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FGPA > FPGA #316

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2 changes: 1 addition & 1 deletion content/english/hpc/arithmetic/ieee-754.md
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Expand Up @@ -53,7 +53,7 @@ Their availability ranges from chip to chip:
- Extended formats are exclusive to x86, and are available in C as the `long double` type, which falls back to double precision on Arm CPUs. The choice of 64 bits for mantissa is so that every `long long` integer can be represented exactly. There is also a 40-bit format that similarly allocates 32 mantissa bits.
- Quadruple as well as the 256-bit "octuple" formats are only used for specific scientific computations and are not supported by general-purpose hardware.
- Half-precision arithmetic only supports a small subset of operations and is generally used for applications such as machine learning, especially neural networks, because they tend to perform large amounts of calculations but don't require high levels of precision.
- Half-precision is being gradually replaced by bfloat, which trades off 3 mantissa bits to have the same range as single-precision, enabling interoperability with it. It is mostly being adopted by specialized hardware: TPUs, FGPAs, and GPUs. The name stands for "[Brain](https://en.wikipedia.org/wiki/Google_Brain) float."
- Half-precision is being gradually replaced by bfloat, which trades off 3 mantissa bits to have the same range as single-precision, enabling interoperability with it. It is mostly being adopted by specialized hardware: TPUs, FPGAs, and GPUs. The name stands for "[Brain](https://en.wikipedia.org/wiki/Google_Brain) float."

Lower-precision types need less memory bandwidth to move them around and usually take fewer cycles to operate on (e.g., the division instruction may take $x$, $y$, or $z$ cycles depending on the type), which is why they are preferred when error tolerance allows it.

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