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authorKenta Murata <mrkn@mrkn.jp>2021-01-12 22:58:17 +0900
committerKenta Murata <mrkn@mrkn.jp>2021-01-13 02:11:18 +0900
commit4ba3a4491e15ed50f26c8f7a602fb4ef5452085a (patch)
tree1acc0f040522a8db6bc9a73dc996afa9c7dbfd7f
parent2175c2c957a711f1c48f42d38db202bf52c8bc6f (diff)
[ruby/bigdecimal] Optimize rb_float_convert_to_BigDecimal by using dtoa
This improve the conversion speed several times faster than before. ``` RUBYLIB= BUNDLER_ORIG_RUBYLIB= /home/mrkn/.rbenv/versions/3.0.0/bin/ruby -v -S benchmark-driver /home/mrkn/src/github.com/ruby/bigdecimal/benchmark/from_float.yml ruby 3.0.0p0 (2020-12-25 revision 95aff21468) [x86_64-linux] Calculating ------------------------------------- bigdecimal 3.0.0 master flt_e0 156.400k 783.356k i/s - 100.000k times in 0.639388s 0.127656s flt_ep10 158.640k 777.978k i/s - 100.000k times in 0.630359s 0.128538s flt_ep100 101.676k 504.259k i/s - 100.000k times in 0.983512s 0.198311s flt_em10 103.439k 726.339k i/s - 100.000k times in 0.966751s 0.137677s flt_em100 79.675k 651.446k i/s - 100.000k times in 1.255095s 0.153505s Comparison: flt_e0 master: 783355.6 i/s bigdecimal 3.0.0: 156399.5 i/s - 5.01x slower flt_ep10 master: 777977.6 i/s bigdecimal 3.0.0: 158639.7 i/s - 4.90x slower flt_ep100 master: 504259.4 i/s bigdecimal 3.0.0: 101676.5 i/s - 4.96x slower flt_em10 master: 726338.6 i/s bigdecimal 3.0.0: 103439.2 i/s - 7.02x slower flt_em100 master: 651446.3 i/s bigdecimal 3.0.0: 79675.3 i/s - 8.18x slower ``` https://github.com/ruby/bigdecimal/commit/5bdaedd530 https://github.com/ruby/bigdecimal/commit/9bfff57f90 https://github.com/ruby/bigdecimal/commit/d071a0abbb
-rw-r--r--ext/bigdecimal/bigdecimal.c117
-rw-r--r--ext/bigdecimal/bigdecimal.gemspec4
-rw-r--r--ext/bigdecimal/bigdecimal.h3
-rw-r--r--ext/bigdecimal/extconf.rb1
-rw-r--r--ext/bigdecimal/missing.c17
-rw-r--r--ext/bigdecimal/missing.h3
-rw-r--r--ext/bigdecimal/missing/dtoa.c3462
7 files changed, 3602 insertions, 5 deletions
diff --git a/ext/bigdecimal/bigdecimal.c b/ext/bigdecimal/bigdecimal.c
index 4997487..2d3f09d 100644
--- a/ext/bigdecimal/bigdecimal.c
+++ b/ext/bigdecimal/bigdecimal.c
@@ -74,7 +74,7 @@ static ID id_half;
#define BASE1 (BASE/10)
#ifndef DBLE_FIG
-#define DBLE_FIG rmpd_double_figures() /* figure of double */
+#define DBLE_FIG RMPD_DOUBLE_FIGURES /* figure of double */
#endif
#define LOG10_2 0.3010299956639812
@@ -205,6 +205,7 @@ cannot_be_coerced_into_BigDecimal(VALUE exc_class, VALUE v)
}
static inline VALUE BigDecimal_div2(VALUE, VALUE, VALUE);
+static VALUE rb_inum_convert_to_BigDecimal(VALUE val, size_t digs, int raise_exception);
static VALUE rb_float_convert_to_BigDecimal(VALUE val, size_t digs, int raise_exception);
static VALUE rb_rational_convert_to_BigDecimal(VALUE val, size_t digs, int raise_exception);
static VALUE rb_cstr_convert_to_BigDecimal(const char *c_str, size_t digs, int raise_exception);
@@ -2824,8 +2825,118 @@ rb_float_convert_to_BigDecimal(VALUE val, size_t digs, int raise_exception)
rb_raise(rb_eArgError, "precision too large.");
}
- val = rb_funcall(val, id_to_r, 0);
- return rb_rational_convert_to_BigDecimal(val, digs, raise_exception);
+ /* Use the same logic in flo_to_s to convert a float to a decimal string */
+ char buf[DBLE_FIG + BASE_FIG + 2 + 1];
+ int decpt, negative_p;
+ char *e;
+ char *p = BigDecimal_dtoa(d, 2, digs, &decpt, &negative_p, &e);
+ int len10 = (int)(e - p);
+ if (len10 >= (int)sizeof(buf))
+ len10 = (int)sizeof(buf) - 1;
+ memcpy(buf, p, len10);
+ xfree(p);
+
+ VALUE inum;
+ size_t RB_UNUSED_VAR(prec) = 0;
+ size_t exp = 0;
+ if (decpt > 0) {
+ if (decpt < len10) {
+ /*
+ * len10 |---------------|
+ * : |-------| frac_len10 = len10 - decpt
+ * decpt |-------| |--| ntz10 = BASE_FIG - frac_len10 % BASE_FIG
+ * : : :
+ * 00 dd dddd.dddd dd 00
+ * prec |-----.----.----.-----| prec = exp + roomof(frac_len, BASE_FIG)
+ * exp |-----.----| exp = roomof(decpt, BASE_FIG)
+ */
+ const size_t frac_len10 = len10 - decpt;
+ const size_t ntz10 = BASE_FIG - frac_len10 % BASE_FIG;
+ memset(buf + len10, '0', ntz10);
+ buf[len10 + ntz10] = '\0';
+ inum = rb_cstr_to_inum(buf, 10, false);
+
+ exp = roomof(decpt, BASE_FIG);
+ prec = exp + roomof(frac_len10, BASE_FIG);
+ }
+ else {
+ /*
+ * decpt |-----------------------|
+ * len10 |----------| :
+ * : |------------| exp10
+ * : : :
+ * 00 dd dddd dd 00 0000 0000.0
+ * : : : :
+ * : |--| ntz10 = exp10 % BASE_FIG
+ * prec |-----.----.-----| :
+ * : |----.----| exp10 / BASE_FIG
+ * exp |-----.----.-----.----.----|
+ */
+ const size_t exp10 = decpt - len10;
+ const size_t ntz10 = exp10 % BASE_FIG;
+
+ memset(buf + len10, '0', ntz10);
+ buf[len10 + ntz10] = '\0';
+ inum = rb_cstr_to_inum(buf, 10, false);
+
+ prec = roomof(len10 + ntz10, BASE_FIG);
+ exp = prec + exp10 / BASE_FIG;
+ }
+ }
+ else if (decpt == 0) {
+ /*
+ * len10 |------------|
+ * : :
+ * 0.dddd dddd dd 00
+ * : : :
+ * : |--| ntz10 = prec * BASE_FIG - len10
+ * prec |----.----.-----| roomof(len10, BASE_FIG)
+ */
+ prec = roomof(len10, BASE_FIG);
+ const size_t ntz10 = prec * BASE_FIG - len10;
+
+ memset(buf + len10, '0', ntz10);
+ buf[len10 + ntz10] = '\0';
+ inum = rb_cstr_to_inum(buf, 10, false);
+ }
+ else {
+ /*
+ * len10 |---------------|
+ * : :
+ * decpt |-------| |--| ntz10 = prec * BASE_FIG - nlz10 - len10
+ * : : :
+ * 0.0000 00 dd dddd dddd dd 00
+ * : : :
+ * nlz10 |--| : decpt % BASE_FIG
+ * prec |-----.----.----.-----| roomof(decpt + len10, BASE_FIG) - exp
+ * exp |----| decpt / BASE_FIG
+ */
+ decpt = -decpt;
+
+ const size_t nlz10 = decpt % BASE_FIG;
+ exp = decpt / BASE_FIG;
+ prec = roomof(decpt + len10, BASE_FIG) - exp;
+ const size_t ntz10 = prec * BASE_FIG - nlz10 - len10;
+
+ if (nlz10 > 0) {
+ memmove(buf + nlz10, buf, len10);
+ memset(buf, '0', nlz10);
+ }
+ memset(buf + nlz10 + len10, '0', ntz10);
+ buf[nlz10 + len10 + ntz10] = '\0';
+ inum = rb_cstr_to_inum(buf, 10, false);
+
+ exp = -exp;
+ }
+
+ VALUE bd = rb_inum_convert_to_BigDecimal(inum, SIZE_MAX, raise_exception);
+ Real *vp;
+ TypedData_Get_Struct(bd, Real, &BigDecimal_data_type, vp);
+ assert(vp->Prec == prec);
+ vp->exponent = exp;
+
+ if (negative_p) VpSetSign(vp, -1);
+ return bd;
}
static VALUE
diff --git a/ext/bigdecimal/bigdecimal.gemspec b/ext/bigdecimal/bigdecimal.gemspec
index 8a2f5b6..79009aa 100644
--- a/ext/bigdecimal/bigdecimal.gemspec
+++ b/ext/bigdecimal/bigdecimal.gemspec
@@ -21,7 +21,9 @@ Gem::Specification.new do |s|
ext/bigdecimal/bigdecimal.h
ext/bigdecimal/bits.h
ext/bigdecimal/feature.h
+ ext/bigdecimal/missing.c
ext/bigdecimal/missing.h
+ ext/bigdecimal/missing/dtoa.c
ext/bigdecimal/static_assert.h
lib/bigdecimal.rb
lib/bigdecimal/jacobian.rb
@@ -40,5 +42,5 @@ Gem::Specification.new do |s|
s.add_development_dependency "rake", ">= 12.3.3"
s.add_development_dependency "rake-compiler", ">= 0.9"
s.add_development_dependency "minitest", "< 5.0.0"
- s.add_development_dependency "pry"
+ s.add_development_dependency "irb"
end
diff --git a/ext/bigdecimal/bigdecimal.h b/ext/bigdecimal/bigdecimal.h
index 6b6ac21..5f343db 100644
--- a/ext/bigdecimal/bigdecimal.h
+++ b/ext/bigdecimal/bigdecimal.h
@@ -77,6 +77,7 @@ extern VALUE rb_cBigDecimal;
# define RMPD_BASE ((DECDIG)100U)
#endif
+#define RMPD_DOUBLE_FIGURES (1+DBL_DIG)
/*
* NaN & Infinity
@@ -175,7 +176,7 @@ rmpd_base_value(void) { return RMPD_BASE; }
static inline size_t
rmpd_component_figures(void) { return RMPD_COMPONENT_FIGURES; }
static inline size_t
-rmpd_double_figures(void) { return 1+DBL_DIG; }
+rmpd_double_figures(void) { return RMPD_DOUBLE_FIGURES; }
#define VpBaseFig() rmpd_component_figures()
#define VpDblFig() rmpd_double_figures()
diff --git a/ext/bigdecimal/extconf.rb b/ext/bigdecimal/extconf.rb
index d5140e8..c92aacb 100644
--- a/ext/bigdecimal/extconf.rb
+++ b/ext/bigdecimal/extconf.rb
@@ -66,6 +66,7 @@ have_func("llabs", "stdlib.h")
have_func("finite", "math.h")
have_func("isfinite", "math.h")
+have_header("ruby/atomic.h")
have_header("ruby/internal/has/builtin.h")
have_header("ruby/internal/static_assert.h")
diff --git a/ext/bigdecimal/missing.c b/ext/bigdecimal/missing.c
new file mode 100644
index 0000000..b0bc6ee
--- /dev/null
+++ b/ext/bigdecimal/missing.c
@@ -0,0 +1,17 @@
+#include <ruby/ruby.h>
+
+#ifdef HAVE_RUBY_ATOMIC_H
+# include <ruby/atomic.h>
+#endif
+
+#ifdef RUBY_ATOMIC_PTR_CAS
+# define ATOMIC_PTR_CAS(var, old, new) RUBY_ATOMIC_PTR_CAS(var, old, new)
+#endif
+
+#undef strtod
+#define strtod BigDecimal_strtod
+#undef dtoa
+#define dtoa BigDecimal_dtoa
+#undef hdtoa
+#define hdtoa BigDecimal_hdtoa
+#include "missing/dtoa.c"
diff --git a/ext/bigdecimal/missing.h b/ext/bigdecimal/missing.h
index aa056c3..11b58c0 100644
--- a/ext/bigdecimal/missing.h
+++ b/ext/bigdecimal/missing.h
@@ -117,6 +117,9 @@ finite(double)
# endif
#endif
+/* dtoa */
+char *BigDecimal_dtoa(double d_, int mode, int ndigits, int *decpt, int *sign, char **rve);
+
/* rational */
#ifndef HAVE_RB_RATIONAL_NUM
diff --git a/ext/bigdecimal/missing/dtoa.c b/ext/bigdecimal/missing/dtoa.c
new file mode 100644
index 0000000..41b0a22
--- /dev/null
+++ b/ext/bigdecimal/missing/dtoa.c
@@ -0,0 +1,3462 @@
+/****************************************************************
+ *
+ * The author of this software is David M. Gay.
+ *
+ * Copyright (c) 1991, 2000, 2001 by Lucent Technologies.
+ *
+ * Permission to use, copy, modify, and distribute this software for any
+ * purpose without fee is hereby granted, provided that this entire notice
+ * is included in all copies of any software which is or includes a copy
+ * or modification of this software and in all copies of the supporting
+ * documentation for such software.
+ *
+ * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
+ * WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY
+ * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
+ * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
+ *
+ ***************************************************************/
+
+/* Please send bug reports to David M. Gay (dmg at acm dot org,
+ * with " at " changed at "@" and " dot " changed to "."). */
+
+/* On a machine with IEEE extended-precision registers, it is
+ * necessary to specify double-precision (53-bit) rounding precision
+ * before invoking strtod or dtoa. If the machine uses (the equivalent
+ * of) Intel 80x87 arithmetic, the call
+ * _control87(PC_53, MCW_PC);
+ * does this with many compilers. Whether this or another call is
+ * appropriate depends on the compiler; for this to work, it may be
+ * necessary to #include "float.h" or another system-dependent header
+ * file.
+ */
+
+/* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
+ *
+ * This strtod returns a nearest machine number to the input decimal
+ * string (or sets errno to ERANGE). With IEEE arithmetic, ties are
+ * broken by the IEEE round-even rule. Otherwise ties are broken by
+ * biased rounding (add half and chop).
+ *
+ * Inspired loosely by William D. Clinger's paper "How to Read Floating
+ * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
+ *
+ * Modifications:
+ *
+ * 1. We only require IEEE, IBM, or VAX double-precision
+ * arithmetic (not IEEE double-extended).
+ * 2. We get by with floating-point arithmetic in a case that
+ * Clinger missed -- when we're computing d * 10^n
+ * for a small integer d and the integer n is not too
+ * much larger than 22 (the maximum integer k for which
+ * we can represent 10^k exactly), we may be able to
+ * compute (d*10^k) * 10^(e-k) with just one roundoff.
+ * 3. Rather than a bit-at-a-time adjustment of the binary
+ * result in the hard case, we use floating-point
+ * arithmetic to determine the adjustment to within
+ * one bit; only in really hard cases do we need to
+ * compute a second residual.
+ * 4. Because of 3., we don't need a large table of powers of 10
+ * for ten-to-e (just some small tables, e.g. of 10^k
+ * for 0 <= k <= 22).
+ */
+
+/*
+ * #define IEEE_LITTLE_ENDIAN for IEEE-arithmetic machines where the least
+ * significant byte has the lowest address.
+ * #define IEEE_BIG_ENDIAN for IEEE-arithmetic machines where the most
+ * significant byte has the lowest address.
+ * #define Long int on machines with 32-bit ints and 64-bit longs.
+ * #define IBM for IBM mainframe-style floating-point arithmetic.
+ * #define VAX for VAX-style floating-point arithmetic (D_floating).
+ * #define No_leftright to omit left-right logic in fast floating-point
+ * computation of dtoa.
+ * #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
+ * and strtod and dtoa should round accordingly.
+ * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
+ * and Honor_FLT_ROUNDS is not #defined.
+ * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
+ * that use extended-precision instructions to compute rounded
+ * products and quotients) with IBM.
+ * #define ROUND_BIASED for IEEE-format with biased rounding.
+ * #define Inaccurate_Divide for IEEE-format with correctly rounded
+ * products but inaccurate quotients, e.g., for Intel i860.
+ * #define NO_LONG_LONG on machines that do not have a "long long"
+ * integer type (of >= 64 bits). On such machines, you can
+ * #define Just_16 to store 16 bits per 32-bit Long when doing
+ * high-precision integer arithmetic. Whether this speeds things
+ * up or slows things down depends on the machine and the number
+ * being converted. If long long is available and the name is
+ * something other than "long long", #define Llong to be the name,
+ * and if "unsigned Llong" does not work as an unsigned version of
+ * Llong, #define #ULLong to be the corresponding unsigned type.
+ * #define KR_headers for old-style C function headers.
+ * #define Bad_float_h if your system lacks a float.h or if it does not
+ * define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
+ * FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
+ * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
+ * if memory is available and otherwise does something you deem
+ * appropriate. If MALLOC is undefined, malloc will be invoked
+ * directly -- and assumed always to succeed.
+ * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making
+ * memory allocations from a private pool of memory when possible.
+ * When used, the private pool is PRIVATE_MEM bytes long: 2304 bytes,
+ * unless #defined to be a different length. This default length
+ * suffices to get rid of MALLOC calls except for unusual cases,
+ * such as decimal-to-binary conversion of a very long string of
+ * digits. The longest string dtoa can return is about 751 bytes
+ * long. For conversions by strtod of strings of 800 digits and
+ * all dtoa conversions in single-threaded executions with 8-byte
+ * pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte
+ * pointers, PRIVATE_MEM >= 7112 appears adequate.
+ * #define INFNAN_CHECK on IEEE systems to cause strtod to check for
+ * Infinity and NaN (case insensitively). On some systems (e.g.,
+ * some HP systems), it may be necessary to #define NAN_WORD0
+ * appropriately -- to the most significant word of a quiet NaN.
+ * (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)
+ * When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined,
+ * strtod also accepts (case insensitively) strings of the form
+ * NaN(x), where x is a string of hexadecimal digits and spaces;
+ * if there is only one string of hexadecimal digits, it is taken
+ * for the 52 fraction bits of the resulting NaN; if there are two
+ * or more strings of hex digits, the first is for the high 20 bits,
+ * the second and subsequent for the low 32 bits, with intervening
+ * white space ignored; but if this results in none of the 52
+ * fraction bits being on (an IEEE Infinity symbol), then NAN_WORD0
+ * and NAN_WORD1 are used instead.
+ * #define MULTIPLE_THREADS if the system offers preemptively scheduled
+ * multiple threads. In this case, you must provide (or suitably
+ * #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed
+ * by FREE_DTOA_LOCK(n) for n = 0 or 1. (The second lock, accessed
+ * in pow5mult, ensures lazy evaluation of only one copy of high
+ * powers of 5; omitting this lock would introduce a small
+ * probability of wasting memory, but would otherwise be harmless.)
+ * You must also invoke freedtoa(s) to free the value s returned by
+ * dtoa. You may do so whether or not MULTIPLE_THREADS is #defined.
+ * #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that
+ * avoids underflows on inputs whose result does not underflow.
+ * If you #define NO_IEEE_Scale on a machine that uses IEEE-format
+ * floating-point numbers and flushes underflows to zero rather
+ * than implementing gradual underflow, then you must also #define
+ * Sudden_Underflow.
+ * #define YES_ALIAS to permit aliasing certain double values with
+ * arrays of ULongs. This leads to slightly better code with
+ * some compilers and was always used prior to 19990916, but it
+ * is not strictly legal and can cause trouble with aggressively
+ * optimizing compilers (e.g., gcc 2.95.1 under -O2).
+ * #define USE_LOCALE to use the current locale's decimal_point value.
+ * #define SET_INEXACT if IEEE arithmetic is being used and extra
+ * computation should be done to set the inexact flag when the
+ * result is inexact and avoid setting inexact when the result
+ * is exact. In this case, dtoa.c must be compiled in
+ * an environment, perhaps provided by #include "dtoa.c" in a
+ * suitable wrapper, that defines two functions,
+ * int get_inexact(void);
+ * void clear_inexact(void);
+ * such that get_inexact() returns a nonzero value if the
+ * inexact bit is already set, and clear_inexact() sets the
+ * inexact bit to 0. When SET_INEXACT is #defined, strtod
+ * also does extra computations to set the underflow and overflow
+ * flags when appropriate (i.e., when the result is tiny and
+ * inexact or when it is a numeric value rounded to +-infinity).
+ * #define NO_ERRNO if strtod should not assign errno = ERANGE when
+ * the result overflows to +-Infinity or underflows to 0.
+ */
+
+#ifdef WORDS_BIGENDIAN
+#define IEEE_BIG_ENDIAN
+#else
+#define IEEE_LITTLE_ENDIAN
+#endif
+
+#ifdef __vax__
+#define VAX
+#undef IEEE_BIG_ENDIAN
+#undef IEEE_LITTLE_ENDIAN
+#endif
+
+#if defined(__arm__) && !defined(__VFP_FP__)
+#define IEEE_BIG_ENDIAN
+#undef IEEE_LITTLE_ENDIAN
+#endif
+
+#undef Long
+#undef ULong
+
+#include <limits.h>
+
+#if (INT_MAX >> 30) && !(INT_MAX >> 31)
+#define Long int
+#define ULong unsigned int
+#elif (LONG_MAX >> 30) && !(LONG_MAX >> 31)
+#define Long long int
+#define ULong unsigned long int
+#else
+#error No 32bit integer
+#endif
+
+#if HAVE_LONG_LONG
+#define Llong LONG_LONG
+#else
+#define NO_LONG_LONG
+#endif
+
+#ifdef DEBUG
+#include <stdio.h>
+#define Bug(x) {fprintf(stderr, "%s\n", (x)); exit(EXIT_FAILURE);}
+#endif
+
+#ifndef ISDIGIT
+#include <ctype.h>
+#define ISDIGIT(c) isdigit(c)
+#endif
+#include <errno.h>
+#include <stdlib.h>
+#include <string.h>
+
+#ifdef USE_LOCALE
+#include <locale.h>
+#endif
+
+#ifdef MALLOC
+extern void *MALLOC(size_t);
+#else
+#define MALLOC xmalloc
+#endif
+#ifdef FREE
+extern void FREE(void*);
+#else
+#define FREE xfree
+#endif
+#ifndef NO_SANITIZE
+#define NO_SANITIZE(x, y) y
+#endif
+
+#ifndef Omit_Private_Memory
+#ifndef PRIVATE_MEM
+#define PRIVATE_MEM 2304
+#endif
+#define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
+static double private_mem[PRIVATE_mem], *pmem_next = private_mem;
+#endif
+
+#undef IEEE_Arith
+#undef Avoid_Underflow
+#ifdef IEEE_BIG_ENDIAN
+#define IEEE_Arith
+#endif
+#ifdef IEEE_LITTLE_ENDIAN
+#define IEEE_Arith
+#endif
+
+#ifdef Bad_float_h
+
+#ifdef IEEE_Arith
+#define DBL_DIG 15
+#define DBL_MAX_10_EXP 308
+#define DBL_MAX_EXP 1024
+#define FLT_RADIX 2
+#endif /*IEEE_Arith*/
+
+#ifdef IBM
+#define DBL_DIG 16
+#define DBL_MAX_10_EXP 75
+#define DBL_MAX_EXP 63
+#define FLT_RADIX 16
+#define DBL_MAX 7.2370055773322621e+75
+#endif
+
+#ifdef VAX
+#define DBL_DIG 16
+#define DBL_MAX_10_EXP 38
+#define DBL_MAX_EXP 127
+#define FLT_RADIX 2
+#define DBL_MAX 1.7014118346046923e+38
+#endif
+
+#ifndef LONG_MAX
+#define LONG_MAX 2147483647
+#endif
+
+#else /* ifndef Bad_float_h */
+#include <float.h>
+#endif /* Bad_float_h */
+
+#include <math.h>
+
+#ifdef __cplusplus
+extern "C" {
+#if 0
+} /* satisfy cc-mode */
+#endif
+#endif
+
+#ifndef hexdigit
+static const char hexdigit[] = "0123456789abcdef0123456789ABCDEF";
+#endif
+
+#if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN) + defined(VAX) + defined(IBM) != 1
+Exactly one of IEEE_LITTLE_ENDIAN, IEEE_BIG_ENDIAN, VAX, or IBM should be defined.
+#endif
+
+typedef union { double d; ULong L[2]; } U;
+
+#ifdef YES_ALIAS
+typedef double double_u;
+# define dval(x) (x)
+# ifdef IEEE_LITTLE_ENDIAN
+# define word0(x) (((ULong *)&(x))[1])
+# define word1(x) (((ULong *)&(x))[0])
+# else
+# define word0(x) (((ULong *)&(x))[0])
+# define word1(x) (((ULong *)&(x))[1])
+# endif
+#else
+typedef U double_u;
+# ifdef IEEE_LITTLE_ENDIAN
+# define word0(x) ((x).L[1])
+# define word1(x) ((x).L[0])
+# else
+# define word0(x) ((x).L[0])
+# define word1(x) ((x).L[1])
+# endif
+# define dval(x) ((x).d)
+#endif
+
+/* The following definition of Storeinc is appropriate for MIPS processors.
+ * An alternative that might be better on some machines is
+ * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
+ */
+#if defined(IEEE_LITTLE_ENDIAN) + defined(VAX) + defined(__arm__)
+#define Storeinc(a,b,c) (((unsigned short *)(a))[1] = (unsigned short)(b), \
+((unsigned short *)(a))[0] = (unsigned short)(c), (a)++)
+#else
+#define Storeinc(a,b,c) (((unsigned short *)(a))[0] = (unsigned short)(b), \
+((unsigned short *)(a))[1] = (unsigned short)(c), (a)++)
+#endif
+
+/* #define P DBL_MANT_DIG */
+/* Ten_pmax = floor(P*log(2)/log(5)) */
+/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
+/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
+/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
+
+#ifdef IEEE_Arith
+#define Exp_shift 20
+#define Exp_shift1 20
+#define Exp_msk1 0x100000
+#define Exp_msk11 0x100000
+#define Exp_mask 0x7ff00000
+#define P 53
+#define Bias 1023
+#define Emin (-1022)
+#define Exp_1 0x3ff00000
+#define Exp_11 0x3ff00000
+#define Ebits 11
+#define Frac_mask 0xfffff
+#define Frac_mask1 0xfffff
+#define Ten_pmax 22
+#define Bletch 0x10
+#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
+#define Rounding rounding
+#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 Bias 65
+#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 Bias 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
+#endif
+
+#ifdef RND_PRODQUOT
+#define rounded_product(a,b) ((a) = rnd_prod((a), (b)))
+#define rounded_quotient(a,b) ((a) = rnd_quot((a), (b)))
+extern double rnd_prod(double, double), rnd_quot(double, double);
+#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
+
+#define FFFFFFFF 0xffffffffUL
+
+#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 */
+
+#define MULTIPLE_THREADS 1
+
+#ifndef MULTIPLE_THREADS
+#define ACQUIRE_DTOA_LOCK(n) /*nothing*/
+#define FREE_DTOA_LOCK(n) /*nothing*/
+#else
+#define ACQUIRE_DTOA_LOCK(n) /*unused right now*/
+#define FREE_DTOA_LOCK(n) /*unused right now*/
+#endif
+
+#ifndef ATOMIC_PTR_CAS
+#define ATOMIC_PTR_CAS(var, old, new) ((var) = (new), (old))
+#endif
+#ifndef LIKELY
+#define LIKELY(x) (x)
+#endif
+#ifndef UNLIKELY
+#define UNLIKELY(x) (x)
+#endif
+#ifndef ASSUME
+#define ASSUME(x) (void)(x)
+#endif
+
+#define Kmax 15
+
+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(int k)
+{
+ int x;
+ Bigint *rv;
+#ifndef Omit_Private_Memory
+ size_t len;
+#endif
+
+ rv = 0;
+ ACQUIRE_DTOA_LOCK(0);
+ if (k <= Kmax) {
+ rv = freelist[k];
+ while (rv) {
+ Bigint *rvn = rv;
+ rv = ATOMIC_PTR_CAS(freelist[k], rv, rv->next);
+ if (LIKELY(rvn == rv)) {
+ ASSUME(rv);
+ break;
+ }
+ }
+ }
+ if (!rv) {
+ 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) {
+ double *pnext = pmem_next;
+ while (pnext - private_mem + len <= PRIVATE_mem) {
+ double *p = pnext;
+ pnext = ATOMIC_PTR_CAS(pmem_next, pnext, pnext + len);
+ if (LIKELY(p == pnext)) {
+ rv = (Bigint*)pnext;
+ ASSUME(rv);
+ break;
+ }
+ }
+ }
+ if (!rv)
+ 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(Bigint *v)
+{
+ Bigint *vn;
+ if (v) {
+ if (v->k > Kmax) {
+ FREE(v);
+ return;
+ }
+ ACQUIRE_DTOA_LOCK(0);
+ do {
+ vn = v->next = freelist[v->k];
+ } while (UNLIKELY(ATOMIC_PTR_CAS(freelist[v->k], vn, v) != vn));
+ 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(Bigint *b, int m, int a) /* multiply by m and add a */
+{
+ int i, wds;
+ ULong *x;
+#ifdef ULLong
+ ULLong carry, y;
+#else
+ ULong carry, 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++ = (ULong)(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++] = (ULong)carry;
+ b->wds = wds;
+ }
+ return b;
+}
+
+static Bigint *
+s2b(const char *s, int nd0, int nd, ULong y9)
+{
+ 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++;
+ }
+ else
+ s += 10;
+ for (; i < nd; i++)
+ b = multadd(b, 10, *s++ - '0');
+ return b;
+}
+
+static int
+hi0bits(register ULong x)
+{
+ register 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(ULong *y)
+{
+ register int k;
+ register 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(int i)
+{
+ Bigint *b;
+
+ b = Balloc(1);
+ b->x[0] = i;
+ b->wds = 1;
+ return b;
+}
+
+static Bigint *
+mult(Bigint *a, Bigint *b)
+{
+ 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++) != 0) {
+ x = xa;
+ xc = xc0;
+ carry = 0;
+ do {
+ z = *x++ * (ULLong)y + *xc + carry;
+ carry = z >> 32;
+ *xc++ = (ULong)(z & FFFFFFFF);
+ } while (x < xae);
+ *xc = (ULong)carry;
+ }
+ }
+#else
+#ifdef Pack_32
+ for (; xb < xbe; xb++, xc0++) {
+ if ((y = *xb & 0xffff) != 0) {
+ 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 = (ULong)carry;
+ }
+ if ((y = *xb >> 16) != 0) {
+ 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 = (ULong)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(Bigint *b, int k)
+{
+ Bigint *b1, *p5, *p51;
+ Bigint *p5tmp;
+ int i;
+ static const int p05[3] = { 5, 25, 125 };
+
+ if ((i = k & 3) != 0)
+ b = multadd(b, p05[i-1], 0);
+
+ if (!(k >>= 2))
+ return b;
+ if (!(p5 = p5s)) {
+ /* first time */
+ ACQUIRE_DTOA_LOCK(1);
+ if (!(p5 = p5s)) {
+ p5 = i2b(625);
+ p5->next = 0;
+ p5tmp = ATOMIC_PTR_CAS(p5s, NULL, p5);
+ if (UNLIKELY(p5tmp)) {
+ Bfree(p5);
+ p5 = p5tmp;
+ }
+ }
+ FREE_DTOA_LOCK(1);
+ }
+ for (;;) {
+ if (k & 1) {
+ b1 = mult(b, p5);
+ Bfree(b);
+ b = b1;
+ }
+ if (!(k >>= 1))
+ break;
+ if (!(p51 = p5->next)) {
+ ACQUIRE_DTOA_LOCK(1);
+ if (!(p51 = p5->next)) {
+ p51 = mult(p5,p5);
+ p51->next = 0;
+ p5tmp = ATOMIC_PTR_CAS(p5->next, NULL, p51);
+ if (UNLIKELY(p5tmp)) {
+ Bfree(p51);
+ p51 = p5tmp;
+ }
+ }
+ FREE_DTOA_LOCK(1);
+ }
+ p5 = p51;
+ }
+ return b;
+}
+
+static Bigint *
+lshift(Bigint *b, int k)
+{
+ 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) != 0)
+ ++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(Bigint *a, Bigint *b)
+{
+ 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;
+}
+
+NO_SANITIZE("unsigned-integer-overflow", static Bigint * diff(Bigint *a, Bigint *b));
+static Bigint *
+diff(Bigint *a, Bigint *b)
+{
+ 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++ = (ULong)(y & FFFFFFFF);
+ } while (xb < xbe);
+ while (xa < xae) {
+ y = *xa++ - borrow;
+ borrow = y >> 32 & (ULong)1;
+ *xc++ = (ULong)(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(double x_)
+{
+ register Long L;
+ double_u x, a;
+ dval(x) = x_;
+
+ 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(a) = L;
+ word1(a) = 0;
+#ifndef Avoid_Underflow
+#ifndef Sudden_Underflow
+ }
+ else {
+ L = -L >> Exp_shift;
+ if (L < Exp_shift) {
+ word0(a) = 0x80000 >> L;
+ word1(a) = 0;
+ }
+ else {
+ word0(a) = 0;
+ L -= Exp_shift;
+ word1(a) = L >= 31 ? 1 : 1 << 31 - L;
+ }
+ }
+#endif
+#endif
+ return dval(a);
+}
+
+static double
+b2d(Bigint *a, int *e)
+{
+ ULong *xa, *xa0, w, y, z;
+ int k;
+ double_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(double d_, int *e, int *bits)
+{
+ double_u d;
+ Bigint *b;
+ int de, k;
+ ULong *x, y, z;
+#ifndef Sudden_Underflow
+ int i;
+#endif
+#ifdef VAX
+ ULong d0, d1;
+#endif
+ dval(d) = d_;
+#ifdef VAX
+ 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)) != 0)
+ z |= Exp_msk1;
+#endif
+#ifdef Pack_32
+ if ((y = d1) != 0) {
+ if ((k = lo0bits(&y)) != 0) {
+ 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 {
+#ifdef DEBUG
+ if (!z)
+ Bug("Zero passed to d2b");
+#endif
+ 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(Bigint *a, Bigint *b)
+{
+ double_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-53 */
+#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
+
+#ifndef IEEE_Arith
+#undef INFNAN_CHECK
+#endif
+
+#ifdef INFNAN_CHECK
+
+#ifndef NAN_WORD0
+#define NAN_WORD0 0x7ff80000
+#endif
+
+#ifndef NAN_WORD1
+#define NAN_WORD1 0
+#endif
+
+static int
+match(const char **sp, char *t)
+{
+ 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(double *rvp, const char **sp)
+{
+ ULong c, x[2];
+ const char *s;
+ int havedig, udx0, xshift;
+
+ x[0] = x[1] = 0;
+ havedig = xshift = 0;
+ udx0 = 1;
+ s = *sp;
+ while (c = *(const unsigned char*)++s) {
+ if (c >= '0' && c <= '9')
+ c -= '0';
+ else if (c >= 'a' && c <= 'f')
+ c += 10 - 'a';
+ else if (c >= 'A' && c <= 'F')
+ c += 10 - 'A';
+ else if (c <= ' ') {
+ if (udx0 && havedig) {
+ udx0 = 0;
+ xshift = 1;
+ }
+ continue;
+ }
+ else if (/*(*/ c == ')' && havedig) {
+ *sp = s + 1;
+ break;
+ }
+ else
+ return; /* invalid form: don't change *sp */
+ 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 */
+
+NO_SANITIZE("unsigned-integer-overflow", double strtod(const char *s00, char **se));
+double
+strtod(const char *s00, char **se)
+{
+#ifdef Avoid_Underflow
+ int scale;
+#endif
+ int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
+ e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
+ const char *s, *s0, *s1;
+ double aadj, adj;
+ double_u aadj1, rv, rv0;
+ Long L;
+ ULong y, z;
+ Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
+#ifdef SET_INEXACT
+ int inexact, oldinexact;
+#endif
+#ifdef Honor_FLT_ROUNDS
+ int rounding;
+#endif
+#ifdef USE_LOCALE
+ const char *s2;
+#endif
+
+ errno = 0;
+ sign = nz0 = nz = 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') {
+ if (s[1] == 'x' || s[1] == 'X') {
+ s0 = ++s;
+ adj = 0;
+ aadj = 1.0;
+ nd0 = -4;
+
+ if (!*++s || !(s1 = strchr(hexdigit, *s))) goto ret0;
+ if (*s == '0') {
+ while (*++s == '0');
+ s1 = strchr(hexdigit, *s);
+ }
+ if (s1 != NULL) {
+ do {
+ adj += aadj * ((s1 - hexdigit) & 15);
+ nd0 += 4;
+ aadj /= 16;
+ } while (*++s && (s1 = strchr(hexdigit, *s)));
+ }
+
+ if (*s == '.') {
+ dsign = 1;
+ if (!*++s || !(s1 = strchr(hexdigit, *s))) goto ret0;
+ if (nd0 < 0) {
+ while (*s == '0') {
+ s++;
+ nd0 -= 4;
+ }
+ }
+ for (; *s && (s1 = strchr(hexdigit, *s)); ++s) {
+ adj += aadj * ((s1 - hexdigit) & 15);
+ if ((aadj /= 16) == 0.0) {
+ while (strchr(hexdigit, *++s));
+ break;
+ }
+ }
+ }
+ else {
+ dsign = 0;
+ }
+
+ if (*s == 'P' || *s == 'p') {
+ dsign = 0x2C - *++s; /* +: 2B, -: 2D */
+ if (abs(dsign) == 1) s++;
+ else dsign = 1;
+
+ nd = 0;
+ c = *s;
+ if (c < '0' || '9' < c) goto ret0;
+ do {
+ nd *= 10;
+ nd += c;
+ nd -= '0';
+ c = *++s;
+ /* Float("0x0."+("0"*267)+"1fp2095") */
+ if (nd + dsign * nd0 > 2095) {
+ while ('0' <= c && c <= '9') c = *++s;
+ break;
+ }
+ } while ('0' <= c && c <= '9');
+ nd0 += nd * dsign;
+ }
+ else {
+ if (dsign) goto ret0;
+ }
+ dval(rv) = ldexp(adj, nd0);
+ goto ret;
+ }
+ 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 < DBL_DIG + 2)
+ z = 10*z + c - '0';
+ nd0 = nd;
+#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 == '.') {
+ if (!ISDIGIT(s[1]))
+ goto dig_done;
+ c = *++s;
+ if (!nd) {
+ for (; c == '0'; c = *++s)
+ nz++;
+ if (c > '0' && c <= '9') {
+ s0 = s;
+ nf += nz;
+ nz = 0;
+ goto have_dig;
+ }
+ goto dig_done;
+ }
+ for (; c >= '0' && c <= '9'; c = *++s) {
+have_dig:
+ nz++;
+ if (nd > DBL_DIG * 4) {
+ continue;
+ }
+ if (c -= '0') {
+ nf += nz;
+ for (i = 1; i < nz; i++)
+ if (nd++ < 9)
+ y *= 10;
+ else if (nd <= DBL_DIG + 2)
+ z *= 10;
+ if (nd++ < 9)
+ y = 10*y + c;
+ else if (nd <= DBL_DIG + 2)
+ z = 10*z + c;
+ nz = 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 */
+ 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;
+ }
+ 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 + 2 ? nd : DBL_DIG + 2;
+ 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 = bb = bd = bs = delta = 0;
+ if (nd <= DBL_DIG
+#ifndef RND_PRODQUOT
+#ifndef Honor_FLT_ROUNDS
+ && Flt_Rounds == 1
+#endif
+#endif
+ ) {
+ if (!e)
+ goto ret;
+ 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) {
+ dval(rv) = -dval(rv);
+ 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) {
+ dval(rv) = -dval(rv);
+ 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) {
+ dval(rv) = -dval(rv);
+ sign = 0;
+ }
+#endif
+ /* rv = */ rounded_quotient(dval(rv), tens[-e]);
+ goto ret;
+ }
+#endif
+ }
+ e1 += nd - k;
+
+#ifdef IEEE_Arith
+#ifdef SET_INEXACT
+ inexact = 1;
+ if (k <= DBL_DIG)
+ oldinexact = get_inexact();
+#endif
+#ifdef Avoid_Underflow
+ scale = 0;
+#endif
+#ifdef Honor_FLT_ROUNDS
+ if ((rounding = Flt_Rounds) >= 2) {
+ if (sign)
+ rounding = rounding == 2 ? 0 : 2;
+ else
+ if (rounding != 2)
+ rounding = 0;
+ }
+#endif
+#endif /*IEEE_Arith*/
+
+ /* Get starting approximation = rv * 10**e1 */
+
+ if (e1 > 0) {
+ if ((i = e1 & 15) != 0)
+ dval(rv) *= tens[i];
+ if (e1 &= ~15) {
+ if (e1 > DBL_MAX_10_EXP) {
+ovfl:
+#ifndef NO_ERRNO
+ errno = ERANGE;
+#endif
+ /* Can't trust HUGE_VAL */
+#ifdef IEEE_Arith
+#ifdef Honor_FLT_ROUNDS
+ switch (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*/
+ if (bd0)
+ goto retfree;
+ 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) != 0)
+ dval(rv) /= tens[i];
+ if (e1 >>= 4) {
+ if (e1 >= 1 << n_bigtens)
+ goto undfl;
+#ifdef Avoid_Underflow
+ if (e1 & Scale_Bit)
+ scale = 2*P;
+ for (j = 0; e1 > 0; j++, e1 >>= 1)
+ if (e1 & 1)
+ dval(rv) *= tinytens[j];
+ if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask)
+ >> Exp_shift)) > 0) {
+ /* scaled rv is denormal; zap j low bits */
+ if (j >= 32) {
+ 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.;
+#ifndef NO_ERRNO
+ errno = ERANGE;
+#endif
+ if (bd0)
+ goto retfree;
+ goto ret;
+ }
+#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 */
+
+ bd0 = s2b(s0, nd0, nd, y);
+
+ for (;;) {
+ bd = Balloc(bd0->k);
+ Bcopy(bd, bd0);
+ bb = d2b(dval(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 (rounding != 1)
+ bs2++;
+#endif
+#ifdef Avoid_Underflow
+ j = bbe - scale;
+ i = j + bbbits - 1; /* logb(rv) */
+ if (i < Emin) /* denormal */
+ j += P - Emin;
+ else
+ j = P + 1 - bbbits;
+#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 += 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);
+ dsign = delta->sign;
+ delta->sign = 0;
+ i = cmp(delta, bs);
+#ifdef Honor_FLT_ROUNDS
+ if (rounding != 1) {
+ if (i < 0) {
+ /* Error is less than an ulp */
+ if (!delta->x[0] && delta->wds <= 1) {
+ /* exact */
+#ifdef SET_INEXACT
+ inexact = 0;
+#endif
+ break;
+ }
+ if (rounding) {
+ if (dsign) {
+ adj = 1.;
+ goto apply_adj;
+ }
+ }
+ else if (!dsign) {
+ adj = -1.;
+ if (!word1(rv)
+ && !(word0(rv) & Frac_mask)) {
+ y = word0(rv) & Exp_mask;
+#ifdef Avoid_Underflow
+ if (!scale || y > 2*P*Exp_msk1)
+#else
+ if (y)
+#endif
+ {
+ delta = lshift(delta,Log2P);
+ if (cmp(delta, bs) <= 0)
+ adj = -0.5;
+ }
+ }
+apply_adj:
+#ifdef Avoid_Underflow
+ if (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*ulp(dval(rv));
+ word0(rv) -= P*Exp_msk1;
+ }
+ else
+#endif /*Sudden_Underflow*/
+#endif /*Avoid_Underflow*/
+ dval(rv) += adj*ulp(dval(rv));
+ }
+ break;
+ }
+ adj = ratio(delta, bs);
+ if (adj < 1.)
+ adj = 1.;
+ if (adj <= 0x7ffffffe) {
+ /* adj = rounding ? ceil(adj) : floor(adj); */
+ y = adj;
+ if (y != adj) {
+ if (!((rounding>>1) ^ dsign))
+ y++;
+ adj = y;
+ }
+ }
+#ifdef Avoid_Underflow
+ if (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 *= ulp(dval(rv));
+ if (dsign)
+ dval(rv) += adj;
+ else
+ dval(rv) -= adj;
+ word0(rv) -= P*Exp_msk1;
+ goto cont;
+ }
+#endif /*Sudden_Underflow*/
+#endif /*Avoid_Underflow*/
+ adj *= ulp(dval(rv));
+ if (dsign)
+ dval(rv) += adj;
+ else
+ dval(rv) -= adj;
+ 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 (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)
+ inexact = 0;
+#endif
+ break;
+ }
+ if (!delta->x[0] && delta->wds <= 1) {
+ /* exact result */
+#ifdef SET_INEXACT
+ 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 (dsign) {
+ if ((word0(rv) & Bndry_mask1) == Bndry_mask1
+ && word1(rv) == (
+#ifdef Avoid_Underflow
+ (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
+ ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
+#endif
+ 0xffffffff)) {
+ /*boundary case -- increment exponent*/
+ word0(rv) = (word0(rv) & Exp_mask)
+ + Exp_msk1
+#ifdef IBM
+ | Exp_msk1 >> 4
+#endif
+ ;
+ word1(rv) = 0;
+#ifdef Avoid_Underflow
+ 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 <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
+#else
+ if (L <= Exp_msk1)
+#endif /*Avoid_Underflow*/
+#endif /*IBM*/
+ goto undfl;
+ L -= Exp_msk1;
+#else /*Sudden_Underflow}{*/
+#ifdef Avoid_Underflow
+ if (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 */
+ 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
+ break;
+#endif
+ }
+#ifndef ROUND_BIASED
+ if (!(word1(rv) & LSB))
+ break;
+#endif
+ if (dsign)
+ dval(rv) += ulp(dval(rv));
+#ifndef ROUND_BIASED
+ else {
+ dval(rv) -= ulp(dval(rv));
+#ifndef Sudden_Underflow
+ if (!dval(rv))
+ goto undfl;
+#endif
+ }
+#ifdef Avoid_Underflow
+ dsign = 1 - dsign;
+#endif
+#endif
+ break;
+ }
+ if ((aadj = ratio(delta, bs)) <= 2.) {
+ if (dsign)
+ aadj = dval(aadj1) = 1.;
+ else if (word1(rv) || word0(rv) & Bndry_mask) {
+#ifndef Sudden_Underflow
+ if (word1(rv) == Tiny1 && !word0(rv))
+ goto undfl;
+#endif
+ aadj = 1.;
+ dval(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;
+ dval(aadj1) = -aadj;
+ }
+ }
+ else {
+ aadj *= 0.5;
+ dval(aadj1) = dsign ? aadj : -aadj;
+#ifdef Check_FLT_ROUNDS
+ switch (Rounding) {
+ case 2: /* towards +infinity */
+ dval(aadj1) -= 0.5;
+ break;
+ case 0: /* towards 0 */
+ case 3: /* towards -infinity */
+ dval(aadj1) += 0.5;
+ }
+#else
+ if (Flt_Rounds == 0)
+ dval(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 = dval(aadj1) * ulp(dval(rv));
+ dval(rv) += adj;
+ 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 (scale && y <= 2*P*Exp_msk1) {
+ if (aadj <= 0x7fffffff) {
+ if ((z = (int)aadj) <= 0)
+ z = 1;
+ aadj = z;
+ dval(aadj1) = dsign ? aadj : -aadj;
+ }
+ word0(aadj1) += (2*P+1)*Exp_msk1 - y;
+ }
+ adj = dval(aadj1) * ulp(dval(rv));
+ dval(rv) += adj;
+#else
+#ifdef Sudden_Underflow
+ if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
+ dval(rv0) = dval(rv);
+ word0(rv) += P*Exp_msk1;
+ adj = dval(aadj1) * ulp(dval(rv));
+ dval(rv) += adj;
+#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)
+ goto undfl;
+ word0(rv) = Tiny0;
+ word1(rv) = Tiny1;
+ goto cont;
+ }
+ else
+ word0(rv) -= P*Exp_msk1;
+ }
+ else {
+ adj = dval(aadj1) * ulp(dval(rv));
+ dval(rv) += adj;
+ }
+#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.) {
+ dval(aadj1) = (double)(int)(aadj + 0.5);
+ if (!dsign)
+ dval(aadj1) = -dval(aadj1);
+ }
+ adj = dval(aadj1) * ulp(dval(rv));
+ dval(rv) += adj;
+#endif /*Sudden_Underflow*/
+#endif /*Avoid_Underflow*/
+ }
+ z = word0(rv) & Exp_mask;
+#ifndef SET_INEXACT
+#ifdef Avoid_Underflow
+ if (!scale)
+#endif
+ if (y == z) {
+ /* Can we stop now? */
+ L = (Long)aadj;
+ aadj -= L;
+ /* The tolerances below are conservative. */
+ if (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);
+ }
+#ifdef SET_INEXACT
+ if (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 (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 */
+ if (word0(rv) == 0 && word1(rv) == 0)
+ errno = ERANGE;
+#endif
+ }
+#endif /* Avoid_Underflow */
+#ifdef SET_INEXACT
+ if (inexact && !(word0(rv) & Exp_mask)) {
+ /* set underflow bit */
+ dval(rv0) = 1e-300;
+ dval(rv0) *= dval(rv0);
+ }
+#endif
+retfree:
+ Bfree(bb);
+ Bfree(bd);
+ Bfree(bs);
+ Bfree(bd0);
+ Bfree(delta);
+ret:
+ if (se)
+ *se = (char *)s;
+ return sign ? -dval(rv) : dval(rv);
+}
+
+NO_SANITIZE("unsigned-integer-overflow", static int quorem(Bigint *b, Bigint *S));
+static int
+quorem(Bigint *b, Bigint *S)
+{
+ 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
+ /*debug*/ if (q > 9)
+ /*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++ = (ULong)(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++ = (ULong)(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;
+}
+
+#ifndef MULTIPLE_THREADS
+static char *dtoa_result;
+#endif
+
+#ifndef MULTIPLE_THREADS
+static char *
+rv_alloc(int i)
+{
+ return dtoa_result = MALLOC(i);
+}
+#else
+#define rv_alloc(i) MALLOC(i)
+#endif
+
+static char *
+nrv_alloc(const char *s, char **rve, size_t n)
+{
+ char *rv, *t;
+
+ t = rv = rv_alloc(n);
+ while ((*t = *s++) != 0) t++;
+ if (rve)
+ *rve = t;
+ return rv;
+}
+
+#define rv_strdup(s, rve) nrv_alloc((s), (rve), strlen(s)+1)
+
+#ifndef MULTIPLE_THREADS
+/* 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.
+ */
+
+static void
+freedtoa(char *s)
+{
+ FREE(s);
+}
+#endif
+
+static const char INFSTR[] = "Infinity";
+static const char NANSTR[] = "NaN";
+static const char ZEROSTR[] = "0";
+
+/* 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(double d_, int mode, int ndigits, int *decpt, int *sign, char **rve)
+{
+ /* 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, half = 0;
+ Long L;
+#ifndef Sudden_Underflow
+ int denorm;
+ ULong x;
+#endif
+ Bigint *b, *b1, *delta, *mlo = 0, *mhi = 0, *S;
+ double ds;
+ double_u d, d2, eps;
+ char *s, *s0;
+#ifdef Honor_FLT_ROUNDS
+ int rounding;
+#endif
+#ifdef SET_INEXACT
+ int inexact, oldinexact;
+#endif
+
+ dval(d) = d_;
+
+#ifndef MULTIPLE_THREADS
+ if (dtoa_result) {
+ freedtoa(dtoa_result);
+ dtoa_result = 0;
+ }
+#endif
+
+ if (word0(d) & Sign_bit) {
+ /* set sign for everything, including 0's and NaNs */
+ *sign = 1;
+ word0(d) &= ~Sign_bit; /* clear sign bit */
+ }
+ else
+ *sign = 0;
+
+#if defined(IEEE_Arith) + defined(VAX)
+#ifdef IEEE_Arith
+ if ((word0(d) & Exp_mask) == Exp_mask)
+#else
+ if (word0(d) == 0x8000)
+#endif
+ {
+ /* Infinity or NaN */
+ *decpt = 9999;
+#ifdef IEEE_Arith
+ if (!word1(d) && !(word0(d) & 0xfffff))
+ return rv_strdup(INFSTR, rve);
+#endif
+ return rv_strdup(NANSTR, rve);
+ }
+#endif
+#ifdef IBM
+ dval(d) += 0; /* normalize */
+#endif
+ if (!dval(d)) {
+ *decpt = 1;
+ return rv_strdup(ZEROSTR, rve);
+ }
+
+#ifdef SET_INEXACT
+ try_quick = oldinexact = get_inexact();
+ inexact = 1;
+#endif
+#ifdef Honor_FLT_ROUNDS
+ if ((rounding = Flt_Rounds) >= 2) {
+ if (*sign)
+ rounding = rounding == 2 ? 0 : 2;
+ else
+ if (rounding != 2)
+ rounding = 0;
+ }
+#endif
+
+ b = d2b(dval(d), &be, &bbits);
+#ifdef Sudden_Underflow
+ i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
+#else
+ if ((i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1))) != 0) {
+#endif
+ dval(d2) = dval(d);
+ 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(d) << (64 - i) | word1(d) >> (i - 32)
+ : word1(d) << (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(d) < 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;
+ 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+1);
+
+#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(d);
+ 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(d) /= bigtens[n_bigtens-1];
+ ieps++;
+ }
+ for (; j; j >>= 1, i++)
+ if (j & 1) {
+ ieps++;
+ ds *= bigtens[i];
+ }
+ dval(d) /= ds;
+ }
+ else if ((j1 = -k) != 0) {
+ dval(d) *= tens[j1 & 0xf];
+ for (j = j1 >> 4; j; j >>= 1, i++)
+ if (j & 1) {
+ ieps++;
+ dval(d) *= bigtens[i];
+ }
+ }
+ if (k_check && dval(d) < 1. && ilim > 0) {
+ if (ilim1 <= 0)
+ goto fast_failed;
+ ilim = ilim1;
+ k--;
+ dval(d) *= 10.;
+ ieps++;
+ }
+ dval(eps) = ieps*dval(d) + 7.;
+ word0(eps) -= (P-1)*Exp_msk1;
+ if (ilim == 0) {
+ S = mhi = 0;
+ dval(d) -= 5.;
+ if (dval(d) > dval(eps))
+ goto one_digit;
+ if (dval(d) < -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);
+ for (i = 0;;) {
+ L = (int)dval(d);
+ dval(d) -= L;
+ *s++ = '0' + (int)L;
+ if (dval(d) < dval(eps))
+ goto ret1;
+ if (1. - dval(d) < dval(eps))
+ goto bump_up;
+ if (++i >= ilim)
+ break;
+ dval(eps) *= 10.;
+ dval(d) *= 10.;
+ }
+ }
+ else {
+#endif
+ /* Generate ilim digits, then fix them up. */
+ dval(eps) *= tens[ilim-1];
+ for (i = 1;; i++, dval(d) *= 10.) {
+ L = (Long)(dval(d));
+ if (!(dval(d) -= L))
+ ilim = i;
+ *s++ = '0' + (int)L;
+ if (i == ilim) {
+ if (dval(d) > 0.5 + dval(eps))
+ goto bump_up;
+ else if (dval(d) < 0.5 - dval(eps)) {
+ while (*--s == '0') ;
+ s++;
+ goto ret1;
+ }
+ half = 1;
+ if ((*(s-1) - '0') & 1) {
+ goto bump_up;
+ }
+ break;
+ }
+ }
+#ifndef No_leftright
+ }
+#endif
+fast_failed:
+ s = s0;
+ dval(d) = 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(d) <= 5*ds)
+ goto no_digits;
+ goto one_digit;
+ }
+ for (i = 1;; i++, dval(d) *= 10.) {
+ L = (Long)(dval(d) / ds);
+ dval(d) -= L*ds;
+#ifdef Check_FLT_ROUNDS
+ /* If FLT_ROUNDS == 2, L will usually be high by 1 */
+ if (dval(d) < 0) {
+ L--;
+ dval(d) += ds;
+ }
+#endif
+ *s++ = '0' + (int)L;
+ if (!dval(d)) {
+#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(d) += dval(d);
+ if (dval(d) > ds || (dval(d) == ds && (L & 1))) {
+bump_up:
+ while (*--s == '9')
+ if (s == s0) {
+ k++;
+ *s = '0';
+ break;
+ }
+ ++*s++;
+ }
+ break;
+ }
+ }
+ goto ret1;
+ }
+
+ m2 = b2;
+ m5 = b5;
+ 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) != 0)
+ 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(d) && !(word0(d) & Bndry_mask)
+#ifndef Sudden_Underflow
+ && word0(d) & (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.
+ */
+#ifdef Pack_32
+ if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f) != 0)
+ i = 32 - i;
+#else
+ if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf) != 0)
+ i = 16 - i;
+#endif
+ if (i > 4) {
+ i -= 4;
+ b2 += i;
+ m2 += i;
+ s2 += i;
+ }
+ else if (i < 4) {
+ i += 28;
+ 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(d) & 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(d) & 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);
+ if ((j1 > 0 || (j1 == 0 && (dig & 1))) && 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);
+ if (j > 0 || (j == 0 && (dig & 1))) {
+ roundoff:
+ while (*--s == '9')
+ if (s == s0) {
+ k++;
+ *s++ = '1';
+ goto ret;
+ }
+ if (!half || (*s - '0') & 1)
+ ++*s;
+ }
+ else {
+ 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(d) = Exp_1 + (70 << Exp_shift);
+ word1(d) = 0;
+ dval(d) += 1.;
+ }
+ }
+ else if (!oldinexact)
+ clear_inexact();
+#endif
+ Bfree(b);
+ *s = 0;
+ *decpt = k + 1;
+ if (rve)
+ *rve = s;
+ return s0;
+}
+
+/*-
+ * Copyright (c) 2004-2008 David Schultz <das@FreeBSD.ORG>
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ * notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ * notice, this list of conditions and the following disclaimer in the
+ * documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+#define DBL_MANH_SIZE 20
+#define DBL_MANL_SIZE 32
+#define DBL_ADJ (DBL_MAX_EXP - 2)
+#define SIGFIGS ((DBL_MANT_DIG + 3) / 4 + 1)
+#define dexp_get(u) ((int)(word0(u) >> Exp_shift) & ~Exp_msk1)
+#define dexp_set(u,v) (word0(u) = (((int)(word0(u)) & ~Exp_mask) | ((v) << Exp_shift)))
+#define dmanh_get(u) ((uint32_t)(word0(u) & Frac_mask))
+#define dmanl_get(u) ((uint32_t)word1(u))
+
+
+/*
+ * This procedure converts a double-precision number in IEEE format
+ * into a string of hexadecimal digits and an exponent of 2. Its
+ * behavior is bug-for-bug compatible with dtoa() in mode 2, with the
+ * following exceptions:
+ *
+ * - An ndigits < 0 causes it to use as many digits as necessary to
+ * represent the number exactly.
+ * - The additional xdigs argument should point to either the string
+ * "0123456789ABCDEF" or the string "0123456789abcdef", depending on
+ * which case is desired.
+ * - This routine does not repeat dtoa's mistake of setting decpt
+ * to 9999 in the case of an infinity or NaN. INT_MAX is used
+ * for this purpose instead.
+ *
+ * Note that the C99 standard does not specify what the leading digit
+ * should be for non-zero numbers. For instance, 0x1.3p3 is the same
+ * as 0x2.6p2 is the same as 0x4.cp3. This implementation always makes
+ * the leading digit a 1. This ensures that the exponent printed is the
+ * actual base-2 exponent, i.e., ilogb(d).
+ *
+ * Inputs: d, xdigs, ndigits
+ * Outputs: decpt, sign, rve
+ */
+char *
+hdtoa(double d, const char *xdigs, int ndigits, int *decpt, int *sign, char **rve)
+{
+ U u;
+ char *s, *s0;
+ int bufsize;
+ uint32_t manh, manl;
+
+ u.d = d;
+ 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 (isinf(d)) { /* FP_INFINITE */
+ *decpt = INT_MAX;
+ return rv_strdup(INFSTR, rve);
+ }
+ else if (isnan(d)) { /* FP_NAN */
+ *decpt = INT_MAX;
+ return rv_strdup(NANSTR, rve);
+ }
+ else if (d == 0.0) { /* FP_ZERO */
+ *decpt = 1;
+ return rv_strdup(ZEROSTR, rve);
+ }
+ else if (dexp_get(u)) { /* FP_NORMAL */
+ *decpt = dexp_get(u) - DBL_ADJ;
+ }
+ else { /* FP_SUBNORMAL */
+ u.d *= 5.363123171977039e+154 /* 0x1p514 */;
+ *decpt = dexp_get(u) - (514 + DBL_ADJ);
+ }
+
+ if (ndigits == 0) /* dtoa() compatibility */
+ ndigits = 1;
+
+ /*
+ * If ndigits < 0, we are expected to auto-size, so we allocate
+ * enough space for all the digits.
+ */
+ bufsize = (ndigits > 0) ? ndigits : SIGFIGS;
+ s0 = rv_alloc(bufsize+1);
+
+ /* Round to the desired number of digits. */
+ if (SIGFIGS > ndigits && ndigits > 0) {
+ float redux = 1.0f;
+ int offset = 4 * ndigits + DBL_MAX_EXP - 4 - DBL_MANT_DIG;
+ dexp_set(u, offset);
+ u.d += redux;
+ u.d -= redux;
+ *decpt += dexp_get(u) - offset;
+ }
+
+ manh = dmanh_get(u);
+ manl = dmanl_get(u);
+ *s0 = '1';
+ for (s = s0 + 1; s < s0 + bufsize; s++) {
+ *s = xdigs[(manh >> (DBL_MANH_SIZE - 4)) & 0xf];
+ manh = (manh << 4) | (manl >> (DBL_MANL_SIZE - 4));
+ manl <<= 4;
+ }
+
+ /* If ndigits < 0, we are expected to auto-size the precision. */
+ if (ndigits < 0) {
+ for (ndigits = SIGFIGS; s0[ndigits - 1] == '0'; ndigits--)
+ ;
+ }
+
+ s = s0 + ndigits;
+ *s = '\0';
+ if (rve != NULL)
+ *rve = s;
+ return (s0);
+}
+
+#ifdef __cplusplus
+#if 0
+{ /* satisfy cc-mode */
+#endif
+}
+#endif