gh-140443: Use fma in loghelper to improve accuracy of log for very large integers

Misc/ACKS

@@ -1921,6 +1921,7 @@ Tim Tisdall
 Jason Tishler
 Christian Tismer
 Jim Tittsler
+Abhishek Tiwari
 Frank J. Tobin
 James Tocknell
 Bennett Todd

Misc/NEWS.d/next/Core_and_Builtins/2025-10-22-23-26-37.gh-issue-140443.wT5i1A.rst

@@ -0,0 +1,5 @@
+The logarithm functions (such as :func:`math.log10` and :func:`math.log`) may now produce
+slightly different results for extremely large integers that cannot be
+converted to floats without overflow. These results are generally more
+accurate, with reduced worst-case error and a tighter overall error
+distribution.

Modules/mathmodule.c

@@ -2309,7 +2309,7 @@ loghelper(PyObject* arg, double (*func)(double))
             assert(e >= 0);
             assert(!PyErr_Occurred());
             /* Value is ~= x * 2**e, so the log ~= log(x) + log(2) * e. */
-            result = func(x) + func(2.0) * e;
+            result = fma(func(2.0), (double)e, func(x));
         }
         else
             /* Successfully converted x to a double. */