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Thread: OpenCL spec -- Table 7.1: Where do the ULP values come from?

  1. #1
    Junior Member
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    OpenCL spec -- Table 7.1: Where do the ULP values come from?

    Hi --

    I'm perusing the OpenCL spec as a source of information regarding modern floating point math specifications. In section 7.4, there is a table (table 7.1) listing the minimum accuracy required of various math functions in the OpenCL API. Each function has a required ULP which must be obeyed.

    My question: Where do the ULP values come from? For example, the table calls out that exp(x) must be accurate to within 3 ULPs of the mathematically correct result. Fair enough, but what information was used to create the spec of 3 ULPs? I'm looking for pointers to the literature, estimates based on the "best" implementation of the function, or other considerations which led to this spec.

    Thanks!

    Stuart

  2. #2
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    Re: OpenCL spec -- Table 7.1: Where do the ULP values come from?

    Stuart,
    My understanding is that those specs were a compromise between the ultimate goal of exact and what the hardware vendors could do with reasonable performance. I would expect that over time the requirements will improve in accuracy, with the native and fast versions existing for greater speed. As for implementations, that's a really tricky subject. I know a lot of system math libraries have difficulty meeting those standards across the full range, so it's really quite difficult to get it right. Unfortunately I'm not a numerics guy so I can't be more helpful than that.

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