The Tor Browser / file revision

 /****************************************************************

  *

  * The author of this software is David M. Gay.

  *

  * Copyright (c) 1991, 2000, 2001 by Lucent Technologies.

  *

  * Permission to use, copy, modify, and distribute this software for any

  * purpose without fee is hereby granted, provided that this entire notice

  * is included in all copies of any software which is or includes a copy

  * or modification of this software and in all copies of the supporting

  * documentation for such software.

  *

  * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED

  * WARRANTY.  IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY

  * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY

  * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.

  *

  ***************************************************************/

 /* Please send bug reports to David M. Gay (dmg at acm dot org,

  * with " at " changed at "@" and " dot " changed to ".").	*/

 /* On a machine with IEEE extended-precision registers, it is

  * necessary to specify double-precision (53-bit) rounding precision

  * before invoking strtod or dtoa.  If the machine uses (the equivalent

  * of) Intel 80x87 arithmetic, the call

  *	_control87(PC_53, MCW_PC);

  * does this with many compilers.  Whether this or another call is

  * appropriate depends on the compiler; for this to work, it may be

  * necessary to #include "float.h" or another system-dependent header

  * file.

  */

 /* strtod for IEEE-, VAX-, and IBM-arithmetic machines.

  *

  * This strtod returns a nearest machine number to the input decimal

  * string (or sets errno to ERANGE).  With IEEE arithmetic, ties are

  * broken by the IEEE round-even rule.  Otherwise ties are broken by

  * biased rounding (add half and chop).

  *

  * Inspired loosely by William D. Clinger's paper "How to Read Floating

  * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].

  *

  * Modifications:

  *

  *	1. We only require IEEE, IBM, or VAX double-precision

  *		arithmetic (not IEEE double-extended).

  *	2. We get by with floating-point arithmetic in a case that

  *		Clinger missed -- when we're computing d * 10^n

  *		for a small integer d and the integer n is not too

  *		much larger than 22 (the maximum integer k for which

  *		we can represent 10^k exactly), we may be able to

  *		compute (d*10^k) * 10^(e-k) with just one roundoff.

  *	3. Rather than a bit-at-a-time adjustment of the binary

  *		result in the hard case, we use floating-point

  *		arithmetic to determine the adjustment to within

  *		one bit; only in really hard cases do we need to

  *		compute a second residual.

  *	4. Because of 3., we don't need a large table of powers of 10

  *		for ten-to-e (just some small tables, e.g. of 10^k

  *		for 0 <= k <= 22).

  */

 /*

  * #define IEEE_8087 for IEEE-arithmetic machines where the least

  *	significant byte has the lowest address.

  * #define IEEE_MC68k for IEEE-arithmetic machines where the most

  *	significant byte has the lowest address.

  * #define Long int on machines with 32-bit ints and 64-bit longs.

  * #define IBM for IBM mainframe-style floating-point arithmetic.

  * #define VAX for VAX-style floating-point arithmetic (D_floating).

  * #define No_leftright to omit left-right logic in fast floating-point

  *	computation of dtoa.  This will cause dtoa modes 4 and 5 to be

  *	treated the same as modes 2 and 3 for some inputs.

  * #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3

  *	and strtod and dtoa should round accordingly.  Unless Trust_FLT_ROUNDS

  *	is also #defined, fegetround() will be queried for the rounding mode.

  *	Note that both FLT_ROUNDS and fegetround() are specified by the C99

  *	standard (and are specified to be consistent, with fesetround()

  *	affecting the value of FLT_ROUNDS), but that some (Linux) systems

  *	do not work correctly in this regard, so using fegetround() is more

  *	portable than using FLT_ROUNDS directly.

  * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3

  *	and Honor_FLT_ROUNDS is not #defined.

  * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines

  *	that use extended-precision instructions to compute rounded

  *	products and quotients) with IBM.

  * #define ROUND_BIASED for IEEE-format with biased rounding and arithmetic

  *	that rounds toward +Infinity.

  * #define ROUND_BIASED_without_Round_Up for IEEE-format with biased

  *	rounding when the underlying floating-point arithmetic uses

  *	unbiased rounding.  This prevent using ordinary floating-point

  *	arithmetic when the result could be computed with one rounding error.

  * #define Inaccurate_Divide for IEEE-format with correctly rounded

  *	products but inaccurate quotients, e.g., for Intel i860.

  * #define NO_LONG_LONG on machines that do not have a "long long"

  *	integer type (of >= 64 bits).  On such machines, you can

  *	#define Just_16 to store 16 bits per 32-bit Long when doing

  *	high-precision integer arithmetic.  Whether this speeds things

  *	up or slows things down depends on the machine and the number

  *	being converted.  If long long is available and the name is

  *	something other than "long long", #define Llong to be the name,

  *	and if "unsigned Llong" does not work as an unsigned version of

  *	Llong, #define #ULLong to be the corresponding unsigned type.

  * #define KR_headers for old-style C function headers.

  * #define Bad_float_h if your system lacks a float.h or if it does not

  *	define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,

  *	FLT_RADIX, FLT_ROUNDS, and DBL_MAX.

  * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)

  *	if memory is available and otherwise does something you deem

  *	appropriate.  If MALLOC is undefined, malloc will be invoked

  *	directly -- and assumed always to succeed.  Similarly, if you

  *	want something other than the system's free() to be called to

  *	recycle memory acquired from MALLOC, #define FREE to be the

  *	name of the alternate routine.  (FREE or free is only called in

  *	pathological cases, e.g., in a dtoa call after a dtoa return in

  *	mode 3 with thousands of digits requested.)

  * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making

  *	memory allocations from a private pool of memory when possible.

  *	When used, the private pool is PRIVATE_MEM bytes long:  2304 bytes,

  *	unless #defined to be a different length.  This default length

  *	suffices to get rid of MALLOC calls except for unusual cases,

  *	such as decimal-to-binary conversion of a very long string of

  *	digits.  The longest string dtoa can return is about 751 bytes

  *	long.  For conversions by strtod of strings of 800 digits and

  *	all dtoa conversions in single-threaded executions with 8-byte

  *	pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte

  *	pointers, PRIVATE_MEM >= 7112 appears adequate.

  * #define NO_INFNAN_CHECK if you do not wish to have INFNAN_CHECK

  *	#defined automatically on IEEE systems.  On such systems,

  *	when INFNAN_CHECK is #defined, strtod checks

  *	for Infinity and NaN (case insensitively).  On some systems

  *	(e.g., some HP systems), it may be necessary to #define NAN_WORD0

  *	appropriately -- to the most significant word of a quiet NaN.

  *	(On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)

  *	When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined,

  *	strtod also accepts (case insensitively) strings of the form

  *	NaN(x), where x is a string of hexadecimal digits and spaces;

  *	if there is only one string of hexadecimal digits, it is taken

  *	for the 52 fraction bits of the resulting NaN; if there are two

  *	or more strings of hex digits, the first is for the high 20 bits,

  *	the second and subsequent for the low 32 bits, with intervening

  *	white space ignored; but if this results in none of the 52

  *	fraction bits being on (an IEEE Infinity symbol), then NAN_WORD0

  *	and NAN_WORD1 are used instead.

  * #define MULTIPLE_THREADS if the system offers preemptively scheduled

  *	multiple threads.  In this case, you must provide (or suitably

  *	#define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed

  *	by FREE_DTOA_LOCK(n) for n = 0 or 1.  (The second lock, accessed

  *	in pow5mult, ensures lazy evaluation of only one copy of high

  *	powers of 5; omitting this lock would introduce a small

  *	probability of wasting memory, but would otherwise be harmless.)

  *	You must also invoke freedtoa(s) to free the value s returned by

  *	dtoa.  You may do so whether or not MULTIPLE_THREADS is #defined.

  * #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that

  *	avoids underflows on inputs whose result does not underflow.

  *	If you #define NO_IEEE_Scale on a machine that uses IEEE-format

  *	floating-point numbers and flushes underflows to zero rather

  *	than implementing gradual underflow, then you must also #define

  *	Sudden_Underflow.

  * #define USE_LOCALE to use the current locale's decimal_point value.

  * #define SET_INEXACT if IEEE arithmetic is being used and extra

  *	computation should be done to set the inexact flag when the

  *	result is inexact and avoid setting inexact when the result

  *	is exact.  In this case, dtoa.c must be compiled in

  *	an environment, perhaps provided by #include "dtoa.c" in a

  *	suitable wrapper, that defines two functions,

  *		int get_inexact(void);

  *		void clear_inexact(void);

  *	such that get_inexact() returns a nonzero value if the

  *	inexact bit is already set, and clear_inexact() sets the

  *	inexact bit to 0.  When SET_INEXACT is #defined, strtod

  *	also does extra computations to set the underflow and overflow

  *	flags when appropriate (i.e., when the result is tiny and

  *	inexact or when it is a numeric value rounded to +-infinity).

  * #define NO_ERRNO if strtod should not assign errno = ERANGE when

  *	the result overflows to +-Infinity or underflows to 0.

  * #define NO_HEX_FP to omit recognition of hexadecimal floating-point

  *	values by strtod.

  * #define NO_STRTOD_BIGCOMP (on IEEE-arithmetic systems only for now)

  *	to disable logic for "fast" testing of very long input strings

  *	to strtod.  This testing proceeds by initially truncating the

  *	input string, then if necessary comparing the whole string with

  *	a decimal expansion to decide close cases. This logic is only

  *	used for input more than STRTOD_DIGLIM digits long (default 40).

  */

 #ifndef Long

 #define Long long

 #endif

 #ifndef ULong

 typedef unsigned Long ULong;

 #endif

 #ifdef DEBUG

 #include "stdio.h"

 #define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}

 #endif

 #include "stdlib.h"

 #include "string.h"

 #ifdef USE_LOCALE

 #include "locale.h"

 #endif

 #ifdef Honor_FLT_ROUNDS

 #ifndef Trust_FLT_ROUNDS

 #include <fenv.h>

 #endif

 #endif

 #ifdef MALLOC

 #ifdef KR_headers

 extern char *MALLOC();

 #else

 extern void *MALLOC(size_t);

 #endif

 #else

 #define MALLOC malloc

 #endif

 #ifndef Omit_Private_Memory

 #ifndef PRIVATE_MEM

 #define PRIVATE_MEM 2304

 #endif

 #define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))

 static double private_mem[PRIVATE_mem], *pmem_next = private_mem;

 #endif

 #undef IEEE_Arith

 #undef Avoid_Underflow

 #ifdef IEEE_MC68k

 #define IEEE_Arith

 #endif

 #ifdef IEEE_8087

 #define IEEE_Arith

 #endif

 #ifdef IEEE_Arith

 #ifndef NO_INFNAN_CHECK

 #undef INFNAN_CHECK

 #define INFNAN_CHECK

 #endif

 #else

 #undef INFNAN_CHECK

 #define NO_STRTOD_BIGCOMP

 #endif

 #include "errno.h"

 #ifdef Bad_float_h

 #ifdef IEEE_Arith

 #define DBL_DIG 15

 #define DBL_MAX_10_EXP 308

 #define DBL_MAX_EXP 1024

 #define FLT_RADIX 2

 #endif /*IEEE_Arith*/

 #ifdef IBM

 #define DBL_DIG 16

 #define DBL_MAX_10_EXP 75

 #define DBL_MAX_EXP 63

 #define FLT_RADIX 16

 #define DBL_MAX 7.2370055773322621e+75

 #endif

 #ifdef VAX

 #define DBL_DIG 16

 #define DBL_MAX_10_EXP 38

 #define DBL_MAX_EXP 127

 #define FLT_RADIX 2

 #define DBL_MAX 1.7014118346046923e+38

 #endif

 #ifndef LONG_MAX

 #define LONG_MAX 2147483647

 #endif

 #else /* ifndef Bad_float_h */

 #include "float.h"

 #endif /* Bad_float_h */

 #ifndef __MATH_H__

 #include "math.h"

 #endif

 #ifdef __cplusplus

 extern "C" {

 #endif

 #ifndef CONST

 #ifdef KR_headers

 #define CONST /* blank */

 #else

 #define CONST const

 #endif

 #endif

 #if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1

 Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined.

 #endif

 typedef union { double d; ULong L[2]; } U;

 #ifdef IEEE_8087

 #define word0(x) (x)->L[1]

 #define word1(x) (x)->L[0]

 #else

 #define word0(x) (x)->L[0]

 #define word1(x) (x)->L[1]

 #endif

 #define dval(x) (x)->d

 #ifndef STRTOD_DIGLIM

 #define STRTOD_DIGLIM 40

 #endif

 #ifdef DIGLIM_DEBUG

 extern int strtod_diglim;

 #else

 #define strtod_diglim STRTOD_DIGLIM

 #endif

 /* The following definition of Storeinc is appropriate for MIPS processors.

  * An alternative that might be better on some machines is

  * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)

  */

 #if defined(IEEE_8087) + defined(VAX)

 #define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \

 ((unsigned short *)a)[0] = (unsigned short)c, a++)

 #else

 #define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \

 ((unsigned short *)a)[1] = (unsigned short)c, a++)

 #endif

 /* #define P DBL_MANT_DIG */

 /* Ten_pmax = floor(P*log(2)/log(5)) */

 /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */

 /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */

 /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */

 #ifdef IEEE_Arith

 #define Exp_shift  20

 #define Exp_shift1 20

 #define Exp_msk1    0x100000

 #define Exp_msk11   0x100000

 #define Exp_mask  0x7ff00000

 #define P 53

 #define Nbits 53

 #define Bias 1023

 #define Emax 1023

 #define Emin (-1022)

 #define Exp_1  0x3ff00000

 #define Exp_11 0x3ff00000

 #define Ebits 11

 #define Frac_mask  0xfffff

 #define Frac_mask1 0xfffff

 #define Ten_pmax 22

 #define Bletch 0x10

 #define Bndry_mask  0xfffff

 #define Bndry_mask1 0xfffff

 #define LSB 1

 #define Sign_bit 0x80000000

 #define Log2P 1

 #define Tiny0 0

 #define Tiny1 1

 #define Quick_max 14

 #define Int_max 14

 #ifndef NO_IEEE_Scale

 #define Avoid_Underflow

 #ifdef Flush_Denorm	/* debugging option */

 #undef Sudden_Underflow

 #endif

 #endif

 #ifndef Flt_Rounds

 #ifdef FLT_ROUNDS

 #define Flt_Rounds FLT_ROUNDS

 #else

 #define Flt_Rounds 1

 #endif

 #endif /*Flt_Rounds*/

 #ifdef Honor_FLT_ROUNDS

 #undef Check_FLT_ROUNDS

 #define Check_FLT_ROUNDS

 #else

 #define Rounding Flt_Rounds

 #endif

 #else /* ifndef IEEE_Arith */

 #undef Check_FLT_ROUNDS

 #undef Honor_FLT_ROUNDS

 #undef SET_INEXACT

 #undef  Sudden_Underflow

 #define Sudden_Underflow

 #ifdef IBM

 #undef Flt_Rounds

 #define Flt_Rounds 0

 #define Exp_shift  24

 #define Exp_shift1 24

 #define Exp_msk1   0x1000000

 #define Exp_msk11  0x1000000

 #define Exp_mask  0x7f000000

 #define P 14

 #define Nbits 56

 #define Bias 65

 #define Emax 248

 #define Emin (-260)

 #define Exp_1  0x41000000

 #define Exp_11 0x41000000

 #define Ebits 8	/* exponent has 7 bits, but 8 is the right value in b2d */

 #define Frac_mask  0xffffff

 #define Frac_mask1 0xffffff

 #define Bletch 4

 #define Ten_pmax 22

 #define Bndry_mask  0xefffff

 #define Bndry_mask1 0xffffff

 #define LSB 1

 #define Sign_bit 0x80000000

 #define Log2P 4

 #define Tiny0 0x100000

 #define Tiny1 0

 #define Quick_max 14

 #define Int_max 15

 #else /* VAX */

 #undef Flt_Rounds

 #define Flt_Rounds 1

 #define Exp_shift  23

 #define Exp_shift1 7

 #define Exp_msk1    0x80

 #define Exp_msk11   0x800000

 #define Exp_mask  0x7f80

 #define P 56

 #define Nbits 56

 #define Bias 129

 #define Emax 126

 #define Emin (-129)

 #define Exp_1  0x40800000

 #define Exp_11 0x4080

 #define Ebits 8

 #define Frac_mask  0x7fffff

 #define Frac_mask1 0xffff007f

 #define Ten_pmax 24

 #define Bletch 2

 #define Bndry_mask  0xffff007f

 #define Bndry_mask1 0xffff007f

 #define LSB 0x10000

 #define Sign_bit 0x8000

 #define Log2P 1

 #define Tiny0 0x80

 #define Tiny1 0

 #define Quick_max 15

 #define Int_max 15

 #endif /* IBM, VAX */

 #endif /* IEEE_Arith */

 #ifndef IEEE_Arith

 #define ROUND_BIASED

 #else

 #ifdef ROUND_BIASED_without_Round_Up

 #undef  ROUND_BIASED

 #define ROUND_BIASED

 #endif

 #endif

 #ifdef RND_PRODQUOT

 #define rounded_product(a,b) a = rnd_prod(a, b)

 #define rounded_quotient(a,b) a = rnd_quot(a, b)

 #ifdef KR_headers

 extern double rnd_prod(), rnd_quot();

 #else

 extern double rnd_prod(double, double), rnd_quot(double, double);

 #endif

 #else

 #define rounded_product(a,b) a *= b

 #define rounded_quotient(a,b) a /= b

 #endif

 #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))

 #define Big1 0xffffffff

 #ifndef Pack_32

 #define Pack_32

 #endif

 typedef struct BCinfo BCinfo;

  struct

 BCinfo { int dp0, dp1, dplen, dsign, e0, inexact, nd, nd0, rounding, scale, uflchk; };

 #ifdef KR_headers

 #define FFFFFFFF ((((unsigned long)0xffff)<<16)|(unsigned long)0xffff)

 #else

 #define FFFFFFFF 0xffffffffUL

 #endif

 #ifdef NO_LONG_LONG

 #undef ULLong

 #ifdef Just_16

 #undef Pack_32

 /* When Pack_32 is not defined, we store 16 bits per 32-bit Long.

  * This makes some inner loops simpler and sometimes saves work

  * during multiplications, but it often seems to make things slightly

  * slower.  Hence the default is now to store 32 bits per Long.

  */

 #endif

 #else	/* long long available */

 #ifndef Llong

 #define Llong long long

 #endif

 #ifndef ULLong

 #define ULLong unsigned Llong

 #endif

 #endif /* NO_LONG_LONG */

 #ifndef MULTIPLE_THREADS

 #define ACQUIRE_DTOA_LOCK(n)	/*nothing*/

 #define FREE_DTOA_LOCK(n)	/*nothing*/

 #endif

 #define Kmax 7

 #ifdef __cplusplus

 extern "C" double strtod(const char *s00, char **se);

 extern "C" char *dtoa(double d, int mode, int ndigits,

 			int *decpt, int *sign, char **rve);

 #endif

  struct

 Bigint {

 	struct Bigint *next;

 	int k, maxwds, sign, wds;

 	ULong x[1];

 	};

  typedef struct Bigint Bigint;

  static Bigint *freelist[Kmax+1];

  static Bigint *

 Balloc

 #ifdef KR_headers

 	(k) int k;

 #else

 	(int k)

 #endif

 {

 	int x;

 	Bigint *rv;

 #ifndef Omit_Private_Memory

 	unsigned int len;

 #endif

 	ACQUIRE_DTOA_LOCK(0);

 	/* The k > Kmax case does not need ACQUIRE_DTOA_LOCK(0), */

 	/* but this case seems very unlikely. */

 	if (k <= Kmax && (rv = freelist[k]))

 		freelist[k] = rv->next;

 	else {

 		x = 1 << k;

 #ifdef Omit_Private_Memory

 		rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong));

 #else

 		len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)

 			/sizeof(double);

 		if (k <= Kmax && pmem_next - private_mem + len <= PRIVATE_mem) {

 			rv = (Bigint*)pmem_next;

 			pmem_next += len;

 			}

 		else

 			rv = (Bigint*)MALLOC(len*sizeof(double));

 #endif

 		rv->k = k;

 		rv->maxwds = x;

 		}

 	FREE_DTOA_LOCK(0);

 	rv->sign = rv->wds = 0;

 	return rv;

 	}

  static void

 Bfree

 #ifdef KR_headers

 	(v) Bigint *v;

 #else

 	(Bigint *v)

 #endif

 {

 	if (v) {

 		if (v->k > Kmax)

 #ifdef FREE

 			FREE((void*)v);

 #else

 			free((void*)v);

 #endif

 		else {

 			ACQUIRE_DTOA_LOCK(0);

 			v->next = freelist[v->k];

 			freelist[v->k] = v;

 			FREE_DTOA_LOCK(0);

 			}

 		}

 	}

 #define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \

 y->wds*sizeof(Long) + 2*sizeof(int))

  static Bigint *

 multadd

 #ifdef KR_headers

 	(b, m, a) Bigint *b; int m, a;

 #else

 	(Bigint *b, int m, int a)	/* multiply by m and add a */

 #endif

 {

 	int i, wds;

 #ifdef ULLong

 	ULong *x;

 	ULLong carry, y;

 #else

 	ULong carry, *x, y;

 #ifdef Pack_32

 	ULong xi, z;

 #endif

 #endif

 	Bigint *b1;

 	wds = b->wds;

 	x = b->x;

 	i = 0;

 	carry = a;

 	do {

 #ifdef ULLong

 		y = *x * (ULLong)m + carry;

 		carry = y >> 32;

 		*x++ = y & FFFFFFFF;

 #else

 #ifdef Pack_32

 		xi = *x;

 		y = (xi & 0xffff) * m + carry;

 		z = (xi >> 16) * m + (y >> 16);

 		carry = z >> 16;

 		*x++ = (z << 16) + (y & 0xffff);

 #else

 		y = *x * m + carry;

 		carry = y >> 16;

 		*x++ = y & 0xffff;

 #endif

 #endif

 		}

 		while(++i < wds);

 	if (carry) {

 		if (wds >= b->maxwds) {

 			b1 = Balloc(b->k+1);

 			Bcopy(b1, b);

 			Bfree(b);

 			b = b1;

 			}

 		b->x[wds++] = carry;

 		b->wds = wds;

 		}

 	return b;

 	}

  static Bigint *

 s2b

 #ifdef KR_headers

 	(s, nd0, nd, y9, dplen) CONST char *s; int nd0, nd, dplen; ULong y9;

 #else

 	(const char *s, int nd0, int nd, ULong y9, int dplen)

 #endif

 {

 	Bigint *b;

 	int i, k;

 	Long x, y;

 	x = (nd + 8) / 9;

 	for(k = 0, y = 1; x > y; y <<= 1, k++) ;

 #ifdef Pack_32

 	b = Balloc(k);

 	b->x[0] = y9;

 	b->wds = 1;

 #else

 	b = Balloc(k+1);

 	b->x[0] = y9 & 0xffff;

 	b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;

 #endif

 	i = 9;

 	if (9 < nd0) {

 		s += 9;

 		do b = multadd(b, 10, *s++ - '0');

 			while(++i < nd0);

 		s += dplen;

 		}

 	else

 		s += dplen + 9;

 	for(; i < nd; i++)

 		b = multadd(b, 10, *s++ - '0');

 	return b;

 	}

  static int

 hi0bits

 #ifdef KR_headers

 	(x) ULong x;

 #else

 	(ULong x)

 #endif

 {

 	int k = 0;

 	if (!(x & 0xffff0000)) {

 		k = 16;

 		x <<= 16;

 		}

 	if (!(x & 0xff000000)) {

 		k += 8;

 		x <<= 8;

 		}

 	if (!(x & 0xf0000000)) {

 		k += 4;

 		x <<= 4;

 		}

 	if (!(x & 0xc0000000)) {

 		k += 2;

 		x <<= 2;

 		}

 	if (!(x & 0x80000000)) {

 		k++;

 		if (!(x & 0x40000000))

 			return 32;

 		}

 	return k;

 	}

  static int

 lo0bits

 #ifdef KR_headers

 	(y) ULong *y;

 #else

 	(ULong *y)

 #endif

 {

 	int k;

 	ULong x = *y;

 	if (x & 7) {

 		if (x & 1)

 			return 0;

 		if (x & 2) {

 			*y = x >> 1;

 			return 1;

 			}

 		*y = x >> 2;

 		return 2;

 		}

 	k = 0;

 	if (!(x & 0xffff)) {

 		k = 16;

 		x >>= 16;

 		}

 	if (!(x & 0xff)) {

 		k += 8;

 		x >>= 8;

 		}

 	if (!(x & 0xf)) {

 		k += 4;

 		x >>= 4;

 		}

 	if (!(x & 0x3)) {

 		k += 2;

 		x >>= 2;

 		}

 	if (!(x & 1)) {

 		k++;

 		x >>= 1;

 		if (!x)

 			return 32;

 		}

 	*y = x;

 	return k;

 	}

  static Bigint *

 i2b

 #ifdef KR_headers

 	(i) int i;

 #else

 	(int i)

 #endif

 {

 	Bigint *b;

 	b = Balloc(1);

 	b->x[0] = i;

 	b->wds = 1;

 	return b;

 	}

  static Bigint *

 mult

 #ifdef KR_headers

 	(a, b) Bigint *a, *b;

 #else

 	(Bigint *a, Bigint *b)

 #endif

 {

 	Bigint *c;

 	int k, wa, wb, wc;

 	ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;

 	ULong y;

 #ifdef ULLong

 	ULLong carry, z;

 #else

 	ULong carry, z;

 #ifdef Pack_32

 	ULong z2;

 #endif

 #endif

 	if (a->wds < b->wds) {

 		c = a;

 		a = b;

 		b = c;

 		}

 	k = a->k;

 	wa = a->wds;

 	wb = b->wds;

 	wc = wa + wb;

 	if (wc > a->maxwds)

 		k++;

 	c = Balloc(k);

 	for(x = c->x, xa = x + wc; x < xa; x++)

 		*x = 0;

 	xa = a->x;

 	xae = xa + wa;

 	xb = b->x;

 	xbe = xb + wb;

 	xc0 = c->x;

 #ifdef ULLong

 	for(; xb < xbe; xc0++) {

 		if ((y = *xb++)) {

 			x = xa;

 			xc = xc0;

 			carry = 0;

 			do {

 				z = *x++ * (ULLong)y + *xc + carry;

 				carry = z >> 32;

 				*xc++ = z & FFFFFFFF;

 				}

 				while(x < xae);

 			*xc = carry;

 			}

 		}

 #else

 #ifdef Pack_32

 	for(; xb < xbe; xb++, xc0++) {

 		if (y = *xb & 0xffff) {

 			x = xa;

 			xc = xc0;

 			carry = 0;

 			do {

 				z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;

 				carry = z >> 16;

 				z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;

 				carry = z2 >> 16;

 				Storeinc(xc, z2, z);

 				}

 				while(x < xae);

 			*xc = carry;

 			}

 		if (y = *xb >> 16) {

 			x = xa;

 			xc = xc0;

 			carry = 0;

 			z2 = *xc;

 			do {

 				z = (*x & 0xffff) * y + (*xc >> 16) + carry;

 				carry = z >> 16;

 				Storeinc(xc, z, z2);

 				z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;

 				carry = z2 >> 16;

 				}

 				while(x < xae);

 			*xc = z2;

 			}

 		}

 #else

 	for(; xb < xbe; xc0++) {

 		if (y = *xb++) {

 			x = xa;

 			xc = xc0;

 			carry = 0;

 			do {

 				z = *x++ * y + *xc + carry;

 				carry = z >> 16;

 				*xc++ = z & 0xffff;

 				}

 				while(x < xae);

 			*xc = carry;

 			}

 		}

 #endif

 #endif

 	for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;

 	c->wds = wc;

 	return c;

 	}

  static Bigint *p5s;

  static Bigint *

 pow5mult

 #ifdef KR_headers

 	(b, k) Bigint *b; int k;

 #else

 	(Bigint *b, int k)

 #endif

 {

 	Bigint *b1, *p5, *p51;

 	int i;

 	static int p05[3] = { 5, 25, 125 };

 	if ((i = k & 3))

 		b = multadd(b, p05[i-1], 0);

 	if (!(k >>= 2))

 		return b;

 	if (!(p5 = p5s)) {

 		/* first time */

 #ifdef MULTIPLE_THREADS

 		ACQUIRE_DTOA_LOCK(1);

 		if (!(p5 = p5s)) {

 			p5 = p5s = i2b(625);

 			p5->next = 0;

 			}

 		FREE_DTOA_LOCK(1);

 #else

 		p5 = p5s = i2b(625);

 		p5->next = 0;

 #endif

 		}

 	for(;;) {

 		if (k & 1) {

 			b1 = mult(b, p5);

 			Bfree(b);

 			b = b1;

 			}

 		if (!(k >>= 1))

 			break;

 		if (!(p51 = p5->next)) {

 #ifdef MULTIPLE_THREADS

 			ACQUIRE_DTOA_LOCK(1);

 			if (!(p51 = p5->next)) {

 				p51 = p5->next = mult(p5,p5);

 				p51->next = 0;

 				}

 			FREE_DTOA_LOCK(1);

 #else

 			p51 = p5->next = mult(p5,p5);

 			p51->next = 0;

 #endif

 			}

 		p5 = p51;

 		}

 	return b;

 	}

  static Bigint *

 lshift

 #ifdef KR_headers

 	(b, k) Bigint *b; int k;

 #else

 	(Bigint *b, int k)

 #endif

 {

 	int i, k1, n, n1;

 	Bigint *b1;

 	ULong *x, *x1, *xe, z;

 #ifdef Pack_32

 	n = k >> 5;

 #else

 	n = k >> 4;

 #endif

 	k1 = b->k;

 	n1 = n + b->wds + 1;

 	for(i = b->maxwds; n1 > i; i <<= 1)

 		k1++;

 	b1 = Balloc(k1);

 	x1 = b1->x;

 	for(i = 0; i < n; i++)

 		*x1++ = 0;

 	x = b->x;

 	xe = x + b->wds;

 #ifdef Pack_32

 	if (k &= 0x1f) {

 		k1 = 32 - k;

 		z = 0;

 		do {

 			*x1++ = *x << k | z;

 			z = *x++ >> k1;

 			}

 			while(x < xe);

 		if ((*x1 = z))

 			++n1;

 		}

 #else

 	if (k &= 0xf) {

 		k1 = 16 - k;

 		z = 0;

 		do {

 			*x1++ = *x << k  & 0xffff | z;

 			z = *x++ >> k1;

 			}

 			while(x < xe);

 		if (*x1 = z)

 			++n1;

 		}

 #endif

 	else do

 		*x1++ = *x++;

 		while(x < xe);

 	b1->wds = n1 - 1;

 	Bfree(b);

 	return b1;

 	}

  static int

 cmp

 #ifdef KR_headers

 	(a, b) Bigint *a, *b;

 #else

 	(Bigint *a, Bigint *b)

 #endif

 {

 	ULong *xa, *xa0, *xb, *xb0;

 	int i, j;

 	i = a->wds;

 	j = b->wds;

 #ifdef DEBUG

 	if (i > 1 && !a->x[i-1])

 		Bug("cmp called with a->x[a->wds-1] == 0");

 	if (j > 1 && !b->x[j-1])

 		Bug("cmp called with b->x[b->wds-1] == 0");

 #endif

 	if (i -= j)

 		return i;

 	xa0 = a->x;

 	xa = xa0 + j;

 	xb0 = b->x;

 	xb = xb0 + j;

 	for(;;) {

 		if (*--xa != *--xb)

 			return *xa < *xb ? -1 : 1;

 		if (xa <= xa0)

 			break;

 		}

 	return 0;

 	}

  static Bigint *

 diff

 #ifdef KR_headers

 	(a, b) Bigint *a, *b;

 #else

 	(Bigint *a, Bigint *b)

 #endif

 {

 	Bigint *c;

 	int i, wa, wb;

 	ULong *xa, *xae, *xb, *xbe, *xc;

 #ifdef ULLong

 	ULLong borrow, y;

 #else

 	ULong borrow, y;

 #ifdef Pack_32

 	ULong z;

 #endif

 #endif

 	i = cmp(a,b);

 	if (!i) {

 		c = Balloc(0);

 		c->wds = 1;

 		c->x[0] = 0;

 		return c;

 		}

 	if (i < 0) {

 		c = a;

 		a = b;

 		b = c;

 		i = 1;

 		}

 	else

 		i = 0;

 	c = Balloc(a->k);

 	c->sign = i;

 	wa = a->wds;

 	xa = a->x;

 	xae = xa + wa;

 	wb = b->wds;

 	xb = b->x;

 	xbe = xb + wb;

 	xc = c->x;

 	borrow = 0;

 #ifdef ULLong

 	do {

 		y = (ULLong)*xa++ - *xb++ - borrow;

 		borrow = y >> 32 & (ULong)1;

 		*xc++ = y & FFFFFFFF;

 		}

 		while(xb < xbe);

 	while(xa < xae) {

 		y = *xa++ - borrow;

 		borrow = y >> 32 & (ULong)1;

 		*xc++ = y & FFFFFFFF;

 		}

 #else

 #ifdef Pack_32

 	do {

 		y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;

 		borrow = (y & 0x10000) >> 16;

 		z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;

 		borrow = (z & 0x10000) >> 16;

 		Storeinc(xc, z, y);

 		}

 		while(xb < xbe);

 	while(xa < xae) {

 		y = (*xa & 0xffff) - borrow;

 		borrow = (y & 0x10000) >> 16;

 		z = (*xa++ >> 16) - borrow;

 		borrow = (z & 0x10000) >> 16;

 		Storeinc(xc, z, y);

 		}

 #else

 	do {

 		y = *xa++ - *xb++ - borrow;

 		borrow = (y & 0x10000) >> 16;

 		*xc++ = y & 0xffff;

 		}

 		while(xb < xbe);

 	while(xa < xae) {

 		y = *xa++ - borrow;

 		borrow = (y & 0x10000) >> 16;

 		*xc++ = y & 0xffff;

 		}

 #endif

 #endif

 	while(!*--xc)

 		wa--;

 	c->wds = wa;

 	return c;

 	}

  static double

 ulp

 #ifdef KR_headers

 	(x) U *x;

 #else

 	(U *x)

 #endif

 {

 	Long L;

 	U u;

 	L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;

 #ifndef Avoid_Underflow

 #ifndef Sudden_Underflow

 	if (L > 0) {

 #endif

 #endif

 #ifdef IBM

 		L |= Exp_msk1 >> 4;

 #endif

 		word0(&u) = L;

 		word1(&u) = 0;

 #ifndef Avoid_Underflow

 #ifndef Sudden_Underflow

 		}

 	else {

 		L = -L >> Exp_shift;

 		if (L < Exp_shift) {

 			word0(&u) = 0x80000 >> L;

 			word1(&u) = 0;

 			}

 		else {

 			word0(&u) = 0;

 			L -= Exp_shift;

 			word1(&u) = L >= 31 ? 1 : 1 << 31 - L;

 			}

 		}

 #endif

 #endif

 	return dval(&u);

 	}

  static double

 b2d

 #ifdef KR_headers

 	(a, e) Bigint *a; int *e;

 #else

 	(Bigint *a, int *e)

 #endif

 {

 	ULong *xa, *xa0, w, y, z;

 	int k;

 	U d;

 #ifdef VAX

 	ULong d0, d1;

 #else

 #define d0 word0(&d)

 #define d1 word1(&d)

 #endif

 	xa0 = a->x;

 	xa = xa0 + a->wds;

 	y = *--xa;

 #ifdef DEBUG

 	if (!y) Bug("zero y in b2d");

 #endif

 	k = hi0bits(y);

 	*e = 32 - k;

 #ifdef Pack_32

 	if (k < Ebits) {

 		d0 = Exp_1 | y >> (Ebits - k);

 		w = xa > xa0 ? *--xa : 0;

 		d1 = y << ((32-Ebits) + k) | w >> (Ebits - k);

 		goto ret_d;

 		}

 	z = xa > xa0 ? *--xa : 0;

 	if (k -= Ebits) {

 		d0 = Exp_1 | y << k | z >> (32 - k);

 		y = xa > xa0 ? *--xa : 0;

 		d1 = z << k | y >> (32 - k);

 		}

 	else {

 		d0 = Exp_1 | y;

 		d1 = z;

 		}

 #else

 	if (k < Ebits + 16) {

 		z = xa > xa0 ? *--xa : 0;

 		d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;

 		w = xa > xa0 ? *--xa : 0;

 		y = xa > xa0 ? *--xa : 0;

 		d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;

 		goto ret_d;

 		}

 	z = xa > xa0 ? *--xa : 0;

 	w = xa > xa0 ? *--xa : 0;

 	k -= Ebits + 16;

 	d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;

 	y = xa > xa0 ? *--xa : 0;

 	d1 = w << k + 16 | y << k;

 #endif

  ret_d:

 #ifdef VAX

 	word0(&d) = d0 >> 16 | d0 << 16;

 	word1(&d) = d1 >> 16 | d1 << 16;

 #else

 #undef d0

 #undef d1

 #endif

 	return dval(&d);

 	}

  static Bigint *

 d2b

 #ifdef KR_headers

 	(d, e, bits) U *d; int *e, *bits;

 #else

 	(U *d, int *e, int *bits)

 #endif

 {

 	Bigint *b;

 	int de, k;

 	ULong *x, y, z;

 #ifndef Sudden_Underflow

 	int i;

 #endif

 #ifdef VAX

 	ULong d0, d1;

 	d0 = word0(d) >> 16 | word0(d) << 16;

 	d1 = word1(d) >> 16 | word1(d) << 16;

 #else

 #define d0 word0(d)

 #define d1 word1(d)

 #endif

 #ifdef Pack_32

 	b = Balloc(1);

 #else

 	b = Balloc(2);

 #endif

 	x = b->x;

 	z = d0 & Frac_mask;

 	d0 &= 0x7fffffff;	/* clear sign bit, which we ignore */

 #ifdef Sudden_Underflow

 	de = (int)(d0 >> Exp_shift);

 #ifndef IBM

 	z |= Exp_msk11;

 #endif

 #else

 	if ((de = (int)(d0 >> Exp_shift)))

 		z |= Exp_msk1;

 #endif

 #ifdef Pack_32

 	if ((y = d1)) {

 		if ((k = lo0bits(&y))) {

 			x[0] = y | z << (32 - k);

 			z >>= k;

 			}

 		else

 			x[0] = y;

 #ifndef Sudden_Underflow

 		i =

 #endif

 		    b->wds = (x[1] = z) ? 2 : 1;

 		}

 	else {

 		k = lo0bits(&z);

 		x[0] = z;

 #ifndef Sudden_Underflow

 		i =

 #endif

 		    b->wds = 1;

 		k += 32;

 		}

 #else

 	if (y = d1) {

 		if (k = lo0bits(&y))

 			if (k >= 16) {

 				x[0] = y | z << 32 - k & 0xffff;

 				x[1] = z >> k - 16 & 0xffff;

 				x[2] = z >> k;

 				i = 2;

 				}

 			else {

 				x[0] = y & 0xffff;

 				x[1] = y >> 16 | z << 16 - k & 0xffff;

 				x[2] = z >> k & 0xffff;

 				x[3] = z >> k+16;

 				i = 3;

 				}

 		else {

 			x[0] = y & 0xffff;

 			x[1] = y >> 16;

 			x[2] = z & 0xffff;

 			x[3] = z >> 16;

 			i = 3;

 			}

 		}

 	else {

 #ifdef DEBUG

 		if (!z)

 			Bug("Zero passed to d2b");

 #endif

 		k = lo0bits(&z);

 		if (k >= 16) {

 			x[0] = z;

 			i = 0;

 			}

 		else {

 			x[0] = z & 0xffff;

 			x[1] = z >> 16;

 			i = 1;

 			}

 		k += 32;

 		}

 	while(!x[i])

 		--i;

 	b->wds = i + 1;

 #endif

 #ifndef Sudden_Underflow

 	if (de) {

 #endif

 #ifdef IBM

 		*e = (de - Bias - (P-1) << 2) + k;

 		*bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);

 #else

 		*e = de - Bias - (P-1) + k;

 		*bits = P - k;

 #endif

 #ifndef Sudden_Underflow

 		}

 	else {

 		*e = de - Bias - (P-1) + 1 + k;

 #ifdef Pack_32

 		*bits = 32*i - hi0bits(x[i-1]);

 #else

 		*bits = (i+2)*16 - hi0bits(x[i]);

 #endif

 		}

 #endif

 	return b;

 	}

 #undef d0

 #undef d1

  static double

 ratio

 #ifdef KR_headers

 	(a, b) Bigint *a, *b;

 #else

 	(Bigint *a, Bigint *b)

 #endif

 {

 	U da, db;

 	int k, ka, kb;

 	dval(&da) = b2d(a, &ka);

 	dval(&db) = b2d(b, &kb);

 #ifdef Pack_32

 	k = ka - kb + 32*(a->wds - b->wds);

 #else

 	k = ka - kb + 16*(a->wds - b->wds);

 #endif

 #ifdef IBM

 	if (k > 0) {

 		word0(&da) += (k >> 2)*Exp_msk1;

 		if (k &= 3)

 			dval(&da) *= 1 << k;

 		}

 	else {

 		k = -k;

 		word0(&db) += (k >> 2)*Exp_msk1;

 		if (k &= 3)

 			dval(&db) *= 1 << k;

 		}

 #else

 	if (k > 0)

 		word0(&da) += k*Exp_msk1;

 	else {

 		k = -k;

 		word0(&db) += k*Exp_msk1;

 		}

 #endif

 	return dval(&da) / dval(&db);

 	}

  static CONST double

 tens[] = {

 		1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,

 		1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,

 		1e20, 1e21, 1e22

 #ifdef VAX

 		, 1e23, 1e24

 #endif

 		};

  static CONST double

 #ifdef IEEE_Arith

 bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };

 static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,

 #ifdef Avoid_Underflow

 		9007199254740992.*9007199254740992.e-256

 		/* = 2^106 * 1e-256 */

 #else

 		1e-256

 #endif

 		};

 /* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */

 /* flag unnecessarily.  It leads to a song and dance at the end of strtod. */

 #define Scale_Bit 0x10

 #define n_bigtens 5

 #else

 #ifdef IBM

 bigtens[] = { 1e16, 1e32, 1e64 };

 static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 };

 #define n_bigtens 3

 #else

 bigtens[] = { 1e16, 1e32 };

 static CONST double tinytens[] = { 1e-16, 1e-32 };

 #define n_bigtens 2

 #endif

 #endif

 #undef Need_Hexdig

 #ifdef INFNAN_CHECK

 #ifndef No_Hex_NaN

 #define Need_Hexdig

 #endif

 #endif

 #ifndef Need_Hexdig

 #ifndef NO_HEX_FP

 #define Need_Hexdig

 #endif

 #endif

 #ifdef Need_Hexdig /*{*/

 static unsigned char hexdig[256];

  static void

 #ifdef KR_headers

 htinit(h, s, inc) unsigned char *h; unsigned char *s; int inc;

 #else

 htinit(unsigned char *h, unsigned char *s, int inc)

 #endif

 {

 	int i, j;

 	for(i = 0; (j = s[i]) !=0; i++)

 		h[j] = i + inc;

 	}

  static void

 #ifdef KR_headers

 hexdig_init()

 #else

 hexdig_init(void)

 #endif

 {

 #define USC (unsigned char *)

 	htinit(hexdig, USC "0123456789", 0x10);

 	htinit(hexdig, USC "abcdef", 0x10 + 10);

 	htinit(hexdig, USC "ABCDEF", 0x10 + 10);

 	}

 #endif /* } Need_Hexdig */

 #ifdef INFNAN_CHECK

 #ifndef NAN_WORD0

 #define NAN_WORD0 0x7ff80000

 #endif

 #ifndef NAN_WORD1

 #define NAN_WORD1 0

 #endif

  static int

 match

 #ifdef KR_headers

 	(sp, t) char **sp, *t;

 #else

 	(const char **sp, const char *t)

 #endif

 {

 	int c, d;

 	CONST char *s = *sp;

 	while((d = *t++)) {

 		if ((c = *++s) >= 'A' && c <= 'Z')

 			c += 'a' - 'A';

 		if (c != d)

 			return 0;

 		}

 	*sp = s + 1;

 	return 1;

 	}

 #ifndef No_Hex_NaN

  static void

 hexnan

 #ifdef KR_headers

 	(rvp, sp) U *rvp; CONST char **sp;

 #else

 	(U *rvp, const char **sp)

 #endif

 {

 	ULong c, x[2];

 	CONST char *s;

 	int c1, havedig, udx0, xshift;

 	if (!hexdig['0'])

 		hexdig_init();

 	x[0] = x[1] = 0;

 	havedig = xshift = 0;

 	udx0 = 1;

 	s = *sp;

 	/* allow optional initial 0x or 0X */

 	while((c = *(CONST unsigned char*)(s+1)) && c <= ' ')

 		++s;

 	if (s[1] == '0' && (s[2] == 'x' || s[2] == 'X'))

 		s += 2;

 	while((c = *(CONST unsigned char*)++s)) {

 		if ((c1 = hexdig[c]))

 			c  = c1 & 0xf;

 		else if (c <= ' ') {

 			if (udx0 && havedig) {

 				udx0 = 0;

 				xshift = 1;

 				}

 			continue;

 			}

 #ifdef GDTOA_NON_PEDANTIC_NANCHECK

 		else if (/*(*/ c == ')' && havedig) {

 			*sp = s + 1;

 			break;

 			}

 		else

 			return;	/* invalid form: don't change *sp */

 #else

 		else {

 			do {

 				if (/*(*/ c == ')') {

 					*sp = s + 1;

 					break;

 					}

 				} while((c = *++s));

 			break;

 			}

 #endif

 		havedig = 1;

 		if (xshift) {

 			xshift = 0;

 			x[0] = x[1];

 			x[1] = 0;

 			}

 		if (udx0)

 			x[0] = (x[0] << 4) | (x[1] >> 28);

 		x[1] = (x[1] << 4) | c;

 		}

 	if ((x[0] &= 0xfffff) || x[1]) {

 		word0(rvp) = Exp_mask | x[0];

 		word1(rvp) = x[1];

 		}

 	}

 #endif /*No_Hex_NaN*/

 #endif /* INFNAN_CHECK */

 #ifdef Pack_32

 #define ULbits 32

 #define kshift 5

 #define kmask 31

 #else

 #define ULbits 16

 #define kshift 4

 #define kmask 15

 #endif

 #if !defined(NO_HEX_FP) || defined(Honor_FLT_ROUNDS) /*{*/

  static Bigint *

 #ifdef KR_headers

 increment(b) Bigint *b;

 #else

 increment(Bigint *b)

 #endif

 {

 	ULong *x, *xe;

 	Bigint *b1;

 	x = b->x;

 	xe = x + b->wds;

 	do {

 		if (*x < (ULong)0xffffffffL) {

 			++*x;

 			return b;

 			}

 		*x++ = 0;

 		} while(x < xe);

 	{

 		if (b->wds >= b->maxwds) {

 			b1 = Balloc(b->k+1);

 			Bcopy(b1,b);

 			Bfree(b);

 			b = b1;

 			}

 		b->x[b->wds++] = 1;

 		}

 	return b;

 	}

 #endif /*}*/

 #ifndef NO_HEX_FP /*{*/

  static void

 #ifdef KR_headers

 rshift(b, k) Bigint *b; int k;

 #else

 rshift(Bigint *b, int k)

 #endif

 {

 	ULong *x, *x1, *xe, y;

 	int n;

 	x = x1 = b->x;

 	n = k >> kshift;

 	if (n < b->wds) {

 		xe = x + b->wds;

 		x += n;

 		if (k &= kmask) {

 			n = 32 - k;

 			y = *x++ >> k;

 			while(x < xe) {

 				*x1++ = (y | (*x << n)) & 0xffffffff;

 				y = *x++ >> k;

 				}

 			if ((*x1 = y) !=0)

 				x1++;

 			}

 		else

 			while(x < xe)

 				*x1++ = *x++;

 		}

 	if ((b->wds = x1 - b->x) == 0)

 		b->x[0] = 0;

 	}

  static ULong

 #ifdef KR_headers

 any_on(b, k) Bigint *b; int k;

 #else

 any_on(Bigint *b, int k)

 #endif

 {

 	int n, nwds;

 	ULong *x, *x0, x1, x2;

 	x = b->x;

 	nwds = b->wds;

 	n = k >> kshift;

 	if (n > nwds)

 		n = nwds;

 	else if (n < nwds && (k &= kmask)) {

 		x1 = x2 = x[n];

 		x1 >>= k;

 		x1 <<= k;

 		if (x1 != x2)

 			return 1;

 		}

 	x0 = x;

 	x += n;

 	while(x > x0)

 		if (*--x)

 			return 1;

 	return 0;

 	}

 enum {	/* rounding values: same as FLT_ROUNDS */

 	Round_zero = 0,

 	Round_near = 1,

 	Round_up = 2,

 	Round_down = 3

 	};

  void

 #ifdef KR_headers

 gethex(sp, rvp, rounding, sign)

 	CONST char **sp; U *rvp; int rounding, sign;

 #else

 gethex( CONST char **sp, U *rvp, int rounding, int sign)

 #endif

 {

 	Bigint *b;

 	CONST unsigned char *decpt, *s0, *s, *s1;

 	Long e, e1;

 	ULong L, lostbits, *x;

 	int big, denorm, esign, havedig, k, n, nbits, up, zret;

 #ifdef IBM

 	int j;

 #endif

 	enum {

 #ifdef IEEE_Arith /*{{*/

 		emax = 0x7fe - Bias - P + 1,

 		emin = Emin - P + 1

 #else /*}{*/

 		emin = Emin - P,

 #ifdef VAX

 		emax = 0x7ff - Bias - P + 1

 #endif

 #ifdef IBM

 		emax = 0x7f - Bias - P

 #endif

 #endif /*}}*/

 		};

 #ifdef USE_LOCALE

 	int i;

 #ifdef NO_LOCALE_CACHE

 	const unsigned char *decimalpoint = (unsigned char*)

 		localeconv()->decimal_point;

 #else

 	const unsigned char *decimalpoint;

 	static unsigned char *decimalpoint_cache;

 	if (!(s0 = decimalpoint_cache)) {

 		s0 = (unsigned char*)localeconv()->decimal_point;

 		if ((decimalpoint_cache = (unsigned char*)

 				MALLOC(strlen((CONST char*)s0) + 1))) {

 			strcpy((char*)decimalpoint_cache, (CONST char*)s0);

 			s0 = decimalpoint_cache;

 			}

 		}

 	decimalpoint = s0;

 #endif

 #endif

 	if (!hexdig['0'])

 		hexdig_init();

 	havedig = 0;

 	s0 = *(CONST unsigned char **)sp + 2;

 	while(s0[havedig] == '0')

 		havedig++;

 	s0 += havedig;

 	s = s0;

 	decpt = 0;

 	zret = 0;

 	e = 0;

 	if (hexdig[*s])

 		havedig++;

 	else {

 		zret = 1;

 #ifdef USE_LOCALE

 		for(i = 0; decimalpoint[i]; ++i) {

 			if (s[i] != decimalpoint[i])

 				goto pcheck;

 			}

 		decpt = s += i;

 #else

 		if (*s != '.')

 			goto pcheck;

 		decpt = ++s;

 #endif

 		if (!hexdig[*s])

 			goto pcheck;

 		while(*s == '0')

 			s++;

 		if (hexdig[*s])

 			zret = 0;

 		havedig = 1;

 		s0 = s;

 		}

 	while(hexdig[*s])

 		s++;

 #ifdef USE_LOCALE

 	if (*s == *decimalpoint && !decpt) {

 		for(i = 1; decimalpoint[i]; ++i) {

 			if (s[i] != decimalpoint[i])

 				goto pcheck;

 			}

 		decpt = s += i;

 #else

 	if (*s == '.' && !decpt) {

 		decpt = ++s;

 #endif

 		while(hexdig[*s])

 			s++;

 		}/*}*/

 	if (decpt)

 		e = -(((Long)(s-decpt)) << 2);

  pcheck:

 	s1 = s;

 	big = esign = 0;

 	switch(*s) {

 	  case 'p':

 	  case 'P':

 		switch(*++s) {

 		  case '-':

 			esign = 1;

 			/* no break */

 		  case '+':

 			s++;

 		  }

 		if ((n = hexdig[*s]) == 0 || n > 0x19) {

 			s = s1;

 			break;

 			}

 		e1 = n - 0x10;

 		while((n = hexdig[*++s]) !=0 && n <= 0x19) {

 			if (e1 & 0xf8000000)

 				big = 1;

 			e1 = 10*e1 + n - 0x10;

 			}

 		if (esign)

 			e1 = -e1;

 		e += e1;

 	  }

 	*sp = (char*)s;

 	if (!havedig)

 		*sp = (char*)s0 - 1;

 	if (zret)

 		goto retz1;

 	if (big) {

 		if (esign) {

 #ifdef IEEE_Arith

 			switch(rounding) {

 			  case Round_up:

 				if (sign)

 					break;

 				goto ret_tiny;

 			  case Round_down:

 				if (!sign)

 					break;

 				goto ret_tiny;

 			  }

 #endif

 			goto retz;

 #ifdef IEEE_Arith

  ret_tiny:

 #ifndef NO_ERRNO

 			errno = ERANGE;

 #endif

 			word0(rvp) = 0;

 			word1(rvp) = 1;

 			return;

 #endif /* IEEE_Arith */

 			}

 		switch(rounding) {

 		  case Round_near:

 			goto ovfl1;

 		  case Round_up:

 			if (!sign)

 				goto ovfl1;

 			goto ret_big;

 		  case Round_down:

 			if (sign)

 				goto ovfl1;

 			goto ret_big;

 		  }

  ret_big:

 		word0(rvp) = Big0;

 		word1(rvp) = Big1;

 		return;

 		}

 	n = s1 - s0 - 1;

 	for(k = 0; n > (1 << (kshift-2)) - 1; n >>= 1)

 		k++;

 	b = Balloc(k);

 	x = b->x;

 	n = 0;

 	L = 0;

 #ifdef USE_LOCALE

 	for(i = 0; decimalpoint[i+1]; ++i);

 #endif

 	while(s1 > s0) {

 #ifdef USE_LOCALE

 		if (*--s1 == decimalpoint[i]) {

 			s1 -= i;

 			continue;

 			}

 #else

 		if (*--s1 == '.')

 			continue;

 #endif

 		if (n == ULbits) {

 			*x++ = L;

 			L = 0;

 			n = 0;

 			}

 		L |= (hexdig[*s1] & 0x0f) << n;

 		n += 4;

 		}

 	*x++ = L;

 	b->wds = n = x - b->x;

 	n = ULbits*n - hi0bits(L);

 	nbits = Nbits;

 	lostbits = 0;

 	x = b->x;

 	if (n > nbits) {

 		n -= nbits;

 		if (any_on(b,n)) {

 			lostbits = 1;

 			k = n - 1;

 			if (x[k>>kshift] & 1 << (k & kmask)) {

 				lostbits = 2;

 				if (k > 0 && any_on(b,k))

 					lostbits = 3;

 				}

 			}

 		rshift(b, n);

 		e += n;

 		}

 	else if (n < nbits) {

 		n = nbits - n;

 		b = lshift(b, n);

 		e -= n;

 		x = b->x;

 		}

 	if (e > Emax) {

  ovfl:

 		Bfree(b);

  ovfl1:

 #ifndef NO_ERRNO

 		errno = ERANGE;

 #endif

 		word0(rvp) = Exp_mask;

 		word1(rvp) = 0;

 		return;

 		}

 	denorm = 0;

 	if (e < emin) {

 		denorm = 1;

 		n = emin - e;

 		if (n >= nbits) {

 #ifdef IEEE_Arith /*{*/

 			switch (rounding) {

 			  case Round_near:

 				if (n == nbits && (n < 2 || any_on(b,n-1)))

 					goto ret_tiny;

 				break;

 			  case Round_up:

 				if (!sign)

 					goto ret_tiny;

 				break;

 			  case Round_down:

 				if (sign)

 					goto ret_tiny;

 			  }

 #endif /* } IEEE_Arith */

 			Bfree(b);

  retz:

 #ifndef NO_ERRNO

 			errno = ERANGE;

 #endif

  retz1:

 			rvp->d = 0.;

 			return;

 			}

 		k = n - 1;

 		if (lostbits)

 			lostbits = 1;

 		else if (k > 0)

 			lostbits = any_on(b,k);

 		if (x[k>>kshift] & 1 << (k & kmask))

 			lostbits |= 2;

 		nbits -= n;

 		rshift(b,n);

 		e = emin;

 		}

 	if (lostbits) {

 		up = 0;

 		switch(rounding) {

 		  case Round_zero:

 			break;

 		  case Round_near:

 			if (lostbits & 2

 			 && (lostbits & 1) | (x[0] & 1))

 				up = 1;

 			break;

 		  case Round_up:

 			up = 1 - sign;

 			break;

 		  case Round_down:

 			up = sign;

 		  }

 		if (up) {

 			k = b->wds;

 			b = increment(b);

 			x = b->x;

 			if (denorm) {

 #if 0

 				if (nbits == Nbits - 1

 				 && x[nbits >> kshift] & 1 << (nbits & kmask))

 					denorm = 0; /* not currently used */

 #endif

 				}

 			else if (b->wds > k

 			 || ((n = nbits & kmask) !=0

 			     && hi0bits(x[k-1]) < 32-n)) {

 				rshift(b,1);

 				if (++e > Emax)

 					goto ovfl;

 				}

 			}

 		}

 #ifdef IEEE_Arith

 	if (denorm)

 		word0(rvp) = b->wds > 1 ? b->x[1] & ~0x100000 : 0;

 	else

 		word0(rvp) = (b->x[1] & ~0x100000) | ((e + 0x3ff + 52) << 20);

 	word1(rvp) = b->x[0];

 #endif

 #ifdef IBM

 	if ((j = e & 3)) {

 		k = b->x[0] & ((1 << j) - 1);

 		rshift(b,j);

 		if (k) {

 			switch(rounding) {

 			  case Round_up:

 				if (!sign)

 					increment(b);

 				break;

 			  case Round_down:

 				if (sign)

 					increment(b);

 				break;

 			  case Round_near:

 				j = 1 << (j-1);

 				if (k & j && ((k & (j-1)) | lostbits))

 					increment(b);

 			  }

 			}

 		}

 	e >>= 2;

 	word0(rvp) = b->x[1] | ((e + 65 + 13) << 24);

 	word1(rvp) = b->x[0];

 #endif

 #ifdef VAX

 	/* The next two lines ignore swap of low- and high-order 2 bytes. */

 	/* word0(rvp) = (b->x[1] & ~0x800000) | ((e + 129 + 55) << 23); */

 	/* word1(rvp) = b->x[0]; */

 	word0(rvp) = ((b->x[1] & ~0x800000) >> 16) | ((e + 129 + 55) << 7) | (b->x[1] << 16);

 	word1(rvp) = (b->x[0] >> 16) | (b->x[0] << 16);

 #endif

 	Bfree(b);

 	}

 #endif /*!NO_HEX_FP}*/

  static int

 #ifdef KR_headers

 dshift(b, p2) Bigint *b; int p2;

 #else

 dshift(Bigint *b, int p2)

 #endif

 {

 	int rv = hi0bits(b->x[b->wds-1]) - 4;

 	if (p2 > 0)

 		rv -= p2;

 	return rv & kmask;

 	}

  static int

 quorem

 #ifdef KR_headers

 	(b, S) Bigint *b, *S;

 #else

 	(Bigint *b, Bigint *S)

 #endif

 {

 	int n;

 	ULong *bx, *bxe, q, *sx, *sxe;

 #ifdef ULLong

 	ULLong borrow, carry, y, ys;

 #else

 	ULong borrow, carry, y, ys;

 #ifdef Pack_32

 	ULong si, z, zs;

 #endif

 #endif

 	n = S->wds;

 #ifdef DEBUG

 	/*debug*/ if (b->wds > n)

 	/*debug*/	Bug("oversize b in quorem");

 #endif

 	if (b->wds < n)

 		return 0;

 	sx = S->x;

 	sxe = sx + --n;

 	bx = b->x;

 	bxe = bx + n;

 	q = *bxe / (*sxe + 1);	/* ensure q <= true quotient */

 #ifdef DEBUG

 #ifdef NO_STRTOD_BIGCOMP

 	/*debug*/ if (q > 9)

 #else

 	/* An oversized q is possible when quorem is called from bigcomp and */

 	/* the input is near, e.g., twice the smallest denormalized number. */

 	/*debug*/ if (q > 15)

 #endif

 	/*debug*/	Bug("oversized quotient in quorem");

 #endif

 	if (q) {

 		borrow = 0;

 		carry = 0;

 		do {

 #ifdef ULLong

 			ys = *sx++ * (ULLong)q + carry;

 			carry = ys >> 32;

 			y = *bx - (ys & FFFFFFFF) - borrow;

 			borrow = y >> 32 & (ULong)1;

 			*bx++ = y & FFFFFFFF;

 #else

 #ifdef Pack_32

 			si = *sx++;

 			ys = (si & 0xffff) * q + carry;

 			zs = (si >> 16) * q + (ys >> 16);

 			carry = zs >> 16;

 			y = (*bx & 0xffff) - (ys & 0xffff) - borrow;

 			borrow = (y & 0x10000) >> 16;

 			z = (*bx >> 16) - (zs & 0xffff) - borrow;

 			borrow = (z & 0x10000) >> 16;

 			Storeinc(bx, z, y);

 #else

 			ys = *sx++ * q + carry;

 			carry = ys >> 16;

 			y = *bx - (ys & 0xffff) - borrow;

 			borrow = (y & 0x10000) >> 16;

 			*bx++ = y & 0xffff;

 #endif

 #endif

 			}

 			while(sx <= sxe);

 		if (!*bxe) {

 			bx = b->x;

 			while(--bxe > bx && !*bxe)

 				--n;

 			b->wds = n;

 			}

 		}

 	if (cmp(b, S) >= 0) {

 		q++;

 		borrow = 0;

 		carry = 0;

 		bx = b->x;

 		sx = S->x;

 		do {

 #ifdef ULLong

 			ys = *sx++ + carry;

 			carry = ys >> 32;

 			y = *bx - (ys & FFFFFFFF) - borrow;

 			borrow = y >> 32 & (ULong)1;

 			*bx++ = y & FFFFFFFF;

 #else

 #ifdef Pack_32

 			si = *sx++;

 			ys = (si & 0xffff) + carry;

 			zs = (si >> 16) + (ys >> 16);

 			carry = zs >> 16;

 			y = (*bx & 0xffff) - (ys & 0xffff) - borrow;

 			borrow = (y & 0x10000) >> 16;

 			z = (*bx >> 16) - (zs & 0xffff) - borrow;

 			borrow = (z & 0x10000) >> 16;

 			Storeinc(bx, z, y);

 #else

 			ys = *sx++ + carry;

 			carry = ys >> 16;

 			y = *bx - (ys & 0xffff) - borrow;

 			borrow = (y & 0x10000) >> 16;

 			*bx++ = y & 0xffff;

 #endif

 #endif

 			}

 			while(sx <= sxe);

 		bx = b->x;

 		bxe = bx + n;

 		if (!*bxe) {

 			while(--bxe > bx && !*bxe)

 				--n;

 			b->wds = n;

 			}

 		}

 	return q;

 	}

 #if defined(Avoid_Underflow) || !defined(NO_STRTOD_BIGCOMP) /*{*/

  static double

 sulp

 #ifdef KR_headers

 	(x, bc) U *x; BCinfo *bc;

 #else

 	(U *x, BCinfo *bc)

 #endif

 {

 	U u;

 	double rv;

 	int i;

 	rv = ulp(x);

 	if (!bc->scale || (i = 2*P + 1 - ((word0(x) & Exp_mask) >> Exp_shift)) <= 0)

 		return rv; /* Is there an example where i <= 0 ? */

 	word0(&u) = Exp_1 + (i << Exp_shift);

 	word1(&u) = 0;

 	return rv * u.d;

 	}

 #endif /*}*/

 #ifndef NO_STRTOD_BIGCOMP

  static void

 bigcomp

 #ifdef KR_headers

 	(rv, s0, bc)

 	U *rv; CONST char *s0; BCinfo *bc;

 #else

 	(U *rv, const char *s0, BCinfo *bc)

 #endif

 {

 	Bigint *b, *d;

 	int b2, bbits, d2, dd, dig, dsign, i, j, nd, nd0, p2, p5, speccase;

 	dsign = bc->dsign;

 	nd = bc->nd;

 	nd0 = bc->nd0;

 	p5 = nd + bc->e0 - 1;

 	speccase = 0;

 #ifndef Sudden_Underflow

 	if (rv->d == 0.) {	/* special case: value near underflow-to-zero */

 				/* threshold was rounded to zero */

 		b = i2b(1);

 		p2 = Emin - P + 1;

 		bbits = 1;

 #ifdef Avoid_Underflow

 		word0(rv) = (P+2) << Exp_shift;

 #else

 		word1(rv) = 1;

 #endif

 		i = 0;

 #ifdef Honor_FLT_ROUNDS

 		if (bc->rounding == 1)

 #endif

 			{

 			speccase = 1;

 			--p2;

 			dsign = 0;

 			goto have_i;

 			}

 		}

 	else

 #endif

 		b = d2b(rv, &p2, &bbits);

 #ifdef Avoid_Underflow

 	p2 -= bc->scale;

 #endif

 	/* floor(log2(rv)) == bbits - 1 + p2 */

 	/* Check for denormal case. */

 	i = P - bbits;

 	if (i > (j = P - Emin - 1 + p2)) {

 #ifdef Sudden_Underflow

 		Bfree(b);

 		b = i2b(1);

 		p2 = Emin;

 		i = P - 1;

 #ifdef Avoid_Underflow

 		word0(rv) = (1 + bc->scale) << Exp_shift;

 #else

 		word0(rv) = Exp_msk1;

 #endif

 		word1(rv) = 0;

 #else

 		i = j;

 #endif

 		}

 #ifdef Honor_FLT_ROUNDS

 	if (bc->rounding != 1) {

 		if (i > 0)

 			b = lshift(b, i);

 		if (dsign)

 			b = increment(b);

 		}

 	else

 #endif

 		{

 		b = lshift(b, ++i);

 		b->x[0] |= 1;

 		}

 #ifndef Sudden_Underflow

  have_i:

 #endif

 	p2 -= p5 + i;

 	d = i2b(1);

 	/* Arrange for convenient computation of quotients:

 	 * shift left if necessary so divisor has 4 leading 0 bits.

 	 */

 	if (p5 > 0)

 		d = pow5mult(d, p5);

 	else if (p5 < 0)

 		b = pow5mult(b, -p5);

 	if (p2 > 0) {

 		b2 = p2;

 		d2 = 0;

 		}

 	else {

 		b2 = 0;

 		d2 = -p2;

 		}

 	i = dshift(d, d2);

 	if ((b2 += i) > 0)

 		b = lshift(b, b2);

 	if ((d2 += i) > 0)

 		d = lshift(d, d2);

 	/* Now b/d = exactly half-way between the two floating-point values */

 	/* on either side of the input string.  Compute first digit of b/d. */

 	if (!(dig = quorem(b,d))) {

 		b = multadd(b, 10, 0);	/* very unlikely */

 		dig = quorem(b,d);

 		}

 	/* Compare b/d with s0 */

 	for(i = 0; i < nd0; ) {

 		if ((dd = s0[i++] - '0' - dig))

 			goto ret;

 		if (!b->x[0] && b->wds == 1) {

 			if (i < nd)

 				dd = 1;

 			goto ret;

 			}

 		b = multadd(b, 10, 0);

 		dig = quorem(b,d);

 		}

 	for(j = bc->dp1; i++ < nd;) {

 		if ((dd = s0[j++] - '0' - dig))

 			goto ret;

 		if (!b->x[0] && b->wds == 1) {

 			if (i < nd)

 				dd = 1;

 			goto ret;

 			}

 		b = multadd(b, 10, 0);

 		dig = quorem(b,d);

 		}

 	if (b->x[0] || b->wds > 1 || dig > 0)

 		dd = -1;

  ret:

 	Bfree(b);

 	Bfree(d);

 #ifdef Honor_FLT_ROUNDS

 	if (bc->rounding != 1) {

 		if (dd < 0) {

 			if (bc->rounding == 0) {

 				if (!dsign)

 					goto retlow1;

 				}

 			else if (dsign)

 				goto rethi1;

 			}

 		else if (dd > 0) {

 			if (bc->rounding == 0) {

 				if (dsign)

 					goto rethi1;

 				goto ret1;

 				}

 			if (!dsign)

 				goto rethi1;

 			dval(rv) += 2.*sulp(rv,bc);

 			}

 		else {

 			bc->inexact = 0;

 			if (dsign)

 				goto rethi1;

 			}

 		}

 	else

 #endif

 	if (speccase) {

 		if (dd <= 0)

 			rv->d = 0.;

 		}

 	else if (dd < 0) {

 		if (!dsign)	/* does not happen for round-near */

 retlow1:

 			dval(rv) -= sulp(rv,bc);

 		}

 	else if (dd > 0) {

 		if (dsign) {

  rethi1:

 			dval(rv) += sulp(rv,bc);

 			}

 		}

 	else {

 		/* Exact half-way case:  apply round-even rule. */

 		if ((j = ((word0(rv) & Exp_mask) >> Exp_shift) - bc->scale) <= 0) {

 			i = 1 - j;

 			if (i <= 31) {

 				if (word1(rv) & (0x1 << i))

 					goto odd;

 				}

 			else if (word0(rv) & (0x1 << (i-32)))

 				goto odd;

 			}

 		else if (word1(rv) & 1) {

  odd:

 			if (dsign)

 				goto rethi1;

 			goto retlow1;

 			}

 		}

 #ifdef Honor_FLT_ROUNDS

  ret1:

 #endif

 	return;

 	}

 #endif /* NO_STRTOD_BIGCOMP */

  double

 strtod

 #ifdef KR_headers

 	(s00, se) CONST char *s00; char **se;

 #else

 	(const char *s00, char **se)

 #endif

 {

 	int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, e, e1;

 	int esign, i, j, k, nd, nd0, nf, nz, nz0, nz1, sign;

 	CONST char *s, *s0, *s1;

 	double aadj, aadj1;

 	Long L;

 	U aadj2, adj, rv, rv0;

 	ULong y, z;

 	BCinfo bc;

 	Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;

 #ifdef Avoid_Underflow

 	ULong Lsb, Lsb1;

 #endif

 #ifdef SET_INEXACT

 	int oldinexact;

 #endif

 #ifndef NO_STRTOD_BIGCOMP

 	int req_bigcomp = 0;

 #endif

 #ifdef Honor_FLT_ROUNDS /*{*/

 #ifdef Trust_FLT_ROUNDS /*{{ only define this if FLT_ROUNDS really works! */

 	bc.rounding = Flt_Rounds;

 #else /*}{*/

 	bc.rounding = 1;

 	switch(fegetround()) {

 	  case FE_TOWARDZERO:	bc.rounding = 0; break;

 	  case FE_UPWARD:	bc.rounding = 2; break;

 	  case FE_DOWNWARD:	bc.rounding = 3;

 	  }

 #endif /*}}*/

 #endif /*}*/

 #ifdef USE_LOCALE

 	CONST char *s2;

 #endif

 	sign = nz0 = nz1 = nz = bc.dplen = bc.uflchk = 0;

 	dval(&rv) = 0.;

 	for(s = s00;;s++) switch(*s) {

 		case '-':

 			sign = 1;

 			/* no break */

 		case '+':

 			if (*++s)

 				goto break2;

 			/* no break */

 		case 0:

 			goto ret0;

 		case '\t':

 		case '\n':

 		case '\v':

 		case '\f':

 		case '\r':

 		case ' ':

 			continue;

 		default:

 			goto break2;

 		}

  break2:

 	if (*s == '0') {

 #ifndef NO_HEX_FP /*{*/

 		switch(s[1]) {

 		  case 'x':

 		  case 'X':

 #ifdef Honor_FLT_ROUNDS

 			gethex(&s, &rv, bc.rounding, sign);

 #else

 			gethex(&s, &rv, 1, sign);

 #endif

 			goto ret;

 		  }

 #endif /*}*/

 		nz0 = 1;

 		while(*++s == '0') ;

 		if (!*s)

 			goto ret;

 		}

 	s0 = s;

 	y = z = 0;

 	for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)

 		if (nd < 9)

 			y = 10*y + c - '0';

 		else if (nd < 16)

 			z = 10*z + c - '0';

 	nd0 = nd;

 	bc.dp0 = bc.dp1 = s - s0;

 	for(s1 = s; s1 > s0 && *--s1 == '0'; )

 		++nz1;

 #ifdef USE_LOCALE

 	s1 = localeconv()->decimal_point;

 	if (c == *s1) {

 		c = '.';

 		if (*++s1) {

 			s2 = s;

 			for(;;) {

 				if (*++s2 != *s1) {

 					c = 0;

 					break;

 					}

 				if (!*++s1) {

 					s = s2;

 					break;

 					}

 				}

 			}

 		}

 #endif

 	if (c == '.') {

 		c = *++s;

 		bc.dp1 = s - s0;

 		bc.dplen = bc.dp1 - bc.dp0;

 		if (!nd) {

 			for(; c == '0'; c = *++s)

 				nz++;

 			if (c > '0' && c <= '9') {

 				bc.dp0 = s0 - s;

 				bc.dp1 = bc.dp0 + bc.dplen;

 				s0 = s;

 				nf += nz;

 				nz = 0;

 				goto have_dig;

 				}

 			goto dig_done;

 			}

 		for(; c >= '0' && c <= '9'; c = *++s) {

  have_dig:

 			nz++;

 			if (c -= '0') {

 				nf += nz;

 				for(i = 1; i < nz; i++)

 					if (nd++ < 9)

 						y *= 10;

 					else if (nd <= DBL_DIG + 1)

 						z *= 10;

 				if (nd++ < 9)

 					y = 10*y + c;

 				else if (nd <= DBL_DIG + 1)

 					z = 10*z + c;

 				nz = nz1 = 0;

 				}

 			}

 		}

  dig_done:

 	e = 0;

 	if (c == 'e' || c == 'E') {

 		if (!nd && !nz && !nz0) {

 			goto ret0;

 			}

 		s00 = s;

 		esign = 0;

 		switch(c = *++s) {

 			case '-':

 				esign = 1;

 			case '+':

 				c = *++s;

 			}

 		if (c >= '0' && c <= '9') {

 			while(c == '0')

 				c = *++s;

 			if (c > '0' && c <= '9') {

 				L = c - '0';

 				s1 = s;

 				while((c = *++s) >= '0' && c <= '9')

 					L = 10*L + c - '0';

 				if (s - s1 > 8 || L > 19999)

 					/* Avoid confusion from exponents

 					 * so large that e might overflow.

 					 */

 					e = 19999; /* safe for 16 bit ints */