Re: about boost::math

From: Matt Borland (matt_at_[hidden])
Date: 2023-04-14 13:37:23

> Hi Matt,
> Thanks for your comments. But I don't want to go that far, since the rest of the math functions will hopefully be constexpr with C++26 (https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2023/p1383r1.pdf). An implementation in ccmath would be very elaborate.
> My questions were related to how I can now provide additional math functions without much effort; to stay with the cot example (simplified):
>
> 1) without constexpr
> template <typename Type> inline auto cot(const Type x) noexcept { return 1/std::tan(x); }
> This would have the disadvantage that performance might be wasted if the compiler already provides std::tan constexpr (e.g. gcc).
>
> 2) "optimistic" with constexpr
> template <typename Type> inline constexpr auto cot ...
> constexpr auto y = cot(2); // gcc ok else error "not constexpr"
> This may give a CT error. The question is if this would be acceptable from your side.
>
> 3) additional macro e.g. BOOST_MATH_CONSTEXPR
> #if (BOOST_GCC && __cplusplus >= 201103L) || (defined(__cpp_lib_constexpr_cmath) && __cpp_lib_constexpr_cmath >= 202202L)
> #define BOOST_MATH_CONSTEXPR constexpr
> #else
> #define BOOST_MATH_CONSTEXPR
> #endif
> template <typename Type> inline BOOST_MATH_CONSTEXPR auto cot ...
> BOOST_MATH_CONSTEXPR auto y = cot(2);
> Disadvantage: the macro must always be kept up to date (maintenance effort).
>
> Which would be the best solution?
>
> thx
> Gero

Gero,

For seemingly trivial functions like cot = 1 / tan having an accurate implementation is non-trivial. You will want to implement this using a minmax polynomial instead https://en.wikipedia.org/wiki/Remez_algorithm. If you look in various standard library implementations they use these polynomials instead of trigonometric identities (e.g. sin = cos(pi/2 - theta)) for accuracy*. These are certainly more elaborate to implement. The current ccmath functions are all cross-platform so we do not have a dependency on GCC. I would recommend that if you want to proceed that you follow the way we implement functions we already ship in ccmath.

Matt

*https://github.com/bpowers/musl/blob/master/src/math/__sin.c and https://github.com/bpowers/musl/blob/master/src/math/__cos.c