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main_repo / deps / v8 / src / third_party / dtoa / dtoa.c @ 40c0f755
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/****************************************************************
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*
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* The author of this software is David M. Gay.
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*
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* Copyright (c) 1991, 2000, 2001 by Lucent Technologies.
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*
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* Permission to use, copy, modify, and distribute this software for any
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* purpose without fee is hereby granted, provided that this entire notice
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* is included in all copies of any software which is or includes a copy
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* or modification of this software and in all copies of the supporting
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* documentation for such software.
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*
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* THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
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* WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY
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* REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
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* OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
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*
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***************************************************************/
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/* Please send bug reports to David M. Gay (dmg at acm dot org,
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* with " at " changed at "@" and " dot " changed to "."). */
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/* On a machine with IEEE extended-precision registers, it is
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* necessary to specify double-precision (53-bit) rounding precision
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* before invoking strtod or dtoa. If the machine uses (the equivalent
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* of) Intel 80x87 arithmetic, the call
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* _control87(PC_53, MCW_PC);
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* does this with many compilers. Whether this or another call is
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* appropriate depends on the compiler; for this to work, it may be
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* necessary to #include "float.h" or another system-dependent header
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* file.
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*/
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/* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
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*
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* This strtod returns a nearest machine number to the input decimal
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* string (or sets errno to ERANGE). With IEEE arithmetic, ties are
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* broken by the IEEE round-even rule. Otherwise ties are broken by
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* biased rounding (add half and chop).
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*
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* Inspired loosely by William D. Clinger's paper "How to Read Floating
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* Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
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*
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* Modifications:
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*
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* 1. We only require IEEE, IBM, or VAX double-precision
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* arithmetic (not IEEE double-extended).
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* 2. We get by with floating-point arithmetic in a case that
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* Clinger missed -- when we're computing d * 10^n
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* for a small integer d and the integer n is not too
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* much larger than 22 (the maximum integer k for which
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* we can represent 10^k exactly), we may be able to
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* compute (d*10^k) * 10^(e-k) with just one roundoff.
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* 3. Rather than a bit-at-a-time adjustment of the binary
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* result in the hard case, we use floating-point
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* arithmetic to determine the adjustment to within
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* one bit; only in really hard cases do we need to
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* compute a second residual.
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* 4. Because of 3., we don't need a large table of powers of 10
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* for ten-to-e (just some small tables, e.g. of 10^k
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* for 0 <= k <= 22).
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*/
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/*
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* #define IEEE_8087 for IEEE-arithmetic machines where the least
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* significant byte has the lowest address.
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* #define IEEE_MC68k for IEEE-arithmetic machines where the most
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* significant byte has the lowest address.
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* #define Long int on machines with 32-bit ints and 64-bit longs.
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* #define IBM for IBM mainframe-style floating-point arithmetic.
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* #define VAX for VAX-style floating-point arithmetic (D_floating).
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* #define No_leftright to omit left-right logic in fast floating-point
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* computation of dtoa.
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* #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
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* and strtod and dtoa should round accordingly.
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* #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
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* and Honor_FLT_ROUNDS is not #defined.
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* #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
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* that use extended-precision instructions to compute rounded
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* products and quotients) with IBM.
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* #define ROUND_BIASED for IEEE-format with biased rounding.
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* #define Inaccurate_Divide for IEEE-format with correctly rounded
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* products but inaccurate quotients, e.g., for Intel i860.
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* #define NO_LONG_LONG on machines that do not have a "long long"
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* integer type (of >= 64 bits). On such machines, you can
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* #define Just_16 to store 16 bits per 32-bit Long when doing
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* high-precision integer arithmetic. Whether this speeds things
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* up or slows things down depends on the machine and the number
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* being converted. If long long is available and the name is
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* something other than "long long", #define Llong to be the name,
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* and if "unsigned Llong" does not work as an unsigned version of
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* Llong, #define #ULLong to be the corresponding unsigned type.
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* #define KR_headers for old-style C function headers.
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* #define Bad_float_h if your system lacks a float.h or if it does not
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* define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
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* FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
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* #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
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* if memory is available and otherwise does something you deem
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* appropriate. If MALLOC is undefined, malloc will be invoked
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* directly -- and assumed always to succeed.
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* #define Omit_Private_Memory to omit logic (added Jan. 1998) for making
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* memory allocations from a private pool of memory when possible.
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* When used, the private pool is PRIVATE_MEM bytes long: 2304 bytes,
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* unless #defined to be a different length. This default length
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* suffices to get rid of MALLOC calls except for unusual cases,
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* such as decimal-to-binary conversion of a very long string of
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* digits. The longest string dtoa can return is about 751 bytes
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* long. For conversions by strtod of strings of 800 digits and
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* all dtoa conversions in single-threaded executions with 8-byte
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* pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte
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* pointers, PRIVATE_MEM >= 7112 appears adequate.
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* #define INFNAN_CHECK on IEEE systems to cause strtod to check for
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* Infinity and NaN (case insensitively). On some systems (e.g.,
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* some HP systems), it may be necessary to #define NAN_WORD0
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* appropriately -- to the most significant word of a quiet NaN.
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* (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)
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* When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined,
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* strtod also accepts (case insensitively) strings of the form
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* NaN(x), where x is a string of hexadecimal digits and spaces;
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* if there is only one string of hexadecimal digits, it is taken
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* for the 52 fraction bits of the resulting NaN; if there are two
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* or more strings of hex digits, the first is for the high 20 bits,
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* the second and subsequent for the low 32 bits, with intervening
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* white space ignored; but if this results in none of the 52
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* fraction bits being on (an IEEE Infinity symbol), then NAN_WORD0
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* and NAN_WORD1 are used instead.
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* #define MULTIPLE_THREADS if the system offers preemptively scheduled
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* multiple threads. In this case, you must provide (or suitably
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* #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed
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* by FREE_DTOA_LOCK(n) for n = 0 or 1. (The second lock, accessed
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* in pow5mult, ensures lazy evaluation of only one copy of high
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* powers of 5; omitting this lock would introduce a small
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* probability of wasting memory, but would otherwise be harmless.)
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* You must also invoke freedtoa(s) to free the value s returned by
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* dtoa. You may do so whether or not MULTIPLE_THREADS is #defined.
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* #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that
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* avoids underflows on inputs whose result does not underflow.
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* If you #define NO_IEEE_Scale on a machine that uses IEEE-format
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* floating-point numbers and flushes underflows to zero rather
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* than implementing gradual underflow, then you must also #define
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* Sudden_Underflow.
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* #define YES_ALIAS to permit aliasing certain double values with
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* arrays of ULongs. This leads to slightly better code with
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* some compilers and was always used prior to 19990916, but it
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* is not strictly legal and can cause trouble with aggressively
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* optimizing compilers (e.g., gcc 2.95.1 under -O2).
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* #define USE_LOCALE to use the current locale's decimal_point value.
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* #define SET_INEXACT if IEEE arithmetic is being used and extra
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* computation should be done to set the inexact flag when the
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* result is inexact and avoid setting inexact when the result
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* is exact. In this case, dtoa.c must be compiled in
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* an environment, perhaps provided by #include "dtoa.c" in a
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* suitable wrapper, that defines two functions,
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* int get_inexact(void);
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* void clear_inexact(void);
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* such that get_inexact() returns a nonzero value if the
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* inexact bit is already set, and clear_inexact() sets the
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* inexact bit to 0. When SET_INEXACT is #defined, strtod
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* also does extra computations to set the underflow and overflow
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* flags when appropriate (i.e., when the result is tiny and
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* inexact or when it is a numeric value rounded to +-infinity).
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* #define NO_ERRNO if strtod should not assign errno = ERANGE when
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* the result overflows to +-Infinity or underflows to 0.
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*/
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#ifndef Long
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#define Long long |
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#endif
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#ifndef ULong
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typedef unsigned Long ULong; |
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#endif
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#ifdef DEBUG
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#include "stdio.h" |
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#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);} |
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#endif
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#include "stdlib.h" |
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#include "string.h" |
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#ifdef USE_LOCALE
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#include "locale.h" |
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#endif
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#ifdef MALLOC
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#ifdef KR_headers
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extern char *MALLOC(); |
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#else
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extern void *MALLOC(size_t); |
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#endif
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#else
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#define MALLOC malloc
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#endif
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#ifndef Omit_Private_Memory
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#ifndef PRIVATE_MEM
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#define PRIVATE_MEM 2304 |
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#endif
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#define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double)) |
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static double private_mem[PRIVATE_mem], *pmem_next = private_mem; |
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#endif
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#undef IEEE_Arith
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#undef Avoid_Underflow
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#ifdef IEEE_MC68k
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#define IEEE_Arith
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#endif
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#ifdef IEEE_8087
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#define IEEE_Arith
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#endif
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#include "errno.h" |
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#ifdef Bad_float_h
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#ifdef IEEE_Arith
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#define DBL_DIG 15 |
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#define DBL_MAX_10_EXP 308 |
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#define DBL_MAX_EXP 1024 |
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#define FLT_RADIX 2 |
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#endif /*IEEE_Arith*/ |
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#ifdef IBM
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#define DBL_DIG 16 |
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#define DBL_MAX_10_EXP 75 |
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#define DBL_MAX_EXP 63 |
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#define FLT_RADIX 16 |
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#define DBL_MAX 7.2370055773322621e+75 |
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#endif
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#ifdef VAX
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#define DBL_DIG 16 |
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#define DBL_MAX_10_EXP 38 |
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#define DBL_MAX_EXP 127 |
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#define FLT_RADIX 2 |
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#define DBL_MAX 1.7014118346046923e+38 |
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#endif
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#ifndef LONG_MAX
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#define LONG_MAX 2147483647 |
| 241 |
#endif
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#else /* ifndef Bad_float_h */ |
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#include "float.h" |
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#endif /* Bad_float_h */ |
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#ifndef __MATH_H__
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#include "math.h" |
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#endif
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#ifdef __cplusplus
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extern "C" { |
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#endif
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#ifndef CONST
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#ifdef KR_headers
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#define CONST /* blank */ |
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#else
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#define CONST const |
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#endif
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#endif
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#if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1 |
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Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined. |
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#endif
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typedef union { double d; ULong L[2]; } U; |
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#ifdef YES_ALIAS
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#define dval(x) x
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#ifdef IEEE_8087
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#define word0(x) ((ULong *)&x)[1] |
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#define word1(x) ((ULong *)&x)[0] |
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#else
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#define word0(x) ((ULong *)&x)[0] |
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#define word1(x) ((ULong *)&x)[1] |
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#endif
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#else
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#ifdef IEEE_8087
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#define word0(x) ((U*)&x)->L[1] |
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#define word1(x) ((U*)&x)->L[0] |
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#else
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#define word0(x) ((U*)&x)->L[0] |
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#define word1(x) ((U*)&x)->L[1] |
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#endif
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#define dval(x) ((U*)&x)->d
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#endif
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/* The following definition of Storeinc is appropriate for MIPS processors.
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* An alternative that might be better on some machines is
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* #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
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*/
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#if defined(IEEE_8087) + defined(VAX)
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#define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \ |
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((unsigned short *)a)[0] = (unsigned short)c, a++) |
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#else
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#define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \ |
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((unsigned short *)a)[1] = (unsigned short)c, a++) |
| 299 |
#endif
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| 300 |
|
| 301 |
/* #define P DBL_MANT_DIG */
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/* Ten_pmax = floor(P*log(2)/log(5)) */
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/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
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| 304 |
/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
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| 305 |
/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
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| 306 |
|
| 307 |
#ifdef IEEE_Arith
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| 308 |
#define Exp_shift 20 |
| 309 |
#define Exp_shift1 20 |
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#define Exp_msk1 0x100000 |
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#define Exp_msk11 0x100000 |
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#define Exp_mask 0x7ff00000 |
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#define P 53 |
| 314 |
#define Bias 1023 |
| 315 |
#define Emin (-1022) |
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#define Exp_1 0x3ff00000 |
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#define Exp_11 0x3ff00000 |
| 318 |
#define Ebits 11 |
| 319 |
#define Frac_mask 0xfffff |
| 320 |
#define Frac_mask1 0xfffff |
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#define Ten_pmax 22 |
| 322 |
#define Bletch 0x10 |
| 323 |
#define Bndry_mask 0xfffff |
| 324 |
#define Bndry_mask1 0xfffff |
| 325 |
#define LSB 1 |
| 326 |
#define Sign_bit 0x80000000 |
| 327 |
#define Log2P 1 |
| 328 |
#define Tiny0 0 |
| 329 |
#define Tiny1 1 |
| 330 |
#define Quick_max 14 |
| 331 |
#define Int_max 14 |
| 332 |
#ifndef NO_IEEE_Scale
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| 333 |
#define Avoid_Underflow
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| 334 |
#ifdef Flush_Denorm /* debugging option */ |
| 335 |
#undef Sudden_Underflow
|
| 336 |
#endif
|
| 337 |
#endif
|
| 338 |
|
| 339 |
#ifndef Flt_Rounds
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| 340 |
#ifdef FLT_ROUNDS
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| 341 |
#define Flt_Rounds FLT_ROUNDS
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| 342 |
#else
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| 343 |
#define Flt_Rounds 1 |
| 344 |
#endif
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| 345 |
#endif /*Flt_Rounds*/ |
| 346 |
|
| 347 |
#ifdef Honor_FLT_ROUNDS
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| 348 |
#define Rounding rounding
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| 349 |
#undef Check_FLT_ROUNDS
|
| 350 |
#define Check_FLT_ROUNDS
|
| 351 |
#else
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| 352 |
#define Rounding Flt_Rounds
|
| 353 |
#endif
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| 354 |
|
| 355 |
#else /* ifndef IEEE_Arith */ |
| 356 |
#undef Check_FLT_ROUNDS
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| 357 |
#undef Honor_FLT_ROUNDS
|
| 358 |
#undef SET_INEXACT
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| 359 |
#undef Sudden_Underflow
|
| 360 |
#define Sudden_Underflow
|
| 361 |
#ifdef IBM
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| 362 |
#undef Flt_Rounds
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| 363 |
#define Flt_Rounds 0 |
| 364 |
#define Exp_shift 24 |
| 365 |
#define Exp_shift1 24 |
| 366 |
#define Exp_msk1 0x1000000 |
| 367 |
#define Exp_msk11 0x1000000 |
| 368 |
#define Exp_mask 0x7f000000 |
| 369 |
#define P 14 |
| 370 |
#define Bias 65 |
| 371 |
#define Exp_1 0x41000000 |
| 372 |
#define Exp_11 0x41000000 |
| 373 |
#define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */ |
| 374 |
#define Frac_mask 0xffffff |
| 375 |
#define Frac_mask1 0xffffff |
| 376 |
#define Bletch 4 |
| 377 |
#define Ten_pmax 22 |
| 378 |
#define Bndry_mask 0xefffff |
| 379 |
#define Bndry_mask1 0xffffff |
| 380 |
#define LSB 1 |
| 381 |
#define Sign_bit 0x80000000 |
| 382 |
#define Log2P 4 |
| 383 |
#define Tiny0 0x100000 |
| 384 |
#define Tiny1 0 |
| 385 |
#define Quick_max 14 |
| 386 |
#define Int_max 15 |
| 387 |
#else /* VAX */ |
| 388 |
#undef Flt_Rounds
|
| 389 |
#define Flt_Rounds 1 |
| 390 |
#define Exp_shift 23 |
| 391 |
#define Exp_shift1 7 |
| 392 |
#define Exp_msk1 0x80 |
| 393 |
#define Exp_msk11 0x800000 |
| 394 |
#define Exp_mask 0x7f80 |
| 395 |
#define P 56 |
| 396 |
#define Bias 129 |
| 397 |
#define Exp_1 0x40800000 |
| 398 |
#define Exp_11 0x4080 |
| 399 |
#define Ebits 8 |
| 400 |
#define Frac_mask 0x7fffff |
| 401 |
#define Frac_mask1 0xffff007f |
| 402 |
#define Ten_pmax 24 |
| 403 |
#define Bletch 2 |
| 404 |
#define Bndry_mask 0xffff007f |
| 405 |
#define Bndry_mask1 0xffff007f |
| 406 |
#define LSB 0x10000 |
| 407 |
#define Sign_bit 0x8000 |
| 408 |
#define Log2P 1 |
| 409 |
#define Tiny0 0x80 |
| 410 |
#define Tiny1 0 |
| 411 |
#define Quick_max 15 |
| 412 |
#define Int_max 15 |
| 413 |
#endif /* IBM, VAX */ |
| 414 |
#endif /* IEEE_Arith */ |
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|
| 416 |
#ifndef IEEE_Arith
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| 417 |
#define ROUND_BIASED
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| 418 |
#endif
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|
| 420 |
#ifdef RND_PRODQUOT
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#define rounded_product(a,b) a = rnd_prod(a, b)
|
| 422 |
#define rounded_quotient(a,b) a = rnd_quot(a, b)
|
| 423 |
#ifdef KR_headers
|
| 424 |
extern double rnd_prod(), rnd_quot(); |
| 425 |
#else
|
| 426 |
extern double rnd_prod(double, double), rnd_quot(double, double); |
| 427 |
#endif
|
| 428 |
#else
|
| 429 |
#define rounded_product(a,b) a *= b
|
| 430 |
#define rounded_quotient(a,b) a /= b
|
| 431 |
#endif
|
| 432 |
|
| 433 |
#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1)) |
| 434 |
#define Big1 0xffffffff |
| 435 |
|
| 436 |
#ifndef Pack_32
|
| 437 |
#define Pack_32
|
| 438 |
#endif
|
| 439 |
|
| 440 |
#ifdef KR_headers
|
| 441 |
#define FFFFFFFF ((((unsigned long)0xffff)<<16)|(unsigned long)0xffff) |
| 442 |
#else
|
| 443 |
#define FFFFFFFF 0xffffffffUL |
| 444 |
#endif
|
| 445 |
|
| 446 |
#ifdef NO_LONG_LONG
|
| 447 |
#undef ULLong
|
| 448 |
#ifdef Just_16
|
| 449 |
#undef Pack_32
|
| 450 |
/* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
|
| 451 |
* This makes some inner loops simpler and sometimes saves work
|
| 452 |
* during multiplications, but it often seems to make things slightly
|
| 453 |
* slower. Hence the default is now to store 32 bits per Long.
|
| 454 |
*/
|
| 455 |
#endif
|
| 456 |
#else /* long long available */ |
| 457 |
#ifndef Llong
|
| 458 |
#define Llong long long |
| 459 |
#endif
|
| 460 |
#ifndef ULLong
|
| 461 |
#define ULLong unsigned Llong |
| 462 |
#endif
|
| 463 |
#endif /* NO_LONG_LONG */ |
| 464 |
|
| 465 |
#ifndef MULTIPLE_THREADS
|
| 466 |
#define ACQUIRE_DTOA_LOCK(n) /*nothing*/ |
| 467 |
#define FREE_DTOA_LOCK(n) /*nothing*/ |
| 468 |
#endif
|
| 469 |
|
| 470 |
#define Kmax 15 |
| 471 |
|
| 472 |
#ifdef __cplusplus
|
| 473 |
extern "C" double strtod(const char *s00, char **se); |
| 474 |
extern "C" char *dtoa(double d, int mode, int ndigits, |
| 475 |
int *decpt, int *sign, char **rve); |
| 476 |
#endif
|
| 477 |
|
| 478 |
struct
|
| 479 |
Bigint {
|
| 480 |
struct Bigint *next;
|
| 481 |
int k, maxwds, sign, wds;
|
| 482 |
ULong x[1];
|
| 483 |
}; |
| 484 |
|
| 485 |
typedef struct Bigint Bigint; |
| 486 |
|
| 487 |
static Bigint *freelist[Kmax+1]; |
| 488 |
|
| 489 |
static Bigint *
|
| 490 |
Balloc |
| 491 |
#ifdef KR_headers
|
| 492 |
(k) int k;
|
| 493 |
#else
|
| 494 |
(int k)
|
| 495 |
#endif
|
| 496 |
{
|
| 497 |
int x;
|
| 498 |
Bigint *rv; |
| 499 |
#ifndef Omit_Private_Memory
|
| 500 |
unsigned int len; |
| 501 |
#endif
|
| 502 |
|
| 503 |
ACQUIRE_DTOA_LOCK(0);
|
| 504 |
if ((rv = freelist[k])) {
|
| 505 |
freelist[k] = rv->next; |
| 506 |
} |
| 507 |
else {
|
| 508 |
x = 1 << k;
|
| 509 |
#ifdef Omit_Private_Memory
|
| 510 |
rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong)); |
| 511 |
#else
|
| 512 |
len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1) |
| 513 |
/sizeof(double); |
| 514 |
if (pmem_next - private_mem + len <= PRIVATE_mem) {
|
| 515 |
rv = (Bigint*)pmem_next; |
| 516 |
pmem_next += len; |
| 517 |
} |
| 518 |
else
|
| 519 |
rv = (Bigint*)MALLOC(len*sizeof(double)); |
| 520 |
#endif
|
| 521 |
rv->k = k; |
| 522 |
rv->maxwds = x; |
| 523 |
} |
| 524 |
FREE_DTOA_LOCK(0);
|
| 525 |
rv->sign = rv->wds = 0;
|
| 526 |
return rv;
|
| 527 |
} |
| 528 |
|
| 529 |
static void |
| 530 |
Bfree |
| 531 |
#ifdef KR_headers
|
| 532 |
(v) Bigint *v; |
| 533 |
#else
|
| 534 |
(Bigint *v) |
| 535 |
#endif
|
| 536 |
{
|
| 537 |
if (v) {
|
| 538 |
ACQUIRE_DTOA_LOCK(0);
|
| 539 |
v->next = freelist[v->k]; |
| 540 |
freelist[v->k] = v; |
| 541 |
FREE_DTOA_LOCK(0);
|
| 542 |
} |
| 543 |
} |
| 544 |
|
| 545 |
#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \ |
| 546 |
y->wds*sizeof(Long) + 2*sizeof(int)) |
| 547 |
|
| 548 |
static Bigint *
|
| 549 |
multadd |
| 550 |
#ifdef KR_headers
|
| 551 |
(b, m, a) Bigint *b; int m, a;
|
| 552 |
#else
|
| 553 |
(Bigint *b, int m, int a) /* multiply by m and add a */ |
| 554 |
#endif
|
| 555 |
{
|
| 556 |
int i, wds;
|
| 557 |
#ifdef ULLong
|
| 558 |
ULong *x; |
| 559 |
ULLong carry, y; |
| 560 |
#else
|
| 561 |
ULong carry, *x, y; |
| 562 |
#ifdef Pack_32
|
| 563 |
ULong xi, z; |
| 564 |
#endif
|
| 565 |
#endif
|
| 566 |
Bigint *b1; |
| 567 |
|
| 568 |
wds = b->wds; |
| 569 |
x = b->x; |
| 570 |
i = 0;
|
| 571 |
carry = a; |
| 572 |
do {
|
| 573 |
#ifdef ULLong
|
| 574 |
y = *x * (ULLong)m + carry; |
| 575 |
carry = y >> 32;
|
| 576 |
*x++ = y & FFFFFFFF; |
| 577 |
#else
|
| 578 |
#ifdef Pack_32
|
| 579 |
xi = *x; |
| 580 |
y = (xi & 0xffff) * m + carry;
|
| 581 |
z = (xi >> 16) * m + (y >> 16); |
| 582 |
carry = z >> 16;
|
| 583 |
*x++ = (z << 16) + (y & 0xffff); |
| 584 |
#else
|
| 585 |
y = *x * m + carry; |
| 586 |
carry = y >> 16;
|
| 587 |
*x++ = y & 0xffff;
|
| 588 |
#endif
|
| 589 |
#endif
|
| 590 |
} |
| 591 |
while(++i < wds);
|
| 592 |
if (carry) {
|
| 593 |
if (wds >= b->maxwds) {
|
| 594 |
b1 = Balloc(b->k+1);
|
| 595 |
Bcopy(b1, b); |
| 596 |
Bfree(b); |
| 597 |
b = b1; |
| 598 |
} |
| 599 |
b->x[wds++] = carry; |
| 600 |
b->wds = wds; |
| 601 |
} |
| 602 |
return b;
|
| 603 |
} |
| 604 |
|
| 605 |
static Bigint *
|
| 606 |
s2b |
| 607 |
#ifdef KR_headers
|
| 608 |
(s, nd0, nd, y9) CONST char *s; int nd0, nd; ULong y9; |
| 609 |
#else
|
| 610 |
(CONST char *s, int nd0, int nd, ULong y9) |
| 611 |
#endif
|
| 612 |
{
|
| 613 |
Bigint *b; |
| 614 |
int i, k;
|
| 615 |
Long x, y; |
| 616 |
|
| 617 |
x = (nd + 8) / 9; |
| 618 |
for(k = 0, y = 1; x > y; y <<= 1, k++) ; |
| 619 |
#ifdef Pack_32
|
| 620 |
b = Balloc(k); |
| 621 |
b->x[0] = y9;
|
| 622 |
b->wds = 1;
|
| 623 |
#else
|
| 624 |
b = Balloc(k+1);
|
| 625 |
b->x[0] = y9 & 0xffff; |
| 626 |
b->wds = (b->x[1] = y9 >> 16) ? 2 : 1; |
| 627 |
#endif
|
| 628 |
|
| 629 |
i = 9;
|
| 630 |
if (9 < nd0) { |
| 631 |
s += 9;
|
| 632 |
do b = multadd(b, 10, *s++ - '0'); |
| 633 |
while(++i < nd0);
|
| 634 |
s++; |
| 635 |
} |
| 636 |
else
|
| 637 |
s += 10;
|
| 638 |
for(; i < nd; i++)
|
| 639 |
b = multadd(b, 10, *s++ - '0'); |
| 640 |
return b;
|
| 641 |
} |
| 642 |
|
| 643 |
static int |
| 644 |
hi0bits |
| 645 |
#ifdef KR_headers
|
| 646 |
(x) register ULong x;
|
| 647 |
#else
|
| 648 |
(register ULong x)
|
| 649 |
#endif
|
| 650 |
{
|
| 651 |
register int k = 0; |
| 652 |
|
| 653 |
if (!(x & 0xffff0000)) { |
| 654 |
k = 16;
|
| 655 |
x <<= 16;
|
| 656 |
} |
| 657 |
if (!(x & 0xff000000)) { |
| 658 |
k += 8;
|
| 659 |
x <<= 8;
|
| 660 |
} |
| 661 |
if (!(x & 0xf0000000)) { |
| 662 |
k += 4;
|
| 663 |
x <<= 4;
|
| 664 |
} |
| 665 |
if (!(x & 0xc0000000)) { |
| 666 |
k += 2;
|
| 667 |
x <<= 2;
|
| 668 |
} |
| 669 |
if (!(x & 0x80000000)) { |
| 670 |
k++; |
| 671 |
if (!(x & 0x40000000)) |
| 672 |
return 32; |
| 673 |
} |
| 674 |
return k;
|
| 675 |
} |
| 676 |
|
| 677 |
static int |
| 678 |
lo0bits |
| 679 |
#ifdef KR_headers
|
| 680 |
(y) ULong *y; |
| 681 |
#else
|
| 682 |
(ULong *y) |
| 683 |
#endif
|
| 684 |
{
|
| 685 |
register int k; |
| 686 |
register ULong x = *y;
|
| 687 |
|
| 688 |
if (x & 7) { |
| 689 |
if (x & 1) |
| 690 |
return 0; |
| 691 |
if (x & 2) { |
| 692 |
*y = x >> 1;
|
| 693 |
return 1; |
| 694 |
} |
| 695 |
*y = x >> 2;
|
| 696 |
return 2; |
| 697 |
} |
| 698 |
k = 0;
|
| 699 |
if (!(x & 0xffff)) { |
| 700 |
k = 16;
|
| 701 |
x >>= 16;
|
| 702 |
} |
| 703 |
if (!(x & 0xff)) { |
| 704 |
k += 8;
|
| 705 |
x >>= 8;
|
| 706 |
} |
| 707 |
if (!(x & 0xf)) { |
| 708 |
k += 4;
|
| 709 |
x >>= 4;
|
| 710 |
} |
| 711 |
if (!(x & 0x3)) { |
| 712 |
k += 2;
|
| 713 |
x >>= 2;
|
| 714 |
} |
| 715 |
if (!(x & 1)) { |
| 716 |
k++; |
| 717 |
x >>= 1;
|
| 718 |
if (!x)
|
| 719 |
return 32; |
| 720 |
} |
| 721 |
*y = x; |
| 722 |
return k;
|
| 723 |
} |
| 724 |
|
| 725 |
static Bigint *
|
| 726 |
i2b |
| 727 |
#ifdef KR_headers
|
| 728 |
(i) int i;
|
| 729 |
#else
|
| 730 |
(int i)
|
| 731 |
#endif
|
| 732 |
{
|
| 733 |
Bigint *b; |
| 734 |
|
| 735 |
b = Balloc(1);
|
| 736 |
b->x[0] = i;
|
| 737 |
b->wds = 1;
|
| 738 |
return b;
|
| 739 |
} |
| 740 |
|
| 741 |
static Bigint *
|
| 742 |
mult |
| 743 |
#ifdef KR_headers
|
| 744 |
(a, b) Bigint *a, *b; |
| 745 |
#else
|
| 746 |
(Bigint *a, Bigint *b) |
| 747 |
#endif
|
| 748 |
{
|
| 749 |
Bigint *c; |
| 750 |
int k, wa, wb, wc;
|
| 751 |
ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0; |
| 752 |
ULong y; |
| 753 |
#ifdef ULLong
|
| 754 |
ULLong carry, z; |
| 755 |
#else
|
| 756 |
ULong carry, z; |
| 757 |
#ifdef Pack_32
|
| 758 |
ULong z2; |
| 759 |
#endif
|
| 760 |
#endif
|
| 761 |
|
| 762 |
if (a->wds < b->wds) {
|
| 763 |
c = a; |
| 764 |
a = b; |
| 765 |
b = c; |
| 766 |
} |
| 767 |
k = a->k; |
| 768 |
wa = a->wds; |
| 769 |
wb = b->wds; |
| 770 |
wc = wa + wb; |
| 771 |
if (wc > a->maxwds)
|
| 772 |
k++; |
| 773 |
c = Balloc(k); |
| 774 |
for(x = c->x, xa = x + wc; x < xa; x++)
|
| 775 |
*x = 0;
|
| 776 |
xa = a->x; |
| 777 |
xae = xa + wa; |
| 778 |
xb = b->x; |
| 779 |
xbe = xb + wb; |
| 780 |
xc0 = c->x; |
| 781 |
#ifdef ULLong
|
| 782 |
for(; xb < xbe; xc0++) {
|
| 783 |
if ((y = *xb++)) {
|
| 784 |
x = xa; |
| 785 |
xc = xc0; |
| 786 |
carry = 0;
|
| 787 |
do {
|
| 788 |
z = *x++ * (ULLong)y + *xc + carry; |
| 789 |
carry = z >> 32;
|
| 790 |
*xc++ = z & FFFFFFFF; |
| 791 |
} |
| 792 |
while(x < xae);
|
| 793 |
*xc = carry; |
| 794 |
} |
| 795 |
} |
| 796 |
#else
|
| 797 |
#ifdef Pack_32
|
| 798 |
for(; xb < xbe; xb++, xc0++) {
|
| 799 |
if (y = *xb & 0xffff) { |
| 800 |
x = xa; |
| 801 |
xc = xc0; |
| 802 |
carry = 0;
|
| 803 |
do {
|
| 804 |
z = (*x & 0xffff) * y + (*xc & 0xffff) + carry; |
| 805 |
carry = z >> 16;
|
| 806 |
z2 = (*x++ >> 16) * y + (*xc >> 16) + carry; |
| 807 |
carry = z2 >> 16;
|
| 808 |
Storeinc(xc, z2, z); |
| 809 |
} |
| 810 |
while(x < xae);
|
| 811 |
*xc = carry; |
| 812 |
} |
| 813 |
if (y = *xb >> 16) { |
| 814 |
x = xa; |
| 815 |
xc = xc0; |
| 816 |
carry = 0;
|
| 817 |
z2 = *xc; |
| 818 |
do {
|
| 819 |
z = (*x & 0xffff) * y + (*xc >> 16) + carry; |
| 820 |
carry = z >> 16;
|
| 821 |
Storeinc(xc, z, z2); |
| 822 |
z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry; |
| 823 |
carry = z2 >> 16;
|
| 824 |
} |
| 825 |
while(x < xae);
|
| 826 |
*xc = z2; |
| 827 |
} |
| 828 |
} |
| 829 |
#else
|
| 830 |
for(; xb < xbe; xc0++) {
|
| 831 |
if (y = *xb++) {
|
| 832 |
x = xa; |
| 833 |
xc = xc0; |
| 834 |
carry = 0;
|
| 835 |
do {
|
| 836 |
z = *x++ * y + *xc + carry; |
| 837 |
carry = z >> 16;
|
| 838 |
*xc++ = z & 0xffff;
|
| 839 |
} |
| 840 |
while(x < xae);
|
| 841 |
*xc = carry; |
| 842 |
} |
| 843 |
} |
| 844 |
#endif
|
| 845 |
#endif
|
| 846 |
for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ; |
| 847 |
c->wds = wc; |
| 848 |
return c;
|
| 849 |
} |
| 850 |
|
| 851 |
static Bigint *p5s;
|
| 852 |
|
| 853 |
static Bigint *
|
| 854 |
pow5mult |
| 855 |
#ifdef KR_headers
|
| 856 |
(b, k) Bigint *b; int k;
|
| 857 |
#else
|
| 858 |
(Bigint *b, int k)
|
| 859 |
#endif
|
| 860 |
{
|
| 861 |
Bigint *b1, *p5, *p51; |
| 862 |
int i;
|
| 863 |
static int p05[3] = { 5, 25, 125 }; |
| 864 |
|
| 865 |
if ((i = k & 3)) |
| 866 |
b = multadd(b, p05[i-1], 0); |
| 867 |
|
| 868 |
if (!(k >>= 2)) |
| 869 |
return b;
|
| 870 |
if (!(p5 = p5s)) {
|
| 871 |
/* first time */
|
| 872 |
#ifdef MULTIPLE_THREADS
|
| 873 |
ACQUIRE_DTOA_LOCK(1);
|
| 874 |
if (!(p5 = p5s)) {
|
| 875 |
p5 = p5s = i2b(625);
|
| 876 |
p5->next = 0;
|
| 877 |
} |
| 878 |
FREE_DTOA_LOCK(1);
|
| 879 |
#else
|
| 880 |
p5 = p5s = i2b(625);
|
| 881 |
p5->next = 0;
|
| 882 |
#endif
|
| 883 |
} |
| 884 |
for(;;) {
|
| 885 |
if (k & 1) { |
| 886 |
b1 = mult(b, p5); |
| 887 |
Bfree(b); |
| 888 |
b = b1; |
| 889 |
} |
| 890 |
if (!(k >>= 1)) |
| 891 |
break;
|
| 892 |
if (!(p51 = p5->next)) {
|
| 893 |
#ifdef MULTIPLE_THREADS
|
| 894 |
ACQUIRE_DTOA_LOCK(1);
|
| 895 |
if (!(p51 = p5->next)) {
|
| 896 |
p51 = p5->next = mult(p5,p5); |
| 897 |
p51->next = 0;
|
| 898 |
} |
| 899 |
FREE_DTOA_LOCK(1);
|
| 900 |
#else
|
| 901 |
p51 = p5->next = mult(p5,p5); |
| 902 |
p51->next = 0;
|
| 903 |
#endif
|
| 904 |
} |
| 905 |
p5 = p51; |
| 906 |
} |
| 907 |
return b;
|
| 908 |
} |
| 909 |
|
| 910 |
static Bigint *
|
| 911 |
lshift |
| 912 |
#ifdef KR_headers
|
| 913 |
(b, k) Bigint *b; int k;
|
| 914 |
#else
|
| 915 |
(Bigint *b, int k)
|
| 916 |
#endif
|
| 917 |
{
|
| 918 |
int i, k1, n, n1;
|
| 919 |
Bigint *b1; |
| 920 |
ULong *x, *x1, *xe, z; |
| 921 |
|
| 922 |
#ifdef Pack_32
|
| 923 |
n = k >> 5;
|
| 924 |
#else
|
| 925 |
n = k >> 4;
|
| 926 |
#endif
|
| 927 |
k1 = b->k; |
| 928 |
n1 = n + b->wds + 1;
|
| 929 |
for(i = b->maxwds; n1 > i; i <<= 1) |
| 930 |
k1++; |
| 931 |
b1 = Balloc(k1); |
| 932 |
x1 = b1->x; |
| 933 |
for(i = 0; i < n; i++) |
| 934 |
*x1++ = 0;
|
| 935 |
x = b->x; |
| 936 |
xe = x + b->wds; |
| 937 |
#ifdef Pack_32
|
| 938 |
if (k &= 0x1f) { |
| 939 |
k1 = 32 - k;
|
| 940 |
z = 0;
|
| 941 |
do {
|
| 942 |
*x1++ = *x << k | z; |
| 943 |
z = *x++ >> k1; |
| 944 |
} |
| 945 |
while(x < xe);
|
| 946 |
if ((*x1 = z))
|
| 947 |
++n1; |
| 948 |
} |
| 949 |
#else
|
| 950 |
if (k &= 0xf) { |
| 951 |
k1 = 16 - k;
|
| 952 |
z = 0;
|
| 953 |
do {
|
| 954 |
*x1++ = *x << k & 0xffff | z;
|
| 955 |
z = *x++ >> k1; |
| 956 |
} |
| 957 |
while(x < xe);
|
| 958 |
if (*x1 = z)
|
| 959 |
++n1; |
| 960 |
} |
| 961 |
#endif
|
| 962 |
else do |
| 963 |
*x1++ = *x++; |
| 964 |
while(x < xe);
|
| 965 |
b1->wds = n1 - 1;
|
| 966 |
Bfree(b); |
| 967 |
return b1;
|
| 968 |
} |
| 969 |
|
| 970 |
static int |
| 971 |
cmp |
| 972 |
#ifdef KR_headers
|
| 973 |
(a, b) Bigint *a, *b; |
| 974 |
#else
|
| 975 |
(Bigint *a, Bigint *b) |
| 976 |
#endif
|
| 977 |
{
|
| 978 |
ULong *xa, *xa0, *xb, *xb0; |
| 979 |
int i, j;
|
| 980 |
|
| 981 |
i = a->wds; |
| 982 |
j = b->wds; |
| 983 |
#ifdef DEBUG
|
| 984 |
if (i > 1 && !a->x[i-1]) |
| 985 |
Bug("cmp called with a->x[a->wds-1] == 0");
|
| 986 |
if (j > 1 && !b->x[j-1]) |
| 987 |
Bug("cmp called with b->x[b->wds-1] == 0");
|
| 988 |
#endif
|
| 989 |
if (i -= j)
|
| 990 |
return i;
|
| 991 |
xa0 = a->x; |
| 992 |
xa = xa0 + j; |
| 993 |
xb0 = b->x; |
| 994 |
xb = xb0 + j; |
| 995 |
for(;;) {
|
| 996 |
if (*--xa != *--xb)
|
| 997 |
return *xa < *xb ? -1 : 1; |
| 998 |
if (xa <= xa0)
|
| 999 |
break;
|
| 1000 |
} |
| 1001 |
return 0; |
| 1002 |
} |
| 1003 |
|
| 1004 |
static Bigint *
|
| 1005 |
diff |
| 1006 |
#ifdef KR_headers
|
| 1007 |
(a, b) Bigint *a, *b; |
| 1008 |
#else
|
| 1009 |
(Bigint *a, Bigint *b) |
| 1010 |
#endif
|
| 1011 |
{
|
| 1012 |
Bigint *c; |
| 1013 |
int i, wa, wb;
|
| 1014 |
ULong *xa, *xae, *xb, *xbe, *xc; |
| 1015 |
#ifdef ULLong
|
| 1016 |
ULLong borrow, y; |
| 1017 |
#else
|
| 1018 |
ULong borrow, y; |
| 1019 |
#ifdef Pack_32
|
| 1020 |
ULong z; |
| 1021 |
#endif
|
| 1022 |
#endif
|
| 1023 |
|
| 1024 |
i = cmp(a,b); |
| 1025 |
if (!i) {
|
| 1026 |
c = Balloc(0);
|
| 1027 |
c->wds = 1;
|
| 1028 |
c->x[0] = 0; |
| 1029 |
return c;
|
| 1030 |
} |
| 1031 |
if (i < 0) { |
| 1032 |
c = a; |
| 1033 |
a = b; |
| 1034 |
b = c; |
| 1035 |
i = 1;
|
| 1036 |
} |
| 1037 |
else
|
| 1038 |
i = 0;
|
| 1039 |
c = Balloc(a->k); |
| 1040 |
c->sign = i; |
| 1041 |
wa = a->wds; |
| 1042 |
xa = a->x; |
| 1043 |
xae = xa + wa; |
| 1044 |
wb = b->wds; |
| 1045 |
xb = b->x; |
| 1046 |
xbe = xb + wb; |
| 1047 |
xc = c->x; |
| 1048 |
borrow = 0;
|
| 1049 |
#ifdef ULLong
|
| 1050 |
do {
|
| 1051 |
y = (ULLong)*xa++ - *xb++ - borrow; |
| 1052 |
borrow = y >> 32 & (ULong)1; |
| 1053 |
*xc++ = y & FFFFFFFF; |
| 1054 |
} |
| 1055 |
while(xb < xbe);
|
| 1056 |
while(xa < xae) {
|
| 1057 |
y = *xa++ - borrow; |
| 1058 |
borrow = y >> 32 & (ULong)1; |
| 1059 |
*xc++ = y & FFFFFFFF; |
| 1060 |
} |
| 1061 |
#else
|
| 1062 |
#ifdef Pack_32
|
| 1063 |
do {
|
| 1064 |
y = (*xa & 0xffff) - (*xb & 0xffff) - borrow; |
| 1065 |
borrow = (y & 0x10000) >> 16; |
| 1066 |
z = (*xa++ >> 16) - (*xb++ >> 16) - borrow; |
| 1067 |
borrow = (z & 0x10000) >> 16; |
| 1068 |
Storeinc(xc, z, y); |
| 1069 |
} |
| 1070 |
while(xb < xbe);
|
| 1071 |
while(xa < xae) {
|
| 1072 |
y = (*xa & 0xffff) - borrow;
|
| 1073 |
borrow = (y & 0x10000) >> 16; |
| 1074 |
z = (*xa++ >> 16) - borrow;
|
| 1075 |
borrow = (z & 0x10000) >> 16; |
| 1076 |
Storeinc(xc, z, y); |
| 1077 |
} |
| 1078 |
#else
|
| 1079 |
do {
|
| 1080 |
y = *xa++ - *xb++ - borrow; |
| 1081 |
borrow = (y & 0x10000) >> 16; |
| 1082 |
*xc++ = y & 0xffff;
|
| 1083 |
} |
| 1084 |
while(xb < xbe);
|
| 1085 |
while(xa < xae) {
|
| 1086 |
y = *xa++ - borrow; |
| 1087 |
borrow = (y & 0x10000) >> 16; |
| 1088 |
*xc++ = y & 0xffff;
|
| 1089 |
} |
| 1090 |
#endif
|
| 1091 |
#endif
|
| 1092 |
while(!*--xc)
|
| 1093 |
wa--; |
| 1094 |
c->wds = wa; |
| 1095 |
return c;
|
| 1096 |
} |
| 1097 |
|
| 1098 |
static double |
| 1099 |
ulp |
| 1100 |
#ifdef KR_headers
|
| 1101 |
(x) double x;
|
| 1102 |
#else
|
| 1103 |
(double x)
|
| 1104 |
#endif
|
| 1105 |
{
|
| 1106 |
register Long L;
|
| 1107 |
double a;
|
| 1108 |
|
| 1109 |
L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
|
| 1110 |
#ifndef Avoid_Underflow
|
| 1111 |
#ifndef Sudden_Underflow
|
| 1112 |
if (L > 0) { |
| 1113 |
#endif
|
| 1114 |
#endif
|
| 1115 |
#ifdef IBM
|
| 1116 |
L |= Exp_msk1 >> 4;
|
| 1117 |
#endif
|
| 1118 |
word0(a) = L; |
| 1119 |
word1(a) = 0;
|
| 1120 |
#ifndef Avoid_Underflow
|
| 1121 |
#ifndef Sudden_Underflow
|
| 1122 |
} |
| 1123 |
else {
|
| 1124 |
L = -L >> Exp_shift; |
| 1125 |
if (L < Exp_shift) {
|
| 1126 |
word0(a) = 0x80000 >> L;
|
| 1127 |
word1(a) = 0;
|
| 1128 |
} |
| 1129 |
else {
|
| 1130 |
word0(a) = 0;
|
| 1131 |
L -= Exp_shift; |
| 1132 |
word1(a) = L >= 31 ? 1 : 1 << 31 - L; |
| 1133 |
} |
| 1134 |
} |
| 1135 |
#endif
|
| 1136 |
#endif
|
| 1137 |
return dval(a);
|
| 1138 |
} |
| 1139 |
|
| 1140 |
static double |
| 1141 |
b2d |
| 1142 |
#ifdef KR_headers
|
| 1143 |
(a, e) Bigint *a; int *e;
|
| 1144 |
#else
|
| 1145 |
(Bigint *a, int *e)
|
| 1146 |
#endif
|
| 1147 |
{
|
| 1148 |
ULong *xa, *xa0, w, y, z; |
| 1149 |
int k;
|
| 1150 |
double d;
|
| 1151 |
#ifdef VAX
|
| 1152 |
ULong d0, d1; |
| 1153 |
#else
|
| 1154 |
#define d0 word0(d)
|
| 1155 |
#define d1 word1(d)
|
| 1156 |
#endif
|
| 1157 |
|
| 1158 |
xa0 = a->x; |
| 1159 |
xa = xa0 + a->wds; |
| 1160 |
y = *--xa; |
| 1161 |
#ifdef DEBUG
|
| 1162 |
if (!y) Bug("zero y in b2d"); |
| 1163 |
#endif
|
| 1164 |
k = hi0bits(y); |
| 1165 |
*e = 32 - k;
|
| 1166 |
#ifdef Pack_32
|
| 1167 |
if (k < Ebits) {
|
| 1168 |
d0 = Exp_1 | (y >> (Ebits - k)); |
| 1169 |
w = xa > xa0 ? *--xa : 0;
|
| 1170 |
d1 = (y << ((32-Ebits) + k)) | (w >> (Ebits - k));
|
| 1171 |
goto ret_d;
|
| 1172 |
} |
| 1173 |
z = xa > xa0 ? *--xa : 0;
|
| 1174 |
if (k -= Ebits) {
|
| 1175 |
d0 = Exp_1 | (y << k) | (z >> (32 - k));
|
| 1176 |
y = xa > xa0 ? *--xa : 0;
|
| 1177 |
d1 = (z << k) | (y >> (32 - k));
|
| 1178 |
} |
| 1179 |
else {
|
| 1180 |
d0 = Exp_1 | y; |
| 1181 |
d1 = z; |
| 1182 |
} |
| 1183 |
#else
|
| 1184 |
if (k < Ebits + 16) { |
| 1185 |
z = xa > xa0 ? *--xa : 0;
|
| 1186 |
d0 = Exp_1 | (y << (k - Ebits)) | (z >> (Ebits + 16 - k));
|
| 1187 |
w = xa > xa0 ? *--xa : 0;
|
| 1188 |
y = xa > xa0 ? *--xa : 0;
|
| 1189 |
d1 = (z << (k + 16 - Ebits)) | (w << (k - Ebits)) | (y >> (16 + Ebits - k)); |
| 1190 |
goto ret_d;
|
| 1191 |
} |
| 1192 |
z = xa > xa0 ? *--xa : 0;
|
| 1193 |
w = xa > xa0 ? *--xa : 0;
|
| 1194 |
k -= Ebits + 16;
|
| 1195 |
d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k; |
| 1196 |
y = xa > xa0 ? *--xa : 0;
|
| 1197 |
d1 = w << k + 16 | y << k;
|
| 1198 |
#endif
|
| 1199 |
ret_d:
|
| 1200 |
#ifdef VAX
|
| 1201 |
word0(d) = d0 >> 16 | d0 << 16; |
| 1202 |
word1(d) = d1 >> 16 | d1 << 16; |
| 1203 |
#else
|
| 1204 |
#undef d0
|
| 1205 |
#undef d1
|
| 1206 |
#endif
|
| 1207 |
return dval(d);
|
| 1208 |
} |
| 1209 |
|
| 1210 |
static Bigint *
|
| 1211 |
d2b |
| 1212 |
#ifdef KR_headers
|
| 1213 |
(d, e, bits) double d; int *e, *bits; |
| 1214 |
#else
|
| 1215 |
(double d, int *e, int *bits) |
| 1216 |
#endif
|
| 1217 |
{
|
| 1218 |
Bigint *b; |
| 1219 |
int de, k;
|
| 1220 |
ULong *x, y, z; |
| 1221 |
#ifndef Sudden_Underflow
|
| 1222 |
int i;
|
| 1223 |
#endif
|
| 1224 |
#ifdef VAX
|
| 1225 |
ULong d0, d1; |
| 1226 |
d0 = word0(d) >> 16 | word0(d) << 16; |
| 1227 |
d1 = word1(d) >> 16 | word1(d) << 16; |
| 1228 |
#else
|
| 1229 |
#define d0 word0(d)
|
| 1230 |
#define d1 word1(d)
|
| 1231 |
#endif
|
| 1232 |
|
| 1233 |
#ifdef Pack_32
|
| 1234 |
b = Balloc(1);
|
| 1235 |
#else
|
| 1236 |
b = Balloc(2);
|
| 1237 |
#endif
|
| 1238 |
x = b->x; |
| 1239 |
|
| 1240 |
z = d0 & Frac_mask; |
| 1241 |
d0 &= 0x7fffffff; /* clear sign bit, which we ignore */ |
| 1242 |
#ifdef Sudden_Underflow
|
| 1243 |
de = (int)(d0 >> Exp_shift);
|
| 1244 |
#ifndef IBM
|
| 1245 |
z |= Exp_msk11; |
| 1246 |
#endif
|
| 1247 |
#else
|
| 1248 |
if ((de = (int)(d0 >> Exp_shift))) |
| 1249 |
z |= Exp_msk1; |
| 1250 |
#endif
|
| 1251 |
#ifdef Pack_32
|
| 1252 |
if ((y = d1)) {
|
| 1253 |
if ((k = lo0bits(&y))) {
|
| 1254 |
x[0] = y | (z << (32 - k)); |
| 1255 |
z >>= k; |
| 1256 |
} |
| 1257 |
else
|
| 1258 |
x[0] = y;
|
| 1259 |
#ifndef Sudden_Underflow
|
| 1260 |
i = |
| 1261 |
#endif
|
| 1262 |
b->wds = (x[1] = z) ? 2 : 1; |
| 1263 |
} |
| 1264 |
else {
|
| 1265 |
/* This assertion fails for "1e-500" and other very
|
| 1266 |
* small numbers. It provides the right result (0)
|
| 1267 |
* though. This assert has also been removed from KJS's
|
| 1268 |
* version of dtoa.c.
|
| 1269 |
*
|
| 1270 |
* #ifdef DEBUG
|
| 1271 |
* if (!z) Bug("zero z in b2d");
|
| 1272 |
* #endif
|
| 1273 |
*/
|
| 1274 |
k = lo0bits(&z); |
| 1275 |
x[0] = z;
|
| 1276 |
#ifndef Sudden_Underflow
|
| 1277 |
i = |
| 1278 |
#endif
|
| 1279 |
b->wds = 1;
|
| 1280 |
k += 32;
|
| 1281 |
} |
| 1282 |
#else
|
| 1283 |
if (y = d1) {
|
| 1284 |
if (k = lo0bits(&y))
|
| 1285 |
if (k >= 16) { |
| 1286 |
x[0] = y | z << 32 - k & 0xffff; |
| 1287 |
x[1] = z >> k - 16 & 0xffff; |
| 1288 |
x[2] = z >> k;
|
| 1289 |
i = 2;
|
| 1290 |
} |
| 1291 |
else {
|
| 1292 |
x[0] = y & 0xffff; |
| 1293 |
x[1] = y >> 16 | z << 16 - k & 0xffff; |
| 1294 |
x[2] = z >> k & 0xffff; |
| 1295 |
x[3] = z >> k+16; |
| 1296 |
i = 3;
|
| 1297 |
} |
| 1298 |
else {
|
| 1299 |
x[0] = y & 0xffff; |
| 1300 |
x[1] = y >> 16; |
| 1301 |
x[2] = z & 0xffff; |
| 1302 |
x[3] = z >> 16; |
| 1303 |
i = 3;
|
| 1304 |
} |
| 1305 |
} |
| 1306 |
else {
|
| 1307 |
#ifdef DEBUG
|
| 1308 |
if (!z)
|
| 1309 |
Bug("Zero passed to d2b");
|
| 1310 |
#endif
|
| 1311 |
k = lo0bits(&z); |
| 1312 |
if (k >= 16) { |
| 1313 |
x[0] = z;
|
| 1314 |
i = 0;
|
| 1315 |
} |
| 1316 |
else {
|
| 1317 |
x[0] = z & 0xffff; |
| 1318 |
x[1] = z >> 16; |
| 1319 |
i = 1;
|
| 1320 |
} |
| 1321 |
k += 32;
|
| 1322 |
} |
| 1323 |
while(!x[i])
|
| 1324 |
--i; |
| 1325 |
b->wds = i + 1;
|
| 1326 |
#endif
|
| 1327 |
#ifndef Sudden_Underflow
|
| 1328 |
if (de) {
|
| 1329 |
#endif
|
| 1330 |
#ifdef IBM
|
| 1331 |
*e = (de - Bias - (P-1) << 2) + k; |
| 1332 |
*bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask); |
| 1333 |
#else
|
| 1334 |
*e = de - Bias - (P-1) + k;
|
| 1335 |
*bits = P - k; |
| 1336 |
#endif
|
| 1337 |
#ifndef Sudden_Underflow
|
| 1338 |
} |
| 1339 |
else {
|
| 1340 |
*e = de - Bias - (P-1) + 1 + k; |
| 1341 |
#ifdef Pack_32
|
| 1342 |
*bits = 32*i - hi0bits(x[i-1]); |
| 1343 |
#else
|
| 1344 |
*bits = (i+2)*16 - hi0bits(x[i]); |
| 1345 |
#endif
|
| 1346 |
} |
| 1347 |
#endif
|
| 1348 |
return b;
|
| 1349 |
} |
| 1350 |
#undef d0
|
| 1351 |
#undef d1
|
| 1352 |
|
| 1353 |
static double |
| 1354 |
ratio |
| 1355 |
#ifdef KR_headers
|
| 1356 |
(a, b) Bigint *a, *b; |
| 1357 |
#else
|
| 1358 |
(Bigint *a, Bigint *b) |
| 1359 |
#endif
|
| 1360 |
{
|
| 1361 |
double da, db;
|
| 1362 |
int k, ka, kb;
|
| 1363 |
|
| 1364 |
dval(da) = b2d(a, &ka); |
| 1365 |
dval(db) = b2d(b, &kb); |
| 1366 |
#ifdef Pack_32
|
| 1367 |
k = ka - kb + 32*(a->wds - b->wds);
|
| 1368 |
#else
|
| 1369 |
k = ka - kb + 16*(a->wds - b->wds);
|
| 1370 |
#endif
|
| 1371 |
#ifdef IBM
|
| 1372 |
if (k > 0) { |
| 1373 |
word0(da) += (k >> 2)*Exp_msk1;
|
| 1374 |
if (k &= 3) |
| 1375 |
dval(da) *= 1 << k;
|
| 1376 |
} |
| 1377 |
else {
|
| 1378 |
k = -k; |
| 1379 |
word0(db) += (k >> 2)*Exp_msk1;
|
| 1380 |
if (k &= 3) |
| 1381 |
dval(db) *= 1 << k;
|
| 1382 |
} |
| 1383 |
#else
|
| 1384 |
if (k > 0) |
| 1385 |
word0(da) += k*Exp_msk1; |
| 1386 |
else {
|
| 1387 |
k = -k; |
| 1388 |
word0(db) += k*Exp_msk1; |
| 1389 |
} |
| 1390 |
#endif
|
| 1391 |
return dval(da) / dval(db);
|
| 1392 |
} |
| 1393 |
|
| 1394 |
static CONST double |
| 1395 |
tens[] = {
|
| 1396 |
1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, |
| 1397 |
1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, |
| 1398 |
1e20, 1e21, 1e22 |
| 1399 |
#ifdef VAX
|
| 1400 |
, 1e23, 1e24 |
| 1401 |
#endif
|
| 1402 |
}; |
| 1403 |
|
| 1404 |
static CONST double |
| 1405 |
#ifdef IEEE_Arith
|
| 1406 |
bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
|
| 1407 |
static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, |
| 1408 |
#ifdef Avoid_Underflow
|
| 1409 |
9007199254740992.*9007199254740992.e-256 |
| 1410 |
/* = 2^106 * 1e-53 */
|
| 1411 |
#else
|
| 1412 |
1e-256 |
| 1413 |
#endif
|
| 1414 |
}; |
| 1415 |
/* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
|
| 1416 |
/* flag unnecessarily. It leads to a song and dance at the end of strtod. */
|
| 1417 |
#define Scale_Bit 0x10 |
| 1418 |
#define n_bigtens 5 |
| 1419 |
#else
|
| 1420 |
#ifdef IBM
|
| 1421 |
bigtens[] = { 1e16, 1e32, 1e64 };
|
| 1422 |
static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 }; |
| 1423 |
#define n_bigtens 3 |
| 1424 |
#else
|
| 1425 |
bigtens[] = { 1e16, 1e32 };
|
| 1426 |
static CONST double tinytens[] = { 1e-16, 1e-32 }; |
| 1427 |
#define n_bigtens 2 |
| 1428 |
#endif
|
| 1429 |
#endif
|
| 1430 |
|
| 1431 |
#ifndef IEEE_Arith
|
| 1432 |
#undef INFNAN_CHECK
|
| 1433 |
#endif
|
| 1434 |
|
| 1435 |
#ifdef INFNAN_CHECK
|
| 1436 |
|
| 1437 |
#ifndef NAN_WORD0
|
| 1438 |
#define NAN_WORD0 0x7ff80000 |
| 1439 |
#endif
|
| 1440 |
|
| 1441 |
#ifndef NAN_WORD1
|
| 1442 |
#define NAN_WORD1 0 |
| 1443 |
#endif
|
| 1444 |
|
| 1445 |
static int |
| 1446 |
match |
| 1447 |
#ifdef KR_headers
|
| 1448 |
(sp, t) char **sp, *t;
|
| 1449 |
#else
|
| 1450 |
(CONST char **sp, char *t) |
| 1451 |
#endif
|
| 1452 |
{
|
| 1453 |
int c, d;
|
| 1454 |
CONST char *s = *sp;
|
| 1455 |
|
| 1456 |
while(d = *t++) {
|
| 1457 |
if ((c = *++s) >= 'A' && c <= 'Z') |
| 1458 |
c += 'a' - 'A'; |
| 1459 |
if (c != d)
|
| 1460 |
return 0; |
| 1461 |
} |
| 1462 |
*sp = s + 1;
|
| 1463 |
return 1; |
| 1464 |
} |
| 1465 |
|
| 1466 |
#ifndef No_Hex_NaN
|
| 1467 |
static void |
| 1468 |
hexnan |
| 1469 |
#ifdef KR_headers
|
| 1470 |
(rvp, sp) double *rvp; CONST char **sp; |
| 1471 |
#else
|
| 1472 |
(double *rvp, CONST char **sp) |
| 1473 |
#endif
|
| 1474 |
{
|
| 1475 |
ULong c, x[2];
|
| 1476 |
CONST char *s;
|
| 1477 |
int havedig, udx0, xshift;
|
| 1478 |
|
| 1479 |
x[0] = x[1] = 0; |
| 1480 |
havedig = xshift = 0;
|
| 1481 |
udx0 = 1;
|
| 1482 |
s = *sp; |
| 1483 |
while(c = *(CONST unsigned char*)++s) { |
| 1484 |
if (c >= '0' && c <= '9') |
| 1485 |
c -= '0';
|
| 1486 |
else if (c >= 'a' && c <= 'f') |
| 1487 |
c += 10 - 'a'; |
| 1488 |
else if (c >= 'A' && c <= 'F') |
| 1489 |
c += 10 - 'A'; |
| 1490 |
else if (c <= ' ') { |
| 1491 |
if (udx0 && havedig) {
|
| 1492 |
udx0 = 0;
|
| 1493 |
xshift = 1;
|
| 1494 |
} |
| 1495 |
continue;
|
| 1496 |
} |
| 1497 |
else if (/*(*/ c == ')' && havedig) { |
| 1498 |
*sp = s + 1;
|
| 1499 |
break;
|
| 1500 |
} |
| 1501 |
else
|
| 1502 |
return; /* invalid form: don't change *sp */ |
| 1503 |
havedig = 1;
|
| 1504 |
if (xshift) {
|
| 1505 |
xshift = 0;
|
| 1506 |
x[0] = x[1]; |
| 1507 |
x[1] = 0; |
| 1508 |
} |
| 1509 |
if (udx0)
|
| 1510 |
x[0] = (x[0] << 4) | (x[1] >> 28); |
| 1511 |
x[1] = (x[1] << 4) | c; |
| 1512 |
} |
| 1513 |
if ((x[0] &= 0xfffff) || x[1]) { |
| 1514 |
word0(*rvp) = Exp_mask | x[0];
|
| 1515 |
word1(*rvp) = x[1];
|
| 1516 |
} |
| 1517 |
} |
| 1518 |
#endif /*No_Hex_NaN*/ |
| 1519 |
#endif /* INFNAN_CHECK */ |
| 1520 |
|
| 1521 |
double
|
| 1522 |
strtod |
| 1523 |
#ifdef KR_headers
|
| 1524 |
(s00, se) CONST char *s00; char **se; |
| 1525 |
#else
|
| 1526 |
(CONST char *s00, char **se) |
| 1527 |
#endif
|
| 1528 |
{
|
| 1529 |
#ifdef Avoid_Underflow
|
| 1530 |
int scale;
|
| 1531 |
#endif
|
| 1532 |
int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
|
| 1533 |
e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign; |
| 1534 |
CONST char *s, *s0, *s1;
|
| 1535 |
double aadj, aadj1, adj, rv, rv0;
|
| 1536 |
Long L; |
| 1537 |
ULong y, z; |
| 1538 |
Bigint *bb, *bb1, *bd, *bd0, *bs, *delta; |
| 1539 |
#ifdef SET_INEXACT
|
| 1540 |
int inexact, oldinexact;
|
| 1541 |
#endif
|
| 1542 |
#ifdef Honor_FLT_ROUNDS
|
| 1543 |
int rounding;
|
| 1544 |
#endif
|
| 1545 |
#ifdef USE_LOCALE
|
| 1546 |
CONST char *s2;
|
| 1547 |
#endif
|
| 1548 |
|
| 1549 |
sign = nz0 = nz = 0;
|
| 1550 |
dval(rv) = 0.;
|
| 1551 |
for(s = s00;;s++) switch(*s) { |
| 1552 |
case '-': |
| 1553 |
sign = 1;
|
| 1554 |
/* no break */
|
| 1555 |
case '+': |
| 1556 |
if (*++s)
|
| 1557 |
goto break2;
|
| 1558 |
/* no break */
|
| 1559 |
case 0: |
| 1560 |
goto ret0;
|
| 1561 |
case '\t': |
| 1562 |
case '\n': |
| 1563 |
case '\v': |
| 1564 |
case '\f': |
| 1565 |
case '\r': |
| 1566 |
case ' ': |
| 1567 |
continue;
|
| 1568 |
default:
|
| 1569 |
goto break2;
|
| 1570 |
} |
| 1571 |
break2:
|
| 1572 |
if (*s == '0') { |
| 1573 |
nz0 = 1;
|
| 1574 |
while(*++s == '0') ; |
| 1575 |
if (!*s)
|
| 1576 |
goto ret;
|
| 1577 |
} |
| 1578 |
s0 = s; |
| 1579 |
y = z = 0;
|
| 1580 |
for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++) |
| 1581 |
if (nd < 9) |
| 1582 |
y = 10*y + c - '0'; |
| 1583 |
else if (nd < 16) |
| 1584 |
z = 10*z + c - '0'; |
| 1585 |
nd0 = nd; |
| 1586 |
#ifdef USE_LOCALE
|
| 1587 |
s1 = localeconv()->decimal_point; |
| 1588 |
if (c == *s1) {
|
| 1589 |
c = '.';
|
| 1590 |
if (*++s1) {
|
| 1591 |
s2 = s; |
| 1592 |
for(;;) {
|
| 1593 |
if (*++s2 != *s1) {
|
| 1594 |
c = 0;
|
| 1595 |
break;
|
| 1596 |
} |
| 1597 |
if (!*++s1) {
|
| 1598 |
s = s2; |
| 1599 |
break;
|
| 1600 |
} |
| 1601 |
} |
| 1602 |
} |
| 1603 |
} |
| 1604 |
#endif
|
| 1605 |
if (c == '.') { |
| 1606 |
c = *++s; |
| 1607 |
if (!nd) {
|
| 1608 |
for(; c == '0'; c = *++s) |
| 1609 |
nz++; |
| 1610 |
if (c > '0' && c <= '9') { |
| 1611 |
s0 = s; |
| 1612 |
nf += nz; |
| 1613 |
nz = 0;
|
| 1614 |
goto have_dig;
|
| 1615 |
} |
| 1616 |
goto dig_done;
|
| 1617 |
} |
| 1618 |
for(; c >= '0' && c <= '9'; c = *++s) { |
| 1619 |
have_dig:
|
| 1620 |
nz++; |
| 1621 |
if (c -= '0') { |
| 1622 |
nf += nz; |
| 1623 |
for(i = 1; i < nz; i++) |
| 1624 |
if (nd++ < 9) |
| 1625 |
y *= 10;
|
| 1626 |
else if (nd <= DBL_DIG + 1) |
| 1627 |
z *= 10;
|
| 1628 |
if (nd++ < 9) |
| 1629 |
y = 10*y + c;
|
| 1630 |
else if (nd <= DBL_DIG + 1) |
| 1631 |
z = 10*z + c;
|
| 1632 |
nz = 0;
|
| 1633 |
} |
| 1634 |
} |
| 1635 |
} |
| 1636 |
dig_done:
|
| 1637 |
e = 0;
|
| 1638 |
if (c == 'e' || c == 'E') { |
| 1639 |
if (!nd && !nz && !nz0) {
|
| 1640 |
goto ret0;
|
| 1641 |
} |
| 1642 |
s00 = s; |
| 1643 |
esign = 0;
|
| 1644 |
switch(c = *++s) {
|
| 1645 |
case '-': |
| 1646 |
esign = 1;
|
| 1647 |
case '+': |
| 1648 |
c = *++s; |
| 1649 |
} |
| 1650 |
if (c >= '0' && c <= '9') { |
| 1651 |
while(c == '0') |
| 1652 |
c = *++s; |
| 1653 |
if (c > '0' && c <= '9') { |
| 1654 |
L = c - '0';
|
| 1655 |
s1 = s; |
| 1656 |
while((c = *++s) >= '0' && c <= '9') |
| 1657 |
L = 10*L + c - '0'; |
| 1658 |
if (s - s1 > 8 || L > 19999) |
| 1659 |
/* Avoid confusion from exponents
|
| 1660 |
* so large that e might overflow.
|
| 1661 |
*/
|
| 1662 |
e = 19999; /* safe for 16 bit ints */ |
| 1663 |
else
|
| 1664 |
e = (int)L;
|
| 1665 |
if (esign)
|
| 1666 |
e = -e; |
| 1667 |
} |
| 1668 |
else
|
| 1669 |
e = 0;
|
| 1670 |
} |
| 1671 |
else
|
| 1672 |
s = s00; |
| 1673 |
} |
| 1674 |
if (!nd) {
|
| 1675 |
if (!nz && !nz0) {
|
| 1676 |
#ifdef INFNAN_CHECK
|
| 1677 |
/* Check for Nan and Infinity */
|
| 1678 |
switch(c) {
|
| 1679 |
case 'i': |
| 1680 |
case 'I': |
| 1681 |
if (match(&s,"nf")) { |
| 1682 |
--s; |
| 1683 |
if (!match(&s,"inity")) |
| 1684 |
++s; |
| 1685 |
word0(rv) = 0x7ff00000;
|
| 1686 |
word1(rv) = 0;
|
| 1687 |
goto ret;
|
| 1688 |
} |
| 1689 |
break;
|
| 1690 |
case 'n': |
| 1691 |
case 'N': |
| 1692 |
if (match(&s, "an")) { |
| 1693 |
word0(rv) = NAN_WORD0; |
| 1694 |
word1(rv) = NAN_WORD1; |
| 1695 |
#ifndef No_Hex_NaN
|
| 1696 |
if (*s == '(') /*)*/ |
| 1697 |
hexnan(&rv, &s); |
| 1698 |
#endif
|
| 1699 |
goto ret;
|
| 1700 |
} |
| 1701 |
} |
| 1702 |
#endif /* INFNAN_CHECK */ |
| 1703 |
ret0:
|
| 1704 |
s = s00; |
| 1705 |
sign = 0;
|
| 1706 |
} |
| 1707 |
goto ret;
|
| 1708 |
} |
| 1709 |
e1 = e -= nf; |
| 1710 |
|
| 1711 |
/* Now we have nd0 digits, starting at s0, followed by a
|
| 1712 |
* decimal point, followed by nd-nd0 digits. The number we're
|
| 1713 |
* after is the integer represented by those digits times
|
| 1714 |
* 10**e */
|
| 1715 |
|
| 1716 |
if (!nd0)
|
| 1717 |
nd0 = nd; |
| 1718 |
k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1; |
| 1719 |
dval(rv) = y; |
| 1720 |
if (k > 9) { |
| 1721 |
#ifdef SET_INEXACT
|
| 1722 |
if (k > DBL_DIG)
|
| 1723 |
oldinexact = get_inexact(); |
| 1724 |
#endif
|
| 1725 |
dval(rv) = tens[k - 9] * dval(rv) + z;
|
| 1726 |
} |
| 1727 |
bd0 = 0;
|
| 1728 |
if (nd <= DBL_DIG
|
| 1729 |
#ifndef RND_PRODQUOT
|
| 1730 |
#ifndef Honor_FLT_ROUNDS
|
| 1731 |
&& Flt_Rounds == 1
|
| 1732 |
#endif
|
| 1733 |
#endif
|
| 1734 |
) {
|
| 1735 |
if (!e)
|
| 1736 |
goto ret;
|
| 1737 |
if (e > 0) { |
| 1738 |
if (e <= Ten_pmax) {
|
| 1739 |
#ifdef VAX
|
| 1740 |
goto vax_ovfl_check;
|
| 1741 |
#else
|
| 1742 |
#ifdef Honor_FLT_ROUNDS
|
| 1743 |
/* round correctly FLT_ROUNDS = 2 or 3 */
|
| 1744 |
if (sign) {
|
| 1745 |
rv = -rv; |
| 1746 |
sign = 0;
|
| 1747 |
} |
| 1748 |
#endif
|
| 1749 |
/* rv = */ rounded_product(dval(rv), tens[e]);
|
| 1750 |
goto ret;
|
| 1751 |
#endif
|
| 1752 |
} |
| 1753 |
i = DBL_DIG - nd; |
| 1754 |
if (e <= Ten_pmax + i) {
|
| 1755 |
/* A fancier test would sometimes let us do
|
| 1756 |
* this for larger i values.
|
| 1757 |
*/
|
| 1758 |
#ifdef Honor_FLT_ROUNDS
|
| 1759 |
/* round correctly FLT_ROUNDS = 2 or 3 */
|
| 1760 |
if (sign) {
|
| 1761 |
rv = -rv; |
| 1762 |
sign = 0;
|
| 1763 |
} |
| 1764 |
#endif
|
| 1765 |
e -= i; |
| 1766 |
dval(rv) *= tens[i]; |
| 1767 |
#ifdef VAX
|
| 1768 |
/* VAX exponent range is so narrow we must
|
| 1769 |
* worry about overflow here...
|
| 1770 |
*/
|
| 1771 |
vax_ovfl_check:
|
| 1772 |
word0(rv) -= P*Exp_msk1; |
| 1773 |
/* rv = */ rounded_product(dval(rv), tens[e]);
|
| 1774 |
if ((word0(rv) & Exp_mask)
|
| 1775 |
> Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
|
| 1776 |
goto ovfl;
|
| 1777 |
word0(rv) += P*Exp_msk1; |
| 1778 |
#else
|
| 1779 |
/* rv = */ rounded_product(dval(rv), tens[e]);
|
| 1780 |
#endif
|
| 1781 |
goto ret;
|
| 1782 |
} |
| 1783 |
} |
| 1784 |
#ifndef Inaccurate_Divide
|
| 1785 |
else if (e >= -Ten_pmax) { |
| 1786 |
#ifdef Honor_FLT_ROUNDS
|
| 1787 |
/* round correctly FLT_ROUNDS = 2 or 3 */
|
| 1788 |
if (sign) {
|
| 1789 |
rv = -rv; |
| 1790 |
sign = 0;
|
| 1791 |
} |
| 1792 |
#endif
|
| 1793 |
/* rv = */ rounded_quotient(dval(rv), tens[-e]);
|
| 1794 |
goto ret;
|
| 1795 |
} |
| 1796 |
#endif
|
| 1797 |
} |
| 1798 |
e1 += nd - k; |
| 1799 |
|
| 1800 |
#ifdef IEEE_Arith
|
| 1801 |
#ifdef SET_INEXACT
|
| 1802 |
inexact = 1;
|
| 1803 |
if (k <= DBL_DIG)
|
| 1804 |
oldinexact = get_inexact(); |
| 1805 |
#endif
|
| 1806 |
#ifdef Avoid_Underflow
|
| 1807 |
scale = 0;
|
| 1808 |
#endif
|
| 1809 |
#ifdef Honor_FLT_ROUNDS
|
| 1810 |
if ((rounding = Flt_Rounds) >= 2) { |
| 1811 |
if (sign)
|
| 1812 |
rounding = rounding == 2 ? 0 : 2; |
| 1813 |
else
|
| 1814 |
if (rounding != 2) |
| 1815 |
rounding = 0;
|
| 1816 |
} |
| 1817 |
#endif
|
| 1818 |
#endif /*IEEE_Arith*/ |
| 1819 |
|
| 1820 |
/* Get starting approximation = rv * 10**e1 */
|
| 1821 |
|
| 1822 |
if (e1 > 0) { |
| 1823 |
if ((i = e1 & 15)) |
| 1824 |
dval(rv) *= tens[i]; |
| 1825 |
if (e1 &= ~15) { |
| 1826 |
if (e1 > DBL_MAX_10_EXP) {
|
| 1827 |
ovfl:
|
| 1828 |
#ifndef NO_ERRNO
|
| 1829 |
errno = ERANGE; |
| 1830 |
#endif
|
| 1831 |
/* Can't trust HUGE_VAL */
|
| 1832 |
#ifdef IEEE_Arith
|
| 1833 |
#ifdef Honor_FLT_ROUNDS
|
| 1834 |
switch(rounding) {
|
| 1835 |
case 0: /* toward 0 */ |
| 1836 |
case 3: /* toward -infinity */ |
| 1837 |
word0(rv) = Big0; |
| 1838 |
word1(rv) = Big1; |
| 1839 |
break;
|
| 1840 |
default:
|
| 1841 |
word0(rv) = Exp_mask; |
| 1842 |
word1(rv) = 0;
|
| 1843 |
} |
| 1844 |
#else /*Honor_FLT_ROUNDS*/ |
| 1845 |
word0(rv) = Exp_mask; |
| 1846 |
word1(rv) = 0;
|
| 1847 |
#endif /*Honor_FLT_ROUNDS*/ |
| 1848 |
#ifdef SET_INEXACT
|
| 1849 |
/* set overflow bit */
|
| 1850 |
dval(rv0) = 1e300;
|
| 1851 |
dval(rv0) *= dval(rv0); |
| 1852 |
#endif
|
| 1853 |
#else /*IEEE_Arith*/ |
| 1854 |
word0(rv) = Big0; |
| 1855 |
word1(rv) = Big1; |
| 1856 |
#endif /*IEEE_Arith*/ |
| 1857 |
if (bd0)
|
| 1858 |
goto retfree;
|
| 1859 |
goto ret;
|
| 1860 |
} |
| 1861 |
e1 >>= 4;
|
| 1862 |
for(j = 0; e1 > 1; j++, e1 >>= 1) |
| 1863 |
if (e1 & 1) |
| 1864 |
dval(rv) *= bigtens[j]; |
| 1865 |
/* The last multiplication could overflow. */
|
| 1866 |
word0(rv) -= P*Exp_msk1; |
| 1867 |
dval(rv) *= bigtens[j]; |
| 1868 |
if ((z = word0(rv) & Exp_mask)
|
| 1869 |
> Exp_msk1*(DBL_MAX_EXP+Bias-P)) |
| 1870 |
goto ovfl;
|
| 1871 |
if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) { |
| 1872 |
/* set to largest number */
|
| 1873 |
/* (Can't trust DBL_MAX) */
|
| 1874 |
word0(rv) = Big0; |
| 1875 |
word1(rv) = Big1; |
| 1876 |
} |
| 1877 |
else
|
| 1878 |
word0(rv) += P*Exp_msk1; |
| 1879 |
} |
| 1880 |
} |
| 1881 |
else if (e1 < 0) { |
| 1882 |
e1 = -e1; |
| 1883 |
if ((i = e1 & 15)) |
| 1884 |
dval(rv) /= tens[i]; |
| 1885 |
if (e1 >>= 4) { |
| 1886 |
if (e1 >= 1 << n_bigtens) |
| 1887 |
goto undfl;
|
| 1888 |
#ifdef Avoid_Underflow
|
| 1889 |
if (e1 & Scale_Bit)
|
| 1890 |
scale = 2*P;
|
| 1891 |
for(j = 0; e1 > 0; j++, e1 >>= 1) |
| 1892 |
if (e1 & 1) |
| 1893 |
dval(rv) *= tinytens[j]; |
| 1894 |
if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask) |
| 1895 |
>> Exp_shift)) > 0) {
|
| 1896 |
/* scaled rv is denormal; zap j low bits */
|
| 1897 |
if (j >= 32) { |
| 1898 |
word1(rv) = 0;
|
| 1899 |
if (j >= 53) |
| 1900 |
word0(rv) = (P+2)*Exp_msk1;
|
| 1901 |
else
|
| 1902 |
word0(rv) &= 0xffffffff << (j-32); |
| 1903 |
} |
| 1904 |
else
|
| 1905 |
word1(rv) &= 0xffffffff << j;
|
| 1906 |
} |
| 1907 |
#else
|
| 1908 |
for(j = 0; e1 > 1; j++, e1 >>= 1) |
| 1909 |
if (e1 & 1) |
| 1910 |
dval(rv) *= tinytens[j]; |
| 1911 |
/* The last multiplication could underflow. */
|
| 1912 |
dval(rv0) = dval(rv); |
| 1913 |
dval(rv) *= tinytens[j]; |
| 1914 |
if (!dval(rv)) {
|
| 1915 |
dval(rv) = 2.*dval(rv0);
|
| 1916 |
dval(rv) *= tinytens[j]; |
| 1917 |
#endif
|
| 1918 |
if (!dval(rv)) {
|
| 1919 |
undfl:
|
| 1920 |
dval(rv) = 0.;
|
| 1921 |
#ifndef NO_ERRNO
|
| 1922 |
errno = ERANGE; |
| 1923 |
#endif
|
| 1924 |
if (bd0)
|
| 1925 |
goto retfree;
|
| 1926 |
goto ret;
|
| 1927 |
} |
| 1928 |
#ifndef Avoid_Underflow
|
| 1929 |
word0(rv) = Tiny0; |
| 1930 |
word1(rv) = Tiny1; |
| 1931 |
/* The refinement below will clean
|
| 1932 |
* this approximation up.
|
| 1933 |
*/
|
| 1934 |
} |
| 1935 |
#endif
|
| 1936 |
} |
| 1937 |
} |
| 1938 |
|
| 1939 |
/* Now the hard part -- adjusting rv to the correct value.*/
|
| 1940 |
|
| 1941 |
/* Put digits into bd: true value = bd * 10^e */
|
| 1942 |
|
| 1943 |
bd0 = s2b(s0, nd0, nd, y); |
| 1944 |
|
| 1945 |
for(;;) {
|
| 1946 |
bd = Balloc(bd0->k); |
| 1947 |
Bcopy(bd, bd0); |
| 1948 |
bb = d2b(dval(rv), &bbe, &bbbits); /* rv = bb * 2^bbe */
|
| 1949 |
bs = i2b(1);
|
| 1950 |
|
| 1951 |
if (e >= 0) { |
| 1952 |
bb2 = bb5 = 0;
|
| 1953 |
bd2 = bd5 = e; |
| 1954 |
} |
| 1955 |
else {
|
| 1956 |
bb2 = bb5 = -e; |
| 1957 |
bd2 = bd5 = 0;
|
| 1958 |
} |
| 1959 |
if (bbe >= 0) |
| 1960 |
bb2 += bbe; |
| 1961 |
else
|
| 1962 |
bd2 -= bbe; |
| 1963 |
bs2 = bb2; |
| 1964 |
#ifdef Honor_FLT_ROUNDS
|
| 1965 |
if (rounding != 1) |
| 1966 |
bs2++; |
| 1967 |
#endif
|
| 1968 |
#ifdef Avoid_Underflow
|
| 1969 |
j = bbe - scale; |
| 1970 |
i = j + bbbits - 1; /* logb(rv) */ |
| 1971 |
if (i < Emin) /* denormal */ |
| 1972 |
j += P - Emin; |
| 1973 |
else
|
| 1974 |
j = P + 1 - bbbits;
|
| 1975 |
#else /*Avoid_Underflow*/ |
| 1976 |
#ifdef Sudden_Underflow
|
| 1977 |
#ifdef IBM
|
| 1978 |
j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3); |
| 1979 |
#else
|
| 1980 |
j = P + 1 - bbbits;
|
| 1981 |
#endif
|
| 1982 |
#else /*Sudden_Underflow*/ |
| 1983 |
j = bbe; |
| 1984 |
i = j + bbbits - 1; /* logb(rv) */ |
| 1985 |
if (i < Emin) /* denormal */ |
| 1986 |
j += P - Emin; |
| 1987 |
else
|
| 1988 |
j = P + 1 - bbbits;
|
| 1989 |
#endif /*Sudden_Underflow*/ |
| 1990 |
#endif /*Avoid_Underflow*/ |
| 1991 |
bb2 += j; |
| 1992 |
bd2 += j; |
| 1993 |
#ifdef Avoid_Underflow
|
| 1994 |
bd2 += scale; |
| 1995 |
#endif
|
| 1996 |
i = bb2 < bd2 ? bb2 : bd2; |
| 1997 |
if (i > bs2)
|
| 1998 |
i = bs2; |
| 1999 |
if (i > 0) { |
| 2000 |
bb2 -= i; |
| 2001 |
bd2 -= i; |
| 2002 |
bs2 -= i; |
| 2003 |
} |
| 2004 |
if (bb5 > 0) { |
| 2005 |
bs = pow5mult(bs, bb5); |
| 2006 |
bb1 = mult(bs, bb); |
| 2007 |
Bfree(bb); |
| 2008 |
bb = bb1; |
| 2009 |
} |
| 2010 |
if (bb2 > 0) |
| 2011 |
bb = lshift(bb, bb2); |
| 2012 |
if (bd5 > 0) |
| 2013 |
bd = pow5mult(bd, bd5); |
| 2014 |
if (bd2 > 0) |
| 2015 |
bd = lshift(bd, bd2); |
| 2016 |
if (bs2 > 0) |
| 2017 |
bs = lshift(bs, bs2); |
| 2018 |
delta = diff(bb, bd); |
| 2019 |
dsign = delta->sign; |
| 2020 |
delta->sign = 0;
|
| 2021 |
i = cmp(delta, bs); |
| 2022 |
#ifdef Honor_FLT_ROUNDS
|
| 2023 |
if (rounding != 1) { |
| 2024 |
if (i < 0) { |
| 2025 |
/* Error is less than an ulp */
|
| 2026 |
if (!delta->x[0] && delta->wds <= 1) { |
| 2027 |
/* exact */
|
| 2028 |
#ifdef SET_INEXACT
|
| 2029 |
inexact = 0;
|
| 2030 |
#endif
|
| 2031 |
break;
|
| 2032 |
} |
| 2033 |
if (rounding) {
|
| 2034 |
if (dsign) {
|
| 2035 |
adj = 1.;
|
| 2036 |
goto apply_adj;
|
| 2037 |
} |
| 2038 |
} |
| 2039 |
else if (!dsign) { |
| 2040 |
adj = -1.;
|
| 2041 |
if (!word1(rv)
|
| 2042 |
&& !(word0(rv) & Frac_mask)) {
|
| 2043 |
y = word0(rv) & Exp_mask; |
| 2044 |
#ifdef Avoid_Underflow
|
| 2045 |
if (!scale || y > 2*P*Exp_msk1) |
| 2046 |
#else
|
| 2047 |
if (y)
|
| 2048 |
#endif
|
| 2049 |
{
|
| 2050 |
delta = lshift(delta,Log2P); |
| 2051 |
if (cmp(delta, bs) <= 0) |
| 2052 |
adj = -0.5; |
| 2053 |
} |
| 2054 |
} |
| 2055 |
apply_adj:
|
| 2056 |
#ifdef Avoid_Underflow
|
| 2057 |
if (scale && (y = word0(rv) & Exp_mask)
|
| 2058 |
<= 2*P*Exp_msk1)
|
| 2059 |
word0(adj) += (2*P+1)*Exp_msk1 - y; |
| 2060 |
#else
|
| 2061 |
#ifdef Sudden_Underflow
|
| 2062 |
if ((word0(rv) & Exp_mask) <=
|
| 2063 |
P*Exp_msk1) {
|
| 2064 |
word0(rv) += P*Exp_msk1; |
| 2065 |
dval(rv) += adj*ulp(dval(rv)); |
| 2066 |
word0(rv) -= P*Exp_msk1; |
| 2067 |
} |
| 2068 |
else
|
| 2069 |
#endif /*Sudden_Underflow*/ |
| 2070 |
#endif /*Avoid_Underflow*/ |
| 2071 |
dval(rv) += adj*ulp(dval(rv)); |
| 2072 |
} |
| 2073 |
break;
|
| 2074 |
} |
| 2075 |
adj = ratio(delta, bs); |
| 2076 |
if (adj < 1.) |
| 2077 |
adj = 1.;
|
| 2078 |
if (adj <= 0x7ffffffe) { |
| 2079 |
/* adj = rounding ? ceil(adj) : floor(adj); */
|
| 2080 |
y = adj; |
| 2081 |
if (y != adj) {
|
| 2082 |
if (!((rounding>>1) ^ dsign)) |
| 2083 |
y++; |
| 2084 |
adj = y; |
| 2085 |
} |
| 2086 |
} |
| 2087 |
#ifdef Avoid_Underflow
|
| 2088 |
if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1) |
| 2089 |
word0(adj) += (2*P+1)*Exp_msk1 - y; |
| 2090 |
#else
|
| 2091 |
#ifdef Sudden_Underflow
|
| 2092 |
if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
|
| 2093 |
word0(rv) += P*Exp_msk1; |
| 2094 |
adj *= ulp(dval(rv)); |
| 2095 |
if (dsign)
|
| 2096 |
dval(rv) += adj; |
| 2097 |
else
|
| 2098 |
dval(rv) -= adj; |
| 2099 |
word0(rv) -= P*Exp_msk1; |
| 2100 |
goto cont;
|
| 2101 |
} |
| 2102 |
#endif /*Sudden_Underflow*/ |
| 2103 |
#endif /*Avoid_Underflow*/ |
| 2104 |
adj *= ulp(dval(rv)); |
| 2105 |
if (dsign)
|
| 2106 |
dval(rv) += adj; |
| 2107 |
else
|
| 2108 |
dval(rv) -= adj; |
| 2109 |
goto cont;
|
| 2110 |
} |
| 2111 |
#endif /*Honor_FLT_ROUNDS*/ |
| 2112 |
|
| 2113 |
if (i < 0) { |
| 2114 |
/* Error is less than half an ulp -- check for
|
| 2115 |
* special case of mantissa a power of two.
|
| 2116 |
*/
|
| 2117 |
if (dsign || word1(rv) || word0(rv) & Bndry_mask
|
| 2118 |
#ifdef IEEE_Arith
|
| 2119 |
#ifdef Avoid_Underflow
|
| 2120 |
|| (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1 |
| 2121 |
#else
|
| 2122 |
|| (word0(rv) & Exp_mask) <= Exp_msk1 |
| 2123 |
#endif
|
| 2124 |
#endif
|
| 2125 |
) {
|
| 2126 |
#ifdef SET_INEXACT
|
| 2127 |
if (!delta->x[0] && delta->wds <= 1) |
| 2128 |
inexact = 0;
|
| 2129 |
#endif
|
| 2130 |
break;
|
| 2131 |
} |
| 2132 |
if (!delta->x[0] && delta->wds <= 1) { |
| 2133 |
/* exact result */
|
| 2134 |
#ifdef SET_INEXACT
|
| 2135 |
inexact = 0;
|
| 2136 |
#endif
|
| 2137 |
break;
|
| 2138 |
} |
| 2139 |
delta = lshift(delta,Log2P); |
| 2140 |
if (cmp(delta, bs) > 0) |
| 2141 |
goto drop_down;
|
| 2142 |
break;
|
| 2143 |
} |
| 2144 |
if (i == 0) { |
| 2145 |
/* exactly half-way between */
|
| 2146 |
if (dsign) {
|
| 2147 |
if ((word0(rv) & Bndry_mask1) == Bndry_mask1
|
| 2148 |
&& word1(rv) == ( |
| 2149 |
#ifdef Avoid_Underflow
|
| 2150 |
(scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
|
| 2151 |
? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) : |
| 2152 |
#endif
|
| 2153 |
0xffffffff)) {
|
| 2154 |
/*boundary case -- increment exponent*/
|
| 2155 |
word0(rv) = (word0(rv) & Exp_mask) |
| 2156 |
+ Exp_msk1 |
| 2157 |
#ifdef IBM
|
| 2158 |
| Exp_msk1 >> 4
|
| 2159 |
#endif
|
| 2160 |
; |
| 2161 |
word1(rv) = 0;
|
| 2162 |
#ifdef Avoid_Underflow
|
| 2163 |
dsign = 0;
|
| 2164 |
#endif
|
| 2165 |
break;
|
| 2166 |
} |
| 2167 |
} |
| 2168 |
else if (!(word0(rv) & Bndry_mask) && !word1(rv)) { |
| 2169 |
drop_down:
|
| 2170 |
/* boundary case -- decrement exponent */
|
| 2171 |
#ifdef Sudden_Underflow /*{{*/ |
| 2172 |
L = word0(rv) & Exp_mask; |
| 2173 |
#ifdef IBM
|
| 2174 |
if (L < Exp_msk1)
|
| 2175 |
#else
|
| 2176 |
#ifdef Avoid_Underflow
|
| 2177 |
if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1)) |
| 2178 |
#else
|
| 2179 |
if (L <= Exp_msk1)
|
| 2180 |
#endif /*Avoid_Underflow*/ |
| 2181 |
#endif /*IBM*/ |
| 2182 |
goto undfl;
|
| 2183 |
L -= Exp_msk1; |
| 2184 |
#else /*Sudden_Underflow}{*/ |
| 2185 |
#ifdef Avoid_Underflow
|
| 2186 |
if (scale) {
|
| 2187 |
L = word0(rv) & Exp_mask; |
| 2188 |
if (L <= (2*P+1)*Exp_msk1) { |
| 2189 |
if (L > (P+2)*Exp_msk1) |
| 2190 |
/* round even ==> */
|
| 2191 |
/* accept rv */
|
| 2192 |
break;
|
| 2193 |
/* rv = smallest denormal */
|
| 2194 |
goto undfl;
|
| 2195 |
} |
| 2196 |
} |
| 2197 |
#endif /*Avoid_Underflow*/ |
| 2198 |
L = (word0(rv) & Exp_mask) - Exp_msk1; |
| 2199 |
#endif /*Sudden_Underflow}}*/ |
| 2200 |
word0(rv) = L | Bndry_mask1; |
| 2201 |
word1(rv) = 0xffffffff;
|
| 2202 |
#ifdef IBM
|
| 2203 |
goto cont;
|
| 2204 |
#else
|
| 2205 |
break;
|
| 2206 |
#endif
|
| 2207 |
} |
| 2208 |
#ifndef ROUND_BIASED
|
| 2209 |
if (!(word1(rv) & LSB))
|
| 2210 |
break;
|
| 2211 |
#endif
|
| 2212 |
if (dsign)
|
| 2213 |
dval(rv) += ulp(dval(rv)); |
| 2214 |
#ifndef ROUND_BIASED
|
| 2215 |
else {
|
| 2216 |
dval(rv) -= ulp(dval(rv)); |
| 2217 |
#ifndef Sudden_Underflow
|
| 2218 |
if (!dval(rv))
|
| 2219 |
goto undfl;
|
| 2220 |
#endif
|
| 2221 |
} |
| 2222 |
#ifdef Avoid_Underflow
|
| 2223 |
dsign = 1 - dsign;
|
| 2224 |
#endif
|
| 2225 |
#endif
|
| 2226 |
break;
|
| 2227 |
} |
| 2228 |
if ((aadj = ratio(delta, bs)) <= 2.) { |
| 2229 |
if (dsign)
|
| 2230 |
aadj = aadj1 = 1.;
|
| 2231 |
else if (word1(rv) || word0(rv) & Bndry_mask) { |
| 2232 |
#ifndef Sudden_Underflow
|
| 2233 |
if (word1(rv) == Tiny1 && !word0(rv))
|
| 2234 |
goto undfl;
|
| 2235 |
#endif
|
| 2236 |
aadj = 1.;
|
| 2237 |
aadj1 = -1.;
|
| 2238 |
} |
| 2239 |
else {
|
| 2240 |
/* special case -- power of FLT_RADIX to be */
|
| 2241 |
/* rounded down... */
|
| 2242 |
|
| 2243 |
if (aadj < 2./FLT_RADIX) |
| 2244 |
aadj = 1./FLT_RADIX;
|
| 2245 |
else
|
| 2246 |
aadj *= 0.5; |
| 2247 |
aadj1 = -aadj; |
| 2248 |
} |
| 2249 |
} |
| 2250 |
else {
|
| 2251 |
aadj *= 0.5; |
| 2252 |
aadj1 = dsign ? aadj : -aadj; |
| 2253 |
#ifdef Check_FLT_ROUNDS
|
| 2254 |
switch(Rounding) {
|
| 2255 |
case 2: /* towards +infinity */ |
| 2256 |
aadj1 -= 0.5; |
| 2257 |
break;
|
| 2258 |
case 0: /* towards 0 */ |
| 2259 |
case 3: /* towards -infinity */ |
| 2260 |
aadj1 += 0.5; |
| 2261 |
} |
| 2262 |
#else
|
| 2263 |
if (Flt_Rounds == 0) |
| 2264 |
aadj1 += 0.5; |
| 2265 |
#endif /*Check_FLT_ROUNDS*/ |
| 2266 |
} |
| 2267 |
y = word0(rv) & Exp_mask; |
| 2268 |
|
| 2269 |
/* Check for overflow */
|
| 2270 |
|
| 2271 |
if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) { |
| 2272 |
dval(rv0) = dval(rv); |
| 2273 |
word0(rv) -= P*Exp_msk1; |
| 2274 |
adj = aadj1 * ulp(dval(rv)); |
| 2275 |
dval(rv) += adj; |
| 2276 |
if ((word0(rv) & Exp_mask) >=
|
| 2277 |
Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
|
| 2278 |
if (word0(rv0) == Big0 && word1(rv0) == Big1)
|
| 2279 |
goto ovfl;
|
| 2280 |
word0(rv) = Big0; |
| 2281 |
word1(rv) = Big1; |
| 2282 |
goto cont;
|
| 2283 |
} |
| 2284 |
else
|
| 2285 |
word0(rv) += P*Exp_msk1; |
| 2286 |
} |
| 2287 |
else {
|
| 2288 |
#ifdef Avoid_Underflow
|
| 2289 |
if (scale && y <= 2*P*Exp_msk1) { |
| 2290 |
if (aadj <= 0x7fffffff) { |
| 2291 |
if ((z = aadj) <= 0) |
| 2292 |
z = 1;
|
| 2293 |
aadj = z; |
| 2294 |
aadj1 = dsign ? aadj : -aadj; |
| 2295 |
} |
| 2296 |
word0(aadj1) += (2*P+1)*Exp_msk1 - y; |
| 2297 |
} |
| 2298 |
adj = aadj1 * ulp(dval(rv)); |
| 2299 |
dval(rv) += adj; |
| 2300 |
#else
|
| 2301 |
#ifdef Sudden_Underflow
|
| 2302 |
if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
|
| 2303 |
dval(rv0) = dval(rv); |
| 2304 |
word0(rv) += P*Exp_msk1; |
| 2305 |
adj = aadj1 * ulp(dval(rv)); |
| 2306 |
dval(rv) += adj; |
| 2307 |
#ifdef IBM
|
| 2308 |
if ((word0(rv) & Exp_mask) < P*Exp_msk1)
|
| 2309 |
#else
|
| 2310 |
if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
|
| 2311 |
#endif
|
| 2312 |
{
|
| 2313 |
if (word0(rv0) == Tiny0
|
| 2314 |
&& word1(rv0) == Tiny1) |
| 2315 |
goto undfl;
|
| 2316 |
word0(rv) = Tiny0; |
| 2317 |
word1(rv) = Tiny1; |
| 2318 |
goto cont;
|
| 2319 |
} |
| 2320 |
else
|
| 2321 |
word0(rv) -= P*Exp_msk1; |
| 2322 |
} |
| 2323 |
else {
|
| 2324 |
adj = aadj1 * ulp(dval(rv)); |
| 2325 |
dval(rv) += adj; |
| 2326 |
} |
| 2327 |
#else /*Sudden_Underflow*/ |
| 2328 |
/* Compute adj so that the IEEE rounding rules will
|
| 2329 |
* correctly round rv + adj in some half-way cases.
|
| 2330 |
* If rv * ulp(rv) is denormalized (i.e.,
|
| 2331 |
* y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
|
| 2332 |
* trouble from bits lost to denormalization;
|
| 2333 |
* example: 1.2e-307 .
|
| 2334 |
*/
|
| 2335 |
if (y <= (P-1)*Exp_msk1 && aadj > 1.) { |
| 2336 |
aadj1 = (double)(int)(aadj + 0.5); |
| 2337 |
if (!dsign)
|
| 2338 |
aadj1 = -aadj1; |
| 2339 |
} |
| 2340 |
adj = aadj1 * ulp(dval(rv)); |
| 2341 |
dval(rv) += adj; |
| 2342 |
#endif /*Sudden_Underflow*/ |
| 2343 |
#endif /*Avoid_Underflow*/ |
| 2344 |
} |
| 2345 |
z = word0(rv) & Exp_mask; |
| 2346 |
#ifndef SET_INEXACT
|
| 2347 |
#ifdef Avoid_Underflow
|
| 2348 |
if (!scale)
|
| 2349 |
#endif
|
| 2350 |
if (y == z) {
|
| 2351 |
/* Can we stop now? */
|
| 2352 |
L = (Long)aadj; |
| 2353 |
aadj -= L; |
| 2354 |
/* The tolerances below are conservative. */
|
| 2355 |
if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
|
| 2356 |
if (aadj < .4999999 || aadj > .5000001) |
| 2357 |
break;
|
| 2358 |
} |
| 2359 |
else if (aadj < .4999999/FLT_RADIX) |
| 2360 |
break;
|
| 2361 |
} |
| 2362 |
#endif
|
| 2363 |
cont:
|
| 2364 |
Bfree(bb); |
| 2365 |
Bfree(bd); |
| 2366 |
Bfree(bs); |
| 2367 |
Bfree(delta); |
| 2368 |
} |
| 2369 |
#ifdef SET_INEXACT
|
| 2370 |
if (inexact) {
|
| 2371 |
if (!oldinexact) {
|
| 2372 |
word0(rv0) = Exp_1 + (70 << Exp_shift);
|
| 2373 |
word1(rv0) = 0;
|
| 2374 |
dval(rv0) += 1.;
|
| 2375 |
} |
| 2376 |
} |
| 2377 |
else if (!oldinexact) |
| 2378 |
clear_inexact(); |
| 2379 |
#endif
|
| 2380 |
#ifdef Avoid_Underflow
|
| 2381 |
if (scale) {
|
| 2382 |
word0(rv0) = Exp_1 - 2*P*Exp_msk1;
|
| 2383 |
word1(rv0) = 0;
|
| 2384 |
dval(rv) *= dval(rv0); |
| 2385 |
#ifndef NO_ERRNO
|
| 2386 |
/* try to avoid the bug of testing an 8087 register value */
|
| 2387 |
if (word0(rv) == 0 && word1(rv) == 0) |
| 2388 |
errno = ERANGE; |
| 2389 |
#endif
|
| 2390 |
} |
| 2391 |
#endif /* Avoid_Underflow */ |
| 2392 |
#ifdef SET_INEXACT
|
| 2393 |
if (inexact && !(word0(rv) & Exp_mask)) {
|
| 2394 |
/* set underflow bit */
|
| 2395 |
dval(rv0) = 1e-300; |
| 2396 |
dval(rv0) *= dval(rv0); |
| 2397 |
} |
| 2398 |
#endif
|
| 2399 |
retfree:
|
| 2400 |
Bfree(bb); |
| 2401 |
Bfree(bd); |
| 2402 |
Bfree(bs); |
| 2403 |
Bfree(bd0); |
| 2404 |
Bfree(delta); |
| 2405 |
ret:
|
| 2406 |
if (se)
|
| 2407 |
*se = (char *)s;
|
| 2408 |
return sign ? -dval(rv) : dval(rv);
|
| 2409 |
} |
| 2410 |
|
| 2411 |
static int |
| 2412 |
quorem |
| 2413 |
#ifdef KR_headers
|
| 2414 |
(b, S) Bigint *b, *S; |
| 2415 |
#else
|
| 2416 |
(Bigint *b, Bigint *S) |
| 2417 |
#endif
|
| 2418 |
{
|
| 2419 |
int n;
|
| 2420 |
ULong *bx, *bxe, q, *sx, *sxe; |
| 2421 |
#ifdef ULLong
|
| 2422 |
ULLong borrow, carry, y, ys; |
| 2423 |
#else
|
| 2424 |
ULong borrow, carry, y, ys; |
| 2425 |
#ifdef Pack_32
|
| 2426 |
ULong si, z, zs; |
| 2427 |
#endif
|
| 2428 |
#endif
|
| 2429 |
|
| 2430 |
n = S->wds; |
| 2431 |
#ifdef DEBUG
|
| 2432 |
/*debug*/ if (b->wds > n) |
| 2433 |
/*debug*/ Bug("oversize b in quorem"); |
| 2434 |
#endif
|
| 2435 |
if (b->wds < n)
|
| 2436 |
return 0; |
| 2437 |
sx = S->x; |
| 2438 |
sxe = sx + --n; |
| 2439 |
bx = b->x; |
| 2440 |
bxe = bx + n; |
| 2441 |
q = *bxe / (*sxe + 1); /* ensure q <= true quotient */ |
| 2442 |
#ifdef DEBUG
|
| 2443 |
/*debug*/ if (q > 9) |
| 2444 |
/*debug*/ Bug("oversized quotient in quorem"); |
| 2445 |
#endif
|
| 2446 |
if (q) {
|
| 2447 |
borrow = 0;
|
| 2448 |
carry = 0;
|
| 2449 |
do {
|
| 2450 |
#ifdef ULLong
|
| 2451 |
ys = *sx++ * (ULLong)q + carry; |
| 2452 |
carry = ys >> 32;
|
| 2453 |
y = *bx - (ys & FFFFFFFF) - borrow; |
| 2454 |
borrow = y >> 32 & (ULong)1; |
| 2455 |
*bx++ = y & FFFFFFFF; |
| 2456 |
#else
|
| 2457 |
#ifdef Pack_32
|
| 2458 |
si = *sx++; |
| 2459 |
ys = (si & 0xffff) * q + carry;
|
| 2460 |
zs = (si >> 16) * q + (ys >> 16); |
| 2461 |
carry = zs >> 16;
|
| 2462 |
y = (*bx & 0xffff) - (ys & 0xffff) - borrow; |
| 2463 |
borrow = (y & 0x10000) >> 16; |
| 2464 |
z = (*bx >> 16) - (zs & 0xffff) - borrow; |
| 2465 |
borrow = (z & 0x10000) >> 16; |
| 2466 |
Storeinc(bx, z, y); |
| 2467 |
#else
|
| 2468 |
ys = *sx++ * q + carry; |
| 2469 |
carry = ys >> 16;
|
| 2470 |
y = *bx - (ys & 0xffff) - borrow;
|
| 2471 |
borrow = (y & 0x10000) >> 16; |
| 2472 |
*bx++ = y & 0xffff;
|
| 2473 |
#endif
|
| 2474 |
#endif
|
| 2475 |
} |
| 2476 |
while(sx <= sxe);
|
| 2477 |
if (!*bxe) {
|
| 2478 |
bx = b->x; |
| 2479 |
while(--bxe > bx && !*bxe)
|
| 2480 |
--n; |
| 2481 |
b->wds = n; |
| 2482 |
} |
| 2483 |
} |
| 2484 |
if (cmp(b, S) >= 0) { |
| 2485 |
q++; |
| 2486 |
borrow = 0;
|
| 2487 |
carry = 0;
|
| 2488 |
bx = b->x; |
| 2489 |
sx = S->x; |
| 2490 |
do {
|
| 2491 |
#ifdef ULLong
|
| 2492 |
ys = *sx++ + carry; |
| 2493 |
carry = ys >> 32;
|
| 2494 |
y = *bx - (ys & FFFFFFFF) - borrow; |
| 2495 |
borrow = y >> 32 & (ULong)1; |
| 2496 |
*bx++ = y & FFFFFFFF; |
| 2497 |
#else
|
| 2498 |
#ifdef Pack_32
|
| 2499 |
si = *sx++; |
| 2500 |
ys = (si & 0xffff) + carry;
|
| 2501 |
zs = (si >> 16) + (ys >> 16); |
| 2502 |
carry = zs >> 16;
|
| 2503 |
y = (*bx & 0xffff) - (ys & 0xffff) - borrow; |
| 2504 |
borrow = (y & 0x10000) >> 16; |
| 2505 |
z = (*bx >> 16) - (zs & 0xffff) - borrow; |
| 2506 |
borrow = (z & 0x10000) >> 16; |
| 2507 |
Storeinc(bx, z, y); |
| 2508 |
#else
|
| 2509 |
ys = *sx++ + carry; |
| 2510 |
carry = ys >> 16;
|
| 2511 |
y = *bx - (ys & 0xffff) - borrow;
|
| 2512 |
borrow = (y & 0x10000) >> 16; |
| 2513 |
*bx++ = y & 0xffff;
|
| 2514 |
#endif
|
| 2515 |
#endif
|
| 2516 |
} |
| 2517 |
while(sx <= sxe);
|
| 2518 |
bx = b->x; |
| 2519 |
bxe = bx + n; |
| 2520 |
if (!*bxe) {
|
| 2521 |
while(--bxe > bx && !*bxe)
|
| 2522 |
--n; |
| 2523 |
b->wds = n; |
| 2524 |
} |
| 2525 |
} |
| 2526 |
return q;
|
| 2527 |
} |
| 2528 |
|
| 2529 |
#ifndef MULTIPLE_THREADS
|
| 2530 |
static char *dtoa_result; |
| 2531 |
#endif
|
| 2532 |
|
| 2533 |
static char * |
| 2534 |
#ifdef KR_headers
|
| 2535 |
rv_alloc(i) int i;
|
| 2536 |
#else
|
| 2537 |
rv_alloc(int i)
|
| 2538 |
#endif
|
| 2539 |
{
|
| 2540 |
int j, k, *r;
|
| 2541 |
|
| 2542 |
j = sizeof(ULong);
|
| 2543 |
for(k = 0; |
| 2544 |
sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= i; |
| 2545 |
j <<= 1)
|
| 2546 |
k++; |
| 2547 |
r = (int*)Balloc(k);
|
| 2548 |
*r = k; |
| 2549 |
return
|
| 2550 |
#ifndef MULTIPLE_THREADS
|
| 2551 |
dtoa_result = |
| 2552 |
#endif
|
| 2553 |
(char *)(r+1); |
| 2554 |
} |
| 2555 |
|
| 2556 |
static char * |
| 2557 |
#ifdef KR_headers
|
| 2558 |
nrv_alloc(s, rve, n) char *s, **rve; int n; |
| 2559 |
#else
|
| 2560 |
nrv_alloc(const char *s, char **rve, int n) |
| 2561 |
#endif
|
| 2562 |
{
|
| 2563 |
char *rv, *t;
|
| 2564 |
|
| 2565 |
t = rv = rv_alloc(n); |
| 2566 |
while ((*t = *s++)) t++;
|
| 2567 |
if (rve)
|
| 2568 |
*rve = t; |
| 2569 |
return rv;
|
| 2570 |
} |
| 2571 |
|
| 2572 |
/* freedtoa(s) must be used to free values s returned by dtoa
|
| 2573 |
* when MULTIPLE_THREADS is #defined. It should be used in all cases,
|
| 2574 |
* but for consistency with earlier versions of dtoa, it is optional
|
| 2575 |
* when MULTIPLE_THREADS is not defined.
|
| 2576 |
*/
|
| 2577 |
|
| 2578 |
void
|
| 2579 |
#ifdef KR_headers
|
| 2580 |
freedtoa(s) char *s;
|
| 2581 |
#else
|
| 2582 |
freedtoa(char *s)
|
| 2583 |
#endif
|
| 2584 |
{
|
| 2585 |
Bigint *b = (Bigint *)((int *)s - 1); |
| 2586 |
b->maxwds = 1 << (b->k = *(int*)b); |
| 2587 |
Bfree(b); |
| 2588 |
#ifndef MULTIPLE_THREADS
|
| 2589 |
if (s == dtoa_result)
|
| 2590 |
dtoa_result = 0;
|
| 2591 |
#endif
|
| 2592 |
} |
| 2593 |
|
| 2594 |
/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
|
| 2595 |
*
|
| 2596 |
* Inspired by "How to Print Floating-Point Numbers Accurately" by
|
| 2597 |
* Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126].
|
| 2598 |
*
|
| 2599 |
* Modifications:
|
| 2600 |
* 1. Rather than iterating, we use a simple numeric overestimate
|
| 2601 |
* to determine k = floor(log10(d)). We scale relevant
|
| 2602 |
* quantities using O(log2(k)) rather than O(k) multiplications.
|
| 2603 |
* 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
|
| 2604 |
* try to generate digits strictly left to right. Instead, we
|
| 2605 |
* compute with fewer bits and propagate the carry if necessary
|
| 2606 |
* when rounding the final digit up. This is often faster.
|
| 2607 |
* 3. Under the assumption that input will be rounded nearest,
|
| 2608 |
* mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
|
| 2609 |
* That is, we allow equality in stopping tests when the
|
| 2610 |
* round-nearest rule will give the same floating-point value
|
| 2611 |
* as would satisfaction of the stopping test with strict
|
| 2612 |
* inequality.
|
| 2613 |
* 4. We remove common factors of powers of 2 from relevant
|
| 2614 |
* quantities.
|
| 2615 |
* 5. When converting floating-point integers less than 1e16,
|
| 2616 |
* we use floating-point arithmetic rather than resorting
|
| 2617 |
* to multiple-precision integers.
|
| 2618 |
* 6. When asked to produce fewer than 15 digits, we first try
|
| 2619 |
* to get by with floating-point arithmetic; we resort to
|
| 2620 |
* multiple-precision integer arithmetic only if we cannot
|
| 2621 |
* guarantee that the floating-point calculation has given
|
| 2622 |
* the correctly rounded result. For k requested digits and
|
| 2623 |
* "uniformly" distributed input, the probability is
|
| 2624 |
* something like 10^(k-15) that we must resort to the Long
|
| 2625 |
* calculation.
|
| 2626 |
*/
|
| 2627 |
|
| 2628 |
char *
|
| 2629 |
dtoa |
| 2630 |
#ifdef KR_headers
|
| 2631 |
(d, mode, ndigits, decpt, sign, rve) |
| 2632 |
double d; int mode, ndigits, *decpt, *sign; char **rve; |
| 2633 |
#else
|
| 2634 |
(double d, int mode, int ndigits, int *decpt, int *sign, char **rve) |
| 2635 |
#endif
|
| 2636 |
{
|
| 2637 |
/* Arguments ndigits, decpt, sign are similar to those
|
| 2638 |
of ecvt and fcvt; trailing zeros are suppressed from
|
| 2639 |
the returned string. If not null, *rve is set to point
|
| 2640 |
to the end of the return value. If d is +-Infinity or NaN,
|
| 2641 |
then *decpt is set to 9999.
|
| 2642 |
|
| 2643 |
mode:
|
| 2644 |
0 ==> shortest string that yields d when read in
|
| 2645 |
and rounded to nearest.
|
| 2646 |
1 ==> like 0, but with Steele & White stopping rule;
|
| 2647 |
e.g. with IEEE P754 arithmetic , mode 0 gives
|
| 2648 |
1e23 whereas mode 1 gives 9.999999999999999e22.
|
| 2649 |
2 ==> max(1,ndigits) significant digits. This gives a
|
| 2650 |
return value similar to that of ecvt, except
|
| 2651 |
that trailing zeros are suppressed.
|
| 2652 |
3 ==> through ndigits past the decimal point. This
|
| 2653 |
gives a return value similar to that from fcvt,
|
| 2654 |
except that trailing zeros are suppressed, and
|
| 2655 |
ndigits can be negative.
|
| 2656 |
4,5 ==> similar to 2 and 3, respectively, but (in
|
| 2657 |
round-nearest mode) with the tests of mode 0 to
|
| 2658 |
possibly return a shorter string that rounds to d.
|
| 2659 |
With IEEE arithmetic and compilation with
|
| 2660 |
-DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
|
| 2661 |
as modes 2 and 3 when FLT_ROUNDS != 1.
|
| 2662 |
6-9 ==> Debugging modes similar to mode - 4: don't try
|
| 2663 |
fast floating-point estimate (if applicable).
|
| 2664 |
|
| 2665 |
Values of mode other than 0-9 are treated as mode 0.
|
| 2666 |
|
| 2667 |
Sufficient space is allocated to the return value
|
| 2668 |
to hold the suppressed trailing zeros.
|
| 2669 |
*/
|
| 2670 |
|
| 2671 |
int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
|
| 2672 |
j, j1, k, k0, k_check, leftright, m2, m5, s2, s5, |
| 2673 |
spec_case, try_quick, bias_round_up; |
| 2674 |
Long L; |
| 2675 |
#ifndef Sudden_Underflow
|
| 2676 |
int denorm;
|
| 2677 |
ULong x; |
| 2678 |
#endif
|
| 2679 |
Bigint *b, *b1, *delta, *mlo, *mhi, *S; |
| 2680 |
double d2, ds, eps;
|
| 2681 |
char *s, *s0;
|
| 2682 |
#ifdef Honor_FLT_ROUNDS
|
| 2683 |
int rounding;
|
| 2684 |
#endif
|
| 2685 |
#ifdef SET_INEXACT
|
| 2686 |
int inexact, oldinexact;
|
| 2687 |
#endif
|
| 2688 |
|
| 2689 |
/* In mode 2 and 3 we bias rounding up when there are ties. */
|
| 2690 |
bias_round_up = mode == 2 || mode == 3; |
| 2691 |
|
| 2692 |
ilim = ilim1 = 0; /* to avoid Google3 compiler warnings */ |
| 2693 |
|
| 2694 |
#ifndef MULTIPLE_THREADS
|
| 2695 |
if (dtoa_result) {
|
| 2696 |
freedtoa(dtoa_result); |
| 2697 |
dtoa_result = 0;
|
| 2698 |
} |
| 2699 |
#endif
|
| 2700 |
|
| 2701 |
if (word0(d) & Sign_bit) {
|
| 2702 |
/* set sign for everything, including 0's and NaNs */
|
| 2703 |
*sign = 1;
|
| 2704 |
word0(d) &= ~Sign_bit; /* clear sign bit */
|
| 2705 |
} |
| 2706 |
else
|
| 2707 |
*sign = 0;
|
| 2708 |
|
| 2709 |
#if defined(IEEE_Arith) + defined(VAX)
|
| 2710 |
#ifdef IEEE_Arith
|
| 2711 |
if ((word0(d) & Exp_mask) == Exp_mask)
|
| 2712 |
#else
|
| 2713 |
if (word0(d) == 0x8000) |
| 2714 |
#endif
|
| 2715 |
{
|
| 2716 |
/* Infinity or NaN */
|
| 2717 |
*decpt = 9999;
|
| 2718 |
#ifdef IEEE_Arith
|
| 2719 |
if (!word1(d) && !(word0(d) & 0xfffff)) |
| 2720 |
return nrv_alloc("Infinity", rve, 8); |
| 2721 |
#endif
|
| 2722 |
return nrv_alloc("NaN", rve, 3); |
| 2723 |
} |
| 2724 |
#endif
|
| 2725 |
#ifdef IBM
|
| 2726 |
dval(d) += 0; /* normalize */ |
| 2727 |
#endif
|
| 2728 |
if (!dval(d)) {
|
| 2729 |
*decpt = 1;
|
| 2730 |
return nrv_alloc("0", rve, 1); |
| 2731 |
} |
| 2732 |
|
| 2733 |
#ifdef SET_INEXACT
|
| 2734 |
try_quick = oldinexact = get_inexact(); |
| 2735 |
inexact = 1;
|
| 2736 |
#endif
|
| 2737 |
#ifdef Honor_FLT_ROUNDS
|
| 2738 |
if ((rounding = Flt_Rounds) >= 2) { |
| 2739 |
if (*sign)
|
| 2740 |
rounding = rounding == 2 ? 0 : 2; |
| 2741 |
else
|
| 2742 |
if (rounding != 2) |
| 2743 |
rounding = 0;
|
| 2744 |
} |
| 2745 |
#endif
|
| 2746 |
|
| 2747 |
b = d2b(dval(d), &be, &bbits); |
| 2748 |
#ifdef Sudden_Underflow
|
| 2749 |
i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
|
| 2750 |
#else
|
| 2751 |
if ((i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1)))) { |
| 2752 |
#endif
|
| 2753 |
dval(d2) = dval(d); |
| 2754 |
word0(d2) &= Frac_mask1; |
| 2755 |
word0(d2) |= Exp_11; |
| 2756 |
#ifdef IBM
|
| 2757 |
if (j = 11 - hi0bits(word0(d2) & Frac_mask)) |
| 2758 |
dval(d2) /= 1 << j;
|
| 2759 |
#endif
|
| 2760 |
|
| 2761 |
/* log(x) ~=~ log(1.5) + (x-1.5)/1.5
|
| 2762 |
* log10(x) = log(x) / log(10)
|
| 2763 |
* ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
|
| 2764 |
* log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
|
| 2765 |
*
|
| 2766 |
* This suggests computing an approximation k to log10(d) by
|
| 2767 |
*
|
| 2768 |
* k = (i - Bias)*0.301029995663981
|
| 2769 |
* + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
|
| 2770 |
*
|
| 2771 |
* We want k to be too large rather than too small.
|
| 2772 |
* The error in the first-order Taylor series approximation
|
| 2773 |
* is in our favor, so we just round up the constant enough
|
| 2774 |
* to compensate for any error in the multiplication of
|
| 2775 |
* (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
|
| 2776 |
* and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
|
| 2777 |
* adding 1e-13 to the constant term more than suffices.
|
| 2778 |
* Hence we adjust the constant term to 0.1760912590558.
|
| 2779 |
* (We could get a more accurate k by invoking log10,
|
| 2780 |
* but this is probably not worthwhile.)
|
| 2781 |
*/
|
| 2782 |
|
| 2783 |
i -= Bias; |
| 2784 |
#ifdef IBM
|
| 2785 |
i <<= 2;
|
| 2786 |
i += j; |
| 2787 |
#endif
|
| 2788 |
#ifndef Sudden_Underflow
|
| 2789 |
denorm = 0;
|
| 2790 |
} |
| 2791 |
else {
|
| 2792 |
/* d is denormalized */
|
| 2793 |
|
| 2794 |
i = bbits + be + (Bias + (P-1) - 1); |
| 2795 |
x = i > 32 ? (word0(d) << (64 - i)) | (word1(d) >> (i - 32)) |
| 2796 |
: word1(d) << (32 - i);
|
| 2797 |
dval(d2) = x; |
| 2798 |
word0(d2) -= 31*Exp_msk1; /* adjust exponent */ |
| 2799 |
i -= (Bias + (P-1) - 1) + 1; |
| 2800 |
denorm = 1;
|
| 2801 |
} |
| 2802 |
#endif
|
| 2803 |
ds = (dval(d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981; |
| 2804 |
k = (int)ds;
|
| 2805 |
if (ds < 0. && ds != k) |
| 2806 |
k--; /* want k = floor(ds) */
|
| 2807 |
k_check = 1;
|
| 2808 |
if (k >= 0 && k <= Ten_pmax) { |
| 2809 |
if (dval(d) < tens[k])
|
| 2810 |
k--; |
| 2811 |
k_check = 0;
|
| 2812 |
} |
| 2813 |
j = bbits - i - 1;
|
| 2814 |
if (j >= 0) { |
| 2815 |
b2 = 0;
|
| 2816 |
s2 = j; |
| 2817 |
} |
| 2818 |
else {
|
| 2819 |
b2 = -j; |
| 2820 |
s2 = 0;
|
| 2821 |
} |
| 2822 |
if (k >= 0) { |
| 2823 |
b5 = 0;
|
| 2824 |
s5 = k; |
| 2825 |
s2 += k; |
| 2826 |
} |
| 2827 |
else {
|
| 2828 |
b2 -= k; |
| 2829 |
b5 = -k; |
| 2830 |
s5 = 0;
|
| 2831 |
} |
| 2832 |
if (mode < 0 || mode > 9) |
| 2833 |
mode = 0;
|
| 2834 |
|
| 2835 |
#ifndef SET_INEXACT
|
| 2836 |
#ifdef Check_FLT_ROUNDS
|
| 2837 |
try_quick = Rounding == 1;
|
| 2838 |
#else
|
| 2839 |
try_quick = 1;
|
| 2840 |
#endif
|
| 2841 |
#endif /*SET_INEXACT*/ |
| 2842 |
|
| 2843 |
if (mode > 5) { |
| 2844 |
mode -= 4;
|
| 2845 |
try_quick = 0;
|
| 2846 |
} |
| 2847 |
leftright = 1;
|
| 2848 |
switch(mode) {
|
| 2849 |
case 0: |
| 2850 |
case 1: |
| 2851 |
ilim = ilim1 = -1;
|
| 2852 |
i = 18;
|
| 2853 |
ndigits = 0;
|
| 2854 |
break;
|
| 2855 |
case 2: |
| 2856 |
leftright = 0;
|
| 2857 |
/* no break */
|
| 2858 |
case 4: |
| 2859 |
if (ndigits <= 0) |
| 2860 |
ndigits = 1;
|
| 2861 |
ilim = ilim1 = i = ndigits; |
| 2862 |
break;
|
| 2863 |
case 3: |
| 2864 |
leftright = 0;
|
| 2865 |
/* no break */
|
| 2866 |
case 5: |
| 2867 |
i = ndigits + k + 1;
|
| 2868 |
ilim = i; |
| 2869 |
ilim1 = i - 1;
|
| 2870 |
if (i <= 0) |
| 2871 |
i = 1;
|
| 2872 |
} |
| 2873 |
s = s0 = rv_alloc(i); |
| 2874 |
|
| 2875 |
#ifdef Honor_FLT_ROUNDS
|
| 2876 |
if (mode > 1 && rounding != 1) |
| 2877 |
leftright = 0;
|
| 2878 |
#endif
|
| 2879 |
|
| 2880 |
if (ilim >= 0 && ilim <= Quick_max && try_quick) { |
| 2881 |
|
| 2882 |
/* Try to get by with floating-point arithmetic. */
|
| 2883 |
|
| 2884 |
i = 0;
|
| 2885 |
dval(d2) = dval(d); |
| 2886 |
k0 = k; |
| 2887 |
ilim0 = ilim; |
| 2888 |
ieps = 2; /* conservative */ |
| 2889 |
if (k > 0) { |
| 2890 |
ds = tens[k&0xf];
|
| 2891 |
j = k >> 4;
|
| 2892 |
if (j & Bletch) {
|
| 2893 |
/* prevent overflows */
|
| 2894 |
j &= Bletch - 1;
|
| 2895 |
dval(d) /= bigtens[n_bigtens-1];
|
| 2896 |
ieps++; |
| 2897 |
} |
| 2898 |
for(; j; j >>= 1, i++) |
| 2899 |
if (j & 1) { |
| 2900 |
ieps++; |
| 2901 |
ds *= bigtens[i]; |
| 2902 |
} |
| 2903 |
dval(d) /= ds; |
| 2904 |
} |
| 2905 |
else if ((j1 = -k)) { |
| 2906 |
dval(d) *= tens[j1 & 0xf];
|
| 2907 |
for(j = j1 >> 4; j; j >>= 1, i++) |
| 2908 |
if (j & 1) { |
| 2909 |
ieps++; |
| 2910 |
dval(d) *= bigtens[i]; |
| 2911 |
} |
| 2912 |
} |
| 2913 |
if (k_check && dval(d) < 1. && ilim > 0) { |
| 2914 |
if (ilim1 <= 0) |
| 2915 |
goto fast_failed;
|
| 2916 |
ilim = ilim1; |
| 2917 |
k--; |
| 2918 |
dval(d) *= 10.; |
| 2919 |
ieps++; |
| 2920 |
} |
| 2921 |
dval(eps) = ieps*dval(d) + 7.;
|
| 2922 |
word0(eps) -= (P-1)*Exp_msk1;
|
| 2923 |
if (ilim == 0) { |
| 2924 |
S = mhi = 0;
|
| 2925 |
dval(d) -= 5.;
|
| 2926 |
if (dval(d) > dval(eps))
|
| 2927 |
goto one_digit;
|
| 2928 |
if (dval(d) < -dval(eps))
|
| 2929 |
goto no_digits;
|
| 2930 |
goto fast_failed;
|
| 2931 |
} |
| 2932 |
#ifndef No_leftright
|
| 2933 |
if (leftright) {
|
| 2934 |
/* Use Steele & White method of only
|
| 2935 |
* generating digits needed.
|
| 2936 |
*/
|
| 2937 |
dval(eps) = 0.5/tens[ilim-1] - dval(eps); |
| 2938 |
for(i = 0;;) { |
| 2939 |
L = dval(d); |
| 2940 |
dval(d) -= L; |
| 2941 |
*s++ = '0' + (int)L; |
| 2942 |
if (dval(d) < dval(eps))
|
| 2943 |
goto ret1;
|
| 2944 |
if (1. - dval(d) < dval(eps)) |
| 2945 |
goto bump_up;
|
| 2946 |
if (++i >= ilim)
|
| 2947 |
break;
|
| 2948 |
dval(eps) *= 10.; |
| 2949 |
dval(d) *= 10.; |
| 2950 |
} |
| 2951 |
} |
| 2952 |
else {
|
| 2953 |
#endif
|
| 2954 |
/* Generate ilim digits, then fix them up. */
|
| 2955 |
dval(eps) *= tens[ilim-1];
|
| 2956 |
for(i = 1;; i++, dval(d) *= 10.) { |
| 2957 |
L = (Long)(dval(d)); |
| 2958 |
if (!(dval(d) -= L))
|
| 2959 |
ilim = i; |
| 2960 |
*s++ = '0' + (int)L; |
| 2961 |
if (i == ilim) {
|
| 2962 |
if (dval(d) > 0.5 + dval(eps)) |
| 2963 |
goto bump_up;
|
| 2964 |
else if (dval(d) < 0.5 - dval(eps)) { |
| 2965 |
while(*--s == '0'); |
| 2966 |
s++; |
| 2967 |
goto ret1;
|
| 2968 |
} |
| 2969 |
break;
|
| 2970 |
} |
| 2971 |
} |
| 2972 |
#ifndef No_leftright
|
| 2973 |
} |
| 2974 |
#endif
|
| 2975 |
fast_failed:
|
| 2976 |
s = s0; |
| 2977 |
dval(d) = dval(d2); |
| 2978 |
k = k0; |
| 2979 |
ilim = ilim0; |
| 2980 |
} |
| 2981 |
|
| 2982 |
/* Do we have a "small" integer? */
|
| 2983 |
|
| 2984 |
if (be >= 0 && k <= Int_max) { |
| 2985 |
/* Yes. */
|
| 2986 |
ds = tens[k]; |
| 2987 |
if (ndigits < 0 && ilim <= 0) { |
| 2988 |
S = mhi = 0;
|
| 2989 |
if (ilim < 0 || dval(d) < 5*ds || ((dval(d) == 5*ds) && !bias_round_up)) |
| 2990 |
goto no_digits;
|
| 2991 |
goto one_digit;
|
| 2992 |
} |
| 2993 |
|
| 2994 |
/* Limit looping by the number of digits to produce.
|
| 2995 |
* Firefox had a crash bug because some plugins reduce
|
| 2996 |
* the precision of double arithmetic. With reduced
|
| 2997 |
* precision "dval(d) -= L*ds" might be imprecise and
|
| 2998 |
* d might not become zero and the loop might not
|
| 2999 |
* terminate.
|
| 3000 |
*
|
| 3001 |
* See https://bugzilla.mozilla.org/show_bug.cgi?id=358569
|
| 3002 |
*/
|
| 3003 |
for(i = 1; i <= k+1; i++, dval(d) *= 10.) { |
| 3004 |
L = (Long)(dval(d) / ds); |
| 3005 |
dval(d) -= L*ds; |
| 3006 |
#ifdef Check_FLT_ROUNDS
|
| 3007 |
/* If FLT_ROUNDS == 2, L will usually be high by 1 */
|
| 3008 |
if (dval(d) < 0) { |
| 3009 |
L--; |
| 3010 |
dval(d) += ds; |
| 3011 |
} |
| 3012 |
#endif
|
| 3013 |
*s++ = '0' + (int)L; |
| 3014 |
if (!dval(d)) {
|
| 3015 |
#ifdef SET_INEXACT
|
| 3016 |
inexact = 0;
|
| 3017 |
#endif
|
| 3018 |
break;
|
| 3019 |
} |
| 3020 |
if (i == ilim) {
|
| 3021 |
#ifdef Honor_FLT_ROUNDS
|
| 3022 |
if (mode > 1) |
| 3023 |
switch(rounding) {
|
| 3024 |
case 0: goto ret1; |
| 3025 |
case 2: goto bump_up; |
| 3026 |
} |
| 3027 |
#endif
|
| 3028 |
dval(d) += dval(d); |
| 3029 |
if (dval(d) > ds || (dval(d) == ds && ((L & 1) || bias_round_up))) { |
| 3030 |
bump_up:
|
| 3031 |
while(*--s == '9') |
| 3032 |
if (s == s0) {
|
| 3033 |
k++; |
| 3034 |
*s = '0';
|
| 3035 |
break;
|
| 3036 |
} |
| 3037 |
++*s++; |
| 3038 |
} |
| 3039 |
break;
|
| 3040 |
} |
| 3041 |
} |
| 3042 |
goto ret1;
|
| 3043 |
} |
| 3044 |
|
| 3045 |
m2 = b2; |
| 3046 |
m5 = b5; |
| 3047 |
mhi = mlo = 0;
|
| 3048 |
if (leftright) {
|
| 3049 |
i = |
| 3050 |
#ifndef Sudden_Underflow
|
| 3051 |
denorm ? be + (Bias + (P-1) - 1 + 1) : |
| 3052 |
#endif
|
| 3053 |
#ifdef IBM
|
| 3054 |
1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3); |
| 3055 |
#else
|
| 3056 |
1 + P - bbits;
|
| 3057 |
#endif
|
| 3058 |
b2 += i; |
| 3059 |
s2 += i; |
| 3060 |
mhi = i2b(1);
|
| 3061 |
} |
| 3062 |
if (m2 > 0 && s2 > 0) { |
| 3063 |
i = m2 < s2 ? m2 : s2; |
| 3064 |
b2 -= i; |
| 3065 |
m2 -= i; |
| 3066 |
s2 -= i; |
| 3067 |
} |
| 3068 |
if (b5 > 0) { |
| 3069 |
if (leftright) {
|
| 3070 |
if (m5 > 0) { |
| 3071 |
mhi = pow5mult(mhi, m5); |
| 3072 |
b1 = mult(mhi, b); |
| 3073 |
Bfree(b); |
| 3074 |
b = b1; |
| 3075 |
} |
| 3076 |
if ((j = b5 - m5))
|
| 3077 |
b = pow5mult(b, j); |
| 3078 |
} |
| 3079 |
else
|
| 3080 |
b = pow5mult(b, b5); |
| 3081 |
} |
| 3082 |
S = i2b(1);
|
| 3083 |
if (s5 > 0) |
| 3084 |
S = pow5mult(S, s5); |
| 3085 |
|
| 3086 |
/* Check for special case that d is a normalized power of 2. */
|
| 3087 |
|
| 3088 |
spec_case = 0;
|
| 3089 |
if ((mode < 2 || leftright) |
| 3090 |
#ifdef Honor_FLT_ROUNDS
|
| 3091 |
&& rounding == 1
|
| 3092 |
#endif
|
| 3093 |
) {
|
| 3094 |
if (!word1(d) && !(word0(d) & Bndry_mask)
|
| 3095 |
#ifndef Sudden_Underflow
|
| 3096 |
&& word0(d) & (Exp_mask & ~Exp_msk1) |
| 3097 |
#endif
|
| 3098 |
) {
|
| 3099 |
/* The special case */
|
| 3100 |
b2 += Log2P; |
| 3101 |
s2 += Log2P; |
| 3102 |
spec_case = 1;
|
| 3103 |
} |
| 3104 |
} |
| 3105 |
|
| 3106 |
/* Arrange for convenient computation of quotients:
|
| 3107 |
* shift left if necessary so divisor has 4 leading 0 bits.
|
| 3108 |
*
|
| 3109 |
* Perhaps we should just compute leading 28 bits of S once
|
| 3110 |
* and for all and pass them and a shift to quorem, so it
|
| 3111 |
* can do shifts and ors to compute the numerator for q.
|
| 3112 |
*/
|
| 3113 |
#ifdef Pack_32
|
| 3114 |
if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f)) |
| 3115 |
i = 32 - i;
|
| 3116 |
#else
|
| 3117 |
if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf)) |
| 3118 |
i = 16 - i;
|
| 3119 |
#endif
|
| 3120 |
if (i > 4) { |
| 3121 |
i -= 4;
|
| 3122 |
b2 += i; |
| 3123 |
m2 += i; |
| 3124 |
s2 += i; |
| 3125 |
} |
| 3126 |
else if (i < 4) { |
| 3127 |
i += 28;
|
| 3128 |
b2 += i; |
| 3129 |
m2 += i; |
| 3130 |
s2 += i; |
| 3131 |
} |
| 3132 |
if (b2 > 0) |
| 3133 |
b = lshift(b, b2); |
| 3134 |
if (s2 > 0) |
| 3135 |
S = lshift(S, s2); |
| 3136 |
if (k_check) {
|
| 3137 |
if (cmp(b,S) < 0) { |
| 3138 |
k--; |
| 3139 |
b = multadd(b, 10, 0); /* we botched the k estimate */ |
| 3140 |
if (leftright)
|
| 3141 |
mhi = multadd(mhi, 10, 0); |
| 3142 |
ilim = ilim1; |
| 3143 |
} |
| 3144 |
} |
| 3145 |
if (ilim <= 0 && (mode == 3 || mode == 5)) { |
| 3146 |
S = multadd(S, 5, 0); |
| 3147 |
if (ilim < 0 || cmp(b, S) < 0 || ((cmp(b, S) == 0) && !bias_round_up)) { |
| 3148 |
/* no digits, fcvt style */
|
| 3149 |
no_digits:
|
| 3150 |
k = -1 - ndigits;
|
| 3151 |
goto ret;
|
| 3152 |
} |
| 3153 |
one_digit:
|
| 3154 |
*s++ = '1';
|
| 3155 |
k++; |
| 3156 |
goto ret;
|
| 3157 |
} |
| 3158 |
if (leftright) {
|
| 3159 |
if (m2 > 0) |
| 3160 |
mhi = lshift(mhi, m2); |
| 3161 |
|
| 3162 |
/* Compute mlo -- check for special case
|
| 3163 |
* that d is a normalized power of 2.
|
| 3164 |
*/
|
| 3165 |
|
| 3166 |
mlo = mhi; |
| 3167 |
if (spec_case) {
|
| 3168 |
mhi = Balloc(mhi->k); |
| 3169 |
Bcopy(mhi, mlo); |
| 3170 |
mhi = lshift(mhi, Log2P); |
| 3171 |
} |
| 3172 |
|
| 3173 |
for(i = 1;;i++) { |
| 3174 |
dig = quorem(b,S) + '0';
|
| 3175 |
/* Do we yet have the shortest decimal string
|
| 3176 |
* that will round to d?
|
| 3177 |
*/
|
| 3178 |
j = cmp(b, mlo); |
| 3179 |
delta = diff(S, mhi); |
| 3180 |
j1 = delta->sign ? 1 : cmp(b, delta);
|
| 3181 |
Bfree(delta); |
| 3182 |
#ifndef ROUND_BIASED
|
| 3183 |
if (j1 == 0 && mode != 1 && !(word1(d) & 1) |
| 3184 |
#ifdef Honor_FLT_ROUNDS
|
| 3185 |
&& rounding >= 1
|
| 3186 |
#endif
|
| 3187 |
) {
|
| 3188 |
if (dig == '9') |
| 3189 |
goto round_9_up;
|
| 3190 |
if (j > 0) |
| 3191 |
dig++; |
| 3192 |
#ifdef SET_INEXACT
|
| 3193 |
else if (!b->x[0] && b->wds <= 1) |
| 3194 |
inexact = 0;
|
| 3195 |
#endif
|
| 3196 |
*s++ = dig; |
| 3197 |
goto ret;
|
| 3198 |
} |
| 3199 |
#endif
|
| 3200 |
if (j < 0 || (j == 0 && mode != 1 |
| 3201 |
#ifndef ROUND_BIASED
|
| 3202 |
&& !(word1(d) & 1)
|
| 3203 |
#endif
|
| 3204 |
)) {
|
| 3205 |
if (!b->x[0] && b->wds <= 1) { |
| 3206 |
#ifdef SET_INEXACT
|
| 3207 |
inexact = 0;
|
| 3208 |
#endif
|
| 3209 |
goto accept_dig;
|
| 3210 |
} |
| 3211 |
#ifdef Honor_FLT_ROUNDS
|
| 3212 |
if (mode > 1) |
| 3213 |
switch(rounding) {
|
| 3214 |
case 0: goto accept_dig; |
| 3215 |
case 2: goto keep_dig; |
| 3216 |
} |
| 3217 |
#endif /*Honor_FLT_ROUNDS*/ |
| 3218 |
if (j1 > 0) { |
| 3219 |
b = lshift(b, 1);
|
| 3220 |
j1 = cmp(b, S); |
| 3221 |
if ((j1 > 0 || (j1 == 0 && ((dig & 1) || bias_round_up))) |
| 3222 |
&& dig++ == '9')
|
| 3223 |
goto round_9_up;
|
| 3224 |
} |
| 3225 |
accept_dig:
|
| 3226 |
*s++ = dig; |
| 3227 |
goto ret;
|
| 3228 |
} |
| 3229 |
if (j1 > 0) { |
| 3230 |
#ifdef Honor_FLT_ROUNDS
|
| 3231 |
if (!rounding)
|
| 3232 |
goto accept_dig;
|
| 3233 |
#endif
|
| 3234 |
if (dig == '9') { /* possible if i == 1 */ |
| 3235 |
round_9_up:
|
| 3236 |
*s++ = '9';
|
| 3237 |
goto roundoff;
|
| 3238 |
} |
| 3239 |
*s++ = dig + 1;
|
| 3240 |
goto ret;
|
| 3241 |
} |
| 3242 |
#ifdef Honor_FLT_ROUNDS
|
| 3243 |
keep_dig:
|
| 3244 |
#endif
|
| 3245 |
*s++ = dig; |
| 3246 |
if (i == ilim)
|
| 3247 |
break;
|
| 3248 |
b = multadd(b, 10, 0); |
| 3249 |
if (mlo == mhi)
|
| 3250 |
mlo = mhi = multadd(mhi, 10, 0); |
| 3251 |
else {
|
| 3252 |
mlo = multadd(mlo, 10, 0); |
| 3253 |
mhi = multadd(mhi, 10, 0); |
| 3254 |
} |
| 3255 |
} |
| 3256 |
} |
| 3257 |
else
|
| 3258 |
for(i = 1;; i++) { |
| 3259 |
*s++ = dig = quorem(b,S) + '0';
|
| 3260 |
if (!b->x[0] && b->wds <= 1) { |
| 3261 |
#ifdef SET_INEXACT
|
| 3262 |
inexact = 0;
|
| 3263 |
#endif
|
| 3264 |
goto ret;
|
| 3265 |
} |
| 3266 |
if (i >= ilim)
|
| 3267 |
break;
|
| 3268 |
b = multadd(b, 10, 0); |
| 3269 |
} |
| 3270 |
|
| 3271 |
/* Round off last digit */
|
| 3272 |
|
| 3273 |
#ifdef Honor_FLT_ROUNDS
|
| 3274 |
switch(rounding) {
|
| 3275 |
case 0: goto trimzeros; |
| 3276 |
case 2: goto roundoff; |
| 3277 |
} |
| 3278 |
#endif
|
| 3279 |
b = lshift(b, 1);
|
| 3280 |
j = cmp(b, S); |
| 3281 |
if (j > 0 || (j == 0 && ((dig & 1) || bias_round_up))) { |
| 3282 |
roundoff:
|
| 3283 |
while(*--s == '9') |
| 3284 |
if (s == s0) {
|
| 3285 |
k++; |
| 3286 |
*s++ = '1';
|
| 3287 |
goto ret;
|
| 3288 |
} |
| 3289 |
++*s++; |
| 3290 |
} |
| 3291 |
else {
|
| 3292 |
/* trimzeros: (never used) */
|
| 3293 |
while(*--s == '0'); |
| 3294 |
s++; |
| 3295 |
} |
| 3296 |
ret:
|
| 3297 |
Bfree(S); |
| 3298 |
if (mhi) {
|
| 3299 |
if (mlo && mlo != mhi)
|
| 3300 |
Bfree(mlo); |
| 3301 |
Bfree(mhi); |
| 3302 |
} |
| 3303 |
ret1:
|
| 3304 |
#ifdef SET_INEXACT
|
| 3305 |
if (inexact) {
|
| 3306 |
if (!oldinexact) {
|
| 3307 |
word0(d) = Exp_1 + (70 << Exp_shift);
|
| 3308 |
word1(d) = 0;
|
| 3309 |
dval(d) += 1.;
|
| 3310 |
} |
| 3311 |
} |
| 3312 |
else if (!oldinexact) |
| 3313 |
clear_inexact(); |
| 3314 |
#endif
|
| 3315 |
Bfree(b); |
| 3316 |
*s = 0;
|
| 3317 |
*decpt = k + 1;
|
| 3318 |
if (rve)
|
| 3319 |
*rve = s; |
| 3320 |
return s0;
|
| 3321 |
} |
| 3322 |
#ifdef __cplusplus
|
| 3323 |
} |
| 3324 |
#endif
|