32 research outputs found
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
,ulp, and we give the worst ones. In particular, the worst case
for is . 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