/*		 
 * Sux: Succinct data structures
 *
 * Copyright (C) 2007-2013 Sebastiano Vigna 
 *
 *  This library is free software; you can redistribute it and/or modify it
 *  under the terms of the GNU Lesser General Public License as published by the Free
 *  Software Foundation; either version 3 of the License, or (at your option)
 *  any later version.
 *
 *  This library is distributed in the hope that it will be useful, but
 *  WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
 *  or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public License
 *  for more details.
 *
 *  You should have received a copy of the GNU Lesser General Public License
 *  along with this program; if not, see <http://www.gnu.org/licenses/>.
 *
 */

#ifndef select_h
#define select_h
#include <stdint.h>
#include "macros.hpp"


const unsigned char select_in_byte[2048] = {
	8, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 5, 0, 1, 0, 2, 0, 1,
	0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 6, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0,
	1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2,
	0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 7, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0,
	2, 0, 1, 0, 5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 6, 0, 1,
	0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 5, 0, 1, 0, 2, 0, 1, 0, 3, 0,
	1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 8, 8, 8, 1, 8, 2, 2, 1, 8, 3, 3, 1, 3, 2, 2, 1, 8,
	4, 4, 1, 4, 2, 2, 1, 4, 3, 3, 1, 3, 2, 2, 1, 8, 5, 5, 1, 5, 2, 2, 1, 5, 3, 3, 1, 3, 2, 2, 1, 5, 4, 4, 1, 4, 2, 2, 1,
	4, 3, 3, 1, 3, 2, 2, 1, 8, 6, 6, 1, 6, 2, 2, 1, 6, 3, 3, 1, 3, 2, 2, 1, 6, 4, 4, 1, 4, 2, 2, 1, 4, 3, 3, 1, 3, 2, 2,
	1, 6, 5, 5, 1, 5, 2, 2, 1, 5, 3, 3, 1, 3, 2, 2, 1, 5, 4, 4, 1, 4, 2, 2, 1, 4, 3, 3, 1, 3, 2, 2, 1, 8, 7, 7, 1, 7, 2,
	2, 1, 7, 3, 3, 1, 3, 2, 2, 1, 7, 4, 4, 1, 4, 2, 2, 1, 4, 3, 3, 1, 3, 2, 2, 1, 7, 5, 5, 1, 5, 2, 2, 1, 5, 3, 3, 1, 3,
	2, 2, 1, 5, 4, 4, 1, 4, 2, 2, 1, 4, 3, 3, 1, 3, 2, 2, 1, 7, 6, 6, 1, 6, 2, 2, 1, 6, 3, 3, 1, 3, 2, 2, 1, 6, 4, 4, 1,
	4, 2, 2, 1, 4, 3, 3, 1, 3, 2, 2, 1, 6, 5, 5, 1, 5, 2, 2, 1, 5, 3, 3, 1, 3, 2, 2, 1, 5, 4, 4, 1, 4, 2, 2, 1, 4, 3, 3,
	1, 3, 2, 2, 1, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 3, 8, 3, 3, 2, 8, 8, 8, 4, 8, 4, 4, 2, 8, 4, 4, 3, 4, 3, 3, 2, 8, 8,
	8, 5, 8, 5, 5, 2, 8, 5, 5, 3, 5, 3, 3, 2, 8, 5, 5, 4, 5, 4, 4, 2, 5, 4, 4, 3, 4, 3, 3, 2, 8, 8, 8, 6, 8, 6, 6, 2, 8,
	6, 6, 3, 6, 3, 3, 2, 8, 6, 6, 4, 6, 4, 4, 2, 6, 4, 4, 3, 4, 3, 3, 2, 8, 6, 6, 5, 6, 5, 5, 2, 6, 5, 5, 3, 5, 3, 3, 2,
	6, 5, 5, 4, 5, 4, 4, 2, 5, 4, 4, 3, 4, 3, 3, 2, 8, 8, 8, 7, 8, 7, 7, 2, 8, 7, 7, 3, 7, 3, 3, 2, 8, 7, 7, 4, 7, 4, 4,
	2, 7, 4, 4, 3, 4, 3, 3, 2, 8, 7, 7, 5, 7, 5, 5, 2, 7, 5, 5, 3, 5, 3, 3, 2, 7, 5, 5, 4, 5, 4, 4, 2, 5, 4, 4, 3, 4, 3,
	3, 2, 8, 7, 7, 6, 7, 6, 6, 2, 7, 6, 6, 3, 6, 3, 3, 2, 7, 6, 6, 4, 6, 4, 4, 2, 6, 4, 4, 3, 4, 3, 3, 2, 7, 6, 6, 5, 6,
	5, 5, 2, 6, 5, 5, 3, 5, 3, 3, 2, 6, 5, 5, 4, 5, 4, 4, 2, 5, 4, 4, 3, 4, 3, 3, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
	8, 8, 8, 3, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 4, 8, 4, 4, 3, 8, 8, 8, 8, 8, 8, 8, 5, 8, 8, 8, 5, 8, 5, 5, 3, 8, 8, 8,
	5, 8, 5, 5, 4, 8, 5, 5, 4, 5, 4, 4, 3, 8, 8, 8, 8, 8, 8, 8, 6, 8, 8, 8, 6, 8, 6, 6, 3, 8, 8, 8, 6, 8, 6, 6, 4, 8, 6,
	6, 4, 6, 4, 4, 3, 8, 8, 8, 6, 8, 6, 6, 5, 8, 6, 6, 5, 6, 5, 5, 3, 8, 6, 6, 5, 6, 5, 5, 4, 6, 5, 5, 4, 5, 4, 4, 3, 8,
	8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 7, 8, 7, 7, 3, 8, 8, 8, 7, 8, 7, 7, 4, 8, 7, 7, 4, 7, 4, 4, 3, 8, 8, 8, 7, 8, 7, 7, 5,
	8, 7, 7, 5, 7, 5, 5, 3, 8, 7, 7, 5, 7, 5, 5, 4, 7, 5, 5, 4, 5, 4, 4, 3, 8, 8, 8, 7, 8, 7, 7, 6, 8, 7, 7, 6, 7, 6, 6,
	3, 8, 7, 7, 6, 7, 6, 6, 4, 7, 6, 6, 4, 6, 4, 4, 3, 8, 7, 7, 6, 7, 6, 6, 5, 7, 6, 6, 5, 6, 5, 5, 3, 7, 6, 6, 5, 6, 5,
	5, 4, 6, 5, 5, 4, 5, 4, 4, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
	8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 8, 8, 8, 8, 8, 8, 8, 5, 8, 8, 8, 5, 8, 5, 5, 4, 8, 8, 8, 8,
	8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 8, 8, 8, 8, 8, 8, 8, 6, 8, 8, 8, 6, 8, 6, 6, 4, 8, 8, 8, 8, 8, 8, 8, 6, 8, 8, 8,
	6, 8, 6, 6, 5, 8, 8, 8, 6, 8, 6, 6, 5, 8, 6, 6, 5, 6, 5, 5, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8,
	8, 8, 8, 8, 8, 7, 8, 8, 8, 7, 8, 7, 7, 4, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 7, 8, 7, 7, 5, 8, 8, 8, 7, 8, 7, 7, 5, 8,
	7, 7, 5, 7, 5, 5, 4, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 7, 8, 7, 7, 6, 8, 8, 8, 7, 8, 7, 7, 6, 8, 7, 7, 6, 7, 6, 6, 4,
	8, 8, 8, 7, 8, 7, 7, 6, 8, 7, 7, 6, 7, 6, 6, 5, 8, 7, 7, 6, 7, 6, 6, 5, 7, 6, 6, 5, 6, 5, 5, 4, 8, 8, 8, 8, 8, 8, 8,
	8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
	8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
	8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 8, 8, 8, 8, 8, 8, 8, 6, 8, 8, 8, 6,
	8, 6, 6, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8,
	8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 7, 8, 7, 7, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
	8, 8, 8, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 7, 8, 7, 7, 6, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 7, 8, 7, 7, 6, 8,
	8, 8, 7, 8, 7, 7, 6, 8, 7, 7, 6, 7, 6, 6, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
	8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
	8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
	8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
	8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
	8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
	8, 8, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 7, 8, 7, 7, 6, 8, 8,
	8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
	8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
	8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
	8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
	8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
	8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
	8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7
};

const uint64_t overflow[] = {
	0x7f7f7f7f7f7f7f7fULL,
	0x7e7e7e7e7e7e7e7eULL,
	0x7d7d7d7d7d7d7d7dULL,
	0x7c7c7c7c7c7c7c7cULL,
	0x7b7b7b7b7b7b7b7bULL,
	0x7a7a7a7a7a7a7a7aULL,
	0x7979797979797979ULL,
	0x7878787878787878ULL,
	0x7777777777777777ULL,
	0x7676767676767676ULL,
	0x7575757575757575ULL,
	0x7474747474747474ULL,
	0x7373737373737373ULL,
	0x7272727272727272ULL,
	0x7171717171717171ULL,
	0x7070707070707070ULL,
	0x6f6f6f6f6f6f6f6fULL,
	0x6e6e6e6e6e6e6e6eULL,
	0x6d6d6d6d6d6d6d6dULL,
	0x6c6c6c6c6c6c6c6cULL,
	0x6b6b6b6b6b6b6b6bULL,
	0x6a6a6a6a6a6a6a6aULL,
	0x6969696969696969ULL,
	0x6868686868686868ULL,
	0x6767676767676767ULL,
	0x6666666666666666ULL,
	0x6565656565656565ULL,
	0x6464646464646464ULL,
	0x6363636363636363ULL,
	0x6262626262626262ULL,
	0x6161616161616161ULL,
	0x6060606060606060ULL,
	0x5f5f5f5f5f5f5f5fULL,
	0x5e5e5e5e5e5e5e5eULL,
	0x5d5d5d5d5d5d5d5dULL,
	0x5c5c5c5c5c5c5c5cULL,
	0x5b5b5b5b5b5b5b5bULL,
	0x5a5a5a5a5a5a5a5aULL,
	0x5959595959595959ULL,
	0x5858585858585858ULL,
	0x5757575757575757ULL,
	0x5656565656565656ULL,
	0x5555555555555555ULL,
	0x5454545454545454ULL,
	0x5353535353535353ULL,
	0x5252525252525252ULL,
	0x5151515151515151ULL,
	0x5050505050505050ULL,
	0x4f4f4f4f4f4f4f4fULL,
	0x4e4e4e4e4e4e4e4eULL,
	0x4d4d4d4d4d4d4d4dULL,
	0x4c4c4c4c4c4c4c4cULL,
	0x4b4b4b4b4b4b4b4bULL,
	0x4a4a4a4a4a4a4a4aULL,
	0x4949494949494949ULL,
	0x4848484848484848ULL,
	0x4747474747474747ULL,
	0x4646464646464646ULL,
	0x4545454545454545ULL,
	0x4444444444444444ULL,
	0x4343434343434343ULL,
	0x4242424242424242ULL,
	0x4141414141414141ULL,
	0x4040404040404040ULL
};

// A slightly faster version of Gog & Petri's select.

__inline int select_in_word( const uint64_t x, const int k ) {
	// Phase 1: sums by byte
	uint64_t byte_sums = x - ( x >> 1 & 0x5ULL * ONES_STEP_4 );
	byte_sums = ( byte_sums & 3ULL * ONES_STEP_4 ) + ( ( byte_sums >> 2 ) & 3ULL * ONES_STEP_4 );
	byte_sums = ( byte_sums + ( byte_sums >> 4 ) ) & 0x0fULL * ONES_STEP_8;
	byte_sums *= ONES_STEP_8;

	// Phase 2: compare each byte sum with k
	const uint64_t k_step_8 = k * ONES_STEP_8;
	// Giuseppe Ottaviano's improvement
	const int place = __builtin_popcountll( EASY_LEQ_STEP_8_MSBS( byte_sums, k_step_8 ) ) * 8;

	// Phase 3: Locate the relevant byte and look up the result in select_in_byte
	return place + select_in_byte[ ( x >> place & 0xFFULL) | ( k - ( ( byte_sums << 8 ) >> place & 0xFFULL ) ) << 8 ];
}
#endif