Fast decimal floating-point division

A new implementation for decimal floating-point (DFP) division is introduced. The algorithm is based on high-radix SRT division The SRT division algorithm is named after D. Sweeney, J. E. Robertson, and T. D. Tocher. with the recurrence in a new decimal signed-digit format. Quotient digits are selected using comparison multiples, where the magnitude of the quotient digit is calculated by comparing the truncated partial remainder with limited precision multiples of the divisor. The sign is determined concurrently by investigating the polarity of the truncated partial remainder. A timing evaluation using a logic synthesis shows a significant decrease in the division execution time in contrast with one of the fastest DFP dividers reported in the open literatureHooman Nikmehr, Braden Phillips and Cheng-Chew Li

Worst Cases for the Exponential Function in the IEEE 754r decimal64 Format

We searched for the worst cases for correct rounding of the exponential function in the IEEE 754r decimal64 format, and computed all the bad cases whose distance from a breakpoint (for all rounding modes) is less than $10^{-15}$,ulp, and we give the worst ones. In particular, the worst case for $|x| geq 3 imes 10^{-11}$ is $exp(9.407822313572878 imes 10^{-2}) = 1.098645682066338,5,0000000000000000,278ldots$. This work can be extended to other elementary functions in the decimal64 format and allows the design of reasonably fast routines that will evaluate these functions with correct rounding, at least in some domains

Radix Conversion for IEEE754-2008 Mixed Radix Floating-Point Arithmetic

Conversion between binary and decimal floating-point representations is ubiquitous. Floating-point radix conversion means converting both the exponent and the mantissa. We develop an atomic operation for FP radix conversion with simple straight-line algorithm, suitable for hardware design. Exponent conversion is performed with a small multiplication and a lookup table. It yields the correct result without error. Mantissa conversion uses a few multiplications and a small lookup table that is shared amongst all types of conversions. The accuracy changes by adjusting the computing precision

Hardware Design of a Binary Integer Decimal-based

Abstract Because of the growing importance of decimal floating-point (DFP