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>

Modules/mathmodule.c

@@ -3864,13 +3864,20 @@ math.nextafter
     x: double
     y: double
     /
+    *
+    steps: object = None
 
-Return the next floating-point value after x towards y.
+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.
+
+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);
+        }
+    }
 }