Current problems Currently, the math configuration mainly test for some math functions, and configure numpy accordingly. But instead of testing each desired function independently, the current system has been developed more as workarounds particular platform oddities, using platform implicit knowledge. This is against the normal philosophy of testing for capabilities only, which is the autoconf philosophy, which showed the path toward portability (on Unix at least) 1 This causes problems because modifying or adding configuration on existing platforms break the implicit assumption, without a clear solution. For example, on windows, when numpy is built with mingw, it would be nice to enforce the configuration sizeof(long double) sizeof(double) because mingw uses the MS runtime, and the MS runtime does not support long double. Unfortunately, doing so breaks the mingw math function detection, because of the implicit assumption that mingw has a configuration sizeof(long double)!= sizeof(double). Another example is the testing for set of functions using only one function: if expf is found, it is assumed that all basic float functions are available.
Instead, each function should be tested independently (expf, sinf, etc). Proposal We suggest to break any implicit assumption, and test each math function independently from each other, as usually done by autoconf. Since testing for a vast set of functions can be time consuming, we will use a scheme similar to ACCHECKFUNCSONCE in autoconf, that is test for a set of function at once, and only in the case it breaks, do the per function check.
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When the first check works, it should be as fast as the current scheme, except that the assumptions are explicitly checked (all functions implied by HAVELONGDOUBLEFUNCS would be checked together, for example).