/util.c

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/**********************************************************************

  util.c -

  $Author$
  created at: Fri Mar 10 17:22:34 JST 1995

  Copyright (C) 1993-2008 Yukihiro Matsumoto

**********************************************************************/

#include "ruby/ruby.h"

#include <ctype.h>
#include <stdio.h>
#include <errno.h>
#include <math.h>
#include <float.h>

#ifdef _WIN32
#include "missing/file.h"
#endif

#include "ruby/util.h"

unsigned long
ruby_scan_oct(const char *start, size_t len, size_t *retlen)
{
    register const char *s = start;
    register unsigned long retval = 0;

    while (len-- && *s >= '0' && *s <= '7') {
	retval <<= 3;
	retval |= *s++ - '0';
    }
    *retlen = (int)(s - start);	/* less than len */
    return retval;
}

unsigned long
ruby_scan_hex(const char *start, size_t len, size_t *retlen)
{
    static const char hexdigit[] = "0123456789abcdef0123456789ABCDEF";
    register const char *s = start;
    register unsigned long retval = 0;
    const char *tmp;

    while (len-- && *s && (tmp = strchr(hexdigit, *s))) {
	retval <<= 4;
	retval |= (tmp - hexdigit) & 15;
	s++;
    }
    *retlen = (int)(s - start);	/* less than len */
    return retval;
}

static unsigned long
scan_digits(const char *str, int base, size_t *retlen, int *overflow)
{
    static signed char table[] = {
        /*     0  1  2  3  4  5  6  7  8  9  a  b  c  d  e  f */
        /*0*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
        /*1*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
        /*2*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
        /*3*/  0, 1, 2, 3, 4, 5, 6, 7, 8, 9,-1,-1,-1,-1,-1,-1,
        /*4*/ -1,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,
        /*5*/ 25,26,27,28,29,30,31,32,33,34,35,-1,-1,-1,-1,-1,
        /*6*/ -1,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,
        /*7*/ 25,26,27,28,29,30,31,32,33,34,35,-1,-1,-1,-1,-1,
        /*8*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
        /*9*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
        /*a*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
        /*b*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
        /*c*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
        /*d*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
        /*e*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
        /*f*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
    };

    const char *start = str;
    unsigned long ret = 0, x;
    unsigned long mul_overflow = (~(unsigned long)0) / base;
    int c;
    *overflow = 0;

    while ((c = (unsigned char)*str++) != '\0') {
        int d = table[c];
        if (d == -1 || base <= d) {
            *retlen = (str-1) - start;
            return ret;
        }
        if (mul_overflow < ret)
            *overflow = 1;
        ret *= base;
        x = ret;
        ret += d;
        if (ret < x)
            *overflow = 1;
    }
    *retlen = (str-1) - start;
    return ret;
}

unsigned long
ruby_strtoul(const char *str, char **endptr, int base)
{
    int c, b, overflow;
    int sign = 0;
    size_t len;
    unsigned long ret;
    const char *subject_found = str;

    if (base == 1 || 36 < base) {
        errno = EINVAL;
        return 0;
    }

    while ((c = *str) && ISSPACE(c))
        str++;

    if (c == '+') {
        sign = 1;
        str++;
    }
    else if (c == '-') {
        sign = -1;
        str++;
    }

    if (str[0] == '0') {
        subject_found = str+1;
        if (base == 0 || base == 16) {
            if (str[1] == 'x' || str[1] == 'X') {
                b = 16;
                str += 2;
            }
            else {
                b = base == 0 ? 8 : 16;
                str++;
            }
        }
        else {
            b = base;
            str++;
        }
    }
    else {
        b = base == 0 ? 10 : base;
    }

    ret = scan_digits(str, b, &len, &overflow);

    if (0 < len)
        subject_found = str+len;

    if (endptr)
        *endptr = (char*)subject_found;

    if (overflow) {
        errno = ERANGE;
        return ULONG_MAX;
    }

    if (sign < 0) {
        ret = (unsigned long)(-(long)ret);
        return ret;
    }
    else {
        return ret;
    }
}

#include <sys/types.h>
#include <sys/stat.h>
#ifdef HAVE_UNISTD_H
#include <unistd.h>
#endif
#if defined(HAVE_FCNTL_H)
#include <fcntl.h>
#endif

#ifndef S_ISDIR
#   define S_ISDIR(m) ((m & S_IFMT) == S_IFDIR)
#endif

#if defined(__CYGWIN32__) || defined(_WIN32)
/*
 *  Copyright (c) 1993, Intergraph Corporation
 *
 *  You may distribute under the terms of either the GNU General Public
 *  License or the Artistic License, as specified in the perl README file.
 *
 *  Various Unix compatibility functions and NT specific functions.
 *
 *  Some of this code was derived from the MSDOS port(s) and the OS/2 port.
 *
 */


/*
 * Suffix appending for in-place editing under MS-DOS and OS/2 (and now NT!).
 *
 * Here are the rules:
 *
 * Style 0:  Append the suffix exactly as standard perl would do it.
 *           If the filesystem groks it, use it.  (HPFS will always
 *           grok it.  So will NTFS. FAT will rarely accept it.)
 *
 * Style 1:  The suffix begins with a '.'.  The extension is replaced.
 *           If the name matches the original name, use the fallback method.
 *
 * Style 2:  The suffix is a single character, not a '.'.  Try to add the
 *           suffix to the following places, using the first one that works.
 *               [1] Append to extension.
 *               [2] Append to filename,
 *               [3] Replace end of extension,
 *               [4] Replace end of filename.
 *           If the name matches the original name, use the fallback method.
 *
 * Style 3:  Any other case:  Ignore the suffix completely and use the
 *           fallback method.
 *
 * Fallback method:  Change the extension to ".$$$".  If that matches the
 *           original name, then change the extension to ".~~~".
 *
 * If filename is more than 1000 characters long, we die a horrible
 * death.  Sorry.
 *
 * The filename restriction is a cheat so that we can use buf[] to store
 * assorted temporary goo.
 *
 * Examples, assuming style 0 failed.
 *
 * suffix = ".bak" (style 1)
 *                foo.bar => foo.bak
 *                foo.bak => foo.$$$	(fallback)
 *                foo.$$$ => foo.~~~	(fallback)
 *                makefile => makefile.bak
 *
 * suffix = "~" (style 2)
 *                foo.c => foo.c~
 *                foo.c~ => foo.c~~
 *                foo.c~~ => foo~.c~~
 *                foo~.c~~ => foo~~.c~~
 *                foo~~~~~.c~~ => foo~~~~~.$$$ (fallback)
 *
 *                foo.pas => foo~.pas
 *                makefile => makefile.~
 *                longname.fil => longname.fi~
 *                longname.fi~ => longnam~.fi~
 *                longnam~.fi~ => longnam~.$$$
 *
 */


static int valid_filename(const char *s);

static const char suffix1[] = ".$$$";
static const char suffix2[] = ".~~~";

#define strEQ(s1,s2) (strcmp(s1,s2) == 0)

extern const char *ruby_find_basename(const char *, long *, long *);
extern const char *ruby_find_extname(const char *, long *);

void
ruby_add_suffix(VALUE str, const char *suffix)
{
    int baselen;
    int extlen = strlen(suffix);
    char *p, *q;
    long slen;
    char buf[1024];
    const char *name;
    const char *ext;
    long len;

    name = StringValueCStr(str);
    slen = strlen(name);
    if (slen > sizeof(buf) - 1)
	rb_fatal("Cannot do inplace edit on long filename (%ld characters)",
		 slen);

    /* Style 0 */
    rb_str_cat(str, suffix, extlen);
    if (valid_filename(RSTRING_PTR(str))) return;

    /* Fooey, style 0 failed.  Fix str before continuing. */
    rb_str_resize(str, slen);
    name = StringValueCStr(str);
    ext = ruby_find_extname(name, &len);

    if (*suffix == '.') {        /* Style 1 */
	if (ext) {
	    if (strEQ(ext, suffix)) goto fallback;
	    slen = ext - name;
	}
	rb_str_resize(str, slen);
	rb_str_cat(str, suffix, extlen);
    }
    else {
	strncpy(buf, name, slen);
	if (ext)
	    p = buf + (ext - name);
	else
	    p = buf + slen;
	p[len] = '\0';
	if (suffix[1] == '\0') {  /* Style 2 */
	    if (len <= 3) {
		p[len] = *suffix;
		p[++len] = '\0';
	    }
	    else if ((q = (char *)ruby_find_basename(buf, &baselen, 0)) &&
		     baselen < 8) {
		q += baselen;
		*q++ = *suffix;
		if (ext) {
		    strncpy(q, ext, ext - name);
		    q[ext - name + 1] = '\0';
		}
		else
		    *q = '\0';
	    }
	    else if (len == 4 && p[3] != *suffix)
		p[3] = *suffix;
	    else if (baselen == 8 && q[7] != *suffix)
		q[7] = *suffix;
	    else
		goto fallback;
	}
	else { /* Style 3:  Panic */
	  fallback:
	    (void)memcpy(p, !ext || strEQ(ext, suffix1) ? suffix2 : suffix1, 5);
	}
    }
    rb_str_resize(str, strlen(buf));
    memcpy(RSTRING_PTR(str), buf, RSTRING_LEN(str));
}

static int
valid_filename(const char *s)
{
    int fd;

    /*
    // It doesn't exist, so see if we can open it.
    */

    if ((fd = open(s, O_CREAT|O_EXCL, 0666)) >= 0) {
	close(fd);
	unlink(s);	/* don't leave it laying around */
	return 1;
    }
    else if (errno == EEXIST) {
	/* if the file exists, then it's a valid filename! */
	return 1;
    }
    return 0;
}
#endif


/* mm.c */

#define A ((int*)a)
#define B ((int*)b)
#define C ((int*)c)
#define D ((int*)d)

#define mmprepare(base, size) do {\
 if (((long)base & (0x3)) == 0)\
   if (size >= 16) mmkind = 1;\
   else            mmkind = 0;\
 else              mmkind = -1;\
 high = (size & (~0xf));\
 low  = (size &  0x0c);\
} while (0)\

#define mmarg mmkind, size, high, low

static void mmswap_(register char *a, register char *b, int mmkind, size_t size, size_t high, size_t low)
{
 register int s;
 if (a == b) return;
 if (mmkind >= 0) {
   if (mmkind > 0) {
     register char *t = a + high;
     do {
       s = A[0]; A[0] = B[0]; B[0] = s;
       s = A[1]; A[1] = B[1]; B[1] = s;
       s = A[2]; A[2] = B[2]; B[2] = s;
       s = A[3]; A[3] = B[3]; B[3] = s;  a += 16; b += 16;
     } while (a < t);
   }
   if (low != 0) { s = A[0]; A[0] = B[0]; B[0] = s;
     if (low >= 8) { s = A[1]; A[1] = B[1]; B[1] = s;
       if (low == 12) {s = A[2]; A[2] = B[2]; B[2] = s;}}}
 }
 else {
   register char *t = a + size;
   do {s = *a; *a++ = *b; *b++ = s;} while (a < t);
 }
}
#define mmswap(a,b) mmswap_((a),(b),mmarg)

static void mmrot3_(register char *a, register char *b, register char *c, int mmkind, size_t size, size_t high, size_t low)
{
 register int s;
 if (mmkind >= 0) {
   if (mmkind > 0) {
     register char *t = a + high;
     do {
       s = A[0]; A[0] = B[0]; B[0] = C[0]; C[0] = s;
       s = A[1]; A[1] = B[1]; B[1] = C[1]; C[1] = s;
       s = A[2]; A[2] = B[2]; B[2] = C[2]; C[2] = s;
       s = A[3]; A[3] = B[3]; B[3] = C[3]; C[3] = s; a += 16; b += 16; c += 16;
     } while (a < t);
   }
   if (low != 0) { s = A[0]; A[0] = B[0]; B[0] = C[0]; C[0] = s;
     if (low >= 8) { s = A[1]; A[1] = B[1]; B[1] = C[1]; C[1] = s;
       if (low == 12) {s = A[2]; A[2] = B[2]; B[2] = C[2]; C[2] = s;}}}
 }
 else {
   register char *t = a + size;
   do {s = *a; *a++ = *b; *b++ = *c; *c++ = s;} while (a < t);
 }
}
#define mmrot3(a,b,c) mmrot3_((a),(b),(c),mmarg)

/* qs6.c */
/*****************************************************/
/*                                                   */
/*          qs6   (Quick sort function)              */
/*                                                   */
/* by  Tomoyuki Kawamura              1995.4.21      */
/* kawamura@tokuyama.ac.jp                           */
/*****************************************************/

typedef struct { char *LL, *RR; } stack_node; /* Stack structure for L,l,R,r */
#define PUSH(ll,rr) do { top->LL = (ll); top->RR = (rr); ++top; } while (0)  /* Push L,l,R,r */
#define POP(ll,rr)  do { --top; ll = top->LL; rr = top->RR; } while (0)      /* Pop L,l,R,r */

#define med3(a,b,c) ((*cmp)(a,b,d)<0 ?                                   \
                       ((*cmp)(b,c,d)<0 ? b : ((*cmp)(a,c,d)<0 ? c : a)) : \
                       ((*cmp)(b,c,d)>0 ? b : ((*cmp)(a,c,d)<0 ? a : c)))

void
ruby_qsort(void* base, const size_t nel, const size_t size,
	   int (*cmp)(const void*, const void*, void*), void *d)
{
  register char *l, *r, *m;          	/* l,r:left,right group   m:median point */
  register int t, eq_l, eq_r;       	/* eq_l: all items in left group are equal to S */
  char *L = base;                    	/* left end of current region */
  char *R = (char*)base + size*(nel-1); /* right end of current region */
  size_t chklim = 63;                   /* threshold of ordering element check */
  stack_node stack[32], *top = stack;   /* 32 is enough for 32bit CPU */
  int mmkind;
  size_t high, low, n;

  if (nel <= 1) return;        /* need not to sort */
  mmprepare(base, size);
  goto start;

  nxt:
  if (stack == top) return;    /* return if stack is empty */
  POP(L,R);

  for (;;) {
    start:
    if (L + size == R) {       /* 2 elements */
      if ((*cmp)(L,R,d) > 0) mmswap(L,R); goto nxt;
    }

    l = L; r = R;
    n = (r - l + size) / size;  /* number of elements */
    m = l + size * (n >> 1);    /* calculate median value */

    if (n >= 60) {
      register char *m1;
      register char *m3;
      if (n >= 200) {
	n = size*(n>>3); /* number of bytes in splitting 8 */
	{
	  register char *p1 = l  + n;
	  register char *p2 = p1 + n;
	  register char *p3 = p2 + n;
	  m1 = med3(p1, p2, p3);
	  p1 = m  + n;
	  p2 = p1 + n;
	  p3 = p2 + n;
	  m3 = med3(p1, p2, p3);
	}
      }
      else {
	n = size*(n>>2); /* number of bytes in splitting 4 */
	m1 = l + n;
	m3 = m + n;
      }
      m = med3(m1, m, m3);
    }

    if ((t = (*cmp)(l,m,d)) < 0) {                           /*3-5-?*/
      if ((t = (*cmp)(m,r,d)) < 0) {                         /*3-5-7*/
	if (chklim && nel >= chklim) {   /* check if already ascending order */
	  char *p;
	  chklim = 0;
	  for (p=l; p<r; p+=size) if ((*cmp)(p,p+size,d) > 0) goto fail;
	  goto nxt;
	}
	fail: goto loopA;                                    /*3-5-7*/
      }
      if (t > 0) {
	if ((*cmp)(l,r,d) <= 0) {mmswap(m,r); goto loopA;}     /*3-5-4*/
	mmrot3(r,m,l); goto loopA;                           /*3-5-2*/
      }
      goto loopB;                                            /*3-5-5*/
    }

    if (t > 0) {                                             /*7-5-?*/
      if ((t = (*cmp)(m,r,d)) > 0) {                         /*7-5-3*/
	if (chklim && nel >= chklim) {   /* check if already ascending order */
	  char *p;
	  chklim = 0;
	  for (p=l; p<r; p+=size) if ((*cmp)(p,p+size,d) < 0) goto fail2;
	  while (l<r) {mmswap(l,r); l+=size; r-=size;}  /* reverse region */
	  goto nxt;
	}
	fail2: mmswap(l,r); goto loopA;                      /*7-5-3*/
      }
      if (t < 0) {
	if ((*cmp)(l,r,d) <= 0) {mmswap(l,m); goto loopB;}   /*7-5-8*/
	mmrot3(l,m,r); goto loopA;                           /*7-5-6*/
      }
      mmswap(l,r); goto loopA;                               /*7-5-5*/
    }

    if ((t = (*cmp)(m,r,d)) < 0)  {goto loopA;}              /*5-5-7*/
    if (t > 0) {mmswap(l,r); goto loopB;}                    /*5-5-3*/

    /* determining splitting type in case 5-5-5 */           /*5-5-5*/
    for (;;) {
      if ((l += size) == r)      goto nxt;                   /*5-5-5*/
      if (l == m) continue;
      if ((t = (*cmp)(l,m,d)) > 0) {mmswap(l,r); l = L; goto loopA;}/*575-5*/
      if (t < 0)                 {mmswap(L,l); l = L; goto loopB;}  /*535-5*/
    }

    loopA: eq_l = 1; eq_r = 1;  /* splitting type A */ /* left <= median < right */
    for (;;) {
      for (;;) {
	if ((l += size) == r)
	  {l -= size; if (l != m) mmswap(m,l); l -= size; goto fin;}
	if (l == m) continue;
	if ((t = (*cmp)(l,m,d)) > 0) {eq_r = 0; break;}
	if (t < 0) eq_l = 0;
      }
      for (;;) {
	if (l == (r -= size))
	  {l -= size; if (l != m) mmswap(m,l); l -= size; goto fin;}
	if (r == m) {m = l; break;}
	if ((t = (*cmp)(r,m,d)) < 0) {eq_l = 0; break;}
	if (t == 0) break;
      }
      mmswap(l,r);    /* swap left and right */
    }

    loopB: eq_l = 1; eq_r = 1;  /* splitting type B */ /* left < median <= right */
    for (;;) {
      for (;;) {
	if (l == (r -= size))
	  {r += size; if (r != m) mmswap(r,m); r += size; goto fin;}
	if (r == m) continue;
	if ((t = (*cmp)(r,m,d)) < 0) {eq_l = 0; break;}
	if (t > 0) eq_r = 0;
      }
      for (;;) {
	if ((l += size) == r)
	  {r += size; if (r != m) mmswap(r,m); r += size; goto fin;}
	if (l == m) {m = r; break;}
	if ((t = (*cmp)(l,m,d)) > 0) {eq_r = 0; break;}
	if (t == 0) break;
      }
      mmswap(l,r);    /* swap left and right */
    }

    fin:
    if (eq_l == 0)                         /* need to sort left side */
      if (eq_r == 0)                       /* need to sort right side */
	if (l-L < R-r) {PUSH(r,R); R = l;} /* sort left side first */
	else           {PUSH(L,l); L = r;} /* sort right side first */
      else R = l;                          /* need to sort left side only */
    else if (eq_r == 0) L = r;             /* need to sort right side only */
    else goto nxt;                         /* need not to sort both sides */
  }
}

char *
ruby_strdup(const char *str)
{
    char *tmp;
    size_t len = strlen(str) + 1;

    tmp = xmalloc(len);
    memcpy(tmp, str, len);

    return tmp;
}

char *
ruby_getcwd(void)
{
#ifdef HAVE_GETCWD
    int size = 200;
    char *buf = xmalloc(size);

    while (!getcwd(buf, size)) {
	if (errno != ERANGE) {
	    xfree(buf);
	    rb_sys_fail("getcwd");
	}
	size *= 2;
	buf = xrealloc(buf, size);
    }
#else
# ifndef PATH_MAX
#  define PATH_MAX 8192
# endif
    char *buf = xmalloc(PATH_MAX+1);

    if (!getwd(buf)) {
	xfree(buf);
	rb_sys_fail("getwd");
    }
#endif
    return buf;
}

/****************************************************************
 *
 * 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

#if SIZEOF_INT == 4
#define Long int
#define ULong unsigned int
#elif SIZEOF_LONG == 4
#define Long long int
#define ULong unsigned long int
#endif

#if HAVE_LONG_LONG
#define Llong LONG_LONG
#endif

#ifdef DEBUG
#include "stdio.h"
#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
#endif

#include "stdlib.h"
#include "string.h"

#ifdef USE_LOCALE
#include "locale.h"
#endif

#ifdef MALLOC
extern void *MALLOC(size_t);
#else
#define MALLOC malloc
#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 */

#ifndef __MATH_H__
#include "math.h"
#endif

#ifdef __cplusplus
extern "C" {
#if 0
}
#endif
#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

#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

    ACQUIRE_DTOA_LOCK(0);
    if ((rv = freelist[k]) != 0) {
        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 (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(Bigint *v)
{
    if (v) {
        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(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) {
            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) {
            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;
    int i;
    static 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 */
#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(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;
}

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 fact…