test_sf.c

math library from gnu

  local_s |= test_sf_check_result(message_buff, r, val_in, tol);
  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("  %22.18e  %22.18e\n", r.val, r.err);
  }
  return local_s;
}

int
test_sf_e10 (gsl_sf_result_e10 re, double val_in, int e10_in, double tol, int status,
             int expect_return, const char * desc)
{
  char message_buff[4096];
  int local_s = 0;
  gsl_sf_result r;
  r.val = re.val; r.err = re.err;

  message_buff[0] = '\0';

  local_s |= test_sf_check_result(message_buff, r, val_in, tol);
  local_s |= test_sf_check_e10(message_buff, re.e10, e10_in);
  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("  %22.18e  %22.18e  10^%d\n", re.val, re.err, re.e10);
  }
  return local_s;
}


int
test_sf_val (double val, double val_in, double tol, const char * desc)
{
  char message_buff[4096];
  int local_s = 0;

  message_buff[0] = '\0';

  local_s |= test_sf_check_val(message_buff, val, val_in, tol);

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


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

  message_buff[0] = '\0';

  local_s |= test_sf_check_result_relax(message_buff, r, val_in, tol);
  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("  %22.18e  %22.18e\n", r.val, r.err);
  }
  return local_s;
}


int
test_sf_2 (gsl_sf_result r1, double val1, double tol1, 
           gsl_sf_result r2, double val2, double tol2,
           int status, int expect_return, const char * desc)
{
  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("  %22.18e  %22.18e\n", r1.val, r1.err);
    printf("  %22.18e  %22.18e\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("  %22.18e  %22.18e\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;
}