Hardware implementations of elementary functions regularly deploy piecewise polynomial approximations. This work determines the complete design space of piecewise polynomial approximations meeting a given accuracy specification. Knowledge of this design ...

The reptile search algorithm (RSA) is a dynamic and effective meta-heuristic algorithm inspired by the behavior of crocodiles in nature and the way of hunting prey. Unlike other crawler search algorithms, it uses four novel mechanisms to update the ...

The evaluation of small degree polynomials is critical for the computation of elementary functions. It has been extensively studied and is well documented. In this article, we evaluate existing methods for polynomial evaluation on superscalar ...

Many important workloads depend on the efficient computation of elementary functions like square root and logarithm. Accurate computation of these functions is time-consuming, and hard for compilers to schedule, because of conditional execution. These ...

The IEEE 754-2008 standard recommends the correct rounding of some elementary functions. This requires solving the Table Maker’s Dilemma (TMD), which implies a huge amount of CPU computation time. In this article, we consider accelerating such ...

In the current article, the capability and flexibility of field programmable gate-arrays (FPGAs) to implement IEEE-754 double-precision floating-point elementary functions are explored. To perform various elementary functions on the unified hardware ...

In this article, a unified VLIW coprocessor, based on a common group of atomic operation units, for Quad arithmetic and elementary functions (QP_VELP) is presented. The explicitly parallel scheme of VLIW instruction and Estrin's evaluation scheme for ...

Efficient elementary function implementations require primitives optimized for modern FPGAs. Fixed-point function generators are one such type of primitives. When built around piecewise polynomial approximations they make use of memory blocks and ...

This paper explores the capability of FPGA solutions to accelerate scientific applications with variable-precision floating-point (VP) arithmetic. First, we present a special-purpose Very Large Instruction Word (VLIW) architecture for VP arithmetic (VV-...

In many numerical programs there is a need for a high-quality floating-point approximation of useful functions f, such as such as exp, sin, erf. In the actual implementation, the function is replaced by a polynomial p, which leads to an approximation ...

This paper presents implementation of the double precision exponential function. A novel table-based architecture, together with short Taylor expansion, provides low latency (30 clock cycles) which is comparable to 32-bit implementations. Low area ...

This article presents a multiple-precision binary floating-point library, written in the ISO C language, and based on the GNU MP library. Its particularity is to extend to arbitrary-precision, ideas from the IEEE 754 standard, by providing correct ...

The growth of the Internet has triggered tremendous opportunities for cooperative computation, where people are jointly conducting computation tasks based on the private inputs they each supply. These computations could occur between mutually untrusted ...

Each coordinate rotation digital computer iteration selects the rotation direction by analyzing the results of the previous iteration. In this paper, we introduce two arctangent radices and show that about 2/3 of the rotation directions can be derived ...