* Derived quantities.
 */

#define TEN_PMAX	22	/* floor(FP_PRECISION*log(2)/log(5)) */
#define QUICK_MAX	14	/* floor((FP_PRECISION-1)*log(2)/log(10))-1 */
#define BLETCH		0x10	/* Highest power of two that is greater than
				 * DBL_MAX_10_EXP, divided by 16. */
#define DIGIT_GROUP	8	/* floor(DIGIT_BIT*log(2)/log(10)) */
#define DIGIT_GROUP	8	/* floor(MP_DIGIT_BIT*log(2)/log(10)) */

/*
 * Union used to dismantle floating point numbers.
 */

typedef union Double {
    struct {

		bignumRepPtr);
	mp_add_d(bignumRepPtr, (mp_digit) digit, bignumRepPtr);
    } 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 DIGIT_BIT is at least 27. The
	 * 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
	 * multiply (this presumes that DIGIT_BIT >= 24).
	 * multiply (this presumes that MP_DIGIT_BIT >= 24).
	 */

	n = numZeros + 1;
	mp_mul_d(bignumRepPtr, (mp_digit) pow10_wide[n&0x7], bignumRepPtr);
	for (i=3; i<=7; ++i) {
	    if (n & (1 << i)) {
		mp_mul(bignumRepPtr, pow5+i, bignumRepPtr);

/*
 *----------------------------------------------------------------------
 *
 * ShouldBankerRoundUpPowD --
 *
 *	Test whether bankers' rounding should round a digit up. Assumption is
 *	made that the denominator of the fraction being tested is a power of
 *	2**DIGIT_BIT.
 *	2**MP_DIGIT_BIT.
 *
 * 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
ShouldBankerRoundUpPowD(
    mp_int *b,			/* Numerator of the fraction. */
    int sd,			/* Denominator is 2**(sd*DIGIT_BIT). */
    int sd,			/* Denominator is 2**(sd*MP_DIGIT_BIT). */
    int isodd)			/* 1 if the digit is odd, 0 if even. */
{
    int i;
    static const mp_digit topbit = ((mp_digit)1) << (MP_DIGIT_BIT - 1);

    if (b->used < sd || (b->dp[sd-1] & topbit) == 0) {
	return 0;

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

static inline int
ShouldBankerRoundUpToNextPowD(
    mp_int *b,			/* Numerator of the fraction. */
    mp_int *m,			/* Numerator of the rounding tolerance. */
    int sd,			/* Common denominator is 2**(sd*DIGIT_BIT). */
    int sd,			/* Common denominator is 2**(sd*MP_DIGIT_BIT). */
    int isodd,			/* 1 if the integer significand is odd. */
    mp_int *temp)		/* Work area for the calculation. */
{
    int i;

    /*
     * 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**(DIGIT_BIT*sd)
     * 2**(MP_DIGIT_BIT*sd)
     */

    mp_add(b, m, temp);
    if (temp->used <= sd) {	/* Too few digits to be > s */
	return 0;
    }
    if (temp->used > sd+1 || temp->dp[sd] > 1) {

 *----------------------------------------------------------------------
 *
 * ShorteningBignumConversionPowD --
 *
 *	Converts a double-precision number to the shortest string of digits
 *	that reconverts exactly to the given number, or to 'ilim' digits if
 *	that will yield a shorter result. The denominator in David Gay's
 *	conversion algorithm is known to be a power of 2**DIGIT_BIT, and hence
 *	conversion algorithm is known to be a power of 2**MP_DIGIT_BIT, and hence
 *	the division in the main loop may be replaced by a digit shift and
 *	mask.
 *
 * Results:
 *	Returns the string of significant decimal digits, in newly allocated
 *	memory
 *

    if (m2plus > m2minus) {
	mp_init_copy(&mplus, &mminus);
	mp_mul_2d(&mplus, m2plus-m2minus, &mplus);
    }
    mp_init(&temp);

    /*
     * Loop through the digits. Do division and mod by s == 2**(sd*DIGIT_BIT)
     * Loop through the digits. Do division and mod by s == 2**(sd*MP_DIGIT_BIT)
     * by mp_digit extraction.
     */

    i = 0;
    for (;;) {
	if (b.used <= sd) {
	    digit = 0;

 *----------------------------------------------------------------------
 *
 * StrictBignumConversionPowD --
 *
 *	Converts a double-precision number to a fixed-lengt string of 'ilim'
 *	digits (or 'ilim1' if log10(d) has been overestimated).  The
 *	denominator in David Gay's conversion algorithm is known to be a power
 *	of 2**DIGIT_BIT, and hence the division in the main loop may be
 *	of 2**MP_DIGIT_BIT, and hence the division in the main loop may be
 *	replaced by a digit shift and mask.
 *
 * Results:
 *	Returns the string of significant decimal digits, in newly allocated
 *	memory.
 *
 * Side effects:

    if (b.used <= sd) {
	mp_mul_d(&b, 10, &b);
	ilim = ilim1;
	--k;
    }

    /*
     * Loop through the digits. Do division and mod by s == 2**(sd*DIGIT_BIT)
     * Loop through the digits. Do division and mod by s == 2**(sd*MP_DIGIT_BIT)
     * by mp_digit extraction.
     */

    i = 1;
    for (;;) {
	if (b.used <= sd) {
	    digit = 0;

	     */

	    return ShorteningInt64Conversion(&d, bw, b2, b5, m2plus,
		    m2minus, m5, s2, s5, k, len, ilim, ilim1, decpt, endPtr);
	} else if (s5 == 0) {
	    /*
	     * The denominator is a power of 2, so we can replace division by
	     * digit shifts. First we round up s2 to a multiple of DIGIT_BIT,
	     * digit shifts. First we round up s2 to a multiple of MP_DIGIT_BIT,
	     * and adjust m2 and b2 accordingly. Then we launch into a version
	     * of the comparison that's specialized for the 'power of mp_digit
	     * in the denominator' case.
	     */

	    if (s2 % MP_DIGIT_BIT != 0) {
		int delta = MP_DIGIT_BIT - (s2 % MP_DIGIT_BIT);

	     */

	    return StrictInt64Conversion(&d, bw, b2, b5, s2, s5, k,
		    len, ilim, ilim1, decpt, endPtr);
	} else if (s5 == 0) {
	    /*
	     * The denominator is a power of 2, so we can replace division by
	     * digit shifts. First we round up s2 to a multiple of DIGIT_BIT,
	     * digit shifts. First we round up s2 to a multiple of MP_DIGIT_BIT,
	     * and adjust m2 and b2 accordingly. Then we launch into a version
	     * of the comparison that's specialized for the 'power of mp_digit
	     * in the denominator' case.
	     */

	    if (s2 % MP_DIGIT_BIT != 0) {
		int delta = MP_DIGIT_BIT - (s2 % MP_DIGIT_BIT);