added missing headers for thiersort3
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Richard Thier
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109
thiersort3.h
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109
thiersort3.h
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#ifndef THIER_SORT3_H
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#define THIER_SORT3_H
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#include <stdint.h>
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#include "threepass_xbit.h"
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/* A non-implace tricky float-hackz based bucket sort variant. Uses threepass_xbit and removes some compies! */
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/* Float and unsigned32 reinterpreter */
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union th3_fu {
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float f;
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uint32_t u;
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};
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typedef union th3_fu th3_fu;
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/** Tells from the key which bucket it is in. */
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static inline uint32_t witch_bucket3(uint32_t key) {
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/* This is hackz to misuse int->float converter HEAVILY and IEE for bucketing */
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/* https://en.wikipedia.org/wiki/Single-precision_floating-point_format */
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/* Old Hungarian ASM trick I know from Tomcat/Abaddon mailing list and prog.hu */
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/* "A következő nagyon fontos gondolat, hogy két lebegőpontos számot, */
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/* amennyiben pozitív, "simán" is összehasonlíthatunk" */
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/* See: https://prog.hu/cikkek/100239/fpu-gems */
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/* This approach uses 12 bits from a 32 bit float to map onto a byte bucket index */
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th3_fu as;
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as.f = (float) key;
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uint32_t witch_base = (key <= 2) ? 0 : (as.u >> 23) - 128; // 0, [127..159] -> [0..31]
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// return witch_base * 8 + ((as.u >> (23 - 3)) & 7); // 0..255
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return witch_base * 128 + ((as.u >> (23 - 7)) & 127); // 0..2047
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/* Alternative (but I measure it being worse):
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return (as.u >> 23);
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*/
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}
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/**
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* Sort the array using the temporary array of the same size with fast bucket sort thiersort.
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*
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* @param arr The array to sort, will contain result afterwards
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* @param temparr The temporary array with same size
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* @param n Number of elements in arr and temparr
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* @param rstate Create with sch_rand_state rstate = schwab_rand_state(junk_uint32_t);
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*/
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static inline void thiersort3(uint32_t *arr, uint32_t *temparr, int n) {
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int bucket[4096]; /* Inclusive */
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int bucket_end[4096]; /* Not inclusive */
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/* Check if need to sort at all - needed for invariants later */
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if(n < 2) {
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return;
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}
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/* Count */
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#pragma GCC unroll 64
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for(int i = 0; i < 4096; ++i) {
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bucket[i] = 0;
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}
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#pragma GCC unroll 64
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for(int i = 0; i < n; ++i) {
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++bucket[witch_bucket3(arr[i])];
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}
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/* Prefix sum (like in Magyarsort) */
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uint32_t prev = 0;
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#pragma GCC unroll 4
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for (int i = 0; i < 4096; i++) {
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bucket[i] += prev;
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prev = bucket[i];
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}
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/* Save end-offsets */
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#pragma GCC unroll 64
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for(int i = 0; i < 4096; ++i) {
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bucket_end[i] = bucket[i];
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}
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/* arr -> temparr */
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/* Move to the buckets */
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/* Rem.: This also changes bucket[i] so they will point to bucket beginnings */
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#pragma GCC unroll 64
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for(int i = 0; i < n; ++i) {
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uint32_t num = arr[i];
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uint32_t witch = witch_bucket3(num);
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int offset = (--bucket[witch]);
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temparr[offset] = num;
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}
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/* temparr -> arr each bucket and sort them in-place */
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#pragma GCC unroll 64
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for(int b = 0; b < 4096; ++b) {
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int begin = bucket[b];
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int end = bucket_end[b];
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/* Ensure exists */
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if(begin >= end) {
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continue;
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}
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/* Use our specialized threepass */
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/* - which does not use up all the bits */
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/* - which does not allocate and copy back to arr here */
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uint32_t n = end - begin;
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uint32_t *a = &(temparr[begin]);
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uint32_t *buf = &(arr[begin]);
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threepass_xb(a, buf, n);
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}
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}
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#endif /* THIER_SORT3_H */
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136
threepass_xbit.h
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136
threepass_xbit.h
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#ifndef THREE_PASS_XB_H
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#define THREE_PASS_XB_H
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/* Basically like threepass.h but but fewer bits - only for thiersort3! */
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/* How the 28-30 bits gets separated? This is chosen because I saw that: */
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/* - in float trickery I saw at around 4 billion the buckets change around 200 million */
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/* - 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 */
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/* - This means those bits in numbers DO get used when we are running as internal sort of thier3 */
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/* - But the numbers high bits (29..32th bits) stay the same inside each bucket so we spare it! */
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/* - If you know your data does not have all the range of 32 bits you can #define these by #define CUSTOM_TPBX_BITS */
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#ifndef CUSTOM_TPBX_BITS
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#define TPBX1 10 // top
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#define TPBX2 9 // mid
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#define TPBX3 9 // bottom
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#endif /* CUSTOM_TPBX_BITS */
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static inline constexpr uint32_t min3u32_xb(uint32_t a, uint32_t b, uint32_t c) noexcept {
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return (a <= b) ?
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((a <= c) ? a : c) :
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((b <= c) ? b : c);
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}
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/**
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* Simple three-pass (ok: 3 + 1) bottom-up internal radix sort writter for thiersort3
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*
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* @param a The array to sort - will be changed too!
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* @param buf Result array with the same size - result will be here
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* @param n The number of elements
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*/
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static inline void threepass_xb(uint32_t *a, uint32_t *buf, int n) noexcept {
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assert(buf != NULL);
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constexpr int shr1 = TPBX3 + TPBX2;
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constexpr int shr2 = TPBX3;
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constexpr int shr3 = 0;
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constexpr int mask1 = (1 << TPBX1) - 1;
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constexpr int mask2 = (1 << TPBX2) - 1;
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constexpr int mask3 = (1 << TPBX3) - 1;
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/* helper buffers. */
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int sz = n * sizeof(a[0]);
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static thread_local uint32_t bucket1[1 << TPBX1];
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memset(bucket1, 0, (1 << TPBX1) * sizeof(uint32_t));
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static thread_local uint32_t bucket2[1 << TPBX2];
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memset(bucket2, 0, (1 << TPBX2) * sizeof(uint32_t));
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static thread_local uint32_t bucket3[1 << TPBX3];
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memset(bucket3, 0, (1 << TPBX3) * sizeof(uint32_t));
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/* Count occurences (can count together with good ILP) */
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#pragma GCC unroll 64
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for(uint32_t i = 0; i < n; ++i) {
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++bucket1[(a[i] >> shr1) & mask1];
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++bucket2[(a[i] >> shr2) & mask2];
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++bucket3[(a[i] >> shr3) & mask3];
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}
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/* Count prefix sums - try as much ILP as possible because bigger arrays than usual! */
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uint32_t prev1 = 0;
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uint32_t prev2 = 0;
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uint32_t prev3 = 0;
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uint32_t common = min3u32_xb(
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(1 << TPBX1),
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(1 << TPBX2),
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(1 << TPBX3)
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);
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int i = 0;
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#pragma GCC unroll 8
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for (; i < common; ++i) {
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bucket1[i] += prev1;
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prev1 = bucket1[i];
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bucket2[i] += prev2;
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prev2 = bucket2[i];
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bucket3[i] += prev3;
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prev3 = bucket3[i];
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}
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/* Do remaining 1 */
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for (int j = i; j < (1 << TPBX1); ++j) {
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bucket1[j] += prev1;
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prev1 = bucket1[j];
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}
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/* Do remaining 2 */
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for (int j = i; j< (1 << TPBX2); ++j) {
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bucket2[j] += prev2;
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prev2 = bucket2[j];
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}
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/* Do remaining 3 */
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for (int j = i; j < (1 << TPBX3); ++j) {
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bucket3[j] += prev3;
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prev3 = bucket3[j];
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}
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// Bottom digit a->buf
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// right-to-left to ensure already sorted digits order we keep for iterations
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#pragma GCC unroll 48
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for(uint32_t i = n; i > 0; --i) {
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// Prefetch caches
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//__builtin_prefetch(&a[i-8]);
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// Get num and its new offset / location
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auto num = a[i - 1];
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auto bkeyni = (num >> shr3) & mask3;
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auto offset = --bucket3[bkeyni];
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// Add to the proper target location
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buf[offset] = num;
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}
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// Mid digit buf->a
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// right-to-left to ensure already sorted digits order we keep for iterations
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#pragma GCC unroll 48
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for(uint32_t i = n; i > 0; --i) {
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// Prefetch caches
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//__builtin_prefetch(&buf[i-8]);
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// Get num and its new offset / location
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auto num = buf[i - 1];
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auto bkeyni = (num >> shr2) & mask2;
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auto offset = --bucket2[bkeyni];
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// Add to the proper target location
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a[offset] = num;
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}
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// Top digit a->buf
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// right-to-left to ensure already sorted digits order we keep for iterations
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#pragma GCC unroll 48
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for(uint32_t i = n; i > 0; --i) {
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// Prefetch caches
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// __builtin_prefetch(&a[i-16]);
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// Get num and its new offset / location
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auto num = a[i - 1];
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auto bkeyni = (num >> shr1) & mask1;
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auto offset = --bucket1[bkeyni];
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// Add to the proper target location
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buf[offset] = num;
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}
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}
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#endif /* THREE_PASS_XB_H */
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