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ma_dtoa.c
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/* Copyright (c) 2007, 2012, Oracle and/or its affiliates. All rights reserved.
2016,2022 MariaDB Corporation AB
This library is free software; you can redistribute it and/or
modify it under the terms of the GNU Library General Public
License as published by the Free Software Foundation; version 2
of the License.
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 St, Fifth Floor, Boston, MA 02110-1301 USA */
/****************************************************************
This file incorporates work covered by the following copyright and
permission notice:
The author of this software is David M. Gay.
Copyright (c) 1991, 2000, 2001 by Lucent Technologies.
Permission to use, copy, modify, and distribute this software for any
purpose without fee is hereby granted, provided that this entire notice
is included in all copies of any software which is or includes a copy
or modification of this software and in all copies of the supporting
documentation for such software.
THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY
REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
***************************************************************/
//#include "strings_def.h"
//#include <my_base.h> /* for EOVERFLOW on Windows */
#include <ma_global.h>
#include <memory.h>
#include "ma_string.h"
/**
Appears to suffice to not call malloc() in most cases.
@todo
see if it is possible to get rid of malloc().
this constant is sufficient to avoid malloc() on all inputs I have tried.
*/
#define DTOA_BUFF_SIZE (460 * sizeof(void *))
/* Magic value returned by dtoa() to indicate overflow */
#define DTOA_OVERFLOW 9999
static char *dtoa(double, int, int, int *, int *, char **, char *, size_t);
static void dtoa_free(char *, char *, size_t);
/**
@brief
Converts a given floating point number to a zero-terminated string
representation using the 'f' format.
@details
This function is a wrapper around dtoa() to do the same as
sprintf(to, "%-.*f", precision, x), though the conversion is usually more
precise. The only difference is in handling [-,+]infinity and nan values,
in which case we print '0\0' to the output string and indicate an overflow.
@param x the input floating point number.
@param precision the number of digits after the decimal point.
All properties of sprintf() apply:
- if the number of significant digits after the decimal
point is less than precision, the resulting string is
right-padded with zeros
- if the precision is 0, no decimal point appears
- if a decimal point appears, at least one digit appears
before it
@param to pointer to the output buffer. The longest string which
my_fcvt() can return is FLOATING_POINT_BUFFER bytes
(including the terminating '\0').
@param error if not NULL, points to a location where the status of
conversion is stored upon return.
FALSE successful conversion
TRUE the input number is [-,+]infinity or nan.
The output string in this case is always '0'.
@return number of written characters (excluding terminating '\0')
*/
size_t ma_fcvt(double x, int precision, char *to, my_bool *error)
{
int decpt, sign, len, i;
char *res, *src, *end, *dst= to;
char buf[DTOA_BUFF_SIZE];
DBUG_ASSERT(precision >= 0 && precision < NOT_FIXED_DEC && to != NULL);
res= dtoa(x, 5, precision, &decpt, &sign, &end, buf, sizeof(buf));
if (decpt == DTOA_OVERFLOW)
{
dtoa_free(res, buf, sizeof(buf));
*to++= '0';
*to= '\0';
if (error != NULL)
*error= TRUE;
return 1;
}
src= res;
len= (int)(end - src);
if (sign)
*dst++= '-';
if (decpt <= 0)
{
*dst++= '0';
*dst++= '.';
for (i= decpt; i < 0; i++)
*dst++= '0';
}
for (i= 1; i <= len; i++)
{
*dst++= *src++;
if (i == decpt && i < len)
*dst++= '.';
}
while (i++ <= decpt)
*dst++= '0';
if (precision > 0)
{
if (len <= decpt)
*dst++= '.';
for (i= precision - MAX(0, (len - decpt)); i > 0; i--)
*dst++= '0';
}
*dst= '\0';
if (error != NULL)
*error= FALSE;
dtoa_free(res, buf, sizeof(buf));
return dst - to;
}
/**
@brief
Converts a given floating point number to a zero-terminated string
representation with a given field width using the 'e' format
(aka scientific notation) or the 'f' one.
@details
The format is chosen automatically to provide the most number of significant
digits (and thus, precision) with a given field width. In many cases, the
result is similar to that of sprintf(to, "%g", x) with a few notable
differences:
- the conversion is usually more precise than C library functions.
- there is no 'precision' argument. instead, we specify the number of
characters available for conversion (i.e. a field width).
- the result never exceeds the specified field width. If the field is too
short to contain even a rounded decimal representation, ma_gcvt()
indicates overflow and truncates the output string to the specified width.
- float-type arguments are handled differently than double ones. For a
float input number (i.e. when the 'type' argument is MY_GCVT_ARG_FLOAT)
we deliberately limit the precision of conversion by FLT_DIG digits to
avoid garbage past the significant digits.
- unlike sprintf(), in cases where the 'e' format is preferred, we don't
zero-pad the exponent to save space for significant digits. The '+' sign
for a positive exponent does not appear for the same reason.
@param x the input floating point number.
@param type is either MY_GCVT_ARG_FLOAT or MY_GCVT_ARG_DOUBLE.
Specifies the type of the input number (see notes above).
@param width field width in characters. The minimal field width to
hold any number representation (albeit rounded) is 7
characters ("-Ne-NNN").
@param to pointer to the output buffer. The result is always
zero-terminated, and the longest returned string is thus
'width + 1' bytes.
@param error if not NULL, points to a location where the status of
conversion is stored upon return.
FALSE successful conversion
TRUE the input number is [-,+]infinity or nan.
The output string in this case is always '0'.
@return number of written characters (excluding terminating '\0')
@todo
Check if it is possible and makes sense to do our own rounding on top of
dtoa() instead of calling dtoa() twice in (rare) cases when the resulting
string representation does not fit in the specified field width and we want
to re-round the input number with fewer significant digits. Examples:
ma_gcvt(-9e-3, ..., 4, ...);
ma_gcvt(-9e-3, ..., 2, ...);
ma_gcvt(1.87e-3, ..., 4, ...);
ma_gcvt(55, ..., 1, ...);
We do our best to minimize such cases by:
- passing to dtoa() the field width as the number of significant digits
- removing the sign of the number early (and decreasing the width before
passing it to dtoa())
- choosing the proper format to preserve the most number of significant
digits.
*/
size_t ma_gcvt(double x, my_gcvt_arg_type type, int width, char *to,
my_bool *error)
{
int decpt, sign, len, exp_len;
char *res, *src, *end, *dst= to, *dend= dst + width;
char buf[DTOA_BUFF_SIZE];
my_bool have_space, force_e_format;
DBUG_ASSERT(width > 0 && to != NULL);
/* We want to remove '-' from equations early */
if (x < 0.)
width--;
res= dtoa(x, 4, type == MY_GCVT_ARG_DOUBLE ? width : MIN(width, FLT_DIG),
&decpt, &sign, &end, buf, sizeof(buf));
if (decpt == DTOA_OVERFLOW)
{
dtoa_free(res, buf, sizeof(buf));
*to++= '0';
*to= '\0';
if (error != NULL)
*error= TRUE;
return 1;
}
if (error != NULL)
*error= FALSE;
src= res;
len= (int)(end - res);
/*
Number of digits in the exponent from the 'e' conversion.
The sign of the exponent is taken into account separately, we don't need
to count it here.
*/
exp_len= 1 + (decpt >= 101 || decpt <= -99) + (decpt >= 11 || decpt <= -9);
/*
Do we have enough space for all digits in the 'f' format?
Let 'len' be the number of significant digits returned by dtoa,
and F be the length of the resulting decimal representation.
Consider the following cases:
1. decpt <= 0, i.e. we have "0.NNN" => F = len - decpt + 2
2. 0 < decpt < len, i.e. we have "NNN.NNN" => F = len + 1
3. len <= decpt, i.e. we have "NNN00" => F = decpt
*/
have_space= (decpt <= 0 ? len - decpt + 2 :
decpt > 0 && decpt < len ? len + 1 :
decpt) <= width;
/*
The following is true when no significant digits can be placed with the
specified field width using the 'f' format, and the 'e' format
will not be truncated.
*/
force_e_format= (decpt <= 0 && width <= 2 - decpt && width >= 3 + exp_len);
/*
Assume that we don't have enough space to place all significant digits in
the 'f' format. We have to choose between the 'e' format and the 'f' one
to keep as many significant digits as possible.
Let E and F be the lengths of decimal representation in the 'e' and 'f'
formats, respectively. We want to use the 'f' format if, and only if F <= E.
Consider the following cases:
1. decpt <= 0.
F = len - decpt + 2 (see above)
E = len + (len > 1) + 1 + 1 (decpt <= -99) + (decpt <= -9) + 1
("N.NNe-MMM")
(F <= E) <=> (len == 1 && decpt >= -1) || (len > 1 && decpt >= -2)
We also need to ensure that if the 'f' format is chosen,
the field width allows us to place at least one significant digit
(i.e. width > 2 - decpt). If not, we prefer the 'e' format.
2. 0 < decpt < len
F = len + 1 (see above)
E = len + 1 + 1 + ... ("N.NNeMMM")
F is always less than E.
3. len <= decpt <= width
In this case we have enough space to represent the number in the 'f'
format, so we prefer it with some exceptions.
4. width < decpt
The number cannot be represented in the 'f' format at all, always use
the 'e' 'one.
*/
if ((have_space ||
/*
Not enough space, let's see if the 'f' format provides the most number
of significant digits.
*/
((decpt <= width && (decpt >= -1 || (decpt == -2 &&
(len > 1 || !force_e_format)))) &&
!force_e_format)) &&
/*
Use the 'e' format in some cases even if we have enough space for the
'f' one. See comment for DBL_DIG.
*/
(!have_space || (decpt >= -DBL_DIG + 1 &&
(decpt <= DBL_DIG || len > decpt))))
{
/* 'f' format */
int i;
width-= (decpt < len) + (decpt <= 0 ? 1 - decpt : 0);
/* Do we have to truncate any digits? */
if (width < len)
{
if (width < decpt)
{
if (error != NULL)
*error= TRUE;
width= decpt;
}
/*
We want to truncate (len - width) least significant digits after the
decimal point. For this we are calling dtoa with mode=5, passing the
number of significant digits = (len-decpt) - (len-width) = width-decpt
*/
dtoa_free(res, buf, sizeof(buf));
res= dtoa(x, 5, width - decpt, &decpt, &sign, &end, buf, sizeof(buf));
src= res;
len= (int)(end - res);
}
if (len == 0)
{
/* Underflow. Just print '0' and exit */
*dst++= '0';
goto end;
}
/*
At this point we are sure we have enough space to put all digits
returned by dtoa
*/
if (sign && dst < dend)
*dst++= '-';
if (decpt <= 0)
{
if (dst < dend)
*dst++= '0';
if (len > 0 && dst < dend)
*dst++= '.';
for (; decpt < 0 && dst < dend; decpt++)
*dst++= '0';
}
for (i= 1; i <= len && dst < dend; i++)
{
*dst++= *src++;
if (i == decpt && i < len && dst < dend)
*dst++= '.';
}
while (i++ <= decpt && dst < dend)
*dst++= '0';
}
else
{
/* 'e' format */
int decpt_sign= 0;
if (--decpt < 0)
{
decpt= -decpt;
width--;
decpt_sign= 1;
}
width-= 1 + exp_len; /* eNNN */
if (len > 1)
width--;
if (width <= 0)
{
/* Overflow */
if (error != NULL)
*error= TRUE;
width= 0;
}
/* Do we have to truncate any digits? */
if (width < len)
{
/* Yes, re-convert with a smaller width */
dtoa_free(res, buf, sizeof(buf));
res= dtoa(x, 4, width, &decpt, &sign, &end, buf, sizeof(buf));
src= res;
len= (int)(end - res);
if (--decpt < 0)
decpt= -decpt;
}
/*
At this point we are sure we have enough space to put all digits
returned by dtoa
*/
if (sign && dst < dend)
*dst++= '-';
if (dst < dend)
*dst++= *src++;
if (len > 1 && dst < dend)
{
*dst++= '.';
while (src < end && dst < dend)
*dst++= *src++;
}
if (dst < dend)
*dst++= 'e';
if (decpt_sign && dst < dend)
*dst++= '-';
if (decpt >= 100 && dst < dend)
{
*dst++= decpt / 100 + '0';
decpt%= 100;
if (dst < dend)
*dst++= decpt / 10 + '0';
}
else if (decpt >= 10 && dst < dend)
*dst++= decpt / 10 + '0';
if (dst < dend)
*dst++= decpt % 10 + '0';
}
end:
dtoa_free(res, buf, sizeof(buf));
*dst= '\0';
return dst - to;
}
/****************************************************************
*
* The author of this software is David M. Gay.
*
* Copyright (c) 1991, 2000, 2001 by Lucent Technologies.
*
* Permission to use, copy, modify, and distribute this software for any
* purpose without fee is hereby granted, provided that this entire notice
* is included in all copies of any software which is or includes a copy
* or modification of this software and in all copies of the supporting
* documentation for such software.
*
* THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
* WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY
* REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
* OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
*
***************************************************************/
/* Please send bug reports to David M. Gay (dmg at acm dot org,
* with " at " changed at "@" and " dot " changed to "."). */
/*
Original copy of the software is located at http://www.netlib.org/fp/dtoa.c
It was adjusted to serve MySQL server needs:
* strtod() was modified to not expect a zero-terminated string.
It now honors 'se' (end of string) argument as the input parameter,
not just as the output one.
* in dtoa(), in case of overflow/underflow/NaN result string now contains "0";
decpt is set to DTOA_OVERFLOW to indicate overflow.
* support for VAX, IBM mainframe and 16-bit hardware removed
* we always assume that 64-bit integer type is available
* support for Kernigan-Ritchie style headers (pre-ANSI compilers)
removed
* all gcc warnings ironed out
* we always assume multithreaded environment, so we had to change
memory allocation procedures to use stack in most cases;
malloc is used as the last resort.
* pow5mult rewritten to use pre-calculated pow5 list instead of
the one generated on the fly.
*/
/*
On a machine with IEEE extended-precision registers, it is
necessary to specify double-precision (53-bit) rounding precision
before invoking strtod or dtoa. If the machine uses (the equivalent
of) Intel 80x87 arithmetic, the call
_control87(PC_53, MCW_PC);
does this with many compilers. Whether this or another call is
appropriate depends on the compiler; for this to work, it may be
necessary to #include "float.h" or another system-dependent header
file.
*/
/*
#define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
and dtoa should round accordingly.
#define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
and Honor_FLT_ROUNDS is not #defined.
TODO: check if we can get rid of the above two
*/
typedef int32 Long;
typedef uint32 ULong;
typedef int64 LLong;
typedef uint64 ULLong;
typedef union { double d; ULong L[2]; } U;
#if defined(HAVE_BIGENDIAN) || defined(WORDS_BIGENDIAN) || \
(defined(__FLOAT_WORD_ORDER) && (__FLOAT_WORD_ORDER == __BIG_ENDIAN))
#define word0(x) ((x)->L[0])
#define word1(x) ((x)->L[1])
#else
#define word0(x) ((x)->L[1])
#define word1(x) ((x)->L[0])
#endif
#define dval(x) ((x)->d)
/* #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) */
#define Exp_shift 20
#define Exp_shift1 20
#define Exp_msk1 0x100000
#define Exp_mask 0x7ff00000
#define P 53
#define Bias 1023
#define Emin (-1022)
#define Exp_1 0x3ff00000
#define Exp_11 0x3ff00000
#define Ebits 11
#define Frac_mask 0xfffff
#define Frac_mask1 0xfffff
#define Ten_pmax 22
#define Bletch 0x10
#define Bndry_mask 0xfffff
#define Bndry_mask1 0xfffff
#define LSB 1
#define Sign_bit 0x80000000
#define Log2P 1
#define Tiny1 1
#define Quick_max 14
#define Int_max 14
#ifndef Flt_Rounds
#ifdef FLT_ROUNDS
#define Flt_Rounds FLT_ROUNDS
#else
#define Flt_Rounds 1
#endif
#endif /*Flt_Rounds*/
#ifdef Honor_FLT_ROUNDS
#define Rounding rounding
#undef Check_FLT_ROUNDS
#define Check_FLT_ROUNDS
#else
#define Rounding Flt_Rounds
#endif
#define rounded_product(a,b) ((a)*= (b))
#define rounded_quotient(a,b) ((a)/= (b))
#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
#define Big1 0xffffffff
#define FFFFFFFF 0xffffffffUL
/* This is tested to be enough for dtoa */
#define Kmax 15
#define Bcopy(x,y) memcpy((char *)&(x)->sign, (char *)&(y)->sign, \
2*sizeof(int) + (y)->wds*sizeof(ULong))
/* Arbitrary-length integer */
typedef struct Bigint
{
union {
ULong *x; /* points right after this Bigint object */
struct Bigint *next; /* to maintain free lists */
} p;
int k; /* 2^k = maxwds */
int maxwds; /* maximum length in 32-bit words */
int sign; /* not zero if number is negative */
int wds; /* current length in 32-bit words */
} Bigint;
/* A simple stack-memory based allocator for Bigints */
typedef struct Stack_alloc
{
char *begin;
char *free;
char *end;
/*
Having list of free blocks lets us reduce maximum required amount
of memory from ~4000 bytes to < 1680 (tested on x86).
*/
Bigint *freelist[Kmax+1];
} Stack_alloc;
/*
Try to allocate object on stack, and resort to malloc if all
stack memory is used. Ensure allocated objects to be aligned by the pointer
size in order to not break the alignment rules when storing a pointer to a
Bigint.
*/
static Bigint *Balloc(int k, Stack_alloc *alloc)
{
Bigint *rv;
DBUG_ASSERT(k <= Kmax);
if (k <= Kmax && alloc->freelist[k])
{
rv= alloc->freelist[k];
alloc->freelist[k]= rv->p.next;
}
else
{
int x, len;
x= 1 << k;
len= MY_ALIGN(sizeof(Bigint) + x * sizeof(ULong), SIZEOF_CHARP);
if (alloc->free + len <= alloc->end)
{
rv= (Bigint*) alloc->free;
alloc->free+= len;
}
else
rv= (Bigint*) malloc(len);
rv->k= k;
rv->maxwds= x;
}
rv->sign= rv->wds= 0;
rv->p.x= (ULong*) (rv + 1);
return rv;
}
/*
If object was allocated on stack, try putting it to the free
list. Otherwise call free().
*/
static void Bfree(Bigint *v, Stack_alloc *alloc)
{
char *gptr= (char*) v; /* generic pointer */
if (gptr < alloc->begin || gptr >= alloc->end)
free(gptr);
else if (v->k <= Kmax)
{
/*
Maintain free lists only for stack objects: this way we don't
have to bother with freeing lists in the end of dtoa;
heap should not be used normally anyway.
*/
v->p.next= alloc->freelist[v->k];
alloc->freelist[v->k]= v;
}
}
/*
This is to place return value of dtoa in: tries to use stack
as well, but passes by free lists management and just aligns len by
the pointer size in order to not break the alignment rules when storing a
pointer to a Bigint.
*/
static char *dtoa_alloc(int i, Stack_alloc *alloc)
{
char *rv;
int aligned_size= MY_ALIGN(i, SIZEOF_CHARP);
if (alloc->free + aligned_size <= alloc->end)
{
rv= alloc->free;
alloc->free+= aligned_size;
}
else
rv= malloc(i);
return rv;
}
/*
dtoa_free() must be used to free values s returned by dtoa()
This is the counterpart of dtoa_alloc()
*/
static void dtoa_free(char *gptr, char *buf, size_t buf_size)
{
if (gptr < buf || gptr >= buf + buf_size)
free(gptr);
}
/* Bigint arithmetic functions */
/* Multiply by m and add a */
static Bigint *multadd(Bigint *b, int m, int a, Stack_alloc *alloc)
{
int i, wds;
ULong *x;
ULLong carry, y;
Bigint *b1;
wds= b->wds;
x= b->p.x;
i= 0;
carry= a;
do
{
y= *x * (ULLong)m + carry;
carry= y >> 32;
*x++= (ULong)(y & FFFFFFFF);
}
while (++i < wds);
if (carry)
{
if (wds >= b->maxwds)
{
b1= Balloc(b->k+1, alloc);
Bcopy(b1, b);
Bfree(b, alloc);
b= b1;
}
b->p.x[wds++]= (ULong) carry;
b->wds= wds;
}
return b;
}
static int hi0bits(register ULong x)
{
register int k= 0;
if (!(x & 0xffff0000))
{
k= 16;
x<<= 16;
}
if (!(x & 0xff000000))
{
k+= 8;
x<<= 8;
}
if (!(x & 0xf0000000))
{
k+= 4;
x<<= 4;
}
if (!(x & 0xc0000000))
{
k+= 2;
x<<= 2;
}
if (!(x & 0x80000000))
{
k++;
if (!(x & 0x40000000))
return 32;
}
return k;
}
static int lo0bits(ULong *y)
{
register int k;
register ULong x= *y;
if (x & 7)
{
if (x & 1)
return 0;
if (x & 2)
{
*y= x >> 1;
return 1;
}
*y= x >> 2;
return 2;
}
k= 0;
if (!(x & 0xffff))
{
k= 16;
x>>= 16;
}
if (!(x & 0xff))
{
k+= 8;
x>>= 8;
}
if (!(x & 0xf))
{
k+= 4;
x>>= 4;
}
if (!(x & 0x3))
{
k+= 2;
x>>= 2;
}
if (!(x & 1))
{
k++;
x>>= 1;
if (!x)
return 32;
}
*y= x;
return k;
}
/* Convert integer to Bigint number */
static Bigint *i2b(int i, Stack_alloc *alloc)
{
Bigint *b;
b= Balloc(1, alloc);
b->p.x[0]= i;
b->wds= 1;
return b;
}
/* Multiply two Bigint numbers */
static Bigint *mult(Bigint *a, Bigint *b, Stack_alloc *alloc)
{
Bigint *c;
int k, wa, wb, wc;
ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
ULong y;
ULLong carry, z;
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, alloc);
for (x= c->p.x, xa= x + wc; x < xa; x++)
*x= 0;
xa= a->p.x;
xae= xa + wa;
xb= b->p.x;
xbe= xb + wb;
xc0= c->p.x;
for (; xb < xbe; xc0++)
{
if ((y= *xb++))
{
x= xa;
xc= xc0;
carry= 0;
do
{
z= *x++ * (ULLong)y + *xc + carry;
carry= z >> 32;
*xc++= (ULong) (z & FFFFFFFF);
}
while (x < xae);
*xc= (ULong) carry;
}
}
for (xc0= c->p.x, xc= xc0 + wc; wc > 0 && !*--xc; --wc) ;
c->wds= wc;
return c;
}
/*
Precalculated array of powers of 5: tested to be enough for
vasting majority of dtoa_r cases.
*/
static ULong powers5[]=
{
625UL,
390625UL,
2264035265UL, 35UL,
2242703233UL, 762134875UL, 1262UL,
3211403009UL, 1849224548UL, 3668416493UL, 3913284084UL, 1593091UL,
781532673UL, 64985353UL, 253049085UL, 594863151UL, 3553621484UL,
3288652808UL, 3167596762UL, 2788392729UL, 3911132675UL, 590UL,
2553183233UL, 3201533787UL, 3638140786UL, 303378311UL, 1809731782UL,
3477761648UL, 3583367183UL, 649228654UL, 2915460784UL, 487929380UL,
1011012442UL, 1677677582UL, 3428152256UL, 1710878487UL, 1438394610UL,
2161952759UL, 4100910556UL, 1608314830UL, 349175UL
};
static Bigint p5_a[]=
{
/* { x } - k - maxwds - sign - wds */
{ { powers5 }, 1, 1, 0, 1 },
{ { powers5 + 1 }, 1, 1, 0, 1 },
{ { powers5 + 2 }, 1, 2, 0, 2 },
{ { powers5 + 4 }, 2, 3, 0, 3 },
{ { powers5 + 7 }, 3, 5, 0, 5 },
{ { powers5 + 12 }, 4, 10, 0, 10 },
{ { powers5 + 22 }, 5, 19, 0, 19 }
};
#define P5A_MAX (sizeof(p5_a)/sizeof(*p5_a) - 1)
static Bigint *pow5mult(Bigint *b, int k, Stack_alloc *alloc)
{
Bigint *b1, *p5, *p51=NULL;
int i;
static int p05[3]= { 5, 25, 125 };
my_bool overflow= FALSE;
if ((i= k & 3))
b= multadd(b, p05[i-1], 0, alloc);
if (!(k>>= 2))
return b;
p5= p5_a;
for (;;)
{
if (k & 1)
{
b1= mult(b, p5, alloc);
Bfree(b, alloc);
b= b1;
}
if (!(k>>= 1))
break;
/* Calculate next power of 5 */
if (overflow)
{
p51= mult(p5, p5, alloc);
Bfree(p5, alloc);
p5= p51;
}
else if (p5 < p5_a + P5A_MAX)
++p5;
else if (p5 == p5_a + P5A_MAX)
{
p5= mult(p5, p5, alloc);
overflow= TRUE;
}
}
if (p51)
Bfree(p51, alloc);
return b;
}
static Bigint *lshift(Bigint *b, int k, Stack_alloc *alloc)
{
int i, k1, n, n1;
Bigint *b1;
ULong *x, *x1, *xe, z;
n= k >> 5;
k1= b->k;
n1= n + b->wds + 1;
for (i= b->maxwds; n1 > i; i<<= 1)
k1++;
b1= Balloc(k1, alloc);
x1= b1->p.x;
for (i= 0; i < n; i++)
*x1++= 0;
x= b->p.x;