Apparently IEEE-754 guarantees bit-identical (≤½ ulp error) results for +, -, ×, ÷, and √ — but only those? Do processors usually comply?
Can't vouch for hardware-supported √. GPUs - AFAIK can be made to work on new ones, can be tough: https://developer.nvidia.com/sites/default/files/akamai/cuda/files/NVIDIA-CUDA-Floating-Point.pdf …
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oh man. apparently due to the introduction of FMA, even a*a+b can now produce non-bit-identical results "correctly".
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reasonable compilers let you disable FMAs. If I got it right, NVIDIA's won't, gives you intrinsics for non-fused MACs. Painful!
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Oh, this is awesome. Thanks!
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