/* real.c - software floating point emulation.
- Copyright (C) 1993, 1994, 1995, 1996, 1997, 1998, 1999,
- 2000, 2002, 2003, 2004, 2005, 2007 Free Software Foundation, Inc.
+ Copyright (C) 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2002,
+ 2003, 2004, 2005, 2007, 2008, 2009, 2010, 2011
+ Free Software Foundation, Inc.
Contributed by Stephen L. Moshier (moshier@world.std.com).
Re-written by Richard Henderson <rth@redhat.com>
GCC 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, or (at your option) any later
+ Software Foundation; either version 3, or (at your option) any later
version.
GCC is distributed in the hope that it will be useful, but WITHOUT ANY
for more details.
You should have received a copy of the GNU General Public License
- along with GCC; see the file COPYING. If not, write to the Free
- Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA
- 02110-1301, USA. */
+ along with GCC; see the file COPYING3. If not see
+ <http://www.gnu.org/licenses/>. */
#include "config.h"
#include "system.h"
#include "coretypes.h"
#include "tm.h"
#include "tree.h"
-#include "toplev.h"
+#include "diagnostic-core.h"
#include "real.h"
+#include "realmpfr.h"
#include "tm_p.h"
#include "dfp.h"
Both of these requirements are easily satisfied. The largest target
significand is 113 bits; we store at least 160. The smallest
- denormal number fits in 17 exponent bits; we store 27.
+ denormal number fits in 17 exponent bits; we store 26.
Note that the decimal string conversion routines are sensitive to
rounding errors. Since the raw arithmetic routines do not themselves
static void do_fix_trunc (REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *);
static unsigned long rtd_divmod (REAL_VALUE_TYPE *, REAL_VALUE_TYPE *);
+static void decimal_from_integer (REAL_VALUE_TYPE *);
+static void decimal_integer_string (char *, const REAL_VALUE_TYPE *,
+ size_t);
static const REAL_VALUE_TYPE * ten_to_ptwo (int);
static const REAL_VALUE_TYPE * ten_to_mptwo (int);
/* Sign of zero doesn't matter for compares. */
return 0;
+ case CLASS2 (rvc_normal, rvc_zero):
+ /* Decimal float zero is special and uses rvc_normal, not rvc_zero. */
+ if (a->decimal)
+ return decimal_do_compare (a, b, nan_result);
+ /* Fall through. */
case CLASS2 (rvc_inf, rvc_zero):
case CLASS2 (rvc_inf, rvc_normal):
- case CLASS2 (rvc_normal, rvc_zero):
return (a->sign ? -1 : 1);
case CLASS2 (rvc_inf, rvc_inf):
return -a->sign - -b->sign;
case CLASS2 (rvc_zero, rvc_normal):
+ /* Decimal float zero is special and uses rvc_normal, not rvc_zero. */
+ if (b->decimal)
+ return decimal_do_compare (a, b, nan_result);
+ /* Fall through. */
case CLASS2 (rvc_zero, rvc_inf):
case CLASS2 (rvc_normal, rvc_inf):
return (b->sign ? 1 : -1);
real_arithmetic (REAL_VALUE_TYPE *r, int icode, const REAL_VALUE_TYPE *op0,
const REAL_VALUE_TYPE *op1)
{
- enum tree_code code = icode;
+ enum tree_code code = (enum tree_code) icode;
if (op0->decimal || (op1 && op1->decimal))
- return decimal_real_arithmetic (r, icode, op0, op1);
+ return decimal_real_arithmetic (r, code, op0, op1);
switch (code)
{
case PLUS_EXPR:
+ /* Clear any padding areas in *r if it isn't equal to one of the
+ operands so that we can later do bitwise comparisons later on. */
+ if (r != op0 && r != op1)
+ memset (r, '\0', sizeof (*r));
return do_add (r, op0, op1, 0);
case MINUS_EXPR:
+ if (r != op0 && r != op1)
+ memset (r, '\0', sizeof (*r));
return do_add (r, op0, op1, 1);
case MULT_EXPR:
+ if (r != op0 && r != op1)
+ memset (r, '\0', sizeof (*r));
return do_multiply (r, op0, op1);
case RDIV_EXPR:
+ if (r != op0 && r != op1)
+ memset (r, '\0', sizeof (*r));
return do_divide (r, op0, op1);
case MIN_EXPR:
return false;
}
-/* Legacy. Similar, but return the result directly. */
+REAL_VALUE_TYPE
+real_value_negate (const REAL_VALUE_TYPE *op0)
+{
+ REAL_VALUE_TYPE r;
+ real_arithmetic (&r, NEGATE_EXPR, op0, NULL);
+ return r;
+}
REAL_VALUE_TYPE
-real_arithmetic2 (int icode, const REAL_VALUE_TYPE *op0,
- const REAL_VALUE_TYPE *op1)
+real_value_abs (const REAL_VALUE_TYPE *op0)
{
REAL_VALUE_TYPE r;
- real_arithmetic (&r, icode, op0, op1);
+ real_arithmetic (&r, ABS_EXPR, op0, NULL);
return r;
}
real_compare (int icode, const REAL_VALUE_TYPE *op0,
const REAL_VALUE_TYPE *op1)
{
- enum tree_code code = icode;
+ enum tree_code code = (enum tree_code) icode;
switch (code)
{
*r = u;
return true;
}
+
+/* Return true if arithmetic on values in IMODE that were promoted
+ from values in TMODE is equivalent to direct arithmetic on values
+ in TMODE. */
+
+bool
+real_can_shorten_arithmetic (enum machine_mode imode, enum machine_mode tmode)
+{
+ const struct real_format *tfmt, *ifmt;
+ tfmt = REAL_MODE_FORMAT (tmode);
+ ifmt = REAL_MODE_FORMAT (imode);
+ /* These conditions are conservative rather than trying to catch the
+ exact boundary conditions; the main case to allow is IEEE float
+ and double. */
+ return (ifmt->b == tfmt->b
+ && ifmt->p > 2 * tfmt->p
+ && ifmt->emin < 2 * tfmt->emin - tfmt->p - 2
+ && ifmt->emin < tfmt->emin - tfmt->emax - tfmt->p - 2
+ && ifmt->emax > 2 * tfmt->emax + 2
+ && ifmt->emax > tfmt->emax - tfmt->emin + tfmt->p + 2
+ && ifmt->round_towards_zero == tfmt->round_towards_zero
+ && (ifmt->has_sign_dependent_rounding
+ == tfmt->has_sign_dependent_rounding)
+ && ifmt->has_nans >= tfmt->has_nans
+ && ifmt->has_inf >= tfmt->has_inf
+ && ifmt->has_signed_zero >= tfmt->has_signed_zero
+ && !MODE_COMPOSITE_P (tmode)
+ && !MODE_COMPOSITE_P (imode));
+}
\f
/* Render R as an integer. */
if (HOST_BITS_PER_WIDE_INT == HOST_BITS_PER_LONG)
i = r->sig[SIGSZ-1];
- else
+ else
{
gcc_assert (HOST_BITS_PER_WIDE_INT == 2 * HOST_BITS_PER_LONG);
i = r->sig[SIGSZ-1];
case rvc_normal:
if (r->decimal)
- {
+ {
decimal_real_to_integer2 (plow, phigh, r);
return;
}
-
+
exp = REAL_EXP (r);
if (exp <= 0)
goto underflow;
high = t.sig[SIGSZ-1];
low = t.sig[SIGSZ-2];
}
- else
+ else
{
gcc_assert (HOST_BITS_PER_WIDE_INT == 2*HOST_BITS_PER_LONG);
high = t.sig[SIGSZ-1];
/* Render R as a decimal floating point constant. Emit DIGITS significant
digits in the result, bounded by BUF_SIZE. If DIGITS is 0, choose the
maximum for the representation. If CROP_TRAILING_ZEROS, strip trailing
- zeros. */
+ zeros. If MODE is VOIDmode, round to nearest value. Otherwise, round
+ to a string that, when parsed back in mode MODE, yields the same value. */
#define M_LOG10_2 0.30102999566398119521
void
-real_to_decimal (char *str, const REAL_VALUE_TYPE *r_orig, size_t buf_size,
- size_t digits, int crop_trailing_zeros)
+real_to_decimal_for_mode (char *str, const REAL_VALUE_TYPE *r_orig,
+ size_t buf_size, size_t digits,
+ int crop_trailing_zeros, enum machine_mode mode)
{
+ const struct real_format *fmt = NULL;
const REAL_VALUE_TYPE *one, *ten;
REAL_VALUE_TYPE r, pten, u, v;
int dec_exp, cmp_one, digit;
size_t max_digits;
char *p, *first, *last;
bool sign;
+ bool round_up;
+
+ if (mode != VOIDmode)
+ {
+ fmt = REAL_MODE_FORMAT (mode);
+ gcc_assert (fmt);
+ }
r = *r_orig;
switch (r.cl)
return;
case rvc_nan:
/* ??? Print the significand as well, if not canonical? */
- strcpy (str, (r.sign ? "-NaN" : "+NaN"));
+ sprintf (str, "%c%cNaN", (r_orig->sign ? '-' : '+'),
+ (r_orig->signalling ? 'S' : 'Q'));
return;
default:
gcc_unreachable ();
digit = rtd_divmod (&r, &pten);
/* Round the result. */
- if (digit == 5)
+ if (fmt && fmt->round_towards_zero)
{
- /* Round to nearest. If R is nonzero there are additional
- nonzero digits to be extracted. */
+ /* If the format uses round towards zero when parsing the string
+ back in, we need to always round away from zero here. */
if (cmp_significand_0 (&r))
digit++;
- /* Round to even. */
- else if ((p[-1] - '0') & 1)
- digit++;
+ round_up = digit > 0;
}
- if (digit > 5)
+ else
+ {
+ if (digit == 5)
+ {
+ /* Round to nearest. If R is nonzero there are additional
+ nonzero digits to be extracted. */
+ if (cmp_significand_0 (&r))
+ digit++;
+ /* Round to even. */
+ else if ((p[-1] - '0') & 1)
+ digit++;
+ }
+
+ round_up = digit > 5;
+ }
+
+ if (round_up)
{
while (p > first)
{
/* Append the exponent. */
sprintf (last, "e%+d", dec_exp);
+
+#ifdef ENABLE_CHECKING
+ /* Verify that we can read the original value back in. */
+ if (mode != VOIDmode)
+ {
+ real_from_string (&r, str);
+ real_convert (&r, mode, &r);
+ gcc_assert (real_identical (&r, r_orig));
+ }
+#endif
+}
+
+/* Likewise, except always uses round-to-nearest. */
+
+void
+real_to_decimal (char *str, const REAL_VALUE_TYPE *r_orig, size_t buf_size,
+ size_t digits, int crop_trailing_zeros)
+{
+ real_to_decimal_for_mode (str, r_orig, buf_size,
+ digits, crop_trailing_zeros, VOIDmode);
}
/* Render R as a hexadecimal floating point constant. Emit DIGITS
return;
case rvc_nan:
/* ??? Print the significand as well, if not canonical? */
- strcpy (str, (r->sign ? "-NaN" : "+NaN"));
+ sprintf (str, "%c%cNaN", (r->sign ? '-' : '+'),
+ (r->signalling ? 'S' : 'Q'));
return;
default:
gcc_unreachable ();
else if (*str == '+')
str++;
+ if (!strncmp (str, "QNaN", 4))
+ {
+ get_canonical_qnan (r, sign);
+ return 0;
+ }
+ else if (!strncmp (str, "SNaN", 4))
+ {
+ get_canonical_snan (r, sign);
+ return 0;
+ }
+ else if (!strncmp (str, "Inf", 3))
+ {
+ get_inf (r, sign);
+ return 0;
+ }
+
if (str[0] == '0' && (str[1] == 'x' || str[1] == 'X'))
{
/* Hexadecimal floating point. */
/* Initialize R from string S and desired MODE. */
-void
+void
real_from_string3 (REAL_VALUE_TYPE *r, const char *s, enum machine_mode mode)
{
if (DECIMAL_FLOAT_MODE_P (mode))
real_from_string (r, s);
if (mode != VOIDmode)
- real_convert (r, mode, r);
-}
+ real_convert (r, mode, r);
+}
/* Initialize R from the integer pair HIGH+LOW. */
normalize (r);
}
- if (mode != VOIDmode)
+ if (DECIMAL_FLOAT_MODE_P (mode))
+ decimal_from_integer (r);
+ else if (mode != VOIDmode)
real_convert (r, mode, r);
}
+/* Render R, an integral value, as a floating point constant with no
+ specified exponent. */
+
+static void
+decimal_integer_string (char *str, const REAL_VALUE_TYPE *r_orig,
+ size_t buf_size)
+{
+ int dec_exp, digit, digits;
+ REAL_VALUE_TYPE r, pten;
+ char *p;
+ bool sign;
+
+ r = *r_orig;
+
+ if (r.cl == rvc_zero)
+ {
+ strcpy (str, "0.");
+ return;
+ }
+
+ sign = r.sign;
+ r.sign = 0;
+
+ dec_exp = REAL_EXP (&r) * M_LOG10_2;
+ digits = dec_exp + 1;
+ gcc_assert ((digits + 2) < (int)buf_size);
+
+ pten = *real_digit (1);
+ times_pten (&pten, dec_exp);
+
+ p = str;
+ if (sign)
+ *p++ = '-';
+
+ digit = rtd_divmod (&r, &pten);
+ gcc_assert (digit >= 0 && digit <= 9);
+ *p++ = digit + '0';
+ while (--digits > 0)
+ {
+ times_pten (&r, 1);
+ digit = rtd_divmod (&r, &pten);
+ *p++ = digit + '0';
+ }
+ *p++ = '.';
+ *p++ = '\0';
+}
+
+/* Convert a real with an integral value to decimal float. */
+
+static void
+decimal_from_integer (REAL_VALUE_TYPE *r)
+{
+ char str[256];
+
+ decimal_integer_string (str, r, sizeof (str) - 1);
+ decimal_real_from_string (r, str);
+}
+
/* Returns 10**2**N. */
static const REAL_VALUE_TYPE *
do_divide (r, r, &pten);
}
+/* Returns the special REAL_VALUE_TYPE corresponding to 'e'. */
+
+const REAL_VALUE_TYPE *
+dconst_e_ptr (void)
+{
+ static REAL_VALUE_TYPE value;
+
+ /* Initialize mathematical constants for constant folding builtins.
+ These constants need to be given to at least 160 bits precision. */
+ if (value.cl == rvc_zero)
+ {
+ mpfr_t m;
+ mpfr_init2 (m, SIGNIFICAND_BITS);
+ mpfr_set_ui (m, 1, GMP_RNDN);
+ mpfr_exp (m, m, GMP_RNDN);
+ real_from_mpfr (&value, m, NULL_TREE, GMP_RNDN);
+ mpfr_clear (m);
+
+ }
+ return &value;
+}
+
+/* Returns the special REAL_VALUE_TYPE corresponding to 1/3. */
+
+const REAL_VALUE_TYPE *
+dconst_third_ptr (void)
+{
+ static REAL_VALUE_TYPE value;
+
+ /* Initialize mathematical constants for constant folding builtins.
+ These constants need to be given to at least 160 bits precision. */
+ if (value.cl == rvc_zero)
+ {
+ real_arithmetic (&value, RDIV_EXPR, &dconst1, real_digit (3));
+ }
+ return &value;
+}
+
+/* Returns the special REAL_VALUE_TYPE corresponding to sqrt(2). */
+
+const REAL_VALUE_TYPE *
+dconst_sqrt2_ptr (void)
+{
+ static REAL_VALUE_TYPE value;
+
+ /* Initialize mathematical constants for constant folding builtins.
+ These constants need to be given to at least 160 bits precision. */
+ if (value.cl == rvc_zero)
+ {
+ mpfr_t m;
+ mpfr_init2 (m, SIGNIFICAND_BITS);
+ mpfr_sqrt_ui (m, 2, GMP_RNDN);
+ real_from_mpfr (&value, m, NULL_TREE, GMP_RNDN);
+ mpfr_clear (m);
+ }
+ return &value;
+}
+
/* Fills R with +Inf. */
void
fmt = REAL_MODE_FORMAT (mode);
gcc_assert (fmt);
memset (r, 0, sizeof (*r));
-
+
if (fmt->b == 10)
decimal_real_maxval (r, sign, mode);
else
required to be the value of the long double rounded to the
nearest double. Rounding means we need a slightly smaller
value for LDBL_MAX. */
- clear_significand_bit (r, SIGNIFICAND_BITS - fmt->pnan);
+ clear_significand_bit (r, SIGNIFICAND_BITS - fmt->pnan - 1);
}
}
/* Fills R with 2**N. */
void
-real_2expN (REAL_VALUE_TYPE *r, int n)
+real_2expN (REAL_VALUE_TYPE *r, int n, enum machine_mode fmode)
{
memset (r, 0, sizeof (*r));
SET_REAL_EXP (r, n);
r->sig[SIGSZ-1] = SIG_MSB;
}
+ if (DECIMAL_FLOAT_MODE_P (fmode))
+ decimal_real_convert (r, fmode, r);
}
\f
round_for_format (const struct real_format *fmt, REAL_VALUE_TYPE *r)
{
int p2, np2, i, w;
- unsigned long sticky;
- bool guard, lsb;
int emin2m1, emax2;
+ bool round_up = false;
if (r->decimal)
{
}
}
- /* There are P2 true significand bits, followed by one guard bit,
- followed by one sticky bit, followed by stuff. Fold nonzero
- stuff into the sticky bit. */
+ if (!fmt->round_towards_zero)
+ {
+ /* There are P2 true significand bits, followed by one guard bit,
+ followed by one sticky bit, followed by stuff. Fold nonzero
+ stuff into the sticky bit. */
+ unsigned long sticky;
+ bool guard, lsb;
- sticky = 0;
- for (i = 0, w = (np2 - 1) / HOST_BITS_PER_LONG; i < w; ++i)
- sticky |= r->sig[i];
- sticky |=
- r->sig[w] & (((unsigned long)1 << ((np2 - 1) % HOST_BITS_PER_LONG)) - 1);
+ sticky = 0;
+ for (i = 0, w = (np2 - 1) / HOST_BITS_PER_LONG; i < w; ++i)
+ sticky |= r->sig[i];
+ sticky |= r->sig[w]
+ & (((unsigned long)1 << ((np2 - 1) % HOST_BITS_PER_LONG)) - 1);
- guard = test_significand_bit (r, np2 - 1);
- lsb = test_significand_bit (r, np2);
+ guard = test_significand_bit (r, np2 - 1);
+ lsb = test_significand_bit (r, np2);
- /* Round to even. */
- if (guard && (sticky || lsb))
+ /* Round to even. */
+ round_up = guard && (sticky || lsb);
+ }
+
+ if (round_up)
{
REAL_VALUE_TYPE u;
get_zero (&u, 0);
128,
31,
31,
+ false,
+ true,
true,
true,
true,
128,
31,
31,
+ false,
+ true,
true,
true,
true,
128,
31,
31,
+ false,
+ true,
true,
true,
true,
true,
true
};
+
+/* SPU Single Precision (Extended-Range Mode) format is the same as IEEE
+ single precision with the following differences:
+ - Infinities are not supported. Instead MAX_FLOAT or MIN_FLOAT
+ are generated.
+ - NaNs are not supported.
+ - The range of non-zero numbers in binary is
+ (001)[1.]000...000 to (255)[1.]111...111.
+ - Denormals can be represented, but are treated as +0.0 when
+ used as an operand and are never generated as a result.
+ - -0.0 can be represented, but a zero result is always +0.0.
+ - the only supported rounding mode is trunction (towards zero). */
+const struct real_format spu_single_format =
+ {
+ encode_ieee_single,
+ decode_ieee_single,
+ 2,
+ 24,
+ 24,
+ -125,
+ 129,
+ 31,
+ 31,
+ true,
+ false,
+ false,
+ false,
+ true,
+ true,
+ false,
+ false
+ };
\f
/* IEEE double-precision format. */
1024,
63,
63,
+ false,
+ true,
true,
true,
true,
1024,
63,
63,
+ false,
+ true,
true,
true,
true,
1024,
63,
63,
+ false,
+ true,
true,
true,
true,
16384,
95,
95,
+ false,
+ true,
true,
true,
true,
16384,
79,
79,
+ false,
+ true,
true,
true,
true,
16384,
79,
79,
+ false,
+ true,
true,
true,
true,
16384,
79,
79,
+ false,
+ true,
true,
true,
true,
base_fmt = fmt->qnan_msb_set ? &ieee_double_format : &mips_double_format;
- /* Renormlize R before doing any arithmetic on it. */
+ /* Renormalize R before doing any arithmetic on it. */
normr = *r;
if (normr.cl == rvc_normal)
normalize (&normr);
1024,
127,
-1,
+ false,
+ true,
true,
true,
true,
1024,
127,
-1,
+ false,
+ true,
true,
true,
true,
16384,
127,
127,
+ false,
+ true,
true,
true,
true,
16384,
127,
127,
+ false,
+ true,
true,
true,
true,
false,
false,
false,
+ false,
+ false,
false
};
false,
false,
false,
+ false,
+ false,
false
};
false,
false,
false,
+ false,
+ false,
false
};
\f
/* Encode real R into a single precision DFP value in BUF. */
static void
encode_decimal_single (const struct real_format *fmt ATTRIBUTE_UNUSED,
- long *buf ATTRIBUTE_UNUSED,
+ long *buf ATTRIBUTE_UNUSED,
const REAL_VALUE_TYPE *r ATTRIBUTE_UNUSED)
{
encode_decimal32 (fmt, buf, r);
}
/* Decode a single precision DFP value in BUF into a real R. */
-static void
+static void
decode_decimal_single (const struct real_format *fmt ATTRIBUTE_UNUSED,
- REAL_VALUE_TYPE *r ATTRIBUTE_UNUSED,
+ REAL_VALUE_TYPE *r ATTRIBUTE_UNUSED,
const long *buf ATTRIBUTE_UNUSED)
{
decode_decimal32 (fmt, r, buf);
}
/* Encode real R into a double precision DFP value in BUF. */
-static void
+static void
encode_decimal_double (const struct real_format *fmt ATTRIBUTE_UNUSED,
- long *buf ATTRIBUTE_UNUSED,
+ long *buf ATTRIBUTE_UNUSED,
const REAL_VALUE_TYPE *r ATTRIBUTE_UNUSED)
{
encode_decimal64 (fmt, buf, r);
}
/* Decode a double precision DFP value in BUF into a real R. */
-static void
+static void
decode_decimal_double (const struct real_format *fmt ATTRIBUTE_UNUSED,
- REAL_VALUE_TYPE *r ATTRIBUTE_UNUSED,
+ REAL_VALUE_TYPE *r ATTRIBUTE_UNUSED,
const long *buf ATTRIBUTE_UNUSED)
{
decode_decimal64 (fmt, r, buf);
}
/* Encode real R into a quad precision DFP value in BUF. */
-static void
+static void
encode_decimal_quad (const struct real_format *fmt ATTRIBUTE_UNUSED,
long *buf ATTRIBUTE_UNUSED,
const REAL_VALUE_TYPE *r ATTRIBUTE_UNUSED)
}
/* Decode a quad precision DFP value in BUF into a real R. */
-static void
+static void
decode_decimal_quad (const struct real_format *fmt ATTRIBUTE_UNUSED,
REAL_VALUE_TYPE *r ATTRIBUTE_UNUSED,
const long *buf ATTRIBUTE_UNUSED)
decode_decimal128 (fmt, r, buf);
}
-/* Single precision decimal floating point (IEEE 754R). */
+/* Single precision decimal floating point (IEEE 754). */
const struct real_format decimal_single_format =
{
encode_decimal_single,
decode_decimal_single,
- 10,
+ 10,
7,
7,
- -95,
- 96,
+ -94,
+ 97,
31,
31,
+ false,
+ true,
+ true,
true,
true,
true,
- true,
true,
false
};
-/* Double precision decimal floating point (IEEE 754R). */
+/* Double precision decimal floating point (IEEE 754). */
const struct real_format decimal_double_format =
{
encode_decimal_double,
10,
16,
16,
- -383,
- 384,
+ -382,
+ 385,
63,
63,
+ false,
+ true,
true,
true,
true,
false
};
-/* Quad precision decimal floating point (IEEE 754R). */
+/* Quad precision decimal floating point (IEEE 754). */
const struct real_format decimal_quad_format =
{
encode_decimal_quad,
10,
34,
34,
- -6143,
- 6144,
+ -6142,
+ 6145,
127,
127,
+ false,
+ true,
+ true,
+ true,
true,
true,
- true,
- true,
true,
false
};
\f
-/* The "twos-complement" c4x format is officially defined as
-
- x = s(~s).f * 2**e
-
- This is rather misleading. One must remember that F is signed.
- A better description would be
-
- x = -1**s * ((s + 1 + .f) * 2**e
-
- So if we have a (4 bit) fraction of .1000 with a sign bit of 1,
- that's -1 * (1+1+(-.5)) == -1.5. I think.
-
- The constructions here are taken from Tables 5-1 and 5-2 of the
- TMS320C4x User's Guide wherein step-by-step instructions for
- conversion from IEEE are presented. That's close enough to our
- internal representation so as to make things easy.
-
- See http://www-s.ti.com/sc/psheets/spru063c/spru063c.pdf */
-
-static void encode_c4x_single (const struct real_format *fmt,
- long *, const REAL_VALUE_TYPE *);
-static void decode_c4x_single (const struct real_format *,
- REAL_VALUE_TYPE *, const long *);
-static void encode_c4x_extended (const struct real_format *fmt,
- long *, const REAL_VALUE_TYPE *);
-static void decode_c4x_extended (const struct real_format *,
- REAL_VALUE_TYPE *, const long *);
-
+/* Encode half-precision floats. This routine is used both for the IEEE
+ ARM alternative encodings. */
static void
-encode_c4x_single (const struct real_format *fmt ATTRIBUTE_UNUSED,
- long *buf, const REAL_VALUE_TYPE *r)
+encode_ieee_half (const struct real_format *fmt, long *buf,
+ const REAL_VALUE_TYPE *r)
{
- unsigned long image, exp, sig;
+ unsigned long image, sig, exp;
+ unsigned long sign = r->sign;
+ bool denormal = (r->sig[SIGSZ-1] & SIG_MSB) == 0;
+
+ image = sign << 15;
+ sig = (r->sig[SIGSZ-1] >> (HOST_BITS_PER_LONG - 11)) & 0x3ff;
switch (r->cl)
{
case rvc_zero:
- exp = -128;
- sig = 0;
break;
case rvc_inf:
- case rvc_nan:
- exp = 127;
- sig = 0x800000 - r->sign;
+ if (fmt->has_inf)
+ image |= 31 << 10;
+ else
+ image |= 0x7fff;
break;
- case rvc_normal:
- exp = REAL_EXP (r) - 1;
- sig = (r->sig[SIGSZ-1] >> (HOST_BITS_PER_LONG - 24)) & 0x7fffff;
- if (r->sign)
+ case rvc_nan:
+ if (fmt->has_nans)
{
- if (sig)
- sig = -sig;
+ if (r->canonical)
+ sig = (fmt->canonical_nan_lsbs_set ? (1 << 9) - 1 : 0);
+ if (r->signalling == fmt->qnan_msb_set)
+ sig &= ~(1 << 9);
else
- exp--;
- sig |= 0x800000;
+ sig |= 1 << 9;
+ if (sig == 0)
+ sig = 1 << 8;
+
+ image |= 31 << 10;
+ image |= sig;
}
+ else
+ image |= 0x3ff;
+ break;
+
+ case rvc_normal:
+ /* Recall that IEEE numbers are interpreted as 1.F x 2**exp,
+ whereas the intermediate representation is 0.F x 2**exp.
+ Which means we're off by one. */
+ if (denormal)
+ exp = 0;
+ else
+ exp = REAL_EXP (r) + 15 - 1;
+ image |= exp << 10;
+ image |= sig;
break;
default:
gcc_unreachable ();
}
- image = ((exp & 0xff) << 24) | (sig & 0xffffff);
buf[0] = image;
}
+/* Decode half-precision floats. This routine is used both for the IEEE
+ ARM alternative encodings. */
static void
-decode_c4x_single (const struct real_format *fmt ATTRIBUTE_UNUSED,
- REAL_VALUE_TYPE *r, const long *buf)
+decode_ieee_half (const struct real_format *fmt, REAL_VALUE_TYPE *r,
+ const long *buf)
{
- unsigned long image = buf[0];
- unsigned long sig;
- int exp, sf;
-
- exp = (((image >> 24) & 0xff) ^ 0x80) - 0x80;
- sf = ((image & 0xffffff) ^ 0x800000) - 0x800000;
+ unsigned long image = buf[0] & 0xffff;
+ bool sign = (image >> 15) & 1;
+ int exp = (image >> 10) & 0x1f;
memset (r, 0, sizeof (*r));
+ image <<= HOST_BITS_PER_LONG - 11;
+ image &= ~SIG_MSB;
- if (exp != -128)
+ if (exp == 0)
{
- r->cl = rvc_normal;
-
- sig = sf & 0x7fffff;
- if (sf < 0)
+ if (image && fmt->has_denorm)
{
- r->sign = 1;
- if (sig)
- sig = -sig;
- else
- exp++;
+ r->cl = rvc_normal;
+ r->sign = sign;
+ SET_REAL_EXP (r, -14);
+ r->sig[SIGSZ-1] = image << 1;
+ normalize (r);
}
- sig = (sig << (HOST_BITS_PER_LONG - 24)) | SIG_MSB;
-
- SET_REAL_EXP (r, exp + 1);
- r->sig[SIGSZ-1] = sig;
+ else if (fmt->has_signed_zero)
+ r->sign = sign;
}
-}
-
-static void
-encode_c4x_extended (const struct real_format *fmt ATTRIBUTE_UNUSED,
- long *buf, const REAL_VALUE_TYPE *r)
-{
- unsigned long exp, sig;
-
- switch (r->cl)
+ else if (exp == 31 && (fmt->has_nans || fmt->has_inf))
{
- case rvc_zero:
- exp = -128;
- sig = 0;
- break;
-
- case rvc_inf:
- case rvc_nan:
- exp = 127;
- sig = 0x80000000 - r->sign;
- break;
-
- case rvc_normal:
- exp = REAL_EXP (r) - 1;
-
- sig = r->sig[SIGSZ-1];
- if (HOST_BITS_PER_LONG == 64)
- sig = sig >> 1 >> 31;
- sig &= 0x7fffffff;
-
- if (r->sign)
+ if (image)
{
- if (sig)
- sig = -sig;
- else
- exp--;
- sig |= 0x80000000;
+ r->cl = rvc_nan;
+ r->sign = sign;
+ r->signalling = (((image >> (HOST_BITS_PER_LONG - 2)) & 1)
+ ^ fmt->qnan_msb_set);
+ r->sig[SIGSZ-1] = image;
+ }
+ else
+ {
+ r->cl = rvc_inf;
+ r->sign = sign;
}
- break;
-
- default:
- gcc_unreachable ();
}
-
- exp = (exp & 0xff) << 24;
- sig &= 0xffffffff;
-
- if (FLOAT_WORDS_BIG_ENDIAN)
- buf[0] = exp, buf[1] = sig;
else
- buf[0] = sig, buf[0] = exp;
-}
-
-static void
-decode_c4x_extended (const struct real_format *fmt ATTRIBUTE_UNUSED,
- REAL_VALUE_TYPE *r, const long *buf)
-{
- unsigned long sig;
- int exp, sf;
-
- if (FLOAT_WORDS_BIG_ENDIAN)
- exp = buf[0], sf = buf[1];
- else
- sf = buf[0], exp = buf[1];
-
- exp = (((exp >> 24) & 0xff) & 0x80) - 0x80;
- sf = ((sf & 0xffffffff) ^ 0x80000000) - 0x80000000;
-
- memset (r, 0, sizeof (*r));
-
- if (exp != -128)
{
r->cl = rvc_normal;
-
- sig = sf & 0x7fffffff;
- if (sf < 0)
- {
- r->sign = 1;
- if (sig)
- sig = -sig;
- else
- exp++;
- }
- if (HOST_BITS_PER_LONG == 64)
- sig = sig << 1 << 31;
- sig |= SIG_MSB;
-
- SET_REAL_EXP (r, exp + 1);
- r->sig[SIGSZ-1] = sig;
+ r->sign = sign;
+ SET_REAL_EXP (r, exp - 15 + 1);
+ r->sig[SIGSZ-1] = image | SIG_MSB;
}
}
-const struct real_format c4x_single_format =
+/* Half-precision format, as specified in IEEE 754R. */
+const struct real_format ieee_half_format =
{
- encode_c4x_single,
- decode_c4x_single,
+ encode_ieee_half,
+ decode_ieee_half,
2,
- 24,
- 24,
- -126,
- 128,
- 23,
- -1,
- false,
- false,
- false,
- false,
+ 11,
+ 11,
+ -13,
+ 16,
+ 15,
+ 15,
false,
+ true,
+ true,
+ true,
+ true,
+ true,
+ true,
false
};
-const struct real_format c4x_extended_format =
+/* ARM's alternative half-precision format, similar to IEEE but with
+ no reserved exponent value for NaNs and infinities; rather, it just
+ extends the range of exponents by one. */
+const struct real_format arm_half_format =
{
- encode_c4x_extended,
- decode_c4x_extended,
+ encode_ieee_half,
+ decode_ieee_half,
2,
- 32,
- 32,
- -126,
- 128,
- 31,
- -1,
- false,
+ 11,
+ 11,
+ -13,
+ 17,
+ 15,
+ 15,
false,
+ true,
false,
false,
+ true,
+ true,
false,
false
};
-
\f
/* A synthetic "format" for internal arithmetic. It's the size of the
internal significand minus the two bits needed for proper rounding.
MAX_EXP,
-1,
-1,
+ false,
+ false,
true,
true,
false,
r->sign = x->sign;
}
-/* Convert from REAL_VALUE_TYPE to MPFR. The caller is responsible
- for initializing and clearing the MPFR parameter. */
-
-void
-mpfr_from_real (mpfr_ptr m, const REAL_VALUE_TYPE *r, mp_rnd_t rndmode)
-{
- /* We use a string as an intermediate type. */
- char buf[128];
- int ret;
-
- /* Take care of Infinity and NaN. */
- if (r->cl == rvc_inf)
- {
- mpfr_set_inf (m, r->sign == 1 ? -1 : 1);
- return;
- }
-
- if (r->cl == rvc_nan)
- {
- mpfr_set_nan (m);
- return;
- }
-
- real_to_hexadecimal (buf, r, sizeof (buf), 0, 1);
- /* mpfr_set_str() parses hexadecimal floats from strings in the same
- format that GCC will output them. Nothing extra is needed. */
- ret = mpfr_set_str (m, buf, 16, rndmode);
- gcc_assert (ret == 0);
-}
-
-/* Convert from MPFR to REAL_VALUE_TYPE, for a given type TYPE and rounding
- mode RNDMODE. TYPE is only relevant if M is a NaN. */
-
-void
-real_from_mpfr (REAL_VALUE_TYPE *r, mpfr_srcptr m, tree type, mp_rnd_t rndmode)
-{
- /* We use a string as an intermediate type. */
- char buf[128], *rstr;
- mp_exp_t exp;
-
- /* Take care of Infinity and NaN. */
- if (mpfr_inf_p (m))
- {
- real_inf (r);
- if (mpfr_sgn (m) < 0)
- *r = REAL_VALUE_NEGATE (*r);
- return;
- }
-
- if (mpfr_nan_p (m))
- {
- real_nan (r, "", 1, TYPE_MODE (type));
- return;
- }
-
- rstr = mpfr_get_str (NULL, &exp, 16, 0, m, rndmode);
-
- /* The additional 12 chars add space for the sprintf below. This
- leaves 6 digits for the exponent which is supposedly enough. */
- gcc_assert (rstr != NULL && strlen (rstr) < sizeof (buf) - 12);
-
- /* REAL_VALUE_ATOF expects the exponent for mantissa * 2**exp,
- mpfr_get_str returns the exponent for mantissa * 16**exp, adjust
- for that. */
- exp *= 4;
-
- if (rstr[0] == '-')
- sprintf (buf, "-0x.%sp%d", &rstr[1], (int) exp);
- else
- sprintf (buf, "0x.%sp%d", rstr, (int) exp);
-
- mpfr_free_str (rstr);
-
- real_from_string (r, buf);
-}
-
/* Check whether the real constant value given is an integer. */
bool
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