English Edition: how are real numbers e.g. 0.1 represented on computers? What can go wrong with using their representation in calculations? And does it matter? These and other questions are the subject of this ByteSized episode with my guests Prof. Ulrich Ruede (University of Erlangen-Nuernberg), Andreas Herten and Edoardo di Napoli (both Research Centre Juelich). 

Links:

• https://www.h-schmidt.net/FloatConverter/IEEE754.html  an online tool to convert numbers into their bit/hex equivalent - also showing the rounding errors
• https://dl.acm.org/doi/10.1145/103162.103163  Goldberg Paper: What every computer scientist should know about floating points
• https://arxiv.org/abs/2012.02492 revisiting Goldberg, Vincent Lafage
• https://en.wikipedia.org/wiki/IEEE_754 the Wiki entry on the IEEE 754 standard for floating points (the standard itself is not accessible for free)
• https://en.wikipedia.org/wiki/Unit_in_the_last_place definition von "ulp"
• https://developer.nvidia.com/blog/floating-point-8-an-introduction-to-efficient-lower-precision-ai-training/ NVidia’s take on lower precision numbers 
• https://indico.esa.int/event/445/contributions/8473/attachments/5559/9378/gernigon_cedric_EDHPC2023.pdf list of lower precision formats
• https://en.wikipedia.org/wiki/Chinese_remainder_theorem Chinese remainder theorem

I would like to thank the STEP-UP project in the UK for supporting this series of ByteSized episodes. 

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