static floatx80 fyl2x(floatx80 a, floatx80 b)
{
UINT64 aSig = extractFloatx80Frac(a);
INT32 aExp = extractFloatx80Exp(a);
int aSign = extractFloatx80Sign(a);
UINT64 bSig = extractFloatx80Frac(b);
INT32 bExp = extractFloatx80Exp(b);
int bSign = extractFloatx80Sign(b);
int zSign = bSign ^ 1;
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 (aSign && (UINT64)(aExp | aSig)) goto invalid;
if (aSig && (aExp == 0))
float_raise(float_flag_denormal);
if (aExp < 0x3FFF) {
return packFloatx80(zSign, 0x7FFF, U64(0x8000000000000000));
}
if (aExp == 0x3FFF && ((UINT64) (aSig<<1) == 0)) goto invalid;
return packFloatx80(bSign, 0x7FFF, U64(0x8000000000000000));
}
if (aExp == 0) {
if (aSig == 0) {
if ((bExp | bSig) == 0) goto invalid;
float_raise(float_flag_divbyzero);
return packFloatx80(zSign, 0x7FFF, U64(0x8000000000000000));
}
if (aSign) goto invalid;
float_raise(float_flag_denormal);
normalizeFloatx80Subnormal(aSig, &aExp, &aSig);
}
if (aSign) goto invalid;
if (bExp == 0) {
if (bSig == 0) {
if (aExp < 0x3FFF) return packFloatx80(zSign, 0, 0);
return packFloatx80(bSign, 0, 0);
}
float_raise(float_flag_denormal);
normalizeFloatx80Subnormal(bSig, &bExp, &bSig);
}
if (aExp == 0x3FFF && ((UINT64) (aSig<<1) == 0))
return packFloatx80(bSign, 0, 0);
float_raise(float_flag_inexact);
int ExpDiff = aExp - 0x3FFF;
aExp = 0;
if (aSig >= SQRT2_HALF_SIG) {
ExpDiff++;
aExp--;
}
/* ******************************** */
/* using float128 for approximation */
/* ******************************** */
UINT64 zSig0, zSig1;
shift128Right(aSig<<1, 0, 16, &zSig0, &zSig1);
float128 x = packFloat128(0, aExp+0x3FFF, zSig0, zSig1);
x = poly_l2(x);
x = float128_add(x, int64_to_float128((INT64) ExpDiff));
return floatx80_mul(b, float128_to_floatx80(x));
}
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));
}
/*============================================================================
* Written for Bochs (x86 achitecture simulator) by
* Stanislav Shwartsman [sshwarts at sourceforge net]
* ==========================================================================*/
#define FLOAT128
#include "softfloatx80.h"
#include "softfloat-round-pack.h"
#include "fpu_constant.h"
#define FPATAN_ARR_SIZE 11
static const float128 float128_one =
packFloat128(BX_CONST64(0x3fff000000000000), BX_CONST64(0x0000000000000000));
static const float128 float128_sqrt3 =
packFloat128(BX_CONST64(0x3fffbb67ae8584ca), BX_CONST64(0xa73b25742d7078b8));
static const floatx80 floatx80_pi =
packFloatx80(0, 0x4000, BX_CONST64(0xc90fdaa22168c235));
static const float128 float128_pi2 =
packFloat128(BX_CONST64(0x3fff921fb54442d1), BX_CONST64(0x8469898CC5170416));
static const float128 float128_pi4 =
packFloat128(BX_CONST64(0x3ffe921fb54442d1), BX_CONST64(0x8469898CC5170416));
static const float128 float128_pi6 =
packFloat128(BX_CONST64(0x3ffe0c152382d736), BX_CONST64(0x58465BB32E0F580F));
static float128 atan_arr[FPATAN_ARR_SIZE] =
{
PACK_FLOAT_128(0x3fff000000000000, 0x0000000000000000), /* 1 */
