test_sf.c

math library from gnu

  sa += ( re.err > TEST_TOL5 );
  sa += ( re.e10 != 868 );
  gsl_test(sa, "  gsl_sf_exp_e10_e(2000.0, &re)");


  TEST_SF(s, gsl_sf_exp_err_e, (-10.0, TEST_TOL1, &r), exp(-10.0), TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_exp_err_e, ( 10.0, TEST_TOL1, &r), exp( 10.0), TEST_TOL1, GSL_SUCCESS);

  sa = 0;
  sa += gsl_sf_exp_err_e10_e(1.0, TEST_SQRT_TOL0, &re);
  sa += ( test_sf_frac_diff(re.val, M_E ) > TEST_TOL1 );
  sa += ( re.err > 32.0 * TEST_SQRT_TOL0 );
  sa += ( re.e10 != 0 );
  gsl_test(sa, "  gsl_sf_exp_err_e10_e(1.0, TEST_SQRT_TOL0, &re)");

  sa = 0;
  sa += gsl_sf_exp_err_e10_e(2000.0, 1.0e-10, &re);
  sa += ( test_sf_frac_diff(re.val, 3.88118019428363725 ) > TEST_TOL3 );
  sa += ( re.err > 1.0e-07 );
  sa += ( re.e10 != 868 );
  gsl_test(sa, "  gsl_sf_exp_err_e10_e(2000.0, 1.0e-10, &re)");


  x = 0.8*GSL_LOG_DBL_MAX;
  TEST_SF(s, gsl_sf_exp_mult_e, (-10.0,  1.0e-06, &r), 1.0e-06*exp(-10.0), TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_exp_mult_e, (-10.0,  2.0, &r),     2.0*exp(-10.0),     TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_exp_mult_e, (-10.0, -2.0, &r),    -2.0*exp(-10.0),     TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_exp_mult_e, ( 10.0,  1.0e-06, &r), 1.0e-06*exp( 10.0), TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_exp_mult_e, ( 10.0, -2.0, &r),    -2.0*exp( 10.0),     TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_exp_mult_e, (x, 1.00001, &r),      1.00001*exp(x),     TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_exp_mult_e, (x, 1.000001, &r),     1.000001*exp(x),    TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_exp_mult_e, (x, 1.000000001, &r),  1.000000001*exp(x), TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_exp_mult_e, (x, 100.0, &r),        100.0*exp(x),       TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_exp_mult_e, (x, 1.0e+20, &r),      1.0e+20*exp(x),     TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_exp_mult_e, (x, exp(-x)*exp(M_LN2), &r),  2.0, TEST_TOL4, GSL_SUCCESS );

  TEST_SF(s, gsl_sf_exp_mult_err_e, (-10.0, TEST_SQRT_TOL0, 2.0, TEST_SQRT_TOL0, &r), 2.0*exp(-10.0), TEST_SQRT_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_exp_mult_err_e, (x, TEST_SQRT_TOL0*x, exp(-x)*exp(M_LN2), TEST_SQRT_TOL0*exp(-x)*exp(M_LN2), &r),  2.0, TEST_SQRT_TOL0, GSL_SUCCESS );

  sa = 0;
  sa += gsl_sf_exp_mult_e10_e(1.0, 1.0, &re);
  sa += ( test_sf_frac_diff(re.val, M_E ) > TEST_TOL0 );
  sa += ( re.err > TEST_TOL2 );
  sa += ( re.e10 != 0 );
  gsl_test(sa, "gsl_sf_exp_mult_e10_e(1.0, 1.0, &re)");
  TEST_SF_E10(s,  gsl_sf_exp_mult_e10_e, (1.0, 1.0, &re), M_E, 0, TEST_TOL0, GSL_SUCCESS);

  sa = 0;
  sa += gsl_sf_exp_mult_e10_e(1000.0, 1.0e+200, &re);
  sa += ( test_sf_frac_diff(re.val, 1.970071114017046993888879352) > TEST_TOL3 );
  sa += ( re.err > 1.0e-11 );
  sa += ( re.e10 != 634 );
  gsl_test(sa, "gsl_sf_exp_mult_e10_e(1000.0, 1.0e+200, &re)");
  TEST_SF_E10(s,  gsl_sf_exp_mult_e10_e, (1000.0, 1.0e+200, &re), 1.970071114017046993888879352, 634, TEST_TOL3, GSL_SUCCESS);

  sa = 0;
  sa += gsl_sf_exp_mult_err_e10_e(1.0, TEST_TOL0, 1.0, TEST_TOL0, &re);
  sa += ( test_sf_frac_diff(re.val, M_E ) > TEST_TOL0 );
  sa += ( re.err > TEST_TOL2 );
  sa += ( re.e10 != 0 );
  gsl_test(sa, "gsl_sf_exp_mult_err_e10_e(1.0, TEST_TOL0, 1.0, TEST_TOL0, &re)");
  TEST_SF_E10(s,  gsl_sf_exp_mult_err_e10_e, (1.0, TEST_TOL0, 1.0, TEST_TOL0, &re), M_E, 0, TEST_TOL0, GSL_SUCCESS);

  sa = 0;
  sa += gsl_sf_exp_mult_err_e10_e(1000.0, 1.0e-12, 1.0e+200, 1.0e+190, &re);
  sa += ( test_sf_frac_diff(re.val, 1.9700711140165661 ) > TEST_TOL3 );
  sa += ( re.err > 1.0e-09 );
  sa += ( re.e10 != 634 );
  gsl_test(sa, "gsl_sf_exp_mult_err_e10_e(1.0e-12, 1.0e+200, &re)");
  TEST_SF_E10(s,  gsl_sf_exp_mult_err_e10_e, (1000.0, 1.0e-12, 1.0e+200, 1.0e+190, &re), 1.9700711140165661,634, TEST_TOL3, GSL_SUCCESS);

  /* Test cases from Szymon Jaroszewicz */

  TEST_SF_E10(s,  gsl_sf_exp_mult_e10_e, (10000.0, 1.0, &re), 8.806818225662921587261496007, 4342, TEST_TOL5, GSL_SUCCESS);
  TEST_SF_E10(s,  gsl_sf_exp_mult_e10_e, (100.0, 1.0, &re), 2.688117141816135448412625551e43, 0, TEST_TOL2, GSL_SUCCESS);
  TEST_SF_E10(s,  gsl_sf_exp_e10_e, (100.0, &re), 2.688117141816135448412625551e43, 0, TEST_TOL2, GSL_SUCCESS);
  TEST_SF_E10(s,  gsl_sf_exp_e10_e, (1000.0, &re), 1.970071114017046993888879352, 434, TEST_TOL3, GSL_SUCCESS);
  TEST_SF_E10(s,  gsl_sf_exp_e10_e, (-100.0, &re), 3.720075976020835962959695803e-44, 0, TEST_TOL2, GSL_SUCCESS);
  TEST_SF_E10(s,  gsl_sf_exp_e10_e, (-1000.0, &re), 5.075958897549456765291809479, -435, TEST_TOL3, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_expm1_e, (-10.0, &r), exp(-10.0)-1.0, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expm1_e, (-0.001, &r), -0.00099950016662500845, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expm1_e, (-1.0e-8, &r), -1.0e-08 + 0.5e-16, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expm1_e, ( 1.0e-8, &r), 1.0e-08 + 0.5e-16, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expm1_e, ( 0.001, &r), 0.0010005001667083417, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expm1_e, ( 10.0, &r), exp(10.0)-1.0, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_exprel_e, (-10.0, &r), 0.0999954600070237515, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_e, (-0.001, &r), 0.9995001666250084, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_e, (-1.0e-8, &r), 1.0 - 0.5e-08, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_e, ( 1.0e-8, &r), 1.0 + 0.5e-08, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_e, ( 0.001, &r), 1.0005001667083417, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_e, ( 10.0, &r), 2202.5465794806716517, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_exprel_2_e, (-10.0, &r), 0.18000090799859524970, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_2_e, (-0.001, &r), 0.9996667499833361107, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_2_e, (-1.0e-8, &r), 0.9999999966666666750, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_2_e, ( 1.0e-8, &r), 1.0000000033333333417, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_2_e, ( 0.001, &r), 1.0003334166833361115, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_2_e, ( 10.0, &r), 440.3093158961343303, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_exprel_n_e, (3, -1000.0, &r), 0.00299400600000000000, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_n_e, (3, -100.0, &r), 0.02940600000000000000, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_n_e, (3, -10.0, &r), 0.24599972760042142509, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_n_e, (3, -3.0, &r), 0.5444917625849191238, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_n_e, (3, -0.001, &r), 0.9997500499916678570, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_n_e, (3, -1.0e-8, &r), 0.9999999975000000050, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_n_e, (3,  1.0e-8, &r), 1.0000000025000000050, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_n_e, (3,  0.001, &r), 1.0002500500083345240, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_n_e, (3,  3.0, &r), 2.5745637607083706091, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_n_e, (3,  3.1, &r), 2.6772417068460206247, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_n_e, (3,  10.0, &r), 131.79279476884029910, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_n_e, (3,  100.0, &r), 1.6128702850896812690e+38, TEST_TOL2, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_exprel_n_e, (50, -1000.0, &r), 0.04766231609253975959, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_n_e, (50, -100.0, &r), 0.3348247572345889317, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_n_e, (50, -10.0, &r), 0.8356287051853286482, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_n_e, (50, -3.0, &r), 0.9443881609152163615, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_n_e, (50, -1.0, &r), 0.980762245565660617, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_n_e, (50, -1.0e-8, &r), 1.0 -1.0e-8/51.0, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_n_e, (50,  1.0e-8, &r), 1.0 +1.0e-8/51.0, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_n_e, (50,  1.0, &r), 1.01999216583666790, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_n_e, (50,  3.0, &r), 1.0624205757460368307, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_n_e, (50,  48.0, &r), 7.499573876877194416, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_n_e, (50,  50.1, &r), 9.311803306230992272, TEST_TOL4, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_n_e, (50,  100.0, &r), 8.175664432485807634e+07, TEST_TOL4, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_n_e, (50,  500.0, &r), 4.806352370663185330e+146, TEST_TOL3, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_exprel_n_e, (500, -1000.0, &r), 0.3334815803127619256, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_n_e, (500, -100.0, &r), 0.8335646217536183909, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_n_e, (500, -10.0, &r), 0.9804297803131823066, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_n_e, (500, -3.0, &r), 0.9940475488850672997, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_n_e, (500, -1.0, &r), 0.9980079602383488808, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_n_e, (500, -1.0e-8, &r), 1.0 -1.0e-8/501.0, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_n_e, (500,  1.0e-8, &r), 1.0 +1.0e-8/501.0, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_n_e, (500,  1.0, &r), 1.0019999920160634252, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_n_e, (500,  3.0, &r), 1.0060240236632444934, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_n_e, (500,  48.0, &r), 1.1059355517981272174, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_n_e, (500,  100.0, &r), 1.2492221464878287204, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_n_e, (500,  500.0, &r), 28.363019877927630858, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_n_e, (500,  1000.0, &r), 2.4037563160335300322e+68, TEST_TOL4, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_n_e, (500,  1600.0, &r), 7.899293535320607403e+226, TEST_TOL4, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_exprel_n_e, (1263131.0, 1261282.3637, &r), 545.0113107238425900305428360, TEST_TOL4, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exprel_n_CF_e, (6.315655e+05, 6.302583168053568806e+05, &r), 385.425369029433473098652465720, TEST_TOL4, GSL_SUCCESS);

  return s;
}


int test_expint(void)
{
  gsl_sf_result r;
  int s = 0;

  TEST_SF(s,  gsl_sf_expint_E1_e, (-1.0, &r), -1.8951178163559367555, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_E1_e, (1.0e-10, &r), 22.448635265138923980, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_E1_e, (1.0e-05, &r), 10.935719800043695615, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_E1_e, (0.1, &r), 1.82292395841939066610, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_E1_e, (1.0, &r), 0.21938393439552027368, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_E1_e, (10.0, &r), 4.156968929685324277e-06, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_E1_e, (50.0, &r), 3.783264029550459019e-24, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_E1_e, (300.0, &r), 1.710384276804510115e-133, TEST_TOL2, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_expint_E2_e, (-1.0, &r), 0.8231640121031084799, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_E2_e, (0.0, &r), 1.0, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_E2_e, (1.0/4294967296.0, &r), 0.9999999947372139168, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_E2_e, (1.0/65536.0, &r), 0.9998243233207178845, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_E2_e, (0.1, &r), 0.7225450221940205066, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_E2_e, (1.0, &r), 0.14849550677592204792, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_E2_e, (10.0, &r), 3.830240465631608762e-06, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_E2_e, (50.0, &r), 3.711783318868827367e-24, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_E2_e, (300.0, &r), 1.7047391998483433998e-133, TEST_TOL2, GSL_SUCCESS);

  /* Tests for E_n(x) */

  TEST_SF(s,  gsl_sf_expint_En_e, (1,-1.0, &r), -1.8951178163559367555, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_En_e, (1,1.0e-10, &r), 22.448635265138923980, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_En_e, (1,1.0e-05, &r), 10.935719800043695615, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_En_e, (1,0.1, &r), 1.82292395841939066610, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_En_e, (1,1.0, &r), 0.21938393439552027368, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_En_e, (1,10.0, &r), 4.156968929685324277e-06, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_En_e, (1,50.0, &r), 3.783264029550459019e-24, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_En_e, (1,300.0, &r), 1.710384276804510115e-133, TEST_TOL2, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_expint_En_e, (2,-1.0, &r), 0.8231640121031084799, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_En_e, (2,0.0, &r), 1.0, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_En_e, (2,1.0/4294967296.0, &r), 0.9999999947372139168, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_En_e, (2,1.0/65536.0, &r), 0.9998243233207178845, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_En_e, (2,0.1, &r), 0.7225450221940205066, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_En_e, (2,1.0, &r), 0.14849550677592204792, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_En_e, (2,10.0, &r), 3.830240465631608762e-06, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_En_e, (2,50.0, &r), 3.711783318868827367e-24, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_En_e, (2,300.0, &r), 1.7047391998483433998e-133, TEST_TOL2, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_expint_En_e, (3,0.0, &r), 0.5, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_En_e, (3,1.0/4294967296.0, &r), 0.499999999767169356972, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_En_e, (3,1.0/65536.0, &r), 0.4999847426094515610, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_En_e, (3,0.1, &r), 0.4162914579082787612543, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_En_e, (3,1.0, &r), 0.10969196719776013683858, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_En_e, (3,10.0, &r),0.000003548762553084381959981, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_En_e, (3,50.0, &r), 3.6429094264752049812e-24, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_En_e, (3,300.0, &r),1.699131143349179084e-133, TEST_TOL2, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_expint_En_e, (10,0.0, &r), 0.111111111111111111, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_En_e, (10,1.0/4294967296.0, &r), 0.111111111082007280658, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_En_e, (10,1.0/65536.0, &r), 0.11110920377910896018606, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_En_e, (10,0.1, &r), 0.099298432000896813567905, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_En_e, (10,1.0, &r), 0.036393994031416401634164534, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_En_e, (10,10.0, &r), 0.00000232530265702821081778968, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_En_e, (10,50.0, &r), 3.223296586749110919572e-24, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_En_e, (10,300.0, &r), 1.6608815083360041367294736e-133, TEST_TOL2, GSL_SUCCESS);

  /* Tests for Ei(x) */

  TEST_SF(s,  gsl_sf_expint_Ei_e, (-1.0, &r), -0.21938393439552027368, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_Ei_e, (1.0/4294967296.0, &r), -21.603494112783886397, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_Ei_e, (1.0, &r), 1.8951178163559367555, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_expint_E1_scaled_e, (-10000.0, &r), -0.00010001000200060024012, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_E1_scaled_e, (-1000.0, &r), -0.0010010020060241207251, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_E1_scaled_e, (-10.0, &r), -0.11314702047341077803, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_E1_scaled_e, (-1.0, &r), -0.69717488323506606877, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_E1_scaled_e, (1.0e-10, &r), 22.448635267383787506, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_E1_scaled_e, (1.0e-05, &r), 10.935829157788483865, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_E1_scaled_e, (0.1, &r), 2.0146425447084516791, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_E1_scaled_e, (1.0, &r), 0.59634736232319407434, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_E1_scaled_e, (10.0, &r), 0.091563333939788081876, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_E1_scaled_e, (50.0, &r), 0.019615109930114870365, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_E1_scaled_e, (300.0, &r), 0.0033222955652707070644, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_E1_scaled_e, (1000.0, &r), 0.00099900199402388071500, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_expint_E1