magyarsort/thiersort3.h

#ifndef THIER_SORT3_H
#define THIER_SORT3_H
#include <stdint.h>
#include "threepass_xbit.h"
/* A non-implace tricky float-hackz based bucket sort variant. Uses threepass_xbit and removes some compies! */

/* Float and unsigned32 reinterpreter */
union th3_fu {
	float f;
	uint32_t u;
};
typedef union th3_fu th3_fu;

/** Tells from the key which bucket it is in. */
static inline uint32_t witch_bucket3(uint32_t key) {
	/* This is hackz to misuse int->float converter HEAVILY and IEE for bucketing */
	/* https://en.wikipedia.org/wiki/Single-precision_floating-point_format */

	/* Old Hungarian ASM trick I know from Tomcat/Abaddon mailing list and prog.hu */
	/* "A következő nagyon fontos gondolat, hogy két lebegőpontos számot, */
	/* amennyiben pozitív, "simán" is összehasonlíthatunk" */
	/* See: https://prog.hu/cikkek/100239/fpu-gems */

	/* This approach uses 12 bits from a 32 bit float to map onto a byte bucket index */
	th3_fu as;
	as.f = (float) key;

	uint32_t witch_base = (key <= 2) ? 0 : (as.u >> 23) - 128; // 0, [127..159] -> [0..31]
	// return witch_base * 8 + ((as.u >> (23 - 3)) & 7); // 0..255
	return witch_base * 128 + ((as.u >> (23 - 7)) & 127); // 0..2047
	/* Alternative (but I measure it being worse):
	return (as.u >> 23);
	*/
}

/**
 * Sort the array using the temporary array of the same size with fast bucket sort thiersort.
 *
 * @param arr The array to sort, will contain result afterwards
 * @param temparr The temporary array with same size
 * @param n Number of elements in arr and temparr
 * @param rstate Create with sch_rand_state rstate = schwab_rand_state(junk_uint32_t);
 */
static inline void thiersort3(uint32_t *arr, uint32_t *temparr, int n) {
	int bucket[4096]; /* Inclusive */
	int bucket_end[4096]; /* Not inclusive */

	/* Check if need to sort at all - needed for invariants later */
	if(n < 2) {
		return;
	}

	/* Count */
	#pragma GCC unroll 64
	for(int i = 0; i < 4096; ++i) {
		bucket[i] = 0;
	}
	#pragma GCC unroll 64
	for(int i = 0; i < n; ++i) {
		++bucket[witch_bucket3(arr[i])];
	}

	/* Prefix sum (like in Magyarsort) */
	uint32_t prev = 0;
	#pragma GCC unroll 4
	for (int i = 0; i < 4096; i++) {
		bucket[i] += prev;
		prev = bucket[i];
	}

	/* Save end-offsets */
	#pragma GCC unroll 64
	for(int i = 0; i < 4096; ++i) {
		bucket_end[i] = bucket[i];
	}

	/* arr -> temparr */
	/* Move to the buckets */
	/* Rem.: This also changes bucket[i] so they will point to bucket beginnings */
	#pragma GCC unroll 64
	for(int i = 0; i < n; ++i) {
		uint32_t num = arr[i];
		uint32_t witch = witch_bucket3(num);
		int offset = (--bucket[witch]);
		temparr[offset] = num;
	}

	/* temparr -> arr each bucket and sort them in-place */
	#pragma GCC unroll 64
	for(int b = 0; b < 4096; ++b) {
		int begin = bucket[b];
		int end = bucket_end[b];

		/* Ensure exists */
		if(begin >= end) {
			continue;
		}

		/* Use our specialized threepass */
		/* - which does not use up all the bits */
		/* - which does not allocate and copy back to arr here */
		uint32_t n = end - begin;
		uint32_t *a = &(temparr[begin]);
		uint32_t *buf = &(arr[begin]);
		threepass_xb(a, buf, n);
	}
}

#endif /* THIER_SORT3_H */