xref: /openbmc/qemu/libdecnumber/dpd/decimal64.c (revision 6a4cff8e1a80bafc4b8fe2bfb10081f4880d1b3b)

/* Decimal 64-bit format module for the decNumber C Library.
   Copyright (C) 2005, 2007 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 2, or (at your option) any later
   version.

   In addition to the permissions in the GNU General Public License,
   the Free Software Foundation gives you unlimited permission to link
   the compiled version of this file into combinations with other
   programs, and to distribute those combinations without any
   restriction coming from the use of this file.  (The General Public
   License restrictions do apply in other respects; for example, they
   cover modification of the file, and distribution when not linked
   into a combine executable.)

   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.

   You should have received a copy of the GNU General Public License
   along with GCC; see the file COPYING.  If not, write to the Free
   Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA
   02110-1301, USA.  */

/* ------------------------------------------------------------------ */
/* 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 "qemu/osdep.h"

#include "libdecnumber/dconfig.h"
#define	 DECNUMDIGITS 16      /* make decNumbers with space for 16 */
#include "libdecnumber/decNumber.h"
#include "libdecnumber/decNumberLocal.h"
#include "libdecnumber/dpd/decimal64.h"

/* Utility routines and tables [in decimal64.c]; externs for C++ */
extern const uInt COMBEXP[32], COMBMSD[32];
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 "libdecnumber/decDPD.h"

/* ------------------------------------------------------------------ */
/* 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 *pu;			   /* .. */
  uInt comb, exp;		   /* .. */
  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 */
  pu=(uInt *)d64->bytes;	   /* overlay */
  if (DECLITEND) {
    pu[0]=targar[0];		   /* directly store the low int */
    pu[1]=targar[1];		   /* then the high int */
    }
   else {
    pu[0]=targar[1];		   /* directly store the high int */
    pu[1]=targar[0];		   /* then the low int */
    }

  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 */
  const uInt *pu;		   /* work */
  Int  need;			   /* .. */
  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 */
  pu=(const uInt *)d64->bytes;	   /* overlay */
  if (DECLITEND) {
    sourlo=pu[0];		   /* directly load the low int */
    sourhi=pu[1];		   /* then the high int */
    }
   else {
    sourhi=pu[0];		   /* directly load the high int */
    sourlo=pu[1];		   /* 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 uInt *pu;		   /* work */
  char *s, *t;			   /* .. (source, target) */
  Int  dpd;			   /* .. */
  Int  pre, e;			   /* .. */
  const uByte *u;		   /* .. */

  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 */
  pu=(const uInt *)d64->bytes;	   /* overlay */
  if (DECLITEND) {
    sourlo=pu[0];		   /* directly load the low int */
    sourhi=pu[1];		   /* then the high int */
    }
   else {
    sourhi=pu[0];		   /* directly load the high int */
    sourlo=pu[1];		   /* 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.					      */
/* ------------------------------------------------------------------ */
uint32_t 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]|=(uint8_t)((e)>>6);				      \
  (d)->bytes[1]|=(uint8_t)(((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 "libdecnumber/decDPD.h"

/* 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  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

  while (digits > 0) {             /* 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 */