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binutils-gdb/sim/rx/fpu.c

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/* fpu.c --- FPU emulator for stand-alone RX simulator.
Copyright (C) 2008-2014 Free Software Foundation, Inc.
Contributed by Red Hat, Inc.
This file is part of the GNU simulators.
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 3 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, see <http://www.gnu.org/licenses/>. */
#include "config.h"
#include <stdio.h>
#include <stdlib.h>
#include "cpu.h"
#include "fpu.h"
/* FPU encodings are as follows:
S EXPONENT MANTISSA
1 12345678 12345678901234567890123
0 00000000 00000000000000000000000 +0
1 00000000 00000000000000000000000 -0
X 00000000 00000000000000000000001 Denormals
X 00000000 11111111111111111111111
X 00000001 XXXXXXXXXXXXXXXXXXXXXXX Normals
X 11111110 XXXXXXXXXXXXXXXXXXXXXXX
0 11111111 00000000000000000000000 +Inf
1 11111111 00000000000000000000000 -Inf
X 11111111 0XXXXXXXXXXXXXXXXXXXXXX SNaN (X != 0)
X 11111111 1XXXXXXXXXXXXXXXXXXXXXX QNaN (X != 0)
*/
#define trace 0
#define tprintf if (trace) printf
/* Some magic numbers. */
#define PLUS_MAX 0x7f7fffffUL
#define MINUS_MAX 0xff7fffffUL
#define PLUS_INF 0x7f800000UL
#define MINUS_INF 0xff800000UL
#define PLUS_ZERO 0x00000000UL
#define MINUS_ZERO 0x80000000UL
#define FP_RAISE(e) fp_raise(FPSWBITS_C##e)
static void
fp_raise (int mask)
{
regs.r_fpsw |= mask;
if (mask != FPSWBITS_CE)
{
if (regs.r_fpsw & (mask << FPSW_CESH))
regs.r_fpsw |= (mask << FPSW_CFSH);
if (regs.r_fpsw & FPSWBITS_FMASK)
regs.r_fpsw |= FPSWBITS_FSUM;
else
regs.r_fpsw &= ~FPSWBITS_FSUM;
}
}
/* We classify all numbers as one of these. They correspond to the
rows/colums in the exception tables. */
typedef enum {
FP_NORMAL,
FP_PZERO,
FP_NZERO,
FP_PINFINITY,
FP_NINFINITY,
FP_DENORMAL,
FP_QNAN,
FP_SNAN
} FP_Type;
#if defined DEBUG0
static const char *fpt_names[] = {
"Normal", "+0", "-0", "+Inf", "-Inf", "Denormal", "QNaN", "SNaN"
};
#endif
#define EXP_BIAS 127
#define EXP_ZERO -127
#define EXP_INF 128
#define MANT_BIAS 0x00080000UL
typedef struct {
int exp;
unsigned int mant; /* 24 bits */
char type;
char sign;
fp_t orig_value;
} FP_Parts;
static void
fp_explode (fp_t f, FP_Parts *p)
{
int exp, mant, sign;
exp = ((f & 0x7f800000UL) >> 23);
mant = f & 0x007fffffUL;
sign = f & 0x80000000UL;
/*printf("explode: %08x %x %2x %6x\n", f, sign, exp, mant);*/
p->sign = sign ? -1 : 1;
p->exp = exp - EXP_BIAS;
p->orig_value = f;
p->mant = mant | 0x00800000UL;
if (p->exp == EXP_ZERO)
{
if (regs.r_fpsw & FPSWBITS_DN)
mant = 0;
if (mant)
p->type = FP_DENORMAL;
else
{
p->mant = 0;
p->type = sign ? FP_NZERO : FP_PZERO;
}
}
else if (p->exp == EXP_INF)
{
if (mant == 0)
p->type = sign ? FP_NINFINITY : FP_PINFINITY;
else if (mant & 0x00400000UL)
p->type = FP_QNAN;
else
p->type = FP_SNAN;
}
else
p->type = FP_NORMAL;
}
static fp_t
fp_implode (FP_Parts *p)
{
int exp, mant;
exp = p->exp + EXP_BIAS;
mant = p->mant;
/*printf("implode: exp %d mant 0x%x\n", exp, mant);*/
if (p->type == FP_NORMAL)
{
while (mant
&& exp > 0
&& mant < 0x00800000UL)
{
mant <<= 1;
exp --;
}
while (mant > 0x00ffffffUL)
{
mant >>= 1;
exp ++;
}
if (exp < 0)
{
/* underflow */
exp = 0;
mant = 0;
FP_RAISE (E);
}
if (exp >= 255)
{
/* overflow */
exp = 255;
mant = 0;
FP_RAISE (O);
}
}
mant &= 0x007fffffUL;
exp &= 0xff;
mant |= exp << 23;
if (p->sign < 0)
mant |= 0x80000000UL;
return mant;
}
typedef union {
unsigned long long ll;
double d;
} U_d_ll;
static int checked_format = 0;
/* We assume a double format like this:
S[1] E[11] M[52]
*/
static double
fp_to_double (FP_Parts *p)
{
U_d_ll u;
if (!checked_format)
{
u.d = 1.5;
if (u.ll != 0x3ff8000000000000ULL)
abort ();
u.d = -225;
if (u.ll != 0xc06c200000000000ULL)
abort ();
u.d = 10.1;
if (u.ll != 0x4024333333333333ULL)
abort ();
checked_format = 1;
}
u.ll = 0;
if (p->sign < 0)
u.ll |= (1ULL << 63);
/* Make sure a zero encoding stays a zero. */
if (p->exp != -EXP_BIAS)
u.ll |= ((unsigned long long)p->exp + 1023ULL) << 52;
u.ll |= (unsigned long long) (p->mant & 0x007fffffUL) << (52 - 23);
return u.d;
}
static void
double_to_fp (double d, FP_Parts *p)
{
int exp;
U_d_ll u;
int sign;
u.d = d;
sign = (u.ll & 0x8000000000000000ULL) ? 1 : 0;
exp = u.ll >> 52;
exp = (exp & 0x7ff);
if (exp == 0)
{
/* A generated denormal should show up as an underflow, not
here. */
if (sign)
fp_explode (MINUS_ZERO, p);
else
fp_explode (PLUS_ZERO, p);
return;
}
exp = exp - 1023;
if ((exp + EXP_BIAS) > 254)
{
FP_RAISE (O);
switch (regs.r_fpsw & FPSWBITS_RM)
{
case FPRM_NEAREST:
if (sign)
fp_explode (MINUS_INF, p);
else
fp_explode (PLUS_INF, p);
break;
case FPRM_ZERO:
if (sign)
fp_explode (MINUS_MAX, p);
else
fp_explode (PLUS_MAX, p);
break;
case FPRM_PINF:
if (sign)
fp_explode (MINUS_MAX, p);
else
fp_explode (PLUS_INF, p);
break;
case FPRM_NINF:
if (sign)
fp_explode (MINUS_INF, p);
else
fp_explode (PLUS_MAX, p);
break;
}
return;
}
if ((exp + EXP_BIAS) < 1)
{
if (sign)
fp_explode (MINUS_ZERO, p);
else
fp_explode (PLUS_ZERO, p);
FP_RAISE (U);
}
p->sign = sign ? -1 : 1;
p->exp = exp;
p->mant = u.ll >> (52-23) & 0x007fffffUL;
p->mant |= 0x00800000UL;
p->type = FP_NORMAL;
if (u.ll & 0x1fffffffULL)
{
switch (regs.r_fpsw & FPSWBITS_RM)
{
case FPRM_NEAREST:
if (u.ll & 0x10000000ULL)
p->mant ++;
break;
case FPRM_ZERO:
break;
case FPRM_PINF:
if (sign == 1)
p->mant ++;
break;
case FPRM_NINF:
if (sign == -1)
p->mant ++;
break;
}
FP_RAISE (X);
}
}
typedef enum {
eNR, /* Use the normal result. */
ePZ, eNZ, /* +- zero */
eSZ, /* signed zero - XOR signs of ops together. */
eRZ, /* +- zero depending on rounding mode. */
ePI, eNI, /* +- Infinity */
eSI, /* signed infinity - XOR signs of ops together. */
eQN, eSN, /* Quiet/Signalling NANs */
eIn, /* Invalid. */
eUn, /* Unimplemented. */
eDZ, /* Divide-by-zero. */
eLT, /* less than */
eGT, /* greater than */
eEQ, /* equal to */
} FP_ExceptionCases;
#if defined DEBUG0
static const char *ex_names[] = {
"NR", "PZ", "NZ", "SZ", "RZ", "PI", "NI", "SI", "QN", "SN", "IN", "Un", "DZ", "LT", "GT", "EQ"
};
#endif
/* This checks for all exceptional cases (not all FP exceptions) and
returns TRUE if it is providing the result in *c. If it returns
FALSE, the caller should do the "normal" operation. */
int
check_exceptions (FP_Parts *a, FP_Parts *b, fp_t *c,
FP_ExceptionCases ex_tab[5][5],
FP_ExceptionCases *case_ret)
{
FP_ExceptionCases fpec;
if (a->type == FP_SNAN
|| b->type == FP_SNAN)
fpec = eIn;
else if (a->type == FP_QNAN
|| b->type == FP_QNAN)
fpec = eQN;
else if (a->type == FP_DENORMAL
|| b->type == FP_DENORMAL)
fpec = eUn;
else
fpec = ex_tab[(int)(a->type)][(int)(b->type)];
/*printf("%s %s -> %s\n", fpt_names[(int)(a->type)], fpt_names[(int)(b->type)], ex_names[(int)(fpec)]);*/
if (case_ret)
*case_ret = fpec;
switch (fpec)
{
case eNR: /* Use the normal result. */
return 0;
case ePZ: /* + zero */
*c = 0x00000000;
return 1;
case eNZ: /* - zero */
*c = 0x80000000;
return 1;
case eSZ: /* signed zero */
*c = (a->sign == b->sign) ? PLUS_ZERO : MINUS_ZERO;
return 1;
case eRZ: /* +- zero depending on rounding mode. */
if ((regs.r_fpsw & FPSWBITS_RM) == FPRM_NINF)
*c = 0x80000000;
else
*c = 0x00000000;
return 1;
case ePI: /* + Infinity */
*c = 0x7F800000;
return 1;
case eNI: /* - Infinity */
*c = 0xFF800000;
return 1;
case eSI: /* sign Infinity */
*c = (a->sign == b->sign) ? PLUS_INF : MINUS_INF;
return 1;
case eQN: /* Quiet NANs */
if (a->type == FP_QNAN)
*c = a->orig_value;
else
*c = b->orig_value;
return 1;
case eSN: /* Signalling NANs */
if (a->type == FP_SNAN)
*c = a->orig_value;
else
*c = b->orig_value;
FP_RAISE (V);
return 1;
case eIn: /* Invalid. */
FP_RAISE (V);
if (a->type == FP_SNAN)
*c = a->orig_value | 0x00400000;
else if (a->type == FP_SNAN)
*c = b->orig_value | 0x00400000;
else
*c = 0x7fc00000;
return 1;
case eUn: /* Unimplemented. */
FP_RAISE (E);
return 1;
case eDZ: /* Division-by-zero. */
*c = (a->sign == b->sign) ? PLUS_INF : MINUS_INF;
FP_RAISE (Z);
return 1;
default:
return 0;
}
}
#define CHECK_EXCEPTIONS(FPPa, FPPb, fpc, ex_tab) \
if (check_exceptions (&FPPa, &FPPb, &fpc, ex_tab, 0)) \
return fpc;
/* For each operation, we have two tables of how nonnormal cases are
handled. The DN=0 case is first, followed by the DN=1 case, with
each table using the following layout: */
static FP_ExceptionCases ex_add_tab[5][5] = {
/* N +0 -0 +In -In */
{ eNR, eNR, eNR, ePI, eNI }, /* Normal */
{ eNR, ePZ, eRZ, ePI, eNI }, /* +0 */
{ eNR, eRZ, eNZ, ePI, eNI }, /* -0 */
{ ePI, ePI, ePI, ePI, eIn }, /* +Inf */
{ eNI, eNI, eNI, eIn, eNI }, /* -Inf */
};
fp_t
rxfp_add (fp_t fa, fp_t fb)
{
FP_Parts a, b, c;
fp_t rv;
double da, db;
fp_explode (fa, &a);
fp_explode (fb, &b);
CHECK_EXCEPTIONS (a, b, rv, ex_add_tab);
da = fp_to_double (&a);
db = fp_to_double (&b);
tprintf("%g + %g = %g\n", da, db, da+db);
double_to_fp (da+db, &c);
rv = fp_implode (&c);
return rv;
}
static FP_ExceptionCases ex_sub_tab[5][5] = {
/* N +0 -0 +In -In */
{ eNR, eNR, eNR, eNI, ePI }, /* Normal */
{ eNR, eRZ, ePZ, eNI, ePI }, /* +0 */
{ eNR, eNZ, eRZ, eNI, ePI }, /* -0 */
{ ePI, ePI, ePI, eIn, ePI }, /* +Inf */
{ eNI, eNI, eNI, eNI, eIn }, /* -Inf */
};
fp_t
rxfp_sub (fp_t fa, fp_t fb)
{
FP_Parts a, b, c;
fp_t rv;
double da, db;
fp_explode (fa, &a);
fp_explode (fb, &b);
CHECK_EXCEPTIONS (a, b, rv, ex_sub_tab);
da = fp_to_double (&a);
db = fp_to_double (&b);
tprintf("%g - %g = %g\n", da, db, da-db);
double_to_fp (da-db, &c);
rv = fp_implode (&c);
return rv;
}
static FP_ExceptionCases ex_mul_tab[5][5] = {
/* N +0 -0 +In -In */
{ eNR, eNR, eNR, eSI, eSI }, /* Normal */
{ eNR, ePZ, eNZ, eIn, eIn }, /* +0 */
{ eNR, eNZ, ePZ, eIn, eIn }, /* -0 */
{ eSI, eIn, eIn, ePI, eNI }, /* +Inf */
{ eSI, eIn, eIn, eNI, ePI }, /* -Inf */
};
fp_t
rxfp_mul (fp_t fa, fp_t fb)
{
FP_Parts a, b, c;
fp_t rv;
double da, db;
fp_explode (fa, &a);
fp_explode (fb, &b);
CHECK_EXCEPTIONS (a, b, rv, ex_mul_tab);
da = fp_to_double (&a);
db = fp_to_double (&b);
tprintf("%g x %g = %g\n", da, db, da*db);
double_to_fp (da*db, &c);
rv = fp_implode (&c);
return rv;
}
static FP_ExceptionCases ex_div_tab[5][5] = {
/* N +0 -0 +In -In */
{ eNR, eDZ, eDZ, eSZ, eSZ }, /* Normal */
{ eSZ, eIn, eIn, ePZ, eNZ }, /* +0 */
{ eSZ, eIn, eIn, eNZ, ePZ }, /* -0 */
{ eSI, ePI, eNI, eIn, eIn }, /* +Inf */
{ eSI, eNI, ePI, eIn, eIn }, /* -Inf */
};
fp_t
rxfp_div (fp_t fa, fp_t fb)
{
FP_Parts a, b, c;
fp_t rv;
double da, db;
fp_explode (fa, &a);
fp_explode (fb, &b);
CHECK_EXCEPTIONS (a, b, rv, ex_div_tab);
da = fp_to_double (&a);
db = fp_to_double (&b);
tprintf("%g / %g = %g\n", da, db, da/db);
double_to_fp (da/db, &c);
rv = fp_implode (&c);
return rv;
}
static FP_ExceptionCases ex_cmp_tab[5][5] = {
/* N +0 -0 +In -In */
{ eNR, eNR, eNR, eLT, eGT }, /* Normal */
{ eNR, eEQ, eEQ, eLT, eGT }, /* +0 */
{ eNR, eEQ, eEQ, eLT, eGT }, /* -0 */
{ eGT, eGT, eGT, eEQ, eGT }, /* +Inf */
{ eLT, eLT, eLT, eLT, eEQ }, /* -Inf */
};
void
rxfp_cmp (fp_t fa, fp_t fb)
{
FP_Parts a, b;
fp_t c;
FP_ExceptionCases reason;
int flags = 0;
double da, db;
fp_explode (fa, &a);
fp_explode (fb, &b);
if (check_exceptions (&a, &b, &c, ex_cmp_tab, &reason))
{
if (reason == eQN)
{
/* Special case - incomparable. */
set_flags (FLAGBIT_Z | FLAGBIT_S | FLAGBIT_O, FLAGBIT_O);
return;
}
return;
}
switch (reason)
{
case eEQ:
flags = FLAGBIT_Z;
break;
case eLT:
flags = FLAGBIT_S;
break;
case eGT:
flags = 0;
break;
case eNR:
da = fp_to_double (&a);
db = fp_to_double (&b);
tprintf("fcmp: %g cmp %g\n", da, db);
if (da < db)
flags = FLAGBIT_S;
else if (da == db)
flags = FLAGBIT_Z;
else
flags = 0;
break;
default:
abort();
}
set_flags (FLAGBIT_Z | FLAGBIT_S | FLAGBIT_O, flags);
}
long
rxfp_ftoi (fp_t fa, int round_mode)
{
FP_Parts a;
fp_t rv;
int sign;
int whole_bits, frac_bits;
fp_explode (fa, &a);
sign = fa & 0x80000000UL;
switch (a.type)
{
case FP_NORMAL:
break;
case FP_PZERO:
case FP_NZERO:
return 0;
case FP_PINFINITY:
FP_RAISE (V);
return 0x7fffffffL;
case FP_NINFINITY:
FP_RAISE (V);
return 0x80000000L;
case FP_DENORMAL:
FP_RAISE (E);
return 0;
case FP_QNAN:
case FP_SNAN:
FP_RAISE (V);
return sign ? 0x80000000U : 0x7fffffff;
}
if (a.exp >= 31)
{
FP_RAISE (V);
return sign ? 0x80000000U : 0x7fffffff;
}
a.exp -= 23;
if (a.exp <= -25)
{
/* Less than 0.49999 */
frac_bits = a.mant;
whole_bits = 0;
}
else if (a.exp < 0)
{
frac_bits = a.mant << (32 + a.exp);
whole_bits = a.mant >> (-a.exp);
}
else
{
frac_bits = 0;
whole_bits = a.mant << a.exp;
}
if (frac_bits)
{
switch (round_mode & 3)
{
case FPRM_NEAREST:
if (frac_bits & 0x80000000UL)
whole_bits ++;
break;
case FPRM_ZERO:
break;
case FPRM_PINF:
if (!sign)
whole_bits ++;
break;
case FPRM_NINF:
if (sign)
whole_bits ++;
break;
}
}
rv = sign ? -whole_bits : whole_bits;
return rv;
}
fp_t
rxfp_itof (long fa, int round_mode)
{
fp_t rv;
int sign = 0;
unsigned int frac_bits;
volatile unsigned int whole_bits;
FP_Parts a;
if (fa == 0)
return PLUS_ZERO;
if (fa < 0)
{
fa = -fa;
sign = 1;
a.sign = -1;
}
else
a.sign = 1;
whole_bits = fa;
a.exp = 31;
while (! (whole_bits & 0x80000000UL))
{
a.exp --;
whole_bits <<= 1;
}
frac_bits = whole_bits & 0xff;
whole_bits = whole_bits >> 8;
if (frac_bits)
{
/* We must round */
switch (round_mode & 3)
{
case FPRM_NEAREST:
if (frac_bits & 0x80)
whole_bits ++;
break;
case FPRM_ZERO:
break;
case FPRM_PINF:
if (!sign)
whole_bits ++;
break;
case FPRM_NINF:
if (sign)
whole_bits ++;
break;
}
}
a.mant = whole_bits;
if (whole_bits & 0xff000000UL)
{
a.mant >>= 1;
a.exp ++;
}
rv = fp_implode (&a);
return rv;
}
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