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Julia High Performance by Avik Sengupta

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Trading performance for accuracy

In this book, we largely focus on performance. However, at this stage, it should be said that accurate math is usually an even bigger concern. All basic floating-point arithmetic in Julia follows strict IEEE 754 semantics. Rounding is handled carefully in all base library code to guarantee the theoretical best error limits. In some situations, however, it is possible to trade off performance for accuracy and vice versa.

The fastmath macro

The @fastmath macro is a tool to loosen the constraints of IEEE floating point operations in order to achieve greater performance. It can rearrange the order of evaluation to something with is mathematically equivalent but that would not be the same for discrete floating point numbers ...

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