On the Precision Attainable with Various Floating-Point Number Systems

On the precision attainable with various floating-point number systems

For scientific computations on a digital computer the set of real numbers is usually approximated by a finite set F of “floating-point” numbers. We compare the numerical accuracy possible with different choices of F having approximately the same range and requiring the same word length. In particular, we compare different choices of base (or radix) in the usual floating-point systems. The empha...

Double precision floating-point arithmetic on FPGAs

We present low cost FPGA floating-point arithmetic circuits for all the common operations, i.e. addition/subtraction, multiplication, division and square root. Such circuits can be extremely useful in the FPGA implementation of complex systems that benefit from the reprogrammability and parallelism of the FPGA device but also require a general purpose arithmetic unit. While previous work has co...

Reduced-Precision Floating-Point Analysis

Adaptive Precision Floating Point LLL

The LLL algorithm is one of the most studied lattice basis reduction algorithms in the literature. Among all of its variants, the floating point version, also known as L, is the most popular one, due to its efficiency and its practicality. In its classic setting, the floating point precision is a fixed value, determined by the dimension of the input basis at the initiation of the algorithm. We ...

Automated Floating-Point Precision Analysis

Title of dissertation: Automated Floating-Point Precision Analysis Michael O. Lam, Doctor of Philosophy, 2014 Dissertation directed by: Professor Jeffrey K. Hollingsworth Department of Computer Science As scientific computation continues to scale upward, correct and efficient use of floating-point arithmetic is crucially important. Users of floating-point arithmetic encounter many problems, inc...