Additional benchmarks based on https://github.com/lemire/Code-used-on-Daniel-Lemire-s-blog/blob/master/2016/06/25/fastrange.c

main.c

/**
* Demonstrates how can map a 32-bit integer to a range faster than
* a modulo reduction.
* Assumes x64 processor.
* gcc -O3 -o fastrange fastrange.c
*/
#include <stdint.h>
#include <stdlib.h>
#include <stdio.h>

#define RDTSC_START(cycles)                                                   \
    do {                                                                      \
        register unsigned cyc_high, cyc_low;                                  \
        __asm volatile(                                                       \
            "cpuid\n\t"                                                       \
            "rdtsc\n\t"                                                       \
            "mov %%edx, %0\n\t"                                               \
            "mov %%eax, %1\n\t"                                               \
            : "=r"(cyc_high), "=r"(cyc_low)::"%rax", "%rbx", "%rcx", "%rdx"); \
        (cycles) = ((uint64_t)cyc_high << 32) | cyc_low;                      \
    } while (0)

#define RDTSC_FINAL(cycles)                                                   \
    do {                                                                      \
        register unsigned cyc_high, cyc_low;                                  \
        __asm volatile(                                                       \
            "rdtscp\n\t"                                                      \
            "mov %%edx, %0\n\t"                                               \
            "mov %%eax, %1\n\t"                                               \
            "cpuid\n\t"                                                       \
            : "=r"(cyc_high), "=r"(cyc_low)::"%rax", "%rbx", "%rcx", "%rdx"); \
        (cycles) = ((uint64_t)cyc_high << 32) | cyc_low;                      \
    } while (0)

/*
 * Prints the best number of operations per cycle where
 * test is the function call, answer is the expected answer generated by
 * test, repeat is the number of times we should repeat and size is the
 * number of operations represented by test.
 */
#define BEST_TIME(test, answer, repeat, size)                         \
    do {                                                              \
        printf("%s: ", #test);                                        \
        fflush(NULL);                                                 \
        uint64_t cycles_start, cycles_final, cycles_diff;             \
        uint64_t min_diff = (uint64_t)-1;                             \
        int wrong_answer = 0;                                         \
        for (int i = 0; i < repeat; i++) {                            \
            __asm volatile("" ::: /* pretend to clobber */ "memory"); \
            RDTSC_START(cycles_start);                                \
            if (test != answer) wrong_answer = 1;                     \
            RDTSC_FINAL(cycles_final);                                \
            cycles_diff = (cycles_final - cycles_start);              \
            if (cycles_diff < min_diff) min_diff = cycles_diff;       \
        }                                                             \
        uint64_t S = (uint64_t)size;                                  \
        float cycle_per_op = (min_diff) / (float)S;                   \
        printf(" %.2f cycles per operation", cycle_per_op);           \
        if (wrong_answer) printf(" [ERROR]");                         \
        printf("\n");                                                 \
        fflush(NULL);                                                 \
    } while (0)

#define MODSUM_OPT(N)                      \
	uint32_t modsum_##N (uint32_t *z, uint32_t n, uint32_t *accesses, uint32_t nmbr) { \
		uint32_t sum = 0; \
		for (uint32_t j = 0; j < nmbr; ++j) { \
			sum += z[accesses[j] % (1 << N)]; \
		} \
		return sum; \
	}

MODSUM_OPT(24)
MODSUM_OPT(16)
MODSUM_OPT(8)

uint32_t modsum(uint32_t * z, uint32_t N, uint32_t * accesses, uint32_t nmbr) {
  uint32_t sum = 0;
  for(uint32_t j = 0; j < nmbr ; ++j ) {
    sum += z[accesses[j] % N];
  }
  return sum;
}

uint32_t fastsum(uint32_t * z, uint32_t N, uint32_t * accesses, uint32_t nmbr) {
  uint32_t sum = 0;
  uint64_t N64 = (uint64_t) N;
  for(uint32_t j = 0; j < nmbr ; ++j ) {
    sum += z[(accesses[j] * N64)>> 32] ;
  }
  return sum;
}

// N is a power of two
uint32_t maskedsum(uint32_t * z, uint32_t N, uint32_t * accesses, uint32_t nmbr) {
  uint32_t sum = 0;
  for(uint32_t j = 0; j < nmbr ; ++j ) {
    sum += z[accesses[j] & (N-1)] ;
  }
  return sum;
}



void demo(uint32_t N) {
  printf("N = %d\n", N);
  uint32_t * z = malloc(N * sizeof(uint32_t));
  for(uint32_t i = 0 ; i < N; ++i) z[i] = rand(); // some rand. number
  uint32_t nmbr = 500;
  uint32_t * accesses = malloc(nmbr * sizeof(uint32_t));
  for(uint32_t i = 0 ; i < nmbr; ++i) accesses[i] = rand(); // some rand. number
  uint32_t expected1 = modsum(z,N,accesses,nmbr);
  uint32_t expected2 = fastsum(z,N,accesses,nmbr);
  BEST_TIME(modsum(z,N,accesses,nmbr), expected1, 1000, nmbr);
  BEST_TIME(fastsum(z,N,accesses,nmbr), expected2, 1000, nmbr);
  free(z);
  free(accesses);
}

void demopoweroftwo(uint32_t N) {
  printf("N = %d\n", N);
  uint32_t * z = malloc(N * sizeof(uint32_t));
  for(uint32_t i = 0 ; i < N; ++i) z[i] = rand(); // some rand. number
  uint32_t nmbr = 500;
  uint32_t * accesses = malloc(nmbr * sizeof(uint32_t));
  for(uint32_t i = 0 ; i < nmbr; ++i) accesses[i] = rand(); // some rand. number
  uint32_t expected1 = modsum(z,N,accesses,nmbr);
  uint32_t expected2 = fastsum(z,N,accesses,nmbr);

  BEST_TIME(modsum(z,N,accesses,nmbr), expected1, 1000, nmbr);
  BEST_TIME(fastsum(z,N,accesses,nmbr), expected2, 1000, nmbr);
  BEST_TIME(maskedsum(z,N,accesses,nmbr), expected1, 1000, nmbr);

  switch(N){
	case 1<<8:
		BEST_TIME(modsum_8(z,N,accesses,nmbr),expected1, 1000, nmbr);
		break;
	case 1<<16:
		BEST_TIME(modsum_16(z,N,accesses,nmbr), expected1, 1000, nmbr);
		break;
	case 1<<24:
		BEST_TIME(modsum_24(z,N,accesses,nmbr), expected1, 1000, nmbr);
		break;
  }
  free(z);
  free(accesses);
}

int main() {
  demo(1 << 24);
  demo(1 << 8);
  demo(1 << 16);
  demo(1 << 24);
  demopoweroftwo(1 << 8);
  demopoweroftwo(1 << 16);
  demopoweroftwo(1 << 24);
}