Floating-point Approximation Research Articles

A method for exact computation with rational numbers

An easily programmed method is presented for solving N linear equations in N unknowns exactly for the rational answers, given that all coefficients and constants appearing in the equations are rational numbers. The rational answers are deduced from floating point approximations to the answers obtained by any of the standard solution algorithms. Criteria are given for determining for a particular set of equations the floating point precision needed.

A 16-bit A-D-A conversion system for high-fidelity audio research

An A-D and D-A converter system with exceptionally wide dynamic range and low distortion is discussed. The system utilizes 12-bit floating-point approximation at conversion instead of true 16-bit conversion. A deglitching track and hold is illustrated which avoids heterodyning between signal components and the sample clock. Rate-limiting during the transition from hold to track is discussed.