gh-132876: workaround broken ldexp() on Windows 10

Misc/NEWS.d/next/Library/2025-04-29-11-48-46.gh-issue-132876.lyTQGZ.rst

@@ -0,0 +1,4 @@
+`ldexp()` on Windows doesn't round subnormal results before Windows 11,
+but should.  Python's :func:`math.ldexp` wrapper now does round them, so
+results may change slightly, in rare cases of very small results, on
+Windows versions before 11.

Modules/mathmodule.c

@@ -2163,6 +2163,27 @@ math_ldexp_impl(PyObject *module, double x, PyObject *i)
     } else {
         errno = 0;
         r = ldexp(x, (int)exp);
+#ifdef _MSC_VER
+        if (DBL_MIN > r && r > -DBL_MIN) {
+            /* Denormal (or zero) results can be incorrectly rounded here (rather,
+               truncated).  Fixed in newer versions of the C runtime, included
+               with Windows 11. */
+            int original_exp;
+            frexp(x, &original_exp);
+            if (original_exp > DBL_MIN_EXP) {
+                /* Shift down to the smallest normal binade.  No bits lost. */
+                int shift = DBL_MIN_EXP - original_exp;
+                x = ldexp(x, shift);
+                exp -= shift;
+            }
+            /* Multiplying by 2**exp finishes the job, and the HW will round as
+               appropriate.  Note: if exp < -DBL_MANT_DIG, all of x is shifted
+               to be < 0.5ULP of smallest denorm, so should be thrown away.  If
+               exp is so very negative that ldexp underflows to 0, that's fine;
+               no need to check in advance. */
+            r = x*ldexp(1.0, (int)exp);
+        }
+#endif
         if (isinf(r))
             errno = ERANGE;
     }