Implement computation of spacing according to the TeXBook

This implements the relevant math typography rules described in the
Appendix G of the TeXbook. More precisely, for each atom

  + the class is computed by implementing rules 5 and 6 of Appendix G

  + the spacing is computed according to the table p. 170

This code is not used at this point.

src/mathed/MathClass.cpp

@@ -11,10 +11,17 @@
 #include <config.h>
 
 #include "MathClass.h"
+#include "MathSupport.h"
 
+#include "MetricsInfo.h"
+#include "FontInfo.h"
+
+#include "support/debug.h"
 #include "support/docstring.h"
 #include "support/lassert.h"
 
+#include <ostream>
+
 using namespace std;
 
 namespace lyx {
@@ -79,4 +86,95 @@ MathClass string_to_class(docstring const &s)
 }
 
 
+/*
+ * The TeXbook presents in Appendix G a set of 22 rules (!) explaining
+ * how to typeset mathematic formulas. Of interest here are rules 5
+ * and 6:
+
+ * 5. If the current item is a Bin atom, and if this was the first
+ *    atom in the list, or if the most recent previous atom was Bin,
+ *    Op, Rel, Open, or Punct, change the current Bin to Ord [and
+ *    continue with Rule 14. Otherwise continue with Rule 17]
+ *
+ * 6. If the current item is a Rel or Close or Punct atom, and if the
+ *    most recent previous atom was Bin, change that previous Bin to
+ *    Ord. [Continue with Rule 17.]
+ */
+void update_class(MathClass & mc, MathClass const prev, MathClass const next)
+{
+	if (mc == MC_BIN
+		&& (prev == MC_BIN || prev == MC_OP || prev == MC_OPEN
+			|| prev == MC_PUNCT || prev == MC_REL
+			|| next == MC_CLOSE || next == MC_PUNCT || next == MC_REL))
+		mc = MC_ORD;
+}
+
+
+/*
+ * This table of spacing between two classes can be found p. 170 of
+ * The TeXbook.
+ *
+ * The line is the class of the first class, and the column the second
+ * class. The number encodes the spacing between the two atoms, as
+ * follows
+ *
+ * + 0: no spacing
+ * + 1: thin mu skip
+ * + 2: med mu skip
+ * + 3: thick mu skip
+ * + 9: should never happen
+ * + negative value: either 0 if the atom is in script or scriptscript mode,
+ *   or the spacing given by the absolute value.
+ */
+int pair_spc[MC_UNKNOWN][MC_UNKNOWN] = {
+//	 ORD    OP   BIN   REL  OPEN CLOSE PUNCT INNER
+	{  0,    1,   -2,   -3,    0,    0,    0,   -1}, // ORD
+	{  1,    1,    9,   -3,    0,    0,    0,   -1}, // OP
+	{ -2,   -2,    9,    9,   -2,    9,    9,   -2}, // BIN
+	{ -3,   -3,    9,    0,   -3,    0,    0,   -3}, // REL
+	{  0,    0,    9,    0,    0,    0,    0,    0}, // OPEN
+	{  0,    1,   -2,   -3,    0,    0,    0,   -1}, // CLOSE
+	{ -1,   -1,    9,   -1,   -1,   -1,   -1,   -1}, // PUNCT
+	{ -1,    1,   -2,   -3,   -1,    0,   -1,   -1}, // INNER
+};
+
+
+int class_spacing(MathClass const mc1, MathClass const mc2,
+                  MetricsBase const & mb)
+{
+	int spc_code = pair_spc[mc1][mc2];
+	//lyxerr << class_to_string(mc1) << "+" << class_to_string(mc2)
+	//	   << "=" << spc_code << " @" << mb.style << endl;
+	if (spc_code < 0) {
+		switch (mb.style) {
+		case LM_ST_DISPLAY:
+		case LM_ST_TEXT:
+			spc_code = abs(spc_code);
+			break;
+		case LM_ST_SCRIPT:
+		case LM_ST_SCRIPTSCRIPT:
+			spc_code = 0;
+		}
+	}
+
+	int spc = 0;
+	switch(spc_code) {
+	case 0:
+		break;
+	case 1:
+		spc = mathed_thinmuskip(mb.font);
+		break;
+	case 2:
+		spc = mathed_medmuskip(mb.font);
+		break;
+	case 3:
+		spc = mathed_thickmuskip(mb.font);
+		break;
+	default:
+		LYXERR0("Impossible pair of classes: (" << mc1 << ", " << mc2 << ")");
+		LATTEST(false);
+	}
+	return spc;
+}
+
 } // namespace lyx

src/mathed/MathClass.h

@@ -16,6 +16,7 @@
 
 namespace lyx {
 
+class MetricsBase;
 
 /* The TeXbook, p. 158:
  *
@@ -58,6 +59,10 @@ MathClass string_to_class(docstring const &);
 
 docstring const class_to_string(MathClass);
 
+void update_class(MathClass & mc, MathClass const prev, MathClass const next);
+
+int class_spacing(MathClass const mc1, MathClass const mc2,
+                  MetricsBase const & mb);
 
 } // namespace lyx
 

src/mathed/MathSupport.cpp

@@ -528,6 +528,9 @@ int mathed_font_em(FontInfo const & font)
  * punctuation, and is put around inner objects, except where these
  * are followed by a close or preceded by an open symbol, and except
  * if the other object is a large operator or a binary relation.
+ *
+ * See the file MathClass.cpp for a formal implementation of the rules
+ * above.
  */
 
 int mathed_thinmuskip(FontInfo font)