test.c

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    gsl_function f = make_function(&f15, &alpha);
    gsl_function fc = make_counter(&f, &p) ;

    status = gsl_integration_qagiu (&fc, 0.0, 0.0, 1.0e-7, w->limit,
                                    w, 
                                    &result, &abserr) ;
    
    gsl_test_rel(result,exp_result,1e-14,"qagiu(f15) smooth result") ;
    gsl_test_rel(abserr,exp_abserr,1e-5,"qagiu(f15) smooth abserr") ;
    gsl_test_int((int)(p.neval),exp_neval,"qagiu(f15) smooth neval") ;  
    gsl_test_int((int)(w->size),exp_last,"qagiu(f15) smooth last") ;  
    gsl_test_int(status,exp_ier,"qagiu(f15) smooth status") ;

    for (i = 0; i < 10 ; i++) 
        gsl_test_rel(w->alist[i],a[i],1e-15,"qagiu(f15) smooth alist") ;

    for (i = 0; i < 10 ; i++) 
        gsl_test_rel(w->blist[i],b[i],1e-15,"qagiu(f15) smooth blist") ;

    for (i = 0; i < 10 ; i++) 
        gsl_test_rel(w->rlist[i],r[i],1e-15,"qagiu(f15) smooth rlist") ;

    for (i = 0; i < 10 ; i++) 
        gsl_test_rel(w->elist[i],e[i],1e-4,"qagiu(f15) smooth elist") ;

    for (i = 0; i < 10 ; i++) 
        gsl_test_int((int)w->order[i],order[i]-1,"qagiu(f15) smooth order");

    gsl_integration_workspace_free (w) ;

  }

  /* Test infinite range integral f16 using an absolute error bound */

  {
    int status = 0, i; struct counter_params p;
    double result = 0, abserr=0;

    gsl_integration_workspace * w = gsl_integration_workspace_alloc (1000) ;

    /* All results are for GSL_IEEE_MODE=double-precision */

    double exp_result = 1.000000000006713292E-04;
    double exp_abserr = 3.084062020905636316E-09;
    int exp_neval  =      165;
    int exp_ier    =        0;
    int exp_last   =        6;

    double a[6] = { 0.000000000000000000E+00,
                    5.000000000000000000E-01,
                    2.500000000000000000E-01,
                    1.250000000000000000E-01,
                    6.250000000000000000E-02,
                    3.125000000000000000E-02 } ;
    double b[6] = { 3.125000000000000000E-02,
                    1.000000000000000000E+00,
                    5.000000000000000000E-01,
                    2.500000000000000000E-01,
                    1.250000000000000000E-01,
                    6.250000000000000000E-02 } ;
    double r[6] = { 7.633587786326674618E-05,
                    9.900990099009899620E-07,
                    1.922522349322310737E-06,
                    3.629434715543053753E-06,
                    6.501422186103209199E-06,
                    1.062064387653501389E-05 } ;
    double e[6] = { 3.084061858351569051E-09,
                    3.112064814755089674E-17,
                    4.543453652226561245E-17,
                    4.908618166361344548E-17,
                    3.014338672269481784E-17,
                    6.795996738013555461E-18 } ;
    int order[6] = { 1, 4, 3, 2, 5, 6 } ;

    double alpha = 1.0;

    gsl_function f = make_function(&f16, &alpha);
    gsl_function fc = make_counter(&f, &p) ;

    status = gsl_integration_qagiu (&fc, 99.9, 1.0e-7, 0.0, w->limit,
                                    w, 
                                    &result, &abserr) ;
    
    gsl_test_rel(result,exp_result,1e-14,"qagiu(f16) smooth result") ;
    gsl_test_rel(abserr,exp_abserr,1e-5,"qagiu(f16) smooth abserr") ;
    gsl_test_int((int)(p.neval),exp_neval,"qagiu(f16) smooth neval") ;  
    gsl_test_int((int)(w->size),exp_last,"qagiu(f16) smooth last") ;  
    gsl_test_int(status,exp_ier,"qagiu(f16) smooth status") ;

    for (i = 0; i < 6 ; i++) 
        gsl_test_rel(w->alist[i],a[i],1e-15,"qagiu(f16) smooth alist") ;

    for (i = 0; i < 6 ; i++) 
        gsl_test_rel(w->blist[i],b[i],1e-15,"qagiu(f16) smooth blist") ;

    for (i = 0; i < 6 ; i++) 
        gsl_test_rel(w->rlist[i],r[i],1e-15,"qagiu(f16) smooth rlist") ;

    for (i = 0; i < 6 ; i++) 
        gsl_test_rel(w->elist[i],e[i],1e-4,"qagiu(f16) smooth elist") ;

    for (i = 0; i < 6 ; i++) 
        gsl_test_int((int)w->order[i],order[i]-1,"qagiu(f16) smooth order");

    gsl_integration_workspace_free (w) ;

  }

  /* Test infinite range integral myfn1 using an absolute error bound */

  {
    int status = 0, i; struct counter_params p;
    double result = 0, abserr=0;

    gsl_integration_workspace * w = gsl_integration_workspace_alloc (1000) ;

    /* All results are for GSL_IEEE_MODE=double-precision */

    double exp_result = 2.275875794468747770E+00;
    double exp_abserr = 7.436490118267390744E-09;
    int exp_neval  =      270;
    int exp_ier    =        0;
    int exp_last   =        5;

    double a[5] = { 1.250000000000000000E-01,
                    5.000000000000000000E-01,
                    2.500000000000000000E-01,
                    0.000000000000000000E+00,
                    3.750000000000000000E-01 } ;
    double b[5] = { 2.500000000000000000E-01,
                    1.000000000000000000E+00,
                    3.750000000000000000E-01,
                    1.250000000000000000E-01,
                    5.000000000000000000E-01 } ;
    double r[5] = { 4.639317228058405717E-04,
                    1.691664195356748834E+00,
                    1.146307471900291086E-01,
                    4.379392477350953574E-20,
                    4.691169201991640669E-01 } ;
    double e[5] = { 3.169263960393051137E-09,
                    4.265988974874425043E-09,
                    1.231954072964969637E-12,
                    8.360902986775307673E-20,
                    5.208244060463541433E-15 } ;
    int order[5] = { 2, 1, 3, 5, 4 } ;

    gsl_function f = make_function(&myfn1, 0);
    gsl_function fc = make_counter(&f, &p) ;

    status = gsl_integration_qagi (&fc, 1.0e-7, 0.0, w->limit,
                                   w, 
                                   &result, &abserr) ;
    
    gsl_test_rel(result,exp_result,1e-14,"qagiu(myfn1) smooth result") ;
    gsl_test_rel(abserr,exp_abserr,1e-5,"qagiu(myfn1) smooth abserr") ;
    gsl_test_int((int)(p.neval),exp_neval,"qagiu(myfn1) smooth neval") ;  
    gsl_test_int((int)(w->size),exp_last,"qagiu(myfn1) smooth last") ;  
    gsl_test_int(status,exp_ier,"qagiu(myfn1) smooth status") ;

    for (i = 0; i < 5 ; i++) 
        gsl_test_rel(w->alist[i],a[i],1e-15,"qagiu(myfn1) smooth alist") ;

    for (i = 0; i < 5 ; i++) 
        gsl_test_rel(w->blist[i],b[i],1e-15,"qagiu(myfn1) smooth blist") ;

    for (i = 0; i < 5 ; i++) 
        gsl_test_rel(w->rlist[i],r[i],1e-14,"qagiu(myfn1) smooth rlist") ;

    for (i = 0; i < 5 ; i++) 
        gsl_test_rel(w->elist[i],e[i],1e-4,"qagiu(myfn1) smooth elist") ;

    for (i = 0; i < 5 ; i++) 
        gsl_test_int((int)w->order[i],order[i]-1,"qagiu(myfn1) smooth order");

    gsl_integration_workspace_free (w) ;

  }

  /* Test infinite range integral myfn1 using an absolute error bound */

  {
    int status = 0, i; struct counter_params p;
    double result = 0, abserr=0;

    gsl_integration_workspace * w = gsl_integration_workspace_alloc (1000) ;

    /* All results are for GSL_IEEE_MODE=double-precision */

    double exp_result = 2.718281828459044647E+00;
    double exp_abserr = 1.588185109253204805E-10;
    int exp_neval  =      135;
    int exp_ier    =        0;
    int exp_last   =        5;

    double a[5] = { 0.000000000000000000E+00,
                    5.000000000000000000E-01,
                    2.500000000000000000E-01,
                    1.250000000000000000E-01,
                    6.250000000000000000E-02 } ;
    double b[5] = { 6.250000000000000000E-02,
                    1.000000000000000000E+00,
                    5.000000000000000000E-01,
                    2.500000000000000000E-01,
                    1.250000000000000000E-01 } ;
    double r[5] = { 8.315287189746029816E-07,
                    1.718281828459045091E+00,
                    8.646647167633871867E-01,
                    1.328565310599463256E-01,
                    2.477920647947255521E-03 } ;
    double e[5] = { 1.533437090413525935E-10,
                    4.117868247943567505E-12,
                    7.802455785301941044E-13,
                    5.395586026138397182E-13,
                    3.713312434866150125E-14 } ;
    int order[5] = { 1, 2, 3, 4, 5 } ;

    double alpha = 1.0 ;
    gsl_function f = make_function(&myfn2, &alpha);
    gsl_function fc = make_counter(&f, &p) ;

    status = gsl_integration_qagil (&fc, 1.0, 1.0e-7, 0.0, w->limit,
                                    w, 
                                    &result, &abserr) ;
    
    gsl_test_rel(result,exp_result,1e-14,"qagiu(myfn2) smooth result") ;
    gsl_test_rel(abserr,exp_abserr,1e-5,"qagiu(myfn2) smooth abserr") ;
    gsl_test_int((int)(p.neval),exp_neval,"qagiu(myfn2) smooth neval") ;  
    gsl_test_int((int)(w->size),exp_last,"qagiu(myfn2) smooth last") ;  
    gsl_test_int(status,exp_ier,"qagiu(myfn2) smooth status") ;

    for (i = 0; i < 5 ; i++) 
        gsl_test_rel(w->alist[i],a[i],1e-15,"qagiu(myfn2) smooth alist") ;

    for (i = 0; i < 5 ; i++) 
        gsl_test_rel(w->blist[i],b[i],1e-15,"qagiu(myfn2) smooth blist") ;

    for (i = 0; i < 5 ; i++) 
        gsl_test_rel(w->rlist[i],r[i],1e-14,"qagiu(myfn2) smooth rlist") ;

    for (i = 0; i < 5 ; i++) 
        gsl_test_rel(w->elist[i],e[i],1e-4,"qagiu(myfn2) smooth elist") ;

    for (i = 0; i < 5 ; i++) 
        gsl_test_int((int)w->order[i],order[i]-1,"qagiu(myfn2) smooth order");

    gsl_integration_workspace_free (w) ;

  }

  /* Test integral f454 with integrable singular points */

  {
    int status = 0, i; struct counter_params p;
    double result = 0, abserr=0;

    gsl_integration_workspace * w = gsl_integration_workspace_alloc (1000) ;

    /* All results are for GSL_IEEE_MODE=double-precision */

    double exp_result = 5.274080611672716401E+01;
    double exp_abserr = 1.755703848687062418E-04;
    int exp_neval  =        777;
    int exp_ier    =          0;
    int exp_last   =         20;

    double a[20] = { 9.687500000000000000E-01,
                    1.401269388548935790E+00,
                    1.414213562373095145E+00,
                    1.000000000000000000E+00,
                    0.000000000000000000E+00,
                    2.207106781186547462E+00,
                    1.810660171779821415E+00,
                    1.207106781186547462E+00,
                    5.000000000000000000E-01,
                    1.103553390593273731E+00,
                    1.612436867076458391E+00,
                    1.310660171779821415E+00,
                    7.500000000000000000E-01,
                    1.051776695296636976E+00,
                    1.513325214724776657E+00,
                    1.362436867076458391E+00,
                    8.750000000000000000E-01,
                    1.463769388548935790E+00,
                    1.388325214724776657E+00,
                    9.375000000000000000E-01} ;
    double b[20] = { 1.000000000000000000E+00,
                     1.414213562373095145E+00,
                     1.463769388548935790E+00,
                     1.051776695296636976E+00,
                     5.000000000000000000E-01,
                     3.000000000000000000E+00,
                     2.207106781186547462E+00,
                     1.310660171779821415E+00,
                     7.500000000000000000E-01,
                     1.207106781186547462E+00,
                     1.810660171779821415E+00,
                     1.362436867076458391E+00,
                     8.750000000000000000E-01,
                     1.103553390593273731E+00,
                     1.612436867076458391E+00,
                     1.388325214724776657E+00,
                     9.375000000000000000E-01,
                     1.513325214724776657E+00,
                     1.401269388548935790E+00,
                     9.687500000000000000E-01} ;
    double r[20] = { -1.125078814079027711E-01,
                     -1.565132123531515207E-01,
                     -4.225328513207429193E-01,
                     -1.830392049835374568E-01,
                     6.575875041899758092E-03,
                     4.873920540843067783E+01,
                     6.032891565603589079E+00,
                     -2.991531901645863023E-01,
                     -7.326282608704996063E-03,
                     -2.431894410706912923E-01,
                     5.911661670635662835E-01,
                     -2.236786562536174916E-01,
                     -5.647871991778510847E-02,
                     -1.305470403178642658E-01,
                     -1.721363984401322045E-01,
                     -1.5893454545