Computation of cyclic redundancy checks may use whichever form is more convenient. Parallel update for a byte or a word at a time can also be done explicitly, without a table. This is normally used in high-speed hardware implementations. For each bit an equation is solved after 8 bits have been shifted in. The following tables list the equations for some commonly used polynomials, using following symbols: As the CRC-32 polynomial has a large number of terms, when computing the remainder a byte at a time each bit depends on several bits of the previous iteration. In byte-parallel hardware implementations this calls for either multiple-input
Stochastic computing rough estimate very rapidly. This property is usually referred to as "progressive precision", which suggests that the precision of stochastic numbers (bit streams) increases as computation proceeds. It is as if the most significant bits of the number arrive before its least significant bits; unlike the conventional arithmetic circuits where the most significant bits usually arrive last. In some iterative systems the partial solutions obtained through progressive precision can provide faster feedback than through traditional computing methods, leading to faster convergence. Stochastic computing is, by its very nature, random. When we examine a random bit stream and try to reconstruct