Sacado_trad2.hpp

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// @HEADER
// ***********************************************************************
//
//                           Sacado Package
//                 Copyright (2007) Sandia Corporation
//
// Under the terms of Contract DE-AC04-94AL85000 with Sandia Corporation,
// the U.S. Government retains certain rights in this software.
//
// This library is free software; you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as
// published by the Free Software Foundation; either version 2.1 of the
// License, or (at your option) any later version.
//
// This library is distributed in the hope that it will be useful, but
// WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
// Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307
// USA
// Questions? Contact David M. Gay (dmgay@sandia.gov) or Eric T. Phipps
// (etphipp@sandia.gov).
//
// ***********************************************************************
// @HEADER

// Extension of the RAD package (Reverse Automatic Differentiation) --
// a package specialized for function and gradient evaluations -- to
// Hessian-vector products.
// Written in 2007 by David M. Gay at Sandia National Labs, Albuquerque, NM.

#ifndef SACADO_TRAD2_H
#define SACADO_TRAD2_H

#include "Sacado_ConfigDefs.h"
#include "Sacado_trad_Traits.hpp"

#include <stddef.h>
#include <cmath>
#include <math.h>

#ifdef RAD_Const_WARN // ==> RAD_AUTO_AD_Const and RAD_DEBUG
#ifndef RAD_AUTO_AD_Const
#define RAD_AUTO_AD_Const
#endif
#ifndef RAD_DEBUG
#define RAD_DEBUG
#endif
extern "C" int RAD_Const_Warn(const void*);// outside any namespace for
          // ease in setting breakpoints
#endif // RAD_Const_WARN

#ifdef RAD_DEBUG
#include <cstdio>
#include <stdlib.h>
#endif

#ifndef RAD_AUTO_AD_Const
#ifdef RAD_DEBUG_BLOCKKEEP
#include <complex>  // must be here when SACADO_NAMESPACE is #defined
#endif
#endif

namespace Sacado {
namespace Rad2 {

// -DRAD_NO_USING_STDCC is needed, e.g., with Sun CC 5.7
#ifndef RAD_NO_USING_STDCC
  // Bring math functions into scope
  using std::exp;
  using std::log;
  using std::log10;
  using std::sqrt;
  using std::cos;
  using std::sin;
  using std::tan;
  using std::acos;
  using std::asin;
  using std::atan;
  using std::cosh;
  using std::sinh;
  using std::tanh;
  using std::abs;
  using std::fabs;
  using std::atan2;
  using std::pow;
#endif 

#ifdef RAD_AUTO_AD_Const
#undef RAD_DEBUG_BLOCKKEEP
#else 
#ifdef RAD_DEBUG_BLOCKKEEP
#if !(RAD_DEBUG_BLOCKKEEP > 0)
#undef RAD_DEBUG_BLOCKKEEP
#else
extern "C" void _uninit_f2c(void *x, int type, long len);

template <typename T>
struct UninitType {};

template <>
struct UninitType<float> {
  static const int utype = 4;
};

template <>
struct UninitType<double> {
  static const int utype = 5;
};

template <typename T>
struct UninitType< std::complex<T> > {
  static const int utype = UninitType<T>::utype + 2;
};

#endif /*RAD_DEBUG_BLOCKKEEP > 0*/
#endif /*RAD_DEBUG_BLOCKKEEP*/
#endif /*RAD_AUTO_AD_Const*/

 class RAD_DoubleIgnore {};

 template<typename T> class
DoubleAvoid {
 public:
  typedef double  dtype;
  typedef T ttype;
  };
 template<> class
DoubleAvoid<double> {
 public:
  typedef RAD_DoubleIgnore &dtype;
  typedef RAD_DoubleIgnore &ttype;
  };

#define Dtype typename DoubleAvoid<Double>::dtype
#define Ttype typename DoubleAvoid<Double>::ttype

 template<typename Double> class IndepADvar;
 template<typename Double> class ConstADvar;
 template<typename Double> class ConstADvari;
 template<typename Double> class ADvar;
 template<typename Double> class ADvar1;
 template<typename Double> class ADvar1g;
 template<typename Double> class ADvar1s;
 template<typename Double> class ADvar2;
 template<typename Double> class ADvar2g;
 template<typename Double> class ADvar2q;
 template<typename Double> class ADvari;
 template<typename Double> class ADvari_block;
 template<typename Double> class ADvarn;
 template<typename Double> class Derp;

 template<typename Double> struct
ADmemblock {  // We get memory in ADmemblock chunks and never give it back,
    // but reuse it once computations start anew after call(s) on
    // ADcontext::Gradcomp() or ADcontext::Weighted_Gradcomp().
  ADmemblock *next;
  Double memblk[2000];
  };

 template<typename Double> class
ADvari_block {
 public:
  typedef ADvari<Double> ADVari;
  enum { Gulp = 1021 };
  ADvari_block *next, *prev;
  ADVari **limit;
  ADVari *pADvari[Gulp];
  };

 template<typename Double> class
ADcontext { // A singleton class: one instance in radops.c
  typedef ADmemblock<Double> ADMemblock;
  typedef ADvari <Double> ADVari;
  typedef ADvar1 <Double> ADVar1;
  typedef ADvar2 <Double> ADVar2;
  typedef ADvarn <Double> ADVarn;
  typedef ADvar1g<Double> ADVar1g;
  typedef ADvar1s<Double> ADVar1s;
  typedef ADvar2g<Double> ADVar2g;
  typedef ADvar2q<Double> ADVar2q;
  typedef ADvari_block<Double> ADVari_block;
  ADMemblock *Busy, *Free;
  char *Mbase;
  size_t Mleft;
  ADVari **Ailimit, **Ainext;
  ADVari_block *Aibusy, *Aifree;
  ADMemblock *First;
  ADVari_block *AiFirst;
  double First0[(sizeof(ADMemblock) + sizeof(double) - 1) / sizeof(double)];
  double First1[(sizeof(ADVari_block) + sizeof(double) - 1) / sizeof(double)];
  void *new_ADmemblock(size_t);
  void new_ADvari_block();
  typedef ADvar<Double> ADVar;
  typedef Derp<Double> DErp;
  int rad_need_reinit;
  size_t rad_mleft_save;
#ifdef RAD_DEBUG_BLOCKKEEP
  int rad_busy_blocks;
  ADMemblock *rad_Oldcurmb;
#endif
 public:
  static const Double One, negOne;
  ADcontext();
  void *Memalloc(size_t len);
  static void Gradcomp();
  static void Hvprod(int, ADVar**, Double*, Double*);
  static void aval_reset(void);
  static void Weighted_Gradcomp(int, ADVar**, Double*);
  inline void ADvari_record(ADVari *x) {
    if (Ainext >= Ailimit)
      new_ADvari_block();
    *Ainext++ = x;
    }
  };

 template<typename Double> class
CADcontext: public ADcontext<Double> {  // for possibly constant ADvar values
 protected:
  bool fpval_implies_const;
 public:
  friend class ADvar<Double>;
  CADcontext(): ADcontext<Double>() { fpval_implies_const = false; }
  };

 template<typename Double> class
Derp {    // one derivative-propagation operation
 public:
  friend class ADvarn<Double>;
  typedef ADvari<Double> ADVari;
  static Derp *LastDerp;
  Derp *next;
  const Double *a;
  const ADVari *b;
  mutable ADVari *c;
  Derp(){};
  Derp(const ADVari *);
  Derp(const Double *, const ADVari *);
  Derp(const Double *, const ADVari *, const ADVari *);
  /* c->aval += a * b->aval; */
  };


// Now we use #define to overcome bad design in the C++ templating system

#define Ai const ADvari<Double>&
#define AI const IndepADvar<Double>&
#define T template<typename Double>
#define D Double
#define T1(f) \
T F f (AI); \
T F f (Ai);
#define T2(r,f) \
 T r f(Ai,Ai); \
 T r f(Ai,D); \
 T r f(Ai,Dtype); \
 T r f(Ai,long); \
 T r f(Ai,int); \
 T r f(D,Ai); \
 T r f(Dtype,Ai); \
 T r f(long,Ai); \
 T r f(int,Ai); \
 T r f(AI,D); \
 T r f(AI,Dtype); \
 T r f(AI,long); \
 T r f(AI,int); \
 T r f(D,AI); \
 T r f(Dtype,AI); \
 T r f(long,AI); \
 T r f(int,AI); \
 T r f(Ai,AI);\
 T r f(AI,Ai);\
 T r f(AI,AI);

#define F ADvari<Double>&
T2(F, operator+)
T2(F, operator-)
T2(F, operator*)
T2(F, operator/)
T2(F, atan2)
T2(F, pow)
T2(F, max)
T2(F, min)
T2(int, operator<)
T2(int, operator<=)
T2(int, operator==)
T2(int, operator!=)
T2(int, operator>=)
T2(int, operator>)
T1(operator+)
T1(operator-)
T1(abs)
T1(acos)
T1(acosh)
T1(asin)
T1(asinh)
T1(atan)
T1(atanh)
T1(cos)
T1(cosh)
T1(exp)
T1(log)
T1(log10)
T1(sin)
T1(sinh)
T1(sqrt)
T1(tan)
T1(tanh)
T1(fabs)

T F copy(AI);
T F copy(Ai);

#undef F
#undef T2
#undef T1
#undef D
#undef T
#undef AI
#undef Ai

} /* namespace Rad2 */
} /* namespace Sacado */
#define SNS Sacado::Rad2
namespace std { // Moved here from bottom for use in testing nesting of Rad with itself.
  using SNS::exp;
  using SNS::log;
  using SNS::log10;
  using SNS::sqrt;
  using SNS::cos;
  using SNS::sin;
  using SNS::tan;
  using SNS::acos;
  using SNS::asin;
  using SNS::atan;
  using SNS::cosh;
  using SNS::sinh;
  using SNS::tanh;
  using SNS::abs;
  using SNS::fabs;
  using SNS::atan2;
  using SNS::pow;
}
#undef SNS
namespace Sacado {
namespace Rad2 {

 template<typename Double>ADvari<Double>& ADf1(Double f, Double g, const IndepADvar<Double> &x);
 template<typename Double>ADvari<Double>& ADf2(Double f, Double gx, Double gy,
  const IndepADvar<Double> &x, const IndepADvar<Double> &y);
 template<typename Double>ADvari<Double>& ADfn(Double f, int n,
  const IndepADvar<Double> *x, const Double *g);

 template<typename Double> IndepADvar<Double>& ADvar_operatoreq(IndepADvar<Double>*,
  const ADvari<Double>&);
 template<typename Double> ADvar<Double>& ADvar_operatoreq(ADvar<Double>*, const ADvari<Double>&);
 template<typename Double> void AD_Const(const IndepADvar<Double>&);
 template<typename Double> void AD_Const1(Double*, const IndepADvar<Double>&);
 template<typename Double> ADvari<Double>& ADf1(Double, Double, const ADvari<Double>&);
 template<typename Double> ADvari<Double>& ADf2(Double, Double, Double,
  const ADvari<Double>&, const ADvari<Double>&);
 template<typename Double> ADvari<Double>& ADf2(Double, Double, Double,
  const IndepADvar<Double>&, const ADvari<Double>&);
 template<typename Double> ADvari<Double>& ADf2(Double, Double, Double,
  const ADvari<Double>&, const IndepADvar<Double>&);
 template<typename Double> Double val(const ADvari<Double>&);

 enum Advari_Opclass {
  Hv_const,
  Hv_copy,
  Hv_binary,
  Hv_unary,
  Hv_negate,
  Hv_plusLR,
  Hv_minusLR,
  Hv_timesL,
  Hv_timesLR,
  Hv_quotLR,
  Hv_nary
  };

 template<typename Double> ADvari<Double>&
ADf1(Double f, Double g, Double h, const ADvari<Double> &x);

 template<typename Double> ADvari<Double>&
ADf2(Double f, Double gx, Double gy, Double hxx,
      Double hxy, Double hyy, const ADvari<Double> &x, const ADvari<Double> &y);

 template<typename Double> ADvari<Double>&
ADfn(Double f, int n, const IndepADvar<Double> *x, const Double *g, const Double *h);

 template<typename Double> class
ADvari {  // implementation of an ADvar
 public:
  typedef Double value_type;
  typedef IndepADvar<Double> IndepADVar;
#ifdef RAD_AUTO_AD_Const
  friend class IndepADvar<Double>;
#ifdef RAD_Const_WARN
  mutable const IndepADVar *padv;
#else
 protected:
  mutable const IndepADVar *padv;
#endif //RAD_Const_WARN
 private:
  ADvari *Next;
  static ADvari *First_ADvari, **Last_ADvari;
 public:
#endif //RAD_AUTO_AD_Const
#ifdef RAD_DEBUG
  int gcgen;
  int opno;
  static int gcgen_cur, last_opno, zap_gcgen, zap_gcgen1, zap_opno;
  static FILE *debug_file;
#endif
  static ADcontext<Double> adc;
  Advari_Opclass opclass;
  Double Val;   // result of this operation
  mutable Double aval;  // adjoint -- partial of final result w.r.t. this Val
  mutable Double dO;  // deriv of op w.r.t. t in x + t*p
  mutable Double aO;  // adjoint (in Hv computation) of op
  mutable Double adO; // adjoint (in Hv computation) of dO
  void *operator new(size_t len) {
#ifdef RAD_DEBUG
    ADvari *rv = (ADvari*)ADvari::adc.Memalloc(len);
    rv->gcgen = gcgen_cur;
    rv->opno = ++last_opno;
    if (last_opno == zap_opno && gcgen_cur == zap_gcgen)
      printf("");
    return rv;
#else
    return ADvari::adc.Memalloc(len);
#endif
    }
  void operator delete(void*) {} /*Should never be called.*/
  inline ADvari(Advari_Opclass oc, Double t):
    opclass(oc), Val(t), aval(0.), dO(0.)
    { if (oc != Hv_const) ADvari::adc.ADvari_record(this); }
  inline ADvari(Advari_Opclass oc, Double t, Double ta):
    opclass(oc), Val(t), aval(ta), dO(0.)
    { if (oc != Hv_const) ADvari::adc.ADvari_record(this); }
 private:
  inline ADvari(): Val(0.), aval(0.), dO(0.) {} // prevent construction without value (?)
 public:
  friend class ConstADvari<Double>;
#ifdef RAD_AUTO_AD_Const
  friend class ADcontext<Double>;
  friend class ADvar<Double>;
  friend class ADvar1<Double>;
  friend class ADvar1s<Double>;
  friend class ADvar2<Double>;
  friend class ADvar2q<Double>;
  friend class ConstADvar<Double>;
  ADvari(const IndepADVar *, Double);
  ADvari(const IndepADVar *, Double, Double);
  ADvari(const IndepADVar *, Double, Double, int);
#endif
#define F friend
#define R ADvari&
#define Ai const ADvari&
#define T1(r,f) F r f <>(Ai);
#define T2(r,f) \
F r f <>(Ai,Ai); \
F r f <>(Ttype,Ai); \
F r f <>(Ai,Ttype); \
F r f <>(double,Ai); \
F r f <>(Ai,double); \
F r f <>(long,Ai); \
F r f <>(Ai,long); \
F r f <>(int,Ai); \
F r f <>(Ai,int);
  T1(R,operator+)
  T2(R,operator+)
  T1(R,operator-)
  T2(R,operator-)
  T2(R,operator*)
  T2(R,operator/)
  T1(R,abs)
  T1(R,acos)
  T1(R,acosh)
  T1(R,asin)
  T1(R,asinh)
  T1(R,atan)
  T1(R,atanh)
  T2(R,atan2)
  T2(R,max)
  T2(R,min)
  T1(R,cos)
  T1(R,cosh)
  T1(R,exp)
  T1(R,log)
  T1(R,log10)
  T2(R,pow)
  T1(R,sin)
  T1(R,sinh)
  T1(R,sqrt)
  T1(R,tan)
  T1(R,tanh)
  T1(R,fabs)
  T1(R,copy)
  T2(int,operator<)
  T2(int,operator<=)
  T2(int,operator==)
  T2(int,operator!=)
  T2(int,operator>=)
  T2(int,operator>)
#undef T2
#undef T1
#undef Ai
#undef R
#undef F

  friend ADvari& ADf1<>(Double f, Double g, Double h, const ADvari &x);
  friend ADvari& ADf2<>(Double f, Double gx, Double gy, Double hxx,
      Double hxy, Double hyy, const ADvari &x, const ADvari &y);
  friend ADvari& ADfn<>(Double f, int n, const IndepADVar *x,
      const Double *g, const Double *h);

  inline operator Double() { return this->Val; }
  inline operator Double() const { return this->Val; }
  };

 template<typename Double> class
ADvar1: public ADvari<Double> { // simplest unary ops
 public:
  typedef ADvari<Double> ADVari;
  Derp<Double> d;
  ADvar1(Advari_Opclass oc, Double val1, const Double *a1, const ADVari *c1):
    ADVari(oc,val1), d(a1,this,c1) {}
#ifdef RAD_AUTO_AD_Const
  typedef typename ADVari::IndepADVar IndepADVar;
  typedef ADvar<Double> ADVar;
  ADvar1(const IndepADVar*, const IndepADVar&);
  ADvar1(const IndepADVar*, const ADVari&);
  ADvar1(const Double val1, const Double *a1, const ADVari *c1, const ADVar *v):
      ADVari(val1), d(a1,this,c1) {
    c1->padv = 0;
    *ADVari::Last_ADvari = this;
    ADVari::Last_ADvari = &this->Next;
    this->padv = v;
    }
#endif
  };


 template<typename Double> class
ConstADvari: public ADvari<Double> {
 private:
  ConstADvari *prevcad;
  ConstADvari() {}; // prevent construction without value (?)
  static ConstADvari *lastcad;
 public:
  typedef ADvari<Double> ADVari;
  typedef Derp<Double> DErp;
  static CADcontext<Double> cadc;
  inline void *operator new(size_t len) { return ConstADvari::cadc.Memalloc(len); }
  inline ConstADvari(Double t): ADVari(Hv_copy, t) { prevcad = lastcad; lastcad = this; }
  static void aval_reset(void);
  };


 template<typename Double> class
IndepADvar {    // an independent ADvar
 private:
  IndepADvar& operator=(IndepADvar&x) {
    /* private to prevent assignment */
#ifdef RAD_AUTO_AD_Const
    if (cv)
      cv->padv = 0;
    cv = new ADvar1<Double>(this,x);
    return *this;
#else
#ifdef RAD_EQ_ALIAS
    this->cv = x.cv;
    return *this;
#else
    return ADvar_operatoreq(this,*x.cv);
#endif
#endif
    }
 protected:
  static void AD_Const(const IndepADvar&);
  mutable ADvari<Double> *cv;
 public:
  typedef Double value_type;
  friend class ADvar<Double>;
  friend class ADcontext<Double>;
  friend class ADvar1<Double>;
  friend class ADvarn<Double>;
  typedef ADvari<Double> ADVari;
  typedef ADvar<Double> ADVar;
  IndepADvar(Ttype);
  IndepADvar(double);
  IndepADvar(int);
  IndepADvar(long);
  IndepADvar& operator= (Double);
#ifdef RAD_AUTO_AD_Const
  inline IndepADvar(const IndepADvar &x) { cv = x.cv ? new ADvar1<Double>(this, x) : 0; };
  inline IndepADvar() { cv = 0; }
  inline ~IndepADvar() {
          if (cv)
            cv->padv = 0;
          }
#else
  inline IndepADvar() {
#ifndef RAD_EQ_ALIAS
    cv = 0;
#endif
    }
  inline ~IndepADvar() {}
  friend IndepADvar& ADvar_operatoreq<>(IndepADvar*, const ADVari&);
#endif

#ifdef RAD_Const_WARN
  inline operator ADVari&() const {
    ADVari *tcv = this->cv;
    if (tcv->opno < 0)
      RAD_Const_Warn(tcv);
    return *tcv;
    }
  inline operator ADVari*() const {
    ADVari *tcv = this->cv;
    if (tcv->opno < 0)
      RAD_Const_Warn(tcv);
    return tcv;
    }
#else //RAD_Const_WARN
  inline operator ADVari&() const { return *this->cv; }
  inline operator ADVari*() const { return this->cv; }
#endif //RAD_Const_WARN

  Double val() const { return cv->Val; }
  Double adj() const { return cv->aval; }

  friend void AD_Const1<>(Double*, const IndepADvar&);

  friend ADVari& ADf1<>(Double, Double, const IndepADvar&);
  friend ADVari& ADf2<>(Double, Double, Double, const IndepADvar&, const IndepADvar&);
  friend ADVari& ADf2<>(Double, Double, Double, const ADVari&, const IndepADvar&);
  friend ADVari& ADf2<>(Double, Double, Double, const IndepADvar&, const ADVari&);

  static inline void Gradcomp() { ADcontext<Double>::Gradcomp(); }
  static inline void Hvprod(int n, ADVar **vp, Double *v, Double *hv)
        { ADcontext<Double>::Hvprod(n, vp, v, hv); }
  static inline void aval_reset() { ConstADvari<Double>::aval_reset(); }
  static inline void Weighted_Gradcomp(int n, ADVar **v, Double *w)
        { ADcontext<Double>::Weighted_Gradcomp(n, v, w); }

  /* We use #define to deal with bizarre templating rules that apparently */
  /* require us to spell the some conversion explicitly */


#define Ai const ADVari&
#define AI const IndepADvar&
#define D Double
#define T2(r,f) \
 r f <>(AI,AI);\
 r f <>(Ai,AI);\
 r f <>(AI,Ai);\
 r f <>(Ttype,AI);\
 r f <>(double,AI);\
 r f <>(long,AI);\
 r f <>(int,AI);\
 r f <>(AI,Ttype);\
 r f <>(AI,double);\
 r f <>(AI,long);\
 r f <>(AI,int);
#define T1(f) friend ADVari& f<> (AI);

#define F friend ADVari&
T2(F, operator+)
T2(F, operator-)
T2(F, operator*)
T2(F, operator/)
T2(F, atan2)
T2(F, max)
T2(F, min)
T2(F, pow)
#undef F
#define F friend int
T2(F, operator<)
T2(F, operator<=)
T2(F, operator==)
T2(F, operator!=)
T2(F, operator>=)
T2(F, operator>)

T1(operator+)
T1(operator-)
T1(abs)
T1(acos)
T1(acosh)
T1(asin)
T1(asinh)
T1(atan)
T1(atanh)
T1(cos)
T1(cosh)
T1(exp)
T1(log)
T1(log10)
T1(sin)
T1(sinh)
T1(sqrt)
T1(tan)
T1(tanh)
T1(fabs)
T1(copy)

#undef F
#undef T1
#undef T2
#undef D
#undef AI
#undef Ai

  };

 template<typename Double> class
ADvar: public IndepADvar<Double> {  // an "active" variable
 public:
  typedef IndepADvar<Double> IndepADVar;
  typedef typename IndepADVar::ADVari ADVari;
  typedef ConstADvari<Double> ConstADVari;
 private:
  void ADvar_ctr(Double d) {
    ADVari *x = ConstADVari::cadc.fpval_implies_const
      ? new ConstADVari(d)
#ifdef RAD_AUTO_AD_Const
      : new ADVari((IndepADVar*)this, d);
#else
      : new ADVari(Hv_const, d);
#endif
    this->cv = x;
    }
 public:
  friend class ADvar1<Double>;
  typedef ADvar1<Double> ADVar1;
  ADvar() { /* cv = 0; */ }
  ADvar(Ttype d)  { ADvar_ctr(d); }
  ADvar(double i) { ADvar_ctr(Double(i)); }
  ADvar(int i)  { ADvar_ctr(Double(i)); }
  ADvar(long i) { ADvar_ctr(Double(i)); }
  inline ~ADvar() {}
#ifdef RAD_AUTO_AD_Const
  inline ADvar(IndepADVar &x) {
    this->cv = x.cv ? new ADVar1(this, x) : 0;
    }
  inline ADvar(ADVari &x) { this->cv = &x; x.padv = this; }
  inline ADvar& operator=(IndepADVar &x) {
    if (this->cv)
      this->cv->padv = 0;
    this->cv = new ADVar1(this,x);
    return *this;
    }
  inline ADvar& operator=(ADVari &x) {
    if (this->cv)
      this->cv->padv = 0;
    this->cv = new ADVar1(this, x);
    return *this;
    }
#else 
  friend ADvar& ADvar_operatoreq<>(ADvar*, const ADVari&);
#ifdef RAD_EQ_ALIAS
  /* allow aliasing v and w after "v = w;" */
  inline ADvar(const IndepADVar &x) { this->cv = (ADVari*)x.cv; }
  inline ADvar(const ADVari &x) { this->cv = (ADVari*)&x; }
  inline ADvar& operator=(IndepADVar &x) { this->cv = (ADVari*)x.cv; return *this; }
  inline ADvar& operator=(const ADVari &x) { this->cv = (ADVari*)&x; return *this; }
#else 
  ADvar(const IndepADVar &x) { this->cv = x.cv ? new ADVar1(x.cv->Val, &this->cv->adc.One, x.cv) : 0; }
  ADvar(const ADvar&x) { this->cv = x.cv ?
    new ADVar1(Hv_copy, x.cv->Val, &this->cv->adc.One, (ADVari*)x.cv) : 0; }
  ADvar(const ADVari &x) { this->cv = new ADVar1(Hv_copy, x.Val, &this->cv->adc.One, &x); }
  inline ADvar& operator=(IndepADVar &x) { return ADvar_operatoreq(this,*x.cv); };
  inline ADvar& operator=(const ADVari &x) { return ADvar_operatoreq(this,x); };
#endif /* RAD_EQ_ALIAS */
#endif /* RAD_AUTO_AD_Const */
  ADvar& operator=(Double);
  ADvar& operator+=(const ADVari&);
  ADvar& operator+=(Double);
  ADvar& operator-=(const ADVari&);
  ADvar& operator-=(Double);
  ADvar& operator*=(const ADVari&);
  ADvar& operator*=(Double);
  ADvar& operator/=(const ADVari&);
  ADvar& operator/=(Double);
  inline static bool get_fpval_implies_const(void)
    { return ConstADVari::cadc.fpval_implies_const; }
  inline static void set_fpval_implies_const(bool newval)
    { ConstADVari::cadc.fpval_implies_const = newval; }
  inline static bool setget_fpval_implies_const(bool newval) {
    bool oldval = ConstADVari::cadc.fpval_implies_const;
    ConstADVari::cadc.fpval_implies_const = newval;
    return oldval;
    }
  static inline void Gradcomp() { ADcontext<Double>::Gradcomp(); }
  static inline void aval_reset() { ConstADVari::aval_reset(); }
  static inline void Weighted_Gradcomp(int n, ADvar **v, Double *w)
        { ADcontext<Double>::Weighted_Gradcomp(n, v, w); }
  };

template<typename Double>
 inline void AD_Const1(Double *notused, const IndepADvar<Double>&v)
{ IndepADvar<Double>::AD_Const(v); }

template<typename Double>
 inline void AD_Const(const IndepADvar<Double>&v) { AD_Const1((Double*)0, v); }

 template<typename Double> class
ConstADvar: public ADvar<Double> {
 public:
  typedef ADvar<Double> ADVar;
  typedef typename ADVar::ADVari ADVari;
  typedef typename ADVar::ConstADVari ConstADVari;
  typedef Derp<Double> DErp;
  typedef typename ADVar::IndepADVar IndepADVar;
 private: // disable op=
  ConstADvar& operator+=(ADVari&);
  ConstADvar& operator+=(Double);
  ConstADvar& operator-=(ADVari&);
  ConstADvar& operator-=(Double);
  ConstADvar& operator*=(ADVari&);
  ConstADvar& operator*=(Double);
  ConstADvar& operator/=(ADVari&);
  ConstADvar& operator/=(Double);
  void ConstADvar_ctr(Double);
 public:
  ConstADvar(Ttype d) { ConstADvar_ctr(d); }
  ConstADvar(double i)  { ConstADvar_ctr(Double(i)); }
  ConstADvar(int i) { ConstADvar_ctr(Double(i)); }
  ConstADvar(long i)  { ConstADvar_ctr(Double(i)); }
  ConstADvar(const IndepADVar&);
  ConstADvar(const ConstADvar&);
  ConstADvar(const ADVari&);
  inline ~ConstADvar() {}
#ifdef RAD_NO_CONST_UPDATE
 private:
#endif
  ConstADvar();
  inline ConstADvar& operator=(Double d) { this->cv->Val = d; return *this; }
  inline ConstADvar& operator=(ADVari& d) { this->cv->Val = d.Val; return *this; }
 };

 template<typename Double> class
ADvar1s: public ADvar1<Double> { // unary ops with partials
 public:
  typedef ADvar1<Double> ADVar1;
  typedef typename ADVar1::ADVari ADVari;
  Double pL;  // deriv of op w.r.t. left operand L
  ADvar1s(Double val1, Double a1, const ADVari *c1):
    ADVar1(Hv_timesL,val1,&pL,c1), pL(a1) {}
#ifdef RAD_AUTO_AD_Const
  typedef typename ADVar1::ADVar ADVar;
  ADvar1s(Double val1, Double a1, const ADVari *c1, const ADVar *v):
    ADVar1(val1,&a,c1,v), a(a1) {}
#endif
  };

 template<typename Double> class
ADvar1g: public ADvar1<Double> { // unary ops with partials
 public:
  typedef ADvar1<Double> ADVar1;
  typedef typename ADVar1::ADVari ADVari;
  Double pL;  // deriv of op w.r.t. left operand L
  Double pL2; // partial of op w.r.t. L,L
  ADvar1g(Double val1, Double d1, Double d2, const ADVari *c1):
    ADVar1(Hv_unary,val1,&pL,c1), pL(d1), pL2(d2) {}
  };

 template<typename Double> class
ADvar2: public ADvari<Double> { // basic binary ops
 public:
  typedef ADvari<Double> ADVari;
  typedef Derp<Double> DErp;
  DErp dL, dR;
  ADvar2(Advari_Opclass oc, Double val1, const ADVari *Lcv, const Double *Lc,
    const ADVari *Rcv, const Double *Rc):
      ADVari(oc,val1) {
    dR.next = DErp::LastDerp;
    dL.next = &dR;
    DErp::LastDerp = &dL;
    dL.a = Lc;
    dL.c = (ADVari*)Lcv;
    dR.a = Rc;
    dR.c = (ADVari*)Rcv;
    dL.b = dR.b = this;
    }
#ifdef RAD_AUTO_AD_Const
  typedef ADvar<Double> ADVar;
  ADvar2(Double val1, const ADVari *Lcv, const Double *Lc,
    const ADVari *Rcv, const Double *Rc, ADVar *v):
      ADVari(val1) {
    dR.next = DErp::LastDerp;
    dL.next = &dR;
    DErp::LastDerp = &dL;
    dL.a = Lc;
    dL.c = Lcv;
    dR.a = Rc;
    dR.c = Rcv;
    dL.b = dR.b = this;
    Lcv->padv = 0;
    *ADVari::Last_ADvari = this;
    ADVari::Last_ADvari = &this->Next;
    this->padv = v;
    }
#endif
  };

 template<typename Double> class
ADvar2q: public ADvar2<Double> { // binary ops with partials
 public:
  typedef ADvar2<Double> ADVar2;
  typedef typename ADVar2::ADVari ADVari;
  typedef typename ADVar2::DErp DErp;
  Double pL;  // deriv of op w.r.t. left operand L
  Double pR;  // deriv of op w.r.t. right operand R
  Double pLR; // second partial w.r.t. L,R
  Double pR2; // second partial w.r.t. R,R
  ADvar2q(Double val1, Double Lp, Double Rp, Double LR, Double R2,
    const ADVari *Lcv, const ADVari *Rcv):
      ADVar2(Hv_quotLR,val1,Lcv,&pL,Rcv,&pR),
      pL(Lp), pR(Rp), pLR(LR), pR2(R2) {}
#ifdef RAD_AUTO_AD_Const
  typedef typename ADVar2::ADVar ADVar;
  ADvar2q(Double val1, Double Lp, Double Rp, Double LR, Double R2,
    const ADVari *Lcv, const ADVari *Rcv, const ADVar *v):
      ADVar2(Hv_quotLR,val1,Lcv,&pL,Rcv,&pR,v),
      pL(Lp), pR(Rp), pLR(LR), pR2(R2) {}
#endif
  };

 template<typename Double> class
ADvar2g: public ADvar2<Double> { // general binary ops with partials
 public:
  typedef ADvar2<Double> ADVar2;
  typedef typename ADVar2::ADVari ADVari;
  Double pL;  // deriv of op w.r.t. left operand L
  Double pR;  // deriv of op w.r.t. right operand R
  Double pL2; // second partial w.r.t. L,L
  Double pLR; // second partial w.r.t. L,R
  Double pR2; // second partial w.r.t. R,R
  ADvar2g(Double val1, Double Lp, Double Rp, Double L2, Double LR, Double R2,
    const ADVari *Lcv, const ADVari *Rcv):
      ADVar2(Hv_binary,val1,Lcv,&pL,Rcv,&pR),
      pL(Lp), pR(Rp), pL2(L2), pLR(LR), pR2(R2) { }
  };

 template<typename Double> class
ADvarn: public ADvari<Double> { // n-ary ops with partials g and
        // 2nd partials h (lower triangle, rowwise)
 public:
  typedef ADvari<Double> ADVari;
  typedef ADvar<Double> ADVar;
  typedef typename ADVari::IndepADVar IndepADVar;
  typedef Derp<Double> DErp;
  int n;
  Double *G, *H;
  DErp *D;
  ADvarn(Double val1, int n1, const IndepADVar *x, const Double *g, const Double *h):
      ADVari(Hv_nary,val1), n(n1) {
    DErp *d1, *dlast;
    Double *a1;
    int i, nh;

    a1 = G = (Double*)ADVari::adc.Memalloc(n*sizeof(*g));
    d1 = D = (DErp*)ADVari::adc.Memalloc(n*sizeof(DErp));
    dlast = DErp::LastDerp;
    for(i = 0; i < n1; i++, d1++) {
      d1->next = dlast;
      dlast = d1;
      a1[i] = g[i];
      d1->a = &a1[i];
      d1->b = this;
      d1->c = x[i].cv;
      }
    DErp::LastDerp = dlast;
    nh = (n*(n+1)) >> 1;
    a1 = H = (double*)ADVari::adc.Memalloc(nh * sizeof(*h));
    for(i = 0; i < nh; i++)
      a1[i] = h[i];
    }
  };

template<typename Double>
 inline ADvari<Double>& operator+(const ADvari<Double> &T) { return *(ADvari<Double>*)&T; }

template<typename Double>
 inline int operator<(const ADvari<Double> &L, const ADvari<Double> &R) { return L.Val < R.Val; }
template<typename Double>
 inline int operator<(const ADvari<Double> &L, Double R) { return L.Val < R; }
template<typename Double>
 inline int operator<(Double L, const ADvari<Double> &R) { return L < R.Val; }

template<typename Double>
 inline int operator<=(const ADvari<Double> &L, const ADvari<Double> &R) { return L.Val <= R.Val; }
template<typename Double>
 inline int operator<=(const ADvari<Double> &L, Double R) { return L.Val <= R; }
template<typename Double>
 inline int operator<=(Double L, const ADvari<Double> &R) { return L <= R.Val; }

template<typename Double>
 inline int operator==(const ADvari<Double> &L, const ADvari<Double> &R) { return L.Val == R.Val; }
template<typename Double>
 inline int operator==(const ADvari<Double> &L, Double R) { return L.Val == R; }
template<typename Double>
 inline int operator==(Double L, const ADvari<Double> &R) { return L == R.Val; }

template<typename Double>
 inline int operator!=(const ADvari<Double> &L, const ADvari<Double> &R) { return L.Val != R.Val; }
template<typename Double>
 inline int operator!=(const ADvari<Double> &L, Double R) { return L.Val != R; }
template<typename Double>
 inline int operator!=(Double L, const ADvari<Double> &R) { return L != R.Val; }

template<typename Double>
 inline int operator>=(const ADvari<Double> &L, const ADvari<Double> &R) { return L.Val >= R.Val; }
template<typename Double>
 inline int operator>=(const ADvari<Double> &L, Double R) { return L.Val >= R; }
template<typename Double>
 inline int operator>=(Double L, const ADvari<Double> &R) { return L >= R.Val; }

template<typename Double>
 inline int operator>(const ADvari<Double> &L, const ADvari<Double> &R) { return L.Val > R.Val; }
template<typename Double>
 inline int operator>(const ADvari<Double> &L, Double R) { return L.Val > R; }
template<typename Double>
 inline int operator>(Double L, const ADvari<Double> &R) { return L > R.Val; }

template<typename Double>
 inline void *ADcontext<Double>::Memalloc(size_t len) {
    if (Mleft >= len)
      return Mbase + (Mleft -= len);
    return new_ADmemblock(len);
    }

template<typename Double>
 inline Derp<Double>::Derp(const ADVari *c1): c((ADVari*)c1) {
    next = LastDerp;
    LastDerp = this;
    }

template<typename Double>
 inline Derp<Double>::Derp(const Double *a1, const ADVari *c1): a(a1), c((ADVari*)c1) {
    next = LastDerp;
    LastDerp = this;
    }

template<typename Double>
 inline Derp<Double>::Derp(const Double *a1, const ADVari *b1, const ADVari *c1):
  a(a1), b(b1), c((ADVari*)c1) {
    next = LastDerp;
    LastDerp = this;
    }

/**** radops ****/

template<typename Double> Derp<Double> *Derp<Double>::LastDerp = 0;
template<typename Double> ADcontext<Double> ADvari<Double>::adc;
template<typename Double> const Double ADcontext<Double>::One = 1.;
template<typename Double> const Double ADcontext<Double>::negOne = -1.;
template<typename Double> CADcontext<Double> ConstADvari<Double>::cadc;
template<typename Double> ConstADvari<Double> *ConstADvari<Double>::lastcad;

#ifdef RAD_AUTO_AD_Const
template<typename Double> ADvari<Double>*   ADvari<Double>::First_ADvari;
template<typename Double> ADvari<Double>**  ADvari<Double>::Last_ADvari = &ADvari<Double>::First_ADvari;
#endif

#ifdef RAD_DEBUG
#ifndef RAD_DEBUG_gcgen1
#define RAD_DEBUG_gcgen1 -1
#endif
template<typename Double> int ADvari<Double>::gcgen_cur;
template<typename Double> int ADvari<Double>::last_opno;
template<typename Double> int ADvari<Double>::zap_gcgen;
template<typename Double> int ADvari<Double>::zap_gcgen1 = RAD_DEBUG_gcgen1;
template<typename Double> int ADvari<Double>::zap_opno;
template<typename Double> FILE *ADvari<Double>::debug_file;
#endif


 template<typename Double>
ADcontext<Double>::ADcontext()
{
  ADVari_block *fb;

  First = (ADMemblock*)First0;
  First->next = 0;
  Busy = First;
  Free = 0;
  Mbase = (char*)First->memblk;
  Mleft = sizeof(First->memblk);
  AiFirst = Aibusy = fb = (ADVari_block*)First1;
  Aifree = 0;
  Ainext = fb->pADvari;
  fb->next = fb->prev = 0;
  fb->limit = Ailimit = fb->pADvari + ADVari_block::Gulp;
  rad_need_reinit = 0;
#ifdef RAD_DEBUG_BLOCKKEEP
  rad_busy_blocks = 0;
  rad_mleft_save = 0;
  rad_Oldcurmb = 0;
#endif
  }

template<typename Double> void*
ADcontext<Double>::new_ADmemblock(size_t len)
{
  ADMemblock *mb, *mb0, *mb1, *mbf, *x;
  ADVari_block *b;

  if ((rad_need_reinit & 1) && this == &ADVari::adc) {
    rad_need_reinit &= ~1;
    DErp::LastDerp = 0;
    Aibusy = b = AiFirst;
    Aifree = b->next;
    b->next = b->prev = 0;
    Ailimit = b->limit = (Ainext = b->pADvari) + ADVari_block::Gulp;
#ifdef RAD_DEBUG_BLOCKKEEP
    Mleft = rad_mleft_save;
    if (Mleft < sizeof(First->memblk))
      _uninit_f2c(Mbase + Mleft,
        UninitType<Double>::utype,
        (sizeof(First->memblk) - Mleft)
        /sizeof(typename Sacado::ValueType<Double>::type));
    if (mb = Busy->next) {
      if (!(mb0 = rad_Oldcurmb))
        mb0 = (ADMemblock*)First0;
      for(;; mb = mb->next) {
        _uninit_f2c(mb->memblk,
          UninitType<Double>::utype,
          sizeof(First->memblk)
          /sizeof(typename Sacado::ValueType<Double>::type));
        if (mb == mb0)
          break;
        }
      }
    rad_Oldcurmb = Busy;
    if (rad_busy_blocks >= RAD_DEBUG_BLOCKKEEP) {
      rad_busy_blocks = 0;
      rad_Oldcurmb = 0;
      mb0 = (ADMemblock*)First0;
      mbf =  Free;
      for(mb = Busy; mb != mb0; mb = mb1) {
        mb1 = mb->next;
        mb->next = mbf;
        mbf = mb;
        }
      Free = mbf;
      Busy = mb;
      Mbase = (char*)First->memblk;
      Mleft = sizeof(First->memblk);
      }

#else /* !RAD_DEBUG_BLOCKKEEP */

    mb0 = First;
    mbf =  Free;
    for(mb = Busy; mb != mb0; mb = mb1) {
      mb1 = mb->next;
      mb->next = mbf;
      mbf = mb;
      }
    Free = mbf;
    Busy = mb;
    Mbase = (char*)First->memblk;
    Mleft = sizeof(First->memblk);
#endif /*RAD_DEBUG_BLOCKKEEP*/
    if (Mleft >= len)
      return Mbase + (Mleft -= len);
    }

  if ((x = Free))
    Free = x->next;
  else
    x = new ADMemblock;
#ifdef RAD_DEBUG_BLOCKKEEP
  rad_busy_blocks++;
#endif
  x->next = Busy;
  Busy = x;
  return (Mbase = (char*)x->memblk) +
    (Mleft = sizeof(First->memblk) - len);
  }

template<typename Double> void
ADcontext<Double>::new_ADvari_block()
{
  ADVari_block *ob, *nb;
  ob = Aibusy;
  ob->limit = Ailimit;  // should be unnecessary, but harmless
  if (nb = Aifree)
    Aifree = nb->next;
  else
    nb = new ADVari_block;
  Aibusy = Aibusy->next = nb;
  nb->limit = Ailimit = (Ainext = nb->pADvari) + ADVari_block::Gulp;
  ob->next = nb;
  nb->prev = ob;
  nb->next = 0;
  }

template<typename Double> void
ADcontext<Double>::Gradcomp()
{
  DErp *d;
#ifdef RAD_AUTO_AD_Const
  ADVari *a, *anext;
  IndepADvar<Double> *v;
#ifdef RAD_Const_WARN
  ADVari *cv;
  int i, j;
#endif
#endif /*RAD_AUTO_AD_Const*/

  if (ADVari::adc.rad_need_reinit) {
    for(d = DErp::LastDerp; d; d = d->next)
      d->c->aval = 0;
    }
  if (!(ADVari::adc.rad_need_reinit & 1)) {
    ADVari::adc.rad_need_reinit = 1;
    ADVari::adc.rad_mleft_save = ADVari::adc.Mleft;
    ADVari::adc.Mleft = 0;
    }
#ifdef RAD_DEBUG
  if (ADVari::gcgen_cur == ADVari::zap_gcgen1) {
    const char *fname;
    if (!(fname = getenv("RAD_DEBUG_FILE")))
      fname = "rad_debug.out";
    else if (!*fname)
      fname = 0;
    if (fname)
      ADVari::debug_file = fopen(fname, "w");
    ADVari::zap_gcgen1 = -1;
    }
#endif
  if ((d = DErp::LastDerp)) {
    d->b->aval = 1;
#ifdef RAD_DEBUG
    if (ADVari::debug_file)
      do {
        fprintf(ADVari::debug_file, "%d\t%d\t%g + %g * %g",
          d->c->opno, d->b->opno, d->c->aval, *d->a, d->b->aval);
        d->c->aval += *d->a * d->b->aval;
        fprintf(ADVari::debug_file, " = %g\n", d->c->aval);
        fflush(ADVari::debug_file);
        } while(d = d->next);
    else
#endif
    do d->c->aval += *d->a * d->b->aval;
    while((d = d->next));
    }
#ifdef RAD_DEBUG
  if (ADVari::debug_file) {
    fclose(ADVari::debug_file);
    ADVari::debug_file = 0;
    }
#endif //RAD_DEBUG
#ifdef RAD_AUTO_AD_Const
  *ADVari::Last_ADvari = 0;
  ADVari::Last_ADvari = &ADVari::First_ADvari;
  if ((anext = ADVari::First_ADvari) && !(ADVari::adc.rad_need_reinit & 2)) {
    ADVari::adc.rad_need_reinit = 3;
    while((a = anext)) {
      anext = a->Next;
      if ((v = (IndepADvar<Double> *)a->padv)) {
#ifdef RAD_Const_WARN
        if ((i = a->opno) > 0)
          i = -i;
        j = a->gcgen;
        v->cv = cv = new ADVari(v, a->Val, a->aval);
        cv->opno = i;
        cv->gcgen = j;
#else
        v->cv = new ADVari(v, a->Val, a->aval);
#endif
        }
      }
    DErp::LastDerp = 0;
    }
#endif /*RAD_AUTO_AD_Const*/
#ifdef RAD_DEBUG
  ADVari::gcgen_cur++;
  ADVari::last_opno = 0;
#endif
  }

template<typename Double> void
ADcontext<Double>::Weighted_Gradcomp(int n, ADVar **V, Double *w)
{
  DErp *d;
  int i;
#ifdef RAD_Const_WARN
  ADVari *cv;
  int j;
#endif
#ifdef RAD_AUTO_AD_Const
  ADVari *a, *anext;
  IndepADvar<Double> *v;
#endif /*RAD_AUTO_AD_Const*/

  if (ADVari::adc.rad_need_reinit) {
    for(d = DErp::LastDerp; d; d = d->next)
      d->c->aval = 0;
    }
  if (!(ADVari::adc.rad_need_reinit & 1)) {
    ADVari::adc.rad_need_reinit = 1;
    ADVari::adc.rad_mleft_save = ADVari::adc.Mleft;
    ADVari::adc.Mleft = 0;
    }
#ifdef RAD_DEBUG
  if (ADVari::gcgen_cur == ADVari::zap_gcgen1) {
    const char *fname;
    if (!(fname = getenv("RAD_DEBUG_FILE")))
      fname = "rad_debug.out";
    else if (!*fname)
      fname = 0;
    if (fname)
      ADVari::debug_file = fopen(fname, "w");
    ADVari::zap_gcgen1 = -1;
    }
#endif
  if (d = DErp::LastDerp) {
    for(i = 0; i < n; i++)
      V[i]->cv->aval = w[i];
#ifdef RAD_DEBUG
    if (ADVari::debug_file)
      do {
        fprintf(ADVari::debug_file, "%d\t%d\t%g + %g * %g",
          d->c->opno, d->b->opno, d->c->aval, *d->a, d->b->aval);
        d->c->aval += *d->a * d->b->aval;
        fprintf(ADVari::debug_file, " = %g\n", d->c->aval);
        fflush(ADVari::debug_file);
        } while(d = d->next);
    else
#endif
    do d->c->aval += *d->a * d->b->aval;
    while(d = d->next);
    }
#ifdef RAD_DEBUG
  if (ADVari::debug_file) {
    fclose(ADVari::debug_file);
    ADVari::debug_file = 0;
    }
#endif //RAD_DEBUG
#ifdef RAD_AUTO_AD_Const
  *ADVari::Last_ADvari = 0;
  ADVari::Last_ADvari = &ADVari::First_ADvari;
  if ((anext = ADVari::First_ADvari) && !(ADVari::adc.rad_need_reinit & 2)) {
    ADVari::adc.rad_need_reinit = 3;
    while(a = anext) {
      anext = a->Next;
      if (v = (IndepADvar<Double> *)a->padv) {
#ifdef RAD_Const_WARN
        if ((i = a->opno) > 0)
          i = -i;
        j = a->gcgen;
        v->cv = cv = new ADVari(v, a->Val, a->aval);
        cv->opno = i;
        cv->gcgen = j;
#else
        v->cv = new ADVari(v, a->Val, a->aval);
#endif
        }
      }
    DErp::LastDerp = 0;
    }
#endif /*RAD_AUTO_AD_Const*/
#ifdef RAD_DEBUG
  ADVari::gcgen_cur++;
  ADVari::last_opno = 0;
#endif
    }

 template<typename Double>
IndepADvar<Double>::IndepADvar(Ttype d)
{

  ADVari *x = new ADVari(Hv_const, d);
  cv = x;
  }

 template<typename Double>
IndepADvar<Double>::IndepADvar(double i)
{

  ADVari *x = new ADVari(Hv_const, Double(i));
  cv = x;
  }

 template<typename Double>
IndepADvar<Double>::IndepADvar(int i)
{

  ADVari *x = new ADVari(Hv_const, Double(i));
  cv = x;
  }

 template<typename Double>
IndepADvar<Double>::IndepADvar(long i)
{

  ADVari *x = new ADVari(Hv_const, Double(i));
  cv = x;
  }

 template<typename Double>
ConstADvar<Double>::ConstADvar()
{
  ConstADVari *x = new ConstADVari(0.);
  this->cv = x;
  }

 template<typename Double> void
ConstADvar<Double>::ConstADvar_ctr(Double d)
{
  ConstADVari *x = new ConstADVari(d);
  this->cv = x;
  }

 template<typename Double>
ConstADvar<Double>::ConstADvar(const IndepADVar &x)
{
  ConstADVari *y = new ConstADVari(x.cv->Val);
  DErp *d = new DErp(&x.adc.One, y, x.cv);
  this->cv = y;
  }

 template<typename Double>
ConstADvar<Double>::ConstADvar(const ConstADvar &x)
{
  ConstADVari *y = new ConstADVari(x.cv->Val);
  DErp *d = new DErp(&x.cv->adc.One, y, (ADVari*)x.cv);
  this->cv = y;
  }

 template<typename Double>
ConstADvar<Double>::ConstADvar(const ADVari &x)
{
  ConstADVari *y = new ConstADVari(x.Val);
  DErp *d = new DErp(&x.adc.One, y, &x);
  this->cv = y;
  }

 template<typename Double>
 void
IndepADvar<Double>::AD_Const(const IndepADvar &v)
{
  typedef ConstADvari<Double> ConstADVari;

  ConstADVari *ncv = new ConstADVari(v.val());
#ifdef RAD_AUTO_AD_Const
  v.cv->padv = 0;
#endif
  v.cv = ncv;
  }

 template<typename Double>
 void
ConstADvari<Double>::aval_reset()
{
  ConstADvari *x = ConstADvari::lastcad;
  while(x) {
    x->aval = 0;
    x = x->prevcad;
    }
  }

#ifdef RAD_AUTO_AD_Const

 template<typename Double>
ADvari<Double>::ADvari(const IndepADVar *x, Double d): Val(d), aval(0.)
{
  opclass = Hv_const;
  *Last_ADvari = this;
  Last_ADvari = &Next;
  this->padv = (IndepADVar*)x;
  }

 template<typename Double>
ADvari<Double>::ADvari(const IndepADVar *x, Double d, Double g): Val(d), aval(g)
{
  *Last_ADvari = this;
  Last_ADvari = &Next;
  this->padv = (IndepADVar*)x;
  }

 template<typename Double>
ADvar1<Double>::ADvar1(const IndepADVar *x, const IndepADVar &y):
  ADVari(Hv_copy, y.cv->Val), d((const Double*)&ADcontext<Double>::One, (ADVari*)this, y.cv)
{
  *ADVari::Last_ADvari = this;
  ADVari::Last_ADvari = &this->Next;
  this->padv = x;
  }

 template<typename Double>
ADvar1<Double>::ADvar1(const IndepADVar *x, const ADVari &y):
  ADVari(Hv_copy, y.Val), d((const Double*)&ADcontext<Double>::One, this, &y)
{
  *ADVari::Last_ADvari = this;
  ADVari::Last_ADvari = &this->Next;
  this->padv = x;
  }

#else /* !RAD_AUTO_AD_Const */

 template<typename Double>
 IndepADvar<Double>&
ADvar_operatoreq(IndepADvar<Double> *This, const ADvari<Double> &x)
{ This->cv = new ADvar1<Double>(Hv_copy, x.Val, &x.adc.One, &x);
  return *(IndepADvar<Double>*) This; }

 template<typename Double>
 ADvar<Double>&
ADvar_operatoreq(ADvar<Double> *This, const ADvari<Double> &x)
{ This->cv = new ADvar1<Double>(Hv_copy, x.Val, &x.adc.One, &x); return *(ADvar<Double>*) This; }

#endif /* RAD_AUTO_AD_Const */


 template<typename Double>
 IndepADvar<Double>&
IndepADvar<Double>::operator=(Double d)
{
#ifdef RAD_AUTO_AD_Const
  if (this->cv)
    this->cv->padv = 0;
  this->cv = new ADVari(Hv_const, this,d);
#else
  this->cv = new ADVari(Hv_const, d);
#endif
  return *this;
  }

 template<typename Double>
 ADvar<Double>&
ADvar<Double>::operator=(Double d)
{
#ifdef RAD_AUTO_AD_Const
  if (this->cv)
    this->cv->padv = 0;
  this->cv = new ADVari(Hv_const, this,d);
#else
  this->cv = ConstADVari::cadc.fpval_implies_const
    ? new ConstADVari(d)
    : new ADVari(Hv_const, d);
#endif
  return *this;
  }

 template<typename Double>
 ADvari<Double>&
operator-(const ADvari<Double> &T) {
  return *(new ADvar1<Double>(Hv_negate, -T.Val, &T.adc.negOne, &T));
  }

 template<typename Double>
 ADvari<Double>&
operator+(const ADvari<Double> &L, const ADvari<Double> &R) {
  return *(new ADvar2<Double>(Hv_plusLR, L.Val + R.Val, &L, &L.adc.One, &R, &L.adc.One));
  }

#ifdef RAD_AUTO_AD_Const
#define RAD_ACA ,this
#else
#define RAD_ACA /*nothing*/
#endif

 template<typename Double>
 ADvar<Double>&
ADvar<Double>::operator+=(const ADVari &R) {
  ADVari *Lcv = this->cv;
  this->cv = new ADvar2<Double>(Hv_plusLR, Lcv->Val + R.Val, Lcv,
          &R.adc.One, &R, &R.adc.One RAD_ACA);
  return *this;
  }

 template<typename Double>
 ADvari<Double>&
operator+(const ADvari<Double> &L, Double R) {
  return *(new ADvar1<Double>(Hv_copy, L.Val + R, &L.adc.One, &L));
  }

 template<typename Double>
 ADvar<Double>&
ADvar<Double>::operator+=(Double R) {
  ADVari *tcv = this->cv;
  this->cv = new ADVar1(Hv_copy, tcv->Val + R, &tcv->adc.One, tcv RAD_ACA);
  return *this;
  }

 template<typename Double>
 ADvari<Double>&
operator+(Double L, const ADvari<Double> &R) {
  return *(new ADvar1<Double>(Hv_copy, L + R.Val, &R.adc.One, &R));
  }

 template<typename Double>
 ADvari<Double>&
operator-(const ADvari<Double> &L, const ADvari<Double> &R) {
  return *(new ADvar2<Double>(Hv_minusLR, L.Val - R.Val, &L, &L.adc.One, &R, &L.adc.negOne));
  }

 template<typename Double>
 ADvar<Double>&
ADvar<Double>::operator-=(const ADVari &R) {
  ADVari *Lcv = this->cv;
  this->cv = new ADvar2<Double>(Hv_minusLR,Lcv->Val - R.Val, Lcv,
          &R.adc.One, &R, &R.adc.negOne RAD_ACA);
  return *this;
  }

 template<typename Double>
 ADvari<Double>&
operator-(const ADvari<Double> &L, Double R) {
  return *(new ADvar1<Double>(Hv_copy, L.Val - R, &L.adc.One, &L));
  }

 template<typename Double>
 ADvar<Double>&
ADvar<Double>::operator-=(Double R) {
  ADVari *tcv = this->cv;
  this->cv = new ADVar1(Hv_copy, tcv->Val - R, &tcv->adc.One, tcv RAD_ACA);
  return *this;
  }

 template<typename Double>
 ADvari<Double>&
operator-(Double L, const ADvari<Double> &R) {
  return *(new ADvar1<Double>(Hv_negate, L - R.Val, &R.adc.negOne, &R));
  }

 template<typename Double>
 ADvari<Double>&
operator*(const ADvari<Double> &L, const ADvari<Double> &R) {
  return *(new ADvar2<Double>(Hv_timesLR, L.Val * R.Val, &L, &R.Val, &R, &L.Val));
  }

 template<typename Double>
 ADvar<Double>&
ADvar<Double>::operator*=(const ADVari &R) {
  ADVari *Lcv = this->cv;
  this->cv = new ADvar2<Double>(Hv_timesLR, Lcv->Val * R.Val, Lcv,
          &R.Val, &R, &Lcv->Val RAD_ACA);
  return *this;
  }

 template<typename Double>
 ADvari<Double>&
operator*(const ADvari<Double> &L, Double R) {
  return *(new ADvar1s<Double>(L.Val * R, R, &L));
  }

 template<typename Double>
 ADvar<Double>&
ADvar<Double>::operator*=(Double R) {
  ADVari *Lcv = this->cv;
  this->cv = new ADvar1s<Double>(Lcv->Val * R, R, Lcv RAD_ACA);
  return *this;
  }

 template<typename Double>
 ADvari<Double>&
operator*(Double L, const ADvari<Double> &R) {
  return *(new ADvar1s<Double>(L * R.Val, L, &R));
  }

 template<typename Double>
 ADvari<Double>&
operator/(const ADvari<Double> &L, const ADvari<Double> &R) {
  Double Lv = L.Val, Rv = R.Val, pL = 1. / Rv, q = Lv/Rv, qpL = q*pL;
  return *(new ADvar2q<Double>(q, pL, -qpL, -pL*pL, 2.*pL*qpL, &L, &R));
  }

 template<typename Double>
 ADvar<Double>&
ADvar<Double>::operator/=(const ADVari &R) {
  ADVari *Lcv = this->cv;
  Double Lv = Lcv->Val, Rv = R.Val, pL = 1. / Rv, q = Lv/Rv, qpL = q*pL;
  this->cv = new ADvar2q<Double>(q, pL, -qpL, -pL*pL, 2.*pL*qpL, Lcv, &R RAD_ACA);
  return *this;
  }

 template<typename Double>
 ADvari<Double>&
operator/(const ADvari<Double> &L, Double R) {
  return *(new ADvar1s<Double>(L.Val / R, 1./R, &L));
  }

 template<typename Double>
 ADvari<Double>&
operator/(Double L, const ADvari<Double> &R) {
  Double recip = 1. / R.Val;
  Double q = L * recip;
  Double d1 = -q*recip;
  return *(new ADvar1g<Double>(q, d1, -q*d1, &R));
  }

 template<typename Double>
 ADvar<Double>&
ADvar<Double>::operator/=(Double R) {
  ADVari *Lcv = this->cv;
  this->cv = new ADvar1s<Double>(Lcv->Val / R, 1./R, Lcv RAD_ACA);
  return *this;
  }

 template<typename Double>
 ADvari<Double>&
acos(const ADvari<Double> &v) {
  Double t = v.Val, t1 = 1. - t*t, d1 = -1./std::sqrt(t1);
  return *(new ADvar1g<Double>(std::acos(t), d1, t*d1/t1, &v));
  }

 template<typename Double>
 ADvari<Double>&
acosh(const ADvari<Double> &v) {
  Double d1, t, t1, t2;
  t = v.Val;
  t1 = std::sqrt(t2 = t*t - 1.);
  d1 = 1. / t1;
  return *(new ADvar1g<Double>(std::log(t + t1), d1, -t*d1/t2, &v));
  }

 template<typename Double>
 ADvari<Double>&
asin(const ADvari<Double> &v) {
  Double d1, t, t1;
  t = v.Val;
  d1 = 1. / std::sqrt(t1 = 1. - t*t);
  return *(new ADvar1g<Double>(std::asin(t), d1, t*d1/t1, &v));
  }

 template<typename Double>
 ADvari<Double>&
asinh(const ADvari<Double> &v) {
  Double d1, t, t1, t2, td;
  t = v.Val;
  t1 = std::sqrt(t2 = t*t + 1.);
  d1 = 1. / t1;
  td = 1.;
  if (t < 0.)
    td = -1.;
  return *(new ADvar1g<Double>(td*std::log(t*td + t1), d1, -(t/t2)*d1, &v));
  }

 template<typename Double>
 ADvari<Double>&
atan(const ADvari<Double> &v) {
  Double t = v.Val, d1 = 1./(1. + t*t);
  return *(new ADvar1g<Double>(std::atan(t), d1, -(t+t)*d1*d1, &v));
  }

 template<typename Double>
 ADvari<Double>&
atanh(const ADvari<Double> &v) {
  Double t = v.Val, d1 = 1./(1. - t*t);
  return *(new ADvar1g<Double>(0.5*std::log((1.+t)/(1.-t)), d1, (t+t)*d1*d1, &v));
  }

 template<typename Double>
 ADvari<Double>&
atan2(const ADvari<Double> &L, const ADvari<Double> &R) {
  Double R2, t, t2, x, x2, y, y2;
  x = L.Val;
  y = R.Val;
  x2 = x*x;
  y2 = y*y;
  t = 1./(x2 + y2);
  t2 = t*t;
  R2 = 2.*t2*x*y;
  return *(new ADvar2g<Double>(std::atan2(x,y), y*t, -x*t, -R2, t2*(x2 - y2), R2, &L, &R));
  }

 template<typename Double>
 ADvari<Double>&
atan2(Double x, const ADvari<Double> &R) {
  Double t, x2, y, y2;
  y = R.Val;
  x2 = x*x;
  y2 = y*y;
  t = 1./(x2 + y2);
  return *(new ADvar1g<Double>(std::atan2(x,y), -x*t, 2.*t*t*x*y, &R));
  }

 template<typename Double>
 ADvari<Double>&
atan2(const ADvari<Double> &L, Double y) {
  Double t, x, x2, y2;
  x = L.Val;
  x2 = x*x;
  y2 = y*y;
  t = 1./(x2 + y2);
  return *(new ADvar1g<Double>(std::atan2(x,y), y*t, -2.*t*t*x*y, &L));
  }

 template<typename Double>
 ADvari<Double>&
max(const ADvari<Double> &L, const ADvari<Double> &R) {
  const ADvari<Double> &x = L.Val >= R.Val ? L : R;
  return *(new ADvar1<Double>(Hv_copy, x.Val, &x.adc.One, &x));
  }

 template<typename Double>
 ADvari<Double>&
max(Double L, const ADvari<Double> &R) {
  if (L >= R.Val)
    return *(new ADvari<Double>(Hv_const, L));
  return *(new ADvar1<Double>(Hv_copy, R.Val, &R.adc.One, &R));
  }

 template<typename Double>
 ADvari<Double>&
max(const ADvari<Double> &L, Double R) {
  if (L.Val >= R)
    return *(new ADvar1<Double>(Hv_copy, L.Val, &L.adc.One, &L));
  return *(new ADvari<Double>(Hv_const, R));
  }

 template<typename Double>
 ADvari<Double>&
min(const ADvari<Double> &L, const ADvari<Double> &R) {
  const ADvari<Double> &x = L.Val <= R.Val ? L : R;
  return *(new ADvar1<Double>(Hv_copy, x.Val, &x.adc.One, &x));
  }

 template<typename Double>
 ADvari<Double>&
min(Double L, const ADvari<Double> &R) {
  if (L <= R.Val)
    return *(new ADvari<Double>(Hv_const, L));
  return *(new ADvar1<Double>(Hv_copy, R.Val, &R.adc.One, &R));
  }

 template<typename Double>
 ADvari<Double>&
min(const ADvari<Double> &L, Double R) {
  if (L.Val <= R)
    return *(new ADvar1<Double>(Hv_copy, L.Val, &L.adc.One, &L));
  return *(new ADvari<Double>(Hv_const, R));
  }

 template<typename Double>
 ADvari<Double>&
cos(const ADvari<Double> &v) {
  Double t = std::cos(v.Val);
  return *(new ADvar1g<Double>(t, -std::sin(v.Val), -t, &v));
  }

 template<typename Double>
 ADvari<Double>&
cosh(const ADvari<Double> &v) {
  Double t = std::cosh(v.Val);
  return *(new ADvar1g<Double>(t, std::sinh(v.Val), t, &v));
  }

 template<typename Double>
 ADvari<Double>&
exp(const ADvari<Double> &v) {
  Double t = std::exp(v.Val);
  return *(new ADvar1g<Double>(t, t, t, &v));
  }

 template<typename Double>
 ADvari<Double>&
log(const ADvari<Double> &v) {
  Double x = v.Val, d1 = 1. / x;
  return *(new ADvar1g<Double>(std::log(x), d1, -d1*d1, &v));
  }

 template<typename Double>
 ADvari<Double>&
log10(const ADvari<Double> &v) {
  static double num = 1. / std::log(10.);
  Double d1, t, x;
  x = v.Val;
  t = 1. / x;
  d1 = num * t;
  return *(new ADvar1g<Double>(std::log10(x), d1, -d1*t, &v));
  }

 template<typename Double>
 ADvari<Double>&
pow(const ADvari<Double> &L, const ADvari<Double> &R) {
  Double dx, dy, t, x, xlog, xym1, y;
  x = L.Val;
  y = R.Val;
  t = std::pow(x,y);
  xym1 = t / x;
  xlog = std::log(x);
  dx = y*xym1;
  dy = t * xlog;
  return *(new ADvar2g<Double>(t, dx, dy, (y-1.)*dx/x, xym1*(1. + y*xlog), dy*xlog, &L, &R));
  }

 template<typename Double>
 ADvari<Double>&
pow(Double x, const ADvari<Double> &R) {
  Double dy, t, xlog, y;
  y = R.Val;
  t = std::pow(x,y);
  xlog = std::log(x);
  dy = t * xlog;
  return *(new ADvar1g<Double>(t, dy, dy*xlog, &R));
  }

 template<typename Double>
 ADvari<Double>&
pow(const ADvari<Double> &L, Double y) {
  Double dx, t, x;
  x = L.Val;
  t = std::pow(x,y);
  dx = y*t/x;
  return *(new ADvar1g<Double>(t, dx, (y-1.)*dx/x, &L));
  }

 template<typename Double>
 ADvari<Double>&
sin(const ADvari<Double> &v) {
  Double t = std::sin(v.Val);
  return *(new ADvar1g<Double>(t, std::cos(v.Val), -t, &v));
  }

 template<typename Double>
 ADvari<Double>&
sinh(const ADvari<Double> &v) {
  Double t = std::sinh(v.Val);
  return *(new ADvar1g<Double>(t, std::cosh(v.Val), t, &v));
  }

 template<typename Double>
 ADvari<Double>&
sqrt(const ADvari<Double> &v) {
  Double t = std::sqrt(v.Val);
  Double d1 = 0.5 / t;
  return *(new ADvar1g<Double>(t, d1, -0.5*d1/v.Val, &v));
  }

 template<typename Double>
 ADvari<Double>&
tan(const ADvari<Double> &v) {
  Double d1, rv, t;
  rv = std::tan(v.Val);
  t = 1. / std::cos(v.Val);
  d1 = t*t;
  return *(new ADvar1g<Double>(rv, d1, (rv+rv)*d1, &v));
  }

 template<typename Double>
 ADvari<Double>&
tanh(const ADvari<Double> &v) {
  Double d1, rv, t;
  rv = std::tanh(v.Val);
  t = 1. / std::cosh(v.Val);
  d1 = t*t;
  return *(new ADvar1g<Double>(rv, d1, -(rv+rv)*d1, &v));
  }

 template<typename Double>
 ADvari<Double>&
abs(const ADvari<Double> &v) {
  Double t, p;
  p = 1.;
  if ((t = v.Val) < 0) {
    t = -t;
    p = -p;
    }
  return *(new ADvar1g<Double>(t, p, 0., &v));
  }

 template<typename Double>
 ADvari<Double>&
fabs(const ADvari<Double> &v) { // Synonym for "abs"
        // "fabs" is not the best choice of name,
        // but this name is used at Sandia.
  Double t, p;
  p = 1.;
  if ((t = v.Val) < 0) {
    t = -t;
    p = -p;
    }
  return *(new ADvar1g<Double>(t, p, 0., &v));
  }

 template<typename Double>
 ADvari<Double>&
ADf1(Double f, Double g, Double h, const ADvari<Double> &x) {
  return *(new ADvar1g<Double>(f, g, h, &x));
  }

 template<typename Double>
 inline ADvari<Double>&
ADf1(Double f, Double g, Double h, const IndepADvar<Double> &x) {
  return *(new ADvar1g<Double>(f, g, h, x.cv));
  }

 template<typename Double>
 ADvari<Double>&
ADf2(Double f, Double gx, Double gy, Double hxx, Double hxy, Double hyy,
    const ADvari<Double> &x, const ADvari<Double> &y) {
  return *(new ADvar2g<Double>(f, gx, gy, hxx, hxy, hyy, &x, &y));
  }

 template<typename Double>
 ADvari<Double>&
ADf2(Double f, Double gx, Double gy, Double hxx, Double hxy, Double hyy,
    const ADvari<Double> &x, const IndepADvar<Double> &y) {
  return *(new ADvar2g<Double>(f, gx, gy, hxx, hxy, hyy, &x, y.cv));
  }

 template<typename Double>
 ADvari<Double>&
ADf2(Double f, Double gx, Double gy, Double hxx, Double hxy, Double hyy,
    const IndepADvar<Double> &x, const ADvari<Double> &y) {
  return *(new ADvar2g<Double>(f, gx, gy, hxx, hxy, hyy, x.cv, &y));
  }

 template<typename Double>
 ADvari<Double>&
ADf2(Double f, Double gx, Double gy, Double hxx, Double hxy, Double hyy,
    const IndepADvar<Double> &x, const IndepADvar<Double> &y) {
  return *(new ADvar2g<Double>(f, gx, gy, hxx, hxy, hyy, x.cv, y.cv));
  }

 template<typename Double>
 ADvari<Double>&
ADfn(Double f, int n, const IndepADvar<Double> *x, const Double *g, const Double *h) {
  return *(new ADvarn<Double>(f, n, x, g, h));
  }

 template<typename Double>
 inline ADvari<Double>&
ADfn(Double f, int n, const ADvar<Double> *x, const Double *g, const Double *h) {
  return ADfn<Double>(f, n, (IndepADvar<Double>*)x, g, h);
  }

 template<typename Double>
 void
ADcontext<Double>::Hvprod(int n, ADvar<Double> **x, Double *v, Double *hv)
{
  ADVari *a, *aL, *aR, **ap, **ape;
  ADVari_block *b, *b0;
  DErp *d;
  Double aO, adO, *g, *h, *h0, t, tL, tR;
  int i, j, k, m;
  for(i = 0; i < n; i++) {
    a = x[i]->cv;
    a->dO = v[i];
    a->aO = a->adO = 0.;
    }
  ADVari::adc.Aibusy->limit = ADVari::adc.Ainext;
  a = 0;
  for(b0 = 0, b = ADVari::adc.AiFirst; b; b0 = b, b = b->next) {
    ap = b->pADvari;
    ape = b->limit;
    while(ap < ape) {
      a = *ap++;
      a->aO = a->adO = 0.;
      switch(a->opclass) {
       case Hv_copy:
        a->dO = ((ADVar1*)a)->d.c->dO;
        break;
       case Hv_binary:
        a->dO =   ((ADVar2g*)a)->pL * ((ADVar2g*)a)->dL.c->dO
          + ((ADVar2g*)a)->pR * ((ADVar2g*)a)->dR.c->dO;
        break;
       case Hv_unary:
        a->dO = ((ADVar1g*)a)->pL * ((ADVar1g*)a)->d.c->dO;
        break;
       case Hv_negate:
        a->dO = -((ADVar1*)a)->d.c->dO;
        break;
       case Hv_plusLR:
        a->dO = ((ADVar2*)a)->dL.c->dO + ((ADVar2*)a)->dR.c->dO;
        break;
       case Hv_minusLR:
        a->dO = ((ADVar2*)a)->dL.c->dO - ((ADVar2*)a)->dR.c->dO;
        break;
       case Hv_timesL:
        a->dO = ((ADVar1s*)a)->pL * ((ADVar1s*)a)->d.c->dO;
        break;
       case Hv_timesLR:
        a->dO =   ((ADVar2*)a)->dR.c->Val * ((ADVar2*)a)->dL.c->dO
          + ((ADVar2*)a)->dL.c->Val * ((ADVar2*)a)->dR.c->dO;
        break;
       case Hv_quotLR:
        a->dO =   ((ADVar2q*)a)->pL * ((ADVar2q*)a)->dL.c->dO
          + ((ADVar2q*)a)->pR * ((ADVar2q*)a)->dR.c->dO;
        break;
       case Hv_nary:
        d = ((ADVarn*)a)->D;
        m = ((ADVarn*)a)->n;
        g = ((ADVarn*)a)->G;
        t = 0.;
        for(i = 0; i < m; i++)
          t += g[i] * d[i].c->dO;
        a->dO = t;
       }
      }
    }
  if (a)
    a->adO = 1.;
  for(b = b0; b; b = b->prev) {
    ape = b->pADvari;
    ap = b->limit;
    while(ap > ape) {
      a = *--ap;
      aO = a->aO;
      adO = a->adO;
      switch(a->opclass) {
       case Hv_copy:
        aL = ((ADVar1*)a)->d.c;
        aL->aO += aO;
        aL->adO += adO;
        break;
       case Hv_binary:
        aL = ((ADVar2g*)a)->dL.c;
        aR = ((ADVar2g*)a)->dR.c;
        tL = adO*aL->dO;
        tR = adO*aR->dO;
        aL->aO += aO*((ADVar2g*)a)->pL
          + tL*((ADVar2g*)a)->pL2
          + tR*((ADVar2g*)a)->pLR;
        aR->aO += aO*((ADVar2g*)a)->pR
          + tL*((ADVar2g*)a)->pLR
          + tR*((ADVar2g*)a)->pR2;
        aL->adO += adO * ((ADVar2g*)a)->pL;
        aR->adO += adO * ((ADVar2g*)a)->pR;
        break;
       case Hv_unary:
        aL = ((ADVar1g*)a)->d.c;
        aL->aO += aO * ((ADVar1g*)a)->pL
          + adO * aL->dO * ((ADVar1g*)a)->pL2;
        aL->adO += adO * ((ADVar1g*)a)->pL;
        break;
       case Hv_negate:
        aL = ((ADVar1*)a)->d.c;
        aL->aO -= aO;
        aL->adO -= adO;
        break;
       case Hv_plusLR:
        aL = ((ADVar2*)a)->dL.c;
        aR = ((ADVar2*)a)->dR.c;
        aL->aO += aO;
        aL->adO += adO;
        aR->aO += aO;
        aR->adO += adO;
        break;
       case Hv_minusLR:
        aL = ((ADVar2*)a)->dL.c;
        aR = ((ADVar2*)a)->dR.c;
        aL->aO += aO;
        aL->adO += adO;
        aR->aO -= aO;
        aR->adO -= adO;
        break;
       case Hv_timesL:
        aL = ((ADVar1s*)a)->d.c;
        aL->aO += aO * (tL = ((ADVar1s*)a)->pL);
        aL->adO += adO * tL;
        break;
       case Hv_timesLR:
        aL = ((ADVar2*)a)->dL.c;
        aR = ((ADVar2*)a)->dR.c;
        aL->aO += aO * (tL = aR->Val) + adO*aR->dO;
        aR->aO += aO * (tR = aL->Val) + adO*aL->dO;
        aL->adO += adO * tL;
        aR->adO += adO * tR;
        break;
       case Hv_quotLR:
        aL = ((ADVar2q*)a)->dL.c;
        aR = ((ADVar2q*)a)->dR.c;
        tL = adO*aL->dO;
        tR = adO*aR->dO;
        aL->aO += aO*((ADVar2q*)a)->pL
          + tR*((ADVar2q*)a)->pLR;
        aR->aO += aO*((ADVar2q*)a)->pR
          + tL*((ADVar2q*)a)->pLR
          + tR*((ADVar2q*)a)->pR2;
        aL->adO += adO * ((ADVar2q*)a)->pL;
        aR->adO += adO * ((ADVar2q*)a)->pR;
        break;
       case Hv_nary:
        d  = ((ADVarn*)a)->D;
        m  = ((ADVarn*)a)->n;
        g  = ((ADVarn*)a)->G;
        h0 = ((ADVarn*)a)->H;
        for(i = 0; i < m; i++) {
          aL = d[i].c;
          aL->adO += adO * (t = g[i]);
          aL->aO += t*aO;
          t = adO * aL->dO;
          for(h = h0, j = 0; j <= i; j++)
            d[j].c->aO += t * *h++;
          h0 = h--;
          for(k = j; j < m; j++)
            d[j].c->aO += t * *(h += k++);
          }
       }
      }
    }
  for(i = 0; i < n; i++) {
    a = x[i]->cv;
    a->dO = 0.;
    hv[i] = a->aO;
    }
  }

 template<typename Double>
 inline Double
val(const ADvari<Double> &x) {
  return x.Val;
  }

#undef RAD_ACA
#define A (ADvari<Double>*)
#ifdef RAD_Const_WARN
#define C(x) (((x)->opno < 0) ? RAD_Const_Warn(x) : 0, *A x)
#else
#define C(x) *A x
#endif
#define T template<typename Double> inline
#define F ADvari<Double>&
#define Ai const ADvari<Double>&
#define AI const IndepADvar<Double>&
#define D Double
#define T2(r,f) \
 T r f(Ai L, AI R) { return f(L, C(R.cv)); }\
 T r f(AI L, Ai R) { return f(C(L.cv), R); }\
 T r f(AI L, AI R) { return f(C(L.cv), C(R.cv)); }\
 T r f(AI L, D R) { return f(C(L.cv), R); }\
 T r f(Ai L, Dtype R) { return f(L, (D)R); }\
 T r f(AI L, Dtype R) { return f(C(L.cv), (D)R); }\
 T r f(Ai L, long R) { return f(L, (D)R); }\
 T r f(AI L, long R) { return f(C(L.cv), (D)R); }\
 T r f(Ai L, int R) { return f(L, (D)R); }\
 T r f(AI L, int R) { return f(C(L.cv), (D)R); }\
 T r f(D L, AI R) { return f(L, C(R.cv)); }\
 T r f(Dtype L, Ai R) { return f((D)L, R); }\
 T r f(Dtype L, AI R) { return f((D)L, C(R.cv)); }\
 T r f(long L, Ai R) { return f((D)L, R); }\
 T r f(long L, AI R) { return f((D)L, C(R.cv)); }\
 T r f(int L, Ai R) { return f((D)L, R); }\
 T r f(int L, AI R) { return f((D)L, C(R.cv)); }

T2(F, operator+)
T2(F, operator-)
T2(F, operator*)
T2(F, operator/)
T2(F, atan2)
T2(F, pow)
T2(F, max)
T2(F, min)
T2(int, operator<)
T2(int, operator<=)
T2(int, operator==)
T2(int, operator!=)
T2(int, operator>=)
T2(int, operator>)

#undef T2
#undef D

#define T1(f)\
 T F f(AI x) { return f(C(x.cv)); }

T1(operator+)
T1(operator-)
T1(abs)
T1(acos)
T1(acosh)
T1(asin)
T1(asinh)
T1(atan)
T1(atanh)
T1(cos)
T1(cosh)
T1(exp)
T1(log)
T1(log10)
T1(sin)
T1(sinh)
T1(sqrt)
T1(tan)
T1(tanh)
T1(fabs)

T F copy(AI x)
{ return *(new ADvar1<Double>(Hv_copy, x.cv->Val, &ADcontext<Double>::One, (ADvari<Double>*)x.cv)); }

T F copy(Ai x)
{ return *(new ADvar1<Double>(Hv_copy, x.Val, &ADcontext<Double>::One, (ADvari<Double>*)&x)); }

#undef T1
#undef AI
#undef Ai
#undef F
#undef T
#undef A
#undef C
#undef Ttype
#undef Dtype

} /* namespace Rad2 */
} /* namespace Sacado */

#endif /* SACADO_TRAD2_H */

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