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vasnprintf.c
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/* vsprintf with automatic memory allocation.
Copyright (C) 1999, 2002-2010 Free Software Foundation, Inc.
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 3, or (at your option)
any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License along
with this program; if not, write to the Free Software Foundation,
Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. */
/* This file can be parametrized with the following macros:
VASNPRINTF The name of the function being defined.
FCHAR_T The element type of the format string.
DCHAR_T The element type of the destination (result) string.
FCHAR_T_ONLY_ASCII Set to 1 to enable verification that all characters
in the format string are ASCII. MUST be set if
FCHAR_T and DCHAR_T are not the same type.
DIRECTIVE Structure denoting a format directive.
Depends on FCHAR_T.
DIRECTIVES Structure denoting the set of format directives of a
format string. Depends on FCHAR_T.
PRINTF_PARSE Function that parses a format string.
Depends on FCHAR_T.
DCHAR_CPY memcpy like function for DCHAR_T[] arrays.
DCHAR_SET memset like function for DCHAR_T[] arrays.
DCHAR_MBSNLEN mbsnlen like function for DCHAR_T[] arrays.
SNPRINTF The system's snprintf (or similar) function.
This may be either snprintf or swprintf.
TCHAR_T The element type of the argument and result string
of the said SNPRINTF function. This may be either
char or wchar_t. The code exploits that
sizeof (TCHAR_T) | sizeof (DCHAR_T) and
alignof (TCHAR_T) <= alignof (DCHAR_T).
DCHAR_IS_TCHAR Set to 1 if DCHAR_T and TCHAR_T are the same type.
DCHAR_CONV_FROM_ENCODING A function to convert from char[] to DCHAR[].
DCHAR_IS_UINT8_T Set to 1 if DCHAR_T is uint8_t.
DCHAR_IS_UINT16_T Set to 1 if DCHAR_T is uint16_t.
DCHAR_IS_UINT32_T Set to 1 if DCHAR_T is uint32_t. */
/* Tell glibc's <stdio.h> to provide a prototype for snprintf().
This must come before <config.h> because <config.h> may include
<features.h>, and once <features.h> has been included, it's too late. */
#ifndef _GNU_SOURCE
# define _GNU_SOURCE 1
#endif
#ifndef VASNPRINTF
# include <config.h>
#endif
#ifndef IN_LIBINTL
# include <alloca.h>
#endif
/* Specification. */
#ifndef VASNPRINTF
# if WIDE_CHAR_VERSION
# include "vasnwprintf.h"
# else
# include "vasnprintf.h"
# endif
#endif
#include <locale.h> /* localeconv() */
#include <stdio.h> /* snprintf(), sprintf() */
#include <stdlib.h> /* abort(), malloc(), realloc(), free() */
#include <string.h> /* memcpy(), strlen() */
#include <errno.h> /* errno */
#include <limits.h> /* CHAR_BIT */
#include <float.h> /* DBL_MAX_EXP, LDBL_MAX_EXP */
#if HAVE_NL_LANGINFO
# include <langinfo.h>
#endif
#ifndef VASNPRINTF
# if WIDE_CHAR_VERSION
# include "wprintf-parse.h"
# else
# include "printf-parse.h"
# endif
#endif
/* Checked size_t computations. */
#include "xsize.h"
#if (NEED_PRINTF_DOUBLE || NEED_PRINTF_LONG_DOUBLE) && !defined IN_LIBINTL
# include <math.h>
# include "float+.h"
#endif
#if (NEED_PRINTF_DOUBLE || NEED_PRINTF_INFINITE_DOUBLE) && !defined IN_LIBINTL
# include <math.h>
# include "isnand-nolibm.h"
#endif
#if (NEED_PRINTF_LONG_DOUBLE || NEED_PRINTF_INFINITE_LONG_DOUBLE) && !defined IN_LIBINTL
# include <math.h>
# include "isnanl-nolibm.h"
# include "fpucw.h"
#endif
#if (NEED_PRINTF_DIRECTIVE_A || NEED_PRINTF_DOUBLE) && !defined IN_LIBINTL
# include <math.h>
# include "isnand-nolibm.h"
# include "printf-frexp.h"
#endif
#if (NEED_PRINTF_DIRECTIVE_A || NEED_PRINTF_LONG_DOUBLE) && !defined IN_LIBINTL
# include <math.h>
# include "isnanl-nolibm.h"
# include "printf-frexpl.h"
# include "fpucw.h"
#endif
/* Default parameters. */
#ifndef VASNPRINTF
# if WIDE_CHAR_VERSION
# define VASNPRINTF vasnwprintf
# define FCHAR_T wchar_t
# define DCHAR_T wchar_t
# define TCHAR_T wchar_t
# define DCHAR_IS_TCHAR 1
# define DIRECTIVE wchar_t_directive
# define DIRECTIVES wchar_t_directives
# define PRINTF_PARSE wprintf_parse
# define DCHAR_CPY wmemcpy
# define DCHAR_SET wmemset
# else
# define VASNPRINTF vasnprintf
# define FCHAR_T char
# define DCHAR_T char
# define TCHAR_T char
# define DCHAR_IS_TCHAR 1
# define DIRECTIVE char_directive
# define DIRECTIVES char_directives
# define PRINTF_PARSE printf_parse
# define DCHAR_CPY memcpy
# define DCHAR_SET memset
# endif
#endif
#if WIDE_CHAR_VERSION
/* TCHAR_T is wchar_t. */
# define USE_SNPRINTF 1
# if HAVE_DECL__SNWPRINTF
/* On Windows, the function swprintf() has a different signature than
on Unix; we use the function _snwprintf() or - on mingw - snwprintf()
instead. The mingw function snwprintf() has fewer bugs than the
MSVCRT function _snwprintf(), so prefer that. */
# if defined __MINGW32__
# define SNPRINTF snwprintf
# else
# define SNPRINTF _snwprintf
# endif
# else
/* Unix. */
# define SNPRINTF swprintf
# endif
#else
/* TCHAR_T is char. */
/* Use snprintf if it exists under the name 'snprintf' or '_snprintf'.
But don't use it on BeOS, since BeOS snprintf produces no output if the
size argument is >= 0x3000000.
Also don't use it on Linux libc5, since there snprintf with size = 1
writes any output without bounds, like sprintf. */
# if (HAVE_DECL__SNPRINTF || HAVE_SNPRINTF) && !defined __BEOS__ && !(__GNU_LIBRARY__ == 1)
# define USE_SNPRINTF 1
# else
# define USE_SNPRINTF 0
# endif
# if HAVE_DECL__SNPRINTF
/* Windows. The mingw function snprintf() has fewer bugs than the MSVCRT
function _snprintf(), so prefer that. */
# if defined __MINGW32__
# define SNPRINTF snprintf
/* Here we need to call the native snprintf, not rpl_snprintf. */
# undef snprintf
# else
# define SNPRINTF _snprintf
# endif
# else
/* Unix. */
# define SNPRINTF snprintf
/* Here we need to call the native snprintf, not rpl_snprintf. */
# undef snprintf
# endif
#endif
/* Here we need to call the native sprintf, not rpl_sprintf. */
#undef sprintf
/* GCC >= 4.0 with -Wall emits unjustified "... may be used uninitialized"
warnings in this file. Use -Dlint to suppress them. */
#ifdef lint
# define IF_LINT(Code) Code
#else
# define IF_LINT(Code) /* empty */
#endif
/* Avoid some warnings from "gcc -Wshadow".
This file doesn't use the exp() and remainder() functions. */
#undef exp
#define exp expo
#undef remainder
#define remainder rem
#if (!USE_SNPRINTF || !HAVE_SNPRINTF_RETVAL_C99) && !WIDE_CHAR_VERSION
# if (HAVE_STRNLEN && !defined _AIX)
# define local_strnlen strnlen
# else
# ifndef local_strnlen_defined
# define local_strnlen_defined 1
static size_t
local_strnlen (const char *string, size_t maxlen)
{
const char *end = memchr (string, '\0', maxlen);
return end ? (size_t) (end - string) : maxlen;
}
# endif
# endif
#endif
#if (((!USE_SNPRINTF || !HAVE_SNPRINTF_RETVAL_C99) && WIDE_CHAR_VERSION) || ((!USE_SNPRINTF || !HAVE_SNPRINTF_RETVAL_C99 || (NEED_PRINTF_DIRECTIVE_LS && !defined IN_LIBINTL)) && !WIDE_CHAR_VERSION && DCHAR_IS_TCHAR)) && HAVE_WCHAR_T
# if HAVE_WCSLEN
# define local_wcslen wcslen
# else
/* Solaris 2.5.1 has wcslen() in a separate library libw.so. To avoid
a dependency towards this library, here is a local substitute.
Define this substitute only once, even if this file is included
twice in the same compilation unit. */
# ifndef local_wcslen_defined
# define local_wcslen_defined 1
static size_t
local_wcslen (const wchar_t *s)
{
const wchar_t *ptr;
for (ptr = s; *ptr != (wchar_t) 0; ptr++)
;
return ptr - s;
}
# endif
# endif
#endif
#if (!USE_SNPRINTF || !HAVE_SNPRINTF_RETVAL_C99) && HAVE_WCHAR_T && WIDE_CHAR_VERSION
# if HAVE_WCSNLEN
# define local_wcsnlen wcsnlen
# else
# ifndef local_wcsnlen_defined
# define local_wcsnlen_defined 1
static size_t
local_wcsnlen (const wchar_t *s, size_t maxlen)
{
const wchar_t *ptr;
for (ptr = s; maxlen > 0 && *ptr != (wchar_t) 0; ptr++, maxlen--)
;
return ptr - s;
}
# endif
# endif
#endif
#if (NEED_PRINTF_DIRECTIVE_A || NEED_PRINTF_LONG_DOUBLE || NEED_PRINTF_INFINITE_LONG_DOUBLE || NEED_PRINTF_DOUBLE || NEED_PRINTF_INFINITE_DOUBLE) && !defined IN_LIBINTL
/* Determine the decimal-point character according to the current locale. */
# ifndef decimal_point_char_defined
# define decimal_point_char_defined 1
static char
decimal_point_char (void)
{
const char *point;
/* Determine it in a multithread-safe way. We know nl_langinfo is
multithread-safe on glibc systems and MacOS X systems, but is not required
to be multithread-safe by POSIX. sprintf(), however, is multithread-safe.
localeconv() is rarely multithread-safe. */
# if HAVE_NL_LANGINFO && (__GLIBC__ || (defined __APPLE__ && defined __MACH__))
point = nl_langinfo (RADIXCHAR);
# elif 1
char pointbuf[5];
sprintf (pointbuf, "%#.0f", 1.0);
point = &pointbuf[1];
# else
point = localeconv () -> decimal_point;
# endif
/* The decimal point is always a single byte: either '.' or ','. */
return (point[0] != '\0' ? point[0] : '.');
}
# endif
#endif
#if NEED_PRINTF_INFINITE_DOUBLE && !NEED_PRINTF_DOUBLE && !defined IN_LIBINTL
/* Equivalent to !isfinite(x) || x == 0, but does not require libm. */
static int
is_infinite_or_zero (double x)
{
return isnand (x) || x + x == x;
}
#endif
#if NEED_PRINTF_INFINITE_LONG_DOUBLE && !NEED_PRINTF_LONG_DOUBLE && !defined IN_LIBINTL
/* Equivalent to !isfinite(x) || x == 0, but does not require libm. */
static int
is_infinite_or_zerol (long double x)
{
return isnanl (x) || x + x == x;
}
#endif
#if (NEED_PRINTF_LONG_DOUBLE || NEED_PRINTF_DOUBLE) && !defined IN_LIBINTL
/* Converting 'long double' to decimal without rare rounding bugs requires
real bignums. We use the naming conventions of GNU gmp, but vastly simpler
(and slower) algorithms. */
typedef unsigned int mp_limb_t;
# define GMP_LIMB_BITS 32
typedef int mp_limb_verify[2 * (sizeof (mp_limb_t) * CHAR_BIT == GMP_LIMB_BITS) - 1];
typedef unsigned long long mp_twolimb_t;
# define GMP_TWOLIMB_BITS 64
typedef int mp_twolimb_verify[2 * (sizeof (mp_twolimb_t) * CHAR_BIT == GMP_TWOLIMB_BITS) - 1];
/* Representation of a bignum >= 0. */
typedef struct
{
size_t nlimbs;
mp_limb_t *limbs; /* Bits in little-endian order, allocated with malloc(). */
} mpn_t;
/* Compute the product of two bignums >= 0.
Return the allocated memory in case of success, NULL in case of memory
allocation failure. */
static void *
multiply (mpn_t src1, mpn_t src2, mpn_t *dest)
{
const mp_limb_t *p1;
const mp_limb_t *p2;
size_t len1;
size_t len2;
if (src1.nlimbs <= src2.nlimbs)
{
len1 = src1.nlimbs;
p1 = src1.limbs;
len2 = src2.nlimbs;
p2 = src2.limbs;
}
else
{
len1 = src2.nlimbs;
p1 = src2.limbs;
len2 = src1.nlimbs;
p2 = src1.limbs;
}
/* Now 0 <= len1 <= len2. */
if (len1 == 0)
{
/* src1 or src2 is zero. */
dest->nlimbs = 0;
dest->limbs = (mp_limb_t *) malloc (1);
}
else
{
/* Here 1 <= len1 <= len2. */
size_t dlen;
mp_limb_t *dp;
size_t k, i, j;
dlen = len1 + len2;
dp = (mp_limb_t *) malloc (dlen * sizeof (mp_limb_t));
if (dp == NULL)
return NULL;
for (k = len2; k > 0; )
dp[--k] = 0;
for (i = 0; i < len1; i++)
{
mp_limb_t digit1 = p1[i];
mp_twolimb_t carry = 0;
for (j = 0; j < len2; j++)
{
mp_limb_t digit2 = p2[j];
carry += (mp_twolimb_t) digit1 * (mp_twolimb_t) digit2;
carry += dp[i + j];
dp[i + j] = (mp_limb_t) carry;
carry = carry >> GMP_LIMB_BITS;
}
dp[i + len2] = (mp_limb_t) carry;
}
/* Normalise. */
while (dlen > 0 && dp[dlen - 1] == 0)
dlen--;
dest->nlimbs = dlen;
dest->limbs = dp;
}
return dest->limbs;
}
/* Compute the quotient of a bignum a >= 0 and a bignum b > 0.
a is written as a = q * b + r with 0 <= r < b. q is the quotient, r
the remainder.
Finally, round-to-even is performed: If r > b/2 or if r = b/2 and q is odd,
q is incremented.
Return the allocated memory in case of success, NULL in case of memory
allocation failure. */
static void *
divide (mpn_t a, mpn_t b, mpn_t *q)
{
/* Algorithm:
First normalise a and b: a=[a[m-1],...,a[0]], b=[b[n-1],...,b[0]]
with m>=0 and n>0 (in base beta = 2^GMP_LIMB_BITS).
If m<n, then q:=0 and r:=a.
If m>=n=1, perform a single-precision division:
r:=0, j:=m,
while j>0 do
{Here (q[m-1]*beta^(m-1)+...+q[j]*beta^j) * b[0] + r*beta^j =
= a[m-1]*beta^(m-1)+...+a[j]*beta^j und 0<=r<b[0]<beta}
j:=j-1, r:=r*beta+a[j], q[j]:=floor(r/b[0]), r:=r-b[0]*q[j].
Normalise [q[m-1],...,q[0]], yields q.
If m>=n>1, perform a multiple-precision division:
We have a/b < beta^(m-n+1).
s:=intDsize-1-(highest bit in b[n-1]), 0<=s<intDsize.
Shift a and b left by s bits, copying them. r:=a.
r=[r[m],...,r[0]], b=[b[n-1],...,b[0]] with b[n-1]>=beta/2.
For j=m-n,...,0: {Here 0 <= r < b*beta^(j+1).}
Compute q* :
q* := floor((r[j+n]*beta+r[j+n-1])/b[n-1]).
In case of overflow (q* >= beta) set q* := beta-1.
Compute c2 := ((r[j+n]*beta+r[j+n-1]) - q* * b[n-1])*beta + r[j+n-2]
and c3 := b[n-2] * q*.
{We have 0 <= c2 < 2*beta^2, even 0 <= c2 < beta^2 if no overflow
occurred. Furthermore 0 <= c3 < beta^2.
If there was overflow and
r[j+n]*beta+r[j+n-1] - q* * b[n-1] >= beta, i.e. c2 >= beta^2,
the next test can be skipped.}
While c3 > c2, {Here 0 <= c2 < c3 < beta^2}
Put q* := q* - 1, c2 := c2 + b[n-1]*beta, c3 := c3 - b[n-2].
If q* > 0:
Put r := r - b * q* * beta^j. In detail:
[r[n+j],...,r[j]] := [r[n+j],...,r[j]] - q* * [b[n-1],...,b[0]].
hence: u:=0, for i:=0 to n-1 do
u := u + q* * b[i],
r[j+i]:=r[j+i]-(u mod beta) (+ beta, if carry),
u:=u div beta (+ 1, if carry in subtraction)
r[n+j]:=r[n+j]-u.
{Since always u = (q* * [b[i-1],...,b[0]] div beta^i) + 1
< q* + 1 <= beta,
the carry u does not overflow.}
If a negative carry occurs, put q* := q* - 1
and [r[n+j],...,r[j]] := [r[n+j],...,r[j]] + [0,b[n-1],...,b[0]].
Set q[j] := q*.
Normalise [q[m-n],..,q[0]]; this yields the quotient q.
Shift [r[n-1],...,r[0]] right by s bits and normalise; this yields the
rest r.
The room for q[j] can be allocated at the memory location of r[n+j].
Finally, round-to-even:
Shift r left by 1 bit.
If r > b or if r = b and q[0] is odd, q := q+1.
*/
const mp_limb_t *a_ptr = a.limbs;
size_t a_len = a.nlimbs;
const mp_limb_t *b_ptr = b.limbs;
size_t b_len = b.nlimbs;
mp_limb_t *roomptr;
mp_limb_t *tmp_roomptr = NULL;
mp_limb_t *q_ptr;
size_t q_len;
mp_limb_t *r_ptr;
size_t r_len;
/* Allocate room for a_len+2 digits.
(Need a_len+1 digits for the real division and 1 more digit for the
final rounding of q.) */
roomptr = (mp_limb_t *) malloc ((a_len + 2) * sizeof (mp_limb_t));
if (roomptr == NULL)
return NULL;
/* Normalise a. */
while (a_len > 0 && a_ptr[a_len - 1] == 0)
a_len--;
/* Normalise b. */
for (;;)
{
if (b_len == 0)
/* Division by zero. */
abort ();
if (b_ptr[b_len - 1] == 0)
b_len--;
else
break;
}
/* Here m = a_len >= 0 and n = b_len > 0. */
if (a_len < b_len)
{
/* m<n: trivial case. q=0, r := copy of a. */
r_ptr = roomptr;
r_len = a_len;
memcpy (r_ptr, a_ptr, a_len * sizeof (mp_limb_t));
q_ptr = roomptr + a_len;
q_len = 0;
}
else if (b_len == 1)
{
/* n=1: single precision division.
beta^(m-1) <= a < beta^m ==> beta^(m-2) <= a/b < beta^m */
r_ptr = roomptr;
q_ptr = roomptr + 1;
{
mp_limb_t den = b_ptr[0];
mp_limb_t remainder = 0;
const mp_limb_t *sourceptr = a_ptr + a_len;
mp_limb_t *destptr = q_ptr + a_len;
size_t count;
for (count = a_len; count > 0; count--)
{
mp_twolimb_t num =
((mp_twolimb_t) remainder << GMP_LIMB_BITS) | *--sourceptr;
*--destptr = num / den;
remainder = num % den;
}
/* Normalise and store r. */
if (remainder > 0)
{
r_ptr[0] = remainder;
r_len = 1;
}
else
r_len = 0;
/* Normalise q. */
q_len = a_len;
if (q_ptr[q_len - 1] == 0)
q_len--;
}
}
else
{
/* n>1: multiple precision division.
beta^(m-1) <= a < beta^m, beta^(n-1) <= b < beta^n ==>
beta^(m-n-1) <= a/b < beta^(m-n+1). */
/* Determine s. */
size_t s;
{
mp_limb_t msd = b_ptr[b_len - 1]; /* = b[n-1], > 0 */
s = 31;
if (msd >= 0x10000)
{
msd = msd >> 16;
s -= 16;
}
if (msd >= 0x100)
{
msd = msd >> 8;
s -= 8;
}
if (msd >= 0x10)
{
msd = msd >> 4;
s -= 4;
}
if (msd >= 0x4)
{
msd = msd >> 2;
s -= 2;
}
if (msd >= 0x2)
{
msd = msd >> 1;
s -= 1;
}
}
/* 0 <= s < GMP_LIMB_BITS.
Copy b, shifting it left by s bits. */
if (s > 0)
{
tmp_roomptr = (mp_limb_t *) malloc (b_len * sizeof (mp_limb_t));
if (tmp_roomptr == NULL)
{
free (roomptr);
return NULL;
}
{
const mp_limb_t *sourceptr = b_ptr;
mp_limb_t *destptr = tmp_roomptr;
mp_twolimb_t accu = 0;
size_t count;
for (count = b_len; count > 0; count--)
{
accu += (mp_twolimb_t) *sourceptr++ << s;
*destptr++ = (mp_limb_t) accu;
accu = accu >> GMP_LIMB_BITS;
}
/* accu must be zero, since that was how s was determined. */
if (accu != 0)
abort ();
}
b_ptr = tmp_roomptr;
}
/* Copy a, shifting it left by s bits, yields r.
Memory layout:
At the beginning: r = roomptr[0..a_len],
at the end: r = roomptr[0..b_len-1], q = roomptr[b_len..a_len] */
r_ptr = roomptr;
if (s == 0)
{
memcpy (r_ptr, a_ptr, a_len * sizeof (mp_limb_t));
r_ptr[a_len] = 0;
}
else
{
const mp_limb_t *sourceptr = a_ptr;
mp_limb_t *destptr = r_ptr;
mp_twolimb_t accu = 0;
size_t count;
for (count = a_len; count > 0; count--)
{
accu += (mp_twolimb_t) *sourceptr++ << s;
*destptr++ = (mp_limb_t) accu;
accu = accu >> GMP_LIMB_BITS;
}
*destptr++ = (mp_limb_t) accu;
}
q_ptr = roomptr + b_len;
q_len = a_len - b_len + 1; /* q will have m-n+1 limbs */
{
size_t j = a_len - b_len; /* m-n */
mp_limb_t b_msd = b_ptr[b_len - 1]; /* b[n-1] */
mp_limb_t b_2msd = b_ptr[b_len - 2]; /* b[n-2] */
mp_twolimb_t b_msdd = /* b[n-1]*beta+b[n-2] */
((mp_twolimb_t) b_msd << GMP_LIMB_BITS) | b_2msd;
/* Division loop, traversed m-n+1 times.
j counts down, b is unchanged, beta/2 <= b[n-1] < beta. */
for (;;)
{
mp_limb_t q_star;
mp_limb_t c1;
if (r_ptr[j + b_len] < b_msd) /* r[j+n] < b[n-1] ? */
{
/* Divide r[j+n]*beta+r[j+n-1] by b[n-1], no overflow. */
mp_twolimb_t num =
((mp_twolimb_t) r_ptr[j + b_len] << GMP_LIMB_BITS)
| r_ptr[j + b_len - 1];
q_star = num / b_msd;
c1 = num % b_msd;
}
else
{
/* Overflow, hence r[j+n]*beta+r[j+n-1] >= beta*b[n-1]. */
q_star = (mp_limb_t)~(mp_limb_t)0; /* q* = beta-1 */
/* Test whether r[j+n]*beta+r[j+n-1] - (beta-1)*b[n-1] >= beta
<==> r[j+n]*beta+r[j+n-1] + b[n-1] >= beta*b[n-1]+beta
<==> b[n-1] < floor((r[j+n]*beta+r[j+n-1]+b[n-1])/beta)
{<= beta !}.
If yes, jump directly to the subtraction loop.
(Otherwise, r[j+n]*beta+r[j+n-1] - (beta-1)*b[n-1] < beta
<==> floor((r[j+n]*beta+r[j+n-1]+b[n-1])/beta) = b[n-1] ) */
if (r_ptr[j + b_len] > b_msd
|| (c1 = r_ptr[j + b_len - 1] + b_msd) < b_msd)
/* r[j+n] >= b[n-1]+1 or
r[j+n] = b[n-1] and the addition r[j+n-1]+b[n-1] gives a
carry. */
goto subtract;
}
/* q_star = q*,
c1 = (r[j+n]*beta+r[j+n-1]) - q* * b[n-1] (>=0, <beta). */
{
mp_twolimb_t c2 = /* c1*beta+r[j+n-2] */
((mp_twolimb_t) c1 << GMP_LIMB_BITS) | r_ptr[j + b_len - 2];
mp_twolimb_t c3 = /* b[n-2] * q* */
(mp_twolimb_t) b_2msd * (mp_twolimb_t) q_star;
/* While c2 < c3, increase c2 and decrease c3.
Consider c3-c2. While it is > 0, decrease it by
b[n-1]*beta+b[n-2]. Because of b[n-1]*beta+b[n-2] >= beta^2/2
this can happen only twice. */
if (c3 > c2)
{
q_star = q_star - 1; /* q* := q* - 1 */
if (c3 - c2 > b_msdd)
q_star = q_star - 1; /* q* := q* - 1 */
}
}
if (q_star > 0)
subtract:
{
/* Subtract r := r - b * q* * beta^j. */
mp_limb_t cr;
{
const mp_limb_t *sourceptr = b_ptr;
mp_limb_t *destptr = r_ptr + j;
mp_twolimb_t carry = 0;
size_t count;
for (count = b_len; count > 0; count--)
{
/* Here 0 <= carry <= q*. */
carry =
carry
+ (mp_twolimb_t) q_star * (mp_twolimb_t) *sourceptr++
+ (mp_limb_t) ~(*destptr);
/* Here 0 <= carry <= beta*q* + beta-1. */
*destptr++ = ~(mp_limb_t) carry;
carry = carry >> GMP_LIMB_BITS; /* <= q* */
}
cr = (mp_limb_t) carry;
}
/* Subtract cr from r_ptr[j + b_len], then forget about
r_ptr[j + b_len]. */
if (cr > r_ptr[j + b_len])
{
/* Subtraction gave a carry. */
q_star = q_star - 1; /* q* := q* - 1 */
/* Add b back. */
{
const mp_limb_t *sourceptr = b_ptr;
mp_limb_t *destptr = r_ptr + j;
mp_limb_t carry = 0;
size_t count;
for (count = b_len; count > 0; count--)
{
mp_limb_t source1 = *sourceptr++;
mp_limb_t source2 = *destptr;
*destptr++ = source1 + source2 + carry;
carry =
(carry
? source1 >= (mp_limb_t) ~source2
: source1 > (mp_limb_t) ~source2);
}
}
/* Forget about the carry and about r[j+n]. */
}
}
/* q* is determined. Store it as q[j]. */
q_ptr[j] = q_star;
if (j == 0)
break;
j--;
}
}
r_len = b_len;
/* Normalise q. */
if (q_ptr[q_len - 1] == 0)
q_len--;
# if 0 /* Not needed here, since we need r only to compare it with b/2, and
b is shifted left by s bits. */
/* Shift r right by s bits. */
if (s > 0)
{
mp_limb_t ptr = r_ptr + r_len;
mp_twolimb_t accu = 0;
size_t count;
for (count = r_len; count > 0; count--)
{
accu = (mp_twolimb_t) (mp_limb_t) accu << GMP_LIMB_BITS;
accu += (mp_twolimb_t) *--ptr << (GMP_LIMB_BITS - s);
*ptr = (mp_limb_t) (accu >> GMP_LIMB_BITS);
}
}
# endif
/* Normalise r. */
while (r_len > 0 && r_ptr[r_len - 1] == 0)
r_len--;
}
/* Compare r << 1 with b. */
if (r_len > b_len)
goto increment_q;
{
size_t i;
for (i = b_len;;)
{
mp_limb_t r_i =
(i <= r_len && i > 0 ? r_ptr[i - 1] >> (GMP_LIMB_BITS - 1) : 0)
| (i < r_len ? r_ptr[i] << 1 : 0);
mp_limb_t b_i = (i < b_len ? b_ptr[i] : 0);
if (r_i > b_i)
goto increment_q;
if (r_i < b_i)
goto keep_q;
if (i == 0)
break;
i--;
}
}
if (q_len > 0 && ((q_ptr[0] & 1) != 0))
/* q is odd. */
increment_q:
{
size_t i;
for (i = 0; i < q_len; i++)
if (++(q_ptr[i]) != 0)
goto keep_q;
q_ptr[q_len++] = 1;
}
keep_q:
if (tmp_roomptr != NULL)
free (tmp_roomptr);
q->limbs = q_ptr;
q->nlimbs = q_len;
return roomptr;
}
/* Convert a bignum a >= 0, multiplied with 10^extra_zeroes, to decimal
representation.
Destroys the contents of a.
Return the allocated memory - containing the decimal digits in low-to-high
order, terminated with a NUL character - in case of success, NULL in case
of memory allocation failure. */
static char *
convert_to_decimal (mpn_t a, size_t extra_zeroes)
{
mp_limb_t *a_ptr = a.limbs;
size_t a_len = a.nlimbs;
/* 0.03345 is slightly larger than log(2)/(9*log(10)). */
size_t c_len = 9 * ((size_t)(a_len * (GMP_LIMB_BITS * 0.03345f)) + 1);
char *c_ptr = (char *) malloc (xsum (c_len, extra_zeroes));
if (c_ptr != NULL)
{
char *d_ptr = c_ptr;
for (; extra_zeroes > 0; extra_zeroes--)
*d_ptr++ = '0';
while (a_len > 0)
{
/* Divide a by 10^9, in-place. */
mp_limb_t remainder = 0;
mp_limb_t *ptr = a_ptr + a_len;
size_t count;
for (count = a_len; count > 0; count--)
{
mp_twolimb_t num =
((mp_twolimb_t) remainder << GMP_LIMB_BITS) | *--ptr;
*ptr = num / 1000000000;
remainder = num % 1000000000;
}
/* Store the remainder as 9 decimal digits. */
for (count = 9; count > 0; count--)
{
*d_ptr++ = '0' + (remainder % 10);
remainder = remainder / 10;
}
/* Normalize a. */
if (a_ptr[a_len - 1] == 0)
a_len--;
}
/* Remove leading zeroes. */
while (d_ptr > c_ptr && d_ptr[-1] == '0')
d_ptr--;
/* But keep at least one zero. */
if (d_ptr == c_ptr)
*d_ptr++ = '0';
/* Terminate the string. */
*d_ptr = '\0';
}
return c_ptr;
}
# if NEED_PRINTF_LONG_DOUBLE
/* Assuming x is finite and >= 0:
write x as x = 2^e * m, where m is a bignum.
Return the allocated memory in case of success, NULL in case of memory
allocation failure. */
static void *
decode_long_double (long double x, int *ep, mpn_t *mp)
{
mpn_t m;
int exp;
long double y;
size_t i;
/* Allocate memory for result. */
m.nlimbs = (LDBL_MANT_BIT + GMP_LIMB_BITS - 1) / GMP_LIMB_BITS;
m.limbs = (mp_limb_t *) malloc (m.nlimbs * sizeof (mp_limb_t));
if (m.limbs == NULL)
return NULL;
/* Split into exponential part and mantissa. */
y = frexpl (x, &exp);
if (!(y >= 0.0L && y < 1.0L))
abort ();
/* x = 2^exp * y = 2^(exp - LDBL_MANT_BIT) * (y * LDBL_MANT_BIT), and the
latter is an integer. */
/* Convert the mantissa (y * LDBL_MANT_BIT) to a sequence of limbs.
I'm not sure whether it's safe to cast a 'long double' value between
2^31 and 2^32 to 'unsigned int', therefore play safe and cast only
'long double' values between 0 and 2^16 (to 'unsigned int' or 'int',
doesn't matter). */
# if (LDBL_MANT_BIT % GMP_LIMB_BITS) != 0
# if (LDBL_MANT_BIT % GMP_LIMB_BITS) > GMP_LIMB_BITS / 2
{
mp_limb_t hi, lo;
y *= (mp_limb_t) 1 << (LDBL_MANT_BIT % (GMP_LIMB_BITS / 2));
hi = (int) y;
y -= hi;
if (!(y >= 0.0L && y < 1.0L))
abort ();
y *= (mp_limb_t) 1 << (GMP_LIMB_BITS / 2);
lo = (int) y;
y -= lo;
if (!(y >= 0.0L && y < 1.0L))
abort ();
m.limbs[LDBL_MANT_BIT / GMP_LIMB_BITS] = (hi << (GMP_LIMB_BITS / 2)) | lo;
}
# else
{
mp_limb_t d;
y *= (mp_limb_t) 1 << (LDBL_MANT_BIT % GMP_LIMB_BITS);
d = (int) y;
y -= d;
if (!(y >= 0.0L && y < 1.0L))
abort ();
m.limbs[LDBL_MANT_BIT / GMP_LIMB_BITS] = d;
}
# endif
# endif
for (i = LDBL_MANT_BIT / GMP_LIMB_BITS; i > 0; )
{
mp_limb_t hi, lo;
y *= (mp_limb_t) 1 << (GMP_LIMB_BITS / 2);
hi = (int) y;
y -= hi;
if (!(y >= 0.0L && y < 1.0L))
abort ();
y *= (mp_limb_t) 1 << (GMP_LIMB_BITS / 2);
lo = (int) y;
y -= lo;
if (!(y >= 0.0L && y < 1.0L))
abort ();
m.limbs[--i] = (hi << (GMP_LIMB_BITS / 2)) | lo;
}
#if 0 /* On FreeBSD 6.1/x86, 'long double' numbers sometimes have excess
precision. */
if (!(y == 0.0L))
abort ();
#endif
/* Normalise. */
while (m.nlimbs > 0 && m.limbs[m.nlimbs - 1] == 0)
m.nlimbs--;
*mp = m;
*ep = exp - LDBL_MANT_BIT;
return m.limbs;
}
# endif
# if NEED_PRINTF_DOUBLE
/* Assuming x is finite and >= 0:
write x as x = 2^e * m, where m is a bignum.
Return the allocated memory in case of success, NULL in case of memory
allocation failure. */
static void *
decode_double (double x, int *ep, mpn_t *mp)
{
mpn_t m;
int exp;
double y;
size_t i;
/* Allocate memory for result. */
m.nlimbs = (DBL_MANT_BIT + GMP_LIMB_BITS - 1) / GMP_LIMB_BITS;
m.limbs = (mp_limb_t *) malloc (m.nlimbs * sizeof (mp_limb_t));
if (m.limbs == NULL)
return NULL;
/* Split into exponential part and mantissa. */
y = frexp (x, &exp);
if (!(y >= 0.0 && y < 1.0))
abort ();
/* x = 2^exp * y = 2^(exp - DBL_MANT_BIT) * (y * DBL_MANT_BIT), and the
latter is an integer. */
/* Convert the mantissa (y * DBL_MANT_BIT) to a sequence of limbs.
I'm not sure whether it's safe to cast a 'double' value between
2^31 and 2^32 to 'unsigned int', therefore play safe and cast only
'double' values between 0 and 2^16 (to 'unsigned int' or 'int',
doesn't matter). */
# if (DBL_MANT_BIT % GMP_LIMB_BITS) != 0
# if (DBL_MANT_BIT % GMP_LIMB_BITS) > GMP_LIMB_BITS / 2
{
mp_limb_t hi, lo;
y *= (mp_limb_t) 1 << (DBL_MANT_BIT % (GMP_LIMB_BITS / 2));
hi = (int) y;
y -= hi;
if (!(y >= 0.0 && y < 1.0))
abort ();
y *= (mp_limb_t) 1 << (GMP_LIMB_BITS / 2);
lo = (int) y;
y -= lo;
if (!(y >= 0.0 && y < 1.0))
abort ();
m.limbs[DBL_MANT_BIT / GMP_LIMB_BITS] = (hi << (GMP_LIMB_BITS / 2)) | lo;
}
# else
{
mp_limb_t d;
y *= (mp_limb_t) 1 << (DBL_MANT_BIT % GMP_LIMB_BITS);