/* Convert a s32 to register */
static void convert_l2reg(s32 const *arg, int deststnr)
{
int tag;
s32 num = *arg;
u_char sign;
FPU_REG *dest = &st(deststnr);
if (num == 0)
{
FPU_copy_to_regi(&CONST_Z, TAG_Zero, deststnr);
return;
}
if (num > 0)
{ sign = SIGN_POS; }
else
{ num = -num; sign = SIGN_NEG; }
dest->sigh = num;
dest->sigl = 0;
setexponent16(dest, 31);
tag = FPU_normalize_nuo(dest,
EXTENDED_Ebias); /* No underflow or overflow
is possible */
FPU_settagi(deststnr, tag);
setsign(dest, sign);
return;
}
static void convert_l2reg(long const *arg, int deststnr)
{
int tag;
long num = *arg;
u_char sign;
FPU_REG *dest = &st(deststnr);
if (num == 0) {
FPU_copy_to_regi(&CONST_Z, TAG_Zero, deststnr);
return;
}
if (num > 0) {
sign = SIGN_POS;
} else {
num = -num;
sign = SIGN_NEG;
}
dest->sigh = num;
dest->sigl = 0;
setexponent16(dest, 31);
tag = FPU_normalize(dest);
FPU_settagi(deststnr, tag);
setsign(dest, sign);
return;
}
static int trig_arg(FPU_REG *st0_ptr, int even)
{
FPU_REG tmp;
u_char tmptag;
unsigned long long q;
int old_cw = control_word, saved_status = partial_status;
int tag, st0_tag = TAG_Valid;
if (exponent(st0_ptr) >= 63) {
partial_status |= SW_C2;
return -1;
}
control_word &= ~CW_RC;
control_word |= RC_CHOP;
setpositive(st0_ptr);
tag = FPU_u_div(st0_ptr, &CONST_PI2, &tmp, PR_64_BITS | RC_CHOP | 0x3f,
SIGN_POS);
FPU_round_to_int(&tmp, tag);
q = significand(&tmp);
if (q) {
rem_kernel(significand(st0_ptr),
&significand(&tmp),
significand(&CONST_PI2),
q, exponent(st0_ptr) - exponent(&CONST_PI2));
setexponent16(&tmp, exponent(&CONST_PI2));
st0_tag = FPU_normalize(&tmp);
FPU_copy_to_reg0(&tmp, st0_tag);
}
if ((even && !(q & 1)) || (!even && (q & 1))) {
st0_tag =
FPU_sub(REV | LOADED | TAG_Valid, (int)&CONST_PI2,
FULL_PRECISION);
#ifdef BETTER_THAN_486
if ((exponent(st0_ptr) <= exponent(&CONST_PI2extra) + 64)
|| (q > 1)) {
significand(&tmp) = q + 1;
setexponent16(&tmp, 63);
FPU_normalize(&tmp);
tmptag =
FPU_u_mul(&CONST_PI2extra, &tmp, &tmp,
FULL_PRECISION, SIGN_POS,
exponent(&CONST_PI2extra) +
exponent(&tmp));
setsign(&tmp, getsign(&CONST_PI2extra));
st0_tag = FPU_add(&tmp, tmptag, 0, FULL_PRECISION);
if (signnegative(st0_ptr)) {
setpositive(st0_ptr);
q++;
}
}
#endif
}
#ifdef BETTER_THAN_486
else {
if (((q > 0)
&& (exponent(st0_ptr) <= exponent(&CONST_PI2extra) + 64))
|| (q > 1)) {
significand(&tmp) = q;
setexponent16(&tmp, 63);
FPU_normalize(&tmp);
tmptag =
FPU_u_mul(&CONST_PI2extra, &tmp, &tmp,
FULL_PRECISION, SIGN_POS,
exponent(&CONST_PI2extra) +
exponent(&tmp));
setsign(&tmp, getsign(&CONST_PI2extra));
st0_tag = FPU_sub(LOADED | (tmptag & 0x0f), (int)&tmp,
FULL_PRECISION);
if ((exponent(st0_ptr) == exponent(&CONST_PI2)) &&
((st0_ptr->sigh > CONST_PI2.sigh)
|| ((st0_ptr->sigh == CONST_PI2.sigh)
&& (st0_ptr->sigl > CONST_PI2.sigl)))) {
st0_tag =
FPU_sub(REV | LOADED | TAG_Valid,
(int)&CONST_PI2, FULL_PRECISION);
q++;
}
}
}
#endif
FPU_settag0(st0_tag);
control_word = old_cw;
partial_status = saved_status & ~SW_C2;
return (q & 3) | even;
}
static
int add_sub_specials(FPU_REG const *a, u_char taga, u_char signa,
FPU_REG const *b, u_char tagb, u_char signb,
FPU_REG * dest, int deststnr, int control_w)
{
if (((taga == TW_Denormal) || (tagb == TW_Denormal))
&& (denormal_operand() < 0))
return FPU_Exception;
if (taga == TAG_Zero) {
if (tagb == TAG_Zero) {
u_char different_signs = signa ^ signb;
FPU_copy_to_regi(a, TAG_Zero, deststnr);
if (different_signs) {
setsign(dest, ((control_w & CW_RC) != RC_DOWN)
? SIGN_POS : SIGN_NEG);
} else
setsign(dest, signa);
return TAG_Zero;
} else {
reg_copy(b, dest);
if ((tagb == TW_Denormal) && (b->sigh & 0x80000000)) {
addexponent(dest, 1);
tagb = TAG_Valid;
} else if (tagb > TAG_Empty)
tagb = TAG_Special;
setsign(dest, signb);
FPU_settagi(deststnr, tagb);
return tagb;
}
} else if (tagb == TAG_Zero) {
reg_copy(a, dest);
if ((taga == TW_Denormal) && (a->sigh & 0x80000000)) {
addexponent(dest, 1);
taga = TAG_Valid;
} else if (taga > TAG_Empty)
taga = TAG_Special;
setsign(dest, signa);
FPU_settagi(deststnr, taga);
return taga;
} else if (taga == TW_Infinity) {
if ((tagb != TW_Infinity) || (signa == signb)) {
FPU_copy_to_regi(a, TAG_Special, deststnr);
setsign(dest, signa);
return taga;
}
return arith_invalid(deststnr);
} else if (tagb == TW_Infinity) {
FPU_copy_to_regi(b, TAG_Special, deststnr);
setsign(dest, signb);
return tagb;
}
#ifdef PARANOID
EXCEPTION(EX_INTERNAL | 0x101);
#endif
return FPU_Exception;
}
int FPU_add(FPU_REG const *b, u_char tagb, int deststnr, int control_w)
{
FPU_REG *a = &st(0);
FPU_REG *dest = &st(deststnr);
u_char signb = getsign(b);
u_char taga = FPU_gettag0();
u_char signa = getsign(a);
u_char saved_sign = getsign(dest);
int diff, tag, expa, expb;
if (!(taga | tagb)) {
expa = exponent(a);
expb = exponent(b);
valid_add:
if (!(signa ^ signb)) {
tag =
FPU_u_add(a, b, dest, control_w, signa, expa, expb);
} else {
diff = expa - expb;
if (!diff) {
diff = a->sigh - b->sigh;
if (!diff) {
diff = a->sigl > b->sigl;
if (!diff)
diff = -(a->sigl < b->sigl);
}
}
if (diff > 0) {
tag =
FPU_u_sub(a, b, dest, control_w, signa,
expa, expb);
} else if (diff < 0) {
tag =
FPU_u_sub(b, a, dest, control_w, signb,
expb, expa);
} else {
FPU_copy_to_regi(&CONST_Z, TAG_Zero, deststnr);
setsign(dest, ((control_w & CW_RC) != RC_DOWN)
? SIGN_POS : SIGN_NEG);
return TAG_Zero;
}
}
if (tag < 0) {
setsign(dest, saved_sign);
return tag;
}
FPU_settagi(deststnr, tag);
return tag;
}
if (taga == TAG_Special)
taga = FPU_Special(a);
if (tagb == TAG_Special)
tagb = FPU_Special(b);
if (((taga == TAG_Valid) && (tagb == TW_Denormal))
|| ((taga == TW_Denormal) && (tagb == TAG_Valid))
|| ((taga == TW_Denormal) && (tagb == TW_Denormal))) {
FPU_REG x, y;
if (denormal_operand() < 0)
return FPU_Exception;
FPU_to_exp16(a, &x);
FPU_to_exp16(b, &y);
a = &x;
b = &y;
expa = exponent16(a);
expb = exponent16(b);
goto valid_add;
}
if ((taga == TW_NaN) || (tagb == TW_NaN)) {
if (deststnr == 0)
return real_2op_NaN(b, tagb, deststnr, a);
else
return real_2op_NaN(a, taga, deststnr, a);
}
return add_sub_specials(a, taga, signa, b, tagb, signb,
dest, deststnr, control_w);
}
int FPU_sub(int flags, int rm, int control_w)
{
FPU_REG const *a, *b;
FPU_REG *dest;
u_char taga, tagb, signa, signb, saved_sign, sign;
int diff, tag = 0, expa, expb, deststnr;
a = &st(0);
taga = FPU_gettag0();
deststnr = 0;
if (flags & LOADED) {
b = (FPU_REG *) rm;
tagb = flags & 0x0f;
} else {
b = &st(rm);
tagb = FPU_gettagi(rm);
if (flags & DEST_RM)
deststnr = rm;
}
signa = getsign(a);
signb = getsign(b);
if (flags & REV) {
signa ^= SIGN_NEG;
signb ^= SIGN_NEG;
}
dest = &st(deststnr);
saved_sign = getsign(dest);
if (!(taga | tagb)) {
expa = exponent(a);
expb = exponent(b);
valid_subtract:
diff = expa - expb;
if (!diff) {
diff = a->sigh - b->sigh;
if (!diff) {
diff = a->sigl > b->sigl;
if (!diff)
diff = -(a->sigl < b->sigl);
}
}
switch ((((int)signa) * 2 + signb) / SIGN_NEG) {
case 0:
case 3:
if (diff > 0) {
tag =
FPU_u_sub(a, b, dest, control_w, signa,
expa, expb);
} else if (diff == 0) {
FPU_copy_to_regi(&CONST_Z, TAG_Zero, deststnr);
setsign(dest, ((control_w & CW_RC) != RC_DOWN)
? SIGN_POS : SIGN_NEG);
return TAG_Zero;
} else {
sign = signa ^ SIGN_NEG;
tag =
FPU_u_sub(b, a, dest, control_w, sign, expb,
expa);
}
break;
case 1:
tag =
FPU_u_add(a, b, dest, control_w, SIGN_POS, expa,
expb);
break;
case 2:
tag =
FPU_u_add(a, b, dest, control_w, SIGN_NEG, expa,
expb);
break;
#ifdef PARANOID
default:
EXCEPTION(EX_INTERNAL | 0x111);
return -1;
#endif
}
if (tag < 0) {
setsign(dest, saved_sign);
return tag;
}
FPU_settagi(deststnr, tag);
return tag;
}
if (taga == TAG_Special)
taga = FPU_Special(a);
if (tagb == TAG_Special)
tagb = FPU_Special(b);
if (((taga == TAG_Valid) && (tagb == TW_Denormal))
|| ((taga == TW_Denormal) && (tagb == TAG_Valid))
|| ((taga == TW_Denormal) && (tagb == TW_Denormal))) {
FPU_REG x, y;
if (denormal_operand() < 0)
return FPU_Exception;
FPU_to_exp16(a, &x);
FPU_to_exp16(b, &y);
a = &x;
b = &y;
expa = exponent16(a);
expb = exponent16(b);
goto valid_subtract;
}
if ((taga == TW_NaN) || (tagb == TW_NaN)) {
FPU_REG const *d1, *d2;
if (flags & REV) {
d1 = b;
d2 = a;
} else {
d1 = a;
d2 = b;
}
if (flags & LOADED)
return real_2op_NaN(b, tagb, deststnr, d1);
if (flags & DEST_RM)
return real_2op_NaN(a, taga, deststnr, d2);
else
return real_2op_NaN(b, tagb, deststnr, d2);
}
return add_sub_specials(a, taga, signa, b, tagb, signb ^ SIGN_NEG,
dest, deststnr, control_w);
}
static
int add_sub_specials(FPU_REG const *a, u_char taga, u_char signa,
FPU_REG const *b, u_char tagb, u_char signb,
FPU_REG *dest, int deststnr, int control_w)
{
if ( ((taga == TW_Denormal) || (tagb == TW_Denormal))
&& (denormal_operand() < 0) )
return FPU_Exception;
if (taga == TAG_Zero)
{
if (tagb == TAG_Zero)
{
/* Both are zero, result will be zero. */
u_char different_signs = signa ^ signb;
FPU_copy_to_regi(a, TAG_Zero, deststnr);
if ( different_signs )
{
/* Signs are different. */
/* Sign of answer depends upon rounding mode. */
setsign(dest, ((control_w & CW_RC) != RC_DOWN)
? SIGN_POS : SIGN_NEG);
}
else
setsign(dest, signa); /* signa may differ from the sign of a. */
return TAG_Zero;
}
else
{
reg_copy(b, dest);
if ( (tagb == TW_Denormal) && (b->sigh & 0x80000000) )
{
/* A pseudoDenormal, convert it. */
addexponent(dest, 1);
tagb = TAG_Valid;
}
else if ( tagb > TAG_Empty )
tagb = TAG_Special;
setsign(dest, signb); /* signb may differ from the sign of b. */
FPU_settagi(deststnr, tagb);
return tagb;
}
}
else if (tagb == TAG_Zero)
{
reg_copy(a, dest);
if ( (taga == TW_Denormal) && (a->sigh & 0x80000000) )
{
/* A pseudoDenormal */
addexponent(dest, 1);
taga = TAG_Valid;
}
else if ( taga > TAG_Empty )
taga = TAG_Special;
setsign(dest, signa); /* signa may differ from the sign of a. */
FPU_settagi(deststnr, taga);
return taga;
}
else if (taga == TW_Infinity)
{
if ( (tagb != TW_Infinity) || (signa == signb) )
{
FPU_copy_to_regi(a, TAG_Special, deststnr);
setsign(dest, signa); /* signa may differ from the sign of a. */
return taga;
}
/* Infinity-Infinity is undefined. */
return arith_invalid(deststnr);
}
else if (tagb == TW_Infinity)
{
FPU_copy_to_regi(b, TAG_Special, deststnr);
setsign(dest, signb); /* signb may differ from the sign of b. */
return tagb;
}
#ifdef PARANOID
EXCEPTION(EX_INTERNAL|0x101);
#endif
return FPU_Exception;
}
/*
Operates on st(0) and st(n), or on st(0) and temporary data.
The destination must be one of the source st(x).
*/
int FPU_add(FPU_REG const *b, u_char tagb, int deststnr, u16 control_w)
{
FPU_REG *a = &st(0);
FPU_REG *dest = &st(deststnr);
u_char signb = getsign(b);
u_char taga = FPU_gettag0();
u_char signa = getsign(a);
u_char saved_sign = getsign(dest);
int diff, tag, expa, expb;
if ( !(taga | tagb) )
{
expa = exponent(a);
expb = exponent(b);
valid_add:
/* Both registers are valid */
if (!(signa ^ signb))
{
/* signs are the same */
tag = FPU_u_add(a, b, dest, control_w, signa, expa, expb);
}
else
{
/* The signs are different, so do a subtraction */
diff = expa - expb;
if (!diff)
{
diff = a->sigh - b->sigh; /* This works only if the ms bits
are identical. */
if (!diff)
{
diff = a->sigl > b->sigl;
if (!diff)
diff = -(a->sigl < b->sigl);
}
}
if (diff > 0)
{
tag = FPU_u_sub(a, b, dest, control_w, signa, expa, expb);
}
else if ( diff < 0 )
{
tag = FPU_u_sub(b, a, dest, control_w, signb, expb, expa);
}
else
{
FPU_copy_to_regi(&CONST_Z, TAG_Zero, deststnr);
/* sign depends upon rounding mode */
setsign(dest, ((control_w & CW_RC) != RC_DOWN)
? SIGN_POS : SIGN_NEG);
return TAG_Zero;
}
}
if ( tag < 0 )
{
setsign(dest, saved_sign);
return tag;
}
FPU_settagi(deststnr, tag);
return tag;
}
if ( taga == TAG_Special )
taga = FPU_Special(a);
if ( tagb == TAG_Special )
tagb = FPU_Special(b);
if ( ((taga == TAG_Valid) && (tagb == TW_Denormal))
|| ((taga == TW_Denormal) && (tagb == TAG_Valid))
|| ((taga == TW_Denormal) && (tagb == TW_Denormal)) )
{
FPU_REG x, y;
if ( denormal_operand() < 0 )
return FPU_Exception;
FPU_to_exp16(a, &x);
FPU_to_exp16(b, &y);
a = &x;
b = &y;
expa = exponent16(a);
expb = exponent16(b);
goto valid_add;
}
if ( (taga == TW_NaN) || (tagb == TW_NaN) )
{
if ( deststnr == 0 )
return real_2op_NaN(b, tagb, deststnr, a);
else
return real_2op_NaN(a, taga, deststnr, a);
}
return add_sub_specials(a, taga, signa, b, tagb, signb,
dest, deststnr, control_w);
}
/* Limited measurements show no results worse than 64 bit precision
except for the results for arguments close to 2^63, where the
precision of the result sometimes degrades to about 63.9 bits */
static int trig_arg(FPU_REG *st0_ptr, int even)
{
FPU_REG tmp;
u_char tmptag;
unsigned long long q;
int old_cw = control_word, saved_status = partial_status;
int tag, st0_tag = TAG_Valid;
if (exponent(st0_ptr) >= 63) {
partial_status |= SW_C2; /* Reduction incomplete. */
return -1;
}
control_word &= ~CW_RC;
control_word |= RC_CHOP;
setpositive(st0_ptr);
tag = FPU_u_div(st0_ptr, &CONST_PI2, &tmp, PR_64_BITS | RC_CHOP | 0x3f,
SIGN_POS);
FPU_round_to_int(&tmp, tag); /* Fortunately, this can't overflow
to 2^64 */
q = significand(&tmp);
if (q) {
rem_kernel(significand(st0_ptr),
&significand(&tmp),
significand(&CONST_PI2),
q, exponent(st0_ptr) - exponent(&CONST_PI2));
setexponent16(&tmp, exponent(&CONST_PI2));
st0_tag = FPU_normalize(&tmp);
FPU_copy_to_reg0(&tmp, st0_tag);
}
if ((even && !(q & 1)) || (!even && (q & 1))) {
st0_tag =
FPU_sub(REV | LOADED | TAG_Valid, (int)&CONST_PI2,
FULL_PRECISION);
#ifdef BETTER_THAN_486
/* So far, the results are exact but based upon a 64 bit
precision approximation to pi/2. The technique used
now is equivalent to using an approximation to pi/2 which
is accurate to about 128 bits. */
if ((exponent(st0_ptr) <= exponent(&CONST_PI2extra) + 64)
|| (q > 1)) {
/* This code gives the effect of having pi/2 to better than
128 bits precision. */
significand(&tmp) = q + 1;
setexponent16(&tmp, 63);
FPU_normalize(&tmp);
tmptag =
FPU_u_mul(&CONST_PI2extra, &tmp, &tmp,
FULL_PRECISION, SIGN_POS,
exponent(&CONST_PI2extra) +
exponent(&tmp));
setsign(&tmp, getsign(&CONST_PI2extra));
st0_tag = FPU_add(&tmp, tmptag, 0, FULL_PRECISION);
if (signnegative(st0_ptr)) {
/* CONST_PI2extra is negative, so the result of the addition
can be negative. This means that the argument is actually
in a different quadrant. The correction is always < pi/2,
so it can't overflow into yet another quadrant. */
setpositive(st0_ptr);
q++;
}
}
#endif /* BETTER_THAN_486 */
}
#ifdef BETTER_THAN_486
else {
/* So far, the results are exact but based upon a 64 bit
precision approximation to pi/2. The technique used
now is equivalent to using an approximation to pi/2 which
is accurate to about 128 bits. */
if (((q > 0)
&& (exponent(st0_ptr) <= exponent(&CONST_PI2extra) + 64))
|| (q > 1)) {
/* This code gives the effect of having p/2 to better than
128 bits precision. */
significand(&tmp) = q;
setexponent16(&tmp, 63);
FPU_normalize(&tmp); /* This must return TAG_Valid */
tmptag =
FPU_u_mul(&CONST_PI2extra, &tmp, &tmp,
FULL_PRECISION, SIGN_POS,
exponent(&CONST_PI2extra) +
exponent(&tmp));
setsign(&tmp, getsign(&CONST_PI2extra));
st0_tag = FPU_sub(LOADED | (tmptag & 0x0f), (int)&tmp,
FULL_PRECISION);
if ((exponent(st0_ptr) == exponent(&CONST_PI2)) &&
((st0_ptr->sigh > CONST_PI2.sigh)
|| ((st0_ptr->sigh == CONST_PI2.sigh)
&& (st0_ptr->sigl > CONST_PI2.sigl)))) {
/* CONST_PI2extra is negative, so the result of the
subtraction can be larger than pi/2. This means
that the argument is actually in a different quadrant.
The correction is always < pi/2, so it can't overflow
into yet another quadrant. */
st0_tag =
FPU_sub(REV | LOADED | TAG_Valid,
(int)&CONST_PI2, FULL_PRECISION);
q++;
}
}
}
#endif /* BETTER_THAN_486 */
FPU_settag0(st0_tag);
control_word = old_cw;
partial_status = saved_status & ~SW_C2; /* Reduction complete. */
return (q & 3) | even;
}
static void fptan(FPU_REG *st0_ptr, u_char st0_tag)
{
FPU_REG *st_new_ptr;
int q;
u_char arg_sign = getsign(st0_ptr);
/* Stack underflow has higher priority */
if (st0_tag == TAG_Empty) {
FPU_stack_underflow(); /* Puts a QNaN in st(0) */
if (control_word & CW_Invalid) {
st_new_ptr = &st(-1);
push();
FPU_stack_underflow(); /* Puts a QNaN in the new st(0) */
}
return;
}
if (STACK_OVERFLOW) {
FPU_stack_overflow();
return;
}
if (st0_tag == TAG_Valid) {
if (exponent(st0_ptr) > -40) {
if ((q = trig_arg(st0_ptr, 0)) == -1) {
/* Operand is out of range */
return;
}
poly_tan(st0_ptr);
setsign(st0_ptr, (q & 1) ^ (arg_sign != 0));
set_precision_flag_up(); /* We do not really know if up or down */
} else {
/* For a small arg, the result == the argument */
/* Underflow may happen */
denormal_arg:
FPU_to_exp16(st0_ptr, st0_ptr);
st0_tag =
FPU_round(st0_ptr, 1, 0, FULL_PRECISION, arg_sign);
FPU_settag0(st0_tag);
}
push();
FPU_copy_to_reg0(&CONST_1, TAG_Valid);
return;
}
if (st0_tag == TAG_Zero) {
push();
FPU_copy_to_reg0(&CONST_1, TAG_Valid);
setcc(0);
return;
}
if (st0_tag == TAG_Special)
st0_tag = FPU_Special(st0_ptr);
if (st0_tag == TW_Denormal) {
if (denormal_operand() < 0)
return;
goto denormal_arg;
}
if (st0_tag == TW_Infinity) {
/* The 80486 treats infinity as an invalid operand */
if (arith_invalid(0) >= 0) {
st_new_ptr = &st(-1);
push();
arith_invalid(0);
}
return;
}
single_arg_2_error(st0_ptr, st0_tag);
}
int poly_2xm1(u_char sign, FPU_REG *arg, FPU_REG *result)
{
long int exponent, shift;
unsigned long long Xll;
Xsig accumulator, Denom, argSignif;
u_char tag;
exponent = exponent16(arg);
#ifdef PARANOID
if (exponent >= 0) { /* */
/* */
EXCEPTION(EX_INTERNAL | 0x127);
return 1;
}
#endif /* */
argSignif.lsw = 0;
XSIG_LL(argSignif) = Xll = significand(arg);
if (exponent == -1) {
shift = (argSignif.msw & 0x40000000) ? 3 : 2;
/* */
exponent -= 2;
XSIG_LL(argSignif) <<= 2;
Xll <<= 2;
} else if (exponent == -2) {
shift = 1;
/* */
exponent--;
XSIG_LL(argSignif) <<= 1;
Xll <<= 1;
} else
shift = 0;
if (exponent < -2) {
/* */
if (FPU_shrx(&Xll, -2 - exponent) >= 0x80000000U)
Xll++; /* */
}
accumulator.lsw = accumulator.midw = accumulator.msw = 0;
polynomial_Xsig(&accumulator, &Xll, lterms, HIPOWER - 1);
mul_Xsig_Xsig(&accumulator, &argSignif);
shr_Xsig(&accumulator, 3);
mul_Xsig_Xsig(&argSignif, &hiterm); /* */
add_two_Xsig(&accumulator, &argSignif, &exponent);
if (shift) {
/*
*/
shr_Xsig(&accumulator, -exponent);
accumulator.msw |= 0x80000000; /* */
mul_Xsig_Xsig(&accumulator, shiftterm[shift]);
accumulator.msw &= 0x3fffffff; /* */
exponent = 1;
}
if (sign != SIGN_POS) {
/*
*/
Denom.lsw = accumulator.lsw;
XSIG_LL(Denom) = XSIG_LL(accumulator);
if (exponent < 0)
shr_Xsig(&Denom, -exponent);
else if (exponent > 0) {
/* */
XSIG_LL(Denom) <<= 1;
if (Denom.lsw & 0x80000000)
XSIG_LL(Denom) |= 1;
(Denom.lsw) <<= 1;
}
Denom.msw |= 0x80000000; /* */
div_Xsig(&accumulator, &Denom, &accumulator);
}
/* */
exponent += round_Xsig(&accumulator);
result = &st(0);
significand(result) = XSIG_LL(accumulator);
setexponent16(result, exponent);
tag = FPU_round(result, 1, 0, FULL_PRECISION, sign);
setsign(result, sign);
FPU_settag0(tag);
return 0;
}
/*
Divide one register by another and put the result into a third register.
*/
int FPU_div(int flags, int rm, int control_w)
{
FPU_REG x, y;
FPU_REG const *a, *b, *st0_ptr, *st_ptr;
FPU_REG *dest;
u_char taga, tagb, signa, signb, sign, saved_sign;
int tag, deststnr;
if (flags & DEST_RM)
deststnr = rm;
else
deststnr = 0;
if (flags & REV) {
b = &st(0);
st0_ptr = b;
tagb = FPU_gettag0();
if (flags & LOADED) {
a = (FPU_REG *) rm;
taga = flags & 0x0f;
} else {
a = &st(rm);
st_ptr = a;
taga = FPU_gettagi(rm);
}
} else {
a = &st(0);
st0_ptr = a;
taga = FPU_gettag0();
if (flags & LOADED) {
b = (FPU_REG *) rm;
tagb = flags & 0x0f;
} else {
b = &st(rm);
st_ptr = b;
tagb = FPU_gettagi(rm);
}
}
signa = getsign(a);
signb = getsign(b);
sign = signa ^ signb;
dest = &st(deststnr);
saved_sign = getsign(dest);
if (!(taga | tagb)) {
/* Both regs Valid, this should be the most common case. */
reg_copy(a, &x);
reg_copy(b, &y);
setpositive(&x);
setpositive(&y);
tag = FPU_u_div(&x, &y, dest, control_w, sign);
if (tag < 0)
return tag;
FPU_settagi(deststnr, tag);
return tag;
}
if (taga == TAG_Special)
taga = FPU_Special(a);
if (tagb == TAG_Special)
tagb = FPU_Special(b);
if (((taga == TAG_Valid) && (tagb == TW_Denormal))
|| ((taga == TW_Denormal) && (tagb == TAG_Valid))
|| ((taga == TW_Denormal) && (tagb == TW_Denormal))) {
if (denormal_operand() < 0)
return FPU_Exception;
FPU_to_exp16(a, &x);
FPU_to_exp16(b, &y);
tag = FPU_u_div(&x, &y, dest, control_w, sign);
if (tag < 0)
return tag;
FPU_settagi(deststnr, tag);
return tag;
} else if ((taga <= TW_Denormal) && (tagb <= TW_Denormal)) {
if (tagb != TAG_Zero) {
/* Want to find Zero/Valid */
if (tagb == TW_Denormal) {
if (denormal_operand() < 0)
return FPU_Exception;
}
/* The result is zero. */
FPU_copy_to_regi(&CONST_Z, TAG_Zero, deststnr);
setsign(dest, sign);
return TAG_Zero;
}
/* We have an exception condition, either 0/0 or Valid/Zero. */
if (taga == TAG_Zero) {
/* 0/0 */
return arith_invalid(deststnr);
}
/* Valid/Zero */
return FPU_divide_by_zero(deststnr, sign);
}
/* Must have infinities, NaNs, etc */
else if ((taga == TW_NaN) || (tagb == TW_NaN)) {
if (flags & LOADED)
return real_2op_NaN((FPU_REG *) rm, flags & 0x0f, 0,
st0_ptr);
if (flags & DEST_RM) {
int tag;
tag = FPU_gettag0();
if (tag == TAG_Special)
tag = FPU_Special(st0_ptr);
return real_2op_NaN(st0_ptr, tag, rm,
(flags & REV) ? st0_ptr : &st(rm));
} else {
int tag;
tag = FPU_gettagi(rm);
if (tag == TAG_Special)
tag = FPU_Special(&st(rm));
return real_2op_NaN(&st(rm), tag, 0,
(flags & REV) ? st0_ptr : &st(rm));
}
} else if (taga == TW_Infinity) {
if (tagb == TW_Infinity) {
/* infinity/infinity */
return arith_invalid(deststnr);
} else {
/* tagb must be Valid or Zero */
if ((tagb == TW_Denormal) && (denormal_operand() < 0))
return FPU_Exception;
/* Infinity divided by Zero or Valid does
not raise and exception, but returns Infinity */
FPU_copy_to_regi(a, TAG_Special, deststnr);
setsign(dest, sign);
return taga;
}
} else if (tagb == TW_Infinity) {
if ((taga == TW_Denormal) && (denormal_operand() < 0))
return FPU_Exception;
/* The result is zero. */
FPU_copy_to_regi(&CONST_Z, TAG_Zero, deststnr);
setsign(dest, sign);
return TAG_Zero;
}
#ifdef PARANOID
else {
EXCEPTION(EX_INTERNAL | 0x102);
return FPU_Exception;
}
#endif /* PARANOID */
return 0;
}
int FPU_mul(FPU_REG const *b, u_char tagb, int deststnr, int control_w)
{
FPU_REG *a = &st(deststnr);
FPU_REG *dest = a;
u_char taga = FPU_gettagi(deststnr);
u_char saved_sign = getsign(dest);
u_char sign = (getsign(a) ^ getsign(b));
int tag;
if (!(taga | tagb)) {
tag =
FPU_u_mul(a, b, dest, control_w, sign,
exponent(a) + exponent(b));
if (tag < 0) {
setsign(dest, saved_sign);
return tag;
}
FPU_settagi(deststnr, tag);
return tag;
}
if (taga == TAG_Special)
taga = FPU_Special(a);
if (tagb == TAG_Special)
tagb = FPU_Special(b);
if (((taga == TAG_Valid) && (tagb == TW_Denormal))
|| ((taga == TW_Denormal) && (tagb == TAG_Valid))
|| ((taga == TW_Denormal) && (tagb == TW_Denormal))) {
FPU_REG x, y;
if (denormal_operand() < 0)
return FPU_Exception;
FPU_to_exp16(a, &x);
FPU_to_exp16(b, &y);
tag = FPU_u_mul(&x, &y, dest, control_w, sign,
exponent16(&x) + exponent16(&y));
if (tag < 0) {
setsign(dest, saved_sign);
return tag;
}
FPU_settagi(deststnr, tag);
return tag;
} else if ((taga <= TW_Denormal) && (tagb <= TW_Denormal)) {
if (((tagb == TW_Denormal) || (taga == TW_Denormal))
&& (denormal_operand() < 0))
return FPU_Exception;
FPU_copy_to_regi(&CONST_Z, TAG_Zero, deststnr);
setsign(dest, sign);
return TAG_Zero;
}
else if ((taga == TW_NaN) || (tagb == TW_NaN)) {
return real_2op_NaN(b, tagb, deststnr, &st(0));
} else if (((taga == TW_Infinity) && (tagb == TAG_Zero))
|| ((tagb == TW_Infinity) && (taga == TAG_Zero))) {
return arith_invalid(deststnr);
} else if (((taga == TW_Denormal) || (tagb == TW_Denormal))
&& (denormal_operand() < 0)) {
return FPU_Exception;
} else if (taga == TW_Infinity) {
FPU_copy_to_regi(a, TAG_Special, deststnr);
setsign(dest, sign);
return TAG_Special;
} else if (tagb == TW_Infinity) {
FPU_copy_to_regi(b, TAG_Special, deststnr);
setsign(dest, sign);
return TAG_Special;
}
#ifdef PARANOID
else {
EXCEPTION(EX_INTERNAL | 0x102);
return FPU_Exception;
}
#endif
return 0;
}
void poly_sine(FPU_REG *st0_ptr)
{
int exponent, echange;
Xsig accumulator, argSqrd, argTo4;
unsigned long fix_up, adj;
unsigned long long fixed_arg;
FPU_REG result;
exponent = exponent(st0_ptr);
accumulator.lsw = accumulator.midw = accumulator.msw = 0;
if ((exponent < -1)
|| ((exponent == -1) && (st0_ptr->sigh <= 0xe21240aa))) {
argSqrd.msw = st0_ptr->sigh;
argSqrd.midw = st0_ptr->sigl;
argSqrd.lsw = 0;
mul64_Xsig(&argSqrd, &significand(st0_ptr));
shr_Xsig(&argSqrd, 2 * (-1 - exponent));
argTo4.msw = argSqrd.msw;
argTo4.midw = argSqrd.midw;
argTo4.lsw = argSqrd.lsw;
mul_Xsig_Xsig(&argTo4, &argTo4);
polynomial_Xsig(&accumulator, &XSIG_LL(argTo4), neg_terms_l,
N_COEFF_N - 1);
mul_Xsig_Xsig(&accumulator, &argSqrd);
negate_Xsig(&accumulator);
polynomial_Xsig(&accumulator, &XSIG_LL(argTo4), pos_terms_l,
N_COEFF_P - 1);
shr_Xsig(&accumulator, 2);
accumulator.msw |= 0x80000000;
mul64_Xsig(&accumulator, &significand(st0_ptr));
mul64_Xsig(&accumulator, &significand(st0_ptr));
mul64_Xsig(&accumulator, &significand(st0_ptr));
exponent = 3 * exponent;
shr_Xsig(&accumulator, exponent(st0_ptr) - exponent);
negate_Xsig(&accumulator);
XSIG_LL(accumulator) += significand(st0_ptr);
echange = round_Xsig(&accumulator);
setexponentpos(&result, exponent(st0_ptr) + echange);
} else {
fixed_arg = significand(st0_ptr);
if (exponent == 0) {
fixed_arg <<= 1;
}
fixed_arg = 0x921fb54442d18469LL - fixed_arg;
if (fixed_arg == 0xffffffffffffffffLL)
fixed_arg = 0;
XSIG_LL(argSqrd) = fixed_arg;
argSqrd.lsw = 0;
mul64_Xsig(&argSqrd, &fixed_arg);
XSIG_LL(argTo4) = XSIG_LL(argSqrd);
argTo4.lsw = argSqrd.lsw;
mul_Xsig_Xsig(&argTo4, &argTo4);
polynomial_Xsig(&accumulator, &XSIG_LL(argTo4), neg_terms_h,
N_COEFF_NH - 1);
mul_Xsig_Xsig(&accumulator, &argSqrd);
negate_Xsig(&accumulator);
polynomial_Xsig(&accumulator, &XSIG_LL(argTo4), pos_terms_h,
N_COEFF_PH - 1);
negate_Xsig(&accumulator);
mul64_Xsig(&accumulator, &fixed_arg);
mul64_Xsig(&accumulator, &fixed_arg);
shr_Xsig(&accumulator, 3);
negate_Xsig(&accumulator);
add_Xsig_Xsig(&accumulator, &argSqrd);
shr_Xsig(&accumulator, 1);
accumulator.lsw |= 1;
negate_Xsig(&accumulator);
fix_up = 0x898cc517;
if (argSqrd.msw & 0xffc00000) {
fix_up -= mul_32_32(0x898cc517, argSqrd.msw) / 6;
}
fix_up = mul_32_32(fix_up, LL_MSW(fixed_arg));
adj = accumulator.lsw;
accumulator.lsw -= fix_up;
if (accumulator.lsw > adj)
XSIG_LL(accumulator)--;
echange = round_Xsig(&accumulator);
setexponentpos(&result, echange - 1);
}
significand(&result) = XSIG_LL(accumulator);
setsign(&result, getsign(st0_ptr));
FPU_copy_to_reg0(&result, TAG_Valid);
#ifdef PARANOID
if ((exponent(&result) >= 0)
&& (significand(&result) > 0x8000000000000000LL)) {
EXCEPTION(EX_INTERNAL | 0x150);
}
#endif
}
static void fptan(FPU_REG *st0_ptr, u_char st0_tag)
{
FPU_REG *st_new_ptr;
int q;
u_char arg_sign = getsign(st0_ptr);
if (st0_tag == TAG_Empty) {
FPU_stack_underflow();
if (control_word & CW_Invalid) {
st_new_ptr = &st(-1);
push();
FPU_stack_underflow();
}
return;
}
if (STACK_OVERFLOW) {
FPU_stack_overflow();
return;
}
if (st0_tag == TAG_Valid) {
if (exponent(st0_ptr) > -40) {
if ((q = trig_arg(st0_ptr, 0)) == -1) {
return;
}
poly_tan(st0_ptr);
setsign(st0_ptr, (q & 1) ^ (arg_sign != 0));
set_precision_flag_up();
} else {
denormal_arg:
FPU_to_exp16(st0_ptr, st0_ptr);
st0_tag =
FPU_round(st0_ptr, 1, 0, FULL_PRECISION, arg_sign);
FPU_settag0(st0_tag);
}
push();
FPU_copy_to_reg0(&CONST_1, TAG_Valid);
return;
}
if (st0_tag == TAG_Zero) {
push();
FPU_copy_to_reg0(&CONST_1, TAG_Valid);
setcc(0);
return;
}
if (st0_tag == TAG_Special)
st0_tag = FPU_Special(st0_ptr);
if (st0_tag == TW_Denormal) {
if (denormal_operand() < 0)
return;
goto denormal_arg;
}
if (st0_tag == TW_Infinity) {
if (arith_invalid(0) >= 0) {
st_new_ptr = &st(-1);
push();
arith_invalid(0);
}
return;
}
single_arg_2_error(st0_ptr, st0_tag);
}
/*--- poly_2xm1() -----------------------------------------------------------+
| Requires st(0) which is TAG_Valid and < 1. |
+---------------------------------------------------------------------------*/
int poly_2xm1(u_char sign, FPU_REG *arg, FPU_REG *result)
{
s32 exponent, shift;
u64 Xll;
Xsig accumulator, Denom, argSignif;
u_char tag;
exponent = exponent16(arg);
#ifdef PARANOID
if ( exponent >= 0 ) /* Don't want a |number| >= 1.0 */
{
/* Number negative, too large, or not Valid. */
EXCEPTION(EX_INTERNAL|0x127);
return 1;
}
#endif /* PARANOID */
argSignif.lsw = 0;
XSIG_LL(argSignif) = Xll = significand(arg);
if ( exponent == -1 )
{
shift = (argSignif.msw & 0x40000000) ? 3 : 2;
/* subtract 0.5 or 0.75 */
exponent -= 2;
XSIG_LL(argSignif) <<= 2;
Xll <<= 2;
}
else if ( exponent == -2 )
{
shift = 1;
/* subtract 0.25 */
exponent--;
XSIG_LL(argSignif) <<= 1;
Xll <<= 1;
}
else
shift = 0;
if ( exponent < -2 )
{
/* Shift the argument right by the required places. */
if ( FPU_shrx(&Xll, -2-exponent) >= 0x80000000U )
Xll++; /* round up */
}
accumulator.lsw = accumulator.midw = accumulator.msw = 0;
polynomial_Xsig(&accumulator, &Xll, lterms, HIPOWER-1);
mul_Xsig_Xsig(&accumulator, &argSignif);
shr_Xsig(&accumulator, 3);
mul_Xsig_Xsig(&argSignif, &hiterm); /* The leading term */
add_two_Xsig(&accumulator, &argSignif, &exponent);
if ( shift )
{
/* The argument is large, use the identity:
f(x+a) = f(a) * (f(x) + 1) - 1;
*/
shr_Xsig(&accumulator, - exponent);
accumulator.msw |= 0x80000000; /* add 1.0 */
mul_Xsig_Xsig(&accumulator, shiftterm[shift]);
accumulator.msw &= 0x3fffffff; /* subtract 1.0 */
exponent = 1;
}
if ( sign != SIGN_POS )
{
/* The argument is negative, use the identity:
f(-x) = -f(x) / (1 + f(x))
*/
Denom.lsw = accumulator.lsw;
XSIG_LL(Denom) = XSIG_LL(accumulator);
if ( exponent < 0 )
shr_Xsig(&Denom, - exponent);
else if ( exponent > 0 )
{
/* exponent must be 1 here */
XSIG_LL(Denom) <<= 1;
if ( Denom.lsw & 0x80000000 )
XSIG_LL(Denom) |= 1;
(Denom.lsw) <<= 1;
}
Denom.msw |= 0x80000000; /* add 1.0 */
div_Xsig(&accumulator, &Denom, &accumulator);
}
/* Convert to 64 bit signed-compatible */
exponent += round_Xsig(&accumulator);
result = &st(0);
significand(result) = XSIG_LL(accumulator);
setexponent16(result, exponent);
tag = FPU_round(result, 1, 0, FULL_PRECISION, sign);
setsign(result, sign);
FPU_settag0(tag);
return 0;
}
static void fxtract(FPU_REG *st0_ptr, u_char st0_tag)
{
FPU_REG *st_new_ptr;
u_char sign;
register FPU_REG *st1_ptr = st0_ptr;
if (STACK_OVERFLOW) {
FPU_stack_overflow();
return;
}
clear_C1();
if (st0_tag == TAG_Valid) {
long e;
push();
sign = getsign(st1_ptr);
reg_copy(st1_ptr, st_new_ptr);
setexponent16(st_new_ptr, exponent(st_new_ptr));
denormal_arg:
e = exponent16(st_new_ptr);
convert_l2reg(&e, 1);
setexponentpos(st_new_ptr, 0);
setsign(st_new_ptr, sign);
FPU_settag0(TAG_Valid);
return;
} else if (st0_tag == TAG_Zero) {
sign = getsign(st0_ptr);
if (FPU_divide_by_zero(0, SIGN_NEG) < 0)
return;
push();
FPU_copy_to_reg0(&CONST_Z, TAG_Zero);
setsign(st_new_ptr, sign);
return;
}
if (st0_tag == TAG_Special)
st0_tag = FPU_Special(st0_ptr);
if (st0_tag == TW_Denormal) {
if (denormal_operand() < 0)
return;
push();
sign = getsign(st1_ptr);
FPU_to_exp16(st1_ptr, st_new_ptr);
goto denormal_arg;
} else if (st0_tag == TW_Infinity) {
sign = getsign(st0_ptr);
setpositive(st0_ptr);
push();
FPU_copy_to_reg0(&CONST_INF, TAG_Special);
setsign(st_new_ptr, sign);
return;
} else if (st0_tag == TW_NaN) {
if (real_1op_NaN(st0_ptr) < 0)
return;
push();
FPU_copy_to_reg0(st0_ptr, TAG_Special);
return;
} else if (st0_tag == TAG_Empty) {
if (control_word & EX_Invalid) {
FPU_stack_underflow();
push();
FPU_stack_underflow();
} else
EXCEPTION(EX_StackUnder);
}
#ifdef PARANOID
else
EXCEPTION(EX_INTERNAL | 0x119);
#endif
}
int FPU_div(int flags, int rm, int control_w)
{
FPU_REG x, y;
FPU_REG const *a, *b, *st0_ptr, *st_ptr;
FPU_REG *dest;
u_char taga, tagb, signa, signb, sign, saved_sign;
int tag, deststnr;
if (flags & DEST_RM)
deststnr = rm;
else
deststnr = 0;
if (flags & REV) {
b = &st(0);
st0_ptr = b;
tagb = FPU_gettag0();
if (flags & LOADED) {
a = (FPU_REG *) rm;
taga = flags & 0x0f;
} else {
a = &st(rm);
st_ptr = a;
taga = FPU_gettagi(rm);
}
} else {
a = &st(0);
st0_ptr = a;
taga = FPU_gettag0();
if (flags & LOADED) {
b = (FPU_REG *) rm;
tagb = flags & 0x0f;
} else {
b = &st(rm);
st_ptr = b;
tagb = FPU_gettagi(rm);
}
}
signa = getsign(a);
signb = getsign(b);
sign = signa ^ signb;
dest = &st(deststnr);
saved_sign = getsign(dest);
if (!(taga | tagb)) {
reg_copy(a, &x);
reg_copy(b, &y);
setpositive(&x);
setpositive(&y);
tag = FPU_u_div(&x, &y, dest, control_w, sign);
if (tag < 0)
return tag;
FPU_settagi(deststnr, tag);
return tag;
}
if (taga == TAG_Special)
taga = FPU_Special(a);
if (tagb == TAG_Special)
tagb = FPU_Special(b);
if (((taga == TAG_Valid) && (tagb == TW_Denormal))
|| ((taga == TW_Denormal) && (tagb == TAG_Valid))
|| ((taga == TW_Denormal) && (tagb == TW_Denormal))) {
if (denormal_operand() < 0)
return FPU_Exception;
FPU_to_exp16(a, &x);
FPU_to_exp16(b, &y);
tag = FPU_u_div(&x, &y, dest, control_w, sign);
if (tag < 0)
return tag;
FPU_settagi(deststnr, tag);
return tag;
} else if ((taga <= TW_Denormal) && (tagb <= TW_Denormal)) {
if (tagb != TAG_Zero) {
if (tagb == TW_Denormal) {
if (denormal_operand() < 0)
return FPU_Exception;
}
FPU_copy_to_regi(&CONST_Z, TAG_Zero, deststnr);
setsign(dest, sign);
return TAG_Zero;
}
if (taga == TAG_Zero) {
return arith_invalid(deststnr);
}
return FPU_divide_by_zero(deststnr, sign);
}
else if ((taga == TW_NaN) || (tagb == TW_NaN)) {
if (flags & LOADED)
return real_2op_NaN((FPU_REG *) rm, flags & 0x0f, 0,
st0_ptr);
if (flags & DEST_RM) {
int tag;
tag = FPU_gettag0();
if (tag == TAG_Special)
tag = FPU_Special(st0_ptr);
return real_2op_NaN(st0_ptr, tag, rm,
(flags & REV) ? st0_ptr : &st(rm));
} else {
int tag;
tag = FPU_gettagi(rm);
if (tag == TAG_Special)
tag = FPU_Special(&st(rm));
return real_2op_NaN(&st(rm), tag, 0,
(flags & REV) ? st0_ptr : &st(rm));
}
} else if (taga == TW_Infinity) {
if (tagb == TW_Infinity) {
return arith_invalid(deststnr);
} else {
if ((tagb == TW_Denormal) && (denormal_operand() < 0))
return FPU_Exception;
FPU_copy_to_regi(a, TAG_Special, deststnr);
setsign(dest, sign);
return taga;
}
} else if (tagb == TW_Infinity) {
if ((taga == TW_Denormal) && (denormal_operand() < 0))
return FPU_Exception;
FPU_copy_to_regi(&CONST_Z, TAG_Zero, deststnr);
setsign(dest, sign);
return TAG_Zero;
}
#ifdef PARANOID
else {
EXCEPTION(EX_INTERNAL | 0x102);
return FPU_Exception;
}
#endif
return 0;
}
