5126 lines
133 KiB
C
5126 lines
133 KiB
C
/*
|
||
* tclStrToD.c --
|
||
*
|
||
* This file contains a collection of procedures for managing conversions
|
||
* to/from floating-point in Tcl. They include TclParseNumber, which
|
||
* parses numbers from strings; TclDoubleDigits, which formats numbers
|
||
* into strings of digits, and procedures for interconversion among
|
||
* 'double' and 'mp_int' types.
|
||
*
|
||
* Copyright (c) 2005 by Kevin B. Kenny. All rights reserved.
|
||
*
|
||
* See the file "license.terms" for information on usage and redistribution of
|
||
* this file, and for a DISCLAIMER OF ALL WARRANTIES.
|
||
*/
|
||
|
||
#include "tclInt.h"
|
||
#include "tommath.h"
|
||
#include <float.h>
|
||
#include <math.h>
|
||
|
||
#ifdef _WIN32
|
||
#define copysign _copysign
|
||
#endif
|
||
|
||
/*
|
||
* Define KILL_OCTAL to suppress interpretation of numbers with leading zero
|
||
* as octal. (Ceterum censeo: numeros octonarios delendos esse.)
|
||
*/
|
||
|
||
#undef KILL_OCTAL
|
||
|
||
/*
|
||
* This code supports (at least hypothetically), IBM, Cray, VAX and IEEE-754
|
||
* floating point; of these, only IEEE-754 can represent NaN. IEEE-754 can be
|
||
* uniquely determined by radix and by the widths of significand and exponent.
|
||
*/
|
||
|
||
#if (FLT_RADIX == 2) && (DBL_MANT_DIG == 53) && (DBL_MAX_EXP == 1024)
|
||
# define IEEE_FLOATING_POINT
|
||
#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
|
||
* file exists only on Linux; it is missing on Cygwin and MinGW. Most gcc-isms
|
||
* and ix86-isms are factored out here.
|
||
*/
|
||
|
||
#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
|
||
#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.
|
||
*/
|
||
#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.
|
||
*/
|
||
|
||
#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)
|
||
#else
|
||
# define NAN_START 0x7FF8
|
||
# define NAN_MASK (((Tcl_WideUInt) 1) << 51)
|
||
#endif
|
||
|
||
/*
|
||
* Constants used by this file (most of which are only ever calculated at
|
||
* runtime).
|
||
*/
|
||
|
||
/* Magic constants */
|
||
|
||
#define LOG10_2 0.3010299956639812
|
||
#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
|
||
/* 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)
|
||
/* 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(MP_DIGIT_BIT*log(2)/log(10)) */
|
||
|
||
/*
|
||
* Union used to dismantle floating point numbers.
|
||
*/
|
||
|
||
typedef union Double {
|
||
struct {
|
||
#ifdef WORDS_BIGENDIAN
|
||
int word0;
|
||
int word1;
|
||
#else
|
||
int word1;
|
||
int word0;
|
||
#endif
|
||
} w;
|
||
double d;
|
||
Tcl_WideUInt q;
|
||
} Double;
|
||
|
||
static int maxpow10_wide; /* The powers of ten that can be represented
|
||
* exactly as wide integers. */
|
||
static Tcl_WideUInt *pow10_wide;
|
||
#define MAXPOW 22
|
||
static double pow10vals[MAXPOW+1];
|
||
/* The powers of ten that can be represented
|
||
* exactly as IEEE754 doubles. */
|
||
static int mmaxpow; /* Largest power of ten that can be
|
||
* represented exactly in a 'double'. */
|
||
static int log10_DIGIT_MAX; /* The number of decimal digits that fit in an
|
||
* mp_digit. */
|
||
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 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
|
||
* of the decimal point in a double. */
|
||
static const double pow_10_2_n[] = { /* Inexact higher powers of ten. */
|
||
1.0,
|
||
100.0,
|
||
10000.0,
|
||
1.0e+8,
|
||
1.0e+16,
|
||
1.0e+32,
|
||
1.0e+64,
|
||
1.0e+128,
|
||
1.0e+256
|
||
};
|
||
|
||
static int n770_fp; /* Flag is 1 on Nokia N770 floating point.
|
||
* Nokia's floating point has the words
|
||
* reversed: if big-endian is 7654 3210,
|
||
* and little-endian is 0123 4567,
|
||
* then Nokia's FP is 4567 0123;
|
||
* little-endian within the 32-bit words but
|
||
* big-endian between them. */
|
||
|
||
/*
|
||
* 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,
|
||
625, 3125, 15625, 78125,
|
||
390625, 1953125, 9765625, 48828125,
|
||
244140625
|
||
};
|
||
|
||
/*
|
||
* 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[] = {
|
||
1e00, 1e01, 1e02, 1e03, 1e04, 1e05, 1e06, 1e07, 1e08, 1e09,
|
||
1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
|
||
1e20, 1e21, 1e22
|
||
};
|
||
|
||
static const int itens [] = {
|
||
1,
|
||
10,
|
||
100,
|
||
1000,
|
||
10000,
|
||
100000,
|
||
1000000,
|
||
10000000,
|
||
100000000
|
||
};
|
||
|
||
static const double bigtens[] = {
|
||
1e016, 1e032, 1e064, 1e128, 1e256
|
||
};
|
||
#define N_BIGTENS 5
|
||
|
||
static const int log2pow5[27] = {
|
||
01, 3, 5, 7, 10, 12, 14, 17, 19, 21,
|
||
24, 26, 28, 31, 33, 35, 38, 40, 42, 45,
|
||
47, 49, 52, 54, 56, 59, 61
|
||
};
|
||
#define N_LOG2POW5 27
|
||
|
||
static const Tcl_WideUInt wuipow5[27] = {
|
||
(Tcl_WideUInt) 1, /* 5**0 */
|
||
(Tcl_WideUInt) 5,
|
||
(Tcl_WideUInt) 25,
|
||
(Tcl_WideUInt) 125,
|
||
(Tcl_WideUInt) 625,
|
||
(Tcl_WideUInt) 3125, /* 5**5 */
|
||
(Tcl_WideUInt) 3125*5,
|
||
(Tcl_WideUInt) 3125*25,
|
||
(Tcl_WideUInt) 3125*125,
|
||
(Tcl_WideUInt) 3125*625,
|
||
(Tcl_WideUInt) 3125*3125, /* 5**10 */
|
||
(Tcl_WideUInt) 3125*3125*5,
|
||
(Tcl_WideUInt) 3125*3125*25,
|
||
(Tcl_WideUInt) 3125*3125*125,
|
||
(Tcl_WideUInt) 3125*3125*625,
|
||
(Tcl_WideUInt) 3125*3125*3125, /* 5**15 */
|
||
(Tcl_WideUInt) 3125*3125*3125*5,
|
||
(Tcl_WideUInt) 3125*3125*3125*25,
|
||
(Tcl_WideUInt) 3125*3125*3125*125,
|
||
(Tcl_WideUInt) 3125*3125*3125*625,
|
||
(Tcl_WideUInt) 3125*3125*3125*3125, /* 5**20 */
|
||
(Tcl_WideUInt) 3125*3125*3125*3125*5,
|
||
(Tcl_WideUInt) 3125*3125*3125*3125*25,
|
||
(Tcl_WideUInt) 3125*3125*3125*3125*125,
|
||
(Tcl_WideUInt) 3125*3125*3125*3125*625,
|
||
(Tcl_WideUInt) 3125*3125*3125*3125*3125, /* 5**25 */
|
||
(Tcl_WideUInt) 3125*3125*3125*3125*3125*5 /* 5**26 */
|
||
};
|
||
|
||
/*
|
||
* Static functions defined in this file.
|
||
*/
|
||
|
||
static int AccumulateDecimalDigit(unsigned, int,
|
||
Tcl_WideUInt *, mp_int *, int);
|
||
static double MakeHighPrecisionDouble(int signum,
|
||
mp_int *significand, int nSigDigs, long exponent);
|
||
static double MakeLowPrecisionDouble(int signum,
|
||
Tcl_WideUInt significand, int nSigDigs,
|
||
long 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 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 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,
|
||
int, int, int, int, int, int, int, int, int,
|
||
int, int, int *, char **);
|
||
static char * StrictInt64Conversion(Double *, int, Tcl_WideUInt,
|
||
int, int, int, int, int, int,
|
||
int, int, int *, char **);
|
||
static int ShouldBankerRoundUpPowD(mp_int *, int, int);
|
||
static int ShouldBankerRoundUpToNextPowD(mp_int *, mp_int *,
|
||
int, int, int, mp_int *);
|
||
static char * ShorteningBignumConversionPowD(Double *dPtr,
|
||
int convType, Tcl_WideUInt bw, int b2, int b5,
|
||
int m2plus, int m2minus, int m5,
|
||
int sd, int k, int len,
|
||
int ilim, int ilim1, int *decpt,
|
||
char **endPtr);
|
||
static char * StrictBignumConversionPowD(Double *dPtr, int convType,
|
||
Tcl_WideUInt bw, int b2, int b5,
|
||
int sd, int k, int len,
|
||
int ilim, int ilim1, int *decpt,
|
||
char **endPtr);
|
||
static int ShouldBankerRoundUp(mp_int *, mp_int *, int);
|
||
static int ShouldBankerRoundUpToNext(mp_int *, mp_int *,
|
||
mp_int *, int, int, mp_int *);
|
||
static char * ShorteningBignumConversion(Double *dPtr, int convType,
|
||
Tcl_WideUInt bw, int b2,
|
||
int m2plus, int m2minus,
|
||
int s2, int s5, int k, int len,
|
||
int ilim, int ilim1, int *decpt,
|
||
char **endPtr);
|
||
static char * StrictBignumConversion(Double *dPtr, int convType,
|
||
Tcl_WideUInt bw, int b2,
|
||
int s2, int s5, int k, int len,
|
||
int ilim, int ilim1, int *decpt,
|
||
char **endPtr);
|
||
static double BignumToBiasedFrExp(const mp_int *big, int *machexp);
|
||
static double Pow10TimesFrExp(int exponent, double fraction,
|
||
int *machexp);
|
||
static double SafeLdExp(double fraction, int exponent);
|
||
#ifdef IEEE_FLOATING_POINT
|
||
static Tcl_WideUInt Nokia770Twiddle(Tcl_WideUInt w);
|
||
#endif
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* TclParseNumber --
|
||
*
|
||
* Scans bytes, interpreted as characters in Tcl's internal encoding, and
|
||
* parses the longest prefix that is the string representation of a
|
||
* number in a format recognized by Tcl.
|
||
*
|
||
* The arguments bytes, numBytes, and objPtr are the inputs which
|
||
* determine the string to be parsed. If bytes is non-NULL, it points to
|
||
* the first byte to be scanned. If bytes is NULL, then objPtr must be
|
||
* non-NULL, and the string representation of objPtr will be scanned
|
||
* (generated first, if necessary). The numBytes argument determines the
|
||
* number of bytes to be scanned. If numBytes is negative, the first NUL
|
||
* byte encountered will terminate the scan. If numBytes is non-negative,
|
||
* then no more than numBytes bytes will be scanned.
|
||
*
|
||
* The argument flags is an input that controls the numeric formats
|
||
* recognized by the parser. The flag bits are:
|
||
*
|
||
* - TCL_PARSE_INTEGER_ONLY: accept only integer values; reject
|
||
* strings that denote floating point values (or accept only the
|
||
* leading portion of them that are integer values).
|
||
* - 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_BINARY_ONLY: parse only in the binary format, whether
|
||
* or not a prefix is present that would lead to binary parsing.
|
||
* Use only in combination with TCL_PARSE_INTEGER_ONLY.
|
||
* - 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,
|
||
* 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
|
||
* matter whether a 0 prefix would normally force a different
|
||
* base.
|
||
* - TCL_PARSE_NO_WHITESPACE: reject any leading/trailing whitespace
|
||
*
|
||
* The arguments interp and expected are inputs that control error
|
||
* message generation. If interp is NULL, no error message will be
|
||
* generated. If interp is non-NULL, then expected must also be non-NULL.
|
||
* When TCL_ERROR is returned, an error message will be left in the
|
||
* result of interp, and the expected argument will appear in the error
|
||
* message as the thing TclParseNumber expected, but failed to find in
|
||
* the string.
|
||
*
|
||
* The arguments objPtr and endPtrPtr as well as the return code are the
|
||
* outputs.
|
||
*
|
||
* When the parser cannot find any prefix of the string that matches a
|
||
* format it is looking for, TCL_ERROR is returned and an error message
|
||
* may be generated and returned as described above. The contents of
|
||
* objPtr will not be changed. If endPtrPtr is non-NULL, a pointer to the
|
||
* character in the string that terminated the scan will be written to
|
||
* *endPtrPtr.
|
||
*
|
||
* When the parser determines that the entire string matches a format it
|
||
* is looking for, TCL_OK is returned, and if objPtr is non-NULL, then
|
||
* the internal rep and Tcl_ObjType of objPtr are set to the "canonical"
|
||
* numeric value that matches the scanned string. If endPtrPtr is not
|
||
* NULL, a pointer to the end of the string will be written to *endPtrPtr
|
||
* (that is, either bytes+numBytes or a pointer to a terminating NUL
|
||
* byte).
|
||
*
|
||
* When the parser determines that a partial string matches a format it
|
||
* is looking for, the value of endPtrPtr determines what happens:
|
||
*
|
||
* - If endPtrPtr is NULL, then TCL_ERROR is returned, with error message
|
||
* generation as above.
|
||
*
|
||
* - If endPtrPtr is non-NULL, then TCL_OK is returned and objPtr
|
||
* internals are set as above. Also, a pointer to the first
|
||
* character following the parsed numeric string is written to
|
||
* *endPtrPtr.
|
||
*
|
||
* In some cases where the string being scanned is the string rep of
|
||
* objPtr, this routine can leave objPtr in an inconsistent state where
|
||
* its string rep and its internal rep do not agree. In these cases the
|
||
* internal rep will be in agreement with only some substring of the
|
||
* string rep. This might happen if the caller passes in a non-NULL bytes
|
||
* value that points somewhere into the string rep. It might happen if
|
||
* the caller passes in a numBytes value that limits the scan to only a
|
||
* prefix of the string rep. Or it might happen if a non-NULL value of
|
||
* endPtrPtr permits a TCL_OK return from only a partial string match. It
|
||
* is the responsibility of the caller to detect and correct such
|
||
* inconsistencies when they can and do arise.
|
||
*
|
||
* Results:
|
||
* Returns a standard Tcl result.
|
||
*
|
||
* Side effects:
|
||
* The string representaton of objPtr may be generated.
|
||
*
|
||
* The internal representation and Tcl_ObjType of objPtr may be changed.
|
||
* This may involve allocation and/or freeing of memory.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
int
|
||
TclParseNumber(
|
||
Tcl_Interp *interp, /* Used for error reporting. May be NULL. */
|
||
Tcl_Obj *objPtr, /* Object to receive the internal rep. */
|
||
const char *expected, /* Description of the type of number the
|
||
* caller expects to be able to parse
|
||
* ("integer", "boolean value", etc.). */
|
||
const char *bytes, /* Pointer to the start of the string to
|
||
* scan. */
|
||
int numBytes, /* Maximum number of bytes to scan, see
|
||
* above. */
|
||
const char **endPtrPtr, /* Place to store pointer to the character
|
||
* that terminated the scan. */
|
||
int flags) /* Flags governing the parse. */
|
||
{
|
||
enum State {
|
||
INITIAL, SIGNUM, ZERO, ZERO_X,
|
||
ZERO_O, ZERO_B, BINARY,
|
||
HEXADECIMAL, OCTAL, BAD_OCTAL, DECIMAL,
|
||
LEADING_RADIX_POINT, FRACTION,
|
||
EXPONENT_START, EXPONENT_SIGNUM, EXPONENT,
|
||
sI, sIN, sINF, sINFI, sINFIN, sINFINI, sINFINIT, sINFINITY
|
||
#ifdef IEEE_FLOATING_POINT
|
||
, sN, sNA, sNAN, sNANPAREN, sNANHEX, sNANFINISH
|
||
#endif
|
||
} state = INITIAL;
|
||
enum State acceptState = INITIAL;
|
||
|
||
int signum = 0; /* Sign of the number being parsed. */
|
||
Tcl_WideUInt significandWide = 0;
|
||
/* Significand of the number being parsed (if
|
||
* no overflow). */
|
||
mp_int significandBig; /* Significand of the number being parsed (if
|
||
* it overflows significandWide). */
|
||
int significandOverflow = 0;/* Flag==1 iff significandBig is used. */
|
||
Tcl_WideUInt octalSignificandWide = 0;
|
||
/* Significand of an octal number; needed
|
||
* because we don't know whether a number with
|
||
* a leading zero is octal or decimal until
|
||
* we've scanned forward to a '.' or 'e'. */
|
||
mp_int octalSignificandBig; /* Significand of octal number once
|
||
* octalSignificandWide overflows. */
|
||
int octalSignificandOverflow = 0;
|
||
/* Flag==1 if octalSignificandBig is used. */
|
||
int numSigDigs = 0; /* Number of significant digits in the decimal
|
||
* significand. */
|
||
int numTrailZeros = 0; /* Number of trailing zeroes at the current
|
||
* point in the parse. */
|
||
int numDigitsAfterDp = 0; /* Number of digits scanned after the decimal
|
||
* point. */
|
||
int exponentSignum = 0; /* Signum of the exponent of a floating point
|
||
* 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. */
|
||
size_t acceptLen; /* Number of characters following that
|
||
* point. */
|
||
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 */
|
||
int explicitOctal = 0;
|
||
|
||
#define ALL_BITS (~(Tcl_WideUInt)0)
|
||
#define MOST_BITS (ALL_BITS >> 1)
|
||
|
||
/*
|
||
* Initialize bytes to start of the object's string rep if the caller
|
||
* didn't pass anything else.
|
||
*/
|
||
|
||
if (bytes == NULL) {
|
||
bytes = TclGetString(objPtr);
|
||
}
|
||
|
||
p = bytes;
|
||
len = numBytes;
|
||
acceptPoint = p;
|
||
acceptLen = len;
|
||
while (1) {
|
||
char c = len ? *p : '\0';
|
||
switch (state) {
|
||
|
||
case INITIAL:
|
||
/*
|
||
* Initial state. Acceptable characters are +, -, digits, period,
|
||
* I, N, and whitespace.
|
||
*/
|
||
|
||
if (TclIsSpaceProcM(c)) {
|
||
if (flags & TCL_PARSE_NO_WHITESPACE) {
|
||
goto endgame;
|
||
}
|
||
break;
|
||
} else if (c == '+') {
|
||
state = SIGNUM;
|
||
break;
|
||
} else if (c == '-') {
|
||
signum = 1;
|
||
state = SIGNUM;
|
||
break;
|
||
}
|
||
/* FALLTHROUGH */
|
||
|
||
case SIGNUM:
|
||
/*
|
||
* Scanned a leading + or -. Acceptable characters are digits,
|
||
* period, I, and N.
|
||
*/
|
||
|
||
if (c == '0') {
|
||
if (flags & TCL_PARSE_DECIMAL_ONLY) {
|
||
state = DECIMAL;
|
||
} else {
|
||
state = ZERO;
|
||
}
|
||
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))) {
|
||
significandWide = c - '0';
|
||
numSigDigs = 1;
|
||
state = DECIMAL;
|
||
break;
|
||
} else if (flags & TCL_PARSE_INTEGER_ONLY) {
|
||
goto endgame;
|
||
} else if (c == '.') {
|
||
state = LEADING_RADIX_POINT;
|
||
break;
|
||
} else if (c == 'I' || c == 'i') {
|
||
state = sI;
|
||
break;
|
||
#ifdef IEEE_FLOATING_POINT
|
||
} else if (c == 'N' || c == 'n') {
|
||
state = sN;
|
||
break;
|
||
#endif
|
||
}
|
||
goto endgame;
|
||
|
||
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'.
|
||
*/
|
||
|
||
acceptState = state;
|
||
acceptPoint = p;
|
||
acceptLen = len;
|
||
if (c == 'x' || c == 'X') {
|
||
if (flags & (TCL_PARSE_OCTAL_ONLY|TCL_PARSE_BINARY_ONLY)) {
|
||
goto endgame;
|
||
}
|
||
state = ZERO_X;
|
||
break;
|
||
}
|
||
if (flags & TCL_PARSE_HEXADECIMAL_ONLY) {
|
||
goto zerox;
|
||
}
|
||
if (flags & TCL_PARSE_SCAN_PREFIXES) {
|
||
goto zeroo;
|
||
}
|
||
if (c == 'b' || c == 'B') {
|
||
if (flags & TCL_PARSE_OCTAL_ONLY) {
|
||
goto endgame;
|
||
}
|
||
state = ZERO_B;
|
||
break;
|
||
}
|
||
if (flags & TCL_PARSE_BINARY_ONLY) {
|
||
goto zerob;
|
||
}
|
||
if (c == 'o' || c == 'O') {
|
||
explicitOctal = 1;
|
||
state = ZERO_O;
|
||
break;
|
||
}
|
||
#ifdef KILL_OCTAL
|
||
goto decimal;
|
||
#endif
|
||
/* FALLTHROUGH */
|
||
|
||
case OCTAL:
|
||
/*
|
||
* Scanned an optional + or -, followed by a string of octal
|
||
* digits. Acceptable inputs are more digits, period, or E. If 8
|
||
* or 9 is encountered, commit to floating point.
|
||
*/
|
||
|
||
acceptState = state;
|
||
acceptPoint = p;
|
||
acceptLen = len;
|
||
/* FALLTHROUGH */
|
||
case ZERO_O:
|
||
zeroo:
|
||
if (c == '0') {
|
||
numTrailZeros++;
|
||
state = OCTAL;
|
||
break;
|
||
} else if (c >= '1' && c <= '7') {
|
||
if (objPtr != NULL) {
|
||
shift = 3 * (numTrailZeros + 1);
|
||
significandOverflow = AccumulateDecimalDigit(
|
||
(unsigned)(c-'0'), numTrailZeros,
|
||
&significandWide, &significandBig,
|
||
significandOverflow);
|
||
|
||
if (!octalSignificandOverflow) {
|
||
/*
|
||
* Shifting by more bits than are in the value being
|
||
* shifted is at least de facto nonportable. Check for
|
||
* too large shifts first.
|
||
*/
|
||
|
||
if ((octalSignificandWide != 0)
|
||
&& (((size_t)shift >=
|
||
CHAR_BIT*sizeof(Tcl_WideUInt))
|
||
|| (octalSignificandWide >
|
||
(~(Tcl_WideUInt)0 >> shift)))) {
|
||
octalSignificandOverflow = 1;
|
||
TclBNInitBignumFromWideUInt(&octalSignificandBig,
|
||
octalSignificandWide);
|
||
}
|
||
}
|
||
if (!octalSignificandOverflow) {
|
||
octalSignificandWide =
|
||
(octalSignificandWide << shift) + (c - '0');
|
||
} else {
|
||
mp_mul_2d(&octalSignificandBig, shift,
|
||
&octalSignificandBig);
|
||
mp_add_d(&octalSignificandBig, (mp_digit)(c - '0'),
|
||
&octalSignificandBig);
|
||
}
|
||
}
|
||
if (numSigDigs != 0) {
|
||
numSigDigs += numTrailZeros+1;
|
||
} else {
|
||
numSigDigs = 1;
|
||
}
|
||
numTrailZeros = 0;
|
||
state = OCTAL;
|
||
break;
|
||
}
|
||
/* FALLTHROUGH */
|
||
|
||
case BAD_OCTAL:
|
||
if (explicitOctal) {
|
||
/*
|
||
* No forgiveness for bad digits in explicitly octal numbers.
|
||
*/
|
||
|
||
goto endgame;
|
||
}
|
||
if (flags & TCL_PARSE_INTEGER_ONLY) {
|
||
/*
|
||
* No seeking floating point when parsing only integer.
|
||
*/
|
||
|
||
goto endgame;
|
||
}
|
||
#ifndef KILL_OCTAL
|
||
|
||
/*
|
||
* Scanned a number with a leading zero that contains an 8, 9,
|
||
* radix point or E. This is an invalid octal number, but might
|
||
* still be floating point.
|
||
*/
|
||
|
||
if (c == '0') {
|
||
numTrailZeros++;
|
||
state = BAD_OCTAL;
|
||
break;
|
||
} else if (isdigit(UCHAR(c))) {
|
||
if (objPtr != NULL) {
|
||
significandOverflow = AccumulateDecimalDigit(
|
||
(unsigned)(c-'0'), numTrailZeros,
|
||
&significandWide, &significandBig,
|
||
significandOverflow);
|
||
}
|
||
if (numSigDigs != 0) {
|
||
numSigDigs += (numTrailZeros + 1);
|
||
} else {
|
||
numSigDigs = 1;
|
||
}
|
||
numTrailZeros = 0;
|
||
state = BAD_OCTAL;
|
||
break;
|
||
} else if (c == '.') {
|
||
state = FRACTION;
|
||
break;
|
||
} else if (c == 'E' || c == 'e') {
|
||
state = EXPONENT_START;
|
||
break;
|
||
}
|
||
#endif
|
||
goto endgame;
|
||
|
||
/*
|
||
* Scanned 0x. If state is HEXADECIMAL, scanned at least one
|
||
* character following the 0x. The only acceptable inputs are
|
||
* hexadecimal digits.
|
||
*/
|
||
|
||
case HEXADECIMAL:
|
||
acceptState = state;
|
||
acceptPoint = p;
|
||
acceptLen = len;
|
||
/* FALLTHROUGH */
|
||
|
||
case ZERO_X:
|
||
zerox:
|
||
if (c == '0') {
|
||
numTrailZeros++;
|
||
state = HEXADECIMAL;
|
||
break;
|
||
} else if (isdigit(UCHAR(c))) {
|
||
d = (c-'0');
|
||
} else if (c >= 'A' && c <= 'F') {
|
||
d = (c-'A'+10);
|
||
} else if (c >= 'a' && c <= 'f') {
|
||
d = (c-'a'+10);
|
||
} else {
|
||
goto endgame;
|
||
}
|
||
if (objPtr != NULL) {
|
||
shift = 4 * (numTrailZeros + 1);
|
||
if (!significandOverflow) {
|
||
/*
|
||
* Shifting by more bits than are in the value being
|
||
* shifted is at least de facto nonportable. Check for too
|
||
* large shifts first.
|
||
*/
|
||
|
||
if (significandWide != 0 &&
|
||
((size_t)shift >= CHAR_BIT*sizeof(Tcl_WideUInt) ||
|
||
significandWide > (~(Tcl_WideUInt)0 >> shift))) {
|
||
significandOverflow = 1;
|
||
TclBNInitBignumFromWideUInt(&significandBig,
|
||
significandWide);
|
||
}
|
||
}
|
||
if (!significandOverflow) {
|
||
significandWide = (significandWide << shift) + d;
|
||
} else {
|
||
mp_mul_2d(&significandBig, shift, &significandBig);
|
||
mp_add_d(&significandBig, (mp_digit) d, &significandBig);
|
||
}
|
||
}
|
||
numTrailZeros = 0;
|
||
state = HEXADECIMAL;
|
||
break;
|
||
|
||
case BINARY:
|
||
acceptState = state;
|
||
acceptPoint = p;
|
||
acceptLen = len;
|
||
/* FALLTHRU */
|
||
case ZERO_B:
|
||
zerob:
|
||
if (c == '0') {
|
||
numTrailZeros++;
|
||
state = BINARY;
|
||
break;
|
||
} else if (c != '1') {
|
||
goto endgame;
|
||
}
|
||
if (objPtr != NULL) {
|
||
shift = numTrailZeros + 1;
|
||
if (!significandOverflow) {
|
||
/*
|
||
* Shifting by more bits than are in the value being
|
||
* shifted is at least de facto nonportable. Check for too
|
||
* large shifts first.
|
||
*/
|
||
|
||
if (significandWide != 0 &&
|
||
((size_t)shift >= CHAR_BIT*sizeof(Tcl_WideUInt) ||
|
||
significandWide > (~(Tcl_WideUInt)0 >> shift))) {
|
||
significandOverflow = 1;
|
||
TclBNInitBignumFromWideUInt(&significandBig,
|
||
significandWide);
|
||
}
|
||
}
|
||
if (!significandOverflow) {
|
||
significandWide = (significandWide << shift) + 1;
|
||
} else {
|
||
mp_mul_2d(&significandBig, shift, &significandBig);
|
||
mp_add_d(&significandBig, (mp_digit) 1, &significandBig);
|
||
}
|
||
}
|
||
numTrailZeros = 0;
|
||
state = BINARY;
|
||
break;
|
||
|
||
case DECIMAL:
|
||
/*
|
||
* Scanned an optional + or - followed by a string of decimal
|
||
* digits.
|
||
*/
|
||
|
||
#ifdef KILL_OCTAL
|
||
decimal:
|
||
#endif
|
||
acceptState = state;
|
||
acceptPoint = p;
|
||
acceptLen = len;
|
||
if (c == '0') {
|
||
numTrailZeros++;
|
||
state = DECIMAL;
|
||
break;
|
||
} else if (isdigit(UCHAR(c))) {
|
||
if (objPtr != NULL) {
|
||
significandOverflow = AccumulateDecimalDigit(
|
||
(unsigned)(c - '0'), numTrailZeros,
|
||
&significandWide, &significandBig,
|
||
significandOverflow);
|
||
}
|
||
numSigDigs += numTrailZeros+1;
|
||
numTrailZeros = 0;
|
||
state = DECIMAL;
|
||
break;
|
||
} else if (flags & TCL_PARSE_INTEGER_ONLY) {
|
||
goto endgame;
|
||
} else if (c == '.') {
|
||
state = FRACTION;
|
||
break;
|
||
} else if (c == 'E' || c == 'e') {
|
||
state = EXPONENT_START;
|
||
break;
|
||
}
|
||
goto endgame;
|
||
|
||
/*
|
||
* Found a decimal point. If no digits have yet been scanned, E is
|
||
* not allowed; otherwise, it introduces the exponent. If at least
|
||
* one digit has been found, we have a possible complete number.
|
||
*/
|
||
|
||
case FRACTION:
|
||
acceptState = state;
|
||
acceptPoint = p;
|
||
acceptLen = len;
|
||
if (c == 'E' || c=='e') {
|
||
state = EXPONENT_START;
|
||
break;
|
||
}
|
||
/* FALLTHROUGH */
|
||
|
||
case LEADING_RADIX_POINT:
|
||
if (c == '0') {
|
||
numDigitsAfterDp++;
|
||
numTrailZeros++;
|
||
state = FRACTION;
|
||
break;
|
||
} else if (isdigit(UCHAR(c))) {
|
||
numDigitsAfterDp++;
|
||
if (objPtr != NULL) {
|
||
significandOverflow = AccumulateDecimalDigit(
|
||
(unsigned)(c-'0'), numTrailZeros,
|
||
&significandWide, &significandBig,
|
||
significandOverflow);
|
||
}
|
||
if (numSigDigs != 0) {
|
||
numSigDigs += numTrailZeros+1;
|
||
} else {
|
||
numSigDigs = 1;
|
||
}
|
||
numTrailZeros = 0;
|
||
state = FRACTION;
|
||
break;
|
||
}
|
||
goto endgame;
|
||
|
||
case EXPONENT_START:
|
||
/*
|
||
* Scanned the E at the start of an exponent. Make sure a legal
|
||
* character follows before using the C library strtol routine,
|
||
* which allows whitespace.
|
||
*/
|
||
|
||
if (c == '+') {
|
||
state = EXPONENT_SIGNUM;
|
||
break;
|
||
} else if (c == '-') {
|
||
exponentSignum = 1;
|
||
state = EXPONENT_SIGNUM;
|
||
break;
|
||
}
|
||
/* FALLTHROUGH */
|
||
|
||
case EXPONENT_SIGNUM:
|
||
/*
|
||
* Found the E at the start of the exponent, followed by a sign
|
||
* character.
|
||
*/
|
||
|
||
if (isdigit(UCHAR(c))) {
|
||
exponent = c - '0';
|
||
state = EXPONENT;
|
||
break;
|
||
}
|
||
goto endgame;
|
||
|
||
case EXPONENT:
|
||
/*
|
||
* Found an exponent with at least one digit. Accumulate it,
|
||
* making sure to hard-pin it to LONG_MAX on overflow.
|
||
*/
|
||
|
||
acceptState = state;
|
||
acceptPoint = p;
|
||
acceptLen = len;
|
||
if (isdigit(UCHAR(c))) {
|
||
if (exponent < (LONG_MAX - 9) / 10) {
|
||
exponent = 10 * exponent + (c - '0');
|
||
} else {
|
||
exponent = LONG_MAX;
|
||
}
|
||
state = EXPONENT;
|
||
break;
|
||
}
|
||
goto endgame;
|
||
|
||
/*
|
||
* Parse out INFINITY by simply spelling it out. INF is accepted
|
||
* as an abbreviation; other prefices are not.
|
||
*/
|
||
|
||
case sI:
|
||
if (c == 'n' || c == 'N') {
|
||
state = sIN;
|
||
break;
|
||
}
|
||
goto endgame;
|
||
case sIN:
|
||
if (c == 'f' || c == 'F') {
|
||
state = sINF;
|
||
break;
|
||
}
|
||
goto endgame;
|
||
case sINF:
|
||
acceptState = state;
|
||
acceptPoint = p;
|
||
acceptLen = len;
|
||
if (c == 'i' || c == 'I') {
|
||
state = sINFI;
|
||
break;
|
||
}
|
||
goto endgame;
|
||
case sINFI:
|
||
if (c == 'n' || c == 'N') {
|
||
state = sINFIN;
|
||
break;
|
||
}
|
||
goto endgame;
|
||
case sINFIN:
|
||
if (c == 'i' || c == 'I') {
|
||
state = sINFINI;
|
||
break;
|
||
}
|
||
goto endgame;
|
||
case sINFINI:
|
||
if (c == 't' || c == 'T') {
|
||
state = sINFINIT;
|
||
break;
|
||
}
|
||
goto endgame;
|
||
case sINFINIT:
|
||
if (c == 'y' || c == 'Y') {
|
||
state = sINFINITY;
|
||
break;
|
||
}
|
||
goto endgame;
|
||
|
||
/*
|
||
* Parse NaN's.
|
||
*/
|
||
#ifdef IEEE_FLOATING_POINT
|
||
case sN:
|
||
if (c == 'a' || c == 'A') {
|
||
state = sNA;
|
||
break;
|
||
}
|
||
goto endgame;
|
||
case sNA:
|
||
if (c == 'n' || c == 'N') {
|
||
state = sNAN;
|
||
break;
|
||
}
|
||
goto endgame;
|
||
case sNAN:
|
||
acceptState = state;
|
||
acceptPoint = p;
|
||
acceptLen = len;
|
||
if (c == '(') {
|
||
state = sNANPAREN;
|
||
break;
|
||
}
|
||
goto endgame;
|
||
|
||
/*
|
||
* Parse NaN(hexdigits)
|
||
*/
|
||
case sNANHEX:
|
||
if (c == ')') {
|
||
state = sNANFINISH;
|
||
break;
|
||
}
|
||
/* FALLTHROUGH */
|
||
case sNANPAREN:
|
||
if (TclIsSpaceProcM(c)) {
|
||
break;
|
||
}
|
||
if (numSigDigs < 13) {
|
||
if (c >= '0' && c <= '9') {
|
||
d = c - '0';
|
||
} else if (c >= 'a' && c <= 'f') {
|
||
d = 10 + c - 'a';
|
||
} else if (c >= 'A' && c <= 'F') {
|
||
d = 10 + c - 'A';
|
||
} else {
|
||
goto endgame;
|
||
}
|
||
numSigDigs++;
|
||
significandWide = (significandWide << 4) + d;
|
||
state = sNANHEX;
|
||
break;
|
||
}
|
||
goto endgame;
|
||
case sNANFINISH:
|
||
#endif
|
||
|
||
case sINFINITY:
|
||
acceptState = state;
|
||
acceptPoint = p;
|
||
acceptLen = len;
|
||
goto endgame;
|
||
}
|
||
p++;
|
||
len--;
|
||
}
|
||
|
||
endgame:
|
||
if (acceptState == INITIAL) {
|
||
/*
|
||
* No numeric string at all found.
|
||
*/
|
||
|
||
status = TCL_ERROR;
|
||
if (endPtrPtr != NULL) {
|
||
*endPtrPtr = p;
|
||
}
|
||
} else {
|
||
/*
|
||
* Back up to the last accepting state in the lexer.
|
||
*/
|
||
|
||
p = acceptPoint;
|
||
len = acceptLen;
|
||
if (!(flags & TCL_PARSE_NO_WHITESPACE)) {
|
||
/*
|
||
* Accept trailing whitespace.
|
||
*/
|
||
|
||
while (len != 0 && TclIsSpaceProcM(*p)) {
|
||
p++;
|
||
len--;
|
||
}
|
||
}
|
||
if (endPtrPtr == NULL) {
|
||
if ((len != 0) && ((numBytes > 0) || (*p != '\0'))) {
|
||
status = TCL_ERROR;
|
||
}
|
||
} else {
|
||
*endPtrPtr = p;
|
||
}
|
||
}
|
||
|
||
/*
|
||
* Generate and store the appropriate internal rep.
|
||
*/
|
||
|
||
if (status == TCL_OK && objPtr != NULL) {
|
||
TclFreeIntRep(objPtr);
|
||
switch (acceptState) {
|
||
case SIGNUM:
|
||
case BAD_OCTAL:
|
||
case ZERO_X:
|
||
case ZERO_O:
|
||
case ZERO_B:
|
||
case LEADING_RADIX_POINT:
|
||
case EXPONENT_START:
|
||
case EXPONENT_SIGNUM:
|
||
case sI:
|
||
case sIN:
|
||
case sINFI:
|
||
case sINFIN:
|
||
case sINFINI:
|
||
case sINFINIT:
|
||
#ifdef IEEE_FLOATING_POINT
|
||
case sN:
|
||
case sNA:
|
||
case sNANPAREN:
|
||
case sNANHEX:
|
||
#endif
|
||
Tcl_Panic("TclParseNumber: bad acceptState %d parsing '%s'",
|
||
acceptState, bytes);
|
||
case BINARY:
|
||
shift = numTrailZeros;
|
||
if (!significandOverflow && significandWide != 0 &&
|
||
((size_t)shift >= CHAR_BIT*sizeof(Tcl_WideUInt) ||
|
||
significandWide > (MOST_BITS + signum) >> shift)) {
|
||
significandOverflow = 1;
|
||
TclBNInitBignumFromWideUInt(&significandBig, significandWide);
|
||
}
|
||
if (shift) {
|
||
if (!significandOverflow) {
|
||
significandWide <<= shift;
|
||
} else {
|
||
mp_mul_2d(&significandBig, shift, &significandBig);
|
||
}
|
||
}
|
||
goto returnInteger;
|
||
|
||
case HEXADECIMAL:
|
||
/*
|
||
* Returning a hex integer. Final scaling step.
|
||
*/
|
||
|
||
shift = 4 * numTrailZeros;
|
||
if (!significandOverflow && significandWide !=0 &&
|
||
((size_t)shift >= CHAR_BIT*sizeof(Tcl_WideUInt) ||
|
||
significandWide > (MOST_BITS + signum) >> shift)) {
|
||
significandOverflow = 1;
|
||
TclBNInitBignumFromWideUInt(&significandBig, significandWide);
|
||
}
|
||
if (shift) {
|
||
if (!significandOverflow) {
|
||
significandWide <<= shift;
|
||
} else {
|
||
mp_mul_2d(&significandBig, shift, &significandBig);
|
||
}
|
||
}
|
||
goto returnInteger;
|
||
|
||
case OCTAL:
|
||
/*
|
||
* Returning an octal integer. Final scaling step.
|
||
*/
|
||
|
||
shift = 3 * numTrailZeros;
|
||
if (!octalSignificandOverflow && octalSignificandWide != 0 &&
|
||
((size_t)shift >= CHAR_BIT*sizeof(Tcl_WideUInt) ||
|
||
octalSignificandWide > (MOST_BITS + signum) >> shift)) {
|
||
octalSignificandOverflow = 1;
|
||
TclBNInitBignumFromWideUInt(&octalSignificandBig,
|
||
octalSignificandWide);
|
||
}
|
||
if (shift) {
|
||
if (!octalSignificandOverflow) {
|
||
octalSignificandWide <<= shift;
|
||
} else {
|
||
mp_mul_2d(&octalSignificandBig, shift,
|
||
&octalSignificandBig);
|
||
}
|
||
}
|
||
if (!octalSignificandOverflow) {
|
||
if (octalSignificandWide >
|
||
(Tcl_WideUInt)(((~(unsigned long)0) >> 1) + signum)) {
|
||
#ifndef TCL_WIDE_INT_IS_LONG
|
||
if (octalSignificandWide <= (MOST_BITS + signum)) {
|
||
objPtr->typePtr = &tclWideIntType;
|
||
if (signum) {
|
||
objPtr->internalRep.wideValue =
|
||
- (Tcl_WideInt) octalSignificandWide;
|
||
} else {
|
||
objPtr->internalRep.wideValue =
|
||
(Tcl_WideInt) octalSignificandWide;
|
||
}
|
||
break;
|
||
}
|
||
#endif
|
||
TclBNInitBignumFromWideUInt(&octalSignificandBig,
|
||
octalSignificandWide);
|
||
octalSignificandOverflow = 1;
|
||
} else {
|
||
objPtr->typePtr = &tclIntType;
|
||
if (signum) {
|
||
objPtr->internalRep.longValue =
|
||
- (long) octalSignificandWide;
|
||
} else {
|
||
objPtr->internalRep.longValue =
|
||
(long) octalSignificandWide;
|
||
}
|
||
}
|
||
}
|
||
if (octalSignificandOverflow) {
|
||
if (signum) {
|
||
(void)mp_neg(&octalSignificandBig, &octalSignificandBig);
|
||
}
|
||
TclSetBignumInternalRep(objPtr, &octalSignificandBig);
|
||
}
|
||
break;
|
||
|
||
case ZERO:
|
||
case DECIMAL:
|
||
significandOverflow = AccumulateDecimalDigit(0, numTrailZeros-1,
|
||
&significandWide, &significandBig, significandOverflow);
|
||
if (!significandOverflow && (significandWide > MOST_BITS+signum)) {
|
||
significandOverflow = 1;
|
||
TclBNInitBignumFromWideUInt(&significandBig, significandWide);
|
||
}
|
||
returnInteger:
|
||
if (!significandOverflow) {
|
||
if (significandWide >
|
||
(Tcl_WideUInt)(((~(unsigned long)0) >> 1) + signum)) {
|
||
#ifndef TCL_WIDE_INT_IS_LONG
|
||
if (significandWide <= MOST_BITS+signum) {
|
||
objPtr->typePtr = &tclWideIntType;
|
||
if (signum) {
|
||
objPtr->internalRep.wideValue =
|
||
- (Tcl_WideInt) significandWide;
|
||
} else {
|
||
objPtr->internalRep.wideValue =
|
||
(Tcl_WideInt) significandWide;
|
||
}
|
||
break;
|
||
}
|
||
#endif
|
||
TclBNInitBignumFromWideUInt(&significandBig,
|
||
significandWide);
|
||
significandOverflow = 1;
|
||
} else {
|
||
objPtr->typePtr = &tclIntType;
|
||
if (signum) {
|
||
objPtr->internalRep.longValue =
|
||
- (long) significandWide;
|
||
} else {
|
||
objPtr->internalRep.longValue =
|
||
(long) significandWide;
|
||
}
|
||
}
|
||
}
|
||
if (significandOverflow) {
|
||
if (signum) {
|
||
(void)mp_neg(&significandBig, &significandBig);
|
||
}
|
||
TclSetBignumInternalRep(objPtr, &significandBig);
|
||
}
|
||
break;
|
||
|
||
case FRACTION:
|
||
case EXPONENT:
|
||
|
||
/*
|
||
* Here, we're parsing a floating-point number. 'significandWide'
|
||
* or 'significandBig' contains the exact significand, according
|
||
* to whether 'significandOverflow' is set. The desired floating
|
||
* point value is significand * 10**k, where
|
||
* k = numTrailZeros+exponent-numDigitsAfterDp.
|
||
*/
|
||
|
||
objPtr->typePtr = &tclDoubleType;
|
||
if (exponentSignum) {
|
||
/*
|
||
* At this point exponent>=0, so the following calculation
|
||
* cannot underflow.
|
||
*/
|
||
exponent = -exponent;
|
||
}
|
||
|
||
/*
|
||
* Adjust the exponent for the number of trailing zeros that
|
||
* have not been accumulated, and the number of digits after
|
||
* the decimal point. Pin any overflow to LONG_MAX/LONG_MIN
|
||
* respectively.
|
||
*/
|
||
|
||
if (exponent >= 0) {
|
||
if (exponent - numDigitsAfterDp > LONG_MAX - numTrailZeros) {
|
||
exponent = LONG_MAX;
|
||
} else {
|
||
exponent = exponent - numDigitsAfterDp + numTrailZeros;
|
||
}
|
||
} else {
|
||
if (exponent + numTrailZeros < LONG_MIN + numDigitsAfterDp) {
|
||
exponent = LONG_MIN;
|
||
} else {
|
||
exponent = exponent + numTrailZeros - numDigitsAfterDp;
|
||
}
|
||
}
|
||
|
||
/*
|
||
* The desired number is now significandWide * 10**exponent
|
||
* or significandBig * 10**exponent, depending on whether
|
||
* the significand has overflowed a wide int.
|
||
*/
|
||
if (!significandOverflow) {
|
||
objPtr->internalRep.doubleValue = MakeLowPrecisionDouble(
|
||
signum, significandWide, numSigDigs, exponent);
|
||
} else {
|
||
objPtr->internalRep.doubleValue = MakeHighPrecisionDouble(
|
||
signum, &significandBig, numSigDigs, exponent);
|
||
}
|
||
break;
|
||
|
||
case sINF:
|
||
case sINFINITY:
|
||
if (signum) {
|
||
objPtr->internalRep.doubleValue = -HUGE_VAL;
|
||
} else {
|
||
objPtr->internalRep.doubleValue = HUGE_VAL;
|
||
}
|
||
objPtr->typePtr = &tclDoubleType;
|
||
break;
|
||
|
||
#ifdef IEEE_FLOATING_POINT
|
||
case sNAN:
|
||
case sNANFINISH:
|
||
objPtr->internalRep.doubleValue = MakeNaN(signum, significandWide);
|
||
objPtr->typePtr = &tclDoubleType;
|
||
break;
|
||
#endif
|
||
case INITIAL:
|
||
/* This case only to silence compiler warning. */
|
||
Tcl_Panic("TclParseNumber: state INITIAL can't happen here");
|
||
}
|
||
}
|
||
|
||
/*
|
||
* Format an error message when an invalid number is encountered.
|
||
*/
|
||
|
||
if (status != TCL_OK) {
|
||
if (interp != NULL) {
|
||
Tcl_Obj *msg = Tcl_ObjPrintf("expected %s but got \"",
|
||
expected);
|
||
|
||
Tcl_AppendLimitedToObj(msg, bytes, numBytes, 50, "");
|
||
Tcl_AppendToObj(msg, "\"", -1);
|
||
if (state == BAD_OCTAL) {
|
||
Tcl_AppendToObj(msg, " (looks like invalid octal number)", -1);
|
||
}
|
||
Tcl_SetObjResult(interp, msg);
|
||
Tcl_SetErrorCode(interp, "TCL", "VALUE", "NUMBER", NULL);
|
||
}
|
||
}
|
||
|
||
/*
|
||
* Free memory.
|
||
*/
|
||
|
||
if (octalSignificandOverflow) {
|
||
mp_clear(&octalSignificandBig);
|
||
}
|
||
if (significandOverflow) {
|
||
mp_clear(&significandBig);
|
||
}
|
||
return status;
|
||
}
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* AccumulateDecimalDigit --
|
||
*
|
||
* Consume a decimal digit in a number being scanned.
|
||
*
|
||
* Results:
|
||
* Returns 1 if the number has overflowed to a bignum, 0 if it still fits
|
||
* in a wide integer.
|
||
*
|
||
* Side effects:
|
||
* Updates either the wide or bignum representation.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
static int
|
||
AccumulateDecimalDigit(
|
||
unsigned digit, /* Digit being scanned. */
|
||
int numZeros, /* Count of zero digits preceding the digit
|
||
* being scanned. */
|
||
Tcl_WideUInt *wideRepPtr, /* Representation of the partial number as a
|
||
* wide integer. */
|
||
mp_int *bignumRepPtr, /* Representation of the partial number as a
|
||
* bignum. */
|
||
int bignumFlag) /* Flag == 1 if the number overflowed previous
|
||
* to this digit. */
|
||
{
|
||
int i, n;
|
||
Tcl_WideUInt w;
|
||
|
||
/*
|
||
* Try wide multiplication first.
|
||
*/
|
||
|
||
if (!bignumFlag) {
|
||
w = *wideRepPtr;
|
||
if (w == 0) {
|
||
/*
|
||
* There's no need to multiply if the multiplicand is zero.
|
||
*/
|
||
|
||
*wideRepPtr = digit;
|
||
return 0;
|
||
} else if (numZeros >= maxpow10_wide
|
||
|| 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.
|
||
*/
|
||
|
||
TclBNInitBignumFromWideUInt(bignumRepPtr, w);
|
||
} else {
|
||
/*
|
||
* Wide multiplication.
|
||
*/
|
||
|
||
*wideRepPtr = w * pow10_wide[numZeros+1] + digit;
|
||
return 0;
|
||
}
|
||
}
|
||
|
||
/*
|
||
* Bignum multiplication.
|
||
*/
|
||
|
||
if (numZeros < log10_DIGIT_MAX) {
|
||
/*
|
||
* Up to about 8 zeros - single digit multiplication.
|
||
*/
|
||
|
||
mp_mul_d(bignumRepPtr, (mp_digit) pow10_wide[numZeros+1],
|
||
bignumRepPtr);
|
||
mp_add_d(bignumRepPtr, (mp_digit) digit, bignumRepPtr);
|
||
} else {
|
||
/*
|
||
* More than single digit multiplication. Multiply by the appropriate
|
||
* small powers of 5, and then shift. Large strings of zeroes are
|
||
* eaten 256 at a time; this is less efficient than it could be, but
|
||
* seems implausible. We presume that MP_DIGIT_BIT is at least 27. The
|
||
* first multiplication, by up to 10**7, is done with a one-DIGIT
|
||
* multiply (this presumes that MP_DIGIT_BIT >= 24).
|
||
*/
|
||
|
||
n = numZeros + 1;
|
||
mp_mul_d(bignumRepPtr, (mp_digit) pow10_wide[n&0x7], bignumRepPtr);
|
||
for (i=3; i<=7; ++i) {
|
||
if (n & (1 << i)) {
|
||
mp_mul(bignumRepPtr, pow5+i, bignumRepPtr);
|
||
}
|
||
}
|
||
while (n >= 256) {
|
||
mp_mul(bignumRepPtr, pow5+8, bignumRepPtr);
|
||
n -= 256;
|
||
}
|
||
mp_mul_2d(bignumRepPtr, (int)(numZeros+1)&~0x7, bignumRepPtr);
|
||
mp_add_d(bignumRepPtr, (mp_digit) digit, bignumRepPtr);
|
||
}
|
||
|
||
return 1;
|
||
}
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* MakeLowPrecisionDouble --
|
||
*
|
||
* Makes the double precision number, signum*significand*10**exponent.
|
||
*
|
||
* Results:
|
||
* Returns the constructed number.
|
||
*
|
||
* Common cases, where there are few enough digits that the number can be
|
||
* represented with at most roundoff, are handled specially here. If the
|
||
* number requires more than one rounded operation to compute, the code
|
||
* promotes the significand to a bignum and calls MakeHighPrecisionDouble
|
||
* to do it instead.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
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 */
|
||
long exponent) /* Power of ten */
|
||
{
|
||
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.
|
||
* This causes the result of double-precision calculations to be rounded
|
||
* twice: once to the precision of double-extended and then again to the
|
||
* precision of double. Double-rounding introduces gratuitous errors of 1
|
||
* ulp, so we need to change rounding mode to 53-bits.
|
||
*/
|
||
|
||
TCL_IEEE_DOUBLE_ROUNDING;
|
||
|
||
/*
|
||
* Test for the easy cases.
|
||
*/
|
||
|
||
if (significand == 0) {
|
||
return copysign(0.0, -signum);
|
||
}
|
||
if (numSigDigs <= QUICK_MAX) {
|
||
if (exponent >= 0) {
|
||
if (exponent <= mmaxpow) {
|
||
/*
|
||
* The significand is an exact integer, and so is
|
||
* 10**exponent. The product will be correct to within 1/2 ulp
|
||
* without special handling.
|
||
*/
|
||
|
||
retval = (double)
|
||
((Tcl_WideInt)significand * pow10vals[exponent]);
|
||
goto returnValue;
|
||
} else {
|
||
int diff = QUICK_MAX - numSigDigs;
|
||
|
||
if (exponent-diff <= mmaxpow) {
|
||
/*
|
||
* 10**exponent is not an exact integer, but
|
||
* 10**(exponent-diff) is exact, and so is
|
||
* significand*10**diff, so we can still compute the value
|
||
* with only one roundoff.
|
||
*/
|
||
|
||
volatile double factor = (double)
|
||
((Tcl_WideInt)significand * pow10vals[diff]);
|
||
retval = factor * pow10vals[exponent-diff];
|
||
goto returnValue;
|
||
}
|
||
}
|
||
} else {
|
||
if (exponent >= -mmaxpow) {
|
||
/*
|
||
* 10**-exponent is an exact integer, and so is the
|
||
* significand. Compute the result by one division, again with
|
||
* only one rounding.
|
||
*/
|
||
|
||
retval = (double)
|
||
((Tcl_WideInt)significand / pow10vals[-exponent]);
|
||
goto returnValue;
|
||
}
|
||
}
|
||
}
|
||
|
||
/*
|
||
* All the easy cases have failed. Promote ths significand to bignum and
|
||
* call MakeHighPrecisionDouble to do it the hard way.
|
||
*/
|
||
|
||
TclBNInitBignumFromWideUInt(&significandBig, significand);
|
||
retval = MakeHighPrecisionDouble(0, &significandBig, numSigDigs,
|
||
exponent);
|
||
mp_clear(&significandBig);
|
||
|
||
/*
|
||
* Come here to return the computed value.
|
||
*/
|
||
|
||
returnValue:
|
||
if (signum) {
|
||
retval = -retval;
|
||
}
|
||
|
||
/*
|
||
* On gcc on x86, restore the floating point mode word.
|
||
*/
|
||
|
||
TCL_DEFAULT_DOUBLE_ROUNDING;
|
||
|
||
return retval;
|
||
}
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* MakeHighPrecisionDouble --
|
||
*
|
||
* Makes the double precision number, signum*significand*10**exponent.
|
||
*
|
||
* Results:
|
||
* Returns the constructed number.
|
||
*
|
||
* MakeHighPrecisionDouble is used when arbitrary-precision arithmetic is
|
||
* needed to ensure correct rounding. It begins by calculating a
|
||
* low-precision approximation to the desired number, and then refines
|
||
* the answer in high precision.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
static double
|
||
MakeHighPrecisionDouble(
|
||
int signum, /* 1=negative, 0=nonnegative */
|
||
mp_int *significand, /* Exact significand of the number */
|
||
int numSigDigs, /* Number of significant digits */
|
||
long exponent) /* Power of 10 by which to multiply */
|
||
{
|
||
double retval;
|
||
int machexp; /* Machine exponent of a power of 10. */
|
||
|
||
/*
|
||
* With gcc on x86, the floating point rounding mode is double-extended.
|
||
* This causes the result of double-precision calculations to be rounded
|
||
* twice: once to the precision of double-extended and then again to the
|
||
* precision of double. Double-rounding introduces gratuitous errors of 1
|
||
* ulp, so we need to change rounding mode to 53-bits.
|
||
*/
|
||
|
||
TCL_IEEE_DOUBLE_ROUNDING;
|
||
|
||
/*
|
||
* Quick checks for zero, and over/underflow. Be careful to avoid
|
||
* integer overflow when calculating with 'exponent'.
|
||
*/
|
||
|
||
if (mp_iszero(significand)) {
|
||
return copysign(0.0, -signum);
|
||
}
|
||
if (exponent >= 0 && exponent-1 > maxDigits-numSigDigs) {
|
||
retval = HUGE_VAL;
|
||
goto returnValue;
|
||
} else if (exponent < 0 && numSigDigs+exponent < minDigits+1) {
|
||
retval = 0.0;
|
||
goto returnValue;
|
||
}
|
||
|
||
/*
|
||
* Develop a first approximation to the significand. It is tempting simply
|
||
* to force bignum to double, but that will overflow on input numbers like
|
||
* 1.[string repeat 0 1000]1; while this is a not terribly likely
|
||
* scenario, we still have to deal with it. Use fraction and exponent
|
||
* instead. Once we have the significand, multiply by 10**exponent. Test
|
||
* for overflow. Convert back to a double, and test for underflow.
|
||
*/
|
||
|
||
retval = BignumToBiasedFrExp(significand, &machexp);
|
||
retval = Pow10TimesFrExp(exponent, retval, &machexp);
|
||
if (machexp > DBL_MAX_EXP*log2FLT_RADIX) {
|
||
retval = HUGE_VAL;
|
||
goto returnValue;
|
||
}
|
||
retval = SafeLdExp(retval, machexp);
|
||
if (tiny == 0.0) {
|
||
tiny = SafeLdExp(1.0, DBL_MIN_EXP * log2FLT_RADIX - mantBits);
|
||
}
|
||
if (retval < tiny) {
|
||
retval = tiny;
|
||
}
|
||
|
||
/*
|
||
* Refine the result twice. (The second refinement should be necessary
|
||
* only if the best approximation is a power of 2 minus 1/2 ulp).
|
||
*/
|
||
|
||
retval = RefineApproximation(retval, significand, exponent);
|
||
retval = RefineApproximation(retval, significand, exponent);
|
||
|
||
/*
|
||
* Come here to return the computed value.
|
||
*/
|
||
|
||
returnValue:
|
||
if (signum) {
|
||
retval = -retval;
|
||
}
|
||
|
||
/*
|
||
* On gcc on x86, restore the floating point mode word.
|
||
*/
|
||
|
||
TCL_DEFAULT_DOUBLE_ROUNDING;
|
||
|
||
return retval;
|
||
}
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* MakeNaN --
|
||
*
|
||
* Makes a "Not a Number" given a set of bits to put in the tag bits
|
||
*
|
||
* Note that a signalling NaN is never returned.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
#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. */
|
||
{
|
||
union {
|
||
Tcl_WideUInt iv;
|
||
double dv;
|
||
} theNaN;
|
||
|
||
theNaN.iv = tags;
|
||
theNaN.iv &= (((Tcl_WideUInt) 1) << 51) - 1;
|
||
if (signum) {
|
||
theNaN.iv |= ((Tcl_WideUInt) (0x8000 | NAN_START)) << 48;
|
||
} else {
|
||
theNaN.iv |= ((Tcl_WideUInt) NAN_START) << 48;
|
||
}
|
||
if (n770_fp) {
|
||
theNaN.iv = Nokia770Twiddle(theNaN.iv);
|
||
}
|
||
return theNaN.dv;
|
||
}
|
||
#endif
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* RefineApproximation --
|
||
*
|
||
* Given a poor approximation to a floating point number, returns a
|
||
* better one. (The better approximation is correct to within 1 ulp, and
|
||
* is entirely correct if the poor approximation is correct to 1 ulp.)
|
||
*
|
||
* Results:
|
||
* Returns the improved result.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
static double
|
||
RefineApproximation(
|
||
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. */
|
||
int msb; /* Most significant bit position of an
|
||
* intermediate result. */
|
||
int nDigits; /* Number of mp_digit's in an intermediate
|
||
* result. */
|
||
mp_int twoMv; /* Approx binary value expressed as an exact
|
||
* 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. */
|
||
double num, den; /* Numerator and denominator of the correction
|
||
* term. */
|
||
double quot; /* Correction term. */
|
||
double minincr; /* Lower bound on the absolute value of the
|
||
* correction term. */
|
||
int roundToEven = 0; /* Flag == TRUE if we need to invoke
|
||
* "round to even" functionality */
|
||
double rteSignificand; /* Significand of the round-to-even result */
|
||
int rteExponent; /* Exponent of the round-to-even result */
|
||
int shift; /* Shift count for converting numerator
|
||
* and denominator of corrector to floating
|
||
* point */
|
||
Tcl_WideInt rteSigWide; /* Wide integer version of the significand
|
||
* for testing evenness */
|
||
int i;
|
||
|
||
/*
|
||
* The first approximation is always low. If we find that it's HUGE_VAL,
|
||
* we're done.
|
||
*/
|
||
|
||
if (approxResult == HUGE_VAL) {
|
||
return approxResult;
|
||
}
|
||
significand = frexp(approxResult, &binExponent);
|
||
|
||
/*
|
||
* We are trying to compute a corrector term that, when added to the
|
||
* approximate result, will yield close to the exact result.
|
||
* The exact result is exactSignificand * 10**exponent.
|
||
* The approximate result is significand * 2**binExponent
|
||
* If exponent<0, we need to multiply the exact value by 10**-exponent
|
||
* to make it an integer, plus another factor of 2 to decide on rounding.
|
||
* Similarly if binExponent<FP_PRECISION, we need
|
||
* to multiply by 2**FP_PRECISION to make the approximate value an integer.
|
||
*
|
||
* Let M = 2**M2 * 5**M5 be the least common multiple of these two
|
||
* multipliers.
|
||
*/
|
||
|
||
i = mantBits - binExponent;
|
||
if (i < 0) {
|
||
M2 = 0;
|
||
} else {
|
||
M2 = i;
|
||
}
|
||
if (exponent > 0) {
|
||
M5 = 0;
|
||
} else {
|
||
M5 = -exponent;
|
||
if (M5 - 1 > M2) {
|
||
M2 = M5 - 1;
|
||
}
|
||
}
|
||
|
||
/*
|
||
* Compute twoMv as 2*M*v, where v is the approximate value.
|
||
* This is done by bit-whacking to calculate 2**(M2+1)*significand,
|
||
* and then multiplying by 5**M5.
|
||
*/
|
||
|
||
msb = binExponent + M2; /* 1008 */
|
||
nDigits = msb / MP_DIGIT_BIT + 1;
|
||
mp_init_size(&twoMv, nDigits);
|
||
i = (msb % MP_DIGIT_BIT + 1);
|
||
twoMv.used = nDigits;
|
||
significand *= SafeLdExp(1.0, i);
|
||
while (--nDigits >= 0) {
|
||
twoMv.dp[nDigits] = (mp_digit) significand;
|
||
significand -= (mp_digit) significand;
|
||
significand = SafeLdExp(significand, MP_DIGIT_BIT);
|
||
}
|
||
for (i = 0; i <= 8; ++i) {
|
||
if (M5 & (1 << i)) {
|
||
mp_mul(&twoMv, pow5+i, &twoMv);
|
||
}
|
||
}
|
||
|
||
/*
|
||
* Compute twoMd as 2*M*d, where d is the exact value.
|
||
* This is done by multiplying by 5**(M5+exponent) and then multiplying
|
||
* by 2**(M5+exponent+1), which is, of couse, a left shift.
|
||
*/
|
||
|
||
mp_init_copy(&twoMd, exactSignificand);
|
||
for (i=0; i<=8; ++i) {
|
||
if ((M5 + exponent) & (1 << i)) {
|
||
mp_mul(&twoMd, pow5+i, &twoMd);
|
||
}
|
||
}
|
||
mp_mul_2d(&twoMd, M2+exponent+1, &twoMd);
|
||
|
||
/*
|
||
* Now let twoMd = twoMd - twoMv, the difference between the exact and
|
||
* approximate values.
|
||
*/
|
||
|
||
mp_sub(&twoMd, &twoMv, &twoMd);
|
||
|
||
/*
|
||
* 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. Place that factor
|
||
* times 1/2 ULP into twoMd.
|
||
*/
|
||
|
||
scale = binExponent - mantBits - 1;
|
||
mp_set(&twoMv, 1);
|
||
for (i=0; i<=8; ++i) {
|
||
if (M5 & (1 << i)) {
|
||
mp_mul(&twoMv, pow5+i, &twoMv);
|
||
}
|
||
}
|
||
multiplier = M2 + scale + 1;
|
||
if (multiplier > 0) {
|
||
mp_mul_2d(&twoMv, multiplier, &twoMv);
|
||
} else if (multiplier < 0) {
|
||
mp_div_2d(&twoMv, -multiplier, &twoMv, NULL);
|
||
}
|
||
|
||
/*
|
||
* Will the eventual correction term be less than, equal to, or
|
||
* greater than 1/2 ULP?
|
||
*/
|
||
|
||
switch (mp_cmp_mag(&twoMd, &twoMv)) {
|
||
case MP_LT:
|
||
/*
|
||
* If the error is less than 1/2 ULP, there's no correction to make.
|
||
*/
|
||
mp_clear(&twoMd);
|
||
mp_clear(&twoMv);
|
||
return approxResult;
|
||
case MP_EQ:
|
||
/*
|
||
* If the error is exactly 1/2 ULP, we need to round to even.
|
||
*/
|
||
roundToEven = 1;
|
||
break;
|
||
case MP_GT:
|
||
/*
|
||
* We need to correct the result if the error exceeds 1/2 ULP.
|
||
*/
|
||
break;
|
||
}
|
||
|
||
/*
|
||
* If we're in the 'round to even' case, and the significand is already
|
||
* even, we're done. Return the approximate result.
|
||
*/
|
||
if (roundToEven) {
|
||
rteSignificand = frexp(approxResult, &rteExponent);
|
||
rteSigWide = (Tcl_WideInt) ldexp(rteSignificand, FP_PRECISION);
|
||
if ((rteSigWide & 1) == 0) {
|
||
mp_clear(&twoMd);
|
||
mp_clear(&twoMv);
|
||
return approxResult;
|
||
}
|
||
}
|
||
|
||
/*
|
||
* Reduce the numerator and denominator of the corrector term so that
|
||
* they will fit in the floating point precision.
|
||
*/
|
||
shift = mp_count_bits(&twoMv) - FP_PRECISION - 1;
|
||
if (shift > 0) {
|
||
mp_div_2d(&twoMv, shift, &twoMv, NULL);
|
||
mp_div_2d(&twoMd, shift, &twoMd, NULL);
|
||
}
|
||
|
||
/*
|
||
* Convert the numerator and denominator of the corrector term accurately
|
||
* to floating point numbers.
|
||
*/
|
||
|
||
num = TclBignumToDouble(&twoMd);
|
||
den = TclBignumToDouble(&twoMv);
|
||
|
||
quot = SafeLdExp(num/den, scale);
|
||
minincr = SafeLdExp(1.0, binExponent-mantBits);
|
||
|
||
if (quot<0. && quot>-minincr) {
|
||
quot = -minincr;
|
||
} else if (quot>0. && quot<minincr) {
|
||
quot = minincr;
|
||
}
|
||
|
||
mp_clear(&twoMd);
|
||
mp_clear(&twoMv);
|
||
|
||
return approxResult + quot;
|
||
}
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* MultPow5 --
|
||
*
|
||
* Multiply a bignum by a power of 5.
|
||
*
|
||
* Side effects:
|
||
* Stores base*5**n in result.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
static inline void
|
||
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;
|
||
int n13 = n / 13;
|
||
int r = n % 13;
|
||
|
||
if (r != 0) {
|
||
mp_mul_d(p, dpow5[r], result);
|
||
p = result;
|
||
}
|
||
r = 0;
|
||
while (n13 != 0) {
|
||
if (n13 & 1) {
|
||
mp_mul(p, pow5_13+r, result);
|
||
p = result;
|
||
}
|
||
n13 >>= 1;
|
||
++r;
|
||
}
|
||
if (p != result) {
|
||
mp_copy(p, result);
|
||
}
|
||
}
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* NormalizeRightward --
|
||
*
|
||
* 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.
|
||
*
|
||
* Side effects:
|
||
* Shifts the number in place; *wPtr is replaced by the shifted number.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
static inline int
|
||
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;
|
||
}
|
||
if (!(w & (Tcl_WideUInt) 0xFF)) {
|
||
w >>= 8; rv += 8;
|
||
}
|
||
if (!(w & (Tcl_WideUInt) 0xF)) {
|
||
w >>= 4; rv += 4;
|
||
}
|
||
if (!(w & 0x3)) {
|
||
w >>= 2; rv += 2;
|
||
}
|
||
if (!(w & 0x1)) {
|
||
w >>= 1; ++rv;
|
||
}
|
||
*wPtr = w;
|
||
return rv;
|
||
}
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* 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.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
static int
|
||
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 {
|
||
wi = (unsigned long) w; rv = 0;
|
||
}
|
||
if (wi & 0xFFFF0000) {
|
||
wi >>= 16; rv += 16;
|
||
}
|
||
if (wi & 0xFF00) {
|
||
wi >>= 8; rv += 8;
|
||
}
|
||
if (wi & 0xF0) {
|
||
wi >>= 4; rv += 4;
|
||
}
|
||
if (wi & 0xC) {
|
||
wi >>= 2; rv += 2;
|
||
}
|
||
if (wi & 0x2) {
|
||
wi >>= 1; ++rv;
|
||
}
|
||
if (wi & 0x1) {
|
||
++rv;
|
||
}
|
||
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'.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
static inline 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. */
|
||
{
|
||
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.
|
||
*/
|
||
|
||
de = (d.w.word0 & EXP_MASK) >> EXP_SHIFT;
|
||
z = d.q & SIG_MASK;
|
||
if (de != 0) {
|
||
z |= HIDDEN_BIT;
|
||
k = NormalizeRightward(&z);
|
||
*bits = FP_PRECISION - k;
|
||
*expon = k + (de - EXPONENT_BIAS) - (FP_PRECISION-1);
|
||
} else {
|
||
k = NormalizeRightward(&z);
|
||
*expon = k + (de - EXPONENT_BIAS) - (FP_PRECISION-1) + 1;
|
||
*bits = RequiredPrecision(z);
|
||
}
|
||
*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.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
static inline void
|
||
TakeAbsoluteValue(
|
||
Double *d, /* Number to replace with absolute value. */
|
||
int *sign) /* Place to put the signum. */
|
||
{
|
||
if (d->w.word0 & SIGN_BIT) {
|
||
*sign = 1;
|
||
d->w.word0 &= ~SIGN_BIT;
|
||
} else {
|
||
*sign = 0;
|
||
}
|
||
}
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* FormatInfAndNaN --
|
||
*
|
||
* Bailout for formatting infinities and Not-A-Number.
|
||
*
|
||
* Results:
|
||
* 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.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
static inline 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;
|
||
|
||
*decpt = 9999;
|
||
if (!(d->w.word1) && !(d->w.word0 & HI_ORDER_SIG_MASK)) {
|
||
retval = ckalloc(9);
|
||
strcpy(retval, "Infinity");
|
||
if (endPtr) {
|
||
*endPtr = retval + 8;
|
||
}
|
||
} else {
|
||
retval = ckalloc(4);
|
||
strcpy(retval, "NaN");
|
||
if (endPtr) {
|
||
*endPtr = retval + 3;
|
||
}
|
||
}
|
||
return retval;
|
||
}
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* FormatZero --
|
||
*
|
||
* Bailout to format a zero floating-point number.
|
||
*
|
||
* Results:
|
||
* Returns the constant string "0"
|
||
*
|
||
* Side effects:
|
||
* Stores 1 in '*decpt' and puts a pointer to the NUL byte terminating
|
||
* the string in '*endPtr' if 'endPtr' is not NULL.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
static inline char *
|
||
FormatZero(
|
||
int *decpt, /* Location of the decimal point. */
|
||
char **endPtr) /* Pointer to the end of the formatted data */
|
||
{
|
||
char *retval = ckalloc(2);
|
||
|
||
strcpy(retval, "0");
|
||
if (endPtr) {
|
||
*endPtr = retval+1;
|
||
}
|
||
*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.
|
||
*
|
||
* Results:
|
||
* Return an approximation to floor(log10(bw*2**be)) that is either exact
|
||
* or 1 too high.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
static inline 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. */
|
||
{
|
||
int i; /* Log base 2 of the number. */
|
||
int k; /* Floor(Log base 10 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)
|
||
* + (significand-1.5)/(1.5 * log(10))
|
||
*/
|
||
|
||
d2.q = bw << (FP_PRECISION - bbits) & SIG_MASK;
|
||
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;
|
||
k = (int) ds;
|
||
if (k > ds) {
|
||
--k;
|
||
}
|
||
return k;
|
||
}
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* BetterLog10 --
|
||
*
|
||
* Improves the result of ApproximateLog10 for numbers in the range
|
||
* 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.
|
||
*
|
||
* Results:
|
||
* Returns the improved approximation to log10(d).
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
static inline 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. */
|
||
{
|
||
/*
|
||
* 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--;
|
||
}
|
||
*k_check = 0;
|
||
} else {
|
||
*k_check = 1;
|
||
}
|
||
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.
|
||
*
|
||
* 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.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
static inline 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. */
|
||
{
|
||
/*
|
||
* 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;
|
||
} else {
|
||
*b2 = be;
|
||
*s2 = 0;
|
||
}
|
||
|
||
/*
|
||
* Scale numerator and denominator so that the output decimal number is
|
||
* the ratio of integers.
|
||
*/
|
||
|
||
if (k >= 0) {
|
||
*b5 = 0;
|
||
*s5 = k;
|
||
*s2 += k;
|
||
} else {
|
||
*b2 -= k;
|
||
*b5 = -k;
|
||
*s5 = 0;
|
||
}
|
||
}
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* SetPrecisionLimits --
|
||
*
|
||
* 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 '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.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
static inline void
|
||
SetPrecisionLimits(
|
||
int convType, /* Type of conversion: TCL_DD_SHORTEST,
|
||
* TCL_DD_STEELE0, TCL_DD_E_FMT,
|
||
* TCL_DD_F_FMT. */
|
||
int k, /* Floor(log10(number to convert)) */
|
||
int *ndigitsPtr, /* IN/OUT: Number of digits requested (will be
|
||
* adjusted if needed). */
|
||
int *iPtr, /* OUT: Maximum number of digits to return. */
|
||
int *iLimPtr, /* OUT: Number of digits of significance if
|
||
* the bignum method is used.*/
|
||
int *iLim1Ptr) /* OUT: Number of digits of significance if
|
||
* the quick method is used. */
|
||
{
|
||
switch (convType) {
|
||
case TCL_DD_SHORTEST0:
|
||
case TCL_DD_STEELE0:
|
||
*iLimPtr = *iLim1Ptr = -1;
|
||
*iPtr = 18;
|
||
*ndigitsPtr = 0;
|
||
break;
|
||
case TCL_DD_E_FORMAT:
|
||
if (*ndigitsPtr <= 0) {
|
||
*ndigitsPtr = 1;
|
||
}
|
||
*iLimPtr = *iLim1Ptr = *iPtr = *ndigitsPtr;
|
||
break;
|
||
case TCL_DD_F_FORMAT:
|
||
*iPtr = *ndigitsPtr + k + 1;
|
||
*iLimPtr = *iPtr;
|
||
*iLim1Ptr = *iPtr - 1;
|
||
if (*iPtr <= 0) {
|
||
*iPtr = 1;
|
||
}
|
||
break;
|
||
default:
|
||
*iPtr = -1;
|
||
*iLimPtr = -1;
|
||
*iLim1Ptr = -1;
|
||
Tcl_Panic("impossible conversion type in TclDoubleDigits");
|
||
}
|
||
}
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* BumpUp --
|
||
*
|
||
* 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.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
static inline 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) {
|
||
++(*kPtr);
|
||
*s = '1';
|
||
return s+1;
|
||
}
|
||
}
|
||
++*s;
|
||
++s;
|
||
return s;
|
||
}
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* AdjustRange --
|
||
*
|
||
* 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.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
static inline int
|
||
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. */
|
||
double ds;
|
||
int i, j, j1;
|
||
|
||
ieps = 2;
|
||
|
||
if (k > 0) {
|
||
/*
|
||
* The number must be reduced to bring it into range.
|
||
*/
|
||
|
||
ds = tens[k & 0xF];
|
||
j = k >> 4;
|
||
if (j & BLETCH) {
|
||
j &= (BLETCH-1);
|
||
d /= bigtens[N_BIGTENS - 1];
|
||
ieps++;
|
||
}
|
||
i = 0;
|
||
for (; j != 0; j>>=1) {
|
||
if (j & 1) {
|
||
ds *= bigtens[i];
|
||
++ieps;
|
||
}
|
||
++i;
|
||
}
|
||
d /= ds;
|
||
} else if ((j1 = -k) != 0) {
|
||
/*
|
||
* The number must be increased to bring it into range.
|
||
*/
|
||
|
||
d *= tens[j1 & 0xF];
|
||
i = 0;
|
||
for (j = j1>>4; j; j>>=1) {
|
||
if (j & 1) {
|
||
ieps++;
|
||
d *= bigtens[i];
|
||
}
|
||
++i;
|
||
}
|
||
}
|
||
|
||
*dPtr = d;
|
||
return ieps;
|
||
}
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* 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.
|
||
*
|
||
* Results:
|
||
* 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'.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
static inline 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. */
|
||
int i;
|
||
|
||
eps = 0.5 / tens[ilim-1] - eps;
|
||
i = 0;
|
||
for (;;) {
|
||
/*
|
||
* 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.
|
||
*/
|
||
|
||
if (d < eps) {
|
||
*kPtr = k;
|
||
return s;
|
||
}
|
||
if ((1. - d) < eps) {
|
||
*kPtr = k;
|
||
return BumpUp(s, retval, kPtr);
|
||
}
|
||
|
||
/*
|
||
* Bail out if the conversion fails to converge to a sufficiently
|
||
* precise value.
|
||
*/
|
||
|
||
if (++i >= ilim) {
|
||
return NULL;
|
||
}
|
||
|
||
/*
|
||
* Bring the next digit to the integer part.
|
||
*/
|
||
|
||
eps *= 10;
|
||
d *= 10.0;
|
||
}
|
||
}
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* StrictQuickFormat --
|
||
*
|
||
* 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.
|
||
*
|
||
* Side effects:
|
||
* Stores the position of the decimal point in '*kPtr'.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
static inline 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. */
|
||
int i;
|
||
|
||
eps *= tens[ilim-1];
|
||
i = 1;
|
||
for (;;) {
|
||
/*
|
||
* Extract a digit.
|
||
*/
|
||
|
||
digit = (int) d;
|
||
d -= digit;
|
||
if (d == 0.0) {
|
||
ilim = i;
|
||
}
|
||
*s++ = '0' + digit;
|
||
|
||
/*
|
||
* When the given digit count is reached, handle trailing strings of 0
|
||
* and 9.
|
||
*/
|
||
|
||
if (i == ilim) {
|
||
if (d > 0.5 + eps) {
|
||
*kPtr = k;
|
||
return BumpUp(s, retval, kPtr);
|
||
} else if (d < 0.5 - eps) {
|
||
while (*--s == '0') {
|
||
/* do nothing */
|
||
}
|
||
s++;
|
||
*kPtr = k;
|
||
return s;
|
||
} else {
|
||
return NULL;
|
||
}
|
||
}
|
||
|
||
/*
|
||
* Advance to the next digit.
|
||
*/
|
||
|
||
++i;
|
||
d *= 10.0;
|
||
}
|
||
}
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* QuickConversion --
|
||
*
|
||
* Converts a floating point number the 'quick' way, when only a limited
|
||
* number of digits is required and floating point arithmetic can
|
||
* therefore be used for the intermediate results.
|
||
*
|
||
* Results:
|
||
* Returns the converted string, or NULL if the bignum method must be
|
||
* used.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
static inline 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 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. */
|
||
volatile double d; /* Workaround for a bug in mingw gcc 3.4.5 */
|
||
|
||
/*
|
||
* 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 (k_check && d < 1. && ilim > 0) {
|
||
if (ilim1 < 0) {
|
||
return NULL;
|
||
}
|
||
ilim = ilim1;
|
||
--k;
|
||
d = d * 10.0;
|
||
++ieps;
|
||
}
|
||
|
||
/*
|
||
* 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.
|
||
*/
|
||
|
||
retval = ckalloc(len + 1);
|
||
if (ilim == 0) {
|
||
d = d - 5.;
|
||
if (d > eps.d) {
|
||
*retval = '1';
|
||
*decpt = k;
|
||
return retval;
|
||
} else if (d < -eps.d) {
|
||
*decpt = k;
|
||
return retval;
|
||
} else {
|
||
ckfree(retval);
|
||
return NULL;
|
||
}
|
||
}
|
||
|
||
/*
|
||
* Format the digit string.
|
||
*/
|
||
|
||
if (flags & TCL_DD_SHORTEN_FLAG) {
|
||
end = ShorteningQuickFormat(d, k, ilim, eps.d, retval, decpt);
|
||
} else {
|
||
end = StrictQuickFormat(d, k, ilim, eps.d, retval, decpt);
|
||
}
|
||
if (end == NULL) {
|
||
ckfree(retval);
|
||
return NULL;
|
||
}
|
||
*end = '\0';
|
||
if (endPtr != NULL) {
|
||
*endPtr = end;
|
||
}
|
||
return retval;
|
||
}
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* 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.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
static inline 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. */
|
||
{
|
||
int i;
|
||
|
||
if (*m2 > 0 && *s2 > 0) { /* Find the smallest power of 2 in the
|
||
* numerator. */
|
||
if (*m2 < *s2) { /* Find the lowest common denominator. */
|
||
i = *m2;
|
||
} else {
|
||
i = *s2;
|
||
}
|
||
*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.
|
||
*
|
||
* Results:
|
||
* 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'.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
static inline char *
|
||
ShorteningInt64Conversion(
|
||
Double *dPtr, /* Original number to convert. */
|
||
int convType, /* Type of conversion (shortest, Steele,
|
||
* E format, F format). */
|
||
Tcl_WideUInt bw, /* Integer significand. */
|
||
int b2, int b5, /* Scale factor for the significand in the
|
||
* numerator. */
|
||
int m2plus, int m2minus, int m5,
|
||
/* Scale factors for 1/2 ulp in the numerator
|
||
* (will be different if bw == 1. */
|
||
int s2, int s5, /* Scale factors for the denominator. */
|
||
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. */
|
||
Tcl_WideUInt b = (bw * wuipow5[b5]) << b2;
|
||
/* 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. */
|
||
|
||
/*
|
||
* Adjust if the logarithm was guessed wrong.
|
||
*/
|
||
|
||
if (b < S) {
|
||
b = 10 * b;
|
||
++m2plus; ++m2minus; ++m5;
|
||
ilim = ilim1;
|
||
--k;
|
||
}
|
||
|
||
/*
|
||
* Compute roundoff ranges.
|
||
*/
|
||
|
||
mplus = wuipow5[m5] << m2plus;
|
||
mminus = wuipow5[m5] << m2minus;
|
||
|
||
/*
|
||
* Loop through the digits.
|
||
*/
|
||
|
||
i = 1;
|
||
for (;;) {
|
||
digit = (int)(b / S);
|
||
if (digit > 10) {
|
||
Tcl_Panic("wrong digit!");
|
||
}
|
||
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)) {
|
||
/*
|
||
* Make sure we shouldn't be rounding *up* instead, in case the
|
||
* next number above is closer.
|
||
*/
|
||
|
||
if (2 * b > S || (2 * b == S && (digit & 1) != 0)) {
|
||
++digit;
|
||
if (digit == 10) {
|
||
*s++ = '9';
|
||
s = BumpUp(s, retval, &k);
|
||
break;
|
||
}
|
||
}
|
||
|
||
/*
|
||
* Stash the current digit.
|
||
*/
|
||
|
||
*s++ = '0' + digit;
|
||
break;
|
||
}
|
||
|
||
/*
|
||
* Does one plus the current digit put us within roundoff of the
|
||
* number?
|
||
*/
|
||
|
||
if (b > S - mminus || (b == S - mminus
|
||
&& convType != TCL_DD_STEELE0 && (dPtr->w.word1 & 1) == 0)) {
|
||
if (digit == 9) {
|
||
*s++ = '9';
|
||
s = BumpUp(s, retval, &k);
|
||
break;
|
||
}
|
||
++digit;
|
||
*s++ = '0' + digit;
|
||
break;
|
||
}
|
||
|
||
/*
|
||
* Have we converted all the requested digits?
|
||
*/
|
||
|
||
*s++ = '0' + digit;
|
||
if (i == ilim) {
|
||
if (2*b > S || (2*b == S && (digit & 1) != 0)) {
|
||
s = BumpUp(s, retval, &k);
|
||
}
|
||
break;
|
||
}
|
||
|
||
/*
|
||
* 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) {
|
||
*endPtr = s;
|
||
}
|
||
return retval;
|
||
}
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* 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.
|
||
*
|
||
* Results:
|
||
* 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'.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
static inline char *
|
||
StrictInt64Conversion(
|
||
Double *dPtr, /* Original number to convert. */
|
||
int convType, /* Type of conversion (shortest, Steele,
|
||
* E format, F format). */
|
||
Tcl_WideUInt bw, /* Integer significand. */
|
||
int b2, int b5, /* Scale factor for the significand in the
|
||
* numerator. */
|
||
int s2, int s5, /* Scale factors for the denominator. */
|
||
int k, /* Number of output digits before the decimal
|
||
* point. */
|
||
int len, /* Number of digits to allocate. */
|
||
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. */
|
||
Tcl_WideUInt b = (bw * wuipow5[b5]) << b2;
|
||
/* 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. */
|
||
|
||
/*
|
||
* Adjust if the logarithm was guessed wrong.
|
||
*/
|
||
|
||
if (b < S) {
|
||
b = 10 * b;
|
||
ilim = ilim1;
|
||
--k;
|
||
}
|
||
|
||
/*
|
||
* Loop through the digits.
|
||
*/
|
||
|
||
i = 1;
|
||
for (;;) {
|
||
digit = (int)(b / S);
|
||
if (digit > 10) {
|
||
Tcl_Panic("wrong digit!");
|
||
}
|
||
b = b % S;
|
||
|
||
/*
|
||
* Have we converted all the requested digits?
|
||
*/
|
||
|
||
*s++ = '0' + digit;
|
||
if (i == ilim) {
|
||
if (2*b > S || (2*b == S && (digit & 1) != 0)) {
|
||
s = BumpUp(s, retval, &k);
|
||
} else {
|
||
while (*--s == '0') {
|
||
/* do nothing */
|
||
}
|
||
++s;
|
||
}
|
||
break;
|
||
}
|
||
|
||
/*
|
||
* 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) {
|
||
*endPtr = s;
|
||
}
|
||
return retval;
|
||
}
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* 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**MP_DIGIT_BIT.
|
||
*
|
||
* Results:
|
||
* Returns 1 iff the fraction is more than 1/2, or if the fraction is
|
||
* exactly 1/2 and the digit is odd.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
static inline int
|
||
ShouldBankerRoundUpPowD(
|
||
mp_int *b, /* Numerator of the fraction. */
|
||
int sd, /* Denominator is 2**(sd*MP_DIGIT_BIT). */
|
||
int isodd) /* 1 if the digit is odd, 0 if even. */
|
||
{
|
||
int i;
|
||
static const mp_digit topbit = ((mp_digit)1) << (MP_DIGIT_BIT - 1);
|
||
|
||
if (b->used < sd || (b->dp[sd-1] & topbit) == 0) {
|
||
return 0;
|
||
}
|
||
if (b->dp[sd-1] != topbit) {
|
||
return 1;
|
||
}
|
||
for (i = sd-2; i >= 0; --i) {
|
||
if (b->dp[i] != 0) {
|
||
return 1;
|
||
}
|
||
}
|
||
return isodd;
|
||
}
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* ShouldBankerRoundUpToNextPowD --
|
||
*
|
||
* Tests whether bankers' rounding will round down in the "denominator is
|
||
* a power of 2**MP_DIGIT" case.
|
||
*
|
||
* Results:
|
||
* Returns 1 if the rounding will be performed - which increases the
|
||
* digit by one - and 0 otherwise.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
static inline int
|
||
ShouldBankerRoundUpToNextPowD(
|
||
mp_int *b, /* Numerator of the fraction. */
|
||
mp_int *m, /* Numerator of the rounding tolerance. */
|
||
int sd, /* Common denominator is 2**(sd*MP_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
|
||
* 2**(MP_DIGIT_BIT*sd)
|
||
*/
|
||
|
||
mp_add(b, m, temp);
|
||
if (temp->used <= sd) { /* Too few digits to be > s */
|
||
return 0;
|
||
}
|
||
if (temp->used > sd+1 || temp->dp[sd] > 1) {
|
||
/* >= 2s */
|
||
return 1;
|
||
}
|
||
for (i = sd-1; i >= 0; --i) {
|
||
/* Check for ==s */
|
||
if (temp->dp[i] != 0) { /* > s */
|
||
return 1;
|
||
}
|
||
}
|
||
if (convType == TCL_DD_STEELE0) {
|
||
/* Biased rounding. */
|
||
return 0;
|
||
}
|
||
return isodd;
|
||
}
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* ShorteningBignumConversionPowD --
|
||
*
|
||
* 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**MP_DIGIT_BIT, and hence
|
||
* the division in the main loop may be replaced by a digit shift and
|
||
* mask.
|
||
*
|
||
* Results:
|
||
* Returns the string of significant decimal digits, in newly allocated
|
||
* memory
|
||
*
|
||
* Side effects:
|
||
* Stores the location of the decimal point in '*decpt' and the location
|
||
* of the terminal null byte in '*endPtr'.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
static inline char *
|
||
ShorteningBignumConversionPowD(
|
||
Double *dPtr, /* Original number to convert. */
|
||
int convType, /* Type of conversion (shortest, Steele,
|
||
* E format, F format). */
|
||
Tcl_WideUInt bw, /* Integer significand. */
|
||
int b2, int b5, /* Scale factor for the significand in the
|
||
* numerator. */
|
||
int m2plus, int m2minus, int m5,
|
||
/* Scale factors for 1/2 ulp in the numerator
|
||
* (will be different if bw == 1). */
|
||
int sd, /* Scale factor for the denominator. */
|
||
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. */
|
||
mp_int temp;
|
||
int r1;
|
||
|
||
/*
|
||
* b = bw * 2**b2 * 5**b5
|
||
* mminus = 5**m5
|
||
*/
|
||
|
||
TclBNInitBignumFromWideUInt(&b, bw);
|
||
mp_init_set(&mminus, 1);
|
||
MulPow5(&b, b5, &b);
|
||
mp_mul_2d(&b, b2, &b);
|
||
|
||
/*
|
||
* Adjust if the logarithm was guessed wrong.
|
||
*/
|
||
|
||
if (b.used <= sd) {
|
||
mp_mul_d(&b, 10, &b);
|
||
++m2plus; ++m2minus; ++m5;
|
||
ilim = ilim1;
|
||
--k;
|
||
}
|
||
|
||
/*
|
||
* mminus = 5**m5 * 2**m2minus
|
||
* mplus = 5**m5 * 2**m2plus
|
||
*/
|
||
|
||
mp_mul_2d(&mminus, m2minus, &mminus);
|
||
MulPow5(&mminus, m5, &mminus);
|
||
if (m2plus > m2minus) {
|
||
mp_init_copy(&mplus, &mminus);
|
||
mp_mul_2d(&mplus, m2plus-m2minus, &mplus);
|
||
}
|
||
mp_init(&temp);
|
||
|
||
/*
|
||
* Loop through the digits. Do division and mod by s == 2**(sd*MP_DIGIT_BIT)
|
||
* by mp_digit extraction.
|
||
*/
|
||
|
||
i = 0;
|
||
for (;;) {
|
||
if (b.used <= sd) {
|
||
digit = 0;
|
||
} else {
|
||
digit = b.dp[sd];
|
||
if (b.used > sd+1 || digit >= 10) {
|
||
Tcl_Panic("wrong digit!");
|
||
}
|
||
--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)) {
|
||
/*
|
||
* 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) {
|
||
*s++ = '9';
|
||
s = BumpUp(s, retval, &k);
|
||
break;
|
||
}
|
||
}
|
||
|
||
/*
|
||
* Stash the last digit.
|
||
*/
|
||
|
||
*s++ = '0' + digit;
|
||
break;
|
||
}
|
||
|
||
/*
|
||
* Does one plus the current digit put us within roundoff of the
|
||
* number?
|
||
*/
|
||
|
||
if (ShouldBankerRoundUpToNextPowD(&b, &mminus, sd, convType,
|
||
dPtr->w.word1 & 1, &temp)) {
|
||
if (digit == 9) {
|
||
*s++ = '9';
|
||
s = BumpUp(s, retval, &k);
|
||
break;
|
||
}
|
||
++digit;
|
||
*s++ = '0' + digit;
|
||
break;
|
||
}
|
||
|
||
/*
|
||
* Have we converted all the requested digits?
|
||
*/
|
||
|
||
*s++ = '0' + digit;
|
||
if (i == ilim) {
|
||
if (ShouldBankerRoundUpPowD(&b, sd, digit&1)) {
|
||
s = BumpUp(s, retval, &k);
|
||
}
|
||
break;
|
||
}
|
||
|
||
/*
|
||
* Advance to the next digit.
|
||
*/
|
||
|
||
mp_mul_d(&b, 10, &b);
|
||
mp_mul_d(&mminus, 10, &mminus);
|
||
if (m2plus > m2minus) {
|
||
mp_mul_2d(&mminus, m2plus-m2minus, &mplus);
|
||
}
|
||
++i;
|
||
}
|
||
|
||
/*
|
||
* Endgame - store the location of the decimal point and the end of the
|
||
* string.
|
||
*/
|
||
|
||
if (m2plus > m2minus) {
|
||
mp_clear(&mplus);
|
||
}
|
||
mp_clear_multi(&b, &mminus, &temp, NULL);
|
||
*s = '\0';
|
||
*decpt = k;
|
||
if (endPtr) {
|
||
*endPtr = s;
|
||
}
|
||
return retval;
|
||
}
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* 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**MP_DIGIT_BIT, and hence the division in the main loop may be
|
||
* replaced by a digit shift and mask.
|
||
*
|
||
* Results:
|
||
* Returns the string of significant decimal digits, in newly allocated
|
||
* memory.
|
||
*
|
||
* Side effects:
|
||
* Stores the location of the decimal point in '*decpt' and the location
|
||
* of the terminal null byte in '*endPtr'.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
static inline char *
|
||
StrictBignumConversionPowD(
|
||
Double *dPtr, /* Original number to convert. */
|
||
int convType, /* Type of conversion (shortest, Steele,
|
||
* E format, F format). */
|
||
Tcl_WideUInt bw, /* Integer significand. */
|
||
int b2, int b5, /* Scale factor for the significand in the
|
||
* numerator. */
|
||
int sd, /* Scale factor for the denominator. */
|
||
int k, /* Number of output digits before the decimal
|
||
* point. */
|
||
int len, /* Number of digits to allocate. */
|
||
int ilim, /* Number of digits to convert if b >= s */
|
||
int ilim1, /* Number of digits to convert if b < s */
|
||
int *decpt, /* OUTPUT: Position of the decimal point. */
|
||
char **endPtr) /* OUTPUT: Position of the terminal '\0' at
|
||
* the end of the returned string. */
|
||
{
|
||
char *retval = ckalloc(len + 1);
|
||
/* Output buffer. */
|
||
mp_int b; /* Numerator of the fraction being
|
||
* converted. */
|
||
mp_digit digit; /* Current output digit. */
|
||
char *s = retval; /* Cursor in the output buffer. */
|
||
int i; /* Index in the output buffer. */
|
||
mp_int temp;
|
||
|
||
/*
|
||
* b = bw * 2**b2 * 5**b5
|
||
*/
|
||
|
||
TclBNInitBignumFromWideUInt(&b, bw);
|
||
MulPow5(&b, b5, &b);
|
||
mp_mul_2d(&b, b2, &b);
|
||
|
||
/*
|
||
* Adjust if the logarithm was guessed wrong.
|
||
*/
|
||
|
||
if (b.used <= sd) {
|
||
mp_mul_d(&b, 10, &b);
|
||
ilim = ilim1;
|
||
--k;
|
||
}
|
||
mp_init(&temp);
|
||
|
||
/*
|
||
* Loop through the digits. Do division and mod by s == 2**(sd*MP_DIGIT_BIT)
|
||
* by mp_digit extraction.
|
||
*/
|
||
|
||
i = 1;
|
||
for (;;) {
|
||
if (b.used <= sd) {
|
||
digit = 0;
|
||
} else {
|
||
digit = b.dp[sd];
|
||
if (b.used > sd+1 || digit >= 10) {
|
||
Tcl_Panic("wrong digit!");
|
||
}
|
||
--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);
|
||
}
|
||
while (*--s == '0') {
|
||
/* do nothing */
|
||
}
|
||
++s;
|
||
break;
|
||
}
|
||
|
||
/*
|
||
* 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;
|
||
if (endPtr) {
|
||
*endPtr = s;
|
||
}
|
||
return retval;
|
||
}
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* ShouldBankerRoundUp --
|
||
*
|
||
* Tests whether a digit should be rounded up or down when finishing
|
||
* bignum-based floating point conversion.
|
||
*
|
||
* Results:
|
||
* Returns 1 if the number needs to be rounded up, 0 otherwise.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
static inline 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. */
|
||
{
|
||
int r = mp_cmp_mag(twor, S);
|
||
|
||
switch (r) {
|
||
case MP_LT:
|
||
return 0;
|
||
case MP_EQ:
|
||
return isodd;
|
||
case MP_GT:
|
||
return 1;
|
||
}
|
||
Tcl_Panic("in ShouldBankerRoundUp, trichotomy fails!");
|
||
return 0;
|
||
}
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* ShouldBankerRoundUpToNext --
|
||
*
|
||
* Tests whether the remainder is great enough to force rounding to the
|
||
* next higher digit.
|
||
*
|
||
* Results:
|
||
* Returns 1 if the number should be rounded up, 0 otherwise.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
static inline int
|
||
ShouldBankerRoundUpToNext(
|
||
mp_int *b, /* Remainder from the division that produced
|
||
* the last digit. */
|
||
mp_int *m, /* Numerator of the rounding tolerance. */
|
||
mp_int *S, /* Denominator. */
|
||
int convType, /* Conversion type: STEELE0 defeats
|
||
* round-to-even. (Not sure why one would want
|
||
* this; I coped it from Gay). FIXME */
|
||
int isodd, /* 1 if the integer significand is odd. */
|
||
mp_int *temp) /* Work area needed for the calculation. */
|
||
{
|
||
int r;
|
||
|
||
/*
|
||
* Compare b and S-m: this is the same as comparing B+m and S.
|
||
*/
|
||
|
||
mp_add(b, m, temp);
|
||
r = mp_cmp_mag(temp, S);
|
||
switch(r) {
|
||
case MP_LT:
|
||
return 0;
|
||
case MP_EQ:
|
||
if (convType == TCL_DD_STEELE0) {
|
||
return 0;
|
||
} else {
|
||
return isodd;
|
||
}
|
||
case MP_GT:
|
||
return 1;
|
||
}
|
||
Tcl_Panic("in ShouldBankerRoundUpToNext, trichotomy fails!");
|
||
return 0;
|
||
}
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* ShorteningBignumConversion --
|
||
*
|
||
* Convert a floating point number to a variable-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.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
static inline char *
|
||
ShorteningBignumConversion(
|
||
Double *dPtr, /* Original number being converted. */
|
||
int convType, /* Conversion type. */
|
||
Tcl_WideUInt bw, /* Integer significand and exponent. */
|
||
int b2, /* Scale factor for the significand. */
|
||
int m2plus, int m2minus, /* Scale factors for 1/2 ulp in numerator. */
|
||
int s2, int s5, /* Scale factors for denominator. */
|
||
int k, /* Guessed position of the decimal point. */
|
||
int len, /* Size of the digit buffer to allocate. */
|
||
int ilim, /* Number of digits to convert if b >= s */
|
||
int ilim1, /* Number of digits to convert if b < s */
|
||
int *decpt, /* OUTPUT: Position of the decimal point. */
|
||
char **endPtr) /* OUTPUT: Pointer to the end of the number */
|
||
{
|
||
char *retval = ckalloc(len+1);
|
||
/* Buffer of digits to return. */
|
||
char *s = retval; /* Cursor in the return value. */
|
||
mp_int b; /* Numerator of the result. */
|
||
mp_int mminus; /* 1/2 ulp below the result. */
|
||
mp_int mplus; /* 1/2 ulp above the result. */
|
||
mp_int S; /* Denominator of the result. */
|
||
mp_int dig; /* Current digit of the result. */
|
||
int digit; /* Current digit of the result. */
|
||
mp_int temp; /* Work area. */
|
||
int minit = 1; /* Fudge factor for when we misguess k. */
|
||
int i;
|
||
int r1;
|
||
|
||
/*
|
||
* b = bw * 2**b2 * 5**b5
|
||
* S = 2**s2 * 5*s5
|
||
*/
|
||
|
||
TclBNInitBignumFromWideUInt(&b, bw);
|
||
mp_mul_2d(&b, b2, &b);
|
||
mp_init_set(&S, 1);
|
||
MulPow5(&S, s5, &S); mp_mul_2d(&S, s2, &S);
|
||
|
||
/*
|
||
* Handle the case where we guess the position of the decimal point wrong.
|
||
*/
|
||
|
||
if (mp_cmp_mag(&b, &S) == MP_LT) {
|
||
mp_mul_d(&b, 10, &b);
|
||
minit = 10;
|
||
ilim =ilim1;
|
||
--k;
|
||
}
|
||
|
||
/*
|
||
* mminus = 2**m2minus * 5**m5
|
||
*/
|
||
|
||
mp_init_set(&mminus, minit);
|
||
mp_mul_2d(&mminus, m2minus, &mminus);
|
||
if (m2plus > m2minus) {
|
||
mp_init_copy(&mplus, &mminus);
|
||
mp_mul_2d(&mplus, m2plus-m2minus, &mplus);
|
||
}
|
||
mp_init(&temp);
|
||
|
||
/*
|
||
* Loop through the digits.
|
||
*/
|
||
|
||
mp_init(&dig);
|
||
i = 1;
|
||
for (;;) {
|
||
mp_div(&b, &S, &dig, &b);
|
||
if (dig.used > 1 || dig.dp[0] >= 10) {
|
||
Tcl_Panic("wrong digit!");
|
||
}
|
||
digit = dig.dp[0];
|
||
|
||
/*
|
||
* Does the current digit leave us with a remainder small enough to
|
||
* round to it?
|
||
*/
|
||
|
||
r1 = mp_cmp_mag(&b, (m2plus > m2minus)? &mplus : &mminus);
|
||
if (r1 == MP_LT || (r1 == MP_EQ
|
||
&& convType != TCL_DD_STEELE0 && (dPtr->w.word1 & 1) == 0)) {
|
||
mp_mul_2d(&b, 1, &b);
|
||
if (ShouldBankerRoundUp(&b, &S, digit&1)) {
|
||
++digit;
|
||
if (digit == 10) {
|
||
*s++ = '9';
|
||
s = BumpUp(s, retval, &k);
|
||
break;
|
||
}
|
||
}
|
||
*s++ = '0' + digit;
|
||
break;
|
||
}
|
||
|
||
/*
|
||
* Does the current digit leave us with a remainder large enough to
|
||
* commit to rounding up to the next higher digit?
|
||
*/
|
||
|
||
if (ShouldBankerRoundUpToNext(&b, &mminus, &S, convType,
|
||
dPtr->w.word1 & 1, &temp)) {
|
||
++digit;
|
||
if (digit == 10) {
|
||
*s++ = '9';
|
||
s = BumpUp(s, retval, &k);
|
||
break;
|
||
}
|
||
*s++ = '0' + digit;
|
||
break;
|
||
}
|
||
|
||
/*
|
||
* 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);
|
||
}
|
||
break;
|
||
}
|
||
|
||
/*
|
||
* Advance to the next digit.
|
||
*/
|
||
|
||
if (s5 > 0) {
|
||
/*
|
||
* Can possibly shorten the denominator.
|
||
*/
|
||
|
||
mp_mul_2d(&b, 1, &b);
|
||
mp_mul_2d(&mminus, 1, &mminus);
|
||
if (m2plus > m2minus) {
|
||
mp_mul_2d(&mplus, 1, &mplus);
|
||
}
|
||
mp_div_d(&S, 5, &S, NULL);
|
||
--s5;
|
||
|
||
/*
|
||
* IDEA: It might possibly be a win to fall back to int64_t
|
||
* 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**29 3 trips
|
||
* 10**30 4 trips
|
||
* 10**31 5 trips
|
||
* 10**32 6 trips
|
||
* 10**33 7 trips
|
||
* 10**34 8 trips
|
||
* 10**35 9 trips
|
||
* 10**36 10 trips
|
||
* 10**37 11 trips
|
||
* 10**38 12 trips
|
||
* 10**39 13 trips
|
||
* 10**40 14 trips
|
||
* 10**41 15 trips
|
||
* 10**42 16 trips
|
||
* thereafter no gain.
|
||
*/
|
||
} else {
|
||
mp_mul_d(&b, 10, &b);
|
||
mp_mul_d(&mminus, 10, &mminus);
|
||
if (m2plus > m2minus) {
|
||
mp_mul_2d(&mplus, 10, &mplus);
|
||
}
|
||
}
|
||
|
||
++i;
|
||
}
|
||
|
||
/*
|
||
* Endgame - store the location of the decimal point and the end of the
|
||
* string.
|
||
*/
|
||
|
||
if (m2plus > m2minus) {
|
||
mp_clear(&mplus);
|
||
}
|
||
mp_clear_multi(&b, &mminus, &temp, &dig, &S, NULL);
|
||
*s = '\0';
|
||
*decpt = k;
|
||
if (endPtr) {
|
||
*endPtr = s;
|
||
}
|
||
return retval;
|
||
}
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* StrictBignumConversion --
|
||
*
|
||
* 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.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
static inline char *
|
||
StrictBignumConversion(
|
||
Double *dPtr, /* Original number being converted. */
|
||
int convType, /* Conversion type. */
|
||
Tcl_WideUInt bw, /* Integer significand and exponent. */
|
||
int b2, /* Scale factor for the significand. */
|
||
int s2, int s5, /* Scale factors for denominator. */
|
||
int k, /* Guessed position of the decimal point. */
|
||
int len, /* Size of the digit buffer to allocate. */
|
||
int ilim, /* Number of digits to convert if b >= s */
|
||
int ilim1, /* Number of digits to convert if b < s */
|
||
int *decpt, /* OUTPUT: Position of the decimal point. */
|
||
char **endPtr) /* OUTPUT: Pointer to the end of the number */
|
||
{
|
||
char *retval = ckalloc(len+1);
|
||
/* Buffer of digits to return. */
|
||
char *s = retval; /* Cursor in the return value. */
|
||
mp_int b; /* Numerator of the result. */
|
||
mp_int S; /* Denominator of the result. */
|
||
mp_int dig; /* Current digit of the result. */
|
||
int digit; /* Current digit of the result. */
|
||
mp_int temp; /* Work area. */
|
||
int g; /* Size of the current digit ground. */
|
||
int i, j;
|
||
|
||
/*
|
||
* b = bw * 2**b2 * 5**b5
|
||
* S = 2**s2 * 5*s5
|
||
*/
|
||
|
||
mp_init_multi(&temp, &dig, NULL);
|
||
TclBNInitBignumFromWideUInt(&b, bw);
|
||
mp_mul_2d(&b, b2, &b);
|
||
mp_init_set(&S, 1);
|
||
MulPow5(&S, s5, &S); mp_mul_2d(&S, s2, &S);
|
||
|
||
/*
|
||
* Handle the case where we guess the position of the decimal point wrong.
|
||
*/
|
||
|
||
if (mp_cmp_mag(&b, &S) == MP_LT) {
|
||
mp_mul_d(&b, 10, &b);
|
||
ilim =ilim1;
|
||
--k;
|
||
}
|
||
|
||
/*
|
||
* Convert the leading digit.
|
||
*/
|
||
|
||
i = 0;
|
||
mp_div(&b, &S, &dig, &b);
|
||
if (dig.used > 1 || dig.dp[0] >= 10) {
|
||
Tcl_Panic("wrong digit!");
|
||
}
|
||
digit = dig.dp[0];
|
||
|
||
/*
|
||
* 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);
|
||
}
|
||
} else {
|
||
for (;;) {
|
||
/*
|
||
* Shift by a group of digits.
|
||
*/
|
||
|
||
g = ilim - i;
|
||
if (g > DIGIT_GROUP) {
|
||
g = DIGIT_GROUP;
|
||
}
|
||
if (s5 >= g) {
|
||
mp_div_d(&S, dpow5[g], &S, NULL);
|
||
s5 -= g;
|
||
} else if (s5 > 0) {
|
||
mp_div_d(&S, dpow5[s5], &S, NULL);
|
||
mp_mul_d(&b, dpow5[g - s5], &b);
|
||
s5 = 0;
|
||
} else {
|
||
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_t 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.
|
||
*/
|
||
|
||
mp_div(&b, &S, &dig, &b);
|
||
if (dig.used > 1) {
|
||
Tcl_Panic("wrong digit!");
|
||
}
|
||
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?
|
||
*/
|
||
|
||
if (i == ilim) {
|
||
mp_mul_2d(&b, 1, &b);
|
||
if (ShouldBankerRoundUp(&b, &S, digit&1)) {
|
||
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;
|
||
if (endPtr) {
|
||
*endPtr = s;
|
||
}
|
||
return retval;
|
||
}
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* TclDoubleDigits --
|
||
*
|
||
* 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.
|
||
*
|
||
* 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.
|
||
* For floating point numbers that are exactly between two
|
||
* decimal numbers, it resolves using the 'round to even' rule.
|
||
* With this value, the 'ndigits' parameter is ignored.
|
||
* TCL_DD_STEELE - This value is not recommended and may be removed in
|
||
* the future. It follows the conversion algorithm outlined in
|
||
* "How to Print Floating-Point Numbers Accurately" by Guy
|
||
* L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90,
|
||
* pp. 112-126]. This rule has the effect of rendering 1e23 as
|
||
* 9.9999999999999999e22 - which is a 'better' approximation in
|
||
* the sense that it will reconvert correctly even if a
|
||
* subsequent input conversion is 'round up' or 'round down'
|
||
* rather than 'round to nearest', but is surprising otherwise.
|
||
* TCL_DD_E_FORMAT - This value is used to prepare numbers for %e format
|
||
* conversion (or for default floating->string if tcl_precision
|
||
* is not 0). It constructs a string of at most 'ndigits' digits,
|
||
* choosing the one that is closest to the given number (and
|
||
* resolving ties with 'round to even'). It is allowed to return
|
||
* fewer than 'ndigits' if the number converts exactly; if the
|
||
* TCL_DD_E_FORMAT|TCL_DD_SHORTEN_FLAG is supplied instead, it
|
||
* 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.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
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, or TCL_DD_F_FORMAT. */
|
||
Double d; /* Union for deconstructing doubles. */
|
||
Tcl_WideUInt bw; /* Integer significand. */
|
||
int be; /* Power of 2 by which b must be multiplied */
|
||
int bbits; /* Number of bits needed to represent b. */
|
||
int denorm; /* Flag == 1 iff the input number was
|
||
* denormalized. */
|
||
int k; /* Estimate of floor(log10(d)). */
|
||
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. */
|
||
int i = -1;
|
||
|
||
/*
|
||
* 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.
|
||
*/
|
||
|
||
TakeAbsoluteValue(&d, sign);
|
||
if ((d.w.word0 & EXP_MASK) == EXP_MASK) {
|
||
return FormatInfAndNaN(&d, decpt, endPtr);
|
||
}
|
||
if (d.d == 0.0) {
|
||
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)).
|
||
*/
|
||
|
||
denorm = ((d.w.word0 & EXP_MASK) == 0);
|
||
DoubleToExpAndSig(d.d, &bw, &be, &bbits);
|
||
k = ApproximateLog10(bw, be, bbits);
|
||
k = BetterLog10(d.d, k, &k_check);
|
||
|
||
/* At this point, we have:
|
||
* d is the number to convert.
|
||
* 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
|
||
* 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.
|
||
*/
|
||
|
||
ComputeScale(be, k, &b2, &b5, &s2, &s5);
|
||
|
||
/*
|
||
* Correct an incorrect caller-supplied 'ndigits'. Also determine:
|
||
* i = The maximum number of decimal digits that will be returned in the
|
||
* formatted string. This is k + 1 + ndigits for F format, 18 for
|
||
* shortest and Steele, and ndigits for E format.
|
||
* ilim = The number of significant digits to convert if k has been
|
||
* guessed correctly. This is -1 for shortest and Steele (which
|
||
* stop when all significance has been lost), 'ndigits' for E
|
||
* format, and 'k + 1 + ndigits' for F format.
|
||
* ilim1 = The minimum number of significant digits to convert if k has
|
||
* been guessed 1 too high. This, too, is -1 for shortest and
|
||
* Steele, and 'ndigits' for E format, but it's 'ndigits-1' for F
|
||
* format.
|
||
*/
|
||
|
||
SetPrecisionLimits(convType, k, &ndigits, &i, &ilim, &ilim1);
|
||
|
||
/*
|
||
* Try to do low-precision conversion in floating point rather than
|
||
* resorting to expensive multiprecision arithmetic.
|
||
*/
|
||
|
||
if (ilim >= 0 && ilim <= QUICK_MAX && !(flags & TCL_DD_NO_QUICK)) {
|
||
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.
|
||
*/
|
||
|
||
if (flags & TCL_DD_SHORTEN_FLAG) {
|
||
int m2minus = b2;
|
||
int m2plus;
|
||
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.
|
||
*/
|
||
|
||
if (denorm) {
|
||
i = be + EXPONENT_BIAS + (FP_PRECISION-1);
|
||
} else {
|
||
i = 1 + FP_PRECISION - bbits;
|
||
}
|
||
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.
|
||
*/
|
||
|
||
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;
|
||
++s2;
|
||
++m2plus;
|
||
}
|
||
|
||
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]).
|
||
*/
|
||
|
||
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 MP_DIGIT_BIT,
|
||
* and adjust m2 and b2 accordingly. Then we launch into a version
|
||
* of the comparison that's specialized for the 'power of mp_digit
|
||
* in the denominator' case.
|
||
*/
|
||
|
||
if (s2 % MP_DIGIT_BIT != 0) {
|
||
int delta = MP_DIGIT_BIT - (s2 % MP_DIGIT_BIT);
|
||
|
||
b2 += delta;
|
||
m2plus += delta;
|
||
m2minus += delta;
|
||
s2 += delta;
|
||
}
|
||
return ShorteningBignumConversionPowD(&d, convType, bw, b2, b5,
|
||
m2plus, m2minus, m5, s2/MP_DIGIT_BIT, k, len, ilim, ilim1,
|
||
decpt, endPtr);
|
||
} else {
|
||
/*
|
||
* Alas, there's no helpful special case; use full-up bignum
|
||
* arithmetic for the conversion.
|
||
*/
|
||
|
||
return ShorteningBignumConversion(&d, convType, bw, b2, m2plus,
|
||
m2minus, s2, s5, k, len, ilim, ilim1, decpt, endPtr);
|
||
}
|
||
} else {
|
||
/*
|
||
* Non-shortening conversion.
|
||
*/
|
||
|
||
int len = i;
|
||
|
||
/*
|
||
* Reduce numerator and denominator to lowest terms.
|
||
*/
|
||
|
||
if (b2 >= s2 && s2 > 0) {
|
||
b2 -= s2; s2 = 0;
|
||
} else if (s2 >= b2 && b2 > 0) {
|
||
s2 -= b2; b2 = 0;
|
||
}
|
||
|
||
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.
|
||
*/
|
||
|
||
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 MP_DIGIT_BIT,
|
||
* and adjust m2 and b2 accordingly. Then we launch into a version
|
||
* of the comparison that's specialized for the 'power of mp_digit
|
||
* in the denominator' case.
|
||
*/
|
||
|
||
if (s2 % MP_DIGIT_BIT != 0) {
|
||
int delta = MP_DIGIT_BIT - (s2 % MP_DIGIT_BIT);
|
||
|
||
b2 += delta;
|
||
s2 += delta;
|
||
}
|
||
return StrictBignumConversionPowD(&d, convType, bw, b2, b5,
|
||
s2/MP_DIGIT_BIT, k, len, ilim, ilim1, decpt, endPtr);
|
||
} else {
|
||
/*
|
||
* There are no helpful special cases, but at least we know in
|
||
* advance how many digits we will convert. We can run the
|
||
* conversion in steps of DIGIT_GROUP digits, so as to have many
|
||
* fewer mp_int divisions.
|
||
*/
|
||
|
||
return StrictBignumConversion(&d, convType, bw, b2, s2, s5, k,
|
||
len, ilim, ilim1, decpt, endPtr);
|
||
}
|
||
}
|
||
}
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* TclInitDoubleConversion --
|
||
*
|
||
* Initializes constants that are needed for conversions to and from
|
||
* 'double'
|
||
*
|
||
* Results:
|
||
* None.
|
||
*
|
||
* Side effects:
|
||
* The log base 2 of the floating point radix, the number of bits in a
|
||
* double mantissa, and a table of the powers of five and ten are
|
||
* computed and stored.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
void
|
||
TclInitDoubleConversion(void)
|
||
{
|
||
int i;
|
||
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;
|
||
|
||
mipsCR.fc_word = get_fpc_csr();
|
||
mipsCR.fc_struct.flush = 0;
|
||
set_fpc_csr(mipsCR.fc_word);
|
||
#endif
|
||
|
||
/*
|
||
* Initialize table of powers of 10 expressed as wide integers.
|
||
*/
|
||
|
||
maxpow10_wide = (int)
|
||
floor(sizeof(Tcl_WideUInt) * CHAR_BIT * log(2.) / log(10.));
|
||
pow10_wide = (Tcl_WideUInt *)
|
||
ckalloc((maxpow10_wide + 1) * sizeof(Tcl_WideUInt));
|
||
u = 1;
|
||
for (i = 0; i < maxpow10_wide; ++i) {
|
||
pow10_wide[i] = u;
|
||
u *= 10;
|
||
}
|
||
pow10_wide[i] = u;
|
||
|
||
/*
|
||
* 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) {
|
||
Tcl_Panic("This code doesn't work on a decimal machine!");
|
||
}
|
||
log2FLT_RADIX--;
|
||
mantBits = DBL_MANT_DIG * log2FLT_RADIX;
|
||
d = 1.0;
|
||
|
||
/*
|
||
* 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));
|
||
if (x < MAXPOW) {
|
||
mmaxpow = x;
|
||
} else {
|
||
mmaxpow = MAXPOW;
|
||
}
|
||
for (i=0 ; i<=mmaxpow ; ++i) {
|
||
pow10vals[i] = d;
|
||
d *= 10.0;
|
||
}
|
||
|
||
/*
|
||
* Initialize a table of large powers of five.
|
||
*/
|
||
|
||
for (i=0; i<9; ++i) {
|
||
mp_init(pow5 + i);
|
||
}
|
||
mp_set(pow5, 5);
|
||
for (i=0; i<8; ++i) {
|
||
mp_sqr(pow5+i, pow5+i+1);
|
||
}
|
||
mp_init_set_int(pow5_13, 1220703125);
|
||
for (i = 1; i < 5; ++i) {
|
||
mp_init(pow5_13 + i);
|
||
mp_sqr(pow5_13 + i - 1, pow5_13 + i);
|
||
}
|
||
|
||
/*
|
||
* Determine the number of decimal digits to the left and right of the
|
||
* decimal point in the largest and smallest double, the smallest double
|
||
* that differs from zero, and the number of mp_digits needed to represent
|
||
* the significand of a double.
|
||
*/
|
||
|
||
maxDigits = (int) ((DBL_MAX_EXP * log((double) FLT_RADIX)
|
||
+ 0.5 * log(10.)) / log(10.));
|
||
minDigits = (int) floor((DBL_MIN_EXP - DBL_MANT_DIG)
|
||
* log((double) FLT_RADIX) / log(10.));
|
||
log10_DIGIT_MAX = (int) floor(MP_DIGIT_BIT * log(2.) / log(10.));
|
||
|
||
/*
|
||
* Nokia 770's software-emulated floating point is "middle endian": the
|
||
* bytes within a 32-bit word are little-endian (like the native
|
||
* integers), but the two words of a 'double' are presented most
|
||
* significant word first.
|
||
*/
|
||
|
||
#ifdef IEEE_FLOATING_POINT
|
||
bitwhack.dv = 1.000000238418579;
|
||
/* 3ff0 0000 4000 0000 */
|
||
if ((bitwhack.iv >> 32) == 0x3FF00000) {
|
||
n770_fp = 0;
|
||
} else if ((bitwhack.iv & 0xFFFFFFFF) == 0x3FF00000) {
|
||
n770_fp = 1;
|
||
} else {
|
||
Tcl_Panic("unknown floating point word order on this machine");
|
||
}
|
||
#endif
|
||
}
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* TclFinalizeDoubleConversion --
|
||
*
|
||
* Cleans up this file on exit.
|
||
*
|
||
* Results:
|
||
* None
|
||
*
|
||
* Side effects:
|
||
* Memory allocated by TclInitDoubleConversion is freed.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
void
|
||
TclFinalizeDoubleConversion(void)
|
||
{
|
||
int i;
|
||
|
||
ckfree(pow10_wide);
|
||
for (i=0; i<9; ++i) {
|
||
mp_clear(pow5 + i);
|
||
}
|
||
for (i=0; i < 5; ++i) {
|
||
mp_clear(pow5_13 + i);
|
||
}
|
||
}
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* Tcl_InitBignumFromDouble --
|
||
*
|
||
* Extracts the integer part of a double and converts it to an arbitrary
|
||
* precision integer.
|
||
*
|
||
* Results:
|
||
* None.
|
||
*
|
||
* Side effects:
|
||
* Initializes the bignum supplied, and stores the converted number in
|
||
* it.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
int
|
||
Tcl_InitBignumFromDouble(
|
||
Tcl_Interp *interp, /* For error message. */
|
||
double d, /* Number to convert. */
|
||
mp_int *b) /* Place to store the result. */
|
||
{
|
||
double fract;
|
||
int expt;
|
||
|
||
/*
|
||
* Infinite values can't convert to bignum.
|
||
*/
|
||
|
||
if (TclIsInfinite(d)) {
|
||
if (interp != NULL) {
|
||
const char *s = "integer value too large to represent";
|
||
|
||
Tcl_SetObjResult(interp, Tcl_NewStringObj(s, -1));
|
||
Tcl_SetErrorCode(interp, "ARITH", "IOVERFLOW", s, NULL);
|
||
}
|
||
return TCL_ERROR;
|
||
}
|
||
|
||
fract = frexp(d,&expt);
|
||
if (expt <= 0) {
|
||
mp_init(b);
|
||
mp_zero(b);
|
||
} else {
|
||
Tcl_WideInt w = (Tcl_WideInt) ldexp(fract, mantBits);
|
||
int shift = expt - mantBits;
|
||
|
||
TclBNInitBignumFromWideInt(b, w);
|
||
if (shift < 0) {
|
||
mp_div_2d(b, -shift, b, NULL);
|
||
} else if (shift > 0) {
|
||
mp_mul_2d(b, shift, b);
|
||
}
|
||
}
|
||
return TCL_OK;
|
||
}
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* TclBignumToDouble --
|
||
*
|
||
* Convert an arbitrary-precision integer to a native floating point
|
||
* number.
|
||
*
|
||
* Results:
|
||
* Returns the converted number. Sets errno to ERANGE if the number is
|
||
* too large to convert.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
double
|
||
TclBignumToDouble(
|
||
const mp_int *a) /* Integer to convert. */
|
||
{
|
||
mp_int b;
|
||
int bits, shift, i, lsb;
|
||
double r;
|
||
|
||
|
||
/*
|
||
* We need a 'mantBits'-bit significand. Determine what shift will
|
||
* give us that.
|
||
*/
|
||
|
||
bits = mp_count_bits(a);
|
||
if (bits > DBL_MAX_EXP*log2FLT_RADIX) {
|
||
errno = ERANGE;
|
||
if (mp_isneg(a)) {
|
||
return -HUGE_VAL;
|
||
} else {
|
||
return HUGE_VAL;
|
||
}
|
||
}
|
||
shift = mantBits - bits;
|
||
|
||
/*
|
||
* If shift > 0, shift the significand left by the requisite number of
|
||
* bits. If shift == 0, the significand is already exactly 'mantBits'
|
||
* in length. If shift < 0, we will need to shift the significand right
|
||
* by the requisite number of bits, and round it. If the '1-shift'
|
||
* least significant bits are 0, but the 'shift'th bit is nonzero,
|
||
* then the significand lies exactly between two values and must be
|
||
* 'rounded to even'.
|
||
*/
|
||
|
||
mp_init(&b);
|
||
if (shift == 0) {
|
||
mp_copy(a, &b);
|
||
} else if (shift > 0) {
|
||
mp_mul_2d(a, shift, &b);
|
||
} else if (shift < 0) {
|
||
lsb = mp_cnt_lsb(a);
|
||
if (lsb == -1-shift) {
|
||
|
||
/*
|
||
* Round to even
|
||
*/
|
||
|
||
mp_div_2d(a, -shift, &b, NULL);
|
||
if (mp_isodd(&b)) {
|
||
if (mp_isneg(&b)) {
|
||
mp_sub_d(&b, 1, &b);
|
||
} else {
|
||
mp_add_d(&b, 1, &b);
|
||
}
|
||
}
|
||
} else {
|
||
|
||
/*
|
||
* Ordinary rounding
|
||
*/
|
||
|
||
mp_div_2d(a, -1-shift, &b, NULL);
|
||
if (mp_isneg(&b)) {
|
||
mp_sub_d(&b, 1, &b);
|
||
} else {
|
||
mp_add_d(&b, 1, &b);
|
||
}
|
||
mp_div_2d(&b, 1, &b, NULL);
|
||
}
|
||
}
|
||
|
||
/*
|
||
* Accumulate the result, one mp_digit at a time.
|
||
*/
|
||
|
||
r = 0.0;
|
||
for (i=b.used-1 ; i>=0 ; --i) {
|
||
r = ldexp(r, MP_DIGIT_BIT) + b.dp[i];
|
||
}
|
||
mp_clear(&b);
|
||
|
||
/*
|
||
* Scale the result to the correct number of bits.
|
||
*/
|
||
|
||
r = ldexp(r, bits - mantBits);
|
||
|
||
/*
|
||
* Return the result with the appropriate sign.
|
||
*/
|
||
|
||
if (mp_isneg(a)) {
|
||
return -r;
|
||
} else {
|
||
return r;
|
||
}
|
||
}
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* TclCeil --
|
||
*
|
||
* Computes the smallest floating point number that is at least the
|
||
* mp_int argument.
|
||
*
|
||
* Results:
|
||
* Returns the floating point number.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
double
|
||
TclCeil(
|
||
const mp_int *a) /* Integer to convert. */
|
||
{
|
||
double r = 0.0;
|
||
mp_int b;
|
||
|
||
mp_init(&b);
|
||
if (mp_cmp_d(a, 0) == MP_LT) {
|
||
mp_neg(a, &b);
|
||
r = -TclFloor(&b);
|
||
} else {
|
||
int bits = mp_count_bits(a);
|
||
|
||
if (bits > DBL_MAX_EXP*log2FLT_RADIX) {
|
||
r = HUGE_VAL;
|
||
} else {
|
||
int i, exact = 1, shift = mantBits - bits;
|
||
|
||
if (shift > 0) {
|
||
mp_mul_2d(a, shift, &b);
|
||
} else if (shift < 0) {
|
||
mp_int d;
|
||
mp_init(&d);
|
||
mp_div_2d(a, -shift, &b, &d);
|
||
exact = mp_iszero(&d);
|
||
mp_clear(&d);
|
||
} else {
|
||
mp_copy(a, &b);
|
||
}
|
||
if (!exact) {
|
||
mp_add_d(&b, 1, &b);
|
||
}
|
||
for (i=b.used-1 ; i>=0 ; --i) {
|
||
r = ldexp(r, MP_DIGIT_BIT) + b.dp[i];
|
||
}
|
||
r = ldexp(r, bits - mantBits);
|
||
}
|
||
}
|
||
mp_clear(&b);
|
||
return r;
|
||
}
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* TclFloor --
|
||
*
|
||
* Computes the largest floating point number less than or equal to the
|
||
* mp_int argument.
|
||
*
|
||
* Results:
|
||
* Returns the floating point value.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
double
|
||
TclFloor(
|
||
const mp_int *a) /* Integer to convert. */
|
||
{
|
||
double r = 0.0;
|
||
mp_int b;
|
||
|
||
mp_init(&b);
|
||
if (mp_cmp_d(a, 0) == MP_LT) {
|
||
mp_neg(a, &b);
|
||
r = -TclCeil(&b);
|
||
} else {
|
||
int bits = mp_count_bits(a);
|
||
|
||
if (bits > DBL_MAX_EXP*log2FLT_RADIX) {
|
||
r = DBL_MAX;
|
||
} else {
|
||
int i, shift = mantBits - bits;
|
||
|
||
if (shift > 0) {
|
||
mp_mul_2d(a, shift, &b);
|
||
} else if (shift < 0) {
|
||
mp_div_2d(a, -shift, &b, NULL);
|
||
} else {
|
||
mp_copy(a, &b);
|
||
}
|
||
for (i=b.used-1 ; i>=0 ; --i) {
|
||
r = ldexp(r, MP_DIGIT_BIT) + b.dp[i];
|
||
}
|
||
r = ldexp(r, bits - mantBits);
|
||
}
|
||
}
|
||
mp_clear(&b);
|
||
return r;
|
||
}
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* BignumToBiasedFrExp --
|
||
*
|
||
* Convert an arbitrary-precision integer to a native floating point
|
||
* number in the range [0.5,1) times a power of two. NOTE: Intentionally
|
||
* converts to a number that's a few ulp too small, so that
|
||
* RefineApproximation will not overflow near the high end of the
|
||
* machine's arithmetic range.
|
||
*
|
||
* Results:
|
||
* Returns the converted number.
|
||
*
|
||
* Side effects:
|
||
* Stores the exponent of two in 'machexp'.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
static double
|
||
BignumToBiasedFrExp(
|
||
const mp_int *a, /* Integer to convert. */
|
||
int *machexp) /* Power of two. */
|
||
{
|
||
mp_int b;
|
||
int bits;
|
||
int shift;
|
||
int i;
|
||
double r;
|
||
|
||
/*
|
||
* Determine how many bits we need, and extract that many from the input.
|
||
* Round to nearest unit in the last place.
|
||
*/
|
||
|
||
bits = mp_count_bits(a);
|
||
shift = mantBits - 2 - bits;
|
||
mp_init(&b);
|
||
if (shift > 0) {
|
||
mp_mul_2d(a, shift, &b);
|
||
} else if (shift < 0) {
|
||
mp_div_2d(a, -shift, &b, NULL);
|
||
} else {
|
||
mp_copy(a, &b);
|
||
}
|
||
|
||
/*
|
||
* Accumulate the result, one mp_digit at a time.
|
||
*/
|
||
|
||
r = 0.0;
|
||
for (i=b.used-1; i>=0; --i) {
|
||
r = ldexp(r, MP_DIGIT_BIT) + b.dp[i];
|
||
}
|
||
mp_clear(&b);
|
||
|
||
/*
|
||
* Return the result with the appropriate sign.
|
||
*/
|
||
|
||
*machexp = bits - mantBits + 2;
|
||
return (mp_isneg(a) ? -r : r);
|
||
}
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* Pow10TimesFrExp --
|
||
*
|
||
* Multiply a power of ten by a number expressed as fraction and
|
||
* exponent.
|
||
*
|
||
* Results:
|
||
* Returns the significand of the result.
|
||
*
|
||
* Side effects:
|
||
* Overwrites the 'machexp' parameter with the exponent of the result.
|
||
*
|
||
* Assumes that 'exponent' is such that 10**exponent would be a double, even
|
||
* though 'fraction*10**(machexp+exponent)' might overflow.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
static double
|
||
Pow10TimesFrExp(
|
||
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. */
|
||
{
|
||
int i, j;
|
||
int expt = *machexp;
|
||
double retval = fraction;
|
||
|
||
if (exponent > 0) {
|
||
/*
|
||
* Multiply by 10**exponent.
|
||
*/
|
||
|
||
retval = frexp(retval * pow10vals[exponent&0xF], &j);
|
||
expt += j;
|
||
for (i=4; i<9; ++i) {
|
||
if (exponent & (1<<i)) {
|
||
retval = frexp(retval * pow_10_2_n[i], &j);
|
||
expt += j;
|
||
}
|
||
}
|
||
} else if (exponent < 0) {
|
||
/*
|
||
* Divide by 10**-exponent.
|
||
*/
|
||
|
||
retval = frexp(retval / pow10vals[(-exponent) & 0xF], &j);
|
||
expt += j;
|
||
for (i=4; i<9; ++i) {
|
||
if ((-exponent) & (1<<i)) {
|
||
retval = frexp(retval / pow_10_2_n[i], &j);
|
||
expt += j;
|
||
}
|
||
}
|
||
}
|
||
|
||
*machexp = expt;
|
||
return retval;
|
||
}
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* SafeLdExp --
|
||
*
|
||
* Do an 'ldexp' operation, but handle denormals gracefully.
|
||
*
|
||
* Results:
|
||
* Returns the appropriately scaled value.
|
||
*
|
||
* On some platforms, 'ldexp' fails when presented with a number too
|
||
* small to represent as a normalized double. This routine does 'ldexp'
|
||
* in two steps for those numbers, to return correctly denormalized
|
||
* values.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
static double
|
||
SafeLdExp(
|
||
double fract,
|
||
int expt)
|
||
{
|
||
int minexpt = DBL_MIN_EXP * log2FLT_RADIX;
|
||
volatile double a, b, retval;
|
||
|
||
if (expt < minexpt) {
|
||
a = ldexp(fract, expt - mantBits - minexpt);
|
||
b = ldexp(1.0, mantBits + minexpt);
|
||
retval = a * b;
|
||
} else {
|
||
retval = ldexp(fract, expt);
|
||
}
|
||
return retval;
|
||
}
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* TclFormatNaN --
|
||
*
|
||
* Makes the string representation of a "Not a Number"
|
||
*
|
||
* Results:
|
||
* None.
|
||
*
|
||
* Side effects:
|
||
* Stores the string representation in the supplied buffer, which must be
|
||
* at least TCL_DOUBLE_SPACE characters.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
void
|
||
TclFormatNaN(
|
||
double value, /* The Not-a-Number to format. */
|
||
char *buffer) /* String representation. */
|
||
{
|
||
#ifndef IEEE_FLOATING_POINT
|
||
strcpy(buffer, "NaN");
|
||
return;
|
||
#else
|
||
union {
|
||
double dv;
|
||
Tcl_WideUInt iv;
|
||
} bitwhack;
|
||
|
||
bitwhack.dv = value;
|
||
if (n770_fp) {
|
||
bitwhack.iv = Nokia770Twiddle(bitwhack.iv);
|
||
}
|
||
if (bitwhack.iv & ((Tcl_WideUInt) 1 << 63)) {
|
||
bitwhack.iv &= ~ ((Tcl_WideUInt) 1 << 63);
|
||
*buffer++ = '-';
|
||
}
|
||
*buffer++ = 'N';
|
||
*buffer++ = 'a';
|
||
*buffer++ = 'N';
|
||
bitwhack.iv &= (((Tcl_WideUInt) 1) << 51) - 1;
|
||
if (bitwhack.iv != 0) {
|
||
sprintf(buffer, "(%" TCL_LL_MODIFIER "x)", bitwhack.iv);
|
||
} else {
|
||
*buffer = '\0';
|
||
}
|
||
#endif /* IEEE_FLOATING_POINT */
|
||
}
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* Nokia770Twiddle --
|
||
*
|
||
* 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. */
|
||
{
|
||
return (((w >> 32) & 0xFFFFFFFF) | (w << 32));
|
||
}
|
||
#endif
|
||
|
||
/*
|
||
*----------------------------------------------------------------------
|
||
*
|
||
* TclNokia770Doubles --
|
||
*
|
||
* Transpose the two words of a number for Nokia 770 floating point
|
||
* handling.
|
||
*
|
||
*----------------------------------------------------------------------
|
||
*/
|
||
|
||
int
|
||
TclNokia770Doubles(void)
|
||
{
|
||
return n770_fp;
|
||
}
|
||
|
||
/*
|
||
* Local Variables:
|
||
* mode: c
|
||
* c-basic-offset: 4
|
||
* fill-column: 78
|
||
* End:
|
||
*/
|