1 /* -*- Mode: C; tab-width: 8; indent-tabs-mode: t; c-basic-offset: 8 -*- */
2 /****************************************************************
3  *
4  * The author of this software is David M. Gay.
5  *
6  * Copyright (c) 1991, 2000, 2001 by Lucent Technologies.
7  *
8  * Permission to use, copy, modify, and distribute this software for any
9  * purpose without fee is hereby granted, provided that this entire notice
10  * is included in all copies of any software which is or includes a copy
11  * or modification of this software and in all copies of the supporting
12  * documentation for such software.
13  *
14  * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
15  * WARRANTY.  IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY
16  * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
17  * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
18  *
19  ***************************************************************/
20 
21 /* Please send bug reports to David M. Gay (dmg at acm dot org,
22  * with " at " changed at "@" and " dot " changed to ".").	*/
23 
24 /* On a machine with IEEE extended-precision registers, it is
25  * necessary to specify double-precision (53-bit) rounding precision
26  * before invoking strtod or dtoa.  If the machine uses (the equivalent
27  * of) Intel 80x87 arithmetic, the call
28  *	_control87(PC_53, MCW_PC);
29  * does this with many compilers.  Whether this or another call is
30  * appropriate depends on the compiler; for this to work, it may be
31  * necessary to #include "float.h" or another system-dependent header
32  * file.
33  */
34 
35 /* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
36  *
37  * This strtod returns a nearest machine number to the input decimal
38  * string (or sets errno to ERANGE).  With IEEE arithmetic, ties are
39  * broken by the IEEE round-even rule.  Otherwise ties are broken by
40  * biased rounding (add half and chop).
41  *
42  * Inspired loosely by William D. Clinger's paper "How to Read Floating
43  * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
44  *
45  * Modifications:
46  *
47  *	1. We only require IEEE, IBM, or VAX double-precision
48  *		arithmetic (not IEEE double-extended).
49  *	2. We get by with floating-point arithmetic in a case that
50  *		Clinger missed -- when we're computing d * 10^n
51  *		for a small integer d and the integer n is not too
52  *		much larger than 22 (the maximum integer k for which
53  *		we can represent 10^k exactly), we may be able to
54  *		compute (d*10^k) * 10^(e-k) with just one roundoff.
55  *	3. Rather than a bit-at-a-time adjustment of the binary
56  *		result in the hard case, we use floating-point
57  *		arithmetic to determine the adjustment to within
58  *		one bit; only in really hard cases do we need to
59  *		compute a second residual.
60  *	4. Because of 3., we don't need a large table of powers of 10
61  *		for ten-to-e (just some small tables, e.g. of 10^k
62  *		for 0 <= k <= 22).
63  */
64 
65 /*
66  * #define IEEE_8087 for IEEE-arithmetic machines where the least
67  *	significant byte has the lowest address.
68  * #define IEEE_MC68k for IEEE-arithmetic machines where the most
69  *	significant byte has the lowest address.
70  * #define Long int on machines with 32-bit ints and 64-bit longs.
71  * #define IBM for IBM mainframe-style floating-point arithmetic.
72  * #define VAX for VAX-style floating-point arithmetic (D_floating).
73  * #define No_leftright to omit left-right logic in fast floating-point
74  *	computation of dtoa.
75  * #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
76  *	and strtod and dtoa should round accordingly.
77  * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
78  *	and Honor_FLT_ROUNDS is not #defined.
79  * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
80  *	that use extended-precision instructions to compute rounded
81  *	products and quotients) with IBM.
82  * #define ROUND_BIASED for IEEE-format with biased rounding.
83  * #define Inaccurate_Divide for IEEE-format with correctly rounded
84  *	products but inaccurate quotients, e.g., for Intel i860.
85  * #define NO_LONG_LONG on machines that do not have a "long long"
86  *	integer type (of >= 64 bits).  On such machines, you can
87  *	#define Just_16 to store 16 bits per 32-bit Long when doing
88  *	high-precision integer arithmetic.  Whether this speeds things
89  *	up or slows things down depends on the machine and the number
90  *	being converted.  If long long is available and the name is
91  *	something other than "long long", #define Llong to be the name,
92  *	and if "unsigned Llong" does not work as an unsigned version of
93  *	Llong, #define #ULLong to be the corresponding unsigned type.
94  * #define KR_headers for old-style C function headers.
95  * #define Bad_float_h if your system lacks a float.h or if it does not
96  *	define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
97  *	FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
98  * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
99  *	if memory is available and otherwise does something you deem
100  *	appropriate.  If MALLOC is undefined, malloc will be invoked
101  *	directly -- and assumed always to succeed.  Similarly, if you
102  *	want something other than the system's free() to be called to
103  *	recycle memory acquired from MALLOC, #define FREE to be the
104  *	name of the alternate routine.  (Unless you #define
105  *	NO_GLOBAL_STATE and call destroydtoa, FREE or free is only
106  *	called in pathological cases, e.g., in a dtoa call after a dtoa
107  *	return in mode 3 with thousands of digits requested.)
108  * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making
109  *	memory allocations from a private pool of memory when possible.
110  *	When used, the private pool is PRIVATE_MEM bytes long:  2304 bytes,
111  *	unless #defined to be a different length.  This default length
112  *	suffices to get rid of MALLOC calls except for unusual cases,
113  *	such as decimal-to-binary conversion of a very long string of
114  *	digits.  The longest string dtoa can return is about 751 bytes
115  *	long.  For conversions by strtod of strings of 800 digits and
116  *	all dtoa conversions in single-threaded executions with 8-byte
117  *	pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte
118  *	pointers, PRIVATE_MEM >= 7112 appears adequate.
119  * #define MULTIPLE_THREADS if the system offers preemptively scheduled
120  *	multiple threads.  In this case, you must provide (or suitably
121  *	#define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed
122  *	by FREE_DTOA_LOCK(n) for n = 0 or 1.  (The second lock, accessed
123  *	in pow5mult, ensures lazy evaluation of only one copy of high
124  *	powers of 5; omitting this lock would introduce a small
125  *	probability of wasting memory, but would otherwise be harmless.)
126  *	You must also invoke freedtoa(s) to free the value s returned by
127  *	dtoa.  You may do so whether or not MULTIPLE_THREADS is #defined.
128  * #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that
129  *	avoids underflows on inputs whose result does not underflow.
130  *	If you #define NO_IEEE_Scale on a machine that uses IEEE-format
131  *	floating-point numbers and flushes underflows to zero rather
132  *	than implementing gradual underflow, then you must also #define
133  *	Sudden_Underflow.
134  * #define USE_LOCALE to use the current locale's decimal_point value.
135  * #define SET_INEXACT if IEEE arithmetic is being used and extra
136  *	computation should be done to set the inexact flag when the
137  *	result is inexact and avoid setting inexact when the result
138  *	is exact.  In this case, dtoa.c must be compiled in
139  *	an environment, perhaps provided by #include "dtoa.c" in a
140  *	suitable wrapper, that defines two functions,
141  *		int get_inexact(void);
142  *		void clear_inexact(void);
143  *	such that get_inexact() returns a nonzero value if the
144  *	inexact bit is already set, and clear_inexact() sets the
145  *	inexact bit to 0.  When SET_INEXACT is #defined, strtod
146  *	also does extra computations to set the underflow and overflow
147  *	flags when appropriate (i.e., when the result is tiny and
148  *	inexact or when it is a numeric value rounded to +-infinity).
149  * #define NO_ERRNO if strtod should not assign errno = ERANGE when
150  *	the result overflows to +-Infinity or underflows to 0.
151  * #define NO_GLOBAL_STATE to avoid defining any non-const global or
152  *	static variables. Instead the necessary state is stored in an
153  *	opaque struct, DtoaState, a pointer to which must be passed to
154  *	every entry point. Two new functions are added to the API:
155  *		DtoaState *newdtoa(void);
156  *		void destroydtoa(DtoaState *);
157  */
158 
159 #ifndef Long
160 #define Long long
161 #endif
162 #ifndef ULong
163 typedef unsigned Long ULong;
164 #endif
165 
166 #ifdef DEBUG
167 #include <stdio.h>
168 #define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
169 #endif
170 
171 #include <stdlib.h>
172 #include <string.h>
173 
174 #ifdef USE_LOCALE
175 #include <locale.h>
176 #endif
177 
178 #ifdef MALLOC
179 #ifdef KR_headers
180 extern char *MALLOC();
181 #else
182 extern void *MALLOC(size_t);
183 #endif
184 #else
185 #define MALLOC malloc
186 #endif
187 
188 #ifndef FREE
189 #define FREE free
190 #endif
191 
192 #ifndef Omit_Private_Memory
193 #ifndef PRIVATE_MEM
194 #define PRIVATE_MEM 2304
195 #endif
196 #define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
197 #endif
198 
199 #undef IEEE_Arith
200 #undef Avoid_Underflow
201 #ifdef IEEE_MC68k
202 #define IEEE_Arith
203 #endif
204 #ifdef IEEE_8087
205 #define IEEE_Arith
206 #endif
207 
208 #include <errno.h>
209 
210 #ifdef Bad_float_h
211 
212 #ifdef IEEE_Arith
213 #define DBL_DIG 15
214 #define DBL_MAX_10_EXP 308
215 #define DBL_MAX_EXP 1024
216 #define FLT_RADIX 2
217 #endif /*IEEE_Arith*/
218 
219 #ifdef IBM
220 #define DBL_DIG 16
221 #define DBL_MAX_10_EXP 75
222 #define DBL_MAX_EXP 63
223 #define FLT_RADIX 16
224 #define DBL_MAX 7.2370055773322621e+75
225 #endif
226 
227 #ifdef VAX
228 #define DBL_DIG 16
229 #define DBL_MAX_10_EXP 38
230 #define DBL_MAX_EXP 127
231 #define FLT_RADIX 2
232 #define DBL_MAX 1.7014118346046923e+38
233 #endif
234 
235 #ifndef LONG_MAX
236 #define LONG_MAX 2147483647
237 #endif
238 
239 #else /* ifndef Bad_float_h */
240 #include <float.h>
241 #endif /* Bad_float_h */
242 
243 #ifndef __MATH_H__
244 #include <math.h>
245 #endif
246 
247 #ifndef CONST
248 #ifdef KR_headers
249 #define CONST /* blank */
250 #else
251 #define CONST const
252 #endif
253 #endif
254 
255 #if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1
256 Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined.
257 #endif
258 
259 typedef union { double d; ULong L[2]; } U;
260 
261 #define dval(x) ((x).d)
262 #ifdef IEEE_8087
263 #define word0(x) ((x).L[1])
264 #define word1(x) ((x).L[0])
265 #else
266 #define word0(x) ((x).L[0])
267 #define word1(x) ((x).L[1])
268 #endif
269 
270 /* The following definition of Storeinc is appropriate for MIPS processors.
271  * An alternative that might be better on some machines is
272  * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
273  */
274 #if defined(IEEE_8087) + defined(VAX)
275 #define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
276 ((unsigned short *)a)[0] = (unsigned short)c, a++)
277 #else
278 #define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
279 ((unsigned short *)a)[1] = (unsigned short)c, a++)
280 #endif
281 
282 /* #define P DBL_MANT_DIG */
283 /* Ten_pmax = floor(P*log(2)/log(5)) */
284 /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
285 /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
286 /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
287 
288 #ifdef IEEE_Arith
289 #define Exp_shift  20
290 #define Exp_shift1 20
291 #define Exp_msk1    0x100000
292 #define Exp_msk11   0x100000
293 #define Exp_mask  0x7ff00000
294 #define P 53
295 #define Bias 1023
296 #define Emin (-1022)
297 #define Exp_1  0x3ff00000
298 #define Exp_11 0x3ff00000
299 #define Ebits 11
300 #define Frac_mask  0xfffff
301 #define Frac_mask1 0xfffff
302 #define Ten_pmax 22
303 #define Bletch 0x10
304 #define Bndry_mask  0xfffff
305 #define Bndry_mask1 0xfffff
306 #define LSB 1
307 #define Sign_bit 0x80000000
308 #define Log2P 1
309 #define Tiny0 0
310 #define Tiny1 1
311 #define Quick_max 14
312 #define Int_max 14
313 #ifndef NO_IEEE_Scale
314 #define Avoid_Underflow
315 #ifdef Flush_Denorm	/* debugging option */
316 #undef Sudden_Underflow
317 #endif
318 #endif
319 
320 #ifndef Flt_Rounds
321 #ifdef FLT_ROUNDS
322 #define Flt_Rounds FLT_ROUNDS
323 #else
324 #define Flt_Rounds 1
325 #endif
326 #endif /*Flt_Rounds*/
327 
328 #ifdef Honor_FLT_ROUNDS
329 #define Rounding rounding
330 #undef Check_FLT_ROUNDS
331 #define Check_FLT_ROUNDS
332 #else
333 #define Rounding Flt_Rounds
334 #endif
335 
336 #else /* ifndef IEEE_Arith */
337 #undef Check_FLT_ROUNDS
338 #undef Honor_FLT_ROUNDS
339 #undef SET_INEXACT
340 #undef  Sudden_Underflow
341 #define Sudden_Underflow
342 #ifdef IBM
343 #undef Flt_Rounds
344 #define Flt_Rounds 0
345 #define Exp_shift  24
346 #define Exp_shift1 24
347 #define Exp_msk1   0x1000000
348 #define Exp_msk11  0x1000000
349 #define Exp_mask  0x7f000000
350 #define P 14
351 #define Bias 65
352 #define Exp_1  0x41000000
353 #define Exp_11 0x41000000
354 #define Ebits 8	/* exponent has 7 bits, but 8 is the right value in b2d */
355 #define Frac_mask  0xffffff
356 #define Frac_mask1 0xffffff
357 #define Bletch 4
358 #define Ten_pmax 22
359 #define Bndry_mask  0xefffff
360 #define Bndry_mask1 0xffffff
361 #define LSB 1
362 #define Sign_bit 0x80000000
363 #define Log2P 4
364 #define Tiny0 0x100000
365 #define Tiny1 0
366 #define Quick_max 14
367 #define Int_max 15
368 #else /* VAX */
369 #undef Flt_Rounds
370 #define Flt_Rounds 1
371 #define Exp_shift  23
372 #define Exp_shift1 7
373 #define Exp_msk1    0x80
374 #define Exp_msk11   0x800000
375 #define Exp_mask  0x7f80
376 #define P 56
377 #define Bias 129
378 #define Exp_1  0x40800000
379 #define Exp_11 0x4080
380 #define Ebits 8
381 #define Frac_mask  0x7fffff
382 #define Frac_mask1 0xffff007f
383 #define Ten_pmax 24
384 #define Bletch 2
385 #define Bndry_mask  0xffff007f
386 #define Bndry_mask1 0xffff007f
387 #define LSB 0x10000
388 #define Sign_bit 0x8000
389 #define Log2P 1
390 #define Tiny0 0x80
391 #define Tiny1 0
392 #define Quick_max 15
393 #define Int_max 15
394 #endif /* IBM, VAX */
395 #endif /* IEEE_Arith */
396 
397 #ifndef IEEE_Arith
398 #define ROUND_BIASED
399 #endif
400 
401 #ifdef RND_PRODQUOT
402 #define rounded_product(a,b) a = rnd_prod(a, b)
403 #define rounded_quotient(a,b) a = rnd_quot(a, b)
404 #ifdef KR_headers
405 extern double rnd_prod(), rnd_quot();
406 #else
407 extern double rnd_prod(double, double), rnd_quot(double, double);
408 #endif
409 #else
410 #define rounded_product(a,b) a *= b
411 #define rounded_quotient(a,b) a /= b
412 #endif
413 
414 #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
415 #define Big1 0xffffffff
416 
417 #ifndef Pack_32
418 #define Pack_32
419 #endif
420 
421 #ifdef KR_headers
422 #define FFFFFFFF ((((unsigned long)0xffff)<<16)|(unsigned long)0xffff)
423 #else
424 #define FFFFFFFF 0xffffffffUL
425 #endif
426 
427 #ifdef NO_LONG_LONG
428 #undef ULLong
429 #ifdef Just_16
430 #undef Pack_32
431 /* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
432  * This makes some inner loops simpler and sometimes saves work
433  * during multiplications, but it often seems to make things slightly
434  * slower.  Hence the default is now to store 32 bits per Long.
435  */
436 #endif
437 #else	/* long long available */
438 #ifndef Llong
439 #define Llong long long
440 #endif
441 #ifndef ULLong
442 #define ULLong unsigned Llong
443 #endif
444 #endif /* NO_LONG_LONG */
445 
446 #ifndef MULTIPLE_THREADS
447 #define ACQUIRE_DTOA_LOCK(n)	/*nothing*/
448 #define FREE_DTOA_LOCK(n)	/*nothing*/
449 #endif
450 
451 #define Kmax 7
452 
453  struct
454 Bigint {
455 	struct Bigint *next;
456 	int k, maxwds, sign, wds;
457 	ULong x[1];
458 	};
459 
460  typedef struct Bigint Bigint;
461 
462 #ifdef NO_GLOBAL_STATE
463 #ifdef MULTIPLE_THREADS
464 #error "cannot have both NO_GLOBAL_STATE and MULTIPLE_THREADS"
465 #endif
466  struct
467 DtoaState {
468 #define DECLARE_GLOBAL_STATE  /* nothing */
469 #else
470 #define DECLARE_GLOBAL_STATE static
471 #endif
472 
473 	DECLARE_GLOBAL_STATE Bigint *freelist[Kmax+1];
474 	DECLARE_GLOBAL_STATE Bigint *p5s;
475 #ifndef Omit_Private_Memory
476 	DECLARE_GLOBAL_STATE double private_mem[PRIVATE_mem];
477 	DECLARE_GLOBAL_STATE double *pmem_next
478 #ifndef NO_GLOBAL_STATE
479 	                                       = private_mem
480 #endif
481 	                                                    ;
482 #endif
483 #ifdef NO_GLOBAL_STATE
484 	};
485  typedef struct DtoaState DtoaState;
486 #ifdef KR_headers
487 #define STATE_PARAM state,
488 #define STATE_PARAM_DECL DtoaState *state;
489 #else
490 #define STATE_PARAM DtoaState *state,
491 #endif
492 #define PASS_STATE state,
493 #define GET_STATE(field) (state->field)
494 
495  static DtoaState *
newdtoa(void)496 newdtoa(void)
497 {
498 	DtoaState *state = (DtoaState *) MALLOC(sizeof(DtoaState));
499 	if (state) {
500 		memset(state, 0, sizeof(DtoaState));
501 #ifndef Omit_Private_Memory
502 		state->pmem_next = state->private_mem;
503 #endif
504 		}
505 	return state;
506 }
507 
508  static void
destroydtoa(state)509 destroydtoa
510 #ifdef KR_headers
511 	(state) STATE_PARAM_DECL
512 #else
513 	(DtoaState *state)
514 #endif
515 {
516 	int i;
517 	Bigint *v, *next;
518 
519 	for (i = 0; i <= Kmax; i++) {
520 		for (v = GET_STATE(freelist)[i]; v; v = next) {
521 			next = v->next;
522 #ifndef Omit_Private_Memory
523 			if ((double*)v < GET_STATE(private_mem) ||
524 			    (double*)v >= GET_STATE(private_mem) + PRIVATE_mem)
525 #endif
526 				FREE((void*)v);
527 			}
528 		}
529 	FREE((void *)state);
530 }
531 
532 #else
533 #define STATE_PARAM      /* nothing */
534 #define STATE_PARAM_DECL /* nothing */
535 #define PASS_STATE       /* nothing */
536 #define GET_STATE(name) name
537 #endif
538 
539  static Bigint *
540 Balloc
541 #ifdef KR_headers
542 	(STATE_PARAM k) STATE_PARAM_DECL int k;
543 #else
544 	(STATE_PARAM int k)
545 #endif
546 {
547 	int x;
548 	Bigint *rv;
549 #ifndef Omit_Private_Memory
550 	size_t len;
551 #endif
552 
553 	ACQUIRE_DTOA_LOCK(0);
554 	/* The k > Kmax case does not need ACQUIRE_DTOA_LOCK(0), */
555 	/* but this case seems very unlikely. */
556 	if (k <= Kmax && (rv = GET_STATE(freelist)[k]))
557 		GET_STATE(freelist)[k] = rv->next;
558 	else {
559 		x = 1 << k;
560 #ifdef Omit_Private_Memory
561 		rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong));
562 #else
563 		len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)
564 			/sizeof(double);
565 		if (k <= Kmax && GET_STATE(pmem_next) - GET_STATE(private_mem) + len <= PRIVATE_mem) {
566 			rv = (Bigint*)GET_STATE(pmem_next);
567 			GET_STATE(pmem_next) += len;
568 			}
569 		else
570 			rv = (Bigint*)MALLOC(len*sizeof(double));
571 #endif
572 		rv->k = k;
573 		rv->maxwds = x;
574 		}
575 	FREE_DTOA_LOCK(0);
576 	rv->sign = rv->wds = 0;
577 	return rv;
578 	}
579 
580  static void
581 Bfree
582 #ifdef KR_headers
583 	(STATE_PARAM v) STATE_PARAM_DECL Bigint *v;
584 #else
585 	(STATE_PARAM Bigint *v)
586 #endif
587 {
588 	if (v) {
589 		if (v->k > Kmax)
590 			FREE((void*)v);
591 		else {
592 			ACQUIRE_DTOA_LOCK(0);
593 			v->next = GET_STATE(freelist)[v->k];
594 			GET_STATE(freelist)[v->k] = v;
595 			FREE_DTOA_LOCK(0);
596 			}
597 		}
598 	}
599 
600 #define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
601 y->wds*sizeof(Long) + 2*sizeof(int))
602 
603  static Bigint *
604 multadd
605 #ifdef KR_headers
606 	(STATE_PARAM b, m, a) STATE_PARAM_DECL Bigint *b; int m, a;
607 #else
608 	(STATE_PARAM Bigint *b, int m, int a)	/* multiply by m and add a */
609 #endif
610 {
611 	int i, wds;
612 #ifdef ULLong
613 	ULong *x;
614 	ULLong carry, y;
615 #else
616 	ULong carry, *x, y;
617 #ifdef Pack_32
618 	ULong xi, z;
619 #endif
620 #endif
621 	Bigint *b1;
622 
623 	wds = b->wds;
624 	x = b->x;
625 	i = 0;
626 	carry = a;
627 	do {
628 #ifdef ULLong
629 		y = *x * (ULLong)m + carry;
630 		carry = y >> 32;
631 		*x++ = (ULong) y & FFFFFFFF;
632 #else
633 #ifdef Pack_32
634 		xi = *x;
635 		y = (xi & 0xffff) * m + carry;
636 		z = (xi >> 16) * m + (y >> 16);
637 		carry = z >> 16;
638 		*x++ = (z << 16) + (y & 0xffff);
639 #else
640 		y = *x * m + carry;
641 		carry = y >> 16;
642 		*x++ = y & 0xffff;
643 #endif
644 #endif
645 		}
646 		while(++i < wds);
647 	if (carry) {
648 		if (wds >= b->maxwds) {
649 			b1 = Balloc(PASS_STATE b->k+1);
650 			Bcopy(b1, b);
651 			Bfree(PASS_STATE b);
652 			b = b1;
653 			}
654 		b->x[wds++] = (ULong) carry;
655 		b->wds = wds;
656 		}
657 	return b;
658 	}
659 
660  static Bigint *
661 s2b
662 #ifdef KR_headers
663 	(STATE_PARAM s, nd0, nd, y9) STATE_PARAM_DECL CONST char *s; int nd0, nd; ULong y9;
664 #else
665 	(STATE_PARAM CONST char *s, int nd0, int nd, ULong y9)
666 #endif
667 {
668 	Bigint *b;
669 	int i, k;
670 	Long x, y;
671 
672 	x = (nd + 8) / 9;
673 	for(k = 0, y = 1; x > y; y <<= 1, k++) ;
674 #ifdef Pack_32
675 	b = Balloc(PASS_STATE k);
676 	b->x[0] = y9;
677 	b->wds = 1;
678 #else
679 	b = Balloc(PASS_STATE k+1);
680 	b->x[0] = y9 & 0xffff;
681 	b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
682 #endif
683 
684 	i = 9;
685 	if (9 < nd0) {
686 		s += 9;
687 		do b = multadd(PASS_STATE b, 10, *s++ - '0');
688 			while(++i < nd0);
689 		s++;
690 		}
691 	else
692 		s += 10;
693 	for(; i < nd; i++)
694 		b = multadd(PASS_STATE b, 10, *s++ - '0');
695 	return b;
696 	}
697 
698  static int
hi0bits(x)699 hi0bits
700 #ifdef KR_headers
701 	(x) ULong x;
702 #else
703 	(ULong x)
704 #endif
705 {
706 	int k = 0;
707 
708 	if (!(x & 0xffff0000)) {
709 		k = 16;
710 		x <<= 16;
711 		}
712 	if (!(x & 0xff000000)) {
713 		k += 8;
714 		x <<= 8;
715 		}
716 	if (!(x & 0xf0000000)) {
717 		k += 4;
718 		x <<= 4;
719 		}
720 	if (!(x & 0xc0000000)) {
721 		k += 2;
722 		x <<= 2;
723 		}
724 	if (!(x & 0x80000000)) {
725 		k++;
726 		if (!(x & 0x40000000))
727 			return 32;
728 		}
729 	return k;
730 	}
731 
732  static int
lo0bits(y)733 lo0bits
734 #ifdef KR_headers
735 	(y) ULong *y;
736 #else
737 	(ULong *y)
738 #endif
739 {
740 	int k;
741 	ULong x = *y;
742 
743 	if (x & 7) {
744 		if (x & 1)
745 			return 0;
746 		if (x & 2) {
747 			*y = x >> 1;
748 			return 1;
749 			}
750 		*y = x >> 2;
751 		return 2;
752 		}
753 	k = 0;
754 	if (!(x & 0xffff)) {
755 		k = 16;
756 		x >>= 16;
757 		}
758 	if (!(x & 0xff)) {
759 		k += 8;
760 		x >>= 8;
761 		}
762 	if (!(x & 0xf)) {
763 		k += 4;
764 		x >>= 4;
765 		}
766 	if (!(x & 0x3)) {
767 		k += 2;
768 		x >>= 2;
769 		}
770 	if (!(x & 1)) {
771 		k++;
772 		x >>= 1;
773 		if (!x)
774 			return 32;
775 		}
776 	*y = x;
777 	return k;
778 	}
779 
780  static Bigint *
781 i2b
782 #ifdef KR_headers
783 	(STATE_PARAM i) STATE_PARAM_DECL int i;
784 #else
785 	(STATE_PARAM int i)
786 #endif
787 {
788 	Bigint *b;
789 
790 	b = Balloc(PASS_STATE 1);
791 	b->x[0] = i;
792 	b->wds = 1;
793 	return b;
794 	}
795 
796  static Bigint *
797 mult
798 #ifdef KR_headers
799 	(STATE_PARAM a, b) STATE_PARAM_DECL Bigint *a, *b;
800 #else
801 	(STATE_PARAM Bigint *a, Bigint *b)
802 #endif
803 {
804 	Bigint *c;
805 	int k, wa, wb, wc;
806 	ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
807 	ULong y;
808 #ifdef ULLong
809 	ULLong carry, z;
810 #else
811 	ULong carry, z;
812 #ifdef Pack_32
813 	ULong z2;
814 #endif
815 #endif
816 
817 	if (a->wds < b->wds) {
818 		c = a;
819 		a = b;
820 		b = c;
821 		}
822 	k = a->k;
823 	wa = a->wds;
824 	wb = b->wds;
825 	wc = wa + wb;
826 	if (wc > a->maxwds)
827 		k++;
828 	c = Balloc(PASS_STATE k);
829 	for(x = c->x, xa = x + wc; x < xa; x++)
830 		*x = 0;
831 	xa = a->x;
832 	xae = xa + wa;
833 	xb = b->x;
834 	xbe = xb + wb;
835 	xc0 = c->x;
836 #ifdef ULLong
837 	for(; xb < xbe; xc0++) {
838 		if ((y = *xb++)) {
839 			x = xa;
840 			xc = xc0;
841 			carry = 0;
842 			do {
843 				z = *x++ * (ULLong)y + *xc + carry;
844 				carry = z >> 32;
845 				*xc++ = (ULong) z & FFFFFFFF;
846 				}
847 				while(x < xae);
848 			*xc = (ULong) carry;
849 			}
850 		}
851 #else
852 #ifdef Pack_32
853 	for(; xb < xbe; xb++, xc0++) {
854 		if (y = *xb & 0xffff) {
855 			x = xa;
856 			xc = xc0;
857 			carry = 0;
858 			do {
859 				z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
860 				carry = z >> 16;
861 				z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
862 				carry = z2 >> 16;
863 				Storeinc(xc, z2, z);
864 				}
865 				while(x < xae);
866 			*xc = carry;
867 			}
868 		if (y = *xb >> 16) {
869 			x = xa;
870 			xc = xc0;
871 			carry = 0;
872 			z2 = *xc;
873 			do {
874 				z = (*x & 0xffff) * y + (*xc >> 16) + carry;
875 				carry = z >> 16;
876 				Storeinc(xc, z, z2);
877 				z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
878 				carry = z2 >> 16;
879 				}
880 				while(x < xae);
881 			*xc = z2;
882 			}
883 		}
884 #else
885 	for(; xb < xbe; xc0++) {
886 		if (y = *xb++) {
887 			x = xa;
888 			xc = xc0;
889 			carry = 0;
890 			do {
891 				z = *x++ * y + *xc + carry;
892 				carry = z >> 16;
893 				*xc++ = z & 0xffff;
894 				}
895 				while(x < xae);
896 			*xc = carry;
897 			}
898 		}
899 #endif
900 #endif
901 	for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
902 	c->wds = wc;
903 	return c;
904 	}
905 
906  static Bigint *
907 pow5mult
908 #ifdef KR_headers
909 	(STATE_PARAM b, k) STATE_PARAM_DECL Bigint *b; int k;
910 #else
911 	(STATE_PARAM Bigint *b, int k)
912 #endif
913 {
914 	Bigint *b1, *p5, *p51;
915 	int i;
916 	static CONST int p05[3] = { 5, 25, 125 };
917 
918 	if ((i = k & 3))
919 		b = multadd(PASS_STATE b, p05[i-1], 0);
920 
921 	if (!(k >>= 2))
922 		return b;
923 	if (!(p5 = GET_STATE(p5s))) {
924 		/* first time */
925 #ifdef MULTIPLE_THREADS
926 		ACQUIRE_DTOA_LOCK(1);
927 		if (!(p5 = p5s)) {
928 			p5 = p5s = i2b(625);
929 			p5->next = 0;
930 			}
931 		FREE_DTOA_LOCK(1);
932 #else
933 		p5 = GET_STATE(p5s) = i2b(PASS_STATE 625);
934 		p5->next = 0;
935 #endif
936 		}
937 	for(;;) {
938 		if (k & 1) {
939 			b1 = mult(PASS_STATE b, p5);
940 			Bfree(PASS_STATE b);
941 			b = b1;
942 			}
943 		if (!(k >>= 1))
944 			break;
945 		if (!(p51 = p5->next)) {
946 #ifdef MULTIPLE_THREADS
947 			ACQUIRE_DTOA_LOCK(1);
948 			if (!(p51 = p5->next)) {
949 				p51 = p5->next = mult(p5,p5);
950 				p51->next = 0;
951 				}
952 			FREE_DTOA_LOCK(1);
953 #else
954 			p51 = p5->next = mult(PASS_STATE p5,p5);
955 			p51->next = 0;
956 #endif
957 			}
958 		p5 = p51;
959 		}
960 	return b;
961 	}
962 
963  static Bigint *
964 lshift
965 #ifdef KR_headers
966 	(STATE_PARAM b, k) STATE_PARAM_DECL Bigint *b; int k;
967 #else
968 	(STATE_PARAM Bigint *b, int k)
969 #endif
970 {
971 	int i, k1, n, n1;
972 	Bigint *b1;
973 	ULong *x, *x1, *xe, z;
974 
975 #ifdef Pack_32
976 	n = k >> 5;
977 #else
978 	n = k >> 4;
979 #endif
980 	k1 = b->k;
981 	n1 = n + b->wds + 1;
982 	for(i = b->maxwds; n1 > i; i <<= 1)
983 		k1++;
984 	b1 = Balloc(PASS_STATE k1);
985 	x1 = b1->x;
986 	for(i = 0; i < n; i++)
987 		*x1++ = 0;
988 	x = b->x;
989 	xe = x + b->wds;
990 #ifdef Pack_32
991 	if (k &= 0x1f) {
992 		k1 = 32 - k;
993 		z = 0;
994 		do {
995 			*x1++ = *x << k | z;
996 			z = *x++ >> k1;
997 			}
998 			while(x < xe);
999 		if ((*x1 = z))
1000 			++n1;
1001 		}
1002 #else
1003 	if (k &= 0xf) {
1004 		k1 = 16 - k;
1005 		z = 0;
1006 		do {
1007 			*x1++ = *x << k  & 0xffff | z;
1008 			z = *x++ >> k1;
1009 			}
1010 			while(x < xe);
1011 		if (*x1 = z)
1012 			++n1;
1013 		}
1014 #endif
1015 	else do
1016 		*x1++ = *x++;
1017 		while(x < xe);
1018 	b1->wds = n1 - 1;
1019 	Bfree(PASS_STATE b);
1020 	return b1;
1021 	}
1022 
1023  static int
cmp(a,b)1024 cmp
1025 #ifdef KR_headers
1026 	(a, b) Bigint *a, *b;
1027 #else
1028 	(Bigint *a, Bigint *b)
1029 #endif
1030 {
1031 	ULong *xa, *xa0, *xb, *xb0;
1032 	int i, j;
1033 
1034 	i = a->wds;
1035 	j = b->wds;
1036 #ifdef DEBUG
1037 	if (i > 1 && !a->x[i-1])
1038 		Bug("cmp called with a->x[a->wds-1] == 0");
1039 	if (j > 1 && !b->x[j-1])
1040 		Bug("cmp called with b->x[b->wds-1] == 0");
1041 #endif
1042 	if (i -= j)
1043 		return i;
1044 	xa0 = a->x;
1045 	xa = xa0 + j;
1046 	xb0 = b->x;
1047 	xb = xb0 + j;
1048 	for(;;) {
1049 		if (*--xa != *--xb)
1050 			return *xa < *xb ? -1 : 1;
1051 		if (xa <= xa0)
1052 			break;
1053 		}
1054 	return 0;
1055 	}
1056 
1057  static Bigint *
1058 diff
1059 #ifdef KR_headers
1060 	(STATE_PARAM a, b) STATE_PARAM_DECL Bigint *a, *b;
1061 #else
1062 	(STATE_PARAM Bigint *a, Bigint *b)
1063 #endif
1064 {
1065 	Bigint *c;
1066 	int i, wa, wb;
1067 	ULong *xa, *xae, *xb, *xbe, *xc;
1068 #ifdef ULLong
1069 	ULLong borrow, y;
1070 #else
1071 	ULong borrow, y;
1072 #ifdef Pack_32
1073 	ULong z;
1074 #endif
1075 #endif
1076 
1077 	i = cmp(a,b);
1078 	if (!i) {
1079 		c = Balloc(PASS_STATE 0);
1080 		c->wds = 1;
1081 		c->x[0] = 0;
1082 		return c;
1083 		}
1084 	if (i < 0) {
1085 		c = a;
1086 		a = b;
1087 		b = c;
1088 		i = 1;
1089 		}
1090 	else
1091 		i = 0;
1092 	c = Balloc(PASS_STATE a->k);
1093 	c->sign = i;
1094 	wa = a->wds;
1095 	xa = a->x;
1096 	xae = xa + wa;
1097 	wb = b->wds;
1098 	xb = b->x;
1099 	xbe = xb + wb;
1100 	xc = c->x;
1101 	borrow = 0;
1102 #ifdef ULLong
1103 	do {
1104 		y = (ULLong)*xa++ - *xb++ - borrow;
1105 		borrow = y >> 32 & (ULong)1;
1106 		*xc++ = (ULong) y & FFFFFFFF;
1107 		}
1108 		while(xb < xbe);
1109 	while(xa < xae) {
1110 		y = *xa++ - borrow;
1111 		borrow = y >> 32 & (ULong)1;
1112 		*xc++ = (ULong) y & FFFFFFFF;
1113 		}
1114 #else
1115 #ifdef Pack_32
1116 	do {
1117 		y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
1118 		borrow = (y & 0x10000) >> 16;
1119 		z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
1120 		borrow = (z & 0x10000) >> 16;
1121 		Storeinc(xc, z, y);
1122 		}
1123 		while(xb < xbe);
1124 	while(xa < xae) {
1125 		y = (*xa & 0xffff) - borrow;
1126 		borrow = (y & 0x10000) >> 16;
1127 		z = (*xa++ >> 16) - borrow;
1128 		borrow = (z & 0x10000) >> 16;
1129 		Storeinc(xc, z, y);
1130 		}
1131 #else
1132 	do {
1133 		y = *xa++ - *xb++ - borrow;
1134 		borrow = (y & 0x10000) >> 16;
1135 		*xc++ = y & 0xffff;
1136 		}
1137 		while(xb < xbe);
1138 	while(xa < xae) {
1139 		y = *xa++ - borrow;
1140 		borrow = (y & 0x10000) >> 16;
1141 		*xc++ = y & 0xffff;
1142 		}
1143 #endif
1144 #endif
1145 	while(!*--xc)
1146 		wa--;
1147 	c->wds = wa;
1148 	return c;
1149 	}
1150 
1151  static double
ulp(x)1152 ulp
1153 #ifdef KR_headers
1154 	(x) U x;
1155 #else
1156 	(U x)
1157 #endif
1158 {
1159 	Long L;
1160 	U a;
1161 
1162 	L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
1163 #ifndef Avoid_Underflow
1164 #ifndef Sudden_Underflow
1165 	if (L > 0) {
1166 #endif
1167 #endif
1168 #ifdef IBM
1169 		L |= Exp_msk1 >> 4;
1170 #endif
1171 		word0(a) = L;
1172 		word1(a) = 0;
1173 #ifndef Avoid_Underflow
1174 #ifndef Sudden_Underflow
1175 		}
1176 	else {
1177 		L = -L >> Exp_shift;
1178 		if (L < Exp_shift) {
1179 			word0(a) = 0x80000 >> L;
1180 			word1(a) = 0;
1181 			}
1182 		else {
1183 			word0(a) = 0;
1184 			L -= Exp_shift;
1185 			word1(a) = L >= 31 ? 1 : 1 << 31 - L;
1186 			}
1187 		}
1188 #endif
1189 #endif
1190 	return dval(a);
1191 	}
1192 
1193  static double
b2d(a,e)1194 b2d
1195 #ifdef KR_headers
1196 	(a, e) Bigint *a; int *e;
1197 #else
1198 	(Bigint *a, int *e)
1199 #endif
1200 {
1201 	ULong *xa, *xa0, w, y, z;
1202 	int k;
1203 	U d;
1204 #ifdef VAX
1205 	ULong d0, d1;
1206 #else
1207 #define d0 word0(d)
1208 #define d1 word1(d)
1209 #endif
1210 
1211 	xa0 = a->x;
1212 	xa = xa0 + a->wds;
1213 	y = *--xa;
1214 #ifdef DEBUG
1215 	if (!y) Bug("zero y in b2d");
1216 #endif
1217 	k = hi0bits(y);
1218 	*e = 32 - k;
1219 #ifdef Pack_32
1220 	if (k < Ebits) {
1221 		d0 = Exp_1 | y >> (Ebits - k);
1222 		w = xa > xa0 ? *--xa : 0;
1223 		d1 = y << ((32-Ebits) + k) | w >> (Ebits - k);
1224 		goto ret_d;
1225 		}
1226 	z = xa > xa0 ? *--xa : 0;
1227 	if (k -= Ebits) {
1228 		d0 = Exp_1 | y << k | z >> (32 - k);
1229 		y = xa > xa0 ? *--xa : 0;
1230 		d1 = z << k | y >> (32 - k);
1231 		}
1232 	else {
1233 		d0 = Exp_1 | y;
1234 		d1 = z;
1235 		}
1236 #else
1237 	if (k < Ebits + 16) {
1238 		z = xa > xa0 ? *--xa : 0;
1239 		d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
1240 		w = xa > xa0 ? *--xa : 0;
1241 		y = xa > xa0 ? *--xa : 0;
1242 		d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
1243 		goto ret_d;
1244 		}
1245 	z = xa > xa0 ? *--xa : 0;
1246 	w = xa > xa0 ? *--xa : 0;
1247 	k -= Ebits + 16;
1248 	d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
1249 	y = xa > xa0 ? *--xa : 0;
1250 	d1 = w << k + 16 | y << k;
1251 #endif
1252  ret_d:
1253 #ifdef VAX
1254 	word0(d) = d0 >> 16 | d0 << 16;
1255 	word1(d) = d1 >> 16 | d1 << 16;
1256 #else
1257 #undef d0
1258 #undef d1
1259 #endif
1260 	return dval(d);
1261 	}
1262 
1263  static Bigint *
1264 d2b
1265 #ifdef KR_headers
1266 	(STATE_PARAM d, e, bits) STATE_PARAM_DECL U d; int *e, *bits;
1267 #else
1268 	(STATE_PARAM U d, int *e, int *bits)
1269 #endif
1270 {
1271 	Bigint *b;
1272 	int de, k;
1273 	ULong *x, y, z;
1274 #ifndef Sudden_Underflow
1275 	int i;
1276 #endif
1277 #ifdef VAX
1278 	ULong d0, d1;
1279 	d0 = word0(d) >> 16 | word0(d) << 16;
1280 	d1 = word1(d) >> 16 | word1(d) << 16;
1281 #else
1282 #define d0 word0(d)
1283 #define d1 word1(d)
1284 #endif
1285 
1286 #ifdef Pack_32
1287 	b = Balloc(PASS_STATE 1);
1288 #else
1289 	b = Balloc(PASS_STATE 2);
1290 #endif
1291 	x = b->x;
1292 
1293 	z = d0 & Frac_mask;
1294 	d0 &= 0x7fffffff;	/* clear sign bit, which we ignore */
1295 #ifdef Sudden_Underflow
1296 	de = (int)(d0 >> Exp_shift);
1297 #ifndef IBM
1298 	z |= Exp_msk11;
1299 #endif
1300 #else
1301 	if ((de = (int)(d0 >> Exp_shift)))
1302 		z |= Exp_msk1;
1303 #endif
1304 #ifdef Pack_32
1305 	if ((y = d1)) {
1306 		if ((k = lo0bits(&y))) {
1307 			x[0] = y | z << (32 - k);
1308 			z >>= k;
1309 			}
1310 		else
1311 			x[0] = y;
1312 #ifndef Sudden_Underflow
1313 		i =
1314 #endif
1315 		    b->wds = (x[1] = z) ? 2 : 1;
1316 		}
1317 	else {
1318 		k = lo0bits(&z);
1319 		x[0] = z;
1320 #ifndef Sudden_Underflow
1321 		i =
1322 #endif
1323 		    b->wds = 1;
1324 		k += 32;
1325 		}
1326 #else
1327 	if (y = d1) {
1328 		if (k = lo0bits(&y))
1329 			if (k >= 16) {
1330 				x[0] = y | z << 32 - k & 0xffff;
1331 				x[1] = z >> k - 16 & 0xffff;
1332 				x[2] = z >> k;
1333 				i = 2;
1334 				}
1335 			else {
1336 				x[0] = y & 0xffff;
1337 				x[1] = y >> 16 | z << 16 - k & 0xffff;
1338 				x[2] = z >> k & 0xffff;
1339 				x[3] = z >> k+16;
1340 				i = 3;
1341 				}
1342 		else {
1343 			x[0] = y & 0xffff;
1344 			x[1] = y >> 16;
1345 			x[2] = z & 0xffff;
1346 			x[3] = z >> 16;
1347 			i = 3;
1348 			}
1349 		}
1350 	else {
1351 #ifdef DEBUG
1352 		if (!z)
1353 			Bug("Zero passed to d2b");
1354 #endif
1355 		k = lo0bits(&z);
1356 		if (k >= 16) {
1357 			x[0] = z;
1358 			i = 0;
1359 			}
1360 		else {
1361 			x[0] = z & 0xffff;
1362 			x[1] = z >> 16;
1363 			i = 1;
1364 			}
1365 		k += 32;
1366 		}
1367 	while(!x[i])
1368 		--i;
1369 	b->wds = i + 1;
1370 #endif
1371 #ifndef Sudden_Underflow
1372 	if (de) {
1373 #endif
1374 #ifdef IBM
1375 		*e = (de - Bias - (P-1) << 2) + k;
1376 		*bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
1377 #else
1378 		*e = de - Bias - (P-1) + k;
1379 		*bits = P - k;
1380 #endif
1381 #ifndef Sudden_Underflow
1382 		}
1383 	else {
1384 		*e = de - Bias - (P-1) + 1 + k;
1385 #ifdef Pack_32
1386 		*bits = 32*i - hi0bits(x[i-1]);
1387 #else
1388 		*bits = (i+2)*16 - hi0bits(x[i]);
1389 #endif
1390 		}
1391 #endif
1392 	return b;
1393 	}
1394 #undef d0
1395 #undef d1
1396 
1397  static double
ratio(a,b)1398 ratio
1399 #ifdef KR_headers
1400 	(a, b) Bigint *a, *b;
1401 #else
1402 	(Bigint *a, Bigint *b)
1403 #endif
1404 {
1405 	U da, db;
1406 	int k, ka, kb;
1407 
1408 	dval(da) = b2d(a, &ka);
1409 	dval(db) = b2d(b, &kb);
1410 #ifdef Pack_32
1411 	k = ka - kb + 32*(a->wds - b->wds);
1412 #else
1413 	k = ka - kb + 16*(a->wds - b->wds);
1414 #endif
1415 #ifdef IBM
1416 	if (k > 0) {
1417 		word0(da) += (k >> 2)*Exp_msk1;
1418 		if (k &= 3)
1419 			dval(da) *= 1 << k;
1420 		}
1421 	else {
1422 		k = -k;
1423 		word0(db) += (k >> 2)*Exp_msk1;
1424 		if (k &= 3)
1425 			dval(db) *= 1 << k;
1426 		}
1427 #else
1428 	if (k > 0)
1429 		word0(da) += k*Exp_msk1;
1430 	else {
1431 		k = -k;
1432 		word0(db) += k*Exp_msk1;
1433 		}
1434 #endif
1435 	return dval(da) / dval(db);
1436 	}
1437 
1438  static CONST double
1439 tens[] = {
1440 		1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1441 		1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
1442 		1e20, 1e21, 1e22
1443 #ifdef VAX
1444 		, 1e23, 1e24
1445 #endif
1446 		};
1447 
1448  static CONST double
1449 #ifdef IEEE_Arith
1450 bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
1451 static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
1452 #ifdef Avoid_Underflow
1453 		9007199254740992.*9007199254740992.e-256
1454 		/* = 2^106 * 1e-53 */
1455 #else
1456 		1e-256
1457 #endif
1458 		};
1459 /* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
1460 /* flag unnecessarily.  It leads to a song and dance at the end of strtod. */
1461 #define Scale_Bit 0x10
1462 #define n_bigtens 5
1463 #else
1464 #ifdef IBM
1465 bigtens[] = { 1e16, 1e32, 1e64 };
1466 static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 };
1467 #define n_bigtens 3
1468 #else
1469 bigtens[] = { 1e16, 1e32 };
1470 static CONST double tinytens[] = { 1e-16, 1e-32 };
1471 #define n_bigtens 2
1472 #endif
1473 #endif
1474 
1475  static double
1476 _strtod
1477 #ifdef KR_headers
1478 	(STATE_PARAM s00, se) STATE_PARAM_DECL CONST char *s00; char **se;
1479 #else
1480 	(STATE_PARAM CONST char *s00, char **se)
1481 #endif
1482 {
1483 #ifdef Avoid_Underflow
1484 	int scale;
1485 #endif
1486 	int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
1487 		 e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
1488 	CONST char *s, *s0, *s1;
1489 	double aadj, adj;
1490 	U aadj1, rv, rv0;
1491 	Long L;
1492 	ULong y, z;
1493 	Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
1494 #ifdef SET_INEXACT
1495 	int inexact, oldinexact;
1496 #endif
1497 #ifdef Honor_FLT_ROUNDS
1498 	int rounding;
1499 #endif
1500 #ifdef USE_LOCALE
1501 	CONST char *s2;
1502 #endif
1503 
1504 #ifdef __GNUC__
1505 	delta = bb = bd = bs = 0;
1506 #endif
1507 
1508 	sign = nz0 = nz = 0;
1509 	dval(rv) = 0.;
1510 	for(s = s00;;s++) switch(*s) {
1511 		case '-':
1512 			sign = 1;
1513 			/* no break */
1514 		case '+':
1515 			if (*++s)
1516 				goto break2;
1517 			/* no break */
1518 		case 0:
1519 			goto ret0;
1520 		case '\t':
1521 		case '\n':
1522 		case '\v':
1523 		case '\f':
1524 		case '\r':
1525 		case ' ':
1526 			continue;
1527 		default:
1528 			goto break2;
1529 		}
1530  break2:
1531 	if (*s == '0') {
1532 		nz0 = 1;
1533 		while(*++s == '0') ;
1534 		if (!*s)
1535 			goto ret;
1536 		}
1537 	s0 = s;
1538 	y = z = 0;
1539 	for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
1540 		if (nd < 9)
1541 			y = 10*y + c - '0';
1542 		else if (nd < 16)
1543 			z = 10*z + c - '0';
1544 	nd0 = nd;
1545 #ifdef USE_LOCALE
1546 	s1 = localeconv()->decimal_point;
1547 	if (c == *s1) {
1548 		c = '.';
1549 		if (*++s1) {
1550 			s2 = s;
1551 			for(;;) {
1552 				if (*++s2 != *s1) {
1553 					c = 0;
1554 					break;
1555 					}
1556 				if (!*++s1) {
1557 					s = s2;
1558 					break;
1559 					}
1560 				}
1561 			}
1562 		}
1563 #endif
1564 	if (c == '.') {
1565 		c = *++s;
1566 		if (!nd) {
1567 			for(; c == '0'; c = *++s)
1568 				nz++;
1569 			if (c > '0' && c <= '9') {
1570 				s0 = s;
1571 				nf += nz;
1572 				nz = 0;
1573 				goto have_dig;
1574 				}
1575 			goto dig_done;
1576 			}
1577 		for(; c >= '0' && c <= '9'; c = *++s) {
1578  have_dig:
1579 			nz++;
1580 			if (c -= '0') {
1581 				nf += nz;
1582 				for(i = 1; i < nz; i++)
1583 					if (nd++ < 9)
1584 						y *= 10;
1585 					else if (nd <= DBL_DIG + 1)
1586 						z *= 10;
1587 				if (nd++ < 9)
1588 					y = 10*y + c;
1589 				else if (nd <= DBL_DIG + 1)
1590 					z = 10*z + c;
1591 				nz = 0;
1592 				}
1593 			}
1594 		}
1595  dig_done:
1596 	e = 0;
1597 	if (c == 'e' || c == 'E') {
1598 		if (!nd && !nz && !nz0) {
1599 			goto ret0;
1600 			}
1601 		s00 = s;
1602 		esign = 0;
1603 		switch(c = *++s) {
1604 			case '-':
1605 				esign = 1;
1606 			case '+':
1607 				c = *++s;
1608 			}
1609 		if (c >= '0' && c <= '9') {
1610 			while(c == '0')
1611 				c = *++s;
1612 			if (c > '0' && c <= '9') {
1613 				L = c - '0';
1614 				s1 = s;
1615 				while((c = *++s) >= '0' && c <= '9')
1616 					L = 10*L + c - '0';
1617 				if (s - s1 > 8 || L > 19999)
1618 					/* Avoid confusion from exponents
1619 					 * so large that e might overflow.
1620 					 */
1621 					e = 19999; /* safe for 16 bit ints */
1622 				else
1623 					e = (int)L;
1624 				if (esign)
1625 					e = -e;
1626 				}
1627 			else
1628 				e = 0;
1629 			}
1630 		else
1631 			s = s00;
1632 		}
1633 	if (!nd) {
1634 		if (!nz && !nz0) {
1635  ret0:
1636 			s = s00;
1637 			sign = 0;
1638 			}
1639 		goto ret;
1640 		}
1641 	e1 = e -= nf;
1642 
1643 	/* Now we have nd0 digits, starting at s0, followed by a
1644 	 * decimal point, followed by nd-nd0 digits.  The number we're
1645 	 * after is the integer represented by those digits times
1646 	 * 10**e */
1647 
1648 	if (!nd0)
1649 		nd0 = nd;
1650 	k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
1651 	dval(rv) = y;
1652 	if (k > 9) {
1653 #ifdef SET_INEXACT
1654 		if (k > DBL_DIG)
1655 			oldinexact = get_inexact();
1656 #endif
1657 		dval(rv) = tens[k - 9] * dval(rv) + z;
1658 		}
1659 	bd0 = 0;
1660 	if (nd <= DBL_DIG
1661 #ifndef RND_PRODQUOT
1662 #ifndef Honor_FLT_ROUNDS
1663 		&& Flt_Rounds == 1
1664 #endif
1665 #endif
1666 			) {
1667 		if (!e)
1668 			goto ret;
1669 		if (e > 0) {
1670 			if (e <= Ten_pmax) {
1671 #ifdef VAX
1672 				goto vax_ovfl_check;
1673 #else
1674 #ifdef Honor_FLT_ROUNDS
1675 				/* round correctly FLT_ROUNDS = 2 or 3 */
1676 				if (sign) {
1677 					rv = -rv;
1678 					sign = 0;
1679 					}
1680 #endif
1681 				/* rv = */ rounded_product(dval(rv), tens[e]);
1682 				goto ret;
1683 #endif
1684 				}
1685 			i = DBL_DIG - nd;
1686 			if (e <= Ten_pmax + i) {
1687 				/* A fancier test would sometimes let us do
1688 				 * this for larger i values.
1689 				 */
1690 #ifdef Honor_FLT_ROUNDS
1691 				/* round correctly FLT_ROUNDS = 2 or 3 */
1692 				if (sign) {
1693 					rv = -rv;
1694 					sign = 0;
1695 					}
1696 #endif
1697 				e -= i;
1698 				dval(rv) *= tens[i];
1699 #ifdef VAX
1700 				/* VAX exponent range is so narrow we must
1701 				 * worry about overflow here...
1702 				 */
1703  vax_ovfl_check:
1704 				word0(rv) -= P*Exp_msk1;
1705 				/* rv = */ rounded_product(dval(rv), tens[e]);
1706 				if ((word0(rv) & Exp_mask)
1707 				 > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
1708 					goto ovfl;
1709 				word0(rv) += P*Exp_msk1;
1710 #else
1711 				/* rv = */ rounded_product(dval(rv), tens[e]);
1712 #endif
1713 				goto ret;
1714 				}
1715 			}
1716 #ifndef Inaccurate_Divide
1717 		else if (e >= -Ten_pmax) {
1718 #ifdef Honor_FLT_ROUNDS
1719 			/* round correctly FLT_ROUNDS = 2 or 3 */
1720 			if (sign) {
1721 				rv = -rv;
1722 				sign = 0;
1723 				}
1724 #endif
1725 			/* rv = */ rounded_quotient(dval(rv), tens[-e]);
1726 			goto ret;
1727 			}
1728 #endif
1729 		}
1730 	e1 += nd - k;
1731 
1732 #ifdef IEEE_Arith
1733 #ifdef SET_INEXACT
1734 	inexact = 1;
1735 	if (k <= DBL_DIG)
1736 		oldinexact = get_inexact();
1737 #endif
1738 #ifdef Avoid_Underflow
1739 	scale = 0;
1740 #endif
1741 #ifdef Honor_FLT_ROUNDS
1742 	if ((rounding = Flt_Rounds) >= 2) {
1743 		if (sign)
1744 			rounding = rounding == 2 ? 0 : 2;
1745 		else
1746 			if (rounding != 2)
1747 				rounding = 0;
1748 		}
1749 #endif
1750 #endif /*IEEE_Arith*/
1751 
1752 	/* Get starting approximation = rv * 10**e1 */
1753 
1754 	if (e1 > 0) {
1755 		if ((i = e1 & 15))
1756 			dval(rv) *= tens[i];
1757 		if (e1 &= ~15) {
1758 			if (e1 > DBL_MAX_10_EXP) {
1759  ovfl:
1760 #ifndef NO_ERRNO
1761 				errno = ERANGE;
1762 #endif
1763 				/* Can't trust HUGE_VAL */
1764 #ifdef IEEE_Arith
1765 #ifdef Honor_FLT_ROUNDS
1766 				switch(rounding) {
1767 				  case 0: /* toward 0 */
1768 				  case 3: /* toward -infinity */
1769 					word0(rv) = Big0;
1770 					word1(rv) = Big1;
1771 					break;
1772 				  default:
1773 					word0(rv) = Exp_mask;
1774 					word1(rv) = 0;
1775 				  }
1776 #else /*Honor_FLT_ROUNDS*/
1777 				word0(rv) = Exp_mask;
1778 				word1(rv) = 0;
1779 #endif /*Honor_FLT_ROUNDS*/
1780 #ifdef SET_INEXACT
1781 				/* set overflow bit */
1782 				dval(rv0) = 1e300;
1783 				dval(rv0) *= dval(rv0);
1784 #endif
1785 #else /*IEEE_Arith*/
1786 				word0(rv) = Big0;
1787 				word1(rv) = Big1;
1788 #endif /*IEEE_Arith*/
1789 				if (bd0)
1790 					goto retfree;
1791 				goto ret;
1792 				}
1793 			e1 >>= 4;
1794 			for(j = 0; e1 > 1; j++, e1 >>= 1)
1795 				if (e1 & 1)
1796 					dval(rv) *= bigtens[j];
1797 		/* The last multiplication could overflow. */
1798 			word0(rv) -= P*Exp_msk1;
1799 			dval(rv) *= bigtens[j];
1800 			if ((z = word0(rv) & Exp_mask)
1801 			 > Exp_msk1*(DBL_MAX_EXP+Bias-P))
1802 				goto ovfl;
1803 			if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
1804 				/* set to largest number */
1805 				/* (Can't trust DBL_MAX) */
1806 				word0(rv) = Big0;
1807 				word1(rv) = Big1;
1808 				}
1809 			else
1810 				word0(rv) += P*Exp_msk1;
1811 			}
1812 		}
1813 	else if (e1 < 0) {
1814 		e1 = -e1;
1815 		if ((i = e1 & 15))
1816 			dval(rv) /= tens[i];
1817 		if (e1 >>= 4) {
1818 			if (e1 >= 1 << n_bigtens)
1819 				goto undfl;
1820 #ifdef Avoid_Underflow
1821 			if (e1 & Scale_Bit)
1822 				scale = 2*P;
1823 			for(j = 0; e1 > 0; j++, e1 >>= 1)
1824 				if (e1 & 1)
1825 					dval(rv) *= tinytens[j];
1826 			if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask)
1827 						>> Exp_shift)) > 0) {
1828 				/* scaled rv is denormal; zap j low bits */
1829 				if (j >= 32) {
1830 					word1(rv) = 0;
1831 					if (j >= 53)
1832 					 word0(rv) = (P+2)*Exp_msk1;
1833 					else
1834 					 word0(rv) &= 0xffffffff << (j-32);
1835 					}
1836 				else
1837 					word1(rv) &= 0xffffffff << j;
1838 				}
1839 #else
1840 			for(j = 0; e1 > 1; j++, e1 >>= 1)
1841 				if (e1 & 1)
1842 					dval(rv) *= tinytens[j];
1843 			/* The last multiplication could underflow. */
1844 			dval(rv0) = dval(rv);
1845 			dval(rv) *= tinytens[j];
1846 			if (!dval(rv)) {
1847 				dval(rv) = 2.*dval(rv0);
1848 				dval(rv) *= tinytens[j];
1849 #endif
1850 				if (!dval(rv)) {
1851  undfl:
1852 					dval(rv) = 0.;
1853 #ifndef NO_ERRNO
1854 					errno = ERANGE;
1855 #endif
1856 					if (bd0)
1857 						goto retfree;
1858 					goto ret;
1859 					}
1860 #ifndef Avoid_Underflow
1861 				word0(rv) = Tiny0;
1862 				word1(rv) = Tiny1;
1863 				/* The refinement below will clean
1864 				 * this approximation up.
1865 				 */
1866 				}
1867 #endif
1868 			}
1869 		}
1870 
1871 	/* Now the hard part -- adjusting rv to the correct value.*/
1872 
1873 	/* Put digits into bd: true value = bd * 10^e */
1874 
1875 	bd0 = s2b(PASS_STATE s0, nd0, nd, y);
1876 
1877 	for(;;) {
1878 		bd = Balloc(PASS_STATE bd0->k);
1879 		Bcopy(bd, bd0);
1880 		bb = d2b(PASS_STATE rv, &bbe, &bbbits);	/* rv = bb * 2^bbe */
1881 		bs = i2b(PASS_STATE 1);
1882 
1883 		if (e >= 0) {
1884 			bb2 = bb5 = 0;
1885 			bd2 = bd5 = e;
1886 			}
1887 		else {
1888 			bb2 = bb5 = -e;
1889 			bd2 = bd5 = 0;
1890 			}
1891 		if (bbe >= 0)
1892 			bb2 += bbe;
1893 		else
1894 			bd2 -= bbe;
1895 		bs2 = bb2;
1896 #ifdef Honor_FLT_ROUNDS
1897 		if (rounding != 1)
1898 			bs2++;
1899 #endif
1900 #ifdef Avoid_Underflow
1901 		j = bbe - scale;
1902 		i = j + bbbits - 1;	/* logb(rv) */
1903 		if (i < Emin)	/* denormal */
1904 			j += P - Emin;
1905 		else
1906 			j = P + 1 - bbbits;
1907 #else /*Avoid_Underflow*/
1908 #ifdef Sudden_Underflow
1909 #ifdef IBM
1910 		j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
1911 #else
1912 		j = P + 1 - bbbits;
1913 #endif
1914 #else /*Sudden_Underflow*/
1915 		j = bbe;
1916 		i = j + bbbits - 1;	/* logb(rv) */
1917 		if (i < Emin)	/* denormal */
1918 			j += P - Emin;
1919 		else
1920 			j = P + 1 - bbbits;
1921 #endif /*Sudden_Underflow*/
1922 #endif /*Avoid_Underflow*/
1923 		bb2 += j;
1924 		bd2 += j;
1925 #ifdef Avoid_Underflow
1926 		bd2 += scale;
1927 #endif
1928 		i = bb2 < bd2 ? bb2 : bd2;
1929 		if (i > bs2)
1930 			i = bs2;
1931 		if (i > 0) {
1932 			bb2 -= i;
1933 			bd2 -= i;
1934 			bs2 -= i;
1935 			}
1936 		if (bb5 > 0) {
1937 			bs = pow5mult(PASS_STATE bs, bb5);
1938 			bb1 = mult(PASS_STATE bs, bb);
1939 			Bfree(PASS_STATE bb);
1940 			bb = bb1;
1941 			}
1942 		if (bb2 > 0)
1943 			bb = lshift(PASS_STATE bb, bb2);
1944 		if (bd5 > 0)
1945 			bd = pow5mult(PASS_STATE bd, bd5);
1946 		if (bd2 > 0)
1947 			bd = lshift(PASS_STATE bd, bd2);
1948 		if (bs2 > 0)
1949 			bs = lshift(PASS_STATE bs, bs2);
1950 		delta = diff(PASS_STATE bb, bd);
1951 		dsign = delta->sign;
1952 		delta->sign = 0;
1953 		i = cmp(delta, bs);
1954 #ifdef Honor_FLT_ROUNDS
1955 		if (rounding != 1) {
1956 			if (i < 0) {
1957 				/* Error is less than an ulp */
1958 				if (!delta->x[0] && delta->wds <= 1) {
1959 					/* exact */
1960 #ifdef SET_INEXACT
1961 					inexact = 0;
1962 #endif
1963 					break;
1964 					}
1965 				if (rounding) {
1966 					if (dsign) {
1967 						adj = 1.;
1968 						goto apply_adj;
1969 						}
1970 					}
1971 				else if (!dsign) {
1972 					adj = -1.;
1973 					if (!word1(rv)
1974 					 && !(word0(rv) & Frac_mask)) {
1975 						y = word0(rv) & Exp_mask;
1976 #ifdef Avoid_Underflow
1977 						if (!scale || y > 2*P*Exp_msk1)
1978 #else
1979 						if (y)
1980 #endif
1981 						  {
1982 						  delta = lshift(PASS_STATE delta,Log2P);
1983 						  if (cmp(delta, bs) <= 0)
1984 							adj = -0.5;
1985 						  }
1986 						}
1987  apply_adj:
1988 #ifdef Avoid_Underflow
1989 					if (scale && (y = word0(rv) & Exp_mask)
1990 						<= 2*P*Exp_msk1)
1991 					  word0(adj) += (2*P+1)*Exp_msk1 - y;
1992 #else
1993 #ifdef Sudden_Underflow
1994 					if ((word0(rv) & Exp_mask) <=
1995 							P*Exp_msk1) {
1996 						word0(rv) += P*Exp_msk1;
1997 						dval(rv) += adj*ulp(rv);
1998 						word0(rv) -= P*Exp_msk1;
1999 						}
2000 					else
2001 #endif /*Sudden_Underflow*/
2002 #endif /*Avoid_Underflow*/
2003 					dval(rv) += adj*ulp(rv);
2004 					}
2005 				break;
2006 				}
2007 			adj = ratio(delta, bs);
2008 			if (adj < 1.)
2009 				adj = 1.;
2010 			if (adj <= 0x7ffffffe) {
2011 				/* adj = rounding ? ceil(adj) : floor(adj); */
2012 				y = adj;
2013 				if (y != adj) {
2014 					if (!((rounding>>1) ^ dsign))
2015 						y++;
2016 					adj = y;
2017 					}
2018 				}
2019 #ifdef Avoid_Underflow
2020 			if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
2021 				word0(adj) += (2*P+1)*Exp_msk1 - y;
2022 #else
2023 #ifdef Sudden_Underflow
2024 			if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2025 				word0(rv) += P*Exp_msk1;
2026 				adj *= ulp(rv);
2027 				if (dsign)
2028 					dval(rv) += adj;
2029 				else
2030 					dval(rv) -= adj;
2031 				word0(rv) -= P*Exp_msk1;
2032 				goto cont;
2033 				}
2034 #endif /*Sudden_Underflow*/
2035 #endif /*Avoid_Underflow*/
2036 			adj *= ulp(rv);
2037 			if (dsign)
2038 				dval(rv) += adj;
2039 			else
2040 				dval(rv) -= adj;
2041 			goto cont;
2042 			}
2043 #endif /*Honor_FLT_ROUNDS*/
2044 
2045 		if (i < 0) {
2046 			/* Error is less than half an ulp -- check for
2047 			 * special case of mantissa a power of two.
2048 			 */
2049 			if (dsign || word1(rv) || word0(rv) & Bndry_mask
2050 #ifdef IEEE_Arith
2051 #ifdef Avoid_Underflow
2052 			 || (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1
2053 #else
2054 			 || (word0(rv) & Exp_mask) <= Exp_msk1
2055 #endif
2056 #endif
2057 				) {
2058 #ifdef SET_INEXACT
2059 				if (!delta->x[0] && delta->wds <= 1)
2060 					inexact = 0;
2061 #endif
2062 				break;
2063 				}
2064 			if (!delta->x[0] && delta->wds <= 1) {
2065 				/* exact result */
2066 #ifdef SET_INEXACT
2067 				inexact = 0;
2068 #endif
2069 				break;
2070 				}
2071 			delta = lshift(PASS_STATE delta,Log2P);
2072 			if (cmp(delta, bs) > 0)
2073 				goto drop_down;
2074 			break;
2075 			}
2076 		if (i == 0) {
2077 			/* exactly half-way between */
2078 			if (dsign) {
2079 				if ((word0(rv) & Bndry_mask1) == Bndry_mask1
2080 				 &&  word1(rv) == (
2081 #ifdef Avoid_Underflow
2082 			(scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
2083 		? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
2084 #endif
2085 						   0xffffffff)) {
2086 					/*boundary case -- increment exponent*/
2087 					word0(rv) = (word0(rv) & Exp_mask)
2088 						+ Exp_msk1
2089 #ifdef IBM
2090 						| Exp_msk1 >> 4
2091 #endif
2092 						;
2093 					word1(rv) = 0;
2094 #ifdef Avoid_Underflow
2095 					dsign = 0;
2096 #endif
2097 					break;
2098 					}
2099 				}
2100 			else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
2101  drop_down:
2102 				/* boundary case -- decrement exponent */
2103 #ifdef Sudden_Underflow /*{{*/
2104 				L = word0(rv) & Exp_mask;
2105 #ifdef IBM
2106 				if (L <  Exp_msk1)
2107 #else
2108 #ifdef Avoid_Underflow
2109 				if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
2110 #else
2111 				if (L <= Exp_msk1)
2112 #endif /*Avoid_Underflow*/
2113 #endif /*IBM*/
2114 					goto undfl;
2115 				L -= Exp_msk1;
2116 #else /*Sudden_Underflow}{*/
2117 #ifdef Avoid_Underflow
2118 				if (scale) {
2119 					L = word0(rv) & Exp_mask;
2120 					if (L <= (2*P+1)*Exp_msk1) {
2121 						if (L > (P+2)*Exp_msk1)
2122 							/* round even ==> */
2123 							/* accept rv */
2124 							break;
2125 						/* rv = smallest denormal */
2126 						goto undfl;
2127 						}
2128 					}
2129 #endif /*Avoid_Underflow*/
2130 				L = (word0(rv) & Exp_mask) - Exp_msk1;
2131 #endif /*Sudden_Underflow}}*/
2132 				word0(rv) = L | Bndry_mask1;
2133 				word1(rv) = 0xffffffff;
2134 #ifdef IBM
2135 				goto cont;
2136 #else
2137 				break;
2138 #endif
2139 				}
2140 #ifndef ROUND_BIASED
2141 			if (!(word1(rv) & LSB))
2142 				break;
2143 #endif
2144 			if (dsign)
2145 				dval(rv) += ulp(rv);
2146 #ifndef ROUND_BIASED
2147 			else {
2148 				dval(rv) -= ulp(rv);
2149 #ifndef Sudden_Underflow
2150 				if (!dval(rv))
2151 					goto undfl;
2152 #endif
2153 				}
2154 #ifdef Avoid_Underflow
2155 			dsign = 1 - dsign;
2156 #endif
2157 #endif
2158 			break;
2159 			}
2160 		if ((aadj = ratio(delta, bs)) <= 2.) {
2161 			if (dsign)
2162 				aadj = dval(aadj1) = 1.;
2163 			else if (word1(rv) || word0(rv) & Bndry_mask) {
2164 #ifndef Sudden_Underflow
2165 				if (word1(rv) == Tiny1 && !word0(rv))
2166 					goto undfl;
2167 #endif
2168 				aadj = 1.;
2169 				dval(aadj1) = -1.;
2170 				}
2171 			else {
2172 				/* special case -- power of FLT_RADIX to be */
2173 				/* rounded down... */
2174 
2175 				if (aadj < 2./FLT_RADIX)
2176 					aadj = 1./FLT_RADIX;
2177 				else
2178 					aadj *= 0.5;
2179 				dval(aadj1) = -aadj;
2180 				}
2181 			}
2182 		else {
2183 			aadj *= 0.5;
2184 			dval(aadj1) = dsign ? aadj : -aadj;
2185 #ifdef Check_FLT_ROUNDS
2186 			switch(Rounding) {
2187 				case 2: /* towards +infinity */
2188 					dval(aadj1) -= 0.5;
2189 					break;
2190 				case 0: /* towards 0 */
2191 				case 3: /* towards -infinity */
2192 					dval(aadj1) += 0.5;
2193 				}
2194 #else
2195 			if (Flt_Rounds == 0)
2196 				dval(aadj1) += 0.5;
2197 #endif /*Check_FLT_ROUNDS*/
2198 			}
2199 		y = word0(rv) & Exp_mask;
2200 
2201 		/* Check for overflow */
2202 
2203 		if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
2204 			dval(rv0) = dval(rv);
2205 			word0(rv) -= P*Exp_msk1;
2206 			adj = dval(aadj1) * ulp(rv);
2207 			dval(rv) += adj;
2208 			if ((word0(rv) & Exp_mask) >=
2209 					Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
2210 				if (word0(rv0) == Big0 && word1(rv0) == Big1)
2211 					goto ovfl;
2212 				word0(rv) = Big0;
2213 				word1(rv) = Big1;
2214 				goto cont;
2215 				}
2216 			else
2217 				word0(rv) += P*Exp_msk1;
2218 			}
2219 		else {
2220 #ifdef Avoid_Underflow
2221 			if (scale && y <= 2*P*Exp_msk1) {
2222 				if (aadj <= 0x7fffffff) {
2223 					if ((z = (ULong) aadj) <= 0)
2224 						z = 1;
2225 					aadj = z;
2226 					dval(aadj1) = dsign ? aadj : -aadj;
2227 					}
2228 				word0(aadj1) += (2*P+1)*Exp_msk1 - y;
2229 				}
2230 			adj = dval(aadj1) * ulp(rv);
2231 			dval(rv) += adj;
2232 #else
2233 #ifdef Sudden_Underflow
2234 			if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2235 				dval(rv0) = dval(rv);
2236 				word0(rv) += P*Exp_msk1;
2237 				adj = dval(aadj1) * ulp(rv);
2238 				dval(rv) += adj;
2239 #ifdef IBM
2240 				if ((word0(rv) & Exp_mask) <  P*Exp_msk1)
2241 #else
2242 				if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
2243 #endif
2244 					{
2245 					if (word0(rv0) == Tiny0
2246 					 && word1(rv0) == Tiny1)
2247 						goto undfl;
2248 					word0(rv) = Tiny0;
2249 					word1(rv) = Tiny1;
2250 					goto cont;
2251 					}
2252 				else
2253 					word0(rv) -= P*Exp_msk1;
2254 				}
2255 			else {
2256 				adj = dval(aadj1) * ulp(rv);
2257 				dval(rv) += adj;
2258 				}
2259 #else /*Sudden_Underflow*/
2260 			/* Compute adj so that the IEEE rounding rules will
2261 			 * correctly round rv + adj in some half-way cases.
2262 			 * If rv * ulp(rv) is denormalized (i.e.,
2263 			 * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
2264 			 * trouble from bits lost to denormalization;
2265 			 * example: 1.2e-307 .
2266 			 */
2267 			if (y <= (P-1)*Exp_msk1 && aadj > 1.) {
2268 				dval(aadj1) = (double)(int)(aadj + 0.5);
2269 				if (!dsign)
2270 					dval(aadj1) = -dval(aadj1);
2271 				}
2272 			adj = dval(aadj1) * ulp(rv);
2273 			dval(rv) += adj;
2274 #endif /*Sudden_Underflow*/
2275 #endif /*Avoid_Underflow*/
2276 			}
2277 		z = word0(rv) & Exp_mask;
2278 #ifndef SET_INEXACT
2279 #ifdef Avoid_Underflow
2280 		if (!scale)
2281 #endif
2282 		if (y == z) {
2283 			/* Can we stop now? */
2284 			L = (Long)aadj;
2285 			aadj -= L;
2286 			/* The tolerances below are conservative. */
2287 			if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
2288 				if (aadj < .4999999 || aadj > .5000001)
2289 					break;
2290 				}
2291 			else if (aadj < .4999999/FLT_RADIX)
2292 				break;
2293 			}
2294 #endif
2295  cont:
2296 		Bfree(PASS_STATE bb);
2297 		Bfree(PASS_STATE bd);
2298 		Bfree(PASS_STATE bs);
2299 		Bfree(PASS_STATE delta);
2300 		}
2301 #ifdef SET_INEXACT
2302 	if (inexact) {
2303 		if (!oldinexact) {
2304 			word0(rv0) = Exp_1 + (70 << Exp_shift);
2305 			word1(rv0) = 0;
2306 			dval(rv0) += 1.;
2307 			}
2308 		}
2309 	else if (!oldinexact)
2310 		clear_inexact();
2311 #endif
2312 #ifdef Avoid_Underflow
2313 	if (scale) {
2314 		word0(rv0) = Exp_1 - 2*P*Exp_msk1;
2315 		word1(rv0) = 0;
2316 		dval(rv) *= dval(rv0);
2317 #ifndef NO_ERRNO
2318 		/* try to avoid the bug of testing an 8087 register value */
2319 		if (word0(rv) == 0 && word1(rv) == 0)
2320 			errno = ERANGE;
2321 #endif
2322 		}
2323 #endif /* Avoid_Underflow */
2324 #ifdef SET_INEXACT
2325 	if (inexact && !(word0(rv) & Exp_mask)) {
2326 		/* set underflow bit */
2327 		dval(rv0) = 1e-300;
2328 		dval(rv0) *= dval(rv0);
2329 		}
2330 #endif
2331  retfree:
2332 	Bfree(PASS_STATE bb);
2333 	Bfree(PASS_STATE bd);
2334 	Bfree(PASS_STATE bs);
2335 	Bfree(PASS_STATE bd0);
2336 	Bfree(PASS_STATE delta);
2337  ret:
2338 	if (se)
2339 		*se = (char *)s;
2340 	return sign ? -dval(rv) : dval(rv);
2341 	}
2342 
2343  static int
quorem(b,S)2344 quorem
2345 #ifdef KR_headers
2346 	(b, S) Bigint *b, *S;
2347 #else
2348 	(Bigint *b, Bigint *S)
2349 #endif
2350 {
2351 	int n;
2352 	ULong *bx, *bxe, q, *sx, *sxe;
2353 #ifdef ULLong
2354 	ULLong borrow, carry, y, ys;
2355 #else
2356 	ULong borrow, carry, y, ys;
2357 #ifdef Pack_32
2358 	ULong si, z, zs;
2359 #endif
2360 #endif
2361 
2362 	n = S->wds;
2363 #ifdef DEBUG
2364 	/*debug*/ if (b->wds > n)
2365 	/*debug*/	Bug("oversize b in quorem");
2366 #endif
2367 	if (b->wds < n)
2368 		return 0;
2369 	sx = S->x;
2370 	sxe = sx + --n;
2371 	bx = b->x;
2372 	bxe = bx + n;
2373 	q = *bxe / (*sxe + 1);	/* ensure q <= true quotient */
2374 #ifdef DEBUG
2375 	/*debug*/ if (q > 9)
2376 	/*debug*/	Bug("oversized quotient in quorem");
2377 #endif
2378 	if (q) {
2379 		borrow = 0;
2380 		carry = 0;
2381 		do {
2382 #ifdef ULLong
2383 			ys = *sx++ * (ULLong)q + carry;
2384 			carry = ys >> 32;
2385 			y = *bx - (ys & FFFFFFFF) - borrow;
2386 			borrow = y >> 32 & (ULong)1;
2387 			*bx++ = (ULong) y & FFFFFFFF;
2388 #else
2389 #ifdef Pack_32
2390 			si = *sx++;
2391 			ys = (si & 0xffff) * q + carry;
2392 			zs = (si >> 16) * q + (ys >> 16);
2393 			carry = zs >> 16;
2394 			y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
2395 			borrow = (y & 0x10000) >> 16;
2396 			z = (*bx >> 16) - (zs & 0xffff) - borrow;
2397 			borrow = (z & 0x10000) >> 16;
2398 			Storeinc(bx, z, y);
2399 #else
2400 			ys = *sx++ * q + carry;
2401 			carry = ys >> 16;
2402 			y = *bx - (ys & 0xffff) - borrow;
2403 			borrow = (y & 0x10000) >> 16;
2404 			*bx++ = y & 0xffff;
2405 #endif
2406 #endif
2407 			}
2408 			while(sx <= sxe);
2409 		if (!*bxe) {
2410 			bx = b->x;
2411 			while(--bxe > bx && !*bxe)
2412 				--n;
2413 			b->wds = n;
2414 			}
2415 		}
2416 	if (cmp(b, S) >= 0) {
2417 		q++;
2418 		borrow = 0;
2419 		carry = 0;
2420 		bx = b->x;
2421 		sx = S->x;
2422 		do {
2423 #ifdef ULLong
2424 			ys = *sx++ + carry;
2425 			carry = ys >> 32;
2426 			y = *bx - (ys & FFFFFFFF) - borrow;
2427 			borrow = y >> 32 & (ULong)1;
2428 			*bx++ = (ULong) y & FFFFFFFF;
2429 #else
2430 #ifdef Pack_32
2431 			si = *sx++;
2432 			ys = (si & 0xffff) + carry;
2433 			zs = (si >> 16) + (ys >> 16);
2434 			carry = zs >> 16;
2435 			y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
2436 			borrow = (y & 0x10000) >> 16;
2437 			z = (*bx >> 16) - (zs & 0xffff) - borrow;
2438 			borrow = (z & 0x10000) >> 16;
2439 			Storeinc(bx, z, y);
2440 #else
2441 			ys = *sx++ + carry;
2442 			carry = ys >> 16;
2443 			y = *bx - (ys & 0xffff) - borrow;
2444 			borrow = (y & 0x10000) >> 16;
2445 			*bx++ = y & 0xffff;
2446 #endif
2447 #endif
2448 			}
2449 			while(sx <= sxe);
2450 		bx = b->x;
2451 		bxe = bx + n;
2452 		if (!*bxe) {
2453 			while(--bxe > bx && !*bxe)
2454 				--n;
2455 			b->wds = n;
2456 			}
2457 		}
2458 	return q;
2459 	}
2460 
2461 #if !defined(MULTIPLE_THREADS) && !defined(NO_GLOBAL_STATE)
2462 #define USE_DTOA_RESULT 1
2463  static char *dtoa_result;
2464 #endif
2465 
2466  static char *
2467 #ifdef KR_headers
2468 rv_alloc(STATE_PARAM i) STATE_PARAM_DECL int i;
2469 #else
2470 rv_alloc(STATE_PARAM int i)
2471 #endif
2472 {
2473 	int j, k, *r;
2474 
2475 	j = sizeof(ULong);
2476 	for(k = 0;
2477 		sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= (unsigned) i;
2478 		j <<= 1)
2479 			k++;
2480 	r = (int*)Balloc(PASS_STATE k);
2481 	*r = k;
2482 	return
2483 #ifdef USE_DTOA_RESULT
2484 	dtoa_result =
2485 #endif
2486 		(char *)(r+1);
2487 	}
2488 
2489  static char *
2490 #ifdef KR_headers
2491 nrv_alloc(STATE_PARAM s, rve, n) STATE_PARAM_DECL char *s, **rve; int n;
2492 #else
2493 nrv_alloc(STATE_PARAM CONST char *s, char **rve, int n)
2494 #endif
2495 {
2496 	char *rv, *t;
2497 
2498 	t = rv = rv_alloc(PASS_STATE n);
2499 	while((*t = *s++)) t++;
2500 	if (rve)
2501 		*rve = t;
2502 	return rv;
2503 	}
2504 
2505 /* freedtoa(s) must be used to free values s returned by dtoa
2506  * when MULTIPLE_THREADS is #defined.  It should be used in all cases,
2507  * but for consistency with earlier versions of dtoa, it is optional
2508  * when MULTIPLE_THREADS is not defined.
2509  */
2510 
2511  static void
2512 #ifdef KR_headers
2513 freedtoa(STATE_PARAM s) STATE_PARAM_DECL char *s;
2514 #else
2515 freedtoa(STATE_PARAM char *s)
2516 #endif
2517 {
2518 	Bigint *b = (Bigint *)((int *)s - 1);
2519 	b->maxwds = 1 << (b->k = *(int*)b);
2520 	Bfree(PASS_STATE b);
2521 #ifdef USE_DTOA_RESULT
2522 	if (s == dtoa_result)
2523 		dtoa_result = 0;
2524 #endif
2525 	}
2526 
2527 /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
2528  *
2529  * Inspired by "How to Print Floating-Point Numbers Accurately" by
2530  * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126].
2531  *
2532  * Modifications:
2533  *	1. Rather than iterating, we use a simple numeric overestimate
2534  *	   to determine k = floor(log10(d)).  We scale relevant
2535  *	   quantities using O(log2(k)) rather than O(k) multiplications.
2536  *	2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
2537  *	   try to generate digits strictly left to right.  Instead, we
2538  *	   compute with fewer bits and propagate the carry if necessary
2539  *	   when rounding the final digit up.  This is often faster.
2540  *	3. Under the assumption that input will be rounded nearest,
2541  *	   mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
2542  *	   That is, we allow equality in stopping tests when the
2543  *	   round-nearest rule will give the same floating-point value
2544  *	   as would satisfaction of the stopping test with strict
2545  *	   inequality.
2546  *	4. We remove common factors of powers of 2 from relevant
2547  *	   quantities.
2548  *	5. When converting floating-point integers less than 1e16,
2549  *	   we use floating-point arithmetic rather than resorting
2550  *	   to multiple-precision integers.
2551  *	6. When asked to produce fewer than 15 digits, we first try
2552  *	   to get by with floating-point arithmetic; we resort to
2553  *	   multiple-precision integer arithmetic only if we cannot
2554  *	   guarantee that the floating-point calculation has given
2555  *	   the correctly rounded result.  For k requested digits and
2556  *	   "uniformly" distributed input, the probability is
2557  *	   something like 10^(k-15) that we must resort to the Long
2558  *	   calculation.
2559  */
2560 
2561  static char *
2562 dtoa
2563 #ifdef KR_headers
2564 	(STATE_PARAM d, mode, ndigits, decpt, sign, rve)
2565 	STATE_PARAM_DECL U d; int mode, ndigits, *decpt, *sign; char **rve;
2566 #else
2567 	(STATE_PARAM U d, int mode, int ndigits, int *decpt, int *sign, char **rve)
2568 #endif
2569 {
2570  /*	Arguments ndigits, decpt, sign are similar to those
2571 	of ecvt and fcvt; trailing zeros are suppressed from
2572 	the returned string.  If not null, *rve is set to point
2573 	to the end of the return value.  If d is +-Infinity or NaN,
2574 	then *decpt is set to 9999.
2575 
2576 	mode:
2577 		0 ==> shortest string that yields d when read in
2578 			and rounded to nearest.
2579 		1 ==> like 0, but with Steele & White stopping rule;
2580 			e.g. with IEEE P754 arithmetic , mode 0 gives
2581 			1e23 whereas mode 1 gives 9.999999999999999e22.
2582 		2 ==> max(1,ndigits) significant digits.  This gives a
2583 			return value similar to that of ecvt, except
2584 			that trailing zeros are suppressed.
2585 		3 ==> through ndigits past the decimal point.  This
2586 			gives a return value similar to that from fcvt,
2587 			except that trailing zeros are suppressed, and
2588 			ndigits can be negative.
2589 		4,5 ==> similar to 2 and 3, respectively, but (in
2590 			round-nearest mode) with the tests of mode 0 to
2591 			possibly return a shorter string that rounds to d.
2592 			With IEEE arithmetic and compilation with
2593 			-DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
2594 			as modes 2 and 3 when FLT_ROUNDS != 1.
2595 		6-9 ==> Debugging modes similar to mode - 4:  don't try
2596 			fast floating-point estimate (if applicable).
2597 
2598 		Values of mode other than 0-9 are treated as mode 0.
2599 
2600 		Sufficient space is allocated to the return value
2601 		to hold the suppressed trailing zeros.
2602 	*/
2603 
2604 	int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
2605 		j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
2606 		spec_case, try_quick;
2607 	Long L;
2608 #ifndef Sudden_Underflow
2609 	int denorm;
2610 	ULong x;
2611 #endif
2612 	Bigint *b, *b1, *delta, *mlo, *mhi, *S;
2613 	U d2, eps;
2614 	double ds;
2615 	char *s, *s0;
2616 #ifdef Honor_FLT_ROUNDS
2617 	int rounding;
2618 #endif
2619 #ifdef SET_INEXACT
2620 	int inexact, oldinexact;
2621 #endif
2622 
2623 #ifdef __GNUC__
2624 	ilim = ilim1 = 0;
2625 	mlo = NULL;
2626 #endif
2627 
2628 #ifdef USE_DTOA_RESULT
2629 	if (dtoa_result) {
2630 		freedtoa(PASS_STATE dtoa_result);
2631 		dtoa_result = 0;
2632 		}
2633 #endif
2634 
2635 	if (word0(d) & Sign_bit) {
2636 		/* set sign for everything, including 0's and NaNs */
2637 		*sign = 1;
2638 		word0(d) &= ~Sign_bit;	/* clear sign bit */
2639 		}
2640 	else
2641 		*sign = 0;
2642 
2643 #if defined(IEEE_Arith) + defined(VAX)
2644 #ifdef IEEE_Arith
2645 	if ((word0(d) & Exp_mask) == Exp_mask)
2646 #else
2647 	if (word0(d)  == 0x8000)
2648 #endif
2649 		{
2650 		/* Infinity or NaN */
2651 		*decpt = 9999;
2652 #ifdef IEEE_Arith
2653 		if (!word1(d) && !(word0(d) & 0xfffff))
2654 			return nrv_alloc(PASS_STATE "Infinity", rve, 8);
2655 #endif
2656 		return nrv_alloc(PASS_STATE "NaN", rve, 3);
2657 		}
2658 #endif
2659 #ifdef IBM
2660 	dval(d) += 0; /* normalize */
2661 #endif
2662 	if (!dval(d)) {
2663 		*decpt = 1;
2664 		return nrv_alloc(PASS_STATE "0", rve, 1);
2665 		}
2666 
2667 #ifdef SET_INEXACT
2668 	try_quick = oldinexact = get_inexact();
2669 	inexact = 1;
2670 #endif
2671 #ifdef Honor_FLT_ROUNDS
2672 	if ((rounding = Flt_Rounds) >= 2) {
2673 		if (*sign)
2674 			rounding = rounding == 2 ? 0 : 2;
2675 		else
2676 			if (rounding != 2)
2677 				rounding = 0;
2678 		}
2679 #endif
2680 
2681 	b = d2b(PASS_STATE d, &be, &bbits);
2682 #ifdef Sudden_Underflow
2683 	i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
2684 #else
2685 	if ((i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1)))) {
2686 #endif
2687 		dval(d2) = dval(d);
2688 		word0(d2) &= Frac_mask1;
2689 		word0(d2) |= Exp_11;
2690 #ifdef IBM
2691 		if (j = 11 - hi0bits(word0(d2) & Frac_mask))
2692 			dval(d2) /= 1 << j;
2693 #endif
2694 
2695 		/* log(x)	~=~ log(1.5) + (x-1.5)/1.5
2696 		 * log10(x)	 =  log(x) / log(10)
2697 		 *		~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
2698 		 * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
2699 		 *
2700 		 * This suggests computing an approximation k to log10(d) by
2701 		 *
2702 		 * k = (i - Bias)*0.301029995663981
2703 		 *	+ ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
2704 		 *
2705 		 * We want k to be too large rather than too small.
2706 		 * The error in the first-order Taylor series approximation
2707 		 * is in our favor, so we just round up the constant enough
2708 		 * to compensate for any error in the multiplication of
2709 		 * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
2710 		 * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
2711 		 * adding 1e-13 to the constant term more than suffices.
2712 		 * Hence we adjust the constant term to 0.1760912590558.
2713 		 * (We could get a more accurate k by invoking log10,
2714 		 *  but this is probably not worthwhile.)
2715 		 */
2716 
2717 		i -= Bias;
2718 #ifdef IBM
2719 		i <<= 2;
2720 		i += j;
2721 #endif
2722 #ifndef Sudden_Underflow
2723 		denorm = 0;
2724 		}
2725 	else {
2726 		/* d is denormalized */
2727 
2728 		i = bbits + be + (Bias + (P-1) - 1);
2729 		x = i > 32  ? word0(d) << (64 - i) | word1(d) >> (i - 32)
2730 			    : word1(d) << (32 - i);
2731 		dval(d2) = x;
2732 		word0(d2) -= 31*Exp_msk1; /* adjust exponent */
2733 		i -= (Bias + (P-1) - 1) + 1;
2734 		denorm = 1;
2735 		}
2736 #endif
2737 	ds = (dval(d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
2738 	k = (int)ds;
2739 	if (ds < 0. && ds != k)
2740 		k--;	/* want k = floor(ds) */
2741 	k_check = 1;
2742 	if (k >= 0 && k <= Ten_pmax) {
2743 		if (dval(d) < tens[k])
2744 			k--;
2745 		k_check = 0;
2746 		}
2747 	j = bbits - i - 1;
2748 	if (j >= 0) {
2749 		b2 = 0;
2750 		s2 = j;
2751 		}
2752 	else {
2753 		b2 = -j;
2754 		s2 = 0;
2755 		}
2756 	if (k >= 0) {
2757 		b5 = 0;
2758 		s5 = k;
2759 		s2 += k;
2760 		}
2761 	else {
2762 		b2 -= k;
2763 		b5 = -k;
2764 		s5 = 0;
2765 		}
2766 	if (mode < 0 || mode > 9)
2767 		mode = 0;
2768 
2769 #ifndef SET_INEXACT
2770 #ifdef Check_FLT_ROUNDS
2771 	try_quick = Rounding == 1;
2772 #else
2773 	try_quick = 1;
2774 #endif
2775 #endif /*SET_INEXACT*/
2776 
2777 	if (mode > 5) {
2778 		mode -= 4;
2779 		try_quick = 0;
2780 		}
2781 	leftright = 1;
2782 	switch(mode) {
2783 		case 0:
2784 		case 1:
2785 			ilim = ilim1 = -1;
2786 			i = 18;
2787 			ndigits = 0;
2788 			break;
2789 		case 2:
2790 			leftright = 0;
2791 			/* no break */
2792 		case 4:
2793 			if (ndigits <= 0)
2794 				ndigits = 1;
2795 			ilim = ilim1 = i = ndigits;
2796 			break;
2797 		case 3:
2798 			leftright = 0;
2799 			/* no break */
2800 		case 5:
2801 			i = ndigits + k + 1;
2802 			ilim = i;
2803 			ilim1 = i - 1;
2804 			if (i <= 0)
2805 				i = 1;
2806 		}
2807 	s = s0 = rv_alloc(PASS_STATE i);
2808 
2809 #ifdef Honor_FLT_ROUNDS
2810 	if (mode > 1 && rounding != 1)
2811 		leftright = 0;
2812 #endif
2813 
2814 	if (ilim >= 0 && ilim <= Quick_max && try_quick) {
2815 
2816 		/* Try to get by with floating-point arithmetic. */
2817 
2818 		i = 0;
2819 		dval(d2) = dval(d);
2820 		k0 = k;
2821 		ilim0 = ilim;
2822 		ieps = 2; /* conservative */
2823 		if (k > 0) {
2824 			ds = tens[k&0xf];
2825 			j = k >> 4;
2826 			if (j & Bletch) {
2827 				/* prevent overflows */
2828 				j &= Bletch - 1;
2829 				dval(d) /= bigtens[n_bigtens-1];
2830 				ieps++;
2831 				}
2832 			for(; j; j >>= 1, i++)
2833 				if (j & 1) {
2834 					ieps++;
2835 					ds *= bigtens[i];
2836 					}
2837 			dval(d) /= ds;
2838 			}
2839 		else if ((j1 = -k)) {
2840 			dval(d) *= tens[j1 & 0xf];
2841 			for(j = j1 >> 4; j; j >>= 1, i++)
2842 				if (j & 1) {
2843 					ieps++;
2844 					dval(d) *= bigtens[i];
2845 					}
2846 			}
2847 		if (k_check && dval(d) < 1. && ilim > 0) {
2848 			if (ilim1 <= 0)
2849 				goto fast_failed;
2850 			ilim = ilim1;
2851 			k--;
2852 			dval(d) *= 10.;
2853 			ieps++;
2854 			}
2855 		dval(eps) = ieps*dval(d) + 7.;
2856 		word0(eps) -= (P-1)*Exp_msk1;
2857 		if (ilim == 0) {
2858 			S = mhi = 0;
2859 			dval(d) -= 5.;
2860 			if (dval(d) > dval(eps))
2861 				goto one_digit;
2862 			if (dval(d) < -dval(eps))
2863 				goto no_digits;
2864 			goto fast_failed;
2865 			}
2866 #ifndef No_leftright
2867 		if (leftright) {
2868 			/* Use Steele & White method of only
2869 			 * generating digits needed.
2870 			 */
2871 			dval(eps) = 0.5/tens[ilim-1] - dval(eps);
2872 			for(i = 0;;) {
2873 				L = (ULong) dval(d);
2874 				dval(d) -= L;
2875 				*s++ = '0' + (int)L;
2876 				if (dval(d) < dval(eps))
2877 					goto ret1;
2878 				if (1. - dval(d) < dval(eps))
2879 					goto bump_up;
2880 				if (++i >= ilim)
2881 					break;
2882 				dval(eps) *= 10.;
2883 				dval(d) *= 10.;
2884 				}
2885 			}
2886 		else {
2887 #endif
2888 			/* Generate ilim digits, then fix them up. */
2889 			dval(eps) *= tens[ilim-1];
2890 			for(i = 1;; i++, dval(d) *= 10.) {
2891 				L = (Long)(dval(d));
2892 				if (!(dval(d) -= L))
2893 					ilim = i;
2894 				*s++ = '0' + (int)L;
2895 				if (i == ilim) {
2896 					if (dval(d) > 0.5 + dval(eps))
2897 						goto bump_up;
2898 					else if (dval(d) < 0.5 - dval(eps)) {
2899 						while(*--s == '0');
2900 						s++;
2901 						goto ret1;
2902 						}
2903 					break;
2904 					}
2905 				}
2906 #ifndef No_leftright
2907 			}
2908 #endif
2909  fast_failed:
2910 		s = s0;
2911 		dval(d) = dval(d2);
2912 		k = k0;
2913 		ilim = ilim0;
2914 		}
2915 
2916 	/* Do we have a "small" integer? */
2917 
2918 	if (be >= 0 && k <= Int_max) {
2919 		/* Yes. */
2920 		ds = tens[k];
2921 		if (ndigits < 0 && ilim <= 0) {
2922 			S = mhi = 0;
2923 			if (ilim < 0 || dval(d) < 5*ds)
2924 				goto no_digits;
2925 			goto one_digit;
2926 			}
2927 		for(i = 1;; i++, dval(d) *= 10.) {
2928 			L = (Long)(dval(d) / ds);
2929 			dval(d) -= L*ds;
2930 #ifdef Check_FLT_ROUNDS
2931 			/* If FLT_ROUNDS == 2, L will usually be high by 1 */
2932 			if (dval(d) < 0) {
2933 				L--;
2934 				dval(d) += ds;
2935 				}
2936 #endif
2937 			*s++ = '0' + (int)L;
2938 			if (!dval(d)) {
2939 #ifdef SET_INEXACT
2940 				inexact = 0;
2941 #endif
2942 				break;
2943 				}
2944 			if (i == ilim) {
2945 #ifdef Honor_FLT_ROUNDS
2946 				if (mode > 1)
2947 				switch(rounding) {
2948 				  case 0: goto ret1;
2949 				  case 2: goto bump_up;
2950 				  }
2951 #endif
2952 				dval(d) += dval(d);
2953 				if (dval(d) > ds || (dval(d) == ds && L & 1)) {
2954  bump_up:
2955 					while(*--s == '9')
2956 						if (s == s0) {
2957 							k++;
2958 							*s = '0';
2959 							break;
2960 							}
2961 					++*s++;
2962 					}
2963 				break;
2964 				}
2965 			}
2966 		goto ret1;
2967 		}
2968 
2969 	m2 = b2;
2970 	m5 = b5;
2971 	mhi = mlo = 0;
2972 	if (leftright) {
2973 		i =
2974 #ifndef Sudden_Underflow
2975 			denorm ? be + (Bias + (P-1) - 1 + 1) :
2976 #endif
2977 #ifdef IBM
2978 			1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
2979 #else
2980 			1 + P - bbits;
2981 #endif
2982 		b2 += i;
2983 		s2 += i;
2984 		mhi = i2b(PASS_STATE 1);
2985 		}
2986 	if (m2 > 0 && s2 > 0) {
2987 		i = m2 < s2 ? m2 : s2;
2988 		b2 -= i;
2989 		m2 -= i;
2990 		s2 -= i;
2991 		}
2992 	if (b5 > 0) {
2993 		if (leftright) {
2994 			if (m5 > 0) {
2995 				mhi = pow5mult(PASS_STATE mhi, m5);
2996 				b1 = mult(PASS_STATE mhi, b);
2997 				Bfree(PASS_STATE b);
2998 				b = b1;
2999 				}
3000 			if ((j = b5 - m5))
3001 				b = pow5mult(PASS_STATE b, j);
3002 			}
3003 		else
3004 			b = pow5mult(PASS_STATE b, b5);
3005 		}
3006 	S = i2b(PASS_STATE 1);
3007 	if (s5 > 0)
3008 		S = pow5mult(PASS_STATE S, s5);
3009 
3010 	/* Check for special case that d is a normalized power of 2. */
3011 
3012 	spec_case = 0;
3013 	if ((mode < 2 || leftright)
3014 #ifdef Honor_FLT_ROUNDS
3015 			&& rounding == 1
3016 #endif
3017 				) {
3018 		if (!word1(d) && !(word0(d) & Bndry_mask)
3019 #ifndef Sudden_Underflow
3020 		 && word0(d) & (Exp_mask & ~Exp_msk1)
3021 #endif
3022 				) {
3023 			/* The special case */
3024 			b2 += Log2P;
3025 			s2 += Log2P;
3026 			spec_case = 1;
3027 			}
3028 		}
3029 
3030 	/* Arrange for convenient computation of quotients:
3031 	 * shift left if necessary so divisor has 4 leading 0 bits.
3032 	 *
3033 	 * Perhaps we should just compute leading 28 bits of S once
3034 	 * and for all and pass them and a shift to quorem, so it
3035 	 * can do shifts and ors to compute the numerator for q.
3036 	 */
3037 #ifdef Pack_32
3038 	if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f))
3039 		i = 32 - i;
3040 #else
3041 	if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf)
3042 		i = 16 - i;
3043 #endif
3044 	if (i > 4) {
3045 		i -= 4;
3046 		b2 += i;
3047 		m2 += i;
3048 		s2 += i;
3049 		}
3050 	else if (i < 4) {
3051 		i += 28;
3052 		b2 += i;
3053 		m2 += i;
3054 		s2 += i;
3055 		}
3056 	if (b2 > 0)
3057 		b = lshift(PASS_STATE b, b2);
3058 	if (s2 > 0)
3059 		S = lshift(PASS_STATE S, s2);
3060 	if (k_check) {
3061 		if (cmp(b,S) < 0) {
3062 			k--;
3063 			b = multadd(PASS_STATE b, 10, 0);	/* we botched the k estimate */
3064 			if (leftright)
3065 				mhi = multadd(PASS_STATE mhi, 10, 0);
3066 			ilim = ilim1;
3067 			}
3068 		}
3069 	if (ilim <= 0 && (mode == 3 || mode == 5)) {
3070 		if (ilim < 0 || cmp(b,S = multadd(PASS_STATE S,5,0)) < 0) {
3071 			/* no digits, fcvt style */
3072  no_digits:
3073 			/* MOZILLA CHANGE: Always return a non-empty string. */
3074 			*s++ = '0';
3075 			k = 0;
3076 			goto ret;
3077 			}
3078  one_digit:
3079 		*s++ = '1';
3080 		k++;
3081 		goto ret;
3082 		}
3083 	if (leftright) {
3084 		if (m2 > 0)
3085 			mhi = lshift(PASS_STATE mhi, m2);
3086 
3087 		/* Compute mlo -- check for special case
3088 		 * that d is a normalized power of 2.
3089 		 */
3090 
3091 		mlo = mhi;
3092 		if (spec_case) {
3093 			mhi = Balloc(PASS_STATE mhi->k);
3094 			Bcopy(mhi, mlo);
3095 			mhi = lshift(PASS_STATE mhi, Log2P);
3096 			}
3097 
3098 		for(i = 1;;i++) {
3099 			dig = quorem(b,S) + '0';
3100 			/* Do we yet have the shortest decimal string
3101 			 * that will round to d?
3102 			 */
3103 			j = cmp(b, mlo);
3104 			delta = diff(PASS_STATE S, mhi);
3105 			j1 = delta->sign ? 1 : cmp(b, delta);
3106 			Bfree(PASS_STATE delta);
3107 #ifndef ROUND_BIASED
3108 			if (j1 == 0 && mode != 1 && !(word1(d) & 1)
3109 #ifdef Honor_FLT_ROUNDS
3110 				&& rounding >= 1
3111 #endif
3112 								   ) {
3113 				if (dig == '9')
3114 					goto round_9_up;
3115 				if (j > 0)
3116 					dig++;
3117 #ifdef SET_INEXACT
3118 				else if (!b->x[0] && b->wds <= 1)
3119 					inexact = 0;
3120 #endif
3121 				*s++ = dig;
3122 				goto ret;
3123 				}
3124 #endif
3125 			if (j < 0 || (j == 0 && mode != 1
3126 #ifndef ROUND_BIASED
3127 							&& !(word1(d) & 1)
3128 #endif
3129 					)) {
3130 				if (!b->x[0] && b->wds <= 1) {
3131 #ifdef SET_INEXACT
3132 					inexact = 0;
3133 #endif
3134 					goto accept_dig;
3135 					}
3136 #ifdef Honor_FLT_ROUNDS
3137 				if (mode > 1)
3138 				 switch(rounding) {
3139 				  case 0: goto accept_dig;
3140 				  case 2: goto keep_dig;
3141 				  }
3142 #endif /*Honor_FLT_ROUNDS*/
3143 				if (j1 > 0) {
3144 					b = lshift(PASS_STATE b, 1);
3145 					j1 = cmp(b, S);
3146 					if ((j1 > 0 || (j1 == 0 && dig & 1))
3147 					&& dig++ == '9')
3148 						goto round_9_up;
3149 					}
3150  accept_dig:
3151 				*s++ = dig;
3152 				goto ret;
3153 				}
3154 			if (j1 > 0) {
3155 #ifdef Honor_FLT_ROUNDS
3156 				if (!rounding)
3157 					goto accept_dig;
3158 #endif
3159 				if (dig == '9') { /* possible if i == 1 */
3160  round_9_up:
3161 					*s++ = '9';
3162 					goto roundoff;
3163 					}
3164 				*s++ = dig + 1;
3165 				goto ret;
3166 				}
3167 #ifdef Honor_FLT_ROUNDS
3168  keep_dig:
3169 #endif
3170 			*s++ = dig;
3171 			if (i == ilim)
3172 				break;
3173 			b = multadd(PASS_STATE b, 10, 0);
3174 			if (mlo == mhi)
3175 				mlo = mhi = multadd(PASS_STATE mhi, 10, 0);
3176 			else {
3177 				mlo = multadd(PASS_STATE mlo, 10, 0);
3178 				mhi = multadd(PASS_STATE mhi, 10, 0);
3179 				}
3180 			}
3181 		}
3182 	else
3183 		for(i = 1;; i++) {
3184 			*s++ = dig = quorem(b,S) + '0';
3185 			if (!b->x[0] && b->wds <= 1) {
3186 #ifdef SET_INEXACT
3187 				inexact = 0;
3188 #endif
3189 				goto ret;
3190 				}
3191 			if (i >= ilim)
3192 				break;
3193 			b = multadd(PASS_STATE b, 10, 0);
3194 			}
3195 
3196 	/* Round off last digit */
3197 
3198 #ifdef Honor_FLT_ROUNDS
3199 	switch(rounding) {
3200 	  case 0: goto trimzeros;
3201 	  case 2: goto roundoff;
3202 	  }
3203 #endif
3204 	b = lshift(PASS_STATE b, 1);
3205 	j = cmp(b, S);
3206 	if (j >= 0) {  /* ECMA compatible rounding needed by Spidermonkey */
3207  roundoff:
3208 		while(*--s == '9')
3209 			if (s == s0) {
3210 				k++;
3211 				*s++ = '1';
3212 				goto ret;
3213 				}
3214 		++*s++;
3215 		}
3216 	else {
3217 #ifdef Honor_FLT_ROUNDS
3218  trimzeros:
3219 #endif
3220 		while(*--s == '0');
3221 		s++;
3222 		}
3223  ret:
3224 	Bfree(PASS_STATE S);
3225 	if (mhi) {
3226 		if (mlo && mlo != mhi)
3227 			Bfree(PASS_STATE mlo);
3228 		Bfree(PASS_STATE mhi);
3229 		}
3230  ret1:
3231 #ifdef SET_INEXACT
3232 	if (inexact) {
3233 		if (!oldinexact) {
3234 			word0(d) = Exp_1 + (70 << Exp_shift);
3235 			word1(d) = 0;
3236 			dval(d) += 1.;
3237 			}
3238 		}
3239 	else if (!oldinexact)
3240 		clear_inexact();
3241 #endif
3242 	Bfree(PASS_STATE b);
3243 	*s = 0;
3244 	*decpt = k + 1;
3245 	if (rve)
3246 		*rve = s;
3247 	return s0;
3248 	}
3249 #undef CONST
3250