Worst Cases for the Exponential Function in the IEEE 754r decimal64 Format
نویسندگان
چکیده
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 ulp, and we give the worst ones. In particular, the worst case for |x| ≥ 3 × 10 is exp(9.407822313572878 × 10) = 1.098645682066338 5 0000000000000000 278 . . .. 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.
منابع مشابه
Reduced Area Low Power High Throughput BCD Adders for IEEE 754r Format
IEEE 754r is the ongoing revision to the IEEE 754 floating point standard and a major enhancement to the standard is the addition of decimal format. Firstly, this paper proposes novel two transistor AND and OR gates. The proposed AND gate has no power supply, thus it can be referred as the Powerless AND gate. Similarly, the proposed two transistor OR gate has no ground and can be referred as Gr...
متن کاملPartial Reversible Gates(PRG) for Reversible BCD Arithmetic
IEEE 754r is the ongoing revision to the IEEE 754 floating point standard and a major enhancement to the standard is the addition of decimal format. Furthermore, in the recent years reversible logic has emerged as a promising computing paradigm having its applications in low power CMOS, quantum computing, nanotechnology, and optical computing. The major goal in reversible logic is to minimize t...
متن کاملModified Carry Look Ahead BCD Adder With CMOS and Reversible Logic Implementation
IEEE 754r is the ongoing revision to the IEEE 754 floating point standard and a major enhancement to the standard is the addition of decimal format. Firstly, this paper proposes novel two transistor AND & OR gates. The proposed AND gate has no power supply, thus it can be referred as the Powerless AND gate. Similarly, the proposed two transistor OR gate has no ground and can be referred as Grou...
متن کاملFormal Correctness of Comparison Algorithms Between Binary64 and Decimal64 Floating-Point Numbers
We present a full Coq formalisation of the correctness of some comparison algorithms between binary64 and decimal64 floatingpoint numbers.
متن کامل