static floatx80 sincos_approximation(int neg, float128 r, Bit64u quotient, float_status_t &status)
{
if (quotient & 0x1) {
r = poly_cos(r, status);
neg = 0;
} else {
r = poly_sin(r, status);
}
floatx80 result = float128_to_floatx80(r, status);
if (quotient & 0x2)
neg = ! neg;
if (neg)
floatx80_chs(result);
return result;
}
static floatx80 sincos_approximation(int neg, float128 r, UINT64 quotient)
{
if (quotient & 0x1) {
r = poly_cos(r);
neg = 0;
} else {
r = poly_sin(r);
}
floatx80 result = float128_to_floatx80(r);
if (quotient & 0x2)
neg = ! neg;
if (neg)
result = floatx80_chs(result);
return result;
}
/* DF /4 */
void BX_CPP_AttrRegparmN(1) BX_CPU_C::FBLD_PACKED_BCD(bxInstruction_c *i)
{
#if BX_SUPPORT_FPU
BX_CPU_THIS_PTR prepareFPU(i);
// read packed bcd from memory
Bit16u hi2 = read_virtual_word (i->seg(), RMAddr(i) + 8);
Bit64u lo8 = read_virtual_qword(i->seg(), RMAddr(i));
clear_C1();
if (! IS_TAG_EMPTY(-1))
{
BX_CPU_THIS_PTR FPU_stack_overflow();
return;
}
// convert packed BCD to 64-bit integer
Bit64s scale = 1;
Bit64s val64 = 0;
for (int n = 0; n < 16; n++)
{
val64 += (lo8 & 0x0f) * scale;
lo8 >>= 4;
scale *= 10;
}
val64 += (hi2 & 0x0f) * scale;
val64 += ((hi2>>4) & 0x0f) * scale * 10;
floatx80 result = int64_to_floatx80(val64);
if (hi2 & 0x8000) // set negative
floatx80_chs(result);
BX_CPU_THIS_PTR the_i387.FPU_push();
BX_WRITE_FPU_REG(result, 0);
#else
BX_INFO(("FBLD_PACKED_BCD: required FPU, configure --enable-fpu"));
#endif
}
/* DF /4 */
BX_INSF_TYPE BX_CPP_AttrRegparmN(1) BX_CPU_C::FBLD_PACKED_BCD(bxInstruction_c *i)
{
BX_CPU_THIS_PTR prepareFPU(i);
RMAddr(i) = BX_CPU_CALL_METHODR(i->ResolveModrm, (i));
Bit16u hi2 = read_virtual_word(i->seg(), (RMAddr(i) + 8) & i->asize_mask());
Bit64u lo8 = read_virtual_qword(i->seg(), RMAddr(i));
FPU_update_last_instruction(i);
clear_C1();
if (! IS_TAG_EMPTY(-1))
{
FPU_stack_overflow();
BX_NEXT_INSTR(i);
}
// convert packed BCD to 64-bit integer
Bit64s scale = 1;
Bit64s val64 = 0;
for (int n = 0; n < 16; n++)
{
val64 += (lo8 & 0x0f) * scale;
lo8 >>= 4;
scale *= 10;
}
val64 += (hi2 & 0x0f) * scale;
val64 += ((hi2>>4) & 0x0f) * scale * 10;
floatx80 result = int64_to_floatx80(val64);
if (hi2 & 0x8000) // set negative
floatx80_chs(result);
BX_CPU_THIS_PTR the_i387.FPU_push();
BX_WRITE_FPU_REG(result, 0);
BX_NEXT_INSTR(i);
}
int ftan(floatx80 &a, float_status_t &status)
{
Bit64u aSig0, aSig1 = 0;
Bit32s aExp, zExp, expDiff;
int aSign, zSign;
int q = 0;
// handle unsupported extended double-precision floating encodings
if (floatx80_is_unsupported(a))
{
goto invalid;
}
aSig0 = extractFloatx80Frac(a);
aExp = extractFloatx80Exp(a);
aSign = extractFloatx80Sign(a);
/* invalid argument */
if (aExp == 0x7FFF) {
if ((Bit64u) (aSig0<<1))
{
a = propagateFloatx80NaN(a, status);
return 0;
}
invalid:
float_raise(status, float_flag_invalid);
a = floatx80_default_nan;
return 0;
}
if (aExp == 0) {
if (aSig0 == 0) return 0;
float_raise(status, float_flag_denormal);
/* handle pseudo denormals */
if (! (aSig0 & BX_CONST64(0x8000000000000000)))
{
float_raise(status, float_flag_inexact | float_flag_underflow);
return 0;
}
normalizeFloatx80Subnormal(aSig0, &aExp, &aSig0);
}
zSign = aSign;
zExp = EXP_BIAS;
expDiff = aExp - zExp;
/* argument is out-of-range */
if (expDiff >= 63)
return -1;
float_raise(status, float_flag_inexact);
if (expDiff < -1) { // doesn't require reduction
if (expDiff <= -68) {
a = packFloatx80(aSign, aExp, aSig0);
return 0;
}
zExp = aExp;
}
else {
q = reduce_trig_arg(expDiff, zSign, aSig0, aSig1);
}
/* **************************** */
/* argument reduction completed */
/* **************************** */
/* using float128 for approximation */
float128 r = normalizeRoundAndPackFloat128(0, zExp-0x10, aSig0, aSig1, status);
float128 sin_r = poly_sin(r, status);
float128 cos_r = poly_cos(r, status);
if (q & 0x1) {
r = float128_div(cos_r, sin_r, status);
zSign = ! zSign;
} else {
r = float128_div(sin_r, cos_r, status);
}
a = float128_to_floatx80(r, status);
if (zSign)
floatx80_chs(a);
return 0;
}
int floatx80_ftan(floatx80 &a)
{
UINT64 aSig0, aSig1 = 0;
INT32 aExp, zExp, expDiff;
int aSign, zSign;
int q = 0;
aSig0 = extractFloatx80Frac(a);
aExp = extractFloatx80Exp(a);
aSign = extractFloatx80Sign(a);
/* invalid argument */
if (aExp == 0x7FFF) {
if ((UINT64) (aSig0<<1))
{
a = propagateFloatx80NaNOneArg(a);
return 0;
}
float_raise(float_flag_invalid);
a = floatx80_default_nan;
return 0;
}
if (aExp == 0) {
if (aSig0 == 0) return 0;
// float_raise(float_flag_denormal);
/* handle pseudo denormals */
if (! (aSig0 & U64(0x8000000000000000)))
{
float_raise(float_flag_inexact | float_flag_underflow);
return 0;
}
normalizeFloatx80Subnormal(aSig0, &aExp, &aSig0);
}
zSign = aSign;
zExp = EXP_BIAS;
expDiff = aExp - zExp;
/* argument is out-of-range */
if (expDiff >= 63)
return -1;
float_raise(float_flag_inexact);
if (expDiff < -1) { // doesn't require reduction
if (expDiff <= -68) {
a = packFloatx80(aSign, aExp, aSig0);
return 0;
}
zExp = aExp;
}
else {
q = reduce_trig_arg(expDiff, zSign, aSig0, aSig1);
}
/* **************************** */
/* argument reduction completed */
/* **************************** */
/* using float128 for approximation */
float128 r = normalizeRoundAndPackFloat128(0, zExp-0x10, aSig0, aSig1);
float128 sin_r = poly_sin(r);
float128 cos_r = poly_cos(r);
if (q & 0x1) {
r = float128_div(cos_r, sin_r);
zSign = ! zSign;
} else {
r = float128_div(sin_r, cos_r);
}
a = float128_to_floatx80(r);
if (zSign)
a = floatx80_chs(a);
return 0;
}
floatx80 fpatan(floatx80 a, floatx80 b, float_status_t &status)
{
// handle unsupported extended double-precision floating encodings
if (floatx80_is_unsupported(a) || floatx80_is_unsupported(b)) {
float_raise(status, float_flag_invalid);
return floatx80_default_nan;
}
Bit64u aSig = extractFloatx80Frac(a);
Bit32s aExp = extractFloatx80Exp(a);
int aSign = extractFloatx80Sign(a);
Bit64u bSig = extractFloatx80Frac(b);
Bit32s bExp = extractFloatx80Exp(b);
int bSign = extractFloatx80Sign(b);
int zSign = aSign ^ bSign;
if (bExp == 0x7FFF)
{
if ((Bit64u) (bSig<<1))
return propagateFloatx80NaN(a, b, status);
if (aExp == 0x7FFF) {
if ((Bit64u) (aSig<<1))
return propagateFloatx80NaN(a, b, status);
if (aSign) { /* return 3PI/4 */
return roundAndPackFloatx80(80, bSign,
FLOATX80_3PI4_EXP, FLOAT_3PI4_HI, FLOAT_3PI4_LO, status);
}
else { /* return PI/4 */
return roundAndPackFloatx80(80, bSign,
FLOATX80_PI4_EXP, FLOAT_PI_HI, FLOAT_PI_LO, status);
}
}
if (aSig && (aExp == 0))
float_raise(status, float_flag_denormal);
/* return PI/2 */
return roundAndPackFloatx80(80, bSign, FLOATX80_PI2_EXP, FLOAT_PI_HI, FLOAT_PI_LO, status);
}
if (aExp == 0x7FFF)
{
if ((Bit64u) (aSig<<1))
return propagateFloatx80NaN(a, b, status);
if (bSig && (bExp == 0))
float_raise(status, float_flag_denormal);
return_PI_or_ZERO:
if (aSign) { /* return PI */
return roundAndPackFloatx80(80, bSign, FLOATX80_PI_EXP, FLOAT_PI_HI, FLOAT_PI_LO, status);
} else { /* return 0 */
return packFloatx80(bSign, 0, 0);
}
}
if (bExp == 0)
{
if (bSig == 0) {
if (aSig && (aExp == 0)) float_raise(status, float_flag_denormal);
goto return_PI_or_ZERO;
}
float_raise(status, float_flag_denormal);
normalizeFloatx80Subnormal(bSig, &bExp, &bSig);
}
if (aExp == 0)
{
if (aSig == 0) /* return PI/2 */
return roundAndPackFloatx80(80, bSign, FLOATX80_PI2_EXP, FLOAT_PI_HI, FLOAT_PI_LO, status);
float_raise(status, float_flag_denormal);
normalizeFloatx80Subnormal(aSig, &aExp, &aSig);
}
float_raise(status, float_flag_inexact);
/* |a| = |b| ==> return PI/4 */
if (aSig == bSig && aExp == bExp)
return roundAndPackFloatx80(80, bSign, FLOATX80_PI4_EXP, FLOAT_PI_HI, FLOAT_PI_LO, status);
/* ******************************** */
/* using float128 for approximation */
/* ******************************** */
float128 a128 = normalizeRoundAndPackFloat128(0, aExp-0x10, aSig, 0, status);
float128 b128 = normalizeRoundAndPackFloat128(0, bExp-0x10, bSig, 0, status);
float128 x;
int swap = 0, add_pi6 = 0, add_pi4 = 0;
if (aExp > bExp || (aExp == bExp && aSig > bSig))
{
x = float128_div(b128, a128, status);
}
else {
x = float128_div(a128, b128, status);
swap = 1;
}
Bit32s xExp = extractFloat128Exp(x);
if (xExp <= EXP_BIAS-40)
goto approximation_completed;
if (x.hi >= BX_CONST64(0x3ffe800000000000)) // 3/4 < x < 1
{
/*
arctan(x) = arctan((x-1)/(x+1)) + pi/4
*/
float128 t1 = float128_sub(x, float128_one, status);
float128 t2 = float128_add(x, float128_one, status);
x = float128_div(t1, t2, status);
add_pi4 = 1;
}
else
{
/* argument correction */
if (xExp >= 0x3FFD) // 1/4 < x < 3/4
{
/*
arctan(x) = arctan((x*sqrt(3)-1)/(x+sqrt(3))) + pi/6
*/
float128 t1 = float128_mul(x, float128_sqrt3, status);
float128 t2 = float128_add(x, float128_sqrt3, status);
x = float128_sub(t1, float128_one, status);
x = float128_div(x, t2, status);
add_pi6 = 1;
}
}
x = poly_atan(x, status);
if (add_pi6) x = float128_add(x, float128_pi6, status);
if (add_pi4) x = float128_add(x, float128_pi4, status);
approximation_completed:
if (swap) x = float128_sub(float128_pi2, x, status);
floatx80 result = float128_to_floatx80(x, status);
if (zSign) floatx80_chs(result);
int rSign = extractFloatx80Sign(result);
if (!bSign && rSign)
return floatx80_add(result, floatx80_pi, status);
if (bSign && !rSign)
return floatx80_sub(result, floatx80_pi, status);
return result;
}