deka 0.4.0.4 → 0.6.0.0

raw patch · 61 files changed

+4989/−17850 lines, 61 filesdep +containersdep +dekadep +parsecdep ~QuickCheckdep ~tastydep ~tasty-quickchecksetup-changedPVP ok

version bump matches the API change (PVP)

Dependencies added: containers, deka, parsec, pipes, transformers

Dependency ranges changed: QuickCheck, tasty, tasty-quickcheck

API changes (from Hackage documentation)

Files

• ChangeLog +9/−0
• README.md +30/−29
• Setup.hs +1/−1
• configure +0/−4449
• current-versions.txt +10/−8
• decnumber/src/decBasic.c +0/−3908
• decnumber/src/decCommon.c +0/−1835
• decnumber/src/decContext.c +0/−437
• decnumber/src/decContext.h +0/−254
• decnumber/src/decDPD.h +0/−1185
• decnumber/src/decNumberLocal.h.in +0/−757
• decnumber/src/decQuad.c +0/−135
• decnumber/src/decQuad.h +0/−177
• dectest/AllModules.hs +22/−0
• dectest/Arity.hs +131/−0
• dectest/Conditions.hs +50/−0
• dectest/Directives.hs +142/−0
• dectest/NumTests.hs +61/−0
• dectest/Operand.hs +67/−0
• dectest/Parse.hs +99/−0
• dectest/Parse/Tokenizer.hs +220/−0
• dectest/Parse/Tokens.hs +70/−0
• dectest/Result.hs +74/−0
• dectest/Runner.hs +164/−0
• dectest/Specials.hs +85/−0
• dectest/TestHelpers.hs +35/−0
• dectest/TestLog.hs +64/−0
• dectest/Types.hs +36/−0
• dectest/Util.hs +28/−0
• dectest/dectest.hs +7/−0
• deka.cabal +78/−57
• lib/Data/Deka.hs +0/−168
• lib/Data/Deka/Decnumber.hsc +0/−731
• lib/Data/Deka/Docs.hs +0/−23
• lib/Data/Deka/Docs/Examples.lhs +0/−282
• lib/Data/Deka/Internal.hs +0/−163
• lib/Data/Deka/Quad.hs +0/−1688
• lib/Deka.hs +173/−0
• lib/Deka/Context.hs +112/−0
• lib/Deka/Dec.hs +123/−0
• lib/Deka/Docs.hs +24/−0
• lib/Deka/Docs/Examples.lhs +268/−0
• lib/Deka/Internal/Context.hs +637/−0
• lib/Deka/Internal/Dec/Ctx.hs +364/−0
• lib/Deka/Internal/Dec/CtxFree.hs +141/−0
• lib/Deka/Internal/Mpdec.hsc +838/−0
• lib/Deka/Internal/Unsafe.hs +19/−0
• lib/Deka/Internal/Util/Ctx.hs +48/−0
• lib/Deka/Native.hs +88/−0
• lib/Deka/Native/Abstract.hs +330/−0
• lib/Deka/Native/FromString.hs +227/−0
• minimum-versions.txt +17/−25
• native/AllModules.hs +5/−0
• native/Generators.hs +58/−0
• native/Properties.hs +25/−0
• native/native.hs +9/−0
• test/DataDir.hs +0/−12
• test/DataDir/DekaDir.hs +0/−10
• test/DataDir/DekaDir/QuadTest.hs +0/−1422
• test/DataDir/DekaTest.hs +0/−81
• test/tasty-test.hs +0/−13

@@ -1,3 +1,12 @@+version 0.6.0.0:++* switch to mpdecimal for the underlying C library.  This allows+higher limits on exponents and precision.  All arithmetic is now+(practically speaking) arbitrary precision.  This also allows more+operations, such as logarithms and all exponents.  As a possible+disadvantage, this might be slower than decNumber (but I have not+benchmarked this.)+ version 0.4.0.4:  * test with GHC 7.8.2

@@ -2,31 +2,27 @@  deka provides correctly rounded decimal arithmetic for Haskell. -The core of deka is a binding to the C library decNumber. As the-author of deka, I have no association with the author of decNumber,-and any errors in this library are mine and should be reported to-omari@smileystation.com or to the Github tracker at+The core of deka is a binding to the C library mpdecimal.  You need+to install mpdecimal; otherwise, your executables will not link.+mpdecimal is available here: -http://www.github.com/massysett/deka+http://www.bytereef.org/mpdecimal/index.html -deka uses the decQuad functions in decNumber.  This means that deka-is limited to 34 digits of precision.  Because 1 quadrillion (that-is, one thousand trillion) has only 16 digits of precision, I figure-that 34 should be sufficient for many uses.  Also, you are limited-to exponents no smaller than -6176 and no greater than 6111.  deka-will notify you if you perform calculations that must be rounded in-order to fit within the 34 digits of precision or within the size-limits for the exponent.+mpdecimal has also been packaged for some Linux distributions, such+as Debian (libmpdec-dev) and Arch (mpdecimal).  deka has been tested+with mpdecimal version 2.4.0. -You will want to understand decNumber and the General Decimal-Arithmetic Specification in order to fully understand deka.  The-specification is at+As the author of deka, I have no association with the author of+mpdecimal, and any errors in this library are mine and should be+reported to omari@smileystation.com or to the Github tracker at -http://speleotrove.com/decimal/decarith.html+http://www.github.com/massysett/deka -and decNumber is at+You will want to understand the General Decimal Arithmetic+Specification in order to fully understand deka.  The specification+is at -http://speleotrove.com/decimal/decnumber.html+http://speleotrove.com/decimal/decarith.html  and more about decimal arithmetic generally at @@ -34,13 +30,22 @@  ## Dependencies -The main deka library depends only on `base` and `bytestring`, so it-shouldn't be difficult to build.  The-tests use [tasty](http://documentup.com/feuerbach/tasty) and-[QuickCheck](http://hackage.haskell.org/package/QuickCheck).  The-decNumber C library is bundled in; GHC will build it and link it for-you when you install deka.+The main deka library depends only on `base`, `bytestring`, and+`parsec`, so it shouldn't be difficult to build.  The tests use+[tasty](http://documentup.com/feuerbach/tasty) and+[QuickCheck](http://hackage.haskell.org/package/QuickCheck). +## Test status++deka is tested using the tests available on the General Decimal+Arithmetic website:++http://speleotrove.com/decimal/dectest.html++Some of these tests currently fail.  The failures are in edge cases+that should not affect most usage.  Diagnosing these failures is on+the TODO list.+ ## More documentation  Much more documentation is available in the Haddock comments in the@@ -55,8 +60,4 @@ ## License  deka is licensed under the BSD license, see the LICENSE file.--## Build status--[![Build Status](https://travis-ci.org/massysett/deka.png?branch=master)](https://travis-ci.org/massysett/deka) 

@@ -1,2 +1,2 @@ import Distribution.Simple-main = defaultMainWithHooks autoconfUserHooks+main = defaultMain

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@@ -1,7 +1,7 @@ This package was tested to work with these dependency versions and compiler version. These are the default versions fetched by cabal install.-Tested as of: 2014-04-17 19:37:00.007331 UTC+Tested as of: 2014-05-20 16:07:05.864819 UTC Path to compiler: ghc-7.8.2 Compiler description: 7.8.2 @@ -33,24 +33,26 @@     transformers-0.3.0.0     unix-2.7.0.1 -/home/massysett/deka/sunlight-20121/db:+/home/massysett/deka/sunlight-730/db:     QuickCheck-2.7.3     ansi-terminal-0.6.1.1     ansi-wl-pprint-0.6.7.1     async-2.0.1.5-    deka-0.4.0.4+    deka-0.6.0.0+    mmorph-1.0.3     mtl-2.1.3.1-    optparse-applicative-0.8.0.1+    optparse-applicative-0.8.1     parsec-3.1.5-    primitive-0.5.2.1+    pipes-4.1.2+    primitive-0.5.3.0     random-1.0.1.1     regex-base-0.93.2     regex-tdfa-1.2.0     stm-2.4.3-    tagged-0.7.1+    tagged-0.7.2     tasty-0.8.0.4-    tasty-quickcheck-0.8.0.3-    text-1.1.0.1+    tasty-quickcheck-0.8.1+    text-1.1.1.2     tf-random-0.5     unbounded-delays-0.1.0.7 

@@ -1,3908 +0,0 @@-/* ------------------------------------------------------------------ */
-/* decBasic.c -- common base code for Basic decimal types             */
-/* ------------------------------------------------------------------ */
-/* Copyright (c) IBM Corporation, 2000, 2010.  All rights reserved.   */
-/*                                                                    */
-/* This software is made available under the terms of the             */
-/* ICU License -- ICU 1.8.1 and later.                                */
-/*                                                                    */
-/* The description and User's Guide ("The decNumber C Library") for   */
-/* this software is included in the package as decNumber.pdf.  This   */
-/* document is also available in HTML, together with specifications,  */
-/* testcases, and Web links, on the General Decimal Arithmetic page.  */
-/*                                                                    */
-/* Please send comments, suggestions, and corrections to the author:  */
-/*   mfc@uk.ibm.com                                                   */
-/*   Mike Cowlishaw, IBM Fellow                                       */
-/*   IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK         */
-/* ------------------------------------------------------------------ */
-/* This module comprises code that is shared between decDouble and    */
-/* decQuad (but not decSingle).  The main arithmetic operations are   */
-/* here (Add, Subtract, Multiply, FMA, and Division operators).       */
-/*                                                                    */
-/* Unlike decNumber, parameterization takes place at compile time     */
-/* rather than at runtime.  The parameters are set in the decDouble.c */
-/* (etc.) files, which then include this one to produce the compiled  */
-/* code.  The functions here, therefore, are code shared between      */
-/* multiple formats.                                                  */
-/*                                                                    */
-/* This must be included after decCommon.c.                           */
-/* ------------------------------------------------------------------ */
-// Names here refer to decFloat rather than to decDouble, etc., and
-// the functions are in strict alphabetical order.
-
-// The compile-time flags SINGLE, DOUBLE, and QUAD are set up in
-// decCommon.c
-#if !defined(QUAD)
-  #error decBasic.c must be included after decCommon.c
-#endif
-#if SINGLE
-  #error Routines in decBasic.c are for decDouble and decQuad only
-#endif
-
-/* Private constants */
-#define DIVIDE      0x80000000     // Divide operations [as flags]
-#define REMAINDER   0x40000000     // ..
-#define DIVIDEINT   0x20000000     // ..
-#define REMNEAR     0x10000000     // ..
-
-/* Private functions (local, used only by routines in this module) */
-static decFloat *decDivide(decFloat *, const decFloat *,
-                              const decFloat *, decContext *, uInt);
-static decFloat *decCanonical(decFloat *, const decFloat *);
-static void      decFiniteMultiply(bcdnum *, uByte *, const decFloat *,
-                              const decFloat *);
-static decFloat *decInfinity(decFloat *, const decFloat *);
-static decFloat *decInvalid(decFloat *, decContext *);
-static decFloat *decNaNs(decFloat *, const decFloat *, const decFloat *,
-                              decContext *);
-static Int       decNumCompare(const decFloat *, const decFloat *, Flag);
-static decFloat *decToIntegral(decFloat *, const decFloat *, decContext *,
-                              enum rounding, Flag);
-static uInt      decToInt32(const decFloat *, decContext *, enum rounding,
-                              Flag, Flag);
-
-/* ------------------------------------------------------------------ */
-/* decCanonical -- copy a decFloat, making canonical                  */
-/*                                                                    */
-/*   result gets the canonicalized df                                 */
-/*   df     is the decFloat to copy and make canonical                */
-/*   returns result                                                   */
-/*                                                                    */
-/* This is exposed via decFloatCanonical for Double and Quad only.    */
-/* This works on specials, too; no error or exception is possible.    */
-/* ------------------------------------------------------------------ */
-static decFloat * decCanonical(decFloat *result, const decFloat *df) {
-  uInt encode, precode, dpd;       // work
-  uInt inword, uoff, canon;        // ..
-  Int  n;                          // counter (down)
-  if (df!=result) *result=*df;     // effect copy if needed
-  if (DFISSPECIAL(result)) {
-    if (DFISINF(result)) return decInfinity(result, df); // clean Infinity
-    // is a NaN
-    DFWORD(result, 0)&=~ECONNANMASK;    // clear ECON except selector
-    if (DFISCCZERO(df)) return result;  // coefficient continuation is 0
-    // drop through to check payload
-    }
-  // return quickly if the coefficient continuation is canonical
-  { // declare block
-  #if DOUBLE
-    uInt sourhi=DFWORD(df, 0);
-    uInt sourlo=DFWORD(df, 1);
-    if (CANONDPDOFF(sourhi, 8)
-     && CANONDPDTWO(sourhi, sourlo, 30)
-     && CANONDPDOFF(sourlo, 20)
-     && CANONDPDOFF(sourlo, 10)
-     && CANONDPDOFF(sourlo, 0)) return result;
-  #elif QUAD
-    uInt sourhi=DFWORD(df, 0);
-    uInt sourmh=DFWORD(df, 1);
-    uInt sourml=DFWORD(df, 2);
-    uInt sourlo=DFWORD(df, 3);
-    if (CANONDPDOFF(sourhi, 4)
-     && CANONDPDTWO(sourhi, sourmh, 26)
-     && CANONDPDOFF(sourmh, 16)
-     && CANONDPDOFF(sourmh, 6)
-     && CANONDPDTWO(sourmh, sourml, 28)
-     && CANONDPDOFF(sourml, 18)
-     && CANONDPDOFF(sourml, 8)
-     && CANONDPDTWO(sourml, sourlo, 30)
-     && CANONDPDOFF(sourlo, 20)
-     && CANONDPDOFF(sourlo, 10)
-     && CANONDPDOFF(sourlo, 0)) return result;
-  #endif
-  } // block
-
-  // Loop to repair a non-canonical coefficent, as needed
-  inword=DECWORDS-1;               // current input word
-  uoff=0;                          // bit offset of declet
-  encode=DFWORD(result, inword);
-  for (n=DECLETS-1; n>=0; n--) {   // count down declets of 10 bits
-    dpd=encode>>uoff;
-    uoff+=10;
-    if (uoff>32) {                 // crossed uInt boundary
-      inword--;
-      encode=DFWORD(result, inword);
-      uoff-=32;
-      dpd|=encode<<(10-uoff);      // get pending bits
-      }
-    dpd&=0x3ff;                    // clear uninteresting bits
-    if (dpd<0x16e) continue;       // must be canonical
-    canon=BIN2DPD[DPD2BIN[dpd]];   // determine canonical declet
-    if (canon==dpd) continue;      // have canonical declet
-    // need to replace declet
-    if (uoff>=10) {                // all within current word
-      encode&=~(0x3ff<<(uoff-10)); // clear the 10 bits ready for replace
-      encode|=canon<<(uoff-10);    // insert the canonical form
-      DFWORD(result, inword)=encode;    // .. and save
-      continue;
-      }
-    // straddled words
-    precode=DFWORD(result, inword+1);   // get previous
-    precode&=0xffffffff>>(10-uoff);     // clear top bits
-    DFWORD(result, inword+1)=precode|(canon<<(32-(10-uoff)));
-    encode&=0xffffffff<<uoff;           // clear bottom bits
-    encode|=canon>>(10-uoff);           // insert canonical
-    DFWORD(result, inword)=encode;      // .. and save
-    } // n
-  return result;
-  } // decCanonical
-
-/* ------------------------------------------------------------------ */
-/* decDivide -- divide operations                                     */
-/*                                                                    */
-/*   result gets the result of dividing dfl by dfr:                   */
-/*   dfl    is the first decFloat (lhs)                               */
-/*   dfr    is the second decFloat (rhs)                              */
-/*   set    is the context                                            */
-/*   op     is the operation selector                                 */
-/*   returns result                                                   */
-/*                                                                    */
-/* op is one of DIVIDE, REMAINDER, DIVIDEINT, or REMNEAR.             */
-/* ------------------------------------------------------------------ */
-#define DIVCOUNT  0                // 1 to instrument subtractions counter
-#define DIVBASE   ((uInt)BILLION)  // the base used for divide
-#define DIVOPLEN  DECPMAX9         // operand length ('digits' base 10**9)
-#define DIVACCLEN (DIVOPLEN*3)     // accumulator length (ditto)
-static decFloat * decDivide(decFloat *result, const decFloat *dfl,
-                            const decFloat *dfr, decContext *set, uInt op) {
-  decFloat quotient;               // for remainders
-  bcdnum num;                      // for final conversion
-  uInt   acc[DIVACCLEN];           // coefficent in base-billion ..
-  uInt   div[DIVOPLEN];            // divisor in base-billion ..
-  uInt   quo[DIVOPLEN+1];          // quotient in base-billion ..
-  uByte  bcdacc[(DIVOPLEN+1)*9+2]; // for quotient in BCD, +1, +1
-  uInt   *msua, *msud, *msuq;      // -> msu of acc, div, and quo
-  Int    divunits, accunits;       // lengths
-  Int    quodigits;                // digits in quotient
-  uInt   *lsua, *lsuq;             // -> current acc and quo lsus
-  Int    length, multiplier;       // work
-  uInt   carry, sign;              // ..
-  uInt   *ua, *ud, *uq;            // ..
-  uByte  *ub;                      // ..
-  uInt   uiwork;                   // for macros
-  uInt   divtop;                   // top unit of div adjusted for estimating
-  #if DIVCOUNT
-  static uInt maxcount=0;          // worst-seen subtractions count
-  uInt   divcount=0;               // subtractions count [this divide]
-  #endif
-
-  // calculate sign
-  num.sign=(DFWORD(dfl, 0)^DFWORD(dfr, 0)) & DECFLOAT_Sign;
-
-  if (DFISSPECIAL(dfl) || DFISSPECIAL(dfr)) { // either is special?
-    // NaNs are handled as usual
-    if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set);
-    // one or two infinities
-    if (DFISINF(dfl)) {
-      if (DFISINF(dfr)) return decInvalid(result, set); // Two infinities bad
-      if (op&(REMAINDER|REMNEAR)) return decInvalid(result, set); // as is rem
-      // Infinity/x is infinite and quiet, even if x=0
-      DFWORD(result, 0)=num.sign;
-      return decInfinity(result, result);
-      }
-    // must be x/Infinity -- remainders are lhs
-    if (op&(REMAINDER|REMNEAR)) return decCanonical(result, dfl);
-    // divides: return zero with correct sign and exponent depending
-    // on op (Etiny for divide, 0 for divideInt)
-    decFloatZero(result);
-    if (op==DIVIDEINT) DFWORD(result, 0)|=num.sign; // add sign
-     else DFWORD(result, 0)=num.sign;        // zeros the exponent, too
-    return result;
-    }
-  // next, handle zero operands (x/0 and 0/x)
-  if (DFISZERO(dfr)) {                       // x/0
-    if (DFISZERO(dfl)) {                     // 0/0 is undefined
-      decFloatZero(result);
-      DFWORD(result, 0)=DECFLOAT_qNaN;
-      set->status|=DEC_Division_undefined;
-      return result;
-      }
-    if (op&(REMAINDER|REMNEAR)) return decInvalid(result, set); // bad rem
-    set->status|=DEC_Division_by_zero;
-    DFWORD(result, 0)=num.sign;
-    return decInfinity(result, result);      // x/0 -> signed Infinity
-    }
-  num.exponent=GETEXPUN(dfl)-GETEXPUN(dfr);  // ideal exponent
-  if (DFISZERO(dfl)) {                       // 0/x (x!=0)
-    // if divide, result is 0 with ideal exponent; divideInt has
-    // exponent=0, remainders give zero with lower exponent
-    if (op&DIVIDEINT) {
-      decFloatZero(result);
-      DFWORD(result, 0)|=num.sign;           // add sign
-      return result;
-      }
-    if (!(op&DIVIDE)) {                      // a remainder
-      // exponent is the minimum of the operands
-      num.exponent=MINI(GETEXPUN(dfl), GETEXPUN(dfr));
-      // if the result is zero the sign shall be sign of dfl
-      num.sign=DFWORD(dfl, 0)&DECFLOAT_Sign;
-      }
-    bcdacc[0]=0;
-    num.msd=bcdacc;                          // -> 0
-    num.lsd=bcdacc;                          // ..
-    return decFinalize(result, &num, set);   // [divide may clamp exponent]
-    } // 0/x
-  // [here, both operands are known to be finite and non-zero]
-
-  // extract the operand coefficents into 'units' which are
-  // base-billion; the lhs is high-aligned in acc and the msu of both
-  // acc and div is at the right-hand end of array (offset length-1);
-  // the quotient can need one more unit than the operands as digits
-  // in it are not necessarily aligned neatly; further, the quotient
-  // may not start accumulating until after the end of the initial
-  // operand in acc if that is small (e.g., 1) so the accumulator
-  // must have at least that number of units extra (at the ls end)
-  GETCOEFFBILL(dfl, acc+DIVACCLEN-DIVOPLEN);
-  GETCOEFFBILL(dfr, div);
-  // zero the low uInts of acc
-  acc[0]=0;
-  acc[1]=0;
-  acc[2]=0;
-  acc[3]=0;
-  #if DOUBLE
-    #if DIVOPLEN!=2
-      #error Unexpected Double DIVOPLEN
-    #endif
-  #elif QUAD
-  acc[4]=0;
-  acc[5]=0;
-  acc[6]=0;
-  acc[7]=0;
-    #if DIVOPLEN!=4
-      #error Unexpected Quad DIVOPLEN
-    #endif
-  #endif
-
-  // set msu and lsu pointers
-  msua=acc+DIVACCLEN-1;       // [leading zeros removed below]
-  msuq=quo+DIVOPLEN;
-  //[loop for div will terminate because operands are non-zero]
-  for (msud=div+DIVOPLEN-1; *msud==0;) msud--;
-  // the initial least-significant unit of acc is set so acc appears
-  // to have the same length as div.
-  // This moves one position towards the least possible for each
-  // iteration
-  divunits=(Int)(msud-div+1); // precalculate
-  lsua=msua-divunits+1;       // initial working lsu of acc
-  lsuq=msuq;                  // and of quo
-
-  // set up the estimator for the multiplier; this is the msu of div,
-  // plus two bits from the unit below (if any) rounded up by one if
-  // there are any non-zero bits or units below that [the extra two
-  // bits makes for a much better estimate when the top unit is small]
-  divtop=*msud<<2;
-  if (divunits>1) {
-    uInt *um=msud-1;
-    uInt d=*um;
-    if (d>=750000000) {divtop+=3; d-=750000000;}
-     else if (d>=500000000) {divtop+=2; d-=500000000;}
-     else if (d>=250000000) {divtop++; d-=250000000;}
-    if (d) divtop++;
-     else for (um--; um>=div; um--) if (*um) {
-      divtop++;
-      break;
-      }
-    } // >1 unit
-
-  #if DECTRACE
-  {Int i;
-  printf("----- div=");
-  for (i=divunits-1; i>=0; i--) printf("%09ld ", (LI)div[i]);
-  printf("\n");}
-  #endif
-
-  // now collect up to DECPMAX+1 digits in the quotient (this may
-  // need OPLEN+1 uInts if unaligned)
-  quodigits=0;                // no digits yet
-  for (;; lsua--) {           // outer loop -- each input position
-    #if DECCHECK
-    if (lsua<acc) {
-      printf("Acc underrun...\n");
-      break;
-      }
-    #endif
-    #if DECTRACE
-    printf("Outer: quodigits=%ld acc=", (LI)quodigits);
-    for (ua=msua; ua>=lsua; ua--) printf("%09ld ", (LI)*ua);
-    printf("\n");
-    #endif
-    *lsuq=0;                  // default unit result is 0
-    for (;;) {                // inner loop -- calculate quotient unit
-      // strip leading zero units from acc (either there initially or
-      // from subtraction below); this may strip all if exactly 0
-      for (; *msua==0 && msua>=lsua;) msua--;
-      accunits=(Int)(msua-lsua+1);                // [maybe 0]
-      // subtraction is only necessary and possible if there are as
-      // least as many units remaining in acc for this iteration as
-      // there are in div
-      if (accunits<divunits) {
-        if (accunits==0) msua++;                  // restore
-        break;
-        }
-
-      // If acc is longer than div then subtraction is definitely
-      // possible (as msu of both is non-zero), but if they are the
-      // same length a comparison is needed.
-      // If a subtraction is needed then a good estimate of the
-      // multiplier for the subtraction is also needed in order to
-      // minimise the iterations of this inner loop because the
-      // subtractions needed dominate division performance.
-      if (accunits==divunits) {
-        // compare the high divunits of acc and div:
-        // acc<div:  this quotient unit is unchanged; subtraction
-        //           will be possible on the next iteration
-        // acc==div: quotient gains 1, set acc=0
-        // acc>div:  subtraction necessary at this position
-        for (ud=msud, ua=msua; ud>div; ud--, ua--) if (*ud!=*ua) break;
-        // [now at first mismatch or lsu]
-        if (*ud>*ua) break;                       // next time...
-        if (*ud==*ua) {                           // all compared equal
-          *lsuq+=1;                               // increment result
-          msua=lsua;                              // collapse acc units
-          *msua=0;                                // .. to a zero
-          break;
-          }
-
-        // subtraction necessary; estimate multiplier [see above]
-        // if both *msud and *msua are small it is cost-effective to
-        // bring in part of the following units (if any) to get a
-        // better estimate (assume some other non-zero in div)
-        #define DIVLO 1000000U
-        #define DIVHI (DIVBASE/DIVLO)
-        #if DECUSE64
-          if (divunits>1) {
-            // there cannot be a *(msud-2) for DECDOUBLE so next is
-            // an exact calculation unless DECQUAD (which needs to
-            // assume bits out there if divunits>2)
-            uLong mul=(uLong)*msua * DIVBASE + *(msua-1);
-            uLong div=(uLong)*msud * DIVBASE + *(msud-1);
-            #if QUAD
-            if (divunits>2) div++;
-            #endif
-            mul/=div;
-            multiplier=(Int)mul;
-            }
-           else multiplier=*msua/(*msud);
-        #else
-          if (divunits>1 && *msua<DIVLO && *msud<DIVLO) {
-            multiplier=(*msua*DIVHI + *(msua-1)/DIVLO)
-                      /(*msud*DIVHI + *(msud-1)/DIVLO +1);
-            }
-           else multiplier=(*msua<<2)/divtop;
-        #endif
-        }
-       else {                                     // accunits>divunits
-        // msud is one unit 'lower' than msua, so estimate differently
-        #if DECUSE64
-          uLong mul;
-          // as before, bring in extra digits if possible
-          if (divunits>1 && *msua<DIVLO && *msud<DIVLO) {
-            mul=((uLong)*msua * DIVHI * DIVBASE) + *(msua-1) * DIVHI
-               + *(msua-2)/DIVLO;
-            mul/=(*msud*DIVHI + *(msud-1)/DIVLO +1);
-            }
-           else if (divunits==1) {
-            mul=(uLong)*msua * DIVBASE + *(msua-1);
-            mul/=*msud;       // no more to the right
-            }
-           else {
-            mul=(uLong)(*msua) * (uInt)(DIVBASE<<2)
-                + (*(msua-1)<<2);
-            mul/=divtop;      // [divtop already allows for sticky bits]
-            }
-          multiplier=(Int)mul;
-        #else
-          multiplier=*msua * ((DIVBASE<<2)/divtop);
-        #endif
-        }
-      if (multiplier==0) multiplier=1;            // marginal case
-      *lsuq+=multiplier;
-
-      #if DIVCOUNT
-      // printf("Multiplier: %ld\n", (LI)multiplier);
-      divcount++;
-      #endif
-
-      // Carry out the subtraction  acc-(div*multiplier); for each
-      // unit in div, do the multiply, split to units (see
-      // decFloatMultiply for the algorithm), and subtract from acc
-      #define DIVMAGIC  2305843009U               // 2**61/10**9
-      #define DIVSHIFTA 29
-      #define DIVSHIFTB 32
-      carry=0;
-      for (ud=div, ua=lsua; ud<=msud; ud++, ua++) {
-        uInt lo, hop;
-        #if DECUSE64
-          uLong sub=(uLong)multiplier*(*ud)+carry;
-          if (sub<DIVBASE) {
-            carry=0;
-            lo=(uInt)sub;
-            }
-           else {
-            hop=(uInt)(sub>>DIVSHIFTA);
-            carry=(uInt)(((uLong)hop*DIVMAGIC)>>DIVSHIFTB);
-            // the estimate is now in hi; now calculate sub-hi*10**9
-            // to get the remainder (which will be <DIVBASE))
-            lo=(uInt)sub;
-            lo-=carry*DIVBASE;                    // low word of result
-            if (lo>=DIVBASE) {
-              lo-=DIVBASE;                        // correct by +1
-              carry++;
-              }
-            }
-        #else // 32-bit
-          uInt hi;
-          // calculate multiplier*(*ud) into hi and lo
-          LONGMUL32HI(hi, *ud, multiplier);       // get the high word
-          lo=multiplier*(*ud);                    // .. and the low
-          lo+=carry;                              // add the old hi
-          carry=hi+(lo<carry);                    // .. with any carry
-          if (carry || lo>=DIVBASE) {             // split is needed
-            hop=(carry<<3)+(lo>>DIVSHIFTA);       // hi:lo/2**29
-            LONGMUL32HI(carry, hop, DIVMAGIC);    // only need the high word
-            // [DIVSHIFTB is 32, so carry can be used directly]
-            // the estimate is now in carry; now calculate hi:lo-est*10**9;
-            // happily the top word of the result is irrelevant because it
-            // will always be zero so this needs only one multiplication
-            lo-=(carry*DIVBASE);
-            // the correction here will be at most +1; do it
-            if (lo>=DIVBASE) {
-              lo-=DIVBASE;
-              carry++;
-              }
-            }
-        #endif
-        if (lo>*ua) {              // borrow needed
-          *ua+=DIVBASE;
-          carry++;
-          }
-        *ua-=lo;
-        } // ud loop
-      if (carry) *ua-=carry;       // accdigits>divdigits [cannot borrow]
-      } // inner loop
-
-    // the outer loop terminates when there is either an exact result
-    // or enough digits; first update the quotient digit count and
-    // pointer (if any significant digits)
-    #if DECTRACE
-    if (*lsuq || quodigits) printf("*lsuq=%09ld\n", (LI)*lsuq);
-    #endif
-    if (quodigits) {
-      quodigits+=9;                // had leading unit earlier
-      lsuq--;
-      if (quodigits>DECPMAX+1) break;   // have enough
-      }
-     else if (*lsuq) {             // first quotient digits
-      const uInt *pow;
-      for (pow=DECPOWERS; *lsuq>=*pow; pow++) quodigits++;
-      lsuq--;
-      // [cannot have >DECPMAX+1 on first unit]
-      }
-
-    if (*msua!=0) continue;        // not an exact result
-    // acc is zero iff used all of original units and zero down to lsua
-    // (must also continue to original lsu for correct quotient length)
-    if (lsua>acc+DIVACCLEN-DIVOPLEN) continue;
-    for (; msua>lsua && *msua==0;) msua--;
-    if (*msua==0 && msua==lsua) break;
-    } // outer loop
-
-  // all of the original operand in acc has been covered at this point
-  // quotient now has at least DECPMAX+2 digits
-  // *msua is now non-0 if inexact and sticky bits
-  // lsuq is one below the last uint of the quotient
-  lsuq++;                          // set -> true lsu of quo
-  if (*msua) *lsuq|=1;             // apply sticky bit
-
-  // quo now holds the (unrounded) quotient in base-billion; one
-  // base-billion 'digit' per uInt.
-  #if DECTRACE
-  printf("DivQuo:");
-  for (uq=msuq; uq>=lsuq; uq--) printf(" %09ld", (LI)*uq);
-  printf("\n");
-  #endif
-
-  // Now convert to BCD for rounding and cleanup, starting from the
-  // most significant end [offset by one into bcdacc to leave room
-  // for a possible carry digit if rounding for REMNEAR is needed]
-  for (uq=msuq, ub=bcdacc+1; uq>=lsuq; uq--, ub+=9) {
-    uInt top, mid, rem;                 // work
-    if (*uq==0) {                       // no split needed
-      UBFROMUI(ub, 0);                  // clear 9 BCD8s
-      UBFROMUI(ub+4, 0);                // ..
-      *(ub+8)=0;                        // ..
-      continue;
-      }
-    // *uq is non-zero -- split the base-billion digit into
-    // hi, mid, and low three-digits
-    #define divsplit9 1000000           // divisor
-    #define divsplit6 1000              // divisor
-    // The splitting is done by simple divides and remainders,
-    // assuming the compiler will optimize these [GCC does]
-    top=*uq/divsplit9;
-    rem=*uq%divsplit9;
-    mid=rem/divsplit6;
-    rem=rem%divsplit6;
-    // lay out the nine BCD digits (plus one unwanted byte)
-    UBFROMUI(ub,   UBTOUI(&BIN2BCD8[top*4]));
-    UBFROMUI(ub+3, UBTOUI(&BIN2BCD8[mid*4]));
-    UBFROMUI(ub+6, UBTOUI(&BIN2BCD8[rem*4]));
-    } // BCD conversion loop
-  ub--;                                 // -> lsu
-
-  // complete the bcdnum; quodigits is correct, so the position of
-  // the first non-zero is known
-  num.msd=bcdacc+1+(msuq-lsuq+1)*9-quodigits;
-  num.lsd=ub;
-
-  // make exponent adjustments, etc
-  if (lsua<acc+DIVACCLEN-DIVOPLEN) {    // used extra digits
-    num.exponent-=(Int)((acc+DIVACCLEN-DIVOPLEN-lsua)*9);
-    // if the result was exact then there may be up to 8 extra
-    // trailing zeros in the overflowed quotient final unit
-    if (*msua==0) {
-      for (; *ub==0;) ub--;             // drop zeros
-      num.exponent+=(Int)(num.lsd-ub);  // and adjust exponent
-      num.lsd=ub;
-      }
-    } // adjustment needed
-
-  #if DIVCOUNT
-  if (divcount>maxcount) {              // new high-water nark
-    maxcount=divcount;
-    printf("DivNewMaxCount: %ld\n", (LI)maxcount);
-    }
-  #endif
-
-  if (op&DIVIDE) return decFinalize(result, &num, set); // all done
-
-  // Is DIVIDEINT or a remainder; there is more to do -- first form
-  // the integer (this is done 'after the fact', unlike as in
-  // decNumber, so as not to tax DIVIDE)
-
-  // The first non-zero digit will be in the first 9 digits, known
-  // from quodigits and num.msd, so there is always space for DECPMAX
-  // digits
-
-  length=(Int)(num.lsd-num.msd+1);
-  //printf("Length exp: %ld %ld\n", (LI)length, (LI)num.exponent);
-
-  if (length+num.exponent>DECPMAX) { // cannot fit
-    decFloatZero(result);
-    DFWORD(result, 0)=DECFLOAT_qNaN;
-    set->status|=DEC_Division_impossible;
-    return result;
-    }
-
-  if (num.exponent>=0) {           // already an int, or need pad zeros
-    for (ub=num.lsd+1; ub<=num.lsd+num.exponent; ub++) *ub=0;
-    num.lsd+=num.exponent;
-    }
-   else {                          // too long: round or truncate needed
-    Int drop=-num.exponent;
-    if (!(op&REMNEAR)) {           // simple truncate
-      num.lsd-=drop;
-      if (num.lsd<num.msd) {       // truncated all
-        num.lsd=num.msd;           // make 0
-        *num.lsd=0;                // .. [sign still relevant]
-        }
-      }
-     else {                        // round to nearest even [sigh]
-      // round-to-nearest, in-place; msd is at or to right of bcdacc+1
-      // (this is a special case of Quantize -- q.v. for commentary)
-      uByte *roundat;              // -> re-round digit
-      uByte reround;               // reround value
-      *(num.msd-1)=0;              // in case of left carry, or make 0
-      if (drop<length) roundat=num.lsd-drop+1;
-       else if (drop==length) roundat=num.msd;
-       else roundat=num.msd-1;     // [-> 0]
-      reround=*roundat;
-      for (ub=roundat+1; ub<=num.lsd; ub++) {
-        if (*ub!=0) {
-          reround=DECSTICKYTAB[reround];
-          break;
-          }
-        } // check stickies
-      if (roundat>num.msd) num.lsd=roundat-1;
-       else {
-        num.msd--;                           // use the 0 ..
-        num.lsd=num.msd;                     // .. at the new MSD place
-        }
-      if (reround!=0) {                      // discarding non-zero
-        uInt bump=0;
-        // rounding is DEC_ROUND_HALF_EVEN always
-        if (reround>5) bump=1;               // >0.5 goes up
-         else if (reround==5)                // exactly 0.5000 ..
-          bump=*(num.lsd) & 0x01;            // .. up iff [new] lsd is odd
-        if (bump!=0) {                       // need increment
-          // increment the coefficient; this might end up with 1000...
-          ub=num.lsd;
-          for (; UBTOUI(ub-3)==0x09090909; ub-=4) UBFROMUI(ub-3, 0);
-          for (; *ub==9; ub--) *ub=0;        // at most 3 more
-          *ub+=1;
-          if (ub<num.msd) num.msd--;         // carried
-          } // bump needed
-        } // reround!=0
-      } // remnear
-    } // round or truncate needed
-  num.exponent=0;                            // all paths
-  //decShowNum(&num, "int");
-
-  if (op&DIVIDEINT) return decFinalize(result, &num, set); // all done
-
-  // Have a remainder to calculate
-  decFinalize(&quotient, &num, set);         // lay out the integer so far
-  DFWORD(&quotient, 0)^=DECFLOAT_Sign;       // negate it
-  sign=DFWORD(dfl, 0);                       // save sign of dfl
-  decFloatFMA(result, &quotient, dfr, dfl, set);
-  if (!DFISZERO(result)) return result;
-  // if the result is zero the sign shall be sign of dfl
-  DFWORD(&quotient, 0)=sign;                 // construct decFloat of sign
-  return decFloatCopySign(result, result, &quotient);
-  } // decDivide
-
-/* ------------------------------------------------------------------ */
-/* decFiniteMultiply -- multiply two finite decFloats                 */
-/*                                                                    */
-/*   num    gets the result of multiplying dfl and dfr                */
-/*   bcdacc .. with the coefficient in this array                     */
-/*   dfl    is the first decFloat (lhs)                               */
-/*   dfr    is the second decFloat (rhs)                              */
-/*                                                                    */
-/* This effects the multiplication of two decFloats, both known to be */
-/* finite, leaving the result in a bcdnum ready for decFinalize (for  */
-/* use in Multiply) or in a following addition (FMA).                 */
-/*                                                                    */
-/* bcdacc must have space for at least DECPMAX9*18+1 bytes.           */
-/* No error is possible and no status is set.                         */
-/* ------------------------------------------------------------------ */
-// This routine has two separate implementations of the core
-// multiplication; both using base-billion.  One uses only 32-bit
-// variables (Ints and uInts) or smaller; the other uses uLongs (for
-// multiplication and addition only).  Both implementations cover
-// both arithmetic sizes (DOUBLE and QUAD) in order to allow timing
-// comparisons.  In any one compilation only one implementation for
-// each size can be used, and if DECUSE64 is 0 then use of the 32-bit
-// version is forced.
-//
-// Historical note: an earlier version of this code also supported the
-// 256-bit format and has been preserved.  That is somewhat trickier
-// during lazy carry splitting because the initial quotient estimate
-// (est) can exceed 32 bits.
-
-#define MULTBASE  ((uInt)BILLION)  // the base used for multiply
-#define MULOPLEN  DECPMAX9         // operand length ('digits' base 10**9)
-#define MULACCLEN (MULOPLEN*2)              // accumulator length (ditto)
-#define LEADZEROS (MULACCLEN*9 - DECPMAX*2) // leading zeros always
-
-// Assertions: exponent not too large and MULACCLEN is a multiple of 4
-#if DECEMAXD>9
-  #error Exponent may overflow when doubled for Multiply
-#endif
-#if MULACCLEN!=(MULACCLEN/4)*4
-  // This assumption is used below only for initialization
-  #error MULACCLEN is not a multiple of 4
-#endif
-
-static void decFiniteMultiply(bcdnum *num, uByte *bcdacc,
-                              const decFloat *dfl, const decFloat *dfr) {
-  uInt   bufl[MULOPLEN];           // left  coefficient (base-billion)
-  uInt   bufr[MULOPLEN];           // right coefficient (base-billion)
-  uInt   *ui, *uj;                 // work
-  uByte  *ub;                      // ..
-  uInt   uiwork;                   // for macros
-
-  #if DECUSE64
-  uLong  accl[MULACCLEN];          // lazy accumulator (base-billion+)
-  uLong  *pl;                      // work -> lazy accumulator
-  uInt   acc[MULACCLEN];           // coefficent in base-billion ..
-  #else
-  uInt   acc[MULACCLEN*2];         // accumulator in base-billion ..
-  #endif
-  uInt   *pa;                      // work -> accumulator
-  //printf("Base10**9: OpLen=%d MulAcclen=%d\n", OPLEN, MULACCLEN);
-
-  /* Calculate sign and exponent */
-  num->sign=(DFWORD(dfl, 0)^DFWORD(dfr, 0)) & DECFLOAT_Sign;
-  num->exponent=GETEXPUN(dfl)+GETEXPUN(dfr); // [see assertion above]
-
-  /* Extract the coefficients and prepare the accumulator */
-  // the coefficients of the operands are decoded into base-billion
-  // numbers in uInt arrays (bufl and bufr, LSD at offset 0) of the
-  // appropriate size.
-  GETCOEFFBILL(dfl, bufl);
-  GETCOEFFBILL(dfr, bufr);
-  #if DECTRACE && 0
-    printf("CoeffbL:");
-    for (ui=bufl+MULOPLEN-1; ui>=bufl; ui--) printf(" %08lx", (LI)*ui);
-    printf("\n");
-    printf("CoeffbR:");
-    for (uj=bufr+MULOPLEN-1; uj>=bufr; uj--) printf(" %08lx", (LI)*uj);
-    printf("\n");
-  #endif
-
-  // start the 64-bit/32-bit differing paths...
-#if DECUSE64
-
-  // zero the accumulator
-  #if MULACCLEN==4
-    accl[0]=0; accl[1]=0; accl[2]=0; accl[3]=0;
-  #else                                      // use a loop
-    // MULACCLEN is a multiple of four, asserted above
-    for (pl=accl; pl<accl+MULACCLEN; pl+=4) {
-      *pl=0; *(pl+1)=0; *(pl+2)=0; *(pl+3)=0;// [reduce overhead]
-      } // pl
-  #endif
-
-  /* Effect the multiplication */
-  // The multiplcation proceeds using MFC's lazy-carry resolution
-  // algorithm from decNumber.  First, the multiplication is
-  // effected, allowing accumulation of the partial products (which
-  // are in base-billion at each column position) into 64 bits
-  // without resolving back to base=billion after each addition.
-  // These 64-bit numbers (which may contain up to 19 decimal digits)
-  // are then split using the Clark & Cowlishaw algorithm (see below).
-  // [Testing for 0 in the inner loop is not really a 'win']
-  for (ui=bufr; ui<bufr+MULOPLEN; ui++) { // over each item in rhs
-    if (*ui==0) continue;                 // product cannot affect result
-    pl=accl+(ui-bufr);                    // where to add the lhs
-    for (uj=bufl; uj<bufl+MULOPLEN; uj++, pl++) { // over each item in lhs
-      // if (*uj==0) continue;            // product cannot affect result
-      *pl+=((uLong)*ui)*(*uj);
-      } // uj
-    } // ui
-
-  // The 64-bit carries must now be resolved; this means that a
-  // quotient/remainder has to be calculated for base-billion (1E+9).
-  // For this, Clark & Cowlishaw's quotient estimation approach (also
-  // used in decNumber) is needed, because 64-bit divide is generally
-  // extremely slow on 32-bit machines, and may be slower than this
-  // approach even on 64-bit machines.  This algorithm splits X
-  // using:
-  //
-  //   magic=2**(A+B)/1E+9;   // 'magic number'
-  //   hop=X/2**A;            // high order part of X (by shift)
-  //   est=magic*hop/2**B     // quotient estimate (may be low by 1)
-  //
-  // A and B are quite constrained; hop and magic must fit in 32 bits,
-  // and 2**(A+B) must be as large as possible (which is 2**61 if
-  // magic is to fit).  Further, maxX increases with the length of
-  // the operands (and hence the number of partial products
-  // accumulated); maxX is OPLEN*(10**18), which is up to 19 digits.
-  //
-  // It can be shown that when OPLEN is 2 then the maximum error in
-  // the estimated quotient is <1, but for larger maximum x the
-  // maximum error is above 1 so a correction that is >1 may be
-  // needed.  Values of A and B are chosen to satisfy the constraints
-  // just mentioned while minimizing the maximum error (and hence the
-  // maximum correction), as shown in the following table:
-  //
-  //   Type    OPLEN   A   B     maxX    maxError  maxCorrection
-  //   ---------------------------------------------------------
-  //   DOUBLE    2    29  32  <2*10**18    0.63       1
-  //   QUAD      4    30  31  <4*10**18    1.17       2
-  //
-  // In the OPLEN==2 case there is most choice, but the value for B
-  // of 32 has a big advantage as then the calculation of the
-  // estimate requires no shifting; the compiler can extract the high
-  // word directly after multiplying magic*hop.
-  #define MULMAGIC 2305843009U          // 2**61/10**9  [both cases]
-  #if DOUBLE
-    #define MULSHIFTA 29
-    #define MULSHIFTB 32
-  #elif QUAD
-    #define MULSHIFTA 30
-    #define MULSHIFTB 31
-  #else
-    #error Unexpected type
-  #endif
-
-  #if DECTRACE
-  printf("MulAccl:");
-  for (pl=accl+MULACCLEN-1; pl>=accl; pl--)
-    printf(" %08lx:%08lx", (LI)(*pl>>32), (LI)(*pl&0xffffffff));
-  printf("\n");
-  #endif
-
-  for (pl=accl, pa=acc; pl<accl+MULACCLEN; pl++, pa++) { // each column position
-    uInt lo, hop;                       // work
-    uInt est;                           // cannot exceed 4E+9
-    if (*pl>=MULTBASE) {
-      // *pl holds a binary number which needs to be split
-      hop=(uInt)(*pl>>MULSHIFTA);
-      est=(uInt)(((uLong)hop*MULMAGIC)>>MULSHIFTB);
-      // the estimate is now in est; now calculate hi:lo-est*10**9;
-      // happily the top word of the result is irrelevant because it
-      // will always be zero so this needs only one multiplication
-      lo=(uInt)(*pl-((uLong)est*MULTBASE));  // low word of result
-      // If QUAD, the correction here could be +2
-      if (lo>=MULTBASE) {
-        lo-=MULTBASE;                   // correct by +1
-        est++;
-        #if QUAD
-        // may need to correct by +2
-        if (lo>=MULTBASE) {
-          lo-=MULTBASE;
-          est++;
-          }
-        #endif
-        }
-      // finally place lo as the new coefficient 'digit' and add est to
-      // the next place up [this is safe because this path is never
-      // taken on the final iteration as *pl will fit]
-      *pa=lo;
-      *(pl+1)+=est;
-      } // *pl needed split
-     else {                             // *pl<MULTBASE
-      *pa=(uInt)*pl;                    // just copy across
-      }
-    } // pl loop
-
-#else  // 32-bit
-  for (pa=acc;; pa+=4) {                     // zero the accumulator
-    *pa=0; *(pa+1)=0; *(pa+2)=0; *(pa+3)=0;  // [reduce overhead]
-    if (pa==acc+MULACCLEN*2-4) break;        // multiple of 4 asserted
-    } // pa
-
-  /* Effect the multiplication */
-  // uLongs are not available (and in particular, there is no uLong
-  // divide) but it is still possible to use MFC's lazy-carry
-  // resolution algorithm from decNumber.  First, the multiplication
-  // is effected, allowing accumulation of the partial products
-  // (which are in base-billion at each column position) into 64 bits
-  // [with the high-order 32 bits in each position being held at
-  // offset +ACCLEN from the low-order 32 bits in the accumulator].
-  // These 64-bit numbers (which may contain up to 19 decimal digits)
-  // are then split using the Clark & Cowlishaw algorithm (see
-  // below).
-  for (ui=bufr;; ui++) {                // over each item in rhs
-    uInt hi, lo;                        // words of exact multiply result
-    pa=acc+(ui-bufr);                   // where to add the lhs
-    for (uj=bufl;; uj++, pa++) {        // over each item in lhs
-      LONGMUL32HI(hi, *ui, *uj);        // calculate product of digits
-      lo=(*ui)*(*uj);                   // ..
-      *pa+=lo;                          // accumulate low bits and ..
-      *(pa+MULACCLEN)+=hi+(*pa<lo);     // .. high bits with any carry
-      if (uj==bufl+MULOPLEN-1) break;
-      }
-    if (ui==bufr+MULOPLEN-1) break;
-    }
-
-  // The 64-bit carries must now be resolved; this means that a
-  // quotient/remainder has to be calculated for base-billion (1E+9).
-  // For this, Clark & Cowlishaw's quotient estimation approach (also
-  // used in decNumber) is needed, because 64-bit divide is generally
-  // extremely slow on 32-bit machines.  This algorithm splits X
-  // using:
-  //
-  //   magic=2**(A+B)/1E+9;   // 'magic number'
-  //   hop=X/2**A;            // high order part of X (by shift)
-  //   est=magic*hop/2**B     // quotient estimate (may be low by 1)
-  //
-  // A and B are quite constrained; hop and magic must fit in 32 bits,
-  // and 2**(A+B) must be as large as possible (which is 2**61 if
-  // magic is to fit).  Further, maxX increases with the length of
-  // the operands (and hence the number of partial products
-  // accumulated); maxX is OPLEN*(10**18), which is up to 19 digits.
-  //
-  // It can be shown that when OPLEN is 2 then the maximum error in
-  // the estimated quotient is <1, but for larger maximum x the
-  // maximum error is above 1 so a correction that is >1 may be
-  // needed.  Values of A and B are chosen to satisfy the constraints
-  // just mentioned while minimizing the maximum error (and hence the
-  // maximum correction), as shown in the following table:
-  //
-  //   Type    OPLEN   A   B     maxX    maxError  maxCorrection
-  //   ---------------------------------------------------------
-  //   DOUBLE    2    29  32  <2*10**18    0.63       1
-  //   QUAD      4    30  31  <4*10**18    1.17       2
-  //
-  // In the OPLEN==2 case there is most choice, but the value for B
-  // of 32 has a big advantage as then the calculation of the
-  // estimate requires no shifting; the high word is simply
-  // calculated from multiplying magic*hop.
-  #define MULMAGIC 2305843009U          // 2**61/10**9  [both cases]
-  #if DOUBLE
-    #define MULSHIFTA 29
-    #define MULSHIFTB 32
-  #elif QUAD
-    #define MULSHIFTA 30
-    #define MULSHIFTB 31
-  #else
-    #error Unexpected type
-  #endif
-
-  #if DECTRACE
-  printf("MulHiLo:");
-  for (pa=acc+MULACCLEN-1; pa>=acc; pa--)
-    printf(" %08lx:%08lx", (LI)*(pa+MULACCLEN), (LI)*pa);
-  printf("\n");
-  #endif
-
-  for (pa=acc;; pa++) {                 // each low uInt
-    uInt hi, lo;                        // words of exact multiply result
-    uInt hop, estlo;                    // work
-    #if QUAD
-    uInt esthi;                         // ..
-    #endif
-
-    lo=*pa;
-    hi=*(pa+MULACCLEN);                 // top 32 bits
-    // hi and lo now hold a binary number which needs to be split
-
-    #if DOUBLE
-      hop=(hi<<3)+(lo>>MULSHIFTA);      // hi:lo/2**29
-      LONGMUL32HI(estlo, hop, MULMAGIC);// only need the high word
-      // [MULSHIFTB is 32, so estlo can be used directly]
-      // the estimate is now in estlo; now calculate hi:lo-est*10**9;
-      // happily the top word of the result is irrelevant because it
-      // will always be zero so this needs only one multiplication
-      lo-=(estlo*MULTBASE);
-      // esthi=0;                       // high word is ignored below
-      // the correction here will be at most +1; do it
-      if (lo>=MULTBASE) {
-        lo-=MULTBASE;
-        estlo++;
-        }
-    #elif QUAD
-      hop=(hi<<2)+(lo>>MULSHIFTA);      // hi:lo/2**30
-      LONGMUL32HI(esthi, hop, MULMAGIC);// shift will be 31 ..
-      estlo=hop*MULMAGIC;               // .. so low word needed
-      estlo=(esthi<<1)+(estlo>>MULSHIFTB); // [just the top bit]
-      // esthi=0;                       // high word is ignored below
-      lo-=(estlo*MULTBASE);             // as above
-      // the correction here could be +1 or +2
-      if (lo>=MULTBASE) {
-        lo-=MULTBASE;
-        estlo++;
-        }
-      if (lo>=MULTBASE) {
-        lo-=MULTBASE;
-        estlo++;
-        }
-    #else
-      #error Unexpected type
-    #endif
-
-    // finally place lo as the new accumulator digit and add est to
-    // the next place up; this latter add could cause a carry of 1
-    // to the high word of the next place
-    *pa=lo;
-    *(pa+1)+=estlo;
-    // esthi is always 0 for DOUBLE and QUAD so this is skipped
-    // *(pa+1+MULACCLEN)+=esthi;
-    if (*(pa+1)<estlo) *(pa+1+MULACCLEN)+=1; // carry
-    if (pa==acc+MULACCLEN-2) break;          // [MULACCLEN-1 will never need split]
-    } // pa loop
-#endif
-
-  // At this point, whether using the 64-bit or the 32-bit paths, the
-  // accumulator now holds the (unrounded) result in base-billion;
-  // one base-billion 'digit' per uInt.
-  #if DECTRACE
-  printf("MultAcc:");
-  for (pa=acc+MULACCLEN-1; pa>=acc; pa--) printf(" %09ld", (LI)*pa);
-  printf("\n");
-  #endif
-
-  // Now convert to BCD for rounding and cleanup, starting from the
-  // most significant end
-  pa=acc+MULACCLEN-1;
-  if (*pa!=0) num->msd=bcdacc+LEADZEROS;// drop known lead zeros
-   else {                               // >=1 word of leading zeros
-    num->msd=bcdacc;                    // known leading zeros are gone
-    pa--;                               // skip first word ..
-    for (; *pa==0; pa--) if (pa==acc) break; // .. and any more leading 0s
-    }
-  for (ub=bcdacc;; pa--, ub+=9) {
-    if (*pa!=0) {                       // split(s) needed
-      uInt top, mid, rem;               // work
-      // *pa is non-zero -- split the base-billion acc digit into
-      // hi, mid, and low three-digits
-      #define mulsplit9 1000000         // divisor
-      #define mulsplit6 1000            // divisor
-      // The splitting is done by simple divides and remainders,
-      // assuming the compiler will optimize these where useful
-      // [GCC does]
-      top=*pa/mulsplit9;
-      rem=*pa%mulsplit9;
-      mid=rem/mulsplit6;
-      rem=rem%mulsplit6;
-      // lay out the nine BCD digits (plus one unwanted byte)
-      UBFROMUI(ub,   UBTOUI(&BIN2BCD8[top*4]));
-      UBFROMUI(ub+3, UBTOUI(&BIN2BCD8[mid*4]));
-      UBFROMUI(ub+6, UBTOUI(&BIN2BCD8[rem*4]));
-      }
-     else {                             // *pa==0
-      UBFROMUI(ub, 0);                  // clear 9 BCD8s
-      UBFROMUI(ub+4, 0);                // ..
-      *(ub+8)=0;                        // ..
-      }
-    if (pa==acc) break;
-    } // BCD conversion loop
-
-  num->lsd=ub+8;                        // complete the bcdnum ..
-
-  #if DECTRACE
-  decShowNum(num, "postmult");
-  decFloatShow(dfl, "dfl");
-  decFloatShow(dfr, "dfr");
-  #endif
-  return;
-  } // decFiniteMultiply
-
-/* ------------------------------------------------------------------ */
-/* decFloatAbs -- absolute value, heeding NaNs, etc.                  */
-/*                                                                    */
-/*   result gets the canonicalized df with sign 0                     */
-/*   df     is the decFloat to abs                                    */
-/*   set    is the context                                            */
-/*   returns result                                                   */
-/*                                                                    */
-/* This has the same effect as decFloatPlus unless df is negative,    */
-/* in which case it has the same effect as decFloatMinus.  The        */
-/* effect is also the same as decFloatCopyAbs except that NaNs are    */
-/* handled normally (the sign of a NaN is not affected, and an sNaN   */
-/* will signal) and the result will be canonical.                     */
-/* ------------------------------------------------------------------ */
-decFloat * decFloatAbs(decFloat *result, const decFloat *df,
-                       decContext *set) {
-  if (DFISNAN(df)) return decNaNs(result, df, NULL, set);
-  decCanonical(result, df);             // copy and check
-  DFBYTE(result, 0)&=~0x80;             // zero sign bit
-  return result;
-  } // decFloatAbs
-
-/* ------------------------------------------------------------------ */
-/* decFloatAdd -- add two decFloats                                   */
-/*                                                                    */
-/*   result gets the result of adding dfl and dfr:                    */
-/*   dfl    is the first decFloat (lhs)                               */
-/*   dfr    is the second decFloat (rhs)                              */
-/*   set    is the context                                            */
-/*   returns result                                                   */
-/*                                                                    */
-/* ------------------------------------------------------------------ */
-#if QUAD
-// Table for testing MSDs for fastpath elimination; returns the MSD of
-// a decDouble or decQuad (top 6 bits tested) ignoring the sign.
-// Infinities return -32 and NaNs return -128 so that summing the two
-// MSDs also allows rapid tests for the Specials (see code below).
-const Int DECTESTMSD[64]={
-  0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5,   6,    7,
-  0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 9, 8, 9, -32, -128,
-  0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5,   6,    7,
-  0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 9, 8, 9, -32, -128};
-#else
-// The table for testing MSDs is shared between the modules
-extern const Int DECTESTMSD[64];
-#endif
-
-decFloat * decFloatAdd(decFloat *result,
-                       const decFloat *dfl, const decFloat *dfr,
-                       decContext *set) {
-  bcdnum num;                      // for final conversion
-  Int    bexpl, bexpr;             // left and right biased exponents
-  uByte  *ub, *us, *ut;            // work
-  uInt   uiwork;                   // for macros
-  #if QUAD
-  uShort uswork;                   // ..
-  #endif
-
-  uInt sourhil, sourhir;           // top words from source decFloats
-                                   // [valid only through end of
-                                   // fastpath code -- before swap]
-  uInt diffsign;                   // non-zero if signs differ
-  uInt carry;                      // carry: 0 or 1 before add loop
-  Int  overlap;                    // coefficient overlap (if full)
-  Int  summ;                       // sum of the MSDs
-  // the following buffers hold coefficients with various alignments
-  // (see commentary and diagrams below)
-  uByte acc[4+2+DECPMAX*3+8];
-  uByte buf[4+2+DECPMAX*2];
-  uByte *umsd, *ulsd;              // local MSD and LSD pointers
-
-  #if DECLITEND
-    #define CARRYPAT 0x01000000    // carry=1 pattern
-  #else
-    #define CARRYPAT 0x00000001    // carry=1 pattern
-  #endif
-
-  /* Start decoding the arguments */
-  // The initial exponents are placed into the opposite Ints to
-  // that which might be expected; there are two sets of data to
-  // keep track of (each decFloat and the corresponding exponent),
-  // and this scheme means that at the swap point (after comparing
-  // exponents) only one pair of words needs to be swapped
-  // whichever path is taken (thereby minimising worst-case path).
-  // The calculated exponents will be nonsense when the arguments are
-  // Special, but are not used in that path
-  sourhil=DFWORD(dfl, 0);          // LHS top word
-  summ=DECTESTMSD[sourhil>>26];    // get first MSD for testing
-  bexpr=DECCOMBEXP[sourhil>>26];   // get exponent high bits (in place)
-  bexpr+=GETECON(dfl);             // .. + continuation
-
-  sourhir=DFWORD(dfr, 0);          // RHS top word
-  summ+=DECTESTMSD[sourhir>>26];   // sum MSDs for testing
-  bexpl=DECCOMBEXP[sourhir>>26];
-  bexpl+=GETECON(dfr);
-
-  // here bexpr has biased exponent from lhs, and vice versa
-
-  diffsign=(sourhil^sourhir)&DECFLOAT_Sign;
-
-  // now determine whether to take a fast path or the full-function
-  // slow path.  The slow path must be taken when:
-  //   -- both numbers are finite, and:
-  //         the exponents are different, or
-  //         the signs are different, or
-  //         the sum of the MSDs is >8 (hence might overflow)
-  // specialness and the sum of the MSDs can be tested at once using
-  // the summ value just calculated, so the test for specials is no
-  // longer on the worst-case path (as of 3.60)
-
-  if (summ<=8) {                   // MSD+MSD is good, or there is a special
-    if (summ<0) {                  // there is a special
-      // Inf+Inf would give -64; Inf+finite is -32 or higher
-      if (summ<-64) return decNaNs(result, dfl, dfr, set);  // one or two NaNs
-      // two infinities with different signs is invalid
-      if (summ==-64 && diffsign) return decInvalid(result, set);
-      if (DFISINF(dfl)) return decInfinity(result, dfl);    // LHS is infinite
-      return decInfinity(result, dfr);                      // RHS must be Inf
-      }
-    // Here when both arguments are finite; fast path is possible
-    // (currently only for aligned and same-sign)
-    if (bexpr==bexpl && !diffsign) {
-      uInt tac[DECLETS+1];              // base-1000 coefficient
-      uInt encode;                      // work
-
-      // Get one coefficient as base-1000 and add the other
-      GETCOEFFTHOU(dfl, tac);           // least-significant goes to [0]
-      ADDCOEFFTHOU(dfr, tac);
-      // here the sum of the MSDs (plus any carry) will be <10 due to
-      // the fastpath test earlier
-
-      // construct the result; low word is the same for both formats
-      encode =BIN2DPD[tac[0]];
-      encode|=BIN2DPD[tac[1]]<<10;
-      encode|=BIN2DPD[tac[2]]<<20;
-      encode|=BIN2DPD[tac[3]]<<30;
-      DFWORD(result, (DECBYTES/4)-1)=encode;
-
-      // collect next two declets (all that remains, for Double)
-      encode =BIN2DPD[tac[3]]>>2;
-      encode|=BIN2DPD[tac[4]]<<8;
-
-      #if QUAD
-      // complete and lay out middling words
-      encode|=BIN2DPD[tac[5]]<<18;
-      encode|=BIN2DPD[tac[6]]<<28;
-      DFWORD(result, 2)=encode;
-
-      encode =BIN2DPD[tac[6]]>>4;
-      encode|=BIN2DPD[tac[7]]<<6;
-      encode|=BIN2DPD[tac[8]]<<16;
-      encode|=BIN2DPD[tac[9]]<<26;
-      DFWORD(result, 1)=encode;
-
-      // and final two declets
-      encode =BIN2DPD[tac[9]]>>6;
-      encode|=BIN2DPD[tac[10]]<<4;
-      #endif
-
-      // add exponent continuation and sign (from either argument)
-      encode|=sourhil & (ECONMASK | DECFLOAT_Sign);
-
-      // create lookup index = MSD + top two bits of biased exponent <<4
-      tac[DECLETS]|=(bexpl>>DECECONL)<<4;
-      encode|=DECCOMBFROM[tac[DECLETS]]; // add constructed combination field
-      DFWORD(result, 0)=encode;          // complete
-
-      // decFloatShow(result, ">");
-      return result;
-      } // fast path OK
-    // drop through to slow path
-    } // low sum or Special(s)
-
-  /* Slow path required -- arguments are finite and might overflow,   */
-  /* or require alignment, or might have different signs              */
-
-  // now swap either exponents or argument pointers
-  if (bexpl<=bexpr) {
-    // original left is bigger
-    Int bexpswap=bexpl;
-    bexpl=bexpr;
-    bexpr=bexpswap;
-    // printf("left bigger\n");
-    }
-   else {
-    const decFloat *dfswap=dfl;
-    dfl=dfr;
-    dfr=dfswap;
-    // printf("right bigger\n");
-    }
-  // [here dfl and bexpl refer to the datum with the larger exponent,
-  // of if the exponents are equal then the original LHS argument]
-
-  // if lhs is zero then result will be the rhs (now known to have
-  // the smaller exponent), which also may need to be tested for zero
-  // for the weird IEEE 754 sign rules
-  if (DFISZERO(dfl)) {
-    decCanonical(result, dfr);               // clean copy
-    // "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 '-'."
-    if (diffsign && DFISZERO(result)) {
-      DFWORD(result, 0)&=~DECFLOAT_Sign;     // assume sign 0
-      if (set->round==DEC_ROUND_FLOOR) DFWORD(result, 0)|=DECFLOAT_Sign;
-      }
-    return result;
-    } // numfl is zero
-  // [here, LHS is non-zero; code below assumes that]
-
-  // Coefficients layout during the calculations to follow:
-  //
-  //       Overlap case:
-  //       +------------------------------------------------+
-  // acc:  |0000|      coeffa      | tail B |               |
-  //       +------------------------------------------------+
-  // buf:  |0000| pad0s |      coeffb       |               |
-  //       +------------------------------------------------+
-  //
-  //       Touching coefficients or gap:
-  //       +------------------------------------------------+
-  // acc:  |0000|      coeffa      | gap |      coeffb      |
-  //       +------------------------------------------------+
-  //       [buf not used or needed; gap clamped to Pmax]
-
-  // lay out lhs coefficient into accumulator; this starts at acc+4
-  // for decDouble or acc+6 for decQuad so the LSD is word-
-  // aligned; the top word gap is there only in case a carry digit
-  // is prefixed after the add -- it does not need to be zeroed
-  #if DOUBLE
-    #define COFF 4                      // offset into acc
-  #elif QUAD
-    UBFROMUS(acc+4, 0);                 // prefix 00
-    #define COFF 6                      // offset into acc
-  #endif
-
-  GETCOEFF(dfl, acc+COFF);              // decode from decFloat
-  ulsd=acc+COFF+DECPMAX-1;
-  umsd=acc+4;                           // [having this here avoids
-
-  #if DECTRACE
-  {bcdnum tum;
-  tum.msd=umsd;
-  tum.lsd=ulsd;
-  tum.exponent=bexpl-DECBIAS;
-  tum.sign=DFWORD(dfl, 0) & DECFLOAT_Sign;
-  decShowNum(&tum, "dflx");}
-  #endif
-
-  // if signs differ, take ten's complement of lhs (here the
-  // coefficient is subtracted from all-nines; the 1 is added during
-  // the later add cycle -- zeros to the right do not matter because
-  // the complement of zero is zero); these are fixed-length inverts
-  // where the lsd is known to be at a 4-byte boundary (so no borrow
-  // possible)
-  carry=0;                              // assume no carry
-  if (diffsign) {
-    carry=CARRYPAT;                     // for +1 during add
-    UBFROMUI(acc+ 4, 0x09090909-UBTOUI(acc+ 4));
-    UBFROMUI(acc+ 8, 0x09090909-UBTOUI(acc+ 8));
-    UBFROMUI(acc+12, 0x09090909-UBTOUI(acc+12));
-    UBFROMUI(acc+16, 0x09090909-UBTOUI(acc+16));
-    #if QUAD
-    UBFROMUI(acc+20, 0x09090909-UBTOUI(acc+20));
-    UBFROMUI(acc+24, 0x09090909-UBTOUI(acc+24));
-    UBFROMUI(acc+28, 0x09090909-UBTOUI(acc+28));
-    UBFROMUI(acc+32, 0x09090909-UBTOUI(acc+32));
-    UBFROMUI(acc+36, 0x09090909-UBTOUI(acc+36));
-    #endif
-    } // diffsign
-
-  // now process the rhs coefficient; if it cannot overlap lhs then
-  // it can be put straight into acc (with an appropriate gap, if
-  // needed) because no actual addition will be needed (except
-  // possibly to complete ten's complement)
-  overlap=DECPMAX-(bexpl-bexpr);
-  #if DECTRACE
-  printf("exps: %ld %ld\n", (LI)(bexpl-DECBIAS), (LI)(bexpr-DECBIAS));
-  printf("Overlap=%ld carry=%08lx\n", (LI)overlap, (LI)carry);
-  #endif
-
-  if (overlap<=0) {                     // no overlap possible
-    uInt gap;                           // local work
-    // since a full addition is not needed, a ten's complement
-    // calculation started above may need to be completed
-    if (carry) {
-      for (ub=ulsd; *ub==9; ub--) *ub=0;
-      *ub+=1;
-      carry=0;                          // taken care of
-      }
-    // up to DECPMAX-1 digits of the final result can extend down
-    // below the LSD of the lhs, so if the gap is >DECPMAX then the
-    // rhs will be simply sticky bits.  In this case the gap is
-    // clamped to DECPMAX and the exponent adjusted to suit [this is
-    // safe because the lhs is non-zero].
-    gap=-overlap;
-    if (gap>DECPMAX) {
-      bexpr+=gap-1;
-      gap=DECPMAX;
-      }
-    ub=ulsd+gap+1;                      // where MSD will go
-    // Fill the gap with 0s; note that there is no addition to do
-    ut=acc+COFF+DECPMAX;                // start of gap
-    for (; ut<ub; ut+=4) UBFROMUI(ut, 0); // mind the gap
-    if (overlap<-DECPMAX) {             // gap was > DECPMAX
-      *ub=(uByte)(!DFISZERO(dfr));      // make sticky digit
-      }
-     else {                             // need full coefficient
-      GETCOEFF(dfr, ub);                // decode from decFloat
-      ub+=DECPMAX-1;                    // new LSD...
-      }
-    ulsd=ub;                            // save new LSD
-    } // no overlap possible
-
-   else {                               // overlap>0
-    // coefficients overlap (perhaps completely, although also
-    // perhaps only where zeros)
-    if (overlap==DECPMAX) {             // aligned
-      ub=buf+COFF;                      // where msd will go
-      #if QUAD
-      UBFROMUS(buf+4, 0);               // clear quad's 00
-      #endif
-      GETCOEFF(dfr, ub);                // decode from decFloat
-      }
-     else {                             // unaligned
-      ub=buf+COFF+DECPMAX-overlap;      // where MSD will go
-      // Fill the prefix gap with 0s; 8 will cover most common
-      // unalignments, so start with direct assignments (a loop is
-      // then used for any remaining -- the loop (and the one in a
-      // moment) is not then on the critical path because the number
-      // of additions is reduced by (at least) two in this case)
-      UBFROMUI(buf+4, 0);               // [clears decQuad 00 too]
-      UBFROMUI(buf+8, 0);
-      if (ub>buf+12) {
-        ut=buf+12;                      // start any remaining
-        for (; ut<ub; ut+=4) UBFROMUI(ut, 0); // fill them
-        }
-      GETCOEFF(dfr, ub);                // decode from decFloat
-
-      // now move tail of rhs across to main acc; again use direct
-      // copies for 8 digits-worth
-      UBFROMUI(acc+COFF+DECPMAX,   UBTOUI(buf+COFF+DECPMAX));
-      UBFROMUI(acc+COFF+DECPMAX+4, UBTOUI(buf+COFF+DECPMAX+4));
-      if (buf+COFF+DECPMAX+8<ub+DECPMAX) {
-        us=buf+COFF+DECPMAX+8;          // source
-        ut=acc+COFF+DECPMAX+8;          // target
-        for (; us<ub+DECPMAX; us+=4, ut+=4) UBFROMUI(ut, UBTOUI(us));
-        }
-      } // unaligned
-
-    ulsd=acc+(ub-buf+DECPMAX-1);        // update LSD pointer
-
-    // Now do the add of the non-tail; this is all nicely aligned,
-    // and is over a multiple of four digits (because for Quad two
-    // zero digits were added on the left); words in both acc and
-    // buf (buf especially) will often be zero
-    // [byte-by-byte add, here, is about 15% slower total effect than
-    // the by-fours]
-
-    // Now effect the add; this is harder on a little-endian
-    // machine as the inter-digit carry cannot use the usual BCD
-    // addition trick because the bytes are loaded in the wrong order
-    // [this loop could be unrolled, but probably scarcely worth it]
-
-    ut=acc+COFF+DECPMAX-4;              // target LSW (acc)
-    us=buf+COFF+DECPMAX-4;              // source LSW (buf, to add to acc)
-
-    #if !DECLITEND
-    for (; ut>=acc+4; ut-=4, us-=4) {   // big-endian add loop
-      // bcd8 add
-      carry+=UBTOUI(us);                // rhs + carry
-      if (carry==0) continue;           // no-op
-      carry+=UBTOUI(ut);                // lhs
-      // Big-endian BCD adjust (uses internal carry)
-      carry+=0x76f6f6f6;                // note top nibble not all bits
-      // apply BCD adjust and save
-      UBFROMUI(ut, (carry & 0x0f0f0f0f) - ((carry & 0x60606060)>>4));
-      carry>>=31;                       // true carry was at far left
-      } // add loop
-    #else
-    for (; ut>=acc+4; ut-=4, us-=4) {   // little-endian add loop
-      // bcd8 add
-      carry+=UBTOUI(us);                // rhs + carry
-      if (carry==0) continue;           // no-op [common if unaligned]
-      carry+=UBTOUI(ut);                // lhs
-      // Little-endian BCD adjust; inter-digit carry must be manual
-      // because the lsb from the array will be in the most-significant
-      // byte of carry
-      carry+=0x76767676;                // note no inter-byte carries
-      carry+=(carry & 0x80000000)>>15;
-      carry+=(carry & 0x00800000)>>15;
-      carry+=(carry & 0x00008000)>>15;
-      carry-=(carry & 0x60606060)>>4;   // BCD adjust back
-      UBFROMUI(ut, carry & 0x0f0f0f0f); // clear debris and save
-      // here, final carry-out bit is at 0x00000080; move it ready
-      // for next word-add (i.e., to 0x01000000)
-      carry=(carry & 0x00000080)<<17;
-      } // add loop
-    #endif
-
-    #if DECTRACE
-    {bcdnum tum;
-    printf("Add done, carry=%08lx, diffsign=%ld\n", (LI)carry, (LI)diffsign);
-    tum.msd=umsd;  // acc+4;
-    tum.lsd=ulsd;
-    tum.exponent=0;
-    tum.sign=0;
-    decShowNum(&tum, "dfadd");}
-    #endif
-    } // overlap possible
-
-  // ordering here is a little strange in order to have slowest path
-  // first in GCC asm listing
-  if (diffsign) {                  // subtraction
-    if (!carry) {                  // no carry out means RHS<LHS
-      // borrowed -- take ten's complement
-      // sign is lhs sign
-      num.sign=DFWORD(dfl, 0) & DECFLOAT_Sign;
-
-      // invert the coefficient first by fours, then add one; space
-      // at the end of the buffer ensures the by-fours is always
-      // safe, but lsd+1 must be cleared to prevent a borrow
-      // if big-endian
-      #if !DECLITEND
-      *(ulsd+1)=0;
-      #endif
-      // there are always at least four coefficient words
-      UBFROMUI(umsd,    0x09090909-UBTOUI(umsd));
-      UBFROMUI(umsd+4,  0x09090909-UBTOUI(umsd+4));
-      UBFROMUI(umsd+8,  0x09090909-UBTOUI(umsd+8));
-      UBFROMUI(umsd+12, 0x09090909-UBTOUI(umsd+12));
-      #if DOUBLE
-        #define BNEXT 16
-      #elif QUAD
-        UBFROMUI(umsd+16, 0x09090909-UBTOUI(umsd+16));
-        UBFROMUI(umsd+20, 0x09090909-UBTOUI(umsd+20));
-        UBFROMUI(umsd+24, 0x09090909-UBTOUI(umsd+24));
-        UBFROMUI(umsd+28, 0x09090909-UBTOUI(umsd+28));
-        UBFROMUI(umsd+32, 0x09090909-UBTOUI(umsd+32));
-        #define BNEXT 36
-      #endif
-      if (ulsd>=umsd+BNEXT) {           // unaligned
-        // eight will handle most unaligments for Double; 16 for Quad
-        UBFROMUI(umsd+BNEXT,   0x09090909-UBTOUI(umsd+BNEXT));
-        UBFROMUI(umsd+BNEXT+4, 0x09090909-UBTOUI(umsd+BNEXT+4));
-        #if DOUBLE
-        #define BNEXTY (BNEXT+8)
-        #elif QUAD
-        UBFROMUI(umsd+BNEXT+8,  0x09090909-UBTOUI(umsd+BNEXT+8));
-        UBFROMUI(umsd+BNEXT+12, 0x09090909-UBTOUI(umsd+BNEXT+12));
-        #define BNEXTY (BNEXT+16)
-        #endif
-        if (ulsd>=umsd+BNEXTY) {        // very unaligned
-          ut=umsd+BNEXTY;               // -> continue
-          for (;;ut+=4) {
-            UBFROMUI(ut, 0x09090909-UBTOUI(ut)); // invert four digits
-            if (ut>=ulsd-3) break;      // all done
-            }
-          }
-        }
-      // complete the ten's complement by adding 1
-      for (ub=ulsd; *ub==9; ub--) *ub=0;
-      *ub+=1;
-      } // borrowed
-
-     else {                        // carry out means RHS>=LHS
-      num.sign=DFWORD(dfr, 0) & DECFLOAT_Sign;
-      // all done except for the special IEEE 754 exact-zero-result
-      // rule (see above); while testing for zero, strip leading
-      // zeros (which will save decFinalize doing it) (this is in
-      // diffsign path, so carry impossible and true umsd is
-      // acc+COFF)
-
-      // Check the initial coefficient area using the fast macro;
-      // this will often be all that needs to be done (as on the
-      // worst-case path when the subtraction was aligned and
-      // full-length)
-      if (ISCOEFFZERO(acc+COFF)) {
-        umsd=acc+COFF+DECPMAX-1;   // so far, so zero
-        if (ulsd>umsd) {           // more to check
-          umsd++;                  // to align after checked area
-          for (; UBTOUI(umsd)==0 && umsd+3<ulsd;) umsd+=4;
-          for (; *umsd==0 && umsd<ulsd;) umsd++;
-          }
-        if (*umsd==0) {            // must be true zero (and diffsign)
-          num.sign=0;              // assume +
-          if (set->round==DEC_ROUND_FLOOR) num.sign=DECFLOAT_Sign;
-          }
-        }
-      // [else was not zero, might still have leading zeros]
-      } // subtraction gave positive result
-    } // diffsign
-
-   else { // same-sign addition
-    num.sign=DFWORD(dfl, 0)&DECFLOAT_Sign;
-    #if DOUBLE
-    if (carry) {                   // only possible with decDouble
-      *(acc+3)=1;                  // [Quad has leading 00]
-      umsd=acc+3;
-      }
-    #endif
-    } // same sign
-
-  num.msd=umsd;                    // set MSD ..
-  num.lsd=ulsd;                    // .. and LSD
-  num.exponent=bexpr-DECBIAS;      // set exponent to smaller, unbiassed
-
-  #if DECTRACE
-  decFloatShow(dfl, "dfl");
-  decFloatShow(dfr, "dfr");
-  decShowNum(&num, "postadd");
-  #endif
-  return decFinalize(result, &num, set); // round, check, and lay out
-  } // decFloatAdd
-
-/* ------------------------------------------------------------------ */
-/* decFloatAnd -- logical digitwise AND of two decFloats              */
-/*                                                                    */
-/*   result gets the result of ANDing dfl and dfr                     */
-/*   dfl    is the first decFloat (lhs)                               */
-/*   dfr    is the second decFloat (rhs)                              */
-/*   set    is the context                                            */
-/*   returns result, which will be canonical with sign=0              */
-/*                                                                    */
-/* The operands must be positive, finite with exponent q=0, and       */
-/* comprise just zeros and ones; if not, Invalid operation results.   */
-/* ------------------------------------------------------------------ */
-decFloat * decFloatAnd(decFloat *result,
-                       const decFloat *dfl, const decFloat *dfr,
-                       decContext *set) {
-  if (!DFISUINT01(dfl) || !DFISUINT01(dfr)
-   || !DFISCC01(dfl)   || !DFISCC01(dfr)) return decInvalid(result, set);
-  // the operands are positive finite integers (q=0) with just 0s and 1s
-  #if DOUBLE
-   DFWORD(result, 0)=ZEROWORD
-                   |((DFWORD(dfl, 0) & DFWORD(dfr, 0))&0x04009124);
-   DFWORD(result, 1)=(DFWORD(dfl, 1) & DFWORD(dfr, 1))&0x49124491;
-  #elif QUAD
-   DFWORD(result, 0)=ZEROWORD
-                   |((DFWORD(dfl, 0) & DFWORD(dfr, 0))&0x04000912);
-   DFWORD(result, 1)=(DFWORD(dfl, 1) & DFWORD(dfr, 1))&0x44912449;
-   DFWORD(result, 2)=(DFWORD(dfl, 2) & DFWORD(dfr, 2))&0x12449124;
-   DFWORD(result, 3)=(DFWORD(dfl, 3) & DFWORD(dfr, 3))&0x49124491;
-  #endif
-  return result;
-  } // decFloatAnd
-
-/* ------------------------------------------------------------------ */
-/* decFloatCanonical -- copy a decFloat, making canonical             */
-/*                                                                    */
-/*   result gets the canonicalized df                                 */
-/*   df     is the decFloat to copy and make canonical                */
-/*   returns result                                                   */
-/*                                                                    */
-/* This works on specials, too; no error or exception is possible.    */
-/* ------------------------------------------------------------------ */
-decFloat * decFloatCanonical(decFloat *result, const decFloat *df) {
-  return decCanonical(result, df);
-  } // decFloatCanonical
-
-/* ------------------------------------------------------------------ */
-/* decFloatClass -- return the class of a decFloat                    */
-/*                                                                    */
-/*   df is the decFloat to test                                       */
-/*   returns the decClass that df falls into                          */
-/* ------------------------------------------------------------------ */
-enum decClass decFloatClass(const decFloat *df) {
-  Int exp;                         // exponent
-  if (DFISSPECIAL(df)) {
-    if (DFISQNAN(df)) return DEC_CLASS_QNAN;
-    if (DFISSNAN(df)) return DEC_CLASS_SNAN;
-    // must be an infinity
-    if (DFISSIGNED(df)) return DEC_CLASS_NEG_INF;
-    return DEC_CLASS_POS_INF;
-    }
-  if (DFISZERO(df)) {              // quite common
-    if (DFISSIGNED(df)) return DEC_CLASS_NEG_ZERO;
-    return DEC_CLASS_POS_ZERO;
-    }
-  // is finite and non-zero; similar code to decFloatIsNormal, here
-  // [this could be speeded up slightly by in-lining decFloatDigits]
-  exp=GETEXPUN(df)                 // get unbiased exponent ..
-     +decFloatDigits(df)-1;        // .. and make adjusted exponent
-  if (exp>=DECEMIN) {              // is normal
-    if (DFISSIGNED(df)) return DEC_CLASS_NEG_NORMAL;
-    return DEC_CLASS_POS_NORMAL;
-    }
-  // is subnormal
-  if (DFISSIGNED(df)) return DEC_CLASS_NEG_SUBNORMAL;
-  return DEC_CLASS_POS_SUBNORMAL;
-  } // decFloatClass
-
-/* ------------------------------------------------------------------ */
-/* decFloatClassString -- return the class of a decFloat as a string  */
-/*                                                                    */
-/*   df is the decFloat to test                                       */
-/*   returns a constant string describing the class df falls into     */
-/* ------------------------------------------------------------------ */
-const char *decFloatClassString(const decFloat *df) {
-  enum decClass eclass=decFloatClass(df);
-  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
-  } // decFloatClassString
-
-/* ------------------------------------------------------------------ */
-/* decFloatCompare -- compare two decFloats; quiet NaNs allowed       */
-/*                                                                    */
-/*   result gets the result of comparing dfl and dfr                  */
-/*   dfl    is the first decFloat (lhs)                               */
-/*   dfr    is the second decFloat (rhs)                              */
-/*   set    is the context                                            */
-/*   returns result, which may be -1, 0, 1, or NaN (Unordered)        */
-/* ------------------------------------------------------------------ */
-decFloat * decFloatCompare(decFloat *result,
-                           const decFloat *dfl, const decFloat *dfr,
-                           decContext *set) {
-  Int comp;                                  // work
-  // NaNs are handled as usual
-  if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set);
-  // numeric comparison needed
-  comp=decNumCompare(dfl, dfr, 0);
-  decFloatZero(result);
-  if (comp==0) return result;
-  DFBYTE(result, DECBYTES-1)=0x01;      // LSD=1
-  if (comp<0) DFBYTE(result, 0)|=0x80;  // set sign bit
-  return result;
-  } // decFloatCompare
-
-/* ------------------------------------------------------------------ */
-/* decFloatCompareSignal -- compare two decFloats; all NaNs signal    */
-/*                                                                    */
-/*   result gets the result of comparing dfl and dfr                  */
-/*   dfl    is the first decFloat (lhs)                               */
-/*   dfr    is the second decFloat (rhs)                              */
-/*   set    is the context                                            */
-/*   returns result, which may be -1, 0, 1, or NaN (Unordered)        */
-/* ------------------------------------------------------------------ */
-decFloat * decFloatCompareSignal(decFloat *result,
-                                 const decFloat *dfl, const decFloat *dfr,
-                                 decContext *set) {
-  Int comp;                                  // work
-  // NaNs are handled as usual, except that all NaNs signal
-  if (DFISNAN(dfl) || DFISNAN(dfr)) {
-    set->status|=DEC_Invalid_operation;
-    return decNaNs(result, dfl, dfr, set);
-    }
-  // numeric comparison needed
-  comp=decNumCompare(dfl, dfr, 0);
-  decFloatZero(result);
-  if (comp==0) return result;
-  DFBYTE(result, DECBYTES-1)=0x01;      // LSD=1
-  if (comp<0) DFBYTE(result, 0)|=0x80;  // set sign bit
-  return result;
-  } // decFloatCompareSignal
-
-/* ------------------------------------------------------------------ */
-/* decFloatCompareTotal -- compare two decFloats with total ordering  */
-/*                                                                    */
-/*   result gets the result of comparing dfl and dfr                  */
-/*   dfl    is the first decFloat (lhs)                               */
-/*   dfr    is the second decFloat (rhs)                              */
-/*   returns result, which may be -1, 0, or 1                         */
-/* ------------------------------------------------------------------ */
-decFloat * decFloatCompareTotal(decFloat *result,
-                                const decFloat *dfl, const decFloat *dfr) {
-  Int  comp;                                 // work
-  uInt uiwork;                               // for macros
-  #if QUAD
-  uShort uswork;                             // ..
-  #endif
-  if (DFISNAN(dfl) || DFISNAN(dfr)) {
-    Int nanl, nanr;                          // work
-    // morph NaNs to +/- 1 or 2, leave numbers as 0
-    nanl=DFISSNAN(dfl)+DFISQNAN(dfl)*2;      // quiet > signalling
-    if (DFISSIGNED(dfl)) nanl=-nanl;
-    nanr=DFISSNAN(dfr)+DFISQNAN(dfr)*2;
-    if (DFISSIGNED(dfr)) nanr=-nanr;
-    if (nanl>nanr) comp=+1;
-     else if (nanl<nanr) comp=-1;
-     else { // NaNs are the same type and sign .. must compare payload
-      // buffers need +2 for QUAD
-      uByte bufl[DECPMAX+4];                 // for LHS coefficient + foot
-      uByte bufr[DECPMAX+4];                 // for RHS coefficient + foot
-      uByte *ub, *uc;                        // work
-      Int sigl;                              // signum of LHS
-      sigl=(DFISSIGNED(dfl) ? -1 : +1);
-
-      // decode the coefficients
-      // (shift both right two if Quad to make a multiple of four)
-      #if QUAD
-        UBFROMUS(bufl, 0);
-        UBFROMUS(bufr, 0);
-      #endif
-      GETCOEFF(dfl, bufl+QUAD*2);            // decode from decFloat
-      GETCOEFF(dfr, bufr+QUAD*2);            // ..
-      // all multiples of four, here
-      comp=0;                                // assume equal
-      for (ub=bufl, uc=bufr; ub<bufl+DECPMAX+QUAD*2; ub+=4, uc+=4) {
-        uInt ui=UBTOUI(ub);
-        if (ui==UBTOUI(uc)) continue; // so far so same
-        // about to find a winner; go by bytes in case little-endian
-        for (;; ub++, uc++) {
-          if (*ub==*uc) continue;
-          if (*ub>*uc) comp=sigl;            // difference found
-           else comp=-sigl;                  // ..
-           break;
-          }
-        }
-      } // same NaN type and sign
-    }
-   else {
-    // numeric comparison needed
-    comp=decNumCompare(dfl, dfr, 1);    // total ordering
-    }
-  decFloatZero(result);
-  if (comp==0) return result;
-  DFBYTE(result, DECBYTES-1)=0x01;      // LSD=1
-  if (comp<0) DFBYTE(result, 0)|=0x80;  // set sign bit
-  return result;
-  } // decFloatCompareTotal
-
-/* ------------------------------------------------------------------ */
-/* decFloatCompareTotalMag -- compare magnitudes with total ordering  */
-/*                                                                    */
-/*   result gets the result of comparing abs(dfl) and abs(dfr)        */
-/*   dfl    is the first decFloat (lhs)                               */
-/*   dfr    is the second decFloat (rhs)                              */
-/*   returns result, which may be -1, 0, or 1                         */
-/* ------------------------------------------------------------------ */
-decFloat * decFloatCompareTotalMag(decFloat *result,
-                                const decFloat *dfl, const decFloat *dfr) {
-  decFloat a, b;                        // for copy if needed
-  // copy and redirect signed operand(s)
-  if (DFISSIGNED(dfl)) {
-    decFloatCopyAbs(&a, dfl);
-    dfl=&a;
-    }
-  if (DFISSIGNED(dfr)) {
-    decFloatCopyAbs(&b, dfr);
-    dfr=&b;
-    }
-  return decFloatCompareTotal(result, dfl, dfr);
-  } // decFloatCompareTotalMag
-
-/* ------------------------------------------------------------------ */
-/* decFloatCopy -- copy a decFloat as-is                              */
-/*                                                                    */
-/*   result gets the copy of dfl                                      */
-/*   dfl    is the decFloat to copy                                   */
-/*   returns result                                                   */
-/*                                                                    */
-/* This is a bitwise operation; no errors or exceptions are possible. */
-/* ------------------------------------------------------------------ */
-decFloat * decFloatCopy(decFloat *result, const decFloat *dfl) {
-  if (dfl!=result) *result=*dfl;             // copy needed
-  return result;
-  } // decFloatCopy
-
-/* ------------------------------------------------------------------ */
-/* decFloatCopyAbs -- copy a decFloat as-is and set sign bit to 0     */
-/*                                                                    */
-/*   result gets the copy of dfl with sign bit 0                      */
-/*   dfl    is the decFloat to copy                                   */
-/*   returns result                                                   */
-/*                                                                    */
-/* This is a bitwise operation; no errors or exceptions are possible. */
-/* ------------------------------------------------------------------ */
-decFloat * decFloatCopyAbs(decFloat *result, const decFloat *dfl) {
-  if (dfl!=result) *result=*dfl;        // copy needed
-  DFBYTE(result, 0)&=~0x80;             // zero sign bit
-  return result;
-  } // decFloatCopyAbs
-
-/* ------------------------------------------------------------------ */
-/* decFloatCopyNegate -- copy a decFloat as-is with inverted sign bit */
-/*                                                                    */
-/*   result gets the copy of dfl with sign bit inverted               */
-/*   dfl    is the decFloat to copy                                   */
-/*   returns result                                                   */
-/*                                                                    */
-/* This is a bitwise operation; no errors or exceptions are possible. */
-/* ------------------------------------------------------------------ */
-decFloat * decFloatCopyNegate(decFloat *result, const decFloat *dfl) {
-  if (dfl!=result) *result=*dfl;        // copy needed
-  DFBYTE(result, 0)^=0x80;              // invert sign bit
-  return result;
-  } // decFloatCopyNegate
-
-/* ------------------------------------------------------------------ */
-/* decFloatCopySign -- copy a decFloat with the sign of another       */
-/*                                                                    */
-/*   result gets the result of copying dfl with the sign of dfr       */
-/*   dfl    is the first decFloat (lhs)                               */
-/*   dfr    is the second decFloat (rhs)                              */
-/*   returns result                                                   */
-/*                                                                    */
-/* This is a bitwise operation; no errors or exceptions are possible. */
-/* ------------------------------------------------------------------ */
-decFloat * decFloatCopySign(decFloat *result,
-                            const decFloat *dfl, const decFloat *dfr) {
-  uByte sign=(uByte)(DFBYTE(dfr, 0)&0x80);   // save sign bit
-  if (dfl!=result) *result=*dfl;             // copy needed
-  DFBYTE(result, 0)&=~0x80;                  // clear sign ..
-  DFBYTE(result, 0)=(uByte)(DFBYTE(result, 0)|sign); // .. and set saved
-  return result;
-  } // decFloatCopySign
-
-/* ------------------------------------------------------------------ */
-/* decFloatDigits -- return the number of digits in a decFloat        */
-/*                                                                    */
-/*   df is the decFloat to investigate                                */
-/*   returns the number of significant digits in the decFloat; a      */
-/*     zero coefficient returns 1 as does an infinity (a NaN returns  */
-/*     the number of digits in the payload)                           */
-/* ------------------------------------------------------------------ */
-// private macro to extract a declet according to provided formula
-// (form), and if it is non-zero then return the calculated digits
-// depending on the declet number (n), where n=0 for the most
-// significant declet; uses uInt dpd for work
-#define dpdlenchk(n, form)  dpd=(form)&0x3ff;     \
-  if (dpd) return (DECPMAX-1-3*(n))-(3-DPD2BCD8[dpd*4+3])
-// next one is used when it is known that the declet must be
-// non-zero, or is the final zero declet
-#define dpdlendun(n, form)  dpd=(form)&0x3ff;     \
-  if (dpd==0) return 1;                           \
-  return (DECPMAX-1-3*(n))-(3-DPD2BCD8[dpd*4+3])
-
-uInt decFloatDigits(const decFloat *df) {
-  uInt dpd;                        // work
-  uInt sourhi=DFWORD(df, 0);       // top word from source decFloat
-  #if QUAD
-  uInt sourmh, sourml;
-  #endif
-  uInt sourlo;
-
-  if (DFISINF(df)) return 1;
-  // A NaN effectively has an MSD of 0; otherwise if non-zero MSD
-  // then the coefficient is full-length
-  if (!DFISNAN(df) && DECCOMBMSD[sourhi>>26]) return DECPMAX;
-
-  #if DOUBLE
-    if (sourhi&0x0003ffff) {     // ends in first
-      dpdlenchk(0, sourhi>>8);
-      sourlo=DFWORD(df, 1);
-      dpdlendun(1, (sourhi<<2) | (sourlo>>30));
-      } // [cannot drop through]
-    sourlo=DFWORD(df, 1);  // sourhi not involved now
-    if (sourlo&0xfff00000) {     // in one of first two
-      dpdlenchk(1, sourlo>>30);  // very rare
-      dpdlendun(2, sourlo>>20);
-      } // [cannot drop through]
-    dpdlenchk(3, sourlo>>10);
-    dpdlendun(4, sourlo);
-    // [cannot drop through]
-
-  #elif QUAD
-    if (sourhi&0x00003fff) {     // ends in first
-      dpdlenchk(0, sourhi>>4);
-      sourmh=DFWORD(df, 1);
-      dpdlendun(1, ((sourhi)<<6) | (sourmh>>26));
-      } // [cannot drop through]
-    sourmh=DFWORD(df, 1);
-    if (sourmh) {
-      dpdlenchk(1, sourmh>>26);
-      dpdlenchk(2, sourmh>>16);
-      dpdlenchk(3, sourmh>>6);
-      sourml=DFWORD(df, 2);
-      dpdlendun(4, ((sourmh)<<4) | (sourml>>28));
-      } // [cannot drop through]
-    sourml=DFWORD(df, 2);
-    if (sourml) {
-      dpdlenchk(4, sourml>>28);
-      dpdlenchk(5, sourml>>18);
-      dpdlenchk(6, sourml>>8);
-      sourlo=DFWORD(df, 3);
-      dpdlendun(7, ((sourml)<<2) | (sourlo>>30));
-      } // [cannot drop through]
-    sourlo=DFWORD(df, 3);
-    if (sourlo&0xfff00000) {     // in one of first two
-      dpdlenchk(7, sourlo>>30);  // very rare
-      dpdlendun(8, sourlo>>20);
-      } // [cannot drop through]
-    dpdlenchk(9, sourlo>>10);
-    dpdlendun(10, sourlo);
-    // [cannot drop through]
-  #endif
-  } // decFloatDigits
-
-/* ------------------------------------------------------------------ */
-/* decFloatDivide -- divide a decFloat by another                     */
-/*                                                                    */
-/*   result gets the result of dividing dfl by dfr:                   */
-/*   dfl    is the first decFloat (lhs)                               */
-/*   dfr    is the second decFloat (rhs)                              */
-/*   set    is the context                                            */
-/*   returns result                                                   */
-/*                                                                    */
-/* ------------------------------------------------------------------ */
-// This is just a wrapper.
-decFloat * decFloatDivide(decFloat *result,
-                          const decFloat *dfl, const decFloat *dfr,
-                          decContext *set) {
-  return decDivide(result, dfl, dfr, set, DIVIDE);
-  } // decFloatDivide
-
-/* ------------------------------------------------------------------ */
-/* decFloatDivideInteger -- integer divide a decFloat by another      */
-/*                                                                    */
-/*   result gets the result of dividing dfl by dfr:                   */
-/*   dfl    is the first decFloat (lhs)                               */
-/*   dfr    is the second decFloat (rhs)                              */
-/*   set    is the context                                            */
-/*   returns result                                                   */
-/*                                                                    */
-/* ------------------------------------------------------------------ */
-decFloat * decFloatDivideInteger(decFloat *result,
-                             const decFloat *dfl, const decFloat *dfr,
-                             decContext *set) {
-  return decDivide(result, dfl, dfr, set, DIVIDEINT);
-  } // decFloatDivideInteger
-
-/* ------------------------------------------------------------------ */
-/* decFloatFMA -- multiply and add three decFloats, fused             */
-/*                                                                    */
-/*   result gets the result of (dfl*dfr)+dff with a single rounding   */
-/*   dfl    is the first decFloat (lhs)                               */
-/*   dfr    is the second decFloat (rhs)                              */
-/*   dff    is the final decFloat (fhs)                               */
-/*   set    is the context                                            */
-/*   returns result                                                   */
-/*                                                                    */
-/* ------------------------------------------------------------------ */
-decFloat * decFloatFMA(decFloat *result, const decFloat *dfl,
-                       const decFloat *dfr, const decFloat *dff,
-                       decContext *set) {
-
-  // The accumulator has the bytes needed for FiniteMultiply, plus
-  // one byte to the left in case of carry, plus DECPMAX+2 to the
-  // right for the final addition (up to full fhs + round & sticky)
-  #define FMALEN (ROUNDUP4(1+ (DECPMAX9*18+1) +DECPMAX+2))
-  uByte  acc[FMALEN];              // for multiplied coefficient in BCD
-                                   // .. and for final result
-  bcdnum mul;                      // for multiplication result
-  bcdnum fin;                      // for final operand, expanded
-  uByte  coe[ROUNDUP4(DECPMAX)];   // dff coefficient in BCD
-  bcdnum *hi, *lo;                 // bcdnum with higher/lower exponent
-  uInt   diffsign;                 // non-zero if signs differ
-  uInt   hipad;                    // pad digit for hi if needed
-  Int    padding;                  // excess exponent
-  uInt   carry;                    // +1 for ten's complement and during add
-  uByte  *ub, *uh, *ul;            // work
-  uInt   uiwork;                   // for macros
-
-  // handle all the special values [any special operand leads to a
-  // special result]
-  if (DFISSPECIAL(dfl) || DFISSPECIAL(dfr) || DFISSPECIAL(dff)) {
-    decFloat proxy;                // multiplication result proxy
-    // NaNs are handled as usual, giving priority to sNaNs
-    if (DFISSNAN(dfl) || DFISSNAN(dfr)) return decNaNs(result, dfl, dfr, set);
-    if (DFISSNAN(dff)) return decNaNs(result, dff, NULL, set);
-    if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set);
-    if (DFISNAN(dff)) return decNaNs(result, dff, NULL, set);
-    // One or more of the three is infinite
-    // infinity times zero is bad
-    decFloatZero(&proxy);
-    if (DFISINF(dfl)) {
-      if (DFISZERO(dfr)) return decInvalid(result, set);
-      decInfinity(&proxy, &proxy);
-      }
-     else if (DFISINF(dfr)) {
-      if (DFISZERO(dfl)) return decInvalid(result, set);
-      decInfinity(&proxy, &proxy);
-      }
-    // compute sign of multiplication and place in proxy
-    DFWORD(&proxy, 0)|=(DFWORD(dfl, 0)^DFWORD(dfr, 0))&DECFLOAT_Sign;
-    if (!DFISINF(dff)) return decFloatCopy(result, &proxy);
-    // dff is Infinite
-    if (!DFISINF(&proxy)) return decInfinity(result, dff);
-    // both sides of addition are infinite; different sign is bad
-    if ((DFWORD(dff, 0)&DECFLOAT_Sign)!=(DFWORD(&proxy, 0)&DECFLOAT_Sign))
-      return decInvalid(result, set);
-    return decFloatCopy(result, &proxy);
-    }
-
-  /* Here when all operands are finite */
-
-  // First multiply dfl*dfr
-  decFiniteMultiply(&mul, acc+1, dfl, dfr);
-  // The multiply is complete, exact and unbounded, and described in
-  // mul with the coefficient held in acc[1...]
-
-  // now add in dff; the algorithm is essentially the same as
-  // decFloatAdd, but the code is different because the code there
-  // is highly optimized for adding two numbers of the same size
-  fin.exponent=GETEXPUN(dff);           // get dff exponent and sign
-  fin.sign=DFWORD(dff, 0)&DECFLOAT_Sign;
-  diffsign=mul.sign^fin.sign;           // note if signs differ
-  fin.msd=coe;
-  fin.lsd=coe+DECPMAX-1;
-  GETCOEFF(dff, coe);                   // extract the coefficient
-
-  // now set hi and lo so that hi points to whichever of mul and fin
-  // has the higher exponent and lo points to the other [don't care,
-  // if the same].  One coefficient will be in acc, the other in coe.
-  if (mul.exponent>=fin.exponent) {
-    hi=&mul;
-    lo=&fin;
-    }
-   else {
-    hi=&fin;
-    lo=&mul;
-    }
-
-  // remove leading zeros on both operands; this will save time later
-  // and make testing for zero trivial (tests are safe because acc
-  // and coe are rounded up to uInts)
-  for (; UBTOUI(hi->msd)==0 && hi->msd+3<hi->lsd;) hi->msd+=4;
-  for (; *hi->msd==0 && hi->msd<hi->lsd;) hi->msd++;
-  for (; UBTOUI(lo->msd)==0 && lo->msd+3<lo->lsd;) lo->msd+=4;
-  for (; *lo->msd==0 && lo->msd<lo->lsd;) lo->msd++;
-
-  // if hi is zero then result will be lo (which has the smaller
-  // exponent), which also may need to be tested for zero for the
-  // weird IEEE 754 sign rules
-  if (*hi->msd==0) {                         // hi is zero
-    // "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 '-'."
-    if (diffsign) {
-      if (*lo->msd==0) {                     // lo is zero
-        lo->sign=0;
-        if (set->round==DEC_ROUND_FLOOR) lo->sign=DECFLOAT_Sign;
-        } // diffsign && lo=0
-      } // diffsign
-    return decFinalize(result, lo, set);     // may need clamping
-    } // numfl is zero
-  // [here, both are minimal length and hi is non-zero]
-  // (if lo is zero then padding with zeros may be needed, below)
-
-  // if signs differ, take the ten's complement of hi (zeros to the
-  // right do not matter because the complement of zero is zero); the
-  // +1 is done later, as part of the addition, inserted at the
-  // correct digit
-  hipad=0;
-  carry=0;
-  if (diffsign) {
-    hipad=9;
-    carry=1;
-    // exactly the correct number of digits must be inverted
-    for (uh=hi->msd; uh<hi->lsd-3; uh+=4) UBFROMUI(uh, 0x09090909-UBTOUI(uh));
-    for (; uh<=hi->lsd; uh++) *uh=(uByte)(0x09-*uh);
-    }
-
-  // ready to add; note that hi has no leading zeros so gap
-  // calculation does not have to be as pessimistic as in decFloatAdd
-  // (this is much more like the arbitrary-precision algorithm in
-  // Rexx and decNumber)
-
-  // padding is the number of zeros that would need to be added to hi
-  // for its lsd to be aligned with the lsd of lo
-  padding=hi->exponent-lo->exponent;
-  // printf("FMA pad %ld\n", (LI)padding);
-
-  // the result of the addition will be built into the accumulator,
-  // starting from the far right; this could be either hi or lo, and
-  // will be aligned
-  ub=acc+FMALEN-1;                 // where lsd of result will go
-  ul=lo->lsd;                      // lsd of rhs
-
-  if (padding!=0) {                // unaligned
-    // if the msd of lo is more than DECPMAX+2 digits to the right of
-    // the original msd of hi then it can be reduced to a single
-    // digit at the right place, as it stays clear of hi digits
-    // [it must be DECPMAX+2 because during a subtraction the msd
-    // could become 0 after a borrow from 1.000 to 0.9999...]
-
-    Int hilen=(Int)(hi->lsd-hi->msd+1); // length of hi
-    Int lolen=(Int)(lo->lsd-lo->msd+1); // and of lo
-
-    if (hilen+padding-lolen > DECPMAX+2) {   // can reduce lo to single
-      // make sure it is virtually at least DECPMAX from hi->msd, at
-      // least to right of hi->lsd (in case of destructive subtract),
-      // and separated by at least two digits from either of those
-      // (the tricky DOUBLE case is when hi is a 1 that will become a
-      // 0.9999... by subtraction:
-      //   hi:   1                                   E+16
-      //   lo:    .................1000000000000000  E-16
-      // which for the addition pads to:
-      //   hi:   1000000000000000000                 E-16
-      //   lo:    .................1000000000000000  E-16
-      Int newexp=MINI(hi->exponent, hi->exponent+hilen-DECPMAX)-3;
-
-      // printf("FMA reduce: %ld\n", (LI)reduce);
-      lo->lsd=lo->msd;                       // to single digit [maybe 0]
-      lo->exponent=newexp;                   // new lowest exponent
-      padding=hi->exponent-lo->exponent;     // recalculate
-      ul=lo->lsd;                            // .. and repoint
-      }
-
-    // padding is still > 0, but will fit in acc (less leading carry slot)
-    #if DECCHECK
-      if (padding<=0) printf("FMA low padding: %ld\n", (LI)padding);
-      if (hilen+padding+1>FMALEN)
-        printf("FMA excess hilen+padding: %ld+%ld \n", (LI)hilen, (LI)padding);
-      // printf("FMA padding: %ld\n", (LI)padding);
-    #endif
-
-    // padding digits can now be set in the result; one or more of
-    // these will come from lo; others will be zeros in the gap
-    for (; ul-3>=lo->msd && padding>3; padding-=4, ul-=4, ub-=4) {
-      UBFROMUI(ub-3, UBTOUI(ul-3));          // [cannot overlap]
-      }
-    for (; ul>=lo->msd && padding>0; padding--, ul--, ub--) *ub=*ul;
-    for (;padding>0; padding--, ub--) *ub=0; // mind the gap
-    }
-
-  // addition now complete to the right of the rightmost digit of hi
-  uh=hi->lsd;
-
-  // dow do the add from hi->lsd to the left
-  // [bytewise, because either operand can run out at any time]
-  // carry was set up depending on ten's complement above
-  // first assume both operands have some digits
-  for (;; ub--) {
-    if (uh<hi->msd || ul<lo->msd) break;
-    *ub=(uByte)(carry+(*uh--)+(*ul--));
-    carry=0;
-    if (*ub<10) continue;
-    *ub-=10;
-    carry=1;
-    } // both loop
-
-  if (ul<lo->msd) {           // to left of lo
-    for (;; ub--) {
-      if (uh<hi->msd) break;
-      *ub=(uByte)(carry+(*uh--));  // [+0]
-      carry=0;
-      if (*ub<10) continue;
-      *ub-=10;
-      carry=1;
-      } // hi loop
-    }
-   else {                     // to left of hi
-    for (;; ub--) {
-      if (ul<lo->msd) break;
-      *ub=(uByte)(carry+hipad+(*ul--));
-      carry=0;
-      if (*ub<10) continue;
-      *ub-=10;
-      carry=1;
-      } // lo loop
-    }
-
-  // addition complete -- now handle carry, borrow, etc.
-  // use lo to set up the num (its exponent is already correct, and
-  // sign usually is)
-  lo->msd=ub+1;
-  lo->lsd=acc+FMALEN-1;
-  // decShowNum(lo, "lo");
-  if (!diffsign) {                 // same-sign addition
-    if (carry) {                   // carry out
-      *ub=1;                       // place the 1 ..
-      lo->msd--;                   // .. and update
-      }
-    } // same sign
-   else {                          // signs differed (subtraction)
-    if (!carry) {                  // no carry out means hi<lo
-      // borrowed -- take ten's complement of the right digits
-      lo->sign=hi->sign;           // sign is lhs sign
-      for (ul=lo->msd; ul<lo->lsd-3; ul+=4) UBFROMUI(ul, 0x09090909-UBTOUI(ul));
-      for (; ul<=lo->lsd; ul++) *ul=(uByte)(0x09-*ul); // [leaves ul at lsd+1]
-      // complete the ten's complement by adding 1 [cannot overrun]
-      for (ul--; *ul==9; ul--) *ul=0;
-      *ul+=1;
-      } // borrowed
-     else {                        // carry out means hi>=lo
-      // sign to use is lo->sign
-      // all done except for the special IEEE 754 exact-zero-result
-      // rule (see above); while testing for zero, strip leading
-      // zeros (which will save decFinalize doing it)
-      for (; UBTOUI(lo->msd)==0 && lo->msd+3<lo->lsd;) lo->msd+=4;
-      for (; *lo->msd==0 && lo->msd<lo->lsd;) lo->msd++;
-      if (*lo->msd==0) {           // must be true zero (and diffsign)
-        lo->sign=0;                // assume +
-        if (set->round==DEC_ROUND_FLOOR) lo->sign=DECFLOAT_Sign;
-        }
-      // [else was not zero, might still have leading zeros]
-      } // subtraction gave positive result
-    } // diffsign
-
-  #if DECCHECK
-  // assert no left underrun
-  if (lo->msd<acc) {
-    printf("FMA underrun by %ld \n", (LI)(acc-lo->msd));
-    }
-  #endif
-
-  return decFinalize(result, lo, set);  // round, check, and lay out
-  } // decFloatFMA
-
-/* ------------------------------------------------------------------ */
-/* decFloatFromInt -- initialise a decFloat from an Int               */
-/*                                                                    */
-/*   result gets the converted Int                                    */
-/*   n      is the Int to convert                                     */
-/*   returns result                                                   */
-/*                                                                    */
-/* The result is Exact; no errors or exceptions are possible.         */
-/* ------------------------------------------------------------------ */
-decFloat * decFloatFromInt32(decFloat *result, Int n) {
-  uInt u=(uInt)n;                       // copy as bits
-  uInt encode;                          // work
-  DFWORD(result, 0)=ZEROWORD;           // always
-  #if QUAD
-    DFWORD(result, 1)=0;
-    DFWORD(result, 2)=0;
-  #endif
-  if (n<0) {                            // handle -n with care
-    // [This can be done without the test, but is then slightly slower]
-    u=(~u)+1;
-    DFWORD(result, 0)|=DECFLOAT_Sign;
-    }
-  // Since the maximum value of u now is 2**31, only the low word of
-  // result is affected
-  encode=BIN2DPD[u%1000];
-  u/=1000;
-  encode|=BIN2DPD[u%1000]<<10;
-  u/=1000;
-  encode|=BIN2DPD[u%1000]<<20;
-  u/=1000;                              // now 0, 1, or 2
-  encode|=u<<30;
-  DFWORD(result, DECWORDS-1)=encode;
-  return result;
-  } // decFloatFromInt32
-
-/* ------------------------------------------------------------------ */
-/* decFloatFromUInt -- initialise a decFloat from a uInt              */
-/*                                                                    */
-/*   result gets the converted uInt                                   */
-/*   n      is the uInt to convert                                    */
-/*   returns result                                                   */
-/*                                                                    */
-/* The result is Exact; no errors or exceptions are possible.         */
-/* ------------------------------------------------------------------ */
-decFloat * decFloatFromUInt32(decFloat *result, uInt u) {
-  uInt encode;                          // work
-  DFWORD(result, 0)=ZEROWORD;           // always
-  #if QUAD
-    DFWORD(result, 1)=0;
-    DFWORD(result, 2)=0;
-  #endif
-  encode=BIN2DPD[u%1000];
-  u/=1000;
-  encode|=BIN2DPD[u%1000]<<10;
-  u/=1000;
-  encode|=BIN2DPD[u%1000]<<20;
-  u/=1000;                              // now 0 -> 4
-  encode|=u<<30;
-  DFWORD(result, DECWORDS-1)=encode;
-  DFWORD(result, DECWORDS-2)|=u>>2;     // rarely non-zero
-  return result;
-  } // decFloatFromUInt32
-
-/* ------------------------------------------------------------------ */
-/* decFloatInvert -- logical digitwise INVERT of a decFloat           */
-/*                                                                    */
-/*   result gets the result of INVERTing df                           */
-/*   df     is the decFloat to invert                                 */
-/*   set    is the context                                            */
-/*   returns result, which will be canonical with sign=0              */
-/*                                                                    */
-/* The operand must be positive, finite with exponent q=0, and        */
-/* comprise just zeros and ones; if not, Invalid operation results.   */
-/* ------------------------------------------------------------------ */
-decFloat * decFloatInvert(decFloat *result, const decFloat *df,
-                          decContext *set) {
-  uInt sourhi=DFWORD(df, 0);            // top word of dfs
-
-  if (!DFISUINT01(df) || !DFISCC01(df)) return decInvalid(result, set);
-  // the operand is a finite integer (q=0)
-  #if DOUBLE
-   DFWORD(result, 0)=ZEROWORD|((~sourhi)&0x04009124);
-   DFWORD(result, 1)=(~DFWORD(df, 1))   &0x49124491;
-  #elif QUAD
-   DFWORD(result, 0)=ZEROWORD|((~sourhi)&0x04000912);
-   DFWORD(result, 1)=(~DFWORD(df, 1))   &0x44912449;
-   DFWORD(result, 2)=(~DFWORD(df, 2))   &0x12449124;
-   DFWORD(result, 3)=(~DFWORD(df, 3))   &0x49124491;
-  #endif
-  return result;
-  } // decFloatInvert
-
-/* ------------------------------------------------------------------ */
-/* decFloatIs -- decFloat tests (IsSigned, etc.)                      */
-/*                                                                    */
-/*   df is the decFloat to test                                       */
-/*   returns 0 or 1 in a uInt                                         */
-/*                                                                    */
-/* Many of these could be macros, but having them as real functions   */
-/* is a little cleaner (and they can be referred to here by the       */
-/* generic names)                                                     */
-/* ------------------------------------------------------------------ */
-uInt decFloatIsCanonical(const decFloat *df) {
-  if (DFISSPECIAL(df)) {
-    if (DFISINF(df)) {
-      if (DFWORD(df, 0)&ECONMASK) return 0;  // exponent continuation
-      if (!DFISCCZERO(df)) return 0;         // coefficient continuation
-      return 1;
-      }
-    // is a NaN
-    if (DFWORD(df, 0)&ECONNANMASK) return 0; // exponent continuation
-    if (DFISCCZERO(df)) return 1;            // coefficient continuation
-    // drop through to check payload
-    }
-  { // declare block
-  #if DOUBLE
-    uInt sourhi=DFWORD(df, 0);
-    uInt sourlo=DFWORD(df, 1);
-    if (CANONDPDOFF(sourhi, 8)
-     && CANONDPDTWO(sourhi, sourlo, 30)
-     && CANONDPDOFF(sourlo, 20)
-     && CANONDPDOFF(sourlo, 10)
-     && CANONDPDOFF(sourlo, 0)) return 1;
-  #elif QUAD
-    uInt sourhi=DFWORD(df, 0);
-    uInt sourmh=DFWORD(df, 1);
-    uInt sourml=DFWORD(df, 2);
-    uInt sourlo=DFWORD(df, 3);
-    if (CANONDPDOFF(sourhi, 4)
-     && CANONDPDTWO(sourhi, sourmh, 26)
-     && CANONDPDOFF(sourmh, 16)
-     && CANONDPDOFF(sourmh, 6)
-     && CANONDPDTWO(sourmh, sourml, 28)
-     && CANONDPDOFF(sourml, 18)
-     && CANONDPDOFF(sourml, 8)
-     && CANONDPDTWO(sourml, sourlo, 30)
-     && CANONDPDOFF(sourlo, 20)
-     && CANONDPDOFF(sourlo, 10)
-     && CANONDPDOFF(sourlo, 0)) return 1;
-  #endif
-  } // block
-  return 0;    // a declet is non-canonical
-  }
-
-uInt decFloatIsFinite(const decFloat *df) {
-  return !DFISSPECIAL(df);
-  }
-uInt decFloatIsInfinite(const decFloat *df) {
-  return DFISINF(df);
-  }
-uInt decFloatIsInteger(const decFloat *df) {
-  return DFISINT(df);
-  }
-uInt decFloatIsLogical(const decFloat *df) {
-  return DFISUINT01(df) & DFISCC01(df);
-  }
-uInt decFloatIsNaN(const decFloat *df) {
-  return DFISNAN(df);
-  }
-uInt decFloatIsNegative(const decFloat *df) {
-  return DFISSIGNED(df) && !DFISZERO(df) && !DFISNAN(df);
-  }
-uInt decFloatIsNormal(const decFloat *df) {
-  Int exp;                         // exponent
-  if (DFISSPECIAL(df)) return 0;
-  if (DFISZERO(df)) return 0;
-  // is finite and non-zero
-  exp=GETEXPUN(df)                 // get unbiased exponent ..
-     +decFloatDigits(df)-1;        // .. and make adjusted exponent
-  return (exp>=DECEMIN);           // < DECEMIN is subnormal
-  }
-uInt decFloatIsPositive(const decFloat *df) {
-  return !DFISSIGNED(df) && !DFISZERO(df) && !DFISNAN(df);
-  }
-uInt decFloatIsSignaling(const decFloat *df) {
-  return DFISSNAN(df);
-  }
-uInt decFloatIsSignalling(const decFloat *df) {
-  return DFISSNAN(df);
-  }
-uInt decFloatIsSigned(const decFloat *df) {
-  return DFISSIGNED(df);
-  }
-uInt decFloatIsSubnormal(const decFloat *df) {
-  if (DFISSPECIAL(df)) return 0;
-  // is finite
-  if (decFloatIsNormal(df)) return 0;
-  // it is <Nmin, but could be zero
-  if (DFISZERO(df)) return 0;
-  return 1;                                  // is subnormal
-  }
-uInt decFloatIsZero(const decFloat *df) {
-  return DFISZERO(df);
-  } // decFloatIs...
-
-/* ------------------------------------------------------------------ */
-/* decFloatLogB -- return adjusted exponent, by 754 rules             */
-/*                                                                    */
-/*   result gets the adjusted exponent as an integer, or a NaN etc.   */
-/*   df     is the decFloat to be examined                            */
-/*   set    is the context                                            */
-/*   returns result                                                   */
-/*                                                                    */
-/* 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                                     */
-/* ------------------------------------------------------------------ */
-decFloat * decFloatLogB(decFloat *result, const decFloat *df,
-                        decContext *set) {
-  Int ae;                                    // adjusted exponent
-  if (DFISNAN(df)) return decNaNs(result, df, NULL, set);
-  if (DFISINF(df)) {
-    DFWORD(result, 0)=0;                     // need +ve
-    return decInfinity(result, result);      // canonical +Infinity
-    }
-  if (DFISZERO(df)) {
-    set->status|=DEC_Division_by_zero;       // as per 754
-    DFWORD(result, 0)=DECFLOAT_Sign;         // make negative
-    return decInfinity(result, result);      // canonical -Infinity
-    }
-  ae=GETEXPUN(df)                       // get unbiased exponent ..
-    +decFloatDigits(df)-1;              // .. and make adjusted exponent
-  // ae has limited range (3 digits for DOUBLE and 4 for QUAD), so
-  // it is worth using a special case of decFloatFromInt32
-  DFWORD(result, 0)=ZEROWORD;           // always
-  if (ae<0) {
-    DFWORD(result, 0)|=DECFLOAT_Sign;   // -0 so far
-    ae=-ae;
-    }
-  #if DOUBLE
-    DFWORD(result, 1)=BIN2DPD[ae];      // a single declet
-  #elif QUAD
-    DFWORD(result, 1)=0;
-    DFWORD(result, 2)=0;
-    DFWORD(result, 3)=(ae/1000)<<10;    // is <10, so need no DPD encode
-    DFWORD(result, 3)|=BIN2DPD[ae%1000];
-  #endif
-  return result;
-  } // decFloatLogB
-
-/* ------------------------------------------------------------------ */
-/* decFloatMax -- return maxnum of two operands                       */
-/*                                                                    */
-/*   result gets the chosen decFloat                                  */
-/*   dfl    is the first decFloat (lhs)                               */
-/*   dfr    is the second decFloat (rhs)                              */
-/*   set    is the context                                            */
-/*   returns result                                                   */
-/*                                                                    */
-/* If just one operand is a quiet NaN it is ignored.                  */
-/* ------------------------------------------------------------------ */
-decFloat * decFloatMax(decFloat *result,
-                       const decFloat *dfl, const decFloat *dfr,
-                       decContext *set) {
-  Int comp;
-  if (DFISNAN(dfl)) {
-    // sNaN or both NaNs leads to normal NaN processing
-    if (DFISNAN(dfr) || DFISSNAN(dfl)) return decNaNs(result, dfl, dfr, set);
-    return decCanonical(result, dfr);        // RHS is numeric
-    }
-  if (DFISNAN(dfr)) {
-    // sNaN leads to normal NaN processing (both NaN handled above)
-    if (DFISSNAN(dfr)) return decNaNs(result, dfl, dfr, set);
-    return decCanonical(result, dfl);        // LHS is numeric
-    }
-  // Both operands are numeric; numeric comparison needed -- use
-  // total order for a well-defined choice (and +0 > -0)
-  comp=decNumCompare(dfl, dfr, 1);
-  if (comp>=0) return decCanonical(result, dfl);
-  return decCanonical(result, dfr);
-  } // decFloatMax
-
-/* ------------------------------------------------------------------ */
-/* decFloatMaxMag -- return maxnummag of two operands                 */
-/*                                                                    */
-/*   result gets the chosen decFloat                                  */
-/*   dfl    is the first decFloat (lhs)                               */
-/*   dfr    is the second decFloat (rhs)                              */
-/*   set    is the context                                            */
-/*   returns result                                                   */
-/*                                                                    */
-/* Returns according to the magnitude comparisons if both numeric and */
-/* unequal, otherwise returns maxnum                                  */
-/* ------------------------------------------------------------------ */
-decFloat * decFloatMaxMag(decFloat *result,
-                       const decFloat *dfl, const decFloat *dfr,
-                       decContext *set) {
-  Int comp;
-  decFloat absl, absr;
-  if (DFISNAN(dfl) || DFISNAN(dfr)) return decFloatMax(result, dfl, dfr, set);
-
-  decFloatCopyAbs(&absl, dfl);
-  decFloatCopyAbs(&absr, dfr);
-  comp=decNumCompare(&absl, &absr, 0);
-  if (comp>0) return decCanonical(result, dfl);
-  if (comp<0) return decCanonical(result, dfr);
-  return decFloatMax(result, dfl, dfr, set);
-  } // decFloatMaxMag
-
-/* ------------------------------------------------------------------ */
-/* decFloatMin -- return minnum of two operands                       */
-/*                                                                    */
-/*   result gets the chosen decFloat                                  */
-/*   dfl    is the first decFloat (lhs)                               */
-/*   dfr    is the second decFloat (rhs)                              */
-/*   set    is the context                                            */
-/*   returns result                                                   */
-/*                                                                    */
-/* If just one operand is a quiet NaN it is ignored.                  */
-/* ------------------------------------------------------------------ */
-decFloat * decFloatMin(decFloat *result,
-                       const decFloat *dfl, const decFloat *dfr,
-                       decContext *set) {
-  Int comp;
-  if (DFISNAN(dfl)) {
-    // sNaN or both NaNs leads to normal NaN processing
-    if (DFISNAN(dfr) || DFISSNAN(dfl)) return decNaNs(result, dfl, dfr, set);
-    return decCanonical(result, dfr);        // RHS is numeric
-    }
-  if (DFISNAN(dfr)) {
-    // sNaN leads to normal NaN processing (both NaN handled above)
-    if (DFISSNAN(dfr)) return decNaNs(result, dfl, dfr, set);
-    return decCanonical(result, dfl);        // LHS is numeric
-    }
-  // Both operands are numeric; numeric comparison needed -- use
-  // total order for a well-defined choice (and +0 > -0)
-  comp=decNumCompare(dfl, dfr, 1);
-  if (comp<=0) return decCanonical(result, dfl);
-  return decCanonical(result, dfr);
-  } // decFloatMin
-
-/* ------------------------------------------------------------------ */
-/* decFloatMinMag -- return minnummag of two operands                 */
-/*                                                                    */
-/*   result gets the chosen decFloat                                  */
-/*   dfl    is the first decFloat (lhs)                               */
-/*   dfr    is the second decFloat (rhs)                              */
-/*   set    is the context                                            */
-/*   returns result                                                   */
-/*                                                                    */
-/* Returns according to the magnitude comparisons if both numeric and */
-/* unequal, otherwise returns minnum                                  */
-/* ------------------------------------------------------------------ */
-decFloat * decFloatMinMag(decFloat *result,
-                       const decFloat *dfl, const decFloat *dfr,
-                       decContext *set) {
-  Int comp;
-  decFloat absl, absr;
-  if (DFISNAN(dfl) || DFISNAN(dfr)) return decFloatMin(result, dfl, dfr, set);
-
-  decFloatCopyAbs(&absl, dfl);
-  decFloatCopyAbs(&absr, dfr);
-  comp=decNumCompare(&absl, &absr, 0);
-  if (comp<0) return decCanonical(result, dfl);
-  if (comp>0) return decCanonical(result, dfr);
-  return decFloatMin(result, dfl, dfr, set);
-  } // decFloatMinMag
-
-/* ------------------------------------------------------------------ */
-/* decFloatMinus -- negate value, heeding NaNs, etc.                  */
-/*                                                                    */
-/*   result gets the canonicalized 0-df                               */
-/*   df     is the decFloat to minus                                  */
-/*   set    is the context                                            */
-/*   returns result                                                   */
-/*                                                                    */
-/* This has the same effect as 0-df where the exponent of the zero is */
-/* the same as that of df (if df is finite).                          */
-/* The effect is also the same as decFloatCopyNegate except that NaNs */
-/* are handled normally (the sign of a NaN is not affected, and an    */
-/* sNaN will signal), the result is canonical, and zero gets sign 0.  */
-/* ------------------------------------------------------------------ */
-decFloat * decFloatMinus(decFloat *result, const decFloat *df,
-                         decContext *set) {
-  if (DFISNAN(df)) return decNaNs(result, df, NULL, set);
-  decCanonical(result, df);                       // copy and check
-  if (DFISZERO(df)) DFBYTE(result, 0)&=~0x80;     // turn off sign bit
-   else DFBYTE(result, 0)^=0x80;                  // flip sign bit
-  return result;
-  } // decFloatMinus
-
-/* ------------------------------------------------------------------ */
-/* decFloatMultiply -- multiply two decFloats                         */
-/*                                                                    */
-/*   result gets the result of multiplying dfl and dfr:               */
-/*   dfl    is the first decFloat (lhs)                               */
-/*   dfr    is the second decFloat (rhs)                              */
-/*   set    is the context                                            */
-/*   returns result                                                   */
-/*                                                                    */
-/* ------------------------------------------------------------------ */
-decFloat * decFloatMultiply(decFloat *result,
-                            const decFloat *dfl, const decFloat *dfr,
-                            decContext *set) {
-  bcdnum num;                      // for final conversion
-  uByte  bcdacc[DECPMAX9*18+1];    // for coefficent in BCD
-
-  if (DFISSPECIAL(dfl) || DFISSPECIAL(dfr)) { // either is special?
-    // NaNs are handled as usual
-    if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set);
-    // infinity times zero is bad
-    if (DFISINF(dfl) && DFISZERO(dfr)) return decInvalid(result, set);
-    if (DFISINF(dfr) && DFISZERO(dfl)) return decInvalid(result, set);
-    // both infinite; return canonical infinity with computed sign
-    DFWORD(result, 0)=DFWORD(dfl, 0)^DFWORD(dfr, 0); // compute sign
-    return decInfinity(result, result);
-    }
-
-  /* Here when both operands are finite */
-  decFiniteMultiply(&num, bcdacc, dfl, dfr);
-  return decFinalize(result, &num, set); // round, check, and lay out
-  } // decFloatMultiply
-
-/* ------------------------------------------------------------------ */
-/* decFloatNextMinus -- next towards -Infinity                        */
-/*                                                                    */
-/*   result gets the next lesser decFloat                             */
-/*   dfl    is the decFloat to start with                             */
-/*   set    is the context                                            */
-/*   returns result                                                   */
-/*                                                                    */
-/* This is 754 nextdown; Invalid is the only status possible (from    */
-/* an sNaN).                                                          */
-/* ------------------------------------------------------------------ */
-decFloat * decFloatNextMinus(decFloat *result, const decFloat *dfl,
-                             decContext *set) {
-  decFloat delta;                       // tiny increment
-  uInt savestat;                        // saves status
-  enum rounding saveround;              // .. and mode
-
-  // +Infinity is the special case
-  if (DFISINF(dfl) && !DFISSIGNED(dfl)) {
-    DFSETNMAX(result);
-    return result;                      // [no status to set]
-    }
-  // other cases are effected by sutracting a tiny delta -- this
-  // should be done in a wider format as the delta is unrepresentable
-  // here (but can be done with normal add if the sign of zero is
-  // treated carefully, because no Inexactitude is interesting);
-  // rounding to -Infinity then pushes the result to next below
-  decFloatZero(&delta);                 // set up tiny delta
-  DFWORD(&delta, DECWORDS-1)=1;         // coefficient=1
-  DFWORD(&delta, 0)=DECFLOAT_Sign;      // Sign=1 + biased exponent=0
-  // set up for the directional round
-  saveround=set->round;                 // save mode
-  set->round=DEC_ROUND_FLOOR;           // .. round towards -Infinity
-  savestat=set->status;                 // save status
-  decFloatAdd(result, dfl, &delta, set);
-  // Add rules mess up the sign when going from +Ntiny to 0
-  if (DFISZERO(result)) DFWORD(result, 0)^=DECFLOAT_Sign; // correct
-  set->status&=DEC_Invalid_operation;   // preserve only sNaN status
-  set->status|=savestat;                // restore pending flags
-  set->round=saveround;                 // .. and mode
-  return result;
-  } // decFloatNextMinus
-
-/* ------------------------------------------------------------------ */
-/* decFloatNextPlus -- next towards +Infinity                         */
-/*                                                                    */
-/*   result gets the next larger decFloat                             */
-/*   dfl    is the decFloat to start with                             */
-/*   set    is the context                                            */
-/*   returns result                                                   */
-/*                                                                    */
-/* This is 754 nextup; Invalid is the only status possible (from      */
-/* an sNaN).                                                          */
-/* ------------------------------------------------------------------ */
-decFloat * decFloatNextPlus(decFloat *result, const decFloat *dfl,
-                            decContext *set) {
-  uInt savestat;                        // saves status
-  enum rounding saveround;              // .. and mode
-  decFloat delta;                       // tiny increment
-
-  // -Infinity is the special case
-  if (DFISINF(dfl) && DFISSIGNED(dfl)) {
-    DFSETNMAX(result);
-    DFWORD(result, 0)|=DECFLOAT_Sign;   // make negative
-    return result;                      // [no status to set]
-    }
-  // other cases are effected by sutracting a tiny delta -- this
-  // should be done in a wider format as the delta is unrepresentable
-  // here (but can be done with normal add if the sign of zero is
-  // treated carefully, because no Inexactitude is interesting);
-  // rounding to +Infinity then pushes the result to next above
-  decFloatZero(&delta);                 // set up tiny delta
-  DFWORD(&delta, DECWORDS-1)=1;         // coefficient=1
-  DFWORD(&delta, 0)=0;                  // Sign=0 + biased exponent=0
-  // set up for the directional round
-  saveround=set->round;                 // save mode
-  set->round=DEC_ROUND_CEILING;         // .. round towards +Infinity
-  savestat=set->status;                 // save status
-  decFloatAdd(result, dfl, &delta, set);
-  // Add rules mess up the sign when going from -Ntiny to -0
-  if (DFISZERO(result)) DFWORD(result, 0)^=DECFLOAT_Sign; // correct
-  set->status&=DEC_Invalid_operation;   // preserve only sNaN status
-  set->status|=savestat;                // restore pending flags
-  set->round=saveround;                 // .. and mode
-  return result;
-  } // decFloatNextPlus
-
-/* ------------------------------------------------------------------ */
-/* decFloatNextToward -- next towards a decFloat                      */
-/*                                                                    */
-/*   result gets the next decFloat                                    */
-/*   dfl    is the decFloat to start with                             */
-/*   dfr    is the decFloat to move toward                            */
-/*   set    is the context                                            */
-/*   returns result                                                   */
-/*                                                                    */
-/* This is 754-1985 nextafter, as modified during revision (dropped   */
-/* from 754-2008); status may be set unless the result is a normal    */
-/* number.                                                            */
-/* ------------------------------------------------------------------ */
-decFloat * decFloatNextToward(decFloat *result,
-                              const decFloat *dfl, const decFloat *dfr,
-                              decContext *set) {
-  decFloat delta;                       // tiny increment or decrement
-  decFloat pointone;                    // 1e-1
-  uInt  savestat;                       // saves status
-  enum  rounding saveround;             // .. and mode
-  uInt  deltatop;                       // top word for delta
-  Int   comp;                           // work
-
-  if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set);
-  // Both are numeric, so Invalid no longer a possibility
-  comp=decNumCompare(dfl, dfr, 0);
-  if (comp==0) return decFloatCopySign(result, dfl, dfr); // equal
-  // unequal; do NextPlus or NextMinus but with different status rules
-
-  if (comp<0) { // lhs<rhs, do NextPlus, see above for commentary
-    if (DFISINF(dfl) && DFISSIGNED(dfl)) {   // -Infinity special case
-      DFSETNMAX(result);
-      DFWORD(result, 0)|=DECFLOAT_Sign;
-      return result;
-      }
-    saveround=set->round;                    // save mode
-    set->round=DEC_ROUND_CEILING;            // .. round towards +Infinity
-    deltatop=0;                              // positive delta
-    }
-   else { // lhs>rhs, do NextMinus, see above for commentary
-    if (DFISINF(dfl) && !DFISSIGNED(dfl)) {  // +Infinity special case
-      DFSETNMAX(result);
-      return result;
-      }
-    saveround=set->round;                    // save mode
-    set->round=DEC_ROUND_FLOOR;              // .. round towards -Infinity
-    deltatop=DECFLOAT_Sign;                  // negative delta
-    }
-  savestat=set->status;                      // save status
-  // Here, Inexact is needed where appropriate (and hence Underflow,
-  // etc.).  Therefore the tiny delta which is otherwise
-  // unrepresentable (see NextPlus and NextMinus) is constructed
-  // using the multiplication of FMA.
-  decFloatZero(&delta);                 // set up tiny delta
-  DFWORD(&delta, DECWORDS-1)=1;         // coefficient=1
-  DFWORD(&delta, 0)=deltatop;           // Sign + biased exponent=0
-  decFloatFromString(&pointone, "1E-1", set); // set up multiplier
-  decFloatFMA(result, &delta, &pointone, dfl, set);
-  // [Delta is truly tiny, so no need to correct sign of zero]
-  // use new status unless the result is normal
-  if (decFloatIsNormal(result)) set->status=savestat; // else goes forward
-  set->round=saveround;                 // restore mode
-  return result;
-  } // decFloatNextToward
-
-/* ------------------------------------------------------------------ */
-/* decFloatOr -- logical digitwise OR of two decFloats                */
-/*                                                                    */
-/*   result gets the result of ORing dfl and dfr                      */
-/*   dfl    is the first decFloat (lhs)                               */
-/*   dfr    is the second decFloat (rhs)                              */
-/*   set    is the context                                            */
-/*   returns result, which will be canonical with sign=0              */
-/*                                                                    */
-/* The operands must be positive, finite with exponent q=0, and       */
-/* comprise just zeros and ones; if not, Invalid operation results.   */
-/* ------------------------------------------------------------------ */
-decFloat * decFloatOr(decFloat *result,
-                       const decFloat *dfl, const decFloat *dfr,
-                       decContext *set) {
-  if (!DFISUINT01(dfl) || !DFISUINT01(dfr)
-   || !DFISCC01(dfl)   || !DFISCC01(dfr)) return decInvalid(result, set);
-  // the operands are positive finite integers (q=0) with just 0s and 1s
-  #if DOUBLE
-   DFWORD(result, 0)=ZEROWORD
-                   |((DFWORD(dfl, 0) | DFWORD(dfr, 0))&0x04009124);
-   DFWORD(result, 1)=(DFWORD(dfl, 1) | DFWORD(dfr, 1))&0x49124491;
-  #elif QUAD
-   DFWORD(result, 0)=ZEROWORD
-                   |((DFWORD(dfl, 0) | DFWORD(dfr, 0))&0x04000912);
-   DFWORD(result, 1)=(DFWORD(dfl, 1) | DFWORD(dfr, 1))&0x44912449;
-   DFWORD(result, 2)=(DFWORD(dfl, 2) | DFWORD(dfr, 2))&0x12449124;
-   DFWORD(result, 3)=(DFWORD(dfl, 3) | DFWORD(dfr, 3))&0x49124491;
-  #endif
-  return result;
-  } // decFloatOr
-
-/* ------------------------------------------------------------------ */
-/* decFloatPlus -- add value to 0, heeding NaNs, etc.                 */
-/*                                                                    */
-/*   result gets the canonicalized 0+df                               */
-/*   df     is the decFloat to plus                                   */
-/*   set    is the context                                            */
-/*   returns result                                                   */
-/*                                                                    */
-/* This has the same effect as 0+df where the exponent of the zero is */
-/* the same as that of df (if df is finite).                          */
-/* The effect is also the same as decFloatCopy except that NaNs       */
-/* are handled normally (the sign of a NaN is not affected, and an    */
-/* sNaN will signal), the result is canonical, and zero gets sign 0.  */
-/* ------------------------------------------------------------------ */
-decFloat * decFloatPlus(decFloat *result, const decFloat *df,
-                        decContext *set) {
-  if (DFISNAN(df)) return decNaNs(result, df, NULL, set);
-  decCanonical(result, df);                       // copy and check
-  if (DFISZERO(df)) DFBYTE(result, 0)&=~0x80;     // turn off sign bit
-  return result;
-  } // decFloatPlus
-
-/* ------------------------------------------------------------------ */
-/* decFloatQuantize -- quantize a decFloat                            */
-/*                                                                    */
-/*   result gets the result of quantizing dfl to match dfr            */
-/*   dfl    is the first decFloat (lhs)                               */
-/*   dfr    is the second decFloat (rhs), which sets the exponent     */
-/*   set    is the context                                            */
-/*   returns result                                                   */
-/*                                                                    */
-/* Unless there is an error or the result is infinite, the exponent   */
-/* of result is guaranteed to be the same as that of dfr.             */
-/* ------------------------------------------------------------------ */
-decFloat * decFloatQuantize(decFloat *result,
-                            const decFloat *dfl, const decFloat *dfr,
-                            decContext *set) {
-  Int   explb, exprb;         // left and right biased exponents
-  uByte *ulsd;                // local LSD pointer
-  uByte *ub, *uc;             // work
-  Int   drop;                 // ..
-  uInt  dpd;                  // ..
-  uInt  encode;               // encoding accumulator
-  uInt  sourhil, sourhir;     // top words from source decFloats
-  uInt  uiwork;               // for macros
-  #if QUAD
-  uShort uswork;              // ..
-  #endif
-  // the following buffer holds the coefficient for manipulation
-  uByte buf[4+DECPMAX*3+2*QUAD];   // + space for zeros to left or right
-  #if DECTRACE
-  bcdnum num;                      // for trace displays
-  #endif
-
-  /* Start decoding the arguments */
-  sourhil=DFWORD(dfl, 0);          // LHS top word
-  explb=DECCOMBEXP[sourhil>>26];   // get exponent high bits (in place)
-  sourhir=DFWORD(dfr, 0);          // RHS top word
-  exprb=DECCOMBEXP[sourhir>>26];
-
-  if (EXPISSPECIAL(explb | exprb)) { // either is special?
-    // NaNs are handled as usual
-    if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set);
-    // one infinity but not both is bad
-    if (DFISINF(dfl)!=DFISINF(dfr)) return decInvalid(result, set);
-    // both infinite; return canonical infinity with sign of LHS
-    return decInfinity(result, dfl);
-    }
-
-  /* Here when both arguments are finite */
-  // complete extraction of the exponents [no need to unbias]
-  explb+=GETECON(dfl);             // + continuation
-  exprb+=GETECON(dfr);             // ..
-
-  // calculate the number of digits to drop from the coefficient
-  drop=exprb-explb;                // 0 if nothing to do
-  if (drop==0) return decCanonical(result, dfl); // return canonical
-
-  // the coefficient is needed; lay it out into buf, offset so zeros
-  // can be added before or after as needed -- an extra heading is
-  // added so can safely pad Quad DECPMAX-1 zeros to the left by
-  // fours
-  #define BUFOFF (buf+4+DECPMAX)
-  GETCOEFF(dfl, BUFOFF);           // decode from decFloat
-  // [now the msd is at BUFOFF and the lsd is at BUFOFF+DECPMAX-1]
-
-  #if DECTRACE
-  num.msd=BUFOFF;
-  num.lsd=BUFOFF+DECPMAX-1;
-  num.exponent=explb-DECBIAS;
-  num.sign=sourhil & DECFLOAT_Sign;
-  decShowNum(&num, "dfl");
-  #endif
-
-  if (drop>0) {                         // [most common case]
-    // (this code is very similar to that in decFloatFinalize, but
-    // has many differences so is duplicated here -- so any changes
-    // may need to be made there, too)
-    uByte *roundat;                          // -> re-round digit
-    uByte reround;                           // reround value
-    // printf("Rounding; drop=%ld\n", (LI)drop);
-
-    // there is at least one zero needed to the left, in all but one
-    // exceptional (all-nines) case, so place four zeros now; this is
-    // needed almost always and makes rounding all-nines by fours safe
-    UBFROMUI(BUFOFF-4, 0);
-
-    // Three cases here:
-    //   1. new LSD is in coefficient (almost always)
-    //   2. new LSD is digit to left of coefficient (so MSD is
-    //      round-for-reround digit)
-    //   3. new LSD is to left of case 2 (whole coefficient is sticky)
-    // Note that leading zeros can safely be treated as useful digits
-
-    // [duplicate check-stickies code to save a test]
-    // [by-digit check for stickies as runs of zeros are rare]
-    if (drop<DECPMAX) {                      // NB lengths not addresses
-      roundat=BUFOFF+DECPMAX-drop;
-      reround=*roundat;
-      for (ub=roundat+1; ub<BUFOFF+DECPMAX; ub++) {
-        if (*ub!=0) {                        // non-zero to be discarded
-          reround=DECSTICKYTAB[reround];     // apply sticky bit
-          break;                             // [remainder don't-care]
-          }
-        } // check stickies
-      ulsd=roundat-1;                        // set LSD
-      }
-     else {                                  // edge case
-      if (drop==DECPMAX) {
-        roundat=BUFOFF;
-        reround=*roundat;
-        }
-       else {
-        roundat=BUFOFF-1;
-        reround=0;
-        }
-      for (ub=roundat+1; ub<BUFOFF+DECPMAX; ub++) {
-        if (*ub!=0) {                        // non-zero to be discarded
-          reround=DECSTICKYTAB[reround];     // apply sticky bit
-          break;                             // [remainder don't-care]
-          }
-        } // check stickies
-      *BUFOFF=0;                             // make a coefficient of 0
-      ulsd=BUFOFF;                           // .. at the MSD place
-      }
-
-    if (reround!=0) {                        // discarding non-zero
-      uInt bump=0;
-      set->status|=DEC_Inexact;
-
-      // next decide whether to increment the coefficient
-      if (set->round==DEC_ROUND_HALF_EVEN) { // fastpath slowest case
-        if (reround>5) bump=1;               // >0.5 goes up
-         else if (reround==5)                // exactly 0.5000 ..
-          bump=*ulsd & 0x01;                 // .. up iff [new] lsd is odd
-        } // r-h-e
-       else switch (set->round) {
-        case DEC_ROUND_DOWN: {
-          // no change
-          break;} // r-d
-        case DEC_ROUND_HALF_DOWN: {
-          if (reround>5) bump=1;
-          break;} // r-h-d
-        case DEC_ROUND_HALF_UP: {
-          if (reround>=5) bump=1;
-          break;} // r-h-u
-        case DEC_ROUND_UP: {
-          if (reround>0) bump=1;
-          break;} // r-u
-        case DEC_ROUND_CEILING: {
-          // same as _UP for positive numbers, and as _DOWN for negatives
-          if (!(sourhil&DECFLOAT_Sign) && reround>0) bump=1;
-          break;} // r-c
-        case DEC_ROUND_FLOOR: {
-          // same as _UP for negative numbers, and as _DOWN for positive
-          // [negative reround cannot occur on 0]
-          if (sourhil&DECFLOAT_Sign && reround>0) bump=1;
-          break;} // r-f
-        case DEC_ROUND_05UP: {
-          if (reround>0) { // anything out there is 'sticky'
-            // bump iff lsd=0 or 5; this cannot carry so it could be
-            // effected immediately with no bump -- but the code
-            // is clearer if this is done the same way as the others
-            if (*ulsd==0 || *ulsd==5) bump=1;
-            }
-          break;} // r-r
-        default: {      // e.g., DEC_ROUND_MAX
-          set->status|=DEC_Invalid_context;
-          #if DECCHECK
-          printf("Unknown rounding mode: %ld\n", (LI)set->round);
-          #endif
-          break;}
-        } // switch (not r-h-e)
-      // printf("ReRound: %ld  bump: %ld\n", (LI)reround, (LI)bump);
-
-      if (bump!=0) {                         // need increment
-        // increment the coefficient; this could give 1000... (after
-        // the all nines case)
-        ub=ulsd;
-        for (; UBTOUI(ub-3)==0x09090909; ub-=4) UBFROMUI(ub-3, 0);
-        // now at most 3 digits left to non-9 (usually just the one)
-        for (; *ub==9; ub--) *ub=0;
-        *ub+=1;
-        // [the all-nines case will have carried one digit to the
-        // left of the original MSD -- just where it is needed]
-        } // bump needed
-      } // inexact rounding
-
-    // now clear zeros to the left so exactly DECPMAX digits will be
-    // available in the coefficent -- the first word to the left was
-    // cleared earlier for safe carry; now add any more needed
-    if (drop>4) {
-      UBFROMUI(BUFOFF-8, 0);                 // must be at least 5
-      for (uc=BUFOFF-12; uc>ulsd-DECPMAX-3; uc-=4) UBFROMUI(uc, 0);
-      }
-    } // need round (drop>0)
-
-   else { // drop<0; padding with -drop digits is needed
-    // This is the case where an error can occur if the padded
-    // coefficient will not fit; checking for this can be done in the
-    // same loop as padding for zeros if the no-hope and zero cases
-    // are checked first
-    if (-drop>DECPMAX-1) {                   // cannot fit unless 0
-      if (!ISCOEFFZERO(BUFOFF)) return decInvalid(result, set);
-      // a zero can have any exponent; just drop through and use it
-      ulsd=BUFOFF+DECPMAX-1;
-      }
-     else { // padding will fit (but may still be too long)
-      // final-word mask depends on endianess
-      #if DECLITEND
-      static const uInt dmask[]={0, 0x000000ff, 0x0000ffff, 0x00ffffff};
-      #else
-      static const uInt dmask[]={0, 0xff000000, 0xffff0000, 0xffffff00};
-      #endif
-      // note that here zeros to the right are added by fours, so in
-      // the Quad case this could write 36 zeros if the coefficient has
-      // fewer than three significant digits (hence the +2*QUAD for buf)
-      for (uc=BUFOFF+DECPMAX;; uc+=4) {
-        UBFROMUI(uc, 0);
-        if (UBTOUI(uc-DECPMAX)!=0) {              // could be bad
-          // if all four digits should be zero, definitely bad
-          if (uc<=BUFOFF+DECPMAX+(-drop)-4)
-            return decInvalid(result, set);
-          // must be a 1- to 3-digit sequence; check more carefully
-          if ((UBTOUI(uc-DECPMAX)&dmask[(-drop)%4])!=0)
-            return decInvalid(result, set);
-          break;    // no need for loop end test
-          }
-        if (uc>=BUFOFF+DECPMAX+(-drop)-4) break;  // done
-        }
-      ulsd=BUFOFF+DECPMAX+(-drop)-1;
-      } // pad and check leading zeros
-    } // drop<0
-
-  #if DECTRACE
-  num.msd=ulsd-DECPMAX+1;
-  num.lsd=ulsd;
-  num.exponent=explb-DECBIAS;
-  num.sign=sourhil & DECFLOAT_Sign;
-  decShowNum(&num, "res");
-  #endif
-
-  /*------------------------------------------------------------------*/
-  /* At this point the result is DECPMAX digits, ending at ulsd, so   */
-  /* fits the encoding exactly; there is no possibility of error      */
-  /*------------------------------------------------------------------*/
-  encode=((exprb>>DECECONL)<<4) + *(ulsd-DECPMAX+1); // make index
-  encode=DECCOMBFROM[encode];                // indexed by (0-2)*16+msd
-  // the exponent continuation can be extracted from the original RHS
-  encode|=sourhir & ECONMASK;
-  encode|=sourhil&DECFLOAT_Sign;             // add the sign from LHS
-
-  // finally encode the coefficient
-  // private macro to encode a declet; this version can be used
-  // because all coefficient digits exist
-  #define getDPD3q(dpd, n) ub=ulsd-(3*(n))-2;                   \
-    dpd=BCD2DPD[(*ub*256)+(*(ub+1)*16)+*(ub+2)];
-
-  #if DOUBLE
-    getDPD3q(dpd, 4); encode|=dpd<<8;
-    getDPD3q(dpd, 3); encode|=dpd>>2;
-    DFWORD(result, 0)=encode;
-    encode=dpd<<30;
-    getDPD3q(dpd, 2); encode|=dpd<<20;
-    getDPD3q(dpd, 1); encode|=dpd<<10;
-    getDPD3q(dpd, 0); encode|=dpd;
-    DFWORD(result, 1)=encode;
-
-  #elif QUAD
-    getDPD3q(dpd,10); encode|=dpd<<4;
-    getDPD3q(dpd, 9); encode|=dpd>>6;
-    DFWORD(result, 0)=encode;
-    encode=dpd<<26;
-    getDPD3q(dpd, 8); encode|=dpd<<16;
-    getDPD3q(dpd, 7); encode|=dpd<<6;
-    getDPD3q(dpd, 6); encode|=dpd>>4;
-    DFWORD(result, 1)=encode;
-    encode=dpd<<28;
-    getDPD3q(dpd, 5); encode|=dpd<<18;
-    getDPD3q(dpd, 4); encode|=dpd<<8;
-    getDPD3q(dpd, 3); encode|=dpd>>2;
-    DFWORD(result, 2)=encode;
-    encode=dpd<<30;
-    getDPD3q(dpd, 2); encode|=dpd<<20;
-    getDPD3q(dpd, 1); encode|=dpd<<10;
-    getDPD3q(dpd, 0); encode|=dpd;
-    DFWORD(result, 3)=encode;
-  #endif
-  return result;
-  } // decFloatQuantize
-
-/* ------------------------------------------------------------------ */
-/* decFloatReduce -- reduce finite coefficient to minimum length      */
-/*                                                                    */
-/*   result gets the reduced decFloat                                 */
-/*   df     is the source decFloat                                    */
-/*   set    is the context                                            */
-/*   returns result, which will be canonical                          */
-/*                                                                    */
-/* This removes all possible trailing zeros from the coefficient;     */
-/* some may remain when the number is very close to Nmax.             */
-/* Special values are unchanged and no status is set unless df=sNaN.  */
-/* Reduced zero has an exponent q=0.                                  */
-/* ------------------------------------------------------------------ */
-decFloat * decFloatReduce(decFloat *result, const decFloat *df,
-                          decContext *set) {
-  bcdnum num;                           // work
-  uByte buf[DECPMAX], *ub;              // coefficient and pointer
-  if (df!=result) *result=*df;          // copy, if needed
-  if (DFISNAN(df)) return decNaNs(result, df, NULL, set);   // sNaN
-  // zeros and infinites propagate too
-  if (DFISINF(df)) return decInfinity(result, df);     // canonical
-  if (DFISZERO(df)) {
-    uInt sign=DFWORD(df, 0)&DECFLOAT_Sign;
-    decFloatZero(result);
-    DFWORD(result, 0)|=sign;
-    return result;                      // exponent dropped, sign OK
-    }
-  // non-zero finite
-  GETCOEFF(df, buf);
-  ub=buf+DECPMAX-1;                     // -> lsd
-  if (*ub) return result;               // no trailing zeros
-  for (ub--; *ub==0;) ub--;             // terminates because non-zero
-  // *ub is the first non-zero from the right
-  num.sign=DFWORD(df, 0)&DECFLOAT_Sign; // set up number...
-  num.exponent=GETEXPUN(df)+(Int)(buf+DECPMAX-1-ub); // adjusted exponent
-  num.msd=buf;
-  num.lsd=ub;
-  return decFinalize(result, &num, set);
-  } // decFloatReduce
-
-/* ------------------------------------------------------------------ */
-/* decFloatRemainder -- integer divide and return remainder           */
-/*                                                                    */
-/*   result gets the remainder of dividing dfl by dfr:                */
-/*   dfl    is the first decFloat (lhs)                               */
-/*   dfr    is the second decFloat (rhs)                              */
-/*   set    is the context                                            */
-/*   returns result                                                   */
-/*                                                                    */
-/* ------------------------------------------------------------------ */
-decFloat * decFloatRemainder(decFloat *result,
-                             const decFloat *dfl, const decFloat *dfr,
-                             decContext *set) {
-  return decDivide(result, dfl, dfr, set, REMAINDER);
-  } // decFloatRemainder
-
-/* ------------------------------------------------------------------ */
-/* decFloatRemainderNear -- integer divide to nearest and remainder   */
-/*                                                                    */
-/*   result gets the remainder of dividing dfl by dfr:                */
-/*   dfl    is the first decFloat (lhs)                               */
-/*   dfr    is the second decFloat (rhs)                              */
-/*   set    is the context                                            */
-/*   returns result                                                   */
-/*                                                                    */
-/* This is the IEEE remainder, where the nearest integer is used.     */
-/* ------------------------------------------------------------------ */
-decFloat * decFloatRemainderNear(decFloat *result,
-                             const decFloat *dfl, const decFloat *dfr,
-                             decContext *set) {
-  return decDivide(result, dfl, dfr, set, REMNEAR);
-  } // decFloatRemainderNear
-
-/* ------------------------------------------------------------------ */
-/* decFloatRotate -- rotate the coefficient of a decFloat left/right  */
-/*                                                                    */
-/*   result gets the result of rotating dfl                           */
-/*   dfl    is the source decFloat to rotate                          */
-/*   dfr    is the count of digits to rotate, an integer (with q=0)   */
-/*   set    is the context                                            */
-/*   returns result                                                   */
-/*                                                                    */
-/* The digits of the coefficient of dfl are rotated to the left (if   */
-/* dfr is positive) or to the right (if dfr is negative) without      */
-/* adjusting the exponent or the sign of dfl.                         */
-/*                                                                    */
-/* dfr must be in the range -DECPMAX through +DECPMAX.                */
-/* NaNs are propagated as usual.  An infinite dfl is unaffected (but  */
-/* dfr must be valid).  No status is set unless dfr is invalid or an  */
-/* operand is an sNaN.  The result is canonical.                      */
-/* ------------------------------------------------------------------ */
-#define PHALF (ROUNDUP(DECPMAX/2, 4))   // half length, rounded up
-decFloat * decFloatRotate(decFloat *result,
-                         const decFloat *dfl, const decFloat *dfr,
-                         decContext *set) {
-  Int rotate;                           // dfr as an Int
-  uByte buf[DECPMAX+PHALF];             // coefficient + half
-  uInt digits, savestat;                // work
-  bcdnum num;                           // ..
-  uByte *ub;                            // ..
-
-  if (DFISNAN(dfl)||DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set);
-  if (!DFISINT(dfr)) return decInvalid(result, set);
-  digits=decFloatDigits(dfr);                    // calculate digits
-  if (digits>2) return decInvalid(result, set);  // definitely out of range
-  rotate=DPD2BIN[DFWORD(dfr, DECWORDS-1)&0x3ff]; // is in bottom declet
-  if (rotate>DECPMAX) return decInvalid(result, set); // too big
-  // [from here on no error or status change is possible]
-  if (DFISINF(dfl)) return decInfinity(result, dfl);  // canonical
-  // handle no-rotate cases
-  if (rotate==0 || rotate==DECPMAX) return decCanonical(result, dfl);
-  // a real rotate is needed: 0 < rotate < DECPMAX
-  // reduce the rotation to no more than half to reduce copying later
-  // (for QUAD in fact half + 2 digits)
-  if (DFISSIGNED(dfr)) rotate=-rotate;
-  if (abs(rotate)>PHALF) {
-    if (rotate<0) rotate=DECPMAX+rotate;
-     else rotate=rotate-DECPMAX;
-    }
-  // now lay out the coefficient, leaving room to the right or the
-  // left depending on the direction of rotation
-  ub=buf;
-  if (rotate<0) ub+=PHALF;    // rotate right, so space to left
-  GETCOEFF(dfl, ub);
-  // copy half the digits to left or right, and set num.msd
-  if (rotate<0) {
-    memcpy(buf, buf+DECPMAX, PHALF);
-    num.msd=buf+PHALF+rotate;
-    }
-   else {
-    memcpy(buf+DECPMAX, buf, PHALF);
-    num.msd=buf+rotate;
-    }
-  // fill in rest of num
-  num.lsd=num.msd+DECPMAX-1;
-  num.sign=DFWORD(dfl, 0)&DECFLOAT_Sign;
-  num.exponent=GETEXPUN(dfl);
-  savestat=set->status;                 // record
-  decFinalize(result, &num, set);
-  set->status=savestat;                 // restore
-  return result;
-  } // decFloatRotate
-
-/* ------------------------------------------------------------------ */
-/* decFloatSameQuantum -- test decFloats for same quantum             */
-/*                                                                    */
-/*   dfl    is the first decFloat (lhs)                               */
-/*   dfr    is the second decFloat (rhs)                              */
-/*   returns 1 if the operands have the same quantum, 0 otherwise     */
-/*                                                                    */
-/* No error is possible and no status results.                        */
-/* ------------------------------------------------------------------ */
-uInt decFloatSameQuantum(const decFloat *dfl, const decFloat *dfr) {
-  if (DFISSPECIAL(dfl) || DFISSPECIAL(dfr)) {
-    if (DFISNAN(dfl) && DFISNAN(dfr)) return 1;
-    if (DFISINF(dfl) && DFISINF(dfr)) return 1;
-    return 0;  // any other special mixture gives false
-    }
-  if (GETEXP(dfl)==GETEXP(dfr)) return 1; // biased exponents match
-  return 0;
-  } // decFloatSameQuantum
-
-/* ------------------------------------------------------------------ */
-/* decFloatScaleB -- multiply by a power of 10, as per 754            */
-/*                                                                    */
-/*   result gets the result of the operation                          */
-/*   dfl    is the first decFloat (lhs)                               */
-/*   dfr    is the second decFloat (rhs), am integer (with q=0)       */
-/*   set    is the context                                            */
-/*   returns result                                                   */
-/*                                                                    */
-/* This computes result=dfl x 10**dfr where dfr is an integer in the  */
-/* range +/-2*(emax+pmax), typically resulting from LogB.             */
-/* Underflow and Overflow (with Inexact) may occur.  NaNs propagate   */
-/* as usual.                                                          */
-/* ------------------------------------------------------------------ */
-#define SCALEBMAX 2*(DECEMAX+DECPMAX)   // D=800, Q=12356
-decFloat * decFloatScaleB(decFloat *result,
-                          const decFloat *dfl, const decFloat *dfr,
-                          decContext *set) {
-  uInt digits;                          // work
-  Int  expr;                            // dfr as an Int
-
-  if (DFISNAN(dfl)||DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set);
-  if (!DFISINT(dfr)) return decInvalid(result, set);
-  digits=decFloatDigits(dfr);                // calculate digits
-
-  #if DOUBLE
-  if (digits>3) return decInvalid(result, set);   // definitely out of range
-  expr=DPD2BIN[DFWORD(dfr, 1)&0x3ff];             // must be in bottom declet
-  #elif QUAD
-  if (digits>5) return decInvalid(result, set);   // definitely out of range
-  expr=DPD2BIN[DFWORD(dfr, 3)&0x3ff]              // in bottom 2 declets ..
-      +DPD2BIN[(DFWORD(dfr, 3)>>10)&0x3ff]*1000;  // ..
-  #endif
-  if (expr>SCALEBMAX) return decInvalid(result, set);  // oops
-  // [from now on no error possible]
-  if (DFISINF(dfl)) return decInfinity(result, dfl);   // canonical
-  if (DFISSIGNED(dfr)) expr=-expr;
-  // dfl is finite and expr is valid
-  *result=*dfl;                              // copy to target
-  return decFloatSetExponent(result, set, GETEXPUN(result)+expr);
-  } // decFloatScaleB
-
-/* ------------------------------------------------------------------ */
-/* decFloatShift -- shift the coefficient of a decFloat left or right */
-/*                                                                    */
-/*   result gets the result of shifting dfl                           */
-/*   dfl    is the source decFloat to shift                           */
-/*   dfr    is the count of digits to shift, an integer (with q=0)    */
-/*   set    is the context                                            */
-/*   returns result                                                   */
-/*                                                                    */
-/* The digits of the coefficient of dfl are shifted to the left (if   */
-/* dfr is positive) or to the right (if dfr is negative) without      */
-/* adjusting the exponent or the sign of dfl.                         */
-/*                                                                    */
-/* dfr must be in the range -DECPMAX through +DECPMAX.                */
-/* NaNs are propagated as usual.  An infinite dfl is unaffected (but  */
-/* dfr must be valid).  No status is set unless dfr is invalid or an  */
-/* operand is an sNaN.  The result is canonical.                      */
-/* ------------------------------------------------------------------ */
-decFloat * decFloatShift(decFloat *result,
-                         const decFloat *dfl, const decFloat *dfr,
-                         decContext *set) {
-  Int    shift;                         // dfr as an Int
-  uByte  buf[DECPMAX*2];                // coefficient + padding
-  uInt   digits, savestat;              // work
-  bcdnum num;                           // ..
-  uInt   uiwork;                        // for macros
-
-  if (DFISNAN(dfl)||DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set);
-  if (!DFISINT(dfr)) return decInvalid(result, set);
-  digits=decFloatDigits(dfr);                     // calculate digits
-  if (digits>2) return decInvalid(result, set);   // definitely out of range
-  shift=DPD2BIN[DFWORD(dfr, DECWORDS-1)&0x3ff];   // is in bottom declet
-  if (shift>DECPMAX) return decInvalid(result, set);   // too big
-  // [from here on no error or status change is possible]
-
-  if (DFISINF(dfl)) return decInfinity(result, dfl); // canonical
-  // handle no-shift and all-shift (clear to zero) cases
-  if (shift==0) return decCanonical(result, dfl);
-  if (shift==DECPMAX) {                      // zero with sign
-    uByte sign=(uByte)(DFBYTE(dfl, 0)&0x80); // save sign bit
-    decFloatZero(result);                    // make +0
-    DFBYTE(result, 0)=(uByte)(DFBYTE(result, 0)|sign); // and set sign
-    // [cannot safely use CopySign]
-    return result;
-    }
-  // a real shift is needed: 0 < shift < DECPMAX
-  num.sign=DFWORD(dfl, 0)&DECFLOAT_Sign;
-  num.exponent=GETEXPUN(dfl);
-  num.msd=buf;
-  GETCOEFF(dfl, buf);
-  if (DFISSIGNED(dfr)) { // shift right
-    // edge cases are taken care of, so this is easy
-    num.lsd=buf+DECPMAX-shift-1;
-    }
-   else { // shift left -- zero padding needed to right
-    UBFROMUI(buf+DECPMAX, 0);           // 8 will handle most cases
-    UBFROMUI(buf+DECPMAX+4, 0);         // ..
-    if (shift>8) memset(buf+DECPMAX+8, 0, 8+QUAD*18); // all other cases
-    num.msd+=shift;
-    num.lsd=num.msd+DECPMAX-1;
-    }
-  savestat=set->status;                 // record
-  decFinalize(result, &num, set);
-  set->status=savestat;                 // restore
-  return result;
-  } // decFloatShift
-
-/* ------------------------------------------------------------------ */
-/* decFloatSubtract -- subtract a decFloat from another               */
-/*                                                                    */
-/*   result gets the result of subtracting dfr from dfl:              */
-/*   dfl    is the first decFloat (lhs)                               */
-/*   dfr    is the second decFloat (rhs)                              */
-/*   set    is the context                                            */
-/*   returns result                                                   */
-/*                                                                    */
-/* ------------------------------------------------------------------ */
-decFloat * decFloatSubtract(decFloat *result,
-                            const decFloat *dfl, const decFloat *dfr,
-                            decContext *set) {
-  decFloat temp;
-  // NaNs must propagate without sign change
-  if (DFISNAN(dfr)) return decFloatAdd(result, dfl, dfr, set);
-  temp=*dfr;                                   // make a copy
-  DFBYTE(&temp, 0)^=0x80;                      // flip sign
-  return decFloatAdd(result, dfl, &temp, set); // and add to the lhs
-  } // decFloatSubtract
-
-/* ------------------------------------------------------------------ */
-/* decFloatToInt -- round to 32-bit binary integer (4 flavours)       */
-/*                                                                    */
-/*   df    is the decFloat to round                                   */
-/*   set   is the context                                             */
-/*   round is the rounding mode to use                                */
-/*   returns a uInt or an Int, rounded according to the name          */
-/*                                                                    */
-/* Invalid will always be signaled if df is a NaN, is Infinite, or is */
-/* outside the range of the target; Inexact will not be signaled for  */
-/* simple rounding unless 'Exact' appears in the name.                */
-/* ------------------------------------------------------------------ */
-uInt decFloatToUInt32(const decFloat *df, decContext *set,
-                      enum rounding round) {
-  return decToInt32(df, set, round, 0, 1);}
-
-uInt decFloatToUInt32Exact(const decFloat *df, decContext *set,
-                           enum rounding round) {
-  return decToInt32(df, set, round, 1, 1);}
-
-Int decFloatToInt32(const decFloat *df, decContext *set,
-                    enum rounding round) {
-  return (Int)decToInt32(df, set, round, 0, 0);}
-
-Int decFloatToInt32Exact(const decFloat *df, decContext *set,
-                         enum rounding round) {
-  return (Int)decToInt32(df, set, round, 1, 0);}
-
-/* ------------------------------------------------------------------ */
-/* decFloatToIntegral -- round to integral value (two flavours)       */
-/*                                                                    */
-/*   result gets the result                                           */
-/*   df     is the decFloat to round                                  */
-/*   set    is the context                                            */
-/*   round  is the rounding mode to use                               */
-/*   returns result                                                   */
-/*                                                                    */
-/* No exceptions, even Inexact, are raised except for sNaN input, or  */
-/* if 'Exact' appears in the name.                                    */
-/* ------------------------------------------------------------------ */
-decFloat * decFloatToIntegralValue(decFloat *result, const decFloat *df,
-                                   decContext *set, enum rounding round) {
-  return decToIntegral(result, df, set, round, 0);}
-
-decFloat * decFloatToIntegralExact(decFloat *result, const decFloat *df,
-                                   decContext *set) {
-  return decToIntegral(result, df, set, set->round, 1);}
-
-/* ------------------------------------------------------------------ */
-/* decFloatXor -- logical digitwise XOR of two decFloats              */
-/*                                                                    */
-/*   result gets the result of XORing dfl and dfr                     */
-/*   dfl    is the first decFloat (lhs)                               */
-/*   dfr    is the second decFloat (rhs)                              */
-/*   set    is the context                                            */
-/*   returns result, which will be canonical with sign=0              */
-/*                                                                    */
-/* The operands must be positive, finite with exponent q=0, and       */
-/* comprise just zeros and ones; if not, Invalid operation results.   */
-/* ------------------------------------------------------------------ */
-decFloat * decFloatXor(decFloat *result,
-                       const decFloat *dfl, const decFloat *dfr,
-                       decContext *set) {
-  if (!DFISUINT01(dfl) || !DFISUINT01(dfr)
-   || !DFISCC01(dfl)   || !DFISCC01(dfr)) return decInvalid(result, set);
-  // the operands are positive finite integers (q=0) with just 0s and 1s
-  #if DOUBLE
-   DFWORD(result, 0)=ZEROWORD
-                   |((DFWORD(dfl, 0) ^ DFWORD(dfr, 0))&0x04009124);
-   DFWORD(result, 1)=(DFWORD(dfl, 1) ^ DFWORD(dfr, 1))&0x49124491;
-  #elif QUAD
-   DFWORD(result, 0)=ZEROWORD
-                   |((DFWORD(dfl, 0) ^ DFWORD(dfr, 0))&0x04000912);
-   DFWORD(result, 1)=(DFWORD(dfl, 1) ^ DFWORD(dfr, 1))&0x44912449;
-   DFWORD(result, 2)=(DFWORD(dfl, 2) ^ DFWORD(dfr, 2))&0x12449124;
-   DFWORD(result, 3)=(DFWORD(dfl, 3) ^ DFWORD(dfr, 3))&0x49124491;
-  #endif
-  return result;
-  } // decFloatXor
-
-/* ------------------------------------------------------------------ */
-/* decInvalid -- set Invalid_operation result                         */
-/*                                                                    */
-/*   result gets a canonical NaN                                      */
-/*   set    is the context                                            */
-/*   returns result                                                   */
-/*                                                                    */
-/* status has Invalid_operation added                                 */
-/* ------------------------------------------------------------------ */
-static decFloat *decInvalid(decFloat *result, decContext *set) {
-  decFloatZero(result);
-  DFWORD(result, 0)=DECFLOAT_qNaN;
-  set->status|=DEC_Invalid_operation;
-  return result;
-  } // decInvalid
-
-/* ------------------------------------------------------------------ */
-/* decInfinity -- set canonical Infinity with sign from a decFloat    */
-/*                                                                    */
-/*   result gets a canonical Infinity                                 */
-/*   df     is source decFloat (only the sign is used)                */
-/*   returns result                                                   */
-/*                                                                    */
-/* df may be the same as result                                       */
-/* ------------------------------------------------------------------ */
-static decFloat *decInfinity(decFloat *result, const decFloat *df) {
-  uInt sign=DFWORD(df, 0);         // save source signword
-  decFloatZero(result);            // clear everything
-  DFWORD(result, 0)=DECFLOAT_Inf | (sign & DECFLOAT_Sign);
-  return result;
-  } // decInfinity
-
-/* ------------------------------------------------------------------ */
-/* decNaNs -- handle NaN argument(s)                                  */
-/*                                                                    */
-/*   result gets the result of handling dfl and dfr, one or both of   */
-/*          which is a NaN                                            */
-/*   dfl    is the first decFloat (lhs)                               */
-/*   dfr    is the second decFloat (rhs) -- may be NULL for a single- */
-/*          operand operation                                         */
-/*   set    is the context                                            */
-/*   returns result                                                   */
-/*                                                                    */
-/* 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 decFloat *decNaNs(decFloat *result,
-                         const decFloat *dfl, const decFloat *dfr,
-                         decContext *set) {
-  // handle sNaNs first
-  if (dfr!=NULL && DFISSNAN(dfr) && !DFISSNAN(dfl)) dfl=dfr; // use RHS
-  if (DFISSNAN(dfl)) {
-    decCanonical(result, dfl);          // propagate canonical sNaN
-    DFWORD(result, 0)&=~(DECFLOAT_qNaN ^ DECFLOAT_sNaN); // quiet
-    set->status|=DEC_Invalid_operation;
-    return result;
-    }
-  // one or both is a quiet NaN
-  if (!DFISNAN(dfl)) dfl=dfr;           // RHS must be NaN, use it
-  return decCanonical(result, dfl);     // propagate canonical qNaN
-  } // decNaNs
-
-/* ------------------------------------------------------------------ */
-/* decNumCompare -- numeric comparison of two decFloats               */
-/*                                                                    */
-/*   dfl    is the left-hand decFloat, which is not a NaN             */
-/*   dfr    is the right-hand decFloat, which is not a NaN            */
-/*   tot    is 1 for total order compare, 0 for simple numeric        */
-/*   returns -1, 0, or +1 for dfl<dfr, dfl=dfr, dfl>dfr               */
-/*                                                                    */
-/* No error is possible; status and mode are unchanged.               */
-/* ------------------------------------------------------------------ */
-static Int decNumCompare(const decFloat *dfl, const decFloat *dfr, Flag tot) {
-  Int   sigl, sigr;                     // LHS and RHS non-0 signums
-  Int   shift;                          // shift needed to align operands
-  uByte *ub, *uc;                       // work
-  uInt  uiwork;                         // for macros
-  // buffers +2 if Quad (36 digits), need double plus 4 for safe padding
-  uByte bufl[DECPMAX*2+QUAD*2+4];       // for LHS coefficient + padding
-  uByte bufr[DECPMAX*2+QUAD*2+4];       // for RHS coefficient + padding
-
-  sigl=1;
-  if (DFISSIGNED(dfl)) {
-    if (!DFISSIGNED(dfr)) {             // -LHS +RHS
-      if (DFISZERO(dfl) && DFISZERO(dfr) && !tot) return 0;
-      return -1;                        // RHS wins
-      }
-    sigl=-1;
-    }
-  if (DFISSIGNED(dfr)) {
-    if (!DFISSIGNED(dfl)) {             // +LHS -RHS
-      if (DFISZERO(dfl) && DFISZERO(dfr) && !tot) return 0;
-      return +1;                        // LHS wins
-      }
-    }
-
-  // signs are the same; operand(s) could be zero
-  sigr=-sigl;                           // sign to return if abs(RHS) wins
-
-  if (DFISINF(dfl)) {
-    if (DFISINF(dfr)) return 0;         // both infinite & same sign
-    return sigl;                        // inf > n
-    }
-  if (DFISINF(dfr)) return sigr;        // n < inf [dfl is finite]
-
-  // here, both are same sign and finite; calculate their offset
-  shift=GETEXP(dfl)-GETEXP(dfr);        // [0 means aligned]
-  // [bias can be ignored -- the absolute exponent is not relevant]
-
-  if (DFISZERO(dfl)) {
-    if (!DFISZERO(dfr)) return sigr;    // LHS=0, RHS!=0
-    // both are zero, return 0 if both same exponent or numeric compare
-    if (shift==0 || !tot) return 0;
-    if (shift>0) return sigl;
-    return sigr;                        // [shift<0]
-    }
-   else {                               // LHS!=0
-    if (DFISZERO(dfr)) return sigl;     // LHS!=0, RHS=0
-    }
-  // both are known to be non-zero at this point
-
-  // if the exponents are so different that the coefficients do not
-  // overlap (by even one digit) then a full comparison is not needed
-  if (abs(shift)>=DECPMAX) {            // no overlap
-    // coefficients are known to be non-zero
-    if (shift>0) return sigl;
-    return sigr;                        // [shift<0]
-    }
-
-  // decode the coefficients
-  // (shift both right two if Quad to make a multiple of four)
-  #if QUAD
-    UBFROMUI(bufl, 0);
-    UBFROMUI(bufr, 0);
-  #endif
-  GETCOEFF(dfl, bufl+QUAD*2);           // decode from decFloat
-  GETCOEFF(dfr, bufr+QUAD*2);           // ..
-  if (shift==0) {                       // aligned; common and easy
-    // all multiples of four, here
-    for (ub=bufl, uc=bufr; ub<bufl+DECPMAX+QUAD*2; ub+=4, uc+=4) {
-      uInt ui=UBTOUI(ub);
-      if (ui==UBTOUI(uc)) continue;     // so far so same
-      // about to find a winner; go by bytes in case little-endian
-      for (;; ub++, uc++) {
-        if (*ub>*uc) return sigl;       // difference found
-        if (*ub<*uc) return sigr;       // ..
-        }
-      }
-    } // aligned
-   else if (shift>0) {                  // lhs to left
-    ub=bufl;                            // RHS pointer
-    // pad bufl so right-aligned; most shifts will fit in 8
-    UBFROMUI(bufl+DECPMAX+QUAD*2, 0);   // add eight zeros
-    UBFROMUI(bufl+DECPMAX+QUAD*2+4, 0); // ..
-    if (shift>8) {
-      // more than eight; fill the rest, and also worth doing the
-      // lead-in by fours
-      uByte *up;                        // work
-      uByte *upend=bufl+DECPMAX+QUAD*2+shift;
-      for (up=bufl+DECPMAX+QUAD*2+8; up<upend; up+=4) UBFROMUI(up, 0);
-      // [pads up to 36 in all for Quad]
-      for (;; ub+=4) {
-        if (UBTOUI(ub)!=0) return sigl;
-        if (ub+4>bufl+shift-4) break;
-        }
-      }
-    // check remaining leading digits
-    for (; ub<bufl+shift; ub++) if (*ub!=0) return sigl;
-    // now start the overlapped part; bufl has been padded, so the
-    // comparison can go for the full length of bufr, which is a
-    // multiple of 4 bytes
-    for (uc=bufr; ; uc+=4, ub+=4) {
-      uInt ui=UBTOUI(ub);
-      if (ui!=UBTOUI(uc)) {             // mismatch found
-        for (;; uc++, ub++) {           // check from left [little-endian?]
-          if (*ub>*uc) return sigl;     // difference found
-          if (*ub<*uc) return sigr;     // ..
-          }
-        } // mismatch
-      if (uc==bufr+QUAD*2+DECPMAX-4) break; // all checked
-      }
-    } // shift>0
-
-   else { // shift<0) .. RHS is to left of LHS; mirror shift>0
-    uc=bufr;                            // RHS pointer
-    // pad bufr so right-aligned; most shifts will fit in 8
-    UBFROMUI(bufr+DECPMAX+QUAD*2, 0);   // add eight zeros
-    UBFROMUI(bufr+DECPMAX+QUAD*2+4, 0); // ..
-    if (shift<-8) {
-      // more than eight; fill the rest, and also worth doing the
-      // lead-in by fours
-      uByte *up;                        // work
-      uByte *upend=bufr+DECPMAX+QUAD*2-shift;
-      for (up=bufr+DECPMAX+QUAD*2+8; up<upend; up+=4) UBFROMUI(up, 0);
-      // [pads up to 36 in all for Quad]
-      for (;; uc+=4) {
-        if (UBTOUI(uc)!=0) return sigr;
-        if (uc+4>bufr-shift-4) break;
-        }
-      }
-    // check remaining leading digits
-    for (; uc<bufr-shift; uc++) if (*uc!=0) return sigr;
-    // now start the overlapped part; bufr has been padded, so the
-    // comparison can go for the full length of bufl, which is a
-    // multiple of 4 bytes
-    for (ub=bufl; ; ub+=4, uc+=4) {
-      uInt ui=UBTOUI(ub);
-      if (ui!=UBTOUI(uc)) {             // mismatch found
-        for (;; ub++, uc++) {           // check from left [little-endian?]
-          if (*ub>*uc) return sigl;     // difference found
-          if (*ub<*uc) return sigr;     // ..
-          }
-        } // mismatch
-      if (ub==bufl+QUAD*2+DECPMAX-4) break; // all checked
-      }
-    } // shift<0
-
-  // Here when compare equal
-  if (!tot) return 0;                   // numerically equal
-  // total ordering .. exponent matters
-  if (shift>0) return sigl;             // total order by exponent
-  if (shift<0) return sigr;             // ..
-  return 0;
-  } // decNumCompare
-
-/* ------------------------------------------------------------------ */
-/* decToInt32 -- local routine to effect ToInteger conversions        */
-/*                                                                    */
-/*   df     is the decFloat to convert                                */
-/*   set    is the context                                            */
-/*   rmode  is the rounding mode to use                               */
-/*   exact  is 1 if Inexact should be signalled                       */
-/*   unsign is 1 if the result a uInt, 0 if an Int (cast to uInt)     */
-/*   returns 32-bit result as a uInt                                  */
-/*                                                                    */
-/* Invalid is set is df is a NaN, is infinite, or is out-of-range; in */
-/* these cases 0 is returned.                                         */
-/* ------------------------------------------------------------------ */
-static uInt decToInt32(const decFloat *df, decContext *set,
-                       enum rounding rmode, Flag exact, Flag unsign) {
-  Int  exp;                        // exponent
-  uInt sourhi, sourpen, sourlo;    // top word from source decFloat ..
-  uInt hi, lo;                     // .. penultimate, least, etc.
-  decFloat zero, result;           // work
-  Int  i;                          // ..
-
-  /* Start decoding the argument */
-  sourhi=DFWORD(df, 0);                 // top word
-  exp=DECCOMBEXP[sourhi>>26];           // get exponent high bits (in place)
-  if (EXPISSPECIAL(exp)) {              // is special?
-    set->status|=DEC_Invalid_operation; // signal
-    return 0;
-    }
-
-  /* Here when the argument is finite */
-  if (GETEXPUN(df)==0) result=*df;      // already a true integer
-   else {                               // need to round to integer
-    enum rounding saveround;            // saver
-    uInt savestatus;                    // ..
-    saveround=set->round;               // save rounding mode ..
-    savestatus=set->status;             // .. and status
-    set->round=rmode;                   // set mode
-    decFloatZero(&zero);                // make 0E+0
-    set->status=0;                      // clear
-    decFloatQuantize(&result, df, &zero, set); // [this may fail]
-    set->round=saveround;               // restore rounding mode ..
-    if (exact) set->status|=savestatus; // include Inexact
-     else set->status=savestatus;       // .. or just original status
-    }
-
-  // only the last four declets of the coefficient can contain
-  // non-zero; check for others (and also NaN or Infinity from the
-  // Quantize) first (see DFISZERO for explanation):
-  // decFloatShow(&result, "sofar");
-  #if DOUBLE
-  if ((DFWORD(&result, 0)&0x1c03ff00)!=0
-   || (DFWORD(&result, 0)&0x60000000)==0x60000000) {
-  #elif QUAD
-  if ((DFWORD(&result, 2)&0xffffff00)!=0
-   ||  DFWORD(&result, 1)!=0
-   || (DFWORD(&result, 0)&0x1c003fff)!=0
-   || (DFWORD(&result, 0)&0x60000000)==0x60000000) {
-  #endif
-    set->status|=DEC_Invalid_operation; // Invalid or out of range
-    return 0;
-    }
-  // get last twelve digits of the coefficent into hi & ho, base
-  // 10**9 (see GETCOEFFBILL):
-  sourlo=DFWORD(&result, DECWORDS-1);
-  lo=DPD2BIN0[sourlo&0x3ff]
-    +DPD2BINK[(sourlo>>10)&0x3ff]
-    +DPD2BINM[(sourlo>>20)&0x3ff];
-  sourpen=DFWORD(&result, DECWORDS-2);
-  hi=DPD2BIN0[((sourpen<<2) | (sourlo>>30))&0x3ff];
-
-  // according to request, check range carefully
-  if (unsign) {
-    if (hi>4 || (hi==4 && lo>294967295) || (hi+lo!=0 && DFISSIGNED(&result))) {
-      set->status|=DEC_Invalid_operation; // out of range
-      return 0;
-      }
-    return hi*BILLION+lo;
-    }
-  // signed
-  if (hi>2 || (hi==2 && lo>147483647)) {
-    // handle the usual edge case
-    if (lo==147483648 && hi==2 && DFISSIGNED(&result)) return 0x80000000;
-    set->status|=DEC_Invalid_operation; // truly out of range
-    return 0;
-    }
-  i=hi*BILLION+lo;
-  if (DFISSIGNED(&result)) i=-i;
-  return (uInt)i;
-  } // decToInt32
-
-/* ------------------------------------------------------------------ */
-/* decToIntegral -- local routine to effect ToIntegral value          */
-/*                                                                    */
-/*   result gets the result                                           */
-/*   df     is the decFloat to round                                  */
-/*   set    is the context                                            */
-/*   rmode  is the rounding mode to use                               */
-/*   exact  is 1 if Inexact should be signalled                       */
-/*   returns result                                                   */
-/* ------------------------------------------------------------------ */
-static decFloat * decToIntegral(decFloat *result, const decFloat *df,
-                                decContext *set, enum rounding rmode,
-                                Flag exact) {
-  Int  exp;                        // exponent
-  uInt sourhi;                     // top word from source decFloat
-  enum rounding saveround;         // saver
-  uInt savestatus;                 // ..
-  decFloat zero;                   // work
-
-  /* Start decoding the argument */
-  sourhi=DFWORD(df, 0);            // top word
-  exp=DECCOMBEXP[sourhi>>26];      // get exponent high bits (in place)
-
-  if (EXPISSPECIAL(exp)) {         // is special?
-    // NaNs are handled as usual
-    if (DFISNAN(df)) return decNaNs(result, df, NULL, set);
-    // must be infinite; return canonical infinity with sign of df
-    return decInfinity(result, df);
-    }
-
-  /* Here when the argument is finite */
-  // complete extraction of the exponent
-  exp+=GETECON(df)-DECBIAS;             // .. + continuation and unbias
-
-  if (exp>=0) return decCanonical(result, df); // already integral
-
-  saveround=set->round;                 // save rounding mode ..
-  savestatus=set->status;               // .. and status
-  set->round=rmode;                     // set mode
-  decFloatZero(&zero);                  // make 0E+0
-  decFloatQuantize(result, df, &zero, set); // 'integrate'; cannot fail
-  set->round=saveround;                 // restore rounding mode ..
-  if (!exact) set->status=savestatus;   // .. and status, unless exact
-  return result;
-  } // decToIntegral