static Zs find(const Z& n)
{
Z limit = 0;
Z sqn = sqrt(n);
for ( ; limit<primes.size() && primes[limit] <= sqn; ++limit )
;
// quadroot
Z qrn = 2;
while ( qrn*qrn*qrn*qrn < n ) ++qrn;
Z limitc = 0;
for ( ; limitc<primes.size() && primes[limitc] <= qrn; ++limitc ) {
Z l=primes[limitc];
l = l*l*l*l;
if ( l >= n )
break;
}
// cuberoot
Z crn = 2;
while ( crn*crn*crn < n ) ++crn;
Z limitb = 0;
for ( ; limitb<primes.size() && primes[limitb] <= crn; ++limitb ) {
Z l=primes[limitb];
l = l*l*l;
if ( l >= n )
break;
}
for ( Z c=0; c<limitc; ++c ) {
Z pc = primes[c];
pc = pc*pc*pc*pc;
for ( Z b=0; b<limitb; ++b ) {
Z pb = primes[b];
pb = pb*pb*pb;
if ( pb+pc >= n )
continue;
for ( Z a=0; a<limit; ++a )
{
Z pa = primes[a];
pa = pa*pa;
if ( pa+pb+pc == n ) {
Zs v(3);
v[0] = primes[a];
v[1] = primes[b];
v[2] = primes[c];
return v;
}
}
}
}
return Zs();
}
int main()
{
cout << "Max prime: " << primes[primes.size()-1] << endl;
assert(count(50) == 4);
assert(count(1000) == 98);
assert(count(100000) == 4704);
cout << count(2000000) << endl;
}
int main()
{
cout << "Sieving primes" << endl;
cout.flush();
const prime_sieve<Z, MAXNUM> primes;
cout << "Starting loop" << endl;
cout.flush();
for ( size_t i=0; primes[i]<MAX && i<primes.size(); ++i ) {
const Z a = primes[i];
for ( size_t j=0; primes[j]*a<MAX && j<=i; ++j ) {
const Z b = primes[j];
check(b*b);
check(a*b);
}
}
cout << "Count: " << cnt << endl;
cout << "Expect: 17427258" << endl;
}
INT phi(const INT& n)
{
static prime_sieve<INT, PRIMES> primes;
// Negative numbers
if ( n < 0 )
return phi<PRIMES, INT>(-n);
// By definition
if ( n == 1 )
return 1;
// Base case
if ( n < 2 )
return 0;
// Lehmer's conjecture
if ( less(n, primes.size()) && primes.isprime(n) )
return n-1;
// Even number?
if ( (n & 1) == 0 ) {
INT m = n / 2;
return (m & 1) == 0 ?
2*phi<PRIMES, INT>(m)
: phi<PRIMES, INT>(m);
}
// For all primes less than n ...
const INT sqrt_n = 1+sqrt(n);
for ( typename std::vector<INT>::const_iterator p = primes.first();
p != primes.last() && *p <= sqrt_n; ++p )
{
INT m = *p;
// Is m not a factor?
if ( (n % m) != 0 )
continue;
// Phi is multiplicative
INT o = n/m;
INT d = binary_gcd<INT>(m, o);
return d==1?
phi<PRIMES, INT>(m) * phi<PRIMES, INT>(o)
: phi<PRIMES, INT>(m) * phi<PRIMES, INT>(o) * d / phi<PRIMES, INT>(d);
}
// Find out if n is really prime
INT p;
for ( p=2+*(primes.last()-1); p < n && (n % p) != 0; p += 2 )
; // loop
// If n is prime, use Lehmer's conjecture
if ( p >= n )
return n-1;
// n must be composite, so divide up and recurse
INT o = n/p;
INT d = binary_gcd<INT>(p, o);
return d==1?
phi<PRIMES, INT>(p) * phi<PRIMES, INT>(o)
: phi<PRIMES, INT>(p) * phi<PRIMES, INT>(o) * d / phi<PRIMES, INT>(d);
}