source: vbox/trunk/src/libs/liblzma-5.8.1/check/crc_clmul_consts_gen.c@ 109307

// SPDX-License-Identifier: 0BSD

///////////////////////////////////////////////////////////////////////////////
//
/// \file       crc_clmul_consts_gen.c
/// \brief      Generate constants for CLMUL CRC code
///
/// Compiling: gcc -std=c99 -o crc_clmul_consts_gen crc_clmul_consts_gen.c
///
/// This is for CRCs that use reversed bit order (bit reflection).
/// The same CLMUL CRC code can be used with CRC64 and smaller ones like
/// CRC32 apart from one special case: CRC64 needs an extra step in the
/// Barrett reduction to handle the 65th bit; the smaller ones don't.
/// Otherwise it's enough to just change the polynomial and the derived
/// constants and use the same code.
///
/// See the Intel white paper "Fast CRC Computation for Generic Polynomials
/// Using PCLMULQDQ Instruction" from 2009.
//
//  Author:     Lasse Collin
//
///////////////////////////////////////////////////////////////////////////////

#include <inttypes.h>
#include <stdio.h>


/// CRC32 (Ethernet) polynomial in reversed representation
static const uint64_t p32 = 0xedb88320;

// CRC64 (ECMA-182) polynomial in reversed representation
static const uint64_t p64 = 0xc96c5795d7870f42;


/// Calculates floor(x^128 / p) where p is a CRC64 polynomial in
/// reversed representation. The result is in reversed representation too.
static uint64_t
calc_cldiv(uint64_t p)
{
        // Quotient
        uint64_t q = 0;

        // Align the x^64 term with the x^128 (the implied high bits of the
        // divisor and the dividend) and do the first step of polynomial long
        // division, calculating the first remainder. The variable q remains
        // zero because the highest bit of the quotient is an implied bit 1
        // (we kind of set q = 1 << -1).
        uint64_t r = p;

        // Then process the remaining 64 terms. Note that r has no implied
        // high bit, only q and p do. (And remember that a high bit in the
        // polynomial is stored at a low bit in the variable due to the
        // reversed bit order.)
        for (unsigned i = 0; i < 64; ++i) {
                q |= (r & 1) << i;
                r = (r >> 1) ^ (r & 1 ? p : 0);
        }

        return q;
}


/// Calculate the remainder of carryless division:
///
///     x^(bits + n - 1) % p, where n=64 (for CRC64)
///
/// p must be in reversed representation which omits the bit of
/// the highest term of the polynomial. Instead, it is an implied bit
/// at kind of like "1 << -1" position, as if it had just been shifted out.
///
/// The return value is in the reversed bit order. (There are no implied bits.)
static uint64_t
calc_clrem(uint64_t p, unsigned bits)
{
        // Do the first step of polynomial long division.
        uint64_t r = p;

        // Then process the remaining terms. Start with i = 1 instead of i = 0
        // to account for the -1 in x^(bits + n - 1). This -1 is convenient
        // with the reversed bit order. See the "Bit-Reflection" section in
        // the Intel white paper.
        for (unsigned i = 1; i < bits; ++i)
                r = (r >> 1) ^ (r & 1 ? p : 0);

        return r;
}


extern int
main(void)
{
        puts("// CRC64");

        // The order of the two 64-bit constants in a vector don't matter.
        // It feels logical to put them in this order as it matches the
        // order in which the input bytes are read.
        printf("const __m128i fold512 = _mm_set_epi64x("
                "0x%016" PRIx64 ", 0x%016" PRIx64 ");\n",
                calc_clrem(p64, 4 * 128 - 64),
                calc_clrem(p64, 4 * 128));

        printf("const __m128i fold128 = _mm_set_epi64x("
                "0x%016" PRIx64 ", 0x%016" PRIx64 ");\n",
                calc_clrem(p64, 128 - 64),
                calc_clrem(p64, 128));

        // When we multiply by mu, we care about the high bits of the result
        // (in reversed bit order!). It doesn't matter that the low bit gets
        // shifted out because the affected output bits will be ignored.
        // Below we add the implied high bit with "| 1" after the shifting
        // so that the high bits of the multiplication will be correct.
        //
        // p64 is shifted left by one so that the final multiplication
        // in Barrett reduction won't be misaligned by one bit. We could
        // use "(p64 << 1) | 1" instead of "p64 << 1" too but it makes
        // no difference as that bit won't affect the relevant output bits
        // (we only care about the lowest 64 bits of the result, that is,
        // lowest in the reversed bit order).
        //
        // NOTE: The 65rd bit of p64 gets shifted out. It needs to be
        // compensated with 64-bit shift and xor in the CRC64 code.
        printf("const __m128i mu_p = _mm_set_epi64x("
                "0x%016" PRIx64 ", 0x%016" PRIx64 ");\n",
                (calc_cldiv(p64) << 1) | 1,
                p64 << 1);

        puts("");

        puts("// CRC32");

        printf("const __m128i fold512 = _mm_set_epi64x("
                "0x%08" PRIx64 ", 0x%08" PRIx64 ");\n",
                calc_clrem(p32, 4 * 128 - 64),
                calc_clrem(p32, 4 * 128));

        printf("const __m128i fold128 = _mm_set_epi64x("
                "0x%08" PRIx64 ", 0x%08" PRIx64 ");\n",
                calc_clrem(p32, 128 - 64),
                calc_clrem(p32, 128));

        // CRC32 calculation is done by modulus scaling it to a CRC64.
        // Since the CRC is in reversed representation, only the mu
        // constant changes with the modulus scaling. This method avoids
        // one additional constant and one additional clmul in the final
        // reduction steps, making the code both simpler and faster.
        //
        // p32 is shifted left by one so that the final multiplication
        // in Barrett reduction won't be misaligned by one bit. We could
        // use "(p32 << 1) | 1" instead of "p32 << 1" too but it makes
        // no difference as that bit won't affect the relevant output bits.
        //
        // NOTE: The 33-bit value fits in 64 bits so, unlike with CRC64,
        // there is no need to compensate for any missing bits in the code.
        printf("const __m128i mu_p = _mm_set_epi64x("
                "0x%016" PRIx64 ", 0x%" PRIx64 ");\n",
                (calc_cldiv(p32) << 1) | 1,
                p32 << 1);

        return 0;
}