This commit changes the semantics of the out_of_range_tolerance[]

parameter-table entry to allow the min/max ends of the grid to be
handled differently.  (We'll need this for the multiprocessor interpolation.)

***** IMPORTANT *****
This change is *NOT* backwards-compatible: if you are calling
CCTK_InterpLocalUniform()  from this thorn (CactusBase/LocalInterp),
and you have set  out_of_range_tolerance[]  to a non-default value,
you must (slightly) change your code, or else you'll get an error
return from the interpolator.

If you don't use  out_of_range_tolerance[] , then you don't need
to do anything.

The semantics of  out_of_range_tolerance[]  are now as follows:

  @var          out_of_range_tolerance
  @vdesc        Specifies how out-of-range interpolation points should
                be handled.  The array elements are matched up with
                the axes and minimum/maximum ends of the grid in the
                order [x_min, x_max, y_min, y_max, z_min, z_max, ...].
                An array value TOL is interpreted as follows:
                If TOL >= 0.0,
                   then an interpolation point is considered to be
                        "out of range" if and only if the interpolation
                        point is > TOL * coord_delta[axis]
                        outside the grid in this coordinate direction.
                If TOL == -1.0,
                   then an interpolation point is considered to be
                        "out of range" if and only if a centered molecule
                        (or more generally, a molecule whose centering
                        is chosen pretending that the grid is of infinite
                        extent), would require data from outside the grid
                        in this direction.
                Other values of TOL are illegal (reserved for future use).
  @vtype        const CCTK_REAL out_of_range_tolerance[2*N_dims]
  @endvar

The change is that it used to have only N_dims elements, one for
each axis -- now there are 2*N_dims elements, one for each min/max
end of each axis.



----------------------------------------------------------------------

Modified Files:
	doc/documentation.tex
	src/GeneralizedPolynomial-Uniform/InterpLocalUniform.c
	src/GeneralizedPolynomial-Uniform/InterpLocalUniform.h
	src/GeneralizedPolynomial-Uniform/interpolate.maple
	src/GeneralizedPolynomial-Uniform/molecule_posn.c
	src/GeneralizedPolynomial-Uniform/template.c
	src/GeneralizedPolynomial-Uniform/test_molecule_posn.c


git-svn-id: http://svn.cactuscode.org/arrangements/CactusBase/LocalInterp/trunk@88 df1f8a13-aa1d-4dd4-9681-27ded5b42416

6 files changed, 342 insertions, 223 deletions

diff --git a/src/GeneralizedPolynomial-Uniform/InterpLocalUniform.c b/src/GeneralizedPolynomial-Uniform/InterpLocalUniform.c
index f6982ac..b4eef31 100644
--- a/src/GeneralizedPolynomial-Uniform/InterpLocalUniform.c
+++ b/src/GeneralizedPolynomial-Uniform/InterpLocalUniform.c
@@ -348,23 +348,26 @@ return LocalInterp_InterpLocalUniform(interp_operator_Hermite,
   @vtype	CCTK_INT order
   @endvar
 
-  @var		out_of_range_tolerance
+  @var		out_of_range_tolerance,
   @vdesc	Specifies how out-of-range interpolation points should
-		be handled:
-		If out_of_range_tolerance[axis] >= 0.0,
+		be handled.  The array elements are matched up with
+		the axes and minimum/maximum ends of the grid in the
+		order [x_min, x_max, y_min, y_max, z_min, z_max, ...].
+		An array value TOL is interpreted as follows:
+		If TOL >= 0.0,
 		   then an interpolation point is considered to be
 			"out of range" if and only if the interpolation
-			point is > out_of_range_tolerance[axis]
-				   * coord_delta[axis]
-			outside the grid in any coordinate.
-		If out_of_range_tolerance[axis] == -1.0,
+			point is > TOL * coord_delta[axis]
+			outside the grid in this coordinate direction.
+		If TOL == -1.0,
 		   then an interpolation point is considered to be
 			"out of range" if and only if a centered molecule
 			(or more generally, a molecule whose centering
 			is chosen pretending that the grid is of infinite
-			extent), would require data from outside the grid.
-		Other values of out_of_range_tolerance[axis] are illegal.
-  @vtype	const CCTK_REAL out_of_range_tolerance[N_dims]
+			extent), would require data from outside the grid
+			in this direction.
+		Other values of TOL are illegal.
+  @vtype	const CCTK_REAL out_of_range_tolerance[2*N_dims]
   @endvar
 
   @var		input_array_offsets
@@ -710,34 +713,38 @@ if ((order < 1) || (order > MAX_ORDER))
  * out-of-range interpolation-point handling
  */
   {
-CCTK_REAL out_of_range_tolerance[MAX_N_DIMS];
+CCTK_REAL out_of_range_tolerance[2*MAX_N_DIMS];
+const int N_tolerances = 2*N_dims;
 status = Util_TableGetRealArray(param_table_handle,
-				N_dims, out_of_range_tolerance,
+				N_tolerances, out_of_range_tolerance,
 				"out_of_range_tolerance");
 if	(status == UTIL_ERROR_TABLE_NO_SUCH_KEY)
    then {
 	/* default */
-	int axis;
-		for (axis = 0 ; axis < N_dims ; ++axis)
+	int tol_index;
+		for (tol_index = 0 ; tol_index < N_tolerances ; ++tol_index)
 		{
-		out_of_range_tolerance[axis] = OUT_OF_RANGE_TOLERANCE_DEFAULT;
+		out_of_range_tolerance[tol_index]
+			= OUT_OF_RANGE_TOLERANCE_DEFAULT;
 		}
 	}
-else if (status == N_dims)
+else if (status == N_tolerances)
    then {
 	/* check that all values are valid */
-	int axis;
-		for (axis = 0 ; axis < N_dims ; ++axis)
+	int tol_index;
+		for (tol_index = 0 ; tol_index < N_tolerances ; ++tol_index)
 		{
-		if (! (    (out_of_range_tolerance[axis] >=  0.0)
-			|| (out_of_range_tolerance[axis] == -1.0)    )  )
+		if (! (    (out_of_range_tolerance[tol_index] >=  0.0)
+			|| (out_of_range_tolerance[tol_index] == -1.0)    )  )
 		   then {
 			CCTK_VWarn(ERROR_MSG_SEVERITY_LEVEL,
 				   __LINE__, __FILE__, CCTK_THORNSTRING,
 "\n"
-"   CCTK_InterpLocalUniform(): invalid out_of_range_tolerance[axis=%d] = %g!\n"
-"                              (valid values are -1.0 or >= 0.0)",
-				   axis, out_of_range_tolerance[axis]);
+"   CCTK_InterpLocalUniform():\n"
+"        invalid out_of_range_tolerance[tol_index=%d] = %g!\n"
+"        (valid values are -1.0 or >= 0.0)",
+				   tol_index,
+				   out_of_range_tolerance[tol_index]);
 			return UTIL_ERROR_BAD_INPUT;	/*** ERROR RETURN ***/
 			}
 		}
diff --git a/src/GeneralizedPolynomial-Uniform/InterpLocalUniform.h b/src/GeneralizedPolynomial-Uniform/InterpLocalUniform.h
index 1486794..9559393 100644
--- a/src/GeneralizedPolynomial-Uniform/InterpLocalUniform.h
+++ b/src/GeneralizedPolynomial-Uniform/InterpLocalUniform.h
@@ -193,8 +193,9 @@ int LocalInterp_ILU_Hermite(int N_dims,
 /* functions in molecule_posn.c */
 int LocalInterp_molecule_posn(fp grid_origin, fp grid_delta,
 			      int grid_i_min, int grid_i_max,
-			      fp out_of_range_tolerance,
 			      int molecule_size,
+			      fp out_of_range_tolerance_min,
+			      fp out_of_range_tolerance_max,
 			      fp x,
 			      fp *x_rel,
 			      int *molecule_m_min, int *molecule_m_max);
diff --git a/src/GeneralizedPolynomial-Uniform/interpolate.maple b/src/GeneralizedPolynomial-Uniform/interpolate.maple
index 54979ba..23ca9e0 100644
--- a/src/GeneralizedPolynomial-Uniform/interpolate.maple
+++ b/src/GeneralizedPolynomial-Uniform/interpolate.maple
@@ -4,6 +4,7 @@
 #
 # <<<representation of numbers, data values, etc>>>
 # Lagrange_polynomial_interpolant - compute Lagrange polynomial interpolant
+# Hermite_polynomial_interpolant - compute Hermite polynomial interpolant
 # coeff_as_lc_of_data - coefficients of ... (linear combination of data)
 #
 # print_coeff__lc_of_data - print C code to compute coefficients
@@ -83,6 +84,48 @@ end proc;
 ################################################################################
 
 #
+# This function computes a Hermite polynomial interpolant in any
+# number of dimensions.
+#
+# Arguments:
+# fn = The interpolation function.  This should be a procedure in the
+#      coordinates, having the coefficients as global variables.  For
+#      example,
+#	  proc(x,y) c00 + c10*x + c01*y end proc
+# coeff_list = A set of the interpolation coefficients (coefficients in
+#	       the interpolation function), for example [c00, c10, c01].
+# coord_list = A list of the coordinates (independent variables in the
+#	       interpolation function), for example [x,y].
+# posn_list = A list of positions (each a list of numeric values) where the
+#	      interpolant is to use data, for example  hypercube([0,0], [1,1]).
+#	      Any positions may be used; if they're redundant (as in the
+#	      example) the least-squares interpolant is computed.
+#
+# Results:
+# This function returns the interpolating polynomial, in the form of
+# an algebraic expression in the coordinates and the data values.
+#
+Hermite_polynomial_interpolant :=
+proc(
+      fn::procedure, coeff_list::list(name),
+      coord_list::list(name), posn_list::list(list(numeric))
+    )
+local posn, data_eqns, coeff_eqns;
+
+# coefficients of interpolating polynomial
+data_eqns := {  seq( fn(op(posn))='DATA'(op(posn)) , posn=posn_list )  };
+coeff_eqns := linalg[leastsqrs](data_eqns, {op(coeff_list)});
+if (has(coeff_eqns, '_t'))
+   then error "interpolation coefficients aren't uniquely determined!";
+end if;
+
+# interpolant as a polynomial in the coordinates
+return subs(coeff_eqns, eval(fn))(op(coord_list));
+end proc;
+
+################################################################################
+
+#
 # This function takes as input an interpolating polynomial, expresses
 # it as a linear combination of the data values, and returns the coefficeints
 # of that form.
diff --git a/src/GeneralizedPolynomial-Uniform/molecule_posn.c b/src/GeneralizedPolynomial-Uniform/molecule_posn.c
index f67922e..44e78fc 100644
--- a/src/GeneralizedPolynomial-Uniform/molecule_posn.c
+++ b/src/GeneralizedPolynomial-Uniform/molecule_posn.c
@@ -93,9 +93,15 @@ static const char *rcsid = "$Header$";
  @vtype	int grid_i_max
  @endvar
 
- @var	out_of_range_tolerance
+ @var	molecule_size
+ @vdesc	The size (number of points) of the molecule.
+ @vtype	int molecule_size
+ @endvar
+
+ @var	out_of_range_tolerance_min, out_of_range_tolerance_max
  @vdesc	Specifies how out-of-range interpolation points should
-	be handled:
+	be handled for the {minimum,maximum} ends of the grid
+	respectively.
 	If out_of_range_tolerance >= 0.0,
 	   then an interpolation point is considered to be
 		"out of range" if and only if the interpolation
@@ -106,12 +112,7 @@ static const char *rcsid = "$Header$";
 		"out of range" if and only if a centered molecule
 		would require data from outside the grid.
 	Other values of out_of_range_tolerance are illegal.
- @vtype fp
- @endvar
-
- @var	molecule_size
- @vdesc	The size (number of points) of the molecule.
- @vtype	int molecule_size
+ @vtype fp out_of_range_tolerance_min, out_of_range_tolerance_max
  @endvar
 
  @var	x
@@ -128,17 +129,11 @@ static const char *rcsid = "$Header$";
  @vio	pointer to out
  @endvar
 
- @var	molecule_m_min
- @vdesc	A pointer to an int where this function should store the minimum
-	molecule coordinate m of the molecule; or NULL to skip storing this.
- @vtype	int *molecule_m_min
- @vio	pointer to out
- @endvar
-
- @var	p_molecule_m_max
- @vdesc	A pointer to an int where this function should store the maximum
-	molecule coordinate m of the molecule; or NULL to skip storing this.
- @vtype	int *molecle_m_max
+ @var	molecule_m_min, molecule_m_max
+ @vdesc	A pointer to an int where this function should store the
+	{minimum,maximum} molecule coordinate m of the molecule;
+	or NULL to skip storing this.
+ @vtype	int *molecule_m_min, *molecule_m_max
  @vio	pointer to out
  @endvar
 
@@ -155,8 +150,9 @@ static const char *rcsid = "$Header$";
  @@*/
 int LocalInterp_molecule_posn(fp grid_origin, fp grid_delta,
 			      int grid_i_min, int grid_i_max,
-			      fp out_of_range_tolerance,
 			      int molecule_size,
+			      fp out_of_range_tolerance_min,
+			      fp out_of_range_tolerance_max,
 			      fp x,
 			      fp *x_rel,
 			      int *molecule_m_min, int *molecule_m_max)
@@ -169,14 +165,17 @@ const int m_min = m_max - molecule_size + 1;	/* a negative number */
 const fp fp_i = (x - grid_origin) / grid_delta;
 
 /* is point x out-of-range? */
-if (out_of_range_tolerance >= 0.0)
+if (out_of_range_tolerance_min >= 0.0)
    then {
 	const fp fp_effective_grid_i_min
-		= ((fp) grid_i_min) - out_of_range_tolerance;
-	const fp fp_effective_grid_i_max
-		= ((fp) grid_i_max) + out_of_range_tolerance;
+		= ((fp) grid_i_min) - out_of_range_tolerance_min;
 	if (fp_i < fp_effective_grid_i_min)
 	   then return INT_MIN;				/*** ERROR RETURN ***/
+	}
+if (out_of_range_tolerance_max >= 0.0)
+   then {
+	const fp fp_effective_grid_i_max
+		= ((fp) grid_i_max) + out_of_range_tolerance_max;
 	if (fp_i > fp_effective_grid_i_max)
 	   then return INT_MAX;				/*** ERROR RETURN ***/
 	}
@@ -194,13 +193,10 @@ const int centered_i_min = i_center + m_min;
 const int centered_i_max = i_center + m_max;
 
 /* check if off-centered molecules are forbidden? */
-if (out_of_range_tolerance == -1.0)
-   then {
-	if (centered_i_min < grid_i_min)
-	   then return INT_MIN;				/*** ERROR RETURN ***/
-	if (centered_i_max > grid_i_max)
-	   then return INT_MAX;				/*** ERROR RETURN ***/
-	}
+if ((out_of_range_tolerance_min == -1.0) && (centered_i_min < grid_i_min))
+   then return INT_MIN;					/*** ERROR RETURN ***/
+if ((out_of_range_tolerance_max == -1.0) && (centered_i_max > grid_i_max))
+   then return INT_MAX;					/*** ERROR RETURN ***/
 
 /* off-center as needed if we're close to the edge of the grid */
   {
diff --git a/src/GeneralizedPolynomial-Uniform/template.c b/src/GeneralizedPolynomial-Uniform/template.c
index 3cb2c38..5cb934b 100644
--- a/src/GeneralizedPolynomial-Uniform/template.c
+++ b/src/GeneralizedPolynomial-Uniform/template.c
@@ -421,6 +421,17 @@ int FUNCTION_NAME(/***** coordinate system *****/
   #error "N_DIMS may not be > 3!"
 #endif
 
+/* layout of axes and min/max ends in out_of_range_tolerance[] array */
+#define X_AXIS_MIN	0
+#define X_AXIS_MAX	1
+#define Y_AXIS_MIN	2
+#define Y_AXIS_MAX	3
+#define Z_AXIS_MIN	4
+#define Z_AXIS_MAX	5
+#if (N_DIMS > 3)
+  #error "N_DIMS may not be > 3!"
+#endif
+
 /* basic sanity check on molecule size */
 #define MOLECULE_M_COUNT (MOLECULE_MAX_M - MOLECULE_MIN_M + 1)
 #if (MOLECULE_SIZE != MOLECULE_M_COUNT)
@@ -740,8 +751,9 @@ int pt;
 		= LocalInterp_molecule_posn(origin_x, delta_x,
 					    input_array_min_subscripts[X_AXIS],
 					    input_array_max_subscripts[X_AXIS],
-					    out_of_range_tolerance[X_AXIS],
 					    MOLECULE_SIZE,
+					    out_of_range_tolerance[X_AXIS_MIN],
+					    out_of_range_tolerance[X_AXIS_MAX],
 					    interp_coords_fp[X_AXIS],
 					    &x_temp,
 					    (int *) NULL, (int *) NULL);
@@ -753,8 +765,9 @@ int pt;
 		= LocalInterp_molecule_posn(origin_y, delta_y,
 					    input_array_min_subscripts[Y_AXIS],
 					    input_array_max_subscripts[Y_AXIS],
-					    out_of_range_tolerance[Y_AXIS],
 					    MOLECULE_SIZE,
+					    out_of_range_tolerance[Y_AXIS_MIN],
+					    out_of_range_tolerance[Y_AXIS_MAX],
 					    interp_coords_fp[Y_AXIS],
 					    &y_temp,
 					    (int *) NULL, (int *) NULL);
@@ -766,8 +779,9 @@ int pt;
 		= LocalInterp_molecule_posn(origin_z, delta_z,
 					    input_array_min_subscripts[Z_AXIS],
 					    input_array_max_subscripts[Z_AXIS],
-					    out_of_range_tolerance[Z_AXIS],
 					    MOLECULE_SIZE,
+					    out_of_range_tolerance[Z_AXIS_MIN],
+					    out_of_range_tolerance[Z_AXIS_MAX],
 					    interp_coords_fp[Z_AXIS],
 					    &z_temp,
 					    (int *) NULL, (int *) NULL);
diff --git a/src/GeneralizedPolynomial-Uniform/test_molecule_posn.c b/src/GeneralizedPolynomial-Uniform/test_molecule_posn.c
index b4c2379..bd3a1f9 100644
--- a/src/GeneralizedPolynomial-Uniform/test_molecule_posn.c
+++ b/src/GeneralizedPolynomial-Uniform/test_molecule_posn.c
@@ -6,10 +6,14 @@
  *
  * Usage:
  *	test_molecule_posn			# run a preset set of tests
- *	test_molecule_posn molecule_size x	# do a single test as specified
+ *	test_molecule_posn molecule_size		\
+ *	                   out_of_range_tolerance_min	\
+ *	                   out_of_range_tolerance_max	\
+ *	                   x			# do a single test as specified
  */
 
 #include <math.h>
+#include <string.h>
 #include <limits.h>
 #include <stdio.h>
 #include <stdlib.h>
@@ -22,10 +26,6 @@
 
 #define fuzzy_EQ(x,y)	(fabs(x-y) <= 1.0e-10)
 
-/* prototypes */
-void run_interactive_test(fp out_of_range_tolerance, int molecule_size, fp x);
-int run_batch_tests(void);
-
 /* hard-wired arguments for  LocalInterp_molecule_posn() */
 const fp grid_x0 = 3.1;
 const fp grid_dx = 0.1;
@@ -35,6 +35,19 @@ const int grid_i_max = 105;	/* x_max = 13.6 */
 /******************************************************************************/
 
 /*
+ * prototypes for functions local to this file
+*/
+static
+  void run_interactive_test(int molecule_size,
+			    fp out_of_range_tolerance_min,
+			    fp out_of_range_tolerance_max,
+			    fp x);
+static
+  int run_batch_tests(void);
+
+/******************************************************************************/
+
+/*
  * test data for batch tests
  */
 
@@ -42,8 +55,9 @@ const int grid_i_max = 105;	/* x_max = 13.6 */
 struct	args_results
 	{
 	/* args */
-	fp out_of_range_tolerance;
 	int molecule_size;
+	fp out_of_range_tolerance_min;
+	fp out_of_range_tolerance_max;
 	fp x;
 	/* results */
 	int i_center;
@@ -53,139 +67,142 @@ struct	args_results
 
 /* test data */
 static const struct args_results test_data[] =
-      {
-	/* molecule size 2 */
-	{ 1.0,     2,  7.19, INT_MIN, -1.1,       0,+1 },
-	{ 1.0,     2,  7.21,      42, -0.9,       0,+1 },
-	{ 1.0,     2,  7.24,      42, -0.6,       0,+1 },
-	{ 1.0,     2,  7.26,      42, -0.4,       0,+1 },
-	{ 1.0,     2,  7.29,      42, -0.1,       0,+1 },
-	{-1.0,     2,  7.29, INT_MIN, -0.1,       0,+1 },
-	{ 1.0e-12, 2,  7.3,       42,  0.0,       0,+1 }, /* x == grid_x_min */
-	{ 1.0e-12, 2,  7.31,      42, +0.1,       0,+1 },
-	{-1.0    , 2,  7.31,      42, +0.1,       0,+1 },
-	{ 1.0e-12, 2,  7.35,      42, +0.5,       0,+1 },
-	{ 1.0e-12, 2,  7.39,      42, +0.9,       0,+1 },
-	{ 1.0e-12, 2,  7.41,      43,  0.1,       0,+1 },
-	{ 1.0e-12, 2,  9.81,      67, +0.1,       0,+1 },
-	{ 1.0e-12, 2,  9.85,      67, +0.5,       0,+1 },
-	{ 1.0e-12, 2,  9.89,      67, +0.9,       0,+1 },
-	{ 1.0e-12, 2, 13.45,     103, +0.5,       0,+1 },
-	{ 1.0e-12, 2, 13.51,     104, +0.1,       0,+1 },
-	{ 1.0e-12, 2, 13.55,     104, +0.5,       0,+1 },
-	{ 1.0e-12, 2, 13.59,     104, +0.9,       0,+1 },
-	{-1.0,     2, 13.59,     104, +0.9,       0,+1 },
-	{ 1.0e-12, 2, 13.6,      104, +1.0,       0,+1 }, /* x == grid_x_max */
-	{ 1.0,     2, 13.61,     104, +1.1,       0,+1 },
-	{-1.0,     2, 13.61, INT_MAX, +1.1,       0,+1 },
-	{ 1.0,     2, 13.65,     104, +1.5,       0,+1 },
-	{ 1.0,     2, 13.69,     104, +1.9,       0,+1 },
-	{ 1.0,     2, 13.71, INT_MAX, +2.1,       0,+1 },
-	/* molecule size 3 */
-	{ 1.0,     3,  7.19, INT_MIN, -2.1,      -1,+1 },
-	{ 1.0,     3,  7.21,      43, -1.9,      -1,+1 },
-	{ 1.0,     3,  7.24,      43, -1.6,      -1,+1 },
-	{ 1.0,     3,  7.26,      43, -1.4,      -1,+1 },
-	{ 1.0,     3,  7.29,      43, -1.1,      -1,+1 },
-	{-1.0,     3,  7.29, INT_MIN, -1.1,      -1,+1 },
-	{ 1.0e-12, 3,  7.3,       43, -1.0,      -1,+1 }, /* x == grid_x_min */
-	{ 1.0e-12, 3,  7.31,      43, -0.9,      -1,+1 },
-	{ 1.0e-12, 3,  7.34,      43, -0.6,      -1,+1 },
-	{-1.0,     3,  7.34, INT_MIN, -0.6,      -1,+1 },
-	{ 1.0e-12, 3,  7.36,      43, -0.4,      -1,+1 },
-	{-1.0,     3,  7.36,      43, -0.4,      -1,+1 },
-	{ 1.0e-12, 3,  7.39,      43, -0.1,      -1,+1 },
-	{ 1.0e-12, 3,  7.4,       43,  0.0,      -1,+1 },
-	{ 1.0e-12, 3,  7.44,      43, +0.4,      -1,+1 },
-	{ 1.0e-12, 3,  7.46,      44, -0.4,      -1,+1 },
-	{ 1.0e-12, 3,  9.8,       67,  0.0,      -1,+1 },
-	{ 1.0e-12, 3,  9.81,      67, +0.1,      -1,+1 },
-	{ 1.0e-12, 3,  9.84,      67, +0.4,      -1,+1 },
-	{ 1.0e-12, 3,  9.86,      68, -0.4,      -1,+1 },
-	{ 1.0e-12, 3,  9.89,      68, -0.1,      -1,+1 },
-	{ 1.0e-12, 3,  9.9,       68,  0.0,      -1,+1 },
-	{ 1.0e-12, 3, 13.44,     103, +0.4,      -1,+1 },
-	{ 1.0e-12, 3, 13.46,     104, -0.4,      -1,+1 },
-	{ 1.0e-12, 3, 13.5,      104,  0.0,      -1,+1 },
-	{ 1.0e-12, 3, 13.51,     104, +0.1,      -1,+1 },
-	{ 1.0e-12, 3, 13.54,     104, +0.4,      -1,+1 },
-	{-1.0,     3, 13.54,     104, +0.4,      -1,+1 },
-	{ 1.0e-12, 3, 13.56,     104, +0.6,      -1,+1 },
-	{-1.0,     3, 13.56, INT_MAX, +0.6,      -1,+1 },
-	{ 1.0e-12, 3, 13.59,     104, +0.9,      -1,+1 },
-	{ 1.0e-12, 3, 13.6,      104, +1.0,      -1,+1 }, /* x == grid_x_max */
-	{ 1.0,     3, 13.61,     104, +1.1,      -1,+1 },
-	{ 1.0,     3, 13.65,     104, +1.5,      -1,+1 },
-	{ 1.0,     3, 13.69,     104, +1.9,      -1,+1 },
-	{ 1.0,     3, 13.71, INT_MAX, +2.1,      -1,+1 },
-	/* molecule size 4 */
-	{ 0.2,     4,  7.27, INT_MIN, -1.3,      -1,+2 },
-	{ 0.2,     4,  7.29,      43, -1.1,      -1,+2 },
-	{ 1.0e-12, 4,  7.3,       43, -1.0,      -1,+2 }, /* x == grid_x_min */
-	{ 1.0e-12, 4,  7.33,      43, -0.7,      -1,+2 },
-	{ 1.0e-12, 4,  7.39,      43, -0.1,      -1,+2 },
-	{-1.0,     4,  7.39, INT_MIN, -0.1,      -1,+2 },
-	{ 1.0e-12, 4,  7.4,       43,  0.0,      -1,+2 },
-	{-1.0,     4,  7.41,      43, +0.1,      -1,+2 },
-	{ 1.0e-12, 4,  7.42,      43, +0.2,      -1,+2 },
-	{ 1.0e-12, 4,  7.48,      43, +0.8,      -1,+2 },
-	{ 1.0e-12, 4,  7.51,      44, +0.1,      -1,+2 },
-	{ 1.0e-12, 4,  9.81,      67, +0.1,      -1,+2 },
-	{ 1.0e-12, 4,  9.85,      67, +0.5,      -1,+2 },
-	{ 1.0e-12, 4,  9.89,      67, +0.9,      -1,+2 },
-	{ 1.0e-12, 4, 13.39,     102, +0.9,      -1,+2 },
-	{ 1.0e-12, 4, 13.41,     103, +0.1,      -1,+2 },
-	{ 1.0e-12, 4, 13.48,     103, +0.8,      -1,+2 },
-	{-1.0,     4, 13.48,     103, +0.8,      -1,+2 },
-	{ 1.0e-12, 4, 13.5,      103, +1.0,      -1,+2 },
-	{ 1.0e-12, 4, 13.51,     103, +1.1,      -1,+2 },
-	{-1.0,     4, 13.51, INT_MAX, +1.1,      -1,+2 },
-	{ 1.0e-12, 4, 13.55,     103, +1.5,      -1,+2 },
-	{ 1.0e-12, 4, 13.59,     103, +1.9,      -1,+2 },
-	{ 1.0e-12, 4, 13.6,      103, +2.0,      -1,+2 }, /* x == grid_x_max */
-	{ 2.0,     4, 13.79,     103, +3.9,      -1,+2 },
-	{ 2.0,     4, 13.81, INT_MAX, +4.1,      -1,+2 },
-	/* molecule size 5 */
-	{ 3.0,     5,  6.99, INT_MIN, -5.1,      -2,+2 },
-	{ 3.0,     5,  7.01,      44, -4.9,      -2,+2 },
-	{ 1.0e-12, 5,  7.3,       44, -2.0,      -2,+2 }, /* x == grid_x_min */
-	{ 1.0e-12, 5,  7.4,       44, -1.0,      -2,+2 },
-	{ 1.0e-12, 5,  7.44,      44, -0.6,      -2,+2 },
-	{-1.0,     5,  7.44, INT_MIN, -0.6,      -2,+2 },
-	{ 1.0e-12, 5,  7.46,      44, -0.4,      -2,+2 },
-	{-1.0,     5,  7.46,      44, -0.4,      -2,+2 },
-	{ 1.0e-12, 5,  7.49,      44, -0.1,      -2,+2 },
-	{ 1.0e-12, 5,  7.5,       44,  0.0,      -2,+2 },
-	{ 1.0e-12, 5,  7.54,      44, +0.4,      -2,+2 },
-	{ 1.0e-12, 5,  7.56,      45, -0.4,      -2,+2 },
-	{ 1.0e-12, 5,  7.6,       45,  0.0,      -2,+2 },
-	{ 1.0e-12, 5,  7.64,      45, +0.4,      -2,+2 },
-	{ 1.0e-12, 5,  9.8,       67,  0.0,      -2,+2 },
-	{ 1.0e-12, 5,  9.81,      67, +0.1,      -2,+2 },
-	{ 1.0e-12, 5,  9.84,      67, +0.4,      -2,+2 },
-	{ 1.0e-12, 5,  9.86,      68, -0.4,      -2,+2 },
-	{ 1.0e-12, 5,  9.89,      68, -0.1,      -2,+2 },
-	{ 1.0e-12, 5,  9.9,       68,  0.0,      -2,+2 },
-	{ 1.0e-12, 5, 13.34,     102, +0.4,      -2,+2 },
-	{ 1.0e-12, 5, 13.36,     103, -0.4,      -2,+2 },
-	{ 1.0e-12, 5, 13.39,     103, -0.1,      -2,+2 },
-	{ 1.0e-12, 5, 13.41,     103, +0.1,      -2,+2 },
-	{ 1.0e-12, 5, 13.44,     103, +0.4,      -2,+2 },
-	{-1.0,     5, 13.44,     103, +0.4,      -2,+2 },
-	{ 1.0e-12, 5, 13.46,     103, +0.6,      -2,+2 },
-	{-1.0,     5, 13.46, INT_MAX, +0.6,      -2,+2 },
-	{ 1.0e-12, 5, 13.48,     103, +0.8,      -2,+2 },
-	{ 1.0e-12, 5, 13.5,      103, +1.0,      -2,+2 },
-	{ 1.0e-12, 5, 13.51,     103, +1.1,      -2,+2 },
-	{ 1.0e-12, 5, 13.54,     103, +1.4,      -2,+2 },
-	{-1.0,     5, 13.54, INT_MAX, +1.4,      -2,+2 },
-	{ 1.0e-12, 5, 13.56,     103, +1.6,      -2,+2 },
-	{-1.0,     5, 13.56, INT_MAX, +1.6,      -2,+2 },
-	{ 1.0e-12, 5, 13.59,     103, +1.9,      -2,+2 },
-	{ 1.0e-12, 5, 13.6,      103, +2.0,      -2,+2 }, /* x == grid_x_max */
-	{ 1.5,     5, 13.74,     103, +3.4,      -2,+2 },
-	{ 1.5,     5, 13.76, INT_MAX, +3.6,      -2,+2 },
-      };
+  {
+    /* molecule size 2 */
+    { 2,  1.0,      1.0e-12,  7.19, INT_MIN, -1.1,       0,+1 },
+    { 2,  1.0,      1.0e-12,  7.21,      42, -0.9,       0,+1 },
+    { 2,  1.0,      1.0e-12,  7.24,      42, -0.6,       0,+1 },
+    { 2,  1.0,      1.0e-12,  7.26,      42, -0.4,       0,+1 },
+    { 2,  1.0,      1.0e-12,  7.29,      42, -0.1,       0,+1 },
+    { 2, -1.0,      1.0e-12,  7.29, INT_MIN, -0.1,       0,+1 },
+    { 2,  1.0e-12,  1.0e-12,  7.3,       42,  0.0,       0,+1 },/* grid_x_min */
+    { 2,  1.0e-12,  1.0e-12,  7.31,      42, +0.1,       0,+1 },
+    { 2, -1.0    ,  1.0e-12,  7.31,      42, +0.1,       0,+1 },
+    { 2,  1.0e-12,  1.0e-12,  7.35,      42, +0.5,       0,+1 },
+    { 2,  1.0e-12,  1.0e-12,  7.39,      42, +0.9,       0,+1 },
+    { 2,  1.0e-12,  1.0e-12,  7.41,      43,  0.1,       0,+1 },
+    { 2,  1.0e-12,  1.0e-12,  9.81,      67, +0.1,       0,+1 },
+    { 2,  1.0e-12,  1.0e-12,  9.85,      67, +0.5,       0,+1 },
+    { 2,  1.0e-12,  1.0e-12,  9.89,      67, +0.9,       0,+1 },
+    { 2,  1.0e-12,  1.0e-12, 13.45,     103, +0.5,       0,+1 },
+    { 2,  1.0e-12,  1.0e-12, 13.51,     104, +0.1,       0,+1 },
+    { 2,  1.0e-12,  1.0e-12, 13.55,     104, +0.5,       0,+1 },
+    { 2,  1.0e-12,  1.0e-12, 13.59,     104, +0.9,       0,+1 },
+    { 2,  1.0e-12, -1.0,     13.59,     104, +0.9,       0,+1 },
+    { 2,  1.0e-12,  1.0e-12, 13.6,      104, +1.0,       0,+1 },/* grid_x_max */
+    { 2,  1.0e-12,  1.0,     13.61,     104, +1.1,       0,+1 },
+    { 2,  1.0e-12, -1.0,     13.61, INT_MAX, +1.1,       0,+1 },
+    { 2,  1.0e-12,  1.0,     13.65,     104, +1.5,       0,+1 },
+    { 2,  1.0e-12,  1.0,     13.69,     104, +1.9,       0,+1 },
+    { 2,  1.0e-12,  1.0,     13.71, INT_MAX, +2.1,       0,+1 },
+
+    /* molecule size 3 */
+    { 3,  1.0,      1.0e-12,  7.19, INT_MIN, -2.1,      -1,+1 },
+    { 3,  1.0,      1.0e-12,  7.21,      43, -1.9,      -1,+1 },
+    { 3,  1.0,      1.0e-12,  7.24,      43, -1.6,      -1,+1 },
+    { 3,  1.0,      1.0e-12,  7.26,      43, -1.4,      -1,+1 },
+    { 3,  1.0,      1.0e-12,  7.29,      43, -1.1,      -1,+1 },
+    { 3, -1.0,      1.0e-12,  7.29, INT_MIN, -1.1,      -1,+1 },
+    { 3,  1.0e-12,  1.0e-12,  7.3,       43, -1.0,      -1,+1 },/* grid_x_min */
+    { 3,  1.0e-12,  1.0e-12,  7.31,      43, -0.9,      -1,+1 },
+    { 3,  1.0e-12,  1.0e-12,  7.34,      43, -0.6,      -1,+1 },
+    { 3, -1.0,      1.0e-12,  7.34, INT_MIN, -0.6,      -1,+1 },
+    { 3,  1.0e-12,  1.0e-12,  7.36,      43, -0.4,      -1,+1 },
+    { 3, -1.0,      1.0e-12,  7.36,      43, -0.4,      -1,+1 },
+    { 3,  1.0e-12,  1.0e-12,  7.39,      43, -0.1,      -1,+1 },
+    { 3,  1.0e-12,  1.0e-12,  7.4,       43,  0.0,      -1,+1 },
+    { 3,  1.0e-12,  1.0e-12,  7.44,      43, +0.4,      -1,+1 },
+    { 3,  1.0e-12,  1.0e-12,  7.46,      44, -0.4,      -1,+1 },
+    { 3,  1.0e-12,  1.0e-12,  9.8,       67,  0.0,      -1,+1 },
+    { 3,  1.0e-12,  1.0e-12,  9.81,      67, +0.1,      -1,+1 },
+    { 3,  1.0e-12,  1.0e-12,  9.84,      67, +0.4,      -1,+1 },
+    { 3,  1.0e-12,  1.0e-12,  9.86,      68, -0.4,      -1,+1 },
+    { 3,  1.0e-12,  1.0e-12,  9.89,      68, -0.1,      -1,+1 },
+    { 3,  1.0e-12,  1.0e-12,  9.9,       68,  0.0,      -1,+1 },
+    { 3,  1.0e-12,  1.0e-12, 13.44,     103, +0.4,      -1,+1 },
+    { 3,  1.0e-12,  1.0e-12, 13.46,     104, -0.4,      -1,+1 },
+    { 3,  1.0e-12,  1.0e-12, 13.5,      104,  0.0,      -1,+1 },
+    { 3,  1.0e-12,  1.0e-12, 13.51,     104, +0.1,      -1,+1 },
+    { 3,  1.0e-12,  1.0e-12, 13.54,     104, +0.4,      -1,+1 },
+    { 3,  1.0e-12, -1.0,     13.54,     104, +0.4,      -1,+1 },
+    { 3,  1.0e-12,  1.0e-12, 13.56,     104, +0.6,      -1,+1 },
+    { 3,  1.0e-12, -1.0,     13.56, INT_MAX, +0.6,      -1,+1 },
+    { 3,  1.0e-12,  1.0e-12, 13.59,     104, +0.9,      -1,+1 },
+    { 3,  1.0e-12,  1.0e-12, 13.6,      104, +1.0,      -1,+1 },/* grid_x_max */
+    { 3,  1.0e-12,  1.0,     13.61,     104, +1.1,      -1,+1 },
+    { 3,  1.0e-12,  1.0,     13.65,     104, +1.5,      -1,+1 },
+    { 3,  1.0e-12,  1.0,     13.69,     104, +1.9,      -1,+1 },
+    { 3,  1.0e-12,  1.0,     13.71, INT_MAX, +2.1,      -1,+1 },
+
+    /* molecule size 4 */
+    { 4,  0.2,      1.0e-12,  7.27, INT_MIN, -1.3,      -1,+2 },
+    { 4,  0.2,      1.0e-12,  7.29,      43, -1.1,      -1,+2 },
+    { 4,  1.0e-12,  1.0e-12,  7.3,       43, -1.0,      -1,+2 },/* grid_x_min */
+    { 4,  1.0e-12,  1.0e-12,  7.33,      43, -0.7,      -1,+2 },
+    { 4,  1.0e-12,  1.0e-12,  7.39,      43, -0.1,      -1,+2 },
+    { 4, -1.0,      1.0e-12,  7.39, INT_MIN, -0.1,      -1,+2 },
+    { 4,  1.0e-12,  1.0e-12,  7.4,       43,  0.0,      -1,+2 },
+    { 4, -1.0,      1.0e-12,  7.41,      43, +0.1,      -1,+2 },
+    { 4,  1.0e-12,  1.0e-12,  7.42,      43, +0.2,      -1,+2 },
+    { 4,  1.0e-12,  1.0e-12,  7.48,      43, +0.8,      -1,+2 },
+    { 4,  1.0e-12,  1.0e-12,  7.51,      44, +0.1,      -1,+2 },
+    { 4,  1.0e-12,  1.0e-12,  9.81,      67, +0.1,      -1,+2 },
+    { 4,  1.0e-12,  1.0e-12,  9.85,      67, +0.5,      -1,+2 },
+    { 4,  1.0e-12,  1.0e-12,  9.89,      67, +0.9,      -1,+2 },
+    { 4,  1.0e-12,  1.0e-12, 13.39,     102, +0.9,      -1,+2 },
+    { 4,  1.0e-12,  1.0e-12, 13.41,     103, +0.1,      -1,+2 },
+    { 4,  1.0e-12,  1.0e-12, 13.48,     103, +0.8,      -1,+2 },
+    { 4,  1.0e-12, -1.0,     13.48,     103, +0.8,      -1,+2 },
+    { 4,  1.0e-12,  1.0e-12, 13.5,      103, +1.0,      -1,+2 },
+    { 4,  1.0e-12,  1.0e-12, 13.51,     103, +1.1,      -1,+2 },
+    { 4,  1.0e-12, -1.0,     13.51, INT_MAX, +1.1,      -1,+2 },
+    { 4,  1.0e-12,  1.0e-12, 13.55,     103, +1.5,      -1,+2 },
+    { 4,  1.0e-12,  1.0e-12, 13.59,     103, +1.9,      -1,+2 },
+    { 4,  1.0e-12,  1.0e-12, 13.6,      103, +2.0,      -1,+2 },/* grid_x_max */
+    { 4,  1.0e-12,  2.0,     13.79,     103, +3.9,      -1,+2 },
+    { 4,  1.0e-12,  2.0,     13.81, INT_MAX, +4.1,      -1,+2 },
+
+    /* molecule size 5 */
+    { 5,  3.0,      1.0e-12,  6.99, INT_MIN, -5.1,      -2,+2 },
+    { 5,  3.0,      1.0e-12,  7.01,      44, -4.9,      -2,+2 },
+    { 5,  1.0e-12,  1.0e-12,  7.3,       44, -2.0,      -2,+2 },/* grid_x_min */
+    { 5,  1.0e-12,  1.0e-12,  7.4,       44, -1.0,      -2,+2 },
+    { 5,  1.0e-12,  1.0e-12,  7.44,      44, -0.6,      -2,+2 },
+    { 5, -1.0,      1.0e-12,  7.44, INT_MIN, -0.6,      -2,+2 },
+    { 5,  1.0e-12,  1.0e-12,  7.46,      44, -0.4,      -2,+2 },
+    { 5, -1.0,      1.0e-12,  7.46,      44, -0.4,      -2,+2 },
+    { 5,  1.0e-12,  1.0e-12,  7.49,      44, -0.1,      -2,+2 },
+    { 5,  1.0e-12,  1.0e-12,  7.5,       44,  0.0,      -2,+2 },
+    { 5,  1.0e-12,  1.0e-12,  7.54,      44, +0.4,      -2,+2 },
+    { 5,  1.0e-12,  1.0e-12,  7.56,      45, -0.4,      -2,+2 },
+    { 5,  1.0e-12,  1.0e-12,  7.6,       45,  0.0,      -2,+2 },
+    { 5,  1.0e-12,  1.0e-12,  7.64,      45, +0.4,      -2,+2 },
+    { 5,  1.0e-12,  1.0e-12,  9.8,       67,  0.0,      -2,+2 },
+    { 5,  1.0e-12,  1.0e-12,  9.81,      67, +0.1,      -2,+2 },
+    { 5,  1.0e-12,  1.0e-12,  9.84,      67, +0.4,      -2,+2 },
+    { 5,  1.0e-12,  1.0e-12,  9.86,      68, -0.4,      -2,+2 },
+    { 5,  1.0e-12,  1.0e-12,  9.89,      68, -0.1,      -2,+2 },
+    { 5,  1.0e-12,  1.0e-12,  9.9,       68,  0.0,      -2,+2 },
+    { 5,  1.0e-12,  1.0e-12, 13.34,     102, +0.4,      -2,+2 },
+    { 5,  1.0e-12,  1.0e-12, 13.36,     103, -0.4,      -2,+2 },
+    { 5,  1.0e-12,  1.0e-12, 13.39,     103, -0.1,      -2,+2 },
+    { 5,  1.0e-12,  1.0e-12, 13.41,     103, +0.1,      -2,+2 },
+    { 5,  1.0e-12,  1.0e-12, 13.44,     103, +0.4,      -2,+2 },
+    { 5,  1.0e-12, -1.0,     13.44,     103, +0.4,      -2,+2 },
+    { 5,  1.0e-12,  1.0e-12, 13.46,     103, +0.6,      -2,+2 },
+    { 5,  1.0e-12, -1.0,     13.46, INT_MAX, +0.6,      -2,+2 },
+    { 5,  1.0e-12,  1.0e-12, 13.48,     103, +0.8,      -2,+2 },
+    { 5,  1.0e-12,  1.0e-12, 13.5,      103, +1.0,      -2,+2 },
+    { 5,  1.0e-12,  1.0e-12, 13.51,     103, +1.1,      -2,+2 },
+    { 5,  1.0e-12,  1.0e-12, 13.54,     103, +1.4,      -2,+2 },
+    { 5,  1.0e-12, -1.0,     13.54, INT_MAX, +1.4,      -2,+2 },
+    { 5,  1.0e-12,  1.0e-12, 13.56,     103, +1.6,      -2,+2 },
+    { 5,  1.0e-12, -1.0,     13.56, INT_MAX, +1.6,      -2,+2 },
+    { 5,  1.0e-12,  1.0e-12, 13.59,     103, +1.9,      -2,+2 },
+    { 5,  1.0e-12,  1.0e-12, 13.6,      103, +2.0,      -2,+2 },/* grid_x_max */
+    { 5,  1.0e-12,  1.5,     13.74,     103, +3.4,      -2,+2 },
+    { 5,  1.0e-12,  1.5,     13.76, INT_MAX, +3.6,      -2,+2 },
+  };
 #define N_TESTS ((int) (sizeof(test_data)/sizeof(test_data[0])))
 
 
@@ -194,9 +211,9 @@ static const struct args_results test_data[] =
 int main(int argc, const char *const argv[])
 {
 bool N_fail;
-fp out_of_range_tolerance;
 int molecule_size;
-fp x;
+double out_of_range_tolerance_min, out_of_range_tolerance_max;
+double x;
 
 switch	(argc)
 	{
@@ -213,54 +230,88 @@ case 1:
 		return 1;
 		}
 
-case 4:
-	if (    (sscanf(argv[1], "%lf", &out_of_range_tolerance) == 1)
-	     && (sscanf(argv[2], "%d",  &molecule_size) == 1)
-	     && (sscanf(argv[3], "%lf", &x) == 1)    )
+case 5:
+	if (    (sscanf(argv[1], "%d",  &molecule_size) == 1)
+	     && (sscanf(argv[2], "%lf", &out_of_range_tolerance_min) == 1)
+	     && (sscanf(argv[3], "%lf", &out_of_range_tolerance_max) == 1)
+	     && (sscanf(argv[4], "%lf", &x) == 1)    )
 	   then {
-		run_interactive_test(out_of_range_tolerance, molecule_size, x);
+		run_interactive_test(molecule_size,
+				     out_of_range_tolerance_min,
+				     out_of_range_tolerance_max,
+				     x);
 		return 0;
 		}
 	/* fall through */
+
 default:
 	fprintf(stderr,
 		"usage:\n"
 		"# run a single test as specified:\n"
-		"  %s out_of_range_tolerance molecule_size x\n"
+		"  %s molecule_size			\\\n"
+		"  %*s out_of_range_tolerance_min	\\\n"
+		"  %*s out_of_range_tolerance_max	\\\n"
+		"  %*s x\n"
 		"# run a preset set of tests:\n"
 		"  %s\n"
 		,
-		argv[0], argv[0]);
+		argv[0],
+		(int) strlen(argv[0]), "",
+		(int) strlen(argv[0]), "",
+		(int) strlen(argv[0]), "",
+		argv[0]);
 	return 1;
 	}
 }
 
 /******************************************************************************/
 
-/* run a single test as specified */
-void run_interactive_test(fp out_of_range_tolerance, int molecule_size, fp x)
+/*
+ * This function runs a single test as specified.
+ */
+static
+  void run_interactive_test(int molecule_size,
+			    fp out_of_range_tolerance_min,
+			    fp out_of_range_tolerance_max,
+			    fp x)
 {
 fp x_rel;
 int m_min, m_max;
 
-int i_center = LocalInterp_molecule_posn(grid_x0, grid_dx,
-					 grid_i_min, grid_i_max,
-					 out_of_range_tolerance,
-					 molecule_size,
-					 x,
-					 &x_rel,
-					 &m_min, &m_max);
+printf("testing with molecule_size=%d\n", molecule_size);
+printf("             out_of_range_tolerance_[min,max]=[%g,%g]\n",
+       (double) out_of_range_tolerance_min,
+       (double) out_of_range_tolerance_max);
+printf("             x=%g\n", (double) x);
+
+  {
+const int i_center = LocalInterp_molecule_posn(grid_x0, grid_dx,
+					       grid_i_min, grid_i_max,
+					       molecule_size,
+					       out_of_range_tolerance_min,
+					       out_of_range_tolerance_max,
+					       x,
+					       &x_rel,
+					       &m_min, &m_max);
 
 if ((i_center == INT_MIN) || (i_center == INT_MAX))
    then printf("i_center=%d\n", i_center);
    else printf("i_center=%d x_rel=%g m_[min,max]=[%d,%d] i_[min,max]=[%d,%d]\n",
 	       i_center, x_rel, m_min, m_max, i_center+m_min, i_center+m_max);
+  }
 }
 
 /******************************************************************************/
 
-/* run a preset set of tests, return number of failures */
-int run_batch_tests(void)
+/*
+ * This function run the preset set of tests specified by the
+ *  test_data  array
+ *
+ * Results:
+ * This function returns the number of test failures.
+ */
+static
+  int run_batch_tests(void)
 {
 int i;
 int failure_count = 0;
@@ -272,8 +323,9 @@ int failure_count = 0;
 	int m_min = 0, m_max = 0;
 	int i_center = LocalInterp_molecule_posn(grid_x0, grid_dx,
 						 grid_i_min, grid_i_max,
-						 p->out_of_range_tolerance,
 						 p->molecule_size,
+						 p->out_of_range_tolerance_min,
+						 p->out_of_range_tolerance_max,
 						 p->x,
 						 &x_rel,
 						 &m_min, &m_max);
@@ -283,10 +335,16 @@ int failure_count = 0;
 		      && fuzzy_EQ(x_rel, p->x_rel)
 		      && (m_min == p->m_min)
 		      && (m_max == p->m_max)    );
-	int msglen = printf("tol=%g size=%d x=%g ==> ",
-			    p->out_of_range_tolerance, p->molecule_size, p->x);
-	printf("i_center=%d x_rel=%g m_[min,max]=[%d,%d]\n",
-	       i_center, x_rel, m_min, m_max);
+
+	int msglen =
+	  printf("size=%d tol=[%g,%g] x=%g ==> ",
+		 p->molecule_size,
+		 (double) p->out_of_range_tolerance_min,
+		 (double) p->out_of_range_tolerance_max,
+		 (double) p->x);
+	printf("i_center=%d x_rel=%g m=[%d,%d]\n",
+	       i_center, (double) x_rel, m_min, m_max);
+
 	if (! ok)
 	   then {
 		++failure_count;
@@ -294,7 +352,7 @@ int failure_count = 0;
 		int error_msglen = printf("***** FAIL: ");
 		printf("%-*s", msglen-error_msglen, "expected");
 		printf("i_center=%d x_rel=%g m_[min,max]=[%d,%d]\n",
-		       p->i_center, p->x_rel, p->m_min, p->m_max);
+		       p->i_center, (double) p->x_rel, p->m_min, p->m_max);
 		  }
 		}
 	}