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Diff for /OpenXM_contrib2/asir2000/include/interval.h between version 1.11 and 1.18

version 1.11, 2014/01/07 06:22:08 version 1.18, 2019/12/24 10:26:38
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 /*  /*
  * $OpenXM: OpenXM_contrib2/asir2000/include/interval.h,v 1.10 2006/02/05 06:47:03 noro Exp $   * $OpenXM: OpenXM_contrib2/asir2000/include/interval.h,v 1.17 2019/11/12 10:52:04 kondoh Exp $
 */  */
 #ifndef _INTERVAL_H  #ifndef  _INTERVAL_H
 #define _INTERVAL_H  #define  _INTERVAL_H
   
 #define PRINTF_G        0  #define       INT_ASIR_VERSION        20191219
 #define PRINTF_E        1  
   
   #define  PRINTF_G  0
   #define  PRINTF_E  1
   
 #if defined(INTERVAL)  #if defined(INTERVAL)
   #if INTERVAL == 0
   #undef INTERVAL
   #endif
   #endif
   #if defined(INTERVAL)
   
 #include <math.h>  #include <math.h>
   
 #ifdef  sun  #ifdef  sun
 #if OSMajorVersion < 4 || (OSMajorVersion == 4 && OSMinorVersion < 1)  #if OSMajorVersion < 4 || (OSMajorVersion == 4 && OSMinorVersion < 1)
 #include <sys/ieeefp.h>  #include <sys/ieeefp.h>
 #endif  #endif
 #if defined(__svr4__)  #if defined(__svr4__)
 #include        <ieeefp.h>  #include  <ieeefp.h>
 #define FPNEAREST       fpsetround(FP_RN);  #define  FPNEAREST  fpsetround(FP_RN);
 #define FPPLUSINF       fpsetround(FP_RP);  #define  FPPLUSINF  fpsetround(FP_RP);
 #define FPMINUSINF      fpsetround(FP_RM);  #define  FPMINUSINF  fpsetround(FP_RM);
 #define FPTOZERO        fpsetround(FP_RZ);  #define  FPTOZERO  fpsetround(FP_RZ);
 #else  #else
 static char     *Interval_dummy;  static char  *Interval_dummy;
 #define FPNEAREST       ieee_flags("clear", "direction", Interval_dummy, &Interval_dummy);  #define  FPNEAREST  ieee_flags("clear", "direction", Interval_dummy, &Interval_dummy);
 #define FPPLUSINF       ieee_flags("set", "direction", "positive", &Interval_dummy);  #define  FPPLUSINF  ieee_flags("set", "direction", "positive", &Interval_dummy);
 #define FPMINUSINF      ieee_flags("set", "direction", "negative", &Interval_dummy);  #define  FPMINUSINF  ieee_flags("set", "direction", "negative", &Interval_dummy);
 #define FPTOZERO        ieee_flags("set", "direction", "tozero", &Interval_dummy);  #define  FPTOZERO  ieee_flags("set", "direction", "tozero", &Interval_dummy);
 #endif  #endif
 #endif  #endif
   
 #ifdef  linux  #if 0
 #include        <fpu_control.h>  #ifdef  linux
   #include  <fpu_control.h>
 #if 1  #if 1
 #define LINUX_FPU_RC_MASK                               0xf3ff  
 #define LINUX_FPU_SETCW(c)                      \  #if defined(__ARM_ARCH) || defined(ANDROID)
   #ifndef _FPU_RC_NEAREST
   #define _FPU_RC_NEAREST 0x0
   #endif
   #ifndef _FPU_RC_DOWN
   #define _FPU_RC_DOWN    0x400
   #endif
   #ifndef _FPU_RC_UP
   #define _FPU_RC_UP      0x800
   #endif
   #ifndef _FPU_RC_ZERO
   #define _FPU_RC_ZERO    0xC00
   #endif
   #endif /* __ARM_ARCH */
   
   #define  LINUX_FPU_RC_MASK        0xf3ff
   #define  LINUX_FPU_SETCW(c)      \
 {fpu_control_t __tmp__; _FPU_GETCW(__fpu_control);\  {fpu_control_t __tmp__; _FPU_GETCW(__fpu_control);\
  __tmp__ = (__fpu_control & LINUX_FPU_RC_MASK | c);\   __tmp__ = (__fpu_control & LINUX_FPU_RC_MASK | c);\
  _FPU_SETCW(__tmp__);}   _FPU_SETCW(__tmp__);}
 #define FPNEAREST       LINUX_FPU_SETCW(_FPU_RC_NEAREST);  #define  FPNEAREST  LINUX_FPU_SETCW(_FPU_RC_NEAREST);
 #define FPPLUSINF       LINUX_FPU_SETCW(_FPU_RC_UP);  #define  FPPLUSINF  LINUX_FPU_SETCW(_FPU_RC_UP);
 #define FPMINUSINF      LINUX_FPU_SETCW(_FPU_RC_DOWN);  #define  FPMINUSINF  LINUX_FPU_SETCW(_FPU_RC_DOWN);
 #define FPTOZERO                LINUX_FPU_SETCW(_FPU_RC_ZERO);  #define  FPTOZERO    LINUX_FPU_SETCW(_FPU_RC_ZERO);
 #else  #else
 #define _FPU_DEFAULT_p_FPU_RC_UP        0x1b72  #define  _FPU_DEFAULT_p_FPU_RC_UP  0x1b72
 #define _FPU_DEFAULT_p_FPU_RC_DOWN      0x1772  #define  _FPU_DEFAULT_p_FPU_RC_DOWN  0x1772
 #define _FPU_DEFAULT_p_FPU_RC_ZERO      0x1f72  #define  _FPU_DEFAULT_p_FPU_RC_ZERO  0x1f72
 #define FPNEAREST       __setfpucw(_FPU_DEFAULT);  #define  FPNEAREST  __setfpucw(_FPU_DEFAULT);
 #define FPPLUSINF       __setfpucw(_FPU_DEFAULT_p_FPU_RC_UP);  #define  FPPLUSINF  __setfpucw(_FPU_DEFAULT_p_FPU_RC_UP);
 #define FPMINUSINF      __setfpucw(_FPU_DEFAULT_p_FPU_RC_DOWN);  #define  FPMINUSINF  __setfpucw(_FPU_DEFAULT_p_FPU_RC_DOWN);
 #define FPTOZERO        __setfpucw(_FPU_DEFAULT_p_FPU_RC_ZERO);  #define  FPTOZERO  __setfpucw(_FPU_DEFAULT_p_FPU_RC_ZERO);
 #endif  #endif
 #endif  #endif
   
 #if defined(__osf__)  #if defined(__osf__)
 #if 0  #if 0
 #include        <float.h>  #include  <float.h>
 #define FPNEAREST       write_rnd(FP_RND_RN);  #define  FPNEAREST  write_rnd(FP_RND_RN);
 #define FPPLUSINF       write_rnd(FP_RND_RP);  #define  FPPLUSINF  write_rnd(FP_RND_RP);
 #define FPMINUSINF      write_rnd(FP_RND_RM);  #define  FPMINUSINF  write_rnd(FP_RND_RM);
 #define FPTOZERO        write_rnd(FP_RND_RZ);  #define  FPTOZERO  write_rnd(FP_RND_RZ);
 #else  #else
 #define FPNEAREST  #define  FPNEAREST
 #define FPPLUSINF  #define  FPPLUSINF
 #define FPMINUSINF  #define  FPMINUSINF
 #define FPTOZERO  #define  FPTOZERO
 #endif  #endif
 #endif  #endif
   
 #if defined(__FreeBSD__) && defined(__GNUC__)  #if defined(__FreeBSD__) && defined(__GNUC__)
 #include        <floatingpoint.h>  #include  <floatingpoint.h>
 #define FPNEAREST       fpsetround(FP_RN);  #define  FPNEAREST  fpsetround(FP_RN);
 #define FPPLUSINF       fpsetround(FP_RP);  #define  FPPLUSINF  fpsetround(FP_RP);
 #define FPMINUSINF      fpsetround(FP_RM);  #define  FPMINUSINF  fpsetround(FP_RM);
 #define FPTOZERO        fpsetround(FP_RZ);  #define  FPTOZERO  fpsetround(FP_RZ);
 #endif  #endif
   
 #if defined(VISUAL)  #if defined(VISUAL) || defined(__MINGW32__)
 #include <float.h>  #include <float.h>
 #define FPNEAREST _controlfp(_RC_NEAR,_MCW_RC);  #define FPNEAREST _controlfp(_RC_NEAR,_MCW_RC);
 #define FPPLUSINF _controlfp(_RC_UP,_MCW_RC);  #define FPPLUSINF _controlfp(_RC_UP,_MCW_RC);
 #define FPMINUSINF _controlfp(_RC_DOWN,_MCW_RC);  #define FPMINUSINF _controlfp(_RC_DOWN,_MCW_RC);
 #define FPTOZERO _controlfp(_RC_CHOP,_MCW_RC);  #define FPTOZERO _controlfp(_RC_CHOP,_MCW_RC);
 #endif  #endif
   #endif
   #include <fenv.h>
   
   #define FPNEAREST       fesetround(FE_TONEAREST);
   #define FPPLUSINF       fesetround(FE_UPWARD);
   #define FPMINUSINF      fesetround(FE_DOWNWARD);
   #define FPTOZERO        fesetround(FE_TOWARDZERO);
   
   
 /* no control function of floating point rounding */  /* no control function of floating point rounding */
 #ifndef FPNEAREST  #ifndef FPNEAREST
 #define FPNEAREST       fprintf(stderr, "Fpu control FPNEAREST is not supported in this machine yet.\n");  #define  FPNEAREST  fprintf(stderr, "Fpu control FPNEAREST is not supported in this machine yet.\n");
 #endif  #endif
 #ifndef FPMINUSINF  #ifndef FPMINUSINF
 #define FPMINUSINF      fprintf(stderr, "Fpu control FPMINUSINF is not supported in this machine yet.\n");  #define  FPMINUSINF  fprintf(stderr, "Fpu control FPMINUSINF is not supported in this machine yet.\n");
 #endif  #endif
 #ifndef FPPLUSINF  #ifndef FPPLUSINF
 #define FPPLUSINF       fprintf(stderr, "Fpu control FPPLUSINF is not supported in this machine yet.\n");  #define  FPPLUSINF  fprintf(stderr, "Fpu control FPPLUSINF is not supported in this machine yet.\n");
 #endif  #endif
 #ifndef FPTOZERO  #ifndef FPTOZERO
 #define FPTOZERO        fprintf(stderr, "Fpu control FPZERO is not supported in this machine yet.\n");  #define  FPTOZERO  fprintf(stderr, "Fpu control FPZERO is not supported in this machine yet.\n");
 #endif  #endif
 #define FPCLEAR         FPNEAREST  #define FPCLEAR    FPNEAREST
   
 #define MID_PRINTF_G    2  #define  MID_PRINTF_G  2
 #define MID_PRINTF_E    3  #define  MID_PRINTF_E  3
   
   #define DEFAULTPREC     0 //mpfr_get_default_prec()     /* for mpfr */
   
 /* data structures */  /* data structures */
 struct oItv {  struct oItv {
         short   id;          short  id;
         char    nid;          char  nid;
         char    pad;          char  pad;
         Num     inf;          Num  inf;
         Num     sup;          Num  sup;
 };  };
   
 typedef struct oItv *Itv;  typedef struct oItv *Itv;
   
 struct oIntervalDouble {  struct oIntervalDouble {
         short   id;          short  id;
         char    nid;          char  nid;
         char    pad;          char  pad;
         double  inf;          double  inf;
         double  sup;          double  sup;
 };  };
   
 typedef struct oIntervalDouble *IntervalDouble;  typedef struct oIntervalDouble *IntervalDouble;
   
 struct oforth {  struct oforth {
         short   sign;    short  sign;
         short   exp;    short  exp;
         double  u;    double  u;
         double  l;    double  l;
 };  };
   
 typedef struct oforth *forth;  typedef struct oforth *forth;
   
 struct oIntervalQuad {  struct oIntervalQuad {
         short   id;          short  id;
         char    nid;          char  nid;
         char    pad;          char  pad;
         forth   inf;          forth  inf;
         forth   sup;          forth  sup;
 };  };
   
 typedef struct oIntervalQuad *IntervalQuad;  typedef struct oIntervalQuad *IntervalQuad;
   
 struct oIntervalBigFloat {  struct oIntervalBigFloat {
         short   id;          short  id;
         char    nid;          char  nid;
         char    pad;          char  pad;
         BF      inf;          BF  inf;
         BF      sup;          BF  sup;
 };  };
   
 typedef struct oIntervalBigFloat *IntervalBigFloat;  typedef struct oIntervalBigFloat *IntervalBigFloat;
   
 extern int zerorewrite;  extern int zerorewrite;
   extern int zerorewriteCount;
   
   #define ZEROREWRITE       if (zerorewrite && initvp(0,c) ) { *rp = 0; zerorewriteCount++; }
   
 /* general macros */  /* general macros */
 #define INF(p)  ((p)->inf)  #define INF(p)  ((p)->inf)
 #define SUP(p)  ((p)->sup)  #define SUP(p)  ((p)->sup)
   
 #define NEWItvP(q)      ((q)=(Itv)MALLOC(sizeof(struct oItv)),\  #define NEWItvP(q)  ((q)=(Itv)MALLOC(sizeof(struct oItv)),\
                                         OID(q)=O_N,NID(q)=N_IP)            OID(q)=O_N,NID(q)=N_IP)
 #define NEWIntervalDouble(q)    ((q)=(IntervalDouble)MALLOC(sizeof(struct oIntervalDouble)),\  #define NEWIntervalDouble(q)  ((q)=(IntervalDouble)MALLOC(sizeof(struct oIntervalDouble)),\
                                         OID(q)=O_N,NID(q)=N_IntervalDouble)            OID(q)=O_N,NID(q)=N_IntervalDouble)
 #define NEWIntervalQuad(q)      ((q)=(IntervalDouble)MALLOC(sizeof(struct oIntervalQuad)),\  #define NEWIntervalQuad(q)  ((q)=(IntervalDouble)MALLOC(sizeof(struct oIntervalQuad)),\
                                         OID(q)=O_N,NID(q)=N_IntervalQuad)            OID(q)=O_N,NID(q)=N_IntervalQuad)
 #define NEWIntervalBigFloat(q)  ((q)=(IntervalBigFloat)MALLOC(sizeof(struct oIntervalBigFloat)),\  #define NEWIntervalBigFloat(q)  ((q)=(IntervalBigFloat)MALLOC(sizeof(struct oIntervalBigFloat)),\
                                         OID(q)=O_N,NID(q)=N_IntervalBigFloat)            OID(q)=O_N,NID(q)=N_IntervalBigFloat)
 #define MKItvP(a,b,c)   (NEWItvP(c),(INF(c)=(a),SUP(c)=(b)))  #define MKItvP(a,b,c)  (NEWItvP(c),(INF(c)=(a),SUP(c)=(b)))
 #define MKIntervalDouble(a,b,c) if((zerorewrite) && ((a)<=0.0) && ((b)>=0.0)) (c)=0;\  #define MKIntervalDouble(a,b,c)  if((zerorewrite) && ((a)<=0.0) && ((b)>=0.0)) {(c)=0;zerorewriteCount++;}\
                         else (NEWIntervalDouble(c),(INF(c)=(a),SUP(c)=(b)))          else (NEWIntervalDouble(c),(INF(c)=(a),SUP(c)=(b)))
 #define MKIntervalQuad(a,b,c)   (NEWIntervalQuad(c),(INF(c)=(a),SUP(c)=(b)))  #define MKIntervalQuad(a,b,c)  (NEWIntervalQuad(c),(INF(c)=(a),SUP(c)=(b)))
 #define MKIntervalBigFloat(a,b,c)       (NEWIntervalBigFloat(c),(INF(c)=(a),SUP(c)=(b)))  #define MKIntervalBigFloat(a,b,c)  (NEWIntervalBigFloat(c),(INF(c)=(a),SUP(c)=(b)))
   
 #define ToItvP(a,c)     (NEWItvP(c),INF(c)=(a),SUP(c)=(a))  #define ToItvP(a,c)  (NEWItvP(c),INF(c)=(a),SUP(c)=(a))
 #define ToIntervalDouble(a,c)   (NEWIntervalDouble(c),INF(c)=(ToReal(a)),SUP(c)=(ToReal(a)))  #define ToIntervalDouble(a,c)  (NEWIntervalDouble(c),INF(c)=(toRealDown(a)),SUP(c)=(toRealUp(a)))
 #define ToIntervalBigFloat(a,c) (NEWIntervalBigFloat(c),INF(c)=(a),SUP(c)=(a))  #define ToIntervalBigFloat(a,c)  (NEWIntervalBigFloat(c),INF(c)=(a),SUP(c)=(a))
   
 #define ITVP(a) (NID(a)==N_IP)  #define ITVP(a) (NID(a)==N_IP)
 #define ITVD(a) (NID(a)==N_IntervalDouble)  #define ITVD(a) (NID(a)==N_IntervalDouble)
 #define ITVQ(a) (NID(a)==N_IntervalQuad)  #define ITVQ(a) (NID(a)==N_IntervalQuad)
 #define ITVF(a) (NID(a)==N_IntervalBigFloat)  #define ITVF(a) (NID(a)==N_IntervalBigFloat)
   
 /***    engine/itv.c    ***/  #define EvalIntervalDouble              0
   #define EvalIntervalQuad                1
   #define EvalIntervalBigFloat    2
   
   #if 0
 double  ToRealSup(Num);  double  ToRealSup(Num);
 double  ToRealInf(Num);  double  ToRealInf(Num);
 double  RatnToRealUp(Q);  double  RatnToRealUp(Q);
 double  NatToRealUp(N, int *);  double  NatToRealUp(N, int *);
   
 void    double2bf(double, BF *);  void  double2bf(double, BF *);
 double  bf2double(BF);  double  bf2double(BF);
   
 void    itvtois(Itv, Num *, Num *);  
 void    istoitv(Num, Num, Itv *);  
   
 #if 0  
 void    additv(Num, Num, Num *);  void    additv(Num, Num, Num *);
 void    subitv(Num, Num, Num *);  void    subitv(Num, Num, Num *);
 void    mulitv(Num, Num, Num *);  void    mulitv(Num, Num, Num *);
Line 212  void    widthitv(Itv, Num *);
Line 250  void    widthitv(Itv, Num *);
 void    distanceitv(Itv, Itv, Num *);  void    distanceitv(Itv, Itv, Num *);
 #endif  #endif
   
   /***    engine/p-itv.c    ***/
   void  itvtois(Itv, Num *, Num *);
   void  istoitv(Num, Num, Itv *);
   
 void    additvp(Itv, Itv, Itv *);  void    additvp(Itv, Itv, Itv *);
 void    subitvp(Itv, Itv, Itv *);  void    subitvp(Itv, Itv, Itv *);
 void    mulitvp(Itv, Itv, Itv *);  void    mulitvp(Itv, Itv, Itv *);
 void    divitvp(Itv, Itv, Itv *);  void    divitvp(Itv, Itv, Itv *);
 void    chsgnitvp(Itv, Itv *);  
 int     cmpitvp(Itv, Itv);  
 void    pwritvp(Itv, Num, Itv *);  void    pwritvp(Itv, Num, Itv *);
 void    pwritv0p(Itv, int, Itv *);  void    pwritv0p(Itv, int, Itv *);
   void    chsgnitvp(Itv, Itv *);
   int     initvp(Num , Itv );
   int     itvinitvp(Itv, Itv);
   int     cmpitvp(Itv, Itv);
   void miditvp(Itv, Num *);
 void    cupitvp(Itv, Itv, Itv *);  void    cupitvp(Itv, Itv, Itv *);
 void    capitvp(Itv, Itv, Itv *);  void    capitvp(Itv, Itv, Itv *);
 void    widthitvp(Itv, Num *);  void    widthitvp(Itv, Num *);
   void    absitvp(Itv, Num *);
   void    absintvalp(Itv, Itv *);
 void    distanceitvp(Itv, Itv, Num *);  void    distanceitvp(Itv, Itv, Num *);
   
 void    ToBf(Num, BF *);  
 void    double2bf(double, BF *);  
 double  bf2double(BF);  
 void    addulp(IntervalBigFloat, IntervalBigFloat *);  
 void    getulp(BF, BF *);  
   
   /***    engine/f-itv.c    ***/
   
   //void  ToBf(Num, BF *);
   //void  double2bf(double, BF *);
   //double  bf2double(BF);
   //void  addulp(IntervalBigFloat, IntervalBigFloat *);
   //void  getulp(BF, BF *);
   double mpfr2dblDown(mpfr_t);
   double mpfr2dblUp(mpfr_t);
   void toInterval(Num, int, int, Num *);
   
 void    additvf(IntervalBigFloat, IntervalBigFloat, IntervalBigFloat *);  void    additvf(IntervalBigFloat, IntervalBigFloat, IntervalBigFloat *);
 void    subitvf(IntervalBigFloat, IntervalBigFloat, IntervalBigFloat *);  void    subitvf(IntervalBigFloat, IntervalBigFloat, IntervalBigFloat *);
 void    mulitvf(IntervalBigFloat, IntervalBigFloat, IntervalBigFloat *);  void    mulitvf(IntervalBigFloat, IntervalBigFloat, IntervalBigFloat *);
 void    divitvf(IntervalBigFloat, IntervalBigFloat, IntervalBigFloat *);  void    divitvf(IntervalBigFloat, IntervalBigFloat, IntervalBigFloat *);
 void    chsgnitvf(Itv, Itv *);  void    chsgnitvf(IntervalBigFloat, IntervalBigFloat *);
   int     initvf(Num, Itv);
   int     itvinitvf(Itv, Itv);
 int     cmpitvf(Itv, Itv);  int     cmpitvf(Itv, Itv);
 void    pwritvf(Itv, Num, Itv *);  void    pwritvf(Itv, Num, Itv *);
 void    pwritv0f(Itv, int, Itv *);  void    pwritv0f(Itv, int, Itv *);
   void miditvf(Itv, Num *);
   void cupitvf(Itv, Itv, Itv *);
   void capitvf(Itv, Itv, Itv *);
   void widthitvf(Itv, Num *);
   void absitvf(Itv, Num *);
   void distanceitvf(Itv, Itv, Num *);
   
 /***    engine/d-itv.c    ***/  /***    engine/d-itv.c    ***/
 double  ToRealDown(Num);  double  toRealDown(Num);
 double  ToRealUp(Num);  double  toRealUp(Num);
 void    Num2double(Num, double *, double *);  void  Num2double(Num, double *, double *);
   
 void    additvd(Num, Num, IntervalDouble *);  void    additvd(Num, Num, IntervalDouble *);
 void    subitvd(Num, Num, IntervalDouble *);  void    subitvd(Num, Num, IntervalDouble *);
 void    mulitvd(Num, Num, IntervalDouble *);  void    mulitvd(Num, Num, IntervalDouble *);
 void    divitvd(Num, Num, IntervalDouble *);  void    divitvd(Num, Num, IntervalDouble *);
 void    chsgnitvd(IntervalDouble, IntervalDouble *);  void    chsgnitvd(IntervalDouble, IntervalDouble *);
   int     initvd(Num, IntervalDouble);
 int     cmpitvd(IntervalDouble, IntervalDouble);  int     cmpitvd(IntervalDouble, IntervalDouble);
 void    pwritvd(Num, Num, IntervalDouble *);  void    pwritvd(Num, Num, IntervalDouble *);
 void    pwritv0d(IntervalDouble, int, IntervalDouble *);  void    pwritv0d(IntervalDouble, int, IntervalDouble *);
Line 258  void    cupitvd(IntervalDouble, IntervalDouble, Interv
Line 320  void    cupitvd(IntervalDouble, IntervalDouble, Interv
 void    capitvd(IntervalDouble, IntervalDouble, IntervalDouble *);  void    capitvd(IntervalDouble, IntervalDouble, IntervalDouble *);
 void    widthitvd(IntervalDouble, Num *);  void    widthitvd(IntervalDouble, Num *);
 void    absitvd(IntervalDouble, Num *);  void    absitvd(IntervalDouble, Num *);
   void    absintvald(IntervalDouble, IntervalDouble *);
 void    distanceitvd(IntervalDouble, IntervalDouble, Num *);  void    distanceitvd(IntervalDouble, IntervalDouble, Num *);
   
   /***    builtin/itvnum.c    ***/
   
   void evalitvr(VL ,Obj ,int , int , Obj *);
   void evalitvp(VL ,P ,int , int , P *);
   void evalitvv(VL ,V ,int , int , Obj *);
   //void evalitvins(PFINS ,int , int , Obj *);
   extern void (*pi_itv_ft[])();
   extern void (*e_itv_ft[])();
   extern void (*sin_itv_ft[])();
   extern void (*cos_itv_ft[])();
   extern void (*tan_itv_ft[])();
   extern void (*asin_itv_ft[])();
   extern void (*acos_itv_ft[])();
   extern void (*atan_itv_ft[])();
   extern void (*sinh_itv_ft[])();
   extern void (*cosh_itv_ft[])();
   extern void (*tanh_itv_ft[])();
   extern void (*asinh_itv_ft[])();
   extern void (*acosh_itv_ft[])();
   extern void (*atanh_itv_ft[])();
   extern void (*exp_itv_ft[])();
   extern void (*log_itv_ft[])();
   extern void (*abs_itv_ft[])();
   extern void (*pow_itv_ft[])();
   //void devalr(VL ,Obj ,Obj *);
   //void devalp(VL ,P ,P *);
   //void devalv(VL ,V ,Obj *);
   //void devalins(PFINS ,Obj *);
   
   void Pitvbf_pi(NODE ,Obj *);
   void Pitvbf_e(NODE ,Obj *);
   void Pitvbf_sin(NODE ,Obj *);
   void Pitvbf_cos(NODE ,Obj *);
   void Pitvbf_tan(NODE ,Obj *);
   void Pitvbf_asin(NODE ,Obj *);
   void Pitvbf_acos(NODE ,Obj *);
   void Pitvbf_atan(NODE ,Obj *);
   void Pitvbf_sinh(NODE ,Obj *);
   void Pitvbf_cosh(NODE ,Obj *);
   void Pitvbf_tanh(NODE ,Obj *);
   void Pitvbf_asinh(NODE ,Obj *);
   void Pitvbf_acosh(NODE ,Obj *);
   void Pitvbf_atanh(NODE ,Obj *);
   void Pitvbf_exp(NODE ,Obj *);
   void Pitvbf_log(NODE ,Obj *);
   void Pitvbf_abs(NODE ,Obj *);
   //void mp_factorial(NODE ,Num *);
   void Pitvbf_pow(NODE ,Num *);
   
   void Pitvd_pi(NODE ,Obj *);
   void Pitvd_e(NODE ,Obj *);
   void Pitvd_sin(NODE ,Obj *);
   void Pitvd_cos(NODE ,Obj *);
   void Pitvd_tan(NODE ,Obj *);
   void Pitvd_asin(NODE ,Obj *);
   void Pitvd_acos(NODE ,Obj *);
   void Pitvd_atan(NODE ,Obj *);
   void Pitvd_sinh(NODE ,Obj *);
   void Pitvd_cosh(NODE ,Obj *);
   void Pitvd_tanh(NODE ,Obj *);
   void Pitvd_asinh(NODE ,Obj *);
   void Pitvd_acosh(NODE ,Obj *);
   void Pitvd_atanh(NODE ,Obj *);
   void Pitvd_exp(NODE ,Obj *);
   void Pitvd_log(NODE ,Obj *);
   void Pitvd_abs(NODE ,Obj *);
   void Pitvd_pow(NODE ,Num *);
   
 #endif /* end of INTERVAL */  #endif /* end of INTERVAL */
 #endif /* end of _INTERVAL_H */  #endif /* end of _INTERVAL_H */
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  Added in v.1.18
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