/*
*----------------------------------------------------------------------
*
* tclDouble.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.
*
* RCS: @(#) $Id: tclStrToD.c,v 1.11 2005/10/13 15:15:28 dgp Exp $
*
*----------------------------------------------------------------------
*/
#include <tclInt.h>
#include <stdio.h>
#include <stdlib.h>
#include <float.h>
#include <limits.h>
#include <math.h>
#include <ctype.h>
#include <tommath.h>
/*
* Define TIP_114_FORMATS to accept 0b and 0o for binary and octal strings.
* Define KILL_OCTAL as well as TIP_114_FORMATS to suppress interpretation
* of numbers with leading zero as octal. (Ceterum censeo: numeros octonarios
* delendos esse.)
*/
#define TIP_114_FORMATS
#undef KILL_OCTAL
#ifndef TIP_114_FORMATS
#undef KILL_OCTAL
#endif
/*
* 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
/*
* 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__) && defined(__i386)
typedef unsigned int fpu_control_t __attribute__ ((__mode__ (__HI__)));
#define _FPU_GETCW(cw) __asm__ __volatile__ ("fnstcw %0" : "=m" (*&cw))
#define _FPU_SETCW(cw) __asm__ __volatile__ ("fldcw %0" : : "m" (*&cw))
# define FPU_IEEE_ROUNDING 0x027f
# define ADJUST_FPU_CONTROL_WORD
#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
/* The powers of ten that can be represented exactly as wide integers */
static int maxpow10_wide;
static Tcl_WideUInt *pow10_wide;
/* The number of decimal digits that fit in an mp_digit */
static int log10_DIGIT_MAX;
/* The powers of ten that can be represented exactly as IEEE754 doubles. */
#define MAXPOW 22
static double pow10 [MAXPOW+1];
static int mmaxpow; /* Largest power of ten that can be
* represented exactly in a 'double'. */
/* Inexact higher powers of ten */
static CONST double pow_10_2_n [] = {
1.0,
100.0,
10000.0,
1.0e+8,
1.0e+16,
1.0e+32,
1.0e+64,
1.0e+128,
1.0e+256
};
/* Logarithm of the floating point radix. */
static int log2FLT_RADIX;
/* Number of bits in a double's significand */
static int mantBits;
/* Table of powers of 5**(2**n), up to 5**256 */
static mp_int pow5[9];
/* The smallest representable double */
static double tiny;
/* The maximum number of digits to the left of the decimal point of a
* double. */
static int maxDigits;
/* The maximum number of digits to the right of the decimal point in a
* double. */
static int minDigits;
/* Number of mp_digit's needed to hold the significand of a double */
static int mantDIGIT;
/* Static functions defined in this file */
static int AccumulateDecimalDigit _ANSI_ARGS_((unsigned, int,
Tcl_WideUInt*, mp_int*, int));
static double MakeLowPrecisionDouble _ANSI_ARGS_((int signum,
Tcl_WideUInt significand,
int nSigDigs,
int exponent));
static double MakeHighPrecisionDouble _ANSI_ARGS_((int signum,
mp_int* significand,
int nSigDigs,
int exponent));
static double MakeNaN _ANSI_ARGS_(( int signum, Tcl_WideUInt tag ));
static double RefineApproximation _ANSI_ARGS_((double approx,
mp_int* exactSignificand,
int exponent));
static double AbsoluteValue(double v, int* signum);
static int GetIntegerTimesPower(double v, mp_int* r, int* e);
static double BignumToBiasedFrExp _ANSI_ARGS_(( mp_int* big, int* machexp ));
static double Pow10TimesFrExp _ANSI_ARGS_(( int exponent,
double fraction,
int* machexp ));
static double SafeLdExp _ANSI_ARGS_(( double fraction, int exponent ));
/*
*----------------------------------------------------------------------
*
* TclParseNumber --
*
* Place a "numeric" internal representation on a Tcl object.
*
* Results:
* Returns a standard Tcl result.
*
* Side effects:
* Stores an internal representation appropriate to the string.
* The internal representation may be an integer, a wide integer,
* a bignum, or a double.
*
* TclMakeObjNumeric is called as a common scanner in routines
* that expect numbers in Tcl_Obj's. It scans the string representation
* of a given Tcl_Obj and stores an internal rep that represents
* a "canonical" version of its numeric value. The value of the
* canonicalization is that a routine can determine simply by
* examining the type pointer whether an object LooksLikeInt,
* what size of integer is needed to hold it, and similar questions,
* and never needs to refer back to the string representation, even
* for "impure" objects.
*
* The 'strPtr' and 'endPtrPtr' arguments allow for recognizing a number
* that is in a substring of a Tcl_Obj, for example a screen metric or
* "end-" index. If 'strPtr' is not NULL, it designates where the
* number begins within the string. (The default is the start of
* objPtr's string rep, which will be constructed if necessary.)
*
* If 'strPtr' is supplied, 'objPtr' may be NULL. In this case,
* no internal representation will be generated; instead, the routine
* will simply check for a syntactically correct number, returning
* TCL_OK or TCL_ERROR as appropriate, and setting *endPtrPtr if
* necessary.
*
* If 'endPtrPtr' is not NULL, it designates the first character
* after the scanned number. In this case, successfully recognizing
* any digits will yield a return code of TCL_OK. Only in the case
* where no leading string of 'strPtr' (or of objPtr's internal rep)
* represents a number will TCL_ERROR be returned.
*
* When only a partial string is being recognized, it is the caller's
* responsibility to destroy the internal representation, or at
* least change its type. Failure to do so will lead to subsequent
* problems where a string that does not represent a number will
* be recognized as one because it has a numeric internal representation.
*
* When the 'flags' word includes TCL_PARSE_DECIMAL_ONLY, only decimal
* numbers are recognized; leading 0 has no special interpretation as
* octal and leading '0x' is forbidden.
*
*----------------------------------------------------------------------
*/
int
TclParseNumber( Tcl_Interp* interp,
/* Tcl interpreter for error reporting.
* May be NULL */
Tcl_Obj* objPtr,
/* Object to receive the internal rep */
CONST char* type,
/* Type of number being parsed ("integer",
* "wide integer", etc. */
CONST char* string,
/* Pointer to the start of the string to
* scan, see above */
size_t length, /* Maximum length of the string to scan,
* see above. */
CONST char** endPtrPtr,
/* (Output) pointer to the end of the
* scanned number, see above */
int flags) /* Flags governing the parse */
{
enum State {
INITIAL, SIGNUM, ZERO, ZERO_X,
#ifdef TIP_114_FORMATS
ZERO_O, ZERO_B, BINARY,
#endif
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 */
#ifdef TIP_114_FORMATS
int explicitOctal = 0;
#endif
/*
* Initialize string to start of the object's string rep if
* the caller didn't pass anything else.
*/
if ( string == NULL ) {
string = Tcl_GetStringFromObj( objPtr, NULL );
}
p = string;
len = length;
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 (isspace(UCHAR(c))) {
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_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, 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'.
*/
acceptState = state;
acceptPoint = p;
acceptLen = len;
if (c == 'x' || c == 'X') {
state = ZERO_X;
break;
}
if (flags & TCL_PARSE_HEXADECIMAL_ONLY) {
goto zerox;
}
#ifdef TIP_114_FORMATS
if (flags & TCL_PARSE_SCAN_PREFIXES) {
goto zeroo;
}
if (c == 'b' || c == 'B') {
state = ZERO_B;
break;
}
if (c == 'o' || c == 'O') {
explicitOctal = 1;
state = ZERO_O;
break;
}
#ifdef KILL_OCTAL
goto decimal;
#endif
#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;
#ifdef TIP_114_FORMATS
/* FALLTHROUGH */
case ZERO_O:
#endif
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)
&& ((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:
#ifdef TIP_114_FORMATS
if (explicitOctal) {
/* No forgiveness for bad digits in explicitly octal numbers */
goto endgame;
}
#endif
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
&& (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;
#ifdef TIP_114_FORMATS
case BINARY:
acceptState = state;
acceptPoint = p;
acceptLen = len;
case ZERO_B:
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
&& (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;
#endif
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 ( isspace(UCHAR(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';
}
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:
/* Back up to the last accepting state in the lexer */
if (acceptState == INITIAL) {
status = TCL_ERROR;
}
p = acceptPoint;
len = acceptLen;
/* Skip past trailing whitespace */
if (endPtrPtr != NULL) {
*endPtrPtr = p;
}
while (len > 0 && isspace(UCHAR(*p))) {
++p;
--len;
}
/* Determine whether a partial string is acceptable. */
if (endPtrPtr == NULL && len != 0 && *p != '\0') {
status = TCL_ERROR;
}
/* Generate and store the appropriate internal rep */
if (status == TCL_OK && objPtr != NULL) {
if ( acceptState != INITIAL ) {
TclFreeIntRep( objPtr );
}
switch (acceptState) {
case INITIAL:
status = TCL_ERROR;
break;
case SIGNUM:
case BAD_OCTAL:
case ZERO_X:
#ifdef TIP_114_FORMATS
case ZERO_O:
case ZERO_B:
#endif
case LEADING_RADIX_POINT:
case EXPONENT_START:
case EXPONENT_SIGNUM:
case sI:
case sIN:
case sINFI:
case sINFIN:
case sINFINI:
case sINFINIT:
case sN:
case sNA:
case sNANPAREN:
case sNANHEX:
panic("in TclParseNumber: bad acceptState, can't happen.");
#ifdef TIP_114_FORMATS
case BINARY:
shift = numTrailZeros;
if (!significandOverflow) {
if (significandWide !=0
&& (shift >= CHAR_BIT*sizeof(Tcl_WideUInt)
|| significandWide
> (((~(Tcl_WideUInt)0) >> 1) + signum) >> shift )) {
significandOverflow = 1;
TclBNInitBignumFromWideUInt(&significandBig,
significandWide);
}
}
if (shift) {
if ( !significandOverflow ) {
significandWide <<= shift;
} else {
mp_mul_2d( &significandBig, shift, &significandBig );
}
}
goto returnInteger;
#endif
case HEXADECIMAL:
/* Returning a hex integer. Final scaling step */
shift = 4 * numTrailZeros;
if (!significandOverflow) {
if (significandWide !=0
&& (shift >= CHAR_BIT*sizeof(Tcl_WideUInt)
|| significandWide
> (((~(Tcl_WideUInt)0) >> 1) + 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) {
if (octalSignificandWide != 0
&& (shift >= CHAR_BIT*sizeof(Tcl_WideUInt)
|| octalSignificandWide
> (((~(Tcl_WideUInt)0) >> 1) + 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 NO_WIDE_TYPE
if (octalSignificandWide
<= (((~(Tcl_WideUInt)0) >> 1) + 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) {
mp_neg(&octalSignificandBig, &octalSignificandBig);
}
TclSetBignumIntRep(objPtr, &octalSignificandBig);
}
break;
case ZERO:
case DECIMAL:
significandOverflow =
AccumulateDecimalDigit( 0, numTrailZeros-1,
&significandWide, &significandBig,
significandOverflow );
if (!significandOverflow
&& (significandWide
> (((~(Tcl_WideUInt)0) >> 1) + signum))) {
significandOverflow = 1;
TclBNInitBignumFromWideUInt(&significandBig,
significandWide);
}
returnInteger:
if (!significandOverflow) {
if (significandWide >
(Tcl_WideUInt)(((~(unsigned long)0) >> 1) + signum)) {
#ifndef NO_WIDE_TYPE
if (significandWide
<= (((~(Tcl_WideUInt)0) >> 1) + 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) {
mp_neg(&significandBig, &significandBig);
}
TclSetBignumIntRep(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 ) {
exponent = - exponent;
}
if ( !significandOverflow ) {
objPtr->internalRep.doubleValue =
MakeLowPrecisionDouble( signum,
significandWide,
numSigDigs,
( numTrailZeros
+ exponent
- numDigitsAfterDp ) );
} else {
objPtr->internalRep.doubleValue =
MakeHighPrecisionDouble( signum,
&significandBig,
numSigDigs,
( numTrailZeros
+ exponent
- numDigitsAfterDp ) );
}
break;
case sINF:
case sINFINITY:
if ( signum ) {
objPtr->internalRep.doubleValue = -HUGE_VAL;
} else {
objPtr->internalRep.doubleValue = HUGE_VAL;
}
objPtr->typePtr = &tclDoubleType;
break;
case sNAN:
case sNANFINISH:
objPtr->internalRep.doubleValue
= MakeNaN( signum, significandWide );
objPtr->typePtr = &tclDoubleType;
break;
}
}
/* Format an error message when an invalid number is encountered. */
if ( status != TCL_OK ) {
if ( interp != NULL ) {
Tcl_Obj *msg = Tcl_NewStringObj( "expected ", -1 );
Tcl_AppendToObj( msg, type, -1 );
Tcl_AppendToObj( msg, " but got \"", -1 );
TclAppendLimitedToObj( msg, string, length, 50, "" );
Tcl_AppendToObj( msg, "\"", -1 );
if ( state == BAD_OCTAL ) {
Tcl_AppendToObj( msg, " (looks like invalid octal number)",
-1 );
}
Tcl_SetObjResult( interp, msg );
}
}
/* 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;
/* Check if the number still fits in a wide */
if (!bignumFlag) {
if (*wideRepPtr != 0) {
if ((numZeros >= maxpow10_wide)
|| (*wideRepPtr > (((~(Tcl_WideUInt)0) - digit)
/ pow10_wide[numZeros+1]))) {
/* Oops, it's overflowed, have to allocate a bignum */
TclBNInitBignumFromWideUInt (bignumRepPtr, *wideRepPtr);
bignumFlag = 1;
}
}
}
/* Multiply the number by 10**numZeros+1 and add in the new digit. */
if (!bignumFlag) {
/* Wide multiplication */
*wideRepPtr = *wideRepPtr * pow10_wide[numZeros+1] + digit;
} else 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 DIGIT_BIT is at least 27.
* The first multiplication, by up to 10**7, is done with a
* one-DIGIT multiply (this presumes that DIGIT_BIT >= 24).
*/
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);
}
return bignumFlag;
}
/*
*----------------------------------------------------------------------
*
* 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 */
int 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.
*/
#if defined(__GNUC__) && defined(__i386)
fpu_control_t roundTo53Bits = 0x027f;
fpu_control_t oldRoundingMode;
_FPU_GETCW( oldRoundingMode );
_FPU_SETCW( roundTo53Bits );
#endif
/* Test for the easy cases */
if ( numSigDigs <= DBL_DIG ) {
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 * pow10[ exponent ];
goto returnValue;
} else {
int diff = DBL_DIG - 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 * pow10[diff];
retval = factor * pow10[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 / pow10[-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 );
/* Come here to return the computed value */
returnValue:
if ( signum ) {
retval = -retval;
}
/* On gcc on x86, restore the floating point mode word. */
#if defined(__GNUC__) && defined(__i386)
_FPU_SETCW( oldRoundingMode );
#endif
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 */
int 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.
*/
#if defined(__GNUC__) && defined(__i386)
fpu_control_t roundTo53Bits = 0x027f;
fpu_control_t oldRoundingMode;
_FPU_GETCW( oldRoundingMode );
_FPU_SETCW( roundTo53Bits );
#endif
/* Quick checks for over/underflow */
if ( numSigDigs + exponent - 1 > maxDigits ) {
retval = HUGE_VAL;
goto returnValue;
}
if ( numSigDigs + exponent - 1 < minDigits ) {
retval = 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 ( 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. */
#if defined(__GNUC__) && defined(__i386)
_FPU_SETCW( oldRoundingMode );
#endif
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;
}
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 i;
/*
* The first approximation is always low. If we find that
* it's HUGE_VAL, we're done.
*/
if ( approxResult == HUGE_VAL ) {
return approxResult;
}
/*
* Find a common denominator for the decimal and binary fractions.
* The common denominator will be 2**M2 + 5**M5.
*/
significand = frexp( approxResult, &binExponent );
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;
}
}
/*
* The floating point number is significand*2**binExponent.
* Compute the large integer significand*2**(binExponent+M2+1)
* The 2**-1 bit of the significand (the most significant)
* corresponds to the 2**(binExponent+M2 + 1) bit of 2*M2*v.
* Allocate enough digits to hold that quantity, then
* convert the significand to a large integer, scaled
* appropriately. Then multiply by the appropriate power of 5.
*/
msb = binExponent + M2; /* 1008 */
nDigits = msb / DIGIT_BIT + 1;
mp_init_size( &twoMv, nDigits );
i = ( msb % 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, DIGIT_BIT );
}
for ( i = 0; i <= 8; ++i ) {
if ( M5 & ( 1 << i ) ) {
mp_mul( &twoMv, pow5+i, &twoMv );
}
}
/*
* Collect the decimal significand as a high precision integer.
* The least significant bit corresponds to bit M2+exponent+1
* so it will need to be shifted left by that many bits after
* being multiplied by 5**(M5+exponent).
*/
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 );
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
*/
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 );
}
/*
* If the result is less than unity, the error is less than 1/2 unit
* in the last place, so there's no correction to make.
*/
if ( mp_cmp_mag( &twoMd, &twoMv ) == MP_LT ) {
return approxResult;
}
/*
* 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;
}
/*
*----------------------------------------------------------------------
*
* TclDoubleDigits --
*
* Converts a double to a string of digits.
*
* Results:
* Returns the position of the character in the string after which the
* decimal point should appear. Since the string contains only
* significant digits, the position may be less than zero or greater than
* the length of the string.
*
* Side effects:
* Stores the digits in the given buffer and sets 'signum' according to
* the sign of the number.
*
*----------------------------------------------------------------------
*/
int
TclDoubleDigits( char * string, /* Buffer in which to store the result,
* must have at least 18 chars */
double v, /* Number to convert. Must be
* finite, and not NaN */
int *signum ) /* Output: 1 if the number is negative.
* Should handle -0 correctly on the
* IEEE architecture. */
{
int e; /* Power of FLT_RADIX that satisfies
* v = f * FLT_RADIX**e */
int lowOK, highOK;
mp_int r; /* Scaled significand. */
mp_int s; /* Divisor such that v = r / s */
int smallestSig; /* Flag == 1 iff v's significand is
* the smallest that can be represented. */
mp_int mplus; /* Scaled epsilon: (r + 2* mplus) == v(+)
* where v(+) is the floating point successor
* of v. */
mp_int mminus; /* Scaled epsilon: (r - 2*mminus) == v(-)
* where v(-) is the floating point
* predecessor of v. */
mp_int temp;
int rfac2 = 0; /* Powers of 2 and 5 by which large */
int rfac5 = 0; /* integers should be scaled. */
int sfac2 = 0;
int sfac5 = 0;
int mplusfac2 = 0;
int mminusfac2 = 0;
char c;
int i, k, n;
/* Split the number into absolute value and signum. */
v = AbsoluteValue(v, signum);
/*
* Handle zero specially.
*/
if ( v == 0.0 ) {
*string++ = '0';
*string++ = '\0';
return 1;
}
/*
* Find a large integer r, and integer e, such that
* v = r * FLT_RADIX**e
* and r is as small as possible. Also determine whether the
* significand is the smallest possible.
*/
smallestSig = GetIntegerTimesPower(v, &r, &e);
lowOK = highOK = (mp_iseven(&r));
/*
* We are going to want to develop integers r, s, mplus, and mminus such
* that v = r / s, v(+)-v / 2 = mplus / s; v-v(-) / 2 = mminus / s and
* then scale either s or r, mplus, mminus by an appropriate power of ten.
*
* We actually do this by keeping track of the powers of 2 and 5 by which
* f is multiplied to yield v and by which 1 is multiplied to yield s,
* mplus, and mminus.
*/
if (e >= 0) {
int bits = e * log2FLT_RADIX;
if (!smallestSig) {
/*
* Normal case, m+ and m- are both FLT_RADIX**e
*/
rfac2 = bits + 1;
sfac2 = 1;
mplusfac2 = bits;
mminusfac2 = bits;
} else {
/*
* If f is equal to the smallest significand, then we need another
* factor of FLT_RADIX in s to cope with stepping to the next
* smaller exponent when going to e's predecessor.
*/
rfac2 = bits + log2FLT_RADIX + 1;
sfac2 = 1 + log2FLT_RADIX;
mplusfac2 = bits + log2FLT_RADIX;
mminusfac2 = bits;
}
} else {
/*
* v has digits after the binary point
*/
if (e <= DBL_MIN_EXP-DBL_MANT_DIG || !smallestSig) {
/*
* Either f isn't the smallest significand or e is the smallest
* exponent. mplus and mminus will both be 1.
*/
rfac2 = 1;
sfac2 = 1 - e * log2FLT_RADIX;
mplusfac2 = 0;
mminusfac2 = 0;
} else {
/*
* f is the smallest significand, but e is not the smallest
* exponent. We need to scale by FLT_RADIX again to cope with the
* fact that v's predecessor has a smaller exponent.
*/
rfac2 = 1 + log2FLT_RADIX;
sfac2 = 1 + log2FLT_RADIX * (1 - e);
mplusfac2 = FLT_RADIX;
mminusfac2 = 0;
}
}
/*
* Estimate the highest power of ten that will be needed to hold the
* result.
*/
k = (int) ceil(log(v) / log(10.));
if (k >= 0) {
sfac2 += k;
sfac5 = k;
} else {
rfac2 -= k;
mplusfac2 -= k;
mminusfac2 -= k;
rfac5 = -k;
}
/*
* Scale r, s, mplus, mminus by the appropriate powers of 2 and 5.
*/
mp_init_set(&mplus, 1);
for (i=0 ; i<=8 ; ++i) {
if (rfac5 & (1 << i)) {
mp_mul(&mplus, pow5+i, &mplus);
}
}
mp_mul(&r, &mplus, &r);
mp_mul_2d(&r, rfac2, &r);
mp_init_copy(&mminus, &mplus);
mp_mul_2d(&mplus, mplusfac2, &mplus);
mp_mul_2d(&mminus, mminusfac2, &mminus);
mp_init_set(&s, 1);
for (i=0 ; i<=8 ; ++i) {
if (sfac5 & (1 << i)) {
mp_mul(&s, pow5+i, &s);
}
}
mp_mul_2d(&s, sfac2, &s);
/*
* It is possible for k to be off by one because we used an inexact
* logarithm.
*/
mp_init(&temp);
mp_add(&r, &mplus, &temp);
i = mp_cmp_mag(&temp, &s);
if (i>0 || (highOK && i==0)) {
mp_mul_d(&s, 10, &s);
++k;
} else {
mp_mul_d(&temp, 10, &temp);
i = mp_cmp_mag(&temp, &s);
if (i<0 || (highOK && i==0)) {
mp_mul_d(&r, 10, &r);
mp_mul_d(&mplus, 10, &mplus);
mp_mul_d(&mminus, 10, &mminus);
--k;
}
}
/*
* At this point, k contains the power of ten by which we're scaling the
* result. r/s is at least 1/10 and strictly less than ten, and v = r/s *
* 10**k. mplus and mminus give the rounding limits.
*/
for (;;) {
int tc1, tc2;
mp_mul_d(&r, 10, &r);
mp_div(&r, &s, &temp, &r); /* temp = 10r / s; r = 10r mod s */
i = temp.dp[0];
mp_mul_d(&mplus, 10, &mplus);
mp_mul_d(&mminus, 10, &mminus);
tc1 = mp_cmp_mag(&r, &mminus);
if (lowOK) {
tc1 = (tc1 <= 0);
} else {
tc1 = (tc1 < 0);
}
mp_add(&r, &mplus, &temp);
tc2 = mp_cmp_mag(&temp, &s);
if (highOK) {
tc2 = (tc2 >= 0);
} else {
tc2= (tc2 > 0);
}
if ( ! tc1 ) {
if ( !tc2 ) {
*string++ = '0' + i;
} else {
c = (char) (i + '1');
break;
}
} else {
if (!tc2) {
c = (char) (i + '0');
} else {
mp_mul_2d(&r, 1, &r);
n = mp_cmp_mag(&r, &s);
if (n < 0) {
c = (char) (i + '0');
} else {
c = (char) (i + '1');
}
}
break;
}
};
*string++ = c;
*string++ = '\0';
/*
* Free memory, and return.
*/
mp_clear_multi(&r, &s, &mplus, &mminus, &temp, NULL);
return k;
}
/*
*----------------------------------------------------------------------
*
* AbsoluteValue --
*
* Splits a 'double' into its absolute value and sign.
*
* Results:
* Returns the absolute value.
*
* Side effects:
* Stores the signum in '*signum'.
*
*----------------------------------------------------------------------
*/
static double
AbsoluteValue (double v, /* Number to split */
int* signum) /* (Output) Sign of the number 1=-, 0=+ */
{
/*
* Take the absolute value of the number, and report the number's sign.
* Take special steps to preserve signed zeroes in IEEE floating point.
* (We can't use fpclassify, because that's a C9x feature and we still
* have to build on C89 compilers.)
*/
#ifndef IEEE_FLOATING_POINT
if (v >= 0.0) {
*signum = 0;
} else {
*signum = 1;
v = -v;
}
#else
union {
Tcl_WideUInt iv;
double dv;
} bitwhack;
bitwhack.dv = v;
if (bitwhack.iv & ((Tcl_WideUInt) 1 << 63)) {
*signum = 1;
bitwhack.iv &= ~((Tcl_WideUInt) 1 << 63);
v = bitwhack.dv;
} else {
*signum = 0;
}
#endif
return v;
}
/*
*----------------------------------------------------------------------
*
* GetIntegerTimesPower --
*
* Converts a floating point number to an exact integer times a
* power of the floating point radix.
*
* Results:
* Returns 1 if it converted the smallest significand, 0 otherwise.
*
* Side effects:
* Initializes the integer value (does not just assign it),
* and stores the exponent.
*
*----------------------------------------------------------------------
*/
static int
GetIntegerTimesPower(double v, /* Value to convert */
mp_int* rPtr,
/* (Output) Integer value */
int* ePtr) /* (Output) Power of FLT_RADIX by which
* r must be multiplied to yield v*/
{
double a;
double f;
int e;
int i;
int n;
/*
* Develop f and e such that v = f * FLT_RADIX**e, with
* 1.0/FLT_RADIX <= f < 1.
*/
f = frexp(v, &e);
#if FLT_RADIX > 2
n = e % log2FLT_RADIX;
if (n > 0) {
n -= log2FLT_RADIX;
e += 1;
f *= ldexp(1.0, n);
}
e = (e - n) / log2FLT_RADIX;
#endif
if (f == 1.0) {
f = 1.0 / FLT_RADIX;
e += 1;
}
/*
* If the original number was denormalized, adjust e and f to be denormal
* as well.
*/
if (e < DBL_MIN_EXP) {
n = mantBits + (e - DBL_MIN_EXP)*log2FLT_RADIX;
f = ldexp(f, (e - DBL_MIN_EXP)*log2FLT_RADIX);
e = DBL_MIN_EXP;
n = (n + DIGIT_BIT - 1) / DIGIT_BIT;
} else {
n = mantDIGIT;
}
/*
* Now extract the base-2**DIGIT_BIT digits of f into a multi-precision
* integer r. Preserve the invariant v = r * 2**rfac2 * FLT_RADIX**e by
* adjusting e.
*/
a = f;
n = mantDIGIT;
mp_init_size(rPtr, n);
rPtr->used = n;
rPtr->sign = MP_ZPOS;
i = (mantBits % DIGIT_BIT);
if (i == 0) {
i = DIGIT_BIT;
}
while (n > 0) {
a *= ldexp(1.0, i);
i = DIGIT_BIT;
rPtr->dp[--n] = (mp_digit) a;
a -= (mp_digit) a;
}
*ePtr = e - DBL_MANT_DIG;
return (f == 1.0 / FLT_RADIX);
}
/*
*----------------------------------------------------------------------
*
* 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;
/*
* 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*) Tcl_Alloc ((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) {
pow10[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 );
}
/*
* 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.
*/
tiny = SafeLdExp( 1.0, DBL_MIN_EXP * log2FLT_RADIX - mantBits );
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. ) );
mantDIGIT = ( mantBits + DIGIT_BIT - 1 ) / DIGIT_BIT;
log10_DIGIT_MAX = (int) floor (DIGIT_BIT * log(2.) / log (10.));
}
/*
*----------------------------------------------------------------------
*
* TclFinalizeDoubleConversion --
*
* Cleans up this file on exit.
*
* Results:
* None
*
* Side effects:
* Memory allocated by TclInitDoubleConversion is freed.
*
*----------------------------------------------------------------------
*/
void
TclFinalizeDoubleConversion()
{
int i;
Tcl_Free ((char*)pow10_wide);
for ( i = 0; i < 9; ++i ) {
mp_clear( pow5 + i );
}
}
/*
*----------------------------------------------------------------------
*
* TclInitBignumFromDouble --
*
* 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
TclInitBignumFromDouble(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) {
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(mp_int *a) /* Integer to convert. */
{
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);
if (bits > DBL_MAX_EXP*log2FLT_RADIX) {
errno = ERANGE;
if (a->sign == MP_ZPOS) {
return HUGE_VAL;
} else {
return -HUGE_VAL;
}
}
shift = mantBits + 1 - 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);
}
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, 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 (a->sign == MP_ZPOS) {
return r;
} else {
return -r;
}
}
double
TclCeil(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, DIGIT_BIT) + b.dp[i];
}
r = ldexp(r, bits - mantBits);
}
}
mp_clear(&b);
return r;
}
double
TclFloor(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, 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( 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, DIGIT_BIT ) + b.dp[i];
}
mp_clear( &b );
/* Return the result with the appropriate sign. */
*machexp = bits - mantBits + 2;
if ( a->sign == MP_ZPOS ) {
return r;
} else {
return -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 * pow10[ 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 / pow10[ (-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 (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 */
}