path: root/libdecnumber/decCommon.c

/* Common code for fixed-size types in the decNumber C Library.
   Copyright (C) 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.  */

/* ------------------------------------------------------------------ */
/* decCommon.c -- common code for all three fixed-size types	      */
/* ------------------------------------------------------------------ */
/* This module comprises code that is shared between all the formats  */
/* (decSingle, decDouble, and decQuad); it includes set and extract   */
/* of format components, widening, narrowing, and string conversions. */
/*								      */
/* Unlike decNumber, parameterization takes place at compile time     */
/* rather than at runtime.  The parameters are set in the decDouble.c */
/* (etc.) files, which then include this one to produce the compiled  */
/* code.  The functions here, therefore, are code shared between      */
/* multiple formats.						      */
/* ------------------------------------------------------------------ */
/* Names here refer to decFloat rather than to decDouble, etc., and */
/* the functions are in strict alphabetical order. */
/* Constants, tables, and debug function(s) are included only for QUAD */
/* (which will always be compiled if DOUBLE or SINGLE are used). */
/* */
/* Whenever a decContext is used, only the status may be set (using */
/* OR) or the rounding mode read; all other fields are ignored and */
/* untouched. */

/* names for simpler testing and default context */
#if DECPMAX==7
  #define SINGLE     1
  #define DOUBLE     0
  #define QUAD	     0
  #define DEFCONTEXT DEC_INIT_DECIMAL32
#elif DECPMAX==16
  #define SINGLE     0
  #define DOUBLE     1
  #define QUAD	     0
  #define DEFCONTEXT DEC_INIT_DECIMAL64
#elif DECPMAX==34
  #define SINGLE     0
  #define DOUBLE     0
  #define QUAD	     1
  #define DEFCONTEXT DEC_INIT_DECIMAL128
#else
  #error Unexpected DECPMAX value
#endif

/* Assertions */

#if DECPMAX!=7 && DECPMAX!=16 && DECPMAX!=34
  #error Unexpected Pmax (DECPMAX) value for this module
#endif

/* Assert facts about digit characters, etc. */
#if ('9'&0x0f)!=9
  #error This module assumes characters are of the form 0b....nnnn
  /* where .... are don't care 4 bits and nnnn is 0000 through 1001 */
#endif
#if ('9'&0xf0)==('.'&0xf0)
  #error This module assumes '.' has a different mask than a digit
#endif

/* Assert ToString lay-out conditions */
#if DECSTRING<DECPMAX+9
  #error ToString needs at least 8 characters for lead-in and dot
#endif
#if DECPMAX+DECEMAXD+5 > DECSTRING
  #error Exponent form can be too long for ToString to lay out safely
#endif
#if DECEMAXD > 4
  #error Exponent form is too long for ToString to lay out
  /* Note: code for up to 9 digits exists in archives [decOct] */
#endif

/* Private functions used here and possibly in decBasic.c, etc. */
static decFloat * decFinalize(decFloat *, bcdnum *, decContext *);
static Flag decBiStr(const char *, const char *, const char *);

/* Macros and private tables; those which are not format-dependent    */
/* are only included if decQuad is being built.			      */

/* ------------------------------------------------------------------ */
/* Combination field lookup tables (uInts to save measurable work)    */
/*								      */
/*   DECCOMBEXP	 - 2 most-significant-bits of exponent (00, 01, or    */
/*		   10), shifted left for format, or DECFLOAT_Inf/NaN  */
/*   DECCOMBWEXP - The same, for the next-wider format (unless QUAD)  */
/*   DECCOMBMSD	 - 4-bit most-significant-digit			      */
/*		   [0 if the index is a special (Infinity or NaN)]    */
/*   DECCOMBFROM - 5-bit combination field from EXP top bits and MSD  */
/*		   (placed in uInt so no shift is needed)	      */
/*								      */
/* DECCOMBEXP, DECCOMBWEXP, and DECCOMBMSD are indexed by the sign    */
/*   and 5-bit combination field (0-63, the second half of the table  */
/*   identical to the first half)				      */
/* DECCOMBFROM is indexed by expTopTwoBits*16 + msd		      */
/*								      */
/* DECCOMBMSD and DECCOMBFROM are not format-dependent and so are     */
/* only included once, when QUAD is being built			      */
/* ------------------------------------------------------------------ */
static const uInt DECCOMBEXP[64]={
  0, 0, 0, 0, 0, 0, 0, 0,
  1<<DECECONL, 1<<DECECONL, 1<<DECECONL, 1<<DECECONL,
  1<<DECECONL, 1<<DECECONL, 1<<DECECONL, 1<<DECECONL,
  2<<DECECONL, 2<<DECECONL, 2<<DECECONL, 2<<DECECONL,
  2<<DECECONL, 2<<DECECONL, 2<<DECECONL, 2<<DECECONL,
  0,	       0,	    1<<DECECONL, 1<<DECECONL,
  2<<DECECONL, 2<<DECECONL, DECFLOAT_Inf, DECFLOAT_NaN,
  0, 0, 0, 0, 0, 0, 0, 0,
  1<<DECECONL, 1<<DECECONL, 1<<DECECONL, 1<<DECECONL,
  1<<DECECONL, 1<<DECECONL, 1<<DECECONL, 1<<DECECONL,
  2<<DECECONL, 2<<DECECONL, 2<<DECECONL, 2<<DECECONL,
  2<<DECECONL, 2<<DECECONL, 2<<DECECONL, 2<<DECECONL,
  0,	       0,	    1<<DECECONL, 1<<DECECONL,
  2<<DECECONL, 2<<DECECONL, DECFLOAT_Inf, DECFLOAT_NaN};
#if !QUAD
static const uInt DECCOMBWEXP[64]={
  0, 0, 0, 0, 0, 0, 0, 0,
  1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL,
  1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL,
  2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL,
  2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL,
  0,		0,	      1<<DECWECONL, 1<<DECWECONL,
  2<<DECWECONL, 2<<DECWECONL, DECFLOAT_Inf, DECFLOAT_NaN,
  0, 0, 0, 0, 0, 0, 0, 0,
  1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL,
  1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL,
  2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL,
  2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL,
  0,		0,	      1<<DECWECONL, 1<<DECWECONL,
  2<<DECWECONL, 2<<DECWECONL, DECFLOAT_Inf, DECFLOAT_NaN};
#endif

#if QUAD
const uInt DECCOMBMSD[64]={
  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,
  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, 0};

const uInt DECCOMBFROM[48]={
  0x00000000, 0x04000000, 0x08000000, 0x0C000000, 0x10000000, 0x14000000,
  0x18000000, 0x1C000000, 0x60000000, 0x64000000, 0x00000000, 0x00000000,
  0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x20000000, 0x24000000,
  0x28000000, 0x2C000000, 0x30000000, 0x34000000, 0x38000000, 0x3C000000,
  0x68000000, 0x6C000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
  0x00000000, 0x00000000, 0x40000000, 0x44000000, 0x48000000, 0x4C000000,
  0x50000000, 0x54000000, 0x58000000, 0x5C000000, 0x70000000, 0x74000000,
  0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000};

/* ------------------------------------------------------------------ */
/* Request and include the tables to use for conversions	      */
/* ------------------------------------------------------------------ */
#define DEC_BCD2DPD  1	      /* 0-0x999 -> DPD */
#define DEC_BIN2DPD  1	      /* 0-999 -> DPD */
#define DEC_BIN2BCD8 1	      /* 0-999 -> ddd, len */
#define DEC_DPD2BCD8 1	      /* DPD -> ddd, len */
#define DEC_DPD2BIN  1	      /* DPD -> 0-999 */
#define DEC_DPD2BINK 1	      /* DPD -> 0-999000 */
#define DEC_DPD2BINM 1	      /* DPD -> 0-999000000 */
#include "decDPD.h"	      /* source of the lookup tables */

#endif

/* ----------------------------------------------------------------- */
/* decBiStr -- compare string with pairwise options		     */
/*								     */
/*   targ is the string to compare				     */
/*   str1 is one of the strings to compare against (length may be 0) */
/*   str2 is the other; it must be the same length as str1	     */
/*								     */
/*   returns 1 if strings compare equal, (that is, targ is the same  */
/*   length as str1 and str2, and each character of targ is in one   */
/*   of str1 or str2 in the corresponding position), or 0 otherwise  */
/*								     */
/* This is used for generic caseless compare, including the awkward  */
/* case of the Turkish dotted and dotless Is.  Use as (for example): */
/*   if (decBiStr(test, "mike", "MIKE")) ...			     */
/* ----------------------------------------------------------------- */
static Flag decBiStr(const char *targ, const char *str1, const char *str2) {
  for (;;targ++, str1++, str2++) {
    if (*targ!=*str1 && *targ!=*str2) return 0;
    /* *targ has a match in one (or both, if terminator) */
    if (*targ=='\0') break;
    } /* forever */
  return 1;
  } /* decBiStr */

/* ------------------------------------------------------------------ */
/* decFinalize -- adjust and store a final result		      */
/*								      */
/*  df	is the decFloat format number which gets the final result     */
/*  num is the descriptor of the number to be checked and encoded     */
/*	   [its values, including the coefficient, may be modified]   */
/*  set is the context to use					      */
/*  returns df							      */
/*								      */
/* The num descriptor may point to a bcd8 string of any length; this  */
/* string may have leading insignificant zeros.	 If it has more than  */
/* DECPMAX digits then the final digit can be a round-for-reround     */
/* digit (i.e., it may include a sticky bit residue).		      */
/*								      */
/* The exponent (q) may be one of the codes for a special value and   */
/* can be up to 999999999 for conversion from string.		      */
/*								      */
/* No error is possible, but Inexact, Underflow, and/or Overflow may  */
/* be set.							      */
/* ------------------------------------------------------------------ */
/* Constant whose size varies with format; also the check for surprises */
static uByte allnines[DECPMAX]=
#if SINGLE
  {9, 9, 9, 9, 9, 9, 9};
#elif DOUBLE
  {9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9};
#elif QUAD
  {9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
   9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9};
#endif

static decFloat * decFinalize(decFloat *df, bcdnum *num,
			      decContext *set) {
  uByte *ub;		      /* work */
  uInt	 dpd;		      /* .. */
  uByte *umsd=num->msd;	      /* local copy */
  uByte *ulsd=num->lsd;	      /* .. */
  uInt	 encode;	      /* encoding accumulator */
  Int	 length;	      /* coefficient length */

  #if DECCHECK
  Int clen=ulsd-umsd+1;
  #if QUAD
    #define COEXTRA 2			     /* extra-long coefficent */
  #else
    #define COEXTRA 0
  #endif
  if (clen<1 || clen>DECPMAX*3+2+COEXTRA)
    printf("decFinalize: suspect coefficient [length=%ld]\n", (LI)clen);
  if (num->sign!=0 && num->sign!=DECFLOAT_Sign)
    printf("decFinalize: bad sign [%08lx]\n", (LI)num->sign);
  if (!EXPISSPECIAL(num->exponent)
      && (num->exponent>1999999999 || num->exponent<-1999999999))
    printf("decFinalize: improbable exponent [%ld]\n", (LI)num->exponent);
  /* decShowNum(num, "final"); */
  #endif

  /* A special will have an 'exponent' which is very positive and a */
  /* coefficient < DECPMAX */
  length=(uInt)(ulsd-umsd+1);		     /* coefficient length */

  if (!NUMISSPECIAL(num)) {
    Int	  drop;				     /* digits to be dropped */
    /* skip leading insignificant zeros to calculate an exact length */
    /* [this is quite expensive] */
    if (*umsd==0) {
      for (; UINTAT(umsd)==0 && umsd+3<ulsd;) umsd+=4;
      for (; *umsd==0 && umsd<ulsd;) umsd++;
      length=ulsd-umsd+1;		     /* recalculate */
      }
    drop=MAXI(length-DECPMAX, DECQTINY-num->exponent);
    /* drop can now be > digits for bottom-clamp (subnormal) cases */
    if (drop>0) {			     /* rounding needed */
      /* (decFloatQuantize has very similar code to this, so any */
      /* changes may need to be made there, too) */
      uByte *roundat;			     /* -> re-round digit */
      uByte reround;			     /* reround value */
      /* printf("Rounding; drop=%ld\n", (LI)drop); */

      num->exponent+=drop;		     /* always update exponent */

      /* Three cases here: */
      /*   1. new LSD is in coefficient (almost always) */
      /*   2. new LSD is digit to left of coefficient (so MSD is */
      /*      round-for-reround digit) */
      /*   3. new LSD is to left of case 2 (whole coefficient is sticky) */
      /* [duplicate check-stickies code to save a test] */
      /* [by-digit check for stickies as runs of zeros are rare] */
      if (drop<length) {		     /* NB lengths not addresses */
	roundat=umsd+length-drop;
	reround=*roundat;
	for (ub=roundat+1; ub<=ulsd; ub++) {
	  if (*ub!=0) {			     /* non-zero to be discarded */
	    reround=DECSTICKYTAB[reround];   /* apply sticky bit */
	    break;			     /* [remainder don't-care] */
	    }
	  } /* check stickies */
	ulsd=roundat-1;			     /* new LSD */
	}
       else {				     /* edge case */
	if (drop==length) {
	  roundat=umsd;
	  reround=*roundat;
	  }
	 else {
	  roundat=umsd-1;
	  reround=0;
	  }
	for (ub=roundat+1; ub<=ulsd; ub++) {
	  if (*ub!=0) {			     /* non-zero to be discarded */
	    reround=DECSTICKYTAB[reround];   /* apply sticky bit */
	    break;			     /* [remainder don't-care] */
	    }
	  } /* check stickies */
	*umsd=0;			     /* coefficient is a 0 */
	ulsd=umsd;			     /* .. */
	}

      if (reround!=0) {			     /* discarding non-zero */
	uInt bump=0;
	set->status|=DEC_Inexact;
	/* if adjusted exponent [exp+digits-1] is < EMIN then num is */
	/* subnormal -- so raise Underflow */
	if (num->exponent<DECEMIN && (num->exponent+(ulsd-umsd+1)-1)<DECEMIN)
	  set->status|=DEC_Underflow;

	/* next decide whether increment of the coefficient is needed */
	if (set->round==DEC_ROUND_HALF_EVEN) {	  /* fastpath slowest case */
	  if (reround>5) bump=1;		  /* >0.5 goes up */
	   else if (reround==5)			  /* exactly 0.5000 .. */
	    bump=*ulsd & 0x01;			  /* .. up iff [new] lsd is odd */
	  } /* r-h-e */
	 else switch (set->round) {
	  case DEC_ROUND_DOWN: {
	    /* no change */
	    break;} /* r-d */
	  case DEC_ROUND_HALF_DOWN: {
	    if (reround>5) bump=1;
	    break;} /* r-h-d */
	  case DEC_ROUND_HALF_UP: {
	    if (reround>=5) bump=1;
	    break;} /* r-h-u */
	  case DEC_ROUND_UP: {
	    if (reround>0) bump=1;
	    break;} /* r-u */
	  case DEC_ROUND_CEILING: {
	    /* same as _UP for positive numbers, and as _DOWN for negatives */
	    if (!num->sign && reround>0) bump=1;
	    break;} /* r-c */
	  case DEC_ROUND_FLOOR: {
	    /* same as _UP for negative numbers, and as _DOWN for positive */
	    /* [negative reround cannot occur on 0] */
	    if (num->sign && reround>0) bump=1;
	    break;} /* r-f */
	  case DEC_ROUND_05UP: {
	    if (reround>0) { /* anything out there is 'sticky' */
	      /* bump iff lsd=0 or 5; this cannot carry so it could be */
	      /* effected immediately with no bump -- but the code */
	      /* is clearer if this is done the same way as the others */
	      if (*ulsd==0 || *ulsd==5) bump=1;
	      }
	    break;} /* r-r */
	  default: {	  /* e.g., DEC_ROUND_MAX */
	    set->status|=DEC_Invalid_context;
	    #if DECCHECK
	    printf("Unknown rounding mode: %ld\n", (LI)set->round);
	    #endif
	    break;}
	  } /* switch (not r-h-e) */
	/* printf("ReRound: %ld	 bump: %ld\n", (LI)reround, (LI)bump); */

	if (bump!=0) {			     /* need increment */
	  /* increment the coefficient; this might end up with 1000... */
	  /* (after the all nines case) */
	  ub=ulsd;
	  for(; ub-3>=umsd && UINTAT(ub-3)==0x09090909; ub-=4) UINTAT(ub-3)=0;
	  /* [note ub could now be to left of msd, and it is not safe */
	  /* to write to the the left of the msd] */
	  /* now at most 3 digits left to non-9 (usually just the one) */
	  for (; ub>=umsd; *ub=0, ub--) {
	    if (*ub==9) continue;	     /* carry */
	    *ub+=1;
	    break;
	    }
	  if (ub<umsd) {		     /* had all-nines */
	    *umsd=1;			     /* coefficient to 1000... */
	    /* usually the 1000... coefficient can be used as-is */
	    if ((ulsd-umsd+1)==DECPMAX) {
	      num->exponent++;
	      }
	     else {
	      /* if coefficient is shorter than Pmax then num is */
	      /* subnormal, so extend it; this is safe as drop>0 */
	      /* (or, if the coefficient was supplied above, it could */
	      /* not be 9); this may make the result normal. */
	      ulsd++;
	      *ulsd=0;
	      /* [exponent unchanged] */
	      #if DECCHECK
	      if (num->exponent!=DECQTINY) /* sanity check */
		printf("decFinalize: bad all-nines extend [^%ld, %ld]\n",
		       (LI)num->exponent, (LI)(ulsd-umsd+1));
	      #endif
	      } /* subnormal extend */
	    } /* had all-nines */
	  } /* bump needed */
	} /* inexact rounding */

      length=ulsd-umsd+1;		/* recalculate (may be <DECPMAX) */
      } /* need round (drop>0) */

    /* The coefficient will now fit and has final length unless overflow */
    /* decShowNum(num, "rounded"); */

    /* if exponent is >=emax may have to clamp, overflow, or fold-down */
    if (num->exponent>DECEMAX-(DECPMAX-1)) { /* is edge case */
      /* printf("overflow checks...\n"); */
      if (*ulsd==0 && ulsd==umsd) {	/* have zero */
	num->exponent=DECEMAX-(DECPMAX-1); /* clamp to max */
	}
       else if ((num->exponent+length-1)>DECEMAX) { /* > Nmax */
	/* Overflow -- these could go straight to encoding, here, but */
	/* instead num is adjusted to keep the code cleaner */
	Flag needmax=0;			/* 1 for finite result */
	set->status|=(DEC_Overflow | DEC_Inexact);
	switch (set->round) {
	  case DEC_ROUND_DOWN: {
	    needmax=1;			/* never Infinity */
	    break;} /* r-d */
	  case DEC_ROUND_05UP: {
	    needmax=1;			/* never Infinity */
	    break;} /* r-05 */
	  case DEC_ROUND_CEILING: {
	    if (num->sign) needmax=1;	/* Infinity iff non-negative */
	    break;} /* r-c */
	  case DEC_ROUND_FLOOR: {
	    if (!num->sign) needmax=1;	/* Infinity iff negative */
	    break;} /* r-f */
	  default: break;		/* Infinity in all other cases */
	  }
	if (!needmax) {			/* easy .. set Infinity */
	  num->exponent=DECFLOAT_Inf;
	  *umsd=0;			/* be clean: coefficient to 0 */
	  ulsd=umsd;			/* .. */
	  }
	 else {				/* return Nmax */
	  umsd=allnines;		/* use constant array */
	  ulsd=allnines+DECPMAX-1;
	  num->exponent=DECEMAX-(DECPMAX-1);
	  }
	}
       else { /* no overflow but non-zero and may have to fold-down */
	Int shift=num->exponent-(DECEMAX-(DECPMAX-1));
	if (shift>0) {			/* fold-down needed */
	  /* fold down needed; must copy to buffer in order to pad */
	  /* with zeros safely; fortunately this is not the worst case */
	  /* path because cannot have had a round */
	  uByte buffer[ROUNDUP(DECPMAX+3, 4)]; /* [+3 allows uInt padding] */
	  uByte *s=umsd;		/* source */
	  uByte *t=buffer;		/* safe target */
	  uByte *tlsd=buffer+(ulsd-umsd)+shift; /* target LSD */
	  /* printf("folddown shift=%ld\n", (LI)shift); */
	  for (; s<=ulsd; s+=4, t+=4) UINTAT(t)=UINTAT(s);
	  for (t=tlsd-shift+1; t<=tlsd; t+=4) UINTAT(t)=0;  /* pad */
	  num->exponent-=shift;
	  umsd=buffer;
	  ulsd=tlsd;
	  }
	} /* fold-down? */
      length=ulsd-umsd+1;		/* recalculate length */
      } /* high-end edge case */
    } /* finite number */

  /*------------------------------------------------------------------*/
  /* At this point the result will properly fit the decFloat	      */
  /* encoding, and it can be encoded with no possibility of error     */
  /*------------------------------------------------------------------*/
  /* Following code does not alter coefficient (could be allnines array) */

  if (length==DECPMAX) {
    return decFloatFromBCD(df, num->exponent, umsd, num->sign);
    }

  /* Here when length is short */
  if (!NUMISSPECIAL(num)) {		/* is still finite */
    /* encode the combination field and exponent continuation */
    uInt uexp=(uInt)(num->exponent+DECBIAS); /* biased exponent */
    uInt code=(uexp>>DECECONL)<<4;	/* top two bits of exp */
    /* [msd=0] */
    /* look up the combination field and make high word */
    encode=DECCOMBFROM[code];		/* indexed by (0-2)*16+msd */
    encode|=(uexp<<(32-6-DECECONL)) & 0x03ffffff; /* exponent continuation */
    }
   else encode=num->exponent;		/* special [already in word] */
  /* [coefficient length here will be < DECPMAX] */

  encode|=num->sign;			/* add sign */

  /* private macro to extract a declet, n (where 0<=n<DECLETS and 0 */
  /* refers to the declet from the least significant three digits) */
  /* and put the corresponding DPD code into dpd.  Access to umsd and */
  /* ulsd (pointers to the most and least significant digit of the */
  /* variable-length coefficient) is assumed, along with use of a */
  /* working pointer, uInt *ub. */
  /* As not full-length then chances are there are many leading zeros */
  /* [and there may be a partial triad] */
  #define getDPD(dpd, n) ub=ulsd-(3*(n))-2;			      \
    if (ub<umsd-2) dpd=0;					      \
     else if (ub>=umsd) dpd=BCD2DPD[(*ub*256)+(*(ub+1)*16)+*(ub+2)];  \
     else {dpd=*(ub+2); if (ub+1==umsd) dpd+=*(ub+1)*16; dpd=BCD2DPD[dpd];}

  /* place the declets in the encoding words and copy to result (df), */
  /* according to endianness; in all cases complete the sign word */
  /* first */
  #if DECPMAX==7
    getDPD(dpd, 1);
    encode|=dpd<<10;
    getDPD(dpd, 0);
    encode|=dpd;
    DFWORD(df, 0)=encode;     /* just the one word */

  #elif DECPMAX==16
    getDPD(dpd, 4); encode|=dpd<<8;
    getDPD(dpd, 3); encode|=dpd>>2;
    DFWORD(df, 0)=encode;
    encode=dpd<<30;
    getDPD(dpd, 2); encode|=dpd<<20;
    getDPD(dpd, 1); encode|=dpd<<10;
    getDPD(dpd, 0); encode|=dpd;
    DFWORD(df, 1)=encode;

  #elif DECPMAX==34
    getDPD(dpd,10); encode|=dpd<<4;
    getDPD(dpd, 9); encode|=dpd>>6;
    DFWORD(df, 0)=encode;

    encode=dpd<<26;
    getDPD(dpd, 8); encode|=dpd<<16;
    getDPD(dpd, 7); encode|=dpd<<6;
    getDPD(dpd, 6); encode|=dpd>>4;
    DFWORD(df, 1)=encode;

    encode=dpd<<28;
    getDPD(dpd, 5); encode|=dpd<<18;
    getDPD(dpd, 4); encode|=dpd<<8;
    getDPD(dpd, 3); encode|=dpd>>2;
    DFWORD(df, 2)=encode;

    encode=dpd<<30;
    getDPD(dpd, 2); encode|=dpd<<20;
    getDPD(dpd, 1); encode|=dpd<<10;
    getDPD(dpd, 0); encode|=dpd;
    DFWORD(df, 3)=encode;
  #endif

  /* printf("Status: %08lx\n", (LI)set->status); */
  /* decFloatShow(df, "final"); */
  return df;
  } /* decFinalize */

/* ------------------------------------------------------------------ */
/* decFloatFromBCD -- set decFloat from exponent, BCD8, and sign      */
/*								      */
/*  df is the target decFloat					      */
/*  exp is the in-range unbiased exponent, q, or a special value in   */
/*    the form returned by decFloatGetExponent			      */
/*  bcdar holds DECPMAX digits to set the coefficient from, one	      */
/*    digit in each byte (BCD8 encoding); the first (MSD) is ignored  */
/*    if df is a NaN; all are ignored if df is infinite.	      */
/*    All bytes must be in 0-9; results undefined otherwise.	      */
/*  sig is DECFLOAT_Sign to set the sign bit, 0 otherwise	      */
/*  returns df, which will be canonical				      */
/*								      */
/* No error is possible, and no status will be set.		      */
/* ------------------------------------------------------------------ */
decFloat * decFloatFromBCD(decFloat *df, Int exp, const uByte *bcdar,
			   Int sig) {
  uInt encode, dpd;			/* work */
  const uByte *ub;			/* .. */

  if (EXPISSPECIAL(exp)) encode=exp|sig;/* specials already encoded */
   else {				/* is finite */
    /* encode the combination field and exponent continuation */
    uInt uexp=(uInt)(exp+DECBIAS);	/* biased exponent */
    uInt code=(uexp>>DECECONL)<<4;	/* top two bits of exp */
    code+=bcdar[0];			/* add msd */
    /* look up the combination field and make high word */
    encode=DECCOMBFROM[code]|sig;	/* indexed by (0-2)*16+msd */
    encode|=(uexp<<(32-6-DECECONL)) & 0x03ffffff; /* exponent continuation */
    }

  /* private macro to extract a declet, n (where 0<=n<DECLETS and 0 */
  /* refers to the declet from the least significant three digits) */
  /* and put the corresponding DPD code into dpd. */
  /* Use of a working pointer, uInt *ub, is assumed. */

  #define getDPDf(dpd, n) ub=bcdar+DECPMAX-1-(3*(n))-2;	    \
    dpd=BCD2DPD[(*ub*256)+(*(ub+1)*16)+*(ub+2)];

  /* place the declets in the encoding words and copy to result (df), */
  /* according to endianness; in all cases complete the sign word */
  /* first */
  #if DECPMAX==7
    getDPDf(dpd, 1);
    encode|=dpd<<10;
    getDPDf(dpd, 0);
    encode|=dpd;
    DFWORD(df, 0)=encode;     /* just the one word */

  #elif DECPMAX==16
    getDPDf(dpd, 4); encode|=dpd<<8;
    getDPDf(dpd, 3); encode|=dpd>>2;
    DFWORD(df, 0)=encode;
    encode=dpd<<30;
    getDPDf(dpd, 2); encode|=dpd<<20;
    getDPDf(dpd, 1); encode|=dpd<<10;
    getDPDf(dpd, 0); encode|=dpd;
    DFWORD(df, 1)=encode;

  #elif DECPMAX==34
    getDPDf(dpd,10); encode|=dpd<<4;
    getDPDf(dpd, 9); encode|=dpd>>6;
    DFWORD(df, 0)=encode;

    encode=dpd<<26;
    getDPDf(dpd, 8); encode|=dpd<<16;
    getDPDf(dpd, 7); encode|=dpd<<6;
    getDPDf(dpd, 6); encode|=dpd>>4;
    DFWORD(df, 1)=encode;

    encode=dpd<<28;
    getDPDf(dpd, 5); encode|=dpd<<18;
    getDPDf(dpd, 4); encode|=dpd<<8;
    getDPDf(dpd, 3); encode|=dpd>>2;
    DFWORD(df, 2)=encode;

    encode=dpd<<30;
    getDPDf(dpd, 2); encode|=dpd<<20;
    getDPDf(dpd, 1); encode|=dpd<<10;
    getDPDf(dpd, 0); encode|=dpd;
    DFWORD(df, 3)=encode;
  #endif
  /* decFloatShow(df, "final"); */
  return df;
  } /* decFloatFromBCD */

/* ------------------------------------------------------------------ */
/* decFloatFromPacked -- set decFloat from exponent and packed BCD    */
/*								      */
/*  df is the target decFloat					      */
/*  exp is the in-range unbiased exponent, q, or a special value in   */
/*    the form returned by decFloatGetExponent			      */
/*  packed holds DECPMAX packed decimal digits plus a sign nibble     */
/*    (all 6 codes are OK); the first (MSD) is ignored if df is a NaN */
/*    and all except sign are ignored if df is infinite.  For DOUBLE  */
/*    and QUAD the first (pad) nibble is also ignored in all cases.   */
/*    All coefficient nibbles must be in 0-9 and sign in A-F; results */
/*    are undefined otherwise.					      */
/*  returns df, which will be canonical				      */
/*								      */
/* No error is possible, and no status will be set.		      */
/* ------------------------------------------------------------------ */
decFloat * decFloatFromPacked(decFloat *df, Int exp, const uByte *packed) {
  uByte bcdar[DECPMAX+2];		/* work [+1 for pad, +1 for sign] */
  const uByte *ip;			/* .. */
  uByte *op;				/* .. */
  Int	sig=0;				/* sign */

  /* expand coefficient and sign to BCDAR */
  #if SINGLE
  op=bcdar+1;				/* no pad digit */
  #else
  op=bcdar;				/* first (pad) digit ignored */
  #endif
  for (ip=packed; ip<packed+((DECPMAX+2)/2); ip++) {
    *op++=*ip>>4;
    *op++=(uByte)(*ip&0x0f);		/* [final nibble is sign] */
    }
  op--;					/* -> sign byte */
  if (*op==DECPMINUS || *op==DECPMINUSALT) sig=DECFLOAT_Sign;

  if (EXPISSPECIAL(exp)) {		/* Infinity or NaN */
    if (!EXPISINF(exp)) bcdar[1]=0;	/* a NaN: ignore MSD */
     else memset(bcdar+1, 0, DECPMAX);	/* Infinite: coefficient to 0 */
    }
  return decFloatFromBCD(df, exp, bcdar+1, sig);
  } /* decFloatFromPacked */

/* ------------------------------------------------------------------ */
/* decFloatFromString -- conversion from numeric string		      */
/*								      */
/*  result  is the decFloat 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), \0-terminated      */
/*	    If there are too many significant digits in the	      */
/*	    coefficient it will be rounded.			      */
/*  set	    is the context					      */
/*  returns result						      */
/*								      */
/* The length of the coefficient and the size of the exponent are     */
/* checked by this routine, so the correct error (Underflow or	      */
/* Overflow) can be reported or rounding applied, as necessary.	      */
/*								      */
/* There is no limit to the coefficient length for finite inputs;     */
/* NaN payloads must be integers with no more than DECPMAX-1 digits.  */
/* Exponents may have up to nine significant digits.		      */
/*								      */
/* If bad syntax is detected, the result will be a quiet NaN.	      */
/* ------------------------------------------------------------------ */
decFloat * decFloatFromString(decFloat *result, const char *string,
			      decContext *set) {
  Int	 digits;		   /* count of digits in coefficient */
  const	 char *dotchar=NULL;	   /* where dot was found [NULL if none] */
  const	 char *cfirst=string;	   /* -> first character of decimal part */
  const	 char *c;		   /* work */
  uByte *ub;			   /* .. */
  bcdnum num;			   /* collects data for finishing */
  uInt	 error=DEC_Conversion_syntax;	/* assume the worst */
  uByte	 buffer[ROUNDUP(DECSTRING+11, 8)]; /* room for most coefficents, */
				   /* some common rounding, +3, & pad */
  #if DECTRACE
  /* printf("FromString %s ...\n", string); */
  #endif

  for(;;) {				/* once-only 'loop' */
    num.sign=0;				/* assume non-negative */
    num.msd=buffer;			/* MSD is here always */

    /* detect and validate the coefficient, including any leading, */
    /* trailing, or embedded '.' */
    /* [could test four-at-a-time here (saving 10% for decQuads), */
    /* but that risks storage violation because the position of the */
    /* terminator is unknown] */
    for (c=string;; c++) {		/* -> input character */
      if (((unsigned)(*c-'0'))<=9) continue; /* '0' through '9' is good */
      if (*c=='\0') break;		/* most common non-digit */
      if (*c=='.') {
	if (dotchar!=NULL) break;	/* not first '.' */
	dotchar=c;			/* record offset into decimal part */
	continue;}
      if (c==string) {			/* first in string... */
	if (*c=='-') {			/* valid - sign */
	  cfirst++;
	  num.sign=DECFLOAT_Sign;
	  continue;}
	if (*c=='+') {			/* valid + sign */
	  cfirst++;
	  continue;}
	}
      /* *c is not a digit, terminator, or a valid +, -, or '.' */
      break;
      } /* c loop */

    digits=(uInt)(c-cfirst);		/* digits (+1 if a dot) */

    if (digits>0) {			/* had digits and/or dot */
      const char *clast=c-1;		/* note last coefficient char position */
      Int exp=0;			/* exponent accumulator */
      if (*c!='\0') {			/* something follows the coefficient */
	uInt edig;			/* unsigned work */
	/* had some digits and more to come; expect E[+|-]nnn now */
	const char *firstexp;		/* exponent first non-zero */
	if (*c!='E' && *c!='e') break;
	c++;				/* to (optional) sign */
	if (*c=='-' || *c=='+') c++;	/* step over sign (c=clast+2) */
	if (*c=='\0') break;		/* no digits!  (e.g., '1.2E') */
	for (; *c=='0';) c++;		/* skip leading zeros [even last] */
	firstexp=c;			/* remember start [maybe '\0'] */
	/* gather exponent digits */
	edig=(uInt)*c-(uInt)'0';
	if (edig<=9) {			/* [check not bad or terminator] */
	  exp+=edig;			/* avoid initial X10 */
	  c++;
	  for (;; c++) {
	    edig=(uInt)*c-(uInt)'0';
	    if (edig>9) break;
	    exp=exp*10+edig;
	    }
	  }
	/* if not now on the '\0', *c must not be a digit */
	if (*c!='\0') break;

	/* (this next test must be after the syntax checks) */
	/* if definitely more than the possible digits for format then */
	/* the exponent may have wrapped, so simply set it to a certain */
	/* over/underflow value */
	if (c>firstexp+DECEMAXD) exp=DECEMAX*2;
	if (*(clast+2)=='-') exp=-exp;	/* was negative */
	} /* digits>0 */

      if (dotchar!=NULL) {		/* had a '.' */
	digits--;			/* remove from digits count */
	if (digits==0) break;		/* was dot alone: bad syntax */
	exp-=(Int)(clast-dotchar);	/* adjust exponent */
	/* [the '.' can now be ignored] */
	}
      num.exponent=exp;			/* exponent is good; store it */

      /* Here when whole string has been inspected and syntax is good */
      /* cfirst->first digit or dot, clast->last digit or dot */
      error=0;				/* no error possible now */

      /* if the number of digits in the coefficient will fit in buffer */
      /* then it can simply be converted to bcd8 and copied -- decFinalize */
      /* will take care of leading zeros and rounding; the buffer is big */
      /* enough for all canonical coefficients, including 0.00000nn... */
      ub=buffer;
      if (digits<=(Int)(sizeof(buffer)-3)) { /* [-3 allows by-4s copy] */
	c=cfirst;
	if (dotchar!=NULL) {		     /* a dot to worry about */
	  if (*(c+1)=='.') {		     /* common canonical case */
	    *ub++=(uByte)(*c-'0');	     /* copy leading digit */
	    c+=2;			     /* prepare to handle rest */
	    }
	   else for (; c<=clast;) {	     /* '.' could be anywhere */
	    /* as usual, go by fours when safe; NB it has been asserted */
	    /* that a '.' does not have the same mask as a digit */
	    if (c<=clast-3			       /* safe for four */
	     && (UINTAT(c)&0xf0f0f0f0)==CHARMASK) {    /* test four */
	      UINTAT(ub)=UINTAT(c)&0x0f0f0f0f;	       /* to BCD8 */
	      ub+=4;
	      c+=4;
	      continue;
	      }
	    if (*c=='.') {		     /* found the dot */
	      c++;			     /* step over it .. */
	      break;			     /* .. and handle the rest */
	      }
	    *ub++=(uByte)(*c++-'0');
	    }
	  } /* had dot */
	/* Now no dot; do this by fours (where safe) */
	for (; c<=clast-3; c+=4, ub+=4) UINTAT(ub)=UINTAT(c)&0x0f0f0f0f;
	for (; c<=clast; c++, ub++) *ub=(uByte)(*c-'0');
	num.lsd=buffer+digits-1;	     /* record new LSD */
	} /* fits */

       else {				     /* too long for buffer */
	/* [This is a rare and unusual case; arbitrary-length input] */
	/* strip leading zeros [but leave final 0 if all 0's] */
	if (*cfirst=='.') cfirst++;	     /* step past dot at start */
	if (*cfirst=='0') {		     /* [cfirst always -> digit] */
	  for (; cfirst<clast; cfirst++) {
	    if (*cfirst!='0') {		     /* non-zero found */
	      if (*cfirst=='.') continue;    /* [ignore] */
	      break;			     /* done */
	      }
	    digits--;			     /* 0 stripped */
	    } /* cfirst */
	  } /* at least one leading 0 */

	/* the coefficient is now as short as possible, but may still */
	/* be too long; copy up to Pmax+1 digits to the buffer, then */
	/* just record any non-zeros (set round-for-reround digit) */
	for (c=cfirst; c<=clast && ub<=buffer+DECPMAX; c++) {
	  /* (see commentary just above) */
	  if (c<=clast-3			  /* safe for four */
	   && (UINTAT(c)&0xf0f0f0f0)==CHARMASK) { /* four digits */
	    UINTAT(ub)=UINTAT(c)&0x0f0f0f0f;	  /* to BCD8 */
	    ub+=4;
	    c+=3;			     /* [will become 4] */
	    continue;
	    }
	  if (*c=='.') continue;	     /* [ignore] */
	  *ub++=(uByte)(*c-'0');
	  }
	ub--;				     /* -> LSD */
	for (; c<=clast; c++) {		     /* inspect remaining chars */
	  if (*c!='0') {		     /* sticky bit needed */
	    if (*c=='.') continue;	     /* [ignore] */
	    *ub=DECSTICKYTAB[*ub];	     /* update round-for-reround */
	    break;			     /* no need to look at more */
	    }
	  }
	num.lsd=ub;			     /* record LSD */
	/* adjust exponent for dropped digits */
	num.exponent+=digits-(Int)(ub-buffer+1);
	} /* too long for buffer */
      } /* digits or dot */

     else {				/* no digits or dot were found */
      if (*c=='\0') break;		/* nothing to come is bad */
      /* only Infinities and NaNs are allowed, here */
      buffer[0]=0;			/* default a coefficient of 0 */
      num.lsd=buffer;			/* .. */
      if (decBiStr(c, "infinity", "INFINITY")
       || decBiStr(c, "inf", "INF")) num.exponent=DECFLOAT_Inf;
       else {				/* should be a NaN */
	num.exponent=DECFLOAT_qNaN;	/* assume quiet NaN */
	if (*c=='s' || *c=='S') {	/* probably an sNaN */
	  c++;
	  num.exponent=DECFLOAT_sNaN;	/* assume is in fact sNaN */
	  }
	if (*c!='N' && *c!='n') break;	/* check caseless "NaN" */
	c++;
	if (*c!='a' && *c!='A') break;	/* .. */
	c++;
	if (*c!='N' && *c!='n') break;	/* .. */
	c++;
	/* now either nothing, or nnnn payload (no dots), expected */
	/* -> start of integer, and skip leading 0s [including plain 0] */
	for (cfirst=c; *cfirst=='0';) cfirst++;
	if (*cfirst!='\0') {		/* not empty or all-0, payload */
	  /* payload found; check all valid digits and copy to buffer as bcd8 */
	  ub=buffer;
	  for (c=cfirst;; c++, ub++) {
	    if ((unsigned)(*c-'0')>9) break; /* quit if not 0-9 */
	    if (c-cfirst==DECPMAX-1) break;  /* too many digits */
	    *ub=(uByte)(*c-'0');	/* good bcd8 */
	    }
	  if (*c!='\0') break;		/* not all digits, or too many */
	  num.lsd=ub-1;			/* record new LSD */
	  }
	} /* NaN or sNaN */
      error=0;				/* syntax is OK */
      break;				/* done with specials */
      } /* digits=0 (special expected) */
    break;
    }					/* [for(;;) break] */

  /* decShowNum(&num, "fromStr"); */

  if (error!=0) {
    set->status|=error;
    num.exponent=DECFLOAT_qNaN;		/* set up quiet NaN */
    num.sign=0;				/* .. with 0 sign */
    buffer[0]=0;			/* .. and coefficient */
    num.lsd=buffer;			/* .. */
    /* decShowNum(&num, "oops"); */
    }

  /* decShowNum(&num, "dffs"); */
  decFinalize(result, &num, set);	/* round, check, and lay out */
  /* decFloatShow(result, "fromString"); */
  return result;
  } /* decFloatFromString */

/* ------------------------------------------------------------------ */
/* decFloatFromWider -- conversion from next-wider format	      */
/*								      */
/*  result  is the decFloat format number which gets the result of    */
/*	    the conversion					      */
/*  wider   is the decFloatWider format number which will be narrowed */
/*  set	    is the context					      */
/*  returns result						      */
/*								      */
/* Narrowing can cause rounding, overflow, etc., but not Invalid      */
/* operation (sNaNs are copied and do not signal).		      */
/* ------------------------------------------------------------------ */
/* narrow-to is not possible for decQuad format numbers; simply omit */
#if !QUAD
decFloat * decFloatFromWider(decFloat *result, const decFloatWider *wider,
			     decContext *set) {
  bcdnum num;				/* collects data for finishing */
  uByte	 bcdar[DECWPMAX];		/* room for wider coefficient */
  uInt	 widerhi=DFWWORD(wider, 0);	/* top word */
  Int	 exp;

  GETWCOEFF(wider, bcdar);

  num.msd=bcdar;			/* MSD is here always */
  num.lsd=bcdar+DECWPMAX-1;		/* LSD is here always */
  num.sign=widerhi&0x80000000;		/* extract sign [DECFLOAT_Sign=Neg] */

  /* decode the wider combination field to exponent */
  exp=DECCOMBWEXP[widerhi>>26];		/* decode from wider combination field */
  /* if it is a special there's nothing to do unless sNaN; if it's */
  /* finite then add the (wider) exponent continuation and unbias */
  if (EXPISSPECIAL(exp)) exp=widerhi&0x7e000000; /* include sNaN selector */
   else exp+=GETWECON(wider)-DECWBIAS;
  num.exponent=exp;

  /* decShowNum(&num, "dffw"); */
  return decFinalize(result, &num, set);/* round, check, and lay out */
  } /* decFloatFromWider */
#endif

/* ------------------------------------------------------------------ */
/* decFloatGetCoefficient -- get coefficient as BCD8		      */
/*								      */
/*  df is the decFloat from which to extract the coefficient	      */
/*  bcdar is where DECPMAX bytes will be written, one BCD digit in    */
/*    each byte (BCD8 encoding); if df is a NaN the first byte will   */
/*    be zero, and if it is infinite they will all be zero	      */
/*  returns the sign of the coefficient (DECFLOAT_Sign if negative,   */
/*    0 otherwise)						      */
/*								      */
/* No error is possible, and no status will be set.  If df is a	      */
/* special value the array is set to zeros (for Infinity) or to the   */
/* payload of a qNaN or sNaN.					      */
/* ------------------------------------------------------------------ */
Int decFloatGetCoefficient(const decFloat *df, uByte *bcdar) {
  if (DFISINF(df)) memset(bcdar, 0, DECPMAX);
   else {
    GETCOEFF(df, bcdar);	   /* use macro */
    if (DFISNAN(df)) bcdar[0]=0;   /* MSD needs correcting */
    }
  return DFISSIGNED(df);
  } /* decFloatGetCoefficient */

/* ------------------------------------------------------------------ */
/* decFloatGetExponent -- get unbiased exponent			      */
/*								      */
/*  df is the decFloat from which to extract the exponent	      */
/*  returns the exponent, q.					      */
/*								      */
/* No error is possible, and no status will be set.  If df is a	      */
/* special value the first seven bits of the decFloat are returned,   */
/* left adjusted and with the first (sign) bit set to 0 (followed by  */
/* 25 0 bits).	e.g., -sNaN would return 0x7e000000 (DECFLOAT_sNaN).  */
/* ------------------------------------------------------------------ */
Int decFloatGetExponent(const decFloat *df) {
  if (DFISSPECIAL(df)) return DFWORD(df, 0)&0x7e000000;
  return GETEXPUN(df);
  } /* decFloatGetExponent */

/* ------------------------------------------------------------------ */
/* decFloatSetCoefficient -- set coefficient from BCD8		      */
/*								      */
/*  df is the target decFloat (and source of exponent/special value)  */
/*  bcdar holds DECPMAX digits to set the coefficient from, one	      */
/*    digit in each byte (BCD8 encoding); the first (MSD) is ignored  */
/*    if df is a NaN; all are ignored if df is infinite.	      */
/*  sig is DECFLOAT_Sign to set the sign bit, 0 otherwise	      */
/*  returns df, which will be canonical				      */
/*								      */
/* No error is possible, and no status will be set.		      */
/* ------------------------------------------------------------------ */
decFloat * decFloatSetCoefficient(decFloat *df, const uByte *bcdar,
				  Int sig) {
  uInt exp;			   /* for exponent */
  uByte bcdzero[DECPMAX];	   /* for infinities */

  /* Exponent/special code is extracted from df */
  if (DFISSPECIAL(df)) {
    exp=DFWORD(df, 0)&0x7e000000;
    if (DFISINF(df)) {
      memset(bcdzero, 0, DECPMAX);
      return decFloatFromBCD(df, exp, bcdzero, sig);
      }
    }
   else exp=GETEXPUN(df);
  return decFloatFromBCD(df, exp, bcdar, sig);
  } /* decFloatSetCoefficient */

/* ------------------------------------------------------------------ */
/* decFloatSetExponent -- set exponent or special value		      */
/*								      */
/*  df	is the target decFloat (and source of coefficient/payload)    */
/*  set is the context for reporting status			      */
/*  exp is the unbiased exponent, q, or a special value in the form   */
/*    returned by decFloatGetExponent				      */
/*  returns df, which will be canonical				      */
/*								      */
/* No error is possible, but Overflow or Underflow might occur.	      */
/* ------------------------------------------------------------------ */
decFloat * decFloatSetExponent(decFloat *df, decContext *set, Int exp) {
  uByte	 bcdcopy[DECPMAX];	   /* for coefficient */
  bcdnum num;			   /* work */
  num.exponent=exp;
  num.sign=decFloatGetCoefficient(df, bcdcopy); /* extract coefficient */
  if (DFISSPECIAL(df)) {	   /* MSD or more needs correcting */
    if (DFISINF(df)) memset(bcdcopy, 0, DECPMAX);
    bcdcopy[0]=0;
    }
  num.msd=bcdcopy;
  num.lsd=bcdcopy+DECPMAX-1;
  return decFinalize(df, &num, set);
  } /* decFloatSetExponent */

/* ------------------------------------------------------------------ */
/* decFloatRadix -- returns the base (10)			      */
/*								      */
/*   df is any decFloat of this format				      */
/* ------------------------------------------------------------------ */
uInt decFloatRadix(const decFloat *df) {
  if (df) return 10;			     /* to placate compiler */
  return 10;
  } /* decFloatRadix */

/* ------------------------------------------------------------------ */
/* decFloatShow -- printf a decFloat in hexadecimal and decimal	      */
/*   df	 is the decFloat to show				      */
/*   tag is a tag string displayed with the number		      */
/*								      */
/* This is a debug aid; the precise format of the string may change.  */
/* ------------------------------------------------------------------ */
void decFloatShow(const decFloat *df, const char *tag) {
  char hexbuf[DECBYTES*2+DECBYTES/4+1]; /* NB blank after every fourth */
  char buff[DECSTRING];			/* for value in decimal */
  Int i, j=0;

  for (i=0; i<DECBYTES; i++) {
    #if DECLITEND
      sprintf(&hexbuf[j], "%02x", df->bytes[DECBYTES-1-i]);
    #else
      sprintf(&hexbuf[j], "%02x", df->bytes[i]);
    #endif
    j+=2;
    /* the next line adds blank (and terminator) after final pair, too */
    if ((i+1)%4==0) {strcpy(&hexbuf[j], " "); j++;}
    }
  decFloatToString(df, buff);
  printf(">%s> %s [big-endian]	%s\n", tag, hexbuf, buff);
  return;
  } /* decFloatShow */

/* ------------------------------------------------------------------ */
/* decFloatToBCD -- get sign, exponent, and BCD8 from a decFloat      */
/*								      */
/*  df is the source decFloat					      */
/*  exp will be set to the unbiased exponent, q, or to a special      */
/*    value in the form returned by decFloatGetExponent		      */
/*  bcdar is where DECPMAX bytes will be written, one BCD digit in    */
/*    each byte (BCD8 encoding); if df is a NaN the first byte will   */
/*    be zero, and if it is infinite they will all be zero	      */
/*  returns the sign of the coefficient (DECFLOAT_Sign if negative,   */
/*    0 otherwise)						      */
/*								      */
/* No error is possible, and no status will be set.		      */
/* ------------------------------------------------------------------ */
Int decFloatToBCD(const decFloat *df, Int *exp, uByte *bcdar) {
  if (DFISINF(df)) {
    memset(bcdar, 0, DECPMAX);
    *exp=DFWORD(df, 0)&0x7e000000;
    }
   else {
    GETCOEFF(df, bcdar);	   /* use macro */
    if (DFISNAN(df)) {
      bcdar[0]=0;		   /* MSD needs correcting */
      *exp=DFWORD(df, 0)&0x7e000000;
      }
     else {			   /* finite */
      *exp=GETEXPUN(df);
      }
    }
  return DFISSIGNED(df);
  } /* decFloatToBCD */

/* ------------------------------------------------------------------ */
/* decFloatToEngString -- conversion to numeric string, engineering   */
/*								      */
/*  df is the decFloat format number to convert			      */
/*  string is the string where the result will be laid out	      */
/*								      */
/* string must be at least DECPMAX+9 characters (the worst case is    */
/* "-0.00000nnn...nnn\0", which is as long as the exponent form when  */
/* DECEMAXD<=4); this condition is asserted above		      */
/*								      */
/* No error is possible, and no status will be set		      */
/* ------------------------------------------------------------------ */
char * decFloatToEngString(const decFloat *df, 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 */
  char *s, *t;			   /* .. (source, target) */
  Int  pre, e;			   /* work */
  const uByte *u;		   /* .. */

  /* Source words; macro handles endianness */
  uInt sourhi=DFWORD(df, 0);	   /* word with sign */
  #if DECPMAX==16
  uInt sourlo=DFWORD(df, 1);
  #elif DECPMAX==34
  uInt sourmh=DFWORD(df, 1);
  uInt sourml=DFWORD(df, 2);
  uInt sourlo=DFWORD(df, 3);
  #endif

  c=string;			   /* where result will go */
  if (((Int)sourhi)<0) *c++='-';   /* handle sign */
  comb=sourhi>>26;		   /* sign+combination field */
  msd=DECCOMBMSD[comb];		   /* decode the combination field */
  exp=DECCOMBEXP[comb];		   /* .. */

  if (EXPISSPECIAL(exp)) {	   /* special */
    if (exp==DECFLOAT_Inf) {	   /* 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 */
    /* quick exit if the payload is zero */
    #if DECPMAX==7
    if ((sourhi&0x000fffff)==0) return string;
    #elif DECPMAX==16
    if (sourlo==0 && (sourhi&0x0003ffff)==0) return string;
    #elif DECPMAX==34
    if (sourlo==0 && sourml==0 && sourmh==0
     && (sourhi&0x00003fff)==0) return string;
    #endif
    /* otherwise drop through to add integer; set correct exp etc. */
    exp=0; msd=0;		   /* setup for following code */
    }
   else { /* complete exponent; top two bits are in place */
    exp+=GETECON(df)-DECBIAS;	   /* .. + continuation and unbias */
    }

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

  /* Decode the declets.  After extracting each declet, it is */
  /* decoded to a 4-uByte sequence by table lookup; the four uBytes */
  /* are the three encoded BCD8 digits followed by a 1-byte length */
  /* (significant digits, except that 000 has length 0).  This allows */
  /* us to left-align the first declet with non-zero content, then */
  /* the remaining ones are full 3-char length.	 Fixed-length copies */
  /* are used because variable-length memcpy causes a subroutine call */
  /* in at least two compilers.	 (The copies are length 4 for speed */
  /* and are safe because the last item in the array is of length */
  /* three and has the length byte following.) */
  #define dpd2char(dpdin) u=&DPD2BCD8[((dpdin)&0x3ff)*4];	 \
	 if (c!=cstart) {UINTAT(c)=UINTAT(u)|CHARMASK; c+=3;}	 \
	  else if (*(u+3)) {					 \
	   UINTAT(c)=UINTAT(u+3-*(u+3))|CHARMASK; c+=*(u+3);}

  #if DECPMAX==7
  dpd2char(sourhi>>10);			/* declet 1 */
  dpd2char(sourhi);			/* declet 2 */

  #elif DECPMAX==16
  dpd2char(sourhi>>8);			/* declet 1 */
  dpd2char((sourhi<<2) | (sourlo>>30)); /* declet 2 */
  dpd2char(sourlo>>20);			/* declet 3 */
  dpd2char(sourlo>>10);			/* declet 4 */
  dpd2char(sourlo);			/* declet 5 */

  #elif DECPMAX==34
  dpd2char(sourhi>>4);			/* declet 1 */
  dpd2char((sourhi<<6) | (sourmh>>26)); /* declet 2 */
  dpd2char(sourmh>>16);			/* declet 3 */
  dpd2char(sourmh>>6);			/* declet 4 */
  dpd2char((sourmh<<4) | (sourml>>28)); /* declet 5 */
  dpd2char(sourml>>18);			/* declet 6 */
  dpd2char(sourml>>8);			/* declet 7 */
  dpd2char((sourml<<2) | (sourlo>>30)); /* declet 8 */
  dpd2char(sourlo>>20);			/* declet 9 */
  dpd2char(sourlo>>10);			/* declet 10 */
  dpd2char(sourlo);			/* declet 11 */
  #endif

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

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

  e=0;				   /* assume no E */
  pre=(Int)(c-cstart)+exp;	   /* length+exp  [c->LSD+1] */
  /* [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 '.' */
    if (e!=0) {			   /* engineering: may need to adjust */
      Int adj;			   /* adjustment */
      /* The C remainder operator is undefined for negative numbers, so */
      /* a positive remainder calculation must be used here */
      if (e<0) {
	adj=(-e)%3;
	if (adj!=0) adj=3-adj;
	}
       else { /* e>0 */
	adj=e%3;
	}
      e=e-adj;
      /* if dealing with zero still produce an exponent which is a */
      /* multiple of three, as expected, but there will only be the */
      /* one zero before the E, still.	Otherwise note the padding. */
      if (!DFISZERO(df)) pre+=adj;
       else {  /* is zero */
	if (adj!=0) {		   /* 0.00Esnn needed */
	  e=e+3;
	  pre=-(2-adj);
	  }
	} /* zero */
      } /* engineering adjustment */
    } /* exponential form */
  /* printf("e=%ld pre=%ld exp=%ld\n", (LI)e, (LI)pre, (LI)exp); */

  /* modify the coefficient, adding 0s, '.', and E+nn as needed */
  if (pre>0) {			   /* ddd.ddd (plain), perhaps with E */
				   /* or dd00 padding for engineering */
    char *dotat=cstart+pre;
    if (dotat<c) {			/* if embedded dot needed... */
      /* move by fours; there must be space for junk at the end */
      /* because there is still space for exponent */
      s=dotat+ROUNDDOWN4(c-dotat);	/* source */
      t=s+1;				/* target */
      /* open the gap */
      for (; s>=dotat; s-=4, t-=4) UINTAT(t)=UINTAT(s);
      *dotat='.';
      c++;				/* length increased by one */
      } /* need dot? */
     else for (; c<dotat; c++) *c='0';	/* pad for engineering */
    } /* pre>0 */
   else {
    /* -5<=pre<=0: here for plain 0.ddd or 0.000ddd forms (may have
       E, but only for 0.00E+3 kind of case -- with plenty of spare
       space in this case */
    pre=-pre+2;				/* gap width, including "0." */
    t=cstart+ROUNDDOWN4(c-cstart)+pre;	/* preferred first target point */
    /* backoff if too far to the right */
    if (t>string+DECSTRING-5) t=string+DECSTRING-5; /* adjust to fit */
    /* now shift the entire coefficient to the right, being careful not */
    /* to access to the left of string */
    for (s=t-pre; s>=string; s-=4, t-=4) UINTAT(t)=UINTAT(s);
    /* for Quads and Singles there may be a character or two left... */
    s+=3;				/* where next would come from */
    for(; s>=cstart; s--, t--) *(t+3)=*(s);
    /* now have fill 0. through 0.00000; use overlaps to avoid tests */
    if (pre>=4) {
      UINTAT(cstart+pre-4)=UINTAT("0000");
      UINTAT(cstart)=UINTAT("0.00");
      }
     else { /* 2 or 3 */
      *(cstart+pre-1)='0';
      USHORTAT(cstart)=USHORTAT("0.");
      }
    c+=pre;				/* to end */
    }

  /* finally add the E-part, if needed; it will never be 0, and has */
  /* a maximum length of 3 or 4 digits (asserted above) */
  if (e!=0) {
    USHORTAT(c)=USHORTAT("E+");		/* starts with E, assume + */
    c++;
    if (e<0) {
      *c='-';				/* oops, need '-' */
      e=-e;				/* uInt, please */
      }
    c++;
    /* Three-character exponents are easy; 4-character a little trickier */
    #if DECEMAXD<=3
      u=&BIN2BCD8[e*4];			/* -> 3 digits + length byte */
      /* copy fixed 4 characters [is safe], starting at non-zero */
      /* and with character mask to convert BCD to char */
      UINTAT(c)=UINTAT(u+3-*(u+3))|CHARMASK;
      c+=*(u+3);			/* bump pointer appropriately */
    #elif DECEMAXD==4
      if (e<1000) {			/* 3 (or fewer) digits case */
	u=&BIN2BCD8[e*4];		/* -> 3 digits + length byte */
	UINTAT(c)=UINTAT(u+3-*(u+3))|CHARMASK; /* [as above] */
	c+=*(u+3);			/* bump pointer appropriately */
	}
       else {				/* 4-digits */
	Int thou=((e>>3)*1049)>>17;	/* e/1000 */
	Int rem=e-(1000*thou);		/* e%1000 */
	*c++=(char)('0'+(char)thou);	/* the thousands digit */
	u=&BIN2BCD8[rem*4];		/* -> 3 digits + length byte */
	UINTAT(c)=UINTAT(u)|CHARMASK;	/* copy fixed 3+1 characters [is safe] */
	c+=3;				/* bump pointer, always 3 digits */
	}
    #endif
    }
  *c='\0';				/* terminate */
  /*printf("res %s\n", string); */
  return string;
  } /* decFloatToEngString */

/* ------------------------------------------------------------------ */
/* decFloatToPacked -- convert decFloat to Packed decimal + exponent  */
/*								      */
/*  df is the source decFloat					      */
/*  exp will be set to the unbiased exponent, q, or to a special      */
/*    value in the form returned by decFloatGetExponent		      */
/*  packed is where DECPMAX nibbles will be written with the sign as  */
/*    final nibble (0x0c for +, 0x0d for -); a NaN has a first nibble */
/*    of zero, and an infinity is all zeros. decDouble and decQuad    */
/*    have a additional leading zero nibble, leading to result	      */
/*    lengths of 4, 9, and 18 bytes.				      */
/*  returns the sign of the coefficient (DECFLOAT_Sign if negative,   */
/*    0 otherwise)						      */
/*								      */
/* No error is possible, and no status will be set.		      */
/* ------------------------------------------------------------------ */
Int decFloatToPacked(const decFloat *df, Int *exp, uByte *packed) {
  uByte bcdar[DECPMAX+2];	   /* work buffer */
  uByte *ip=bcdar, *op=packed;	   /* work pointers */
  if (DFISINF(df)) {
    memset(bcdar, 0, DECPMAX+2);
    *exp=DECFLOAT_Inf;
    }
   else {
    GETCOEFF(df, bcdar+1);	   /* use macro */
    if (DFISNAN(df)) {
      bcdar[1]=0;		   /* MSD needs clearing */
      *exp=DFWORD(df, 0)&0x7e000000;
      }
     else {			   /* finite */
      *exp=GETEXPUN(df);
      }
    }
  /* now pack; coefficient currently at bcdar+1 */
  #if SINGLE
    ip++;			   /* ignore first byte */
  #else
    *ip=0;			   /* need leading zero */
  #endif
  /* set final byte to Packed BCD sign value */
  bcdar[DECPMAX+1]=(DFISSIGNED(df) ? DECPMINUS : DECPPLUS);
  /* pack an even number of bytes... */
  for (; op<packed+((DECPMAX+2)/2); op++, ip+=2) {
    *op=(uByte)((*ip<<4)+*(ip+1));
    }
  return (bcdar[DECPMAX+1]==DECPMINUS ? DECFLOAT_Sign : 0);
  } /* decFloatToPacked */

/* ------------------------------------------------------------------ */
/* decFloatToString -- conversion to numeric string		      */
/*								      */
/*  df is the decFloat format number to convert			      */
/*  string is the string where the result will be laid out	      */
/*								      */
/* string must be at least DECPMAX+9 characters (the worst case is    */
/* "-0.00000nnn...nnn\0", which is as long as the exponent form when  */
/* DECEMAXD<=4); this condition is asserted above		      */
/*								      */
/* No error is possible, and no status will be set		      */
/* ------------------------------------------------------------------ */
char * decFloatToString(const decFloat *df, 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 */
  char *s, *t;			   /* .. (source, target) */
  Int  pre, e;			   /* work */
  const uByte *u;		   /* .. */

  /* Source words; macro handles endianness */
  uInt sourhi=DFWORD(df, 0);	   /* word with sign */
  #if DECPMAX==16
  uInt sourlo=DFWORD(df, 1);
  #elif DECPMAX==34
  uInt sourmh=DFWORD(df, 1);
  uInt sourml=DFWORD(df, 2);
  uInt sourlo=DFWORD(df, 3);
  #endif

  c=string;			   /* where result will go */
  if (((Int)sourhi)<0) *c++='-';   /* handle sign */
  comb=sourhi>>26;		   /* sign+combination field */
  msd=DECCOMBMSD[comb];		   /* decode the combination field */
  exp=DECCOMBEXP[comb];		   /* .. */

  if (EXPISSPECIAL(exp)) {	   /* special */
    if (exp==DECFLOAT_Inf) {	   /* infinity */
      strcpy(c, "Infinity");
      return string;		   /* easy */
      }
    if (sourhi&0x02000000) *c++='s'; /* sNaN */
    strcpy(c, "NaN");		   /* complete word */
    c+=3;			   /* step past */
    /* quick exit if the payload is zero */
    #if DECPMAX==7
    if ((sourhi&0x000fffff)==0) return string;
    #elif DECPMAX==16
    if (sourlo==0 && (sourhi&0x0003ffff)==0) return string;
    #elif DECPMAX==34
    if (sourlo==0 && sourml==0 && sourmh==0
     && (sourhi&0x00003fff)==0) return string;
    #endif
    /* otherwise drop through to add integer; set correct exp etc. */
    exp=0; msd=0;		   /* setup for following code */
    }
   else { /* complete exponent; top two bits are in place */
    exp+=GETECON(df)-DECBIAS;	   /* .. + continuation and unbias */
    }

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

  /* Decode the declets.  After extracting each declet, it is */
  /* decoded to a 4-uByte sequence by table lookup; the four uBytes */
  /* are the three encoded BCD8 digits followed by a 1-byte length */
  /* (significant digits, except that 000 has length 0).  This allows */
  /* us to left-align the first declet with non-zero content, then */
  /* the remaining ones are full 3-char length.	 Fixed-length copies */
  /* are used because variable-length memcpy causes a subroutine call */
  /* in at least two compilers.	 (The copies are length 4 for speed */
  /* and are safe because the last item in the array is of length */
  /* three and has the length byte following.) */
  #define dpd2char(dpdin) u=&DPD2BCD8[((dpdin)&0x3ff)*4];	 \
	 if (c!=cstart) {UINTAT(c)=UINTAT(u)|CHARMASK; c+=3;}	 \
	  else if (*(u+3)) {					 \
	   UINTAT(c)=UINTAT(u+3-*(u+3))|CHARMASK; c+=*(u+3);}

  #if DECPMAX==7
  dpd2char(sourhi>>10);			/* declet 1 */
  dpd2char(sourhi);			/* declet 2 */

  #elif DECPMAX==16
  dpd2char(sourhi>>8);			/* declet 1 */
  dpd2char((sourhi<<2) | (sourlo>>30)); /* declet 2 */
  dpd2char(sourlo>>20);			/* declet 3 */
  dpd2char(sourlo>>10);			/* declet 4 */
  dpd2char(sourlo);			/* declet 5 */

  #elif DECPMAX==34
  dpd2char(sourhi>>4);			/* declet 1 */
  dpd2char((sourhi<<6) | (sourmh>>26)); /* declet 2 */
  dpd2char(sourmh>>16);			/* declet 3 */
  dpd2char(sourmh>>6);			/* declet 4 */
  dpd2char((sourmh<<4) | (sourml>>28)); /* declet 5 */
  dpd2char(sourml>>18);			/* declet 6 */
  dpd2char(sourml>>8);			/* declet 7 */
  dpd2char((sourml<<2) | (sourlo>>30)); /* declet 8 */
  dpd2char(sourlo>>20);			/* declet 9 */
  dpd2char(sourlo>>10);			/* declet 10 */
  dpd2char(sourlo);			/* declet 11 */
  #endif

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

  /*[This fast path is valid but adds 3-5 cycles to worst case length] */
  /*if (exp==0) {		   // integer or NaN case -- easy */
  /*  *c='\0';			   // terminate */
  /*  return string; */
  /*  } */

  e=0;				   /* assume no E */
  pre=(Int)(c-cstart)+exp;	   /* length+exp  [c->LSD+1] */
  /* [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 */
  if (pre>0) {			   /* ddd.ddd (plain), perhaps with E */
    char *dotat=cstart+pre;
    if (dotat<c) {			/* if embedded dot needed... */
      /* move by fours; there must be space for junk at the end */
      /* because there is still space for exponent */
      s=dotat+ROUNDDOWN4(c-dotat);	/* source */
      t=s+1;				/* target */
      /* open the gap */
      for (; s>=dotat; s-=4, t-=4) UINTAT(t)=UINTAT(s);
      *dotat='.';
      c++;				/* length increased by one */
      } /* need dot? */

    /* finally add the E-part, if needed; it will never be 0, and has */
    /* a maximum length of 3 or 4 digits (asserted above) */
    if (e!=0) {
      USHORTAT(c)=USHORTAT("E+");	/* starts with E, assume + */
      c++;
      if (e<0) {
	*c='-';				/* oops, need '-' */
	e=-e;				/* uInt, please */
	}
      c++;
      /* Three-character exponents are easy; 4-character a little trickier */
      #if DECEMAXD<=3
	u=&BIN2BCD8[e*4];		/* -> 3 digits + length byte */
	/* copy fixed 4 characters [is safe], starting at non-zero */
	/* and with character mask to convert BCD to char */
	UINTAT(c)=UINTAT(u+3-*(u+3))|CHARMASK;
	c+=*(u+3);			/* bump pointer appropriately */
      #elif DECEMAXD==4
	if (e<1000) {			/* 3 (or fewer) digits case */
	  u=&BIN2BCD8[e*4];		/* -> 3 digits + length byte */
	  UINTAT(c)=UINTAT(u+3-*(u+3))|CHARMASK; /* [as above] */
	  c+=*(u+3);			/* bump pointer appropriately */
	  }
	 else {				/* 4-digits */
	  Int thou=((e>>3)*1049)>>17;	/* e/1000 */
	  Int rem=e-(1000*thou);	/* e%1000 */
	  *c++=(char)('0'+(char)thou);	/* the thousands digit */
	  u=&BIN2BCD8[rem*4];		/* -> 3 digits + length byte */
	  UINTAT(c)=UINTAT(u)|CHARMASK; /* copy fixed 3+1 characters [is safe] */
	  c+=3;				/* bump pointer, always 3 digits */
	  }
      #endif
      }
    *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) */
  /* Surprisingly, this is close to being the worst-case path, so the */
  /* shift is done by fours; this is a little tricky because the */
  /* rightmost character to be written must not be beyond where the */
  /* rightmost terminator could be -- so backoff to not touch */
  /* terminator position if need be (this can make exact alignments */
  /* for full Doubles, but in some cases needs care not to access too */
  /* far to the left) */

  pre=-pre+2;				/* gap width, including "0." */
  t=cstart+ROUNDDOWN4(c-cstart)+pre;	/* preferred first target point */
  /* backoff if too far to the right */
  if (t>string+DECSTRING-5) t=string+DECSTRING-5; /* adjust to fit */
  /* now shift the entire coefficient to the right, being careful not */
  /* to access to the left of string */
  for (s=t-pre; s>=string; s-=4, t-=4) UINTAT(t)=UINTAT(s);
  /* for Quads and Singles there may be a character or two left... */
  s+=3;					/* where next would come from */
  for(; s>=cstart; s--, t--) *(t+3)=*(s);
  /* now have fill 0. through 0.00000; use overlaps to avoid tests */
  if (pre>=4) {
    UINTAT(cstart+pre-4)=UINTAT("0000");
    UINTAT(cstart)=UINTAT("0.00");
    }
   else { /* 2 or 3 */
    *(cstart+pre-1)='0';
    USHORTAT(cstart)=USHORTAT("0.");
    }
  *(c+pre)='\0';			/* terminate */
  return string;
  } /* decFloatToString */

/* ------------------------------------------------------------------ */
/* decFloatToWider -- conversion to next-wider format		      */
/*								      */
/*  source  is the decFloat format number which gets the result of    */
/*	    the conversion					      */
/*  wider   is the decFloatWider format number which will be narrowed */
/*  returns wider						      */
/*								      */
/* Widening is always exact; no status is set (sNaNs are copied and   */
/* do not signal).  The result will be canonical if the source is,    */
/* and may or may not be if the source is not.			      */
/* ------------------------------------------------------------------ */
/* widening is not possible for decQuad format numbers; simply omit */
#if !QUAD
decFloatWider * decFloatToWider(const decFloat *source, decFloatWider *wider) {
  uInt msd;

  /* Construct and copy the sign word */
  if (DFISSPECIAL(source)) {
    /* copy sign, combination, and first bit of exponent (sNaN selector) */
    DFWWORD(wider, 0)=DFWORD(source, 0)&0xfe000000;
    msd=0;
    }
   else { /* is finite number */
    uInt exp=GETEXPUN(source)+DECWBIAS; /* get unbiased exponent and rebias */
    uInt code=(exp>>DECWECONL)<<29;	/* set two bits of exp [msd=0] */
    code|=(exp<<(32-6-DECWECONL)) & 0x03ffffff; /* add exponent continuation */
    code|=DFWORD(source, 0)&0x80000000; /* add sign */
    DFWWORD(wider, 0)=code;		/* .. and place top word in wider */
    msd=GETMSD(source);			/* get source coefficient MSD [0-9] */
    }
  /* Copy the coefficient and clear any 'unused' words to left */
  #if SINGLE
    DFWWORD(wider, 1)=(DFWORD(source, 0)&0x000fffff)|(msd<<20);
  #elif DOUBLE
    DFWWORD(wider, 2)=(DFWORD(source, 0)&0x0003ffff)|(msd<<18);
    DFWWORD(wider, 3)=DFWORD(source, 1);
    DFWWORD(wider, 1)=0;
  #endif
  return wider;
  } /* decFloatToWider */
#endif

/* ------------------------------------------------------------------ */
/* decFloatVersion -- return package version string		      */
/*								      */
/*  returns a constant string describing this package		      */
/* ------------------------------------------------------------------ */
const char *decFloatVersion(void) {
  return DECVERSION;
  } /* decFloatVersion */

/* ------------------------------------------------------------------ */
/* decFloatZero -- set to canonical (integer) zero		      */
/*								      */
/*  df is the decFloat format number to integer +0 (q=0, c=+0)	      */
/*  returns df							      */
/*								      */
/* No error is possible, and no status can be set.		      */
/* ------------------------------------------------------------------ */
decFloat * decFloatZero(decFloat *df){
  DFWORD(df, 0)=ZEROWORD;     /* set appropriate top word */
  #if DOUBLE || QUAD
    DFWORD(df, 1)=0;
    #if QUAD
      DFWORD(df, 2)=0;
      DFWORD(df, 3)=0;
    #endif
  #endif
  /* decFloatShow(df, "zero"); */
  return df;
  } /* decFloatZero */

/* ------------------------------------------------------------------ */
/* Private generic function (not format-specific) for development use */
/* ------------------------------------------------------------------ */
/* This is included once only, for all to use */
#if QUAD && (DECCHECK || DECTRACE)
  /* ---------------------------------------------------------------- */
  /* decShowNum -- display bcd8 number in debug form		      */
  /*								      */
  /*   num is the bcdnum to display				      */
  /*   tag is a string to label the display			      */
  /* ---------------------------------------------------------------- */
  void decShowNum(const bcdnum *num, const char *tag) {
    const char *csign="+";		/* sign character */
    uByte *ub;				/* work */
    if (num->sign==DECFLOAT_Sign) csign="-";

    printf(">%s> ", tag);
    if (num->exponent==DECFLOAT_Inf) printf("%sInfinity", csign);
    else if (num->exponent==DECFLOAT_qNaN) printf("%sqNaN", csign);
    else if (num->exponent==DECFLOAT_sNaN) printf("%ssNaN", csign);
    else {				/* finite */
     char qbuf[10];			/* for right-aligned q */
     char *c;				/* work */
     const uByte *u;			/* .. */
     Int e=num->exponent;		/* .. exponent */
     strcpy(qbuf, "q=");
     c=&qbuf[2];			/* where exponent will go */
     /* lay out the exponent */
     if (e<0) {
       *c++='-';			/* add '-' */
       e=-e;				/* uInt, please */
       }
     #if DECEMAXD>4
       #error Exponent form is too long for ShowNum to lay out
     #endif
     if (e==0) *c++='0';		/* 0-length case */
      else if (e<1000) {		/* 3 (or fewer) digits case */
       u=&BIN2BCD8[e*4];		/* -> 3 digits + length byte */
       UINTAT(c)=UINTAT(u+3-*(u+3))|CHARMASK; /* [as above] */
       c+=*(u+3);			/* bump pointer appropriately */
       }
      else {				/* 4-digits */
       Int thou=((e>>3)*1049)>>17;	/* e/1000 */
       Int rem=e-(1000*thou);		/* e%1000 */
       *c++=(char)('0'+(char)thou);	/* the thousands digit */
       u=&BIN2BCD8[rem*4];		/* -> 3 digits + length byte */
       UINTAT(c)=UINTAT(u)|CHARMASK;	/* copy fixed 3+1 characters [is safe] */
       c+=3;				/* bump pointer, always 3 digits */
       }
     *c='\0';				/* add terminator */
     printf("%7s c=%s", qbuf, csign);
     }

    if (!EXPISSPECIAL(num->exponent) || num->msd!=num->lsd || *num->lsd!=0) {
      for (ub=num->msd; ub<=num->lsd; ub++) { /* coefficient... */
	printf("%1x", *ub);
	if ((num->lsd-ub)%3==0 && ub!=num->lsd) printf(" "); /* 4-space */
	}
      }
    printf("\n");
    } /* decShowNum */
#endif