1.0e+16,
    1.0e+32,
    1.0e+64,
    1.0e+128,
    1.0e+256
};

static int n770_fp;		/* Flag is 1 on Nokia N770 floating point.
static bool n770_fp;		/* Flag is true on Nokia N770 floating point.
				 * Nokia's floating point has the words
				 * reversed: if big-endian is 7654 3210,
				 * and little-endian is       0123 4567,
				 * then Nokia's FP is         4567 0123;
				 * little-endian within the 32-bit words but
				 * big-endian between them. */

    (Tcl_WideUInt) 3125U*3125U*3125U*3125U*3125U*25U /* 5**27 */
};

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

static int		AccumulateDecimalDigit(unsigned, int,
static bool		AccumulateDecimalDigit(unsigned, int,
			    Tcl_WideUInt *, mp_int *, int);
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 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,
			    int, int, int *, char **);
static int		ShouldBankerRoundUpPowD(mp_int *, int, int);
static int		ShouldBankerRoundUpToNextPowD(mp_int *, mp_int *,
			    int, int, mp_int *);
static bool		ShouldBankerRoundUpPowD(mp_int *, int, bool);
static bool		ShouldBankerRoundUpToNextPowD(mp_int *, mp_int *,
			    int, bool, mp_int *);
static char *		ShorteningBignumConversionPowD(Double *dPtr,
			    Tcl_WideUInt bw, int b2, int b5,
			    int m2plus, int m2minus, int m5,
			    int sd, int k, int len,
			    int ilim, int ilim1, int *decpt,
			    char **endPtr);
static char *		StrictBignumConversionPowD(
			    Tcl_WideUInt bw, int b2, int b5,
			    int sd, int k, int len,
			    int ilim, int ilim1, int *decpt,
			    char **endPtr);
static int		ShouldBankerRoundUp(mp_int *, mp_int *, int);
static int		ShouldBankerRoundUpToNext(mp_int *, mp_int *,
			    mp_int *, int);
static bool		ShouldBankerRoundUp(mp_int *, mp_int *, bool);
static bool		ShouldBankerRoundUpToNext(mp_int *, mp_int *,
			    mp_int *, bool);
static char *		ShorteningBignumConversion(Double *dPtr,
			    Tcl_WideUInt bw, int b2,
			    int m2plus, int m2minus,
			    int s2, int s5, int k, int len,
			    int ilim, int ilim1, int *decpt,
			    char **endPtr);
static char *		StrictBignumConversion(

    int signum = 0;		/* Sign of the number being parsed. */
    Tcl_WideUInt significandWide = 0;
				/* Significand of the number being parsed (if
				 * no overflow). */
    mp_int significandBig;	/* Significand of the number being parsed (if
				 * it overflows significandWide). */
    int significandOverflow = 0;/* Flag==1 iff significandBig is used. */
    bool significandOverflow = false;/* True iff significandBig is used. */
    Tcl_WideUInt octalSignificandWide = 0;
				/* Significand of an octal number; needed
				 * because we don't know whether a number with
				 * a leading zero is octal or decimal until
				 * we've scanned forward to a '.' or 'e'. */
    mp_int octalSignificandBig;	/* Significand of octal number once
				 * octalSignificandWide overflows. */
    int octalSignificandOverflow = 0;
				/* Flag==1 if octalSignificandBig is used. */
    bool octalSignificandOverflow = false;
				/* True if octalSignificandBig is used. */
    int numSigDigs = 0;		/* Number of significant digits in the decimal
				 * significand. */
    int numTrailZeros = 0;	/* Number of trailing zeroes at the current
				 * point in the parse. */
    int numDigitsAfterDp = 0;	/* Number of digits scanned after the decimal
				 * point. */
    int exponentSignum = 0;	/* Signum of the exponent of a floating point

			 */

			if ((octalSignificandWide != 0)
				&& (((size_t)shift >=
					CHAR_BIT*sizeof(Tcl_WideUInt))
				|| (octalSignificandWide >
					(UWIDE_MAX >> shift)))) {
			    octalSignificandOverflow = 1;
			    octalSignificandOverflow = true;
			    err = mp_init_u64(&octalSignificandBig,
				    octalSignificandWide);
			}
		    }
		    if (!octalSignificandOverflow) {
			/*
			 * When the significand is 0, it is possible for the

		     * value being shifted is undefined behavior. Check
		     * for too large shifts first.
		     */

		    if (significandWide != 0 &&
			    ((size_t)shift >= CHAR_BIT*sizeof(Tcl_WideUInt) ||
			    significandWide > (UWIDE_MAX >> shift))) {
			significandOverflow = 1;
			significandOverflow = true;
			err = mp_init_u64(&significandBig,
				significandWide);
		    }
		}
		if (!significandOverflow) {
		    /*
		     * When the significand is 0, it is possible for the

		     * value being shifted is undefined behavior. Check
		     * for too large shifts first.
		     */

		    if (significandWide != 0 &&
			    ((size_t)shift >= CHAR_BIT*sizeof(Tcl_WideUInt) ||
			    significandWide > (UWIDE_MAX >> shift))) {
			significandOverflow = 1;
			significandOverflow = true;
			err = mp_init_u64(&significandBig,
				significandWide);
		    }
		}
		if (!significandOverflow) {
		    /*
		     * When the significand is 0, it is possible for the

	    Tcl_Panic("TclParseNumber: bad acceptState %d parsing '%s'",
		    acceptState, bytes);
	case BINARY:
	    shift = numTrailZeros;
	    if (!significandOverflow && significandWide != 0 &&
		    ((size_t)shift >= CHAR_BIT*sizeof(Tcl_WideUInt) ||
		    significandWide > (MOST_BITS + signum) >> shift)) {
		significandOverflow = 1;
		significandOverflow = true;
		err = mp_init_u64(&significandBig, significandWide);
	    }
	    if (shift) {
		if (!significandOverflow) {
		    /*
		     * When the significand is 0, it is possible for the
		     * amount to be shifted to equal or exceed the width

	     * Returning a hex integer. Final scaling step.
	     */

	    shift = 4 * numTrailZeros;
	    if (!significandOverflow && significandWide !=0 &&
		    ((size_t)shift >= CHAR_BIT*sizeof(Tcl_WideUInt) ||
		    significandWide > (MOST_BITS + signum) >> shift)) {
		significandOverflow = 1;
		significandOverflow = true;
		err = mp_init_u64(&significandBig, significandWide);
	    }
	    if (shift) {
		if (!significandOverflow) {
		    /*
		     * When the significand is 0, it is possible for the
		     * amount to be shifted to equal or exceed the width

	     * Returning an octal integer. Final scaling step.
	     */

	    shift = 3 * numTrailZeros;
	    if (!octalSignificandOverflow && octalSignificandWide != 0 &&
		    ((size_t)shift >= CHAR_BIT*sizeof(Tcl_WideUInt) ||
		    octalSignificandWide > (MOST_BITS + signum) >> shift)) {
		octalSignificandOverflow = 1;
		octalSignificandOverflow = true;
		err = mp_init_u64(&octalSignificandBig,
			octalSignificandWide);
	    }
	    if (shift) {
		if (!octalSignificandOverflow) {
		    /*
		     * When the significand is 0, it is possible for the

			    &octalSignificandBig);
		}
	    }
	    if (!octalSignificandOverflow) {
		if ((err == MP_OKAY) && (octalSignificandWide > (MOST_BITS + signum))) {
		    err = mp_init_u64(&octalSignificandBig,
			    octalSignificandWide);
		    octalSignificandOverflow = 1;
		    octalSignificandOverflow = true;
		} else {
		    objPtr->typePtr = &tclIntType;
		    if (signum) {
			objPtr->internalRep.wideValue =
				(Tcl_WideInt)(-octalSignificandWide);
		    } else {
			objPtr->internalRep.wideValue =

	    break;

	case ZERO:
	case DECIMAL:
	    significandOverflow = AccumulateDecimalDigit(0, numTrailZeros-1,
		    &significandWide, &significandBig, significandOverflow);
	    if ((err == MP_OKAY) && !significandOverflow && (significandWide > MOST_BITS+signum)) {
		significandOverflow = 1;
		significandOverflow = true;
		err = mp_init_u64(&significandBig, significandWide);
	    }
	returnInteger:
	    if (!significandOverflow) {
		if ((err == MP_OKAY) && (significandWide > MOST_BITS+signum)) {
		    err = mp_init_u64(&significandBig,
			    significandWide);
		    significandOverflow = 1;
		    significandOverflow = true;
		} else {
		    objPtr->typePtr = &tclIntType;
		    if (signum) {
			objPtr->internalRep.wideValue =
				(Tcl_WideInt)(-significandWide);
		    } else {
			objPtr->internalRep.wideValue =

 *----------------------------------------------------------------------
 *
 * AccumulateDecimalDigit --
 *
 *	Consume a decimal digit in a number being scanned.
 *
 * Results:
 *	Returns 1 if the number has overflowed to a bignum, 0 if it still fits
 *	in a wide integer.
 *	Returns true if the number has overflowed to a bignum, false if it
 *	still fits in a wide integer.
 *
 * Side effects:
 *	Updates either the wide or bignum representation.
 *
 *----------------------------------------------------------------------
 */

static int
static bool
AccumulateDecimalDigit(
    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

	Tcl_WideUInt w = *wideRepPtr;
	if (w == 0) {
	    /*
	     * There's no need to multiply if the multiplicand is zero.
	     */

	    *wideRepPtr = digit;
	    return 0;
	    return false;
	} else if (numZeros >= maxpow10_wide
		|| w > (UWIDE_MAX-digit)/pow10_wide[numZeros+1]) {
	    /*
	     * Wide multiplication will overflow.  Expand the number to a
	     * bignum and fall through into the bignum case.
	     */

	    if (mp_init_u64(bignumRepPtr, w) != MP_OKAY) {
		return 0;
		return false;
	    }
	} else {
	    /*
	     * Wide multiplication.
	     */

	    *wideRepPtr = w * pow10_wide[numZeros+1] + digit;
	    return 0;
	    return false;
	}
    }

    /*
     * Bignum multiplication.
     */

    if (numZeros < log10_DIGIT_MAX) {
	/*
	 * Up to about 8 zeros - single digit multiplication.
	 */

	if ((mp_mul_d(bignumRepPtr, (mp_digit) pow10_wide[numZeros+1],
		bignumRepPtr) != MP_OKAY)
		|| (mp_add_d(bignumRepPtr, (mp_digit) digit, bignumRepPtr) != MP_OKAY))
	return 0;
		|| (mp_add_d(bignumRepPtr, (mp_digit) digit, bignumRepPtr) != MP_OKAY)) {
	    return false;
	}
    } else {
	/*
	 * More than single digit multiplication. Multiply by the appropriate
	 * small powers of 5, and then shift. Large strings of zeroes are
	 * eaten 256 at a time; this is less efficient than it could be, but
	 * seems implausible. We presume that MP_DIGIT_BIT is at least 27. The
	 * first multiplication, by up to 10**7, is done with a one-DIGIT

	while ((err == MP_OKAY) && (n >= 256)) {
	    err = mp_mul(bignumRepPtr, pow5+8, bignumRepPtr);
	    n -= 256;
	}
	if ((err != MP_OKAY)
		|| (mp_mul_2d(bignumRepPtr, (int)(numZeros+1)&~0x7, bignumRepPtr) != MP_OKAY)
		|| (mp_add_d(bignumRepPtr, (mp_digit) digit, bignumRepPtr) != MP_OKAY)) {
	    return 0;
	    return false;
	}
    }

    return 1;
    return true;
}

/*
 *----------------------------------------------------------------------
 *
 * MakeLowPrecisionDouble --
 *

    int scale;			/* Scale factor for M. */
    int multiplier;		/* Power of two to scale M. */
    double num, den;		/* Numerator and denominator of the correction
				 * term. */
    double quot;		/* Correction term. */
    double minincr;		/* Lower bound on the absolute value of the
				 * correction term. */
    int roundToEven = 0;	/* Flag == TRUE if we need to invoke
				 * "round to even" functionality */
    bool roundToEven = false;	/* True if we need to invoke "round to even"
				 * functionality */
    double rteSignificand;	/* Significand of the round-to-even result */
    int rteExponent;		/* Exponent of the round-to-even result */
    int shift;			/* Shift count for converting numerator
				 * and denominator of corrector to floating
				 * point */
    Tcl_WideInt rteSigWide;	/* Wide integer version of the significand
				 * for testing evenness */

	mp_clear(&twoMd);
	mp_clear(&twoMv);
	return approxResult;
    case MP_EQ:
	/*
	 * If the error is exactly 1/2 ULP, we need to round to even.
	 */
	roundToEven = 1;
	roundToEven = true;
	break;
    case MP_GT:
	/*
	 * We need to correct the result if the error exceeds 1/2 ULP.
	 */
	break;
    }

 * Results:
 *	Returns 1 iff the fraction is more than 1/2, or if the fraction is
 *	exactly 1/2 and the digit is odd.
 *
 *----------------------------------------------------------------------
 */

static inline int
static inline bool
ShouldBankerRoundUpPowD(
    mp_int *b,			/* Numerator of the fraction. */
    int sd,			/* Denominator is 2**(sd*MP_DIGIT_BIT). */
    int isodd)			/* 1 if the digit is odd, 0 if even. */
    bool isodd)			/* true if the digit is odd, false if even. */
{
    static const mp_digit topbit = ((mp_digit)1) << (MP_DIGIT_BIT - 1);

    if (b->used < sd || (b->dp[sd-1] & topbit) == 0) {
	return 0;
	return false;
    }
    if (b->dp[sd-1] != topbit) {
	return 1;
	return true;
    }
    for (int i = sd-2; i >= 0; --i) {
	if (b->dp[i] != 0) {
	    return 1;
	    return true;
	}
    }
    return isodd;
}

/*
 *----------------------------------------------------------------------
 *
 * ShouldBankerRoundUpToNextPowD --
 *
 *	Tests whether bankers' rounding will round down in the "denominator is
 *	a power of 2**MP_DIGIT" case.
 *
 * Results:
 *	Returns 1 if the rounding will be performed - which increases the
 *	digit by one - and 0 otherwise.
 *	Returns true if the rounding will be performed - which increases the
 *	digit by one - and false otherwise.
 *
 *----------------------------------------------------------------------
 */

static inline int
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). */
    int isodd,			/* 1 if the integer significand is odd. */
    bool isodd,			/* 1 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)
     */

    if ((mp_add(b, m, temp) != MP_OKAY) || (temp->used <= sd)) {
	/* Too few digits to be > s */
	return 0;
	return false;
    }
    if (temp->used > sd+1 || temp->dp[sd] > 1) {
				/* >= 2s */
	return 1;
	return true;
    }
    for (int i = sd-1; i >= 0; --i) {
				/* Check for ==s */
	if (temp->dp[i] != 0) {	/* > s */
	    return 1;
	    return true;
	}
    }
    return isodd;
}

/*
 *----------------------------------------------------------------------

 *
 * ShouldBankerRoundUp --
 *
 *	Tests whether a digit should be rounded up or down when finishing
 *	bignum-based floating point conversion.
 *
 * Results:
 *	Returns 1 if the number needs to be rounded up, 0 otherwise.
 *	Returns true if the number needs to be rounded up, false otherwise.
 *
 *----------------------------------------------------------------------
 */

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

    switch (r) {
    case MP_EQ:
	return isodd;
    case MP_GT:
	return 1;
	return true;
    default:
	return 0;
	return false;
    }
}

/*
 *----------------------------------------------------------------------
 *
 * ShouldBankerRoundUpToNext --
 *
 *	Tests whether the remainder is great enough to force rounding to the
 *	next higher digit.
 *
 * Results:
 *	Returns 1 if the number should be rounded up, 0 otherwise.
 *
 *----------------------------------------------------------------------
 */

static inline int
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. */
    int isodd)			/* 1 if the integer significand is odd. */
    bool isodd)			/* 1 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.
     */

    if ((mp_init(&temp) != MP_OKAY) || (mp_add(b, m, &temp) != MP_OKAY)) {
	return 0;
	return false;
    }
    r = mp_cmp_mag(&temp, S);
    mp_clear(&temp);
    switch (r) {
    case MP_EQ:
	return isodd;
    case MP_GT:
	return 1;
	return true;
    default:
	return 0;
	return false;
    }
}

/*
 *----------------------------------------------------------------------
 *
 * ShorteningBignumConversion --

 */

void
TclInitDoubleConversion(void)
{
    Tcl_WideUInt u;
    double d;
#ifdef IEEE_FLOATING_POINT
    union {
	double dv;
	Tcl_WideUInt iv;
    } bitwhack;
#endif
    mp_err err = MP_OKAY;
#if defined(__sgi) && defined(_COMPILER_VERSION)
    union fpc_csr mipsCR;

    mipsCR.fc_word = get_fpc_csr();
    mipsCR.fc_struct.flush = 0;
    set_fpc_csr(mipsCR.fc_word);

     * Nokia 770's software-emulated floating point is "middle endian": the
     * bytes within a 32-bit word are little-endian (like the native
     * integers), but the two words of a 'double' are presented most
     * significant word first.
     */

#ifdef IEEE_FLOATING_POINT
    union {
	double dv;
	Tcl_WideUInt iv;
    } bitwhack;
    bitwhack.dv = 1.000000238418579;
				/* 3ff0 0000 4000 0000 */
    if ((bitwhack.iv >> 32) == 0x3FF00000) {
	n770_fp = 0;
	n770_fp = false;
    } else if ((bitwhack.iv & 0xFFFFFFFF) == 0x3FF00000) {
	n770_fp = 1;
	n770_fp = true;
    } else {
	Tcl_Panic("unknown floating point word order on this machine");
    }
#endif
}

/*

	r = -TclFloor(&b);
    } else {
	int bits = mp_count_bits(a);

	if (bits > DBL_MAX_EXP*log2FLT_RADIX) {
	    r = HUGE_VAL;
	} else {
	    bool exact = true;
	    int exact = 1, shift = mantBits - bits;
	    int shift = mantBits - bits;

	    if (err != MP_OKAY) {
		/* just skip */
	    } else if (shift > 0) {
		err = mp_mul_2d(a, shift, &b);
	    } else if (shift < 0) {
		mp_int d;

#endif

/*
 *----------------------------------------------------------------------
 *
 * TclNokia770Doubles --
 *
 *	Transpose the two words of a number for Nokia 770 floating point
 *	handling.
 *	Report whether the two words of a number need to be transposed for
 *	Nokia 770 floating point handling.
 *
 *----------------------------------------------------------------------
 */

int
bool
TclNokia770Doubles(void)
{
    return n770_fp;
}

/*
 * Local Variables:
 * mode: c
 * c-basic-offset: 4
 * fill-column: 78
 * End:
 */