burroughs BSP Floating Point Processor free download

File name BSP_Floating_Point_Processor.pdf

I Burroughs ! ( BURROUGHS SCIENTIFIC PROCESSOR FLOATING POINT ARITHMETIC BSP ~~~-~- BURROU(;HS SCIENTIFIC PROCESSOR CONTENTS Section Page 1 INTRODUCTION 1 2 DATA REPRESENTATION IN MEMORY 3 Single Precision Floating Point Word Format 3 Integer Word Format 4 Double Precision Real Floating Point Word Format 5 3 DATA REPRESENTATION IN THE ARITHIVIETIC ELEl\1ENTS 7 Basic Data Representation 7 Representation of Zero 8 Complex Number (Single Precision) 8 4 HARDWARE ERROR CHECKING 9 5 ARITHMETIC ALGORITHMS 11 Implementation of Reciprocation and Square Root 11 Division 13 Square Root 13 6 ROUNDING AND NORMALIZATION 15 Rounding - Single Precision 15 Rounding - Double Precision 17 Normaliza tion 17 Appendix A - Arithmetic Operations 19 Appendix B - Error Estimates for Arithmetic Operations 27 iii ~~p ~~~~~~~~~~~~~~~~~~~~~BURROUGHSSCIENTIFICPROCESSOR BSP 1. INTRODUCTION One of the most important features of any computer is its arithmetic. This docu- ment discusses the implementation of floating point arithmetic in the Burroughs Scientific Processor (BSP). Data representation in both the BSP memory and arithmetic element is described, as are the arithmetic algorithms used in the BSP. Of particular interest are the techniques used for error checking in the arithmetic element and for rounding in both the scalar processor and the parallel processor. The BSP arithmetic operations, including instructions and cycle operations, are described in detail in Appendix A, and the accuracy of arithmetic operations is discussed in Appendix B.