From 399a5f9aa3d7db43f9c13361902da8ef3b4c43f5 Mon Sep 17 00:00:00 2001
From: Arash Partow <partow@gmail.com>
Date: Sun, 28 Jul 2013 21:35:06 +1000
Subject: [PATCH] C++ Mathematical Expression Library (ExprTk) 
 http://www.partow.net/programming/exprtk/index.html

---
 exprtk.hpp                   | 128 ++++++++++++++++++-----------------
 exprtk_benchmark.cpp         |  35 +++++-----
 exprtk_simple_example_02.cpp |  10 +--
 exprtk_simple_example_03.cpp |   6 +-
 exprtk_simple_example_05.cpp |   4 +-
 exprtk_test.cpp              |  46 ++++++-------
 readme.txt                   |  94 ++++++++++++-------------
 7 files changed, 166 insertions(+), 157 deletions(-)

diff --git a/exprtk.hpp b/exprtk.hpp
index fd22846..47ea450 100644
--- a/exprtk.hpp
+++ b/exprtk.hpp
@@ -232,6 +232,12 @@ namespace exprtk
             return (*this);
          }
 
+         inline build_string& operator << (const char* s)
+         {
+            data_ += std::string(s);
+            return (*this);
+         }
+
          inline operator std::string () const
          {
             return data_;
@@ -10216,8 +10222,8 @@ namespace exprtk
          }
 
          if (
-              numeric_check_enabled() ||
-              bracket_check_enabled() ||
+              numeric_check_enabled () ||
+              bracket_check_enabled () ||
               sequence_check_enabled()
             )
          {
@@ -13564,7 +13570,7 @@ namespace exprtk
                                                       const details::operator_type& operation,
                                                       expression_node_ptr (&branch)[2])
             {
-               const Type  c = dynamic_cast<details::literal_node<Type>* >(branch[0])->value();
+               const Type  c = dynamic_cast<details::literal_node<Type>*> (branch[0])->value();
                const Type& v = dynamic_cast<details::variable_node<Type>*>(branch[1])->ref();
                details::free_node(*(expr_gen.node_allocator_),branch[0]);
                switch (operation)
@@ -13585,7 +13591,7 @@ namespace exprtk
                                                       expression_node_ptr (&branch)[2])
             {
                const Type& v = dynamic_cast<details::variable_node<Type>*>(branch[0])->ref();
-               const Type  c = dynamic_cast<details::literal_node<Type>* >(branch[1])->value();
+               const Type  c = dynamic_cast<details::literal_node<Type>*> (branch[1])->value();
                details::free_node(*(expr_gen.node_allocator_),branch[1]);
                if (expr_gen.cardinal_pow_optimizable(operation,c))
                {
@@ -13883,7 +13889,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf3ext_expression::template compile<vtype,vtype,vtype>(expr_gen,id(expr_gen,o0,o1),v0,v1,v2,result))
                   return result;
-               if (!expr_gen.valid_operator(o0,f0))
+               else if (!expr_gen.valid_operator(o0,f0))
                   return error_node();
                else if (!expr_gen.valid_operator(o1,f1))
                   return error_node();
@@ -13920,7 +13926,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf3ext_expression::template compile<vtype,vtype,ctype>(expr_gen,id(expr_gen,o0,o1),v0,v1,c,result))
                   return result;
-               if (!expr_gen.valid_operator(o0,f0))
+               else if (!expr_gen.valid_operator(o0,f0))
                   return error_node();
                else if (!expr_gen.valid_operator(o1,f1))
                   return error_node();
@@ -13956,7 +13962,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf3ext_expression::template compile<vtype,vtype,ctype>(expr_gen,id(expr_gen,o0,o1),v0,v1,c,result))
                   return result;
-               if (!expr_gen.valid_operator(o0,f0))
+               else if (!expr_gen.valid_operator(o0,f0))
                   return error_node();
                else if (!expr_gen.valid_operator(o1,f1))
                   return error_node();
@@ -13992,7 +13998,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf3ext_expression::template compile<vtype,ctype,vtype>(expr_gen,id(expr_gen,o0,o1),v0,c,v1,result))
                   return result;
-               if (!expr_gen.valid_operator(o0,f0))
+               else if (!expr_gen.valid_operator(o0,f0))
                   return error_node();
                else if (!expr_gen.valid_operator(o1,f1))
                   return error_node();
@@ -14028,7 +14034,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf3ext_expression::template compile<vtype,ctype,vtype>(expr_gen,id(expr_gen,o0,o1),v0,c,v1,result))
                   return result;
-               if (!expr_gen.valid_operator(o0,f0))
+               else if (!expr_gen.valid_operator(o0,f0))
                   return error_node();
                else if (!expr_gen.valid_operator(o1,f1))
                   return error_node();
@@ -14064,7 +14070,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf3ext_expression::template compile<ctype,vtype,vtype>(expr_gen,id(expr_gen,o0,o1),c,v0,v1,result))
                   return result;
-               if (!expr_gen.valid_operator(o0,f0))
+               else if (!expr_gen.valid_operator(o0,f0))
                   return error_node();
                else if (!expr_gen.valid_operator(o1,f1))
                   return error_node();
@@ -14101,7 +14107,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf3ext_expression::template compile<ctype,vtype,vtype>(expr_gen,id(expr_gen,o0,o1),c,v0,v1,result))
                   return result;
-               if (!expr_gen.valid_operator(o0,f0))
+               else if (!expr_gen.valid_operator(o0,f0))
                   return error_node();
                else if (!expr_gen.valid_operator(o1,f1))
                   return error_node();
@@ -14137,7 +14143,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf3ext_expression::template compile<ctype,vtype,ctype>(expr_gen,id(expr_gen,o0,o1),c0,v,c1,result))
                   return result;
-               if (!expr_gen.valid_operator(o0,f0))
+               else if (!expr_gen.valid_operator(o0,f0))
                   return error_node();
                else if (!expr_gen.valid_operator(o1,f1))
                   return error_node();
@@ -14174,7 +14180,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf3ext_expression::template compile<ctype,vtype,ctype>(expr_gen,id(expr_gen,o0,o1),c0,v,c1,result))
                   return result;
-               if (!expr_gen.valid_operator(o0,f0))
+               else if (!expr_gen.valid_operator(o0,f0))
                   return error_node();
                else if (!expr_gen.valid_operator(o1,f1))
                   return error_node();
@@ -14221,7 +14227,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf3ext_expression::template compile<ctype,ctype,vtype>(expr_gen,id(expr_gen,o0,o1),c0,c1,v,result))
                   return result;
-               if (!expr_gen.valid_operator(o0,f0))
+               else if (!expr_gen.valid_operator(o0,f0))
                   return error_node();
                else if (!expr_gen.valid_operator(o1,f1))
                   return error_node();
@@ -14257,7 +14263,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf3ext_expression::template compile<vtype,ctype,ctype>(expr_gen,id(expr_gen,o0,o1),v,c0,c1,result))
                   return result;
-               if (!expr_gen.valid_operator(o0,f0))
+               else if (!expr_gen.valid_operator(o0,f0))
                   return error_node();
                else if (!expr_gen.valid_operator(o1,f1))
                   return error_node();
@@ -14313,7 +14319,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),v0,v1,v2,v3,result))
                   return result;
-               if (!expr_gen.valid_operator(o0,f0))
+               else if (!expr_gen.valid_operator(o0,f0))
                   return error_node();
                else if (!expr_gen.valid_operator(o1,f1))
                   return error_node();
@@ -14359,7 +14365,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),v0,v1,v2,c,result))
                   return result;
-               if (!expr_gen.valid_operator(o0,f0))
+               else if (!expr_gen.valid_operator(o0,f0))
                   return error_node();
                else if (!expr_gen.valid_operator(o1,f1))
                   return error_node();
@@ -14406,7 +14412,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),v0,v1,c,v2,result))
                   return result;
-               if (!expr_gen.valid_operator(o0,f0))
+               else if (!expr_gen.valid_operator(o0,f0))
                   return error_node();
                else if (!expr_gen.valid_operator(o1,f1))
                   return error_node();
@@ -14453,7 +14459,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),v0,c,v1,v2,result))
                   return result;
-               if (!expr_gen.valid_operator(o0,f0))
+               else if (!expr_gen.valid_operator(o0,f0))
                   return error_node();
                else if (!expr_gen.valid_operator(o1,f1))
                   return error_node();
@@ -14500,7 +14506,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),c,v0,v1,v2,result))
                   return result;
-               if (!expr_gen.valid_operator(o0,f0))
+               else if (!expr_gen.valid_operator(o0,f0))
                   return error_node();
                else if (!expr_gen.valid_operator(o1,f1))
                   return error_node();
@@ -14547,7 +14553,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),c0,v0,c1,v1,result))
                   return result;
-               if (!expr_gen.valid_operator(o0,f0))
+               else if (!expr_gen.valid_operator(o0,f0))
                   return error_node();
                else if (!expr_gen.valid_operator(o1,f1))
                   return error_node();
@@ -14594,7 +14600,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),v0,c0,v1,c1,result))
                   return result;
-               if (!expr_gen.valid_operator(o0,f0))
+               else if (!expr_gen.valid_operator(o0,f0))
                   return error_node();
                else if (!expr_gen.valid_operator(o1,f1))
                   return error_node();
@@ -14641,7 +14647,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),c0,v0,v1,c1,result))
                   return result;
-               if (!expr_gen.valid_operator(o0,f0))
+               else if (!expr_gen.valid_operator(o0,f0))
                   return error_node();
                else if (!expr_gen.valid_operator(o1,f1))
                   return error_node();
@@ -14688,7 +14694,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),v0,c0,c1,v1,result))
                   return result;
-               if (!expr_gen.valid_operator(o0,f0))
+               else if (!expr_gen.valid_operator(o0,f0))
                   return error_node();
                else if (!expr_gen.valid_operator(o1,f1))
                   return error_node();
@@ -14734,7 +14740,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),v0,v1,v2,v3,result))
                   return result;
-               if (!expr_gen.valid_operator(o0,f0))
+               else if (!expr_gen.valid_operator(o0,f0))
                   return error_node();
                else
                   return node_type::allocate(*(expr_gen.node_allocator_),v0,v1,v2,v3,f0,f1,f2);
@@ -14776,7 +14782,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),v0,v1,v2,c,result))
                   return result;
-               if (!expr_gen.valid_operator(o0,f0))
+               else if (!expr_gen.valid_operator(o0,f0))
                   return error_node();
                else
                   return node_type::allocate(*(expr_gen.node_allocator_),v0,v1,v2,c,f0,f1,f2);
@@ -14847,7 +14853,7 @@ namespace exprtk
                typedef typename synthesize_covov_expression1::node_type covov_t;
                const covov_t* covov = dynamic_cast<const covov_t*>(branch[1]);
                const T& v0 = dynamic_cast<details::variable_node<Type>*>(branch[0])->ref();
-               const T&  c = covov->t0();
+               const T   c = covov->t0();
                const T& v1 = covov->t1();
                const T& v2 = covov->t2();
                const details::operator_type o0 = operation;
@@ -14860,7 +14866,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),v0,c,v1,v2,result))
                   return result;
-               if (!expr_gen.valid_operator(o0,f0))
+               else if (!expr_gen.valid_operator(o0,f0))
                   return error_node();
                else
                   return node_type::allocate(*(expr_gen.node_allocator_),v0,c,v1,v2,f0,f1,f2);
@@ -14888,7 +14894,7 @@ namespace exprtk
                // c o0 (v0 o1 (v1 o2 v2))
                typedef typename synthesize_vovov_expression1::node_type vovov_t;
                const vovov_t* vovov = dynamic_cast<const vovov_t*>(branch[1]);
-               const T&  c = dynamic_cast<details::literal_node<Type>*>(branch[0])->value();
+               const T   c = dynamic_cast<details::literal_node<Type>*>(branch[0])->value();
                const T& v0 = vovov->t0();
                const T& v1 = vovov->t1();
                const T& v2 = vovov->t2();
@@ -14946,7 +14952,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),c0,v0,c1,v1,result))
                   return result;
-               if (!expr_gen.valid_operator(o0,f0))
+               else if (!expr_gen.valid_operator(o0,f0))
                   return error_node();
                else
                   return node_type::allocate(*(expr_gen.node_allocator_),c0,v0,c1,v1,f0,f1,f2);
@@ -14988,7 +14994,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),v0,c0,v1,c1,result))
                   return result;
-               if (!expr_gen.valid_operator(o0,f0))
+               else if (!expr_gen.valid_operator(o0,f0))
                   return error_node();
                else
                   return node_type::allocate(*(expr_gen.node_allocator_),v0,c0,v1,c1,f0,f1,f2);
@@ -15031,7 +15037,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),c0,v0,v1,c1,result))
                   return result;
-               if (!expr_gen.valid_operator(o0,f0))
+               else if (!expr_gen.valid_operator(o0,f0))
                   return error_node();
                else
                   return node_type::allocate(*(expr_gen.node_allocator_),c0,v0,v1,c1,f0,f1,f2);
@@ -15073,7 +15079,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),v0,c0,c1,v1,result))
                   return result;
-               if (!expr_gen.valid_operator(o0,f0))
+               else if (!expr_gen.valid_operator(o0,f0))
                   return error_node();
                else
                   return node_type::allocate(*(expr_gen.node_allocator_),v0,c0,c1,v1,f0,f1,f2);
@@ -15115,7 +15121,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),v0,v1,v2,v3,result))
                   return result;
-               if (!expr_gen.valid_operator(o0,f0))
+               else if (!expr_gen.valid_operator(o0,f0))
                   return error_node();
                else
                   return node_type::allocate(*(expr_gen.node_allocator_),v0,v1,v2,v3,f0,f1,f2);
@@ -15157,7 +15163,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),v0,v1,v2,c,result))
                   return result;
-               if (!expr_gen.valid_operator(o0,f0))
+               else if (!expr_gen.valid_operator(o0,f0))
                   return error_node();
                else
                   return node_type::allocate(*(expr_gen.node_allocator_),v0,v1,v2,c,f0,f1,f2);
@@ -15199,7 +15205,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),v0,v1,c,v2,result))
                   return result;
-               if (!expr_gen.valid_operator(o0,f0))
+               else if (!expr_gen.valid_operator(o0,f0))
                   return error_node();
                else
                   return node_type::allocate(*(expr_gen.node_allocator_),v0,v1,c,v2,f0,f1,f2);
@@ -15241,7 +15247,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),v0,c,v1,v2,result))
                   return result;
-               if (!expr_gen.valid_operator(o0,f0))
+               else if (!expr_gen.valid_operator(o0,f0))
                   return error_node();
                else
                   return node_type::allocate(*(expr_gen.node_allocator_),v0,c,v1,v2,f0,f1,f2);
@@ -15284,7 +15290,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),c,v0,v1,v2,result))
                   return result;
-               if (!expr_gen.valid_operator(o0,f0))
+               else if (!expr_gen.valid_operator(o0,f0))
                   return error_node();
                else
                   return node_type::allocate(*(expr_gen.node_allocator_),c,v0,v1,v2,f0,f1,f2);
@@ -15327,7 +15333,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),c0,v0,c1,v1,result))
                   return result;
-               if (!expr_gen.valid_operator(o0,f0))
+               else if (!expr_gen.valid_operator(o0,f0))
                   return error_node();
                else
                   return node_type::allocate(*(expr_gen.node_allocator_),c0,v0,c1,v1,f0,f1,f2);
@@ -15356,9 +15362,9 @@ namespace exprtk
                typedef typename synthesize_covoc_expression0::node_type covoc_t;
                const covoc_t* covoc = dynamic_cast<const covoc_t*>(branch[1]);
                const T& v0 = dynamic_cast<details::variable_node<Type>*>(branch[0])->ref();
-               const T& c0 = covoc->t0();
+               const T  c0 = covoc->t0();
                const T& v1 = covoc->t1();
-               const T& c1 = covoc->t2();
+               const T  c1 = covoc->t2();
                const details::operator_type o0 = operation;
                const details::operator_type o1 = expr_gen.get_operator(covoc->f0());
                const details::operator_type o2 = expr_gen.get_operator(covoc->f1());
@@ -15369,7 +15375,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),v0,c0,v1,c1,result))
                   return result;
-               if (!expr_gen.valid_operator(o0,f0))
+               else if (!expr_gen.valid_operator(o0,f0))
                   return error_node();
                else
                   return node_type::allocate(*(expr_gen.node_allocator_),v0,c0,v1,c1,f0,f1,f2);
@@ -15412,7 +15418,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),c0,v0,v1,c1,result))
                   return result;
-               if (!expr_gen.valid_operator(o0,f0))
+               else if (!expr_gen.valid_operator(o0,f0))
                   return error_node();
                else
                   return node_type::allocate(*(expr_gen.node_allocator_),c0,v0,v1,c1,f0,f1,f2);
@@ -15470,7 +15476,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),v0,v1,v2,v3,result))
                   return result;
-               if (!expr_gen.valid_operator(o2,f2))
+               else if (!expr_gen.valid_operator(o2,f2))
                   return error_node();
                else
                   return node_type::allocate(*(expr_gen.node_allocator_),v0,v1,v2,v3,f0,f1,f2);
@@ -15513,7 +15519,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),v0,v1,v2,c,result))
                   return result;
-               if (!expr_gen.valid_operator(o2,f2))
+               else if (!expr_gen.valid_operator(o2,f2))
                   return error_node();
                else
                   return node_type::allocate(*(expr_gen.node_allocator_),v0,v1,v2,c,f0,f1,f2);
@@ -15555,7 +15561,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),v0,v1,c,v2,result))
                   return result;
-               if (!expr_gen.valid_operator(o2,f2))
+               else if (!expr_gen.valid_operator(o2,f2))
                   return error_node();
                else
                   return node_type::allocate(*(expr_gen.node_allocator_),v0,v1,c,v2,f0,f1,f2);
@@ -15584,7 +15590,7 @@ namespace exprtk
                typedef typename synthesize_vocov_expression0::node_type vocov_t;
                const vocov_t* vocov = dynamic_cast<const vocov_t*>(branch[0]);
                const T& v0 = vocov->t0();
-               const T&  c = vocov->t1();
+               const T   c = vocov->t1();
                const T& v1 = vocov->t2();
                const T& v2 = dynamic_cast<details::variable_node<Type>*>(branch[1])->ref();
                const details::operator_type o0 = expr_gen.get_operator(vocov->f0());
@@ -15597,7 +15603,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),v0,c,v1,v2,result))
                   return result;
-               if (!expr_gen.valid_operator(o2,f2))
+               else if (!expr_gen.valid_operator(o2,f2))
                   return error_node();
                else
                   return node_type::allocate(*(expr_gen.node_allocator_),v0,c,v1,v2,f0,f1,f2);
@@ -15639,7 +15645,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),c,v0,v1,v2,result))
                   return result;
-               if (!expr_gen.valid_operator(o2,f2))
+               else if (!expr_gen.valid_operator(o2,f2))
                   return error_node();
                else
                   return node_type::allocate(*(expr_gen.node_allocator_),c,v0,v1,v2,f0,f1,f2);
@@ -15681,7 +15687,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),c0,v0,c1,v1,result))
                   return result;
-               if (!expr_gen.valid_operator(o2,f2))
+               else if (!expr_gen.valid_operator(o2,f2))
                   return error_node();
                else
                   return node_type::allocate(*(expr_gen.node_allocator_),c0,v0,c1,v1,f0,f1,f2);
@@ -15724,7 +15730,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),v0,c0,v1,c1,result))
                   return result;
-               if (!expr_gen.valid_operator(o2,f2))
+               else if (!expr_gen.valid_operator(o2,f2))
                   return error_node();
                else
                   return node_type::allocate(*(expr_gen.node_allocator_),v0,c0,v1,c1,f0,f1,f2);
@@ -15767,7 +15773,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),c0,v0,v1,c1,result))
                   return result;
-               if (!expr_gen.valid_operator(o2,f2))
+               else if (!expr_gen.valid_operator(o2,f2))
                   return error_node();
                else
                   return node_type::allocate(*(expr_gen.node_allocator_),c0,v0,v1,c1,f0,f1,f2);
@@ -15809,7 +15815,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),v0,c0,c1,v1,result))
                   return result;
-               if (!expr_gen.valid_operator(o2,f2))
+               else if (!expr_gen.valid_operator(o2,f2))
                   return error_node();
                else
                   return node_type::allocate(*(expr_gen.node_allocator_),v0,c0,c1,v1,f0,f1,f2);
@@ -15851,7 +15857,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),v0,v1,v2,v3,result))
                   return result;
-               if (!expr_gen.valid_operator(o2,f2))
+               else if (!expr_gen.valid_operator(o2,f2))
                   return error_node();
                else
                   return node_type::allocate(*(expr_gen.node_allocator_),v0,v1,v2,v3,f0,f1,f2);
@@ -15894,7 +15900,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),v0,v1,v2,c,result))
                   return result;
-               if (!expr_gen.valid_operator(o2,f2))
+               else if (!expr_gen.valid_operator(o2,f2))
                   return error_node();
                else
                   return node_type::allocate(*(expr_gen.node_allocator_),v0,v1,v2,c,f0,f1,f2);
@@ -15936,7 +15942,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),v0,v1,c,v2,result))
                   return result;
-               if (!expr_gen.valid_operator(o2,f2))
+               else if (!expr_gen.valid_operator(o2,f2))
                   return error_node();
                else
                   return node_type::allocate(*(expr_gen.node_allocator_),v0,v1,c,v2,f0,f1,f2);
@@ -15978,7 +15984,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),v0,c,v1,v2,result))
                   return result;
-               if (!expr_gen.valid_operator(o2,f2))
+               else if (!expr_gen.valid_operator(o2,f2))
                   return error_node();
                else
                   return node_type::allocate(*(expr_gen.node_allocator_),v0,c,v1,v2,f0,f1,f2);
@@ -16020,7 +16026,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),c,v0,v1,v2,result))
                   return result;
-               if (!expr_gen.valid_operator(o2,f2))
+               else if (!expr_gen.valid_operator(o2,f2))
                   return error_node();
                else
                   return node_type::allocate(*(expr_gen.node_allocator_),c,v0,v1,v2,f0,f1,f2);
@@ -16062,7 +16068,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),c0,v0,c1,v1,result))
                   return result;
-               if (!expr_gen.valid_operator(o2,f2))
+               else if (!expr_gen.valid_operator(o2,f2))
                   return error_node();
                else
                   return node_type::allocate(*(expr_gen.node_allocator_),c0,v0,c1,v1,f0,f1,f2);
@@ -16105,7 +16111,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),v0,c0,v1,c1,result))
                   return result;
-               if (!expr_gen.valid_operator(o2,f2))
+               else if (!expr_gen.valid_operator(o2,f2))
                   return error_node();
                else
                   return node_type::allocate(*(expr_gen.node_allocator_),v0,c0,v1,c1,f0,f1,f2);
@@ -16148,7 +16154,7 @@ namespace exprtk
                expression_node_ptr result = error_node();
                if (synthesize_sf4ext_expression::template compile<T0,T1,T2,T3>(expr_gen,id(expr_gen,o0,o1,o2),c0,v0,v1,c1,result))
                   return result;
-               if (!expr_gen.valid_operator(o2,f2))
+               else if (!expr_gen.valid_operator(o2,f2))
                   return error_node();
                else
                   return node_type::allocate(*(expr_gen.node_allocator_),c0,v0,v1,c1,f0,f1,f2);
diff --git a/exprtk_benchmark.cpp b/exprtk_benchmark.cpp
index 19699b1..cce68ab 100644
--- a/exprtk_benchmark.cpp
+++ b/exprtk_benchmark.cpp
@@ -37,7 +37,7 @@ const std::string expression_list[] = {
                                          "sin(2 * x) + cos(pi / y)",
                                          "1 - sin(2 * x) + cos(pi / y)",
                                          "sqrt(111.111 - sin(2 * x) + cos(pi / y) / 333.333)",
-                                         "(x^2 / sin(2 * pi / y)) -x / 2",
+                                         "(x^2 / sin(2 * pi / y)) - x / 2",
                                          "x + (cos(y - sin(2 / x * pi)) - sin(x - cos(2 * y / pi))) - y",
                                          "clamp(-1.0, sin(2 * pi * x) + cos(y / 2 * pi), +1.0)",
                                          "max(3.33, min(sqrt(1 - sin(2 * x) + cos(pi / y) / 3), 1.11))",
@@ -82,7 +82,7 @@ void run_exprtk_benchmark(T& x, T& y,
                           exprtk::expression<T>& expression,
                           const std::string& expr_string)
 {
-   T total = 0.0;
+   T total = T(0);
    unsigned int count = 0;
    exprtk::timer timer;
    timer.start();
@@ -95,7 +95,7 @@ void run_exprtk_benchmark(T& x, T& y,
       }
    }
    timer.stop();
-   if (T(0.0) != total)
+   if (T(0) != total)
       printf("[exprtk] Total Time:%12.8f  Rate:%14.3fevals/sec Expression: %s\n",
              timer.time(),
              count / timer.time(),
@@ -109,7 +109,7 @@ template <typename T> struct native;
 template <typename T, typename NativeFunction>
 void run_native_benchmark(T& x, T& y, NativeFunction f, const std::string& expr_string)
 {
-   T total = 0.0;
+   T total = T(0);
    unsigned int count = 0;
    exprtk::timer timer;
    timer.start();
@@ -122,7 +122,7 @@ void run_native_benchmark(T& x, T& y, NativeFunction f, const std::string& expr_
       }
    }
    timer.stop();
-   if (T(0.0) != total)
+   if (T(0) != total)
       printf("[native] Total Time:%12.8f  Rate:%14.3fevals/sec Expression: %s\n",
              timer.time(),
              count / timer.time(),
@@ -173,7 +173,7 @@ struct native
 
    static inline T avg(Type x, Type y)
    {
-      return (x + y) / T(2.0);
+      return (x + y) / T(2);
    }
 
    static inline T clamp(const Type l, const Type v, const Type u)
@@ -188,12 +188,12 @@ struct native
 
    static inline T func01(Type x, Type y)
    {
-      return T(2.0) * (y + x);
+      return T(2) * (y + x);
    }
 
    static inline T func02(Type x, Type y)
    {
-      return (T(2.0) * y + T(2.0) * x);
+      return (T(2) * y + T(2) * x);
    }
 
    static inline T func03(Type x, Type y)
@@ -213,7 +213,7 @@ struct native
 
    static inline T func06(Type x, Type y)
    {
-      return T(1.0) - ((x * y) + (y / x)) - T(3.0);
+      return T(1) - ((x * y) + (y / x)) - T(3);
    }
 
    static inline T func07(Type x, Type y)
@@ -223,27 +223,28 @@ struct native
 
    static inline T func08(Type x, Type y)
    {
-      return (1.1*pow(x,T(1.0))+2.2*pow(y,T(2.0))-3.3*pow(x,T(3.0))+4.4*pow(y,T(15.0))-5.5*pow(x,T(23.0))+6.6*pow(y,T(55.0)));
+      using namespace std;
+      return (T(1.1)*pow(x,T(1))+T(2.2)*pow(y,T(2))-T(3.3)*pow(x,T(3))+T(4.4)*pow(y,T(15))-T(5.5)*pow(x,T(23))+T(6.6)*pow(y,T(55)));
    }
 
    static inline T func09(Type x, Type y)
    {
-      return std::sin(T(2.0) * x) + std::cos(pi / y);
+      return std::sin(T(2) * x) + std::cos(pi / y);
    }
 
    static inline T func10(Type x, Type y)
    {
-      return T(1.0) - std::sin(2.0 * x) + std::cos(pi / y);
+      return T(1) - std::sin(T(2) * x) + std::cos(pi / y);
    }
 
    static inline T func11(Type x, Type y)
    {
-      return std::sqrt(T(111.111) - std::sin(T(2.0) * x) + std::cos(pi / y) / T(333.333));
+      return std::sqrt(T(111.111) - std::sin(T(2) * x) + std::cos(pi / y) / T(333.333));
    }
 
    static inline T func12(Type x, Type y)
    {
-      return ((x * x) / std::sin(T(2.0) * pi / y)) -x / T(2.0);
+      return ((x * x) / std::sin(T(2) * pi / y)) - x / T(2);
    }
 
    static inline T func13(Type x, Type y)
@@ -253,17 +254,17 @@ struct native
 
    static inline T func14(Type x, Type y)
    {
-      return clamp(T(-1.0), std::sin(T(2.0) * pi * x) + std::cos(y / T(2.0) * pi), + T(1.0));
+      return clamp(T(-1), std::sin(T(2) * pi * x) + std::cos(y / T(2) * pi), + T(1));
    }
 
    static inline T func15(Type x, Type y)
    {
-      return std::max(T(3.33), std::min(sqrt(T(1.0) - std::sin(T(2.0) * x) + std::cos(pi / y) / T(3.0)), T(1.11)));
+      return std::max(T(3.33), std::min(sqrt(T(1) - std::sin(T(2) * x) + std::cos(pi / y) / T(3)), T(1.11)));
    }
 
    static inline T func16(Type x, Type y)
    {
-      return (((y + (x * T(2.2))) <= (x + y + T(1.1))) ? x - y : x * y) + T(2.0) * pi / x;
+      return (((y + (x * T(2.2))) <= (x + y + T(1.1))) ? x - y : x * y) + T(2) * pi / x;
    }
 };
 
diff --git a/exprtk_simple_example_02.cpp b/exprtk_simple_example_02.cpp
index 2ae670c..d6b2958 100644
--- a/exprtk_simple_example_02.cpp
+++ b/exprtk_simple_example_02.cpp
@@ -33,9 +33,9 @@ void square_wave()
                              " (1/21)*sin(42*pi*f*t)+(1/23)*sin(46*pi*f*t)+"
                              " (1/25)*sin(50*pi*f*t)+(1/27)*sin(54*pi*f*t))";
    static const T pi = T(3.14159265358979323846);
-   T f = pi/10.0;
-   T t = T(0.0);
-   T a = T(10.0);
+   T f = pi / T(10);
+   T t = T(0);
+   T a = T(10);
 
    exprtk::symbol_table<T> symbol_table;
    symbol_table.add_variable("f",f);
@@ -49,8 +49,8 @@ void square_wave()
    exprtk::parser<T> parser;
    parser.compile(expr_string,expression);
 
-   const T delta = (4.0*pi)/1000.0;
-   for (t = -2.0*pi; t <= +2.0*pi; t+=delta)
+   const T delta = (T(4) * pi) / T(1000);
+   for (t = (T(-2) * pi); t <= (T(+2) * pi); t += delta)
    {
       T result = expression.value();
       printf("%19.15f\t%19.15f\n",t,result);
diff --git a/exprtk_simple_example_03.cpp b/exprtk_simple_example_03.cpp
index 3f97659..ad1b193 100644
--- a/exprtk_simple_example_03.cpp
+++ b/exprtk_simple_example_03.cpp
@@ -25,9 +25,9 @@ template<typename T>
 void polynomial()
 {
    std::string expression_string = "25x^5 - 35x^4 - 15x^3 + 40x^2 - 15x + 1";
-   T r0 = T(0.0);
-   T r1 = T(1.0);
-   T  x = T(0.0);
+   T r0 = T(0);
+   T r1 = T(1);
+   T  x = T(0);
 
    exprtk::symbol_table<T> symbol_table;
    symbol_table.add_variable("x",x);
diff --git a/exprtk_simple_example_05.cpp b/exprtk_simple_example_05.cpp
index 438deb5..45de3d4 100644
--- a/exprtk_simple_example_05.cpp
+++ b/exprtk_simple_example_05.cpp
@@ -39,8 +39,8 @@ void custom_function()
 {
    typedef exprtk::expression<T> expression_t;
    std::string expression_string = "myfunc(sin(x*pi),y/2)";
-   T x = T(1.0);
-   T y = T(2.0);
+   T x = T(1);
+   T y = T(2);
    myfunc<T> mf;
 
    exprtk::symbol_table<T> symbol_table;
diff --git a/exprtk_test.cpp b/exprtk_test.cpp
index 5d1d00a..da3e3e7 100644
--- a/exprtk_test.cpp
+++ b/exprtk_test.cpp
@@ -1008,7 +1008,7 @@ inline bool not_equal_impl(const T& t1,
    if (t1 != t1) return true;
    if (t2 != t2) return true;
    T diff = std::abs(t1 - t2);
-   T eps_norm = (std::max(T(1.0),std::max(std::abs(t1),std::abs(t2))) * epsilon);
+   T eps_norm = (std::max(T(1),std::max(std::abs(t1),std::abs(t2))) * epsilon);
    return diff > eps_norm;
 }
 
@@ -1505,28 +1505,28 @@ inline bool run_test02()
                               test_ab<T>("'456'                == a[r0+2:r1] ","01234567890123456789","",T(1.0)),
                               test_ab<T>("'4567890123456789'   == a[r1-r0:]  ","01234567890123456789","",T(1.0)),
                               test_ab<T>("'01234'              == a[:r1-r0]  ","01234567890123456789","",T(1.0)),
-                              test_ab<T>("a[r0: 6]   == b "                   ,"01234567890123456789","23456",T(1.0)),
-                              test_ab<T>("a[2: r1]   == b "                   ,"01234567890123456789","23456",T(1.0)),
-                              test_ab<T>("a[r0:3*2]  == b "                   ,"01234567890123456789","23456",T(1.0)),
-                              test_ab<T>("a[1+1:r1]  == b "                   ,"01234567890123456789","23456",T(1.0)),
-                              test_ab<T>("a[r0:  ]   == b "                   ,"01234567890123456789","234567890123456789",T(1.0)),
-                              test_ab<T>("a[:  r1]   == b "                   ,"01234567890123456789","0123456",T(1.0)),
-                              test_ab<T>("a[r0:r1]   == b "                   ,"01234567890123456789","23456",T(1.0)),
-                              test_ab<T>("a[r0:r1+2] == b "                   ,"01234567890123456789","2345678",T(1.0)),
-                              test_ab<T>("a[r0+2:r1] == b "                   ,"01234567890123456789","456",T(1.0)),
-                              test_ab<T>("a[r1-r0:]  == b "                   ,"01234567890123456789","4567890123456789",T(1.0)),
-                              test_ab<T>("a[:r1-r0]  == b "                   ,"01234567890123456789","01234",T(1.0)),
-                              test_ab<T>("b == a[r0: 6]   "                   ,"01234567890123456789","23456",T(1.0)),
-                              test_ab<T>("b == a[2: r1]   "                   ,"01234567890123456789","23456",T(1.0)),
-                              test_ab<T>("b == a[r0:3*2]  "                   ,"01234567890123456789","23456",T(1.0)),
-                              test_ab<T>("b == a[1+1:r1]  "                   ,"01234567890123456789","23456",T(1.0)),
-                              test_ab<T>("b == a[r0:  ]   "                   ,"01234567890123456789","234567890123456789",T(1.0)),
-                              test_ab<T>("b == a[:  r1]   "                   ,"01234567890123456789","0123456",T(1.0)),
-                              test_ab<T>("b == a[r0:r1]   "                   ,"01234567890123456789","23456",T(1.0)),
-                              test_ab<T>("b == a[r0:r1+2] "                   ,"01234567890123456789","2345678",T(1.0)),
-                              test_ab<T>("b == a[r0+2:r1] "                   ,"01234567890123456789","456",T(1.0)),
-                              test_ab<T>("b == a[r1-r0:]  "                   ,"01234567890123456789","4567890123456789",T(1.0)),
-                              test_ab<T>("b == a[:r1-r0]  "                   ,"01234567890123456789","01234",T(1.0)),
+                              test_ab<T>("a[r0: 6]   == b                    ","01234567890123456789","23456",T(1.0)),
+                              test_ab<T>("a[2: r1]   == b                    ","01234567890123456789","23456",T(1.0)),
+                              test_ab<T>("a[r0:3*2]  == b                    ","01234567890123456789","23456",T(1.0)),
+                              test_ab<T>("a[1+1:r1]  == b                    ","01234567890123456789","23456",T(1.0)),
+                              test_ab<T>("a[r0:  ]   == b                    ","01234567890123456789","234567890123456789",T(1.0)),
+                              test_ab<T>("a[:  r1]   == b                    ","01234567890123456789","0123456",T(1.0)),
+                              test_ab<T>("a[r0:r1]   == b                    ","01234567890123456789","23456",T(1.0)),
+                              test_ab<T>("a[r0:r1+2] == b                    ","01234567890123456789","2345678",T(1.0)),
+                              test_ab<T>("a[r0+2:r1] == b                    ","01234567890123456789","456",T(1.0)),
+                              test_ab<T>("a[r1-r0:]  == b                    ","01234567890123456789","4567890123456789",T(1.0)),
+                              test_ab<T>("a[:r1-r0]  == b                    ","01234567890123456789","01234",T(1.0)),
+                              test_ab<T>("b == a[r0: 6]                      ","01234567890123456789","23456",T(1.0)),
+                              test_ab<T>("b == a[2: r1]                      ","01234567890123456789","23456",T(1.0)),
+                              test_ab<T>("b == a[r0:3*2]                     ","01234567890123456789","23456",T(1.0)),
+                              test_ab<T>("b == a[1+1:r1]                     ","01234567890123456789","23456",T(1.0)),
+                              test_ab<T>("b == a[r0:  ]                      ","01234567890123456789","234567890123456789",T(1.0)),
+                              test_ab<T>("b == a[:  r1]                      ","01234567890123456789","0123456",T(1.0)),
+                              test_ab<T>("b == a[r0:r1]                      ","01234567890123456789","23456",T(1.0)),
+                              test_ab<T>("b == a[r0:r1+2]                    ","01234567890123456789","2345678",T(1.0)),
+                              test_ab<T>("b == a[r0+2:r1]                    ","01234567890123456789","456",T(1.0)),
+                              test_ab<T>("b == a[r1-r0:]                     ","01234567890123456789","4567890123456789",T(1.0)),
+                              test_ab<T>("b == a[:r1-r0]                     ","01234567890123456789","01234",T(1.0)),
                               test_ab<T>("'01234567890123456789'[0:9] == a     ","0123456789","",T(1.0)),
                               test_ab<T>("'01234567890123456789'[0:9] == a[:]  ","0123456789","",T(1.0)),
                               test_ab<T>("'01234567890123456789'[0:9] == a[0:] ","0123456789","",T(1.0)),
diff --git a/readme.txt b/readme.txt
index 9a6b2c2..bdd189d 100644
--- a/readme.txt
+++ b/readme.txt
@@ -134,9 +134,6 @@ include path (e.g: /usr/include/).
 |  :=      | Assign the value of x to y. (eg: y := x)                |
 |          | Where y is a variable type.                             |
 +----------+---------------------------------------------------------+
-|  <=>     | Swap the values of x and y. (eg: x <=> y)               |
-|          | Where both x and y are variables.                       |
-+----------+---------------------------------------------------------+
 
 (1) Equalities & Inequalities
 +----------+---------------------------------------------------------+
@@ -144,7 +141,7 @@ include path (e.g: /usr/include/).
 +----------+---------------------------------------------------------+
 | == or =  | True only if x is strictly equal to y. (eg: x == y)     |
 +----------+---------------------------------------------------------+
-| <> or != | True only if x does not equal y (eg: x <> y or x != y)  |
+| <> or != | True only if x does not equal y. (eg: x <> y or x != y) |
 +----------+---------------------------------------------------------+
 |  <       | True only if x is less than y. (eg: x < y)              |
 +----------+---------------------------------------------------------+
@@ -152,7 +149,7 @@ include path (e.g: /usr/include/).
 +----------+---------------------------------------------------------+
 |  >       | True only if x is greater than y. (eg: x > y)           |
 +----------+---------------------------------------------------------+
-|  >=      | True only if x greater than or equal to y (eg: x >= y)  |
+|  >=      | True only if x greater than or equal to y. (eg: x >= y) |
 +----------+---------------------------------------------------------+
 
 (2) Boolean Operations
@@ -214,29 +211,29 @@ include path (e.g: /usr/include/).
 +----------+---------------------------------------------------------+
 | equal    | Equality test between x and y using normalized epsilon  |
 +----------+---------------------------------------------------------+
-| erf      | Error function of x                                     |
+| erf      | Error function of x.                                    |
 +----------+---------------------------------------------------------+
-| erfc     | Complimentary error function of x                       |
+| erfc     | Complimentary error function of x.                      |
 +----------+---------------------------------------------------------+
-| exp      | e to the power of x                                     |
+| exp      | e to the power of x.                                    |
 +----------+---------------------------------------------------------+
 | expm1    | e to the power of x minus 1, where x is very small.     |
 |          | (eg: expm1(x))                                          |
 +----------+---------------------------------------------------------+
 | floor    | Largest integer that is less than or equal to x.        |
 +----------+---------------------------------------------------------+
-| frac     | Fractional portion of x                                 |
+| frac     | Fractional portion of x.                                |
 +----------+---------------------------------------------------------+
 | hypot    | Hypotenuse of x and y (eg: hypot(x,y) = sqrt(x*x + y*y))|
 +----------+---------------------------------------------------------+
-| log      | Natural logarithm of x                                  |
+| log      | Natural logarithm of x.                                 |
 +----------+---------------------------------------------------------+
-| log10    | Base 10 logarithm of x                                  |
+| log10    | Base 10 logarithm of x.                                 |
 +----------+---------------------------------------------------------+
 | log1p    | Natural logarithm of 1 + x, where x is very small.      |
 |          | (eg: log1p(x))                                          |
 +----------+---------------------------------------------------------+
-| log2     | Base 2 logarithm of x                                   |
+| log2     | Base 2 logarithm of x.                                  |
 +----------+---------------------------------------------------------+
 | logn     | Base N logarithm of x (eg: logn(1235,8))                |
 |          | where n > 0 and is an integer.                          |
@@ -266,7 +263,7 @@ include path (e.g: /usr/include/).
 | sum      | Sum of all the inputs.                                  |
 |          | (eg: sum(x,y,z,w,u,v,t) == (x + y + z + w + u + v + t)) |
 +----------+---------------------------------------------------------+
-| trunc    | Integer portion of x                                    |
+| trunc    | Integer portion of x.                                   |
 +----------+---------------------------------------------------------+
 
 (4) Trigonometry Functions
@@ -282,38 +279,38 @@ include path (e.g: /usr/include/).
 | atan2    | Arc tangent of (x/y) expressed in radians. [-pi,+pi]    |
 |          | eg: atan2(x,y)                                          |
 +----------+---------------------------------------------------------+
-| cos      | Cosine of x                                             |
+| cos      | Cosine of x.                                            |
 +----------+---------------------------------------------------------+
-| cosh     | Hyperbolic cosine of x                                  |
+| cosh     | Hyperbolic cosine of x.                                 |
 +----------+---------------------------------------------------------+
-| cot      | Cotangent of x                                          |
+| cot      | Cotangent of x.                                         |
 +----------+---------------------------------------------------------+
-| csc      | Cosecant of x                                           |
+| csc      | Cosecant of x.                                          |
 +----------+---------------------------------------------------------+
-| sec      | Secant of x                                             |
+| sec      | Secant of x.                                            |
 +----------+---------------------------------------------------------+
-| sin      | Sine of x                                               |
+| sin      | Sine of x.                                              |
 +----------+---------------------------------------------------------+
-| sinh     | Hyperbolic sine of x                                    |
+| sinh     | Hyperbolic sine of x.                                   |
 +----------+---------------------------------------------------------+
-| tan      | Tangent of x                                            |
+| tan      | Tangent of x.                                           |
 +----------+---------------------------------------------------------+
-| tanh     | Hyperbolic tangent of x                                 |
+| tanh     | Hyperbolic tangent of x.                                |
 +----------+---------------------------------------------------------+
-| deg2rad  | Convert x from degrees to radians                       |
+| deg2rad  | Convert x from degrees to radians.                      |
 +----------+---------------------------------------------------------+
-| deg2grad | Convert x from degrees to gradians                      |
+| deg2grad | Convert x from degrees to gradians.                     |
 +----------+---------------------------------------------------------+
-| rad2deg  | Convert x from radians to degrees                       |
+| rad2deg  | Convert x from radians to degrees.                      |
 +----------+---------------------------------------------------------+
-| grad2deg | Convert x from gradians to degrees                      |
+| grad2deg | Convert x from gradians to degrees.                     |
 +----------+---------------------------------------------------------+
 
 (5) String Processing
 +----------+---------------------------------------------------------+
 | FUNCTION | DEFINITION                                              |
 +----------+---------------------------------------------------------+
-| in       | True only if x is a substring of y                      |
+| in       | True only if x is a substring of y.                     |
 |          | (eg: x in y or 'abc' in 'abcdefgh')                     |
 +----------+---------------------------------------------------------+
 | like     | True only if the string x matches the pattern y.        |
@@ -471,59 +468,64 @@ correctly optimize such expressions for a given architecture.
 
  (02) Standard mathematical operator precedence is applied (BEDMAS).
 
- (03) Supported user defined types are numeric and string variables
+ (03) Results of expressions that are deemed as being 'valid' are to
+      exist within the set of Real numbers. All other results will be
+      of the value Not-A-Number (NaN).
+
+ (04) Supported user defined types are numeric and string variables
       and functions.
 
- (04) All variable and function names are case-insensitive
+ (05) All variable and function names are case-insensitive.
 
- (05) Variable and function names must begin with a letter
+ (06) Variable and function names must begin with a letter
       (A-Z or a-z), then can be comprised of any combination of
       letters, digits and underscores. (eg: x, var1 or power_func99)
 
- (06) Expression lengths and sub-expression lists are limited only by
+ (07) Expression lengths and sub-expression lists are limited only by
       storage capacity.
 
- (07) The life-time of objects registered with or created from a
-      specific symbol-table must span at least the life-time of
-      expressions generated using that symbol-table, otherwise
-      the result will be undefined behavior.
+ (08) The life-time of objects registered with or created from a
+      specific symbol-table must span at least the life-time of the
+      compiled expressions which utilize objects, such as variables,
+      of that symbol-table, otherwise the result will be undefined
+      behavior.
 
- (08) Equal/Nequal are normalized equality routines, which use
+ (09) Equal/Nequal are normalized equality routines, which use
       epsilons of 0.0000000001 and 0.000001 for double and float
       types respectively.
 
- (09) All trigonometric functions assume radian input unless
+ (10) All trigonometric functions assume radian input unless
       stated otherwise.
 
- (10) Expressions may contain white-space characters such as
+ (11) Expressions may contain white-space characters such as
       space,  tabs, new-lines, control-feed et al.
       ('\n', '\r', '\t', '\b', '\v', '\f')
 
- (11) Strings may be constructed from any letters, digits or special
+ (12) Strings may be constructed from any letters, digits or special
       characters such as (~!@#$%^&*()[]|=+ ,./?<>;:"`~_), and must
       be enclosed with single-quotes.
       eg: 'Frankly, my dear, I do not give a damn!'
 
- (12) User defined normal functions can have up to 20 parameters,
+ (13) User defined normal functions can have up to 20 parameters,
       where as user defined vararg-functions can have an unlimited
       number of parameters.
 
- (13) The inbuilt polynomial functions can be at most of degree 12.
+ (14) The inbuilt polynomial functions can be at most of degree 12.
 
- (14) Where appropriate constant folding optimisations will be
+ (15) Where appropriate constant folding optimisations will be
       applied. (eg: The expression '2+(3-(x/y))' becomes '5-(x/y)')
 
- (15) String processing capabilities are available by default.
+ (16) String processing capabilities are available by default.
       To turn them off, the following needs to be defined at
       compile time: exprtk_disable_string_capabilities
 
- (16) Composited functions can call themselves or any other functions
+ (17) Composited functions can call themselves or any other functions
       that have been defined prior to their own definition.
 
- (17) Recursive calls made from within composited functions will have
+ (18) Recursive calls made from within composited functions will have
       a stack size bound by the stack of the executing architecture.
 
- (18) Expressions may contain any of the following comment styles:
+ (19) Expressions may contain any of the following comment styles:
       1. // .... \n
       2. #  .... \n
       3. /* .... */