Abstract: Methods and an apparatus for compiling a transcendental floating-point operation are disclosed. The disclosed techniques compile a transcendental floating-point operation by replacing the transcendental floating-point operation with an integer-based routine (e.g., a single routine) hand-coded to perform the transcendental floating-point operation. Each of the instructions in the integer-based routine, including the integer operations, is compiled directly into opcodes without primitive floating-point emulation calls. As a result, function nesting is reduced and more efficient algorithms are used. The disclosed system does not simply emulate basic floating-point operations using integer operations. Instead, portions of the computation are isolated where fixed-point accuracy is sufficient and thus native integer computations can be used. For example, computing (log(1+Z)?Z)/Z instead of computing log(1+Z).

Abstract: Methods and an apparatus for compiling a transcendental floating-point operation are disclosed. The disclosed techniques compile a transcendental floating-point operation by replacing the transcendental floating-point operation with an integer-based routine (e.g., a single routine) hand-coded to perform the transcendental floating-point operation. Each of the instructions in the integer-based routine, including the integer operations, is compiled directly into opcodes without primitive floating-point emulation calls. As a result, function nesting is reduced and more efficient algorithms are used. The disclosed system does not simply emulate basic floating-point operations using integer operations. Instead, portions of the computation are isolated where fixed-point accuracy is sufficient and thus native integer computations can be used. For example, computing (log(1+Z)−Z)/Z instead of computing log(1+Z).

Abstract: The division and square root systems include a multiplier. The systems also include a multipartite table system, a folding inverter, and a complement inverter, each coupled to the multiplier. The division and square root functions can be performed using three scaling iterations. The system first determines both a first and a second scaling value. The first scaling value is a semi-complement term computed using the folding inverter to invert selected bits of the input. The second scaling value is a table lookup value obtained from the multipartite table system. In the first iteration, the system scales the input by the semi-complement term. In the second iteration, the resulting approximation is scaled by a function of the table lookup value. In the third iteration, the approximation is scaled by a value obtained from a function of the semi-complement term and the table lookup value. After the third iteration, the approximation is available for rounding.