floatx80 fyl2xp1(floatx80 a, floatx80 b)
{
INT32 aExp, bExp;
UINT64 aSig, bSig, zSig0, zSig1, zSig2;
int aSign, bSign;
aSig = extractFloatx80Frac(a);
aExp = extractFloatx80Exp(a);
aSign = extractFloatx80Sign(a);
bSig = extractFloatx80Frac(b);
bExp = extractFloatx80Exp(b);
bSign = extractFloatx80Sign(b);
int zSign = aSign ^ bSign;
if (aExp == 0x7FFF) {
if ((UINT64) (aSig<<1)
|| ((bExp == 0x7FFF) && (UINT64) (bSig<<1)))
{
return propagateFloatx80NaN(a, b);
}
if (aSign)
{
invalid:
float_raise(float_flag_invalid);
return floatx80_default_nan;
}
else {
if (bExp == 0) {
if (bSig == 0) goto invalid;
float_raise(float_flag_denormal);
}
return packFloatx80(bSign, 0x7FFF, U64(0x8000000000000000));
}
}
if (bExp == 0x7FFF)
{
if ((UINT64) (bSig<<1))
return propagateFloatx80NaN(a, b);
if (aExp == 0) {
if (aSig == 0) goto invalid;
float_raise(float_flag_denormal);
}
return packFloatx80(zSign, 0x7FFF, U64(0x8000000000000000));
}
if (aExp == 0) {
if (aSig == 0) {
if (bSig && (bExp == 0)) float_raise(float_flag_denormal);
return packFloatx80(zSign, 0, 0);
}
float_raise(float_flag_denormal);
normalizeFloatx80Subnormal(aSig, &aExp, &aSig);
}
if (bExp == 0) {
if (bSig == 0) return packFloatx80(zSign, 0, 0);
float_raise(float_flag_denormal);
normalizeFloatx80Subnormal(bSig, &bExp, &bSig);
}
float_raise(float_flag_inexact);
if (aSign && aExp >= 0x3FFF)
return a;
if (aExp >= 0x3FFC) // big argument
{
return fyl2x(floatx80_add(a, floatx80_one), b);
}
// handle tiny argument
if (aExp < EXP_BIAS-70)
{
// first order approximation, return (a*b)/ln(2)
INT32 zExp = aExp + FLOAT_LN2INV_EXP - 0x3FFE;
mul128By64To192(FLOAT_LN2INV_HI, FLOAT_LN2INV_LO, aSig, &zSig0, &zSig1, &zSig2);
if (0 < (INT64) zSig0) {
shortShift128Left(zSig0, zSig1, 1, &zSig0, &zSig1);
--zExp;
}
zExp = zExp + bExp - 0x3FFE;
mul128By64To192(zSig0, zSig1, bSig, &zSig0, &zSig1, &zSig2);
if (0 < (INT64) zSig0) {
shortShift128Left(zSig0, zSig1, 1, &zSig0, &zSig1);
--zExp;
}
return
roundAndPackFloatx80(80, aSign ^ bSign, zExp, zSig0, zSig1);
}
/* ******************************** */
/* using float128 for approximation */
/* ******************************** */
shift128Right(aSig<<1, 0, 16, &zSig0, &zSig1);
float128 x = packFloat128(aSign, aExp, zSig0, zSig1);
x = poly_l2p1(x);
return floatx80_mul(b, float128_to_floatx80(x));
}
floatx80 floatx80_scale(floatx80 a, floatx80 b)
{
sbits32 aExp, bExp;
bits64 aSig, bSig;
// handle unsupported extended double-precision floating encodings
/* if (floatx80_is_unsupported(a) || floatx80_is_unsupported(b))
{
float_raise(float_flag_invalid);
return floatx80_default_nan;
}*/
aSig = extractFloatx80Frac(a);
aExp = extractFloatx80Exp(a);
int aSign = extractFloatx80Sign(a);
bSig = extractFloatx80Frac(b);
bExp = extractFloatx80Exp(b);
int bSign = extractFloatx80Sign(b);
if (aExp == 0x7FFF) {
if ((bits64) (aSig<<1) || ((bExp == 0x7FFF) && (bits64) (bSig<<1)))
{
return propagateFloatx80NaN(a, b);
}
if ((bExp == 0x7FFF) && bSign) {
float_raise(float_flag_invalid);
return floatx80_default_nan;
}
if (bSig && (bExp == 0)) float_raise(float_flag_denormal);
return a;
}
if (bExp == 0x7FFF) {
if ((bits64) (bSig<<1)) return propagateFloatx80NaN(a, b);
if ((aExp | aSig) == 0) {
if (! bSign) {
float_raise(float_flag_invalid);
return floatx80_default_nan;
}
return a;
}
if (aSig && (aExp == 0)) float_raise(float_flag_denormal);
if (bSign) return packFloatx80(aSign, 0, 0);
return packFloatx80(aSign, 0x7FFF, U64(0x8000000000000000));
}
if (aExp == 0) {
if (aSig == 0) return a;
float_raise(float_flag_denormal);
normalizeFloatx80Subnormal(aSig, &aExp, &aSig);
}
if (bExp == 0) {
if (bSig == 0) return a;
float_raise(float_flag_denormal);
normalizeFloatx80Subnormal(bSig, &bExp, &bSig);
}
if (bExp > 0x400E) {
/* generate appropriate overflow/underflow */
return roundAndPackFloatx80(80, aSign,
bSign ? -0x3FFF : 0x7FFF, aSig, 0);
}
if (bExp < 0x3FFF) return a;
int shiftCount = 0x403E - bExp;
bSig >>= shiftCount;
sbits32 scale = bSig;
if (bSign) scale = -scale; /* -32768..32767 */
return
roundAndPackFloatx80(80, aSign, aExp+scale, aSig, 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;
}
