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mariadb/strings/decimal.c
unknown a0d5302e17 Fix for bug 8416 (bigint test fails on PPC) 
strings/decimal.c:
  <0 doesn't work properly on PPC in that case.
2005-02-13 01:36:35 +04:00

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/* Copyright (C) 2000 MySQL AB
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 2 of the License, 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., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
#line __LINE__ "decimal.c"
/*
=======================================================================
NOTE: this library implements SQL standard "exact numeric" type
and is not at all generic, but rather intentinally crippled to
follow the standard :)
=======================================================================
Quoting the standard
(SQL:2003, Part 2 Foundations, aka ISO/IEC 9075-2:2003)
4.4.2 Characteristics of numbers, page 27:
An exact numeric type has a precision P and a scale S. P is a positive
integer that determines the number of significant digits in a
particular radix R, where R is either 2 or 10. S is a non-negative
integer. Every value of an exact numeric type of scale S is of the
form n*10^{-S}, where n is an integer such that ­-R^P <= n <= R^P.
[...]
If an assignment of some number would result in a loss of its most
significant digit, an exception condition is raised. If least
significant digits are lost, implementation-defined rounding or
truncating occurs, with no exception condition being raised.
[...]
Whenever an exact or approximate numeric value is assigned to an exact
numeric value site, an approximation of its value that preserves
leading significant digits after rounding or truncating is represented
in the declared type of the target. The value is converted to have the
precision and scale of the target. The choice of whether to truncate
or round is implementation-defined.
[...]
All numeric values between the smallest and the largest value,
inclusive, in a given exact numeric type have an approximation
obtained by rounding or truncation for that type; it is
implementation-defined which other numeric values have such
approximations.
5.3 <literal>, page 143
<exact numeric literal> ::=
<unsigned integer> [ <period> [ <unsigned integer> ] ]
| <period> <unsigned integer>
6.1 <data type>, page 165:
19) The <scale> of an <exact numeric type> shall not be greater than
the <precision> of the <exact numeric type>.
20) For the <exact numeric type>s DECIMAL and NUMERIC:
a) The maximum value of <precision> is implementation-defined.
<precision> shall not be greater than this value.
b) The maximum value of <scale> is implementation-defined. <scale>
shall not be greater than this maximum value.
21) NUMERIC specifies the data type exact numeric, with the decimal
precision and scale specified by the <precision> and <scale>.
22) DECIMAL specifies the data type exact numeric, with the decimal
scale specified by the <scale> and the implementation-defined
decimal precision equal to or greater than the value of the
specified <precision>.
6.26 <numeric value expression>, page 241:
1) If the declared type of both operands of a dyadic arithmetic
operator is exact numeric, then the declared type of the result is
an implementation-defined exact numeric type, with precision and
scale determined as follows:
a) Let S1 and S2 be the scale of the first and second operands
respectively.
b) The precision of the result of addition and subtraction is
implementation-defined, and the scale is the maximum of S1 and S2.
c) The precision of the result of multiplication is
implementation-defined, and the scale is S1 + S2.
d) The precision and scale of the result of division are
implementation-defined.
*/
#include <my_global.h>
#include <m_ctype.h>
#include <myisampack.h>
#include <my_sys.h> /* for my_alloca */
#include <m_string.h>
#include <decimal.h>
typedef decimal_digit dec1;
typedef longlong dec2;
#define DIG_PER_DEC1 9
#define DIG_MASK 100000000
#define DIG_BASE 1000000000
#define DIG_MAX 999999999
#define DIG_BASE2 LL(1000000000000000000)
#define ROUND_UP(X) (((X)+DIG_PER_DEC1-1)/DIG_PER_DEC1)
static const dec1 powers10[DIG_PER_DEC1+1]={
1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000};
static const int dig2bytes[DIG_PER_DEC1+1]={0, 1, 1, 2, 2, 3, 3, 4, 4, 4};
static const dec1 frac_max[DIG_PER_DEC1-1]={
900000000, 990000000, 999000000,
999900000, 999990000, 999999000,
999999900, 999999990 };
#define sanity(d) DBUG_ASSERT((d)->len >0 && ((d)->buf[0] | \
(d)->buf[(d)->len-1] | 1))
#define FIX_INTG_FRAC_ERROR(len, intg1, frac1, error) \
do \
{ \
if (unlikely(intg1+frac1 > (len))) \
{ \
if (unlikely(intg1 > (len))) \
{ \
intg1=(len); \
frac1=0; \
error=E_DEC_OVERFLOW; \
} \
else \
{ \
frac1=(len)-intg1; \
error=E_DEC_TRUNCATED; \
} \
} \
else \
error=E_DEC_OK; \
} while(0)
#define ADD(to, from1, from2, carry) /* assume carry <= 1 */ \
do \
{ \
dec1 a=(from1)+(from2)+(carry); \
if (((carry)= a >= DIG_BASE)) /* no division here! */ \
a-=DIG_BASE; \
(to)=a; \
} while(0)
#define ADD2(to, from1, from2, carry) \
do \
{ \
dec1 a=(from1)+(from2)+(carry); \
if (((carry)= a >= DIG_BASE)) \
a-=DIG_BASE; \
if (unlikely(a >= DIG_BASE)) \
{ \
a-=DIG_BASE; \
carry++; \
} \
(to)=a; \
} while(0)
#define SUB(to, from1, from2, carry) /* to=from1-from2 */ \
do \
{ \
dec1 a=(from1)-(from2)-(carry); \
if (((carry)= a < 0)) \
a+=DIG_BASE; \
(to)=a; \
} while(0)
#define SUB2(to, from1, from2, carry) /* to=from1-from2 */ \
do \
{ \
dec1 a=(from1)-(from2)-(carry); \
if (((carry)= a < 0)) \
a+=DIG_BASE; \
if (unlikely(a < 0)) \
{ \
a+=DIG_BASE; \
carry++; \
} \
(to)=a; \
} while(0)
/*
Get maximum value for given precision and scale
SYNOPSIS
max_decimal()
precision/scale - see decimal_bin_size() below
to - decimal where where the result will be stored
to->buf and to->len must be set.
*/
void max_decimal(int precision, int frac, decimal *to)
{
int intpart;
dec1 *buf= to->buf;
DBUG_ASSERT(precision && precision >= frac);
to->sign= 0;
if ((intpart= to->intg= (precision - frac)))
{
int firstdigits= intpart % DIG_PER_DEC1;
if (firstdigits)
*buf++= powers10[firstdigits] - 1; /* get 9 99 999 ... */
for(intpart/= DIG_PER_DEC1; intpart; intpart--)
*buf++= DIG_MAX;
}
if ((to->frac= frac))
{
int lastdigits= frac % DIG_PER_DEC1;
for(frac/= DIG_PER_DEC1; frac; frac--)
*buf++= DIG_MAX;
if (lastdigits)
*buf= frac_max[lastdigits - 1];
}
}
static dec1 *remove_leading_zeroes(decimal *from, int *intg_result)
{
int intg= from->intg, i;
dec1 *buf0= from->buf;
i= ((intg - 1) % DIG_PER_DEC1) + 1;
while (intg > 0 && *buf0 == 0)
{
intg-= i;
i= DIG_PER_DEC1;
buf0++;
}
if (intg > 0)
{
for (i= (intg - 1) % DIG_PER_DEC1; *buf0 < powers10[i--]; intg--) ;
DBUG_ASSERT(intg > 0);
}
else
intg=0;
*intg_result= intg;
return buf0;
}
/*
Remove ending 0 digits from fraction part
SYNOPSIS
decimal_optimize_fraction()
from number for processing
*/
void decimal_optimize_fraction(decimal *from)
{
int frac= from->frac, i;
dec1 *buf0= from->buf + ROUND_UP(from->intg) + ROUND_UP(frac) - 1;
if (frac == 0)
return;
i= ((frac - 1) % DIG_PER_DEC1 + 1);
while (frac > 0 && *buf0 == 0)
{
frac-= i;
i= DIG_PER_DEC1;
buf0--;
}
if (frac > 0)
{
for (i= DIG_PER_DEC1 - ((frac - 1) % DIG_PER_DEC1);
*buf0 % powers10[i++] == 0;
frac--);
}
from->frac= frac;
}
/*
Convert decimal to its printable string representation
SYNOPSIS
decimal2string()
from - value to convert
to - points to buffer where string representation
should be stored
*to_len - in: size of to buffer
out: length of the actually written string
fixed_precision - 0 if representation can be variable length and
fixed_decimals will not be checked in this case.
Put number as with fixed point position with this
number of digits (sign counted and decimal point is
counted)
fixed_decimals - number digits after point.
filler - character to fill gaps in case of fixed_precision > 0
RETURN VALUE
E_DEC_OK/E_DEC_TRUNCATED/E_DEC_OVERFLOW
*/
int decimal2string(decimal *from, char *to, int *to_len,
int fixed_precision, int fixed_decimals,
char filler)
{
int len, intg, frac=from->frac, i, intg_len, frac_len, fill;
/* number digits before decimal point */
int fixed_intg= (fixed_precision ?
(fixed_precision -
(from->sign ? 1 : 0) -
(fixed_decimals ? 1 : 0) -
fixed_decimals) :
0);
int error=E_DEC_OK;
char *s=to;
dec1 *buf, *buf0=from->buf, tmp;
DBUG_ASSERT(*to_len >= 2+from->sign);
DBUG_ASSERT(fixed_precision == 0 ||
(fixed_precision < *to_len &&
fixed_precision > ((from->sign ? 1 : 0) +
(fixed_decimals ? 1 : 0))));
/* removing leading zeroes */
buf0= remove_leading_zeroes(from, &intg);
if (unlikely(intg+frac==0))
{
intg=1;
tmp=0;
buf0=&tmp;
}
intg_len= fixed_precision ? fixed_intg : (intg ? intg : 1);
frac_len= fixed_precision ? fixed_decimals : frac;
len= from->sign + intg_len + test(frac) + frac_len;
if (fixed_precision)
{
if (frac > fixed_decimals)
{
error= E_DEC_TRUNCATED;
frac= fixed_decimals;
}
if (intg > fixed_intg)
{
error= E_DEC_OVERFLOW;
intg= fixed_intg;
}
}
else if (unlikely(len > --*to_len)) /* reserve one byte for \0 */
{
int i=len-*to_len;
error= (frac && i <= frac + 1) ? E_DEC_TRUNCATED : E_DEC_OVERFLOW;
if (frac && i >= frac + 1) i--;
if (i > frac)
{
intg-= i-frac;
frac= 0;
}
else
frac-=i;
len= from->sign + intg_len + test(frac) + frac_len;
}
*to_len=len;
s[len]=0;
if (from->sign)
*s++='-';
if (frac)
{
char *s1= s + intg_len;
fill= frac_len - frac;
buf=buf0+ROUND_UP(intg);
*s1++='.';
for (; frac>0; frac-=DIG_PER_DEC1)
{
dec1 x=*buf++;
for (i=min(frac, DIG_PER_DEC1); i; i--)
{
dec1 y=x/DIG_MASK;
*s1++='0'+(uchar)y;
x-=y*DIG_MASK;
x*=10;
}
}
for(; fill; fill--)
*s1++=filler;
}
fill= intg_len - intg;
if (intg == 0)
fill--; /* symbol 0 before digital point */
for(; fill; fill--)
*s++=filler;
if (intg)
{
s+=intg;
for (buf=buf0+ROUND_UP(intg); intg>0; intg-=DIG_PER_DEC1)
{
dec1 x=*--buf;
for (i=min(intg, DIG_PER_DEC1); i; i--)
{
dec1 y=x/10;
*--s='0'+(uchar)(x-y*10);
x=y;
}
}
}
else
*s= '0';
return error;
}
/*
Return bounds of decimal digits in the number
SYNOPSIS
digits_bounds()
from - decimal number for processing
start_result - index (from 0 ) of first decimal digits will
be written by this address
end_result - index of position just after last decimal digit
be written by this address
*/
static void digits_bounds(decimal *from, int *start_result, int *end_result)
{
int start, stop, i;
dec1 *buf_beg= from->buf;
dec1 *end= from->buf + ROUND_UP(from->intg) + ROUND_UP(from->frac);
dec1 *buf_end= end - 1;
/* find non-zero digit from number begining */
while (buf_beg < end && *buf_beg == 0)
buf_beg++;
if (buf_beg >= end)
{
/* it is zero */
*start_result= *end_result= 0;
return;
}
/* find non-zero decimal digit from number begining */
if (buf_beg == from->buf && from->intg)
{
start= DIG_PER_DEC1 - (i= ((from->intg-1) % DIG_PER_DEC1 + 1));
i--;
}
else
{
i= DIG_PER_DEC1 - 1;
start= (buf_beg - from->buf) * DIG_PER_DEC1;
}
if (buf_beg < end)
for (; *buf_beg < powers10[i--]; start++) ;
*start_result= start; /* index of first decimal digit (from 0) */
/* find non-zero digit at the end */
while (buf_end > buf_beg && *buf_end == 0)
buf_end--;
/* find non-zero decimal digit from the end */
if (buf_end == end - 1 && from->frac)
{
stop= ((buf_end - from->buf) * DIG_PER_DEC1 +
(i= ((from->frac - 1) % DIG_PER_DEC1 + 1)));
i= DIG_PER_DEC1 - i + 1;
}
else
{
stop= (buf_end - from->buf + 1) * DIG_PER_DEC1;
i= 1;
}
for (; *buf_end % powers10[i++] == 0; stop--);
*end_result= stop; /* index of position after last decimal digit (from 0) */
}
/*
Left shift for alignment of data in buffer
SYNOPSIS
do_mini_left_shift()
dec pointer to decimal number which have to be shifted
shift number of decimal digits on which it should be shifted
beg/end bounds of decimal digits (see digits_bounds())
NOTE
Result fitting in the buffer should be garanted.
'shift' have to be from 1 to DIG_PER_DEC1-1 (inclusive)
*/
void do_mini_left_shift(decimal *dec, int shift, int beg, int last)
{
dec1 *from= dec->buf + ROUND_UP(beg + 1) - 1;
dec1 *end= dec->buf + ROUND_UP(last) - 1;
int c_shift= DIG_PER_DEC1 - shift;
DBUG_ASSERT(from >= dec->buf);
DBUG_ASSERT(end < dec->buf + dec->len);
if (beg % DIG_PER_DEC1 < shift)
*(from - 1)= (*from) / powers10[c_shift];
for(; from < end; from++)
*from= ((*from % powers10[c_shift]) * powers10[shift] +
(*(from + 1)) / powers10[c_shift]);
*from= (*from % powers10[c_shift]) * powers10[shift];
}
/*
Right shift for alignment of data in buffer
SYNOPSIS
do_mini_left_shift()
dec pointer to decimal number which have to be shifted
shift number of decimal digits on which it should be shifted
beg/end bounds of decimal digits (see digits_bounds())
NOTE
Result fitting in the buffer should be garanted.
'shift' have to be from 1 to DIG_PER_DEC1-1 (inclusive)
*/
void do_mini_right_shift(decimal *dec, int shift, int beg, int last)
{
dec1 *from= dec->buf + ROUND_UP(last) - 1;
dec1 *end= dec->buf + ROUND_UP(beg + 1) - 1;
int c_shift= DIG_PER_DEC1 - shift;
DBUG_ASSERT(from < dec->buf + dec->len);
DBUG_ASSERT(end >= dec->buf);
if (DIG_PER_DEC1 - ((last - 1) % DIG_PER_DEC1 + 1) < shift)
*(from + 1)= (*from % powers10[shift]) * powers10[c_shift];
for(; from > end; from--)
*from= (*from / powers10[shift] +
(*(from - 1) % powers10[shift]) * powers10[c_shift]);
*from= *from / powers10[shift];
}
/*
Shift of decimal digits in given number (with rounding if it need)
SYNOPSIS
decimal_shift()
dec number to be shifted
shift number of decimal positions
shift > 0 means shift to left shift
shift < 0 meand right shift
NOTE
In fact it is multipling on 10^shift.
RETURN
E_DEC_OK OK
E_DEC_OVERFLOW operation lead to overflow, number is untoched
E_DEC_TRUNCATED number was rounded to fit into buffer
*/
int decimal_shift(decimal *dec, int shift)
{
/* index of first non zero digit (all indexes from 0) */
int beg;
/* index of position after last decimal digit */
int end;
/* index of digit position just after point */
int point= ROUND_UP(dec->intg) * DIG_PER_DEC1;
/* new point position */
int new_point= point + shift;
/* number of digits in result */
int digits_int, digits_frac;
/* length of result and new fraction in big digits*/
int new_len, new_frac_len;
/* return code */
int err= E_DEC_OK;
int new_front;
if (shift == 0)
return E_DEC_OK;
digits_bounds(dec, &beg, &end);
if (beg == end)
{
decimal_make_zero(dec);
return E_DEC_OK;
}
digits_int= new_point - beg;
set_if_bigger(digits_int, 0);
digits_frac= end - new_point;
set_if_bigger(digits_frac, 0);
if ((new_len= ROUND_UP(digits_int) + (new_frac_len= ROUND_UP(digits_frac))) >
dec->len)
{
int lack= new_len - dec->len;
int diff;
if (new_frac_len < lack)
return E_DEC_OVERFLOW; /* lack more then we have in fraction */
/* cat off fraction part to allow new number to fit in our buffer */
err= E_DEC_TRUNCATED;
new_frac_len-= lack;
diff= digits_frac - (new_frac_len * DIG_PER_DEC1);
/* Make rounding method as parameter? */
decimal_round(dec, dec, end - point - diff, HALF_UP);
end-= diff;
digits_frac= new_frac_len * DIG_PER_DEC1;
if (end <= beg)
{
/*
we lost all digits (they will be shifted out of buffer), so we can
just return 0
*/
decimal_make_zero(dec);
return E_DEC_TRUNCATED;
}
}
if (shift % DIG_PER_DEC1)
{
int l_mini_shift, r_mini_shift, mini_shift;
int do_left;
/*
Calculate left/right shift to align decimal digits inside our bug
digits correctly
*/
if (shift > 0)
{
l_mini_shift= shift % DIG_PER_DEC1;
r_mini_shift= DIG_PER_DEC1 - l_mini_shift;
/*
It is left shift so prefer left shift, but if we have not place from
left, we have to have it from right, because we checked length of
result
*/
do_left= l_mini_shift <= beg;
DBUG_ASSERT(do_left || (dec->len * DIG_PER_DEC1 - end) >= r_mini_shift);
}
else
{
r_mini_shift= (-shift) % DIG_PER_DEC1;
l_mini_shift= DIG_PER_DEC1 - r_mini_shift;
/* see comment above */
do_left= !((dec->len * DIG_PER_DEC1 - end) >= r_mini_shift);
DBUG_ASSERT(!do_left || l_mini_shift <= beg);
}
if (do_left)
{
do_mini_left_shift(dec, l_mini_shift, beg, end);
mini_shift=- l_mini_shift;
}
else
{
do_mini_right_shift(dec, r_mini_shift, beg, end);
mini_shift= r_mini_shift;
}
new_point+= mini_shift;
/*
If number is shifted and correctly aligned in buffer we can
finish
*/
if (!(shift+= mini_shift) && (new_point - digits_int) < DIG_PER_DEC1)
{
dec->intg= digits_int;
dec->frac= digits_frac;
return err; /* already shifted as it should be */
}
beg+= mini_shift;
end+= mini_shift;
}
/* if new 'decimal front' is in first digit, we do not need move digits */
if ((new_front= (new_point - digits_int)) >= DIG_PER_DEC1 ||
new_front < 0)
{
/* need to move digits */
int d_shift;
dec1 *to, *barier;
if (new_front > 0)
{
/* move left */
d_shift= new_front / DIG_PER_DEC1;
to= dec->buf + (ROUND_UP(beg + 1) - 1 - d_shift);
barier= dec->buf + (ROUND_UP(end) - 1 - d_shift);
DBUG_ASSERT(to >= dec->buf);
DBUG_ASSERT(barier + d_shift < dec->buf + dec->len);
for(; to <= barier; to++)
*to= *(to + d_shift);
for(barier+= d_shift; to <= barier; to++)
*to= 0;
d_shift= -d_shift;
}
else
{
/* move right */
d_shift= (1 - new_front) / DIG_PER_DEC1;
to= dec->buf + ROUND_UP(end) - 1 + d_shift;
barier= dec->buf + ROUND_UP(beg + 1) - 1 + d_shift;
DBUG_ASSERT(to < dec->buf + dec->len);
DBUG_ASSERT(barier - d_shift >= dec->buf);
for(; to >= barier; to--)
*to= *(to - d_shift);
for(barier-= d_shift; to >= barier; to--)
*to= 0;
}
d_shift*= DIG_PER_DEC1;
beg+= d_shift;
end+= d_shift;
new_point+= d_shift;
}
/*
If there are gaps then fill ren with 0.
Only one of following 'for' loops will work becouse beg <= end
*/
beg= ROUND_UP(beg + 1) - 1;
end= ROUND_UP(end) - 1;
DBUG_ASSERT(new_point >= 0);
new_point= ROUND_UP(new_point) - 1;
for(; new_point > end; new_point--)
dec->buf[new_point]= 0;
for(; new_point < beg; new_point++)
dec->buf[new_point]= 0;
dec->intg= digits_int;
dec->frac= digits_frac;
return err;
}
/*
Convert string to decimal
SYNOPSIS
str2decl()
from - value to convert
to - decimal where where the result will be stored
to->buf and to->len must be set.
end - if not NULL, *end will be set to the char where
conversion ended
fixed - use to->intg, to->frac as limits for input number
NOTE
to->intg and to->frac can be modified even when fixed=1
(but only decreased, in this case)
RETURN VALUE
E_DEC_OK/E_DEC_TRUNCATED/E_DEC_OVERFLOW/E_DEC_BAD_NUM/E_DEC_OOM
*/
static int str2dec(char *from, decimal *to, char **end, my_bool fixed)
{
char *s=from, *s1, *endp;
int i, intg, frac, error, intg1, frac1;
dec1 x,*buf;
LINT_INIT(error);
sanity(to);
while (my_isspace(&my_charset_latin1, *s))
s++;
if ((to->sign= (*s == '-')))
s++;
else if (*s == '+')
s++;
s1=s;
while (my_isdigit(&my_charset_latin1, *s))
s++;
intg=s-s1;
if (*s=='.')
{
endp= s+1;
while (my_isdigit(&my_charset_latin1, *endp))
endp++;
frac= endp - s - 1;
}
else
{
frac= 0;
endp= s;
}
if (end)
*end= endp;
if (frac+intg == 0)
return E_DEC_BAD_NUM;
if (fixed)
{
if (frac > to->frac)
{
error=E_DEC_TRUNCATED;
frac=to->frac;
}
if (intg > to->intg)
{
error=E_DEC_OVERFLOW;
intg=to->intg;
}
intg1=ROUND_UP(intg);
frac1=ROUND_UP(frac);
if (intg1+frac1 > to->len)
return E_DEC_OOM;
}
else
{
intg1=ROUND_UP(intg);
frac1=ROUND_UP(frac);
FIX_INTG_FRAC_ERROR(to->len, intg1, frac1, error);
if (unlikely(error))
{
frac=frac1*DIG_PER_DEC1;
if (error == E_DEC_OVERFLOW)
intg=intg1*DIG_PER_DEC1;
}
}
/* Error is guranteed to be set here */
to->intg=intg;
to->frac=frac;
buf=to->buf+intg1;
s1=s;
for (x=0, i=0; intg; intg--)
{
x+= (*--s - '0')*powers10[i];
if (unlikely(++i == DIG_PER_DEC1))
{
*--buf=x;
x=0;
i=0;
}
}
if (i)
*--buf=x;
buf=to->buf+intg1;
for (x=0, i=0; frac; frac--)
{
x= (*++s1 - '0') + x*10;
if (unlikely(++i == DIG_PER_DEC1))
{
*buf++=x;
x=0;
i=0;
}
}
if (i)
*buf=x*powers10[DIG_PER_DEC1-i];
if (*endp == 'e' || *endp == 'E')
{
long exp= strtol(endp + 1, &endp, 10);
if (end)
*end= endp;
if (exp > INT_MAX/2)
return E_DEC_OVERFLOW;
if (exp < INT_MIN/2 && error != E_DEC_OVERFLOW)
return E_DEC_TRUNCATED;
if(error != E_DEC_OVERFLOW)
error= decimal_shift(to, exp);
}
return error;
}
int string2decimal(char *from, decimal *to, char **end)
{
return str2dec(from, to, end, 0);
}
int string2decimal_fixed(char *from, decimal *to, char **end)
{
return str2dec(from, to, end, 1);
}
/*
Convert decimal to double
SYNOPSIS
decimal2double()
from - value to convert
to - result will be stored there
RETURN VALUE
E_DEC_OK
*/
int decimal2double(decimal *from, double *to)
{
double x=0, t=DIG_BASE;
int intg, frac;
dec1 *buf=from->buf;
for (intg=from->intg; intg > 0; intg-=DIG_PER_DEC1)
x=x*DIG_BASE + *buf++;
for (frac=from->frac; frac > 0; frac-=DIG_PER_DEC1, t*=DIG_BASE)
x+=*buf++/t;
*to=from->sign ? -x : x;
return E_DEC_OK;
}
/*
Convert double to decimal
SYNOPSIS
double2decimal()
from - value to convert
to - result will be stored there
RETURN VALUE
E_DEC_OK/E_DEC_OVERFLOW/E_DEC_TRUNCATED
*/
int double2decimal(double from, decimal *to)
{
/* TODO: fix it, when we'll have dtoa */
char s[400];
sprintf(s, "%f", from);
return string2decimal(s, to, 0);
}
static int ull2dec(ulonglong from, decimal *to)
{
int intg1, error=E_DEC_OK;
ulonglong x=from;
dec1 *buf;
sanity(to);
for (intg1=1; from >= DIG_BASE; intg1++, from/=DIG_BASE);
if (unlikely(intg1 > to->len))
{
intg1=to->len;
error=E_DEC_OVERFLOW;
}
to->frac=0;
to->intg=intg1*DIG_PER_DEC1;
for (buf=to->buf+intg1; intg1; intg1--)
{
ulonglong y=x/DIG_BASE;
*--buf=(dec1)(x-y*DIG_BASE);
x=y;
}
return error;
}
int ulonglong2decimal(ulonglong from, decimal *to)
{
to->sign=0;
return ull2dec(from, to);
}
int longlong2decimal(longlong from, decimal *to)
{
if ((to->sign= from < 0))
return ull2dec(-from, to);
return ull2dec(from, to);
}
int decimal2ulonglong(decimal *from, ulonglong *to)
{
dec1 *buf=from->buf;
ulonglong x=0;
int intg, frac;
if (from->sign)
{
*to=ULL(0);
return E_DEC_OVERFLOW;
}
for (intg=from->intg; intg > 0; intg-=DIG_PER_DEC1)
{
ulonglong y=x;
x=x*DIG_BASE + *buf++;
if (unlikely(y > (ULONGLONG_MAX/DIG_BASE) || x < y))
{
*to=y;
return E_DEC_OVERFLOW;
}
}
*to=x;
for (frac=from->frac; unlikely(frac > 0); frac-=DIG_PER_DEC1)
if (*buf++)
return E_DEC_TRUNCATED;
return E_DEC_OK;
}
int decimal2longlong(decimal *from, longlong *to)
{
dec1 *buf=from->buf;
longlong x=0;
int intg, frac;
for (intg=from->intg; intg > 0; intg-=DIG_PER_DEC1)
{
longlong y=x;
/*
Attention: trick!
we're calculating -|from| instead of |from| here
because |LONGLONG_MIN| > LONGLONG_MAX
so we can convert -9223372036854775808 correctly
*/
x=x*DIG_BASE - *buf++;
if (unlikely(y < (LONGLONG_MIN/DIG_BASE) || x > y))
{
*to= from->sign ? y : -y;
return E_DEC_OVERFLOW;
}
}
/* boundary case: 9223372036854775808 */
if (unlikely(from->sign==0 && x < 0 && -x < 0))
{
*to= -1-x;
return E_DEC_OVERFLOW;
}
*to=from->sign ? x : -x;
for (frac=from->frac; unlikely(frac > 0); frac-=DIG_PER_DEC1)
if (*buf++)
return E_DEC_TRUNCATED;
return E_DEC_OK;
}
/*
Convert decimal to its binary fixed-length representation
two representations of the same length can be compared with memcmp
with the correct -1/0/+1 result
SYNOPSIS
decimal2bin()
from - value to convert
to - points to buffer where string representation should be stored
precision/scale - see decimal_bin_size() below
NOTE
the buffer is assumed to be of the size decimal_bin_size(precision, scale)
RETURN VALUE
E_DEC_OK/E_DEC_TRUNCATED/E_DEC_OVERFLOW
*/
int decimal2bin(decimal *from, char *to, int precision, int frac)
{
dec1 mask=from->sign ? -1 : 0, *buf1=from->buf, *stop1;
int error=E_DEC_OK, intg=precision-frac,
isize1, intg1, intg1x, from_intg,
intg0=intg/DIG_PER_DEC1,
frac0=frac/DIG_PER_DEC1,
intg0x=intg-intg0*DIG_PER_DEC1,
frac0x=frac-frac0*DIG_PER_DEC1,
frac1=from->frac/DIG_PER_DEC1,
frac1x=from->frac-frac1*DIG_PER_DEC1,
isize0=intg0*sizeof(dec1)+dig2bytes[intg0x],
fsize0=frac0*sizeof(dec1)+dig2bytes[frac0x],
fsize1=frac1*sizeof(dec1)+dig2bytes[frac1x];
char *orig_to= to;
buf1= remove_leading_zeroes(from, &from_intg);
if (unlikely(from_intg+fsize1==0))
{
mask=0; /* just in case */
intg=1;
buf1=&mask;
}
intg1=from_intg/DIG_PER_DEC1;
intg1x=from_intg-intg1*DIG_PER_DEC1;
isize1=intg1*sizeof(dec1)+dig2bytes[intg1x];
if (intg < from_intg)
{
buf1+=intg1-intg0+(intg1x>0)-(intg0x>0);
intg1=intg0; intg1x=intg0x;
error=E_DEC_OVERFLOW;
}
else if (isize0 > isize1)
{
while (isize0-- > isize1)
*to++= (char)mask;
}
if (fsize0 < fsize1)
{
frac1=frac0; frac1x=frac0x;
error=E_DEC_TRUNCATED;
}
else if (fsize0 > fsize1 && frac1x)
{
if (frac0 == frac1)
frac1x=frac0x;
else
{
frac1++;
frac1x=0;
}
}
/* intg1x part */
if (intg1x)
{
int i=dig2bytes[intg1x];
dec1 x=(*buf1++ % powers10[intg1x]) ^ mask;
switch (i)
{
case 1: mi_int1store(to, x); break;
case 2: mi_int2store(to, x); break;
case 3: mi_int3store(to, x); break;
case 4: mi_int4store(to, x); break;
default: DBUG_ASSERT(0);
}
to+=i;
}
/* intg1+frac1 part */
for (stop1=buf1+intg1+frac1; buf1 < stop1; to+=sizeof(dec1))
{
dec1 x=*buf1++ ^ mask;
DBUG_ASSERT(sizeof(dec1) == 4);
mi_int4store(to, x);
}
/* frac1x part */
if (frac1x)
{
dec1 x;
int i=dig2bytes[frac1x],
lim=(frac1 < frac0 ? DIG_PER_DEC1 : frac0x);
while (frac1x < lim && dig2bytes[frac1x] == i)
frac1x++;
x=(*buf1 / powers10[DIG_PER_DEC1 - frac1x]) ^ mask;
switch (i)
{
case 1: mi_int1store(to, x); break;
case 2: mi_int2store(to, x); break;
case 3: mi_int3store(to, x); break;
case 4: mi_int4store(to, x); break;
default: DBUG_ASSERT(0);
}
to+=i;
}
if (fsize0 > fsize1)
{
while (fsize0-- > fsize1)
*to++=(uchar)mask;
}
orig_to[0]^= 0x80;
return error;
}
/*
Restores decimal from its binary fixed-length representation
SYNOPSIS
bin2decimal()
from - value to convert
to - result
precision/scale - see decimal_bin_size() below
NOTE
see decimal2bin()
the buffer is assumed to be of the size decimal_bin_size(precision, scale)
RETURN VALUE
E_DEC_OK/E_DEC_TRUNCATED/E_DEC_OVERFLOW
*/
int bin2decimal(char *from, decimal *to, int precision, int scale)
{
int error=E_DEC_OK, intg=precision-scale,
intg0=intg/DIG_PER_DEC1, frac0=scale/DIG_PER_DEC1,
intg0x=intg-intg0*DIG_PER_DEC1, frac0x=scale-frac0*DIG_PER_DEC1,
intg1=intg0+(intg0x>0), frac1=frac0+(frac0x>0);
dec1 *buf=to->buf, mask=(*from & 0x80) ? 0 : -1;
char *stop;
char *d_copy;
int bin_size= decimal_bin_size(precision, scale);
sanity(to);
d_copy= (char *)my_alloca(bin_size);
memcpy(d_copy, from, bin_size);
d_copy[0]^= 0x80;
from= d_copy;
FIX_INTG_FRAC_ERROR(to->len, intg1, frac1, error);
if (unlikely(error))
{
if (intg1 < intg0+(intg0x>0))
{
from+=dig2bytes[intg0x]+sizeof(dec1)*(intg0-intg1);
frac0=frac0x=intg0x=0;
intg0=intg1;
}
else
{
frac0x=0;
frac0=frac1;
}
}
to->sign=(mask != 0);
to->intg=intg0*DIG_PER_DEC1+intg0x;
to->frac=frac0*DIG_PER_DEC1+frac0x;
if (intg0x)
{
int i=dig2bytes[intg0x];
dec1 x;
switch (i)
{
case 1: x=mi_sint1korr(from); break;
case 2: x=mi_sint2korr(from); break;
case 3: x=mi_sint3korr(from); break;
case 4: x=mi_sint4korr(from); break;
default: DBUG_ASSERT(0);
}
from+=i;
*buf=x ^ mask;
if (buf > to->buf || *buf != 0)
buf++;
else
to->intg-=intg0x;
}
for (stop=from+intg0*sizeof(dec1); from < stop; from+=sizeof(dec1))
{
DBUG_ASSERT(sizeof(dec1) == 4);
*buf=mi_sint4korr(from) ^ mask;
if (buf > to->buf || *buf != 0)
buf++;
else
to->intg-=DIG_PER_DEC1;
}
DBUG_ASSERT(to->intg >=0);
for (stop=from+frac0*sizeof(dec1); from < stop; from+=sizeof(dec1))
{
DBUG_ASSERT(sizeof(dec1) == 4);
*buf=mi_sint4korr(from) ^ mask;
buf++;
}
if (frac0x)
{
int i=dig2bytes[frac0x];
dec1 x;
switch (i)
{
case 1: x=mi_sint1korr(from); break;
case 2: x=mi_sint2korr(from); break;
case 3: x=mi_sint3korr(from); break;
case 4: x=mi_sint4korr(from); break;
default: DBUG_ASSERT(0);
}
*buf=(x ^ mask) * powers10[DIG_PER_DEC1 - frac0x];
buf++;
}
my_afree(d_copy);
return error;
}
/*
Returns the size of array to hold a decimal with given precision and scale
RETURN VALUE
size in dec1
(multiply by sizeof(dec1) to get the size if bytes)
*/
int decimal_size(int precision, int scale)
{
DBUG_ASSERT(scale >= 0 && precision > 0 && scale <= precision);
return ROUND_UP(precision-scale)+ROUND_UP(scale);
}
/*
Returns the size of array to hold a binary representation of a decimal
RETURN VALUE
size in bytes
*/
int decimal_bin_size(int precision, int scale)
{
int intg=precision-scale,
intg0=intg/DIG_PER_DEC1, frac0=scale/DIG_PER_DEC1,
intg0x=intg-intg0*DIG_PER_DEC1, frac0x=scale-frac0*DIG_PER_DEC1;
DBUG_ASSERT(scale >= 0 && precision > 0 && scale <= precision);
return intg0*sizeof(dec1)+dig2bytes[intg0x]+
frac0*sizeof(dec1)+dig2bytes[frac0x];
}
/*
Rounds the decimal to "scale" digits
SYNOPSIS
decimal_round()
from - decimal to round,
to - result buffer. from==to is allowed
scale - to what position to round. can be negative!
mode - round to nearest even or truncate
NOTES
scale can be negative !
one TRUNCATED error (line XXX below) isn't treated very logical :(
RETURN VALUE
E_DEC_OK/E_DEC_TRUNCATED
*/
int decimal_round(decimal *from, decimal *to, int scale, decimal_round_mode mode)
{
int frac0=scale>0 ? ROUND_UP(scale) : scale/DIG_PER_DEC1,
frac1=ROUND_UP(from->frac), round_digit,
intg0=ROUND_UP(from->intg), error=E_DEC_OK, len=to->len,
intg1=ROUND_UP(from->intg +
(((intg0 + frac0)>0) && (from->buf[0] == DIG_MAX)));
dec1 *buf0=from->buf, *buf1=to->buf, x, y, carry=0;
sanity(to);
switch (mode) {
case HALF_UP:
case HALF_EVEN: round_digit=5; break;
case CEILING: round_digit= from->sign ? 10 : 0; break;
case FLOOR: round_digit= from->sign ? 0 : 10; break;
case TRUNCATE: round_digit=10; break;
default: DBUG_ASSERT(0);
}
if (unlikely(frac0+intg0 > len))
{
frac0=len-intg0;
scale=frac0*DIG_PER_DEC1;
error=E_DEC_TRUNCATED;
}
if (scale+from->intg < 0)
{
decimal_make_zero(to);
return E_DEC_OK;
}
if (to != from || intg1>intg0)
{
dec1 *p0= buf0+intg0+max(frac1, frac0);
dec1 *p1= buf1+intg1+max(frac1, frac0);
to->buf[0]= 0;
while (buf0 < p0)
*(--p1) = *(--p0);
intg0= intg1;
buf0=to->buf;
buf1=to->buf;
to->sign=from->sign;
to->intg=min(intg0, len)*DIG_PER_DEC1;
}
if (frac0 > frac1)
{
buf1+=intg0+frac1;
while (frac0-- > frac1)
*buf1++=0;
goto done;
}
if (scale >= from->frac)
goto done; /* nothing to do */
buf0+=intg0+frac0-1;
buf1+=intg0+frac0-1;
if (scale == frac0*DIG_PER_DEC1)
{
DBUG_ASSERT(frac0+intg0 >= 0);
x=buf0[1]/DIG_MASK;
if (x > round_digit ||
(round_digit == 5 && x == 5 && (mode == HALF_UP ||
(frac0+intg0 > 0 && *buf0 & 1))))
{
if (frac0+intg0>0)
(*buf1)++;
else
*(++buf1)=DIG_BASE;
}
}
else
{
int pos=frac0*DIG_PER_DEC1-scale-1;
DBUG_ASSERT(frac0+intg0 > 0);
x=*buf1 / powers10[pos];
y=x % 10;
if (y > round_digit ||
(round_digit == 5 && y == 5 && (mode == HALF_UP || (x/10) & 1)))
x+=10;
*buf1=powers10[pos]*(x-y);
}
if (frac0 < 0)
{
dec1 *end=to->buf+intg0, *buf=buf1+1;
while (buf < end)
*buf++=0;
}
if (*buf1 >= DIG_BASE)
{
carry=1;
*buf1-=DIG_BASE;
while (carry && --buf1 >= to->buf)
ADD(*buf1, *buf1, 0, carry);
if (unlikely(carry))
{
/* shifting the number to create space for new digit */
if (frac0+intg0 >= len)
{
frac0--;
scale=frac0*DIG_PER_DEC1;
error=E_DEC_TRUNCATED; /* XXX */
}
for (buf1=to->buf+intg0+max(frac0,0); buf1 > to->buf; buf1--)
{
buf1[0]=buf1[-1];
}
*buf1=1;
to->intg++;
}
}
else
{
while (unlikely(*buf1 == 0) && buf1 >= to->buf)
buf1--;
if (buf1 < to->buf)
{
decimal_make_zero(to);
return E_DEC_OK;
}
}
if (scale<0) scale=0;
done:
to->frac=scale;
return error;
}
/*
Returns the size of the result of the operation
SYNOPSIS
decimal_result_size()
from1 - operand of the unary operation or first operand of the
binary operation
from2 - second operand of the binary operation
op - operation. one char '+', '-', '*', '/' are allowed
others may be added later
param - extra param to the operation. unused for '+', '-', '*'
scale increment for '/'
NOTE
returned valued may be larger than the actual buffer requred
in the operation, as decimal_result_size, by design, operates on
precision/scale values only and not on the actual decimal number
RETURN VALUE
size of to->buf array in dec1 elements. to get size in bytes
multiply by sizeof(dec1)
*/
int decimal_result_size(decimal *from1, decimal *from2, char op, int param)
{
switch (op) {
case '-':
return ROUND_UP(max(from1->intg, from2->intg)) +
ROUND_UP(max(from1->frac, from2->frac));
case '+':
return ROUND_UP(max(from1->intg, from2->intg)+1) +
ROUND_UP(max(from1->frac, from2->frac));
case '*':
return ROUND_UP(from1->intg+from2->intg)+
ROUND_UP(from1->frac)+ROUND_UP(from2->frac);
case '/':
return ROUND_UP(from1->intg+from2->intg+1+from1->frac+from2->frac+param);
default: DBUG_ASSERT(0);
}
return -1; /* shut up the warning */
}
static int do_add(decimal *from1, decimal *from2, decimal *to)
{
int intg1=ROUND_UP(from1->intg), intg2=ROUND_UP(from2->intg),
frac1=ROUND_UP(from1->frac), frac2=ROUND_UP(from2->frac),
frac0=max(frac1, frac2), intg0=max(intg1, intg2), error;
dec1 *buf1, *buf2, *buf0, *stop, *stop2, x, carry;
sanity(to);
/* is there a need for extra word because of carry ? */
x=intg1 > intg2 ? from1->buf[0] :
intg2 > intg1 ? from2->buf[0] :
from1->buf[0] + from2->buf[0] ;
if (unlikely(x > DIG_MASK*9)) /* yes, there is */
{
intg0++;
to->buf[0]=0; /* safety */
}
FIX_INTG_FRAC_ERROR(to->len, intg0, frac0, error);
buf0=to->buf+intg0+frac0;
to->sign=from1->sign;
to->frac=max(from1->frac, from2->frac);
to->intg=intg0*DIG_PER_DEC1;
if (unlikely(error))
{
set_if_smaller(to->frac, frac0*DIG_PER_DEC1);
set_if_smaller(frac1, frac0);
set_if_smaller(frac2, frac0);
set_if_smaller(intg1, intg0);
set_if_smaller(intg2, intg0);
}
/* part 1 - max(frac) ... min (frac) */
if (frac1 > frac2)
{
buf1=from1->buf+intg1+frac1;
stop=from1->buf+intg1+frac2;
buf2=from2->buf+intg2+frac2;
stop2=from1->buf+(intg1 > intg2 ? intg1-intg2 : 0);
}
else
{
buf1=from2->buf+intg2+frac2;
stop=from2->buf+intg2+frac1;
buf2=from1->buf+intg1+frac1;
stop2=from2->buf+(intg2 > intg1 ? intg2-intg1 : 0);
}
while (buf1 > stop)
*--buf0=*--buf1;
/* part 2 - min(frac) ... min(intg) */
carry=0;
while (buf1 > stop2)
{
ADD(*--buf0, *--buf1, *--buf2, carry);
}
/* part 3 - min(intg) ... max(intg) */
buf1= intg1 > intg2 ? ((stop=from1->buf)+intg1-intg2) :
((stop=from2->buf)+intg2-intg1) ;
while (buf1 > stop)
{
ADD(*--buf0, *--buf1, 0, carry);
}
if (unlikely(carry))
*--buf0=1;
DBUG_ASSERT(buf0 == to->buf || buf0 == to->buf+1);
return error;
}
/* to=from1-from2.
if to==0, return -1/0/+1 - the result of the comparison */
static int do_sub(decimal *from1, decimal *from2, decimal *to)
{
int intg1=ROUND_UP(from1->intg), intg2=ROUND_UP(from2->intg),
frac1=ROUND_UP(from1->frac), frac2=ROUND_UP(from2->frac);
int frac0=max(frac1, frac2), error;
dec1 *buf1, *buf2, *buf0, *stop1, *stop2, *start1, *start2, carry=0;
/* let carry:=1 if from2 > from1 */
start1=buf1=from1->buf; stop1=buf1+intg1;
start2=buf2=from2->buf; stop2=buf2+intg2;
if (unlikely(*buf1 == 0))
{
while (buf1 < stop1 && *buf1 == 0)
buf1++;
start1=buf1;
intg1=stop1-buf1;
}
if (unlikely(*buf2 == 0))
{
while (buf2 < stop2 && *buf2 == 0)
buf2++;
start2=buf2;
intg2=stop2-buf2;
}
if (intg2 > intg1)
carry=1;
else if (intg2 == intg1)
{
while (unlikely(stop1[frac1-1] == 0))
frac1--;
while (unlikely(stop2[frac2-1] == 0))
frac2--;
while (buf1 < stop1+frac1 && buf2 < stop2+frac2 && *buf1 == *buf2)
buf1++, buf2++;
if (buf1 < stop1+frac1)
if (buf2 < stop2+frac2)
carry= *buf2 > *buf1;
else
carry= 0;
else
if (buf2 < stop2+frac2)
carry=1;
else /* short-circuit everything: from1 == from2 */
{
if (to == 0) /* decimal_cmp() */
return 0;
decimal_make_zero(to);
return E_DEC_OK;
}
}
if (to == 0) /* decimal_cmp() */
return carry == from1->sign ? 1 : -1;
sanity(to);
to->sign=from1->sign;
/* ensure that always from1 > from2 (and intg1 >= intg2) */
if (carry)
{
swap_variables(decimal *,from1,from1);
swap_variables(dec1 *,start1, start2);
swap_variables(int,intg1,intg2);
swap_variables(int,frac1,frac2);
to->sign= 1 - to->sign;
}
FIX_INTG_FRAC_ERROR(to->len, intg1, frac0, error);
buf0=to->buf+intg1+frac0;
to->frac=max(from1->frac, from2->frac);
to->intg=intg1*DIG_PER_DEC1;
if (unlikely(error))
{
set_if_smaller(to->frac, frac0*DIG_PER_DEC1);
set_if_smaller(frac1, frac0);
set_if_smaller(frac2, frac0);
set_if_smaller(intg2, intg1);
}
carry=0;
/* part 1 - max(frac) ... min (frac) */
if (frac1 > frac2)
{
buf1=start1+intg1+frac1;
stop1=start1+intg1+frac2;
buf2=start2+intg2+frac2;
while (frac0-- > frac1)
*--buf0=0;
while (buf1 > stop1)
*--buf0=*--buf1;
}
else
{
buf1=start1+intg1+frac1;
buf2=start2+intg2+frac2;
stop2=start2+intg2+frac1;
while (frac0-- > frac2)
*--buf0=0;
while (buf2 > stop2)
{
SUB(*--buf0, 0, *--buf2, carry);
}
}
/* part 2 - min(frac) ... intg2 */
while (buf2 > start2)
{
SUB(*--buf0, *--buf1, *--buf2, carry);
}
/* part 3 - intg2 ... intg1 */
while (carry && buf1 > start1)
{
SUB(*--buf0, *--buf1, 0, carry);
}
while (buf1 > start1)
*--buf0=*--buf1;
while (buf0 > to->buf)
*--buf0=0;
return error;
}
int decimal_add(decimal *from1, decimal *from2, decimal *to)
{
if (likely(from1->sign == from2->sign))
return do_add(from1, from2, to);
return do_sub(from1, from2, to);
}
int decimal_sub(decimal *from1, decimal *from2, decimal *to)
{
if (likely(from1->sign == from2->sign))
return do_sub(from1, from2, to);
return do_add(from1, from2, to);
}
int decimal_cmp(decimal *from1, decimal *from2)
{
if (likely(from1->sign == from2->sign))
return do_sub(from1, from2, 0);
return from1->sign > from2->sign ? -1 : 1;
}
int decimal_is_zero(decimal *from)
{
dec1 *buf1=from->buf,
*end=buf1+ROUND_UP(from->intg)+ROUND_UP(from->frac);
while (buf1 < end)
if (*buf1++)
return 0;
return 1;
}
/*
multiply two decimals
SYNOPSIS
decimal_mul()
from1, from2 - factors
to - product
RETURN VALUE
E_DEC_OK/E_DEC_TRUNCATED/E_DEC_OVERFLOW;
NOTES
in this implementation, with sizeof(dec1)=4 we have DIG_PER_DEC1=9,
and 63-digit number will take only 7 dec1 words (basically a 7-digit
"base 999999999" number). Thus there's no need in fast multiplication
algorithms, 7-digit numbers can be multiplied with a naive O(n*n)
method.
XXX if this library is to be used with huge numbers of thousands of
digits, fast multiplication must be implemented.
*/
int decimal_mul(decimal *from1, decimal *from2, decimal *to)
{
int intg1=ROUND_UP(from1->intg), intg2=ROUND_UP(from2->intg),
frac1=ROUND_UP(from1->frac), frac2=ROUND_UP(from2->frac),
intg0=ROUND_UP(from1->intg+from2->intg),
frac0=frac1+frac2, error, i, j;
dec1 *buf1=from1->buf+intg1, *buf2=from2->buf+intg2, *buf0,
*start2, *stop2, *stop1, *start0, carry;
sanity(to);
i=intg0;
j=frac0;
FIX_INTG_FRAC_ERROR(to->len, intg0, frac0, error);
to->sign=from1->sign != from2->sign;
to->frac=from1->frac+from2->frac;
to->intg=intg0*DIG_PER_DEC1;
if (unlikely(error))
{
set_if_smaller(to->frac, frac0*DIG_PER_DEC1);
set_if_smaller(to->intg, intg0*DIG_PER_DEC1);
if (unlikely(i > intg0))
{
i-=intg0;
j=i >> 1;
intg1-= j;
intg2-=i-j;
frac1=frac2=0; /* frac0 is already 0 here */
}
else
{
j-=frac0;
i=j >> 1;
frac1-= i;
frac2-=j-i;
}
}
start0=to->buf+intg0+frac0-1;
start2=buf2+frac2-1;
stop1=buf1-intg1;
stop2=buf2-intg2;
bzero(to->buf, (intg0+frac0)*sizeof(dec1));
for (buf1+=frac1-1; buf1 >= stop1; buf1--, start0--)
{
carry=0;
for (buf0=start0, buf2=start2; buf2 >= stop2; buf2--, buf0--)
{
dec1 hi, lo;
dec2 p= ((dec2)*buf1) * ((dec2)*buf2);
hi=(dec1)(p/DIG_BASE);
lo=(dec1)(p-((dec2)hi)*DIG_BASE);
ADD2(*buf0, *buf0, lo, carry);
carry+=hi;
}
for (; carry; buf0--)
ADD(*buf0, *buf0, 0, carry);
}
return error;
}
/*
naive division algorithm (Knuth's Algorithm D in 4.3.1) -
it's ok for short numbers
also we're using alloca() to allocate a temporary buffer
XXX if this library is to be used with huge numbers of thousands of
digits, fast division must be implemented and alloca should be
changed to malloc (or at least fallback to malloc if alloca() fails)
but then, decimal_mod() should be rewritten too :(
*/
static int do_div_mod(decimal *from1, decimal *from2,
decimal *to, decimal *mod, int scale_incr)
{
int frac1=ROUND_UP(from1->frac)*DIG_PER_DEC1, prec1=from1->intg+frac1,
frac2=ROUND_UP(from2->frac)*DIG_PER_DEC1, prec2=from2->intg+frac2,
error, i, intg0, frac0, len1, len2, dlen1, dintg, div=(!mod);
dec1 *buf0, *buf1=from1->buf, *buf2=from2->buf, *tmp1,
*start2, *stop2, *stop1, *stop0, norm2, carry, *start1;
dec2 norm_factor, x, guess, y;
LINT_INIT(error);
if (mod)
to=mod;
sanity(to);
/* removing all the leading zeroes */
i=((prec1-1) % DIG_PER_DEC1)+1;
while (prec1 > 0 && *buf1 == 0)
{
prec1-=i;
i=DIG_PER_DEC1;
buf1++;
}
if (prec1 <= 0)
{ /* short-circuit everything: from1 == 0 */
decimal_make_zero(to);
return E_DEC_OK;
}
for (i=(prec1-1) % DIG_PER_DEC1; *buf1 < powers10[i--]; prec1--) ;
DBUG_ASSERT(prec1 > 0);
i=((prec2-1) % DIG_PER_DEC1)+1;
while (prec2 > 0 && *buf2 == 0)
{
prec2-=i;
i=DIG_PER_DEC1;
buf2++;
}
if (prec2 <= 0) /* short-circuit everything: from2 == 0 */
return E_DEC_DIV_ZERO;
for (i=(prec2-1) % DIG_PER_DEC1; *buf2 < powers10[i--]; prec2--) ;
DBUG_ASSERT(prec2 > 0);
/* let's fix scale_incr, taking into account frac1,frac2 increase */
if ((scale_incr-= frac1 - from1->frac + frac2 - from2->frac) < 0)
scale_incr=0;
dintg=(prec1-frac1)-(prec2-frac2)+(*buf1 >= *buf2);
if (dintg < 0)
{
dintg/=DIG_PER_DEC1;
intg0=0;
}
else
intg0=ROUND_UP(dintg);
if (mod)
{
/* we're calculating N1 % N2.
The result will have
frac=max(frac1, frac2), as for subtraction
intg=intg2
*/
to->sign=from1->sign;
to->frac=max(from1->frac, from2->frac);
frac0=0;
}
else
{
/*
we're calculating N1/N2. N1 is in the buf1, has prec1 digits
N2 is in the buf2, has prec2 digits. Scales are frac1 and
frac2 accordingly.
Thus, the result will have
frac = ROUND_UP(frac1+frac2+scale_incr)
and
intg = (prec1-frac1) - (prec2-frac2) + 1
prec = intg+frac
*/
frac0=ROUND_UP(frac1+frac2+scale_incr);
FIX_INTG_FRAC_ERROR(to->len, intg0, frac0, error);
to->sign=from1->sign != from2->sign;
to->intg=intg0*DIG_PER_DEC1;
to->frac=frac0*DIG_PER_DEC1;
}
buf0=to->buf;
stop0=buf0+intg0+frac0;
if (likely(div))
while (dintg++ < 0)
*buf0++=0;
len1=(i=ROUND_UP(prec1))+ROUND_UP(2*frac2+scale_incr+1) + 1;
set_if_bigger(len1, 3);
if (!(tmp1=(dec1 *)my_alloca(len1*sizeof(dec1))))
return E_DEC_OOM;
memcpy(tmp1, buf1, i*sizeof(dec1));
bzero(tmp1+i, (len1-i)*sizeof(dec1));
start1=tmp1;
stop1=start1+len1;
start2=buf2;
stop2=buf2+ROUND_UP(prec2)-1;
/* removing end zeroes */
while (*stop2 == 0 && stop2 >= start2)
stop2--;
len2= ++stop2 - start2;
/*
calculating norm2 (normalized *start2) - we need *start2 to be large
(at least > DIG_BASE/2), but unlike Knuth's Alg. D we don't want to
normalize input numbers (as we don't make a copy of the divisor).
Thus we normalize first dec1 of buf2 only, and we'll normalize *start1
on the fly for the purpose of guesstimation only.
It's also faster, as we're saving on normalization of buf2
*/
norm_factor=DIG_BASE/(*start2+1);
norm2=(dec1)(norm_factor*start2[0]);
if (likely(len2>1))
norm2+=(dec1)(norm_factor*start2[1]/DIG_BASE);
/* main loop */
for ( ; buf0 < stop0; buf0++)
{
/* short-circuit, if possible */
if (unlikely(*start1 == 0))
{
start1++;
if (likely(div))
*buf0=0;
continue;
}
/* D3: make a guess */
if (*start1 >= *start2)
{
x=start1[0];
y=start1[1];
dlen1=len2-1;
}
else
{
x=((dec2)start1[0])*DIG_BASE+start1[1];
y=start1[2];
dlen1=len2;
}
guess=(norm_factor*x+norm_factor*y/DIG_BASE)/norm2;
if (unlikely(guess >= DIG_BASE))
guess=DIG_BASE-1;
if (likely(len2>1))
{
/* hmm, this is a suspicious trick - I removed normalization here */
if (start2[1]*guess > (x-guess*start2[0])*DIG_BASE+y)
guess--;
if (unlikely(start2[1]*guess > (x-guess*start2[0])*DIG_BASE+y))
guess--;
DBUG_ASSERT(start2[1]*guess <= (x-guess*start2[0])*DIG_BASE+y);
}
/* D4: multiply and subtract */
buf2=stop2;
buf1=start1+dlen1;
DBUG_ASSERT(buf1 < stop1);
for (carry=0; buf2 > start2; buf1--)
{
dec1 hi, lo;
x=guess * (*--buf2);
hi=(dec1)(x/DIG_BASE);
lo=(dec1)(x-((dec2)hi)*DIG_BASE);
SUB2(*buf1, *buf1, lo, carry);
carry+=hi;
}
for (; buf1 >= start1; buf1--)
{
SUB2(*buf1, *buf1, 0, carry);
}
/* D5: check the remainder */
if (unlikely(carry))
{
DBUG_ASSERT(carry==1);
/* D6: correct the guess */
guess--;
buf2=stop2;
buf1=start1+dlen1;
for (carry=0; buf2 > start2; buf1--)
{
ADD(*buf1, *buf1, *--buf2, carry);
}
for (; buf1 >= start1; buf1--)
{
SUB2(*buf1, *buf1, 0, carry);
}
DBUG_ASSERT(carry==1);
}
if (likely(div))
*buf0=(dec1)guess;
if (*start1 == 0)
start1++;
}
if (mod)
{
/*
now the result is in tmp1, it has
intg=prec1-frac1
frac=max(frac1, frac2)=to->frac
*/
buf0=to->buf;
intg0=ROUND_UP(prec1-frac1)-(start1-tmp1);
frac0=ROUND_UP(to->frac);
error=E_DEC_OK;
if (unlikely(frac0==0 && intg0==0))
{
decimal_make_zero(to);
goto done;
}
if (intg0<=0)
{
if (unlikely(-intg0 >= to->len))
{
decimal_make_zero(to);
error=E_DEC_TRUNCATED;
goto done;
}
stop1=start1+frac0;
frac0+=intg0;
to->intg=0;
while (intg0++ < 0)
*buf0++=0;
}
else
{
if (unlikely(intg0 > to->len))
{
frac0=0;
intg0=to->len;
error=E_DEC_OVERFLOW;
goto done;
}
DBUG_ASSERT(intg0 <= ROUND_UP(from2->intg));
stop1=start1+frac0+intg0;
to->intg=min(intg0*DIG_PER_DEC1, from2->intg);
}
if (unlikely(intg0+frac0 > to->len))
{
stop1-=to->len-frac0-intg0;
frac0=to->len-intg0;
to->frac=frac0*DIG_PER_DEC1;
error=E_DEC_TRUNCATED;
}
while (start1 < stop1)
*buf0++=*start1++;
}
done:
my_afree(tmp1);
return error;
}
/*
division of two decimals
SYNOPSIS
decimal_div()
from1 - dividend
from2 - divisor
to - quotient
RETURN VALUE
E_DEC_OK/E_DEC_TRUNCATED/E_DEC_OVERFLOW/E_DEC_DIV_ZERO;
NOTES
see do_div_mod()
*/
int decimal_div(decimal *from1, decimal *from2, decimal *to, int scale_incr)
{
return do_div_mod(from1, from2, to, 0, scale_incr);
}
/*
modulus
SYNOPSIS
decimal_mod()
from1 - dividend
from2 - divisor
to - modulus
RETURN VALUE
E_DEC_OK/E_DEC_TRUNCATED/E_DEC_OVERFLOW/E_DEC_DIV_ZERO;
NOTES
see do_div_mod()
DESCRIPTION
the modulus R in R = M mod N
is defined as
0 <= |R| < |M|
sign R == sign M
R = M - k*N, where k is integer
thus, there's no requirement for M or N to be integers
*/
int decimal_mod(decimal *from1, decimal *from2, decimal *to)
{
return do_div_mod(from1, from2, 0, to, 0);
}
#ifdef MAIN
int full= 0;
decimal a, b, c;
char buf1[100], buf2[100], buf3[100];
void dump_decimal(decimal *d)
{
int i;
printf("/* intg=%d, frac=%d, sign=%d, buf[]={", d->intg, d->frac, d->sign);
for (i=0; i < ROUND_UP(d->frac)+ROUND_UP(d->intg)-1; i++)
printf("%09d, ", d->buf[i]);
printf("%09d} */ ", d->buf[i]);
}
void check_result_code(int actual, int want)
{
if (actual != want)
{
printf("\n^^^^^^^^^^^^^ mast return %d\n", want);
exit(1);
}
}
void print_decimal(decimal *d, char *orig, int actual, int want)
{
char s[100];
int slen=sizeof(s);
if (full) dump_decimal(d);
decimal2string(d, s, &slen, 0, 0, 0);
printf("'%s'", s);
check_result_code(actual, want);
if (orig && strcmp(orig, s))
{
printf("\n^^^^^^^^^^^^^ must've been '%s'\n", orig);
exit(1);
}
}
void test_d2s()
{
char s[100];
int slen, res;
/***********************************/
printf("==== decimal2string ====\n");
a.buf[0]=12345; a.intg=5; a.frac=0; a.sign=0;
slen=sizeof(s);
res=decimal2string(&a, s, &slen, 0, 0, 0);
dump_decimal(&a); printf(" --> res=%d str='%s' len=%d\n", res, s, slen);
a.buf[1]=987000000; a.frac=3;
slen=sizeof(s);
res=decimal2string(&a, s, &slen, 0, 0, 0);
dump_decimal(&a); printf(" --> res=%d str='%s' len=%d\n", res, s, slen);
a.sign=1;
slen=sizeof(s);
res=decimal2string(&a, s, &slen, 0, 0, 0);
dump_decimal(&a); printf(" --> res=%d str='%s' len=%d\n", res, s, slen);
slen=8;
res=decimal2string(&a, s, &slen, 0, 0, 0);
dump_decimal(&a); printf(" --> res=%d str='%s' len=%d\n", res, s, slen);
slen=5;
res=decimal2string(&a, s, &slen, 0, 0, 0);
dump_decimal(&a); printf(" --> res=%d str='%s' len=%d\n", res, s, slen);
a.buf[0]=987000000; a.frac=3; a.intg=0;
slen=sizeof(s);
res=decimal2string(&a, s, &slen, 0, 0, 0);
dump_decimal(&a); printf(" --> res=%d str='%s' len=%d\n", res, s, slen);
}
void test_s2d(char *s, char *orig, int ex)
{
char s1[100];
int res;
sprintf(s1, "'%s'", s);
printf("len=%2d %-30s => res=%d ", a.len, s1,
(res= string2decimal(s, &a, 0)));
print_decimal(&a, orig, res, ex);
printf("\n");
}
void test_d2f(char *s, int ex)
{
char s1[100];
double x;
int res;
sprintf(s1, "'%s'", s);
string2decimal(s, &a, 0);
res=decimal2double(&a, &x);
if (full) dump_decimal(&a);
printf("%-40s => res=%d %.*g\n", s1, res, a.intg+a.frac, x);
check_result_code(res, ex);
}
void test_d2b2d(char *str, int p, int s, char *orig, int ex)
{
char s1[100], buf[100];
int res, i, size=decimal_bin_size(p, s);
sprintf(s1, "'%s'", str);
string2decimal(str, &a, 0);
res=decimal2bin(&a, buf, p, s);
printf("%-31s {%2d, %2d} => res=%d size=%-2d ", s1, p, s, res, size);
if (full)
{
printf("0x");
for (i=0; i < size; i++)
printf("%02x", ((uchar *)buf)[i]);
}
res=bin2decimal(buf, &a, p, s);
printf(" => res=%d ", res);
print_decimal(&a, orig, res, ex);
printf("\n");
}
void test_f2d(double from, int ex)
{
int res;
res=double2decimal(from, &a);
printf("%-40.*f => res=%d ", DBL_DIG-2, from, res);
print_decimal(&a, 0, res, ex);
printf("\n");
}
void test_ull2d(ulonglong from, char *orig, int ex)
{
char s[100];
int res;
res=ulonglong2decimal(from, &a);
longlong10_to_str(from,s,10);
printf("%-40s => res=%d ", s, res);
print_decimal(&a, orig, res, ex);
printf("\n");
}
void test_ll2d(longlong from, char *orig, int ex)
{
char s[100];
int res;
res=longlong2decimal(from, &a);
longlong10_to_str(from,s,-10);
printf("%-40s => res=%d ", s, res);
print_decimal(&a, orig, res, ex);
printf("\n");
}
void test_d2ull(char *s, char *orig, int ex)
{
char s1[100];
ulonglong x;
int res;
string2decimal(s, &a, 0);
res=decimal2ulonglong(&a, &x);
if (full) dump_decimal(&a);
longlong10_to_str(x,s1,10);
printf("%-40s => res=%d %s\n", s, res, s1);
check_result_code(res, ex);
if (orig && strcmp(orig, s1))
{
printf("\n^^^^^^^^^^^^^ must've been '%s'\n", orig);
exit(1);
}
}
void test_d2ll(char *s, char *orig, int ex)
{
char s1[100];
longlong x;
int res;
string2decimal(s, &a, 0);
res=decimal2longlong(&a, &x);
if (full) dump_decimal(&a);
longlong10_to_str(x,s1,-10);
printf("%-40s => res=%d %s\n", s, res, s1);
check_result_code(res, ex);
if (orig && strcmp(orig, s1))
{
printf("\n^^^^^^^^^^^^^ must've been '%s'\n", orig);
exit(1);
}
}
void test_da(char *s1, char *s2, char *orig, int ex)
{
char s[100];
int res;
sprintf(s, "'%s' + '%s'", s1, s2);
string2decimal(s1, &a, 0);
string2decimal(s2, &b, 0);
res=decimal_add(&a, &b, &c);
printf("%-40s => res=%d ", s, res);
print_decimal(&c, orig, res, ex);
printf("\n");
}
void test_ds(char *s1, char *s2, char *orig, int ex)
{
char s[100];
int res;
sprintf(s, "'%s' - '%s'", s1, s2);
string2decimal(s1, &a, 0);
string2decimal(s2, &b, 0);
res=decimal_sub(&a, &b, &c);
printf("%-40s => res=%d ", s, res);
print_decimal(&c, orig, res, ex);
printf("\n");
}
void test_dc(char *s1, char *s2, int orig)
{
char s[100];
int res;
sprintf(s, "'%s' <=> '%s'", s1, s2);
string2decimal(s1, &a, 0);
string2decimal(s2, &b, 0);
res=decimal_cmp(&a, &b);
printf("%-40s => res=%d\n", s, res);
if (orig != res)
{
printf("\n^^^^^^^^^^^^^ must've been %d\n", orig);
exit(1);
}
}
void test_dm(char *s1, char *s2, char *orig, int ex)
{
char s[100];
int res;
sprintf(s, "'%s' * '%s'", s1, s2);
string2decimal(s1, &a, 0);
string2decimal(s2, &b, 0);
res=decimal_mul(&a, &b, &c);
printf("%-40s => res=%d ", s, res);
print_decimal(&c, orig, res, ex);
printf("\n");
}
void test_dv(char *s1, char *s2, char *orig, int ex)
{
char s[100];
int res;
sprintf(s, "'%s' / '%s'", s1, s2);
string2decimal(s1, &a, 0);
string2decimal(s2, &b, 0);
res=decimal_div(&a, &b, &c, 5);
printf("%-40s => res=%d ", s, res);
check_result_code(res, ex);
if (res == E_DEC_DIV_ZERO)
printf("E_DEC_DIV_ZERO");
else
print_decimal(&c, orig, res, ex);
printf("\n");
}
void test_md(char *s1, char *s2, char *orig, int ex)
{
char s[100];
int res;
sprintf(s, "'%s' %% '%s'", s1, s2);
string2decimal(s1, &a, 0);
string2decimal(s2, &b, 0);
res=decimal_mod(&a, &b, &c);
printf("%-40s => res=%d ", s, res);
check_result_code(res, ex);
if (res == E_DEC_DIV_ZERO)
printf("E_DEC_DIV_ZERO");
else
print_decimal(&c, orig, res, ex);
printf("\n");
}
char *round_mode[]={"TRUNCATE", "HALF_EVEN", "HALF_UP", "CEILING", "FLOOR"};
void test_ro(char *s1, int n, decimal_round_mode mode, char *orig, int ex)
{
char s[100];
int res;
sprintf(s, "'%s', %d, %s", s1, n, round_mode[mode]);
string2decimal(s1, &a, 0);
res=decimal_round(&a, &b, n, mode);
printf("%-40s => res=%d ", s, res);
print_decimal(&b, orig, res, ex);
printf("\n");
}
void test_mx(int precision, int frac, char *orig)
{
char s[100];
sprintf(s, "%d, %d", precision, frac);
max_decimal(precision, frac, &a);
printf("%-40s => ", s);
print_decimal(&a, orig, 0, 0);
printf("\n");
}
void test_pr(char *s1, int prec, int dec, char filler, char *orig, int ex)
{
char s[100];
char s2[100];
int slen= sizeof(s2);
int res;
sprintf(s, "'%s', %d, %d, '%c'", s1, prec, dec, filler);
string2decimal(s1, &a, 0);
res= decimal2string(&a, s2, &slen, prec, dec, filler);
printf("%-40s => res=%d '%s'", s, res, s2);
check_result_code(res, ex);
if (orig && strcmp(orig, s2))
{
printf("\n^^^^^^^^^^^^^ must've been '%s'\n", orig);
exit(1);
}
printf("\n");
}
void test_sh(char *s1, int shift, char *orig, int ex)
{
char s[100];
int res;
sprintf(s, "'%s' %s %d", s1, ((shift < 0) ? ">>" : "<<"), abs(shift));
string2decimal(s1, &a, 0);
res= decimal_shift(&a, shift);
printf("%-40s => res=%d ", s, res);
print_decimal(&a, orig, res, ex);
printf("\n");
}
void test_fr(char *s1, char *orig)
{
char s[100];
sprintf(s, "'%s'", s1);
printf("%-40s => ", s);
string2decimal(s1, &a, 0);
decimal_optimize_fraction(&a);
print_decimal(&a, orig, 0, 0);
printf("\n");
}
int main()
{
a.buf=(void*)buf1;
a.len=sizeof(buf1)/sizeof(dec1);
b.buf=(void*)buf2;
b.len=sizeof(buf2)/sizeof(dec1);
c.buf=(void*)buf3;
c.len=sizeof(buf3)/sizeof(dec1);
if (full)
test_d2s();
printf("==== string2decimal ====\n");
test_s2d("12345", "12345", 0);
test_s2d("12345.", "12345", 0);
test_s2d("123.45", "123.45", 0);
test_s2d("-123.45", "-123.45", 0);
test_s2d(".00012345000098765", "0.00012345000098765", 0);
test_s2d(".12345000098765", "0.12345000098765", 0);
test_s2d("-.000000012345000098765", "-0.000000012345000098765", 0);
test_s2d("1234500009876.5", "1234500009876.5", 0);
a.len=1;
test_s2d("123450000098765", "98765", 2);
test_s2d("123450.000098765", "123450", 1);
a.len=sizeof(buf1)/sizeof(dec1);
test_s2d("123E5", "12300000", 0);
test_s2d("123E-2", "1.23", 0);
printf("==== decimal2double ====\n");
test_d2f("12345", 0);
test_d2f("123.45", 0);
test_d2f("-123.45", 0);
test_d2f("0.00012345000098765", 0);
test_d2f("1234500009876.5", 0);
printf("==== double2decimal ====\n");
test_f2d(12345, 0);
test_f2d(1.0/3, 0);
test_f2d(-123.45, 0);
test_f2d(0.00012345000098765, 0);
test_f2d(1234500009876.5, 0);
printf("==== ulonglong2decimal ====\n");
test_ull2d(ULL(12345), "12345", 0);
test_ull2d(ULL(0), "0", 0);
test_ull2d(ULL(18446744073709551615), "18446744073709551615", 0);
printf("==== decimal2ulonglong ====\n");
test_d2ull("12345", "12345", 0);
test_d2ull("0", "0", 0);
test_d2ull("18446744073709551615", "18446744073709551615", 0);
test_d2ull("18446744073709551616", "18446744073", 2);
test_d2ull("-1", "0", 2);
test_d2ull("1.23", "1", 1);
test_d2ull("9999999999999999999999999.000", "9999999999999999", 2);
printf("==== longlong2decimal ====\n");
test_ll2d(LL(-12345), "-12345", 0);
test_ll2d(LL(-1), "-1", 0);
test_ll2d(LL(-9223372036854775807), "-9223372036854775807", 0);
test_ll2d(ULL(9223372036854775808), "-9223372036854775808", 0);
printf("==== decimal2longlong ====\n");
test_d2ll("18446744073709551615", "18446744073", 2);
test_d2ll("-1", "-1", 0);
test_d2ll("-1.23", "-1", 1);
test_d2ll("-9223372036854775807", "-9223372036854775807", 0);
test_d2ll("-9223372036854775808", "-9223372036854775808", 0);
test_d2ll("9223372036854775808", "9223372036854775807", 2);
printf("==== do_add ====\n");
test_da(".00012345000098765" ,"123.45", "123.45012345000098765", 0);
test_da(".1" ,".45", "0.55", 0);
test_da("1234500009876.5" ,".00012345000098765", "1234500009876.50012345000098765", 0);
test_da("9999909999999.5" ,".555", "9999910000000.055", 0);
test_da("99999999" ,"1", "100000000", 0);
test_da("989999999" ,"1", "990000000", 0);
test_da("999999999" ,"1", "1000000000", 0);
test_da("12345" ,"123.45", "12468.45", 0);
test_da("-12345" ,"-123.45", "-12468.45", 0);
test_ds("-12345" ,"123.45", "-12468.45", 0);
test_ds("12345" ,"-123.45", "12468.45", 0);
printf("==== do_sub ====\n");
test_ds(".00012345000098765", "123.45","-123.44987654999901235", 0);
test_ds("1234500009876.5", ".00012345000098765","1234500009876.49987654999901235", 0);
test_ds("9999900000000.5", ".555","9999899999999.945", 0);
test_ds("1111.5551", "1111.555","0.0001", 0);
test_ds(".555", ".555","0", 0);
test_ds("10000000", "1","9999999", 0);
test_ds("1000001000", ".1","1000000999.9", 0);
test_ds("1000000000", ".1","999999999.9", 0);
test_ds("12345", "123.45","12221.55", 0);
test_ds("-12345", "-123.45","-12221.55", 0);
test_da("-12345", "123.45","-12221.55", 0);
test_da("12345", "-123.45","12221.55", 0);
test_ds("123.45", "12345","-12221.55", 0);
test_ds("-123.45", "-12345","12221.55", 0);
test_da("123.45", "-12345","-12221.55", 0);
test_da("-123.45", "12345","12221.55", 0);
test_da("5", "-6.0","-1.0", 0);
printf("==== decimal_mul ====\n");
test_dm("12", "10","120", 0);
test_dm("-123.456", "98765.4321","-12193185.1853376", 0);
test_dm("-123456000000", "98765432100000","-12193185185337600000000000", 0);
test_dm("123456", "987654321","121931851853376", 0);
test_dm("123456", "9876543210","1219318518533760", 0);
test_dm("123", "0.01","1.23", 0);
test_dm("123", "0","0", 0);
printf("==== decimal_div ====\n");
test_dv("120", "10","12.000000000", 0);
test_dv("123", "0.01","12300.000000000", 0);
test_dv("120", "100000000000.00000","0.000000001200000000", 0);
test_dv("123", "0","", 4);
test_dv("-12193185.1853376", "98765.4321","-123.456000000000000000", 0);
test_dv("121931851853376", "987654321","123456.000000000", 0);
test_dv("0", "987","0", 0);
test_dv("1", "3","0.333333333", 0);
test_dv("1.000000000000", "3","0.333333333333333333", 0);
test_dv("1", "1","1.000000000", 0);
test_dv("0.0123456789012345678912345", "9999999999","0.000000000001234567890246913578148141", 0);
printf("==== decimal_mod ====\n");
test_md("234","10","4", 0);
test_md("234.567","10.555","2.357", 0);
test_md("-234.567","10.555","-2.357", 0);
test_md("234.567","-10.555","2.357", 0);
if (full)
{
c.buf[1]=0x3ABECA;
test_md("99999999999999999999999999999999999999","3","0", 0);
printf("%X\n", c.buf[1]);
}
printf("==== decimal2bin/bin2decimal ====\n");
test_d2b2d("-10.55", 4, 2,"-10.55", 0);
test_d2b2d("0.0123456789012345678912345", 30, 25,"0.0123456789012345678912345", 0);
test_d2b2d("12345", 5, 0,"12345", 0);
test_d2b2d("12345", 10, 3,"12345.000", 0);
test_d2b2d("123.45", 10, 3,"123.450", 0);
test_d2b2d("-123.45", 20, 10,"-123.4500000000", 0);
test_d2b2d(".00012345000098765", 15, 14,"0.00012345000098", 0);
test_d2b2d(".00012345000098765", 22, 20,"0.00012345000098765000", 0);
test_d2b2d(".12345000098765", 30, 20,"0.12345000098765000000", 0);
test_d2b2d("-.000000012345000098765", 30, 20,"-0.00000001234500009876", 0);
test_d2b2d("1234500009876.5", 30, 5,"1234500009876.50000", 0);
test_d2b2d("111111111.11", 10, 2,"11111111.11", 0);
test_d2b2d("000000000.01", 7, 3,"0.010", 0);
test_d2b2d("123.4", 10, 2, "123.40", 0);
printf("==== decimal_cmp ====\n");
test_dc("12","13",-1);
test_dc("13","12",1);
test_dc("-10","10",-1);
test_dc("10","-10",1);
test_dc("-12","-13",1);
test_dc("0","12",-1);
test_dc("-10","0",-1);
test_dc("4","4",0);
printf("==== decimal_round ====\n");
test_ro("5678.123451",-4,TRUNCATE,"0", 0);
test_ro("5678.123451",-3,TRUNCATE,"5000", 0);
test_ro("5678.123451",-2,TRUNCATE,"5600", 0);
test_ro("5678.123451",-1,TRUNCATE,"5670", 0);
test_ro("5678.123451",0,TRUNCATE,"5678", 0);
test_ro("5678.123451",1,TRUNCATE,"5678.1", 0);
test_ro("5678.123451",2,TRUNCATE,"5678.12", 0);
test_ro("5678.123451",3,TRUNCATE,"5678.123", 0);
test_ro("5678.123451",4,TRUNCATE,"5678.1234", 0);
test_ro("5678.123451",5,TRUNCATE,"5678.12345", 0);
test_ro("5678.123451",6,TRUNCATE,"5678.123451", 0);
test_ro("-5678.123451",-4,TRUNCATE,"0", 0);
memset(buf2, 33, sizeof(buf2));
test_ro("99999999999999999999999999999999999999",-31,TRUNCATE,"99999990000000000000000000000000000000", 0);
test_ro("15.1",0,HALF_UP,"15", 0);
test_ro("15.5",0,HALF_UP,"16", 0);
test_ro("15.9",0,HALF_UP,"16", 0);
test_ro("-15.1",0,HALF_UP,"-15", 0);
test_ro("-15.5",0,HALF_UP,"-16", 0);
test_ro("-15.9",0,HALF_UP,"-16", 0);
test_ro("15.1",1,HALF_UP,"15.1", 0);
test_ro("-15.1",1,HALF_UP,"-15.1", 0);
test_ro("15.17",1,HALF_UP,"15.2", 0);
test_ro("15.4",-1,HALF_UP,"20", 0);
test_ro("-15.4",-1,HALF_UP,"-20", 0);
test_ro("5.4",-1,HALF_UP,"10", 0);
test_ro(".999", 0, HALF_UP, "1", 0);
memset(buf2, 33, sizeof(buf2));
test_ro("999999999", -9, HALF_UP, "1000000000", 0);
test_ro("15.1",0,HALF_EVEN,"15", 0);
test_ro("15.5",0,HALF_EVEN,"16", 0);
test_ro("14.5",0,HALF_EVEN,"14", 0);
test_ro("15.9",0,HALF_EVEN,"16", 0);
test_ro("15.1",0,CEILING,"16", 0);
test_ro("-15.1",0,CEILING,"-15", 0);
test_ro("15.1",0,FLOOR,"15", 0);
test_ro("-15.1",0,FLOOR,"-16", 0);
test_ro("999999999999999999999.999", 0, CEILING,"1000000000000000000000", 0);
test_ro("-999999999999999999999.999", 0, FLOOR,"-1000000000000000000000", 0);
printf("==== max_decimal ====\n");
test_mx(1,1,"0.9");
test_mx(1,0,"9");
test_mx(2,1,"9.9");
test_mx(4,2,"99.99");
test_mx(6,3,"999.999");
test_mx(8,4,"9999.9999");
test_mx(10,5,"99999.99999");
test_mx(12,6,"999999.999999");
test_mx(14,7,"9999999.9999999");
test_mx(16,8,"99999999.99999999");
test_mx(18,9,"999999999.999999999");
test_mx(20,10,"9999999999.9999999999");
test_mx(20,20,"0.99999999999999999999");
test_mx(20,0,"99999999999999999999");
test_mx(40,20,"99999999999999999999.99999999999999999999");
printf("==== decimal2string ====\n");
test_pr("123.123", 0, 0, 0, "123.123", 0);
test_pr("123.123", 7, 3, '0', "123.123", 0);
test_pr("123.123", 9, 3, '0', "00123.123", 0);
test_pr("123.123", 9, 4, '0', "0123.1230", 0);
test_pr("123.123", 9, 5, '0', "123.12300", 0);
test_pr("123.123", 9, 2, '0', "000123.12", 1);
test_pr("123.123", 9, 6, '0', "23.123000", 2);
printf("==== decimal_shift ====\n");
test_sh("123.123", 1, "1231.23", 0);
test_sh("123457189.123123456789000", 1, "1234571891.23123456789", 0);
test_sh("123457189.123123456789000", 4, "1234571891231.23456789", 0);
test_sh("123457189.123123456789000", 8, "12345718912312345.6789", 0);
test_sh("123457189.123123456789000", 9, "123457189123123456.789", 0);
test_sh("123457189.123123456789000", 10, "1234571891231234567.89", 0);
test_sh("123457189.123123456789000", 17, "12345718912312345678900000", 0);
test_sh("123457189.123123456789000", 18, "123457189123123456789000000", 0);
test_sh("123457189.123123456789000", 19, "1234571891231234567890000000", 0);
test_sh("123457189.123123456789000", 26, "12345718912312345678900000000000000", 0);
test_sh("123457189.123123456789000", 27, "123457189123123456789000000000000000", 0);
test_sh("123457189.123123456789000", 28, "1234571891231234567890000000000000000", 0);
test_sh("000000000000000000000000123457189.123123456789000", 26, "12345718912312345678900000000000000", 0);
test_sh("00000000123457189.123123456789000", 27, "123457189123123456789000000000000000", 0);
test_sh("00000000000000000123457189.123123456789000", 28, "1234571891231234567890000000000000000", 0);
test_sh("123", 1, "1230", 0);
test_sh("123", 10, "1230000000000", 0);
test_sh(".123", 1, "1.23", 0);
test_sh(".123", 10, "1230000000", 0);
test_sh(".123", 14, "12300000000000", 0);
test_sh("000.000", 1000, "0", 0);
test_sh("000.", 1000, "0", 0);
test_sh(".000", 1000, "0", 0);
test_sh("1", 1000, "1", 2);
test_sh("123.123", -1, "12.3123", 0);
test_sh("123987654321.123456789000", -1, "12398765432.1123456789", 0);
test_sh("123987654321.123456789000", -2, "1239876543.21123456789", 0);
test_sh("123987654321.123456789000", -3, "123987654.321123456789", 0);
test_sh("123987654321.123456789000", -8, "1239.87654321123456789", 0);
test_sh("123987654321.123456789000", -9, "123.987654321123456789", 0);
test_sh("123987654321.123456789000", -10, "12.3987654321123456789", 0);
test_sh("123987654321.123456789000", -11, "1.23987654321123456789", 0);
test_sh("123987654321.123456789000", -12, "0.123987654321123456789", 0);
test_sh("123987654321.123456789000", -13, "0.0123987654321123456789", 0);
test_sh("123987654321.123456789000", -14, "0.00123987654321123456789", 0);
test_sh("00000087654321.123456789000", -14, "0.00000087654321123456789", 0);
a.len= 2;
test_sh("123.123", -2, "1.23123", 0);
test_sh("123.123", -3, "0.123123", 0);
test_sh("123.123", -6, "0.000123123", 0);
test_sh("123.123", -7, "0.0000123123", 0);
test_sh("123.123", -15, "0.000000000000123123", 0);
test_sh("123.123", -16, "0.000000000000012312", 1);
test_sh("123.123", -17, "0.000000000000001231", 1);
test_sh("123.123", -18, "0.000000000000000123", 1);
test_sh("123.123", -19, "0.000000000000000012", 1);
test_sh("123.123", -20, "0.000000000000000001", 1);
test_sh("123.123", -21, "0", 1);
test_sh(".000000000123", -1, "0.0000000000123", 0);
test_sh(".000000000123", -6, "0.000000000000000123", 0);
test_sh(".000000000123", -7, "0.000000000000000012", 1);
test_sh(".000000000123", -8, "0.000000000000000001", 1);
test_sh(".000000000123", -9, "0", 1);
test_sh(".000000000123", 1, "0.00000000123", 0);
test_sh(".000000000123", 8, "0.0123", 0);
test_sh(".000000000123", 9, "0.123", 0);
test_sh(".000000000123", 10, "1.23", 0);
test_sh(".000000000123", 17, "12300000", 0);
test_sh(".000000000123", 18, "123000000", 0);
test_sh(".000000000123", 19, "1230000000", 0);
test_sh(".000000000123", 20, "12300000000", 0);
test_sh(".000000000123", 21, "123000000000", 0);
test_sh(".000000000123", 22, "1230000000000", 0);
test_sh(".000000000123", 23, "12300000000000", 0);
test_sh(".000000000123", 24, "123000000000000", 0);
test_sh(".000000000123", 25, "1230000000000000", 0);
test_sh(".000000000123", 26, "12300000000000000", 0);
test_sh(".000000000123", 27, "123000000000000000", 0);
test_sh(".000000000123", 28, "0.000000000123", 2);
test_sh("123456789.987654321", -1, "12345678.998765432", 1);
test_sh("123456789.987654321", -2, "1234567.899876543", 1);
test_sh("123456789.987654321", -8, "1.234567900", 1);
test_sh("123456789.987654321", -9, "0.123456789987654321", 0);
test_sh("123456789.987654321", -10, "0.012345678998765432", 1);
test_sh("123456789.987654321", -17, "0.000000001234567900", 1);
test_sh("123456789.987654321", -18, "0.000000000123456790", 1);
test_sh("123456789.987654321", -19, "0.000000000012345679", 1);
test_sh("123456789.987654321", -26, "0.000000000000000001", 1);
test_sh("123456789.987654321", -27, "0", 1);
test_sh("123456789.987654321", 1, "1234567900", 1);
test_sh("123456789.987654321", 2, "12345678999", 1);
test_sh("123456789.987654321", 4, "1234567899877", 1);
test_sh("123456789.987654321", 8, "12345678998765432", 1);
test_sh("123456789.987654321", 9, "123456789987654321", 0);
test_sh("123456789.987654321", 10, "123456789.987654321", 2);
test_sh("123456789.987654321", 0, "123456789.987654321", 0);
a.len= sizeof(buf1)/sizeof(dec1);
printf("==== decimal_optimize_fraction ====\n");
test_fr("1.123456789000000000", "1.123456789");
test_fr("1.12345678000000000", "1.12345678");
test_fr("1.1234567000000000", "1.1234567");
test_fr("1.123456000000000", "1.123456");
test_fr("1.12345000000000", "1.12345");
test_fr("1.1234000000000", "1.1234");
test_fr("1.123000000000", "1.123");
test_fr("1.12000000000", "1.12");
test_fr("1.1000000000", "1.1");
test_fr("1.000000000", "1");
test_fr("1.0", "1");
test_fr("10000000000000000000.0", "10000000000000000000");
return 0;
}
#endif
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