test_sf.c

This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY without ev

  char message_buff[4096];
  int local_s = 0;

  message_buff[0] = '\0';

  local_s |= test_sf_check_result(message_buff, r1, val1, tol1);
  local_s |= test_sf_check_result(message_buff, r2, val2, tol2);
  local_s |= test_sf_check_return(message_buff, status, expect_return);

  gsl_test(local_s, desc);
  if(local_s != 0) {
    /* printf("  %s %d\n", __FILE__, __LINE__); */
    printf("%s", message_buff);
    printf("  %22.18g  %22.18g\n", r1.val, r1.err);
    printf("  %22.18g  %22.18g\n", r2.val, r2.err);
  }
  return local_s;
}

int
test_sf_sgn (gsl_sf_result r, double sgn, double val_in, double tol, double expect_sgn, int status,
             int expect_return, const char * desc)
{
  char message_buff[4096];
  gsl_sf_result local_r;
  int local_s = 0;

  message_buff[0] = '\0';

  local_r.val = sgn;
  local_r.err = 0.0;
  local_s |= test_sf_check_result(message_buff, r, val_in, tol);
  local_s |= test_sf_check_result(message_buff, local_r, expect_sgn, 0.0);
  local_s |= test_sf_check_return(message_buff, status, expect_return);

  gsl_test(local_s, desc);
  if(local_s != 0) {
    /* printf("  %s %d\n", __FILE__, __LINE__); */
    printf("%s", message_buff);
    printf("  %22.18g  %22.18g\n", r.val, r.err);
  }
  return local_s;
}

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

  TEST_SF(s,  gsl_sf_clausen_e, (M_PI/20.0, &r), 0.4478882448133546, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_clausen_e, (M_PI/6.0, &r), 0.8643791310538927, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_clausen_e, (M_PI/3.0, &r), 1.0149416064096535, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_clausen_e, (  2.0*M_PI + M_PI/3.0, &r), 1.0149416064096535, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_clausen_e, (100.0*M_PI + M_PI/3.0, &r), 1.0149416064096535, TEST_TOL0, GSL_SUCCESS);

  return s;
}


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

  /* Test 3j */

  TEST_SF(s, gsl_sf_coupling_3j_e, (0, 1, 1, 0,  1, -1, &r), sqrt(1.0/2.0), TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_coupling_3j_e, (1, 1, 2, 1, -1,  0, &r), sqrt(1.0/6.0), TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_coupling_3j_e, (2, 4, 6, 0,  2, -2, &r), sqrt(8.0/105.0), TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_coupling_3j_e, (4, 4, 8, 0,  0,  0, &r), sqrt(2.0/35.0), TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_coupling_3j_e, (4, 4, 8, 2, -2,  0, &r), 2.0/3.0*sqrt(2.0/35.0), TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_coupling_3j_e, (4, 4, 8, 4, -4,  0, &r), 1.0/(3.0*sqrt(70.0)), TEST_TOL2, GSL_SUCCESS);

  /* Test 3j error checking */

  TEST_SF(s, gsl_sf_coupling_3j_e, (-1, 1, 2, 1, -1, 0, &r), GSL_NAN, GSL_NAN, GSL_EDOM);
  TEST_SF(s, gsl_sf_coupling_3j_e, (1, -1, 2, 1, -1, 0, &r), GSL_NAN, GSL_NAN, GSL_EDOM);
  TEST_SF(s, gsl_sf_coupling_3j_e, (1, 1, -2, 1, -1, 0, &r), GSL_NAN, GSL_NAN, GSL_EDOM);

  /* Test |m_i|<=j_i */

  TEST_SF(s, gsl_sf_coupling_3j_e, (1, 1, 2, 2, -1, 0, &r), 0, 0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_coupling_3j_e, (1, 1, 2, 1, -2, 0, &r), 0, 0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_coupling_3j_e, (1, 1, 2, 1, -1, 3, &r), 0, 0, GSL_SUCCESS);

  /* Test triangle condition j1 + j2 >= j, j >= j2 - j1, j>= j1 - j2 */

  TEST_SF(s, gsl_sf_coupling_3j_e, (1, 1, 3, 1, -1, 0, &r), 0, 0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_coupling_3j_e, (1, 4, 2, 1, -1, 0, &r), 0, 0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_coupling_3j_e, (4, 1, 2, 1, -1, 0, &r), 0, 0, GSL_SUCCESS);

  /* Test 6j */

  TEST_SF(s, gsl_sf_coupling_6j_e, (2, 2, 4, 2, 2, 2, &r),  1.0/6.0, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_coupling_6j_e, (4, 4, 2, 4, 4, 4, &r), -1.0/10.0, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_coupling_6j_e, (4, 4, 2, 4, 4, 2, &r),  1.0/6.0, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_coupling_6j_e, (4, 4, 2, 2, 2, 2, &r), -0.5/sqrt(5.0), TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_coupling_6j_e, (4, 4, 4, 2, 2, 2, &r),  sqrt(7.0/3.0)/10.0, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_coupling_6j_e, (6, 6, 6, 4, 4, 4, &r), -sqrt(3.0/5.0)/14.0, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_coupling_6j_e, (6, 6, 6, 4, 4, 2, &r), -sqrt(3.0/5.0)/7.0, TEST_TOL0, GSL_SUCCESS);

  /* Test 6j error checking */

  TEST_SF(s, gsl_sf_coupling_6j_e, (-2, 2, 4, 2, 2, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM);
  TEST_SF(s, gsl_sf_coupling_6j_e, (2, -2, 4, 2, 2, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM);
  TEST_SF(s, gsl_sf_coupling_6j_e, (2, 2, -4, 2, 2, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM);
  TEST_SF(s, gsl_sf_coupling_6j_e, (2, 2, 4, -2, 2, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM);
  TEST_SF(s, gsl_sf_coupling_6j_e, (2, 2, 4, 2, -2, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM);
  TEST_SF(s, gsl_sf_coupling_6j_e, (2, 2, 4, 2, 2, -2, &r), GSL_NAN, GSL_NAN, GSL_EDOM);

  /* Test 6j triangle conditions */

  TEST_SF(s, gsl_sf_coupling_6j_e, (2, 2, 4, 2, 2, 7, &r), 0, 0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_coupling_6j_e, (2, 2, 4, 2, 7, 2, &r), 0, 0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_coupling_6j_e, (2, 2, 4, 7, 2, 2, &r), 0, 0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_coupling_6j_e, (2, 2, 7, 2, 2, 2, &r), 0, 0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_coupling_6j_e, (2, 7, 4, 2, 2, 2, &r), 0, 0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_coupling_6j_e, (7, 2, 4, 2, 2, 2, &r), 0, 0, GSL_SUCCESS);

  /* Test 9j */

  TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2,  4, 3, 3, 2, 1, 1, 2, &r), -sqrt(1.0/6.0)/10.0, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_coupling_9j_e, (8, 4, 10, 7, 3, 8, 1, 1, 2, &r),  sqrt(7.0/3.0)/60.0, TEST_TOL2, GSL_SUCCESS);

  /* Test 9j error checking */

  TEST_SF(s, gsl_sf_coupling_9j_e, (-4, 2, 4, 3, 3, 2, 1, 1, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM);
  TEST_SF(s, gsl_sf_coupling_9j_e, (4, -2, 4, 3, 3, 2, 1, 1, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM);
  TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, -4, 3, 3, 2, 1, 1, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM);
  TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, -3, 3, 2, 1, 1, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM);
  TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, 3, -3, 2, 1, 1, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM);
  TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, 3, 3, -2, 1, 1, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM);
  TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, 3, 3, 2, -1, 1, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM);
  TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, 3, 3, 2, 1, -1, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM);
  TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, 3, 3, 2, 1, 1, -2, &r), GSL_NAN, GSL_NAN, GSL_EDOM);

  TEST_SF(s, gsl_sf_coupling_9j_e, (10, 2, 4, 3, 3, 2, 1, 1, 2, &r), 0, 0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_coupling_9j_e, (4, 10, 4, 3, 3, 2, 1, 1, 2, &r), 0, 0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 10, 3, 3, 2, 1, 1, 2, &r), 0, 0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, 10, 3, 2, 1, 1, 2, &r), 0, 0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, 3, 10, 2, 1, 1, 2, &r), 0, 0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, 3, 3, 10, 1, 1, 2, &r), 0, 0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, 3, 3, 2, 10, 1, 2, &r), 0, 0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, 3, 3, 2, 1, 10, 2, &r), 0, 0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, 3, 3, 2, 1, 1, 10, &r), 0, 0, GSL_SUCCESS);
  return s;
}

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

  TEST_SF(s, gsl_sf_dawson_e, (1.0e-15, &r), 1.0e-15, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_dawson_e, (0.5, &r), 0.4244363835020222959, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_dawson_e, (2.0, &r), 0.30134038892379196603, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_dawson_e, (1000.0, &r), 0.0005000002500003750009, TEST_TOL0, GSL_SUCCESS);
  
  return s;
}

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

  TEST_SF(s, gsl_sf_debye_1_e, (0.1, &r),  0.975277750004723276, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_debye_1_e, (1.0, &r),  0.777504634112248239, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_debye_1_e, (10.0, &r), 0.164443465679946027, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_debye_2_e, (0.1, &r),  0.967083287045302664,  TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_debye_2_e, (1.0, &r),  0.70787847562782924,   TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_debye_2_e, (10.0, &r), 0.0479714980201218708, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_debye_3_e, (0.1, &r),  0.962999940487211048,  TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_debye_3_e, (1.0, &r),  0.674415564077814667,  TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_debye_3_e, (10.0, &r), 0.0192957656903454886, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_debye_4_e, (0.1, &r),  0.960555486124335944,   TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_debye_4_e, (1.0, &r),  0.654874068886737049,   TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_debye_4_e, (10.0, &r), 0.00967367556027115896, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_debye_5_e, (0.1, &r),  0.95892849428310568745,  TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_debye_5_e, (1.0, &r),  0.6421002580217790246,   TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_debye_5_e, (10.0, &r), 0.005701535852992908538, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_debye_6_e, (0.1, &r),  0.95776777382605465878,  TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_debye_6_e, (1.0, &r),  0.63311142583495107588,  TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_debye_6_e, (10.0, &r), 3.7938493294615955279e-3, TEST_TOL0, GSL_SUCCESS);

  return s;
}


int test_elementary(void)
{
  gsl_sf_result r;
  double x = 0.2*DBL_MAX;
  int s = 0;

  TEST_SF(s,  gsl_sf_multiply_e, (-3.0,2.0, &r), -6.0,          TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_multiply_e, (x, 1.0/x, &r),  1.0,          TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_multiply_e, (x, 0.2, &r),    0.04*DBL_MAX, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_multiply_e, (x, 4.0, &r),    0.8*DBL_MAX,  TEST_TOL1, GSL_SUCCESS);
  s += ( gsl_sf_multiply_e(DBL_MAX, 1.1, &r) != GSL_EOVRFLW);
  s += ( gsl_sf_multiply_e(DBL_MIN,  DBL_MIN, &r) != GSL_EUNDRFLW);
  s += ( gsl_sf_multiply_e(DBL_MIN, -DBL_MIN, &r) != GSL_EUNDRFLW);

  return s;
}


int test_ellint(void)
{
  gsl_sf_result r;
  gsl_mode_t mode = GSL_MODE_DEFAULT;
  int s = 0;
  
  TEST_SF(s,  gsl_sf_ellint_Kcomp_e, ( 0.99, mode, &r), 3.3566005233611923760, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_ellint_Kcomp_e, ( 0.50, mode, &r), 1.6857503548125960429, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_ellint_Kcomp_e, (0.010, mode, &r), 1.5708355989121522360, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_ellint_Ecomp_e, (0.99, mode, &r), 1.0284758090288040010, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_ellint_Ecomp_e, (0.50, mode, &r), 1.4674622093394271555, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_ellint_Ecomp_e, (0.01, mode, &r), 1.5707570561503852873, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_ellint_F_e, (M_PI/3.0, 0.99, mode, &r), 1.3065333392738766762, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_ellint_F_e, (M_PI/3.0, 0.50, mode, &r), 1.0895506700518854093, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_ellint_F_e, (M_PI/3.0, 0.01, mode, &r), 1.0472129063770918952, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_ellint_E_e, (M_PI/3.0, 0.99, mode, &r), 0.8704819220377943536, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_ellint_E_e, (M_PI/3.0, 0.50, mode, &r), 1.0075555551444720293, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_ellint_E_e, (M_PI/3.0, 0.01, mode, &r), 1.0471821963889481104, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_ellint_P_e, (M_PI/3.0, 0.99, 0.5, mode, &r), 1.1288726598764099882, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_ellint_P_e, (M_PI/3.0, 0.50, 0.5, mode, &r), 0.9570574331323584890, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_ellint_P_e, (M_PI/3.0, 0.01, 0.5, mode, &r), 0.9228868127118118465, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_ellint_RF_e, (5.0e-11, 1.0e-10, 1.0, mode, &r), 12.36441982979439, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_ellint_RF_e, (1.0, 2.0, 3.0, mode, &r), 0.7269459354689082, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_ellint_RD_e, (5.0e-11, 1.0e-10, 1.0, mode, &r), 34.0932594919337362, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_ellint_RD_e, (1.0, 2.0, 3.0, mode, &r), 0.2904602810289906, TEST_TOL0, GSL_SUCCESS);