From 61e9ffa191aa3a3270c5efcd3f1d05810419b63f Mon Sep 17 00:00:00 2001 From: Tim Peters Date: Sat, 5 Oct 2013 16:53:52 -0500 Subject: [PATCH] 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. (grafted from f34c59494420765b013136ca93f63b716d9f1d30) --- Objects/longobject.c | 14 ++++++++++---- 1 file changed, 10 insertions(+), 4 deletions(-) diff --git a/Objects/longobject.c b/Objects/longobject.c index fb740dc4d6..405be2e045 100644 --- a/Objects/longobject.c +++ b/Objects/longobject.c @@ -3474,10 +3474,16 @@ 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); -- 2.50.1