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 #ifndef _ERASURE_CODE_H_
 #define _ERASURE_CODE_H_
 
 /**
  *  @file erasure_code.h
  *  @brief Interface to functions supporting erasure code encode and decode.
  *
  *  This file defines the interface to optimized functions used in erasure
  *  codes.  Encode and decode of erasures in GF(2^8) are made by calculating the
  *  dot product of the symbols (bytes in GF(2^8)) across a set of buffers and a
  *  set of coefficients.  Values for the coefficients are determined by the type
  *  of erasure code.  Using a general dot product means that any sequence of
  *  coefficients may be used including erasure codes based on random
  *  coefficients.
  *  Multiple versions of dot product are supplied to calculate 1-6 output
  *  vectors in one pass.
  *  Base GF multiply and divide functions can be sped up by defining
  *  GF_LARGE_TABLES at the expense of memory size.
  *
  */
 
 #include "gf_vect_mul.h"
 
 #ifdef __cplusplus
 extern "C" {
 #endif
 
 /**
  * @brief Initialize tables for fast Erasure Code encode and decode.
  *
  * Generates the expanded tables needed for fast encode or decode for erasure
  * codes on blocks of data.  32bytes is generated for each input coefficient.
  *
  * @param k      The number of vector sources or rows in the generator matrix
  *               for coding.
  * @param rows   The number of output vectors to concurrently encode/decode.
  * @param a      Pointer to sets of arrays of input coefficients used to encode
  *               or decode data.
  * @param gftbls Pointer to start of space for concatenated output tables
  *               generated from input coefficients.  Must be of size 32*k*rows.
  * @returns none
  */
 
 void
 ec_init_tables(int k, int rows, unsigned char *a, unsigned char *gftbls);
 
 /**
  * @brief Initialize tables for fast Erasure Code encode and decode, runs baseline version.
  *
  * Baseline version of ec_encode_data() with same parameters.
  */
 
 void
 ec_init_tables_base(int k, int rows, unsigned char *a, unsigned char *gftbls);
 
 /**
  * @brief Generate or decode erasure codes on blocks of data, runs appropriate version.
  *
  * Given a list of source data blocks, generate one or multiple blocks of
  * encoded data as specified by a matrix of GF(2^8) coefficients. When given a
  * suitable set of coefficients, this function will perform the fast generation
  * or decoding of Reed-Solomon type erasure codes.
  *
  * This function determines what instruction sets are enabled and
  * selects the appropriate version at runtime.
  *
  * @param len    Length of each block of data (vector) of source or dest data.
  * @param k      The number of vector sources or rows in the generator matrix
  *       for coding.
  * @param rows   The number of output vectors to concurrently encode/decode.
  * @param gftbls Pointer to array of input tables generated from coding
  *       coefficients in ec_init_tables(). Must be of size 32*k*rows
  * @param data   Array of pointers to source input buffers.
  * @param coding Array of pointers to coded output buffers.
  * @returns none
  */
 
 void
 ec_encode_data(int len, int k, int rows, unsigned char *gftbls, unsigned char **data,
                unsigned char **coding);
 
 /**
  * @brief Generate or decode erasure codes on blocks of data, runs baseline version.
  *
  * Baseline version of ec_encode_data() with same parameters.
  */
 void
 ec_encode_data_base(int len, int srcs, int dests, unsigned char *v, unsigned char **src,
                     unsigned char **dest);
 
 /**
  * @brief Generate update for encode or decode of erasure codes from single source, runs appropriate
  * version.
  *
  * Given one source data block, update one or multiple blocks of encoded data as
  * specified by a matrix of GF(2^8) coefficients. When given a suitable set of
  * coefficients, this function will perform the fast generation or decoding of
  * Reed-Solomon type erasure codes from one input source at a time.
  *
  * This function determines what instruction sets are enabled and selects the
  * appropriate version at runtime.
  *
  * @param len    Length of each block of data (vector) of source or dest data.
  * @param k      The number of vector sources or rows in the generator matrix
  *       for coding.
  * @param rows   The number of output vectors to concurrently encode/decode.
  * @param vec_i  The vector index corresponding to the single input source.
  * @param g_tbls Pointer to array of input tables generated from coding
  *       coefficients in ec_init_tables(). Must be of size 32*k*rows
  * @param data   Pointer to single input source used to update output parity.
  * @param coding Array of pointers to coded output buffers.
  * @returns none
  */
 void
 ec_encode_data_update(int len, int k, int rows, int vec_i, unsigned char *g_tbls,
                       unsigned char *data, unsigned char **coding);
 
 /**
  * @brief Generate update for encode or decode of erasure codes from single source.
  *
  * Baseline version of ec_encode_data_update().
  */
 
 void
 ec_encode_data_update_base(int len, int k, int rows, int vec_i, unsigned char *v,
                            unsigned char *data, unsigned char **dest);
 
 /**
  * @brief GF(2^8) vector dot product, runs baseline version.
  *
  * Does a GF(2^8) dot product across each byte of the input array and a constant
  * set of coefficients to produce each byte of the output. Can be used for
  * erasure coding encode and decode. Function requires pre-calculation of a
  * 32*vlen byte constant array based on the input coefficients.
  *
  * @param len    Length of each vector in bytes. Must be >= 16.
  * @param vlen   Number of vector sources.
  * @param gftbls Pointer to 32*vlen byte array of pre-calculated constants based
  *               on the array of input coefficients. Only elements 32*CONST*j + 1
  *               of this array are used, where j = (0, 1, 2...) and CONST is the
  *               number of elements in the array of input coefficients. The
  *               elements used correspond to the original input coefficients.
  * @param src    Array of pointers to source inputs.
  * @param dest   Pointer to destination data array.
  * @returns none
  */
 
 void
 gf_vect_dot_prod_base(int len, int vlen, unsigned char *gftbls, unsigned char **src,
                       unsigned char *dest);
 
 /**
  * @brief GF(2^8) vector dot product, runs appropriate version.
  *
  * Does a GF(2^8) dot product across each byte of the input array and a constant
  * set of coefficients to produce each byte of the output. Can be used for
  * erasure coding encode and decode. Function requires pre-calculation of a
  * 32*vlen byte constant array based on the input coefficients.
  *
  * This function determines what instruction sets are enabled and
  * selects the appropriate version at runtime.
  *
  * @param len    Length of each vector in bytes. Must be >= 32.
  * @param vlen   Number of vector sources.
  * @param gftbls Pointer to 32*vlen byte array of pre-calculated constants based
  *               on the array of input coefficients.
  * @param src    Array of pointers to source inputs.
  * @param dest   Pointer to destination data array.
  * @returns none
  */
 
 void
 gf_vect_dot_prod(int len, int vlen, unsigned char *gftbls, unsigned char **src,
                  unsigned char *dest);
 
 /**
  * @brief GF(2^8) vector multiply accumulate, runs appropriate version.
  *
  * Does a GF(2^8) multiply across each byte of input source with expanded
  * constant and add to destination array. Can be used for erasure coding encode
  * and decode update when only one source is available at a time. Function
  * requires pre-calculation of a 32*vec byte constant array based on the input
  * coefficients.
  *
  * This function determines what instruction sets are enabled and selects the
  * appropriate version at runtime.
  *
  * @param len    Length of each vector in bytes. Must be >= 64.
  * @param vec    The number of vector sources or rows in the generator matrix
  *       for coding.
  * @param vec_i  The vector index corresponding to the single input source.
  * @param gftbls Pointer to array of input tables generated from coding
  *       coefficients in ec_init_tables(). Must be of size 32*vec.
  * @param src    Array of pointers to source inputs.
  * @param dest   Pointer to destination data array.
  * @returns none
  */
 
 void
 gf_vect_mad(int len, int vec, int vec_i, unsigned char *gftbls, unsigned char *src,
             unsigned char *dest);
 
 /**
  * @brief GF(2^8) vector multiply accumulate, baseline version.
  *
  * Baseline version of gf_vect_mad() with same parameters.
  */
 
 void
 gf_vect_mad_base(int len, int vec, int vec_i, unsigned char *v, unsigned char *src,
                  unsigned char *dest);
 
 // x86 only
 #if defined(__i386__) || defined(__x86_64__)
 
 /**
  * @brief Generate or decode erasure codes on blocks of data.
  *
  * Arch specific version of ec_encode_data() with same parameters.
  * @requires SSE4.1
  */
 void
 ec_encode_data_sse(int len, int k, int rows, unsigned char *gftbls, unsigned char **data,
                    unsigned char **coding);
 
 /**
  * @brief Generate or decode erasure codes on blocks of data.
  *
  * Arch specific version of ec_encode_data() with same parameters.
  * @requires AVX
  */
 void
 ec_encode_data_avx(int len, int k, int rows, unsigned char *gftbls, unsigned char **data,
                    unsigned char **coding);
 
 /**
  * @brief Generate or decode erasure codes on blocks of data.
  *
  * Arch specific version of ec_encode_data() with same parameters.
  * @requires AVX2
  */
 void
 ec_encode_data_avx2(int len, int k, int rows, unsigned char *gftbls, unsigned char **data,
                     unsigned char **coding);
 
 /**
  * @brief Generate update for encode or decode of erasure codes from single source.
  *
  * Arch specific version of ec_encode_data_update() with same parameters.
  * @requires SSE4.1
  */
 
 void
 ec_encode_data_update_sse(int len, int k, int rows, int vec_i, unsigned char *g_tbls,
                           unsigned char *data, unsigned char **coding);
 
 /**
  * @brief Generate update for encode or decode of erasure codes from single source.
  *
  * Arch specific version of ec_encode_data_update() with same parameters.
  * @requires AVX
  */
 
 void
 ec_encode_data_update_avx(int len, int k, int rows, int vec_i, unsigned char *g_tbls,
                           unsigned char *data, unsigned char **coding);
 
 /**
  * @brief Generate update for encode or decode of erasure codes from single source.
  *
  * Arch specific version of ec_encode_data_update() with same parameters.
  * @requires AVX2
  */
 
 void
 ec_encode_data_update_avx2(int len, int k, int rows, int vec_i, unsigned char *g_tbls,
                            unsigned char *data, unsigned char **coding);
 
 /**
  * @brief GF(2^8) vector dot product.
  *
  * Does a GF(2^8) dot product across each byte of the input array and a constant
  * set of coefficients to produce each byte of the output. Can be used for
  * erasure coding encode and decode. Function requires pre-calculation of a
  * 32*vlen byte constant array based on the input coefficients.
  * @requires SSE4.1
  *
  * @param len    Length of each vector in bytes. Must be >= 16.
  * @param vlen   Number of vector sources.
  * @param gftbls Pointer to 32*vlen byte array of pre-calculated constants based
  *               on the array of input coefficients.
  * @param src    Array of pointers to source inputs.
  * @param dest   Pointer to destination data array.
  * @returns none
  */
 
 void
 gf_vect_dot_prod_sse(int len, int vlen, unsigned char *gftbls, unsigned char **src,
                      unsigned char *dest);
 
 /**
  * @brief GF(2^8) vector dot product.
  *
  * Does a GF(2^8) dot product across each byte of the input array and a constant
  * set of coefficients to produce each byte of the output. Can be used for
  * erasure coding encode and decode. Function requires pre-calculation of a
  * 32*vlen byte constant array based on the input coefficients.
  * @requires AVX
  *
  * @param len    Length of each vector in bytes. Must be >= 16.
  * @param vlen   Number of vector sources.
  * @param gftbls Pointer to 32*vlen byte array of pre-calculated constants based
  *               on the array of input coefficients.
  * @param src    Array of pointers to source inputs.
  * @param dest   Pointer to destination data array.
  * @returns none
  */
 
 void
 gf_vect_dot_prod_avx(int len, int vlen, unsigned char *gftbls, unsigned char **src,
                      unsigned char *dest);
 
 /**
  * @brief GF(2^8) vector dot product.
  *
  * Does a GF(2^8) dot product across each byte of the input array and a constant
  * set of coefficients to produce each byte of the output. Can be used for
  * erasure coding encode and decode. Function requires pre-calculation of a
  * 32*vlen byte constant array based on the input coefficients.
  * @requires AVX2
  *
  * @param len    Length of each vector in bytes. Must be >= 32.
  * @param vlen   Number of vector sources.
  * @param gftbls Pointer to 32*vlen byte array of pre-calculated constants based
  *               on the array of input coefficients.
  * @param src    Array of pointers to source inputs.
  * @param dest   Pointer to destination data array.
  * @returns none
  */
 
 void
 gf_vect_dot_prod_avx2(int len, int vlen, unsigned char *gftbls, unsigned char **src,
                       unsigned char *dest);
 
 /**
  * @brief GF(2^8) vector dot product with two outputs.
  *
  * Vector dot product optimized to calculate two outputs at a time. Does two
  * GF(2^8) dot products across each byte of the input array and two constant
  * sets of coefficients to produce each byte of the outputs. Can be used for
  * erasure coding encode and decode. Function requires pre-calculation of a
  * 2*32*vlen byte constant array based on the two sets of input coefficients.
  * @requires SSE4.1
  *
  * @param len    Length of each vector in bytes. Must be >= 16.
  * @param vlen   Number of vector sources.
  * @param gftbls Pointer to 2*32*vlen byte array of pre-calculated constants
  *               based on the array of input coefficients.
  * @param src    Array of pointers to source inputs.
  * @param dest   Array of pointers to destination data buffers.
  * @returns none
  */
 
 void
 gf_2vect_dot_prod_sse(int len, int vlen, unsigned char *gftbls, unsigned char **src,
                       unsigned char **dest);
 
 /**
  * @brief GF(2^8) vector dot product with two outputs.
  *
  * Vector dot product optimized to calculate two outputs at a time. Does two
  * GF(2^8) dot products across each byte of the input array and two constant
  * sets of coefficients to produce each byte of the outputs. Can be used for
  * erasure coding encode and decode. Function requires pre-calculation of a
  * 2*32*vlen byte constant array based on the two sets of input coefficients.
  * @requires AVX
  *
  * @param len    Length of each vector in bytes. Must be >= 16.
  * @param vlen   Number of vector sources.
  * @param gftbls Pointer to 2*32*vlen byte array of pre-calculated constants
  *               based on the array of input coefficients.
  * @param src    Array of pointers to source inputs.
  * @param dest   Array of pointers to destination data buffers.
  * @returns none
  */
 
 void
 gf_2vect_dot_prod_avx(int len, int vlen, unsigned char *gftbls, unsigned char **src,
                       unsigned char **dest);
 
 /**
  * @brief GF(2^8) vector dot product with two outputs.
  *
  * Vector dot product optimized to calculate two outputs at a time. Does two
  * GF(2^8) dot products across each byte of the input array and two constant
  * sets of coefficients to produce each byte of the outputs. Can be used for
  * erasure coding encode and decode. Function requires pre-calculation of a
  * 2*32*vlen byte constant array based on the two sets of input coefficients.
  * @requires AVX2
  *
  * @param len    Length of each vector in bytes. Must be >= 32.
  * @param vlen   Number of vector sources.
  * @param gftbls Pointer to 2*32*vlen byte array of pre-calculated constants
  *               based on the array of input coefficients.
  * @param src    Array of pointers to source inputs.
  * @param dest   Array of pointers to destination data buffers.
  * @returns none
  */
 
 void
 gf_2vect_dot_prod_avx2(int len, int vlen, unsigned char *gftbls, unsigned char **src,
                        unsigned char **dest);
 
 /**
  * @brief GF(2^8) vector dot product with three outputs.
  *
  * Vector dot product optimized to calculate three outputs at a time. Does three
  * GF(2^8) dot products across each byte of the input array and three constant
  * sets of coefficients to produce each byte of the outputs. Can be used for
  * erasure coding encode and decode. Function requires pre-calculation of a
  * 3*32*vlen byte constant array based on the three sets of input coefficients.
  * @requires SSE4.1
  *
  * @param len    Length of each vector in bytes. Must be >= 16.
  * @param vlen   Number of vector sources.
  * @param gftbls Pointer to 3*32*vlen byte array of pre-calculated constants
  *               based on the array of input coefficients.
  * @param src    Array of pointers to source inputs.
  * @param dest   Array of pointers to destination data buffers.
  * @returns none
  */
 
 void
 gf_3vect_dot_prod_sse(int len, int vlen, unsigned char *gftbls, unsigned char **src,
                       unsigned char **dest);
 
 /**
  * @brief GF(2^8) vector dot product with three outputs.
  *
  * Vector dot product optimized to calculate three outputs at a time. Does three
  * GF(2^8) dot products across each byte of the input array and three constant
  * sets of coefficients to produce each byte of the outputs. Can be used for
  * erasure coding encode and decode. Function requires pre-calculation of a
  * 3*32*vlen byte constant array based on the three sets of input coefficients.
  * @requires AVX
  *
  * @param len    Length of each vector in bytes. Must be >= 16.
  * @param vlen   Number of vector sources.
  * @param gftbls Pointer to 3*32*vlen byte array of pre-calculated constants
  *               based on the array of input coefficients.
  * @param src    Array of pointers to source inputs.
  * @param dest   Array of pointers to destination data buffers.
  * @returns none
  */
 
 void
 gf_3vect_dot_prod_avx(int len, int vlen, unsigned char *gftbls, unsigned char **src,
                       unsigned char **dest);
 
 /**
  * @brief GF(2^8) vector dot product with three outputs.
  *
  * Vector dot product optimized to calculate three outputs at a time. Does three
  * GF(2^8) dot products across each byte of the input array and three constant
  * sets of coefficients to produce each byte of the outputs. Can be used for
  * erasure coding encode and decode. Function requires pre-calculation of a
  * 3*32*vlen byte constant array based on the three sets of input coefficients.
  * @requires AVX2
  *
  * @param len    Length of each vector in bytes. Must be >= 32.
  * @param vlen   Number of vector sources.
  * @param gftbls Pointer to 3*32*vlen byte array of pre-calculated constants
  *               based on the array of input coefficients.
  * @param src    Array of pointers to source inputs.
  * @param dest   Array of pointers to destination data buffers.
  * @returns none
  */
 
 void
 gf_3vect_dot_prod_avx2(int len, int vlen, unsigned char *gftbls, unsigned char **src,
                        unsigned char **dest);
 
 /**
  * @brief GF(2^8) vector dot product with four outputs.
  *
  * Vector dot product optimized to calculate four outputs at a time. Does four
  * GF(2^8) dot products across each byte of the input array and four constant
  * sets of coefficients to produce each byte of the outputs. Can be used for
  * erasure coding encode and decode. Function requires pre-calculation of a
  * 4*32*vlen byte constant array based on the four sets of input coefficients.
  * @requires SSE4.1
  *
  * @param len    Length of each vector in bytes. Must be >= 16.
  * @param vlen   Number of vector sources.
  * @param gftbls Pointer to 4*32*vlen byte array of pre-calculated constants
  *               based on the array of input coefficients.
  * @param src    Array of pointers to source inputs.
  * @param dest   Array of pointers to destination data buffers.
  * @returns none
  */
 
 void
 gf_4vect_dot_prod_sse(int len, int vlen, unsigned char *gftbls, unsigned char **src,
                       unsigned char **dest);
 
 /**
  * @brief GF(2^8) vector dot product with four outputs.
  *
  * Vector dot product optimized to calculate four outputs at a time. Does four
  * GF(2^8) dot products across each byte of the input array and four constant
  * sets of coefficients to produce each byte of the outputs. Can be used for
  * erasure coding encode and decode. Function requires pre-calculation of a
  * 4*32*vlen byte constant array based on the four sets of input coefficients.
  * @requires AVX
  *
  * @param len    Length of each vector in bytes. Must be >= 16.
  * @param vlen   Number of vector sources.
  * @param gftbls Pointer to 4*32*vlen byte array of pre-calculated constants
  *               based on the array of input coefficients.
  * @param src    Array of pointers to source inputs.
  * @param dest   Array of pointers to destination data buffers.
  * @returns none
  */
 
 void
 gf_4vect_dot_prod_avx(int len, int vlen, unsigned char *gftbls, unsigned char **src,
                       unsigned char **dest);
 
 /**
  * @brief GF(2^8) vector dot product with four outputs.
  *
  * Vector dot product optimized to calculate four outputs at a time. Does four
  * GF(2^8) dot products across each byte of the input array and four constant
  * sets of coefficients to produce each byte of the outputs. Can be used for
  * erasure coding encode and decode. Function requires pre-calculation of a
  * 4*32*vlen byte constant array based on the four sets of input coefficients.
  * @requires AVX2
  *
  * @param len    Length of each vector in bytes. Must be >= 32.
  * @param vlen   Number of vector sources.
  * @param gftbls Pointer to 4*32*vlen byte array of pre-calculated constants
  *               based on the array of input coefficients.
  * @param src    Array of pointers to source inputs.
  * @param dest   Array of pointers to destination data buffers.
  * @returns none
  */
 
 void
 gf_4vect_dot_prod_avx2(int len, int vlen, unsigned char *gftbls, unsigned char **src,
                        unsigned char **dest);
 
 /**
  * @brief GF(2^8) vector dot product with five outputs.
  *
  * Vector dot product optimized to calculate five outputs at a time. Does five
  * GF(2^8) dot products across each byte of the input array and five constant
  * sets of coefficients to produce each byte of the outputs. Can be used for
  * erasure coding encode and decode. Function requires pre-calculation of a
  * 5*32*vlen byte constant array based on the five sets of input coefficients.
  * @requires SSE4.1
  *
  * @param len    Length of each vector in bytes. Must >= 16.
  * @param vlen   Number of vector sources.
  * @param gftbls Pointer to 5*32*vlen byte array of pre-calculated constants
  *               based on the array of input coefficients.
  * @param src    Array of pointers to source inputs.
  * @param dest   Array of pointers to destination data buffers.
  * @returns none
  */
 
 void
 gf_5vect_dot_prod_sse(int len, int vlen, unsigned char *gftbls, unsigned char **src,
                       unsigned char **dest);
 
 /**
  * @brief GF(2^8) vector dot product with five outputs.
  *
  * Vector dot product optimized to calculate five outputs at a time. Does five
  * GF(2^8) dot products across each byte of the input array and five constant
  * sets of coefficients to produce each byte of the outputs. Can be used for
  * erasure coding encode and decode. Function requires pre-calculation of a
  * 5*32*vlen byte constant array based on the five sets of input coefficients.
  * @requires AVX
  *
  * @param len    Length of each vector in bytes. Must >= 16.
  * @param vlen   Number of vector sources.
  * @param gftbls Pointer to 5*32*vlen byte array of pre-calculated constants
  *               based on the array of input coefficients.
  * @param src    Array of pointers to source inputs.
  * @param dest   Array of pointers to destination data buffers.
  * @returns none
  */
 
 void
 gf_5vect_dot_prod_avx(int len, int vlen, unsigned char *gftbls, unsigned char **src,
                       unsigned char **dest);
 
 /**
  * @brief GF(2^8) vector dot product with five outputs.
  *
  * Vector dot product optimized to calculate five outputs at a time. Does five
  * GF(2^8) dot products across each byte of the input array and five constant
  * sets of coefficients to produce each byte of the outputs. Can be used for
  * erasure coding encode and decode. Function requires pre-calculation of a
  * 5*32*vlen byte constant array based on the five sets of input coefficients.
  * @requires AVX2
  *
  * @param len    Length of each vector in bytes. Must >= 32.
  * @param vlen   Number of vector sources.
  * @param gftbls Pointer to 5*32*vlen byte array of pre-calculated constants
  *               based on the array of input coefficients.
  * @param src    Array of pointers to source inputs.
  * @param dest   Array of pointers to destination data buffers.
  * @returns none
  */
 
 void
 gf_5vect_dot_prod_avx2(int len, int vlen, unsigned char *gftbls, unsigned char **src,
                        unsigned char **dest);
 
 /**
  * @brief GF(2^8) vector dot product with six outputs.
  *
  * Vector dot product optimized to calculate six outputs at a time. Does six
  * GF(2^8) dot products across each byte of the input array and six constant
  * sets of coefficients to produce each byte of the outputs. Can be used for
  * erasure coding encode and decode. Function requires pre-calculation of a
  * 6*32*vlen byte constant array based on the six sets of input coefficients.
  * @requires SSE4.1
  *
  * @param len    Length of each vector in bytes. Must be >= 16.
  * @param vlen   Number of vector sources.
  * @param gftbls Pointer to 6*32*vlen byte array of pre-calculated constants
  *               based on the array of input coefficients.
  * @param src    Array of pointers to source inputs.
  * @param dest   Array of pointers to destination data buffers.
  * @returns none
  */
 
 void
 gf_6vect_dot_prod_sse(int len, int vlen, unsigned char *gftbls, unsigned char **src,
                       unsigned char **dest);
 
 /**
  * @brief GF(2^8) vector dot product with six outputs.
  *
  * Vector dot product optimized to calculate six outputs at a time. Does six
  * GF(2^8) dot products across each byte of the input array and six constant
  * sets of coefficients to produce each byte of the outputs. Can be used for
  * erasure coding encode and decode. Function requires pre-calculation of a
  * 6*32*vlen byte constant array based on the six sets of input coefficients.
  * @requires AVX
  *
  * @param len    Length of each vector in bytes. Must be >= 16.
  * @param vlen   Number of vector sources.
  * @param gftbls Pointer to 6*32*vlen byte array of pre-calculated constants
  *               based on the array of input coefficients.
  * @param src    Array of pointers to source inputs.
  * @param dest   Array of pointers to destination data buffers.
  * @returns none
  */
 
 void
 gf_6vect_dot_prod_avx(int len, int vlen, unsigned char *gftbls, unsigned char **src,
                       unsigned char **dest);
 
 /**
  * @brief GF(2^8) vector dot product with six outputs.
  *
  * Vector dot product optimized to calculate six outputs at a time. Does six
  * GF(2^8) dot products across each byte of the input array and six constant
  * sets of coefficients to produce each byte of the outputs. Can be used for
  * erasure coding encode and decode. Function requires pre-calculation of a
  * 6*32*vlen byte constant array based on the six sets of input coefficients.
  * @requires AVX2
  *
  * @param len    Length of each vector in bytes. Must be >= 32.
  * @param vlen   Number of vector sources.
  * @param gftbls Pointer to 6*32*vlen byte array of pre-calculated constants
  *               based on the array of input coefficients.
  * @param src    Array of pointers to source inputs.
  * @param dest   Array of pointers to destination data buffers.
  * @returns none
  */
 
 void
 gf_6vect_dot_prod_avx2(int len, int vlen, unsigned char *gftbls, unsigned char **src,
                        unsigned char **dest);
 
 /**
  * @brief GF(2^8) vector multiply accumulate, arch specific version.
  *
  * Arch specific version of gf_vect_mad() with same parameters.
  * @requires SSE4.1
  */
 
 void
 gf_vect_mad_sse(int len, int vec, int vec_i, unsigned char *gftbls, unsigned char *src,
                 unsigned char *dest);
 /**
  * @brief GF(2^8) vector multiply accumulate, arch specific version.
  *
  * Arch specific version of gf_vect_mad() with same parameters.
  * @requires AVX
  */
 
 void
 gf_vect_mad_avx(int len, int vec, int vec_i, unsigned char *gftbls, unsigned char *src,
                 unsigned char *dest);
 
 /**
  * @brief GF(2^8) vector multiply accumulate, arch specific version.
  *
  * Arch specific version of gf_vect_mad() with same parameters.
  * @requires AVX2
  */
 
 void
 gf_vect_mad_avx2(int len, int vec, int vec_i, unsigned char *gftbls, unsigned char *src,
                  unsigned char *dest);
 
 /**
  * @brief GF(2^8) vector multiply with 2 accumulate.  SSE version.
  *
  * Does a GF(2^8) multiply across each byte of input source with expanded
  * constants and add to destination arrays. Can be used for erasure coding
  * encode and decode update when only one source is available at a
  * time. Function requires pre-calculation of a 32*vec byte constant array based
  * on the input coefficients.
  * @requires SSE4.1
  *
  * @param len    Length of each vector in bytes. Must be >= 32.
  * @param vec    The number of vector sources or rows in the generator matrix
  *       for coding.
  * @param vec_i  The vector index corresponding to the single input source.
  * @param gftbls Pointer to array of input tables generated from coding
  *       coefficients in ec_init_tables(). Must be of size 32*vec.
  * @param src    Pointer to source input array.
  * @param dest   Array of pointers to destination input/outputs.
  * @returns none
  */
 
 void
 gf_2vect_mad_sse(int len, int vec, int vec_i, unsigned char *gftbls, unsigned char *src,
                  unsigned char **dest);
 
 /**
  * @brief GF(2^8) vector multiply with 2 accumulate. AVX version of gf_2vect_mad_sse().
  * @requires AVX
  */
 void
 gf_2vect_mad_avx(int len, int vec, int vec_i, unsigned char *gftbls, unsigned char *src,
                  unsigned char **dest);
 /**
  * @brief GF(2^8) vector multiply with 2 accumulate. AVX2 version of gf_2vect_mad_sse().
  * @requires AVX2
  */
 void
 gf_2vect_mad_avx2(int len, int vec, int vec_i, unsigned char *gftbls, unsigned char *src,
                   unsigned char **dest);
 
 /**
  * @brief GF(2^8) vector multiply with 3 accumulate. SSE version.
  *
  * Does a GF(2^8) multiply across each byte of input source with expanded
  * constants and add to destination arrays. Can be used for erasure coding
  * encode and decode update when only one source is available at a
  * time. Function requires pre-calculation of a 32*vec byte constant array based
  * on the input coefficients.
  * @requires SSE4.1
  *
  * @param len    Length of each vector in bytes. Must be >= 32.
  * @param vec    The number of vector sources or rows in the generator matrix
  *       for coding.
  * @param vec_i  The vector index corresponding to the single input source.
  * @param gftbls Pointer to array of input tables generated from coding
  *       coefficients in ec_init_tables(). Must be of size 32*vec.
  * @param src    Pointer to source input array.
  * @param dest   Array of pointers to destination input/outputs.
  * @returns none
  */
 
 void
 gf_3vect_mad_sse(int len, int vec, int vec_i, unsigned char *gftbls, unsigned char *src,
                  unsigned char **dest);
 
 /**
  * @brief GF(2^8) vector multiply with 3 accumulate. AVX version of gf_3vect_mad_sse().
  * @requires AVX
  */
 void
 gf_3vect_mad_avx(int len, int vec, int vec_i, unsigned char *gftbls, unsigned char *src,
                  unsigned char **dest);
 
 /**
  * @brief GF(2^8) vector multiply with 3 accumulate. AVX2 version of gf_3vect_mad_sse().
  * @requires AVX2
  */
 void
 gf_3vect_mad_avx2(int len, int vec, int vec_i, unsigned char *gftbls, unsigned char *src,
                   unsigned char **dest);
 
 /**
  * @brief GF(2^8) vector multiply with 4 accumulate. SSE version.
  *
  * Does a GF(2^8) multiply across each byte of input source with expanded
  * constants and add to destination arrays. Can be used for erasure coding
  * encode and decode update when only one source is available at a
  * time. Function requires pre-calculation of a 32*vec byte constant array based
  * on the input coefficients.
  * @requires SSE4.1
  *
  * @param len    Length of each vector in bytes. Must be >= 32.
  * @param vec    The number of vector sources or rows in the generator matrix
  *       for coding.
  * @param vec_i  The vector index corresponding to the single input source.
  * @param gftbls Pointer to array of input tables generated from coding
  *       coefficients in ec_init_tables(). Must be of size 32*vec.
  * @param src    Pointer to source input array.
  * @param dest   Array of pointers to destination input/outputs.
  * @returns none
  */
 
 void
 gf_4vect_mad_sse(int len, int vec, int vec_i, unsigned char *gftbls, unsigned char *src,
                  unsigned char **dest);
 
 /**
  * @brief GF(2^8) vector multiply with 4 accumulate. AVX version of gf_4vect_mad_sse().
  * @requires AVX
  */
 void
 gf_4vect_mad_avx(int len, int vec, int vec_i, unsigned char *gftbls, unsigned char *src,
                  unsigned char **dest);
 /**
  * @brief GF(2^8) vector multiply with 4 accumulate. AVX2 version of gf_4vect_mad_sse().
  * @requires AVX2
  */
 void
 gf_4vect_mad_avx2(int len, int vec, int vec_i, unsigned char *gftbls, unsigned char *src,
                   unsigned char **dest);
 
 /**
  * @brief GF(2^8) vector multiply with 5 accumulate. SSE version.
  * @requires SSE4.1
  */
 void
 gf_5vect_mad_sse(int len, int vec, int vec_i, unsigned char *gftbls, unsigned char *src,
                  unsigned char **dest);
 
 /**
  * @brief GF(2^8) vector multiply with 5 accumulate. AVX version.
  * @requires AVX
  */
 void
 gf_5vect_mad_avx(int len, int vec, int vec_i, unsigned char *gftbls, unsigned char *src,
                  unsigned char **dest);
 /**
  * @brief GF(2^8) vector multiply with 5 accumulate. AVX2 version.
  * @requires AVX2
  */
 void
 gf_5vect_mad_avx2(int len, int vec, int vec_i, unsigned char *gftbls, unsigned char *src,
                   unsigned char **dest);
 
 /**
  * @brief GF(2^8) vector multiply with 6 accumulate. SSE version.
  * @requires SSE4.1
  */
 void
 gf_6vect_mad_sse(int len, int vec, int vec_i, unsigned char *gftbls, unsigned char *src,
                  unsigned char **dest);
 /**
  * @brief GF(2^8) vector multiply with 6 accumulate. AVX version.
  * @requires AVX
  */
 void
 gf_6vect_mad_avx(int len, int vec, int vec_i, unsigned char *gftbls, unsigned char *src,
                  unsigned char **dest);
 
 /**
  * @brief GF(2^8) vector multiply with 6 accumulate. AVX2 version.
  * @requires AVX2
  */
 void
 gf_6vect_mad_avx2(int len, int vec, int vec_i, unsigned char *gftbls, unsigned char *src,
                   unsigned char **dest);
 
 #endif
 
 /**********************************************************************
  * The remaining are lib support functions used in GF(2^8) operations.
  */
 
 /**
  * @brief Single element GF(2^8) multiply.
  *
  * @param a  Multiplicand a
  * @param b  Multiplicand b
  * @returns  Product of a and b in GF(2^8)
  */
 
 unsigned char
 gf_mul(unsigned char a, unsigned char b);
 
 /**
  * @brief Single element GF(2^8) inverse.
  *
  * @param a  Input element
  * @returns  Field element b such that a x b = {1}
  */
 
 unsigned char
 gf_inv(unsigned char a);
 
 /**
  * @brief Generate a matrix of coefficients to be used for encoding.
  *
  * Vandermonde matrix example of encoding coefficients where high portion of
  * matrix is identity matrix I and lower portion is constructed as 2^{i*(j-k+1)}
  * i:{0,k-1} j:{k,m-1}. Commonly used method for choosing coefficients in
  * erasure encoding but does not guarantee invertable for every sub matrix. For
  * large pairs of m and k it is possible to find cases where the decode matrix
  * chosen from sources and parity is not invertable. Users may want to adjust
  * for certain pairs m and k. If m and k satisfy one of the following
  * inequalities, no adjustment is required:
  *
  * - k <= 3
  * - k = 4, m <= 25
  * - k = 5, m <= 10
  * - k <= 21, m-k = 4
  * - m - k <= 3.
  *
  * @param a  [m x k] array to hold coefficients
  * @param m  number of rows in matrix corresponding to srcs + parity.
  * @param k  number of columns in matrix corresponding to srcs.
  * @returns  none
  */
 
 void
 gf_gen_rs_matrix(unsigned char *a, int m, int k);
 
 /**
  * @brief Generate a Cauchy matrix of coefficients to be used for encoding.
  *
  * Cauchy matrix example of encoding coefficients where high portion of matrix
  * is identity matrix I and lower portion is constructed as 1/(i + j) | i != j,
  * i:{0,k-1} j:{k,m-1}.  Any sub-matrix of a Cauchy matrix should be invertable.
  *
  * @param a  [m x k] array to hold coefficients
  * @param m  number of rows in matrix corresponding to srcs + parity.
  * @param k  number of columns in matrix corresponding to srcs.
  * @returns  none
  */
 
 void
 gf_gen_cauchy1_matrix(unsigned char *a, int m, int k);
 
 /**
  * @brief Invert a matrix in GF(2^8)
  *
  * Attempts to construct an n x n inverse of the input matrix. Returns non-zero
  * if singular. Will always destroy input matrix in process.
  *
  * @param in  input matrix, destroyed by invert process
  * @param out output matrix such that [in] x [out] = [I] - identity matrix
  * @param n   size of matrix [nxn]
  * @returns 0 successful, other fail on singular input matrix
  */
 
 int
 gf_invert_matrix(unsigned char *in, unsigned char *out, const int n);
 
 /*************************************************************/
 
 #ifdef __cplusplus
 }
 #endif
 
 #endif //_ERASURE_CODE_H_

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