File: decNumber.c

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

   This file is part of GCC.

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

   GCC is distributed in the hope that it will be useful, but WITHOUT ANY
   WARRANTY; without even the implied warranty of MERCHANTABILITY or
   FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
   for more details.

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

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

/* ------------------------------------------------------------------ */
/* Decimal Number arithmetic module				      */
/* ------------------------------------------------------------------ */
/* This module comprises the routines for arbitrary-precision General */
/* Decimal Arithmetic as defined in the specification which may be    */
/* found on the General Decimal Arithmetic pages.  It implements both */
/* the full ('extended') arithmetic and the simpler ('subset')	      */
/* arithmetic.							      */
/*								      */
/* Usage notes: 						      */
/*								      */
/* 1. This code is ANSI C89 except:				      */
/*								      */
/*    a) C99 line comments (double forward slash) are used.  (Most C  */
/*	 compilers accept these.  If yours does not, a simple script  */
/*	 can be used to convert them to ANSI C comments.)	      */
/*								      */
/*    b) Types from C99 stdint.h are used.  If you do not have this   */
/*	 header file, see the User's Guide section of the decNumber   */
/*	 documentation; this lists the necessary definitions.	      */
/*								      */
/*    c) If DECDPUN>4 or DECUSE64=1, the C99 64-bit int64_t and       */
/*	 uint64_t types may be used.  To avoid these, set DECUSE64=0  */
/*	 and DECDPUN<=4 (see documentation).			      */
/*								      */
/*    The code also conforms to C99 restrictions; in particular,      */
/*    strict aliasing rules are observed.			      */
/*								      */
/* 2. The decNumber format which this library uses is optimized for   */
/*    efficient processing of relatively short numbers; in particular */
/*    it allows the use of fixed sized structures and minimizes copy  */
/*    and move operations.  It does, however, support arbitrary       */
/*    precision (up to 999,999,999 digits) and arbitrary exponent     */
/*    range (Emax in the range 0 through 999,999,999 and Emin in the  */
/*    range -999,999,999 through 0).  Mathematical functions (for     */
/*    example decNumberExp) as identified below are restricted more   */
/*    tightly: digits, emax, and -emin in the context must be <=      */
/*    DEC_MAX_MATH (999999), and their operand(s) must be within      */
/*    these bounds.						      */
/*								      */
/* 3. Logical functions are further restricted; their operands must   */
/*    be finite, positive, have an exponent of zero, and all digits   */
/*    must be either 0 or 1.  The result will only contain digits     */
/*    which are 0 or 1 (and will have exponent=0 and a sign of 0).    */
/*								      */
/* 4. Operands to operator functions are never modified unless they   */
/*    are also specified to be the result number (which is always     */
/*    permitted).  Other than that case, operands must not overlap.   */
/*								      */
/* 5. Error handling: the type of the error is ORed into the status   */
/*    flags in the current context (decContext structure).  The       */
/*    SIGFPE signal is then raised if the corresponding trap-enabler  */
/*    flag in the decContext is set (is 1).			      */
/*								      */
/*    It is the responsibility of the caller to clear the status      */
/*    flags as required.					      */
/*								      */
/*    The result of any routine which returns a number will always    */
/*    be a valid number (which may be a special value, such as an     */
/*    Infinity or NaN). 					      */
/*								      */
/* 6. The decNumber format is not an exchangeable concrete	      */
/*    representation as it comprises fields which may be machine-     */
/*    dependent (packed or unpacked, or special length, for example). */
/*    Canonical conversions to and from strings are provided; other   */
/*    conversions are available in separate modules.		      */
/*								      */
/* 7. Normally, input operands are assumed to be valid.  Set DECCHECK */
/*    to 1 for extended operand checking (including NULL operands).   */
/*    Results are undefined if a badly-formed structure (or a NULL    */
/*    pointer to a structure) is provided, though with DECCHECK       */
/*    enabled the operator routines are protected against exceptions. */
/*    (Except if the result pointer is NULL, which is unrecoverable.) */
/*								      */
/*    However, the routines will never cause exceptions if they are   */
/*    given well-formed operands, even if the value of the operands   */
/*    is inappropriate for the operation and DECCHECK is not set.     */
/*    (Except for SIGFPE, as and where documented.)		      */
/*								      */
/* 8. Subset arithmetic is available only if DECSUBSET is set to 1.   */
/* ------------------------------------------------------------------ */
/* Implementation notes for maintenance of this module: 	      */
/*								      */
/* 1. Storage leak protection:	Routines which use malloc are not     */
/*    permitted to use return for fastpath or error exits (i.e.,      */
/*    they follow strict structured programming conventions).	      */
/*    Instead they have a do{}while(0); construct surrounding the     */
/*    code which is protected -- break may be used to exit this.      */
/*    Other routines can safely use the return statement inline.      */
/*								      */
/*    Storage leak accounting can be enabled using DECALLOC.	      */
/*								      */
/* 2. All loops use the for(;;) construct.  Any do construct does     */
/*    not loop; it is for allocation protection as just described.    */
/*								      */
/* 3. Setting status in the context must always be the very last      */
/*    action in a routine, as non-0 status may raise a trap and hence */
/*    the call to set status may not return (if the handler uses long */
/*    jump).  Therefore all cleanup must be done first.  In general,  */
/*    to achieve this status is accumulated and is only applied just  */
/*    before return by calling decContextSetStatus (via decStatus).   */
/*								      */
/*    Routines which allocate storage cannot, in general, use the     */
/*    'top level' routines which could cause a non-returning	      */
/*    transfer of control.  The decXxxxOp routines are safe (do not   */
/*    call decStatus even if traps are set in the context) and should */
/*    be used instead (they are also a little faster).		      */
/*								      */
/* 4. Exponent checking is minimized by allowing the exponent to      */
/*    grow outside its limits during calculations, provided that      */
/*    the decFinalize function is called later.  Multiplication and   */
/*    division, and intermediate calculations in exponentiation,      */
/*    require more careful checks because of the risk of 31-bit       */
/*    overflow (the most negative valid exponent is -1999999997, for  */
/*    a 999999999-digit number with adjusted exponent of -999999999). */
/*								      */
/* 5. Rounding is deferred until finalization of results, with any    */
/*    'off to the right' data being represented as a single digit     */
/*    residue (in the range -1 through 9).  This avoids any double-   */
/*    rounding when more than one shortening takes place (for	      */
/*    example, when a result is subnormal).			      */
/*								      */
/* 6. The digits count is allowed to rise to a multiple of DECDPUN    */
/*    during many operations, so whole Units are handled and exact    */
/*    accounting of digits is not needed.  The correct digits value   */
/*    is found by decGetDigits, which accounts for leading zeros.     */
/*    This must be called before any rounding if the number of digits */
/*    is not known exactly.					      */
/*								      */
/* 7. The multiply-by-reciprocal 'trick' is used for partitioning     */
/*    numbers up to four digits, using appropriate constants.  This   */
/*    is not useful for longer numbers because overflow of 32 bits    */
/*    would lead to 4 multiplies, which is almost as expensive as     */
/*    a divide (unless a floating-point or 64-bit multiply is	      */
/*    assumed to be available). 				      */
/*								      */
/* 8. Unusual abbreviations that may be used in the commentary:       */
/*	lhs -- left hand side (operand, of an operation)	      */
/*	lsd -- least significant digit (of coefficient) 	      */
/*	lsu -- least significant Unit (of coefficient)		      */
/*	msd -- most significant digit (of coefficient)		      */
/*	msi -- most significant item (in an array)		      */
/*	msu -- most significant Unit (of coefficient)		      */
/*	rhs -- right hand side (operand, of an operation)	      */
/*	+ve -- positive 					      */
/*	-ve -- negative 					      */
/*	**  -- raise to the power				      */
/* ------------------------------------------------------------------ */

#include <stdlib.h>		   /* for malloc, free, etc. */
#include <stdio.h>		   /* for printf [if needed] */
#include <string.h>		   /* for strcpy */
#include <ctype.h>		   /* for lower */
#include "dconfig.h"		   /* for GCC definitions */
#include "decNumber.h"		   /* base number library */
#include "decNumberLocal.h"	   /* decNumber local types, etc. */

/* Constants */
/* Public lookup table used by the D2U macro */
const uByte d2utable[DECMAXD2U+1]=D2UTABLE;

#define DECVERB     1		   /* set to 1 for verbose DECCHECK */
#define powers	    DECPOWERS	   /* old internal name */

/* Local constants */
#define DIVIDE	    0x80	   /* Divide operators */
#define REMAINDER   0x40	   /* .. */
#define DIVIDEINT   0x20	   /* .. */
#define REMNEAR     0x10	   /* .. */
#define COMPARE     0x01	   /* Compare operators */
#define COMPMAX     0x02	   /* .. */
#define COMPMIN     0x03	   /* .. */
#define COMPTOTAL   0x04	   /* .. */
#define COMPNAN     0x05	   /* .. [NaN processing] */
#define COMPSIG     0x06	   /* .. [signaling COMPARE] */
#define COMPMAXMAG  0x07	   /* .. */
#define COMPMINMAG  0x08	   /* .. */

#define DEC_sNaN     0x40000000    /* local status: sNaN signal */
#define BADINT	(Int)0x80000000    /* most-negative Int; error indicator */
/* Next two indicate an integer >= 10**6, and its parity (bottom bit) */
#define BIGEVEN (Int)0x80000002
#define BIGODD	(Int)0x80000003

static Unit uarrone[1]={1};   /* Unit array of 1, used for incrementing */

/* Granularity-dependent code */
#if DECDPUN<=4
  #define eInt	Int	      /* extended integer */
  #define ueInt uInt	      /* unsigned extended integer */
  /* 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)
#else
  /* For DECDPUN>4 non-ANSI-89 64-bit types are needed. */
  #if !DECUSE64
    #error decNumber.c: DECUSE64 must be 1 when DECDPUN>4
  #endif
  #define eInt	Long	      /* extended integer */
  #define ueInt uLong	      /* unsigned extended integer */
#endif

/* Local routines */
static decNumber * decAddOp(decNumber *, const decNumber *, const decNumber *,
			      decContext *, uByte, uInt *);
static Flag	   decBiStr(const char *, const char *, const char *);
static uInt	   decCheckMath(const decNumber *, decContext *, uInt *);
static void	   decApplyRound(decNumber *, decContext *, Int, uInt *);
static Int	   decCompare(const decNumber *lhs, const decNumber *rhs, Flag);
static decNumber * decCompareOp(decNumber *, const decNumber *,
			      const decNumber *, decContext *,
			      Flag, uInt *);
static void	   decCopyFit(decNumber *, const decNumber *, decContext *,
			      Int *, uInt *);
static decNumber * decDecap(decNumber *, Int);
static decNumber * decDivideOp(decNumber *, const decNumber *,
			      const decNumber *, decContext *, Flag, uInt *);
static decNumber * decExpOp(decNumber *, const decNumber *,
			      decContext *, uInt *);
static void	   decFinalize(decNumber *, decContext *, Int *, uInt *);
static Int	   decGetDigits(Unit *, Int);
static Int	   decGetInt(const decNumber *);
static decNumber * decLnOp(decNumber *, const decNumber *,
			      decContext *, uInt *);
static decNumber * decMultiplyOp(decNumber *, const decNumber *,
			      const decNumber *, decContext *,
			      uInt *);
static decNumber * decNaNs(decNumber *, const decNumber *,
			      const decNumber *, decContext *, uInt *);
static decNumber * decQuantizeOp(decNumber *, const decNumber *,
			      const decNumber *, decContext *, Flag,
			      uInt *);
static void	   decReverse(Unit *, Unit *);
static void	   decSetCoeff(decNumber *, decContext *, const Unit *,
			      Int, Int *, uInt *);
static void	   decSetMaxValue(decNumber *, decContext *);
static void	   decSetOverflow(decNumber *, decContext *, uInt *);
static void	   decSetSubnormal(decNumber *, decContext *, Int *, uInt *);
static Int	   decShiftToLeast(Unit *, Int, Int);
static Int	   decShiftToMost(Unit *, Int, Int);
static void	   decStatus(decNumber *, uInt, decContext *);
static void	   decToString(const decNumber *, char[], Flag);
static decNumber * decTrim(decNumber *, decContext *, Flag, Flag, Int *);
static Int	   decUnitAddSub(const Unit *, Int, const Unit *, Int, Int,
			      Unit *, Int);
static Int	   decUnitCompare(const Unit *, Int, const Unit *, Int, Int);

#if !DECSUBSET
/* decFinish == decFinalize when no subset arithmetic needed */
#define decFinish(a,b,c,d) decFinalize(a,b,c,d)
#else
static void	   decFinish(decNumber *, decContext *, Int *, uInt *);
static decNumber * decRoundOperand(const decNumber *, decContext *, uInt *);
#endif

/* Local macros */
/* masked special-values bits */
#define SPECIALARG  (rhs->bits & DECSPECIAL)
#define SPECIALARGS ((lhs->bits | rhs->bits) & DECSPECIAL)

/* Diagnostic macros, etc. */
#if DECALLOC
/* Handle malloc/free accounting.  If enabled, our accountable routines */
/* are used; otherwise the code just goes straight to the system malloc */
/* and free routines. */
#define malloc(a) decMalloc(a)
#define free(a) decFree(a)
#define DECFENCE 0x5a		   /* corruption detector */
/* 'Our' malloc and free: */
static void *decMalloc(size_t);
static void  decFree(void *);
uInt decAllocBytes=0;		   /* count of bytes allocated */
/* Note that DECALLOC code only checks for storage buffer overflow. */
/* To check for memory leaks, the decAllocBytes variable must be */
/* checked to be 0 at appropriate times (e.g., after the test */
/* harness completes a set of tests).  This checking may be unreliable */
/* if the testing is done in a multi-thread environment. */
#endif

#if DECCHECK
/* Optional checking routines.	Enabling these means that decNumber */
/* and decContext operands to operator routines are checked for */
/* correctness.  This roughly doubles the execution time of the */
/* fastest routines (and adds 600+ bytes), so should not normally be */
/* used in 'production'. */
/* decCheckInexact is used to check that inexact results have a full */
/* complement of digits (where appropriate -- this is not the case */
/* for Quantize, for example) */
#define DECUNRESU ((decNumber *)(void *)0xffffffff)
#define DECUNUSED ((const decNumber *)(void *)0xffffffff)
#define DECUNCONT ((decContext *)(void *)(0xffffffff))
static Flag decCheckOperands(decNumber *, const decNumber *,
			     const decNumber *, decContext *);
static Flag decCheckNumber(const decNumber *);
static void decCheckInexact(const decNumber *, decContext *);
#endif

#if DECTRACE || DECCHECK
/* Optional trace/debugging routines (may or may not be used) */
void decNumberShow(const decNumber *);	/* displays the components of a number */
static void decDumpAr(char, const Unit *, Int);
#endif

/* ================================================================== */
/* Conversions							      */
/* ================================================================== */

/* ------------------------------------------------------------------ */
/* from-int32 -- conversion from Int or uInt			      */
/*								      */
/*  dn is the decNumber to receive the integer			      */
/*  in or uin is the integer to be converted			      */
/*  returns dn							      */
/*								      */
/* No error is possible.					      */
/* ------------------------------------------------------------------ */
decNumber * decNumberFromInt32(decNumber *dn, Int in) {
  uInt unsig;
  if (in>=0) unsig=in;
   else {				/* negative (possibly BADINT) */
    if (in==BADINT) unsig=(uInt)1073741824*2; /* special case */
     else unsig=-in;			/* invert */
    }
  /* in is now positive */
  decNumberFromUInt32(dn, unsig);
  if (in<0) dn->bits=DECNEG;		/* sign needed */
  return dn;
  } /* decNumberFromInt32 */

decNumber * decNumberFromUInt32(decNumber *dn, uInt uin) {
  Unit *up;				/* work pointer */
  decNumberZero(dn);			/* clean */
  if (uin==0) return dn;		/* [or decGetDigits bad call] */
  for (up=dn->lsu; uin>0; up++) {
    *up=(Unit)(uin%(DECDPUNMAX+1));
    uin=uin/(DECDPUNMAX+1);
    }
  dn->digits=decGetDigits(dn->lsu, up-dn->lsu);
  return dn;
  } /* decNumberFromUInt32 */

/* ------------------------------------------------------------------ */
/* to-int32 -- conversion to Int or uInt			      */
/*								      */
/*  dn is the decNumber to convert				      */
/*  set is the context for reporting errors			      */
/*  returns the converted decNumber, or 0 if Invalid is set	      */
/*								      */
/* Invalid is set if the decNumber does not have exponent==0 or if    */
/* it is a NaN, Infinite, or out-of-range.			      */
/* ------------------------------------------------------------------ */
Int decNumberToInt32(const decNumber *dn, decContext *set) {
  #if DECCHECK
  if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
  #endif

  /* special or too many digits, or bad exponent */
  if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0) ; /* bad */
   else { /* is a finite integer with 10 or fewer digits */
    Int d;			   /* work */
    const Unit *up;		   /* .. */
    uInt hi=0, lo;		   /* .. */
    up=dn->lsu; 		   /* -> lsu */
    lo=*up;			   /* get 1 to 9 digits */
    #if DECDPUN>1		   /* split to higher */
      hi=lo/10;
      lo=lo%10;
    #endif
    up++;
    /* collect remaining Units, if any, into hi */
    for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1];
    /* now low has the lsd, hi the remainder */
    if (hi>214748364 || (hi==214748364 && lo>7)) { /* out of range? */
      /* most-negative is a reprieve */
      if (dn->bits&DECNEG && hi==214748364 && lo==8) return 0x80000000;
      /* bad -- drop through */
      }
     else { /* in-range always */
      Int i=X10(hi)+lo;
      if (dn->bits&DECNEG) return -i;
      return i;
      }
    } /* integer */
  decContextSetStatus(set, DEC_Invalid_operation); /* [may not return] */
  return 0;
  } /* decNumberToInt32 */

uInt decNumberToUInt32(const decNumber *dn, decContext *set) {
  #if DECCHECK
  if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
  #endif
  /* special or too many digits, or bad exponent, or negative (<0) */
  if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0
    || (dn->bits&DECNEG && !ISZERO(dn)));		    /* bad */
   else { /* is a finite integer with 10 or fewer digits */
    Int d;			   /* work */
    const Unit *up;		   /* .. */
    uInt hi=0, lo;		   /* .. */
    up=dn->lsu; 		   /* -> lsu */
    lo=*up;			   /* get 1 to 9 digits */
    #if DECDPUN>1		   /* split to higher */
      hi=lo/10;
      lo=lo%10;
    #endif
    up++;
    /* collect remaining Units, if any, into hi */
    for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1];

    /* now low has the lsd, hi the remainder */
    if (hi>429496729 || (hi==429496729 && lo>5)) ; /* no reprieve possible */
     else return X10(hi)+lo;
    } /* integer */
  decContextSetStatus(set, DEC_Invalid_operation); /* [may not return] */
  return 0;
  } /* decNumberToUInt32 */

/* ------------------------------------------------------------------ */
/* to-scientific-string -- conversion to numeric string 	      */
/* to-engineering-string -- conversion to numeric string	      */
/*								      */
/*   decNumberToString(dn, string);				      */
/*   decNumberToEngString(dn, string);				      */
/*								      */
/*  dn is the decNumber to convert				      */
/*  string is the string where the result will be laid out	      */
/*								      */
/*  string must be at least dn->digits+14 characters long	      */
/*								      */
/*  No error is possible, and no status can be set.		      */
/* ------------------------------------------------------------------ */
char * decNumberToString(const decNumber *dn, char *string){
  decToString(dn, string, 0);
  return string;
  } /* DecNumberToString */

char * decNumberToEngString(const decNumber *dn, char *string){
  decToString(dn, string, 1);
  return string;
  } /* DecNumberToEngString */

/* ------------------------------------------------------------------ */
/* to-number -- conversion from numeric string			      */
/*								      */
/* decNumberFromString -- convert string to decNumber		      */
/*   dn        -- the number structure to fill			      */
/*   chars[]   -- the string to convert ('\0' terminated)	      */
/*   set       -- the context used for processing any error,	      */
/*		  determining the maximum precision available	      */
/*		  (set.digits), determining the maximum and minimum   */
/*		  exponent (set.emax and set.emin), determining if    */
/*		  extended values are allowed, and checking the       */
/*		  rounding mode if overflow occurs or rounding is     */
/*		  needed.					      */
/*								      */
/* 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.       */
/*								      */
/* If bad syntax is detected, the result will be a quiet NaN.	      */
/* ------------------------------------------------------------------ */
decNumber * decNumberFromString(decNumber *dn, const char chars[],
				decContext *set) {
  Int	exponent=0;		   /* working exponent [assume 0] */
  uByte bits=0; 		   /* working flags [assume +ve] */
  Unit	*res;			   /* where result will be built */
  Unit	resbuff[SD2U(DECBUFFER+9)];/* local buffer in case need temporary */
				   /* [+9 allows for ln() constants] */
  Unit	*allocres=NULL; 	   /* -> allocated result, iff allocated */
  Int	d=0;			   /* count of digits found in decimal part */
  const char *dotchar=NULL;	   /* where dot was found */
  const char *cfirst=chars;	   /* -> first character of decimal part */
  const char *last=NULL;	   /* -> last digit of decimal part */
  const char *c;		   /* work */
  Unit	*up;			   /* .. */
  #if DECDPUN>1
  Int	cut, out;		   /* .. */
  #endif
  Int	residue;		   /* rounding residue */
  uInt	status=0;		   /* error code */

  #if DECCHECK
  if (decCheckOperands(DECUNRESU, DECUNUSED, DECUNUSED, set))
    return decNumberZero(dn);
  #endif

  do {				   /* status & malloc protection */
    for (c=chars;; c++) {	   /* -> input character */
      if (*c>='0' && *c<='9') {    /* test for Arabic digit */
	last=c;
	d++;			   /* count of real digits */
	continue;		   /* still in decimal part */
	}
      if (*c=='.' && dotchar==NULL) { /* first '.' */
	dotchar=c;		   /* record offset into decimal part */
	if (c==cfirst) cfirst++;   /* first digit must follow */
	continue;}
      if (c==chars) {		   /* first in string... */
	if (*c=='-') {		   /* valid - sign */
	  cfirst++;
	  bits=DECNEG;
	  continue;}
	if (*c=='+') {		   /* valid + sign */
	  cfirst++;
	  continue;}
	}
      /* *c is not a digit, or a valid +, -, or '.' */
      break;
      } /* c */

    if (last==NULL) {		   /* no digits yet */
      status=DEC_Conversion_syntax;/* assume the worst */
      if (*c=='\0') break;	   /* and no more to come... */
      #if DECSUBSET
      /* if subset then infinities and NaNs are not allowed */
      if (!set->extended) break;   /* hopeless */
      #endif
      /* Infinities and NaNs are possible, here */
      if (dotchar!=NULL) break;    /* .. unless had a dot */
      decNumberZero(dn);	   /* be optimistic */
      if (decBiStr(c, "infinity", "INFINITY")
       || decBiStr(c, "inf", "INF")) {
	dn->bits=bits | DECINF;
	status=0;		   /* is OK */
	break; /* all done */
	}
      /* a NaN expected */
      /* 2003.09.10 NaNs are now permitted to have a sign */
      dn->bits=bits | DECNAN;	   /* assume simple NaN */
      if (*c=='s' || *c=='S') {    /* looks like an sNaN */
	c++;
	dn->bits=bits | DECSNAN;
	}
      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, expected */
      /* -> start of integer and skip leading 0s [including plain 0] */
      for (cfirst=c; *cfirst=='0';) cfirst++;
      if (*cfirst=='\0') {	   /* "NaN" or "sNaN", maybe with all 0s */
	status=0;		   /* it's good */
	break;			   /* .. */
	}
      /* something other than 0s; setup last and d as usual [no dots] */
      for (c=cfirst;; c++, d++) {
	if (*c<'0' || *c>'9') break; /* test for Arabic digit */
	last=c;
	}
      if (*c!='\0') break;	   /* not all digits */
      if (d>set->digits-1) {
	/* [NB: payload in a decNumber can be full length unless */
	/* clamped, in which case can only be digits-1] */
	if (set->clamp) break;
	if (d>set->digits) break;
	} /* too many digits? */
      /* good; drop through to convert the integer to coefficient */
      status=0; 		   /* syntax is OK */
      bits=dn->bits;		   /* for copy-back */
      } /* last==NULL */

     else if (*c!='\0') {	   /* more to process... */
      /* had some digits; exponent is only valid sequence now */
      Flag nege;		   /* 1=negative exponent */
      const char *firstexp;	   /* -> first significant exponent digit */
      status=DEC_Conversion_syntax;/* assume the worst */
      if (*c!='e' && *c!='E') break;
      /* Found 'e' or 'E' -- now process explicit exponent */
      /* 1998.07.11: sign no longer required */
      nege=0;
      c++;			   /* to (possible) sign */
      if (*c=='-') {nege=1; c++;}
       else if (*c=='+') c++;
      if (*c=='\0') break;

      for (; *c=='0' && *(c+1)!='\0';) c++;  /* strip insignificant zeros */
      firstexp=c;			     /* save exponent digit place */
      for (; ;c++) {
	if (*c<'0' || *c>'9') break;	     /* not a digit */
	exponent=X10(exponent)+(Int)*c-(Int)'0';
	} /* c */
      /* if not now on a '\0', *c must not be a digit */
      if (*c!='\0') break;

      /* (this next test must be after the syntax checks) */
      /* if it was too long the exponent may have wrapped, so check */
      /* carefully and set it to a certain overflow if wrap possible */
      if (c>=firstexp+9+1) {
	if (c>firstexp+9+1 || *firstexp>'1') exponent=DECNUMMAXE*2;
	/* [up to 1999999999 is OK, for example 1E-1000000998] */
	}
      if (nege) exponent=-exponent;	/* was negative */
      status=0; 			/* is OK */
      } /* stuff after digits */

    /* Here when whole string has been inspected; syntax is good */
    /* cfirst->first digit (never dot), last->last digit (ditto) */

    /* strip leading zeros/dot [leave final 0 if all 0's] */
    if (*cfirst=='0') { 		/* [cfirst has stepped over .] */
      for (c=cfirst; c<last; c++, cfirst++) {
	if (*c=='.') continue;		/* ignore dots */
	if (*c!='0') break;		/* non-zero found */
	d--;				/* 0 stripped */
	} /* c */
      #if DECSUBSET
      /* make a rapid exit for easy zeros if !extended */
      if (*cfirst=='0' && !set->extended) {
	decNumberZero(dn);		/* clean result */
	break;				/* [could be return] */
	}
      #endif
      } /* at least one leading 0 */

    /* Handle decimal point... */
    if (dotchar!=NULL && dotchar<last)	/* non-trailing '.' found? */
      exponent-=(last-dotchar); 	/* adjust exponent */
    /* [we can now ignore the .] */

    /* OK, the digits string is good.  Assemble in the decNumber, or in */
    /* a temporary units array if rounding is needed */
    if (d<=set->digits) res=dn->lsu;	/* fits into supplied decNumber */
     else {				/* rounding needed */
      Int needbytes=D2U(d)*sizeof(Unit);/* bytes needed */
      res=resbuff;			/* assume use local buffer */
      if (needbytes>(Int)sizeof(resbuff)) { /* too big for local */
	allocres=(Unit *)malloc(needbytes);
	if (allocres==NULL) {status|=DEC_Insufficient_storage; break;}
	res=allocres;
	}
      }
    /* res now -> number lsu, buffer, or allocated storage for Unit array */

    /* Place the coefficient into the selected Unit array */
    /* [this is often 70% of the cost of this function when DECDPUN>1] */
    #if DECDPUN>1
    out=0;			   /* accumulator */
    up=res+D2U(d)-1;		   /* -> msu */
    cut=d-(up-res)*DECDPUN;	   /* digits in top unit */
    for (c=cfirst;; c++) {	   /* along the digits */
      if (*c=='.') continue;	   /* ignore '.' [don't decrement cut] */
      out=X10(out)+(Int)*c-(Int)'0';
      if (c==last) break;	   /* done [never get to trailing '.'] */
      cut--;
      if (cut>0) continue;	   /* more for this unit */
      *up=(Unit)out;		   /* write unit */
      up--;			   /* prepare for unit below.. */
      cut=DECDPUN;		   /* .. */
      out=0;			   /* .. */
      } /* c */
    *up=(Unit)out;		   /* write lsu */

    #else
    /* DECDPUN==1 */
    up=res;			   /* -> lsu */
    for (c=last; c>=cfirst; c--) { /* over each character, from least */
      if (*c=='.') continue;	   /* ignore . [don't step up] */
      *up=(Unit)((Int)*c-(Int)'0');
      up++;
      } /* c */
    #endif

    dn->bits=bits;
    dn->exponent=exponent;
    dn->digits=d;

    /* if not in number (too long) shorten into the number */
    if (d>set->digits) {
      residue=0;
      decSetCoeff(dn, set, res, d, &residue, &status);
      /* always check for overflow or subnormal and round as needed */
      decFinalize(dn, set, &residue, &status);
      }
     else { /* no rounding, but may still have overflow or subnormal */
      /* [these tests are just for performance; finalize repeats them] */
      if ((dn->exponent-1<set->emin-dn->digits)
       || (dn->exponent-1>set->emax-set->digits)) {
	residue=0;
	decFinalize(dn, set, &residue, &status);
	}
      }
    /* decNumberShow(dn); */
    } while(0); 			/* [for break] */

  free(allocres);	/* drop any storage used */
  if (status!=0) decStatus(dn, status, set);
  return dn;
  } /* decNumberFromString */

/* ================================================================== */
/* Operators							      */
/* ================================================================== */

/* ------------------------------------------------------------------ */
/* decNumberAbs -- absolute value operator			      */
/*								      */
/*   This computes C = abs(A)					      */
/*								      */
/*   res is C, the result.  C may be A				      */
/*   rhs is A							      */
/*   set is the context 					      */
/*								      */
/* See also decNumberCopyAbs for a quiet bitwise version of this.     */
/* C must have space for set->digits digits.			      */
/* ------------------------------------------------------------------ */
/* This has the same effect as decNumberPlus unless A is negative,    */
/* in which case it has the same effect as decNumberMinus.	      */
/* ------------------------------------------------------------------ */
decNumber * decNumberAbs(decNumber *res, const decNumber *rhs,
			 decContext *set) {
  decNumber dzero;			/* for 0 */
  uInt status=0;			/* accumulator */

  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  decNumberZero(&dzero);		/* set 0 */
  dzero.exponent=rhs->exponent; 	/* [no coefficient expansion] */
  decAddOp(res, &dzero, rhs, set, (uByte)(rhs->bits & DECNEG), &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } /* decNumberAbs */

/* ------------------------------------------------------------------ */
/* decNumberAdd -- add two Numbers				      */
/*								      */
/*   This computes C = A + B					      */
/*								      */
/*   res is C, the result.  C may be A and/or B (e.g., X=X+X)	      */
/*   lhs is A							      */
/*   rhs is B							      */
/*   set is the context 					      */
/*								      */
/* C must have space for set->digits digits.			      */
/* ------------------------------------------------------------------ */
/* This just calls the routine shared with Subtract		      */
decNumber * decNumberAdd(decNumber *res, const decNumber *lhs,
			 const decNumber *rhs, decContext *set) {
  uInt status=0;			/* accumulator */
  decAddOp(res, lhs, rhs, set, 0, &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } /* decNumberAdd */

/* ------------------------------------------------------------------ */
/* decNumberAnd -- AND two Numbers, digitwise			      */
/*								      */
/*   This computes C = A & B					      */
/*								      */
/*   res is C, the result.  C may be A and/or B (e.g., X=X&X)	      */
/*   lhs is A							      */
/*   rhs is B							      */
/*   set is the context (used for result length and error report)     */
/*								      */
/* C must have space for set->digits digits.			      */
/*								      */
/* Logical function restrictions apply (see above); a NaN is	      */
/* returned with Invalid_operation if a restriction is violated.      */
/* ------------------------------------------------------------------ */
decNumber * decNumberAnd(decNumber *res, const decNumber *lhs,
			 const decNumber *rhs, decContext *set) {
  const Unit *ua, *ub;			/* -> operands */
  const Unit *msua, *msub;		/* -> operand msus */
  Unit *uc,  *msuc;			/* -> result and its msu */
  Int	msudigs;			/* digits in res msu */
  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)
   || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
    decStatus(res, DEC_Invalid_operation, set);
    return res;
    }

  /* operands are valid */
  ua=lhs->lsu;				/* bottom-up */
  ub=rhs->lsu;				/* .. */
  uc=res->lsu;				/* .. */
  msua=ua+D2U(lhs->digits)-1;		/* -> msu of lhs */
  msub=ub+D2U(rhs->digits)-1;		/* -> msu of rhs */
  msuc=uc+D2U(set->digits)-1;		/* -> msu of result */
  msudigs=MSUDIGITS(set->digits);	/* [faster than remainder] */
  for (; uc<=msuc; ua++, ub++, uc++) {	/* Unit loop */
    Unit a, b;				/* extract units */
    if (ua>msua) a=0;
     else a=*ua;
    if (ub>msub) b=0;
     else b=*ub;
    *uc=0;				/* can now write back */
    if (a|b) {				/* maybe 1 bits to examine */
      Int i, j;
      *uc=0;				/* can now write back */
      /* This loop could be unrolled and/or use BIN2BCD tables */
      for (i=0; i<DECDPUN; i++) {
	if (a&b&1) *uc=*uc+(Unit)powers[i];  /* effect AND */
	j=a%10;
	a=a/10;
	j|=b%10;
	b=b/10;
	if (j>1) {
	  decStatus(res, DEC_Invalid_operation, set);
	  return res;
	  }
	if (uc==msuc && i==msudigs-1) break; /* just did final digit */
	} /* each digit */
      } /* both OK */
    } /* each unit */
  /* [here uc-1 is the msu of the result] */
  res->digits=decGetDigits(res->lsu, uc-res->lsu);
  res->exponent=0;			/* integer */
  res->bits=0;				/* sign=0 */
  return res;  /* [no status to set] */
  } /* decNumberAnd */

/* ------------------------------------------------------------------ */
/* decNumberCompare -- compare two Numbers			      */
/*								      */
/*   This computes C = A ? B					      */
/*								      */
/*   res is C, the result.  C may be A and/or B (e.g., X=X?X)	      */
/*   lhs is A							      */
/*   rhs is B							      */
/*   set is the context 					      */
/*								      */
/* C must have space for one digit (or NaN).			      */
/* ------------------------------------------------------------------ */
decNumber * decNumberCompare(decNumber *res, const decNumber *lhs,
			     const decNumber *rhs, decContext *set) {
  uInt status=0;			/* accumulator */
  decCompareOp(res, lhs, rhs, set, COMPARE, &status);
  if (status!=0) decStatus(res, status, set);
  return res;
  } /* decNumberCompare */

/* ------------------------------------------------------------------ */
/* decNumberCompareSignal -- compare, signalling on all NaNs	      */
/*								      */
/*   This computes C = A ? B					      */
/*								      */
/*   res is C, the result.  C may be A and/or B (e.g., X=X?X)	      */
/*   lhs is A							      */
/*   rhs is B							      */
/*   set is the context 					      */
/*								      */
/* C must have space for one digit (or NaN).			      */
/* ------------------------------------------------------------------ */
decNumber * decNumberCompareSignal(decNumber *res, const decNumber *lhs,
				   const decNumber *rhs, decContext *set) {
  uInt status=0;			/* accumulator */
  decCompareOp(res, lhs, rhs, set, COMPSIG, &status);
  if (status!=0) decStatus(res, status, set);
  return res;
  } /* decNumberCompareSignal */

/* ------------------------------------------------------------------ */
/* decNumberCompareTotal -- compare two Numbers, using total ordering */
/*								      */
/*   This computes C = A ? B, under total ordering		      */
/*								      */
/*   res is C, the result.  C may be A and/or B (e.g., X=X?X)	      */
/*   lhs is A							      */
/*   rhs is B							      */
/*   set is the context 					      */
/*								      */
/* C must have space for one digit; the result will always be one of  */
/* -1, 0, or 1. 						      */
/* ------------------------------------------------------------------ */
decNumber * decNumberCompareTotal(decNumber *res, const decNumber *lhs,
				  const decNumber *rhs, decContext *set) {
  uInt status=0;			/* accumulator */
  decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status);
  if (status!=0) decStatus(res, status, set);
  return res;
  } /* decNumberCompareTotal */

/* ------------------------------------------------------------------ */
/* decNumberCompareTotalMag -- compare, total ordering of magnitudes  */
/*								      */
/*   This computes C = |A| ? |B|, under total ordering		      */
/*								      */
/*   res is C, the result.  C may be A and/or B (e.g., X=X?X)	      */
/*   lhs is A							      */
/*   rhs is B							      */
/*   set is the context 					      */
/*								      */
/* C must have space for one digit; the result will always be one of  */
/* -1, 0, or 1. 						      */
/* ------------------------------------------------------------------ */
decNumber * decNumberCompareTotalMag(decNumber *res, const decNumber *lhs,
				     const decNumber *rhs, decContext *set) {
  uInt status=0;		   /* accumulator */
  uInt needbytes;		   /* for space calculations */
  decNumber bufa[D2N(DECBUFFER+1)];/* +1 in case DECBUFFER=0 */
  decNumber *allocbufa=NULL;	   /* -> allocated bufa, iff allocated */
  decNumber bufb[D2N(DECBUFFER+1)];
  decNumber *allocbufb=NULL;	   /* -> allocated bufb, iff allocated */
  decNumber *a, *b;		   /* temporary pointers */

  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  do {					/* protect allocated storage */
    /* if either is negative, take a copy and absolute */
    if (decNumberIsNegative(lhs)) {	/* lhs<0 */
      a=bufa;
      needbytes=sizeof(decNumber)+(D2U(lhs->digits)-1)*sizeof(Unit);
      if (needbytes>sizeof(bufa)) {	/* need malloc space */
	allocbufa=(decNumber *)malloc(needbytes);
	if (allocbufa==NULL) {		/* hopeless -- abandon */
	  status|=DEC_Insufficient_storage;
	  break;}
	a=allocbufa;			/* use the allocated space */
	}
      decNumberCopy(a, lhs);		/* copy content */
      a->bits&=~DECNEG; 		/* .. and clear the sign */
      lhs=a;				/* use copy from here on */
      }
    if (decNumberIsNegative(rhs)) {	/* rhs<0 */
      b=bufb;
      needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);
      if (needbytes>sizeof(bufb)) {	/* need malloc space */
	allocbufb=(decNumber *)malloc(needbytes);
	if (allocbufb==NULL) {		/* hopeless -- abandon */
	  status|=DEC_Insufficient_storage;
	  break;}
	b=allocbufb;			/* use the allocated space */
	}
      decNumberCopy(b, rhs);		/* copy content */
      b->bits&=~DECNEG; 		/* .. and clear the sign */
      rhs=b;				/* use copy from here on */
      }
    decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status);
    } while(0); 			/* end protected */

  free(allocbufa); /* drop any storage used */
  free(allocbufb); /* .. */
  if (status!=0) decStatus(res, status, set);
  return res;
  } /* decNumberCompareTotalMag */

/* ------------------------------------------------------------------ */
/* decNumberDivide -- divide one number by another		      */
/*								      */
/*   This computes C = A / B					      */
/*								      */
/*   res is C, the result.  C may be A and/or B (e.g., X=X/X)	      */
/*   lhs is A							      */
/*   rhs is B							      */
/*   set is the context 					      */
/*								      */
/* C must have space for set->digits digits.			      */
/* ------------------------------------------------------------------ */
decNumber * decNumberDivide(decNumber *res, const decNumber *lhs,
			    const decNumber *rhs, decContext *set) {
  uInt status=0;			/* accumulator */
  decDivideOp(res, lhs, rhs, set, DIVIDE, &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } /* decNumberDivide */

/* ------------------------------------------------------------------ */
/* decNumberDivideInteger -- divide and return integer quotient       */
/*								      */
/*   This computes C = A # B, where # is the integer divide operator  */
/*								      */
/*   res is C, the result.  C may be A and/or B (e.g., X=X#X)	      */
/*   lhs is A							      */
/*   rhs is B							      */
/*   set is the context 					      */
/*								      */
/* C must have space for set->digits digits.			      */
/* ------------------------------------------------------------------ */
decNumber * decNumberDivideInteger(decNumber *res, const decNumber *lhs,
				   const decNumber *rhs, decContext *set) {
  uInt status=0;			/* accumulator */
  decDivideOp(res, lhs, rhs, set, DIVIDEINT, &status);
  if (status!=0) decStatus(res, status, set);
  return res;
  } /* decNumberDivideInteger */

/* ------------------------------------------------------------------ */
/* decNumberExp -- exponentiation				      */
/*								      */
/*   This computes C = exp(A)					      */
/*								      */
/*   res is C, the result.  C may be A				      */
/*   rhs is A							      */
/*   set is the context; note that rounding mode has no effect	      */
/*								      */
/* C must have space for set->digits digits.			      */
/*								      */
/* Mathematical function restrictions apply (see above); a NaN is     */
/* returned with Invalid_operation if a restriction is violated.      */
/*								      */
/* Finite results will always be full precision and Inexact, except   */
/* when A is a zero or -Infinity (giving 1 or 0 respectively).	      */
/*								      */
/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will    */
/* almost always be correctly rounded, but may be up to 1 ulp in      */
/* error in rare cases. 					      */
/* ------------------------------------------------------------------ */
/* This is a wrapper for decExpOp which can handle the slightly wider */
/* (double) range needed by Ln (which has to be able to calculate     */
/* exp(-a) where a can be the tiniest number (Ntiny).		      */
/* ------------------------------------------------------------------ */
decNumber * decNumberExp(decNumber *res, const decNumber *rhs,
			 decContext *set) {
  uInt status=0;			/* accumulator */
  #if DECSUBSET
  decNumber *allocrhs=NULL;	   /* non-NULL if rounded rhs allocated */
  #endif

  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  /* Check restrictions; these restrictions ensure that if h=8 (see */
  /* decExpOp) then the result will either overflow or underflow to 0. */
  /* Other math functions restrict the input range, too, for inverses. */
  /* If not violated then carry out the operation. */
  if (!decCheckMath(rhs, set, &status)) do { /* protect allocation */
    #if DECSUBSET
    if (!set->extended) {
      /* reduce operand and set lostDigits status, as needed */
      if (rhs->digits>set->digits) {
	allocrhs=decRoundOperand(rhs, set, &status);
	if (allocrhs==NULL) break;
	rhs=allocrhs;
	}
      }
    #endif
    decExpOp(res, rhs, set, &status);
    } while(0); 			/* end protected */

  #if DECSUBSET
  free(allocrhs);	/* drop any storage used */
  #endif
  /* apply significant status */
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } /* decNumberExp */

/* ------------------------------------------------------------------ */
/* decNumberFMA -- fused multiply add				      */
/*								      */
/*   This computes D = (A * B) + C with only one rounding	      */
/*								      */
/*   res is D, the result.  D may be A or B or C (e.g., X=FMA(X,X,X)) */
/*   lhs is A							      */
/*   rhs is B							      */
/*   fhs is C [far hand side]					      */
/*   set is the context 					      */
/*								      */
/* Mathematical function restrictions apply (see above); a NaN is     */
/* returned with Invalid_operation if a restriction is violated.      */
/*								      */
/* C must have space for set->digits digits.			      */
/* ------------------------------------------------------------------ */
decNumber * decNumberFMA(decNumber *res, const decNumber *lhs,
			 const decNumber *rhs, const decNumber *fhs,
			 decContext *set) {
  uInt status=0;		   /* accumulator */
  decContext dcmul;		   /* context for the multiplication */
  uInt needbytes;		   /* for space calculations */
  decNumber bufa[D2N(DECBUFFER*2+1)];
  decNumber *allocbufa=NULL;	   /* -> allocated bufa, iff allocated */
  decNumber *acc;		   /* accumulator pointer */
  decNumber dzero;		   /* work */

  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  if (decCheckOperands(res, fhs, DECUNUSED, set)) return res;
  #endif

  do {					/* protect allocated storage */
    #if DECSUBSET
    if (!set->extended) {		/* [undefined if subset] */
      status|=DEC_Invalid_operation;
      break;}
    #endif
    /* Check math restrictions [these ensure no overflow or underflow] */
    if ((!decNumberIsSpecial(lhs) && decCheckMath(lhs, set, &status))
     || (!decNumberIsSpecial(rhs) && decCheckMath(rhs, set, &status))
     || (!decNumberIsSpecial(fhs) && decCheckMath(fhs, set, &status))) break;
    /* set up context for multiply */
    dcmul=*set;
    dcmul.digits=lhs->digits+rhs->digits; /* just enough */
    /* [The above may be an over-estimate for subset arithmetic, but that's OK] */
    dcmul.emax=DEC_MAX_EMAX;		/* effectively unbounded .. */
    dcmul.emin=DEC_MIN_EMIN;		/* [thanks to Math restrictions] */
    /* set up decNumber space to receive the result of the multiply */
    acc=bufa;				/* may fit */
    needbytes=sizeof(decNumber)+(D2U(dcmul.digits)-1)*sizeof(Unit);
    if (needbytes>sizeof(bufa)) {	/* need malloc space */
      allocbufa=(decNumber *)malloc(needbytes);
      if (allocbufa==NULL) {		/* hopeless -- abandon */
	status|=DEC_Insufficient_storage;
	break;}
      acc=allocbufa;			/* use the allocated space */
      }
    /* multiply with extended range and necessary precision */
    /*printf("emin=%ld\n", dcmul.emin); */
    decMultiplyOp(acc, lhs, rhs, &dcmul, &status);
    /* Only Invalid operation (from sNaN or Inf * 0) is possible in */
    /* status; if either is seen than ignore fhs (in case it is */
    /* another sNaN) and set acc to NaN unless we had an sNaN */
    /* [decMultiplyOp leaves that to caller] */
    /* Note sNaN has to go through addOp to shorten payload if */
    /* necessary */
    if ((status&DEC_Invalid_operation)!=0) {
      if (!(status&DEC_sNaN)) { 	/* but be true invalid */
	decNumberZero(res);		/* acc not yet set */
	res->bits=DECNAN;
	break;
	}
      decNumberZero(&dzero);		/* make 0 (any non-NaN would do) */
      fhs=&dzero;			/* use that */
      }
    #if DECCHECK
     else { /* multiply was OK */
      if (status!=0) printf("Status=%08lx after FMA multiply\n", (LI)status);
      }
    #endif
    /* add the third operand and result -> res, and all is done */
    decAddOp(res, acc, fhs, set, 0, &status);
    } while(0); 			/* end protected */

  free(allocbufa); /* drop any storage used */
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } /* decNumberFMA */

/* ------------------------------------------------------------------ */
/* decNumberInvert -- invert a Number, digitwise		      */
/*								      */
/*   This computes C = ~A					      */
/*								      */
/*   res is C, the result.  C may be A (e.g., X=~X)		      */
/*   rhs is A							      */
/*   set is the context (used for result length and error report)     */
/*								      */
/* C must have space for set->digits digits.			      */
/*								      */
/* Logical function restrictions apply (see above); a NaN is	      */
/* returned with Invalid_operation if a restriction is violated.      */
/* ------------------------------------------------------------------ */
decNumber * decNumberInvert(decNumber *res, const decNumber *rhs,
			    decContext *set) {
  const Unit *ua, *msua;		/* -> operand and its msu */
  Unit	*uc, *msuc;			/* -> result and its msu */
  Int	msudigs;			/* digits in res msu */
  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  if (rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
    decStatus(res, DEC_Invalid_operation, set);
    return res;
    }
  /* operand is valid */
  ua=rhs->lsu;				/* bottom-up */
  uc=res->lsu;				/* .. */
  msua=ua+D2U(rhs->digits)-1;		/* -> msu of rhs */
  msuc=uc+D2U(set->digits)-1;		/* -> msu of result */
  msudigs=MSUDIGITS(set->digits);	/* [faster than remainder] */
  for (; uc<=msuc; ua++, uc++) {	/* Unit loop */
    Unit a;				/* extract unit */
    Int  i, j;				/* work */
    if (ua>msua) a=0;
     else a=*ua;
    *uc=0;				/* can now write back */
    /* always need to examine all bits in rhs */
    /* This loop could be unrolled and/or use BIN2BCD tables */
    for (i=0; i<DECDPUN; i++) {
      if ((~a)&1) *uc=*uc+(Unit)powers[i];   /* effect INVERT */
      j=a%10;
      a=a/10;
      if (j>1) {
	decStatus(res, DEC_Invalid_operation, set);
	return res;
	}
      if (uc==msuc && i==msudigs-1) break;   /* just did final digit */
      } /* each digit */
    } /* each unit */
  /* [here uc-1 is the msu of the result] */
  res->digits=decGetDigits(res->lsu, uc-res->lsu);
  res->exponent=0;			/* integer */
  res->bits=0;				/* sign=0 */
  return res;  /* [no status to set] */
  } /* decNumberInvert */

/* ------------------------------------------------------------------ */
/* decNumberLn -- natural logarithm				      */
/*								      */
/*   This computes C = ln(A)					      */
/*								      */
/*   res is C, the result.  C may be A				      */
/*   rhs is A							      */
/*   set is the context; note that rounding mode has no effect	      */
/*								      */
/* C must have space for set->digits digits.			      */
/*								      */
/* Notable cases:						      */
/*   A<0 -> Invalid						      */
/*   A=0 -> -Infinity (Exact)					      */
/*   A=+Infinity -> +Infinity (Exact)				      */
/*   A=1 exactly -> 0 (Exact)					      */
/*								      */
/* Mathematical function restrictions apply (see above); a NaN is     */
/* returned with Invalid_operation if a restriction is violated.      */
/*								      */
/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will    */
/* almost always be correctly rounded, but may be up to 1 ulp in      */
/* error in rare cases. 					      */
/* ------------------------------------------------------------------ */
/* This is a wrapper for decLnOp which can handle the slightly wider  */
/* (+11) range needed by Ln, Log10, etc. (which may have to be able   */
/* to calculate at p+e+2).					      */
/* ------------------------------------------------------------------ */
decNumber * decNumberLn(decNumber *res, const decNumber *rhs,
			decContext *set) {
  uInt status=0;		   /* accumulator */
  #if DECSUBSET
  decNumber *allocrhs=NULL;	   /* non-NULL if rounded rhs allocated */
  #endif

  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  /* Check restrictions; this is a math function; if not violated */
  /* then carry out the operation. */
  if (!decCheckMath(rhs, set, &status)) do { /* protect allocation */
    #if DECSUBSET
    if (!set->extended) {
      /* reduce operand and set lostDigits status, as needed */
      if (rhs->digits>set->digits) {
	allocrhs=decRoundOperand(rhs, set, &status);
	if (allocrhs==NULL) break;
	rhs=allocrhs;
	}
      /* special check in subset for rhs=0 */
      if (ISZERO(rhs)) {		/* +/- zeros -> error */
	status|=DEC_Invalid_operation;
	break;}
      } /* extended=0 */
    #endif
    decLnOp(res, rhs, set, &status);
    } while(0); 			/* end protected */

  #if DECSUBSET
  free(allocrhs);	/* drop any storage used */
  #endif
  /* apply significant status */
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } /* decNumberLn */

/* ------------------------------------------------------------------ */
/* decNumberLogB - get adjusted exponent, by 754 rules		      */
/*								      */
/*   This computes C = adjustedexponent(A)			      */
/*								      */
/*   res is C, the result.  C may be A				      */
/*   rhs is A							      */
/*   set is the context, used only for digits and status	      */
/*								      */
/* C must have space for 10 digits (A might have 10**9 digits and     */
/* an exponent of +999999999, or one digit and an exponent of	      */
/* -1999999999).						      */
/*								      */
/* This returns the adjusted exponent of A after (in theory) padding  */
/* with zeros on the right to set->digits digits while keeping the    */
/* same value.	The exponent is not limited by emin/emax.	      */
/*								      */
/* Notable cases:						      */
/*   A<0 -> Use |A|						      */
/*   A=0 -> -Infinity (Division by zero)			      */
/*   A=Infinite -> +Infinity (Exact)				      */
/*   A=1 exactly -> 0 (Exact)					      */
/*   NaNs are propagated as usual				      */
/* ------------------------------------------------------------------ */
decNumber * decNumberLogB(decNumber *res, const decNumber *rhs,
			  decContext *set) {
  uInt status=0;		   /* accumulator */

  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  /* NaNs as usual; Infinities return +Infinity; 0->oops */
  if (decNumberIsNaN(rhs)) decNaNs(res, rhs, NULL, set, &status);
   else if (decNumberIsInfinite(rhs)) decNumberCopyAbs(res, rhs);
   else if (decNumberIsZero(rhs)) {
    decNumberZero(res); 		/* prepare for Infinity */
    res->bits=DECNEG|DECINF;		/* -Infinity */
    status|=DEC_Division_by_zero;	/* as per 754 */
    }
   else { /* finite non-zero */
    Int ae=rhs->exponent+rhs->digits-1; /* adjusted exponent */
    decNumberFromInt32(res, ae);	/* lay it out */
    }

  if (status!=0) decStatus(res, status, set);
  return res;
  } /* decNumberLogB */

/* ------------------------------------------------------------------ */
/* decNumberLog10 -- logarithm in base 10			      */
/*								      */
/*   This computes C = log10(A) 				      */
/*								      */
/*   res is C, the result.  C may be A				      */
/*   rhs is A							      */
/*   set is the context; note that rounding mode has no effect	      */
/*								      */
/* C must have space for set->digits digits.			      */
/*								      */
/* Notable cases:						      */
/*   A<0 -> Invalid						      */
/*   A=0 -> -Infinity (Exact)					      */
/*   A=+Infinity -> +Infinity (Exact)				      */
/*   A=10**n (if n is an integer) -> n (Exact)			      */
/*								      */
/* Mathematical function restrictions apply (see above); a NaN is     */
/* returned with Invalid_operation if a restriction is violated.      */
/*								      */
/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will    */
/* almost always be correctly rounded, but may be up to 1 ulp in      */
/* error in rare cases. 					      */
/* ------------------------------------------------------------------ */
/* This calculates ln(A)/ln(10) using appropriate precision.  For     */
/* ln(A) this is the max(p, rhs->digits + t) + 3, where p is the      */
/* requested digits and t is the number of digits in the exponent     */
/* (maximum 6).  For ln(10) it is p + 3; this is often handled by the */
/* fastpath in decLnOp.  The final division is done to the requested  */
/* precision.							      */
/* ------------------------------------------------------------------ */
decNumber * decNumberLog10(decNumber *res, const decNumber *rhs,
			  decContext *set) {
  uInt status=0, ignore=0;	   /* status accumulators */
  uInt needbytes;		   /* for space calculations */
  Int p;			   /* working precision */
  Int t;			   /* digits in exponent of A */

  /* buffers for a and b working decimals */
  /* (adjustment calculator, same size) */
  decNumber bufa[D2N(DECBUFFER+2)];
  decNumber *allocbufa=NULL;	   /* -> allocated bufa, iff allocated */
  decNumber *a=bufa;		   /* temporary a */
  decNumber bufb[D2N(DECBUFFER+2)];
  decNumber *allocbufb=NULL;	   /* -> allocated bufb, iff allocated */
  decNumber *b=bufb;		   /* temporary b */
  decNumber bufw[D2N(10)];	   /* working 2-10 digit number */
  decNumber *w=bufw;		   /* .. */
  #if DECSUBSET
  decNumber *allocrhs=NULL;	   /* non-NULL if rounded rhs allocated */
  #endif

  decContext aset;		   /* working context */

  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  /* Check restrictions; this is a math function; if not violated */
  /* then carry out the operation. */
  if (!decCheckMath(rhs, set, &status)) do { /* protect malloc */
    #if DECSUBSET
    if (!set->extended) {
      /* reduce operand and set lostDigits status, as needed */
      if (rhs->digits>set->digits) {
	allocrhs=decRoundOperand(rhs, set, &status);
	if (allocrhs==NULL) break;
	rhs=allocrhs;
	}
      /* special check in subset for rhs=0 */
      if (ISZERO(rhs)) {		/* +/- zeros -> error */
	status|=DEC_Invalid_operation;
	break;}
      } /* extended=0 */
    #endif

    decContextDefault(&aset, DEC_INIT_DECIMAL64); /* clean context */

    /* handle exact powers of 10; only check if +ve finite */
    if (!(rhs->bits&(DECNEG|DECSPECIAL)) && !ISZERO(rhs)) {
      Int residue=0;		   /* (no residue) */
      uInt copystat=0;		   /* clean status */

      /* round to a single digit... */
      aset.digits=1;
      decCopyFit(w, rhs, &aset, &residue, &copystat); /* copy & shorten */
      /* if exact and the digit is 1, rhs is a power of 10 */
      if (!(copystat&DEC_Inexact) && w->lsu[0]==1) {
	/* the exponent, conveniently, is the power of 10; making */
	/* this the result needs a little care as it might not fit, */
	/* so first convert it into the working number, and then move */
	/* to res */
	decNumberFromInt32(w, w->exponent);
	residue=0;
	decCopyFit(res, w, set, &residue, &status); /* copy & round */
	decFinish(res, set, &residue, &status);     /* cleanup/set flags */
	break;
	} /* not a power of 10 */
      } /* not a candidate for exact */

    /* simplify the information-content calculation to use 'total */
    /* number of digits in a, including exponent' as compared to the */
    /* requested digits, as increasing this will only rarely cost an */
    /* iteration in ln(a) anyway */
    t=6;				/* it can never be >6 */

    /* allocate space when needed... */
    p=(rhs->digits+t>set->digits?rhs->digits+t:set->digits)+3;
    needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit);
    if (needbytes>sizeof(bufa)) {	/* need malloc space */
      allocbufa=(decNumber *)malloc(needbytes);
      if (allocbufa==NULL) {		/* hopeless -- abandon */
	status|=DEC_Insufficient_storage;
	break;}
      a=allocbufa;			/* use the allocated space */
      }
    aset.digits=p;			/* as calculated */
    aset.emax=DEC_MAX_MATH;		/* usual bounds */
    aset.emin=-DEC_MAX_MATH;		/* .. */
    aset.clamp=0;			/* and no concrete format */
    decLnOp(a, rhs, &aset, &status);	/* a=ln(rhs) */

    /* skip the division if the result so far is infinite, NaN, or */
    /* zero, or there was an error; note NaN from sNaN needs copy */
    if (status&DEC_NaNs && !(status&DEC_sNaN)) break;
    if (a->bits&DECSPECIAL || ISZERO(a)) {
      decNumberCopy(res, a);		/* [will fit] */
      break;}

    /* for ln(10) an extra 3 digits of precision are needed */
    p=set->digits+3;
    needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit);
    if (needbytes>sizeof(bufb)) {	/* need malloc space */
      allocbufb=(decNumber *)malloc(needbytes);
      if (allocbufb==NULL) {		/* hopeless -- abandon */
	status|=DEC_Insufficient_storage;
	break;}
      b=allocbufb;			/* use the allocated space */
      }
    decNumberZero(w);			/* set up 10... */
    #if DECDPUN==1
    w->lsu[1]=1; w->lsu[0]=0;		/* .. */
    #else
    w->lsu[0]=10;			/* .. */
    #endif
    w->digits=2;			/* .. */

    aset.digits=p;
    decLnOp(b, w, &aset, &ignore);	/* b=ln(10) */

    aset.digits=set->digits;		/* for final divide */
    decDivideOp(res, a, b, &aset, DIVIDE, &status); /* into result */
    } while(0); 			/* [for break] */

  free(allocbufa); /* drop any storage used */
  free(allocbufb); /* .. */
  #if DECSUBSET
  free(allocrhs);	/* .. */
  #endif
  /* apply significant status */
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } /* decNumberLog10 */

/* ------------------------------------------------------------------ */
/* decNumberMax -- compare two Numbers and return the maximum	      */
/*								      */
/*   This computes C = A ? B, returning the maximum by 754 rules      */
/*								      */
/*   res is C, the result.  C may be A and/or B (e.g., X=X?X)	      */
/*   lhs is A							      */
/*   rhs is B							      */
/*   set is the context 					      */
/*								      */
/* C must have space for set->digits digits.			      */
/* ------------------------------------------------------------------ */
decNumber * decNumberMax(decNumber *res, const decNumber *lhs,
			 const decNumber *rhs, decContext *set) {
  uInt status=0;			/* accumulator */
  decCompareOp(res, lhs, rhs, set, COMPMAX, &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } /* decNumberMax */

/* ------------------------------------------------------------------ */
/* decNumberMaxMag -- compare and return the maximum by magnitude     */
/*								      */
/*   This computes C = A ? B, returning the maximum by 754 rules      */
/*								      */
/*   res is C, the result.  C may be A and/or B (e.g., X=X?X)	      */
/*   lhs is A							      */
/*   rhs is B							      */
/*   set is the context 					      */
/*								      */
/* C must have space for set->digits digits.			      */
/* ------------------------------------------------------------------ */
decNumber * decNumberMaxMag(decNumber *res, const decNumber *lhs,
			 const decNumber *rhs, decContext *set) {
  uInt status=0;			/* accumulator */
  decCompareOp(res, lhs, rhs, set, COMPMAXMAG, &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } /* decNumberMaxMag */

/* ------------------------------------------------------------------ */
/* decNumberMin -- compare two Numbers and return the minimum	      */
/*								      */
/*   This computes C = A ? B, returning the minimum by 754 rules      */
/*								      */
/*   res is C, the result.  C may be A and/or B (e.g., X=X?X)	      */
/*   lhs is A							      */
/*   rhs is B							      */
/*   set is the context 					      */
/*								      */
/* C must have space for set->digits digits.			      */
/* ------------------------------------------------------------------ */
decNumber * decNumberMin(decNumber *res, const decNumber *lhs,
			 const decNumber *rhs, decContext *set) {
  uInt status=0;			/* accumulator */
  decCompareOp(res, lhs, rhs, set, COMPMIN, &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } /* decNumberMin */

/* ------------------------------------------------------------------ */
/* decNumberMinMag -- compare and return the minimum by magnitude     */
/*								      */
/*   This computes C = A ? B, returning the minimum by 754 rules      */
/*								      */
/*   res is C, the result.  C may be A and/or B (e.g., X=X?X)	      */
/*   lhs is A							      */
/*   rhs is B							      */
/*   set is the context 					      */
/*								      */
/* C must have space for set->digits digits.			      */
/* ------------------------------------------------------------------ */
decNumber * decNumberMinMag(decNumber *res, const decNumber *lhs,
			 const decNumber *rhs, decContext *set) {
  uInt status=0;			/* accumulator */
  decCompareOp(res, lhs, rhs, set, COMPMINMAG, &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } /* decNumberMinMag */

/* ------------------------------------------------------------------ */
/* decNumberMinus -- prefix minus operator			      */
/*								      */
/*   This computes C = 0 - A					      */
/*								      */
/*   res is C, the result.  C may be A				      */
/*   rhs is A							      */
/*   set is the context 					      */
/*								      */
/* See also decNumberCopyNegate for a quiet bitwise version of this.  */
/* C must have space for set->digits digits.			      */
/* ------------------------------------------------------------------ */
/* Simply use AddOp for the subtract, which will do the necessary.    */
/* ------------------------------------------------------------------ */
decNumber * decNumberMinus(decNumber *res, const decNumber *rhs,
			   decContext *set) {
  decNumber dzero;
  uInt status=0;			/* accumulator */

  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  decNumberZero(&dzero);		/* make 0 */
  dzero.exponent=rhs->exponent; 	/* [no coefficient expansion] */
  decAddOp(res, &dzero, rhs, set, DECNEG, &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } /* decNumberMinus */

/* ------------------------------------------------------------------ */
/* decNumberNextMinus -- next towards -Infinity 		      */
/*								      */
/*   This computes C = A - infinitesimal, rounded towards -Infinity   */
/*								      */
/*   res is C, the result.  C may be A				      */
/*   rhs is A							      */
/*   set is the context 					      */
/*								      */
/* This is a generalization of 754 NextDown.			      */
/* ------------------------------------------------------------------ */
decNumber * decNumberNextMinus(decNumber *res, const decNumber *rhs,
			       decContext *set) {
  decNumber dtiny;			     /* constant */
  decContext workset=*set;		     /* work */
  uInt status=0;			     /* accumulator */
  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  /* +Infinity is the special case */
  if ((rhs->bits&(DECINF|DECNEG))==DECINF) {
    decSetMaxValue(res, set);		     /* is +ve */
    /* there is no status to set */
    return res;
    }
  decNumberZero(&dtiny);		     /* start with 0 */
  dtiny.lsu[0]=1;			     /* make number that is .. */
  dtiny.exponent=DEC_MIN_EMIN-1;	     /* .. smaller than tiniest */
  workset.round=DEC_ROUND_FLOOR;
  decAddOp(res, rhs, &dtiny, &workset, DECNEG, &status);
  status&=DEC_Invalid_operation|DEC_sNaN;    /* only sNaN Invalid please */
  if (status!=0) decStatus(res, status, set);
  return res;
  } /* decNumberNextMinus */

/* ------------------------------------------------------------------ */
/* decNumberNextPlus -- next towards +Infinity			      */
/*								      */
/*   This computes C = A + infinitesimal, rounded towards +Infinity   */
/*								      */
/*   res is C, the result.  C may be A				      */
/*   rhs is A							      */
/*   set is the context 					      */
/*								      */
/* This is a generalization of 754 NextUp.			      */
/* ------------------------------------------------------------------ */
decNumber * decNumberNextPlus(decNumber *res, const decNumber *rhs,
			      decContext *set) {
  decNumber dtiny;			     /* constant */
  decContext workset=*set;		     /* work */
  uInt status=0;			     /* accumulator */
  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  /* -Infinity is the special case */
  if ((rhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) {
    decSetMaxValue(res, set);
    res->bits=DECNEG;			     /* negative */
    /* there is no status to set */
    return res;
    }
  decNumberZero(&dtiny);		     /* start with 0 */
  dtiny.lsu[0]=1;			     /* make number that is .. */
  dtiny.exponent=DEC_MIN_EMIN-1;	     /* .. smaller than tiniest */
  workset.round=DEC_ROUND_CEILING;
  decAddOp(res, rhs, &dtiny, &workset, 0, &status);
  status&=DEC_Invalid_operation|DEC_sNaN;    /* only sNaN Invalid please */
  if (status!=0) decStatus(res, status, set);
  return res;
  } /* decNumberNextPlus */

/* ------------------------------------------------------------------ */
/* decNumberNextToward -- next towards rhs			      */
/*								      */
/*   This computes C = A +/- infinitesimal, rounded towards	      */
/*   +/-Infinity in the direction of B, as per 754-1985 nextafter     */
/*   modified during revision but dropped from 754-2008.	      */
/*								      */
/*   res is C, the result.  C may be A or B.			      */
/*   lhs is A							      */
/*   rhs is B							      */
/*   set is the context 					      */
/*								      */
/* This is a generalization of 754-1985 NextAfter.		      */
/* ------------------------------------------------------------------ */
decNumber * decNumberNextToward(decNumber *res, const decNumber *lhs,
				const decNumber *rhs, decContext *set) {
  decNumber dtiny;			     /* constant */
  decContext workset=*set;		     /* work */
  Int result;				     /* .. */
  uInt status=0;			     /* accumulator */
  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) {
    decNaNs(res, lhs, rhs, set, &status);
    }
   else { /* Is numeric, so no chance of sNaN Invalid, etc. */
    result=decCompare(lhs, rhs, 0);	/* sign matters */
    if (result==BADINT) status|=DEC_Insufficient_storage; /* rare */
     else { /* valid compare */
      if (result==0) decNumberCopySign(res, lhs, rhs); /* easy */
       else { /* differ: need NextPlus or NextMinus */
	uByte sub;			/* add or subtract */
	if (result<0) { 		/* lhs<rhs, do nextplus */
	  /* -Infinity is the special case */
	  if ((lhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) {
	    decSetMaxValue(res, set);
	    res->bits=DECNEG;		/* negative */
	    return res; 		/* there is no status to set */
	    }
	  workset.round=DEC_ROUND_CEILING;
	  sub=0;			/* add, please */
	  } /* plus */
	 else { 			/* lhs>rhs, do nextminus */
	  /* +Infinity is the special case */
	  if ((lhs->bits&(DECINF|DECNEG))==DECINF) {
	    decSetMaxValue(res, set);
	    return res; 		/* there is no status to set */
	    }
	  workset.round=DEC_ROUND_FLOOR;
	  sub=DECNEG;			/* subtract, please */
	  } /* minus */
	decNumberZero(&dtiny);		/* start with 0 */
	dtiny.lsu[0]=1; 		/* make number that is .. */
	dtiny.exponent=DEC_MIN_EMIN-1;	/* .. smaller than tiniest */
	decAddOp(res, lhs, &dtiny, &workset, sub, &status); /* + or - */
	/* turn off exceptions if the result is a normal number */
	/* (including Nmin), otherwise let all status through */
	if (decNumberIsNormal(res, set)) status=0;
	} /* unequal */
      } /* compare OK */
    } /* numeric */
  if (status!=0) decStatus(res, status, set);
  return res;
  } /* decNumberNextToward */

/* ------------------------------------------------------------------ */
/* decNumberOr -- OR two Numbers, digitwise			      */
/*								      */
/*   This computes C = A | B					      */
/*								      */
/*   res is C, the result.  C may be A and/or B (e.g., X=X|X)	      */
/*   lhs is A							      */
/*   rhs is B							      */
/*   set is the context (used for result length and error report)     */
/*								      */
/* C must have space for set->digits digits.			      */
/*								      */
/* Logical function restrictions apply (see above); a NaN is	      */
/* returned with Invalid_operation if a restriction is violated.      */
/* ------------------------------------------------------------------ */
decNumber * decNumberOr(decNumber *res, const decNumber *lhs,
			const decNumber *rhs, decContext *set) {
  const Unit *ua, *ub;			/* -> operands */
  const Unit *msua, *msub;		/* -> operand msus */
  Unit	*uc, *msuc;			/* -> result and its msu */
  Int	msudigs;			/* digits in res msu */
  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)
   || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
    decStatus(res, DEC_Invalid_operation, set);
    return res;
    }
  /* operands are valid */
  ua=lhs->lsu;				/* bottom-up */
  ub=rhs->lsu;				/* .. */
  uc=res->lsu;				/* .. */
  msua=ua+D2U(lhs->digits)-1;		/* -> msu of lhs */
  msub=ub+D2U(rhs->digits)-1;		/* -> msu of rhs */
  msuc=uc+D2U(set->digits)-1;		/* -> msu of result */
  msudigs=MSUDIGITS(set->digits);	/* [faster than remainder] */
  for (; uc<=msuc; ua++, ub++, uc++) {	/* Unit loop */
    Unit a, b;				/* extract units */
    if (ua>msua) a=0;
     else a=*ua;
    if (ub>msub) b=0;
     else b=*ub;
    *uc=0;				/* can now write back */
    if (a|b) {				/* maybe 1 bits to examine */
      Int i, j;
      /* This loop could be unrolled and/or use BIN2BCD tables */
      for (i=0; i<DECDPUN; i++) {
	if ((a|b)&1) *uc=*uc+(Unit)powers[i];	  /* effect OR */
	j=a%10;
	a=a/10;
	j|=b%10;
	b=b/10;
	if (j>1) {
	  decStatus(res, DEC_Invalid_operation, set);
	  return res;
	  }
	if (uc==msuc && i==msudigs-1) break;	  /* just did final digit */
	} /* each digit */
      } /* non-zero */
    } /* each unit */
  /* [here uc-1 is the msu of the result] */
  res->digits=decGetDigits(res->lsu, uc-res->lsu);
  res->exponent=0;			/* integer */
  res->bits=0;				/* sign=0 */
  return res;  /* [no status to set] */
  } /* decNumberOr */

/* ------------------------------------------------------------------ */
/* decNumberPlus -- prefix plus operator			      */
/*								      */
/*   This computes C = 0 + A					      */
/*								      */
/*   res is C, the result.  C may be A				      */
/*   rhs is A							      */
/*   set is the context 					      */
/*								      */
/* See also decNumberCopy for a quiet bitwise version of this.	      */
/* C must have space for set->digits digits.			      */
/* ------------------------------------------------------------------ */
/* This simply uses AddOp; Add will take fast path after preparing A. */
/* Performance is a concern here, as this routine is often used to    */
/* check operands and apply rounding and overflow/underflow testing.  */
/* ------------------------------------------------------------------ */
decNumber * decNumberPlus(decNumber *res, const decNumber *rhs,
			  decContext *set) {
  decNumber dzero;
  uInt status=0;			/* accumulator */
  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  decNumberZero(&dzero);		/* make 0 */
  dzero.exponent=rhs->exponent; 	/* [no coefficient expansion] */
  decAddOp(res, &dzero, rhs, set, 0, &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } /* decNumberPlus */

/* ------------------------------------------------------------------ */
/* decNumberMultiply -- multiply two Numbers			      */
/*								      */
/*   This computes C = A x B					      */
/*								      */
/*   res is C, the result.  C may be A and/or B (e.g., X=X+X)	      */
/*   lhs is A							      */
/*   rhs is B							      */
/*   set is the context 					      */
/*								      */
/* C must have space for set->digits digits.			      */
/* ------------------------------------------------------------------ */
decNumber * decNumberMultiply(decNumber *res, const decNumber *lhs,
			      const decNumber *rhs, decContext *set) {
  uInt status=0;		   /* accumulator */
  decMultiplyOp(res, lhs, rhs, set, &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } /* decNumberMultiply */

/* ------------------------------------------------------------------ */
/* decNumberPower -- raise a number to a power			      */
/*								      */
/*   This computes C = A ** B					      */
/*								      */
/*   res is C, the result.  C may be A and/or B (e.g., X=X**X)	      */
/*   lhs is A							      */
/*   rhs is B							      */
/*   set is the context 					      */
/*								      */
/* C must have space for set->digits digits.			      */
/*								      */
/* Mathematical function restrictions apply (see above); a NaN is     */
/* returned with Invalid_operation if a restriction is violated.      */
/*								      */
/* However, if 1999999997<=B<=999999999 and B is an integer then the  */
/* restrictions on A and the context are relaxed to the usual bounds, */
/* for compatibility with the earlier (integer power only) version    */
/* of this function.						      */
/*								      */
/* When B is an integer, the result may be exact, even if rounded.    */
/*								      */
/* The final result is rounded according to the context; it will      */
/* almost always be correctly rounded, but may be up to 1 ulp in      */
/* error in rare cases. 					      */
/* ------------------------------------------------------------------ */
decNumber * decNumberPower(decNumber *res, const decNumber *lhs,
			   const decNumber *rhs, decContext *set) {
  #if DECSUBSET
  decNumber *alloclhs=NULL;	   /* non-NULL if rounded lhs allocated */
  decNumber *allocrhs=NULL;	   /* .., rhs */
  #endif
  decNumber *allocdac=NULL;	   /* -> allocated acc buffer, iff used */
  decNumber *allocinv=NULL;	   /* -> allocated 1/x buffer, iff used */
  Int	reqdigits=set->digits;	   /* requested DIGITS */
  Int	n;			   /* rhs in binary */
  Flag	rhsint=0;		   /* 1 if rhs is an integer */
  Flag	useint=0;		   /* 1 if can use integer calculation */
  Flag	isoddint=0;		   /* 1 if rhs is an integer and odd */
  Int	i;			   /* work */
  #if DECSUBSET
  Int	dropped;		   /* .. */
  #endif
  uInt	needbytes;		   /* buffer size needed */
  Flag	seenbit;		   /* seen a bit while powering */
  Int	residue=0;		   /* rounding residue */
  uInt	status=0;		   /* accumulators */
  uByte bits=0; 		   /* result sign if errors */
  decContext aset;		   /* working context */
  decNumber dnOne;		   /* work value 1... */
  /* local accumulator buffer [a decNumber, with digits+elength+1 digits] */
  decNumber dacbuff[D2N(DECBUFFER+9)];
  decNumber *dac=dacbuff;	   /* -> result accumulator */
  /* same again for possible 1/lhs calculation */
  decNumber invbuff[D2N(DECBUFFER+9)];

  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  do {				   /* protect allocated storage */
    #if DECSUBSET
    if (!set->extended) { /* reduce operands and set status, as needed */
      if (lhs->digits>reqdigits) {
	alloclhs=decRoundOperand(lhs, set, &status);
	if (alloclhs==NULL) break;
	lhs=alloclhs;
	}
      if (rhs->digits>reqdigits) {
	allocrhs=decRoundOperand(rhs, set, &status);
	if (allocrhs==NULL) break;
	rhs=allocrhs;
	}
      }
    #endif
    /* [following code does not require input rounding] */

    /* handle NaNs and rhs Infinity (lhs infinity is harder) */
    if (SPECIALARGS) {
      if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) { /* NaNs */
	decNaNs(res, lhs, rhs, set, &status);
	break;}
      if (decNumberIsInfinite(rhs)) {	/* rhs Infinity */
	Flag rhsneg=rhs->bits&DECNEG;	/* save rhs sign */
	if (decNumberIsNegative(lhs)	/* lhs<0 */
	 && !decNumberIsZero(lhs))	/* .. */
	  status|=DEC_Invalid_operation;
	 else { 			/* lhs >=0 */
	  decNumberZero(&dnOne);	/* set up 1 */
	  dnOne.lsu[0]=1;
	  decNumberCompare(dac, lhs, &dnOne, set); /* lhs ? 1 */
	  decNumberZero(res);		/* prepare for 0/1/Infinity */
	  if (decNumberIsNegative(dac)) {    /* lhs<1 */
	    if (rhsneg) res->bits|=DECINF;   /* +Infinity [else is +0] */
	    }
	   else if (dac->lsu[0]==0) {	     /* lhs=1 */
	    /* 1**Infinity is inexact, so return fully-padded 1.0000 */
	    Int shift=set->digits-1;
	    *res->lsu=1;		     /* was 0, make int 1 */
	    res->digits=decShiftToMost(res->lsu, 1, shift);
	    res->exponent=-shift;	     /* make 1.0000... */
	    status|=DEC_Inexact|DEC_Rounded; /* deemed inexact */
	    }
	   else {			     /* lhs>1 */
	    if (!rhsneg) res->bits|=DECINF;  /* +Infinity [else is +0] */
	    }
	  } /* lhs>=0 */
	break;}
      /* [lhs infinity drops through] */
      } /* specials */

    /* Original rhs may be an integer that fits and is in range */
    n=decGetInt(rhs);
    if (n!=BADINT) {			/* it is an integer */
      rhsint=1; 			/* record the fact for 1**n */
      isoddint=(Flag)n&1;		/* [works even if big] */
      if (n!=BIGEVEN && n!=BIGODD)	/* can use integer path? */
	useint=1;			/* looks good */
      }

    if (decNumberIsNegative(lhs)	/* -x .. */
      && isoddint) bits=DECNEG; 	/* .. to an odd power */

    /* handle LHS infinity */
    if (decNumberIsInfinite(lhs)) {	/* [NaNs already handled] */
      uByte rbits=rhs->bits;		/* save */
      decNumberZero(res);		/* prepare */
      if (n==0) *res->lsu=1;		/* [-]Inf**0 => 1 */
       else {
	/* -Inf**nonint -> error */
	if (!rhsint && decNumberIsNegative(lhs)) {
	  status|=DEC_Invalid_operation;     /* -Inf**nonint is error */
	  break;}
	if (!(rbits & DECNEG)) bits|=DECINF; /* was not a **-n */
	/* [otherwise will be 0 or -0] */
	res->bits=bits;
	}
      break;}

    /* similarly handle LHS zero */
    if (decNumberIsZero(lhs)) {
      if (n==0) {			     /* 0**0 => Error */
	#if DECSUBSET
	if (!set->extended) {		     /* [unless subset] */
	  decNumberZero(res);
	  *res->lsu=1;			     /* return 1 */
	  break;}
	#endif
	status|=DEC_Invalid_operation;
	}
       else {				     /* 0**x */
	uByte rbits=rhs->bits;		     /* save */
	if (rbits & DECNEG) {		     /* was a 0**(-n) */
	  #if DECSUBSET
	  if (!set->extended) { 	     /* [bad if subset] */
	    status|=DEC_Invalid_operation;
	    break;}
	  #endif
	  bits|=DECINF;
	  }
	decNumberZero(res);		     /* prepare */
	/* [otherwise will be 0 or -0] */
	res->bits=bits;
	}
      break;}

    /* here both lhs and rhs are finite; rhs==0 is handled in the */
    /* integer path.  Next handle the non-integer cases */
    if (!useint) {			/* non-integral rhs */
      /* any -ve lhs is bad, as is either operand or context out of */
      /* bounds */
      if (decNumberIsNegative(lhs)) {
	status|=DEC_Invalid_operation;
	break;}
      if (decCheckMath(lhs, set, &status)
       || decCheckMath(rhs, set, &status)) break; /* variable status */

      decContextDefault(&aset, DEC_INIT_DECIMAL64); /* clean context */
      aset.emax=DEC_MAX_MATH;		/* usual bounds */
      aset.emin=-DEC_MAX_MATH;		/* .. */
      aset.clamp=0;			/* and no concrete format */

      /* calculate the result using exp(ln(lhs)*rhs), which can */
      /* all be done into the accumulator, dac.  The precision needed */
      /* is enough to contain the full information in the lhs (which */
      /* is the total digits, including exponent), or the requested */
      /* precision, if larger, + 4; 6 is used for the exponent */
      /* maximum length, and this is also used when it is shorter */
      /* than the requested digits as it greatly reduces the >0.5 ulp */
      /* cases at little cost (because Ln doubles digits each */
      /* iteration so a few extra digits rarely causes an extra */
      /* iteration) */
      aset.digits=MAXI(lhs->digits, set->digits)+6+4;
      } /* non-integer rhs */

     else { /* rhs is in-range integer */
      if (n==0) {			/* x**0 = 1 */
	/* (0**0 was handled above) */
	decNumberZero(res);		/* result=1 */
	*res->lsu=1;			/* .. */
	break;}
      /* rhs is a non-zero integer */
      if (n<0) n=-n;			/* use abs(n) */

      aset=*set;			/* clone the context */
      aset.round=DEC_ROUND_HALF_EVEN;	/* internally use balanced */
      /* calculate the working DIGITS */
      aset.digits=reqdigits+(rhs->digits+rhs->exponent)+2;
      #if DECSUBSET
      if (!set->extended) aset.digits--;     /* use classic precision */
      #endif
      /* it's an error if this is more than can be handled */
      if (aset.digits>DECNUMMAXP) {status|=DEC_Invalid_operation; break;}
      } /* integer path */

    /* aset.digits is the count of digits for the accumulator needed */
    /* if accumulator is too long for local storage, then allocate */
    needbytes=sizeof(decNumber)+(D2U(aset.digits)-1)*sizeof(Unit);
    /* [needbytes also used below if 1/lhs needed] */
    if (needbytes>sizeof(dacbuff)) {
      allocdac=(decNumber *)malloc(needbytes);
      if (allocdac==NULL) {   /* hopeless -- abandon */
	status|=DEC_Insufficient_storage;
	break;}
      dac=allocdac;	      /* use the allocated space */
      }
    /* here, aset is set up and accumulator is ready for use */

    if (!useint) {			     /* non-integral rhs */
      /* x ** y; special-case x=1 here as it will otherwise always */
      /* reduce to integer 1; decLnOp has a fastpath which detects */
      /* the case of x=1 */
      decLnOp(dac, lhs, &aset, &status);     /* dac=ln(lhs) */
      /* [no error possible, as lhs 0 already handled] */
      if (ISZERO(dac)) {		     /* x==1, 1.0, etc. */
	/* need to return fully-padded 1.0000 etc., but rhsint->1 */
	*dac->lsu=1;			     /* was 0, make int 1 */
	if (!rhsint) {			     /* add padding */
	  Int shift=set->digits-1;
	  dac->digits=decShiftToMost(dac->lsu, 1, shift);
	  dac->exponent=-shift; 	     /* make 1.0000... */
	  status|=DEC_Inexact|DEC_Rounded;   /* deemed inexact */
	  }
	}
       else {
	decMultiplyOp(dac, dac, rhs, &aset, &status);  /* dac=dac*rhs */
	decExpOp(dac, dac, &aset, &status);	       /* dac=exp(dac) */
	}
      /* and drop through for final rounding */
      } /* non-integer rhs */

     else {				/* carry on with integer */
      decNumberZero(dac);		/* acc=1 */
      *dac->lsu=1;			/* .. */

      /* if a negative power the constant 1 is needed, and if not subset */
      /* invert the lhs now rather than inverting the result later */
      if (decNumberIsNegative(rhs)) {	/* was a **-n [hence digits>0] */
	decNumber *inv=invbuff; 	/* assume use fixed buffer */
	decNumberCopy(&dnOne, dac);	/* dnOne=1;  [needed now or later] */
	#if DECSUBSET
	if (set->extended) {		/* need to calculate 1/lhs */
	#endif
	  /* divide lhs into 1, putting result in dac [dac=1/dac] */
	  decDivideOp(dac, &dnOne, lhs, &aset, DIVIDE, &status);
	  /* now locate or allocate space for the inverted lhs */
	  if (needbytes>sizeof(invbuff)) {
	    allocinv=(decNumber *)malloc(needbytes);
	    if (allocinv==NULL) {	/* hopeless -- abandon */
	      status|=DEC_Insufficient_storage;
	      break;}
	    inv=allocinv;		/* use the allocated space */
	    }
	  /* [inv now points to big-enough buffer or allocated storage] */
	  decNumberCopy(inv, dac);	/* copy the 1/lhs */
	  decNumberCopy(dac, &dnOne);	/* restore acc=1 */
	  lhs=inv;			/* .. and go forward with new lhs */
	#if DECSUBSET
	  }
	#endif
	}

      /* Raise-to-the-power loop... */
      seenbit=0;		   /* set once a 1-bit is encountered */
      for (i=1;;i++){		   /* for each bit [top bit ignored] */
	/* abandon if had overflow or terminal underflow */
	if (status & (DEC_Overflow|DEC_Underflow)) { /* interesting? */
	  if (status&DEC_Overflow || ISZERO(dac)) break;
	  }
	/* [the following two lines revealed an optimizer bug in a C++ */
	/* compiler, with symptom: 5**3 -> 25, when n=n+n was used] */
	n=n<<1; 		   /* move next bit to testable position */
	if (n<0) {		   /* top bit is set */
	  seenbit=1;		   /* OK, significant bit seen */
	  decMultiplyOp(dac, dac, lhs, &aset, &status); /* dac=dac*x */
	  }
	if (i==31) break;	   /* that was the last bit */
	if (!seenbit) continue;    /* no need to square 1 */
	decMultiplyOp(dac, dac, dac, &aset, &status); /* dac=dac*dac [square] */
	} /*i*/ /* 32 bits */

      /* complete internal overflow or underflow processing */
      if (status & (DEC_Overflow|DEC_Underflow)) {
	#if DECSUBSET
	/* If subset, and power was negative, reverse the kind of -erflow */
	/* [1/x not yet done] */
	if (!set->extended && decNumberIsNegative(rhs)) {
	  if (status & DEC_Overflow)
	    status^=DEC_Overflow | DEC_Underflow | DEC_Subnormal;
	   else { /* trickier -- Underflow may or may not be set */
	    status&=~(DEC_Underflow | DEC_Subnormal); /* [one or both] */
	    status|=DEC_Overflow;
	    }
	  }
	#endif
	dac->bits=(dac->bits & ~DECNEG) | bits; /* force correct sign */
	/* round subnormals [to set.digits rather than aset.digits] */
	/* or set overflow result similarly as required */
	decFinalize(dac, set, &residue, &status);
	decNumberCopy(res, dac);   /* copy to result (is now OK length) */
	break;
	}

      #if DECSUBSET
      if (!set->extended &&		     /* subset math */
	  decNumberIsNegative(rhs)) {	     /* was a **-n [hence digits>0] */
	/* so divide result into 1 [dac=1/dac] */
	decDivideOp(dac, &dnOne, dac, &aset, DIVIDE, &status);
	}
      #endif
      } /* rhs integer path */

    /* reduce result to the requested length and copy to result */
    decCopyFit(res, dac, set, &residue, &status);
    decFinish(res, set, &residue, &status);  /* final cleanup */
    #if DECSUBSET
    if (!set->extended) decTrim(res, set, 0, 1, &dropped); /* trailing zeros */
    #endif
    } while(0); 			/* end protected */

  free(allocdac);	/* drop any storage used */
  free(allocinv);	/* .. */
  #if DECSUBSET
  free(alloclhs);	/* .. */
  free(allocrhs);	/* .. */
  #endif
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } /* decNumberPower */

/* ------------------------------------------------------------------ */
/* decNumberQuantize -- force exponent to requested value	      */
/*								      */
/*   This computes C = op(A, B), where op adjusts the coefficient     */
/*   of C (by rounding or shifting) such that the exponent (-scale)   */
/*   of C has exponent of B.  The numerical value of C will equal A,  */
/*   except for the effects of any rounding that occurred.	      */
/*								      */
/*   res is C, the result.  C may be A or B			      */
/*   lhs is A, the number to adjust				      */
/*   rhs is B, the number with exponent to match		      */
/*   set is the context 					      */
/*								      */
/* C must have space for set->digits digits.			      */
/*								      */
/* Unless there is an error or the result is infinite, the exponent   */
/* after the operation is guaranteed to be equal to that of B.	      */
/* ------------------------------------------------------------------ */
decNumber * decNumberQuantize(decNumber *res, const decNumber *lhs,
			      const decNumber *rhs, decContext *set) {
  uInt status=0;			/* accumulator */
  decQuantizeOp(res, lhs, rhs, set, 1, &status);
  if (status!=0) decStatus(res, status, set);
  return res;
  } /* decNumberQuantize */

/* ------------------------------------------------------------------ */
/* decNumberReduce -- remove trailing zeros			      */
/*								      */
/*   This computes C = 0 + A, and normalizes the result 	      */
/*								      */
/*   res is C, the result.  C may be A				      */
/*   rhs is A							      */
/*   set is the context 					      */
/*								      */
/* C must have space for set->digits digits.			      */
/* ------------------------------------------------------------------ */
/* Previously known as Normalize */
decNumber * decNumberNormalize(decNumber *res, const decNumber *rhs,
			       decContext *set) {
  return decNumberReduce(res, rhs, set);
  } /* decNumberNormalize */

decNumber * decNumberReduce(decNumber *res, const decNumber *rhs,
			    decContext *set) {
  #if DECSUBSET
  decNumber *allocrhs=NULL;	   /* non-NULL if rounded rhs allocated */
  #endif
  uInt status=0;		   /* as usual */
  Int  residue=0;		   /* as usual */
  Int  dropped; 		   /* work */

  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  do {				   /* protect allocated storage */
    #if DECSUBSET
    if (!set->extended) {
      /* reduce operand and set lostDigits status, as needed */
      if (rhs->digits>set->digits) {
	allocrhs=decRoundOperand(rhs, set, &status);
	if (allocrhs==NULL) break;
	rhs=allocrhs;
	}
      }
    #endif
    /* [following code does not require input rounding] */

    /* Infinities copy through; NaNs need usual treatment */
    if (decNumberIsNaN(rhs)) {
      decNaNs(res, rhs, NULL, set, &status);
      break;
      }

    /* reduce result to the requested length and copy to result */
    decCopyFit(res, rhs, set, &residue, &status); /* copy & round */
    decFinish(res, set, &residue, &status);	  /* cleanup/set flags */
    decTrim(res, set, 1, 0, &dropped);		  /* normalize in place */
						  /* [may clamp] */
    } while(0); 			     /* end protected */

  #if DECSUBSET
  free(allocrhs);	     /* .. */
  #endif
  if (status!=0) decStatus(res, status, set);/* then report status */
  return res;
  } /* decNumberReduce */

/* ------------------------------------------------------------------ */
/* decNumberRescale -- force exponent to requested value	      */
/*								      */
/*   This computes C = op(A, B), where op adjusts the coefficient     */
/*   of C (by rounding or shifting) such that the exponent (-scale)   */
/*   of C has the value B.  The numerical value of C will equal A,    */
/*   except for the effects of any rounding that occurred.	      */
/*								      */
/*   res is C, the result.  C may be A or B			      */
/*   lhs is A, the number to adjust				      */
/*   rhs is B, the requested exponent				      */
/*   set is the context 					      */
/*								      */
/* C must have space for set->digits digits.			      */
/*								      */
/* Unless there is an error or the result is infinite, the exponent   */
/* after the operation is guaranteed to be equal to B.		      */
/* ------------------------------------------------------------------ */
decNumber * decNumberRescale(decNumber *res, const decNumber *lhs,
			     const decNumber *rhs, decContext *set) {
  uInt status=0;			/* accumulator */
  decQuantizeOp(res, lhs, rhs, set, 0, &status);
  if (status!=0) decStatus(res, status, set);
  return res;
  } /* decNumberRescale */

/* ------------------------------------------------------------------ */
/* decNumberRemainder -- divide and return remainder		      */
/*								      */
/*   This computes C = A % B					      */
/*								      */
/*   res is C, the result.  C may be A and/or B (e.g., X=X%X)	      */
/*   lhs is A							      */
/*   rhs is B							      */
/*   set is the context 					      */
/*								      */
/* C must have space for set->digits digits.			      */
/* ------------------------------------------------------------------ */
decNumber * decNumberRemainder(decNumber *res, const decNumber *lhs,
			       const decNumber *rhs, decContext *set) {
  uInt status=0;			/* accumulator */
  decDivideOp(res, lhs, rhs, set, REMAINDER, &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } /* decNumberRemainder */

/* ------------------------------------------------------------------ */
/* decNumberRemainderNear -- divide and return remainder from nearest */
/*								      */
/*   This computes C = A % B, where % is the IEEE remainder operator  */
/*								      */
/*   res is C, the result.  C may be A and/or B (e.g., X=X%X)	      */
/*   lhs is A							      */
/*   rhs is B							      */
/*   set is the context 					      */
/*								      */
/* C must have space for set->digits digits.			      */
/* ------------------------------------------------------------------ */
decNumber * decNumberRemainderNear(decNumber *res, const decNumber *lhs,
				   const decNumber *rhs, decContext *set) {
  uInt status=0;			/* accumulator */
  decDivideOp(res, lhs, rhs, set, REMNEAR, &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } /* decNumberRemainderNear */

/* ------------------------------------------------------------------ */
/* decNumberRotate -- rotate the coefficient of a Number left/right   */
/*								      */
/*   This computes C = A rot B	(in base ten and rotating set->digits */
/*   digits).							      */
/*								      */
/*   res is C, the result.  C may be A and/or B (e.g., X=XrotX)       */
/*   lhs is A							      */
/*   rhs is B, the number of digits to rotate (-ve to right)	      */
/*   set is the context 					      */
/*								      */
/* The digits of the coefficient of A are rotated to the left (if B   */
/* is positive) or to the right (if B is negative) without adjusting  */
/* the exponent or the sign of A.  If lhs->digits is less than	      */
/* set->digits the coefficient is padded with zeros on the left       */
/* before the rotate.  Any leading zeros in the result are removed    */
/* as usual.							      */
/*								      */
/* B must be an integer (q=0) and in the range -set->digits through   */
/* +set->digits.						      */
/* C must have space for set->digits digits.			      */
/* NaNs are propagated as usual.  Infinities are unaffected (but      */
/* B must be valid).  No status is set unless B is invalid or an      */
/* operand is an sNaN.						      */
/* ------------------------------------------------------------------ */
decNumber * decNumberRotate(decNumber *res, const decNumber *lhs,
			   const decNumber *rhs, decContext *set) {
  uInt status=0;	      /* accumulator */
  Int  rotate;		      /* rhs as an Int */

  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  /* NaNs propagate as normal */
  if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))
    decNaNs(res, lhs, rhs, set, &status);
   /* rhs must be an integer */
   else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)
    status=DEC_Invalid_operation;
   else { /* both numeric, rhs is an integer */
    rotate=decGetInt(rhs);		     /* [cannot fail] */
    if (rotate==BADINT			     /* something bad .. */
     || rotate==BIGODD || rotate==BIGEVEN    /* .. very big .. */
     || abs(rotate)>set->digits)	     /* .. or out of range */
      status=DEC_Invalid_operation;
     else {				     /* rhs is OK */
      decNumberCopy(res, lhs);
      /* convert -ve rotate to equivalent positive rotation */
      if (rotate<0) rotate=set->digits+rotate;
      if (rotate!=0 && rotate!=set->digits   /* zero or full rotation */
       && !decNumberIsInfinite(res)) {	     /* lhs was infinite */
	/* left-rotate to do; 0 < rotate < set->digits */
	uInt units, shift;		     /* work */
	uInt msudigits; 		     /* digits in result msu */
	Unit *msu=res->lsu+D2U(res->digits)-1;	  /* current msu */
	Unit *msumax=res->lsu+D2U(set->digits)-1; /* rotation msu */
	for (msu++; msu<=msumax; msu++) *msu=0;   /* ensure high units=0 */
	res->digits=set->digits;		  /* now full-length */
	msudigits=MSUDIGITS(res->digits);	  /* actual digits in msu */

	/* rotation here is done in-place, in three steps */
	/* 1. shift all to least up to one unit to unit-align final */
	/*    lsd [any digits shifted out are rotated to the left, */
	/*    abutted to the original msd (which may require split)] */
	/* */
	/*    [if there are no whole units left to rotate, the */
	/*    rotation is now complete] */
	/* */
	/* 2. shift to least, from below the split point only, so that */
	/*    the final msd is in the right place in its Unit [any */
	/*    digits shifted out will fit exactly in the current msu, */
	/*    left aligned, no split required] */
	/* */
	/* 3. rotate all the units by reversing left part, right */
	/*    part, and then whole */
	/* */
	/* example: rotate right 8 digits (2 units + 2), DECDPUN=3. */
	/* */
	/*   start: 00a bcd efg hij klm npq */
	/* */
	/*	1a  000 0ab cde fgh|ijk lmn [pq saved] */
	/*	1b  00p qab cde fgh|ijk lmn */
	/* */
	/*	2a  00p qab cde fgh|00i jkl [mn saved] */
	/*	2b  mnp qab cde fgh|00i jkl */
	/* */
	/*	3a  fgh cde qab mnp|00i jkl */
	/*	3b  fgh cde qab mnp|jkl 00i */
	/*	3c  00i jkl mnp qab cde fgh */

	/* Step 1: amount to shift is the partial right-rotate count */
	rotate=set->digits-rotate;	/* make it right-rotate */
	units=rotate/DECDPUN;		/* whole units to rotate */
	shift=rotate%DECDPUN;		/* left-over digits count */
	if (shift>0) {			/* not an exact number of units */
	  uInt save=res->lsu[0]%powers[shift];	  /* save low digit(s) */
	  decShiftToLeast(res->lsu, D2U(res->digits), shift);
	  if (shift>msudigits) {	/* msumax-1 needs >0 digits */
	    uInt rem=save%powers[shift-msudigits];/* split save */
	    *msumax=(Unit)(save/powers[shift-msudigits]); /* and insert */
	    *(msumax-1)=*(msumax-1)
		       +(Unit)(rem*powers[DECDPUN-(shift-msudigits)]); /* .. */
	    }
	   else { /* all fits in msumax */
	    *msumax=*msumax+(Unit)(save*powers[msudigits-shift]); /* [maybe *1] */
	    }
	  } /* digits shift needed */

	/* If whole units to rotate... */
	if (units>0) {			/* some to do */
	  /* Step 2: the units to touch are the whole ones in rotate, */
	  /*   if any, and the shift is DECDPUN-msudigits (which may be */
	  /*   0, again) */
	  shift=DECDPUN-msudigits;
	  if (shift>0) {		/* not an exact number of units */
	    uInt save=res->lsu[0]%powers[shift];  /* save low digit(s) */
	    decShiftToLeast(res->lsu, units, shift);
	    *msumax=*msumax+(Unit)(save*powers[msudigits]);
	    } /* partial shift needed */

	  /* Step 3: rotate the units array using triple reverse */
	  /* (reversing is easy and fast) */
	  decReverse(res->lsu+units, msumax);	  /* left part */
	  decReverse(res->lsu, res->lsu+units-1); /* right part */
	  decReverse(res->lsu, msumax); 	  /* whole */
	  } /* whole units to rotate */
	/* the rotation may have left an undetermined number of zeros */
	/* on the left, so true length needs to be calculated */
	res->digits=decGetDigits(res->lsu, msumax-res->lsu+1);
	} /* rotate needed */
      } /* rhs OK */
    } /* numerics */
  if (status!=0) decStatus(res, status, set);
  return res;
  } /* decNumberRotate */

/* ------------------------------------------------------------------ */
/* decNumberSameQuantum -- test for equal exponents		      */
/*								      */
/*   res is the result number, which will contain either 0 or 1       */
/*   lhs is a number to test					      */
/*   rhs is the second (usually a pattern)			      */
/*								      */
/* No errors are possible and no context is needed.		      */
/* ------------------------------------------------------------------ */
decNumber * decNumberSameQuantum(decNumber *res, const decNumber *lhs,
				 const decNumber *rhs) {
  Unit ret=0;			   /* return value */

  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, DECUNCONT)) return res;
  #endif

  if (SPECIALARGS) {
    if (decNumberIsNaN(lhs) && decNumberIsNaN(rhs)) ret=1;
     else if (decNumberIsInfinite(lhs) && decNumberIsInfinite(rhs)) ret=1;
     /* [anything else with a special gives 0] */
    }
   else if (lhs->exponent==rhs->exponent) ret=1;

  decNumberZero(res);		   /* OK to overwrite an operand now */
  *res->lsu=ret;
  return res;
  } /* decNumberSameQuantum */

/* ------------------------------------------------------------------ */
/* decNumberScaleB -- multiply by a power of 10 		      */
/*								      */
/* This computes C = A x 10**B where B is an integer (q=0) with       */
/* maximum magnitude 2*(emax+digits)				      */
/*								      */
/*   res is C, the result.  C may be A or B			      */
/*   lhs is A, the number to adjust				      */
/*   rhs is B, the requested power of ten to use		      */
/*   set is the context 					      */
/*								      */
/* C must have space for set->digits digits.			      */
/*								      */
/* The result may underflow or overflow.			      */
/* ------------------------------------------------------------------ */
decNumber * decNumberScaleB(decNumber *res, const decNumber *lhs,
			    const decNumber *rhs, decContext *set) {
  Int  reqexp;		      /* requested exponent change [B] */
  uInt status=0;	      /* accumulator */
  Int  residue; 	      /* work */

  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  /* Handle special values except lhs infinite */
  if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))
    decNaNs(res, lhs, rhs, set, &status);
    /* rhs must be an integer */
   else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)
    status=DEC_Invalid_operation;
   else {
    /* lhs is a number; rhs is a finite with q==0 */
    reqexp=decGetInt(rhs);		     /* [cannot fail] */
    if (reqexp==BADINT			     /* something bad .. */
     || reqexp==BIGODD || reqexp==BIGEVEN    /* .. very big .. */
     || abs(reqexp)>(2*(set->digits+set->emax))) /* .. or out of range */
      status=DEC_Invalid_operation;
     else {				     /* rhs is OK */
      decNumberCopy(res, lhs);		     /* all done if infinite lhs */
      if (!decNumberIsInfinite(res)) {	     /* prepare to scale */
	res->exponent+=reqexp;		     /* adjust the exponent */
	residue=0;
	decFinalize(res, set, &residue, &status); /* .. and check */
	} /* finite LHS */
      } /* rhs OK */
    } /* rhs finite */
  if (status!=0) decStatus(res, status, set);
  return res;
  } /* decNumberScaleB */

/* ------------------------------------------------------------------ */
/* decNumberShift -- shift the coefficient of a Number left or right  */
/*								      */
/*   This computes C = A << B or C = A >> -B  (in base ten).	      */
/*								      */
/*   res is C, the result.  C may be A and/or B (e.g., X=X<<X)	      */
/*   lhs is A							      */
/*   rhs is B, the number of digits to shift (-ve to right)	      */
/*   set is the context 					      */
/*								      */
/* The digits of the coefficient of A are shifted to the left (if B   */
/* is positive) or to the right (if B is negative) without adjusting  */
/* the exponent or the sign of A.				      */
/*								      */
/* B must be an integer (q=0) and in the range -set->digits through   */
/* +set->digits.						      */
/* C must have space for set->digits digits.			      */
/* NaNs are propagated as usual.  Infinities are unaffected (but      */
/* B must be valid).  No status is set unless B is invalid or an      */
/* operand is an sNaN.						      */
/* ------------------------------------------------------------------ */
decNumber * decNumberShift(decNumber *res, const decNumber *lhs,
			   const decNumber *rhs, decContext *set) {
  uInt status=0;	      /* accumulator */
  Int  shift;		      /* rhs as an Int */

  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  /* NaNs propagate as normal */
  if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))
    decNaNs(res, lhs, rhs, set, &status);
   /* rhs must be an integer */
   else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)
    status=DEC_Invalid_operation;
   else { /* both numeric, rhs is an integer */
    shift=decGetInt(rhs);		     /* [cannot fail] */
    if (shift==BADINT			     /* something bad .. */
     || shift==BIGODD || shift==BIGEVEN      /* .. very big .. */
     || abs(shift)>set->digits) 	     /* .. or out of range */
      status=DEC_Invalid_operation;
     else {				     /* rhs is OK */
      decNumberCopy(res, lhs);
      if (shift!=0 && !decNumberIsInfinite(res)) { /* something to do */
	if (shift>0) {			     /* to left */
	  if (shift==set->digits) {	     /* removing all */
	    *res->lsu=0;		     /* so place 0 */
	    res->digits=1;		     /* .. */
	    }
	   else {			     /* */
	    /* first remove leading digits if necessary */
	    if (res->digits+shift>set->digits) {
	      decDecap(res, res->digits+shift-set->digits);
	      /* that updated res->digits; may have gone to 1 (for a */
	      /* single digit or for zero */
	      }
	    if (res->digits>1 || *res->lsu)  /* if non-zero.. */
	      res->digits=decShiftToMost(res->lsu, res->digits, shift);
	    } /* partial left */
	  } /* left */
	 else { /* to right */
	  if (-shift>=res->digits) {	     /* discarding all */
	    *res->lsu=0;		     /* so place 0 */
	    res->digits=1;		     /* .. */
	    }
	   else {
	    decShiftToLeast(res->lsu, D2U(res->digits), -shift);
	    res->digits-=(-shift);
	    }
	  } /* to right */
	} /* non-0 non-Inf shift */
      } /* rhs OK */
    } /* numerics */
  if (status!=0) decStatus(res, status, set);
  return res;
  } /* decNumberShift */

/* ------------------------------------------------------------------ */
/* decNumberSquareRoot -- square root operator			      */
/*								      */
/*   This computes C = squareroot(A)				      */
/*								      */
/*   res is C, the result.  C may be A				      */
/*   rhs is A							      */
/*   set is the context; note that rounding mode has no effect	      */
/*								      */
/* C must have space for set->digits digits.			      */
/* ------------------------------------------------------------------ */
/* This uses the following varying-precision algorithm in:	      */
/*								      */
/*   Properly Rounded Variable Precision Square Root, T. E. Hull and  */
/*   A. Abrham, ACM Transactions on Mathematical Software, Vol 11 #3, */
/*   pp229-237, ACM, September 1985.				      */
/*								      */
/* The square-root is calculated using Newton's method, after which   */
/* a check is made to ensure the result is correctly rounded.	      */
/*								      */
/* % [Reformatted original Numerical Turing source code follows.]     */
/* function sqrt(x : real) : real				      */
/* % sqrt(x) returns the properly rounded approximation to the square */
/* % root of x, in the precision of the calling environment, or it    */
/* % fails if x < 0.						      */
/* % t e hull and a abrham, august, 1984			      */
/* if x <= 0 then						      */
/*   if x < 0 then						      */
/*     assert false						      */
/*   else							      */
/*     result 0 						      */
/*   end if							      */
/* end if							      */
/* var f := setexp(x, 0)  % fraction part of x	 [0.1 <= x < 1]       */
/* var e := getexp(x)	  % exponent part of x			      */
/* var approx : real						      */
/* if e mod 2 = 0  then 					      */
/*   approx := .259 + .819 * f	 % approx to root of f		      */
/* else 							      */
/*   f := f/l0			 % adjustments			      */
/*   e := e + 1 		 %   for odd			      */
/*   approx := .0819 + 2.59 * f  %   exponent			      */
/* end if							      */
/*								      */
/* var p:= 3							      */
/* const maxp := currentprecision + 2				      */
/* loop 							      */
/*   p := min(2*p - 2, maxp)	 % p = 4,6,10, . . . , maxp	      */
/*   precision p						      */
/*   approx := .5 * (approx + f/approx) 			      */
/*   exit when p = maxp 					      */
/* end loop							      */
/*								      */
/* % approx is now within 1 ulp of the properly rounded square root   */
/* % of f; to ensure proper rounding, compare squares of (approx -    */
/* % l/2 ulp) and (approx + l/2 ulp) with f.			      */
/* p := currentprecision					      */
/* begin							      */
/*   precision p + 2						      */
/*   const approxsubhalf := approx - setexp(.5, -p)		      */
/*   if mulru(approxsubhalf, approxsubhalf) > f then		      */
/*     approx := approx - setexp(.l, -p + 1)			      */
/*   else							      */
/*     const approxaddhalf := approx + setexp(.5, -p)		      */
/*     if mulrd(approxaddhalf, approxaddhalf) < f then		      */
/*	 approx := approx + setexp(.l, -p + 1)			      */
/*     end if							      */
/*   end if							      */
/* end								      */
/* result setexp(approx, e div 2)  % fix exponent		      */
/* end sqrt							      */
/* ------------------------------------------------------------------ */
decNumber * decNumberSquareRoot(decNumber *res, const decNumber *rhs,
				decContext *set) {
  decContext workset, approxset;   /* work contexts */
  decNumber dzero;		   /* used for constant zero */
  Int  maxp;			   /* largest working precision */
  Int  workp;			   /* working precision */
  Int  residue=0;		   /* rounding residue */
  uInt status=0, ignore=0;	   /* status accumulators */
  uInt rstatus; 		   /* .. */
  Int  exp;			   /* working exponent */
  Int  ideal;			   /* ideal (preferred) exponent */
  Int  needbytes;		   /* work */
  Int  dropped; 		   /* .. */

  #if DECSUBSET
  decNumber *allocrhs=NULL;	   /* non-NULL if rounded rhs allocated */
  #endif
  /* buffer for f [needs +1 in case DECBUFFER 0] */
  decNumber buff[D2N(DECBUFFER+1)];
  /* buffer for a [needs +2 to match likely maxp] */
  decNumber bufa[D2N(DECBUFFER+2)];
  /* buffer for temporary, b [must be same size as a] */
  decNumber bufb[D2N(DECBUFFER+2)];
  decNumber *allocbuff=NULL;	   /* -> allocated buff, iff allocated */
  decNumber *allocbufa=NULL;	   /* -> allocated bufa, iff allocated */
  decNumber *allocbufb=NULL;	   /* -> allocated bufb, iff allocated */
  decNumber *f=buff;		   /* reduced fraction */
  decNumber *a=bufa;		   /* approximation to result */
  decNumber *b=bufb;		   /* intermediate result */
  /* buffer for temporary variable, up to 3 digits */
  decNumber buft[D2N(3)];
  decNumber *t=buft;		   /* up-to-3-digit constant or work */

  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  do {				   /* protect allocated storage */
    #if DECSUBSET
    if (!set->extended) {
      /* reduce operand and set lostDigits status, as needed */
      if (rhs->digits>set->digits) {
	allocrhs=decRoundOperand(rhs, set, &status);
	if (allocrhs==NULL) break;
	/* [Note: 'f' allocation below could reuse this buffer if */
	/* used, but as this is rare they are kept separate for clarity.] */
	rhs=allocrhs;
	}
      }
    #endif
    /* [following code does not require input rounding] */

    /* handle infinities and NaNs */
    if (SPECIALARG) {
      if (decNumberIsInfinite(rhs)) {	      /* an infinity */
	if (decNumberIsNegative(rhs)) status|=DEC_Invalid_operation;
	 else decNumberCopy(res, rhs);	      /* +Infinity */
	}
       else decNaNs(res, rhs, NULL, set, &status); /* a NaN */
      break;
      }

    /* calculate the ideal (preferred) exponent [floor(exp/2)] */
    /* [It would be nicer to write: ideal=rhs->exponent>>1, but this */
    /* generates a compiler warning.  Generated code is the same.] */
    ideal=(rhs->exponent&~1)/2; 	/* target */

    /* handle zeros */
    if (ISZERO(rhs)) {
      decNumberCopy(res, rhs);		/* could be 0 or -0 */
      res->exponent=ideal;		/* use the ideal [safe] */
      /* use decFinish to clamp any out-of-range exponent, etc. */
      decFinish(res, set, &residue, &status);
      break;
      }

    /* any other -x is an oops */
    if (decNumberIsNegative(rhs)) {
      status|=DEC_Invalid_operation;
      break;
      }

    /* space is needed for three working variables */
    /*	 f -- the same precision as the RHS, reduced to 0.01->0.99... */
    /*	 a -- Hull's approximation -- precision, when assigned, is */
    /*	      currentprecision+1 or the input argument precision, */
    /*	      whichever is larger (+2 for use as temporary) */
    /*	 b -- intermediate temporary result (same size as a) */
    /* if any is too long for local storage, then allocate */
    workp=MAXI(set->digits+1, rhs->digits);  /* actual rounding precision */
    workp=MAXI(workp, 7);		     /* at least 7 for low cases */
    maxp=workp+2;			     /* largest working precision */

    needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);
    if (needbytes>(Int)sizeof(buff)) {
      allocbuff=(decNumber *)malloc(needbytes);
      if (allocbuff==NULL) {  /* hopeless -- abandon */
	status|=DEC_Insufficient_storage;
	break;}
      f=allocbuff;	      /* use the allocated space */
      }
    /* a and b both need to be able to hold a maxp-length number */
    needbytes=sizeof(decNumber)+(D2U(maxp)-1)*sizeof(Unit);
    if (needbytes>(Int)sizeof(bufa)) {		  /* [same applies to b] */
      allocbufa=(decNumber *)malloc(needbytes);
      allocbufb=(decNumber *)malloc(needbytes);
      if (allocbufa==NULL || allocbufb==NULL) {   /* hopeless */
	status|=DEC_Insufficient_storage;
	break;}
      a=allocbufa;	      /* use the allocated spaces */
      b=allocbufb;	      /* .. */
      }

    /* copy rhs -> f, save exponent, and reduce so 0.1 <= f < 1 */
    decNumberCopy(f, rhs);
    exp=f->exponent+f->digits;		     /* adjusted to Hull rules */
    f->exponent=-(f->digits);		     /* to range */

    /* set up working context */
    decContextDefault(&workset, DEC_INIT_DECIMAL64);
    workset.emax=DEC_MAX_EMAX;
    workset.emin=DEC_MIN_EMIN;

    /* [Until further notice, no error is possible and status bits */
    /* (Rounded, etc.) should be ignored, not accumulated.] */

    /* Calculate initial approximation, and allow for odd exponent */
    workset.digits=workp;		     /* p for initial calculation */
    t->bits=0; t->digits=3;
    a->bits=0; a->digits=3;
    if ((exp & 1)==0) { 		     /* even exponent */
      /* Set t=0.259, a=0.819 */
      t->exponent=-3;
      a->exponent=-3;
      #if DECDPUN>=3
	t->lsu[0]=259;
	a->lsu[0]=819;
      #elif DECDPUN==2
	t->lsu[0]=59; t->lsu[1]=2;
	a->lsu[0]=19; a->lsu[1]=8;
      #else
	t->lsu[0]=9; t->lsu[1]=5; t->lsu[2]=2;
	a->lsu[0]=9; a->lsu[1]=1; a->lsu[2]=8;
      #endif
      }
     else {				     /* odd exponent */
      /* Set t=0.0819, a=2.59 */
      f->exponent--;			     /* f=f/10 */
      exp++;				     /* e=e+1 */
      t->exponent=-4;
      a->exponent=-2;
      #if DECDPUN>=3
	t->lsu[0]=819;
	a->lsu[0]=259;
      #elif DECDPUN==2
	t->lsu[0]=19; t->lsu[1]=8;
	a->lsu[0]=59; a->lsu[1]=2;
      #else
	t->lsu[0]=9; t->lsu[1]=1; t->lsu[2]=8;
	a->lsu[0]=9; a->lsu[1]=5; a->lsu[2]=2;
      #endif
      }

    decMultiplyOp(a, a, f, &workset, &ignore);	  /* a=a*f */
    decAddOp(a, a, t, &workset, 0, &ignore);	  /* ..+t */
    /* [a is now the initial approximation for sqrt(f), calculated with */
    /* currentprecision, which is also a's precision.] */

    /* the main calculation loop */
    decNumberZero(&dzero);		     /* make 0 */
    decNumberZero(t);			     /* set t = 0.5 */
    t->lsu[0]=5;			     /* .. */
    t->exponent=-1;			     /* .. */
    workset.digits=3;			     /* initial p */
    for (; workset.digits<maxp;) {
      /* set p to min(2*p - 2, maxp)  [hence 3; or: 4, 6, 10, ... , maxp] */
      workset.digits=MINI(workset.digits*2-2, maxp);
      /* a = 0.5 * (a + f/a) */
      /* [calculated at p then rounded to currentprecision] */
      decDivideOp(b, f, a, &workset, DIVIDE, &ignore); /* b=f/a */
      decAddOp(b, b, a, &workset, 0, &ignore);	       /* b=b+a */
      decMultiplyOp(a, b, t, &workset, &ignore);       /* a=b*0.5 */
      } /* loop */

    /* Here, 0.1 <= a < 1 [Hull], and a has maxp digits */
    /* now reduce to length, etc.; this needs to be done with a */
    /* having the correct exponent so as to handle subnormals */
    /* correctly */
    approxset=*set;			     /* get emin, emax, etc. */
    approxset.round=DEC_ROUND_HALF_EVEN;
    a->exponent+=exp/2; 		     /* set correct exponent */
    rstatus=0;				     /* clear status */
    residue=0;				     /* .. and accumulator */
    decCopyFit(a, a, &approxset, &residue, &rstatus);  /* reduce (if needed) */
    decFinish(a, &approxset, &residue, &rstatus);      /* clean and finalize */

    /* Overflow was possible if the input exponent was out-of-range, */
    /* in which case quit */
    if (rstatus&DEC_Overflow) {
      status=rstatus;			     /* use the status as-is */
      decNumberCopy(res, a);		     /* copy to result */
      break;
      }

    /* Preserve status except Inexact/Rounded */
    status|=(rstatus & ~(DEC_Rounded|DEC_Inexact));

    /* Carry out the Hull correction */
    a->exponent-=exp/2; 		     /* back to 0.1->1 */

    /* a is now at final precision and within 1 ulp of the properly */
    /* rounded square root of f; to ensure proper rounding, compare */
    /* squares of (a - l/2 ulp) and (a + l/2 ulp) with f. */
    /* Here workset.digits=maxp and t=0.5, and a->digits determines */
    /* the ulp */
    workset.digits--;				  /* maxp-1 is OK now */
    t->exponent=-a->digits-1;			  /* make 0.5 ulp */
    decAddOp(b, a, t, &workset, DECNEG, &ignore); /* b = a - 0.5 ulp */
    workset.round=DEC_ROUND_UP;
    decMultiplyOp(b, b, b, &workset, &ignore);	  /* b = mulru(b, b) */
    decCompareOp(b, f, b, &workset, COMPARE, &ignore); /* b ? f, reversed */
    if (decNumberIsNegative(b)) {		  /* f < b [i.e., b > f] */
      /* this is the more common adjustment, though both are rare */
      t->exponent++;				  /* make 1.0 ulp */
      t->lsu[0]=1;				  /* .. */
      decAddOp(a, a, t, &workset, DECNEG, &ignore); /* a = a - 1 ulp */
      /* assign to approx [round to length] */
      approxset.emin-=exp/2;			  /* adjust to match a */
      approxset.emax-=exp/2;
      decAddOp(a, &dzero, a, &approxset, 0, &ignore);
      }
     else {
      decAddOp(b, a, t, &workset, 0, &ignore);	  /* b = a + 0.5 ulp */
      workset.round=DEC_ROUND_DOWN;
      decMultiplyOp(b, b, b, &workset, &ignore);  /* b = mulrd(b, b) */
      decCompareOp(b, b, f, &workset, COMPARE, &ignore);   /* b ? f */
      if (decNumberIsNegative(b)) {		  /* b < f */
	t->exponent++;				  /* make 1.0 ulp */
	t->lsu[0]=1;				  /* .. */
	decAddOp(a, a, t, &workset, 0, &ignore);  /* a = a + 1 ulp */
	/* assign to approx [round to length] */
	approxset.emin-=exp/2;			  /* adjust to match a */
	approxset.emax-=exp/2;
	decAddOp(a, &dzero, a, &approxset, 0, &ignore);
	}
      }
    /* [no errors are possible in the above, and rounding/inexact during */
    /* estimation are irrelevant, so status was not accumulated] */

    /* Here, 0.1 <= a < 1  (still), so adjust back */
    a->exponent+=exp/2; 		     /* set correct exponent */

    /* count droppable zeros [after any subnormal rounding] by */
    /* trimming a copy */
    decNumberCopy(b, a);
    decTrim(b, set, 1, 1, &dropped);	     /* [drops trailing zeros] */

    /* Set Inexact and Rounded.  The answer can only be exact if */
    /* it is short enough so that squaring it could fit in workp */
    /* digits, so this is the only (relatively rare) condition that */
    /* a careful check is needed */
    if (b->digits*2-1 > workp) {	     /* cannot fit */
      status|=DEC_Inexact|DEC_Rounded;
      }
     else {				     /* could be exact/unrounded */
      uInt mstatus=0;			     /* local status */
      decMultiplyOp(b, b, b, &workset, &mstatus); /* try the multiply */
      if (mstatus&DEC_Overflow) {	     /* result just won't fit */
	status|=DEC_Inexact|DEC_Rounded;
	}
       else {				     /* plausible */
	decCompareOp(t, b, rhs, &workset, COMPARE, &mstatus); /* b ? rhs */
	if (!ISZERO(t)) status|=DEC_Inexact|DEC_Rounded; /* not equal */
	 else { 			     /* is Exact */
	  /* here, dropped is the count of trailing zeros in 'a' */
	  /* use closest exponent to ideal... */
	  Int todrop=ideal-a->exponent;      /* most that can be dropped */
	  if (todrop<0) status|=DEC_Rounded; /* ideally would add 0s */
	   else {			     /* unrounded */
	    /* there are some to drop, but emax may not allow all */
	    Int maxexp=set->emax-set->digits+1;
	    Int maxdrop=maxexp-a->exponent;
	    if (todrop>maxdrop && set->clamp) { /* apply clamping */
	      todrop=maxdrop;
	      status|=DEC_Clamped;
	      }
	    if (dropped<todrop) {	     /* clamp to those available */
	      todrop=dropped;
	      status|=DEC_Clamped;
	      }
	    if (todrop>0) {		     /* have some to drop */
	      decShiftToLeast(a->lsu, D2U(a->digits), todrop);
	      a->exponent+=todrop;	     /* maintain numerical value */
	      a->digits-=todrop;	     /* new length */
	      }
	    }
	  }
	}
      }

    /* double-check Underflow, as perhaps the result could not have */
    /* been subnormal (initial argument too big), or it is now Exact */
    if (status&DEC_Underflow) {
      Int ae=rhs->exponent+rhs->digits-1;    /* adjusted exponent */
      /* check if truly subnormal */
      #if DECEXTFLAG			     /* DEC_Subnormal too */
	if (ae>=set->emin*2) status&=~(DEC_Subnormal|DEC_Underflow);
      #else
	if (ae>=set->emin*2) status&=~DEC_Underflow;
      #endif
      /* check if truly inexact */
      if (!(status&DEC_Inexact)) status&=~DEC_Underflow;
      }

    decNumberCopy(res, a);		     /* a is now the result */
    } while(0); 			     /* end protected */

  free(allocbuff);      /* drop any storage used */
  free(allocbufa);      /* .. */
  free(allocbufb);      /* .. */
  #if DECSUBSET
  free(allocrhs);	     /* .. */
  #endif
  if (status!=0) decStatus(res, status, set);/* then report status */
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } /* decNumberSquareRoot */

/* ------------------------------------------------------------------ */
/* decNumberSubtract -- subtract two Numbers			      */
/*								      */
/*   This computes C = A - B					      */
/*								      */
/*   res is C, the result.  C may be A and/or B (e.g., X=X-X)	      */
/*   lhs is A							      */
/*   rhs is B							      */
/*   set is the context 					      */
/*								      */
/* C must have space for set->digits digits.			      */
/* ------------------------------------------------------------------ */
decNumber * decNumberSubtract(decNumber *res, const decNumber *lhs,
			      const decNumber *rhs, decContext *set) {
  uInt status=0;			/* accumulator */

  decAddOp(res, lhs, rhs, set, DECNEG, &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } /* decNumberSubtract */

/* ------------------------------------------------------------------ */
/* decNumberToIntegralExact -- round-to-integral-value with InExact   */
/* decNumberToIntegralValue -- round-to-integral-value		      */
/*								      */
/*   res is the result						      */
/*   rhs is input number					      */
/*   set is the context 					      */
/*								      */
/* res must have space for any value of rhs.			      */
/*								      */
/* This implements the IEEE special operators and therefore treats    */
/* special values as valid.  For finite numbers it returns	      */
/* rescale(rhs, 0) if rhs->exponent is <0.			      */
/* Otherwise the result is rhs (so no error is possible, except for   */
/* sNaN).							      */
/*								      */
/* The context is used for rounding mode and status after sNaN, but   */
/* the digits setting is ignored.  The Exact version will signal      */
/* Inexact if the result differs numerically from rhs; the other      */
/* never signals Inexact.					      */
/* ------------------------------------------------------------------ */
decNumber * decNumberToIntegralExact(decNumber *res, const decNumber *rhs,
				     decContext *set) {
  decNumber dn;
  decContext workset;		   /* working context */
  uInt status=0;		   /* accumulator */

  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  /* handle infinities and NaNs */
  if (SPECIALARG) {
    if (decNumberIsInfinite(rhs)) decNumberCopy(res, rhs); /* an Infinity */
     else decNaNs(res, rhs, NULL, set, &status); /* a NaN */
    }
   else { /* finite */
    /* have a finite number; no error possible (res must be big enough) */
    if (rhs->exponent>=0) return decNumberCopy(res, rhs);
    /* that was easy, but if negative exponent there is work to do... */
    workset=*set;		   /* clone rounding, etc. */
    workset.digits=rhs->digits;    /* no length rounding */
    workset.traps=0;		   /* no traps */
    decNumberZero(&dn); 	   /* make a number with exponent 0 */
    decNumberQuantize(res, rhs, &dn, &workset);
    status|=workset.status;
    }
  if (status!=0) decStatus(res, status, set);
  return res;
  } /* decNumberToIntegralExact */

decNumber * decNumberToIntegralValue(decNumber *res, const decNumber *rhs,
				     decContext *set) {
  decContext workset=*set;	   /* working context */
  workset.traps=0;		   /* no traps */
  decNumberToIntegralExact(res, rhs, &workset);
  /* this never affects set, except for sNaNs; NaN will have been set */
  /* or propagated already, so no need to call decStatus */
  set->status|=workset.status&DEC_Invalid_operation;
  return res;
  } /* decNumberToIntegralValue */

/* ------------------------------------------------------------------ */
/* decNumberXor -- XOR two Numbers, digitwise			      */
/*								      */
/*   This computes C = A ^ B					      */
/*								      */
/*   res is C, the result.  C may be A and/or B (e.g., X=X^X)	      */
/*   lhs is A							      */
/*   rhs is B							      */
/*   set is the context (used for result length and error report)     */
/*								      */
/* C must have space for set->digits digits.			      */
/*								      */
/* Logical function restrictions apply (see above); a NaN is	      */
/* returned with Invalid_operation if a restriction is violated.      */
/* ------------------------------------------------------------------ */
decNumber * decNumberXor(decNumber *res, const decNumber *lhs,
			 const decNumber *rhs, decContext *set) {
  const Unit *ua, *ub;			/* -> operands */
  const Unit *msua, *msub;		/* -> operand msus */
  Unit	*uc, *msuc;			/* -> result and its msu */
  Int	msudigs;			/* digits in res msu */
  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)
   || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
    decStatus(res, DEC_Invalid_operation, set);
    return res;
    }
  /* operands are valid */
  ua=lhs->lsu;				/* bottom-up */
  ub=rhs->lsu;				/* .. */
  uc=res->lsu;				/* .. */
  msua=ua+D2U(lhs->digits)-1;		/* -> msu of lhs */
  msub=ub+D2U(rhs->digits)-1;		/* -> msu of rhs */
  msuc=uc+D2U(set->digits)-1;		/* -> msu of result */
  msudigs=MSUDIGITS(set->digits);	/* [faster than remainder] */
  for (; uc<=msuc; ua++, ub++, uc++) {	/* Unit loop */
    Unit a, b;				/* extract units */
    if (ua>msua) a=0;
     else a=*ua;
    if (ub>msub) b=0;
     else b=*ub;
    *uc=0;				/* can now write back */
    if (a|b) {				/* maybe 1 bits to examine */
      Int i, j;
      /* This loop could be unrolled and/or use BIN2BCD tables */
      for (i=0; i<DECDPUN; i++) {
	if ((a^b)&1) *uc=*uc+(Unit)powers[i];	  /* effect XOR */
	j=a%10;
	a=a/10;
	j|=b%10;
	b=b/10;
	if (j>1) {
	  decStatus(res, DEC_Invalid_operation, set);
	  return res;
	  }
	if (uc==msuc && i==msudigs-1) break;	  /* just did final digit */
	} /* each digit */
      } /* non-zero */
    } /* each unit */
  /* [here uc-1 is the msu of the result] */
  res->digits=decGetDigits(res->lsu, uc-res->lsu);
  res->exponent=0;			/* integer */
  res->bits=0;				/* sign=0 */
  return res;  /* [no status to set] */
  } /* decNumberXor */


/* ================================================================== */
/* Utility routines						      */
/* ================================================================== */

/* ------------------------------------------------------------------ */
/* decNumberClass -- return the decClass of a decNumber 	      */
/*   dn -- the decNumber to test				      */
/*   set -- the context to use for Emin 			      */
/*   returns the decClass enum					      */
/* ------------------------------------------------------------------ */
enum decClass decNumberClass(const decNumber *dn, decContext *set) {
  if (decNumberIsSpecial(dn)) {
    if (decNumberIsQNaN(dn)) return DEC_CLASS_QNAN;
    if (decNumberIsSNaN(dn)) return DEC_CLASS_SNAN;
    /* must be an infinity */
    if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_INF;
    return DEC_CLASS_POS_INF;
    }
  /* is finite */
  if (decNumberIsNormal(dn, set)) { /* most common */
    if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_NORMAL;
    return DEC_CLASS_POS_NORMAL;
    }
  /* is subnormal or zero */
  if (decNumberIsZero(dn)) {	/* most common */
    if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_ZERO;
    return DEC_CLASS_POS_ZERO;
    }
  if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_SUBNORMAL;
  return DEC_CLASS_POS_SUBNORMAL;
  } /* decNumberClass */

/* ------------------------------------------------------------------ */
/* decNumberClassToString -- convert decClass to a string	      */
/*								      */
/*  eclass is a valid decClass					      */
/*  returns a constant string describing the class (max 13+1 chars)   */
/* ------------------------------------------------------------------ */
const char *decNumberClassToString(enum decClass eclass) {
  if (eclass==DEC_CLASS_POS_NORMAL)    return DEC_ClassString_PN;
  if (eclass==DEC_CLASS_NEG_NORMAL)    return DEC_ClassString_NN;
  if (eclass==DEC_CLASS_POS_ZERO)      return DEC_ClassString_PZ;
  if (eclass==DEC_CLASS_NEG_ZERO)      return DEC_ClassString_NZ;
  if (eclass==DEC_CLASS_POS_SUBNORMAL) return DEC_ClassString_PS;
  if (eclass==DEC_CLASS_NEG_SUBNORMAL) return DEC_ClassString_NS;
  if (eclass==DEC_CLASS_POS_INF)       return DEC_ClassString_PI;
  if (eclass==DEC_CLASS_NEG_INF)       return DEC_ClassString_NI;
  if (eclass==DEC_CLASS_QNAN)	       return DEC_ClassString_QN;
  if (eclass==DEC_CLASS_SNAN)	       return DEC_ClassString_SN;
  return DEC_ClassString_UN;	       /* Unknown */
  } /* decNumberClassToString */

/* ------------------------------------------------------------------ */
/* decNumberCopy -- copy a number				      */
/*								      */
/*   dest is the target decNumber				      */
/*   src  is the source decNumber				      */
/*   returns dest						      */
/*								      */
/* (dest==src is allowed and is a no-op)			      */
/* All fields are updated as required.	This is a utility operation,  */
/* so special values are unchanged and no error is possible.	      */
/* ------------------------------------------------------------------ */
decNumber * decNumberCopy(decNumber *dest, const decNumber *src) {

  #if DECCHECK
  if (src==NULL) return decNumberZero(dest);
  #endif

  if (dest==src) return dest;		     /* no copy required */

  /* Use explicit assignments here as structure assignment could copy */
  /* more than just the lsu (for small DECDPUN).  This would not affect */
  /* the value of the results, but could disturb test harness spill */
  /* checking. */
  dest->bits=src->bits;
  dest->exponent=src->exponent;
  dest->digits=src->digits;
  dest->lsu[0]=src->lsu[0];
  if (src->digits>DECDPUN) {		     /* more Units to come */
    const Unit *smsup, *s;		     /* work */
    Unit  *d;				     /* .. */
    /* memcpy for the remaining Units would be safe as they cannot */
    /* overlap.  However, this explicit loop is faster in short cases. */
    d=dest->lsu+1;			     /* -> first destination */
    smsup=src->lsu+D2U(src->digits);	     /* -> source msu+1 */
    for (s=src->lsu+1; s<smsup; s++, d++) *d=*s;
    }
  return dest;
  } /* decNumberCopy */

/* ------------------------------------------------------------------ */
/* decNumberCopyAbs -- quiet absolute value operator		      */
/*								      */
/*   This sets C = abs(A)					      */
/*								      */
/*   res is C, the result.  C may be A				      */
/*   rhs is A							      */
/*								      */
/* C must have space for set->digits digits.			      */
/* No exception or error can occur; this is a quiet bitwise operation.*/
/* See also decNumberAbs for a checking version of this.	      */
/* ------------------------------------------------------------------ */
decNumber * decNumberCopyAbs(decNumber *res, const decNumber *rhs) {
  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res;
  #endif
  decNumberCopy(res, rhs);
  res->bits&=~DECNEG;			/* turn off sign */
  return res;
  } /* decNumberCopyAbs */

/* ------------------------------------------------------------------ */
/* decNumberCopyNegate -- quiet negate value operator		      */
/*								      */
/*   This sets C = negate(A)					      */
/*								      */
/*   res is C, the result.  C may be A				      */
/*   rhs is A							      */
/*								      */
/* C must have space for set->digits digits.			      */
/* No exception or error can occur; this is a quiet bitwise operation.*/
/* See also decNumberMinus for a checking version of this.	      */
/* ------------------------------------------------------------------ */
decNumber * decNumberCopyNegate(decNumber *res, const decNumber *rhs) {
  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res;
  #endif
  decNumberCopy(res, rhs);
  res->bits^=DECNEG;			/* invert the sign */
  return res;
  } /* decNumberCopyNegate */

/* ------------------------------------------------------------------ */
/* decNumberCopySign -- quiet copy and set sign operator	      */
/*								      */
/*   This sets C = A with the sign of B 			      */
/*								      */
/*   res is C, the result.  C may be A				      */
/*   lhs is A							      */
/*   rhs is B							      */
/*								      */
/* C must have space for set->digits digits.			      */
/* No exception or error can occur; this is a quiet bitwise operation.*/
/* ------------------------------------------------------------------ */
decNumber * decNumberCopySign(decNumber *res, const decNumber *lhs,
			      const decNumber *rhs) {
  uByte sign;				/* rhs sign */
  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res;
  #endif
  sign=rhs->bits & DECNEG;		/* save sign bit */
  decNumberCopy(res, lhs);
  res->bits&=~DECNEG;			/* clear the sign */
  res->bits|=sign;			/* set from rhs */
  return res;
  } /* decNumberCopySign */

/* ------------------------------------------------------------------ */
/* decNumberGetBCD -- get the coefficient in BCD8		      */
/*   dn is the source decNumber 				      */
/*   bcd is the uInt array that will receive dn->digits BCD bytes,    */
/*     most-significant at offset 0				      */
/*   returns bcd						      */
/*								      */
/* bcd must have at least dn->digits bytes.  No error is possible; if */
/* dn is a NaN or Infinite, digits must be 1 and the coefficient 0.   */
/* ------------------------------------------------------------------ */
uByte * decNumberGetBCD(const decNumber *dn, uByte *bcd) {
  uByte *ub=bcd+dn->digits-1;	   /* -> lsd */
  const Unit *up=dn->lsu;	   /* Unit pointer, -> lsu */

  #if DECDPUN==1		   /* trivial simple copy */
    for (; ub>=bcd; ub--, up++) *ub=*up;
  #else 			   /* chopping needed */
    uInt u=*up; 		   /* work */
    uInt cut=DECDPUN;		   /* downcounter through unit */
    for (; ub>=bcd; ub--) {
      *ub=(uByte)(u%10);	   /* [*6554 trick inhibits, here] */
      u=u/10;
      cut--;
      if (cut>0) continue;	   /* more in this unit */
      up++;
      u=*up;
      cut=DECDPUN;
      }
  #endif
  return bcd;
  } /* decNumberGetBCD */

/* ------------------------------------------------------------------ */
/* decNumberSetBCD -- set (replace) the coefficient from BCD8	      */
/*   dn is the target decNumber 				      */
/*   bcd is the uInt array that will source n BCD bytes, most-	      */
/*     significant at offset 0					      */
/*   n is the number of digits in the source BCD array (bcd)	      */
/*   returns dn 						      */
/*								      */
/* dn must have space for at least n digits.  No error is possible;   */
/* if dn is a NaN, or Infinite, or is to become a zero, n must be 1   */
/* and bcd[0] zero.						      */
/* ------------------------------------------------------------------ */
decNumber * decNumberSetBCD(decNumber *dn, const uByte *bcd, uInt n) {
  Unit *up=dn->lsu+D2U(dn->digits)-1;	/* -> msu [target pointer] */
  const uByte *ub=bcd;			/* -> source msd */

  #if DECDPUN==1			/* trivial simple copy */
    for (; ub<bcd+n; ub++, up--) *up=*ub;
  #else 				/* some assembly needed */
    /* calculate how many digits in msu, and hence first cut */
    Int cut=MSUDIGITS(n);		/* [faster than remainder] */
    for (;up>=dn->lsu; up--) {		/* each Unit from msu */
      *up=0;				/* will take <=DECDPUN digits */
      for (; cut>0; ub++, cut--) *up=X10(*up)+*ub;
      cut=DECDPUN;			/* next Unit has all digits */
      }
  #endif
  dn->digits=n; 			/* set digit count */
  return dn;
  } /* decNumberSetBCD */

/* ------------------------------------------------------------------ */
/* decNumberIsNormal -- test normality of a decNumber		      */
/*   dn is the decNumber to test				      */
/*   set is the context to use for Emin 			      */
/*   returns 1 if |dn| is finite and >=Nmin, 0 otherwise	      */
/* ------------------------------------------------------------------ */
Int decNumberIsNormal(const decNumber *dn, decContext *set) {
  Int ae;				/* adjusted exponent */
  #if DECCHECK
  if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
  #endif

  if (decNumberIsSpecial(dn)) return 0; /* not finite */
  if (decNumberIsZero(dn)) return 0;	/* not non-zero */

  ae=dn->exponent+dn->digits-1; 	/* adjusted exponent */
  if (ae<set->emin) return 0;		/* is subnormal */
  return 1;
  } /* decNumberIsNormal */

/* ------------------------------------------------------------------ */
/* decNumberIsSubnormal -- test subnormality of a decNumber	      */
/*   dn is the decNumber to test				      */
/*   set is the context to use for Emin 			      */
/*   returns 1 if |dn| is finite, non-zero, and <Nmin, 0 otherwise    */
/* ------------------------------------------------------------------ */
Int decNumberIsSubnormal(const decNumber *dn, decContext *set) {
  Int ae;				/* adjusted exponent */
  #if DECCHECK
  if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
  #endif

  if (decNumberIsSpecial(dn)) return 0; /* not finite */
  if (decNumberIsZero(dn)) return 0;	/* not non-zero */

  ae=dn->exponent+dn->digits-1; 	/* adjusted exponent */
  if (ae<set->emin) return 1;		/* is subnormal */
  return 0;
  } /* decNumberIsSubnormal */

/* ------------------------------------------------------------------ */
/* decNumberTrim -- remove insignificant zeros			      */
/*								      */
/*   dn is the number to trim					      */
/*   returns dn 						      */
/*								      */
/* All fields are updated as required.	This is a utility operation,  */
/* so special values are unchanged and no error is possible.  The     */
/* zeros are removed unconditionally.				      */
/* ------------------------------------------------------------------ */
decNumber * decNumberTrim(decNumber *dn) {
  Int  dropped; 		   /* work */
  decContext set;		   /* .. */
  #if DECCHECK
  if (decCheckOperands(DECUNRESU, DECUNUSED, dn, DECUNCONT)) return dn;
  #endif
  decContextDefault(&set, DEC_INIT_BASE);    /* clamp=0 */
  return decTrim(dn, &set, 0, 1, &dropped);
  } /* decNumberTrim */

/* ------------------------------------------------------------------ */
/* decNumberVersion -- return the name and version of this module     */
/*								      */
/* No error is possible.					      */
/* ------------------------------------------------------------------ */
const char * decNumberVersion(void) {
  return DECVERSION;
  } /* decNumberVersion */

/* ------------------------------------------------------------------ */
/* decNumberZero -- set a number to 0				      */
/*								      */
/*   dn is the number to set, with space for one digit		      */
/*   returns dn 						      */
/*								      */
/* No error is possible.					      */
/* ------------------------------------------------------------------ */
/* Memset is not used as it is much slower in some environments. */
decNumber * decNumberZero(decNumber *dn) {

  #if DECCHECK
  if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn;
  #endif

  dn->bits=0;
  dn->exponent=0;
  dn->digits=1;
  dn->lsu[0]=0;
  return dn;
  } /* decNumberZero */

/* ================================================================== */
/* Local routines						      */
/* ================================================================== */

/* ------------------------------------------------------------------ */
/* decToString -- lay out a number into a string		      */
/*								      */
/*   dn     is the number to lay out				      */
/*   string is where to lay out the number			      */
/*   eng    is 1 if Engineering, 0 if Scientific		      */
/*								      */
/* string must be at least dn->digits+14 characters long	      */
/* No error is possible.					      */
/*								      */
/* Note that this routine can generate a -0 or 0.000.  These are      */
/* never generated in subset to-number or arithmetic, but can occur   */
/* in non-subset arithmetic (e.g., -1*0 or 1.234-1.234).	      */
/* ------------------------------------------------------------------ */
/* If DECCHECK is enabled the string "?" is returned if a number is */
/* invalid. */
static void decToString(const decNumber *dn, char *string, Flag eng) {
  Int exp=dn->exponent;       /* local copy */
  Int e;		      /* E-part value */
  Int pre;		      /* digits before the '.' */
  Int cut;		      /* for counting digits in a Unit */
  char *c=string;	      /* work [output pointer] */
  const Unit *up=dn->lsu+D2U(dn->digits)-1; /* -> msu [input pointer] */
  uInt u, pow;		      /* work */

  #if DECCHECK
  if (decCheckOperands(DECUNRESU, dn, DECUNUSED, DECUNCONT)) {
    strcpy(string, "?");
    return;}
  #endif

  if (decNumberIsNegative(dn)) {   /* Negatives get a minus */
    *c='-';
    c++;
    }
  if (dn->bits&DECSPECIAL) {	   /* Is a special value */
    if (decNumberIsInfinite(dn)) {
      strcpy(c,   "Inf");
      strcpy(c+3, "inity");
      return;}
    /* a NaN */
    if (dn->bits&DECSNAN) {	   /* signalling NaN */
      *c='s';
      c++;
      }
    strcpy(c, "NaN");
    c+=3;			   /* step past */
    /* if not a clean non-zero coefficient, that's all there is in a */
    /* NaN string */
    if (exp!=0 || (*dn->lsu==0 && dn->digits==1)) return;
    /* [drop through to add integer] */
    }

  /* calculate how many digits in msu, and hence first cut */
  cut=MSUDIGITS(dn->digits);	   /* [faster than remainder] */
  cut--;			   /* power of ten for digit */

  if (exp==0) { 		   /* simple integer [common fastpath] */
    for (;up>=dn->lsu; up--) {	   /* each Unit from msu */
      u=*up;			   /* contains DECDPUN digits to lay out */
      for (; cut>=0; c++, cut--) TODIGIT(u, cut, c, pow);
      cut=DECDPUN-1;		   /* next Unit has all digits */
      }
    *c='\0';			   /* terminate the string */
    return;}

  /* non-0 exponent -- assume plain form */
  pre=dn->digits+exp;		   /* digits before '.' */
  e=0;				   /* no E */
  if ((exp>0) || (pre<-5)) {	   /* need exponential form */
    e=exp+dn->digits-1; 	   /* calculate E value */
    pre=1;			   /* assume one digit before '.' */
    if (eng && (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 (!ISZERO(dn)) pre+=adj;
       else {  /* is zero */
	if (adj!=0) {		   /* 0.00Esnn needed */
	  e=e+3;
	  pre=-(2-adj);
	  }
	} /* zero */
      } /* eng */
    } /* need exponent */

  /* lay out the digits of the coefficient, adding 0s and . as needed */
  u=*up;
  if (pre>0) {			   /* xxx.xxx or xx00 (engineering) form */
    Int n=pre;
    for (; pre>0; pre--, c++, cut--) {
      if (cut<0) {		   /* need new Unit */
	if (up==dn->lsu) break;    /* out of input digits (pre>digits) */
	up--;
	cut=DECDPUN-1;
	u=*up;
	}
      TODIGIT(u, cut, c, pow);
      }
    if (n<dn->digits) { 	   /* more to come, after '.' */
      *c='.'; c++;
      for (;; c++, cut--) {
	if (cut<0) {		   /* need new Unit */
	  if (up==dn->lsu) break;  /* out of input digits */
	  up--;
	  cut=DECDPUN-1;
	  u=*up;
	  }
	TODIGIT(u, cut, c, pow);
	}
      }
     else for (; pre>0; pre--, c++) *c='0'; /* 0 padding (for engineering) needed */
    }
   else {			   /* 0.xxx or 0.000xxx form */
    *c='0'; c++;
    *c='.'; c++;
    for (; pre<0; pre++, c++) *c='0';	/* add any 0's after '.' */
    for (; ; c++, cut--) {
      if (cut<0) {		   /* need new Unit */
	if (up==dn->lsu) break;    /* out of input digits */
	up--;
	cut=DECDPUN-1;
	u=*up;
	}
      TODIGIT(u, cut, c, pow);
      }
    }

  /* Finally add the E-part, if needed.  It will never be 0, has a
     base maximum and minimum of +999999999 through -999999999, but
     could range down to -1999999998 for anormal numbers */
  if (e!=0) {
    Flag had=0; 	      /* 1=had non-zero */
    *c='E'; c++;
    *c='+'; c++;	      /* assume positive */
    u=e;		      /* .. */
    if (e<0) {
      *(c-1)='-';	      /* oops, need - */
      u=-e;		      /* uInt, please */
      }
    /* lay out the exponent [_itoa or equivalent is not ANSI C] */
    for (cut=9; cut>=0; cut--) {
      TODIGIT(u, cut, c, pow);
      if (*c=='0' && !had) continue;	/* skip leading zeros */
      had=1;				/* had non-0 */
      c++;				/* step for next */
      } /* cut */
    }
  *c='\0';	    /* terminate the string (all paths) */
  return;
  } /* decToString */

/* ------------------------------------------------------------------ */
/* decAddOp -- add/subtract operation				      */
/*								      */
/*   This computes C = A + B					      */
/*								      */
/*   res is C, the result.  C may be A and/or B (e.g., X=X+X)	      */
/*   lhs is A							      */
/*   rhs is B							      */
/*   set is the context 					      */
/*   negate is DECNEG if rhs should be negated, or 0 otherwise	      */
/*   status accumulates status for the caller			      */
/*								      */
/* C must have space for set->digits digits.			      */
/* Inexact in status must be 0 for correct Exact zero sign in result  */
/* ------------------------------------------------------------------ */
/* If possible, the coefficient is calculated directly into C.	      */
/* However, if: 						      */
/*   -- a digits+1 calculation is needed because the numbers are      */
/*	unaligned and span more than set->digits digits 	      */
/*   -- a carry to digits+1 digits looks possible		      */
/*   -- C is the same as A or B, and the result would destructively   */
/*	overlap the A or B coefficient				      */
/* then the result must be calculated into a temporary buffer.	In    */
/* this case a local (stack) buffer is used if possible, and only if  */
/* too long for that does malloc become the final resort.	      */
/*								      */
/* Misalignment is handled as follows:				      */
/*   Apad: (AExp>BExp) Swap operands and proceed as for BExp>AExp.    */
/*   BPad: Apply the padding by a combination of shifting (whole      */
/*	   units) and multiplication (part units).		      */
/*								      */
/* Addition, especially x=x+1, is speed-critical.		      */
/* The static buffer is larger than might be expected to allow for    */
/* calls from higher-level funtions (notable exp).		      */
/* ------------------------------------------------------------------ */
static decNumber * decAddOp(decNumber *res, const decNumber *lhs,
			    const decNumber *rhs, decContext *set,
			    uByte negate, uInt *status) {
  #if DECSUBSET
  decNumber *alloclhs=NULL;	   /* non-NULL if rounded lhs allocated */
  decNumber *allocrhs=NULL;	   /* .., rhs */
  #endif
  Int	rhsshift;		   /* working shift (in Units) */
  Int	maxdigits;		   /* longest logical length */
  Int	mult;			   /* multiplier */
  Int	residue;		   /* rounding accumulator */
  uByte bits;			   /* result bits */
  Flag	diffsign;		   /* non-0 if arguments have different sign */
  Unit	*acc;			   /* accumulator for result */
  Unit	accbuff[SD2U(DECBUFFER*2+20)]; /* local buffer [*2+20 reduces many */
				   /* allocations when called from */
				   /* other operations, notable exp] */
  Unit	*allocacc=NULL; 	   /* -> allocated acc buffer, iff allocated */
  Int	reqdigits=set->digits;	   /* local copy; requested DIGITS */
  Int	padding;		   /* work */

  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  do {				   /* protect allocated storage */
    #if DECSUBSET
    if (!set->extended) {
      /* reduce operands and set lostDigits status, as needed */
      if (lhs->digits>reqdigits) {
	alloclhs=decRoundOperand(lhs, set, status);
	if (alloclhs==NULL) break;
	lhs=alloclhs;
	}
      if (rhs->digits>reqdigits) {
	allocrhs=decRoundOperand(rhs, set, status);
	if (allocrhs==NULL) break;
	rhs=allocrhs;
	}
      }
    #endif
    /* [following code does not require input rounding] */

    /* note whether signs differ [used all paths] */
    diffsign=(Flag)((lhs->bits^rhs->bits^negate)&DECNEG);

    /* handle infinities and NaNs */
    if (SPECIALARGS) {			/* a special bit set */
      if (SPECIALARGS & (DECSNAN | DECNAN))  /* a NaN */
	decNaNs(res, lhs, rhs, set, status);
       else { /* one or two infinities */
	if (decNumberIsInfinite(lhs)) { /* LHS is infinity */
	  /* two infinities with different signs is invalid */
	  if (decNumberIsInfinite(rhs) && diffsign) {
	    *status|=DEC_Invalid_operation;
	    break;
	    }
	  bits=lhs->bits & DECNEG;	/* get sign from LHS */
	  }
	 else bits=(rhs->bits^negate) & DECNEG;/* RHS must be Infinity */
	bits|=DECINF;
	decNumberZero(res);
	res->bits=bits; 		/* set +/- infinity */
	} /* an infinity */
      break;
      }

    /* Quick exit for add 0s; return the non-0, modified as need be */
    if (ISZERO(lhs)) {
      Int adjust;			/* work */
      Int lexp=lhs->exponent;		/* save in case LHS==RES */
      bits=lhs->bits;			/* .. */
      residue=0;			/* clear accumulator */
      decCopyFit(res, rhs, set, &residue, status); /* copy (as needed) */
      res->bits^=negate;		/* flip if rhs was negated */
      #if DECSUBSET
      if (set->extended) {		/* exponents on zeros count */
      #endif
	/* exponent will be the lower of the two */
	adjust=lexp-res->exponent;	/* adjustment needed [if -ve] */
	if (ISZERO(res)) {		/* both 0: special IEEE 754 rules */
	  if (adjust<0) res->exponent=lexp;  /* set exponent */
	  /* 0-0 gives +0 unless rounding to -infinity, and -0-0 gives -0 */
	  if (diffsign) {
	    if (set->round!=DEC_ROUND_FLOOR) res->bits=0;
	     else res->bits=DECNEG;	/* preserve 0 sign */
	    }
	  }
	 else { /* non-0 res */
	  if (adjust<0) {     /* 0-padding needed */
	    if ((res->digits-adjust)>set->digits) {
	      adjust=res->digits-set->digits;	  /* to fit exactly */
	      *status|=DEC_Rounded;		  /* [but exact] */
	      }
	    res->digits=decShiftToMost(res->lsu, res->digits, -adjust);
	    res->exponent+=adjust;		  /* set the exponent. */
	    }
	  } /* non-0 res */
      #if DECSUBSET
	} /* extended */
      #endif
      decFinish(res, set, &residue, status);	  /* clean and finalize */
      break;}

    if (ISZERO(rhs)) {			/* [lhs is non-zero] */
      Int adjust;			/* work */
      Int rexp=rhs->exponent;		/* save in case RHS==RES */
      bits=rhs->bits;			/* be clean */
      residue=0;			/* clear accumulator */
      decCopyFit(res, lhs, set, &residue, status); /* copy (as needed) */
      #if DECSUBSET
      if (set->extended) {		/* exponents on zeros count */
      #endif
	/* exponent will be the lower of the two */
	/* [0-0 case handled above] */
	adjust=rexp-res->exponent;	/* adjustment needed [if -ve] */
	if (adjust<0) {     /* 0-padding needed */
	  if ((res->digits-adjust)>set->digits) {
	    adjust=res->digits-set->digits;	/* to fit exactly */
	    *status|=DEC_Rounded;		/* [but exact] */
	    }
	  res->digits=decShiftToMost(res->lsu, res->digits, -adjust);
	  res->exponent+=adjust;		/* set the exponent. */
	  }
      #if DECSUBSET
	} /* extended */
      #endif
      decFinish(res, set, &residue, status);	  /* clean and finalize */
      break;}

    /* [NB: both fastpath and mainpath code below assume these cases */
    /* (notably 0-0) have already been handled] */

    /* calculate the padding needed to align the operands */
    padding=rhs->exponent-lhs->exponent;

    /* Fastpath cases where the numbers are aligned and normal, the RHS */
    /* is all in one unit, no operand rounding is needed, and no carry, */
    /* lengthening, or borrow is needed */
    if (padding==0
	&& rhs->digits<=DECDPUN
	&& rhs->exponent>=set->emin	/* [some normals drop through] */
	&& rhs->exponent<=set->emax-set->digits+1 /* [could clamp] */
	&& rhs->digits<=reqdigits
	&& lhs->digits<=reqdigits) {
      Int partial=*lhs->lsu;
      if (!diffsign) {			/* adding */
	partial+=*rhs->lsu;
	if ((partial<=DECDPUNMAX)	/* result fits in unit */
	 && (lhs->digits>=DECDPUN ||	/* .. and no digits-count change */
	     partial<(Int)powers[lhs->digits])) { /* .. */
	  if (res!=lhs) decNumberCopy(res, lhs);  /* not in place */
	  *res->lsu=(Unit)partial;	/* [copy could have overwritten RHS] */
	  break;
	  }
	/* else drop out for careful add */
	}
       else {				/* signs differ */
	partial-=*rhs->lsu;
	if (partial>0) { /* no borrow needed, and non-0 result */
	  if (res!=lhs) decNumberCopy(res, lhs);  /* not in place */
	  *res->lsu=(Unit)partial;
	  /* this could have reduced digits [but result>0] */
	  res->digits=decGetDigits(res->lsu, D2U(res->digits));
	  break;
	  }
	/* else drop out for careful subtract */
	}
      }

    /* Now align (pad) the lhs or rhs so they can be added or */
    /* subtracted, as necessary.  If one number is much larger than */
    /* the other (that is, if in plain form there is a least one */
    /* digit between the lowest digit of one and the highest of the */
    /* other) padding with up to DIGITS-1 trailing zeros may be */
    /* needed; then apply rounding (as exotic rounding modes may be */
    /* affected by the residue). */
    rhsshift=0; 	      /* rhs shift to left (padding) in Units */
    bits=lhs->bits;	      /* assume sign is that of LHS */
    mult=1;		      /* likely multiplier */

    /* [if padding==0 the operands are aligned; no padding is needed] */
    if (padding!=0) {
      /* some padding needed; always pad the RHS, as any required */
      /* padding can then be effected by a simple combination of */
      /* shifts and a multiply */
      Flag swapped=0;
      if (padding<0) {			/* LHS needs the padding */
	const decNumber *t;
	padding=-padding;		/* will be +ve */
	bits=(uByte)(rhs->bits^negate); /* assumed sign is now that of RHS */
	t=lhs; lhs=rhs; rhs=t;
	swapped=1;
	}

      /* If, after pad, rhs would be longer than lhs by digits+1 or */
      /* more then lhs cannot affect the answer, except as a residue, */
      /* so only need to pad up to a length of DIGITS+1. */
      if (rhs->digits+padding > lhs->digits+reqdigits+1) {
	/* The RHS is sufficient */
	/* for residue use the relative sign indication... */
	Int shift=reqdigits-rhs->digits;     /* left shift needed */
	residue=1;			     /* residue for rounding */
	if (diffsign) residue=-residue;      /* signs differ */
	/* copy, shortening if necessary */
	decCopyFit(res, rhs, set, &residue, status);
	/* if it was already shorter, then need to pad with zeros */
	if (shift>0) {
	  res->digits=decShiftToMost(res->lsu, res->digits, shift);
	  res->exponent-=shift; 	     /* adjust the exponent. */
	  }
	/* flip the result sign if unswapped and rhs was negated */
	if (!swapped) res->bits^=negate;
	decFinish(res, set, &residue, status);	  /* done */
	break;}

      /* LHS digits may affect result */
      rhsshift=D2U(padding+1)-1;	/* this much by Unit shift .. */
      mult=powers[padding-(rhsshift*DECDPUN)]; /* .. this by multiplication */
      } /* padding needed */

    if (diffsign) mult=-mult;		/* signs differ */

    /* determine the longer operand */
    maxdigits=rhs->digits+padding;	/* virtual length of RHS */
    if (lhs->digits>maxdigits) maxdigits=lhs->digits;

    /* Decide on the result buffer to use; if possible place directly */
    /* into result. */
    acc=res->lsu;			/* assume add direct to result */
    /* If destructive overlap, or the number is too long, or a carry or */
    /* borrow to DIGITS+1 might be possible, a buffer must be used. */
    /* [Might be worth more sophisticated tests when maxdigits==reqdigits] */
    if ((maxdigits>=reqdigits)		/* is, or could be, too large */
     || (res==rhs && rhsshift>0)) {	/* destructive overlap */
      /* buffer needed, choose it; units for maxdigits digits will be */
      /* needed, +1 Unit for carry or borrow */
      Int need=D2U(maxdigits)+1;
      acc=accbuff;			/* assume use local buffer */
      if (need*sizeof(Unit)>sizeof(accbuff)) {
	/* printf("malloc add %ld %ld\n", need, sizeof(accbuff)); */
	allocacc=(Unit *)malloc(need*sizeof(Unit));
	if (allocacc==NULL) {		/* hopeless -- abandon */
	  *status|=DEC_Insufficient_storage;
	  break;}
	acc=allocacc;
	}
      }

    res->bits=(uByte)(bits&DECNEG);	/* it's now safe to overwrite.. */
    res->exponent=lhs->exponent;	/* .. operands (even if aliased) */

    #if DECTRACE
      decDumpAr('A', lhs->lsu, D2U(lhs->digits));
      decDumpAr('B', rhs->lsu, D2U(rhs->digits));
      printf("	:h: %ld %ld\n", rhsshift, mult);
    #endif

    /* add [A+B*m] or subtract [A+B*(-m)] */
    res->digits=decUnitAddSub(lhs->lsu, D2U(lhs->digits),
			      rhs->lsu, D2U(rhs->digits),
			      rhsshift, acc, mult)
	       *DECDPUN;	   /* [units -> digits] */
    if (res->digits<0) {	   /* borrowed... */
      res->digits=-res->digits;
      res->bits^=DECNEG;	   /* flip the sign */
      }
    #if DECTRACE
      decDumpAr('+', acc, D2U(res->digits));
    #endif

    /* If a buffer was used the result must be copied back, possibly */
    /* shortening.  (If no buffer was used then the result must have */
    /* fit, so can't need rounding and residue must be 0.) */
    residue=0;			   /* clear accumulator */
    if (acc!=res->lsu) {
      #if DECSUBSET
      if (set->extended) {	   /* round from first significant digit */
      #endif
	/* remove leading zeros that were added due to rounding up to */
	/* integral Units -- before the test for rounding. */
	if (res->digits>reqdigits)
	  res->digits=decGetDigits(acc, D2U(res->digits));
	decSetCoeff(res, set, acc, res->digits, &residue, status);
      #if DECSUBSET
	}
       else { /* subset arithmetic rounds from original significant digit */
	/* May have an underestimate.  This only occurs when both */
	/* numbers fit in DECDPUN digits and are padding with a */
	/* negative multiple (-10, -100...) and the top digit(s) become */
	/* 0.  (This only matters when using X3.274 rules where the */
	/* leading zero could be included in the rounding.) */
	if (res->digits<maxdigits) {
	  *(acc+D2U(res->digits))=0; /* ensure leading 0 is there */
	  res->digits=maxdigits;
	  }
	 else {
	  /* remove leading zeros that added due to rounding up to */
	  /* integral Units (but only those in excess of the original */
	  /* maxdigits length, unless extended) before test for rounding. */
	  if (res->digits>reqdigits) {
	    res->digits=decGetDigits(acc, D2U(res->digits));
	    if (res->digits<maxdigits) res->digits=maxdigits;
	    }
	  }
	decSetCoeff(res, set, acc, res->digits, &residue, status);
	/* Now apply rounding if needed before removing leading zeros. */
	/* This is safe because subnormals are not a possibility */
	if (residue!=0) {
	  decApplyRound(res, set, residue, status);
	  residue=0;		     /* did what needed to be done */
	  }
	} /* subset */
      #endif
      } /* used buffer */

    /* strip leading zeros [these were left on in case of subset subtract] */
    res->digits=decGetDigits(res->lsu, D2U(res->digits));

    /* apply checks and rounding */
    decFinish(res, set, &residue, status);

    /* "When the sum of two operands with opposite signs is exactly */
    /* zero, the sign of that sum shall be '+' in all rounding modes */
    /* except round toward -Infinity, in which mode that sign shall be */
    /* '-'."  [Subset zeros also never have '-', set by decFinish.] */
    if (ISZERO(res) && diffsign
     #if DECSUBSET
     && set->extended
     #endif
     && (*status&DEC_Inexact)==0) {
      if (set->round==DEC_ROUND_FLOOR) res->bits|=DECNEG;   /* sign - */
				  else res->bits&=~DECNEG;  /* sign + */
      }
    } while(0); 			     /* end protected */

  free(allocacc);	     /* drop any storage used */
  #if DECSUBSET
  free(allocrhs);	     /* .. */
  free(alloclhs);	     /* .. */
  #endif
  return res;
  } /* decAddOp */

/* ------------------------------------------------------------------ */
/* decDivideOp -- division operation				      */
/*								      */
/*  This routine performs the calculations for all four division      */
/*  operators (divide, divideInteger, remainder, remainderNear).      */
/*								      */
/*  C=A op B							      */
/*								      */
/*   res is C, the result.  C may be A and/or B (e.g., X=X/X)	      */
/*   lhs is A							      */
/*   rhs is B							      */
/*   set is the context 					      */
/*   op  is DIVIDE, DIVIDEINT, REMAINDER, or REMNEAR respectively.    */
/*   status is the usual accumulator				      */
/*								      */
/* C must have space for set->digits digits.			      */
/*								      */
/* ------------------------------------------------------------------ */
/*   The underlying algorithm of this routine is the same as in the   */
/*   1981 S/370 implementation, that is, non-restoring long division  */
/*   with bi-unit (rather than bi-digit) estimation for each unit     */
/*   multiplier.  In this pseudocode overview, complications for the  */
/*   Remainder operators and division residues for exact rounding are */
/*   omitted for clarity.					      */
/*								      */
/*     Prepare operands and handle special values		      */
/*     Test for x/0 and then 0/x				      */
/*     Exp =Exp1 - Exp2 					      */
/*     Exp =Exp +len(var1) -len(var2)				      */
/*     Sign=Sign1 * Sign2					      */
/*     Pad accumulator (Var1) to double-length with 0's (pad1)	      */
/*     Pad Var2 to same length as Var1				      */
/*     msu2pair/plus=1st 2 or 1 units of var2, +1 to allow for round  */
/*     have=0							      */
/*     Do until (have=digits+1 OR residue=0)			      */
/*	 if exp<0 then if integer divide/residue then leave	      */
/*	 this_unit=0						      */
/*	 Do forever						      */
/*	    compare numbers					      */
/*	    if <0 then leave inner_loop 			      */
/*	    if =0 then (* quick exit without subtract *) do	      */
/*	       this_unit=this_unit+1; output this_unit		      */
/*	       leave outer_loop; end				      */
/*	    Compare lengths of numbers (mantissae):		      */
/*	    If same then tops2=msu2pair -- {units 1&2 of var2}	      */
/*		    else tops2=msu2plus -- {0, unit 1 of var2}	      */
/*	    tops1=first_unit_of_Var1*10**DECDPUN +second_unit_of_var1 */
/*	    mult=tops1/tops2  -- Good and safe guess at divisor       */
/*	    if mult=0 then mult=1				      */
/*	    this_unit=this_unit+mult				      */
/*	    subtract						      */
/*	    end inner_loop					      */
/*	  if have\=0 | this_unit\=0 then do			      */
/*	    output this_unit					      */
/*	    have=have+1; end					      */
/*	  var2=var2/10						      */
/*	  exp=exp-1						      */
/*	  end outer_loop					      */
/*     exp=exp+1   -- set the proper exponent			      */
/*     if have=0 then generate answer=0 			      */
/*     Return (Result is defined by Var1)			      */
/*								      */
/* ------------------------------------------------------------------ */
/* Two working buffers are needed during the division; one (digits+   */
/* 1) to accumulate the result, and the other (up to 2*digits+1) for  */
/* long subtractions.  These are acc and var1 respectively.	      */
/* var1 is a copy of the lhs coefficient, var2 is the rhs coefficient.*/
/* The static buffers may be larger than might be expected to allow   */
/* for calls from higher-level funtions (notable exp).		      */
/* ------------------------------------------------------------------ */
static decNumber * decDivideOp(decNumber *res,
			       const decNumber *lhs, const decNumber *rhs,
			       decContext *set, Flag op, uInt *status) {
  #if DECSUBSET
  decNumber *alloclhs=NULL;	   /* non-NULL if rounded lhs allocated */
  decNumber *allocrhs=NULL;	   /* .., rhs */
  #endif
  Unit	accbuff[SD2U(DECBUFFER+DECDPUN+10)]; /* local buffer */
  Unit	*acc=accbuff;		   /* -> accumulator array for result */
  Unit	*allocacc=NULL; 	   /* -> allocated buffer, iff allocated */
  Unit	*accnext;		   /* -> where next digit will go */
  Int	acclength;		   /* length of acc needed [Units] */
  Int	accunits;		   /* count of units accumulated */
  Int	accdigits;		   /* count of digits accumulated */

  Unit	varbuff[SD2U(DECBUFFER*2+DECDPUN)];  /* buffer for var1 */
  Unit	*var1=varbuff;		   /* -> var1 array for long subtraction */
  Unit	*varalloc=NULL; 	   /* -> allocated buffer, iff used */
  Unit	*msu1;			   /* -> msu of var1 */

  const Unit *var2;		   /* -> var2 array */
  const Unit *msu2;		   /* -> msu of var2 */
  Int	msu2plus;		   /* msu2 plus one [does not vary] */
  eInt	msu2pair;		   /* msu2 pair plus one [does not vary] */

  Int	var1units, var2units;	   /* actual lengths */
  Int	var2ulen;		   /* logical length (units) */
  Int	var1initpad=0;		   /* var1 initial padding (digits) */
  Int	maxdigits;		   /* longest LHS or required acc length */
  Int	mult;			   /* multiplier for subtraction */
  Unit	thisunit;		   /* current unit being accumulated */
  Int	residue;		   /* for rounding */
  Int	reqdigits=set->digits;	   /* requested DIGITS */
  Int	exponent;		   /* working exponent */
  Int	maxexponent=0;		   /* DIVIDE maximum exponent if unrounded */
  uByte bits;			   /* working sign */
  Unit	*target;		   /* work */
  const Unit *source;		   /* .. */
  uInt	const *pow;		   /* .. */
  Int	shift, cut;		   /* .. */
  #if DECSUBSET
  Int	dropped;		   /* work */
  #endif

  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  do {				   /* protect allocated storage */
    #if DECSUBSET
    if (!set->extended) {
      /* reduce operands and set lostDigits status, as needed */
      if (lhs->digits>reqdigits) {
	alloclhs=decRoundOperand(lhs, set, status);
	if (alloclhs==NULL) break;
	lhs=alloclhs;
	}
      if (rhs->digits>reqdigits) {
	allocrhs=decRoundOperand(rhs, set, status);
	if (allocrhs==NULL) break;
	rhs=allocrhs;
	}
      }
    #endif
    /* [following code does not require input rounding] */

    bits=(lhs->bits^rhs->bits)&DECNEG;	/* assumed sign for divisions */

    /* handle infinities and NaNs */
    if (SPECIALARGS) {			/* a special bit set */
      if (SPECIALARGS & (DECSNAN | DECNAN)) { /* one or two NaNs */
	decNaNs(res, lhs, rhs, set, status);
	break;
	}
      /* one or two infinities */
      if (decNumberIsInfinite(lhs)) {	/* LHS (dividend) is infinite */
	if (decNumberIsInfinite(rhs) || /* two infinities are invalid .. */
	    op & (REMAINDER | REMNEAR)) { /* as is remainder of infinity */
	  *status|=DEC_Invalid_operation;
	  break;
	  }
	/* [Note that infinity/0 raises no exceptions] */
	decNumberZero(res);
	res->bits=bits|DECINF;		/* set +/- infinity */
	break;
	}
       else {				/* RHS (divisor) is infinite */
	residue=0;
	if (op&(REMAINDER|REMNEAR)) {
	  /* result is [finished clone of] lhs */
	  decCopyFit(res, lhs, set, &residue, status);
	  }
	 else {  /* a division */
	  decNumberZero(res);
	  res->bits=bits;		/* set +/- zero */
	  /* for DIVIDEINT the exponent is always 0.  For DIVIDE, result */
	  /* is a 0 with infinitely negative exponent, clamped to minimum */
	  if (op&DIVIDE) {
	    res->exponent=set->emin-set->digits+1;
	    *status|=DEC_Clamped;
	    }
	  }
	decFinish(res, set, &residue, status);
	break;
	}
      }

    /* handle 0 rhs (x/0) */
    if (ISZERO(rhs)) {			/* x/0 is always exceptional */
      if (ISZERO(lhs)) {
	decNumberZero(res);		/* [after lhs test] */
	*status|=DEC_Division_undefined;/* 0/0 will become NaN */
	}
       else {
	decNumberZero(res);
	if (op&(REMAINDER|REMNEAR)) *status|=DEC_Invalid_operation;
	 else {
	  *status|=DEC_Division_by_zero; /* x/0 */
	  res->bits=bits|DECINF;	 /* .. is +/- Infinity */
	  }
	}
      break;}

    /* handle 0 lhs (0/x) */
    if (ISZERO(lhs)) {			/* 0/x [x!=0] */
      #if DECSUBSET
      if (!set->extended) decNumberZero(res);
       else {
      #endif
	if (op&DIVIDE) {
	  residue=0;
	  exponent=lhs->exponent-rhs->exponent; /* ideal exponent */
	  decNumberCopy(res, lhs);	/* [zeros always fit] */
	  res->bits=bits;		/* sign as computed */
	  res->exponent=exponent;	/* exponent, too */
	  decFinalize(res, set, &residue, status);   /* check exponent */
	  }
	 else if (op&DIVIDEINT) {
	  decNumberZero(res);		/* integer 0 */
	  res->bits=bits;		/* sign as computed */
	  }
	 else { 			/* a remainder */
	  exponent=rhs->exponent;	/* [save in case overwrite] */
	  decNumberCopy(res, lhs);	/* [zeros always fit] */
	  if (exponent<res->exponent) res->exponent=exponent; /* use lower */
	  }
      #if DECSUBSET
	}
      #endif
      break;}

    /* Precalculate exponent.  This starts off adjusted (and hence fits */
    /* in 31 bits) and becomes the usual unadjusted exponent as the */
    /* division proceeds.  The order of evaluation is important, here, */
    /* to avoid wrap. */
    exponent=(lhs->exponent+lhs->digits)-(rhs->exponent+rhs->digits);

    /* If the working exponent is -ve, then some quick exits are */
    /* possible because the quotient is known to be <1 */
    /* [for REMNEAR, it needs to be < -1, as -0.5 could need work] */
    if (exponent<0 && !(op==DIVIDE)) {
      if (op&DIVIDEINT) {
	decNumberZero(res);		     /* integer part is 0 */
	#if DECSUBSET
	if (set->extended)
	#endif
	  res->bits=bits;		     /* set +/- zero */
	break;}
      /* fastpath remainders so long as the lhs has the smaller */
      /* (or equal) exponent */
      if (lhs->exponent<=rhs->exponent) {
	if (op&REMAINDER || exponent<-1) {
	  /* It is REMAINDER or safe REMNEAR; result is [finished */
	  /* clone of] lhs  (r = x - 0*y) */
	  residue=0;
	  decCopyFit(res, lhs, set, &residue, status);
	  decFinish(res, set, &residue, status);
	  break;
	  }
	/* [unsafe REMNEAR drops through] */
	}
      } /* fastpaths */

    /* Long (slow) division is needed; roll up the sleeves... */

    /* The accumulator will hold the quotient of the division. */
    /* If it needs to be too long for stack storage, then allocate. */
    acclength=D2U(reqdigits+DECDPUN);	/* in Units */
    if (acclength*sizeof(Unit)>sizeof(accbuff)) {
      /* printf("malloc dvacc %ld units\n", acclength); */
      allocacc=(Unit *)malloc(acclength*sizeof(Unit));
      if (allocacc==NULL) {		/* hopeless -- abandon */
	*status|=DEC_Insufficient_storage;
	break;}
      acc=allocacc;			/* use the allocated space */
      }

    /* var1 is the padded LHS ready for subtractions. */
    /* If it needs to be too long for stack storage, then allocate. */
    /* The maximum units needed for var1 (long subtraction) is: */
    /* Enough for */
    /*	   (rhs->digits+reqdigits-1) -- to allow full slide to right */
    /* or  (lhs->digits)	     -- to allow for long lhs */
    /* whichever is larger */
    /*	 +1		   -- for rounding of slide to right */
    /*	 +1		   -- for leading 0s */
    /*	 +1		   -- for pre-adjust if a remainder or DIVIDEINT */
    /* [Note: unused units do not participate in decUnitAddSub data] */
    maxdigits=rhs->digits+reqdigits-1;
    if (lhs->digits>maxdigits) maxdigits=lhs->digits;
    var1units=D2U(maxdigits)+2;
    /* allocate a guard unit above msu1 for REMAINDERNEAR */
    if (!(op&DIVIDE)) var1units++;
    if ((var1units+1)*sizeof(Unit)>sizeof(varbuff)) {
      /* printf("malloc dvvar %ld units\n", var1units+1); */
      varalloc=(Unit *)malloc((var1units+1)*sizeof(Unit));
      if (varalloc==NULL) {		/* hopeless -- abandon */
	*status|=DEC_Insufficient_storage;
	break;}
      var1=varalloc;			/* use the allocated space */
      }

    /* Extend the lhs and rhs to full long subtraction length.	The lhs */
    /* is truly extended into the var1 buffer, with 0 padding, so a */
    /* subtract in place is always possible.  The rhs (var2) has */
    /* virtual padding (implemented by decUnitAddSub). */
    /* One guard unit was allocated above msu1 for rem=rem+rem in */
    /* REMAINDERNEAR. */
    msu1=var1+var1units-1;		/* msu of var1 */
    source=lhs->lsu+D2U(lhs->digits)-1; /* msu of input array */
    for (target=msu1; source>=lhs->lsu; source--, target--) *target=*source;
    for (; target>=var1; target--) *target=0;

    /* rhs (var2) is left-aligned with var1 at the start */
    var2ulen=var1units; 		/* rhs logical length (units) */
    var2units=D2U(rhs->digits); 	/* rhs actual length (units) */
    var2=rhs->lsu;			/* -> rhs array */
    msu2=var2+var2units-1;		/* -> msu of var2 [never changes] */
    /* now set up the variables which will be used for estimating the */
    /* multiplication factor.  If these variables are not exact, add */
    /* 1 to make sure that the multiplier is never overestimated. */
    msu2plus=*msu2;			/* it's value .. */
    if (var2units>1) msu2plus++;	/* .. +1 if any more */
    msu2pair=(eInt)*msu2*(DECDPUNMAX+1);/* top two pair .. */
    if (var2units>1) {			/* .. [else treat 2nd as 0] */
      msu2pair+=*(msu2-1);		/* .. */
      if (var2units>2) msu2pair++;	/* .. +1 if any more */
      }

    /* The calculation is working in units, which may have leading zeros, */
    /* but the exponent was calculated on the assumption that they are */
    /* both left-aligned.  Adjust the exponent to compensate: add the */
    /* number of leading zeros in var1 msu and subtract those in var2 msu. */
    /* [This is actually done by counting the digits and negating, as */
    /* lead1=DECDPUN-digits1, and similarly for lead2.] */
    for (pow=&powers[1]; *msu1>=*pow; pow++) exponent--;
    for (pow=&powers[1]; *msu2>=*pow; pow++) exponent++;

    /* Now, if doing an integer divide or remainder, ensure that */
    /* the result will be Unit-aligned.  To do this, shift the var1 */
    /* accumulator towards least if need be.  (It's much easier to */
    /* do this now than to reassemble the residue afterwards, if */
    /* doing a remainder.)  Also ensure the exponent is not negative. */
    if (!(op&DIVIDE)) {
      Unit *u;				/* work */
      /* save the initial 'false' padding of var1, in digits */
      var1initpad=(var1units-D2U(lhs->digits))*DECDPUN;
      /* Determine the shift to do. */
      if (exponent<0) cut=-exponent;
       else cut=DECDPUN-exponent%DECDPUN;
      decShiftToLeast(var1, var1units, cut);
      exponent+=cut;			/* maintain numerical value */
      var1initpad-=cut; 		/* .. and reduce padding */
      /* clean any most-significant units which were just emptied */
      for (u=msu1; cut>=DECDPUN; cut-=DECDPUN, u--) *u=0;
      } /* align */
     else { /* is DIVIDE */
      maxexponent=lhs->exponent-rhs->exponent;	  /* save */
      /* optimization: if the first iteration will just produce 0, */
      /* preadjust to skip it [valid for DIVIDE only] */
      if (*msu1<*msu2) {
	var2ulen--;			/* shift down */
	exponent-=DECDPUN;		/* update the exponent */
	}
      }

    /* ---- start the long-division loops ------------------------------ */
    accunits=0; 			/* no units accumulated yet */
    accdigits=0;			/* .. or digits */
    accnext=acc+acclength-1;		/* -> msu of acc [NB: allows digits+1] */
    for (;;) {				/* outer forever loop */
      thisunit=0;			/* current unit assumed 0 */
      /* find the next unit */
      for (;;) {			/* inner forever loop */
	/* strip leading zero units [from either pre-adjust or from */
	/* subtract last time around].	Leave at least one unit. */
	for (; *msu1==0 && msu1>var1; msu1--) var1units--;

	if (var1units<var2ulen) break;	     /* var1 too low for subtract */
	if (var1units==var2ulen) {	     /* unit-by-unit compare needed */
	  /* compare the two numbers, from msu */
	  const Unit *pv1, *pv2;
	  Unit v2;			     /* units to compare */
	  pv2=msu2;			     /* -> msu */
	  for (pv1=msu1; ; pv1--, pv2--) {
	    /* v1=*pv1 -- always OK */
	    v2=0;			     /* assume in padding */
	    if (pv2>=var2) v2=*pv2;	     /* in range */
	    if (*pv1!=v2) break;	     /* no longer the same */
	    if (pv1==var1) break;	     /* done; leave pv1 as is */
	    }
	  /* here when all inspected or a difference seen */
	  if (*pv1<v2) break;		     /* var1 too low to subtract */
	  if (*pv1==v2) {		     /* var1 == var2 */
	    /* reach here if var1 and var2 are identical; subtraction */
	    /* would increase digit by one, and the residue will be 0 so */
	    /* the calculation is done; leave the loop with residue=0. */
	    thisunit++; 		     /* as though subtracted */
	    *var1=0;			     /* set var1 to 0 */
	    var1units=1;		     /* .. */
	    break;  /* from inner */
	    } /* var1 == var2 */
	  /* *pv1>v2.  Prepare for real subtraction; the lengths are equal */
	  /* Estimate the multiplier (there's always a msu1-1)... */
	  /* Bring in two units of var2 to provide a good estimate. */
	  mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2pair);
	  } /* lengths the same */
	 else { /* var1units > var2ulen, so subtraction is safe */
	  /* The var2 msu is one unit towards the lsu of the var1 msu, */
	  /* so only one unit for var2 can be used. */
	  mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2plus);
	  }
	if (mult==0) mult=1;		     /* must always be at least 1 */
	/* subtraction needed; var1 is > var2 */
	thisunit=(Unit)(thisunit+mult);      /* accumulate */
	/* subtract var1-var2, into var1; only the overlap needs */
	/* processing, as this is an in-place calculation */
	shift=var2ulen-var2units;
	#if DECTRACE
	  decDumpAr('1', &var1[shift], var1units-shift);
	  decDumpAr('2', var2, var2units);
	  printf("m=%ld\n", -mult);
	#endif
	decUnitAddSub(&var1[shift], var1units-shift,
		      var2, var2units, 0,
		      &var1[shift], -mult);
	#if DECTRACE
	  decDumpAr('#', &var1[shift], var1units-shift);
	#endif
	/* var1 now probably has leading zeros; these are removed at the */
	/* top of the inner loop. */
	} /* inner loop */

      /* The next unit has been calculated in full; unless it's a */
      /* leading zero, add to acc */
      if (accunits!=0 || thisunit!=0) {      /* is first or non-zero */
	*accnext=thisunit;		     /* store in accumulator */
	/* account exactly for the new digits */
	if (accunits==0) {
	  accdigits++;			     /* at least one */
	  for (pow=&powers[1]; thisunit>=*pow; pow++) accdigits++;
	  }
	 else accdigits+=DECDPUN;
	accunits++;			     /* update count */
	accnext--;			     /* ready for next */
	if (accdigits>reqdigits) break;      /* have enough digits */
	}

      /* if the residue is zero, the operation is done (unless divide */
      /* or divideInteger and still not enough digits yet) */
      if (*var1==0 && var1units==1) {	     /* residue is 0 */
	if (op&(REMAINDER|REMNEAR)) break;
	if ((op&DIVIDE) && (exponent<=maxexponent)) break;
	/* [drop through if divideInteger] */
	}
      /* also done enough if calculating remainder or integer */
      /* divide and just did the last ('units') unit */
      if (exponent==0 && !(op&DIVIDE)) break;

      /* to get here, var1 is less than var2, so divide var2 by the per- */
      /* Unit power of ten and go for the next digit */
      var2ulen--;			     /* shift down */
      exponent-=DECDPUN;		     /* update the exponent */
      } /* outer loop */

    /* ---- division is complete --------------------------------------- */
    /* here: acc      has at least reqdigits+1 of good results (or fewer */
    /*		      if early stop), starting at accnext+1 (its lsu) */
    /*	     var1     has any residue at the stopping point */
    /*	     accunits is the number of digits collected in acc */
    if (accunits==0) {		   /* acc is 0 */
      accunits=1;		   /* show have a unit .. */
      accdigits=1;		   /* .. */
      *accnext=0;		   /* .. whose value is 0 */
      }
     else accnext++;		   /* back to last placed */
    /* accnext now -> lowest unit of result */

    residue=0;			   /* assume no residue */
    if (op&DIVIDE) {
      /* record the presence of any residue, for rounding */
      if (*var1!=0 || var1units>1) residue=1;
       else { /* no residue */
	/* Had an exact division; clean up spurious trailing 0s. */
	/* There will be at most DECDPUN-1, from the final multiply, */
	/* and then only if the result is non-0 (and even) and the */
	/* exponent is 'loose'. */
	#if DECDPUN>1
	Unit lsu=*accnext;
	if (!(lsu&0x01) && (lsu!=0)) {
	  /* count the trailing zeros */
	  Int drop=0;
	  for (;; drop++) {    /* [will terminate because lsu!=0] */
	    if (exponent>=maxexponent) break;	  /* don't chop real 0s */
	    #if DECDPUN<=4
	      if ((lsu-QUOT10(lsu, drop+1)
		  *powers[drop+1])!=0) break;	  /* found non-0 digit */
	    #else
	      if (lsu%powers[drop+1]!=0) break;   /* found non-0 digit */
	    #endif
	    exponent++;
	    }
	  if (drop>0) {
	    accunits=decShiftToLeast(accnext, accunits, drop);
	    accdigits=decGetDigits(accnext, accunits);
	    accunits=D2U(accdigits);
	    /* [exponent was adjusted in the loop] */
	    }
	  } /* neither odd nor 0 */
	#endif
	} /* exact divide */
      } /* divide */
     else /* op!=DIVIDE */ {
      /* check for coefficient overflow */
      if (accdigits+exponent>reqdigits) {
	*status|=DEC_Division_impossible;
	break;
	}
      if (op & (REMAINDER|REMNEAR)) {
	/* [Here, the exponent will be 0, because var1 was adjusted */
	/* appropriately.] */
	Int postshift;			     /* work */
	Flag wasodd=0;			     /* integer was odd */
	Unit *quotlsu;			     /* for save */
	Int  quotdigits;		     /* .. */

	bits=lhs->bits; 		     /* remainder sign is always as lhs */

	/* Fastpath when residue is truly 0 is worthwhile [and */
	/* simplifies the code below] */
	if (*var1==0 && var1units==1) {      /* residue is 0 */
	  Int exp=lhs->exponent;	     /* save min(exponents) */
	  if (rhs->exponent<exp) exp=rhs->exponent;
	  decNumberZero(res);		     /* 0 coefficient */
	  #if DECSUBSET
	  if (set->extended)
	  #endif
	  res->exponent=exp;		     /* .. with proper exponent */
	  res->bits=(uByte)(bits&DECNEG);	   /* [cleaned] */
	  decFinish(res, set, &residue, status);   /* might clamp */
	  break;
	  }
	/* note if the quotient was odd */
	if (*accnext & 0x01) wasodd=1;	     /* acc is odd */
	quotlsu=accnext;		     /* save in case need to reinspect */
	quotdigits=accdigits;		     /* .. */

	/* treat the residue, in var1, as the value to return, via acc */
	/* calculate the unused zero digits.  This is the smaller of: */
	/*   var1 initial padding (saved above) */
	/*   var2 residual padding, which happens to be given by: */
	postshift=var1initpad+exponent-lhs->exponent+rhs->exponent;
	/* [the 'exponent' term accounts for the shifts during divide] */
	if (var1initpad<postshift) postshift=var1initpad;

	/* shift var1 the requested amount, and adjust its digits */
	var1units=decShiftToLeast(var1, var1units, postshift);
	accnext=var1;
	accdigits=decGetDigits(var1, var1units);
	accunits=D2U(accdigits);

	exponent=lhs->exponent; 	/* exponent is smaller of lhs & rhs */
	if (rhs->exponent<exponent) exponent=rhs->exponent;

	/* Now correct the result if doing remainderNear; if it */
	/* (looking just at coefficients) is > rhs/2, or == rhs/2 and */
	/* the integer was odd then the result should be rem-rhs. */
	if (op&REMNEAR) {
	  Int compare, tarunits;	/* work */
	  Unit *up;			/* .. */
	  /* calculate remainder*2 into the var1 buffer (which has */
	  /* 'headroom' of an extra unit and hence enough space) */
	  /* [a dedicated 'double' loop would be faster, here] */
	  tarunits=decUnitAddSub(accnext, accunits, accnext, accunits,
				 0, accnext, 1);
	  /* decDumpAr('r', accnext, tarunits); */

	  /* Here, accnext (var1) holds tarunits Units with twice the */
	  /* remainder's coefficient, which must now be compared to the */
	  /* RHS.  The remainder's exponent may be smaller than the RHS's. */
	  compare=decUnitCompare(accnext, tarunits, rhs->lsu, D2U(rhs->digits),
				 rhs->exponent-exponent);
	  if (compare==BADINT) {	     /* deep trouble */
	    *status|=DEC_Insufficient_storage;
	    break;}

	  /* now restore the remainder by dividing by two; the lsu */
	  /* is known to be even. */
	  for (up=accnext; up<accnext+tarunits; up++) {
	    Int half;		   /* half to add to lower unit */
	    half=*up & 0x01;
	    *up/=2;		   /* [shift] */
	    if (!half) continue;
	    *(up-1)+=(DECDPUNMAX+1)/2;
	    }
	  /* [accunits still describes the original remainder length] */

	  if (compare>0 || (compare==0 && wasodd)) { /* adjustment needed */
	    Int exp, expunits, exprem;	     /* work */
	    /* This is effectively causing round-up of the quotient, */
	    /* so if it was the rare case where it was full and all */
	    /* nines, it would overflow and hence division-impossible */
	    /* should be raised */
	    Flag allnines=0;		     /* 1 if quotient all nines */
	    if (quotdigits==reqdigits) {     /* could be borderline */
	      for (up=quotlsu; ; up++) {
		if (quotdigits>DECDPUN) {
		  if (*up!=DECDPUNMAX) break;/* non-nines */
		  }
		 else { 		     /* this is the last Unit */
		  if (*up==powers[quotdigits]-1) allnines=1;
		  break;
		  }
		quotdigits-=DECDPUN;	     /* checked those digits */
		} /* up */
	      } /* borderline check */
	    if (allnines) {
	      *status|=DEC_Division_impossible;
	      break;}

	    /* rem-rhs is needed; the sign will invert.  Again, var1 */
	    /* can safely be used for the working Units array. */
	    exp=rhs->exponent-exponent;      /* RHS padding needed */
	    /* Calculate units and remainder from exponent. */
	    expunits=exp/DECDPUN;
	    exprem=exp%DECDPUN;
	    /* subtract [A+B*(-m)]; the result will always be negative */
	    accunits=-decUnitAddSub(accnext, accunits,
				    rhs->lsu, D2U(rhs->digits),
				    expunits, accnext, -(Int)powers[exprem]);
	    accdigits=decGetDigits(accnext, accunits); /* count digits exactly */
	    accunits=D2U(accdigits);	/* and recalculate the units for copy */
	    /* [exponent is as for original remainder] */
	    bits^=DECNEG;		/* flip the sign */
	    }
	  } /* REMNEAR */
	} /* REMAINDER or REMNEAR */
      } /* not DIVIDE */

    /* Set exponent and bits */
    res->exponent=exponent;
    res->bits=(uByte)(bits&DECNEG);	     /* [cleaned] */

    /* Now the coefficient. */
    decSetCoeff(res, set, accnext, accdigits, &residue, status);

    decFinish(res, set, &residue, status);   /* final cleanup */

    #if DECSUBSET
    /* If a divide then strip trailing zeros if subset [after round] */
    if (!set->extended && (op==DIVIDE)) decTrim(res, set, 0, 1, &dropped);
    #endif
    } while(0); 			     /* end protected */

  free(varalloc);	/* drop any storage used */
  free(allocacc);	/* .. */
  #if DECSUBSET
  free(allocrhs);	/* .. */
  free(alloclhs);	/* .. */
  #endif
  return res;
  } /* decDivideOp */

/* ------------------------------------------------------------------ */
/* decMultiplyOp -- multiplication operation			      */
/*								      */
/*  This routine performs the multiplication C=A x B.		      */
/*								      */
/*   res is C, the result.  C may be A and/or B (e.g., X=X*X)	      */
/*   lhs is A							      */
/*   rhs is B							      */
/*   set is the context 					      */
/*   status is the usual accumulator				      */
/*								      */
/* C must have space for set->digits digits.			      */
/*								      */
/* ------------------------------------------------------------------ */
/* 'Classic' multiplication is used rather than Karatsuba, as the     */
/* latter would give only a minor improvement for the short numbers   */
/* expected to be handled most (and uses much more memory).	      */
/*								      */
/* There are two major paths here: the general-purpose ('old code')   */
/* path which handles all DECDPUN values, and a fastpath version      */
/* which is used if 64-bit ints are available, DECDPUN<=4, and more   */
/* than two calls to decUnitAddSub would be made.		      */
/*								      */
/* The fastpath version lumps units together into 8-digit or 9-digit  */
/* chunks, and also uses a lazy carry strategy to minimise expensive  */
/* 64-bit divisions.  The chunks are then broken apart again into     */
/* units for continuing processing.  Despite this overhead, the       */
/* fastpath can speed up some 16-digit operations by 10x (and much    */
/* more for higher-precision calculations).			      */
/*								      */
/* A buffer always has to be used for the accumulator; in the	      */
/* fastpath, buffers are also always needed for the chunked copies of */
/* of the operand coefficients. 				      */
/* Static buffers are larger than needed just for multiply, to allow  */
/* for calls from other operations (notably exp).		      */
/* ------------------------------------------------------------------ */
#define FASTMUL (DECUSE64 && DECDPUN<5)
static decNumber * decMultiplyOp(decNumber *res, const decNumber *lhs,
				 const decNumber *rhs, decContext *set,
				 uInt *status) {
  Int	 accunits;		   /* Units of accumulator in use */
  Int	 exponent;		   /* work */
  Int	 residue=0;		   /* rounding residue */
  uByte  bits;			   /* result sign */
  Unit	*acc;			   /* -> accumulator Unit array */
  Int	 needbytes;		   /* size calculator */
  void	*allocacc=NULL; 	   /* -> allocated accumulator, iff allocated */
  Unit	accbuff[SD2U(DECBUFFER*4+1)]; /* buffer (+1 for DECBUFFER==0, */
				   /* *4 for calls from other operations) */
  const Unit *mer, *mermsup;	   /* work */
  Int	madlength;		   /* Units in multiplicand */
  Int	shift;			   /* Units to shift multiplicand by */

  #if FASTMUL
    /* if DECDPUN is 1 or 3 work in base 10**9, otherwise */
    /* (DECDPUN is 2 or 4) then work in base 10**8 */
    #if DECDPUN & 1		   /* odd */
      #define FASTBASE 1000000000  /* base */
      #define FASTDIGS		9  /* digits in base */
      #define FASTLAZY	       18  /* carry resolution point [1->18] */
    #else
      #define FASTBASE	100000000
      #define FASTDIGS		8
      #define FASTLAZY	     1844  /* carry resolution point [1->1844] */
    #endif
    /* three buffers are used, two for chunked copies of the operands */
    /* (base 10**8 or base 10**9) and one base 2**64 accumulator with */
    /* lazy carry evaluation */
    uInt   zlhibuff[(DECBUFFER*2+1)/8+1]; /* buffer (+1 for DECBUFFER==0) */
    uInt  *zlhi=zlhibuff;		  /* -> lhs array */
    uInt  *alloclhi=NULL;		  /* -> allocated buffer, iff allocated */
    uInt   zrhibuff[(DECBUFFER*2+1)/8+1]; /* buffer (+1 for DECBUFFER==0) */
    uInt  *zrhi=zrhibuff;		  /* -> rhs array */
    uInt  *allocrhi=NULL;		  /* -> allocated buffer, iff allocated */
    uLong  zaccbuff[(DECBUFFER*2+1)/4+2]; /* buffer (+1 for DECBUFFER==0) */
    /* [allocacc is shared for both paths, as only one will run] */
    uLong *zacc=zaccbuff;	   /* -> accumulator array for exact result */
    #if DECDPUN==1
    Int    zoff;		   /* accumulator offset */
    #endif
    uInt  *lip, *rip;		   /* item pointers */
    uInt  *lmsi, *rmsi; 	   /* most significant items */
    Int    ilhs, irhs, iacc;	   /* item counts in the arrays */
    Int    lazy;		   /* lazy carry counter */
    uLong  lcarry;		   /* uLong carry */
    uInt   carry;		   /* carry (NB not uLong) */
    Int    count;		   /* work */
    const  Unit *cup;		   /* .. */
    Unit  *up;			   /* .. */
    uLong *lp;			   /* .. */
    Int    p;			   /* .. */
  #endif

  #if DECSUBSET
    decNumber *alloclhs=NULL;	   /* -> allocated buffer, iff allocated */
    decNumber *allocrhs=NULL;	   /* -> allocated buffer, iff allocated */
  #endif

  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  /* precalculate result sign */
  bits=(uByte)((lhs->bits^rhs->bits)&DECNEG);

  /* handle infinities and NaNs */
  if (SPECIALARGS) {		   /* a special bit set */
    if (SPECIALARGS & (DECSNAN | DECNAN)) { /* one or two NaNs */
      decNaNs(res, lhs, rhs, set, status);
      return res;}
    /* one or two infinities; Infinity * 0 is invalid */
    if (((lhs->bits & DECINF)==0 && ISZERO(lhs))
      ||((rhs->bits & DECINF)==0 && ISZERO(rhs))) {
      *status|=DEC_Invalid_operation;
      return res;}
    decNumberZero(res);
    res->bits=bits|DECINF;	   /* infinity */
    return res;}

  /* For best speed, as in DMSRCN [the original Rexx numerics */
  /* module], use the shorter number as the multiplier (rhs) and */
  /* the longer as the multiplicand (lhs) to minimise the number of */
  /* adds (partial products) */
  if (lhs->digits<rhs->digits) {   /* swap... */
    const decNumber *hold=lhs;
    lhs=rhs;
    rhs=hold;
    }

  do {				   /* protect allocated storage */
    #if DECSUBSET
    if (!set->extended) {
      /* reduce operands and set lostDigits status, as needed */
      if (lhs->digits>set->digits) {
	alloclhs=decRoundOperand(lhs, set, status);
	if (alloclhs==NULL) break;
	lhs=alloclhs;
	}
      if (rhs->digits>set->digits) {
	allocrhs=decRoundOperand(rhs, set, status);
	if (allocrhs==NULL) break;
	rhs=allocrhs;
	}
      }
    #endif
    /* [following code does not require input rounding] */

    #if FASTMUL 		   /* fastpath can be used */
    /* use the fast path if there are enough digits in the shorter */
    /* operand to make the setup and takedown worthwhile */
    #define NEEDTWO (DECDPUN*2)    /* within two decUnitAddSub calls */
    if (rhs->digits>NEEDTWO) {	   /* use fastpath... */
      /* calculate the number of elements in each array */
      ilhs=(lhs->digits+FASTDIGS-1)/FASTDIGS; /* [ceiling] */
      irhs=(rhs->digits+FASTDIGS-1)/FASTDIGS; /* .. */
      iacc=ilhs+irhs;

      /* allocate buffers if required, as usual */
      needbytes=ilhs*sizeof(uInt);
      if (needbytes>(Int)sizeof(zlhibuff)) {
	alloclhi=(uInt *)malloc(needbytes);
	zlhi=alloclhi;}
      needbytes=irhs*sizeof(uInt);
      if (needbytes>(Int)sizeof(zrhibuff)) {
	allocrhi=(uInt *)malloc(needbytes);
	zrhi=allocrhi;}

      /* Allocating the accumulator space needs a special case when */
      /* DECDPUN=1 because when converting the accumulator to Units */
      /* after the multiplication each 8-byte item becomes 9 1-byte */
      /* units.  Therefore iacc extra bytes are needed at the front */
      /* (rounded up to a multiple of 8 bytes), and the uLong */
      /* accumulator starts offset the appropriate number of units */
      /* to the right to avoid overwrite during the unchunking. */
      needbytes=iacc*sizeof(uLong);
      #if DECDPUN==1
      zoff=(iacc+7)/8;	      /* items to offset by */
      needbytes+=zoff*8;
      #endif
      if (needbytes>(Int)sizeof(zaccbuff)) {
	allocacc=(uLong *)malloc(needbytes);
	zacc=(uLong *)allocacc;}
      if (zlhi==NULL||zrhi==NULL||zacc==NULL) {
	*status|=DEC_Insufficient_storage;
	break;}

      acc=(Unit *)zacc;       /* -> target Unit array */
      #if DECDPUN==1
      zacc+=zoff;	      /* start uLong accumulator to right */
      #endif

      /* assemble the chunked copies of the left and right sides */
      for (count=lhs->digits, cup=lhs->lsu, lip=zlhi; count>0; lip++)
	for (p=0, *lip=0; p<FASTDIGS && count>0;
	     p+=DECDPUN, cup++, count-=DECDPUN)
	  *lip+=*cup*powers[p];
      lmsi=lip-1;     /* save -> msi */
      for (count=rhs->digits, cup=rhs->lsu, rip=zrhi; count>0; rip++)
	for (p=0, *rip=0; p<FASTDIGS && count>0;
	     p+=DECDPUN, cup++, count-=DECDPUN)
	  *rip+=*cup*powers[p];
      rmsi=rip-1;     /* save -> msi */

      /* zero the accumulator */
      for (lp=zacc; lp<zacc+iacc; lp++) *lp=0;

      /* Start the multiplication */
      /* Resolving carries can dominate the cost of accumulating the */
      /* partial products, so this is only done when necessary. */
      /* Each uLong item in the accumulator can hold values up to */
      /* 2**64-1, and each partial product can be as large as */
      /* (10**FASTDIGS-1)**2.  When FASTDIGS=9, this can be added to */
      /* itself 18.4 times in a uLong without overflowing, so during */
      /* the main calculation resolution is carried out every 18th */
      /* add -- every 162 digits.  Similarly, when FASTDIGS=8, the */
      /* partial products can be added to themselves 1844.6 times in */
      /* a uLong without overflowing, so intermediate carry */
      /* resolution occurs only every 14752 digits.  Hence for common */
      /* short numbers usually only the one final carry resolution */
      /* occurs. */
      /* (The count is set via FASTLAZY to simplify experiments to */
      /* measure the value of this approach: a 35% improvement on a */
      /* [34x34] multiply.) */
      lazy=FASTLAZY;			     /* carry delay count */
      for (rip=zrhi; rip<=rmsi; rip++) {     /* over each item in rhs */
	lp=zacc+(rip-zrhi);		     /* where to add the lhs */
	for (lip=zlhi; lip<=lmsi; lip++, lp++) { /* over each item in lhs */
	  *lp+=(uLong)(*lip)*(*rip);	     /* [this should in-line] */
	  } /* lip loop */
	lazy--;
	if (lazy>0 && rip!=rmsi) continue;
	lazy=FASTLAZY;			     /* reset delay count */
	/* spin up the accumulator resolving overflows */
	for (lp=zacc; lp<zacc+iacc; lp++) {
	  if (*lp<FASTBASE) continue;	     /* it fits */
	  lcarry=*lp/FASTBASE;		     /* top part [slow divide] */
	  /* lcarry can exceed 2**32-1, so check again; this check */
	  /* and occasional extra divide (slow) is well worth it, as */
	  /* it allows FASTLAZY to be increased to 18 rather than 4 */
	  /* in the FASTDIGS=9 case */
	  if (lcarry<FASTBASE) carry=(uInt)lcarry;  /* [usual] */
	   else { /* two-place carry [fairly rare] */
	    uInt carry2=(uInt)(lcarry/FASTBASE);    /* top top part */
	    *(lp+2)+=carry2;			    /* add to item+2 */
	    *lp-=((uLong)FASTBASE*FASTBASE*carry2); /* [slow] */
	    carry=(uInt)(lcarry-((uLong)FASTBASE*carry2)); /* [inline] */
	    }
	  *(lp+1)+=carry;		     /* add to item above [inline] */
	  *lp-=((uLong)FASTBASE*carry);      /* [inline] */
	  } /* carry resolution */
	} /* rip loop */

      /* The multiplication is complete; time to convert back into */
      /* units.  This can be done in-place in the accumulator and in */
      /* 32-bit operations, because carries were resolved after the */
      /* final add.  This needs N-1 divides and multiplies for */
      /* each item in the accumulator (which will become up to N */
      /* units, where 2<=N<=9). */
      for (lp=zacc, up=acc; lp<zacc+iacc; lp++) {
	uInt item=(uInt)*lp;		     /* decapitate to uInt */
	for (p=0; p<FASTDIGS-DECDPUN; p+=DECDPUN, up++) {
	  uInt part=item/(DECDPUNMAX+1);
	  *up=(Unit)(item-(part*(DECDPUNMAX+1)));
	  item=part;
	  } /* p */
	*up=(Unit)item; up++;		     /* [final needs no division] */
	} /* lp */
      accunits=up-acc;			     /* count of units */
      }
     else { /* here to use units directly, without chunking ['old code'] */
    #endif

      /* if accumulator will be too long for local storage, then allocate */
      acc=accbuff;		   /* -> assume buffer for accumulator */
      needbytes=(D2U(lhs->digits)+D2U(rhs->digits))*sizeof(Unit);
      if (needbytes>(Int)sizeof(accbuff)) {
	allocacc=(Unit *)malloc(needbytes);
	if (allocacc==NULL) {*status|=DEC_Insufficient_storage; break;}
	acc=(Unit *)allocacc;		     /* use the allocated space */
	}

      /* Now the main long multiplication loop */
      /* Unlike the equivalent in the IBM Java implementation, there */
      /* is no advantage in calculating from msu to lsu.  So, do it */
      /* by the book, as it were. */
      /* Each iteration calculates ACC=ACC+MULTAND*MULT */
      accunits=1;		   /* accumulator starts at '0' */
      *acc=0;			   /* .. (lsu=0) */
      shift=0;			   /* no multiplicand shift at first */
      madlength=D2U(lhs->digits);  /* this won't change */
      mermsup=rhs->lsu+D2U(rhs->digits); /* -> msu+1 of multiplier */

      for (mer=rhs->lsu; mer<mermsup; mer++) {
	/* Here, *mer is the next Unit in the multiplier to use */
	/* If non-zero [optimization] add it... */
	if (*mer!=0) accunits=decUnitAddSub(&acc[shift], accunits-shift,
					    lhs->lsu, madlength, 0,
					    &acc[shift], *mer)
					    + shift;
	 else { /* extend acc with a 0; it will be used shortly */
	  *(acc+accunits)=0;	   /* [this avoids length of <=0 later] */
	  accunits++;
	  }
	/* multiply multiplicand by 10**DECDPUN for next Unit to left */
	shift++;		   /* add this for 'logical length' */
	} /* n */
    #if FASTMUL
      } /* unchunked units */
    #endif
    /* common end-path */
    #if DECTRACE
      decDumpAr('*', acc, accunits);	     /* Show exact result */
    #endif

    /* acc now contains the exact result of the multiplication, */
    /* possibly with a leading zero unit; build the decNumber from */
    /* it, noting if any residue */
    res->bits=bits;			     /* set sign */
    res->digits=decGetDigits(acc, accunits); /* count digits exactly */

    /* There can be a 31-bit wrap in calculating the exponent. */
    /* This can only happen if both input exponents are negative and */
    /* both their magnitudes are large.  If there was a wrap, set a */
    /* safe very negative exponent, from which decFinalize() will */
    /* raise a hard underflow shortly. */
    exponent=lhs->exponent+rhs->exponent;    /* calculate exponent */
    if (lhs->exponent<0 && rhs->exponent<0 && exponent>0)
      exponent=-2*DECNUMMAXE;		     /* force underflow */
    res->exponent=exponent;		     /* OK to overwrite now */


    /* Set the coefficient.  If any rounding, residue records */
    decSetCoeff(res, set, acc, res->digits, &residue, status);
    decFinish(res, set, &residue, status);   /* final cleanup */
    } while(0); 			/* end protected */

  free(allocacc);	/* drop any storage used */
  #if DECSUBSET
  free(allocrhs);	/* .. */
  free(alloclhs);	/* .. */
  #endif
  #if FASTMUL
  free(allocrhi);	/* .. */
  free(alloclhi);	/* .. */
  #endif
  return res;
  } /* decMultiplyOp */

/* ------------------------------------------------------------------ */
/* decExpOp -- effect exponentiation				      */
/*								      */
/*   This computes C = exp(A)					      */
/*								      */
/*   res is C, the result.  C may be A				      */
/*   rhs is A							      */
/*   set is the context; note that rounding mode has no effect	      */
/*								      */
/* C must have space for set->digits digits. status is updated but    */
/* not set.							      */
/*								      */
/* Restrictions:						      */
/*								      */
/*   digits, emax, and -emin in the context must be less than	      */
/*   2*DEC_MAX_MATH (1999998), and the rhs must be within these       */
/*   bounds or a zero.	This is an internal routine, so these	      */
/*   restrictions are contractual and not enforced.		      */
/*								      */
/* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will      */
/* almost always be correctly rounded, but may be up to 1 ulp in      */
/* error in rare cases. 					      */
/*								      */
/* Finite results will always be full precision and Inexact, except   */
/* when A is a zero or -Infinity (giving 1 or 0 respectively).	      */
/* ------------------------------------------------------------------ */
/* This approach used here is similar to the algorithm described in   */
/*								      */
/*   Variable Precision Exponential Function, T. E. Hull and	      */
/*   A. Abrham, ACM Transactions on Mathematical Software, Vol 12 #2, */
/*   pp79-91, ACM, June 1986.					      */
/*								      */
/* with the main difference being that the iterations in the series   */
/* evaluation are terminated dynamically (which does not require the  */
/* extra variable-precision variables which are expensive in this     */
/* context).							      */
/*								      */
/* The error analysis in Hull & Abrham's paper applies except for the */
/* round-off error accumulation during the series evaluation.  This   */
/* code does not precalculate the number of iterations and so cannot  */
/* use Horner's scheme.  Instead, the accumulation is done at double- */
/* precision, which ensures that the additions of the terms are exact */
/* and do not accumulate round-off (and any round-off errors in the   */
/* terms themselves move 'to the right' faster than they can	      */
/* accumulate).  This code also extends the calculation by allowing,  */
/* in the spirit of other decNumber operators, the input to be more   */
/* precise than the result (the precision used is based on the more   */
/* precise of the input or requested result).			      */
/*								      */
/* Implementation notes:					      */
/*								      */
/* 1. This is separated out as decExpOp so it can be called from      */
/*    other Mathematical functions (notably Ln) with a wider range    */
/*    than normal.  In particular, it can handle the slightly wider   */
/*    (double) range needed by Ln (which has to be able to calculate  */
/*    exp(-x) where x can be the tiniest number (Ntiny).	      */
/*								      */
/* 2. Normalizing x to be <=0.1 (instead of <=1) reduces loop	      */
/*    iterations by approximately a third with additional (although    */
/*    diminishing) returns as the range is reduced to even smaller    */
/*    fractions.  However, h (the power of 10 used to correct the     */
/*    result at the end, see below) must be kept <=8 as otherwise     */
/*    the final result cannot be computed.  Hence the leverage is a   */
/*    sliding value (8-h), where potentially the range is reduced     */
/*    more for smaller values.					      */
/*								      */
/*    The leverage that can be applied in this way is severely	      */
/*    limited by the cost of the raise-to-the power at the end,       */
/*    which dominates when the number of iterations is small (less    */
/*    than ten) or when rhs is short.  As an example, the adjustment  */
/*    x**10,000,000 needs 31 multiplications, all but one full-width. */
/*								      */
/* 3. The restrictions (especially precision) could be raised with    */
/*    care, but the full decNumber range seems very hard within the   */
/*    32-bit limits.						      */
/*								      */
/* 4. The working precisions for the static buffers are twice the     */
/*    obvious size to allow for calls from decNumberPower.	      */
/* ------------------------------------------------------------------ */
decNumber * decExpOp(decNumber *res, const decNumber *rhs,
			 decContext *set, uInt *status) {
  uInt ignore=0;		   /* working status */
  Int h;			   /* adjusted exponent for 0.xxxx */
  Int p;			   /* working precision */
  Int residue;			   /* rounding residue */
  uInt needbytes;		   /* for space calculations */
  const decNumber *x=rhs;	   /* (may point to safe copy later) */
  decContext aset, tset, dset;	   /* working contexts */
  Int comp;			   /* work */

  /* the argument is often copied to normalize it, so (unusually) it */
  /* is treated like other buffers, using DECBUFFER, +1 in case */
  /* DECBUFFER is 0 */
  decNumber bufr[D2N(DECBUFFER*2+1)];
  decNumber *allocrhs=NULL;	   /* non-NULL if rhs buffer allocated */

  /* the working precision will be no more than set->digits+8+1 */
  /* so for on-stack buffers DECBUFFER+9 is used, +1 in case DECBUFFER */
  /* is 0 (and twice that for the accumulator) */

  /* buffer for t, term (working precision plus) */
  decNumber buft[D2N(DECBUFFER*2+9+1)];
  decNumber *allocbuft=NULL;	   /* -> allocated buft, iff allocated */
  decNumber *t=buft;		   /* term */
  /* buffer for a, accumulator (working precision * 2), at least 9 */
  decNumber bufa[D2N(DECBUFFER*4+18+1)];
  decNumber *allocbufa=NULL;	   /* -> allocated bufa, iff allocated */
  decNumber *a=bufa;		   /* accumulator */
  /* decNumber for the divisor term; this needs at most 9 digits */
  /* and so can be fixed size [16 so can use standard context] */
  decNumber bufd[D2N(16)];
  decNumber *d=bufd;		   /* divisor */
  decNumber numone;		   /* constant 1 */

  #if DECCHECK
  Int iterations=0;		   /* for later sanity check */
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  do {					/* protect allocated storage */
    if (SPECIALARG) {			/* handle infinities and NaNs */
      if (decNumberIsInfinite(rhs)) {	/* an infinity */
	if (decNumberIsNegative(rhs))	/* -Infinity -> +0 */
	  decNumberZero(res);
	 else decNumberCopy(res, rhs);	/* +Infinity -> self */
	}
       else decNaNs(res, rhs, NULL, set, status); /* a NaN */
      break;}

    if (ISZERO(rhs)) {			/* zeros -> exact 1 */
      decNumberZero(res);		/* make clean 1 */
      *res->lsu=1;			/* .. */
      break;}				/* [no status to set] */

    /* e**x when 0 < x < 0.66 is < 1+3x/2, hence can fast-path */
    /* positive and negative tiny cases which will result in inexact */
    /* 1.  This also allows the later add-accumulate to always be */
    /* exact (because its length will never be more than twice the */
    /* working precision). */
    /* The comparator (tiny) needs just one digit, so use the */
    /* decNumber d for it (reused as the divisor, etc., below); its */
    /* exponent is such that if x is positive it will have */
    /* set->digits-1 zeros between the decimal point and the digit, */
    /* which is 4, and if x is negative one more zero there as the */
    /* more precise result will be of the form 0.9999999 rather than */
    /* 1.0000001.  Hence, tiny will be 0.0000004  if digits=7 and x>0 */
    /* or 0.00000004 if digits=7 and x<0.  If RHS not larger than */
    /* this then the result will be 1.000000 */
    decNumberZero(d);			/* clean */
    *d->lsu=4;				/* set 4 .. */
    d->exponent=-set->digits;		/* * 10**(-d) */
    if (decNumberIsNegative(rhs)) d->exponent--;  /* negative case */
    comp=decCompare(d, rhs, 1); 	/* signless compare */
    if (comp==BADINT) {
      *status|=DEC_Insufficient_storage;
      break;}
    if (comp>=0) {			/* rhs < d */
      Int shift=set->digits-1;
      decNumberZero(res);		/* set 1 */
      *res->lsu=1;			/* .. */
      res->digits=decShiftToMost(res->lsu, 1, shift);
      res->exponent=-shift;		     /* make 1.0000... */
      *status|=DEC_Inexact | DEC_Rounded;    /* .. inexactly */
      break;} /* tiny */

    /* set up the context to be used for calculating a, as this is */
    /* used on both paths below */
    decContextDefault(&aset, DEC_INIT_DECIMAL64);
    /* accumulator bounds are as requested (could underflow) */
    aset.emax=set->emax;		/* usual bounds */
    aset.emin=set->emin;		/* .. */
    aset.clamp=0;			/* and no concrete format */

    /* calculate the adjusted (Hull & Abrham) exponent (where the */
    /* decimal point is just to the left of the coefficient msd) */
    h=rhs->exponent+rhs->digits;
    /* if h>8 then 10**h cannot be calculated safely; however, when */
    /* h=8 then exp(|rhs|) will be at least exp(1E+7) which is at */
    /* least 6.59E+4342944, so (due to the restriction on Emax/Emin) */
    /* overflow (or underflow to 0) is guaranteed -- so this case can */
    /* be handled by simply forcing the appropriate excess */
    if (h>8) {				/* overflow/underflow */
      /* set up here so Power call below will over or underflow to */
      /* zero; set accumulator to either 2 or 0.02 */
      /* [stack buffer for a is always big enough for this] */
      decNumberZero(a);
      *a->lsu=2;			/* not 1 but < exp(1) */
      if (decNumberIsNegative(rhs)) a->exponent=-2; /* make 0.02 */
      h=8;				/* clamp so 10**h computable */
      p=9;				/* set a working precision */
      }
     else {				/* h<=8 */
      Int maxlever=(rhs->digits>8?1:0);
      /* [could/should increase this for precisions >40 or so, too] */

      /* if h is 8, cannot normalize to a lower upper limit because */
      /* the final result will not be computable (see notes above), */
      /* but leverage can be applied whenever h is less than 8. */
      /* Apply as much as possible, up to a MAXLEVER digits, which */
      /* sets the tradeoff against the cost of the later a**(10**h). */
      /* As h is increased, the working precision below also */
      /* increases to compensate for the "constant digits at the */
      /* front" effect. */
      Int lever=MINI(8-h, maxlever);	/* leverage attainable */
      Int use=-rhs->digits-lever;	/* exponent to use for RHS */
      h+=lever; 			/* apply leverage selected */
      if (h<0) {			/* clamp */
	use+=h; 			/* [may end up subnormal] */
	h=0;
	}
      /* Take a copy of RHS if it needs normalization (true whenever x>=1) */
      if (rhs->exponent!=use) {
	decNumber *newrhs=bufr; 	/* assume will fit on stack */
	needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);
	if (needbytes>sizeof(bufr)) {	/* need malloc space */
	  allocrhs=(decNumber *)malloc(needbytes);
	  if (allocrhs==NULL) { 	/* hopeless -- abandon */
	    *status|=DEC_Insufficient_storage;
	    break;}
	  newrhs=allocrhs;		/* use the allocated space */
	  }
	decNumberCopy(newrhs, rhs);	/* copy to safe space */
	newrhs->exponent=use;		/* normalize; now <1 */
	x=newrhs;			/* ready for use */
	/* decNumberShow(x); */
	}

      /* Now use the usual power series to evaluate exp(x).  The */
      /* series starts as 1 + x + x^2/2 ... so prime ready for the */
      /* third term by setting the term variable t=x, the accumulator */
      /* a=1, and the divisor d=2. */

      /* First determine the working precision.  From Hull & Abrham */
      /* this is set->digits+h+2.  However, if x is 'over-precise' we */
      /* need to allow for all its digits to potentially participate */
      /* (consider an x where all the excess digits are 9s) so in */
      /* this case use x->digits+h+2 */
      p=MAXI(x->digits, set->digits)+h+2;    /* [h<=8] */

      /* a and t are variable precision, and depend on p, so space */
      /* must be allocated for them if necessary */

      /* the accumulator needs to be able to hold 2p digits so that */
      /* the additions on the second and subsequent iterations are */
      /* sufficiently exact. */
      needbytes=sizeof(decNumber)+(D2U(p*2)-1)*sizeof(Unit);
      if (needbytes>sizeof(bufa)) {	/* need malloc space */
	allocbufa=(decNumber *)malloc(needbytes);
	if (allocbufa==NULL) {		/* hopeless -- abandon */
	  *status|=DEC_Insufficient_storage;
	  break;}
	a=allocbufa;			/* use the allocated space */
	}
      /* the term needs to be able to hold p digits (which is */
      /* guaranteed to be larger than x->digits, so the initial copy */
      /* is safe); it may also be used for the raise-to-power */
      /* calculation below, which needs an extra two digits */
      needbytes=sizeof(decNumber)+(D2U(p+2)-1)*sizeof(Unit);
      if (needbytes>sizeof(buft)) {	/* need malloc space */
	allocbuft=(decNumber *)malloc(needbytes);
	if (allocbuft==NULL) {		/* hopeless -- abandon */
	  *status|=DEC_Insufficient_storage;
	  break;}
	t=allocbuft;			/* use the allocated space */
	}

      decNumberCopy(t, x);		/* term=x */
      decNumberZero(a); *a->lsu=1;	/* accumulator=1 */
      decNumberZero(d); *d->lsu=2;	/* divisor=2 */
      decNumberZero(&numone); *numone.lsu=1; /* constant 1 for increment */

      /* set up the contexts for calculating a, t, and d */
      decContextDefault(&tset, DEC_INIT_DECIMAL64);
      dset=tset;
      /* accumulator bounds are set above, set precision now */
      aset.digits=p*2;			/* double */
      /* term bounds avoid any underflow or overflow */
      tset.digits=p;
      tset.emin=DEC_MIN_EMIN;		/* [emax is plenty] */
      /* [dset.digits=16, etc., are sufficient] */

      /* finally ready to roll */
      for (;;) {
	#if DECCHECK
	iterations++;
	#endif
	/* only the status from the accumulation is interesting */
	/* [but it should remain unchanged after first add] */
	decAddOp(a, a, t, &aset, 0, status);	       /* a=a+t */
	decMultiplyOp(t, t, x, &tset, &ignore);        /* t=t*x */
	decDivideOp(t, t, d, &tset, DIVIDE, &ignore);  /* t=t/d */
	/* the iteration ends when the term cannot affect the result, */
	/* if rounded to p digits, which is when its value is smaller */
	/* than the accumulator by p+1 digits.	There must also be */
	/* full precision in a. */
	if (((a->digits+a->exponent)>=(t->digits+t->exponent+p+1))
	    && (a->digits>=p)) break;
	decAddOp(d, d, &numone, &dset, 0, &ignore);    /* d=d+1 */
	} /* iterate */

      #if DECCHECK
      /* just a sanity check; comment out test to show always */
      if (iterations>p+3)
	printf("Exp iterations=%ld, status=%08lx, p=%ld, d=%ld\n",
	       (LI)iterations, (LI)*status, (LI)p, (LI)x->digits);
      #endif
      } /* h<=8 */

    /* apply postconditioning: a=a**(10**h) -- this is calculated */
    /* at a slightly higher precision than Hull & Abrham suggest */
    if (h>0) {
      Int seenbit=0;		   /* set once a 1-bit is seen */
      Int i;			   /* counter */
      Int n=powers[h];		   /* always positive */
      aset.digits=p+2;		   /* sufficient precision */
      /* avoid the overhead and many extra digits of decNumberPower */
      /* as all that is needed is the short 'multipliers' loop; here */
      /* accumulate the answer into t */
      decNumberZero(t); *t->lsu=1; /* acc=1 */
      for (i=1;;i++){		   /* for each bit [top bit ignored] */
	/* abandon if have had overflow or terminal underflow */
	if (*status & (DEC_Overflow|DEC_Underflow)) { /* interesting? */
	  if (*status&DEC_Overflow || ISZERO(t)) break;}
	n=n<<1; 		   /* move next bit to testable position */
	if (n<0) {		   /* top bit is set */
	  seenbit=1;		   /* OK, have a significant bit */
	  decMultiplyOp(t, t, a, &aset, status); /* acc=acc*x */
	  }
	if (i==31) break;	   /* that was the last bit */
	if (!seenbit) continue;    /* no need to square 1 */
	decMultiplyOp(t, t, t, &aset, status); /* acc=acc*acc [square] */
	} /*i*/ /* 32 bits */
      /* decNumberShow(t); */
      a=t;			   /* and carry on using t instead of a */
      }

    /* Copy and round the result to res */
    residue=1;				/* indicate dirt to right .. */
    if (ISZERO(a)) residue=0;		/* .. unless underflowed to 0 */
    aset.digits=set->digits;		/* [use default rounding] */
    decCopyFit(res, a, &aset, &residue, status); /* copy & shorten */
    decFinish(res, set, &residue, status);	 /* cleanup/set flags */
    } while(0); 			/* end protected */

  free(allocrhs);	/* drop any storage used */
  free(allocbufa); /* .. */
  free(allocbuft); /* .. */
  /* [status is handled by caller] */
  return res;
  } /* decExpOp */

/* ------------------------------------------------------------------ */
/* Initial-estimate natural logarithm table			      */
/*								      */
/*   LNnn -- 90-entry 16-bit table for values from .10 through .99.   */
/*	     The result is a 4-digit encode of the coefficient (c=the */
/*	     top 14 bits encoding 0-9999) and a 2-digit encode of the */
/*	     exponent (e=the bottom 2 bits encoding 0-3)	      */
/*								      */
/*	     The resulting value is given by:			      */
/*								      */
/*	       v = -c * 10**(-e-3)				      */
/*								      */
/*	     where e and c are extracted from entry k = LNnn[x-10]    */
/*	     where x is truncated (NB) into the range 10 through 99,  */
/*	     and then c = k>>2 and e = k&3.			      */
/* ------------------------------------------------------------------ */
const uShort LNnn[90]={9016,  8652,  8316,  8008,  7724,  7456,  7208,
  6972,  6748,	6540,  6340,  6148,  5968,  5792,  5628,  5464,  5312,
  5164,  5020,	4884,  4748,  4620,  4496,  4376,  4256,  4144,  4032,
 39233, 38181, 37157, 36157, 35181, 34229, 33297, 32389, 31501, 30629,
 29777, 28945, 28129, 27329, 26545, 25777, 25021, 24281, 23553, 22837,
 22137, 21445, 20769, 20101, 19445, 18801, 18165, 17541, 16925, 16321,
 15721, 15133, 14553, 13985, 13421, 12865, 12317, 11777, 11241, 10717,
 10197,  9685,	9177,  8677,  8185,  7697,  7213,  6737,  6269,  5801,
  5341,  4889,	4437, 39930, 35534, 31186, 26886, 22630, 18418, 14254,
 10130,  6046, 20055};

/* ------------------------------------------------------------------ */
/* decLnOp -- effect natural logarithm				      */
/*								      */
/*   This computes C = ln(A)					      */
/*								      */
/*   res is C, the result.  C may be A				      */
/*   rhs is A							      */
/*   set is the context; note that rounding mode has no effect	      */
/*								      */
/* C must have space for set->digits digits.			      */
/*								      */
/* Notable cases:						      */
/*   A<0 -> Invalid						      */
/*   A=0 -> -Infinity (Exact)					      */
/*   A=+Infinity -> +Infinity (Exact)				      */
/*   A=1 exactly -> 0 (Exact)					      */
/*								      */
/* Restrictions (as for Exp):					      */
/*								      */
/*   digits, emax, and -emin in the context must be less than	      */
/*   DEC_MAX_MATH+11 (1000010), and the rhs must be within these      */
/*   bounds or a zero.	This is an internal routine, so these	      */
/*   restrictions are contractual and not enforced.		      */
/*								      */
/* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will      */
/* almost always be correctly rounded, but may be up to 1 ulp in      */
/* error in rare cases. 					      */
/* ------------------------------------------------------------------ */
/* The result is calculated using Newton's method, with each	      */
/* iteration calculating a' = a + x * exp(-a) - 1.  See, for example, */
/* Epperson 1989.						      */
/*								      */
/* The iteration ends when the adjustment x*exp(-a)-1 is tiny enough. */
/* This has to be calculated at the sum of the precision of x and the */
/* working precision.						      */
/*								      */
/* Implementation notes:					      */
/*								      */
/* 1. This is separated out as decLnOp so it can be called from       */
/*    other Mathematical functions (e.g., Log 10) with a wider range  */
/*    than normal.  In particular, it can handle the slightly wider   */
/*    (+9+2) range needed by a power function.			      */
/*								      */
/* 2. The speed of this function is about 10x slower than exp, as     */
/*    it typically needs 4-6 iterations for short numbers, and the    */
/*    extra precision needed adds a squaring effect, twice.	      */
/*								      */
/* 3. Fastpaths are included for ln(10) and ln(2), up to length 40,   */
/*    as these are common requests.  ln(10) is used by log10(x).      */
/*								      */
/* 4. An iteration might be saved by widening the LNnn table, and     */
/*    would certainly save at least one if it were made ten times     */
/*    bigger, too (for truncated fractions 0.100 through 0.999).      */
/*    However, for most practical evaluations, at least four or five  */
/*    iterations will be neede -- so this would only speed up by      */
/*    20-25% and that probably does not justify increasing the table  */
/*    size.							      */
/*								      */
/* 5. The static buffers are larger than might be expected to allow   */
/*    for calls from decNumberPower.				      */
/* ------------------------------------------------------------------ */
decNumber * decLnOp(decNumber *res, const decNumber *rhs,
		    decContext *set, uInt *status) {
  uInt ignore=0;		   /* working status accumulator */
  uInt needbytes;		   /* for space calculations */
  Int residue;			   /* rounding residue */
  Int r;			   /* rhs=f*10**r [see below] */
  Int p;			   /* working precision */
  Int pp;			   /* precision for iteration */
  Int t;			   /* work */

  /* buffers for a (accumulator, typically precision+2) and b */
  /* (adjustment calculator, same size) */
  decNumber bufa[D2N(DECBUFFER+12)];
  decNumber *allocbufa=NULL;	   /* -> allocated bufa, iff allocated */
  decNumber *a=bufa;		   /* accumulator/work */
  decNumber bufb[D2N(DECBUFFER*2+2)];
  decNumber *allocbufb=NULL;	   /* -> allocated bufa, iff allocated */
  decNumber *b=bufb;		   /* adjustment/work */

  decNumber  numone;		   /* constant 1 */
  decNumber  cmp;		   /* work */
  decContext aset, bset;	   /* working contexts */

  #if DECCHECK
  Int iterations=0;		   /* for later sanity check */
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  do {					/* protect allocated storage */
    if (SPECIALARG) {			/* handle infinities and NaNs */
      if (decNumberIsInfinite(rhs)) {	/* an infinity */
	if (decNumberIsNegative(rhs))	/* -Infinity -> error */
	  *status|=DEC_Invalid_operation;
	 else decNumberCopy(res, rhs);	/* +Infinity -> self */
	}
       else decNaNs(res, rhs, NULL, set, status); /* a NaN */
      break;}

    if (ISZERO(rhs)) {			/* +/- zeros -> -Infinity */
      decNumberZero(res);		/* make clean */
      res->bits=DECINF|DECNEG;		/* set - infinity */
      break;}				/* [no status to set] */

    /* Non-zero negatives are bad... */
    if (decNumberIsNegative(rhs)) {	/* -x -> error */
      *status|=DEC_Invalid_operation;
      break;}

    /* Here, rhs is positive, finite, and in range */

    /* lookaside fastpath code for ln(2) and ln(10) at common lengths */
    if (rhs->exponent==0 && set->digits<=40) {
      #if DECDPUN==1
      if (rhs->lsu[0]==0 && rhs->lsu[1]==1 && rhs->digits==2) { /* ln(10) */
      #else
      if (rhs->lsu[0]==10 && rhs->digits==2) {			/* ln(10) */
      #endif
	aset=*set; aset.round=DEC_ROUND_HALF_EVEN;
	#define LN10 "2.302585092994045684017991454684364207601"
	decNumberFromString(res, LN10, &aset);
	*status|=(DEC_Inexact | DEC_Rounded); /* is inexact */
	break;}
      if (rhs->lsu[0]==2 && rhs->digits==1) { /* ln(2) */
	aset=*set; aset.round=DEC_ROUND_HALF_EVEN;
	#define LN2 "0.6931471805599453094172321214581765680755"
	decNumberFromString(res, LN2, &aset);
	*status|=(DEC_Inexact | DEC_Rounded);
	break;}
      } /* integer and short */

    /* Determine the working precision.  This is normally the */
    /* requested precision + 2, with a minimum of 9.  However, if */
    /* the rhs is 'over-precise' then allow for all its digits to */
    /* potentially participate (consider an rhs where all the excess */
    /* digits are 9s) so in this case use rhs->digits+2. */
    p=MAXI(rhs->digits, MAXI(set->digits, 7))+2;

    /* Allocate space for the accumulator and the high-precision */
    /* adjustment calculator, if necessary.  The accumulator must */
    /* be able to hold p digits, and the adjustment up to */
    /* rhs->digits+p digits.  They are also made big enough for 16 */
    /* digits so that they can be used for calculating the initial */
    /* estimate. */
    needbytes=sizeof(decNumber)+(D2U(MAXI(p,16))-1)*sizeof(Unit);
    if (needbytes>sizeof(bufa)) {     /* need malloc space */
      allocbufa=(decNumber *)malloc(needbytes);
      if (allocbufa==NULL) {	      /* hopeless -- abandon */
	*status|=DEC_Insufficient_storage;
	break;}
      a=allocbufa;		      /* use the allocated space */
      }
    pp=p+rhs->digits;
    needbytes=sizeof(decNumber)+(D2U(MAXI(pp,16))-1)*sizeof(Unit);
    if (needbytes>sizeof(bufb)) {     /* need malloc space */
      allocbufb=(decNumber *)malloc(needbytes);
      if (allocbufb==NULL) {	      /* hopeless -- abandon */
	*status|=DEC_Insufficient_storage;
	break;}
      b=allocbufb;		      /* use the allocated space */
      }

    /* Prepare an initial estimate in acc. Calculate this by */
    /* considering the coefficient of x to be a normalized fraction, */
    /* f, with the decimal point at far left and multiplied by */
    /* 10**r.  Then, rhs=f*10**r and 0.1<=f<1, and */
    /*	 ln(x) = ln(f) + ln(10)*r */
    /* Get the initial estimate for ln(f) from a small lookup */
    /* table (see above) indexed by the first two digits of f, */
    /* truncated. */

    decContextDefault(&aset, DEC_INIT_DECIMAL64); /* 16-digit extended */
    r=rhs->exponent+rhs->digits;	/* 'normalised' exponent */
    decNumberFromInt32(a, r);		/* a=r */
    decNumberFromInt32(b, 2302585);	/* b=ln(10) (2.302585) */
    b->exponent=-6;			/*  .. */
    decMultiplyOp(a, a, b, &aset, &ignore);  /* a=a*b */
    /* now get top two digits of rhs into b by simple truncate and */
    /* force to integer */
    residue=0;				/* (no residue) */
    aset.digits=2; aset.round=DEC_ROUND_DOWN;
    decCopyFit(b, rhs, &aset, &residue, &ignore); /* copy & shorten */
    b->exponent=0;			/* make integer */
    t=decGetInt(b);			/* [cannot fail] */
    if (t<10) t=X10(t); 		/* adjust single-digit b */
    t=LNnn[t-10];			/* look up ln(b) */
    decNumberFromInt32(b, t>>2);	/* b=ln(b) coefficient */
    b->exponent=-(t&3)-3;		/* set exponent */
    b->bits=DECNEG;			/* ln(0.10)->ln(0.99) always -ve */
    aset.digits=16; aset.round=DEC_ROUND_HALF_EVEN; /* restore */
    decAddOp(a, a, b, &aset, 0, &ignore); /* acc=a+b */
    /* the initial estimate is now in a, with up to 4 digits correct. */
    /* When rhs is at or near Nmax the estimate will be low, so we */
    /* will approach it from below, avoiding overflow when calling exp. */

    decNumberZero(&numone); *numone.lsu=1;   /* constant 1 for adjustment */

    /* accumulator bounds are as requested (could underflow, but */
    /* cannot overflow) */
    aset.emax=set->emax;
    aset.emin=set->emin;
    aset.clamp=0;			/* no concrete format */
    /* set up a context to be used for the multiply and subtract */
    bset=aset;
    bset.emax=DEC_MAX_MATH*2;		/* use double bounds for the */
    bset.emin=-DEC_MAX_MATH*2;		/* adjustment calculation */
					/* [see decExpOp call below] */
    /* for each iteration double the number of digits to calculate, */
    /* up to a maximum of p */
    pp=9;				/* initial precision */
    /* [initially 9 as then the sequence starts 7+2, 16+2, and */
    /* 34+2, which is ideal for standard-sized numbers] */
    aset.digits=pp;			/* working context */
    bset.digits=pp+rhs->digits; 	/* wider context */
    for (;;) {				/* iterate */
      #if DECCHECK
      iterations++;
      if (iterations>24) break; 	/* consider 9 * 2**24 */
      #endif
      /* calculate the adjustment (exp(-a)*x-1) into b.  This is a */
      /* catastrophic subtraction but it really is the difference */
      /* from 1 that is of interest. */
      /* Use the internal entry point to Exp as it allows the double */
      /* range for calculating exp(-a) when a is the tiniest subnormal. */
      a->bits^=DECNEG;			/* make -a */
      decExpOp(b, a, &bset, &ignore);	/* b=exp(-a) */
      a->bits^=DECNEG;			/* restore sign of a */
      /* now multiply by rhs and subtract 1, at the wider precision */
      decMultiplyOp(b, b, rhs, &bset, &ignore);        /* b=b*rhs */
      decAddOp(b, b, &numone, &bset, DECNEG, &ignore); /* b=b-1 */

      /* the iteration ends when the adjustment cannot affect the */
      /* result by >=0.5 ulp (at the requested digits), which */
      /* is when its value is smaller than the accumulator by */
      /* set->digits+1 digits (or it is zero) -- this is a looser */
      /* requirement than for Exp because all that happens to the */
      /* accumulator after this is the final rounding (but note that */
      /* there must also be full precision in a, or a=0). */

      if (decNumberIsZero(b) ||
	  (a->digits+a->exponent)>=(b->digits+b->exponent+set->digits+1)) {
	if (a->digits==p) break;
	if (decNumberIsZero(a)) {
	  decCompareOp(&cmp, rhs, &numone, &aset, COMPARE, &ignore); /* rhs=1 ? */
	  if (cmp.lsu[0]==0) a->exponent=0;	       /* yes, exact 0 */
	   else *status|=(DEC_Inexact | DEC_Rounded);  /* no, inexact */
	  break;
	  }
	/* force padding if adjustment has gone to 0 before full length */
	if (decNumberIsZero(b)) b->exponent=a->exponent-p;
	}

      /* not done yet ... */
      decAddOp(a, a, b, &aset, 0, &ignore);  /* a=a+b for next estimate */
      if (pp==p) continue;		     /* precision is at maximum */
      /* lengthen the next calculation */
      pp=pp*2;				     /* double precision */
      if (pp>p) pp=p;			     /* clamp to maximum */
      aset.digits=pp;			     /* working context */
      bset.digits=pp+rhs->digits;	     /* wider context */
      } /* Newton's iteration */

    #if DECCHECK
    /* just a sanity check; remove the test to show always */
    if (iterations>24)
      printf("Ln iterations=%ld, status=%08lx, p=%ld, d=%ld\n",
	    (LI)iterations, (LI)*status, (LI)p, (LI)rhs->digits);
    #endif

    /* Copy and round the result to res */
    residue=1;				/* indicate dirt to right */
    if (ISZERO(a)) residue=0;		/* .. unless underflowed to 0 */
    aset.digits=set->digits;		/* [use default rounding] */
    decCopyFit(res, a, &aset, &residue, status); /* copy & shorten */
    decFinish(res, set, &residue, status);	 /* cleanup/set flags */
    } while(0); 			/* end protected */

  free(allocbufa); /* drop any storage used */
  free(allocbufb); /* .. */
  /* [status is handled by caller] */
  return res;
  } /* decLnOp */

/* ------------------------------------------------------------------ */
/* decQuantizeOp  -- force exponent to requested value		      */
/*								      */
/*   This computes C = op(A, B), where op adjusts the coefficient     */
/*   of C (by rounding or shifting) such that the exponent (-scale)   */
/*   of C has the value B or matches the exponent of B. 	      */
/*   The numerical value of C will equal A, except for the effects of */
/*   any rounding that occurred.				      */
/*								      */
/*   res is C, the result.  C may be A or B			      */
/*   lhs is A, the number to adjust				      */
/*   rhs is B, the requested exponent				      */
/*   set is the context 					      */
/*   quant is 1 for quantize or 0 for rescale			      */
/*   status is the status accumulator (this can be called without     */
/*	    risk of control loss)				      */
/*								      */
/* C must have space for set->digits digits.			      */
/*								      */
/* Unless there is an error or the result is infinite, the exponent   */
/* after the operation is guaranteed to be that requested.	      */
/* ------------------------------------------------------------------ */
static decNumber * decQuantizeOp(decNumber *res, const decNumber *lhs,
				 const decNumber *rhs, decContext *set,
				 Flag quant, uInt *status) {
  #if DECSUBSET
  decNumber *alloclhs=NULL;	   /* non-NULL if rounded lhs allocated */
  decNumber *allocrhs=NULL;	   /* .., rhs */
  #endif
  const decNumber *inrhs=rhs;	   /* save original rhs */
  Int	reqdigits=set->digits;	   /* requested DIGITS */
  Int	reqexp; 		   /* requested exponent [-scale] */
  Int	residue=0;		   /* rounding residue */
  Int	etiny=set->emin-(reqdigits-1);

  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  do {				   /* protect allocated storage */
    #if DECSUBSET
    if (!set->extended) {
      /* reduce operands and set lostDigits status, as needed */
      if (lhs->digits>reqdigits) {
	alloclhs=decRoundOperand(lhs, set, status);
	if (alloclhs==NULL) break;
	lhs=alloclhs;
	}
      if (rhs->digits>reqdigits) { /* [this only checks lostDigits] */
	allocrhs=decRoundOperand(rhs, set, status);
	if (allocrhs==NULL) break;
	rhs=allocrhs;
	}
      }
    #endif
    /* [following code does not require input rounding] */

    /* Handle special values */
    if (SPECIALARGS) {
      /* NaNs get usual processing */
      if (SPECIALARGS & (DECSNAN | DECNAN))
	decNaNs(res, lhs, rhs, set, status);
      /* one infinity but not both is bad */
      else if ((lhs->bits ^ rhs->bits) & DECINF)
	*status|=DEC_Invalid_operation;
      /* both infinity: return lhs */
      else decNumberCopy(res, lhs);	     /* [nop if in place] */
      break;
      }

    /* set requested exponent */
    if (quant) reqexp=inrhs->exponent;	/* quantize -- match exponents */
     else {				/* rescale -- use value of rhs */
      /* Original rhs must be an integer that fits and is in range, */
      /* which could be from -1999999997 to +999999999, thanks to */
      /* subnormals */
      reqexp=decGetInt(inrhs);		     /* [cannot fail] */
      }

    #if DECSUBSET
    if (!set->extended) etiny=set->emin;     /* no subnormals */
    #endif

    if (reqexp==BADINT			     /* bad (rescale only) or .. */
     || reqexp==BIGODD || reqexp==BIGEVEN    /* very big (ditto) or .. */
     || (reqexp<etiny)			     /* < lowest */
     || (reqexp>set->emax)) {		     /* > emax */
      *status|=DEC_Invalid_operation;
      break;}

    /* the RHS has been processed, so it can be overwritten now if necessary */
    if (ISZERO(lhs)) {			     /* zero coefficient unchanged */
      decNumberCopy(res, lhs);		     /* [nop if in place] */
      res->exponent=reqexp;		     /* .. just set exponent */
      #if DECSUBSET
      if (!set->extended) res->bits=0;	     /* subset specification; no -0 */
      #endif
      }
     else {				     /* non-zero lhs */
      Int adjust=reqexp-lhs->exponent;	     /* digit adjustment needed */
      /* if adjusted coefficient will definitely not fit, give up now */
      if ((lhs->digits-adjust)>reqdigits) {
	*status|=DEC_Invalid_operation;
	break;
	}

      if (adjust>0) {			     /* increasing exponent */
	/* this will decrease the length of the coefficient by adjust */
	/* digits, and must round as it does so */
	decContext workset;		     /* work */
	workset=*set;			     /* clone rounding, etc. */
	workset.digits=lhs->digits-adjust;   /* set requested length */
	/* [note that the latter can be <1, here] */
	decCopyFit(res, lhs, &workset, &residue, status); /* fit to result */
	decApplyRound(res, &workset, residue, status);	  /* .. and round */
	residue=0;					  /* [used] */
	/* If just rounded a 999s case, exponent will be off by one; */
	/* adjust back (after checking space), if so. */
	if (res->exponent>reqexp) {
	  /* re-check needed, e.g., for quantize(0.9999, 0.001) under */
	  /* set->digits==3 */
	  if (res->digits==reqdigits) {      /* cannot shift by 1 */
	    *status&=~(DEC_Inexact | DEC_Rounded); /* [clean these] */
	    *status|=DEC_Invalid_operation;
	    break;
	    }
	  res->digits=decShiftToMost(res->lsu, res->digits, 1); /* shift */
	  res->exponent--;		     /* (re)adjust the exponent. */
	  }
	#if DECSUBSET
	if (ISZERO(res) && !set->extended) res->bits=0; /* subset; no -0 */
	#endif
	} /* increase */
       else /* adjust<=0 */ {		     /* decreasing or = exponent */
	/* this will increase the length of the coefficient by -adjust */
	/* digits, by adding zero or more trailing zeros; this is */
	/* already checked for fit, above */
	decNumberCopy(res, lhs);	     /* [it will fit] */
	/* if padding needed (adjust<0), add it now... */
	if (adjust<0) {
	  res->digits=decShiftToMost(res->lsu, res->digits, -adjust);
	  res->exponent+=adjust;	     /* adjust the exponent */
	  }
	} /* decrease */
      } /* non-zero */

    /* Check for overflow [do not use Finalize in this case, as an */
    /* overflow here is a "don't fit" situation] */
    if (res->exponent>set->emax-res->digits+1) {  /* too big */
      *status|=DEC_Invalid_operation;
      break;
      }
     else {
      decFinalize(res, set, &residue, status);	  /* set subnormal flags */
      *status&=~DEC_Underflow;		/* suppress Underflow [as per 754] */
      }
    } while(0); 			/* end protected */

  #if DECSUBSET
  free(allocrhs);	/* drop any storage used */
  free(alloclhs);	/* .. */
  #endif
  return res;
  } /* decQuantizeOp */

/* ------------------------------------------------------------------ */
/* decCompareOp -- compare, min, or max two Numbers		      */
/*								      */
/*   This computes C = A ? B and carries out one of four operations:  */
/*     COMPARE	  -- returns the signum (as a number) giving the      */
/*		     result of a comparison unless one or both	      */
/*		     operands is a NaN (in which case a NaN results)  */
/*     COMPSIG	  -- as COMPARE except that a quiet NaN raises	      */
/*		     Invalid operation. 			      */
/*     COMPMAX	  -- returns the larger of the operands, using the    */
/*		     754 maxnum operation			      */
/*     COMPMAXMAG -- ditto, comparing absolute values		      */
/*     COMPMIN	  -- the 754 minnum operation			      */
/*     COMPMINMAG -- ditto, comparing absolute values		      */
/*     COMTOTAL   -- returns the signum (as a number) giving the      */
/*		     result of a comparison using 754 total ordering  */
/*								      */
/*   res is C, the result.  C may be A and/or B (e.g., X=X?X)	      */
/*   lhs is A							      */
/*   rhs is B							      */
/*   set is the context 					      */
/*   op  is the operation flag					      */
/*   status is the usual accumulator				      */
/*								      */
/* C must have space for one digit for COMPARE or set->digits for     */
/* COMPMAX, COMPMIN, COMPMAXMAG, or COMPMINMAG. 		      */
/* ------------------------------------------------------------------ */
/* The emphasis here is on speed for common cases, and avoiding       */
/* coefficient comparison if possible.				      */
/* ------------------------------------------------------------------ */
decNumber * decCompareOp(decNumber *res, const decNumber *lhs,
			 const decNumber *rhs, decContext *set,
			 Flag op, uInt *status) {
  #if DECSUBSET
  decNumber *alloclhs=NULL;	   /* non-NULL if rounded lhs allocated */
  decNumber *allocrhs=NULL;	   /* .., rhs */
  #endif
  Int	result=0;		   /* default result value */
  uByte merged; 		   /* work */

  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  do {				   /* protect allocated storage */
    #if DECSUBSET
    if (!set->extended) {
      /* reduce operands and set lostDigits status, as needed */
      if (lhs->digits>set->digits) {
	alloclhs=decRoundOperand(lhs, set, status);
	if (alloclhs==NULL) {result=BADINT; break;}
	lhs=alloclhs;
	}
      if (rhs->digits>set->digits) {
	allocrhs=decRoundOperand(rhs, set, status);
	if (allocrhs==NULL) {result=BADINT; break;}
	rhs=allocrhs;
	}
      }
    #endif
    /* [following code does not require input rounding] */

    /* If total ordering then handle differing signs 'up front' */
    if (op==COMPTOTAL) {		/* total ordering */
      if (decNumberIsNegative(lhs) && !decNumberIsNegative(rhs)) {
	result=-1;
	break;
	}
      if (!decNumberIsNegative(lhs) && decNumberIsNegative(rhs)) {
	result=+1;
	break;
	}
      }

    /* handle NaNs specially; let infinities drop through */
    /* This assumes sNaN (even just one) leads to NaN. */
    merged=(lhs->bits | rhs->bits) & (DECSNAN | DECNAN);
    if (merged) {			/* a NaN bit set */
      if (op==COMPARE); 		/* result will be NaN */
       else if (op==COMPSIG)		/* treat qNaN as sNaN */
	*status|=DEC_Invalid_operation | DEC_sNaN;
       else if (op==COMPTOTAL) {	/* total ordering, always finite */
	/* signs are known to be the same; compute the ordering here */
	/* as if the signs are both positive, then invert for negatives */
	if (!decNumberIsNaN(lhs)) result=-1;
	 else if (!decNumberIsNaN(rhs)) result=+1;
	 /* here if both NaNs */
	 else if (decNumberIsSNaN(lhs) && decNumberIsQNaN(rhs)) result=-1;
	 else if (decNumberIsQNaN(lhs) && decNumberIsSNaN(rhs)) result=+1;
	 else { /* both NaN or both sNaN */
	  /* now it just depends on the payload */
	  result=decUnitCompare(lhs->lsu, D2U(lhs->digits),
				rhs->lsu, D2U(rhs->digits), 0);
	  /* [Error not possible, as these are 'aligned'] */
	  } /* both same NaNs */
	if (decNumberIsNegative(lhs)) result=-result;
	break;
	} /* total order */

       else if (merged & DECSNAN);	     /* sNaN -> qNaN */
       else { /* here if MIN or MAX and one or two quiet NaNs */
	/* min or max -- 754 rules ignore single NaN */
	if (!decNumberIsNaN(lhs) || !decNumberIsNaN(rhs)) {
	  /* just one NaN; force choice to be the non-NaN operand */
	  op=COMPMAX;
	  if (lhs->bits & DECNAN) result=-1; /* pick rhs */
			     else result=+1; /* pick lhs */
	  break;
	  }
	} /* max or min */
      op=COMPNAN;			     /* use special path */
      decNaNs(res, lhs, rhs, set, status);   /* propagate NaN */
      break;
      }
    /* have numbers */
    if (op==COMPMAXMAG || op==COMPMINMAG) result=decCompare(lhs, rhs, 1);
     else result=decCompare(lhs, rhs, 0);    /* sign matters */
    } while(0); 			     /* end protected */

  if (result==BADINT) *status|=DEC_Insufficient_storage; /* rare */
   else {
    if (op==COMPARE || op==COMPSIG ||op==COMPTOTAL) { /* returning signum */
      if (op==COMPTOTAL && result==0) {
	/* operands are numerically equal or same NaN (and same sign, */
	/* tested first); if identical, leave result 0 */
	if (lhs->exponent!=rhs->exponent) {
	  if (lhs->exponent<rhs->exponent) result=-1;
	   else result=+1;
	  if (decNumberIsNegative(lhs)) result=-result;
	  } /* lexp!=rexp */
	} /* total-order by exponent */
      decNumberZero(res);		/* [always a valid result] */
      if (result!=0) {			/* must be -1 or +1 */
	*res->lsu=1;
	if (result<0) res->bits=DECNEG;
	}
      }
     else if (op==COMPNAN);		/* special, drop through */
     else {				/* MAX or MIN, non-NaN result */
      Int residue=0;			/* rounding accumulator */
      /* choose the operand for the result */
      const decNumber *choice;
      if (result==0) { /* operands are numerically equal */
	/* choose according to sign then exponent (see 754) */
	uByte slhs=(lhs->bits & DECNEG);
	uByte srhs=(rhs->bits & DECNEG);
	#if DECSUBSET
	if (!set->extended) {		/* subset: force left-hand */
	  op=COMPMAX;
	  result=+1;
	  }
	else
	#endif
	if (slhs!=srhs) {	   /* signs differ */
	  if (slhs) result=-1;	   /* rhs is max */
	       else result=+1;	   /* lhs is max */
	  }
	 else if (slhs && srhs) {  /* both negative */
	  if (lhs->exponent<rhs->exponent) result=+1;
				      else result=-1;
	  /* [if equal, use lhs, technically identical] */
	  }
	 else { 		   /* both positive */
	  if (lhs->exponent>rhs->exponent) result=+1;
				      else result=-1;
	  /* [ditto] */
	  }
	} /* numerically equal */
      /* here result will be non-0; reverse if looking for MIN */
      if (op==COMPMIN || op==COMPMINMAG) result=-result;
      choice=(result>0 ? lhs : rhs);	/* choose */
      /* copy chosen to result, rounding if need be */
      decCopyFit(res, choice, set, &residue, status);
      decFinish(res, set, &residue, status);
      }
    }
  #if DECSUBSET
  free(allocrhs);	/* free any storage used */
  free(alloclhs);	/* .. */
  #endif
  return res;
  } /* decCompareOp */

/* ------------------------------------------------------------------ */
/* decCompare -- compare two decNumbers by numerical value	      */
/*								      */
/*  This routine compares A ? B without altering them.		      */
/*								      */
/*  Arg1 is A, a decNumber which is not a NaN			      */
/*  Arg2 is B, a decNumber which is not a NaN			      */
/*  Arg3 is 1 for a sign-independent compare, 0 otherwise	      */
/*								      */
/*  returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure   */
/*  (the only possible failure is an allocation error)		      */
/* ------------------------------------------------------------------ */
static Int decCompare(const decNumber *lhs, const decNumber *rhs,
		      Flag abs) {
  Int	result; 		   /* result value */
  Int	sigr;			   /* rhs signum */
  Int	compare;		   /* work */

  result=1;				     /* assume signum(lhs) */
  if (ISZERO(lhs)) result=0;
  if (abs) {
    if (ISZERO(rhs)) return result;	     /* LHS wins or both 0 */
    /* RHS is non-zero */
    if (result==0) return -1;		     /* LHS is 0; RHS wins */
    /* [here, both non-zero, result=1] */
    }
   else {				     /* signs matter */
    if (result && decNumberIsNegative(lhs)) result=-1;
    sigr=1;				     /* compute signum(rhs) */
    if (ISZERO(rhs)) sigr=0;
     else if (decNumberIsNegative(rhs)) sigr=-1;
    if (result > sigr) return +1;	     /* L > R, return 1 */
    if (result < sigr) return -1;	     /* L < R, return -1 */
    if (result==0) return 0;		       /* both 0 */
    }

  /* signums are the same; both are non-zero */
  if ((lhs->bits | rhs->bits) & DECINF) {    /* one or more infinities */
    if (decNumberIsInfinite(rhs)) {
      if (decNumberIsInfinite(lhs)) result=0;/* both infinite */
       else result=-result;		     /* only rhs infinite */
      }
    return result;
    }
  /* must compare the coefficients, allowing for exponents */
  if (lhs->exponent>rhs->exponent) {	     /* LHS exponent larger */
    /* swap sides, and sign */
    const decNumber *temp=lhs;
    lhs=rhs;
    rhs=temp;
    result=-result;
    }
  compare=decUnitCompare(lhs->lsu, D2U(lhs->digits),
			 rhs->lsu, D2U(rhs->digits),
			 rhs->exponent-lhs->exponent);
  if (compare!=BADINT) compare*=result;      /* comparison succeeded */
  return compare;
  } /* decCompare */

/* ------------------------------------------------------------------ */
/* decUnitCompare -- compare two >=0 integers in Unit arrays	      */
/*								      */
/*  This routine compares A ? B*10**E where A and B are unit arrays   */
/*  A is a plain integer					      */
/*  B has an exponent of E (which must be non-negative) 	      */
/*								      */
/*  Arg1 is A first Unit (lsu)					      */
/*  Arg2 is A length in Units					      */
/*  Arg3 is B first Unit (lsu)					      */
/*  Arg4 is B length in Units					      */
/*  Arg5 is E (0 if the units are aligned)			      */
/*								      */
/*  returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure   */
/*  (the only possible failure is an allocation error, which can      */
/*  only occur if E!=0) 					      */
/* ------------------------------------------------------------------ */
static Int decUnitCompare(const Unit *a, Int alength,
			  const Unit *b, Int blength, Int exp) {
  Unit	*acc;			   /* accumulator for result */
  Unit	accbuff[SD2U(DECBUFFER*2+1)]; /* local buffer */
  Unit	*allocacc=NULL; 	   /* -> allocated acc buffer, iff allocated */
  Int	accunits, need; 	   /* units in use or needed for acc */
  const Unit *l, *r, *u;	   /* work */
  Int	expunits, exprem, result;  /* .. */

  if (exp==0) { 		   /* aligned; fastpath */
    if (alength>blength) return 1;
    if (alength<blength) return -1;
    /* same number of units in both -- need unit-by-unit compare */
    l=a+alength-1;
    r=b+alength-1;
    for (;l>=a; l--, r--) {
      if (*l>*r) return 1;
      if (*l<*r) return -1;
      }
    return 0;			   /* all units match */
    } /* aligned */

  /* Unaligned.  If one is >1 unit longer than the other, padded */
  /* approximately, then can return easily */
  if (alength>blength+(Int)D2U(exp)) return 1;
  if (alength+1<blength+(Int)D2U(exp)) return -1;

  /* Need to do a real subtract.  For this, a result buffer is needed */
  /* even though only the sign is of interest.	Its length needs */
  /* to be the larger of alength and padded blength, +2 */
  need=blength+D2U(exp);		/* maximum real length of B */
  if (need<alength) need=alength;
  need+=2;
  acc=accbuff;				/* assume use local buffer */
  if (need*sizeof(Unit)>sizeof(accbuff)) {
    allocacc=(Unit *)malloc(need*sizeof(Unit));
    if (allocacc==NULL) return BADINT;	/* hopeless -- abandon */
    acc=allocacc;
    }
  /* Calculate units and remainder from exponent. */
  expunits=exp/DECDPUN;
  exprem=exp%DECDPUN;
  /* subtract [A+B*(-m)] */
  accunits=decUnitAddSub(a, alength, b, blength, expunits, acc,
			 -(Int)powers[exprem]);
  /* [UnitAddSub result may have leading zeros, even on zero] */
  if (accunits<0) result=-1;		/* negative result */
   else {				/* non-negative result */
    /* check units of the result before freeing any storage */
    for (u=acc; u<acc+accunits-1 && *u==0;) u++;
    result=(*u==0 ? 0 : +1);
    }
  /* clean up and return the result */
  free(allocacc);	/* drop any storage used */
  return result;
  } /* decUnitCompare */

/* ------------------------------------------------------------------ */
/* decUnitAddSub -- add or subtract two >=0 integers in Unit arrays   */
/*								      */
/*  This routine performs the calculation:			      */
/*								      */
/*  C=A+(B*M)							      */
/*								      */
/*  Where M is in the range -DECDPUNMAX through +DECDPUNMAX.	      */
/*								      */
/*  A may be shorter or longer than B.				      */
/*								      */
/*  Leading zeros are not removed after a calculation.	The result is */
/*  either the same length as the longer of A and B (adding any       */
/*  shift), or one Unit longer than that (if a Unit carry occurred).  */
/*								      */
/*  A and B content are not altered unless C is also A or B.	      */
/*  C may be the same array as A or B, but only if no zero padding is */
/*  requested (that is, C may be B only if bshift==0).		      */
/*  C is filled from the lsu; only those units necessary to complete  */
/*  the calculation are referenced.				      */
/*								      */
/*  Arg1 is A first Unit (lsu)					      */
/*  Arg2 is A length in Units					      */
/*  Arg3 is B first Unit (lsu)					      */
/*  Arg4 is B length in Units					      */
/*  Arg5 is B shift in Units  (>=0; pads with 0 units if positive)    */
/*  Arg6 is C first Unit (lsu)					      */
/*  Arg7 is M, the multiplier					      */
/*								      */
/*  returns the count of Units written to C, which will be non-zero   */
/*  and negated if the result is negative.  That is, the sign of the  */
/*  returned Int is the sign of the result (positive for zero) and    */
/*  the absolute value of the Int is the count of Units.	      */
/*								      */
/*  It is the caller's responsibility to make sure that C size is     */
/*  safe, allowing space if necessary for a one-Unit carry.	      */
/*								      */
/*  This routine is severely performance-critical; *any* change here  */
/*  must be measured (timed) to assure no performance degradation.    */
/*  In particular, trickery here tends to be counter-productive, as   */
/*  increased complexity of code hurts register optimizations on      */
/*  register-poor architectures.  Avoiding divisions is nearly	      */
/*  always a Good Idea, however.				      */
/*								      */
/* Special thanks to Rick McGuire (IBM Cambridge, MA) and Dave Clark  */
/* (IBM Warwick, UK) for some of the ideas used in this routine.      */
/* ------------------------------------------------------------------ */
static Int decUnitAddSub(const Unit *a, Int alength,
			 const Unit *b, Int blength, Int bshift,
			 Unit *c, Int m) {
  const Unit *alsu=a;		   /* A lsu [need to remember it] */
  Unit *clsu=c; 		   /* C ditto */
  Unit *minC;			   /* low water mark for C */
  Unit *maxC;			   /* high water mark for C */
  eInt carry=0; 		   /* carry integer (could be Long) */
  Int  add;			   /* work */
  #if DECDPUN<=4		   /* myriadal, millenary, etc. */
  Int  est;			   /* estimated quotient */
  #endif

  #if DECTRACE
  if (alength<1 || blength<1)
    printf("decUnitAddSub: alen blen m %ld %ld [%ld]\n", alength, blength, m);
  #endif

  maxC=c+alength;		   /* A is usually the longer */
  minC=c+blength;		   /* .. and B the shorter */
  if (bshift!=0) {		   /* B is shifted; low As copy across */
    minC+=bshift;
    /* if in place [common], skip copy unless there's a gap [rare] */
    if (a==c && bshift<=alength) {
      c+=bshift;
      a+=bshift;
      }
     else for (; c<clsu+bshift; a++, c++) {  /* copy needed */
      if (a<alsu+alength) *c=*a;
       else *c=0;
      }
    }
  if (minC>maxC) { /* swap */
    Unit *hold=minC;
    minC=maxC;
    maxC=hold;
    }

  /* For speed, do the addition as two loops; the first where both A */
  /* and B contribute, and the second (if necessary) where only one or */
  /* other of the numbers contribute. */
  /* Carry handling is the same (i.e., duplicated) in each case. */
  for (; c<minC; c++) {
    carry+=*a;
    a++;
    carry+=((eInt)*b)*m;		/* [special-casing m=1/-1 */
    b++;				/* here is not a win] */
    /* here carry is new Unit of digits; it could be +ve or -ve */
    if ((ueInt)carry<=DECDPUNMAX) {	/* fastpath 0-DECDPUNMAX */
      *c=(Unit)carry;
      carry=0;
      continue;
      }
    #if DECDPUN==4			     /* use divide-by-multiply */
      if (carry>=0) {
	est=(((ueInt)carry>>11)*53687)>>18;
	*c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
	carry=est;			     /* likely quotient [89%] */
	if (*c<DECDPUNMAX+1) continue;	     /* estimate was correct */
	carry++;
	*c-=DECDPUNMAX+1;
	continue;
	}
      /* negative case */
      carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
      est=(((ueInt)carry>>11)*53687)>>18;
      *c=(Unit)(carry-est*(DECDPUNMAX+1));
      carry=est-(DECDPUNMAX+1); 	     /* correctly negative */
      if (*c<DECDPUNMAX+1) continue;	     /* was OK */
      carry++;
      *c-=DECDPUNMAX+1;
    #elif DECDPUN==3
      if (carry>=0) {
	est=(((ueInt)carry>>3)*16777)>>21;
	*c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
	carry=est;			     /* likely quotient [99%] */
	if (*c<DECDPUNMAX+1) continue;	     /* estimate was correct */
	carry++;
	*c-=DECDPUNMAX+1;
	continue;
	}
      /* negative case */
      carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
      est=(((ueInt)carry>>3)*16777)>>21;
      *c=(Unit)(carry-est*(DECDPUNMAX+1));
      carry=est-(DECDPUNMAX+1); 	     /* correctly negative */
      if (*c<DECDPUNMAX+1) continue;	     /* was OK */
      carry++;
      *c-=DECDPUNMAX+1;
    #elif DECDPUN<=2
      /* Can use QUOT10 as carry <= 4 digits */
      if (carry>=0) {
	est=QUOT10(carry, DECDPUN);
	*c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
	carry=est;			     /* quotient */
	continue;
	}
      /* negative case */
      carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
      est=QUOT10(carry, DECDPUN);
      *c=(Unit)(carry-est*(DECDPUNMAX+1));
      carry=est-(DECDPUNMAX+1); 	     /* correctly negative */
    #else
      /* remainder operator is undefined if negative, so must test */
      if ((ueInt)carry<(DECDPUNMAX+1)*2) {   /* fastpath carry +1 */
	*c=(Unit)(carry-(DECDPUNMAX+1));     /* [helps additions] */
	carry=1;
	continue;
	}
      if (carry>=0) {
	*c=(Unit)(carry%(DECDPUNMAX+1));
	carry=carry/(DECDPUNMAX+1);
	continue;
	}
      /* negative case */
      carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
      *c=(Unit)(carry%(DECDPUNMAX+1));
      carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1);
    #endif
    } /* c */

  /* now may have one or other to complete */
  /* [pretest to avoid loop setup/shutdown] */
  if (c<maxC) for (; c<maxC; c++) {
    if (a<alsu+alength) {		/* still in A */
      carry+=*a;
      a++;
      }
     else {				/* inside B */
      carry+=((eInt)*b)*m;
      b++;
      }
    /* here carry is new Unit of digits; it could be +ve or -ve and */
    /* magnitude up to DECDPUNMAX squared */
    if ((ueInt)carry<=DECDPUNMAX) {	/* fastpath 0-DECDPUNMAX */
      *c=(Unit)carry;
      carry=0;
      continue;
      }
    /* result for this unit is negative or >DECDPUNMAX */
    #if DECDPUN==4			     /* use divide-by-multiply */
      if (carry>=0) {
	est=(((ueInt)carry>>11)*53687)>>18;
	*c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
	carry=est;			     /* likely quotient [79.7%] */
	if (*c<DECDPUNMAX+1) continue;	     /* estimate was correct */
	carry++;
	*c-=DECDPUNMAX+1;
	continue;
	}
      /* negative case */
      carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
      est=(((ueInt)carry>>11)*53687)>>18;
      *c=(Unit)(carry-est*(DECDPUNMAX+1));
      carry=est-(DECDPUNMAX+1); 	     /* correctly negative */
      if (*c<DECDPUNMAX+1) continue;	     /* was OK */
      carry++;
      *c-=DECDPUNMAX+1;
    #elif DECDPUN==3
      if (carry>=0) {
	est=(((ueInt)carry>>3)*16777)>>21;
	*c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
	carry=est;			     /* likely quotient [99%] */
	if (*c<DECDPUNMAX+1) continue;	     /* estimate was correct */
	carry++;
	*c-=DECDPUNMAX+1;
	continue;
	}
      /* negative case */
      carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
      est=(((ueInt)carry>>3)*16777)>>21;
      *c=(Unit)(carry-est*(DECDPUNMAX+1));
      carry=est-(DECDPUNMAX+1); 	     /* correctly negative */
      if (*c<DECDPUNMAX+1) continue;	     /* was OK */
      carry++;
      *c-=DECDPUNMAX+1;
    #elif DECDPUN<=2
      if (carry>=0) {
	est=QUOT10(carry, DECDPUN);
	*c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
	carry=est;			     /* quotient */
	continue;
	}
      /* negative case */
      carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
      est=QUOT10(carry, DECDPUN);
      *c=(Unit)(carry-est*(DECDPUNMAX+1));
      carry=est-(DECDPUNMAX+1); 	     /* correctly negative */
    #else
      if ((ueInt)carry<(DECDPUNMAX+1)*2){    /* fastpath carry 1 */
	*c=(Unit)(carry-(DECDPUNMAX+1));
	carry=1;
	continue;
	}
      /* remainder operator is undefined if negative, so must test */
      if (carry>=0) {
	*c=(Unit)(carry%(DECDPUNMAX+1));
	carry=carry/(DECDPUNMAX+1);
	continue;
	}
      /* negative case */
      carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
      *c=(Unit)(carry%(DECDPUNMAX+1));
      carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1);
    #endif
    } /* c */

  /* OK, all A and B processed; might still have carry or borrow */
  /* return number of Units in the result, negated if a borrow */
  if (carry==0) return c-clsu;	   /* no carry, so no more to do */
  if (carry>0) {		   /* positive carry */
    *c=(Unit)carry;		   /* place as new unit */
    c++;			   /* .. */
    return c-clsu;
    }
  /* -ve carry: it's a borrow; complement needed */
  add=1;			   /* temporary carry... */
  for (c=clsu; c<maxC; c++) {
    add=DECDPUNMAX+add-*c;
    if (add<=DECDPUNMAX) {
      *c=(Unit)add;
      add=0;
      }
     else {
      *c=0;
      add=1;
      }
    }
  /* add an extra unit iff it would be non-zero */
  #if DECTRACE
    printf("UAS borrow: add %ld, carry %ld\n", add, carry);
  #endif
  if ((add-carry-1)!=0) {
    *c=(Unit)(add-carry-1);
    c++;		      /* interesting, include it */
    }
  return clsu-c;	      /* -ve result indicates borrowed */
  } /* decUnitAddSub */

/* ------------------------------------------------------------------ */
/* decTrim -- trim trailing zeros or normalize			      */
/*								      */
/*   dn is the number to trim or normalize			      */
/*   set is the context to use to check for clamp		      */
/*   all is 1 to remove all trailing zeros, 0 for just fraction ones  */
/*   noclamp is 1 to unconditional (unclamped) trim		      */
/*   dropped returns the number of discarded trailing zeros	      */
/*   returns dn 						      */
/*								      */
/* If clamp is set in the context then the number of zeros trimmed    */
/* may be limited if the exponent is high.			      */
/* All fields are updated as required.	This is a utility operation,  */
/* so special values are unchanged and no error is possible.	      */
/* ------------------------------------------------------------------ */
static decNumber * decTrim(decNumber *dn, decContext *set, Flag all,
			   Flag noclamp, Int *dropped) {
  Int	d, exp; 		   /* work */
  uInt	cut;			   /* .. */
  Unit	*up;			   /* -> current Unit */

  #if DECCHECK
  if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn;
  #endif

  *dropped=0;				/* assume no zeros dropped */
  if ((dn->bits & DECSPECIAL)		/* fast exit if special .. */
    || (*dn->lsu & 0x01)) return dn;	/* .. or odd */
  if (ISZERO(dn)) {			/* .. or 0 */
    dn->exponent=0;			/* (sign is preserved) */
    return dn;
    }

  /* have a finite number which is even */
  exp=dn->exponent;
  cut=1;			   /* digit (1-DECDPUN) in Unit */
  up=dn->lsu;			   /* -> current Unit */
  for (d=0; d<dn->digits-1; d++) { /* [don't strip the final digit] */
    /* slice by powers */
    #if DECDPUN<=4
      uInt quot=QUOT10(*up, cut);
      if ((*up-quot*powers[cut])!=0) break;  /* found non-0 digit */
    #else
      if (*up%powers[cut]!=0) break;	     /* found non-0 digit */
    #endif
    /* have a trailing 0 */
    if (!all) { 		   /* trimming */
      /* [if exp>0 then all trailing 0s are significant for trim] */
      if (exp<=0) {		   /* if digit might be significant */
	if (exp==0) break;	   /* then quit */
	exp++;			   /* next digit might be significant */
	}
      }
    cut++;			   /* next power */
    if (cut>DECDPUN) {		   /* need new Unit */
      up++;
      cut=1;
      }
    } /* d */
  if (d==0) return dn;		   /* none to drop */

  /* may need to limit drop if clamping */
  if (set->clamp && !noclamp) {
    Int maxd=set->emax-set->digits+1-dn->exponent;
    if (maxd<=0) return dn;	   /* nothing possible */
    if (d>maxd) d=maxd;
    }

  /* effect the drop */
  decShiftToLeast(dn->lsu, D2U(dn->digits), d);
  dn->exponent+=d;		   /* maintain numerical value */
  dn->digits-=d;		   /* new length */
  *dropped=d;			   /* report the count */
  return dn;
  } /* decTrim */

/* ------------------------------------------------------------------ */
/* decReverse -- reverse a Unit array in place			      */
/*								      */
/*   ulo    is the start of the array				      */
/*   uhi    is the end of the array (highest Unit to include)	      */
/*								      */
/* The units ulo through uhi are reversed in place (if the number     */
/* of units is odd, the middle one is untouched).  Note that the      */
/* digit(s) in each unit are unaffected.			      */
/* ------------------------------------------------------------------ */
static void decReverse(Unit *ulo, Unit *uhi) {
  Unit temp;
  for (; ulo<uhi; ulo++, uhi--) {
    temp=*ulo;
    *ulo=*uhi;
    *uhi=temp;
    }
  return;
  } /* decReverse */

/* ------------------------------------------------------------------ */
/* decShiftToMost -- shift digits in array towards most significant   */
/*								      */
/*   uar    is the array					      */
/*   digits is the count of digits in use in the array		      */
/*   shift  is the number of zeros to pad with (least significant);   */
/*     it must be zero or positive				      */
/*								      */
/*   returns the new length of the integer in the array, in digits    */
/*								      */
/* No overflow is permitted (that is, the uar array must be known to  */
/* be large enough to hold the result, after shifting). 	      */
/* ------------------------------------------------------------------ */
static Int decShiftToMost(Unit *uar, Int digits, Int shift) {
  Unit	*target, *source, *first;  /* work */
  Int	cut;			   /* odd 0's to add */
  uInt	next;			   /* work */

  if (shift==0) return digits;	   /* [fastpath] nothing to do */
  if ((digits+shift)<=DECDPUN) {   /* [fastpath] single-unit case */
    *uar=(Unit)(*uar*powers[shift]);
    return digits+shift;
    }

  next=0;			   /* all paths */
  source=uar+D2U(digits)-1;	   /* where msu comes from */
  target=source+D2U(shift);	   /* where upper part of first cut goes */
  cut=DECDPUN-MSUDIGITS(shift);    /* where to slice */
  if (cut==0) { 		   /* unit-boundary case */
    for (; source>=uar; source--, target--) *target=*source;
    }
   else {
    first=uar+D2U(digits+shift)-1; /* where msu of source will end up */
    for (; source>=uar; source--, target--) {
      /* split the source Unit and accumulate remainder for next */
      #if DECDPUN<=4
	uInt quot=QUOT10(*source, cut);
	uInt rem=*source-quot*powers[cut];
	next+=quot;
      #else
	uInt rem=*source%powers[cut];
	next+=*source/powers[cut];
      #endif
      if (target<=first) *target=(Unit)next;   /* write to target iff valid */
      next=rem*powers[DECDPUN-cut];	       /* save remainder for next Unit */
      }
    } /* shift-move */

  /* propagate any partial unit to one below and clear the rest */
  for (; target>=uar; target--) {
    *target=(Unit)next;
    next=0;
    }
  return digits+shift;
  } /* decShiftToMost */

/* ------------------------------------------------------------------ */
/* decShiftToLeast -- shift digits in array towards least significant */
/*								      */
/*   uar   is the array 					      */
/*   units is length of the array, in units			      */
/*   shift is the number of digits to remove from the lsu end; it     */
/*     must be zero or positive and <= than units*DECDPUN.	      */
/*								      */
/*   returns the new length of the integer in the array, in units     */
/*								      */
/* Removed digits are discarded (lost).  Units not required to hold   */
/* the final result are unchanged.				      */
/* ------------------------------------------------------------------ */
static Int decShiftToLeast(Unit *uar, Int units, Int shift) {
  Unit	*target, *up;		   /* work */
  Int	cut, count;		   /* work */
  Int	quot, rem;		   /* for division */

  if (shift==0) return units;	   /* [fastpath] nothing to do */
  if (shift==units*DECDPUN) {	   /* [fastpath] little to do */
    *uar=0;			   /* all digits cleared gives zero */
    return 1;			   /* leaves just the one */
    }

  target=uar;			   /* both paths */
  cut=MSUDIGITS(shift);
  if (cut==DECDPUN) {		   /* unit-boundary case; easy */
    up=uar+D2U(shift);
    for (; up<uar+units; target++, up++) *target=*up;
    return target-uar;
    }

  /* messier */
  up=uar+D2U(shift-cut);	   /* source; correct to whole Units */
  count=units*DECDPUN-shift;	   /* the maximum new length */
  #if DECDPUN<=4
    quot=QUOT10(*up, cut);
  #else
    quot=*up/powers[cut];
  #endif
  for (; ; target++) {
    *target=(Unit)quot;
    count-=(DECDPUN-cut);
    if (count<=0) break;
    up++;
    quot=*up;
    #if DECDPUN<=4
      quot=QUOT10(quot, cut);
      rem=*up-quot*powers[cut];
    #else
      rem=quot%powers[cut];
      quot=quot/powers[cut];
    #endif
    *target=(Unit)(*target+rem*powers[DECDPUN-cut]);
    count-=cut;
    if (count<=0) break;
    }
  return target-uar+1;
  } /* decShiftToLeast */

#if DECSUBSET
/* ------------------------------------------------------------------ */
/* decRoundOperand -- round an operand	[used for subset only]	      */
/*								      */
/*   dn is the number to round (dn->digits is > set->digits)	      */
/*   set is the relevant context				      */
/*   status is the status accumulator				      */
/*								      */
/*   returns an allocated decNumber with the rounded result.	      */
/*								      */
/* lostDigits and other status may be set by this.		      */
/*								      */
/* Since the input is an operand, it must not be modified.	      */
/* Instead, return an allocated decNumber, rounded as required.       */
/* It is the caller's responsibility to free the allocated storage.   */
/*								      */
/* If no storage is available then the result cannot be used, so NULL */
/* is returned. 						      */
/* ------------------------------------------------------------------ */
static decNumber *decRoundOperand(const decNumber *dn, decContext *set,
				  uInt *status) {
  decNumber *res;			/* result structure */
  uInt newstatus=0;			/* status from round */
  Int  residue=0;			/* rounding accumulator */

  /* Allocate storage for the returned decNumber, big enough for the */
  /* length specified by the context */
  res=(decNumber *)malloc(sizeof(decNumber)
			  +(D2U(set->digits)-1)*sizeof(Unit));
  if (res==NULL) {
    *status|=DEC_Insufficient_storage;
    return NULL;
    }
  decCopyFit(res, dn, set, &residue, &newstatus);
  decApplyRound(res, set, residue, &newstatus);

  /* If that set Inexact then "lost digits" is raised... */
  if (newstatus & DEC_Inexact) newstatus|=DEC_Lost_digits;
  *status|=newstatus;
  return res;
  } /* decRoundOperand */
#endif

/* ------------------------------------------------------------------ */
/* decCopyFit -- copy a number, truncating the coefficient if needed  */
/*								      */
/*   dest is the target decNumber				      */
/*   src  is the source decNumber				      */
/*   set is the context [used for length (digits) and rounding mode]  */
/*   residue is the residue accumulator 			      */
/*   status contains the current status to be updated		      */
/*								      */
/* (dest==src is allowed and will be a no-op if fits)		      */
/* All fields are updated as required.				      */
/* ------------------------------------------------------------------ */
static void decCopyFit(decNumber *dest, const decNumber *src,
		       decContext *set, Int *residue, uInt *status) {
  dest->bits=src->bits;
  dest->exponent=src->exponent;
  decSetCoeff(dest, set, src->lsu, src->digits, residue, status);
  } /* decCopyFit */

/* ------------------------------------------------------------------ */
/* decSetCoeff -- set the coefficient of a number		      */
/*								      */
/*   dn    is the number whose coefficient array is to be set.	      */
/*	   It must have space for set->digits digits		      */
/*   set   is the context [for size]				      */
/*   lsu   -> lsu of the source coefficient [may be dn->lsu]	      */
/*   len   is digits in the source coefficient [may be dn->digits]    */
/*   residue is the residue accumulator.  This has values as in       */
/*	   decApplyRound, and will be unchanged unless the	      */
/*	   target size is less than len.  In this case, the	      */
/*	   coefficient is truncated and the residue is updated to     */
/*	   reflect the previous residue and the dropped digits.       */
/*   status is the status accumulator, as usual 		      */
/*								      */
/* The coefficient may already be in the number, or it can be an      */
/* external intermediate array.  If it is in the number, lsu must ==  */
/* dn->lsu and len must == dn->digits.				      */
/*								      */
/* Note that the coefficient length (len) may be < set->digits, and   */
/* in this case this merely copies the coefficient (or is a no-op     */
/* if dn->lsu==lsu).						      */
/*								      */
/* Note also that (only internally, from decQuantizeOp and	      */
/* decSetSubnormal) the value of set->digits may be less than one,    */
/* indicating a round to left.	This routine handles that case	      */
/* correctly; caller ensures space.				      */
/*								      */
/* dn->digits, dn->lsu (and as required), and dn->exponent are	      */
/* updated as necessary.   dn->bits (sign) is unchanged.	      */
/*								      */
/* DEC_Rounded status is set if any digits are discarded.	      */
/* DEC_Inexact status is set if any non-zero digits are discarded, or */
/*			 incoming residue was non-0 (implies rounded) */
/* ------------------------------------------------------------------ */
/* mapping array: maps 0-9 to canonical residues, so that a residue */
/* can be adjusted in the range [-1, +1] and achieve correct rounding */
/*			       0  1  2	3  4  5  6  7  8  9 */
static const uByte resmap[10]={0, 3, 3, 3, 3, 5, 7, 7, 7, 7};
static void decSetCoeff(decNumber *dn, decContext *set, const Unit *lsu,
			Int len, Int *residue, uInt *status) {
  Int	discard;	      /* number of digits to discard */
  uInt	cut;		      /* cut point in Unit */
  const Unit *up;	      /* work */
  Unit	*target;	      /* .. */
  Int	count;		      /* .. */
  #if DECDPUN<=4
  uInt	temp;		      /* .. */
  #endif

  discard=len-set->digits;    /* digits to discard */
  if (discard<=0) {	      /* no digits are being discarded */
    if (dn->lsu!=lsu) {       /* copy needed */
      /* copy the coefficient array to the result number; no shift needed */
      count=len;	      /* avoids D2U */
      up=lsu;
      for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN)
	*target=*up;
      dn->digits=len;	      /* set the new length */
      }
    /* dn->exponent and residue are unchanged, record any inexactitude */
    if (*residue!=0) *status|=(DEC_Inexact | DEC_Rounded);
    return;
    }

  /* some digits must be discarded ... */
  dn->exponent+=discard;      /* maintain numerical value */
  *status|=DEC_Rounded;       /* accumulate Rounded status */
  if (*residue>1) *residue=1; /* previous residue now to right, so reduce */

  if (discard>len) {	      /* everything, +1, is being discarded */
    /* guard digit is 0 */
    /* residue is all the number [NB could be all 0s] */
    if (*residue<=0) {	      /* not already positive */
      count=len;	      /* avoids D2U */
      for (up=lsu; count>0; up++, count-=DECDPUN) if (*up!=0) { /* found non-0 */
	*residue=1;
	break;		      /* no need to check any others */
	}
      }
    if (*residue!=0) *status|=DEC_Inexact; /* record inexactitude */
    *dn->lsu=0; 	      /* coefficient will now be 0 */
    dn->digits=1;	      /* .. */
    return;
    } /* total discard */

  /* partial discard [most common case] */
  /* here, at least the first (most significant) discarded digit exists */

  /* spin up the number, noting residue during the spin, until get to */
  /* the Unit with the first discarded digit.  When reach it, extract */
  /* it and remember its position */
  count=0;
  for (up=lsu;; up++) {
    count+=DECDPUN;
    if (count>=discard) break; /* full ones all checked */
    if (*up!=0) *residue=1;
    } /* up */

  /* here up -> Unit with first discarded digit */
  cut=discard-(count-DECDPUN)-1;
  if (cut==DECDPUN-1) {       /* unit-boundary case (fast) */
    Unit half=(Unit)powers[DECDPUN]>>1;
    /* set residue directly */
    if (*up>=half) {
      if (*up>half) *residue=7;
      else *residue+=5;       /* add sticky bit */
      }
     else { /* <half */
      if (*up!=0) *residue=3; /* [else is 0, leave as sticky bit] */
      }
    if (set->digits<=0) {     /* special for Quantize/Subnormal :-( */
      *dn->lsu=0;	      /* .. result is 0 */
      dn->digits=1;	      /* .. */
      }
     else {		      /* shift to least */
      count=set->digits;      /* now digits to end up with */
      dn->digits=count;       /* set the new length */
      up++;		      /* move to next */
      /* on unit boundary, so shift-down copy loop is simple */
      for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN)
	*target=*up;
      }
    } /* unit-boundary case */

   else { /* discard digit is in low digit(s), and not top digit */
    uInt  discard1;		   /* first discarded digit */
    uInt  quot, rem;		   /* for divisions */
    if (cut==0) quot=*up;	   /* is at bottom of unit */
     else /* cut>0 */ { 	   /* it's not at bottom of unit */
      #if DECDPUN<=4
	quot=QUOT10(*up, cut);
	rem=*up-quot*powers[cut];
      #else
	rem=*up%powers[cut];
	quot=*up/powers[cut];
      #endif
      if (rem!=0) *residue=1;
      }
    /* discard digit is now at bottom of quot */
    #if DECDPUN<=4
      temp=(quot*6554)>>16;	   /* fast /10 */
      /* Vowels algorithm here not a win (9 instructions) */
      discard1=quot-X10(temp);
      quot=temp;
    #else
      discard1=quot%10;
      quot=quot/10;
    #endif
    /* here, discard1 is the guard digit, and residue is everything */
    /* else [use mapping array to accumulate residue safely] */
    *residue+=resmap[discard1];
    cut++;			   /* update cut */
    /* here: up -> Unit of the array with bottom digit */
    /*	     cut is the division point for each Unit */
    /*	     quot holds the uncut high-order digits for the current unit */
    if (set->digits<=0) {	   /* special for Quantize/Subnormal :-( */
      *dn->lsu=0;		   /* .. result is 0 */
      dn->digits=1;		   /* .. */
      }
     else {			   /* shift to least needed */
      count=set->digits;	   /* now digits to end up with */
      dn->digits=count; 	   /* set the new length */
      /* shift-copy the coefficient array to the result number */
      for (target=dn->lsu; ; target++) {
	*target=(Unit)quot;
	count-=(DECDPUN-cut);
	if (count<=0) break;
	up++;
	quot=*up;
	#if DECDPUN<=4
	  quot=QUOT10(quot, cut);
	  rem=*up-quot*powers[cut];
	#else
	  rem=quot%powers[cut];
	  quot=quot/powers[cut];
	#endif
	*target=(Unit)(*target+rem*powers[DECDPUN-cut]);
	count-=cut;
	if (count<=0) break;
	} /* shift-copy loop */
      } /* shift to least */
    } /* not unit boundary */

  if (*residue!=0) *status|=DEC_Inexact; /* record inexactitude */
  return;
  } /* decSetCoeff */

/* ------------------------------------------------------------------ */
/* decApplyRound -- apply pending rounding to a number		      */
/*								      */
/*   dn    is the number, with space for set->digits digits	      */
/*   set   is the context [for size and rounding mode]		      */
/*   residue indicates pending rounding, being any accumulated	      */
/*	   guard and sticky information.  It may be:		      */
/*	   6-9: rounding digit is >5				      */
/*	   5:	rounding digit is exactly half-way		      */
/*	   1-4: rounding digit is <5 and >0			      */
/*	   0:	the coefficient is exact			      */
/*	  -1:	as 1, but the hidden digits are subtractive, that     */
/*		is, of the opposite sign to dn.  In this case the     */
/*		coefficient must be non-0.  This case occurs when     */
/*		subtracting a small number (which can be reduced to   */
/*		a sticky bit); see decAddOp.			      */
/*   status is the status accumulator, as usual 		      */
/*								      */
/* This routine applies rounding while keeping the length of the      */
/* coefficient constant.  The exponent and status are unchanged       */
/* except if:							      */
/*								      */
/*   -- the coefficient was increased and is all nines (in which      */
/*	case Overflow could occur, and is handled directly here so    */
/*	the caller does not need to re-test for overflow)	      */
/*								      */
/*   -- the coefficient was decreased and becomes all nines (in which */
/*	case Underflow could occur, and is also handled directly).    */
/*								      */
/* All fields in dn are updated as required.			      */
/*								      */
/* ------------------------------------------------------------------ */
static void decApplyRound(decNumber *dn, decContext *set, Int residue,
			  uInt *status) {
  Int  bump;		      /* 1 if coefficient needs to be incremented */
			      /* -1 if coefficient needs to be decremented */

  if (residue==0) return;     /* nothing to apply */

  bump=0;		      /* assume a smooth ride */

  /* now decide whether, and how, to round, depending on mode */
  switch (set->round) {
    case DEC_ROUND_05UP: {    /* round zero or five up (for reround) */
      /* This is the same as DEC_ROUND_DOWN unless there is a */
      /* positive residue and the lsd of dn is 0 or 5, in which case */
      /* it is bumped; when residue is <0, the number is therefore */
      /* bumped down unless the final digit was 1 or 6 (in which */
      /* case it is bumped down and then up -- a no-op) */
      Int lsd5=*dn->lsu%5;     /* get lsd and quintate */
      if (residue<0 && lsd5!=1) bump=-1;
       else if (residue>0 && lsd5==0) bump=1;
      /* [bump==1 could be applied directly; use common path for clarity] */
      break;} /* r-05 */

    case DEC_ROUND_DOWN: {
      /* no change, except if negative residue */
      if (residue<0) bump=-1;
      break;} /* r-d */

    case DEC_ROUND_HALF_DOWN: {
      if (residue>5) bump=1;
      break;} /* r-h-d */

    case DEC_ROUND_HALF_EVEN: {
      if (residue>5) bump=1;		/* >0.5 goes up */
       else if (residue==5) {		/* exactly 0.5000... */
	/* 0.5 goes up iff [new] lsd is odd */
	if (*dn->lsu & 0x01) bump=1;
	}
      break;} /* r-h-e */

    case DEC_ROUND_HALF_UP: {
      if (residue>=5) bump=1;
      break;} /* r-h-u */

    case DEC_ROUND_UP: {
      if (residue>0) bump=1;
      break;} /* r-u */

    case DEC_ROUND_CEILING: {
      /* same as _UP for positive numbers, and as _DOWN for negatives */
      /* [negative residue cannot occur on 0] */
      if (decNumberIsNegative(dn)) {
	if (residue<0) bump=-1;
	}
       else {
	if (residue>0) bump=1;
	}
      break;} /* r-c */

    case DEC_ROUND_FLOOR: {
      /* same as _UP for negative numbers, and as _DOWN for positive */
      /* [negative residue cannot occur on 0] */
      if (!decNumberIsNegative(dn)) {
	if (residue<0) bump=-1;
	}
       else {
	if (residue>0) bump=1;
	}
      break;} /* r-f */

    default: {	    /* e.g., DEC_ROUND_MAX */
      *status|=DEC_Invalid_context;
      #if DECTRACE || (DECCHECK && DECVERB)
      printf("Unknown rounding mode: %d\n", set->round);
      #endif
      break;}
    } /* switch */

  /* now bump the number, up or down, if need be */
  if (bump==0) return;			     /* no action required */

  /* Simply use decUnitAddSub unless bumping up and the number is */
  /* all nines.  In this special case set to 100... explicitly */
  /* and adjust the exponent by one (as otherwise could overflow */
  /* the array) */
  /* Similarly handle all-nines result if bumping down. */
  if (bump>0) {
    Unit *up;				     /* work */
    uInt count=dn->digits;		     /* digits to be checked */
    for (up=dn->lsu; ; up++) {
      if (count<=DECDPUN) {
	/* this is the last Unit (the msu) */
	if (*up!=powers[count]-1) break;     /* not still 9s */
	/* here if it, too, is all nines */
	*up=(Unit)powers[count-1];	     /* here 999 -> 100 etc. */
	for (up=up-1; up>=dn->lsu; up--) *up=0; /* others all to 0 */
	dn->exponent++; 		     /* and bump exponent */
	/* [which, very rarely, could cause Overflow...] */
	if ((dn->exponent+dn->digits)>set->emax+1) {
	  decSetOverflow(dn, set, status);
	  }
	return; 			     /* done */
	}
      /* a full unit to check, with more to come */
      if (*up!=DECDPUNMAX) break;	     /* not still 9s */
      count-=DECDPUN;
      } /* up */
    } /* bump>0 */
   else {				     /* -1 */
    /* here checking for a pre-bump of 1000... (leading 1, all */
    /* other digits zero) */
    Unit *up, *sup;			     /* work */
    uInt count=dn->digits;		     /* digits to be checked */
    for (up=dn->lsu; ; up++) {
      if (count<=DECDPUN) {
	/* this is the last Unit (the msu) */
	if (*up!=powers[count-1]) break;     /* not 100.. */
	/* here if have the 1000... case */
	sup=up; 			     /* save msu pointer */
	*up=(Unit)powers[count]-1;	     /* here 100 in msu -> 999 */
	/* others all to all-nines, too */
	for (up=up-1; up>=dn->lsu; up--) *up=(Unit)powers[DECDPUN]-1;
	dn->exponent--; 		     /* and bump exponent */

	/* iff the number was at the subnormal boundary (exponent=etiny) */
	/* then the exponent is now out of range, so it will in fact get */
	/* clamped to etiny and the final 9 dropped. */
	/* printf(">> emin=%d exp=%d sdig=%d\n", set->emin, */
	/*	  dn->exponent, set->digits); */
	if (dn->exponent+1==set->emin-set->digits+1) {
	  if (count==1 && dn->digits==1) *sup=0;  /* here 9 -> 0[.9] */
	   else {
	    *sup=(Unit)powers[count-1]-1;    /* here 999.. in msu -> 99.. */
	    dn->digits--;
	    }
	  dn->exponent++;
	  *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded;
	  }
	return; 			     /* done */
	}

      /* a full unit to check, with more to come */
      if (*up!=0) break;		     /* not still 0s */
      count-=DECDPUN;
      } /* up */

    } /* bump<0 */

  /* Actual bump needed.  Do it. */
  decUnitAddSub(dn->lsu, D2U(dn->digits), uarrone, 1, 0, dn->lsu, bump);
  } /* decApplyRound */

#if DECSUBSET
/* ------------------------------------------------------------------ */
/* decFinish -- finish processing a number			      */
/*								      */
/*   dn is the number						      */
/*   set is the context 					      */
/*   residue is the rounding accumulator (as in decApplyRound)	      */
/*   status is the accumulator					      */
/*								      */
/* This finishes off the current number by:			      */
/*    1. If not extended:					      */
/*	 a. Converting a zero result to clean '0'		      */
/*	 b. Reducing positive exponents to 0, if would fit in digits  */
/*    2. Checking for overflow and subnormals (always)		      */
/* Note this is just Finalize when no subset arithmetic.	      */
/* All fields are updated as required.				      */
/* ------------------------------------------------------------------ */
static void decFinish(decNumber *dn, decContext *set, Int *residue,
		      uInt *status) {
  if (!set->extended) {
    if ISZERO(dn) {		   /* value is zero */
      dn->exponent=0;		   /* clean exponent .. */
      dn->bits=0;		   /* .. and sign */
      return;			   /* no error possible */
      }
    if (dn->exponent>=0) {	   /* non-negative exponent */
      /* >0; reduce to integer if possible */
      if (set->digits >= (dn->exponent+dn->digits)) {
	dn->digits=decShiftToMost(dn->lsu, dn->digits, dn->exponent);
	dn->exponent=0;
	}
      }
    } /* !extended */

  decFinalize(dn, set, residue, status);
  } /* decFinish */
#endif

/* ------------------------------------------------------------------ */
/* decFinalize -- final check, clamp, and round of a number	      */
/*								      */
/*   dn is the number						      */
/*   set is the context 					      */
/*   residue is the rounding accumulator (as in decApplyRound)	      */
/*   status is the status accumulator				      */
/*								      */
/* This finishes off the current number by checking for subnormal     */
/* results, applying any pending rounding, checking for overflow,     */
/* and applying any clamping.					      */
/* Underflow and overflow conditions are raised as appropriate.       */
/* All fields are updated as required.				      */
/* ------------------------------------------------------------------ */
static void decFinalize(decNumber *dn, decContext *set, Int *residue,
			uInt *status) {
  Int shift;				/* shift needed if clamping */
  Int tinyexp=set->emin-dn->digits+1;	/* precalculate subnormal boundary */

  /* Must be careful, here, when checking the exponent as the */
  /* adjusted exponent could overflow 31 bits [because it may already */
  /* be up to twice the expected]. */

  /* First test for subnormal.	This must be done before any final */
  /* round as the result could be rounded to Nmin or 0. */
  if (dn->exponent<=tinyexp) {		/* prefilter */
    Int comp;
    decNumber nmin;
    /* A very nasty case here is dn == Nmin and residue<0 */
    if (dn->exponent<tinyexp) {
      /* Go handle subnormals; this will apply round if needed. */
      decSetSubnormal(dn, set, residue, status);
      return;
      }
    /* Equals case: only subnormal if dn=Nmin and negative residue */
    decNumberZero(&nmin);
    nmin.lsu[0]=1;
    nmin.exponent=set->emin;
    comp=decCompare(dn, &nmin, 1);		  /* (signless compare) */
    if (comp==BADINT) { 			  /* oops */
      *status|=DEC_Insufficient_storage;	  /* abandon... */
      return;
      }
    if (*residue<0 && comp==0) {		  /* neg residue and dn==Nmin */
      decApplyRound(dn, set, *residue, status);   /* might force down */
      decSetSubnormal(dn, set, residue, status);
      return;
      }
    }

  /* now apply any pending round (this could raise overflow). */
  if (*residue!=0) decApplyRound(dn, set, *residue, status);

  /* Check for overflow [redundant in the 'rare' case] or clamp */
  if (dn->exponent<=set->emax-set->digits+1) return;   /* neither needed */


  /* here when might have an overflow or clamp to do */
  if (dn->exponent>set->emax-dn->digits+1) {	       /* too big */
    decSetOverflow(dn, set, status);
    return;
    }
  /* here when the result is normal but in clamp range */
  if (!set->clamp) return;

  /* here when need to apply the IEEE exponent clamp (fold-down) */
  shift=dn->exponent-(set->emax-set->digits+1);

  /* shift coefficient (if non-zero) */
  if (!ISZERO(dn)) {
    dn->digits=decShiftToMost(dn->lsu, dn->digits, shift);
    }
  dn->exponent-=shift;	 /* adjust the exponent to match */
  *status|=DEC_Clamped;  /* and record the dirty deed */
  return;
  } /* decFinalize */

/* ------------------------------------------------------------------ */
/* decSetOverflow -- set number to proper overflow value	      */
/*								      */
/*   dn is the number (used for sign [only] and result) 	      */
/*   set is the context [used for the rounding mode, etc.]	      */
/*   status contains the current status to be updated		      */
/*								      */
/* This sets the sign of a number and sets its value to either	      */
/* Infinity or the maximum finite value, depending on the sign of     */
/* dn and the rounding mode, following IEEE 754 rules.		      */
/* ------------------------------------------------------------------ */
static void decSetOverflow(decNumber *dn, decContext *set, uInt *status) {
  Flag needmax=0;		   /* result is maximum finite value */
  uByte sign=dn->bits&DECNEG;	   /* clean and save sign bit */

  if (ISZERO(dn)) {		   /* zero does not overflow magnitude */
    Int emax=set->emax; 		     /* limit value */
    if (set->clamp) emax-=set->digits-1;     /* lower if clamping */
    if (dn->exponent>emax) {		     /* clamp required */
      dn->exponent=emax;
      *status|=DEC_Clamped;
      }
    return;
    }

  decNumberZero(dn);
  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 (sign) needmax=1;	   /* Infinity if non-negative */
      break;} /* r-c */
    case DEC_ROUND_FLOOR: {
      if (!sign) needmax=1;	   /* Infinity if negative */
      break;} /* r-f */
    default: break;		   /* Infinity in all other cases */
    }
  if (needmax) {
    decSetMaxValue(dn, set);
    dn->bits=sign;		   /* set sign */
    }
   else dn->bits=sign|DECINF;	   /* Value is +/-Infinity */
  *status|=DEC_Overflow | DEC_Inexact | DEC_Rounded;
  } /* decSetOverflow */

/* ------------------------------------------------------------------ */
/* decSetMaxValue -- set number to +Nmax (maximum normal value)       */
/*								      */
/*   dn is the number to set					      */
/*   set is the context [used for digits and emax]		      */
/*								      */
/* This sets the number to the maximum positive value.		      */
/* ------------------------------------------------------------------ */
static void decSetMaxValue(decNumber *dn, decContext *set) {
  Unit *up;			   /* work */
  Int count=set->digits;	   /* nines to add */
  dn->digits=count;
  /* fill in all nines to set maximum value */
  for (up=dn->lsu; ; up++) {
    if (count>DECDPUN) *up=DECDPUNMAX;	/* unit full o'nines */
     else {				/* this is the msu */
      *up=(Unit)(powers[count]-1);
      break;
      }
    count-=DECDPUN;		   /* filled those digits */
    } /* up */
  dn->bits=0;			   /* + sign */
  dn->exponent=set->emax-set->digits+1;
  } /* decSetMaxValue */

/* ------------------------------------------------------------------ */
/* decSetSubnormal -- process value whose exponent is <Emin	      */
/*								      */
/*   dn is the number (used as input as well as output; it may have   */
/*	   an allowed subnormal value, which may need to be rounded)  */
/*   set is the context [used for the rounding mode]		      */
/*   residue is any pending residue				      */
/*   status contains the current status to be updated		      */
/*								      */
/* If subset mode, set result to zero and set Underflow flags.	      */
/*								      */
/* Value may be zero with a low exponent; this does not set Subnormal */
/* but the exponent will be clamped to Etiny.			      */
/*								      */
/* Otherwise ensure exponent is not out of range, and round as	      */
/* necessary.  Underflow is set if the result is Inexact.	      */
/* ------------------------------------------------------------------ */
static void decSetSubnormal(decNumber *dn, decContext *set, Int *residue,
			    uInt *status) {
  decContext workset;	      /* work */
  Int	     etiny, adjust;   /* .. */

  #if DECSUBSET
  /* simple set to zero and 'hard underflow' for subset */
  if (!set->extended) {
    decNumberZero(dn);
    /* always full overflow */
    *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded;
    return;
    }
  #endif

  /* Full arithmetic -- allow subnormals, rounded to minimum exponent */
  /* (Etiny) if needed */
  etiny=set->emin-(set->digits-1);	/* smallest allowed exponent */

  if ISZERO(dn) {			/* value is zero */
    /* residue can never be non-zero here */
    #if DECCHECK
      if (*residue!=0) {
	printf("++ Subnormal 0 residue %ld\n", (LI)*residue);
	*status|=DEC_Invalid_operation;
	}
    #endif
    if (dn->exponent<etiny) {		/* clamp required */
      dn->exponent=etiny;
      *status|=DEC_Clamped;
      }
    return;
    }

  *status|=DEC_Subnormal;		/* have a non-zero subnormal */
  adjust=etiny-dn->exponent;		/* calculate digits to remove */
  if (adjust<=0) {			/* not out of range; unrounded */
    /* residue can never be non-zero here, except in the Nmin-residue */
    /* case (which is a subnormal result), so can take fast-path here */
    /* it may already be inexact (from setting the coefficient) */
    if (*status&DEC_Inexact) *status|=DEC_Underflow;
    return;
    }

  /* adjust>0, so need to rescale the result so exponent becomes Etiny */
  /* [this code is similar to that in rescale] */
  workset=*set; 			/* clone rounding, etc. */
  workset.digits=dn->digits-adjust;	/* set requested length */
  workset.emin-=adjust; 		/* and adjust emin to match */
  /* [note that the latter can be <1, here, similar to Rescale case] */
  decSetCoeff(dn, &workset, dn->lsu, dn->digits, residue, status);
  decApplyRound(dn, &workset, *residue, status);

  /* Use 754 default rule: Underflow is set iff Inexact */
  /* [independent of whether trapped] */
  if (*status&DEC_Inexact) *status|=DEC_Underflow;

  /* if rounded up a 999s case, exponent will be off by one; adjust */
  /* back if so [it will fit, because it was shortened earlier] */
  if (dn->exponent>etiny) {
    dn->digits=decShiftToMost(dn->lsu, dn->digits, 1);
    dn->exponent--;			/* (re)adjust the exponent. */
    }

  /* if rounded to zero, it is by definition clamped... */
  if (ISZERO(dn)) *status|=DEC_Clamped;
  } /* decSetSubnormal */

/* ------------------------------------------------------------------ */
/* decCheckMath - check entry conditions for a math function	      */
/*								      */
/*   This checks the context and the operand			      */
/*								      */
/*   rhs is the operand to check				      */
/*   set is the context to check				      */
/*   status is unchanged if both are good			      */
/*								      */
/* returns non-zero if status is changed, 0 otherwise		      */
/*								      */
/* Restrictions enforced:					      */
/*								      */
/*   digits, emax, and -emin in the context must be less than	      */
/*   DEC_MAX_MATH (999999), and A must be within these bounds if      */
/*   non-zero.	Invalid_operation is set in the status if a	      */
/*   restriction is violated.					      */
/* ------------------------------------------------------------------ */
static uInt decCheckMath(const decNumber *rhs, decContext *set,
			 uInt *status) {
  uInt save=*status;			     /* record */
  if (set->digits>DEC_MAX_MATH
   || set->emax>DEC_MAX_MATH
   || -set->emin>DEC_MAX_MATH) *status|=DEC_Invalid_context;
   else if ((rhs->digits>DEC_MAX_MATH
     || rhs->exponent+rhs->digits>DEC_MAX_MATH+1
     || rhs->exponent+rhs->digits<2*(1-DEC_MAX_MATH))
     && !ISZERO(rhs)) *status|=DEC_Invalid_operation;
  return (*status!=save);
  } /* decCheckMath */

/* ------------------------------------------------------------------ */
/* decGetInt -- get integer from a number			      */
/*								      */
/*   dn is the number [which will not be altered]		      */
/*								      */
/*   returns one of:						      */
/*     BADINT if there is a non-zero fraction			      */
/*     the converted integer					      */
/*     BIGEVEN if the integer is even and magnitude > 2*10**9	      */
/*     BIGODD  if the integer is odd  and magnitude > 2*10**9	      */
/*								      */
/* This checks and gets a whole number from the input decNumber.      */
/* The sign can be determined from dn by the caller when BIGEVEN or   */
/* BIGODD is returned.						      */
/* ------------------------------------------------------------------ */
static Int decGetInt(const decNumber *dn) {
  Int  theInt;				/* result accumulator */
  const Unit *up;			/* work */
  Int  got;				/* digits (real or not) processed */
  Int  ilength=dn->digits+dn->exponent; /* integral length */
  Flag neg=decNumberIsNegative(dn);	/* 1 if -ve */

  /* The number must be an integer that fits in 10 digits */
  /* Assert, here, that 10 is enough for any rescale Etiny */
  #if DEC_MAX_EMAX > 999999999
    #error GetInt may need updating [for Emax]
  #endif
  #if DEC_MIN_EMIN < -999999999
    #error GetInt may need updating [for Emin]
  #endif
  if (ISZERO(dn)) return 0;		/* zeros are OK, with any exponent */

  up=dn->lsu;				/* ready for lsu */
  theInt=0;				/* ready to accumulate */
  if (dn->exponent>=0) {		/* relatively easy */
    /* no fractional part [usual]; allow for positive exponent */
    got=dn->exponent;
    }
   else { /* -ve exponent; some fractional part to check and discard */
    Int count=-dn->exponent;		/* digits to discard */
    /* spin up whole units until reach the Unit with the unit digit */
    for (; count>=DECDPUN; up++) {
      if (*up!=0) return BADINT;	/* non-zero Unit to discard */
      count-=DECDPUN;
      }
    if (count==0) got=0;		/* [a multiple of DECDPUN] */
     else {				/* [not multiple of DECDPUN] */
      Int rem;				/* work */
      /* slice off fraction digits and check for non-zero */
      #if DECDPUN<=4
	theInt=QUOT10(*up, count);
	rem=*up-theInt*powers[count];
      #else
	rem=*up%powers[count];		/* slice off discards */
	theInt=*up/powers[count];
      #endif
      if (rem!=0) return BADINT;	/* non-zero fraction */
      /* it looks good */
      got=DECDPUN-count;		/* number of digits so far */
      up++;				/* ready for next */
      }
    }
  /* now it's known there's no fractional part */

  /* tricky code now, to accumulate up to 9.3 digits */
  if (got==0) {theInt=*up; got+=DECDPUN; up++;} /* ensure lsu is there */

  if (ilength<11) {
    Int save=theInt;
    /* collect any remaining unit(s) */
    for (; got<ilength; up++) {
      theInt+=*up*powers[got];
      got+=DECDPUN;
      }
    if (ilength==10) {			/* need to check for wrap */
      if (theInt/(Int)powers[got-DECDPUN]!=(Int)*(up-1)) ilength=11;
	 /* [that test also disallows the BADINT result case] */
       else if (neg && theInt>1999999997) ilength=11;
       else if (!neg && theInt>999999999) ilength=11;
      if (ilength==11) theInt=save;	/* restore correct low bit */
      }
    }

  if (ilength>10) {			/* too big */
    if (theInt&1) return BIGODD;	/* bottom bit 1 */
    return BIGEVEN;			/* bottom bit 0 */
    }

  if (neg) theInt=-theInt;		/* apply sign */
  return theInt;
  } /* decGetInt */

/* ------------------------------------------------------------------ */
/* decDecap -- decapitate the coefficient of a number		      */
/*								      */
/*   dn   is the number to be decapitated			      */
/*   drop is the number of digits to be removed from the left of dn;  */
/*     this must be <= dn->digits (if equal, the coefficient is       */
/*     set to 0)						      */
/*								      */
/* Returns dn; dn->digits will be <= the initial digits less drop     */
/* (after removing drop digits there may be leading zero digits       */
/* which will also be removed).  Only dn->lsu and dn->digits change.  */
/* ------------------------------------------------------------------ */
static decNumber *decDecap(decNumber *dn, Int drop) {
  Unit *msu;				/* -> target cut point */
  Int cut;				/* work */
  if (drop>=dn->digits) {		/* losing the whole thing */
    #if DECCHECK
    if (drop>dn->digits)
      printf("decDecap called with drop>digits [%ld>%ld]\n",
	     (LI)drop, (LI)dn->digits);
    #endif
    dn->lsu[0]=0;
    dn->digits=1;
    return dn;
    }
  msu=dn->lsu+D2U(dn->digits-drop)-1;	/* -> likely msu */
  cut=MSUDIGITS(dn->digits-drop);	/* digits to be in use in msu */
  if (cut!=DECDPUN) *msu%=powers[cut];	/* clear left digits */
  /* that may have left leading zero digits, so do a proper count... */
  dn->digits=decGetDigits(dn->lsu, msu-dn->lsu+1);
  return dn;
  } /* decDecap */

/* ------------------------------------------------------------------ */
/* 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, it is the same     */
/*   length as str1 and str2, and each character of targ is in either */
/*   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 */

/* ------------------------------------------------------------------ */
/* decNaNs -- handle NaN operand or operands			      */
/*								      */
/*   res     is the result number				      */
/*   lhs     is the first operand				      */
/*   rhs     is the second operand, or NULL if none		      */
/*   context is used to limit payload length			      */
/*   status  contains the current status			      */
/*   returns res in case convenient				      */
/*								      */
/* Called when one or both operands is a NaN, and propagates the      */
/* appropriate result to res.  When an sNaN is found, it is changed   */
/* to a qNaN and Invalid operation is set.			      */
/* ------------------------------------------------------------------ */
static decNumber * decNaNs(decNumber *res, const decNumber *lhs,
			   const decNumber *rhs, decContext *set,
			   uInt *status) {
  /* This decision tree ends up with LHS being the source pointer, */
  /* and status updated if need be */
  if (lhs->bits & DECSNAN)
    *status|=DEC_Invalid_operation | DEC_sNaN;
   else if (rhs==NULL);
   else if (rhs->bits & DECSNAN) {
    lhs=rhs;
    *status|=DEC_Invalid_operation | DEC_sNaN;
    }
   else if (lhs->bits & DECNAN);
   else lhs=rhs;

  /* propagate the payload */
  if (lhs->digits<=set->digits) decNumberCopy(res, lhs); /* easy */
   else { /* too long */
    const Unit *ul;
    Unit *ur, *uresp1;
    /* copy safe number of units, then decapitate */
    res->bits=lhs->bits;		/* need sign etc. */
    uresp1=res->lsu+D2U(set->digits);
    for (ur=res->lsu, ul=lhs->lsu; ur<uresp1; ur++, ul++) *ur=*ul;
    res->digits=D2U(set->digits)*DECDPUN;
    /* maybe still too long */
    if (res->digits>set->digits) decDecap(res, res->digits-set->digits);
    }

  res->bits&=~DECSNAN;	      /* convert any sNaN to NaN, while */
  res->bits|=DECNAN;	      /* .. preserving sign */
  res->exponent=0;	      /* clean exponent */
			      /* [coefficient was copied/decapitated] */
  return res;
  } /* decNaNs */

/* ------------------------------------------------------------------ */
/* decStatus -- apply non-zero status				      */
/*								      */
/*   dn     is the number to set if error			      */
/*   status contains the current status (not yet in context)	      */
/*   set    is the context					      */
/*								      */
/* If the status is an error status, the number is set to a NaN,      */
/* unless the error was an overflow, divide-by-zero, or underflow,    */
/* in which case the number will have already been set. 	      */
/*								      */
/* The context status is then updated with the new status.  Note that */
/* this may raise a signal, so control may never return from this     */
/* routine (hence resources must be recovered before it is called).   */
/* ------------------------------------------------------------------ */
static void decStatus(decNumber *dn, uInt status, decContext *set) {
  if (status & DEC_NaNs) {		/* error status -> NaN */
    /* if cause was an sNaN, clear and propagate [NaN is already set up] */
    if (status & DEC_sNaN) status&=~DEC_sNaN;
     else {
      decNumberZero(dn);		/* other error: clean throughout */
      dn->bits=DECNAN;			/* and make a quiet NaN */
      }
    }
  decContextSetStatus(set, status);	/* [may not return] */
  return;
  } /* decStatus */

/* ------------------------------------------------------------------ */
/* decGetDigits -- count digits in a Units array		      */
/*								      */
/*   uar is the Unit array holding the number (this is often an       */
/*	    accumulator of some sort)				      */
/*   len is the length of the array in units [>=1]		      */
/*								      */
/*   returns the number of (significant) digits in the array	      */
/*								      */
/* All leading zeros are excluded, except the last if the array has   */
/* only zero Units.						      */
/* ------------------------------------------------------------------ */
/* This may be called twice during some operations. */
static Int decGetDigits(Unit *uar, Int len) {
  Unit *up=uar+(len-1); 	   /* -> msu */
  Int  digits=(len-1)*DECDPUN+1;   /* possible digits excluding msu */
  #if DECDPUN>4
  uInt const *pow;		   /* work */
  #endif
				   /* (at least 1 in final msu) */
  #if DECCHECK
  if (len<1) printf("decGetDigits called with len<1 [%ld]\n", (LI)len);
  #endif

  for (; up>=uar; up--) {
    if (*up==0) {		   /* unit is all 0s */
      if (digits==1) break;	   /* a zero has one digit */
      digits-=DECDPUN;		   /* adjust for 0 unit */
      continue;}
    /* found the first (most significant) non-zero Unit */
    #if DECDPUN>1		   /* not done yet */
    if (*up<10) break;		   /* is 1-9 */
    digits++;
    #if DECDPUN>2		   /* not done yet */
    if (*up<100) break; 	   /* is 10-99 */
    digits++;
    #if DECDPUN>3		   /* not done yet */
    if (*up<1000) break;	   /* is 100-999 */
    digits++;
    #if DECDPUN>4		   /* count the rest ... */
    for (pow=&powers[4]; *up>=*pow; pow++) digits++;
    #endif
    #endif
    #endif
    #endif
    break;
    } /* up */
  return digits;
  } /* decGetDigits */

#if DECTRACE | DECCHECK
/* ------------------------------------------------------------------ */
/* decNumberShow -- display a number [debug aid]		      */
/*   dn is the number to show					      */
/*								      */
/* Shows: sign, exponent, coefficient (msu first), digits	      */
/*    or: sign, special-value					      */
/* ------------------------------------------------------------------ */
/* this is public so other modules can use it */
void decNumberShow(const decNumber *dn) {
  const Unit *up;		   /* work */
  uInt u, d;			   /* .. */
  Int cut;			   /* .. */
  char isign='+';		   /* main sign */
  if (dn==NULL) {
    printf("NULL\n");
    return;}
  if (decNumberIsNegative(dn)) isign='-';
  printf(" >> %c ", isign);
  if (dn->bits&DECSPECIAL) {	   /* Is a special value */
    if (decNumberIsInfinite(dn)) printf("Infinity");
     else {				     /* a NaN */
      if (dn->bits&DECSNAN) printf("sNaN");  /* signalling NaN */
       else printf("NaN");
      }
    /* if coefficient and exponent are 0, no more to do */
    if (dn->exponent==0 && dn->digits==1 && *dn->lsu==0) {
      printf("\n");
      return;}
    /* drop through to report other information */
    printf(" ");
    }

  /* now carefully display the coefficient */
  up=dn->lsu+D2U(dn->digits)-1; 	/* msu */
  printf("%ld", (LI)*up);
  for (up=up-1; up>=dn->lsu; up--) {
    u=*up;
    printf(":");
    for (cut=DECDPUN-1; cut>=0; cut--) {
      d=u/powers[cut];
      u-=d*powers[cut];
      printf("%ld", (LI)d);
      } /* cut */
    } /* up */
  if (dn->exponent!=0) {
    char esign='+';
    if (dn->exponent<0) esign='-';
    printf(" E%c%ld", esign, (LI)abs(dn->exponent));
    }
  printf(" [%ld]\n", (LI)dn->digits);
  } /* decNumberShow */
#endif

#if DECTRACE || DECCHECK
/* ------------------------------------------------------------------ */
/* decDumpAr -- display a unit array [debug/check aid]		      */
/*   name is a single-character tag name			      */
/*   ar   is the array to display				      */
/*   len  is the length of the array in Units			      */
/* ------------------------------------------------------------------ */
static void decDumpAr(char name, const Unit *ar, Int len) {
  Int i;
  const char *spec;
  #if DECDPUN==9
    spec="%09d ";
  #elif DECDPUN==8
    spec="%08d ";
  #elif DECDPUN==7
    spec="%07d ";
  #elif DECDPUN==6
    spec="%06d ";
  #elif DECDPUN==5
    spec="%05d ";
  #elif DECDPUN==4
    spec="%04d ";
  #elif DECDPUN==3
    spec="%03d ";
  #elif DECDPUN==2
    spec="%02d ";
  #else
    spec="%d ";
  #endif
  printf("  :%c: ", name);
  for (i=len-1; i>=0; i--) {
    if (i==len-1) printf("%ld ", (LI)ar[i]);
     else printf(spec, ar[i]);
    }
  printf("\n");
  return;}
#endif

#if DECCHECK
/* ------------------------------------------------------------------ */
/* decCheckOperands -- check operand(s) to a routine		      */
/*   res is the result structure (not checked; it will be set to      */
/*	    quiet NaN if error found (and it is not NULL))	      */
/*   lhs is the first operand (may be DECUNRESU)		      */
/*   rhs is the second (may be DECUNUSED)			      */
/*   set is the context (may be DECUNCONT)			      */
/*   returns 0 if both operands, and the context are clean, or 1      */
/*     otherwise (in which case the context will show an error,       */
/*     unless NULL).  Note that res is not cleaned; caller should     */
/*     handle this so res=NULL case is safe.			      */
/* The caller is expected to abandon immediately if 1 is returned.    */
/* ------------------------------------------------------------------ */
static Flag decCheckOperands(decNumber *res, const decNumber *lhs,
			     const decNumber *rhs, decContext *set) {
  Flag bad=0;
  if (set==NULL) {		   /* oops; hopeless */
    #if DECTRACE || DECVERB
    printf("Reference to context is NULL.\n");
    #endif
    bad=1;
    return 1;}
   else if (set!=DECUNCONT
     && (set->digits<1 || set->round>=DEC_ROUND_MAX)) {
    bad=1;
    #if DECTRACE || DECVERB
    printf("Bad context [digits=%ld round=%ld].\n",
	   (LI)set->digits, (LI)set->round);
    #endif
    }
   else {
    if (res==NULL) {
      bad=1;
      #if DECTRACE
      /* this one not DECVERB as standard tests include NULL */
      printf("Reference to result is NULL.\n");
      #endif
      }
    if (!bad && lhs!=DECUNUSED) bad=(decCheckNumber(lhs));
    if (!bad && rhs!=DECUNUSED) bad=(decCheckNumber(rhs));
    }
  if (bad) {
    if (set!=DECUNCONT) decContextSetStatus(set, DEC_Invalid_operation);
    if (res!=DECUNRESU && res!=NULL) {
      decNumberZero(res);
      res->bits=DECNAN;       /* qNaN */
      }
    }
  return bad;
  } /* decCheckOperands */

/* ------------------------------------------------------------------ */
/* decCheckNumber -- check a number				      */
/*   dn is the number to check					      */
/*   returns 0 if the number is clean, or 1 otherwise		      */
/*								      */
/* The number is considered valid if it could be a result from some   */
/* operation in some valid context.				      */
/* ------------------------------------------------------------------ */
static Flag decCheckNumber(const decNumber *dn) {
  const Unit *up;	      /* work */
  uInt maxuint; 	      /* .. */
  Int ae, d, digits;	      /* .. */
  Int emin, emax;	      /* .. */

  if (dn==NULL) {	      /* hopeless */
    #if DECTRACE
    /* this one not DECVERB as standard tests include NULL */
    printf("Reference to decNumber is NULL.\n");
    #endif
    return 1;}

  /* check special values */
  if (dn->bits & DECSPECIAL) {
    if (dn->exponent!=0) {
      #if DECTRACE || DECVERB
      printf("Exponent %ld (not 0) for a special value [%02x].\n",
	     (LI)dn->exponent, dn->bits);
      #endif
      return 1;}

    /* 2003.09.08: NaNs may now have coefficients, so next tests Inf only */
    if (decNumberIsInfinite(dn)) {
      if (dn->digits!=1) {
	#if DECTRACE || DECVERB
	printf("Digits %ld (not 1) for an infinity.\n", (LI)dn->digits);
	#endif
	return 1;}
      if (*dn->lsu!=0) {
	#if DECTRACE || DECVERB
	printf("LSU %ld (not 0) for an infinity.\n", (LI)*dn->lsu);
	#endif
	decDumpAr('I', dn->lsu, D2U(dn->digits));
	return 1;}
      } /* Inf */
    /* 2002.12.26: negative NaNs can now appear through proposed IEEE */
    /*		   concrete formats (decimal64, etc.). */
    return 0;
    }

  /* check the coefficient */
  if (dn->digits<1 || dn->digits>DECNUMMAXP) {
    #if DECTRACE || DECVERB
    printf("Digits %ld in number.\n", (LI)dn->digits);
    #endif
    return 1;}

  d=dn->digits;

  for (up=dn->lsu; d>0; up++) {
    if (d>DECDPUN) maxuint=DECDPUNMAX;
     else {		      /* reached the msu */
      maxuint=powers[d]-1;
      if (dn->digits>1 && *up<powers[d-1]) {
	#if DECTRACE || DECVERB
	printf("Leading 0 in number.\n");
	decNumberShow(dn);
	#endif
	return 1;}
      }
    if (*up>maxuint) {
      #if DECTRACE || DECVERB
      printf("Bad Unit [%08lx] in %ld-digit number at offset %ld [maxuint %ld].\n",
	      (LI)*up, (LI)dn->digits, (LI)(up-dn->lsu), (LI)maxuint);
      #endif
      return 1;}
    d-=DECDPUN;
    }

  /* check the exponent.  Note that input operands can have exponents */
  /* which are out of the set->emin/set->emax and set->digits range */
  /* (just as they can have more digits than set->digits). */
  ae=dn->exponent+dn->digits-1;    /* adjusted exponent */
  emax=DECNUMMAXE;
  emin=DECNUMMINE;
  digits=DECNUMMAXP;
  if (ae<emin-(digits-1)) {
    #if DECTRACE || DECVERB
    printf("Adjusted exponent underflow [%ld].\n", (LI)ae);
    decNumberShow(dn);
    #endif
    return 1;}
  if (ae>+emax) {
    #if DECTRACE || DECVERB
    printf("Adjusted exponent overflow [%ld].\n", (LI)ae);
    decNumberShow(dn);
    #endif
    return 1;}

  return 0;		 /* it's OK */
  } /* decCheckNumber */

/* ------------------------------------------------------------------ */
/* decCheckInexact -- check a normal finite inexact result has digits */
/*   dn is the number to check					      */
/*   set is the context (for status and precision)		      */
/*   sets Invalid operation, etc., if some digits are missing	      */
/* [this check is not made for DECSUBSET compilation or when	      */
/* subnormal is not set]					      */
/* ------------------------------------------------------------------ */
static void decCheckInexact(const decNumber *dn, decContext *set) {
  #if !DECSUBSET && DECEXTFLAG
    if ((set->status & (DEC_Inexact|DEC_Subnormal))==DEC_Inexact
     && (set->digits!=dn->digits) && !(dn->bits & DECSPECIAL)) {
      #if DECTRACE || DECVERB
      printf("Insufficient digits [%ld] on normal Inexact result.\n",
	     (LI)dn->digits);
      decNumberShow(dn);
      #endif
      decContextSetStatus(set, DEC_Invalid_operation);
      }
  #else
    /* next is a noop for quiet compiler */
    if (dn!=NULL && dn->digits==0) set->status|=DEC_Invalid_operation;
  #endif
  return;
  } /* decCheckInexact */
#endif

#if DECALLOC
#undef malloc
#undef free
/* ------------------------------------------------------------------ */
/* decMalloc -- accountable allocation routine			      */
/*   n is the number of bytes to allocate			      */
/*								      */
/* Semantics is the same as the stdlib malloc routine, but bytes      */
/* allocated are accounted for globally, and corruption fences are    */
/* added before and after the 'actual' storage. 		      */
/* ------------------------------------------------------------------ */
/* This routine allocates storage with an extra twelve bytes; 8 are   */
/* at the start and hold:					      */
/*   0-3 the original length requested				      */
/*   4-7 buffer corruption detection fence (DECFENCE, x4)	      */
/* The 4 bytes at the end also hold a corruption fence (DECFENCE, x4) */
/* ------------------------------------------------------------------ */
static void *decMalloc(size_t n) {
  uInt	size=n+12;		   /* true size */
  void	*alloc; 		   /* -> allocated storage */
  uByte *b, *b0;		   /* work */
  uInt	uiwork; 		   /* for macros */

  alloc=malloc(size);		   /* -> allocated storage */
  if (alloc==NULL) return NULL;    /* out of strorage */
  b0=(uByte *)alloc;		   /* as bytes */
  decAllocBytes+=n;		   /* account for storage */
  UBFROMUI(alloc, n);		   /* save n */
  /* printf(" alloc ++ dAB: %ld (%ld)\n", (LI)decAllocBytes, (LI)n); */
  for (b=b0+4; b<b0+8; b++) *b=DECFENCE;
  for (b=b0+n+8; b<b0+n+12; b++) *b=DECFENCE;
  return b0+8;			   /* -> play area */
  } /* decMalloc */

/* ------------------------------------------------------------------ */
/* decFree -- accountable free routine				      */
/*   alloc is the storage to free				      */
/*								      */
/* Semantics is the same as the stdlib malloc routine, except that    */
/* the global storage accounting is updated and the fences are	      */
/* checked to ensure that no routine has written 'out of bounds'.     */
/* ------------------------------------------------------------------ */
/* This routine first checks that the fences have not been corrupted. */
/* It then frees the storage using the 'truw' storage address (that   */
/* is, offset by 8).						      */
/* ------------------------------------------------------------------ */
static void decFree(void *alloc) {
  uInt	n;			   /* original length */
  uByte *b, *b0;		   /* work */
  uInt	uiwork; 		   /* for macros */

  if (alloc==NULL) return;	   /* allowed; it's a nop */
  b0=(uByte *)alloc;		   /* as bytes */
  b0-=8;			   /* -> true start of storage */
  n=UBTOUI(b0); 		   /* lift length */
  for (b=b0+4; b<b0+8; b++) if (*b!=DECFENCE)
    printf("=== Corrupt byte [%02x] at offset %d from %ld ===\n", *b,
	   b-b0-8, (LI)b0);
  for (b=b0+n+8; b<b0+n+12; b++) if (*b!=DECFENCE)
    printf("=== Corrupt byte [%02x] at offset +%d from %ld, n=%ld ===\n", *b,
	   b-b0-8, (LI)b0, (LI)n);
  free(b0);			   /* drop the storage */
  decAllocBytes-=n;		   /* account for storage */
  /* printf(" free -- dAB: %d (%d)\n", decAllocBytes, -n); */
  } /* decFree */
#define malloc(a) decMalloc(a)
#define free(a) decFree(a)
#endif