How to use sqrt and ceil with Boost::multiprecisio

Do you know how to do this simple line of code without error using Boost::multiprecison ?

boost::multiprecision::cpp_int v, uMax, candidate;
//...
v += 6 * ceil((sqrt(uMax * uMax - candidate) - v) / 6);

Using MSVC there is an error for "sqrt" and it's possible to fix it with:

v += 6 * ceil((sqrt(static_cast<boost::multiprecision::cpp_int>(uMax * uMax - candidate)) - v) / 6);

Then there is an error for "ceil" and it's possible to fix it with:

namespace bmp = boost::multiprecision;
typedef bmp::number<bmp::cpp_dec_float<0>> float_bmp;
v += 6 * ceil(static_cast<float_bmp>((sqrt(static_cast<bmp::cpp_int>(uMax * uMax - candidate)) - v) / 6));

Then there is an error of "generic interconvertion" !?!

I think there should be a more elegant way to realize a so simple line of code, isn't it? Let me know if you have some ideas about it please.

Regards.

回答1:

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:

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<>).

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>();

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:

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#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);
    }
}

回答2:

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