gh-94906: Support multiple steps in math.nextafter

Doc/library/math.rst

@@ -224,11 +224,11 @@ Number-theoretic and representation functions
  of *x* and are floats.
 
 
-.. function:: nextafter(x, y)
+.. function:: nextafter(x, y, steps=1)
 
- Return the next floating-point value after *x* towards *y*.
+ Return the floating-point value *steps* steps after *x* towards *y*.
 
- If *x* is equal to *y*, return *y*.
+ If *x* is equal to *y*, return *y*, unless *steps* is zero.
 
  Examples:
 
@@ -239,6 +239,9 @@ Number-theoretic and representation functions
 
  See also :func:`math.ulp`.
 
+ .. versionchanged:: 3.12
+ Added the *steps* argument.
+
  .. versionadded:: 3.9
 
 .. function:: perm(n, k=None)

Include/internal/pycore_global_strings.h

@@ -680,6 +680,7 @@ struct _Py_global_strings{
  STRUCT_FOR_ID(stdin)
  STRUCT_FOR_ID(stdout)
  STRUCT_FOR_ID(step)
+ STRUCT_FOR_ID(steps)
  STRUCT_FOR_ID(store_name)
  STRUCT_FOR_ID(strategy)
  STRUCT_FOR_ID(strftime)

Lib/test/test_math.py

@@ -2296,11 +2296,20 @@ def test_nextafter(self):
  float.fromhex('0x1.fffffffffffffp-1'))
  self.assertEqual(math.nextafter(1.0, INF),
  float.fromhex('0x1.0000000000001p+0'))
+ self.assertEqual(math.nextafter(1.0, -INF, steps=1),
+ float.fromhex('0x1.fffffffffffffp-1'))
+ self.assertEqual(math.nextafter(1.0, INF, steps=1),
+ float.fromhex('0x1.0000000000001p+0'))
+ self.assertEqual(math.nextafter(1.0, -INF, steps=3),
+ float.fromhex('0x1.ffffffffffffdp-1'))
+ self.assertEqual(math.nextafter(1.0, INF, steps=3),
+ float.fromhex('0x1.0000000000003p+0'))
 
  # x == y: y is returned
- self.assertEqual(math.nextafter(2.0, 2.0), 2.0)
- self.assertEqualSign(math.nextafter(-0.0, +0.0), +0.0)
- self.assertEqualSign(math.nextafter(+0.0, -0.0), -0.0)
+ for steps in range(1, 5):
+ self.assertEqual(math.nextafter(2.0, 2.0, steps=steps), 2.0)
+ self.assertEqualSign(math.nextafter(-0.0, +0.0, steps=steps), +0.0)
+ self.assertEqualSign(math.nextafter(+0.0, -0.0, steps=steps), -0.0)
 
  # around 0.0
  smallest_subnormal = sys.float_info.min * sys.float_info.epsilon
@@ -2325,6 +2334,11 @@ def test_nextafter(self):
  self.assertIsNaN(math.nextafter(1.0, NAN))
  self.assertIsNaN(math.nextafter(NAN, NAN))
 
+ self.assertEqual(1.0, math.nextafter(1.0, INF, steps=0))
+ with self.assertRaises(ValueError):
+ math.nextafter(1.0, INF, steps=-1)
+
+
  @requires_IEEE_754
  def test_ulp(self):
  self.assertEqual(math.ulp(1.0), sys.float_info.epsilon)

Lib/test/test_math_property.py

@@ -0,0 +1,41 @@
+import functools
+import unittest
+from math import isnan, nextafter
+from test.support import requires_IEEE_754
+from test.support.hypothesis_helper import hypothesis
+
+floats = hypothesis.strategies.floats
+integers = hypothesis.strategies.integers
+
+
+def assert_equal_float(x, y):
+ assert isnan(x) and isnan(y) or x == y
+
+
+def via_reduce(x, y, steps):
+ return functools.reduce(nextafter, [y] * steps, x)
+
+
+class NextafterTests(unittest.TestCase):
+ @requires_IEEE_754
+ @hypothesis.given(
+ x=floats(),
+ y=floats(),
+ steps=integers(min_value=0, max_value=2**16))
+ def test_count(self, x, y, steps):
+ assert_equal_float(via_reduce(x, y, steps),
+ nextafter(x, y, steps=steps))
+
+ @requires_IEEE_754
+ @hypothesis.given(
+ x=floats(),
+ y=floats(),
+ a=integers(min_value=0),
+ b=integers(min_value=0))
+ def test_addition_commutes(self, x, y, a, b):
+ first = nextafter(x, y, steps=a)
+ second = nextafter(first, y, steps=b)
+ combined = nextafter(x, y, steps=a+b)
+ hypothesis.note(f"{first} ->{second} =={combined}")
+
+ assert_equal_float(second, combined)

Misc/NEWS.d/next/Library/2022-07-16-17-15-29.gh-issue-94906.C4G8DG.rst

@@ -0,0 +1 @@
+Support multiple steps in :func:`math.nextafter`. Patch by Shantanu Jain and Matthias Gorgens.

Modules/mathmodule.c

@@ -3864,13 +3864,20 @@ math.nextafter
  x: double
  y: double
  /
+ *
+ steps: object = None
+
+Return the floating-point value the given number of steps after x towards y.
+
+If steps is not specified or is None, it defaults to 1.
 
-Return the next floating-point value after x towards y.
+Raises a TypeError, if x or y is not a double, or if steps is not an integer.
+Raises ValueError if steps is negative.
 [clinic start generated code]*/
 
 static PyObject *
-math_nextafter_impl(PyObject *module, double x, double y)
-/*[clinic end generated code: output=750c8266c1c540ce input=02b2d50cd1d9f9b6]*/
+math_nextafter_impl(PyObject *module, double x, double y, PyObject *steps)
+/*[clinic end generated code: output=cc6511f02afc099e input=7f2a5842112af2b4]*/
 {
 #if defined(_AIX)
  if (x == y){
@@ -3885,7 +3892,101 @@ math_nextafter_impl(PyObject *module, double x, double y)
  return PyFloat_FromDouble(y);
  }
 #endif
- return PyFloat_FromDouble(nextafter(x, y));
+ if (steps == Py_None){
+ // fast path: we default to one step.
+ return PyFloat_FromDouble(nextafter(x, y));
+ }
+ steps = PyNumber_Index(steps);
+ if (steps == NULL){
+ return NULL;
+ }
+ assert(PyLong_CheckExact(steps));
+ if (_PyLong_IsNegative((PyLongObject *)steps)){
+ PyErr_SetString(PyExc_ValueError,
+ "steps must be a non-negative integer");
+ Py_DECREF(steps);
+ return NULL;
+ }
+
+ unsigned long long usteps_ull = PyLong_AsUnsignedLongLong(steps);
+ // Conveniently, uint64_t and double have the same number of bits
+ // on all the platforms we care about.
+ // So if an overflow occurs, we can just use UINT64_MAX.
+ Py_DECREF(steps);
+ if (usteps_ull >= UINT64_MAX){
+ // This branch includes the case where an error occurred, since
+ // (unsigned long long)(-1) = ULLONG_MAX >= UINT64_MAX. Note that
+ // usteps_ull can be strictly larger than UINT64_MAX on a machine
+ // where unsigned long long has width > 64 bits.
+ if (PyErr_Occurred()){
+ if (PyErr_ExceptionMatches(PyExc_OverflowError)){
+ PyErr_Clear();
+ }
+ else{
+ return NULL;
+ }
+ }
+ usteps_ull = UINT64_MAX;
+ }
+ assert(usteps_ull <= UINT64_MAX);
+ uint64_t usteps = (uint64_t)usteps_ull;
+
+ if (usteps == 0){
+ return PyFloat_FromDouble(x);
+ }
+ if (Py_IS_NAN(x)){
+ return PyFloat_FromDouble(x);
+ }
+ if (Py_IS_NAN(y)){
+ return PyFloat_FromDouble(y);
+ }
+
+ // We assume that double and uint64_t have the same endianness.
+ // This is not guaranteed by the C-standard, but it is true for
+ // all platforms we care about. (The most likely form of violation
+ // would be a "mixed-endian" double.)
+ union pun{double f; uint64_t i};
+ union pun ux ={x}, uy ={y};
+ if (ux.i == uy.i){
+ return PyFloat_FromDouble(x);
+ }
+
+ const uint64_t sign_bit = 1ULL<<63;
+
+ uint64_t ax = ux.i & ~sign_bit;
+ uint64_t ay = uy.i & ~sign_bit;
+
+ // opposite signs
+ if (((ux.i ^ uy.i) & sign_bit)){
+ // NOTE: ax + ay can never overflow, because their most significant bit
+ // ain't set.
+ if (ax + ay <= usteps){
+ return PyFloat_FromDouble(uy.f);
+ // This comparison has to use <, because <= would get +0.0 vs -0.0
+ // wrong.
+ } else if (ax < usteps){
+ union pun result ={.i = (uy.i & sign_bit) | (usteps - ax)};
+ return PyFloat_FromDouble(result.f);
+ } else{
+ ux.i -= usteps;
+ return PyFloat_FromDouble(ux.f);
+ }
+ // same sign
+ } else if (ax > ay){
+ if (ax - ay >= usteps){
+ ux.i -= usteps;
+ return PyFloat_FromDouble(ux.f);
+ } else{
+ return PyFloat_FromDouble(uy.f);
+ }
+ } else{
+ if (ay - ax >= usteps){
+ ux.i += usteps;
+ return PyFloat_FromDouble(ux.f);
+ } else{
+ return PyFloat_FromDouble(uy.f);
+ }
+ }
 }