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Sure, and as I've stated many times in this conversation, I would like for C to be more strongly specified. However, defining something like signed integer overflow as guaranteed to wrap would be a step backwards for implementations that want to make it safer such as trapping.
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It's always implemented in software via hardware features. The features vary in performance. Jump-on-overflow is a lot worse than architectures with support for enabling a trapping mode, whether it's strict or propagates a poison value that can never be accessed (since it traps).
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Hardware doesn't implement C, so there isn't a standard behavior defined by hardware. It's up to the compiler to map C onto the hardware or the virtual machine. They get to choose how to handle each kind of undefined or implementation defined behavior, and everything else.
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No, that's not what I've been saying. I think it would be a serious regression to break compatibility with safe implementations by making it correct to be incompatible with them. You want to massively roll back safety and security, especially if you want to remove it by default.
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Trapping on signed integer overflow isn't a new behavior. It has been around as a compiler feature for ages and is broadly deployed. Trapping on unsigned integer overflow is a newer feature, and it's far harder to deploy largely due to it not being standards compliant.
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