I applaud such efforts, but users (or WG21 reviewers) of a linear algebra library might be scared away if they think they need deep understanding of floating-point semantics in order to use the library : - ) Also, I don't think we need most of this. Different algorithms have different requirements for the matrix element type. For example, most BLAS operations work fine with just addition and multiplication. That covers the GraphBLAS / "graph algorithms in the language of linear algebra" case. Some BLAS operations and a lot of matrix factorizations really would like division. Some algorithms need comparison, some need absolute values, and some ask for numeric_limits - style traits like the underflow threshold. The requirements really should be per algorithm, so that users with more restrictive types could still get some functionality.

mfh

On 3/7/19, 12:01 PM, "SG14 on behalf of Jayesh Badwaik" <sg14-bounces_at_lists.isocpp.org on behalf of badwaik.jayesh_at_gmail.com> wrote:

    http://homepage.divms.uiowa.edu/~tinelli/papers/BraEtAl-ARITH-15.pdf
    
    I have sent a link to a paper which tries to have formal semantics
    for floating point numbers. We have shifted to manually specifying
    types which should be matrix elements by using `is_matrix_element`
    trait. However, I feel this would be instructive to look at anyway.
    
    
    
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    Best
    Jayesh Badwaik
    https://jayeshbadwaik.github.io
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