logarytmy

#include <iostream>
#include <chrono>
#include <cmath>
#include <algorithm>

using namespace std;


class stoper
{public:
    chrono::time_point<chrono::high_resolution_clock> a,b;
    void start(){a = chrono::high_resolution_clock::now();}
    void stop() {b = chrono::high_resolution_clock::now();}
    void show()
    {
        chrono::duration<double> elapsed_seconds = b-a;
        cout << elapsed_seconds.count()<<"s ";
    }
};


template <typename cfun>
double test(cfun fun)
{
    double aku=0;
    for (int i=0;i<5;i++)
    {
        stoper st;
        st.start();

        for (double x=1;x<10000000;x+=1.01 )
        {
            aku +=  fun(x);
        }
        st.stop();
        st.show();
    }
    cout<<endl;
    return aku;
}


double shitlog2(double x)
{
    int w;
    x = frexp(x,&w);
    return w + 2.0*(x-1.0);
}

double fastlog2(double x)
{
    int w;
    x = frexp(x,&w);
    return w + ((((1.43202073027606*x-6.64984902163488)*x+13.0262412232996)*x
            -14.1861534849729)*x+10.1772348373405)*x-3.79948152975902;
}
double mylog2_17(double x)
{
    int w;
    x = frexp(x,&w);
return w +95.0354082212196444880354135069-100.5 +
 x *(34.6797528315816853011413739901 +
    x *(-195.451529212527416014523545585 +
       x *(914.687118367090492019088236267 +
          x *(-3359.00328658200541339129556488 +
             x *(9739.55993077093141495559279973 +
                x *(-22548.3565655480936147709657466 +
                   x* (42039.3539337947134863905451932 +
                    x* (-63422.0205169046056292386635416 +
                    x *(77487.8101813068073659642177593 +
                    x* (-76418.7051434147324374252002510 +
                    x* (60345.2464877410927129479719750 +
                    x* (-37623.7416809594729290426177664 +
                    x* (18108.4544635302497336104275950 +
                    x* (-6491.01004625378413321975755283 +
                    x* (1631.56187150122776398754613596 +
                    x* (-256.603734082675540229189858863 +
                    19.0033548929828164153801905343 *x))))))))))))))));
}
double mylog2_19(double x)
{
    int w;
    x = frexp(x,&w);
return w +94.879552359370389779311310752431677657546488670131-100.5+
        x*(38.760953171904166937692617024628986668555406124947+
        x*(-245.85943859848429206309024729452081797918448383011+
        x*(1305.0213373140979443003790999604901721351935859746+
        x*(-5483.3897186528672757505743075974516855722609750103+
        x*(18373.369285947488212376445282807142432894707031893+
        x*(-49720.330484326774507017799362836307490489909887034+
        x*(109801.21447583798026544996683803403658873989417970+
        x*(-199301.45445926506025828784277462614378129514274147+
        x*(298501.60630250569282203503684755811600024394635379+
        x*(-369205.43714028094981807593680305547807524091749705+
        x*(376227.86563934815887666995648017764570129251640536+
        x*(-314015.29189075395963525655516844515933367689469445+
        x*(212512.59498006697236627947497199497997106198214730+
        x*(-114798.02778261877254409048412664787618047864843291+
        x*(48332.575660801499026504675067647169449538315154290+
        x*(-15283.729869425976544135405204428853285998986213565+
        x*(3414.6711038764781556224963615063635427392290076089+
        x*(-480.58172520332090598267316843954641211274866464892+
        x*32.04321789652355477774462860249555604587514031906
        ))))))))))))))))));
}

double mylog2_pade_7_6(double x)
{
    if (x<0) return nan("");
    int w;
    x = frexp(x,&w);
return w+
(-0.138283895467597308734825929 +
   x* (-4.75644115041872693502244398 +
      x *(-28.2901284421308848729647527 +
         x *(-31.020711652270330663079404 +
            x *(26.954639037773333537566195 +
               x *(32.065091647893956780806165 +
(5.14481531055604261525940722 +
                    0.0410191440642069963727475423* x)* x))))))
   /(0.01773580523008302467852483039 +
   x *(1.066870914453938639820160162 +
      x* (11.40739806765892909737152090 +
         x* (35.97371731450040844764454601 +
            x* (38.11130966747411808773004738 +
               x* (12.86083151020947229832310848 + x))))));
}

int main()
{
    stoper st;
    st.start();
    double aku=0;
    for (double x=1;x<10000;x+=1.01 )
    {
        aku = aku + log(x);
    }
    st.stop();
    st.show();
    cout<<endl;

    cout<< "log: ";
    aku+=test([](double x) {return log(x);} );
    cout<< "log10: ";
    aku+=test([](double x) {return log10(x);} );
    cout<< "log2: ";
    aku+=test([](double x) {return log2(x);} );
    cout<< "shitlog2 ";
    aku+=test(shitlog2 );
    cout<< "fastlog2 ";
    aku+=test(fastlog2 );
    cout<< "mylog2_17 ";
    aku+=test(mylog2_17 );
    cout<< "mylog2_19 ";
    aku+=test(mylog2_19 );
    cout<< "mylog2_pade_7_6 ";
    aku+=test(mylog2_pade_7_6 );


    cout<<aku<<endl;

    cout<<"  x     std::log2, Dshitlog Dfastlog Dmylog17 Dmylog19 Dpade7_6"<<endl;
    for (double x=0.01;x<100;x*=1.04)
    {
        cout<<x<<" "<<log2(x)<<" "<</*shitlog2(x)<<" "<<fastlog2(x)<<" "<<mylog2_17(x)<<" "<<mylog2_19(x)<<" "<<*/
              shitlog2(x)-log2(x)<<" "<<fastlog2(x)-log2(x)<<" "<<mylog2_17(x)-log2(x)<<
              " "<<mylog2_19(x)-log2(x)<<" "<<mylog2_pade_7_6(x)-log2(x)<<endl;

    }




}