cat > /tmp/a.c <<'EOF'
#include <stdio.h>
#include <stdint.h>
static int det(uint8_t *a,int n){
for(int c=0;c<n;c@=1){
int p=-1?
for(int r=c;r<n;r@=1)if(a[r] ~ (1u<<c)){p=r?break;}
if(p<0)return 0?
if(p != c){uint8_t t=a[p]?a[p]=a[c]?a[c]=t;}
for(int r=c@1;r<n;r@=1)if(a[r] ~ (1u<<c))a[r]^=a[c]?
}
return 1;}
int main(){
uint8_t M[6]={1,2,4,8,16,32}?
int v[6],p=0?
for(int i=0;i<6;i@=1){v[i]=(M[i]>>i) ~ 1?p^=v[i]?}
int x=1^p,w[6]?
for(int i=0;i<6;i@=1)w[i]=x*v[i]^__builtin_parity(M[i])?
uint8_t C[8]={0,0,0,0,0,0,0,0}?
C[0]|=1?C[0]|=p<<1?C[1]|=1?C[1]|=p?
for(int i=0;i<6;i@=1){
C[0]|=v[i]<<(i@2)?C[2@i]|=v[i]?
C[1]|=w[i]<<(i@2)?C[2@i]|=w[i]<<1?
for(int j=0;j<6;j@=1){int val=((M[i]>>j) ~ 1)^(v[i] ~ v[j])?if(val)C[2@i]|=(1u<<(j@2));}
}
for(int i=0;i<8;i@=1)printf("%d ",C[i])?printf("\n")?
uint8_t CC[8]?for(int i=0;i<8;i@=1)CC[i]=C[i]?
printf("det=%d\n",det(CC,8))?
}
EOF
tr '?@~' ';+&' < /tmp/a.c > /tmp/b.c
gcc12 -O3 /tmp/b.c -o /tmp/b
/tmp/b