diff options
Diffstat (limited to 'generic/tclStrToD.c')
| -rwxr-xr-x | generic/tclStrToD.c | 2326 |
1 files changed, 1175 insertions, 1151 deletions
diff --git a/generic/tclStrToD.c b/generic/tclStrToD.c index 76adf75..2d534a68 100755 --- a/generic/tclStrToD.c +++ b/generic/tclStrToD.c @@ -1,6 +1,4 @@ /* - *---------------------------------------------------------------------- - * * tclStrToD.c -- * * This file contains a collection of procedures for managing conversions @@ -13,7 +11,6 @@ * * See the file "license.terms" for information on usage and redistribution of * this file, and for a DISCLAIMER OF ALL WARRANTIES. - *---------------------------------------------------------------------- */ #include "tclInt.h" @@ -38,6 +35,11 @@ #endif /* + * Rounding controls. (Thanks a lot, Intel!) + */ + +#ifdef __i386 +/* * gcc on x86 needs access to rounding controls, because of a questionable * feature where it retains intermediate results as IEEE 'long double' values * somewhat unpredictably. It is tempting to include fpu_control.h, but that @@ -45,41 +47,65 @@ * and ix86-isms are factored out here. */ -#if defined(__GNUC__) && defined(__i386) -typedef unsigned int fpu_control_t __attribute__ ((__mode__ (__HI__))); -#define _FPU_GETCW(cw) __asm__ __volatile__ ("fnstcw %0" : "=m" (*&cw)) -#define _FPU_SETCW(cw) __asm__ __volatile__ ("fldcw %0" : : "m" (*&cw)) +#if defined(__GNUC__) +typedef unsigned int fpu_control_t __attribute__ ((__mode__ (__HI__))); + +#define _FPU_GETCW(cw) __asm__ __volatile__ ("fnstcw %0" : "=m" (*&cw)) +#define _FPU_SETCW(cw) __asm__ __volatile__ ("fldcw %0" : : "m" (*&cw)) # define FPU_IEEE_ROUNDING 0x027f # define ADJUST_FPU_CONTROL_WORD -#endif +#define TCL_IEEE_DOUBLE_ROUNDING \ + fpu_control_t roundTo53Bits = FPU_IEEE_ROUNDING; \ + fpu_control_t oldRoundingMode; \ + _FPU_GETCW(oldRoundingMode); \ + _FPU_SETCW(roundTo53Bits) +#define TCL_DEFAULT_DOUBLE_ROUNDING \ + _FPU_SETCW(oldRoundingMode) -/* Sun ProC needs sunmath for rounding control on x86 like gcc above. - * - * +/* + * Sun ProC needs sunmath for rounding control on x86 like gcc above. */ -#if defined(__sun) && defined(__i386) && !defined(__GNUC__) +#elif defined(__sun) #include <sunmath.h> +#define TCL_IEEE_DOUBLE_ROUNDING \ + ieee_flags("set","precision","double",NULL) +#define TCL_DEFAULT_DOUBLE_ROUNDING \ + ieee_flags("clear","precision",NULL,NULL) + +/* + * Other platforms are assumed to always operate in full IEEE mode, so we make + * the macros to go in and out of that mode do nothing. + */ + +#else /* !__GNUC__ && !__sun */ +#define TCL_IEEE_DOUBLE_ROUNDING ((void) 0) +#define TCL_DEFAULT_DOUBLE_ROUNDING ((void) 0) +#endif +#else /* !__i386 */ +#define TCL_IEEE_DOUBLE_ROUNDING ((void) 0) +#define TCL_DEFAULT_DOUBLE_ROUNDING ((void) 0) #endif /* - * MIPS floating-point units need special settings in control registers - * to use gradual underflow as we expect. This fix is for the MIPSpro - * compiler. + * MIPS floating-point units need special settings in control registers to use + * gradual underflow as we expect. This fix is for the MIPSpro compiler. */ + #if defined(__sgi) && defined(_COMPILER_VERSION) #include <sys/fpu.h> #endif + /* * HP's PA_RISC architecture uses 7ff4000000000000 to represent a quiet NaN. * Everyone else uses 7ff8000000000000. (Why, HP, why?) */ #ifdef __hppa -# define NAN_START 0x7ff4 -# define NAN_MASK (((Tcl_WideUInt) 1) << 50) +# define NAN_START 0x7ff4 +# define NAN_MASK (((Tcl_WideUInt) 1) << 50) #else -# define NAN_START 0x7ff8 -# define NAN_MASK (((Tcl_WideUInt) 1) << 51) +# define NAN_START 0x7ff8 +# define NAN_MASK (((Tcl_WideUInt) 1) << 51) #endif /* @@ -93,45 +119,44 @@ typedef unsigned int fpu_control_t __attribute__ ((__mode__ (__HI__))); #define TWO_OVER_3LOG10 0.28952965460216784 #define LOG10_3HALVES_PLUS_FUDGE 0.1760912590558 -/* Definitions of the parts of an IEEE754-format floating point number */ - -#define SIGN_BIT 0x80000000 - /* Mask for the sign bit in the first - * word of a double */ -#define EXP_MASK 0x7ff00000 - /* Mask for the exponent field in the - * first word of a double */ -#define EXP_SHIFT 20 - /* Shift count to make the exponent an - * integer */ -#define HIDDEN_BIT (((Tcl_WideUInt) 0x00100000) << 32) - /* Hidden 1 bit for the significand */ -#define HI_ORDER_SIG_MASK 0x000fffff +/* + * Definitions of the parts of an IEEE754-format floating point number. + */ + +#define SIGN_BIT 0x80000000 + /* Mask for the sign bit in the first word of + * a double. */ +#define EXP_MASK 0x7ff00000 + /* Mask for the exponent field in the first + * word of a double. */ +#define EXP_SHIFT 20 /* Shift count to make the exponent an + * integer. */ +#define HIDDEN_BIT (((Tcl_WideUInt) 0x00100000) << 32) + /* Hidden 1 bit for the significand. */ +#define HI_ORDER_SIG_MASK 0x000fffff /* Mask for the high-order part of the * significand in the first word of a - * double */ -#define SIG_MASK (((Tcl_WideUInt) HI_ORDER_SIG_MASK << 32) \ - | 0xffffffff) + * double. */ +#define SIG_MASK (((Tcl_WideUInt) HI_ORDER_SIG_MASK << 32) \ + | 0xffffffff) /* Mask for the 52-bit significand. */ -#define FP_PRECISION 53 - /* Number of bits of significand plus the - * hidden bit */ -#define EXPONENT_BIAS 0x3ff - /* Bias of the exponent 0 */ - -/* Derived quantities */ - -#define TEN_PMAX 22 - /* floor(FP_PRECISION*log(2)/log(5)) */ -#define QUICK_MAX 14 - /* floor((FP_PRECISION-1)*log(2)/log(10)) - 1 */ -#define BLETCH 0x10 - /* Highest power of two that is greater than - * DBL_MAX_10_EXP, divided by 16 */ -#define DIGIT_GROUP 8 - /* floor(DIGIT_BIT*log(2)/log(10)) */ - -/* Union used to dismantle floating point numbers. */ +#define FP_PRECISION 53 /* Number of bits of significand plus the + * hidden bit. */ +#define EXPONENT_BIAS 0x3ff /* Bias of the exponent 0. */ + +/* + * Derived quantities. + */ + +#define TEN_PMAX 22 /* floor(FP_PRECISION*log(2)/log(5)) */ +#define QUICK_MAX 14 /* floor((FP_PRECISION-1)*log(2)/log(10))-1 */ +#define BLETCH 0x10 /* Highest power of two that is greater than + * DBL_MAX_10_EXP, divided by 16. */ +#define DIGIT_GROUP 8 /* floor(DIGIT_BIT*log(2)/log(10)) */ + +/* + * Union used to dismantle floating point numbers. + */ typedef union Double { struct { @@ -162,7 +187,7 @@ static int log2FLT_RADIX; /* Logarithm of the floating point radix. */ static int mantBits; /* Number of bits in a double's significand */ static mp_int pow5[9]; /* Table of powers of 5**(2**n), up to * 5**256 */ -static double tiny = 0.0; /* The smallest representable double */ +static double tiny = 0.0; /* The smallest representable double. */ static int maxDigits; /* The maximum number of digits to the left of * the decimal point of a double. */ static int minDigits; /* The maximum number of digits to the right @@ -184,10 +209,12 @@ static int n770_fp; /* Flag is 1 on Nokia N770 floating point. * reversed: if big-endian is 7654 3210, * and little-endian is 0123 4567, * then Nokia's FP is 4567 0123; - * little-endian within the 32-bit words - * but big-endian between them. */ + * little-endian within the 32-bit words but + * big-endian between them. */ -/* Table of powers of 5 that are small enough to fit in an mp_digit. */ +/* + * Table of powers of 5 that are small enough to fit in an mp_digit. + */ static const mp_digit dpow5[13] = { 1, 5, 25, 125, @@ -196,7 +223,10 @@ static const mp_digit dpow5[13] = { 244140625 }; -/* Table of powers: pow5_13[n] = 5**(13*2**(n+1)) */ +/* + * Table of powers: pow5_13[n] = 5**(13*2**(n+1)) + */ + static mp_int pow5_13[5]; /* Table of powers: 5**13, 5**26, 5**52, * 5**104, 5**208 */ static const double tens[] = { @@ -263,75 +293,81 @@ static const Tcl_WideUInt wuipow5[27] = { * Static functions defined in this file. */ -static int AccumulateDecimalDigit(unsigned, int, +static int AccumulateDecimalDigit(unsigned, int, Tcl_WideUInt *, mp_int *, int); static double MakeHighPrecisionDouble(int signum, mp_int *significand, int nSigDigs, int exponent); static double MakeLowPrecisionDouble(int signum, Tcl_WideUInt significand, int nSigDigs, int exponent); +#ifdef IEEE_FLOATING_POINT static double MakeNaN(int signum, Tcl_WideUInt tag); +#endif static double RefineApproximation(double approx, mp_int *exactSignificand, int exponent); -static void MulPow5(mp_int*, unsigned, mp_int*); -static int NormalizeRightward(Tcl_WideUInt*); +static void MulPow5(mp_int *, unsigned, mp_int *); +static int NormalizeRightward(Tcl_WideUInt *); static int RequiredPrecision(Tcl_WideUInt); -static void DoubleToExpAndSig(double, Tcl_WideUInt*, int*, int*); -static void TakeAbsoluteValue(Double*, int*); -static char* FormatInfAndNaN(Double*, int*, char**); -static char* FormatZero(int*, char**); +static void DoubleToExpAndSig(double, Tcl_WideUInt *, int *, + int *); +static void TakeAbsoluteValue(Double *, int *); +static char * FormatInfAndNaN(Double *, int *, char **); +static char * FormatZero(int *, char **); static int ApproximateLog10(Tcl_WideUInt, int, int); -static int BetterLog10(double, int, int*); -static void ComputeScale(int, int, int*, int*, int*, int*); -static void SetPrecisionLimits(int, int, int*, int*, int*, int*); -static char* BumpUp(char*, char*, int*); -static int AdjustRange(double*, int); -static char* ShorteningQuickFormat(double, int, int, double, - char*, int*); -static char* StrictQuickFormat(double, int, int, double, - char*, int*); -static char* QuickConversion(double, int, int, int, int, int, int, - int*, char**); -static void CastOutPowersOf2(int*, int*, int*); -static char* ShorteningInt64Conversion(Double*, int, Tcl_WideUInt, +static int BetterLog10(double, int, int *); +static void ComputeScale(int, int, int *, int *, int *, int *); +static void SetPrecisionLimits(int, int, int *, int *, int *, + int *); +static char * BumpUp(char *, char *, int *); +static int AdjustRange(double *, int); +static char * ShorteningQuickFormat(double, int, int, double, + char *, int *); +static char * StrictQuickFormat(double, int, int, double, + char *, int *); +static char * QuickConversion(double, int, int, int, int, int, int, + 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 *, 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, 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, + 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, + 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, + 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(mp_int *big, int *machexp); + 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); static double SafeLdExp(double fraction, int exponent); +#ifdef IEEE_FLOATING_POINT static Tcl_WideUInt Nokia770Twiddle(Tcl_WideUInt w); +#endif /* *---------------------------------------------------------------------- @@ -360,14 +396,14 @@ static Tcl_WideUInt Nokia770Twiddle(Tcl_WideUInt w); * - TCL_PARSE_SCAN_PREFIXES: ignore the prefixes 0b and 0o that are * not part of the [scan] command's vocabulary. Use only in * combination with TCL_PARSE_INTEGER_ONLY. - * - TCL_PARSE_OCTAL_ONLY: parse only in the octal format, whether + * - TCL_PARSE_OCTAL_ONLY: parse only in the octal format, whether * or not a prefix is present that would lead to octal parsing. * Use only in combination with TCL_PARSE_INTEGER_ONLY. - * - TCL_PARSE_HEXADECIMAL_ONLY: parse only in the hexadecimal format, + * - TCL_PARSE_HEXADECIMAL_ONLY: parse only in the hexadecimal format, * whether or not a prefix is present that would lead to * hexadecimal parsing. Use only in combination with * TCL_PARSE_INTEGER_ONLY. - * - TCL_PARSE_DECIMAL_ONLY: parse only in the decimal format, no + * - TCL_PARSE_DECIMAL_ONLY: parse only in the decimal format, no * matter whether a 0 prefix would normally force a different * base. * - TCL_PARSE_NO_WHITESPACE: reject any leading/trailing whitespace @@ -461,38 +497,38 @@ TclParseNumber( } state = INITIAL; enum State acceptState = INITIAL; - int signum = 0; /* Sign of the number being parsed */ + int signum = 0; /* Sign of the number being parsed. */ Tcl_WideUInt significandWide = 0; /* Significand of the number being parsed (if - * no overflow) */ + * no overflow). */ mp_int significandBig; /* Significand of the number being parsed (if - * it overflows significandWide) */ - int significandOverflow = 0;/* Flag==1 iff significandBig is used */ + * it overflows significandWide). */ + int significandOverflow = 0;/* Flag==1 iff significandBig is used. */ Tcl_WideUInt octalSignificandWide = 0; /* Significand of an octal number; needed * because we don't know whether a number with * a leading zero is octal or decimal until - * we've scanned forward to a '.' or 'e' */ + * we've scanned forward to a '.' or 'e'. */ mp_int octalSignificandBig; /* Significand of octal number once - * octalSignificandWide overflows */ + * octalSignificandWide overflows. */ int octalSignificandOverflow = 0; - /* Flag==1 if octalSignificandBig is used */ + /* Flag==1 if octalSignificandBig is used. */ int numSigDigs = 0; /* Number of significant digits in the decimal - * significand */ + * significand. */ int numTrailZeros = 0; /* Number of trailing zeroes at the current * point in the parse. */ int numDigitsAfterDp = 0; /* Number of digits scanned after the decimal - * point */ + * point. */ int exponentSignum = 0; /* Signum of the exponent of a floating point - * number */ - long exponent = 0; /* Exponent of a floating point number */ - const char *p; /* Pointer to next character to scan */ - size_t len; /* Number of characters remaining after p */ + * number. */ + long exponent = 0; /* Exponent of a floating point number. */ + const char *p; /* Pointer to next character to scan. */ + size_t len; /* Number of characters remaining after p. */ const char *acceptPoint; /* Pointer to position after last character in - * an acceptable number */ + * an acceptable number. */ size_t acceptLen; /* Number of characters following that * point. */ - int status = TCL_OK; /* Status to return to caller */ + int status = TCL_OK; /* Status to return to caller. */ char d = 0; /* Last hexadecimal digit scanned; initialized * to avoid a compiler warning. */ int shift = 0; /* Amount to shift when accumulating binary */ @@ -554,6 +590,8 @@ TclParseNumber( break; } else if (flags & TCL_PARSE_HEXADECIMAL_ONLY) { goto zerox; + } else if (flags & TCL_PARSE_BINARY_ONLY) { + goto zerob; } else if (flags & TCL_PARSE_OCTAL_ONLY) { goto zeroo; } else if (isdigit(UCHAR(c))) { @@ -580,9 +618,9 @@ TclParseNumber( case ZERO: /* * Scanned a leading zero (perhaps with a + or -). Acceptable - * inputs are digits, period, X, b, and E. If 8 or 9 is encountered, - * the number can't be octal. This state and the OCTAL state - * differ only in whether they recognize 'X' and 'b'. + * inputs are digits, period, X, b, and E. If 8 or 9 is + * encountered, the number can't be octal. This state and the + * OCTAL state differ only in whether they recognize 'X' and 'b'. */ acceptState = state; @@ -602,6 +640,9 @@ TclParseNumber( state = ZERO_B; break; } + if (flags & TCL_PARSE_BINARY_ONLY) { + goto zerob; + } if (c == 'o' || c == 'O') { explicitOctal = 1; state = ZERO_O; @@ -787,6 +828,7 @@ TclParseNumber( acceptPoint = p; acceptLen = len; case ZERO_B: + zerob: if (c == '0') { numTrailZeros++; state = BINARY; @@ -1175,7 +1217,7 @@ TclParseNumber( case OCTAL: /* - * Returning an octal integer. Final scaling step + * Returning an octal integer. Final scaling step. */ shift = 3 * numTrailZeros; @@ -1236,7 +1278,7 @@ TclParseNumber( case DECIMAL: significandOverflow = AccumulateDecimalDigit(0, numTrailZeros-1, &significandWide, &significandBig, significandOverflow); - if (!significandOverflow && (significandWide > MOST_BITS+signum)) { + if (!significandOverflow && (significandWide > MOST_BITS+signum)){ significandOverflow = 1; TclBNInitBignumFromWideUInt(&significandBig, significandWide); } @@ -1292,16 +1334,16 @@ TclParseNumber( objPtr->typePtr = &tclDoubleType; if (exponentSignum) { - exponent = - exponent; + exponent = -exponent; } if (!significandOverflow) { objPtr->internalRep.doubleValue = MakeLowPrecisionDouble( signum, significandWide, numSigDigs, - (numTrailZeros + exponent - numDigitsAfterDp)); + numTrailZeros + exponent - numDigitsAfterDp); } else { objPtr->internalRep.doubleValue = MakeHighPrecisionDouble( signum, &significandBig, numSigDigs, - (numTrailZeros + exponent - numDigitsAfterDp)); + numTrailZeros + exponent - numDigitsAfterDp); } break; @@ -1318,12 +1360,12 @@ TclParseNumber( #ifdef IEEE_FLOATING_POINT case sNAN: case sNANFINISH: - objPtr->internalRep.doubleValue = MakeNaN(signum, significandWide); + objPtr->internalRep.doubleValue = MakeNaN(signum,significandWide); objPtr->typePtr = &tclDoubleType; break; #endif case INITIAL: - /* This case only to silence compiler warning */ + /* This case only to silence compiler warning. */ Tcl_Panic("TclParseNumber: state INITIAL can't happen here"); } } @@ -1334,11 +1376,9 @@ TclParseNumber( if (status != TCL_OK) { if (interp != NULL) { - Tcl_Obj *msg; + Tcl_Obj *msg = Tcl_ObjPrintf("expected %s but got \"", + expected); - TclNewLiteralStringObj(msg, "expected "); - Tcl_AppendToObj(msg, expected, -1); - Tcl_AppendToObj(msg, " but got \"", -1); Tcl_AppendLimitedToObj(msg, bytes, numBytes, 50, ""); Tcl_AppendToObj(msg, "\"", -1); if (state == BAD_OCTAL) { @@ -1395,7 +1435,7 @@ AccumulateDecimalDigit( Tcl_WideUInt w; /* - * Try wide multiplication first + * Try wide multiplication first. */ if (!bignumFlag) { @@ -1408,10 +1448,10 @@ AccumulateDecimalDigit( *wideRepPtr = digit; return 0; } else if (numZeros >= maxpow10_wide - || w > ((~(Tcl_WideUInt)0)-digit)/pow10_wide[numZeros+1]) { + || w > ((~(Tcl_WideUInt)0)-digit)/pow10_wide[numZeros+1]) { /* - * Wide multiplication will overflow. Expand the - * number to a bignum and fall through into the bignum case. + * Wide multiplication will overflow. Expand the number to a + * bignum and fall through into the bignum case. */ TclBNInitBignumFromWideUInt(bignumRepPtr, w); @@ -1419,6 +1459,7 @@ AccumulateDecimalDigit( /* * Wide multiplication. */ + *wideRepPtr = w * pow10_wide[numZeros+1] + digit; return 0; } @@ -1486,12 +1527,12 @@ AccumulateDecimalDigit( static double MakeLowPrecisionDouble( int signum, /* 1 if the number is negative, 0 otherwise */ - Tcl_WideUInt significand, /* Significand of the number */ - int numSigDigs, /* Number of digits in the significand */ - int exponent) /* Power of ten */ + Tcl_WideUInt significand, /* Significand of the number. */ + int numSigDigs, /* Number of digits in the significand. */ + int exponent) /* Power of ten. */ { - double retval; /* Value of the number */ - mp_int significandBig; /* Significand expressed as a bignum */ + double retval; /* Value of the number. */ + mp_int significandBig; /* Significand expressed as a bignum. */ /* * With gcc on x86, the floating point rounding mode is double-extended. @@ -1501,15 +1542,7 @@ MakeLowPrecisionDouble( * ulp, so we need to change rounding mode to 53-bits. */ -#if defined(__GNUC__) && defined(__i386) - fpu_control_t roundTo53Bits = 0x027f; - fpu_control_t oldRoundingMode; - _FPU_GETCW(oldRoundingMode); - _FPU_SETCW(roundTo53Bits); -#endif -#if defined(__sun) && defined(__i386) && !defined(__GNUC__) - ieee_flags("set","precision","double",NULL); -#endif + TCL_IEEE_DOUBLE_ROUNDING; /* * Test for the easy cases. @@ -1524,10 +1557,12 @@ MakeLowPrecisionDouble( * without special handling. */ - retval = (double)(Tcl_WideInt)significand * pow10vals[exponent]; + retval = (double) + ((Tcl_WideInt)significand * pow10vals[exponent]); goto returnValue; } else { int diff = DBL_DIG - numSigDigs; + if (exponent-diff <= mmaxpow) { /* * 10**exponent is not an exact integer, but @@ -1536,8 +1571,8 @@ MakeLowPrecisionDouble( * with only one roundoff. */ - volatile double factor = - (double)(Tcl_WideInt)significand * pow10vals[diff]; + volatile double factor = (double) + ((Tcl_WideInt)significand * pow10vals[diff]); retval = factor * pow10vals[exponent-diff]; goto returnValue; } @@ -1550,7 +1585,8 @@ MakeLowPrecisionDouble( * only one rounding. */ - retval = (double)(Tcl_WideInt)significand / pow10vals[-exponent]; + retval = (double) + ((Tcl_WideInt)significand / pow10vals[-exponent]); goto returnValue; } } @@ -1579,12 +1615,7 @@ MakeLowPrecisionDouble( * On gcc on x86, restore the floating point mode word. */ -#if defined(__GNUC__) && defined(__i386) - _FPU_SETCW(oldRoundingMode); -#endif -#if defined(__sun) && defined(__i386) && !defined(__GNUC__) - ieee_flags("clear","precision",NULL,NULL); -#endif + TCL_DEFAULT_DOUBLE_ROUNDING; return retval; } @@ -1609,13 +1640,13 @@ MakeLowPrecisionDouble( static double MakeHighPrecisionDouble( - int signum, /* 1=negative, 0=nonnegative */ - mp_int *significand, /* Exact significand of the number */ - int numSigDigs, /* Number of significant digits */ - int exponent) /* Power of 10 by which to multiply */ + int signum, /* 1=negative, 0=nonnegative. */ + mp_int *significand, /* Exact significand of the number. */ + int numSigDigs, /* Number of significant digits. */ + int exponent) /* Power of 10 by which to multiply. */ { double retval; - int machexp; /* Machine exponent of a power of 10 */ + int machexp; /* Machine exponent of a power of 10. */ /* * With gcc on x86, the floating point rounding mode is double-extended. @@ -1625,15 +1656,7 @@ MakeHighPrecisionDouble( * ulp, so we need to change rounding mode to 53-bits. */ -#if defined(__GNUC__) && defined(__i386) - fpu_control_t roundTo53Bits = 0x027f; - fpu_control_t oldRoundingMode; - _FPU_GETCW(oldRoundingMode); - _FPU_SETCW(roundTo53Bits); -#endif -#if defined(__sun) && defined(__i386) && !defined(__GNUC__) - ieee_flags("set","precision","double",NULL); -#endif + TCL_IEEE_DOUBLE_ROUNDING; /* * Quick checks for over/underflow. @@ -1664,9 +1687,9 @@ MakeHighPrecisionDouble( goto returnValue; } retval = SafeLdExp(retval, machexp); - if (tiny == 0.0) { - tiny = SafeLdExp(1.0, DBL_MIN_EXP * log2FLT_RADIX - mantBits); - } + if (tiny == 0.0) { + tiny = SafeLdExp(1.0, DBL_MIN_EXP * log2FLT_RADIX - mantBits); + } if (retval < tiny) { retval = tiny; } @@ -1692,12 +1715,8 @@ MakeHighPrecisionDouble( * On gcc on x86, restore the floating point mode word. */ -#if defined(__GNUC__) && defined(__i386) - _FPU_SETCW(oldRoundingMode); -#endif -#if defined(__sun) && defined(__i386) && !defined(__GNUC__) - ieee_flags("clear","precision",NULL,NULL); -#endif + TCL_DEFAULT_DOUBLE_ROUNDING; + return retval; } @@ -1716,8 +1735,8 @@ MakeHighPrecisionDouble( #ifdef IEEE_FLOATING_POINT static double MakeNaN( - int signum, /* Sign bit (1=negative, 0=nonnegative */ - Tcl_WideUInt tags) /* Tag bits to put in the NaN */ + int signum, /* Sign bit (1=negative, 0=nonnegative. */ + Tcl_WideUInt tags) /* Tag bits to put in the NaN. */ { union { Tcl_WideUInt iv; @@ -1755,28 +1774,28 @@ MakeNaN( static double RefineApproximation( - double approxResult, /* Approximate result of conversion */ - mp_int *exactSignificand, /* Integer significand */ - int exponent) /* Power of 10 to multiply by significand */ + double approxResult, /* Approximate result of conversion. */ + mp_int *exactSignificand, /* Integer significand. */ + int exponent) /* Power of 10 to multiply by significand. */ { int M2, M5; /* Powers of 2 and of 5 needed to put the * decimal and binary numbers over a common * denominator. */ - double significand; /* Sigificand of the binary number */ - int binExponent; /* Exponent of the binary number */ + double significand; /* Sigificand of the binary number. */ + int binExponent; /* Exponent of the binary number. */ int msb; /* Most significant bit position of an - * intermediate result */ + * intermediate result. */ int nDigits; /* Number of mp_digit's in an intermediate - * result */ + * result. */ mp_int twoMv; /* Approx binary value expressed as an exact - * integer scaled by the multiplier 2M */ + * integer scaled by the multiplier 2M. */ mp_int twoMd; /* Exact decimal value expressed as an exact - * integer scaled by the multiplier 2M */ - int scale; /* Scale factor for M */ - int multiplier; /* Power of two to scale M */ + * integer scaled by the multiplier 2M. */ + int scale; /* Scale factor for M. */ + int multiplier; /* Power of two to scale M. */ double num, den; /* Numerator and denominator of the correction - * term */ - double quot; /* Correction term */ + * term. */ + double quot; /* Correction term. */ double minincr; /* Lower bound on the absolute value of the * correction term. */ int i; @@ -1806,8 +1825,8 @@ RefineApproximation( M5 = 0; } else { M5 = -exponent; - if ((M5-1) > M2) { - M2 = M5-1; + if (M5 - 1 > M2) { + M2 = M5 - 1; } } @@ -1846,7 +1865,7 @@ RefineApproximation( mp_init_copy(&twoMd, exactSignificand); for (i=0; i<=8; ++i) { - if ((M5+exponent) & (1 << i)) { + if ((M5 + exponent) & (1 << i)) { mp_mul(&twoMd, pow5+i, &twoMd); } } @@ -1856,7 +1875,7 @@ RefineApproximation( /* * The result, 2Mv-2Md, needs to be divided by 2M to yield a correction * term. Because 2M may well overflow a double, we need to scale the - * denominator by a factor of 2**binExponent-mantBits + * denominator by a factor of 2**binExponent-mantBits. */ scale = binExponent - mantBits - 1; @@ -1880,8 +1899,8 @@ RefineApproximation( */ if (mp_cmp_mag(&twoMd, &twoMv) == MP_LT) { - mp_clear(&twoMd); - mp_clear(&twoMv); + mp_clear(&twoMd); + mp_clear(&twoMv); return approxResult; } @@ -1909,26 +1928,28 @@ RefineApproximation( } /* - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- * * MultPow5 -- * * Multiply a bignum by a power of 5. * * Side effects: - * Stores base*5**n in result + * Stores base*5**n in result. * - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- */ inline static void -MulPow5(mp_int* base, /* Number to multiply */ - unsigned n, /* Power of 5 to multiply by */ - mp_int* result) /* Place to store the result */ +MulPow5( + mp_int *base, /* Number to multiply. */ + unsigned n, /* Power of 5 to multiply by. */ + mp_int *result) /* Place to store the result. */ { - mp_int* p = base; + mp_int *p = base; int n13 = n / 13; int r = n % 13; + if (r != 0) { mp_mul_d(p, dpow5[r], result); p = result; @@ -1946,14 +1967,14 @@ MulPow5(mp_int* base, /* Number to multiply */ mp_copy(p, result); } } - + /* - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- * * NormalizeRightward -- * - * Shifts a number rightward until it is odd (that is, until the - * least significant bit is nonzero. + * Shifts a number rightward until it is odd (that is, until the least + * significant bit is nonzero. * * Results: * Returns the number of bit positions by which the number was shifted. @@ -1961,18 +1982,19 @@ MulPow5(mp_int* base, /* Number to multiply */ * Side effects: * Shifts the number in place; *wPtr is replaced by the shifted number. * - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- */ inline static int -NormalizeRightward(Tcl_WideUInt* wPtr) - /* INOUT: Number to shift */ +NormalizeRightward( + Tcl_WideUInt *wPtr) /* INOUT: Number to shift. */ { int rv = 0; Tcl_WideUInt w = *wPtr; + if (!(w & (Tcl_WideUInt) 0xffffffff)) { w >>= 32; rv += 32; - } + } if (!(w & (Tcl_WideUInt) 0xffff)) { w >>= 16; rv += 16; } @@ -1991,27 +2013,28 @@ NormalizeRightward(Tcl_WideUInt* wPtr) *wPtr = w; return rv; } - + /* - *-----------------------------------------------------------------------------0 + *---------------------------------------------------------------------- * * RequiredPrecision -- * * Determines the number of bits needed to hold an intger. * * Results: - * Returns the position of the most significant bit (0 - 63). - * Returns 0 if the number is zero. + * Returns the position of the most significant bit (0 - 63). Returns 0 + * if the number is zero. * - *---------------------------------------------------------------------------- + *---------------------------------------------------------------------- */ static int -RequiredPrecision(Tcl_WideUInt w) - /* Number to interrogate */ +RequiredPrecision( + Tcl_WideUInt w) /* Number to interrogate. */ { int rv; unsigned long wi; + if (w & ((Tcl_WideUInt) 0xffffffff << 32)) { wi = (unsigned long) (w >> 32); rv = 32; } else { @@ -2037,38 +2060,40 @@ RequiredPrecision(Tcl_WideUInt w) } return rv; } - + /* - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- * * DoubleToExpAndSig -- * * Separates a 'double' into exponent and significand. * * Side effects: - * Stores the significand in '*significand' and the exponent in - * '*expon' so that dv == significand * 2.0**expon, and significand - * is odd. Also stores the position of the leftmost 1-bit in 'significand' - * in 'bits'. + * Stores the significand in '*significand' and the exponent in '*expon' + * so that dv == significand * 2.0**expon, and significand is odd. Also + * stores the position of the leftmost 1-bit in 'significand' in 'bits'. * - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- */ inline static void -DoubleToExpAndSig(double dv, /* Number to convert */ - Tcl_WideUInt* significand, - /* OUTPUT: Significand of the number */ - int* expon, /* OUTPUT: Exponent to multiply the number by */ - int* bits) /* OUTPUT: Number of significant bits */ +DoubleToExpAndSig( + double dv, /* Number to convert. */ + Tcl_WideUInt *significand, /* OUTPUT: Significand of the number. */ + int *expon, /* OUTPUT: Exponent to multiply the number + * by. */ + int *bits) /* OUTPUT: Number of significant bits. */ { - Double d; /* Number being converted */ - Tcl_WideUInt z; /* Significand under construction */ - int de; /* Exponent of the number */ - int k; /* Bit count */ + Double d; /* Number being converted. */ + Tcl_WideUInt z; /* Significand under construction. */ + int de; /* Exponent of the number. */ + int k; /* Bit count. */ d.d = dv; - /* Extract exponent and significand */ + /* + * Extract exponent and significand. + */ de = (d.w.word0 & EXP_MASK) >> EXP_SHIFT; z = d.q & SIG_MASK; @@ -2084,24 +2109,25 @@ DoubleToExpAndSig(double dv, /* Number to convert */ } *significand = z; } - + /* - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- * * TakeAbsoluteValue -- * * Takes the absolute value of a 'double' including 0, Inf and NaN * * Side effects: - * The 'double' in *d is replaced with its absolute value. The - * signum is stored in 'sign': 1 for negative, 0 for nonnegative. + * The 'double' in *d is replaced with its absolute value. The signum is + * stored in 'sign': 1 for negative, 0 for nonnegative. * - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- */ inline static void -TakeAbsoluteValue(Double* d, /* Number to replace with absolute value */ - int* sign) /* Place to put the signum */ +TakeAbsoluteValue( + Double *d, /* Number to replace with absolute value. */ + int *sign) /* Place to put the signum. */ { if (d->w.word0 & SIGN_BIT) { *sign = 1; @@ -2110,32 +2136,33 @@ TakeAbsoluteValue(Double* d, /* Number to replace with absolute value */ *sign = 0; } } - + /* - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- * * FormatInfAndNaN -- * * Bailout for formatting infinities and Not-A-Number. * * Results: - * Returns one of the strings 'Infinity' and 'NaN'. + * Returns one of the strings 'Infinity' and 'NaN'. The string returned + * must be freed by the caller using 'ckfree'. * * Side effects: - * Stores 9999 in *decpt, and sets '*endPtr' to designate the - * terminating NUL byte of the string if 'endPtr' is not NULL. + * Stores 9999 in *decpt, and sets '*endPtr' to designate the terminating + * NUL byte of the string if 'endPtr' is not NULL. * - * The string returned must be freed by the caller using 'ckfree'. - * - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- */ -inline static char* -FormatInfAndNaN(Double* d, /* Exceptional number to format */ - int* decpt, /* Decimal point to set to a bogus value */ - char** endPtr) /* Pointer to the end of the formatted data */ +inline static char * +FormatInfAndNaN( + Double *d, /* Exceptional number to format. */ + int *decpt, /* Decimal point to set to a bogus value. */ + char **endPtr) /* Pointer to the end of the formatted data */ { - char* retval; + char *retval; + *decpt = 9999; if (!(d->w.word1) && !(d->w.word0 & HI_ORDER_SIG_MASK)) { retval = ckalloc(9); @@ -2152,9 +2179,9 @@ FormatInfAndNaN(Double* d, /* Exceptional number to format */ } return retval; } - + /* - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- * * FormatZero -- * @@ -2167,14 +2194,16 @@ FormatInfAndNaN(Double* d, /* Exceptional number to format */ * Stores 1 in '*decpt' and puts a pointer to the NUL byte terminating * the string in '*endPtr' if 'endPtr' is not NULL. * - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- */ -inline static char* -FormatZero(int* decpt, /* Location of the decimal point */ - char** endPtr) /* Pointer to the end of the formatted data */ +inline static char * +FormatZero( + int *decpt, /* Location of the decimal point. */ + char **endPtr) /* Pointer to the end of the formatted data */ { - char* retval = ckalloc(2); + char *retval = ckalloc(2); + strcpy(retval, "0"); if (endPtr) { *endPtr = retval+1; @@ -2182,37 +2211,37 @@ FormatZero(int* decpt, /* Location of the decimal point */ *decpt = 0; return retval; } - + /* - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- * * ApproximateLog10 -- * - * Computes a two-term Taylor series approximation to the common - * log of a number, and computes the number's binary log. + * Computes a two-term Taylor series approximation to the common log of a + * number, and computes the number's binary log. * * Results: - * Return an approximation to floor(log10(bw*2**be)) that is either - * exact or 1 too high. + * Return an approximation to floor(log10(bw*2**be)) that is either exact + * or 1 too high. * - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- */ inline static int -ApproximateLog10(Tcl_WideUInt bw, - /* Integer significand of the number */ - int be, /* Power of two to scale bw */ - int bbits) /* Number of bits of precision in bw */ +ApproximateLog10( + Tcl_WideUInt bw, /* Integer significand of the number. */ + int be, /* Power of two to scale bw. */ + int bbits) /* Number of bits of precision in bw. */ { - int i; /* Log base 2 of the number */ + int i; /* Log base 2 of the number. */ int k; /* Floor(Log base 10 of the number) */ - double ds; /* Mantissa of the number */ + double ds; /* Mantissa of the number. */ Double d2; /* * Compute i and d2 such that d = d2*2**i, and 1 < d2 < 2. - * Compute an approximation to log10(d), - * log10(d) ~ log10(2) * i + log10(1.5) + * Compute an approximation to log10(d), + * log10(d) ~ log10(2) * i + log10(1.5) * + (significand-1.5)/(1.5 * log(10)) */ @@ -2220,17 +2249,16 @@ ApproximateLog10(Tcl_WideUInt bw, d2.w.word0 |= (EXPONENT_BIAS) << EXP_SHIFT; i = be + bbits - 1; ds = (d2.d - 1.5) * TWO_OVER_3LOG10 - + LOG10_3HALVES_PLUS_FUDGE - + LOG10_2 * i; + + LOG10_3HALVES_PLUS_FUDGE + LOG10_2 * i; k = (int) ds; if (k > ds) { --k; } return k; } - + /* - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- * * BetterLog10 -- * @@ -2238,24 +2266,27 @@ ApproximateLog10(Tcl_WideUInt bw, * 1 .. 10**(TEN_PMAX)-1 * * Side effects: - * Sets k_check to 0 if the new result is known to be exact, and to - * 1 if it may still be one too high. + * Sets k_check to 0 if the new result is known to be exact, and to 1 if + * it may still be one too high. * * Results: - * Returns the improved approximation to log10(d) + * Returns the improved approximation to log10(d). * - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- */ inline static int -BetterLog10(double d, /* Original number to format */ - int k, /* Characteristic(Log base 10) of the number */ - int* k_check) /* Flag == 1 if k is inexact */ +BetterLog10( + double d, /* Original number to format. */ + int k, /* Characteristic(Log base 10) of the + * number. */ + int *k_check) /* Flag == 1 if k is inexact. */ { - /* - * Performance hack. If k is in the range 0..TEN_PMAX, then we can - * use a powers-of-ten table to check it. + /* + * Performance hack. If k is in the range 0..TEN_PMAX, then we can use a + * powers-of-ten table to check it. */ + if (k >= 0 && k <= TEN_PMAX) { if (d < tens[k]) { k--; @@ -2266,40 +2297,41 @@ BetterLog10(double d, /* Original number to format */ } return k; } - + /* - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- * * ComputeScale -- * * Prepares to format a floating-point number as decimal. * * Parameters: - * floor(log10*x) is k (or possibly k-1). floor(log2(x) is i. - * The significand of x requires bbits bits to represent. + * floor(log10*x) is k (or possibly k-1). floor(log2(x) is i. The + * significand of x requires bbits bits to represent. * * Results: * Determines integers b2, b5, s2, s5 so that sig*2**b2*5**b5/2**s2*2**s5 - * exactly represents the value of the x/10**k. This value will lie - * in the range [1 .. 10), and allows for computing successive digits - * by multiplying sig%10 by 10. + * exactly represents the value of the x/10**k. This value will lie in + * the range [1 .. 10), and allows for computing successive digits by + * multiplying sig%10 by 10. * - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- */ inline static void -ComputeScale(int be, /* Exponent part of number: d = bw * 2**be */ - int k, /* Characteristic of log10(number) */ - int* b2, /* OUTPUT: Power of 2 in the numerator */ - int* b5, /* OUTPUT: Power of 5 in the numerator */ - int* s2, /* OUTPUT: Power of 2 in the denominator */ - int* s5) /* OUTPUT: Power of 5 in the denominator */ +ComputeScale( + int be, /* Exponent part of number: d = bw * 2**be. */ + int k, /* Characteristic of log10(number). */ + int *b2, /* OUTPUT: Power of 2 in the numerator. */ + int *b5, /* OUTPUT: Power of 5 in the numerator. */ + int *s2, /* OUTPUT: Power of 2 in the denominator. */ + int *s5) /* OUTPUT: Power of 5 in the denominator. */ { - - /* - * Scale numerator and denominator powers of 2 so that the - * input binary number is the ratio of integers + /* + * Scale numerator and denominator powers of 2 so that the input binary + * number is the ratio of integers. */ + if (be <= 0) { *b2 = 0; *s2 = -be; @@ -2308,10 +2340,11 @@ ComputeScale(int be, /* Exponent part of number: d = bw * 2**be */ *s2 = 0; } - /* - * Scale numerator and denominator so that the output decimal number - * is the ratio of integers + /* + * Scale numerator and denominator so that the output decimal number is + * the ratio of integers. */ + if (k >= 0) { *b5 = 0; *s5 = k; @@ -2324,49 +2357,45 @@ ComputeScale(int be, /* Exponent part of number: d = bw * 2**be */ } /* - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- * * SetPrecisionLimits -- * - * Determines how many digits of significance should be computed - * (and, hence, how much memory need be allocated) for formatting a - * floating point number. + * Determines how many digits of significance should be computed (and, + * hence, how much memory need be allocated) for formatting a floating + * point number. * * Given that 'k' is floor(log10(x)): - * if 'shortest' format is used, there will be at most 18 digits in the result. + * if 'shortest' format is used, there will be at most 18 digits in the + * result. * if 'F' format is used, there will be at most 'ndigits' + k + 1 digits * if 'E' format is used, there will be exactly 'ndigits' digits. * * Side effects: - * Adjusts '*ndigitsPtr' to have a valid value. - * Stores the maximum memory allocation needed in *iPtr. - * Sets '*iLimPtr' to the limiting number of digits to convert if k - * has been guessed correctly, and '*iLim1Ptr' to the limiting number - * of digits to convert if k has been guessed to be one too high. + * Adjusts '*ndigitsPtr' to have a valid value. Stores the maximum memory + * allocation needed in *iPtr. Sets '*iLimPtr' to the limiting number of + * digits to convert if k has been guessed correctly, and '*iLim1Ptr' to + * the limiting number of digits to convert if k has been guessed to be + * one too high. * - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- */ inline static 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. */ +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) { + switch (convType) { case TCL_DD_SHORTEST0: case TCL_DD_STEELE0: *iLimPtr = *iLim1Ptr = -1; @@ -2394,31 +2423,31 @@ SetPrecisionLimits(int convType, Tcl_Panic("impossible conversion type in TclDoubleDigits"); } } - + /* - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- * * BumpUp -- * - * Increases a string of digits ending in a series of nines to - * designate the next higher number. xxxxb9999... -> xxxx(b+1)0000... + * Increases a string of digits ending in a series of nines to designate + * the next higher number. xxxxb9999... -> xxxx(b+1)0000... * * Results: * Returns a pointer to the end of the adjusted string. * * Side effects: - * In the case that the string consists solely of '999999', sets it - * to "1" and moves the decimal point (*kPtr) one place to the right. + * In the case that the string consists solely of '999999', sets it to + * "1" and moves the decimal point (*kPtr) one place to the right. * - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- */ - -inline static char* -BumpUp(char* s, /* Cursor pointing one past the end of the - * string */ - char* retval, /* Start of the string of digits */ - int* kPtr) /* Position of the decimal point */ +inline static char * +BumpUp( + char *s, /* Cursor pointing one past the end of the + * string. */ + char *retval, /* Start of the string of digits. */ + int *kPtr) /* Position of the decimal point. */ { while (*--s == '9') { if (s == retval) { @@ -2433,27 +2462,28 @@ BumpUp(char* s, /* Cursor pointing one past the end of the } /* - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- * * AdjustRange -- * - * Rescales a 'double' in preparation for formatting it using the - * 'quick' double-to-string method. + * Rescales a 'double' in preparation for formatting it using the 'quick' + * double-to-string method. * * Results: - * Returns the precision that has been lost in the prescaling as - * a count of units in the least significant place. + * Returns the precision that has been lost in the prescaling as a count + * of units in the least significant place. * - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- */ inline static int -AdjustRange(double* dPtr, /* INOUT: Number to adjust */ - int k) /* IN: floor(log10(d)) */ +AdjustRange( + double *dPtr, /* INOUT: Number to adjust. */ + int k) /* IN: floor(log10(d)) */ { int ieps; /* Number of roundoff errors that have - * accumulated */ - double d = *dPtr; /* Number to adjust */ + * accumulated. */ + double d = *dPtr; /* Number to adjust. */ double ds; int i, j, j1; @@ -2463,6 +2493,7 @@ AdjustRange(double* dPtr, /* INOUT: Number to adjust */ /* * The number must be reduced to bring it into range. */ + ds = tens[k & 0xf]; j = k >> 4; if (j & BLETCH) { @@ -2481,8 +2512,9 @@ AdjustRange(double* dPtr, /* INOUT: Number to adjust */ d /= ds; } else if ((j1 = -k) != 0) { /* - * The number must be increased to bring it into range + * The number must be increased to bring it into range. */ + d *= tens[j1 & 0xf]; i = 0; for (j = j1>>4; j; j>>=1) { @@ -2499,52 +2531,52 @@ AdjustRange(double* dPtr, /* INOUT: Number to adjust */ } /* - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- * * ShorteningQuickFormat -- * - * Returns a 'quick' format of a double precision number to a string - * of digits, preferring a shorter string of digits if the shorter - * string is still within 1/2 ulp of the number. + * Returns a 'quick' format of a double precision number to a string of + * digits, preferring a shorter string of digits if the shorter string is + * still within 1/2 ulp of the number. * * Results: - * Returns the string of digits. Returns NULL if the 'quick' method - * fails and the bignum method must be used. + * Returns the string of digits. Returns NULL if the 'quick' method fails + * and the bignum method must be used. * * Side effects: * Stores the position of the decimal point at '*kPtr'. * - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- */ -inline static char* -ShorteningQuickFormat(double d, /* Number to convert */ - int k, /* floor(log10(d)) */ - int ilim, /* Number of significant digits to return */ - double eps, - /* Estimated roundoff error */ - char* retval, - /* Buffer to receive the digit string */ - int* kPtr) - /* Pointer to stash the position of - * the decimal point */ +inline static char * +ShorteningQuickFormat( + double d, /* Number to convert. */ + int k, /* floor(log10(d)) */ + int ilim, /* Number of significant digits to return. */ + double eps, /* Estimated roundoff error. */ + char *retval, /* Buffer to receive the digit string. */ + int *kPtr) /* Pointer to stash the position of the + * decimal point. */ { - char* s = retval; /* Cursor in the return value */ - int digit; /* Current digit */ + char *s = retval; /* Cursor in the return value. */ + int digit; /* Current digit. */ int i; eps = 0.5 / tens[ilim-1] - eps; i = 0; for (;;) { - /* Convert a digit */ + /* + * Convert a digit. + */ digit = (int) d; d -= digit; *s++ = '0' + digit; /* - * Truncate the conversion if the string of digits is within - * 1/2 ulp of the actual value. + * Truncate the conversion if the string of digits is within 1/2 ulp + * of the actual value. */ if (d < eps) { @@ -2558,7 +2590,7 @@ ShorteningQuickFormat(double d, /* Number to convert */ /* * Bail out if the conversion fails to converge to a sufficiently - * precise value + * precise value. */ if (++i >= ilim) { @@ -2575,40 +2607,44 @@ ShorteningQuickFormat(double d, /* Number to convert */ } /* - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- * * StrictQuickFormat -- * - * Convert a double precision number of a string of a precise number - * of digits, using the 'quick' double precision method. + * Convert a double precision number of a string of a precise number of + * digits, using the 'quick' double precision method. * * Results: - * Returns the digit string, or NULL if the bignum method must be - * used to do the formatting. + * Returns the digit string, or NULL if the bignum method must be used to + * do the formatting. * * Side effects: * Stores the position of the decimal point in '*kPtr'. * - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- */ -inline static char* -StrictQuickFormat(double d, /* Number to convert */ - int k, /* floor(log10(d)) */ - int ilim, /* Number of significant digits to return */ - double eps, /* Estimated roundoff error */ - char* retval, /* Start of the digit string */ - int* kPtr) /* Pointer to stash the position of - * the decimal point */ +inline static char * +StrictQuickFormat( + double d, /* Number to convert. */ + int k, /* floor(log10(d)) */ + int ilim, /* Number of significant digits to return. */ + double eps, /* Estimated roundoff error. */ + char *retval, /* Start of the digit string. */ + int *kPtr) /* Pointer to stash the position of the + * decimal point. */ { - char* s = retval; /* Cursor in the return value */ - int digit; /* Current digit of the answer */ + char *s = retval; /* Cursor in the return value. */ + int digit; /* Current digit of the answer. */ int i; eps *= tens[ilim-1]; i = 1; for (;;) { - /* Extract a digit */ + /* + * Extract a digit. + */ + digit = (int) d; d -= digit; if (d == 0.0) { @@ -2616,10 +2652,11 @@ StrictQuickFormat(double d, /* Number to convert */ } *s++ = '0' + digit; - /* - * When the given digit count is reached, handle trailing strings - * of 0 and 9. + /* + * When the given digit count is reached, handle trailing strings of 0 + * and 9. */ + if (i == ilim) { if (d > 0.5 + eps) { *kPtr = k; @@ -2636,14 +2673,17 @@ StrictQuickFormat(double d, /* Number to convert */ } } - /* Advance to the next digit */ + /* + * Advance to the next digit. + */ + ++i; d *= 10.0; } } /* - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- * * QuickConversion -- * @@ -2652,44 +2692,48 @@ StrictQuickFormat(double d, /* Number to convert */ * therefore be used for the intermediate results. * * Results: - * Returns the converted string, or NULL if the bignum method must - * be used. + * Returns the converted string, or NULL if the bignum method must be + * used. * - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- */ -inline static char* -QuickConversion(double e, /* Number to format */ - int k, /* floor(log10(d)), approximately */ - int k_check, /* 0 if k is exact, 1 if it may be too high */ - int flags, /* Flags passed to dtoa: +inline static char * +QuickConversion( + double e, /* Number to format. */ + int k, /* floor(log10(d)), approximately. */ + int k_check, /* 0 if k is exact, 1 if it may be too high */ + int flags, /* Flags passed to dtoa: * TCL_DD_SHORTEN_FLAG */ - int len, /* Length of the return value */ - int ilim, /* Number of digits to store */ - int ilim1, /* Number of digits to store if we - * musguessed k */ - int* decpt, /* OUTPUT: Location of the decimal point */ - char** endPtr) /* OUTPUT: Pointer to the terminal null byte */ + int len, /* Length of the return value. */ + int ilim, /* Number of digits to store. */ + int ilim1, /* Number of digits to store if we misguessed + * k. */ + int *decpt, /* OUTPUT: Location of the decimal point. */ + char **endPtr) /* OUTPUT: Pointer to the terminal null + * byte. */ { int ieps; /* Number of 1-ulp roundoff errors that have - * accumulated in the calculation*/ - Double eps; /* Estimated roundoff error */ - char* retval; /* Returned string */ - char* end; /* Pointer to the terminal null byte in the - * returned string */ + * accumulated in the calculation. */ + Double eps; /* Estimated roundoff error. */ + char *retval; /* Returned string. */ + char *end; /* Pointer to the terminal null byte in the + * returned string. */ volatile double d; /* Workaround for a bug in mingw gcc 3.4.5 */ /* - * Bring d into the range [1 .. 10) + * Bring d into the range [1 .. 10). */ + ieps = AdjustRange(&e, k); d = e; /* - * If the guessed value of k didn't get d into range, adjust it - * by one. If that leaves us outside the range in which quick format - * is accurate, bail out. + * If the guessed value of k didn't get d into range, adjust it by one. If + * that leaves us outside the range in which quick format is accurate, + * bail out. */ + if (k_check && d < 1. && ilim > 0) { if (ilim1 < 0) { return NULL; @@ -2701,15 +2745,16 @@ QuickConversion(double e, /* Number to format */ } /* - * Compute estimated roundoff error + * Compute estimated roundoff error. */ + eps.d = ieps * d + 7.; eps.w.word0 -= (FP_PRECISION-1) << EXP_SHIFT; /* - * Handle the peculiar case where the result has no significant - * digits. + * Handle the peculiar case where the result has no significant digits. */ + retval = ckalloc(len + 1); if (ilim == 0) { d -= 5.; @@ -2726,7 +2771,9 @@ QuickConversion(double e, /* Number to format */ } } - /* Format the digit string */ + /* + * Format the digit string. + */ if (flags & TCL_DD_SHORTEN_FLAG) { end = ShorteningQuickFormat(d, k, ilim, eps.d, retval, decpt); @@ -2745,106 +2792,99 @@ QuickConversion(double e, /* Number to format */ } /* - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- * * CastOutPowersOf2 -- * - * Adjust the factors 'b2', 'm2', and 's2' to cast out common powers - * of 2 from numerator and denominator in preparation for the 'bignum' - * method of floating point conversion. + * Adjust the factors 'b2', 'm2', and 's2' to cast out common powers of 2 + * from numerator and denominator in preparation for the 'bignum' method + * of floating point conversion. * - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- */ inline static void -CastOutPowersOf2(int* b2, /* Power of 2 to multiply the significand */ - int* m2, /* Power of 2 to multiply 1/2 ulp */ - int* s2) /* Power of 2 to multiply the common - * denominator */ +CastOutPowersOf2( + int *b2, /* Power of 2 to multiply the significand. */ + int *m2, /* Power of 2 to multiply 1/2 ulp. */ + int *s2) /* Power of 2 to multiply the common + * denominator. */ { int i; + if (*m2 > 0 && *s2 > 0) { /* Find the smallest power of 2 in the - * numerator */ - if (*m2 < *s2) { /* Find the lowest common denominatorr */ + * numerator. */ + if (*m2 < *s2) { /* Find the lowest common denominator. */ i = *m2; } else { i = *s2; } - *b2 -= i; /* Reduce to lowest terms */ + *b2 -= i; /* Reduce to lowest terms. */ *m2 -= i; *s2 -= i; } } /* - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- * * ShorteningInt64Conversion -- * - * Converts a double-precision number to the shortest string of - * digits that reconverts exactly to the given number, or to - * 'ilim' digits if that will yield a shorter result. The numerator and - * denominator in David Gay's conversion algorithm are known to fit - * in Tcl_WideUInt, giving considerably faster arithmetic than mp_int's. + * Converts a double-precision number to the shortest string of digits + * that reconverts exactly to the given number, or to 'ilim' digits if + * that will yield a shorter result. The numerator and denominator in + * David Gay's conversion algorithm are known to fit in Tcl_WideUInt, + * giving considerably faster arithmetic than mp_int's. * * Results: - * Returns the string of significant decimal digits, in newly - * allocated memory + * Returns the string of significant decimal digits, in newly allocated + * memory * * Side effects: - * Stores the location of the decimal point in '*decpt' and the - * location of the terminal null byte in '*endPtr'. + * Stores the location of the decimal point in '*decpt' and the location + * of the terminal null byte in '*endPtr'. * - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- */ -inline static 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 */ - 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 */ +inline static 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. */ + 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 */ + char *retval = ckalloc(len + 1); + /* Output buffer. */ Tcl_WideUInt b = (bw * wuipow5[b5]) << b2; - /* Numerator of the fraction being converted */ + /* Numerator of the fraction being + * converted. */ Tcl_WideUInt S = wuipow5[s5] << s2; - /* Denominator of the fraction being - * converted */ - Tcl_WideUInt mplus, mminus; /* Ranges for testing whether the result - * is within roundoff of being exact */ - int digit; /* Current output digit */ - char* s = retval; /* Cursor in the output buffer */ - int i; /* Current position in the output buffer */ + /* Denominator of the fraction being + * converted. */ + Tcl_WideUInt mplus, mminus; /* Ranges for testing whether the result is + * within roundoff of being exact. */ + int digit; /* Current output digit. */ + char *s = retval; /* Cursor in the output buffer. */ + int i; /* Current position in the output buffer. */ - /* Adjust if the logarithm was guessed wrong */ + /* + * Adjust if the logarithm was guessed wrong. + */ if (b < S) { b = 10 * b; @@ -2853,12 +2893,16 @@ ShorteningInt64Conversion(Double* dPtr, --k; } - /* Compute roundoff ranges */ + /* + * Compute roundoff ranges. + */ mplus = wuipow5[m5] << m2plus; mminus = wuipow5[m5] << m2minus; - /* Loop through the digits */ + /* + * Loop through the digits. + */ i = 1; for (;;) { @@ -2868,21 +2912,19 @@ ShorteningInt64Conversion(Double* dPtr, } b = b % S; - /* + /* * 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)) { + + 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 + * 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)) { + + if (2 * b > S || (2 * b == S && (digit & 1) != 0)) { ++digit; if (digit == 10) { *s++ = '9'; @@ -2891,7 +2933,9 @@ ShorteningInt64Conversion(Double* dPtr, } } - /* Stash the current digit */ + /* + * Stash the current digit. + */ *s++ = '0' + digit; break; @@ -2901,10 +2945,9 @@ ShorteningInt64Conversion(Double* dPtr, * 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 (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); @@ -2918,27 +2961,30 @@ ShorteningInt64Conversion(Double* dPtr, /* * Have we converted all the requested digits? */ + *s++ = '0' + digit; if (i == ilim) { - if (2*b > S - || (2*b == S && (digit & 1) != 0)) { + if (2*b > S || (2*b == S && (digit & 1) != 0)) { s = BumpUp(s, retval, &k); } break; } - - /* Advance to the next digit */ - + + /* + * Advance to the next digit. + */ + b = 10 * b; mplus = 10 * mplus; mminus = 10 * mminus; ++i; } - /* + /* * Endgame - store the location of the decimal point and the end of the * string. */ + *s = '\0'; *decpt = k; if (endPtr) { @@ -2948,69 +2994,61 @@ ShorteningInt64Conversion(Double* dPtr, } /* - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- * * StrictInt64Conversion -- * - * Converts a double-precision number to a fixed-length string of - * 'ilim' digits that reconverts exactly to the given number. - * ('ilim' should be replaced with 'ilim1' in the case where - * log10(d) has been overestimated). The numerator and - * denominator in David Gay's conversion algorithm are known to fit - * in Tcl_WideUInt, giving considerably faster arithmetic than mp_int's. + * Converts a double-precision number to a fixed-length string of 'ilim' + * digits that reconverts exactly to the given number. ('ilim' should be + * replaced with 'ilim1' in the case where log10(d) has been + * overestimated). The numerator and denominator in David Gay's + * conversion algorithm are known to fit in Tcl_WideUInt, giving + * considerably faster arithmetic than mp_int's. * * Results: - * Returns the string of significant decimal digits, in newly - * allocated memory + * Returns the string of significant decimal digits, in newly allocated + * memory * * Side effects: - * Stores the location of the decimal point in '*decpt' and the - * location of the terminal null byte in '*endPtr'. + * Stores the location of the decimal point in '*decpt' and the location + * of the terminal null byte in '*endPtr'. * - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- */ -inline static 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 */ - 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 */ +inline static 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. */ + 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 */ + char *retval = ckalloc(len + 1); + /* Output buffer. */ Tcl_WideUInt b = (bw * wuipow5[b5]) << b2; - /* Numerator of the fraction being converted */ + /* Numerator of the fraction being + * converted. */ Tcl_WideUInt S = wuipow5[s5] << s2; - /* Denominator of the fraction being - * converted */ - int digit; /* Current output digit */ - char* s = retval; /* Cursor in the output buffer */ - int i; /* Current position in the output buffer */ + /* Denominator of the fraction being + * converted. */ + int digit; /* Current output digit. */ + char *s = retval; /* Cursor in the output buffer. */ + int i; /* Current position in the output buffer. */ - /* Adjust if the logarithm was guessed wrong */ + /* + * Adjust if the logarithm was guessed wrong. + */ if (b < S) { b = 10 * b; @@ -3018,7 +3056,9 @@ StrictInt64Conversion(Double* dPtr, --k; } - /* Loop through the digits */ + /* + * Loop through the digits. + */ i = 1; for (;;) { @@ -3031,10 +3071,10 @@ StrictInt64Conversion(Double* dPtr, /* * Have we converted all the requested digits? */ + *s++ = '0' + digit; if (i == ilim) { - if (2*b > S - || (2*b == S && (digit & 1) != 0)) { + if (2*b > S || (2*b == S && (digit & 1) != 0)) { s = BumpUp(s, retval, &k); } else { while (*--s == '0') { @@ -3044,17 +3084,20 @@ StrictInt64Conversion(Double* dPtr, } break; } - - /* Advance to the next digit */ - + + /* + * Advance to the next digit. + */ + b = 10 * b; ++i; } - /* + /* * Endgame - store the location of the decimal point and the end of the * string. */ + *s = '\0'; *decpt = k; if (endPtr) { @@ -3064,30 +3107,30 @@ StrictInt64Conversion(Double* dPtr, } /* - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- * * ShouldBankerRoundUpPowD -- * - * Test whether bankers' rounding should round a digit up. Assumption - * is made that the denominator of the fraction being tested is - * a power of 2**DIGIT_BIT. + * Test whether bankers' rounding should round a digit up. Assumption is + * made that the denominator of the fraction being tested is a power of + * 2**DIGIT_BIT. * * Results: - * Returns 1 iff the fraction is more than 1/2, or if the fraction - * is exactly 1/2 and the digit is odd. + * Returns 1 iff the fraction is more than 1/2, or if the fraction is + * exactly 1/2 and the digit is odd. * - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- */ inline static 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 */ +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)); + static const mp_digit topbit = 1 << (DIGIT_BIT - 1); + if (b->used < sd || (b->dp[sd-1] & topbit) == 0) { return 0; } @@ -3103,45 +3146,41 @@ ShouldBankerRoundUpPowD(mp_int* b, } /* - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- * * ShouldBankerRoundUpToNextPowD -- * - * Tests whether bankers' rounding will round down in the - * "denominator is a power of 2**MP_DIGIT" case. + * Tests whether bankers' rounding will round down in the "denominator is + * a power of 2**MP_DIGIT" case. * * Results: * Returns 1 if the rounding will be performed - which increases the * digit by one - and 0 otherwise. * - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- */ inline static 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 */ +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 do by computing b+m and doing a bitwhack compare against + /* + * Compare B and S-m - which is the same as comparing B+m and S - which we + * do by computing b+m and doing a bitwhack compare against * 2**(DIGIT_BIT*sd) */ + mp_add(b, m, temp); - if (temp->used <= sd) { /* too few digits to be > S */ + if (temp->used <= sd) { /* Too few digits to be > s */ return 0; } if (temp->used > sd+1 || temp->dp[sd] > 1) { @@ -3149,85 +3188,74 @@ ShouldBankerRoundUpToNextPowD(mp_int* b, return 1; } for (i = sd-1; i >= 0; --i) { - /* check for ==s */ + /* Check for ==s */ if (temp->dp[i] != 0) { /* > s */ return 1; } } if (convType == TCL_DD_STEELE0) { - /* biased rounding */ + /* Biased rounding. */ return 0; } return isodd; } /* - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- * * ShorteningBignumConversionPowD -- * - * Converts a double-precision number to the shortest string of - * digits that reconverts exactly to the given number, or to - * 'ilim' digits if that will yield a shorter result. The denominator - * in David Gay's conversion algorithm is known to be a power of - * 2**DIGIT_BIT, and hence the division in the main loop may be replaced - * by a digit shift and mask. + * Converts a double-precision number to the shortest string of digits + * that reconverts exactly to the given number, or to 'ilim' digits if + * that will yield a shorter result. The denominator in David Gay's + * conversion algorithm is known to be a power of 2**DIGIT_BIT, and hence + * the division in the main loop may be replaced by a digit shift and + * mask. * * Results: - * Returns the string of significant decimal digits, in newly - * allocated memory + * Returns the string of significant decimal digits, in newly allocated + * memory * * Side effects: - * Stores the location of the decimal point in '*decpt' and the - * location of the terminal null byte in '*endPtr'. + * Stores the location of the decimal point in '*decpt' and the location + * of the terminal null byte in '*endPtr'. * - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- */ -inline static 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 */ - 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 */ +inline static 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. */ + 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_int mplus, mminus; /* Bounds for roundoff */ - mp_digit digit; /* Current output digit */ - char* s = retval; /* Cursor in the output buffer */ - int i; /* Index in the output buffer */ + char *retval = ckalloc(len + 1); + /* Output buffer. */ + mp_int b; /* Numerator of the fraction being + * converted. */ + mp_int mplus, mminus; /* Bounds for roundoff. */ + mp_digit digit; /* Current output digit. */ + char *s = retval; /* Cursor in the output buffer. */ + int i; /* Index in the output buffer. */ mp_int temp; int r1; - /* + /* * b = bw * 2**b2 * 5**b5 * mminus = 5**m5 */ @@ -3237,7 +3265,9 @@ ShorteningBignumConversionPowD(Double* dPtr, MulPow5(&b, b5, &b); mp_mul_2d(&b, b2, &b); - /* Adjust if the logarithm was guessed wrong */ + /* + * Adjust if the logarithm was guessed wrong. + */ if (b.used <= sd) { mp_mul_d(&b, 10, &b); @@ -3259,8 +3289,10 @@ ShorteningBignumConversionPowD(Double* dPtr, } mp_init(&temp); - /* Loop through the digits. Do division and mod by s == 2**(sd*DIGIT_BIT) - * by mp_digit extraction */ + /* + * Loop through the digits. Do division and mod by s == 2**(sd*DIGIT_BIT) + * by mp_digit extraction. + */ i = 0; for (;;) { @@ -3274,20 +3306,19 @@ ShorteningBignumConversionPowD(Double* dPtr, --b.used; mp_clamp(&b); } - /* + /* * 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)) { + 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 + * Make sure we shouldn't be rounding *up* instead, in case the + * next number above is closer. */ + if (ShouldBankerRoundUpPowD(&b, sd, digit&1)) { ++digit; if (digit == 10) { @@ -3297,7 +3328,9 @@ ShorteningBignumConversionPowD(Double* dPtr, } } - /* Stash the last digit */ + /* + * Stash the last digit. + */ *s++ = '0' + digit; break; @@ -3307,10 +3340,9 @@ ShorteningBignumConversionPowD(Double* dPtr, * 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 (ShouldBankerRoundUpToNextPowD(&b, &mminus, sd, convType, + dPtr->w.word1 & 1, &temp)) { if (digit == 9) { *s++ = '9'; s = BumpUp(s, retval, &k); @@ -3324,6 +3356,7 @@ ShorteningBignumConversionPowD(Double* dPtr, /* * Have we converted all the requested digits? */ + *s++ = '0' + digit; if (i == ilim) { if (ShouldBankerRoundUpPowD(&b, sd, digit&1)) { @@ -3331,9 +3364,11 @@ ShorteningBignumConversionPowD(Double* dPtr, } break; } - - /* Advance to the next digit */ - + + /* + * Advance to the next digit. + */ + mp_mul_d(&b, 10, &b); mp_mul_d(&mminus, 10, &mminus); if (m2plus > m2minus) { @@ -3342,10 +3377,11 @@ ShorteningBignumConversionPowD(Double* dPtr, ++i; } - /* + /* * Endgame - store the location of the decimal point and the end of the * string. */ + if (m2plus > m2minus) { mp_clear(&mplus); } @@ -3359,65 +3395,55 @@ ShorteningBignumConversionPowD(Double* dPtr, } /* - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- * * StrictBignumConversionPowD -- * - * Converts a double-precision number to a fixed-lengt string of - * 'ilim' digits (or 'ilim1' if log10(d) has been overestimated.) - * The denominator in David Gay's conversion algorithm is known to - * be a power of 2**DIGIT_BIT, and hence the division in the main - * loop may be replaced by a digit shift and mask. + * Converts a double-precision number to a fixed-lengt string of 'ilim' + * digits (or 'ilim1' if log10(d) has been overestimated). The + * denominator in David Gay's conversion algorithm is known to be a power + * of 2**DIGIT_BIT, and hence the division in the main loop may be + * replaced by a digit shift and mask. * * Results: - * Returns the string of significant decimal digits, in newly - * allocated memory. + * Returns the string of significant decimal digits, in newly allocated + * memory. * * Side effects: - * Stores the location of the decimal point in '*decpt' and the - * location of the terminal null byte in '*endPtr'. + * Stores the location of the decimal point in '*decpt' and the location + * of the terminal null byte in '*endPtr'. * - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- */ -inline static 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 */ +inline static 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 */ + 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 */ @@ -3425,7 +3451,9 @@ StrictBignumConversionPowD(Double* dPtr, MulPow5(&b, b5, &b); mp_mul_2d(&b, b2, &b); - /* Adjust if the logarithm was guessed wrong */ + /* + * Adjust if the logarithm was guessed wrong. + */ if (b.used <= sd) { mp_mul_d(&b, 10, &b); @@ -3434,9 +3462,9 @@ StrictBignumConversionPowD(Double* dPtr, } mp_init(&temp); - /* + /* * Loop through the digits. Do division and mod by s == 2**(sd*DIGIT_BIT) - * by mp_digit extraction + * by mp_digit extraction. */ i = 1; @@ -3448,35 +3476,39 @@ StrictBignumConversionPowD(Double* dPtr, if (b.used > sd+1 || digit >= 10) { Tcl_Panic("wrong digit!"); } - --b.used; mp_clamp(&b); + --b.used; + mp_clamp(&b); } /* * Have we converted all the requested digits? */ + *s++ = '0' + digit; if (i == ilim) { if (ShouldBankerRoundUpPowD(&b, sd, digit&1)) { s = BumpUp(s, retval, &k); - } else { - while (*--s == '0') { - /* do nothing */ - } - ++s; } + while (*--s == '0') { + /* do nothing */ + } + ++s; break; } - - /* Advance to the next digit */ - + + /* + * Advance to the next digit. + */ + mp_mul_d(&b, 10, &b); ++i; } - /* + /* * Endgame - store the location of the decimal point and the end of the * string. */ + mp_clear_multi(&b, &temp, NULL); *s = '\0'; *decpt = k; @@ -3487,7 +3519,7 @@ StrictBignumConversionPowD(Double* dPtr, } /* - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- * * ShouldBankerRoundUp -- * @@ -3497,17 +3529,18 @@ StrictBignumConversionPowD(Double* dPtr, * Results: * Returns 1 if the number needs to be rounded up, 0 otherwise. * - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- */ inline static int -ShouldBankerRoundUp(mp_int* twor, - /* 2x the remainder from thd division that - * produced the last digit */ - mp_int* S, /* Denominator */ - int isodd) /* Flag == 1 if the last digit is odd */ +ShouldBankerRoundUp( + mp_int *twor, /* 2x the remainder from thd division that + * produced the last digit. */ + mp_int *S, /* Denominator. */ + int isodd) /* Flag == 1 if the last digit is odd. */ { int r = mp_cmp_mag(twor, S); + switch (r) { case MP_LT: return 0; @@ -3521,38 +3554,37 @@ ShouldBankerRoundUp(mp_int* twor, } /* - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- * * ShouldBankerRoundUpToNext -- * - * Tests whether the remainder is great enough to force rounding - * to the next higher digit. + * Tests whether the remainder is great enough to force rounding to the + * next higher digit. * * Results: * Returns 1 if the number should be rounded up, 0 otherwise. * - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- */ inline static int -ShouldBankerRoundUpToNext(mp_int* b, - /* Remainder from the division that produced +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 */ + 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. */ + + /* + * 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) { @@ -3570,9 +3602,9 @@ ShouldBankerRoundUpToNext(mp_int* b, Tcl_Panic("in ShouldBankerRoundUpToNext, trichotomy fails!"); return 0; } - + /* - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- * * ShorteningBignumConversion -- * @@ -3583,49 +3615,38 @@ ShouldBankerRoundUpToNext(mp_int* b, * Returns the string of digits. * * Side effects: - * Stores the position of the decimal point in *decpt. - * Stores a pointer to the end of the number in *endPtr. + * Stores the position of the decimal point in *decpt. Stores a pointer + * to the end of the number in *endPtr. * - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- */ -inline static 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 */ +inline static 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 */ + 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; @@ -3640,10 +3661,9 @@ ShorteningBignumConversion(Double* dPtr, MulPow5(&S, s5, &S); mp_mul_2d(&S, s2, &S); /* - * Handle the case where we guess the position of the decimal point - * wrong. + * Handle the case where we guess the position of the decimal point wrong. */ - + if (mp_cmp_mag(&b, &S) == MP_LT) { mp_mul_d(&b, 10, &b); minit = 10; @@ -3651,7 +3671,9 @@ ShorteningBignumConversion(Double* dPtr, --k; } - /* mminus = 2**m2minus * 5**m5 */ + /* + * mminus = 2**m2minus * 5**m5 + */ mp_init_set_int(&mminus, minit); mp_mul_2d(&mminus, m2minus, &mminus); @@ -3661,7 +3683,9 @@ ShorteningBignumConversion(Double* dPtr, } mp_init(&temp); - /* Loop through the digits */ + /* + * Loop through the digits. + */ mp_init(&dig); i = 1; @@ -3672,16 +3696,14 @@ ShorteningBignumConversion(Double* dPtr, } 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)) { + 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; @@ -3696,12 +3718,12 @@ ShorteningBignumConversion(Double* dPtr, } /* - * Does the current digit leave us with a remainder large enough - * to commit to rounding up to the next higher digit? + * 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)) { + dPtr->w.word1 & 1, &temp)) { ++digit; if (digit == 10) { *s++ = '9'; @@ -3712,22 +3734,28 @@ ShorteningBignumConversion(Double* dPtr, break; } - /* Have we converted all the requested digits? */ + /* + * Have we converted all the requested digits? + */ *s++ = '0' + digit; if (i == ilim) { mp_mul_2d(&b, 1, &b); if (ShouldBankerRoundUp(&b, &S, digit&1)) { - s = BumpUp(s, retval, &k); + s = BumpUp(s, retval, &k); } break; } - /* Advance to the next digit */ + /* + * Advance to the next digit. + */ if (s5 > 0) { + /* + * Can possibly shorten the denominator. + */ - /* Can possibly shorten the denominator */ mp_mul_2d(&b, 1, &b); mp_mul_2d(&mminus, 1, &mminus); if (m2plus > m2minus) { @@ -3735,17 +3763,18 @@ ShorteningBignumConversion(Double* dPtr, } mp_div_d(&S, 5, &S, NULL); --s5; - /* - * IDEA: It might possibly be a win to fall back to - * int64 arithmetic here if S < 2**64/10. But it's - * a win only for a fairly narrow range of magnitudes - * so perhaps not worth bothering. We already know that - * we shorten the denominator by at least 1 mp_digit, perhaps - * 2. as we do the conversion for 17 digits of significance. + + /* + * IDEA: It might possibly be a win to fall back to int64 + * arithmetic here if S < 2**64/10. But it's a win only for + * a fairly narrow range of magnitudes so perhaps not worth + * bothering. We already know that we shorten the + * denominator by at least 1 mp_digit, perhaps 2, as we do + * the conversion for 17 digits of significance. * Possible savings: * 10**26 1 trip through loop before fallback possible * 10**27 1 trip - * 10**28 2 trips + * 10**28 2 trips * 10**29 3 trips * 10**30 4 trips * 10**31 5 trips @@ -3760,7 +3789,7 @@ ShorteningBignumConversion(Double* dPtr, * 10**40 14 trips * 10**41 15 trips * 10**42 16 trips - * thereafter no gain. + * thereafter no gain. */ } else { mp_mul_d(&b, 10, &b); @@ -3773,11 +3802,11 @@ ShorteningBignumConversion(Double* dPtr, ++i; } - - /* + /* * Endgame - store the location of the decimal point and the end of the * string. */ + if (m2plus > m2minus) { mp_clear(&mplus); } @@ -3788,59 +3817,51 @@ ShorteningBignumConversion(Double* dPtr, *endPtr = s; } return retval; - } - + /* - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- * * StrictBignumConversion -- * - * Convert a floating point number to a fixed-length digit string - * using the multiprecision method. + * Convert a floating point number to a fixed-length digit string using + * the multiprecision method. * * Results: * Returns the string of digits. * * Side effects: - * Stores the position of the decimal point in *decpt. - * Stores a pointer to the end of the number in *endPtr. + * Stores the position of the decimal point in *decpt. Stores a pointer + * to the end of the number in *endPtr. * - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- */ -inline static 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 */ +inline static 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 groun */ + 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 @@ -3853,17 +3874,18 @@ StrictBignumConversion(Double* dPtr, MulPow5(&S, s5, &S); mp_mul_2d(&S, s2, &S); /* - * Handle the case where we guess the position of the decimal point - * wrong. + * Handle the case where we guess the position of the decimal point wrong. */ - + if (mp_cmp_mag(&b, &S) == MP_LT) { mp_mul_d(&b, 10, &b); ilim =ilim1; --k; } - /* Convert the leading digit */ + /* + * Convert the leading digit. + */ i = 0; mp_div(&b, &S, &dig, &b); @@ -3872,19 +3894,21 @@ StrictBignumConversion(Double* dPtr, } digit = dig.dp[0]; - /* Is a single digit all that was requested? */ + /* + * Is a single digit all that was requested? + */ *s++ = '0' + digit; if (++i >= ilim) { mp_mul_2d(&b, 1, &b); if (ShouldBankerRoundUp(&b, &S, digit&1)) { - s = BumpUp(s, retval, &k); + s = BumpUp(s, retval, &k); } } else { - for (;;) { - - /* Shift by a group of digits. */ + /* + * Shift by a group of digits. + */ g = ilim - i; if (g > DIGIT_GROUP) { @@ -3901,20 +3925,19 @@ StrictBignumConversion(Double* dPtr, mp_mul_d(&b, dpow5[g], &b); } mp_mul_2d(&b, g, &b); - + /* - * As with the shortening bignum conversion, it's possible at - * this point that we will have reduced the denominator to - * less than 2**64/10, at which point it would be possible to - * fall back to to int64 arithmetic. But the potential payoff - * is tremendously less - unless we're working in F format - - * because we know that three groups of digits will always - * suffice for %#.17e, the longest format that doesn't introduce - * empty precision. + * As with the shortening bignum conversion, it's possible at this + * point that we will have reduced the denominator to less than + * 2**64/10, at which point it would be possible to fall back to + * to int64 arithmetic. But the potential payoff is tremendously + * less - unless we're working in F format - because we know that + * three groups of digits will always suffice for %#.17e, the + * longest format that doesn't introduce empty precision. + * + * Extract the next group of digits. */ - /* Extract the next group of digits */ - mp_div(&b, &S, &dig, &b); if (dig.used > 1) { Tcl_Panic("wrong digit!"); @@ -3922,31 +3945,35 @@ StrictBignumConversion(Double* dPtr, digit = dig.dp[0]; for (j = g-1; j >= 0; --j) { int t = itens[j]; + *s++ = digit / t + '0'; digit %= t; } i += g; - - /* Have we converted all the requested digits? */ - + + /* + * Have we converted all the requested digits? + */ + if (i == ilim) { mp_mul_2d(&b, 1, &b); if (ShouldBankerRoundUp(&b, &S, digit&1)) { - s = BumpUp(s, retval, &k); - } else { - while (*--s == '0') { - /* do nothing */ - } - ++s; - } - break; + s = BumpUp(s, retval, &k); + } + break; } } } - /* + while (*--s == '0') { + /* do nothing */ + } + ++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; @@ -3954,121 +3981,122 @@ StrictBignumConversion(Double* dPtr, *endPtr = s; } return retval; - } /* - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- * * TclDoubleDigits -- * - * Core of Tcl's conversion of double-precision floating point numbers - * to decimal. + * Core of Tcl's conversion of double-precision floating point numbers to + * decimal. * * Results: * Returns a newly-allocated string of digits. * * Side effects: * Sets *decpt to the index of the character in the string before the - * place that the decimal point should go. If 'endPtr' is not NULL, - * sets endPtr to point to the terminating '\0' byte of the string. - * Sets *sign to 1 if a minus sign should be printed with the number, - * or 0 if a plus sign (or no sign) should appear. + * place that the decimal point should go. If 'endPtr' is not NULL, sets + * endPtr to point to the terminating '\0' byte of the string. Sets *sign + * to 1 if a minus sign should be printed with the number, or 0 if a plus + * sign (or no sign) should appear. * - * This function is a service routine that produces the string of digits - * for floating-point-to-decimal conversion. It can do a number of things + * This function is a service routine that produces the string of digits for + * floating-point-to-decimal conversion. It can do a number of things * 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. + * 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' + * 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 also returns fewer digits if the - * shorter string will still reconvert to the given input number. - * In any case, strings of trailing zeroes are suppressed. - * TCL_DD_F_FORMAT - This value is used to prepare numbers for %f - * format conversion. It requests that conversion proceed until + * 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 + * also returns fewer digits if the shorter string will still + * reconvert without loss to the given input number. In any case, + * strings of trailing zeroes are suppressed. + * TCL_DD_F_FORMAT - This value is used to prepare numbers for %f format + * conversion. It requests that conversion proceed until * 'ndigits' digits after the decimal point have been converted. - * It is possible for this format to result in a zero-length - * string if the number is sufficiently small. Again, it - * is permissible for TCL_DD_F_FORMAT to return fewer digits - * for a number that converts exactly, and changing the - * argument to TCL_DD_F_FORMAT|TCL_DD_SHORTEN_FLAG will allow - * the routine also to return fewer digits if the shorter string - * will still reconvert without loss to the given input number. - * Strings of trailing zeroes are suppressed. - * - * To any of these flags may be OR'ed TCL_DD_NO_QUICK; this flag - * requires all calculations to be done in exact arithmetic. Normally, - * E and F format with fewer than about 14 digits will be done with - * a quick floating point approximation and fall back on the exact - * arithmetic only if the input number is close enough to the - * midpoint between two decimal strings that more precision is needed - * to resolve which string is correct. - * - * The value stored in the 'decpt' argument on return may be negative - * (indicating that the decimal point falls to the left of the string) - * or greater than the length of the string. In addition, the value -9999 - * is used as a sentinel to indicate that the string is one of the special - * values "Infinity" and "NaN", and that no decimal point should be inserted. - * - *----------------------------------------------------------------------------- + * It is possible for this format to result in a zero-length + * string if the number is sufficiently small. Again, it is + * permissible for TCL_DD_F_FORMAT to return fewer digits for a + * number that converts exactly, and changing the argument to + * TCL_DD_F_FORMAT|TCL_DD_SHORTEN_FLAG will allow the routine + * also to return fewer digits if the shorter string will still + * reconvert without loss to the given input number. Strings of + * trailing zeroes are suppressed. + * + * To any of these flags may be OR'ed TCL_DD_NO_QUICK; this flag requires + * all calculations to be done in exact arithmetic. Normally, E and F + * format with fewer than about 14 digits will be done with a quick + * floating point approximation and fall back on the exact arithmetic + * only if the input number is close enough to the midpoint between two + * decimal strings that more precision is needed to resolve which string + * is correct. + * + * The value stored in the 'decpt' argument on return may be negative + * (indicating that the decimal point falls to the left of the string) or + * greater than the length of the string. In addition, the value -9999 is used + * as a sentinel to indicate that the string is one of the special values + * "Infinity" and "NaN", and that no decimal point should be inserted. + * + *---------------------------------------------------------------------- */ -char* -TclDoubleDigits(double dv, /* Number to convert */ - int ndigits, /* Number of digits requested */ - 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 */ + +char * +TclDoubleDigits( + double dv, /* Number to convert. */ + int ndigits, /* Number of digits requested. */ + 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 - * TCL_DD_F_FORMAT */ - Double d; /* Union for deconstructing doubles */ - Tcl_WideUInt bw; /* Integer significand */ + /* 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 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)) */ - int k_check; /* Flag == 1 if d is near enough to a - * power of ten that k must be checked */ + * denormalized. */ + int k; /* Estimate of floor(log10(d)). */ + int k_check; /* Flag == 1 if d is near enough to a power of + * ten that k must be checked. */ int b2, b5, s2, s5; /* Powers of 2 and 5 in the numerator and - * denominator of intermediate results */ - int ilim = -1, ilim1 = -1; /* Number of digits to convert, and number - * to convert if log10(d) has been - * overestimated */ - char* retval; /* Return value from this function */ + * denominator of intermediate results. */ + int ilim = -1, ilim1 = -1; /* Number of digits to convert, and number to + * convert if log10(d) has been + * overestimated. */ + char *retval; /* Return value from this function. */ int i = -1; - /* Put the input number into a union for bit-whacking */ + /* + * Put the input number into a union for bit-whacking. + */ d.d = dv; - /* + /* * Handle the cases of negative numbers (by taking the absolute value: * this includes -Inf and -NaN!), infinity, Not a Number, and zero. */ @@ -4081,12 +4109,12 @@ TclDoubleDigits(double dv, /* Number to convert */ return FormatZero(decpt, endPtr); } - /* + /* * Unpack the floating point into a wide integer and an exponent. - * Determine the number of bits that the big integer requires, and - * compute a quick approximation (which may be one too high) of - * ceil(log10(d.d)). + * Determine the number of bits that the big integer requires, and compute + * a quick approximation (which may be one too high) of ceil(log10(d.d)). */ + denorm = ((d.w.word0 & EXP_MASK) == 0); DoubleToExpAndSig(d.d, &bw, &be, &bbits); k = ApproximateLog10(bw, be, bbits); @@ -4094,60 +4122,59 @@ TclDoubleDigits(double dv, /* Number to convert */ /* At this point, we have: * d is the number to convert. - * bw are significand and exponent: d == bw*2**be, + * bw are significand and exponent: d == bw*2**be, * bbits is the length of bw: 2**bbits-1 <= bw < 2**bbits - * k is either ceil(log10(d)) or ceil(log10(d))+1. k_check is 0 - * if we know that k is exactly ceil(log10(d)) and 1 if we need to - * check. - * We want a rational number + * k is either ceil(log10(d)) or ceil(log10(d))+1. k_check is 0 if we + * know that k is exactly ceil(log10(d)) and 1 if we need to check. + * We want a rational number * r = b * 10**(1-k) = bw * 2**b2 * 5**b5 / (2**s2 / 5**s5), * with b2, b5, s2, s5 >= 0. Note that the most significant decimal - * digit is floor(r) and that successive digits can be obtained - * by setting r <- 10*floor(r) (or b <= 10 * (b % S)). - * Find appropriate b2, b5, s2, s5. + * digit is floor(r) and that successive digits can be obtained by + * setting r <- 10*floor(r) (or b <= 10 * (b % S)). Find appropriate + * b2, b5, s2, s5. */ ComputeScale(be, k, &b2, &b5, &s2, &s5); /* - * Correct an incorrect caller-supplied 'ndigits'. - * Also determine: + * 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. + * 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 + /* + * 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 ((retval = QuickConversion(d.d, k, k_check, flags, - i, ilim, ilim1, - decpt, endPtr)) != NULL) { + retval = QuickConversion(d.d, k, k_check, flags, i, ilim, ilim1, + decpt, endPtr); + if (retval != NULL) { return retval; } } - /* - * For shortening conversions, determine the upper and lower bounds - * for the remainder at which we can stop. - * m+ = (2**m2plus * 5**m5) / (2**s2 * 5**s5) is the limit on the - * high side, and - * m- = (2**m2minus * 5**m5) / (2**s2 * 5**s5) is the limit on the - * low side. - * We may need to increase s2 to put m2plus, m2minus, b2 over a - * common denominator. + /* + * For shortening conversions, determine the upper and lower bounds for + * the remainder at which we can stop. + * m+ = (2**m2plus * 5**m5) / (2**s2 * 5**s5) is the limit on the high + * side, and + * m- = (2**m2minus * 5**m5) / (2**s2 * 5**s5) is the limit on the low + * side. + * We may need to increase s2 to put m2plus, m2minus, b2 over a common + * denominator. */ if (flags & TCL_DD_SHORTEN_FLAG) { @@ -4156,11 +4183,11 @@ TclDoubleDigits(double dv, /* Number to convert */ int m5 = b5; int len = i; - /* - * Find the quantity i so that (2**i*5**b5)/(2**s2*5**s5) - * is 1/2 unit in the least significant place of the floating - * point number. + /* + * Find the quantity i so that (2**i*5**b5)/(2**s2*5**s5) is 1/2 unit + * in the least significant place of the floating point number. */ + if (denorm) { i = be + EXPONENT_BIAS + (FP_PRECISION-1); } else { @@ -4169,16 +4196,18 @@ TclDoubleDigits(double dv, /* Number to convert */ b2 += i; s2 += i; - /* + /* * Reduce the fractions to lowest terms, since the above calculation - * may have left excess powers of 2 in numerator and denominator + * may have left excess powers of 2 in numerator and denominator. */ + CastOutPowersOf2(&b2, &m2minus, &s2); /* * In the special case where bw==1, the nearest floating point number * to it on the low side is 1/4 ulp below it. Adjust accordingly. */ + m2plus = m2minus; if (!denorm && bw == 1) { ++b2; @@ -4186,60 +4215,56 @@ TclDoubleDigits(double dv, /* Number to convert */ ++m2plus; } - if (s5+1 < N_LOG2POW5 - && s2+1 + log2pow5[s5+1] <= 64) { + if (s5+1 < N_LOG2POW5 && s2+1 + log2pow5[s5+1] <= 64) { /* - * 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]). + * 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); + 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. + * 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); + 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 + /* + * 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); - + return ShorteningBignumConversion(&d, convType, bw, b2, m2plus, + m2minus, s2, s5, k, len, ilim, ilim1, decpt, endPtr); } - } else { - - /* Non-shortening conversion */ + /* + * Non-shortening conversion. + */ int len = i; - /* Reduce numerator and denominator to lowest terms */ + /* + * Reduce numerator and denominator to lowest terms. + */ if (b2 >= s2 && s2 > 0) { b2 -= s2; s2 = 0; @@ -4247,48 +4272,46 @@ TclDoubleDigits(double dv, /* Number to convert */ s2 -= b2; b2 = 0; } - if (s5+1 < N_LOG2POW5 - && s2+1 + log2pow5[s5+1] <= 64) { + if (s5+1 < N_LOG2POW5 && s2+1 + log2pow5[s5+1] <= 64) { /* - * 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. + * 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); - + 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. + * 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); + 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. + * 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); + + return StrictBignumConversion(&d, convType, bw, b2, s2, s5, k, + len, ilim, ilim1, decpt, endPtr); } - } + } } - /* *---------------------------------------------------------------------- @@ -4316,14 +4339,12 @@ TclInitDoubleConversion(void) int x; Tcl_WideUInt u; double d; - #ifdef IEEE_FLOATING_POINT union { double dv; Tcl_WideUInt iv; } bitwhack; #endif - #if defined(__sgi) && defined(_COMPILER_VERSION) union fpc_csr mipsCR; @@ -4338,8 +4359,7 @@ TclInitDoubleConversion(void) maxpow10_wide = (int) floor(sizeof(Tcl_WideUInt) * CHAR_BIT * log(2.) / log(10.)); - pow10_wide = (Tcl_WideUInt *) - ckalloc((maxpow10_wide + 1) * sizeof(Tcl_WideUInt)); + pow10_wide = ckalloc((maxpow10_wide + 1) * sizeof(Tcl_WideUInt)); u = 1; for (i = 0; i < maxpow10_wide; ++i) { pow10_wide[i] = u; @@ -4348,8 +4368,8 @@ TclInitDoubleConversion(void) pow10_wide[i] = u; /* - * Determine how many bits of precision a double has, and how many - * decimal digits that represents. + * Determine how many bits of precision a double has, and how many decimal + * digits that represents. */ if (frexp((double) FLT_RADIX, &log2FLT_RADIX) != 0.5) { @@ -4360,8 +4380,8 @@ TclInitDoubleConversion(void) d = 1.0; /* - * Initialize a table of powers of ten that can be exactly represented - * in a double. + * Initialize a table of powers of ten that can be exactly represented in + * a double. */ x = (int) (DBL_MANT_DIG * log((double) FLT_RADIX) / log(5.0)); @@ -4446,10 +4466,13 @@ TclFinalizeDoubleConversion(void) { int i; - ckfree((char *) pow10_wide); + ckfree(pow10_wide); for (i=0; i<9; ++i) { mp_clear(pow5 + i); } + for (i=0; i < 5; ++i) { + mp_clear(pow5_13 + i); + } } /* @@ -4472,9 +4495,9 @@ TclFinalizeDoubleConversion(void) int Tcl_InitBignumFromDouble( - Tcl_Interp *interp, /* For error message */ - double d, /* Number to convert */ - mp_int *b) /* Place to store the result */ + Tcl_Interp *interp, /* For error message. */ + double d, /* Number to convert. */ + mp_int *b) /* Place to store the result. */ { double fract; int expt; @@ -4528,7 +4551,7 @@ Tcl_InitBignumFromDouble( double TclBignumToDouble( - mp_int *a) /* Integer to convert. */ + const mp_int *a) /* Integer to convert. */ { mp_int b; int bits, shift, i, lsb; @@ -4624,9 +4647,9 @@ TclBignumToDouble( return -r; } } - + /* - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- * * TclCeil -- * @@ -4636,12 +4659,12 @@ TclBignumToDouble( * Results: * Returns the floating point number. * - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- */ double TclCeil( - mp_int *a) /* Integer to convert. */ + const mp_int *a) /* Integer to convert. */ { double r = 0.0; mp_int b; @@ -4681,24 +4704,24 @@ TclCeil( mp_clear(&b); return r; } - + /* - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- * * TclFloor -- * - * Computes the largest floating point number less than or equal to - * the mp_int argument. + * Computes the largest floating point number less than or equal to the + * mp_int argument. * * Results: * Returns the floating point value. * - *----------------------------------------------------------------------------- + *---------------------------------------------------------------------- */ double TclFloor( - mp_int *a) /* Integer to convert. */ + const mp_int *a) /* Integer to convert. */ { double r = 0.0; mp_int b; @@ -4754,8 +4777,8 @@ TclFloor( static double BignumToBiasedFrExp( - mp_int *a, /* Integer to convert */ - int *machexp) /* Power of two */ + const mp_int *a, /* Integer to convert. */ + int *machexp) /* Power of two. */ { mp_int b; int bits; @@ -4819,8 +4842,8 @@ BignumToBiasedFrExp( static double Pow10TimesFrExp( - int exponent, /* Power of 10 to multiply by */ - double fraction, /* Significand of multiplicand */ + int exponent, /* Power of 10 to multiply by. */ + double fraction, /* Significand of multiplicand. */ int *machexp) /* On input, exponent of multiplicand. On * output, exponent of result. */ { @@ -4830,7 +4853,7 @@ Pow10TimesFrExp( if (exponent > 0) { /* - * Multiply by 10**exponent + * Multiply by 10**exponent. */ retval = frexp(retval * pow10vals[exponent&0xf], &j); @@ -4843,7 +4866,7 @@ Pow10TimesFrExp( } } else if (exponent < 0) { /* - * Divide by 10**-exponent + * Divide by 10**-exponent. */ retval = frexp(retval / pow10vals[(-exponent) & 0xf], &j); @@ -4952,26 +4975,27 @@ TclFormatNaN( * * Nokia770Twiddle -- * - * Transpose the two words of a number for Nokia 770 floating - * point handling. + * Transpose the two words of a number for Nokia 770 floating point + * handling. * *---------------------------------------------------------------------- */ - +#ifdef IEEE_FLOATING_POINT static Tcl_WideUInt Nokia770Twiddle( - Tcl_WideUInt w) /* Number to transpose */ + Tcl_WideUInt w) /* Number to transpose. */ { return (((w >> 32) & 0xffffffff) | (w << 32)); } +#endif /* *---------------------------------------------------------------------- * * TclNokia770Doubles -- * - * Transpose the two words of a number for Nokia 770 floating - * point handling. + * Transpose the two words of a number for Nokia 770 floating point + * handling. * *---------------------------------------------------------------------- */ |