Issue #19171: speed some cases of 3-argument long pow().

Reduce the base by the modulus when the base is larger than
the modulus.  This can unboundedly speed the "startup costs"
of doing modular exponentiation, particularly in cases where
the base is much larger than the modulus.  Original patch
by Armin Rigo, inspired by https://github.com/pyca/ed25519.

diff --git a/Objects/longobject.c b/Objects/longobject.c
index 985b1ec83c6dbcb7ccf90a625c2be716c82ce3ca..6383507a5c6ab39fb42442d6d9b89ed684eade63 100644 (file)
--- a/Objects/longobject.c
+++ b/Objects/longobject.c
@@ -3868,10 +3868,16 @@ long_pow(PyObject *v, PyObject *w, PyObject *x)
             goto Done;
         }
 
-        /* if base < 0:
-               base = base % modulus
-           Having the base positive just makes things easier. */
-        if (Py_SIZE(a) < 0) {
+        /* Reduce base by modulus in some cases:
+           1. If base < 0.  Forcing the base non-negative makes things easier.
+           2. If base is obviously larger than the modulus.  The "small
+              exponent" case later can multiply directly by base repeatedly,
+              while the "large exponent" case multiplies directly by base 31
+              times.  It can be unboundedly faster to multiply by
+              base % modulus instead.
+           We could _always_ do this reduction, but l_divmod() isn't cheap,
+           so we only do it when it buys something. */
+        if (Py_SIZE(a) < 0 || Py_SIZE(a) > Py_SIZE(c)) {
             if (l_divmod(a, c, NULL, &temp) < 0)
                 goto Error;
             Py_DECREF(a);