QuadMP.cpp

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#include <math.h>
#include <complex>
extern "C" {
#include <quadmath.h>
}
#include "mpreal.h"
#include "Lib3_GK.h"
#include "SD.h"
 
/* error return codes */
#define SUCCESS 0
#define FAILURE 1
 
using namespace std;
namespace {
    typedef mpfr::mpreal mpREAL;
    typedef const mpREAL & mpREAL_t;
    typedef complex<mpREAL> mpCOMPLEX;
    typedef std::function<int(unsigned yn, mpREAL *y, mpREAL *e, const mpREAL & x, void *fdata)> f1Type;
    typedef const f1Type & f1Type_t;
    typedef std::function<int(unsigned yn, mpREAL *y, mpREAL *e, unsigned xdim, const mpREAL *x, void *fdata)> fnType;
    typedef const fnType & fnType_t;
    typedef void (*PrintHookerType) (mpREAL *, mpREAL *, size_t *, void *);
}
 
extern mpREAL mpPi;
extern mpREAL mpEuler;
extern mpCOMPLEX mpiEpsilon;
 
namespace {
    size_t _nGK_ = 10000;
    size_t _mGK_ = 10; // sets (2m+1)-point Gauss-Kronrod
    
    int QuadPack1(unsigned yn, mpREAL *oval, mpREAL *oerr, f1Type_t f, mpREAL_t epsabs, PrintHookerType PrintHooker, void *fdata) {
        GK gk(_nGK_, _mGK_);
        Function F(yn,f,fdata);
        try {
            return gk.QAG(F, 0, 1, epsabs, 0, oval, oerr, PrintHooker);
        } catch (const char* reason) {
            cout << reason << endl;
            throw reason;
        }
        return SUCCESS;
    }
    
    int QuadPackN(unsigned yn, mpREAL *oval, mpREAL *oerr, unsigned xdim, fnType_t f, mpREAL_t eps, PrintHookerType PrintHooker, void *fdata) {
        if(xdim==1) {
            auto f1 = [f,eps](unsigned yn, mpREAL *y, mpREAL *e, mpREAL_t x, void *fdata)->int {
                mpREAL xs[1];
                xs[0] = x;
                return f(yn,y,e,1,xs,fdata);
            };
            return QuadPack1(yn, oval, oerr, f1, eps, PrintHooker, fdata);
        }
        
        auto f1 = [f,eps,xdim](unsigned yn, mpREAL *y, mpREAL *e, mpREAL_t x, void *fdata)->int {
            auto f2 =[f,x](unsigned yn, mpREAL *y1, mpREAL *e1, unsigned xdim1, const mpREAL *xs1, void *fdata1)->int {
                mpREAL xs[xdim1+1];
                if(true) { // insert first
                    xs[0] = x;
                    for(int i=0; i<xdim1; i++) xs[i+1] = xs1[i];
                } else { // insert last
                    for(int i=0; i<xdim1; i++) xs[i] = xs1[i];
                    xs[xdim1] = x;
                }
                return f(yn,y1,e1,xdim1+1,xs,fdata1);
            };
            return QuadPackN(yn,y,e,xdim-1,f2,eps/xdim,NULL,fdata);
        };
        return QuadPack1(yn, oval, oerr, f1, eps, PrintHooker, fdata);
    }
    
}
 
namespace HepLib::SD {
 
/*-----------------------------------------------------*/
// QuadMP Classes
/*-----------------------------------------------------*/
 
ex QuadMP::mp2ex(const mpREAL & num) {
    ostringstream oss;
    oss.precision(MPDigits);
    oss << num;
    string sn = oss.str();
    numeric ret(sn.c_str());
    return ret;
}
 
int QuadMP::Wrapper(unsigned ydim, mpREAL *y, mpREAL *e, unsigned xdim, const mpREAL *x, void *fdata) {
    auto self = (QuadMP*)fdata;
    self->IntegrandMP(xdim, x, ydim, y, self->mpParameter, self->mpLambda);
    // Check NaN/Inf
    bool ok = true;
    for(int j=0; j<ydim; j++) {
        if(!isfinite(y[j])) { ok = false; break; }
    }
    if(!ok) {
        mpfr::mpreal::set_default_prec(mpfr::digits2bits(self->MPDigits*10));
        self->IntegrandMP(xdim, x, ydim, y, self->mpParameter, self->mpLambda);
        mpfr::mpreal::set_default_prec(mpfr::digits2bits(self->MPDigits));
    }
    for(int j=0; j<ydim; j++) e[j] = 0; // assume error can be ignored
    return SUCCESS;
}
 
void QuadMP::DefaultPrintHooker(mpREAL* result, mpREAL* epsabs, size_t * nrun, void *fdata) {
    auto self = (QuadMP*)fdata;
    if(*nrun == self->nGK + 1979) return;
    if(self->RunTime>0) {
        auto cur_timer = time(NULL);
        auto used_time = difftime(cur_timer,self->StartTimer);
        if(used_time>self->RunTime) {
            self->NEval = *nrun;
            *nrun = self->nGK + 1979;
            if(Verbose>10) cout << WarnColor << "     Exit with Run out of Time: " << used_time << RESET << endl;
            return;
        }
    }
    if(Verbose>10) {
        auto r0 = result[0];
        auto r1 = result[1];
        auto e0 = epsabs[0].toString(3);
        auto e1 = epsabs[1].toString(3);
        cout << "     L: " << (*nrun) << ", ";
        if(self->ReIm==3 || self->ReIm==1) cout << "[" << r0 << ", " << e0 << "]";
        if(self->ReIm==3 || self->ReIm==2) cout << "+I*[" << r1 << ", " << e1 << "]";
        cout << endl;
    }
    self->NEval = *nrun;
 
    bool rExit = (epsabs[0] < self->EpsAbs+1E-50Q) || (epsabs[0] < fabs(result[0])*self->EpsRel+1E-50Q);
    bool iExit = (epsabs[1] < self->EpsAbs+1E-50Q) || (epsabs[1] < fabs(result[1])*self->EpsRel+1E-50Q);
    if(rExit && iExit) {
        *nrun = self->nGK + 1979;
        return;
    }
 
    auto pid = getpid();
    ostringstream fn;
    fn << pid << ".int.done";
    if(file_exists(fn.str().c_str())) {
        self->NEval = *nrun;
        *nrun = self->nGK + 1979;
        ostringstream cmd;
        cmd << "rm " << fn.str();
        auto rc = system(cmd.str().c_str());
        if(Verbose>10) cout << "     Exit: " << fn.str() << endl;
    }
}
 
ex QuadMP::Integrate(size_t n) {
    if(mpfr_buildopt_tls_p()<=0) throw Error("Integrate: mpfr_buildopt_tls_p()<=0.");
    mpfr_free_cache();
    mpfr::mpreal::set_default_prec(mpfr::digits2bits(MPDigits));
    mpPi = mpfr::const_pi();
    mpEuler = mpfr::const_euler();
    mpiEpsilon = complex<mpREAL>(0,mpfr::machine_epsilon()*100);
    
    unsigned int xdim = XDim;
    unsigned int ydim = 2;
    mpREAL result[ydim], estabs[ydim];
 
    NEval = 0;
    _mGK_ = mGK;
    _nGK_ = n==0 ? nGK : n;
    StartTimer = time(NULL);
    auto nok = QuadPackN(ydim, result, estabs, xdim, Wrapper, EpsAbs, n==0 ? PrintHooker : NULL, this);
    
    if(nok) {
        mpREAL abs_res = sqrt(result[0]*result[0]+result[1]*result[1]);
        mpREAL abs_est = sqrt(estabs[0]*estabs[0]+estabs[1]*estabs[1]);
        mpREAL mpfr_eps = 10*mpfr::machine_epsilon();
        if( (abs_res < mpfr_eps) && (abs_est < mpfr_eps) ) {
            cout << ErrColor << "QuadMP Failed with 0 result returned!" << RESET << endl;
            return NaN;
        }
    }
    
    ex FResult = 0;
    if(isnan(result[0]) || isnan(result[1])) FResult += NaN;
    else {
        try{
            FResult += VE(mp2ex(result[0]), mp2ex(estabs[0]));
            FResult += VE(mp2ex(result[1]), mp2ex(estabs[1])) * I;
        } catch(...) {
            FResult += NaN;
        }
    }
 
    return FResult;
}
 
}