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Commit6e39fa1

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gh-94906: Support multiple steps in math.nextafter (#103881)
This PR updates `math.nextafter` to add a new `steps` argument. The behaviour is as though `math.nextafter` had been called `steps` times in succession.---------Co-authored-by: Mark Dickinson <mdickinson@enthought.com>
1 parentc3f43bf commit6e39fa1

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10 files changed

+223
-18
lines changed

10 files changed

+223
-18
lines changed

‎Doc/library/math.rst‎

Lines changed: 6 additions & 3 deletions
Original file line numberDiff line numberDiff line change
@@ -224,11 +224,11 @@ Number-theoretic and representation functions
224224
of *x* and are floats.
225225

226226

227-
..function::nextafter(x, y)
227+
..function::nextafter(x, y, steps=1)
228228

229-
Return thenextfloating-point value after *x* towards *y*.
229+
Return the floating-point value *steps* steps after *x* towards *y*.
230230

231-
If *x* is equal to *y*, return *y*.
231+
If *x* is equal to *y*, return *y*, unless *steps* is zero.
232232

233233
Examples:
234234

@@ -239,6 +239,9 @@ Number-theoretic and representation functions
239239

240240
See also:func:`math.ulp`.
241241

242+
..versionchanged::3.12
243+
Added the *steps* argument.
244+
242245
..versionadded::3.9
243246

244247
..function::perm(n, k=None)

‎Include/internal/pycore_global_objects_fini_generated.h‎

Lines changed: 1 addition & 0 deletions
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‎Include/internal/pycore_global_strings.h‎

Lines changed: 1 addition & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -681,6 +681,7 @@ struct _Py_global_strings {
681681
STRUCT_FOR_ID(stdin)
682682
STRUCT_FOR_ID(stdout)
683683
STRUCT_FOR_ID(step)
684+
STRUCT_FOR_ID(steps)
684685
STRUCT_FOR_ID(store_name)
685686
STRUCT_FOR_ID(strategy)
686687
STRUCT_FOR_ID(strftime)

‎Include/internal/pycore_runtime_init_generated.h‎

Lines changed: 1 addition & 0 deletions
Some generated files are not rendered by default. Learn more aboutcustomizing how changed files appear on GitHub.

‎Include/internal/pycore_unicodeobject_generated.h‎

Lines changed: 3 additions & 0 deletions
Some generated files are not rendered by default. Learn more aboutcustomizing how changed files appear on GitHub.

‎Lib/test/test_math.py‎

Lines changed: 17 additions & 3 deletions
Original file line numberDiff line numberDiff line change
@@ -2296,11 +2296,20 @@ def test_nextafter(self):
22962296
float.fromhex('0x1.fffffffffffffp-1'))
22972297
self.assertEqual(math.nextafter(1.0,INF),
22982298
float.fromhex('0x1.0000000000001p+0'))
2299+
self.assertEqual(math.nextafter(1.0,-INF,steps=1),
2300+
float.fromhex('0x1.fffffffffffffp-1'))
2301+
self.assertEqual(math.nextafter(1.0,INF,steps=1),
2302+
float.fromhex('0x1.0000000000001p+0'))
2303+
self.assertEqual(math.nextafter(1.0,-INF,steps=3),
2304+
float.fromhex('0x1.ffffffffffffdp-1'))
2305+
self.assertEqual(math.nextafter(1.0,INF,steps=3),
2306+
float.fromhex('0x1.0000000000003p+0'))
22992307

23002308
# x == y: y is returned
2301-
self.assertEqual(math.nextafter(2.0,2.0),2.0)
2302-
self.assertEqualSign(math.nextafter(-0.0,+0.0),+0.0)
2303-
self.assertEqualSign(math.nextafter(+0.0,-0.0),-0.0)
2309+
forstepsinrange(1,5):
2310+
self.assertEqual(math.nextafter(2.0,2.0,steps=steps),2.0)
2311+
self.assertEqualSign(math.nextafter(-0.0,+0.0,steps=steps),+0.0)
2312+
self.assertEqualSign(math.nextafter(+0.0,-0.0,steps=steps),-0.0)
23042313

23052314
# around 0.0
23062315
smallest_subnormal=sys.float_info.min*sys.float_info.epsilon
@@ -2325,6 +2334,11 @@ def test_nextafter(self):
23252334
self.assertIsNaN(math.nextafter(1.0,NAN))
23262335
self.assertIsNaN(math.nextafter(NAN,NAN))
23272336

2337+
self.assertEqual(1.0,math.nextafter(1.0,INF,steps=0))
2338+
withself.assertRaises(ValueError):
2339+
math.nextafter(1.0,INF,steps=-1)
2340+
2341+
23282342
@requires_IEEE_754
23292343
deftest_ulp(self):
23302344
self.assertEqual(math.ulp(1.0),sys.float_info.epsilon)

‎Lib/test/test_math_property.py‎

Lines changed: 41 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,41 @@
1+
importfunctools
2+
importunittest
3+
frommathimportisnan,nextafter
4+
fromtest.supportimportrequires_IEEE_754
5+
fromtest.support.hypothesis_helperimporthypothesis
6+
7+
floats=hypothesis.strategies.floats
8+
integers=hypothesis.strategies.integers
9+
10+
11+
defassert_equal_float(x,y):
12+
assertisnan(x)andisnan(y)orx==y
13+
14+
15+
defvia_reduce(x,y,steps):
16+
returnfunctools.reduce(nextafter, [y]*steps,x)
17+
18+
19+
classNextafterTests(unittest.TestCase):
20+
@requires_IEEE_754
21+
@hypothesis.given(
22+
x=floats(),
23+
y=floats(),
24+
steps=integers(min_value=0,max_value=2**16))
25+
deftest_count(self,x,y,steps):
26+
assert_equal_float(via_reduce(x,y,steps),
27+
nextafter(x,y,steps=steps))
28+
29+
@requires_IEEE_754
30+
@hypothesis.given(
31+
x=floats(),
32+
y=floats(),
33+
a=integers(min_value=0),
34+
b=integers(min_value=0))
35+
deftest_addition_commutes(self,x,y,a,b):
36+
first=nextafter(x,y,steps=a)
37+
second=nextafter(first,y,steps=b)
38+
combined=nextafter(x,y,steps=a+b)
39+
hypothesis.note(f"{first} ->{second} =={combined}")
40+
41+
assert_equal_float(second,combined)
Lines changed: 1 addition & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1 @@
1+
Support multiple steps in:func:`math.nextafter`. Patch by Shantanu Jain and Matthias Gorgens.

‎Modules/clinic/mathmodule.c.h‎

Lines changed: 47 additions & 8 deletions
Some generated files are not rendered by default. Learn more aboutcustomizing how changed files appear on GitHub.

‎Modules/mathmodule.c‎

Lines changed: 105 additions & 4 deletions
Original file line numberDiff line numberDiff line change
@@ -3864,13 +3864,20 @@ math.nextafter
38643864
x: double
38653865
y: double
38663866
/
3867+
*
3868+
steps: object = None
3869+
3870+
Return the floating-point value the given number of steps after x towards y.
3871+
3872+
If steps is not specified or is None, it defaults to 1.
38673873
3868-
Return the next floating-point value after x towards y.
3874+
Raises a TypeError, if x or y is not a double, or if steps is not an integer.
3875+
Raises ValueError if steps is negative.
38693876
[clinic start generated code]*/
38703877

38713878
staticPyObject*
3872-
math_nextafter_impl(PyObject*module,doublex,doubley)
3873-
/*[clinic end generated code: output=750c8266c1c540ce input=02b2d50cd1d9f9b6]*/
3879+
math_nextafter_impl(PyObject*module,doublex,doubley,PyObject*steps)
3880+
/*[clinic end generated code: output=cc6511f02afc099e input=7f2a5842112af2b4]*/
38743881
{
38753882
#if defined(_AIX)
38763883
if (x==y) {
@@ -3885,7 +3892,101 @@ math_nextafter_impl(PyObject *module, double x, double y)
38853892
returnPyFloat_FromDouble(y);
38863893
}
38873894
#endif
3888-
returnPyFloat_FromDouble(nextafter(x,y));
3895+
if (steps==Py_None) {
3896+
// fast path: we default to one step.
3897+
returnPyFloat_FromDouble(nextafter(x,y));
3898+
}
3899+
steps=PyNumber_Index(steps);
3900+
if (steps==NULL) {
3901+
returnNULL;
3902+
}
3903+
assert(PyLong_CheckExact(steps));
3904+
if (_PyLong_IsNegative((PyLongObject*)steps)) {
3905+
PyErr_SetString(PyExc_ValueError,
3906+
"steps must be a non-negative integer");
3907+
Py_DECREF(steps);
3908+
returnNULL;
3909+
}
3910+
3911+
unsigned long longusteps_ull=PyLong_AsUnsignedLongLong(steps);
3912+
// Conveniently, uint64_t and double have the same number of bits
3913+
// on all the platforms we care about.
3914+
// So if an overflow occurs, we can just use UINT64_MAX.
3915+
Py_DECREF(steps);
3916+
if (usteps_ull >=UINT64_MAX) {
3917+
// This branch includes the case where an error occurred, since
3918+
// (unsigned long long)(-1) = ULLONG_MAX >= UINT64_MAX. Note that
3919+
// usteps_ull can be strictly larger than UINT64_MAX on a machine
3920+
// where unsigned long long has width > 64 bits.
3921+
if (PyErr_Occurred()) {
3922+
if (PyErr_ExceptionMatches(PyExc_OverflowError)) {
3923+
PyErr_Clear();
3924+
}
3925+
else {
3926+
returnNULL;
3927+
}
3928+
}
3929+
usteps_ull=UINT64_MAX;
3930+
}
3931+
assert(usteps_ull <=UINT64_MAX);
3932+
uint64_tusteps= (uint64_t)usteps_ull;
3933+
3934+
if (usteps==0) {
3935+
returnPyFloat_FromDouble(x);
3936+
}
3937+
if (Py_IS_NAN(x)) {
3938+
returnPyFloat_FromDouble(x);
3939+
}
3940+
if (Py_IS_NAN(y)) {
3941+
returnPyFloat_FromDouble(y);
3942+
}
3943+
3944+
// We assume that double and uint64_t have the same endianness.
3945+
// This is not guaranteed by the C-standard, but it is true for
3946+
// all platforms we care about. (The most likely form of violation
3947+
// would be a "mixed-endian" double.)
3948+
unionpun {doublef;uint64_ti;};
3949+
unionpunux= {x},uy= {y};
3950+
if (ux.i==uy.i) {
3951+
returnPyFloat_FromDouble(x);
3952+
}
3953+
3954+
constuint64_tsign_bit=1ULL<<63;
3955+
3956+
uint64_tax=ux.i& ~sign_bit;
3957+
uint64_tay=uy.i& ~sign_bit;
3958+
3959+
// opposite signs
3960+
if (((ux.i ^uy.i)&sign_bit)) {
3961+
// NOTE: ax + ay can never overflow, because their most significant bit
3962+
// ain't set.
3963+
if (ax+ay <=usteps) {
3964+
returnPyFloat_FromDouble(uy.f);
3965+
// This comparison has to use <, because <= would get +0.0 vs -0.0
3966+
// wrong.
3967+
}elseif (ax<usteps) {
3968+
unionpunresult= {.i= (uy.i&sign_bit) | (usteps-ax)};
3969+
returnPyFloat_FromDouble(result.f);
3970+
}else {
3971+
ux.i-=usteps;
3972+
returnPyFloat_FromDouble(ux.f);
3973+
}
3974+
// same sign
3975+
}elseif (ax>ay) {
3976+
if (ax-ay >=usteps) {
3977+
ux.i-=usteps;
3978+
returnPyFloat_FromDouble(ux.f);
3979+
}else {
3980+
returnPyFloat_FromDouble(uy.f);
3981+
}
3982+
}else {
3983+
if (ay-ax >=usteps) {
3984+
ux.i+=usteps;
3985+
returnPyFloat_FromDouble(ux.f);
3986+
}else {
3987+
returnPyFloat_FromDouble(uy.f);
3988+
}
3989+
}
38893990
}
38903991

38913992

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