median.c

#include "median.h"
#include "hex.h"
#include <strings.h>   // size_t
#include <stdio.h>     // fprintf
#include <stdlib.h>    // qsort
#include <string.h>    // memcpy

// The structure of the data buffer is this:
// ----------------------------------------------------------------------------
// | Metadata | BlockData | Data * nMembers | BlockData | Data * nMembers .....
// ----------------------------------------------------------------------------
// Where the number of blocks is nLevels and stored in Metadata, and nMembers
// is stored in Metadata as well.
// The buffer is cast into this struct.
typedef struct bufferdata {
  unsigned int id;           // Block identity.
  size_t level;              // The level of this buffer.
  size_t occupancy;          // Number of occupants for this buffer.
  median_data_t data[0];     // The data for this buffer.
} blockdata_t;

typedef struct metadata {
  unsigned int gid;        // The next available global id
  size_t nLevels;          // Number of buffers available.
  size_t nMembers;         // The number of members in each block.
  size_t currentBufferIdx; // The index of the currently active buffer.
  unsigned char data[0];   // The start of the data.
  blockdata_t blocks[0];   // Makes the code cleaner and avoids unnecessary casting.
} metadata_t;

typedef struct sortrec {
  median_data_t d;
  size_t        sz;
} sort_rec_t;

typedef struct spare_buffer {
  size_t spareSize;             // Size in bytes of the spare block.
  size_t recordSize;            // Size in SortRecords
  size_t datumSize;             // Size in number of Datum elements.
  unsigned char data[0];        // Start of the data block.
  sort_rec_t records[0];        // The same point cast as a sort_rec
  median_data_t median_data[0]; // The same point cast as a median datum
  size_t sizes[0];              // The same point case as size_t
} spare_buffer_t;


// ----------------------------------------------------------------------------
// Helper functions.
//
// This turns epsilon into a suggested size for each block.
size_t calculate_nMembers(double epsilon) {
  return (size_t) ((1.0 / epsilon) + 1);
}

// This turns maxN into the number of levels needed. It's ceiling(log2(maxN)).
size_t calculate_nLevels(size_t maxN) {
  size_t nLevels = 1;
  while((maxN = (maxN >> 1))) nLevels++;
  return nLevels;
}

// This returns the blocksize in bytes.
size_t blocksize(metadata_t * m) {
  return sizeof(blockdata_t) + m->nMembers * sizeof(median_data_t);
}

// This return the start of the next block given
// a pointer to a block.
blockdata_t * nextblock(blockdata_t * blk, metadata_t * m) {
  return (blockdata_t *) (blk->data + m->nMembers);
}

// This returns the size of the entire buffer.
size_t buffersize(metadata_t * m) {
  return sizeof(metadata_t) + m->nLevels * blocksize(m);
}

// This is largely so that the "output" function
// can be run without ruining the buffer.
size_t sparespace(metadata_t * m) {
  return sizeof(spare_buffer_t) + m->nLevels * m->nMembers * sizeof(sort_rec_t);
}

// Returns the first byte address which is too high to start a block regardless
// of size..  One blockdata worth less than the actual end of the buffer plus
// one.
blockdata_t * out_of_bounds(metadata_t * m) {
  return (blockdata_t *) (m->data + buffersize(m) - blocksize(m));
}

// Get the current block.
blockdata_t * get_current_block(metadata_t *m) {
  size_t offset = m->currentBufferIdx * blocksize(m);
  return (blockdata_t *)(m->data + offset);
}

// Does the current block have space?
unsigned int current_block_has_space(metadata_t* m) {
  return (get_current_block(m)->occupancy < m->nMembers);
}

// This will only be called in a safe situation. It's an internal function.
// Does not bound check!
// Do not call it unless you know what you are doing.
void insert_data_into_current_block(metadata_t *m, median_data_t data) {
  blockdata_t * b = get_current_block(m);
  b->data[b->occupancy++] = data;
}

// Check if there is space in some block and if there is, then
// make that block the current block.
unsigned int occupy_available_empty_block(metadata_t * m) {
  // Iterate over the blocks.
  for(blockdata_t * b = m->blocks; b < out_of_bounds(m); b = nextblock(b,m)) {
    if(b->occupancy < m->nMembers) {
      // Empty block found!
      m->currentBufferIdx = b->id;
      return 1;
    }
  }
  // Failed to find an empty block.
  return 0;
}

// A simple compare operator for the qsort routine.
int compare_data(const void *a, const void *b){
  median_data_t * i = (median_data_t *)a;
  median_data_t * j = (median_data_t *)b;
  return (*i < *j)?-1:+1;
}

unsigned int  merge_blocks(metadata_t *m,blockdata_t *i,blockdata_t *j, median_scratch_buffer_t spare){
  // Prepare an array for the data.
  unsigned char * d = spare->data;
  size_t datasz = m->nMembers * sizeof(median_data_t);
  if (2*datasz > spare->spareSize) {
    return 0;
  }
  bzero(d, 2*datasz);

  // This is the size of the data.
  // Copy the data to where it needs to be.
  memcpy(d, i->data, datasz);
  memcpy(d + datasz, j->data, datasz);

  // Sort it. In principle we do not need to
  // sort things, instead we should only sort
  // when level is 0 and merge otherwise.
  // For now, since most of the time, we will
  // be consuming level 0 buffers, I have left this
  // inefficiency in.
  // But we should fix it.
  qsort(d,2*m->nMembers,sizeof(median_data_t),&compare_data);
  median_data_t * sorted_data = spare->median_data;

  // Now interleave the sorted buffer.
  // We should track parity and take the
  // odd and even values alternately for each
  // merge.
  for(size_t idx = 0; idx < 2*m->nMembers; idx+=2){
    i->data[idx/2] = sorted_data[idx];
  }

  // Update the metadata. i is full, j is empty.
  // half the items are gone.
  i->level++;

  // Reset j to clean state.
  j->level = 0;
  j->occupancy = 0;
  bzero(j->data, datasz);
  return 1;
}

// Find the smallest level such that there are two blocks at the same level.
unsigned int identify_qualified_level(metadata_t *m, size_t *lvl, median_scratch_buffer_t spare) {
  // Zero out the count buffer after validating the
  // spare space buffer.
  size_t datasz = m->nLevels * sizeof(size_t);
  if (datasz > spare->spareSize) {
    return 0;
  }

  // Prepare the size array.
  size_t * levelcount = spare->sizes;
  bzero(levelcount, datasz);

  // Count up the level population.
  for(blockdata_t * b = m->blocks; b < out_of_bounds(m); b = nextblock(b,m)) {
    levelcount[b->level]++;
  }

  // Look for a level where the count is at least 2.
  for(size_t idx = 0; idx < m->nLevels; idx++) {
     if(levelcount[idx] > 1) {
       // Found one, return it.
       *lvl = idx;
       return 1;
     }
  }

  // There is no such thing.
  return 0;
}

// This identifies the pair of blocks to merge.
unsigned int identify_compatible_block_pair(metadata_t *m, blockdata_t ** i, blockdata_t ** j, median_scratch_buffer_t spare) {
  // The qualified level will reside here.
  // Find the qualified level.
  size_t qualified_level = 0;
  if (!identify_qualified_level(m,&qualified_level,spare)) {
    return 0;
  }

  // Initial values to return.
  *i = 0;
  *j = 0;

  // State machine to find the two buffers.
  // Iterate over the blocks.
  for(blockdata_t * b = m->blocks; b < out_of_bounds(m); b = nextblock(b,m)) {
    if (!(*i) && (b->level == qualified_level)) {
      *i = b; continue; // Found the first one.
    }
    if (!(*j) && (b->level == qualified_level)) {
      *j = b; return 1; // Found the second one.
    }
  }
  // Loop should not exit before the two are found.
  return 0;
}


// THis routine creates an empty block by merging two available blocks into a
// single block. Consequently this frees up one of them.
// If two compatible blocks cannot be found, then this routine returns 0.
// It also returns 0 if for some reason the two blocks cannot be merged.
unsigned int create_empty_block(metadata_t * m, median_scratch_buffer_t spare) {
  blockdata_t *i,*j;
  if(!identify_compatible_block_pair(m, &i, &j, spare)){
    return 0;
  }
  return merge_blocks(m,i,j,spare);
}

// Shift the current block. If there is an empty block, great!
// If not, then empty a block by merging two blocks and then occupy the
// freed up block.
unsigned int shift_current_block(metadata_t * m, median_scratch_buffer_t spare) {
  if(!occupy_available_empty_block(m)) {
    if(create_empty_block(m,spare)) { // Now there should be an empty block!
      if(!occupy_available_empty_block(m)) {
        return 0; // Stuck we are. Empty block is not, even though create it we did.
      }
    } else {
      return 0; // Stuck we are. Block not.
    }
  }
  return 1; // Occupy a block we did.
}


// ----------------------------------------------------------------------------
// Implementation of the interface functions (specified in median.h).
// ----------------------------------------------------------------------------

// ----------------------------------------------------------------------------
// Suggest the size of the buffer needed for a fixed epsilon and maxN.
// ----------------------------------------------------------------------------
median_error_t median_suggest_buffer_size(double epsilon, size_t maxN, size_t *suggested_size){
  // First check for sane parameters.

  // Check that maxN is not zero.
  if (maxN <= 0) return MEDIAN_ERROR_INVALID_PARAMETERS;

  // If n is too large, (i.e. epsilon is too small), you are looking for too fine an approximation.
  // This is not the right algorithm. Maybe consider random sampling instead.
  if (calculate_nMembers(epsilon) > 100000) return MEDIAN_ERROR_INVALID_PARAMETERS;

  // Calculate the required buffer size for the right nLevels and nMembers
  // value.
  metadata_t m;
  m.nLevels = calculate_nLevels(maxN);
  m.nMembers = calculate_nMembers(epsilon);

  // The size is the size of the buffer and the spare needed for merging
  // and outputing. If we have many ongoing buffers, we can do with a single
  // spare space buffer. We can figure out that optimization later.
  // Ideally, this will be done by keeping a pointer to the global spare space
  // within the metadata_t block. I prefer keeping this data structure
  // relocatable and serializable. So we may need to think about what the
  // alternatives are.
  *suggested_size = buffersize(&m);

  // Things worked. Return MEDIAN_OK
  return MEDIAN_OK;
}

// ----------------------------------------------------------------------------
// Suggest a buffer size for the scratch buffer.
// ----------------------------------------------------------------------------
median_error_t median_suggest_scratch_buffer_size(median_buffer_t m, size_t *suggested_size){
  metadata_t * md = (metadata_t *) m;
  *suggested_size = sparespace(md);
  return MEDIAN_OK;
}

// ----------------------------------------------------------------------------
// Initialize an allocated buffer.
// ----------------------------------------------------------------------------
median_error_t median_init_buffer(void * buffer, size_t buffer_size, double epsilon, size_t maxN, median_buffer_t *initialized_buffer){

  // Initialize.
  size_t expectedSize = 0;
  median_error_t error = MEDIAN_OK;

  // First run median_suggest_buffer_size
  if ((error = median_suggest_buffer_size(epsilon,maxN,&expectedSize)) != MEDIAN_OK) return error;
  // Ensure that the buffer is large enough.
  if (expectedSize > buffer_size) return MEDIAN_ERROR_BUFFER_TOO_SMALL;
  // Cast the buffer as metadata_t so that we can initialize the metadata block.
  metadata_t * m = (metadata_t *)buffer;
  // Initialize the metadata block.
  m->gid = 0;
  m->nMembers = calculate_nMembers(epsilon);
  m->nLevels = calculate_nLevels(maxN);
  m->currentBufferIdx = 0;
  // Zero all the data following the metadata block.
  // Strictly this should not be necessary, but I'm a coward!
  bzero(m->data, buffersize(m) - sizeof(metadata_t));

  // cast the data part as an array of blockdata_t fronted blocks.
  // and initialize each of the blocks.
  // Iterate over the blocks.
  for(blockdata_t * b = m->blocks; b < out_of_bounds(m); b = nextblock(b,m)) {
    b->id = (m->gid)++;
    b->level  = 0;
    b->occupancy = 0;
  }

  // Populate the return value.
  *initialized_buffer = (median_buffer_t)buffer;
  return error;
}

// ----------------------------------------------------------------------------
// Initialize the scratch buffer.
// ----------------------------------------------------------------------------
median_error_t median_init_scratch_buffer(void * buffer, size_t buffer_size, median_buffer_t m, median_scratch_buffer_t * initialized_buffer){
  median_scratch_buffer_t s = buffer;
  s->spareSize = buffer_size - sizeof(spare_buffer_t);
  *initialized_buffer = s;
  return MEDIAN_OK;
}

// ----------------------------------------------------------------------------
// Insert data into the buffer.
// We could have made this more concise and pretty if we used short-circuit
// execution of the boolean condition..
//
// if (current_block_has_space(m) || shift_current_block(m)) {
//   insert_data_into_current_block(m,data);
//   return MEDIAN_OK;
// } else {
//   return MEDIAN_ERROR_MAX_N_EXCEEDED;
// }
//
// But this code is harder to read, because of the side
// effect issue.
// ----------------------------------------------------------------------------
median_error_t median_insert_data(median_buffer_t buffer,
                                  median_data_t data,
                                  median_scratch_buffer_t scratch){
  metadata_t * m = (metadata_t *) buffer;
  // If there is space in the current block..
  if(current_block_has_space(m)) {
    // Insert data into the current block. This
    // call is to an unchecked method, which will
    // never fail.
    insert_data_into_current_block(m,data);
  } else {
    // Current block is full. So try and shift it.
    if(shift_current_block(m, scratch)) {
      // The current block has shifted successfully.
      // So we can now call the unchecked method again.
      insert_data_into_current_block(m,data);
    } else {
      // Failed to shift block. Stuck we are.
      return MEDIAN_ERROR_MAX_N_EXCEEDED;
    }
  }
  // Everything worked. So return MEDIAN_OK.
  return MEDIAN_OK;
}

// ----------------------------------------------------------------------------
// Compare two sort records.
// ----------------------------------------------------------------------------
int compare_sort_rec(const void * a, const void *b) {
  return ((sort_rec_t *)a)->d < ((sort_rec_t*)b)->d?-1:1;
}

// ----------------------------------------------------------------------------
// Output the estimated median.
// ----------------------------------------------------------------------------
median_error_t median_output_median(const median_buffer_t buffer,
                                    median_data_t *approximate_median,
                                    median_scratch_buffer_t scratch){
  // Initialize the data buffer to zero.
  metadata_t * m = (metadata_t *) buffer;
  size_t datasz = m->nMembers * m->nLevels * sizeof(sort_rec_t);
  if(datasz > scratch->spareSize) {
    return MEDIAN_ERROR_BUFFER_TOO_SMALL;
  }
  sort_rec_t * s = (sort_rec_t *) scratch->data;
  bzero(s, datasz);
  // Initialize the count and weight values.
  size_t count = 0;
  size_t weight = 0;
  // First construct the sort buffer.
  for(blockdata_t * b = m->blocks; b < out_of_bounds(m); b = nextblock(b,m)) {
    for(size_t i = 0; i < b->occupancy; i++) {
      s->d = b->data[i];
      s->sz = (1 << b->level);
      weight += s->sz;
      s++; count++;
    }
  }
  qsort(scratch->data,count,sizeof(sort_rec_t),&compare_sort_rec);

  // This is the weight at which the median will be found.
  weight = weight/2;

  // We now need to pick out the
  // median.
  for(s = (sort_rec_t *) scratch->data;
      weight > s->sz;
      weight -= (s++)->sz) ;

  *approximate_median = s->d;
  return MEDIAN_OK;
}

// ----------------------------------------------------------------------------
// Dump the state to stderr.
// ----------------------------------------------------------------------------
median_error_t median_dump_stderr(const median_buffer_t buffer){
  // First print out all the metadata.
  metadata_t * m = (metadata_t *) buffer;
  blockdata_t * current = get_current_block(m);
  fprintf(stderr, "Metadata:\n Next GID:%d\n nMembers:%d\n nLevels:%d\n CurrentBlock:%d\n",m->gid,(unsigned)m->nMembers,(unsigned)m->nLevels, current->id);

  for(blockdata_t * b = m->blocks; b < out_of_bounds(m); b = nextblock(b,m)) {
  // Now dump the blocks.
    fprintf(stderr, "Block:%d\n Level:%d\n Occupancy:%d\n", b->id,(unsigned)b->level,(unsigned)b->occupancy);
    // For every block, dump the first 8 keys in the block.
    stderr_hexdmp("Data:",(unsigned char *)(b->data),8*sizeof(median_data_t));
  }

  // Done, return MEDIAN_OK.
  return MEDIAN_OK;
}
// ----------------------------------------------------------------------------