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 /* -*- Mode: C; tab-width: 8; indent-tabs-mode: t; c-basic-offset: 8 -*- */

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

  *

  * 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.

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

  *	and strtod and dtoa should round accordingly.

  * #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.

  * #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.  (Unless you #define

  *	NO_GLOBAL_STATE and call destroydtoa, 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 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_GLOBAL_STATE to avoid defining any non-const global or

  *	static variables. Instead the necessary state is stored in an

  *	opaque struct, DtoaState, a pointer to which must be passed to

  *	every entry point. Two new functions are added to the API:

  *		DtoaState *newdtoa(void);

  *		void destroydtoa(DtoaState *);

  */

 #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 MALLOC

 #ifdef KR_headers

 extern char *MALLOC();

 #else

 extern void *MALLOC(size_t);

 #endif

 #else

 #define MALLOC malloc

 #endif

 #ifndef FREE

 #define FREE free

 #endif

 #ifndef Omit_Private_Memory

 #ifndef PRIVATE_MEM

 #define PRIVATE_MEM 2304

 #endif

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

 #endif

 #undef IEEE_Arith

 #undef Avoid_Underflow

 #ifdef IEEE_MC68k

 #define IEEE_Arith

 #endif

 #ifdef IEEE_8087

 #define IEEE_Arith

 #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

 #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;

 #define dval(x) ((x).d)

 #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

 /* 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 Bias 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

 #define Rounding rounding

 #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 Bias 65

 #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 Bias 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

 #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

 #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

  struct

 Bigint {

 	struct Bigint *next;

 	int k, maxwds, sign, wds;

 	ULong x[1];

 	};

  typedef struct Bigint Bigint;

 #ifdef NO_GLOBAL_STATE

 #ifdef MULTIPLE_THREADS

 #error "cannot have both NO_GLOBAL_STATE and MULTIPLE_THREADS"

 #endif

  struct

 DtoaState {

 #define DECLARE_GLOBAL_STATE  /* nothing */

 #else

 #define DECLARE_GLOBAL_STATE static

 #endif

 	DECLARE_GLOBAL_STATE Bigint *freelist[Kmax+1];

 	DECLARE_GLOBAL_STATE Bigint *p5s;

 #ifndef Omit_Private_Memory

 	DECLARE_GLOBAL_STATE double private_mem[PRIVATE_mem];

 	DECLARE_GLOBAL_STATE double *pmem_next

 #ifndef NO_GLOBAL_STATE

 	                                       = private_mem

 #endif

 	                                                    ;

 #endif

 #ifdef NO_GLOBAL_STATE

 	};

  typedef struct DtoaState DtoaState;

 #ifdef KR_headers

 #define STATE_PARAM state,

 #define STATE_PARAM_DECL DtoaState *state;

 #else

 #define STATE_PARAM DtoaState *state,

 #endif

 #define PASS_STATE state,

 #define GET_STATE(field) (state->field)

  static DtoaState *

 newdtoa(void)

 {

 	DtoaState *state = (DtoaState *) MALLOC(sizeof(DtoaState));

 	if (state) {

 		memset(state, 0, sizeof(DtoaState));

 #ifndef Omit_Private_Memory

 		state->pmem_next = state->private_mem;

 #endif

 		}

 	return state;

 }

  static void

 destroydtoa

 #ifdef KR_headers

 	(state) STATE_PARAM_DECL

 #else

 	(DtoaState *state)

 #endif

 {

 	int i;

 	Bigint *v, *next;

 	for (i = 0; i <= Kmax; i++) {

 		for (v = GET_STATE(freelist)[i]; v; v = next) {

 			next = v->next;

 #ifndef Omit_Private_Memory

 			if ((double*)v < GET_STATE(private_mem) ||

 			    (double*)v >= GET_STATE(private_mem) + PRIVATE_mem)

 #endif

 				FREE((void*)v);

 			}

 		}

 	FREE((void *)state);

 }

 #else

 #define STATE_PARAM      /* nothing */

 #define STATE_PARAM_DECL /* nothing */

 #define PASS_STATE       /* nothing */

 #define GET_STATE(name) name

 #endif

  static Bigint *

 Balloc

 #ifdef KR_headers

 	(STATE_PARAM k) STATE_PARAM_DECL int k;

 #else

 	(STATE_PARAM int k)

 #endif

 {

 	int x;

 	Bigint *rv;

 #ifndef Omit_Private_Memory

 	size_t 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 = GET_STATE(freelist)[k]))

 		GET_STATE(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 && GET_STATE(pmem_next) - GET_STATE(private_mem) + len <= PRIVATE_mem) {

 			rv = (Bigint*)GET_STATE(pmem_next);

 			GET_STATE(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

 	(STATE_PARAM v) STATE_PARAM_DECL Bigint *v;

 #else

 	(STATE_PARAM Bigint *v)

 #endif

 {

 	if (v) {

 		if (v->k > Kmax)

 			FREE((void*)v);

 		else {

 			ACQUIRE_DTOA_LOCK(0);

 			v->next = GET_STATE(freelist)[v->k];

 			GET_STATE(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

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

 #else

 	(STATE_PARAM 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++ = (ULong) 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(PASS_STATE b->k+1);

 			Bcopy(b1, b);

 			Bfree(PASS_STATE b);

 			b = b1;

 			}

 		b->x[wds++] = (ULong) carry;

 		b->wds = wds;

 		}

 	return b;

 	}

  static Bigint *

 s2b

 #ifdef KR_headers

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

 #else

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

 #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(PASS_STATE k);

 	b->x[0] = y9;

 	b->wds = 1;

 #else

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

 			while(++i < nd0);

 		s++;

 		}

 	else

 		s += 10;

 	for(; i < nd; i++)

 		b = multadd(PASS_STATE 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

 	(STATE_PARAM i) STATE_PARAM_DECL int i;

 #else

 	(STATE_PARAM int i)

 #endif

 {

 	Bigint *b;

 	b = Balloc(PASS_STATE 1);

 	b->x[0] = i;

 	b->wds = 1;

 	return b;

 	}

  static Bigint *

 mult

 #ifdef KR_headers

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

 #else

 	(STATE_PARAM 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(PASS_STATE 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++ = (ULong) z & FFFFFFFF;

 				}

 				while(x < xae);

 			*xc = (ULong) 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 *

 pow5mult

 #ifdef KR_headers

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

 #else

 	(STATE_PARAM Bigint *b, int k)

 #endif

 {

 	Bigint *b1, *p5, *p51;

 	int i;

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

 	if ((i = k & 3))

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

 	if (!(k >>= 2))

 		return b;

 	if (!(p5 = GET_STATE(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 = GET_STATE(p5s) = i2b(PASS_STATE 625);

 		p5->next = 0;

 #endif

 		}

 	for(;;) {

 		if (k & 1) {

 			b1 = mult(PASS_STATE b, p5);

 			Bfree(PASS_STATE 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(PASS_STATE p5,p5);

 			p51->next = 0;

 #endif

 			}

 		p5 = p51;

 		}

 	return b;

 	}

  static Bigint *

 lshift

 #ifdef KR_headers

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

 #else

 	(STATE_PARAM 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(PASS_STATE 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(PASS_STATE 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

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

 #else

 	(STATE_PARAM 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(PASS_STATE 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(PASS_STATE 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++ = (ULong) y & FFFFFFFF;

 		}

 		while(xb < xbe);

 	while(xa < xae) {

 		y = *xa++ - borrow;

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

 		*xc++ = (ULong) 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 a;

 	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(a) = L;

 		word1(a) = 0;

 #ifndef Avoid_Underflow

 #ifndef Sudden_Underflow

 		}

 	else {

 		L = -L >> Exp_shift;

 		if (L < Exp_shift) {

 			word0(a) = 0x80000 >> L;

 			word1(a) = 0;

 			}

 		else {

 			word0(a) = 0;

 			L -= Exp_shift;

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

 			}

 		}

 #endif

 #endif

 	return dval(a);

 	}

  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

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

 #else

 	(STATE_PARAM 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(PASS_STATE 1);

 #else

 	b = Balloc(PASS_STATE 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-53 */

 #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

  static double

 _strtod

 #ifdef KR_headers

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

 #else

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

 #endif

 {

 #ifdef Avoid_Underflow

 	int scale;

 #endif

 	int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,

 		 e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;

 	CONST char *s, *s0, *s1;

 	double aadj, adj;

 	U aadj1, rv, rv0;

 	Long L;

 	ULong y, z;

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

 #ifdef SET_INEXACT

 	int inexact, oldinexact;

 #endif

 #ifdef Honor_FLT_ROUNDS

 	int rounding;

 #endif

 #ifdef USE_LOCALE

 	CONST char *s2;

 #endif

 #ifdef __GNUC__

 	delta = bb = bd = bs = 0;

 #endif

 	sign = nz0 = nz = 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') {

 		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;

 #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;

 		if (!nd) {

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

 				nz++;

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

 				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 = 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 */

 				else

 					e = (int)L;

 				if (esign)

 					e = -e;

 				}

 			else

 				e = 0;

 			}

 		else

 			s = s00;

 		}

 	if (!nd) {

 		if (!nz && !nz0) {

  ret0:

 			s = s00;

 			sign = 0;

 			}

 		goto ret;

 		}

 	e1 = e -= nf;

 	/* Now we have nd0 digits, starting at s0, followed by a

 	 * decimal point, followed by nd-nd0 digits.  The number we're

 	 * after is the integer represented by those digits times

 	 * 10**e */

 	if (!nd0)

 		nd0 = nd;

 	k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;

 	dval(rv) = y;

 	if (k > 9) {

 #ifdef SET_INEXACT

 		if (k > DBL_DIG)

 			oldinexact = get_inexact();

 #endif

 		dval(rv) = tens[k - 9] * dval(rv) + z;

 		}

 	bd0 = 0;

 	if (nd <= DBL_DIG

 #ifndef RND_PRODQUOT

 #ifndef Honor_FLT_ROUNDS

 		&& Flt_Rounds == 1

 #endif

 #endif

 			) {

 		if (!e)

 			goto ret;

 		if (e > 0) {

 			if (e <= Ten_pmax) {

 #ifdef VAX

 				goto vax_ovfl_check;

 #else

 #ifdef Honor_FLT_ROUNDS

 				/* round correctly FLT_ROUNDS = 2 or 3 */

 				if (sign) {

 					rv = -rv;

 					sign = 0;

 					}

 #endif

 				/* rv = */ rounded_product(dval(rv), tens[e]);

 				goto ret;

 #endif

 				}

 			i = DBL_DIG - nd;

 			if (e <= Ten_pmax + i) {

 				/* A fancier test would sometimes let us do

 				 * this for larger i values.

 				 */

 #ifdef Honor_FLT_ROUNDS

 				/* round correctly FLT_ROUNDS = 2 or 3 */

 				if (sign) {

 					rv = -rv;

 					sign = 0;

 					}

 #endif

 				e -= i;

 				dval(rv) *= tens[i];

 #ifdef VAX

 				/* VAX exponent range is so narrow we must

 				 * worry about overflow here...

 				 */

  vax_ovfl_check:

 				word0(rv) -= P*Exp_msk1;

 				/* rv = */ rounded_product(dval(rv), tens[e]);

 				if ((word0(rv) & Exp_mask)

 				 > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))

 					goto ovfl;

 				word0(rv) += P*Exp_msk1;

 #else

 				/* rv = */ rounded_product(dval(rv), tens[e]);

 #endif

 				goto ret;

 				}

 			}

 #ifndef Inaccurate_Divide

 		else if (e >= -Ten_pmax) {

 #ifdef Honor_FLT_ROUNDS

 			/* round correctly FLT_ROUNDS = 2 or 3 */

 			if (sign) {

 				rv = -rv;

 				sign = 0;

 				}

 #endif

 			/* rv = */ rounded_quotient(dval(rv), tens[-e]);

 			goto ret;

 			}

 #endif

 		}

 	e1 += nd - k;

 #ifdef IEEE_Arith

 #ifdef SET_INEXACT

 	inexact = 1;

 	if (k <= DBL_DIG)

 		oldinexact = get_inexact();

 #endif

 #ifdef Avoid_Underflow

 	scale = 0;

 #endif

 #ifdef Honor_FLT_ROUNDS

 	if ((rounding = Flt_Rounds) >= 2) {

 		if (sign)

 			rounding = rounding == 2 ? 0 : 2;

 		else

 			if (rounding != 2)

 				rounding = 0;

 		}

 #endif

 #endif /*IEEE_Arith*/

 	/* Get starting approximation = rv * 10**e1 */

 	if (e1 > 0) {

 		if ((i = e1 & 15))

 			dval(rv) *= tens[i];

 		if (e1 &= ~15) {

 			if (e1 > DBL_MAX_10_EXP) {

  ovfl:

 #ifndef NO_ERRNO

 				errno = ERANGE;

 #endif

 				/* Can't trust HUGE_VAL */

 #ifdef IEEE_Arith

 #ifdef Honor_FLT_ROUNDS

 				switch(rounding) {

 				  case 0: /* toward 0 */

 				  case 3: /* toward -infinity */

 					word0(rv) = Big0;

 					word1(rv) = Big1;

 					break;

 				  default:

 					word0(rv) = Exp_mask;

 					word1(rv) = 0;

 				  }

 #else /*Honor_FLT_ROUNDS*/

 				word0(rv) = Exp_mask;

 				word1(rv) = 0;

 #endif /*Honor_FLT_ROUNDS*/

 #ifdef SET_INEXACT

 				/* set overflow bit */

 				dval(rv0) = 1e300;

 				dval(rv0) *= dval(rv0);

 #endif

 #else /*IEEE_Arith*/

 				word0(rv) = Big0;

 				word1(rv) = Big1;

 #endif /*IEEE_Arith*/

 				if (bd0)

 					goto retfree;

 				goto ret;

 				}

 			e1 >>= 4;

 			for(j = 0; e1 > 1; j++, e1 >>= 1)

 				if (e1 & 1)

 					dval(rv) *= bigtens[j];

 		/* The last multiplication could overflow. */

 			word0(rv) -= P*Exp_msk1;

 			dval(rv) *= bigtens[j];

 			if ((z = word0(rv) & Exp_mask)

 			 > Exp_msk1*(DBL_MAX_EXP+Bias-P))

 				goto ovfl;

 			if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {

 				/* set to largest number */

 				/* (Can't trust DBL_MAX) */

 				word0(rv) = Big0;

 				word1(rv) = Big1;

 				}

 			else

 				word0(rv) += P*Exp_msk1;

 			}

 		}

 	else if (e1 < 0) {

 		e1 = -e1;

 		if ((i = e1 & 15))

 			dval(rv) /= tens[i];

 		if (e1 >>= 4) {

 			if (e1 >= 1 << n_bigtens)

 				goto undfl;

 #ifdef Avoid_Underflow

 			if (e1 & Scale_Bit)

 				scale = 2*P;

 			for(j = 0; e1 > 0; j++, e1 >>= 1)

 				if (e1 & 1)

 					dval(rv) *= tinytens[j];

 			if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask)

 						>> Exp_shift)) > 0) {

 				/* scaled rv is denormal; zap j low bits */

 				if (j >= 32) {

 					word1(rv) = 0;

 					if (j >= 53)

 					 word0(rv) = (P+2)*Exp_msk1;

 					else

 					 word0(rv) &= 0xffffffff << (j-32);

 					}

 				else

 					word1(rv) &= 0xffffffff << j;

 				}

 #else

 			for(j = 0; e1 > 1; j++, e1 >>= 1)

 				if (e1 & 1)

 					dval(rv) *= tinytens[j];

 			/* The last multiplication could underflow. */

 			dval(rv0) = dval(rv);

 			dval(rv) *= tinytens[j];

 			if (!dval(rv)) {

 				dval(rv) = 2.*dval(rv0);

 				dval(rv) *= tinytens[j];

 #endif

 				if (!dval(rv)) {

  undfl:

 					dval(rv) = 0.;

 #ifndef NO_ERRNO

 					errno = ERANGE;

 #endif

 					if (bd0)

 						goto retfree;

 					goto ret;

 					}

 #ifndef Avoid_Underflow

 				word0(rv) = Tiny0;

 				word1(rv) = Tiny1;

 				/* The refinement below will clean

 				 * this approximation up.

 				 */

 				}

 #endif

 			}

 		}

 	/* Now the hard part -- adjusting rv to the correct value.*/

 	/* Put digits into bd: true value = bd * 10^e */

 	bd0 = s2b(PASS_STATE s0, nd0, nd, y);

 	for(;;) {

 		bd = Balloc(PASS_STATE bd0->k);

 		Bcopy(bd, bd0);

 		bb = d2b(PASS_STATE rv, &bbe, &bbbits);	/* rv = bb * 2^bbe */

 		bs = i2b(PASS_STATE 1);

 		if (e >= 0) {

 			bb2 = bb5 = 0;

 			bd2 = bd5 = e;

 			}

 		else {

 			bb2 = bb5 = -e;

 			bd2 = bd5 = 0;

 			}

 		if (bbe >= 0)

 			bb2 += bbe;

 		else

 			bd2 -= bbe;

 		bs2 = bb2;

 #ifdef Honor_FLT_ROUNDS

 		if (rounding != 1)

 			bs2++;

 #endif

 #ifdef Avoid_Underflow

 		j = bbe - scale;

 		i = j + bbbits - 1;	/* logb(rv) */

 		if (i < Emin)	/* denormal */

 			j += P - Emin;

 		else

 			j = P + 1 - bbbits;

 #else /*Avoid_Underflow*/

 #ifdef Sudden_Underflow

 #ifdef IBM

 		j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);

 #else

 		j = P + 1 - bbbits;

 #endif

 #else /*Sudden_Underflow*/

 		j = bbe;

 		i = j + bbbits - 1;	/* logb(rv) */

 		if (i < Emin)	/* denormal */

 			j += P - Emin;

 		else

 			j = P + 1 - bbbits;

 #endif /*Sudden_Underflow*/

 #endif /*Avoid_Underflow*/

 		bb2 += j;

 		bd2 += j;

 #ifdef Avoid_Underflow

 		bd2 += scale;

 #endif

 		i = bb2 < bd2 ? bb2 : bd2;

 		if (i > bs2)

 			i = bs2;

 		if (i > 0) {

 			bb2 -= i;

 			bd2 -= i;

 			bs2 -= i;

 			}

 		if (bb5 > 0) {

 			bs = pow5mult(PASS_STATE bs, bb5);

 			bb1 = mult(PASS_STATE bs, bb);

 			Bfree(PASS_STATE bb);

 			bb = bb1;

 			}

 		if (bb2 > 0)

 			bb = lshift(PASS_STATE bb, bb2);

 		if (bd5 > 0)

 			bd = pow5mult(PASS_STATE bd, bd5);

 		if (bd2 > 0)

 			bd = lshift(PASS_STATE bd, bd2);

 		if (bs2 > 0)

 			bs = lshift(PASS_STATE bs, bs2);

 		delta = diff(PASS_STATE bb, bd);

 		dsign = delta->sign;

 		delta->sign = 0;

 		i = cmp(delta, bs);

 #ifdef Honor_FLT_ROUNDS

 		if (rounding != 1) {

 			if (i < 0) {

 				/* Error is less than an ulp */

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

 					/* exact */

 #ifdef SET_INEXACT

 					inexact = 0;

 #endif

 					break;

 					}

 				if (rounding) {

 					if (dsign) {

 						adj = 1.;

 						goto apply_adj;

 						}

 					}

 				else if (!dsign) {

 					adj = -1.;

 					if (!word1(rv)

 					 && !(word0(rv) & Frac_mask)) {

 						y = word0(rv) & Exp_mask;

 #ifdef Avoid_Underflow

 						if (!scale || y > 2*P*Exp_msk1)

 #else

 						if (y)

 #endif

 						  {

 						  delta = lshift(PASS_STATE delta,Log2P);

 						  if (cmp(delta, bs) <= 0)

 							adj = -0.5;

 						  }

 						}

  apply_adj:

 #ifdef Avoid_Underflow

 					if (scale && (y = word0(rv) & Exp_mask)

 						<= 2*P*Exp_msk1)

 					  word0(adj) += (2*P+1)*Exp_msk1 - y;

 #else

 #ifdef Sudden_Underflow

 					if ((word0(rv) & Exp_mask) <=

 							P*Exp_msk1) {

 						word0(rv) += P*Exp_msk1;

 						dval(rv) += adj*ulp(rv);

 						word0(rv) -= P*Exp_msk1;

 						}

 					else

 #endif /*Sudden_Underflow*/

 #endif /*Avoid_Underflow*/

 					dval(rv) += adj*ulp(rv);

 					}

 				break;

 				}

 			adj = ratio(delta, bs);

 			if (adj < 1.)

 				adj = 1.;

 			if (adj <= 0x7ffffffe) {

 				/* adj = rounding ? ceil(adj) : floor(adj); */

 				y = adj;

 				if (y != adj) {

 					if (!((rounding>>1) ^ dsign))

 						y++;

 					adj = y;

 					}

 				}

 #ifdef Avoid_Underflow

 			if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)

 				word0(adj) += (2*P+1)*Exp_msk1 - y;

 #else

 #ifdef Sudden_Underflow

 			if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {

 				word0(rv) += P*Exp_msk1;

 				adj *= ulp(rv);

 				if (dsign)

 					dval(rv) += adj;

 				else

 					dval(rv) -= adj;

 				word0(rv) -= P*Exp_msk1;

 				goto cont;

 				}

 #endif /*Sudden_Underflow*/

 #endif /*Avoid_Underflow*/

 			adj *= ulp(rv);

 			if (dsign)

 				dval(rv) += adj;

 			else

 				dval(rv) -= adj;

 			goto cont;

 			}

 #endif /*Honor_FLT_ROUNDS*/

 		if (i < 0) {

 			/* Error is less than half an ulp -- check for

 			 * special case of mantissa a power of two.

 			 */

 			if (dsign || word1(rv) || word0(rv) & Bndry_mask

 #ifdef IEEE_Arith

 #ifdef Avoid_Underflow

 			 || (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1

 #else

 			 || (word0(rv) & Exp_mask) <= Exp_msk1

 #endif

 #endif

 				) {

 #ifdef SET_INEXACT

 				if (!delta->x[0] && delta->wds <= 1)

 					inexact = 0;

 #endif

 				break;

 				}

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

 				/* exact result */

 #ifdef SET_INEXACT

 				inexact = 0;

 #endif

 				break;

 				}

 			delta = lshift(PASS_STATE delta,Log2P);

 			if (cmp(delta, bs) > 0)

 				goto drop_down;

 			break;

 			}

 		if (i == 0) {

 			/* exactly half-way between */

 			if (dsign) {

 				if ((word0(rv) & Bndry_mask1) == Bndry_mask1

 				 &&  word1(rv) == (

 #ifdef Avoid_Underflow

 			(scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)

 		? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :

 #endif

 						   0xffffffff)) {

 					/*boundary case -- increment exponent*/

 					word0(rv) = (word0(rv) & Exp_mask)

 						+ Exp_msk1

 #ifdef IBM

 						| Exp_msk1 >> 4

 #endif

 						;

 					word1(rv) = 0;

 #ifdef Avoid_Underflow

 					dsign = 0;

 #endif

 					break;

 					}

 				}

 			else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {

  drop_down:

 				/* boundary case -- decrement exponent */

 #ifdef Sudden_Underflow /*{{*/

 				L = word0(rv) & Exp_mask;

 #ifdef IBM

 				if (L <  Exp_msk1)

 #else

 #ifdef Avoid_Underflow

 				if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1))

 #else

 				if (L <= Exp_msk1)

 #endif /*Avoid_Underflow*/

 #endif /*IBM*/

 					goto undfl;

 				L -= Exp_msk1;

 #else /*Sudden_Underflow}{*/

 #ifdef Avoid_Underflow

 				if (scale) {

 					L = word0(rv) & Exp_mask;

 					if (L <= (2*P+1)*Exp_msk1) {

 						if (L > (P+2)*Exp_msk1)

 							/* round even ==> */

 							/* accept rv */

 							break;

 						/* rv = smallest denormal */

 						goto undfl;

 						}

 					}

 #endif /*Avoid_Underflow*/

 				L = (word0(rv) & Exp_mask) - Exp_msk1;

 #endif /*Sudden_Underflow}}*/

 				word0(rv) = L | Bndry_mask1;

 				word1(rv) = 0xffffffff;

 #ifdef IBM

 				goto cont;

 #else

 				break;

 #endif

 				}

 #ifndef ROUND_BIASED

 			if (!(word1(rv) & LSB))

 				break;

 #endif

 			if (dsign)

 				dval(rv) += ulp(rv);

 #ifndef ROUND_BIASED

 			else {

 				dval(rv) -= ulp(rv);

 #ifndef Sudden_Underflow

 				if (!dval(rv))

 					goto undfl;

 #endif

 				}

 #ifdef Avoid_Underflow

 			dsign = 1 - dsign;

 #endif

 #endif

 			break;

 			}

 		if ((aadj = ratio(delta, bs)) <= 2.) {

 			if (dsign)

 				aadj = dval(aadj1) = 1.;

 			else if (word1(rv) || word0(rv) & Bndry_mask) {

 #ifndef Sudden_Underflow

 				if (word1(rv) == Tiny1 && !word0(rv))

 					goto undfl;

 #endif

 				aadj = 1.;

 				dval(aadj1) = -1.;

 				}

 			else {

 				/* special case -- power of FLT_RADIX to be */

 				/* rounded down... */

 				if (aadj < 2./FLT_RADIX)

 					aadj = 1./FLT_RADIX;

 				else

 					aadj *= 0.5;

 				dval(aadj1) = -aadj;

 				}

 			}

 		else {

 			aadj *= 0.5;

 			dval(aadj1) = dsign ? aadj : -aadj;

 #ifdef Check_FLT_ROUNDS

 			switch(Rounding) {

 				case 2: /* towards +infinity */

 					dval(aadj1) -= 0.5;

 					break;

 				case 0: /* towards 0 */

 				case 3: /* towards -infinity */

 					dval(aadj1) += 0.5;

 				}

 #else

 			if (Flt_Rounds == 0)

 				dval(aadj1) += 0.5;

 #endif /*Check_FLT_ROUNDS*/

 			}

 		y = word0(rv) & Exp_mask;

 		/* Check for overflow */

 		if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {

 			dval(rv0) = dval(rv);

 			word0(rv) -= P*Exp_msk1;

 			adj = dval(aadj1) * ulp(rv);

 			dval(rv) += adj;

 			if ((word0(rv) & Exp_mask) >=

 					Exp_msk1*(DBL_MAX_EXP+Bias-P)) {

 				if (word0(rv0) == Big0 && word1(rv0) == Big1)

 					goto ovfl;

 				word0(rv) = Big0;

 				word1(rv) = Big1;

 				goto cont;

 				}

 			else

 				word0(rv) += P*Exp_msk1;

 			}

 		else {

 #ifdef Avoid_Underflow

 			if (scale && y <= 2*P*Exp_msk1) {

 				if (aadj <= 0x7fffffff) {

 					if ((z = (ULong) aadj) <= 0)

 						z = 1;

 					aadj = z;

 					dval(aadj1) = dsign ? aadj : -aadj;

 					}

 				word0(aadj1) += (2*P+1)*Exp_msk1 - y;

 				}

 			adj = dval(aadj1) * ulp(rv);

 			dval(rv) += adj;

 #else

 #ifdef Sudden_Underflow

 			if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {

 				dval(rv0) = dval(rv);

 				word0(rv) += P*Exp_msk1;

 				adj = dval(aadj1) * ulp(rv);

 				dval(rv) += adj;

 #ifdef IBM

 				if ((word0(rv) & Exp_mask) <  P*Exp_msk1)

 #else

 				if ((word0(rv) & Exp_mask) <= P*Exp_msk1)

 #endif

 					{

 					if (word0(rv0) == Tiny0

 					 && word1(rv0) == Tiny1)

 						goto undfl;

 					word0(rv) = Tiny0;

 					word1(rv) = Tiny1;

 					goto cont;

 					}

 				else

 					word0(rv) -= P*Exp_msk1;

 				}

 			else {

 				adj = dval(aadj1) * ulp(rv);

 				dval(rv) += adj;

 				}

 #else /*Sudden_Underflow*/

 			/* Compute adj so that the IEEE rounding rules will

 			 * correctly round rv + adj in some half-way cases.

 			 * If rv * ulp(rv) is denormalized (i.e.,

 			 * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid

 			 * trouble from bits lost to denormalization;

 			 * example: 1.2e-307 .

 			 */

 			if (y <= (P-1)*Exp_msk1 && aadj > 1.) {

 				dval(aadj1) = (double)(int)(aadj + 0.5);

 				if (!dsign)

 					dval(aadj1) = -dval(aadj1);

 				}

 			adj = dval(aadj1) * ulp(rv);

 			dval(rv) += adj;

 #endif /*Sudden_Underflow*/

 #endif /*Avoid_Underflow*/

 			}

 		z = word0(rv) & Exp_mask;

 #ifndef SET_INEXACT

 #ifdef Avoid_Underflow

 		if (!scale)

 #endif

 		if (y == z) {

 			/* Can we stop now? */

 			L = (Long)aadj;

 			aadj -= L;

 			/* The tolerances below are conservative. */

 			if (dsign || word1(rv) || word0(rv) & Bndry_mask) {

 				if (aadj < .4999999 || aadj > .5000001)

 					break;

 				}

 			else if (aadj < .4999999/FLT_RADIX)

 				break;

 			}

 #endif

  cont:

 		Bfree(PASS_STATE bb);

 		Bfree(PASS_STATE bd);

 		Bfree(PASS_STATE bs);

 		Bfree(PASS_STATE delta);

 		}

 #ifdef SET_INEXACT

 	if (inexact) {

 		if (!oldinexact) {

 			word0(rv0) = Exp_1 + (70 << Exp_shift);

 			word1(rv0) = 0;

 			dval(rv0) += 1.;

 			}

 		}

 	else if (!oldinexact)

 		clear_inexact();

 #endif

 #ifdef Avoid_Underflow

 	if (scale) {

 		word0(rv0) = Exp_1 - 2*P*Exp_msk1;

 		word1(rv0) = 0;

 		dval(rv) *= dval(rv0);

 #ifndef NO_ERRNO

 		/* try to avoid the bug of testing an 8087 register value */

 		if (word0(rv) == 0 && word1(rv) == 0)

 			errno = ERANGE;

 #endif

 		}

 #endif /* Avoid_Underflow */

 #ifdef SET_INEXACT

 	if (inexact && !(word0(rv) & Exp_mask)) {

 		/* set underflow bit */

 		dval(rv0) = 1e-300;

 		dval(rv0) *= dval(rv0);

 		}

 #endif

  retfree:

 	Bfree(PASS_STATE bb);

 	Bfree(PASS_STATE bd);

 	Bfree(PASS_STATE bs);

 	Bfree(PASS_STATE bd0);

 	Bfree(PASS_STATE delta);

  ret:

 	if (se)

 		*se = (char *)s;

 	return sign ? -dval(rv) : dval(rv);

 	}

  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

 	/*debug*/ if (q > 9)

 	/*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++ = (ULong) 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++ = (ULong) 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(MULTIPLE_THREADS) && !defined(NO_GLOBAL_STATE)

 #define USE_DTOA_RESULT 1

  static char *dtoa_result;

 #endif

  static char *

 #ifdef KR_headers

 rv_alloc(STATE_PARAM i) STATE_PARAM_DECL int i;

 #else

 rv_alloc(STATE_PARAM int i)

 #endif

 {

 	int j, k, *r;

 	j = sizeof(ULong);

 	for(k = 0;

 		sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= (unsigned) i;

 		j <<= 1)

 			k++;

 	r = (int*)Balloc(PASS_STATE k);

 	*r = k;

 	return

 #ifdef USE_DTOA_RESULT

 	dtoa_result =

 #endif

 		(char *)(r+1);

 	}

  static char *

 #ifdef KR_headers

 nrv_alloc(STATE_PARAM s, rve, n) STATE_PARAM_DECL char *s, **rve; int n;

 #else

 nrv_alloc(STATE_PARAM CONST char *s, char **rve, int n)

 #endif

 {

 	char *rv, *t;

 	t = rv = rv_alloc(PASS_STATE n);

 	while((*t = *s++)) t++;

 	if (rve)

 		*rve = t;

 	return rv;

 	}

 /* freedtoa(s) must be used to free values s returned by dtoa

  * when MULTIPLE_THREADS is #defined.  It should be used in all cases,

  * but for consistency with earlier versions of dtoa, it is optional

  * when MULTIPLE_THREADS is not defined.

  */

  static void

 #ifdef KR_headers

 freedtoa(STATE_PARAM s) STATE_PARAM_DECL char *s;

 #else

 freedtoa(STATE_PARAM char *s)

 #endif

 {

 	Bigint *b = (Bigint *)((int *)s - 1);

 	b->maxwds = 1 << (b->k = *(int*)b);

 	Bfree(PASS_STATE b);

 #ifdef USE_DTOA_RESULT

 	if (s == dtoa_result)

 		dtoa_result = 0;

 #endif

 	}

 /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.

  *

  * Inspired by "How to Print Floating-Point Numbers Accurately" by

  * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126].

  *

  * Modifications:

  *	1. Rather than iterating, we use a simple numeric overestimate

  *	   to determine k = floor(log10(d)).  We scale relevant

  *	   quantities using O(log2(k)) rather than O(k) multiplications.

  *	2. For some modes > 2 (corresponding to ecvt and fcvt), we don't

  *	   try to generate digits strictly left to right.  Instead, we

  *	   compute with fewer bits and propagate the carry if necessary

  *	   when rounding the final digit up.  This is often faster.

  *	3. Under the assumption that input will be rounded nearest,

  *	   mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.

  *	   That is, we allow equality in stopping tests when the

  *	   round-nearest rule will give the same floating-point value

  *	   as would satisfaction of the stopping test with strict

  *	   inequality.

  *	4. We remove common factors of powers of 2 from relevant

  *	   quantities.

  *	5. When converting floating-point integers less than 1e16,

  *	   we use floating-point arithmetic rather than resorting

  *	   to multiple-precision integers.

  *	6. When asked to produce fewer than 15 digits, we first try

  *	   to get by with floating-point arithmetic; we resort to

  *	   multiple-precision integer arithmetic only if we cannot

  *	   guarantee that the floating-point calculation has given

  *	   the correctly rounded result.  For k requested digits and

  *	   "uniformly" distributed input, the probability is

  *	   something like 10^(k-15) that we must resort to the Long

  *	   calculation.

  */

  static char *

 dtoa

 #ifdef KR_headers

 	(STATE_PARAM d, mode, ndigits, decpt, sign, rve)

 	STATE_PARAM_DECL U d; int mode, ndigits, *decpt, *sign; char **rve;

 #else

 	(STATE_PARAM U d, int mode, int ndigits, int *decpt, int *sign, char **rve)

 #endif

 {

  /*	Arguments ndigits, decpt, sign are similar to those

 	of ecvt and fcvt; trailing zeros are suppressed from

 	the returned string.  If not null, *rve is set to point

 	to the end of the return value.  If d is +-Infinity or NaN,

 	then *decpt is set to 9999.

 	mode:

 		0 ==> shortest string that yields d when read in

 			and rounded to nearest.

 		1 ==> like 0, but with Steele & White stopping rule;

 			e.g. with IEEE P754 arithmetic , mode 0 gives

 			1e23 whereas mode 1 gives 9.999999999999999e22.

 		2 ==> max(1,ndigits) significant digits.  This gives a

 			return value similar to that of ecvt, except

 			that trailing zeros are suppressed.

 		3 ==> through ndigits past the decimal point.  This

 			gives a return value similar to that from fcvt,

 			except that trailing zeros are suppressed, and

 			ndigits can be negative.

 		4,5 ==> similar to 2 and 3, respectively, but (in

 			round-nearest mode) with the tests of mode 0 to

 			possibly return a shorter string that rounds to d.

 			With IEEE arithmetic and compilation with

 			-DHonor_FLT_ROUNDS, modes 4 and 5 behave the same

 			as modes 2 and 3 when FLT_ROUNDS != 1.

 		6-9 ==> Debugging modes similar to mode - 4:  don't try

 			fast floating-point estimate (if applicable).

 		Values of mode other than 0-9 are treated as mode 0.

 		Sufficient space is allocated to the return value

 		to hold the suppressed trailing zeros.

 	*/

 	int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,

 		j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,

 		spec_case, try_quick;

 	Long L;

 #ifndef Sudden_Underflow

 	int denorm;

 	ULong x;

 #endif

 	Bigint *b, *b1, *delta, *mlo, *mhi, *S;

 	U d2, eps;

 	double ds;

 	char *s, *s0;

 #ifdef Honor_FLT_ROUNDS

 	int rounding;

 #endif

 #ifdef SET_INEXACT

 	int inexact, oldinexact;

 #endif

 #ifdef __GNUC__

 	ilim = ilim1 = 0;

 	mlo = NULL;

 #endif

 #ifdef USE_DTOA_RESULT

 	if (dtoa_result) {

 		freedtoa(PASS_STATE dtoa_result);

 		dtoa_result = 0;

 		}

 #endif

 	if (word0(d) & Sign_bit) {

 		/* set sign for everything, including 0's and NaNs */

 		*sign = 1;

 		word0(d) &= ~Sign_bit;	/* clear sign bit */

 		}

 	else

 		*sign = 0;

 #if defined(IEEE_Arith) + defined(VAX)

 #ifdef IEEE_Arith

 	if ((word0(d) & Exp_mask) == Exp_mask)

 #else

 	if (word0(d)  == 0x8000)