/* -*-c-*-
*
- * $Id: exp.h,v 1.1.4.1 2004/03/20 00:13:31 mdw Exp $
+ * $Id: exp.h,v 1.3 2004/03/22 02:19:10 mdw Exp $
*
* Generalized exponentiation
*
/*----- Revision history --------------------------------------------------*
*
* $Log: exp.h,v $
+ * Revision 1.3 2004/03/22 02:19:10 mdw
+ * Rationalise the sliding-window threshold. Drop guarantee that right
+ * arguments to EC @add@ are canonical, and fix up projective implementations
+ * to cope.
+ *
+ * Revision 1.2 2004/03/21 22:52:06 mdw
+ * Merge and close elliptic curve branch.
+ *
* Revision 1.1.4.1 2004/03/20 00:13:31 mdw
* Projective coordinates for prime curves
*
# define EXP_WINSZ 4 /* Predefine if you need to */
#endif
-/* --- These are determined from the window size --- */
+/* --- These are determined from the window size --- *
+ *
+ * Given a %$k$%-bit exponent, I expect to do %$k/2$% multiplies if I use the
+ * simple way. If I use an n-bit sliding window, then I do %$2^n$%
+ * multiplies up front, but I only do %$(2^n - 1)/2^n k/n$% multiplies for
+ * the exponentiation. This is a win when
+ *
+ * %$k \ge \frac{n 2^{n+1}}{n - 2}$%
+ */
#define EXP_TABSZ (1 << EXP_WINSZ)
-#define EXP_THRESH (((MPW_BITS / EXP_WINSZ) << 2) + 1)
+#define EXP_THRESH \
+ ((EXP_WINSZ * (2 << EXP_WINSZ))/((EXP_WINSZ - 2) * MPW_BITS))
/* --- Required operations --- *
*