magyarsort/threepass_xbit.h

#ifndef THREE_PASS_XB_H
#define THREE_PASS_XB_H
/* Basically like threepass.h but but fewer bits - only for thiersort3! */

/* How the 28-30 bits gets separated? This is chosen because I saw that: */
/* - in float trickery I saw at around 4 billion the buckets change around 200 million */
/* - Which is smaller than 1/2 or 1/4 or 1/8 or 1/16 of it because 16*200 mil = 3.2 bill 28 bit is needed */
/* - This means those bits in numbers DO get used when we are running as internal sort of thier3 */
/* - But the numbers high bits (29..32th bits) stay the same inside each bucket so we spare it! */
/* - If you know your data does not have all the range of 32 bits you can #define these by #define CUSTOM_TPBX_BITS */
#ifndef CUSTOM_TPBX_BITS
#define TPBX1 10 // top
#define TPBX2 9 // mid
#define TPBX3 9 // bottom
#endif /* CUSTOM_TPBX_BITS */

static inline constexpr uint32_t min3u32_xb(uint32_t a, uint32_t b, uint32_t c) noexcept {
	return (a <= b) ?
		((a <= c) ? a : c) :
		((b <= c) ? b : c);
}

/**
 * Simple three-pass (ok: 3 + 1) bottom-up internal radix sort writter for thiersort3
 *
 * @param a The array to sort - will be changed too!
 * @param buf Result array with the same size - result will be here
 * @param n The number of elements
 */
static inline void threepass_xb(uint32_t *a, uint32_t *buf, int n) noexcept {
	assert(buf != NULL);
	constexpr int shr1 = TPBX3 + TPBX2;
	constexpr int shr2 = TPBX3;
	constexpr int shr3 = 0;
	constexpr int mask1 = (1 << TPBX1) - 1;
	constexpr int mask2 = (1 << TPBX2) - 1;
	constexpr int mask3 = (1 << TPBX3) - 1;

	/* helper buffers. */
	int sz = n * sizeof(a[0]);

	static thread_local uint32_t bucket1[1 << TPBX1];
	memset(bucket1, 0, (1 << TPBX1) * sizeof(uint32_t));
	static thread_local uint32_t bucket2[1 << TPBX2];
	memset(bucket2, 0, (1 << TPBX2) * sizeof(uint32_t));
	static thread_local uint32_t bucket3[1 << TPBX3];
	memset(bucket3, 0, (1 << TPBX3) * sizeof(uint32_t));

	/* Count occurences (can count together with good ILP) */
	#pragma GCC unroll 64
	for(uint32_t i = 0; i < n; ++i) {
		++bucket1[(a[i] >> shr1) & mask1];
		++bucket2[(a[i] >> shr2) & mask2];
		++bucket3[(a[i] >> shr3) & mask3];
	}

	/* Count prefix sums - try as much ILP as possible because bigger arrays than usual! */
	int prev1 = -1;
	int prev2 = -1;
	int prev3 = -1;
	uint32_t common = min3u32_xb(
		(1 << TPBX1),
		(1 << TPBX2),
		(1 << TPBX3)
	);
	int i = 0;
	#pragma GCC unroll 8
	for (; i < common; ++i) {
		bucket1[i] += prev1;
		prev1 = bucket1[i];
		bucket2[i] += prev2;
		prev2 = bucket2[i];
		bucket3[i] += prev3;
		prev3 = bucket3[i];
	}
	/* Do remaining 1 */
	for (int j = i; j < (1 << TPBX1); ++j) {
		bucket1[j] += prev1;
		prev1 = bucket1[j];
	}
	/* Do remaining 2 */
	for (int j = i; j< (1 << TPBX2); ++j) {
		bucket2[j] += prev2;
		prev2 = bucket2[j];
	}
	/* Do remaining 3 */
	for (int j = i; j < (1 << TPBX3); ++j) {
		bucket3[j] += prev3;
		prev3 = bucket3[j];
	}

	/* Move elements (the 3 pass): This utilizes frewr trick to overwrite keys (elements) by ror-ing them */
	/* This rewrites the key into its rotated state to save some pipeline stalls. (3 rotates happen and in the end its ok) */
	/* right-to-left to ensure already sorted digits order we keep for iterations */

	/* Bottom digit a->buf */
	#pragma GCC unroll 64
	for(int i = n - 1; i >= 0; --i) {
		uint32_t num = a[i];
		/* save rotated into the masked, bucketed loc */
		buf[bucket3[num & mask3]--] = (num >> TPBX3) | (num << (32 - TPBX3));
		//__builtin_prefetch(&buf[bucket3[num & mask3] - 2]);
	}

	/* Mid digit buf->a */
	#pragma GCC unroll 64
	for(int i = n - 1; i >= 0; --i) {
		uint32_t num = buf[i];
		/* save rotated into the masked, bucketed loc */
		a[bucket2[num & mask2]--] = (num >> TPBX2) | (num << (32 - TPBX2));
		//__builtin_prefetch(&a[bucket2[num & mask2] - 2]);
	}

	/* Top digit a->buf */
	#pragma GCC unroll 64
	for(int i = n - 1; i >= 0; --i) {
		uint32_t num = a[i];
		/* Reconstruct the original key in this element by where its stuff is stored */
		constexpr int rot = TPBX1 + (32 - TPBX1 - TPBX2 - TPBX3);
		/* save rotated into the masked, bucketed loc */
		buf[bucket1[num & mask1]--] = (num >> rot) | (num << (32 - rot));
		//__builtin_prefetch(&buf[bucket1[num & mask1] - 2]);
	}
}

#endif /* THREE_PASS_XB_H */