Re: [boost] [Units] test_trig fails on Sandia-darwin-4.4 (caused by compile-time evaluation of math functions)

Subject: Re: [boost] [Units] test_trig fails on Sandia-darwin-4.4 (caused by compile-time evaluation of math functions)
From: Mathias Gaunard (mathias.gaunard_at_[hidden])
Date: 2011-08-21 10:56:19

On 08/21/2011 04:19 PM, Michel MORIN wrote:
> The Units' test (libs/units/test/test_trig.cpp) fails on Sandia-darwin-4.4:
>      http://tinyurl.com/3wherck
>
> The failure is caused by the fact that the results of `std::acos(0.2)` and
> `std::acos(d)` (double d = 0.2) are NOT equal on Sandia-darwin-4.4.
>
> On gcc-4.3 and newer versions, built-in math functions having
> constant arguments are evaluated at compile time
> using the MPFR (Multiple Precision Floating-Point Reliable) library.
> This happens even if optimization is disabled.
>
> So, the results of
>      std::acos(0.2); // evaluated by the MPFR library at compile time
> and
>      double d = 0.2;
>      std::acos(d); // evaluated by the built-in function at run time
> are different. (If we compile with optimization enabled,
> the latter code is also evaluated by the MPFR library at compile time.)
>
> The solution to this problem is
>    * Change BOOST_CHECK_EQUAL to BOOST_CHECK_CLOSE_FRACTION.
> or
>    * Change `std::acos(0.2)` to `std::acos(d)` (with `double d = 0.2`)
>
> An interesting thing is that the test fails only on Sandia-darwin
> (x86-64) platform. On other platforms using gcc 4.3-4.6, the test runs
> successfully. I suspect that they have 80-bit registers and so the result
> of `std::acos(d)` is as accurate as the result of the MPFR library.
> Do you have any thoughts about this?

This seems correct.

The compile-time evaluation of GCC yields correctly-rounded results, 
which is not the case of the runtime evaluation.

I don't know what BOOST_CHECK_CLOSE_FRACTION does, but I don't think 
there is any guarantee at all about the accuracy of the standard 
mathematical functions.