#!/usr/bin/env perl
# ====================================================================
# Written by Andy Polyakov <appro@openssl.org> for the OpenSSL
# project. The module is, however, dual licensed under OpenSSL and
# CRYPTOGAMS licenses depending on where you obtain it. For further
# details see http://www.openssl.org/~appro/cryptogams/.
# ====================================================================
# March 2015
#
# "Teaser" Montgomery multiplication module for ARMv8. Needs more
# work. While it does improve RSA sign performance by 20-30% (less for
# longer keys) on most processors, for some reason RSA2048 is not
# faster and RSA4096 goes 15-20% slower on Cortex-A57. Multiplication
# instruction issue rate is limited on processor in question, meaning
# that dedicated squaring procedure is a must. Well, actually all
# contemporary AArch64 processors seem to have limited multiplication
# issue rate, i.e. they can't issue multiplication every cycle, which
# explains moderate improvement coefficients in comparison to
# compiler-generated code. Recall that compiler is instructed to use
# umulh and therefore uses same amount of multiplication instructions
# to do the job. Assembly's edge is to minimize number of "collateral"
# instructions and of course instruction scheduling.
#
# April 2015
#
# Squaring procedure that handles lengths divisible by 8 improves
# RSA/DSA performance by 25-40-60% depending on processor and key
# length. Overall improvement coefficients are always positive in
# comparison to compiler-generated code. On Cortex-A57 improv