Abstract: The apparatus and method for calculating and retaining a bound on error during floating-point operations inserts an additional bounding field into the standard floating-point format that records the retained significant bits of the calculation with notification upon insufficient retention. The bounding field, accounting for both rounding and cancellation errors, includes the lost bits D Field and the accumulated rounding error R Field. The D Field states the number of bits in the floating-point representation that are no longer meaningful. The bounds on the represented real value are determined by the truncated floating-point value and the addition of the error determined by the number of lost bits. The true, real value is absolutely contained by these bounds. The allowable loss (optionally programmable) of significant digits provides a fail-safe, real-time notification of loss of significant digits. This allows representation of real numbers accurate to the last digit.

Abstract: The apparatus and method for calculating and retaining a bound on error during floating-point operations inserts an additional bounding field into the standard floating-point format that records the retained significant bits of the calculation with notification upon insufficient retention. The bounding field, accounting for both rounding and cancellation errors, includes the lost bits D Field and the accumulated rounding error R Field. The D Field states the number of bits in the floating-point representation that are no longer meaningful. The bounds on the represented real value are determined by the truncated floating-point value and the addition of the error determined by the number of lost bits. The true, real value is absolutely contained by these bounds. The allowable loss (optionally programmable) of significant digits provides a fail-safe, real-time notification of loss of significant digits. This allows representation of real numbers accurate to the last digit.

Abstract: The apparatus and method for calculating and retaining a bound on error during floating-point operations inserts an additional bounding field into the standard floating-point format that records the retained significant bits of the calculation with notification upon insufficient retention. The bounding field, accounting for both rounding and cancellation errors, includes the lost bits D Field and the accumulated rounding error R Field. The D Field states the number of bits in the floating-point representation that are no longer meaningful. The bounds on the represented real value are determined by the truncated floating-point value and the addition of the error determined by the number of lost bits. The true, real value is absolutely contained by these bounds. The allowable loss (optionally programmable) of significant digits provides a fail-safe, real-time notification of loss of significant digits. This allows representation of real numbers accurate to the last digit.

Abstract: The apparatus and method for calculating and retaining a bound on error during floating-point operations inserts an additional bounding field into the standard floating-point format that records the retained significant bits of the calculation with notification upon insufficient retention. The bounding field, accounting for both rounding and cancellation errors, includes the lost bits D Field and the accumulated rounding error R Field. The D Field states the number of bits in the floating-point representation that are no longer meaningful. The bounds on the represented real value are determined by the truncated floating-point value and the addition of the error determined by the number of lost bits. The true, real value is absolutely contained by these bounds. The allowable loss (optionally programmable) of significant digits provides a fail-safe, real-time notification of loss of significant digits. This allows representation of real numbers accurate to the last digit.

Abstract: The apparatus and method for calculating and retaining a bound on error during floating point operations inserts an additional bounding field into the standard floating-point format that records the retained significant bits of the calculation with notification upon insufficient retention. The bounding field, accounting for both rounding and cancellation errors, includes the lost bits D Field and the accumulated rounding error R Field. The D Field states the number of bits in the floating point representation that are no longer meaningful. The bounds on the represented real value are determined by the truncated floating point value and the addition of the error determined by the number of lost bits. The true, real value is absolutely contained by these bounds. The allowable loss (optionally programmable) of significant digits provides a fail-safe, real-time notification of loss of significant digits. This allows representation of real numbers accurate to the last digit.

Abstract: The apparatus and method for calculating and retaining a bound on error during floating point operations inserts an additional bounding field into the standard floating-point format that records the retained significant bits of the calculation with notification upon insufficient retention. The bounding field, accounting for both rounding and cancellation errors, includes the lost bits D Field and the accumulated rounding error R Field. The D Field states the number of bits in the floating point representation that are no longer meaningful. The bounds on the represented real value are determined by the truncated floating point value and the addition of the error determined by the number of lost bits. The true, real value is absolutely contained by these bounds. The allowable loss (optionally programmable) of significant digits provides a fail-safe, real-time notification of loss of significant digits. This allows representation of real numbers accurate to the last digit.

Abstract: The apparatus and method for calculating and retaining a bound on error during floating point operations inserts an additional bounding field into the standard floating-point format that records the retained significant bits of the calculation with notification upon insufficient retention. The bounding field, which accounts for both rounding and cancellation errors, has two parts, the lost bits D Field and the accumulated rounding error R Field. The D Field states the number of bits in the floating point representation that are no longer meaningful. The bounds on the real value represented are determined from the truncated floating point value (first bound) and the addition of the error determined by the number of lost bits (second bound). The true, real value is absolutely contained by the first and second bounds. The allowed loss (optionally programmable) of significant bits provides a fail-safe, real-time notification of loss of significant bits.

Abstract: The apparatus and method for calculating and retaining a bound on error during floating point operations inserts an additional bounding field into the standard floating-point format that records the retained significant bits of the calculation with notification upon insufficient retention. The bounding field, which accounts for both rounding and cancellation errors, has two parts, the lost bits D Field and the accumulated rounding error R Field. The D Field states the number of bits in the floating point representation that are no longer meaningful. The bounds on the real value represented are determined from the truncated floating point value (first bound) and the addition of the error determined by the number of lost bits (second bound). The true, real value is absolutely contained by the first and second bounds. The allowed loss (optionally programmable) of significant bits provides a fail-safe, real-time notification of loss of significant bits.