2018-02-24 21:18:00 +01:00
|
|
|
/*
|
|
|
|
|
* 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"
|
2018-03-05 21:39:04 +01:00
|
|
|
#include "softfloat_fpsp_tables.h"
|
2018-02-24 21:18:00 +01:00
|
|
|
|
2018-03-12 21:27:24 +01:00
|
|
|
#define pi_exp 0x4000
|
2018-03-12 21:27:22 +01:00
|
|
|
#define piby2_exp 0x3FFF
|
|
|
|
|
#define pi_sig LIT64(0xc90fdaa22168c235)
|
|
|
|
|
|
2018-02-24 21:18:02 +01:00
|
|
|
static floatx80 propagateFloatx80NaNOneArg(floatx80 a, float_status *status)
|
|
|
|
|
{
|
|
|
|
|
if (floatx80_is_signaling_nan(a, status)) {
|
|
|
|
|
float_raise(float_flag_invalid, status);
|
2018-05-10 22:49:00 +02:00
|
|
|
a = floatx80_silence_nan(a, status);
|
2018-02-24 21:18:02 +01:00
|
|
|
}
|
|
|
|
|
|
|
|
|
|
if (status->default_nan_mode) {
|
|
|
|
|
return floatx80_default_nan(status);
|
|
|
|
|
}
|
|
|
|
|
|
2018-05-10 22:49:00 +02:00
|
|
|
return a;
|
2018-02-24 21:18:02 +01:00
|
|
|
}
|
|
|
|
|
|
2018-02-24 21:18:00 +01:00
|
|
|
/*----------------------------------------------------------------------------
|
|
|
|
|
| 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);
|
2018-05-08 22:39:37 +02:00
|
|
|
expDiff -= 62;
|
2018-02-24 21:18:00 +01:00
|
|
|
}
|
|
|
|
|
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);
|
|
|
|
|
}
|
2018-02-24 21:18:02 +01:00
|
|
|
|
|
|
|
|
/*----------------------------------------------------------------------------
|
|
|
|
|
| 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);
|
|
|
|
|
}
|
2018-03-05 21:39:03 +01:00
|
|
|
|
|
|
|
|
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);
|
|
|
|
|
}
|
2018-03-05 21:39:04 +01:00
|
|
|
|
|
|
|
|
/*----------------------------------------------------------------------------
|
|
|
|
|
| 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);
|
2018-04-30 19:01:55 +02:00
|
|
|
return packFloatx80(aSign, floatx80_infinity.high,
|
|
|
|
|
floatx80_infinity.low);
|
2018-03-05 21:39:04 +01:00
|
|
|
}
|
|
|
|
|
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;
|
|
|
|
|
}
|
|
|
|
|
}
|
2018-03-05 21:39:05 +01:00
|
|
|
|
|
|
|
|
/*----------------------------------------------------------------------------
|
|
|
|
|
| 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;
|
|
|
|
|
}
|
|
|
|
|
}
|
2018-03-05 21:39:06 +01:00
|
|
|
|
|
|
|
|
/*----------------------------------------------------------------------------
|
|
|
|
|
| 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;
|
|
|
|
|
}
|
2018-03-05 21:39:07 +01:00
|
|
|
|
|
|
|
|
/*----------------------------------------------------------------------------
|
|
|
|
|
| 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;
|
|
|
|
|
}
|
2018-03-05 21:39:08 +01:00
|
|
|
|
|
|
|
|
/*----------------------------------------------------------------------------
|
|
|
|
|
| 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;
|
|
|
|
|
}
|
|
|
|
|
}
|
2018-03-05 21:39:09 +01:00
|
|
|
|
|
|
|
|
/*----------------------------------------------------------------------------
|
|
|
|
|
| 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 */
|
|
|
|
|
|
2018-03-05 21:39:10 +01:00
|
|
|
/* 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 */
|
|
|
|
|
|
2018-03-05 21:39:09 +01:00
|
|
|
/* 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;
|
|
|
|
|
}
|
|
|
|
|
}
|
2018-03-12 21:27:18 +01:00
|
|
|
|
|
|
|
|
/*----------------------------------------------------------------------------
|
|
|
|
|
| Tangent
|
|
|
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
|
|
|
|
|
|
floatx80 floatx80_tan(floatx80 a, float_status *status)
|
|
|
|
|
{
|
|
|
|
|
flag aSign, xSign;
|
|
|
|
|
int32_t aExp, xExp;
|
|
|
|
|
uint64_t aSig, xSig;
|
|
|
|
|
|
|
|
|
|
int8_t user_rnd_mode, user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
int32_t compact, l, n, j;
|
|
|
|
|
floatx80 fp0, fp1, fp2, fp3, fp4, fp5, invtwopi, twopi1, twopi2;
|
|
|
|
|
float32 twoto63;
|
|
|
|
|
flag endflag;
|
|
|
|
|
|
|
|
|
|
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 && aSig == 0) {
|
|
|
|
|
return packFloatx80(aSign, 0, 0);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
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;
|
|
|
|
|
|
|
|
|
|
if (compact < 0x3FD78000 || compact > 0x4004BC7E) {
|
|
|
|
|
/* 2^(-40) > |X| > 15 PI */
|
|
|
|
|
if (compact > 0x3FFF8000) { /* |X| >= 15 PI */
|
|
|
|
|
/* REDUCEX */
|
|
|
|
|
fp1 = packFloatx80(0, 0, 0);
|
|
|
|
|
if (compact == 0x7FFEFFFF) {
|
|
|
|
|
twopi1 = packFloatx80(aSign ^ 1, 0x7FFE,
|
|
|
|
|
LIT64(0xC90FDAA200000000));
|
|
|
|
|
twopi2 = packFloatx80(aSign ^ 1, 0x7FDC,
|
|
|
|
|
LIT64(0x85A308D300000000));
|
|
|
|
|
fp0 = floatx80_add(fp0, twopi1, status);
|
|
|
|
|
fp1 = fp0;
|
|
|
|
|
fp0 = floatx80_add(fp0, twopi2, status);
|
|
|
|
|
fp1 = floatx80_sub(fp1, fp0, status);
|
|
|
|
|
fp1 = floatx80_add(fp1, twopi2, status);
|
|
|
|
|
}
|
|
|
|
|
loop:
|
|
|
|
|
xSign = extractFloatx80Sign(fp0);
|
|
|
|
|
xExp = extractFloatx80Exp(fp0);
|
|
|
|
|
xExp -= 0x3FFF;
|
|
|
|
|
if (xExp <= 28) {
|
|
|
|
|
l = 0;
|
|
|
|
|
endflag = 1;
|
|
|
|
|
} else {
|
|
|
|
|
l = xExp - 27;
|
|
|
|
|
endflag = 0;
|
|
|
|
|
}
|
|
|
|
|
invtwopi = packFloatx80(0, 0x3FFE - l,
|
|
|
|
|
LIT64(0xA2F9836E4E44152A)); /* INVTWOPI */
|
|
|
|
|
twopi1 = packFloatx80(0, 0x3FFF + l, LIT64(0xC90FDAA200000000));
|
|
|
|
|
twopi2 = packFloatx80(0, 0x3FDD + l, LIT64(0x85A308D300000000));
|
|
|
|
|
|
|
|
|
|
/* SIGN(INARG)*2^63 IN SGL */
|
|
|
|
|
twoto63 = packFloat32(xSign, 0xBE, 0);
|
|
|
|
|
|
|
|
|
|
fp2 = floatx80_mul(fp0, invtwopi, status);
|
|
|
|
|
fp2 = floatx80_add(fp2, float32_to_floatx80(twoto63, status),
|
|
|
|
|
status); /* THE FRACT PART OF FP2 IS ROUNDED */
|
|
|
|
|
fp2 = floatx80_sub(fp2, float32_to_floatx80(twoto63, status),
|
|
|
|
|
status); /* FP2 is N */
|
|
|
|
|
fp4 = floatx80_mul(twopi1, fp2, status); /* W = N*P1 */
|
|
|
|
|
fp5 = floatx80_mul(twopi2, fp2, status); /* w = N*P2 */
|
|
|
|
|
fp3 = floatx80_add(fp4, fp5, status); /* FP3 is P */
|
|
|
|
|
fp4 = floatx80_sub(fp4, fp3, status); /* W-P */
|
|
|
|
|
fp0 = floatx80_sub(fp0, fp3, status); /* FP0 is A := R - P */
|
|
|
|
|
fp4 = floatx80_add(fp4, fp5, status); /* FP4 is p = (W-P)+w */
|
|
|
|
|
fp3 = fp0; /* FP3 is A */
|
|
|
|
|
fp1 = floatx80_sub(fp1, fp4, status); /* FP1 is a := r - p */
|
|
|
|
|
fp0 = floatx80_add(fp0, fp1, status); /* FP0 is R := A+a */
|
|
|
|
|
|
|
|
|
|
if (endflag > 0) {
|
|
|
|
|
n = floatx80_to_int32(fp2, status);
|
|
|
|
|
goto tancont;
|
|
|
|
|
}
|
|
|
|
|
fp3 = floatx80_sub(fp3, fp0, status); /* A-R */
|
|
|
|
|
fp1 = floatx80_add(fp1, fp3, status); /* FP1 is r := (A-R)+a */
|
|
|
|
|
goto loop;
|
|
|
|
|
} else {
|
|
|
|
|
status->float_rounding_mode = user_rnd_mode;
|
|
|
|
|
status->floatx80_rounding_precision = user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
a = floatx80_move(a, status);
|
|
|
|
|
|
|
|
|
|
float_raise(float_flag_inexact, status);
|
|
|
|
|
|
|
|
|
|
return a;
|
|
|
|
|
}
|
|
|
|
|
} else {
|
|
|
|
|
fp1 = floatx80_mul(fp0, float64_to_floatx80(
|
|
|
|
|
make_float64(0x3FE45F306DC9C883), status),
|
|
|
|
|
status); /* X*2/PI */
|
|
|
|
|
|
|
|
|
|
n = floatx80_to_int32(fp1, status);
|
|
|
|
|
j = 32 + n;
|
|
|
|
|
|
|
|
|
|
fp0 = floatx80_sub(fp0, pi_tbl[j], status); /* X-Y1 */
|
|
|
|
|
fp0 = floatx80_sub(fp0, float32_to_floatx80(pi_tbl2[j], status),
|
|
|
|
|
status); /* FP0 IS R = (X-Y1)-Y2 */
|
|
|
|
|
|
|
|
|
|
tancont:
|
|
|
|
|
if (n & 1) {
|
|
|
|
|
/* NODD */
|
|
|
|
|
fp1 = fp0; /* R */
|
|
|
|
|
fp0 = floatx80_mul(fp0, fp0, status); /* S = R*R */
|
|
|
|
|
fp3 = float64_to_floatx80(make_float64(0x3EA0B759F50F8688),
|
|
|
|
|
status); /* Q4 */
|
|
|
|
|
fp2 = float64_to_floatx80(make_float64(0xBEF2BAA5A8924F04),
|
|
|
|
|
status); /* P3 */
|
|
|
|
|
fp3 = floatx80_mul(fp3, fp0, status); /* SQ4 */
|
|
|
|
|
fp2 = floatx80_mul(fp2, fp0, status); /* SP3 */
|
|
|
|
|
fp3 = floatx80_add(fp3, float64_to_floatx80(
|
|
|
|
|
make_float64(0xBF346F59B39BA65F), status),
|
|
|
|
|
status); /* Q3+SQ4 */
|
|
|
|
|
fp4 = packFloatx80(0, 0x3FF6, LIT64(0xE073D3FC199C4A00));
|
|
|
|
|
fp2 = floatx80_add(fp2, fp4, status); /* P2+SP3 */
|
|
|
|
|
fp3 = floatx80_mul(fp3, fp0, status); /* S(Q3+SQ4) */
|
|
|
|
|
fp2 = floatx80_mul(fp2, fp0, status); /* S(P2+SP3) */
|
|
|
|
|
fp4 = packFloatx80(0, 0x3FF9, LIT64(0xD23CD68415D95FA1));
|
|
|
|
|
fp3 = floatx80_add(fp3, fp4, status); /* Q2+S(Q3+SQ4) */
|
|
|
|
|
fp4 = packFloatx80(1, 0x3FFC, LIT64(0x8895A6C5FB423BCA));
|
|
|
|
|
fp2 = floatx80_add(fp2, fp4, status); /* P1+S(P2+SP3) */
|
|
|
|
|
fp3 = floatx80_mul(fp3, fp0, status); /* S(Q2+S(Q3+SQ4)) */
|
|
|
|
|
fp2 = floatx80_mul(fp2, fp0, status); /* S(P1+S(P2+SP3)) */
|
|
|
|
|
fp4 = packFloatx80(1, 0x3FFD, LIT64(0xEEF57E0DA84BC8CE));
|
|
|
|
|
fp3 = floatx80_add(fp3, fp4, status); /* Q1+S(Q2+S(Q3+SQ4)) */
|
|
|
|
|
fp2 = floatx80_mul(fp2, fp1, status); /* RS(P1+S(P2+SP3)) */
|
|
|
|
|
fp0 = floatx80_mul(fp0, fp3, status); /* S(Q1+S(Q2+S(Q3+SQ4))) */
|
|
|
|
|
fp1 = floatx80_add(fp1, fp2, status); /* R+RS(P1+S(P2+SP3)) */
|
|
|
|
|
fp0 = floatx80_add(fp0, float32_to_floatx80(
|
|
|
|
|
make_float32(0x3F800000), status),
|
|
|
|
|
status); /* 1+S(Q1+S(Q2+S(Q3+SQ4))) */
|
|
|
|
|
|
|
|
|
|
xSign = extractFloatx80Sign(fp1);
|
|
|
|
|
xExp = extractFloatx80Exp(fp1);
|
|
|
|
|
xSig = extractFloatx80Frac(fp1);
|
|
|
|
|
xSign ^= 1;
|
|
|
|
|
fp1 = packFloatx80(xSign, xExp, xSig);
|
|
|
|
|
|
|
|
|
|
status->float_rounding_mode = user_rnd_mode;
|
|
|
|
|
status->floatx80_rounding_precision = user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
a = floatx80_div(fp0, fp1, status);
|
|
|
|
|
|
|
|
|
|
float_raise(float_flag_inexact, status);
|
|
|
|
|
|
|
|
|
|
return a;
|
|
|
|
|
} else {
|
|
|
|
|
fp1 = floatx80_mul(fp0, fp0, status); /* S = R*R */
|
|
|
|
|
fp3 = float64_to_floatx80(make_float64(0x3EA0B759F50F8688),
|
|
|
|
|
status); /* Q4 */
|
|
|
|
|
fp2 = float64_to_floatx80(make_float64(0xBEF2BAA5A8924F04),
|
|
|
|
|
status); /* P3 */
|
|
|
|
|
fp3 = floatx80_mul(fp3, fp1, status); /* SQ4 */
|
|
|
|
|
fp2 = floatx80_mul(fp2, fp1, status); /* SP3 */
|
|
|
|
|
fp3 = floatx80_add(fp3, float64_to_floatx80(
|
|
|
|
|
make_float64(0xBF346F59B39BA65F), status),
|
|
|
|
|
status); /* Q3+SQ4 */
|
|
|
|
|
fp4 = packFloatx80(0, 0x3FF6, LIT64(0xE073D3FC199C4A00));
|
|
|
|
|
fp2 = floatx80_add(fp2, fp4, status); /* P2+SP3 */
|
|
|
|
|
fp3 = floatx80_mul(fp3, fp1, status); /* S(Q3+SQ4) */
|
|
|
|
|
fp2 = floatx80_mul(fp2, fp1, status); /* S(P2+SP3) */
|
|
|
|
|
fp4 = packFloatx80(0, 0x3FF9, LIT64(0xD23CD68415D95FA1));
|
|
|
|
|
fp3 = floatx80_add(fp3, fp4, status); /* Q2+S(Q3+SQ4) */
|
|
|
|
|
fp4 = packFloatx80(1, 0x3FFC, LIT64(0x8895A6C5FB423BCA));
|
|
|
|
|
fp2 = floatx80_add(fp2, fp4, status); /* P1+S(P2+SP3) */
|
|
|
|
|
fp3 = floatx80_mul(fp3, fp1, status); /* S(Q2+S(Q3+SQ4)) */
|
|
|
|
|
fp2 = floatx80_mul(fp2, fp1, status); /* S(P1+S(P2+SP3)) */
|
|
|
|
|
fp4 = packFloatx80(1, 0x3FFD, LIT64(0xEEF57E0DA84BC8CE));
|
|
|
|
|
fp3 = floatx80_add(fp3, fp4, status); /* Q1+S(Q2+S(Q3+SQ4)) */
|
|
|
|
|
fp2 = floatx80_mul(fp2, fp0, status); /* RS(P1+S(P2+SP3)) */
|
|
|
|
|
fp1 = floatx80_mul(fp1, fp3, status); /* S(Q1+S(Q2+S(Q3+SQ4))) */
|
|
|
|
|
fp0 = floatx80_add(fp0, fp2, status); /* R+RS(P1+S(P2+SP3)) */
|
|
|
|
|
fp1 = floatx80_add(fp1, float32_to_floatx80(
|
|
|
|
|
make_float32(0x3F800000), status),
|
|
|
|
|
status); /* 1+S(Q1+S(Q2+S(Q3+SQ4))) */
|
|
|
|
|
|
|
|
|
|
status->float_rounding_mode = user_rnd_mode;
|
|
|
|
|
status->floatx80_rounding_precision = user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
a = floatx80_div(fp0, fp1, status);
|
|
|
|
|
|
|
|
|
|
float_raise(float_flag_inexact, status);
|
|
|
|
|
|
|
|
|
|
return a;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
}
|
2018-03-12 21:27:19 +01:00
|
|
|
|
|
|
|
|
/*----------------------------------------------------------------------------
|
|
|
|
|
| Sine
|
|
|
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
|
|
|
|
|
|
floatx80 floatx80_sin(floatx80 a, float_status *status)
|
|
|
|
|
{
|
|
|
|
|
flag aSign, xSign;
|
|
|
|
|
int32_t aExp, xExp;
|
|
|
|
|
uint64_t aSig, xSig;
|
|
|
|
|
|
|
|
|
|
int8_t user_rnd_mode, user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
int32_t compact, l, n, j;
|
|
|
|
|
floatx80 fp0, fp1, fp2, fp3, fp4, fp5, x, invtwopi, twopi1, twopi2;
|
|
|
|
|
float32 posneg1, twoto63;
|
2018-04-30 19:01:56 +02:00
|
|
|
flag endflag;
|
2018-03-12 21:27:19 +01:00
|
|
|
|
|
|
|
|
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 && aSig == 0) {
|
|
|
|
|
return packFloatx80(aSign, 0, 0);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
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;
|
|
|
|
|
|
|
|
|
|
if (compact < 0x3FD78000 || compact > 0x4004BC7E) {
|
|
|
|
|
/* 2^(-40) > |X| > 15 PI */
|
|
|
|
|
if (compact > 0x3FFF8000) { /* |X| >= 15 PI */
|
|
|
|
|
/* REDUCEX */
|
|
|
|
|
fp1 = packFloatx80(0, 0, 0);
|
|
|
|
|
if (compact == 0x7FFEFFFF) {
|
|
|
|
|
twopi1 = packFloatx80(aSign ^ 1, 0x7FFE,
|
|
|
|
|
LIT64(0xC90FDAA200000000));
|
|
|
|
|
twopi2 = packFloatx80(aSign ^ 1, 0x7FDC,
|
|
|
|
|
LIT64(0x85A308D300000000));
|
|
|
|
|
fp0 = floatx80_add(fp0, twopi1, status);
|
|
|
|
|
fp1 = fp0;
|
|
|
|
|
fp0 = floatx80_add(fp0, twopi2, status);
|
|
|
|
|
fp1 = floatx80_sub(fp1, fp0, status);
|
|
|
|
|
fp1 = floatx80_add(fp1, twopi2, status);
|
|
|
|
|
}
|
|
|
|
|
loop:
|
|
|
|
|
xSign = extractFloatx80Sign(fp0);
|
|
|
|
|
xExp = extractFloatx80Exp(fp0);
|
|
|
|
|
xExp -= 0x3FFF;
|
|
|
|
|
if (xExp <= 28) {
|
|
|
|
|
l = 0;
|
|
|
|
|
endflag = 1;
|
|
|
|
|
} else {
|
|
|
|
|
l = xExp - 27;
|
|
|
|
|
endflag = 0;
|
|
|
|
|
}
|
|
|
|
|
invtwopi = packFloatx80(0, 0x3FFE - l,
|
|
|
|
|
LIT64(0xA2F9836E4E44152A)); /* INVTWOPI */
|
|
|
|
|
twopi1 = packFloatx80(0, 0x3FFF + l, LIT64(0xC90FDAA200000000));
|
|
|
|
|
twopi2 = packFloatx80(0, 0x3FDD + l, LIT64(0x85A308D300000000));
|
|
|
|
|
|
|
|
|
|
/* SIGN(INARG)*2^63 IN SGL */
|
|
|
|
|
twoto63 = packFloat32(xSign, 0xBE, 0);
|
|
|
|
|
|
|
|
|
|
fp2 = floatx80_mul(fp0, invtwopi, status);
|
|
|
|
|
fp2 = floatx80_add(fp2, float32_to_floatx80(twoto63, status),
|
|
|
|
|
status); /* THE FRACT PART OF FP2 IS ROUNDED */
|
|
|
|
|
fp2 = floatx80_sub(fp2, float32_to_floatx80(twoto63, status),
|
|
|
|
|
status); /* FP2 is N */
|
|
|
|
|
fp4 = floatx80_mul(twopi1, fp2, status); /* W = N*P1 */
|
|
|
|
|
fp5 = floatx80_mul(twopi2, fp2, status); /* w = N*P2 */
|
|
|
|
|
fp3 = floatx80_add(fp4, fp5, status); /* FP3 is P */
|
|
|
|
|
fp4 = floatx80_sub(fp4, fp3, status); /* W-P */
|
|
|
|
|
fp0 = floatx80_sub(fp0, fp3, status); /* FP0 is A := R - P */
|
|
|
|
|
fp4 = floatx80_add(fp4, fp5, status); /* FP4 is p = (W-P)+w */
|
|
|
|
|
fp3 = fp0; /* FP3 is A */
|
|
|
|
|
fp1 = floatx80_sub(fp1, fp4, status); /* FP1 is a := r - p */
|
|
|
|
|
fp0 = floatx80_add(fp0, fp1, status); /* FP0 is R := A+a */
|
|
|
|
|
|
|
|
|
|
if (endflag > 0) {
|
|
|
|
|
n = floatx80_to_int32(fp2, status);
|
|
|
|
|
goto sincont;
|
|
|
|
|
}
|
|
|
|
|
fp3 = floatx80_sub(fp3, fp0, status); /* A-R */
|
|
|
|
|
fp1 = floatx80_add(fp1, fp3, status); /* FP1 is r := (A-R)+a */
|
|
|
|
|
goto loop;
|
|
|
|
|
} else {
|
|
|
|
|
/* SINSM */
|
|
|
|
|
fp0 = float32_to_floatx80(make_float32(0x3F800000),
|
|
|
|
|
status); /* 1 */
|
|
|
|
|
|
|
|
|
|
status->float_rounding_mode = user_rnd_mode;
|
|
|
|
|
status->floatx80_rounding_precision = user_rnd_prec;
|
|
|
|
|
|
2018-04-30 19:01:56 +02:00
|
|
|
/* SINTINY */
|
|
|
|
|
a = floatx80_move(a, status);
|
2018-03-12 21:27:19 +01:00
|
|
|
float_raise(float_flag_inexact, status);
|
|
|
|
|
|
|
|
|
|
return a;
|
|
|
|
|
}
|
|
|
|
|
} else {
|
|
|
|
|
fp1 = floatx80_mul(fp0, float64_to_floatx80(
|
|
|
|
|
make_float64(0x3FE45F306DC9C883), status),
|
|
|
|
|
status); /* X*2/PI */
|
|
|
|
|
|
|
|
|
|
n = floatx80_to_int32(fp1, status);
|
|
|
|
|
j = 32 + n;
|
|
|
|
|
|
|
|
|
|
fp0 = floatx80_sub(fp0, pi_tbl[j], status); /* X-Y1 */
|
|
|
|
|
fp0 = floatx80_sub(fp0, float32_to_floatx80(pi_tbl2[j], status),
|
|
|
|
|
status); /* FP0 IS R = (X-Y1)-Y2 */
|
|
|
|
|
|
|
|
|
|
sincont:
|
2018-04-30 19:01:56 +02:00
|
|
|
if (n & 1) {
|
2018-03-12 21:27:19 +01:00
|
|
|
/* COSPOLY */
|
|
|
|
|
fp0 = floatx80_mul(fp0, fp0, status); /* FP0 IS S */
|
|
|
|
|
fp1 = floatx80_mul(fp0, fp0, status); /* FP1 IS T */
|
|
|
|
|
fp2 = float64_to_floatx80(make_float64(0x3D2AC4D0D6011EE3),
|
|
|
|
|
status); /* B8 */
|
|
|
|
|
fp3 = float64_to_floatx80(make_float64(0xBDA9396F9F45AC19),
|
|
|
|
|
status); /* B7 */
|
|
|
|
|
|
|
|
|
|
xSign = extractFloatx80Sign(fp0); /* X IS S */
|
|
|
|
|
xExp = extractFloatx80Exp(fp0);
|
|
|
|
|
xSig = extractFloatx80Frac(fp0);
|
|
|
|
|
|
2018-04-30 19:01:56 +02:00
|
|
|
if ((n >> 1) & 1) {
|
2018-03-12 21:27:19 +01:00
|
|
|
xSign ^= 1;
|
|
|
|
|
posneg1 = make_float32(0xBF800000); /* -1 */
|
|
|
|
|
} else {
|
|
|
|
|
xSign ^= 0;
|
|
|
|
|
posneg1 = make_float32(0x3F800000); /* 1 */
|
|
|
|
|
} /* X IS NOW R'= SGN*R */
|
|
|
|
|
|
|
|
|
|
fp2 = floatx80_mul(fp2, fp1, status); /* TB8 */
|
|
|
|
|
fp3 = floatx80_mul(fp3, fp1, status); /* TB7 */
|
|
|
|
|
fp2 = floatx80_add(fp2, float64_to_floatx80(
|
|
|
|
|
make_float64(0x3E21EED90612C972), status),
|
|
|
|
|
status); /* B6+TB8 */
|
|
|
|
|
fp3 = floatx80_add(fp3, float64_to_floatx80(
|
|
|
|
|
make_float64(0xBE927E4FB79D9FCF), status),
|
|
|
|
|
status); /* B5+TB7 */
|
|
|
|
|
fp2 = floatx80_mul(fp2, fp1, status); /* T(B6+TB8) */
|
|
|
|
|
fp3 = floatx80_mul(fp3, fp1, status); /* T(B5+TB7) */
|
|
|
|
|
fp2 = floatx80_add(fp2, float64_to_floatx80(
|
|
|
|
|
make_float64(0x3EFA01A01A01D423), status),
|
|
|
|
|
status); /* B4+T(B6+TB8) */
|
|
|
|
|
fp4 = packFloatx80(1, 0x3FF5, LIT64(0xB60B60B60B61D438));
|
|
|
|
|
fp3 = floatx80_add(fp3, fp4, status); /* B3+T(B5+TB7) */
|
|
|
|
|
fp2 = floatx80_mul(fp2, fp1, status); /* T(B4+T(B6+TB8)) */
|
|
|
|
|
fp1 = floatx80_mul(fp1, fp3, status); /* T(B3+T(B5+TB7)) */
|
|
|
|
|
fp4 = packFloatx80(0, 0x3FFA, LIT64(0xAAAAAAAAAAAAAB5E));
|
|
|
|
|
fp2 = floatx80_add(fp2, fp4, status); /* B2+T(B4+T(B6+TB8)) */
|
|
|
|
|
fp1 = floatx80_add(fp1, float32_to_floatx80(
|
|
|
|
|
make_float32(0xBF000000), status),
|
|
|
|
|
status); /* B1+T(B3+T(B5+TB7)) */
|
|
|
|
|
fp0 = floatx80_mul(fp0, fp2, status); /* S(B2+T(B4+T(B6+TB8))) */
|
|
|
|
|
fp0 = floatx80_add(fp0, fp1, status); /* [B1+T(B3+T(B5+TB7))]+
|
|
|
|
|
* [S(B2+T(B4+T(B6+TB8)))]
|
|
|
|
|
*/
|
|
|
|
|
|
|
|
|
|
x = packFloatx80(xSign, xExp, xSig);
|
|
|
|
|
fp0 = floatx80_mul(fp0, x, status);
|
|
|
|
|
|
|
|
|
|
status->float_rounding_mode = user_rnd_mode;
|
|
|
|
|
status->floatx80_rounding_precision = user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
a = floatx80_add(fp0, float32_to_floatx80(posneg1, status), status);
|
|
|
|
|
|
|
|
|
|
float_raise(float_flag_inexact, status);
|
|
|
|
|
|
|
|
|
|
return a;
|
|
|
|
|
} else {
|
|
|
|
|
/* SINPOLY */
|
|
|
|
|
xSign = extractFloatx80Sign(fp0); /* X IS R */
|
|
|
|
|
xExp = extractFloatx80Exp(fp0);
|
|
|
|
|
xSig = extractFloatx80Frac(fp0);
|
|
|
|
|
|
2018-04-30 19:01:56 +02:00
|
|
|
xSign ^= (n >> 1) & 1; /* X IS NOW R'= SGN*R */
|
2018-03-12 21:27:19 +01:00
|
|
|
|
|
|
|
|
fp0 = floatx80_mul(fp0, fp0, status); /* FP0 IS S */
|
|
|
|
|
fp1 = floatx80_mul(fp0, fp0, status); /* FP1 IS T */
|
|
|
|
|
fp3 = float64_to_floatx80(make_float64(0xBD6AAA77CCC994F5),
|
|
|
|
|
status); /* A7 */
|
|
|
|
|
fp2 = float64_to_floatx80(make_float64(0x3DE612097AAE8DA1),
|
|
|
|
|
status); /* A6 */
|
|
|
|
|
fp3 = floatx80_mul(fp3, fp1, status); /* T*A7 */
|
|
|
|
|
fp2 = floatx80_mul(fp2, fp1, status); /* T*A6 */
|
|
|
|
|
fp3 = floatx80_add(fp3, float64_to_floatx80(
|
|
|
|
|
make_float64(0xBE5AE6452A118AE4), status),
|
|
|
|
|
status); /* A5+T*A7 */
|
|
|
|
|
fp2 = floatx80_add(fp2, float64_to_floatx80(
|
|
|
|
|
make_float64(0x3EC71DE3A5341531), status),
|
|
|
|
|
status); /* A4+T*A6 */
|
|
|
|
|
fp3 = floatx80_mul(fp3, fp1, status); /* T(A5+TA7) */
|
|
|
|
|
fp2 = floatx80_mul(fp2, fp1, status); /* T(A4+TA6) */
|
|
|
|
|
fp3 = floatx80_add(fp3, float64_to_floatx80(
|
|
|
|
|
make_float64(0xBF2A01A01A018B59), status),
|
|
|
|
|
status); /* A3+T(A5+TA7) */
|
|
|
|
|
fp4 = packFloatx80(0, 0x3FF8, LIT64(0x88888888888859AF));
|
|
|
|
|
fp2 = floatx80_add(fp2, fp4, status); /* A2+T(A4+TA6) */
|
|
|
|
|
fp1 = floatx80_mul(fp1, fp3, status); /* T(A3+T(A5+TA7)) */
|
|
|
|
|
fp2 = floatx80_mul(fp2, fp0, status); /* S(A2+T(A4+TA6)) */
|
|
|
|
|
fp4 = packFloatx80(1, 0x3FFC, LIT64(0xAAAAAAAAAAAAAA99));
|
|
|
|
|
fp1 = floatx80_add(fp1, fp4, status); /* A1+T(A3+T(A5+TA7)) */
|
|
|
|
|
fp1 = floatx80_add(fp1, fp2,
|
|
|
|
|
status); /* [A1+T(A3+T(A5+TA7))]+
|
|
|
|
|
* [S(A2+T(A4+TA6))]
|
|
|
|
|
*/
|
|
|
|
|
|
|
|
|
|
x = packFloatx80(xSign, xExp, xSig);
|
|
|
|
|
fp0 = floatx80_mul(fp0, x, status); /* R'*S */
|
|
|
|
|
fp0 = floatx80_mul(fp0, fp1, status); /* SIN(R')-R' */
|
|
|
|
|
|
|
|
|
|
status->float_rounding_mode = user_rnd_mode;
|
|
|
|
|
status->floatx80_rounding_precision = user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
a = floatx80_add(fp0, x, status);
|
|
|
|
|
|
|
|
|
|
float_raise(float_flag_inexact, status);
|
|
|
|
|
|
|
|
|
|
return a;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
}
|
2018-03-12 21:27:20 +01:00
|
|
|
|
|
|
|
|
/*----------------------------------------------------------------------------
|
|
|
|
|
| Cosine
|
|
|
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
|
|
|
|
|
|
floatx80 floatx80_cos(floatx80 a, float_status *status)
|
|
|
|
|
{
|
|
|
|
|
flag aSign, xSign;
|
|
|
|
|
int32_t aExp, xExp;
|
|
|
|
|
uint64_t aSig, xSig;
|
|
|
|
|
|
|
|
|
|
int8_t user_rnd_mode, user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
int32_t compact, l, n, j;
|
|
|
|
|
floatx80 fp0, fp1, fp2, fp3, fp4, fp5, x, invtwopi, twopi1, twopi2;
|
|
|
|
|
float32 posneg1, twoto63;
|
2018-04-30 19:01:56 +02:00
|
|
|
flag endflag;
|
2018-03-12 21:27:20 +01:00
|
|
|
|
|
|
|
|
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 && 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;
|
|
|
|
|
|
|
|
|
|
compact = floatx80_make_compact(aExp, aSig);
|
|
|
|
|
|
|
|
|
|
fp0 = a;
|
|
|
|
|
|
|
|
|
|
if (compact < 0x3FD78000 || compact > 0x4004BC7E) {
|
|
|
|
|
/* 2^(-40) > |X| > 15 PI */
|
|
|
|
|
if (compact > 0x3FFF8000) { /* |X| >= 15 PI */
|
|
|
|
|
/* REDUCEX */
|
|
|
|
|
fp1 = packFloatx80(0, 0, 0);
|
|
|
|
|
if (compact == 0x7FFEFFFF) {
|
|
|
|
|
twopi1 = packFloatx80(aSign ^ 1, 0x7FFE,
|
|
|
|
|
LIT64(0xC90FDAA200000000));
|
|
|
|
|
twopi2 = packFloatx80(aSign ^ 1, 0x7FDC,
|
|
|
|
|
LIT64(0x85A308D300000000));
|
|
|
|
|
fp0 = floatx80_add(fp0, twopi1, status);
|
|
|
|
|
fp1 = fp0;
|
|
|
|
|
fp0 = floatx80_add(fp0, twopi2, status);
|
|
|
|
|
fp1 = floatx80_sub(fp1, fp0, status);
|
|
|
|
|
fp1 = floatx80_add(fp1, twopi2, status);
|
|
|
|
|
}
|
|
|
|
|
loop:
|
|
|
|
|
xSign = extractFloatx80Sign(fp0);
|
|
|
|
|
xExp = extractFloatx80Exp(fp0);
|
|
|
|
|
xExp -= 0x3FFF;
|
|
|
|
|
if (xExp <= 28) {
|
|
|
|
|
l = 0;
|
|
|
|
|
endflag = 1;
|
|
|
|
|
} else {
|
|
|
|
|
l = xExp - 27;
|
|
|
|
|
endflag = 0;
|
|
|
|
|
}
|
|
|
|
|
invtwopi = packFloatx80(0, 0x3FFE - l,
|
|
|
|
|
LIT64(0xA2F9836E4E44152A)); /* INVTWOPI */
|
|
|
|
|
twopi1 = packFloatx80(0, 0x3FFF + l, LIT64(0xC90FDAA200000000));
|
|
|
|
|
twopi2 = packFloatx80(0, 0x3FDD + l, LIT64(0x85A308D300000000));
|
|
|
|
|
|
|
|
|
|
/* SIGN(INARG)*2^63 IN SGL */
|
|
|
|
|
twoto63 = packFloat32(xSign, 0xBE, 0);
|
|
|
|
|
|
|
|
|
|
fp2 = floatx80_mul(fp0, invtwopi, status);
|
|
|
|
|
fp2 = floatx80_add(fp2, float32_to_floatx80(twoto63, status),
|
|
|
|
|
status); /* THE FRACT PART OF FP2 IS ROUNDED */
|
|
|
|
|
fp2 = floatx80_sub(fp2, float32_to_floatx80(twoto63, status),
|
|
|
|
|
status); /* FP2 is N */
|
|
|
|
|
fp4 = floatx80_mul(twopi1, fp2, status); /* W = N*P1 */
|
|
|
|
|
fp5 = floatx80_mul(twopi2, fp2, status); /* w = N*P2 */
|
|
|
|
|
fp3 = floatx80_add(fp4, fp5, status); /* FP3 is P */
|
|
|
|
|
fp4 = floatx80_sub(fp4, fp3, status); /* W-P */
|
|
|
|
|
fp0 = floatx80_sub(fp0, fp3, status); /* FP0 is A := R - P */
|
|
|
|
|
fp4 = floatx80_add(fp4, fp5, status); /* FP4 is p = (W-P)+w */
|
|
|
|
|
fp3 = fp0; /* FP3 is A */
|
|
|
|
|
fp1 = floatx80_sub(fp1, fp4, status); /* FP1 is a := r - p */
|
|
|
|
|
fp0 = floatx80_add(fp0, fp1, status); /* FP0 is R := A+a */
|
|
|
|
|
|
|
|
|
|
if (endflag > 0) {
|
|
|
|
|
n = floatx80_to_int32(fp2, status);
|
|
|
|
|
goto sincont;
|
|
|
|
|
}
|
|
|
|
|
fp3 = floatx80_sub(fp3, fp0, status); /* A-R */
|
|
|
|
|
fp1 = floatx80_add(fp1, fp3, status); /* FP1 is r := (A-R)+a */
|
|
|
|
|
goto loop;
|
|
|
|
|
} else {
|
|
|
|
|
/* SINSM */
|
|
|
|
|
fp0 = float32_to_floatx80(make_float32(0x3F800000), status); /* 1 */
|
|
|
|
|
|
|
|
|
|
status->float_rounding_mode = user_rnd_mode;
|
|
|
|
|
status->floatx80_rounding_precision = user_rnd_prec;
|
|
|
|
|
|
2018-04-30 19:01:56 +02:00
|
|
|
/* COSTINY */
|
|
|
|
|
a = floatx80_sub(fp0, float32_to_floatx80(
|
|
|
|
|
make_float32(0x00800000), status),
|
|
|
|
|
status);
|
2018-03-12 21:27:20 +01:00
|
|
|
float_raise(float_flag_inexact, status);
|
|
|
|
|
|
|
|
|
|
return a;
|
|
|
|
|
}
|
|
|
|
|
} else {
|
|
|
|
|
fp1 = floatx80_mul(fp0, float64_to_floatx80(
|
|
|
|
|
make_float64(0x3FE45F306DC9C883), status),
|
|
|
|
|
status); /* X*2/PI */
|
|
|
|
|
|
|
|
|
|
n = floatx80_to_int32(fp1, status);
|
|
|
|
|
j = 32 + n;
|
|
|
|
|
|
|
|
|
|
fp0 = floatx80_sub(fp0, pi_tbl[j], status); /* X-Y1 */
|
|
|
|
|
fp0 = floatx80_sub(fp0, float32_to_floatx80(pi_tbl2[j], status),
|
|
|
|
|
status); /* FP0 IS R = (X-Y1)-Y2 */
|
|
|
|
|
|
|
|
|
|
sincont:
|
2018-04-30 19:01:56 +02:00
|
|
|
if ((n + 1) & 1) {
|
2018-03-12 21:27:20 +01:00
|
|
|
/* COSPOLY */
|
|
|
|
|
fp0 = floatx80_mul(fp0, fp0, status); /* FP0 IS S */
|
|
|
|
|
fp1 = floatx80_mul(fp0, fp0, status); /* FP1 IS T */
|
|
|
|
|
fp2 = float64_to_floatx80(make_float64(0x3D2AC4D0D6011EE3),
|
|
|
|
|
status); /* B8 */
|
|
|
|
|
fp3 = float64_to_floatx80(make_float64(0xBDA9396F9F45AC19),
|
|
|
|
|
status); /* B7 */
|
|
|
|
|
|
|
|
|
|
xSign = extractFloatx80Sign(fp0); /* X IS S */
|
|
|
|
|
xExp = extractFloatx80Exp(fp0);
|
|
|
|
|
xSig = extractFloatx80Frac(fp0);
|
|
|
|
|
|
2018-04-30 19:01:56 +02:00
|
|
|
if (((n + 1) >> 1) & 1) {
|
2018-03-12 21:27:20 +01:00
|
|
|
xSign ^= 1;
|
|
|
|
|
posneg1 = make_float32(0xBF800000); /* -1 */
|
|
|
|
|
} else {
|
|
|
|
|
xSign ^= 0;
|
|
|
|
|
posneg1 = make_float32(0x3F800000); /* 1 */
|
|
|
|
|
} /* X IS NOW R'= SGN*R */
|
|
|
|
|
|
|
|
|
|
fp2 = floatx80_mul(fp2, fp1, status); /* TB8 */
|
|
|
|
|
fp3 = floatx80_mul(fp3, fp1, status); /* TB7 */
|
|
|
|
|
fp2 = floatx80_add(fp2, float64_to_floatx80(
|
|
|
|
|
make_float64(0x3E21EED90612C972), status),
|
|
|
|
|
status); /* B6+TB8 */
|
|
|
|
|
fp3 = floatx80_add(fp3, float64_to_floatx80(
|
|
|
|
|
make_float64(0xBE927E4FB79D9FCF), status),
|
|
|
|
|
status); /* B5+TB7 */
|
|
|
|
|
fp2 = floatx80_mul(fp2, fp1, status); /* T(B6+TB8) */
|
|
|
|
|
fp3 = floatx80_mul(fp3, fp1, status); /* T(B5+TB7) */
|
|
|
|
|
fp2 = floatx80_add(fp2, float64_to_floatx80(
|
|
|
|
|
make_float64(0x3EFA01A01A01D423), status),
|
|
|
|
|
status); /* B4+T(B6+TB8) */
|
|
|
|
|
fp4 = packFloatx80(1, 0x3FF5, LIT64(0xB60B60B60B61D438));
|
|
|
|
|
fp3 = floatx80_add(fp3, fp4, status); /* B3+T(B5+TB7) */
|
|
|
|
|
fp2 = floatx80_mul(fp2, fp1, status); /* T(B4+T(B6+TB8)) */
|
|
|
|
|
fp1 = floatx80_mul(fp1, fp3, status); /* T(B3+T(B5+TB7)) */
|
|
|
|
|
fp4 = packFloatx80(0, 0x3FFA, LIT64(0xAAAAAAAAAAAAAB5E));
|
|
|
|
|
fp2 = floatx80_add(fp2, fp4, status); /* B2+T(B4+T(B6+TB8)) */
|
|
|
|
|
fp1 = floatx80_add(fp1, float32_to_floatx80(
|
|
|
|
|
make_float32(0xBF000000), status),
|
|
|
|
|
status); /* B1+T(B3+T(B5+TB7)) */
|
|
|
|
|
fp0 = floatx80_mul(fp0, fp2, status); /* S(B2+T(B4+T(B6+TB8))) */
|
|
|
|
|
fp0 = floatx80_add(fp0, fp1, status);
|
|
|
|
|
/* [B1+T(B3+T(B5+TB7))]+[S(B2+T(B4+T(B6+TB8)))] */
|
|
|
|
|
|
|
|
|
|
x = packFloatx80(xSign, xExp, xSig);
|
|
|
|
|
fp0 = floatx80_mul(fp0, x, status);
|
|
|
|
|
|
|
|
|
|
status->float_rounding_mode = user_rnd_mode;
|
|
|
|
|
status->floatx80_rounding_precision = user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
a = floatx80_add(fp0, float32_to_floatx80(posneg1, status), status);
|
|
|
|
|
|
|
|
|
|
float_raise(float_flag_inexact, status);
|
|
|
|
|
|
|
|
|
|
return a;
|
|
|
|
|
} else {
|
|
|
|
|
/* SINPOLY */
|
|
|
|
|
xSign = extractFloatx80Sign(fp0); /* X IS R */
|
|
|
|
|
xExp = extractFloatx80Exp(fp0);
|
|
|
|
|
xSig = extractFloatx80Frac(fp0);
|
|
|
|
|
|
2018-04-30 19:01:56 +02:00
|
|
|
xSign ^= ((n + 1) >> 1) & 1; /* X IS NOW R'= SGN*R */
|
2018-03-12 21:27:20 +01:00
|
|
|
|
|
|
|
|
fp0 = floatx80_mul(fp0, fp0, status); /* FP0 IS S */
|
|
|
|
|
fp1 = floatx80_mul(fp0, fp0, status); /* FP1 IS T */
|
|
|
|
|
fp3 = float64_to_floatx80(make_float64(0xBD6AAA77CCC994F5),
|
|
|
|
|
status); /* A7 */
|
|
|
|
|
fp2 = float64_to_floatx80(make_float64(0x3DE612097AAE8DA1),
|
|
|
|
|
status); /* A6 */
|
|
|
|
|
fp3 = floatx80_mul(fp3, fp1, status); /* T*A7 */
|
|
|
|
|
fp2 = floatx80_mul(fp2, fp1, status); /* T*A6 */
|
|
|
|
|
fp3 = floatx80_add(fp3, float64_to_floatx80(
|
|
|
|
|
make_float64(0xBE5AE6452A118AE4), status),
|
|
|
|
|
status); /* A5+T*A7 */
|
|
|
|
|
fp2 = floatx80_add(fp2, float64_to_floatx80(
|
|
|
|
|
make_float64(0x3EC71DE3A5341531), status),
|
|
|
|
|
status); /* A4+T*A6 */
|
|
|
|
|
fp3 = floatx80_mul(fp3, fp1, status); /* T(A5+TA7) */
|
|
|
|
|
fp2 = floatx80_mul(fp2, fp1, status); /* T(A4+TA6) */
|
|
|
|
|
fp3 = floatx80_add(fp3, float64_to_floatx80(
|
|
|
|
|
make_float64(0xBF2A01A01A018B59), status),
|
|
|
|
|
status); /* A3+T(A5+TA7) */
|
|
|
|
|
fp4 = packFloatx80(0, 0x3FF8, LIT64(0x88888888888859AF));
|
|
|
|
|
fp2 = floatx80_add(fp2, fp4, status); /* A2+T(A4+TA6) */
|
|
|
|
|
fp1 = floatx80_mul(fp1, fp3, status); /* T(A3+T(A5+TA7)) */
|
|
|
|
|
fp2 = floatx80_mul(fp2, fp0, status); /* S(A2+T(A4+TA6)) */
|
|
|
|
|
fp4 = packFloatx80(1, 0x3FFC, LIT64(0xAAAAAAAAAAAAAA99));
|
|
|
|
|
fp1 = floatx80_add(fp1, fp4, status); /* A1+T(A3+T(A5+TA7)) */
|
|
|
|
|
fp1 = floatx80_add(fp1, fp2, status);
|
|
|
|
|
/* [A1+T(A3+T(A5+TA7))]+[S(A2+T(A4+TA6))] */
|
|
|
|
|
|
|
|
|
|
x = packFloatx80(xSign, xExp, xSig);
|
|
|
|
|
fp0 = floatx80_mul(fp0, x, status); /* R'*S */
|
|
|
|
|
fp0 = floatx80_mul(fp0, fp1, status); /* SIN(R')-R' */
|
|
|
|
|
|
|
|
|
|
status->float_rounding_mode = user_rnd_mode;
|
|
|
|
|
status->floatx80_rounding_precision = user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
a = floatx80_add(fp0, x, status);
|
|
|
|
|
|
|
|
|
|
float_raise(float_flag_inexact, status);
|
|
|
|
|
|
|
|
|
|
return a;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
}
|
2018-03-12 21:27:22 +01:00
|
|
|
|
|
|
|
|
/*----------------------------------------------------------------------------
|
|
|
|
|
| Arc tangent
|
|
|
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
|
|
|
|
|
|
floatx80 floatx80_atan(floatx80 a, float_status *status)
|
|
|
|
|
{
|
|
|
|
|
flag aSign;
|
|
|
|
|
int32_t aExp;
|
|
|
|
|
uint64_t aSig;
|
|
|
|
|
|
|
|
|
|
int8_t user_rnd_mode, user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
int32_t compact, tbl_index;
|
|
|
|
|
floatx80 fp0, fp1, fp2, fp3, xsave;
|
|
|
|
|
|
|
|
|
|
aSig = extractFloatx80Frac(a);
|
|
|
|
|
aExp = extractFloatx80Exp(a);
|
|
|
|
|
aSign = extractFloatx80Sign(a);
|
|
|
|
|
|
|
|
|
|
if (aExp == 0x7FFF) {
|
|
|
|
|
if ((uint64_t) (aSig << 1)) {
|
|
|
|
|
return propagateFloatx80NaNOneArg(a, status);
|
|
|
|
|
}
|
|
|
|
|
a = packFloatx80(aSign, piby2_exp, pi_sig);
|
|
|
|
|
float_raise(float_flag_inexact, status);
|
|
|
|
|
return floatx80_move(a, status);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
if (aExp == 0 && aSig == 0) {
|
|
|
|
|
return packFloatx80(aSign, 0, 0);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
compact = floatx80_make_compact(aExp, aSig);
|
|
|
|
|
|
|
|
|
|
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 (compact < 0x3FFB8000 || compact > 0x4002FFFF) {
|
|
|
|
|
/* |X| >= 16 or |X| < 1/16 */
|
|
|
|
|
if (compact > 0x3FFF8000) { /* |X| >= 16 */
|
|
|
|
|
if (compact > 0x40638000) { /* |X| > 2^(100) */
|
|
|
|
|
fp0 = packFloatx80(aSign, piby2_exp, pi_sig);
|
|
|
|
|
fp1 = packFloatx80(aSign, 0x0001, one_sig);
|
|
|
|
|
|
|
|
|
|
status->float_rounding_mode = user_rnd_mode;
|
|
|
|
|
status->floatx80_rounding_precision = user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
a = floatx80_sub(fp0, fp1, status);
|
|
|
|
|
|
|
|
|
|
float_raise(float_flag_inexact, status);
|
|
|
|
|
|
|
|
|
|
return a;
|
|
|
|
|
} else {
|
|
|
|
|
fp0 = a;
|
|
|
|
|
fp1 = packFloatx80(1, one_exp, one_sig); /* -1 */
|
|
|
|
|
fp1 = floatx80_div(fp1, fp0, status); /* X' = -1/X */
|
|
|
|
|
xsave = fp1;
|
|
|
|
|
fp0 = floatx80_mul(fp1, fp1, status); /* Y = X'*X' */
|
|
|
|
|
fp1 = floatx80_mul(fp0, fp0, status); /* Z = Y*Y */
|
|
|
|
|
fp3 = float64_to_floatx80(make_float64(0xBFB70BF398539E6A),
|
|
|
|
|
status); /* C5 */
|
|
|
|
|
fp2 = float64_to_floatx80(make_float64(0x3FBC7187962D1D7D),
|
|
|
|
|
status); /* C4 */
|
|
|
|
|
fp3 = floatx80_mul(fp3, fp1, status); /* Z*C5 */
|
|
|
|
|
fp2 = floatx80_mul(fp2, fp1, status); /* Z*C4 */
|
|
|
|
|
fp3 = floatx80_add(fp3, float64_to_floatx80(
|
|
|
|
|
make_float64(0xBFC24924827107B8), status),
|
|
|
|
|
status); /* C3+Z*C5 */
|
|
|
|
|
fp2 = floatx80_add(fp2, float64_to_floatx80(
|
|
|
|
|
make_float64(0x3FC999999996263E), status),
|
|
|
|
|
status); /* C2+Z*C4 */
|
|
|
|
|
fp1 = floatx80_mul(fp1, fp3, status); /* Z*(C3+Z*C5) */
|
|
|
|
|
fp2 = floatx80_mul(fp2, fp0, status); /* Y*(C2+Z*C4) */
|
|
|
|
|
fp1 = floatx80_add(fp1, float64_to_floatx80(
|
|
|
|
|
make_float64(0xBFD5555555555536), status),
|
|
|
|
|
status); /* C1+Z*(C3+Z*C5) */
|
|
|
|
|
fp0 = floatx80_mul(fp0, xsave, status); /* X'*Y */
|
|
|
|
|
/* [Y*(C2+Z*C4)]+[C1+Z*(C3+Z*C5)] */
|
|
|
|
|
fp1 = floatx80_add(fp1, fp2, status);
|
|
|
|
|
/* X'*Y*([B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))]) ?? */
|
|
|
|
|
fp0 = floatx80_mul(fp0, fp1, status);
|
|
|
|
|
fp0 = floatx80_add(fp0, xsave, status);
|
|
|
|
|
fp1 = packFloatx80(aSign, piby2_exp, pi_sig);
|
|
|
|
|
|
|
|
|
|
status->float_rounding_mode = user_rnd_mode;
|
|
|
|
|
status->floatx80_rounding_precision = user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
a = floatx80_add(fp0, fp1, status);
|
|
|
|
|
|
|
|
|
|
float_raise(float_flag_inexact, status);
|
|
|
|
|
|
|
|
|
|
return a;
|
|
|
|
|
}
|
|
|
|
|
} else { /* |X| < 1/16 */
|
|
|
|
|
if (compact < 0x3FD78000) { /* |X| < 2^(-40) */
|
|
|
|
|
status->float_rounding_mode = user_rnd_mode;
|
|
|
|
|
status->floatx80_rounding_precision = user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
a = floatx80_move(a, status);
|
|
|
|
|
|
|
|
|
|
float_raise(float_flag_inexact, status);
|
|
|
|
|
|
|
|
|
|
return a;
|
|
|
|
|
} else {
|
|
|
|
|
fp0 = a;
|
|
|
|
|
xsave = a;
|
|
|
|
|
fp0 = floatx80_mul(fp0, fp0, status); /* Y = X*X */
|
|
|
|
|
fp1 = floatx80_mul(fp0, fp0, status); /* Z = Y*Y */
|
|
|
|
|
fp2 = float64_to_floatx80(make_float64(0x3FB344447F876989),
|
|
|
|
|
status); /* B6 */
|
|
|
|
|
fp3 = float64_to_floatx80(make_float64(0xBFB744EE7FAF45DB),
|
|
|
|
|
status); /* B5 */
|
|
|
|
|
fp2 = floatx80_mul(fp2, fp1, status); /* Z*B6 */
|
|
|
|
|
fp3 = floatx80_mul(fp3, fp1, status); /* Z*B5 */
|
|
|
|
|
fp2 = floatx80_add(fp2, float64_to_floatx80(
|
|
|
|
|
make_float64(0x3FBC71C646940220), status),
|
|
|
|
|
status); /* B4+Z*B6 */
|
|
|
|
|
fp3 = floatx80_add(fp3, float64_to_floatx80(
|
|
|
|
|
make_float64(0xBFC24924921872F9),
|
|
|
|
|
status), status); /* B3+Z*B5 */
|
|
|
|
|
fp2 = floatx80_mul(fp2, fp1, status); /* Z*(B4+Z*B6) */
|
|
|
|
|
fp1 = floatx80_mul(fp1, fp3, status); /* Z*(B3+Z*B5) */
|
|
|
|
|
fp2 = floatx80_add(fp2, float64_to_floatx80(
|
|
|
|
|
make_float64(0x3FC9999999998FA9), status),
|
|
|
|
|
status); /* B2+Z*(B4+Z*B6) */
|
|
|
|
|
fp1 = floatx80_add(fp1, float64_to_floatx80(
|
|
|
|
|
make_float64(0xBFD5555555555555), status),
|
|
|
|
|
status); /* B1+Z*(B3+Z*B5) */
|
|
|
|
|
fp2 = floatx80_mul(fp2, fp0, status); /* Y*(B2+Z*(B4+Z*B6)) */
|
|
|
|
|
fp0 = floatx80_mul(fp0, xsave, status); /* X*Y */
|
|
|
|
|
/* [B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))] */
|
|
|
|
|
fp1 = floatx80_add(fp1, fp2, status);
|
|
|
|
|
/* X*Y*([B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))]) */
|
|
|
|
|
fp0 = floatx80_mul(fp0, fp1, status);
|
|
|
|
|
|
|
|
|
|
status->float_rounding_mode = user_rnd_mode;
|
|
|
|
|
status->floatx80_rounding_precision = user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
a = floatx80_add(fp0, xsave, status);
|
|
|
|
|
|
|
|
|
|
float_raise(float_flag_inexact, status);
|
|
|
|
|
|
|
|
|
|
return a;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
} else {
|
|
|
|
|
aSig &= LIT64(0xF800000000000000);
|
|
|
|
|
aSig |= LIT64(0x0400000000000000);
|
|
|
|
|
xsave = packFloatx80(aSign, aExp, aSig); /* F */
|
|
|
|
|
fp0 = a;
|
|
|
|
|
fp1 = a; /* X */
|
|
|
|
|
fp2 = packFloatx80(0, one_exp, one_sig); /* 1 */
|
|
|
|
|
fp1 = floatx80_mul(fp1, xsave, status); /* X*F */
|
|
|
|
|
fp0 = floatx80_sub(fp0, xsave, status); /* X-F */
|
|
|
|
|
fp1 = floatx80_add(fp1, fp2, status); /* 1 + X*F */
|
|
|
|
|
fp0 = floatx80_div(fp0, fp1, status); /* U = (X-F)/(1+X*F) */
|
|
|
|
|
|
|
|
|
|
tbl_index = compact;
|
|
|
|
|
|
|
|
|
|
tbl_index &= 0x7FFF0000;
|
|
|
|
|
tbl_index -= 0x3FFB0000;
|
|
|
|
|
tbl_index >>= 1;
|
|
|
|
|
tbl_index += compact & 0x00007800;
|
|
|
|
|
tbl_index >>= 11;
|
|
|
|
|
|
|
|
|
|
fp3 = atan_tbl[tbl_index];
|
|
|
|
|
|
|
|
|
|
fp3.high |= aSign ? 0x8000 : 0; /* ATAN(F) */
|
|
|
|
|
|
|
|
|
|
fp1 = floatx80_mul(fp0, fp0, status); /* V = U*U */
|
|
|
|
|
fp2 = float64_to_floatx80(make_float64(0xBFF6687E314987D8),
|
|
|
|
|
status); /* A3 */
|
|
|
|
|
fp2 = floatx80_add(fp2, fp1, status); /* A3+V */
|
|
|
|
|
fp2 = floatx80_mul(fp2, fp1, status); /* V*(A3+V) */
|
|
|
|
|
fp1 = floatx80_mul(fp1, fp0, status); /* U*V */
|
|
|
|
|
fp2 = floatx80_add(fp2, float64_to_floatx80(
|
|
|
|
|
make_float64(0x4002AC6934A26DB3), status),
|
|
|
|
|
status); /* A2+V*(A3+V) */
|
|
|
|
|
fp1 = floatx80_mul(fp1, float64_to_floatx80(
|
|
|
|
|
make_float64(0xBFC2476F4E1DA28E), status),
|
|
|
|
|
status); /* A1+U*V */
|
|
|
|
|
fp1 = floatx80_mul(fp1, fp2, status); /* A1*U*V*(A2+V*(A3+V)) */
|
|
|
|
|
fp0 = floatx80_add(fp0, fp1, status); /* ATAN(U) */
|
|
|
|
|
|
|
|
|
|
status->float_rounding_mode = user_rnd_mode;
|
|
|
|
|
status->floatx80_rounding_precision = user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
a = floatx80_add(fp0, fp3, status); /* ATAN(X) */
|
|
|
|
|
|
|
|
|
|
float_raise(float_flag_inexact, status);
|
|
|
|
|
|
|
|
|
|
return a;
|
|
|
|
|
}
|
|
|
|
|
}
|
2018-03-12 21:27:23 +01:00
|
|
|
|
|
|
|
|
/*----------------------------------------------------------------------------
|
|
|
|
|
| Arc sine
|
|
|
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
|
|
|
|
|
|
floatx80 floatx80_asin(floatx80 a, float_status *status)
|
|
|
|
|
{
|
|
|
|
|
flag aSign;
|
|
|
|
|
int32_t aExp;
|
|
|
|
|
uint64_t aSig;
|
|
|
|
|
|
|
|
|
|
int8_t user_rnd_mode, user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
int32_t compact;
|
|
|
|
|
floatx80 fp0, fp1, fp2, one;
|
|
|
|
|
|
|
|
|
|
aSig = extractFloatx80Frac(a);
|
|
|
|
|
aExp = extractFloatx80Exp(a);
|
|
|
|
|
aSign = extractFloatx80Sign(a);
|
|
|
|
|
|
|
|
|
|
if (aExp == 0x7FFF && (uint64_t) (aSig << 1)) {
|
|
|
|
|
return propagateFloatx80NaNOneArg(a, status);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
if (aExp == 0 && aSig == 0) {
|
|
|
|
|
return packFloatx80(aSign, 0, 0);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
compact = floatx80_make_compact(aExp, aSig);
|
|
|
|
|
|
|
|
|
|
if (compact >= 0x3FFF8000) { /* |X| >= 1 */
|
|
|
|
|
if (aExp == one_exp && aSig == one_sig) { /* |X| == 1 */
|
|
|
|
|
float_raise(float_flag_inexact, status);
|
|
|
|
|
a = packFloatx80(aSign, piby2_exp, pi_sig);
|
|
|
|
|
return floatx80_move(a, status);
|
|
|
|
|
} else { /* |X| > 1 */
|
|
|
|
|
float_raise(float_flag_invalid, status);
|
|
|
|
|
return floatx80_default_nan(status);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
} /* |X| < 1 */
|
|
|
|
|
|
|
|
|
|
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;
|
|
|
|
|
|
|
|
|
|
one = packFloatx80(0, one_exp, one_sig);
|
|
|
|
|
fp0 = a;
|
|
|
|
|
|
|
|
|
|
fp1 = floatx80_sub(one, fp0, status); /* 1 - X */
|
|
|
|
|
fp2 = floatx80_add(one, fp0, status); /* 1 + X */
|
|
|
|
|
fp1 = floatx80_mul(fp2, fp1, status); /* (1+X)*(1-X) */
|
|
|
|
|
fp1 = floatx80_sqrt(fp1, status); /* SQRT((1+X)*(1-X)) */
|
|
|
|
|
fp0 = floatx80_div(fp0, fp1, status); /* X/SQRT((1+X)*(1-X)) */
|
|
|
|
|
|
|
|
|
|
status->float_rounding_mode = user_rnd_mode;
|
|
|
|
|
status->floatx80_rounding_precision = user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
a = floatx80_atan(fp0, status); /* ATAN(X/SQRT((1+X)*(1-X))) */
|
|
|
|
|
|
|
|
|
|
float_raise(float_flag_inexact, status);
|
|
|
|
|
|
|
|
|
|
return a;
|
|
|
|
|
}
|
2018-03-12 21:27:24 +01:00
|
|
|
|
|
|
|
|
/*----------------------------------------------------------------------------
|
|
|
|
|
| Arc cosine
|
|
|
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
|
|
|
|
|
|
floatx80 floatx80_acos(floatx80 a, float_status *status)
|
|
|
|
|
{
|
|
|
|
|
flag aSign;
|
|
|
|
|
int32_t aExp;
|
|
|
|
|
uint64_t aSig;
|
|
|
|
|
|
|
|
|
|
int8_t user_rnd_mode, user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
int32_t compact;
|
|
|
|
|
floatx80 fp0, fp1, one;
|
|
|
|
|
|
|
|
|
|
aSig = extractFloatx80Frac(a);
|
|
|
|
|
aExp = extractFloatx80Exp(a);
|
|
|
|
|
aSign = extractFloatx80Sign(a);
|
|
|
|
|
|
|
|
|
|
if (aExp == 0x7FFF && (uint64_t) (aSig << 1)) {
|
|
|
|
|
return propagateFloatx80NaNOneArg(a, status);
|
|
|
|
|
}
|
|
|
|
|
if (aExp == 0 && aSig == 0) {
|
|
|
|
|
float_raise(float_flag_inexact, status);
|
|
|
|
|
return roundAndPackFloatx80(status->floatx80_rounding_precision, 0,
|
|
|
|
|
piby2_exp, pi_sig, 0, status);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
compact = floatx80_make_compact(aExp, aSig);
|
|
|
|
|
|
|
|
|
|
if (compact >= 0x3FFF8000) { /* |X| >= 1 */
|
|
|
|
|
if (aExp == one_exp && aSig == one_sig) { /* |X| == 1 */
|
|
|
|
|
if (aSign) { /* X == -1 */
|
|
|
|
|
a = packFloatx80(0, pi_exp, pi_sig);
|
|
|
|
|
float_raise(float_flag_inexact, status);
|
|
|
|
|
return floatx80_move(a, status);
|
|
|
|
|
} else { /* X == +1 */
|
|
|
|
|
return packFloatx80(0, 0, 0);
|
|
|
|
|
}
|
|
|
|
|
} else { /* |X| > 1 */
|
|
|
|
|
float_raise(float_flag_invalid, status);
|
|
|
|
|
return floatx80_default_nan(status);
|
|
|
|
|
}
|
|
|
|
|
} /* |X| < 1 */
|
|
|
|
|
|
|
|
|
|
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;
|
|
|
|
|
|
|
|
|
|
one = packFloatx80(0, one_exp, one_sig);
|
|
|
|
|
fp0 = a;
|
|
|
|
|
|
|
|
|
|
fp1 = floatx80_add(one, fp0, status); /* 1 + X */
|
|
|
|
|
fp0 = floatx80_sub(one, fp0, status); /* 1 - X */
|
|
|
|
|
fp0 = floatx80_div(fp0, fp1, status); /* (1-X)/(1+X) */
|
|
|
|
|
fp0 = floatx80_sqrt(fp0, status); /* SQRT((1-X)/(1+X)) */
|
|
|
|
|
fp0 = floatx80_atan(fp0, status); /* ATAN(SQRT((1-X)/(1+X))) */
|
|
|
|
|
|
|
|
|
|
status->float_rounding_mode = user_rnd_mode;
|
|
|
|
|
status->floatx80_rounding_precision = user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
a = floatx80_add(fp0, fp0, status); /* 2 * ATAN(SQRT((1-X)/(1+X))) */
|
|
|
|
|
|
|
|
|
|
float_raise(float_flag_inexact, status);
|
|
|
|
|
|
|
|
|
|
return a;
|
|
|
|
|
}
|
2018-03-12 21:27:25 +01:00
|
|
|
|
|
|
|
|
/*----------------------------------------------------------------------------
|
|
|
|
|
| Hyperbolic arc tangent
|
|
|
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
|
|
|
|
|
|
floatx80 floatx80_atanh(floatx80 a, float_status *status)
|
|
|
|
|
{
|
|
|
|
|
flag aSign;
|
|
|
|
|
int32_t aExp;
|
|
|
|
|
uint64_t aSig;
|
|
|
|
|
|
|
|
|
|
int8_t user_rnd_mode, user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
int32_t compact;
|
|
|
|
|
floatx80 fp0, fp1, fp2, one;
|
|
|
|
|
|
|
|
|
|
aSig = extractFloatx80Frac(a);
|
|
|
|
|
aExp = extractFloatx80Exp(a);
|
|
|
|
|
aSign = extractFloatx80Sign(a);
|
|
|
|
|
|
|
|
|
|
if (aExp == 0x7FFF && (uint64_t) (aSig << 1)) {
|
|
|
|
|
return propagateFloatx80NaNOneArg(a, status);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
if (aExp == 0 && aSig == 0) {
|
|
|
|
|
return packFloatx80(aSign, 0, 0);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
compact = floatx80_make_compact(aExp, aSig);
|
|
|
|
|
|
|
|
|
|
if (compact >= 0x3FFF8000) { /* |X| >= 1 */
|
|
|
|
|
if (aExp == one_exp && aSig == one_sig) { /* |X| == 1 */
|
|
|
|
|
float_raise(float_flag_divbyzero, status);
|
|
|
|
|
return packFloatx80(aSign, floatx80_infinity.high,
|
|
|
|
|
floatx80_infinity.low);
|
|
|
|
|
} else { /* |X| > 1 */
|
|
|
|
|
float_raise(float_flag_invalid, status);
|
|
|
|
|
return floatx80_default_nan(status);
|
|
|
|
|
}
|
|
|
|
|
} /* |X| < 1 */
|
|
|
|
|
|
|
|
|
|
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;
|
|
|
|
|
|
|
|
|
|
one = packFloatx80(0, one_exp, one_sig);
|
|
|
|
|
fp2 = packFloatx80(aSign, 0x3FFE, one_sig); /* SIGN(X) * (1/2) */
|
|
|
|
|
fp0 = packFloatx80(0, aExp, aSig); /* Y = |X| */
|
|
|
|
|
fp1 = packFloatx80(1, aExp, aSig); /* -Y */
|
|
|
|
|
fp0 = floatx80_add(fp0, fp0, status); /* 2Y */
|
|
|
|
|
fp1 = floatx80_add(fp1, one, status); /* 1-Y */
|
|
|
|
|
fp0 = floatx80_div(fp0, fp1, status); /* Z = 2Y/(1-Y) */
|
|
|
|
|
fp0 = floatx80_lognp1(fp0, status); /* LOG1P(Z) */
|
|
|
|
|
|
|
|
|
|
status->float_rounding_mode = user_rnd_mode;
|
|
|
|
|
status->floatx80_rounding_precision = user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
a = floatx80_mul(fp0, fp2,
|
|
|
|
|
status); /* ATANH(X) = SIGN(X) * (1/2) * LOG1P(Z) */
|
|
|
|
|
|
|
|
|
|
float_raise(float_flag_inexact, status);
|
|
|
|
|
|
|
|
|
|
return a;
|
|
|
|
|
}
|
2018-03-12 21:27:26 +01:00
|
|
|
|
|
|
|
|
/*----------------------------------------------------------------------------
|
|
|
|
|
| e to x minus 1
|
|
|
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
|
|
|
|
|
|
floatx80 floatx80_etoxm1(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, m, m1;
|
|
|
|
|
floatx80 fp0, fp1, fp2, fp3, l2, sc, onebysc;
|
|
|
|
|
|
|
|
|
|
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(aSign, one_exp, one_sig);
|
|
|
|
|
}
|
|
|
|
|
return packFloatx80(0, floatx80_infinity.high,
|
|
|
|
|
floatx80_infinity.low);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
if (aExp == 0 && aSig == 0) {
|
|
|
|
|
return packFloatx80(aSign, 0, 0);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
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 (aExp >= 0x3FFD) { /* |X| >= 1/4 */
|
|
|
|
|
compact = floatx80_make_compact(aExp, aSig);
|
|
|
|
|
|
|
|
|
|
if (compact <= 0x4004C215) { /* |X| <= 70 log2 */
|
|
|
|
|
fp0 = a;
|
|
|
|
|
fp1 = a;
|
|
|
|
|
fp0 = floatx80_mul(fp0, float32_to_floatx80(
|
|
|
|
|
make_float32(0x42B8AA3B), status),
|
|
|
|
|
status); /* 64/log2 * X */
|
|
|
|
|
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--;
|
|
|
|
|
}
|
|
|
|
|
m1 = -m;
|
|
|
|
|
/*m += 0x3FFF; // biased exponent of 2^(M) */
|
|
|
|
|
/*m1 += 0x3FFF; // biased exponent of -2^(-M) */
|
|
|
|
|
|
|
|
|
|
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(0x3950097B),
|
|
|
|
|
status); /* A6 */
|
|
|
|
|
fp2 = floatx80_mul(fp2, fp1, status); /* fp2 is S*A6 */
|
|
|
|
|
fp3 = floatx80_mul(float32_to_floatx80(make_float32(0x3AB60B6A),
|
|
|
|
|
status), fp1, status); /* fp3 is S*A5 */
|
|
|
|
|
fp2 = floatx80_add(fp2, float64_to_floatx80(
|
|
|
|
|
make_float64(0x3F81111111174385), status),
|
|
|
|
|
status); /* fp2 IS A4+S*A6 */
|
|
|
|
|
fp3 = floatx80_add(fp3, float64_to_floatx80(
|
|
|
|
|
make_float64(0x3FA5555555554F5A), status),
|
|
|
|
|
status); /* fp3 is A3+S*A5 */
|
|
|
|
|
fp2 = floatx80_mul(fp2, fp1, status); /* fp2 IS S*(A4+S*A6) */
|
|
|
|
|
fp3 = floatx80_mul(fp3, fp1, status); /* fp3 IS S*(A3+S*A5) */
|
|
|
|
|
fp2 = floatx80_add(fp2, float64_to_floatx80(
|
|
|
|
|
make_float64(0x3FC5555555555555), status),
|
|
|
|
|
status); /* fp2 IS A2+S*(A4+S*A6) */
|
|
|
|
|
fp3 = floatx80_add(fp3, float32_to_floatx80(
|
|
|
|
|
make_float32(0x3F000000), status),
|
|
|
|
|
status); /* fp3 IS A1+S*(A3+S*A5) */
|
|
|
|
|
fp2 = floatx80_mul(fp2, fp1,
|
|
|
|
|
status); /* fp2 IS S*(A2+S*(A4+S*A6)) */
|
|
|
|
|
fp1 = floatx80_mul(fp1, fp3,
|
|
|
|
|
status); /* fp1 IS S*(A1+S*(A3+S*A5)) */
|
|
|
|
|
fp2 = floatx80_mul(fp2, fp0,
|
|
|
|
|
status); /* fp2 IS R*S*(A2+S*(A4+S*A6)) */
|
|
|
|
|
fp0 = floatx80_add(fp0, fp1,
|
|
|
|
|
status); /* fp0 IS R+S*(A1+S*(A3+S*A5)) */
|
|
|
|
|
fp0 = floatx80_add(fp0, fp2, status); /* fp0 IS EXP(R) - 1 */
|
|
|
|
|
|
|
|
|
|
fp0 = floatx80_mul(fp0, exp_tbl[j],
|
|
|
|
|
status); /* 2^(J/64)*(Exp(R)-1) */
|
|
|
|
|
|
|
|
|
|
if (m >= 64) {
|
|
|
|
|
fp1 = float32_to_floatx80(exp_tbl2[j], status);
|
|
|
|
|
onebysc = packFloatx80(1, m1 + 0x3FFF, one_sig); /* -2^(-M) */
|
|
|
|
|
fp1 = floatx80_add(fp1, onebysc, status);
|
|
|
|
|
fp0 = floatx80_add(fp0, fp1, status);
|
|
|
|
|
fp0 = floatx80_add(fp0, exp_tbl[j], status);
|
|
|
|
|
} else if (m < -3) {
|
|
|
|
|
fp0 = floatx80_add(fp0, float32_to_floatx80(exp_tbl2[j],
|
|
|
|
|
status), status);
|
|
|
|
|
fp0 = floatx80_add(fp0, exp_tbl[j], status);
|
|
|
|
|
onebysc = packFloatx80(1, m1 + 0x3FFF, one_sig); /* -2^(-M) */
|
|
|
|
|
fp0 = floatx80_add(fp0, onebysc, status);
|
|
|
|
|
} else { /* -3 <= m <= 63 */
|
|
|
|
|
fp1 = exp_tbl[j];
|
|
|
|
|
fp0 = floatx80_add(fp0, float32_to_floatx80(exp_tbl2[j],
|
|
|
|
|
status), status);
|
|
|
|
|
onebysc = packFloatx80(1, m1 + 0x3FFF, one_sig); /* -2^(-M) */
|
|
|
|
|
fp1 = floatx80_add(fp1, onebysc, status);
|
|
|
|
|
fp0 = floatx80_add(fp0, fp1, status);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
sc = packFloatx80(0, m + 0x3FFF, one_sig);
|
|
|
|
|
|
|
|
|
|
status->float_rounding_mode = user_rnd_mode;
|
|
|
|
|
status->floatx80_rounding_precision = user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
a = floatx80_mul(fp0, sc, status);
|
|
|
|
|
|
|
|
|
|
float_raise(float_flag_inexact, status);
|
|
|
|
|
|
|
|
|
|
return a;
|
|
|
|
|
} else { /* |X| > 70 log2 */
|
|
|
|
|
if (aSign) {
|
|
|
|
|
fp0 = float32_to_floatx80(make_float32(0xBF800000),
|
|
|
|
|
status); /* -1 */
|
|
|
|
|
|
|
|
|
|
status->float_rounding_mode = user_rnd_mode;
|
|
|
|
|
status->floatx80_rounding_precision = user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
a = floatx80_add(fp0, float32_to_floatx80(
|
|
|
|
|
make_float32(0x00800000), status),
|
|
|
|
|
status); /* -1 + 2^(-126) */
|
|
|
|
|
|
|
|
|
|
float_raise(float_flag_inexact, status);
|
|
|
|
|
|
|
|
|
|
return a;
|
|
|
|
|
} else {
|
|
|
|
|
status->float_rounding_mode = user_rnd_mode;
|
|
|
|
|
status->floatx80_rounding_precision = user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
return floatx80_etox(a, status);
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
} else { /* |X| < 1/4 */
|
|
|
|
|
if (aExp >= 0x3FBE) {
|
|
|
|
|
fp0 = a;
|
|
|
|
|
fp0 = floatx80_mul(fp0, fp0, status); /* S = X*X */
|
|
|
|
|
fp1 = float32_to_floatx80(make_float32(0x2F30CAA8),
|
|
|
|
|
status); /* B12 */
|
|
|
|
|
fp1 = floatx80_mul(fp1, fp0, status); /* S * B12 */
|
|
|
|
|
fp2 = float32_to_floatx80(make_float32(0x310F8290),
|
|
|
|
|
status); /* B11 */
|
|
|
|
|
fp1 = floatx80_add(fp1, float32_to_floatx80(
|
|
|
|
|
make_float32(0x32D73220), status),
|
|
|
|
|
status); /* B10 */
|
|
|
|
|
fp2 = floatx80_mul(fp2, fp0, status);
|
|
|
|
|
fp1 = floatx80_mul(fp1, fp0, status);
|
|
|
|
|
fp2 = floatx80_add(fp2, float32_to_floatx80(
|
|
|
|
|
make_float32(0x3493F281), status),
|
|
|
|
|
status); /* B9 */
|
|
|
|
|
fp1 = floatx80_add(fp1, float64_to_floatx80(
|
|
|
|
|
make_float64(0x3EC71DE3A5774682), status),
|
|
|
|
|
status); /* B8 */
|
|
|
|
|
fp2 = floatx80_mul(fp2, fp0, status);
|
|
|
|
|
fp1 = floatx80_mul(fp1, fp0, status);
|
|
|
|
|
fp2 = floatx80_add(fp2, float64_to_floatx80(
|
|
|
|
|
make_float64(0x3EFA01A019D7CB68), status),
|
|
|
|
|
status); /* B7 */
|
|
|
|
|
fp1 = floatx80_add(fp1, float64_to_floatx80(
|
|
|
|
|
make_float64(0x3F2A01A01A019DF3), status),
|
|
|
|
|
status); /* B6 */
|
|
|
|
|
fp2 = floatx80_mul(fp2, fp0, status);
|
|
|
|
|
fp1 = floatx80_mul(fp1, fp0, status);
|
|
|
|
|
fp2 = floatx80_add(fp2, float64_to_floatx80(
|
|
|
|
|
make_float64(0x3F56C16C16C170E2), status),
|
|
|
|
|
status); /* B5 */
|
|
|
|
|
fp1 = floatx80_add(fp1, float64_to_floatx80(
|
|
|
|
|
make_float64(0x3F81111111111111), status),
|
|
|
|
|
status); /* B4 */
|
|
|
|
|
fp2 = floatx80_mul(fp2, fp0, status);
|
|
|
|
|
fp1 = floatx80_mul(fp1, fp0, status);
|
|
|
|
|
fp2 = floatx80_add(fp2, float64_to_floatx80(
|
|
|
|
|
make_float64(0x3FA5555555555555), status),
|
|
|
|
|
status); /* B3 */
|
|
|
|
|
fp3 = packFloatx80(0, 0x3FFC, LIT64(0xAAAAAAAAAAAAAAAB));
|
|
|
|
|
fp1 = floatx80_add(fp1, fp3, status); /* B2 */
|
|
|
|
|
fp2 = floatx80_mul(fp2, fp0, status);
|
|
|
|
|
fp1 = floatx80_mul(fp1, fp0, status);
|
|
|
|
|
|
|
|
|
|
fp2 = floatx80_mul(fp2, fp0, status);
|
|
|
|
|
fp1 = floatx80_mul(fp1, a, status);
|
|
|
|
|
|
|
|
|
|
fp0 = floatx80_mul(fp0, float32_to_floatx80(
|
|
|
|
|
make_float32(0x3F000000), status),
|
|
|
|
|
status); /* S*B1 */
|
|
|
|
|
fp1 = floatx80_add(fp1, fp2, status); /* Q */
|
|
|
|
|
fp0 = floatx80_add(fp0, fp1, status); /* S*B1+Q */
|
|
|
|
|
|
|
|
|
|
status->float_rounding_mode = user_rnd_mode;
|
|
|
|
|
status->floatx80_rounding_precision = user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
a = floatx80_add(fp0, a, status);
|
|
|
|
|
|
|
|
|
|
float_raise(float_flag_inexact, status);
|
|
|
|
|
|
|
|
|
|
return a;
|
|
|
|
|
} else { /* |X| < 2^(-65) */
|
|
|
|
|
sc = packFloatx80(1, 1, one_sig);
|
|
|
|
|
fp0 = a;
|
|
|
|
|
|
|
|
|
|
if (aExp < 0x0033) { /* |X| < 2^(-16382) */
|
|
|
|
|
fp0 = floatx80_mul(fp0, float64_to_floatx80(
|
|
|
|
|
make_float64(0x48B0000000000000), status),
|
|
|
|
|
status);
|
|
|
|
|
fp0 = floatx80_add(fp0, sc, status);
|
|
|
|
|
|
|
|
|
|
status->float_rounding_mode = user_rnd_mode;
|
|
|
|
|
status->floatx80_rounding_precision = user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
a = floatx80_mul(fp0, float64_to_floatx80(
|
|
|
|
|
make_float64(0x3730000000000000), status),
|
|
|
|
|
status);
|
|
|
|
|
} else {
|
|
|
|
|
status->float_rounding_mode = user_rnd_mode;
|
|
|
|
|
status->floatx80_rounding_precision = user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
a = floatx80_add(fp0, sc, status);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
float_raise(float_flag_inexact, status);
|
|
|
|
|
|
|
|
|
|
return a;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
/*----------------------------------------------------------------------------
|
|
|
|
|
| Hyperbolic tangent
|
|
|
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
|
|
|
|
|
|
floatx80 floatx80_tanh(floatx80 a, float_status *status)
|
|
|
|
|
{
|
|
|
|
|
flag aSign, vSign;
|
|
|
|
|
int32_t aExp, vExp;
|
|
|
|
|
uint64_t aSig, vSig;
|
|
|
|
|
|
|
|
|
|
int8_t user_rnd_mode, user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
int32_t compact;
|
|
|
|
|
floatx80 fp0, fp1;
|
|
|
|
|
uint32_t sign;
|
|
|
|
|
|
|
|
|
|
aSig = extractFloatx80Frac(a);
|
|
|
|
|
aExp = extractFloatx80Exp(a);
|
|
|
|
|
aSign = extractFloatx80Sign(a);
|
|
|
|
|
|
|
|
|
|
if (aExp == 0x7FFF) {
|
|
|
|
|
if ((uint64_t) (aSig << 1)) {
|
|
|
|
|
return propagateFloatx80NaNOneArg(a, status);
|
|
|
|
|
}
|
|
|
|
|
return packFloatx80(aSign, one_exp, one_sig);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
if (aExp == 0 && aSig == 0) {
|
|
|
|
|
return packFloatx80(aSign, 0, 0);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
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 < 0x3FD78000 || compact > 0x3FFFDDCE) {
|
|
|
|
|
/* TANHBORS */
|
|
|
|
|
if (compact < 0x3FFF8000) {
|
|
|
|
|
/* TANHSM */
|
|
|
|
|
status->float_rounding_mode = user_rnd_mode;
|
|
|
|
|
status->floatx80_rounding_precision = user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
a = floatx80_move(a, status);
|
|
|
|
|
|
|
|
|
|
float_raise(float_flag_inexact, status);
|
|
|
|
|
|
|
|
|
|
return a;
|
|
|
|
|
} else {
|
|
|
|
|
if (compact > 0x40048AA1) {
|
|
|
|
|
/* TANHHUGE */
|
|
|
|
|
sign = 0x3F800000;
|
|
|
|
|
sign |= aSign ? 0x80000000 : 0x00000000;
|
|
|
|
|
fp0 = float32_to_floatx80(make_float32(sign), status);
|
|
|
|
|
sign &= 0x80000000;
|
|
|
|
|
sign ^= 0x80800000; /* -SIGN(X)*EPS */
|
|
|
|
|
|
|
|
|
|
status->float_rounding_mode = user_rnd_mode;
|
|
|
|
|
status->floatx80_rounding_precision = user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
a = floatx80_add(fp0, float32_to_floatx80(make_float32(sign),
|
|
|
|
|
status), status);
|
|
|
|
|
|
|
|
|
|
float_raise(float_flag_inexact, status);
|
|
|
|
|
|
|
|
|
|
return a;
|
|
|
|
|
} else {
|
|
|
|
|
fp0 = packFloatx80(0, aExp + 1, aSig); /* Y = 2|X| */
|
|
|
|
|
fp0 = floatx80_etox(fp0, status); /* FP0 IS EXP(Y) */
|
|
|
|
|
fp0 = floatx80_add(fp0, float32_to_floatx80(
|
|
|
|
|
make_float32(0x3F800000),
|
|
|
|
|
status), status); /* EXP(Y)+1 */
|
|
|
|
|
sign = aSign ? 0x80000000 : 0x00000000;
|
|
|
|
|
fp1 = floatx80_div(float32_to_floatx80(make_float32(
|
|
|
|
|
sign ^ 0xC0000000), status), fp0,
|
|
|
|
|
status); /* -SIGN(X)*2 / [EXP(Y)+1] */
|
|
|
|
|
fp0 = float32_to_floatx80(make_float32(sign | 0x3F800000),
|
|
|
|
|
status); /* SIGN */
|
|
|
|
|
|
|
|
|
|
status->float_rounding_mode = user_rnd_mode;
|
|
|
|
|
status->floatx80_rounding_precision = user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
a = floatx80_add(fp1, fp0, status);
|
|
|
|
|
|
|
|
|
|
float_raise(float_flag_inexact, status);
|
|
|
|
|
|
|
|
|
|
return a;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
} else { /* 2**(-40) < |X| < (5/2)LOG2 */
|
|
|
|
|
fp0 = packFloatx80(0, aExp + 1, aSig); /* Y = 2|X| */
|
|
|
|
|
fp0 = floatx80_etoxm1(fp0, status); /* FP0 IS Z = EXPM1(Y) */
|
|
|
|
|
fp1 = floatx80_add(fp0, float32_to_floatx80(make_float32(0x40000000),
|
|
|
|
|
status),
|
|
|
|
|
status); /* Z+2 */
|
|
|
|
|
|
|
|
|
|
vSign = extractFloatx80Sign(fp1);
|
|
|
|
|
vExp = extractFloatx80Exp(fp1);
|
|
|
|
|
vSig = extractFloatx80Frac(fp1);
|
|
|
|
|
|
|
|
|
|
fp1 = packFloatx80(vSign ^ aSign, vExp, vSig);
|
|
|
|
|
|
|
|
|
|
status->float_rounding_mode = user_rnd_mode;
|
|
|
|
|
status->floatx80_rounding_precision = user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
a = floatx80_div(fp0, fp1, status);
|
|
|
|
|
|
|
|
|
|
float_raise(float_flag_inexact, status);
|
|
|
|
|
|
|
|
|
|
return a;
|
|
|
|
|
}
|
|
|
|
|
}
|
2018-03-12 21:27:27 +01:00
|
|
|
|
|
|
|
|
/*----------------------------------------------------------------------------
|
|
|
|
|
| Hyperbolic sine
|
|
|
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
|
|
|
|
|
|
floatx80 floatx80_sinh(floatx80 a, float_status *status)
|
|
|
|
|
{
|
|
|
|
|
flag aSign;
|
|
|
|
|
int32_t aExp;
|
|
|
|
|
uint64_t aSig;
|
|
|
|
|
|
|
|
|
|
int8_t user_rnd_mode, user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
int32_t compact;
|
|
|
|
|
floatx80 fp0, fp1, fp2;
|
|
|
|
|
float32 fact;
|
|
|
|
|
|
|
|
|
|
aSig = extractFloatx80Frac(a);
|
|
|
|
|
aExp = extractFloatx80Exp(a);
|
|
|
|
|
aSign = extractFloatx80Sign(a);
|
|
|
|
|
|
|
|
|
|
if (aExp == 0x7FFF) {
|
|
|
|
|
if ((uint64_t) (aSig << 1)) {
|
|
|
|
|
return propagateFloatx80NaNOneArg(a, status);
|
|
|
|
|
}
|
|
|
|
|
return packFloatx80(aSign, floatx80_infinity.high,
|
|
|
|
|
floatx80_infinity.low);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
if (aExp == 0 && aSig == 0) {
|
|
|
|
|
return packFloatx80(aSign, 0, 0);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
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 > 0x400CB167) {
|
|
|
|
|
/* SINHBIG */
|
|
|
|
|
if (compact > 0x400CB2B3) {
|
|
|
|
|
status->float_rounding_mode = user_rnd_mode;
|
|
|
|
|
status->floatx80_rounding_precision = user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
return roundAndPackFloatx80(status->floatx80_rounding_precision,
|
|
|
|
|
aSign, 0x8000, aSig, 0, status);
|
|
|
|
|
} else {
|
|
|
|
|
fp0 = floatx80_abs(a); /* Y = |X| */
|
|
|
|
|
fp0 = floatx80_sub(fp0, float64_to_floatx80(
|
|
|
|
|
make_float64(0x40C62D38D3D64634), status),
|
|
|
|
|
status); /* (|X|-16381LOG2_LEAD) */
|
|
|
|
|
fp0 = floatx80_sub(fp0, float64_to_floatx80(
|
|
|
|
|
make_float64(0x3D6F90AEB1E75CC7), status),
|
|
|
|
|
status); /* |X| - 16381 LOG2, ACCURATE */
|
|
|
|
|
fp0 = floatx80_etox(fp0, status);
|
|
|
|
|
fp2 = packFloatx80(aSign, 0x7FFB, one_sig);
|
|
|
|
|
|
|
|
|
|
status->float_rounding_mode = user_rnd_mode;
|
|
|
|
|
status->floatx80_rounding_precision = user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
a = floatx80_mul(fp0, fp2, status);
|
|
|
|
|
|
|
|
|
|
float_raise(float_flag_inexact, status);
|
|
|
|
|
|
|
|
|
|
return a;
|
|
|
|
|
}
|
|
|
|
|
} else { /* |X| < 16380 LOG2 */
|
|
|
|
|
fp0 = floatx80_abs(a); /* Y = |X| */
|
|
|
|
|
fp0 = floatx80_etoxm1(fp0, status); /* FP0 IS Z = EXPM1(Y) */
|
|
|
|
|
fp1 = floatx80_add(fp0, float32_to_floatx80(make_float32(0x3F800000),
|
|
|
|
|
status), status); /* 1+Z */
|
|
|
|
|
fp2 = fp0;
|
|
|
|
|
fp0 = floatx80_div(fp0, fp1, status); /* Z/(1+Z) */
|
|
|
|
|
fp0 = floatx80_add(fp0, fp2, status);
|
|
|
|
|
|
|
|
|
|
fact = packFloat32(aSign, 0x7E, 0);
|
|
|
|
|
|
|
|
|
|
status->float_rounding_mode = user_rnd_mode;
|
|
|
|
|
status->floatx80_rounding_precision = user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
a = floatx80_mul(fp0, float32_to_floatx80(fact, status), status);
|
|
|
|
|
|
|
|
|
|
float_raise(float_flag_inexact, status);
|
|
|
|
|
|
|
|
|
|
return a;
|
|
|
|
|
}
|
|
|
|
|
}
|
2018-03-12 21:27:28 +01:00
|
|
|
|
|
|
|
|
/*----------------------------------------------------------------------------
|
|
|
|
|
| Hyperbolic cosine
|
|
|
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
|
|
|
|
|
|
floatx80 floatx80_cosh(floatx80 a, float_status *status)
|
|
|
|
|
{
|
|
|
|
|
int32_t aExp;
|
|
|
|
|
uint64_t aSig;
|
|
|
|
|
|
|
|
|
|
int8_t user_rnd_mode, user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
int32_t compact;
|
|
|
|
|
floatx80 fp0, fp1;
|
|
|
|
|
|
|
|
|
|
aSig = extractFloatx80Frac(a);
|
|
|
|
|
aExp = extractFloatx80Exp(a);
|
|
|
|
|
|
|
|
|
|
if (aExp == 0x7FFF) {
|
|
|
|
|
if ((uint64_t) (aSig << 1)) {
|
|
|
|
|
return propagateFloatx80NaNOneArg(a, status);
|
|
|
|
|
}
|
|
|
|
|
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;
|
|
|
|
|
|
|
|
|
|
compact = floatx80_make_compact(aExp, aSig);
|
|
|
|
|
|
|
|
|
|
if (compact > 0x400CB167) {
|
|
|
|
|
if (compact > 0x400CB2B3) {
|
|
|
|
|
status->float_rounding_mode = user_rnd_mode;
|
|
|
|
|
status->floatx80_rounding_precision = user_rnd_prec;
|
|
|
|
|
return roundAndPackFloatx80(status->floatx80_rounding_precision, 0,
|
|
|
|
|
0x8000, one_sig, 0, status);
|
|
|
|
|
} else {
|
|
|
|
|
fp0 = packFloatx80(0, aExp, aSig);
|
|
|
|
|
fp0 = floatx80_sub(fp0, float64_to_floatx80(
|
|
|
|
|
make_float64(0x40C62D38D3D64634), status),
|
|
|
|
|
status);
|
|
|
|
|
fp0 = floatx80_sub(fp0, float64_to_floatx80(
|
|
|
|
|
make_float64(0x3D6F90AEB1E75CC7), status),
|
|
|
|
|
status);
|
|
|
|
|
fp0 = floatx80_etox(fp0, status);
|
|
|
|
|
fp1 = packFloatx80(0, 0x7FFB, one_sig);
|
|
|
|
|
|
|
|
|
|
status->float_rounding_mode = user_rnd_mode;
|
|
|
|
|
status->floatx80_rounding_precision = user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
a = floatx80_mul(fp0, fp1, status);
|
|
|
|
|
|
|
|
|
|
float_raise(float_flag_inexact, status);
|
|
|
|
|
|
|
|
|
|
return a;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
fp0 = packFloatx80(0, aExp, aSig); /* |X| */
|
|
|
|
|
fp0 = floatx80_etox(fp0, status); /* EXP(|X|) */
|
|
|
|
|
fp0 = floatx80_mul(fp0, float32_to_floatx80(make_float32(0x3F000000),
|
|
|
|
|
status), status); /* (1/2)*EXP(|X|) */
|
|
|
|
|
fp1 = float32_to_floatx80(make_float32(0x3E800000), status); /* 1/4 */
|
|
|
|
|
fp1 = floatx80_div(fp1, fp0, status); /* 1/(2*EXP(|X|)) */
|
|
|
|
|
|
|
|
|
|
status->float_rounding_mode = user_rnd_mode;
|
|
|
|
|
status->floatx80_rounding_precision = user_rnd_prec;
|
|
|
|
|
|
|
|
|
|
a = floatx80_add(fp0, fp1, status);
|
|
|
|
|
|
|
|
|
|
float_raise(float_flag_inexact, status);
|
|
|
|
|
|
|
|
|
|
return a;
|
|
|
|
|
}
|
