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The next index method is index_read_idx(). It is similar to the index_read() method but is called from other portions of the optimizer (e.g., where there is at most one matching row see sql_select.cc for details). This method sets the row buffer to the row in the file that matches the key. If the key passed in is null, then the method should return the first key value and the first row in the file. Locate the index_read_idx() method and add the code to get the file position from the index and read a row from the data file. Listing 7-50 shows the method with the changes. Listing 7-50. Changes to the index_read_idx() Method in ha_spartan.cc int ha_spartan::index_read_idx(byte * buf, uint index, const byte * key, uint key_len __attribute__((unused)), enum ha_rkey_function find_flag __attribute__((unused))) { long long pos; DBUG_ENTER("ha_spartan::index_read_idx"); pos = share->index_class->get_index_pos((byte *)key, key_len); if (pos == -1) DBUG_RETURN(HA_ERR_KEY_NOT_FOUND); share->data_class->read_row(buf, table->s->rec_buff_length, pos); DBUG_RETURN(0); } The next index method is index_next(). This method gets the next key in the index and returns the matching row from the data file. It is called during range index scans. Locate the index_next() method and add the code to get the next key from the index and read a row from the data file. Listing 7-51 shows the method with the changes. Listing 7-51. Changes to the index_next() Method in ha_spartan.cc int ha_spartan::index_next(byte * buf) { byte *key = 0; long long pos; DBUG_ENTER("ha_spartan::index_next"); key = share->index_class->get_next_key(); if (key == 0) DBUG_RETURN(HA_ERR_END_OF_FILE); pos = share->index_class->get_index_pos((byte *)key, get_key_len()); share->index_class->seek_index(key, get_key_len()); share->index_class->get_next_key(); if (pos == -1) DBUG_RETURN(HA_ERR_KEY_NOT_FOUND); share->data_class->read_row(buf, table->s->rec_buff_length, pos); DBUG_RETURN(0); }

member While : (unit -> bool) * M<'T> -> M<'T> member Using : 'T * ('T -> M<'T>) -> M<'T> when 'T :> IDisposable member Combine : M<'T> * M<'T> -> M<'T>

> bddBuilderEquiv (nBitCarryRippleAdder 8 (vec 8 "x") (vec 8 "y") (vec 8 "sum") (vec 9 "carry")) (nBitCarryRippleAdder 8 (vec 8 "y") (vec 8 "x") (vec 8 "sum") (vec 9 "carry"));; val it : bool = true Thirty-three variables are involved in this circuit A naive exploration of this space would involve searching a truth table of more than eight billion entries The BDD implementation takes moments on any modern computer Efficient symbolic representations pay off! A more substantial verification problem involves checking the equivalence of circuits that have substantial structural differences To explore this, let s take a different implementation of addition called a carry select adder.

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The next index method is also one of the range queries. The index_prev() method gets the previous key in the index and returns the matching row from the data file. It is called during range index scans. Locate the index_prev() method and add the code to get the previous key from the index and read a row from the data file. Listing 7-52 shows the method with the changes. Listing 7-52. Changes to the index_prev() Method in ha_spartan.cc int ha_spartan::index_prev(byte * buf) { byte *key = 0; long long pos; DBUG_ENTER("ha_spartan::index_prev"); key = share->index_class->get_prev_key(); if (key == 0) DBUG_RETURN(HA_ERR_END_OF_FILE); pos = share->index_class->get_index_pos((byte *)key, get_key_len()); share->index_class->seek_index(key, get_key_len()); share->index_class->get_prev_key(); if (pos == -1) DBUG_RETURN(HA_ERR_KEY_NOT_FOUND); share->data_class->read_row(buf, table->s->rec_buff_length, pos); DBUG_RETURN(0); } Notice that I had to move the index pointers around a bit to get the code for the next and previous to work. Range queries generate two calls to the index class the first time it is used: the first one gets the first key (index_read), and then the second calls the next key (index_next). Subsequent index calls are made to index_next(). Therefore, I must call the Spartan_index class method get_prev_key() to reset the keys correctly. This would be another great opportunity to rework the index class to work better with range queries in MySQL. The next index method is also one of the range queries. The index_first() method gets the first key in the index and returns it. Locate the index_first() method and add the code to get the first key from the index and return the key. Listing 7-53 shows the method with the changes. Listing 7-53. Changes to the index_first() Method in ha_spartan.cc int ha_spartan::index_first(byte * buf) { byte *key = 0; DBUG_ENTER("ha_spartan::index_first"); key = share->index_class->get_first_key(); if (key == 0) DBUG_RETURN(HA_ERR_END_OF_FILE); memcpy(buf, key, get_key_len()); DBUG_RETURN(0); }

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