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# /home/coin/SVN-release/OS-2.3.5/OS/src/OSUtils/OSdtoa.cpp

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    00001 /* $Id: OSdtoa.cpp 4120 2011-03-30 06:28:16Z kmartin $ */
    00002 /****************************************************************
    00003  *
    00004  * The author of this software is David M. Gay.
    00005  *
    00006  * Copyright (c) 1991, 2000, 2001 by Lucent Technologies.
    00007  *
    00008  * Permission to use, copy, modify, and distribute this software for any
    00009  * purpose without fee is hereby granted, provided that this entire notice
    00010  * is included in all copies of any software which is or includes a copy
    00011  * or modification of this software and in all copies of the supporting
    00012  * documentation for such software.
    00013  *
    00014  * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
    00015  * WARRANTY.  IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY
    00016  * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
    00017  * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
    00018  *
    00019  ***************************************************************/
    00020
    00021 /* Please send bug reports to David M. Gay (dmg at acm dot org,
    00022  * with " at " changed at "@" and " dot " changed to ".").      */
    00023
    00024 /* On a machine with IEEE extended-precision registers, it is
    00025  * necessary to specify double-precision (53-bit) rounding precision
    00026  * before invoking strtod or dtoa.  If the machine uses (the equivalent
    00027  * of) Intel 80x87 arithmetic, the call
    00028  *      _control87(PC_53, MCW_PC);
    00029  * does this with many compilers.  Whether this or another call is
    00030  * appropriate depends on the compiler; for this to work, it may be
    00031  * necessary to #include "float.h" or another system-dependent header
    00032  * file.
    00033  */
    00034
    00035 /* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
    00036  *
    00037  * This strtod returns a nearest machine number to the input decimal
    00038  * string (or sets errno to ERANGE).  With IEEE arithmetic, ties are
    00039  * broken by the IEEE round-even rule.  Otherwise ties are broken by
    00040  * biased rounding (add half and chop).
    00041  *
    00042  * Inspired loosely by William D. Clinger's paper "How to Read Floating
    00043  * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
    00044  *
    00045  * Modifications:
    00046  *
    00047  *      1. We only require IEEE, IBM, or VAX double-precision
    00048  *              arithmetic (not IEEE double-extended).
    00049  *      2. We get by with floating-point arithmetic in a case that
    00050  *              Clinger missed -- when we're computing d * 10^n
    00051  *              for a small integer d and the integer n is not too
    00052  *              much larger than 22 (the maximum integer k for which
    00053  *              we can represent 10^k exactly), we may be able to
    00054  *              compute (d*10^k) * 10^(e-k) with just one roundoff.
    00055  *      3. Rather than a bit-at-a-time adjustment of the binary
    00056  *              result in the hard case, we use floating-point
    00057  *              arithmetic to determine the adjustment to within
    00058  *              one bit; only in really hard cases do we need to
    00059  *              compute a second residual.
    00060  *      4. Because of 3., we don't need a large table of powers of 10
    00061  *              for ten-to-e (just some small tables, e.g. of 10^k
    00062  *              for 0 <= k <= 22).
    00063  */
    00064
    00065 /*
    00066  * #define IEEE_8087 for IEEE-arithmetic machines where the least
    00067  *      significant byte has the lowest address.
    00068  * #define IEEE_MC68k for IEEE-arithmetic machines where the most
    00069  *      significant byte has the lowest address.
    00070  * #define Long int on machines with 32-bit ints and 64-bit longs.
    00071  * #define IBM for IBM mainframe-style floating-point arithmetic.
    00072  * #define VAX for VAX-style floating-point arithmetic (D_floating).
    00073  * #define No_leftright to omit left-right logic in fast floating-point
    00074  *      computation of dtoa.
    00075  * #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
    00076  *      and strtod and dtoa should round accordingly.
    00077  * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
    00078  *      and Honor_FLT_ROUNDS is not #defined.
    00079  * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
    00080  *      that use extended-precision instructions to compute rounded
    00081  *      products and quotients) with IBM.
    00082  * #define ROUND_BIASED for IEEE-format with biased rounding.
    00083  * #define Inaccurate_Divide for IEEE-format with correctly rounded
    00084  *      products but inaccurate quotients, e.g., for Intel i860.
    00085  * #define NO_LONG_LONG on machines that do not have a "long long"
    00086  *      integer type (of >= 64 bits).  On such machines, you can
    00087  *      #define Just_16 to store 16 bits per 32-bit Long when doing
    00088  *      high-precision integer arithmetic.  Whether this speeds things
    00089  *      up or slows things down depends on the machine and the number
    00090  *      being converted.  If long long is available and the name is
    00091  *      something other than "long long", #define Llong to be the name,
    00092  *      and if "unsigned Llong" does not work as an unsigned version of
    00093  *      Llong, #define #ULLong to be the corresponding unsigned type.
    00094  * #define KR_headers for old-style C function headers.
    00095  * #define Bad_float_h if your system lacks a float.h or if it does not
    00096  *      define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
    00097  *      FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
    00098  * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
    00099  *      if memory is available and otherwise does something you deem
    00100  *      appropriate.  If MALLOC is undefined, malloc will be invoked
    00101  *      directly -- and assumed always to succeed.
    00102  * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making
    00103  *      memory allocations from a private pool of memory when possible.
    00104  *      When used, the private pool is PRIVATE_MEM bytes long:  2304 bytes,
    00105  *      unless #defined to be a different length.  This default length
    00106  *      suffices to get rid of MALLOC calls except for unusual cases,
    00107  *      such as decimal-to-binary conversion of a very long string of
    00108  *      digits.  The longest string dtoa can return is about 751 bytes
    00109  *      long.  For conversions by strtod of strings of 800 digits and
    00110  *      all dtoa conversions in single-threaded executions with 8-byte
    00111  *      pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte
    00112  *      pointers, PRIVATE_MEM >= 7112 appears adequate.
    00113  * #define NO_INFNAN_CHECK if you do not wish to have INFNAN_CHECK
    00114  *      #defined automatically on IEEE systems.  On such systems,
    00115  *      when INFNAN_CHECK is #defined, strtod checks
    00116  *      for Infinity and NaN (case insensitively).  On some systems
    00117  *      (e.g., some HP systems), it may be necessary to #define NAN_WORD0
    00118  *      appropriately -- to the most significant word of a quiet NaN.
    00119  *      (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)
    00120  *      When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined,
    00121  *      strtod also accepts (case insensitively) strings of the form
    00122  *      NaN(x), where x is a string of hexadecimal digits and spaces;
    00123  *      if there is only one string of hexadecimal digits, it is taken
    00124  *      for the 52 fraction bits of the resulting NaN; if there are two
    00125  *      or more strings of hex digits, the first is for the high 20 bits,
    00126  *      the second and subsequent for the low 32 bits, with intervening
    00127  *      white space ignored; but if this results in none of the 52
    00128  *      fraction bits being on (an IEEE Infinity symbol), then NAN_WORD0
    00129  *      and NAN_WORD1 are used instead.
    00130  * #define MULTIPLE_THREADS if the system offers preemptively scheduled
    00131  *      multiple threads.  In this case, you must provide (or suitably
    00132  *      #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed
    00133  *      by FREE_DTOA_LOCK(n) for n = 0 or 1.  (The second lock, accessed
    00134  *      in pow5mult, ensures lazy evaluation of only one copy of high
    00135  *      powers of 5; omitting this lock would introduce a small
    00136  *      probability of wasting memory, but would otherwise be harmless.)
    00137  *      You must also invoke freedtoa(s) to free the value s returned by
    00138  *      dtoa.  You may do so whether or not MULTIPLE_THREADS is #defined.
    00139  * #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that
    00140  *      avoids underflows on inputs whose result does not underflow.
    00141  *      If you #define NO_IEEE_Scale on a machine that uses IEEE-format
    00142  *      floating-point numbers and flushes underflows to zero rather
    00143  *      than implementing gradual underflow, then you must also #define
    00144  *      Sudden_Underflow.
    00145  * #define YES_ALIAS to permit aliasing certain double values with
    00146  *      arrays of ULongs.  This leads to slightly better code with
    00147  *      some compilers and was always used prior to 19990916, but it
    00148  *      is not strictly legal and can cause trouble with aggressively
    00149  *      optimizing compilers (e.g., gcc 2.95.1 under -O2).
    00150  * #define USE_LOCALE to use the current locale's decimal_point value.
    00151  * #define SET_INEXACT if IEEE arithmetic is being used and extra
    00152  *      computation should be done to set the inexact flag when the
    00153  *      result is inexact and avoid setting inexact when the result
    00154  *      is exact.  In this case, dtoa.c must be compiled in
    00155  *      an environment, perhaps provided by #include "dtoa.c" in a
    00156  *      suitable wrapper, that defines two functions,
    00157  *              int get_inexact(void);
    00158  *              void clear_inexact(void);
    00159  *      such that get_inexact() returns a nonzero value if the
    00160  *      inexact bit is already set, and clear_inexact() sets the
    00161  *      inexact bit to 0.  When SET_INEXACT is #defined, strtod
    00162  *      also does extra computations to set the underflow and overflow
    00163  *      flags when appropriate (i.e., when the result is tiny and
    00164  *      inexact or when it is a numeric value rounded to +-infinity).
    00165  * #define NO_ERRNO if strtod should not assign errno = ERANGE when
    00166  *      the result overflows to +-Infinity or underflows to 0.
    00167  */
    00168
    00175 #include "OSConfig.h"
    00176 #include "OSdtoa.h"
    00177 #include "OSParameters.h"
    00178
    00179
    00180
    00181 #ifdef WORDS_BIGENDIAN
    00182 #define IEEE_MC68k
    00183 #else
    00184 #define IEEE_8087
    00185 #endif
    00186
    00187 #define INFNAN_CHECK
    00188
    00189
    00190
    00191 #define NO_LONG_LONG
    00192 #define Just_16
    00193
    00194 /*
    00195 #if  SIZEOF_LONG_LONG < 8
    00196 #define NO_LONG_LONG
    00197 #define Just_16
    00198 #endif
    00199 */
    00200
    00201 #if  SIZEOF_LONG == 2*SIZEOF_INT
    00202 #define Long int
    00203 #define Intcast (int)(long)
    00204 #endif
    00205
    00206
    00217 #ifndef Long
    00218 #define Long long
    00219 #endif
    00220
    00221
    00222 #ifndef ULong
    00223 typedef unsigned Long ULong;
    00224 #endif
    00225
    00226 #ifdef DEBUG
    00227 #include "stdio.h"
    00228 #define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
    00229 #endif
    00230
    00231 #include "stdlib.h"
    00232 #include "string.h"
    00233
    00234 #ifdef USE_LOCALE
    00235 #include "locale.h"
    00236 #endif
    00237
    00238 #ifdef MALLOC
    00239 #ifdef KR_headers
    00240 extern char *MALLOC();
    00241 #else
    00242 extern void *MALLOC(size_t);
    00243 #endif
    00244 #else
    00245 #define MALLOC malloc
    00246 #endif
    00247
    00248 #ifndef Omit_Private_Memory
    00249 #ifndef PRIVATE_MEM
    00250 #define PRIVATE_MEM 2304
    00251 #endif
    00252 #define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
    00253 static double private_mem[PRIVATE_mem], *pmem_next = private_mem;
    00254 #endif
    00255
    00256 #undef IEEE_Arith
    00257 #undef Avoid_Underflow
    00258 #ifdef IEEE_MC68k
    00259 #define IEEE_Arith
    00260 #endif
    00261 #ifdef IEEE_8087
    00262 #define IEEE_Arith
    00263 #endif
    00264
    00265 #ifdef IEEE_Arith
    00266 #ifndef NO_INFNAN_CHECK
    00267 #undef INFNAN_CHECK
    00268 #define INFNAN_CHECK
    00269 #endif
    00270 #else
    00271 #undef INFNAN_CHECK
    00272 #endif
    00273
    00274 #include "errno.h"
    00275
    00276 #ifdef Bad_float_h
    00277
    00278 #ifdef IEEE_Arith
    00279 #define DBL_DIG 15
    00280 #define DBL_MAX_10_EXP 308
    00281 #define DBL_MAX_EXP 1024
    00282 #define FLT_RADIX 2
    00283 #endif /*IEEE_Arith*/
    00284
    00285 #ifdef IBM
    00286 #define DBL_DIG 16
    00287 #define DBL_MAX_10_EXP 75
    00288 #define DBL_MAX_EXP 63
    00289 #define FLT_RADIX 16
    00290 #define DBL_MAX 7.2370055773322621e+75
    00291 #endif
    00292
    00293 #ifdef VAX
    00294 #define DBL_DIG 16
    00295 #define DBL_MAX_10_EXP 38
    00296 #define DBL_MAX_EXP 127
    00297 #define FLT_RADIX 2
    00298 #define DBL_MAX 1.7014118346046923e+38
    00299 #endif
    00300
    00301 #ifndef LONG_MAX
    00302 #define LONG_MAX 2147483647
    00303 #endif
    00304
    00305 #else /* ifndef Bad_float_h */
    00306 #include "float.h"
    00307 #endif /* Bad_float_h */
    00308
    00309 #ifndef __MATH_H__
    00310 #include "math.h"
    00311 #endif
    00312
    00313 #ifdef __cplusplus
    00314 extern "C" {
    00315 #endif
    00316
    00317 #ifndef CONST
    00318 #ifdef KR_headers
    00319 #define CONST /* blank */
    00320 #else
    00321 #define CONST const
    00322 #endif
    00323 #endif
    00324
    00325 #if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1
    00326 Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined.
    00327 #endif
    00328
    00329 typedef union { double d; ULong L[2]; } U;
    00330
    00331 #ifdef YES_ALIAS
    00332 #define dval(x) x
    00333 #ifdef IEEE_8087
    00334 #define word0(x) ((ULong *)&x)[1]
    00335 #define word1(x) ((ULong *)&x)[0]
    00336 #else
    00337 #define word0(x) ((ULong *)&x)[0]
    00338 #define word1(x) ((ULong *)&x)[1]
    00339 #endif
    00340 #else
    00341 #ifdef IEEE_8087
    00342 #define word0(x) ((U*)&x)->L[1]
    00343 #define word1(x) ((U*)&x)->L[0]
    00344 #else
    00345 #define word0(x) ((U*)&x)->L[0]
    00346 #define word1(x) ((U*)&x)->L[1]
    00347 #endif
    00348 #define dval(x) ((U*)&x)->d
    00349 #endif
    00350
    00351 /* The following definition of Storeinc is appropriate for MIPS processors.
    00352  * An alternative that might be better on some machines is
    00353  * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
    00354  */
    00355 #if defined(IEEE_8087) + defined(VAX)
    00356 #define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
    00357 ((unsigned short *)a)[0] = (unsigned short)c, a++)
    00358 #else
    00359 #define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
    00360 ((unsigned short *)a)[1] = (unsigned short)c, a++)
    00361 #endif
    00362
    00363 /* #define P DBL_MANT_DIG */
    00364 /* Ten_pmax = floor(P*log(2)/log(5)) */
    00365 /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
    00366 /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
    00367 /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
    00368
    00369 #ifdef IEEE_Arith
    00370 #define Exp_shift  20
    00371 #define Exp_shift1 20
    00372 #define Exp_msk1    0x100000
    00373 #define Exp_msk11   0x100000
    00374 #define Exp_mask  0x7ff00000
    00375 #define P 53
    00376 #define Bias 1023
    00377 #define Emin (-1022)
    00378 #define Exp_1  0x3ff00000
    00379 #define Exp_11 0x3ff00000
    00380 #define Ebits 11
    00381 #define Frac_mask  0xfffff
    00382 #define Frac_mask1 0xfffff
    00383 #define Ten_pmax 22
    00384 #define Bletch 0x10
    00385 #define Bndry_mask  0xfffff
    00386 #define Bndry_mask1 0xfffff
    00387 #define LSB 1
    00388 #define Sign_bit 0x80000000
    00389 #define Log2P 1
    00390 #define Tiny0 0
    00391 #define Tiny1 1
    00392 #define Quick_max 14
    00393 #define Int_max 14
    00394 #ifndef NO_IEEE_Scale
    00395 #define Avoid_Underflow
    00396 #ifdef Flush_Denorm     /* debugging option */
    00397 #undef Sudden_Underflow
    00398 #endif
    00399 #endif
    00400
    00401 #ifndef Flt_Rounds
    00402 #ifdef FLT_ROUNDS
    00403 #define Flt_Rounds FLT_ROUNDS
    00404 #else
    00405 #define Flt_Rounds 1
    00406 #endif
    00407 #endif /*Flt_Rounds*/
    00408
    00409 #ifdef Honor_FLT_ROUNDS
    00410 #define Rounding rounding
    00411 #undef Check_FLT_ROUNDS
    00412 #define Check_FLT_ROUNDS
    00413 #else
    00414 #define Rounding Flt_Rounds
    00415 #endif
    00416
    00417 #else /* ifndef IEEE_Arith */
    00418 #undef Check_FLT_ROUNDS
    00419 #undef Honor_FLT_ROUNDS
    00420 #undef SET_INEXACT
    00421 #undef  Sudden_Underflow
    00422 #define Sudden_Underflow
    00423 #ifdef IBM
    00424 #undef Flt_Rounds
    00425 #define Flt_Rounds 0
    00426 #define Exp_shift  24
    00427 #define Exp_shift1 24
    00428 #define Exp_msk1   0x1000000
    00429 #define Exp_msk11  0x1000000
    00430 #define Exp_mask  0x7f000000
    00431 #define P 14
    00432 #define Bias 65
    00433 #define Exp_1  0x41000000
    00434 #define Exp_11 0x41000000
    00435 #define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
    00436 #define Frac_mask  0xffffff
    00437 #define Frac_mask1 0xffffff
    00438 #define Bletch 4
    00439 #define Ten_pmax 22
    00440 #define Bndry_mask  0xefffff
    00441 #define Bndry_mask1 0xffffff
    00442 #define LSB 1
    00443 #define Sign_bit 0x80000000
    00444 #define Log2P 4
    00445 #define Tiny0 0x100000
    00446 #define Tiny1 0
    00447 #define Quick_max 14
    00448 #define Int_max 15
    00449 #else /* VAX */
    00450 #undef Flt_Rounds
    00451 #define Flt_Rounds 1
    00452 #define Exp_shift  23
    00453 #define Exp_shift1 7
    00454 #define Exp_msk1    0x80
    00455 #define Exp_msk11   0x800000
    00456 #define Exp_mask  0x7f80
    00457 #define P 56
    00458 #define Bias 129
    00459 #define Exp_1  0x40800000
    00460 #define Exp_11 0x4080
    00461 #define Ebits 8
    00462 #define Frac_mask  0x7fffff
    00463 #define Frac_mask1 0xffff007f
    00464 #define Ten_pmax 24
    00465 #define Bletch 2
    00466 #define Bndry_mask  0xffff007f
    00467 #define Bndry_mask1 0xffff007f
    00468 #define LSB 0x10000
    00469 #define Sign_bit 0x8000
    00470 #define Log2P 1
    00471 #define Tiny0 0x80
    00472 #define Tiny1 0
    00473 #define Quick_max 15
    00474 #define Int_max 15
    00475 #endif /* IBM, VAX */
    00476 #endif /* IEEE_Arith */
    00477
    00478 #ifndef IEEE_Arith
    00479 #define ROUND_BIASED
    00480 #endif
    00481
    00482 #ifdef RND_PRODQUOT
    00483 #define rounded_product(a,b) a = rnd_prod(a, b)
    00484 #define rounded_quotient(a,b) a = rnd_quot(a, b)
    00485 #ifdef KR_headers
    00486 extern double rnd_prod(), rnd_quot();
    00487 #else
    00488 extern double rnd_prod(double, double), rnd_quot(double, double);
    00489 #endif
    00490 #else
    00491 #define rounded_product(a,b) a *= b
    00492 #define rounded_quotient(a,b) a /= b
    00493 #endif
    00494
    00495 #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
    00496 #define Big1 0xffffffff
    00497
    00498 #ifndef Pack_32
    00499 #define Pack_32
    00500 #endif
    00501
    00502 #ifdef KR_headers
    00503 #define FFFFFFFF ((((unsigned long)0xffff)<<16)|(unsigned long)0xffff)
    00504 #else
    00505 #define FFFFFFFF 0xffffffffUL
    00506 #endif
    00507
    00508 #ifdef NO_LONG_LONG
    00509 #undef ULLong
    00510 #ifdef Just_16
    00511 #undef Pack_32
    00512 /* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
    00513  * This makes some inner loops simpler and sometimes saves work
    00514  * during multiplications, but it often seems to make things slightly
    00515  * slower.  Hence the default is now to store 32 bits per Long.
    00516  */
    00517 #endif
    00518 #else   /* long long available */
    00519 #ifndef Llong
    00520 #define Llong long long
    00521 #endif
    00522 #ifndef ULLong
    00523 #define ULLong unsigned Llong
    00524 #endif
    00525 #endif /* NO_LONG_LONG */
    00526
    00527 #ifndef MULTIPLE_THREADS
    00528 #define ACQUIRE_DTOA_LOCK(n)    /*nothing*/
    00529 #define FREE_DTOA_LOCK(n)       /*nothing*/
    00530 #endif
    00531
    00532 #define Kmax 15
    00533
    00534 #ifdef __cplusplus
    00535 extern "C" double os_strtod(const char *s00, char **se);
    00536 extern "C" char *os_dtoa(double d, int mode, int ndigits,
    00537                         int *decpt, int *sign, char **rve);
    00538 #endif
    00539
    00540  struct
    00541 Bigint {
    00542         struct Bigint *next;
    00543         int k, maxwds, sign, wds;
    00544         ULong x[1];
    00545         };
    00546
    00547  typedef struct Bigint Bigint;
    00548
    00549  static Bigint *freelist[Kmax+1];
    00550
    00551  static Bigint *
    00552 Balloc
    00553 #ifdef KR_headers
    00554         (k) int k;
    00555 #else
    00556         (int k)
    00557 #endif
    00558 {
    00559         int x;
    00560         Bigint *rv;
    00561 #ifndef Omit_Private_Memory
    00562         unsigned int len;
    00563 #endif
    00564
    00565         ACQUIRE_DTOA_LOCK(0);
    00566         if ( (rv = freelist[k]) ) {
    00567                 freelist[k] = rv->next;
    00568                 }
    00569         else {
    00570                 x = 1 << k;
    00571 #ifdef Omit_Private_Memory
    00572                 rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong));
    00573 #else
    00574                 len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)
    00575                         /sizeof(double);
    00576                 unsigned int tmpInt  = PRIVATE_mem;
    00577                 //if (pmem_next - private_mem + len <= PRIVATE_mem) {
    00578                 if (pmem_next - private_mem + len <= tmpInt) {
    00579                         rv = (Bigint*)pmem_next;
    00580                         pmem_next += len;
    00581                         }
    00582                 else
    00583                         rv = (Bigint*)MALLOC(len*sizeof(double));
    00584 #endif
    00585                 rv->k = k;
    00586                 rv->maxwds = x;
    00587                 }
    00588         FREE_DTOA_LOCK(0);
    00589         rv->sign = rv->wds = 0;
    00590         return rv;
    00591         }
    00592
    00593  static void
    00594 Bfree
    00595 #ifdef KR_headers
    00596         (v) Bigint *v;
    00597 #else
    00598         (Bigint *v)
    00599 #endif
    00600 {
    00601         if (v) {
    00602                 ACQUIRE_DTOA_LOCK(0);
    00603                 v->next = freelist[v->k];
    00604                 freelist[v->k] = v;
    00605                 FREE_DTOA_LOCK(0);
    00606                 }
    00607         }
    00608
    00609 #define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
    00610 y->wds*sizeof(Long) + 2*sizeof(int))
    00611
    00612  static Bigint *
    00613 multadd
    00614 #ifdef KR_headers
    00615         (b, m, a) Bigint *b; int m, a;
    00616 #else
    00617         (Bigint *b, int m, int a)       /* multiply by m and add a */
    00618 #endif
    00619 {
    00620         int i, wds;
    00621 #ifdef ULLong
    00622         ULong *x;
    00623         ULLong carry, y;
    00624 #else
    00625         ULong carry, *x, y;
    00626 #ifdef Pack_32
    00627         ULong xi, z;
    00628 #endif
    00629 #endif
    00630         Bigint *b1;
    00631
    00632         wds = b->wds;
    00633         x = b->x;
    00634         i = 0;
    00635         carry = a;
    00636         do {
    00637 #ifdef ULLong
    00638                 y = *x * (ULLong)m + carry;
    00639                 carry = y >> 32;
    00640                 *x++ = y & FFFFFFFF;
    00641 #else
    00642 #ifdef Pack_32
    00643                 xi = *x;
    00644                 y = (xi & 0xffff) * m + carry;
    00645                 z = (xi >> 16) * m + (y >> 16);
    00646                 carry = z >> 16;
    00647                 *x++ = (z << 16) + (y & 0xffff);
    00648 #else
    00649                 y = *x * m + carry;
    00650                 carry = y >> 16;
    00651                 *x++ = y & 0xffff;
    00652 #endif
    00653 #endif
    00654                 }
    00655                 while(++i < wds);
    00656         if (carry) {
    00657                 if (wds >= b->maxwds) {
    00658                         b1 = Balloc(b->k+1);
    00659                         Bcopy(b1, b);
    00660                         Bfree(b);
    00661                         b = b1;
    00662                         }
    00663                 b->x[wds++] = carry;
    00664                 b->wds = wds;
    00665                 }
    00666         return b;
    00667         }
    00668
    00669  static Bigint *
    00670 s2b
    00671 #ifdef KR_headers
    00672         (s, nd0, nd, y9) CONST char *s; int nd0, nd; ULong y9;
    00673 #else
    00674         (CONST char *s, int nd0, int nd, ULong y9)
    00675 #endif
    00676 {
    00677         Bigint *b;
    00678         int i, k;
    00679         Long x, y;
    00680
    00681         x = (nd + 8) / 9;
    00682         for(k = 0, y = 1; x > y; y <<= 1, k++) ;
    00683 #ifdef Pack_32
    00684         b = Balloc(k);
    00685         b->x[0] = y9;
    00686         b->wds = 1;
    00687 #else
    00688         b = Balloc(k+1);
    00689         b->x[0] = y9 & 0xffff;
    00690         b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
    00691 #endif
    00692
    00693         i = 9;
    00694         if (9 < nd0) {
    00695                 s += 9;
    00696                 do b = multadd(b, 10, *s++ - '0');
    00697                         while(++i < nd0);
    00698                 s++;
    00699                 }
    00700         else
    00701                 s += 10;
    00702         for(; i < nd; i++)
    00703                 b = multadd(b, 10, *s++ - '0');
    00704         return b;
    00705         }
    00706
    00707  static int
    00708 hi0bits
    00709 #ifdef KR_headers
    00710         (x) register ULong x;
    00711 #else
    00712         (register ULong x)
    00713 #endif
    00714 {
    00715         register int k = 0;
    00716
    00717         if (!(x & 0xffff0000)) {
    00718                 k = 16;
    00719                 x <<= 16;
    00720                 }
    00721         if (!(x & 0xff000000)) {
    00722                 k += 8;
    00723                 x <<= 8;
    00724                 }
    00725         if (!(x & 0xf0000000)) {
    00726                 k += 4;
    00727                 x <<= 4;
    00728                 }
    00729         if (!(x & 0xc0000000)) {
    00730                 k += 2;
    00731                 x <<= 2;
    00732                 }
    00733         if (!(x & 0x80000000)) {
    00734                 k++;
    00735                 if (!(x & 0x40000000))
    00736                         return 32;
    00737                 }
    00738         return k;
    00739         }
    00740
    00741  static int
    00742 lo0bits
    00743 #ifdef KR_headers
    00744         (y) ULong *y;
    00745 #else
    00746         (ULong *y)
    00747 #endif
    00748 {
    00749         register int k;
    00750         register ULong x = *y;
    00751
    00752         if (x & 7) {
    00753                 if (x & 1)
    00754                         return 0;
    00755                 if (x & 2) {
    00756                         *y = x >> 1;
    00757                         return 1;
    00758                         }
    00759                 *y = x >> 2;
    00760                 return 2;
    00761                 }
    00762         k = 0;
    00763         if (!(x & 0xffff)) {
    00764                 k = 16;
    00765                 x >>= 16;
    00766                 }
    00767         if (!(x & 0xff)) {
    00768                 k += 8;
    00769                 x >>= 8;
    00770                 }
    00771         if (!(x & 0xf)) {
    00772                 k += 4;
    00773                 x >>= 4;
    00774                 }
    00775         if (!(x & 0x3)) {
    00776                 k += 2;
    00777                 x >>= 2;
    00778                 }
    00779         if (!(x & 1)) {
    00780                 k++;
    00781                 x >>= 1;
    00782                 if (!x)
    00783                         return 32;
    00784                 }
    00785         *y = x;
    00786         return k;
    00787         }
    00788
    00789  static Bigint *
    00790 i2b
    00791 #ifdef KR_headers
    00792         (i) int i;
    00793 #else
    00794         (int i)
    00795 #endif
    00796 {
    00797         Bigint *b;
    00798
    00799         b = Balloc(1);
    00800         b->x[0] = i;
    00801         b->wds = 1;
    00802         return b;
    00803         }
    00804
    00805  static Bigint *
    00806 mult
    00807 #ifdef KR_headers
    00808         (a, b) Bigint *a, *b;
    00809 #else
    00810         (Bigint *a, Bigint *b)
    00811 #endif
    00812 {
    00813         Bigint *c;
    00814         int k, wa, wb, wc;
    00815         ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
    00816         ULong y;
    00817 #ifdef ULLong
    00818         ULLong carry, z;
    00819 #else
    00820         ULong carry, z;
    00821 #ifdef Pack_32
    00822         ULong z2;
    00823 #endif
    00824 #endif
    00825
    00826         if (a->wds < b->wds) {
    00827                 c = a;
    00828                 a = b;
    00829                 b = c;
    00830                 }
    00831         k = a->k;
    00832         wa = a->wds;
    00833         wb = b->wds;
    00834         wc = wa + wb;
    00835         if (wc > a->maxwds)
    00836                 k++;
    00837         c = Balloc(k);
    00838         for(x = c->x, xa = x + wc; x < xa; x++)
    00839                 *x = 0;
    00840         xa = a->x;
    00841         xae = xa + wa;
    00842         xb = b->x;
    00843         xbe = xb + wb;
    00844         xc0 = c->x;
    00845 #ifdef ULLong
    00846         for(; xb < xbe; xc0++) {
    00847                 if (y = *xb++) {
    00848                         x = xa;
    00849                         xc = xc0;
    00850                         carry = 0;
    00851                         do {
    00852                                 z = *x++ * (ULLong)y + *xc + carry;
    00853                                 carry = z >> 32;
    00854                                 *xc++ = z & FFFFFFFF;
    00855                                 }
    00856                                 while(x < xae);
    00857                         *xc = carry;
    00858                         }
    00859                 }
    00860 #else
    00861 #ifdef Pack_32
    00862         for(; xb < xbe; xb++, xc0++) {
    00863                 if (y = *xb & 0xffff) {
    00864                         x = xa;
    00865                         xc = xc0;
    00866                         carry = 0;
    00867                         do {
    00868                                 z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
    00869                                 carry = z >> 16;
    00870                                 z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
    00871                                 carry = z2 >> 16;
    00872                                 Storeinc(xc, z2, z);
    00873                                 }
    00874                                 while(x < xae);
    00875                         *xc = carry;
    00876                         }
    00877                 if (y = *xb >> 16) {
    00878                         x = xa;
    00879                         xc = xc0;
    00880                         carry = 0;
    00881                         z2 = *xc;
    00882                         do {
    00883                                 z = (*x & 0xffff) * y + (*xc >> 16) + carry;
    00884                                 carry = z >> 16;
    00885                                 Storeinc(xc, z, z2);
    00886                                 z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
    00887                                 carry = z2 >> 16;
    00888                                 }
    00889                                 while(x < xae);
    00890                         *xc = z2;
    00891                         }
    00892                 }
    00893 #else
    00894         for(; xb < xbe; xc0++) {
    00895                 if ( (y = *xb++) ) {
    00896                         x = xa;
    00897                         xc = xc0;
    00898                         carry = 0;
    00899                         do {
    00900                                 z = *x++ * y + *xc + carry;
    00901                                 carry = z >> 16;
    00902                                 *xc++ = z & 0xffff;
    00903                                 }
    00904                                 while(x < xae);
    00905                         *xc = carry;
    00906                         }
    00907                 }
    00908 #endif
    00909 #endif
    00910         for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
    00911         c->wds = wc;
    00912         return c;
    00913         }
    00914
    00915  static Bigint *p5s;
    00916
    00917  static Bigint *
    00918 pow5mult
    00919 #ifdef KR_headers
    00920         (b, k) Bigint *b; int k;
    00921 #else
    00922         (Bigint *b, int k)
    00923 #endif
    00924 {
    00925         Bigint *b1, *p5, *p51;
    00926         int i;
    00927         static int p05[3] = { 5, 25, 125 };
    00928
    00929         if ( (i = k & 3 ))
    00930                 b = multadd(b, p05[i-1], 0);
    00931
    00932         if (!(k >>= 2))
    00933                 return b;
    00934         if (!(p5 = p5s)) {
    00935                 /* first time */
    00936 #ifdef MULTIPLE_THREADS
    00937                 ACQUIRE_DTOA_LOCK(1);
    00938                 if (!(p5 = p5s)) {
    00939                         p5 = p5s = i2b(625);
    00940                         p5->next = 0;
    00941                         }
    00942                 FREE_DTOA_LOCK(1);
    00943 #else
    00944                 p5 = p5s = i2b(625);
    00945                 p5->next = 0;
    00946 #endif
    00947                 }
    00948         for(;;) {
    00949                 if (k & 1) {
    00950                         b1 = mult(b, p5);
    00951                         Bfree(b);
    00952                         b = b1;
    00953                         }
    00954                 if (!(k >>= 1))
    00955                         break;
    00956                 if (!(p51 = p5->next)) {
    00957 #ifdef MULTIPLE_THREADS
    00958                         ACQUIRE_DTOA_LOCK(1);
    00959                         if (!(p51 = p5->next)) {
    00960                                 p51 = p5->next = mult(p5,p5);
    00961                                 p51->next = 0;
    00962                                 }
    00963                         FREE_DTOA_LOCK(1);
    00964 #else
    00965                         p51 = p5->next = mult(p5,p5);
    00966                         p51->next = 0;
    00967 #endif
    00968                         }
    00969                 p5 = p51;
    00970                 }
    00971         return b;
    00972         }
    00973
    00974  static Bigint *
    00975 lshift
    00976 #ifdef KR_headers
    00977         (b, k) Bigint *b; int k;
    00978 #else
    00979         (Bigint *b, int k)
    00980 #endif
    00981 {
    00982         int i, k1, n, n1;
    00983         Bigint *b1;
    00984         ULong *x, *x1, *xe, z;
    00985
    00986 #ifdef Pack_32
    00987         n = k >> 5;
    00988 #else
    00989         n = k >> 4;
    00990 #endif
    00991         k1 = b->k;
    00992         n1 = n + b->wds + 1;
    00993         for(i = b->maxwds; n1 > i; i <<= 1)
    00994                 k1++;
    00995         b1 = Balloc(k1);
    00996         x1 = b1->x;
    00997         for(i = 0; i < n; i++)
    00998                 *x1++ = 0;
    00999         x = b->x;
    01000         xe = x + b->wds;
    01001 #ifdef Pack_32
    01002         if (k &= 0x1f) {
    01003                 k1 = 32 - k;
    01004                 z = 0;
    01005                 do {
    01006                         *x1++ = *x << k | z;
    01007                         z = *x++ >> k1;
    01008                         }
    01009                         while(x < xe);
    01010                 if (*x1 = z)
    01011                         ++n1;
    01012                 }
    01013 #else
    01014         if (k &= 0xf) {
    01015                 k1 = 16 - k;
    01016                 z = 0;
    01017                 do {
    01018                         *x1++ = *x << k  & 0xffff | z;
    01019                         z = *x++ >> k1;
    01020                         }
    01021                         while(x < xe);
    01022                 if ( (*x1 = z ))
    01023                         ++n1;
    01024                 }
    01025 #endif
    01026         else do
    01027                 *x1++ = *x++;
    01028                 while(x < xe);
    01029         b1->wds = n1 - 1;
    01030         Bfree(b);
    01031         return b1;
    01032         }
    01033
    01034  static int
    01035 cmp
    01036 #ifdef KR_headers
    01037         (a, b) Bigint *a, *b;
    01038 #else
    01039         (Bigint *a, Bigint *b)
    01040 #endif
    01041 {
    01042         ULong *xa, *xa0, *xb, *xb0;
    01043         int i, j;
    01044
    01045         i = a->wds;
    01046         j = b->wds;
    01047 #ifdef DEBUG
    01048         if (i > 1 && !a->x[i-1])
    01049                 Bug("cmp called with a->x[a->wds-1] == 0");
    01050         if (j > 1 && !b->x[j-1])
    01051                 Bug("cmp called with b->x[b->wds-1] == 0");
    01052 #endif
    01053         if (i -= j)
    01054                 return i;
    01055         xa0 = a->x;
    01056         xa = xa0 + j;
    01057         xb0 = b->x;
    01058         xb = xb0 + j;
    01059         for(;;) {
    01060                 if (*--xa != *--xb)
    01061                         return *xa < *xb ? -1 : 1;
    01062                 if (xa <= xa0)
    01063                         break;
    01064                 }
    01065         return 0;
    01066         }
    01067
    01068  static Bigint *
    01069 diff
    01070 #ifdef KR_headers
    01071         (a, b) Bigint *a, *b;
    01072 #else
    01073         (Bigint *a, Bigint *b)
    01074 #endif
    01075 {
    01076         Bigint *c;
    01077         int i, wa, wb;
    01078         ULong *xa, *xae, *xb, *xbe, *xc;
    01079 #ifdef ULLong
    01080         ULLong borrow, y;
    01081 #else
    01082         ULong borrow, y;
    01083 #ifdef Pack_32
    01084         ULong z;
    01085 #endif
    01086 #endif
    01087
    01088         i = cmp(a,b);
    01089         if (!i) {
    01090                 c = Balloc(0);
    01091                 c->wds = 1;
    01092                 c->x[0] = 0;
    01093                 return c;
    01094                 }
    01095         if (i < 0) {
    01096                 c = a;
    01097                 a = b;
    01098                 b = c;
    01099                 i = 1;
    01100                 }
    01101         else
    01102                 i = 0;
    01103         c = Balloc(a->k);
    01104         c->sign = i;
    01105         wa = a->wds;
    01106         xa = a->x;
    01107         xae = xa + wa;
    01108         wb = b->wds;
    01109         xb = b->x;
    01110         xbe = xb + wb;
    01111         xc = c->x;
    01112         borrow = 0;
    01113 #ifdef ULLong
    01114         do {
    01115                 y = (ULLong)*xa++ - *xb++ - borrow;
    01116                 borrow = y >> 32 & (ULong)1;
    01117                 *xc++ = y & FFFFFFFF;
    01118                 }
    01119                 while(xb < xbe);
    01120         while(xa < xae) {
    01121                 y = *xa++ - borrow;
    01122                 borrow = y >> 32 & (ULong)1;
    01123                 *xc++ = y & FFFFFFFF;
    01124                 }
    01125 #else
    01126 #ifdef Pack_32
    01127         do {
    01128                 y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
    01129                 borrow = (y & 0x10000) >> 16;
    01130                 z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
    01131                 borrow = (z & 0x10000) >> 16;
    01132                 Storeinc(xc, z, y);
    01133                 }
    01134                 while(xb < xbe);
    01135         while(xa < xae) {
    01136                 y = (*xa & 0xffff) - borrow;
    01137                 borrow = (y & 0x10000) >> 16;
    01138                 z = (*xa++ >> 16) - borrow;
    01139                 borrow = (z & 0x10000) >> 16;
    01140                 Storeinc(xc, z, y);
    01141                 }
    01142 #else
    01143         do {
    01144                 y = *xa++ - *xb++ - borrow;
    01145                 borrow = (y & 0x10000) >> 16;
    01146                 *xc++ = y & 0xffff;
    01147                 }
    01148                 while(xb < xbe);
    01149         while(xa < xae) {
    01150                 y = *xa++ - borrow;
    01151                 borrow = (y & 0x10000) >> 16;
    01152                 *xc++ = y & 0xffff;
    01153                 }
    01154 #endif
    01155 #endif
    01156         while(!*--xc)
    01157                 wa--;
    01158         c->wds = wa;
    01159         return c;
    01160         }
    01161
    01162  static double
    01163 ulp
    01164 #ifdef KR_headers
    01165         (x) double x;
    01166 #else
    01167         (double x)
    01168 #endif
    01169 {
    01170         register Long L;
    01171         double a;
    01172
    01173         L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
    01174 #ifndef Avoid_Underflow
    01175 #ifndef Sudden_Underflow
    01176         if (L > 0) {
    01177 #endif
    01178 #endif
    01179 #ifdef IBM
    01180                 L |= Exp_msk1 >> 4;
    01181 #endif
    01182                 word0(a) = L;
    01183                 word1(a) = 0;
    01184 #ifndef Avoid_Underflow
    01185 #ifndef Sudden_Underflow
    01186                 }
    01187         else {
    01188                 L = -L >> Exp_shift;
    01189                 if (L < Exp_shift) {
    01190                         word0(a) = 0x80000 >> L;
    01191                         word1(a) = 0;
    01192                         }
    01193                 else {
    01194                         word0(a) = 0;
    01195                         L -= Exp_shift;
    01196                         word1(a) = L >= 31 ? 1 : 1 << 31 - L;
    01197                         }
    01198                 }
    01199 #endif
    01200 #endif
    01201         return dval(a);
    01202         }
    01203
    01204  static double
    01205 b2d
    01206 #ifdef KR_headers
    01207         (a, e) Bigint *a; int *e;
    01208 #else
    01209         (Bigint *a, int *e)
    01210 #endif
    01211 {
    01212         ULong *xa, *xa0, w, y, z;
    01213         int k;
    01214         double d;
    01215 #ifdef VAX
    01216         ULong d0, d1;
    01217 #else
    01218 #define d0 word0(d)
    01219 #define d1 word1(d)
    01220 #endif
    01221
    01222         xa0 = a->x;
    01223         xa = xa0 + a->wds;
    01224         y = *--xa;
    01225 #ifdef DEBUG
    01226         if (!y) Bug("zero y in b2d");
    01227 #endif
    01228         k = hi0bits(y);
    01229         *e = 32 - k;
    01230 #ifdef Pack_32
    01231         if (k < Ebits) {
    01232                 d0 = Exp_1 | y >> Ebits - k;
    01233                 w = xa > xa0 ? *--xa : 0;
    01234                 d1 = y << (32-Ebits) + k | w >> Ebits - k;
    01235                 goto ret_d;
    01236                 }
    01237         z = xa > xa0 ? *--xa : 0;
    01238         if (k -= Ebits) {
    01239                 d0 = Exp_1 | y << k | z >> 32 - k;
    01240                 y = xa > xa0 ? *--xa : 0;
    01241                 d1 = z << k | y >> 32 - k;
    01242                 }
    01243         else {
    01244                 d0 = Exp_1 | y;
    01245                 d1 = z;
    01246                 }
    01247 #else
    01248         if (k < Ebits + 16) {
    01249                 z = xa > xa0 ? *--xa : 0;
    01250                 d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
    01251                 w = xa > xa0 ? *--xa : 0;
    01252                 y = xa > xa0 ? *--xa : 0;
    01253                 d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
    01254                 goto ret_d;
    01255                 }
    01256         z = xa > xa0 ? *--xa : 0;
    01257         w = xa > xa0 ? *--xa : 0;
    01258         k -= Ebits + 16;
    01259         d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
    01260         y = xa > xa0 ? *--xa : 0;
    01261         d1 = w << k + 16 | y << k;
    01262 #endif
    01263  ret_d:
    01264 #ifdef VAX
    01265         word0(d) = d0 >> 16 | d0 << 16;
    01266         word1(d) = d1 >> 16 | d1 << 16;
    01267 #else
    01268 #undef d0
    01269 #undef d1
    01270 #endif
    01271         return dval(d);
    01272         }
    01273
    01274  static Bigint *
    01275 d2b
    01276 #ifdef KR_headers
    01277         (d, e, bits) double d; int *e, *bits;
    01278 #else
    01279         (double d, int *e, int *bits)
    01280 #endif
    01281 {
    01282         Bigint *b;
    01283         int de, k;
    01284         ULong *x, y, z;
    01285 #ifndef Sudden_Underflow
    01286         int i;
    01287 #endif
    01288 #ifdef VAX
    01289         ULong d0, d1;
    01290         d0 = word0(d) >> 16 | word0(d) << 16;
    01291         d1 = word1(d) >> 16 | word1(d) << 16;
    01292 #else
    01293 #define d0 word0(d)
    01294 #define d1 word1(d)
    01295 #endif
    01296
    01297 #ifdef Pack_32
    01298         b = Balloc(1);
    01299 #else
    01300         b = Balloc(2);
    01301 #endif
    01302         x = b->x;
    01303
    01304         z = d0 & Frac_mask;
    01305         d0 &= 0x7fffffff;       /* clear sign bit, which we ignore */
    01306 #ifdef Sudden_Underflow
    01307         de = (int)(d0 >> Exp_shift);
    01308 #ifndef IBM
    01309         z |= Exp_msk11;
    01310 #endif
    01311 #else
    01312         if ( (de = (int)(d0 >> Exp_shift) ))
    01313                 z |= Exp_msk1;
    01314 #endif
    01315 #ifdef Pack_32
    01316         if (y = d1) {
    01317                 if (k = lo0bits(&y)) {
    01318                         x[0] = y | z << 32 - k;
    01319                         z >>= k;
    01320                         }
    01321                 else
    01322                         x[0] = y;
    01323 #ifndef Sudden_Underflow
    01324                 i =
    01325 #endif
    01326                     b->wds = (x[1] = z) ? 2 : 1;
    01327                 }
    01328         else {
    01329 #ifdef DEBUG
    01330                 if (!z)
    01331                         Bug("Zero passed to d2b");
    01332 #endif
    01333                 k = lo0bits(&z);
    01334                 x[0] = z;
    01335 #ifndef Sudden_Underflow
    01336                 i =
    01337 #endif
    01338                     b->wds = 1;
    01339                 k += 32;
    01340                 }
    01341 #else
    01342         if ( (y = d1) ) {
    01343                 if ( (k = lo0bits(&y)) )
    01344                         if (k >= 16) {
    01345                                 x[0] = y | z << 32 - k & 0xffff;
    01346                                 x[1] = z >> k - 16 & 0xffff;
    01347                                 x[2] = z >> k;
    01348                                 i = 2;
    01349                                 }
    01350                         else {
    01351                                 x[0] = y & 0xffff;
    01352                                 x[1] = y >> 16 | z << 16 - k & 0xffff;
    01353                                 x[2] = z >> k & 0xffff;
    01354                                 x[3] = z >> k+16;
    01355                                 i = 3;
    01356                                 }
    01357                 else {
    01358                         x[0] = y & 0xffff;
    01359                         x[1] = y >> 16;
    01360                         x[2] = z & 0xffff;
    01361                         x[3] = z >> 16;
    01362                         i = 3;
    01363                         }
    01364                 }
    01365         else {
    01366 #ifdef DEBUG
    01367                 if (!z)
    01368                         Bug("Zero passed to d2b");
    01369 #endif
    01370                 k = lo0bits(&z);
    01371                 if (k >= 16) {
    01372                         x[0] = z;
    01373                         i = 0;
    01374                         }
    01375                 else {
    01376                         x[0] = z & 0xffff;
    01377                         x[1] = z >> 16;
    01378                         i = 1;
    01379                         }
    01380                 k += 32;
    01381                 }
    01382         while(!x[i])
    01383                 --i;
    01384         b->wds = i + 1;
    01385 #endif
    01386 #ifndef Sudden_Underflow
    01387         if (de) {
    01388 #endif
    01389 #ifdef IBM
    01390                 *e = (de - Bias - (P-1) << 2) + k;
    01391                 *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
    01392 #else
    01393                 *e = de - Bias - (P-1) + k;
    01394                 *bits = P - k;
    01395 #endif
    01396 #ifndef Sudden_Underflow
    01397                 }
    01398         else {
    01399                 *e = de - Bias - (P-1) + 1 + k;
    01400 #ifdef Pack_32
    01401                 *bits = 32*i - hi0bits(x[i-1]);
    01402 #else
    01403                 *bits = (i+2)*16 - hi0bits(x[i]);
    01404 #endif
    01405                 }
    01406 #endif
    01407         return b;
    01408         }
    01409 #undef d0
    01410 #undef d1
    01411
    01412  static double
    01413 ratio
    01414 #ifdef KR_headers
    01415         (a, b) Bigint *a, *b;
    01416 #else
    01417         (Bigint *a, Bigint *b)
    01418 #endif
    01419 {
    01420         double da, db;
    01421         int k, ka, kb;
    01422
    01423         dval(da) = b2d(a, &ka);
    01424         dval(db) = b2d(b, &kb);
    01425 #ifdef Pack_32
    01426         k = ka - kb + 32*(a->wds - b->wds);
    01427 #else
    01428         k = ka - kb + 16*(a->wds - b->wds);
    01429 #endif
    01430 #ifdef IBM
    01431         if (k > 0) {
    01432                 word0(da) += (k >> 2)*Exp_msk1;
    01433                 if (k &= 3)
    01434                         dval(da) *= 1 << k;
    01435                 }
    01436         else {
    01437                 k = -k;
    01438                 word0(db) += (k >> 2)*Exp_msk1;
    01439                 if (k &= 3)
    01440                         dval(db) *= 1 << k;
    01441                 }
    01442 #else
    01443         if (k > 0)
    01444                 word0(da) += k*Exp_msk1;
    01445         else {
    01446                 k = -k;
    01447                 word0(db) += k*Exp_msk1;
    01448                 }
    01449 #endif
    01450         return dval(da) / dval(db);
    01451         }
    01452
    01453  static CONST double
    01454 tens[] = {
    01455                 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
    01456                 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
    01457                 1e20, 1e21, 1e22
    01458 #ifdef VAX
    01459                 , 1e23, 1e24
    01460 #endif
    01461                 };
    01462
    01463  static CONST double
    01464 #ifdef IEEE_Arith
    01465 bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
    01466 static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
    01467 #ifdef Avoid_Underflow
    01468                 9007199254740992.*9007199254740992.e-256
    01469                 /* = 2^106 * 1e-53 */
    01470 #else
    01471                 1e-256
    01472 #endif
    01473                 };
    01474 /* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
    01475 /* flag unnecessarily.  It leads to a song and dance at the end of strtod. */
    01476 #define Scale_Bit 0x10
    01477 #define n_bigtens 5
    01478 #else
    01479 #ifdef IBM
    01480 bigtens[] = { 1e16, 1e32, 1e64 };
    01481 static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 };
    01482 #define n_bigtens 3
    01483 #else
    01484 bigtens[] = { 1e16, 1e32 };
    01485 static CONST double tinytens[] = { 1e-16, 1e-32 };
    01486 #define n_bigtens 2
    01487 #endif
    01488 #endif
    01489
    01490 #ifdef INFNAN_CHECK
    01491
    01492 #ifndef NAN_WORD0
    01493 #define NAN_WORD0 0x7ff80000
    01494 #endif
    01495
    01496 #ifndef NAN_WORD1
    01497 #define NAN_WORD1 0
    01498 #endif
    01499
    01500  static int
    01501 match
    01502 #ifdef KR_headers
    01503         (sp, t) char **sp; CONST char *t;
    01504 #else
    01505         (CONST char **sp, CONST char *t)
    01506 #endif
    01507 {
    01508         int c, d;
    01509         CONST char *s = *sp;
    01510
    01511         while( (d = *t++) ) {
    01512                 if ((c = *++s) >= 'A' && c <= 'Z')
    01513                         c += 'a' - 'A';
    01514                 if (c != d)
    01515                         return 0;
    01516                 }
    01517         *sp = s + 1;
    01518         return 1;
    01519         }
    01520
    01521 #ifndef No_Hex_NaN
    01522  static void
    01523 hexnan
    01524 #ifdef KR_headers
    01525         (rvp, sp) double *rvp; CONST char **sp;
    01526 #else
    01527         (double *rvp, CONST char **sp)
    01528 #endif
    01529 {
    01530         ULong c, x[2];
    01531         CONST char *s;
    01532         int havedig, udx0, xshift;
    01533
    01534         x[0] = x[1] = 0;
    01535         havedig = xshift = 0;
    01536         udx0 = 1;
    01537         s = *sp;
    01538         while( (c = *(CONST unsigned char*)++s) ) {
    01539                 if (c >= '0' && c <= '9')
    01540                         c -= '0';
    01541                 else if (c >= 'a' && c <= 'f')
    01542                         c += 10 - 'a';
    01543                 else if (c >= 'A' && c <= 'F')
    01544                         c += 10 - 'A';
    01545                 else if (c <= ' ') {
    01546                         if (udx0 && havedig) {
    01547                                 udx0 = 0;
    01548                                 xshift = 1;
    01549                                 }
    01550                         continue;
    01551                         }
    01552                 else if (/*(*/ c == ')' && havedig) {
    01553                         *sp = s + 1;
    01554                         break;
    01555                         }
    01556                 else
    01557                         return; /* invalid form: don't change *sp */
    01558                 havedig = 1;
    01559                 if (xshift) {
    01560                         xshift = 0;
    01561                         x[0] = x[1];
    01562                         x[1] = 0;
    01563                         }
    01564                 if (udx0)
    01565                         x[0] = (x[0] << 4) | (x[1] >> 28);
    01566                 x[1] = (x[1] << 4) | c;
    01567                 }
    01568         if ((x[0] &= 0xfffff) || x[1]) {
    01569                 word0(*rvp) = Exp_mask | x[0];
    01570                 word1(*rvp) = x[1];
    01571                 }
    01572         }
    01573 #endif /*No_Hex_NaN*/
    01574 #endif /* INFNAN_CHECK */
    01575
    01576  double
    01577 os_strtod
    01578 #ifdef KR_headers
    01579         (s00, se) CONST char *s00; char **se;
    01580 #else
    01581         (CONST char *s00, char **se)
    01582 #endif
    01583 {
    01584 #ifdef Avoid_Underflow
    01585         int scale;
    01586 #endif
    01587         int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
    01588                  e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
    01589         CONST char *s, *s0, *s1;
    01590         double aadj, aadj1, adj, rv, rv0;
    01591         Long L;
    01592         ULong y, z;
    01593         Bigint *bb = NULL, *bb1 = NULL, *bd = NULL,
    01594                 *bd0 = NULL, *bs = NULL, *delta = NULL;
    01595 #ifdef SET_INEXACT
    01596         int inexact, oldinexact;
    01597 #endif
    01598 #ifdef Honor_FLT_ROUNDS
    01599         int rounding;
    01600 #endif
    01601 #ifdef USE_LOCALE
    01602         CONST char *s2;
    01603 #endif
    01604
    01605         sign = nz0 = nz = 0;
    01606         dval(rv) = 0.;
    01607         for(s = s00;;s++) switch(*s) {
    01608                 case '-':
    01609                         sign = 1;
    01610                         /* no break */
    01611                 case '+':
    01612                         if (*++s)
    01613                                 goto break2;
    01614                         /* no break */
    01615                 case 0:
    01616                         goto ret0;
    01617                 case '\t':
    01618                 case '\n':
    01619                 case '\v':
    01620                 case '\f':
    01621                 case '\r':
    01622                 case ' ':
    01623                         continue;
    01624                 default:
    01625                         goto break2;
    01626                 }
    01627  break2:
    01628         if (*s == '0') {
    01629                 nz0 = 1;
    01630                 while(*++s == '0') ;
    01631                 if (!*s)
    01632                         goto ret;
    01633                 }
    01634         s0 = s;
    01635         y = z = 0;
    01636         for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
    01637                 if (nd < 9)
    01638                         y = 10*y + c - '0';
    01639                 else if (nd < 16)
    01640                         z = 10*z + c - '0';
    01641         nd0 = nd;
    01642 #ifdef USE_LOCALE
    01643         s1 = localeconv()->decimal_point;
    01644         if (c == *s1) {
    01645                 c = '.';
    01646                 if (*++s1) {
    01647                         s2 = s;
    01648                         for(;;) {
    01649                                 if (*++s2 != *s1) {
    01650                                         c = 0;
    01651                                         break;
    01652                                         }
    01653                                 if (!*++s1) {
    01654                                         s = s2;
    01655                                         break;
    01656                                         }
    01657                                 }
    01658                         }
    01659                 }
    01660 #endif
    01661         if (c == '.') {
    01662                 c = *++s;
    01663                 if (!nd) {
    01664                         for(; c == '0'; c = *++s)
    01665                                 nz++;
    01666                         if (c > '0' && c <= '9') {
    01667                                 s0 = s;
    01668                                 nf += nz;
    01669                                 nz = 0;
    01670                                 goto have_dig;
    01671                                 }
    01672                         goto dig_done;
    01673                         }
    01674                 for(; c >= '0' && c <= '9'; c = *++s) {
    01675  have_dig:
    01676                         nz++;
    01677                         if (c -= '0') {
    01678                                 nf += nz;
    01679                                 for(i = 1; i < nz; i++)
    01680                                         if (nd++ < 9)
    01681                                                 y *= 10;
    01682                                         else if (nd <= DBL_DIG + 1)
    01683                                                 z *= 10;
    01684                                 if (nd++ < 9)
    01685                                         y = 10*y + c;
    01686                                 else if (nd <= DBL_DIG + 1)
    01687                                         z = 10*z + c;
    01688                                 nz = 0;
    01689                                 }
    01690                         }
    01691                 }
    01692  dig_done:
    01693         e = 0;
    01694         if (c == 'e' || c == 'E') {
    01695                 if (!nd && !nz && !nz0) {
    01696                         goto ret0;
    01697                         }
    01698                 s00 = s;
    01699                 esign = 0;
    01700                 switch(c = *++s) {
    01701                         case '-':
    01702                                 esign = 1;
    01703                         case '+':
    01704                                 c = *++s;
    01705                         }
    01706                 if (c >= '0' && c <= '9') {
    01707                         while(c == '0')
    01708                                 c = *++s;
    01709                         if (c > '0' && c <= '9') {
    01710                                 L = c - '0';
    01711                                 s1 = s;
    01712                                 while((c = *++s) >= '0' && c <= '9')
    01713                                         L = 10*L + c - '0';
    01714                                 if (s - s1 > 8 || L > 19999)
    01715                                         /* Avoid confusion from exponents
    01716                                          * so large that e might overflow.
    01717                                          */
    01718                                         e = 19999; /* safe for 16 bit ints */
    01719                                 else
    01720                                         e = (int)L;
    01721                                 if (esign)
    01722                                         e = -e;
    01723                                 }
    01724                         else
    01725                                 e = 0;
    01726                         }
    01727                 else
    01728                         s = s00;
    01729                 }
    01730         if (!nd) {
    01731                 if (!nz && !nz0) {
    01732 #ifdef INFNAN_CHECK
    01733                         /* Check for Nan and Infinity */
    01734                         switch(c) {
    01735                           case 'i':
    01736                           case 'I':
    01737                                 if (match(&s,"nf")) {
    01738                                         --s;
    01739                                         if (!match(&s,"inity"))
    01740                                                 ++s;
    01741 //                                      word0(rv) = 0x7ff00000;
    01742 //                                      word1(rv) = 0;
    01743                                         rv = OSDBL_MAX;
    01744                                         goto ret;
    01745                                         }
    01746                                 break;
    01747                           case 'n':
    01748                           case 'N':
    01749                                 if (match(&s, "an")) {
    01750                                         word0(rv) = NAN_WORD0;
    01751                                         word1(rv) = NAN_WORD1;
    01752 #ifndef No_Hex_NaN
    01753                                         if (*s == '(') /*)*/
    01754                                                 hexnan(&rv, &s);
    01755 #endif
    01756                                         goto ret;
    01757                                         }
    01758                           }
    01759 #endif /* INFNAN_CHECK */
    01760  ret0:
    01761                         s = s00;
    01762                         sign = 0;
    01763                         }
    01764                 goto ret;
    01765                 }
    01766         e1 = e -= nf;
    01767
    01768         /* Now we have nd0 digits, starting at s0, followed by a
    01769          * decimal point, followed by nd-nd0 digits.  The number we're
    01770          * after is the integer represented by those digits times
    01771          * 10**e */
    01772
    01773         if (!nd0)
    01774                 nd0 = nd;
    01775         k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
    01776         dval(rv) = y;
    01777         if (k > 9) {
    01778 #ifdef SET_INEXACT
    01779                 if (k > DBL_DIG)
    01780                         oldinexact = get_inexact();
    01781 #endif
    01782                 dval(rv) = tens[k - 9] * dval(rv) + z;
    01783                 }
    01784         bd0 = 0;
    01785         if (nd <= DBL_DIG
    01786 #ifndef RND_PRODQUOT
    01787 #ifndef Honor_FLT_ROUNDS
    01788                 && Flt_Rounds == 1
    01789 #endif
    01790 #endif
    01791                         ) {
    01792                 if (!e)
    01793                         goto ret;
    01794                 if (e > 0) {
    01795                         if (e <= Ten_pmax) {
    01796 #ifdef VAX
    01797                                 goto vax_ovfl_check;
    01798 #else
    01799 #ifdef Honor_FLT_ROUNDS
    01800                                 /* round correctly FLT_ROUNDS = 2 or 3 */
    01801                                 if (sign) {
    01802                                         rv = -rv;
    01803                                         sign = 0;
    01804                                         }
    01805 #endif
    01806                                 /* rv = */ rounded_product(dval(rv), tens[e]);
    01807                                 goto ret;
    01808 #endif
    01809                                 }
    01810                         i = DBL_DIG - nd;
    01811                         if (e <= Ten_pmax + i) {
    01812                                 /* A fancier test would sometimes let us do
    01813                                  * this for larger i values.
    01814                                  */
    01815 #ifdef Honor_FLT_ROUNDS
    01816                                 /* round correctly FLT_ROUNDS = 2 or 3 */
    01817                                 if (sign) {
    01818                                         rv = -rv;
    01819                                         sign = 0;
    01820                                         }
    01821 #endif
    01822                                 e -= i;
    01823                                 dval(rv) *= tens[i];
    01824 #ifdef VAX
    01825                                 /* VAX exponent range is so narrow we must
    01826                                  * worry about overflow here...
    01827                                  */
    01828  vax_ovfl_check:
    01829                                 word0(rv) -= P*Exp_msk1;
    01830                                 /* rv = */ rounded_product(dval(rv), tens[e]);
    01831                                 if ((word0(rv) & Exp_mask)
    01832                                  > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
    01833                                         goto ovfl;
    01834                                 word0(rv) += P*Exp_msk1;
    01835 #else
    01836                                 /* rv = */ rounded_product(dval(rv), tens[e]);
    01837 #endif
    01838                                 goto ret;
    01839                                 }
    01840                         }
    01841 #ifndef Inaccurate_Divide
    01842                 else if (e >= -Ten_pmax) {
    01843 #ifdef Honor_FLT_ROUNDS
    01844                         /* round correctly FLT_ROUNDS = 2 or 3 */
    01845                         if (sign) {
    01846                                 rv = -rv;
    01847                                 sign = 0;
    01848                                 }
    01849 #endif
    01850                         /* rv = */ rounded_quotient(dval(rv), tens[-e]);
    01851                         goto ret;
    01852                         }
    01853 #endif
    01854                 }
    01855         e1 += nd - k;
    01856
    01857 #ifdef IEEE_Arith
    01858 #ifdef SET_INEXACT
    01859         inexact = 1;
    01860         if (k <= DBL_DIG)
    01861                 oldinexact = get_inexact();
    01862 #endif
    01863 #ifdef Avoid_Underflow
    01864         scale = 0;
    01865 #endif
    01866 #ifdef Honor_FLT_ROUNDS
    01867         if ((rounding = Flt_Rounds) >= 2) {
    01868                 if (sign)
    01869                         rounding = rounding == 2 ? 0 : 2;
    01870                 else
    01871                         if (rounding != 2)
    01872                                 rounding = 0;
    01873                 }
    01874 #endif
    01875 #endif /*IEEE_Arith*/
    01876
    01877         /* Get starting approximation = rv * 10**e1 */
    01878
    01879         if (e1 > 0) {
    01880                 if ( (i = e1 & 15) )
    01881                         dval(rv) *= tens[i];
    01882                 if (e1 &= ~15) {
    01883                         if (e1 > DBL_MAX_10_EXP) {
    01884  ovfl:
    01885 #ifndef NO_ERRNO
    01886                                 errno = ERANGE;
    01887 #endif
    01888                                 /* Can't trust HUGE_VAL */
    01889 #ifdef IEEE_Arith
    01890 #ifdef Honor_FLT_ROUNDS
    01891                                 switch(rounding) {
    01892                                   case 0: /* toward 0 */
    01893                                   case 3: /* toward -infinity */
    01894                                         word0(rv) = Big0;
    01895                                         word1(rv) = Big1;
    01896                                         break;
    01897                                   default:
    01898                                         word0(rv) = Exp_mask;
    01899                                         word1(rv) = 0;
    01900                                   }
    01901 #else /*Honor_FLT_ROUNDS*/
    01902                                 word0(rv) = Exp_mask;
    01903                                 word1(rv) = 0;
    01904 #endif /*Honor_FLT_ROUNDS*/
    01905 #ifdef SET_INEXACT
    01906                                 /* set overflow bit */
    01907                                 dval(rv0) = 1e300;
    01908                                 dval(rv0) *= dval(rv0);
    01909 #endif
    01910 #else /*IEEE_Arith*/
    01911                                 word0(rv) = Big0;
    01912                                 word1(rv) = Big1;
    01913 #endif /*IEEE_Arith*/
    01914                                 if (bd0)
    01915                                         goto retfree;
    01916                                 goto ret;
    01917                                 }
    01918                         e1 >>= 4;
    01919                         for(j = 0; e1 > 1; j++, e1 >>= 1)
    01920                                 if (e1 & 1)
    01921                                         dval(rv) *= bigtens[j];
    01922                 /* The last multiplication could overflow. */
    01923                         word0(rv) -= P*Exp_msk1;
    01924                         dval(rv) *= bigtens[j];
    01925                         if ((z = word0(rv) & Exp_mask)
    01926                          > Exp_msk1*(DBL_MAX_EXP+Bias-P))
    01927                                 goto ovfl;
    01928                         if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
    01929                                 /* set to largest number */
    01930                                 /* (Can't trust DBL_MAX) */
    01931                                 word0(rv) = Big0;
    01932                                 word1(rv) = Big1;
    01933                                 }
    01934                         else
    01935                                 word0(rv) += P*Exp_msk1;
    01936                         }
    01937                 }
    01938         else if (e1 < 0) {
    01939                 e1 = -e1;
    01940                 if ( (i = e1 & 15) )
    01941                         dval(rv) /= tens[i];
    01942                 if (e1 >>= 4) {
    01943                         if (e1 >= 1 << n_bigtens)
    01944                                 goto undfl;
    01945 #ifdef Avoid_Underflow
    01946                         if (e1 & Scale_Bit)
    01947                                 scale = 2*P;
    01948                         for(j = 0; e1 > 0; j++, e1 >>= 1)
    01949                                 if (e1 & 1)
    01950                                         dval(rv) *= tinytens[j];
    01951                         if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask)
    01952                                                 >> Exp_shift)) > 0) {
    01953                                 /* scaled rv is denormal; zap j low bits */
    01954                                 if (j >= 32) {
    01955                                         word1(rv) = 0;
    01956                                         if (j >= 53)
    01957                                          word0(rv) = (P+2)*Exp_msk1;
    01958                                         else
    01959                                          word0(rv) &= 0xffffffff << j-32;
    01960                                         }
    01961                                 else
    01962                                         word1(rv) &= 0xffffffff << j;
    01963                                 }
    01964 #else
    01965                         for(j = 0; e1 > 1; j++, e1 >>= 1)
    01966                                 if (e1 & 1)
    01967                                         dval(rv) *= tinytens[j];
    01968                         /* The last multiplication could underflow. */
    01969                         dval(rv0) = dval(rv);
    01970                         dval(rv) *= tinytens[j];
    01971                         if (!dval(rv)) {
    01972                                 dval(rv) = 2.*dval(rv0);
    01973                                 dval(rv) *= tinytens[j];
    01974 #endif
    01975                                 if (!dval(rv)) {
    01976  undfl:
    01977                                         dval(rv) = 0.;
    01978 #ifndef NO_ERRNO
    01979                                         errno = ERANGE;
    01980 #endif
    01981                                         if (bd0)
    01982                                                 goto retfree;
    01983                                         goto ret;
    01984                                         }
    01985 #ifndef Avoid_Underflow
    01986                                 word0(rv) = Tiny0;
    01987                                 word1(rv) = Tiny1;
    01988                                 /* The refinement below will clean
    01989                                  * this approximation up.
    01990                                  */
    01991                                 }
    01992 #endif
    01993                         }
    01994                 }
    01995
    01996         /* Now the hard part -- adjusting rv to the correct value.*/
    01997
    01998         /* Put digits into bd: true value = bd * 10^e */
    01999
    02000         bd0 = s2b(s0, nd0, nd, y);
    02001
    02002         for(;;) {
    02003                 bd = Balloc(bd0->k);
    02004                 Bcopy(bd, bd0);
    02005                 bb = d2b(dval(rv), &bbe, &bbbits);      /* rv = bb * 2^bbe */
    02006                 bs = i2b(1);
    02007
    02008                 if (e >= 0) {
    02009                         bb2 = bb5 = 0;
    02010                         bd2 = bd5 = e;
    02011                         }
    02012                 else {
    02013                         bb2 = bb5 = -e;
    02014                         bd2 = bd5 = 0;
    02015                         }
    02016                 if (bbe >= 0)
    02017                         bb2 += bbe;
    02018                 else
    02019                         bd2 -= bbe;
    02020                 bs2 = bb2;
    02021 #ifdef Honor_FLT_ROUNDS
    02022                 if (rounding != 1)
    02023                         bs2++;
    02024 #endif
    02025 #ifdef Avoid_Underflow
    02026                 j = bbe - scale;
    02027                 i = j + bbbits - 1;     /* logb(rv) */
    02028                 if (i < Emin)   /* denormal */
    02029                         j += P - Emin;
    02030                 else
    02031                         j = P + 1 - bbbits;
    02032 #else /*Avoid_Underflow*/
    02033 #ifdef Sudden_Underflow
    02034 #ifdef IBM
    02035                 j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
    02036 #else
    02037                 j = P + 1 - bbbits;
    02038 #endif
    02039 #else /*Sudden_Underflow*/
    02040                 j = bbe;
    02041                 i = j + bbbits - 1;     /* logb(rv) */
    02042                 if (i < Emin)   /* denormal */
    02043                         j += P - Emin;
    02044                 else
    02045                         j = P + 1 - bbbits;
    02046 #endif /*Sudden_Underflow*/
    02047 #endif /*Avoid_Underflow*/
    02048                 bb2 += j;
    02049                 bd2 += j;
    02050 #ifdef Avoid_Underflow
    02051                 bd2 += scale;
    02052 #endif
    02053                 i = bb2 < bd2 ? bb2 : bd2;
    02054                 if (i > bs2)
    02055                         i = bs2;
    02056                 if (i > 0) {
    02057                         bb2 -= i;
    02058                         bd2 -= i;
    02059                         bs2 -= i;
    02060                         }
    02061                 if (bb5 > 0) {
    02062                         bs = pow5mult(bs, bb5);
    02063                         bb1 = mult(bs, bb);
    02064                         Bfree(bb);
    02065                         bb = bb1;
    02066                         }
    02067                 if (bb2 > 0)
    02068                         bb = lshift(bb, bb2);
    02069                 if (bd5 > 0)
    02070                         bd = pow5mult(bd, bd5);
    02071                 if (bd2 > 0)
    02072                         bd = lshift(bd, bd2);
    02073                 if (bs2 > 0)
    02074                         bs = lshift(bs, bs2);
    02075                 delta = diff(bb, bd);
    02076                 dsign = delta->sign;
    02077                 delta->sign = 0;
    02078                 i = cmp(delta, bs);
    02079 #ifdef Honor_FLT_ROUNDS
    02080                 if (rounding != 1) {
    02081                         if (i < 0) {
    02082                                 /* Error is less than an ulp */
    02083                                 if (!delta->x[0] && delta->wds <= 1) {
    02084                                         /* exact */
    02085 #ifdef SET_INEXACT
    02086                                         inexact = 0;
    02087 #endif
    02088                                         break;
    02089                                         }
    02090                                 if (rounding) {
    02091                                         if (dsign) {
    02092                                                 adj = 1.;
    02093                                                 goto apply_adj;
    02094                                                 }
    02095                                         }
    02096                                 else if (!dsign) {
    02097                                         adj = -1.;
    02098                                         if (!word1(rv)
    02099                                          && !(word0(rv) & Frac_mask)) {
    02100                                                 y = word0(rv) & Exp_mask;
    02101 #ifdef Avoid_Underflow
    02102                                                 if (!scale || y > 2*P*Exp_msk1)
    02103 #else
    02104                                                 if (y)
    02105 #endif
    02106                                                   {
    02107                                                   delta = lshift(delta,Log2P);
    02108                                                   if (cmp(delta, bs) <= 0)
    02109                                                         adj = -0.5;
    02110                                                   }
    02111                                                 }
    02112  apply_adj:
    02113 #ifdef Avoid_Underflow
    02114                                         if (scale && (y = word0(rv) & Exp_mask)
    02115                                                 <= 2*P*Exp_msk1)
    02116                                           word0(adj) += (2*P+1)*Exp_msk1 - y;
    02117 #else
    02118 #ifdef Sudden_Underflow
    02119                                         if ((word0(rv) & Exp_mask) <=
    02120                                                         P*Exp_msk1) {
    02121                                                 word0(rv) += P*Exp_msk1;
    02122                                                 dval(rv) += adj*ulp(dval(rv));
    02123                                                 word0(rv) -= P*Exp_msk1;
    02124                                                 }
    02125                                         else
    02126 #endif /*Sudden_Underflow*/
    02127 #endif /*Avoid_Underflow*/
    02128                                         dval(rv) += adj*ulp(dval(rv));
    02129                                         }
    02130                                 break;
    02131                                 }
    02132                         adj = ratio(delta, bs);
    02133                         if (adj < 1.)
    02134                                 adj = 1.;
    02135                         if (adj <= 0x7ffffffe) {
    02136                                 /* adj = rounding ? ceil(adj) : floor(adj); */
    02137                                 y = adj;
    02138                                 if (y != adj) {
    02139                                         if (!((rounding>>1) ^ dsign))
    02140                                                 y++;
    02141                                         adj = y;
    02142                                         }
    02143                                 }
    02144 #ifdef Avoid_Underflow
    02145                         if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
    02146                                 word0(adj) += (2*P+1)*Exp_msk1 - y;
    02147 #else
    02148 #ifdef Sudden_Underflow
    02149                         if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
    02150                                 word0(rv) += P*Exp_msk1;
    02151                                 adj *= ulp(dval(rv));
    02152                                 if (dsign)
    02153                                         dval(rv) += adj;
    02154                                 else
    02155                                         dval(rv) -= adj;
    02156                                 word0(rv) -= P*Exp_msk1;
    02157                                 goto cont;
    02158                                 }
    02159 #endif /*Sudden_Underflow*/
    02160 #endif /*Avoid_Underflow*/
    02161                         adj *= ulp(dval(rv));
    02162                         if (dsign)
    02163                                 dval(rv) += adj;
    02164                         else
    02165                                 dval(rv) -= adj;
    02166                         goto cont;
    02167                         }
    02168 #endif /*Honor_FLT_ROUNDS*/
    02169
    02170                 if (i < 0) {
    02171                         /* Error is less than half an ulp -- check for
    02172                          * special case of mantissa a power of two.
    02173                          */
    02174                         if (dsign || word1(rv) || word0(rv) & Bndry_mask
    02175 #ifdef IEEE_Arith
    02176 #ifdef Avoid_Underflow
    02177                          || (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1
    02178 #else
    02179                          || (word0(rv) & Exp_mask) <= Exp_msk1
    02180 #endif
    02181 #endif
    02182                                 ) {
    02183 #ifdef SET_INEXACT
    02184                                 if (!delta->x[0] && delta->wds <= 1)
    02185                                         inexact = 0;
    02186 #endif
    02187                                 break;
    02188                                 }
    02189                         if (!delta->x[0] && delta->wds <= 1) {
    02190                                 /* exact result */
    02191 #ifdef SET_INEXACT
    02192                                 inexact = 0;
    02193 #endif
    02194                                 break;
    02195                                 }
    02196                         delta = lshift(delta,Log2P);
    02197                         if (cmp(delta, bs) > 0)
    02198                                 goto drop_down;
    02199                         break;
    02200                         }
    02201                 if (i == 0) {
    02202                         /* exactly half-way between */
    02203                         if (dsign) {
    02204                                 if ((word0(rv) & Bndry_mask1) == Bndry_mask1
    02205                                  &&  word1(rv) == (
    02206 #ifdef Avoid_Underflow
    02207                         (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
    02208                 ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
    02209 #endif
    02210                                                    0xffffffff)) {
    02211                                         /*boundary case -- increment exponent*/
    02212                                         word0(rv) = (word0(rv) & Exp_mask)
    02213                                                 + Exp_msk1
    02214 #ifdef IBM
    02215                                                 | Exp_msk1 >> 4
    02216 #endif
    02217                                                 ;
    02218                                         word1(rv) = 0;
    02219 #ifdef Avoid_Underflow
    02220                                         dsign = 0;
    02221 #endif
    02222                                         break;
    02223                                         }
    02224                                 }
    02225                         else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
    02226  drop_down:
    02227                                 /* boundary case -- decrement exponent */
    02228 #ifdef Sudden_Underflow /*{{*/
    02229                                 L = word0(rv) & Exp_mask;
    02230 #ifdef IBM
    02231                                 if (L <  Exp_msk1)
    02232 #else
    02233 #ifdef Avoid_Underflow
    02234                                 if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
    02235 #else
    02236                                 if (L <= Exp_msk1)
    02237 #endif /*Avoid_Underflow*/
    02238 #endif /*IBM*/
    02239                                         goto undfl;
    02240                                 L -= Exp_msk1;
    02241 #else /*Sudden_Underflow}{*/
    02242 #ifdef Avoid_Underflow
    02243                                 if (scale) {
    02244                                         L = word0(rv) & Exp_mask;
    02245                                         if (L <= (2*P+1)*Exp_msk1) {
    02246                                                 if (L > (P+2)*Exp_msk1)
    02247                                                         /* round even ==> */
    02248                                                         /* accept rv */
    02249                                                         break;
    02250                                                 /* rv = smallest denormal */
    02251                                                 goto undfl;
    02252                                                 }
    02253                                         }
    02254 #endif /*Avoid_Underflow*/
    02255                                 L = (word0(rv) & Exp_mask) - Exp_msk1;
    02256 #endif /*Sudden_Underflow}}*/
    02257                                 word0(rv) = L | Bndry_mask1;
    02258                                 word1(rv) = 0xffffffff;
    02259 #ifdef IBM
    02260                                 goto cont;
    02261 #else
    02262                                 break;
    02263 #endif
    02264                                 }
    02265 #ifndef ROUND_BIASED
    02266                         if (!(word1(rv) & LSB))
    02267                                 break;
    02268 #endif
    02269                         if (dsign)
    02270                                 dval(rv) += ulp(dval(rv));
    02271 #ifndef ROUND_BIASED
    02272                         else {
    02273                                 dval(rv) -= ulp(dval(rv));
    02274 #ifndef Sudden_Underflow
    02275                                 if (!dval(rv))
    02276                                         goto undfl;
    02277 #endif
    02278                                 }
    02279 #ifdef Avoid_Underflow
    02280                         dsign = 1 - dsign;
    02281 #endif
    02282 #endif
    02283                         break;
    02284                         }
    02285                 if ((aadj = ratio(delta, bs)) <= 2.) {
    02286                         if (dsign)
    02287                                 aadj = aadj1 = 1.;
    02288                         else if (word1(rv) || word0(rv) & Bndry_mask) {
    02289 #ifndef Sudden_Underflow
    02290                                 if (word1(rv) == Tiny1 && !word0(rv))
    02291                                         goto undfl;
    02292 #endif
    02293                                 aadj = 1.;
    02294                                 aadj1 = -1.;
    02295                                 }
    02296                         else {
    02297                                 /* special case -- power of FLT_RADIX to be */
    02298                                 /* rounded down... */
    02299
    02300                                 if (aadj < 2./FLT_RADIX)
    02301                                         aadj = 1./FLT_RADIX;
    02302                                 else
    02303                                         aadj *= 0.5;
    02304                                 aadj1 = -aadj;
    02305                                 }
    02306                         }
    02307                 else {
    02308                         aadj *= 0.5;
    02309                         aadj1 = dsign ? aadj : -aadj;
    02310 #ifdef Check_FLT_ROUNDS
    02311                         switch(Rounding) {
    02312                                 case 2: /* towards +infinity */
    02313                                         aadj1 -= 0.5;
    02314                                         break;
    02315                                 case 0: /* towards 0 */
    02316                                 case 3: /* towards -infinity */
    02317                                         aadj1 += 0.5;
    02318                                 }
    02319 #else
    02320                         if (Flt_Rounds == 0)
    02321                                 aadj1 += 0.5;
    02322 #endif /*Check_FLT_ROUNDS*/
    02323                         }
    02324                 y = word0(rv) & Exp_mask;
    02325
    02326                 /* Check for overflow */
    02327
    02328                 if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
    02329                         dval(rv0) = dval(rv);
    02330                         word0(rv) -= P*Exp_msk1;
    02331                         adj = aadj1 * ulp(dval(rv));
    02332                         dval(rv) += adj;
    02333                         if ((word0(rv) & Exp_mask) >=
    02334                                         Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
    02335                                 if (word0(rv0) == Big0 && word1(rv0) == Big1)
    02336                                         goto ovfl;
    02337                                 word0(rv) = Big0;
    02338                                 word1(rv) = Big1;
    02339                                 goto cont;
    02340                                 }
    02341                         else
    02342                                 word0(rv) += P*Exp_msk1;
    02343                         }
    02344                 else {
    02345 #ifdef Avoid_Underflow
    02346                         if (scale && y <= 2*P*Exp_msk1) {
    02347                                 if (aadj <= 0x7fffffff) {
    02348                                         if ((z = (ULong)aadj) <= 0)
    02349                                                 z = 1;
    02350                                         aadj = z;
    02351                                         aadj1 = dsign ? aadj : -aadj;
    02352                                         }
    02353                                 word0(aadj1) += (2*P+1)*Exp_msk1 - y;
    02354                                 }
    02355                         adj = aadj1 * ulp(dval(rv));
    02356                         dval(rv) += adj;
    02357 #else
    02358 #ifdef Sudden_Underflow
    02359                         if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
    02360                                 dval(rv0) = dval(rv);
    02361                                 word0(rv) += P*Exp_msk1;
    02362                                 adj = aadj1 * ulp(dval(rv));
    02363                                 dval(rv) += adj;
    02364 #ifdef IBM
    02365                                 if ((word0(rv) & Exp_mask) <  P*Exp_msk1)
    02366 #else
    02367                                 if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
    02368 #endif
    02369                                         {
    02370                                         if (word0(rv0) == Tiny0
    02371                                          && word1(rv0) == Tiny1)
    02372                                                 goto undfl;
    02373                                         word0(rv) = Tiny0;
    02374                                         word1(rv) = Tiny1;
    02375                                         goto cont;
    02376                                         }
    02377                                 else
    02378                                         word0(rv) -= P*Exp_msk1;
    02379                                 }
    02380                         else {
    02381                                 adj = aadj1 * ulp(dval(rv));
    02382                                 dval(rv) += adj;
    02383                                 }
    02384 #else /*Sudden_Underflow*/
    02385                         /* Compute adj so that the IEEE rounding rules will
    02386                          * correctly round rv + adj in some half-way cases.
    02387                          * If rv * ulp(rv) is denormalized (i.e.,
    02388                          * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
    02389                          * trouble from bits lost to denormalization;
    02390                          * example: 1.2e-307 .
    02391                          */
    02392                         if (y <= (P-1)*Exp_msk1 && aadj > 1.) {
    02393                                 aadj1 = (double)(int)(aadj + 0.5);
    02394                                 if (!dsign)
    02395                                         aadj1 = -aadj1;
    02396                                 }
    02397                         adj = aadj1 * ulp(dval(rv));
    02398                         dval(rv) += adj;
    02399 #endif /*Sudden_Underflow*/
    02400 #endif /*Avoid_Underflow*/
    02401                         }
    02402                 z = word0(rv) & Exp_mask;
    02403 #ifndef SET_INEXACT
    02404 #ifdef Avoid_Underflow
    02405                 if (!scale)
    02406 #endif
    02407                 if (y == z) {
    02408                         /* Can we stop now? */
    02409                         L = (Long)aadj;
    02410                         aadj -= L;
    02411                         /* The tolerances below are conservative. */
    02412                         if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
    02413                                 if (aadj < .4999999 || aadj > .5000001)
    02414                                         break;
    02415                                 }
    02416                         else if (aadj < .4999999/FLT_RADIX)
    02417                                 break;
    02418                         }
    02419 #endif
    02420  cont:
    02421                 Bfree(bb);
    02422                 Bfree(bd);
    02423                 Bfree(bs);
    02424                 Bfree(delta);
    02425                 }
    02426 #ifdef SET_INEXACT
    02427         if (inexact) {
    02428                 if (!oldinexact) {
    02429                         word0(rv0) = Exp_1 + (70 << Exp_shift);
    02430                         word1(rv0) = 0;
    02431                         dval(rv0) += 1.;
    02432                         }
    02433                 }
    02434         else if (!oldinexact)
    02435                 clear_inexact();
    02436 #endif
    02437 #ifdef Avoid_Underflow
    02438         if (scale) {
    02439                 word0(rv0) = Exp_1 - 2*P*Exp_msk1;
    02440                 word1(rv0) = 0;
    02441                 dval(rv) *= dval(rv0);
    02442 #ifndef NO_ERRNO
    02443                 /* try to avoid the bug of testing an 8087 register value */
    02444                 if (word0(rv) == 0 && word1(rv) == 0)
    02445                         errno = ERANGE;
    02446 #endif
    02447                 }
    02448 #endif /* Avoid_Underflow */
    02449 #ifdef SET_INEXACT
    02450         if (inexact && !(word0(rv) & Exp_mask)) {
    02451                 /* set underflow bit */
    02452                 dval(rv0) = 1e-300;
    02453                 dval(rv0) *= dval(rv0);
    02454                 }
    02455 #endif
    02456  retfree:
    02457         Bfree(bb);
    02458         Bfree(bd);
    02459         Bfree(bs);
    02460         Bfree(bd0);
    02461         Bfree(delta);
    02462  ret:
    02463         if (se)
    02464                 *se = const_cast<char*>(s);
    02465         return sign ? -dval(rv) : dval(rv);
    02466         }
    02467
    02468  static int
    02469 quorem
    02470 #ifdef KR_headers
    02471         (b, S) Bigint *b, *S;
    02472 #else
    02473         (Bigint *b, Bigint *S)
    02474 #endif
    02475 {
    02476         int n;
    02477         ULong *bx, *bxe, q, *sx, *sxe;
    02478 #ifdef ULLong
    02479         ULLong borrow, carry, y, ys;
    02480 #else
    02481         ULong borrow, carry, y, ys;
    02482 #ifdef Pack_32
    02483         ULong si, z, zs;
    02484 #endif
    02485 #endif
    02486
    02487         n = S->wds;
    02488 #ifdef DEBUG
    02489         /*debug*/ if (b->wds > n)
    02490         /*debug*/       Bug("oversize b in quorem");
    02491 #endif
    02492         if (b->wds < n)
    02493                 return 0;
    02494         sx = S->x;
    02495         sxe = sx + --n;
    02496         bx = b->x;
    02497         bxe = bx + n;
    02498         q = *bxe / (*sxe + 1);  /* ensure q <= true quotient */
    02499 #ifdef DEBUG
    02500         /*debug*/ if (q > 9)
    02501         /*debug*/       Bug("oversized quotient in quorem");
    02502 #endif
    02503         if (q) {
    02504                 borrow = 0;
    02505                 carry = 0;
    02506                 do {
    02507 #ifdef ULLong
    02508                         ys = *sx++ * (ULLong)q + carry;
    02509                         carry = ys >> 32;
    02510                         y = *bx - (ys & FFFFFFFF) - borrow;
    02511                         borrow = y >> 32 & (ULong)1;
    02512                         *bx++ = y & FFFFFFFF;
    02513 #else
    02514 #ifdef Pack_32
    02515                         si = *sx++;
    02516                         ys = (si & 0xffff) * q + carry;
    02517                         zs = (si >> 16) * q + (ys >> 16);
    02518                         carry = zs >> 16;
    02519                         y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
    02520                         borrow = (y & 0x10000) >> 16;
    02521                         z = (*bx >> 16) - (zs & 0xffff) - borrow;
    02522                         borrow = (z & 0x10000) >> 16;
    02523                         Storeinc(bx, z, y);
    02524 #else
    02525                         ys = *sx++ * q + carry;
    02526                         carry = ys >> 16;
    02527                         y = *bx - (ys & 0xffff) - borrow;
    02528                         borrow = (y & 0x10000) >> 16;
    02529                         *bx++ = y & 0xffff;
    02530 #endif
    02531 #endif
    02532                         }
    02533                         while(sx <= sxe);
    02534                 if (!*bxe) {
    02535                         bx = b->x;
    02536                         while(--bxe > bx && !*bxe)
    02537                                 --n;
    02538                         b->wds = n;
    02539                         }
    02540                 }
    02541         if (cmp(b, S) >= 0) {
    02542                 q++;
    02543                 borrow = 0;
    02544                 carry = 0;
    02545                 bx = b->x;
    02546                 sx = S->x;
    02547                 do {
    02548 #ifdef ULLong
    02549                         ys = *sx++ + carry;
    02550                         carry = ys >> 32;
    02551                         y = *bx - (ys & FFFFFFFF) - borrow;
    02552                         borrow = y >> 32 & (ULong)1;
    02553                         *bx++ = y & FFFFFFFF;
    02554 #else
    02555 #ifdef Pack_32
    02556                         si = *sx++;
    02557                         ys = (si & 0xffff) + carry;
    02558                         zs = (si >> 16) + (ys >> 16);
    02559                         carry = zs >> 16;
    02560                         y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
    02561                         borrow = (y & 0x10000) >> 16;
    02562                         z = (*bx >> 16) - (zs & 0xffff) - borrow;
    02563                         borrow = (z & 0x10000) >> 16;
    02564                         Storeinc(bx, z, y);
    02565 #else
    02566                         ys = *sx++ + carry;
    02567                         carry = ys >> 16;
    02568                         y = *bx - (ys & 0xffff) - borrow;
    02569                         borrow = (y & 0x10000) >> 16;
    02570                         *bx++ = y & 0xffff;
    02571 #endif
    02572 #endif
    02573                         }
    02574                         while(sx <= sxe);
    02575                 bx = b->x;
    02576                 bxe = bx + n;
    02577                 if (!*bxe) {
    02578                         while(--bxe > bx && !*bxe)
    02579                                 --n;
    02580                         b->wds = n;
    02581                         }
    02582                 }
    02583         return q;
    02584         }
    02585
    02586 #ifndef MULTIPLE_THREADS
    02587  static char *dtoa_result;
    02588 #endif
    02589
    02590  static char *
    02591 #ifdef KR_headers
    02592 rv_alloc(i) int i;
    02593 #else
    02594 rv_alloc(int i)
    02595 #endif
    02596 {
    02597         int j, k, *r;
    02598
    02599         j = sizeof(ULong);
    02600         for(k = 0;
    02601                 sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= (unsigned)i;
    02602                 j <<= 1)
    02603                         k++;
    02604         r = (int*)Balloc(k);
    02605         *r = k;
    02606         return
    02607 #ifndef MULTIPLE_THREADS
    02608         dtoa_result =
    02609 #endif
    02610                 (char *)(r+1);
    02611         }
    02612
    02613  static char *
    02614 #ifdef KR_headers
    02615  nrv_alloc(s, rve, n) CONST char *s; char **rve; int n;
    02616 #else
    02617 nrv_alloc(CONST char *s, char **rve, int n)
    02618 #endif
    02619 {
    02620         char *rv, *t;
    02621
    02622         t = rv = rv_alloc(n);
    02623         while( (*t = *s++) ) t++;
    02624         if (rve)
    02625                 *rve = t;
    02626         return rv;
    02627         }
    02628
    02629 /* freedtoa(s) must be used to free values s returned by dtoa
    02630  * when MULTIPLE_THREADS is #defined.  It should be used in all cases,
    02631  * but for consistency with earlier versions of dtoa, it is optional
    02632  * when MULTIPLE_THREADS is not defined.
    02633  */
    02634
    02635  void
    02636 #ifdef KR_headers
    02637 os_freedtoa(s) char *s;
    02638 #else
    02639 os_freedtoa(char *s)
    02640 #endif
    02641 {
    02642         Bigint *b = (Bigint *)((int *)s - 1);
    02643         b->maxwds = 1 << (b->k = *(int*)b);
    02644         Bfree(b);
    02645 #ifndef MULTIPLE_THREADS
    02646         if (s == dtoa_result)
    02647                 dtoa_result = 0;
    02648 #endif
    02649         }
    02650
    02651 /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
    02652  *
    02653  * Inspired by "How to Print Floating-Point Numbers Accurately" by
    02654  * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126].
    02655  *
    02656  * Modifications:
    02657  *      1. Rather than iterating, we use a simple numeric overestimate
    02658  *         to determine k = floor(log10(d)).  We scale relevant
    02659  *         quantities using O(log2(k)) rather than O(k) multiplications.
    02660  *      2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
    02661  *         try to generate digits strictly left to right.  Instead, we
    02662  *         compute with fewer bits and propagate the carry if necessary
    02663  *         when rounding the final digit up.  This is often faster.
    02664  *      3. Under the assumption that input will be rounded nearest,
    02665  *         mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
    02666  *         That is, we allow equality in stopping tests when the
    02667  *         round-nearest rule will give the same floating-point value
    02668  *         as would satisfaction of the stopping test with strict
    02669  *         inequality.
    02670  *      4. We remove common factors of powers of 2 from relevant
    02671  *         quantities.
    02672  *      5. When converting floating-point integers less than 1e16,
    02673  *         we use floating-point arithmetic rather than resorting
    02674  *         to multiple-precision integers.
    02675  *      6. When asked to produce fewer than 15 digits, we first try
    02676  *         to get by with floating-point arithmetic; we resort to
    02677  *         multiple-precision integer arithmetic only if we cannot
    02678  *         guarantee that the floating-point calculation has given
    02679  *         the correctly rounded result.  For k requested digits and
    02680  *         "uniformly" distributed input, the probability is
    02681  *         something like 10^(k-15) that we must resort to the Long
    02682  *         calculation.
    02683  */
    02684
    02685  char *
    02686 os_dtoa
    02687 #ifdef KR_headers
    02688         (d, mode, ndigits, decpt, sign, rve)
    02689         double d; int mode, ndigits, *decpt, *sign; char **rve;
    02690 #else
    02691         (double d, int mode, int ndigits, int *decpt, int *sign, char **rve)
    02692 #endif
    02693 {
    02694  /*     Arguments ndigits, decpt, sign are similar to those
    02695         of ecvt and fcvt; trailing zeros are suppressed from
    02696         the returned string.  If not null, *rve is set to point
    02697         to the end of the return value.  If d is +-Infinity or NaN,
    02698         then *decpt is set to 9999.
    02699
    02700         mode:
    02701                 0 ==> shortest string that yields d when read in
    02702                         and rounded to nearest.
    02703                 1 ==> like 0, but with Steele & White stopping rule;
    02704                         e.g. with IEEE P754 arithmetic , mode 0 gives
    02705                         1e23 whereas mode 1 gives 9.999999999999999e22.
    02706                 2 ==> max(1,ndigits) significant digits.  This gives a
    02707                         return value similar to that of ecvt, except
    02708                         that trailing zeros are suppressed.
    02709                 3 ==> through ndigits past the decimal point.  This
    02710                         gives a return value similar to that from fcvt,
    02711                         except that trailing zeros are suppressed, and
    02712                         ndigits can be negative.
    02713                 4,5 ==> similar to 2 and 3, respectively, but (in
    02714                         round-nearest mode) with the tests of mode 0 to
    02715                         possibly return a shorter string that rounds to d.
    02716                         With IEEE arithmetic and compilation with
    02717                         -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
    02718                         as modes 2 and 3 when FLT_ROUNDS != 1.
    02719                 6-9 ==> Debugging modes similar to mode - 4:  don't try
    02720                         fast floating-point estimate (if applicable).
    02721
    02722                 Values of mode other than 0-9 are treated as mode 0.
    02723
    02724                 Sufficient space is allocated to the return value
    02725                 to hold the suppressed trailing zeros.
    02726         */
    02727
    02728         int bbits, b2, b5, be, dig, i, ieps, ilim = 0, ilim0, ilim1 =0,
    02729                 j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
    02730                 spec_case, try_quick;
    02731         Long L;
    02732 #ifndef Sudden_Underflow
    02733         int denorm;
    02734         ULong x;
    02735 #endif
    02736         Bigint *b, *b1, *delta, *mlo = NULL, *mhi, *S;
    02737         double d2, ds, eps;
    02738         char *s, *s0;
    02739 #ifdef Honor_FLT_ROUNDS
    02740         int rounding;
    02741 #endif
    02742 #ifdef SET_INEXACT
    02743         int inexact, oldinexact;
    02744 #endif
    02745
    02746 #ifndef MULTIPLE_THREADS
    02747         if (dtoa_result) {
    02748                 os_freedtoa(dtoa_result);
    02749                 dtoa_result = 0;
    02750                 }
    02751 #endif
    02752
    02753         if (word0(d) & Sign_bit) {
    02754                 /* set sign for everything, including 0's and NaNs */
    02755                 *sign = 1;
    02756                 word0(d) &= ~Sign_bit;  /* clear sign bit */
    02757                 }
    02758         else
    02759                 *sign = 0;
    02760
    02761 #if defined(IEEE_Arith) + defined(VAX)
    02762 #ifdef IEEE_Arith
    02763         if ((word0(d) & Exp_mask) == Exp_mask)
    02764 #else
    02765         if (word0(d)  == 0x8000)
    02766 #endif
    02767                 {
    02768                 /* Infinity or NaN */
    02769                 *decpt = 9999;
    02770 #ifdef IEEE_Arith
    02771                 if (!word1(d) && !(word0(d) & 0xfffff))
    02772                         return nrv_alloc("Infinity", rve, 8);
    02773 #endif
    02774                 return nrv_alloc("NaN", rve, 3);
    02775                 }
    02776 #endif
    02777 #ifdef IBM
    02778         dval(d) += 0; /* normalize */
    02779 #endif
    02780         if (!dval(d)) {
    02781                 *decpt = 1;
    02782                 return nrv_alloc("0", rve, 1);
    02783                 }
    02784
    02785 #ifdef SET_INEXACT
    02786         try_quick = oldinexact = get_inexact();
    02787         inexact = 1;
    02788 #endif
    02789 #ifdef Honor_FLT_ROUNDS
    02790         if ((rounding = Flt_Rounds) >= 2) {
    02791                 if (*sign)
    02792                         rounding = rounding == 2 ? 0 : 2;
    02793                 else
    02794                         if (rounding != 2)
    02795                                 rounding = 0;
    02796                 }
    02797 #endif
    02798
    02799         b = d2b(dval(d), &be, &bbits);
    02800 #ifdef Sudden_Underflow
    02801         i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
    02802 #else
    02803         if ( (i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1))  ) ) {
    02804 #endif
    02805                 dval(d2) = dval(d);
    02806                 word0(d2) &= Frac_mask1;
    02807                 word0(d2) |= Exp_11;
    02808 #ifdef IBM
    02809                 if (j = 11 - hi0bits(word0(d2) & Frac_mask))
    02810                         dval(d2) /= 1 << j;
    02811 #endif
    02812
    02813                 /* log(x)       ~=~ log(1.5) + (x-1.5)/1.5
    02814                  * log10(x)      =  log(x) / log(10)
    02815                  *              ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
    02816                  * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
    02817                  *
    02818                  * This suggests computing an approximation k to log10(d) by
    02819                  *
    02820                  * k = (i - Bias)*0.301029995663981
    02821                  *      + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
    02822                  *
    02823                  * We want k to be too large rather than too small.
    02824                  * The error in the first-order Taylor series approximation
    02825                  * is in our favor, so we just round up the constant enough
    02826                  * to compensate for any error in the multiplication of
    02827                  * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
    02828                  * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
    02829                  * adding 1e-13 to the constant term more than suffices.
    02830                  * Hence we adjust the constant term to 0.1760912590558.
    02831                  * (We could get a more accurate k by invoking log10,
    02832                  *  but this is probably not worthwhile.)
    02833                  */
    02834
    02835                 i -= Bias;
    02836 #ifdef IBM
    02837                 i <<= 2;
    02838                 i += j;
    02839 #endif
    02840 #ifndef Sudden_Underflow
    02841                 denorm = 0;
    02842                 }
    02843         else {
    02844                 /* d is denormalized */
    02845
    02846                 i = bbits + be + (Bias + (P-1) - 1);
    02847                 x = i > 32  ? word0(d) << 64 - i | word1(d) >> i - 32
    02848                             : word1(d) << 32 - i;
    02849                 dval(d2) = x;
    02850                 word0(d2) -= 31*Exp_msk1; /* adjust exponent */
    02851                 i -= (Bias + (P-1) - 1) + 1;
    02852                 denorm = 1;
    02853                 }
    02854 #endif
    02855         ds = (dval(d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
    02856         k = (int)ds;
    02857         if (ds < 0. && ds != k)
    02858                 k--;    /* want k = floor(ds) */
    02859         k_check = 1;
    02860         if (k >= 0 && k <= Ten_pmax) {
    02861                 if (dval(d) < tens[k])
    02862                         k--;
    02863                 k_check = 0;
    02864                 }
    02865         j = bbits - i - 1;
    02866         if (j >= 0) {
    02867                 b2 = 0;
    02868                 s2 = j;
    02869                 }
    02870         else {
    02871                 b2 = -j;
    02872                 s2 = 0;
    02873                 }
    02874         if (k >= 0) {
    02875                 b5 = 0;
    02876                 s5 = k;
    02877                 s2 += k;
    02878                 }
    02879         else {
    02880                 b2 -= k;
    02881                 b5 = -k;
    02882                 s5 = 0;
    02883                 }
    02884         if (mode < 0 || mode > 9)
    02885                 mode = 0;
    02886
    02887 #ifndef SET_INEXACT
    02888 #ifdef Check_FLT_ROUNDS
    02889         try_quick = Rounding == 1;
    02890 #else
    02891         try_quick = 1;
    02892 #endif
    02893 #endif /*SET_INEXACT*/
    02894
    02895         if (mode > 5) {
    02896                 mode -= 4;
    02897                 try_quick = 0;
    02898                 }
    02899         leftright = 1;
    02900         switch(mode) {
    02901                 case 0:
    02902                 case 1:
    02903                         ilim = ilim1 = -1;
    02904                         i = 18;
    02905                         ndigits = 0;
    02906                         break;
    02907                 case 2:
    02908                         leftright = 0;
    02909                         /* no break */
    02910                 case 4:
    02911                         if (ndigits <= 0)
    02912                                 ndigits = 1;
    02913                         ilim = ilim1 = i = ndigits;
    02914                         break;
    02915                 case 3:
    02916                         leftright = 0;
    02917                         /* no break */
    02918                 case 5:
    02919                         i = ndigits + k + 1;
    02920                         ilim = i;
    02921                         ilim1 = i - 1;
    02922                         if (i <= 0)
    02923                                 i = 1;
    02924                 }
    02925         s = s0 = rv_alloc(i);
    02926
    02927 #ifdef Honor_FLT_ROUNDS
    02928         if (mode > 1 && rounding != 1)
    02929                 leftright = 0;
    02930 #endif
    02931
    02932         if (ilim >= 0 && ilim <= Quick_max && try_quick) {
    02933
    02934                 /* Try to get by with floating-point arithmetic. */
    02935
    02936                 i = 0;
    02937                 dval(d2) = dval(d);
    02938                 k0 = k;
    02939                 ilim0 = ilim;
    02940                 ieps = 2; /* conservative */
    02941                 if (k > 0) {
    02942                         ds = tens[k&0xf];
    02943                         j = k >> 4;
    02944                         if (j & Bletch) {
    02945                                 /* prevent overflows */
    02946                                 j &= Bletch - 1;
    02947                                 dval(d) /= bigtens[n_bigtens-1];
    02948                                 ieps++;
    02949                                 }
    02950                         for(; j; j >>= 1, i++)
    02951                                 if (j & 1) {
    02952                                         ieps++;
    02953                                         ds *= bigtens[i];
    02954                                         }
    02955                         dval(d) /= ds;
    02956                         }
    02957                 else if ( (j1 = -k) ) {
    02958                         dval(d) *= tens[j1 & 0xf];
    02959                         for(j = j1 >> 4; j; j >>= 1, i++)
    02960                                 if (j & 1) {
    02961                                         ieps++;
    02962                                         dval(d) *= bigtens[i];
    02963                                         }
    02964                         }
    02965                 if (k_check && dval(d) < 1. && ilim > 0) {
    02966                         if (ilim1 <= 0)
    02967                                 goto fast_failed;
    02968                         ilim = ilim1;
    02969                         k--;
    02970                         dval(d) *= 10.;
    02971                         ieps++;
    02972                         }
    02973                 dval(eps) = ieps*dval(d) + 7.;
    02974                 word0(eps) -= (P-1)*Exp_msk1;
    02975                 if (ilim == 0) {
    02976                         S = mhi = 0;
    02977                         dval(d) -= 5.;
    02978                         if (dval(d) > dval(eps))
    02979                                 goto one_digit;
    02980                         if (dval(d) < -dval(eps))
    02981                                 goto no_digits;
    02982                         goto fast_failed;
    02983                         }
    02984 #ifndef No_leftright
    02985                 if (leftright) {
    02986                         /* Use Steele & White method of only
    02987                          * generating digits needed.
    02988                          */
    02989                         dval(eps) = 0.5/tens[ilim-1] - dval(eps);
    02990                         for(i = 0;;) {
    02991                                 L = (long int) dval(d);
    02992                                 dval(d) -= L;
    02993                                 *s++ = '0' + (int)L;
    02994                                 if (dval(d) < dval(eps))
    02995                                         goto ret1;
    02996                                 if (1. - dval(d) < dval(eps))
    02997                                         goto bump_up;
    02998                                 if (++i >= ilim)
    02999                                         break;
    03000                                 dval(eps) *= 10.;
    03001                                 dval(d) *= 10.;
    03002                                 }
    03003                         }
    03004                 else {
    03005 #endif
    03006                         /* Generate ilim digits, then fix them up. */
    03007                         dval(eps) *= tens[ilim-1];
    03008                         for(i = 1;; i++, dval(d) *= 10.) {
    03009                                 L = (Long)(dval(d));
    03010                                 if (!(dval(d) -= L))
    03011                                         ilim = i;
    03012                                 *s++ = '0' + (int)L;
    03013                                 if (i == ilim) {
    03014                                         if (dval(d) > 0.5 + dval(eps))
    03015                                                 goto bump_up;
    03016                                         else if (dval(d) < 0.5 - dval(eps)) {
    03017                                                 while(*--s == '0');
    03018                                                 s++;
    03019                                                 goto ret1;
    03020                                                 }
    03021                                         break;
    03022                                         }
    03023                                 }
    03024 #ifndef No_leftright
    03025                         }
    03026 #endif
    03027  fast_failed:
    03028                 s = s0;
    03029                 dval(d) = dval(d2);
    03030                 k = k0;
    03031                 ilim = ilim0;
    03032                 }
    03033
    03034         /* Do we have a "small" integer? */
    03035
    03036         if (be >= 0 && k <= Int_max) {
    03037                 /* Yes. */
    03038                 ds = tens[k];
    03039                 if (ndigits < 0 && ilim <= 0) {
    03040                         S = mhi = 0;
    03041                         if (ilim < 0 || dval(d) <= 5*ds)
    03042                                 goto no_digits;
    03043                         goto one_digit;
    03044                         }
    03045                 for(i = 1;; i++, dval(d) *= 10.) {
    03046                         L = (Long)(dval(d) / ds);
    03047                         dval(d) -= L*ds;
    03048 #ifdef Check_FLT_ROUNDS
    03049                         /* If FLT_ROUNDS == 2, L will usually be high by 1 */
    03050                         if (dval(d) < 0) {
    03051                                 L--;
    03052                                 dval(d) += ds;
    03053                                 }
    03054 #endif
    03055                         *s++ = '0' + (int)L;
    03056                         if (!dval(d)) {
    03057 #ifdef SET_INEXACT
    03058                                 inexact = 0;
    03059 #endif
    03060                                 break;
    03061                                 }
    03062                         if (i == ilim) {
    03063 #ifdef Honor_FLT_ROUNDS
    03064                                 if (mode > 1)
    03065                                 switch(rounding) {
    03066                                   case 0: goto ret1;
    03067                                   case 2: goto bump_up;
    03068                                   }
    03069 #endif
    03070                                 dval(d) += dval(d);
    03071                                 if (dval(d) > ds || dval(d) == ds && L & 1) {
    03072  bump_up:
    03073                                         while(*--s == '9')
    03074                                                 if (s == s0) {
    03075                                                         k++;
    03076                                                         *s = '0';
    03077                                                         break;
    03078                                                         }
    03079                                         ++*s++;
    03080                                         }
    03081                                 break;
    03082                                 }
    03083                         }
    03084                 goto ret1;
    03085                 }
    03086
    03087         m2 = b2;
    03088         m5 = b5;
    03089         mhi = mlo = 0;
    03090         if (leftright) {
    03091                 i =
    03092 #ifndef Sudden_Underflow
    03093                         denorm ? be + (Bias + (P-1) - 1 + 1) :
    03094 #endif
    03095 #ifdef IBM
    03096                         1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
    03097 #else
    03098                         1 + P - bbits;
    03099 #endif
    03100                 b2 += i;
    03101                 s2 += i;
    03102                 mhi = i2b(1);
    03103                 }
    03104         if (m2 > 0 && s2 > 0) {
    03105                 i = m2 < s2 ? m2 : s2;
    03106                 b2 -= i;
    03107                 m2 -= i;
    03108                 s2 -= i;
    03109                 }
    03110         if (b5 > 0) {
    03111                 if (leftright) {
    03112                         if (m5 > 0) {
    03113                                 mhi = pow5mult(mhi, m5);
    03114                                 b1 = mult(mhi, b);
    03115                                 Bfree(b);
    03116                                 b = b1;
    03117                                 }
    03118                         if ( (j = b5 - m5) )
    03119                                 b = pow5mult(b, j);
    03120                         }
    03121                 else
    03122                         b = pow5mult(b, b5);
    03123                 }
    03124         S = i2b(1);
    03125         if (s5 > 0)
    03126                 S = pow5mult(S, s5);
    03127
    03128         /* Check for special case that d is a normalized power of 2. */
    03129
    03130         spec_case = 0;
    03131         if ((mode < 2 || leftright)
    03132 #ifdef Honor_FLT_ROUNDS
    03133                         && rounding == 1
    03134 #endif
    03135                                 ) {
    03136                 if (!word1(d) && !(word0(d) & Bndry_mask)
    03137 #ifndef Sudden_Underflow
    03138                  && word0(d) & (Exp_mask & ~Exp_msk1)
    03139 #endif
    03140                                 ) {
    03141                         /* The special case */
    03142                         b2 += Log2P;
    03143                         s2 += Log2P;
    03144                         spec_case = 1;
    03145                         }
    03146                 }
    03147
    03148         /* Arrange for convenient computation of quotients:
    03149          * shift left if necessary so divisor has 4 leading 0 bits.
    03150          *
    03151          * Perhaps we should just compute leading 28 bits of S once
    03152          * and for all and pass them and a shift to quorem, so it
    03153          * can do shifts and ors to compute the numerator for q.
    03154          */
    03155 #ifdef Pack_32
    03156         if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f)
    03157                 i = 32 - i;
    03158 #else
    03159         if ( (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf) )
    03160                 i = 16 - i;
    03161 #endif
    03162         if (i > 4) {
    03163                 i -= 4;
    03164                 b2 += i;
    03165                 m2 += i;
    03166                 s2 += i;
    03167                 }
    03168         else if (i < 4) {
    03169                 i += 28;
    03170                 b2 += i;
    03171                 m2 += i;
    03172                 s2 += i;
    03173                 }
    03174         if (b2 > 0)
    03175                 b = lshift(b, b2);
    03176         if (s2 > 0)
    03177                 S = lshift(S, s2);
    03178         if (k_check) {
    03179                 if (cmp(b,S) < 0) {
    03180                         k--;
    03181                         b = multadd(b, 10, 0);  /* we botched the k estimate */
    03182                         if (leftright)
    03183                                 mhi = multadd(mhi, 10, 0);
    03184                         ilim = ilim1;
    03185                         }
    03186                 }
    03187         if (ilim <= 0 && (mode == 3 || mode == 5)) {
    03188                 if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) {
    03189                         /* no digits, fcvt style */
    03190  no_digits:
    03191                         k = -1 - ndigits;
    03192                         goto ret;
    03193                         }
    03194  one_digit:
    03195                 *s++ = '1';
    03196                 k++;
    03197                 goto ret;
    03198                 }
    03199         if (leftright) {
    03200                 if (m2 > 0)
    03201                         mhi = lshift(mhi, m2);
    03202
    03203                 /* Compute mlo -- check for special case
    03204                  * that d is a normalized power of 2.
    03205                  */
    03206
    03207                 mlo = mhi;
    03208                 if (spec_case) {
    03209                         mhi = Balloc(mhi->k);
    03210                         Bcopy(mhi, mlo);
    03211                         mhi = lshift(mhi, Log2P);
    03212                         }
    03213
    03214                 for(i = 1;;i++) {
    03215                         dig = quorem(b,S) + '0';
    03216                         /* Do we yet have the shortest decimal string
    03217                          * that will round to d?
    03218                          */
    03219                         j = cmp(b, mlo);
    03220                         delta = diff(S, mhi);
    03221                         j1 = delta->sign ? 1 : cmp(b, delta);
    03222                         Bfree(delta);
    03223 #ifndef ROUND_BIASED
    03224                         if (j1 == 0 && mode != 1 && !(word1(d) & 1)
    03225 #ifdef Honor_FLT_ROUNDS
    03226                                 && rounding >= 1
    03227 #endif
    03228                                                                    ) {
    03229                                 if (dig == '9')
    03230                                         goto round_9_up;
    03231                                 if (j > 0)
    03232                                         dig++;
    03233 #ifdef SET_INEXACT
    03234                                 else if (!b->x[0] && b->wds <= 1)
    03235                                         inexact = 0;
    03236 #endif
    03237                                 *s++ = dig;
    03238                                 goto ret;
    03239                                 }
    03240 #endif
    03241                         if (j < 0 || j == 0 && mode != 1
    03242 #ifndef ROUND_BIASED
    03243                                                         && !(word1(d) & 1)
    03244 #endif
    03245                                         ) {
    03246                                 if (!b->x[0] && b->wds <= 1) {
    03247 #ifdef SET_INEXACT
    03248                                         inexact = 0;
    03249 #endif
    03250                                         goto accept_dig;
    03251                                         }
    03252 #ifdef Honor_FLT_ROUNDS
    03253                                 if (mode > 1)
    03254                                  switch(rounding) {
    03255                                   case 0: goto accept_dig;
    03256                                   case 2: goto keep_dig;
    03257                                   }
    03258 #endif /*Honor_FLT_ROUNDS*/
    03259                                 if (j1 > 0) {
    03260                                         b = lshift(b, 1);
    03261                                         j1 = cmp(b, S);
    03262                                         if ((j1 > 0 || j1 == 0 && dig & 1)
    03263                                         && dig++ == '9')
    03264                                                 goto round_9_up;
    03265                                         }
    03266  accept_dig:
    03267                                 *s++ = dig;
    03268                                 goto ret;
    03269                                 }
    03270                         if (j1 > 0) {
    03271 #ifdef Honor_FLT_ROUNDS
    03272                                 if (!rounding)
    03273                                         goto accept_dig;
    03274 #endif
    03275                                 if (dig == '9') { /* possible if i == 1 */
    03276  round_9_up:
    03277                                         *s++ = '9';
    03278                                         goto roundoff;
    03279                                         }
    03280                                 *s++ = dig + 1;
    03281                                 goto ret;
    03282                                 }
    03283 #ifdef Honor_FLT_ROUNDS
    03284  keep_dig:
    03285 #endif
    03286                         *s++ = dig;
    03287                         if (i == ilim)
    03288                                 break;
    03289                         b = multadd(b, 10, 0);
    03290                         if (mlo == mhi)
    03291                                 mlo = mhi = multadd(mhi, 10, 0);
    03292                         else {
    03293                                 mlo = multadd(mlo, 10, 0);
    03294                                 mhi = multadd(mhi, 10, 0);
    03295                                 }
    03296                         }
    03297                 }
    03298         else
    03299                 for(i = 1;; i++) {
    03300                         *s++ = dig = quorem(b,S) + '0';
    03301                         if (!b->x[0] && b->wds <= 1) {
    03302 #ifdef SET_INEXACT
    03303                                 inexact = 0;
    03304 #endif
    03305                                 goto ret;
    03306                                 }
    03307                         if (i >= ilim)
    03308                                 break;
    03309                         b = multadd(b, 10, 0);
    03310                         }
    03311
    03312         /* Round off last digit */
    03313
    03314 #ifdef Honor_FLT_ROUNDS
    03315         switch(rounding) {
    03316           case 0: goto trimzeros;
    03317           case 2: goto roundoff;
    03318           }
    03319 #endif
    03320         b = lshift(b, 1);
    03321         j = cmp(b, S);
    03322         if (j > 0 || j == 0 && dig & 1) {
    03323  roundoff:
    03324                 while(*--s == '9')
    03325                         if (s == s0) {
    03326                                 k++;
    03327                                 *s++ = '1';
    03328                                 goto ret;
    03329                                 }
    03330                 ++*s++;
    03331                 }
    03332         else {
    03333 #ifdef Honor_FLT_ROUNDS
    03334  trimzeros:
    03335 #endif
    03336                 while(*--s == '0');
    03337                 s++;
    03338                 }
    03339  ret:
    03340         Bfree(S);
    03341         if (mhi) {
    03342                 if (mlo && mlo != mhi)
    03343                         Bfree(mlo);
    03344                 Bfree(mhi);
    03345                 }
    03346  ret1:
    03347 #ifdef SET_INEXACT
    03348         if (inexact) {
    03349                 if (!oldinexact) {
    03350                         word0(d) = Exp_1 + (70 << Exp_shift);
    03351                         word1(d) = 0;
    03352                         dval(d) += 1.;
    03353                         }
    03354                 }
    03355         else if (!oldinexact)
    03356                 clear_inexact();
    03357 #endif
    03358         Bfree(b);
    03359         *s = 0;
    03360         *decpt = k + 1;
    03361         if (rve)
    03362                 *rve = s;
    03363         return s0;
    03364         }
    03365 #ifdef __cplusplus
    03366 }
    03367 #endif