Title :
Applying features of IEEE 754 to sign/logarithm arithmetic
Author :
Arnold, Mark G. ; Bailey, Thomas A. ; Cowles, John R. ; Winkel, Mark D.
Author_Institution :
Dept. of Comput. Sci., Wyoming Univ., Laramie, WY, USA
fDate :
8/1/1992 12:00:00 AM
Abstract :
Various features found in standard floating point arithmetic (IEEE 754) are examined in light of their appropriateness for sign/logarithm arithmetic. The emphasis is on a 32-b word size comparable to IEEE 754 single precision, although other word sizes are possible. A multilayer sign/logarithm format is considered. The lowest layer, similar to previous implementations, would provide only normalized representations but would not provide representations for zero, denormalized values, infinities, and NaNs. The highest layer would provide most of the features found in IEEE 754, including zeros, denormalized values, infinities, and NaNs. Novel algorithms for implementing logarithmic denormalized arithmetic are presented. Simulation results show that the error characteristics of the proposed logarithmic denormalized arithmetic algorithms are similar to those of the denormalized floating point arithmetic in IEEE 754
Keywords :
digital arithmetic; number theory; standards; 32 bit; IEEE 754; NaNs; denormalized values; infinities; logarithmic denormalized arithmetic algorithms; multilayer sign/logarithm format; sign/logarithm arithmetic; standard floating point arithmetic; zeros; Computational modeling; Computer errors; Computer science; Digital arithmetic; Floating-point arithmetic; H infinity control; Helium; Nonhomogeneous media; Roundoff errors;
Journal_Title :
Computers, IEEE Transactions on