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 #error "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 #ifdef Omit_Private_Memory
530 	Bigint* p5 = GET_STATE(p5s);
531 	while (p5) {
532 		Bigint* tmp = p5;
533 		p5 = p5->next;
534 		FREE(tmp);
535 		}
536 #endif
537 	FREE((void *)state);
538 }
539 
540 #else
541 #define STATE_PARAM      /* nothing */
542 #define STATE_PARAM_DECL /* nothing */
543 #define PASS_STATE       /* nothing */
544 #define GET_STATE(name) name
545 #endif
546 
547  static Bigint *
548 Balloc
549 #ifdef KR_headers
550 	(STATE_PARAM k) STATE_PARAM_DECL int k;
551 #else
552 	(STATE_PARAM int k)
553 #endif
554 {
555 	int x;
556 	Bigint *rv;
557 #ifndef Omit_Private_Memory
558 	size_t len;
559 #endif
560 
561 	ACQUIRE_DTOA_LOCK(0);
562 	/* The k > Kmax case does not need ACQUIRE_DTOA_LOCK(0), */
563 	/* but this case seems very unlikely. */
564 	if (k <= Kmax && (rv = GET_STATE(freelist)[k]))
565 		GET_STATE(freelist)[k] = rv->next;
566 	else {
567 		x = 1 << k;
568 #ifdef Omit_Private_Memory
569 		rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong));
570 #else
571 		len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)
572 			/sizeof(double);
573 		if (k <= Kmax && GET_STATE(pmem_next) - GET_STATE(private_mem) + len <= PRIVATE_mem) {
574 			rv = (Bigint*)GET_STATE(pmem_next);
575 			GET_STATE(pmem_next) += len;
576 			}
577 		else
578 			rv = (Bigint*)MALLOC(len*sizeof(double));
579 #endif
580 		rv->k = k;
581 		rv->maxwds = x;
582 		}
583 	FREE_DTOA_LOCK(0);
584 	rv->sign = rv->wds = 0;
585 	return rv;
586 	}
587 
588  static void
589 Bfree
590 #ifdef KR_headers
591 	(STATE_PARAM v) STATE_PARAM_DECL Bigint *v;
592 #else
593 	(STATE_PARAM Bigint *v)
594 #endif
595 {
596 	if (v) {
597 		if (v->k > Kmax)
598 			FREE((void*)v);
599 		else {
600 			ACQUIRE_DTOA_LOCK(0);
601 			v->next = GET_STATE(freelist)[v->k];
602 			GET_STATE(freelist)[v->k] = v;
603 			FREE_DTOA_LOCK(0);
604 			}
605 		}
606 	}
607 
608 #define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
609 y->wds*sizeof(Long) + 2*sizeof(int))
610 
611  static Bigint *
612 multadd
613 #ifdef KR_headers
614 	(STATE_PARAM b, m, a) STATE_PARAM_DECL Bigint *b; int m, a;
615 #else
616 	(STATE_PARAM Bigint *b, int m, int a)	/* multiply by m and add a */
617 #endif
618 {
619 	int i, wds;
620 #ifdef ULLong
621 	ULong *x;
622 	ULLong carry, y;
623 #else
624 	ULong carry, *x, y;
625 #ifdef Pack_32
626 	ULong xi, z;
627 #endif
628 #endif
629 	Bigint *b1;
630 
631 	wds = b->wds;
632 	x = b->x;
633 	i = 0;
634 	carry = a;
635 	do {
636 #ifdef ULLong
637 		y = *x * (ULLong)m + carry;
638 		carry = y >> 32;
639 		*x++ = (ULong) y & FFFFFFFF;
640 #else
641 #ifdef Pack_32
642 		xi = *x;
643 		y = (xi & 0xffff) * m + carry;
644 		z = (xi >> 16) * m + (y >> 16);
645 		carry = z >> 16;
646 		*x++ = (z << 16) + (y & 0xffff);
647 #else
648 		y = *x * m + carry;
649 		carry = y >> 16;
650 		*x++ = y & 0xffff;
651 #endif
652 #endif
653 		}
654 		while(++i < wds);
655 	if (carry) {
656 		if (wds >= b->maxwds) {
657 			b1 = Balloc(PASS_STATE b->k+1);
658 			Bcopy(b1, b);
659 			Bfree(PASS_STATE b);
660 			b = b1;
661 			}
662 		b->x[wds++] = (ULong) carry;
663 		b->wds = wds;
664 		}
665 	return b;
666 	}
667 
668  static Bigint *
669 s2b
670 #ifdef KR_headers
671 	(STATE_PARAM s, nd0, nd, y9) STATE_PARAM_DECL CONST char *s; int nd0, nd; ULong y9;
672 #else
673 	(STATE_PARAM CONST char *s, int nd0, int nd, ULong y9)
674 #endif
675 {
676 	Bigint *b;
677 	int i, k;
678 	Long x, y;
679 
680 	x = (nd + 8) / 9;
681 	for(k = 0, y = 1; x > y; y <<= 1, k++) ;
682 #ifdef Pack_32
683 	b = Balloc(PASS_STATE k);
684 	b->x[0] = y9;
685 	b->wds = 1;
686 #else
687 	b = Balloc(PASS_STATE k+1);
688 	b->x[0] = y9 & 0xffff;
689 	b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
690 #endif
691 
692 	i = 9;
693 	if (9 < nd0) {
694 		s += 9;
695 		do b = multadd(PASS_STATE b, 10, *s++ - '0');
696 			while(++i < nd0);
697 		s++;
698 		}
699 	else
700 		s += 10;
701 	for(; i < nd; i++)
702 		b = multadd(PASS_STATE b, 10, *s++ - '0');
703 	return b;
704 	}
705 
706  static int
hi0bits(x)707 hi0bits
708 #ifdef KR_headers
709 	(x) ULong x;
710 #else
711 	(ULong x)
712 #endif
713 {
714 	int k = 0;
715 
716 	if (!(x & 0xffff0000)) {
717 		k = 16;
718 		x <<= 16;
719 		}
720 	if (!(x & 0xff000000)) {
721 		k += 8;
722 		x <<= 8;
723 		}
724 	if (!(x & 0xf0000000)) {
725 		k += 4;
726 		x <<= 4;
727 		}
728 	if (!(x & 0xc0000000)) {
729 		k += 2;
730 		x <<= 2;
731 		}
732 	if (!(x & 0x80000000)) {
733 		k++;
734 		if (!(x & 0x40000000))
735 			return 32;
736 		}
737 	return k;
738 	}
739 
740  static int
lo0bits(y)741 lo0bits
742 #ifdef KR_headers
743 	(y) ULong *y;
744 #else
745 	(ULong *y)
746 #endif
747 {
748 	int k;
749 	ULong x = *y;
750 
751 	if (x & 7) {
752 		if (x & 1)
753 			return 0;
754 		if (x & 2) {
755 			*y = x >> 1;
756 			return 1;
757 			}
758 		*y = x >> 2;
759 		return 2;
760 		}
761 	k = 0;
762 	if (!(x & 0xffff)) {
763 		k = 16;
764 		x >>= 16;
765 		}
766 	if (!(x & 0xff)) {
767 		k += 8;
768 		x >>= 8;
769 		}
770 	if (!(x & 0xf)) {
771 		k += 4;
772 		x >>= 4;
773 		}
774 	if (!(x & 0x3)) {
775 		k += 2;
776 		x >>= 2;
777 		}
778 	if (!(x & 1)) {
779 		k++;
780 		x >>= 1;
781 		if (!x)
782 			return 32;
783 		}
784 	*y = x;
785 	return k;
786 	}
787 
788  static Bigint *
789 i2b
790 #ifdef KR_headers
791 	(STATE_PARAM i) STATE_PARAM_DECL int i;
792 #else
793 	(STATE_PARAM int i)
794 #endif
795 {
796 	Bigint *b;
797 
798 	b = Balloc(PASS_STATE 1);
799 	b->x[0] = i;
800 	b->wds = 1;
801 	return b;
802 	}
803 
804  static Bigint *
805 mult
806 #ifdef KR_headers
807 	(STATE_PARAM a, b) STATE_PARAM_DECL Bigint *a, *b;
808 #else
809 	(STATE_PARAM Bigint *a, Bigint *b)
810 #endif
811 {
812 	Bigint *c;
813 	int k, wa, wb, wc;
814 	ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
815 	ULong y;
816 #ifdef ULLong
817 	ULLong carry, z;
818 #else
819 	ULong carry, z;
820 #ifdef Pack_32
821 	ULong z2;
822 #endif
823 #endif
824 
825 	if (a->wds < b->wds) {
826 		c = a;
827 		a = b;
828 		b = c;
829 		}
830 	k = a->k;
831 	wa = a->wds;
832 	wb = b->wds;
833 	wc = wa + wb;
834 	if (wc > a->maxwds)
835 		k++;
836 	c = Balloc(PASS_STATE k);
837 	for(x = c->x, xa = x + wc; x < xa; x++)
838 		*x = 0;
839 	xa = a->x;
840 	xae = xa + wa;
841 	xb = b->x;
842 	xbe = xb + wb;
843 	xc0 = c->x;
844 #ifdef ULLong
845 	for(; xb < xbe; xc0++) {
846 		if ((y = *xb++)) {
847 			x = xa;
848 			xc = xc0;
849 			carry = 0;
850 			do {
851 				z = *x++ * (ULLong)y + *xc + carry;
852 				carry = z >> 32;
853 				*xc++ = (ULong) z & FFFFFFFF;
854 				}
855 				while(x < xae);
856 			*xc = (ULong) carry;
857 			}
858 		}
859 #else
860 #ifdef Pack_32
861 	for(; xb < xbe; xb++, xc0++) {
862 		if (y = *xb & 0xffff) {
863 			x = xa;
864 			xc = xc0;
865 			carry = 0;
866 			do {
867 				z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
868 				carry = z >> 16;
869 				z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
870 				carry = z2 >> 16;
871 				Storeinc(xc, z2, z);
872 				}
873 				while(x < xae);
874 			*xc = carry;
875 			}
876 		if (y = *xb >> 16) {
877 			x = xa;
878 			xc = xc0;
879 			carry = 0;
880 			z2 = *xc;
881 			do {
882 				z = (*x & 0xffff) * y + (*xc >> 16) + carry;
883 				carry = z >> 16;
884 				Storeinc(xc, z, z2);
885 				z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
886 				carry = z2 >> 16;
887 				}
888 				while(x < xae);
889 			*xc = z2;
890 			}
891 		}
892 #else
893 	for(; xb < xbe; xc0++) {
894 		if (y = *xb++) {
895 			x = xa;
896 			xc = xc0;
897 			carry = 0;
898 			do {
899 				z = *x++ * y + *xc + carry;
900 				carry = z >> 16;
901 				*xc++ = z & 0xffff;
902 				}
903 				while(x < xae);
904 			*xc = carry;
905 			}
906 		}
907 #endif
908 #endif
909 	for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
910 	c->wds = wc;
911 	return c;
912 	}
913 
914  static Bigint *
915 pow5mult
916 #ifdef KR_headers
917 	(STATE_PARAM b, k) STATE_PARAM_DECL Bigint *b; int k;
918 #else
919 	(STATE_PARAM Bigint *b, int k)
920 #endif
921 {
922 	Bigint *b1, *p5, *p51;
923 	int i;
924 	static CONST int p05[3] = { 5, 25, 125 };
925 
926 	if ((i = k & 3))
927 		b = multadd(PASS_STATE b, p05[i-1], 0);
928 
929 	if (!(k >>= 2))
930 		return b;
931 	if (!(p5 = GET_STATE(p5s))) {
932 		/* first time */
933 #ifdef MULTIPLE_THREADS
934 		ACQUIRE_DTOA_LOCK(1);
935 		if (!(p5 = p5s)) {
936 			p5 = p5s = i2b(625);
937 			p5->next = 0;
938 			}
939 		FREE_DTOA_LOCK(1);
940 #else
941 		p5 = GET_STATE(p5s) = i2b(PASS_STATE 625);
942 		p5->next = 0;
943 #endif
944 		}
945 	for(;;) {
946 		if (k & 1) {
947 			b1 = mult(PASS_STATE b, p5);
948 			Bfree(PASS_STATE b);
949 			b = b1;
950 			}
951 		if (!(k >>= 1))
952 			break;
953 		if (!(p51 = p5->next)) {
954 #ifdef MULTIPLE_THREADS
955 			ACQUIRE_DTOA_LOCK(1);
956 			if (!(p51 = p5->next)) {
957 				p51 = p5->next = mult(p5,p5);
958 				p51->next = 0;
959 				}
960 			FREE_DTOA_LOCK(1);
961 #else
962 			p51 = p5->next = mult(PASS_STATE p5,p5);
963 			p51->next = 0;
964 #endif
965 			}
966 		p5 = p51;
967 		}
968 	return b;
969 	}
970 
971  static Bigint *
972 lshift
973 #ifdef KR_headers
974 	(STATE_PARAM b, k) STATE_PARAM_DECL Bigint *b; int k;
975 #else
976 	(STATE_PARAM Bigint *b, int k)
977 #endif
978 {
979 	int i, k1, n, n1;
980 	Bigint *b1;
981 	ULong *x, *x1, *xe, z;
982 
983 #ifdef Pack_32
984 	n = k >> 5;
985 #else
986 	n = k >> 4;
987 #endif
988 	k1 = b->k;
989 	n1 = n + b->wds + 1;
990 	for(i = b->maxwds; n1 > i; i <<= 1)
991 		k1++;
992 	b1 = Balloc(PASS_STATE k1);
993 	x1 = b1->x;
994 	for(i = 0; i < n; i++)
995 		*x1++ = 0;
996 	x = b->x;
997 	xe = x + b->wds;
998 #ifdef Pack_32
999 	if (k &= 0x1f) {
1000 		k1 = 32 - k;
1001 		z = 0;
1002 		do {
1003 			*x1++ = *x << k | z;
1004 			z = *x++ >> k1;
1005 			}
1006 			while(x < xe);
1007 		if ((*x1 = z))
1008 			++n1;
1009 		}
1010 #else
1011 	if (k &= 0xf) {
1012 		k1 = 16 - k;
1013 		z = 0;
1014 		do {
1015 			*x1++ = *x << k  & 0xffff | z;
1016 			z = *x++ >> k1;
1017 			}
1018 			while(x < xe);
1019 		if (*x1 = z)
1020 			++n1;
1021 		}
1022 #endif
1023 	else do
1024 		*x1++ = *x++;
1025 		while(x < xe);
1026 	b1->wds = n1 - 1;
1027 	Bfree(PASS_STATE b);
1028 	return b1;
1029 	}
1030 
1031  static int
cmp(a,b)1032 cmp
1033 #ifdef KR_headers
1034 	(a, b) Bigint *a, *b;
1035 #else
1036 	(Bigint *a, Bigint *b)
1037 #endif
1038 {
1039 	ULong *xa, *xa0, *xb, *xb0;
1040 	int i, j;
1041 
1042 	i = a->wds;
1043 	j = b->wds;
1044 #ifdef DEBUG
1045 	if (i > 1 && !a->x[i-1])
1046 		Bug("cmp called with a->x[a->wds-1] == 0");
1047 	if (j > 1 && !b->x[j-1])
1048 		Bug("cmp called with b->x[b->wds-1] == 0");
1049 #endif
1050 	if (i -= j)
1051 		return i;
1052 	xa0 = a->x;
1053 	xa = xa0 + j;
1054 	xb0 = b->x;
1055 	xb = xb0 + j;
1056 	for(;;) {
1057 		if (*--xa != *--xb)
1058 			return *xa < *xb ? -1 : 1;
1059 		if (xa <= xa0)
1060 			break;
1061 		}
1062 	return 0;
1063 	}
1064 
1065  static Bigint *
1066 diff
1067 #ifdef KR_headers
1068 	(STATE_PARAM a, b) STATE_PARAM_DECL Bigint *a, *b;
1069 #else
1070 	(STATE_PARAM Bigint *a, Bigint *b)
1071 #endif
1072 {
1073 	Bigint *c;
1074 	int i, wa, wb;
1075 	ULong *xa, *xae, *xb, *xbe, *xc;
1076 #ifdef ULLong
1077 	ULLong borrow, y;
1078 #else
1079 	ULong borrow, y;
1080 #ifdef Pack_32
1081 	ULong z;
1082 #endif
1083 #endif
1084 
1085 	i = cmp(a,b);
1086 	if (!i) {
1087 		c = Balloc(PASS_STATE 0);
1088 		c->wds = 1;
1089 		c->x[0] = 0;
1090 		return c;
1091 		}
1092 	if (i < 0) {
1093 		c = a;
1094 		a = b;
1095 		b = c;
1096 		i = 1;
1097 		}
1098 	else
1099 		i = 0;
1100 	c = Balloc(PASS_STATE a->k);
1101 	c->sign = i;
1102 	wa = a->wds;
1103 	xa = a->x;
1104 	xae = xa + wa;
1105 	wb = b->wds;
1106 	xb = b->x;
1107 	xbe = xb + wb;
1108 	xc = c->x;
1109 	borrow = 0;
1110 #ifdef ULLong
1111 	do {
1112 		y = (ULLong)*xa++ - *xb++ - borrow;
1113 		borrow = y >> 32 & (ULong)1;
1114 		*xc++ = (ULong) y & FFFFFFFF;
1115 		}
1116 		while(xb < xbe);
1117 	while(xa < xae) {
1118 		y = *xa++ - borrow;
1119 		borrow = y >> 32 & (ULong)1;
1120 		*xc++ = (ULong) y & FFFFFFFF;
1121 		}
1122 #else
1123 #ifdef Pack_32
1124 	do {
1125 		y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
1126 		borrow = (y & 0x10000) >> 16;
1127 		z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
1128 		borrow = (z & 0x10000) >> 16;
1129 		Storeinc(xc, z, y);
1130 		}
1131 		while(xb < xbe);
1132 	while(xa < xae) {
1133 		y = (*xa & 0xffff) - borrow;
1134 		borrow = (y & 0x10000) >> 16;
1135 		z = (*xa++ >> 16) - borrow;
1136 		borrow = (z & 0x10000) >> 16;
1137 		Storeinc(xc, z, y);
1138 		}
1139 #else
1140 	do {
1141 		y = *xa++ - *xb++ - borrow;
1142 		borrow = (y & 0x10000) >> 16;
1143 		*xc++ = y & 0xffff;
1144 		}
1145 		while(xb < xbe);
1146 	while(xa < xae) {
1147 		y = *xa++ - borrow;
1148 		borrow = (y & 0x10000) >> 16;
1149 		*xc++ = y & 0xffff;
1150 		}
1151 #endif
1152 #endif
1153 	while(!*--xc)
1154 		wa--;
1155 	c->wds = wa;
1156 	return c;
1157 	}
1158 
1159  static double
ulp(x)1160 ulp
1161 #ifdef KR_headers
1162 	(x) U x;
1163 #else
1164 	(U x)
1165 #endif
1166 {
1167 	Long L;
1168 	U a;
1169 
1170 	L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
1171 #ifndef Avoid_Underflow
1172 #ifndef Sudden_Underflow
1173 	if (L > 0) {
1174 #endif
1175 #endif
1176 #ifdef IBM
1177 		L |= Exp_msk1 >> 4;
1178 #endif
1179 		word0(a) = L;
1180 		word1(a) = 0;
1181 #ifndef Avoid_Underflow
1182 #ifndef Sudden_Underflow
1183 		}
1184 	else {
1185 		L = -L >> Exp_shift;
1186 		if (L < Exp_shift) {
1187 			word0(a) = 0x80000 >> L;
1188 			word1(a) = 0;
1189 			}
1190 		else {
1191 			word0(a) = 0;
1192 			L -= Exp_shift;
1193 			word1(a) = L >= 31 ? 1 : 1 << 31 - L;
1194 			}
1195 		}
1196 #endif
1197 #endif
1198 	return dval(a);
1199 	}
1200 
1201  static double
b2d(a,e)1202 b2d
1203 #ifdef KR_headers
1204 	(a, e) Bigint *a; int *e;
1205 #else
1206 	(Bigint *a, int *e)
1207 #endif
1208 {
1209 	ULong *xa, *xa0, w, y, z;
1210 	int k;
1211 	U d;
1212 #ifdef VAX
1213 	ULong d0, d1;
1214 #else
1215 #define d0 word0(d)
1216 #define d1 word1(d)
1217 #endif
1218 
1219 	xa0 = a->x;
1220 	xa = xa0 + a->wds;
1221 	y = *--xa;
1222 #ifdef DEBUG
1223 	if (!y) Bug("zero y in b2d");
1224 #endif
1225 	k = hi0bits(y);
1226 	*e = 32 - k;
1227 #ifdef Pack_32
1228 	if (k < Ebits) {
1229 		d0 = Exp_1 | y >> (Ebits - k);
1230 		w = xa > xa0 ? *--xa : 0;
1231 		d1 = y << ((32-Ebits) + k) | w >> (Ebits - k);
1232 		goto ret_d;
1233 		}
1234 	z = xa > xa0 ? *--xa : 0;
1235 	if (k -= Ebits) {
1236 		d0 = Exp_1 | y << k | z >> (32 - k);
1237 		y = xa > xa0 ? *--xa : 0;
1238 		d1 = z << k | y >> (32 - k);
1239 		}
1240 	else {
1241 		d0 = Exp_1 | y;
1242 		d1 = z;
1243 		}
1244 #else
1245 	if (k < Ebits + 16) {
1246 		z = xa > xa0 ? *--xa : 0;
1247 		d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
1248 		w = xa > xa0 ? *--xa : 0;
1249 		y = xa > xa0 ? *--xa : 0;
1250 		d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
1251 		goto ret_d;
1252 		}
1253 	z = xa > xa0 ? *--xa : 0;
1254 	w = xa > xa0 ? *--xa : 0;
1255 	k -= Ebits + 16;
1256 	d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
1257 	y = xa > xa0 ? *--xa : 0;
1258 	d1 = w << k + 16 | y << k;
1259 #endif
1260  ret_d:
1261 #ifdef VAX
1262 	word0(d) = d0 >> 16 | d0 << 16;
1263 	word1(d) = d1 >> 16 | d1 << 16;
1264 #else
1265 #undef d0
1266 #undef d1
1267 #endif
1268 	return dval(d);
1269 	}
1270 
1271  static Bigint *
1272 d2b
1273 #ifdef KR_headers
1274 	(STATE_PARAM d, e, bits) STATE_PARAM_DECL U d; int *e, *bits;
1275 #else
1276 	(STATE_PARAM U d, int *e, int *bits)
1277 #endif
1278 {
1279 	Bigint *b;
1280 	int de, k;
1281 	ULong *x, y, z;
1282 #ifndef Sudden_Underflow
1283 	int i;
1284 #endif
1285 #ifdef VAX
1286 	ULong d0, d1;
1287 	d0 = word0(d) >> 16 | word0(d) << 16;
1288 	d1 = word1(d) >> 16 | word1(d) << 16;
1289 #else
1290 #define d0 word0(d)
1291 #define d1 word1(d)
1292 #endif
1293 
1294 #ifdef Pack_32
1295 	b = Balloc(PASS_STATE 1);
1296 #else
1297 	b = Balloc(PASS_STATE 2);
1298 #endif
1299 	x = b->x;
1300 
1301 	z = d0 & Frac_mask;
1302 	d0 &= 0x7fffffff;	/* clear sign bit, which we ignore */
1303 #ifdef Sudden_Underflow
1304 	de = (int)(d0 >> Exp_shift);
1305 #ifndef IBM
1306 	z |= Exp_msk11;
1307 #endif
1308 #else
1309 	if ((de = (int)(d0 >> Exp_shift)))
1310 		z |= Exp_msk1;
1311 #endif
1312 #ifdef Pack_32
1313 	if ((y = d1)) {
1314 		if ((k = lo0bits(&y))) {
1315 			x[0] = y | z << (32 - k);
1316 			z >>= k;
1317 			}
1318 		else
1319 			x[0] = y;
1320 #ifndef Sudden_Underflow
1321 		i =
1322 #endif
1323 		    b->wds = (x[1] = z) ? 2 : 1;
1324 		}
1325 	else {
1326 		k = lo0bits(&z);
1327 		x[0] = z;
1328 #ifndef Sudden_Underflow
1329 		i =
1330 #endif
1331 		    b->wds = 1;
1332 		k += 32;
1333 		}
1334 #else
1335 	if (y = d1) {
1336 		if (k = lo0bits(&y))
1337 			if (k >= 16) {
1338 				x[0] = y | z << 32 - k & 0xffff;
1339 				x[1] = z >> k - 16 & 0xffff;
1340 				x[2] = z >> k;
1341 				i = 2;
1342 				}
1343 			else {
1344 				x[0] = y & 0xffff;
1345 				x[1] = y >> 16 | z << 16 - k & 0xffff;
1346 				x[2] = z >> k & 0xffff;
1347 				x[3] = z >> k+16;
1348 				i = 3;
1349 				}
1350 		else {
1351 			x[0] = y & 0xffff;
1352 			x[1] = y >> 16;
1353 			x[2] = z & 0xffff;
1354 			x[3] = z >> 16;
1355 			i = 3;
1356 			}
1357 		}
1358 	else {
1359 #ifdef DEBUG
1360 		if (!z)
1361 			Bug("Zero passed to d2b");
1362 #endif
1363 		k = lo0bits(&z);
1364 		if (k >= 16) {
1365 			x[0] = z;
1366 			i = 0;
1367 			}
1368 		else {
1369 			x[0] = z & 0xffff;
1370 			x[1] = z >> 16;
1371 			i = 1;
1372 			}
1373 		k += 32;
1374 		}
1375 	while(!x[i])
1376 		--i;
1377 	b->wds = i + 1;
1378 #endif
1379 #ifndef Sudden_Underflow
1380 	if (de) {
1381 #endif
1382 #ifdef IBM
1383 		*e = (de - Bias - (P-1) << 2) + k;
1384 		*bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
1385 #else
1386 		*e = de - Bias - (P-1) + k;
1387 		*bits = P - k;
1388 #endif
1389 #ifndef Sudden_Underflow
1390 		}
1391 	else {
1392 		*e = de - Bias - (P-1) + 1 + k;
1393 #ifdef Pack_32
1394 		*bits = 32*i - hi0bits(x[i-1]);
1395 #else
1396 		*bits = (i+2)*16 - hi0bits(x[i]);
1397 #endif
1398 		}
1399 #endif
1400 	return b;
1401 	}
1402 #undef d0
1403 #undef d1
1404 
1405  static double
ratio(a,b)1406 ratio
1407 #ifdef KR_headers
1408 	(a, b) Bigint *a, *b;
1409 #else
1410 	(Bigint *a, Bigint *b)
1411 #endif
1412 {
1413 	U da, db;
1414 	int k, ka, kb;
1415 
1416 	dval(da) = b2d(a, &ka);
1417 	dval(db) = b2d(b, &kb);
1418 #ifdef Pack_32
1419 	k = ka - kb + 32*(a->wds - b->wds);
1420 #else
1421 	k = ka - kb + 16*(a->wds - b->wds);
1422 #endif
1423 #ifdef IBM
1424 	if (k > 0) {
1425 		word0(da) += (k >> 2)*Exp_msk1;
1426 		if (k &= 3)
1427 			dval(da) *= 1 << k;
1428 		}
1429 	else {
1430 		k = -k;
1431 		word0(db) += (k >> 2)*Exp_msk1;
1432 		if (k &= 3)
1433 			dval(db) *= 1 << k;
1434 		}
1435 #else
1436 	if (k > 0)
1437 		word0(da) += k*Exp_msk1;
1438 	else {
1439 		k = -k;
1440 		word0(db) += k*Exp_msk1;
1441 		}
1442 #endif
1443 	return dval(da) / dval(db);
1444 	}
1445 
1446  static CONST double
1447 tens[] = {
1448 		1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1449 		1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
1450 		1e20, 1e21, 1e22
1451 #ifdef VAX
1452 		, 1e23, 1e24
1453 #endif
1454 		};
1455 
1456  static CONST double
1457 #ifdef IEEE_Arith
1458 bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
1459 static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
1460 #ifdef Avoid_Underflow
1461 		9007199254740992.*9007199254740992.e-256
1462 		/* = 2^106 * 1e-53 */
1463 #else
1464 		1e-256
1465 #endif
1466 		};
1467 /* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
1468 /* flag unnecessarily.  It leads to a song and dance at the end of strtod. */
1469 #define Scale_Bit 0x10
1470 #define n_bigtens 5
1471 #else
1472 #ifdef IBM
1473 bigtens[] = { 1e16, 1e32, 1e64 };
1474 static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 };
1475 #define n_bigtens 3
1476 #else
1477 bigtens[] = { 1e16, 1e32 };
1478 static CONST double tinytens[] = { 1e-16, 1e-32 };
1479 #define n_bigtens 2
1480 #endif
1481 #endif
1482 
1483  static double
1484 _strtod
1485 #ifdef KR_headers
1486 	(STATE_PARAM s00, se) STATE_PARAM_DECL CONST char *s00; char **se;
1487 #else
1488 	(STATE_PARAM CONST char *s00, char **se)
1489 #endif
1490 {
1491 #ifdef Avoid_Underflow
1492 	int scale;
1493 #endif
1494 	int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
1495 		 e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
1496 	CONST char *s, *s0, *s1;
1497 	double aadj, adj;
1498 	U aadj1, rv, rv0;
1499 	Long L;
1500 	ULong y, z;
1501 	Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
1502 #ifdef SET_INEXACT
1503 	int inexact, oldinexact;
1504 #endif
1505 #ifdef Honor_FLT_ROUNDS
1506 	int rounding;
1507 #endif
1508 #ifdef USE_LOCALE
1509 	CONST char *s2;
1510 #endif
1511 
1512 #ifdef __GNUC__
1513 	delta = bb = bd = bs = 0;
1514 #endif
1515 
1516 	sign = nz0 = nz = 0;
1517 	dval(rv) = 0.;
1518 	for(s = s00;;s++) switch(*s) {
1519 		case '-':
1520 			sign = 1;
1521 			/* no break */
1522 		case '+':
1523 			if (*++s)
1524 				goto break2;
1525 			/* no break */
1526 		case 0:
1527 			goto ret0;
1528 		case '\t':
1529 		case '\n':
1530 		case '\v':
1531 		case '\f':
1532 		case '\r':
1533 		case ' ':
1534 			continue;
1535 		default:
1536 			goto break2;
1537 		}
1538  break2:
1539 	if (*s == '0') {
1540 		nz0 = 1;
1541 		while(*++s == '0') ;
1542 		if (!*s)
1543 			goto ret;
1544 		}
1545 	s0 = s;
1546 	y = z = 0;
1547 	for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
1548 		if (nd < 9)
1549 			y = 10*y + c - '0';
1550 		else if (nd < 16)
1551 			z = 10*z + c - '0';
1552 	nd0 = nd;
1553 #ifdef USE_LOCALE
1554 	s1 = localeconv()->decimal_point;
1555 	if (c == *s1) {
1556 		c = '.';
1557 		if (*++s1) {
1558 			s2 = s;
1559 			for(;;) {
1560 				if (*++s2 != *s1) {
1561 					c = 0;
1562 					break;
1563 					}
1564 				if (!*++s1) {
1565 					s = s2;
1566 					break;
1567 					}
1568 				}
1569 			}
1570 		}
1571 #endif
1572 	if (c == '.') {
1573 		c = *++s;
1574 		if (!nd) {
1575 			for(; c == '0'; c = *++s)
1576 				nz++;
1577 			if (c > '0' && c <= '9') {
1578 				s0 = s;
1579 				nf += nz;
1580 				nz = 0;
1581 				goto have_dig;
1582 				}
1583 			goto dig_done;
1584 			}
1585 		for(; c >= '0' && c <= '9'; c = *++s) {
1586  have_dig:
1587 			nz++;
1588 			if (c -= '0') {
1589 				nf += nz;
1590 				for(i = 1; i < nz; i++)
1591 					if (nd++ < 9)
1592 						y *= 10;
1593 					else if (nd <= DBL_DIG + 1)
1594 						z *= 10;
1595 				if (nd++ < 9)
1596 					y = 10*y + c;
1597 				else if (nd <= DBL_DIG + 1)
1598 					z = 10*z + c;
1599 				nz = 0;
1600 				}
1601 			}
1602 		}
1603  dig_done:
1604 	e = 0;
1605 	if (c == 'e' || c == 'E') {
1606 		if (!nd && !nz && !nz0) {
1607 			goto ret0;
1608 			}
1609 		s00 = s;
1610 		esign = 0;
1611 		switch(c = *++s) {
1612 			case '-':
1613 				esign = 1;
1614 			case '+':
1615 				c = *++s;
1616 			}
1617 		if (c >= '0' && c <= '9') {
1618 			while(c == '0')
1619 				c = *++s;
1620 			if (c > '0' && c <= '9') {
1621 				L = c - '0';
1622 				s1 = s;
1623 				while((c = *++s) >= '0' && c <= '9')
1624 					L = 10*L + c - '0';
1625 				if (s - s1 > 8 || L > 19999)
1626 					/* Avoid confusion from exponents
1627 					 * so large that e might overflow.
1628 					 */
1629 					e = 19999; /* safe for 16 bit ints */
1630 				else
1631 					e = (int)L;
1632 				if (esign)
1633 					e = -e;
1634 				}
1635 			else
1636 				e = 0;
1637 			}
1638 		else
1639 			s = s00;
1640 		}
1641 	if (!nd) {
1642 		if (!nz && !nz0) {
1643  ret0:
1644 			s = s00;
1645 			sign = 0;
1646 			}
1647 		goto ret;
1648 		}
1649 	e1 = e -= nf;
1650 
1651 	/* Now we have nd0 digits, starting at s0, followed by a
1652 	 * decimal point, followed by nd-nd0 digits.  The number we're
1653 	 * after is the integer represented by those digits times
1654 	 * 10**e */
1655 
1656 	if (!nd0)
1657 		nd0 = nd;
1658 	k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
1659 	dval(rv) = y;
1660 	if (k > 9) {
1661 #ifdef SET_INEXACT
1662 		if (k > DBL_DIG)
1663 			oldinexact = get_inexact();
1664 #endif
1665 		dval(rv) = tens[k - 9] * dval(rv) + z;
1666 		}
1667 	bd0 = 0;
1668 	if (nd <= DBL_DIG
1669 #ifndef RND_PRODQUOT
1670 #ifndef Honor_FLT_ROUNDS
1671 		&& Flt_Rounds == 1
1672 #endif
1673 #endif
1674 			) {
1675 		if (!e)
1676 			goto ret;
1677 		if (e > 0) {
1678 			if (e <= Ten_pmax) {
1679 #ifdef VAX
1680 				goto vax_ovfl_check;
1681 #else
1682 #ifdef Honor_FLT_ROUNDS
1683 				/* round correctly FLT_ROUNDS = 2 or 3 */
1684 				if (sign) {
1685 					rv = -rv;
1686 					sign = 0;
1687 					}
1688 #endif
1689 				/* rv = */ rounded_product(dval(rv), tens[e]);
1690 				goto ret;
1691 #endif
1692 				}
1693 			i = DBL_DIG - nd;
1694 			if (e <= Ten_pmax + i) {
1695 				/* A fancier test would sometimes let us do
1696 				 * this for larger i values.
1697 				 */
1698 #ifdef Honor_FLT_ROUNDS
1699 				/* round correctly FLT_ROUNDS = 2 or 3 */
1700 				if (sign) {
1701 					rv = -rv;
1702 					sign = 0;
1703 					}
1704 #endif
1705 				e -= i;
1706 				dval(rv) *= tens[i];
1707 #ifdef VAX
1708 				/* VAX exponent range is so narrow we must
1709 				 * worry about overflow here...
1710 				 */
1711  vax_ovfl_check:
1712 				word0(rv) -= P*Exp_msk1;
1713 				/* rv = */ rounded_product(dval(rv), tens[e]);
1714 				if ((word0(rv) & Exp_mask)
1715 				 > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
1716 					goto ovfl;
1717 				word0(rv) += P*Exp_msk1;
1718 #else
1719 				/* rv = */ rounded_product(dval(rv), tens[e]);
1720 #endif
1721 				goto ret;
1722 				}
1723 			}
1724 #ifndef Inaccurate_Divide
1725 		else if (e >= -Ten_pmax) {
1726 #ifdef Honor_FLT_ROUNDS
1727 			/* round correctly FLT_ROUNDS = 2 or 3 */
1728 			if (sign) {
1729 				rv = -rv;
1730 				sign = 0;
1731 				}
1732 #endif
1733 			/* rv = */ rounded_quotient(dval(rv), tens[-e]);
1734 			goto ret;
1735 			}
1736 #endif
1737 		}
1738 	e1 += nd - k;
1739 
1740 #ifdef IEEE_Arith
1741 #ifdef SET_INEXACT
1742 	inexact = 1;
1743 	if (k <= DBL_DIG)
1744 		oldinexact = get_inexact();
1745 #endif
1746 #ifdef Avoid_Underflow
1747 	scale = 0;
1748 #endif
1749 #ifdef Honor_FLT_ROUNDS
1750 	if ((rounding = Flt_Rounds) >= 2) {
1751 		if (sign)
1752 			rounding = rounding == 2 ? 0 : 2;
1753 		else
1754 			if (rounding != 2)
1755 				rounding = 0;
1756 		}
1757 #endif
1758 #endif /*IEEE_Arith*/
1759 
1760 	/* Get starting approximation = rv * 10**e1 */
1761 
1762 	if (e1 > 0) {
1763 		if ((i = e1 & 15))
1764 			dval(rv) *= tens[i];
1765 		if (e1 &= ~15) {
1766 			if (e1 > DBL_MAX_10_EXP) {
1767  ovfl:
1768 #ifndef NO_ERRNO
1769 				errno = ERANGE;
1770 #endif
1771 				/* Can't trust HUGE_VAL */
1772 #ifdef IEEE_Arith
1773 #ifdef Honor_FLT_ROUNDS
1774 				switch(rounding) {
1775 				  case 0: /* toward 0 */
1776 				  case 3: /* toward -infinity */
1777 					word0(rv) = Big0;
1778 					word1(rv) = Big1;
1779 					break;
1780 				  default:
1781 					word0(rv) = Exp_mask;
1782 					word1(rv) = 0;
1783 				  }
1784 #else /*Honor_FLT_ROUNDS*/
1785 				word0(rv) = Exp_mask;
1786 				word1(rv) = 0;
1787 #endif /*Honor_FLT_ROUNDS*/
1788 #ifdef SET_INEXACT
1789 				/* set overflow bit */
1790 				dval(rv0) = 1e300;
1791 				dval(rv0) *= dval(rv0);
1792 #endif
1793 #else /*IEEE_Arith*/
1794 				word0(rv) = Big0;
1795 				word1(rv) = Big1;
1796 #endif /*IEEE_Arith*/
1797 				if (bd0)
1798 					goto retfree;
1799 				goto ret;
1800 				}
1801 			e1 >>= 4;
1802 			for(j = 0; e1 > 1; j++, e1 >>= 1)
1803 				if (e1 & 1)
1804 					dval(rv) *= bigtens[j];
1805 		/* The last multiplication could overflow. */
1806 			word0(rv) -= P*Exp_msk1;
1807 			dval(rv) *= bigtens[j];
1808 			if ((z = word0(rv) & Exp_mask)
1809 			 > Exp_msk1*(DBL_MAX_EXP+Bias-P))
1810 				goto ovfl;
1811 			if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
1812 				/* set to largest number */
1813 				/* (Can't trust DBL_MAX) */
1814 				word0(rv) = Big0;
1815 				word1(rv) = Big1;
1816 				}
1817 			else
1818 				word0(rv) += P*Exp_msk1;
1819 			}
1820 		}
1821 	else if (e1 < 0) {
1822 		e1 = -e1;
1823 		if ((i = e1 & 15))
1824 			dval(rv) /= tens[i];
1825 		if (e1 >>= 4) {
1826 			if (e1 >= 1 << n_bigtens)
1827 				goto undfl;
1828 #ifdef Avoid_Underflow
1829 			if (e1 & Scale_Bit)
1830 				scale = 2*P;
1831 			for(j = 0; e1 > 0; j++, e1 >>= 1)
1832 				if (e1 & 1)
1833 					dval(rv) *= tinytens[j];
1834 			if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask)
1835 						>> Exp_shift)) > 0) {
1836 				/* scaled rv is denormal; zap j low bits */
1837 				if (j >= 32) {
1838 					word1(rv) = 0;
1839 					if (j >= 53)
1840 					 word0(rv) = (P+2)*Exp_msk1;
1841 					else
1842 					 word0(rv) &= 0xffffffff << (j-32);
1843 					}
1844 				else
1845 					word1(rv) &= 0xffffffff << j;
1846 				}
1847 #else
1848 			for(j = 0; e1 > 1; j++, e1 >>= 1)
1849 				if (e1 & 1)
1850 					dval(rv) *= tinytens[j];
1851 			/* The last multiplication could underflow. */
1852 			dval(rv0) = dval(rv);
1853 			dval(rv) *= tinytens[j];
1854 			if (!dval(rv)) {
1855 				dval(rv) = 2.*dval(rv0);
1856 				dval(rv) *= tinytens[j];
1857 #endif
1858 				if (!dval(rv)) {
1859  undfl:
1860 					dval(rv) = 0.;
1861 #ifndef NO_ERRNO
1862 					errno = ERANGE;
1863 #endif
1864 					if (bd0)
1865 						goto retfree;
1866 					goto ret;
1867 					}
1868 #ifndef Avoid_Underflow
1869 				word0(rv) = Tiny0;
1870 				word1(rv) = Tiny1;
1871 				/* The refinement below will clean
1872 				 * this approximation up.
1873 				 */
1874 				}
1875 #endif
1876 			}
1877 		}
1878 
1879 	/* Now the hard part -- adjusting rv to the correct value.*/
1880 
1881 	/* Put digits into bd: true value = bd * 10^e */
1882 
1883 	bd0 = s2b(PASS_STATE s0, nd0, nd, y);
1884 
1885 	for(;;) {
1886 		bd = Balloc(PASS_STATE bd0->k);
1887 		Bcopy(bd, bd0);
1888 		bb = d2b(PASS_STATE rv, &bbe, &bbbits);	/* rv = bb * 2^bbe */
1889 		bs = i2b(PASS_STATE 1);
1890 
1891 		if (e >= 0) {
1892 			bb2 = bb5 = 0;
1893 			bd2 = bd5 = e;
1894 			}
1895 		else {
1896 			bb2 = bb5 = -e;
1897 			bd2 = bd5 = 0;
1898 			}
1899 		if (bbe >= 0)
1900 			bb2 += bbe;
1901 		else
1902 			bd2 -= bbe;
1903 		bs2 = bb2;
1904 #ifdef Honor_FLT_ROUNDS
1905 		if (rounding != 1)
1906 			bs2++;
1907 #endif
1908 #ifdef Avoid_Underflow
1909 		j = bbe - scale;
1910 		i = j + bbbits - 1;	/* logb(rv) */
1911 		if (i < Emin)	/* denormal */
1912 			j += P - Emin;
1913 		else
1914 			j = P + 1 - bbbits;
1915 #else /*Avoid_Underflow*/
1916 #ifdef Sudden_Underflow
1917 #ifdef IBM
1918 		j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
1919 #else
1920 		j = P + 1 - bbbits;
1921 #endif
1922 #else /*Sudden_Underflow*/
1923 		j = bbe;
1924 		i = j + bbbits - 1;	/* logb(rv) */
1925 		if (i < Emin)	/* denormal */
1926 			j += P - Emin;
1927 		else
1928 			j = P + 1 - bbbits;
1929 #endif /*Sudden_Underflow*/
1930 #endif /*Avoid_Underflow*/
1931 		bb2 += j;
1932 		bd2 += j;
1933 #ifdef Avoid_Underflow
1934 		bd2 += scale;
1935 #endif
1936 		i = bb2 < bd2 ? bb2 : bd2;
1937 		if (i > bs2)
1938 			i = bs2;
1939 		if (i > 0) {
1940 			bb2 -= i;
1941 			bd2 -= i;
1942 			bs2 -= i;
1943 			}
1944 		if (bb5 > 0) {
1945 			bs = pow5mult(PASS_STATE bs, bb5);
1946 			bb1 = mult(PASS_STATE bs, bb);
1947 			Bfree(PASS_STATE bb);
1948 			bb = bb1;
1949 			}
1950 		if (bb2 > 0)
1951 			bb = lshift(PASS_STATE bb, bb2);
1952 		if (bd5 > 0)
1953 			bd = pow5mult(PASS_STATE bd, bd5);
1954 		if (bd2 > 0)
1955 			bd = lshift(PASS_STATE bd, bd2);
1956 		if (bs2 > 0)
1957 			bs = lshift(PASS_STATE bs, bs2);
1958 		delta = diff(PASS_STATE bb, bd);
1959 		dsign = delta->sign;
1960 		delta->sign = 0;
1961 		i = cmp(delta, bs);
1962 #ifdef Honor_FLT_ROUNDS
1963 		if (rounding != 1) {
1964 			if (i < 0) {
1965 				/* Error is less than an ulp */
1966 				if (!delta->x[0] && delta->wds <= 1) {
1967 					/* exact */
1968 #ifdef SET_INEXACT
1969 					inexact = 0;
1970 #endif
1971 					break;
1972 					}
1973 				if (rounding) {
1974 					if (dsign) {
1975 						adj = 1.;
1976 						goto apply_adj;
1977 						}
1978 					}
1979 				else if (!dsign) {
1980 					adj = -1.;
1981 					if (!word1(rv)
1982 					 && !(word0(rv) & Frac_mask)) {
1983 						y = word0(rv) & Exp_mask;
1984 #ifdef Avoid_Underflow
1985 						if (!scale || y > 2*P*Exp_msk1)
1986 #else
1987 						if (y)
1988 #endif
1989 						  {
1990 						  delta = lshift(PASS_STATE delta,Log2P);
1991 						  if (cmp(delta, bs) <= 0)
1992 							adj = -0.5;
1993 						  }
1994 						}
1995  apply_adj:
1996 #ifdef Avoid_Underflow
1997 					if (scale && (y = word0(rv) & Exp_mask)
1998 						<= 2*P*Exp_msk1)
1999 					  word0(adj) += (2*P+1)*Exp_msk1 - y;
2000 #else
2001 #ifdef Sudden_Underflow
2002 					if ((word0(rv) & Exp_mask) <=
2003 							P*Exp_msk1) {
2004 						word0(rv) += P*Exp_msk1;
2005 						dval(rv) += adj*ulp(rv);
2006 						word0(rv) -= P*Exp_msk1;
2007 						}
2008 					else
2009 #endif /*Sudden_Underflow*/
2010 #endif /*Avoid_Underflow*/
2011 					dval(rv) += adj*ulp(rv);
2012 					}
2013 				break;
2014 				}
2015 			adj = ratio(delta, bs);
2016 			if (adj < 1.)
2017 				adj = 1.;
2018 			if (adj <= 0x7ffffffe) {
2019 				/* adj = rounding ? ceil(adj) : floor(adj); */
2020 				y = adj;
2021 				if (y != adj) {
2022 					if (!((rounding>>1) ^ dsign))
2023 						y++;
2024 					adj = y;
2025 					}
2026 				}
2027 #ifdef Avoid_Underflow
2028 			if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
2029 				word0(adj) += (2*P+1)*Exp_msk1 - y;
2030 #else
2031 #ifdef Sudden_Underflow
2032 			if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2033 				word0(rv) += P*Exp_msk1;
2034 				adj *= ulp(rv);
2035 				if (dsign)
2036 					dval(rv) += adj;
2037 				else
2038 					dval(rv) -= adj;
2039 				word0(rv) -= P*Exp_msk1;
2040 				goto cont;
2041 				}
2042 #endif /*Sudden_Underflow*/
2043 #endif /*Avoid_Underflow*/
2044 			adj *= ulp(rv);
2045 			if (dsign)
2046 				dval(rv) += adj;
2047 			else
2048 				dval(rv) -= adj;
2049 			goto cont;
2050 			}
2051 #endif /*Honor_FLT_ROUNDS*/
2052 
2053 		if (i < 0) {
2054 			/* Error is less than half an ulp -- check for
2055 			 * special case of mantissa a power of two.
2056 			 */
2057 			if (dsign || word1(rv) || word0(rv) & Bndry_mask
2058 #ifdef IEEE_Arith
2059 #ifdef Avoid_Underflow
2060 			 || (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1
2061 #else
2062 			 || (word0(rv) & Exp_mask) <= Exp_msk1
2063 #endif
2064 #endif
2065 				) {
2066 #ifdef SET_INEXACT
2067 				if (!delta->x[0] && delta->wds <= 1)
2068 					inexact = 0;
2069 #endif
2070 				break;
2071 				}
2072 			if (!delta->x[0] && delta->wds <= 1) {
2073 				/* exact result */
2074 #ifdef SET_INEXACT
2075 				inexact = 0;
2076 #endif
2077 				break;
2078 				}
2079 			delta = lshift(PASS_STATE delta,Log2P);
2080 			if (cmp(delta, bs) > 0)
2081 				goto drop_down;
2082 			break;
2083 			}
2084 		if (i == 0) {
2085 			/* exactly half-way between */
2086 			if (dsign) {
2087 				if ((word0(rv) & Bndry_mask1) == Bndry_mask1
2088 				 &&  word1(rv) == (
2089 #ifdef Avoid_Underflow
2090 			(scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
2091 		? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
2092 #endif
2093 						   0xffffffff)) {
2094 					/*boundary case -- increment exponent*/
2095 					word0(rv) = (word0(rv) & Exp_mask)
2096 						+ Exp_msk1
2097 #ifdef IBM
2098 						| Exp_msk1 >> 4
2099 #endif
2100 						;
2101 					word1(rv) = 0;
2102 #ifdef Avoid_Underflow
2103 					dsign = 0;
2104 #endif
2105 					break;
2106 					}
2107 				}
2108 			else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
2109  drop_down:
2110 				/* boundary case -- decrement exponent */
2111 #ifdef Sudden_Underflow /*{{*/
2112 				L = word0(rv) & Exp_mask;
2113 #ifdef IBM
2114 				if (L <  Exp_msk1)
2115 #else
2116 #ifdef Avoid_Underflow
2117 				if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
2118 #else
2119 				if (L <= Exp_msk1)
2120 #endif /*Avoid_Underflow*/
2121 #endif /*IBM*/
2122 					goto undfl;
2123 				L -= Exp_msk1;
2124 #else /*Sudden_Underflow}{*/
2125 #ifdef Avoid_Underflow
2126 				if (scale) {
2127 					L = word0(rv) & Exp_mask;
2128 					if (L <= (2*P+1)*Exp_msk1) {
2129 						if (L > (P+2)*Exp_msk1)
2130 							/* round even ==> */
2131 							/* accept rv */
2132 							break;
2133 						/* rv = smallest denormal */
2134 						goto undfl;
2135 						}
2136 					}
2137 #endif /*Avoid_Underflow*/
2138 				L = (word0(rv) & Exp_mask) - Exp_msk1;
2139 #endif /*Sudden_Underflow}}*/
2140 				word0(rv) = L | Bndry_mask1;
2141 				word1(rv) = 0xffffffff;
2142 #ifdef IBM
2143 				goto cont;
2144 #else
2145 				break;
2146 #endif
2147 				}
2148 #ifndef ROUND_BIASED
2149 			if (!(word1(rv) & LSB))
2150 				break;
2151 #endif
2152 			if (dsign)
2153 				dval(rv) += ulp(rv);
2154 #ifndef ROUND_BIASED
2155 			else {
2156 				dval(rv) -= ulp(rv);
2157 #ifndef Sudden_Underflow
2158 				if (!dval(rv))
2159 					goto undfl;
2160 #endif
2161 				}
2162 #ifdef Avoid_Underflow
2163 			dsign = 1 - dsign;
2164 #endif
2165 #endif
2166 			break;
2167 			}
2168 		if ((aadj = ratio(delta, bs)) <= 2.) {
2169 			if (dsign)
2170 				aadj = dval(aadj1) = 1.;
2171 			else if (word1(rv) || word0(rv) & Bndry_mask) {
2172 #ifndef Sudden_Underflow
2173 				if (word1(rv) == Tiny1 && !word0(rv))
2174 					goto undfl;
2175 #endif
2176 				aadj = 1.;
2177 				dval(aadj1) = -1.;
2178 				}
2179 			else {
2180 				/* special case -- power of FLT_RADIX to be */
2181 				/* rounded down... */
2182 
2183 				if (aadj < 2./FLT_RADIX)
2184 					aadj = 1./FLT_RADIX;
2185 				else
2186 					aadj *= 0.5;
2187 				dval(aadj1) = -aadj;
2188 				}
2189 			}
2190 		else {
2191 			aadj *= 0.5;
2192 			dval(aadj1) = dsign ? aadj : -aadj;
2193 #ifdef Check_FLT_ROUNDS
2194 			switch(Rounding) {
2195 				case 2: /* towards +infinity */
2196 					dval(aadj1) -= 0.5;
2197 					break;
2198 				case 0: /* towards 0 */
2199 				case 3: /* towards -infinity */
2200 					dval(aadj1) += 0.5;
2201 				}
2202 #else
2203 			if (Flt_Rounds == 0)
2204 				dval(aadj1) += 0.5;
2205 #endif /*Check_FLT_ROUNDS*/
2206 			}
2207 		y = word0(rv) & Exp_mask;
2208 
2209 		/* Check for overflow */
2210 
2211 		if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
2212 			dval(rv0) = dval(rv);
2213 			word0(rv) -= P*Exp_msk1;
2214 			adj = dval(aadj1) * ulp(rv);
2215 			dval(rv) += adj;
2216 			if ((word0(rv) & Exp_mask) >=
2217 					Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
2218 				if (word0(rv0) == Big0 && word1(rv0) == Big1)
2219 					goto ovfl;
2220 				word0(rv) = Big0;
2221 				word1(rv) = Big1;
2222 				goto cont;
2223 				}
2224 			else
2225 				word0(rv) += P*Exp_msk1;
2226 			}
2227 		else {
2228 #ifdef Avoid_Underflow
2229 			if (scale && y <= 2*P*Exp_msk1) {
2230 				if (aadj <= 0x7fffffff) {
2231 					if ((z = (ULong) aadj) <= 0)
2232 						z = 1;
2233 					aadj = z;
2234 					dval(aadj1) = dsign ? aadj : -aadj;
2235 					}
2236 				word0(aadj1) += (2*P+1)*Exp_msk1 - y;
2237 				}
2238 			adj = dval(aadj1) * ulp(rv);
2239 			dval(rv) += adj;
2240 #else
2241 #ifdef Sudden_Underflow
2242 			if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2243 				dval(rv0) = dval(rv);
2244 				word0(rv) += P*Exp_msk1;
2245 				adj = dval(aadj1) * ulp(rv);
2246 				dval(rv) += adj;
2247 #ifdef IBM
2248 				if ((word0(rv) & Exp_mask) <  P*Exp_msk1)
2249 #else
2250 				if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
2251 #endif
2252 					{
2253 					if (word0(rv0) == Tiny0
2254 					 && word1(rv0) == Tiny1)
2255 						goto undfl;
2256 					word0(rv) = Tiny0;
2257 					word1(rv) = Tiny1;
2258 					goto cont;
2259 					}
2260 				else
2261 					word0(rv) -= P*Exp_msk1;
2262 				}
2263 			else {
2264 				adj = dval(aadj1) * ulp(rv);
2265 				dval(rv) += adj;
2266 				}
2267 #else /*Sudden_Underflow*/
2268 			/* Compute adj so that the IEEE rounding rules will
2269 			 * correctly round rv + adj in some half-way cases.
2270 			 * If rv * ulp(rv) is denormalized (i.e.,
2271 			 * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
2272 			 * trouble from bits lost to denormalization;
2273 			 * example: 1.2e-307 .
2274 			 */
2275 			if (y <= (P-1)*Exp_msk1 && aadj > 1.) {
2276 				dval(aadj1) = (double)(int)(aadj + 0.5);
2277 				if (!dsign)
2278 					dval(aadj1) = -dval(aadj1);
2279 				}
2280 			adj = dval(aadj1) * ulp(rv);
2281 			dval(rv) += adj;
2282 #endif /*Sudden_Underflow*/
2283 #endif /*Avoid_Underflow*/
2284 			}
2285 		z = word0(rv) & Exp_mask;
2286 #ifndef SET_INEXACT
2287 #ifdef Avoid_Underflow
2288 		if (!scale)
2289 #endif
2290 		if (y == z) {
2291 			/* Can we stop now? */
2292 			L = (Long)aadj;
2293 			aadj -= L;
2294 			/* The tolerances below are conservative. */
2295 			if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
2296 				if (aadj < .4999999 || aadj > .5000001)
2297 					break;
2298 				}
2299 			else if (aadj < .4999999/FLT_RADIX)
2300 				break;
2301 			}
2302 #endif
2303  cont:
2304 		Bfree(PASS_STATE bb);
2305 		Bfree(PASS_STATE bd);
2306 		Bfree(PASS_STATE bs);
2307 		Bfree(PASS_STATE delta);
2308 		}
2309 #ifdef SET_INEXACT
2310 	if (inexact) {
2311 		if (!oldinexact) {
2312 			word0(rv0) = Exp_1 + (70 << Exp_shift);
2313 			word1(rv0) = 0;
2314 			dval(rv0) += 1.;
2315 			}
2316 		}
2317 	else if (!oldinexact)
2318 		clear_inexact();
2319 #endif
2320 #ifdef Avoid_Underflow
2321 	if (scale) {
2322 		word0(rv0) = Exp_1 - 2*P*Exp_msk1;
2323 		word1(rv0) = 0;
2324 		dval(rv) *= dval(rv0);
2325 #ifndef NO_ERRNO
2326 		/* try to avoid the bug of testing an 8087 register value */
2327 		if (word0(rv) == 0 && word1(rv) == 0)
2328 			errno = ERANGE;
2329 #endif
2330 		}
2331 #endif /* Avoid_Underflow */
2332 #ifdef SET_INEXACT
2333 	if (inexact && !(word0(rv) & Exp_mask)) {
2334 		/* set underflow bit */
2335 		dval(rv0) = 1e-300;
2336 		dval(rv0) *= dval(rv0);
2337 		}
2338 #endif
2339  retfree:
2340 	Bfree(PASS_STATE bb);
2341 	Bfree(PASS_STATE bd);
2342 	Bfree(PASS_STATE bs);
2343 	Bfree(PASS_STATE bd0);
2344 	Bfree(PASS_STATE delta);
2345  ret:
2346 	if (se)
2347 		*se = (char *)s;
2348 	return sign ? -dval(rv) : dval(rv);
2349 	}
2350 
2351  static int
quorem(b,S)2352 quorem
2353 #ifdef KR_headers
2354 	(b, S) Bigint *b, *S;
2355 #else
2356 	(Bigint *b, Bigint *S)
2357 #endif
2358 {
2359 	int n;
2360 	ULong *bx, *bxe, q, *sx, *sxe;
2361 #ifdef ULLong
2362 	ULLong borrow, carry, y, ys;
2363 #else
2364 	ULong borrow, carry, y, ys;
2365 #ifdef Pack_32
2366 	ULong si, z, zs;
2367 #endif
2368 #endif
2369 
2370 	n = S->wds;
2371 #ifdef DEBUG
2372 	/*debug*/ if (b->wds > n)
2373 	/*debug*/	Bug("oversize b in quorem");
2374 #endif
2375 	if (b->wds < n)
2376 		return 0;
2377 	sx = S->x;
2378 	sxe = sx + --n;
2379 	bx = b->x;
2380 	bxe = bx + n;
2381 	q = *bxe / (*sxe + 1);	/* ensure q <= true quotient */
2382 #ifdef DEBUG
2383 	/*debug*/ if (q > 9)
2384 	/*debug*/	Bug("oversized quotient in quorem");
2385 #endif
2386 	if (q) {
2387 		borrow = 0;
2388 		carry = 0;
2389 		do {
2390 #ifdef ULLong
2391 			ys = *sx++ * (ULLong)q + carry;
2392 			carry = ys >> 32;
2393 			y = *bx - (ys & FFFFFFFF) - borrow;
2394 			borrow = y >> 32 & (ULong)1;
2395 			*bx++ = (ULong) y & FFFFFFFF;
2396 #else
2397 #ifdef Pack_32
2398 			si = *sx++;
2399 			ys = (si & 0xffff) * q + carry;
2400 			zs = (si >> 16) * q + (ys >> 16);
2401 			carry = zs >> 16;
2402 			y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
2403 			borrow = (y & 0x10000) >> 16;
2404 			z = (*bx >> 16) - (zs & 0xffff) - borrow;
2405 			borrow = (z & 0x10000) >> 16;
2406 			Storeinc(bx, z, y);
2407 #else
2408 			ys = *sx++ * q + carry;
2409 			carry = ys >> 16;
2410 			y = *bx - (ys & 0xffff) - borrow;
2411 			borrow = (y & 0x10000) >> 16;
2412 			*bx++ = y & 0xffff;
2413 #endif
2414 #endif
2415 			}
2416 			while(sx <= sxe);
2417 		if (!*bxe) {
2418 			bx = b->x;
2419 			while(--bxe > bx && !*bxe)
2420 				--n;
2421 			b->wds = n;
2422 			}
2423 		}
2424 	if (cmp(b, S) >= 0) {
2425 		q++;
2426 		borrow = 0;
2427 		carry = 0;
2428 		bx = b->x;
2429 		sx = S->x;
2430 		do {
2431 #ifdef ULLong
2432 			ys = *sx++ + carry;
2433 			carry = ys >> 32;
2434 			y = *bx - (ys & FFFFFFFF) - borrow;
2435 			borrow = y >> 32 & (ULong)1;
2436 			*bx++ = (ULong) y & FFFFFFFF;
2437 #else
2438 #ifdef Pack_32
2439 			si = *sx++;
2440 			ys = (si & 0xffff) + carry;
2441 			zs = (si >> 16) + (ys >> 16);
2442 			carry = zs >> 16;
2443 			y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
2444 			borrow = (y & 0x10000) >> 16;
2445 			z = (*bx >> 16) - (zs & 0xffff) - borrow;
2446 			borrow = (z & 0x10000) >> 16;
2447 			Storeinc(bx, z, y);
2448 #else
2449 			ys = *sx++ + carry;
2450 			carry = ys >> 16;
2451 			y = *bx - (ys & 0xffff) - borrow;
2452 			borrow = (y & 0x10000) >> 16;
2453 			*bx++ = y & 0xffff;
2454 #endif
2455 #endif
2456 			}
2457 			while(sx <= sxe);
2458 		bx = b->x;
2459 		bxe = bx + n;
2460 		if (!*bxe) {
2461 			while(--bxe > bx && !*bxe)
2462 				--n;
2463 			b->wds = n;
2464 			}
2465 		}
2466 	return q;
2467 	}
2468 
2469 #if !defined(MULTIPLE_THREADS) && !defined(NO_GLOBAL_STATE)
2470 #define USE_DTOA_RESULT 1
2471  static char *dtoa_result;
2472 #endif
2473 
2474  static char *
2475 #ifdef KR_headers
2476 rv_alloc(STATE_PARAM i) STATE_PARAM_DECL int i;
2477 #else
2478 rv_alloc(STATE_PARAM int i)
2479 #endif
2480 {
2481 	int j, k, *r;
2482 
2483 	j = sizeof(ULong);
2484 	for(k = 0;
2485 		sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= (unsigned) i;
2486 		j <<= 1)
2487 			k++;
2488 	r = (int*)Balloc(PASS_STATE k);
2489 	*r = k;
2490 	return
2491 #ifdef USE_DTOA_RESULT
2492 	dtoa_result =
2493 #endif
2494 		(char *)(r+1);
2495 	}
2496 
2497  static char *
2498 #ifdef KR_headers
2499 nrv_alloc(STATE_PARAM s, rve, n) STATE_PARAM_DECL char *s, **rve; int n;
2500 #else
2501 nrv_alloc(STATE_PARAM CONST char *s, char **rve, int n)
2502 #endif
2503 {
2504 	char *rv, *t;
2505 
2506 	t = rv = rv_alloc(PASS_STATE n);
2507 	while((*t = *s++)) t++;
2508 	if (rve)
2509 		*rve = t;
2510 	return rv;
2511 	}
2512 
2513 /* freedtoa(s) must be used to free values s returned by dtoa
2514  * when MULTIPLE_THREADS is #defined.  It should be used in all cases,
2515  * but for consistency with earlier versions of dtoa, it is optional
2516  * when MULTIPLE_THREADS is not defined.
2517  */
2518 
2519  static void
2520 #ifdef KR_headers
2521 freedtoa(STATE_PARAM s) STATE_PARAM_DECL char *s;
2522 #else
2523 freedtoa(STATE_PARAM char *s)
2524 #endif
2525 {
2526 	Bigint *b = (Bigint *)((int *)s - 1);
2527 	b->maxwds = 1 << (b->k = *(int*)b);
2528 	Bfree(PASS_STATE b);
2529 #ifdef USE_DTOA_RESULT
2530 	if (s == dtoa_result)
2531 		dtoa_result = 0;
2532 #endif
2533 	}
2534 
2535 /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
2536  *
2537  * Inspired by "How to Print Floating-Point Numbers Accurately" by
2538  * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126].
2539  *
2540  * Modifications:
2541  *	1. Rather than iterating, we use a simple numeric overestimate
2542  *	   to determine k = floor(log10(d)).  We scale relevant
2543  *	   quantities using O(log2(k)) rather than O(k) multiplications.
2544  *	2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
2545  *	   try to generate digits strictly left to right.  Instead, we
2546  *	   compute with fewer bits and propagate the carry if necessary
2547  *	   when rounding the final digit up.  This is often faster.
2548  *	3. Under the assumption that input will be rounded nearest,
2549  *	   mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
2550  *	   That is, we allow equality in stopping tests when the
2551  *	   round-nearest rule will give the same floating-point value
2552  *	   as would satisfaction of the stopping test with strict
2553  *	   inequality.
2554  *	4. We remove common factors of powers of 2 from relevant
2555  *	   quantities.
2556  *	5. When converting floating-point integers less than 1e16,
2557  *	   we use floating-point arithmetic rather than resorting
2558  *	   to multiple-precision integers.
2559  *	6. When asked to produce fewer than 15 digits, we first try
2560  *	   to get by with floating-point arithmetic; we resort to
2561  *	   multiple-precision integer arithmetic only if we cannot
2562  *	   guarantee that the floating-point calculation has given
2563  *	   the correctly rounded result.  For k requested digits and
2564  *	   "uniformly" distributed input, the probability is
2565  *	   something like 10^(k-15) that we must resort to the Long
2566  *	   calculation.
2567  */
2568 
2569  static char *
2570 dtoa
2571 #ifdef KR_headers
2572 	(STATE_PARAM d, mode, ndigits, decpt, sign, rve)
2573 	STATE_PARAM_DECL U d; int mode, ndigits, *decpt, *sign; char **rve;
2574 #else
2575 	(STATE_PARAM U d, int mode, int ndigits, int *decpt, int *sign, char **rve)
2576 #endif
2577 {
2578  /*	Arguments ndigits, decpt, sign are similar to those
2579 	of ecvt and fcvt; trailing zeros are suppressed from
2580 	the returned string.  If not null, *rve is set to point
2581 	to the end of the return value.  If d is +-Infinity or NaN,
2582 	then *decpt is set to 9999.
2583 
2584 	mode:
2585 		0 ==> shortest string that yields d when read in
2586 			and rounded to nearest.
2587 		1 ==> like 0, but with Steele & White stopping rule;
2588 			e.g. with IEEE P754 arithmetic , mode 0 gives
2589 			1e23 whereas mode 1 gives 9.999999999999999e22.
2590 		2 ==> max(1,ndigits) significant digits.  This gives a
2591 			return value similar to that of ecvt, except
2592 			that trailing zeros are suppressed.
2593 		3 ==> through ndigits past the decimal point.  This
2594 			gives a return value similar to that from fcvt,
2595 			except that trailing zeros are suppressed, and
2596 			ndigits can be negative.
2597 		4,5 ==> similar to 2 and 3, respectively, but (in
2598 			round-nearest mode) with the tests of mode 0 to
2599 			possibly return a shorter string that rounds to d.
2600 			With IEEE arithmetic and compilation with
2601 			-DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
2602 			as modes 2 and 3 when FLT_ROUNDS != 1.
2603 		6-9 ==> Debugging modes similar to mode - 4:  don't try
2604 			fast floating-point estimate (if applicable).
2605 
2606 		Values of mode other than 0-9 are treated as mode 0.
2607 
2608 		Sufficient space is allocated to the return value
2609 		to hold the suppressed trailing zeros.
2610 	*/
2611 
2612 	int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
2613 		j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
2614 		spec_case, try_quick;
2615 	Long L;
2616 #ifndef Sudden_Underflow
2617 	int denorm;
2618 	ULong x;
2619 #endif
2620 	Bigint *b, *b1, *delta, *mlo, *mhi, *S;
2621 	U d2, eps;
2622 	double ds;
2623 	char *s, *s0;
2624 #ifdef Honor_FLT_ROUNDS
2625 	int rounding;
2626 #endif
2627 #ifdef SET_INEXACT
2628 	int inexact, oldinexact;
2629 #endif
2630 
2631 #ifdef __GNUC__
2632 	ilim = ilim1 = 0;
2633 	mlo = NULL;
2634 #endif
2635 
2636 #ifdef USE_DTOA_RESULT
2637 	if (dtoa_result) {
2638 		freedtoa(PASS_STATE dtoa_result);
2639 		dtoa_result = 0;
2640 		}
2641 #endif
2642 
2643 	if (word0(d) & Sign_bit) {
2644 		/* set sign for everything, including 0's and NaNs */
2645 		*sign = 1;
2646 		word0(d) &= ~Sign_bit;	/* clear sign bit */
2647 		}
2648 	else
2649 		*sign = 0;
2650 
2651 #if defined(IEEE_Arith) + defined(VAX)
2652 #ifdef IEEE_Arith
2653 	if ((word0(d) & Exp_mask) == Exp_mask)
2654 #else
2655 	if (word0(d)  == 0x8000)
2656 #endif
2657 		{
2658 		/* Infinity or NaN */
2659 		*decpt = 9999;
2660 #ifdef IEEE_Arith
2661 		if (!word1(d) && !(word0(d) & 0xfffff))
2662 			return nrv_alloc(PASS_STATE "Infinity", rve, 8);
2663 #endif
2664 		return nrv_alloc(PASS_STATE "NaN", rve, 3);
2665 		}
2666 #endif
2667 #ifdef IBM
2668 	dval(d) += 0; /* normalize */
2669 #endif
2670 	if (!dval(d)) {
2671 		*decpt = 1;
2672 		return nrv_alloc(PASS_STATE "0", rve, 1);
2673 		}
2674 
2675 #ifdef SET_INEXACT
2676 	try_quick = oldinexact = get_inexact();
2677 	inexact = 1;
2678 #endif
2679 #ifdef Honor_FLT_ROUNDS
2680 	if ((rounding = Flt_Rounds) >= 2) {
2681 		if (*sign)
2682 			rounding = rounding == 2 ? 0 : 2;
2683 		else
2684 			if (rounding != 2)
2685 				rounding = 0;
2686 		}
2687 #endif
2688 
2689 	b = d2b(PASS_STATE d, &be, &bbits);
2690 #ifdef Sudden_Underflow
2691 	i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
2692 #else
2693 	if ((i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1)))) {
2694 #endif
2695 		dval(d2) = dval(d);
2696 		word0(d2) &= Frac_mask1;
2697 		word0(d2) |= Exp_11;
2698 #ifdef IBM
2699 		if (j = 11 - hi0bits(word0(d2) & Frac_mask))
2700 			dval(d2) /= 1 << j;
2701 #endif
2702 
2703 		/* log(x)	~=~ log(1.5) + (x-1.5)/1.5
2704 		 * log10(x)	 =  log(x) / log(10)
2705 		 *		~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
2706 		 * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
2707 		 *
2708 		 * This suggests computing an approximation k to log10(d) by
2709 		 *
2710 		 * k = (i - Bias)*0.301029995663981
2711 		 *	+ ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
2712 		 *
2713 		 * We want k to be too large rather than too small.
2714 		 * The error in the first-order Taylor series approximation
2715 		 * is in our favor, so we just round up the constant enough
2716 		 * to compensate for any error in the multiplication of
2717 		 * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
2718 		 * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
2719 		 * adding 1e-13 to the constant term more than suffices.
2720 		 * Hence we adjust the constant term to 0.1760912590558.
2721 		 * (We could get a more accurate k by invoking log10,
2722 		 *  but this is probably not worthwhile.)
2723 		 */
2724 
2725 		i -= Bias;
2726 #ifdef IBM
2727 		i <<= 2;
2728 		i += j;
2729 #endif
2730 #ifndef Sudden_Underflow
2731 		denorm = 0;
2732 		}
2733 	else {
2734 		/* d is denormalized */
2735 
2736 		i = bbits + be + (Bias + (P-1) - 1);
2737 		x = i > 32  ? word0(d) << (64 - i) | word1(d) >> (i - 32)
2738 			    : word1(d) << (32 - i);
2739 		dval(d2) = x;
2740 		word0(d2) -= 31*Exp_msk1; /* adjust exponent */
2741 		i -= (Bias + (P-1) - 1) + 1;
2742 		denorm = 1;
2743 		}
2744 #endif
2745 	ds = (dval(d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
2746 	k = (int)ds;
2747 	if (ds < 0. && ds != k)
2748 		k--;	/* want k = floor(ds) */
2749 	k_check = 1;
2750 	if (k >= 0 && k <= Ten_pmax) {
2751 		if (dval(d) < tens[k])
2752 			k--;
2753 		k_check = 0;
2754 		}
2755 	j = bbits - i - 1;
2756 	if (j >= 0) {
2757 		b2 = 0;
2758 		s2 = j;
2759 		}
2760 	else {
2761 		b2 = -j;
2762 		s2 = 0;
2763 		}
2764 	if (k >= 0) {
2765 		b5 = 0;
2766 		s5 = k;
2767 		s2 += k;
2768 		}
2769 	else {
2770 		b2 -= k;
2771 		b5 = -k;
2772 		s5 = 0;
2773 		}
2774 	if (mode < 0 || mode > 9)
2775 		mode = 0;
2776 
2777 #ifndef SET_INEXACT
2778 #ifdef Check_FLT_ROUNDS
2779 	try_quick = Rounding == 1;
2780 #else
2781 	try_quick = 1;
2782 #endif
2783 #endif /*SET_INEXACT*/
2784 
2785 	if (mode > 5) {
2786 		mode -= 4;
2787 		try_quick = 0;
2788 		}
2789 	leftright = 1;
2790 	switch(mode) {
2791 		case 0:
2792 		case 1:
2793 			ilim = ilim1 = -1;
2794 			i = 18;
2795 			ndigits = 0;
2796 			break;
2797 		case 2:
2798 			leftright = 0;
2799 			/* no break */
2800 		case 4:
2801 			if (ndigits <= 0)
2802 				ndigits = 1;
2803 			ilim = ilim1 = i = ndigits;
2804 			break;
2805 		case 3:
2806 			leftright = 0;
2807 			/* no break */
2808 		case 5:
2809 			i = ndigits + k + 1;
2810 			ilim = i;
2811 			ilim1 = i - 1;
2812 			if (i <= 0)
2813 				i = 1;
2814 		}
2815 	s = s0 = rv_alloc(PASS_STATE i);
2816 
2817 #ifdef Honor_FLT_ROUNDS
2818 	if (mode > 1 && rounding != 1)
2819 		leftright = 0;
2820 #endif
2821 
2822 	if (ilim >= 0 && ilim <= Quick_max && try_quick) {
2823 
2824 		/* Try to get by with floating-point arithmetic. */
2825 
2826 		i = 0;
2827 		dval(d2) = dval(d);
2828 		k0 = k;
2829 		ilim0 = ilim;
2830 		ieps = 2; /* conservative */
2831 		if (k > 0) {
2832 			ds = tens[k&0xf];
2833 			j = k >> 4;
2834 			if (j & Bletch) {
2835 				/* prevent overflows */
2836 				j &= Bletch - 1;
2837 				dval(d) /= bigtens[n_bigtens-1];
2838 				ieps++;
2839 				}
2840 			for(; j; j >>= 1, i++)
2841 				if (j & 1) {
2842 					ieps++;
2843 					ds *= bigtens[i];
2844 					}
2845 			dval(d) /= ds;
2846 			}
2847 		else if ((j1 = -k)) {
2848 			dval(d) *= tens[j1 & 0xf];
2849 			for(j = j1 >> 4; j; j >>= 1, i++)
2850 				if (j & 1) {
2851 					ieps++;
2852 					dval(d) *= bigtens[i];
2853 					}
2854 			}
2855 		if (k_check && dval(d) < 1. && ilim > 0) {
2856 			if (ilim1 <= 0)
2857 				goto fast_failed;
2858 			ilim = ilim1;
2859 			k--;
2860 			dval(d) *= 10.;
2861 			ieps++;
2862 			}
2863 		dval(eps) = ieps*dval(d) + 7.;
2864 		word0(eps) -= (P-1)*Exp_msk1;
2865 		if (ilim == 0) {
2866 			S = mhi = 0;
2867 			dval(d) -= 5.;
2868 			if (dval(d) > dval(eps))
2869 				goto one_digit;
2870 			if (dval(d) < -dval(eps))
2871 				goto no_digits;
2872 			goto fast_failed;
2873 			}
2874 #ifndef No_leftright
2875 		if (leftright) {
2876 			/* Use Steele & White method of only
2877 			 * generating digits needed.
2878 			 */
2879 			dval(eps) = 0.5/tens[ilim-1] - dval(eps);
2880 			for(i = 0;;) {
2881 				L = (ULong) dval(d);
2882 				dval(d) -= L;
2883 				*s++ = '0' + (int)L;
2884 				if (dval(d) < dval(eps))
2885 					goto ret1;
2886 				if (1. - dval(d) < dval(eps))
2887 					goto bump_up;
2888 				if (++i >= ilim)
2889 					break;
2890 				dval(eps) *= 10.;
2891 				dval(d) *= 10.;
2892 				}
2893 			}
2894 		else {
2895 #endif
2896 			/* Generate ilim digits, then fix them up. */
2897 			dval(eps) *= tens[ilim-1];
2898 			for(i = 1;; i++, dval(d) *= 10.) {
2899 				L = (Long)(dval(d));
2900 				if (!(dval(d) -= L))
2901 					ilim = i;
2902 				*s++ = '0' + (int)L;
2903 				if (i == ilim) {
2904 					if (dval(d) > 0.5 + dval(eps))
2905 						goto bump_up;
2906 					else if (dval(d) < 0.5 - dval(eps)) {
2907 						while(*--s == '0');
2908 						s++;
2909 						goto ret1;
2910 						}
2911 					break;
2912 					}
2913 				}
2914 #ifndef No_leftright
2915 			}
2916 #endif
2917  fast_failed:
2918 		s = s0;
2919 		dval(d) = dval(d2);
2920 		k = k0;
2921 		ilim = ilim0;
2922 		}
2923 
2924 	/* Do we have a "small" integer? */
2925 
2926 	if (be >= 0 && k <= Int_max) {
2927 		/* Yes. */
2928 		ds = tens[k];
2929 		if (ndigits < 0 && ilim <= 0) {
2930 			S = mhi = 0;
2931 			if (ilim < 0 || dval(d) < 5*ds)
2932 				goto no_digits;
2933 			goto one_digit;
2934 			}
2935 		for(i = 1;; i++, dval(d) *= 10.) {
2936 			L = (Long)(dval(d) / ds);
2937 			dval(d) -= L*ds;
2938 #ifdef Check_FLT_ROUNDS
2939 			/* If FLT_ROUNDS == 2, L will usually be high by 1 */
2940 			if (dval(d) < 0) {
2941 				L--;
2942 				dval(d) += ds;
2943 				}
2944 #endif
2945 			*s++ = '0' + (int)L;
2946 			if (!dval(d)) {
2947 #ifdef SET_INEXACT
2948 				inexact = 0;
2949 #endif
2950 				break;
2951 				}
2952 			if (i == ilim) {
2953 #ifdef Honor_FLT_ROUNDS
2954 				if (mode > 1)
2955 				switch(rounding) {
2956 				  case 0: goto ret1;
2957 				  case 2: goto bump_up;
2958 				  }
2959 #endif
2960 				dval(d) += dval(d);
2961 				if (dval(d) > ds || (dval(d) == ds && L & 1)) {
2962  bump_up:
2963 					while(*--s == '9')
2964 						if (s == s0) {
2965 							k++;
2966 							*s = '0';
2967 							break;
2968 							}
2969 					++*s++;
2970 					}
2971 				break;
2972 				}
2973 			}
2974 		goto ret1;
2975 		}
2976 
2977 	m2 = b2;
2978 	m5 = b5;
2979 	mhi = mlo = 0;
2980 	if (leftright) {
2981 		i =
2982 #ifndef Sudden_Underflow
2983 			denorm ? be + (Bias + (P-1) - 1 + 1) :
2984 #endif
2985 #ifdef IBM
2986 			1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
2987 #else
2988 			1 + P - bbits;
2989 #endif
2990 		b2 += i;
2991 		s2 += i;
2992 		mhi = i2b(PASS_STATE 1);
2993 		}
2994 	if (m2 > 0 && s2 > 0) {
2995 		i = m2 < s2 ? m2 : s2;
2996 		b2 -= i;
2997 		m2 -= i;
2998 		s2 -= i;
2999 		}
3000 	if (b5 > 0) {
3001 		if (leftright) {
3002 			if (m5 > 0) {
3003 				mhi = pow5mult(PASS_STATE mhi, m5);
3004 				b1 = mult(PASS_STATE mhi, b);
3005 				Bfree(PASS_STATE b);
3006 				b = b1;
3007 				}
3008 			if ((j = b5 - m5))
3009 				b = pow5mult(PASS_STATE b, j);
3010 			}
3011 		else
3012 			b = pow5mult(PASS_STATE b, b5);
3013 		}
3014 	S = i2b(PASS_STATE 1);
3015 	if (s5 > 0)
3016 		S = pow5mult(PASS_STATE S, s5);
3017 
3018 	/* Check for special case that d is a normalized power of 2. */
3019 
3020 	spec_case = 0;
3021 	if ((mode < 2 || leftright)
3022 #ifdef Honor_FLT_ROUNDS
3023 			&& rounding == 1
3024 #endif
3025 				) {
3026 		if (!word1(d) && !(word0(d) & Bndry_mask)
3027 #ifndef Sudden_Underflow
3028 		 && word0(d) & (Exp_mask & ~Exp_msk1)
3029 #endif
3030 				) {
3031 			/* The special case */
3032 			b2 += Log2P;
3033 			s2 += Log2P;
3034 			spec_case = 1;
3035 			}
3036 		}
3037 
3038 	/* Arrange for convenient computation of quotients:
3039 	 * shift left if necessary so divisor has 4 leading 0 bits.
3040 	 *
3041 	 * Perhaps we should just compute leading 28 bits of S once
3042 	 * and for all and pass them and a shift to quorem, so it
3043 	 * can do shifts and ors to compute the numerator for q.
3044 	 */
3045 #ifdef Pack_32
3046 	if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f))
3047 		i = 32 - i;
3048 #else
3049 	if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf)
3050 		i = 16 - i;
3051 #endif
3052 	if (i > 4) {
3053 		i -= 4;
3054 		b2 += i;
3055 		m2 += i;
3056 		s2 += i;
3057 		}
3058 	else if (i < 4) {
3059 		i += 28;
3060 		b2 += i;
3061 		m2 += i;
3062 		s2 += i;
3063 		}
3064 	if (b2 > 0)
3065 		b = lshift(PASS_STATE b, b2);
3066 	if (s2 > 0)
3067 		S = lshift(PASS_STATE S, s2);
3068 	if (k_check) {
3069 		if (cmp(b,S) < 0) {
3070 			k--;
3071 			b = multadd(PASS_STATE b, 10, 0);	/* we botched the k estimate */
3072 			if (leftright)
3073 				mhi = multadd(PASS_STATE mhi, 10, 0);
3074 			ilim = ilim1;
3075 			}
3076 		}
3077 	if (ilim <= 0 && (mode == 3 || mode == 5)) {
3078 		if (ilim < 0 || cmp(b,S = multadd(PASS_STATE S,5,0)) < 0) {
3079 			/* no digits, fcvt style */
3080  no_digits:
3081 			/* MOZILLA CHANGE: Always return a non-empty string. */
3082 			*s++ = '0';
3083 			k = 0;
3084 			goto ret;
3085 			}
3086  one_digit:
3087 		*s++ = '1';
3088 		k++;
3089 		goto ret;
3090 		}
3091 	if (leftright) {
3092 		if (m2 > 0)
3093 			mhi = lshift(PASS_STATE mhi, m2);
3094 
3095 		/* Compute mlo -- check for special case
3096 		 * that d is a normalized power of 2.
3097 		 */
3098 
3099 		mlo = mhi;
3100 		if (spec_case) {
3101 			mhi = Balloc(PASS_STATE mhi->k);
3102 			Bcopy(mhi, mlo);
3103 			mhi = lshift(PASS_STATE mhi, Log2P);
3104 			}
3105 
3106 		for(i = 1;;i++) {
3107 			dig = quorem(b,S) + '0';
3108 			/* Do we yet have the shortest decimal string
3109 			 * that will round to d?
3110 			 */
3111 			j = cmp(b, mlo);
3112 			delta = diff(PASS_STATE S, mhi);
3113 			j1 = delta->sign ? 1 : cmp(b, delta);
3114 			Bfree(PASS_STATE delta);
3115 #ifndef ROUND_BIASED
3116 			if (j1 == 0 && mode != 1 && !(word1(d) & 1)
3117 #ifdef Honor_FLT_ROUNDS
3118 				&& rounding >= 1
3119 #endif
3120 								   ) {
3121 				if (dig == '9')
3122 					goto round_9_up;
3123 				if (j > 0)
3124 					dig++;
3125 #ifdef SET_INEXACT
3126 				else if (!b->x[0] && b->wds <= 1)
3127 					inexact = 0;
3128 #endif
3129 				*s++ = dig;
3130 				goto ret;
3131 				}
3132 #endif
3133 			if (j < 0 || (j == 0 && mode != 1
3134 #ifndef ROUND_BIASED
3135 							&& !(word1(d) & 1)
3136 #endif
3137 					)) {
3138 				if (!b->x[0] && b->wds <= 1) {
3139 #ifdef SET_INEXACT
3140 					inexact = 0;
3141 #endif
3142 					goto accept_dig;
3143 					}
3144 #ifdef Honor_FLT_ROUNDS
3145 				if (mode > 1)
3146 				 switch(rounding) {
3147 				  case 0: goto accept_dig;
3148 				  case 2: goto keep_dig;
3149 				  }
3150 #endif /*Honor_FLT_ROUNDS*/
3151 				if (j1 > 0) {
3152 					b = lshift(PASS_STATE b, 1);
3153 					j1 = cmp(b, S);
3154 					if ((j1 > 0 || (j1 == 0 && dig & 1))
3155 					&& dig++ == '9')
3156 						goto round_9_up;
3157 					}
3158  accept_dig:
3159 				*s++ = dig;
3160 				goto ret;
3161 				}
3162 			if (j1 > 0) {
3163 #ifdef Honor_FLT_ROUNDS
3164 				if (!rounding)
3165 					goto accept_dig;
3166 #endif
3167 				if (dig == '9') { /* possible if i == 1 */
3168  round_9_up:
3169 					*s++ = '9';
3170 					goto roundoff;
3171 					}
3172 				*s++ = dig + 1;
3173 				goto ret;
3174 				}
3175 #ifdef Honor_FLT_ROUNDS
3176  keep_dig:
3177 #endif
3178 			*s++ = dig;
3179 			if (i == ilim)
3180 				break;
3181 			b = multadd(PASS_STATE b, 10, 0);
3182 			if (mlo == mhi)
3183 				mlo = mhi = multadd(PASS_STATE mhi, 10, 0);
3184 			else {
3185 				mlo = multadd(PASS_STATE mlo, 10, 0);
3186 				mhi = multadd(PASS_STATE mhi, 10, 0);
3187 				}
3188 			}
3189 		}
3190 	else
3191 		for(i = 1;; i++) {
3192 			*s++ = dig = quorem(b,S) + '0';
3193 			if (!b->x[0] && b->wds <= 1) {
3194 #ifdef SET_INEXACT
3195 				inexact = 0;
3196 #endif
3197 				goto ret;
3198 				}
3199 			if (i >= ilim)
3200 				break;
3201 			b = multadd(PASS_STATE b, 10, 0);
3202 			}
3203 
3204 	/* Round off last digit */
3205 
3206 #ifdef Honor_FLT_ROUNDS
3207 	switch(rounding) {
3208 	  case 0: goto trimzeros;
3209 	  case 2: goto roundoff;
3210 	  }
3211 #endif
3212 	b = lshift(PASS_STATE b, 1);
3213 	j = cmp(b, S);
3214 	if (j >= 0) {  /* ECMA compatible rounding needed by Spidermonkey */
3215  roundoff:
3216 		while(*--s == '9')
3217 			if (s == s0) {
3218 				k++;
3219 				*s++ = '1';
3220 				goto ret;
3221 				}
3222 		++*s++;
3223 		}
3224 	else {
3225 #ifdef Honor_FLT_ROUNDS
3226  trimzeros:
3227 #endif
3228 		while(*--s == '0');
3229 		s++;
3230 		}
3231  ret:
3232 	Bfree(PASS_STATE S);
3233 	if (mhi) {
3234 		if (mlo && mlo != mhi)
3235 			Bfree(PASS_STATE mlo);
3236 		Bfree(PASS_STATE mhi);
3237 		}
3238  ret1:
3239 #ifdef SET_INEXACT
3240 	if (inexact) {
3241 		if (!oldinexact) {
3242 			word0(d) = Exp_1 + (70 << Exp_shift);
3243 			word1(d) = 0;
3244 			dval(d) += 1.;
3245 			}
3246 		}
3247 	else if (!oldinexact)
3248 		clear_inexact();
3249 #endif
3250 	Bfree(PASS_STATE b);
3251 	*s = 0;
3252 	*decpt = k + 1;
3253 	if (rve)
3254 		*rve = s;
3255 	return s0;
3256 	}
3257 #undef CONST
3258