npy_long, npy_longlong#
* #c = ,,,l,ll#
*/

NPY_NO_EXPORT NPY_GCC_OPT_3 void
Expand Down Expand Up @@ -1132,11 +1133,26 @@ NPY_NO_EXPORT void
}
}

/**begin repeat1
* #kind = gcd, lcm#
**/
NPY_NO_EXPORT void
@TYPE@_@kind@(char **args, npy_intp *dimensions, npy_intp *steps, void *NPY_UNUSED(func))
{
BINARY_LOOP {
const @type@ in1 = *(@type@ *)ip1;
const @type@ in2 = *(@type@ *)ip2;
*((@type@ *)op1) = npy_@kind@@c@(in1, in2);
}
}
/**end repeat1**/

/**end repeat**/

/**begin repeat
* #TYPE = UBYTE, USHORT, UINT, ULONG, ULONGLONG#
* #type = npy_ubyte, npy_ushort, npy_uint, npy_ulong, npy_ulonglong#
* #c = u,u,u,ul,ull#
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The standard codes for these are B, H, I, L and Q. Shouldn't you use those instead?

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@eric-wieser eric-wieser Mar 23, 2017 •
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Possibly. Although I didn't see much point implementing B, H, and I separately, because arithmetic always promotes to int in C anyway, doesn't it?

Can you link me to a file that uses these standard codes? Oh, these are the struct.pack codes, right? I was trying to write this as though it were a free C function, like labs and llabs are to abs. I guess in hindsight they use a prefix though...

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A better example of what I was imitating might be strto{l,ll,ul,ull} from the C standard library.

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...these are the struct.pack codes, right?

They are also documented in numpy; see https://docs.scipy.org/doc/numpy/reference/arrays.scalars.html#built-in-scalar-types and numpy.typecodes['Integer'], numpy.typecodes['UnsignedInteger'], etc.

*/

NPY_NO_EXPORT void
Expand Down Expand Up @@ -1204,6 +1220,20 @@ NPY_NO_EXPORT void
}
}

/**begin repeat1
* #kind = gcd, lcm#
**/
NPY_NO_EXPORT void
@TYPE@_@kind@(char **args, npy_intp *dimensions, npy_intp *steps, void *NPY_UNUSED(func))
{
BINARY_LOOP {
const @type@ in1 = *(@type@ *)ip1;
const @type@ in2 = *(@type@ *)ip2;
*((@type@ *)op1) = npy_@kind@@c@(in1, in2);
}
}
/**end repeat1**/

/**end repeat**/

/*
Expand Down
6 changes: 6 additions & 0 deletions numpy/core/src/umath/loops.h.src
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Expand Up @@ -140,6 +140,12 @@ NPY_NO_EXPORT void
NPY_NO_EXPORT void
@S@@TYPE@_divmod(char **args, npy_intp *dimensions, npy_intp *steps, void *NPY_UNUSED(func));

NPY_NO_EXPORT void
@S@@TYPE@_gcd(char **args, npy_intp *dimensions, npy_intp *steps, void *NPY_UNUSED(func));

NPY_NO_EXPORT void
@S@@TYPE@_lcm(char **args, npy_intp *dimensions, npy_intp *steps, void *NPY_UNUSED(func));

/**end repeat1**/

/**end repeat**/
Expand Down
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