How to use sqrt and ceil with Boost::multiprecision?

北城以北 提交于 2019-12-01 19:35:42

The "problem" (it's actually a feature) is that you are using the number<> frontend with template expressions enabled.

This means that many operations can be greatly optimized or even eliminated before code is generated by the compiler.

You have two options:

  1. break things down

    using BF = boost::multiprecision::cpp_bin_float_100;
    using BI = boost::multiprecision::cpp_int;
    BI v = 1, uMax = 9, candidate = 1;
    
    //v += 6 * ceil((sqrt(uMax * uMax - candidate) - v) / 6);
    BF tmp1(uMax * uMax - candidate);
    BF tmp2(sqrt(tmp1) - BF(v));
    BF tmp3(ceil(tmp2 / 6));
    BI tmp4(tmp3.convert_to<BI>());
    std::cout << tmp1 << " " << tmp2 << " " << tmp3 << " " << tmp4 << "\n";
    
    v = v + 6*tmp4;
    

    So you could write

    v += 6*ceil((sqrt(BF(uMax * uMax - candidate)) - BF(v)) / 6).convert_to<BI>();
    

    Which works by forcing evaluation of expression templates (and potentially lossy conversion from float -> integer using convert_to<>).

  2. In general you could switch to non-expression-template versions of the types:

    using BF = mp::number<mp::cpp_bin_float_100::backend_type, mp::et_off>;
    using BI = mp::number<mp::cpp_int::backend_type, mp::et_off>;
    

    In this particular case it doesn't change much because you still have to do type "coercions" from integer -> float -> integer:

    v += 6 * ceil((sqrt(BF(uMax * uMax - candidate)) - BF(v)) / 6).convert_to<BI>();
    
  3. By simplifying, if you make all types float instead (e.g. cpp_dec_float) you can get rid of these complicating artefacts:

    using BF = mp::number<mp::cpp_dec_float_100::backend_type, mp::et_off>;
    BF v = 1, uMax = 9, candidate = 1;
    
    v += 6 * ceil((sqrt(uMax * uMax - candidate) - v) / 6);
    

    CAVEAT Use your profiler to see that using et_off doesn't cause a performance problem on your code-base

Here's a demo program showing all three approaches:

Live On Coliru

#include <boost/multiprecision/cpp_int.hpp>
#include <boost/multiprecision/cpp_bin_float.hpp>
#include <boost/multiprecision/cpp_dec_float.hpp>
#include <boost/multiprecision/number.hpp>

int main() {
    namespace mp = boost::multiprecision;
    //v += 6 * ceil((sqrt(uMax * uMax - candidate) - v) / 6);
    {
        using BF = mp::cpp_bin_float_100;
        using BI = mp::cpp_int;
        BI v = 1, uMax = 9, candidate = 1;

#ifdef DEBUG
        BF tmp1(uMax * uMax - candidate);
        BF tmp2(sqrt(BF(uMax * uMax - candidate)) - BF(v));
        BF tmp3(ceil(tmp2 / 6));
        BI tmp4(tmp3.convert_to<BI>());
        std::cout << tmp1 << " " << tmp2 << " " << tmp3 << " " << tmp4 << "\n";
#endif

        v += 6*ceil((sqrt(BF(uMax * uMax - candidate)) - BF(v)) / 6).convert_to<BI>();
    }

    {
        using BF = mp::number<mp::cpp_bin_float_100::backend_type, mp::et_off>;
        using BI = mp::number<mp::cpp_int::backend_type, mp::et_off>;
        BI v = 1, uMax = 9, candidate = 1;

        v += 6 * ceil((sqrt(BF(uMax * uMax - candidate)) - BF(v)) / 6).convert_to<BI>();
    }

    {
        using BF = mp::number<mp::cpp_dec_float_100::backend_type, mp::et_off>;
        BF v = 1, uMax = 9, candidate = 1;

        v += 6 * ceil((sqrt(uMax * uMax - candidate) - v) / 6);
    }
}

Use boost::multiprecision::sqrt and boost::multiprecision::ceil.

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