/*
* Ported from a work by Andreas Grabher for Previous, NeXT Computer Emulator,
* derived from NetBSD M68040 FPSP functions,
* derived from release 2a of the SoftFloat IEC/IEEE Floating-point Arithmetic
* Package. Those parts of the code (and some later contributions) are
* provided under that license, as detailed below.
* It has subsequently been modified by contributors to the QEMU Project,
* so some portions are provided under:
* the SoftFloat-2a license
* the BSD license
* GPL-v2-or-later
*
* Any future contributions to this file will be taken to be licensed under
* the Softfloat-2a license unless specifically indicated otherwise.
*/
/* Portions of this work are licensed under the terms of the GNU GPL,
* version 2 or later. See the COPYING file in the top-level directory.
*/
#include "qemu/osdep.h"
#include "softfloat.h"
#include "fpu/softfloat-macros.h"
#include "softfloat_fpsp_tables.h"
static floatx80 propagateFloatx80NaNOneArg(floatx80 a, float_status *status)
{
if (floatx80_is_signaling_nan(a, status)) {
float_raise(float_flag_invalid, status);
}
if (status->default_nan_mode) {
return floatx80_default_nan(status);
}
return floatx80_maybe_silence_nan(a, status);
}
/*----------------------------------------------------------------------------
| Returns the modulo remainder of the extended double-precision floating-point
| value `a' with respect to the corresponding value `b'.
*----------------------------------------------------------------------------*/
floatx80 floatx80_mod(floatx80 a, floatx80 b, float_status *status)
{
flag aSign, zSign;
int32_t aExp, bExp, expDiff;
uint64_t aSig0, aSig1, bSig;
uint64_t qTemp, term0, term1;
aSig0 = extractFloatx80Frac(a);
aExp = extractFloatx80Exp(a);
aSign = extractFloatx80Sign(a);
bSig = extractFloatx80Frac(b);
bExp = extractFloatx80Exp(b);
if (aExp == 0x7FFF) {
if ((uint64_t) (aSig0 << 1)
|| ((bExp == 0x7FFF) && (uint64_t) (bSig << 1))) {
return propagateFloatx80NaN(a, b, status);
}
goto invalid;
}
if (bExp == 0x7FFF) {
if ((uint64_t) (bSig << 1)) {
return propagateFloatx80NaN(a, b, status);
}
return a;
}
if (bExp == 0) {
if (bSig == 0) {
invalid:
float_raise(float_flag_invalid, status);
return floatx80_default_nan(status);
}
normalizeFloatx80Subnormal(bSig, &bExp, &bSig);
}
if (aExp == 0) {
if ((uint64_t) (aSig0 << 1) == 0) {
return a;
}
normalizeFloatx80Subnormal(aSig0, &aExp, &aSig0);
}
bSig |= LIT64(0x8000000000000000);
zSign = aSign;
expDiff = aExp - bExp;
aSig1 = 0;
if (expDiff < 0) {
return a;
}
qTemp = (bSig <= aSig0);
if (qTemp) {
aSig0 -= bSig;
}
expDiff -= 64;
while (0 < expDiff) {
qTemp = estimateDiv128To64(aSig0, aSig1, bSig);
qTemp = (2 < qTemp) ? qTemp - 2 : 0;
mul64To128(bSig, qTemp, &term0, &term1);
sub128(aSig0, aSig1, term0, term1, &aSig0, &aSig1);
shortShift128Left(aSig0, aSig1, 62, &aSig0, &aSig1);
}
expDiff += 64;
if (0 < expDiff) {
qTemp = estimateDiv128To64(aSig0, aSig1, bSig);
qTemp = (2 < qTemp) ? qTemp - 2 : 0;
qTemp >>= 64 - expDiff;
mul64To128(bSig, qTemp << (64 - expDiff), &term0, &term1);
sub128(aSig0, aSig1, term0, term1, &aSig0, &aSig1);
shortShift128Left(0, bSig, 64 - expDiff, &term0, &term1);
while (le128(term0, term1, aSig0, aSig1)) {
++qTemp;
sub128(aSig0, aSig1, term0, term1, &aSig0, &aSig1);
}
}
return
normalizeRoundAndPackFloatx80(
80, zSign, bExp + expDiff, aSig0, aSig1, status);
}
/*----------------------------------------------------------------------------
| Returns the mantissa of the extended double-precision floating-point
| value `a'.
*----------------------------------------------------------------------------*/
floatx80 floatx80_getman(floatx80 a, float_status *status)
{
flag aSign;
int32_t aExp;
uint64_t aSig;
aSig = extractFloatx80Frac(a);
aExp = extractFloatx80Exp(a);
aSign = extractFloatx80Sign(a);
if (aExp == 0x7FFF) {
if ((uint64_t) (aSig << 1)) {
return propagateFloatx80NaNOneArg(a , status);
}
float_raise(float_flag_invalid , status);
return floatx80_default_nan(status);
}
if (aExp == 0) {
if (aSig == 0) {
return packFloatx80(aSign, 0, 0);
}
normalizeFloatx80Subnormal(aSig, &aExp, &aSig);
}
return roundAndPackFloatx80(status->floatx80_rounding_precision, aSign,
0x3FFF, aSig, 0, status);
}
/*----------------------------------------------------------------------------
| Returns the exponent of the extended double-precision floating-point
| value `a' as an extended double-precision value.
*----------------------------------------------------------------------------*/
floatx80 floatx80_getexp(floatx80 a, float_status *status)
{
flag aSign;
int32_t aExp;
uint64_t aSig;
aSig = extractFloatx80Frac(a);
aExp = extractFloatx80Exp(a);
aSign = extractFloatx80Sign(a);
if (aExp == 0x7FFF) {
if ((uint64_t) (aSig << 1)) {
return propagateFloatx80NaNOneArg(a , status);
}
float_raise(float_flag_invalid , status);
return floatx80_default_nan(status);
}
if (aExp == 0) {
if (aSig == 0) {
return packFloatx80(aSign, 0, 0);
}
normalizeFloatx80Subnormal(aSig, &aExp, &aSig);
}
return int32_to_floatx80(aExp - 0x3FFF, status);
}
/*----------------------------------------------------------------------------
| Scales extended double-precision floating-point value in operand `a' by
| value `b'. The function truncates the value in the second operand 'b' to
| an integral value and adds that value to the exponent of the operand 'a'.
| The operation performed according to the IEC/IEEE Standard for Binary
| Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
floatx80 floatx80_scale(floatx80 a, floatx80 b, float_status *status)
{
flag aSign, bSign;
int32_t aExp, bExp, shiftCount;
uint64_t aSig, bSig;
aSig = extractFloatx80Frac(a);
aExp = extractFloatx80Exp(a);
aSign = extractFloatx80Sign(a);
bSig = extractFloatx80Frac(b);
bExp = extractFloatx80Exp(b);
bSign = extractFloatx80Sign(b);
if (bExp == 0x7FFF) {
if ((uint64_t) (bSig << 1) ||
((aExp == 0x7FFF) && (uint64_t) (aSig << 1))) {
return propagateFloatx80NaN(a, b, status);
}
float_raise(float_flag_invalid , status);
return floatx80_default_nan(status);
}
if (aExp == 0x7FFF) {
if ((uint64_t) (aSig << 1)) {
return propagateFloatx80NaN(a, b, status);
}
return packFloatx80(aSign, floatx80_infinity.high,
floatx80_infinity.low);
}
if (aExp == 0) {
if (aSig == 0) {
return packFloatx80(aSign, 0, 0);
}
if (bExp < 0x3FFF) {
return a;
}
normalizeFloatx80Subnormal(aSig, &aExp, &aSig);
}
if (bExp < 0x3FFF) {
return a;
}
if (0x400F < bExp) {
aExp = bSign ? -0x6001 : 0xE000;
return roundAndPackFloatx80(status->floatx80_rounding_precision,
aSign, aExp, aSig, 0, status);
}
shiftCount = 0x403E - bExp;
bSig >>= shiftCount;
aExp = bSign ? (aExp - bSig) : (aExp + bSig);
return roundAndPackFloatx80(status->floatx80_rounding_precision,
aSign, aExp, aSig, 0, status);
}
floatx80 floatx80_move(floatx80 a, float_status *status)
{
flag aSign;
int32_t aExp;
uint64_t aSig;
aSig = extractFloatx80Frac(a);
aExp = extractFloatx80Exp(a);
aSign = extractFloatx80Sign(a);
if (aExp == 0x7FFF) {
if ((uint64_t)(aSig << 1)) {
return propagateFloatx80NaNOneArg(a, status);
}
return a;
}
if (aExp == 0) {
if (aSig == 0) {
return a;
}
normalizeRoundAndPackFloatx80(status->floatx80_rounding_precision,
aSign, aExp, aSig, 0, status);
}
return roundAndPackFloatx80(status->floatx80_rounding_precision, aSign,
aExp, aSig, 0, status);
}
/*----------------------------------------------------------------------------
| Algorithms for transcendental functions supported by MC68881 and MC68882
| mathematical coprocessors. The functions are derived from FPSP library.
*----------------------------------------------------------------------------*/
#define one_exp 0x3FFF
#define one_sig LIT64(0x8000000000000000)
/*----------------------------------------------------------------------------
| Function for compactifying extended double-precision floating point values.
*----------------------------------------------------------------------------*/
static int32_t floatx80_make_compact(int32_t aExp, uint64_t aSig)
{
return (aExp << 16) | (aSig >> 48);
}
/*----------------------------------------------------------------------------
| Log base e of x plus 1
*----------------------------------------------------------------------------*/
floatx80 floatx80_lognp1(floatx80 a, float_status *status)
{
flag aSign;
int32_t aExp;
uint64_t aSig, fSig;
int8_t user_rnd_mode, user_rnd_prec;
int32_t compact, j, k;
floatx80 fp0, fp1, fp2, fp3, f, logof2, klog2, saveu;
aSig = extractFloatx80Frac(a);
aExp = extractFloatx80Exp(a);
aSign = extractFloatx80Sign(a);
if (aExp == 0x7FFF) {
if ((uint64_t) (aSig << 1)) {
propagateFloatx80NaNOneArg(a, status);
}
if (aSign) {
float_raise(float_flag_invalid, status);
return floatx80_default_nan(status);
}
return packFloatx80(0, floatx80_infinity.high, floatx80_infinity.low);
}
if (aExp == 0 && aSig == 0) {
return packFloatx80(aSign, 0, 0);
}
if (aSign && aExp >= one_exp) {
if (aExp == one_exp && aSig == one_sig) {
float_raise(float_flag_divbyzero, status);
packFloatx80(aSign, floatx80_infinity.high, floatx80_infinity.low);
}
float_raise(float_flag_invalid, status);
return floatx80_default_nan(status);
}
if (aExp < 0x3f99 || (aExp == 0x3f99 && aSig == one_sig)) {
/* <= min threshold */
float_raise(float_flag_inexact, status);
return floatx80_move(a, status);
}
user_rnd_mode = status->float_rounding_mode;
user_rnd_prec = status->floatx80_rounding_precision;
status->float_rounding_mode = float_round_nearest_even;
status->floatx80_rounding_precision = 80;
compact = floatx80_make_compact(aExp, aSig);
fp0 = a; /* Z */
fp1 = a;
fp0 = floatx80_add(fp0, float32_to_floatx80(make_float32(0x3F800000),
status), status); /* X = (1+Z) */
aExp = extractFloatx80Exp(fp0);
aSig = extractFloatx80Frac(fp0);
compact = floatx80_make_compact(aExp, aSig);
if (compact < 0x3FFE8000 || compact > 0x3FFFC000) {
/* |X| < 1/2 or |X| > 3/2 */
k = aExp - 0x3FFF;
fp1 = int32_to_floatx80(k, status);
fSig = (aSig & LIT64(0xFE00000000000000)) | LIT64(0x0100000000000000);
j = (fSig >> 56) & 0x7E; /* DISPLACEMENT FOR 1/F */
f = packFloatx80(0, 0x3FFF, fSig); /* F */
fp0 = packFloatx80(0, 0x3FFF, aSig); /* Y */
fp0 = floatx80_sub(fp0, f, status); /* Y-F */
lp1cont1:
/* LP1CONT1 */
fp0 = floatx80_mul(fp0, log_tbl[j], status); /* FP0 IS U = (Y-F)/F */
logof2 = packFloatx80(0, 0x3FFE, LIT64(0xB17217F7D1CF79AC));
klog2 = floatx80_mul(fp1, logof2, status); /* FP1 IS K*LOG2 */
fp2 = floatx80_mul(fp0, fp0, status); /* FP2 IS V=U*U */
fp3 = fp2;
fp1 = fp2;
fp1 = floatx80_mul(fp1, float64_to_floatx80(
make_float64(0x3FC2499AB5E4040B), status),
status); /* V*A6 */
fp2 = floatx80_mul(fp2, float64_to_floatx80(
make_float64(0xBFC555B5848CB7DB), status),
status); /* V*A5 */
fp1 = floatx80_add(fp1, float64_to_floatx80(
make_float64(0x3FC99999987D8730), status),
status); /* A4+V*A6 */
fp2 = floatx80_add(fp2, float64_to_floatx80(
make_float64(0xBFCFFFFFFF6F7E97), status),
status); /* A3+V*A5 */
fp1 = floatx80_mul(fp1, fp3, status); /* V*(A4+V*A6) */
fp2 = floatx80_mul(fp2, fp3, status); /* V*(A3+V*A5) */
fp1 = floatx80_add(fp1, float64_to_floatx80(
make_float64(0x3FD55555555555A4), status),
status); /* A2+V*(A4+V*A6) */
fp2 = floatx80_add(fp2, float64_to_floatx80(
make_float64(0xBFE0000000000008), status),
status); /* A1+V*(A3+V*A5) */
fp1 = floatx80_mul(fp1, fp3, status); /* V*(A2+V*(A4+V*A6)) */
fp2 = floatx80_mul(fp2, fp3, status); /* V*(A1+V*(A3+V*A5)) */
fp1 = floatx80_mul(fp1, fp0, status); /* U*V*(A2+V*(A4+V*A6)) */
fp0 = floatx80_add(fp0, fp2, status); /* U+V*(A1+V*(A3+V*A5)) */
fp1 = floatx80_add(fp1, log_tbl[j + 1],
status); /* LOG(F)+U*V*(A2+V*(A4+V*A6)) */
fp0 = floatx80_add(fp0, fp1, status); /* FP0 IS LOG(F) + LOG(1+U) */
status->float_rounding_mode = user_rnd_mode;
status->floatx80_rounding_precision = user_rnd_prec;
a = floatx80_add(fp0, klog2, status);
float_raise(float_flag_inexact, status);
return a;
} else if (compact < 0x3FFEF07D || compact > 0x3FFF8841) {
/* |X| < 1/16 or |X| > -1/16 */
/* LP1CARE */
fSig = (aSig & LIT64(0xFE00000000000000)) | LIT64(0x0100000000000000);
f = packFloatx80(0, 0x3FFF, fSig); /* F */
j = (fSig >> 56) & 0x7E; /* DISPLACEMENT FOR 1/F */
if (compact >= 0x3FFF8000) { /* 1+Z >= 1 */
/* KISZERO */
fp0 = floatx80_sub(float32_to_floatx80(make_float32(0x3F800000),
status), f, status); /* 1-F */
fp0 = floatx80_add(fp0, fp1, status); /* FP0 IS Y-F = (1-F)+Z */
fp1 = packFloatx80(0, 0, 0); /* K = 0 */
} else {
/* KISNEG */
fp0 = floatx80_sub(float32_to_floatx80(make_float32(0x40000000),
status), f, status); /* 2-F */
fp1 = floatx80_add(fp1, fp1, status); /* 2Z */
fp0 = floatx80_add(fp0, fp1, status); /* FP0 IS Y-F = (2-F)+2Z */
fp1 = packFloatx80(1, one_exp, one_sig); /* K = -1 */
}
goto lp1cont1;
} else {
/* LP1ONE16 */
fp1 = floatx80_add(fp1, fp1, status); /* FP1 IS 2Z */
fp0 = floatx80_add(fp0, float32_to_floatx80(make_float32(0x3F800000),
status), status); /* FP0 IS 1+X */
/* LP1CONT2 */
fp1 = floatx80_div(fp1, fp0, status); /* U */
saveu = fp1;
fp0 = floatx80_mul(fp1, fp1, status); /* FP0 IS V = U*U */
fp1 = floatx80_mul(fp0, fp0, status); /* FP1 IS W = V*V */
fp3 = float64_to_floatx80(make_float64(0x3F175496ADD7DAD6),
status); /* B5 */
fp2 = float64_to_floatx80(make_float64(0x3F3C71C2FE80C7E0),
status); /* B4 */
fp3 = floatx80_mul(fp3, fp1, status); /* W*B5 */
fp2 = floatx80_mul(fp2, fp1, status); /* W*B4 */
fp3 = floatx80_add(fp3, float64_to_floatx80(
make_float64(0x3F624924928BCCFF), status),
status); /* B3+W*B5 */
fp2 = floatx80_add(fp2, float64_to_floatx80(
make_float64(0x3F899999999995EC), status),
status); /* B2+W*B4 */
fp1 = floatx80_mul(fp1, fp3, status); /* W*(B3+W*B5) */
fp2 = floatx80_mul(fp2, fp0, status); /* V*(B2+W*B4) */
fp1 = floatx80_add(fp1, float64_to_floatx80(
make_float64(0x3FB5555555555555), status),
status); /* B1+W*(B3+W*B5) */
fp0 = floatx80_mul(fp0, saveu, status); /* FP0 IS U*V */
fp1 = floatx80_add(fp1, fp2,
status); /* B1+W*(B3+W*B5) + V*(B2+W*B4) */
fp0 = floatx80_mul(fp0, fp1,
status); /* U*V*([B1+W*(B3+W*B5)] + [V*(B2+W*B4)]) */
status->float_rounding_mode = user_rnd_mode;
status->floatx80_rounding_precision = user_rnd_prec;
a = floatx80_add(fp0, saveu, status);
/*if (!floatx80_is_zero(a)) { */
float_raise(float_flag_inexact, status);
/*} */
return a;
}
}
/*----------------------------------------------------------------------------
| Log base e
*----------------------------------------------------------------------------*/
floatx80 floatx80_logn(floatx80 a, float_status *status)
{
flag aSign;
int32_t aExp;
uint64_t aSig, fSig;
int8_t user_rnd_mode, user_rnd_prec;
int32_t compact, j, k, adjk;
floatx80 fp0, fp1, fp2, fp3, f, logof2, klog2, saveu;
aSig = extractFloatx80Frac(a);
aExp = extractFloatx80Exp(a);
aSign = extractFloatx80Sign(a);
if (aExp == 0x7FFF) {
if ((uint64_t) (aSig << 1)) {
propagateFloatx80NaNOneArg(a, status);
}
if (aSign == 0) {
return packFloatx80(0, floatx80_infinity.high,
floatx80_infinity.low);
}
}
adjk = 0;
if (aExp == 0) {
if (aSig == 0) { /* zero */
float_raise(float_flag_divbyzero, status);
return packFloatx80(1, floatx80_infinity.high,
floatx80_infinity.low);
}
if ((aSig & one_sig) == 0) { /* denormal */
normalizeFloatx80Subnormal(aSig, &aExp, &aSig);
adjk = -100;
aExp += 100;
a = packFloatx80(aSign, aExp, aSig);
}
}
if (aSign) {
float_raise(float_flag_invalid, status);
return floatx80_default_nan(status);
}
user_rnd_mode = status->float_rounding_mode;
user_rnd_prec = status->floatx80_rounding_precision;
status->float_rounding_mode = float_round_nearest_even;
status->floatx80_rounding_precision = 80;
compact = floatx80_make_compact(aExp, aSig);
if (compact < 0x3FFEF07D || compact > 0x3FFF8841) {
/* |X| < 15/16 or |X| > 17/16 */
k = aExp - 0x3FFF;
k += adjk;
fp1 = int32_to_floatx80(k, status);
fSig = (aSig & LIT64(0xFE00000000000000)) | LIT64(0x0100000000000000);
j = (fSig >> 56) & 0x7E; /* DISPLACEMENT FOR 1/F */
f = packFloatx80(0, 0x3FFF, fSig); /* F */
fp0 = packFloatx80(0, 0x3FFF, aSig); /* Y */
fp0 = floatx80_sub(fp0, f, status); /* Y-F */
/* LP1CONT1 */
fp0 = floatx80_mul(fp0, log_tbl[j], status); /* FP0 IS U = (Y-F)/F */
logof2 = packFloatx80(0, 0x3FFE, LIT64(0xB17217F7D1CF79AC));
klog2 = floatx80_mul(fp1, logof2, status); /* FP1 IS K*LOG2 */
fp2 = floatx80_mul(fp0, fp0, status); /* FP2 IS V=U*U */
fp3 = fp2;
fp1 = fp2;
fp1 = floatx80_mul(fp1, float64_to_floatx80(
make_float64(0x3FC2499AB5E4040B), status),
status); /* V*A6 */
fp2 = floatx80_mul(fp2, float64_to_floatx80(
make_float64(0xBFC555B5848CB7DB), status),
status); /* V*A5 */
fp1 = floatx80_add(fp1, float64_to_floatx80(
make_float64(0x3FC99999987D8730), status),
status); /* A4+V*A6 */
fp2 = floatx80_add(fp2, float64_to_floatx80(
make_float64(0xBFCFFFFFFF6F7E97), status),
status); /* A3+V*A5 */
fp1 = floatx80_mul(fp1, fp3, status); /* V*(A4+V*A6) */
fp2 = floatx80_mul(fp2, fp3, status); /* V*(A3+V*A5) */
fp1 = floatx80_add(fp1, float64_to_floatx80(
make_float64(0x3FD55555555555A4), status),
status); /* A2+V*(A4+V*A6) */
fp2 = floatx80_add(fp2, float64_to_floatx80(
make_float64(0xBFE0000000000008), status),
status); /* A1+V*(A3+V*A5) */
fp1 = floatx80_mul(fp1, fp3, status); /* V*(A2+V*(A4+V*A6)) */
fp2 = floatx80_mul(fp2, fp3, status); /* V*(A1+V*(A3+V*A5)) */
fp1 = floatx80_mul(fp1, fp0, status); /* U*V*(A2+V*(A4+V*A6)) */
fp0 = floatx80_add(fp0, fp2, status); /* U+V*(A1+V*(A3+V*A5)) */
fp1 = floatx80_add(fp1, log_tbl[j + 1],
status); /* LOG(F)+U*V*(A2+V*(A4+V*A6)) */
fp0 = floatx80_add(fp0, fp1, status); /* FP0 IS LOG(F) + LOG(1+U) */
status->float_rounding_mode = user_rnd_mode;
status->floatx80_rounding_precision = user_rnd_prec;
a = floatx80_add(fp0, klog2, status);
float_raise(float_flag_inexact, status);
return a;
} else { /* |X-1| >= 1/16 */
fp0 = a;
fp1 = a;
fp1 = floatx80_sub(fp1, float32_to_floatx80(make_float32(0x3F800000),
status), status); /* FP1 IS X-1 */
fp0 = floatx80_add(fp0, float32_to_floatx80(make_float32(0x3F800000),
status), status); /* FP0 IS X+1 */
fp1 = floatx80_add(fp1, fp1, status); /* FP1 IS 2(X-1) */
/* LP1CONT2 */
fp1 = floatx80_div(fp1, fp0, status); /* U */
saveu = fp1;
fp0 = floatx80_mul(fp1, fp1, status); /* FP0 IS V = U*U */
fp1 = floatx80_mul(fp0, fp0, status); /* FP1 IS W = V*V */
fp3 = float64_to_floatx80(make_float64(0x3F175496ADD7DAD6),
status); /* B5 */
fp2 = float64_to_floatx80(make_float64(0x3F3C71C2FE80C7E0),
status); /* B4 */
fp3 = floatx80_mul(fp3, fp1, status); /* W*B5 */
fp2 = floatx80_mul(fp2, fp1, status); /* W*B4 */
fp3 = floatx80_add(fp3, float64_to_floatx80(
make_float64(0x3F624924928BCCFF), status),
status); /* B3+W*B5 */
fp2 = floatx80_add(fp2, float64_to_floatx80(
make_float64(0x3F899999999995EC), status),
status); /* B2+W*B4 */
fp1 = floatx80_mul(fp1, fp3, status); /* W*(B3+W*B5) */
fp2 = floatx80_mul(fp2, fp0, status); /* V*(B2+W*B4) */
fp1 = floatx80_add(fp1, float64_to_floatx80(
make_float64(0x3FB5555555555555), status),
status); /* B1+W*(B3+W*B5) */
fp0 = floatx80_mul(fp0, saveu, status); /* FP0 IS U*V */
fp1 = floatx80_add(fp1, fp2, status); /* B1+W*(B3+W*B5) + V*(B2+W*B4) */
fp0 = floatx80_mul(fp0, fp1,
status); /* U*V*([B1+W*(B3+W*B5)] + [V*(B2+W*B4)]) */
status->float_rounding_mode = user_rnd_mode;
status->floatx80_rounding_precision = user_rnd_prec;
a = floatx80_add(fp0, saveu, status);
/*if (!floatx80_is_zero(a)) { */
float_raise(float_flag_inexact, status);
/*} */
return a;
}
}
/*----------------------------------------------------------------------------
| Log base 10
*----------------------------------------------------------------------------*/
floatx80 floatx80_log10(floatx80 a, float_status *status)
{
flag aSign;
int32_t aExp;
uint64_t aSig;
int8_t user_rnd_mode, user_rnd_prec;
floatx80 fp0, fp1;
aSig = extractFloatx80Frac(a);
aExp = extractFloatx80Exp(a);
aSign = extractFloatx80Sign(a);
if (aExp == 0x7FFF) {
if ((uint64_t) (aSig << 1)) {
propagateFloatx80NaNOneArg(a, status);
}
if (aSign == 0) {
return packFloatx80(0, floatx80_infinity.high,
floatx80_infinity.low);
}
}
if (aExp == 0 && aSig == 0) {
float_raise(float_flag_divbyzero, status);
return packFloatx80(1, floatx80_infinity.high,
floatx80_infinity.low);
}
if (aSign) {
float_raise(float_flag_invalid, status);
return floatx80_default_nan(status);
}
user_rnd_mode = status->float_rounding_mode;
user_rnd_prec = status->floatx80_rounding_precision;
status->float_rounding_mode = float_round_nearest_even;
status->floatx80_rounding_precision = 80;
fp0 = floatx80_logn(a, status);
fp1 = packFloatx80(0, 0x3FFD, LIT64(0xDE5BD8A937287195)); /* INV_L10 */
status->float_rounding_mode = user_rnd_mode;
status->floatx80_rounding_precision = user_rnd_prec;
a = floatx80_mul(fp0, fp1, status); /* LOGN(X)*INV_L10 */
float_raise(float_flag_inexact, status);
return a;
}
/*----------------------------------------------------------------------------
| Log base 2
*----------------------------------------------------------------------------*/
floatx80 floatx80_log2(floatx80 a, float_status *status)
{
flag aSign;
int32_t aExp;
uint64_t aSig;
int8_t user_rnd_mode, user_rnd_prec;
floatx80 fp0, fp1;
aSig = extractFloatx80Frac(a);
aExp = extractFloatx80Exp(a);
aSign = extractFloatx80Sign(a);
if (aExp == 0x7FFF) {
if ((uint64_t) (aSig << 1)) {
propagateFloatx80NaNOneArg(a, status);
}
if (aSign == 0) {
return packFloatx80(0, floatx80_infinity.high,
floatx80_infinity.low);
}
}
if (aExp == 0) {
if (aSig == 0) {
float_raise(float_flag_divbyzero, status);
return packFloatx80(1, floatx80_infinity.high,
floatx80_infinity.low);
}
normalizeFloatx80Subnormal(aSig, &aExp, &aSig);
}
if (aSign) {
float_raise(float_flag_invalid, status);
return floatx80_default_nan(status);
}
user_rnd_mode = status->float_rounding_mode;
user_rnd_prec = status->floatx80_rounding_precision;
status->float_rounding_mode = float_round_nearest_even;
status->floatx80_rounding_precision = 80;
if (aSig == one_sig) { /* X is 2^k */
status->float_rounding_mode = user_rnd_mode;
status->floatx80_rounding_precision = user_rnd_prec;
a = int32_to_floatx80(aExp - 0x3FFF, status);
} else {
fp0 = floatx80_logn(a, status);
fp1 = packFloatx80(0, 0x3FFF, LIT64(0xB8AA3B295C17F0BC)); /* INV_L2 */
status->float_rounding_mode = user_rnd_mode;
status->floatx80_rounding_precision = user_rnd_prec;
a = floatx80_mul(fp0, fp1, status); /* LOGN(X)*INV_L2 */
}
float_raise(float_flag_inexact, status);
return a;
}
/*----------------------------------------------------------------------------
| e to x
*----------------------------------------------------------------------------*/
floatx80 floatx80_etox(floatx80 a, float_status *status)
{
flag aSign;
int32_t aExp;
uint64_t aSig;
int8_t user_rnd_mode, user_rnd_prec;
int32_t compact, n, j, k, m, m1;
floatx80 fp0, fp1, fp2, fp3, l2, scale, adjscale;
flag adjflag;
aSig = extractFloatx80Frac(a);
aExp = extractFloatx80Exp(a);
aSign = extractFloatx80Sign(a);
if (aExp == 0x7FFF) {
if ((uint64_t) (aSig << 1)) {
return propagateFloatx80NaNOneArg(a, status);
}
if (aSign) {
return packFloatx80(0, 0, 0);
}
return packFloatx80(0, floatx80_infinity.high,
floatx80_infinity.low);
}
if (aExp == 0 && aSig == 0) {
return packFloatx80(0, one_exp, one_sig);
}
user_rnd_mode = status->float_rounding_mode;
user_rnd_prec = status->floatx80_rounding_precision;
status->float_rounding_mode = float_round_nearest_even;
status->floatx80_rounding_precision = 80;
adjflag = 0;
if (aExp >= 0x3FBE) { /* |X| >= 2^(-65) */
compact = floatx80_make_compact(aExp, aSig);
if (compact < 0x400CB167) { /* |X| < 16380 log2 */
fp0 = a;
fp1 = a;
fp0 = floatx80_mul(fp0, float32_to_floatx80(
make_float32(0x42B8AA3B), status),
status); /* 64/log2 * X */
adjflag = 0;
n = floatx80_to_int32(fp0, status); /* int(64/log2*X) */
fp0 = int32_to_floatx80(n, status);
j = n & 0x3F; /* J = N mod 64 */
m = n / 64; /* NOTE: this is really arithmetic right shift by 6 */
if (n < 0 && j) {
/* arithmetic right shift is division and
* round towards minus infinity
*/
m--;
}
m += 0x3FFF; /* biased exponent of 2^(M) */
expcont1:
fp2 = fp0; /* N */
fp0 = floatx80_mul(fp0, float32_to_floatx80(
make_float32(0xBC317218), status),
status); /* N * L1, L1 = lead(-log2/64) */
l2 = packFloatx80(0, 0x3FDC, LIT64(0x82E308654361C4C6));
fp2 = floatx80_mul(fp2, l2, status); /* N * L2, L1+L2 = -log2/64 */
fp0 = floatx80_add(fp0, fp1, status); /* X + N*L1 */
fp0 = floatx80_add(fp0, fp2, status); /* R */
fp1 = floatx80_mul(fp0, fp0, status); /* S = R*R */
fp2 = float32_to_floatx80(make_float32(0x3AB60B70),
status); /* A5 */
fp2 = floatx80_mul(fp2, fp1, status); /* fp2 is S*A5 */
fp3 = floatx80_mul(float32_to_floatx80(make_float32(0x3C088895),
status), fp1,
status); /* fp3 is S*A4 */
fp2 = floatx80_add(fp2, float64_to_floatx80(make_float64(
0x3FA5555555554431), status),
status); /* fp2 is A3+S*A5 */
fp3 = floatx80_add(fp3, float64_to_floatx80(make_float64(
0x3FC5555555554018), status),
status); /* fp3 is A2+S*A4 */
fp2 = floatx80_mul(fp2, fp1, status); /* fp2 is S*(A3+S*A5) */
fp3 = floatx80_mul(fp3, fp1, status); /* fp3 is S*(A2+S*A4) */
fp2 = floatx80_add(fp2, float32_to_floatx80(
make_float32(0x3F000000), status),
status); /* fp2 is A1+S*(A3+S*A5) */
fp3 = floatx80_mul(fp3, fp0, status); /* fp3 IS R*S*(A2+S*A4) */
fp2 = floatx80_mul(fp2, fp1,
status); /* fp2 IS S*(A1+S*(A3+S*A5)) */
fp0 = floatx80_add(fp0, fp3, status); /* fp0 IS R+R*S*(A2+S*A4) */
fp0 = floatx80_add(fp0, fp2, status); /* fp0 IS EXP(R) - 1 */
fp1 = exp_tbl[j];
fp0 = floatx80_mul(fp0, fp1, status); /* 2^(J/64)*(Exp(R)-1) */
fp0 = floatx80_add(fp0, float32_to_floatx80(exp_tbl2[j], status),
status); /* accurate 2^(J/64) */
fp0 = floatx80_add(fp0, fp1,
status); /* 2^(J/64) + 2^(J/64)*(Exp(R)-1) */
scale = packFloatx80(0, m, one_sig);
if (adjflag) {
adjscale = packFloatx80(0, m1, one_sig);
fp0 = floatx80_mul(fp0, adjscale, status);
}
status->float_rounding_mode = user_rnd_mode;
status->floatx80_rounding_precision = user_rnd_prec;
a = floatx80_mul(fp0, scale, status);
float_raise(float_flag_inexact, status);
return a;
} else { /* |X| >= 16380 log2 */
if (compact > 0x400CB27C) { /* |X| >= 16480 log2 */
status->float_rounding_mode = user_rnd_mode;
status->floatx80_rounding_precision = user_rnd_prec;
if (aSign) {
a = roundAndPackFloatx80(
status->floatx80_rounding_precision,
0, -0x1000, aSig, 0, status);
} else {
a = roundAndPackFloatx80(
status->floatx80_rounding_precision,
0, 0x8000, aSig, 0, status);
}
float_raise(float_flag_inexact, status);
return a;
} else {
fp0 = a;
fp1 = a;
fp0 = floatx80_mul(fp0, float32_to_floatx80(
make_float32(0x42B8AA3B), status),
status); /* 64/log2 * X */
adjflag = 1;
n = floatx80_to_int32(fp0, status); /* int(64/log2*X) */
fp0 = int32_to_floatx80(n, status);
j = n & 0x3F; /* J = N mod 64 */
/* NOTE: this is really arithmetic right shift by 6 */
k = n / 64;
if (n < 0 && j) {
/* arithmetic right shift is division and
* round towards minus infinity
*/
k--;
}
/* NOTE: this is really arithmetic right shift by 1 */
m1 = k / 2;
if (k < 0 && (k & 1)) {
/* arithmetic right shift is division and
* round towards minus infinity
*/
m1--;
}
m = k - m1;
m1 += 0x3FFF; /* biased exponent of 2^(M1) */
m += 0x3FFF; /* biased exponent of 2^(M) */
goto expcont1;
}
}
} else { /* |X| < 2^(-65) */
status->float_rounding_mode = user_rnd_mode;
status->floatx80_rounding_precision = user_rnd_prec;
a = floatx80_add(a, float32_to_floatx80(make_float32(0x3F800000),
status), status); /* 1 + X */
float_raise(float_flag_inexact, status);
return a;
}
}
/*----------------------------------------------------------------------------
| 2 to x
*----------------------------------------------------------------------------*/
floatx80 floatx80_twotox(floatx80 a, float_status *status)
{
flag aSign;
int32_t aExp;
uint64_t aSig;
int8_t user_rnd_mode, user_rnd_prec;
int32_t compact, n, j, l, m, m1;
floatx80 fp0, fp1, fp2, fp3, adjfact, fact1, fact2;
aSig = extractFloatx80Frac(a);
aExp = extractFloatx80Exp(a);
aSign = extractFloatx80Sign(a);
if (aExp == 0x7FFF) {
if ((uint64_t) (aSig << 1)) {
return propagateFloatx80NaNOneArg(a, status);
}
if (aSign) {
return packFloatx80(0, 0, 0);
}
return packFloatx80(0, floatx80_infinity.high,
floatx80_infinity.low);
}
if (aExp == 0 && aSig == 0) {
return packFloatx80(0, one_exp, one_sig);
}
user_rnd_mode = status->float_rounding_mode;
user_rnd_prec = status->floatx80_rounding_precision;
status->float_rounding_mode = float_round_nearest_even;
status->floatx80_rounding_precision = 80;
fp0 = a;
compact = floatx80_make_compact(aExp, aSig);
if (compact < 0x3FB98000 || compact > 0x400D80C0) {
/* |X| > 16480 or |X| < 2^(-70) */
if (compact > 0x3FFF8000) { /* |X| > 16480 */
status->float_rounding_mode = user_rnd_mode;
status->floatx80_rounding_precision = user_rnd_prec;
if (aSign) {
return roundAndPackFloatx80(status->floatx80_rounding_precision,
0, -0x1000, aSig, 0, status);
} else {
return roundAndPackFloatx80(status->floatx80_rounding_precision,
0, 0x8000, aSig, 0, status);
}
} else { /* |X| < 2^(-70) */
status->float_rounding_mode = user_rnd_mode;
status->floatx80_rounding_precision = user_rnd_prec;
a = floatx80_add(fp0, float32_to_floatx80(
make_float32(0x3F800000), status),
status); /* 1 + X */
float_raise(float_flag_inexact, status);
return a;
}
} else { /* 2^(-70) <= |X| <= 16480 */
fp1 = fp0; /* X */
fp1 = floatx80_mul(fp1, float32_to_floatx80(
make_float32(0x42800000), status),
status); /* X * 64 */
n = floatx80_to_int32(fp1, status);
fp1 = int32_to_floatx80(n, status);
j = n & 0x3F;
l = n / 64; /* NOTE: this is really arithmetic right shift by 6 */
if (n < 0 && j) {
/* arithmetic right shift is division and
* round towards minus infinity
*/
l--;
}
m = l / 2; /* NOTE: this is really arithmetic right shift by 1 */
if (l < 0 && (l & 1)) {
/* arithmetic right shift is division and
* round towards minus infinity
*/
m--;
}
m1 = l - m;
m1 += 0x3FFF; /* ADJFACT IS 2^(M') */
adjfact = packFloatx80(0, m1, one_sig);
fact1 = exp2_tbl[j];
fact1.high += m;
fact2.high = exp2_tbl2[j] >> 16;
fact2.high += m;
fact2.low = (uint64_t)(exp2_tbl2[j] & 0xFFFF);
fact2.low <<= 48;
fp1 = floatx80_mul(fp1, float32_to_floatx80(
make_float32(0x3C800000), status),
status); /* (1/64)*N */
fp0 = floatx80_sub(fp0, fp1, status); /* X - (1/64)*INT(64 X) */
fp2 = packFloatx80(0, 0x3FFE, LIT64(0xB17217F7D1CF79AC)); /* LOG2 */
fp0 = floatx80_mul(fp0, fp2, status); /* R */
/* EXPR */
fp1 = floatx80_mul(fp0, fp0, status); /* S = R*R */
fp2 = float64_to_floatx80(make_float64(0x3F56C16D6F7BD0B2),
status); /* A5 */
fp3 = float64_to_floatx80(make_float64(0x3F811112302C712C),
status); /* A4 */
fp2 = floatx80_mul(fp2, fp1, status); /* S*A5 */
fp3 = floatx80_mul(fp3, fp1, status); /* S*A4 */
fp2 = floatx80_add(fp2, float64_to_floatx80(
make_float64(0x3FA5555555554CC1), status),
status); /* A3+S*A5 */
fp3 = floatx80_add(fp3, float64_to_floatx80(
make_float64(0x3FC5555555554A54), status),
status); /* A2+S*A4 */
fp2 = floatx80_mul(fp2, fp1, status); /* S*(A3+S*A5) */
fp3 = floatx80_mul(fp3, fp1, status); /* S*(A2+S*A4) */
fp2 = floatx80_add(fp2, float64_to_floatx80(
make_float64(0x3FE0000000000000), status),
status); /* A1+S*(A3+S*A5) */
fp3 = floatx80_mul(fp3, fp0, status); /* R*S*(A2+S*A4) */
fp2 = floatx80_mul(fp2, fp1, status); /* S*(A1+S*(A3+S*A5)) */
fp0 = floatx80_add(fp0, fp3, status); /* R+R*S*(A2+S*A4) */
fp0 = floatx80_add(fp0, fp2, status); /* EXP(R) - 1 */
fp0 = floatx80_mul(fp0, fact1, status);
fp0 = floatx80_add(fp0, fact2, status);
fp0 = floatx80_add(fp0, fact1, status);
status->float_rounding_mode = user_rnd_mode;
status->floatx80_rounding_precision = user_rnd_prec;
a = floatx80_mul(fp0, adjfact, status);
float_raise(float_flag_inexact, status);
return a;
}
}
/*----------------------------------------------------------------------------
| 10 to x
*----------------------------------------------------------------------------*/
floatx80 floatx80_tentox(floatx80 a, float_status *status)
{
flag aSign;
int32_t aExp;
uint64_t aSig;
int8_t user_rnd_mode, user_rnd_prec;
int32_t compact, n, j, l, m, m1;
floatx80 fp0, fp1, fp2, fp3, adjfact, fact1, fact2;
aSig = extractFloatx80Frac(a);
aExp = extractFloatx80Exp(a);
aSign = extractFloatx80Sign(a);
if (aExp == 0x7FFF) {
if ((uint64_t) (aSig << 1)) {
return propagateFloatx80NaNOneArg(a, status);
}
if (aSign) {
return packFloatx80(0, 0, 0);
}
return packFloatx80(0, floatx80_infinity.high,
floatx80_infinity.low);
}
if (aExp == 0 && aSig == 0) {
return packFloatx80(0, one_exp, one_sig);
}
user_rnd_mode = status->float_rounding_mode;
user_rnd_prec = status->floatx80_rounding_precision;
status->float_rounding_mode = float_round_nearest_even;
status->floatx80_rounding_precision = 80;
fp0 = a;
compact = floatx80_make_compact(aExp, aSig);
if (compact < 0x3FB98000 || compact > 0x400B9B07) {
/* |X| > 16480 LOG2/LOG10 or |X| < 2^(-70) */
if (compact > 0x3FFF8000) { /* |X| > 16480 */
status->float_rounding_mode = user_rnd_mode;
status->floatx80_rounding_precision = user_rnd_prec;
if (aSign) {
return roundAndPackFloatx80(status->floatx80_rounding_precision,
0, -0x1000, aSig, 0, status);
} else {
return roundAndPackFloatx80(status->floatx80_rounding_precision,
0, 0x8000, aSig, 0, status);
}
} else { /* |X| < 2^(-70) */
status->float_rounding_mode = user_rnd_mode;
status->floatx80_rounding_precision = user_rnd_prec;
a = floatx80_add(fp0, float32_to_floatx80(
make_float32(0x3F800000), status),
status); /* 1 + X */
float_raise(float_flag_inexact, status);
return a;
}
} else { /* 2^(-70) <= |X| <= 16480 LOG 2 / LOG 10 */
fp1 = fp0; /* X */
fp1 = floatx80_mul(fp1, float64_to_floatx80(
make_float64(0x406A934F0979A371),
status), status); /* X*64*LOG10/LOG2 */
n = floatx80_to_int32(fp1, status); /* N=INT(X*64*LOG10/LOG2) */
fp1 = int32_to_floatx80(n, status);
j = n & 0x3F;
l = n / 64; /* NOTE: this is really arithmetic right shift by 6 */
if (n < 0 && j) {
/* arithmetic right shift is division and
* round towards minus infinity
*/
l--;
}
m = l / 2; /* NOTE: this is really arithmetic right shift by 1 */
if (l < 0 && (l & 1)) {
/* arithmetic right shift is division and
* round towards minus infinity
*/
m--;
}
m1 = l - m;
m1 += 0x3FFF; /* ADJFACT IS 2^(M') */
adjfact = packFloatx80(0, m1, one_sig);
fact1 = exp2_tbl[j];
fact1.high += m;
fact2.high = exp2_tbl2[j] >> 16;
fact2.high += m;
fact2.low = (uint64_t)(exp2_tbl2[j] & 0xFFFF);
fact2.low <<= 48;
fp2 = fp1; /* N */
fp1 = floatx80_mul(fp1, float64_to_floatx80(
make_float64(0x3F734413509F8000), status),
status); /* N*(LOG2/64LOG10)_LEAD */
fp3 = packFloatx80(1, 0x3FCD, LIT64(0xC0219DC1DA994FD2));
fp2 = floatx80_mul(fp2, fp3, status); /* N*(LOG2/64LOG10)_TRAIL */
fp0 = floatx80_sub(fp0, fp1, status); /* X - N L_LEAD */
fp0 = floatx80_sub(fp0, fp2, status); /* X - N L_TRAIL */
fp2 = packFloatx80(0, 0x4000, LIT64(0x935D8DDDAAA8AC17)); /* LOG10 */
fp0 = floatx80_mul(fp0, fp2, status); /* R */
/* EXPR */
fp1 = floatx80_mul(fp0, fp0, status); /* S = R*R */
fp2 = float64_to_floatx80(make_float64(0x3F56C16D6F7BD0B2),
status); /* A5 */
fp3 = float64_to_floatx80(make_float64(0x3F811112302C712C),
status); /* A4 */
fp2 = floatx80_mul(fp2, fp1, status); /* S*A5 */
fp3 = floatx80_mul(fp3, fp1, status); /* S*A4 */
fp2 = floatx80_add(fp2, float64_to_floatx80(
make_float64(0x3FA5555555554CC1), status),
status); /* A3+S*A5 */
fp3 = floatx80_add(fp3, float64_to_floatx80(
make_float64(0x3FC5555555554A54), status),
status); /* A2+S*A4 */
fp2 = floatx80_mul(fp2, fp1, status); /* S*(A3+S*A5) */
fp3 = floatx80_mul(fp3, fp1, status); /* S*(A2+S*A4) */
fp2 = floatx80_add(fp2, float64_to_floatx80(
make_float64(0x3FE0000000000000), status),
status); /* A1+S*(A3+S*A5) */
fp3 = floatx80_mul(fp3, fp0, status); /* R*S*(A2+S*A4) */
fp2 = floatx80_mul(fp2, fp1, status); /* S*(A1+S*(A3+S*A5)) */
fp0 = floatx80_add(fp0, fp3, status); /* R+R*S*(A2+S*A4) */
fp0 = floatx80_add(fp0, fp2, status); /* EXP(R) - 1 */
fp0 = floatx80_mul(fp0, fact1, status);
fp0 = floatx80_add(fp0, fact2, status);
fp0 = floatx80_add(fp0, fact1, status);
status->float_rounding_mode = user_rnd_mode;
status->floatx80_rounding_precision = user_rnd_prec;
a = floatx80_mul(fp0, adjfact, status);
float_raise(float_flag_inexact, status);
return a;
}
}
