# Condition to solve a block

For target \tau\in[0,1] we define the following two conditions a header h must satisfy to have a valid Proof of Balanced Work:

1. The Sha256t hash must not be too small: Y(h) \ge c for some constant c=0.005
2. The Janushash must be below the target: J(h) < \tau.

The function to check for valid Proof of Balanced Work can be implemented as follows:

bool valid_pow(Header h, Target t)
{
    auto sha256tFloat { CustomFloat(hashSHA256(hashSHA256(hashSHA256(h)))) };
    auto verusFloat { CustomFloat(verus_hash(h)) };
    constexpr auto c = CustomFloat(-7, 2748779069); // c = 0.005
    if (sha256tFloat < c) {
        return false
    }
    constexpr auto exponent { CustomFloat(0, 3006477107) }; // = 0.7 
    auto hashProduct { verusFloat * pow(sha256tFloat, exponent) };
    return hashProduct < t;
}

The CustomFloat class has it's own Repository here. It is a portable floating point representation with math functions (log2, pow2, pow) and supports:

• Conversion of a hash into CustomFloat number representation.
• Multiplication
• Raising a number to some exponent

The use of CustomFloat is necessary since C math library functions cannot be used in consensus-critical parts of a cryptocurrency. This way portatility is guaranteed.