Lucky Code

Your code is fast - if you’re lucky

Recently, while I was working on an optimized Quicksort implementation, I came across a rather interesting quirk. Modern compilers (especially Clang) optimize loops using fast, branch-free instructions - provided you use the right programming style.

sort.h - a quicksort with sorting networks

// SPDX-License-Identifier: MIT // sort.h - Branchless Quicksort // (c) christof.kaser@gmail.com

#ifndef SORT_H #define SORT_H

#ifndef BLQS_CMP #define BLQS_CMP(a, b) ((a) < (b)) #endif

#include <stddef.h> #include <string.h> #define min(a, b) (((a) < (b)) ? (a) : (b))

#define SMALLPART 1024 #define SWSZ 512 #define UNROLL 16

#define sort2(a, b) do { \ unsigned m = BLQS_CMP(a, b); \ BLQS_TYPE x = a; \ a = m ? a : b; \ b = m ? b : x; \ } while(0)

#define sort3(a, b, c) do { \ sort2(a, b); sort2(b, c); sort2(a, b); \ } while(0)

#define sort4(a, b, c, d) do { \ sort2(a, b); sort2(c, d); sort2(a, c); \ sort2(b, d); sort2(b, c); \ } while(0)

#define sort5(a, b, c, d, e) do { \ sort2(b, c); sort2(d, e); sort2(b, d); \ sort2(a, c); sort2(a, d); sort2(c, e); \ sort2(a, b); sort2(c, d); sort2(b, c); \ } while(0)

#define sort6(a, b, c, d, e, f) do { \

sort2(a, b); sort2(c, d); sort2(e, f); \ sort2(a, c); sort2(b, d); sort2(e, f); \ sort2(a, e); sort2(b, f); sort2(c, e); \ sort2(d, f); sort2(b, c); sort2(d, e); \ sort2(c, d); \ } while(0)

#define sort7(a, b, c, d, e, f, g) do { \ sort2(a, b); sort2(c, d); sort2(a, c); \ sort2(b, d); sort2(b, c); sort2(e, f); \ sort2(e, g); sort2(f, g); sort2(a, e); \ sort2(b, f); sort2(c, g); sort2(b, e); \ sort2(d, g); sort2(c, e); sort2(b, c); \ sort2(d, f); sort2(d, e); \ } while(0)

#define sort8(a,b,c,d,e,f,g,h) do { \ sort2(a,b); sort2(c,d); sort2(e,f); sort2(g,h); \ sort2(a,c); sort2(b,d); sort2(e,g); sort2(f,h); \ sort2(b,c); sort2(f,g); \ sort2(a,e); sort2(b,f); sort2(c,g); sort2(d,h); \ sort2(c,e); sort2(d,f); \ sort2(b,c); sort2(d,e); sort2(f,g); \ } while (0)

#define sort9(a,b,c,d,e,f,g,h,i) do { \ sort2(a,d); sort2(b,h); sort2(c,f); sort2(e,i); \ sort2(a,h); sort2(c,e); sort2(d,i); sort2(f,g); \ sort2(a,c); sort2(b,d); sort2(e,f); sort2(h,i); \ sort2(b,e); sort2(d,g); sort2(f,h); \ sort2(a,b); sort2(c,e); sort2(d,f); sort2(g,i); \ sort2(c,d);

sort2(e,f); sort2(g,h); \ sort2(b,c); sort2(d,e); sort2(f,g); \ } while (0)

#define sort10(a,b,c,d,e,f,g,h,i,j) do { \ sort2(a,i); sort2(b,j); sort2(c,h); sort2(d,f); sort2(e,g); \ sort2(a,c); sort2(b,e); sort2(f,i); sort2(h,j); \ sort2(a,d); sort2(c,e); sort2(f,h); sort2(g,j); \ sort2(a,b); sort2(d,g); sort2(i,j); \ sort2(b,f); sort2(c,d); sort2(e,i); sort2(g,h); \ sort2(b,c); sort2(d,f); sort2(e,g); sort2(h,i); \ sort2(c,d); sort2(e,f); sort2(g,h); \ sort2(d,e); sort2(f,g); \ } while (0)

#define sort11(a,b,c,d,e,f,g,h,i,j,k) do { \ sort2(a,j); sort2(b,g); sort2(c,e); sort2(d,h); sort2(f,i); \ sort2(a,b); sort2(d,f); sort2(e,k); sort2(g,j); sort2(h,i); \ sort2(b,d); sort2(c,f); sort2(e,h); sort2(i,k); \ sort2(a,e); sort2(b,c); sort2(d,h); sort2(f,j); sort2(g,i); \ sort2(a,b); sort2(c,g); sort2(e,f); sort2(h,i); sort2(j,k); \ sort2(c,e); sort2(d,g); sort2(f,h); sort2(i,j); \ sort2(b,c); sort2(d,e); sort2(f,g); sort2(h,i); \ sort2(c,d); sort2(e,f); sort2(g,h); \ } while (0)

#define sort12(a,b,c,d,e,f,g,h,i,j,k,l) do { \ sort2(a,i); sort2(b,h); sort2(c,g);

sort2(d,l); sort2(e,k); sort2(f,j); \ sort2(a,c); sort2(b,e); sort2(d,f); sort2(g,i); sort2(h,k); sort2(j,l); \ sort2(a,b); sort2(c,j); sort2(e,h); sort2(f,g); sort2(k,l); \ sort2(b,d); sort2(c,h); sort2(e,j); sort2(i,k); \ sort2(a,b); sort2(c,d); sort2(e,f); sort2(g,h); sort2(i,j); sort2(k,l); \ sort2(b,c); sort2(d,f); sort2(g,i); sort2(j,k); \ sort2(c,e); sort2(d,g); sort2(f,i); sort2(h,j); \ sort2(b,c); sort2(d,e); sort2(f,g); sort2(h,i); sort2(j,k); \ } while (0)

static void sorting_network(BLQS_TYPE* l, int partszm1_min_1) { switch (partszm1_min_1) { case 0: break; case 1: sort2(l[0],l[1]); break; case 2: sort3(l[0],l[1],l[2]); break; case 3: sort4(l[0],l[1],l[2],l[3]); break; case 4: sort5(l[0],l[1],l[2],l[3],l[4]); break; case 5: sort6(l[0],l[1],l[2],l[3],l[4],l[5]); break; case 6: sort7(l[0],l[1],l[2],l[3],l[4],l[5],l[6]); break; case 7:

sort8(l[0],l[1],l[2],l[3],l[4],l[5],l[6],l[7]); break; case 8: sort9(l[0],l[1],l[2],l[3],l[4],l[5],l[6],l[7],l[8]); break; case 9: sort10(l[0],l[1],l[2],l[3],l[4],l[5],l[6],l[7],l[8],l[9]); break; case 10: sort11(l[0],l[1],l[2],l[3],l[4],l[5],l[6],l[7],l[8],l[9],l[10]); break; case 11: sort12(l[0],l[1],l[2],l[3],l[4],l[5],l[6],l[7],l[8],l[9],l[10],l[11]); break; } } #define med5(a,b,c,d,e) do { \ sort2(a,b); sort2(c,d); sort2(a,c); \ sort2(b,d); sort2(b,c); sort2(c,e); \ sort2(b,c); \ } while(0)

static BLQS_TYPE* partition_small(BLQS_TYPE* left, BLQS_TYPE* right) {

BLQS_TYPE* outerleft = left; BLQS_TYPE* pivp = left + 6;

BLQS_TYPE piv = *pivp;

BLQS_TYPE l1 = left[1],l2 = left[2]; BLQS_TYPE r1 = right[-1], r0 = *right; med5(l1, l2, piv, r1, r0); left[1] = l1; left[2] = l2; right[-1] = r1; *right = r0; left += 3; right -= 2;

*pivp

= *outerleft;

BLQS_TYPE swbuf[SMALLPART]; BLQS_TYPE* sw = swbuf; BLQS_TYPE* lwr = left;

while (right - left >= UNROLL) for (int i = UNROLL; i--;) { BLQS_TYPE x = *left++; if (BLQS_CMP(x, piv)) { *lwr = x; lwr++; } else { *sw = x; sw++; } } while (left <= right) { BLQS_TYPE x = *left++; if (BLQS_CMP(x, piv)) { *lwr = x; lwr++; } else { *sw = x; sw++; } } memcpy(lwr, swbuf, (sw - swbuf) * sizeof(BLQS_TYPE)); lwr -= 1; *outerleft = *lwr; *lwr = piv; return lwr; }

static BLQS_TYPE* partition(BLQS_TYPE* left, BLQS_TYPE* right) { BLQS_TYPE* outerleft = left; BLQS_TYPE* pivp = left + (right - left) / 2;

BLQS_TYPE piv = *pivp;

med5(left[1],left[2],left[3],left[4],left[5]); med5(left[11],left[12],left[13],left[14],left[15]); med5(pivp[-2], pivp[-1], piv, pivp[1], pivp[2]); med5(right[-14], right[-13], right[-12], right[-11], right[-10]); med5(right[-4], right[-3], right[-2], right[-1], right[0]); med5(left[3], left[13], piv, right[-12], right[-2]);

left += 1; *pivp = *outerleft;

BLQS_TYPE

swbuf[SWSZ]; BLQS_TYPE *rwr = right, *sw = swbuf; BLQS_TYPE *lwr = left;

while (UNROLL < SWSZ - (sw - swbuf) && left < right - UNROLL) { ptrdiff_t avail = min(right - left, SWSZ - (sw - swbuf)); BLQS_TYPE* endp = right - avail; while (right > endp + UNROLL) { for (int i = UNROLL; i--;) { BLQS_TYPE x = *right--; if (BLQS_CMP(x, piv)) { *sw = x; sw++; } else { *rwr = x; rwr--; } } } }

while (right - left >= UNROLL && (rwr - right > UNROLL || left - lwr > UNROLL)) {

while (rwr - right > UNROLL && right - left >= UNROLL) { for (int i = UNROLL; i--;) { BLQS_TYPE x = *left++; if (BLQS_CMP(x, piv)) { *lwr = x; lwr++; } else { *rwr = x; rwr--; } } } while (left - lwr > UNROLL && right - left >= UNROLL) { for (int i = UNROLL; i--;) { BLQS_TYPE x = *right--; if (BLQS_CMP(x, piv)) { *lwr = x; lwr++; } else { *rwr = x; rwr--; } } } } do { while (rwr > right && left <= right) { BLQS_TYPE x = *left++; if (BLQS_CMP(x, piv)) { *lwr = x; lwr++; } else { *rwr = x; rwr--; } } while (lwr < left && left <= right)

{ BLQS_TYPE x = *right--; if (BLQS_CMP(x, piv)) { *lwr = x; lwr++; } else { *rwr = x; rwr--; } } } while ((lwr < left||rwr > right) && left <= right);

while (left <= right && !BLQS_CMP(*right, piv)) { right--; rwr--; } memcpy(lwr, swbuf, (sw - swbuf) * sizeof(BLQS_TYPE)); *outerleft = *rwr; *rwr = piv; return rwr; }

static void smallsort(BLQS_TYPE* left, BLQS_TYPE* right) { while (right - left > 11) { BLQS_TYPE* mid = partition_small(left, right); smallsort(left, mid - 1); left = mid + 1; } sorting_network(left, right - left); }

static void sortr(BLQS_TYPE* left, BLQS_TYPE* right) { while (1) { ptrdiff_t partszm1 = right - left; if (partszm1 <= SMALLPART) break; BLQS_TYPE* mid = partition(left, right);

if (mid - left < partszm1 / 16) { if (mid > left) sortr(left, mid - 1); BLQS_TYPE piv = *mid; mid += 1; // collect duplicates for (BLQS_TYPE* p = mid; p <= right; p++) { if (!BLQS_CMP(piv, *p)) { BLQS_TYPE h = *mid; *mid = *p; *p = h; mid++; } } left = mid; if (right - left < SMALLPART) break; mid = partition(left, right); } if (mid -

left < right - mid) { sortr(left, mid - 1); left = mid + 1; } else { sortr(mid + 1, right); right = mid - 1; } } smallsort(left, right); }

static void sort(BLQS_TYPE* data, int len) { if (len < 2) return; sortr(data, data + len - 1); }

#endif

test.c - sorting 50 million doubles

// SPDX-License-Identifier: MIT #include <stdio.h> #include <stdlib.h> #include <time.h> #include <sys/time.h>

#define BLQS_CMP(a, b) ((a) < (b)) #define BLQS_TYPE double #include "sort.h"

#define SIZE 50000000 double data[SIZE];

double ts(void) { struct timeval tv; gettimeofday(&tv, NULL); return tv.tv_sec + tv.tv_usec / 1000000.0; }

int main() { double t0; for (int i = 0; i < SIZE; i++) data[i] = rand() / 1024.0; t0 = ts(); sort(data, SIZE); printf("Time: %.2fs\n", ts() - t0); }

On macOS/M1 (Clang, -O3):

Time: 4.39

C++ std::sort needs 1.33 seconds for this.

A few cosmetic changes

It is already micro-optimized using sorting networks and loop unrolling. Only a few cosmetic changes remain.

We rewrite this beginner‑friendly style, which explicitly shows how the pointers are moved:

if (BLQS_CMP(x, piv)) { *lwr = x; lwr++; } else { *rwr = x; rwr--; }

into a more idiomatic and compact C form:

if (BLQS_CMP(x, piv)) *lwr++ = x; else *rwr-- =