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Commit 2d007e2a authored by Alexey Kopytov's avatar Alexey Kopytov
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Reconciling different file ids for dtoa.c in trunk and 6.0-codebase.

parents 7dfa66cd 04116597
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strings/dtoa.c 0 → 100644
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/* Copyright (C) 2007 MySQL 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., 59 Temple Place, Suite 330, Boston, MA 02111-1307 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 <my_base.h> /* for EOVERFLOW on Windows */
#include <my_global.h>
#include <m_string.h> /* for memcpy and NOT_FIXED_DEC */
/**
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 (420 * sizeof(void *))
/* Magic value returned by dtoa() to indicate overflow */
#define DTOA_OVERFLOW 9999
static double my_strtod_int(const char *, char **, int *, char *, size_t);
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 my_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= 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, my_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:
my_gcvt(-9e-3, ..., 4, ...);
my_gcvt(-9e-3, ..., 2, ...);
my_gcvt(1.87e-3, ..., 4, ...);
my_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 my_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= end - res;
/*
Number of digits in the exponent from the 'e' conversion.
The sign of the exponent is taken into account separetely, 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 representaion 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 MAX_DECPT_FOR_F_FORMAT.
*/
(!have_space || (decpt >= -MAX_DECPT_FOR_F_FORMAT + 1 &&
(decpt <= MAX_DECPT_FOR_F_FORMAT || 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= 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= 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;
}
/**
@brief
Converts string to double (string does not have to be zero-terminated)
@details
This is a wrapper around dtoa's version of strtod().
@param str input string
@param end address of a pointer to the first character after the input
string. Upon return the pointer is set to point to the first
rejected character.
@param error Upon return is set to EOVERFLOW in case of underflow or
overflow.
@return The resulting double value. In case of underflow, 0.0 is
returned. In case overflow, signed DBL_MAX is returned.
*/
double my_strtod(const char *str, char **end, int *error)
{
char buf[DTOA_BUFF_SIZE];
double res;
DBUG_ASSERT(end != NULL && ((str != NULL && *end != NULL) ||
(str == NULL && *end == NULL)) &&
error != NULL);
res= my_strtod_int(str, end, error, buf, sizeof(buf));
return (*error == 0) ? res : (res < 0 ? -DBL_MAX : DBL_MAX);
}
double my_atof(const char *nptr)
{
int error;
const char *end= nptr+65535; /* Should be enough */
return (my_strtod(nptr, (char**) &end, &error));
}
/****************************************************************
*
* 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(WORDS_BIGENDIAN) || (defined(__FLOAT_WORD_ORDER) && \
(__FLOAT_WORD_ORDER == __BIG_ENDIAN))
#define word0(x) ((U*)&x)->L[0]
#define word1(x) ((U*)&x)->L[1]
#else
#define word0(x) ((U*)&x)->L[1]
#define word1(x) ((U*)&x)->L[0]
#endif
#define dval(x) ((U*)&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;
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 Bigint *s2b(const char *s, int nd0, int nd, ULong y9, Stack_alloc *alloc)
{
Bigint *b;
int i, k;
Long x, y;
x= (nd + 8) / 9;
for (k= 0, y= 1; x > y; y <<= 1, k++) ;
b= Balloc(k, alloc);
b->p.x[0]= y9;
b->wds= 1;
i= 9;
if (9 < nd0)
{
s+= 9;
do
b= multadd(b, 10, *s++ - '0', alloc);
while (++i < nd0);
s++;
}
else
s+= 10;
for(; i < nd; i++)
b= multadd(b, 10, *s++ - '0', alloc);
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;
int i;
static int p05[3]= { 5, 25, 125 };
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 (p5 < p5_a + P5A_MAX)
++p5;
else if (p5 == p5_a + P5A_MAX)
p5= mult(p5, p5, alloc);
else
{
p51= mult(p5, p5, alloc);
Bfree(p5, alloc);
p5= p51;
}
}
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;
xe= x + b->wds;
if (k&= 0x1f)
{
k1= 32 - k;
z= 0;
do
{
*x1++= *x << k | z;
z= *x++ >> k1;
}
while (x < xe);
if ((*x1= z))
++n1;
}
else
do
*x1++= *x++;
while (x < xe);
b1->wds= n1 - 1;
Bfree(b, alloc);
return b1;
}
static int cmp(Bigint *a, Bigint *b)
{
ULong *xa, *xa0, *xb, *xb0;
int i, j;
i= a->wds;
j= b->wds;
if (i-= j)
return i;
xa0= a->p.x;
xa= xa0 + j;
xb0= b->p.x;
xb= xb0 + j;
for (;;)
{
if (*--xa != *--xb)
return *xa < *xb ? -1 : 1;
if (xa <= xa0)
break;
}
return 0;
}
static Bigint *diff(Bigint *a, Bigint *b, Stack_alloc *alloc)
{
Bigint *c;
int i, wa, wb;
ULong *xa, *xae, *xb, *xbe, *xc;
ULLong borrow, y;
i= cmp(a,b);
if (!i)
{
c= Balloc(0, alloc);
c->wds= 1;
c->p.x[0]= 0;
return c;
}
if (i < 0)
{
c= a;
a= b;
b= c;
i= 1;
}
else
i= 0;
c= Balloc(a->k, alloc);
c->sign= i;
wa= a->wds;
xa= a->p.x;
xae= xa + wa;
wb= b->wds;
xb= b->p.x;
xbe= xb + wb;
xc= c->p.x;
borrow= 0;
do
{
y= (ULLong)*xa++ - *xb++ - borrow;
borrow= y >> 32 & (ULong)1;
*xc++= (ULong) (y & FFFFFFFF);
}
while (xb < xbe);
while (xa < xae)
{
y= *xa++ - borrow;
borrow= y >> 32 & (ULong)1;
*xc++= (ULong) (y & FFFFFFFF);
}
while (!*--xc)
wa--;
c->wds= wa;
return c;
}
static double ulp(double x)
{
register Long L;
double a;
L= (word0(x) & Exp_mask) - (P - 1)*Exp_msk1;
word0(a) = L;
word1(a) = 0;
return dval(a);
}
static double b2d(Bigint *a, int *e)
{
ULong *xa, *xa0, w, y, z;
int k;
double d;
#define d0 word0(d)
#define d1 word1(d)
xa0= a->p.x;
xa= xa0 + a->wds;
y= *--xa;
k= hi0bits(y);
*e= 32 - k;
if (k < Ebits)
{
d0= Exp_1 | y >> (Ebits - k);
w= xa > xa0 ? *--xa : 0;
d1= y << ((32-Ebits) + k) | w >> (Ebits - k);
goto ret_d;
}
z= xa > xa0 ? *--xa : 0;
if (k-= Ebits)
{
d0= Exp_1 | y << k | z >> (32 - k);
y= xa > xa0 ? *--xa : 0;
d1= z << k | y >> (32 - k);
}
else
{
d0= Exp_1 | y;
d1= z;
}
ret_d:
#undef d0
#undef d1
return dval(d);
}
static Bigint *d2b(double d, int *e, int *bits, Stack_alloc *alloc)
{
Bigint *b;
int de, k;
ULong *x, y, z;
int i;
#define d0 word0(d)
#define d1 word1(d)
b= Balloc(1, alloc);
x= b->p.x;
z= d0 & Frac_mask;
d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
if ((de= (int)(d0 >> Exp_shift)))
z|= Exp_msk1;
if ((y= d1))
{
if ((k= lo0bits(&y)))
{
x[0]= y | z << (32 - k);
z>>= k;
}
else
x[0]= y;
i= b->wds= (x[1]= z) ? 2 : 1;
}
else
{
k= lo0bits(&z);
x[0]= z;
i= b->wds= 1;
k+= 32;
}
if (de)
{
*e= de - Bias - (P-1) + k;
*bits= P - k;
}
else
{
*e= de - Bias - (P-1) + 1 + k;
*bits= 32*i - hi0bits(x[i-1]);
}
return b;
#undef d0
#undef d1
}
static double ratio(Bigint *a, Bigint *b)
{
double da, db;
int k, ka, kb;
dval(da)= b2d(a, &ka);
dval(db)= b2d(b, &kb);
k= ka - kb + 32*(a->wds - b->wds);
if (k > 0)
word0(da)+= k*Exp_msk1;
else
{
k= -k;
word0(db)+= k*Exp_msk1;
}
return dval(da) / dval(db);
}
static const double tens[] =
{
1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
1e20, 1e21, 1e22
};
static const double bigtens[]= { 1e16, 1e32, 1e64, 1e128, 1e256 };
static const double tinytens[]=
{ 1e-16, 1e-32, 1e-64, 1e-128,
9007199254740992.*9007199254740992.e-256 /* = 2^106 * 1e-53 */
};
/*
The factor of 2^53 in tinytens[4] helps us avoid setting the underflow
flag unnecessarily. It leads to a song and dance at the end of strtod.
*/
#define Scale_Bit 0x10
#define n_bigtens 5
/*
strtod for IEEE--arithmetic machines.
This strtod returns a nearest machine number to the input decimal
string (or sets errno to EOVERFLOW). Ties are broken by the IEEE round-even
rule.
Inspired loosely by William D. Clinger's paper "How to Read Floating
Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
Modifications:
1. We only require IEEE (not IEEE double-extended).
2. We get by with floating-point arithmetic in a case that
Clinger missed -- when we're computing d * 10^n
for a small integer d and the integer n is not too
much larger than 22 (the maximum integer k for which
we can represent 10^k exactly), we may be able to
compute (d*10^k) * 10^(e-k) with just one roundoff.
3. Rather than a bit-at-a-time adjustment of the binary
result in the hard case, we use floating-point
arithmetic to determine the adjustment to within
one bit; only in really hard cases do we need to
compute a second residual.
4. Because of 3., we don't need a large table of powers of 10
for ten-to-e (just some small tables, e.g. of 10^k
for 0 <= k <= 22).
*/
static double my_strtod_int(const char *s00, char **se, int *error, char *buf, size_t buf_size)
{
int scale;
int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
const char *s, *s0, *s1, *end = *se;
double aadj, aadj1, adj, rv, rv0;
Long L;
ULong y, z;
Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
#ifdef SET_INEXACT
int inexact, oldinexact;
#endif
#ifdef Honor_FLT_ROUNDS
int rounding;
#endif
Stack_alloc alloc;
LINT_INIT(c);
*error= 0;
alloc.begin= alloc.free= buf;
alloc.end= buf + buf_size;
memset(alloc.freelist, 0, sizeof(alloc.freelist));
sign= nz0= nz= 0;
dval(rv)= 0.;
for (s= s00; s < end; s++)
switch (*s) {
case '-':
sign= 1;
/* no break */
case '+':
s++;
goto break2;
case '\t':
case '\n':
case '\v':
case '\f':
case '\r':
case ' ':
continue;
default:
goto break2;
}
break2:
if (s >= end)
goto ret0;
if (*s == '0')
{
nz0= 1;
while (++s < end && *s == '0') ;
if (s >= end)
goto ret;
}
s0= s;
y= z= 0;
for (nd= nf= 0; s < end && (c= *s) >= '0' && c <= '9'; nd++, s++)
if (nd < 9)
y= 10*y + c - '0';
else if (nd < 16)
z= 10*z + c - '0';
nd0= nd;
if (s < end - 1 && c == '.')
{
c= *++s;
if (!nd)
{
for (; s < end && c == '0'; c= *++s)
nz++;
if (s < end && c > '0' && c <= '9')
{
s0= s;
nf+= nz;
nz= 0;
goto have_dig;
}
goto dig_done;
}
for (; s < end && c >= '0' && c <= '9'; c = *++s)
{
have_dig:
nz++;
if (c-= '0')
{
nf+= nz;
for (i= 1; i < nz; i++)
if (nd++ < 9)
y*= 10;
else if (nd <= DBL_DIG + 1)
z*= 10;
if (nd++ < 9)
y= 10*y + c;
else if (nd <= DBL_DIG + 1)
z= 10*z + c;
nz= 0;
}
}
}
dig_done:
e= 0;
if (s < end && (c == 'e' || c == 'E'))
{
if (!nd && !nz && !nz0)
goto ret0;
s00= s;
esign= 0;
if (++s < end)
switch (c= *s) {
case '-':
esign= 1;
case '+':
c= *++s;
}
if (s < end && c >= '0' && c <= '9')
{
while (s < end && c == '0')
c= *++s;
if (s < end && c > '0' && c <= '9') {
L= c - '0';
s1= s;
while (++s < end && (c= *s) >= '0' && c <= '9')
L= 10*L + c - '0';
if (s - s1 > 8 || L > 19999)
/* Avoid confusion from exponents
* so large that e might overflow.
*/
e= 19999; /* safe for 16 bit ints */
else
e= (int)L;
if (esign)
e= -e;
}
else
e= 0;
}
else
s= s00;
}
if (!nd)
{
if (!nz && !nz0)
{
ret0:
s= s00;
sign= 0;
}
goto ret;
}
e1= e -= nf;
/*
Now we have nd0 digits, starting at s0, followed by a
decimal point, followed by nd-nd0 digits. The number we're
after is the integer represented by those digits times
10**e
*/
if (!nd0)
nd0= nd;
k= nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
dval(rv)= y;
if (k > 9)
{
#ifdef SET_INEXACT
if (k > DBL_DIG)
oldinexact = get_inexact();
#endif
dval(rv)= tens[k - 9] * dval(rv) + z;
}
bd0= 0;
if (nd <= DBL_DIG
#ifndef Honor_FLT_ROUNDS
&& Flt_Rounds == 1
#endif
)
{
if (!e)
goto ret;
if (e > 0)
{
if (e <= Ten_pmax)
{
#ifdef Honor_FLT_ROUNDS
/* round correctly FLT_ROUNDS = 2 or 3 */
if (sign)
{
rv= -rv;
sign= 0;
}
#endif
/* rv = */ rounded_product(dval(rv), tens[e]);
goto ret;
}
i= DBL_DIG - nd;
if (e <= Ten_pmax + i)
{
/*
A fancier test would sometimes let us do
this for larger i values.
*/
#ifdef Honor_FLT_ROUNDS
/* round correctly FLT_ROUNDS = 2 or 3 */
if (sign)
{
rv= -rv;
sign= 0;
}
#endif
e-= i;
dval(rv)*= tens[i];
/* rv = */ rounded_product(dval(rv), tens[e]);
goto ret;
}
}
#ifndef Inaccurate_Divide
else if (e >= -Ten_pmax)
{
#ifdef Honor_FLT_ROUNDS
/* round correctly FLT_ROUNDS = 2 or 3 */
if (sign)
{
rv= -rv;
sign= 0;
}
#endif
/* rv = */ rounded_quotient(dval(rv), tens[-e]);
goto ret;
}
#endif
}
e1+= nd - k;
#ifdef SET_INEXACT
inexact= 1;
if (k <= DBL_DIG)
oldinexact= get_inexact();
#endif
scale= 0;
#ifdef Honor_FLT_ROUNDS
if ((rounding= Flt_Rounds) >= 2)
{
if (sign)
rounding= rounding == 2 ? 0 : 2;
else
if (rounding != 2)
rounding= 0;
}
#endif
/* Get starting approximation = rv * 10**e1 */
if (e1 > 0)
{
if ((i= e1 & 15))
dval(rv)*= tens[i];
if (e1&= ~15)
{
if (e1 > DBL_MAX_10_EXP)
{
ovfl:
*error= EOVERFLOW;
/* Can't trust HUGE_VAL */
#ifdef Honor_FLT_ROUNDS
switch (rounding)
{
case 0: /* toward 0 */
case 3: /* toward -infinity */
word0(rv)= Big0;
word1(rv)= Big1;
break;
default:
word0(rv)= Exp_mask;
word1(rv)= 0;
}
#else /*Honor_FLT_ROUNDS*/
word0(rv)= Exp_mask;
word1(rv)= 0;
#endif /*Honor_FLT_ROUNDS*/
#ifdef SET_INEXACT
/* set overflow bit */
dval(rv0)= 1e300;
dval(rv0)*= dval(rv0);
#endif
if (bd0)
goto retfree;
goto ret;
}
e1>>= 4;
for(j= 0; e1 > 1; j++, e1>>= 1)
if (e1 & 1)
dval(rv)*= bigtens[j];
/* The last multiplication could overflow. */
word0(rv)-= P*Exp_msk1;
dval(rv)*= bigtens[j];
if ((z= word0(rv) & Exp_mask) > Exp_msk1 * (DBL_MAX_EXP + Bias - P))
goto ovfl;
if (z > Exp_msk1 * (DBL_MAX_EXP + Bias - 1 - P))
{
/* set to largest number (Can't trust DBL_MAX) */
word0(rv)= Big0;
word1(rv)= Big1;
}
else
word0(rv)+= P*Exp_msk1;
}
}
else if (e1 < 0)
{
e1= -e1;
if ((i= e1 & 15))
dval(rv)/= tens[i];
if ((e1>>= 4))
{
if (e1 >= 1 << n_bigtens)
goto undfl;
if (e1 & Scale_Bit)
scale= 2 * P;
for(j= 0; e1 > 0; j++, e1>>= 1)
if (e1 & 1)
dval(rv)*= tinytens[j];
if (scale && (j = 2 * P + 1 - ((word0(rv) & Exp_mask) >> Exp_shift)) > 0)
{
/* scaled rv is denormal; zap j low bits */
if (j >= 32)
{
word1(rv)= 0;
if (j >= 53)
word0(rv)= (P + 2) * Exp_msk1;
else
word0(rv)&= 0xffffffff << (j - 32);
}
else
word1(rv)&= 0xffffffff << j;
}
if (!dval(rv))
{
undfl:
dval(rv)= 0.;
if (bd0)
goto retfree;
goto ret;
}
}
}
/* Now the hard part -- adjusting rv to the correct value.*/
/* Put digits into bd: true value = bd * 10^e */
bd0= s2b(s0, nd0, nd, y, &alloc);
for(;;)
{
bd= Balloc(bd0->k, &alloc);
Bcopy(bd, bd0);
bb= d2b(dval(rv), &bbe, &bbbits, &alloc); /* rv = bb * 2^bbe */
bs= i2b(1, &alloc);
if (e >= 0)
{
bb2= bb5= 0;
bd2= bd5= e;
}
else
{
bb2= bb5= -e;
bd2= bd5= 0;
}
if (bbe >= 0)
bb2+= bbe;
else
bd2-= bbe;
bs2= bb2;
#ifdef Honor_FLT_ROUNDS
if (rounding != 1)
bs2++;
#endif
j= bbe - scale;
i= j + bbbits - 1; /* logb(rv) */
if (i < Emin) /* denormal */
j+= P - Emin;
else
j= P + 1 - bbbits;
bb2+= j;
bd2+= j;
bd2+= scale;
i= bb2 < bd2 ? bb2 : bd2;
if (i > bs2)
i= bs2;
if (i > 0)
{
bb2-= i;
bd2-= i;
bs2-= i;
}
if (bb5 > 0)
{
bs= pow5mult(bs, bb5, &alloc);
bb1= mult(bs, bb, &alloc);
Bfree(bb, &alloc);
bb= bb1;
}
if (bb2 > 0)
bb= lshift(bb, bb2, &alloc);
if (bd5 > 0)
bd= pow5mult(bd, bd5, &alloc);
if (bd2 > 0)
bd= lshift(bd, bd2, &alloc);
if (bs2 > 0)
bs= lshift(bs, bs2, &alloc);
delta= diff(bb, bd, &alloc);
dsign= delta->sign;
delta->sign= 0;
i= cmp(delta, bs);
#ifdef Honor_FLT_ROUNDS
if (rounding != 1)
{
if (i < 0)
{
/* Error is less than an ulp */
if (!delta->x[0] && delta->wds <= 1)
{
/* exact */
#ifdef SET_INEXACT
inexact= 0;
#endif
break;
}
if (rounding)
{
if (dsign)
{
adj= 1.;
goto apply_adj;
}
}
else if (!dsign)
{
adj= -1.;
if (!word1(rv) && !(word0(rv) & Frac_mask))
{
y= word0(rv) & Exp_mask;
if (!scale || y > 2*P*Exp_msk1)
{
delta= lshift(delta,Log2P);
if (cmp(delta, bs) <= 0)
adj= -0.5;
}
}
apply_adj:
if (scale && (y= word0(rv) & Exp_mask) <= 2 * P * Exp_msk1)
word0(adj)+= (2 * P + 1) * Exp_msk1 - y;
dval(rv)+= adj * ulp(dval(rv));
}
break;
}
adj= ratio(delta, bs);
if (adj < 1.)
adj= 1.;
if (adj <= 0x7ffffffe)
{
/* adj = rounding ? ceil(adj) : floor(adj); */
y= adj;
if (y != adj)
{
if (!((rounding >> 1) ^ dsign))
y++;
adj= y;
}
}
if (scale && (y= word0(rv) & Exp_mask) <= 2 * P * Exp_msk1)
word0(adj)+= (2 * P + 1) * Exp_msk1 - y;
adj*= ulp(dval(rv));
if (dsign)
dval(rv)+= adj;
else
dval(rv)-= adj;
goto cont;
}
#endif /*Honor_FLT_ROUNDS*/
if (i < 0)
{
/*
Error is less than half an ulp -- check for special case of mantissa
a power of two.
*/
if (dsign || word1(rv) || word0(rv) & Bndry_mask ||
(word0(rv) & Exp_mask) <= (2 * P + 1) * Exp_msk1)
{
#ifdef SET_INEXACT
if (!delta->x[0] && delta->wds <= 1)
inexact= 0;
#endif
break;
}
if (!delta->p.x[0] && delta->wds <= 1)
{
/* exact result */
#ifdef SET_INEXACT
inexact= 0;
#endif
break;
}
delta= lshift(delta, Log2P, &alloc);
if (cmp(delta, bs) > 0)
goto drop_down;
break;
}
if (i == 0)
{
/* exactly half-way between */
if (dsign)
{
if ((word0(rv) & Bndry_mask1) == Bndry_mask1 &&
word1(rv) ==
((scale && (y = word0(rv) & Exp_mask) <= 2 * P * Exp_msk1) ?
(0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
0xffffffff))
{
/*boundary case -- increment exponent*/
word0(rv)= (word0(rv) & Exp_mask) + Exp_msk1;
word1(rv) = 0;
dsign = 0;
break;
}
}
else if (!(word0(rv) & Bndry_mask) && !word1(rv))
{
drop_down:
/* boundary case -- decrement exponent */
if (scale)
{
L= word0(rv) & Exp_mask;
if (L <= (2 *P + 1) * Exp_msk1)
{
if (L > (P + 2) * Exp_msk1)
/* round even ==> accept rv */
break;
/* rv = smallest denormal */
goto undfl;
}
}
L= (word0(rv) & Exp_mask) - Exp_msk1;
word0(rv)= L | Bndry_mask1;
word1(rv)= 0xffffffff;
break;
}
if (!(word1(rv) & LSB))
break;
if (dsign)
dval(rv)+= ulp(dval(rv));
else
{
dval(rv)-= ulp(dval(rv));
if (!dval(rv))
goto undfl;
}
dsign= 1 - dsign;
break;
}
if ((aadj= ratio(delta, bs)) <= 2.)
{
if (dsign)
aadj= aadj1= 1.;
else if (word1(rv) || word0(rv) & Bndry_mask)
{
if (word1(rv) == Tiny1 && !word0(rv))
goto undfl;
aadj= 1.;
aadj1= -1.;
}
else
{
/* special case -- power of FLT_RADIX to be rounded down... */
if (aadj < 2. / FLT_RADIX)
aadj= 1. / FLT_RADIX;
else
aadj*= 0.5;
aadj1= -aadj;
}
}
else
{
aadj*= 0.5;
aadj1= dsign ? aadj : -aadj;
#ifdef Check_FLT_ROUNDS
switch (Rounding)
{
case 2: /* towards +infinity */
aadj1-= 0.5;
break;
case 0: /* towards 0 */
case 3: /* towards -infinity */
aadj1+= 0.5;
}
#else
if (Flt_Rounds == 0)
aadj1+= 0.5;
#endif /*Check_FLT_ROUNDS*/
}
y= word0(rv) & Exp_mask;
/* Check for overflow */
if (y == Exp_msk1 * (DBL_MAX_EXP + Bias - 1))
{
dval(rv0)= dval(rv);
word0(rv)-= P * Exp_msk1;
adj= aadj1 * ulp(dval(rv));
dval(rv)+= adj;
if ((word0(rv) & Exp_mask) >= Exp_msk1 * (DBL_MAX_EXP + Bias - P))
{
if (word0(rv0) == Big0 && word1(rv0) == Big1)
goto ovfl;
word0(rv)= Big0;
word1(rv)= Big1;
goto cont;
}
else
word0(rv)+= P * Exp_msk1;
}
else
{
if (scale && y <= 2 * P * Exp_msk1)
{
if (aadj <= 0x7fffffff)
{
if ((z= (ULong) aadj) <= 0)
z= 1;
aadj= z;
aadj1= dsign ? aadj : -aadj;
}
word0(aadj1)+= (2 * P + 1) * Exp_msk1 - y;
}
adj = aadj1 * ulp(dval(rv));
dval(rv) += adj;
}
z= word0(rv) & Exp_mask;
#ifndef SET_INEXACT
if (!scale)
if (y == z)
{
/* Can we stop now? */
L= (Long)aadj;
aadj-= L;
/* The tolerances below are conservative. */
if (dsign || word1(rv) || word0(rv) & Bndry_mask)
{
if (aadj < .4999999 || aadj > .5000001)
break;
}
else if (aadj < .4999999 / FLT_RADIX)
break;
}
#endif
cont:
Bfree(bb, &alloc);
Bfree(bd, &alloc);
Bfree(bs, &alloc);
Bfree(delta, &alloc);
}
#ifdef SET_INEXACT
if (inexact)
{
if (!oldinexact)
{
word0(rv0)= Exp_1 + (70 << Exp_shift);
word1(rv0)= 0;
dval(rv0)+= 1.;
}
}
else if (!oldinexact)
clear_inexact();
#endif
if (scale)
{
word0(rv0)= Exp_1 - 2 * P * Exp_msk1;
word1(rv0)= 0;
dval(rv)*= dval(rv0);
}
#ifdef SET_INEXACT
if (inexact && !(word0(rv) & Exp_mask))
{
/* set underflow bit */
dval(rv0)= 1e-300;
dval(rv0)*= dval(rv0);
}
#endif
retfree:
Bfree(bb, &alloc);
Bfree(bd, &alloc);
Bfree(bs, &alloc);
Bfree(bd0, &alloc);
Bfree(delta, &alloc);
ret:
*se= (char *)s;
return sign ? -dval(rv) : dval(rv);
}
static int quorem(Bigint *b, Bigint *S)
{
int n;
ULong *bx, *bxe, q, *sx, *sxe;
ULLong borrow, carry, y, ys;
n= S->wds;
if (b->wds < n)
return 0;
sx= S->p.x;
sxe= sx + --n;
bx= b->p.x;
bxe= bx + n;
q= *bxe / (*sxe + 1); /* ensure q <= true quotient */
if (q)
{
borrow= 0;
carry= 0;
do
{
ys= *sx++ * (ULLong)q + carry;
carry= ys >> 32;
y= *bx - (ys & FFFFFFFF) - borrow;
borrow= y >> 32 & (ULong)1;
*bx++= (ULong) (y & FFFFFFFF);
}
while (sx <= sxe);
if (!*bxe)
{
bx= b->p.x;
while (--bxe > bx && !*bxe)
--n;
b->wds= n;
}
}
if (cmp(b, S) >= 0)
{
q++;
borrow= 0;
carry= 0;
bx= b->p.x;
sx= S->p.x;
do
{
ys= *sx++ + carry;
carry= ys >> 32;
y= *bx - (ys & FFFFFFFF) - borrow;
borrow= y >> 32 & (ULong)1;
*bx++= (ULong) (y & FFFFFFFF);
}
while (sx <= sxe);
bx= b->p.x;
bxe= bx + n;
if (!*bxe)
{
while (--bxe > bx && !*bxe)
--n;
b->wds= n;
}
}
return q;
}
/*
dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
Inspired by "How to Print Floating-Point Numbers Accurately" by
Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126].
Modifications:
1. Rather than iterating, we use a simple numeric overestimate
to determine k= floor(log10(d)). We scale relevant
quantities using O(log2(k)) rather than O(k) multiplications.
2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
try to generate digits strictly left to right. Instead, we
compute with fewer bits and propagate the carry if necessary
when rounding the final digit up. This is often faster.
3. Under the assumption that input will be rounded nearest,
mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
That is, we allow equality in stopping tests when the
round-nearest rule will give the same floating-point value
as would satisfaction of the stopping test with strict
inequality.
4. We remove common factors of powers of 2 from relevant
quantities.
5. When converting floating-point integers less than 1e16,
we use floating-point arithmetic rather than resorting
to multiple-precision integers.
6. When asked to produce fewer than 15 digits, we first try
to get by with floating-point arithmetic; we resort to
multiple-precision integer arithmetic only if we cannot
guarantee that the floating-point calculation has given
the correctly rounded result. For k requested digits and
"uniformly" distributed input, the probability is
something like 10^(k-15) that we must resort to the Long
calculation.
*/
static char *dtoa(double d, int mode, int ndigits, int *decpt, int *sign,
char **rve, char *buf, size_t buf_size)
{
/*
Arguments ndigits, decpt, sign are similar to those
of ecvt and fcvt; trailing zeros are suppressed from
the returned string. If not null, *rve is set to point
to the end of the return value. If d is +-Infinity or NaN,
then *decpt is set to DTOA_OVERFLOW.
mode:
0 ==> shortest string that yields d when read in
and rounded to nearest.
1 ==> like 0, but with Steele & White stopping rule;
e.g. with IEEE P754 arithmetic , mode 0 gives
1e23 whereas mode 1 gives 9.999999999999999e22.
2 ==> max(1,ndigits) significant digits. This gives a
return value similar to that of ecvt, except
that trailing zeros are suppressed.
3 ==> through ndigits past the decimal point. This
gives a return value similar to that from fcvt,
except that trailing zeros are suppressed, and
ndigits can be negative.
4,5 ==> similar to 2 and 3, respectively, but (in
round-nearest mode) with the tests of mode 0 to
possibly return a shorter string that rounds to d.
With IEEE arithmetic and compilation with
-DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
as modes 2 and 3 when FLT_ROUNDS != 1.
6-9 ==> Debugging modes similar to mode - 4: don't try
fast floating-point estimate (if applicable).
Values of mode other than 0-9 are treated as mode 0.
Sufficient space is allocated to the return value
to hold the suppressed trailing zeros.
*/
int bbits, b2, b5, be, dig, i, ieps, UNINIT_VAR(ilim), ilim0,
UNINIT_VAR(ilim1), j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
spec_case, try_quick;
Long L;
int denorm;
ULong x;
Bigint *b, *b1, *delta, *mlo, *mhi, *S;
double d2, ds, eps;
char *s, *s0;
#ifdef Honor_FLT_ROUNDS
int rounding;
#endif
Stack_alloc alloc;
alloc.begin= alloc.free= buf;
alloc.end= buf + buf_size;
memset(alloc.freelist, 0, sizeof(alloc.freelist));
if (word0(d) & Sign_bit)
{
/* set sign for everything, including 0's and NaNs */
*sign= 1;
word0(d) &= ~Sign_bit; /* clear sign bit */
}
else
*sign= 0;
/* If infinity, set decpt to DTOA_OVERFLOW, if 0 set it to 1 */
if (((word0(d) & Exp_mask) == Exp_mask && (*decpt= DTOA_OVERFLOW)) ||
(!dval(d) && (*decpt= 1)))
{
/* Infinity, NaN, 0 */
char *res= (char*) dtoa_alloc(2, &alloc);
res[0]= '0';
res[1]= '\0';
if (rve)
*rve= res + 1;
return res;
}
#ifdef Honor_FLT_ROUNDS
if ((rounding= Flt_Rounds) >= 2)
{
if (*sign)
rounding= rounding == 2 ? 0 : 2;
else
if (rounding != 2)
rounding= 0;
}
#endif
b= d2b(dval(d), &be, &bbits, &alloc);
if ((i= (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1))))
{
dval(d2)= dval(d);
word0(d2) &= Frac_mask1;
word0(d2) |= Exp_11;
/*
log(x) ~=~ log(1.5) + (x-1.5)/1.5
log10(x) = log(x) / log(10)
~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
log10(d)= (i-Bias)*log(2)/log(10) + log10(d2)
This suggests computing an approximation k to log10(d) by
k= (i - Bias)*0.301029995663981
+ ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
We want k to be too large rather than too small.
The error in the first-order Taylor series approximation
is in our favor, so we just round up the constant enough
to compensate for any error in the multiplication of
(i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
adding 1e-13 to the constant term more than suffices.
Hence we adjust the constant term to 0.1760912590558.
(We could get a more accurate k by invoking log10,
but this is probably not worthwhile.)
*/
i-= Bias;
denorm= 0;
}
else
{
/* d is denormalized */
i= bbits + be + (Bias + (P-1) - 1);
x= i > 32 ? word0(d) << (64 - i) | word1(d) >> (i - 32)
: word1(d) << (32 - i);
dval(d2)= x;
word0(d2)-= 31*Exp_msk1; /* adjust exponent */
i-= (Bias + (P-1) - 1) + 1;
denorm= 1;
}
ds= (dval(d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
k= (int)ds;
if (ds < 0. && ds != k)
k--; /* want k= floor(ds) */
k_check= 1;
if (k >= 0 && k <= Ten_pmax)
{
if (dval(d) < tens[k])
k--;
k_check= 0;
}
j= bbits - i - 1;
if (j >= 0)
{
b2= 0;
s2= j;
}
else
{
b2= -j;
s2= 0;
}
if (k >= 0)
{
b5= 0;
s5= k;
s2+= k;
}
else
{
b2-= k;
b5= -k;
s5= 0;
}
if (mode < 0 || mode > 9)
mode= 0;
#ifdef Check_FLT_ROUNDS
try_quick= Rounding == 1;
#else
try_quick= 1;
#endif
if (mode > 5)
{
mode-= 4;
try_quick= 0;
}
leftright= 1;
switch (mode) {
case 0:
case 1:
ilim= ilim1= -1;
i= 18;
ndigits= 0;
break;
case 2:
leftright= 0;
/* no break */
case 4:
if (ndigits <= 0)
ndigits= 1;
ilim= ilim1= i= ndigits;
break;
case 3:
leftright= 0;
/* no break */
case 5:
i= ndigits + k + 1;
ilim= i;
ilim1= i - 1;
if (i <= 0)
i= 1;
}
s= s0= dtoa_alloc(i, &alloc);
#ifdef Honor_FLT_ROUNDS
if (mode > 1 && rounding != 1)
leftright= 0;
#endif
if (ilim >= 0 && ilim <= Quick_max && try_quick)
{
/* Try to get by with floating-point arithmetic. */
i= 0;
dval(d2)= dval(d);
k0= k;
ilim0= ilim;
ieps= 2; /* conservative */
if (k > 0)
{
ds= tens[k&0xf];
j= k >> 4;
if (j & Bletch)
{
/* prevent overflows */
j&= Bletch - 1;
dval(d)/= bigtens[n_bigtens-1];
ieps++;
}
for (; j; j>>= 1, i++)
{
if (j & 1)
{
ieps++;
ds*= bigtens[i];
}
}
dval(d)/= ds;
}
else if ((j1= -k))
{
dval(d)*= tens[j1 & 0xf];
for (j= j1 >> 4; j; j>>= 1, i++)
{
if (j & 1)
{
ieps++;
dval(d)*= bigtens[i];
}
}
}
if (k_check && dval(d) < 1. && ilim > 0)
{
if (ilim1 <= 0)
goto fast_failed;
ilim= ilim1;
k--;
dval(d)*= 10.;
ieps++;
}
dval(eps)= ieps*dval(d) + 7.;
word0(eps)-= (P-1)*Exp_msk1;
if (ilim == 0)
{
S= mhi= 0;
dval(d)-= 5.;
if (dval(d) > dval(eps))
goto one_digit;
if (dval(d) < -dval(eps))
goto no_digits;
goto fast_failed;
}
if (leftright)
{
/* Use Steele & White method of only generating digits needed. */
dval(eps)= 0.5/tens[ilim-1] - dval(eps);
for (i= 0;;)
{
L= (Long) dval(d);
dval(d)-= L;
*s++= '0' + (int)L;
if (dval(d) < dval(eps))
goto ret1;
if (1. - dval(d) < dval(eps))
goto bump_up;
if (++i >= ilim)
break;
dval(eps)*= 10.;
dval(d)*= 10.;
}
}
else
{
/* Generate ilim digits, then fix them up. */
dval(eps)*= tens[ilim-1];
for (i= 1;; i++, dval(d)*= 10.)
{
L= (Long)(dval(d));
if (!(dval(d)-= L))
ilim= i;
*s++= '0' + (int)L;
if (i == ilim)
{
if (dval(d) > 0.5 + dval(eps))
goto bump_up;
else if (dval(d) < 0.5 - dval(eps))
{
while (*--s == '0');
s++;
goto ret1;
}
break;
}
}
}
fast_failed:
s= s0;
dval(d)= dval(d2);
k= k0;
ilim= ilim0;
}
/* Do we have a "small" integer? */
if (be >= 0 && k <= Int_max)
{
/* Yes. */
ds= tens[k];
if (ndigits < 0 && ilim <= 0)
{
S= mhi= 0;
if (ilim < 0 || dval(d) <= 5*ds)
goto no_digits;
goto one_digit;
}
for (i= 1;; i++, dval(d)*= 10.)
{
L= (Long)(dval(d) / ds);
dval(d)-= L*ds;
#ifdef Check_FLT_ROUNDS
/* If FLT_ROUNDS == 2, L will usually be high by 1 */
if (dval(d) < 0)
{
L--;
dval(d)+= ds;
}
#endif
*s++= '0' + (int)L;
if (!dval(d))
{
break;
}
if (i == ilim)
{
#ifdef Honor_FLT_ROUNDS
if (mode > 1)
{
switch (rounding) {
case 0: goto ret1;
case 2: goto bump_up;
}
}
#endif
dval(d)+= dval(d);
if (dval(d) > ds || (dval(d) == ds && L & 1))
{
bump_up:
while (*--s == '9')
if (s == s0)
{
k++;
*s= '0';
break;
}
++*s++;
}
break;
}
}
goto ret1;
}
m2= b2;
m5= b5;
mhi= mlo= 0;
if (leftright)
{
i = denorm ? be + (Bias + (P-1) - 1 + 1) : 1 + P - bbits;
b2+= i;
s2+= i;
mhi= i2b(1, &alloc);
}
if (m2 > 0 && s2 > 0)
{
i= m2 < s2 ? m2 : s2;
b2-= i;
m2-= i;
s2-= i;
}
if (b5 > 0)
{
if (leftright)
{
if (m5 > 0)
{
mhi= pow5mult(mhi, m5, &alloc);
b1= mult(mhi, b, &alloc);
Bfree(b, &alloc);
b= b1;
}
if ((j= b5 - m5))
b= pow5mult(b, j, &alloc);
}
else
b= pow5mult(b, b5, &alloc);
}
S= i2b(1, &alloc);
if (s5 > 0)
S= pow5mult(S, s5, &alloc);
/* Check for special case that d is a normalized power of 2. */
spec_case= 0;
if ((mode < 2 || leftright)
#ifdef Honor_FLT_ROUNDS
&& rounding == 1
#endif
)
{
if (!word1(d) && !(word0(d) & Bndry_mask) &&
word0(d) & (Exp_mask & ~Exp_msk1)
)
{
/* The special case */
b2+= Log2P;
s2+= Log2P;
spec_case= 1;
}
}
/*
Arrange for convenient computation of quotients:
shift left if necessary so divisor has 4 leading 0 bits.
Perhaps we should just compute leading 28 bits of S once
a nd for all and pass them and a shift to quorem, so it
can do shifts and ors to compute the numerator for q.
*/
if ((i= ((s5 ? 32 - hi0bits(S->p.x[S->wds-1]) : 1) + s2) & 0x1f))
i= 32 - i;
if (i > 4)
{
i-= 4;
b2+= i;
m2+= i;
s2+= i;
}
else if (i < 4)
{
i+= 28;
b2+= i;
m2+= i;
s2+= i;
}
if (b2 > 0)
b= lshift(b, b2, &alloc);
if (s2 > 0)
S= lshift(S, s2, &alloc);
if (k_check)
{
if (cmp(b,S) < 0)
{
k--;
/* we botched the k estimate */
b= multadd(b, 10, 0, &alloc);
if (leftright)
mhi= multadd(mhi, 10, 0, &alloc);
ilim= ilim1;
}
}
if (ilim <= 0 && (mode == 3 || mode == 5))
{
if (ilim < 0 || cmp(b,S= multadd(S,5,0, &alloc)) <= 0)
{
/* no digits, fcvt style */
no_digits:
k= -1 - ndigits;
goto ret;
}
one_digit:
*s++= '1';
k++;
goto ret;
}
if (leftright)
{
if (m2 > 0)
mhi= lshift(mhi, m2, &alloc);
/*
Compute mlo -- check for special case that d is a normalized power of 2.
*/
mlo= mhi;
if (spec_case)
{
mhi= Balloc(mhi->k, &alloc);
Bcopy(mhi, mlo);
mhi= lshift(mhi, Log2P, &alloc);
}
for (i= 1;;i++)
{
dig= quorem(b,S) + '0';
/* Do we yet have the shortest decimal string that will round to d? */
j= cmp(b, mlo);
delta= diff(S, mhi, &alloc);
j1= delta->sign ? 1 : cmp(b, delta);
Bfree(delta, &alloc);
if (j1 == 0 && mode != 1 && !(word1(d) & 1)
#ifdef Honor_FLT_ROUNDS
&& rounding >= 1
#endif
)
{
if (dig == '9')
goto round_9_up;
if (j > 0)
dig++;
*s++= dig;
goto ret;
}
if (j < 0 || (j == 0 && mode != 1 && !(word1(d) & 1)))
{
if (!b->p.x[0] && b->wds <= 1)
{
goto accept_dig;
}
#ifdef Honor_FLT_ROUNDS
if (mode > 1)
switch (rounding) {
case 0: goto accept_dig;
case 2: goto keep_dig;
}
#endif /*Honor_FLT_ROUNDS*/
if (j1 > 0)
{
b= lshift(b, 1, &alloc);
j1= cmp(b, S);
if ((j1 > 0 || (j1 == 0 && dig & 1))
&& dig++ == '9')
goto round_9_up;
}
accept_dig:
*s++= dig;
goto ret;
}
if (j1 > 0)
{
#ifdef Honor_FLT_ROUNDS
if (!rounding)
goto accept_dig;
#endif
if (dig == '9')
{ /* possible if i == 1 */
round_9_up:
*s++= '9';
goto roundoff;
}
*s++= dig + 1;
goto ret;
}
#ifdef Honor_FLT_ROUNDS
keep_dig:
#endif
*s++= dig;
if (i == ilim)
break;
b= multadd(b, 10, 0, &alloc);
if (mlo == mhi)
mlo= mhi= multadd(mhi, 10, 0, &alloc);
else
{
mlo= multadd(mlo, 10, 0, &alloc);
mhi= multadd(mhi, 10, 0, &alloc);
}
}
}
else
for (i= 1;; i++)
{
*s++= dig= quorem(b,S) + '0';
if (!b->p.x[0] && b->wds <= 1)
{
goto ret;
}
if (i >= ilim)
break;
b= multadd(b, 10, 0, &alloc);
}
/* Round off last digit */
#ifdef Honor_FLT_ROUNDS
switch (rounding) {
case 0: goto trimzeros;
case 2: goto roundoff;
}
#endif
b= lshift(b, 1, &alloc);
j= cmp(b, S);
if (j > 0 || (j == 0 && dig & 1))
{
roundoff:
while (*--s == '9')
if (s == s0)
{
k++;
*s++= '1';
goto ret;
}
++*s++;
}
else
{
#ifdef Honor_FLT_ROUNDS
trimzeros:
#endif
while (*--s == '0');
s++;
}
ret:
Bfree(S, &alloc);
if (mhi)
{
if (mlo && mlo != mhi)
Bfree(mlo, &alloc);
Bfree(mhi, &alloc);
}
ret1:
Bfree(b, &alloc);
*s= 0;
*decpt= k + 1;
if (rve)
*rve= s;
return s0;
}
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