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In this paper we present a fast radix-4 division algorithm for floating point numbers. This method is based on Svoboda's division algorithm and the radix-4 redundant number system. The algorithm ...involves a simple recurrence with carry-free addition and employs prescaling of the operands. In the proposed divider implementation, each radix-4 digit (belonging to set {-3,...,+3}) of the quotient and partial remainder is encoded using two radix-2 digits (belonging to the set {-1,0,+1}) and this leads to hardware simplicity. The quotient digits are determined by observing three most-significant radix-2 digits of the partial remainder and independent of the divisor. The architecture presented for the proposed algorithm is faster than previously proposed radix-4 dividers, which require at least four digits of the partial remainder to be observed to determine quotient digits.< >
This note points out the close relationship between some of the recently described division techniques, in which the divisor is transformed to a range close to unity. A brief theoretical analysis is ...presented which examines the choice of quotient digit when this type of division technique is used for conventional and signed-digit number systems.
Abstract-The application of a fast division algorithm, particu-larly suitable for floating-point arithmetic, to signed-digit number systems is described. This method, based on the method of A. ...Svo-boda, is performed in two steps: 1) the divisor is adjusted to be of the form (1+e) where e is a fractional quantity, while the dividend is adjusted accordingly, and 2) the generation of each quotient digit is determined by only one digit in the partial remainder together with the transfer digit (or carry/borrow) emanating from it. A working example of radix 16 is given.
A cellular automaton (CA) model coupled with Svoboda’s analytic solution of diffusional phase transformation was established to simulate β-α transition in titanium alloy. A numeric definition of ...diffusion, mixed and interface mode transformation is put forward and simulated by the newly developed CA model. To the best of our knowledge, this is the first model that is capable of quantifying the effect of interface moving (interface mobility coefficient or transformation driving force factor) and solute diffusion process (diffusion coefficient) on phase transformation types. A critical interface mobility coefficient exists for mixed mode transformation, below and above which interface mode and diffusion mode dominate, respectively. This indicated that, in isothermal diffusion/mixed/interface mode phase transformations, solute diffusion distance and solute concentration gradient are decreasing gradually with time. Furthermore, it was found during cooling transformation that diffusion mode transformation at high temperature shifts to interface mode at low temperature, where a high cooling rate corresponds to a high transition temperature.
