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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 "ckd_alloc.h"
00084 #undef USE_LOCALE
00085 
00086 /* Correct totally bogus typedefs in this code. */
00087 #include "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         double 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         double 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 #ifndef Sudden_Underflow
01195         int i;
01196 #endif
01197 #ifdef VAX
01198         ULong d0, d1;
01199         d0 = word0(d) >> 16 | word0(d) << 16;
01200         d1 = word1(d) >> 16 | word1(d) << 16;
01201 #else
01202 #define d0 word0(d)
01203 #define d1 word1(d)
01204 #endif
01205 
01206 #ifdef Pack_32
01207         b = Balloc(1);
01208 #else
01209         b = Balloc(2);
01210 #endif
01211         x = b->x;
01212 
01213         z = d0 & Frac_mask;
01214         d0 &= 0x7fffffff;       /* clear sign bit, which we ignore */
01215 #ifdef Sudden_Underflow
01216         de = (int)(d0 >> Exp_shift);
01217 #ifndef IBM
01218         z |= Exp_msk11;
01219 #endif
01220 #else
01221         if ((de = (int)(d0 >> Exp_shift)))
01222                 z |= Exp_msk1;
01223 #endif
01224 #ifdef Pack_32
01225         if ((y = d1)) {
01226                 if ((k = lo0bits(&y))) {
01227                         x[0] = y | z << (32 - k);
01228                         z >>= k;
01229                         }
01230                 else
01231                         x[0] = y;
01232 #ifndef Sudden_Underflow
01233                 i =
01234 #endif
01235                     b->wds = (x[1] = z) ? 2 : 1;
01236                 }
01237         else {
01238 #ifdef DEBUG
01239                 if (!z)
01240                         Bug("Zero passed to d2b");
01241 #endif
01242                 k = lo0bits(&z);
01243                 x[0] = z;
01244 #ifndef Sudden_Underflow
01245                 i =
01246 #endif
01247                     b->wds = 1;
01248                 k += 32;
01249                 }
01250 #else
01251         if (y = d1) {
01252                 if (k = lo0bits(&y))
01253                         if (k >= 16) {
01254                                 x[0] = y | z << 32 - k & 0xffff;
01255                                 x[1] = z >> k - 16 & 0xffff;
01256                                 x[2] = z >> k;
01257                                 i = 2;
01258                                 }
01259                         else {
01260                                 x[0] = y & 0xffff;
01261                                 x[1] = y >> 16 | z << 16 - k & 0xffff;
01262                                 x[2] = z >> k & 0xffff;
01263                                 x[3] = z >> k+16;
01264                                 i = 3;
01265                                 }
01266                 else {
01267                         x[0] = y & 0xffff;
01268                         x[1] = y >> 16;
01269                         x[2] = z & 0xffff;
01270                         x[3] = z >> 16;
01271                         i = 3;
01272                         }
01273                 }
01274         else {
01275 #ifdef DEBUG
01276                 if (!z)
01277                         Bug("Zero passed to d2b");
01278 #endif
01279                 k = lo0bits(&z);
01280                 if (k >= 16) {
01281                         x[0] = z;
01282                         i = 0;
01283                         }
01284                 else {
01285                         x[0] = z & 0xffff;
01286                         x[1] = z >> 16;
01287                         i = 1;
01288                         }
01289                 k += 32;
01290                 }
01291         while(!x[i])
01292                 --i;
01293         b->wds = i + 1;
01294 #endif
01295 #ifndef Sudden_Underflow
01296         if (de) {
01297 #endif
01298 #ifdef IBM
01299                 *e = (de - Bias - (P-1) << 2) + k;
01300                 *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
01301 #else
01302                 *e = de - Bias - (P-1) + k;
01303                 *bits = P - k;
01304 #endif
01305 #ifndef Sudden_Underflow
01306                 }
01307         else {
01308                 *e = de - Bias - (P-1) + 1 + k;
01309 #ifdef Pack_32
01310                 *bits = 32*i - hi0bits(x[i-1]);
01311 #else
01312                 *bits = (i+2)*16 - hi0bits(x[i]);
01313 #endif
01314                 }
01315 #endif
01316         return b;
01317         }
01318 #undef d0
01319 #undef d1
01320 
01321  static double
01322 ratio
01323 #ifdef KR_headers
01324         (a, b) Bigint *a, *b;
01325 #else
01326         (Bigint *a, Bigint *b)
01327 #endif
01328 {
01329         double da, db;
01330         int k, ka, kb;
01331 
01332         dval(da) = b2d(a, &ka);
01333         dval(db) = b2d(b, &kb);
01334 #ifdef Pack_32
01335         k = ka - kb + 32*(a->wds - b->wds);
01336 #else
01337         k = ka - kb + 16*(a->wds - b->wds);
01338 #endif
01339 #ifdef IBM
01340         if (k > 0) {
01341                 word0(da) += (k >> 2)*Exp_msk1;
01342                 if (k &= 3)
01343                         dval(da) *= 1 << k;
01344                 }
01345         else {
01346                 k = -k;
01347                 word0(db) += (k >> 2)*Exp_msk1;
01348                 if (k &= 3)
01349                         dval(db) *= 1 << k;
01350                 }
01351 #else
01352         if (k > 0)
01353                 word0(da) += k*Exp_msk1;
01354         else {
01355                 k = -k;
01356                 word0(db) += k*Exp_msk1;
01357                 }
01358 #endif
01359         return dval(da) / dval(db);
01360         }
01361 
01362  static CONST double
01363 tens[] = {
01364                 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
01365                 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
01366                 1e20, 1e21, 1e22
01367 #ifdef VAX
01368                 , 1e23, 1e24
01369 #endif
01370                 };
01371 
01372  static CONST double
01373 #ifdef IEEE_Arith
01374 bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
01375 static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
01376 #ifdef Avoid_Underflow
01377                 9007199254740992.*9007199254740992.e-256
01378                 /* = 2^106 * 1e-53 */
01379 #else
01380                 1e-256
01381 #endif
01382                 };
01383 /* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
01384 /* flag unnecessarily.  It leads to a song and dance at the end of strtod. */
01385 #define Scale_Bit 0x10
01386 #define n_bigtens 5
01387 #else
01388 #ifdef IBM
01389 bigtens[] = { 1e16, 1e32, 1e64 };
01390 static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 };
01391 #define n_bigtens 3
01392 #else
01393 bigtens[] = { 1e16, 1e32 };
01394 static CONST double tinytens[] = { 1e-16, 1e-32 };
01395 #define n_bigtens 2
01396 #endif
01397 #endif
01398 
01399 #ifdef INFNAN_CHECK
01400 
01401 #ifndef NAN_WORD0
01402 #define NAN_WORD0 0x7ff80000
01403 #endif
01404 
01405 #ifndef NAN_WORD1
01406 #define NAN_WORD1 0
01407 #endif
01408 
01409  static int
01410 match
01411 #ifdef KR_headers
01412         (sp, t) char **sp, *t;
01413 #else
01414         (CONST char **sp, char *t)
01415 #endif
01416 {
01417         int c, d;
01418         CONST char *s = *sp;
01419 
01420         while((d = *t++)) {
01421                 if ((c = *++s) >= 'A' && c <= 'Z')
01422                         c += 'a' - 'A';
01423                 if (c != d)
01424                         return 0;
01425                 }
01426         *sp = s + 1;
01427         return 1;
01428         }
01429 
01430 #ifndef No_Hex_NaN
01431  static void
01432 hexnan
01433 #ifdef KR_headers
01434         (rvp, sp) double *rvp; CONST char **sp;
01435 #else
01436         (double *rvp, CONST char **sp)
01437 #endif
01438 {
01439         ULong c, x[2];
01440         CONST char *s;
01441         int havedig, udx0, xshift;
01442 
01443         x[0] = x[1] = 0;
01444         havedig = xshift = 0;
01445         udx0 = 1;
01446         s = *sp;
01447         /* allow optional initial 0x or 0X */
01448         while((c = *(CONST unsigned char*)(s+1)) && c <= ' ')
01449                 ++s;
01450         if (s[1] == '0' && (s[2] == 'x' || s[2] == 'X'))
01451                 s += 2;
01452         while((c = *(CONST unsigned char*)++s)) {
01453                 if (c >= '0' && c <= '9')
01454                         c -= '0';
01455                 else if (c >= 'a' && c <= 'f')
01456                         c += 10 - 'a';
01457                 else if (c >= 'A' && c <= 'F')
01458                         c += 10 - 'A';
01459                 else if (c <= ' ') {
01460                         if (udx0 && havedig) {
01461                                 udx0 = 0;
01462                                 xshift = 1;
01463                                 }
01464                         continue;
01465                         }
01466 #ifdef GDTOA_NON_PEDANTIC_NANCHECK
01467                 else if (/*(*/ c == ')' && havedig) {
01468                         *sp = s + 1;
01469                         break;
01470                         }
01471                 else
01472                         return; /* invalid form: don't change *sp */
01473 #else
01474                 else {
01475                         do {
01476                                 if (/*(*/ c == ')') {
01477                                         *sp = s + 1;
01478                                         break;
01479                                         }
01480                         } while((c = *++s));
01481                         break;
01482                 }
01483 #endif
01484                 havedig = 1;
01485                 if (xshift) {
01486                         xshift = 0;
01487                         x[0] = x[1];
01488                         x[1] = 0;
01489                         }
01490                 if (udx0)
01491                         x[0] = (x[0] << 4) | (x[1] >> 28);
01492                 x[1] = (x[1] << 4) | c;
01493                 }
01494         if ((x[0] &= 0xfffff) || x[1]) {
01495                 word0(*rvp) = Exp_mask | x[0];
01496                 word1(*rvp) = x[1];
01497                 }
01498         }
01499 #endif /*No_Hex_NaN*/
01500 #endif /* INFNAN_CHECK */
01501 
01502  double
01503 sb_strtod
01504 #ifdef KR_headers
01505         (s00, se) CONST char *s00; char **se;
01506 #else
01507         (CONST char *s00, char **se)
01508 #endif
01509 {
01510 #ifdef Avoid_Underflow
01511         int scale;
01512 #endif
01513         int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
01514                  e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
01515         CONST char *s, *s0, *s1;
01516         double aadj, aadj1, adj, rv, rv0;
01517         Long L;
01518         ULong y, z;
01519         Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
01520 #ifdef SET_INEXACT
01521         int inexact, oldinexact;
01522 #endif
01523 #ifdef Honor_FLT_ROUNDS
01524         int rounding;
01525 #endif
01526 #ifdef USE_LOCALE
01527         CONST char *s2;
01528 #endif
01529 
01530         sign = nz0 = nz = 0;
01531         dval(rv) = 0.;
01532         for(s = s00;;s++) switch(*s) {
01533                 case '-':
01534                         sign = 1;
01535                         /* no break */
01536                 case '+':
01537                         if (*++s)
01538                                 goto break2;
01539                         /* no break */
01540                 case 0:
01541                         goto ret0;
01542                 case '\t':
01543                 case '\n':
01544                 case '\v':
01545                 case '\f':
01546                 case '\r':
01547                 case ' ':
01548                         continue;
01549                 default:
01550                         goto break2;
01551                 }
01552  break2:
01553         if (*s == '0') {
01554                 nz0 = 1;
01555                 while(*++s == '0') ;
01556                 if (!*s)
01557                         goto ret;
01558                 }
01559         s0 = s;
01560         y = z = 0;
01561         for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
01562                 if (nd < 9)
01563                         y = 10*y + c - '0';
01564                 else if (nd < 16)
01565                         z = 10*z + c - '0';
01566         nd0 = nd;
01567 #ifdef USE_LOCALE
01568         s1 = localeconv()->decimal_point;
01569         if (c == *s1) {
01570                 c = '.';
01571                 if (*++s1) {
01572                         s2 = s;
01573                         for(;;) {
01574                                 if (*++s2 != *s1) {
01575                                         c = 0;
01576                                         break;
01577                                         }
01578                                 if (!*++s1) {
01579                                         s = s2;
01580                                         break;
01581                                         }
01582                                 }
01583                         }
01584                 }
01585 #endif
01586         if (c == '.') {
01587                 c = *++s;
01588                 if (!nd) {
01589                         for(; c == '0'; c = *++s)
01590                                 nz++;
01591                         if (c > '0' && c <= '9') {
01592                                 s0 = s;
01593                                 nf += nz;
01594                                 nz = 0;
01595                                 goto have_dig;
01596                                 }
01597                         goto dig_done;
01598                         }
01599                 for(; c >= '0' && c <= '9'; c = *++s) {
01600  have_dig:
01601                         nz++;
01602                         if (c -= '0') {
01603                                 nf += nz;
01604                                 for(i = 1; i < nz; i++)
01605                                         if (nd++ < 9)
01606                                                 y *= 10;
01607                                         else if (nd <= DBL_DIG + 1)
01608                                                 z *= 10;
01609                                 if (nd++ < 9)
01610                                         y = 10*y + c;
01611                                 else if (nd <= DBL_DIG + 1)
01612                                         z = 10*z + c;
01613                                 nz = 0;
01614                                 }
01615                         }
01616                 }
01617  dig_done:
01618         e = 0;
01619         if (c == 'e' || c == 'E') {
01620                 if (!nd && !nz && !nz0) {
01621                         goto ret0;
01622                         }
01623                 s00 = s;
01624                 esign = 0;
01625                 switch(c = *++s) {
01626                         case '-':
01627                                 esign = 1;
01628                         case '+':
01629                                 c = *++s;
01630                         }
01631                 if (c >= '0' && c <= '9') {
01632                         while(c == '0')
01633                                 c = *++s;
01634                         if (c > '0' && c <= '9') {
01635                                 L = c - '0';
01636                                 s1 = s;
01637                                 while((c = *++s) >= '0' && c <= '9')
01638                                         L = 10*L + c - '0';
01639                                 if (s - s1 > 8 || L > 19999)
01640                                         /* Avoid confusion from exponents
01641                                          * so large that e might overflow.
01642                                          */
01643                                         e = 19999; /* safe for 16 bit ints */
01644                                 else
01645                                         e = (int)L;
01646                                 if (esign)
01647                                         e = -e;
01648                                 }
01649                         else
01650                                 e = 0;
01651                         }
01652                 else
01653                         s = s00;
01654                 }
01655         if (!nd) {
01656                 if (!nz && !nz0) {
01657 #ifdef INFNAN_CHECK
01658                         /* Check for Nan and Infinity */
01659                         switch(c) {
01660                           case 'i':
01661                           case 'I':
01662                                 if (match(&s,"nf")) {
01663                                         --s;
01664                                         if (!match(&s,"inity"))
01665                                                 ++s;
01666                                         word0(rv) = 0x7ff00000;
01667                                         word1(rv) = 0;
01668                                         goto ret;
01669                                         }
01670                                 break;
01671                           case 'n':
01672                           case 'N':
01673                                 if (match(&s, "an")) {
01674                                         word0(rv) = NAN_WORD0;
01675                                         word1(rv) = NAN_WORD1;
01676 #ifndef No_Hex_NaN
01677                                         if (*s == '(') /*)*/
01678                                                 hexnan(&rv, &s);
01679 #endif
01680                                         goto ret;
01681                                         }
01682                           }
01683 #endif /* INFNAN_CHECK */
01684  ret0:
01685                         s = s00;
01686                         sign = 0;
01687                         }
01688                 goto ret;
01689                 }
01690         e1 = e -= nf;
01691 
01692         /* Now we have nd0 digits, starting at s0, followed by a
01693          * decimal point, followed by nd-nd0 digits.  The number we're
01694          * after is the integer represented by those digits times
01695          * 10**e */
01696 
01697         if (!nd0)
01698                 nd0 = nd;
01699         k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
01700         dval(rv) = y;
01701         if (k > 9) {
01702 #ifdef SET_INEXACT
01703                 if (k > DBL_DIG)
01704                         oldinexact = get_inexact();
01705 #endif
01706                 dval(rv) = tens[k - 9] * dval(rv) + z;
01707                 }
01708         bd0 = 0;
01709         if (nd <= DBL_DIG
01710 #ifndef RND_PRODQUOT
01711 #ifndef Honor_FLT_ROUNDS
01712                 && Flt_Rounds == 1
01713 #endif
01714 #endif
01715                         ) {
01716                 if (!e)
01717                         goto ret;
01718                 if (e > 0) {
01719                         if (e <= Ten_pmax) {
01720 #ifdef VAX
01721                                 goto vax_ovfl_check;
01722 #else
01723 #ifdef Honor_FLT_ROUNDS
01724                                 /* round correctly FLT_ROUNDS = 2 or 3 */
01725                                 if (sign) {
01726                                         rv = -rv;
01727                                         sign = 0;
01728                                         }
01729 #endif
01730                                 /* rv = */ rounded_product(dval(rv), tens[e]);
01731                                 goto ret;
01732 #endif
01733                                 }
01734                         i = DBL_DIG - nd;
01735                         if (e <= Ten_pmax + i) {
01736                                 /* A fancier test would sometimes let us do
01737                                  * this for larger i values.
01738                                  */
01739 #ifdef Honor_FLT_ROUNDS
01740                                 /* round correctly FLT_ROUNDS = 2 or 3 */
01741                                 if (sign) {
01742                                         rv = -rv;
01743                                         sign = 0;
01744                                         }
01745 #endif
01746                                 e -= i;
01747                                 dval(rv) *= tens[i];
01748 #ifdef VAX
01749                                 /* VAX exponent range is so narrow we must
01750                                  * worry about overflow here...
01751                                  */
01752  vax_ovfl_check:
01753                                 word0(rv) -= P*Exp_msk1;
01754                                 /* rv = */ rounded_product(dval(rv), tens[e]);
01755                                 if ((word0(rv) & Exp_mask)
01756                                  > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
01757                                         goto ovfl;
01758                                 word0(rv) += P*Exp_msk1;
01759 #else
01760                                 /* rv = */ rounded_product(dval(rv), tens[e]);
01761 #endif
01762                                 goto ret;
01763                                 }
01764                         }
01765 #ifndef Inaccurate_Divide
01766                 else if (e >= -Ten_pmax) {
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                         /* rv = */ rounded_quotient(dval(rv), tens[-e]);
01775                         goto ret;
01776                         }
01777 #endif
01778                 }
01779         e1 += nd - k;
01780 
01781 #ifdef IEEE_Arith
01782 #ifdef SET_INEXACT
01783         inexact = 1;
01784         if (k <= DBL_DIG)
01785                 oldinexact = get_inexact();
01786 #endif
01787 #ifdef Avoid_Underflow
01788         scale = 0;
01789 #endif
01790 #ifdef Honor_FLT_ROUNDS
01791         if ((rounding = Flt_Rounds) >= 2) {
01792                 if (sign)
01793                         rounding = rounding == 2 ? 0 : 2;
01794                 else
01795                         if (rounding != 2)
01796                                 rounding = 0;
01797                 }
01798 #endif
01799 #endif /*IEEE_Arith*/
01800 
01801         /* Get starting approximation = rv * 10**e1 */
01802 
01803         if (e1 > 0) {
01804                 if ((i = e1 & 15))
01805                         dval(rv) *= tens[i];
01806                 if (e1 &= ~15) {
01807                         if (e1 > DBL_MAX_10_EXP) {
01808  ovfl:
01809 #ifndef NO_ERRNO
01810                                 errno = ERANGE;
01811 #endif
01812                                 /* Can't trust HUGE_VAL */
01813 #ifdef IEEE_Arith
01814 #ifdef Honor_FLT_ROUNDS
01815                                 switch(rounding) {
01816                                   case 0: /* toward 0 */
01817                                   case 3: /* toward -infinity */
01818                                         word0(rv) = Big0;
01819                                         word1(rv) = Big1;
01820                                         break;
01821                                   default:
01822                                         word0(rv) = Exp_mask;
01823                                         word1(rv) = 0;
01824                                   }
01825 #else /*Honor_FLT_ROUNDS*/
01826                                 word0(rv) = Exp_mask;
01827                                 word1(rv) = 0;
01828 #endif /*Honor_FLT_ROUNDS*/
01829 #ifdef SET_INEXACT
01830                                 /* set overflow bit */
01831                                 dval(rv0) = 1e300;
01832                                 dval(rv0) *= dval(rv0);
01833 #endif
01834 #else /*IEEE_Arith*/
01835                                 word0(rv) = Big0;
01836                                 word1(rv) = Big1;
01837 #endif /*IEEE_Arith*/
01838                                 if (bd0)
01839                                         goto retfree;
01840                                 goto ret;
01841                                 }
01842                         e1 >>= 4;
01843                         for(j = 0; e1 > 1; j++, e1 >>= 1)
01844                                 if (e1 & 1)
01845                                         dval(rv) *= bigtens[j];
01846                 /* The last multiplication could overflow. */
01847                         word0(rv) -= P*Exp_msk1;
01848                         dval(rv) *= bigtens[j];
01849                         if ((z = word0(rv) & Exp_mask)
01850                          > Exp_msk1*(DBL_MAX_EXP+Bias-P))
01851                                 goto ovfl;
01852                         if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
01853                                 /* set to largest number */
01854                                 /* (Can't trust DBL_MAX) */
01855                                 word0(rv) = Big0;
01856                                 word1(rv) = Big1;
01857                                 }
01858                         else
01859                                 word0(rv) += P*Exp_msk1;
01860                         }
01861                 }
01862         else if (e1 < 0) {
01863                 e1 = -e1;
01864                 if ((i = e1 & 15))
01865                         dval(rv) /= tens[i];
01866                 if (e1 >>= 4) {
01867                         if (e1 >= 1 << n_bigtens)
01868                                 goto undfl;
01869 #ifdef Avoid_Underflow
01870                         if (e1 & Scale_Bit)
01871                                 scale = 2*P;
01872                         for(j = 0; e1 > 0; j++, e1 >>= 1)
01873                                 if (e1 & 1)
01874                                         dval(rv) *= tinytens[j];
01875                         if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask)
01876                                                 >> Exp_shift)) > 0) {
01877                                 /* scaled rv is denormal; zap j low bits */
01878                                 if (j >= 32) {
01879                                         word1(rv) = 0;
01880                                         if (j >= 53)
01881                                          word0(rv) = (P+2)*Exp_msk1;
01882                                         else
01883                                                 word0(rv) &= 0xffffffff << (j-32);
01884                                         }
01885                                 else
01886                                         word1(rv) &= 0xffffffff << j;
01887                                 }
01888 #else
01889                         for(j = 0; e1 > 1; j++, e1 >>= 1)
01890                                 if (e1 & 1)
01891                                         dval(rv) *= tinytens[j];
01892                         /* The last multiplication could underflow. */
01893                         dval(rv0) = dval(rv);
01894                         dval(rv) *= tinytens[j];
01895                         if (!dval(rv)) {
01896                                 dval(rv) = 2.*dval(rv0);
01897                                 dval(rv) *= tinytens[j];
01898 #endif
01899                                 if (!dval(rv)) {
01900  undfl:
01901                                         dval(rv) = 0.;
01902 #ifndef NO_ERRNO
01903                                         errno = ERANGE;
01904 #endif
01905                                         if (bd0)
01906                                                 goto retfree;
01907                                         goto ret;
01908                                         }
01909 #ifndef Avoid_Underflow
01910                                 word0(rv) = Tiny0;
01911                                 word1(rv) = Tiny1;
01912                                 /* The refinement below will clean
01913                                  * this approximation up.
01914                                  */
01915                                 }
01916 #endif
01917                         }
01918                 }
01919 
01920         /* Now the hard part -- adjusting rv to the correct value.*/
01921 
01922         /* Put digits into bd: true value = bd * 10^e */
01923 
01924         bd0 = s2b(s0, nd0, nd, y);
01925 
01926         for(;;) {
01927                 bd = Balloc(bd0->k);
01928                 Bcopy(bd, bd0);
01929                 bb = d2b(dval(rv), &bbe, &bbbits);      /* rv = bb * 2^bbe */
01930                 bs = i2b(1);
01931 
01932                 if (e >= 0) {
01933                         bb2 = bb5 = 0;
01934                         bd2 = bd5 = e;
01935                         }
01936                 else {
01937                         bb2 = bb5 = -e;
01938                         bd2 = bd5 = 0;
01939                         }
01940                 if (bbe >= 0)
01941                         bb2 += bbe;
01942                 else
01943                         bd2 -= bbe;
01944                 bs2 = bb2;
01945 #ifdef Honor_FLT_ROUNDS
01946                 if (rounding != 1)
01947                         bs2++;
01948 #endif
01949 #ifdef Avoid_Underflow
01950                 j = bbe - scale;
01951                 i = j + bbbits - 1;     /* logb(rv) */
01952                 if (i < Emin)   /* denormal */
01953                         j += P - Emin;
01954                 else
01955                         j = P + 1 - bbbits;
01956 #else /*Avoid_Underflow*/
01957 #ifdef Sudden_Underflow
01958 #ifdef IBM
01959                 j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
01960 #else
01961                 j = P + 1 - bbbits;
01962 #endif
01963 #else /*Sudden_Underflow*/
01964                 j = bbe;
01965                 i = j + bbbits - 1;     /* logb(rv) */
01966                 if (i < Emin)   /* denormal */
01967                         j += P - Emin;
01968                 else
01969                         j = P + 1 - bbbits;
01970 #endif /*Sudden_Underflow*/
01971 #endif /*Avoid_Underflow*/
01972                 bb2 += j;
01973                 bd2 += j;
01974 #ifdef Avoid_Underflow
01975                 bd2 += scale;
01976 #endif
01977                 i = bb2 < bd2 ? bb2 : bd2;
01978                 if (i > bs2)
01979                         i = bs2;
01980                 if (i > 0) {
01981                         bb2 -= i;
01982                         bd2 -= i;
01983                         bs2 -= i;
01984                         }
01985                 if (bb5 > 0) {
01986                         bs = pow5mult(bs, bb5);
01987                         bb1 = mult(bs, bb);
01988                         Bfree(bb);
01989                         bb = bb1;
01990                         }
01991                 if (bb2 > 0)
01992                         bb = lshift(bb, bb2);
01993                 if (bd5 > 0)
01994                         bd = pow5mult(bd, bd5);
01995                 if (bd2 > 0)
01996                         bd = lshift(bd, bd2);
01997                 if (bs2 > 0)
01998                         bs = lshift(bs, bs2);
01999                 delta = diff(bb, bd);
02000                 dsign = delta->sign;
02001                 delta->sign = 0;
02002                 i = cmp(delta, bs);
02003 #ifdef Honor_FLT_ROUNDS
02004                 if (rounding != 1) {
02005                         if (i < 0) {
02006                                 /* Error is less than an ulp */
02007                                 if (!delta->x[0] && delta->wds <= 1) {
02008                                         /* exact */
02009 #ifdef SET_INEXACT
02010                                         inexact = 0;
02011 #endif
02012                                         break;
02013                                         }
02014                                 if (rounding) {
02015                                         if (dsign) {
02016                                                 adj = 1.;
02017                                                 goto apply_adj;
02018                                                 }
02019                                         }
02020                                 else if (!dsign) {
02021                                         adj = -1.;
02022                                         if (!word1(rv)
02023                                          && !(word0(rv) & Frac_mask)) {
02024                                                 y = word0(rv) & Exp_mask;
02025 #ifdef Avoid_Underflow
02026                                                 if (!scale || y > 2*P*Exp_msk1)
02027 #else
02028                                                 if (y)
02029 #endif
02030                                                   {
02031                                                   delta = lshift(delta,Log2P);
02032                                                   if (cmp(delta, bs) <= 0)
02033                                                         adj = -0.5;
02034                                                   }
02035                                                 }
02036  apply_adj:
02037 #ifdef Avoid_Underflow
02038                                         if (scale && (y = word0(rv) & Exp_mask)
02039                                                 <= 2*P*Exp_msk1)
02040                                           word0(adj) += (2*P+1)*Exp_msk1 - y;
02041 #else
02042 #ifdef Sudden_Underflow
02043                                         if ((word0(rv) & Exp_mask) <=
02044                                                         P*Exp_msk1) {
02045                                                 word0(rv) += P*Exp_msk1;
02046                                                 dval(rv) += adj*ulp(dval(rv));
02047                                                 word0(rv) -= P*Exp_msk1;
02048                                                 }
02049                                         else
02050 #endif /*Sudden_Underflow*/
02051 #endif /*Avoid_Underflow*/
02052                                         dval(rv) += adj*ulp(dval(rv));
02053                                         }
02054                                 break;
02055                                 }
02056                         adj = ratio(delta, bs);
02057                         if (adj < 1.)
02058                                 adj = 1.;
02059                         if (adj <= 0x7ffffffe) {
02060                                 /* adj = rounding ? ceil(adj) : floor(adj); */
02061                                 y = adj;
02062                                 if (y != adj) {
02063                                         if (!((rounding>>1) ^ dsign))
02064                                                 y++;
02065                                         adj = y;
02066                                         }
02067                                 }
02068 #ifdef Avoid_Underflow
02069                         if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
02070                                 word0(adj) += (2*P+1)*Exp_msk1 - y;
02071 #else
02072 #ifdef Sudden_Underflow
02073                         if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
02074                                 word0(rv) += P*Exp_msk1;
02075                                 adj *= ulp(dval(rv));
02076                                 if (dsign)
02077                                         dval(rv) += adj;
02078                                 else
02079                                         dval(rv) -= adj;
02080                                 word0(rv) -= P*Exp_msk1;
02081                                 goto cont;
02082                                 }
02083 #endif /*Sudden_Underflow*/
02084 #endif /*Avoid_Underflow*/
02085                         adj *= ulp(dval(rv));
02086                         if (dsign)
02087                                 dval(rv) += adj;
02088                         else
02089                                 dval(rv) -= adj;
02090                         goto cont;
02091                         }
02092 #endif /*Honor_FLT_ROUNDS*/
02093 
02094                 if (i < 0) {
02095                         /* Error is less than half an ulp -- check for
02096                          * special case of mantissa a power of two.
02097                          */
02098                         if (dsign || word1(rv) || word0(rv) & Bndry_mask
02099 #ifdef IEEE_Arith
02100 #ifdef Avoid_Underflow
02101                          || (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1
02102 #else
02103                          || (word0(rv) & Exp_mask) <= Exp_msk1
02104 #endif
02105 #endif
02106                                 ) {
02107 #ifdef SET_INEXACT
02108                                 if (!delta->x[0] && delta->wds <= 1)
02109                                         inexact = 0;
02110 #endif
02111                                 break;
02112                                 }
02113                         if (!delta->x[0] && delta->wds <= 1) {
02114                                 /* exact result */
02115 #ifdef SET_INEXACT
02116                                 inexact = 0;
02117 #endif
02118                                 break;
02119                                 }
02120                         delta = lshift(delta,Log2P);
02121                         if (cmp(delta, bs) > 0)
02122                                 goto drop_down;
02123                         break;
02124                         }
02125                 if (i == 0) {
02126                         /* exactly half-way between */
02127                         if (dsign) {
02128                                 if ((word0(rv) & Bndry_mask1) == Bndry_mask1
02129                                  &&  word1(rv) == (
02130 #ifdef Avoid_Underflow
02131                         (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
02132                 ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
02133 #endif
02134                                                    0xffffffff)) {
02135                                         /*boundary case -- increment exponent*/
02136                                         word0(rv) = (word0(rv) & Exp_mask)
02137                                                 + Exp_msk1
02138 #ifdef IBM
02139                                                 | Exp_msk1 >> 4
02140 #endif
02141                                                 ;
02142                                         word1(rv) = 0;
02143 #ifdef Avoid_Underflow
02144                                         dsign = 0;
02145 #endif
02146                                         break;
02147                                         }
02148                                 }
02149                         else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
02150  drop_down:
02151                                 /* boundary case -- decrement exponent */
02152 #ifdef Sudden_Underflow /*{{*/
02153                                 L = word0(rv) & Exp_mask;
02154 #ifdef IBM
02155                                 if (L <  Exp_msk1)
02156 #else
02157 #ifdef Avoid_Underflow
02158                                 if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
02159 #else
02160                                 if (L <= Exp_msk1)
02161 #endif /*Avoid_Underflow*/
02162 #endif /*IBM*/
02163                                         goto undfl;
02164                                 L -= Exp_msk1;
02165 #else /*Sudden_Underflow}{*/
02166 #ifdef Avoid_Underflow
02167                                 if (scale) {
02168                                         L = word0(rv) & Exp_mask;
02169                                         if (L <= (2*P+1)*Exp_msk1) {
02170                                                 if (L > (P+2)*Exp_msk1)
02171                                                         /* round even ==> */
02172                                                         /* accept rv */
02173                                                         break;
02174                                                 /* rv = smallest denormal */
02175                                                 goto undfl;
02176                                                 }
02177                                         }
02178 #endif /*Avoid_Underflow*/
02179                                 L = (word0(rv) & Exp_mask) - Exp_msk1;
02180 #endif /*Sudden_Underflow}}*/
02181                                 word0(rv) = L | Bndry_mask1;
02182                                 word1(rv) = 0xffffffff;
02183 #ifdef IBM
02184                                 goto cont;
02185 #else
02186                                 break;
02187 #endif
02188                                 }
02189 #ifndef ROUND_BIASED
02190                         if (!(word1(rv) & LSB))
02191                                 break;
02192 #endif
02193                         if (dsign)
02194                                 dval(rv) += ulp(dval(rv));
02195 #ifndef ROUND_BIASED
02196                         else {
02197                                 dval(rv) -= ulp(dval(rv));
02198 #ifndef Sudden_Underflow
02199                                 if (!dval(rv))
02200                                         goto undfl;
02201 #endif
02202                                 }
02203 #ifdef Avoid_Underflow
02204                         dsign = 1 - dsign;
02205 #endif
02206 #endif
02207                         break;
02208                         }
02209                 if ((aadj = ratio(delta, bs)) <= 2.) {
02210                         if (dsign)
02211                                 aadj = aadj1 = 1.;
02212                         else if (word1(rv) || word0(rv) & Bndry_mask) {
02213 #ifndef Sudden_Underflow
02214                                 if (word1(rv) == Tiny1 && !word0(rv))
02215                                         goto undfl;
02216 #endif
02217                                 aadj = 1.;
02218                                 aadj1 = -1.;
02219                                 }
02220                         else {
02221                                 /* special case -- power of FLT_RADIX to be */
02222                                 /* rounded down... */
02223 
02224                                 if (aadj < 2./FLT_RADIX)
02225                                         aadj = 1./FLT_RADIX;
02226                                 else
02227                                         aadj *= 0.5;
02228                                 aadj1 = -aadj;
02229                                 }
02230                         }
02231                 else {
02232                         aadj *= 0.5;
02233                         aadj1 = dsign ? aadj : -aadj;
02234 #ifdef Check_FLT_ROUNDS
02235                         switch(Rounding) {
02236                                 case 2: /* towards +infinity */
02237                                         aadj1 -= 0.5;
02238                                         break;
02239                                 case 0: /* towards 0 */
02240                                 case 3: /* towards -infinity */
02241                                         aadj1 += 0.5;
02242                                 }
02243 #else
02244                         if (Flt_Rounds == 0)
02245                                 aadj1 += 0.5;
02246 #endif /*Check_FLT_ROUNDS*/
02247                         }
02248                 y = word0(rv) & Exp_mask;
02249 
02250                 /* Check for overflow */
02251 
02252                 if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
02253                         dval(rv0) = dval(rv);
02254                         word0(rv) -= P*Exp_msk1;
02255                         adj = aadj1 * ulp(dval(rv));
02256                         dval(rv) += adj;
02257                         if ((word0(rv) & Exp_mask) >=
02258                                         Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
02259                                 if (word0(rv0) == Big0 && word1(rv0) == Big1)
02260                                         goto ovfl;
02261                                 word0(rv) = Big0;
02262                                 word1(rv) = Big1;
02263                                 goto cont;
02264                                 }
02265                         else
02266                                 word0(rv) += P*Exp_msk1;
02267                         }
02268                 else {
02269 #ifdef Avoid_Underflow
02270                         if (scale && y <= 2*P*Exp_msk1) {
02271                                 if (aadj <= 0x7fffffff) {
02272                                         if ((z = (uint32)aadj) <= 0)
02273                                                 z = 1;
02274                                         aadj = z;
02275                                         aadj1 = dsign ? aadj : -aadj;
02276                                         }
02277                                 word0(aadj1) += (2*P+1)*Exp_msk1 - y;
02278                                 }
02279                         adj = aadj1 * ulp(dval(rv));
02280                         dval(rv) += adj;
02281 #else
02282 #ifdef Sudden_Underflow
02283                         if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
02284                                 dval(rv0) = dval(rv);
02285                                 word0(rv) += P*Exp_msk1;
02286                                 adj = aadj1 * ulp(dval(rv));
02287                                 dval(rv) += adj;
02288 #ifdef IBM
02289                                 if ((word0(rv) & Exp_mask) <  P*Exp_msk1)
02290 #else
02291                                 if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
02292 #endif
02293                                         {
02294                                         if (word0(rv0) == Tiny0
02295                                          && word1(rv0) == Tiny1)
02296                                                 goto undfl;
02297                                         word0(rv) = Tiny0;
02298                                         word1(rv) = Tiny1;
02299                                         goto cont;
02300                                         }
02301                                 else
02302                                         word0(rv) -= P*Exp_msk1;
02303                                 }
02304                         else {
02305                                 adj = aadj1 * ulp(dval(rv));
02306                                 dval(rv) += adj;
02307                                 }
02308 #else /*Sudden_Underflow*/
02309                         /* Compute adj so that the IEEE rounding rules will
02310                          * correctly round rv + adj in some half-way cases.
02311                          * If rv * ulp(rv) is denormalized (i.e.,
02312                          * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
02313                          * trouble from bits lost to denormalization;
02314                          * example: 1.2e-307 .
02315                          */
02316                         if (y <= (P-1)*Exp_msk1 && aadj > 1.) {
02317                                 aadj1 = (double)(int)(aadj + 0.5);
02318                                 if (!dsign)
02319                                         aadj1 = -aadj1;
02320                                 }
02321                         adj = aadj1 * ulp(dval(rv));
02322                         dval(rv) += adj;
02323 #endif /*Sudden_Underflow*/
02324 #endif /*Avoid_Underflow*/
02325                         }
02326                 z = word0(rv) & Exp_mask;
02327 #ifndef SET_INEXACT
02328 #ifdef Avoid_Underflow
02329                 if (!scale)
02330 #endif
02331                 if (y == z) {
02332                         /* Can we stop now? */
02333                         L = (Long)aadj;
02334                         aadj -= L;
02335                         /* The tolerances below are conservative. */
02336                         if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
02337                                 if (aadj < .4999999 || aadj > .5000001)
02338                                         break;
02339                                 }
02340                         else if (aadj < .4999999/FLT_RADIX)
02341                                 break;
02342                         }
02343 #endif
02344  cont:
02345                 Bfree(bb);
02346                 Bfree(bd);
02347                 Bfree(bs);
02348                 Bfree(delta);
02349                 }
02350 #ifdef SET_INEXACT
02351         if (inexact) {
02352                 if (!oldinexact) {
02353                         word0(rv0) = Exp_1 + (70 << Exp_shift);
02354                         word1(rv0) = 0;
02355                         dval(rv0) += 1.;
02356                         }
02357                 }
02358         else if (!oldinexact)
02359                 clear_inexact();
02360 #endif
02361 #ifdef Avoid_Underflow
02362         if (scale) {
02363                 word0(rv0) = Exp_1 - 2*P*Exp_msk1;
02364                 word1(rv0) = 0;
02365                 dval(rv) *= dval(rv0);
02366 #ifndef NO_ERRNO
02367                 /* try to avoid the bug of testing an 8087 register value */
02368                 if (word0(rv) == 0 && word1(rv) == 0)
02369                         errno = ERANGE;
02370 #endif
02371                 }
02372 #endif /* Avoid_Underflow */
02373 #ifdef SET_INEXACT
02374         if (inexact && !(word0(rv) & Exp_mask)) {
02375                 /* set underflow bit */
02376                 dval(rv0) = 1e-300;
02377                 dval(rv0) *= dval(rv0);
02378                 }
02379 #endif
02380  retfree:
02381         Bfree(bb);
02382         Bfree(bd);
02383         Bfree(bs);
02384         Bfree(bd0);
02385         Bfree(delta);
02386  ret:
02387         if (se)
02388                 *se = (char *)s;
02389         return sign ? -dval(rv) : dval(rv);
02390         }

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