A challenge of running a model predictive control (MPC) algorithm in a production-embedded platform is to provide the certificate of worst-case computation complexity, that is, its maximum execution time needs to always be smaller than the sampling time. This article proposes for the first time a \textit{direct} optimization algorithm for input-constrained MPC: the number of iterations is data-independent and dependent on the problem dimension $n$, with exact value $\left\lceil\frac{\log(\frac{2n}{\epsilon})}{-2\log(\frac{\sqrt{2n}}{\sqrt{2n}+\sqrt{2}-1})}\right\rceil + 1$, where $\epsilon$ denotes a given stopping accuracy.

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