SphinxBase 0.6
src/libsphinxbase/util/dtoa.c
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 David M. Gay (dmg at acm dot org,
00021  * with " at " changed at "@" and " dot " changed to ".").      */
00022 
00023 /* On a machine with IEEE extended-precision registers, it is
00024  * necessary to specify double-precision (53-bit) rounding precision
00025  * before invoking strtod or dtoa.  If the machine uses (the equivalent
00026  * of) Intel 80x87 arithmetic, the call
00027  *      _control87(PC_53, MCW_PC);
00028  * does this with many compilers.  Whether this or another call is
00029  * appropriate depends on the compiler; for this to work, it may be
00030  * necessary to #include "float.h" or another system-dependent header
00031  * file.
00032  */
00033 
00034 /* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
00035  *
00036  * This strtod returns a nearest machine number to the input decimal
00037  * string (or sets errno to ERANGE).  With IEEE arithmetic, ties are
00038  * broken by the IEEE round-even rule.  Otherwise ties are broken by
00039  * biased rounding (add half and chop).
00040  *
00041  * Inspired loosely by William D. Clinger's paper "How to Read Floating
00042  * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
00043  *
00044  * Modifications:
00045  *
00046  *      1. We only require IEEE, IBM, or VAX double-precision
00047  *              arithmetic (not IEEE double-extended).
00048  *      2. We get by with floating-point arithmetic in a case that
00049  *              Clinger missed -- when we're computing d * 10^n
00050  *              for a small integer d and the integer n is not too
00051  *              much larger than 22 (the maximum integer k for which
00052  *              we can represent 10^k exactly), we may be able to
00053  *              compute (d*10^k) * 10^(e-k) with just one roundoff.
00054  *      3. Rather than a bit-at-a-time adjustment of the binary
00055  *              result in the hard case, we use floating-point
00056  *              arithmetic to determine the adjustment to within
00057  *              one bit; only in really hard cases do we need to
00058  *              compute a second residual.
00059  *      4. Because of 3., we don't need a large table of powers of 10
00060  *              for ten-to-e (just some small tables, e.g. of 10^k
00061  *              for 0 <= k <= 22).
00062  */
00063 
00064 /*
00065  * This file has been modified to remove dtoa() and all
00066  * non-reentrancy.  This makes it slower, but it also makes life a lot
00067  * easier on Windows and other platforms without static lock
00068  * initializers (grumble).
00069  */
00070 
00071 /* Added by dhuggins@cs.cmu.edu to use autoconf results. */
00072 /* We do not care about the VAX. */
00073 #include "config.h"
00074 #ifdef WORDS_BIGENDIAN
00075 #define IEEE_MC68k
00076 #else
00077 #define IEEE_8087
00078 #endif
00079 #ifndef HAVE_LONG_LONG
00080 #define NO_LONG_LONG
00081 #endif
00082 #define Omit_Private_Memory
00083 #include "sphinxbase/ckd_alloc.h"
00084 #undef USE_LOCALE
00085 
00086 /* Correct totally bogus typedefs in this code. */
00087 #include "sphinxbase/prim_type.h"
00088 #define Long int32   /* ZOMG */
00089 #define ULong uint32 /* WTF */
00090 
00091 /*
00092  * #define IEEE_8087 for IEEE-arithmetic machines where the least
00093  *      significant byte has the lowest address.
00094  * #define IEEE_MC68k for IEEE-arithmetic machines where the most
00095  *      significant byte has the lowest address.
00096  * #define Long int on machines with 32-bit ints and 64-bit longs.
00097  * #define IBM for IBM mainframe-style floating-point arithmetic.
00098  * #define VAX for VAX-style floating-point arithmetic (D_floating).
00099  * #define No_leftright to omit left-right logic in fast floating-point
00100  *      computation of dtoa.
00101  * #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
00102  *      and strtod and dtoa should round accordingly.
00103  * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
00104  *      and Honor_FLT_ROUNDS is not #defined.
00105  * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
00106  *      that use extended-precision instructions to compute rounded
00107  *      products and quotients) with IBM.
00108  * #define ROUND_BIASED for IEEE-format with biased rounding.
00109  * #define Inaccurate_Divide for IEEE-format with correctly rounded
00110  *      products but inaccurate quotients, e.g., for Intel i860.
00111  * #define NO_LONG_LONG on machines that do not have a "long long"
00112  *      integer type (of >= 64 bits).  On such machines, you can
00113  *      #define Just_16 to store 16 bits per 32-bit Long when doing
00114  *      high-precision integer arithmetic.  Whether this speeds things
00115  *      up or slows things down depends on the machine and the number
00116  *      being converted.  If long long is available and the name is
00117  *      something other than "long long", #define Llong to be the name,
00118  *      and if "unsigned Llong" does not work as an unsigned version of
00119  *      Llong, #define #ULLong to be the corresponding unsigned type.
00120  * #define KR_headers for old-style C function headers.
00121  * #define Bad_float_h if your system lacks a float.h or if it does not
00122  *      define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
00123  *      FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
00124  * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
00125  *      if memory is available and otherwise does something you deem
00126  *      appropriate.  If MALLOC is undefined, malloc will be invoked
00127  *      directly -- and assumed always to succeed.
00128  * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making
00129  *      memory allocations from a private pool of memory when possible.
00130  *      When used, the private pool is PRIVATE_MEM bytes long:  2304 bytes,
00131  *      unless #defined to be a different length.  This default length
00132  *      suffices to get rid of MALLOC calls except for unusual cases,
00133  *      such as decimal-to-binary conversion of a very long string of
00134  *      digits.  The longest string dtoa can return is about 751 bytes
00135  *      long.  For conversions by strtod of strings of 800 digits and
00136  *      all dtoa conversions in single-threaded executions with 8-byte
00137  *      pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte
00138  *      pointers, PRIVATE_MEM >= 7112 appears adequate.
00139  * #define NO_INFNAN_CHECK if you do not wish to have INFNAN_CHECK
00140  *      #defined automatically on IEEE systems.  On such systems,
00141  *      when INFNAN_CHECK is #defined, strtod checks
00142  *      for Infinity and NaN (case insensitively).  On some systems
00143  *      (e.g., some HP systems), it may be necessary to #define NAN_WORD0
00144  *      appropriately -- to the most significant word of a quiet NaN.
00145  *      (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)
00146  *      When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined,
00147  *      strtod also accepts (case insensitively) strings of the form
00148  *      NaN(x), where x is a string of hexadecimal digits and spaces;
00149  *      if there is only one string of hexadecimal digits, it is taken
00150  *      for the 52 fraction bits of the resulting NaN; if there are two
00151  *      or more strings of hex digits, the first is for the high 20 bits,
00152  *      the second and subsequent for the low 32 bits, with intervening
00153  *      white space ignored; but if this results in none of the 52
00154  *      fraction bits being on (an IEEE Infinity symbol), then NAN_WORD0
00155  *      and NAN_WORD1 are used instead.
00156  * #define MULTIPLE_THREADS if the system offers preemptively scheduled
00157  *      multiple threads.  In this case, you must provide (or suitably
00158  *      #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed
00159  *      by FREE_DTOA_LOCK(n) for n = 0 or 1.  (The second lock, accessed
00160  *      in pow5mult, ensures lazy evaluation of only one copy of high
00161  *      powers of 5; omitting this lock would introduce a small
00162  *      probability of wasting memory, but would otherwise be harmless.)
00163  *      You must also invoke freedtoa(s) to free the value s returned by
00164  *      dtoa.  You may do so whether or not MULTIPLE_THREADS is #defined.
00165  * #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that
00166  *      avoids underflows on inputs whose result does not underflow.
00167  *      If you #define NO_IEEE_Scale on a machine that uses IEEE-format
00168  *      floating-point numbers and flushes underflows to zero rather
00169  *      than implementing gradual underflow, then you must also #define
00170  *      Sudden_Underflow.
00171  * #define YES_ALIAS to permit aliasing certain double values with
00172  *      arrays of ULongs.  This leads to slightly better code with
00173  *      some compilers and was always used prior to 19990916, but it
00174  *      is not strictly legal and can cause trouble with aggressively
00175  *      optimizing compilers (e.g., gcc 2.95.1 under -O2).
00176  * #define USE_LOCALE to use the current locale's decimal_point value.
00177  * #define SET_INEXACT if IEEE arithmetic is being used and extra
00178  *      computation should be done to set the inexact flag when the
00179  *      result is inexact and avoid setting inexact when the result
00180  *      is exact.  In this case, dtoa.c must be compiled in
00181  *      an environment, perhaps provided by #include "dtoa.c" in a
00182  *      suitable wrapper, that defines two functions,
00183  *              int get_inexact(void);
00184  *              void clear_inexact(void);
00185  *      such that get_inexact() returns a nonzero value if the
00186  *      inexact bit is already set, and clear_inexact() sets the
00187  *      inexact bit to 0.  When SET_INEXACT is #defined, strtod
00188  *      also does extra computations to set the underflow and overflow
00189  *      flags when appropriate (i.e., when the result is tiny and
00190  *      inexact or when it is a numeric value rounded to +-infinity).
00191  * #define NO_ERRNO if strtod should not assign errno = ERANGE when
00192  *      the result overflows to +-Infinity or underflows to 0.
00193  */
00194 
00195 #ifndef Long
00196 #define Long long
00197 #endif
00198 #ifndef ULong
00199 typedef unsigned Long ULong;
00200 #endif
00201 
00202 #ifdef DEBUG
00203 #include "stdio.h"
00204 #define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
00205 #endif
00206 
00207 #include "stdlib.h"
00208 #include "string.h"
00209 
00210 #ifdef USE_LOCALE
00211 #include "locale.h"
00212 #endif
00213 
00214 /* Private memory and other non-reentrant stuff removed. */
00215 
00216 #undef IEEE_Arith
00217 #undef Avoid_Underflow
00218 #ifdef IEEE_MC68k
00219 #define IEEE_Arith
00220 #endif
00221 #ifdef IEEE_8087
00222 #define IEEE_Arith
00223 #endif
00224 
00225 #ifdef IEEE_Arith
00226 #ifndef NO_INFNAN_CHECK
00227 #undef INFNAN_CHECK
00228 #define INFNAN_CHECK
00229 #endif
00230 #else
00231 #undef INFNAN_CHECK
00232 #endif
00233 
00234 #include "errno.h"
00235 
00236 #ifdef Bad_float_h
00237 
00238 #ifdef IEEE_Arith
00239 #define DBL_DIG 15
00240 #define DBL_MAX_10_EXP 308
00241 #define DBL_MAX_EXP 1024
00242 #define FLT_RADIX 2
00243 #endif /*IEEE_Arith*/
00244 
00245 #ifdef IBM
00246 #define DBL_DIG 16
00247 #define DBL_MAX_10_EXP 75
00248 #define DBL_MAX_EXP 63
00249 #define FLT_RADIX 16
00250 #define DBL_MAX 7.2370055773322621e+75
00251 #endif
00252 
00253 #ifdef VAX
00254 #define DBL_DIG 16
00255 #define DBL_MAX_10_EXP 38
00256 #define DBL_MAX_EXP 127
00257 #define FLT_RADIX 2
00258 #define DBL_MAX 1.7014118346046923e+38
00259 #endif
00260 
00261 #ifndef LONG_MAX
00262 #define LONG_MAX 2147483647
00263 #endif
00264 
00265 #else /* ifndef Bad_float_h */
00266 #include "float.h"
00267 #endif /* Bad_float_h */
00268 
00269 #ifndef __MATH_H__
00270 #include "math.h"
00271 #endif
00272 
00273 #ifdef __cplusplus
00274 extern "C" {
00275 #endif
00276 
00277 #ifndef CONST
00278 #ifdef KR_headers
00279 #define CONST /* blank */
00280 #else
00281 #define CONST const
00282 #endif
00283 #endif
00284 
00285 
00286 #if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1
00287 Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined.
00288 #endif
00289 
00291 typedef union { double d; ULong L[2]; } U;
00292 
00293 #ifdef YES_ALIAS
00294 #define dval(x) x
00295 #ifdef IEEE_8087
00296 #define word0(x) ((ULong *)&x)[1]
00297 #define word1(x) ((ULong *)&x)[0]
00298 #else
00299 #define word0(x) ((ULong *)&x)[0]
00300 #define word1(x) ((ULong *)&x)[1]
00301 #endif
00302 #else
00303 #ifdef IEEE_8087
00304 #define word0(x) ((U*)&x)->L[1]
00305 #define word1(x) ((U*)&x)->L[0]
00306 #else
00307 #define word0(x) ((U*)&x)->L[0]
00308 #define word1(x) ((U*)&x)->L[1]
00309 #endif
00310 #define dval(x) ((U*)&x)->d
00311 #endif
00312 
00313 /* The following definition of Storeinc is appropriate for MIPS processors.
00314  * An alternative that might be better on some machines is
00315  * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
00316  */
00317 #if defined(IEEE_8087) + defined(VAX)
00318 #define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
00319 ((unsigned short *)a)[0] = (unsigned short)c, a++)
00320 #else
00321 #define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
00322 ((unsigned short *)a)[1] = (unsigned short)c, a++)
00323 #endif
00324 
00325 /* #define P DBL_MANT_DIG */
00326 /* Ten_pmax = floor(P*log(2)/log(5)) */
00327 /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
00328 /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
00329 /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
00330 
00331 #ifdef IEEE_Arith
00332 #define Exp_shift  20
00333 #define Exp_shift1 20
00334 #define Exp_msk1    0x100000
00335 #define Exp_msk11   0x100000
00336 #define Exp_mask  0x7ff00000
00337 #define P 53
00338 #define Bias 1023
00339 #define Emin (-1022)
00340 #define Exp_1  0x3ff00000
00341 #define Exp_11 0x3ff00000
00342 #define Ebits 11
00343 #define Frac_mask  0xfffff
00344 #define Frac_mask1 0xfffff
00345 #define Ten_pmax 22
00346 #define Bletch 0x10
00347 #define Bndry_mask  0xfffff
00348 #define Bndry_mask1 0xfffff
00349 #define LSB 1
00350 #define Sign_bit 0x80000000
00351 #define Log2P 1
00352 #define Tiny0 0
00353 #define Tiny1 1
00354 #define Quick_max 14
00355 #define Int_max 14
00356 #ifndef NO_IEEE_Scale
00357 #define Avoid_Underflow
00358 #ifdef Flush_Denorm     /* debugging option */
00359 #undef Sudden_Underflow
00360 #endif
00361 #endif
00362 
00363 #ifndef Flt_Rounds
00364 #ifdef FLT_ROUNDS
00365 #define Flt_Rounds FLT_ROUNDS
00366 #else
00367 #define Flt_Rounds 1
00368 #endif
00369 #endif /*Flt_Rounds*/
00370 
00371 #ifdef Honor_FLT_ROUNDS
00372 #define Rounding rounding
00373 #undef Check_FLT_ROUNDS
00374 #define Check_FLT_ROUNDS
00375 #else
00376 #define Rounding Flt_Rounds
00377 #endif
00378 
00379 #else /* ifndef IEEE_Arith */
00380 #undef Check_FLT_ROUNDS
00381 #undef Honor_FLT_ROUNDS
00382 #undef SET_INEXACT
00383 #undef  Sudden_Underflow
00384 #define Sudden_Underflow
00385 #ifdef IBM
00386 #undef Flt_Rounds
00387 #define Flt_Rounds 0
00388 #define Exp_shift  24
00389 #define Exp_shift1 24
00390 #define Exp_msk1   0x1000000
00391 #define Exp_msk11  0x1000000
00392 #define Exp_mask  0x7f000000
00393 #define P 14
00394 #define Bias 65
00395 #define Exp_1  0x41000000
00396 #define Exp_11 0x41000000
00397 #define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
00398 #define Frac_mask  0xffffff
00399 #define Frac_mask1 0xffffff
00400 #define Bletch 4
00401 #define Ten_pmax 22
00402 #define Bndry_mask  0xefffff
00403 #define Bndry_mask1 0xffffff
00404 #define LSB 1
00405 #define Sign_bit 0x80000000
00406 #define Log2P 4
00407 #define Tiny0 0x100000
00408 #define Tiny1 0
00409 #define Quick_max 14
00410 #define Int_max 15
00411 #else /* VAX */
00412 #undef Flt_Rounds
00413 #define Flt_Rounds 1
00414 #define Exp_shift  23
00415 #define Exp_shift1 7
00416 #define Exp_msk1    0x80
00417 #define Exp_msk11   0x800000
00418 #define Exp_mask  0x7f80
00419 #define P 56
00420 #define Bias 129
00421 #define Exp_1  0x40800000
00422 #define Exp_11 0x4080
00423 #define Ebits 8
00424 #define Frac_mask  0x7fffff
00425 #define Frac_mask1 0xffff007f
00426 #define Ten_pmax 24
00427 #define Bletch 2
00428 #define Bndry_mask  0xffff007f
00429 #define Bndry_mask1 0xffff007f
00430 #define LSB 0x10000
00431 #define Sign_bit 0x8000
00432 #define Log2P 1
00433 #define Tiny0 0x80
00434 #define Tiny1 0
00435 #define Quick_max 15
00436 #define Int_max 15
00437 #endif /* IBM, VAX */
00438 #endif /* IEEE_Arith */
00439 
00440 #ifndef IEEE_Arith
00441 #define ROUND_BIASED
00442 #endif
00443 
00444 #ifdef RND_PRODQUOT
00445 #define rounded_product(a,b) a = rnd_prod(a, b)
00446 #define rounded_quotient(a,b) a = rnd_quot(a, b)
00447 #ifdef KR_headers
00448 extern double rnd_prod(), rnd_quot();
00449 #else
00450 extern double rnd_prod(double, double), rnd_quot(double, double);
00451 #endif
00452 #else
00453 #define rounded_product(a,b) a *= b
00454 #define rounded_quotient(a,b) a /= b
00455 #endif
00456 
00457 #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
00458 #define Big1 0xffffffff
00459 
00460 #ifndef Pack_32
00461 #define Pack_32
00462 #endif
00463 
00464 #ifdef KR_headers
00465 #define FFFFFFFF ((((unsigned long)0xffff)<<16)|(unsigned long)0xffff)
00466 #else
00467 #define FFFFFFFF 0xffffffffUL
00468 #endif
00469 
00470 #ifdef NO_LONG_LONG
00471 #undef ULLong
00472 #ifdef Just_16
00473 #undef Pack_32
00474 /* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
00475  * This makes some inner loops simpler and sometimes saves work
00476  * during multiplications, but it often seems to make things slightly
00477  * slower.  Hence the default is now to store 32 bits per Long.
00478  */
00479 #endif
00480 #else   /* long long available */
00481 #ifndef Llong
00482 #define Llong long long
00483 #endif
00484 #ifndef ULLong
00485 #define ULLong unsigned Llong
00486 #endif
00487 #endif /* NO_LONG_LONG */
00488 
00489 #ifndef MULTIPLE_THREADS
00490 #define ACQUIRE_DTOA_LOCK(n)    /*nothing*/
00491 #define FREE_DTOA_LOCK(n)       /*nothing*/
00492 #endif
00493 
00494 #define Kmax 15
00495 
00496 #ifdef __cplusplus
00497 extern "C" double sb_strtod(const char *s00, char **se);
00498 #endif
00499 
00500  struct
00501 Bigint {
00502         struct Bigint *next;
00503         int k, maxwds, sign, wds;
00504         ULong x[1];
00505         };
00506 
00507  typedef struct Bigint Bigint;
00508 
00509  static Bigint *
00510 Balloc
00511 #ifdef KR_headers
00512         (k) int k;
00513 #else
00514         (int k)
00515 #endif
00516 {
00517         int x;
00518         size_t len;
00519         Bigint *rv;
00520 
00521         x = 1 << k;
00522         len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)
00523                 /sizeof(double);
00524         rv = ckd_malloc(len*sizeof(double));
00525         rv->k = k;
00526         rv->maxwds = x;
00527         rv->sign = rv->wds = 0;
00528         return rv;
00529 }
00530 
00531  static void
00532 Bfree
00533 #ifdef KR_headers
00534         (v) Bigint *v;
00535 #else
00536         (Bigint *v)
00537 #endif
00538 {
00539         ckd_free(v);
00540 }
00541 
00542 #define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
00543 y->wds*sizeof(Long) + 2*sizeof(int))
00544 
00545  static Bigint *
00546 multadd
00547 #ifdef KR_headers
00548         (b, m, a) Bigint *b; int m, a;
00549 #else
00550         (Bigint *b, int m, int a)       /* multiply by m and add a */
00551 #endif
00552 {
00553         int i, wds;
00554 #ifdef ULLong
00555         ULong *x;
00556         ULLong carry, y;
00557 #else
00558         ULong carry, *x, y;
00559 #ifdef Pack_32
00560         ULong xi, z;
00561 #endif
00562 #endif
00563         Bigint *b1;
00564 
00565         wds = b->wds;
00566         x = b->x;
00567         i = 0;
00568         carry = a;
00569         do {
00570 #ifdef ULLong
00571                 y = *x * (ULLong)m + carry;
00572                 carry = y >> 32;
00573                 *x++ = y & FFFFFFFF;
00574 #else
00575 #ifdef Pack_32
00576                 xi = *x;
00577                 y = (xi & 0xffff) * m + carry;
00578                 z = (xi >> 16) * m + (y >> 16);
00579                 carry = z >> 16;
00580                 *x++ = (z << 16) + (y & 0xffff);
00581 #else
00582                 y = *x * m + carry;
00583                 carry = y >> 16;
00584                 *x++ = y & 0xffff;
00585 #endif
00586 #endif
00587                 }
00588                 while(++i < wds);
00589         if (carry) {
00590                 if (wds >= b->maxwds) {
00591                         b1 = Balloc(b->k+1);
00592                         Bcopy(b1, b);
00593                         Bfree(b);
00594                         b = b1;
00595                         }
00596                 b->x[wds++] = carry;
00597                 b->wds = wds;
00598                 }
00599         return b;
00600         }
00601 
00602  static Bigint *
00603 s2b
00604 #ifdef KR_headers
00605         (s, nd0, nd, y9) CONST char *s; int nd0, nd; ULong y9;
00606 #else
00607         (CONST char *s, int nd0, int nd, ULong y9)
00608 #endif
00609 {
00610         Bigint *b;
00611         int i, k;
00612         Long x, y;
00613 
00614         x = (nd + 8) / 9;
00615         for(k = 0, y = 1; x > y; y <<= 1, k++) ;
00616 #ifdef Pack_32
00617         b = Balloc(k);
00618         b->x[0] = y9;
00619         b->wds = 1;
00620 #else
00621         b = Balloc(k+1);
00622         b->x[0] = y9 & 0xffff;
00623         b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
00624 #endif
00625 
00626         i = 9;
00627         if (9 < nd0) {
00628                 s += 9;
00629                 do b = multadd(b, 10, *s++ - '0');
00630                         while(++i < nd0);
00631                 s++;
00632                 }
00633         else
00634                 s += 10;
00635         for(; i < nd; i++)
00636                 b = multadd(b, 10, *s++ - '0');
00637         return b;
00638         }
00639 
00640  static int
00641 hi0bits
00642 #ifdef KR_headers
00643         (x) register ULong x;
00644 #else
00645         (register ULong x)
00646 #endif
00647 {
00648         register int k = 0;
00649 
00650         if (!(x & 0xffff0000)) {
00651                 k = 16;
00652                 x <<= 16;
00653                 }
00654         if (!(x & 0xff000000)) {
00655                 k += 8;
00656                 x <<= 8;
00657                 }
00658         if (!(x & 0xf0000000)) {
00659                 k += 4;
00660                 x <<= 4;
00661                 }
00662         if (!(x & 0xc0000000)) {
00663                 k += 2;
00664                 x <<= 2;
00665                 }
00666         if (!(x & 0x80000000)) {
00667                 k++;
00668                 if (!(x & 0x40000000))
00669                         return 32;
00670                 }
00671         return k;
00672         }
00673 
00674  static int
00675 lo0bits
00676 #ifdef KR_headers
00677         (y) ULong *y;
00678 #else
00679         (ULong *y)
00680 #endif
00681 {
00682         register int k;
00683         register ULong x = *y;
00684 
00685         if (x & 7) {
00686                 if (x & 1)
00687                         return 0;
00688                 if (x & 2) {
00689                         *y = x >> 1;
00690                         return 1;
00691                         }
00692                 *y = x >> 2;
00693                 return 2;
00694                 }
00695         k = 0;
00696         if (!(x & 0xffff)) {
00697                 k = 16;
00698                 x >>= 16;
00699                 }
00700         if (!(x & 0xff)) {
00701                 k += 8;
00702                 x >>= 8;
00703                 }
00704         if (!(x & 0xf)) {
00705                 k += 4;
00706                 x >>= 4;
00707                 }
00708         if (!(x & 0x3)) {
00709                 k += 2;
00710                 x >>= 2;
00711                 }
00712         if (!(x & 1)) {
00713                 k++;
00714                 x >>= 1;
00715                 if (!x)
00716                         return 32;
00717                 }
00718         *y = x;
00719         return k;
00720         }
00721 
00722  static Bigint *
00723 i2b
00724 #ifdef KR_headers
00725         (i) int i;
00726 #else
00727         (int i)
00728 #endif
00729 {
00730         Bigint *b;
00731 
00732         b = Balloc(1);
00733         b->x[0] = i;
00734         b->wds = 1;
00735         return b;
00736         }
00737 
00738  static Bigint *
00739 mult
00740 #ifdef KR_headers
00741         (a, b) Bigint *a, *b;
00742 #else
00743         (Bigint *a, Bigint *b)
00744 #endif
00745 {
00746         Bigint *c;
00747         int k, wa, wb, wc;
00748         ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
00749         ULong y;
00750 #ifdef ULLong
00751         ULLong carry, z;
00752 #else
00753         ULong carry, z;
00754 #ifdef Pack_32
00755         ULong z2;
00756 #endif
00757 #endif
00758 
00759         if (a->wds < b->wds) {
00760                 c = a;
00761                 a = b;
00762                 b = c;
00763                 }
00764         k = a->k;
00765         wa = a->wds;
00766         wb = b->wds;
00767         wc = wa + wb;
00768         if (wc > a->maxwds)
00769                 k++;
00770         c = Balloc(k);
00771         for(x = c->x, xa = x + wc; x < xa; x++)
00772                 *x = 0;
00773         xa = a->x;
00774         xae = xa + wa;
00775         xb = b->x;
00776         xbe = xb + wb;
00777         xc0 = c->x;
00778 #ifdef ULLong
00779         for(; xb < xbe; xc0++) {
00780                 if ((y = *xb++)) {
00781                         x = xa;
00782                         xc = xc0;
00783                         carry = 0;
00784                         do {
00785                                 z = *x++ * (ULLong)y + *xc + carry;
00786                                 carry = z >> 32;
00787                                 *xc++ = z & FFFFFFFF;
00788                                 }
00789                                 while(x < xae);
00790                         *xc = carry;
00791                         }
00792                 }
00793 #else
00794 #ifdef Pack_32
00795         for(; xb < xbe; xb++, xc0++) {
00796                 if (y = *xb & 0xffff) {
00797                         x = xa;
00798                         xc = xc0;
00799                         carry = 0;
00800                         do {
00801                                 z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
00802                                 carry = z >> 16;
00803                                 z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
00804                                 carry = z2 >> 16;
00805                                 Storeinc(xc, z2, z);
00806                                 }
00807                                 while(x < xae);
00808                         *xc = carry;
00809                         }
00810                 if (y = *xb >> 16) {
00811                         x = xa;
00812                         xc = xc0;
00813                         carry = 0;
00814                         z2 = *xc;
00815                         do {
00816                                 z = (*x & 0xffff) * y + (*xc >> 16) + carry;
00817                                 carry = z >> 16;
00818                                 Storeinc(xc, z, z2);
00819                                 z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
00820                                 carry = z2 >> 16;
00821                                 }
00822                                 while(x < xae);
00823                         *xc = z2;
00824                         }
00825                 }
00826 #else
00827         for(; xb < xbe; xc0++) {
00828                 if (y = *xb++) {
00829                         x = xa;
00830                         xc = xc0;
00831                         carry = 0;
00832                         do {
00833                                 z = *x++ * y + *xc + carry;
00834                                 carry = z >> 16;
00835                                 *xc++ = z & 0xffff;
00836                                 }
00837                                 while(x < xae);
00838                         *xc = carry;
00839                         }
00840                 }
00841 #endif
00842 #endif
00843         for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
00844         c->wds = wc;
00845         return c;
00846         }
00847 
00848  static Bigint *
00849 pow5mult
00850 #ifdef KR_headers
00851         (b, k) Bigint *b; int k;
00852 #else
00853         (Bigint *b, int k)
00854 #endif
00855 {
00856         Bigint *b1, *p5, *p51;
00857         int i;
00858         static int CONST p05[3] = { 5, 25, 125 };
00859 
00860         if ((i = k & 3))
00861                 b = multadd(b, p05[i-1], 0);
00862 
00863         if (!(k >>= 2))
00864                 return b;
00865 
00866         p5 = i2b(625);
00867         for(;;) {
00868                 if (k & 1) {
00869                         b1 = mult(b, p5);
00870                         Bfree(b);
00871                         b = b1;
00872                 }
00873                 if (!(k >>= 1))
00874                         break;
00875                 p51 = mult(p5,p5);
00876                 Bfree(p5);
00877                 p5 = p51;
00878         }
00879         Bfree(p5);
00880         return b;
00881 }
00882 
00883  static Bigint *
00884 lshift
00885 #ifdef KR_headers
00886         (b, k) Bigint *b; int k;
00887 #else
00888         (Bigint *b, int k)
00889 #endif
00890 {
00891         int i, k1, n, n1;
00892         Bigint *b1;
00893         ULong *x, *x1, *xe, z;
00894 
00895 #ifdef Pack_32
00896         n = k >> 5;
00897 #else
00898         n = k >> 4;
00899 #endif
00900         k1 = b->k;
00901         n1 = n + b->wds + 1;
00902         for(i = b->maxwds; n1 > i; i <<= 1)
00903                 k1++;
00904         b1 = Balloc(k1);
00905         x1 = b1->x;
00906         for(i = 0; i < n; i++)
00907                 *x1++ = 0;
00908         x = b->x;
00909         xe = x + b->wds;
00910 #ifdef Pack_32
00911         if (k &= 0x1f) {
00912                 k1 = 32 - k;
00913                 z = 0;
00914                 do {
00915                         *x1++ = *x << k | z;
00916                         z = *x++ >> k1;
00917                         }
00918                         while(x < xe);
00919                 if ((*x1 = z))
00920                         ++n1;
00921                 }
00922 #else
00923         if (k &= 0xf) {
00924                 k1 = 16 - k;
00925                 z = 0;
00926                 do {
00927                         *x1++ = *x << k  & 0xffff | z;
00928                         z = *x++ >> k1;
00929                         }
00930                         while(x < xe);
00931                 if (*x1 = z)
00932                         ++n1;
00933                 }
00934 #endif
00935         else do
00936                 *x1++ = *x++;
00937                 while(x < xe);
00938         b1->wds = n1 - 1;
00939         Bfree(b);
00940         return b1;
00941         }
00942 
00943  static int
00944 cmp
00945 #ifdef KR_headers
00946         (a, b) Bigint *a, *b;
00947 #else
00948         (Bigint *a, Bigint *b)
00949 #endif
00950 {
00951         ULong *xa, *xa0, *xb, *xb0;
00952         int i, j;
00953 
00954         i = a->wds;
00955         j = b->wds;
00956 #ifdef DEBUG
00957         if (i > 1 && !a->x[i-1])
00958                 Bug("cmp called with a->x[a->wds-1] == 0");
00959         if (j > 1 && !b->x[j-1])
00960                 Bug("cmp called with b->x[b->wds-1] == 0");
00961 #endif
00962         if (i -= j)
00963                 return i;
00964         xa0 = a->x;
00965         xa = xa0 + j;
00966         xb0 = b->x;
00967         xb = xb0 + j;
00968         for(;;) {
00969                 if (*--xa != *--xb)
00970                         return *xa < *xb ? -1 : 1;
00971                 if (xa <= xa0)
00972                         break;
00973                 }
00974         return 0;
00975         }
00976 
00977  static Bigint *
00978 diff
00979 #ifdef KR_headers
00980         (a, b) Bigint *a, *b;
00981 #else
00982         (Bigint *a, Bigint *b)
00983 #endif
00984 {
00985         Bigint *c;
00986         int i, wa, wb;
00987         ULong *xa, *xae, *xb, *xbe, *xc;
00988 #ifdef ULLong
00989         ULLong borrow, y;
00990 #else
00991         ULong borrow, y;
00992 #ifdef Pack_32
00993         ULong z;
00994 #endif
00995 #endif
00996 
00997         i = cmp(a,b);
00998         if (!i) {
00999                 c = Balloc(0);
01000                 c->wds = 1;
01001                 c->x[0] = 0;
01002                 return c;
01003                 }
01004         if (i < 0) {
01005                 c = a;
01006                 a = b;
01007                 b = c;
01008                 i = 1;
01009                 }
01010         else
01011                 i = 0;
01012         c = Balloc(a->k);
01013         c->sign = i;
01014         wa = a->wds;
01015         xa = a->x;
01016         xae = xa + wa;
01017         wb = b->wds;
01018         xb = b->x;
01019         xbe = xb + wb;
01020         xc = c->x;
01021         borrow = 0;
01022 #ifdef ULLong
01023         do {
01024                 y = (ULLong)*xa++ - *xb++ - borrow;
01025                 borrow = y >> 32 & (ULong)1;
01026                 *xc++ = y & FFFFFFFF;
01027                 }
01028                 while(xb < xbe);
01029         while(xa < xae) {
01030                 y = *xa++ - borrow;
01031                 borrow = y >> 32 & (ULong)1;
01032                 *xc++ = y & FFFFFFFF;
01033                 }
01034 #else
01035 #ifdef Pack_32
01036         do {
01037                 y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
01038                 borrow = (y & 0x10000) >> 16;
01039                 z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
01040                 borrow = (z & 0x10000) >> 16;
01041                 Storeinc(xc, z, y);
01042                 }
01043                 while(xb < xbe);
01044         while(xa < xae) {
01045                 y = (*xa & 0xffff) - borrow;
01046                 borrow = (y & 0x10000) >> 16;
01047                 z = (*xa++ >> 16) - borrow;
01048                 borrow = (z & 0x10000) >> 16;
01049                 Storeinc(xc, z, y);
01050                 }
01051 #else
01052         do {
01053                 y = *xa++ - *xb++ - borrow;
01054                 borrow = (y & 0x10000) >> 16;
01055                 *xc++ = y & 0xffff;
01056                 }
01057                 while(xb < xbe);
01058         while(xa < xae) {
01059                 y = *xa++ - borrow;
01060                 borrow = (y & 0x10000) >> 16;
01061                 *xc++ = y & 0xffff;
01062                 }
01063 #endif
01064 #endif
01065         while(!*--xc)
01066                 wa--;
01067         c->wds = wa;
01068         return c;
01069         }
01070 
01071  static double
01072 ulp
01073 #ifdef KR_headers
01074         (x) double x;
01075 #else
01076         (double x)
01077 #endif
01078 {
01079         register Long L;
01080         U a;
01081 
01082         L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
01083 #ifndef Avoid_Underflow
01084 #ifndef Sudden_Underflow
01085         if (L > 0) {
01086 #endif
01087 #endif
01088 #ifdef IBM
01089                 L |= Exp_msk1 >> 4;
01090 #endif
01091                 word0(a) = L;
01092                 word1(a) = 0;
01093 #ifndef Avoid_Underflow
01094 #ifndef Sudden_Underflow
01095                 }
01096         else {
01097                 L = -L >> Exp_shift;
01098                 if (L < Exp_shift) {
01099                         word0(a) = 0x80000 >> L;
01100                         word1(a) = 0;
01101                         }
01102                 else {
01103                         word0(a) = 0;
01104                         L -= Exp_shift;
01105                         word1(a) = L >= 31 ? 1 : 1 << 31 - L;
01106                         }
01107                 }
01108 #endif
01109 #endif
01110         return dval(a);
01111         }
01112 
01113  static double
01114 b2d
01115 #ifdef KR_headers
01116         (a, e) Bigint *a; int *e;
01117 #else
01118         (Bigint *a, int *e)
01119 #endif
01120 {
01121         ULong *xa, *xa0, w, y, z;
01122         int k;
01123         U d;
01124 #ifdef VAX
01125         ULong d0, d1;
01126 #else
01127 #define d0 word0(d)
01128 #define d1 word1(d)
01129 #endif
01130 
01131         xa0 = a->x;
01132         xa = xa0 + a->wds;
01133         y = *--xa;
01134 #ifdef DEBUG
01135         if (!y) Bug("zero y in b2d");
01136 #endif
01137         k = hi0bits(y);
01138         *e = 32 - k;
01139 #ifdef Pack_32
01140         if (k < Ebits) {
01141                 d0 = Exp_1 | y >> (Ebits - k);
01142                 w = xa > xa0 ? *--xa : 0;
01143                 d1 = y << ((32-Ebits) + k) | w >> (Ebits - k);
01144                 goto ret_d;
01145                 }
01146         z = xa > xa0 ? *--xa : 0;
01147         if (k -= Ebits) {
01148                 d0 = Exp_1 | y << k | z >> (32 - k);
01149                 y = xa > xa0 ? *--xa : 0;
01150                 d1 = z << k | y >> (32 - k);
01151                 }
01152         else {
01153                 d0 = Exp_1 | y;
01154                 d1 = z;
01155                 }
01156 #else
01157         if (k < Ebits + 16) {
01158                 z = xa > xa0 ? *--xa : 0;
01159                 d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
01160                 w = xa > xa0 ? *--xa : 0;
01161                 y = xa > xa0 ? *--xa : 0;
01162                 d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
01163                 goto ret_d;
01164                 }
01165         z = xa > xa0 ? *--xa : 0;
01166         w = xa > xa0 ? *--xa : 0;
01167         k -= Ebits + 16;
01168         d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
01169         y = xa > xa0 ? *--xa : 0;
01170         d1 = w << k + 16 | y << k;
01171 #endif
01172  ret_d:
01173 #ifdef VAX
01174         word0(d) = d0 >> 16 | d0 << 16;
01175         word1(d) = d1 >> 16 | d1 << 16;
01176 #else
01177 #undef d0
01178 #undef d1
01179 #endif
01180         return dval(d);
01181         }
01182 
01183  static Bigint *
01184 d2b
01185 #ifdef KR_headers
01186         (d, e, bits) double d; int *e, *bits;
01187 #else
01188         (double _d, int *e, int *bits)
01189 #endif
01190 {
01191         Bigint *b;
01192         int de, k;
01193         ULong *x, y, z;
01194         U d;
01195 #ifndef Sudden_Underflow
01196         int i;
01197 #endif
01198 #ifdef VAX
01199         ULong d0, d1;
01200         d0 = word0(d) >> 16 | word0(d) << 16;
01201         d1 = word1(d) >> 16 | word1(d) << 16;
01202 #else
01203 #define d0 word0(d)
01204 #define d1 word1(d)
01205 #endif
01206         dval(d) = _d;
01207 
01208 #ifdef Pack_32
01209         b = Balloc(1);
01210 #else
01211         b = Balloc(2);
01212 #endif
01213         x = b->x;
01214 
01215         z = d0 & Frac_mask;
01216         d0 &= 0x7fffffff;       /* clear sign bit, which we ignore */
01217 #ifdef Sudden_Underflow
01218         de = (int)(d0 >> Exp_shift);
01219 #ifndef IBM
01220         z |= Exp_msk11;
01221 #endif
01222 #else
01223         if ((de = (int)(d0 >> Exp_shift)))
01224                 z |= Exp_msk1;
01225 #endif
01226 #ifdef Pack_32
01227         if ((y = d1)) {
01228                 if ((k = lo0bits(&y))) {
01229                         x[0] = y | z << (32 - k);
01230                         z >>= k;
01231                         }
01232                 else
01233                         x[0] = y;
01234 #ifndef Sudden_Underflow
01235                 i =
01236 #endif
01237                     b->wds = (x[1] = z) ? 2 : 1;
01238                 }
01239         else {
01240 #ifdef DEBUG
01241                 if (!z)
01242                         Bug("Zero passed to d2b");
01243 #endif
01244                 k = lo0bits(&z);
01245                 x[0] = z;
01246 #ifndef Sudden_Underflow
01247                 i =
01248 #endif
01249                     b->wds = 1;
01250                 k += 32;
01251                 }
01252 #else
01253         if (y = d1) {
01254                 if (k = lo0bits(&y))
01255                         if (k >= 16) {
01256                                 x[0] = y | z << 32 - k & 0xffff;
01257                                 x[1] = z >> k - 16 & 0xffff;
01258                                 x[2] = z >> k;
01259                                 i = 2;
01260                                 }
01261                         else {
01262                                 x[0] = y & 0xffff;
01263                                 x[1] = y >> 16 | z << 16 - k & 0xffff;
01264                                 x[2] = z >> k & 0xffff;
01265                                 x[3] = z >> k+16;
01266                                 i = 3;
01267                                 }
01268                 else {
01269                         x[0] = y & 0xffff;
01270                         x[1] = y >> 16;
01271                         x[2] = z & 0xffff;
01272                         x[3] = z >> 16;
01273                         i = 3;
01274                         }
01275                 }
01276         else {
01277 #ifdef DEBUG
01278                 if (!z)
01279                         Bug("Zero passed to d2b");
01280 #endif
01281                 k = lo0bits(&z);
01282                 if (k >= 16) {
01283                         x[0] = z;
01284                         i = 0;
01285                         }
01286                 else {
01287                         x[0] = z & 0xffff;
01288                         x[1] = z >> 16;
01289                         i = 1;
01290                         }
01291                 k += 32;
01292                 }
01293         while(!x[i])
01294                 --i;
01295         b->wds = i + 1;
01296 #endif
01297 #ifndef Sudden_Underflow
01298         if (de) {
01299 #endif
01300 #ifdef IBM
01301                 *e = (de - Bias - (P-1) << 2) + k;
01302                 *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
01303 #else
01304                 *e = de - Bias - (P-1) + k;
01305                 *bits = P - k;
01306 #endif
01307 #ifndef Sudden_Underflow
01308                 }
01309         else {
01310                 *e = de - Bias - (P-1) + 1 + k;
01311 #ifdef Pack_32
01312                 *bits = 32*i - hi0bits(x[i-1]);
01313 #else
01314                 *bits = (i+2)*16 - hi0bits(x[i]);
01315 #endif
01316                 }
01317 #endif
01318         return b;
01319         }
01320 #undef d0
01321 #undef d1
01322 
01323  static double
01324 ratio
01325 #ifdef KR_headers
01326         (a, b) Bigint *a, *b;
01327 #else
01328         (Bigint *a, Bigint *b)
01329 #endif
01330 {
01331         U da, db;
01332         int k, ka, kb;
01333 
01334         dval(da) = b2d(a, &ka);
01335         dval(db) = b2d(b, &kb);
01336 #ifdef Pack_32
01337         k = ka - kb + 32*(a->wds - b->wds);
01338 #else
01339         k = ka - kb + 16*(a->wds - b->wds);
01340 #endif
01341 #ifdef IBM
01342         if (k > 0) {
01343                 word0(da) += (k >> 2)*Exp_msk1;
01344                 if (k &= 3)
01345                         dval(da) *= 1 << k;
01346                 }
01347         else {
01348                 k = -k;
01349                 word0(db) += (k >> 2)*Exp_msk1;
01350                 if (k &= 3)
01351                         dval(db) *= 1 << k;
01352                 }
01353 #else
01354         if (k > 0)
01355                 word0(da) += k*Exp_msk1;
01356         else {
01357                 k = -k;
01358                 word0(db) += k*Exp_msk1;
01359                 }
01360 #endif
01361         return dval(da) / dval(db);
01362         }
01363 
01364  static CONST double
01365 tens[] = {
01366                 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
01367                 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
01368                 1e20, 1e21, 1e22
01369 #ifdef VAX
01370                 , 1e23, 1e24
01371 #endif
01372                 };
01373 
01374  static CONST double
01375 #ifdef IEEE_Arith
01376 bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
01377 static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
01378 #ifdef Avoid_Underflow
01379                 9007199254740992.*9007199254740992.e-256
01380                 /* = 2^106 * 1e-53 */
01381 #else
01382                 1e-256
01383 #endif
01384                 };
01385 /* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
01386 /* flag unnecessarily.  It leads to a song and dance at the end of strtod. */
01387 #define Scale_Bit 0x10
01388 #define n_bigtens 5
01389 #else
01390 #ifdef IBM
01391 bigtens[] = { 1e16, 1e32, 1e64 };
01392 static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 };
01393 #define n_bigtens 3
01394 #else
01395 bigtens[] = { 1e16, 1e32 };
01396 static CONST double tinytens[] = { 1e-16, 1e-32 };
01397 #define n_bigtens 2
01398 #endif
01399 #endif
01400 
01401 #ifdef INFNAN_CHECK
01402 
01403 #ifndef NAN_WORD0
01404 #define NAN_WORD0 0x7ff80000
01405 #endif
01406 
01407 #ifndef NAN_WORD1
01408 #define NAN_WORD1 0
01409 #endif
01410 
01411  static int
01412 match
01413 #ifdef KR_headers
01414         (sp, t) char **sp, *t;
01415 #else
01416         (CONST char **sp, char *t)
01417 #endif
01418 {
01419         int c, d;
01420         CONST char *s = *sp;
01421 
01422         while((d = *t++)) {
01423                 if ((c = *++s) >= 'A' && c <= 'Z')
01424                         c += 'a' - 'A';
01425                 if (c != d)
01426                         return 0;
01427                 }
01428         *sp = s + 1;
01429         return 1;
01430         }
01431 
01432 #ifndef No_Hex_NaN
01433  static void
01434 hexnan
01435 #ifdef KR_headers
01436         (rvp, sp) double *rvp; CONST char **sp;
01437 #else
01438         (U *rvp, CONST char **sp)
01439 #endif
01440 {
01441         ULong c, x[2];
01442         CONST char *s;
01443         int havedig, udx0, xshift;
01444 
01445         x[0] = x[1] = 0;
01446         havedig = xshift = 0;
01447         udx0 = 1;
01448         s = *sp;
01449         /* allow optional initial 0x or 0X */
01450         while((c = *(CONST unsigned char*)(s+1)) && c <= ' ')
01451                 ++s;
01452         if (s[1] == '0' && (s[2] == 'x' || s[2] == 'X'))
01453                 s += 2;
01454         while((c = *(CONST unsigned char*)++s)) {
01455                 if (c >= '0' && c <= '9')
01456                         c -= '0';
01457                 else if (c >= 'a' && c <= 'f')
01458                         c += 10 - 'a';
01459                 else if (c >= 'A' && c <= 'F')
01460                         c += 10 - 'A';
01461                 else if (c <= ' ') {
01462                         if (udx0 && havedig) {
01463                                 udx0 = 0;
01464                                 xshift = 1;
01465                                 }
01466                         continue;
01467                         }
01468 #ifdef GDTOA_NON_PEDANTIC_NANCHECK
01469                 else if (/*(*/ c == ')' && havedig) {
01470                         *sp = s + 1;
01471                         break;
01472                         }
01473                 else
01474                         return; /* invalid form: don't change *sp */
01475 #else
01476                 else {
01477                         do {
01478                                 if (/*(*/ c == ')') {
01479                                         *sp = s + 1;
01480                                         break;
01481                                         }
01482                         } while((c = *++s));
01483                         break;
01484                 }
01485 #endif
01486                 havedig = 1;
01487                 if (xshift) {
01488                         xshift = 0;
01489                         x[0] = x[1];
01490                         x[1] = 0;
01491                         }
01492                 if (udx0)
01493                         x[0] = (x[0] << 4) | (x[1] >> 28);
01494                 x[1] = (x[1] << 4) | c;
01495                 }
01496         if ((x[0] &= 0xfffff) || x[1]) {
01497                 word0(*rvp) = Exp_mask | x[0];
01498                 word1(*rvp) = x[1];
01499                 }
01500         }
01501 #endif /*No_Hex_NaN*/
01502 #endif /* INFNAN_CHECK */
01503 
01504  double
01505 sb_strtod
01506 #ifdef KR_headers
01507         (s00, se) CONST char *s00; char **se;
01508 #else
01509         (CONST char *s00, char **se)
01510 #endif
01511 {
01512 #ifdef Avoid_Underflow
01513         int scale;
01514 #endif
01515         int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
01516                  e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
01517         CONST char *s, *s0, *s1;
01518         double aadj, adj;
01519         U rv, rv0, aadj1;
01520         Long L;
01521         ULong y, z;
01522         Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
01523 #ifdef SET_INEXACT
01524         int inexact, oldinexact;
01525 #endif
01526 #ifdef Honor_FLT_ROUNDS
01527         int rounding;
01528 #endif
01529 #ifdef USE_LOCALE
01530         CONST char *s2;
01531 #endif
01532 
01533         sign = nz0 = nz = 0;
01534         dval(rv) = 0.;
01535         for(s = s00;;s++) switch(*s) {
01536                 case '-':
01537                         sign = 1;
01538                         /* no break */
01539                 case '+':
01540                         if (*++s)
01541                                 goto break2;
01542                         /* no break */
01543                 case 0:
01544                         goto ret0;
01545                 case '\t':
01546                 case '\n':
01547                 case '\v':
01548                 case '\f':
01549                 case '\r':
01550                 case ' ':
01551                         continue;
01552                 default:
01553                         goto break2;
01554                 }
01555  break2:
01556         if (*s == '0') {
01557                 nz0 = 1;
01558                 while(*++s == '0') ;
01559                 if (!*s)
01560                         goto ret;
01561                 }
01562         s0 = s;
01563         y = z = 0;
01564         for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
01565                 if (nd < 9)
01566                         y = 10*y + c - '0';
01567                 else if (nd < 16)
01568                         z = 10*z + c - '0';
01569         nd0 = nd;
01570 #ifdef USE_LOCALE
01571         s1 = localeconv()->decimal_point;
01572         if (c == *s1) {
01573                 c = '.';
01574                 if (*++s1) {
01575                         s2 = s;
01576                         for(;;) {
01577                                 if (*++s2 != *s1) {
01578                                         c = 0;
01579                                         break;
01580                                         }
01581                                 if (!*++s1) {
01582                                         s = s2;
01583                                         break;
01584                                         }
01585                                 }
01586                         }
01587                 }
01588 #endif
01589         if (c == '.') {
01590                 c = *++s;
01591                 if (!nd) {
01592                         for(; c == '0'; c = *++s)
01593                                 nz++;
01594                         if (c > '0' && c <= '9') {
01595                                 s0 = s;
01596                                 nf += nz;
01597                                 nz = 0;
01598                                 goto have_dig;
01599                                 }
01600                         goto dig_done;
01601                         }
01602                 for(; c >= '0' && c <= '9'; c = *++s) {
01603  have_dig:
01604                         nz++;
01605                         if (c -= '0') {
01606                                 nf += nz;
01607                                 for(i = 1; i < nz; i++)
01608                                         if (nd++ < 9)
01609                                                 y *= 10;
01610                                         else if (nd <= DBL_DIG + 1)
01611                                                 z *= 10;
01612                                 if (nd++ < 9)
01613                                         y = 10*y + c;
01614                                 else if (nd <= DBL_DIG + 1)
01615                                         z = 10*z + c;
01616                                 nz = 0;
01617                                 }
01618                         }
01619                 }
01620  dig_done:
01621         e = 0;
01622         if (c == 'e' || c == 'E') {
01623                 if (!nd && !nz && !nz0) {
01624                         goto ret0;
01625                         }
01626                 s00 = s;
01627                 esign = 0;
01628                 switch(c = *++s) {
01629                         case '-':
01630                                 esign = 1;
01631                         case '+':
01632                                 c = *++s;
01633                         }
01634                 if (c >= '0' && c <= '9') {
01635                         while(c == '0')
01636                                 c = *++s;
01637                         if (c > '0' && c <= '9') {
01638                                 L = c - '0';
01639                                 s1 = s;
01640                                 while((c = *++s) >= '0' && c <= '9')
01641                                         L = 10*L + c - '0';
01642                                 if (s - s1 > 8 || L > 19999)
01643                                         /* Avoid confusion from exponents
01644                                          * so large that e might overflow.
01645                                          */
01646                                         e = 19999; /* safe for 16 bit ints */
01647                                 else
01648                                         e = (int)L;
01649                                 if (esign)
01650                                         e = -e;
01651                                 }
01652                         else
01653                                 e = 0;
01654                         }
01655                 else
01656                         s = s00;
01657                 }
01658         if (!nd) {
01659                 if (!nz && !nz0) {
01660 #ifdef INFNAN_CHECK
01661                         /* Check for Nan and Infinity */
01662                         switch(c) {
01663                           case 'i':
01664                           case 'I':
01665                                 if (match(&s,"nf")) {
01666                                         --s;
01667                                         if (!match(&s,"inity"))
01668                                                 ++s;
01669                                         word0(rv) = 0x7ff00000;
01670                                         word1(rv) = 0;
01671                                         goto ret;
01672                                         }
01673                                 break;
01674                           case 'n':
01675                           case 'N':
01676                                 if (match(&s, "an")) {
01677                                         word0(rv) = NAN_WORD0;
01678                                         word1(rv) = NAN_WORD1;
01679 #ifndef No_Hex_NaN
01680                                         if (*s == '(') /*)*/
01681                                                 hexnan(&rv, &s);
01682 #endif
01683                                         goto ret;
01684                                         }
01685                           }
01686 #endif /* INFNAN_CHECK */
01687  ret0:
01688                         s = s00;
01689                         sign = 0;
01690                         }
01691                 goto ret;
01692                 }
01693         e1 = e -= nf;
01694 
01695         /* Now we have nd0 digits, starting at s0, followed by a
01696          * decimal point, followed by nd-nd0 digits.  The number we're
01697          * after is the integer represented by those digits times
01698          * 10**e */
01699 
01700         if (!nd0)
01701                 nd0 = nd;
01702         k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
01703         dval(rv) = y;
01704         if (k > 9) {
01705 #ifdef SET_INEXACT
01706                 if (k > DBL_DIG)
01707                         oldinexact = get_inexact();
01708 #endif
01709                 dval(rv) = tens[k - 9] * dval(rv) + z;
01710                 }
01711         bd0 = 0;
01712         if (nd <= DBL_DIG
01713 #ifndef RND_PRODQUOT
01714 #ifndef Honor_FLT_ROUNDS
01715                 && Flt_Rounds == 1
01716 #endif
01717 #endif
01718                         ) {
01719                 if (!e)
01720                         goto ret;
01721                 if (e > 0) {
01722                         if (e <= Ten_pmax) {
01723 #ifdef VAX
01724                                 goto vax_ovfl_check;
01725 #else
01726 #ifdef Honor_FLT_ROUNDS
01727                                 /* round correctly FLT_ROUNDS = 2 or 3 */
01728                                 if (sign) {
01729                                         rv = -rv;
01730                                         sign = 0;
01731                                         }
01732 #endif
01733                                 /* rv = */ rounded_product(dval(rv), tens[e]);
01734                                 goto ret;
01735 #endif
01736                                 }
01737                         i = DBL_DIG - nd;
01738                         if (e <= Ten_pmax + i) {
01739                                 /* A fancier test would sometimes let us do
01740                                  * this for larger i values.
01741                                  */
01742 #ifdef Honor_FLT_ROUNDS
01743                                 /* round correctly FLT_ROUNDS = 2 or 3 */
01744                                 if (sign) {
01745                                         rv = -rv;
01746                                         sign = 0;
01747                                         }
01748 #endif
01749                                 e -= i;
01750                                 dval(rv) *= tens[i];
01751 #ifdef VAX
01752                                 /* VAX exponent range is so narrow we must
01753                                  * worry about overflow here...
01754                                  */
01755  vax_ovfl_check:
01756                                 word0(rv) -= P*Exp_msk1;
01757                                 /* rv = */ rounded_product(dval(rv), tens[e]);
01758                                 if ((word0(rv) & Exp_mask)
01759                                  > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
01760                                         goto ovfl;
01761                                 word0(rv) += P*Exp_msk1;
01762 #else
01763                                 /* rv = */ rounded_product(dval(rv), tens[e]);
01764 #endif
01765                                 goto ret;
01766                                 }
01767                         }
01768 #ifndef Inaccurate_Divide
01769                 else if (e >= -Ten_pmax) {
01770 #ifdef Honor_FLT_ROUNDS
01771                         /* round correctly FLT_ROUNDS = 2 or 3 */
01772                         if (sign) {
01773                                 rv = -rv;
01774                                 sign = 0;
01775                                 }
01776 #endif
01777                         /* rv = */ rounded_quotient(dval(rv), tens[-e]);
01778                         goto ret;
01779                         }
01780 #endif
01781                 }
01782         e1 += nd - k;
01783 
01784 #ifdef IEEE_Arith
01785 #ifdef SET_INEXACT
01786         inexact = 1;
01787         if (k <= DBL_DIG)
01788                 oldinexact = get_inexact();
01789 #endif
01790 #ifdef Avoid_Underflow
01791         scale = 0;
01792 #endif
01793 #ifdef Honor_FLT_ROUNDS
01794         if ((rounding = Flt_Rounds) >= 2) {
01795                 if (sign)
01796                         rounding = rounding == 2 ? 0 : 2;
01797                 else
01798                         if (rounding != 2)
01799                                 rounding = 0;
01800                 }
01801 #endif
01802 #endif /*IEEE_Arith*/
01803 
01804         /* Get starting approximation = rv * 10**e1 */
01805 
01806         if (e1 > 0) {
01807                 if ((i = e1 & 15))
01808                         dval(rv) *= tens[i];
01809                 if (e1 &= ~15) {
01810                         if (e1 > DBL_MAX_10_EXP) {
01811  ovfl:
01812 #ifndef NO_ERRNO
01813                                 errno = ERANGE;
01814 #endif
01815                                 /* Can't trust HUGE_VAL */
01816 #ifdef IEEE_Arith
01817 #ifdef Honor_FLT_ROUNDS
01818                                 switch(rounding) {
01819                                   case 0: /* toward 0 */
01820                                   case 3: /* toward -infinity */
01821                                         word0(rv) = Big0;
01822                                         word1(rv) = Big1;
01823                                         break;
01824                                   default:
01825                                         word0(rv) = Exp_mask;
01826                                         word1(rv) = 0;
01827                                   }
01828 #else /*Honor_FLT_ROUNDS*/
01829                                 word0(rv) = Exp_mask;
01830                                 word1(rv) = 0;
01831 #endif /*Honor_FLT_ROUNDS*/
01832 #ifdef SET_INEXACT
01833                                 /* set overflow bit */
01834                                 dval(rv0) = 1e300;
01835                                 dval(rv0) *= dval(rv0);
01836 #endif
01837 #else /*IEEE_Arith*/
01838                                 word0(rv) = Big0;
01839                                 word1(rv) = Big1;
01840 #endif /*IEEE_Arith*/
01841                                 if (bd0)
01842                                         goto retfree;
01843                                 goto ret;
01844                                 }
01845                         e1 >>= 4;
01846                         for(j = 0; e1 > 1; j++, e1 >>= 1)
01847                                 if (e1 & 1)
01848                                         dval(rv) *= bigtens[j];
01849                 /* The last multiplication could overflow. */
01850                         word0(rv) -= P*Exp_msk1;
01851                         dval(rv) *= bigtens[j];
01852                         if ((z = word0(rv) & Exp_mask)
01853                          > Exp_msk1*(DBL_MAX_EXP+Bias-P))
01854                                 goto ovfl;
01855                         if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
01856                                 /* set to largest number */
01857                                 /* (Can't trust DBL_MAX) */
01858                                 word0(rv) = Big0;
01859                                 word1(rv) = Big1;
01860                                 }
01861                         else
01862                                 word0(rv) += P*Exp_msk1;
01863                         }
01864                 }
01865         else if (e1 < 0) {
01866                 e1 = -e1;
01867                 if ((i = e1 & 15))
01868                         dval(rv) /= tens[i];
01869                 if (e1 >>= 4) {
01870                         if (e1 >= 1 << n_bigtens)
01871                                 goto undfl;
01872 #ifdef Avoid_Underflow
01873                         if (e1 & Scale_Bit)
01874                                 scale = 2*P;
01875                         for(j = 0; e1 > 0; j++, e1 >>= 1)
01876                                 if (e1 & 1)
01877                                         dval(rv) *= tinytens[j];
01878                         if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask)
01879                                                 >> Exp_shift)) > 0) {
01880                                 /* scaled rv is denormal; zap j low bits */
01881                                 if (j >= 32) {
01882                                         word1(rv) = 0;
01883                                         if (j >= 53)
01884                                          word0(rv) = (P+2)*Exp_msk1;
01885                                         else
01886                                                 word0(rv) &= 0xffffffff << (j-32);
01887                                         }
01888                                 else
01889                                         word1(rv) &= 0xffffffff << j;
01890                                 }
01891 #else
01892                         for(j = 0; e1 > 1; j++, e1 >>= 1)
01893                                 if (e1 & 1)
01894                                         dval(rv) *= tinytens[j];
01895                         /* The last multiplication could underflow. */
01896                         dval(rv0) = dval(rv);
01897                         dval(rv) *= tinytens[j];
01898                         if (!dval(rv)) {
01899                                 dval(rv) = 2.*dval(rv0);
01900                                 dval(rv) *= tinytens[j];
01901 #endif
01902                                 if (!dval(rv)) {
01903  undfl:
01904                                         dval(rv) = 0.;
01905 #ifndef NO_ERRNO
01906                                         errno = ERANGE;
01907 #endif
01908                                         if (bd0)
01909                                                 goto retfree;
01910                                         goto ret;
01911                                         }
01912 #ifndef Avoid_Underflow
01913                                 word0(rv) = Tiny0;
01914                                 word1(rv) = Tiny1;
01915                                 /* The refinement below will clean
01916                                  * this approximation up.
01917                                  */
01918                                 }
01919 #endif
01920                         }
01921                 }
01922 
01923         /* Now the hard part -- adjusting rv to the correct value.*/
01924 
01925         /* Put digits into bd: true value = bd * 10^e */
01926 
01927         bd0 = s2b(s0, nd0, nd, y);
01928 
01929         for(;;) {
01930                 bd = Balloc(bd0->k);
01931                 Bcopy(bd, bd0);
01932                 bb = d2b(dval(rv), &bbe, &bbbits);      /* rv = bb * 2^bbe */
01933                 bs = i2b(1);
01934 
01935                 if (e >= 0) {
01936                         bb2 = bb5 = 0;
01937                         bd2 = bd5 = e;
01938                         }
01939                 else {
01940                         bb2 = bb5 = -e;
01941                         bd2 = bd5 = 0;
01942                         }
01943                 if (bbe >= 0)
01944                         bb2 += bbe;
01945                 else
01946                         bd2 -= bbe;
01947                 bs2 = bb2;
01948 #ifdef Honor_FLT_ROUNDS
01949                 if (rounding != 1)
01950                         bs2++;
01951 #endif
01952 #ifdef Avoid_Underflow
01953                 j = bbe - scale;
01954                 i = j + bbbits - 1;     /* logb(rv) */
01955                 if (i < Emin)   /* denormal */
01956                         j += P - Emin;
01957                 else
01958                         j = P + 1 - bbbits;
01959 #else /*Avoid_Underflow*/
01960 #ifdef Sudden_Underflow
01961 #ifdef IBM
01962                 j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
01963 #else
01964                 j = P + 1 - bbbits;
01965 #endif
01966 #else /*Sudden_Underflow*/
01967                 j = bbe;
01968                 i = j + bbbits - 1;     /* logb(rv) */
01969                 if (i < Emin)   /* denormal */
01970                         j += P - Emin;
01971                 else
01972                         j = P + 1 - bbbits;
01973 #endif /*Sudden_Underflow*/
01974 #endif /*Avoid_Underflow*/
01975                 bb2 += j;
01976                 bd2 += j;
01977 #ifdef Avoid_Underflow
01978                 bd2 += scale;
01979 #endif
01980                 i = bb2 < bd2 ? bb2 : bd2;
01981                 if (i > bs2)
01982                         i = bs2;
01983                 if (i > 0) {
01984                         bb2 -= i;
01985                         bd2 -= i;
01986                         bs2 -= i;
01987                         }
01988                 if (bb5 > 0) {
01989                         bs = pow5mult(bs, bb5);
01990                         bb1 = mult(bs, bb);
01991                         Bfree(bb);
01992                         bb = bb1;
01993                         }
01994                 if (bb2 > 0)
01995                         bb = lshift(bb, bb2);
01996                 if (bd5 > 0)
01997                         bd = pow5mult(bd, bd5);
01998                 if (bd2 > 0)
01999                         bd = lshift(bd, bd2);
02000                 if (bs2 > 0)
02001                         bs = lshift(bs, bs2);
02002                 delta = diff(bb, bd);
02003                 dsign = delta->sign;
02004                 delta->sign = 0;
02005                 i = cmp(delta, bs);
02006 #ifdef Honor_FLT_ROUNDS
02007                 if (rounding != 1) {
02008                         if (i < 0) {
02009                                 /* Error is less than an ulp */
02010                                 if (!delta->x[0] && delta->wds <= 1) {
02011                                         /* exact */
02012 #ifdef SET_INEXACT
02013                                         inexact = 0;
02014 #endif
02015                                         break;
02016                                         }
02017                                 if (rounding) {
02018                                         if (dsign) {
02019                                                 adj = 1.;
02020                                                 goto apply_adj;
02021                                                 }
02022                                         }
02023                                 else if (!dsign) {
02024                                         adj = -1.;
02025                                         if (!word1(rv)
02026                                          && !(word0(rv) & Frac_mask)) {
02027                                                 y = word0(rv) & Exp_mask;
02028 #ifdef Avoid_Underflow
02029                                                 if (!scale || y > 2*P*Exp_msk1)
02030 #else
02031                                                 if (y)
02032 #endif
02033                                                   {
02034                                                   delta = lshift(delta,Log2P);
02035                                                   if (cmp(delta, bs) <= 0)
02036                                                         adj = -0.5;
02037                                                   }
02038                                                 }
02039  apply_adj:
02040 #ifdef Avoid_Underflow
02041                                         if (scale && (y = word0(rv) & Exp_mask)
02042                                                 <= 2*P*Exp_msk1)
02043                                           word0(adj) += (2*P+1)*Exp_msk1 - y;
02044 #else
02045 #ifdef Sudden_Underflow
02046                                         if ((word0(rv) & Exp_mask) <=
02047                                                         P*Exp_msk1) {
02048                                                 word0(rv) += P*Exp_msk1;
02049                                                 dval(rv) += adj*ulp(dval(rv));
02050                                                 word0(rv) -= P*Exp_msk1;
02051                                                 }
02052                                         else
02053 #endif /*Sudden_Underflow*/
02054 #endif /*Avoid_Underflow*/
02055                                         dval(rv) += adj*ulp(dval(rv));
02056                                         }
02057                                 break;
02058                                 }
02059                         adj = ratio(delta, bs);
02060                         if (adj < 1.)
02061                                 adj = 1.;
02062                         if (adj <= 0x7ffffffe) {
02063                                 /* adj = rounding ? ceil(adj) : floor(adj); */
02064                                 y = adj;
02065                                 if (y != adj) {
02066                                         if (!((rounding>>1) ^ dsign))
02067                                                 y++;
02068                                         adj = y;
02069                                         }
02070                                 }
02071 #ifdef Avoid_Underflow
02072                         if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
02073                                 word0(adj) += (2*P+1)*Exp_msk1 - y;
02074 #else
02075 #ifdef Sudden_Underflow
02076                         if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
02077                                 word0(rv) += P*Exp_msk1;
02078                                 adj *= ulp(dval(rv));
02079                                 if (dsign)
02080                                         dval(rv) += adj;
02081                                 else
02082                                         dval(rv) -= adj;
02083                                 word0(rv) -= P*Exp_msk1;
02084                                 goto cont;
02085                                 }
02086 #endif /*Sudden_Underflow*/
02087 #endif /*Avoid_Underflow*/
02088                         adj *= ulp(dval(rv));
02089                         if (dsign)
02090                                 dval(rv) += adj;
02091                         else
02092                                 dval(rv) -= adj;
02093                         goto cont;
02094                         }
02095 #endif /*Honor_FLT_ROUNDS*/
02096 
02097                 if (i < 0) {
02098                         /* Error is less than half an ulp -- check for
02099                          * special case of mantissa a power of two.
02100                          */
02101                         if (dsign || word1(rv) || word0(rv) & Bndry_mask
02102 #ifdef IEEE_Arith
02103 #ifdef Avoid_Underflow
02104                          || (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1
02105 #else
02106                          || (word0(rv) & Exp_mask) <= Exp_msk1
02107 #endif
02108 #endif
02109                                 ) {
02110 #ifdef SET_INEXACT
02111                                 if (!delta->x[0] && delta->wds <= 1)
02112                                         inexact = 0;
02113 #endif
02114                                 break;
02115                                 }
02116                         if (!delta->x[0] && delta->wds <= 1) {
02117                                 /* exact result */
02118 #ifdef SET_INEXACT
02119                                 inexact = 0;
02120 #endif
02121                                 break;
02122                                 }
02123                         delta = lshift(delta,Log2P);
02124                         if (cmp(delta, bs) > 0)
02125                                 goto drop_down;
02126                         break;
02127                         }
02128                 if (i == 0) {
02129                         /* exactly half-way between */
02130                         if (dsign) {
02131                                 if ((word0(rv) & Bndry_mask1) == Bndry_mask1
02132                                  &&  word1(rv) == (
02133 #ifdef Avoid_Underflow
02134                         (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
02135                 ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
02136 #endif
02137                                                    0xffffffff)) {
02138                                         /*boundary case -- increment exponent*/
02139                                         word0(rv) = (word0(rv) & Exp_mask)
02140                                                 + Exp_msk1
02141 #ifdef IBM
02142                                                 | Exp_msk1 >> 4
02143 #endif
02144                                                 ;
02145                                         word1(rv) = 0;
02146 #ifdef Avoid_Underflow
02147                                         dsign = 0;
02148 #endif
02149                                         break;
02150                                         }
02151                                 }
02152                         else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
02153  drop_down:
02154                                 /* boundary case -- decrement exponent */
02155 #ifdef Sudden_Underflow /*{{*/
02156                                 L = word0(rv) & Exp_mask;
02157 #ifdef IBM
02158                                 if (L <  Exp_msk1)
02159 #else
02160 #ifdef Avoid_Underflow
02161                                 if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
02162 #else
02163                                 if (L <= Exp_msk1)
02164 #endif /*Avoid_Underflow*/
02165 #endif /*IBM*/
02166                                         goto undfl;
02167                                 L -= Exp_msk1;
02168 #else /*Sudden_Underflow}{*/
02169 #ifdef Avoid_Underflow
02170                                 if (scale) {
02171                                         L = word0(rv) & Exp_mask;
02172                                         if (L <= (2*P+1)*Exp_msk1) {
02173                                                 if (L > (P+2)*Exp_msk1)
02174                                                         /* round even ==> */
02175                                                         /* accept rv */
02176                                                         break;
02177                                                 /* rv = smallest denormal */
02178                                                 goto undfl;
02179                                                 }
02180                                         }
02181 #endif /*Avoid_Underflow*/
02182                                 L = (word0(rv) & Exp_mask) - Exp_msk1;
02183 #endif /*Sudden_Underflow}}*/
02184                                 word0(rv) = L | Bndry_mask1;
02185                                 word1(rv) = 0xffffffff;
02186 #ifdef IBM
02187                                 goto cont;
02188 #else
02189                                 break;
02190 #endif
02191                                 }
02192 #ifndef ROUND_BIASED
02193                         if (!(word1(rv) & LSB))
02194                                 break;
02195 #endif
02196                         if (dsign)
02197                                 dval(rv) += ulp(dval(rv));
02198 #ifndef ROUND_BIASED
02199                         else {
02200                                 dval(rv) -= ulp(dval(rv));
02201 #ifndef Sudden_Underflow
02202                                 if (!dval(rv))
02203                                         goto undfl;
02204 #endif
02205                                 }
02206 #ifdef Avoid_Underflow
02207                         dsign = 1 - dsign;
02208 #endif
02209 #endif
02210                         break;
02211                         }
02212                 if ((aadj = ratio(delta, bs)) <= 2.) {
02213                         if (dsign)
02214                                 aadj = dval(aadj1) = 1.;
02215                         else if (word1(rv) || word0(rv) & Bndry_mask) {
02216 #ifndef Sudden_Underflow
02217                                 if (word1(rv) == Tiny1 && !word0(rv))
02218                                         goto undfl;
02219 #endif
02220                                 aadj = 1.;
02221                                 dval(aadj1) = -1.;
02222                                 }
02223                         else {
02224                                 /* special case -- power of FLT_RADIX to be */
02225                                 /* rounded down... */
02226 
02227                                 if (aadj < 2./FLT_RADIX)
02228                                         aadj = 1./FLT_RADIX;
02229                                 else
02230                                         aadj *= 0.5;
02231                                 dval(aadj1) = -aadj;
02232                                 }
02233                         }
02234                 else {
02235                         aadj *= 0.5;
02236                         dval(aadj1) = dsign ? aadj : -aadj;
02237 #ifdef Check_FLT_ROUNDS
02238                         switch(Rounding) {
02239                                 case 2: /* towards +infinity */
02240                                         dval(aadj1) -= 0.5;
02241                                         break;
02242                                 case 0: /* towards 0 */
02243                                 case 3: /* towards -infinity */
02244                                         dval(aadj1) += 0.5;
02245                                 }
02246 #else
02247                         if (Flt_Rounds == 0)
02248                                 dval(aadj1) += 0.5;
02249 #endif /*Check_FLT_ROUNDS*/
02250                         }
02251                 y = word0(rv) & Exp_mask;
02252 
02253                 /* Check for overflow */
02254 
02255                 if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
02256                         dval(rv0) = dval(rv);
02257                         word0(rv) -= P*Exp_msk1;
02258                         adj = dval(aadj1) * ulp(dval(rv));
02259                         dval(rv) += adj;
02260                         if ((word0(rv) & Exp_mask) >=
02261                                         Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
02262                                 if (word0(rv0) == Big0 && word1(rv0) == Big1)
02263                                         goto ovfl;
02264                                 word0(rv) = Big0;
02265                                 word1(rv) = Big1;
02266                                 goto cont;
02267                                 }
02268                         else
02269                                 word0(rv) += P*Exp_msk1;
02270                         }
02271                 else {
02272 #ifdef Avoid_Underflow
02273                         if (scale && y <= 2*P*Exp_msk1) {
02274                                 if (aadj <= 0x7fffffff) {
02275                                         if ((z = (uint32)aadj) <= 0)
02276                                                 z = 1;
02277                                         aadj = z;
02278                                         dval(aadj1) = dsign ? aadj : -aadj;
02279                                         }
02280                                 word0(aadj1) += (2*P+1)*Exp_msk1 - y;
02281                                 }
02282                         adj = dval(aadj1) * ulp(dval(rv));
02283                         dval(rv) += adj;
02284 #else
02285 #ifdef Sudden_Underflow
02286                         if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
02287                                 dval(rv0) = dval(rv);
02288                                 word0(rv) += P*Exp_msk1;
02289                                 adj = aadj1 * ulp(dval(rv));
02290                                 dval(rv) += adj;
02291 #ifdef IBM
02292                                 if ((word0(rv) & Exp_mask) <  P*Exp_msk1)
02293 #else
02294                                 if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
02295 #endif
02296                                         {
02297                                         if (word0(rv0) == Tiny0
02298                                          && word1(rv0) == Tiny1)
02299                                                 goto undfl;
02300                                         word0(rv) = Tiny0;
02301                                         word1(rv) = Tiny1;
02302                                         goto cont;
02303                                         }
02304                                 else
02305                                         word0(rv) -= P*Exp_msk1;
02306                                 }
02307                         else {
02308                                 adj = aadj1 * ulp(dval(rv));
02309                                 dval(rv) += adj;
02310                                 }
02311 #else /*Sudden_Underflow*/
02312                         /* Compute adj so that the IEEE rounding rules will
02313                          * correctly round rv + adj in some half-way cases.
02314                          * If rv * ulp(rv) is denormalized (i.e.,
02315                          * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
02316                          * trouble from bits lost to denormalization;
02317                          * example: 1.2e-307 .
02318                          */
02319                         if (y <= (P-1)*Exp_msk1 && aadj > 1.) {
02320                                 aadj1 = (double)(int)(aadj + 0.5);
02321                                 if (!dsign)
02322                                         aadj1 = -aadj1;
02323                                 }
02324                         adj = aadj1 * ulp(dval(rv));
02325                         dval(rv) += adj;
02326 #endif /*Sudden_Underflow*/
02327 #endif /*Avoid_Underflow*/
02328                         }
02329                 z = word0(rv) & Exp_mask;
02330 #ifndef SET_INEXACT
02331 #ifdef Avoid_Underflow
02332                 if (!scale)
02333 #endif
02334                 if (y == z) {
02335                         /* Can we stop now? */
02336                         L = (Long)aadj;
02337                         aadj -= L;
02338                         /* The tolerances below are conservative. */
02339                         if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
02340                                 if (aadj < .4999999 || aadj > .5000001)
02341                                         break;
02342                                 }
02343                         else if (aadj < .4999999/FLT_RADIX)
02344                                 break;
02345                         }
02346 #endif
02347  cont:
02348                 Bfree(bb);
02349                 Bfree(bd);
02350                 Bfree(bs);
02351                 Bfree(delta);
02352                 }
02353 #ifdef SET_INEXACT
02354         if (inexact) {
02355                 if (!oldinexact) {
02356                         word0(rv0) = Exp_1 + (70 << Exp_shift);
02357                         word1(rv0) = 0;
02358                         dval(rv0) += 1.;
02359                         }
02360                 }
02361         else if (!oldinexact)
02362                 clear_inexact();
02363 #endif
02364 #ifdef Avoid_Underflow
02365         if (scale) {
02366                 word0(rv0) = Exp_1 - 2*P*Exp_msk1;
02367                 word1(rv0) = 0;
02368                 dval(rv) *= dval(rv0);
02369 #ifndef NO_ERRNO
02370                 /* try to avoid the bug of testing an 8087 register value */
02371                 if (word0(rv) == 0 && word1(rv) == 0)
02372                         errno = ERANGE;
02373 #endif
02374                 }
02375 #endif /* Avoid_Underflow */
02376 #ifdef SET_INEXACT
02377         if (inexact && !(word0(rv) & Exp_mask)) {
02378                 /* set underflow bit */
02379                 dval(rv0) = 1e-300;
02380                 dval(rv0) *= dval(rv0);
02381                 }
02382 #endif
02383  retfree:
02384         Bfree(bb);
02385         Bfree(bd);
02386         Bfree(bs);
02387         Bfree(bd0);
02388         Bfree(delta);
02389  ret:
02390         if (se)
02391                 *se = (char *)s;
02392         return sign ? -dval(rv) : dval(rv);
02393         }