Several implementations on math expression block

1 files changed, 3800 insertions, 0 deletions

diff --git a/Project/fparser/fparser.cc b/Project/fparser/fparser.cc
new file mode 100644
index 0000000..5e77ba5
--- /dev/null
+++ b/Project/fparser/fparser.cc
@@ -0,0 +1,3800 @@
+/***************************************************************************\
+|* Function Parser for C++ v4.5.2                                          *|
+|*-------------------------------------------------------------------------*|
+|* Copyright: Juha Nieminen, Joel Yliluoma                                 *|
+|*                                                                         *|
+|* This library is distributed under the terms of the                      *|
+|* GNU Lesser General Public License version 3.                            *|
+|* (See lgpl.txt and gpl.txt for the license text.)                        *|
+\***************************************************************************/
+
+#include "fpconfig.hh"
+#include "fparser.hh"
+
+#include <set>
+#include <cstdlib>
+#include <cstring>
+#include <cctype>
+#include <cmath>
+#include <cassert>
+#include <limits>
+
+#include "extrasrc/fptypes.hh"
+#include "extrasrc/fpaux.hh"
+using namespace FUNCTIONPARSERTYPES;
+
+#ifdef FP_USE_THREAD_SAFE_EVAL_WITH_ALLOCA
+#ifndef FP_USE_THREAD_SAFE_EVAL
+#define FP_USE_THREAD_SAFE_EVAL
+#endif
+#endif
+
+#ifdef __GNUC__
+# define likely(x)       __builtin_expect(!!(x), 1)
+# define unlikely(x)     __builtin_expect(!!(x), 0)
+#else
+# define likely(x)   (x)
+# define unlikely(x) (x)
+#endif
+
+//=========================================================================
+// Opcode analysis functions
+//=========================================================================
+// These functions are used by the Parse() bytecode optimizer (mostly from
+// code in fp_opcode_add.inc).
+
+bool FUNCTIONPARSERTYPES::IsLogicalOpcode(unsigned op)
+{
+    switch(op)
+    {
+      case cAnd: case cAbsAnd:
+      case cOr:  case cAbsOr:
+      case cNot: case cAbsNot:
+      case cNotNot: case cAbsNotNot:
+      case cEqual: case cNEqual:
+      case cLess: case cLessOrEq:
+      case cGreater: case cGreaterOrEq:
+          return true;
+      default: break;
+    }
+    return false;
+}
+
+bool FUNCTIONPARSERTYPES::IsComparisonOpcode(unsigned op)
+{
+    switch(op)
+    {
+      case cEqual: case cNEqual:
+      case cLess: case cLessOrEq:
+      case cGreater: case cGreaterOrEq:
+          return true;
+      default: break;
+    }
+    return false;
+}
+
+unsigned FUNCTIONPARSERTYPES::OppositeComparisonOpcode(unsigned op)
+{
+    switch(op)
+    {
+      case cLess: return cGreater;
+      case cGreater: return cLess;
+      case cLessOrEq: return cGreaterOrEq;
+      case cGreaterOrEq: return cLessOrEq;
+    }
+    return op;
+}
+
+bool FUNCTIONPARSERTYPES::IsNeverNegativeValueOpcode(unsigned op)
+{
+    switch(op)
+    {
+      case cAnd: case cAbsAnd:
+      case cOr:  case cAbsOr:
+      case cNot: case cAbsNot:
+      case cNotNot: case cAbsNotNot:
+      case cEqual: case cNEqual:
+      case cLess: case cLessOrEq:
+      case cGreater: case cGreaterOrEq:
+      case cSqrt: case cRSqrt: case cSqr:
+      case cHypot:
+      case cAbs:
+      case cAcos: case cCosh:
+          return true;
+      default: break;
+    }
+    return false;
+}
+
+bool FUNCTIONPARSERTYPES::IsAlwaysIntegerOpcode(unsigned op)
+{
+    switch(op)
+    {
+      case cAnd: case cAbsAnd:
+      case cOr:  case cAbsOr:
+      case cNot: case cAbsNot:
+      case cNotNot: case cAbsNotNot:
+      case cEqual: case cNEqual:
+      case cLess: case cLessOrEq:
+      case cGreater: case cGreaterOrEq:
+      case cInt: case cFloor: case cCeil: case cTrunc:
+          return true;
+      default: break;
+    }
+    return false;
+}
+
+bool FUNCTIONPARSERTYPES::IsUnaryOpcode(unsigned op)
+{
+    switch(op)
+    {
+      case cInv: case cNeg:
+      case cNot: case cAbsNot:
+      case cNotNot: case cAbsNotNot:
+      case cSqr: case cRSqrt:
+      case cDeg: case cRad:
+          return true;
+    }
+    return (op < FUNC_AMOUNT && Functions[op].params == 1);
+}
+
+bool FUNCTIONPARSERTYPES::IsBinaryOpcode(unsigned op)
+{
+    switch(op)
+    {
+      case cAdd: case cSub: case cRSub:
+      case cMul: case cDiv: case cRDiv:
+      case cMod:
+      case cEqual: case cNEqual: case cLess:
+      case cLessOrEq: case cGreater: case cGreaterOrEq:
+      case cAnd: case cAbsAnd:
+      case cOr: case cAbsOr:
+          return true;
+    }
+    return (op < FUNC_AMOUNT && Functions[op].params == 2);
+}
+
+bool FUNCTIONPARSERTYPES::IsVarOpcode(unsigned op)
+{
+    // See comment in declaration of FP_ParamGuardMask
+    return int(op) >= VarBegin;
+}
+
+bool FUNCTIONPARSERTYPES::IsCommutativeOrParamSwappableBinaryOpcode(unsigned op)
+{
+    switch(op)
+    {
+      case cAdd:
+      case cMul:
+      case cEqual: case cNEqual:
+      case cAnd: case cAbsAnd:
+      case cOr: case cAbsOr:
+      case cMin: case cMax: case cHypot:
+          return true;
+      case cDiv: case cSub: case cRDiv: case cRSub:
+          return true;
+      case cLess: case cGreater:
+      case cLessOrEq: case cGreaterOrEq: return true;
+    }
+    return false;
+}
+
+unsigned FUNCTIONPARSERTYPES::GetParamSwappedBinaryOpcode(unsigned op)
+{
+    switch(op)
+    {
+      case cAdd:
+      case cMul:
+      case cEqual: case cNEqual:
+      case cAnd: case cAbsAnd:
+      case cOr: case cAbsOr:
+      case cMin: case cMax: case cHypot:
+          return op;
+      case cDiv: return cRDiv;
+      case cSub: return cRSub;
+      case cRDiv: return cDiv;
+      case cRSub: return cSub;
+      case cLess: return cGreater;
+      case cGreater: return cLess;
+      case cLessOrEq: return cGreaterOrEq;
+      case cGreaterOrEq: return cLessOrEq;
+    }
+    return op; // Error
+}
+
+template<bool ComplexType>
+bool FUNCTIONPARSERTYPES::HasInvalidRangesOpcode(unsigned op)
+{
+    // Returns true, if the given opcode has a range of
+    // input values that gives an error.
+    if(ComplexType)
+    {
+        // COMPLEX:
+        switch(op)
+        {
+          case cAtan:  // allowed range: x != +-1i
+          case cAtanh: // allowed range: x != +-1
+          //case cCot: // allowed range: tan(x) != 0
+          //case cCsc: // allowed range: sin(x) != 0
+          case cLog:   // allowed range: x != 0
+          case cLog2:  // allowed range: x != 0
+          case cLog10: // allowed range: x != 0
+    #ifdef FP_SUPPORT_OPTIMIZER
+          case cLog2by:// allowed range: x != 0
+    #endif
+          //case cPow: // allowed when: x != 0 or y != 0
+          //case cSec: // allowed range: cos(x) != 0
+          //case cTan:   // allowed range: cos(x) != 0  --> x != +-(pi/2)
+          //case cTanh:  // allowed range: log(x) != -1 --> x != +-(pi/2)i
+          case cRSqrt: // allowed range: x != 0
+          //case cDiv: // allowed range: y != 0
+          //case cRDiv: // allowed range: x != 0
+          //case cInv: // allowed range: x != 0
+          return true;
+        }
+    }
+    else
+    {
+        // REAL:
+        switch(op)
+        {
+          case cAcos: // allowed range: |x| <= 1
+          case cAsin: // allowed range: |x| <= 1
+          case cAcosh: // allowed range: x >= 1
+          case cAtanh: // allowed range: |x| < 1
+          //case cCot: // allowed range: tan(x) != 0
+          //case cCsc: // allowed range: sin(x) != 0
+          case cLog:   // allowed range: x > 0
+          case cLog2:  // allowed range: x > 0
+          case cLog10: // allowed range: x > 0
+    #ifdef FP_SUPPORT_OPTIMIZER
+          case cLog2by:// allowed range: x > 0
+    #endif
+          //case cPow: // allowed when: x > 0 or (x = 0 and y != 0) or (x<0)
+                       // Technically, when (x<0 and y is not integer),
+                       // it is not allowed, but we allow it anyway
+                       // in order to make nontrivial roots work.
+          //case cSec: // allowed range: cos(x) != 0
+          case cSqrt: // allowed range: x >= 0
+          case cRSqrt: // allowed range: x > 0
+          //case cTan:   // allowed range: cos(x) != 0 --> x != +-(pi/2)
+          //case cDiv: // allowed range: y != 0
+          //case cRDiv: // allowed range: x != 0
+          //case cInv: // allowed range: x != 0
+          return true;
+        }
+    }
+    return false;
+}
+
+template bool FUNCTIONPARSERTYPES::HasInvalidRangesOpcode<false>(unsigned op);
+template bool FUNCTIONPARSERTYPES::HasInvalidRangesOpcode<true>(unsigned op);
+
+
+#if(0) // Implementation moved to fpaux.hh due to linker problems
+//=========================================================================
+// Mathematical template functions
+//=========================================================================
+/* fp_pow() is a wrapper for std::pow()
+ * that produces an identical value for
+ * exp(1) ^ 2.0  (0x4000000000000000)
+ * as exp(2.0)   (0x4000000000000000)
+ * - std::pow() on x86_64
+ * produces 2.0  (0x3FFFFFFFFFFFFFFF) instead!
+ * See comments below for other special traits.
+ */
+namespace
+{
+    template<typename ValueT>
+    inline ValueT fp_pow_with_exp_log(const ValueT& x, const ValueT& y)
+    {
+        // Exponentiation using exp(log(x)*y).
+        // See http://en.wikipedia.org/wiki/Exponentiation#Real_powers
+        // Requirements: x > 0.
+        return fp_exp(fp_log(x) * y);
+    }
+
+    template<typename ValueT>
+    inline ValueT fp_powi(ValueT x, unsigned long y)
+    {
+        // Fast binary exponentiation algorithm
+        // See http://en.wikipedia.org/wiki/Exponentiation_by_squaring
+        // Requirements: y is non-negative integer.
+        ValueT result(1);
+        while(y != 0)
+        {
+            if(y & 1) { result *= x; y -= 1; }
+            else      { x *= x;      y /= 2; }
+        }
+        return result;
+    }
+}
+
+template<typename ValueT>
+ValueT FUNCTIONPARSERTYPES::fp_pow(const ValueT& x, const ValueT& y)
+{
+    if(x == ValueT(1)) return ValueT(1);
+    // y is now zero or positive
+    if(isLongInteger(y))
+    {
+        // Use fast binary exponentiation algorithm
+        if(y >= ValueT(0))
+            return fp_powi(x,              makeLongInteger(y));
+        else
+            return ValueT(1) / fp_powi(x, -makeLongInteger(y));
+    }
+    if(y >= ValueT(0))
+    {
+        // y is now positive. Calculate using exp(log(x)*y).
+        if(x > ValueT(0)) return fp_pow_with_exp_log(x, y);
+        if(x == ValueT(0)) return ValueT(0);
+        // At this point, y > 0.0 and x is known to be < 0.0,
+        // because positive and zero cases are already handled.
+        if(!isInteger(y*ValueT(16)))
+            return -fp_pow_with_exp_log(-x, y);
+        // ^This is not technically correct, but it allows
+        // functions such as cbrt(x^5), that is, x^(5/3),
+        // to be evaluated when x is negative.
+        // It is too complicated (and slow) to test whether y
+        // is a formed from a ratio of an integer to an odd integer.
+        // (And due to floating point inaccuracy, pointless too.)
+        // For example, x^1.30769230769... is
+        // actually x^(17/13), i.e. (x^17) ^ (1/13).
+        // (-5)^(17/13) gives us now -8.204227562330453.
+        // To see whether the result is right, we can test the given
+        // root: (-8.204227562330453)^13 gives us the value of (-5)^17,
+        // which proves that the expression was correct.
+        //
+        // The y*16 check prevents e.g. (-4)^(3/2) from being calculated,
+        // as it would confuse functioninfo when pow() returns no error
+        // but sqrt() does when the formula is converted into sqrt(x)*x.
+        //
+        // The errors in this approach are:
+        //     (-2)^sqrt(2) should produce NaN
+        //                  or actually sqrt(2)I + 2^sqrt(2),
+        //                  produces -(2^sqrt(2)) instead.
+        //                  (Impact: Neglible)
+        // Thus, at worst, we're changing a NaN (or complex)
+        // result into a negative real number result.
+    }
+    else
+    {
+        // y is negative. Utilize the x^y = 1/(x^-y) identity.
+        if(x > ValueT(0)) return fp_pow_with_exp_log(ValueT(1) / x, -y);
+        if(x < ValueT(0))
+        {
+            if(!isInteger(y*ValueT(-16)))
+                return -fp_pow_with_exp_log(ValueT(-1) / x, -y);
+            // ^ See comment above.
+        }
+        // Remaining case: 0.0 ^ negative number
+    }
+    // This is reached when:
+    //      x=0, and y<0
+    //      x<0, and y*16 is either positive or negative integer
+    // It is used for producing error values and as a safe fallback.
+    return fp_pow_base(x, y);
+}
+#endif
+
+
+//=========================================================================
+// Elementary (atom) parsing functions
+//=========================================================================
+namespace
+{
+    const unsigned FP_ParamGuardMask = 1U << (sizeof(unsigned) * 8u - 1u);
+    // ^ This mask is used to prevent cFetch/other opcode's parameters
+    //   from being confused into opcodes or variable indices within the
+    //   bytecode optimizer. Because the way it is tested in bytecoderules.dat
+    //   for speed reasons, it must also be the sign-bit of the "int" datatype.
+    //   Perhaps an "assert(IsVarOpcode(X | FP_ParamGuardMask) == false)"
+    //   might be justified to put somewhere in the code, just in case?
+
+
+    /* Reads an UTF8-encoded sequence which forms a valid identifier name from
+       the given input string and returns its length. If bit 31 is set, the
+       return value also contains the internal function opcode (defined in
+       fptypes.hh) that matches the name.
+    */
+    unsigned readIdentifierCommon(const char* input)
+    {
+        /* Assuming unsigned = 32 bits:
+              76543210 76543210 76543210 76543210
+           Return value if built-in function:
+              1PPPPPPP PPPPPPPP LLLLLLLL LLLLLLLL
+                P = function opcode      (15 bits)
+                L = function name length (16 bits)
+           Return value if not built-in function:
+              0LLLLLLL LLLLLLLL LLLLLLLL LLLLLLLL
+                L = identifier length (31 bits)
+           If unsigned has more than 32 bits, the other
+           higher order bits are to be assumed zero.
+        */
+#include "extrasrc/fp_identifier_parser.inc"
+        return 0;
+    }
+
+    template<typename Value_t>
+    inline unsigned readIdentifier(const char* input)
+    {
+        const unsigned value = readIdentifierCommon(input);
+        if( (value & 0x80000000U) != 0) // Function?
+        {
+            // Verify that the function actually exists for this datatype
+            if(IsIntType<Value_t>::result
+            && !Functions[(value >> 16) & 0x7FFF].okForInt())
+            {
+                // If it does not exist, return it as an identifier instead
+                return value & 0xFFFFu;
+            }
+            if(!IsComplexType<Value_t>::result
+            && Functions[(value >> 16) & 0x7FFF].complexOnly())
+            {
+                // If it does not exist, return it as an identifier instead
+                return value & 0xFFFFu;
+            }
+        }
+        return value;
+    }
+
+    // Returns true if the entire string is a valid identifier
+    template<typename Value_t>
+    bool containsOnlyValidIdentifierChars(const std::string& name)
+    {
+        if(name.empty()) return false;
+        return readIdentifier<Value_t>(name.c_str()) == (unsigned) name.size();
+    }
+
+
+    // -----------------------------------------------------------------------
+    // Wrappers for strto... functions
+    // -----------------------------------------------------------------------
+    template<typename Value_t>
+    inline Value_t fp_parseLiteral(const char* str, char** endptr)
+    {
+        return std::strtod(str, endptr);
+    }
+
+#if defined(FP_USE_STRTOLD) || defined(FP_SUPPORT_CPLUSPLUS11_MATH_FUNCS)
+    template<>
+    inline long double fp_parseLiteral<long double>(const char* str,
+                                                    char** endptr)
+    {
+        using namespace std; // Just in case strtold() is not inside std::
+        return strtold(str, endptr);
+    }
+#endif
+
+#ifdef FP_SUPPORT_LONG_INT_TYPE
+    template<>
+    inline long fp_parseLiteral<long>(const char* str, char** endptr)
+    {
+        return std::strtol(str, endptr, 10);
+    }
+#endif
+
+#ifdef FP_SUPPORT_COMPLEX_NUMBERS
+    template<typename T>
+    inline std::complex<T> fp_parseComplexLiteral(const char* str,
+                                                  char** endptr)
+    {
+        T result = fp_parseLiteral<T> (str,endptr);
+        const char* end = *endptr;
+        if( (*end == 'i'  || *end == 'I')
+        &&  !std::isalnum(end[1]) )
+        {
+            ++*endptr;
+            return std::complex<T> (T(), result);
+        }
+        return std::complex<T> (result, T());
+    }
+#endif
+
+#ifdef FP_SUPPORT_COMPLEX_DOUBLE_TYPE
+    template<>
+    inline std::complex<double> fp_parseLiteral<std::complex<double> >
+    (const char* str, char** endptr)
+    {
+        return fp_parseComplexLiteral<double> (str,endptr);
+    }
+#endif
+
+#ifdef FP_SUPPORT_COMPLEX_FLOAT_TYPE
+    template<>
+    inline std::complex<float> fp_parseLiteral<std::complex<float> >
+    (const char* str, char** endptr)
+    {
+        return fp_parseComplexLiteral<float> (str,endptr);
+    }
+#endif
+
+#ifdef FP_SUPPORT_COMPLEX_LONG_DOUBLE_TYPE
+    template<>
+    inline std::complex<long double> fp_parseLiteral<std::complex<long double> >
+    (const char* str, char** endptr)
+    {
+        return fp_parseComplexLiteral<long double> (str,endptr);
+    }
+#endif
+
+    // -----------------------------------------------------------------------
+    // Hexadecimal floating point literal parsing
+    // -----------------------------------------------------------------------
+    inline int testXdigit(unsigned c)
+    {
+        if((c-'0') < 10u) return c&15; // 0..9
+        if(((c|0x20)-'a') < 6u) return 9+(c&15); // A..F or a..f
+        return -1; // Not a hex digit
+    }
+
+    template<typename elem_t, unsigned n_limbs, unsigned limb_bits>
+    inline void addXdigit(elem_t* buffer, unsigned nibble)
+    {
+        for(unsigned p=0; p<n_limbs; ++p)
+        {
+            unsigned carry = unsigned( buffer[p] >> (elem_t)(limb_bits-4) );
+            buffer[p] = (buffer[p] << 4) | nibble;
+            nibble = carry;
+        }
+    }
+
+    template<typename Value_t>
+    Value_t parseHexLiteral(const char* str, char** endptr)
+    {
+        const unsigned bits_per_char = 8;
+
+        const int MantissaBits =
+            std::numeric_limits<Value_t>::radix == 2
+            ? std::numeric_limits<Value_t>::digits
+            : (((sizeof(Value_t) * bits_per_char) &~ 3) - 4);
+
+        typedef unsigned long elem_t;
+        const int ExtraMantissaBits = 4 + ((MantissaBits+3)&~3); // Store one digit more for correct rounding
+        const unsigned limb_bits = sizeof(elem_t) * bits_per_char;
+        const unsigned n_limbs   = (ExtraMantissaBits + limb_bits-1) / limb_bits;
+        elem_t mantissa_buffer[n_limbs] = { 0 };
+
+        int n_mantissa_bits = 0; // Track the number of bits
+        int exponent = 0; // The exponent that will be used to multiply the mantissa
+        // Read integer portion
+        while(true)
+        {
+            int xdigit = testXdigit(*str);
+            if(xdigit < 0) break;
+            addXdigit<elem_t,n_limbs,limb_bits> (mantissa_buffer, xdigit);
+            ++str;
+
+            n_mantissa_bits += 4;
+            if(n_mantissa_bits >= ExtraMantissaBits)
+            {
+                // Exhausted the precision. Parse the rest (until exponent)
+                // normally but ignore the actual digits.
+                for(; testXdigit(*str) >= 0; ++str)
+                    exponent += 4;
+                // Read but ignore decimals
+                if(*str == '.')
+                    for(++str; testXdigit(*str) >= 0; ++str)
+                        {}
+                goto read_exponent;
+            }
+        }
+        // Read decimals
+        if(*str == '.')
+            for(++str; ; )
+            {
+                int xdigit = testXdigit(*str);
+                if(xdigit < 0) break;
+                addXdigit<elem_t,n_limbs,limb_bits> (mantissa_buffer, xdigit);
+                ++str;
+
+                exponent -= 4;
+                n_mantissa_bits += 4;
+                if(n_mantissa_bits >= ExtraMantissaBits)
+                {
+                    // Exhausted the precision. Skip the rest
+                    // of the decimals, until the exponent.
+                    while(testXdigit(*str) >= 0)
+                        ++str;
+                    break;
+                }
+            }
+
+        // Read exponent
+    read_exponent:
+        if(*str == 'p' || *str == 'P')
+        {
+            const char* str2 = str+1;
+            long p_exponent = strtol(str2, const_cast<char**> (&str2), 10);
+            if(str2 != str+1 && p_exponent == (long)(int)p_exponent)
+            {
+                exponent += (int)p_exponent;
+                str = str2;
+            }
+        }
+
+        if(endptr) *endptr = const_cast<char*> (str);
+
+        Value_t result = std::ldexp(Value_t(mantissa_buffer[0]), exponent);
+        for(unsigned p=1; p<n_limbs; ++p)
+        {
+            exponent += limb_bits;
+            result += ldexp(Value_t(mantissa_buffer[p]), exponent);
+        }
+        return result;
+    }
+
+#ifdef FP_SUPPORT_LONG_INT_TYPE
+    template<>
+    long parseHexLiteral<long>(const char* str, char** endptr)
+    {
+        return std::strtol(str, endptr, 16);
+    }
+#endif
+
+#ifdef FP_SUPPORT_COMPLEX_DOUBLE_TYPE
+    template<>
+    std::complex<double>
+    parseHexLiteral<std::complex<double> >(const char* str, char** endptr)
+    {
+        return parseHexLiteral<double> (str, endptr);
+    }
+#endif
+
+#ifdef FP_SUPPORT_COMPLEX_FLOAT_TYPE
+    template<>
+    std::complex<float>
+    parseHexLiteral<std::complex<float> >(const char* str, char** endptr)
+    {
+        return parseHexLiteral<float> (str, endptr);
+    }
+#endif
+
+#ifdef FP_SUPPORT_COMPLEX_LONG_DOUBLE_TYPE
+    template<>
+    std::complex<long double>
+    parseHexLiteral<std::complex<long double> >(const char* str, char** endptr)
+    {
+        return parseHexLiteral<long double> (str, endptr);
+    }
+#endif
+}
+
+//=========================================================================
+// Utility functions
+//=========================================================================
+namespace
+{
+    // -----------------------------------------------------------------------
+    // Add a new identifier to the specified identifier map
+    // -----------------------------------------------------------------------
+    // Return value will be false if the name already existed
+    template<typename Value_t>
+    bool addNewNameData(NamePtrsMap<Value_t>& namePtrs,
+                        std::pair<NamePtr, NameData<Value_t> >& newName,
+                        bool isVar)
+    {
+        typename NamePtrsMap<Value_t>::iterator nameIter =
+            namePtrs.lower_bound(newName.first);
+
+        if(nameIter != namePtrs.end() && newName.first == nameIter->first)
+        {
+            // redefining a var is not allowed.
+            if(isVar) return false;
+
+            // redefining other tokens is allowed, if the type stays the same.
+            if(nameIter->second.type != newName.second.type)
+                return false;
+
+            // update the data
+            nameIter->second = newName.second;
+            return true;
+        }
+
+        if(!isVar)
+        {
+            // Allocate a copy of the name (pointer stored in the map key)
+            // However, for VARIABLEs, the pointer points to VariableString,
+            // which is managed separately. Thusly, only done when !IsVar.
+            char* namebuf = new char[newName.first.nameLength];
+            memcpy(namebuf, newName.first.name, newName.first.nameLength);
+            newName.first.name = namebuf;
+        }
+
+        namePtrs.insert(nameIter, newName);
+        return true;
+    }
+}
+
+
+//=========================================================================
+// Data struct implementation
+//=========================================================================
+template<typename Value_t>
+FunctionParserBase<Value_t>::Data::Data():
+    mReferenceCounter(1),
+    mDelimiterChar(0),
+    mParseErrorType(NO_FUNCTION_PARSED_YET),
+    mEvalErrorType(0),
+    mUseDegreeConversion(false),
+    mErrorLocation(0),
+    mVariablesAmount(0),
+    mStackSize(0)
+{}
+
+template<typename Value_t>
+FunctionParserBase<Value_t>::Data::Data(const Data& rhs):
+    mReferenceCounter(0),
+    mDelimiterChar(rhs.mDelimiterChar),
+    mParseErrorType(rhs.mParseErrorType),
+    mEvalErrorType(rhs.mEvalErrorType),
+    mUseDegreeConversion(rhs.mUseDegreeConversion),
+    mErrorLocation(rhs.mErrorLocation),
+    mVariablesAmount(rhs.mVariablesAmount),
+    mVariablesString(rhs.mVariablesString),
+    mNamePtrs(),
+    mFuncPtrs(rhs.mFuncPtrs),
+    mFuncParsers(rhs.mFuncParsers),
+    mByteCode(rhs.mByteCode),
+    mImmed(rhs.mImmed),
+#ifndef FP_USE_THREAD_SAFE_EVAL
+    mStack(rhs.mStackSize),
+#endif
+    mStackSize(rhs.mStackSize)
+{
+    for(typename NamePtrsMap<Value_t>::const_iterator i = rhs.mNamePtrs.begin();
+        i != rhs.mNamePtrs.end();
+        ++i)
+    {
+        if(i->second.type == NameData<Value_t>::VARIABLE)
+        {
+            const std::size_t variableStringOffset =
+                i->first.name - rhs.mVariablesString.c_str();
+            std::pair<NamePtr, NameData<Value_t> > tmp
+                (NamePtr(&mVariablesString[variableStringOffset],
+                         i->first.nameLength),
+                 i->second);
+            mNamePtrs.insert(mNamePtrs.end(), tmp);
+        }
+        else
+        {
+            std::pair<NamePtr, NameData<Value_t> > tmp
+                (NamePtr(new char[i->first.nameLength], i->first.nameLength),
+                 i->second );
+            memcpy(const_cast<char*>(tmp.first.name), i->first.name,
+                   tmp.first.nameLength);
+            mNamePtrs.insert(mNamePtrs.end(), tmp);
+        }
+    }
+}
+
+template<typename Value_t>
+FunctionParserBase<Value_t>::Data::~Data()
+{
+    for(typename NamePtrsMap<Value_t>::iterator i = mNamePtrs.begin();
+        i != mNamePtrs.end();
+        ++i)
+    {
+        if(i->second.type != NameData<Value_t>::VARIABLE)
+            delete[] i->first.name;
+    }
+}
+
+template<typename Value_t>
+void FunctionParserBase<Value_t>::incFuncWrapperRefCount
+(FunctionWrapper* wrapper)
+{
+    ++wrapper->mReferenceCount;
+}
+
+template<typename Value_t>
+unsigned FunctionParserBase<Value_t>::decFuncWrapperRefCount
+(FunctionWrapper* wrapper)
+{
+    return --wrapper->mReferenceCount;
+}
+
+template<typename Value_t>
+FunctionParserBase<Value_t>::Data::FuncWrapperPtrData::FuncWrapperPtrData():
+    mRawFuncPtr(0), mFuncWrapperPtr(0), mParams(0)
+{}
+
+template<typename Value_t>
+FunctionParserBase<Value_t>::Data::FuncWrapperPtrData::~FuncWrapperPtrData()
+{
+    if(mFuncWrapperPtr &&
+       FunctionParserBase::decFuncWrapperRefCount(mFuncWrapperPtr) == 0)
+        delete mFuncWrapperPtr;
+}
+
+template<typename Value_t>
+FunctionParserBase<Value_t>::Data::FuncWrapperPtrData::FuncWrapperPtrData
+(const FuncWrapperPtrData& rhs):
+    mRawFuncPtr(rhs.mRawFuncPtr),
+    mFuncWrapperPtr(rhs.mFuncWrapperPtr),
+    mParams(rhs.mParams)
+{
+    if(mFuncWrapperPtr)
+        FunctionParserBase::incFuncWrapperRefCount(mFuncWrapperPtr);
+}
+
+template<typename Value_t>
+typename FunctionParserBase<Value_t>::Data::FuncWrapperPtrData&
+FunctionParserBase<Value_t>::Data::FuncWrapperPtrData::operator=
+(const FuncWrapperPtrData& rhs)
+{
+    if(&rhs != this)
+    {
+        if(mFuncWrapperPtr &&
+           FunctionParserBase::decFuncWrapperRefCount(mFuncWrapperPtr) == 0)
+            delete mFuncWrapperPtr;
+        mRawFuncPtr = rhs.mRawFuncPtr;
+        mFuncWrapperPtr = rhs.mFuncWrapperPtr;
+        mParams = rhs.mParams;
+        if(mFuncWrapperPtr)
+            FunctionParserBase::incFuncWrapperRefCount(mFuncWrapperPtr);
+    }
+    return *this;
+}
+
+
+//=========================================================================
+// FunctionParser constructors, destructor and assignment
+//=========================================================================
+template<typename Value_t>
+FunctionParserBase<Value_t>::FunctionParserBase():
+    mData(new Data),
+    mStackPtr(0)
+{
+}
+
+template<typename Value_t>
+FunctionParserBase<Value_t>::~FunctionParserBase()
+{
+    if(--(mData->mReferenceCounter) == 0)
+        delete mData;
+}
+
+template<typename Value_t>
+FunctionParserBase<Value_t>::FunctionParserBase(const FunctionParserBase& cpy):
+    mData(cpy.mData),
+    mStackPtr(0)
+{
+    ++(mData->mReferenceCounter);
+}
+
+template<typename Value_t>
+FunctionParserBase<Value_t>&
+FunctionParserBase<Value_t>::operator=(const FunctionParserBase& cpy)
+{
+    if(mData != cpy.mData)
+    {
+        if(--(mData->mReferenceCounter) == 0) delete mData;
+
+        mData = cpy.mData;
+        ++(mData->mReferenceCounter);
+    }
+    return *this;
+}
+
+template<typename Value_t>
+typename FunctionParserBase<Value_t>::Data*
+FunctionParserBase<Value_t>::getParserData()
+{
+    return mData;
+}
+
+template<typename Value_t>
+void FunctionParserBase<Value_t>::setDelimiterChar(char c)
+{
+    mData->mDelimiterChar = c;
+}
+
+
+//---------------------------------------------------------------------------
+// Copy-on-write method
+//---------------------------------------------------------------------------
+template<typename Value_t>
+void FunctionParserBase<Value_t>::CopyOnWrite()
+{
+    if(mData->mReferenceCounter > 1)
+    {
+        Data* oldData = mData;
+        mData = new Data(*oldData);
+        --(oldData->mReferenceCounter);
+        mData->mReferenceCounter = 1;
+    }
+}
+
+template<typename Value_t>
+void FunctionParserBase<Value_t>::ForceDeepCopy()
+{
+    CopyOnWrite();
+}
+
+
+//=========================================================================
+// Epsilon
+//=========================================================================
+template<typename Value_t>
+Value_t FunctionParserBase<Value_t>::epsilon()
+{
+    return Epsilon<Value_t>::value;
+}
+
+template<typename Value_t>
+void FunctionParserBase<Value_t>::setEpsilon(Value_t value)
+{
+    Epsilon<Value_t>::value = value;
+}
+
+
+//=========================================================================
+// User-defined identifier addition functions
+//=========================================================================
+template<typename Value_t>
+bool FunctionParserBase<Value_t>::AddConstant(const std::string& name,
+                                              Value_t value)
+{
+    if(!containsOnlyValidIdentifierChars<Value_t>(name)) return false;
+
+    CopyOnWrite();
+    std::pair<NamePtr, NameData<Value_t> > newName
+        (NamePtr(name.data(), unsigned(name.size())),
+         NameData<Value_t>(NameData<Value_t>::CONSTANT, value));
+
+    return addNewNameData(mData->mNamePtrs, newName, false);
+}
+
+template<typename Value_t>
+bool FunctionParserBase<Value_t>::AddUnit(const std::string& name,
+                                          Value_t value)
+{
+    if(!containsOnlyValidIdentifierChars<Value_t>(name)) return false;
+
+    CopyOnWrite();
+    std::pair<NamePtr, NameData<Value_t> > newName
+        (NamePtr(name.data(), unsigned(name.size())),
+         NameData<Value_t>(NameData<Value_t>::UNIT, value));
+    return addNewNameData(mData->mNamePtrs, newName, false);
+}
+
+template<typename Value_t>
+bool FunctionParserBase<Value_t>::AddFunction
+(const std::string& name, FunctionPtr ptr, unsigned paramsAmount)
+{
+    if(!containsOnlyValidIdentifierChars<Value_t>(name)) return false;
+
+    CopyOnWrite();
+    std::pair<NamePtr, NameData<Value_t> > newName
+        (NamePtr(name.data(), unsigned(name.size())),
+         NameData<Value_t>(NameData<Value_t>::FUNC_PTR,
+                           unsigned(mData->mFuncPtrs.size())));
+
+    const bool success = addNewNameData(mData->mNamePtrs, newName, false);
+    if(success)
+    {
+        mData->mFuncPtrs.push_back(typename Data::FuncWrapperPtrData());
+        mData->mFuncPtrs.back().mRawFuncPtr = ptr;
+        mData->mFuncPtrs.back().mParams = paramsAmount;
+    }
+    return success;
+}
+
+template<typename Value_t>
+bool FunctionParserBase<Value_t>::addFunctionWrapperPtr
+(const std::string& name, FunctionWrapper* wrapper, unsigned paramsAmount)
+{
+    if(!AddFunction(name, FunctionPtr(0), paramsAmount)) return false;
+    mData->mFuncPtrs.back().mFuncWrapperPtr = wrapper;
+    return true;
+}
+
+template<typename Value_t>
+typename FunctionParserBase<Value_t>::FunctionWrapper*
+FunctionParserBase<Value_t>::GetFunctionWrapper(const std::string& name)
+{
+    CopyOnWrite();
+    NamePtr namePtr(name.data(), unsigned(name.size()));
+
+    typename NamePtrsMap<Value_t>::iterator nameIter =
+        mData->mNamePtrs.find(namePtr);
+
+    if(nameIter != mData->mNamePtrs.end() &&
+       nameIter->second.type == NameData<Value_t>::FUNC_PTR)
+    {
+        return mData->mFuncPtrs[nameIter->second.index].mFuncWrapperPtr;
+    }
+    return 0;
+}
+
+template<typename Value_t>
+bool FunctionParserBase<Value_t>::CheckRecursiveLinking
+(const FunctionParserBase* fp) const
+{
+    if(fp == this) return true;
+    for(unsigned i = 0; i < fp->mData->mFuncParsers.size(); ++i)
+        if(CheckRecursiveLinking(fp->mData->mFuncParsers[i].mParserPtr))
+            return true;
+    return false;
+}
+
+template<typename Value_t>
+bool FunctionParserBase<Value_t>::AddFunction(const std::string& name,
+                                              FunctionParserBase& fp)
+{
+    if(!containsOnlyValidIdentifierChars<Value_t>(name) ||
+       CheckRecursiveLinking(&fp))
+        return false;
+
+    CopyOnWrite();
+    std::pair<NamePtr, NameData<Value_t> > newName
+        (NamePtr(name.data(), unsigned(name.size())),
+         NameData<Value_t>(NameData<Value_t>::PARSER_PTR,
+                           unsigned(mData->mFuncParsers.size())));
+
+    const bool success = addNewNameData(mData->mNamePtrs, newName, false);
+    if(success)
+    {
+        mData->mFuncParsers.push_back(typename Data::FuncParserPtrData());
+        mData->mFuncParsers.back().mParserPtr = &fp;
+        mData->mFuncParsers.back().mParams = fp.mData->mVariablesAmount;
+    }
+    return success;
+}
+
+template<typename Value_t>
+bool FunctionParserBase<Value_t>::RemoveIdentifier(const std::string& name)
+{
+    CopyOnWrite();
+
+    NamePtr namePtr(name.data(), unsigned(name.size()));
+
+    typename NamePtrsMap<Value_t>::iterator nameIter =
+        mData->mNamePtrs.find(namePtr);
+
+    if(nameIter != mData->mNamePtrs.end())
+    {
+        if(nameIter->second.type == NameData<Value_t>::VARIABLE)
+        {
+            // Illegal attempt to delete variables
+            return false;
+        }
+        delete[] nameIter->first.name;
+        mData->mNamePtrs.erase(nameIter);
+        return true;
+    }
+    return false;
+}
+
+
+//=========================================================================
+// Function parsing
+//=========================================================================
+namespace
+{
+    // Error messages returned by ErrorMsg():
+    const char* const ParseErrorMessage[]=
+    {
+        "Syntax error",                             // 0
+        "Mismatched parenthesis",                   // 1
+        "Missing ')'",                              // 2
+        "Empty parentheses",                        // 3
+        "Syntax error: Operator expected",          // 4
+        "Not enough memory",                        // 5
+        "An unexpected error occurred. Please make a full bug report "
+        "to the author",                            // 6
+        "Syntax error in parameter 'Vars' given to "
+        "FunctionParser::Parse()",                  // 7
+        "Illegal number of parameters to function", // 8
+        "Syntax error: Premature end of string",    // 9
+        "Syntax error: Expecting ( after function", // 10
+        "Syntax error: Unknown identifier",         // 11
+        "(No function has been parsed yet)",
+        ""
+    };
+
+    template<typename Value_t>
+    inline typename FunctionParserBase<Value_t>::ParseErrorType
+    noCommaError(char c)
+    {
+        return c == ')' ?
+            FunctionParserBase<Value_t>::ILL_PARAMS_AMOUNT :
+            FunctionParserBase<Value_t>::SYNTAX_ERROR;
+    }
+
+    template<typename Value_t>
+    inline typename FunctionParserBase<Value_t>::ParseErrorType
+    noParenthError(char c)
+    {
+        return c == ',' ?
+            FunctionParserBase<Value_t>::ILL_PARAMS_AMOUNT :
+            FunctionParserBase<Value_t>::MISSING_PARENTH;
+    }
+
+    template<unsigned offset>
+    struct IntLiteralMask
+    {
+        enum { mask =
+        //    (    1UL << ('-'-offset)) |
+            (0x3FFUL << ('0'-offset)) }; /* 0x3FF = 10 bits worth "1" */
+        // Note: If you change fparser to support negative numbers parsing
+        //       (as opposed to parsing them as cNeg followed by literal),
+        //       enable the '-' line above, and change the offset value
+        //       in BeginsLiteral() to '-' instead of '.'.
+    };
+
+    template<typename Value_t, unsigned offset>
+    struct LiteralMask
+    {
+        enum { mask =
+            (    1UL << ('.'-offset)) |
+            IntLiteralMask<offset>::mask };
+    };
+#ifdef FP_SUPPORT_LONG_INT_TYPE
+    template<unsigned offset>
+    struct LiteralMask<long, offset>: public IntLiteralMask<offset>
+    {
+    };
+#endif
+#ifdef FP_SUPPORT_GMP_INT_TYPE
+    template<unsigned offset>
+    struct LiteralMask<GmpInt, offset>: public IntLiteralMask<offset>
+    {
+    };
+#endif
+
+    template<unsigned offset>
+    struct SimpleSpaceMask
+    {
+        enum { mask =
+            (1UL << ('\r'-offset)) |
+            (1UL << ('\n'-offset)) |
+            (1UL << ('\v'-offset)) |
+            (1UL << ('\t'-offset)) |
+            (1UL << (' ' -offset)) };
+    };
+
+    template<typename Value_t>
+    inline bool BeginsLiteral(unsigned byte)
+    {
+        enum { n = sizeof(unsigned long)>=8 ? 0 : '.' };
+        byte -= n;
+        if(byte > (unsigned char)('9'-n)) return false;
+        unsigned long shifted = 1UL << byte;
+        const unsigned long mask = LiteralMask<Value_t, n>::mask;
+        return (mask & shifted) != 0;
+    }
+
+    template<typename CharPtr>
+    inline void SkipSpace(CharPtr& function)
+    {
+/*
+        Space characters in unicode:
+U+0020  SPACE                      Depends on font, often adjusted (see below)
+U+00A0  NO-BREAK SPACE             As a space, but often not adjusted
+U+2000  EN QUAD                    1 en (= 1/2 em)
+U+2001  EM QUAD                    1 em (nominally, the height of the font)
+U+2002  EN SPACE                   1 en (= 1/2 em)
+U+2003  EM SPACE                   1 em
+U+2004  THREE-PER-EM SPACE         1/3 em
+U+2005  FOUR-PER-EM SPACE          1/4 em
+U+2006  SIX-PER-EM SPACE           1/6 em
+U+2007  FIGURE SPACE               Tabular width, the width of digits
+U+2008  PUNCTUATION SPACE          The width of a period .
+U+2009  THIN SPACE                 1/5 em (or sometimes 1/6 em)
+U+200A  HAIR SPACE                 Narrower than THIN SPACE
+U+200B  ZERO WIDTH SPACE           Nominally no width, but may expand
+U+202F  NARROW NO-BREAK SPACE      Narrower than NO-BREAK SPACE (or SPACE)
+U+205F  MEDIUM MATHEMATICAL SPACE  4/18 em
+U+3000  IDEOGRAPHIC SPACE          The width of ideographic (CJK) characters.
+        Also:
+U+000A  \n
+U+000D  \r
+U+0009  \t
+U+000B  \v
+        As UTF-8 sequences:
+            09
+            0A
+            0B
+            0D
+            20
+            C2 A0
+            E2 80 80-8B
+            E2 80 AF
+            E2 81 9F
+            E3 80 80
+*/
+        while(true)
+        {
+            enum { n = sizeof(unsigned long)>=8 ? 0 : '\t' };
+            typedef signed char schar;
+            unsigned byte = (unsigned char)*function;
+            byte -= n;
+            // ^Note: values smaller than n intentionally become
+            //        big values here due to integer wrap. The
+            //        comparison below thus excludes them, making
+            //        the effective range 0x09..0x20 (32-bit)
+            //        or 0x00..0x20 (64-bit) within the if-clause.
+            if(byte <= (unsigned char)(' '-n))
+            {
+                unsigned long shifted = 1UL << byte;
+                const unsigned long mask = SimpleSpaceMask<n>::mask;
+                if(mask & shifted)
+                    { ++function; continue; } // \r, \n, \t, \v and space
+                break;
+            }
+            if(likely(byte < 0xC2-n)) break;
+
+            if(byte == 0xC2-n && function[1] == char(0xA0))
+                { function += 2; continue; } // U+00A0
+            if(byte == 0xE3-n &&
+               function[1] == char(0x80) && function[2] == char(0x80))
+                { function += 3; continue; } // U+3000
+            if(byte == 0xE2-n)
+            {
+                if(function[1] == char(0x81))
+                {
+                    if(function[2] != char(0x9F)) break;
+                    function += 3; // U+205F
+                    continue;
+                }
+                if(function[1] == char(0x80))
+                if(function[2] == char(0xAF) || // U+202F
+                   schar(function[2]) <= schar(0x8B) // U+2000..U+200B
+                  )
+                {
+                    function += 3;
+                    continue;
+                }
+            }
+            break;
+        } // while(true)
+    } // SkipSpace(CharPtr& function)
+}
+
+// ---------------------------------------------------------------------------
+// Return parse error message
+// ---------------------------------------------------------------------------
+template<typename Value_t>
+const char* FunctionParserBase<Value_t>::ErrorMsg() const
+{
+    return ParseErrorMessage[mData->mParseErrorType];
+}
+
+template<typename Value_t>
+typename FunctionParserBase<Value_t>::ParseErrorType
+FunctionParserBase<Value_t>::GetParseErrorType() const
+{
+    return mData->mParseErrorType;
+}
+
+template<typename Value_t>
+int FunctionParserBase<Value_t>::EvalError() const
+{
+    return mData->mEvalErrorType;
+}
+
+
+// ---------------------------------------------------------------------------
+// Parse variables
+// ---------------------------------------------------------------------------
+template<typename Value_t>
+bool FunctionParserBase<Value_t>::ParseVariables
+(const std::string& inputVarString)
+{
+    if(mData->mVariablesString == inputVarString) return true;
+
+    /* Delete existing variables from mNamePtrs */
+    for(typename NamePtrsMap<Value_t>::iterator i =
+            mData->mNamePtrs.begin();
+        i != mData->mNamePtrs.end(); )
+    {
+        if(i->second.type == NameData<Value_t>::VARIABLE)
+        {
+            typename NamePtrsMap<Value_t>::iterator j (i);
+            ++i;
+            mData->mNamePtrs.erase(j);
+        }
+        else ++i;
+    }
+    mData->mVariablesString = inputVarString;
+
+    const std::string& vars = mData->mVariablesString;
+    const unsigned len = unsigned(vars.size());
+
+    unsigned varNumber = VarBegin;
+
+    const char* beginPtr = vars.c_str();
+    const char* finalPtr = beginPtr + len;
+    while(beginPtr < finalPtr)
+    {
+        SkipSpace(beginPtr);
+        unsigned nameLength = readIdentifier<Value_t>(beginPtr);
+        if(nameLength == 0 || (nameLength & 0x80000000U)) return false;
+        const char* endPtr = beginPtr + nameLength;
+        SkipSpace(endPtr);
+        if(endPtr != finalPtr && *endPtr != ',') return false;
+
+        std::pair<NamePtr, NameData<Value_t> > newName
+            (NamePtr(beginPtr, nameLength),
+             NameData<Value_t>(NameData<Value_t>::VARIABLE, varNumber++));
+
+        if(!addNewNameData(mData->mNamePtrs, newName, true))
+        {
+            return false;
+        }
+
+        beginPtr = endPtr + 1;
+    }
+
+    mData->mVariablesAmount = varNumber - VarBegin;
+    return true;
+}
+
+// ---------------------------------------------------------------------------
+// Parse() public interface functions
+// ---------------------------------------------------------------------------
+template<typename Value_t>
+int FunctionParserBase<Value_t>::Parse(const char* Function,
+                                       const std::string& Vars,
+                                       bool useDegrees)
+{
+    CopyOnWrite();
+
+    if(!ParseVariables(Vars))
+    {
+        mData->mParseErrorType = INVALID_VARS;
+        return int(strlen(Function));
+    }
+
+    return ParseFunction(Function, useDegrees);
+}
+
+template<typename Value_t>
+int FunctionParserBase<Value_t>::Parse(const std::string& Function,
+                                       const std::string& Vars,
+                                       bool useDegrees)
+{
+    CopyOnWrite();
+
+    if(!ParseVariables(Vars))
+    {
+        mData->mParseErrorType = INVALID_VARS;
+        return int(Function.size());
+    }
+
+    return ParseFunction(Function.c_str(), useDegrees);
+}
+
+
+// ---------------------------------------------------------------------------
+// Main parsing function
+// ---------------------------------------------------------------------------
+template<typename Value_t>
+int FunctionParserBase<Value_t>::ParseFunction(const char* function,
+                                               bool useDegrees)
+{
+    mData->mUseDegreeConversion = useDegrees;
+    mData->mParseErrorType = FP_NO_ERROR;
+
+    mData->mInlineVarNames.clear();
+    mData->mByteCode.clear(); mData->mByteCode.reserve(128);
+    mData->mImmed.clear(); mData->mImmed.reserve(128);
+    mData->mStackSize = mStackPtr = 0;
+
+    mData->mHasByteCodeFlags = false;
+
+    const char* ptr = Compile(function);
+    mData->mInlineVarNames.clear();
+
+    if(mData->mHasByteCodeFlags)
+    {
+        for(unsigned i = unsigned(mData->mByteCode.size()); i-- > 0; )
+            mData->mByteCode[i] &= ~FP_ParamGuardMask;
+    }
+
+    if(mData->mParseErrorType != FP_NO_ERROR)
+        return int(mData->mErrorLocation - function);
+
+    assert(ptr); // Should never be null at this point. It's a bug otherwise.
+    if(*ptr)
+    {
+        if(mData->mDelimiterChar == 0 || *ptr != mData->mDelimiterChar)
+            mData->mParseErrorType = EXPECT_OPERATOR;
+        return int(ptr - function);
+    }
+
+#ifndef FP_USE_THREAD_SAFE_EVAL
+    mData->mStack.resize(mData->mStackSize);
+#endif
+
+    return -1;
+}
+
+
+//=========================================================================
+// Parsing and bytecode compiling functions
+//=========================================================================
+template<typename Value_t>
+inline const char* FunctionParserBase<Value_t>::SetErrorType(ParseErrorType t,
+                                                             const char* pos)
+{
+    mData->mParseErrorType = t;
+    mData->mErrorLocation = pos;
+    return 0;
+}
+
+template<typename Value_t>
+inline void FunctionParserBase<Value_t>::incStackPtr()
+{
+    if(++mStackPtr > mData->mStackSize) ++(mData->mStackSize);
+}
+
+namespace
+{
+    const unsigned char powi_factor_table[128] =
+    {
+        0,1,0,0,0,0,0,0, 0, 0,0,0,0,0,0,3,/*   0 -  15 */
+        0,0,0,0,0,0,0,0, 0, 5,0,3,0,0,3,0,/*  16 -  31 */
+        0,0,0,0,0,0,0,3, 0, 0,0,0,0,5,0,0,/*  32 -  47 */
+        0,0,5,3,0,0,3,5, 0, 3,0,0,3,0,0,3,/*  48 -  63 */
+        0,0,0,0,0,0,0,0, 0, 0,0,3,0,0,3,0,/*  64 -  79 */
+        0,9,0,0,0,5,0,3, 0, 0,5,7,0,0,0,5,/*  80 -  95 */
+        0,0,0,3,5,0,3,0, 0, 3,0,0,3,0,5,3,/*  96 - 111 */
+        0,0,3,5,0,9,0,7, 3,11,0,3,0,5,3,0,/* 112 - 127 */
+    };
+
+    inline int get_powi_factor(long abs_int_exponent)
+    {
+        if(abs_int_exponent >= int(sizeof(powi_factor_table))) return 0;
+        return powi_factor_table[abs_int_exponent];
+    }
+
+#if 0
+    int EstimatePowiComplexity(int abs_int_exponent)
+    {
+        int cost = 0;
+        while(abs_int_exponent > 1)
+        {
+            int factor = get_powi_factor(abs_int_exponent);
+            if(factor)
+            {
+                cost += EstimatePowiComplexity(factor);
+                abs_int_exponent /= factor;
+                continue;
+            }
+            if(!(abs_int_exponent & 1))
+            {
+                abs_int_exponent /= 2;
+                cost += 3; // sqr
+            }
+            else
+            {
+                cost += 4; // dup+mul
+                abs_int_exponent -= 1;
+            }
+        }
+        return cost;
+    }
+#endif
+
+    bool IsEligibleIntPowiExponent(long int_exponent)
+    {
+        if(int_exponent == 0) return false;
+        long abs_int_exponent = int_exponent;
+    #if 0
+        int cost = 0;
+
+        if(abs_int_exponent < 0)
+        {
+            cost += 11;
+            abs_int_exponent = -abs_int_exponent;
+        }
+
+        cost += EstimatePowiComplexity(abs_int_exponent);
+
+        return cost < (10*3 + 4*4);
+    #else
+        if(abs_int_exponent < 0) abs_int_exponent = -abs_int_exponent;
+
+        return (abs_int_exponent >= 1)
+            && (abs_int_exponent <= 46 ||
+              (abs_int_exponent <= 1024 &&
+              (abs_int_exponent & (abs_int_exponent - 1)) == 0));
+    #endif
+    }
+
+    /* Needed by fp_opcode_add.inc if tracing is enabled */
+    template<typename Value_t>
+    std::string findName(const NamePtrsMap<Value_t>& nameMap,
+                         unsigned index,
+                         typename NameData<Value_t>::DataType type)
+    {
+        for(typename NamePtrsMap<Value_t>::const_iterator
+                iter = nameMap.begin();
+            iter != nameMap.end();
+            ++iter)
+        {
+            if(iter->second.type == type && iter->second.index == index)
+                return std::string(iter->first.name,
+                                   iter->first.name + iter->first.nameLength);
+        }
+        return "?";
+    }
+}
+
+template<typename Value_t>
+inline void FunctionParserBase<Value_t>::AddImmedOpcode(Value_t value)
+{
+    mData->mImmed.push_back(value);
+    mData->mByteCode.push_back(cImmed);
+}
+
+template<typename Value_t>
+inline void FunctionParserBase<Value_t>::CompilePowi(long abs_int_exponent)
+{
+    int num_muls=0;
+    while(abs_int_exponent > 1)
+    {
+        long factor = get_powi_factor(abs_int_exponent);
+        if(factor)
+        {
+            CompilePowi(factor);
+            abs_int_exponent /= factor;
+            continue;
+        }
+        if(!(abs_int_exponent & 1))
+        {
+            abs_int_exponent /= 2;
+            mData->mByteCode.push_back(cSqr);
+            // ^ Don't put AddFunctionOpcode here,
+            //   it would slow down a great deal.
+        }
+        else
+        {
+            mData->mByteCode.push_back(cDup);
+            incStackPtr();
+            abs_int_exponent -= 1;
+            ++num_muls;
+        }
+    }
+    if(num_muls > 0)
+    {
+        mData->mByteCode.resize(mData->mByteCode.size()+num_muls, cMul);
+        mStackPtr -= num_muls;
+    }
+}
+
+template<typename Value_t>
+inline bool FunctionParserBase<Value_t>::TryCompilePowi(Value_t original_immed)
+{
+    Value_t changed_immed = original_immed;
+    for(int sqrt_count=0; /**/; ++sqrt_count)
+    {
+        long int_exponent = makeLongInteger(changed_immed);
+        if(isLongInteger(changed_immed) &&
+           IsEligibleIntPowiExponent(int_exponent))
+        {
+            long abs_int_exponent = int_exponent;
+            if(abs_int_exponent < 0)
+                abs_int_exponent = -abs_int_exponent;
+
+            mData->mImmed.pop_back(); mData->mByteCode.pop_back();
+            --mStackPtr;
+            // ^Though the above is accounted for by the procedure
+            // that generates cPow, we need it for correct cFetch
+            // indexes in CompilePowi().
+
+            while(sqrt_count > 0)
+            {
+                int opcode = cSqrt;
+                if(sqrt_count == 1 && int_exponent < 0)
+                {
+                    opcode = cRSqrt;
+                    int_exponent = -int_exponent;
+                }
+                mData->mByteCode.push_back(opcode);
+                --sqrt_count;
+            }
+            if((abs_int_exponent & 1) == 0)
+            {
+                // This special rule fixes the optimization
+                // shortcoming of (-x)^2 with minimal overhead.
+                AddFunctionOpcode(cSqr);
+                abs_int_exponent >>= 1;
+            }
+            CompilePowi(abs_int_exponent);
+            if(int_exponent < 0) mData->mByteCode.push_back(cInv);
+            ++mStackPtr; // Needed because cPow adding will assume this.
+            return true;
+        }
+        if(sqrt_count >= 4) break;
+        changed_immed += changed_immed;
+    }
+
+    // When we don't know whether x >= 0, we still know that
+    // x^y can be safely converted into exp(y * log(x))
+    // when y is _not_ integer, because we know that x >= 0.
+    // Otherwise either expression will give a NaN.
+    if(/*!isInteger(original_immed) ||*/
+       IsNeverNegativeValueOpcode(mData->mByteCode[mData->mByteCode.size()-2]))
+    {
+        mData->mImmed.pop_back();
+        mData->mByteCode.pop_back();
+        //--mStackPtr; - accounted for by the procedure that generates cPow
+        AddFunctionOpcode(cLog);
+        AddImmedOpcode(original_immed);
+        //incStackPtr(); - this and the next are redundant because...
+        AddFunctionOpcode(cMul);
+        //--mStackPtr;    - ...because the cImmed was popped earlier.
+        AddFunctionOpcode(cExp);
+        return true;
+    }
+    return false;
+}
+
+//#include "fpoptimizer/opcodename.hh"
+// ^ needed only if FP_TRACE_BYTECODE_OPTIMIZATION() is used
+
+template<typename Value_t>
+inline void FunctionParserBase<Value_t>::AddFunctionOpcode(unsigned opcode)
+{
+#define FP_FLOAT_VERSION 1
+#define FP_COMPLEX_VERSION 0
+#include "extrasrc/fp_opcode_add.inc"
+#undef FP_COMPLEX_VERSION
+#undef FP_FLOAT_VERSION
+}
+
+#ifdef FP_SUPPORT_LONG_INT_TYPE
+template<>
+inline void FunctionParserBase<long>::AddFunctionOpcode(unsigned opcode)
+{
+    typedef long Value_t;
+#define FP_FLOAT_VERSION 0
+#define FP_COMPLEX_VERSION 0
+#include "extrasrc/fp_opcode_add.inc"
+#undef FP_COMPLEX_VERSION
+#undef FP_FLOAT_VERSION
+}
+#endif
+
+#ifdef FP_SUPPORT_GMP_INT_TYPE
+template<>
+inline void FunctionParserBase<GmpInt>::AddFunctionOpcode(unsigned opcode)
+{
+    typedef GmpInt Value_t;
+#define FP_FLOAT_VERSION 0
+#define FP_COMPLEX_VERSION 0
+#include "extrasrc/fp_opcode_add.inc"
+#undef FP_COMPLEX_VERSION
+#undef FP_FLOAT_VERSION
+}
+#endif
+
+#ifdef FP_SUPPORT_COMPLEX_DOUBLE_TYPE
+template<>
+inline void FunctionParserBase<std::complex<double> >::AddFunctionOpcode(unsigned opcode)
+{
+    typedef std::complex<double> Value_t;
+#define FP_FLOAT_VERSION 1
+#define FP_COMPLEX_VERSION 1
+#include "extrasrc/fp_opcode_add.inc"
+#undef FP_COMPLEX_VERSION
+#undef FP_FLOAT_VERSION
+}
+#endif
+
+#ifdef FP_SUPPORT_COMPLEX_FLOAT_TYPE
+template<>
+inline void FunctionParserBase<std::complex<float> >::AddFunctionOpcode(unsigned opcode)
+{
+    typedef std::complex<float> Value_t;
+#define FP_FLOAT_VERSION 1
+#define FP_COMPLEX_VERSION 1
+#include "extrasrc/fp_opcode_add.inc"
+#undef FP_COMPLEX_VERSION
+#undef FP_FLOAT_VERSION
+}
+#endif
+
+#ifdef FP_SUPPORT_COMPLEX_LONG_DOUBLE_TYPE
+template<>
+inline void FunctionParserBase<std::complex<long double> >::AddFunctionOpcode(unsigned opcode)
+{
+    typedef std::complex<long double> Value_t;
+#define FP_FLOAT_VERSION 1
+#define FP_COMPLEX_VERSION 1
+#include "extrasrc/fp_opcode_add.inc"
+#undef FP_COMPLEX_VERSION
+#undef FP_FLOAT_VERSION
+}
+#endif
+
+template<typename Value_t>
+unsigned
+FunctionParserBase<Value_t>::ParseIdentifier(const char* function)
+{
+    return readIdentifier<Value_t>(function);
+}
+
+template<typename Value_t>
+std::pair<const char*, Value_t>
+FunctionParserBase<Value_t>::ParseLiteral(const char* function)
+{
+    char* endptr;
+#if 0 /* Profile the hex literal parser */
+    if(function[0]=='0' && function[1]=='x')
+    {
+        // Parse hexadecimal literal if fp_parseLiteral didn't already
+        Value_t val = parseHexLiteral<Value_t>(function+2, &endptr);
+        if(endptr == function+2)
+            return std::pair<const char*,Value_t> (function, Value_t());
+        return std::pair<const char*, Value_t> (endptr, val);
+    }
+#endif
+    Value_t val = fp_parseLiteral<Value_t>(function, &endptr);
+
+    if(endptr == function+1 && function[0] == '0' && function[1] == 'x')
+    {
+        // Parse hexadecimal literal if fp_parseLiteral didn't already
+        val = parseHexLiteral<Value_t>(function+2, &endptr);
+        if(endptr == function+2)
+            return std::pair<const char*,Value_t> (function, Value_t());
+    }
+    else if(endptr == function)
+        return std::pair<const char*,Value_t> (function, Value_t());
+
+    return std::pair<const char*,Value_t> (endptr, val);
+}
+
+#ifdef FP_SUPPORT_MPFR_FLOAT_TYPE
+template<>
+std::pair<const char*, MpfrFloat>
+FunctionParserBase<MpfrFloat>::ParseLiteral(const char* function)
+{
+    char* endPtr;
+    const MpfrFloat val = MpfrFloat::parseString(function, &endPtr);
+    if(endPtr == function)
+        return std::pair<const char*,MpfrFloat> (function, MpfrFloat());
+    return std::pair<const char*,MpfrFloat> (endPtr, val);
+}
+#endif
+
+#ifdef FP_SUPPORT_GMP_INT_TYPE
+template<>
+std::pair<const char*, GmpInt>
+FunctionParserBase<GmpInt>::ParseLiteral(const char* function)
+{
+    char* endPtr;
+    const GmpInt val = GmpInt::parseString(function, &endPtr);
+    if(endPtr == function)
+        return std::pair<const char*,GmpInt> (function, GmpInt());
+    return std::pair<const char*,GmpInt> (endPtr, val);
+}
+#endif
+
+
+template<typename Value_t>
+inline const char*
+FunctionParserBase<Value_t>::CompileLiteral(const char* function)
+{
+    std::pair<const char*, Value_t> result = ParseLiteral(function);
+
+    if(result.first == function)
+        return SetErrorType(SYNTAX_ERROR, result.first);
+
+    AddImmedOpcode(result.second);
+    incStackPtr();
+    SkipSpace(result.first);
+    return result.first;
+}
+
+template<typename Value_t>
+const char* FunctionParserBase<Value_t>::CompileIf(const char* function)
+{
+    if(*function != '(') return SetErrorType(EXPECT_PARENTH_FUNC, function);
+
+    function = CompileExpression(function+1);
+    if(!function) return 0;
+    if(*function != ',')
+        return SetErrorType(noCommaError<Value_t>(*function), function);
+
+    OPCODE opcode = cIf;
+    if(mData->mByteCode.back() == cNotNot) mData->mByteCode.pop_back();
+    if(IsNeverNegativeValueOpcode(mData->mByteCode.back()))
+    {
+        // If we know that the condition to be tested is always
+        // a positive value (such as when produced by "x<y"),
+        // we can use the faster opcode to evaluate it.
+        // cIf tests whether fabs(cond) >= 0.5,
+        // cAbsIf simply tests whether cond >= 0.5.
+        opcode = cAbsIf;
+    }
+
+    mData->mByteCode.push_back(opcode);
+    const unsigned curByteCodeSize = unsigned(mData->mByteCode.size());
+    PushOpcodeParam<false>(0); // Jump index; to be set later
+    PushOpcodeParam<true> (0); // Immed jump index; to be set later
+
+    --mStackPtr;
+
+    function = CompileExpression(function + 1);
+    if(!function) return 0;
+    if(*function != ',')
+        return SetErrorType(noCommaError<Value_t>(*function), function);
+
+    mData->mByteCode.push_back(cJump);
+    const unsigned curByteCodeSize2 = unsigned(mData->mByteCode.size());
+    const unsigned curImmedSize2 = unsigned(mData->mImmed.size());
+    PushOpcodeParam<false>(0); // Jump index; to be set later
+    PushOpcodeParam<true> (0); // Immed jump index; to be set later
+
+    --mStackPtr;
+
+    function = CompileExpression(function + 1);
+    if(!function) return 0;
+    if(*function != ')')
+        return SetErrorType(noParenthError<Value_t>(*function), function);
+
+    PutOpcodeParamAt<true> ( mData->mByteCode.back(), unsigned(mData->mByteCode.size()-1) );
+    // ^Necessary for guarding against if(x,1,2)+1 being changed
+    //  into if(x,1,3) by fp_opcode_add.inc
+
+    // Set jump indices
+    PutOpcodeParamAt<false>( curByteCodeSize2+1, curByteCodeSize );
+    PutOpcodeParamAt<false>( curImmedSize2,      curByteCodeSize+1 );
+    PutOpcodeParamAt<false>( unsigned(mData->mByteCode.size())-1, curByteCodeSize2);
+    PutOpcodeParamAt<false>( unsigned(mData->mImmed.size()),      curByteCodeSize2+1);
+
+    ++function;
+    SkipSpace(function);
+    return function;
+}
+
+template<typename Value_t>
+const char* FunctionParserBase<Value_t>::CompileFunctionParams
+(const char* function, unsigned requiredParams)
+{
+    if(*function != '(') return SetErrorType(EXPECT_PARENTH_FUNC, function);
+
+    if(requiredParams > 0)
+    {
+        const char* function_end = CompileExpression(function+1);
+        if(!function_end)
+        {
+            // If an error occurred, verify whether it was caused by ()
+            ++function;
+            SkipSpace(function);
+            if(*function == ')')
+                return SetErrorType(ILL_PARAMS_AMOUNT, function);
+            // Not caused by (), use the error message given by CompileExpression()
+            return 0;
+        }
+        function = function_end;
+
+        for(unsigned i = 1; i < requiredParams; ++i)
+        {
+            if(*function != ',')
+                return SetErrorType(noCommaError<Value_t>(*function), function);
+
+            function = CompileExpression(function+1);
+            if(!function) return 0;
+        }
+        // No need for incStackPtr() because each parse parameter calls it
+        mStackPtr -= requiredParams-1;
+    }
+    else
+    {
+        incStackPtr(); // return value of function is pushed onto the stack
+        ++function;
+        SkipSpace(function);
+    }
+
+    if(*function != ')')
+        return SetErrorType(noParenthError<Value_t>(*function), function);
+    ++function;
+    SkipSpace(function);
+    return function;
+}
+
+template<typename Value_t>
+const char* FunctionParserBase<Value_t>::CompileElement(const char* function)
+{
+    if(BeginsLiteral<Value_t>( (unsigned char) *function))
+        return CompileLiteral(function);
+
+    unsigned nameLength = readIdentifier<Value_t>(function);
+    if(nameLength == 0)
+    {
+        // No identifier found
+        if(*function == '(') return CompileParenthesis(function);
+        if(*function == ')') return SetErrorType(MISM_PARENTH, function);
+        return SetErrorType(SYNTAX_ERROR, function);
+    }
+
+    // Function, variable or constant
+    if(nameLength & 0x80000000U) // Function
+    {
+        OPCODE func_opcode = OPCODE( (nameLength >> 16) & 0x7FFF );
+        return CompileFunction(function + (nameLength & 0xFFFF), func_opcode);
+    }
+
+    NamePtr name(function, nameLength);
+    const char* endPtr = function + nameLength;
+    SkipSpace(endPtr);
+
+    typename NamePtrsMap<Value_t>::iterator nameIter =
+        mData->mNamePtrs.find(name);
+    if(nameIter == mData->mNamePtrs.end())
+    {
+        // Check if it's an inline variable:
+        for(typename Data::InlineVarNamesContainer::reverse_iterator iter =
+                mData->mInlineVarNames.rbegin();
+            iter != mData->mInlineVarNames.rend();
+            ++iter)
+        {
+            if(name == iter->mName)
+            {
+                if( iter->mFetchIndex+1 == mStackPtr)
+                {
+                    mData->mByteCode.push_back(cDup);
+                }
+                else
+                {
+                    mData->mByteCode.push_back(cFetch);
+                    PushOpcodeParam<true>(iter->mFetchIndex);
+                }
+                incStackPtr();
+                return endPtr;
+            }
+        }
+
+        return SetErrorType(UNKNOWN_IDENTIFIER, function);
+    }
+
+    const NameData<Value_t>* nameData = &nameIter->second;
+    switch(nameData->type)
+    {
+      case NameData<Value_t>::VARIABLE: // is variable
+          if(unlikely(!mData->mByteCode.empty() &&
+                      mData->mByteCode.back() == nameData->index))
+              mData->mByteCode.push_back(cDup);
+          else
+              mData->mByteCode.push_back(nameData->index);
+          incStackPtr();
+          return endPtr;
+
+      case NameData<Value_t>::CONSTANT: // is constant
+          AddImmedOpcode(nameData->value);
+          incStackPtr();
+          return endPtr;
+
+      case NameData<Value_t>::UNIT: // is unit (error if appears here)
+          break;
+
+      case NameData<Value_t>::FUNC_PTR: // is C++ function
+          function = CompileFunctionParams
+              (endPtr, mData->mFuncPtrs[nameData->index].mParams);
+          //if(!function) return 0;
+          mData->mByteCode.push_back(cFCall);
+          PushOpcodeParam<true>(nameData->index);
+          return function;
+
+      case NameData<Value_t>::PARSER_PTR: // is FunctionParser
+          function = CompileFunctionParams
+              (endPtr, mData->mFuncParsers[nameData->index].mParams);
+          //if(!function) return 0;
+          mData->mByteCode.push_back(cPCall);
+          PushOpcodeParam<true>(nameData->index);
+          return function;
+    }
+
+    // When it's an unit (or unrecognized type):
+    return SetErrorType(SYNTAX_ERROR, function);
+}
+
+template<typename Value_t>
+inline const char* FunctionParserBase<Value_t>::CompileFunction
+(const char* function, unsigned func_opcode)
+{
+    SkipSpace(function);
+    const FuncDefinition& funcDef = Functions[func_opcode];
+
+    if(func_opcode == cIf) // "if" is a special case
+        return CompileIf(function);
+
+    unsigned requiredParams = funcDef.params;
+
+    function = CompileFunctionParams(function, requiredParams);
+    if(!function) return 0;
+
+    if(mData->mUseDegreeConversion)
+    {
+        if(funcDef.flags & FuncDefinition::AngleIn)
+            AddFunctionOpcode(cRad);
+
+        AddFunctionOpcode(func_opcode);
+
+        if(funcDef.flags & FuncDefinition::AngleOut)
+            AddFunctionOpcode(cDeg);
+    }
+    else
+    {
+        AddFunctionOpcode(func_opcode);
+    }
+    return function;
+}
+
+template<typename Value_t>
+inline const char*
+FunctionParserBase<Value_t>::CompileParenthesis(const char* function)
+{
+    ++function; // Skip '('
+
+    SkipSpace(function);
+    if(*function == ')') return SetErrorType(EMPTY_PARENTH, function);
+    function = CompileExpression(function);
+    if(!function) return 0;
+
+    if(*function != ')') return SetErrorType(MISSING_PARENTH, function);
+    ++function; // Skip ')'
+
+    SkipSpace(function);
+    return function;
+}
+
+template<typename Value_t>
+const char*
+FunctionParserBase<Value_t>::CompilePossibleUnit(const char* function)
+{
+    unsigned nameLength = readIdentifier<Value_t>(function);
+    if(nameLength & 0x80000000U) return function; // built-in function name
+    if(nameLength != 0)
+    {
+        NamePtr name(function, nameLength);
+
+        typename NamePtrsMap<Value_t>::iterator nameIter =
+            mData->mNamePtrs.find(name);
+        if(nameIter != mData->mNamePtrs.end())
+        {
+            const NameData<Value_t>* nameData = &nameIter->second;
+            if(nameData->type == NameData<Value_t>::UNIT)
+            {
+                AddImmedOpcode(nameData->value);
+                incStackPtr();
+                AddFunctionOpcode(cMul);
+                --mStackPtr;
+
+                const char* endPtr = function + nameLength;
+                SkipSpace(endPtr);
+                return endPtr;
+            }
+        }
+    }
+
+    return function;
+}
+
+template<typename Value_t>
+inline const char*
+FunctionParserBase<Value_t>::CompilePow(const char* function)
+{
+    function = CompileElement(function);
+    if(!function) return 0;
+    function = CompilePossibleUnit(function);
+
+    if(*function == '^')
+    {
+        ++function;
+        SkipSpace(function);
+
+        unsigned op = cPow;
+        if(mData->mByteCode.back() == cImmed)
+        {
+            if(mData->mImmed.back() == fp_const_e<Value_t>())
+                { op = cExp;  mData->mByteCode.pop_back();
+                    mData->mImmed.pop_back(); --mStackPtr; }
+            else if(mData->mImmed.back() == Value_t(2))
+                { op = cExp2; mData->mByteCode.pop_back();
+                    mData->mImmed.pop_back(); --mStackPtr; }
+        }
+
+        function = CompileUnaryMinus(function);
+        if(!function) return 0;
+
+        // add opcode
+        AddFunctionOpcode(op);
+
+        if(op == cPow) --mStackPtr;
+    }
+    return function;
+}
+
+/* Currently the power operator is skipped for integral types because its
+   usefulness with them is questionable, and in the case of GmpInt, for safety
+   reasons:
+   - With long int almost any power, except for very small ones, would
+     overflow the result, so the usefulness of this is rather questionable.
+   - With GmpInt the power operator could be easily abused to make the program
+     run out of memory (think of a function like "10^10^10^10^1000000").
+*/
+#ifdef FP_SUPPORT_LONG_INT_TYPE
+template<>
+inline const char*
+FunctionParserBase<long>::CompilePow(const char* function)
+{
+    function = CompileElement(function);
+    if(!function) return 0;
+    return CompilePossibleUnit(function);
+}
+#endif
+
+#ifdef FP_SUPPORT_GMP_INT_TYPE
+template<>
+inline const char*
+FunctionParserBase<GmpInt>::CompilePow(const char* function)
+{
+    function = CompileElement(function);
+    if(!function) return 0;
+    return CompilePossibleUnit(function);
+}
+#endif
+
+template<typename Value_t>
+inline const char*
+FunctionParserBase<Value_t>::CompileUnaryMinus(const char* function)
+{
+    char op = *function;
+    switch(op)
+    {
+        case '-':
+        case '!':
+            ++function;
+            SkipSpace(function);
+
+            function = CompileUnaryMinus(function);
+            if(!function) return 0;
+
+            AddFunctionOpcode(op=='-' ? cNeg : cNot);
+
+            return function;
+        default: break;
+    }
+    return CompilePow(function);
+}
+
+template<typename Value_t>
+inline const char*
+FunctionParserBase<Value_t>::CompileMult(const char* function)
+{
+    function = CompileUnaryMinus(function);
+    if(!function) return 0;
+
+    Value_t pending_immed(1);
+    #define FP_FlushImmed(do_reset) \
+        if(pending_immed != Value_t(1)) \
+        { \
+            unsigned op = cMul; \
+            if(!IsIntType<Value_t>::result && mData->mByteCode.back() == cInv) \
+            { \
+                /* (...) cInv 5 cMul -> (...) 5 cRDiv */ \
+                /*           ^               ^      | */ \
+                mData->mByteCode.pop_back(); \
+                op = cRDiv; \
+            } \
+            AddImmedOpcode(pending_immed); \
+            incStackPtr(); \
+            AddFunctionOpcode(op); \
+            --mStackPtr; \
+            if(do_reset) pending_immed = Value_t(1); \
+        }
+    while(true)
+    {
+        char c = *function;
+        if(c == '%')
+        {
+            FP_FlushImmed(true);
+            ++function;
+            SkipSpace(function);
+            function = CompileUnaryMinus(function);
+            if(!function) return 0;
+            AddFunctionOpcode(cMod);
+            --mStackPtr;
+            continue;
+        }
+        if(c != '*' && c != '/') break;
+
+        bool safe_cumulation = (c == '*' || !IsIntType<Value_t>::result);
+        if(!safe_cumulation)
+        {
+            FP_FlushImmed(true);
+        }
+
+        ++function;
+        SkipSpace(function);
+        if(mData->mByteCode.back() == cImmed
+        && (safe_cumulation
+         || mData->mImmed.back() == Value_t(1)))
+        {
+            // 5 (...) cMul --> (...)      ||| 5 cMul
+            // 5 (...) cDiv --> (...) cInv ||| 5 cMul
+            //  ^          |              ^
+            pending_immed *= mData->mImmed.back();
+            mData->mImmed.pop_back();
+            mData->mByteCode.pop_back();
+            --mStackPtr;
+            function = CompileUnaryMinus(function);
+            if(!function) return 0;
+            if(c == '/')
+                AddFunctionOpcode(cInv);
+            continue;
+        }
+        if(safe_cumulation
+        && mData->mByteCode.back() == cMul
+        && mData->mByteCode[mData->mByteCode.size()-2] == cImmed)
+        {
+            // (:::) 5 cMul (...) cMul -> (:::) (...) cMul  ||| 5 cMul
+            // (:::) 5 cMul (...) cDiv -> (:::) (...) cDiv  ||| 5 cMul
+            //             ^                   ^
+            pending_immed *= mData->mImmed.back();
+            mData->mImmed.pop_back();
+            mData->mByteCode.pop_back();
+            mData->mByteCode.pop_back();
+        }
+        // cDiv is not tested here because the bytecode
+        // optimizer will convert this kind of cDivs into cMuls.
+        bool lhs_inverted = false;
+        if(!IsIntType<Value_t>::result && c == '*'
+        && mData->mByteCode.back() == cInv)
+        {
+            // (:::) cInv (...) cMul -> (:::) (...) cRDiv
+            // (:::) cInv (...) cDiv -> (:::) (...) cMul cInv
+            //           ^                   ^            |
+            mData->mByteCode.pop_back();
+            lhs_inverted = true;
+        }
+        function = CompileUnaryMinus(function);
+        if(!function) return 0;
+        if(safe_cumulation
+        && mData->mByteCode.back() == cMul
+        && mData->mByteCode[mData->mByteCode.size()-2] == cImmed)
+        {
+            // (:::) (...) 5 cMul cMul -> (:::) (...) cMul  |||  5 Mul
+            // (:::) (...) 5 cMul cDiv -> (:::) (...) cDiv  ||| /5 Mul
+            //                   ^                        ^
+            if(c == '*')
+                pending_immed *= mData->mImmed.back();
+            else
+                pending_immed /= mData->mImmed.back();
+            mData->mImmed.pop_back();
+            mData->mByteCode.pop_back();
+            mData->mByteCode.pop_back();
+        }
+        else
+        if(safe_cumulation
+        && mData->mByteCode.back() == cRDiv
+        && mData->mByteCode[mData->mByteCode.size()-2] == cImmed)
+        {
+            // (:::) (...) 5 cRDiv cMul -> (:::) (...) cDiv  |||  5 cMul
+            // (:::) (...) 5 cRDiv cDiv -> (:::) (...) cMul  ||| /5 cMul
+            //                    ^                   ^
+            if(c == '*')
+                { c = '/'; pending_immed *= mData->mImmed.back(); }
+            else
+                { c = '*'; pending_immed /= mData->mImmed.back(); }
+            mData->mImmed.pop_back();
+            mData->mByteCode.pop_back();
+            mData->mByteCode.pop_back();
+        }
+        if(!lhs_inverted) // if (/x/y) was changed to /(x*y), add missing cInv
+        {
+            AddFunctionOpcode(c == '*' ? cMul : cDiv);
+            --mStackPtr;
+        }
+        else if(c == '*') // (/x)*y -> rdiv(x,y)
+        {
+            AddFunctionOpcode(cRDiv);
+            --mStackPtr;
+        }
+        else // (/x)/y -> /(x*y)
+        {
+            AddFunctionOpcode(cMul);
+            --mStackPtr;
+            AddFunctionOpcode(cInv);
+        }
+    }
+    FP_FlushImmed(false);
+    #undef FP_FlushImmed
+    return function;
+}
+
+template<typename Value_t>
+inline const char*
+FunctionParserBase<Value_t>::CompileAddition(const char* function)
+{
+    function = CompileMult(function);
+    if(!function) return 0;
+
+    Value_t pending_immed(0);
+    #define FP_FlushImmed(do_reset) \
+        if(pending_immed != Value_t(0)) \
+        { \
+            unsigned op = cAdd; \
+            if(mData->mByteCode.back() == cNeg) \
+            { \
+                /* (...) cNeg 5 cAdd -> (...) 5 cRSub */ \
+                /*           ^               ^      | */ \
+                mData->mByteCode.pop_back(); \
+                op = cRSub; \
+            } \
+            AddImmedOpcode(pending_immed); \
+            incStackPtr(); \
+            AddFunctionOpcode(op); \
+            --mStackPtr; \
+            if(do_reset) pending_immed = Value_t(0); \
+        }
+    while(true)
+    {
+        char c = *function;
+        if(c != '+' && c != '-') break;
+        ++function;
+        SkipSpace(function);
+        if(mData->mByteCode.back() == cImmed)
+        {
+            // 5 (...) cAdd --> (...)      ||| 5 cAdd
+            // 5 (...) cSub --> (...) cNeg ||| 5 cAdd
+            //  ^          |              ^
+            pending_immed += mData->mImmed.back();
+            mData->mImmed.pop_back();
+            mData->mByteCode.pop_back();
+            --mStackPtr;
+            function = CompileMult(function);
+            if(!function) return 0;
+            if(c == '-')
+                AddFunctionOpcode(cNeg);
+            continue;
+        }
+        if(mData->mByteCode.back() == cAdd
+        && mData->mByteCode[mData->mByteCode.size()-2] == cImmed)
+        {
+            // (:::) 5 cAdd (...) cAdd -> (:::) (...) cAdd  ||| 5 cAdd
+            // (:::) 5 cAdd (...) cSub -> (:::) (...) cSub  ||| 5 cAdd
+            //             ^                   ^
+            pending_immed += mData->mImmed.back();
+            mData->mImmed.pop_back();
+            mData->mByteCode.pop_back();
+            mData->mByteCode.pop_back();
+        }
+        // cSub is not tested here because the bytecode
+        // optimizer will convert this kind of cSubs into cAdds.
+        bool lhs_negated = false;
+        if(mData->mByteCode.back() == cNeg)
+        {
+            // (:::) cNeg (...) cAdd -> (:::) (...) cRSub
+            // (:::) cNeg (...) cSub -> (:::) (...) cAdd cNeg
+            //           ^                   ^            |
+            mData->mByteCode.pop_back();
+            lhs_negated = true;
+        }
+        function = CompileMult(function);
+        if(!function) return 0;
+        if(mData->mByteCode.back() == cAdd
+        && mData->mByteCode[mData->mByteCode.size()-2] == cImmed)
+        {
+            // (:::) (...) 5 cAdd cAdd -> (:::) (...) cAdd  |||  5 Add
+            // (:::) (...) 5 cAdd cSub -> (:::) (...) cSub  ||| -5 Add
+            //                   ^                        ^
+            if(c == '+')
+                pending_immed += mData->mImmed.back();
+            else
+                pending_immed -= mData->mImmed.back();
+            mData->mImmed.pop_back();
+            mData->mByteCode.pop_back();
+            mData->mByteCode.pop_back();
+        }
+        else
+        if(mData->mByteCode.back() == cRSub
+        && mData->mByteCode[mData->mByteCode.size()-2] == cImmed)
+        {
+            // (:::) (...) 5 cRSub cAdd -> (:::) (...) cSub  |||  5 cAdd
+            // (:::) (...) 5 cRSub cSub -> (:::) (...) cAdd  ||| -5 cAdd
+            //                    ^                   ^
+            if(c == '+')
+                { c = '-'; pending_immed += mData->mImmed.back(); }
+            else
+                { c = '+'; pending_immed -= mData->mImmed.back(); }
+            mData->mImmed.pop_back();
+            mData->mByteCode.pop_back();
+            mData->mByteCode.pop_back();
+        }
+        if(!lhs_negated) // if (-x-y) was changed to -(x+y), add missing cNeg
+        {
+            AddFunctionOpcode(c == '+' ? cAdd : cSub);
+            --mStackPtr;
+        }
+        else if(c == '+') // (-x)+y -> rsub(x,y)
+        {
+            AddFunctionOpcode(cRSub);
+            --mStackPtr;
+        }
+        else // (-x)-y -> -(x+y)
+        {
+            AddFunctionOpcode(cAdd);
+            --mStackPtr;
+            AddFunctionOpcode(cNeg);
+        }
+    }
+    FP_FlushImmed(false);
+    #undef FP_FlushImmed
+    return function;
+}
+
+template<typename Value_t>
+inline const char*
+FunctionParserBase<Value_t>::CompileComparison(const char* function)
+{
+    unsigned op=0;
+    while(true)
+    {
+        function = CompileAddition(function);
+        if(!function) return 0;
+
+        if(op)
+        {
+            AddFunctionOpcode(op);
+            --mStackPtr;
+        }
+        switch(*function)
+        {
+          case '=':
+              ++function; op = cEqual; break;
+          case '!':
+              if(function[1] == '=')
+              { function += 2; op = cNEqual; break; }
+              // If '=' does not follow '!', a syntax error will
+              // be generated at the outermost parsing level
+              return function;
+          case '<':
+              if(function[1] == '=')
+              { function += 2; op = cLessOrEq; break; }
+              ++function; op = cLess; break;
+          case '>':
+              if(function[1] == '=')
+              { function += 2; op = cGreaterOrEq; break; }
+              ++function; op = cGreater; break;
+          default: return function;
+        }
+        SkipSpace(function);
+    }
+    return function;
+}
+
+template<typename Value_t>
+inline const char* FunctionParserBase<Value_t>::CompileAnd(const char* function)
+{
+    std::size_t param0end=0;
+    while(true)
+    {
+        function = CompileComparison(function);
+        if(!function) return 0;
+
+        if(param0end)
+        {
+            if(mData->mByteCode.back() == cNotNot) mData->mByteCode.pop_back();
+
+            AddFunctionOpcode(cAnd);
+            --mStackPtr;
+        }
+        if(*function != '&') break;
+        ++function;
+        SkipSpace(function);
+        param0end = mData->mByteCode.size();
+    }
+    return function;
+}
+
+template<typename Value_t>
+const char* FunctionParserBase<Value_t>::CompileExpression(const char* function)
+{
+    std::size_t param0end=0;
+    while(true)
+    {
+        SkipSpace(function);
+        function = CompileAnd(function);
+        if(!function) return 0;
+
+        if(param0end)
+        {
+            if(mData->mByteCode.back() == cNotNot) mData->mByteCode.pop_back();
+
+            AddFunctionOpcode(cOr);
+            --mStackPtr;
+        }
+        if(*function != '|') break;
+        ++function;
+        param0end = mData->mByteCode.size();
+    }
+    return function;
+}
+
+template<typename Value_t>
+const char* FunctionParserBase<Value_t>::Compile(const char* function)
+{
+    while(true)
+    {
+        // Check if an identifier appears as first token:
+        SkipSpace(function);
+        unsigned nameLength = readIdentifier<Value_t>(function);
+        if(nameLength > 0 && !(nameLength & 0x80000000U))
+        {
+            typename Data::InlineVariable inlineVar =
+                { NamePtr(function, nameLength), 0 };
+
+            // Check if it's an unknown identifier:
+            typename NamePtrsMap<Value_t>::iterator nameIter =
+                mData->mNamePtrs.find(inlineVar.mName);
+            if(nameIter == mData->mNamePtrs.end())
+            {
+                const char* function2 = function + nameLength;
+                SkipSpace(function2);
+
+                // Check if ":=" follows the unknown identifier:
+                if(function2[0] == ':' && function2[1] == '=')
+                {
+                    // Parse the expression that follows and create the
+                    // inline variable:
+                    function2 = CompileExpression(function2 + 2);
+                    if(!function2) return 0;
+                    if(*function2 != ';') return function2;
+
+                    inlineVar.mFetchIndex = mStackPtr - 1;
+                    mData->mInlineVarNames.push_back(inlineVar);
+
+                    // Continue with the expression after the ';':
+                    function = function2 + 1;
+                    continue;
+                }
+            }
+        }
+        break;
+    }
+
+    return CompileExpression(function);
+}
+
+template<typename Value_t> template<bool PutFlag>
+inline void FunctionParserBase<Value_t>::PushOpcodeParam
+    (unsigned value)
+{
+    mData->mByteCode.push_back(value | (PutFlag ? FP_ParamGuardMask : 0u));
+    if(PutFlag) mData->mHasByteCodeFlags = true;
+}
+
+template<typename Value_t> template<bool PutFlag>
+inline void FunctionParserBase<Value_t>::PutOpcodeParamAt
+    (unsigned value, unsigned offset)
+{
+    mData->mByteCode[offset] = value | (PutFlag ? FP_ParamGuardMask : 0u);
+    if(PutFlag) mData->mHasByteCodeFlags = true;
+}
+
+//===========================================================================
+// Function evaluation
+//===========================================================================
+template<typename Value_t>
+Value_t FunctionParserBase<Value_t>::Eval(const Value_t* Vars)
+{
+    if(mData->mParseErrorType != FP_NO_ERROR) return Value_t(0);
+
+    const unsigned* const byteCode = &(mData->mByteCode[0]);
+    const Value_t* const immed = mData->mImmed.empty() ? 0 : &(mData->mImmed[0]);
+    const unsigned byteCodeSize = unsigned(mData->mByteCode.size());
+    unsigned IP, DP=0;
+    int SP=-1;
+
+#ifdef FP_USE_THREAD_SAFE_EVAL
+    /* If Eval() may be called by multiple threads simultaneously,
+     * then Eval() must allocate its own stack.
+     */
+#ifdef FP_USE_THREAD_SAFE_EVAL_WITH_ALLOCA
+    /* alloca() allocates room from the hardware stack.
+     * It is automatically freed when the function returns.
+     */
+    Value_t* const Stack = (Value_t*)alloca(mData->mStackSize*sizeof(Value_t));
+#else
+    /* Allocate from the heap. Ensure that it is freed
+     * automatically no matter which exit path is taken.
+     */
+    struct AutoDealloc
+    {
+        Value_t* ptr;
+        ~AutoDealloc() { delete[] ptr; }
+    } AutoDeallocStack = { new Value_t[mData->mStackSize] };
+    Value_t*& Stack = AutoDeallocStack.ptr;
+#endif
+#else
+    /* No thread safety, so use a global stack. */
+    std::vector<Value_t>& Stack = mData->mStack;
+#endif
+
+    for(IP=0; IP<byteCodeSize; ++IP)
+    {
+        switch(byteCode[IP])
+        {
+// Functions:
+          case   cAbs: Stack[SP] = fp_abs(Stack[SP]); break;
+
+          case  cAcos:
+              if(IsComplexType<Value_t>::result == false
+              && (Stack[SP] < Value_t(-1) || Stack[SP] > Value_t(1)))
+              { mData->mEvalErrorType=4; return Value_t(0); }
+              Stack[SP] = fp_acos(Stack[SP]); break;
+
+          case cAcosh:
+              if(IsComplexType<Value_t>::result == false
+              && Stack[SP] < Value_t(1))
+              { mData->mEvalErrorType=4; return Value_t(0); }
+              Stack[SP] = fp_acosh(Stack[SP]); break;
+
+          case  cAsin:
+              if(IsComplexType<Value_t>::result == false
+              && (Stack[SP] < Value_t(-1) || Stack[SP] > Value_t(1)))
+              { mData->mEvalErrorType=4; return Value_t(0); }
+              Stack[SP] = fp_asin(Stack[SP]); break;
+
+          case cAsinh: Stack[SP] = fp_asinh(Stack[SP]); break;
+
+          case  cAtan: Stack[SP] = fp_atan(Stack[SP]); break;
+
+          case cAtan2: Stack[SP-1] = fp_atan2(Stack[SP-1], Stack[SP]);
+                       --SP; break;
+
+          case cAtanh:
+              if(IsComplexType<Value_t>::result
+              ?  (Stack[SP] == Value_t(-1) || Stack[SP] == Value_t(1))
+              :  (Stack[SP] <= Value_t(-1) || Stack[SP] >= Value_t(1)))
+              { mData->mEvalErrorType=4; return Value_t(0); }
+              Stack[SP] = fp_atanh(Stack[SP]); break;
+
+          case  cCbrt: Stack[SP] = fp_cbrt(Stack[SP]); break;
+
+          case  cCeil: Stack[SP] = fp_ceil(Stack[SP]); break;
+
+          case   cCos: Stack[SP] = fp_cos(Stack[SP]); break;
+
+          case  cCosh: Stack[SP] = fp_cosh(Stack[SP]); break;
+
+          case   cCot:
+              {
+                  const Value_t t = fp_tan(Stack[SP]);
+                  if(t == Value_t(0))
+                  { mData->mEvalErrorType=1; return Value_t(0); }
+                  Stack[SP] = Value_t(1)/t; break;
+              }
+
+          case   cCsc:
+              {
+                  const Value_t s = fp_sin(Stack[SP]);
+                  if(s == Value_t(0))
+                  { mData->mEvalErrorType=1; return Value_t(0); }
+                  Stack[SP] = Value_t(1)/s; break;
+              }
+
+
+          case   cExp: Stack[SP] = fp_exp(Stack[SP]); break;
+
+          case   cExp2: Stack[SP] = fp_exp2(Stack[SP]); break;
+
+          case cFloor: Stack[SP] = fp_floor(Stack[SP]); break;
+
+          case cHypot:
+              Stack[SP-1] = fp_hypot(Stack[SP-1], Stack[SP]);
+              --SP; break;
+
+          case    cIf:
+                  if(fp_truth(Stack[SP--]))
+                      IP += 2;
+                  else
+                  {
+                      const unsigned* buf = &byteCode[IP+1];
+                      IP = buf[0];
+                      DP = buf[1];
+                  }
+                  break;
+
+          case   cInt: Stack[SP] = fp_int(Stack[SP]); break;
+
+          case   cLog:
+              if(IsComplexType<Value_t>::result
+               ?   Stack[SP] == Value_t(0)
+               :   !(Stack[SP] > Value_t(0)))
+              { mData->mEvalErrorType=3; return Value_t(0); }
+              Stack[SP] = fp_log(Stack[SP]); break;
+
+          case cLog10:
+              if(IsComplexType<Value_t>::result
+               ?   Stack[SP] == Value_t(0)
+               :   !(Stack[SP] > Value_t(0)))
+              { mData->mEvalErrorType=3; return Value_t(0); }
+              Stack[SP] = fp_log10(Stack[SP]);
+              break;
+
+          case  cLog2:
+              if(IsComplexType<Value_t>::result
+               ?   Stack[SP] == Value_t(0)
+               :   !(Stack[SP] > Value_t(0)))
+              { mData->mEvalErrorType=3; return Value_t(0); }
+              Stack[SP] = fp_log2(Stack[SP]);
+              break;
+
+          case   cMax: Stack[SP-1] = fp_max(Stack[SP-1], Stack[SP]);
+                       --SP; break;
+
+          case   cMin: Stack[SP-1] = fp_min(Stack[SP-1], Stack[SP]);
+                       --SP; break;
+
+          case   cPow:
+              // x:Negative ^ y:NonInteger is failure,
+              // except when the reciprocal of y forms an integer
+              /*if(IsComplexType<Value_t>::result == false
+              && Stack[SP-1] < Value_t(0) &&
+                 !isInteger(Stack[SP]) &&
+                 !isInteger(1.0 / Stack[SP]))
+              { mEvalErrorType=3; return Value_t(0); }*/
+              // x:0 ^ y:negative is failure
+              if(Stack[SP-1] == Value_t(0) &&
+                 Stack[SP] < Value_t(0))
+              { mData->mEvalErrorType=3; return Value_t(0); }
+              Stack[SP-1] = fp_pow(Stack[SP-1], Stack[SP]);
+              --SP; break;
+
+          case  cTrunc: Stack[SP] = fp_trunc(Stack[SP]); break;
+
+          case   cSec:
+              {
+                  const Value_t c = fp_cos(Stack[SP]);
+                  if(c == Value_t(0))
+                  { mData->mEvalErrorType=1; return Value_t(0); }
+                  Stack[SP] = Value_t(1)/c; break;
+              }
+
+          case   cSin: Stack[SP] = fp_sin(Stack[SP]); break;
+
+          case  cSinh: Stack[SP] = fp_sinh(Stack[SP]); break;
+
+          case  cSqrt:
+              if(IsComplexType<Value_t>::result == false &&
+                 Stack[SP] < Value_t(0))
+              { mData->mEvalErrorType=2; return Value_t(0); }
+              Stack[SP] = fp_sqrt(Stack[SP]); break;
+
+          case   cTan: Stack[SP] = fp_tan(Stack[SP]); break;
+
+          case  cTanh: Stack[SP] = fp_tanh(Stack[SP]); break;
+
+
+// Misc:
+          case cImmed: Stack[++SP] = immed[DP++]; break;
+
+          case  cJump:
+              {
+                  const unsigned* buf = &byteCode[IP+1];
+                  IP = buf[0];
+                  DP = buf[1];
+                  break;
+              }
+
+// Operators:
+          case   cNeg: Stack[SP] = -Stack[SP]; break;
+          case   cAdd: Stack[SP-1] += Stack[SP]; --SP; break;
+          case   cSub: Stack[SP-1] -= Stack[SP]; --SP; break;
+          case   cMul: Stack[SP-1] *= Stack[SP]; --SP; break;
+
+          case   cDiv:
+              if(Stack[SP] == Value_t(0))
+              { mData->mEvalErrorType=1; return Value_t(0); }
+              Stack[SP-1] /= Stack[SP]; --SP; break;
+
+          case   cMod:
+              if(Stack[SP] == Value_t(0))
+              { mData->mEvalErrorType=1; return Value_t(0); }
+              Stack[SP-1] = fp_mod(Stack[SP-1], Stack[SP]);
+              --SP; break;
+
+          case cEqual:
+              Stack[SP-1] = fp_equal(Stack[SP-1], Stack[SP]);
+              --SP; break;
+
+          case cNEqual:
+              Stack[SP-1] = fp_nequal(Stack[SP-1], Stack[SP]);
+              --SP; break;
+
+          case  cLess:
+              Stack[SP-1] = fp_less(Stack[SP-1], Stack[SP]);
+              --SP; break;
+
+          case  cLessOrEq:
+              Stack[SP-1] = fp_lessOrEq(Stack[SP-1], Stack[SP]);
+              --SP; break;
+
+          case cGreater:
+              Stack[SP-1] = fp_less(Stack[SP], Stack[SP-1]);
+              --SP; break;
+
+          case cGreaterOrEq:
+              Stack[SP-1] = fp_lessOrEq(Stack[SP], Stack[SP-1]);
+              --SP; break;
+
+          case   cNot: Stack[SP] = fp_not(Stack[SP]); break;
+
+          case cNotNot: Stack[SP] = fp_notNot(Stack[SP]); break;
+
+          case   cAnd:
+              Stack[SP-1] = fp_and(Stack[SP-1], Stack[SP]);
+              --SP; break;
+
+          case    cOr:
+              Stack[SP-1] = fp_or(Stack[SP-1], Stack[SP]);
+              --SP; break;
+
+// Degrees-radians conversion:
+          case   cDeg: Stack[SP] = RadiansToDegrees(Stack[SP]); break;
+          case   cRad: Stack[SP] = DegreesToRadians(Stack[SP]); break;
+
+// User-defined function calls:
+          case cFCall:
+              {
+                  const unsigned index = byteCode[++IP];
+                  const unsigned params = mData->mFuncPtrs[index].mParams;
+                  const Value_t retVal =
+                      mData->mFuncPtrs[index].mRawFuncPtr ?
+                      mData->mFuncPtrs[index].mRawFuncPtr(&Stack[SP-params+1]) :
+                      mData->mFuncPtrs[index].mFuncWrapperPtr->callFunction
+                      (&Stack[SP-params+1]);
+                  SP -= int(params)-1;
+                  Stack[SP] = retVal;
+                  break;
+              }
+
+          case cPCall:
+              {
+                  unsigned index = byteCode[++IP];
+                  unsigned params = mData->mFuncParsers[index].mParams;
+                  Value_t retVal =
+                      mData->mFuncParsers[index].mParserPtr->Eval
+                      (&Stack[SP-params+1]);
+                  SP -= int(params)-1;
+                  Stack[SP] = retVal;
+                  const int error =
+                      mData->mFuncParsers[index].mParserPtr->EvalError();
+                  if(error)
+                  {
+                      mData->mEvalErrorType = error;
+                      return 0;
+                  }
+                  break;
+              }
+
+
+          case   cFetch:
+              {
+                  unsigned stackOffs = byteCode[++IP];
+                  Stack[SP+1] = Stack[stackOffs]; ++SP;
+                  break;
+              }
+
+#ifdef FP_SUPPORT_OPTIMIZER
+          case   cPopNMov:
+              {
+                  unsigned stackOffs_target = byteCode[++IP];
+                  unsigned stackOffs_source = byteCode[++IP];
+                  Stack[stackOffs_target] = Stack[stackOffs_source];
+                  SP = stackOffs_target;
+                  break;
+              }
+
+          case  cLog2by:
+              if(IsComplexType<Value_t>::result
+               ?   Stack[SP-1] == Value_t(0)
+               :   !(Stack[SP-1] > Value_t(0)))
+              { mData->mEvalErrorType=3; return Value_t(0); }
+              Stack[SP-1] = fp_log2(Stack[SP-1]) * Stack[SP];
+              --SP;
+              break;
+
+          case cNop: break;
+#endif // FP_SUPPORT_OPTIMIZER
+
+          case cSinCos:
+              fp_sinCos(Stack[SP], Stack[SP+1], Stack[SP]);
+              ++SP;
+              break;
+          case cSinhCosh:
+              fp_sinhCosh(Stack[SP], Stack[SP+1], Stack[SP]);
+              ++SP;
+              break;
+
+          case cAbsNot:
+              Stack[SP] = fp_absNot(Stack[SP]); break;
+          case cAbsNotNot:
+              Stack[SP] = fp_absNotNot(Stack[SP]); break;
+          case cAbsAnd:
+              Stack[SP-1] = fp_absAnd(Stack[SP-1], Stack[SP]);
+              --SP; break;
+          case cAbsOr:
+              Stack[SP-1] = fp_absOr(Stack[SP-1], Stack[SP]);
+              --SP; break;
+          case cAbsIf:
+              if(fp_absTruth(Stack[SP--]))
+                  IP += 2;
+              else
+              {
+                  const unsigned* buf = &byteCode[IP+1];
+                  IP = buf[0];
+                  DP = buf[1];
+              }
+              break;
+
+          case   cDup: Stack[SP+1] = Stack[SP]; ++SP; break;
+
+          case   cInv:
+              if(Stack[SP] == Value_t(0))
+              { mData->mEvalErrorType=1; return Value_t(0); }
+              Stack[SP] = Value_t(1)/Stack[SP];
+              break;
+
+          case   cSqr:
+              Stack[SP] = Stack[SP]*Stack[SP];
+              break;
+
+          case   cRDiv:
+              if(Stack[SP-1] == Value_t(0))
+              { mData->mEvalErrorType=1; return Value_t(0); }
+              Stack[SP-1] = Stack[SP] / Stack[SP-1]; --SP; break;
+
+          case   cRSub: Stack[SP-1] = Stack[SP] - Stack[SP-1]; --SP; break;
+
+          case   cRSqrt:
+              if(Stack[SP] == Value_t(0))
+              { mData->mEvalErrorType=1; return Value_t(0); }
+              Stack[SP] = Value_t(1) / fp_sqrt(Stack[SP]); break;
+
+#ifdef FP_SUPPORT_COMPLEX_NUMBERS
+          case   cReal: Stack[SP] = fp_real(Stack[SP]); break;
+          case   cImag: Stack[SP] = fp_imag(Stack[SP]); break;
+          case   cArg:  Stack[SP] = fp_arg(Stack[SP]); break;
+          case   cConj: Stack[SP] = fp_conj(Stack[SP]); break;
+          case   cPolar:
+              Stack[SP-1] = fp_polar(Stack[SP-1], Stack[SP]);
+              --SP; break;
+#endif
+
+
+// Variables:
+          default:
+              Stack[++SP] = Vars[byteCode[IP]-VarBegin];
+        }
+    }
+
+    mData->mEvalErrorType=0;
+    return Stack[SP];
+}
+
+
+//===========================================================================
+// Variable deduction
+//===========================================================================
+namespace
+{
+    template<typename Value_t>
+    int deduceVariables(FunctionParserBase<Value_t>& fParser,
+                        const char* funcStr,
+                        std::string& destVarString,
+                        int* amountOfVariablesFound,
+                        std::vector<std::string>* destVarNames,
+                        bool useDegrees)
+    {
+        typedef std::set<std::string> StrSet;
+        StrSet varNames;
+
+        int oldIndex = -1;
+
+        while(true)
+        {
+            destVarString.clear();
+            for(StrSet::iterator iter = varNames.begin();
+                iter != varNames.end();
+                ++iter)
+            {
+                if(iter != varNames.begin()) destVarString += ",";
+                destVarString += *iter;
+            }
+
+            const int index =
+                fParser.Parse(funcStr, destVarString, useDegrees);
+            if(index < 0) break;
+            if(index == oldIndex) return index;
+
+            unsigned nameLength = readIdentifier<Value_t>(funcStr + index);
+            if(nameLength & 0x80000000U) return index;
+            if(nameLength == 0) return index;
+
+            varNames.insert(std::string(funcStr + index, nameLength));
+            oldIndex = index;
+        }
+
+        if(amountOfVariablesFound)
+            *amountOfVariablesFound = int(varNames.size());
+
+        if(destVarNames)
+            destVarNames->assign(varNames.begin(), varNames.end());
+
+        return -1;
+    }
+}
+
+template<typename Value_t>
+int FunctionParserBase<Value_t>::ParseAndDeduceVariables
+(const std::string& function,
+ int* amountOfVariablesFound,
+ bool useDegrees)
+{
+    std::string varString;
+    return deduceVariables(*this, function.c_str(), varString,
+                           amountOfVariablesFound, 0, useDegrees);
+}
+
+template<typename Value_t>
+int FunctionParserBase<Value_t>::ParseAndDeduceVariables
+(const std::string& function,
+ std::string& resultVarString,
+ int* amountOfVariablesFound,
+ bool useDegrees)
+{
+    std::string varString;
+    const int index =
+        deduceVariables(*this, function.c_str(), varString,
+                        amountOfVariablesFound, 0, useDegrees);
+    if(index < 0) resultVarString = varString;
+    return index;
+}
+
+template<typename Value_t>
+int FunctionParserBase<Value_t>::ParseAndDeduceVariables
+(const std::string& function,
+ std::vector<std::string>& resultVars,
+ bool useDegrees)
+{
+    std::string varString;
+    std::vector<std::string> vars;
+    const int index =
+        deduceVariables(*this, function.c_str(), varString,
+                        0, &vars, useDegrees);
+    if(index < 0) resultVars.swap(vars);
+    return index;
+}
+
+
+#ifdef FUNCTIONPARSER_SUPPORT_DEBUGGING
+//===========================================================================
+// Bytecode injection
+//===========================================================================
+template<typename Value_t>
+void FunctionParserBase<Value_t>::InjectRawByteCode
+(const unsigned* bytecode, unsigned bytecodeAmount,
+ const Value_t* immed, unsigned immedAmount, unsigned stackSize)
+{
+    CopyOnWrite();
+
+    mData->mByteCode.assign(bytecode, bytecode + bytecodeAmount);
+    mData->mImmed.assign(immed, immed + immedAmount);
+    mData->mStackSize = stackSize;
+
+#ifndef FP_USE_THREAD_SAFE_EVAL
+    mData->mStack.resize(stackSize);
+#endif
+}
+
+//===========================================================================
+// Debug output
+//===========================================================================
+#include <iomanip>
+#include <sstream>
+namespace
+{
+    inline void printHex(std::ostream& dest, unsigned n)
+    {
+        std::ios::fmtflags flags = dest.flags();
+        dest.width(4); dest.fill('0'); std::hex(dest); //uppercase(dest);
+        dest << n;
+        dest.flags(flags);
+    }
+
+    void padLine(std::ostringstream& dest, unsigned destLength)
+    {
+        for(std::size_t currentLength = dest.str().length();
+            currentLength < destLength;
+            ++currentLength)
+        {
+            dest << ' ';
+        }
+    }
+
+    const struct PowiMuliType
+    {
+        unsigned opcode_square;
+        unsigned opcode_cumulate;
+        unsigned opcode_invert;
+        unsigned opcode_half;
+        unsigned opcode_invhalf;
+    } iseq_powi = {cSqr,cMul,cInv,cSqrt,cRSqrt},
+      iseq_muli = {~unsigned(0), cAdd,cNeg, ~unsigned(0),~unsigned(0) };
+
+    template<typename Value_t>
+    Value_t ParsePowiMuli(
+        const PowiMuliType& opcodes,
+        const std::vector<unsigned>& ByteCode, unsigned& IP,
+        unsigned limit,
+        std::size_t factor_stack_base,
+        std::vector<Value_t>& stack,
+        bool IgnoreExcess)
+    {
+        Value_t result = Value_t(1);
+        while(IP < limit)
+        {
+            if(ByteCode[IP] == opcodes.opcode_square)
+            {
+                if(!isInteger(result)) break;
+                result *= Value_t(2);
+                ++IP;
+                continue;
+            }
+            if(ByteCode[IP] == opcodes.opcode_invert)
+            {
+                if(result < Value_t(0)) break;
+                result = -result;
+                ++IP;
+                continue;
+            }
+            if(ByteCode[IP] == opcodes.opcode_half)
+            {
+                if(result > Value_t(0) && isEvenInteger(result))
+                    break;
+                if(isInteger(result * Value_t(0.5))) break;
+                result *= Value_t(0.5);
+                ++IP;
+                continue;
+            }
+            if(ByteCode[IP] == opcodes.opcode_invhalf)
+            {
+                if(result > Value_t(0) && isEvenInteger(result))
+                    break;
+                if(isInteger(result * Value_t(-0.5))) break;
+                result *= Value_t(-0.5);
+                ++IP;
+                continue;
+            }
+
+            unsigned dup_fetch_pos = IP;
+            Value_t lhs = Value_t(1);
+
+            if(ByteCode[IP] == cFetch)
+            {
+                unsigned index = ByteCode[++IP];
+                if(index < factor_stack_base
+                || std::size_t(index-factor_stack_base) >= stack.size())
+                {
+                    // It wasn't a powi-fetch after all
+                    IP = dup_fetch_pos;
+                    break;
+                }
+                lhs = stack[index - factor_stack_base];
+                // Note: ^This assumes that cFetch of recentmost
+                //        is always converted into cDup.
+                goto dup_or_fetch;
+            }
+
+            if(ByteCode[IP] == cDup)
+            {
+                lhs = result;
+                goto dup_or_fetch;
+
+            dup_or_fetch:
+                stack.push_back(result);
+                ++IP;
+                Value_t subexponent = ParsePowiMuli
+                    (opcodes,
+                     ByteCode, IP, limit,
+                     factor_stack_base, stack,
+                     IgnoreExcess);
+                if(IP >= limit && IgnoreExcess)
+                    return lhs*subexponent;
+                if(IP >= limit || ByteCode[IP] != opcodes.opcode_cumulate)
+                {
+                    // It wasn't a powi-dup after all
+                    IP = dup_fetch_pos;
+                    break;
+                }
+                ++IP; // skip opcode_cumulate
+                stack.pop_back();
+                result += lhs*subexponent;
+                continue;
+            }
+            break;
+        }
+        return result;
+    }
+
+    template<typename Value_t>
+    Value_t ParsePowiSequence(const std::vector<unsigned>& ByteCode,
+                              unsigned& IP, unsigned limit,
+                              std::size_t factor_stack_base,
+                              bool IgnoreExcess = false)
+    {
+        std::vector<Value_t> stack;
+        stack.push_back(Value_t(1));
+        return ParsePowiMuli(iseq_powi, ByteCode, IP, limit,
+                             factor_stack_base, stack,
+                             IgnoreExcess);
+    }
+
+    template<typename Value_t>
+    Value_t ParseMuliSequence(const std::vector<unsigned>& ByteCode,
+                              unsigned& IP, unsigned limit,
+                              std::size_t factor_stack_base,
+                              bool IgnoreExcess = false)
+    {
+        std::vector<Value_t> stack;
+        stack.push_back(Value_t(1));
+        return ParsePowiMuli(iseq_muli, ByteCode, IP, limit,
+                             factor_stack_base, stack,
+                             IgnoreExcess);
+    }
+
+    struct IfInfo
+    {
+        std::pair<int,std::string> condition;
+        std::pair<int,std::string> thenbranch;
+        unsigned endif_location;
+
+        IfInfo() : condition(), thenbranch(), endif_location() { }
+    };
+}
+
+template<typename Value_t>
+void FunctionParserBase<Value_t>::PrintByteCode(std::ostream& dest,
+                                                bool showExpression) const
+{
+    dest << "Size of stack: " << mData->mStackSize << "\n";
+
+    std::ostringstream outputBuffer;
+    std::ostream& output = (showExpression ? outputBuffer : dest);
+
+    const std::vector<unsigned>& ByteCode = mData->mByteCode;
+    const std::vector<Value_t>& Immed = mData->mImmed;
+
+    std::vector<std::pair<int,std::string> > stack;
+    std::vector<IfInfo> if_stack;
+
+    for(unsigned IP = 0, DP = 0; IP <= ByteCode.size(); ++IP)
+    {
+    after_powi_or_muli:;
+        std::string n;
+        bool out_params = false;
+        unsigned params = 2, produces = 1, opcode = 0;
+
+        if(showExpression && !if_stack.empty() &&
+          (   // Normal If termination rule:
+              if_stack.back().endif_location == IP
+              // This rule matches when cJumps are threaded:
+           || (IP < ByteCode.size() && ByteCode[IP] == cJump
+               && !if_stack.back().thenbranch.second.empty())
+          ))
+        {
+            printHex(output, IP);
+            if(if_stack.back().endif_location == IP)
+                output << ": ----- (phi)";
+            else
+                output << ": ----- (phi+)";
+
+            stack.resize(stack.size()+2);
+            std::swap(stack[stack.size()-3], stack[stack.size()-1]);
+            std::swap(if_stack.back().condition,  stack[stack.size()-3]);
+            std::swap(if_stack.back().thenbranch, stack[stack.size()-2]);
+            opcode = cIf;
+            params = 3;
+            --IP;
+            if_stack.pop_back();
+        }
+        else
+        {
+            if(IP >= ByteCode.size()) break;
+            opcode = ByteCode[IP];
+
+            if(showExpression && (
+                opcode == cSqr || opcode == cDup
+             || opcode == cInv
+             || opcode == cSqrt || opcode == cRSqrt
+             || opcode == cFetch
+            ))
+            {
+                unsigned changed_ip = IP;
+                Value_t exponent =
+                    ParsePowiSequence<Value_t>
+                    (ByteCode, changed_ip,
+                     if_stack.empty()
+                     ? (unsigned)ByteCode.size()
+                     : if_stack.back().endif_location,
+                     stack.size()-1);
+                std::string        operation_prefix;
+                std::ostringstream operation_value;
+                int prio = 0;
+                if(exponent == Value_t(1.0))
+                {
+                    if(opcode != cDup) goto not_powi_or_muli;
+                    Value_t factor =
+                        ParseMuliSequence<Value_t>
+                        (ByteCode, changed_ip,
+                         if_stack.empty()
+                         ? (unsigned)ByteCode.size()
+                         : if_stack.back().endif_location,
+                         stack.size()-1);
+                    if(factor == Value_t(1) || factor == Value_t(-1))
+                        goto not_powi_or_muli;
+                    operation_prefix = "*";
+                    operation_value << factor;
+                    prio = 3;
+                }
+                else
+                {
+                    prio = 2;
+                    operation_prefix = "^";
+                    operation_value << exponent;
+                }
+
+                //unsigned explanation_before = changed_ip-2;
+                unsigned explanation_before = changed_ip-1;
+
+                const char* explanation_prefix = "_";
+                for(const unsigned first_ip = IP; IP < changed_ip; ++IP)
+                {
+                    printHex(output, IP);
+                    output << ": ";
+
+                    const char* sep = "|";
+                    if(first_ip+1 == changed_ip)
+                    { sep = "="; explanation_prefix = " "; }
+                    else if(IP   == first_ip) sep = "\\";
+                    else if(IP+1 == changed_ip) sep = "/";
+                    else explanation_prefix = "=";
+
+                    switch(ByteCode[IP])
+                    {
+                        case cInv: output << "inv"; break;
+                        case cNeg: output << "neg"; break;
+                        case cDup: output << "dup"; break;
+                        case cSqr: output << "sqr"; break;
+                        case cMul: output << "mul"; break;
+                        case cAdd: output << "add"; break;
+                        case cCbrt: output << "cbrt"; break;
+                        case cSqrt: output << "sqrt"; break;
+                        case cRSqrt: output << "rsqrt"; break;
+                        case cFetch:
+                        {
+                            unsigned index = ByteCode[++IP];
+                            output << "cFetch(" << index << ")";
+                            break;
+                        }
+                        default: break;
+                    }
+                    padLine(outputBuffer, 20);
+                    output << sep;
+                    if(IP >= explanation_before)
+                    {
+                        explanation_before = (unsigned)ByteCode.size();
+                        output << explanation_prefix
+                               << '[' << (stack.size()-1) << ']';
+                        std::string last = stack.back().second;
+                        if(stack.back().first >= prio)
+                            last = "(" + last + ")";
+                        output << last;
+                        output << operation_prefix;
+                        output << operation_value.str();
+                    }
+                    else
+                    {
+                        unsigned p = first_ip;
+                        Value_t exp = operation_prefix=="^" ?
+                            ParsePowiSequence<Value_t>
+                            (ByteCode, p, IP+1, stack.size()-1, true) :
+                            ParseMuliSequence<Value_t>
+                            (ByteCode, p, IP+1, stack.size()-1, true);
+                        std::string last = stack.back().second;
+                        if(stack.back().first >= prio)
+                            last = "(" + last + ")";
+                        output << " ..." << last;
+                        output << operation_prefix;
+                        output << exp;
+                    }
+                    dest << outputBuffer.str() << std::endl;
+                    outputBuffer.str("");
+                }
+
+                std::string& last = stack.back().second;
+                if(stack.back().first >= prio)
+                    last = "(" + last + ")";
+                last += operation_prefix;
+                last += operation_value.str();
+                stack.back().first = prio;
+
+                goto after_powi_or_muli;
+            }
+        not_powi_or_muli:;
+            printHex(output, IP);
+            output << ": ";
+
+            switch(opcode)
+            {
+              case cIf:
+              {
+                  unsigned label = ByteCode[IP+1]+1;
+                  output << "jz ";
+                  printHex(output, label);
+                  params = 1;
+                  produces = 0;
+                  IP += 2;
+
+                  if_stack.resize(if_stack.size() + 1);
+                  std::swap( if_stack.back().condition, stack.back() );
+                  if_stack.back().endif_location = (unsigned) ByteCode.size();
+                  stack.pop_back();
+                  break;
+              }
+              case cAbsIf:
+              {
+                  unsigned dp    = ByteCode[IP+2];
+                  unsigned label = ByteCode[IP+1]+1;
+                  output << "jz_abs " << dp << ",";
+                  printHex(output, label);
+                  params = 1;
+                  produces = 0;
+                  IP += 2;
+
+                  if_stack.resize(if_stack.size() + 1);
+                  std::swap( if_stack.back().condition, stack.back() );
+                  if_stack.back().endif_location = (unsigned) ByteCode.size();
+                  stack.pop_back();
+                  break;
+              }
+
+              case cJump:
+              {
+                  unsigned dp    = ByteCode[IP+2];
+                  unsigned label = ByteCode[IP+1]+1;
+
+                  if(!if_stack.empty() && !stack.empty())
+                  {
+                      std::swap(if_stack.back().thenbranch, stack.back());
+                      if_stack.back().endif_location = label;
+                      stack.pop_back();
+                  }
+
+                  output << "jump " << dp << ",";
+                  printHex(output, label);
+                  params = 0;
+                  produces = 0;
+                  IP += 2;
+                  break;
+              }
+              case cImmed:
+              {
+                  if(showExpression)
+                  {
+                      std::ostringstream buf;
+                      buf.precision(8);
+                      buf << Immed[DP];
+                      stack.push_back( std::make_pair(0, buf.str()) );
+                  }
+                  output.precision(8);
+                  output << "push " << Immed[DP];
+                  ++DP;
+                  produces = 0;
+                  break;
+              }
+
+              case cFCall:
+                  {
+                      const unsigned index = ByteCode[++IP];
+                      params = mData->mFuncPtrs[index].mParams;
+                      static std::string name;
+                      name = "f:" + findName(mData->mNamePtrs, index,
+                                             NameData<Value_t>::FUNC_PTR);
+                      n = name.c_str();
+                      out_params = true;
+                      break;
+                  }
+
+              case cPCall:
+                  {
+                      const unsigned index = ByteCode[++IP];
+                      params = mData->mFuncParsers[index].mParams;
+                      static std::string name;
+                      name = "p:" + findName(mData->mNamePtrs, index,
+                                             NameData<Value_t>::PARSER_PTR);
+                      n = name.c_str();
+                      out_params = true;
+                      break;
+                  }
+
+              default:
+                  if(IsVarOpcode(opcode))
+                  {
+                      if(showExpression)
+                      {
+                          stack.push_back(std::make_pair(0,
+                              (findName(mData->mNamePtrs, opcode,
+                                        NameData<Value_t>::VARIABLE))));
+                      }
+                      output << "push Var" << opcode-VarBegin;
+                      produces = 0;
+                  }
+                  else
+                  {
+                      switch(OPCODE(opcode))
+                      {
+                        case cNeg: n = "neg"; params = 1; break;
+                        case cAdd: n = "add"; break;
+                        case cSub: n = "sub"; break;
+                        case cMul: n = "mul"; break;
+                        case cDiv: n = "div"; break;
+                        case cMod: n = "mod"; break;
+                        case cPow: n = "pow"; break;
+                        case cEqual: n = "eq"; break;
+                        case cNEqual: n = "neq"; break;
+                        case cLess: n = "lt"; break;
+                        case cLessOrEq: n = "le"; break;
+                        case cGreater: n = "gt"; break;
+                        case cGreaterOrEq: n = "ge"; break;
+                        case cAnd: n = "and"; break;
+                        case cOr: n = "or"; break;
+                        case cNot: n = "not"; params = 1; break;
+                        case cNotNot: n = "notnot"; params = 1; break;
+                        case cDeg: n = "deg"; params = 1; break;
+                        case cRad: n = "rad"; params = 1; break;
+
+                        case cFetch:
+                        {
+                            unsigned index = ByteCode[++IP];
+                            if(showExpression && index < stack.size())
+                                stack.push_back(stack[index]);
+                            output << "cFetch(" << index << ")";
+                            produces = 0;
+                            break;
+                        }
+    #ifdef FP_SUPPORT_OPTIMIZER
+                        case cLog2by: n = "log2by"; params = 2; out_params = 1; break;
+                        case cPopNMov:
+                        {
+                            std::size_t a = ByteCode[++IP];
+                            std::size_t b = ByteCode[++IP];
+                            if(showExpression && b < stack.size())
+                            {
+                                std::pair<int, std::string> stacktop(0, "?");
+                                if(b < stack.size()) stacktop = stack[b];
+                                stack.resize(a);
+                                stack.push_back(stacktop);
+                            }
+                            output << "cPopNMov(" << a << ", " << b << ")";
+                            produces = 0;
+                            break;
+                        }
+                        case cNop:
+                            output << "nop"; params = 0; produces = 0;
+                            break;
+    #endif
+                        case cSinCos:
+                        {
+                            if(showExpression)
+                            {
+                                std::pair<int, std::string> sin = stack.back();
+                                std::pair<int, std::string> cos(
+                                    0, "cos(" + sin.second + ")");
+                                sin.first = 0;
+                                sin.second = "sin(" + sin.second + ")";
+                                stack.back() = sin;
+                                stack.push_back(cos);
+                            }
+                            output << "sincos";
+                            produces = 0;
+                            break;
+                        }
+                        case cSinhCosh:
+                        {
+                            if(showExpression)
+                            {
+                                std::pair<int, std::string> sinh = stack.back();
+                                std::pair<int, std::string> cosh(
+                                    0, "cosh(" + sinh.second + ")");
+                                sinh.first = 0;
+                                sinh.second = "sinh(" + sinh.second + ")";
+                                stack.back() = sinh;
+                                stack.push_back(cosh);
+                            }
+                            output << "sinhcosh";
+                            produces = 0;
+                            break;
+                        }
+                        case cAbsAnd: n = "abs_and"; break;
+                        case cAbsOr:  n = "abs_or"; break;
+                        case cAbsNot: n = "abs_not"; params = 1; break;
+                        case cAbsNotNot: n = "abs_notnot"; params = 1; break;
+                        case cDup:
+                        {
+                            if(showExpression)
+                                stack.push_back(stack.back());
+                            output << "dup";
+                            produces = 0;
+                            break;
+                        }
+                        case cInv: n = "inv"; params = 1; break;
+                        case cSqr: n = "sqr"; params = 1; break;
+                        case cRDiv: n = "rdiv"; break;
+                        case cRSub: n = "rsub"; break;
+                        case cRSqrt: n = "rsqrt"; params = 1; break;
+
+                        default:
+                            n = Functions[opcode-cAbs].name;
+                            params = Functions[opcode-cAbs].params;
+                            out_params = params != 1;
+                      }
+                  }
+            }
+        }
+        if(produces) output << n;
+        if(out_params) output << " (" << params << ")";
+        if(showExpression)
+        {
+            padLine(outputBuffer, 20);
+
+            if(produces > 0)
+            {
+                std::ostringstream buf;
+                const char *paramsep = ",", *suff = "";
+                int prio = 0; bool commutative = false;
+                switch(opcode)
+                {
+                  case cIf: buf << "if("; suff = ")";
+                      break;
+                  case cAbsIf: buf << "if("; suff = ")";
+                      break;
+                  case cOr:  prio = 6; paramsep = "|"; commutative = true;
+                      break;
+                  case cAnd: prio = 5; paramsep = "&"; commutative = true;
+                      break;
+                  case cAdd: prio = 4; paramsep = "+"; commutative = true;
+                      break;
+                  case cSub: prio = 4; paramsep = "-";
+                      break;
+                  case cMul: prio = 3; paramsep = "*"; commutative = true;
+                      break;
+                  case cDiv: prio = 3; paramsep = "/";
+                      break;
+                  case cPow: prio = 2; paramsep = "^";
+                      break;
+                  case cAbsOr:  prio = 6; paramsep = "|"; commutative = true;
+                      break;
+                  case cAbsAnd: prio = 5; paramsep = "&"; commutative = true;
+                      break;
+                  case cSqr: prio = 2; suff = "^2";
+                      break;
+                  case cNeg: buf << "(-("; suff = "))";
+                      break;
+                  case cNot: buf << "(!("; suff = "))";
+                      break;
+                  default: buf << n << '('; suff = ")";
+                }
+
+                const char* sep = "";
+                for(unsigned a=0; a<params; ++a)
+                {
+                    buf << sep;
+                    if(stack.size() + a < params)
+                        buf << "?";
+                    else
+                    {
+                        const std::pair<int,std::string>& prev =
+                            stack[stack.size() - params + a];
+                        if(prio > 0 && (prev.first > prio ||
+                                        (prev.first==prio && !commutative)))
+                            buf << '(' << prev.second << ')';
+                        else
+                            buf << prev.second;
+                    }
+                    sep = paramsep;
+                }
+                if(stack.size() >= params)
+                    stack.resize(stack.size() - params);
+                else
+                    stack.clear();
+                buf << suff;
+                stack.push_back(std::make_pair(prio, buf.str()));
+                //if(n.size() <= 4 && !out_params) padLine(outputBuffer, 20);
+            }
+            //padLine(outputBuffer, 20);
+            output << "= ";
+            if(((opcode == cIf || opcode == cAbsIf) && params != 3)
+              || opcode == cJump
+    #ifdef FP_SUPPORT_OPTIMIZER
+              || opcode == cNop
+    #endif
+                )
+                output << "(void)";
+            else if(stack.empty())
+                output << "[?] ?";
+            else
+                output << '[' << (stack.size()-1) << ']'
+                       << stack.back().second;
+        }
+
+        if(showExpression)
+        {
+            dest << outputBuffer.str() << std::endl;
+            outputBuffer.str("");
+        }
+        else
+            output << std::endl;
+    }
+    dest << std::flush;
+}
+#endif
+
+
+#ifndef FP_SUPPORT_OPTIMIZER
+template<typename Value_t>
+void FunctionParserBase<Value_t>::Optimize()
+{
+    // Do nothing if no optimizations are supported.
+}
+#endif
+
+
+#define FUNCTIONPARSER_INSTANTIATE_CLASS(type) \
+    template class FunctionParserBase< type >;
+
+#ifndef FP_DISABLE_DOUBLE_TYPE
+FUNCTIONPARSER_INSTANTIATE_CLASS(double)
+#endif
+
+#ifdef FP_SUPPORT_FLOAT_TYPE
+FUNCTIONPARSER_INSTANTIATE_CLASS(float)
+#endif
+
+#ifdef FP_SUPPORT_LONG_DOUBLE_TYPE
+FUNCTIONPARSER_INSTANTIATE_CLASS(long double)
+#endif
+
+#ifdef FP_SUPPORT_LONG_INT_TYPE
+FUNCTIONPARSER_INSTANTIATE_CLASS(long)
+#endif
+
+#ifdef FP_SUPPORT_MPFR_FLOAT_TYPE
+FUNCTIONPARSER_INSTANTIATE_CLASS(MpfrFloat)
+#endif
+
+#ifdef FP_SUPPORT_GMP_INT_TYPE
+FUNCTIONPARSER_INSTANTIATE_CLASS(GmpInt)
+#endif
+
+#ifdef FP_SUPPORT_COMPLEX_DOUBLE_TYPE
+FUNCTIONPARSER_INSTANTIATE_CLASS(std::complex<double>)
+#endif
+
+#ifdef FP_SUPPORT_COMPLEX_FLOAT_TYPE
+FUNCTIONPARSER_INSTANTIATE_CLASS(std::complex<float>)
+#endif
+
+#ifdef FP_SUPPORT_COMPLEX_LONG_DOUBLE_TYPE
+FUNCTIONPARSER_INSTANTIATE_CLASS(std::complex<long double>)
+#endif