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gdtoaimp.h revision 1.1
      1 /* $NetBSD: gdtoaimp.h,v 1.1 2006/01/25 15:18:48 kleink Exp $ */
      2 
      3 /****************************************************************
      4 
      5 The author of this software is David M. Gay.
      6 
      7 Copyright (C) 1998-2000 by Lucent Technologies
      8 All Rights Reserved
      9 
     10 Permission to use, copy, modify, and distribute this software and
     11 its documentation for any purpose and without fee is hereby
     12 granted, provided that the above copyright notice appear in all
     13 copies and that both that the copyright notice and this
     14 permission notice and warranty disclaimer appear in supporting
     15 documentation, and that the name of Lucent or any of its entities
     16 not be used in advertising or publicity pertaining to
     17 distribution of the software without specific, written prior
     18 permission.
     19 
     20 LUCENT DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE,
     21 INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS.
     22 IN NO EVENT SHALL LUCENT OR ANY OF ITS ENTITIES BE LIABLE FOR ANY
     23 SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
     24 WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER
     25 IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION,
     26 ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF
     27 THIS SOFTWARE.
     28 
     29 ****************************************************************/
     30 
     31 /* This is a variation on dtoa.c that converts arbitary binary
     32    floating-point formats to and from decimal notation.  It uses
     33    double-precision arithmetic internally, so there are still
     34    various #ifdefs that adapt the calculations to the native
     35    double-precision arithmetic (any of IEEE, VAX D_floating,
     36    or IBM mainframe arithmetic).
     37 
     38    Please send bug reports to David M. Gay (dmg at acm dot org,
     39    with " at " changed at "@" and " dot " changed to ".").
     40  */
     41 
     42 /* On a machine with IEEE extended-precision registers, it is
     43  * necessary to specify double-precision (53-bit) rounding precision
     44  * before invoking strtod or dtoa.  If the machine uses (the equivalent
     45  * of) Intel 80x87 arithmetic, the call
     46  *	_control87(PC_53, MCW_PC);
     47  * does this with many compilers.  Whether this or another call is
     48  * appropriate depends on the compiler; for this to work, it may be
     49  * necessary to #include "float.h" or another system-dependent header
     50  * file.
     51  */
     52 
     53 /* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
     54  *
     55  * This strtod returns a nearest machine number to the input decimal
     56  * string (or sets errno to ERANGE).  With IEEE arithmetic, ties are
     57  * broken by the IEEE round-even rule.  Otherwise ties are broken by
     58  * biased rounding (add half and chop).
     59  *
     60  * Inspired loosely by William D. Clinger's paper "How to Read Floating
     61  * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 112-126].
     62  *
     63  * Modifications:
     64  *
     65  *	1. We only require IEEE, IBM, or VAX double-precision
     66  *		arithmetic (not IEEE double-extended).
     67  *	2. We get by with floating-point arithmetic in a case that
     68  *		Clinger missed -- when we're computing d * 10^n
     69  *		for a small integer d and the integer n is not too
     70  *		much larger than 22 (the maximum integer k for which
     71  *		we can represent 10^k exactly), we may be able to
     72  *		compute (d*10^k) * 10^(e-k) with just one roundoff.
     73  *	3. Rather than a bit-at-a-time adjustment of the binary
     74  *		result in the hard case, we use floating-point
     75  *		arithmetic to determine the adjustment to within
     76  *		one bit; only in really hard cases do we need to
     77  *		compute a second residual.
     78  *	4. Because of 3., we don't need a large table of powers of 10
     79  *		for ten-to-e (just some small tables, e.g. of 10^k
     80  *		for 0 <= k <= 22).
     81  */
     82 
     83 /*
     84  * #define IEEE_8087 for IEEE-arithmetic machines where the least
     85  *	significant byte has the lowest address.
     86  * #define IEEE_MC68k for IEEE-arithmetic machines where the most
     87  *	significant byte has the lowest address.
     88  * #define Long int on machines with 32-bit ints and 64-bit longs.
     89  * #define Sudden_Underflow for IEEE-format machines without gradual
     90  *	underflow (i.e., that flush to zero on underflow).
     91  * #define IBM for IBM mainframe-style floating-point arithmetic.
     92  * #define VAX for VAX-style floating-point arithmetic (D_floating).
     93  * #define No_leftright to omit left-right logic in fast floating-point
     94  *	computation of dtoa.
     95  * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3.
     96  * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
     97  *	that use extended-precision instructions to compute rounded
     98  *	products and quotients) with IBM.
     99  * #define ROUND_BIASED for IEEE-format with biased rounding.
    100  * #define Inaccurate_Divide for IEEE-format with correctly rounded
    101  *	products but inaccurate quotients, e.g., for Intel i860.
    102  * #define NO_LONG_LONG on machines that do not have a "long long"
    103  *	integer type (of >= 64 bits).  On such machines, you can
    104  *	#define Just_16 to store 16 bits per 32-bit Long when doing
    105  *	high-precision integer arithmetic.  Whether this speeds things
    106  *	up or slows things down depends on the machine and the number
    107  *	being converted.  If long long is available and the name is
    108  *	something other than "long long", #define Llong to be the name,
    109  *	and if "unsigned Llong" does not work as an unsigned version of
    110  *	Llong, #define #ULLong to be the corresponding unsigned type.
    111  * #define KR_headers for old-style C function headers.
    112  * #define Bad_float_h if your system lacks a float.h or if it does not
    113  *	define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
    114  *	FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
    115  * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
    116  *	if memory is available and otherwise does something you deem
    117  *	appropriate.  If MALLOC is undefined, malloc will be invoked
    118  *	directly -- and assumed always to succeed.
    119  * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making
    120  *	memory allocations from a private pool of memory when possible.
    121  *	When used, the private pool is PRIVATE_MEM bytes long:  2304 bytes,
    122  *	unless #defined to be a different length.  This default length
    123  *	suffices to get rid of MALLOC calls except for unusual cases,
    124  *	such as decimal-to-binary conversion of a very long string of
    125  *	digits.  When converting IEEE double precision values, the
    126  *	longest string gdtoa can return is about 751 bytes long.  For
    127  *	conversions by strtod of strings of 800 digits and all gdtoa
    128  *	conversions of IEEE doubles in single-threaded executions with
    129  *	8-byte pointers, PRIVATE_MEM >= 7400 appears to suffice; with
    130  *	4-byte pointers, PRIVATE_MEM >= 7112 appears adequate.
    131  * #define INFNAN_CHECK on IEEE systems to cause strtod to check for
    132  *	Infinity and NaN (case insensitively).
    133  *	When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined,
    134  *	strtodg also accepts (case insensitively) strings of the form
    135  *	NaN(x), where x is a string of hexadecimal digits and spaces;
    136  *	if there is only one string of hexadecimal digits, it is taken
    137  *	for the fraction bits of the resulting NaN; if there are two or
    138  *	more strings of hexadecimal digits, each string is assigned
    139  *	to the next available sequence of 32-bit words of fractions
    140  *	bits (starting with the most significant), right-aligned in
    141  *	each sequence.
    142  * #define MULTIPLE_THREADS if the system offers preemptively scheduled
    143  *	multiple threads.  In this case, you must provide (or suitably
    144  *	#define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed
    145  *	by FREE_DTOA_LOCK(n) for n = 0 or 1.  (The second lock, accessed
    146  *	in pow5mult, ensures lazy evaluation of only one copy of high
    147  *	powers of 5; omitting this lock would introduce a small
    148  *	probability of wasting memory, but would otherwise be harmless.)
    149  *	You must also invoke freedtoa(s) to free the value s returned by
    150  *	dtoa.  You may do so whether or not MULTIPLE_THREADS is #defined.
    151  * #define IMPRECISE_INEXACT if you do not care about the setting of
    152  *	the STRTOG_Inexact bits in the special case of doing IEEE double
    153  *	precision conversions (which could also be done by the strtog in
    154  *	dtoa.c).
    155  * #define NO_HEX_FP to disable recognition of C9x's hexadecimal
    156  *	floating-point constants.
    157  * #define -DNO_ERRNO to suppress setting errno (in strtod.c and
    158  *	strtodg.c).
    159  * #define NO_STRING_H to use private versions of memcpy.
    160  *	On some K&R systems, it may also be necessary to
    161  *	#define DECLARE_SIZE_T in this case.
    162  * #define YES_ALIAS to permit aliasing certain double values with
    163  *	arrays of ULongs.  This leads to slightly better code with
    164  *	some compilers and was always used prior to 19990916, but it
    165  *	is not strictly legal and can cause trouble with aggressively
    166  *	optimizing compilers (e.g., gcc 2.95.1 under -O2).
    167  * #define USE_LOCALE to use the current locale's decimal_point value.
    168  */
    169 
    170 #ifndef GDTOAIMP_H_INCLUDED
    171 #define GDTOAIMP_H_INCLUDED
    172 #include "gdtoa.h"
    173 #include "gd_qnan.h"
    174 
    175 #ifdef DEBUG
    176 #include "stdio.h"
    177 #define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
    178 #endif
    179 
    180 #include "stdlib.h"
    181 #include "string.h"
    182 
    183 #ifdef KR_headers
    184 #define Char char
    185 #else
    186 #define Char void
    187 #endif
    188 
    189 #ifdef MALLOC
    190 extern Char *MALLOC ANSI((size_t));
    191 #else
    192 #define MALLOC malloc
    193 #endif
    194 
    195 #undef IEEE_Arith
    196 #undef Avoid_Underflow
    197 #ifdef IEEE_MC68k
    198 #define IEEE_Arith
    199 #endif
    200 #ifdef IEEE_8087
    201 #define IEEE_Arith
    202 #endif
    203 
    204 #include "errno.h"
    205 #ifdef Bad_float_h
    206 
    207 #ifdef IEEE_Arith
    208 #define DBL_DIG 15
    209 #define DBL_MAX_10_EXP 308
    210 #define DBL_MAX_EXP 1024
    211 #define FLT_RADIX 2
    212 #define DBL_MAX 1.7976931348623157e+308
    213 #endif
    214 
    215 #ifdef IBM
    216 #define DBL_DIG 16
    217 #define DBL_MAX_10_EXP 75
    218 #define DBL_MAX_EXP 63
    219 #define FLT_RADIX 16
    220 #define DBL_MAX 7.2370055773322621e+75
    221 #endif
    222 
    223 #ifdef VAX
    224 #define DBL_DIG 16
    225 #define DBL_MAX_10_EXP 38
    226 #define DBL_MAX_EXP 127
    227 #define FLT_RADIX 2
    228 #define DBL_MAX 1.7014118346046923e+38
    229 #define n_bigtens 2
    230 #endif
    231 
    232 #ifndef LONG_MAX
    233 #define LONG_MAX 2147483647
    234 #endif
    235 
    236 #else /* ifndef Bad_float_h */
    237 #include "float.h"
    238 #endif /* Bad_float_h */
    239 
    240 #ifdef IEEE_Arith
    241 #define Scale_Bit 0x10
    242 #define n_bigtens 5
    243 #endif
    244 
    245 #ifdef IBM
    246 #define n_bigtens 3
    247 #endif
    248 
    249 #ifdef VAX
    250 #define n_bigtens 2
    251 #endif
    252 
    253 #ifndef __MATH_H__
    254 #include "math.h"
    255 #endif
    256 
    257 #ifdef __cplusplus
    258 extern "C" {
    259 #endif
    260 
    261 #if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1
    262 Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined.
    263 #endif
    264 
    265 typedef union { double d; ULong L[2]; } U;
    266 
    267 #ifdef YES_ALIAS
    268 #define dval(x) x
    269 #ifdef IEEE_8087
    270 #define word0(x) ((ULong *)&x)[1]
    271 #define word1(x) ((ULong *)&x)[0]
    272 #else
    273 #define word0(x) ((ULong *)&x)[0]
    274 #define word1(x) ((ULong *)&x)[1]
    275 #endif
    276 #else /* !YES_ALIAS */
    277 #ifdef IEEE_8087
    278 #define word0(x) ((U*)&x)->L[1]
    279 #define word1(x) ((U*)&x)->L[0]
    280 #else
    281 #define word0(x) ((U*)&x)->L[0]
    282 #define word1(x) ((U*)&x)->L[1]
    283 #endif
    284 #define dval(x) ((U*)&x)->d
    285 #endif /* YES_ALIAS */
    286 
    287 /* The following definition of Storeinc is appropriate for MIPS processors.
    288  * An alternative that might be better on some machines is
    289  * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
    290  */
    291 #if defined(IEEE_8087) + defined(VAX)
    292 #define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
    293 ((unsigned short *)a)[0] = (unsigned short)c, a++)
    294 #else
    295 #define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
    296 ((unsigned short *)a)[1] = (unsigned short)c, a++)
    297 #endif
    298 
    299 /* #define P DBL_MANT_DIG */
    300 /* Ten_pmax = floor(P*log(2)/log(5)) */
    301 /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
    302 /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
    303 /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
    304 
    305 #ifdef IEEE_Arith
    306 #define Exp_shift  20
    307 #define Exp_shift1 20
    308 #define Exp_msk1    0x100000
    309 #define Exp_msk11   0x100000
    310 #define Exp_mask  0x7ff00000
    311 #define P 53
    312 #define Bias 1023
    313 #define Emin (-1022)
    314 #define Exp_1  0x3ff00000
    315 #define Exp_11 0x3ff00000
    316 #define Ebits 11
    317 #define Frac_mask  0xfffff
    318 #define Frac_mask1 0xfffff
    319 #define Ten_pmax 22
    320 #define Bletch 0x10
    321 #define Bndry_mask  0xfffff
    322 #define Bndry_mask1 0xfffff
    323 #define LSB 1
    324 #define Sign_bit 0x80000000
    325 #define Log2P 1
    326 #define Tiny0 0
    327 #define Tiny1 1
    328 #define Quick_max 14
    329 #define Int_max 14
    330 
    331 #ifndef Flt_Rounds
    332 #ifdef FLT_ROUNDS
    333 #define Flt_Rounds FLT_ROUNDS
    334 #else
    335 #define Flt_Rounds 1
    336 #endif
    337 #endif /*Flt_Rounds*/
    338 
    339 #else /* ifndef IEEE_Arith */
    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 #undef  Pack_16
    418 #ifndef Pack_32
    419 #define Pack_32
    420 #endif
    421 
    422 #ifdef NO_LONG_LONG
    423 #undef ULLong
    424 #ifdef Just_16
    425 #undef Pack_32
    426 #define Pack_16
    427 /* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
    428  * This makes some inner loops simpler and sometimes saves work
    429  * during multiplications, but it often seems to make things slightly
    430  * slower.  Hence the default is now to store 32 bits per Long.
    431  */
    432 #endif
    433 #else	/* long long available */
    434 #ifndef Llong
    435 #define Llong long long
    436 #endif
    437 #ifndef ULLong
    438 #define ULLong unsigned Llong
    439 #endif
    440 #endif /* NO_LONG_LONG */
    441 
    442 #ifdef Pack_32
    443 #define ULbits 32
    444 #define kshift 5
    445 #define kmask 31
    446 #define ALL_ON 0xffffffff
    447 #else
    448 #define ULbits 16
    449 #define kshift 4
    450 #define kmask 15
    451 #define ALL_ON 0xffff
    452 #endif
    453 
    454 #ifndef MULTIPLE_THREADS
    455 #define ACQUIRE_DTOA_LOCK(n)	/*nothing*/
    456 #define FREE_DTOA_LOCK(n)	/*nothing*/
    457 #endif
    458 
    459 #define Kmax 15
    460 
    461  struct
    462 Bigint {
    463 	struct Bigint *next;
    464 	int k, maxwds, sign, wds;
    465 	ULong x[1];
    466 	};
    467 
    468  typedef struct Bigint Bigint;
    469 
    470 #ifdef NO_STRING_H
    471 #ifdef DECLARE_SIZE_T
    472 typedef unsigned int size_t;
    473 #endif
    474 extern void memcpy_D2A ANSI((void*, const void*, size_t));
    475 #define Bcopy(x,y) memcpy_D2A(&x->sign,&y->sign,y->wds*sizeof(ULong) + 2*sizeof(int))
    476 #else /* !NO_STRING_H */
    477 #define Bcopy(x,y) memcpy(&x->sign,&y->sign,y->wds*sizeof(ULong) + 2*sizeof(int))
    478 #endif /* NO_STRING_H */
    479 
    480 #define Balloc Balloc_D2A
    481 #define Bfree Bfree_D2A
    482 #define ULtoQ ULtoQ_D2A
    483 #define ULtof ULtof_D2A
    484 #define ULtod ULtod_D2A
    485 #define ULtodd ULtodd_D2A
    486 #define ULtox ULtox_D2A
    487 #define ULtoxL ULtoxL_D2A
    488 #define any_on any_on_D2A
    489 #define b2d b2d_D2A
    490 #define bigtens bigtens_D2A
    491 #define cmp cmp_D2A
    492 #define copybits copybits_D2A
    493 #define d2b d2b_D2A
    494 #define decrement decrement_D2A
    495 #define diff diff_D2A
    496 #define dtoa_result dtoa_result_D2A
    497 #define g__fmt g__fmt_D2A
    498 #define gethex gethex_D2A
    499 #define hexdig hexdig_D2A
    500 #define hexnan hexnan_D2A
    501 #define hi0bits(x) hi0bits_D2A((ULong)(x))
    502 #define i2b i2b_D2A
    503 #define increment increment_D2A
    504 #define lo0bits lo0bits_D2A
    505 #define lshift lshift_D2A
    506 #define match match_D2A
    507 #define mult mult_D2A
    508 #define multadd multadd_D2A
    509 #define nrv_alloc nrv_alloc_D2A
    510 #define pow5mult pow5mult_D2A
    511 #define quorem quorem_D2A
    512 #define ratio ratio_D2A
    513 #define rshift rshift_D2A
    514 #define rv_alloc rv_alloc_D2A
    515 #define s2b s2b_D2A
    516 #define set_ones set_ones_D2A
    517 #define strcp strcp_D2A
    518 #define strtoIg strtoIg_D2A
    519 #define sum sum_D2A
    520 #define tens tens_D2A
    521 #define tinytens tinytens_D2A
    522 #define tinytens tinytens_D2A
    523 #define trailz trailz_D2A
    524 #define ulp ulp_D2A
    525 
    526  extern char *dtoa_result;
    527  extern CONST double bigtens[], tens[], tinytens[];
    528  extern unsigned char hexdig[];
    529 
    530  extern Bigint *Balloc ANSI((int));
    531  extern void Bfree ANSI((Bigint*));
    532  extern void ULtof ANSI((ULong*, ULong*, Long, int));
    533  extern void ULtod ANSI((ULong*, ULong*, Long, int));
    534  extern void ULtodd ANSI((ULong*, ULong*, Long, int));
    535  extern void ULtoQ ANSI((ULong*, ULong*, Long, int));
    536  extern void ULtox ANSI((UShort*, ULong*, Long, int));
    537  extern void ULtoxL ANSI((ULong*, ULong*, Long, int));
    538  extern ULong any_on ANSI((Bigint*, int));
    539  extern double b2d ANSI((Bigint*, int*));
    540  extern int cmp ANSI((Bigint*, Bigint*));
    541  extern void copybits ANSI((ULong*, int, Bigint*));
    542  extern Bigint *d2b ANSI((double, int*, int*));
    543  extern int decrement ANSI((Bigint*));
    544  extern Bigint *diff ANSI((Bigint*, Bigint*));
    545  extern char *dtoa ANSI((double d, int mode, int ndigits,
    546 			int *decpt, int *sign, char **rve));
    547  extern char *g__fmt ANSI((char*, char*, char*, int, ULong));
    548  extern int gethex ANSI((CONST char**, FPI*, Long*, Bigint**, int));
    549  extern void hexdig_init_D2A(Void);
    550  extern int hexnan ANSI((CONST char**, FPI*, ULong*));
    551  extern int hi0bits_D2A ANSI((ULong));
    552  extern Bigint *i2b ANSI((int));
    553  extern Bigint *increment ANSI((Bigint*));
    554  extern int lo0bits ANSI((ULong*));
    555  extern Bigint *lshift ANSI((Bigint*, int));
    556  extern int match ANSI((CONST char**, char*));
    557  extern Bigint *mult ANSI((Bigint*, Bigint*));
    558  extern Bigint *multadd ANSI((Bigint*, int, int));
    559  extern char *nrv_alloc ANSI((char*, char **, int));
    560  extern Bigint *pow5mult ANSI((Bigint*, int));
    561  extern int quorem ANSI((Bigint*, Bigint*));
    562  extern double ratio ANSI((Bigint*, Bigint*));
    563  extern void rshift ANSI((Bigint*, int));
    564  extern char *rv_alloc ANSI((int));
    565  extern Bigint *s2b ANSI((CONST char*, int, int, ULong));
    566  extern Bigint *set_ones ANSI((Bigint*, int));
    567  extern char *strcp ANSI((char*, const char*));
    568  extern int strtoIg ANSI((CONST char*, char**, FPI*, Long*, Bigint**, int*));
    569  extern double strtod ANSI((const char *s00, char **se));
    570  extern Bigint *sum ANSI((Bigint*, Bigint*));
    571  extern int trailz ANSI((Bigint*));
    572  extern double ulp ANSI((double));
    573 
    574 #ifdef __cplusplus
    575 }
    576 #endif
    577 /*
    578  * NAN_WORD0 and NAN_WORD1 are only referenced in strtod.c.  Prior to
    579  * 20050115, they used to be hard-wired here (to 0x7ff80000 and 0,
    580  * respectively), but now are determined by compiling and running
    581  * qnan.c to generate gd_qnan.h, which specifies d_QNAN0 and d_QNAN1.
    582  * Formerly gdtoaimp.h recommended supplying suitable -DNAN_WORD0=...
    583  * and -DNAN_WORD1=...  values if necessary.  This should still work.
    584  * (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)
    585  */
    586 #ifdef IEEE_Arith
    587 #ifdef IEEE_MC68k
    588 #define _0 0
    589 #define _1 1
    590 #ifndef NAN_WORD0
    591 #define NAN_WORD0 d_QNAN0
    592 #endif
    593 #ifndef NAN_WORD1
    594 #define NAN_WORD1 d_QNAN1
    595 #endif
    596 #else
    597 #define _0 1
    598 #define _1 0
    599 #ifndef NAN_WORD0
    600 #define NAN_WORD0 d_QNAN1
    601 #endif
    602 #ifndef NAN_WORD1
    603 #define NAN_WORD1 d_QNAN0
    604 #endif
    605 #endif
    606 #else
    607 #undef INFNAN_CHECK
    608 #endif
    609 
    610 #undef SI
    611 #ifdef Sudden_Underflow
    612 #define SI 1
    613 #else
    614 #define SI 0
    615 #endif
    616 
    617 #endif /* GDTOAIMP_H_INCLUDED */
    618