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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
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SHA3-256: 5293802fe61d615fb577370ba1f31e061703d13965fc94e6f625dac9ab9d7104
User & Date: jan.nijtmans 2019-03-02 18:15:36.228
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
Unified Diff 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 */

#define TCL_DD_SHORTEN_FLAG 		0x4
				/* 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 */

#define TCL_DD_SHORTEN_FLAG 		0x4
				/* 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) {







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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) {
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	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);








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	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);

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 */

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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 */

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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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);







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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);
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 *	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:
	*iPtr = *ndigitsPtr + k + 1;
	*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 --







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2419
2420
2421
2422
2423
2424






2425
2426
2427
2428
2429
2430
2431
2432
2433
2434
2435
2436
2437
2438
2439
2440
2441
2442
2443
2444
2445
2446
2447
2448
2449
2450
 *	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:
	*iPtr = *ndigitsPtr + k + 1;
	*iLimPtr = *iPtr;
	*iLim1Ptr = *iPtr - 1;
	if (*iPtr <= 0) {
	    *iPtr = 1;
	}
	break;
    default:
	*iLimPtr = *iLim1Ptr = -1;
	*iPtr = 18;
	*ndigitsPtr = 0;
	break;
    }
}

/*
 *----------------------------------------------------------------------
 *
 * BumpUp --
2873
2874
2875
2876
2877
2878
2879
2880
2881
2882
2883
2884
2885
2886
2887
2888
 *
 *----------------------------------------------------------------------
 */

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. */







<
<







2866
2867
2868
2869
2870
2871
2872


2873
2874
2875
2876
2877
2878
2879
 *
 *----------------------------------------------------------------------
 */

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. */
2941
2942
2943
2944
2945
2946
2947
2948
2949
2950
2951
2952
2953
2954
2955

	/*
	 * 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;







|







2932
2933
2934
2935
2936
2937
2938
2939
2940
2941
2942
2943
2944
2945
2946

	/*
	 * 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;
2970
2971
2972
2973
2974
2975
2976
2977
2978
2979
2980
2981
2982
2983
2984

	/*
	 * 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;







|







2961
2962
2963
2964
2965
2966
2967
2968
2969
2970
2971
2972
2973
2974
2975

	/*
	 * 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;
3042
3043
3044
3045
3046
3047
3048
3049
3050
3051
3052
3053
3054
3055
3056
3057
 *
 *----------------------------------------------------------------------
 */

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. */







<
<







3033
3034
3035
3036
3037
3038
3039


3040
3041
3042
3043
3044
3045
3046
 *
 *----------------------------------------------------------------------
 */

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. */
3152
3153
3154
3155
3156
3157
3158
3159
3160
3161
3162
3163
3164
3165
3166
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;
    }







|







3141
3142
3143
3144
3145
3146
3147
3148
3149
3150
3151
3152
3153
3154
3155
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;
    }
3188
3189
3190
3191
3192
3193
3194
3195
3196
3197
3198
3199
3200
3201
3202
3203
3204
 */

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







<
<
<







3177
3178
3179
3180
3181
3182
3183



3184
3185
3186
3187
3188
3189
3190
 */

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
3216
3217
3218
3219
3220
3221
3222
3223
3224
3225
3226
3227
3228
3229
3230
3231
3232
3233
    }
    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 --







<
<
<
<







3202
3203
3204
3205
3206
3207
3208




3209
3210
3211
3212
3213
3214
3215
    }
    for (i = sd-1; i >= 0; --i) {
				/* Check for ==s */
	if (temp->dp[i] != 0) {	/* > s */
	    return 1;
	}
    }




    return isodd;
}

/*
 *----------------------------------------------------------------------
 *
 * ShorteningBignumConversionPowD --
3249
3250
3251
3252
3253
3254
3255
3256
3257
3258
3259
3260
3261
3262
3263
3264
 *
 *----------------------------------------------------------------------
 */

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. */







<
<







3231
3232
3233
3234
3235
3236
3237


3238
3239
3240
3241
3242
3243
3244
 *
 *----------------------------------------------------------------------
 */

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. */
3336
3337
3338
3339
3340
3341
3342
3343
3344
3345
3346
3347
3348
3349
3350
	/*
	 * 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;







|







3316
3317
3318
3319
3320
3321
3322
3323
3324
3325
3326
3327
3328
3329
3330
	/*
	 * 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;
3364
3365
3366
3367
3368
3369
3370
3371
3372
3373
3374
3375
3376
3377
3378
	}

	/*
	 * 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;







|







3344
3345
3346
3347
3348
3349
3350
3351
3352
3353
3354
3355
3356
3357
3358
	}

	/*
	 * 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;
3442
3443
3444
3445
3446
3447
3448
3449
3450
3451
3452
3453
3454
3455
3456
3457
3458
3459
3460
3461
3462
3463
3464
3465
3466
3467
3468
3469
3470
3471
3472
3473
3474
3475
3476
3477
3478
3479
3480
3481
3482
3483
3484
3485
3486
3487
3488
3489
3490
3491
3492
3493
3494
3495
3496
3497
 *
 *----------------------------------------------------------------------
 */

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. */
    int ilim,			/* Number of digits to convert if b >= s */
    int ilim1,			/* Number of digits to convert if b < s */
    int *decpt,			/* OUTPUT: Position of the decimal point. */
    char **endPtr)		/* OUTPUT: Position of the terminal '\0' at
				 *	   the end of the returned string. */
{
    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);
    mp_mul_2d(&b, b2, &b);

    /*
     * Adjust if the logarithm was guessed wrong.
     */

    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;







<
<




















<


















<







3422
3423
3424
3425
3426
3427
3428


3429
3430
3431
3432
3433
3434
3435
3436
3437
3438
3439
3440
3441
3442
3443
3444
3445
3446
3447
3448

3449
3450
3451
3452
3453
3454
3455
3456
3457
3458
3459
3460
3461
3462
3463
3464
3465
3466

3467
3468
3469
3470
3471
3472
3473
 *
 *----------------------------------------------------------------------
 */

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. */
    int ilim,			/* Number of digits to convert if b >= s */
    int ilim1,			/* Number of digits to convert if b < s */
    int *decpt,			/* OUTPUT: Position of the decimal point. */
    char **endPtr)		/* OUTPUT: Position of the terminal '\0' at
				 *	   the end of the returned string. */
{
    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);
    mp_mul_2d(&b, b2, &b);

    /*
     * Adjust if the logarithm was guessed wrong.
     */

    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;
3532
3533
3534
3535
3536
3537
3538
3539
3540
3541
3542
3543
3544
3545
3546
    }

    /*
     * 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;
}







|







3508
3509
3510
3511
3512
3513
3514
3515
3516
3517
3518
3519
3520
3521
3522
    }

    /*
     * 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;
}
3596
3597
3598
3599
3600
3601
3602
3603
3604
3605
3606
3607
3608
3609

3610
3611
3612
3613
3614

3615
3616

3617
3618
3619
3620
3621
3622
3623
3624
3625
3626
3627
3628
3629
3630
3631
3632

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;
}








<
<
<
|
<


>





>
|
|
>




<
<
<
|
<







3572
3573
3574
3575
3576
3577
3578



3579

3580
3581
3582
3583
3584
3585
3586
3587
3588
3589
3590
3591
3592
3593
3594
3595



3596

3597
3598
3599
3600
3601
3602
3603

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;
}

3647
3648
3649
3650
3651
3652
3653
3654
3655
3656
3657
3658
3659
3660
3661
3662
3663
3664
3665
3666
3667
3668
3669
3670
3671
3672
3673
3674
3675
3676
3677
3678
3679
3680
3681
3682
 *
 *----------------------------------------------------------------------
 */

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 */
    int ilim1,			/* Number of digits to convert if b < s */
    int *decpt,			/* OUTPUT: Position of the decimal point. */
    char **endPtr)		/* OUTPUT: Pointer to the end of the number */
{
    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 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







<




















<







3618
3619
3620
3621
3622
3623
3624

3625
3626
3627
3628
3629
3630
3631
3632
3633
3634
3635
3636
3637
3638
3639
3640
3641
3642
3643
3644

3645
3646
3647
3648
3649
3650
3651
 *
 *----------------------------------------------------------------------
 */

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 */
    int ilim1,			/* Number of digits to convert if b < s */
    int *decpt,			/* OUTPUT: Position of the decimal point. */
    char **endPtr)		/* OUTPUT: Pointer to the end of the number */
{
    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 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
3704
3705
3706
3707
3708
3709
3710
3711
3712
3713
3714
3715
3716
3717
3718
3719
3720
3721
3722
3723
3724
3725
3726
3727
3728
3729
3730
3731
3732
3733
3734
3735
3736
3737
3738
3739
3740
3741
3742
3743
3744
3745
3746
3747
3748
3749
3750
3751
3752
3753
3754
3755
3756
3757
3758
3759
3760

    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;
    for (;;) {
	mp_div(&b, &S, &dig, &b);
	if (dig.used > 1 || dig.dp[0] >= 10) {
	    Tcl_Panic("wrong digit!");
	}
	digit = dig.dp[0];

	/*
	 * 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;
		}
	    }
	    *s++ = '0' + digit;
	    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;







<




















|
<


















|
|







3673
3674
3675
3676
3677
3678
3679

3680
3681
3682
3683
3684
3685
3686
3687
3688
3689
3690
3691
3692
3693
3694
3695
3696
3697
3698
3699
3700

3701
3702
3703
3704
3705
3706
3707
3708
3709
3710
3711
3712
3713
3714
3715
3716
3717
3718
3719
3720
3721
3722
3723
3724
3725
3726
3727

    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;
    for (;;) {
	mp_div(&b, &S, &dig, &b);
	if (dig.used > 1 || dig.dp[0] >= 10) {
	    Tcl_Panic("wrong digit!");
	}
	digit = dig.dp[0];

	/*
	 * 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;
		}
	    }
	    *s++ = '0' + digit;
	    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;
3833
3834
3835
3836
3837
3838
3839
3840
3841
3842
3843
3844
3845
3846
3847
     * 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;
}







|







3800
3801
3802
3803
3804
3805
3806
3807
3808
3809
3810
3811
3812
3813
3814
     * 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;
}
3863
3864
3865
3866
3867
3868
3869
3870
3871
3872
3873
3874
3875
3876
3877
3878
3879
3880
3881
3882
3883
3884
3885
3886
3887
3888
3889
3890
3891
3892
3893
3894
3895
3896
3897
3898
3899
3900
3901
3902
3903
3904
 *
 *----------------------------------------------------------------------
 */

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 */
    int *decpt,			/* OUTPUT: Position of the decimal point. */
    char **endPtr)		/* OUTPUT: Pointer to the end of the number */
{
    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.







<

















<








|







3830
3831
3832
3833
3834
3835
3836

3837
3838
3839
3840
3841
3842
3843
3844
3845
3846
3847
3848
3849
3850
3851
3852
3853

3854
3855
3856
3857
3858
3859
3860
3861
3862
3863
3864
3865
3866
3867
3868
3869
 *
 *----------------------------------------------------------------------
 */

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 */
    int *decpt,			/* OUTPUT: Position of the decimal point. */
    char **endPtr)		/* OUTPUT: Pointer to the end of the number */
{
    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.
3997
3998
3999
4000
4001
4002
4003
4004
4005
4006
4007
4008
4009
4010
4011
    ++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;
}







|







3962
3963
3964
3965
3966
3967
3968
3969
3970
3971
3972
3973
3974
3975
3976
    ++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;
}
4033
4034
4035
4036
4037
4038
4039
4040
4041
4042
4043
4044
4045
4046
4047
4048
4049
4050
4051
4052
4053
4054
4055
 * 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







<
<
<
<
<
<
<
<
<







3998
3999
4000
4001
4002
4003
4004









4005
4006
4007
4008
4009
4010
4011
 * 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
4092
4093
4094
4095
4096
4097
4098
4099
4100
4101
4102
4103
4104
4105
4106
4107
4108
4109
    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)). */







<
<
<
<







4048
4049
4050
4051
4052
4053
4054




4055
4056
4057
4058
4059
4060
4061
    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)). */
4163
4164
4165
4166
4167
4168
4169
4170
4171
4172
4173
4174
4175
4176
4177
4178
4179
4180
4181
4182
4183
4184
4185
4186
4187
4188

    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)) {







|

|



|
|



|







4115
4116
4117
4118
4119
4120
4121
4122
4123
4124
4125
4126
4127
4128
4129
4130
4131
4132
4133
4134
4135
4136
4137
4138
4139
4140

    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)) {
4247
4248
4249
4250
4251
4252
4253
4254
4255
4256
4257
4258
4259
4260
4261
4262
4263
4264
4265
4266
4267
4268
4269
4270
4271
4272
4273
4274
4275
4276
4277
4278
4279
4280
4281
4282
4283
4284
4285
4286
4287
4288
4289
	     * 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
	     * in the denominator' case.
	     */

	    if (s2 % DIGIT_BIT != 0) {
		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.
	 */








|


















|








|







4199
4200
4201
4202
4203
4204
4205
4206
4207
4208
4209
4210
4211
4212
4213
4214
4215
4216
4217
4218
4219
4220
4221
4222
4223
4224
4225
4226
4227
4228
4229
4230
4231
4232
4233
4234
4235
4236
4237
4238
4239
4240
4241
	     * 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
	     * in the denominator' case.
	     */

	    if (s2 % DIGIT_BIT != 0) {
		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.
	 */

4303
4304
4305
4306
4307
4308
4309
4310
4311
4312
4313
4314
4315
4316
4317
4318
4319
4320
4321
4322
4323
4324
4325
4326
4327
4328
4329
4330
4331
4332
4333
4334
4335
4336
4337
4338
4339
4340
4341
4342
4343
4344
	    /*
	     * 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
	     * in the denominator' case.
	     */

	    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);
	}
    }
}

/*
 *----------------------------------------------------------------------







|
















|









|







4255
4256
4257
4258
4259
4260
4261
4262
4263
4264
4265
4266
4267
4268
4269
4270
4271
4272
4273
4274
4275
4276
4277
4278
4279
4280
4281
4282
4283
4284
4285
4286
4287
4288
4289
4290
4291
4292
4293
4294
4295
4296
	    /*
	     * 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
	     * in the denominator' case.
	     */

	    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.
1697
1698
1699
1700
1701
1702
1703
1704
1705
1706
1707
1708
1709
1710
1711
1712
1713
1714
1715
1716
1717
1718
1719
1720
1721
1722
1723
1724
1725
1726
1727
1728
1729
1730
1731
1732
1733
1734
1735
1736
 *
 * 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,
				/* NULL */
		       Tcl_Interp* interp,
				/* Tcl interpreter */
		       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;







|

















<






<







1697
1698
1699
1700
1701
1702
1703
1704
1705
1706
1707
1708
1709
1710
1711
1712
1713
1714
1715
1716
1717
1718
1719
1720
1721

1722
1723
1724
1725
1726
1727

1728
1729
1730
1731
1732
1733
1734
 *
 * 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,
				/* NULL */
		       Tcl_Interp* interp,
				/* Tcl interpreter */
		       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;