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newlib-cygwin/newlib/libc/stdlib/mprec.c

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/****************************************************************
*
* 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_8087 for IEEE-arithmetic machines where the least
* significant byte has the lowest address.
* #define IEEE_MC68k for IEEE-arithmetic machines where the most
* significant byte has the lowest address.
* #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.
*/
#include <_ansi.h>
#include <stdlib.h>
#include <string.h>
#include <reent.h>
#include "mprec.h"
#ifdef _REENT_THREAD_LOCAL
_Thread_local struct _Bigint *_tls_mp_p5s;
_Thread_local struct _Bigint **_tls_mp_freelist;
#endif
/* This is defined in sys/reent.h as (sizeof (size_t) << 3) now, as in NetBSD.
The old value of 15 was wrong and made newlib vulnerable against buffer
overrun attacks (CVE-2009-0689), same as other implementations of gdtoa
based on BSD code.
#define _Kmax 15
*/
_Bigint *
Balloc (struct _reent *ptr, int k)
{
int x;
_Bigint *rv ;
_REENT_CHECK_MP(ptr);
if (_REENT_MP_FREELIST(ptr) == NULL)
{
/* Allocate a list of pointers to the mprec objects */
_REENT_MP_FREELIST(ptr) = (struct _Bigint **) _calloc_r (ptr,
sizeof (struct _Bigint *),
_Kmax + 1);
if (_REENT_MP_FREELIST(ptr) == NULL)
{
return NULL;
}
}
if ((rv = _REENT_MP_FREELIST(ptr)[k]) != 0)
{
_REENT_MP_FREELIST(ptr)[k] = rv->_next;
}
else
{
x = 1 << k;
/* Allocate an mprec Bigint and stick in in the freelist */
rv = (_Bigint *) _calloc_r (ptr,
1,
sizeof (_Bigint) +
(x-1) * sizeof(rv->_x));
if (rv == NULL) return NULL;
rv->_k = k;
rv->_maxwds = x;
}
rv->_sign = rv->_wds = 0;
return rv;
}
void
Bfree (struct _reent *ptr, _Bigint * v)
{
_REENT_CHECK_MP(ptr);
if (v)
{
v->_next = _REENT_MP_FREELIST(ptr)[v->_k];
_REENT_MP_FREELIST(ptr)[v->_k] = v;
}
}
_Bigint *
multadd (struct _reent *ptr,
_Bigint * b,
int m,
int 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 = eBalloc (ptr, b->_k + 1);
Bcopy (b1, b);
Bfree (ptr, b);
b = b1;
}
b->_x[wds++] = a;
b->_wds = wds;
}
return b;
}
_Bigint *
s2b (struct _reent * ptr,
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 = eBalloc (ptr, k);
b->_x[0] = y9;
b->_wds = 1;
#else
b = eBalloc (ptr, 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 (ptr, b, 10, *s++ - '0');
while (++i < nd0);
s++;
}
else
s += 10;
for (; i < nd; i++)
b = multadd (ptr, b, 10, *s++ - '0');
return b;
}
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;
}
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 & 1)
return 32;
}
*y = x;
return k;
}
_Bigint *
i2b (struct _reent * ptr, int i)
{
_Bigint *b;
b = eBalloc (ptr, 1);
b->_x[0] = i;
b->_wds = 1;
return b;
}
_Bigint *
mult (struct _reent * ptr, _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 = eBalloc (ptr, 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) != 0)
{
x = xa;
xc = xc0;
carry = 0;
do
{
z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
carry = z >> 16;
z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
carry = z2 >> 16;
Storeinc (xc, z2, z);
}
while (x < xae);
*xc = carry;
}
if ((y = *xb >> 16) != 0)
{
x = xa;
xc = xc0;
carry = 0;
z2 = *xc;
do
{
z = (*x & 0xffff) * y + (*xc >> 16) + carry;
carry = z >> 16;
Storeinc (xc, z, z2);
z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
carry = z2 >> 16;
}
while (x < xae);
*xc = z2;
}
}
#else
for (; xb < xbe; xc0++)
{
if (y = *xb++)
{
x = xa;
xc = xc0;
carry = 0;
do
{
z = *x++ * y + *xc + carry;
carry = z >> 16;
*xc++ = z & 0xffff;
}
while (x < xae);
*xc = carry;
}
}
#endif
for (xc0 = c->_x, xc = xc0 + wc; wc > 0 && !*--xc; --wc);
c->_wds = wc;
return c;
}
_Bigint *
pow5mult (struct _reent * ptr, _Bigint * b, int k)
{
_Bigint *b1, *p5, *p51;
int i;
static const int p05[3] = {5, 25, 125};
if ((i = k & 3) != 0)
b = multadd (ptr, b, p05[i - 1], 0);
if (!(k >>= 2))
return b;
_REENT_CHECK_MP(ptr);
if (!(p5 = _REENT_MP_P5S(ptr)))
{
/* first time */
p5 = _REENT_MP_P5S(ptr) = i2b (ptr, 625);
p5->_next = 0;
}
for (;;)
{
if (k & 1)
{
b1 = mult (ptr, b, p5);
Bfree (ptr, b);
b = b1;
}
if (!(k >>= 1))
break;
if (!(p51 = p5->_next))
{
p51 = p5->_next = mult (ptr, p5, p5);
p51->_next = 0;
}
p5 = p51;
}
return b;
}
_Bigint *
lshift (struct _reent * ptr, _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 = eBalloc (ptr, 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 (ptr, b);
return b1;
}
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;
}
_Bigint *
diff (struct _reent * ptr,
_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 = eBalloc (ptr, 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 = eBalloc (ptr, 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;
}
double
ulp (double _x)
{
union double_union x, a;
register __Long L;
x.d = _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;
#ifndef _DOUBLE_IS_32BITS
word1 (a) = 0;
#endif
#ifndef Sudden_Underflow
}
else
{
L = -L >> Exp_shift;
if (L < Exp_shift)
{
word0 (a) = 0x80000 >> L;
#ifndef _DOUBLE_IS_32BITS
word1 (a) = 0;
#endif
}
else
{
word0 (a) = 0;
L -= Exp_shift;
#ifndef _DOUBLE_IS_32BITS
word1 (a) = L >= 31 ? 1 : 1 << (31 - L);
#endif
}
}
#endif
return a.d;
}
double
b2d (_Bigint * a, int *e)
{
__ULong *xa, *xa0, w, y, z;
int k;
union double_union 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;
#ifndef _DOUBLE_IS_32BITS
d1 = y << ((32 - Ebits) + k) | w >> (Ebits - k);
#endif
goto ret_d;
}
z = xa > xa0 ? *--xa : 0;
if (k -= Ebits)
{
d0 = Exp_1 | y << k | z >> (32 - k);
y = xa > xa0 ? *--xa : 0;
#ifndef _DOUBLE_IS_32BITS
d1 = z << k | y >> (32 - k);
#endif
}
else
{
d0 = Exp_1 | y;
#ifndef _DOUBLE_IS_32BITS
d1 = z;
#endif
}
#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 d.d;
}
_Bigint *
d2b (struct _reent * ptr,
double _d,
int *e,
int *bits)
{
union double_union d;
_Bigint *b;
int de, i, k;
__ULong *x, y, z;
#ifdef VAX
__ULong d0, d1;
#endif
d.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)
d.d = _d;
#endif
#ifdef Pack_32
b = eBalloc (ptr, 1);
#else
b = eBalloc (ptr, 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
#ifndef _DOUBLE_IS_32BITS
if (d1)
{
y = d1;
k = lo0bits (&y);
if (k)
{
x[0] = y | z << (32 - k);
z >>= k;
}
else
x[0] = y;
i = b->_wds = (x[1] = z) ? 2 : 1;
}
else
#endif
{
#ifdef DEBUG
if (!z)
Bug ("Zero passed to d2b");
#endif
k = lo0bits (&z);
x[0] = z;
i = b->_wds = 1;
#ifndef _DOUBLE_IS_32BITS
k += 32;
#endif
}
#else
if (d1)
{
y = d1;
k = lo0bits (&y);
if (k)
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
double
ratio (_Bigint * a, _Bigint * b)
{
union double_union da, db;
int k, ka, kb;
da.d = b2d (a, &ka);
db.d = 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.d *= 1 << k;
}
else
{
k = -k;
word0 (db) += (k >> 2) * Exp_msk1;
if (k &= 3)
db.d *= 1 << k;
}
#else
if (k > 0)
word0 (da) += k * Exp_msk1;
else
{
k = -k;
word0 (db) += k * Exp_msk1;
}
#endif
return da.d / db.d;
}
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, 1e23, 1e24
};
#if !defined(_DOUBLE_IS_32BITS) && !defined(__v800)
const double bigtens[] =
{1e16, 1e32, 1e64, 1e128, 1e256};
const double tinytens[] =
{1e-16, 1e-32, 1e-64, 1e-128, 1e-256};
#else
const double bigtens[] =
{1e16, 1e32};
const double tinytens[] =
{1e-16, 1e-32};
#endif
double
_mprec_log10 (int dig)
{
double v = 1.0;
if (dig < 24)
return tens[dig];
while (dig > 0)
{
v *= 10;
dig--;
}
return v;
}
void
copybits (__ULong *c,
int n,
_Bigint *b)
{
__ULong *ce, *x, *xe;
#ifdef Pack_16
int nw, nw1;
#endif
ce = c + ((n-1) >> kshift) + 1;
x = b->_x;
#ifdef Pack_32
xe = x + b->_wds;
while(x < xe)
*c++ = *x++;
#else
nw = b->_wds;
nw1 = nw & 1;
for(xe = x + (nw - nw1); x < xe; x += 2)
Storeinc(c, x[1], x[0]);
if (nw1)
*c++ = *x;
#endif
while(c < ce)
*c++ = 0;
}
__ULong
any_on (_Bigint *b,
int k)
{
int n, nwds;
__ULong *x, *x0, x1, x2;
x = b->_x;
nwds = b->_wds;
n = k >> kshift;
if (n > nwds)
n = nwds;
else if (n < nwds && (k &= kmask)) {
x1 = x2 = x[n];
x1 >>= k;
x1 <<= k;
if (x1 != x2)
return 1;
}
x0 = x;
x += n;
while(x > x0)
if (*--x)
return 1;
return 0;
}
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