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It has taken nearly two decades and an immense amount of work by millions of people for high performance computing to go mainstream with GenAI. And now, we live in a world where AI servers crammed ...

Abstract: The IEEE Standard 754-1985 for binary floating-point arithmetic [19] was revised [20], and an important addition is the definition of decimal floating-point arithmetic [8], [24]. This is ...

Large collection of number systems providing custom arithmetic for mixed-precision algorithm development and optimization for AI, Machine Learning, Computer Vision, Signal Processing, CAE, EDA, ...

A classic and straightforward technique is presented which is not limited to the size or type of number representation used or multiple precision arithmetic.

Multiplication on a common microcontroller is easy. But division is much more difficult. Even with hardware assistance, a 32-bit division on a modern 64-bit x86 CPU can run between 9 and 15 cycles.

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An unfortunate reality of trying to represent continuous real numbers in a fixed space (e.g. with a limited number of bits) is that this comes with an inevitable loss of both precision and accuracy.