Related papers: On Approximate 8-bit Floating-Point Operations Usi…
When sharing or logging numerical data, we must convert binary floating-point numbers into their decimal string representations. For example, the number $\pi$ might become 3.1415927. Engineers have perfected many algorithms for producing…
There is a recent interest in neural network (NN)-based communication algorithms which have shown to achieve (beyond) state-of-the-art performance for a variety of problems or lead to reduced implementation complexity. However, most work on…
Let A be a matrix, c be any linear objective function and x be a fractional vector, say an LP solution to some discrete optimization problem. Then a recurring task in theoretical computer science (and in approximation algorithms in…
Modern lunar-planetary ephemerides are numerically integrated on the observational timespan of more than 100 years (with the last 20 years having very precise astrometrical data). On such long timespans, not only finite difference…
Scientific computing applications, such as computational fluid dynamics and climate modeling, typically rely on 64-bit double-precision floating-point operations, which are extremely costly in terms of computation, memory, and energy. While…
A novel algorithm for producing smooth nonlinearities on digital hardware is presented. The non-linearities are inherently quadratic and have both symmetrical and asymmetrical variants. The integer (and fixed point) implementation is highly…
We contemplate this article to help the teachers of programming in his aspiration for giving some appropriate and interesting examples. The work will be especially useful for students-future programmers, and for their lecturers. Some of the…
We offer a novel approach, MGS (Markov Greedy Sums), to improve the accuracy of low-bitwidth floating-point dot products in neural network computations. In conventional 32-bit floating-point summation, adding values with different exponents…
In many machine learning applications, e.g., tree-based ensembles, floating point numbers are extensively utilized due to their expressiveness. Nowadays performing data analysis on embedded devices from dynamic data masses becomes…
In this paper, we consider a class of Forward--Backward (FB) splitting methods that includes several variants (e.g. inertial schemes, FISTA) for minimizing the sum of two proper convex and lower semi-continuous functions, one of which has a…
Formal proof checkers such as Coq are capable of validating proofs of correction of algorithms for finite field arithmetics but they require extensive training from potential users. The delayed solution of a triangular system over a finite…
This paper explores practical aspects of using a high-level functional language for GPU-based arithmetic on ``midsize'' integers. By this we mean integers of up to about a quarter million bits, which is sufficient for most practical…
Modern processors deliver higher throughput for lower-precision arithmetic than for higher-precision arithmetic. For matrix multiplication, the Ozaki scheme exploits this performance gap by splitting the inputs into lower-precision…
Floating point arithmetic remains expensive on FPGA platforms due to wide datapaths and normalization logic, motivating alternative representations that preserve dynamic range at lower cost. This work introduces the Hybrid Residue Floating…
We present a derivation and numerous applications of a compact explicit formula for the average fidelity of a quantum operation on a finite dimensional quantum system. The formula can be applied to averages over particularly relevant…
Quantum Fourier transform (QFT) is a key function to realize quantum computers. A QFT followed by measurement was demonstrated on a simple circuit based on fiber-optics. The QFT was shown to be robust against imperfections in the rotation…
We present a second-order recursive Fermi-operator expansion scheme using mixed precision floating point operations to perform electronic structure calculations using tensor core units. A performance of over 100 teraFLOPs is achieved for…
With the increasing complexity of machine learning models, managing computational resources like memory and processing power has become a critical concern. Mixed precision techniques, which leverage different numerical precisions during…
Numerical integrations in celestial mechanics often involve the repeated computation of a rotation with a constant angle. A direct evaluation of these rotations yields a linear drift of the distance to the origin. This is due to roundoff in…
Convolutional neural networks (CNNs) achieve state-of-the-art performance at the cost of becoming deeper and larger. Although quantization (both fixed-point and floating-point) has proven effective for reducing storage and memory access,…