6x6 Hotel Key Card Counter

keycount.c

/* 6x6 Hotel Key Card Counter
 * $ cc -fopenmp -O3 -march=native keycount.c
 * Ref: https://possiblywrong.wordpress.com/2020/10/24/counting-hotel-key-cards/
 */
#include <stdio.h>

static long long
transpose(long long x)
{
    return (x <<  5 & 0x408102040) |
           (x << 10 & 0x204081000) |
           (x << 15 & 0x102040000) |
           (x << 20 & 0x081000000) |
           (x << 25 & 0x040000000) |
           (x >>  0 & 0x810204081) |
           (x >>  5 & 0x020408102) |
           (x >> 10 & 0x000810204) |
           (x >> 15 & 0x000020408) |
           (x >> 20 & 0x000000810) |
           (x >> 25 & 0x000000020);
}

static long long
flipv(long long x)
{
    return (x >> 30 & 0x00000003f) |
           (x >> 18 & 0x000000fc0) |
           (x >>  6 & 0x00003f000) |
           (x <<  6 & 0x000fc0000) |
           (x << 18 & 0x03f000000) |
           (x << 30 & 0xfc0000000);
}

static int
valid(long long x)
{
    int v = 0;
    long long a[7];
    a[0] = x;
    a[1] = x = transpose(x);
    v += x < a[0];
    v += x == a[0];
    a[2] = x = flipv(x);
    v += x < a[0];
    v += x == a[0];
    v += x == a[1];
    a[3] = x = transpose(x);
    v += x < a[0];
    v += x == a[0];
    v += x == a[1];
    v += x == a[2];
    a[4] = x = flipv(x);
    v += x < a[0];
    v += x == a[0];
    v += x == a[1];
    v += x == a[2];
    v += x == a[3];
    a[5] = x = transpose(x);
    v += x < a[0];
    v += x == a[0];
    v += x == a[1];
    v += x == a[2];
    v += x == a[3];
    v += x == a[4];
    a[6] = x = flipv(x);
    v += x < a[0];
    v += x == a[0];
    v += x == a[1];
    v += x == a[2];
    v += x == a[3];
    v += x == a[4];
    v += x == a[5];
    x = transpose(x);
    v += x < a[0];
    v += x == a[0];
    v += x == a[1];
    v += x == a[2];
    v += x == a[3];
    v += x == a[4];
    v += x == a[5];
    v += x == a[6];
    return !v;
}

int
main(void)
{
    long long total = 0;
    #pragma omp parallel for
    for (int n = 0; n < 1<<8; n++) {
        long long subtotal = 0;
        for (long long i = 0; i < 1LL<<28; i++) {
            subtotal += valid(i<<8 | n);
        }
        #pragma omp atomic
        total += subtotal;
    }
    printf("%lld\n", total);
}