by Pavel Panchekha with Ian Briggs and Yash Lad on Jun 3, 2024 | Tags: accuracy, approximation, awards, correctness, optimization, type systems
Numerical code needs to carefully balance accuracy and performance. A new DSL, MegaLibm, makes this easier by checking for numerical correctness and offering flexible compilation to efficient code. By reconceptualizing classic numerical techniques like polynomial approximation and range reduction as type-theoric operations like casts and binding operators, MegaLibm makes numerical code composable, and its ability to plug in mathematical an numerical tools (like Sollya) makes it easier and safer to write such code.
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by Santosh Nagarakatte and Jay Lim on Apr 28, 2022 | Tags: awards, correct math libraries, optimization, runtimes
To create a single polynomial approximation that produces correct results for multiple representations and rounding modes, we propose to generate a polynomial that generates the correctly rounded result of f(x) using the non-standard round-to-odd rounding mode with 2 additional precision bits compared to the largest floating point representation that we wish to support. We provide a proof that this method produces correctly rounded results for multiple representations and for all the standard rounding modes. More detailed explanation of our approach can be found in our POPL 2022 distinguished paper.
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by Sara Achour on Dec 14, 2021 | Tags: compilers, hardware, optimization, unconventional computing
Modern analog computers a host of analog behaviors that affect the fidelity of the mapped computation. How can we mitigate these analog behaviors in compilation?
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by Jay Lim and Santosh Nagarakatte on Aug 26, 2021 | Tags: awards, correct math libraries, optimization, program synthesis, runtimes
Everyone uses math libraries. Surprisingly, mainstream math libraries do not produce correct results for several thousands of inputs. Developers are seldom aware of them, which affects reproducibility and portability. We describe our new method for synthesizing elementary functions that produces correct results for all inputs but is also significantly faster than the state of the art libraries, which have been optimized for decades.
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by Kesha Hietala and Robert Rand on Jun 2, 2021 | Tags: compilers, formal verification, optimization, proof engineering, quantum computing
Learn how techniques from traditional compiler verification can be applied to the emerging domain of quantum computing.
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