The simple truth is I never consider this.

When it came up the last time I didn’t really think about it very much as I
was involved in other things and I hoped intereste[d] parties might come to a
consensus without my having to bend my over-stretched brain.

(goes on to discuss workarounds)

这似乎是正确的,在我的测试中只有二进制档案支持inf / nan.

除了nan / inf之外,Xml和文本存档都支持所有精度：

Live On Coliru

using BIA = boost::archive::binary_iarchive;
using BOA = boost::archive::binary_oarchive;
using TIA = boost::archive::text_iarchive;
using TOA = boost::archive::text_oarchive;
using XIA = boost::archive::xml_iarchive;
using XOA = boost::archive::xml_oarchive;

int main() {

    // supported:
    assert((perform_test<BIA,BOA,use_nan,use_inf,use_range>()));
    assert((perform_test<XIA,XOA,no_nan,no_inf,use_range>()));
    assert((perform_test<TIA,TOA,use_range>()));

    // not supported:
    assert(!(perform_test<XIA,use_inf>()));
    assert(!(perform_test<TIA,use_inf>()));

    assert(!(perform_test<XIA,no_inf>()));
    assert(!(perform_test<TIA,no_inf>()));

}

完整清单

后人：

#include <boost/archive/xml_oarchive.hpp>
#include <boost/archive/xml_iarchive.hpp>
#include <boost/archive/binary_oarchive.hpp>
#include <boost/archive/binary_iarchive.hpp>
#include <boost/archive/text_oarchive.hpp>
#include <boost/archive/text_iarchive.hpp>
#include <boost/serialization/vector.hpp>
#include <sstream>

using namespace boost::archive;

static bool equal_or_nan(double a,double b) {
    return (std::isnan(a) && std::isnan(b)) || a==b;
}

template <typename IA,typename OA,bool withNan   = true,bool withInf   = true,bool withRange = true>
bool perform_test() 
{
    std::vector<double> const v {
        withRange? std::numeric_limits<double>::min()       : 0,withRange? std::numeric_limits<double>::max()       : 0,withRange? std::numeric_limits<double>::epsilon()   : 0,withNan?   std::numeric_limits<double>::quiet_NaN() : 0,withInf?   std::numeric_limits<double>::infinity()  : 0,withInf? - std::numeric_limits<double>::infinity()  : 0,};

    std::stringstream ss;
    {
        OA oa(ss);
        oa << boost::serialization::make_nvp("element",v);
    }

    try
    {
        IA ia(ss);
        std::vector<double> w;
        ia >> boost::serialization::make_nvp("element",w);

        return std::equal(v.begin(),v.end(),w.begin(),equal_or_nan);
    } catch(...) {
        return false;
    }
}

static constexpr bool use_inf = true,use_nan = true,use_range = true;
static constexpr bool no_inf  = false,no_nan = false,no_range = false;

using BIA = boost::archive::binary_iarchive;
using BOA = boost::archive::binary_oarchive;
using TIA = boost::archive::text_iarchive;
using TOA = boost::archive::text_oarchive;
using XIA = boost::archive::xml_iarchive;
using XOA = boost::archive::xml_oarchive;

int main() {

    // supported:
    assert((perform_test<BIA,no_inf>()));

}