make #includes consistent

[hiphop-php.git] / hphp / runtime / base / zend / zend_strtod.cpp

/****************************************************************
 *
 * The author of this software is David M. Gay.
 *
 * Copyright (c) 1991 by AT&T.
 *
 * 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 AT&T 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
   AT&T Bell Laboratories, Room 2C-463
   600 Mountain Avenue
   Murray Hill, NJ 07974-2070
   U.S.A.
   dmg@research.att.com or research!dmg
   */

/* 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 Sudden_Underflow for IEEE-format machines without gradual
 *  underflow (i.e., that flush to zero on underflow).
 * #define IBM for IBM mainframe-style floating-point arithmetic.
 * #define VAX for VAX-style floating-point arithmetic.
 * #define Unsigned_Shifts if >> does treats its left operand as unsigned.
 * #define No_leftright to omit left-right logic in fast floating-point
 *  computation of dtoa.
 * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3.
 * #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 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.
 * #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.
 */

#include "hphp/runtime/base/zend/zend_strtod.h"
#include "hphp/runtime/base/util/exceptions.h"
#include "hphp/util/thread_local.h"

namespace HPHP {
///////////////////////////////////////////////////////////////////////////////

#if (defined(__APPLE__) || defined(__APPLE_CC__)) && (defined(__BIG_ENDIAN__) || defined(__LITTLE_ENDIAN__))
# if defined(__LITTLE_ENDIAN__)
#  undef WORDS_BIGENDIAN
# else
#  if defined(__BIG_ENDIAN__)
#   define WORDS_BIGENDIAN
#  endif
# endif
#endif

#ifdef WORDS_BIGENDIAN
#define IEEE_BIG_ENDIAN
#else
#define IEEE_LITTLE_ENDIAN
#endif

#if defined(__arm__) && !defined(__VFP_FP__)
/*
 *  * Although the CPU is little endian the FP has different
 *   * byte and word endianness. The byte order is still little endian
 *    * but the word order is big endian.
 *     */
#define IEEE_BIG_ENDIAN
#undef IEEE_LITTLE_ENDIAN
#endif

#ifdef __vax__
#define VAX
#endif

#if defined(_MSC_VER)
#define int32_t __int32
#define uint32_t unsigned __int32
#define IEEE_LITTLE_ENDIAN
#endif

#define Long    int32_t
#define ULong   uint32_t

#ifdef MALLOC
#ifdef KR_headers
extern char *MALLOC();
#else
extern void *MALLOC(size_t);
#endif
#else
#define MALLOC malloc
#endif

#include <ctype.h>
#include <errno.h>

#ifdef Bad_float_h
#ifdef IEEE_BIG_ENDIAN
#define IEEE_ARITHMETIC
#endif
#ifdef IEEE_LITTLE_ENDIAN
#define IEEE_ARITHMETIC
#endif

#ifdef IEEE_ARITHMETIC
#define DBL_DIG 15
#define DBL_MAX_10_EXP 308
#define DBL_MAX_EXP 1024
#define FLT_RADIX 2
#define FLT_ROUNDS 1
#define DBL_MAX 1.7976931348623157e+308
#endif

#ifdef IBM
#define DBL_DIG 16
#define DBL_MAX_10_EXP 75
#define DBL_MAX_EXP 63
#define FLT_RADIX 16
#define FLT_ROUNDS 0
#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 FLT_ROUNDS 1
#define DBL_MAX 1.7014118346046923e+38
#endif


#ifndef LONG_MAX
#define LONG_MAX 2147483647
#endif
#else
#include <float.h>
#endif
#ifndef __MATH_H__
#include <math.h>
#endif

#ifndef CONST
#ifdef KR_headers
#define CONST /* blank */
#else
#define CONST const
#endif
#endif

#ifdef Unsigned_Shifts
#define Sign_Extend(a,b) if (b < 0) a |= 0xffff0000;
#else
#define Sign_Extend(a,b) /*no-op*/
#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 ul[2];
  } _double;
#define value(x) ((x).d)
#ifdef IEEE_LITTLE_ENDIAN
#define word0(x) ((x).ul[1])
#define word1(x) ((x).ul[0])
#else
#define word0(x) ((x).ul[0])
#define word1(x) ((x).ul[1])
#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) */

#if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN)
#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 IEEE_Arith
#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
#define Infinite(x) (word0(x) == 0x7ff00000) /* sufficient test for here */
#else
#undef  Sudden_Underflow
#define Sudden_Underflow
#ifdef IBM
#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 */
#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
#endif

#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)
#ifdef KR_headers
extern double rnd_prod(), rnd_quot();
#else
extern double rnd_prod(double, double), rnd_quot(double, double);
#endif
#else
#define rounded_product(a,b) a *= b
#define rounded_quotient(a,b) a /= b
#endif

#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
#define Big1 0xffffffff

#ifndef Just_16
/* 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.
 *     */
#ifndef Pack_32
#define Pack_32
#endif
#endif

#define Kmax 15

struct Bigint {
  struct Bigint *next;
  int k, maxwds, sign, wds;
  ULong x[1];
};

typedef struct Bigint Bigint;

void destroy_freelist(void);

class BigintData {
public:
  BigintData() : p5s(nullptr) {
    freelist = (Bigint **)calloc(Kmax + 1, sizeof(Bigint *));
  }
  ~BigintData() {
    destroy_freelist();
    free(freelist);
  }

  Bigint **freelist;
  Bigint *p5s;
};
static IMPLEMENT_THREAD_LOCAL_NO_CHECK(BigintData, s_bigint_data);

void zend_get_bigint_data() {
  s_bigint_data.getCheck();
}

static Bigint * Balloc(int k)
{
  int x;
  Bigint *rv;

  if (k > Kmax) {
    throw FatalErrorException("Balloc() allocation exceeds list boundary");
  }

  Bigint **&freelist = s_bigint_data->freelist;
  if ((rv = freelist[k])) {
    freelist[k] = rv->next;
  } else {
    x = 1 << k;
    rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(Long));
    if (!rv) {
      throw FatalErrorException("Balloc() failed to allocate memory");
    }
    rv->k = k;
    rv->maxwds = x;
  }
  rv->sign = rv->wds = 0;
  return rv;
}

static void Bfree(Bigint *v)
{
  if (v) {
    Bigint **&freelist = s_bigint_data->freelist;
    v->next = freelist[v->k];
    freelist[v->k] = v;
  }
}

#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
    y->wds*sizeof(Long) + 2*sizeof(int))

/* return value is only used as a simple string, so mis-aligned parts
 * inside the Bigint are not at risk on strict align architectures
 */
static char * rv_alloc(int i) {
  int j, k, *r;

  j = sizeof(ULong);
  for(k = 0;
      (int)(sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j) <= i;
      j <<= 1) {
    k++;
  }
  r = (int*)Balloc(k);
  *r = k;
  return (char *)(r+1);
}


static char * nrv_alloc(const char *s, char **rve, int n)
{
  char *rv, *t;

  t = rv = rv_alloc(n);
  while((*t = *s++) !=0) {
    t++;
  }
  if (rve) {
    *rve = t;
  }
  return rv;
}

static Bigint * multadd(Bigint *b, int m, int a) /* multiply by m and add a */
{
  int i, wds;
  ULong *x, y;
#ifdef Pack_32
  ULong xi, z;
#endif
  Bigint *b1;

  wds = b->wds;
  x = b->x;
  i = 0;
  do {
#ifdef Pack_32
    xi = *x;
    y = (xi & 0xffff) * m + a;
    z = (xi >> 16) * m + (y >> 16);
    a = (int)(z >> 16);
    *x++ = (z << 16) + (y & 0xffff);
#else
    y = *x * m + a;
    a = (int)(y >> 16);
    *x++ = y & 0xffff;
#endif
  }
  while(++i < wds);
  if (a) {
    if (wds >= b->maxwds) {
      b1 = Balloc(b->k+1);
      Bcopy(b1, b);
      Bfree(b);
      b = b1;
    }
    b->x[wds++] = a;
    b->wds = wds;
  }
  return b;
}

static int hi0bits(ULong x)
{
  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)
{
  int k;
  ULong x = *y;

  if (x & 7) {
    if (x & 1) {
      return 0;
    }
    if (x & 2) {
      *y = x >> 1;
      return 1;
    }
    *y = x >> 2;
    return 2;
  }
  k = 0;
  if (!(x & 0xffff)) {
    k = 16;
    x >>= 16;
  }
  if (!(x & 0xff)) {
    k += 8;
    x >>= 8;
  }
  if (!(x & 0xf)) {
    k += 4;
    x >>= 4;
  }
  if (!(x & 0x3)) {
    k += 2;
    x >>= 2;
  }
  if (!(x & 1)) {
    k++;
    x >>= 1;
    if (!(x & 1)) {
      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 carry, y, z;
  ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
#ifdef Pack_32
  ULong z2;
#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 Pack_32
  for(; xb < xbe; xb++, xc0++) {
    if ((y = *xb & 0xffff)) {
      x = xa;
      xc = xc0;
      carry = 0;
      do {
        z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
        carry = z >> 16;
        z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
        carry = z2 >> 16;
        Storeinc(xc, z2, z);
      }
      while(x < xae);
      *xc = carry;
    }
    if ((y = *xb >> 16)) {
      x = xa;
      xc = xc0;
      carry = 0;
      z2 = *xc;
      do {
        z = (*x & 0xffff) * y + (*xc >> 16) + carry;
        carry = z >> 16;
        Storeinc(xc, z, z2);
        z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
        carry = z2 >> 16;
      }
      while(x < xae);
      *xc = z2;
    }
  }
#else
  for(; xb < xbe; xc0++) {
    if (y = *xb++) {
      x = xa;
      xc = xc0;
      carry = 0;
      do {
        z = *x++ * y + *xc + carry;
        carry = z >> 16;
        *xc++ = z & 0xffff;
      }
      while(x < xae);
      *xc = carry;
    }
  }
#endif
  for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
  c->wds = wc;
  return c;
}

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 Bigint * pow5mult(Bigint *b, int k)
{
  Bigint *b1, *p5, *p51;
  int i;
  static int p05[3] = { 5, 25, 125 };

  Bigint *&p5s = s_bigint_data->p5s;
  if ((i = k & 3)) {
    b = multadd(b, p05[i-1], 0);
  }

  if (!(k >>= 2)) {
    return b;
  }
  if (!(p5 = p5s)) {
    /* first time */
    p5 = p5s = i2b(625);
    p5->next = 0;
  }
  for(;;) {
    if (k & 1) {
      b1 = mult(b, p5);
      Bfree(b);
      b = b1;
    }
    if (!(k >>= 1)) {
      break;
    }
    if (!(p51 = p5->next)) {
      if (!(p51 = p5->next)) {
        p51 = p5->next = mult(p5,p5);
        p51->next = 0;
      }
    }
    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)) {
      ++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;
  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;
  Long borrow, y; /* We need signed shifts here. */
  ULong *xa, *xae, *xb, *xbe, *xc;
#ifdef Pack_32
  Long z;
#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 Pack_32
  do {
    y = (*xa & 0xffff) - (*xb & 0xffff) + borrow;
    borrow = y >> 16;
    Sign_Extend(borrow, y);
    z = (*xa++ >> 16) - (*xb++ >> 16) + borrow;
    borrow = z >> 16;
    Sign_Extend(borrow, z);
    Storeinc(xc, z, y);
  } while(xb < xbe);
  while(xa < xae) {
    y = (*xa & 0xffff) + borrow;
    borrow = y >> 16;
    Sign_Extend(borrow, y);
    z = (*xa++ >> 16) + borrow;
    borrow = z >> 16;
    Sign_Extend(borrow, z);
    Storeinc(xc, z, y);
  }
#else
  do {
    y = *xa++ - *xb++ + borrow;
    borrow = y >> 16;
    Sign_Extend(borrow, y);
    *xc++ = y & 0xffff;
  } while(xb < xbe);
  while(xa < xae) {
    y = *xa++ + borrow;
    borrow = y >> 16;
    Sign_Extend(borrow, y);
    *xc++ = y & 0xffff;
  }
#endif
  while(!*--xc) {
    wa--;
  }
  c->wds = wa;
  return c;
}

static double ulp (double _x)
{
  _double x;
  register Long L;
  _double a;

  value(x) = _x;
  L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
#ifndef Sudden_Underflow
  if (L > 0) {
#endif
#ifdef IBM
    L |= Exp_msk1 >> 4;
#endif
    word0(a) = L;
    word1(a) = 0;
#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
  return value(a);
}

static double
b2d
#ifdef KR_headers
(a, e) Bigint *a; int *e;
#else
(Bigint *a, int *e)
#endif
{
  ULong *xa, *xa0, w, y, z;
  int k;
  _double 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;
  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 value(d);
}


static Bigint * d2b(double _d, int *e, int *bits)
{
  Bigint *b;
  int de, i, k;
  ULong *x, y, z;
  _double d;
#ifdef VAX
  ULong d0, d1;
#endif

  value(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)))
    z |= Exp_msk1;
#endif
#ifdef Pack_32
  if ((y = d1)) {
    if ((k = lo0bits(&y))) {
      x[0] = y | (z << (32 - k));
      z >>= k;
    } else {
      x[0] = y;
    }
    i = b->wds = (x[1] = z) ? 2 : 1;
  } else {
    k = lo0bits(&z);
    x[0] = z;
    i = 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 {
    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 da, db;
  int k, ka, kb;

  value(da) = b2d(a, &ka);
  value(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) {
      da *= 1 << k;
    }
  } else {
    k = -k;
    word0(db) += (k >> 2)*Exp_msk1;
    if (k &= 3)
      db *= 1 << k;
  }
#else
  if (k > 0) {
    word0(da) += k*Exp_msk1;
  } else {
    k = -k;
    word0(db) += k*Exp_msk1;
  }
#endif
  return value(da) / value(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
};

#ifdef IEEE_Arith
static CONST double bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, 1e-256 };
#define n_bigtens 5
#else
#ifdef IBM
static CONST double bigtens[] = { 1e16, 1e32, 1e64 };
static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 };
#define n_bigtens 3
#else
static CONST double bigtens[] = { 1e16, 1e32 };
static CONST double tinytens[] = { 1e-16, 1e-32 };
#define n_bigtens 2
#endif
#endif


static int quorem(Bigint *b, Bigint *S)
{
  int n;
  Long borrow, y;
  ULong carry, q, ys;
  ULong *bx, *bxe, *sx, *sxe;
#ifdef Pack_32
  Long z;
  ULong si, zs;
#endif

  n = S->wds;
  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 */
  if (q) {
    borrow = 0;
    carry = 0;
    do {
#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 >> 16;
      Sign_Extend(borrow, y);
      z = (*bx >> 16) - (zs & 0xffff) + borrow;
      borrow = z >> 16;
      Sign_Extend(borrow, z);
      Storeinc(bx, z, y);
#else
      ys = *sx++ * q + carry;
      carry = ys >> 16;
      y = *bx - (ys & 0xffff) + borrow;
      borrow = y >> 16;
      Sign_Extend(borrow, y);
      *bx++ = y & 0xffff;
#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 Pack_32
      si = *sx++;
      ys = (si & 0xffff) + carry;
      zs = (si >> 16) + (ys >> 16);
      carry = zs >> 16;
      y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
      borrow = y >> 16;
      Sign_Extend(borrow, y);
      z = (*bx >> 16) - (zs & 0xffff) + borrow;
      borrow = z >> 16;
      Sign_Extend(borrow, z);
      Storeinc(bx, z, y);
#else
      ys = *sx++ + carry;
      carry = ys >> 16;
      y = *bx - (ys & 0xffff) + borrow;
      borrow = y >> 16;
      Sign_Extend(borrow, y);
      *bx++ = y & 0xffff;
#endif
    }
    while(sx <= sxe);
    bx = b->x;
    bxe = bx + n;
    if (!*bxe) {
      while(--bxe > bx && !*bxe)
        --n;
      b->wds = n;
    }
  }
  return q;
}

void destroy_freelist(void)
{
  int i;
  Bigint *tmp;

  Bigint **&freelist = s_bigint_data->freelist;
  for (i = 0; i <= Kmax; i++) {
    Bigint **listp = &freelist[i];
    while ((tmp = *listp) != nullptr) {
      *listp = tmp->next;
      free(tmp);
    }
    freelist[i] = nullptr;
  }

}


void zend_freedtoa(char *s)
{
  Bigint *b = (Bigint *)((int *)s - 1);
  b->maxwds = 1 << (b->k = *(int*)b);
  Bfree(b);
}

/* 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. 92-101].
 *
 * 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 * zend_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.
        4-9 should give the same return values as 2-3, i.e.,
            4 <= mode <= 9 ==> same return as mode
            2 + (mode & 1).  These modes are mainly for
            debugging; often they run slower but sometimes
            faster than modes 2-3.
        4,5,8,9 ==> left-to-right digit generation.
        6-9 ==> 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 = 0, ilim0, ilim1 = 0,
    j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
    spec_case = 0, try_quick;
  Long L;
#ifndef Sudden_Underflow
  int denorm;
  ULong x;
#endif
  Bigint *b, *b1, *delta, *mlo = 0, *mhi, *S, *tmp;
  double ds;
  char *s, *s0;
  _double d, d2, eps;

  value(d) = _d;

  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 nrv_alloc("Infinity", rve, 8);
#endif
      return nrv_alloc("NaN", rve, 3);
    }
#endif
#ifdef IBM
  value(d) += 0; /* normalize */
#endif
  if (!value(d)) {
    *decpt = 1;
    return nrv_alloc("0", rve, 1);
  }

  b = d2b(value(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)))) {
#endif
    value(d2) = value(d);
    word0(d2) &= Frac_mask1;
    word0(d2) |= Exp_11;
#ifdef IBM
    if (j = 11 - hi0bits(word0(d2) & Frac_mask))
      value(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));
    value(d2) = x;
    word0(d2) -= 31*Exp_msk1; /* adjust exponent */
    i -= (Bias + (P-1) - 1) + 1;
    denorm = 1;
  }
#endif
  ds = (value(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 (value(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;
  try_quick = 1;
  if (mode > 5) {
    mode -= 4;
    try_quick = 0;
  }
  leftright = 1;
  switch(mode) {
    case 0:
    case 1:
      ilim = ilim1 = -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);

  if (ilim >= 0 && ilim <= Quick_max && try_quick) {

    /* Try to get by with floating-point arithmetic. */

    i = 0;
    value(d2) = value(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;
        value(d) /= bigtens[n_bigtens-1];
        ieps++;
      }
      for(; j; j >>= 1, i++)
        if (j & 1) {
          ieps++;
          ds *= bigtens[i];
        }
      value(d) /= ds;
    }
    else if ((j1 = -k)) {
      value(d) *= tens[j1 & 0xf];
      for(j = j1 >> 4; j; j >>= 1, i++)
        if (j & 1) {
          ieps++;
          value(d) *= bigtens[i];
        }
    }
    if (k_check && value(d) < 1. && ilim > 0) {
      if (ilim1 <= 0)
        goto fast_failed;
      ilim = ilim1;
      k--;
      value(d) *= 10.;
      ieps++;
    }
    value(eps) = ieps*value(d) + 7.;
    word0(eps) -= (P-1)*Exp_msk1;
    if (ilim == 0) {
      S = mhi = 0;
      value(d) -= 5.;
      if (value(d) > value(eps))
        goto one_digit;
      if (value(d) < -value(eps))
        goto no_digits;
      goto fast_failed;
    }
#ifndef No_leftright
    if (leftright) {
      /* Use Steele & White method of only
       * generating digits needed.
       */
      value(eps) = 0.5/tens[ilim-1] - value(eps);
      for(i = 0;;) {
        L = (int32_t)value(d);
        value(d) -= L;
        *s++ = '0' + (int)L;
        if (value(d) < value(eps))
          goto ret1;
        if (1. - value(d) < value(eps))
          goto bump_up;
        if (++i >= ilim)
          break;
        value(eps) *= 10.;
        value(d) *= 10.;
      }
    }
    else {
#endif
      /* Generate ilim digits, then fix them up. */
      value(eps) *= tens[ilim-1];
      for(i = 1;; i++, value(d) *= 10.) {
        L = (int32_t)value(d);
        value(d) -= L;
        *s++ = '0' + (int)L;
        if (i == ilim) {
          if (value(d) > 0.5 + value(eps))
            goto bump_up;
          else if (value(d) < 0.5 - value(eps)) {
            /* cut ALL traling zeros only if the number of chars is greater than precision
             * otherwise cut only extra zeros
             */
            if (k < ndigits) {
              while(*--s == '0' && (s - s0) > k);
            } else {
              while(*--s == '0');
            }
            s++;
            goto ret1;
          }
          break;
        }
      }
#ifndef No_leftright
    }
#endif
fast_failed:
    s = s0;
    value(d) = value(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 || value(d) <= 5*ds)
        goto no_digits;
      goto one_digit;
    }
    for(i = 1;; i++) {
      L = (int32_t)(value(d) / ds);
      value(d) -= L*ds;
#ifdef Check_FLT_ROUNDS
      /* If FLT_ROUNDS == 2, L will usually be high by 1 */
      if (value(d) < 0) {
        L--;
        value(d) += ds;
      }
#endif
      *s++ = '0' + (int)L;
      if (i == ilim) {
        value(d) += value(d);
        if (value(d) > ds || (value(d) == ds && (L & 1))) {
bump_up:
          while(*--s == '9')
            if (s == s0) {
              k++;
              *s = '0';
              break;
            }
          ++*s++;
        }
        break;
      }
      if (!(value(d) *= 10.))
        break;
    }
    goto ret1;
  }

  m2 = b2;
  m5 = b5;
  mhi = mlo = 0;
  if (leftright) {
    if (mode < 2) {
      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
    }
    else {
      j = ilim - 1;
      if (m5 >= j)
        m5 -= j;
      else {
        s5 += j -= m5;
        b5 += j;
        m5 = 0;
      }
      if ((i = ilim) < 0) {
        m2 -= i;
        i = 0;
      }
    }
    b2 += i;
    s2 += i;
    mhi = i2b(1);
  }
  if (m2 > 0 && s2 > 0) {
    i = m2 < s2 ? m2 : s2;
    b2 -= i;
    m2 -= i;
    s2 -= i;
  }
  if (b5 > 0) {
    if (leftright) {
      if (m5 > 0) {
        mhi = pow5mult(mhi, m5);
        b1 = mult(mhi, b);
        Bfree(b);
        b = b1;
      }
      if ((j = b5 - m5)) {
        b = pow5mult(b, j);
      }
    } else {
      b = pow5mult(b, b5);
    }
  }
  S = i2b(1);
  if (s5 > 0)
    S = pow5mult(S, s5);
  /* Check for special case that d is a normalized power of 2. */

  if (mode < 2) {
    if (!word1(d) && !(word0(d) & Bndry_mask)
#ifndef Sudden_Underflow
        && word0(d) & Exp_mask
#endif
       ) {
      /* The special case */
      b2 += Log2P;
      s2 += Log2P;
      spec_case = 1;
    } else {
      spec_case = 0;
    }
  }

  /* 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))
    i = 32 - i;
#else
  if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf))
    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 > 2) {
    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 && !(word1(d) & 1)) {
        if (dig == '9')
          goto round_9_up;
        if (j > 0)
          dig++;
        *s++ = dig;
        goto ret;
      }
#endif
      if (j < 0 || (j == 0 && !mode
#ifndef ROUND_BIASED
            && !(word1(d) & 1)
#endif
            )) {
        if (j1 > 0) {
          b = lshift(b, 1);
          j1 = cmp(b, S);
          if ((j1 > 0 || (j1 == 0 && (dig & 1)))
              && dig++ == '9')
            goto round_9_up;
        }
        *s++ = dig;
        goto ret;
      }
      if (j1 > 0) {
        if (dig == '9') { /* possible if i == 1 */
round_9_up:
          *s++ = '9';
          goto roundoff;
        }
        *s++ = dig + 1;
        goto ret;
      }
      *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 (i >= ilim)
        break;
      b = multadd(b, 10, 0);
    }

  /* Round off last digit */

  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;
      }
    ++*s++;
  }
  else {
    while(*--s == '0');
    s++;
  }
ret:
  Bfree(S);
  if (mhi) {
    if (mlo && mlo != mhi)
      Bfree(mlo);
    Bfree(mhi);
  }
ret1:

  {
    Bigint *&p5s = s_bigint_data->p5s;
    while (p5s) {
      tmp = p5s;
      p5s = p5s->next;
      free(tmp);
    }
  }

  Bfree(b);

  if (s == s0) {              /* don't return empty string */
    *s++ = '0';
    k = 0;
  }
  *s = 0;
  *decpt = k + 1;
  if (rve)
    *rve = s;
  return s0;
}

double zend_strtod (CONST char *s00, char **se)
{
  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, aadj1, adj;
  _double rv, rv0;
  Long L;
  ULong y, z;
  Bigint *bb = 0, *bb1, *bd = 0, *bd0, *bs = 0, *delta = 0, *tmp;
  double result;

  CONST char decimal_point = '.';

  sign = nz0 = nz = 0;
  value(rv) = 0.;


  for(s = s00; isspace((unsigned char) *s); s++)
    ;

  if (*s == '-') {
    sign = 1;
    s++;
  } else if (*s == '+') {
    s++;
  }

  if (*s == '\0') {
    s = s00;
    goto ret;
  }

  if (*s == '0') {
    nz0 = 1;
    while(*++s == '0') ;
    if (!*s)
      goto ret;
  }
  s0 = s;
  y = z = 0;
  for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
    if (nd < 9)
      y = 10*y + c - '0';
    else if (nd < 16)
      z = 10*z + c - '0';
  nd0 = nd;
  if (c == decimal_point) {
    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 (c -= '0') {
        nf += nz;
        for(i = 1; i < nz; i++)
          if (nd++ < 9)
            y *= 10;
          else if (nd <= DBL_DIG + 1)
            z *= 10;
        if (nd++ < 9)
          y = 10*y + c;
        else if (nd <= DBL_DIG + 1)
          z = 10*z + c;
        nz = 0;
      }
    }
  }
dig_done:
  e = 0;
  if (c == 'e' || c == 'E') {
    if (!nd && !nz && !nz0) {
      s = s00;
      goto ret;
    }
    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)
      s = s00;
    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 + 1 ? nd : DBL_DIG + 1;
  value(rv) = y;
  if (k > 9)
    value(rv) = tens[k - 9] * value(rv) + z;
  bd0 = 0;
  if (nd <= DBL_DIG
#ifndef RND_PRODQUOT
      && FLT_ROUNDS == 1
#endif
     ) {
    if (!e)
      goto ret;
    if (e > 0) {
      if (e <= Ten_pmax) {
#ifdef VAX
        goto vax_ovfl_check;
#else
        /* value(rv) = */ rounded_product(value(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.
         */
        e -= i;
        value(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;
        /* value(rv) = */ rounded_product(value(rv),
            tens[e]);
        if ((word0(rv) & Exp_mask)
            > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
          goto ovfl;
        word0(rv) += P*Exp_msk1;
#else
        /* value(rv) = */ rounded_product(value(rv),
            tens[e]);
#endif
        goto ret;
      }
    }
#ifndef Inaccurate_Divide
    else if (e >= -Ten_pmax) {
      /* value(rv) = */ rounded_quotient(value(rv),
          tens[-e]);
      goto ret;
    }
#endif
  }
  e1 += nd - k;

  /* Get starting approximation = rv * 10**e1 */

  if (e1 > 0) {
    if ((i = e1 & 15))
      value(rv) *= tens[i];
    if (e1 &= ~15) {
      if (e1 > DBL_MAX_10_EXP) {
ovfl:
        errno = ERANGE;
#ifndef Bad_float_h
        value(rv) = HUGE_VAL;
#else
        /* Can't trust HUGE_VAL */
#ifdef IEEE_Arith
        word0(rv) = Exp_mask;
        word1(rv) = 0;
#else
        word0(rv) = Big0;
        word1(rv) = Big1;
#endif
#endif
        if (bd0)
          goto retfree;
        goto ret;
      }
      if (e1 >>= 4) {
        for(j = 0; e1 > 1; j++, e1 >>= 1)
          if (e1 & 1)
            value(rv) *= bigtens[j];
        /* The last multiplication could overflow. */
        word0(rv) -= P*Exp_msk1;
        value(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))
      value(rv) /= tens[i];
    if (e1 &= ~15) {
      e1 >>= 4;
      if (e1 >= 1 << n_bigtens)
        goto undfl;
      for(j = 0; e1 > 1; j++, e1 >>= 1)
        if (e1 & 1)
          value(rv) *= tinytens[j];
      /* The last multiplication could underflow. */
      value(rv0) = value(rv);
      value(rv) *= tinytens[j];
      if (!value(rv)) {
        value(rv) = 2.*value(rv0);
        value(rv) *= tinytens[j];
        if (!value(rv)) {
undfl:
          value(rv) = 0.;
          errno = ERANGE;
          if (bd0)
            goto retfree;
          goto ret;
        }
        word0(rv) = Tiny0;
        word1(rv) = Tiny1;
        /* The refinement below will clean
         * this approximation up.
         */
      }
    }
  }

  /* 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(value(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 Sudden_Underflow
#ifdef IBM
    j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
#else
    j = P + 1 - bbbits;
#endif
#else
    i = bbe + bbbits - 1;  /* logb(rv) */
    if (i < Emin)  /* denormal */
      j = bbe + (P-Emin);
    else
      j = P + 1 - bbbits;
#endif
    bb2 += j;
    bd2 += j;
    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);
    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)
        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) == 0xffffffff) {
          /*boundary case -- increment exponent*/
          word0(rv) = (word0(rv) & Exp_mask)
            + Exp_msk1
#ifdef IBM
            | Exp_msk1 >> 4
#endif
            ;
          word1(rv) = 0;
          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
          if (L <= Exp_msk1)
#endif
            goto undfl;
        L -= Exp_msk1;
#else
        L = (word0(rv) & Exp_mask) - Exp_msk1;
#endif
        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)
        value(rv) += ulp(value(rv));
#ifndef ROUND_BIASED
      else {
        value(rv) -= ulp(value(rv));
#ifndef Sudden_Underflow
        if (!value(rv))
          goto undfl;
#endif
      }
#endif
      break;
    }
    if ((aadj = ratio(delta, bs)) <= 2.) {
      if (dsign)
        aadj = aadj1 = 1.;
      else if (word1(rv) || word0(rv) & Bndry_mask) {
#ifndef Sudden_Underflow
        if (word1(rv) == Tiny1 && !word0(rv))
          goto undfl;
#endif
        aadj = 1.;
        aadj1 = -1.;
      }
      else {
        /* special case -- power of FLT_RADIX to be */
        /* rounded down... */

        if (aadj < 2./FLT_RADIX)
          aadj = 1./FLT_RADIX;
        else
          aadj *= 0.5;
        aadj1 = -aadj;
      }
    }
    else {
      aadj *= 0.5;
      aadj1 = dsign ? aadj : -aadj;
#ifdef Check_FLT_ROUNDS
      switch(FLT_ROUNDS) {
        case 2: /* towards +infinity */
          aadj1 -= 0.5;
          break;
        case 0: /* towards 0 */
        case 3: /* towards -infinity */
          aadj1 += 0.5;
      }
#else
      if (FLT_ROUNDS == 0)
        aadj1 += 0.5;
#endif
    }
    y = word0(rv) & Exp_mask;

    /* Check for overflow */

    if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
      value(rv0) = value(rv);
      word0(rv) -= P*Exp_msk1;
      adj = aadj1 * ulp(value(rv));
      value(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 Sudden_Underflow
      if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
        value(rv0) = value(rv);
        word0(rv) += P*Exp_msk1;
        adj = aadj1 * ulp(value(rv));
        value(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 = aadj1 * ulp(value(rv));
        value(rv) += adj;
      }
#else
      /* Compute adj so that the IEEE rounding rules will
       * correctly round rv + adj in some half-way cases.
       * If rv * ulp(rv) is denormalized (i.e.,
       * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
       * trouble from bits lost to denormalization;
       * example: 1.2e-307 .
       */
      if (y <= (P-1)*Exp_msk1 && aadj >= 1.) {
        aadj1 = (double)(int)(aadj + 0.5);
        if (!dsign)
          aadj1 = -aadj1;
      }
      adj = aadj1 * ulp(value(rv));
      value(rv) += adj;
#endif
    }
    z = word0(rv) & Exp_mask;
    if (y == z) {
      /* Can we stop now? */
      L = (int32_t)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;
    }
cont:
    Bfree(bb);
    Bfree(bd);
    Bfree(bs);
    Bfree(delta);
  }
retfree:
  Bfree(bb);
  Bfree(bd);
  Bfree(bs);
  Bfree(bd0);
  Bfree(delta);
ret:
  if (se)
    *se = (char *)s;
  result = sign ? -value(rv) : value(rv);

  Bigint *&p5s = s_bigint_data->p5s;
  while (p5s) {
    tmp = p5s;
    p5s = p5s->next;
    free(tmp);
  }

  return result;
}

double zend_hex_strtod(const char *str, char **endptr)
{
  const char *s = str;
  char c;
  int any = 0;
  double value = 0;

  if (*s == '0' && (s[1] == 'x' || s[1] == 'X')) {
    s += 2;
  }

  while ((c = *s++)) {
    if (c >= '0' && c <= '9') {
      c -= '0';
    } else if (c >= 'A' && c <= 'F') {
      c -= 'A' - 10;
    } else if (c >= 'a' && c <= 'f') {
      c -= 'a' - 10;
    } else {
      break;
    }

    any = 1;
    value = value * 16 + c;
  }

  if (endptr != nullptr) {
    *endptr = (char *)(any ? s - 1 : str);
  }

  return value;
}

double zend_oct_strtod(const char *str, char **endptr)
{
  const char *s = str;
  char c;
  double value = 0;
  int any = 0;

  /* skip leading zero */
  s++;

  while ((c = *s++)) {
    if (c > '7') {
      /* break and return the current value if the number is not well-formed
       * that's what Linux strtol() does
       */
      break;
    }
    value = value * 8 + c - '0';
    any = 1;
  }

  if (endptr != nullptr) {
    *endptr = (char *)(any ? s - 1 : str);
  }

  return value;
}

///////////////////////////////////////////////////////////////////////////////
}