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/* -*- Mode: C; tab-width: 8; indent-tabs-mode: t; c-basic-offset: 8 -*- */ |
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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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|
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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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|
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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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|
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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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/* |
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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 NO_INFNAN_CHECK if you do not wish to have INFNAN_CHECK |
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* #defined automatically on IEEE systems. On such systems, |
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* when INFNAN_CHECK is #defined, strtod checks |
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* for Infinity and NaN (case insensitively). On some systems |
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* (e.g., 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 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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|
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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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|
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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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|
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#include "stdlib.h" |
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#include "string.h" |
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|
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#ifdef USE_LOCALE |
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#include "locale.h" |
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#endif |
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|
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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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|
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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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|
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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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|
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#ifdef IEEE_Arith |
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#ifndef NO_INFNAN_CHECK |
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#undef INFNAN_CHECK |
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#define INFNAN_CHECK |
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#endif |
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#else |
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#undef INFNAN_CHECK |
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#endif |
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|
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#include "errno.h" |
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|
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#ifdef Bad_float_h |
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|
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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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|
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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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|
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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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|
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#ifndef LONG_MAX |
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#define LONG_MAX 2147483647 |
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#endif |
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|
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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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|
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#ifndef __MATH_H__ |
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#include "math.h" |
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#endif |
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|
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#ifdef __cplusplus |
259 |
extern "C" { |
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#endif |
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|
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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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|
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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 |
273 |
|
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typedef union { double d; ULong L[2]; } U; |
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|
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#define dval(x) ((x).d) |
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#ifdef IEEE_8087 |
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#define word0(x) ((x).L[1]) |
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#define word1(x) ((x).L[0]) |
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#else |
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#define word0(x) ((x).L[0]) |
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#define word1(x) ((x).L[1]) |
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#endif |
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|
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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 |
293 |
#define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \ |
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((unsigned short *)a)[1] = (unsigned short)c, a++) |
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#endif |
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|
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/* #define P DBL_MANT_DIG */ |
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/* Ten_pmax = floor(P*log(2)/log(5)) */ |
299 |
/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */ |
300 |
/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */ |
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/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */ |
302 |
|
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#ifdef IEEE_Arith |
304 |
#define Exp_shift 20 |
305 |
#define Exp_shift1 20 |
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#define Exp_msk1 0x100000 |
307 |
#define Exp_msk11 0x100000 |
308 |
#define Exp_mask 0x7ff00000 |
309 |
#define P 53 |
310 |
#define Bias 1023 |
311 |
#define Emin (-1022) |
312 |
#define Exp_1 0x3ff00000 |
313 |
#define Exp_11 0x3ff00000 |
314 |
#define Ebits 11 |
315 |
#define Frac_mask 0xfffff |
316 |
#define Frac_mask1 0xfffff |
317 |
#define Ten_pmax 22 |
318 |
#define Bletch 0x10 |
319 |
#define Bndry_mask 0xfffff |
320 |
#define Bndry_mask1 0xfffff |
321 |
#define LSB 1 |
322 |
#define Sign_bit 0x80000000 |
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#define Log2P 1 |
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#define Tiny0 0 |
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#define Tiny1 1 |
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#define Quick_max 14 |
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#define Int_max 14 |
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#ifndef NO_IEEE_Scale |
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#define Avoid_Underflow |
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#ifdef Flush_Denorm /* debugging option */ |
331 |
#undef Sudden_Underflow |
332 |
#endif |
333 |
#endif |
334 |
|
335 |
#ifndef Flt_Rounds |
336 |
#ifdef FLT_ROUNDS |
337 |
#define Flt_Rounds FLT_ROUNDS |
338 |
#else |
339 |
#define Flt_Rounds 1 |
340 |
#endif |
341 |
#endif /*Flt_Rounds*/ |
342 |
|
343 |
#ifdef Honor_FLT_ROUNDS |
344 |
#define Rounding rounding |
345 |
#undef Check_FLT_ROUNDS |
346 |
#define Check_FLT_ROUNDS |
347 |
#else |
348 |
#define Rounding Flt_Rounds |
349 |
#endif |
350 |
|
351 |
#else /* ifndef IEEE_Arith */ |
352 |
#undef Check_FLT_ROUNDS |
353 |
#undef Honor_FLT_ROUNDS |
354 |
#undef SET_INEXACT |
355 |
#undef Sudden_Underflow |
356 |
#define Sudden_Underflow |
357 |
#ifdef IBM |
358 |
#undef Flt_Rounds |
359 |
#define Flt_Rounds 0 |
360 |
#define Exp_shift 24 |
361 |
#define Exp_shift1 24 |
362 |
#define Exp_msk1 0x1000000 |
363 |
#define Exp_msk11 0x1000000 |
364 |
#define Exp_mask 0x7f000000 |
365 |
#define P 14 |
366 |
#define Bias 65 |
367 |
#define Exp_1 0x41000000 |
368 |
#define Exp_11 0x41000000 |
369 |
#define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */ |
370 |
#define Frac_mask 0xffffff |
371 |
#define Frac_mask1 0xffffff |
372 |
#define Bletch 4 |
373 |
#define Ten_pmax 22 |
374 |
#define Bndry_mask 0xefffff |
375 |
#define Bndry_mask1 0xffffff |
376 |
#define LSB 1 |
377 |
#define Sign_bit 0x80000000 |
378 |
#define Log2P 4 |
379 |
#define Tiny0 0x100000 |
380 |
#define Tiny1 0 |
381 |
#define Quick_max 14 |
382 |
#define Int_max 15 |
383 |
#else /* VAX */ |
384 |
#undef Flt_Rounds |
385 |
#define Flt_Rounds 1 |
386 |
#define Exp_shift 23 |
387 |
#define Exp_shift1 7 |
388 |
#define Exp_msk1 0x80 |
389 |
#define Exp_msk11 0x800000 |
390 |
#define Exp_mask 0x7f80 |
391 |
#define P 56 |
392 |
#define Bias 129 |
393 |
#define Exp_1 0x40800000 |
394 |
#define Exp_11 0x4080 |
395 |
#define Ebits 8 |
396 |
#define Frac_mask 0x7fffff |
397 |
#define Frac_mask1 0xffff007f |
398 |
#define Ten_pmax 24 |
399 |
#define Bletch 2 |
400 |
#define Bndry_mask 0xffff007f |
401 |
#define Bndry_mask1 0xffff007f |
402 |
#define LSB 0x10000 |
403 |
#define Sign_bit 0x8000 |
404 |
#define Log2P 1 |
405 |
#define Tiny0 0x80 |
406 |
#define Tiny1 0 |
407 |
#define Quick_max 15 |
408 |
#define Int_max 15 |
409 |
#endif /* IBM, VAX */ |
410 |
#endif /* IEEE_Arith */ |
411 |
|
412 |
#ifndef IEEE_Arith |
413 |
#define ROUND_BIASED |
414 |
#endif |
415 |
|
416 |
#ifdef RND_PRODQUOT |
417 |
#define rounded_product(a,b) a = rnd_prod(a, b) |
418 |
#define rounded_quotient(a,b) a = rnd_quot(a, b) |
419 |
#ifdef KR_headers |
420 |
extern double rnd_prod(), rnd_quot(); |
421 |
#else |
422 |
extern double rnd_prod(double, double), rnd_quot(double, double); |
423 |
#endif |
424 |
#else |
425 |
#define rounded_product(a,b) a *= b |
426 |
#define rounded_quotient(a,b) a /= b |
427 |
#endif |
428 |
|
429 |
#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1)) |
430 |
#define Big1 0xffffffff |
431 |
|
432 |
#ifndef Pack_32 |
433 |
#define Pack_32 |
434 |
#endif |
435 |
|
436 |
#ifdef KR_headers |
437 |
#define FFFFFFFF ((((unsigned long)0xffff)<<16)|(unsigned long)0xffff) |
438 |
#else |
439 |
#define FFFFFFFF 0xffffffffUL |
440 |
#endif |
441 |
|
442 |
#ifdef NO_LONG_LONG |
443 |
#undef ULLong |
444 |
#ifdef Just_16 |
445 |
#undef Pack_32 |
446 |
/* When Pack_32 is not defined, we store 16 bits per 32-bit Long. |
447 |
* This makes some inner loops simpler and sometimes saves work |
448 |
* during multiplications, but it often seems to make things slightly |
449 |
* slower. Hence the default is now to store 32 bits per Long. |
450 |
*/ |
451 |
#endif |
452 |
#else /* long long available */ |
453 |
#ifndef Llong |
454 |
#define Llong long long |
455 |
#endif |
456 |
#ifndef ULLong |
457 |
#define ULLong unsigned Llong |
458 |
#endif |
459 |
#endif /* NO_LONG_LONG */ |
460 |
|
461 |
#ifndef MULTIPLE_THREADS |
462 |
#define ACQUIRE_DTOA_LOCK(n) /*nothing*/ |
463 |
#define FREE_DTOA_LOCK(n) /*nothing*/ |
464 |
#endif |
465 |
|
466 |
#define Kmax 15 |
467 |
|
468 |
struct |
469 |
Bigint { |
470 |
struct Bigint *next; |
471 |
int k, maxwds, sign, wds; |
472 |
ULong x[1]; |
473 |
}; |
474 |
|
475 |
typedef struct Bigint Bigint; |
476 |
|
477 |
static Bigint *freelist[Kmax+1]; |
478 |
|
479 |
static Bigint * |
480 |
Balloc |
481 |
#ifdef KR_headers |
482 |
(k) int k; |
483 |
#else |
484 |
(int k) |
485 |
#endif |
486 |
{ |
487 |
int x; |
488 |
Bigint *rv; |
489 |
#ifndef Omit_Private_Memory |
490 |
size_t len; |
491 |
#endif |
492 |
|
493 |
ACQUIRE_DTOA_LOCK(0); |
494 |
if ((rv = freelist[k])) { |
495 |
freelist[k] = rv->next; |
496 |
} |
497 |
else { |
498 |
x = 1 << k; |
499 |
#ifdef Omit_Private_Memory |
500 |
rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong)); |
501 |
#else |
502 |
len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1) |
503 |
/sizeof(double); |
504 |
if (pmem_next - private_mem + len <= PRIVATE_mem) { |
505 |
rv = (Bigint*)pmem_next; |
506 |
pmem_next += len; |
507 |
} |
508 |
else |
509 |
rv = (Bigint*)MALLOC(len*sizeof(double)); |
510 |
#endif |
511 |
rv->k = k; |
512 |
rv->maxwds = x; |
513 |
} |
514 |
FREE_DTOA_LOCK(0); |
515 |
rv->sign = rv->wds = 0; |
516 |
return rv; |
517 |
} |
518 |
|
519 |
static void |
520 |
Bfree |
521 |
#ifdef KR_headers |
522 |
(v) Bigint *v; |
523 |
#else |
524 |
(Bigint *v) |
525 |
#endif |
526 |
{ |
527 |
if (v) { |
528 |
ACQUIRE_DTOA_LOCK(0); |
529 |
v->next = freelist[v->k]; |
530 |
freelist[v->k] = v; |
531 |
FREE_DTOA_LOCK(0); |
532 |
} |
533 |
} |
534 |
|
535 |
#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \ |
536 |
y->wds*sizeof(Long) + 2*sizeof(int)) |
537 |
|
538 |
static Bigint * |
539 |
multadd |
540 |
#ifdef KR_headers |
541 |
(b, m, a) Bigint *b; int m, a; |
542 |
#else |
543 |
(Bigint *b, int m, int a) /* multiply by m and add a */ |
544 |
#endif |
545 |
{ |
546 |
int i, wds; |
547 |
#ifdef ULLong |
548 |
ULong *x; |
549 |
ULLong carry, y; |
550 |
#else |
551 |
ULong carry, *x, y; |
552 |
#ifdef Pack_32 |
553 |
ULong xi, z; |
554 |
#endif |
555 |
#endif |
556 |
Bigint *b1; |
557 |
|
558 |
wds = b->wds; |
559 |
x = b->x; |
560 |
i = 0; |
561 |
carry = a; |
562 |
do { |
563 |
#ifdef ULLong |
564 |
y = *x * (ULLong)m + carry; |
565 |
carry = y >> 32; |
566 |
*x++ = (ULong) y & FFFFFFFF; |
567 |
#else |
568 |
#ifdef Pack_32 |
569 |
xi = *x; |
570 |
y = (xi & 0xffff) * m + carry; |
571 |
z = (xi >> 16) * m + (y >> 16); |
572 |
carry = z >> 16; |
573 |
*x++ = (z << 16) + (y & 0xffff); |
574 |
#else |
575 |
y = *x * m + carry; |
576 |
carry = y >> 16; |
577 |
*x++ = y & 0xffff; |
578 |
#endif |
579 |
#endif |
580 |
} |
581 |
while(++i < wds); |
582 |
if (carry) { |
583 |
if (wds >= b->maxwds) { |
584 |
b1 = Balloc(b->k+1); |
585 |
Bcopy(b1, b); |
586 |
Bfree(b); |
587 |
b = b1; |
588 |
} |
589 |
b->x[wds++] = (ULong) carry; |
590 |
b->wds = wds; |
591 |
} |
592 |
return b; |
593 |
} |
594 |
|
595 |
static Bigint * |
596 |
s2b |
597 |
#ifdef KR_headers |
598 |
(s, nd0, nd, y9) CONST char *s; int nd0, nd; ULong y9; |
599 |
#else |
600 |
(CONST char *s, int nd0, int nd, ULong y9) |
601 |
#endif |
602 |
{ |
603 |
Bigint *b; |
604 |
int i, k; |
605 |
Long x, y; |
606 |
|
607 |
x = (nd + 8) / 9; |
608 |
for(k = 0, y = 1; x > y; y <<= 1, k++) ; |
609 |
#ifdef Pack_32 |
610 |
b = Balloc(k); |
611 |
b->x[0] = y9; |
612 |
b->wds = 1; |
613 |
#else |
614 |
b = Balloc(k+1); |
615 |
b->x[0] = y9 & 0xffff; |
616 |
b->wds = (b->x[1] = y9 >> 16) ? 2 : 1; |
617 |
#endif |
618 |
|
619 |
i = 9; |
620 |
if (9 < nd0) { |
621 |
s += 9; |
622 |
do b = multadd(b, 10, *s++ - '0'); |
623 |
while(++i < nd0); |
624 |
s++; |
625 |
} |
626 |
else |
627 |
s += 10; |
628 |
for(; i < nd; i++) |
629 |
b = multadd(b, 10, *s++ - '0'); |
630 |
return b; |
631 |
} |
632 |
|
633 |
static int |
634 |
hi0bits |
635 |
#ifdef KR_headers |
636 |
(x) register ULong x; |
637 |
#else |
638 |
(register ULong x) |
639 |
#endif |
640 |
{ |
641 |
register int k = 0; |
642 |
|
643 |
if (!(x & 0xffff0000)) { |
644 |
k = 16; |
645 |
x <<= 16; |
646 |
} |
647 |
if (!(x & 0xff000000)) { |
648 |
k += 8; |
649 |
x <<= 8; |
650 |
} |
651 |
if (!(x & 0xf0000000)) { |
652 |
k += 4; |
653 |
x <<= 4; |
654 |
} |
655 |
if (!(x & 0xc0000000)) { |
656 |
k += 2; |
657 |
x <<= 2; |
658 |
} |
659 |
if (!(x & 0x80000000)) { |
660 |
k++; |
661 |
if (!(x & 0x40000000)) |
662 |
return 32; |
663 |
} |
664 |
return k; |
665 |
} |
666 |
|
667 |
static int |
668 |
lo0bits |
669 |
#ifdef KR_headers |
670 |
(y) ULong *y; |
671 |
#else |
672 |
(ULong *y) |
673 |
#endif |
674 |
{ |
675 |
register int k; |
676 |
register ULong x = *y; |
677 |
|
678 |
if (x & 7) { |
679 |
if (x & 1) |
680 |
return 0; |
681 |
if (x & 2) { |
682 |
*y = x >> 1; |
683 |
return 1; |
684 |
} |
685 |
*y = x >> 2; |
686 |
return 2; |
687 |
} |
688 |
k = 0; |
689 |
if (!(x & 0xffff)) { |
690 |
k = 16; |
691 |
x >>= 16; |
692 |
} |
693 |
if (!(x & 0xff)) { |
694 |
k += 8; |
695 |
x >>= 8; |
696 |
} |
697 |
if (!(x & 0xf)) { |
698 |
k += 4; |
699 |
x >>= 4; |
700 |
} |
701 |
if (!(x & 0x3)) { |
702 |
k += 2; |
703 |
x >>= 2; |
704 |
} |
705 |
if (!(x & 1)) { |
706 |
k++; |
707 |
x >>= 1; |
708 |
if (!x) |
709 |
return 32; |
710 |
} |
711 |
*y = x; |
712 |
return k; |
713 |
} |
714 |
|
715 |
static Bigint * |
716 |
i2b |
717 |
#ifdef KR_headers |
718 |
(i) int i; |
719 |
#else |
720 |
(int i) |
721 |
#endif |
722 |
{ |
723 |
Bigint *b; |
724 |
|
725 |
b = Balloc(1); |
726 |
b->x[0] = i; |
727 |
b->wds = 1; |
728 |
return b; |
729 |
} |
730 |
|
731 |
static Bigint * |
732 |
mult |
733 |
#ifdef KR_headers |
734 |
(a, b) Bigint *a, *b; |
735 |
#else |
736 |
(Bigint *a, Bigint *b) |
737 |
#endif |
738 |
{ |
739 |
Bigint *c; |
740 |
int k, wa, wb, wc; |
741 |
ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0; |
742 |
ULong y; |
743 |
#ifdef ULLong |
744 |
ULLong carry, z; |
745 |
#else |
746 |
ULong carry, z; |
747 |
#ifdef Pack_32 |
748 |
ULong z2; |
749 |
#endif |
750 |
#endif |
751 |
|
752 |
if (a->wds < b->wds) { |
753 |
c = a; |
754 |
a = b; |
755 |
b = c; |
756 |
} |
757 |
k = a->k; |
758 |
wa = a->wds; |
759 |
wb = b->wds; |
760 |
wc = wa + wb; |
761 |
if (wc > a->maxwds) |
762 |
k++; |
763 |
c = Balloc(k); |
764 |
for(x = c->x, xa = x + wc; x < xa; x++) |
765 |
*x = 0; |
766 |
xa = a->x; |
767 |
xae = xa + wa; |
768 |
xb = b->x; |
769 |
xbe = xb + wb; |
770 |
xc0 = c->x; |
771 |
#ifdef ULLong |
772 |
for(; xb < xbe; xc0++) { |
773 |
if ((y = *xb++)) { |
774 |
x = xa; |
775 |
xc = xc0; |
776 |
carry = 0; |
777 |
do { |
778 |
z = *x++ * (ULLong)y + *xc + carry; |
779 |
carry = z >> 32; |
780 |
*xc++ = (ULong) z & FFFFFFFF; |
781 |
} |
782 |
while(x < xae); |
783 |
*xc = (ULong) carry; |
784 |
} |
785 |
} |
786 |
#else |
787 |
#ifdef Pack_32 |
788 |
for(; xb < xbe; xb++, xc0++) { |
789 |
if (y = *xb & 0xffff) { |
790 |
x = xa; |
791 |
xc = xc0; |
792 |
carry = 0; |
793 |
do { |
794 |
z = (*x & 0xffff) * y + (*xc & 0xffff) + carry; |
795 |
carry = z >> 16; |
796 |
z2 = (*x++ >> 16) * y + (*xc >> 16) + carry; |
797 |
carry = z2 >> 16; |
798 |
Storeinc(xc, z2, z); |
799 |
} |
800 |
while(x < xae); |
801 |
*xc = carry; |
802 |
} |
803 |
if (y = *xb >> 16) { |
804 |
x = xa; |
805 |
xc = xc0; |
806 |
carry = 0; |
807 |
z2 = *xc; |
808 |
do { |
809 |
z = (*x & 0xffff) * y + (*xc >> 16) + carry; |
810 |
carry = z >> 16; |
811 |
Storeinc(xc, z, z2); |
812 |
z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry; |
813 |
carry = z2 >> 16; |
814 |
} |
815 |
while(x < xae); |
816 |
*xc = z2; |
817 |
} |
818 |
} |
819 |
#else |
820 |
for(; xb < xbe; xc0++) { |
821 |
if (y = *xb++) { |
822 |
x = xa; |
823 |
xc = xc0; |
824 |
carry = 0; |
825 |
do { |
826 |
z = *x++ * y + *xc + carry; |
827 |
carry = z >> 16; |
828 |
*xc++ = z & 0xffff; |
829 |
} |
830 |
while(x < xae); |
831 |
*xc = carry; |
832 |
} |
833 |
} |
834 |
#endif |
835 |
#endif |
836 |
for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ; |
837 |
c->wds = wc; |
838 |
return c; |
839 |
} |
840 |
|
841 |
static Bigint *p5s; |
842 |
|
843 |
static Bigint * |
844 |
pow5mult |
845 |
#ifdef KR_headers |
846 |
(b, k) Bigint *b; int k; |
847 |
#else |
848 |
(Bigint *b, int k) |
849 |
#endif |
850 |
{ |
851 |
Bigint *b1, *p5, *p51; |
852 |
int i; |
853 |
static int p05[3] = { 5, 25, 125 }; |
854 |
|
855 |
if ((i = k & 3)) |
856 |
b = multadd(b, p05[i-1], 0); |
857 |
|
858 |
if (!(k >>= 2)) |
859 |
return b; |
860 |
if (!(p5 = p5s)) { |
861 |
/* first time */ |
862 |
#ifdef MULTIPLE_THREADS |
863 |
ACQUIRE_DTOA_LOCK(1); |
864 |
if (!(p5 = p5s)) { |
865 |
p5 = p5s = i2b(625); |
866 |
p5->next = 0; |
867 |
} |
868 |
FREE_DTOA_LOCK(1); |
869 |
#else |
870 |
p5 = p5s = i2b(625); |
871 |
p5->next = 0; |
872 |
#endif |
873 |
} |
874 |
for(;;) { |
875 |
if (k & 1) { |
876 |
b1 = mult(b, p5); |
877 |
Bfree(b); |
878 |
b = b1; |
879 |
} |
880 |
if (!(k >>= 1)) |
881 |
break; |
882 |
if (!(p51 = p5->next)) { |
883 |
#ifdef MULTIPLE_THREADS |
884 |
ACQUIRE_DTOA_LOCK(1); |
885 |
if (!(p51 = p5->next)) { |
886 |
p51 = p5->next = mult(p5,p5); |
887 |
p51->next = 0; |
888 |
} |
889 |
FREE_DTOA_LOCK(1); |
890 |
#else |
891 |
p51 = p5->next = mult(p5,p5); |
892 |
p51->next = 0; |
893 |
#endif |
894 |
} |
895 |
p5 = p51; |
896 |
} |
897 |
return b; |
898 |
} |
899 |
|
900 |
static Bigint * |
901 |
lshift |
902 |
#ifdef KR_headers |
903 |
(b, k) Bigint *b; int k; |
904 |
#else |
905 |
(Bigint *b, int k) |
906 |
#endif |
907 |
{ |
908 |
int i, k1, n, n1; |
909 |
Bigint *b1; |
910 |
ULong *x, *x1, *xe, z; |
911 |
|
912 |
#ifdef Pack_32 |
913 |
n = k >> 5; |
914 |
#else |
915 |
n = k >> 4; |
916 |
#endif |
917 |
k1 = b->k; |
918 |
n1 = n + b->wds + 1; |
919 |
for(i = b->maxwds; n1 > i; i <<= 1) |
920 |
k1++; |
921 |
b1 = Balloc(k1); |
922 |
x1 = b1->x; |
923 |
for(i = 0; i < n; i++) |
924 |
*x1++ = 0; |
925 |
x = b->x; |
926 |
xe = x + b->wds; |
927 |
#ifdef Pack_32 |
928 |
if (k &= 0x1f) { |
929 |
k1 = 32 - k; |
930 |
z = 0; |
931 |
do { |
932 |
*x1++ = *x << k | z; |
933 |
z = *x++ >> k1; |
934 |
} |
935 |
while(x < xe); |
936 |
if ((*x1 = z)) |
937 |
++n1; |
938 |
} |
939 |
#else |
940 |
if (k &= 0xf) { |
941 |
k1 = 16 - k; |
942 |
z = 0; |
943 |
do { |
944 |
*x1++ = *x << k & 0xffff | z; |
945 |
z = *x++ >> k1; |
946 |
} |
947 |
while(x < xe); |
948 |
if (*x1 = z) |
949 |
++n1; |
950 |
} |
951 |
#endif |
952 |
else do |
953 |
*x1++ = *x++; |
954 |
while(x < xe); |
955 |
b1->wds = n1 - 1; |
956 |
Bfree(b); |
957 |
return b1; |
958 |
} |
959 |
|
960 |
static int |
961 |
cmp |
962 |
#ifdef KR_headers |
963 |
(a, b) Bigint *a, *b; |
964 |
#else |
965 |
(Bigint *a, Bigint *b) |
966 |
#endif |
967 |
{ |
968 |
ULong *xa, *xa0, *xb, *xb0; |
969 |
int i, j; |
970 |
|
971 |
i = a->wds; |
972 |
j = b->wds; |
973 |
#ifdef DEBUG |
974 |
if (i > 1 && !a->x[i-1]) |
975 |
Bug("cmp called with a->x[a->wds-1] == 0"); |
976 |
if (j > 1 && !b->x[j-1]) |
977 |
Bug("cmp called with b->x[b->wds-1] == 0"); |
978 |
#endif |
979 |
if (i -= j) |
980 |
return i; |
981 |
xa0 = a->x; |
982 |
xa = xa0 + j; |
983 |
xb0 = b->x; |
984 |
xb = xb0 + j; |
985 |
for(;;) { |
986 |
if (*--xa != *--xb) |
987 |
return *xa < *xb ? -1 : 1; |
988 |
if (xa <= xa0) |
989 |
break; |
990 |
} |
991 |
return 0; |
992 |
} |
993 |
|
994 |
static Bigint * |
995 |
diff |
996 |
#ifdef KR_headers |
997 |
(a, b) Bigint *a, *b; |
998 |
#else |
999 |
(Bigint *a, Bigint *b) |
1000 |
#endif |
1001 |
{ |
1002 |
Bigint *c; |
1003 |
int i, wa, wb; |
1004 |
ULong *xa, *xae, *xb, *xbe, *xc; |
1005 |
#ifdef ULLong |
1006 |
ULLong borrow, y; |
1007 |
#else |
1008 |
ULong borrow, y; |
1009 |
#ifdef Pack_32 |
1010 |
ULong z; |
1011 |
#endif |
1012 |
#endif |
1013 |
|
1014 |
i = cmp(a,b); |
1015 |
if (!i) { |
1016 |
c = Balloc(0); |
1017 |
c->wds = 1; |
1018 |
c->x[0] = 0; |
1019 |
return c; |
1020 |
} |
1021 |
if (i < 0) { |
1022 |
c = a; |
1023 |
a = b; |
1024 |
b = c; |
1025 |
i = 1; |
1026 |
} |
1027 |
else |
1028 |
i = 0; |
1029 |
c = Balloc(a->k); |
1030 |
c->sign = i; |
1031 |
wa = a->wds; |
1032 |
xa = a->x; |
1033 |
xae = xa + wa; |
1034 |
wb = b->wds; |
1035 |
xb = b->x; |
1036 |
xbe = xb + wb; |
1037 |
xc = c->x; |
1038 |
borrow = 0; |
1039 |
#ifdef ULLong |
1040 |
do { |
1041 |
y = (ULLong)*xa++ - *xb++ - borrow; |
1042 |
borrow = y >> 32 & (ULong)1; |
1043 |
*xc++ = (ULong) y & FFFFFFFF; |
1044 |
} |
1045 |
while(xb < xbe); |
1046 |
while(xa < xae) { |
1047 |
y = *xa++ - borrow; |
1048 |
borrow = y >> 32 & (ULong)1; |
1049 |
*xc++ = (ULong) y & FFFFFFFF; |
1050 |
} |
1051 |
#else |
1052 |
#ifdef Pack_32 |
1053 |
do { |
1054 |
y = (*xa & 0xffff) - (*xb & 0xffff) - borrow; |
1055 |
borrow = (y & 0x10000) >> 16; |
1056 |
z = (*xa++ >> 16) - (*xb++ >> 16) - borrow; |
1057 |
borrow = (z & 0x10000) >> 16; |
1058 |
Storeinc(xc, z, y); |
1059 |
} |
1060 |
while(xb < xbe); |
1061 |
while(xa < xae) { |
1062 |
y = (*xa & 0xffff) - borrow; |
1063 |
borrow = (y & 0x10000) >> 16; |
1064 |
z = (*xa++ >> 16) - borrow; |
1065 |
borrow = (z & 0x10000) >> 16; |
1066 |
Storeinc(xc, z, y); |
1067 |
} |
1068 |
#else |
1069 |
do { |
1070 |
y = *xa++ - *xb++ - borrow; |
1071 |
borrow = (y & 0x10000) >> 16; |
1072 |
*xc++ = y & 0xffff; |
1073 |
} |
1074 |
while(xb < xbe); |
1075 |
while(xa < xae) { |
1076 |
y = *xa++ - borrow; |
1077 |
borrow = (y & 0x10000) >> 16; |
1078 |
*xc++ = y & 0xffff; |
1079 |
} |
1080 |
#endif |
1081 |
#endif |
1082 |
while(!*--xc) |
1083 |
wa--; |
1084 |
c->wds = wa; |
1085 |
return c; |
1086 |
} |
1087 |
|
1088 |
static double |
1089 |
ulp |
1090 |
#ifdef KR_headers |
1091 |
(x) U x; |
1092 |
#else |
1093 |
(U x) |
1094 |
#endif |
1095 |
{ |
1096 |
register Long L; |
1097 |
U a; |
1098 |
|
1099 |
L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1; |
1100 |
#ifndef Avoid_Underflow |
1101 |
#ifndef Sudden_Underflow |
1102 |
if (L > 0) { |
1103 |
#endif |
1104 |
#endif |
1105 |
#ifdef IBM |
1106 |
L |= Exp_msk1 >> 4; |
1107 |
#endif |
1108 |
word0(a) = L; |
1109 |
word1(a) = 0; |
1110 |
#ifndef Avoid_Underflow |
1111 |
#ifndef Sudden_Underflow |
1112 |
} |
1113 |
else { |
1114 |
L = -L >> Exp_shift; |
1115 |
if (L < Exp_shift) { |
1116 |
word0(a) = 0x80000 >> L; |
1117 |
word1(a) = 0; |
1118 |
} |
1119 |
else { |
1120 |
word0(a) = 0; |
1121 |
L -= Exp_shift; |
1122 |
word1(a) = L >= 31 ? 1 : 1 << 31 - L; |
1123 |
} |
1124 |
} |
1125 |
#endif |
1126 |
#endif |
1127 |
return dval(a); |
1128 |
} |
1129 |
|
1130 |
static double |
1131 |
b2d |
1132 |
#ifdef KR_headers |
1133 |
(a, e) Bigint *a; int *e; |
1134 |
#else |
1135 |
(Bigint *a, int *e) |
1136 |
#endif |
1137 |
{ |
1138 |
ULong *xa, *xa0, w, y, z; |
1139 |
int k; |
1140 |
U d; |
1141 |
#ifdef VAX |
1142 |
ULong d0, d1; |
1143 |
#else |
1144 |
#define d0 word0(d) |
1145 |
#define d1 word1(d) |
1146 |
#endif |
1147 |
|
1148 |
xa0 = a->x; |
1149 |
xa = xa0 + a->wds; |
1150 |
y = *--xa; |
1151 |
#ifdef DEBUG |
1152 |
if (!y) Bug("zero y in b2d"); |
1153 |
#endif |
1154 |
k = hi0bits(y); |
1155 |
*e = 32 - k; |
1156 |
#ifdef Pack_32 |
1157 |
if (k < Ebits) { |
1158 |
d0 = Exp_1 | y >> (Ebits - k); |
1159 |
w = xa > xa0 ? *--xa : 0; |
1160 |
d1 = y << ((32-Ebits) + k) | w >> (Ebits - k); |
1161 |
goto ret_d; |
1162 |
} |
1163 |
z = xa > xa0 ? *--xa : 0; |
1164 |
if (k -= Ebits) { |
1165 |
d0 = Exp_1 | y << k | z >> (32 - k); |
1166 |
y = xa > xa0 ? *--xa : 0; |
1167 |
d1 = z << k | y >> (32 - k); |
1168 |
} |
1169 |
else { |
1170 |
d0 = Exp_1 | y; |
1171 |
d1 = z; |
1172 |
} |
1173 |
#else |
1174 |
if (k < Ebits + 16) { |
1175 |
z = xa > xa0 ? *--xa : 0; |
1176 |
d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k; |
1177 |
w = xa > xa0 ? *--xa : 0; |
1178 |
y = xa > xa0 ? *--xa : 0; |
1179 |
d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k; |
1180 |
goto ret_d; |
1181 |
} |
1182 |
z = xa > xa0 ? *--xa : 0; |
1183 |
w = xa > xa0 ? *--xa : 0; |
1184 |
k -= Ebits + 16; |
1185 |
d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k; |
1186 |
y = xa > xa0 ? *--xa : 0; |
1187 |
d1 = w << k + 16 | y << k; |
1188 |
#endif |
1189 |
ret_d: |
1190 |
#ifdef VAX |
1191 |
word0(d) = d0 >> 16 | d0 << 16; |
1192 |
word1(d) = d1 >> 16 | d1 << 16; |
1193 |
#else |
1194 |
#undef d0 |
1195 |
#undef d1 |
1196 |
#endif |
1197 |
return dval(d); |
1198 |
} |
1199 |
|
1200 |
static Bigint * |
1201 |
d2b |
1202 |
#ifdef KR_headers |
1203 |
(d, e, bits) U d; int *e, *bits; |
1204 |
#else |
1205 |
(U d, int *e, int *bits) |
1206 |
#endif |
1207 |
{ |
1208 |
Bigint *b; |
1209 |
int de, k; |
1210 |
ULong *x, y, z; |
1211 |
#ifndef Sudden_Underflow |
1212 |
int i; |
1213 |
#endif |
1214 |
#ifdef VAX |
1215 |
ULong d0, d1; |
1216 |
d0 = word0(d) >> 16 | word0(d) << 16; |
1217 |
d1 = word1(d) >> 16 | word1(d) << 16; |
1218 |
#else |
1219 |
#define d0 word0(d) |
1220 |
#define d1 word1(d) |
1221 |
#endif |
1222 |
|
1223 |
#ifdef Pack_32 |
1224 |
b = Balloc(1); |
1225 |
#else |
1226 |
b = Balloc(2); |
1227 |
#endif |
1228 |
x = b->x; |
1229 |
|
1230 |
z = d0 & Frac_mask; |
1231 |
d0 &= 0x7fffffff; /* clear sign bit, which we ignore */ |
1232 |
#ifdef Sudden_Underflow |
1233 |
de = (int)(d0 >> Exp_shift); |
1234 |
#ifndef IBM |
1235 |
z |= Exp_msk11; |
1236 |
#endif |
1237 |
#else |
1238 |
if ((de = (int)(d0 >> Exp_shift))) |
1239 |
z |= Exp_msk1; |
1240 |
#endif |
1241 |
#ifdef Pack_32 |
1242 |
if ((y = d1)) { |
1243 |
if ((k = lo0bits(&y))) { |
1244 |
x[0] = y | z << (32 - k); |
1245 |
z >>= k; |
1246 |
} |
1247 |
else |
1248 |
x[0] = y; |
1249 |
#ifndef Sudden_Underflow |
1250 |
i = |
1251 |
#endif |
1252 |
b->wds = (x[1] = z) ? 2 : 1; |
1253 |
} |
1254 |
else { |
1255 |
#ifdef DEBUG |
1256 |
if (!z) |
1257 |
Bug("Zero passed to d2b"); |
1258 |
#endif |
1259 |
k = lo0bits(&z); |
1260 |
x[0] = z; |
1261 |
#ifndef Sudden_Underflow |
1262 |
i = |
1263 |
#endif |
1264 |
b->wds = 1; |
1265 |
k += 32; |
1266 |
} |
1267 |
#else |
1268 |
if (y = d1) { |
1269 |
if (k = lo0bits(&y)) |
1270 |
if (k >= 16) { |
1271 |
x[0] = y | z << 32 - k & 0xffff; |
1272 |
x[1] = z >> k - 16 & 0xffff; |
1273 |
x[2] = z >> k; |
1274 |
i = 2; |
1275 |
} |
1276 |
else { |
1277 |
x[0] = y & 0xffff; |
1278 |
x[1] = y >> 16 | z << 16 - k & 0xffff; |
1279 |
x[2] = z >> k & 0xffff; |
1280 |
x[3] = z >> k+16; |
1281 |
i = 3; |
1282 |
} |
1283 |
else { |
1284 |
x[0] = y & 0xffff; |
1285 |
x[1] = y >> 16; |
1286 |
x[2] = z & 0xffff; |
1287 |
x[3] = z >> 16; |
1288 |
i = 3; |
1289 |
} |
1290 |
} |
1291 |
else { |
1292 |
#ifdef DEBUG |
1293 |
if (!z) |
1294 |
Bug("Zero passed to d2b"); |
1295 |
#endif |
1296 |
k = lo0bits(&z); |
1297 |
if (k >= 16) { |
1298 |
x[0] = z; |
1299 |
i = 0; |
1300 |
} |
1301 |
else { |
1302 |
x[0] = z & 0xffff; |
1303 |
x[1] = z >> 16; |
1304 |
i = 1; |
1305 |
} |
1306 |
k += 32; |
1307 |
} |
1308 |
while(!x[i]) |
1309 |
--i; |
1310 |
b->wds = i + 1; |
1311 |
#endif |
1312 |
#ifndef Sudden_Underflow |
1313 |
if (de) { |
1314 |
#endif |
1315 |
#ifdef IBM |
1316 |
*e = (de - Bias - (P-1) << 2) + k; |
1317 |
*bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask); |
1318 |
#else |
1319 |
*e = de - Bias - (P-1) + k; |
1320 |
*bits = P - k; |
1321 |
#endif |
1322 |
#ifndef Sudden_Underflow |
1323 |
} |
1324 |
else { |
1325 |
*e = de - Bias - (P-1) + 1 + k; |
1326 |
#ifdef Pack_32 |
1327 |
*bits = 32*i - hi0bits(x[i-1]); |
1328 |
#else |
1329 |
*bits = (i+2)*16 - hi0bits(x[i]); |
1330 |
#endif |
1331 |
} |
1332 |
#endif |
1333 |
return b; |
1334 |
} |
1335 |
#undef d0 |
1336 |
#undef d1 |
1337 |
|
1338 |
static double |
1339 |
ratio |
1340 |
#ifdef KR_headers |
1341 |
(a, b) Bigint *a, *b; |
1342 |
#else |
1343 |
(Bigint *a, Bigint *b) |
1344 |
#endif |
1345 |
{ |
1346 |
U da, db; |
1347 |
int k, ka, kb; |
1348 |
|
1349 |
dval(da) = b2d(a, &ka); |
1350 |
dval(db) = b2d(b, &kb); |
1351 |
#ifdef Pack_32 |
1352 |
k = ka - kb + 32*(a->wds - b->wds); |
1353 |
#else |
1354 |
k = ka - kb + 16*(a->wds - b->wds); |
1355 |
#endif |
1356 |
#ifdef IBM |
1357 |
if (k > 0) { |
1358 |
word0(da) += (k >> 2)*Exp_msk1; |
1359 |
if (k &= 3) |
1360 |
dval(da) *= 1 << k; |
1361 |
} |
1362 |
else { |
1363 |
k = -k; |
1364 |
word0(db) += (k >> 2)*Exp_msk1; |
1365 |
if (k &= 3) |
1366 |
dval(db) *= 1 << k; |
1367 |
} |
1368 |
#else |
1369 |
if (k > 0) |
1370 |
word0(da) += k*Exp_msk1; |
1371 |
else { |
1372 |
k = -k; |
1373 |
word0(db) += k*Exp_msk1; |
1374 |
} |
1375 |
#endif |
1376 |
return dval(da) / dval(db); |
1377 |
} |
1378 |
|
1379 |
static CONST double |
1380 |
tens[] = { |
1381 |
1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, |
1382 |
1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, |
1383 |
1e20, 1e21, 1e22 |
1384 |
#ifdef VAX |
1385 |
, 1e23, 1e24 |
1386 |
#endif |
1387 |
}; |
1388 |
|
1389 |
static CONST double |
1390 |
#ifdef IEEE_Arith |
1391 |
bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 }; |
1392 |
static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, |
1393 |
#ifdef Avoid_Underflow |
1394 |
9007199254740992.*9007199254740992.e-256 |
1395 |
/* = 2^106 * 1e-53 */ |
1396 |
#else |
1397 |
1e-256 |
1398 |
#endif |
1399 |
}; |
1400 |
/* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */ |
1401 |
/* flag unnecessarily. It leads to a song and dance at the end of strtod. */ |
1402 |
#define Scale_Bit 0x10 |
1403 |
#define n_bigtens 5 |
1404 |
#else |
1405 |
#ifdef IBM |
1406 |
bigtens[] = { 1e16, 1e32, 1e64 }; |
1407 |
static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 }; |
1408 |
#define n_bigtens 3 |
1409 |
#else |
1410 |
bigtens[] = { 1e16, 1e32 }; |
1411 |
static CONST double tinytens[] = { 1e-16, 1e-32 }; |
1412 |
#define n_bigtens 2 |
1413 |
#endif |
1414 |
#endif |
1415 |
|
1416 |
#ifdef INFNAN_CHECK |
1417 |
|
1418 |
#ifndef NAN_WORD0 |
1419 |
#define NAN_WORD0 0x7ff80000 |
1420 |
#endif |
1421 |
|
1422 |
#ifndef NAN_WORD1 |
1423 |
#define NAN_WORD1 0 |
1424 |
#endif |
1425 |
|
1426 |
static int |
1427 |
match |
1428 |
#ifdef KR_headers |
1429 |
(sp, t) char **sp, *t; |
1430 |
#else |
1431 |
(CONST char **sp, CONST char *t) |
1432 |
#endif |
1433 |
{ |
1434 |
int c, d; |
1435 |
CONST char *s = *sp; |
1436 |
|
1437 |
while((d = *t++)) { |
1438 |
if ((c = *++s) >= 'A' && c <= 'Z') |
1439 |
c += 'a' - 'A'; |
1440 |
if (c != d) |
1441 |
return 0; |
1442 |
} |
1443 |
*sp = s + 1; |
1444 |
return 1; |
1445 |
} |
1446 |
|
1447 |
#ifndef No_Hex_NaN |
1448 |
static void |
1449 |
hexnan |
1450 |
#ifdef KR_headers |
1451 |
(rvp, sp) U *rvp; CONST char **sp; |
1452 |
#else |
1453 |
(U *rvp, CONST char **sp) |
1454 |
#endif |
1455 |
{ |
1456 |
ULong c, x[2]; |
1457 |
CONST char *s; |
1458 |
int havedig, udx0, xshift; |
1459 |
|
1460 |
x[0] = x[1] = 0; |
1461 |
havedig = xshift = 0; |
1462 |
udx0 = 1; |
1463 |
s = *sp; |
1464 |
/* allow optional initial 0x or 0X */ |
1465 |
while((c = *(CONST unsigned char*)(s+1)) && c <= ' ') |
1466 |
++s; |
1467 |
if (s[1] == '0' && (s[2] == 'x' || s[2] == 'X')) |
1468 |
s += 2; |
1469 |
while((c = *(CONST unsigned char*)++s)) { |
1470 |
if (c >= '0' && c <= '9') |
1471 |
c -= '0'; |
1472 |
else if (c >= 'a' && c <= 'f') |
1473 |
c += 10 - 'a'; |
1474 |
else if (c >= 'A' && c <= 'F') |
1475 |
c += 10 - 'A'; |
1476 |
else if (c <= ' ') { |
1477 |
if (udx0 && havedig) { |
1478 |
udx0 = 0; |
1479 |
xshift = 1; |
1480 |
} |
1481 |
continue; |
1482 |
} |
1483 |
#ifdef GDTOA_NON_PEDANTIC_NANCHECK |
1484 |
else if (/*(*/ c == ')' && havedig) { |
1485 |
*sp = s + 1; |
1486 |
break; |
1487 |
} |
1488 |
else |
1489 |
return; /* invalid form: don't change *sp */ |
1490 |
#else |
1491 |
else { |
1492 |
do { |
1493 |
if (/*(*/ c == ')') { |
1494 |
*sp = s + 1; |
1495 |
break; |
1496 |
} |
1497 |
} while((c = *++s)); |
1498 |
break; |
1499 |
} |
1500 |
#endif |
1501 |
havedig = 1; |
1502 |
if (xshift) { |
1503 |
xshift = 0; |
1504 |
x[0] = x[1]; |
1505 |
x[1] = 0; |
1506 |
} |
1507 |
if (udx0) |
1508 |
x[0] = (x[0] << 4) | (x[1] >> 28); |
1509 |
x[1] = (x[1] << 4) | c; |
1510 |
} |
1511 |
if ((x[0] &= 0xfffff) || x[1]) { |
1512 |
word0(*rvp) = Exp_mask | x[0]; |
1513 |
word1(*rvp) = x[1]; |
1514 |
} |
1515 |
} |
1516 |
#endif /*No_Hex_NaN*/ |
1517 |
#endif /* INFNAN_CHECK */ |
1518 |
|
1519 |
static double |
1520 |
_strtod |
1521 |
#ifdef KR_headers |
1522 |
(s00, se) CONST char *s00; char **se; |
1523 |
#else |
1524 |
(CONST char *s00, char **se) |
1525 |
#endif |
1526 |
{ |
1527 |
#ifdef Avoid_Underflow |
1528 |
int scale; |
1529 |
#endif |
1530 |
int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign, |
1531 |
e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign; |
1532 |
CONST char *s, *s0, *s1; |
1533 |
double aadj, adj; |
1534 |
U aadj1, rv, rv0; |
1535 |
Long L; |
1536 |
ULong y, z; |
1537 |
Bigint *bb, *bb1, *bd, *bd0, *bs, *delta; |
1538 |
#ifdef SET_INEXACT |
1539 |
int inexact, oldinexact; |
1540 |
#endif |
1541 |
#ifdef Honor_FLT_ROUNDS |
1542 |
int rounding; |
1543 |
#endif |
1544 |
#ifdef USE_LOCALE |
1545 |
CONST char *s2; |
1546 |
#endif |
1547 |
|
1548 |
#ifdef __GNUC__ |
1549 |
delta = bb = bd = bs = 0; |
1550 |
#endif |
1551 |
|
1552 |
sign = nz0 = nz = 0; |
1553 |
dval(rv) = 0.; |
1554 |
for(s = s00;;s++) switch(*s) { |
1555 |
case '-': |
1556 |
sign = 1; |
1557 |
/* no break */ |
1558 |
case '+': |
1559 |
if (*++s) |
1560 |
goto break2; |
1561 |
/* no break */ |
1562 |
case 0: |
1563 |
goto ret0; |
1564 |
case '\t': |
1565 |
case '\n': |
1566 |
case '\v': |
1567 |
case '\f': |
1568 |
case '\r': |
1569 |
case ' ': |
1570 |
continue; |
1571 |
default: |
1572 |
goto break2; |
1573 |
} |
1574 |
break2: |
1575 |
if (*s == '0') { |
1576 |
nz0 = 1; |
1577 |
while(*++s == '0') ; |
1578 |
if (!*s) |
1579 |
goto ret; |
1580 |
} |
1581 |
s0 = s; |
1582 |
y = z = 0; |
1583 |
for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++) |
1584 |
if (nd < 9) |
1585 |
y = 10*y + c - '0'; |
1586 |
else if (nd < 16) |
1587 |
z = 10*z + c - '0'; |
1588 |
nd0 = nd; |
1589 |
#ifdef USE_LOCALE |
1590 |
s1 = localeconv()->decimal_point; |
1591 |
if (c == *s1) { |
1592 |
c = '.'; |
1593 |
if (*++s1) { |
1594 |
s2 = s; |
1595 |
for(;;) { |
1596 |
if (*++s2 != *s1) { |
1597 |
c = 0; |
1598 |
break; |
1599 |
} |
1600 |
if (!*++s1) { |
1601 |
s = s2; |
1602 |
break; |
1603 |
} |
1604 |
} |
1605 |
} |
1606 |
} |
1607 |
#endif |
1608 |
if (c == '.') { |
1609 |
c = *++s; |
1610 |
if (!nd) { |
1611 |
for(; c == '0'; c = *++s) |
1612 |
nz++; |
1613 |
if (c > '0' && c <= '9') { |
1614 |
s0 = s; |
1615 |
nf += nz; |
1616 |
nz = 0; |
1617 |
goto have_dig; |
1618 |
} |
1619 |
goto dig_done; |
1620 |
} |
1621 |
for(; c >= '0' && c <= '9'; c = *++s) { |
1622 |
have_dig: |
1623 |
nz++; |
1624 |
if (c -= '0') { |
1625 |
nf += nz; |
1626 |
for(i = 1; i < nz; i++) |
1627 |
if (nd++ < 9) |
1628 |
y *= 10; |
1629 |
else if (nd <= DBL_DIG + 1) |
1630 |
z *= 10; |
1631 |
if (nd++ < 9) |
1632 |
y = 10*y + c; |
1633 |
else if (nd <= DBL_DIG + 1) |
1634 |
z = 10*z + c; |
1635 |
nz = 0; |
1636 |
} |
1637 |
} |
1638 |
} |
1639 |
dig_done: |
1640 |
e = 0; |
1641 |
if (c == 'e' || c == 'E') { |
1642 |
if (!nd && !nz && !nz0) { |
1643 |
goto ret0; |
1644 |
} |
1645 |
s00 = s; |
1646 |
esign = 0; |
1647 |
switch(c = *++s) { |
1648 |
case '-': |
1649 |
esign = 1; |
1650 |
case '+': |
1651 |
c = *++s; |
1652 |
} |
1653 |
if (c >= '0' && c <= '9') { |
1654 |
while(c == '0') |
1655 |
c = *++s; |
1656 |
if (c > '0' && c <= '9') { |
1657 |
L = c - '0'; |
1658 |
s1 = s; |
1659 |
while((c = *++s) >= '0' && c <= '9') |
1660 |
L = 10*L + c - '0'; |
1661 |
if (s - s1 > 8 || L > 19999) |
1662 |
/* Avoid confusion from exponents |
1663 |
* so large that e might overflow. |
1664 |
*/ |
1665 |
e = 19999; /* safe for 16 bit ints */ |
1666 |
else |
1667 |
e = (int)L; |
1668 |
if (esign) |
1669 |
e = -e; |
1670 |
} |
1671 |
else |
1672 |
e = 0; |
1673 |
} |
1674 |
else |
1675 |
s = s00; |
1676 |
} |
1677 |
if (!nd) { |
1678 |
if (!nz && !nz0) { |
1679 |
#ifdef INFNAN_CHECK |
1680 |
/* Check for Nan and Infinity */ |
1681 |
switch(c) { |
1682 |
case 'i': |
1683 |
case 'I': |
1684 |
if (match(&s,"nf")) { |
1685 |
--s; |
1686 |
if (!match(&s,"inity")) |
1687 |
++s; |
1688 |
word0(rv) = 0x7ff00000; |
1689 |
word1(rv) = 0; |
1690 |
goto ret; |
1691 |
} |
1692 |
break; |
1693 |
case 'n': |
1694 |
case 'N': |
1695 |
if (match(&s, "an")) { |
1696 |
word0(rv) = NAN_WORD0; |
1697 |
word1(rv) = NAN_WORD1; |
1698 |
#ifndef No_Hex_NaN |
1699 |
if (*s == '(') /*)*/ |
1700 |
hexnan(&rv, &s); |
1701 |
#endif |
1702 |
goto ret; |
1703 |
} |
1704 |
} |
1705 |
#endif /* INFNAN_CHECK */ |
1706 |
ret0: |
1707 |
s = s00; |
1708 |
sign = 0; |
1709 |
} |
1710 |
goto ret; |
1711 |
} |
1712 |
e1 = e -= nf; |
1713 |
|
1714 |
/* Now we have nd0 digits, starting at s0, followed by a |
1715 |
* decimal point, followed by nd-nd0 digits. The number we're |
1716 |
* after is the integer represented by those digits times |
1717 |
* 10**e */ |
1718 |
|
1719 |
if (!nd0) |
1720 |
nd0 = nd; |
1721 |
k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1; |
1722 |
dval(rv) = y; |
1723 |
if (k > 9) { |
1724 |
#ifdef SET_INEXACT |
1725 |
if (k > DBL_DIG) |
1726 |
oldinexact = get_inexact(); |
1727 |
#endif |
1728 |
dval(rv) = tens[k - 9] * dval(rv) + z; |
1729 |
} |
1730 |
bd0 = 0; |
1731 |
if (nd <= DBL_DIG |
1732 |
#ifndef RND_PRODQUOT |
1733 |
#ifndef Honor_FLT_ROUNDS |
1734 |
&& Flt_Rounds == 1 |
1735 |
#endif |
1736 |
#endif |
1737 |
) { |
1738 |
if (!e) |
1739 |
goto ret; |
1740 |
if (e > 0) { |
1741 |
if (e <= Ten_pmax) { |
1742 |
#ifdef VAX |
1743 |
goto vax_ovfl_check; |
1744 |
#else |
1745 |
#ifdef Honor_FLT_ROUNDS |
1746 |
/* round correctly FLT_ROUNDS = 2 or 3 */ |
1747 |
if (sign) { |
1748 |
rv = -rv; |
1749 |
sign = 0; |
1750 |
} |
1751 |
#endif |
1752 |
/* rv = */ rounded_product(dval(rv), tens[e]); |
1753 |
goto ret; |
1754 |
#endif |
1755 |
} |
1756 |
i = DBL_DIG - nd; |
1757 |
if (e <= Ten_pmax + i) { |
1758 |
/* A fancier test would sometimes let us do |
1759 |
* this for larger i values. |
1760 |
*/ |
1761 |
#ifdef Honor_FLT_ROUNDS |
1762 |
/* round correctly FLT_ROUNDS = 2 or 3 */ |
1763 |
if (sign) { |
1764 |
rv = -rv; |
1765 |
sign = 0; |
1766 |
} |
1767 |
#endif |
1768 |
e -= i; |
1769 |
dval(rv) *= tens[i]; |
1770 |
#ifdef VAX |
1771 |
/* VAX exponent range is so narrow we must |
1772 |
* worry about overflow here... |
1773 |
*/ |
1774 |
vax_ovfl_check: |
1775 |
word0(rv) -= P*Exp_msk1; |
1776 |
/* rv = */ rounded_product(dval(rv), tens[e]); |
1777 |
if ((word0(rv) & Exp_mask) |
1778 |
> Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) |
1779 |
goto ovfl; |
1780 |
word0(rv) += P*Exp_msk1; |
1781 |
#else |
1782 |
/* rv = */ rounded_product(dval(rv), tens[e]); |
1783 |
#endif |
1784 |
goto ret; |
1785 |
} |
1786 |
} |
1787 |
#ifndef Inaccurate_Divide |
1788 |
else if (e >= -Ten_pmax) { |
1789 |
#ifdef Honor_FLT_ROUNDS |
1790 |
/* round correctly FLT_ROUNDS = 2 or 3 */ |
1791 |
if (sign) { |
1792 |
rv = -rv; |
1793 |
sign = 0; |
1794 |
} |
1795 |
#endif |
1796 |
/* rv = */ rounded_quotient(dval(rv), tens[-e]); |
1797 |
goto ret; |
1798 |
} |
1799 |
#endif |
1800 |
} |
1801 |
e1 += nd - k; |
1802 |
|
1803 |
#ifdef IEEE_Arith |
1804 |
#ifdef SET_INEXACT |
1805 |
inexact = 1; |
1806 |
if (k <= DBL_DIG) |
1807 |
oldinexact = get_inexact(); |
1808 |
#endif |
1809 |
#ifdef Avoid_Underflow |
1810 |
scale = 0; |
1811 |
#endif |
1812 |
#ifdef Honor_FLT_ROUNDS |
1813 |
if ((rounding = Flt_Rounds) >= 2) { |
1814 |
if (sign) |
1815 |
rounding = rounding == 2 ? 0 : 2; |
1816 |
else |
1817 |
if (rounding != 2) |
1818 |
rounding = 0; |
1819 |
} |
1820 |
#endif |
1821 |
#endif /*IEEE_Arith*/ |
1822 |
|
1823 |
/* Get starting approximation = rv * 10**e1 */ |
1824 |
|
1825 |
if (e1 > 0) { |
1826 |
if ((i = e1 & 15)) |
1827 |
dval(rv) *= tens[i]; |
1828 |
if (e1 &= ~15) { |
1829 |
if (e1 > DBL_MAX_10_EXP) { |
1830 |
ovfl: |
1831 |
#ifndef NO_ERRNO |
1832 |
errno = ERANGE; |
1833 |
#endif |
1834 |
/* Can't trust HUGE_VAL */ |
1835 |
#ifdef IEEE_Arith |
1836 |
#ifdef Honor_FLT_ROUNDS |
1837 |
switch(rounding) { |
1838 |
case 0: /* toward 0 */ |
1839 |
case 3: /* toward -infinity */ |
1840 |
word0(rv) = Big0; |
1841 |
word1(rv) = Big1; |
1842 |
break; |
1843 |
default: |
1844 |
word0(rv) = Exp_mask; |
1845 |
word1(rv) = 0; |
1846 |
} |
1847 |
#else /*Honor_FLT_ROUNDS*/ |
1848 |
word0(rv) = Exp_mask; |
1849 |
word1(rv) = 0; |
1850 |
#endif /*Honor_FLT_ROUNDS*/ |
1851 |
#ifdef SET_INEXACT |
1852 |
/* set overflow bit */ |
1853 |
dval(rv0) = 1e300; |
1854 |
dval(rv0) *= dval(rv0); |
1855 |
#endif |
1856 |
#else /*IEEE_Arith*/ |
1857 |
word0(rv) = Big0; |
1858 |
word1(rv) = Big1; |
1859 |
#endif /*IEEE_Arith*/ |
1860 |
if (bd0) |
1861 |
goto retfree; |
1862 |
goto ret; |
1863 |
} |
1864 |
e1 >>= 4; |
1865 |
for(j = 0; e1 > 1; j++, e1 >>= 1) |
1866 |
if (e1 & 1) |
1867 |
dval(rv) *= bigtens[j]; |
1868 |
/* The last multiplication could overflow. */ |
1869 |
word0(rv) -= P*Exp_msk1; |
1870 |
dval(rv) *= bigtens[j]; |
1871 |
if ((z = word0(rv) & Exp_mask) |
1872 |
> Exp_msk1*(DBL_MAX_EXP+Bias-P)) |
1873 |
goto ovfl; |
1874 |
if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) { |
1875 |
/* set to largest number */ |
1876 |
/* (Can't trust DBL_MAX) */ |
1877 |
word0(rv) = Big0; |
1878 |
word1(rv) = Big1; |
1879 |
} |
1880 |
else |
1881 |
word0(rv) += P*Exp_msk1; |
1882 |
} |
1883 |
} |
1884 |
else if (e1 < 0) { |
1885 |
e1 = -e1; |
1886 |
if ((i = e1 & 15)) |
1887 |
dval(rv) /= tens[i]; |
1888 |
if (e1 >>= 4) { |
1889 |
if (e1 >= 1 << n_bigtens) |
1890 |
goto undfl; |
1891 |
#ifdef Avoid_Underflow |
1892 |
if (e1 & Scale_Bit) |
1893 |
scale = 2*P; |
1894 |
for(j = 0; e1 > 0; j++, e1 >>= 1) |
1895 |
if (e1 & 1) |
1896 |
dval(rv) *= tinytens[j]; |
1897 |
if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask) |
1898 |
>> Exp_shift)) > 0) { |
1899 |
/* scaled rv is denormal; zap j low bits */ |
1900 |
if (j >= 32) { |
1901 |
word1(rv) = 0; |
1902 |
if (j >= 53) |
1903 |
word0(rv) = (P+2)*Exp_msk1; |
1904 |
else |
1905 |
word0(rv) &= 0xffffffff << (j-32); |
1906 |
} |
1907 |
else |
1908 |
word1(rv) &= 0xffffffff << j; |
1909 |
} |
1910 |
#else |
1911 |
for(j = 0; e1 > 1; j++, e1 >>= 1) |
1912 |
if (e1 & 1) |
1913 |
dval(rv) *= tinytens[j]; |
1914 |
/* The last multiplication could underflow. */ |
1915 |
dval(rv0) = dval(rv); |
1916 |
dval(rv) *= tinytens[j]; |
1917 |
if (!dval(rv)) { |
1918 |
dval(rv) = 2.*dval(rv0); |
1919 |
dval(rv) *= tinytens[j]; |
1920 |
#endif |
1921 |
if (!dval(rv)) { |
1922 |
undfl: |
1923 |
dval(rv) = 0.; |
1924 |
#ifndef NO_ERRNO |
1925 |
errno = ERANGE; |
1926 |
#endif |
1927 |
if (bd0) |
1928 |
goto retfree; |
1929 |
goto ret; |
1930 |
} |
1931 |
#ifndef Avoid_Underflow |
1932 |
word0(rv) = Tiny0; |
1933 |
word1(rv) = Tiny1; |
1934 |
/* The refinement below will clean |
1935 |
* this approximation up. |
1936 |
*/ |
1937 |
} |
1938 |
#endif |
1939 |
} |
1940 |
} |
1941 |
|
1942 |
/* Now the hard part -- adjusting rv to the correct value.*/ |
1943 |
|
1944 |
/* Put digits into bd: true value = bd * 10^e */ |
1945 |
|
1946 |
bd0 = s2b(s0, nd0, nd, y); |
1947 |
|
1948 |
for(;;) { |
1949 |
bd = Balloc(bd0->k); |
1950 |
Bcopy(bd, bd0); |
1951 |
bb = d2b(rv, &bbe, &bbbits); /* rv = bb * 2^bbe */ |
1952 |
bs = i2b(1); |
1953 |
|
1954 |
if (e >= 0) { |
1955 |
bb2 = bb5 = 0; |
1956 |
bd2 = bd5 = e; |
1957 |
} |
1958 |
else { |
1959 |
bb2 = bb5 = -e; |
1960 |
bd2 = bd5 = 0; |
1961 |
} |
1962 |
if (bbe >= 0) |
1963 |
bb2 += bbe; |
1964 |
else |
1965 |
bd2 -= bbe; |
1966 |
bs2 = bb2; |
1967 |
#ifdef Honor_FLT_ROUNDS |
1968 |
if (rounding != 1) |
1969 |
bs2++; |
1970 |
#endif |
1971 |
#ifdef Avoid_Underflow |
1972 |
j = bbe - scale; |
1973 |
i = j + bbbits - 1; /* logb(rv) */ |
1974 |
if (i < Emin) /* denormal */ |
1975 |
j += P - Emin; |
1976 |
else |
1977 |
j = P + 1 - bbbits; |
1978 |
#else /*Avoid_Underflow*/ |
1979 |
#ifdef Sudden_Underflow |
1980 |
#ifdef IBM |
1981 |
j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3); |
1982 |
#else |
1983 |
j = P + 1 - bbbits; |
1984 |
#endif |
1985 |
#else /*Sudden_Underflow*/ |
1986 |
j = bbe; |
1987 |
i = j + bbbits - 1; /* logb(rv) */ |
1988 |
if (i < Emin) /* denormal */ |
1989 |
j += P - Emin; |
1990 |
else |
1991 |
j = P + 1 - bbbits; |
1992 |
#endif /*Sudden_Underflow*/ |
1993 |
#endif /*Avoid_Underflow*/ |
1994 |
bb2 += j; |
1995 |
bd2 += j; |
1996 |
#ifdef Avoid_Underflow |
1997 |
bd2 += scale; |
1998 |
#endif |
1999 |
i = bb2 < bd2 ? bb2 : bd2; |
2000 |
if (i > bs2) |
2001 |
i = bs2; |
2002 |
if (i > 0) { |
2003 |
bb2 -= i; |
2004 |
bd2 -= i; |
2005 |
bs2 -= i; |
2006 |
} |
2007 |
if (bb5 > 0) { |
2008 |
bs = pow5mult(bs, bb5); |
2009 |
bb1 = mult(bs, bb); |
2010 |
Bfree(bb); |
2011 |
bb = bb1; |
2012 |
} |
2013 |
if (bb2 > 0) |
2014 |
bb = lshift(bb, bb2); |
2015 |
if (bd5 > 0) |
2016 |
bd = pow5mult(bd, bd5); |
2017 |
if (bd2 > 0) |
2018 |
bd = lshift(bd, bd2); |
2019 |
if (bs2 > 0) |
2020 |
bs = lshift(bs, bs2); |
2021 |
delta = diff(bb, bd); |
2022 |
dsign = delta->sign; |
2023 |
delta->sign = 0; |
2024 |
i = cmp(delta, bs); |
2025 |
#ifdef Honor_FLT_ROUNDS |
2026 |
if (rounding != 1) { |
2027 |
if (i < 0) { |
2028 |
/* Error is less than an ulp */ |
2029 |
if (!delta->x[0] && delta->wds <= 1) { |
2030 |
/* exact */ |
2031 |
#ifdef SET_INEXACT |
2032 |
inexact = 0; |
2033 |
#endif |
2034 |
break; |
2035 |
} |
2036 |
if (rounding) { |
2037 |
if (dsign) { |
2038 |
adj = 1.; |
2039 |
goto apply_adj; |
2040 |
} |
2041 |
} |
2042 |
else if (!dsign) { |
2043 |
adj = -1.; |
2044 |
if (!word1(rv) |
2045 |
&& !(word0(rv) & Frac_mask)) { |
2046 |
y = word0(rv) & Exp_mask; |
2047 |
#ifdef Avoid_Underflow |
2048 |
if (!scale || y > 2*P*Exp_msk1) |
2049 |
#else |
2050 |
if (y) |
2051 |
#endif |
2052 |
{ |
2053 |
delta = lshift(delta,Log2P); |
2054 |
if (cmp(delta, bs) <= 0) |
2055 |
adj = -0.5; |
2056 |
} |
2057 |
} |
2058 |
apply_adj: |
2059 |
#ifdef Avoid_Underflow |
2060 |
if (scale && (y = word0(rv) & Exp_mask) |
2061 |
<= 2*P*Exp_msk1) |
2062 |
word0(adj) += (2*P+1)*Exp_msk1 - y; |
2063 |
#else |
2064 |
#ifdef Sudden_Underflow |
2065 |
if ((word0(rv) & Exp_mask) <= |
2066 |
P*Exp_msk1) { |
2067 |
word0(rv) += P*Exp_msk1; |
2068 |
dval(rv) += adj*ulp(rv); |
2069 |
word0(rv) -= P*Exp_msk1; |
2070 |
} |
2071 |
else |
2072 |
#endif /*Sudden_Underflow*/ |
2073 |
#endif /*Avoid_Underflow*/ |
2074 |
dval(rv) += adj*ulp(rv); |
2075 |
} |
2076 |
break; |
2077 |
} |
2078 |
adj = ratio(delta, bs); |
2079 |
if (adj < 1.) |
2080 |
adj = 1.; |
2081 |
if (adj <= 0x7ffffffe) { |
2082 |
/* adj = rounding ? ceil(adj) : floor(adj); */ |
2083 |
y = adj; |
2084 |
if (y != adj) { |
2085 |
if (!((rounding>>1) ^ dsign)) |
2086 |
y++; |
2087 |
adj = y; |
2088 |
} |
2089 |
} |
2090 |
#ifdef Avoid_Underflow |
2091 |
if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1) |
2092 |
word0(adj) += (2*P+1)*Exp_msk1 - y; |
2093 |
#else |
2094 |
#ifdef Sudden_Underflow |
2095 |
if ((word0(rv) & Exp_mask) <= P*Exp_msk1) { |
2096 |
word0(rv) += P*Exp_msk1; |
2097 |
adj *= ulp(rv); |
2098 |
if (dsign) |
2099 |
dval(rv) += adj; |
2100 |
else |
2101 |
dval(rv) -= adj; |
2102 |
word0(rv) -= P*Exp_msk1; |
2103 |
goto cont; |
2104 |
} |
2105 |
#endif /*Sudden_Underflow*/ |
2106 |
#endif /*Avoid_Underflow*/ |
2107 |
adj *= ulp(rv); |
2108 |
if (dsign) |
2109 |
dval(rv) += adj; |
2110 |
else |
2111 |
dval(rv) -= adj; |
2112 |
goto cont; |
2113 |
} |
2114 |
#endif /*Honor_FLT_ROUNDS*/ |
2115 |
|
2116 |
if (i < 0) { |
2117 |
/* Error is less than half an ulp -- check for |
2118 |
* special case of mantissa a power of two. |
2119 |
*/ |
2120 |
if (dsign || word1(rv) || word0(rv) & Bndry_mask |
2121 |
#ifdef IEEE_Arith |
2122 |
#ifdef Avoid_Underflow |
2123 |
|| (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1 |
2124 |
#else |
2125 |
|| (word0(rv) & Exp_mask) <= Exp_msk1 |
2126 |
#endif |
2127 |
#endif |
2128 |
) { |
2129 |
#ifdef SET_INEXACT |
2130 |
if (!delta->x[0] && delta->wds <= 1) |
2131 |
inexact = 0; |
2132 |
#endif |
2133 |
break; |
2134 |
} |
2135 |
if (!delta->x[0] && delta->wds <= 1) { |
2136 |
/* exact result */ |
2137 |
#ifdef SET_INEXACT |
2138 |
inexact = 0; |
2139 |
#endif |
2140 |
break; |
2141 |
} |
2142 |
delta = lshift(delta,Log2P); |
2143 |
if (cmp(delta, bs) > 0) |
2144 |
goto drop_down; |
2145 |
break; |
2146 |
} |
2147 |
if (i == 0) { |
2148 |
/* exactly half-way between */ |
2149 |
if (dsign) { |
2150 |
if ((word0(rv) & Bndry_mask1) == Bndry_mask1 |
2151 |
&& word1(rv) == ( |
2152 |
#ifdef Avoid_Underflow |
2153 |
(scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1) |
2154 |
? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) : |
2155 |
#endif |
2156 |
0xffffffff)) { |
2157 |
/*boundary case -- increment exponent*/ |
2158 |
word0(rv) = (word0(rv) & Exp_mask) |
2159 |
+ Exp_msk1 |
2160 |
#ifdef IBM |
2161 |
| Exp_msk1 >> 4 |
2162 |
#endif |
2163 |
; |
2164 |
word1(rv) = 0; |
2165 |
#ifdef Avoid_Underflow |
2166 |
dsign = 0; |
2167 |
#endif |
2168 |
break; |
2169 |
} |
2170 |
} |
2171 |
else if (!(word0(rv) & Bndry_mask) && !word1(rv)) { |
2172 |
drop_down: |
2173 |
/* boundary case -- decrement exponent */ |
2174 |
#ifdef Sudden_Underflow /*{{*/ |
2175 |
L = word0(rv) & Exp_mask; |
2176 |
#ifdef IBM |
2177 |
if (L < Exp_msk1) |
2178 |
#else |
2179 |
#ifdef Avoid_Underflow |
2180 |
if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1)) |
2181 |
#else |
2182 |
if (L <= Exp_msk1) |
2183 |
#endif /*Avoid_Underflow*/ |
2184 |
#endif /*IBM*/ |
2185 |
goto undfl; |
2186 |
L -= Exp_msk1; |
2187 |
#else /*Sudden_Underflow}{*/ |
2188 |
#ifdef Avoid_Underflow |
2189 |
if (scale) { |
2190 |
L = word0(rv) & Exp_mask; |
2191 |
if (L <= (2*P+1)*Exp_msk1) { |
2192 |
if (L > (P+2)*Exp_msk1) |
2193 |
/* round even ==> */ |
2194 |
/* accept rv */ |
2195 |
break; |
2196 |
/* rv = smallest denormal */ |
2197 |
goto undfl; |
2198 |
} |
2199 |
} |
2200 |
#endif /*Avoid_Underflow*/ |
2201 |
L = (word0(rv) & Exp_mask) - Exp_msk1; |
2202 |
#endif /*Sudden_Underflow}}*/ |
2203 |
word0(rv) = L | Bndry_mask1; |
2204 |
word1(rv) = 0xffffffff; |
2205 |
#ifdef IBM |
2206 |
goto cont; |
2207 |
#else |
2208 |
break; |
2209 |
#endif |
2210 |
} |
2211 |
#ifndef ROUND_BIASED |
2212 |
if (!(word1(rv) & LSB)) |
2213 |
break; |
2214 |
#endif |
2215 |
if (dsign) |
2216 |
dval(rv) += ulp(rv); |
2217 |
#ifndef ROUND_BIASED |
2218 |
else { |
2219 |
dval(rv) -= ulp(rv); |
2220 |
#ifndef Sudden_Underflow |
2221 |
if (!dval(rv)) |
2222 |
goto undfl; |
2223 |
#endif |
2224 |
} |
2225 |
#ifdef Avoid_Underflow |
2226 |
dsign = 1 - dsign; |
2227 |
#endif |
2228 |
#endif |
2229 |
break; |
2230 |
} |
2231 |
if ((aadj = ratio(delta, bs)) <= 2.) { |
2232 |
if (dsign) |
2233 |
aadj = dval(aadj1) = 1.; |
2234 |
else if (word1(rv) || word0(rv) & Bndry_mask) { |
2235 |
#ifndef Sudden_Underflow |
2236 |
if (word1(rv) == Tiny1 && !word0(rv)) |
2237 |
goto undfl; |
2238 |
#endif |
2239 |
aadj = 1.; |
2240 |
dval(aadj1) = -1.; |
2241 |
} |
2242 |
else { |
2243 |
/* special case -- power of FLT_RADIX to be */ |
2244 |
/* rounded down... */ |
2245 |
|
2246 |
if (aadj < 2./FLT_RADIX) |
2247 |
aadj = 1./FLT_RADIX; |
2248 |
else |
2249 |
aadj *= 0.5; |
2250 |
dval(aadj1) = -aadj; |
2251 |
} |
2252 |
} |
2253 |
else { |
2254 |
aadj *= 0.5; |
2255 |
dval(aadj1) = dsign ? aadj : -aadj; |
2256 |
#ifdef Check_FLT_ROUNDS |
2257 |
switch(Rounding) { |
2258 |
case 2: /* towards +infinity */ |
2259 |
dval(aadj1) -= 0.5; |
2260 |
break; |
2261 |
case 0: /* towards 0 */ |
2262 |
case 3: /* towards -infinity */ |
2263 |
dval(aadj1) += 0.5; |
2264 |
} |
2265 |
#else |
2266 |
if (Flt_Rounds == 0) |
2267 |
dval(aadj1) += 0.5; |
2268 |
#endif /*Check_FLT_ROUNDS*/ |
2269 |
} |
2270 |
y = word0(rv) & Exp_mask; |
2271 |
|
2272 |
/* Check for overflow */ |
2273 |
|
2274 |
if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) { |
2275 |
dval(rv0) = dval(rv); |
2276 |
word0(rv) -= P*Exp_msk1; |
2277 |
adj = dval(aadj1) * ulp(rv); |
2278 |
dval(rv) += adj; |
2279 |
if ((word0(rv) & Exp_mask) >= |
2280 |
Exp_msk1*(DBL_MAX_EXP+Bias-P)) { |
2281 |
if (word0(rv0) == Big0 && word1(rv0) == Big1) |
2282 |
goto ovfl; |
2283 |
word0(rv) = Big0; |
2284 |
word1(rv) = Big1; |
2285 |
goto cont; |
2286 |
} |
2287 |
else |
2288 |
word0(rv) += P*Exp_msk1; |
2289 |
} |
2290 |
else { |
2291 |
#ifdef Avoid_Underflow |
2292 |
if (scale && y <= 2*P*Exp_msk1) { |
2293 |
if (aadj <= 0x7fffffff) { |
2294 |
if ((z = (ULong) aadj) <= 0) |
2295 |
z = 1; |
2296 |
aadj = z; |
2297 |
dval(aadj1) = dsign ? aadj : -aadj; |
2298 |
} |
2299 |
word0(aadj1) += (2*P+1)*Exp_msk1 - y; |
2300 |
} |
2301 |
adj = dval(aadj1) * ulp(rv); |
2302 |
dval(rv) += adj; |
2303 |
#else |
2304 |
#ifdef Sudden_Underflow |
2305 |
if ((word0(rv) & Exp_mask) <= P*Exp_msk1) { |
2306 |
dval(rv0) = dval(rv); |
2307 |
word0(rv) += P*Exp_msk1; |
2308 |
adj = dval(aadj1) * ulp(rv); |
2309 |
dval(rv) += adj; |
2310 |
#ifdef IBM |
2311 |
if ((word0(rv) & Exp_mask) < P*Exp_msk1) |
2312 |
#else |
2313 |
if ((word0(rv) & Exp_mask) <= P*Exp_msk1) |
2314 |
#endif |
2315 |
{ |
2316 |
if (word0(rv0) == Tiny0 |
2317 |
&& word1(rv0) == Tiny1) |
2318 |
goto undfl; |
2319 |
word0(rv) = Tiny0; |
2320 |
word1(rv) = Tiny1; |
2321 |
goto cont; |
2322 |
} |
2323 |
else |
2324 |
word0(rv) -= P*Exp_msk1; |
2325 |
} |
2326 |
else { |
2327 |
adj = dval(aadj1) * ulp(rv); |
2328 |
dval(rv) += adj; |
2329 |
} |
2330 |
#else /*Sudden_Underflow*/ |
2331 |
/* Compute adj so that the IEEE rounding rules will |
2332 |
* correctly round rv + adj in some half-way cases. |
2333 |
* If rv * ulp(rv) is denormalized (i.e., |
2334 |
* y <= (P-1)*Exp_msk1), we must adjust aadj to avoid |
2335 |
* trouble from bits lost to denormalization; |
2336 |
* example: 1.2e-307 . |
2337 |
*/ |
2338 |
if (y <= (P-1)*Exp_msk1 && aadj > 1.) { |
2339 |
dval(aadj1) = (double)(int)(aadj + 0.5); |
2340 |
if (!dsign) |
2341 |
dval(aadj1) = -dval(aadj1); |
2342 |
} |
2343 |
adj = dval(aadj1) * ulp(rv); |
2344 |
dval(rv) += adj; |
2345 |
#endif /*Sudden_Underflow*/ |
2346 |
#endif /*Avoid_Underflow*/ |
2347 |
} |
2348 |
z = word0(rv) & Exp_mask; |
2349 |
#ifndef SET_INEXACT |
2350 |
#ifdef Avoid_Underflow |
2351 |
if (!scale) |
2352 |
#endif |
2353 |
if (y == z) { |
2354 |
/* Can we stop now? */ |
2355 |
L = (Long)aadj; |
2356 |
aadj -= L; |
2357 |
/* The tolerances below are conservative. */ |
2358 |
if (dsign || word1(rv) || word0(rv) & Bndry_mask) { |
2359 |
if (aadj < .4999999 || aadj > .5000001) |
2360 |
break; |
2361 |
} |
2362 |
else if (aadj < .4999999/FLT_RADIX) |
2363 |
break; |
2364 |
} |
2365 |
#endif |
2366 |
cont: |
2367 |
Bfree(bb); |
2368 |
Bfree(bd); |
2369 |
Bfree(bs); |
2370 |
Bfree(delta); |
2371 |
} |
2372 |
#ifdef SET_INEXACT |
2373 |
if (inexact) { |
2374 |
if (!oldinexact) { |
2375 |
word0(rv0) = Exp_1 + (70 << Exp_shift); |
2376 |
word1(rv0) = 0; |
2377 |
dval(rv0) += 1.; |
2378 |
} |
2379 |
} |
2380 |
else if (!oldinexact) |
2381 |
clear_inexact(); |
2382 |
#endif |
2383 |
#ifdef Avoid_Underflow |
2384 |
if (scale) { |
2385 |
word0(rv0) = Exp_1 - 2*P*Exp_msk1; |
2386 |
word1(rv0) = 0; |
2387 |
dval(rv) *= dval(rv0); |
2388 |
#ifndef NO_ERRNO |
2389 |
/* try to avoid the bug of testing an 8087 register value */ |
2390 |
if (word0(rv) == 0 && word1(rv) == 0) |
2391 |
errno = ERANGE; |
2392 |
#endif |
2393 |
} |
2394 |
#endif /* Avoid_Underflow */ |
2395 |
#ifdef SET_INEXACT |
2396 |
if (inexact && !(word0(rv) & Exp_mask)) { |
2397 |
/* set underflow bit */ |
2398 |
dval(rv0) = 1e-300; |
2399 |
dval(rv0) *= dval(rv0); |
2400 |
} |
2401 |
#endif |
2402 |
retfree: |
2403 |
Bfree(bb); |
2404 |
Bfree(bd); |
2405 |
Bfree(bs); |
2406 |
Bfree(bd0); |
2407 |
Bfree(delta); |
2408 |
ret: |
2409 |
if (se) |
2410 |
*se = (char *)s; |
2411 |
return sign ? -dval(rv) : dval(rv); |
2412 |
} |
2413 |
|
2414 |
static int |
2415 |
quorem |
2416 |
#ifdef KR_headers |
2417 |
(b, S) Bigint *b, *S; |
2418 |
#else |
2419 |
(Bigint *b, Bigint *S) |
2420 |
#endif |
2421 |
{ |
2422 |
int n; |
2423 |
ULong *bx, *bxe, q, *sx, *sxe; |
2424 |
#ifdef ULLong |
2425 |
ULLong borrow, carry, y, ys; |
2426 |
#else |
2427 |
ULong borrow, carry, y, ys; |
2428 |
#ifdef Pack_32 |
2429 |
ULong si, z, zs; |
2430 |
#endif |
2431 |
#endif |
2432 |
|
2433 |
n = S->wds; |
2434 |
#ifdef DEBUG |
2435 |
/*debug*/ if (b->wds > n) |
2436 |
/*debug*/ Bug("oversize b in quorem"); |
2437 |
#endif |
2438 |
if (b->wds < n) |
2439 |
return 0; |
2440 |
sx = S->x; |
2441 |
sxe = sx + --n; |
2442 |
bx = b->x; |
2443 |
bxe = bx + n; |
2444 |
q = *bxe / (*sxe + 1); /* ensure q <= true quotient */ |
2445 |
#ifdef DEBUG |
2446 |
/*debug*/ if (q > 9) |
2447 |
/*debug*/ Bug("oversized quotient in quorem"); |
2448 |
#endif |
2449 |
if (q) { |
2450 |
borrow = 0; |
2451 |
carry = 0; |
2452 |
do { |
2453 |
#ifdef ULLong |
2454 |
ys = *sx++ * (ULLong)q + carry; |
2455 |
carry = ys >> 32; |
2456 |
y = *bx - (ys & FFFFFFFF) - borrow; |
2457 |
borrow = y >> 32 & (ULong)1; |
2458 |
*bx++ = (ULong) y & FFFFFFFF; |
2459 |
#else |
2460 |
#ifdef Pack_32 |
2461 |
si = *sx++; |
2462 |
ys = (si & 0xffff) * q + carry; |
2463 |
zs = (si >> 16) * q + (ys >> 16); |
2464 |
carry = zs >> 16; |
2465 |
y = (*bx & 0xffff) - (ys & 0xffff) - borrow; |
2466 |
borrow = (y & 0x10000) >> 16; |
2467 |
z = (*bx >> 16) - (zs & 0xffff) - borrow; |
2468 |
borrow = (z & 0x10000) >> 16; |
2469 |
Storeinc(bx, z, y); |
2470 |
#else |
2471 |
ys = *sx++ * q + carry; |
2472 |
carry = ys >> 16; |
2473 |
y = *bx - (ys & 0xffff) - borrow; |
2474 |
borrow = (y & 0x10000) >> 16; |
2475 |
*bx++ = y & 0xffff; |
2476 |
#endif |
2477 |
#endif |
2478 |
} |
2479 |
while(sx <= sxe); |
2480 |
if (!*bxe) { |
2481 |
bx = b->x; |
2482 |
while(--bxe > bx && !*bxe) |
2483 |
--n; |
2484 |
b->wds = n; |
2485 |
} |
2486 |
} |
2487 |
if (cmp(b, S) >= 0) { |
2488 |
q++; |
2489 |
borrow = 0; |
2490 |
carry = 0; |
2491 |
bx = b->x; |
2492 |
sx = S->x; |
2493 |
do { |
2494 |
#ifdef ULLong |
2495 |
ys = *sx++ + carry; |
2496 |
carry = ys >> 32; |
2497 |
y = *bx - (ys & FFFFFFFF) - borrow; |
2498 |
borrow = y >> 32 & (ULong)1; |
2499 |
*bx++ = (ULong) y & FFFFFFFF; |
2500 |
#else |
2501 |
#ifdef Pack_32 |
2502 |
si = *sx++; |
2503 |
ys = (si & 0xffff) + carry; |
2504 |
zs = (si >> 16) + (ys >> 16); |
2505 |
carry = zs >> 16; |
2506 |
y = (*bx & 0xffff) - (ys & 0xffff) - borrow; |
2507 |
borrow = (y & 0x10000) >> 16; |
2508 |
z = (*bx >> 16) - (zs & 0xffff) - borrow; |
2509 |
borrow = (z & 0x10000) >> 16; |
2510 |
Storeinc(bx, z, y); |
2511 |
#else |
2512 |
ys = *sx++ + carry; |
2513 |
carry = ys >> 16; |
2514 |
y = *bx - (ys & 0xffff) - borrow; |
2515 |
borrow = (y & 0x10000) >> 16; |
2516 |
*bx++ = y & 0xffff; |
2517 |
#endif |
2518 |
#endif |
2519 |
} |
2520 |
while(sx <= sxe); |
2521 |
bx = b->x; |
2522 |
bxe = bx + n; |
2523 |
if (!*bxe) { |
2524 |
while(--bxe > bx && !*bxe) |
2525 |
--n; |
2526 |
b->wds = n; |
2527 |
} |
2528 |
} |
2529 |
return q; |
2530 |
} |
2531 |
|
2532 |
#ifndef MULTIPLE_THREADS |
2533 |
static char *dtoa_result; |
2534 |
#endif |
2535 |
|
2536 |
static char * |
2537 |
#ifdef KR_headers |
2538 |
rv_alloc(i) int i; |
2539 |
#else |
2540 |
rv_alloc(int i) |
2541 |
#endif |
2542 |
{ |
2543 |
int j, k, *r; |
2544 |
|
2545 |
j = sizeof(ULong); |
2546 |
for(k = 0; |
2547 |
sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= (unsigned) i; |
2548 |
j <<= 1) |
2549 |
k++; |
2550 |
r = (int*)Balloc(k); |
2551 |
*r = k; |
2552 |
return |
2553 |
#ifndef MULTIPLE_THREADS |
2554 |
dtoa_result = |
2555 |
#endif |
2556 |
(char *)(r+1); |
2557 |
} |
2558 |
|
2559 |
static char * |
2560 |
#ifdef KR_headers |
2561 |
nrv_alloc(s, rve, n) char *s, **rve; int n; |
2562 |
#else |
2563 |
nrv_alloc(CONST char *s, char **rve, int n) |
2564 |
#endif |
2565 |
{ |
2566 |
char *rv, *t; |
2567 |
|
2568 |
t = rv = rv_alloc(n); |
2569 |
while((*t = *s++)) t++; |
2570 |
if (rve) |
2571 |
*rve = t; |
2572 |
return rv; |
2573 |
} |
2574 |
|
2575 |
/* freedtoa(s) must be used to free values s returned by dtoa |
2576 |
* when MULTIPLE_THREADS is #defined. It should be used in all cases, |
2577 |
* but for consistency with earlier versions of dtoa, it is optional |
2578 |
* when MULTIPLE_THREADS is not defined. |
2579 |
*/ |
2580 |
|
2581 |
void |
2582 |
#ifdef KR_headers |
2583 |
freedtoa(s) char *s; |
2584 |
#else |
2585 |
freedtoa(char *s) |
2586 |
#endif |
2587 |
{ |
2588 |
Bigint *b = (Bigint *)((int *)s - 1); |
2589 |
b->maxwds = 1 << (b->k = *(int*)b); |
2590 |
Bfree(b); |
2591 |
#ifndef MULTIPLE_THREADS |
2592 |
if (s == dtoa_result) |
2593 |
dtoa_result = 0; |
2594 |
#endif |
2595 |
} |
2596 |
|
2597 |
/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string. |
2598 |
* |
2599 |
* Inspired by "How to Print Floating-Point Numbers Accurately" by |
2600 |
* Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126]. |
2601 |
* |
2602 |
* Modifications: |
2603 |
* 1. Rather than iterating, we use a simple numeric overestimate |
2604 |
* to determine k = floor(log10(d)). We scale relevant |
2605 |
* quantities using O(log2(k)) rather than O(k) multiplications. |
2606 |
* 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't |
2607 |
* try to generate digits strictly left to right. Instead, we |
2608 |
* compute with fewer bits and propagate the carry if necessary |
2609 |
* when rounding the final digit up. This is often faster. |
2610 |
* 3. Under the assumption that input will be rounded nearest, |
2611 |
* mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22. |
2612 |
* That is, we allow equality in stopping tests when the |
2613 |
* round-nearest rule will give the same floating-point value |
2614 |
* as would satisfaction of the stopping test with strict |
2615 |
* inequality. |
2616 |
* 4. We remove common factors of powers of 2 from relevant |
2617 |
* quantities. |
2618 |
* 5. When converting floating-point integers less than 1e16, |
2619 |
* we use floating-point arithmetic rather than resorting |
2620 |
* to multiple-precision integers. |
2621 |
* 6. When asked to produce fewer than 15 digits, we first try |
2622 |
* to get by with floating-point arithmetic; we resort to |
2623 |
* multiple-precision integer arithmetic only if we cannot |
2624 |
* guarantee that the floating-point calculation has given |
2625 |
* the correctly rounded result. For k requested digits and |
2626 |
* "uniformly" distributed input, the probability is |
2627 |
* something like 10^(k-15) that we must resort to the Long |
2628 |
* calculation. |
2629 |
*/ |
2630 |
|
2631 |
static char * |
2632 |
dtoa |
2633 |
#ifdef KR_headers |
2634 |
(d, mode, ndigits, decpt, sign, rve) |
2635 |
U d; int mode, ndigits, *decpt, *sign; char **rve; |
2636 |
#else |
2637 |
(U d, int mode, int ndigits, int *decpt, int *sign, char **rve) |
2638 |
#endif |
2639 |
{ |
2640 |
/* Arguments ndigits, decpt, sign are similar to those |
2641 |
of ecvt and fcvt; trailing zeros are suppressed from |
2642 |
the returned string. If not null, *rve is set to point |
2643 |
to the end of the return value. If d is +-Infinity or NaN, |
2644 |
then *decpt is set to 9999. |
2645 |
|
2646 |
mode: |
2647 |
0 ==> shortest string that yields d when read in |
2648 |
and rounded to nearest. |
2649 |
1 ==> like 0, but with Steele & White stopping rule; |
2650 |
e.g. with IEEE P754 arithmetic , mode 0 gives |
2651 |
1e23 whereas mode 1 gives 9.999999999999999e22. |
2652 |
2 ==> max(1,ndigits) significant digits. This gives a |
2653 |
return value similar to that of ecvt, except |
2654 |
that trailing zeros are suppressed. |
2655 |
3 ==> through ndigits past the decimal point. This |
2656 |
gives a return value similar to that from fcvt, |
2657 |
except that trailing zeros are suppressed, and |
2658 |
ndigits can be negative. |
2659 |
4,5 ==> similar to 2 and 3, respectively, but (in |
2660 |
round-nearest mode) with the tests of mode 0 to |
2661 |
possibly return a shorter string that rounds to d. |
2662 |
With IEEE arithmetic and compilation with |
2663 |
-DHonor_FLT_ROUNDS, modes 4 and 5 behave the same |
2664 |
as modes 2 and 3 when FLT_ROUNDS != 1. |
2665 |
6-9 ==> Debugging modes similar to mode - 4: don't try |
2666 |
fast floating-point estimate (if applicable). |
2667 |
|
2668 |
Values of mode other than 0-9 are treated as mode 0. |
2669 |
|
2670 |
Sufficient space is allocated to the return value |
2671 |
to hold the suppressed trailing zeros. |
2672 |
*/ |
2673 |
|
2674 |
int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1, |
2675 |
j, j1, k, k0, k_check, leftright, m2, m5, s2, s5, |
2676 |
spec_case, try_quick; |
2677 |
Long L; |
2678 |
#ifndef Sudden_Underflow |
2679 |
int denorm; |
2680 |
ULong x; |
2681 |
#endif |
2682 |
Bigint *b, *b1, *delta, *mlo, *mhi, *S; |
2683 |
U d2, eps; |
2684 |
double ds; |
2685 |
char *s, *s0; |
2686 |
#ifdef Honor_FLT_ROUNDS |
2687 |
int rounding; |
2688 |
#endif |
2689 |
#ifdef SET_INEXACT |
2690 |
int inexact, oldinexact; |
2691 |
#endif |
2692 |
|
2693 |
#ifdef __GNUC__ |
2694 |
ilim = ilim1 = 0; |
2695 |
mlo = NULL; |
2696 |
#endif |
2697 |
|
2698 |
#ifndef MULTIPLE_THREADS |
2699 |
if (dtoa_result) { |
2700 |
freedtoa(dtoa_result); |
2701 |
dtoa_result = 0; |
2702 |
} |
2703 |
#endif |
2704 |
|
2705 |
if (word0(d) & Sign_bit) { |
2706 |
/* set sign for everything, including 0's and NaNs */ |
2707 |
*sign = 1; |
2708 |
word0(d) &= ~Sign_bit; /* clear sign bit */ |
2709 |
} |
2710 |
else |
2711 |
*sign = 0; |
2712 |
|
2713 |
#if defined(IEEE_Arith) + defined(VAX) |
2714 |
#ifdef IEEE_Arith |
2715 |
if ((word0(d) & Exp_mask) == Exp_mask) |
2716 |
#else |
2717 |
if (word0(d) == 0x8000) |
2718 |
#endif |
2719 |
{ |
2720 |
/* Infinity or NaN */ |
2721 |
*decpt = 9999; |
2722 |
#ifdef IEEE_Arith |
2723 |
if (!word1(d) && !(word0(d) & 0xfffff)) |
2724 |
return nrv_alloc("Infinity", rve, 8); |
2725 |
#endif |
2726 |
return nrv_alloc("NaN", rve, 3); |
2727 |
} |
2728 |
#endif |
2729 |
#ifdef IBM |
2730 |
dval(d) += 0; /* normalize */ |
2731 |
#endif |
2732 |
if (!dval(d)) { |
2733 |
*decpt = 1; |
2734 |
return nrv_alloc("0", rve, 1); |
2735 |
} |
2736 |
|
2737 |
#ifdef SET_INEXACT |
2738 |
try_quick = oldinexact = get_inexact(); |
2739 |
inexact = 1; |
2740 |
#endif |
2741 |
#ifdef Honor_FLT_ROUNDS |
2742 |
if ((rounding = Flt_Rounds) >= 2) { |
2743 |
if (*sign) |
2744 |
rounding = rounding == 2 ? 0 : 2; |
2745 |
else |
2746 |
if (rounding != 2) |
2747 |
rounding = 0; |
2748 |
} |
2749 |
#endif |
2750 |
|
2751 |
b = d2b(d, &be, &bbits); |
2752 |
#ifdef Sudden_Underflow |
2753 |
i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1)); |
2754 |
#else |
2755 |
if ((i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1)))) { |
2756 |
#endif |
2757 |
dval(d2) = dval(d); |
2758 |
word0(d2) &= Frac_mask1; |
2759 |
word0(d2) |= Exp_11; |
2760 |
#ifdef IBM |
2761 |
if (j = 11 - hi0bits(word0(d2) & Frac_mask)) |
2762 |
dval(d2) /= 1 << j; |
2763 |
#endif |
2764 |
|
2765 |
/* log(x) ~=~ log(1.5) + (x-1.5)/1.5 |
2766 |
* log10(x) = log(x) / log(10) |
2767 |
* ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10)) |
2768 |
* log10(d) = (i-Bias)*log(2)/log(10) + log10(d2) |
2769 |
* |
2770 |
* This suggests computing an approximation k to log10(d) by |
2771 |
* |
2772 |
* k = (i - Bias)*0.301029995663981 |
2773 |
* + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 ); |
2774 |
* |
2775 |
* We want k to be too large rather than too small. |
2776 |
* The error in the first-order Taylor series approximation |
2777 |
* is in our favor, so we just round up the constant enough |
2778 |
* to compensate for any error in the multiplication of |
2779 |
* (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077, |
2780 |
* and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14, |
2781 |
* adding 1e-13 to the constant term more than suffices. |
2782 |
* Hence we adjust the constant term to 0.1760912590558. |
2783 |
* (We could get a more accurate k by invoking log10, |
2784 |
* but this is probably not worthwhile.) |
2785 |
*/ |
2786 |
|
2787 |
i -= Bias; |
2788 |
#ifdef IBM |
2789 |
i <<= 2; |
2790 |
i += j; |
2791 |
#endif |
2792 |
#ifndef Sudden_Underflow |
2793 |
denorm = 0; |
2794 |
} |
2795 |
else { |
2796 |
/* d is denormalized */ |
2797 |
|
2798 |
i = bbits + be + (Bias + (P-1) - 1); |
2799 |
x = i > 32 ? word0(d) << (64 - i) | word1(d) >> (i - 32) |
2800 |
: word1(d) << (32 - i); |
2801 |
dval(d2) = x; |
2802 |
word0(d2) -= 31*Exp_msk1; /* adjust exponent */ |
2803 |
i -= (Bias + (P-1) - 1) + 1; |
2804 |
denorm = 1; |
2805 |
} |
2806 |
#endif |
2807 |
ds = (dval(d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981; |
2808 |
k = (int)ds; |
2809 |
if (ds < 0. && ds != k) |
2810 |
k--; /* want k = floor(ds) */ |
2811 |
k_check = 1; |
2812 |
if (k >= 0 && k <= Ten_pmax) { |
2813 |
if (dval(d) < tens[k]) |
2814 |
k--; |
2815 |
k_check = 0; |
2816 |
} |
2817 |
j = bbits - i - 1; |
2818 |
if (j >= 0) { |
2819 |
b2 = 0; |
2820 |
s2 = j; |
2821 |
} |
2822 |
else { |
2823 |
b2 = -j; |
2824 |
s2 = 0; |
2825 |
} |
2826 |
if (k >= 0) { |
2827 |
b5 = 0; |
2828 |
s5 = k; |
2829 |
s2 += k; |
2830 |
} |
2831 |
else { |
2832 |
b2 -= k; |
2833 |
b5 = -k; |
2834 |
s5 = 0; |
2835 |
} |
2836 |
if (mode < 0 || mode > 9) |
2837 |
mode = 0; |
2838 |
|
2839 |
#ifndef SET_INEXACT |
2840 |
#ifdef Check_FLT_ROUNDS |
2841 |
try_quick = Rounding == 1; |
2842 |
#else |
2843 |
try_quick = 1; |
2844 |
#endif |
2845 |
#endif /*SET_INEXACT*/ |
2846 |
|
2847 |
if (mode > 5) { |
2848 |
mode -= 4; |
2849 |
try_quick = 0; |
2850 |
} |
2851 |
leftright = 1; |
2852 |
switch(mode) { |
2853 |
case 0: |
2854 |
case 1: |
2855 |
ilim = ilim1 = -1; |
2856 |
i = 18; |
2857 |
ndigits = 0; |
2858 |
break; |
2859 |
case 2: |
2860 |
leftright = 0; |
2861 |
/* no break */ |
2862 |
case 4: |
2863 |
if (ndigits <= 0) |
2864 |
ndigits = 1; |
2865 |
ilim = ilim1 = i = ndigits; |
2866 |
break; |
2867 |
case 3: |
2868 |
leftright = 0; |
2869 |
/* no break */ |
2870 |
case 5: |
2871 |
i = ndigits + k + 1; |
2872 |
ilim = i; |
2873 |
ilim1 = i - 1; |
2874 |
if (i <= 0) |
2875 |
i = 1; |
2876 |
} |
2877 |
s = s0 = rv_alloc(i); |
2878 |
|
2879 |
#ifdef Honor_FLT_ROUNDS |
2880 |
if (mode > 1 && rounding != 1) |
2881 |
leftright = 0; |
2882 |
#endif |
2883 |
|
2884 |
if (ilim >= 0 && ilim <= Quick_max && try_quick) { |
2885 |
|
2886 |
/* Try to get by with floating-point arithmetic. */ |
2887 |
|
2888 |
i = 0; |
2889 |
dval(d2) = dval(d); |
2890 |
k0 = k; |
2891 |
ilim0 = ilim; |
2892 |
ieps = 2; /* conservative */ |
2893 |
if (k > 0) { |
2894 |
ds = tens[k&0xf]; |
2895 |
j = k >> 4; |
2896 |
if (j & Bletch) { |
2897 |
/* prevent overflows */ |
2898 |
j &= Bletch - 1; |
2899 |
dval(d) /= bigtens[n_bigtens-1]; |
2900 |
ieps++; |
2901 |
} |
2902 |
for(; j; j >>= 1, i++) |
2903 |
if (j & 1) { |
2904 |
ieps++; |
2905 |
ds *= bigtens[i]; |
2906 |
} |
2907 |
dval(d) /= ds; |
2908 |
} |
2909 |
else if ((j1 = -k)) { |
2910 |
dval(d) *= tens[j1 & 0xf]; |
2911 |
for(j = j1 >> 4; j; j >>= 1, i++) |
2912 |
if (j & 1) { |
2913 |
ieps++; |
2914 |
dval(d) *= bigtens[i]; |
2915 |
} |
2916 |
} |
2917 |
if (k_check && dval(d) < 1. && ilim > 0) { |
2918 |
if (ilim1 <= 0) |
2919 |
goto fast_failed; |
2920 |
ilim = ilim1; |
2921 |
k--; |
2922 |
dval(d) *= 10.; |
2923 |
ieps++; |
2924 |
} |
2925 |
dval(eps) = ieps*dval(d) + 7.; |
2926 |
word0(eps) -= (P-1)*Exp_msk1; |
2927 |
if (ilim == 0) { |
2928 |
S = mhi = 0; |
2929 |
dval(d) -= 5.; |
2930 |
if (dval(d) > dval(eps)) |
2931 |
goto one_digit; |
2932 |
if (dval(d) < -dval(eps)) |
2933 |
goto no_digits; |
2934 |
goto fast_failed; |
2935 |
} |
2936 |
#ifndef No_leftright |
2937 |
if (leftright) { |
2938 |
/* Use Steele & White method of only |
2939 |
* generating digits needed. |
2940 |
*/ |
2941 |
dval(eps) = 0.5/tens[ilim-1] - dval(eps); |
2942 |
for(i = 0;;) { |
2943 |
L = (ULong) dval(d); |
2944 |
dval(d) -= L; |
2945 |
*s++ = '0' + (int)L; |
2946 |
if (dval(d) < dval(eps)) |
2947 |
goto ret1; |
2948 |
if (1. - dval(d) < dval(eps)) |
2949 |
goto bump_up; |
2950 |
if (++i >= ilim) |
2951 |
break; |
2952 |
dval(eps) *= 10.; |
2953 |
dval(d) *= 10.; |
2954 |
} |
2955 |
} |
2956 |
else { |
2957 |
#endif |
2958 |
/* Generate ilim digits, then fix them up. */ |
2959 |
dval(eps) *= tens[ilim-1]; |
2960 |
for(i = 1;; i++, dval(d) *= 10.) { |
2961 |
L = (Long)(dval(d)); |
2962 |
if (!(dval(d) -= L)) |
2963 |
ilim = i; |
2964 |
*s++ = '0' + (int)L; |
2965 |
if (i == ilim) { |
2966 |
if (dval(d) > 0.5 + dval(eps)) |
2967 |
goto bump_up; |
2968 |
else if (dval(d) < 0.5 - dval(eps)) { |
2969 |
while(*--s == '0'); |
2970 |
s++; |
2971 |
goto ret1; |
2972 |
} |
2973 |
break; |
2974 |
} |
2975 |
} |
2976 |
#ifndef No_leftright |
2977 |
} |
2978 |
#endif |
2979 |
fast_failed: |
2980 |
s = s0; |
2981 |
dval(d) = dval(d2); |
2982 |
k = k0; |
2983 |
ilim = ilim0; |
2984 |
} |
2985 |
|
2986 |
/* Do we have a "small" integer? */ |
2987 |
|
2988 |
if (be >= 0 && k <= Int_max) { |
2989 |
/* Yes. */ |
2990 |
ds = tens[k]; |
2991 |
if (ndigits < 0 && ilim <= 0) { |
2992 |
S = mhi = 0; |
2993 |
if (ilim < 0 || dval(d) < 5*ds) |
2994 |
goto no_digits; |
2995 |
goto one_digit; |
2996 |
} |
2997 |
for(i = 1;; i++, dval(d) *= 10.) { |
2998 |
L = (Long)(dval(d) / ds); |
2999 |
dval(d) -= L*ds; |
3000 |
#ifdef Check_FLT_ROUNDS |
3001 |
/* If FLT_ROUNDS == 2, L will usually be high by 1 */ |
3002 |
if (dval(d) < 0) { |
3003 |
L--; |
3004 |
dval(d) += ds; |
3005 |
} |
3006 |
#endif |
3007 |
*s++ = '0' + (int)L; |
3008 |
if (!dval(d)) { |
3009 |
#ifdef SET_INEXACT |
3010 |
inexact = 0; |
3011 |
#endif |
3012 |
break; |
3013 |
} |
3014 |
if (i == ilim) { |
3015 |
#ifdef Honor_FLT_ROUNDS |
3016 |
if (mode > 1) |
3017 |
switch(rounding) { |
3018 |
case 0: goto ret1; |
3019 |
case 2: goto bump_up; |
3020 |
} |
3021 |
#endif |
3022 |
dval(d) += dval(d); |
3023 |
if (dval(d) > ds || (dval(d) == ds && L & 1)) { |
3024 |
bump_up: |
3025 |
while(*--s == '9') |
3026 |
if (s == s0) { |
3027 |
k++; |
3028 |
*s = '0'; |
3029 |
break; |
3030 |
} |
3031 |
++*s++; |
3032 |
} |
3033 |
break; |
3034 |
} |
3035 |
} |
3036 |
goto ret1; |
3037 |
} |
3038 |
|
3039 |
m2 = b2; |
3040 |
m5 = b5; |
3041 |
mhi = mlo = 0; |
3042 |
if (leftright) { |
3043 |
i = |
3044 |
#ifndef Sudden_Underflow |
3045 |
denorm ? be + (Bias + (P-1) - 1 + 1) : |
3046 |
#endif |
3047 |
#ifdef IBM |
3048 |
1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3); |
3049 |
#else |
3050 |
1 + P - bbits; |
3051 |
#endif |
3052 |
b2 += i; |
3053 |
s2 += i; |
3054 |
mhi = i2b(1); |
3055 |
} |
3056 |
if (m2 > 0 && s2 > 0) { |
3057 |
i = m2 < s2 ? m2 : s2; |
3058 |
b2 -= i; |
3059 |
m2 -= i; |
3060 |
s2 -= i; |
3061 |
} |
3062 |
if (b5 > 0) { |
3063 |
if (leftright) { |
3064 |
if (m5 > 0) { |
3065 |
mhi = pow5mult(mhi, m5); |
3066 |
b1 = mult(mhi, b); |
3067 |
Bfree(b); |
3068 |
b = b1; |
3069 |
} |
3070 |
if ((j = b5 - m5)) |
3071 |
b = pow5mult(b, j); |
3072 |
} |
3073 |
else |
3074 |
b = pow5mult(b, b5); |
3075 |
} |
3076 |
S = i2b(1); |
3077 |
if (s5 > 0) |
3078 |
S = pow5mult(S, s5); |
3079 |
|
3080 |
/* Check for special case that d is a normalized power of 2. */ |
3081 |
|
3082 |
spec_case = 0; |
3083 |
if ((mode < 2 || leftright) |
3084 |
#ifdef Honor_FLT_ROUNDS |
3085 |
&& rounding == 1 |
3086 |
#endif |
3087 |
) { |
3088 |
if (!word1(d) && !(word0(d) & Bndry_mask) |
3089 |
#ifndef Sudden_Underflow |
3090 |
&& word0(d) & (Exp_mask & ~Exp_msk1) |
3091 |
#endif |
3092 |
) { |
3093 |
/* The special case */ |
3094 |
b2 += Log2P; |
3095 |
s2 += Log2P; |
3096 |
spec_case = 1; |
3097 |
} |
3098 |
} |
3099 |
|
3100 |
/* Arrange for convenient computation of quotients: |
3101 |
* shift left if necessary so divisor has 4 leading 0 bits. |
3102 |
* |
3103 |
* Perhaps we should just compute leading 28 bits of S once |
3104 |
* and for all and pass them and a shift to quorem, so it |
3105 |
* can do shifts and ors to compute the numerator for q. |
3106 |
*/ |
3107 |
#ifdef Pack_32 |
3108 |
if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f)) |
3109 |
i = 32 - i; |
3110 |
#else |
3111 |
if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf) |
3112 |
i = 16 - i; |
3113 |
#endif |
3114 |
if (i > 4) { |
3115 |
i -= 4; |
3116 |
b2 += i; |
3117 |
m2 += i; |
3118 |
s2 += i; |
3119 |
} |
3120 |
else if (i < 4) { |
3121 |
i += 28; |
3122 |
b2 += i; |
3123 |
m2 += i; |
3124 |
s2 += i; |
3125 |
} |
3126 |
if (b2 > 0) |
3127 |
b = lshift(b, b2); |
3128 |
if (s2 > 0) |
3129 |
S = lshift(S, s2); |
3130 |
if (k_check) { |
3131 |
if (cmp(b,S) < 0) { |
3132 |
k--; |
3133 |
b = multadd(b, 10, 0); /* we botched the k estimate */ |
3134 |
if (leftright) |
3135 |
mhi = multadd(mhi, 10, 0); |
3136 |
ilim = ilim1; |
3137 |
} |
3138 |
} |
3139 |
if (ilim <= 0 && (mode == 3 || mode == 5)) { |
3140 |
if (ilim < 0 || cmp(b,S = multadd(S,5,0)) < 0) { |
3141 |
/* no digits, fcvt style */ |
3142 |
no_digits: |
3143 |
/* MOZILLA CHANGE: Always return a non-empty string. */ |
3144 |
*s++ = '0'; |
3145 |
k = 0; |
3146 |
goto ret; |
3147 |
} |
3148 |
one_digit: |
3149 |
*s++ = '1'; |
3150 |
k++; |
3151 |
goto ret; |
3152 |
} |
3153 |
if (leftright) { |
3154 |
if (m2 > 0) |
3155 |
mhi = lshift(mhi, m2); |
3156 |
|
3157 |
/* Compute mlo -- check for special case |
3158 |
* that d is a normalized power of 2. |
3159 |
*/ |
3160 |
|
3161 |
mlo = mhi; |
3162 |
if (spec_case) { |
3163 |
mhi = Balloc(mhi->k); |
3164 |
Bcopy(mhi, mlo); |
3165 |
mhi = lshift(mhi, Log2P); |
3166 |
} |
3167 |
|
3168 |
for(i = 1;;i++) { |
3169 |
dig = quorem(b,S) + '0'; |
3170 |
/* Do we yet have the shortest decimal string |
3171 |
* that will round to d? |
3172 |
*/ |
3173 |
j = cmp(b, mlo); |
3174 |
delta = diff(S, mhi); |
3175 |
j1 = delta->sign ? 1 : cmp(b, delta); |
3176 |
Bfree(delta); |
3177 |
#ifndef ROUND_BIASED |
3178 |
if (j1 == 0 && mode != 1 && !(word1(d) & 1) |
3179 |
#ifdef Honor_FLT_ROUNDS |
3180 |
&& rounding >= 1 |
3181 |
#endif |
3182 |
) { |
3183 |
if (dig == '9') |
3184 |
goto round_9_up; |
3185 |
if (j > 0) |
3186 |
dig++; |
3187 |
#ifdef SET_INEXACT |
3188 |
else if (!b->x[0] && b->wds <= 1) |
3189 |
inexact = 0; |
3190 |
#endif |
3191 |
*s++ = dig; |
3192 |
goto ret; |
3193 |
} |
3194 |
#endif |
3195 |
if (j < 0 || (j == 0 && mode != 1 |
3196 |
#ifndef ROUND_BIASED |
3197 |
&& !(word1(d) & 1) |
3198 |
#endif |
3199 |
)) { |
3200 |
if (!b->x[0] && b->wds <= 1) { |
3201 |
#ifdef SET_INEXACT |
3202 |
inexact = 0; |
3203 |
#endif |
3204 |
goto accept_dig; |
3205 |
} |
3206 |
#ifdef Honor_FLT_ROUNDS |
3207 |
if (mode > 1) |
3208 |
switch(rounding) { |
3209 |
case 0: goto accept_dig; |
3210 |
case 2: goto keep_dig; |
3211 |
} |
3212 |
#endif /*Honor_FLT_ROUNDS*/ |
3213 |
if (j1 > 0) { |
3214 |
b = lshift(b, 1); |
3215 |
j1 = cmp(b, S); |
3216 |
if ((j1 > 0 || (j1 == 0 && dig & 1)) |
3217 |
&& dig++ == '9') |
3218 |
goto round_9_up; |
3219 |
} |
3220 |
accept_dig: |
3221 |
*s++ = dig; |
3222 |
goto ret; |
3223 |
} |
3224 |
if (j1 > 0) { |
3225 |
#ifdef Honor_FLT_ROUNDS |
3226 |
if (!rounding) |
3227 |
goto accept_dig; |
3228 |
#endif |
3229 |
if (dig == '9') { /* possible if i == 1 */ |
3230 |
round_9_up: |
3231 |
*s++ = '9'; |
3232 |
goto roundoff; |
3233 |
} |
3234 |
*s++ = dig + 1; |
3235 |
goto ret; |
3236 |
} |
3237 |
#ifdef Honor_FLT_ROUNDS |
3238 |
keep_dig: |
3239 |
#endif |
3240 |
*s++ = dig; |
3241 |
if (i == ilim) |
3242 |
break; |
3243 |
b = multadd(b, 10, 0); |
3244 |
if (mlo == mhi) |
3245 |
mlo = mhi = multadd(mhi, 10, 0); |
3246 |
else { |
3247 |
mlo = multadd(mlo, 10, 0); |
3248 |
mhi = multadd(mhi, 10, 0); |
3249 |
} |
3250 |
} |
3251 |
} |
3252 |
else |
3253 |
for(i = 1;; i++) { |
3254 |
*s++ = dig = quorem(b,S) + '0'; |
3255 |
if (!b->x[0] && b->wds <= 1) { |
3256 |
#ifdef SET_INEXACT |
3257 |
inexact = 0; |
3258 |
#endif |
3259 |
goto ret; |
3260 |
} |
3261 |
if (i >= ilim) |
3262 |
break; |
3263 |
b = multadd(b, 10, 0); |
3264 |
} |
3265 |
|
3266 |
/* Round off last digit */ |
3267 |
|
3268 |
#ifdef Honor_FLT_ROUNDS |
3269 |
switch(rounding) { |
3270 |
case 0: goto trimzeros; |
3271 |
case 2: goto roundoff; |
3272 |
} |
3273 |
#endif |
3274 |
b = lshift(b, 1); |
3275 |
j = cmp(b, S); |
3276 |
if (j >= 0) { /* ECMA compatible rounding needed by Spidermonkey */ |
3277 |
roundoff: |
3278 |
while(*--s == '9') |
3279 |
if (s == s0) { |
3280 |
k++; |
3281 |
*s++ = '1'; |
3282 |
goto ret; |
3283 |
} |
3284 |
++*s++; |
3285 |
} |
3286 |
else { |
3287 |
#ifdef Honor_FLT_ROUNDS |
3288 |
trimzeros: |
3289 |
#endif |
3290 |
while(*--s == '0'); |
3291 |
s++; |
3292 |
} |
3293 |
ret: |
3294 |
Bfree(S); |
3295 |
if (mhi) { |
3296 |
if (mlo && mlo != mhi) |
3297 |
Bfree(mlo); |
3298 |
Bfree(mhi); |
3299 |
} |
3300 |
ret1: |
3301 |
#ifdef SET_INEXACT |
3302 |
if (inexact) { |
3303 |
if (!oldinexact) { |
3304 |
word0(d) = Exp_1 + (70 << Exp_shift); |
3305 |
word1(d) = 0; |
3306 |
dval(d) += 1.; |
3307 |
} |
3308 |
} |
3309 |
else if (!oldinexact) |
3310 |
clear_inexact(); |
3311 |
#endif |
3312 |
Bfree(b); |
3313 |
*s = 0; |
3314 |
*decpt = k + 1; |
3315 |
if (rve) |
3316 |
*rve = s; |
3317 |
return s0; |
3318 |
} |
3319 |
#ifdef __cplusplus |
3320 |
} |
3321 |
#endif |