Algorithms to automatically realize delays in combinational logic circuits to achieve wave pipelining are presented. The algorithms adjust gate speeds and insert a minimal number of active delay elements to balance input-output path lengths in a circuit. For both normal and wave-pipelined circuits, the algorithms also optimally minimize power under delay constraints. The authors analyze the algorithms and comment on their implementation. They report experimental results, including the design and testing of a 63-bit population counter in CML bipolar technology. A brief analysis of circuit technologies shows that CML and super-buffered ECL without stacked structures are well suited for wave pipelining because they have uniform delay. Static CMOS and ordinary ECL including stacked structures and emitter-followers do have some delay variations. A high degree of wave pipelining is still possible in those technologies if special design techniques are followed.>

A class of iterative integer division algorithms is presented based on look-up table and Taylor-series approximations to the reciprocal. The algorithm iterates by using the reciprocal to find an approximate quotient and then subtracting the quotient multiplied by the divisor from the dividend to find a remaining dividend. Fast implementations can produce an average of either 14 or 27 b per iteration, depending on whether the basic or advanced version of this method is implemented. Detailed analyses are presented to support the claimed accuracy per iteration. Speed estimates using state-of-the-art ECL components show that this method is faster than the Newton-Raphson technique and can produce 53-b quotients of 53-b numbers in about 25 ns using the basic method and 21 ns using the advanced method. In addition, these methods naturally produce an exact remainder, which is very useful for implementing precise rounding specifications.>

A class of iterative integer division algorithms is presented based on lookup table Taylor-series approximations to the reciprocal. The algorithm iterates by using the reciprocal to find an approximate quotient and then subtracting the quotient multiplied by the divisor from the dividend to find a remaining dividend. Fast implementations can produce an average of either 14 or 27 b per iteration, depending on whether the basic or advanced version of this method is implemented. Detailed analyses are presented to support the claimed accuracy per iteration. Speed estimates using state-of-the-art ECL (emitted coupled logic) components show that this method is faster than the Newton-Raphson technique and can produce 53-b quotients of 53-b numbers in about 28 or 22 ns for the basic and advanced versions.>

Wave pipelining is a technique for pipelining digital systems that can increase the clock frequency without increasing the number of storage elements. Due to limits and variations in fabrication, the clock frequency can be increased by a factor of 2 to 3 by using the best available design methods. The authors present algorithms that will equalize delays automatically by inserting a minimal number of active delay elements to lengthen short paths. This method can be combined with delay balancing by adjusting gate speeds to design wave-pipelined circuits.>