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Overview
Comment:Various tommath/numeric related optimizations: - Remove the DD_STEEL formatter: it isn't used anywhere in Tcl, and not recommended. - Remove double limit-checks, which are already done inside mp_to_unsigned_bin_n()
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Timelines: family | ancestors | descendants | both | core-8-branch
Files: files | file ages | folders
SHA3-256: 5293802fe61d615fb577370ba1f31e061703d13965fc94e6f625dac9ab9d7104
User & Date: jan.nijtmans 2019-03-02 18:15:36
Context
2019-03-05
17:34
merge 8.6 (TIP#527, New measurement facilities in TCL: New command timerate, performance test suite) check-in: 2d254280f0 user: sebres tags: core-8-branch
2019-03-02
18:15
Various tommath/numeric related optimizations: - Remove the DD_STEEL formatter: it isn't used anywhe... check-in: 5293802fe6 user: jan.nijtmans tags: core-8-branch
17:21
Add build with -DTCL_UTF_MAX=6 to travis CI. Also fix 2 gcc compiler-warnings occurring with -DTCL_U... check-in: 9b2a385a0f user: jan.nijtmans tags: core-8-branch
Changes
Hide Diffs Unified Diffs Ignore Whitespace Patch

Changes to generic/tclBasic.c.

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	    }
	}
	break;
    case TCL_NUMBER_BIG:
	if (Tcl_GetBignumFromObj(interp, objv[1], &big) != TCL_OK) {
	    return TCL_ERROR;
	}
	if (SIGN(&big) == MP_NEG) {
	    mp_clear(&big);
	    goto negarg;
	}
	break;
    default:
	if (TclGetWideIntFromObj(interp, objv[1], &w) != TCL_OK) {
	    return TCL_ERROR;






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	    }
	}
	break;
    case TCL_NUMBER_BIG:
	if (Tcl_GetBignumFromObj(interp, objv[1], &big) != TCL_OK) {
	    return TCL_ERROR;
	}
	if (mp_isneg(&big)) {
	    mp_clear(&big);
	    goto negarg;
	}
	break;
    default:
	if (TclGetWideIntFromObj(interp, objv[1], &w) != TCL_OK) {
	    return TCL_ERROR;

Changes to generic/tclInt.h.

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				/* Procedure that unloads a loaded module */
};

/* Flags for conversion of doubles to digit strings */

#define TCL_DD_SHORTEST 		0x4
				/* Use the shortest possible string */
#define TCL_DD_STEELE   		0x5
				/* Use the original Steele&White algorithm */
#define TCL_DD_E_FORMAT 		0x2
				/* Use a fixed-length string of digits,
				 * suitable for E format*/
#define TCL_DD_F_FORMAT 		0x3
				/* Use a fixed number of digits after the
				 * decimal point, suitable for F format */

................................................................................
				/* Allow return of a shorter digit string
				 * if it converts losslessly */
#define TCL_DD_NO_QUICK 		0x8
				/* Debug flag: forbid quick FP conversion */

#define TCL_DD_CONVERSION_TYPE_MASK	0x3
				/* Mask to isolate the conversion type */
#define TCL_DD_STEELE0 			0x1
				/* 'Steele&White' after masking */
#define TCL_DD_SHORTEST0		0x0
				/* 'Shortest possible' after masking */

/*
 *----------------------------------------------------------------
 * Procedures shared among Tcl modules but not used by the outside world:
 *----------------------------------------------------------------
 */







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				/* Procedure that unloads a loaded module */
};

/* Flags for conversion of doubles to digit strings */

#define TCL_DD_SHORTEST 		0x4
				/* Use the shortest possible string */


#define TCL_DD_E_FORMAT 		0x2
				/* Use a fixed-length string of digits,
				 * suitable for E format*/
#define TCL_DD_F_FORMAT 		0x3
				/* Use a fixed number of digits after the
				 * decimal point, suitable for F format */

................................................................................
				/* Allow return of a shorter digit string
				 * if it converts losslessly */
#define TCL_DD_NO_QUICK 		0x8
				/* Debug flag: forbid quick FP conversion */

#define TCL_DD_CONVERSION_TYPE_MASK	0x3
				/* Mask to isolate the conversion type */





/*
 *----------------------------------------------------------------
 * Procedures shared among Tcl modules but not used by the outside world:
 *----------------------------------------------------------------
 */

Changes to generic/tclObj.c.

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	     * Must check for those bignum values that can fit in a long, even
	     * when auto-narrowing is enabled. Only those values in the signed
	     * long range get auto-narrowed to tclIntType, while all the
	     * values in the unsigned long range will fit in a long.
	     */

	    mp_int big;

	    UNPACK_BIGNUM(objPtr, big);
	    if ((size_t) big.used <= (CHAR_BIT * sizeof(unsigned long) + DIGIT_BIT - 1)
		    / DIGIT_BIT) {
		unsigned long scratch, value = 0, numBytes = sizeof(unsigned long);
		unsigned char *bytes = (unsigned char *) &scratch;


		if (mp_to_unsigned_bin_n(&big, bytes, &numBytes) == MP_OKAY) {
		    while (numBytes-- > 0) {
			value = (value << CHAR_BIT) | *bytes++;
		    }
		    if (big.sign) {
			if (value <= 1 + (unsigned long)LONG_MAX) {
			    *longPtr = - (long) value;
			    return TCL_OK;
			}
		    } else {
			if (value <= (unsigned long)ULONG_MAX) {
			    *longPtr = (long) value;
			    return TCL_OK;
			}
		    }
		}
	    }
#ifndef TCL_WIDE_INT_IS_LONG
	tooLarge:
#endif
	    if (interp != NULL) {
................................................................................
	if (objPtr->typePtr == &tclBignumType) {
	    /*
	     * Must check for those bignum values that can fit in a
	     * Tcl_WideInt, even when auto-narrowing is enabled.
	     */

	    mp_int big;

	    UNPACK_BIGNUM(objPtr, big);
	    if ((size_t) big.used <= (CHAR_BIT * sizeof(Tcl_WideInt)
		     + DIGIT_BIT - 1) / DIGIT_BIT) {
		Tcl_WideUInt value = 0;
		unsigned long numBytes = sizeof(Tcl_WideInt);
		Tcl_WideInt scratch;
		unsigned char *bytes = (unsigned char *) &scratch;


		if (mp_to_unsigned_bin_n(&big, bytes, &numBytes) == MP_OKAY) {
		    while (numBytes-- > 0) {
			value = (value << CHAR_BIT) | *bytes++;
		    }
		    if (big.sign) {
			if (value <= 1 + ~(Tcl_WideUInt)WIDE_MIN) {
			    *wideIntPtr = - (Tcl_WideInt) value;
			    return TCL_OK;
			}
		    } else {
			if (value <= (Tcl_WideUInt)WIDE_MAX) {
			    *wideIntPtr = (Tcl_WideInt) value;
			    return TCL_OK;
			}
		    }
		}
	    }
	    if (interp != NULL) {
		const char *s = "integer value too large to represent";
		Tcl_Obj *msg = Tcl_NewStringObj(s, -1);

................................................................................
 */

void
Tcl_SetBignumObj(
    Tcl_Obj *objPtr,		/* Object to set */
    mp_int *bignumValue)	/* Value to store */
{
    if (Tcl_IsShared(objPtr)) {
	Tcl_Panic("%s called with shared object", "Tcl_SetBignumObj");
    }
    if ((size_t) bignumValue->used
	    <= (CHAR_BIT * sizeof(Tcl_WideUInt) + DIGIT_BIT - 1) / DIGIT_BIT) {
	Tcl_WideUInt value = 0;
	unsigned long numBytes = sizeof(Tcl_WideUInt);
	Tcl_WideUInt scratch;
	unsigned char *bytes = (unsigned char *) &scratch;




	if (mp_to_unsigned_bin_n(bignumValue, bytes, &numBytes) != MP_OKAY) {
	    goto tooLargeForWide;
	}
	while (numBytes-- > 0) {
	    value = (value << CHAR_BIT) | *bytes++;
	}
	if (value > ((Tcl_WideUInt)WIDE_MAX + bignumValue->sign)) {
	    goto tooLargeForWide;
	}
	if (bignumValue->sign) {
	    TclSetIntObj(objPtr, -(Tcl_WideInt)value);
	} else {
	    TclSetIntObj(objPtr, (Tcl_WideInt)value);
	}
	mp_clear(bignumValue);
	return;
    }
  tooLargeForWide:
    TclInvalidateStringRep(objPtr);
    TclFreeIntRep(objPtr);
    TclSetBignumIntRep(objPtr, bignumValue);
}
 
/*






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	     * Must check for those bignum values that can fit in a long, even
	     * when auto-narrowing is enabled. Only those values in the signed
	     * long range get auto-narrowed to tclIntType, while all the
	     * values in the unsigned long range will fit in a long.
	     */

	    mp_int big;




	    unsigned long scratch, value = 0, numBytes = sizeof(unsigned long);
	    unsigned char *bytes = (unsigned char *) &scratch;

	    UNPACK_BIGNUM(objPtr, big);
	    if (mp_to_unsigned_bin_n(&big, bytes, &numBytes) == MP_OKAY) {
		while (numBytes-- > 0) {
			value = (value << CHAR_BIT) | *bytes++;
		}
		if (big.sign) {
		    if (value <= 1 + (unsigned long)LONG_MAX) {
			*longPtr = - (long) value;
			return TCL_OK;
		    }
		} else {
		    if (value <= (unsigned long)ULONG_MAX) {
			*longPtr = (long) value;
			return TCL_OK;

		    }
		}
	    }
#ifndef TCL_WIDE_INT_IS_LONG
	tooLarge:
#endif
	    if (interp != NULL) {
................................................................................
	if (objPtr->typePtr == &tclBignumType) {
	    /*
	     * Must check for those bignum values that can fit in a
	     * Tcl_WideInt, even when auto-narrowing is enabled.
	     */

	    mp_int big;




	    Tcl_WideUInt value = 0;
	    unsigned long numBytes = sizeof(Tcl_WideInt);
	    Tcl_WideInt scratch;
	    unsigned char *bytes = (unsigned char *) &scratch;

	    UNPACK_BIGNUM(objPtr, big);
	    if (mp_to_unsigned_bin_n(&big, bytes, &numBytes) == MP_OKAY) {
		while (numBytes-- > 0) {
		    value = (value << CHAR_BIT) | *bytes++;
		}
		if (big.sign) {
		    if (value <= 1 + ~(Tcl_WideUInt)WIDE_MIN) {
			*wideIntPtr = - (Tcl_WideInt) value;
			return TCL_OK;
		    }
		} else {
		    if (value <= (Tcl_WideUInt)WIDE_MAX) {
			*wideIntPtr = (Tcl_WideInt) value;
			return TCL_OK;

		    }
		}
	    }
	    if (interp != NULL) {
		const char *s = "integer value too large to represent";
		Tcl_Obj *msg = Tcl_NewStringObj(s, -1);

................................................................................
 */

void
Tcl_SetBignumObj(
    Tcl_Obj *objPtr,		/* Object to set */
    mp_int *bignumValue)	/* Value to store */
{





    Tcl_WideUInt value = 0;
    unsigned long numBytes = sizeof(Tcl_WideUInt);
    Tcl_WideUInt scratch;
    unsigned char *bytes = (unsigned char *) &scratch;

    if (Tcl_IsShared(objPtr)) {
	Tcl_Panic("%s called with shared object", "Tcl_SetBignumObj");
    }
    if (mp_to_unsigned_bin_n(bignumValue, bytes, &numBytes) != MP_OKAY) {
	goto tooLargeForWide;
    }
    while (numBytes-- > 0) {
	value = (value << CHAR_BIT) | *bytes++;
    }
    if (value > ((Tcl_WideUInt)WIDE_MAX + bignumValue->sign)) {
	goto tooLargeForWide;
    }
    if (bignumValue->sign) {
	TclSetIntObj(objPtr, -(Tcl_WideInt)value);
    } else {
	TclSetIntObj(objPtr, (Tcl_WideInt)value);
    }
    mp_clear(bignumValue);
    return;

  tooLargeForWide:
    TclInvalidateStringRep(objPtr);
    TclFreeIntRep(objPtr);
    TclSetBignumIntRep(objPtr, bignumValue);
}
 
/*

Changes to generic/tclStrToD.c.

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4344
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,
			    int *, char **);
static void		CastOutPowersOf2(int *, int *, int *);
static char *		ShorteningInt64Conversion(Double *, int, Tcl_WideUInt,
			    int, int, int, int, int, int, int, int, int,
			    int, int, int *, char **);
static char *		StrictInt64Conversion(Double *, int, 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, int, mp_int *);
static char *		ShorteningBignumConversionPowD(Double *dPtr,
			    int convType, 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(Double *dPtr, int convType,
			    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, int, mp_int *);
static char *		ShorteningBignumConversion(Double *dPtr, int convType,
			    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(Double *dPtr, int convType,
			    Tcl_WideUInt bw, int b2,
			    int s2, int s5, int k, int len,
			    int ilim, int ilim1, int *decpt,
			    char **endPtr);
static double		BignumToBiasedFrExp(const mp_int *big, int *machexp);
static double		Pow10TimesFrExp(int exponent, double fraction,
			    int *machexp);
................................................................................
 *	one too high.
 *
 *----------------------------------------------------------------------
 */

static inline void
SetPrecisionLimits(
    int convType,		/* Type of conversion: TCL_DD_SHORTEST,
				 * TCL_DD_STEELE0, TCL_DD_E_FMT,
				 * TCL_DD_F_FMT. */
    int k,			/* Floor(log10(number to convert)) */
    int *ndigitsPtr,		/* IN/OUT: Number of digits requested (will be
				 *         adjusted if needed). */
    int *iPtr,			/* OUT: Maximum number of digits to return. */
    int *iLimPtr,		/* OUT: Number of digits of significance if
				 *      the bignum method is used.*/
    int *iLim1Ptr)		/* OUT: Number of digits of significance if
				 *      the quick method is used. */
{
    switch (convType) {
    case TCL_DD_SHORTEST0:
    case TCL_DD_STEELE0:
	*iLimPtr = *iLim1Ptr = -1;
	*iPtr = 18;
	*ndigitsPtr = 0;
	break;
    case TCL_DD_E_FORMAT:
	if (*ndigitsPtr <= 0) {
	    *ndigitsPtr = 1;
	}
	*iLimPtr = *iLim1Ptr = *iPtr = *ndigitsPtr;
	break;
    case TCL_DD_F_FORMAT:
................................................................................
	*iLimPtr = *iPtr;
	*iLim1Ptr = *iPtr - 1;
	if (*iPtr <= 0) {
	    *iPtr = 1;
	}
	break;
    default:
	*iPtr = -1;
	*iLimPtr = -1;
	*iLim1Ptr = -1;
	Tcl_Panic("impossible conversion type in TclDoubleDigits");
    }
}
 
/*
 *----------------------------------------------------------------------
 *
 * BumpUp --
................................................................................
 *
 *----------------------------------------------------------------------
 */

static inline char *
ShorteningInt64Conversion(
    Double *dPtr,		/* Original number to convert. */
    int convType,		/* Type of conversion (shortest, Steele,
				 * E format, F format). */
    Tcl_WideUInt bw,		/* Integer significand. */
    int b2, int b5,		/* Scale factor for the significand in the
				 * numerator. */
    int m2plus, int m2minus, int m5,
				/* Scale factors for 1/2 ulp in the numerator
				 * (will be different if bw == 1. */
    int s2, int s5,		/* Scale factors for the denominator. */
................................................................................

	/*
	 * Does the current digit put us on the low side of the exact value
	 * but within within roundoff of being exact?
	 */

	if (b < mplus || (b == mplus
		&& convType != TCL_DD_STEELE0 && (dPtr->w.word1 & 1) == 0)) {
	    /*
	     * Make sure we shouldn't be rounding *up* instead, in case the
	     * next number above is closer.
	     */

	    if (2 * b > S || (2 * b == S && (digit & 1) != 0)) {
		++digit;
................................................................................

	/*
	 * Does one plus the current digit put us within roundoff of the
	 * number?
	 */

	if (b > S - mminus || (b == S - mminus
		&& convType != TCL_DD_STEELE0 && (dPtr->w.word1 & 1) == 0)) {
	    if (digit == 9) {
		*s++ = '9';
		s = BumpUp(s, retval, &k);
		break;
	    }
	    ++digit;
	    *s++ = '0' + digit;
................................................................................
 *
 *----------------------------------------------------------------------
 */

static inline char *
StrictInt64Conversion(
    Double *dPtr,		/* Original number to convert. */
    int convType,		/* Type of conversion (shortest, Steele,
				 * E format, F format). */
    Tcl_WideUInt bw,		/* Integer significand. */
    int b2, int b5,		/* Scale factor for the significand in the
				 * numerator. */
    int s2, int s5,		/* Scale factors for the denominator. */
    int k,			/* Number of output digits before the decimal
				 * point. */
    int len,			/* Number of digits to allocate. */
................................................................................
static inline int
ShouldBankerRoundUpPowD(
    mp_int *b,			/* Numerator of the fraction. */
    int sd,			/* Denominator is 2**(sd*DIGIT_BIT). */
    int isodd)			/* 1 if the digit is odd, 0 if even. */
{
    int i;
    static const mp_digit topbit = 1 << (DIGIT_BIT - 1);

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

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 convType,		/* Conversion type: STEELE defeats
				 * round-to-even (not sure why one wants to do
				 * this; I copied it from Gay). FIXME */
    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
................................................................................
    }
    for (i = sd-1; i >= 0; --i) {
				/* Check for ==s */
	if (temp->dp[i] != 0) {	/* > s */
	    return 1;
	}
    }
    if (convType == TCL_DD_STEELE0) {
				/* Biased rounding. */
	return 0;
    }
    return isodd;
}
 
/*
 *----------------------------------------------------------------------
 *
 * ShorteningBignumConversionPowD --
................................................................................
 *
 *----------------------------------------------------------------------
 */

static inline char *
ShorteningBignumConversionPowD(
    Double *dPtr,		/* Original number to convert. */
    int convType,		/* Type of conversion (shortest, Steele,
				 * E format, F format). */
    Tcl_WideUInt bw,		/* Integer significand. */
    int b2, int b5,		/* Scale factor for the significand in the
				 * numerator. */
    int m2plus, int m2minus, int m5,
				/* Scale factors for 1/2 ulp in the numerator
				 * (will be different if bw == 1). */
    int sd,			/* Scale factor for the denominator. */
................................................................................
	/*
	 * Does the current digit put us on the low side of the exact value
	 * but within within roundoff of being exact?
	 */

	r1 = mp_cmp_mag(&b, (m2plus > m2minus)? &mplus : &mminus);
	if (r1 == MP_LT || (r1 == MP_EQ
		&& convType != TCL_DD_STEELE0 && (dPtr->w.word1 & 1) == 0)) {
	    /*
	     * Make sure we shouldn't be rounding *up* instead, in case the
	     * next number above is closer.
	     */

	    if (ShouldBankerRoundUpPowD(&b, sd, digit&1)) {
		++digit;
................................................................................
	}

	/*
	 * Does one plus the current digit put us within roundoff of the
	 * number?
	 */

	if (ShouldBankerRoundUpToNextPowD(&b, &mminus, sd, convType,
		dPtr->w.word1 & 1, &temp)) {
	    if (digit == 9) {
		*s++ = '9';
		s = BumpUp(s, retval, &k);
		break;
	    }
	    ++digit;
................................................................................
 *
 *----------------------------------------------------------------------
 */

static inline char *
StrictBignumConversionPowD(
    Double *dPtr,		/* Original number to convert. */
    int convType,		/* Type of conversion (shortest, Steele,
				 * E format, F format). */
    Tcl_WideUInt bw,		/* Integer significand. */
    int b2, int b5,		/* Scale factor for the significand in the
				 * numerator. */
    int sd,			/* Scale factor for the denominator. */
    int k,			/* Number of output digits before the decimal
				 * point. */
    int len,			/* Number of digits to allocate. */
................................................................................
    char *retval = ckalloc(len + 1);
				/* Output buffer. */
    mp_int b;			/* Numerator of the fraction being
				 * converted. */
    mp_digit digit;		/* Current output digit. */
    char *s = retval;		/* Cursor in the output buffer. */
    int i;			/* Index in the output buffer. */
    mp_int temp;

    /*
     * b = bw * 2**b2 * 5**b5
     */

    TclInitBignumFromWideUInt(&b, bw);
    MulPow5(&b, b5, &b);
................................................................................
     */

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

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

    i = 1;
................................................................................
    }

    /*
     * Endgame - store the location of the decimal point and the end of the
     * string.
     */

    mp_clear_multi(&b, &temp, NULL);
    *s = '\0';
    *decpt = k;
    if (endPtr) {
	*endPtr = s;
    }
    return retval;
}
................................................................................

static inline int
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 convType,		/* Conversion type: STEELE0 defeats
				 * round-to-even. (Not sure why one would want
				 * this; I coped it from Gay). FIXME */
    int isodd,			/* 1 if the integer significand is odd. */
    mp_int *temp)		/* Work area needed for the calculation. */
{
    int r;


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


    mp_add(b, m, temp);
    r = mp_cmp_mag(temp, S);

    switch(r) {
    case MP_LT:
	return 0;
    case MP_EQ:
	if (convType == TCL_DD_STEELE0) {
	    return 0;
	} else {
	    return isodd;
	}
    case MP_GT:
	return 1;
    }
    Tcl_Panic("in ShouldBankerRoundUpToNext, trichotomy fails!");
    return 0;
}
 
................................................................................
 *
 *----------------------------------------------------------------------
 */

static inline char *
ShorteningBignumConversion(
    Double *dPtr,		/* Original number being converted. */
    int convType,		/* Conversion type. */
    Tcl_WideUInt bw,		/* Integer significand and exponent. */
    int b2,			/* Scale factor for the significand. */
    int m2plus, int m2minus,	/* Scale factors for 1/2 ulp in numerator. */
    int s2, int s5,		/* Scale factors for denominator. */
    int k,			/* Guessed position of the decimal point. */
    int len,			/* Size of the digit buffer to allocate. */
    int ilim,			/* Number of digits to convert if b >= s */
................................................................................
    char *s = retval;		/* Cursor in the return value. */
    mp_int b;			/* Numerator of the result. */
    mp_int mminus;		/* 1/2 ulp below the result. */
    mp_int mplus;		/* 1/2 ulp above the result. */
    mp_int S;			/* Denominator of the result. */
    mp_int dig;			/* Current digit of the result. */
    int digit;			/* Current digit of the result. */
    mp_int temp;		/* Work area. */
    int minit = 1;		/* Fudge factor for when we misguess k. */
    int i;
    int r1;

    /*
     * b = bw * 2**b2 * 5**b5
     * S = 2**s2 * 5*s5
................................................................................

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

    /*
     * Loop through the digits.
     */

    mp_init(&dig);
    i = 1;
................................................................................

	/*
	 * Does the current digit leave us with a remainder small enough to
	 * round to it?
	 */

	r1 = mp_cmp_mag(&b, (m2plus > m2minus)? &mplus : &mminus);
	if (r1 == MP_LT || (r1 == MP_EQ
		&& convType != TCL_DD_STEELE0 && (dPtr->w.word1 & 1) == 0)) {
	    mp_mul_2d(&b, 1, &b);
	    if (ShouldBankerRoundUp(&b, &S, digit&1)) {
		++digit;
		if (digit == 10) {
		    *s++ = '9';
		    s = BumpUp(s, retval, &k);
		    break;
................................................................................
	}

	/*
	 * Does the current digit leave us with a remainder large enough to
	 * commit to rounding up to the next higher digit?
	 */

	if (ShouldBankerRoundUpToNext(&b, &mminus, &S, convType,
		dPtr->w.word1 & 1, &temp)) {
	    ++digit;
	    if (digit == 10) {
		*s++ = '9';
		s = BumpUp(s, retval, &k);
		break;
	    }
	    *s++ = '0' + digit;
................................................................................
     * Endgame - store the location of the decimal point and the end of the
     * string.
     */

    if (m2plus > m2minus) {
	mp_clear(&mplus);
    }
    mp_clear_multi(&b, &mminus, &temp, &dig, &S, NULL);
    *s = '\0';
    *decpt = k;
    if (endPtr) {
	*endPtr = s;
    }
    return retval;
}
................................................................................
 *
 *----------------------------------------------------------------------
 */

static inline char *
StrictBignumConversion(
    Double *dPtr,		/* Original number being converted. */
    int convType,		/* Conversion type. */
    Tcl_WideUInt bw,		/* Integer significand and exponent. */
    int b2,			/* Scale factor for the significand. */
    int s2, int s5,		/* Scale factors for denominator. */
    int k,			/* Guessed position of the decimal point. */
    int len,			/* Size of the digit buffer to allocate. */
    int ilim,			/* Number of digits to convert if b >= s */
    int ilim1,			/* Number of digits to convert if b < s */
................................................................................
    char *retval = ckalloc(len+1);
				/* Buffer of digits to return. */
    char *s = retval;		/* Cursor in the return value. */
    mp_int b;			/* Numerator of the result. */
    mp_int S;			/* Denominator of the result. */
    mp_int dig;			/* Current digit of the result. */
    int digit;			/* Current digit of the result. */
    mp_int temp;		/* Work area. */
    int g;			/* Size of the current digit ground. */
    int i, j;

    /*
     * b = bw * 2**b2 * 5**b5
     * S = 2**s2 * 5*s5
     */

    mp_init_multi(&temp, &dig, NULL);
    TclInitBignumFromWideUInt(&b, bw);
    mp_mul_2d(&b, b2, &b);
    mp_init_set_int(&S, 1);
    MulPow5(&S, s5, &S); mp_mul_2d(&S, s2, &S);

    /*
     * Handle the case where we guess the position of the decimal point wrong.
................................................................................
    ++s;

    /*
     * Endgame - store the location of the decimal point and the end of the
     * string.
     */

    mp_clear_multi(&b, &S, &temp, &dig, NULL);
    *s = '\0';
    *decpt = k;
    if (endPtr) {
	*endPtr = s;
    }
    return retval;
}
................................................................................
 * according to the 'flags' argument. Valid values for 'flags' include:
 *	TCL_DD_SHORTEST - This is the default for floating point conversion if
 *		::tcl_precision is 0. It constructs the shortest string of
 *		digits that will reconvert to the given number when scanned.
 *		For floating point numbers that are exactly between two
 *		decimal numbers, it resolves using the 'round to even' rule.
 *		With this value, the 'ndigits' parameter is ignored.
 *	TCL_DD_STEELE - This value is not recommended and may be removed in
 *		the future. It follows the conversion algorithm outlined in
 *		"How to Print Floating-Point Numbers Accurately" by Guy
 *		L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90,
 *		pp. 112-126]. This rule has the effect of rendering 1e23 as
 *		9.9999999999999999e22 - which is a 'better' approximation in
 *		the sense that it will reconvert correctly even if a
 *		subsequent input conversion is 'round up' or 'round down'
 *		rather than 'round to nearest', but is surprising otherwise.
 *	TCL_DD_E_FORMAT - This value is used to prepare numbers for %e format
 *		conversion (or for default floating->string if tcl_precision
 *		is not 0). It constructs a string of at most 'ndigits' digits,
 *		choosing the one that is closest to the given number (and
 *		resolving ties with 'round to even').  It is allowed to return
 *		fewer than 'ndigits' if the number converts exactly; if the
 *		TCL_DD_E_FORMAT|TCL_DD_SHORTEN_FLAG is supplied instead, it
................................................................................
    int flags,			/* Conversion flags. */
    int *decpt,			/* OUTPUT: Position of the decimal point. */
    int *sign,			/* OUTPUT: 1 if the result is negative. */
    char **endPtr)		/* OUTPUT: If not NULL, receives a pointer to
				 *	   one character beyond the end of the
				 *	   returned string. */
{
    int convType = (flags & TCL_DD_CONVERSION_TYPE_MASK);
				/* Type of conversion being performed:
				 * TCL_DD_SHORTEST0, TCL_DD_STEELE0,
				 * TCL_DD_E_FORMAT, or TCL_DD_F_FORMAT. */
    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
				 * denormalized. */
    int k;			/* Estimate of floor(log10(d)). */
................................................................................

    ComputeScale(be, k, &b2, &b5, &s2, &s5);

    /*
     * Correct an incorrect caller-supplied 'ndigits'.  Also determine:
     *	i = The maximum number of decimal digits that will be returned in the
     *      formatted string.  This is k + 1 + ndigits for F format, 18 for
     *      shortest and Steele, and ndigits for E format.
     *  ilim = The number of significant digits to convert if k has been
     *         guessed correctly. This is -1 for shortest and Steele (which
     *         stop when all significance has been lost), 'ndigits' for E
     *         format, and 'k + 1 + ndigits' for F format.
     *  ilim1 = The minimum number of significant digits to convert if k has
     *	        been guessed 1 too high. This, too, is -1 for shortest and
     *	        Steele, and 'ndigits' for E format, but it's 'ndigits-1' for F
     *	        format.
     */

    SetPrecisionLimits(convType, k, &ndigits, &i, &ilim, &ilim1);

    /*
     * Try to do low-precision conversion in floating point rather than
     * resorting to expensive multiprecision arithmetic.
     */

    if (ilim >= 0 && ilim <= QUICK_MAX && !(flags & TCL_DD_NO_QUICK)) {
................................................................................
	     * If 10*2**s2*5**s5 == 2**(s2+1)+5**(s5+1) fits in a 64-bit word,
	     * then all our intermediate calculations can be done using exact
	     * 64-bit arithmetic with no need for expensive multiprecision
	     * operations. (This will be true for all numbers in the range
	     * [1.0e-3 .. 1.0e+24]).
	     */

	    return ShorteningInt64Conversion(&d, convType, 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,
	     * and adjust m2 and b2 accordingly. Then we launch into a version
	     * of the comparison that's specialized for the 'power of mp_digit
................................................................................
		int delta = DIGIT_BIT - (s2 % DIGIT_BIT);

		b2 += delta;
		m2plus += delta;
		m2minus += delta;
		s2 += delta;
	    }
	    return ShorteningBignumConversionPowD(&d, convType, bw, b2, b5,
		    m2plus, m2minus, m5, s2/DIGIT_BIT, k, len, ilim, ilim1,
		    decpt, endPtr);
	} else {
	    /*
	     * Alas, there's no helpful special case; use full-up bignum
	     * arithmetic for the conversion.
	     */

	    return ShorteningBignumConversion(&d, convType, bw, b2, m2plus,
		    m2minus, s2, s5, k, len, ilim, ilim1, decpt, endPtr);
	}
    } else {
	/*
	 * Non-shortening conversion.
	 */

................................................................................
	    /*
	     * If 10*2**s2*5**s5 == 2**(s2+1)+5**(s5+1) fits in a 64-bit word,
	     * then all our intermediate calculations can be done using exact
	     * 64-bit arithmetic with no need for expensive multiprecision
	     * operations.
	     */

	    return StrictInt64Conversion(&d, convType, 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,
	     * and adjust m2 and b2 accordingly. Then we launch into a version
	     * of the comparison that's specialized for the 'power of mp_digit
................................................................................

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

		b2 += delta;
		s2 += delta;
	    }
	    return StrictBignumConversionPowD(&d, convType, bw, b2, b5,
		    s2/DIGIT_BIT, k, len, ilim, ilim1, decpt, endPtr);
	} else {
	    /*
	     * There are no helpful special cases, but at least we know in
	     * advance how many digits we will convert. We can run the
	     * conversion in steps of DIGIT_GROUP digits, so as to have many
	     * fewer mp_int divisions.
	     */

	    return StrictBignumConversion(&d, convType, bw, b2, s2, s5, k,
		    len, ilim, ilim1, decpt, endPtr);
	}
    }
}
 
/*
 *----------------------------------------------------------------------






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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,
			    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(Double *, 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 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(Double *dPtr,
			    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 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(Double *dPtr,
			    Tcl_WideUInt bw, int b2,
			    int s2, int s5, int k, int len,
			    int ilim, int ilim1, int *decpt,
			    char **endPtr);
static double		BignumToBiasedFrExp(const mp_int *big, int *machexp);
static double		Pow10TimesFrExp(int exponent, double fraction,
			    int *machexp);
................................................................................
 *	one too high.
 *
 *----------------------------------------------------------------------
 */

static inline void
SetPrecisionLimits(
    int flags,		/* Type of conversion: TCL_DD_SHORTEST,
				 * TCL_DD_E_FMT, TCL_DD_F_FMT. */

    int k,			/* Floor(log10(number to convert)) */
    int *ndigitsPtr,		/* IN/OUT: Number of digits requested (will be
				 *         adjusted if needed). */
    int *iPtr,			/* OUT: Maximum number of digits to return. */
    int *iLimPtr,		/* OUT: Number of digits of significance if
				 *      the bignum method is used.*/
    int *iLim1Ptr)		/* OUT: Number of digits of significance if
				 *      the quick method is used. */
{
    switch (flags & TCL_DD_CONVERSION_TYPE_MASK) {






    case TCL_DD_E_FORMAT:
	if (*ndigitsPtr <= 0) {
	    *ndigitsPtr = 1;
	}
	*iLimPtr = *iLim1Ptr = *iPtr = *ndigitsPtr;
	break;
    case TCL_DD_F_FORMAT:
................................................................................
	*iLimPtr = *iPtr;
	*iLim1Ptr = *iPtr - 1;
	if (*iPtr <= 0) {
	    *iPtr = 1;
	}
	break;
    default:
	*iLimPtr = *iLim1Ptr = -1;
	*iPtr = 18;
	*ndigitsPtr = 0;
	break;
    }
}
 
/*
 *----------------------------------------------------------------------
 *
 * BumpUp --
................................................................................
 *
 *----------------------------------------------------------------------
 */

static inline char *
ShorteningInt64Conversion(
    Double *dPtr,		/* Original number to convert. */


    Tcl_WideUInt bw,		/* Integer significand. */
    int b2, int b5,		/* Scale factor for the significand in the
				 * numerator. */
    int m2plus, int m2minus, int m5,
				/* Scale factors for 1/2 ulp in the numerator
				 * (will be different if bw == 1. */
    int s2, int s5,		/* Scale factors for the denominator. */
................................................................................

	/*
	 * Does the current digit put us on the low side of the exact value
	 * but within within roundoff of being exact?
	 */

	if (b < mplus || (b == mplus
		&& (dPtr->w.word1 & 1) == 0)) {
	    /*
	     * Make sure we shouldn't be rounding *up* instead, in case the
	     * next number above is closer.
	     */

	    if (2 * b > S || (2 * b == S && (digit & 1) != 0)) {
		++digit;
................................................................................

	/*
	 * Does one plus the current digit put us within roundoff of the
	 * number?
	 */

	if (b > S - mminus || (b == S - mminus
		&& (dPtr->w.word1 & 1) == 0)) {
	    if (digit == 9) {
		*s++ = '9';
		s = BumpUp(s, retval, &k);
		break;
	    }
	    ++digit;
	    *s++ = '0' + digit;
................................................................................
 *
 *----------------------------------------------------------------------
 */

static inline char *
StrictInt64Conversion(
    Double *dPtr,		/* Original number to convert. */


    Tcl_WideUInt bw,		/* Integer significand. */
    int b2, int b5,		/* Scale factor for the significand in the
				 * numerator. */
    int s2, int s5,		/* Scale factors for the denominator. */
    int k,			/* Number of output digits before the decimal
				 * point. */
    int len,			/* Number of digits to allocate. */
................................................................................
static inline int
ShouldBankerRoundUpPowD(
    mp_int *b,			/* Numerator of the fraction. */
    int sd,			/* Denominator is 2**(sd*DIGIT_BIT). */
    int isodd)			/* 1 if the digit is odd, 0 if even. */
{
    int i;
    static const mp_digit topbit = ((mp_digit)1) << (DIGIT_BIT - 1);

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

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 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
................................................................................
    }
    for (i = sd-1; i >= 0; --i) {
				/* Check for ==s */
	if (temp->dp[i] != 0) {	/* > s */
	    return 1;
	}
    }




    return isodd;
}
 
/*
 *----------------------------------------------------------------------
 *
 * ShorteningBignumConversionPowD --
................................................................................
 *
 *----------------------------------------------------------------------
 */

static inline char *
ShorteningBignumConversionPowD(
    Double *dPtr,		/* Original number to convert. */


    Tcl_WideUInt bw,		/* Integer significand. */
    int b2, int b5,		/* Scale factor for the significand in the
				 * numerator. */
    int m2plus, int m2minus, int m5,
				/* Scale factors for 1/2 ulp in the numerator
				 * (will be different if bw == 1). */
    int sd,			/* Scale factor for the denominator. */
................................................................................
	/*
	 * Does the current digit put us on the low side of the exact value
	 * but within within roundoff of being exact?
	 */

	r1 = mp_cmp_mag(&b, (m2plus > m2minus)? &mplus : &mminus);
	if (r1 == MP_LT || (r1 == MP_EQ
		&& (dPtr->w.word1 & 1) == 0)) {
	    /*
	     * Make sure we shouldn't be rounding *up* instead, in case the
	     * next number above is closer.
	     */

	    if (ShouldBankerRoundUpPowD(&b, sd, digit&1)) {
		++digit;
................................................................................
	}

	/*
	 * Does one plus the current digit put us within roundoff of the
	 * number?
	 */

	if (ShouldBankerRoundUpToNextPowD(&b, &mminus, sd,
		dPtr->w.word1 & 1, &temp)) {
	    if (digit == 9) {
		*s++ = '9';
		s = BumpUp(s, retval, &k);
		break;
	    }
	    ++digit;
................................................................................
 *
 *----------------------------------------------------------------------
 */

static inline char *
StrictBignumConversionPowD(
    Double *dPtr,		/* Original number to convert. */


    Tcl_WideUInt bw,		/* Integer significand. */
    int b2, int b5,		/* Scale factor for the significand in the
				 * numerator. */
    int sd,			/* Scale factor for the denominator. */
    int k,			/* Number of output digits before the decimal
				 * point. */
    int len,			/* Number of digits to allocate. */
................................................................................
    char *retval = ckalloc(len + 1);
				/* Output buffer. */
    mp_int b;			/* Numerator of the fraction being
				 * converted. */
    mp_digit digit;		/* Current output digit. */
    char *s = retval;		/* Cursor in the output buffer. */
    int i;			/* Index in the output buffer. */


    /*
     * b = bw * 2**b2 * 5**b5
     */

    TclInitBignumFromWideUInt(&b, bw);
    MulPow5(&b, b5, &b);
................................................................................
     */

    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)
     * by mp_digit extraction.
     */

    i = 1;
................................................................................
    }

    /*
     * Endgame - store the location of the decimal point and the end of the
     * string.
     */

    mp_clear(&b);
    *s = '\0';
    *decpt = k;
    if (endPtr) {
	*endPtr = s;
    }
    return retval;
}
................................................................................

static inline int
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. */

{
    int r;
    mp_int temp;

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

    mp_init(&temp);
    mp_add(b, m, &temp);
    r = mp_cmp_mag(&temp, S);
    mp_clear(&temp);
    switch(r) {
    case MP_LT:
	return 0;
    case MP_EQ:



	return isodd;

    case MP_GT:
	return 1;
    }
    Tcl_Panic("in ShouldBankerRoundUpToNext, trichotomy fails!");
    return 0;
}
 
................................................................................
 *
 *----------------------------------------------------------------------
 */

static inline char *
ShorteningBignumConversion(
    Double *dPtr,		/* Original number being converted. */

    Tcl_WideUInt bw,		/* Integer significand and exponent. */
    int b2,			/* Scale factor for the significand. */
    int m2plus, int m2minus,	/* Scale factors for 1/2 ulp in numerator. */
    int s2, int s5,		/* Scale factors for denominator. */
    int k,			/* Guessed position of the decimal point. */
    int len,			/* Size of the digit buffer to allocate. */
    int ilim,			/* Number of digits to convert if b >= s */
................................................................................
    char *s = retval;		/* Cursor in the return value. */
    mp_int b;			/* Numerator of the result. */
    mp_int mminus;		/* 1/2 ulp below the result. */
    mp_int mplus;		/* 1/2 ulp above the result. */
    mp_int S;			/* Denominator of the result. */
    mp_int dig;			/* Current digit of the result. */
    int digit;			/* Current digit of the result. */

    int minit = 1;		/* Fudge factor for when we misguess k. */
    int i;
    int r1;

    /*
     * b = bw * 2**b2 * 5**b5
     * S = 2**s2 * 5*s5
................................................................................

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


    /*
     * Loop through the digits.
     */

    mp_init(&dig);
    i = 1;
................................................................................

	/*
	 * Does the current digit leave us with a remainder small enough to
	 * round to it?
	 */

	r1 = mp_cmp_mag(&b, (m2plus > m2minus)? &mplus : &mminus);
	if (r1 == MP_LT || (r1 == MP_EQ && (dPtr->w.word1 & 1) == 0)) {

	    mp_mul_2d(&b, 1, &b);
	    if (ShouldBankerRoundUp(&b, &S, digit&1)) {
		++digit;
		if (digit == 10) {
		    *s++ = '9';
		    s = BumpUp(s, retval, &k);
		    break;
................................................................................
	}

	/*
	 * Does the current digit leave us with a remainder large enough to
	 * commit to rounding up to the next higher digit?
	 */

	if (ShouldBankerRoundUpToNext(&b, &mminus, &S,
		dPtr->w.word1 & 1)) {
	    ++digit;
	    if (digit == 10) {
		*s++ = '9';
		s = BumpUp(s, retval, &k);
		break;
	    }
	    *s++ = '0' + digit;
................................................................................
     * Endgame - store the location of the decimal point and the end of the
     * string.
     */

    if (m2plus > m2minus) {
	mp_clear(&mplus);
    }
    mp_clear_multi(&b, &mminus, &dig, &S, NULL);
    *s = '\0';
    *decpt = k;
    if (endPtr) {
	*endPtr = s;
    }
    return retval;
}
................................................................................
 *
 *----------------------------------------------------------------------
 */

static inline char *
StrictBignumConversion(
    Double *dPtr,		/* Original number being converted. */

    Tcl_WideUInt bw,		/* Integer significand and exponent. */
    int b2,			/* Scale factor for the significand. */
    int s2, int s5,		/* Scale factors for denominator. */
    int k,			/* Guessed position of the decimal point. */
    int len,			/* Size of the digit buffer to allocate. */
    int ilim,			/* Number of digits to convert if b >= s */
    int ilim1,			/* Number of digits to convert if b < s */
................................................................................
    char *retval = ckalloc(len+1);
				/* Buffer of digits to return. */
    char *s = retval;		/* Cursor in the return value. */
    mp_int b;			/* Numerator of the result. */
    mp_int S;			/* Denominator of the result. */
    mp_int dig;			/* Current digit of the result. */
    int digit;			/* Current digit of the result. */

    int g;			/* Size of the current digit ground. */
    int i, j;

    /*
     * b = bw * 2**b2 * 5**b5
     * S = 2**s2 * 5*s5
     */

    mp_init_multi(&dig, NULL);
    TclInitBignumFromWideUInt(&b, bw);
    mp_mul_2d(&b, b2, &b);
    mp_init_set_int(&S, 1);
    MulPow5(&S, s5, &S); mp_mul_2d(&S, s2, &S);

    /*
     * Handle the case where we guess the position of the decimal point wrong.
................................................................................
    ++s;

    /*
     * Endgame - store the location of the decimal point and the end of the
     * string.
     */

    mp_clear_multi(&b, &S, &dig, NULL);
    *s = '\0';
    *decpt = k;
    if (endPtr) {
	*endPtr = s;
    }
    return retval;
}
................................................................................
 * according to the 'flags' argument. Valid values for 'flags' include:
 *	TCL_DD_SHORTEST - This is the default for floating point conversion if
 *		::tcl_precision is 0. It constructs the shortest string of
 *		digits that will reconvert to the given number when scanned.
 *		For floating point numbers that are exactly between two
 *		decimal numbers, it resolves using the 'round to even' rule.
 *		With this value, the 'ndigits' parameter is ignored.









 *	TCL_DD_E_FORMAT - This value is used to prepare numbers for %e format
 *		conversion (or for default floating->string if tcl_precision
 *		is not 0). It constructs a string of at most 'ndigits' digits,
 *		choosing the one that is closest to the given number (and
 *		resolving ties with 'round to even').  It is allowed to return
 *		fewer than 'ndigits' if the number converts exactly; if the
 *		TCL_DD_E_FORMAT|TCL_DD_SHORTEN_FLAG is supplied instead, it
................................................................................
    int flags,			/* Conversion flags. */
    int *decpt,			/* OUTPUT: Position of the decimal point. */
    int *sign,			/* OUTPUT: 1 if the result is negative. */
    char **endPtr)		/* OUTPUT: If not NULL, receives a pointer to
				 *	   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
				 * denormalized. */
    int k;			/* Estimate of floor(log10(d)). */
................................................................................

    ComputeScale(be, k, &b2, &b5, &s2, &s5);

    /*
     * Correct an incorrect caller-supplied 'ndigits'.  Also determine:
     *	i = The maximum number of decimal digits that will be returned in the
     *      formatted string.  This is k + 1 + ndigits for F format, 18 for
     *      shortest, and ndigits for E format.
     *  ilim = The number of significant digits to convert if k has been
     *         guessed correctly. This is -1 for shortest (which
     *         stop when all significance has been lost), 'ndigits' for E
     *         format, and 'k + 1 + ndigits' for F format.
     *  ilim1 = The minimum number of significant digits to convert if k has
     *	        been guessed 1 too high. This, too, is -1 for shortest,
     *	        and 'ndigits' for E format, but it's 'ndigits-1' for F
     *	        format.
     */

    SetPrecisionLimits(flags, k, &ndigits, &i, &ilim, &ilim1);

    /*
     * Try to do low-precision conversion in floating point rather than
     * resorting to expensive multiprecision arithmetic.
     */

    if (ilim >= 0 && ilim <= QUICK_MAX && !(flags & TCL_DD_NO_QUICK)) {
................................................................................
	     * If 10*2**s2*5**s5 == 2**(s2+1)+5**(s5+1) fits in a 64-bit word,
	     * then all our intermediate calculations can be done using exact
	     * 64-bit arithmetic with no need for expensive multiprecision
	     * operations. (This will be true for all numbers in the range
	     * [1.0e-3 .. 1.0e+24]).
	     */

	    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,
	     * and adjust m2 and b2 accordingly. Then we launch into a version
	     * of the comparison that's specialized for the 'power of mp_digit
................................................................................
		int delta = DIGIT_BIT - (s2 % DIGIT_BIT);

		b2 += delta;
		m2plus += delta;
		m2minus += delta;
		s2 += delta;
	    }
	    return ShorteningBignumConversionPowD(&d, bw, b2, b5,
		    m2plus, m2minus, m5, s2/DIGIT_BIT, k, len, ilim, ilim1,
		    decpt, endPtr);
	} else {
	    /*
	     * Alas, there's no helpful special case; use full-up bignum
	     * arithmetic for the conversion.
	     */

	    return ShorteningBignumConversion(&d, bw, b2, m2plus,
		    m2minus, s2, s5, k, len, ilim, ilim1, decpt, endPtr);
	}
    } else {
	/*
	 * Non-shortening conversion.
	 */

................................................................................
	    /*
	     * If 10*2**s2*5**s5 == 2**(s2+1)+5**(s5+1) fits in a 64-bit word,
	     * then all our intermediate calculations can be done using exact
	     * 64-bit arithmetic with no need for expensive multiprecision
	     * operations.
	     */

	    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,
	     * and adjust m2 and b2 accordingly. Then we launch into a version
	     * of the comparison that's specialized for the 'power of mp_digit
................................................................................

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

		b2 += delta;
		s2 += delta;
	    }
	    return StrictBignumConversionPowD(&d, bw, b2, b5,
		    s2/DIGIT_BIT, k, len, ilim, ilim1, decpt, endPtr);
	} else {
	    /*
	     * There are no helpful special cases, but at least we know in
	     * advance how many digits we will convert. We can run the
	     * conversion in steps of DIGIT_GROUP digits, so as to have many
	     * fewer mp_int divisions.
	     */

	    return StrictBignumConversion(&d, bw, b2, s2, s5, k,
		    len, ilim, ilim1, decpt, endPtr);
	}
    }
}
 
/*
 *----------------------------------------------------------------------

Changes to generic/tclTest.c.

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 *
 * Usage:
 *	testdoubledigits fpval ndigits type ?shorten"
 *
 * Parameters:
 *	fpval - Floating-point value to format.
 *	ndigits - Digit count to request from Tcl_DoubleDigits
 *	type - One of 'shortest', 'Steele', 'e', 'f'
 *	shorten - Indicates that the 'shorten' flag should be passed in.
 *
 *-----------------------------------------------------------------------------
 */

static int
TestdoubledigitsObjCmd(void *unused,
................................................................................
		       int objc,
				/* Parameter count */
		       Tcl_Obj* const objv[])
				/* Parameter vector */
{
    static const char* options[] = {
	"shortest",
	"Steele",
	"e",
	"f",
	NULL
    };
    static const int types[] = {
	TCL_DD_SHORTEST,
	TCL_DD_STEELE,
	TCL_DD_E_FORMAT,
	TCL_DD_F_FORMAT
    };

    const Tcl_ObjType* doubleType;
    double d;
    int status;






|







 







<






<







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 *
 * Usage:
 *	testdoubledigits fpval ndigits type ?shorten"
 *
 * Parameters:
 *	fpval - Floating-point value to format.
 *	ndigits - Digit count to request from Tcl_DoubleDigits
 *	type - One of 'shortest', 'e', 'f'
 *	shorten - Indicates that the 'shorten' flag should be passed in.
 *
 *-----------------------------------------------------------------------------
 */

static int
TestdoubledigitsObjCmd(void *unused,
................................................................................
		       int objc,
				/* Parameter count */
		       Tcl_Obj* const objv[])
				/* Parameter vector */
{
    static const char* options[] = {
	"shortest",

	"e",
	"f",
	NULL
    };
    static const int types[] = {
	TCL_DD_SHORTEST,

	TCL_DD_E_FORMAT,
	TCL_DD_F_FORMAT
    };

    const Tcl_ObjType* doubleType;
    double d;
    int status;