path: root/libdecnumber/dpd/decimal64.c

/* Decimal 64-bit format module for the decNumber C Library.
   Copyright (C) 2005-2018 Free Software Foundation, Inc.
   Contributed by IBM Corporation.  Author Mike Cowlishaw.

   This file is part of GCC.

   GCC is free software; you can redistribute it and/or modify it under
   the terms of the GNU General Public License as published by the Free
   Software Foundation; either version 3, or (at your option) any later
   version.

   GCC 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 General Public License
   for more details.

Under Section 7 of GPL version 3, you are granted additional
permissions described in the GCC Runtime Library Exception, version
3.1, as published by the Free Software Foundation.

You should have received a copy of the GNU General Public License and
a copy of the GCC Runtime Library Exception along with this program;
see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
<http://www.gnu.org/licenses/>.  */

/* ------------------------------------------------------------------ */
/* Decimal 64-bit format module 				      */
/* ------------------------------------------------------------------ */
/* This module comprises the routines for decimal64 format numbers.   */
/* Conversions are supplied to and from decNumber and String.	      */
/*								      */
/* This is used when decNumber provides operations, either for all    */
/* operations or as a proxy between decNumber and decSingle.	      */
/*								      */
/* Error handling is the same as decNumber (qv.).		      */
/* ------------------------------------------------------------------ */
#include <string.h>	      /* [for memset/memcpy] */
#include <stdio.h>	      /* [for printf] */

#include "dconfig.h"          /* GCC definitions */
#define  DECNUMDIGITS 16      /* make decNumbers with space for 16 */
#include "decNumber.h"	      /* base number library */
#include "decNumberLocal.h"   /* decNumber local types, etc. */
#include "decimal64.h"	      /* our primary include */

/* Utility routines and tables [in decimal64.c]; externs for C++ */
extern const uInt COMBEXP[32], COMBMSD[32];
extern const uShort DPD2BIN[1024];
extern const uShort BIN2DPD[1000];
extern const uByte  BIN2CHAR[4001];

extern void decDigitsFromDPD(decNumber *, const uInt *, Int);
extern void decDigitsToDPD(const decNumber *, uInt *, Int);

#if DECTRACE || DECCHECK
void decimal64Show(const decimal64 *);		  /* for debug */
extern void decNumberShow(const decNumber *);	  /* .. */
#endif

/* Useful macro */
/* Clear a structure (e.g., a decNumber) */
#define DEC_clear(d) memset(d, 0, sizeof(*d))

/* define and include the tables to use for conversions */
#define DEC_BIN2CHAR 1
#define DEC_DPD2BIN  1
#define DEC_BIN2DPD  1		   /* used for all sizes */
#include "decDPD.h"		   /* lookup tables */

/* ------------------------------------------------------------------ */
/* decimal64FromNumber -- convert decNumber to decimal64	      */
/*								      */
/*   ds is the target decimal64 				      */
/*   dn is the source number (assumed valid)			      */
/*   set is the context, used only for reporting errors 	      */
/*								      */
/* The set argument is used only for status reporting and for the     */
/* rounding mode (used if the coefficient is more than DECIMAL64_Pmax */
/* digits or an overflow is detected).	If the exponent is out of the */
/* valid range then Overflow or Underflow will be raised.	      */
/* After Underflow a subnormal result is possible.		      */
/*								      */
/* DEC_Clamped is set if the number has to be 'folded down' to fit,   */
/* by reducing its exponent and multiplying the coefficient by a      */
/* power of ten, or if the exponent on a zero had to be clamped.      */
/* ------------------------------------------------------------------ */
decimal64 * decimal64FromNumber(decimal64 *d64, const decNumber *dn,
				decContext *set) {
  uInt status=0;		   /* status accumulator */
  Int ae;			   /* adjusted exponent */
  decNumber  dw;		   /* work */
  decContext dc;		   /* .. */
  uInt comb, exp;		   /* .. */
  uInt uiwork;			   /* for macros */
  uInt targar[2]={0, 0};	   /* target 64-bit */
  #define targhi targar[1]	   /* name the word with the sign */
  #define targlo targar[0]	   /* and the other */

  /* If the number has too many digits, or the exponent could be */
  /* out of range then reduce the number under the appropriate */
  /* constraints.  This could push the number to Infinity or zero, */
  /* so this check and rounding must be done before generating the */
  /* decimal64] */
  ae=dn->exponent+dn->digits-1; 	     /* [0 if special] */
  if (dn->digits>DECIMAL64_Pmax 	     /* too many digits */
   || ae>DECIMAL64_Emax 		     /* likely overflow */
   || ae<DECIMAL64_Emin) {		     /* likely underflow */
    decContextDefault(&dc, DEC_INIT_DECIMAL64); /* [no traps] */
    dc.round=set->round;		     /* use supplied rounding */
    decNumberPlus(&dw, dn, &dc);	     /* (round and check) */
    /* [this changes -0 to 0, so enforce the sign...] */
    dw.bits|=dn->bits&DECNEG;
    status=dc.status;			     /* save status */
    dn=&dw;				     /* use the work number */
    } /* maybe out of range */

  if (dn->bits&DECSPECIAL) {			  /* a special value */
    if (dn->bits&DECINF) targhi=DECIMAL_Inf<<24;
     else {					  /* sNaN or qNaN */
      if ((*dn->lsu!=0 || dn->digits>1) 	  /* non-zero coefficient */
       && (dn->digits<DECIMAL64_Pmax)) {	  /* coefficient fits */
	decDigitsToDPD(dn, targar, 0);
	}
      if (dn->bits&DECNAN) targhi|=DECIMAL_NaN<<24;
       else targhi|=DECIMAL_sNaN<<24;
      } /* a NaN */
    } /* special */

   else { /* is finite */
    if (decNumberIsZero(dn)) {		     /* is a zero */
      /* set and clamp exponent */
      if (dn->exponent<-DECIMAL64_Bias) {
	exp=0;				     /* low clamp */
	status|=DEC_Clamped;
	}
       else {
	exp=dn->exponent+DECIMAL64_Bias;     /* bias exponent */
	if (exp>DECIMAL64_Ehigh) {	     /* top clamp */
	  exp=DECIMAL64_Ehigh;
	  status|=DEC_Clamped;
	  }
	}
      comb=(exp>>5) & 0x18;		/* msd=0, exp top 2 bits .. */
      }
     else {				/* non-zero finite number */
      uInt msd; 			/* work */
      Int pad=0;			/* coefficient pad digits */

      /* the dn is known to fit, but it may need to be padded */
      exp=(uInt)(dn->exponent+DECIMAL64_Bias);	  /* bias exponent */
      if (exp>DECIMAL64_Ehigh) {		  /* fold-down case */
	pad=exp-DECIMAL64_Ehigh;
	exp=DECIMAL64_Ehigh;			  /* [to maximum] */
	status|=DEC_Clamped;
	}

      /* fastpath common case */
      if (DECDPUN==3 && pad==0) {
	uInt dpd[6]={0,0,0,0,0,0};
	uInt i;
	Int d=dn->digits;
	for (i=0; d>0; i++, d-=3) dpd[i]=BIN2DPD[dn->lsu[i]];
	targlo =dpd[0];
	targlo|=dpd[1]<<10;
	targlo|=dpd[2]<<20;
	if (dn->digits>6) {
	  targlo|=dpd[3]<<30;
	  targhi =dpd[3]>>2;
	  targhi|=dpd[4]<<8;
	  }
	msd=dpd[5];		   /* [did not really need conversion] */
	}
       else { /* general case */
	decDigitsToDPD(dn, targar, pad);
	/* save and clear the top digit */
	msd=targhi>>18;
	targhi&=0x0003ffff;
	}

      /* create the combination field */
      if (msd>=8) comb=0x18 | ((exp>>7) & 0x06) | (msd & 0x01);
	     else comb=((exp>>5) & 0x18) | msd;
      }
    targhi|=comb<<26;		   /* add combination field .. */
    targhi|=(exp&0xff)<<18;	   /* .. and exponent continuation */
    } /* finite */

  if (dn->bits&DECNEG) targhi|=0x80000000; /* add sign bit */

  /* now write to storage; this is now always endian */
  if (DECLITEND) {
    /* lo int then hi */
    UBFROMUI(d64->bytes,   targar[0]);
    UBFROMUI(d64->bytes+4, targar[1]);
    }
   else {
    /* hi int then lo */
    UBFROMUI(d64->bytes,   targar[1]);
    UBFROMUI(d64->bytes+4, targar[0]);
    }

  if (status!=0) decContextSetStatus(set, status); /* pass on status */
  /* decimal64Show(d64); */
  return d64;
  } /* decimal64FromNumber */

/* ------------------------------------------------------------------ */
/* decimal64ToNumber -- convert decimal64 to decNumber		      */
/*   d64 is the source decimal64				      */
/*   dn is the target number, with appropriate space		      */
/* No error is possible.					      */
/* ------------------------------------------------------------------ */
decNumber * decimal64ToNumber(const decimal64 *d64, decNumber *dn) {
  uInt msd;			   /* coefficient MSD */
  uInt exp;			   /* exponent top two bits */
  uInt comb;			   /* combination field */
  Int  need;			   /* work */
  uInt uiwork;			   /* for macros */
  uInt sourar[2];		   /* source 64-bit */
  #define sourhi sourar[1]	   /* name the word with the sign */
  #define sourlo sourar[0]	   /* and the lower word */

  /* load source from storage; this is endian */
  if (DECLITEND) {
    sourlo=UBTOUI(d64->bytes  );   /* directly load the low int */
    sourhi=UBTOUI(d64->bytes+4);   /* then the high int */
    }
   else {
    sourhi=UBTOUI(d64->bytes  );   /* directly load the high int */
    sourlo=UBTOUI(d64->bytes+4);   /* then the low int */
    }

  comb=(sourhi>>26)&0x1f;	   /* combination field */

  decNumberZero(dn);		   /* clean number */
  if (sourhi&0x80000000) dn->bits=DECNEG; /* set sign if negative */

  msd=COMBMSD[comb];		   /* decode the combination field */
  exp=COMBEXP[comb];		   /* .. */

  if (exp==3) { 		   /* is a special */
    if (msd==0) {
      dn->bits|=DECINF;
      return dn;		   /* no coefficient needed */
      }
    else if (sourhi&0x02000000) dn->bits|=DECSNAN;
    else dn->bits|=DECNAN;
    msd=0;			   /* no top digit */
    }
   else {			   /* is a finite number */
    dn->exponent=(exp<<8)+((sourhi>>18)&0xff)-DECIMAL64_Bias; /* unbiased */
    }

  /* get the coefficient */
  sourhi&=0x0003ffff;		   /* clean coefficient continuation */
  if (msd) {			   /* non-zero msd */
    sourhi|=msd<<18;		   /* prefix to coefficient */
    need=6;			   /* process 6 declets */
    }
   else { /* msd=0 */
    if (!sourhi) {		   /* top word 0 */
      if (!sourlo) return dn;	   /* easy: coefficient is 0 */
      need=3;			   /* process at least 3 declets */
      if (sourlo&0xc0000000) need++; /* process 4 declets */
      /* [could reduce some more, here] */
      }
     else {			   /* some bits in top word, msd=0 */
      need=4;			   /* process at least 4 declets */
      if (sourhi&0x0003ff00) need++; /* top declet!=0, process 5 */
      }
    } /*msd=0 */

  decDigitsFromDPD(dn, sourar, need);	/* process declets */
  return dn;
  } /* decimal64ToNumber */


/* ------------------------------------------------------------------ */
/* to-scientific-string -- conversion to numeric string 	      */
/* to-engineering-string -- conversion to numeric string	      */
/*								      */
/*   decimal64ToString(d64, string);				      */
/*   decimal64ToEngString(d64, string); 			      */
/*								      */
/*  d64 is the decimal64 format number to convert		      */
/*  string is the string where the result will be laid out	      */
/*								      */
/*  string must be at least 24 characters			      */
/*								      */
/*  No error is possible, and no status can be set.		      */
/* ------------------------------------------------------------------ */
char * decimal64ToEngString(const decimal64 *d64, char *string){
  decNumber dn; 			/* work */
  decimal64ToNumber(d64, &dn);
  decNumberToEngString(&dn, string);
  return string;
  } /* decimal64ToEngString */

char * decimal64ToString(const decimal64 *d64, char *string){
  uInt msd;			   /* coefficient MSD */
  Int  exp;			   /* exponent top two bits or full */
  uInt comb;			   /* combination field */
  char *cstart; 		   /* coefficient start */
  char *c;			   /* output pointer in string */
  const uByte *u;		   /* work */
  char *s, *t;			   /* .. (source, target) */
  Int  dpd;			   /* .. */
  Int  pre, e;			   /* .. */
  uInt uiwork;			   /* for macros */

  uInt sourar[2];		   /* source 64-bit */
  #define sourhi sourar[1]	   /* name the word with the sign */
  #define sourlo sourar[0]	   /* and the lower word */

  /* load source from storage; this is endian */
  if (DECLITEND) {
    sourlo=UBTOUI(d64->bytes  );   /* directly load the low int */
    sourhi=UBTOUI(d64->bytes+4);   /* then the high int */
    }
   else {
    sourhi=UBTOUI(d64->bytes  );   /* directly load the high int */
    sourlo=UBTOUI(d64->bytes+4);   /* then the low int */
    }

  c=string;			   /* where result will go */
  if (((Int)sourhi)<0) *c++='-';   /* handle sign */

  comb=(sourhi>>26)&0x1f;	   /* combination field */
  msd=COMBMSD[comb];		   /* decode the combination field */
  exp=COMBEXP[comb];		   /* .. */

  if (exp==3) {
    if (msd==0) {		   /* infinity */
      strcpy(c,   "Inf");
      strcpy(c+3, "inity");
      return string;		   /* easy */
      }
    if (sourhi&0x02000000) *c++='s'; /* sNaN */
    strcpy(c, "NaN");		   /* complete word */
    c+=3;			   /* step past */
    if (sourlo==0 && (sourhi&0x0003ffff)==0) return string; /* zero payload */
    /* otherwise drop through to add integer; set correct exp */
    exp=0; msd=0;		   /* setup for following code */
    }
   else exp=(exp<<8)+((sourhi>>18)&0xff)-DECIMAL64_Bias;

  /* convert 16 digits of significand to characters */
  cstart=c;			   /* save start of coefficient */
  if (msd) *c++='0'+(char)msd;	   /* non-zero most significant digit */

  /* Now decode the declets.  After extracting each one, it is */
  /* decoded to binary and then to a 4-char sequence by table lookup; */
  /* the 4-chars are a 1-char length (significant digits, except 000 */
  /* has length 0).  This allows us to left-align the first declet */
  /* with non-zero content, then remaining ones are full 3-char */
  /* length.  We use fixed-length memcpys because variable-length */
  /* causes a subroutine call in GCC.  (These are length 4 for speed */
  /* and are safe because the array has an extra terminator byte.) */
  #define dpd2char u=&BIN2CHAR[DPD2BIN[dpd]*4]; 		  \
		   if (c!=cstart) {memcpy(c, u+1, 4); c+=3;}	  \
		    else if (*u)  {memcpy(c, u+4-*u, 4); c+=*u;}

  dpd=(sourhi>>8)&0x3ff;		     /* declet 1 */
  dpd2char;
  dpd=((sourhi&0xff)<<2) | (sourlo>>30);     /* declet 2 */
  dpd2char;
  dpd=(sourlo>>20)&0x3ff;		     /* declet 3 */
  dpd2char;
  dpd=(sourlo>>10)&0x3ff;		     /* declet 4 */
  dpd2char;
  dpd=(sourlo)&0x3ff;			     /* declet 5 */
  dpd2char;

  if (c==cstart) *c++='0';	   /* all zeros -- make 0 */

  if (exp==0) { 		   /* integer or NaN case -- easy */
    *c='\0';			   /* terminate */
    return string;
    }

  /* non-0 exponent */
  e=0;				   /* assume no E */
  pre=c-cstart+exp;
  /* [here, pre-exp is the digits count (==1 for zero)] */
  if (exp>0 || pre<-5) {	   /* need exponential form */
    e=pre-1;			   /* calculate E value */
    pre=1;			   /* assume one digit before '.' */
    } /* exponential form */

  /* modify the coefficient, adding 0s, '.', and E+nn as needed */
  s=c-1;			   /* source (LSD) */
  if (pre>0) {			   /* ddd.ddd (plain), perhaps with E */
    char *dotat=cstart+pre;
    if (dotat<c) {		   /* if embedded dot needed... */
      t=c;				/* target */
      for (; s>=dotat; s--, t--) *t=*s; /* open the gap; leave t at gap */
      *t='.';				/* insert the dot */
      c++;				/* length increased by one */
      }

    /* finally add the E-part, if needed; it will never be 0, and has */
    /* a maximum length of 3 digits */
    if (e!=0) {
      *c++='E'; 		   /* starts with E */
      *c++='+'; 		   /* assume positive */
      if (e<0) {
	*(c-1)='-';		   /* oops, need '-' */
	e=-e;			   /* uInt, please */
	}
      u=&BIN2CHAR[e*4]; 	   /* -> length byte */
      memcpy(c, u+4-*u, 4);	   /* copy fixed 4 characters [is safe] */
      c+=*u;			   /* bump pointer appropriately */
      }
    *c='\0';			   /* add terminator */
    /*printf("res %s\n", string); */
    return string;
    } /* pre>0 */

  /* -5<=pre<=0: here for plain 0.ddd or 0.000ddd forms (can never have E) */
  t=c+1-pre;
  *(t+1)='\0';				/* can add terminator now */
  for (; s>=cstart; s--, t--) *t=*s;	/* shift whole coefficient right */
  c=cstart;
  *c++='0';				/* always starts with 0. */
  *c++='.';
  for (; pre<0; pre++) *c++='0';	/* add any 0's after '.' */
  /*printf("res %s\n", string); */
  return string;
  } /* decimal64ToString */

/* ------------------------------------------------------------------ */
/* to-number -- conversion from numeric string			      */
/*								      */
/*   decimal64FromString(result, string, set);			      */
/*								      */
/*  result  is the decimal64 format number which gets the result of   */
/*	    the conversion					      */
/*  *string is the character string which should contain a valid      */
/*	    number (which may be a special value)		      */
/*  set     is the context					      */
/*								      */
/* The context is supplied to this routine is used for error handling */
/* (setting of status and traps) and for the rounding mode, only.     */
/* If an error occurs, the result will be a valid decimal64 NaN.      */
/* ------------------------------------------------------------------ */
decimal64 * decimal64FromString(decimal64 *result, const char *string,
				decContext *set) {
  decContext dc;			     /* work */
  decNumber dn; 			     /* .. */

  decContextDefault(&dc, DEC_INIT_DECIMAL64); /* no traps, please */
  dc.round=set->round;			      /* use supplied rounding */

  decNumberFromString(&dn, string, &dc);     /* will round if needed */

  decimal64FromNumber(result, &dn, &dc);
  if (dc.status!=0) {			     /* something happened */
    decContextSetStatus(set, dc.status);     /* .. pass it on */
    }
  return result;
  } /* decimal64FromString */

/* ------------------------------------------------------------------ */
/* decimal64IsCanonical -- test whether encoding is canonical	      */
/*   d64 is the source decimal64				      */
/*   returns 1 if the encoding of d64 is canonical, 0 otherwise       */
/* No error is possible.					      */
/* ------------------------------------------------------------------ */
uInt decimal64IsCanonical(const decimal64 *d64) {
  decNumber dn; 			/* work */
  decimal64 canon;			/* .. */
  decContext dc;			/* .. */
  decContextDefault(&dc, DEC_INIT_DECIMAL64);
  decimal64ToNumber(d64, &dn);
  decimal64FromNumber(&canon, &dn, &dc);/* canon will now be canonical */
  return memcmp(d64, &canon, DECIMAL64_Bytes)==0;
  } /* decimal64IsCanonical */

/* ------------------------------------------------------------------ */
/* decimal64Canonical -- copy an encoding, ensuring it is canonical   */
/*   d64 is the source decimal64				      */
/*   result is the target (may be the same decimal64)		      */
/*   returns result						      */
/* No error is possible.					      */
/* ------------------------------------------------------------------ */
decimal64 * decimal64Canonical(decimal64 *result, const decimal64 *d64) {
  decNumber dn; 			/* work */
  decContext dc;			/* .. */
  decContextDefault(&dc, DEC_INIT_DECIMAL64);
  decimal64ToNumber(d64, &dn);
  decimal64FromNumber(result, &dn, &dc);/* result will now be canonical */
  return result;
  } /* decimal64Canonical */

#if DECTRACE || DECCHECK
/* Macros for accessing decimal64 fields.  These assume the
   argument is a reference (pointer) to the decimal64 structure,
   and the decimal64 is in network byte order (big-endian) */
/* Get sign */
#define decimal64Sign(d)       ((unsigned)(d)->bytes[0]>>7)

/* Get combination field */
#define decimal64Comb(d)       (((d)->bytes[0] & 0x7c)>>2)

/* Get exponent continuation [does not remove bias] */
#define decimal64ExpCon(d)     ((((d)->bytes[0] & 0x03)<<6)	      \
			     | ((unsigned)(d)->bytes[1]>>2))

/* Set sign [this assumes sign previously 0] */
#define decimal64SetSign(d, b) {				      \
  (d)->bytes[0]|=((unsigned)(b)<<7);}

/* Set exponent continuation [does not apply bias] */
/* This assumes range has been checked and exponent previously 0; */
/* type of exponent must be unsigned */
#define decimal64SetExpCon(d, e) {				      \
  (d)->bytes[0]|=(uByte)((e)>>6);				      \
  (d)->bytes[1]|=(uByte)(((e)&0x3F)<<2);}

/* ------------------------------------------------------------------ */
/* decimal64Show -- display a decimal64 in hexadecimal [debug aid]    */
/*   d64 -- the number to show					      */
/* ------------------------------------------------------------------ */
/* Also shows sign/cob/expconfields extracted */
void decimal64Show(const decimal64 *d64) {
  char buf[DECIMAL64_Bytes*2+1];
  Int i, j=0;

  if (DECLITEND) {
    for (i=0; i<DECIMAL64_Bytes; i++, j+=2) {
      sprintf(&buf[j], "%02x", d64->bytes[7-i]);
      }
    printf(" D64> %s [S:%d Cb:%02x Ec:%02x] LittleEndian\n", buf,
	   d64->bytes[7]>>7, (d64->bytes[7]>>2)&0x1f,
	   ((d64->bytes[7]&0x3)<<6)| (d64->bytes[6]>>2));
    }
   else { /* big-endian */
    for (i=0; i<DECIMAL64_Bytes; i++, j+=2) {
      sprintf(&buf[j], "%02x", d64->bytes[i]);
      }
    printf(" D64> %s [S:%d Cb:%02x Ec:%02x] BigEndian\n", buf,
	   decimal64Sign(d64), decimal64Comb(d64), decimal64ExpCon(d64));
    }
  } /* decimal64Show */
#endif

/* ================================================================== */
/* Shared utility routines and tables				      */
/* ================================================================== */
/* define and include the conversion tables to use for shared code */
#if DECDPUN==3
  #define DEC_DPD2BIN 1
#else
  #define DEC_DPD2BCD 1
#endif
#include "decDPD.h"	      /* lookup tables */

/* The maximum number of decNumberUnits needed for a working copy of */
/* the units array is the ceiling of digits/DECDPUN, where digits is */
/* the maximum number of digits in any of the formats for which this */
/* is used.  decimal128.h must not be included in this module, so, as */
/* a very special case, that number is defined as a literal here. */
#define DECMAX754   34
#define DECMAXUNITS ((DECMAX754+DECDPUN-1)/DECDPUN)

/* ------------------------------------------------------------------ */
/* Combination field lookup tables (uInts to save measurable work)    */
/*								      */
/*	COMBEXP - 2-bit most-significant-bits of exponent	      */
/*		  [11 if an Infinity or NaN]			      */
/*	COMBMSD - 4-bit most-significant-digit			      */
/*		  [0=Infinity, 1=NaN if COMBEXP=11]		      */
/*								      */
/* Both are indexed by the 5-bit combination field (0-31)	      */
/* ------------------------------------------------------------------ */
const uInt COMBEXP[32]={0, 0, 0, 0, 0, 0, 0, 0,
			1, 1, 1, 1, 1, 1, 1, 1,
			2, 2, 2, 2, 2, 2, 2, 2,
			0, 0, 1, 1, 2, 2, 3, 3};
const uInt COMBMSD[32]={0, 1, 2, 3, 4, 5, 6, 7,
			0, 1, 2, 3, 4, 5, 6, 7,
			0, 1, 2, 3, 4, 5, 6, 7,
			8, 9, 8, 9, 8, 9, 0, 1};

/* ------------------------------------------------------------------ */
/* decDigitsToDPD -- pack coefficient into DPD form		      */
/*								      */
/*   dn   is the source number (assumed valid, max DECMAX754 digits)  */
/*   targ is 1, 2, or 4-element uInt array, which the caller must     */
/*	  have cleared to zeros 				      */
/*   shift is the number of 0 digits to add on the right (normally 0) */
/*								      */
/* The coefficient must be known small enough to fit.  The full       */
/* coefficient is copied, including the leading 'odd' digit.  This    */
/* digit is retrieved and packed into the combination field by the    */
/* caller.							      */
/*								      */
/* The target uInts are altered only as necessary to receive the      */
/* digits of the decNumber.  When more than one uInt is needed, they  */
/* are filled from left to right (that is, the uInt at offset 0 will  */
/* end up with the least-significant digits).			      */
/*								      */
/* shift is used for 'fold-down' padding.			      */
/*								      */
/* No error is possible.					      */
/* ------------------------------------------------------------------ */
#if DECDPUN<=4
/* Constant multipliers for divide-by-power-of five using reciprocal */
/* multiply, after removing powers of 2 by shifting, and final shift */
/* of 17 [we only need up to **4] */
static const uInt multies[]={131073, 26215, 5243, 1049, 210};
/* QUOT10 -- macro to return the quotient of unit u divided by 10**n */
#define QUOT10(u, n) ((((uInt)(u)>>(n))*multies[n])>>17)
#endif
void decDigitsToDPD(const decNumber *dn, uInt *targ, Int shift) {
  Int  cut;		      /* work */
  Int  n;		      /* output bunch counter */
  Int  digits=dn->digits;     /* digit countdown */
  uInt dpd;		      /* densely packed decimal value */
  uInt bin;		      /* binary value 0-999 */
  uInt *uout=targ;	      /* -> current output uInt */
  uInt	uoff=0; 	      /* -> current output offset [from right] */
  const Unit *inu=dn->lsu;    /* -> current input unit */
  Unit	uar[DECMAXUNITS];     /* working copy of units, iff shifted */
  #if DECDPUN!=3	      /* not fast path */
    Unit in;		      /* current unit */
  #endif

  if (shift!=0) {	      /* shift towards most significant required */
    /* shift the units array to the left by pad digits and copy */
    /* [this code is a special case of decShiftToMost, which could */
    /* be used instead if exposed and the array were copied first] */
    const Unit *source; 		/* .. */
    Unit  *target, *first;		/* .. */
    uInt  next=0;			/* work */

    source=dn->lsu+D2U(digits)-1;	/* where msu comes from */
    target=uar+D2U(digits)-1+D2U(shift);/* where upper part of first cut goes */
    cut=DECDPUN-MSUDIGITS(shift);	/* where to slice */
    if (cut==0) {			/* unit-boundary case */
      for (; source>=dn->lsu; source--, target--) *target=*source;
      }
     else {
      first=uar+D2U(digits+shift)-1;	/* where msu will end up */
      for (; source>=dn->lsu; source--, target--) {
	/* split the source Unit and accumulate remainder for next */
	#if DECDPUN<=4
	  uInt quot=QUOT10(*source, cut);
	  uInt rem=*source-quot*DECPOWERS[cut];
	  next+=quot;
	#else
	  uInt rem=*source%DECPOWERS[cut];
	  next+=*source/DECPOWERS[cut];
	#endif
	if (target<=first) *target=(Unit)next; /* write to target iff valid */
	next=rem*DECPOWERS[DECDPUN-cut];       /* save remainder for next Unit */
	}
      } /* shift-move */
    /* propagate remainder to one below and clear the rest */
    for (; target>=uar; target--) {
      *target=(Unit)next;
      next=0;
      }
    digits+=shift;		   /* add count (shift) of zeros added */
    inu=uar;			   /* use units in working array */
    }

  /* now densely pack the coefficient into DPD declets */

  #if DECDPUN!=3		   /* not fast path */
    in=*inu;			   /* current unit */
    cut=0;			   /* at lowest digit */
    bin=0;			   /* [keep compiler quiet] */
  #endif

  for(n=0; digits>0; n++) {	   /* each output bunch */
    #if DECDPUN==3		   /* fast path, 3-at-a-time */
      bin=*inu; 		   /* 3 digits ready for convert */
      digits-=3;		   /* [may go negative] */
      inu++;			   /* may need another */

    #else			   /* must collect digit-by-digit */
      Unit dig; 		   /* current digit */
      Int j;			   /* digit-in-declet count */
      for (j=0; j<3; j++) {
	#if DECDPUN<=4
	  Unit temp=(Unit)((uInt)(in*6554)>>16);
	  dig=(Unit)(in-X10(temp));
	  in=temp;
	#else
	  dig=in%10;
	  in=in/10;
	#endif
	if (j==0) bin=dig;
	 else if (j==1)  bin+=X10(dig);
	 else /* j==2 */ bin+=X100(dig);
	digits--;
	if (digits==0) break;	   /* [also protects *inu below] */
	cut++;
	if (cut==DECDPUN) {inu++; in=*inu; cut=0;}
	}
    #endif
    /* here there are 3 digits in bin, or have used all input digits */

    dpd=BIN2DPD[bin];

    /* write declet to uInt array */
    *uout|=dpd<<uoff;
    uoff+=10;
    if (uoff<32) continue;	   /* no uInt boundary cross */
    uout++;
    uoff-=32;
    *uout|=dpd>>(10-uoff);	   /* collect top bits */
    } /* n declets */
  return;
  } /* decDigitsToDPD */

/* ------------------------------------------------------------------ */
/* decDigitsFromDPD -- unpack a format's coefficient		      */
/*								      */
/*   dn is the target number, with 7, 16, or 34-digit space.	      */
/*   sour is a 1, 2, or 4-element uInt array containing only declets  */
/*   declets is the number of (right-aligned) declets in sour to      */
/*     be processed.  This may be 1 more than the obvious number in   */
/*     a format, as any top digit is prefixed to the coefficient      */
/*     continuation field.  It also may be as small as 1, as the      */
/*     caller may pre-process leading zero declets.		      */
/*								      */
/* When doing the 'extra declet' case care is taken to avoid writing  */
/* extra digits when there are leading zeros, as these could overflow */
/* the units array when DECDPUN is not 3.			      */
/*								      */
/* The target uInts are used only as necessary to process declets     */
/* declets into the decNumber.	When more than one uInt is needed,    */
/* they are used from left to right (that is, the uInt at offset 0    */
/* provides the least-significant digits).			      */
/*								      */
/* dn->digits is set, but not the sign or exponent.		      */
/* No error is possible [the redundant 888 codes are allowed].	      */
/* ------------------------------------------------------------------ */
void decDigitsFromDPD(decNumber *dn, const uInt *sour, Int declets) {

  uInt	dpd;			   /* collector for 10 bits */
  Int	n;			   /* counter */
  Unit	*uout=dn->lsu;		   /* -> current output unit */
  Unit	*last=uout;		   /* will be unit containing msd */
  const uInt *uin=sour; 	   /* -> current input uInt */
  uInt	uoff=0; 		   /* -> current input offset [from right] */

  #if DECDPUN!=3
  uInt	bcd;			   /* BCD result */
  uInt	nibble; 		   /* work */
  Unit	out=0;			   /* accumulator */
  Int	cut=0;			   /* power of ten in current unit */
  #endif
  #if DECDPUN>4
  uInt const *pow;		   /* work */
  #endif

  /* Expand the densely-packed integer, right to left */
  for (n=declets-1; n>=0; n--) {   /* count down declets of 10 bits */
    dpd=*uin>>uoff;
    uoff+=10;
    if (uoff>32) {		   /* crossed uInt boundary */
      uin++;
      uoff-=32;
      dpd|=*uin<<(10-uoff);	   /* get waiting bits */
      }
    dpd&=0x3ff; 		   /* clear uninteresting bits */

  #if DECDPUN==3
    if (dpd==0) *uout=0;
     else {
      *uout=DPD2BIN[dpd];	   /* convert 10 bits to binary 0-999 */
      last=uout;		   /* record most significant unit */
      }
    uout++;
    } /* n */

  #else /* DECDPUN!=3 */
    if (dpd==0) {		   /* fastpath [e.g., leading zeros] */
      /* write out three 0 digits (nibbles); out may have digit(s) */
      cut++;
      if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
      if (n==0) break;		   /* [as below, works even if MSD=0] */
      cut++;
      if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
      cut++;
      if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
      continue;
      }

    bcd=DPD2BCD[dpd];		   /* convert 10 bits to 12 bits BCD */

    /* now accumulate the 3 BCD nibbles into units */
    nibble=bcd & 0x00f;
    if (nibble) out=(Unit)(out+nibble*DECPOWERS[cut]);
    cut++;
    if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
    bcd>>=4;

    /* if this is the last declet and the remaining nibbles in bcd */
    /* are 00 then process no more nibbles, because this could be */
    /* the 'odd' MSD declet and writing any more Units would then */
    /* overflow the unit array */
    if (n==0 && !bcd) break;

    nibble=bcd & 0x00f;
    if (nibble) out=(Unit)(out+nibble*DECPOWERS[cut]);
    cut++;
    if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
    bcd>>=4;

    nibble=bcd & 0x00f;
    if (nibble) out=(Unit)(out+nibble*DECPOWERS[cut]);
    cut++;
    if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
    } /* n */
  if (cut!=0) { 			/* some more left over */
    *uout=out;				/* write out final unit */
    if (out) last=uout; 		/* and note if non-zero */
    }
  #endif

  /* here, last points to the most significant unit with digits; */
  /* inspect it to get the final digits count -- this is essentially */
  /* the same code as decGetDigits in decNumber.c */
  dn->digits=(last-dn->lsu)*DECDPUN+1;	/* floor of digits, plus */
					/* must be at least 1 digit */
  #if DECDPUN>1
  if (*last<10) return; 		/* common odd digit or 0 */
  dn->digits++; 			/* must be 2 at least */
  #if DECDPUN>2
  if (*last<100) return;		/* 10-99 */
  dn->digits++; 			/* must be 3 at least */
  #if DECDPUN>3
  if (*last<1000) return;		/* 100-999 */
  dn->digits++; 			/* must be 4 at least */
  #if DECDPUN>4
  for (pow=&DECPOWERS[4]; *last>=*pow; pow++) dn->digits++;
  #endif
  #endif
  #endif
  #endif
  return;
  } /*decDigitsFromDPD */