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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. This will cause dtoa modes 4 and 5 to be
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+ * treated the same as modes 2 and 3 for some inputs.
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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. Unless Trust_FLT_ROUNDS
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+ * is also #defined, fegetround() will be queried for the rounding mode.
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+ * Note that both FLT_ROUNDS and fegetround() are specified by the C99
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+ * standard (and are specified to be consistent, with fesetround()
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+ * affecting the value of FLT_ROUNDS), but that some (Linux) systems
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+ * do not work correctly in this regard, so using fegetround() is more
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+ * portable than using FLT_ROUNDS directly.
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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 and arithmetic
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+ * that rounds toward +Infinity.
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+ * #define ROUND_BIASED_without_Round_Up for IEEE-format with biased
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+ * rounding when the underlying floating-point arithmetic uses
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+ * unbiased rounding. This prevent using ordinary floating-point
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+ * arithmetic when the result could be computed with one rounding error.
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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. Similarly, if you
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+ * want something other than the system's free() to be called to
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+ * recycle memory acquired from MALLOC, #define FREE to be the
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+ * name of the alternate routine. (FREE or free is only called in
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+ * pathological cases, e.g., in a dtoa call after a dtoa return in
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+ * mode 3 with thousands of digits requested.)
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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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+ * #define NO_HEX_FP to omit recognition of hexadecimal floating-point
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+ * values by strtod.
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+ * #define NO_STRTOD_BIGCOMP (on IEEE-arithmetic systems only for now)
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+ * to disable logic for "fast" testing of very long input strings
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+ * to strtod. This testing proceeds by initially truncating the
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+ * input string, then if necessary comparing the whole string with
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+ * a decimal expansion to decide close cases. This logic is only
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+ * used for input more than STRTOD_DIGLIM digits long (default 40).
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+ */
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+
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+#include "dtoa_config.h"
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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 Honor_FLT_ROUNDS
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+#ifndef Trust_FLT_ROUNDS
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+#include <fenv.h>
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+#endif
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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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+#define NO_STRTOD_BIGCOMP
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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
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+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
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+
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+typedef union { double d; ULong L[2]; } U;
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+
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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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+#define dval(x) (x)->d
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+
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+#ifndef STRTOD_DIGLIM
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+#define STRTOD_DIGLIM 40
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+#endif
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+
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+#ifdef DIGLIM_DEBUG
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+extern int strtod_diglim;
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+#else
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+#define strtod_diglim STRTOD_DIGLIM
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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
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+#define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
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+((unsigned short *)a)[1] = (unsigned short)c, a++)
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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)) */
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+/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
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+/* 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) */
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+
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+#ifdef IEEE_Arith
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+#define Exp_shift 20
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+#define Exp_shift1 20
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+#define Exp_msk1 0x100000
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+#define Exp_msk11 0x100000
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+#define Exp_mask 0x7ff00000
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+#define P 53
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+#define Nbits 53
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+#define Bias 1023
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+#define Emax 1023
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+#define Emin (-1022)
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+#define Exp_1 0x3ff00000
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+#define Exp_11 0x3ff00000
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+#define Ebits 11
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+#define Frac_mask 0xfffff
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+#define Frac_mask1 0xfffff
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+#define Ten_pmax 22
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+#define Bletch 0x10
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+#define Bndry_mask 0xfffff
|
|
|
+#define Bndry_mask1 0xfffff
|
|
|
+#define LSB 1
|
|
|
+#define Sign_bit 0x80000000
|
|
|
+#define Log2P 1
|
|
|
+#define Tiny0 0
|
|
|
+#define Tiny1 1
|
|
|
+#define Quick_max 14
|
|
|
+#define Int_max 14
|
|
|
+#ifndef NO_IEEE_Scale
|
|
|
+#define Avoid_Underflow
|
|
|
+#ifdef Flush_Denorm /* debugging option */
|
|
|
+#undef Sudden_Underflow
|
|
|
+#endif
|
|
|
+#endif
|
|
|
+
|
|
|
+#ifndef Flt_Rounds
|
|
|
+#ifdef FLT_ROUNDS
|
|
|
+#define Flt_Rounds FLT_ROUNDS
|
|
|
+#else
|
|
|
+#define Flt_Rounds 1
|
|
|
+#endif
|
|
|
+#endif /*Flt_Rounds*/
|
|
|
+
|
|
|
+#ifdef Honor_FLT_ROUNDS
|
|
|
+#undef Check_FLT_ROUNDS
|
|
|
+#define Check_FLT_ROUNDS
|
|
|
+#else
|
|
|
+#define Rounding Flt_Rounds
|
|
|
+#endif
|
|
|
+
|
|
|
+#else /* ifndef IEEE_Arith */
|
|
|
+#undef Check_FLT_ROUNDS
|
|
|
+#undef Honor_FLT_ROUNDS
|
|
|
+#undef SET_INEXACT
|
|
|
+#undef Sudden_Underflow
|
|
|
+#define Sudden_Underflow
|
|
|
+#ifdef IBM
|
|
|
+#undef Flt_Rounds
|
|
|
+#define Flt_Rounds 0
|
|
|
+#define Exp_shift 24
|
|
|
+#define Exp_shift1 24
|
|
|
+#define Exp_msk1 0x1000000
|
|
|
+#define Exp_msk11 0x1000000
|
|
|
+#define Exp_mask 0x7f000000
|
|
|
+#define P 14
|
|
|
+#define Nbits 56
|
|
|
+#define Bias 65
|
|
|
+#define Emax 248
|
|
|
+#define Emin (-260)
|
|
|
+#define Exp_1 0x41000000
|
|
|
+#define Exp_11 0x41000000
|
|
|
+#define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
|
|
|
+#define Frac_mask 0xffffff
|
|
|
+#define Frac_mask1 0xffffff
|
|
|
+#define Bletch 4
|
|
|
+#define Ten_pmax 22
|
|
|
+#define Bndry_mask 0xefffff
|
|
|
+#define Bndry_mask1 0xffffff
|
|
|
+#define LSB 1
|
|
|
+#define Sign_bit 0x80000000
|
|
|
+#define Log2P 4
|
|
|
+#define Tiny0 0x100000
|
|
|
+#define Tiny1 0
|
|
|
+#define Quick_max 14
|
|
|
+#define Int_max 15
|
|
|
+#else /* VAX */
|
|
|
+#undef Flt_Rounds
|
|
|
+#define Flt_Rounds 1
|
|
|
+#define Exp_shift 23
|
|
|
+#define Exp_shift1 7
|
|
|
+#define Exp_msk1 0x80
|
|
|
+#define Exp_msk11 0x800000
|
|
|
+#define Exp_mask 0x7f80
|
|
|
+#define P 56
|
|
|
+#define Nbits 56
|
|
|
+#define Bias 129
|
|
|
+#define Emax 126
|
|
|
+#define Emin (-129)
|
|
|
+#define Exp_1 0x40800000
|
|
|
+#define Exp_11 0x4080
|
|
|
+#define Ebits 8
|
|
|
+#define Frac_mask 0x7fffff
|
|
|
+#define Frac_mask1 0xffff007f
|
|
|
+#define Ten_pmax 24
|
|
|
+#define Bletch 2
|
|
|
+#define Bndry_mask 0xffff007f
|
|
|
+#define Bndry_mask1 0xffff007f
|
|
|
+#define LSB 0x10000
|
|
|
+#define Sign_bit 0x8000
|
|
|
+#define Log2P 1
|
|
|
+#define Tiny0 0x80
|
|
|
+#define Tiny1 0
|
|
|
+#define Quick_max 15
|
|
|
+#define Int_max 15
|
|
|
+#endif /* IBM, VAX */
|
|
|
+#endif /* IEEE_Arith */
|
|
|
+
|
|
|
+#ifndef IEEE_Arith
|
|
|
+#define ROUND_BIASED
|
|
|
+#else
|
|
|
+#ifdef ROUND_BIASED_without_Round_Up
|
|
|
+#undef ROUND_BIASED
|
|
|
+#define ROUND_BIASED
|
|
|
+#endif
|
|
|
+#endif
|
|
|
+
|
|
|
+#ifdef RND_PRODQUOT
|
|
|
+#define rounded_product(a,b) a = rnd_prod(a, b)
|
|
|
+#define rounded_quotient(a,b) a = rnd_quot(a, b)
|
|
|
+#ifdef KR_headers
|
|
|
+extern double rnd_prod(), rnd_quot();
|
|
|
+#else
|
|
|
+extern double rnd_prod(double, double), rnd_quot(double, double);
|
|
|
+#endif
|
|
|
+#else
|
|
|
+#define rounded_product(a,b) a *= b
|
|
|
+#define rounded_quotient(a,b) a /= b
|
|
|
+#endif
|
|
|
+
|
|
|
+#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
|
|
|
+#define Big1 0xffffffff
|
|
|
+
|
|
|
+#ifndef Pack_32
|
|
|
+#define Pack_32
|
|
|
+#endif
|
|
|
+
|
|
|
+typedef struct BCinfo BCinfo;
|
|
|
+ struct
|
|
|
+BCinfo { int dp0, dp1, dplen, dsign, e0, inexact, nd, nd0, rounding, scale, uflchk; };
|
|
|
+
|
|
|
+#ifdef KR_headers
|
|
|
+#define FFFFFFFF ((((unsigned long)0xffff)<<16)|(unsigned long)0xffff)
|
|
|
+#else
|
|
|
+#define FFFFFFFF 0xffffffffUL
|
|
|
+#endif
|
|
|
+
|
|
|
+#ifdef NO_LONG_LONG
|
|
|
+#undef ULLong
|
|
|
+#ifdef Just_16
|
|
|
+#undef Pack_32
|
|
|
+/* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
|
|
|
+ * This makes some inner loops simpler and sometimes saves work
|
|
|
+ * during multiplications, but it often seems to make things slightly
|
|
|
+ * slower. Hence the default is now to store 32 bits per Long.
|
|
|
+ */
|
|
|
+#endif
|
|
|
+#else /* long long available */
|
|
|
+#ifndef Llong
|
|
|
+#define Llong long long
|
|
|
+#endif
|
|
|
+#ifndef ULLong
|
|
|
+#define ULLong unsigned Llong
|
|
|
+#endif
|
|
|
+#endif /* NO_LONG_LONG */
|
|
|
+
|
|
|
+#ifndef MULTIPLE_THREADS
|
|
|
+#define ACQUIRE_DTOA_LOCK(n) /*nothing*/
|
|
|
+#define FREE_DTOA_LOCK(n) /*nothing*/
|
|
|
+#endif
|
|
|
+
|
|
|
+#define Kmax 7
|
|
|
+
|
|
|
+#ifdef __cplusplus
|
|
|
+extern "C" double fpconv_strtod(const char *s00, char **se);
|
|
|
+extern "C" char *dtoa(double d, int mode, int ndigits,
|
|
|
+ int *decpt, int *sign, char **rve);
|
|
|
+#endif
|
|
|
+
|
|
|
+ struct
|
|
|
+Bigint {
|
|
|
+ struct Bigint *next;
|
|
|
+ int k, maxwds, sign, wds;
|
|
|
+ ULong x[1];
|
|
|
+ };
|
|
|
+
|
|
|
+ typedef struct Bigint Bigint;
|
|
|
+
|
|
|
+ static Bigint *freelist[Kmax+1];
|
|
|
+
|
|
|
+ static Bigint *
|
|
|
+Balloc
|
|
|
+#ifdef KR_headers
|
|
|
+ (k) int k;
|
|
|
+#else
|
|
|
+ (int k)
|
|
|
+#endif
|
|
|
+{
|
|
|
+ int x;
|
|
|
+ Bigint *rv;
|
|
|
+#ifndef Omit_Private_Memory
|
|
|
+ unsigned int len;
|
|
|
+#endif
|
|
|
+
|
|
|
+ ACQUIRE_DTOA_LOCK(0);
|
|
|
+ /* The k > Kmax case does not need ACQUIRE_DTOA_LOCK(0), */
|
|
|
+ /* but this case seems very unlikely. */
|
|
|
+ if (k <= Kmax && (rv = freelist[k]))
|
|
|
+ freelist[k] = rv->next;
|
|
|
+ else {
|
|
|
+ x = 1 << k;
|
|
|
+#ifdef Omit_Private_Memory
|
|
|
+ rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong));
|
|
|
+#else
|
|
|
+ len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)
|
|
|
+ /sizeof(double);
|
|
|
+ if (k <= Kmax && pmem_next - private_mem + len <= PRIVATE_mem) {
|
|
|
+ rv = (Bigint*)pmem_next;
|
|
|
+ pmem_next += len;
|
|
|
+ }
|
|
|
+ else
|
|
|
+ rv = (Bigint*)MALLOC(len*sizeof(double));
|
|
|
+#endif
|
|
|
+ rv->k = k;
|
|
|
+ rv->maxwds = x;
|
|
|
+ }
|
|
|
+ FREE_DTOA_LOCK(0);
|
|
|
+ rv->sign = rv->wds = 0;
|
|
|
+ return rv;
|
|
|
+ }
|
|
|
+
|
|
|
+ static void
|
|
|
+Bfree
|
|
|
+#ifdef KR_headers
|
|
|
+ (v) Bigint *v;
|
|
|
+#else
|
|
|
+ (Bigint *v)
|
|
|
+#endif
|
|
|
+{
|
|
|
+ if (v) {
|
|
|
+ if (v->k > Kmax)
|
|
|
+#ifdef FREE
|
|
|
+ FREE((void*)v);
|
|
|
+#else
|
|
|
+ free((void*)v);
|
|
|
+#endif
|
|
|
+ else {
|
|
|
+ ACQUIRE_DTOA_LOCK(0);
|
|
|
+ v->next = freelist[v->k];
|
|
|
+ freelist[v->k] = v;
|
|
|
+ FREE_DTOA_LOCK(0);
|
|
|
+ }
|
|
|
+ }
|
|
|
+ }
|
|
|
+
|
|
|
+#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
|
|
|
+y->wds*sizeof(Long) + 2*sizeof(int))
|
|
|
+
|
|
|
+ static Bigint *
|
|
|
+multadd
|
|
|
+#ifdef KR_headers
|
|
|
+ (b, m, a) Bigint *b; int m, a;
|
|
|
+#else
|
|
|
+ (Bigint *b, int m, int a) /* multiply by m and add a */
|
|
|
+#endif
|
|
|
+{
|
|
|
+ int i, wds;
|
|
|
+#ifdef ULLong
|
|
|
+ ULong *x;
|
|
|
+ ULLong carry, y;
|
|
|
+#else
|
|
|
+ ULong carry, *x, y;
|
|
|
+#ifdef Pack_32
|
|
|
+ ULong xi, z;
|
|
|
+#endif
|
|
|
+#endif
|
|
|
+ Bigint *b1;
|
|
|
+
|
|
|
+ wds = b->wds;
|
|
|
+ x = b->x;
|
|
|
+ i = 0;
|
|
|
+ carry = a;
|
|
|
+ do {
|
|
|
+#ifdef ULLong
|
|
|
+ y = *x * (ULLong)m + carry;
|
|
|
+ carry = y >> 32;
|
|
|
+ *x++ = y & FFFFFFFF;
|
|
|
+#else
|
|
|
+#ifdef Pack_32
|
|
|
+ xi = *x;
|
|
|
+ y = (xi & 0xffff) * m + carry;
|
|
|
+ z = (xi >> 16) * m + (y >> 16);
|
|
|
+ carry = z >> 16;
|
|
|
+ *x++ = (z << 16) + (y & 0xffff);
|
|
|
+#else
|
|
|
+ y = *x * m + carry;
|
|
|
+ carry = y >> 16;
|
|
|
+ *x++ = y & 0xffff;
|
|
|
+#endif
|
|
|
+#endif
|
|
|
+ }
|
|
|
+ while(++i < wds);
|
|
|
+ if (carry) {
|
|
|
+ if (wds >= b->maxwds) {
|
|
|
+ b1 = Balloc(b->k+1);
|
|
|
+ Bcopy(b1, b);
|
|
|
+ Bfree(b);
|
|
|
+ b = b1;
|
|
|
+ }
|
|
|
+ b->x[wds++] = carry;
|
|
|
+ b->wds = wds;
|
|
|
+ }
|
|
|
+ return b;
|
|
|
+ }
|
|
|
+
|
|
|
+ static Bigint *
|
|
|
+s2b
|
|
|
+#ifdef KR_headers
|
|
|
+ (s, nd0, nd, y9, dplen) CONST char *s; int nd0, nd, dplen; ULong y9;
|
|
|
+#else
|
|
|
+ (const char *s, int nd0, int nd, ULong y9, int dplen)
|
|
|
+#endif
|
|
|
+{
|
|
|
+ Bigint *b;
|
|
|
+ int i, k;
|
|
|
+ Long x, y;
|
|
|
+
|
|
|
+ x = (nd + 8) / 9;
|
|
|
+ for(k = 0, y = 1; x > y; y <<= 1, k++) ;
|
|
|
+#ifdef Pack_32
|
|
|
+ b = Balloc(k);
|
|
|
+ b->x[0] = y9;
|
|
|
+ b->wds = 1;
|
|
|
+#else
|
|
|
+ b = Balloc(k+1);
|
|
|
+ b->x[0] = y9 & 0xffff;
|
|
|
+ b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
|
|
|
+#endif
|
|
|
+
|
|
|
+ i = 9;
|
|
|
+ if (9 < nd0) {
|
|
|
+ s += 9;
|
|
|
+ do b = multadd(b, 10, *s++ - '0');
|
|
|
+ while(++i < nd0);
|
|
|
+ s += dplen;
|
|
|
+ }
|
|
|
+ else
|
|
|
+ s += dplen + 9;
|
|
|
+ for(; i < nd; i++)
|
|
|
+ b = multadd(b, 10, *s++ - '0');
|
|
|
+ return b;
|
|
|
+ }
|
|
|
+
|
|
|
+ static int
|
|
|
+hi0bits
|
|
|
+#ifdef KR_headers
|
|
|
+ (x) ULong x;
|
|
|
+#else
|
|
|
+ (ULong x)
|
|
|
+#endif
|
|
|
+{
|
|
|
+ int k = 0;
|
|
|
+
|
|
|
+ if (!(x & 0xffff0000)) {
|
|
|
+ k = 16;
|
|
|
+ x <<= 16;
|
|
|
+ }
|
|
|
+ if (!(x & 0xff000000)) {
|
|
|
+ k += 8;
|
|
|
+ x <<= 8;
|
|
|
+ }
|
|
|
+ if (!(x & 0xf0000000)) {
|
|
|
+ k += 4;
|
|
|
+ x <<= 4;
|
|
|
+ }
|
|
|
+ if (!(x & 0xc0000000)) {
|
|
|
+ k += 2;
|
|
|
+ x <<= 2;
|
|
|
+ }
|
|
|
+ if (!(x & 0x80000000)) {
|
|
|
+ k++;
|
|
|
+ if (!(x & 0x40000000))
|
|
|
+ return 32;
|
|
|
+ }
|
|
|
+ return k;
|
|
|
+ }
|
|
|
+
|
|
|
+ static int
|
|
|
+lo0bits
|
|
|
+#ifdef KR_headers
|
|
|
+ (y) ULong *y;
|
|
|
+#else
|
|
|
+ (ULong *y)
|
|
|
+#endif
|
|
|
+{
|
|
|
+ int k;
|
|
|
+ ULong x = *y;
|
|
|
+
|
|
|
+ if (x & 7) {
|
|
|
+ if (x & 1)
|
|
|
+ return 0;
|
|
|
+ if (x & 2) {
|
|
|
+ *y = x >> 1;
|
|
|
+ return 1;
|
|
|
+ }
|
|
|
+ *y = x >> 2;
|
|
|
+ return 2;
|
|
|
+ }
|
|
|
+ k = 0;
|
|
|
+ if (!(x & 0xffff)) {
|
|
|
+ k = 16;
|
|
|
+ x >>= 16;
|
|
|
+ }
|
|
|
+ if (!(x & 0xff)) {
|
|
|
+ k += 8;
|
|
|
+ x >>= 8;
|
|
|
+ }
|
|
|
+ if (!(x & 0xf)) {
|
|
|
+ k += 4;
|
|
|
+ x >>= 4;
|
|
|
+ }
|
|
|
+ if (!(x & 0x3)) {
|
|
|
+ k += 2;
|
|
|
+ x >>= 2;
|
|
|
+ }
|
|
|
+ if (!(x & 1)) {
|
|
|
+ k++;
|
|
|
+ x >>= 1;
|
|
|
+ if (!x)
|
|
|
+ return 32;
|
|
|
+ }
|
|
|
+ *y = x;
|
|
|
+ return k;
|
|
|
+ }
|
|
|
+
|
|
|
+ static Bigint *
|
|
|
+i2b
|
|
|
+#ifdef KR_headers
|
|
|
+ (i) int i;
|
|
|
+#else
|
|
|
+ (int i)
|
|
|
+#endif
|
|
|
+{
|
|
|
+ Bigint *b;
|
|
|
+
|
|
|
+ b = Balloc(1);
|
|
|
+ b->x[0] = i;
|
|
|
+ b->wds = 1;
|
|
|
+ return b;
|
|
|
+ }
|
|
|
+
|
|
|
+ static Bigint *
|
|
|
+mult
|
|
|
+#ifdef KR_headers
|
|
|
+ (a, b) Bigint *a, *b;
|
|
|
+#else
|
|
|
+ (Bigint *a, Bigint *b)
|
|
|
+#endif
|
|
|
+{
|
|
|
+ Bigint *c;
|
|
|
+ int k, wa, wb, wc;
|
|
|
+ ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
|
|
|
+ ULong y;
|
|
|
+#ifdef ULLong
|
|
|
+ ULLong carry, z;
|
|
|
+#else
|
|
|
+ ULong carry, z;
|
|
|
+#ifdef Pack_32
|
|
|
+ ULong z2;
|
|
|
+#endif
|
|
|
+#endif
|
|
|
+
|
|
|
+ if (a->wds < b->wds) {
|
|
|
+ c = a;
|
|
|
+ a = b;
|
|
|
+ b = c;
|
|
|
+ }
|
|
|
+ k = a->k;
|
|
|
+ wa = a->wds;
|
|
|
+ wb = b->wds;
|
|
|
+ wc = wa + wb;
|
|
|
+ if (wc > a->maxwds)
|
|
|
+ k++;
|
|
|
+ c = Balloc(k);
|
|
|
+ for(x = c->x, xa = x + wc; x < xa; x++)
|
|
|
+ *x = 0;
|
|
|
+ xa = a->x;
|
|
|
+ xae = xa + wa;
|
|
|
+ xb = b->x;
|
|
|
+ xbe = xb + wb;
|
|
|
+ xc0 = c->x;
|
|
|
+#ifdef ULLong
|
|
|
+ for(; xb < xbe; xc0++) {
|
|
|
+ if ((y = *xb++)) {
|
|
|
+ x = xa;
|
|
|
+ xc = xc0;
|
|
|
+ carry = 0;
|
|
|
+ do {
|
|
|
+ z = *x++ * (ULLong)y + *xc + carry;
|
|
|
+ carry = z >> 32;
|
|
|
+ *xc++ = z & FFFFFFFF;
|
|
|
+ }
|
|
|
+ while(x < xae);
|
|
|
+ *xc = carry;
|
|
|
+ }
|
|
|
+ }
|
|
|
+#else
|
|
|
+#ifdef Pack_32
|
|
|
+ for(; xb < xbe; xb++, xc0++) {
|
|
|
+ if (y = *xb & 0xffff) {
|
|
|
+ x = xa;
|
|
|
+ xc = xc0;
|
|
|
+ carry = 0;
|
|
|
+ do {
|
|
|
+ z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
|
|
|
+ carry = z >> 16;
|
|
|
+ z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
|
|
|
+ carry = z2 >> 16;
|
|
|
+ Storeinc(xc, z2, z);
|
|
|
+ }
|
|
|
+ while(x < xae);
|
|
|
+ *xc = carry;
|
|
|
+ }
|
|
|
+ if (y = *xb >> 16) {
|
|
|
+ x = xa;
|
|
|
+ xc = xc0;
|
|
|
+ carry = 0;
|
|
|
+ z2 = *xc;
|
|
|
+ do {
|
|
|
+ z = (*x & 0xffff) * y + (*xc >> 16) + carry;
|
|
|
+ carry = z >> 16;
|
|
|
+ Storeinc(xc, z, z2);
|
|
|
+ z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
|
|
|
+ carry = z2 >> 16;
|
|
|
+ }
|
|
|
+ while(x < xae);
|
|
|
+ *xc = z2;
|
|
|
+ }
|
|
|
+ }
|
|
|
+#else
|
|
|
+ for(; xb < xbe; xc0++) {
|
|
|
+ if (y = *xb++) {
|
|
|
+ x = xa;
|
|
|
+ xc = xc0;
|
|
|
+ carry = 0;
|
|
|
+ do {
|
|
|
+ z = *x++ * y + *xc + carry;
|
|
|
+ carry = z >> 16;
|
|
|
+ *xc++ = z & 0xffff;
|
|
|
+ }
|
|
|
+ while(x < xae);
|
|
|
+ *xc = carry;
|
|
|
+ }
|
|
|
+ }
|
|
|
+#endif
|
|
|
+#endif
|
|
|
+ for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
|
|
|
+ c->wds = wc;
|
|
|
+ return c;
|
|
|
+ }
|
|
|
+
|
|
|
+ static Bigint *p5s;
|
|
|
+
|
|
|
+ static Bigint *
|
|
|
+pow5mult
|
|
|
+#ifdef KR_headers
|
|
|
+ (b, k) Bigint *b; int k;
|
|
|
+#else
|
|
|
+ (Bigint *b, int k)
|
|
|
+#endif
|
|
|
+{
|
|
|
+ Bigint *b1, *p5, *p51;
|
|
|
+ int i;
|
|
|
+ static int p05[3] = { 5, 25, 125 };
|
|
|
+
|
|
|
+ if ((i = k & 3))
|
|
|
+ b = multadd(b, p05[i-1], 0);
|
|
|
+
|
|
|
+ if (!(k >>= 2))
|
|
|
+ return b;
|
|
|
+ if (!(p5 = p5s)) {
|
|
|
+ /* first time */
|
|
|
+#ifdef MULTIPLE_THREADS
|
|
|
+ ACQUIRE_DTOA_LOCK(1);
|
|
|
+ if (!(p5 = p5s)) {
|
|
|
+ p5 = p5s = i2b(625);
|
|
|
+ p5->next = 0;
|
|
|
+ }
|
|
|
+ FREE_DTOA_LOCK(1);
|
|
|
+#else
|
|
|
+ p5 = p5s = i2b(625);
|
|
|
+ p5->next = 0;
|
|
|
+#endif
|
|
|
+ }
|
|
|
+ for(;;) {
|
|
|
+ if (k & 1) {
|
|
|
+ b1 = mult(b, p5);
|
|
|
+ Bfree(b);
|
|
|
+ b = b1;
|
|
|
+ }
|
|
|
+ if (!(k >>= 1))
|
|
|
+ break;
|
|
|
+ if (!(p51 = p5->next)) {
|
|
|
+#ifdef MULTIPLE_THREADS
|
|
|
+ ACQUIRE_DTOA_LOCK(1);
|
|
|
+ if (!(p51 = p5->next)) {
|
|
|
+ p51 = p5->next = mult(p5,p5);
|
|
|
+ p51->next = 0;
|
|
|
+ }
|
|
|
+ FREE_DTOA_LOCK(1);
|
|
|
+#else
|
|
|
+ p51 = p5->next = mult(p5,p5);
|
|
|
+ p51->next = 0;
|
|
|
+#endif
|
|
|
+ }
|
|
|
+ p5 = p51;
|
|
|
+ }
|
|
|
+ return b;
|
|
|
+ }
|
|
|
+
|
|
|
+ static Bigint *
|
|
|
+lshift
|
|
|
+#ifdef KR_headers
|
|
|
+ (b, k) Bigint *b; int k;
|
|
|
+#else
|
|
|
+ (Bigint *b, int k)
|
|
|
+#endif
|
|
|
+{
|
|
|
+ int i, k1, n, n1;
|
|
|
+ Bigint *b1;
|
|
|
+ ULong *x, *x1, *xe, z;
|
|
|
+
|
|
|
+#ifdef Pack_32
|
|
|
+ n = k >> 5;
|
|
|
+#else
|
|
|
+ n = k >> 4;
|
|
|
+#endif
|
|
|
+ k1 = b->k;
|
|
|
+ n1 = n + b->wds + 1;
|
|
|
+ for(i = b->maxwds; n1 > i; i <<= 1)
|
|
|
+ k1++;
|
|
|
+ b1 = Balloc(k1);
|
|
|
+ x1 = b1->x;
|
|
|
+ for(i = 0; i < n; i++)
|
|
|
+ *x1++ = 0;
|
|
|
+ x = b->x;
|
|
|
+ xe = x + b->wds;
|
|
|
+#ifdef Pack_32
|
|
|
+ if (k &= 0x1f) {
|
|
|
+ k1 = 32 - k;
|
|
|
+ z = 0;
|
|
|
+ do {
|
|
|
+ *x1++ = *x << k | z;
|
|
|
+ z = *x++ >> k1;
|
|
|
+ }
|
|
|
+ while(x < xe);
|
|
|
+ if ((*x1 = z))
|
|
|
+ ++n1;
|
|
|
+ }
|
|
|
+#else
|
|
|
+ if (k &= 0xf) {
|
|
|
+ k1 = 16 - k;
|
|
|
+ z = 0;
|
|
|
+ do {
|
|
|
+ *x1++ = *x << k & 0xffff | z;
|
|
|
+ z = *x++ >> k1;
|
|
|
+ }
|
|
|
+ while(x < xe);
|
|
|
+ if (*x1 = z)
|
|
|
+ ++n1;
|
|
|
+ }
|
|
|
+#endif
|
|
|
+ else do
|
|
|
+ *x1++ = *x++;
|
|
|
+ while(x < xe);
|
|
|
+ b1->wds = n1 - 1;
|
|
|
+ Bfree(b);
|
|
|
+ return b1;
|
|
|
+ }
|
|
|
+
|
|
|
+ static int
|
|
|
+cmp
|
|
|
+#ifdef KR_headers
|
|
|
+ (a, b) Bigint *a, *b;
|
|
|
+#else
|
|
|
+ (Bigint *a, Bigint *b)
|
|
|
+#endif
|
|
|
+{
|
|
|
+ ULong *xa, *xa0, *xb, *xb0;
|
|
|
+ int i, j;
|
|
|
+
|
|
|
+ i = a->wds;
|
|
|
+ j = b->wds;
|
|
|
+#ifdef DEBUG
|
|
|
+ if (i > 1 && !a->x[i-1])
|
|
|
+ Bug("cmp called with a->x[a->wds-1] == 0");
|
|
|
+ if (j > 1 && !b->x[j-1])
|
|
|
+ Bug("cmp called with b->x[b->wds-1] == 0");
|
|
|
+#endif
|
|
|
+ if (i -= j)
|
|
|
+ return i;
|
|
|
+ xa0 = a->x;
|
|
|
+ xa = xa0 + j;
|
|
|
+ xb0 = b->x;
|
|
|
+ xb = xb0 + j;
|
|
|
+ for(;;) {
|
|
|
+ if (*--xa != *--xb)
|
|
|
+ return *xa < *xb ? -1 : 1;
|
|
|
+ if (xa <= xa0)
|
|
|
+ break;
|
|
|
+ }
|
|
|
+ return 0;
|
|
|
+ }
|
|
|
+
|
|
|
+ static Bigint *
|
|
|
+diff
|
|
|
+#ifdef KR_headers
|
|
|
+ (a, b) Bigint *a, *b;
|
|
|
+#else
|
|
|
+ (Bigint *a, Bigint *b)
|
|
|
+#endif
|
|
|
+{
|
|
|
+ Bigint *c;
|
|
|
+ int i, wa, wb;
|
|
|
+ ULong *xa, *xae, *xb, *xbe, *xc;
|
|
|
+#ifdef ULLong
|
|
|
+ ULLong borrow, y;
|
|
|
+#else
|
|
|
+ ULong borrow, y;
|
|
|
+#ifdef Pack_32
|
|
|
+ ULong z;
|
|
|
+#endif
|
|
|
+#endif
|
|
|
+
|
|
|
+ i = cmp(a,b);
|
|
|
+ if (!i) {
|
|
|
+ c = Balloc(0);
|
|
|
+ c->wds = 1;
|
|
|
+ c->x[0] = 0;
|
|
|
+ return c;
|
|
|
+ }
|
|
|
+ if (i < 0) {
|
|
|
+ c = a;
|
|
|
+ a = b;
|
|
|
+ b = c;
|
|
|
+ i = 1;
|
|
|
+ }
|
|
|
+ else
|
|
|
+ i = 0;
|
|
|
+ c = Balloc(a->k);
|
|
|
+ c->sign = i;
|
|
|
+ wa = a->wds;
|
|
|
+ xa = a->x;
|
|
|
+ xae = xa + wa;
|
|
|
+ wb = b->wds;
|
|
|
+ xb = b->x;
|
|
|
+ xbe = xb + wb;
|
|
|
+ xc = c->x;
|
|
|
+ borrow = 0;
|
|
|
+#ifdef ULLong
|
|
|
+ do {
|
|
|
+ y = (ULLong)*xa++ - *xb++ - borrow;
|
|
|
+ borrow = y >> 32 & (ULong)1;
|
|
|
+ *xc++ = y & FFFFFFFF;
|
|
|
+ }
|
|
|
+ while(xb < xbe);
|
|
|
+ while(xa < xae) {
|
|
|
+ y = *xa++ - borrow;
|
|
|
+ borrow = y >> 32 & (ULong)1;
|
|
|
+ *xc++ = y & FFFFFFFF;
|
|
|
+ }
|
|
|
+#else
|
|
|
+#ifdef Pack_32
|
|
|
+ do {
|
|
|
+ y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
|
|
|
+ borrow = (y & 0x10000) >> 16;
|
|
|
+ z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
|
|
|
+ borrow = (z & 0x10000) >> 16;
|
|
|
+ Storeinc(xc, z, y);
|
|
|
+ }
|
|
|
+ while(xb < xbe);
|
|
|
+ while(xa < xae) {
|
|
|
+ y = (*xa & 0xffff) - borrow;
|
|
|
+ borrow = (y & 0x10000) >> 16;
|
|
|
+ z = (*xa++ >> 16) - borrow;
|
|
|
+ borrow = (z & 0x10000) >> 16;
|
|
|
+ Storeinc(xc, z, y);
|
|
|
+ }
|
|
|
+#else
|
|
|
+ do {
|
|
|
+ y = *xa++ - *xb++ - borrow;
|
|
|
+ borrow = (y & 0x10000) >> 16;
|
|
|
+ *xc++ = y & 0xffff;
|
|
|
+ }
|
|
|
+ while(xb < xbe);
|
|
|
+ while(xa < xae) {
|
|
|
+ y = *xa++ - borrow;
|
|
|
+ borrow = (y & 0x10000) >> 16;
|
|
|
+ *xc++ = y & 0xffff;
|
|
|
+ }
|
|
|
+#endif
|
|
|
+#endif
|
|
|
+ while(!*--xc)
|
|
|
+ wa--;
|
|
|
+ c->wds = wa;
|
|
|
+ return c;
|
|
|
+ }
|
|
|
+
|
|
|
+ static double
|
|
|
+ulp
|
|
|
+#ifdef KR_headers
|
|
|
+ (x) U *x;
|
|
|
+#else
|
|
|
+ (U *x)
|
|
|
+#endif
|
|
|
+{
|
|
|
+ Long L;
|
|
|
+ U u;
|
|
|
+
|
|
|
+ L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
|
|
|
+#ifndef Avoid_Underflow
|
|
|
+#ifndef Sudden_Underflow
|
|
|
+ if (L > 0) {
|
|
|
+#endif
|
|
|
+#endif
|
|
|
+#ifdef IBM
|
|
|
+ L |= Exp_msk1 >> 4;
|
|
|
+#endif
|
|
|
+ word0(&u) = L;
|
|
|
+ word1(&u) = 0;
|
|
|
+#ifndef Avoid_Underflow
|
|
|
+#ifndef Sudden_Underflow
|
|
|
+ }
|
|
|
+ else {
|
|
|
+ L = -L >> Exp_shift;
|
|
|
+ if (L < Exp_shift) {
|
|
|
+ word0(&u) = 0x80000 >> L;
|
|
|
+ word1(&u) = 0;
|
|
|
+ }
|
|
|
+ else {
|
|
|
+ word0(&u) = 0;
|
|
|
+ L -= Exp_shift;
|
|
|
+ word1(&u) = L >= 31 ? 1 : 1 << 31 - L;
|
|
|
+ }
|
|
|
+ }
|
|
|
+#endif
|
|
|
+#endif
|
|
|
+ return dval(&u);
|
|
|
+ }
|
|
|
+
|
|
|
+ static double
|
|
|
+b2d
|
|
|
+#ifdef KR_headers
|
|
|
+ (a, e) Bigint *a; int *e;
|
|
|
+#else
|
|
|
+ (Bigint *a, int *e)
|
|
|
+#endif
|
|
|
+{
|
|
|
+ ULong *xa, *xa0, w, y, z;
|
|
|
+ int k;
|
|
|
+ U d;
|
|
|
+#ifdef VAX
|
|
|
+ ULong d0, d1;
|
|
|
+#else
|
|
|
+#define d0 word0(&d)
|
|
|
+#define d1 word1(&d)
|
|
|
+#endif
|
|
|
+
|
|
|
+ xa0 = a->x;
|
|
|
+ xa = xa0 + a->wds;
|
|
|
+ y = *--xa;
|
|
|
+#ifdef DEBUG
|
|
|
+ if (!y) Bug("zero y in b2d");
|
|
|
+#endif
|
|
|
+ k = hi0bits(y);
|
|
|
+ *e = 32 - k;
|
|
|
+#ifdef Pack_32
|
|
|
+ if (k < Ebits) {
|
|
|
+ d0 = Exp_1 | y >> (Ebits - k);
|
|
|
+ w = xa > xa0 ? *--xa : 0;
|
|
|
+ d1 = y << ((32-Ebits) + k) | w >> (Ebits - k);
|
|
|
+ goto ret_d;
|
|
|
+ }
|
|
|
+ z = xa > xa0 ? *--xa : 0;
|
|
|
+ if (k -= Ebits) {
|
|
|
+ d0 = Exp_1 | y << k | z >> (32 - k);
|
|
|
+ y = xa > xa0 ? *--xa : 0;
|
|
|
+ d1 = z << k | y >> (32 - k);
|
|
|
+ }
|
|
|
+ else {
|
|
|
+ d0 = Exp_1 | y;
|
|
|
+ d1 = z;
|
|
|
+ }
|
|
|
+#else
|
|
|
+ if (k < Ebits + 16) {
|
|
|
+ z = xa > xa0 ? *--xa : 0;
|
|
|
+ d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
|
|
|
+ w = xa > xa0 ? *--xa : 0;
|
|
|
+ y = xa > xa0 ? *--xa : 0;
|
|
|
+ d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
|
|
|
+ goto ret_d;
|
|
|
+ }
|
|
|
+ z = xa > xa0 ? *--xa : 0;
|
|
|
+ w = xa > xa0 ? *--xa : 0;
|
|
|
+ k -= Ebits + 16;
|
|
|
+ d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
|
|
|
+ y = xa > xa0 ? *--xa : 0;
|
|
|
+ d1 = w << k + 16 | y << k;
|
|
|
+#endif
|
|
|
+ ret_d:
|
|
|
+#ifdef VAX
|
|
|
+ word0(&d) = d0 >> 16 | d0 << 16;
|
|
|
+ word1(&d) = d1 >> 16 | d1 << 16;
|
|
|
+#else
|
|
|
+#undef d0
|
|
|
+#undef d1
|
|
|
+#endif
|
|
|
+ return dval(&d);
|
|
|
+ }
|
|
|
+
|
|
|
+ static Bigint *
|
|
|
+d2b
|
|
|
+#ifdef KR_headers
|
|
|
+ (d, e, bits) U *d; int *e, *bits;
|
|
|
+#else
|
|
|
+ (U *d, int *e, int *bits)
|
|
|
+#endif
|
|
|
+{
|
|
|
+ Bigint *b;
|
|
|
+ int de, k;
|
|
|
+ ULong *x, y, z;
|
|
|
+#ifndef Sudden_Underflow
|
|
|
+ int i;
|
|
|
+#endif
|
|
|
+#ifdef VAX
|
|
|
+ ULong d0, d1;
|
|
|
+ d0 = word0(d) >> 16 | word0(d) << 16;
|
|
|
+ d1 = word1(d) >> 16 | word1(d) << 16;
|
|
|
+#else
|
|
|
+#define d0 word0(d)
|
|
|
+#define d1 word1(d)
|
|
|
+#endif
|
|
|
+
|
|
|
+#ifdef Pack_32
|
|
|
+ b = Balloc(1);
|
|
|
+#else
|
|
|
+ b = Balloc(2);
|
|
|
+#endif
|
|
|
+ x = b->x;
|
|
|
+
|
|
|
+ z = d0 & Frac_mask;
|
|
|
+ d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
|
|
|
+#ifdef Sudden_Underflow
|
|
|
+ de = (int)(d0 >> Exp_shift);
|
|
|
+#ifndef IBM
|
|
|
+ z |= Exp_msk11;
|
|
|
+#endif
|
|
|
+#else
|
|
|
+ if ((de = (int)(d0 >> Exp_shift)))
|
|
|
+ z |= Exp_msk1;
|
|
|
+#endif
|
|
|
+#ifdef Pack_32
|
|
|
+ if ((y = d1)) {
|
|
|
+ if ((k = lo0bits(&y))) {
|
|
|
+ x[0] = y | z << (32 - k);
|
|
|
+ z >>= k;
|
|
|
+ }
|
|
|
+ else
|
|
|
+ x[0] = y;
|
|
|
+#ifndef Sudden_Underflow
|
|
|
+ i =
|
|
|
+#endif
|
|
|
+ b->wds = (x[1] = z) ? 2 : 1;
|
|
|
+ }
|
|
|
+ else {
|
|
|
+ k = lo0bits(&z);
|
|
|
+ x[0] = z;
|
|
|
+#ifndef Sudden_Underflow
|
|
|
+ i =
|
|
|
+#endif
|
|
|
+ b->wds = 1;
|
|
|
+ k += 32;
|
|
|
+ }
|
|
|
+#else
|
|
|
+ if (y = d1) {
|
|
|
+ if (k = lo0bits(&y))
|
|
|
+ if (k >= 16) {
|
|
|
+ x[0] = y | z << 32 - k & 0xffff;
|
|
|
+ x[1] = z >> k - 16 & 0xffff;
|
|
|
+ x[2] = z >> k;
|
|
|
+ i = 2;
|
|
|
+ }
|
|
|
+ else {
|
|
|
+ x[0] = y & 0xffff;
|
|
|
+ x[1] = y >> 16 | z << 16 - k & 0xffff;
|
|
|
+ x[2] = z >> k & 0xffff;
|
|
|
+ x[3] = z >> k+16;
|
|
|
+ i = 3;
|
|
|
+ }
|
|
|
+ else {
|
|
|
+ x[0] = y & 0xffff;
|
|
|
+ x[1] = y >> 16;
|
|
|
+ x[2] = z & 0xffff;
|
|
|
+ x[3] = z >> 16;
|
|
|
+ i = 3;
|
|
|
+ }
|
|
|
+ }
|
|
|
+ else {
|
|
|
+#ifdef DEBUG
|
|
|
+ if (!z)
|
|
|
+ Bug("Zero passed to d2b");
|
|
|
+#endif
|
|
|
+ k = lo0bits(&z);
|
|
|
+ if (k >= 16) {
|
|
|
+ x[0] = z;
|
|
|
+ i = 0;
|
|
|
+ }
|
|
|
+ else {
|
|
|
+ x[0] = z & 0xffff;
|
|
|
+ x[1] = z >> 16;
|
|
|
+ i = 1;
|
|
|
+ }
|
|
|
+ k += 32;
|
|
|
+ }
|
|
|
+ while(!x[i])
|
|
|
+ --i;
|
|
|
+ b->wds = i + 1;
|
|
|
+#endif
|
|
|
+#ifndef Sudden_Underflow
|
|
|
+ if (de) {
|
|
|
+#endif
|
|
|
+#ifdef IBM
|
|
|
+ *e = (de - Bias - (P-1) << 2) + k;
|
|
|
+ *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
|
|
|
+#else
|
|
|
+ *e = de - Bias - (P-1) + k;
|
|
|
+ *bits = P - k;
|
|
|
+#endif
|
|
|
+#ifndef Sudden_Underflow
|
|
|
+ }
|
|
|
+ else {
|
|
|
+ *e = de - Bias - (P-1) + 1 + k;
|
|
|
+#ifdef Pack_32
|
|
|
+ *bits = 32*i - hi0bits(x[i-1]);
|
|
|
+#else
|
|
|
+ *bits = (i+2)*16 - hi0bits(x[i]);
|
|
|
+#endif
|
|
|
+ }
|
|
|
+#endif
|
|
|
+ return b;
|
|
|
+ }
|
|
|
+#undef d0
|
|
|
+#undef d1
|
|
|
+
|
|
|
+ static double
|
|
|
+ratio
|
|
|
+#ifdef KR_headers
|
|
|
+ (a, b) Bigint *a, *b;
|
|
|
+#else
|
|
|
+ (Bigint *a, Bigint *b)
|
|
|
+#endif
|
|
|
+{
|
|
|
+ U da, db;
|
|
|
+ int k, ka, kb;
|
|
|
+
|
|
|
+ dval(&da) = b2d(a, &ka);
|
|
|
+ dval(&db) = b2d(b, &kb);
|
|
|
+#ifdef Pack_32
|
|
|
+ k = ka - kb + 32*(a->wds - b->wds);
|
|
|
+#else
|
|
|
+ k = ka - kb + 16*(a->wds - b->wds);
|
|
|
+#endif
|
|
|
+#ifdef IBM
|
|
|
+ if (k > 0) {
|
|
|
+ word0(&da) += (k >> 2)*Exp_msk1;
|
|
|
+ if (k &= 3)
|
|
|
+ dval(&da) *= 1 << k;
|
|
|
+ }
|
|
|
+ else {
|
|
|
+ k = -k;
|
|
|
+ word0(&db) += (k >> 2)*Exp_msk1;
|
|
|
+ if (k &= 3)
|
|
|
+ dval(&db) *= 1 << k;
|
|
|
+ }
|
|
|
+#else
|
|
|
+ if (k > 0)
|
|
|
+ word0(&da) += k*Exp_msk1;
|
|
|
+ else {
|
|
|
+ k = -k;
|
|
|
+ word0(&db) += k*Exp_msk1;
|
|
|
+ }
|
|
|
+#endif
|
|
|
+ return dval(&da) / dval(&db);
|
|
|
+ }
|
|
|
+
|
|
|
+ static CONST double
|
|
|
+tens[] = {
|
|
|
+ 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
|
|
|
+ 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
|
|
|
+ 1e20, 1e21, 1e22
|
|
|
+#ifdef VAX
|
|
|
+ , 1e23, 1e24
|
|
|
+#endif
|
|
|
+ };
|
|
|
+
|
|
|
+ static CONST double
|
|
|
+#ifdef IEEE_Arith
|
|
|
+bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
|
|
|
+static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
|
|
|
+#ifdef Avoid_Underflow
|
|
|
+ 9007199254740992.*9007199254740992.e-256
|
|
|
+ /* = 2^106 * 1e-256 */
|
|
|
+#else
|
|
|
+ 1e-256
|
|
|
+#endif
|
|
|
+ };
|
|
|
+/* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
|
|
|
+/* flag unnecessarily. It leads to a song and dance at the end of strtod. */
|
|
|
+#define Scale_Bit 0x10
|
|
|
+#define n_bigtens 5
|
|
|
+#else
|
|
|
+#ifdef IBM
|
|
|
+bigtens[] = { 1e16, 1e32, 1e64 };
|
|
|
+static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 };
|
|
|
+#define n_bigtens 3
|
|
|
+#else
|
|
|
+bigtens[] = { 1e16, 1e32 };
|
|
|
+static CONST double tinytens[] = { 1e-16, 1e-32 };
|
|
|
+#define n_bigtens 2
|
|
|
+#endif
|
|
|
+#endif
|
|
|
+
|
|
|
+#undef Need_Hexdig
|
|
|
+#ifdef INFNAN_CHECK
|
|
|
+#ifndef No_Hex_NaN
|
|
|
+#define Need_Hexdig
|
|
|
+#endif
|
|
|
+#endif
|
|
|
+
|
|
|
+#ifndef Need_Hexdig
|
|
|
+#ifndef NO_HEX_FP
|
|
|
+#define Need_Hexdig
|
|
|
+#endif
|
|
|
+#endif
|
|
|
+
|
|
|
+#ifdef Need_Hexdig /*{*/
|
|
|
+static unsigned char hexdig[256];
|
|
|
+
|
|
|
+ static void
|
|
|
+#ifdef KR_headers
|
|
|
+htinit(h, s, inc) unsigned char *h; unsigned char *s; int inc;
|
|
|
+#else
|
|
|
+htinit(unsigned char *h, unsigned char *s, int inc)
|
|
|
+#endif
|
|
|
+{
|
|
|
+ int i, j;
|
|
|
+ for(i = 0; (j = s[i]) !=0; i++)
|
|
|
+ h[j] = i + inc;
|
|
|
+ }
|
|
|
+
|
|
|
+ static void
|
|
|
+#ifdef KR_headers
|
|
|
+hexdig_init()
|
|
|
+#else
|
|
|
+hexdig_init(void)
|
|
|
+#endif
|
|
|
+{
|
|
|
+#define USC (unsigned char *)
|
|
|
+ htinit(hexdig, USC "0123456789", 0x10);
|
|
|
+ htinit(hexdig, USC "abcdef", 0x10 + 10);
|
|
|
+ htinit(hexdig, USC "ABCDEF", 0x10 + 10);
|
|
|
+ }
|
|
|
+#endif /* } Need_Hexdig */
|
|
|
+
|
|
|
+#ifdef INFNAN_CHECK
|
|
|
+
|
|
|
+#ifndef NAN_WORD0
|
|
|
+#define NAN_WORD0 0x7ff80000
|
|
|
+#endif
|
|
|
+
|
|
|
+#ifndef NAN_WORD1
|
|
|
+#define NAN_WORD1 0
|
|
|
+#endif
|
|
|
+
|
|
|
+ static int
|
|
|
+match
|
|
|
+#ifdef KR_headers
|
|
|
+ (sp, t) char **sp, *t;
|
|
|
+#else
|
|
|
+ (const char **sp, const char *t)
|
|
|
+#endif
|
|
|
+{
|
|
|
+ int c, d;
|
|
|
+ CONST char *s = *sp;
|
|
|
+
|
|
|
+ while((d = *t++)) {
|
|
|
+ if ((c = *++s) >= 'A' && c <= 'Z')
|
|
|
+ c += 'a' - 'A';
|
|
|
+ if (c != d)
|
|
|
+ return 0;
|
|
|
+ }
|
|
|
+ *sp = s + 1;
|
|
|
+ return 1;
|
|
|
+ }
|
|
|
+
|
|
|
+#ifndef No_Hex_NaN
|
|
|
+ static void
|
|
|
+hexnan
|
|
|
+#ifdef KR_headers
|
|
|
+ (rvp, sp) U *rvp; CONST char **sp;
|
|
|
+#else
|
|
|
+ (U *rvp, const char **sp)
|
|
|
+#endif
|
|
|
+{
|
|
|
+ ULong c, x[2];
|
|
|
+ CONST char *s;
|
|
|
+ int c1, havedig, udx0, xshift;
|
|
|
+
|
|
|
+ if (!hexdig['0'])
|
|
|
+ hexdig_init();
|
|
|
+ x[0] = x[1] = 0;
|
|
|
+ havedig = xshift = 0;
|
|
|
+ udx0 = 1;
|
|
|
+ s = *sp;
|
|
|
+ /* allow optional initial 0x or 0X */
|
|
|
+ while((c = *(CONST unsigned char*)(s+1)) && c <= ' ')
|
|
|
+ ++s;
|
|
|
+ if (s[1] == '0' && (s[2] == 'x' || s[2] == 'X'))
|
|
|
+ s += 2;
|
|
|
+ while((c = *(CONST unsigned char*)++s)) {
|
|
|
+ if ((c1 = hexdig[c]))
|
|
|
+ c = c1 & 0xf;
|
|
|
+ else if (c <= ' ') {
|
|
|
+ if (udx0 && havedig) {
|
|
|
+ udx0 = 0;
|
|
|
+ xshift = 1;
|
|
|
+ }
|
|
|
+ continue;
|
|
|
+ }
|
|
|
+#ifdef GDTOA_NON_PEDANTIC_NANCHECK
|
|
|
+ else if (/*(*/ c == ')' && havedig) {
|
|
|
+ *sp = s + 1;
|
|
|
+ break;
|
|
|
+ }
|
|
|
+ else
|
|
|
+ return; /* invalid form: don't change *sp */
|
|
|
+#else
|
|
|
+ else {
|
|
|
+ do {
|
|
|
+ if (/*(*/ c == ')') {
|
|
|
+ *sp = s + 1;
|
|
|
+ break;
|
|
|
+ }
|
|
|
+ } while((c = *++s));
|
|
|
+ break;
|
|
|
+ }
|
|
|
+#endif
|
|
|
+ havedig = 1;
|
|
|
+ if (xshift) {
|
|
|
+ xshift = 0;
|
|
|
+ x[0] = x[1];
|
|
|
+ x[1] = 0;
|
|
|
+ }
|
|
|
+ if (udx0)
|
|
|
+ x[0] = (x[0] << 4) | (x[1] >> 28);
|
|
|
+ x[1] = (x[1] << 4) | c;
|
|
|
+ }
|
|
|
+ if ((x[0] &= 0xfffff) || x[1]) {
|
|
|
+ word0(rvp) = Exp_mask | x[0];
|
|
|
+ word1(rvp) = x[1];
|
|
|
+ }
|
|
|
+ }
|
|
|
+#endif /*No_Hex_NaN*/
|
|
|
+#endif /* INFNAN_CHECK */
|
|
|
+
|
|
|
+#ifdef Pack_32
|
|
|
+#define ULbits 32
|
|
|
+#define kshift 5
|
|
|
+#define kmask 31
|
|
|
+#else
|
|
|
+#define ULbits 16
|
|
|
+#define kshift 4
|
|
|
+#define kmask 15
|
|
|
+#endif
|
|
|
+
|
|
|
+#if !defined(NO_HEX_FP) || defined(Honor_FLT_ROUNDS) /*{*/
|
|
|
+ static Bigint *
|
|
|
+#ifdef KR_headers
|
|
|
+increment(b) Bigint *b;
|
|
|
+#else
|
|
|
+increment(Bigint *b)
|
|
|
+#endif
|
|
|
+{
|
|
|
+ ULong *x, *xe;
|
|
|
+ Bigint *b1;
|
|
|
+
|
|
|
+ x = b->x;
|
|
|
+ xe = x + b->wds;
|
|
|
+ do {
|
|
|
+ if (*x < (ULong)0xffffffffL) {
|
|
|
+ ++*x;
|
|
|
+ return b;
|
|
|
+ }
|
|
|
+ *x++ = 0;
|
|
|
+ } while(x < xe);
|
|
|
+ {
|
|
|
+ if (b->wds >= b->maxwds) {
|
|
|
+ b1 = Balloc(b->k+1);
|
|
|
+ Bcopy(b1,b);
|
|
|
+ Bfree(b);
|
|
|
+ b = b1;
|
|
|
+ }
|
|
|
+ b->x[b->wds++] = 1;
|
|
|
+ }
|
|
|
+ return b;
|
|
|
+ }
|
|
|
+
|
|
|
+#endif /*}*/
|
|
|
+
|
|
|
+#ifndef NO_HEX_FP /*{*/
|
|
|
+
|
|
|
+ static void
|
|
|
+#ifdef KR_headers
|
|
|
+rshift(b, k) Bigint *b; int k;
|
|
|
+#else
|
|
|
+rshift(Bigint *b, int k)
|
|
|
+#endif
|
|
|
+{
|
|
|
+ ULong *x, *x1, *xe, y;
|
|
|
+ int n;
|
|
|
+
|
|
|
+ x = x1 = b->x;
|
|
|
+ n = k >> kshift;
|
|
|
+ if (n < b->wds) {
|
|
|
+ xe = x + b->wds;
|
|
|
+ x += n;
|
|
|
+ if (k &= kmask) {
|
|
|
+ n = 32 - k;
|
|
|
+ y = *x++ >> k;
|
|
|
+ while(x < xe) {
|
|
|
+ *x1++ = (y | (*x << n)) & 0xffffffff;
|
|
|
+ y = *x++ >> k;
|
|
|
+ }
|
|
|
+ if ((*x1 = y) !=0)
|
|
|
+ x1++;
|
|
|
+ }
|
|
|
+ else
|
|
|
+ while(x < xe)
|
|
|
+ *x1++ = *x++;
|
|
|
+ }
|
|
|
+ if ((b->wds = x1 - b->x) == 0)
|
|
|
+ b->x[0] = 0;
|
|
|
+ }
|
|
|
+
|
|
|
+ static ULong
|
|
|
+#ifdef KR_headers
|
|
|
+any_on(b, k) Bigint *b; int k;
|
|
|
+#else
|
|
|
+any_on(Bigint *b, int k)
|
|
|
+#endif
|
|
|
+{
|
|
|
+ int n, nwds;
|
|
|
+ ULong *x, *x0, x1, x2;
|
|
|
+
|
|
|
+ x = b->x;
|
|
|
+ nwds = b->wds;
|
|
|
+ n = k >> kshift;
|
|
|
+ if (n > nwds)
|
|
|
+ n = nwds;
|
|
|
+ else if (n < nwds && (k &= kmask)) {
|
|
|
+ x1 = x2 = x[n];
|
|
|
+ x1 >>= k;
|
|
|
+ x1 <<= k;
|
|
|
+ if (x1 != x2)
|
|
|
+ return 1;
|
|
|
+ }
|
|
|
+ x0 = x;
|
|
|
+ x += n;
|
|
|
+ while(x > x0)
|
|
|
+ if (*--x)
|
|
|
+ return 1;
|
|
|
+ return 0;
|
|
|
+ }
|
|
|
+
|
|
|
+enum { /* rounding values: same as FLT_ROUNDS */
|
|
|
+ Round_zero = 0,
|
|
|
+ Round_near = 1,
|
|
|
+ Round_up = 2,
|
|
|
+ Round_down = 3
|
|
|
+ };
|
|
|
+
|
|
|
+ void
|
|
|
+#ifdef KR_headers
|
|
|
+gethex(sp, rvp, rounding, sign)
|
|
|
+ CONST char **sp; U *rvp; int rounding, sign;
|
|
|
+#else
|
|
|
+gethex( CONST char **sp, U *rvp, int rounding, int sign)
|
|
|
+#endif
|
|
|
+{
|
|
|
+ Bigint *b;
|
|
|
+ CONST unsigned char *decpt, *s0, *s, *s1;
|
|
|
+ Long e, e1;
|
|
|
+ ULong L, lostbits, *x;
|
|
|
+ int big, denorm, esign, havedig, k, n, nbits, up, zret;
|
|
|
+#ifdef IBM
|
|
|
+ int j;
|
|
|
+#endif
|
|
|
+ enum {
|
|
|
+#ifdef IEEE_Arith /*{{*/
|
|
|
+ emax = 0x7fe - Bias - P + 1,
|
|
|
+ emin = Emin - P + 1
|
|
|
+#else /*}{*/
|
|
|
+ emin = Emin - P,
|
|
|
+#ifdef VAX
|
|
|
+ emax = 0x7ff - Bias - P + 1
|
|
|
+#endif
|
|
|
+#ifdef IBM
|
|
|
+ emax = 0x7f - Bias - P
|
|
|
+#endif
|
|
|
+#endif /*}}*/
|
|
|
+ };
|
|
|
+#ifdef USE_LOCALE
|
|
|
+ int i;
|
|
|
+#ifdef NO_LOCALE_CACHE
|
|
|
+ const unsigned char *decimalpoint = (unsigned char*)
|
|
|
+ localeconv()->decimal_point;
|
|
|
+#else
|
|
|
+ const unsigned char *decimalpoint;
|
|
|
+ static unsigned char *decimalpoint_cache;
|
|
|
+ if (!(s0 = decimalpoint_cache)) {
|
|
|
+ s0 = (unsigned char*)localeconv()->decimal_point;
|
|
|
+ if ((decimalpoint_cache = (unsigned char*)
|
|
|
+ MALLOC(strlen((CONST char*)s0) + 1))) {
|
|
|
+ strcpy((char*)decimalpoint_cache, (CONST char*)s0);
|
|
|
+ s0 = decimalpoint_cache;
|
|
|
+ }
|
|
|
+ }
|
|
|
+ decimalpoint = s0;
|
|
|
+#endif
|
|
|
+#endif
|
|
|
+
|
|
|
+ if (!hexdig['0'])
|
|
|
+ hexdig_init();
|
|
|
+ havedig = 0;
|
|
|
+ s0 = *(CONST unsigned char **)sp + 2;
|
|
|
+ while(s0[havedig] == '0')
|
|
|
+ havedig++;
|
|
|
+ s0 += havedig;
|
|
|
+ s = s0;
|
|
|
+ decpt = 0;
|
|
|
+ zret = 0;
|
|
|
+ e = 0;
|
|
|
+ if (hexdig[*s])
|
|
|
+ havedig++;
|
|
|
+ else {
|
|
|
+ zret = 1;
|
|
|
+#ifdef USE_LOCALE
|
|
|
+ for(i = 0; decimalpoint[i]; ++i) {
|
|
|
+ if (s[i] != decimalpoint[i])
|
|
|
+ goto pcheck;
|
|
|
+ }
|
|
|
+ decpt = s += i;
|
|
|
+#else
|
|
|
+ if (*s != '.')
|
|
|
+ goto pcheck;
|
|
|
+ decpt = ++s;
|
|
|
+#endif
|
|
|
+ if (!hexdig[*s])
|
|
|
+ goto pcheck;
|
|
|
+ while(*s == '0')
|
|
|
+ s++;
|
|
|
+ if (hexdig[*s])
|
|
|
+ zret = 0;
|
|
|
+ havedig = 1;
|
|
|
+ s0 = s;
|
|
|
+ }
|
|
|
+ while(hexdig[*s])
|
|
|
+ s++;
|
|
|
+#ifdef USE_LOCALE
|
|
|
+ if (*s == *decimalpoint && !decpt) {
|
|
|
+ for(i = 1; decimalpoint[i]; ++i) {
|
|
|
+ if (s[i] != decimalpoint[i])
|
|
|
+ goto pcheck;
|
|
|
+ }
|
|
|
+ decpt = s += i;
|
|
|
+#else
|
|
|
+ if (*s == '.' && !decpt) {
|
|
|
+ decpt = ++s;
|
|
|
+#endif
|
|
|
+ while(hexdig[*s])
|
|
|
+ s++;
|
|
|
+ }/*}*/
|
|
|
+ if (decpt)
|
|
|
+ e = -(((Long)(s-decpt)) << 2);
|
|
|
+ pcheck:
|
|
|
+ s1 = s;
|
|
|
+ big = esign = 0;
|
|
|
+ switch(*s) {
|
|
|
+ case 'p':
|
|
|
+ case 'P':
|
|
|
+ switch(*++s) {
|
|
|
+ case '-':
|
|
|
+ esign = 1;
|
|
|
+ /* no break */
|
|
|
+ case '+':
|
|
|
+ s++;
|
|
|
+ }
|
|
|
+ if ((n = hexdig[*s]) == 0 || n > 0x19) {
|
|
|
+ s = s1;
|
|
|
+ break;
|
|
|
+ }
|
|
|
+ e1 = n - 0x10;
|
|
|
+ while((n = hexdig[*++s]) !=0 && n <= 0x19) {
|
|
|
+ if (e1 & 0xf8000000)
|
|
|
+ big = 1;
|
|
|
+ e1 = 10*e1 + n - 0x10;
|
|
|
+ }
|
|
|
+ if (esign)
|
|
|
+ e1 = -e1;
|
|
|
+ e += e1;
|
|
|
+ }
|
|
|
+ *sp = (char*)s;
|
|
|
+ if (!havedig)
|
|
|
+ *sp = (char*)s0 - 1;
|
|
|
+ if (zret)
|
|
|
+ goto retz1;
|
|
|
+ if (big) {
|
|
|
+ if (esign) {
|
|
|
+#ifdef IEEE_Arith
|
|
|
+ switch(rounding) {
|
|
|
+ case Round_up:
|
|
|
+ if (sign)
|
|
|
+ break;
|
|
|
+ goto ret_tiny;
|
|
|
+ case Round_down:
|
|
|
+ if (!sign)
|
|
|
+ break;
|
|
|
+ goto ret_tiny;
|
|
|
+ }
|
|
|
+#endif
|
|
|
+ goto retz;
|
|
|
+#ifdef IEEE_Arith
|
|
|
+ ret_tiny:
|
|
|
+#ifndef NO_ERRNO
|
|
|
+ errno = ERANGE;
|
|
|
+#endif
|
|
|
+ word0(rvp) = 0;
|
|
|
+ word1(rvp) = 1;
|
|
|
+ return;
|
|
|
+#endif /* IEEE_Arith */
|
|
|
+ }
|
|
|
+ switch(rounding) {
|
|
|
+ case Round_near:
|
|
|
+ goto ovfl1;
|
|
|
+ case Round_up:
|
|
|
+ if (!sign)
|
|
|
+ goto ovfl1;
|
|
|
+ goto ret_big;
|
|
|
+ case Round_down:
|
|
|
+ if (sign)
|
|
|
+ goto ovfl1;
|
|
|
+ goto ret_big;
|
|
|
+ }
|
|
|
+ ret_big:
|
|
|
+ word0(rvp) = Big0;
|
|
|
+ word1(rvp) = Big1;
|
|
|
+ return;
|
|
|
+ }
|
|
|
+ n = s1 - s0 - 1;
|
|
|
+ for(k = 0; n > (1 << (kshift-2)) - 1; n >>= 1)
|
|
|
+ k++;
|
|
|
+ b = Balloc(k);
|
|
|
+ x = b->x;
|
|
|
+ n = 0;
|
|
|
+ L = 0;
|
|
|
+#ifdef USE_LOCALE
|
|
|
+ for(i = 0; decimalpoint[i+1]; ++i);
|
|
|
+#endif
|
|
|
+ while(s1 > s0) {
|
|
|
+#ifdef USE_LOCALE
|
|
|
+ if (*--s1 == decimalpoint[i]) {
|
|
|
+ s1 -= i;
|
|
|
+ continue;
|
|
|
+ }
|
|
|
+#else
|
|
|
+ if (*--s1 == '.')
|
|
|
+ continue;
|
|
|
+#endif
|
|
|
+ if (n == ULbits) {
|
|
|
+ *x++ = L;
|
|
|
+ L = 0;
|
|
|
+ n = 0;
|
|
|
+ }
|
|
|
+ L |= (hexdig[*s1] & 0x0f) << n;
|
|
|
+ n += 4;
|
|
|
+ }
|
|
|
+ *x++ = L;
|
|
|
+ b->wds = n = x - b->x;
|
|
|
+ n = ULbits*n - hi0bits(L);
|
|
|
+ nbits = Nbits;
|
|
|
+ lostbits = 0;
|
|
|
+ x = b->x;
|
|
|
+ if (n > nbits) {
|
|
|
+ n -= nbits;
|
|
|
+ if (any_on(b,n)) {
|
|
|
+ lostbits = 1;
|
|
|
+ k = n - 1;
|
|
|
+ if (x[k>>kshift] & 1 << (k & kmask)) {
|
|
|
+ lostbits = 2;
|
|
|
+ if (k > 0 && any_on(b,k))
|
|
|
+ lostbits = 3;
|
|
|
+ }
|
|
|
+ }
|
|
|
+ rshift(b, n);
|
|
|
+ e += n;
|
|
|
+ }
|
|
|
+ else if (n < nbits) {
|
|
|
+ n = nbits - n;
|
|
|
+ b = lshift(b, n);
|
|
|
+ e -= n;
|
|
|
+ x = b->x;
|
|
|
+ }
|
|
|
+ if (e > Emax) {
|
|
|
+ ovfl:
|
|
|
+ Bfree(b);
|
|
|
+ ovfl1:
|
|
|
+#ifndef NO_ERRNO
|
|
|
+ errno = ERANGE;
|
|
|
+#endif
|
|
|
+ word0(rvp) = Exp_mask;
|
|
|
+ word1(rvp) = 0;
|
|
|
+ return;
|
|
|
+ }
|
|
|
+ denorm = 0;
|
|
|
+ if (e < emin) {
|
|
|
+ denorm = 1;
|
|
|
+ n = emin - e;
|
|
|
+ if (n >= nbits) {
|
|
|
+#ifdef IEEE_Arith /*{*/
|
|
|
+ switch (rounding) {
|
|
|
+ case Round_near:
|
|
|
+ if (n == nbits && (n < 2 || any_on(b,n-1)))
|
|
|
+ goto ret_tiny;
|
|
|
+ break;
|
|
|
+ case Round_up:
|
|
|
+ if (!sign)
|
|
|
+ goto ret_tiny;
|
|
|
+ break;
|
|
|
+ case Round_down:
|
|
|
+ if (sign)
|
|
|
+ goto ret_tiny;
|
|
|
+ }
|
|
|
+#endif /* } IEEE_Arith */
|
|
|
+ Bfree(b);
|
|
|
+ retz:
|
|
|
+#ifndef NO_ERRNO
|
|
|
+ errno = ERANGE;
|
|
|
+#endif
|
|
|
+ retz1:
|
|
|
+ rvp->d = 0.;
|
|
|
+ return;
|
|
|
+ }
|
|
|
+ k = n - 1;
|
|
|
+ if (lostbits)
|
|
|
+ lostbits = 1;
|
|
|
+ else if (k > 0)
|
|
|
+ lostbits = any_on(b,k);
|
|
|
+ if (x[k>>kshift] & 1 << (k & kmask))
|
|
|
+ lostbits |= 2;
|
|
|
+ nbits -= n;
|
|
|
+ rshift(b,n);
|
|
|
+ e = emin;
|
|
|
+ }
|
|
|
+ if (lostbits) {
|
|
|
+ up = 0;
|
|
|
+ switch(rounding) {
|
|
|
+ case Round_zero:
|
|
|
+ break;
|
|
|
+ case Round_near:
|
|
|
+ if (lostbits & 2
|
|
|
+ && (lostbits & 1) | (x[0] & 1))
|
|
|
+ up = 1;
|
|
|
+ break;
|
|
|
+ case Round_up:
|
|
|
+ up = 1 - sign;
|
|
|
+ break;
|
|
|
+ case Round_down:
|
|
|
+ up = sign;
|
|
|
+ }
|
|
|
+ if (up) {
|
|
|
+ k = b->wds;
|
|
|
+ b = increment(b);
|
|
|
+ x = b->x;
|
|
|
+ if (denorm) {
|
|
|
+#if 0
|
|
|
+ if (nbits == Nbits - 1
|
|
|
+ && x[nbits >> kshift] & 1 << (nbits & kmask))
|
|
|
+ denorm = 0; /* not currently used */
|
|
|
+#endif
|
|
|
+ }
|
|
|
+ else if (b->wds > k
|
|
|
+ || ((n = nbits & kmask) !=0
|
|
|
+ && hi0bits(x[k-1]) < 32-n)) {
|
|
|
+ rshift(b,1);
|
|
|
+ if (++e > Emax)
|
|
|
+ goto ovfl;
|
|
|
+ }
|
|
|
+ }
|
|
|
+ }
|
|
|
+#ifdef IEEE_Arith
|
|
|
+ if (denorm)
|
|
|
+ word0(rvp) = b->wds > 1 ? b->x[1] & ~0x100000 : 0;
|
|
|
+ else
|
|
|
+ word0(rvp) = (b->x[1] & ~0x100000) | ((e + 0x3ff + 52) << 20);
|
|
|
+ word1(rvp) = b->x[0];
|
|
|
+#endif
|
|
|
+#ifdef IBM
|
|
|
+ if ((j = e & 3)) {
|
|
|
+ k = b->x[0] & ((1 << j) - 1);
|
|
|
+ rshift(b,j);
|
|
|
+ if (k) {
|
|
|
+ switch(rounding) {
|
|
|
+ case Round_up:
|
|
|
+ if (!sign)
|
|
|
+ increment(b);
|
|
|
+ break;
|
|
|
+ case Round_down:
|
|
|
+ if (sign)
|
|
|
+ increment(b);
|
|
|
+ break;
|
|
|
+ case Round_near:
|
|
|
+ j = 1 << (j-1);
|
|
|
+ if (k & j && ((k & (j-1)) | lostbits))
|
|
|
+ increment(b);
|
|
|
+ }
|
|
|
+ }
|
|
|
+ }
|
|
|
+ e >>= 2;
|
|
|
+ word0(rvp) = b->x[1] | ((e + 65 + 13) << 24);
|
|
|
+ word1(rvp) = b->x[0];
|
|
|
+#endif
|
|
|
+#ifdef VAX
|
|
|
+ /* The next two lines ignore swap of low- and high-order 2 bytes. */
|
|
|
+ /* word0(rvp) = (b->x[1] & ~0x800000) | ((e + 129 + 55) << 23); */
|
|
|
+ /* word1(rvp) = b->x[0]; */
|
|
|
+ word0(rvp) = ((b->x[1] & ~0x800000) >> 16) | ((e + 129 + 55) << 7) | (b->x[1] << 16);
|
|
|
+ word1(rvp) = (b->x[0] >> 16) | (b->x[0] << 16);
|
|
|
+#endif
|
|
|
+ Bfree(b);
|
|
|
+ }
|
|
|
+#endif /*!NO_HEX_FP}*/
|
|
|
+
|
|
|
+ static int
|
|
|
+#ifdef KR_headers
|
|
|
+dshift(b, p2) Bigint *b; int p2;
|
|
|
+#else
|
|
|
+dshift(Bigint *b, int p2)
|
|
|
+#endif
|
|
|
+{
|
|
|
+ int rv = hi0bits(b->x[b->wds-1]) - 4;
|
|
|
+ if (p2 > 0)
|
|
|
+ rv -= p2;
|
|
|
+ return rv & kmask;
|
|
|
+ }
|
|
|
+
|
|
|
+ static int
|
|
|
+quorem
|
|
|
+#ifdef KR_headers
|
|
|
+ (b, S) Bigint *b, *S;
|
|
|
+#else
|
|
|
+ (Bigint *b, Bigint *S)
|
|
|
+#endif
|
|
|
+{
|
|
|
+ int n;
|
|
|
+ ULong *bx, *bxe, q, *sx, *sxe;
|
|
|
+#ifdef ULLong
|
|
|
+ ULLong borrow, carry, y, ys;
|
|
|
+#else
|
|
|
+ ULong borrow, carry, y, ys;
|
|
|
+#ifdef Pack_32
|
|
|
+ ULong si, z, zs;
|
|
|
+#endif
|
|
|
+#endif
|
|
|
+
|
|
|
+ n = S->wds;
|
|
|
+#ifdef DEBUG
|
|
|
+ /*debug*/ if (b->wds > n)
|
|
|
+ /*debug*/ Bug("oversize b in quorem");
|
|
|
+#endif
|
|
|
+ if (b->wds < n)
|
|
|
+ return 0;
|
|
|
+ sx = S->x;
|
|
|
+ sxe = sx + --n;
|
|
|
+ bx = b->x;
|
|
|
+ bxe = bx + n;
|
|
|
+ q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
|
|
|
+#ifdef DEBUG
|
|
|
+#ifdef NO_STRTOD_BIGCOMP
|
|
|
+ /*debug*/ if (q > 9)
|
|
|
+#else
|
|
|
+ /* An oversized q is possible when quorem is called from bigcomp and */
|
|
|
+ /* the input is near, e.g., twice the smallest denormalized number. */
|
|
|
+ /*debug*/ if (q > 15)
|
|
|
+#endif
|
|
|
+ /*debug*/ Bug("oversized quotient in quorem");
|
|
|
+#endif
|
|
|
+ if (q) {
|
|
|
+ borrow = 0;
|
|
|
+ carry = 0;
|
|
|
+ do {
|
|
|
+#ifdef ULLong
|
|
|
+ ys = *sx++ * (ULLong)q + carry;
|
|
|
+ carry = ys >> 32;
|
|
|
+ y = *bx - (ys & FFFFFFFF) - borrow;
|
|
|
+ borrow = y >> 32 & (ULong)1;
|
|
|
+ *bx++ = y & FFFFFFFF;
|
|
|
+#else
|
|
|
+#ifdef Pack_32
|
|
|
+ si = *sx++;
|
|
|
+ ys = (si & 0xffff) * q + carry;
|
|
|
+ zs = (si >> 16) * q + (ys >> 16);
|
|
|
+ carry = zs >> 16;
|
|
|
+ y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
|
|
|
+ borrow = (y & 0x10000) >> 16;
|
|
|
+ z = (*bx >> 16) - (zs & 0xffff) - borrow;
|
|
|
+ borrow = (z & 0x10000) >> 16;
|
|
|
+ Storeinc(bx, z, y);
|
|
|
+#else
|
|
|
+ ys = *sx++ * q + carry;
|
|
|
+ carry = ys >> 16;
|
|
|
+ y = *bx - (ys & 0xffff) - borrow;
|
|
|
+ borrow = (y & 0x10000) >> 16;
|
|
|
+ *bx++ = y & 0xffff;
|
|
|
+#endif
|
|
|
+#endif
|
|
|
+ }
|
|
|
+ while(sx <= sxe);
|
|
|
+ if (!*bxe) {
|
|
|
+ bx = b->x;
|
|
|
+ while(--bxe > bx && !*bxe)
|
|
|
+ --n;
|
|
|
+ b->wds = n;
|
|
|
+ }
|
|
|
+ }
|
|
|
+ if (cmp(b, S) >= 0) {
|
|
|
+ q++;
|
|
|
+ borrow = 0;
|
|
|
+ carry = 0;
|
|
|
+ bx = b->x;
|
|
|
+ sx = S->x;
|
|
|
+ do {
|
|
|
+#ifdef ULLong
|
|
|
+ ys = *sx++ + carry;
|
|
|
+ carry = ys >> 32;
|
|
|
+ y = *bx - (ys & FFFFFFFF) - borrow;
|
|
|
+ borrow = y >> 32 & (ULong)1;
|
|
|
+ *bx++ = y & FFFFFFFF;
|
|
|
+#else
|
|
|
+#ifdef Pack_32
|
|
|
+ si = *sx++;
|
|
|
+ ys = (si & 0xffff) + carry;
|
|
|
+ zs = (si >> 16) + (ys >> 16);
|
|
|
+ carry = zs >> 16;
|
|
|
+ y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
|
|
|
+ borrow = (y & 0x10000) >> 16;
|
|
|
+ z = (*bx >> 16) - (zs & 0xffff) - borrow;
|
|
|
+ borrow = (z & 0x10000) >> 16;
|
|
|
+ Storeinc(bx, z, y);
|
|
|
+#else
|
|
|
+ ys = *sx++ + carry;
|
|
|
+ carry = ys >> 16;
|
|
|
+ y = *bx - (ys & 0xffff) - borrow;
|
|
|
+ borrow = (y & 0x10000) >> 16;
|
|
|
+ *bx++ = y & 0xffff;
|
|
|
+#endif
|
|
|
+#endif
|
|
|
+ }
|
|
|
+ while(sx <= sxe);
|
|
|
+ bx = b->x;
|
|
|
+ bxe = bx + n;
|
|
|
+ if (!*bxe) {
|
|
|
+ while(--bxe > bx && !*bxe)
|
|
|
+ --n;
|
|
|
+ b->wds = n;
|
|
|
+ }
|
|
|
+ }
|
|
|
+ return q;
|
|
|
+ }
|
|
|
+
|
|
|
+#if defined(Avoid_Underflow) || !defined(NO_STRTOD_BIGCOMP) /*{*/
|
|
|
+ static double
|
|
|
+sulp
|
|
|
+#ifdef KR_headers
|
|
|
+ (x, bc) U *x; BCinfo *bc;
|
|
|
+#else
|
|
|
+ (U *x, BCinfo *bc)
|
|
|
+#endif
|
|
|
+{
|
|
|
+ U u;
|
|
|
+ double rv;
|
|
|
+ int i;
|
|
|
+
|
|
|
+ rv = ulp(x);
|
|
|
+ if (!bc->scale || (i = 2*P + 1 - ((word0(x) & Exp_mask) >> Exp_shift)) <= 0)
|
|
|
+ return rv; /* Is there an example where i <= 0 ? */
|
|
|
+ word0(&u) = Exp_1 + (i << Exp_shift);
|
|
|
+ word1(&u) = 0;
|
|
|
+ return rv * u.d;
|
|
|
+ }
|
|
|
+#endif /*}*/
|
|
|
+
|
|
|
+#ifndef NO_STRTOD_BIGCOMP
|
|
|
+ static void
|
|
|
+bigcomp
|
|
|
+#ifdef KR_headers
|
|
|
+ (rv, s0, bc)
|
|
|
+ U *rv; CONST char *s0; BCinfo *bc;
|
|
|
+#else
|
|
|
+ (U *rv, const char *s0, BCinfo *bc)
|
|
|
+#endif
|
|
|
+{
|
|
|
+ Bigint *b, *d;
|
|
|
+ int b2, bbits, d2, dd, dig, dsign, i, j, nd, nd0, p2, p5, speccase;
|
|
|
+
|
|
|
+ dsign = bc->dsign;
|
|
|
+ nd = bc->nd;
|
|
|
+ nd0 = bc->nd0;
|
|
|
+ p5 = nd + bc->e0 - 1;
|
|
|
+ speccase = 0;
|
|
|
+#ifndef Sudden_Underflow
|
|
|
+ if (rv->d == 0.) { /* special case: value near underflow-to-zero */
|
|
|
+ /* threshold was rounded to zero */
|
|
|
+ b = i2b(1);
|
|
|
+ p2 = Emin - P + 1;
|
|
|
+ bbits = 1;
|
|
|
+#ifdef Avoid_Underflow
|
|
|
+ word0(rv) = (P+2) << Exp_shift;
|
|
|
+#else
|
|
|
+ word1(rv) = 1;
|
|
|
+#endif
|
|
|
+ i = 0;
|
|
|
+#ifdef Honor_FLT_ROUNDS
|
|
|
+ if (bc->rounding == 1)
|
|
|
+#endif
|
|
|
+ {
|
|
|
+ speccase = 1;
|
|
|
+ --p2;
|
|
|
+ dsign = 0;
|
|
|
+ goto have_i;
|
|
|
+ }
|
|
|
+ }
|
|
|
+ else
|
|
|
+#endif
|
|
|
+ b = d2b(rv, &p2, &bbits);
|
|
|
+#ifdef Avoid_Underflow
|
|
|
+ p2 -= bc->scale;
|
|
|
+#endif
|
|
|
+ /* floor(log2(rv)) == bbits - 1 + p2 */
|
|
|
+ /* Check for denormal case. */
|
|
|
+ i = P - bbits;
|
|
|
+ if (i > (j = P - Emin - 1 + p2)) {
|
|
|
+#ifdef Sudden_Underflow
|
|
|
+ Bfree(b);
|
|
|
+ b = i2b(1);
|
|
|
+ p2 = Emin;
|
|
|
+ i = P - 1;
|
|
|
+#ifdef Avoid_Underflow
|
|
|
+ word0(rv) = (1 + bc->scale) << Exp_shift;
|
|
|
+#else
|
|
|
+ word0(rv) = Exp_msk1;
|
|
|
+#endif
|
|
|
+ word1(rv) = 0;
|
|
|
+#else
|
|
|
+ i = j;
|
|
|
+#endif
|
|
|
+ }
|
|
|
+#ifdef Honor_FLT_ROUNDS
|
|
|
+ if (bc->rounding != 1) {
|
|
|
+ if (i > 0)
|
|
|
+ b = lshift(b, i);
|
|
|
+ if (dsign)
|
|
|
+ b = increment(b);
|
|
|
+ }
|
|
|
+ else
|
|
|
+#endif
|
|
|
+ {
|
|
|
+ b = lshift(b, ++i);
|
|
|
+ b->x[0] |= 1;
|
|
|
+ }
|
|
|
+#ifndef Sudden_Underflow
|
|
|
+ have_i:
|
|
|
+#endif
|
|
|
+ p2 -= p5 + i;
|
|
|
+ d = i2b(1);
|
|
|
+ /* Arrange for convenient computation of quotients:
|
|
|
+ * shift left if necessary so divisor has 4 leading 0 bits.
|
|
|
+ */
|
|
|
+ if (p5 > 0)
|
|
|
+ d = pow5mult(d, p5);
|
|
|
+ else if (p5 < 0)
|
|
|
+ b = pow5mult(b, -p5);
|
|
|
+ if (p2 > 0) {
|
|
|
+ b2 = p2;
|
|
|
+ d2 = 0;
|
|
|
+ }
|
|
|
+ else {
|
|
|
+ b2 = 0;
|
|
|
+ d2 = -p2;
|
|
|
+ }
|
|
|
+ i = dshift(d, d2);
|
|
|
+ if ((b2 += i) > 0)
|
|
|
+ b = lshift(b, b2);
|
|
|
+ if ((d2 += i) > 0)
|
|
|
+ d = lshift(d, d2);
|
|
|
+
|
|
|
+ /* Now b/d = exactly half-way between the two floating-point values */
|
|
|
+ /* on either side of the input string. Compute first digit of b/d. */
|
|
|
+
|
|
|
+ if (!(dig = quorem(b,d))) {
|
|
|
+ b = multadd(b, 10, 0); /* very unlikely */
|
|
|
+ dig = quorem(b,d);
|
|
|
+ }
|
|
|
+
|
|
|
+ /* Compare b/d with s0 */
|
|
|
+
|
|
|
+ for(i = 0; i < nd0; ) {
|
|
|
+ if ((dd = s0[i++] - '0' - dig))
|
|
|
+ goto ret;
|
|
|
+ if (!b->x[0] && b->wds == 1) {
|
|
|
+ if (i < nd)
|
|
|
+ dd = 1;
|
|
|
+ goto ret;
|
|
|
+ }
|
|
|
+ b = multadd(b, 10, 0);
|
|
|
+ dig = quorem(b,d);
|
|
|
+ }
|
|
|
+ for(j = bc->dp1; i++ < nd;) {
|
|
|
+ if ((dd = s0[j++] - '0' - dig))
|
|
|
+ goto ret;
|
|
|
+ if (!b->x[0] && b->wds == 1) {
|
|
|
+ if (i < nd)
|
|
|
+ dd = 1;
|
|
|
+ goto ret;
|
|
|
+ }
|
|
|
+ b = multadd(b, 10, 0);
|
|
|
+ dig = quorem(b,d);
|
|
|
+ }
|
|
|
+ if (b->x[0] || b->wds > 1)
|
|
|
+ dd = -1;
|
|
|
+ ret:
|
|
|
+ Bfree(b);
|
|
|
+ Bfree(d);
|
|
|
+#ifdef Honor_FLT_ROUNDS
|
|
|
+ if (bc->rounding != 1) {
|
|
|
+ if (dd < 0) {
|
|
|
+ if (bc->rounding == 0) {
|
|
|
+ if (!dsign)
|
|
|
+ goto retlow1;
|
|
|
+ }
|
|
|
+ else if (dsign)
|
|
|
+ goto rethi1;
|
|
|
+ }
|
|
|
+ else if (dd > 0) {
|
|
|
+ if (bc->rounding == 0) {
|
|
|
+ if (dsign)
|
|
|
+ goto rethi1;
|
|
|
+ goto ret1;
|
|
|
+ }
|
|
|
+ if (!dsign)
|
|
|
+ goto rethi1;
|
|
|
+ dval(rv) += 2.*sulp(rv,bc);
|
|
|
+ }
|
|
|
+ else {
|
|
|
+ bc->inexact = 0;
|
|
|
+ if (dsign)
|
|
|
+ goto rethi1;
|
|
|
+ }
|
|
|
+ }
|
|
|
+ else
|
|
|
+#endif
|
|
|
+ if (speccase) {
|
|
|
+ if (dd <= 0)
|
|
|
+ rv->d = 0.;
|
|
|
+ }
|
|
|
+ else if (dd < 0) {
|
|
|
+ if (!dsign) /* does not happen for round-near */
|
|
|
+retlow1:
|
|
|
+ dval(rv) -= sulp(rv,bc);
|
|
|
+ }
|
|
|
+ else if (dd > 0) {
|
|
|
+ if (dsign) {
|
|
|
+ rethi1:
|
|
|
+ dval(rv) += sulp(rv,bc);
|
|
|
+ }
|
|
|
+ }
|
|
|
+ else {
|
|
|
+ /* Exact half-way case: apply round-even rule. */
|
|
|
+ if ((j = ((word0(rv) & Exp_mask) >> Exp_shift) - bc->scale) <= 0) {
|
|
|
+ i = 1 - j;
|
|
|
+ if (i <= 31) {
|
|
|
+ if (word1(rv) & (0x1 << i))
|
|
|
+ goto odd;
|
|
|
+ }
|
|
|
+ else if (word0(rv) & (0x1 << (i-32)))
|
|
|
+ goto odd;
|
|
|
+ }
|
|
|
+ else if (word1(rv) & 1) {
|
|
|
+ odd:
|
|
|
+ if (dsign)
|
|
|
+ goto rethi1;
|
|
|
+ goto retlow1;
|
|
|
+ }
|
|
|
+ }
|
|
|
+
|
|
|
+#ifdef Honor_FLT_ROUNDS
|
|
|
+ ret1:
|
|
|
+#endif
|
|
|
+ return;
|
|
|
+ }
|
|
|
+#endif /* NO_STRTOD_BIGCOMP */
|
|
|
+
|
|
|
+ double
|
|
|
+fpconv_strtod
|
|
|
+#ifdef KR_headers
|
|
|
+ (s00, se) CONST char *s00; char **se;
|
|
|
+#else
|
|
|
+ (const char *s00, char **se)
|
|
|
+#endif
|
|
|
+{
|
|
|
+ int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, e, e1;
|
|
|
+ int esign, i, j, k, nd, nd0, nf, nz, nz0, nz1, sign;
|
|
|
+ CONST char *s, *s0, *s1;
|
|
|
+ double aadj, aadj1;
|
|
|
+ Long L;
|
|
|
+ U aadj2, adj, rv, rv0;
|
|
|
+ ULong y, z;
|
|
|
+ BCinfo bc;
|
|
|
+ Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
|
|
|
+#ifdef Avoid_Underflow
|
|
|
+ ULong Lsb, Lsb1;
|
|
|
+#endif
|
|
|
+#ifdef SET_INEXACT
|
|
|
+ int oldinexact;
|
|
|
+#endif
|
|
|
+#ifndef NO_STRTOD_BIGCOMP
|
|
|
+ int req_bigcomp = 0;
|
|
|
+#endif
|
|
|
+#ifdef Honor_FLT_ROUNDS /*{*/
|
|
|
+#ifdef Trust_FLT_ROUNDS /*{{ only define this if FLT_ROUNDS really works! */
|
|
|
+ bc.rounding = Flt_Rounds;
|
|
|
+#else /*}{*/
|
|
|
+ bc.rounding = 1;
|
|
|
+ switch(fegetround()) {
|
|
|
+ case FE_TOWARDZERO: bc.rounding = 0; break;
|
|
|
+ case FE_UPWARD: bc.rounding = 2; break;
|
|
|
+ case FE_DOWNWARD: bc.rounding = 3;
|
|
|
+ }
|
|
|
+#endif /*}}*/
|
|
|
+#endif /*}*/
|
|
|
+#ifdef USE_LOCALE
|
|
|
+ CONST char *s2;
|
|
|
+#endif
|
|
|
+
|
|
|
+ sign = nz0 = nz1 = nz = bc.dplen = bc.uflchk = 0;
|
|
|
+ dval(&rv) = 0.;
|
|
|
+ for(s = s00;;s++) switch(*s) {
|
|
|
+ case '-':
|
|
|
+ sign = 1;
|
|
|
+ /* no break */
|
|
|
+ case '+':
|
|
|
+ if (*++s)
|
|
|
+ goto break2;
|
|
|
+ /* no break */
|
|
|
+ case 0:
|
|
|
+ goto ret0;
|
|
|
+ case '\t':
|
|
|
+ case '\n':
|
|
|
+ case '\v':
|
|
|
+ case '\f':
|
|
|
+ case '\r':
|
|
|
+ case ' ':
|
|
|
+ continue;
|
|
|
+ default:
|
|
|
+ goto break2;
|
|
|
+ }
|
|
|
+ break2:
|
|
|
+ if (*s == '0') {
|
|
|
+#ifndef NO_HEX_FP /*{*/
|
|
|
+ switch(s[1]) {
|
|
|
+ case 'x':
|
|
|
+ case 'X':
|
|
|
+#ifdef Honor_FLT_ROUNDS
|
|
|
+ gethex(&s, &rv, bc.rounding, sign);
|
|
|
+#else
|
|
|
+ gethex(&s, &rv, 1, sign);
|
|
|
+#endif
|
|
|
+ goto ret;
|
|
|
+ }
|
|
|
+#endif /*}*/
|
|
|
+ nz0 = 1;
|
|
|
+ while(*++s == '0') ;
|
|
|
+ if (!*s)
|
|
|
+ goto ret;
|
|
|
+ }
|
|
|
+ s0 = s;
|
|
|
+ y = z = 0;
|
|
|
+ for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
|
|
|
+ if (nd < 9)
|
|
|
+ y = 10*y + c - '0';
|
|
|
+ else if (nd < 16)
|
|
|
+ z = 10*z + c - '0';
|
|
|
+ nd0 = nd;
|
|
|
+ bc.dp0 = bc.dp1 = s - s0;
|
|
|
+ for(s1 = s; s1 > s0 && *--s1 == '0'; )
|
|
|
+ ++nz1;
|
|
|
+#ifdef USE_LOCALE
|
|
|
+ s1 = localeconv()->decimal_point;
|
|
|
+ if (c == *s1) {
|
|
|
+ c = '.';
|
|
|
+ if (*++s1) {
|
|
|
+ s2 = s;
|
|
|
+ for(;;) {
|
|
|
+ if (*++s2 != *s1) {
|
|
|
+ c = 0;
|
|
|
+ break;
|
|
|
+ }
|
|
|
+ if (!*++s1) {
|
|
|
+ s = s2;
|
|
|
+ break;
|
|
|
+ }
|
|
|
+ }
|
|
|
+ }
|
|
|
+ }
|
|
|
+#endif
|
|
|
+ if (c == '.') {
|
|
|
+ c = *++s;
|
|
|
+ bc.dp1 = s - s0;
|
|
|
+ bc.dplen = bc.dp1 - bc.dp0;
|
|
|
+ if (!nd) {
|
|
|
+ for(; c == '0'; c = *++s)
|
|
|
+ nz++;
|
|
|
+ if (c > '0' && c <= '9') {
|
|
|
+ bc.dp0 = s0 - s;
|
|
|
+ bc.dp1 = bc.dp0 + bc.dplen;
|
|
|
+ s0 = s;
|
|
|
+ nf += nz;
|
|
|
+ nz = 0;
|
|
|
+ goto have_dig;
|
|
|
+ }
|
|
|
+ goto dig_done;
|
|
|
+ }
|
|
|
+ for(; c >= '0' && c <= '9'; c = *++s) {
|
|
|
+ have_dig:
|
|
|
+ nz++;
|
|
|
+ if (c -= '0') {
|
|
|
+ nf += nz;
|
|
|
+ for(i = 1; i < nz; i++)
|
|
|
+ if (nd++ < 9)
|
|
|
+ y *= 10;
|
|
|
+ else if (nd <= DBL_DIG + 1)
|
|
|
+ z *= 10;
|
|
|
+ if (nd++ < 9)
|
|
|
+ y = 10*y + c;
|
|
|
+ else if (nd <= DBL_DIG + 1)
|
|
|
+ z = 10*z + c;
|
|
|
+ nz = nz1 = 0;
|
|
|
+ }
|
|
|
+ }
|
|
|
+ }
|
|
|
+ dig_done:
|
|
|
+ e = 0;
|
|
|
+ if (c == 'e' || c == 'E') {
|
|
|
+ if (!nd && !nz && !nz0) {
|
|
|
+ goto ret0;
|
|
|
+ }
|
|
|
+ s00 = s;
|
|
|
+ esign = 0;
|
|
|
+ switch(c = *++s) {
|
|
|
+ case '-':
|
|
|
+ esign = 1;
|
|
|
+ case '+':
|
|
|
+ c = *++s;
|
|
|
+ }
|
|
|
+ if (c >= '0' && c <= '9') {
|
|
|
+ while(c == '0')
|
|
|
+ c = *++s;
|
|
|
+ if (c > '0' && c <= '9') {
|
|
|
+ L = c - '0';
|
|
|
+ s1 = s;
|
|
|
+ while((c = *++s) >= '0' && c <= '9')
|
|
|
+ L = 10*L + c - '0';
|
|
|
+ if (s - s1 > 8 || L > 19999)
|
|
|
+ /* Avoid confusion from exponents
|
|
|
+ * so large that e might overflow.
|
|
|
+ */
|
|
|
+ e = 19999; /* safe for 16 bit ints */
|
|
|
+ else
|
|
|
+ e = (int)L;
|
|
|
+ if (esign)
|
|
|
+ e = -e;
|
|
|
+ }
|
|
|
+ else
|
|
|
+ e = 0;
|
|
|
+ }
|
|
|
+ else
|
|
|
+ s = s00;
|
|
|
+ }
|
|
|
+ if (!nd) {
|
|
|
+ if (!nz && !nz0) {
|
|
|
+#ifdef INFNAN_CHECK
|
|
|
+ /* Check for Nan and Infinity */
|
|
|
+ if (!bc.dplen)
|
|
|
+ switch(c) {
|
|
|
+ case 'i':
|
|
|
+ case 'I':
|
|
|
+ if (match(&s,"nf")) {
|
|
|
+ --s;
|
|
|
+ if (!match(&s,"inity"))
|
|
|
+ ++s;
|
|
|
+ word0(&rv) = 0x7ff00000;
|
|
|
+ word1(&rv) = 0;
|
|
|
+ goto ret;
|
|
|
+ }
|
|
|
+ break;
|
|
|
+ case 'n':
|
|
|
+ case 'N':
|
|
|
+ if (match(&s, "an")) {
|
|
|
+ word0(&rv) = NAN_WORD0;
|
|
|
+ word1(&rv) = NAN_WORD1;
|
|
|
+#ifndef No_Hex_NaN
|
|
|
+ if (*s == '(') /*)*/
|
|
|
+ hexnan(&rv, &s);
|
|
|
+#endif
|
|
|
+ goto ret;
|
|
|
+ }
|
|
|
+ }
|
|
|
+#endif /* INFNAN_CHECK */
|
|
|
+ ret0:
|
|
|
+ s = s00;
|
|
|
+ sign = 0;
|
|
|
+ }
|
|
|
+ goto ret;
|
|
|
+ }
|
|
|
+ bc.e0 = e1 = e -= nf;
|
|
|
+
|
|
|
+ /* Now we have nd0 digits, starting at s0, followed by a
|
|
|
+ * decimal point, followed by nd-nd0 digits. The number we're
|
|
|
+ * after is the integer represented by those digits times
|
|
|
+ * 10**e */
|
|
|
+
|
|
|
+ if (!nd0)
|
|
|
+ nd0 = nd;
|
|
|
+ k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
|
|
|
+ dval(&rv) = y;
|
|
|
+ if (k > 9) {
|
|
|
+#ifdef SET_INEXACT
|
|
|
+ if (k > DBL_DIG)
|
|
|
+ oldinexact = get_inexact();
|
|
|
+#endif
|
|
|
+ dval(&rv) = tens[k - 9] * dval(&rv) + z;
|
|
|
+ }
|
|
|
+ bd0 = 0;
|
|
|
+ if (nd <= DBL_DIG
|
|
|
+#ifndef RND_PRODQUOT
|
|
|
+#ifndef Honor_FLT_ROUNDS
|
|
|
+ && Flt_Rounds == 1
|
|
|
+#endif
|
|
|
+#endif
|
|
|
+ ) {
|
|
|
+ if (!e)
|
|
|
+ goto ret;
|
|
|
+#ifndef ROUND_BIASED_without_Round_Up
|
|
|
+ if (e > 0) {
|
|
|
+ if (e <= Ten_pmax) {
|
|
|
+#ifdef VAX
|
|
|
+ goto vax_ovfl_check;
|
|
|
+#else
|
|
|
+#ifdef Honor_FLT_ROUNDS
|
|
|
+ /* round correctly FLT_ROUNDS = 2 or 3 */
|
|
|
+ if (sign) {
|
|
|
+ rv.d = -rv.d;
|
|
|
+ sign = 0;
|
|
|
+ }
|
|
|
+#endif
|
|
|
+ /* rv = */ rounded_product(dval(&rv), tens[e]);
|
|
|
+ goto ret;
|
|
|
+#endif
|
|
|
+ }
|
|
|
+ i = DBL_DIG - nd;
|
|
|
+ if (e <= Ten_pmax + i) {
|
|
|
+ /* A fancier test would sometimes let us do
|
|
|
+ * this for larger i values.
|
|
|
+ */
|
|
|
+#ifdef Honor_FLT_ROUNDS
|
|
|
+ /* round correctly FLT_ROUNDS = 2 or 3 */
|
|
|
+ if (sign) {
|
|
|
+ rv.d = -rv.d;
|
|
|
+ sign = 0;
|
|
|
+ }
|
|
|
+#endif
|
|
|
+ e -= i;
|
|
|
+ dval(&rv) *= tens[i];
|
|
|
+#ifdef VAX
|
|
|
+ /* VAX exponent range is so narrow we must
|
|
|
+ * worry about overflow here...
|
|
|
+ */
|
|
|
+ vax_ovfl_check:
|
|
|
+ word0(&rv) -= P*Exp_msk1;
|
|
|
+ /* rv = */ rounded_product(dval(&rv), tens[e]);
|
|
|
+ if ((word0(&rv) & Exp_mask)
|
|
|
+ > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
|
|
|
+ goto ovfl;
|
|
|
+ word0(&rv) += P*Exp_msk1;
|
|
|
+#else
|
|
|
+ /* rv = */ rounded_product(dval(&rv), tens[e]);
|
|
|
+#endif
|
|
|
+ goto ret;
|
|
|
+ }
|
|
|
+ }
|
|
|
+#ifndef Inaccurate_Divide
|
|
|
+ else if (e >= -Ten_pmax) {
|
|
|
+#ifdef Honor_FLT_ROUNDS
|
|
|
+ /* round correctly FLT_ROUNDS = 2 or 3 */
|
|
|
+ if (sign) {
|
|
|
+ rv.d = -rv.d;
|
|
|
+ sign = 0;
|
|
|
+ }
|
|
|
+#endif
|
|
|
+ /* rv = */ rounded_quotient(dval(&rv), tens[-e]);
|
|
|
+ goto ret;
|
|
|
+ }
|
|
|
+#endif
|
|
|
+#endif /* ROUND_BIASED_without_Round_Up */
|
|
|
+ }
|
|
|
+ e1 += nd - k;
|
|
|
+
|
|
|
+#ifdef IEEE_Arith
|
|
|
+#ifdef SET_INEXACT
|
|
|
+ bc.inexact = 1;
|
|
|
+ if (k <= DBL_DIG)
|
|
|
+ oldinexact = get_inexact();
|
|
|
+#endif
|
|
|
+#ifdef Avoid_Underflow
|
|
|
+ bc.scale = 0;
|
|
|
+#endif
|
|
|
+#ifdef Honor_FLT_ROUNDS
|
|
|
+ if (bc.rounding >= 2) {
|
|
|
+ if (sign)
|
|
|
+ bc.rounding = bc.rounding == 2 ? 0 : 2;
|
|
|
+ else
|
|
|
+ if (bc.rounding != 2)
|
|
|
+ bc.rounding = 0;
|
|
|
+ }
|
|
|
+#endif
|
|
|
+#endif /*IEEE_Arith*/
|
|
|
+
|
|
|
+ /* Get starting approximation = rv * 10**e1 */
|
|
|
+
|
|
|
+ if (e1 > 0) {
|
|
|
+ if ((i = e1 & 15))
|
|
|
+ dval(&rv) *= tens[i];
|
|
|
+ if (e1 &= ~15) {
|
|
|
+ if (e1 > DBL_MAX_10_EXP) {
|
|
|
+ ovfl:
|
|
|
+ /* Can't trust HUGE_VAL */
|
|
|
+#ifdef IEEE_Arith
|
|
|
+#ifdef Honor_FLT_ROUNDS
|
|
|
+ switch(bc.rounding) {
|
|
|
+ case 0: /* toward 0 */
|
|
|
+ case 3: /* toward -infinity */
|
|
|
+ word0(&rv) = Big0;
|
|
|
+ word1(&rv) = Big1;
|
|
|
+ break;
|
|
|
+ default:
|
|
|
+ word0(&rv) = Exp_mask;
|
|
|
+ word1(&rv) = 0;
|
|
|
+ }
|
|
|
+#else /*Honor_FLT_ROUNDS*/
|
|
|
+ word0(&rv) = Exp_mask;
|
|
|
+ word1(&rv) = 0;
|
|
|
+#endif /*Honor_FLT_ROUNDS*/
|
|
|
+#ifdef SET_INEXACT
|
|
|
+ /* set overflow bit */
|
|
|
+ dval(&rv0) = 1e300;
|
|
|
+ dval(&rv0) *= dval(&rv0);
|
|
|
+#endif
|
|
|
+#else /*IEEE_Arith*/
|
|
|
+ word0(&rv) = Big0;
|
|
|
+ word1(&rv) = Big1;
|
|
|
+#endif /*IEEE_Arith*/
|
|
|
+ range_err:
|
|
|
+ if (bd0) {
|
|
|
+ Bfree(bb);
|
|
|
+ Bfree(bd);
|
|
|
+ Bfree(bs);
|
|
|
+ Bfree(bd0);
|
|
|
+ Bfree(delta);
|
|
|
+ }
|
|
|
+#ifndef NO_ERRNO
|
|
|
+ errno = ERANGE;
|
|
|
+#endif
|
|
|
+ goto ret;
|
|
|
+ }
|
|
|
+ e1 >>= 4;
|
|
|
+ for(j = 0; e1 > 1; j++, e1 >>= 1)
|
|
|
+ if (e1 & 1)
|
|
|
+ dval(&rv) *= bigtens[j];
|
|
|
+ /* The last multiplication could overflow. */
|
|
|
+ word0(&rv) -= P*Exp_msk1;
|
|
|
+ dval(&rv) *= bigtens[j];
|
|
|
+ if ((z = word0(&rv) & Exp_mask)
|
|
|
+ > Exp_msk1*(DBL_MAX_EXP+Bias-P))
|
|
|
+ goto ovfl;
|
|
|
+ if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
|
|
|
+ /* set to largest number */
|
|
|
+ /* (Can't trust DBL_MAX) */
|
|
|
+ word0(&rv) = Big0;
|
|
|
+ word1(&rv) = Big1;
|
|
|
+ }
|
|
|
+ else
|
|
|
+ word0(&rv) += P*Exp_msk1;
|
|
|
+ }
|
|
|
+ }
|
|
|
+ else if (e1 < 0) {
|
|
|
+ e1 = -e1;
|
|
|
+ if ((i = e1 & 15))
|
|
|
+ dval(&rv) /= tens[i];
|
|
|
+ if (e1 >>= 4) {
|
|
|
+ if (e1 >= 1 << n_bigtens)
|
|
|
+ goto undfl;
|
|
|
+#ifdef Avoid_Underflow
|
|
|
+ if (e1 & Scale_Bit)
|
|
|
+ bc.scale = 2*P;
|
|
|
+ for(j = 0; e1 > 0; j++, e1 >>= 1)
|
|
|
+ if (e1 & 1)
|
|
|
+ dval(&rv) *= tinytens[j];
|
|
|
+ if (bc.scale && (j = 2*P + 1 - ((word0(&rv) & Exp_mask)
|
|
|
+ >> Exp_shift)) > 0) {
|
|
|
+ /* scaled rv is denormal; clear j low bits */
|
|
|
+ if (j >= 32) {
|
|
|
+ if (j > 54)
|
|
|
+ goto undfl;
|
|
|
+ word1(&rv) = 0;
|
|
|
+ if (j >= 53)
|
|
|
+ word0(&rv) = (P+2)*Exp_msk1;
|
|
|
+ else
|
|
|
+ word0(&rv) &= 0xffffffff << (j-32);
|
|
|
+ }
|
|
|
+ else
|
|
|
+ word1(&rv) &= 0xffffffff << j;
|
|
|
+ }
|
|
|
+#else
|
|
|
+ for(j = 0; e1 > 1; j++, e1 >>= 1)
|
|
|
+ if (e1 & 1)
|
|
|
+ dval(&rv) *= tinytens[j];
|
|
|
+ /* The last multiplication could underflow. */
|
|
|
+ dval(&rv0) = dval(&rv);
|
|
|
+ dval(&rv) *= tinytens[j];
|
|
|
+ if (!dval(&rv)) {
|
|
|
+ dval(&rv) = 2.*dval(&rv0);
|
|
|
+ dval(&rv) *= tinytens[j];
|
|
|
+#endif
|
|
|
+ if (!dval(&rv)) {
|
|
|
+ undfl:
|
|
|
+ dval(&rv) = 0.;
|
|
|
+ goto range_err;
|
|
|
+ }
|
|
|
+#ifndef Avoid_Underflow
|
|
|
+ word0(&rv) = Tiny0;
|
|
|
+ word1(&rv) = Tiny1;
|
|
|
+ /* The refinement below will clean
|
|
|
+ * this approximation up.
|
|
|
+ */
|
|
|
+ }
|
|
|
+#endif
|
|
|
+ }
|
|
|
+ }
|
|
|
+
|
|
|
+ /* Now the hard part -- adjusting rv to the correct value.*/
|
|
|
+
|
|
|
+ /* Put digits into bd: true value = bd * 10^e */
|
|
|
+
|
|
|
+ bc.nd = nd - nz1;
|
|
|
+#ifndef NO_STRTOD_BIGCOMP
|
|
|
+ bc.nd0 = nd0; /* Only needed if nd > strtod_diglim, but done here */
|
|
|
+ /* to silence an erroneous warning about bc.nd0 */
|
|
|
+ /* possibly not being initialized. */
|
|
|
+ if (nd > strtod_diglim) {
|
|
|
+ /* ASSERT(strtod_diglim >= 18); 18 == one more than the */
|
|
|
+ /* minimum number of decimal digits to distinguish double values */
|
|
|
+ /* in IEEE arithmetic. */
|
|
|
+ i = j = 18;
|
|
|
+ if (i > nd0)
|
|
|
+ j += bc.dplen;
|
|
|
+ for(;;) {
|
|
|
+ if (--j < bc.dp1 && j >= bc.dp0)
|
|
|
+ j = bc.dp0 - 1;
|
|
|
+ if (s0[j] != '0')
|
|
|
+ break;
|
|
|
+ --i;
|
|
|
+ }
|
|
|
+ e += nd - i;
|
|
|
+ nd = i;
|
|
|
+ if (nd0 > nd)
|
|
|
+ nd0 = nd;
|
|
|
+ if (nd < 9) { /* must recompute y */
|
|
|
+ y = 0;
|
|
|
+ for(i = 0; i < nd0; ++i)
|
|
|
+ y = 10*y + s0[i] - '0';
|
|
|
+ for(j = bc.dp1; i < nd; ++i)
|
|
|
+ y = 10*y + s0[j++] - '0';
|
|
|
+ }
|
|
|
+ }
|
|
|
+#endif
|
|
|
+ bd0 = s2b(s0, nd0, nd, y, bc.dplen);
|
|
|
+
|
|
|
+ for(;;) {
|
|
|
+ bd = Balloc(bd0->k);
|
|
|
+ Bcopy(bd, bd0);
|
|
|
+ bb = d2b(&rv, &bbe, &bbbits); /* rv = bb * 2^bbe */
|
|
|
+ bs = i2b(1);
|
|
|
+
|
|
|
+ if (e >= 0) {
|
|
|
+ bb2 = bb5 = 0;
|
|
|
+ bd2 = bd5 = e;
|
|
|
+ }
|
|
|
+ else {
|
|
|
+ bb2 = bb5 = -e;
|
|
|
+ bd2 = bd5 = 0;
|
|
|
+ }
|
|
|
+ if (bbe >= 0)
|
|
|
+ bb2 += bbe;
|
|
|
+ else
|
|
|
+ bd2 -= bbe;
|
|
|
+ bs2 = bb2;
|
|
|
+#ifdef Honor_FLT_ROUNDS
|
|
|
+ if (bc.rounding != 1)
|
|
|
+ bs2++;
|
|
|
+#endif
|
|
|
+#ifdef Avoid_Underflow
|
|
|
+ Lsb = LSB;
|
|
|
+ Lsb1 = 0;
|
|
|
+ j = bbe - bc.scale;
|
|
|
+ i = j + bbbits - 1; /* logb(rv) */
|
|
|
+ j = P + 1 - bbbits;
|
|
|
+ if (i < Emin) { /* denormal */
|
|
|
+ i = Emin - i;
|
|
|
+ j -= i;
|
|
|
+ if (i < 32)
|
|
|
+ Lsb <<= i;
|
|
|
+ else if (i < 52)
|
|
|
+ Lsb1 = Lsb << (i-32);
|
|
|
+ else
|
|
|
+ Lsb1 = Exp_mask;
|
|
|
+ }
|
|
|
+#else /*Avoid_Underflow*/
|
|
|
+#ifdef Sudden_Underflow
|
|
|
+#ifdef IBM
|
|
|
+ j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
|
|
|
+#else
|
|
|
+ j = P + 1 - bbbits;
|
|
|
+#endif
|
|
|
+#else /*Sudden_Underflow*/
|
|
|
+ j = bbe;
|
|
|
+ i = j + bbbits - 1; /* logb(rv) */
|
|
|
+ if (i < Emin) /* denormal */
|
|
|
+ j += P - Emin;
|
|
|
+ else
|
|
|
+ j = P + 1 - bbbits;
|
|
|
+#endif /*Sudden_Underflow*/
|
|
|
+#endif /*Avoid_Underflow*/
|
|
|
+ bb2 += j;
|
|
|
+ bd2 += j;
|
|
|
+#ifdef Avoid_Underflow
|
|
|
+ bd2 += bc.scale;
|
|
|
+#endif
|
|
|
+ i = bb2 < bd2 ? bb2 : bd2;
|
|
|
+ if (i > bs2)
|
|
|
+ i = bs2;
|
|
|
+ if (i > 0) {
|
|
|
+ bb2 -= i;
|
|
|
+ bd2 -= i;
|
|
|
+ bs2 -= i;
|
|
|
+ }
|
|
|
+ if (bb5 > 0) {
|
|
|
+ bs = pow5mult(bs, bb5);
|
|
|
+ bb1 = mult(bs, bb);
|
|
|
+ Bfree(bb);
|
|
|
+ bb = bb1;
|
|
|
+ }
|
|
|
+ if (bb2 > 0)
|
|
|
+ bb = lshift(bb, bb2);
|
|
|
+ if (bd5 > 0)
|
|
|
+ bd = pow5mult(bd, bd5);
|
|
|
+ if (bd2 > 0)
|
|
|
+ bd = lshift(bd, bd2);
|
|
|
+ if (bs2 > 0)
|
|
|
+ bs = lshift(bs, bs2);
|
|
|
+ delta = diff(bb, bd);
|
|
|
+ bc.dsign = delta->sign;
|
|
|
+ delta->sign = 0;
|
|
|
+ i = cmp(delta, bs);
|
|
|
+#ifndef NO_STRTOD_BIGCOMP /*{*/
|
|
|
+ if (bc.nd > nd && i <= 0) {
|
|
|
+ if (bc.dsign) {
|
|
|
+ /* Must use bigcomp(). */
|
|
|
+ req_bigcomp = 1;
|
|
|
+ break;
|
|
|
+ }
|
|
|
+#ifdef Honor_FLT_ROUNDS
|
|
|
+ if (bc.rounding != 1) {
|
|
|
+ if (i < 0) {
|
|
|
+ req_bigcomp = 1;
|
|
|
+ break;
|
|
|
+ }
|
|
|
+ }
|
|
|
+ else
|
|
|
+#endif
|
|
|
+ i = -1; /* Discarded digits make delta smaller. */
|
|
|
+ }
|
|
|
+#endif /*}*/
|
|
|
+#ifdef Honor_FLT_ROUNDS /*{*/
|
|
|
+ if (bc.rounding != 1) {
|
|
|
+ if (i < 0) {
|
|
|
+ /* Error is less than an ulp */
|
|
|
+ if (!delta->x[0] && delta->wds <= 1) {
|
|
|
+ /* exact */
|
|
|
+#ifdef SET_INEXACT
|
|
|
+ bc.inexact = 0;
|
|
|
+#endif
|
|
|
+ break;
|
|
|
+ }
|
|
|
+ if (bc.rounding) {
|
|
|
+ if (bc.dsign) {
|
|
|
+ adj.d = 1.;
|
|
|
+ goto apply_adj;
|
|
|
+ }
|
|
|
+ }
|
|
|
+ else if (!bc.dsign) {
|
|
|
+ adj.d = -1.;
|
|
|
+ if (!word1(&rv)
|
|
|
+ && !(word0(&rv) & Frac_mask)) {
|
|
|
+ y = word0(&rv) & Exp_mask;
|
|
|
+#ifdef Avoid_Underflow
|
|
|
+ if (!bc.scale || y > 2*P*Exp_msk1)
|
|
|
+#else
|
|
|
+ if (y)
|
|
|
+#endif
|
|
|
+ {
|
|
|
+ delta = lshift(delta,Log2P);
|
|
|
+ if (cmp(delta, bs) <= 0)
|
|
|
+ adj.d = -0.5;
|
|
|
+ }
|
|
|
+ }
|
|
|
+ apply_adj:
|
|
|
+#ifdef Avoid_Underflow /*{*/
|
|
|
+ if (bc.scale && (y = word0(&rv) & Exp_mask)
|
|
|
+ <= 2*P*Exp_msk1)
|
|
|
+ word0(&adj) += (2*P+1)*Exp_msk1 - y;
|
|
|
+#else
|
|
|
+#ifdef Sudden_Underflow
|
|
|
+ if ((word0(&rv) & Exp_mask) <=
|
|
|
+ P*Exp_msk1) {
|
|
|
+ word0(&rv) += P*Exp_msk1;
|
|
|
+ dval(&rv) += adj.d*ulp(dval(&rv));
|
|
|
+ word0(&rv) -= P*Exp_msk1;
|
|
|
+ }
|
|
|
+ else
|
|
|
+#endif /*Sudden_Underflow*/
|
|
|
+#endif /*Avoid_Underflow}*/
|
|
|
+ dval(&rv) += adj.d*ulp(&rv);
|
|
|
+ }
|
|
|
+ break;
|
|
|
+ }
|
|
|
+ adj.d = ratio(delta, bs);
|
|
|
+ if (adj.d < 1.)
|
|
|
+ adj.d = 1.;
|
|
|
+ if (adj.d <= 0x7ffffffe) {
|
|
|
+ /* adj = rounding ? ceil(adj) : floor(adj); */
|
|
|
+ y = adj.d;
|
|
|
+ if (y != adj.d) {
|
|
|
+ if (!((bc.rounding>>1) ^ bc.dsign))
|
|
|
+ y++;
|
|
|
+ adj.d = y;
|
|
|
+ }
|
|
|
+ }
|
|
|
+#ifdef Avoid_Underflow /*{*/
|
|
|
+ if (bc.scale && (y = word0(&rv) & Exp_mask) <= 2*P*Exp_msk1)
|
|
|
+ word0(&adj) += (2*P+1)*Exp_msk1 - y;
|
|
|
+#else
|
|
|
+#ifdef Sudden_Underflow
|
|
|
+ if ((word0(&rv) & Exp_mask) <= P*Exp_msk1) {
|
|
|
+ word0(&rv) += P*Exp_msk1;
|
|
|
+ adj.d *= ulp(dval(&rv));
|
|
|
+ if (bc.dsign)
|
|
|
+ dval(&rv) += adj.d;
|
|
|
+ else
|
|
|
+ dval(&rv) -= adj.d;
|
|
|
+ word0(&rv) -= P*Exp_msk1;
|
|
|
+ goto cont;
|
|
|
+ }
|
|
|
+#endif /*Sudden_Underflow*/
|
|
|
+#endif /*Avoid_Underflow}*/
|
|
|
+ adj.d *= ulp(&rv);
|
|
|
+ if (bc.dsign) {
|
|
|
+ if (word0(&rv) == Big0 && word1(&rv) == Big1)
|
|
|
+ goto ovfl;
|
|
|
+ dval(&rv) += adj.d;
|
|
|
+ }
|
|
|
+ else
|
|
|
+ dval(&rv) -= adj.d;
|
|
|
+ goto cont;
|
|
|
+ }
|
|
|
+#endif /*}Honor_FLT_ROUNDS*/
|
|
|
+
|
|
|
+ if (i < 0) {
|
|
|
+ /* Error is less than half an ulp -- check for
|
|
|
+ * special case of mantissa a power of two.
|
|
|
+ */
|
|
|
+ if (bc.dsign || word1(&rv) || word0(&rv) & Bndry_mask
|
|
|
+#ifdef IEEE_Arith /*{*/
|
|
|
+#ifdef Avoid_Underflow
|
|
|
+ || (word0(&rv) & Exp_mask) <= (2*P+1)*Exp_msk1
|
|
|
+#else
|
|
|
+ || (word0(&rv) & Exp_mask) <= Exp_msk1
|
|
|
+#endif
|
|
|
+#endif /*}*/
|
|
|
+ ) {
|
|
|
+#ifdef SET_INEXACT
|
|
|
+ if (!delta->x[0] && delta->wds <= 1)
|
|
|
+ bc.inexact = 0;
|
|
|
+#endif
|
|
|
+ break;
|
|
|
+ }
|
|
|
+ if (!delta->x[0] && delta->wds <= 1) {
|
|
|
+ /* exact result */
|
|
|
+#ifdef SET_INEXACT
|
|
|
+ bc.inexact = 0;
|
|
|
+#endif
|
|
|
+ break;
|
|
|
+ }
|
|
|
+ delta = lshift(delta,Log2P);
|
|
|
+ if (cmp(delta, bs) > 0)
|
|
|
+ goto drop_down;
|
|
|
+ break;
|
|
|
+ }
|
|
|
+ if (i == 0) {
|
|
|
+ /* exactly half-way between */
|
|
|
+ if (bc.dsign) {
|
|
|
+ if ((word0(&rv) & Bndry_mask1) == Bndry_mask1
|
|
|
+ && word1(&rv) == (
|
|
|
+#ifdef Avoid_Underflow
|
|
|
+ (bc.scale && (y = word0(&rv) & Exp_mask) <= 2*P*Exp_msk1)
|
|
|
+ ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
|
|
|
+#endif
|
|
|
+ 0xffffffff)) {
|
|
|
+ /*boundary case -- increment exponent*/
|
|
|
+ if (word0(&rv) == Big0 && word1(&rv) == Big1)
|
|
|
+ goto ovfl;
|
|
|
+ word0(&rv) = (word0(&rv) & Exp_mask)
|
|
|
+ + Exp_msk1
|
|
|
+#ifdef IBM
|
|
|
+ | Exp_msk1 >> 4
|
|
|
+#endif
|
|
|
+ ;
|
|
|
+ word1(&rv) = 0;
|
|
|
+#ifdef Avoid_Underflow
|
|
|
+ bc.dsign = 0;
|
|
|
+#endif
|
|
|
+ break;
|
|
|
+ }
|
|
|
+ }
|
|
|
+ else if (!(word0(&rv) & Bndry_mask) && !word1(&rv)) {
|
|
|
+ drop_down:
|
|
|
+ /* boundary case -- decrement exponent */
|
|
|
+#ifdef Sudden_Underflow /*{{*/
|
|
|
+ L = word0(&rv) & Exp_mask;
|
|
|
+#ifdef IBM
|
|
|
+ if (L < Exp_msk1)
|
|
|
+#else
|
|
|
+#ifdef Avoid_Underflow
|
|
|
+ if (L <= (bc.scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
|
|
|
+#else
|
|
|
+ if (L <= Exp_msk1)
|
|
|
+#endif /*Avoid_Underflow*/
|
|
|
+#endif /*IBM*/
|
|
|
+ {
|
|
|
+ if (bc.nd >nd) {
|
|
|
+ bc.uflchk = 1;
|
|
|
+ break;
|
|
|
+ }
|
|
|
+ goto undfl;
|
|
|
+ }
|
|
|
+ L -= Exp_msk1;
|
|
|
+#else /*Sudden_Underflow}{*/
|
|
|
+#ifdef Avoid_Underflow
|
|
|
+ if (bc.scale) {
|
|
|
+ L = word0(&rv) & Exp_mask;
|
|
|
+ if (L <= (2*P+1)*Exp_msk1) {
|
|
|
+ if (L > (P+2)*Exp_msk1)
|
|
|
+ /* round even ==> */
|
|
|
+ /* accept rv */
|
|
|
+ break;
|
|
|
+ /* rv = smallest denormal */
|
|
|
+ if (bc.nd >nd) {
|
|
|
+ bc.uflchk = 1;
|
|
|
+ break;
|
|
|
+ }
|
|
|
+ goto undfl;
|
|
|
+ }
|
|
|
+ }
|
|
|
+#endif /*Avoid_Underflow*/
|
|
|
+ L = (word0(&rv) & Exp_mask) - Exp_msk1;
|
|
|
+#endif /*Sudden_Underflow}}*/
|
|
|
+ word0(&rv) = L | Bndry_mask1;
|
|
|
+ word1(&rv) = 0xffffffff;
|
|
|
+#ifdef IBM
|
|
|
+ goto cont;
|
|
|
+#else
|
|
|
+#ifndef NO_STRTOD_BIGCOMP
|
|
|
+ if (bc.nd > nd)
|
|
|
+ goto cont;
|
|
|
+#endif
|
|
|
+ break;
|
|
|
+#endif
|
|
|
+ }
|
|
|
+#ifndef ROUND_BIASED
|
|
|
+#ifdef Avoid_Underflow
|
|
|
+ if (Lsb1) {
|
|
|
+ if (!(word0(&rv) & Lsb1))
|
|
|
+ break;
|
|
|
+ }
|
|
|
+ else if (!(word1(&rv) & Lsb))
|
|
|
+ break;
|
|
|
+#else
|
|
|
+ if (!(word1(&rv) & LSB))
|
|
|
+ break;
|
|
|
+#endif
|
|
|
+#endif
|
|
|
+ if (bc.dsign)
|
|
|
+#ifdef Avoid_Underflow
|
|
|
+ dval(&rv) += sulp(&rv, &bc);
|
|
|
+#else
|
|
|
+ dval(&rv) += ulp(&rv);
|
|
|
+#endif
|
|
|
+#ifndef ROUND_BIASED
|
|
|
+ else {
|
|
|
+#ifdef Avoid_Underflow
|
|
|
+ dval(&rv) -= sulp(&rv, &bc);
|
|
|
+#else
|
|
|
+ dval(&rv) -= ulp(&rv);
|
|
|
+#endif
|
|
|
+#ifndef Sudden_Underflow
|
|
|
+ if (!dval(&rv)) {
|
|
|
+ if (bc.nd >nd) {
|
|
|
+ bc.uflchk = 1;
|
|
|
+ break;
|
|
|
+ }
|
|
|
+ goto undfl;
|
|
|
+ }
|
|
|
+#endif
|
|
|
+ }
|
|
|
+#ifdef Avoid_Underflow
|
|
|
+ bc.dsign = 1 - bc.dsign;
|
|
|
+#endif
|
|
|
+#endif
|
|
|
+ break;
|
|
|
+ }
|
|
|
+ if ((aadj = ratio(delta, bs)) <= 2.) {
|
|
|
+ if (bc.dsign)
|
|
|
+ aadj = aadj1 = 1.;
|
|
|
+ else if (word1(&rv) || word0(&rv) & Bndry_mask) {
|
|
|
+#ifndef Sudden_Underflow
|
|
|
+ if (word1(&rv) == Tiny1 && !word0(&rv)) {
|
|
|
+ if (bc.nd >nd) {
|
|
|
+ bc.uflchk = 1;
|
|
|
+ break;
|
|
|
+ }
|
|
|
+ goto undfl;
|
|
|
+ }
|
|
|
+#endif
|
|
|
+ aadj = 1.;
|
|
|
+ aadj1 = -1.;
|
|
|
+ }
|
|
|
+ else {
|
|
|
+ /* special case -- power of FLT_RADIX to be */
|
|
|
+ /* rounded down... */
|
|
|
+
|
|
|
+ if (aadj < 2./FLT_RADIX)
|
|
|
+ aadj = 1./FLT_RADIX;
|
|
|
+ else
|
|
|
+ aadj *= 0.5;
|
|
|
+ aadj1 = -aadj;
|
|
|
+ }
|
|
|
+ }
|
|
|
+ else {
|
|
|
+ aadj *= 0.5;
|
|
|
+ aadj1 = bc.dsign ? aadj : -aadj;
|
|
|
+#ifdef Check_FLT_ROUNDS
|
|
|
+ switch(bc.rounding) {
|
|
|
+ case 2: /* towards +infinity */
|
|
|
+ aadj1 -= 0.5;
|
|
|
+ break;
|
|
|
+ case 0: /* towards 0 */
|
|
|
+ case 3: /* towards -infinity */
|
|
|
+ aadj1 += 0.5;
|
|
|
+ }
|
|
|
+#else
|
|
|
+ if (Flt_Rounds == 0)
|
|
|
+ aadj1 += 0.5;
|
|
|
+#endif /*Check_FLT_ROUNDS*/
|
|
|
+ }
|
|
|
+ y = word0(&rv) & Exp_mask;
|
|
|
+
|
|
|
+ /* Check for overflow */
|
|
|
+
|
|
|
+ if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
|
|
|
+ dval(&rv0) = dval(&rv);
|
|
|
+ word0(&rv) -= P*Exp_msk1;
|
|
|
+ adj.d = aadj1 * ulp(&rv);
|
|
|
+ dval(&rv) += adj.d;
|
|
|
+ if ((word0(&rv) & Exp_mask) >=
|
|
|
+ Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
|
|
|
+ if (word0(&rv0) == Big0 && word1(&rv0) == Big1)
|
|
|
+ goto ovfl;
|
|
|
+ word0(&rv) = Big0;
|
|
|
+ word1(&rv) = Big1;
|
|
|
+ goto cont;
|
|
|
+ }
|
|
|
+ else
|
|
|
+ word0(&rv) += P*Exp_msk1;
|
|
|
+ }
|
|
|
+ else {
|
|
|
+#ifdef Avoid_Underflow
|
|
|
+ if (bc.scale && y <= 2*P*Exp_msk1) {
|
|
|
+ if (aadj <= 0x7fffffff) {
|
|
|
+ if ((z = aadj) <= 0)
|
|
|
+ z = 1;
|
|
|
+ aadj = z;
|
|
|
+ aadj1 = bc.dsign ? aadj : -aadj;
|
|
|
+ }
|
|
|
+ dval(&aadj2) = aadj1;
|
|
|
+ word0(&aadj2) += (2*P+1)*Exp_msk1 - y;
|
|
|
+ aadj1 = dval(&aadj2);
|
|
|
+ adj.d = aadj1 * ulp(&rv);
|
|
|
+ dval(&rv) += adj.d;
|
|
|
+ if (rv.d == 0.)
|
|
|
+#ifdef NO_STRTOD_BIGCOMP
|
|
|
+ goto undfl;
|
|
|
+#else
|
|
|
+ {
|
|
|
+ if (bc.nd > nd)
|
|
|
+ bc.dsign = 1;
|
|
|
+ break;
|
|
|
+ }
|
|
|
+#endif
|
|
|
+ }
|
|
|
+ else {
|
|
|
+ adj.d = aadj1 * ulp(&rv);
|
|
|
+ dval(&rv) += adj.d;
|
|
|
+ }
|
|
|
+#else
|
|
|
+#ifdef Sudden_Underflow
|
|
|
+ if ((word0(&rv) & Exp_mask) <= P*Exp_msk1) {
|
|
|
+ dval(&rv0) = dval(&rv);
|
|
|
+ word0(&rv) += P*Exp_msk1;
|
|
|
+ adj.d = aadj1 * ulp(&rv);
|
|
|
+ dval(&rv) += adj.d;
|
|
|
+#ifdef IBM
|
|
|
+ if ((word0(&rv) & Exp_mask) < P*Exp_msk1)
|
|
|
+#else
|
|
|
+ if ((word0(&rv) & Exp_mask) <= P*Exp_msk1)
|
|
|
+#endif
|
|
|
+ {
|
|
|
+ if (word0(&rv0) == Tiny0
|
|
|
+ && word1(&rv0) == Tiny1) {
|
|
|
+ if (bc.nd >nd) {
|
|
|
+ bc.uflchk = 1;
|
|
|
+ break;
|
|
|
+ }
|
|
|
+ goto undfl;
|
|
|
+ }
|
|
|
+ word0(&rv) = Tiny0;
|
|
|
+ word1(&rv) = Tiny1;
|
|
|
+ goto cont;
|
|
|
+ }
|
|
|
+ else
|
|
|
+ word0(&rv) -= P*Exp_msk1;
|
|
|
+ }
|
|
|
+ else {
|
|
|
+ adj.d = aadj1 * ulp(&rv);
|
|
|
+ dval(&rv) += adj.d;
|
|
|
+ }
|
|
|
+#else /*Sudden_Underflow*/
|
|
|
+ /* Compute adj so that the IEEE rounding rules will
|
|
|
+ * correctly round rv + adj in some half-way cases.
|
|
|
+ * If rv * ulp(rv) is denormalized (i.e.,
|
|
|
+ * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
|
|
|
+ * trouble from bits lost to denormalization;
|
|
|
+ * example: 1.2e-307 .
|
|
|
+ */
|
|
|
+ if (y <= (P-1)*Exp_msk1 && aadj > 1.) {
|
|
|
+ aadj1 = (double)(int)(aadj + 0.5);
|
|
|
+ if (!bc.dsign)
|
|
|
+ aadj1 = -aadj1;
|
|
|
+ }
|
|
|
+ adj.d = aadj1 * ulp(&rv);
|
|
|
+ dval(&rv) += adj.d;
|
|
|
+#endif /*Sudden_Underflow*/
|
|
|
+#endif /*Avoid_Underflow*/
|
|
|
+ }
|
|
|
+ z = word0(&rv) & Exp_mask;
|
|
|
+#ifndef SET_INEXACT
|
|
|
+ if (bc.nd == nd) {
|
|
|
+#ifdef Avoid_Underflow
|
|
|
+ if (!bc.scale)
|
|
|
+#endif
|
|
|
+ if (y == z) {
|
|
|
+ /* Can we stop now? */
|
|
|
+ L = (Long)aadj;
|
|
|
+ aadj -= L;
|
|
|
+ /* The tolerances below are conservative. */
|
|
|
+ if (bc.dsign || word1(&rv) || word0(&rv) & Bndry_mask) {
|
|
|
+ if (aadj < .4999999 || aadj > .5000001)
|
|
|
+ break;
|
|
|
+ }
|
|
|
+ else if (aadj < .4999999/FLT_RADIX)
|
|
|
+ break;
|
|
|
+ }
|
|
|
+ }
|
|
|
+#endif
|
|
|
+ cont:
|
|
|
+ Bfree(bb);
|
|
|
+ Bfree(bd);
|
|
|
+ Bfree(bs);
|
|
|
+ Bfree(delta);
|
|
|
+ }
|
|
|
+ Bfree(bb);
|
|
|
+ Bfree(bd);
|
|
|
+ Bfree(bs);
|
|
|
+ Bfree(bd0);
|
|
|
+ Bfree(delta);
|
|
|
+#ifndef NO_STRTOD_BIGCOMP
|
|
|
+ if (req_bigcomp) {
|
|
|
+ bd0 = 0;
|
|
|
+ bc.e0 += nz1;
|
|
|
+ bigcomp(&rv, s0, &bc);
|
|
|
+ y = word0(&rv) & Exp_mask;
|
|
|
+ if (y == Exp_mask)
|
|
|
+ goto ovfl;
|
|
|
+ if (y == 0 && rv.d == 0.)
|
|
|
+ goto undfl;
|
|
|
+ }
|
|
|
+#endif
|
|
|
+#ifdef SET_INEXACT
|
|
|
+ if (bc.inexact) {
|
|
|
+ if (!oldinexact) {
|
|
|
+ word0(&rv0) = Exp_1 + (70 << Exp_shift);
|
|
|
+ word1(&rv0) = 0;
|
|
|
+ dval(&rv0) += 1.;
|
|
|
+ }
|
|
|
+ }
|
|
|
+ else if (!oldinexact)
|
|
|
+ clear_inexact();
|
|
|
+#endif
|
|
|
+#ifdef Avoid_Underflow
|
|
|
+ if (bc.scale) {
|
|
|
+ word0(&rv0) = Exp_1 - 2*P*Exp_msk1;
|
|
|
+ word1(&rv0) = 0;
|
|
|
+ dval(&rv) *= dval(&rv0);
|
|
|
+#ifndef NO_ERRNO
|
|
|
+ /* try to avoid the bug of testing an 8087 register value */
|
|
|
+#ifdef IEEE_Arith
|
|
|
+ if (!(word0(&rv) & Exp_mask))
|
|
|
+#else
|
|
|
+ if (word0(&rv) == 0 && word1(&rv) == 0)
|
|
|
+#endif
|
|
|
+ errno = ERANGE;
|
|
|
+#endif
|
|
|
+ }
|
|
|
+#endif /* Avoid_Underflow */
|
|
|
+#ifdef SET_INEXACT
|
|
|
+ if (bc.inexact && !(word0(&rv) & Exp_mask)) {
|
|
|
+ /* set underflow bit */
|
|
|
+ dval(&rv0) = 1e-300;
|
|
|
+ dval(&rv0) *= dval(&rv0);
|
|
|
+ }
|
|
|
+#endif
|
|
|
+ ret:
|
|
|
+ if (se)
|
|
|
+ *se = (char *)s;
|
|
|
+ return sign ? -dval(&rv) : dval(&rv);
|
|
|
+ }
|
|
|
+
|
|
|
+#ifndef MULTIPLE_THREADS
|
|
|
+ static char *dtoa_result;
|
|
|
+#endif
|
|
|
+
|
|
|
+ static char *
|
|
|
+#ifdef KR_headers
|
|
|
+rv_alloc(i) int i;
|
|
|
+#else
|
|
|
+rv_alloc(int i)
|
|
|
+#endif
|
|
|
+{
|
|
|
+ int j, k, *r;
|
|
|
+
|
|
|
+ j = sizeof(ULong);
|
|
|
+ for(k = 0;
|
|
|
+ sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= i;
|
|
|
+ j <<= 1)
|
|
|
+ k++;
|
|
|
+ r = (int*)Balloc(k);
|
|
|
+ *r = k;
|
|
|
+ return
|
|
|
+#ifndef MULTIPLE_THREADS
|
|
|
+ dtoa_result =
|
|
|
+#endif
|
|
|
+ (char *)(r+1);
|
|
|
+ }
|
|
|
+
|
|
|
+ static char *
|
|
|
+#ifdef KR_headers
|
|
|
+nrv_alloc(s, rve, n) char *s, **rve; int n;
|
|
|
+#else
|
|
|
+nrv_alloc(const char *s, char **rve, int n)
|
|
|
+#endif
|
|
|
+{
|
|
|
+ char *rv, *t;
|
|
|
+
|
|
|
+ t = rv = rv_alloc(n);
|
|
|
+ while((*t = *s++)) t++;
|
|
|
+ if (rve)
|
|
|
+ *rve = t;
|
|
|
+ return rv;
|
|
|
+ }
|
|
|
+
|
|
|
+/* freedtoa(s) must be used to free values s returned by dtoa
|
|
|
+ * when MULTIPLE_THREADS is #defined. It should be used in all cases,
|
|
|
+ * but for consistency with earlier versions of dtoa, it is optional
|
|
|
+ * when MULTIPLE_THREADS is not defined.
|
|
|
+ */
|
|
|
+
|
|
|
+ void
|
|
|
+#ifdef KR_headers
|
|
|
+freedtoa(s) char *s;
|
|
|
+#else
|
|
|
+freedtoa(char *s)
|
|
|
+#endif
|
|
|
+{
|
|
|
+ Bigint *b = (Bigint *)((int *)s - 1);
|
|
|
+ b->maxwds = 1 << (b->k = *(int*)b);
|
|
|
+ Bfree(b);
|
|
|
+#ifndef MULTIPLE_THREADS
|
|
|
+ if (s == dtoa_result)
|
|
|
+ dtoa_result = 0;
|
|
|
+#endif
|
|
|
+ }
|
|
|
+
|
|
|
+/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
|
|
|
+ *
|
|
|
+ * Inspired by "How to Print Floating-Point Numbers Accurately" by
|
|
|
+ * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126].
|
|
|
+ *
|
|
|
+ * Modifications:
|
|
|
+ * 1. Rather than iterating, we use a simple numeric overestimate
|
|
|
+ * to determine k = floor(log10(d)). We scale relevant
|
|
|
+ * quantities using O(log2(k)) rather than O(k) multiplications.
|
|
|
+ * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
|
|
|
+ * try to generate digits strictly left to right. Instead, we
|
|
|
+ * compute with fewer bits and propagate the carry if necessary
|
|
|
+ * when rounding the final digit up. This is often faster.
|
|
|
+ * 3. Under the assumption that input will be rounded nearest,
|
|
|
+ * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
|
|
|
+ * That is, we allow equality in stopping tests when the
|
|
|
+ * round-nearest rule will give the same floating-point value
|
|
|
+ * as would satisfaction of the stopping test with strict
|
|
|
+ * inequality.
|
|
|
+ * 4. We remove common factors of powers of 2 from relevant
|
|
|
+ * quantities.
|
|
|
+ * 5. When converting floating-point integers less than 1e16,
|
|
|
+ * we use floating-point arithmetic rather than resorting
|
|
|
+ * to multiple-precision integers.
|
|
|
+ * 6. When asked to produce fewer than 15 digits, we first try
|
|
|
+ * to get by with floating-point arithmetic; we resort to
|
|
|
+ * multiple-precision integer arithmetic only if we cannot
|
|
|
+ * guarantee that the floating-point calculation has given
|
|
|
+ * the correctly rounded result. For k requested digits and
|
|
|
+ * "uniformly" distributed input, the probability is
|
|
|
+ * something like 10^(k-15) that we must resort to the Long
|
|
|
+ * calculation.
|
|
|
+ */
|
|
|
+
|
|
|
+ char *
|
|
|
+dtoa
|
|
|
+#ifdef KR_headers
|
|
|
+ (dd, mode, ndigits, decpt, sign, rve)
|
|
|
+ double dd; int mode, ndigits, *decpt, *sign; char **rve;
|
|
|
+#else
|
|
|
+ (double dd, int mode, int ndigits, int *decpt, int *sign, char **rve)
|
|
|
+#endif
|
|
|
+{
|
|
|
+ /* Arguments ndigits, decpt, sign are similar to those
|
|
|
+ of ecvt and fcvt; trailing zeros are suppressed from
|
|
|
+ the returned string. If not null, *rve is set to point
|
|
|
+ to the end of the return value. If d is +-Infinity or NaN,
|
|
|
+ then *decpt is set to 9999.
|
|
|
+
|
|
|
+ mode:
|
|
|
+ 0 ==> shortest string that yields d when read in
|
|
|
+ and rounded to nearest.
|
|
|
+ 1 ==> like 0, but with Steele & White stopping rule;
|
|
|
+ e.g. with IEEE P754 arithmetic , mode 0 gives
|
|
|
+ 1e23 whereas mode 1 gives 9.999999999999999e22.
|
|
|
+ 2 ==> max(1,ndigits) significant digits. This gives a
|
|
|
+ return value similar to that of ecvt, except
|
|
|
+ that trailing zeros are suppressed.
|
|
|
+ 3 ==> through ndigits past the decimal point. This
|
|
|
+ gives a return value similar to that from fcvt,
|
|
|
+ except that trailing zeros are suppressed, and
|
|
|
+ ndigits can be negative.
|
|
|
+ 4,5 ==> similar to 2 and 3, respectively, but (in
|
|
|
+ round-nearest mode) with the tests of mode 0 to
|
|
|
+ possibly return a shorter string that rounds to d.
|
|
|
+ With IEEE arithmetic and compilation with
|
|
|
+ -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
|
|
|
+ as modes 2 and 3 when FLT_ROUNDS != 1.
|
|
|
+ 6-9 ==> Debugging modes similar to mode - 4: don't try
|
|
|
+ fast floating-point estimate (if applicable).
|
|
|
+
|
|
|
+ Values of mode other than 0-9 are treated as mode 0.
|
|
|
+
|
|
|
+ Sufficient space is allocated to the return value
|
|
|
+ to hold the suppressed trailing zeros.
|
|
|
+ */
|
|
|
+
|
|
|
+ int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
|
|
|
+ j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
|
|
|
+ spec_case, try_quick;
|
|
|
+ Long L;
|
|
|
+#ifndef Sudden_Underflow
|
|
|
+ int denorm;
|
|
|
+ ULong x;
|
|
|
+#endif
|
|
|
+ Bigint *b, *b1, *delta, *mlo, *mhi, *S;
|
|
|
+ U d2, eps, u;
|
|
|
+ double ds;
|
|
|
+ char *s, *s0;
|
|
|
+#ifndef No_leftright
|
|
|
+#ifdef IEEE_Arith
|
|
|
+ U eps1;
|
|
|
+#endif
|
|
|
+#endif
|
|
|
+#ifdef SET_INEXACT
|
|
|
+ int inexact, oldinexact;
|
|
|
+#endif
|
|
|
+#ifdef Honor_FLT_ROUNDS /*{*/
|
|
|
+ int Rounding;
|
|
|
+#ifdef Trust_FLT_ROUNDS /*{{ only define this if FLT_ROUNDS really works! */
|
|
|
+ Rounding = Flt_Rounds;
|
|
|
+#else /*}{*/
|
|
|
+ Rounding = 1;
|
|
|
+ switch(fegetround()) {
|
|
|
+ case FE_TOWARDZERO: Rounding = 0; break;
|
|
|
+ case FE_UPWARD: Rounding = 2; break;
|
|
|
+ case FE_DOWNWARD: Rounding = 3;
|
|
|
+ }
|
|
|
+#endif /*}}*/
|
|
|
+#endif /*}*/
|
|
|
+
|
|
|
+#ifndef MULTIPLE_THREADS
|
|
|
+ if (dtoa_result) {
|
|
|
+ freedtoa(dtoa_result);
|
|
|
+ dtoa_result = 0;
|
|
|
+ }
|
|
|
+#endif
|
|
|
+
|
|
|
+ u.d = dd;
|
|
|
+ if (word0(&u) & Sign_bit) {
|
|
|
+ /* set sign for everything, including 0's and NaNs */
|
|
|
+ *sign = 1;
|
|
|
+ word0(&u) &= ~Sign_bit; /* clear sign bit */
|
|
|
+ }
|
|
|
+ else
|
|
|
+ *sign = 0;
|
|
|
+
|
|
|
+#if defined(IEEE_Arith) + defined(VAX)
|
|
|
+#ifdef IEEE_Arith
|
|
|
+ if ((word0(&u) & Exp_mask) == Exp_mask)
|
|
|
+#else
|
|
|
+ if (word0(&u) == 0x8000)
|
|
|
+#endif
|
|
|
+ {
|
|
|
+ /* Infinity or NaN */
|
|
|
+ *decpt = 9999;
|
|
|
+#ifdef IEEE_Arith
|
|
|
+ if (!word1(&u) && !(word0(&u) & 0xfffff))
|
|
|
+ return nrv_alloc("Infinity", rve, 8);
|
|
|
+#endif
|
|
|
+ return nrv_alloc("NaN", rve, 3);
|
|
|
+ }
|
|
|
+#endif
|
|
|
+#ifdef IBM
|
|
|
+ dval(&u) += 0; /* normalize */
|
|
|
+#endif
|
|
|
+ if (!dval(&u)) {
|
|
|
+ *decpt = 1;
|
|
|
+ return nrv_alloc("0", rve, 1);
|
|
|
+ }
|
|
|
+
|
|
|
+#ifdef SET_INEXACT
|
|
|
+ try_quick = oldinexact = get_inexact();
|
|
|
+ inexact = 1;
|
|
|
+#endif
|
|
|
+#ifdef Honor_FLT_ROUNDS
|
|
|
+ if (Rounding >= 2) {
|
|
|
+ if (*sign)
|
|
|
+ Rounding = Rounding == 2 ? 0 : 2;
|
|
|
+ else
|
|
|
+ if (Rounding != 2)
|
|
|
+ Rounding = 0;
|
|
|
+ }
|
|
|
+#endif
|
|
|
+
|
|
|
+ b = d2b(&u, &be, &bbits);
|
|
|
+#ifdef Sudden_Underflow
|
|
|
+ i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
|
|
|
+#else
|
|
|
+ if ((i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask>>Exp_shift1)))) {
|
|
|
+#endif
|
|
|
+ dval(&d2) = dval(&u);
|
|
|
+ word0(&d2) &= Frac_mask1;
|
|
|
+ word0(&d2) |= Exp_11;
|
|
|
+#ifdef IBM
|
|
|
+ if (j = 11 - hi0bits(word0(&d2) & Frac_mask))
|
|
|
+ dval(&d2) /= 1 << j;
|
|
|
+#endif
|
|
|
+
|
|
|
+ /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
|
|
|
+ * log10(x) = log(x) / log(10)
|
|
|
+ * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
|
|
|
+ * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
|
|
|
+ *
|
|
|
+ * This suggests computing an approximation k to log10(d) by
|
|
|
+ *
|
|
|
+ * k = (i - Bias)*0.301029995663981
|
|
|
+ * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
|
|
|
+ *
|
|
|
+ * We want k to be too large rather than too small.
|
|
|
+ * The error in the first-order Taylor series approximation
|
|
|
+ * is in our favor, so we just round up the constant enough
|
|
|
+ * to compensate for any error in the multiplication of
|
|
|
+ * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
|
|
|
+ * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
|
|
|
+ * adding 1e-13 to the constant term more than suffices.
|
|
|
+ * Hence we adjust the constant term to 0.1760912590558.
|
|
|
+ * (We could get a more accurate k by invoking log10,
|
|
|
+ * but this is probably not worthwhile.)
|
|
|
+ */
|
|
|
+
|
|
|
+ i -= Bias;
|
|
|
+#ifdef IBM
|
|
|
+ i <<= 2;
|
|
|
+ i += j;
|
|
|
+#endif
|
|
|
+#ifndef Sudden_Underflow
|
|
|
+ denorm = 0;
|
|
|
+ }
|
|
|
+ else {
|
|
|
+ /* d is denormalized */
|
|
|
+
|
|
|
+ i = bbits + be + (Bias + (P-1) - 1);
|
|
|
+ x = i > 32 ? word0(&u) << (64 - i) | word1(&u) >> (i - 32)
|
|
|
+ : word1(&u) << (32 - i);
|
|
|
+ dval(&d2) = x;
|
|
|
+ word0(&d2) -= 31*Exp_msk1; /* adjust exponent */
|
|
|
+ i -= (Bias + (P-1) - 1) + 1;
|
|
|
+ denorm = 1;
|
|
|
+ }
|
|
|
+#endif
|
|
|
+ ds = (dval(&d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
|
|
|
+ k = (int)ds;
|
|
|
+ if (ds < 0. && ds != k)
|
|
|
+ k--; /* want k = floor(ds) */
|
|
|
+ k_check = 1;
|
|
|
+ if (k >= 0 && k <= Ten_pmax) {
|
|
|
+ if (dval(&u) < tens[k])
|
|
|
+ k--;
|
|
|
+ k_check = 0;
|
|
|
+ }
|
|
|
+ j = bbits - i - 1;
|
|
|
+ if (j >= 0) {
|
|
|
+ b2 = 0;
|
|
|
+ s2 = j;
|
|
|
+ }
|
|
|
+ else {
|
|
|
+ b2 = -j;
|
|
|
+ s2 = 0;
|
|
|
+ }
|
|
|
+ if (k >= 0) {
|
|
|
+ b5 = 0;
|
|
|
+ s5 = k;
|
|
|
+ s2 += k;
|
|
|
+ }
|
|
|
+ else {
|
|
|
+ b2 -= k;
|
|
|
+ b5 = -k;
|
|
|
+ s5 = 0;
|
|
|
+ }
|
|
|
+ if (mode < 0 || mode > 9)
|
|
|
+ mode = 0;
|
|
|
+
|
|
|
+#ifndef SET_INEXACT
|
|
|
+#ifdef Check_FLT_ROUNDS
|
|
|
+ try_quick = Rounding == 1;
|
|
|
+#else
|
|
|
+ try_quick = 1;
|
|
|
+#endif
|
|
|
+#endif /*SET_INEXACT*/
|
|
|
+
|
|
|
+ if (mode > 5) {
|
|
|
+ mode -= 4;
|
|
|
+ try_quick = 0;
|
|
|
+ }
|
|
|
+ leftright = 1;
|
|
|
+ ilim = ilim1 = -1; /* Values for cases 0 and 1; done here to */
|
|
|
+ /* silence erroneous "gcc -Wall" warning. */
|
|
|
+ switch(mode) {
|
|
|
+ case 0:
|
|
|
+ case 1:
|
|
|
+ i = 18;
|
|
|
+ ndigits = 0;
|
|
|
+ break;
|
|
|
+ case 2:
|
|
|
+ leftright = 0;
|
|
|
+ /* no break */
|
|
|
+ case 4:
|
|
|
+ if (ndigits <= 0)
|
|
|
+ ndigits = 1;
|
|
|
+ ilim = ilim1 = i = ndigits;
|
|
|
+ break;
|
|
|
+ case 3:
|
|
|
+ leftright = 0;
|
|
|
+ /* no break */
|
|
|
+ case 5:
|
|
|
+ i = ndigits + k + 1;
|
|
|
+ ilim = i;
|
|
|
+ ilim1 = i - 1;
|
|
|
+ if (i <= 0)
|
|
|
+ i = 1;
|
|
|
+ }
|
|
|
+ s = s0 = rv_alloc(i);
|
|
|
+
|
|
|
+#ifdef Honor_FLT_ROUNDS
|
|
|
+ if (mode > 1 && Rounding != 1)
|
|
|
+ leftright = 0;
|
|
|
+#endif
|
|
|
+
|
|
|
+ if (ilim >= 0 && ilim <= Quick_max && try_quick) {
|
|
|
+
|
|
|
+ /* Try to get by with floating-point arithmetic. */
|
|
|
+
|
|
|
+ i = 0;
|
|
|
+ dval(&d2) = dval(&u);
|
|
|
+ k0 = k;
|
|
|
+ ilim0 = ilim;
|
|
|
+ ieps = 2; /* conservative */
|
|
|
+ if (k > 0) {
|
|
|
+ ds = tens[k&0xf];
|
|
|
+ j = k >> 4;
|
|
|
+ if (j & Bletch) {
|
|
|
+ /* prevent overflows */
|
|
|
+ j &= Bletch - 1;
|
|
|
+ dval(&u) /= bigtens[n_bigtens-1];
|
|
|
+ ieps++;
|
|
|
+ }
|
|
|
+ for(; j; j >>= 1, i++)
|
|
|
+ if (j & 1) {
|
|
|
+ ieps++;
|
|
|
+ ds *= bigtens[i];
|
|
|
+ }
|
|
|
+ dval(&u) /= ds;
|
|
|
+ }
|
|
|
+ else if ((j1 = -k)) {
|
|
|
+ dval(&u) *= tens[j1 & 0xf];
|
|
|
+ for(j = j1 >> 4; j; j >>= 1, i++)
|
|
|
+ if (j & 1) {
|
|
|
+ ieps++;
|
|
|
+ dval(&u) *= bigtens[i];
|
|
|
+ }
|
|
|
+ }
|
|
|
+ if (k_check && dval(&u) < 1. && ilim > 0) {
|
|
|
+ if (ilim1 <= 0)
|
|
|
+ goto fast_failed;
|
|
|
+ ilim = ilim1;
|
|
|
+ k--;
|
|
|
+ dval(&u) *= 10.;
|
|
|
+ ieps++;
|
|
|
+ }
|
|
|
+ dval(&eps) = ieps*dval(&u) + 7.;
|
|
|
+ word0(&eps) -= (P-1)*Exp_msk1;
|
|
|
+ if (ilim == 0) {
|
|
|
+ S = mhi = 0;
|
|
|
+ dval(&u) -= 5.;
|
|
|
+ if (dval(&u) > dval(&eps))
|
|
|
+ goto one_digit;
|
|
|
+ if (dval(&u) < -dval(&eps))
|
|
|
+ goto no_digits;
|
|
|
+ goto fast_failed;
|
|
|
+ }
|
|
|
+#ifndef No_leftright
|
|
|
+ if (leftright) {
|
|
|
+ /* Use Steele & White method of only
|
|
|
+ * generating digits needed.
|
|
|
+ */
|
|
|
+ dval(&eps) = 0.5/tens[ilim-1] - dval(&eps);
|
|
|
+#ifdef IEEE_Arith
|
|
|
+ if (k0 < 0 && j1 >= 307) {
|
|
|
+ eps1.d = 1.01e256; /* 1.01 allows roundoff in the next few lines */
|
|
|
+ word0(&eps1) -= Exp_msk1 * (Bias+P-1);
|
|
|
+ dval(&eps1) *= tens[j1 & 0xf];
|
|
|
+ for(i = 0, j = (j1-256) >> 4; j; j >>= 1, i++)
|
|
|
+ if (j & 1)
|
|
|
+ dval(&eps1) *= bigtens[i];
|
|
|
+ if (eps.d < eps1.d)
|
|
|
+ eps.d = eps1.d;
|
|
|
+ }
|
|
|
+#endif
|
|
|
+ for(i = 0;;) {
|
|
|
+ L = dval(&u);
|
|
|
+ dval(&u) -= L;
|
|
|
+ *s++ = '0' + (int)L;
|
|
|
+ if (1. - dval(&u) < dval(&eps))
|
|
|
+ goto bump_up;
|
|
|
+ if (dval(&u) < dval(&eps))
|
|
|
+ goto ret1;
|
|
|
+ if (++i >= ilim)
|
|
|
+ break;
|
|
|
+ dval(&eps) *= 10.;
|
|
|
+ dval(&u) *= 10.;
|
|
|
+ }
|
|
|
+ }
|
|
|
+ else {
|
|
|
+#endif
|
|
|
+ /* Generate ilim digits, then fix them up. */
|
|
|
+ dval(&eps) *= tens[ilim-1];
|
|
|
+ for(i = 1;; i++, dval(&u) *= 10.) {
|
|
|
+ L = (Long)(dval(&u));
|
|
|
+ if (!(dval(&u) -= L))
|
|
|
+ ilim = i;
|
|
|
+ *s++ = '0' + (int)L;
|
|
|
+ if (i == ilim) {
|
|
|
+ if (dval(&u) > 0.5 + dval(&eps))
|
|
|
+ goto bump_up;
|
|
|
+ else if (dval(&u) < 0.5 - dval(&eps)) {
|
|
|
+ while(*--s == '0');
|
|
|
+ s++;
|
|
|
+ goto ret1;
|
|
|
+ }
|
|
|
+ break;
|
|
|
+ }
|
|
|
+ }
|
|
|
+#ifndef No_leftright
|
|
|
+ }
|
|
|
+#endif
|
|
|
+ fast_failed:
|
|
|
+ s = s0;
|
|
|
+ dval(&u) = dval(&d2);
|
|
|
+ k = k0;
|
|
|
+ ilim = ilim0;
|
|
|
+ }
|
|
|
+
|
|
|
+ /* Do we have a "small" integer? */
|
|
|
+
|
|
|
+ if (be >= 0 && k <= Int_max) {
|
|
|
+ /* Yes. */
|
|
|
+ ds = tens[k];
|
|
|
+ if (ndigits < 0 && ilim <= 0) {
|
|
|
+ S = mhi = 0;
|
|
|
+ if (ilim < 0 || dval(&u) <= 5*ds)
|
|
|
+ goto no_digits;
|
|
|
+ goto one_digit;
|
|
|
+ }
|
|
|
+ for(i = 1;; i++, dval(&u) *= 10.) {
|
|
|
+ L = (Long)(dval(&u) / ds);
|
|
|
+ dval(&u) -= L*ds;
|
|
|
+#ifdef Check_FLT_ROUNDS
|
|
|
+ /* If FLT_ROUNDS == 2, L will usually be high by 1 */
|
|
|
+ if (dval(&u) < 0) {
|
|
|
+ L--;
|
|
|
+ dval(&u) += ds;
|
|
|
+ }
|
|
|
+#endif
|
|
|
+ *s++ = '0' + (int)L;
|
|
|
+ if (!dval(&u)) {
|
|
|
+#ifdef SET_INEXACT
|
|
|
+ inexact = 0;
|
|
|
+#endif
|
|
|
+ break;
|
|
|
+ }
|
|
|
+ if (i == ilim) {
|
|
|
+#ifdef Honor_FLT_ROUNDS
|
|
|
+ if (mode > 1)
|
|
|
+ switch(Rounding) {
|
|
|
+ case 0: goto ret1;
|
|
|
+ case 2: goto bump_up;
|
|
|
+ }
|
|
|
+#endif
|
|
|
+ dval(&u) += dval(&u);
|
|
|
+#ifdef ROUND_BIASED
|
|
|
+ if (dval(&u) >= ds)
|
|
|
+#else
|
|
|
+ if (dval(&u) > ds || (dval(&u) == ds && L & 1))
|
|
|
+#endif
|
|
|
+ {
|
|
|
+ bump_up:
|
|
|
+ while(*--s == '9')
|
|
|
+ if (s == s0) {
|
|
|
+ k++;
|
|
|
+ *s = '0';
|
|
|
+ break;
|
|
|
+ }
|
|
|
+ ++*s++;
|
|
|
+ }
|
|
|
+ break;
|
|
|
+ }
|
|
|
+ }
|
|
|
+ goto ret1;
|
|
|
+ }
|
|
|
+
|
|
|
+ m2 = b2;
|
|
|
+ m5 = b5;
|
|
|
+ mhi = mlo = 0;
|
|
|
+ if (leftright) {
|
|
|
+ i =
|
|
|
+#ifndef Sudden_Underflow
|
|
|
+ denorm ? be + (Bias + (P-1) - 1 + 1) :
|
|
|
+#endif
|
|
|
+#ifdef IBM
|
|
|
+ 1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
|
|
|
+#else
|
|
|
+ 1 + P - bbits;
|
|
|
+#endif
|
|
|
+ b2 += i;
|
|
|
+ s2 += i;
|
|
|
+ mhi = i2b(1);
|
|
|
+ }
|
|
|
+ if (m2 > 0 && s2 > 0) {
|
|
|
+ i = m2 < s2 ? m2 : s2;
|
|
|
+ b2 -= i;
|
|
|
+ m2 -= i;
|
|
|
+ s2 -= i;
|
|
|
+ }
|
|
|
+ if (b5 > 0) {
|
|
|
+ if (leftright) {
|
|
|
+ if (m5 > 0) {
|
|
|
+ mhi = pow5mult(mhi, m5);
|
|
|
+ b1 = mult(mhi, b);
|
|
|
+ Bfree(b);
|
|
|
+ b = b1;
|
|
|
+ }
|
|
|
+ if ((j = b5 - m5))
|
|
|
+ b = pow5mult(b, j);
|
|
|
+ }
|
|
|
+ else
|
|
|
+ b = pow5mult(b, b5);
|
|
|
+ }
|
|
|
+ S = i2b(1);
|
|
|
+ if (s5 > 0)
|
|
|
+ S = pow5mult(S, s5);
|
|
|
+
|
|
|
+ /* Check for special case that d is a normalized power of 2. */
|
|
|
+
|
|
|
+ spec_case = 0;
|
|
|
+ if ((mode < 2 || leftright)
|
|
|
+#ifdef Honor_FLT_ROUNDS
|
|
|
+ && Rounding == 1
|
|
|
+#endif
|
|
|
+ ) {
|
|
|
+ if (!word1(&u) && !(word0(&u) & Bndry_mask)
|
|
|
+#ifndef Sudden_Underflow
|
|
|
+ && word0(&u) & (Exp_mask & ~Exp_msk1)
|
|
|
+#endif
|
|
|
+ ) {
|
|
|
+ /* The special case */
|
|
|
+ b2 += Log2P;
|
|
|
+ s2 += Log2P;
|
|
|
+ spec_case = 1;
|
|
|
+ }
|
|
|
+ }
|
|
|
+
|
|
|
+ /* Arrange for convenient computation of quotients:
|
|
|
+ * shift left if necessary so divisor has 4 leading 0 bits.
|
|
|
+ *
|
|
|
+ * Perhaps we should just compute leading 28 bits of S once
|
|
|
+ * and for all and pass them and a shift to quorem, so it
|
|
|
+ * can do shifts and ors to compute the numerator for q.
|
|
|
+ */
|
|
|
+ i = dshift(S, s2);
|
|
|
+ b2 += i;
|
|
|
+ m2 += i;
|
|
|
+ s2 += i;
|
|
|
+ if (b2 > 0)
|
|
|
+ b = lshift(b, b2);
|
|
|
+ if (s2 > 0)
|
|
|
+ S = lshift(S, s2);
|
|
|
+ if (k_check) {
|
|
|
+ if (cmp(b,S) < 0) {
|
|
|
+ k--;
|
|
|
+ b = multadd(b, 10, 0); /* we botched the k estimate */
|
|
|
+ if (leftright)
|
|
|
+ mhi = multadd(mhi, 10, 0);
|
|
|
+ ilim = ilim1;
|
|
|
+ }
|
|
|
+ }
|
|
|
+ if (ilim <= 0 && (mode == 3 || mode == 5)) {
|
|
|
+ if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) {
|
|
|
+ /* no digits, fcvt style */
|
|
|
+ no_digits:
|
|
|
+ k = -1 - ndigits;
|
|
|
+ goto ret;
|
|
|
+ }
|
|
|
+ one_digit:
|
|
|
+ *s++ = '1';
|
|
|
+ k++;
|
|
|
+ goto ret;
|
|
|
+ }
|
|
|
+ if (leftright) {
|
|
|
+ if (m2 > 0)
|
|
|
+ mhi = lshift(mhi, m2);
|
|
|
+
|
|
|
+ /* Compute mlo -- check for special case
|
|
|
+ * that d is a normalized power of 2.
|
|
|
+ */
|
|
|
+
|
|
|
+ mlo = mhi;
|
|
|
+ if (spec_case) {
|
|
|
+ mhi = Balloc(mhi->k);
|
|
|
+ Bcopy(mhi, mlo);
|
|
|
+ mhi = lshift(mhi, Log2P);
|
|
|
+ }
|
|
|
+
|
|
|
+ for(i = 1;;i++) {
|
|
|
+ dig = quorem(b,S) + '0';
|
|
|
+ /* Do we yet have the shortest decimal string
|
|
|
+ * that will round to d?
|
|
|
+ */
|
|
|
+ j = cmp(b, mlo);
|
|
|
+ delta = diff(S, mhi);
|
|
|
+ j1 = delta->sign ? 1 : cmp(b, delta);
|
|
|
+ Bfree(delta);
|
|
|
+#ifndef ROUND_BIASED
|
|
|
+ if (j1 == 0 && mode != 1 && !(word1(&u) & 1)
|
|
|
+#ifdef Honor_FLT_ROUNDS
|
|
|
+ && Rounding >= 1
|
|
|
+#endif
|
|
|
+ ) {
|
|
|
+ if (dig == '9')
|
|
|
+ goto round_9_up;
|
|
|
+ if (j > 0)
|
|
|
+ dig++;
|
|
|
+#ifdef SET_INEXACT
|
|
|
+ else if (!b->x[0] && b->wds <= 1)
|
|
|
+ inexact = 0;
|
|
|
+#endif
|
|
|
+ *s++ = dig;
|
|
|
+ goto ret;
|
|
|
+ }
|
|
|
+#endif
|
|
|
+ if (j < 0 || (j == 0 && mode != 1
|
|
|
+#ifndef ROUND_BIASED
|
|
|
+ && !(word1(&u) & 1)
|
|
|
+#endif
|
|
|
+ )) {
|
|
|
+ if (!b->x[0] && b->wds <= 1) {
|
|
|
+#ifdef SET_INEXACT
|
|
|
+ inexact = 0;
|
|
|
+#endif
|
|
|
+ goto accept_dig;
|
|
|
+ }
|
|
|
+#ifdef Honor_FLT_ROUNDS
|
|
|
+ if (mode > 1)
|
|
|
+ switch(Rounding) {
|
|
|
+ case 0: goto accept_dig;
|
|
|
+ case 2: goto keep_dig;
|
|
|
+ }
|
|
|
+#endif /*Honor_FLT_ROUNDS*/
|
|
|
+ if (j1 > 0) {
|
|
|
+ b = lshift(b, 1);
|
|
|
+ j1 = cmp(b, S);
|
|
|
+#ifdef ROUND_BIASED
|
|
|
+ if (j1 >= 0 /*)*/
|
|
|
+#else
|
|
|
+ if ((j1 > 0 || (j1 == 0 && dig & 1))
|
|
|
+#endif
|
|
|
+ && dig++ == '9')
|
|
|
+ goto round_9_up;
|
|
|
+ }
|
|
|
+ accept_dig:
|
|
|
+ *s++ = dig;
|
|
|
+ goto ret;
|
|
|
+ }
|
|
|
+ if (j1 > 0) {
|
|
|
+#ifdef Honor_FLT_ROUNDS
|
|
|
+ if (!Rounding)
|
|
|
+ goto accept_dig;
|
|
|
+#endif
|
|
|
+ if (dig == '9') { /* possible if i == 1 */
|
|
|
+ round_9_up:
|
|
|
+ *s++ = '9';
|
|
|
+ goto roundoff;
|
|
|
+ }
|
|
|
+ *s++ = dig + 1;
|
|
|
+ goto ret;
|
|
|
+ }
|
|
|
+#ifdef Honor_FLT_ROUNDS
|
|
|
+ keep_dig:
|
|
|
+#endif
|
|
|
+ *s++ = dig;
|
|
|
+ if (i == ilim)
|
|
|
+ break;
|
|
|
+ b = multadd(b, 10, 0);
|
|
|
+ if (mlo == mhi)
|
|
|
+ mlo = mhi = multadd(mhi, 10, 0);
|
|
|
+ else {
|
|
|
+ mlo = multadd(mlo, 10, 0);
|
|
|
+ mhi = multadd(mhi, 10, 0);
|
|
|
+ }
|
|
|
+ }
|
|
|
+ }
|
|
|
+ else
|
|
|
+ for(i = 1;; i++) {
|
|
|
+ *s++ = dig = quorem(b,S) + '0';
|
|
|
+ if (!b->x[0] && b->wds <= 1) {
|
|
|
+#ifdef SET_INEXACT
|
|
|
+ inexact = 0;
|
|
|
+#endif
|
|
|
+ goto ret;
|
|
|
+ }
|
|
|
+ if (i >= ilim)
|
|
|
+ break;
|
|
|
+ b = multadd(b, 10, 0);
|
|
|
+ }
|
|
|
+
|
|
|
+ /* Round off last digit */
|
|
|
+
|
|
|
+#ifdef Honor_FLT_ROUNDS
|
|
|
+ switch(Rounding) {
|
|
|
+ case 0: goto trimzeros;
|
|
|
+ case 2: goto roundoff;
|
|
|
+ }
|
|
|
+#endif
|
|
|
+ b = lshift(b, 1);
|
|
|
+ j = cmp(b, S);
|
|
|
+#ifdef ROUND_BIASED
|
|
|
+ if (j >= 0)
|
|
|
+#else
|
|
|
+ if (j > 0 || (j == 0 && dig & 1))
|
|
|
+#endif
|
|
|
+ {
|
|
|
+ roundoff:
|
|
|
+ while(*--s == '9')
|
|
|
+ if (s == s0) {
|
|
|
+ k++;
|
|
|
+ *s++ = '1';
|
|
|
+ goto ret;
|
|
|
+ }
|
|
|
+ ++*s++;
|
|
|
+ }
|
|
|
+ else {
|
|
|
+#ifdef Honor_FLT_ROUNDS
|
|
|
+ trimzeros:
|
|
|
+#endif
|
|
|
+ while(*--s == '0');
|
|
|
+ s++;
|
|
|
+ }
|
|
|
+ ret:
|
|
|
+ Bfree(S);
|
|
|
+ if (mhi) {
|
|
|
+ if (mlo && mlo != mhi)
|
|
|
+ Bfree(mlo);
|
|
|
+ Bfree(mhi);
|
|
|
+ }
|
|
|
+ ret1:
|
|
|
+#ifdef SET_INEXACT
|
|
|
+ if (inexact) {
|
|
|
+ if (!oldinexact) {
|
|
|
+ word0(&u) = Exp_1 + (70 << Exp_shift);
|
|
|
+ word1(&u) = 0;
|
|
|
+ dval(&u) += 1.;
|
|
|
+ }
|
|
|
+ }
|
|
|
+ else if (!oldinexact)
|
|
|
+ clear_inexact();
|
|
|
+#endif
|
|
|
+ Bfree(b);
|
|
|
+ *s = 0;
|
|
|
+ *decpt = k + 1;
|
|
|
+ if (rve)
|
|
|
+ *rve = s;
|
|
|
+ return s0;
|
|
|
+ }
|
|
|
+#ifdef __cplusplus
|
|
|
+}
|
|
|
+#endif
|