};

/*
 * Static functions defined in this file.
 */

static bool		AccumulateDecimalDigit(unsigned, int,
			    Tcl_WideUInt *, mp_int *, int);
			    Tcl_WideUInt *, mp_int *, bool);
static double		MakeHighPrecisionDouble(int signum,
			    mp_int *significand, int nSigDigs, int exponent);
static double		MakeLowPrecisionDouble(int signum,
			    Tcl_WideUInt significand, int nSigDigs,
			    int exponent);
#ifdef IEEE_FLOATING_POINT
static double		MakeNaN(int signum, Tcl_WideUInt tag);
#endif
static double		RefineApproximation(double approx,
			    mp_int *exactSignificand, int exponent);
static mp_err		MulPow5(mp_int *, unsigned, mp_int *) MP_WUR;
static int		NormalizeRightward(Tcl_WideUInt *);
static int		RequiredPrecision(Tcl_WideUInt);
static void		DoubleToExpAndSig(double, Tcl_WideUInt *, int *,
			    int *);
static void		TakeAbsoluteValue(Double *, int *);
static char *		FormatInfAndNaN(Double *, int *, char **);
static char *		FormatZero(int *, char **);
static int		ApproximateLog10(Tcl_WideUInt, int, int);
static int		BetterLog10(double, int, int *);
static int		BetterLog10(double, int, bool *);
static void		ComputeScale(int, int, int *, int *, int *, int *);
static void		SetPrecisionLimits(int, int, int *, int *, int *,
			    int *);
static char *		BumpUp(char *, char *, int *);
static int		AdjustRange(double *, int);
static char *		ShorteningQuickFormat(double, int, int, double,
			    char *, int *);
static char *		StrictQuickFormat(double, int, int, double,
			    char *, int *);
static char *		QuickConversion(double, int, int, int, int, int, int,
static char *		QuickConversion(double, int, bool, int, int, int, int,
			    int *, char **);
static void		CastOutPowersOf2(int *, int *, int *);
static char *		ShorteningInt64Conversion(Double *, Tcl_WideUInt,
			    int, int, int, int, int, int, int, int, int,
			    int, int, int *, char **);
static char *		StrictInt64Conversion(Tcl_WideUInt,
			    int, int, int, int, int, int,

    unsigned digit,		/* Digit being scanned. */
    int numZeros,		/* Count of zero digits preceding the digit
				 * being scanned. */
    Tcl_WideUInt *wideRepPtr,	/* Representation of the partial number as a
				 * wide integer. */
    mp_int *bignumRepPtr,	/* Representation of the partial number as a
				 * bignum. */
    int bignumFlag)		/* Flag == 1 if the number overflowed previous
    bool bignumFlag)		/* True if the number overflowed previous
				 * to this digit. */
{
    /*
     * Try wide multiplication first.
     */

    if (!bignumFlag) {

 */

static inline int
BetterLog10(
    double d,			/* Original number to format. */
    int k,			/* Characteristic(Log base 10) of the
				 * number. */
    int *k_check)		/* Flag == 1 if k is inexact. */
    bool *k_check)		/* True if k is inexact. */
{
    /*
     * Performance hack. If k is in the range 0..TEN_PMAX, then we can use a
     * powers-of-ten table to check it.
     */

    if (k >= 0 && k <= TEN_PMAX) {
	if (d < tens[k]) {
	    k--;
	}
	*k_check = 0;
	*k_check = false;
    } else {
	*k_check = 1;
	*k_check = true;
    }
    return k;
}

/*
 *----------------------------------------------------------------------
 *

 *----------------------------------------------------------------------
 */

static inline char *
QuickConversion(
    double e,			/* Number to format. */
    int k,			/* floor(log10(d)), approximately. */
    int k_check,		/* 0 if k is exact, 1 if it may be too high */
    bool k_check,		/* false if k is exact, true if it may be too high */
    int flags,			/* Flags passed to dtoa:
				 *    TCL_DD_SHORTEST */
    int len,			/* Length of the return value. */
    int ilim,			/* Number of digits to store. */
    int ilim1,			/* Number of digits to store if we misguessed
				 * k. */
    int *decpt,			/* OUTPUT: Location of the decimal point. */

 */

static inline bool
ShouldBankerRoundUpToNextPowD(
    mp_int *b,			/* Numerator of the fraction. */
    mp_int *m,			/* Numerator of the rounding tolerance. */
    int sd,			/* Common denominator is 2**(sd*MP_DIGIT_BIT). */
    bool isodd,			/* 1 if the integer significand is odd. */
    bool isodd,			/* True if the integer significand is odd. */
    mp_int *temp)		/* Work area for the calculation. */
{
    /*
     * Compare B and S-m - which is the same as comparing B+m and S - which we
     * do by computing b+m and doing a bitwhack compare against
     * 2**(MP_DIGIT_BIT*sd)
     */

 */

static inline bool
ShouldBankerRoundUp(
    mp_int *twor,		/* 2x the remainder from thd division that
				 * produced the last digit. */
    mp_int *S,			/* Denominator. */
    bool isodd)			/* Flag == 1 if the last digit is odd. */
    bool isodd)			/* True if the last digit is odd. */
{
    int r = mp_cmp_mag(twor, S);

    switch (r) {
    case MP_EQ:
	return isodd;
    case MP_GT:

static inline bool
ShouldBankerRoundUpToNext(
    mp_int *b,			/* Remainder from the division that produced
				 * the last digit. */
    mp_int *m,			/* Numerator of the rounding tolerance. */
    mp_int *S,			/* Denominator. */
    bool isodd)			/* 1 if the integer significand is odd. */
    bool isodd)			/* True if the integer significand is odd. */
{
    int r;
    mp_int temp;

    /*
     * Compare b and S-m: this is the same as comparing B+m and S.
     */

				 *	   one character beyond the end of the
				 *	   returned string. */
{
    Double d;			/* Union for deconstructing doubles. */
    Tcl_WideUInt bw;		/* Integer significand. */
    int be;			/* Power of 2 by which b must be multiplied */
    int bbits;			/* Number of bits needed to represent b. */
    int denorm;			/* Flag == 1 iff the input number was
    bool denorm;		/* True iff the input number was
				 * denormalized. */
    int k;			/* Estimate of floor(log10(d)). */
    int k_check;		/* Flag == 1 if d is near enough to a power of
    bool k_check;		/* True if d is near enough to a power of
				 * ten that k must be checked. */
    int b2, b5, s2, s5;		/* Powers of 2 and 5 in the numerator and
				 * denominator of intermediate results. */
    int ilim = -1, ilim1 = -1;	/* Number of digits to convert, and number to
				 * convert if log10(d) has been
				 * overestimated. */
    char *retval;		/* Return value from this function. */