library Percent {
  // Solidity automatically throws when dividing by 0
  struct percent {
    uint num;
    uint den;
  }
  
  // storage
  function mul(percent storage p, uint a) internal view returns (uint) {
    if (a == 0) {
      return 0;
    }
    return a*p.num/p.den;
  }

  function div(percent storage p, uint a) internal view returns (uint) {
    return a/p.num*p.den;
  }

  function sub(percent storage p, uint a) internal view returns (uint) {
    uint b = mul(p, a);
    if (b >= a) {
      return 0;
    }
    return a - b;
  }

  function add(percent storage p, uint a) internal view returns (uint) {
    return a + mul(p, a);
  }

  function toMemory(percent storage p) internal view returns (Percent.percent memory) {
    return Percent.percent(p.num, p.den);
  }

  // memory 
  function mmul(percent memory p, uint a) internal pure returns (uint) {
    if (a == 0) {
      return 0;
    }
    return a*p.num/p.den;
  }

  function mdiv(percent memory p, uint a) internal pure returns (uint) {
    return a/p.num*p.den;
  }

  function msub(percent memory p, uint a) internal pure returns (uint) {
    uint b = mmul(p, a);
    if (b >= a) {
      return 0;
    }
    return a - b;
  }

  function madd(percent memory p, uint a) internal pure returns (uint) {
    return a + mmul(p, a);
  }
}
function mul(percent storage p, uint a) internal view returns (uint) {
  if (a == 0) {
    return 0;
  }
  return a*p.num/p.den;
}

// storage