#! /usr/bin/env perl
# Copyright 2010-2016 The OpenSSL Project Authors. All Rights Reserved.
#
# Licensed under the Apache License 2.0 (the "License"). You may not use
# this file except in compliance with the License. You can obtain a copy
# in the file LICENSE in the source distribution or at
# https://www.openssl.org/source/license.html
#
# ====================================================================
# 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, May, June 2010
#
# The module implements "4-bit" GCM GHASH function and underlying
# single multiplication operation in GF(2^128). "4-bit" means that it
# uses 256 bytes per-key table [+64/128 bytes fixed table]. It has two
# code paths: vanilla x86 and vanilla SSE. Former will be executed on
# 486 and Pentium, latter on all others. SSE GHASH features so called
# "528B" variant of "4-bit" method utilizing additional 256+16 bytes
# of per-key storage [+512 bytes shared table]. Performance results
# are for streamed GHASH subroutine and are expressed in cycles per
# processed byte, less is better:
#
# gcc 2.95.3(*) SSE assembler x86 assembler
#
# Pentium 105/111(**) - 50
# PIII 68 /75 12.2 24
# P4 125/125 17.8 84(***)
# Opteron 66 /70 10.1 30
# Core2 54 /67 8.4 18
# Atom 105/105 16.8 53
# VIA Nano 69 /71 13.0 27
#
# (*) gcc 3.4.x was observed to generate few percent slower code,
# which is one of reasons why 2.95.3 results were chosen,
# another reason is lack of 3.4.x results for older CPUs;
# comparison with SSE results is not completely fair, because C
# results are for vanilla "256B" implementation, while
# assembler results are for "528B";-)
# (**) second number is result for code compiled with -fPIC flag,
# which is actually more relevant, because assembler code is
# position-independent;
# (***) see comment in non-MMX routine for further details;
#
# To summarize, it's >2-5 times faster than gcc-generated code. To
# anchor it to something else SHA1 assembler processes one byte in
# ~7 cycles on contemporary x86 cores. As for choice of MMX/SSE
# in particular, see comment at the end of the file...
# May 2010
#
# Add PCLMULQDQ version performing at 2.10 cycles per processed byte.
# The question is how close is it to theoretical limit? The pclmulqdq
# instruction latency appears to be 14 cycles and there can't be more
# than 2 of them executing at any given time. This means that single
# Karatsuba multiplication would take 28 cycles *plus* few cycles for
# pre- and post-processing. Then multiplication has to be followed by
# modulo-reduction. Given that aggregated reduction method [see
# "Carry-less Multiplication and Its Usage for Computing the GCM Mode"
# white paper by Intel] allows you to perform reduction only once in
# a while we can assume that asymptotic performance can be estimated
# as (28+Tmod/Naggr)/16, where Tmod is time to perform reduction
# and Naggr is the aggregation factor.
#
# Before we proceed to this implementation let's have closer look at
# the best-performing code suggested by Intel in their white paper.
# By tracing inter-register dependencies Tmod is estimated as ~19
# cycles and Naggr chosen by Intel is 4, resulting in 2.05 cycles per
# processed byte. As implied, this is quite optimistic estimate,
# because it does not account for Karatsuba pre- and post-processing,
# which for a single multiplication is ~5 cycles. Unfortunately Intel
# does not provide performance data for GHASH alone. But benchmarking
# AES_GCM_encrypt ripped out of Fig. 15 of the white paper with aadt
# alone resulted in 2.46 cycles per byte of out 16KB buffer. Note that
# the result accounts even for pre-computing of degrees of the hash
# key H, but its portion is negligible at 16K