minio/pkg/storage/erasure/ec-base.c

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#include <limits.h>
#include <stdint.h>
#include <string.h>             // for memset
#include "ec-code.h"
#include "ec-base.h"            // for GF tables
#include "ec-ctypes.h"

uint8_t gf_mul(uint8_t a, uint8_t b)
{
#ifndef GF_LARGE_TABLES
        int i;

        if ((a == 0) || (b == 0))
                return 0;

        return gff_base[(i = gflog_base[a] + gflog_base[b]) > 254 ? i - 255 : i];
#else
        return gf_mul_table_base[b * 256 + a];
#endif
}

uint8_t gf_inv(uint8_t a)
{
#ifndef GF_LARGE_TABLES
        if (a == 0)
                return 0;

        return gff_base[255 - gflog_base[a]];
#else
        return gf_inv_table_base[a];
#endif
}

void gf_gen_rs_matrix(uint8_t *a, int m, int k)
{
        int i, j;
        uint8_t p, gen = 1;

        memset(a, 0, k * m);
        for (i = 0; i < k; i++)
                a[k * i + i] = 1;

        for (i = k; i < m; i++) {
                p = 1;
                for (j = 0; j < k; j++) {
                        a[k * i + j] = p;
                        p = gf_mul(p, gen);
                }
                gen = gf_mul(gen, 2);
        }
}

void gf_gen_cauchy1_matrix(uint8_t *a, int m, int k)
{
        int i, j;
        uint8_t *p;

        // Identity matrix in high position
        memset(a, 0, k * m);
        for (i = 0; i < k; i++)
                a[k * i + i] = 1;

        // For the rest choose 1/(i + j) | i != j
        p = &a[k * k];
        for (i = k; i < m; i++)
                for (j = 0; j < k; j++)
                        *p++ = gf_inv(i ^ j);

}

int gf_invert_matrix(uint8_t *in_mat, uint8_t *out_mat, const int n)
{
        int i, j, k;
        uint8_t temp;

        // Set out_mat[] to the identity matrix
        for (i = 0; i < n * n; i++)     // memset(out_mat, 0, n*n)
                out_mat[i] = 0;

        for (i = 0; i < n; i++)
                out_mat[i * n + i] = 1;

        // Inverse
        for (i = 0; i < n; i++) {
                // Check for 0 in pivot element
                if (in_mat[i * n + i] == 0) {
                        // Find a row with non-zero in current column and swap
                        for (j = i + 1; j < n; j++)
                                if (in_mat[j * n + i])
                                        break;

                        if (j == n)     // Couldn't find means it's singular
                                return -1;

                        for (k = 0; k < n; k++) {       // Swap rows i,j
                                temp = in_mat[i * n + k];
                                in_mat[i * n + k] = in_mat[j * n + k];
                                in_mat[j * n + k] = temp;

                                temp = out_mat[i * n + k];
                                out_mat[i * n + k] = out_mat[j * n + k];
                                out_mat[j * n + k] = temp;
                        }
                }

                temp = gf_inv(in_mat[i * n + i]);       // 1/pivot
                for (j = 0; j < n; j++) {       // Scale row i by 1/pivot
                        in_mat[i * n + j] = gf_mul(in_mat[i * n + j], temp);
                        out_mat[i * n + j] = gf_mul(out_mat[i * n + j], temp);
                }

                for (j = 0; j < n; j++) {
                        if (j == i)
                                continue;

                        temp = in_mat[j * n + i];
                        for (k = 0; k < n; k++) {
                                out_mat[j * n + k] ^= gf_mul(temp, out_mat[i * n + k]);
                                in_mat[j * n + k] ^= gf_mul(temp, in_mat[i * n + k]);
                        }
                }
        }
        return 0;
}

// Calculates const table gftbl in GF(2^8) from single input A
// gftbl(A) = {A{00}, A{01}, A{02}, ... , A{0f} }, {A{00}, A{10}, A{20}, ... , A{f0} }

void gf_vect_mul_init(uint8_t c, uint8_t *tbl)
{
        uint8_t c2 = (c << 1) ^ ((c & 0x80) ? 0x1d : 0);  //Mult by GF{2}
        uint8_t c4 = (c2 << 1) ^ ((c2 & 0x80) ? 0x1d : 0);        //Mult by GF{2}
        uint8_t c8 = (c4 << 1) ^ ((c4 & 0x80) ? 0x1d : 0);        //Mult by GF{2}

#if __WORDSIZE == 64 || _WIN64 || __x86_64__
        unsigned long long v1, v2, v4, v8, *t;
        unsigned long long v10, v20, v40, v80;
        uint8_t c17, c18, c20, c24;

        t = (unsigned long long *)tbl;

        v1 = c * 0x0100010001000100ull;
        v2 = c2 * 0x0101000001010000ull;
        v4 = c4 * 0x0101010100000000ull;
        v8 = c8 * 0x0101010101010101ull;

        v4 = v1 ^ v2 ^ v4;
        t[0] = v4;
        t[1] = v8 ^ v4;

        c17 = (c8 << 1) ^ ((c8 & 0x80) ? 0x1d : 0);     //Mult by GF{2}
        c18 = (c17 << 1) ^ ((c17 & 0x80) ? 0x1d : 0);   //Mult by GF{2}
        c20 = (c18 << 1) ^ ((c18 & 0x80) ? 0x1d : 0);   //Mult by GF{2}
        c24 = (c20 << 1) ^ ((c20 & 0x80) ? 0x1d : 0);   //Mult by GF{2}

        v10 = c17 * 0x0100010001000100ull;
        v20 = c18 * 0x0101000001010000ull;
        v40 = c20 * 0x0101010100000000ull;
        v80 = c24 * 0x0101010101010101ull;

        v40 = v10 ^ v20 ^ v40;
        t[2] = v40;
        t[3] = v80 ^ v40;

#else // 32-bit or other
        uint8_t c3, c5, c6, c7, c9, c10, c11, c12, c13, c14, c15;
        uint8_t c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30,
            c31;

        c3 = c2 ^ c;
        c5 = c4 ^ c;
        c6 = c4 ^ c2;
        c7 = c4 ^ c3;

        c9 = c8 ^ c;
        c10 = c8 ^ c2;
        c11 = c8 ^ c3;
        c12 = c8 ^ c4;
        c13 = c8 ^ c5;
        c14 = c8 ^ c6;
        c15 = c8 ^ c7;

        tbl[0] = 0;
        tbl[1] = c;
        tbl[2] = c2;
        tbl[3] = c3;
        tbl[4] = c4;
        tbl[5] = c5;
        tbl[6] = c6;
        tbl[7] = c7;
        tbl[8] = c8;
        tbl[9] = c9;
        tbl[10] = c10;
        tbl[11] = c11;
        tbl[12] = c12;
        tbl[13] = c13;
        tbl[14] = c14;
        tbl[15] = c15;

        c17 = (c8 << 1) ^ ((c8 & 0x80) ? 0x1d : 0);     //Mult by GF{2}
        c18 = (c17 << 1) ^ ((c17 & 0x80) ? 0x1d : 0);   //Mult by GF{2}
        c19 = c18 ^ c17;
        c20 = (c18 << 1) ^ ((c18 & 0x80) ? 0x1d : 0);   //Mult by GF{2}
        c21 = c20 ^ c17;
        c22 = c20 ^ c18;
        c23 = c20 ^ c19;
        c24 = (c20 << 1) ^ ((c20 & 0x80) ? 0x1d : 0);   //Mult by GF{2}
        c25 = c24 ^ c17;
        c26 = c24 ^ c18;
        c27 = c24 ^ c19;
        c28 = c24 ^ c20;
        c29 = c24 ^ c21;
        c30 = c24 ^ c22;
        c31 = c24 ^ c23;

        tbl[16] = 0;
        tbl[17] = c17;
        tbl[18] = c18;
        tbl[19] = c19;
        tbl[20] = c20;
        tbl[21] = c21;
        tbl[22] = c22;
        tbl[23] = c23;
        tbl[24] = c24;
        tbl[25] = c25;
        tbl[26] = c26;
        tbl[27] = c27;
        tbl[28] = c28;
        tbl[29] = c29;
        tbl[30] = c30;
        tbl[31] = c31;

#endif //__WORDSIZE == 64 || _WIN64 || __x86_64__
}

void gf_vect_dot_prod_base(int len, int vlen, uint8_t *v,
                           uint8_t **src, uint8_t *dest)
{
        int i, j;
        uint8_t s;
        for (i = 0; i < len; i++) {
                s = 0;
                for (j = 0; j < vlen; j++)
                        s ^= gf_mul(src[j][i], v[j * 32 + 1]);

                dest[i] = s;
        }
}

void ec_encode_data_base(int len, int srcs, int dests, uint8_t *v,
                         uint8_t **src, uint8_t **dest)
{
        int i, j, l;
        uint8_t s;

        for (l = 0; l < dests; l++) {
                for (i = 0; i < len; i++) {
                        s = 0;
                        for (j = 0; j < srcs; j++)
                                s ^= gf_mul(src[j][i], v[j * 32 + l * srcs * 32 + 1]);

                        dest[l][i] = s;
                }
        }
}

void gf_vect_mul_base(int len, uint8_t *a, uint8_t *src, uint8_t *dest)
{
        //2nd element of table array is ref value used to fill it in
        uint8_t c = a[1];
        while (len-- > 0)
                *dest++ = gf_mul(c, *src++);
}

struct slver {
        UINT16 snum;
        UINT8 ver;
        UINT8 core;
};

// Version info
struct slver gf_vect_mul_init_slver_00020035;
struct slver gf_vect_mul_init_slver = { 0x0035, 0x02, 0x00 };

struct slver ec_encode_data_base_slver_00010135;
struct slver ec_encode_data_base_slver = { 0x0135, 0x01, 0x00 };

struct slver gf_vect_mul_base_slver_00010136;
struct slver gf_vect_mul_base_slver = { 0x0136, 0x01, 0x00 };

struct slver gf_vect_dot_prod_base_slver_00010137;
struct slver gf_vect_dot_prod_base_slver = { 0x0137, 0x01, 0x00 };