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# dtoa.cpp

    00001 /****************************************************************
    00002  *
    00003  * The author of this software is David M. Gay.
    00004  *
    00005  * Copyright (c) 1991, 2000, 2001 by Lucent Technologies.
    00006  *
    00007  * Permission to use, copy, modify, and distribute this software for any
    00008  * purpose without fee is hereby granted, provided that this entire notice
    00009  * is included in all copies of any software which is or includes a copy
    00010  * or modification of this software and in all copies of the supporting
    00011  * documentation for such software.
    00012  *
    00013  * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
    00014  * WARRANTY.  IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY
    00015  * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
    00016  * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
    00017  *
    00018  ***************************************************************/
    00019
    00020 /* Please send bug reports to
    00021     David M. Gay
    00022     Bell Laboratories, Room 2C-463
    00023     600 Mountain Avenue
    00024     Murray Hill, NJ 07974-0636
    00025     U.S.A.
    00026     dmg@bell-labs.com
    00027  */
    00028
    00029 /* On a machine with IEEE extended-precision registers, it is
    00030  * necessary to specify double-precision (53-bit) rounding precision
    00031  * before invoking strtod or dtoa.  If the machine uses (the equivalent
    00032  * of) Intel 80x87 arithmetic, the call
    00033  *  _control87(PC_53, MCW_PC);
    00034  * does this with many compilers.  Whether this or another call is
    00035  * appropriate depends on the compiler; for this to work, it may be
    00036  * necessary to #include "float.h" or another system-dependent header
    00037  * file.
    00038  */
    00039
    00040 /* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
    00041  *
    00042  * This strtod returns a nearest machine number to the input decimal
    00043  * string (or sets errno to ERANGE).  With IEEE arithmetic, ties are
    00044  * broken by the IEEE round-even rule.  Otherwise ties are broken by
    00045  * biased rounding (add half and chop).
    00046  *
    00047  * Inspired loosely by William D. Clinger's paper "How to Read Floating
    00048  * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
    00049  *
    00050  * Modifications:
    00051  *
    00052  *  1. We only require IEEE, IBM, or VAX double-precision
    00053  *      arithmetic (not IEEE double-extended).
    00054  *  2. We get by with floating-point arithmetic in a case that
    00055  *      Clinger missed -- when we're computing d * 10^n
    00056  *      for a small integer d and the integer n is not too
    00057  *      much larger than 22 (the maximum integer k for which
    00058  *      we can represent 10^k exactly), we may be able to
    00059  *      compute (d*10^k) * 10^(e-k) with just one roundoff.
    00060  *  3. Rather than a bit-at-a-time adjustment of the binary
    00061  *      result in the hard case, we use floating-point
    00062  *      arithmetic to determine the adjustment to within
    00063  *      one bit; only in really hard cases do we need to
    00064  *      compute a second residual.
    00065  *  4. Because of 3., we don't need a large table of powers of 10
    00066  *      for ten-to-e (just some small tables, e.g. of 10^k
    00067  *      for 0 <= k <= 22).
    00068  */
    00069
    00070 /*
    00071  * #define IEEE_8087 for IEEE-arithmetic machines where the least
    00072  *  significant byte has the lowest address.
    00073  * #define IEEE_MC68k for IEEE-arithmetic machines where the most
    00074  *  significant byte has the lowest address.
    00075  * #define Long int on machines with 32-bit ints and 64-bit longs.
    00076  * #define IBM for IBM mainframe-style floating-point arithmetic.
    00077  * #define VAX for VAX-style floating-point arithmetic (D_floating).
    00078  * #define No_leftright to omit left-right logic in fast floating-point
    00079  *  computation of dtoa.
    00080  * #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
    00081  *  and strtod and dtoa should round accordingly.
    00082  * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
    00083  *  and Honor_FLT_ROUNDS is not #defined.
    00084  * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
    00085  *  that use extended-precision instructions to compute rounded
    00086  *  products and quotients) with IBM.
    00087  * #define ROUND_BIASED for IEEE-format with biased rounding.
    00088  * #define Inaccurate_Divide for IEEE-format with correctly rounded
    00089  *  products but inaccurate quotients, e.g., for Intel i860.
    00090  * #define NO_LONG_LONG on machines that do not have a "long long"
    00091  *  integer type (of >= 64 bits).  On such machines, you can
    00092  *  #define Just_16 to store 16 bits per 32-bit Long when doing
    00093  *  high-precision integer arithmetic.  Whether this speeds things
    00094  *  up or slows things down depends on the machine and the number
    00095  *  being converted.  If long long is available and the name is
    00096  *  something other than "long long", #define Llong to be the name,
    00097  *  and if "unsigned Llong" does not work as an unsigned version of
    00098  *  Llong, #define #ULLong to be the corresponding unsigned type.
    00099  * #define KR_headers for old-style C function headers.
    00100  * #define Bad_float_h if your system lacks a float.h or if it does not
    00101  *  define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
    00102  *  FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
    00103  * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
    00104  *  if memory is available and otherwise does something you deem
    00105  *  appropriate.  If MALLOC is undefined, malloc will be invoked
    00106  *  directly -- and assumed always to succeed.
    00107  * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making
    00108  *  memory allocations from a private pool of memory when possible.
    00109  *  When used, the private pool is PRIVATE_MEM bytes long:  2304 bytes,
    00110  *  unless #defined to be a different length.  This default length
    00111  *  suffices to get rid of MALLOC calls except for unusual cases,
    00112  *  such as decimal-to-binary conversion of a very long string of
    00113  *  digits.  The longest string dtoa can return is about 751 bytes
    00114  *  long.  For conversions by strtod of strings of 800 digits and
    00115  *  all dtoa conversions in single-threaded executions with 8-byte
    00116  *  pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte
    00117  *  pointers, PRIVATE_MEM >= 7112 appears adequate.
    00118  * #define INFNAN_CHECK on IEEE systems to cause strtod to check for
    00119  *  Infinity and NaN (case insensitively).  On some systems (e.g.,
    00120  *  some HP systems), it may be necessary to #define NAN_WORD0
    00121  *  appropriately -- to the most significant word of a quiet NaN.
    00122  *  (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)
    00123  *  When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined,
    00124  *  strtod also accepts (case insensitively) strings of the form
    00125  *  NaN(x), where x is a string of hexadecimal digits and spaces;
    00126  *  if there is only one string of hexadecimal digits, it is taken
    00127  *  for the 52 fraction bits of the resulting NaN; if there are two
    00128  *  or more strings of hex digits, the first is for the high 20 bits,
    00129  *  the second and subsequent for the low 32 bits, with intervening
    00130  *  white space ignored; but if this results in none of the 52
    00131  *  fraction bits being on (an IEEE Infinity symbol), then NAN_WORD0
    00132  *  and NAN_WORD1 are used instead.
    00133  * #define MULTIPLE_THREADS if the system offers preemptively scheduled
    00134  *  multiple threads.  In this case, you must provide (or suitably
    00135  *  #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed
    00136  *  by FREE_DTOA_LOCK(n) for n = 0 or 1.  (The second lock, accessed
    00137  *  in pow5mult, ensures lazy evaluation of only one copy of high
    00138  *  powers of 5; omitting this lock would introduce a small
    00139  *  probability of wasting memory, but would otherwise be harmless.)
    00140  *  You must also invoke freedtoa(s) to free the value s returned by
    00141  *  dtoa.  You may do so whether or not MULTIPLE_THREADS is #defined.
    00142  * #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that
    00143  *  avoids underflows on inputs whose result does not underflow.
    00144  *  If you #define NO_IEEE_Scale on a machine that uses IEEE-format
    00145  *  floating-point numbers and flushes underflows to zero rather
    00146  *  than implementing gradual underflow, then you must also #define
    00147  *  Sudden_Underflow.
    00148  * #define YES_ALIAS to permit aliasing certain double values with
    00149  *  arrays of ULongs.  This leads to slightly better code with
    00150  *  some compilers and was always used prior to 19990916, but it
    00151  *  is not strictly legal and can cause trouble with aggressively
    00152  *  optimizing compilers (e.g., gcc 2.95.1 under -O2).
    00153  * #define USE_LOCALE to use the current locale's decimal_point value.
    00154  * #define SET_INEXACT if IEEE arithmetic is being used and extra
    00155  *  computation should be done to set the inexact flag when the
    00156  *  result is inexact and avoid setting inexact when the result
    00157  *  is exact.  In this case, dtoa.c must be compiled in
    00158  *  an environment, perhaps provided by #include "dtoa.c" in a
    00159  *  suitable wrapper, that defines two functions,
    00160  *      int get_inexact(void);
    00161  *      void clear_inexact(void);
    00162  *  such that get_inexact() returns a nonzero value if the
    00163  *  inexact bit is already set, and clear_inexact() sets the
    00164  *  inexact bit to 0.  When SET_INEXACT is #defined, strtod
    00165  *  also does extra computations to set the underflow and overflow
    00166  *  flags when appropriate (i.e., when the result is tiny and
    00167  *  inexact or when it is a numeric value rounded to +-infinity).
    00168  * #define NO_ERRNO if strtod should not assign errno = ERANGE when
    00169  *  the result overflows to +-Infinity or underflows to 0.
    00170  */
    00171
    00172 // Put this before anything else that may import a definition of CONST. CONST from grammar.cpp conflicts with this.
    00173 #ifdef KDE_USE_FINAL
    00174 #undef CONST
    00175 #endif
    00176
    00177 #include <config.h>
    00178
    00179 #include "stdlib.h"
    00180
    00181 #ifdef WORDS_BIGENDIAN
    00182 #define IEEE_MC68k
    00183 #else
    00184 #define IEEE_8087
    00185 #endif
    00186 #define INFNAN_CHECK
    00187 #include "dtoa.h"
    00188
    00189
    00190
    00191 #ifndef Long
    00192 #define Long int
    00193 #endif
    00194 #ifndef ULong
    00195 typedef unsigned Long ULong;
    00196 #endif
    00197
    00198 #ifdef DEBUG
    00199 #include "stdio.h"
    00200 #define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
    00201 #endif
    00202
    00203 #include "string.h"
    00204
    00205 #ifdef USE_LOCALE
    00206 #include "locale.h"
    00207 #endif
    00208
    00209 #ifdef MALLOC
    00210 #ifdef KR_headers
    00211 extern char *MALLOC();
    00212 #else
    00213 extern void *MALLOC(size_t);
    00214 #endif
    00215 #else
    00216 #define MALLOC malloc
    00217 #endif
    00218
    00219 #ifndef Omit_Private_Memory
    00220 #ifndef PRIVATE_MEM
    00221 #define PRIVATE_MEM 2304
    00222 #endif
    00223 #define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
    00224 static double private_mem[PRIVATE_mem], *pmem_next = private_mem;
    00225 #endif
    00226
    00227 #undef IEEE_Arith
    00228 #undef Avoid_Underflow
    00229 #ifdef IEEE_MC68k
    00230 #define IEEE_Arith
    00231 #endif
    00232 #ifdef IEEE_8087
    00233 #define IEEE_Arith
    00234 #endif
    00235
    00236 #include "errno.h"
    00237
    00238 #ifdef Bad_float_h
    00239
    00240 #ifdef IEEE_Arith
    00241 #define DBL_DIG 15
    00242 #define DBL_MAX_10_EXP 308
    00243 #define DBL_MAX_EXP 1024
    00244 #define FLT_RADIX 2
    00245 #endif /*IEEE_Arith*/
    00246
    00247 #ifdef IBM
    00248 #define DBL_DIG 16
    00249 #define DBL_MAX_10_EXP 75
    00250 #define DBL_MAX_EXP 63
    00251 #define FLT_RADIX 16
    00252 #define DBL_MAX 7.2370055773322621e+75
    00253 #endif
    00254
    00255 #ifdef VAX
    00256 #define DBL_DIG 16
    00257 #define DBL_MAX_10_EXP 38
    00258 #define DBL_MAX_EXP 127
    00259 #define FLT_RADIX 2
    00260 #define DBL_MAX 1.7014118346046923e+38
    00261 #endif
    00262
    00263 #else /* ifndef Bad_float_h */
    00264 #include "float.h"
    00265 #endif /* Bad_float_h */
    00266
    00267 #ifndef __MATH_H__
    00268 #include "math.h"
    00269 #endif
    00270
    00271 #ifdef __cplusplus
    00272 extern "C" {
    00273 #endif
    00274
    00275 #ifndef CONST
    00276 #ifdef KR_headers
    00277 #define CONST /* blank */
    00278 #else
    00279 #define CONST const
    00280 #endif
    00281 #endif
    00282
    00283 #if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1
    00284 Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined.
    00285 #endif
    00286
    00287 typedef union { double d; ULong L[2]; } U;
    00288
    00289 #ifdef YES_ALIAS
    00290 #define dval(x) x
    00291 #ifdef IEEE_8087
    00292 #define word0(x) ((ULong *)&x)[1]
    00293 #define word1(x) ((ULong *)&x)[0]
    00294 #else
    00295 #define word0(x) ((ULong *)&x)[0]
    00296 #define word1(x) ((ULong *)&x)[1]
    00297 #endif
    00298 #else
    00299 #ifdef IEEE_8087
    00300 #define word0(x) ((U*)&x)->L[1]
    00301 #define word1(x) ((U*)&x)->L[0]
    00302 #else
    00303 #define word0(x) ((U*)&x)->L[0]
    00304 #define word1(x) ((U*)&x)->L[1]
    00305 #endif
    00306 #define dval(x) ((U*)&x)->d
    00307 #endif
    00308
    00309 /* The following definition of Storeinc is appropriate for MIPS processors.
    00310  * An alternative that might be better on some machines is
    00311  * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
    00312  */
    00313 #if defined(IEEE_8087) + defined(VAX)
    00314 #define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
    00315 ((unsigned short *)a)[0] = (unsigned short)c, a++)
    00316 #else
    00317 #define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
    00318 ((unsigned short *)a)[1] = (unsigned short)c, a++)
    00319 #endif
    00320
    00321 /* #define P DBL_MANT_DIG */
    00322 /* Ten_pmax = floor(P*log(2)/log(5)) */
    00323 /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
    00324 /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
    00325 /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
    00326
    00327 #ifdef IEEE_Arith
    00328 #define Exp_shift  20
    00329 #define Exp_shift1 20
    00330 #define Exp_msk1    0x100000
    00331 #define Exp_msk11   0x100000
    00332 #define Exp_mask  0x7ff00000
    00333 #define P 53
    00334 #define Bias 1023
    00335 #define Emin (-1022)
    00336 #define Exp_1  0x3ff00000
    00337 #define Exp_11 0x3ff00000
    00338 #define Ebits 11
    00339 #define Frac_mask  0xfffff
    00340 #define Frac_mask1 0xfffff
    00341 #define Ten_pmax 22
    00342 #define Bletch 0x10
    00343 #define Bndry_mask  0xfffff
    00344 #define Bndry_mask1 0xfffff
    00345 #define LSB 1
    00346 #define Sign_bit 0x80000000
    00347 #define Log2P 1
    00348 #define Tiny0 0
    00349 #define Tiny1 1
    00350 #define Quick_max 14
    00351 #define Int_max 14
    00352 #ifndef NO_IEEE_Scale
    00353 #define Avoid_Underflow
    00354 #ifdef Flush_Denorm /* debugging option */
    00355 #undef Sudden_Underflow
    00356 #endif
    00357 #endif
    00358
    00359 #ifndef Flt_Rounds
    00360 #ifdef FLT_ROUNDS
    00361 #define Flt_Rounds FLT_ROUNDS
    00362 #else
    00363 #define Flt_Rounds 1
    00364 #endif
    00365 #endif /*Flt_Rounds*/
    00366
    00367 #ifdef Honor_FLT_ROUNDS
    00368 #define Rounding rounding
    00369 #undef Check_FLT_ROUNDS
    00370 #define Check_FLT_ROUNDS
    00371 #else
    00372 #define Rounding Flt_Rounds
    00373 #endif
    00374
    00375 #else /* ifndef IEEE_Arith */
    00376 #undef Check_FLT_ROUNDS
    00377 #undef Honor_FLT_ROUNDS
    00378 #undef SET_INEXACT
    00379 #undef  Sudden_Underflow
    00380 #define Sudden_Underflow
    00381 #ifdef IBM
    00382 #undef Flt_Rounds
    00383 #define Flt_Rounds 0
    00384 #define Exp_shift  24
    00385 #define Exp_shift1 24
    00386 #define Exp_msk1   0x1000000
    00387 #define Exp_msk11  0x1000000
    00388 #define Exp_mask  0x7f000000
    00389 #define P 14
    00390 #define Bias 65
    00391 #define Exp_1  0x41000000
    00392 #define Exp_11 0x41000000
    00393 #define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
    00394 #define Frac_mask  0xffffff
    00395 #define Frac_mask1 0xffffff
    00396 #define Bletch 4
    00397 #define Ten_pmax 22
    00398 #define Bndry_mask  0xefffff
    00399 #define Bndry_mask1 0xffffff
    00400 #define LSB 1
    00401 #define Sign_bit 0x80000000
    00402 #define Log2P 4
    00403 #define Tiny0 0x100000
    00404 #define Tiny1 0
    00405 #define Quick_max 14
    00406 #define Int_max 15
    00407 #else /* VAX */
    00408 #undef Flt_Rounds
    00409 #define Flt_Rounds 1
    00410 #define Exp_shift  23
    00411 #define Exp_shift1 7
    00412 #define Exp_msk1    0x80
    00413 #define Exp_msk11   0x800000
    00414 #define Exp_mask  0x7f80
    00415 #define P 56
    00416 #define Bias 129
    00417 #define Exp_1  0x40800000
    00418 #define Exp_11 0x4080
    00419 #define Ebits 8
    00420 #define Frac_mask  0x7fffff
    00421 #define Frac_mask1 0xffff007f
    00422 #define Ten_pmax 24
    00423 #define Bletch 2
    00424 #define Bndry_mask  0xffff007f
    00425 #define Bndry_mask1 0xffff007f
    00426 #define LSB 0x10000
    00427 #define Sign_bit 0x8000
    00428 #define Log2P 1
    00429 #define Tiny0 0x80
    00430 #define Tiny1 0
    00431 #define Quick_max 15
    00432 #define Int_max 15
    00433 #endif /* IBM, VAX */
    00434 #endif /* IEEE_Arith */
    00435
    00436 #ifndef IEEE_Arith
    00437 #define ROUND_BIASED
    00438 #endif
    00439
    00440 #ifdef RND_PRODQUOT
    00441 #define rounded_product(a,b) a = rnd_prod(a, b)
    00442 #define rounded_quotient(a,b) a = rnd_quot(a, b)
    00443 #ifdef KR_headers
    00444 extern double rnd_prod(), rnd_quot();
    00445 #else
    00446 extern double rnd_prod(double, double), rnd_quot(double, double);
    00447 #endif
    00448 #else
    00449 #define rounded_product(a,b) a *= b
    00450 #define rounded_quotient(a,b) a /= b
    00451 #endif
    00452
    00453 #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
    00454 #define Big1 0xffffffff
    00455
    00456 #ifndef Pack_32
    00457 #define Pack_32
    00458 #endif
    00459
    00460 #ifdef KR_headers
    00461 #define FFFFFFFF ((((unsigned long)0xffff)<<16)|(unsigned long)0xffff)
    00462 #else
    00463 #define FFFFFFFF 0xffffffffUL
    00464 #endif
    00465
    00466 #ifdef NO_LONG_LONG
    00467 #undef ULLong
    00468 #ifdef Just_16
    00469 #undef Pack_32
    00470 /* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
    00471  * This makes some inner loops simpler and sometimes saves work
    00472  * during multiplications, but it often seems to make things slightly
    00473  * slower.  Hence the default is now to store 32 bits per Long.
    00474  */
    00475 #endif
    00476 #else   /* long long available */
    00477 #ifndef Llong
    00478 #define Llong long long
    00479 #endif
    00480 #ifndef ULLong
    00481 #define ULLong unsigned Llong
    00482 #endif
    00483 #endif /* NO_LONG_LONG */
    00484
    00485 #ifndef MULTIPLE_THREADS
    00486 #define ACQUIRE_DTOA_LOCK(n)    /*nothing*/
    00487 #define FREE_DTOA_LOCK(n)   /*nothing*/
    00488 #endif
    00489
    00490 #define Kmax 15
    00491
    00492  struct
    00493 Bigint {
    00494     struct Bigint *next;
    00495     int k, maxwds, sign, wds;
    00496     ULong x[1];
    00497     };
    00498
    00499  typedef struct Bigint Bigint;
    00500
    00501  static Bigint *freelist[Kmax+1];
    00502
    00503  static Bigint *
    00504 Balloc
    00505 #ifdef KR_headers
    00506     (k) int k;
    00507 #else
    00508     (int k)
    00509 #endif
    00510 {
    00511     int x;
    00512     Bigint *rv;
    00513 #ifndef Omit_Private_Memory
    00514     unsigned int len;
    00515 #endif
    00516
    00517     ACQUIRE_DTOA_LOCK(0);
    00518     if ((rv = freelist[k])) {
    00519         freelist[k] = rv->next;
    00520         }
    00521     else {
    00522         x = 1 << k;
    00523 #ifdef Omit_Private_Memory
    00524         rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong));
    00525 #else
    00526         len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)
    00527             /sizeof(double);
    00528         if (pmem_next - private_mem + len <= PRIVATE_mem) {
    00529             rv = (Bigint*)pmem_next;
    00530             pmem_next += len;
    00531             }
    00532         else
    00533             rv = (Bigint*)MALLOC(len*sizeof(double));
    00534 #endif
    00535         rv->k = k;
    00536         rv->maxwds = x;
    00537         }
    00538     FREE_DTOA_LOCK(0);
    00539     rv->sign = rv->wds = 0;
    00540     return rv;
    00541     }
    00542
    00543  static void
    00544 Bfree
    00545 #ifdef KR_headers
    00546     (v) Bigint *v;
    00547 #else
    00548     (Bigint *v)
    00549 #endif
    00550 {
    00551     if (v) {
    00552         ACQUIRE_DTOA_LOCK(0);
    00553         v->next = freelist[v->k];
    00554         freelist[v->k] = v;
    00555         FREE_DTOA_LOCK(0);
    00556         }
    00557     }
    00558
    00559 #define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
    00560 y->wds*sizeof(Long) + 2*sizeof(int))
    00561
    00562  static Bigint *
    00563 multadd
    00564 #ifdef KR_headers
    00565     (b, m, a) Bigint *b; int m, a;
    00566 #else
    00567     (Bigint *b, int m, int a)   /* multiply by m and add a */
    00568 #endif
    00569 {
    00570     int i, wds;
    00571 #ifdef ULLong
    00572     ULong *x;
    00573     ULLong carry, y;
    00574 #else
    00575     ULong carry, *x, y;
    00576 #ifdef Pack_32
    00577     ULong xi, z;
    00578 #endif
    00579 #endif
    00580     Bigint *b1;
    00581
    00582     wds = b->wds;
    00583     x = b->x;
    00584     i = 0;
    00585     carry = a;
    00586     do {
    00587 #ifdef ULLong
    00588         y = *x * (ULLong)m + carry;
    00589         carry = y >> 32;
    00590         *x++ = y & FFFFFFFF;
    00591 #else
    00592 #ifdef Pack_32
    00593         xi = *x;
    00594         y = (xi & 0xffff) * m + carry;
    00595         z = (xi >> 16) * m + (y >> 16);
    00596         carry = z >> 16;
    00597         *x++ = (z << 16) + (y & 0xffff);
    00598 #else
    00599         y = *x * m + carry;
    00600         carry = y >> 16;
    00601         *x++ = y & 0xffff;
    00602 #endif
    00603 #endif
    00604         }
    00605         while(++i < wds);
    00606     if (carry) {
    00607         if (wds >= b->maxwds) {
    00608             b1 = Balloc(b->k+1);
    00609             Bcopy(b1, b);
    00610             Bfree(b);
    00611             b = b1;
    00612             }
    00613         b->x[wds++] = carry;
    00614         b->wds = wds;
    00615         }
    00616     return b;
    00617     }
    00618
    00619  static Bigint *
    00620 s2b
    00621 #ifdef KR_headers
    00622     (s, nd0, nd, y9) CONST char *s; int nd0, nd; ULong y9;
    00623 #else
    00624     (CONST char *s, int nd0, int nd, ULong y9)
    00625 #endif
    00626 {
    00627     Bigint *b;
    00628     int i, k;
    00629     Long x, y;
    00630
    00631     x = (nd + 8) / 9;
    00632     for(k = 0, y = 1; x > y; y <<= 1, k++) ;
    00633 #ifdef Pack_32
    00634     b = Balloc(k);
    00635     b->x[0] = y9;
    00636     b->wds = 1;
    00637 #else
    00638     b = Balloc(k+1);
    00639     b->x[0] = y9 & 0xffff;
    00640     b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
    00641 #endif
    00642
    00643     i = 9;
    00644     if (9 < nd0) {
    00645         s += 9;
    00646         do b = multadd(b, 10, *s++ - '0');
    00647             while(++i < nd0);
    00648         s++;
    00649         }
    00650     else
    00651         s += 10;
    00652     for(; i < nd; i++)
    00653         b = multadd(b, 10, *s++ - '0');
    00654     return b;
    00655     }
    00656
    00657  static int
    00658 hi0bits
    00659 #ifdef KR_headers
    00660     (x) register ULong x;
    00661 #else
    00662     (register ULong x)
    00663 #endif
    00664 {
    00665     register int k = 0;
    00666
    00667     if (!(x & 0xffff0000)) {
    00668         k = 16;
    00669         x <<= 16;
    00670         }
    00671     if (!(x & 0xff000000)) {
    00672         k += 8;
    00673         x <<= 8;
    00674         }
    00675     if (!(x & 0xf0000000)) {
    00676         k += 4;
    00677         x <<= 4;
    00678         }
    00679     if (!(x & 0xc0000000)) {
    00680         k += 2;
    00681         x <<= 2;
    00682         }
    00683     if (!(x & 0x80000000)) {
    00684         k++;
    00685         if (!(x & 0x40000000))
    00686             return 32;
    00687         }
    00688     return k;
    00689     }
    00690
    00691  static int
    00692 lo0bits
    00693 #ifdef KR_headers
    00694     (y) ULong *y;
    00695 #else
    00696     (ULong *y)
    00697 #endif
    00698 {
    00699     register int k;
    00700     register ULong x = *y;
    00701
    00702     if (x & 7) {
    00703         if (x & 1)
    00704             return 0;
    00705         if (x & 2) {
    00706             *y = x >> 1;
    00707             return 1;
    00708             }
    00709         *y = x >> 2;
    00710         return 2;
    00711         }
    00712     k = 0;
    00713     if (!(x & 0xffff)) {
    00714         k = 16;
    00715         x >>= 16;
    00716         }
    00717     if (!(x & 0xff)) {
    00718         k += 8;
    00719         x >>= 8;
    00720         }
    00721     if (!(x & 0xf)) {
    00722         k += 4;
    00723         x >>= 4;
    00724         }
    00725     if (!(x & 0x3)) {
    00726         k += 2;
    00727         x >>= 2;
    00728         }
    00729     if (!(x & 1)) {
    00730         k++;
    00731         x >>= 1;
    00732         if (!x & 1)
    00733             return 32;
    00734         }
    00735     *y = x;
    00736     return k;
    00737     }
    00738
    00739  static Bigint *
    00740 i2b
    00741 #ifdef KR_headers
    00742     (i) int i;
    00743 #else
    00744     (int i)
    00745 #endif
    00746 {
    00747     Bigint *b;
    00748
    00749     b = Balloc(1);
    00750     b->x[0] = i;
    00751     b->wds = 1;
    00752     return b;
    00753     }
    00754
    00755  static Bigint *
    00756 mult
    00757 #ifdef KR_headers
    00758     (a, b) Bigint *a, *b;
    00759 #else
    00760     (Bigint *a, Bigint *b)
    00761 #endif
    00762 {
    00763     Bigint *c;
    00764     int k, wa, wb, wc;
    00765     ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
    00766     ULong y;
    00767 #ifdef ULLong
    00768     ULLong carry, z;
    00769 #else
    00770     ULong carry, z;
    00771 #ifdef Pack_32
    00772     ULong z2;
    00773 #endif
    00774 #endif
    00775
    00776     if (a->wds < b->wds) {
    00777         c = a;
    00778         a = b;
    00779         b = c;
    00780         }
    00781     k = a->k;
    00782     wa = a->wds;
    00783     wb = b->wds;
    00784     wc = wa + wb;
    00785     if (wc > a->maxwds)
    00786         k++;
    00787     c = Balloc(k);
    00788     for(x = c->x, xa = x + wc; x < xa; x++)
    00789         *x = 0;
    00790     xa = a->x;
    00791     xae = xa + wa;
    00792     xb = b->x;
    00793     xbe = xb + wb;
    00794     xc0 = c->x;
    00795 #ifdef ULLong
    00796     for(; xb < xbe; xc0++) {
    00797         if ((y = *xb++)) {
    00798             x = xa;
    00799             xc = xc0;
    00800             carry = 0;
    00801             do {
    00802                 z = *x++ * (ULLong)y + *xc + carry;
    00803                 carry = z >> 32;
    00804                 *xc++ = z & FFFFFFFF;
    00805                 }
    00806                 while(x < xae);
    00807             *xc = carry;
    00808             }
    00809         }
    00810 #else
    00811 #ifdef Pack_32
    00812     for(; xb < xbe; xb++, xc0++) {
    00813         if (y = *xb & 0xffff) {
    00814             x = xa;
    00815             xc = xc0;
    00816             carry = 0;
    00817             do {
    00818                 z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
    00819                 carry = z >> 16;
    00820                 z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
    00821                 carry = z2 >> 16;
    00822                 Storeinc(xc, z2, z);
    00823                 }
    00824                 while(x < xae);
    00825             *xc = carry;
    00826             }
    00827         if (y = *xb >> 16) {
    00828             x = xa;
    00829             xc = xc0;
    00830             carry = 0;
    00831             z2 = *xc;
    00832             do {
    00833                 z = (*x & 0xffff) * y + (*xc >> 16) + carry;
    00834                 carry = z >> 16;
    00835                 Storeinc(xc, z, z2);
    00836                 z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
    00837                 carry = z2 >> 16;
    00838                 }
    00839                 while(x < xae);
    00840             *xc = z2;
    00841             }
    00842         }
    00843 #else
    00844     for(; xb < xbe; xc0++) {
    00845         if (y = *xb++) {
    00846             x = xa;
    00847             xc = xc0;
    00848             carry = 0;
    00849             do {
    00850                 z = *x++ * y + *xc + carry;
    00851                 carry = z >> 16;
    00852                 *xc++ = z & 0xffff;
    00853                 }
    00854                 while(x < xae);
    00855             *xc = carry;
    00856             }
    00857         }
    00858 #endif
    00859 #endif
    00860     for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
    00861     c->wds = wc;
    00862     return c;
    00863     }
    00864
    00865  static Bigint *p5s;
    00866
    00867  static Bigint *
    00868 pow5mult
    00869 #ifdef KR_headers
    00870     (b, k) Bigint *b; int k;
    00871 #else
    00872     (Bigint *b, int k)
    00873 #endif
    00874 {
    00875     Bigint *b1, *p5, *p51;
    00876     int i;
    00877     static int p05[3] = { 5, 25, 125 };
    00878
    00879     if ((i = k & 3))
    00880         b = multadd(b, p05[i-1], 0);
    00881
    00882     if (!(k >>= 2))
    00883         return b;
    00884     if (!(p5 = p5s)) {
    00885         /* first time */
    00886 #ifdef MULTIPLE_THREADS
    00887         ACQUIRE_DTOA_LOCK(1);
    00888         if (!(p5 = p5s)) {
    00889             p5 = p5s = i2b(625);
    00890             p5->next = 0;
    00891             }
    00892         FREE_DTOA_LOCK(1);
    00893 #else
    00894         p5 = p5s = i2b(625);
    00895         p5->next = 0;
    00896 #endif
    00897         }
    00898     for(;;) {
    00899         if (k & 1) {
    00900             b1 = mult(b, p5);
    00901             Bfree(b);
    00902             b = b1;
    00903             }
    00904         if (!(k >>= 1))
    00905             break;
    00906         if (!(p51 = p5->next)) {
    00907 #ifdef MULTIPLE_THREADS
    00908             ACQUIRE_DTOA_LOCK(1);
    00909             if (!(p51 = p5->next)) {
    00910                 p51 = p5->next = mult(p5,p5);
    00911                 p51->next = 0;
    00912                 }
    00913             FREE_DTOA_LOCK(1);
    00914 #else
    00915             p51 = p5->next = mult(p5,p5);
    00916             p51->next = 0;
    00917 #endif
    00918             }
    00919         p5 = p51;
    00920         }
    00921     return b;
    00922     }
    00923
    00924  static Bigint *
    00925 lshift
    00926 #ifdef KR_headers
    00927     (b, k) Bigint *b; int k;
    00928 #else
    00929     (Bigint *b, int k)
    00930 #endif
    00931 {
    00932     int i, k1, n, n1;
    00933     Bigint *b1;
    00934     ULong *x, *x1, *xe, z;
    00935
    00936 #ifdef Pack_32
    00937     n = k >> 5;
    00938 #else
    00939     n = k >> 4;
    00940 #endif
    00941     k1 = b->k;
    00942     n1 = n + b->wds + 1;
    00943     for(i = b->maxwds; n1 > i; i <<= 1)
    00944         k1++;
    00945     b1 = Balloc(k1);
    00946     x1 = b1->x;
    00947     for(i = 0; i < n; i++)
    00948         *x1++ = 0;
    00949     x = b->x;
    00950     xe = x + b->wds;
    00951 #ifdef Pack_32
    00952     if (k &= 0x1f) {
    00953         k1 = 32 - k;
    00954         z = 0;
    00955         do {
    00956             *x1++ = *x << k | z;
    00957             z = *x++ >> k1;
    00958             }
    00959             while(x < xe);
    00960         if ((*x1 = z))
    00961             ++n1;
    00962         }
    00963 #else
    00964     if (k &= 0xf) {
    00965         k1 = 16 - k;
    00966         z = 0;
    00967         do {
    00968             *x1++ = *x << k  & 0xffff | z;
    00969             z = *x++ >> k1;
    00970             }
    00971             while(x < xe);
    00972         if (*x1 = z)
    00973             ++n1;
    00974         }
    00975 #endif
    00976     else do
    00977         *x1++ = *x++;
    00978         while(x < xe);
    00979     b1->wds = n1 - 1;
    00980     Bfree(b);
    00981     return b1;
    00982     }
    00983
    00984  static int
    00985 cmp
    00986 #ifdef KR_headers
    00987     (a, b) Bigint *a, *b;
    00988 #else
    00989     (Bigint *a, Bigint *b)
    00990 #endif
    00991 {
    00992     ULong *xa, *xa0, *xb, *xb0;
    00993     int i, j;
    00994
    00995     i = a->wds;
    00996     j = b->wds;
    00997 #ifdef DEBUG
    00998     if (i > 1 && !a->x[i-1])
    00999         Bug("cmp called with a->x[a->wds-1] == 0");
    01000     if (j > 1 && !b->x[j-1])
    01001         Bug("cmp called with b->x[b->wds-1] == 0");
    01002 #endif
    01003     if (i -= j)
    01004         return i;
    01005     xa0 = a->x;
    01006     xa = xa0 + j;
    01007     xb0 = b->x;
    01008     xb = xb0 + j;
    01009     for(;;) {
    01010         if (*--xa != *--xb)
    01011             return *xa < *xb ? -1 : 1;
    01012         if (xa <= xa0)
    01013             break;
    01014         }
    01015     return 0;
    01016     }
    01017
    01018  static Bigint *
    01019 diff
    01020 #ifdef KR_headers
    01021     (a, b) Bigint *a, *b;
    01022 #else
    01023     (Bigint *a, Bigint *b)
    01024 #endif
    01025 {
    01026     Bigint *c;
    01027     int i, wa, wb;
    01028     ULong *xa, *xae, *xb, *xbe, *xc;
    01029 #ifdef ULLong
    01030     ULLong borrow, y;
    01031 #else
    01032     ULong borrow, y;
    01033 #ifdef Pack_32
    01034     ULong z;
    01035 #endif
    01036 #endif
    01037
    01038     i = cmp(a,b);
    01039     if (!i) {
    01040         c = Balloc(0);
    01041         c->wds = 1;
    01042         c->x[0] = 0;
    01043         return c;
    01044         }
    01045     if (i < 0) {
    01046         c = a;
    01047         a = b;
    01048         b = c;
    01049         i = 1;
    01050         }
    01051     else
    01052         i = 0;
    01053     c = Balloc(a->k);
    01054     c->sign = i;
    01055     wa = a->wds;
    01056     xa = a->x;
    01057     xae = xa + wa;
    01058     wb = b->wds;
    01059     xb = b->x;
    01060     xbe = xb + wb;
    01061     xc = c->x;
    01062     borrow = 0;
    01063 #ifdef ULLong
    01064     do {
    01065         y = (ULLong)*xa++ - *xb++ - borrow;
    01066         borrow = y >> 32 & (ULong)1;
    01067         *xc++ = y & FFFFFFFF;
    01068         }
    01069         while(xb < xbe);
    01070     while(xa < xae) {
    01071         y = *xa++ - borrow;
    01072         borrow = y >> 32 & (ULong)1;
    01073         *xc++ = y & FFFFFFFF;
    01074         }
    01075 #else
    01076 #ifdef Pack_32
    01077     do {
    01078         y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
    01079         borrow = (y & 0x10000) >> 16;
    01080         z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
    01081         borrow = (z & 0x10000) >> 16;
    01082         Storeinc(xc, z, y);
    01083         }
    01084         while(xb < xbe);
    01085     while(xa < xae) {
    01086         y = (*xa & 0xffff) - borrow;
    01087         borrow = (y & 0x10000) >> 16;
    01088         z = (*xa++ >> 16) - borrow;
    01089         borrow = (z & 0x10000) >> 16;
    01090         Storeinc(xc, z, y);
    01091         }
    01092 #else
    01093     do {
    01094         y = *xa++ - *xb++ - borrow;
    01095         borrow = (y & 0x10000) >> 16;
    01096         *xc++ = y & 0xffff;
    01097         }
    01098         while(xb < xbe);
    01099     while(xa < xae) {
    01100         y = *xa++ - borrow;
    01101         borrow = (y & 0x10000) >> 16;
    01102         *xc++ = y & 0xffff;
    01103         }
    01104 #endif
    01105 #endif
    01106     while(!*--xc)
    01107         wa--;
    01108     c->wds = wa;
    01109     return c;
    01110     }
    01111
    01112  static double
    01113 ulp
    01114 #ifdef KR_headers
    01115     (x) double x;
    01116 #else
    01117     (double x)
    01118 #endif
    01119 {
    01120     register Long L;
    01121     double a;
    01122
    01123     L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
    01124 #ifndef Avoid_Underflow
    01125 #ifndef Sudden_Underflow
    01126     if (L > 0) {
    01127 #endif
    01128 #endif
    01129 #ifdef IBM
    01130         L |= Exp_msk1 >> 4;
    01131 #endif
    01132         word0(a) = L;
    01133         word1(a) = 0;
    01134 #ifndef Avoid_Underflow
    01135 #ifndef Sudden_Underflow
    01136         }
    01137     else {
    01138         L = -L >> Exp_shift;
    01139         if (L < Exp_shift) {
    01140             word0(a) = 0x80000 >> L;
    01141             word1(a) = 0;
    01142             }
    01143         else {
    01144             word0(a) = 0;
    01145             L -= Exp_shift;
    01146             word1(a) = L >= 31 ? 1 : 1 << 31 - L;
    01147             }
    01148         }
    01149 #endif
    01150 #endif
    01151     return dval(a);
    01152     }
    01153
    01154  static double
    01155 b2d
    01156 #ifdef KR_headers
    01157     (a, e) Bigint *a; int *e;
    01158 #else
    01159     (Bigint *a, int *e)
    01160 #endif
    01161 {
    01162     ULong *xa, *xa0, w, y, z;
    01163     int k;
    01164     double d;
    01165 #ifdef VAX
    01166     ULong d0, d1;
    01167 #else
    01168 #define d0 word0(d)
    01169 #define d1 word1(d)
    01170 #endif
    01171
    01172     xa0 = a->x;
    01173     xa = xa0 + a->wds;
    01174     y = *--xa;
    01175 #ifdef DEBUG
    01176     if (!y) Bug("zero y in b2d");
    01177 #endif
    01178     k = hi0bits(y);
    01179     *e = 32 - k;
    01180 #ifdef Pack_32
    01181     if (k < Ebits) {
    01182         d0 = Exp_1 | y >> Ebits - k;
    01183         w = xa > xa0 ? *--xa : 0;
    01184         d1 = y << (32-Ebits) + k | w >> Ebits - k;
    01185         goto ret_d;
    01186         }
    01187     z = xa > xa0 ? *--xa : 0;
    01188     if (k -= Ebits) {
    01189         d0 = Exp_1 | y << k | z >> 32 - k;
    01190         y = xa > xa0 ? *--xa : 0;
    01191         d1 = z << k | y >> 32 - k;
    01192         }
    01193     else {
    01194         d0 = Exp_1 | y;
    01195         d1 = z;
    01196         }
    01197 #else
    01198     if (k < Ebits + 16) {
    01199         z = xa > xa0 ? *--xa : 0;
    01200         d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
    01201         w = xa > xa0 ? *--xa : 0;
    01202         y = xa > xa0 ? *--xa : 0;
    01203         d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
    01204         goto ret_d;
    01205         }
    01206     z = xa > xa0 ? *--xa : 0;
    01207     w = xa > xa0 ? *--xa : 0;
    01208     k -= Ebits + 16;
    01209     d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
    01210     y = xa > xa0 ? *--xa : 0;
    01211     d1 = w << k + 16 | y << k;
    01212 #endif
    01213  ret_d:
    01214 #ifdef VAX
    01215     word0(d) = d0 >> 16 | d0 << 16;
    01216     word1(d) = d1 >> 16 | d1 << 16;
    01217 #else
    01218 #undef d0
    01219 #undef d1
    01220 #endif
    01221     return dval(d);
    01222     }
    01223
    01224  static Bigint *
    01225 d2b
    01226 #ifdef KR_headers
    01227     (d, e, bits) double d; int *e, *bits;
    01228 #else
    01229     (double d, int *e, int *bits)
    01230 #endif
    01231 {
    01232     Bigint *b;
    01233     int de, k;
    01234     ULong *x, y, z;
    01235 #ifndef Sudden_Underflow
    01236     int i;
    01237 #endif
    01238 #ifdef VAX
    01239     ULong d0, d1;
    01240     d0 = word0(d) >> 16 | word0(d) << 16;
    01241     d1 = word1(d) >> 16 | word1(d) << 16;
    01242 #else
    01243 #define d0 word0(d)
    01244 #define d1 word1(d)
    01245 #endif
    01246
    01247 #ifdef Pack_32
    01248     b = Balloc(1);
    01249 #else
    01250     b = Balloc(2);
    01251 #endif
    01252     x = b->x;
    01253
    01254     z = d0 & Frac_mask;
    01255     d0 &= 0x7fffffff;   /* clear sign bit, which we ignore */
    01256 #ifdef Sudden_Underflow
    01257     de = (int)(d0 >> Exp_shift);
    01258 #ifndef IBM
    01259     z |= Exp_msk11;
    01260 #endif
    01261 #else
    01262     if ((de = (int)(d0 >> Exp_shift)))
    01263         z |= Exp_msk1;
    01264 #endif
    01265 #ifdef Pack_32
    01266     if ((y = d1)) {
    01267         if ((k = lo0bits(&y))) {
    01268             x[0] = y | z << 32 - k;
    01269             z >>= k;
    01270             }
    01271         else
    01272             x[0] = y;
    01273 #ifndef Sudden_Underflow
    01274         i =
    01275 #endif
    01276             b->wds = (x[1] = z) ? 2 : 1;
    01277         }
    01278     else {
    01279 #ifdef DEBUG
    01280         if (!z)
    01281             Bug("Zero passed to d2b");
    01282 #endif
    01283         k = lo0bits(&z);
    01284         x[0] = z;
    01285 #ifndef Sudden_Underflow
    01286         i =
    01287 #endif
    01288             b->wds = 1;
    01289         k += 32;
    01290         }
    01291 #else
    01292     if (y = d1) {
    01293         if (k = lo0bits(&y))
    01294             if (k >= 16) {
    01295                 x[0] = y | z << 32 - k & 0xffff;
    01296                 x[1] = z >> k - 16 & 0xffff;
    01297                 x[2] = z >> k;
    01298                 i = 2;
    01299                 }
    01300             else {
    01301                 x[0] = y & 0xffff;
    01302                 x[1] = y >> 16 | z << 16 - k & 0xffff;
    01303                 x[2] = z >> k & 0xffff;
    01304                 x[3] = z >> k+16;
    01305                 i = 3;
    01306                 }
    01307         else {
    01308             x[0] = y & 0xffff;
    01309             x[1] = y >> 16;
    01310             x[2] = z & 0xffff;
    01311             x[3] = z >> 16;
    01312             i = 3;
    01313             }
    01314         }
    01315     else {
    01316 #ifdef DEBUG
    01317         if (!z)
    01318             Bug("Zero passed to d2b");
    01319 #endif
    01320         k = lo0bits(&z);
    01321         if (k >= 16) {
    01322             x[0] = z;
    01323             i = 0;
    01324             }
    01325         else {
    01326             x[0] = z & 0xffff;
    01327             x[1] = z >> 16;
    01328             i = 1;
    01329             }
    01330         k += 32;
    01331         }
    01332     while(!x[i])
    01333         --i;
    01334     b->wds = i + 1;
    01335 #endif
    01336 #ifndef Sudden_Underflow
    01337     if (de) {
    01338 #endif
    01339 #ifdef IBM
    01340         *e = (de - Bias - (P-1) << 2) + k;
    01341         *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
    01342 #else
    01343         *e = de - Bias - (P-1) + k;
    01344         *bits = P - k;
    01345 #endif
    01346 #ifndef Sudden_Underflow
    01347         }
    01348     else {
    01349         *e = de - Bias - (P-1) + 1 + k;
    01350 #ifdef Pack_32
    01351         *bits = 32*i - hi0bits(x[i-1]);
    01352 #else
    01353         *bits = (i+2)*16 - hi0bits(x[i]);
    01354 #endif
    01355         }
    01356 #endif
    01357     return b;
    01358     }
    01359 #undef d0
    01360 #undef d1
    01361
    01362  static double
    01363 ratio
    01364 #ifdef KR_headers
    01365     (a, b) Bigint *a, *b;
    01366 #else
    01367     (Bigint *a, Bigint *b)
    01368 #endif
    01369 {
    01370     double da, db;
    01371     int k, ka, kb;
    01372
    01373     dval(da) = b2d(a, &ka);
    01374     dval(db) = b2d(b, &kb);
    01375 #ifdef Pack_32
    01376     k = ka - kb + 32*(a->wds - b->wds);
    01377 #else
    01378     k = ka - kb + 16*(a->wds - b->wds);
    01379 #endif
    01380 #ifdef IBM
    01381     if (k > 0) {
    01382         word0(da) += (k >> 2)*Exp_msk1;
    01383         if (k &= 3)
    01384             dval(da) *= 1 << k;
    01385         }
    01386     else {
    01387         k = -k;
    01388         word0(db) += (k >> 2)*Exp_msk1;
    01389         if (k &= 3)
    01390             dval(db) *= 1 << k;
    01391         }
    01392 #else
    01393     if (k > 0)
    01394         word0(da) += k*Exp_msk1;
    01395     else {
    01396         k = -k;
    01397         word0(db) += k*Exp_msk1;
    01398         }
    01399 #endif
    01400     return dval(da) / dval(db);
    01401     }
    01402
    01403  static CONST double
    01404 tens[] = {
    01405         1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
    01406         1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
    01407         1e20, 1e21, 1e22
    01408 #ifdef VAX
    01409         , 1e23, 1e24
    01410 #endif
    01411         };
    01412
    01413  static CONST double
    01414 #ifdef IEEE_Arith
    01415 bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
    01416 static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
    01417 #ifdef Avoid_Underflow
    01418         9007199254740992.*9007199254740992.e-256
    01419         /* = 2^106 * 1e-53 */
    01420 #else
    01421         1e-256
    01422 #endif
    01423         };
    01424 /* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
    01425 /* flag unnecessarily.  It leads to a song and dance at the end of strtod. */
    01426 #define Scale_Bit 0x10
    01427 #define n_bigtens 5
    01428 #else
    01429 #ifdef IBM
    01430 bigtens[] = { 1e16, 1e32, 1e64 };
    01431 static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 };
    01432 #define n_bigtens 3
    01433 #else
    01434 bigtens[] = { 1e16, 1e32 };
    01435 static CONST double tinytens[] = { 1e-16, 1e-32 };
    01436 #define n_bigtens 2
    01437 #endif
    01438 #endif
    01439
    01440 #ifndef IEEE_Arith
    01441 #undef INFNAN_CHECK
    01442 #endif
    01443
    01444 #ifdef INFNAN_CHECK
    01445
    01446 #ifndef NAN_WORD0
    01447 #define NAN_WORD0 0x7ff80000
    01448 #endif
    01449
    01450 #ifndef NAN_WORD1
    01451 #define NAN_WORD1 0
    01452 #endif
    01453
    01454  static int
    01455 match
    01456 #ifdef KR_headers
    01457     (sp, t) char **sp, *t;
    01458 #else
    01459     (CONST char **sp, CONST char *t)
    01460 #endif
    01461 {
    01462     int c, d;
    01463     CONST char *s = *sp;
    01464
    01465     while((d = *t++)) {
    01466         if ((c = *++s) >= 'A' && c <= 'Z')
    01467             c += 'a' - 'A';
    01468         if (c != d)
    01469             return 0;
    01470         }
    01471     *sp = s + 1;
    01472     return 1;
    01473     }
    01474
    01475 #ifndef No_Hex_NaN
    01476  static void
    01477 hexnan
    01478 #ifdef KR_headers
    01479     (rvp, sp) double *rvp; CONST char **sp;
    01480 #else
    01481     (double *rvp, CONST char **sp)
    01482 #endif
    01483 {
    01484     ULong c, x[2];
    01485     CONST char *s;
    01486     int havedig, udx0, xshift;
    01487
    01488     x[0] = x[1] = 0;
    01489     havedig = xshift = 0;
    01490     udx0 = 1;
    01491     s = *sp;
    01492     while((c = *(CONST unsigned char*)++s)) {
    01493         if (c >= '0' && c <= '9')
    01494             c -= '0';
    01495         else if (c >= 'a' && c <= 'f')
    01496             c += 10 - 'a';
    01497         else if (c >= 'A' && c <= 'F')
    01498             c += 10 - 'A';
    01499         else if (c <= ' ') {
    01500             if (udx0 && havedig) {
    01501                 udx0 = 0;
    01502                 xshift = 1;
    01503                 }
    01504             continue;
    01505             }
    01506         else if (/*(*/ c == ')' && havedig) {
    01507             *sp = s + 1;
    01508             break;
    01509             }
    01510         else
    01511             return; /* invalid form: don't change *sp */
    01512         havedig = 1;
    01513         if (xshift) {
    01514             xshift = 0;
    01515             x[0] = x[1];
    01516             x[1] = 0;
    01517             }
    01518         if (udx0)
    01519             x[0] = (x[0] << 4) | (x[1] >> 28);
    01520         x[1] = (x[1] << 4) | c;
    01521         }
    01522     if ((x[0] &= 0xfffff) || x[1]) {
    01523         word0(*rvp) = Exp_mask | x[0];
    01524         word1(*rvp) = x[1];
    01525         }
    01526     }
    01527 #endif /*No_Hex_NaN*/
    01528 #endif /* INFNAN_CHECK */
    01529
    01530  double
    01531 kjs_strtod
    01532 #ifdef KR_headers
    01533     (s00, se) CONST char *s00; char **se;
    01534 #else
    01535     (CONST char *s00, char **se)
    01536 #endif
    01537 {
    01538 #ifdef Avoid_Underflow
    01539     int scale;
    01540 #endif
    01541     int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
    01542          e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
    01543     CONST char *s, *s0, *s1;
    01544     double aadj, aadj1, adj, rv, rv0;
    01545     Long L;
    01546     ULong y, z;
    01547     Bigint *bb = NULL, *bb1 = NULL, *bd = NULL, *bd0 = NULL, *bs = NULL, *delta = NULL;
    01548 #ifdef SET_INEXACT
    01549     int inexact, oldinexact;
    01550 #endif
    01551 #ifdef Honor_FLT_ROUNDS
    01552     int rounding;
    01553 #endif
    01554 #ifdef USE_LOCALE
    01555     CONST char *s2;
    01556 #endif
    01557
    01558     sign = nz0 = nz = 0;
    01559     dval(rv) = 0.;
    01560     for(s = s00;;s++) switch(*s) {
    01561         case '-':
    01562             sign = 1;
    01563             /* no break */
    01564         case '+':
    01565             if (*++s)
    01566                 goto break2;
    01567             /* no break */
    01568         case 0:
    01569             goto ret0;
    01570         case '\t':
    01571         case '\n':
    01572         case '\v':
    01573         case '\f':
    01574         case '\r':
    01575         case ' ':
    01576             continue;
    01577         default:
    01578             goto break2;
    01579         }
    01580  break2:
    01581     if (*s == '0') {
    01582         nz0 = 1;
    01583         while(*++s == '0') ;
    01584         if (!*s)
    01585             goto ret;
    01586         }
    01587     s0 = s;
    01588     y = z = 0;
    01589     for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
    01590         if (nd < 9)
    01591             y = 10*y + c - '0';
    01592         else if (nd < 16)
    01593             z = 10*z + c - '0';
    01594     nd0 = nd;
    01595 #ifdef USE_LOCALE
    01596     s1 = localeconv()->decimal_point;
    01597     if (c == *s1) {
    01598         c = '.';
    01599         if (*++s1) {
    01600             s2 = s;
    01601             for(;;) {
    01602                 if (*++s2 != *s1) {
    01603                     c = 0;
    01604                     break;
    01605                     }
    01606                 if (!*++s1) {
    01607                     s = s2;
    01608                     break;
    01609                     }
    01610                 }
    01611             }
    01612         }
    01613 #endif
    01614     if (c == '.') {
    01615         c = *++s;
    01616         if (!nd) {
    01617             for(; c == '0'; c = *++s)
    01618                 nz++;
    01619             if (c > '0' && c <= '9') {
    01620                 s0 = s;
    01621                 nf += nz;
    01622                 nz = 0;
    01623                 goto have_dig;
    01624                 }
    01625             goto dig_done;
    01626             }
    01627         for(; c >= '0' && c <= '9'; c = *++s) {
    01628  have_dig:
    01629             nz++;
    01630             if (c -= '0') {
    01631                 nf += nz;
    01632                 for(i = 1; i < nz; i++)
    01633                     if (nd++ < 9)
    01634                         y *= 10;
    01635                     else if (nd <= DBL_DIG + 1)
    01636                         z *= 10;
    01637                 if (nd++ < 9)
    01638                     y = 10*y + c;
    01639                 else if (nd <= DBL_DIG + 1)
    01640                     z = 10*z + c;
    01641                 nz = 0;
    01642                 }
    01643             }
    01644         }
    01645  dig_done:
    01646     e = 0;
    01647     if (c == 'e' || c == 'E') {
    01648         if (!nd && !nz && !nz0) {
    01649             goto ret0;
    01650             }
    01651         s00 = s;
    01652         esign = 0;
    01653         switch(c = *++s) {
    01654             case '-':
    01655                 esign = 1;
    01656             case '+':
    01657                 c = *++s;
    01658             }
    01659         if (c >= '0' && c <= '9') {
    01660             while(c == '0')
    01661                 c = *++s;
    01662             if (c > '0' && c <= '9') {
    01663                 L = c - '0';
    01664                 s1 = s;
    01665                 while((c = *++s) >= '0' && c <= '9')
    01666                     L = 10*L + c - '0';
    01667                 if (s - s1 > 8 || L > 19999)
    01668                     /* Avoid confusion from exponents
    01669                      * so large that e might overflow.
    01670                      */
    01671                     e = 19999; /* safe for 16 bit ints */
    01672                 else
    01673                     e = (int)L;
    01674                 if (esign)
    01675                     e = -e;
    01676                 }
    01677             else
    01678                 e = 0;
    01679             }
    01680         else
    01681             s = s00;
    01682         }
    01683     if (!nd) {
    01684         if (!nz && !nz0) {
    01685 #ifdef INFNAN_CHECK
    01686             /* Check for Nan and Infinity */
    01687             switch(c) {
    01688               case 'i':
    01689               case 'I':
    01690                 if (match(&s,"nf")) {
    01691                     --s;
    01692                     if (!match(&s,"inity"))
    01693                         ++s;
    01694                     word0(rv) = 0x7ff00000;
    01695                     word1(rv) = 0;
    01696                     goto ret;
    01697                     }
    01698                 break;
    01699               case 'n':
    01700               case 'N':
    01701                 if (match(&s, "an")) {
    01702                     word0(rv) = NAN_WORD0;
    01703                     word1(rv) = NAN_WORD1;
    01704 #ifndef No_Hex_NaN
    01705                     if (*s == '(') /*)*/
    01706                         hexnan(&rv, &s);
    01707 #endif
    01708                     goto ret;
    01709                     }
    01710               }
    01711 #endif /* INFNAN_CHECK */
    01712  ret0:
    01713             s = s00;
    01714             sign = 0;
    01715             }
    01716         goto ret;
    01717         }
    01718     e1 = e -= nf;
    01719
    01720     /* Now we have nd0 digits, starting at s0, followed by a
    01721      * decimal point, followed by nd-nd0 digits.  The number we're
    01722      * after is the integer represented by those digits times
    01723      * 10**e */
    01724
    01725     if (!nd0)
    01726         nd0 = nd;
    01727     k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
    01728     dval(rv) = y;
    01729     if (k > 9) {
    01730 #ifdef SET_INEXACT
    01731         if (k > DBL_DIG)
    01732             oldinexact = get_inexact();
    01733 #endif
    01734         dval(rv) = tens[k - 9] * dval(rv) + z;
    01735         }
    01736     bd0 = 0;
    01737     if (nd <= DBL_DIG
    01738 #ifndef RND_PRODQUOT
    01739 #ifndef Honor_FLT_ROUNDS
    01740         && Flt_Rounds == 1
    01741 #endif
    01742 #endif
    01743             ) {
    01744         if (!e)
    01745             goto ret;
    01746         if (e > 0) {
    01747             if (e <= Ten_pmax) {
    01748 #ifdef VAX
    01749                 goto vax_ovfl_check;
    01750 #else
    01751 #ifdef Honor_FLT_ROUNDS
    01752                 /* round correctly FLT_ROUNDS = 2 or 3 */
    01753                 if (sign) {
    01754                     rv = -rv;
    01755                     sign = 0;
    01756                     }
    01757 #endif
    01758                 /* rv = */ rounded_product(dval(rv), tens[e]);
    01759                 goto ret;
    01760 #endif
    01761                 }
    01762             i = DBL_DIG - nd;
    01763             if (e <= Ten_pmax + i) {
    01764                 /* A fancier test would sometimes let us do
    01765                  * this for larger i values.
    01766                  */
    01767 #ifdef Honor_FLT_ROUNDS
    01768                 /* round correctly FLT_ROUNDS = 2 or 3 */
    01769                 if (sign) {
    01770                     rv = -rv;
    01771                     sign = 0;
    01772                     }
    01773 #endif
    01774                 e -= i;
    01775                 dval(rv) *= tens[i];
    01776 #ifdef VAX
    01777                 /* VAX exponent range is so narrow we must
    01778                  * worry about overflow here...
    01779                  */
    01780  vax_ovfl_check:
    01781                 word0(rv) -= P*Exp_msk1;
    01782                 /* rv = */ rounded_product(dval(rv), tens[e]);
    01783                 if ((word0(rv) & Exp_mask)
    01784                  > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
    01785                     goto ovfl;
    01786                 word0(rv) += P*Exp_msk1;
    01787 #else
    01788                 /* rv = */ rounded_product(dval(rv), tens[e]);
    01789 #endif
    01790                 goto ret;
    01791                 }
    01792             }
    01793 #ifndef Inaccurate_Divide
    01794         else if (e >= -Ten_pmax) {
    01795 #ifdef Honor_FLT_ROUNDS
    01796             /* round correctly FLT_ROUNDS = 2 or 3 */
    01797             if (sign) {
    01798                 rv = -rv;
    01799                 sign = 0;
    01800                 }
    01801 #endif
    01802             /* rv = */ rounded_quotient(dval(rv), tens[-e]);
    01803             goto ret;
    01804             }
    01805 #endif
    01806         }
    01807     e1 += nd - k;
    01808
    01809 #ifdef IEEE_Arith
    01810 #ifdef SET_INEXACT
    01811     inexact = 1;
    01812     if (k <= DBL_DIG)
    01813         oldinexact = get_inexact();
    01814 #endif
    01815 #ifdef Avoid_Underflow
    01816     scale = 0;
    01817 #endif
    01818 #ifdef Honor_FLT_ROUNDS
    01819     if ((rounding = Flt_Rounds) >= 2) {
    01820         if (sign)
    01821             rounding = rounding == 2 ? 0 : 2;
    01822         else
    01823             if (rounding != 2)
    01824                 rounding = 0;
    01825         }
    01826 #endif
    01827 #endif /*IEEE_Arith*/
    01828
    01829     /* Get starting approximation = rv * 10**e1 */
    01830
    01831     if (e1 > 0) {
    01832         if ((i = e1 & 15))
    01833             dval(rv) *= tens[i];
    01834         if (e1 &= ~15) {
    01835             if (e1 > DBL_MAX_10_EXP) {
    01836  ovfl:
    01837 #ifndef NO_ERRNO
    01838                 errno = ERANGE;
    01839 #endif
    01840                 /* Can't trust HUGE_VAL */
    01841 #ifdef IEEE_Arith
    01842 #ifdef Honor_FLT_ROUNDS
    01843                 switch(rounding) {
    01844                   case 0: /* toward 0 */
    01845                   case 3: /* toward -infinity */
    01846                     word0(rv) = Big0;
    01847                     word1(rv) = Big1;
    01848                     break;
    01849                   default:
    01850                     word0(rv) = Exp_mask;
    01851                     word1(rv) = 0;
    01852                   }
    01853 #else /*Honor_FLT_ROUNDS*/
    01854                 word0(rv) = Exp_mask;
    01855                 word1(rv) = 0;
    01856 #endif /*Honor_FLT_ROUNDS*/
    01857 #ifdef SET_INEXACT
    01858                 /* set overflow bit */
    01859                 dval(rv0) = 1e300;
    01860                 dval(rv0) *= dval(rv0);
    01861 #endif
    01862 #else /*IEEE_Arith*/
    01863                 word0(rv) = Big0;
    01864                 word1(rv) = Big1;
    01865 #endif /*IEEE_Arith*/
    01866                 if (bd0)
    01867                     goto retfree;
    01868                 goto ret;
    01869                 }
    01870             e1 >>= 4;
    01871             for(j = 0; e1 > 1; j++, e1 >>= 1)
    01872                 if (e1 & 1)
    01873                     dval(rv) *= bigtens[j];
    01874         /* The last multiplication could overflow. */
    01875             word0(rv) -= P*Exp_msk1;
    01876             dval(rv) *= bigtens[j];
    01877             if ((z = word0(rv) & Exp_mask)
    01878              > Exp_msk1*(DBL_MAX_EXP+Bias-P))
    01879                 goto ovfl;
    01880             if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
    01881                 /* set to largest number */
    01882                 /* (Can't trust DBL_MAX) */
    01883                 word0(rv) = Big0;
    01884                 word1(rv) = Big1;
    01885                 }
    01886             else
    01887                 word0(rv) += P*Exp_msk1;
    01888             }
    01889         }
    01890     else if (e1 < 0) {
    01891         e1 = -e1;
    01892         if ((i = e1 & 15))
    01893             dval(rv) /= tens[i];
    01894         if (e1 >>= 4) {
    01895             if (e1 >= 1 << n_bigtens)
    01896                 goto undfl;
    01897 #ifdef Avoid_Underflow
    01898             if (e1 & Scale_Bit)
    01899                 scale = 2*P;
    01900             for(j = 0; e1 > 0; j++, e1 >>= 1)
    01901                 if (e1 & 1)
    01902                     dval(rv) *= tinytens[j];
    01903             if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask)
    01904                         >> Exp_shift)) > 0) {
    01905                 /* scaled rv is denormal; zap j low bits */
    01906                 if (j >= 32) {
    01907                     word1(rv) = 0;
    01908                     if (j >= 53)
    01909                      word0(rv) = (P+2)*Exp_msk1;
    01910                     else
    01911                      word0(rv) &= 0xffffffff << j-32;
    01912                     }
    01913                 else
    01914                     word1(rv) &= 0xffffffff << j;
    01915                 }
    01916 #else
    01917             for(j = 0; e1 > 1; j++, e1 >>= 1)
    01918                 if (e1 & 1)
    01919                     dval(rv) *= tinytens[j];
    01920             /* The last multiplication could underflow. */
    01921             dval(rv0) = dval(rv);
    01922             dval(rv) *= tinytens[j];
    01923             if (!dval(rv)) {
    01924                 dval(rv) = 2.*dval(rv0);
    01925                 dval(rv) *= tinytens[j];
    01926 #endif
    01927                 if (!dval(rv)) {
    01928  undfl:
    01929                     dval(rv) = 0.;
    01930 #ifndef NO_ERRNO
    01931                     errno = ERANGE;
    01932 #endif
    01933                     if (bd0)
    01934                         goto retfree;
    01935                     goto ret;
    01936                     }
    01937 #ifndef Avoid_Underflow
    01938                 word0(rv) = Tiny0;
    01939                 word1(rv) = Tiny1;
    01940                 /* The refinement below will clean
    01941                  * this approximation up.
    01942                  */
    01943                 }
    01944 #endif
    01945             }
    01946         }
    01947
    01948     /* Now the hard part -- adjusting rv to the correct value.*/
    01949
    01950     /* Put digits into bd: true value = bd * 10^e */
    01951
    01952     bd0 = s2b(s0, nd0, nd, y);
    01953
    01954     for(;;) {
    01955         bd = Balloc(bd0->k);
    01956         Bcopy(bd, bd0);
    01957         bb = d2b(dval(rv), &bbe, &bbbits);  /* rv = bb * 2^bbe */
    01958         bs = i2b(1);
    01959
    01960         if (e >= 0) {
    01961             bb2 = bb5 = 0;
    01962             bd2 = bd5 = e;
    01963             }
    01964         else {
    01965             bb2 = bb5 = -e;
    01966             bd2 = bd5 = 0;
    01967             }
    01968         if (bbe >= 0)
    01969             bb2 += bbe;
    01970         else
    01971             bd2 -= bbe;
    01972         bs2 = bb2;
    01973 #ifdef Honor_FLT_ROUNDS
    01974         if (rounding != 1)
    01975             bs2++;
    01976 #endif
    01977 #ifdef Avoid_Underflow
    01978         j = bbe - scale;
    01979         i = j + bbbits - 1; /* logb(rv) */
    01980         if (i < Emin)   /* denormal */
    01981             j += P - Emin;
    01982         else
    01983             j = P + 1 - bbbits;
    01984 #else /*Avoid_Underflow*/
    01985 #ifdef Sudden_Underflow
    01986 #ifdef IBM
    01987         j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
    01988 #else
    01989         j = P + 1 - bbbits;
    01990 #endif
    01991 #else /*Sudden_Underflow*/
    01992         j = bbe;
    01993         i = j + bbbits - 1; /* logb(rv) */
    01994         if (i < Emin)   /* denormal */
    01995             j += P - Emin;
    01996         else
    01997             j = P + 1 - bbbits;
    01998 #endif /*Sudden_Underflow*/
    01999 #endif /*Avoid_Underflow*/
    02000         bb2 += j;
    02001         bd2 += j;
    02002 #ifdef Avoid_Underflow
    02003         bd2 += scale;
    02004 #endif
    02005         i = bb2 < bd2 ? bb2 : bd2;
    02006         if (i > bs2)
    02007             i = bs2;
    02008         if (i > 0) {
    02009             bb2 -= i;
    02010             bd2 -= i;
    02011             bs2 -= i;
    02012             }
    02013         if (bb5 > 0) {
    02014             bs = pow5mult(bs, bb5);
    02015             bb1 = mult(bs, bb);
    02016             Bfree(bb);
    02017             bb = bb1;
    02018             }
    02019         if (bb2 > 0)
    02020             bb = lshift(bb, bb2);
    02021         if (bd5 > 0)
    02022             bd = pow5mult(bd, bd5);
    02023         if (bd2 > 0)
    02024             bd = lshift(bd, bd2);
    02025         if (bs2 > 0)
    02026             bs = lshift(bs, bs2);
    02027         delta = diff(bb, bd);
    02028         dsign = delta->sign;
    02029         delta->sign = 0;
    02030         i = cmp(delta, bs);
    02031 #ifdef Honor_FLT_ROUNDS
    02032         if (rounding != 1) {
    02033             if (i < 0) {
    02034                 /* Error is less than an ulp */
    02035                 if (!delta->x[0] && delta->wds <= 1) {
    02036                     /* exact */
    02037 #ifdef SET_INEXACT
    02038                     inexact = 0;
    02039 #endif
    02040                     break;
    02041                     }
    02042                 if (rounding) {
    02043                     if (dsign) {
    02044                         adj = 1.;
    02045                         goto apply_adj;
    02046                         }
    02047                     }
    02048                 else if (!dsign) {
    02049                     adj = -1.;
    02050                     if (!word1(rv)
    02051                      && !(word0(rv) & Frac_mask)) {
    02052                         y = word0(rv) & Exp_mask;
    02053 #ifdef Avoid_Underflow
    02054                         if (!scale || y > 2*P*Exp_msk1)
    02055 #else
    02056                         if (y)
    02057 #endif
    02058                           {
    02059                           delta = lshift(delta,Log2P);
    02060                           if (cmp(delta, bs) <= 0)
    02061                             adj = -0.5;
    02062                           }
    02063                         }
    02064  apply_adj:
    02065 #ifdef Avoid_Underflow
    02066                     if (scale && (y = word0(rv) & Exp_mask)
    02067                         <= 2*P*Exp_msk1)
    02068                       word0(adj) += (2*P+1)*Exp_msk1 - y;
    02069 #else
    02070 #ifdef Sudden_Underflow
    02071                     if ((word0(rv) & Exp_mask) <=
    02072                             P*Exp_msk1) {
    02073                         word0(rv) += P*Exp_msk1;
    02074                         dval(rv) += adj*ulp(dval(rv));
    02075                         word0(rv) -= P*Exp_msk1;
    02076                         }
    02077                     else
    02078 #endif /*Sudden_Underflow*/
    02079 #endif /*Avoid_Underflow*/
    02080                     dval(rv) += adj*ulp(dval(rv));
    02081                     }
    02082                 break;
    02083                 }
    02084             adj = ratio(delta, bs);
    02085             if (adj < 1.)
    02086                 adj = 1.;
    02087             if (adj <= 0x7ffffffe) {
    02088                 /* adj = rounding ? ceil(adj) : floor(adj); */
    02089                 y = adj;
    02090                 if (y != adj) {
    02091                     if (!((rounding>>1) ^ dsign))
    02092                         y++;
    02093                     adj = y;
    02094                     }
    02095                 }
    02096 #ifdef Avoid_Underflow
    02097             if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
    02098                 word0(adj) += (2*P+1)*Exp_msk1 - y;
    02099 #else
    02100 #ifdef Sudden_Underflow
    02101             if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
    02102                 word0(rv) += P*Exp_msk1;
    02103                 adj *= ulp(dval(rv));
    02104                 if (dsign)
    02105                     dval(rv) += adj;
    02106                 else
    02107                     dval(rv) -= adj;
    02108                 word0(rv) -= P*Exp_msk1;
    02109                 goto cont;
    02110                 }
    02111 #endif /*Sudden_Underflow*/
    02112 #endif /*Avoid_Underflow*/
    02113             adj *= ulp(dval(rv));
    02114             if (dsign)
    02115                 dval(rv) += adj;
    02116             else
    02117                 dval(rv) -= adj;
    02118             goto cont;
    02119             }
    02120 #endif /*Honor_FLT_ROUNDS*/
    02121
    02122         if (i < 0) {
    02123             /* Error is less than half an ulp -- check for
    02124              * special case of mantissa a power of two.
    02125              */
    02126             if (dsign || word1(rv) || word0(rv) & Bndry_mask
    02127 #ifdef IEEE_Arith
    02128 #ifdef Avoid_Underflow
    02129              || (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1
    02130 #else
    02131              || (word0(rv) & Exp_mask) <= Exp_msk1
    02132 #endif
    02133 #endif
    02134                 ) {
    02135 #ifdef SET_INEXACT
    02136                 if (!delta->x[0] && delta->wds <= 1)
    02137                     inexact = 0;
    02138 #endif
    02139                 break;
    02140                 }
    02141             if (!delta->x[0] && delta->wds <= 1) {
    02142                 /* exact result */
    02143 #ifdef SET_INEXACT
    02144                 inexact = 0;
    02145 #endif
    02146                 break;
    02147                 }
    02148             delta = lshift(delta,Log2P);
    02149             if (cmp(delta, bs) > 0)
    02150                 goto drop_down;
    02151             break;
    02152             }
    02153         if (i == 0) {
    02154             /* exactly half-way between */
    02155             if (dsign) {
    02156                 if ((word0(rv) & Bndry_mask1) == Bndry_mask1
    02157                  &&  word1(rv) == (
    02158 #ifdef Avoid_Underflow
    02159             (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
    02160         ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
    02161 #endif
    02162                            0xffffffff)) {
    02163                     /*boundary case -- increment exponent*/
    02164                     word0(rv) = (word0(rv) & Exp_mask)
    02165                         + Exp_msk1
    02166 #ifdef IBM
    02167                         | Exp_msk1 >> 4
    02168 #endif
    02169                         ;
    02170                     word1(rv) = 0;
    02171 #ifdef Avoid_Underflow
    02172                     dsign = 0;
    02173 #endif
    02174                     break;
    02175                     }
    02176                 }
    02177             else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
    02178  drop_down:
    02179                 /* boundary case -- decrement exponent */
    02180 #ifdef Sudden_Underflow /*{{*/
    02181                 L = word0(rv) & Exp_mask;
    02182 #ifdef IBM
    02183                 if (L <  Exp_msk1)
    02184 #else
    02185 #ifdef Avoid_Underflow
    02186                 if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
    02187 #else
    02188                 if (L <= Exp_msk1)
    02189 #endif /*Avoid_Underflow*/
    02190 #endif /*IBM*/
    02191                     goto undfl;
    02192                 L -= Exp_msk1;
    02193 #else /*Sudden_Underflow}{*/
    02194 #ifdef Avoid_Underflow
    02195                 if (scale) {
    02196                     L = word0(rv) & Exp_mask;
    02197                     if (L <= (2*P+1)*Exp_msk1) {
    02198                         if (L > (P+2)*Exp_msk1)
    02199                             /* round even ==> */
    02200                             /* accept rv */
    02201                             break;
    02202                         /* rv = smallest denormal */
    02203                         goto undfl;
    02204                         }
    02205                     }
    02206 #endif /*Avoid_Underflow*/
    02207                 L = (word0(rv) & Exp_mask) - Exp_msk1;
    02208 #endif /*Sudden_Underflow}}*/
    02209                 word0(rv) = L | Bndry_mask1;
    02210                 word1(rv) = 0xffffffff;
    02211 #ifdef IBM
    02212                 goto cont;
    02213 #else
    02214                 break;
    02215 #endif
    02216                 }
    02217 #ifndef ROUND_BIASED
    02218             if (!(word1(rv) & LSB))
    02219                 break;
    02220 #endif
    02221             if (dsign)
    02222                 dval(rv) += ulp(dval(rv));
    02223 #ifndef ROUND_BIASED
    02224             else {
    02225                 dval(rv) -= ulp(dval(rv));
    02226 #ifndef Sudden_Underflow
    02227                 if (!dval(rv))
    02228                     goto undfl;
    02229 #endif
    02230                 }
    02231 #ifdef Avoid_Underflow
    02232             dsign = 1 - dsign;
    02233 #endif
    02234 #endif
    02235             break;
    02236             }
    02237         if ((aadj = ratio(delta, bs)) <= 2.) {
    02238             if (dsign)
    02239                 aadj = aadj1 = 1.;
    02240             else if (word1(rv) || word0(rv) & Bndry_mask) {
    02241 #ifndef Sudden_Underflow
    02242                 if (word1(rv) == Tiny1 && !word0(rv))
    02243                     goto undfl;
    02244 #endif
    02245                 aadj = 1.;
    02246                 aadj1 = -1.;
    02247                 }
    02248             else {
    02249                 /* special case -- power of FLT_RADIX to be */
    02250                 /* rounded down... */
    02251
    02252                 if (aadj < 2./FLT_RADIX)
    02253                     aadj = 1./FLT_RADIX;
    02254                 else
    02255                     aadj *= 0.5;
    02256                 aadj1 = -aadj;
    02257                 }
    02258             }
    02259         else {
    02260             aadj *= 0.5;
    02261             aadj1 = dsign ? aadj : -aadj;
    02262 #ifdef Check_FLT_ROUNDS
    02263             switch(Rounding) {
    02264                 case 2: /* towards +infinity */
    02265                     aadj1 -= 0.5;
    02266                     break;
    02267                 case 0: /* towards 0 */
    02268                 case 3: /* towards -infinity */
    02269                     aadj1 += 0.5;
    02270                 }
    02271 #else
    02272             if (Flt_Rounds == 0)
    02273                 aadj1 += 0.5;
    02274 #endif /*Check_FLT_ROUNDS*/
    02275             }
    02276         y = word0(rv) & Exp_mask;
    02277
    02278         /* Check for overflow */
    02279
    02280         if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
    02281             dval(rv0) = dval(rv);
    02282             word0(rv) -= P*Exp_msk1;
    02283             adj = aadj1 * ulp(dval(rv));
    02284             dval(rv) += adj;
    02285             if ((word0(rv) & Exp_mask) >=
    02286                     Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
    02287                 if (word0(rv0) == Big0 && word1(rv0) == Big1)
    02288                     goto ovfl;
    02289                 word0(rv) = Big0;
    02290                 word1(rv) = Big1;
    02291                 goto cont;
    02292                 }
    02293             else
    02294                 word0(rv) += P*Exp_msk1;
    02295             }
    02296         else {
    02297 #ifdef Avoid_Underflow
    02298             if (scale && y <= 2*P*Exp_msk1) {
    02299                 if (aadj <= 0x7fffffff) {
    02300                     if ((z = (ULong)aadj) <= 0)
    02301                         z = 1;
    02302                     aadj = z;
    02303                     aadj1 = dsign ? aadj : -aadj;
    02304                     }
    02305                 word0(aadj1) += (2*P+1)*Exp_msk1 - y;
    02306                 }
    02307             adj = aadj1 * ulp(dval(rv));
    02308             dval(rv) += adj;
    02309 #else
    02310 #ifdef Sudden_Underflow
    02311             if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
    02312                 dval(rv0) = dval(rv);
    02313                 word0(rv) += P*Exp_msk1;
    02314                 adj = aadj1 * ulp(dval(rv));
    02315                 dval(rv) += adj;
    02316 #ifdef IBM
    02317                 if ((word0(rv) & Exp_mask) <  P*Exp_msk1)
    02318 #else
    02319                 if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
    02320 #endif
    02321                     {
    02322                     if (word0(rv0) == Tiny0
    02323                      && word1(rv0) == Tiny1)
    02324                         goto undfl;
    02325                     word0(rv) = Tiny0;
    02326                     word1(rv) = Tiny1;
    02327                     goto cont;
    02328                     }
    02329                 else
    02330                     word0(rv) -= P*Exp_msk1;
    02331                 }
    02332             else {
    02333                 adj = aadj1 * ulp(dval(rv));
    02334                 dval(rv) += adj;
    02335                 }
    02336 #else /*Sudden_Underflow*/
    02337             /* Compute adj so that the IEEE rounding rules will
    02338              * correctly round rv + adj in some half-way cases.
    02339              * If rv * ulp(rv) is denormalized (i.e.,
    02340              * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
    02341              * trouble from bits lost to denormalization;
    02342              * example: 1.2e-307 .
    02343              */
    02344             if (y <= (P-1)*Exp_msk1 && aadj > 1.) {
    02345                 aadj1 = (double)(int)(aadj + 0.5);
    02346                 if (!dsign)
    02347                     aadj1 = -aadj1;
    02348                 }
    02349             adj = aadj1 * ulp(dval(rv));
    02350             dval(rv) += adj;
    02351 #endif /*Sudden_Underflow*/
    02352 #endif /*Avoid_Underflow*/
    02353             }
    02354         z = word0(rv) & Exp_mask;
    02355 #ifndef SET_INEXACT
    02356 #ifdef Avoid_Underflow
    02357         if (!scale)
    02358 #endif
    02359         if (y == z) {
    02360             /* Can we stop now? */
    02361             L = (Long)aadj;
    02362             aadj -= L;
    02363             /* The tolerances below are conservative. */
    02364             if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
    02365                 if (aadj < .4999999 || aadj > .5000001)
    02366                     break;
    02367                 }
    02368             else if (aadj < .4999999/FLT_RADIX)
    02369                 break;
    02370             }
    02371 #endif
    02372  cont:
    02373         Bfree(bb);
    02374         Bfree(bd);
    02375         Bfree(bs);
    02376         Bfree(delta);
    02377         }
    02378 #ifdef SET_INEXACT
    02379     if (inexact) {
    02380         if (!oldinexact) {
    02381             word0(rv0) = Exp_1 + (70 << Exp_shift);
    02382             word1(rv0) = 0;
    02383             dval(rv0) += 1.;
    02384             }
    02385         }
    02386     else if (!oldinexact)
    02387         clear_inexact();
    02388 #endif
    02389 #ifdef Avoid_Underflow
    02390     if (scale) {
    02391         word0(rv0) = Exp_1 - 2*P*Exp_msk1;
    02392         word1(rv0) = 0;
    02393         dval(rv) *= dval(rv0);
    02394 #ifndef NO_ERRNO
    02395         /* try to avoid the bug of testing an 8087 register value */
    02396         if (word0(rv) == 0 && word1(rv) == 0)
    02397             errno = ERANGE;
    02398 #endif
    02399         }
    02400 #endif /* Avoid_Underflow */
    02401 #ifdef SET_INEXACT
    02402     if (inexact && !(word0(rv) & Exp_mask)) {
    02403         /* set underflow bit */
    02404         dval(rv0) = 1e-300;
    02405         dval(rv0) *= dval(rv0);
    02406         }
    02407 #endif
    02408  retfree:
    02409     Bfree(bb);
    02410     Bfree(bd);
    02411     Bfree(bs);
    02412     Bfree(bd0);
    02413     Bfree(delta);
    02414  ret:
    02415     if (se)
    02416         *se = (char *)s;
    02417     return sign ? -dval(rv) : dval(rv);
    02418     }
    02419
    02420  static int
    02421 quorem
    02422 #ifdef KR_headers
    02423     (b, S) Bigint *b, *S;
    02424 #else
    02425     (Bigint *b, Bigint *S)
    02426 #endif
    02427 {
    02428     int n;
    02429     ULong *bx, *bxe, q, *sx, *sxe;
    02430 #ifdef ULLong
    02431     ULLong borrow, carry, y, ys;
    02432 #else
    02433     ULong borrow, carry, y, ys;
    02434 #ifdef Pack_32
    02435     ULong si, z, zs;
    02436 #endif
    02437 #endif
    02438
    02439     n = S->wds;
    02440 #ifdef DEBUG
    02441     /*debug*/ if (b->wds > n)
    02442     /*debug*/   Bug("oversize b in quorem");
    02443 #endif
    02444     if (b->wds < n)
    02445         return 0;
    02446     sx = S->x;
    02447     sxe = sx + --n;
    02448     bx = b->x;
    02449     bxe = bx + n;
    02450     q = *bxe / (*sxe + 1);  /* ensure q <= true quotient */
    02451 #ifdef DEBUG
    02452     /*debug*/ if (q > 9)
    02453     /*debug*/   Bug("oversized quotient in quorem");
    02454 #endif
    02455     if (q) {
    02456         borrow = 0;
    02457         carry = 0;
    02458         do {
    02459 #ifdef ULLong
    02460             ys = *sx++ * (ULLong)q + carry;
    02461             carry = ys >> 32;
    02462             y = *bx - (ys & FFFFFFFF) - borrow;
    02463             borrow = y >> 32 & (ULong)1;
    02464             *bx++ = y & FFFFFFFF;
    02465 #else
    02466 #ifdef Pack_32
    02467             si = *sx++;
    02468             ys = (si & 0xffff) * q + carry;
    02469             zs = (si >> 16) * q + (ys >> 16);
    02470             carry = zs >> 16;
    02471             y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
    02472             borrow = (y & 0x10000) >> 16;
    02473             z = (*bx >> 16) - (zs & 0xffff) - borrow;
    02474             borrow = (z & 0x10000) >> 16;
    02475             Storeinc(bx, z, y);
    02476 #else
    02477             ys = *sx++ * q + carry;
    02478             carry = ys >> 16;
    02479             y = *bx - (ys & 0xffff) - borrow;
    02480             borrow = (y & 0x10000) >> 16;
    02481             *bx++ = y & 0xffff;
    02482 #endif
    02483 #endif
    02484             }
    02485             while(sx <= sxe);
    02486         if (!*bxe) {
    02487             bx = b->x;
    02488             while(--bxe > bx && !*bxe)
    02489                 --n;
    02490             b->wds = n;
    02491             }
    02492         }
    02493     if (cmp(b, S) >= 0) {
    02494         q++;
    02495         borrow = 0;
    02496         carry = 0;
    02497         bx = b->x;
    02498         sx = S->x;
    02499         do {
    02500 #ifdef ULLong
    02501             ys = *sx++ + carry;
    02502             carry = ys >> 32;
    02503             y = *bx - (ys & FFFFFFFF) - borrow;
    02504             borrow = y >> 32 & (ULong)1;
    02505             *bx++ = y & FFFFFFFF;
    02506 #else
    02507 #ifdef Pack_32
    02508             si = *sx++;
    02509             ys = (si & 0xffff) + carry;
    02510             zs = (si >> 16) + (ys >> 16);
    02511             carry = zs >> 16;
    02512             y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
    02513             borrow = (y & 0x10000) >> 16;
    02514             z = (*bx >> 16) - (zs & 0xffff) - borrow;
    02515             borrow = (z & 0x10000) >> 16;
    02516             Storeinc(bx, z, y);
    02517 #else
    02518             ys = *sx++ + carry;
    02519             carry = ys >> 16;
    02520             y = *bx - (ys & 0xffff) - borrow;
    02521             borrow = (y & 0x10000) >> 16;
    02522             *bx++ = y & 0xffff;
    02523 #endif
    02524 #endif
    02525             }
    02526             while(sx <= sxe);
    02527         bx = b->x;
    02528         bxe = bx + n;
    02529         if (!*bxe) {
    02530             while(--bxe > bx && !*bxe)
    02531                 --n;
    02532             b->wds = n;
    02533             }
    02534         }
    02535     return q;
    02536     }
    02537
    02538 #ifndef MULTIPLE_THREADS
    02539  static char *dtoa_result;
    02540 #endif
    02541
    02542  static char *
    02543 #ifdef KR_headers
    02544 rv_alloc(i) int i;
    02545 #else
    02546 rv_alloc(int i)
    02547 #endif
    02548 {
    02549     int j, k, *r;
    02550
    02551     j = sizeof(ULong);
    02552     for(k = 0;
    02553         sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= (unsigned)i;
    02554         j <<= 1)
    02555             k++;
    02556     r = (int*)Balloc(k);
    02557     *r = k;
    02558     return
    02559 #ifndef MULTIPLE_THREADS
    02560     dtoa_result =
    02561 #endif
    02562         (char *)(r+1);
    02563     }
    02564
    02565  static char *
    02566 #ifdef KR_headers
    02567 nrv_alloc(s, rve, n) char *s, **rve; int n;
    02568 #else
    02569 nrv_alloc(CONST char *s, char **rve, int n)
    02570 #endif
    02571 {
    02572     char *rv, *t;
    02573
    02574     t = rv = rv_alloc(n);
    02575     while((*t = *s++)) t++;
    02576     if (rve)
    02577         *rve = t;
    02578     return rv;
    02579     }
    02580
    02581 /* freedtoa(s) must be used to free values s returned by dtoa
    02582  * when MULTIPLE_THREADS is #defined.  It should be used in all cases,
    02583  * but for consistency with earlier versions of dtoa, it is optional
    02584  * when MULTIPLE_THREADS is not defined.
    02585  */
    02586
    02587  void
    02588 #ifdef KR_headers
    02589 kjs_freedtoa(s) char *s;
    02590 #else
    02591 kjs_freedtoa(char *s)
    02592 #endif
    02593 {
    02594     Bigint *b = (Bigint *)((int *)s - 1);
    02595     b->maxwds = 1 << (b->k = *(int*)b);
    02596     Bfree(b);
    02597 #ifndef MULTIPLE_THREADS
    02598     if (s == dtoa_result)
    02599         dtoa_result = 0;
    02600 #endif
    02601     }
    02602
    02603 /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
    02604  *
    02605  * Inspired by "How to Print Floating-Point Numbers Accurately" by
    02606  * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 92-101].
    02607  *
    02608  * Modifications:
    02609  *  1. Rather than iterating, we use a simple numeric overestimate
    02610  *     to determine k = floor(log10(d)).  We scale relevant
    02611  *     quantities using O(log2(k)) rather than O(k) multiplications.
    02612  *  2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
    02613  *     try to generate digits strictly left to right.  Instead, we
    02614  *     compute with fewer bits and propagate the carry if necessary
    02615  *     when rounding the final digit up.  This is often faster.
    02616  *  3. Under the assumption that input will be rounded nearest,
    02617  *     mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
    02618  *     That is, we allow equality in stopping tests when the
    02619  *     round-nearest rule will give the same floating-point value
    02620  *     as would satisfaction of the stopping test with strict
    02621  *     inequality.
    02622  *  4. We remove common factors of powers of 2 from relevant
    02623  *     quantities.
    02624  *  5. When converting floating-point integers less than 1e16,
    02625  *     we use floating-point arithmetic rather than resorting
    02626  *     to multiple-precision integers.
    02627  *  6. When asked to produce fewer than 15 digits, we first try
    02628  *     to get by with floating-point arithmetic; we resort to
    02629  *     multiple-precision integer arithmetic only if we cannot
    02630  *     guarantee that the floating-point calculation has given
    02631  *     the correctly rounded result.  For k requested digits and
    02632  *     "uniformly" distributed input, the probability is
    02633  *     something like 10^(k-15) that we must resort to the Long
    02634  *     calculation.
    02635  */
    02636
    02637  char *
    02638 kjs_dtoa
    02639 #ifdef KR_headers
    02640     (d, mode, ndigits, decpt, sign, rve)
    02641     double d; int mode, ndigits, *decpt, *sign; char **rve;
    02642 #else
    02643     (double d, int mode, int ndigits, int *decpt, int *sign, char **rve)
    02644 #endif
    02645 {
    02646  /* Arguments ndigits, decpt, sign are similar to those
    02647     of ecvt and fcvt; trailing zeros are suppressed from
    02648     the returned string.  If not null, *rve is set to point
    02649     to the end of the return value.  If d is +-Infinity or NaN,
    02650     then *decpt is set to 9999.
    02651
    02652     mode:
    02653         0 ==> shortest string that yields d when read in
    02654             and rounded to nearest.
    02655         1 ==> like 0, but with Steele & White stopping rule;
    02656             e.g. with IEEE P754 arithmetic , mode 0 gives
    02657             1e23 whereas mode 1 gives 9.999999999999999e22.
    02658         2 ==> max(1,ndigits) significant digits.  This gives a
    02659             return value similar to that of ecvt, except
    02660             that trailing zeros are suppressed.
    02661         3 ==> through ndigits past the decimal point.  This
    02662             gives a return value similar to that from fcvt,
    02663             except that trailing zeros are suppressed, and
    02664             ndigits can be negative.
    02665         4,5 ==> similar to 2 and 3, respectively, but (in
    02666             round-nearest mode) with the tests of mode 0 to
    02667             possibly return a shorter string that rounds to d.
    02668             With IEEE arithmetic and compilation with
    02669             -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
    02670             as modes 2 and 3 when FLT_ROUNDS != 1.
    02671         6-9 ==> Debugging modes similar to mode - 4:  don't try
    02672             fast floating-point estimate (if applicable).
    02673
    02674         Values of mode other than 0-9 are treated as mode 0.
    02675
    02676         Sufficient space is allocated to the return value
    02677         to hold the suppressed trailing zeros.
    02678     */
    02679
    02680     int bbits, b2, b5, be, dig, i, ieps, ilim = 0, ilim0, ilim1 = 0,
    02681         j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
    02682         spec_case, try_quick;
    02683     Long L;
    02684 #ifndef Sudden_Underflow
    02685     int denorm;
    02686     ULong x;
    02687 #endif
    02688     Bigint *b, *b1, *delta, *mlo = NULL, *mhi, *S;
    02689     double d2, ds, eps;
    02690     char *s, *s0;
    02691 #ifdef Honor_FLT_ROUNDS
    02692     int rounding;
    02693 #endif
    02694 #ifdef SET_INEXACT
    02695     int inexact, oldinexact;
    02696 #endif
    02697
    02698 #ifndef MULTIPLE_THREADS
    02699     if (dtoa_result) {
    02700         kjs_freedtoa(dtoa_result);
    02701         dtoa_result = 0;
    02702         }
    02703 #endif
    02704
    02705     if (word0(d) & Sign_bit) {
    02706         /* set sign for everything, including 0's and NaNs */
    02707         *sign = 1;
    02708         word0(d) &= ~Sign_bit;  /* clear sign bit */
    02709         }
    02710     else
    02711         *sign = 0;
    02712
    02713 #if defined(IEEE_Arith) + defined(VAX)
    02714 #ifdef IEEE_Arith
    02715     if ((word0(d) & Exp_mask) == Exp_mask)
    02716 #else
    02717     if (word0(d)  == 0x8000)
    02718 #endif
    02719         {
    02720         /* Infinity or NaN */
    02721         *decpt = 9999;
    02722 #ifdef IEEE_Arith
    02723         if (!word1(d) && !(word0(d) & 0xfffff))
    02724             return nrv_alloc("Infinity", rve, 8);
    02725 #endif
    02726         return nrv_alloc("NaN", rve, 3);
    02727         }
    02728 #endif
    02729 #ifdef IBM
    02730     dval(d) += 0; /* normalize */
    02731 #endif
    02732     if (!dval(d)) {
    02733         *decpt = 1;
    02734         return nrv_alloc("0", rve, 1);
    02735         }
    02736
    02737 #ifdef SET_INEXACT
    02738     try_quick = oldinexact = get_inexact();
    02739     inexact = 1;
    02740 #endif
    02741 #ifdef Honor_FLT_ROUNDS
    02742     if ((rounding = Flt_Rounds) >= 2) {
    02743         if (*sign)
    02744             rounding = rounding == 2 ? 0 : 2;
    02745         else
    02746             if (rounding != 2)
    02747                 rounding = 0;
    02748         }
    02749 #endif
    02750
    02751     b = d2b(dval(d), &be, &bbits);
    02752 #ifdef Sudden_Underflow
    02753     i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
    02754 #else
    02755     if ((i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1)))) {
    02756 #endif
    02757         dval(d2) = dval(d);
    02758         word0(d2) &= Frac_mask1;
    02759         word0(d2) |= Exp_11;
    02760 #ifdef IBM
    02761         if (j = 11 - hi0bits(word0(d2) & Frac_mask))
    02762             dval(d2) /= 1 << j;
    02763 #endif
    02764
    02765         /* log(x)   ~=~ log(1.5) + (x-1.5)/1.5
    02766          * log10(x)  =  log(x) / log(10)
    02767          *      ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
    02768          * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
    02769          *
    02770          * This suggests computing an approximation k to log10(d) by
    02771          *
    02772          * k = (i - Bias)*0.301029995663981
    02773          *  + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
    02774          *
    02775          * We want k to be too large rather than too small.
    02776          * The error in the first-order Taylor series approximation
    02777          * is in our favor, so we just round up the constant enough
    02778          * to compensate for any error in the multiplication of
    02779          * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
    02780          * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
    02781          * adding 1e-13 to the constant term more than suffices.
    02782          * Hence we adjust the constant term to 0.1760912590558.
    02783          * (We could get a more accurate k by invoking log10,
    02784          *  but this is probably not worthwhile.)
    02785          */
    02786
    02787         i -= Bias;
    02788 #ifdef IBM
    02789         i <<= 2;
    02790         i += j;
    02791 #endif
    02792 #ifndef Sudden_Underflow
    02793         denorm = 0;
    02794         }
    02795     else {
    02796         /* d is denormalized */
    02797
    02798         i = bbits + be + (Bias + (P-1) - 1);
    02799         x = i > 32  ? word0(d) << 64 - i | word1(d) >> i - 32
    02800                 : word1(d) << 32 - i;
    02801         dval(d2) = x;
    02802         word0(d2) -= 31*Exp_msk1; /* adjust exponent */
    02803         i -= (Bias + (P-1) - 1) + 1;
    02804         denorm = 1;
    02805         }
    02806 #endif
    02807     ds = (dval(d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
    02808     k = (int)ds;
    02809     if (ds < 0. && ds != k)
    02810         k--;    /* want k = floor(ds) */
    02811     k_check = 1;
    02812     if (k >= 0 && k <= Ten_pmax) {
    02813         if (dval(d) < tens[k])
    02814             k--;
    02815         k_check = 0;
    02816         }
    02817     j = bbits - i - 1;
    02818     if (j >= 0) {
    02819         b2 = 0;
    02820         s2 = j;
    02821         }
    02822     else {
    02823         b2 = -j;
    02824         s2 = 0;
    02825         }
    02826     if (k >= 0) {
    02827         b5 = 0;
    02828         s5 = k;
    02829         s2 += k;
    02830         }
    02831     else {
    02832         b2 -= k;
    02833         b5 = -k;
    02834         s5 = 0;
    02835         }
    02836     if (mode < 0 || mode > 9)
    02837         mode = 0;
    02838
    02839 #ifndef SET_INEXACT
    02840 #ifdef Check_FLT_ROUNDS
    02841     try_quick = Rounding == 1;
    02842 #else
    02843     try_quick = 1;
    02844 #endif
    02845 #endif /*SET_INEXACT*/
    02846
    02847     if (mode > 5) {
    02848         mode -= 4;
    02849         try_quick = 0;
    02850         }
    02851     leftright = 1;
    02852     switch(mode) {
    02853         case 0:
    02854         case 1:
    02855             ilim = ilim1 = -1;
    02856             i = 18;
    02857             ndigits = 0;
    02858             break;
    02859         case 2:
    02860             leftright = 0;
    02861             /* no break */
    02862         case 4:
    02863             if (ndigits <= 0)
    02864                 ndigits = 1;
    02865             ilim = ilim1 = i = ndigits;
    02866             break;
    02867         case 3:
    02868             leftright = 0;
    02869             /* no break */
    02870         case 5:
    02871             i = ndigits + k + 1;
    02872             ilim = i;
    02873             ilim1 = i - 1;
    02874             if (i <= 0)
    02875                 i = 1;
    02876         }
    02877     s = s0 = rv_alloc(i);
    02878
    02879 #ifdef Honor_FLT_ROUNDS
    02880     if (mode > 1 && rounding != 1)
    02881         leftright = 0;
    02882 #endif
    02883
    02884     if (ilim >= 0 && ilim <= Quick_max && try_quick) {
    02885
    02886         /* Try to get by with floating-point arithmetic. */
    02887
    02888         i = 0;
    02889         dval(d2) = dval(d);
    02890         k0 = k;
    02891         ilim0 = ilim;
    02892         ieps = 2; /* conservative */
    02893         if (k > 0) {
    02894             ds = tens[k&0xf];
    02895             j = k >> 4;
    02896             if (j & Bletch) {
    02897                 /* prevent overflows */
    02898                 j &= Bletch - 1;
    02899                 dval(d) /= bigtens[n_bigtens-1];
    02900                 ieps++;
    02901                 }
    02902             for(; j; j >>= 1, i++)
    02903                 if (j & 1) {
    02904                     ieps++;
    02905                     ds *= bigtens[i];
    02906                     }
    02907             dval(d) /= ds;
    02908             }
    02909         else if ((j1 = -k)) {
    02910             dval(d) *= tens[j1 & 0xf];
    02911             for(j = j1 >> 4; j; j >>= 1, i++)
    02912                 if (j & 1) {
    02913                     ieps++;
    02914                     dval(d) *= bigtens[i];
    02915                     }
    02916             }
    02917         if (k_check && dval(d) < 1. && ilim > 0) {
    02918             if (ilim1 <= 0)
    02919                 goto fast_failed;
    02920             ilim = ilim1;
    02921             k--;
    02922             dval(d) *= 10.;
    02923             ieps++;
    02924             }
    02925         dval(eps) = ieps*dval(d) + 7.;
    02926         word0(eps) -= (P-1)*Exp_msk1;
    02927         if (ilim == 0) {
    02928             S = mhi = 0;
    02929             dval(d) -= 5.;
    02930             if (dval(d) > dval(eps))
    02931                 goto one_digit;
    02932             if (dval(d) < -dval(eps))
    02933                 goto no_digits;
    02934             goto fast_failed;
    02935             }
    02936 #ifndef No_leftright
    02937         if (leftright) {
    02938             /* Use Steele & White method of only
    02939              * generating digits needed.
    02940              */
    02941             dval(eps) = 0.5/tens[ilim-1] - dval(eps);
    02942             for(i = 0;;) {
    02943                 L = (long int)dval(d);
    02944                 dval(d) -= L;
    02945                 *s++ = '0' + (int)L;
    02946                 if (dval(d) < dval(eps))
    02947                     goto ret1;
    02948                 if (1. - dval(d) < dval(eps))
    02949                     goto bump_up;
    02950                 if (++i >= ilim)
    02951                     break;
    02952                 dval(eps) *= 10.;
    02953                 dval(d) *= 10.;
    02954                 }
    02955             }
    02956         else {
    02957 #endif
    02958             /* Generate ilim digits, then fix them up. */
    02959             dval(eps) *= tens[ilim-1];
    02960             for(i = 1;; i++, dval(d) *= 10.) {
    02961                 L = (Long)(dval(d));
    02962                 if (!(dval(d) -= L))
    02963                     ilim = i;
    02964                 *s++ = '0' + (int)L;
    02965                 if (i == ilim) {
    02966                     if (dval(d) > 0.5 + dval(eps))
    02967                         goto bump_up;
    02968                     else if (dval(d) < 0.5 - dval(eps)) {
    02969                         while(*--s == '0');
    02970                         s++;
    02971                         goto ret1;
    02972                         }
    02973                     break;
    02974                     }
    02975                 }
    02976 #ifndef No_leftright
    02977             }
    02978 #endif
    02979  fast_failed:
    02980         s = s0;
    02981         dval(d) = dval(d2);
    02982         k = k0;
    02983         ilim = ilim0;
    02984         }
    02985
    02986     /* Do we have a "small" integer? */
    02987
    02988     if (be >= 0 && k <= Int_max) {
    02989         /* Yes. */
    02990         ds = tens[k];
    02991         if (ndigits < 0 && ilim <= 0) {
    02992             S = mhi = 0;
    02993             if (ilim < 0 || dval(d) <= 5*ds)
    02994                 goto no_digits;
    02995             goto one_digit;
    02996             }
    02997         for(i = 1;; i++, dval(d) *= 10.) {
    02998             L = (Long)(dval(d) / ds);
    02999             dval(d) -= L*ds;
    03000 #ifdef Check_FLT_ROUNDS
    03001             /* If FLT_ROUNDS == 2, L will usually be high by 1 */
    03002             if (dval(d) < 0) {
    03003                 L--;
    03004                 dval(d) += ds;
    03005                 }
    03006 #endif
    03007             *s++ = '0' + (int)L;
    03008             if (!dval(d)) {
    03009 #ifdef SET_INEXACT
    03010                 inexact = 0;
    03011 #endif
    03012                 break;
    03013                 }
    03014             if (i == ilim) {
    03015 #ifdef Honor_FLT_ROUNDS
    03016                 if (mode > 1)
    03017                 switch(rounding) {
    03018                   case 0: goto ret1;
    03019                   case 2: goto bump_up;
    03020                   }
    03021 #endif
    03022                 dval(d) += dval(d);
    03023                 if (dval(d) > ds || dval(d) == ds && L & 1) {
    03024  bump_up:
    03025                     while(*--s == '9')
    03026                         if (s == s0) {
    03027                             k++;
    03028                             *s = '0';
    03029                             break;
    03030                             }
    03031                     ++*s++;
    03032                     }
    03033                 break;
    03034                 }
    03035             }
    03036         goto ret1;
    03037         }
    03038
    03039     m2 = b2;
    03040     m5 = b5;
    03041     mhi = mlo = 0;
    03042     if (leftright) {
    03043         i =
    03044 #ifndef Sudden_Underflow
    03045             denorm ? be + (Bias + (P-1) - 1 + 1) :
    03046 #endif
    03047 #ifdef IBM
    03048             1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
    03049 #else
    03050             1 + P - bbits;
    03051 #endif
    03052         b2 += i;
    03053         s2 += i;
    03054         mhi = i2b(1);
    03055         }
    03056     if (m2 > 0 && s2 > 0) {
    03057         i = m2 < s2 ? m2 : s2;
    03058         b2 -= i;
    03059         m2 -= i;
    03060         s2 -= i;
    03061         }
    03062     if (b5 > 0) {
    03063         if (leftright) {
    03064             if (m5 > 0) {
    03065                 mhi = pow5mult(mhi, m5);
    03066                 b1 = mult(mhi, b);
    03067                 Bfree(b);
    03068                 b = b1;
    03069                 }
    03070             if ((j = b5 - m5))
    03071                 b = pow5mult(b, j);
    03072             }
    03073         else
    03074             b = pow5mult(b, b5);
    03075         }
    03076     S = i2b(1);
    03077     if (s5 > 0)
    03078         S = pow5mult(S, s5);
    03079
    03080     /* Check for special case that d is a normalized power of 2. */
    03081
    03082     spec_case = 0;
    03083     if ((mode < 2 || leftright)
    03084 #ifdef Honor_FLT_ROUNDS
    03085             && rounding == 1
    03086 #endif
    03087                 ) {
    03088         if (!word1(d) && !(word0(d) & Bndry_mask)
    03089 #ifndef Sudden_Underflow
    03090          && word0(d) & (Exp_mask & ~Exp_msk1)
    03091 #endif
    03092                 ) {
    03093             /* The special case */
    03094             b2 += Log2P;
    03095             s2 += Log2P;
    03096             spec_case = 1;
    03097             }
    03098         }
    03099
    03100     /* Arrange for convenient computation of quotients:
    03101      * shift left if necessary so divisor has 4 leading 0 bits.
    03102      *
    03103      * Perhaps we should just compute leading 28 bits of S once
    03104      * and for all and pass them and a shift to quorem, so it
    03105      * can do shifts and ors to compute the numerator for q.
    03106      */
    03107 #ifdef Pack_32
    03108     if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f))
    03109         i = 32 - i;
    03110 #else
    03111     if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf)
    03112         i = 16 - i;
    03113 #endif
    03114     if (i > 4) {
    03115         i -= 4;
    03116         b2 += i;
    03117         m2 += i;
    03118         s2 += i;
    03119         }
    03120     else if (i < 4) {
    03121         i += 28;
    03122         b2 += i;
    03123         m2 += i;
    03124         s2 += i;
    03125         }
    03126     if (b2 > 0)
    03127         b = lshift(b, b2);
    03128     if (s2 > 0)
    03129         S = lshift(S, s2);
    03130     if (k_check) {
    03131         if (cmp(b,S) < 0) {
    03132             k--;
    03133             b = multadd(b, 10, 0);  /* we botched the k estimate */
    03134             if (leftright)
    03135                 mhi = multadd(mhi, 10, 0);
    03136             ilim = ilim1;
    03137             }
    03138         }
    03139     if (ilim <= 0 && (mode == 3 || mode == 5)) {
    03140         if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) {
    03141             /* no digits, fcvt style */
    03142  no_digits:
    03143             k = -1 - ndigits;
    03144             goto ret;
    03145             }
    03146  one_digit:
    03147         *s++ = '1';
    03148         k++;
    03149         goto ret;
    03150         }
    03151     if (leftright) {
    03152         if (m2 > 0)
    03153             mhi = lshift(mhi, m2);
    03154
    03155         /* Compute mlo -- check for special case
    03156          * that d is a normalized power of 2.
    03157          */
    03158
    03159         mlo = mhi;
    03160         if (spec_case) {
    03161             mhi = Balloc(mhi->k);
    03162             Bcopy(mhi, mlo);
    03163             mhi = lshift(mhi, Log2P);
    03164             }
    03165
    03166         for(i = 1;;i++) {
    03167             dig = quorem(b,S) + '0';
    03168             /* Do we yet have the shortest decimal string
    03169              * that will round to d?
    03170              */
    03171             j = cmp(b, mlo);
    03172             delta = diff(S, mhi);
    03173             j1 = delta->sign ? 1 : cmp(b, delta);
    03174             Bfree(delta);
    03175 #ifndef ROUND_BIASED
    03176             if (j1 == 0 && mode != 1 && !(word1(d) & 1)
    03177 #ifdef Honor_FLT_ROUNDS
    03178                 && rounding >= 1
    03179 #endif
    03180                                    ) {
    03181                 if (dig == '9')
    03182                     goto round_9_up;
    03183                 if (j > 0)
    03184                     dig++;
    03185 #ifdef SET_INEXACT
    03186                 else if (!b->x[0] && b->wds <= 1)
    03187                     inexact = 0;
    03188 #endif
    03189                 *s++ = dig;
    03190                 goto ret;
    03191                 }
    03192 #endif
    03193             if (j < 0 || j == 0 && mode != 1
    03194 #ifndef ROUND_BIASED
    03195                             && !(word1(d) & 1)
    03196 #endif
    03197                     ) {
    03198                 if (!b->x[0] && b->wds <= 1) {
    03199 #ifdef SET_INEXACT
    03200                     inexact = 0;
    03201 #endif
    03202                     goto accept_dig;
    03203                     }
    03204 #ifdef Honor_FLT_ROUNDS
    03205                 if (mode > 1)
    03206                  switch(rounding) {
    03207                   case 0: goto accept_dig;
    03208                   case 2: goto keep_dig;
    03209                   }
    03210 #endif /*Honor_FLT_ROUNDS*/
    03211                 if (j1 > 0) {
    03212                     b = lshift(b, 1);
    03213                     j1 = cmp(b, S);
    03214                     if ((j1 > 0 || j1 == 0 && dig & 1)
    03215                     && dig++ == '9')
    03216                         goto round_9_up;
    03217                     }
    03218  accept_dig:
    03219                 *s++ = dig;
    03220                 goto ret;
    03221                 }
    03222             if (j1 > 0) {
    03223 #ifdef Honor_FLT_ROUNDS
    03224                 if (!rounding)
    03225                     goto accept_dig;
    03226 #endif
    03227                 if (dig == '9') { /* possible if i == 1 */
    03228  round_9_up:
    03229                     *s++ = '9';
    03230                     goto roundoff;
    03231                     }
    03232                 *s++ = dig + 1;
    03233                 goto ret;
    03234                 }
    03235 #ifdef Honor_FLT_ROUNDS
    03236  keep_dig:
    03237 #endif
    03238             *s++ = dig;
    03239             if (i == ilim)
    03240                 break;
    03241             b = multadd(b, 10, 0);
    03242             if (mlo == mhi)
    03243                 mlo = mhi = multadd(mhi, 10, 0);
    03244             else {
    03245                 mlo = multadd(mlo, 10, 0);
    03246                 mhi = multadd(mhi, 10, 0);
    03247                 }
    03248             }
    03249         }
    03250     else
    03251         for(i = 1;; i++) {
    03252             *s++ = dig = quorem(b,S) + '0';
    03253             if (!b->x[0] && b->wds <= 1) {
    03254 #ifdef SET_INEXACT
    03255                 inexact = 0;
    03256 #endif
    03257                 goto ret;
    03258                 }
    03259             if (i >= ilim)
    03260                 break;
    03261             b = multadd(b, 10, 0);
    03262             }
    03263
    03264     /* Round off last digit */
    03265
    03266 #ifdef Honor_FLT_ROUNDS
    03267     switch(rounding) {
    03268       case 0: goto trimzeros;
    03269       case 2: goto roundoff;
    03270       }
    03271 #endif
    03272     b = lshift(b, 1);
    03273     j = cmp(b, S);
    03274     if (j > 0 || j == 0 && dig & 1) {
    03275  roundoff:
    03276         while(*--s == '9')
    03277             if (s == s0) {
    03278                 k++;
    03279                 *s++ = '1';
    03280                 goto ret;
    03281                 }
    03282         ++*s++;
    03283         }
    03284     else {
    03285 #ifdef Honor_FLT_ROUNDS
    03286 trimzeros:
    03287 #endif
    03288         while(*--s == '0');
    03289         s++;
    03290         }
    03291  ret:
    03292     Bfree(S);
    03293     if (mhi) {
    03294         if (mlo && mlo != mhi)
    03295             Bfree(mlo);
    03296         Bfree(mhi);
    03297         }
    03298  ret1:
    03299 #ifdef SET_INEXACT
    03300     if (inexact) {
    03301         if (!oldinexact) {
    03302             word0(d) = Exp_1 + (70 << Exp_shift);
    03303             word1(d) = 0;
    03304             dval(d) += 1.;
    03305             }
    03306         }
    03307     else if (!oldinexact)
    03308         clear_inexact();
    03309 #endif
    03310     Bfree(b);
    03311     *s = 0;
    03312     *decpt = k + 1;
    03313     if (rve)
    03314         *rve = s;
    03315     return s0;
    03316     }
    03317 #ifdef __cplusplus
    03318 }
    03319 #endif

This file is part of the documentation for kjs Library Version 3.4.1.
Documentation copyright © 1996-2004 the KDE developers.
Generated on Sat Jun 11 20:23:05 2005 by doxygen 1.4.1 written by Dimitri van Heesch, © 1997-2003