609 lines
17 KiB
C
609 lines
17 KiB
C
/* IEEE floating point support routines, for GDB, the GNU Debugger.
|
||
Copyright 1991, 1994, 1999, 2000, 2003, 2005
|
||
Free Software Foundation, Inc.
|
||
|
||
This file is part of GDB.
|
||
|
||
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., 51 Franklin Street - Fifth Floor, Boston, MA 02110-1301, USA. */
|
||
|
||
/* This is needed to pick up the NAN macro on some systems. */
|
||
#define _GNU_SOURCE
|
||
|
||
#ifdef HAVE_CONFIG_H
|
||
#include "config.h"
|
||
#endif
|
||
|
||
#include <math.h>
|
||
|
||
#ifdef HAVE_STRING_H
|
||
#include <string.h>
|
||
#endif
|
||
|
||
#include "ansidecl.h"
|
||
#include "libiberty.h"
|
||
#include "floatformat.h"
|
||
|
||
#ifndef INFINITY
|
||
#ifdef HUGE_VAL
|
||
#define INFINITY HUGE_VAL
|
||
#else
|
||
#define INFINITY (1.0 / 0.0)
|
||
#endif
|
||
#endif
|
||
|
||
#ifndef NAN
|
||
#define NAN (0.0 / 0.0)
|
||
#endif
|
||
|
||
static unsigned long get_field (const unsigned char *,
|
||
enum floatformat_byteorders,
|
||
unsigned int,
|
||
unsigned int,
|
||
unsigned int);
|
||
static int floatformat_always_valid (const struct floatformat *fmt,
|
||
const void *from);
|
||
|
||
static int
|
||
floatformat_always_valid (const struct floatformat *fmt ATTRIBUTE_UNUSED,
|
||
const void *from ATTRIBUTE_UNUSED)
|
||
{
|
||
return 1;
|
||
}
|
||
|
||
/* The odds that CHAR_BIT will be anything but 8 are low enough that I'm not
|
||
going to bother with trying to muck around with whether it is defined in
|
||
a system header, what we do if not, etc. */
|
||
#define FLOATFORMAT_CHAR_BIT 8
|
||
|
||
/* floatformats for IEEE single and double, big and little endian. */
|
||
const struct floatformat floatformat_ieee_single_big =
|
||
{
|
||
floatformat_big, 32, 0, 1, 8, 127, 255, 9, 23,
|
||
floatformat_intbit_no,
|
||
"floatformat_ieee_single_big",
|
||
floatformat_always_valid
|
||
};
|
||
const struct floatformat floatformat_ieee_single_little =
|
||
{
|
||
floatformat_little, 32, 0, 1, 8, 127, 255, 9, 23,
|
||
floatformat_intbit_no,
|
||
"floatformat_ieee_single_little",
|
||
floatformat_always_valid
|
||
};
|
||
const struct floatformat floatformat_ieee_double_big =
|
||
{
|
||
floatformat_big, 64, 0, 1, 11, 1023, 2047, 12, 52,
|
||
floatformat_intbit_no,
|
||
"floatformat_ieee_double_big",
|
||
floatformat_always_valid
|
||
};
|
||
const struct floatformat floatformat_ieee_double_little =
|
||
{
|
||
floatformat_little, 64, 0, 1, 11, 1023, 2047, 12, 52,
|
||
floatformat_intbit_no,
|
||
"floatformat_ieee_double_little",
|
||
floatformat_always_valid
|
||
};
|
||
|
||
/* floatformat for IEEE double, little endian byte order, with big endian word
|
||
ordering, as on the ARM. */
|
||
|
||
const struct floatformat floatformat_ieee_double_littlebyte_bigword =
|
||
{
|
||
floatformat_littlebyte_bigword, 64, 0, 1, 11, 1023, 2047, 12, 52,
|
||
floatformat_intbit_no,
|
||
"floatformat_ieee_double_littlebyte_bigword",
|
||
floatformat_always_valid
|
||
};
|
||
|
||
static int floatformat_i387_ext_is_valid (const struct floatformat *fmt,
|
||
const void *from);
|
||
|
||
static int
|
||
floatformat_i387_ext_is_valid (const struct floatformat *fmt, const void *from)
|
||
{
|
||
/* In the i387 double-extended format, if the exponent is all ones,
|
||
then the integer bit must be set. If the exponent is neither 0
|
||
nor ~0, the intbit must also be set. Only if the exponent is
|
||
zero can it be zero, and then it must be zero. */
|
||
unsigned long exponent, int_bit;
|
||
const unsigned char *ufrom = from;
|
||
|
||
exponent = get_field (ufrom, fmt->byteorder, fmt->totalsize,
|
||
fmt->exp_start, fmt->exp_len);
|
||
int_bit = get_field (ufrom, fmt->byteorder, fmt->totalsize,
|
||
fmt->man_start, 1);
|
||
|
||
if ((exponent == 0) != (int_bit == 0))
|
||
return 0;
|
||
else
|
||
return 1;
|
||
}
|
||
|
||
const struct floatformat floatformat_i387_ext =
|
||
{
|
||
floatformat_little, 80, 0, 1, 15, 0x3fff, 0x7fff, 16, 64,
|
||
floatformat_intbit_yes,
|
||
"floatformat_i387_ext",
|
||
floatformat_i387_ext_is_valid
|
||
};
|
||
const struct floatformat floatformat_m68881_ext =
|
||
{
|
||
/* Note that the bits from 16 to 31 are unused. */
|
||
floatformat_big, 96, 0, 1, 15, 0x3fff, 0x7fff, 32, 64,
|
||
floatformat_intbit_yes,
|
||
"floatformat_m68881_ext",
|
||
floatformat_always_valid
|
||
};
|
||
const struct floatformat floatformat_i960_ext =
|
||
{
|
||
/* Note that the bits from 0 to 15 are unused. */
|
||
floatformat_little, 96, 16, 17, 15, 0x3fff, 0x7fff, 32, 64,
|
||
floatformat_intbit_yes,
|
||
"floatformat_i960_ext",
|
||
floatformat_always_valid
|
||
};
|
||
const struct floatformat floatformat_m88110_ext =
|
||
{
|
||
floatformat_big, 80, 0, 1, 15, 0x3fff, 0x7fff, 16, 64,
|
||
floatformat_intbit_yes,
|
||
"floatformat_m88110_ext",
|
||
floatformat_always_valid
|
||
};
|
||
const struct floatformat floatformat_m88110_harris_ext =
|
||
{
|
||
/* Harris uses raw format 128 bytes long, but the number is just an ieee
|
||
double, and the last 64 bits are wasted. */
|
||
floatformat_big,128, 0, 1, 11, 0x3ff, 0x7ff, 12, 52,
|
||
floatformat_intbit_no,
|
||
"floatformat_m88110_ext_harris",
|
||
floatformat_always_valid
|
||
};
|
||
const struct floatformat floatformat_arm_ext_big =
|
||
{
|
||
/* Bits 1 to 16 are unused. */
|
||
floatformat_big, 96, 0, 17, 15, 0x3fff, 0x7fff, 32, 64,
|
||
floatformat_intbit_yes,
|
||
"floatformat_arm_ext_big",
|
||
floatformat_always_valid
|
||
};
|
||
const struct floatformat floatformat_arm_ext_littlebyte_bigword =
|
||
{
|
||
/* Bits 1 to 16 are unused. */
|
||
floatformat_littlebyte_bigword, 96, 0, 17, 15, 0x3fff, 0x7fff, 32, 64,
|
||
floatformat_intbit_yes,
|
||
"floatformat_arm_ext_littlebyte_bigword",
|
||
floatformat_always_valid
|
||
};
|
||
const struct floatformat floatformat_ia64_spill_big =
|
||
{
|
||
floatformat_big, 128, 0, 1, 17, 65535, 0x1ffff, 18, 64,
|
||
floatformat_intbit_yes,
|
||
"floatformat_ia64_spill_big",
|
||
floatformat_always_valid
|
||
};
|
||
const struct floatformat floatformat_ia64_spill_little =
|
||
{
|
||
floatformat_little, 128, 0, 1, 17, 65535, 0x1ffff, 18, 64,
|
||
floatformat_intbit_yes,
|
||
"floatformat_ia64_spill_little",
|
||
floatformat_always_valid
|
||
};
|
||
const struct floatformat floatformat_ia64_quad_big =
|
||
{
|
||
floatformat_big, 128, 0, 1, 15, 16383, 0x7fff, 16, 112,
|
||
floatformat_intbit_no,
|
||
"floatformat_ia64_quad_big",
|
||
floatformat_always_valid
|
||
};
|
||
const struct floatformat floatformat_ia64_quad_little =
|
||
{
|
||
floatformat_little, 128, 0, 1, 15, 16383, 0x7fff, 16, 112,
|
||
floatformat_intbit_no,
|
||
"floatformat_ia64_quad_little",
|
||
floatformat_always_valid
|
||
};
|
||
|
||
/* Extract a field which starts at START and is LEN bits long. DATA and
|
||
TOTAL_LEN are the thing we are extracting it from, in byteorder ORDER. */
|
||
static unsigned long
|
||
get_field (const unsigned char *data, enum floatformat_byteorders order,
|
||
unsigned int total_len, unsigned int start, unsigned int len)
|
||
{
|
||
unsigned long result;
|
||
unsigned int cur_byte;
|
||
int cur_bitshift;
|
||
|
||
/* Start at the least significant part of the field. */
|
||
cur_byte = (start + len) / FLOATFORMAT_CHAR_BIT;
|
||
if (order == floatformat_little)
|
||
cur_byte = (total_len / FLOATFORMAT_CHAR_BIT) - cur_byte - 1;
|
||
cur_bitshift =
|
||
((start + len) % FLOATFORMAT_CHAR_BIT) - FLOATFORMAT_CHAR_BIT;
|
||
result = *(data + cur_byte) >> (-cur_bitshift);
|
||
cur_bitshift += FLOATFORMAT_CHAR_BIT;
|
||
if (order == floatformat_little)
|
||
++cur_byte;
|
||
else
|
||
--cur_byte;
|
||
|
||
/* Move towards the most significant part of the field. */
|
||
while ((unsigned int) cur_bitshift < len)
|
||
{
|
||
if (len - cur_bitshift < FLOATFORMAT_CHAR_BIT)
|
||
/* This is the last byte; zero out the bits which are not part of
|
||
this field. */
|
||
result |=
|
||
(*(data + cur_byte) & ((1 << (len - cur_bitshift)) - 1))
|
||
<< cur_bitshift;
|
||
else
|
||
result |= *(data + cur_byte) << cur_bitshift;
|
||
cur_bitshift += FLOATFORMAT_CHAR_BIT;
|
||
if (order == floatformat_little)
|
||
++cur_byte;
|
||
else
|
||
--cur_byte;
|
||
}
|
||
return result;
|
||
}
|
||
|
||
#ifndef min
|
||
#define min(a, b) ((a) < (b) ? (a) : (b))
|
||
#endif
|
||
|
||
/* Convert from FMT to a double.
|
||
FROM is the address of the extended float.
|
||
Store the double in *TO. */
|
||
|
||
void
|
||
floatformat_to_double (const struct floatformat *fmt,
|
||
const void *from, double *to)
|
||
{
|
||
const unsigned char *ufrom = from;
|
||
double dto;
|
||
long exponent;
|
||
unsigned long mant;
|
||
unsigned int mant_bits, mant_off;
|
||
int mant_bits_left;
|
||
int special_exponent; /* It's a NaN, denorm or zero */
|
||
|
||
exponent = get_field (ufrom, fmt->byteorder, fmt->totalsize,
|
||
fmt->exp_start, fmt->exp_len);
|
||
|
||
/* If the exponent indicates a NaN, we don't have information to
|
||
decide what to do. So we handle it like IEEE, except that we
|
||
don't try to preserve the type of NaN. FIXME. */
|
||
if ((unsigned long) exponent == fmt->exp_nan)
|
||
{
|
||
int nan;
|
||
|
||
mant_off = fmt->man_start;
|
||
mant_bits_left = fmt->man_len;
|
||
nan = 0;
|
||
while (mant_bits_left > 0)
|
||
{
|
||
mant_bits = min (mant_bits_left, 32);
|
||
|
||
if (get_field (ufrom, fmt->byteorder, fmt->totalsize,
|
||
mant_off, mant_bits) != 0)
|
||
{
|
||
/* This is a NaN. */
|
||
nan = 1;
|
||
break;
|
||
}
|
||
|
||
mant_off += mant_bits;
|
||
mant_bits_left -= mant_bits;
|
||
}
|
||
|
||
/* On certain systems (such as GNU/Linux), the use of the
|
||
INFINITY macro below may generate a warning that can not be
|
||
silenced due to a bug in GCC (PR preprocessor/11931). The
|
||
preprocessor fails to recognise the __extension__ keyword in
|
||
conjunction with the GNU/C99 extension for hexadecimal
|
||
floating point constants and will issue a warning when
|
||
compiling with -pedantic. */
|
||
if (nan)
|
||
dto = NAN;
|
||
else
|
||
dto = INFINITY;
|
||
|
||
if (get_field (ufrom, fmt->byteorder, fmt->totalsize, fmt->sign_start, 1))
|
||
dto = -dto;
|
||
|
||
*to = dto;
|
||
|
||
return;
|
||
}
|
||
|
||
mant_bits_left = fmt->man_len;
|
||
mant_off = fmt->man_start;
|
||
dto = 0.0;
|
||
|
||
special_exponent = exponent == 0 || (unsigned long) exponent == fmt->exp_nan;
|
||
|
||
/* Don't bias zero's, denorms or NaNs. */
|
||
if (!special_exponent)
|
||
exponent -= fmt->exp_bias;
|
||
|
||
/* Build the result algebraically. Might go infinite, underflow, etc;
|
||
who cares. */
|
||
|
||
/* If this format uses a hidden bit, explicitly add it in now. Otherwise,
|
||
increment the exponent by one to account for the integer bit. */
|
||
|
||
if (!special_exponent)
|
||
{
|
||
if (fmt->intbit == floatformat_intbit_no)
|
||
dto = ldexp (1.0, exponent);
|
||
else
|
||
exponent++;
|
||
}
|
||
|
||
while (mant_bits_left > 0)
|
||
{
|
||
mant_bits = min (mant_bits_left, 32);
|
||
|
||
mant = get_field (ufrom, fmt->byteorder, fmt->totalsize,
|
||
mant_off, mant_bits);
|
||
|
||
/* Handle denormalized numbers. FIXME: What should we do for
|
||
non-IEEE formats? */
|
||
if (exponent == 0 && mant != 0)
|
||
dto += ldexp ((double)mant,
|
||
(- fmt->exp_bias
|
||
- mant_bits
|
||
- (mant_off - fmt->man_start)
|
||
+ 1));
|
||
else
|
||
dto += ldexp ((double)mant, exponent - mant_bits);
|
||
if (exponent != 0)
|
||
exponent -= mant_bits;
|
||
mant_off += mant_bits;
|
||
mant_bits_left -= mant_bits;
|
||
}
|
||
|
||
/* Negate it if negative. */
|
||
if (get_field (ufrom, fmt->byteorder, fmt->totalsize, fmt->sign_start, 1))
|
||
dto = -dto;
|
||
*to = dto;
|
||
}
|
||
|
||
static void put_field (unsigned char *, enum floatformat_byteorders,
|
||
unsigned int,
|
||
unsigned int,
|
||
unsigned int,
|
||
unsigned long);
|
||
|
||
/* Set a field which starts at START and is LEN bits long. DATA and
|
||
TOTAL_LEN are the thing we are extracting it from, in byteorder ORDER. */
|
||
static void
|
||
put_field (unsigned char *data, enum floatformat_byteorders order,
|
||
unsigned int total_len, unsigned int start, unsigned int len,
|
||
unsigned long stuff_to_put)
|
||
{
|
||
unsigned int cur_byte;
|
||
int cur_bitshift;
|
||
|
||
/* Start at the least significant part of the field. */
|
||
cur_byte = (start + len) / FLOATFORMAT_CHAR_BIT;
|
||
if (order == floatformat_little)
|
||
cur_byte = (total_len / FLOATFORMAT_CHAR_BIT) - cur_byte - 1;
|
||
cur_bitshift =
|
||
((start + len) % FLOATFORMAT_CHAR_BIT) - FLOATFORMAT_CHAR_BIT;
|
||
*(data + cur_byte) &=
|
||
~(((1 << ((start + len) % FLOATFORMAT_CHAR_BIT)) - 1) << (-cur_bitshift));
|
||
*(data + cur_byte) |=
|
||
(stuff_to_put & ((1 << FLOATFORMAT_CHAR_BIT) - 1)) << (-cur_bitshift);
|
||
cur_bitshift += FLOATFORMAT_CHAR_BIT;
|
||
if (order == floatformat_little)
|
||
++cur_byte;
|
||
else
|
||
--cur_byte;
|
||
|
||
/* Move towards the most significant part of the field. */
|
||
while ((unsigned int) cur_bitshift < len)
|
||
{
|
||
if (len - cur_bitshift < FLOATFORMAT_CHAR_BIT)
|
||
{
|
||
/* This is the last byte. */
|
||
*(data + cur_byte) &=
|
||
~((1 << (len - cur_bitshift)) - 1);
|
||
*(data + cur_byte) |= (stuff_to_put >> cur_bitshift);
|
||
}
|
||
else
|
||
*(data + cur_byte) = ((stuff_to_put >> cur_bitshift)
|
||
& ((1 << FLOATFORMAT_CHAR_BIT) - 1));
|
||
cur_bitshift += FLOATFORMAT_CHAR_BIT;
|
||
if (order == floatformat_little)
|
||
++cur_byte;
|
||
else
|
||
--cur_byte;
|
||
}
|
||
}
|
||
|
||
/* The converse: convert the double *FROM to an extended float
|
||
and store where TO points. Neither FROM nor TO have any alignment
|
||
restrictions. */
|
||
|
||
void
|
||
floatformat_from_double (const struct floatformat *fmt,
|
||
const double *from, void *to)
|
||
{
|
||
double dfrom;
|
||
int exponent;
|
||
double mant;
|
||
unsigned int mant_bits, mant_off;
|
||
int mant_bits_left;
|
||
unsigned char *uto = to;
|
||
|
||
dfrom = *from;
|
||
memset (uto, 0, fmt->totalsize / FLOATFORMAT_CHAR_BIT);
|
||
|
||
/* If negative, set the sign bit. */
|
||
if (dfrom < 0)
|
||
{
|
||
put_field (uto, fmt->byteorder, fmt->totalsize, fmt->sign_start, 1, 1);
|
||
dfrom = -dfrom;
|
||
}
|
||
|
||
if (dfrom == 0)
|
||
{
|
||
/* 0.0. */
|
||
return;
|
||
}
|
||
|
||
if (dfrom != dfrom)
|
||
{
|
||
/* NaN. */
|
||
put_field (uto, fmt->byteorder, fmt->totalsize, fmt->exp_start,
|
||
fmt->exp_len, fmt->exp_nan);
|
||
/* Be sure it's not infinity, but NaN value is irrelevant. */
|
||
put_field (uto, fmt->byteorder, fmt->totalsize, fmt->man_start,
|
||
32, 1);
|
||
return;
|
||
}
|
||
|
||
if (dfrom + dfrom == dfrom)
|
||
{
|
||
/* This can only happen for an infinite value (or zero, which we
|
||
already handled above). */
|
||
put_field (uto, fmt->byteorder, fmt->totalsize, fmt->exp_start,
|
||
fmt->exp_len, fmt->exp_nan);
|
||
return;
|
||
}
|
||
|
||
mant = frexp (dfrom, &exponent);
|
||
if (exponent + fmt->exp_bias - 1 > 0)
|
||
put_field (uto, fmt->byteorder, fmt->totalsize, fmt->exp_start,
|
||
fmt->exp_len, exponent + fmt->exp_bias - 1);
|
||
else
|
||
{
|
||
/* Handle a denormalized number. FIXME: What should we do for
|
||
non-IEEE formats? */
|
||
put_field (uto, fmt->byteorder, fmt->totalsize, fmt->exp_start,
|
||
fmt->exp_len, 0);
|
||
mant = ldexp (mant, exponent + fmt->exp_bias - 1);
|
||
}
|
||
|
||
mant_bits_left = fmt->man_len;
|
||
mant_off = fmt->man_start;
|
||
while (mant_bits_left > 0)
|
||
{
|
||
unsigned long mant_long;
|
||
mant_bits = mant_bits_left < 32 ? mant_bits_left : 32;
|
||
|
||
mant *= 4294967296.0;
|
||
mant_long = (unsigned long)mant;
|
||
mant -= mant_long;
|
||
|
||
/* If the integer bit is implicit, and we are not creating a
|
||
denormalized number, then we need to discard it. */
|
||
if ((unsigned int) mant_bits_left == fmt->man_len
|
||
&& fmt->intbit == floatformat_intbit_no
|
||
&& exponent + fmt->exp_bias - 1 > 0)
|
||
{
|
||
mant_long &= 0x7fffffff;
|
||
mant_bits -= 1;
|
||
}
|
||
else if (mant_bits < 32)
|
||
{
|
||
/* The bits we want are in the most significant MANT_BITS bits of
|
||
mant_long. Move them to the least significant. */
|
||
mant_long >>= 32 - mant_bits;
|
||
}
|
||
|
||
put_field (uto, fmt->byteorder, fmt->totalsize,
|
||
mant_off, mant_bits, mant_long);
|
||
mant_off += mant_bits;
|
||
mant_bits_left -= mant_bits;
|
||
}
|
||
}
|
||
|
||
/* Return non-zero iff the data at FROM is a valid number in format FMT. */
|
||
|
||
int
|
||
floatformat_is_valid (const struct floatformat *fmt, const void *from)
|
||
{
|
||
return fmt->is_valid (fmt, from);
|
||
}
|
||
|
||
|
||
#ifdef IEEE_DEBUG
|
||
|
||
#include <stdio.h>
|
||
|
||
/* This is to be run on a host which uses IEEE floating point. */
|
||
|
||
void
|
||
ieee_test (double n)
|
||
{
|
||
double result;
|
||
|
||
floatformat_to_double (&floatformat_ieee_double_little, &n, &result);
|
||
if ((n != result && (! isnan (n) || ! isnan (result)))
|
||
|| (n < 0 && result >= 0)
|
||
|| (n >= 0 && result < 0))
|
||
printf ("Differ(to): %.20g -> %.20g\n", n, result);
|
||
|
||
floatformat_from_double (&floatformat_ieee_double_little, &n, &result);
|
||
if ((n != result && (! isnan (n) || ! isnan (result)))
|
||
|| (n < 0 && result >= 0)
|
||
|| (n >= 0 && result < 0))
|
||
printf ("Differ(from): %.20g -> %.20g\n", n, result);
|
||
|
||
#if 0
|
||
{
|
||
char exten[16];
|
||
|
||
floatformat_from_double (&floatformat_m68881_ext, &n, exten);
|
||
floatformat_to_double (&floatformat_m68881_ext, exten, &result);
|
||
if (n != result)
|
||
printf ("Differ(to+from): %.20g -> %.20g\n", n, result);
|
||
}
|
||
#endif
|
||
|
||
#if IEEE_DEBUG > 1
|
||
/* This is to be run on a host which uses 68881 format. */
|
||
{
|
||
long double ex = *(long double *)exten;
|
||
if (ex != n)
|
||
printf ("Differ(from vs. extended): %.20g\n", n);
|
||
}
|
||
#endif
|
||
}
|
||
|
||
int
|
||
main (void)
|
||
{
|
||
ieee_test (0.0);
|
||
ieee_test (0.5);
|
||
ieee_test (256.0);
|
||
ieee_test (0.12345);
|
||
ieee_test (234235.78907234);
|
||
ieee_test (-512.0);
|
||
ieee_test (-0.004321);
|
||
ieee_test (1.2E-70);
|
||
ieee_test (1.2E-316);
|
||
ieee_test (4.9406564584124654E-324);
|
||
ieee_test (- 4.9406564584124654E-324);
|
||
ieee_test (- 0.0);
|
||
ieee_test (- INFINITY);
|
||
ieee_test (- NAN);
|
||
ieee_test (INFINITY);
|
||
ieee_test (NAN);
|
||
return 0;
|
||
}
|
||
#endif
|