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qemu / qemu / f1dfab0d9b77b8649d60ded3d96870f88d0baccd / . / target / m68k / softfloat.c
blob: b6d0ed7acfe8dd122e052d2ea9348e9ef0f750fe [file] [log] [blame]
/*
* Ported from a work by Andreas Grabher for Previous, NeXT Computer Emulator,
* derived from NetBSD M68040 FPSP functions,
* derived from release 2a of the SoftFloat IEC/IEEE Floating-point Arithmetic
* Package. Those parts of the code (and some later contributions) are
* provided under that license, as detailed below.
* It has subsequently been modified by contributors to the QEMU Project,
* so some portions are provided under:
* the SoftFloat-2a license
* the BSD license
* GPL-v2-or-later
*
* Any future contributions to this file will be taken to be licensed under
* the Softfloat-2a license unless specifically indicated otherwise.
*/
/*
* Portions of this work are licensed under the terms of the GNU GPL,
* version 2 or later. See the COPYING file in the top-level directory.
*/
#include "qemu/osdep.h"
#include "softfloat.h"
#include "fpu/softfloat-macros.h"
#include "softfloat_fpsp_tables.h"
#define pi_exp 0x4000
#define piby2_exp 0x3FFF
#define pi_sig UINT64_C(0xc90fdaa22168c235)
static floatx80 propagateFloatx80NaNOneArg(floatx80 a, float_status *status)
{
if (floatx80_is_signaling_nan(a, status)) {
float_raise(float_flag_invalid, status);
a = floatx80_silence_nan(a, status);
}
if (status->default_nan_mode) {
return floatx80_default_nan(status);
}
return a;
}
/*
* Returns the mantissa of the extended double-precision floating-point
* value `a'.
*/
floatx80 floatx80_getman(floatx80 a, float_status *status)
{
bool 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)
{
bool 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)
{
bool aSign, bSign;
int32_t aExp, bExp, shiftCount;
uint64_t aSig, bSig;
aSig = extractFloatx80Frac(a);
aExp = extractFloatx80Exp(a);
aSign = extractFloatx80Sign(a);
bSig = extractFloatx80Frac(b);
bExp = extractFloatx80Exp(b);
bSign = extractFloatx80Sign(b);
if (bExp == 0x7FFF) {
if ((uint64_t) (bSig << 1) ||
((aExp == 0x7FFF) && (uint64_t) (aSig << 1))) {
return propagateFloatx80NaN(a, b, status);
}
float_raise(float_flag_invalid , status);
return floatx80_default_nan(status);
}
if (aExp == 0x7FFF) {
if ((uint64_t) (aSig << 1)) {
return propagateFloatx80NaN(a, b, status);
}
return packFloatx80(aSign, floatx80_infinity.high,
floatx80_infinity.low);
}
if (aExp == 0) {
if (aSig == 0) {
return packFloatx80(aSign, 0, 0);
}
if (bExp < 0x3FFF) {
return a;
}
normalizeFloatx80Subnormal(aSig, &aExp, &aSig);
}
if (bExp < 0x3FFF) {
return a;
}
if (0x400F < bExp) {
aExp = bSign ? -0x6001 : 0xE000;
return roundAndPackFloatx80(status->floatx80_rounding_precision,
aSign, aExp, aSig, 0, status);
}
shiftCount = 0x403E - bExp;
bSig >>= shiftCount;
aExp = bSign ? (aExp - bSig) : (aExp + bSig);
return roundAndPackFloatx80(status->floatx80_rounding_precision,
aSign, aExp, aSig, 0, status);
}
floatx80 floatx80_move(floatx80 a, float_status *status)
{
bool aSign;
int32_t aExp;
uint64_t aSig;
aSig = extractFloatx80Frac(a);
aExp = extractFloatx80Exp(a);
aSign = extractFloatx80Sign(a);
if (aExp == 0x7FFF) {
if ((uint64_t)(aSig << 1)) {
return propagateFloatx80NaNOneArg(a, status);
}
return a;
}
if (aExp == 0) {
if (aSig == 0) {
return a;
}
normalizeRoundAndPackFloatx80(status->floatx80_rounding_precision,
aSign, aExp, aSig, 0, status);
}
return roundAndPackFloatx80(status->floatx80_rounding_precision, aSign,
aExp, aSig, 0, status);
}
/*
* Algorithms for transcendental functions supported by MC68881 and MC68882
* mathematical coprocessors. The functions are derived from FPSP library.
*/
#define one_exp 0x3FFF
#define one_sig UINT64_C(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)
{
bool 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);
return packFloatx80(aSign, floatx80_infinity.high,
floatx80_infinity.low);
}
float_raise(float_flag_invalid, status);
return floatx80_default_nan(status);
}
if (aExp < 0x3f99 || (aExp == 0x3f99 && aSig == one_sig)) {
/* <= min threshold */
float_raise(float_flag_inexact, status);
return floatx80_move(a, status);
}
user_rnd_mode = status->float_rounding_mode;
user_rnd_prec = status->floatx80_rounding_precision;
status->float_rounding_mode = float_round_nearest_even;
status->floatx80_rounding_precision = 80;
compact = floatx80_make_compact(aExp, aSig);
fp0 = a; /* Z */
fp1 = a;
fp0 = floatx80_add(fp0, float32_to_floatx80(make_float32(0x3F800000),
status), status); /* X = (1+Z) */
aExp = extractFloatx80Exp(fp0);
aSig = extractFloatx80Frac(fp0);
compact = floatx80_make_compact(aExp, aSig);
if (compact < 0x3FFE8000 || compact > 0x3FFFC000) {
/* |X| < 1/2 or |X| > 3/2 */
k = aExp - 0x3FFF;
fp1 = int32_to_floatx80(k, status);
fSig = (aSig & UINT64_C(0xFE00000000000000)) | UINT64_C(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, UINT64_C(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 & UINT64_C(0xFE00000000000000)) | UINT64_C(0x0100000000000000);
f = packFloatx80(0, 0x3FFF, fSig); /* F */
j = (fSig >> 56) & 0x7E; /* DISPLACEMENT FOR 1/F */
if (compact >= 0x3FFF8000) { /* 1+Z >= 1 */
/* KISZERO */
fp0 = floatx80_sub(float32_to_floatx80(make_float32(0x3F800000),
status), f, status); /* 1-F */
fp0 = floatx80_add(fp0, fp1, status); /* FP0 IS Y-F = (1-F)+Z */
fp1 = packFloatx80(0, 0, 0); /* K = 0 */
} else {
/* KISNEG */
fp0 = floatx80_sub(float32_to_floatx80(make_float32(0x40000000),
status), f, status); /* 2-F */
fp1 = floatx80_add(fp1, fp1, status); /* 2Z */
fp0 = floatx80_add(fp0, fp1, status); /* FP0 IS Y-F = (2-F)+2Z */
fp1 = packFloatx80(1, one_exp, one_sig); /* K = -1 */
}
goto lp1cont1;
} else {
/* LP1ONE16 */
fp1 = floatx80_add(fp1, fp1, status); /* FP1 IS 2Z */
fp0 = floatx80_add(fp0, float32_to_floatx80(make_float32(0x3F800000),
status), status); /* FP0 IS 1+X */
/* LP1CONT2 */
fp1 = floatx80_div(fp1, fp0, status); /* U */
saveu = fp1;
fp0 = floatx80_mul(fp1, fp1, status); /* FP0 IS V = U*U */
fp1 = floatx80_mul(fp0, fp0, status); /* FP1 IS W = V*V */
fp3 = float64_to_floatx80(make_float64(0x3F175496ADD7DAD6),
status); /* B5 */
fp2 = float64_to_floatx80(make_float64(0x3F3C71C2FE80C7E0),
status); /* B4 */
fp3 = floatx80_mul(fp3, fp1, status); /* W*B5 */
fp2 = floatx80_mul(fp2, fp1, status); /* W*B4 */
fp3 = floatx80_add(fp3, float64_to_floatx80(
make_float64(0x3F624924928BCCFF), status),
status); /* B3+W*B5 */
fp2 = floatx80_add(fp2, float64_to_floatx80(
make_float64(0x3F899999999995EC), status),
status); /* B2+W*B4 */
fp1 = floatx80_mul(fp1, fp3, status); /* W*(B3+W*B5) */
fp2 = floatx80_mul(fp2, fp0, status); /* V*(B2+W*B4) */
fp1 = floatx80_add(fp1, float64_to_floatx80(
make_float64(0x3FB5555555555555), status),
status); /* B1+W*(B3+W*B5) */
fp0 = floatx80_mul(fp0, saveu, status); /* FP0 IS U*V */
fp1 = floatx80_add(fp1, fp2,
status); /* B1+W*(B3+W*B5) + V*(B2+W*B4) */
fp0 = floatx80_mul(fp0, fp1,
status); /* U*V*([B1+W*(B3+W*B5)] + [V*(B2+W*B4)]) */
status->float_rounding_mode = user_rnd_mode;
status->floatx80_rounding_precision = user_rnd_prec;
a = floatx80_add(fp0, saveu, status);
/*if (!floatx80_is_zero(a)) { */
float_raise(float_flag_inexact, status);
/*} */
return a;
}
}
/*
* Log base e
*/
floatx80 floatx80_logn(floatx80 a, float_status *status)
{
bool 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 & UINT64_C(0xFE00000000000000)) | UINT64_C(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, UINT64_C(0xB17217F7D1CF79AC));
klog2 = floatx80_mul(fp1, logof2, status); /* FP1 IS K*LOG2 */
fp2 = floatx80_mul(fp0, fp0, status); /* FP2 IS V=U*U */
fp3 = fp2;
fp1 = fp2;
fp1 = floatx80_mul(fp1, float64_to_floatx80(
make_float64(0x3FC2499AB5E4040B), status),
status); /* V*A6 */
fp2 = floatx80_mul(fp2, float64_to_floatx80(
make_float64(0xBFC555B5848CB7DB), status),
status); /* V*A5 */
fp1 = floatx80_add(fp1, float64_to_floatx80(
make_float64(0x3FC99999987D8730), status),
status); /* A4+V*A6 */
fp2 = floatx80_add(fp2, float64_to_floatx80(
make_float64(0xBFCFFFFFFF6F7E97), status),
status); /* A3+V*A5 */
fp1 = floatx80_mul(fp1, fp3, status); /* V*(A4+V*A6) */
fp2 = floatx80_mul(fp2, fp3, status); /* V*(A3+V*A5) */
fp1 = floatx80_add(fp1, float64_to_floatx80(
make_float64(0x3FD55555555555A4), status),
status); /* A2+V*(A4+V*A6) */
fp2 = floatx80_add(fp2, float64_to_floatx80(
make_float64(0xBFE0000000000008), status),
status); /* A1+V*(A3+V*A5) */
fp1 = floatx80_mul(fp1, fp3, status); /* V*(A2+V*(A4+V*A6)) */
fp2 = floatx80_mul(fp2, fp3, status); /* V*(A1+V*(A3+V*A5)) */
fp1 = floatx80_mul(fp1, fp0, status); /* U*V*(A2+V*(A4+V*A6)) */
fp0 = floatx80_add(fp0, fp2, status); /* U+V*(A1+V*(A3+V*A5)) */
fp1 = floatx80_add(fp1, log_tbl[j + 1],
status); /* LOG(F)+U*V*(A2+V*(A4+V*A6)) */
fp0 = floatx80_add(fp0, fp1, status); /* FP0 IS LOG(F) + LOG(1+U) */
status->float_rounding_mode = user_rnd_mode;
status->floatx80_rounding_precision = user_rnd_prec;
a = floatx80_add(fp0, klog2, status);
float_raise(float_flag_inexact, status);
return a;
} else { /* |X-1| >= 1/16 */
fp0 = a;
fp1 = a;
fp1 = floatx80_sub(fp1, float32_to_floatx80(make_float32(0x3F800000),
status), status); /* FP1 IS X-1 */
fp0 = floatx80_add(fp0, float32_to_floatx80(make_float32(0x3F800000),
status), status); /* FP0 IS X+1 */
fp1 = floatx80_add(fp1, fp1, status); /* FP1 IS 2(X-1) */
/* LP1CONT2 */
fp1 = floatx80_div(fp1, fp0, status); /* U */
saveu = fp1;
fp0 = floatx80_mul(fp1, fp1, status); /* FP0 IS V = U*U */
fp1 = floatx80_mul(fp0, fp0, status); /* FP1 IS W = V*V */
fp3 = float64_to_floatx80(make_float64(0x3F175496ADD7DAD6),
status); /* B5 */
fp2 = float64_to_floatx80(make_float64(0x3F3C71C2FE80C7E0),
status); /* B4 */
fp3 = floatx80_mul(fp3, fp1, status); /* W*B5 */
fp2 = floatx80_mul(fp2, fp1, status); /* W*B4 */
fp3 = floatx80_add(fp3, float64_to_floatx80(
make_float64(0x3F624924928BCCFF), status),
status); /* B3+W*B5 */
fp2 = floatx80_add(fp2, float64_to_floatx80(
make_float64(0x3F899999999995EC), status),
status); /* B2+W*B4 */
fp1 = floatx80_mul(fp1, fp3, status); /* W*(B3+W*B5) */
fp2 = floatx80_mul(fp2, fp0, status); /* V*(B2+W*B4) */
fp1 = floatx80_add(fp1, float64_to_floatx80(
make_float64(0x3FB5555555555555), status),
status); /* B1+W*(B3+W*B5) */
fp0 = floatx80_mul(fp0, saveu, status); /* FP0 IS U*V */
fp1 = floatx80_add(fp1, fp2, status); /* B1+W*(B3+W*B5) + V*(B2+W*B4) */
fp0 = floatx80_mul(fp0, fp1,
status); /* U*V*([B1+W*(B3+W*B5)] + [V*(B2+W*B4)]) */
status->float_rounding_mode = user_rnd_mode;
status->floatx80_rounding_precision = user_rnd_prec;
a = floatx80_add(fp0, saveu, status);
/*if (!floatx80_is_zero(a)) { */
float_raise(float_flag_inexact, status);
/*} */
return a;
}
}
/*
* Log base 10
*/
floatx80 floatx80_log10(floatx80 a, float_status *status)
{
bool 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, UINT64_C(0xDE5BD8A937287195)); /* INV_L10 */
status->float_rounding_mode = user_rnd_mode;
status->floatx80_rounding_precision = user_rnd_prec;
a = floatx80_mul(fp0, fp1, status); /* LOGN(X)*INV_L10 */
float_raise(float_flag_inexact, status);
return a;
}
/*
* Log base 2
*/
floatx80 floatx80_log2(floatx80 a, float_status *status)
{
bool 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, UINT64_C(0xB8AA3B295C17F0BC)); /* INV_L2 */
status->float_rounding_mode = user_rnd_mode;
status->floatx80_rounding_precision = user_rnd_prec;
a = floatx80_mul(fp0, fp1, status); /* LOGN(X)*INV_L2 */
}
float_raise(float_flag_inexact, status);
return a;
}
/*
* e to x
*/
floatx80 floatx80_etox(floatx80 a, float_status *status)
{
bool 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;
bool 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, UINT64_C(0x82E308654361C4C6));
fp2 = floatx80_mul(fp2, l2, status); /* N * L2, L1+L2 = -log2/64 */
fp0 = floatx80_add(fp0, fp1, status); /* X + N*L1 */
fp0 = floatx80_add(fp0, fp2, status); /* R */
fp1 = floatx80_mul(fp0, fp0, status); /* S = R*R */
fp2 = float32_to_floatx80(make_float32(0x3AB60B70),
status); /* A5 */
fp2 = floatx80_mul(fp2, fp1, status); /* fp2 is S*A5 */
fp3 = floatx80_mul(float32_to_floatx80(make_float32(0x3C088895),
status), fp1,
status); /* fp3 is S*A4 */
fp2 = floatx80_add(fp2, float64_to_floatx80(make_float64(
0x3FA5555555554431), status),
status); /* fp2 is A3+S*A5 */
fp3 = floatx80_add(fp3, float64_to_floatx80(make_float64(
0x3FC5555555554018), status),
status); /* fp3 is A2+S*A4 */
fp2 = floatx80_mul(fp2, fp1, status); /* fp2 is S*(A3+S*A5) */
fp3 = floatx80_mul(fp3, fp1, status); /* fp3 is S*(A2+S*A4) */
fp2 = floatx80_add(fp2, float32_to_floatx80(
make_float32(0x3F000000), status),
status); /* fp2 is A1+S*(A3+S*A5) */
fp3 = floatx80_mul(fp3, fp0, status); /* fp3 IS R*S*(A2+S*A4) */
fp2 = floatx80_mul(fp2, fp1,
status); /* fp2 IS S*(A1+S*(A3+S*A5)) */
fp0 = floatx80_add(fp0, fp3, status); /* fp0 IS R+R*S*(A2+S*A4) */
fp0 = floatx80_add(fp0, fp2, status); /* fp0 IS EXP(R) - 1 */
fp1 = exp_tbl[j];
fp0 = floatx80_mul(fp0, fp1, status); /* 2^(J/64)*(Exp(R)-1) */
fp0 = floatx80_add(fp0, float32_to_floatx80(exp_tbl2[j], status),
status); /* accurate 2^(J/64) */
fp0 = floatx80_add(fp0, fp1,
status); /* 2^(J/64) + 2^(J/64)*(Exp(R)-1) */
scale = packFloatx80(0, m, one_sig);
if (adjflag) {
adjscale = packFloatx80(0, m1, one_sig);
fp0 = floatx80_mul(fp0, adjscale, status);
}
status->float_rounding_mode = user_rnd_mode;
status->floatx80_rounding_precision = user_rnd_prec;
a = floatx80_mul(fp0, scale, status);
float_raise(float_flag_inexact, status);
return a;
} else { /* |X| >= 16380 log2 */
if (compact > 0x400CB27C) { /* |X| >= 16480 log2 */
status->float_rounding_mode = user_rnd_mode;
status->floatx80_rounding_precision = user_rnd_prec;
if (aSign) {
a = roundAndPackFloatx80(
status->floatx80_rounding_precision,
0, -0x1000, aSig, 0, status);
} else {
a = roundAndPackFloatx80(
status->floatx80_rounding_precision,
0, 0x8000, aSig, 0, status);
}
float_raise(float_flag_inexact, status);
return a;
} else {
fp0 = a;
fp1 = a;
fp0 = floatx80_mul(fp0, float32_to_floatx80(
make_float32(0x42B8AA3B), status),
status); /* 64/log2 * X */
adjflag = 1;
n = floatx80_to_int32(fp0, status); /* int(64/log2*X) */
fp0 = int32_to_floatx80(n, status);
j = n & 0x3F; /* J = N mod 64 */
/* NOTE: this is really arithmetic right shift by 6 */
k = n / 64;
if (n < 0 && j) {
/* arithmetic right shift is division and
* round towards minus infinity
*/
k--;
}
/* NOTE: this is really arithmetic right shift by 1 */
m1 = k / 2;
if (k < 0 && (k & 1)) {
/* arithmetic right shift is division and
* round towards minus infinity
*/
m1--;
}
m = k - m1;
m1 += 0x3FFF; /* biased exponent of 2^(M1) */
m += 0x3FFF; /* biased exponent of 2^(M) */
goto expcont1;
}
}
} else { /* |X| < 2^(-65) */
status->float_rounding_mode = user_rnd_mode;
status->floatx80_rounding_precision = user_rnd_prec;
a = floatx80_add(a, float32_to_floatx80(make_float32(0x3F800000),
status), status); /* 1 + X */
float_raise(float_flag_inexact, status);
return a;
}
}
/*
* 2 to x
*/
floatx80 floatx80_twotox(floatx80 a, float_status *status)
{
bool 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, UINT64_C(0xB17217F7D1CF79AC)); /* LOG2 */
fp0 = floatx80_mul(fp0, fp2, status); /* R */
/* EXPR */
fp1 = floatx80_mul(fp0, fp0, status); /* S = R*R */
fp2 = float64_to_floatx80(make_float64(0x3F56C16D6F7BD0B2),
status); /* A5 */
fp3 = float64_to_floatx80(make_float64(0x3F811112302C712C),
status); /* A4 */
fp2 = floatx80_mul(fp2, fp1, status); /* S*A5 */
fp3 = floatx80_mul(fp3, fp1, status); /* S*A4 */
fp2 = floatx80_add(fp2, float64_to_floatx80(
make_float64(0x3FA5555555554CC1), status),
status); /* A3+S*A5 */
fp3 = floatx80_add(fp3, float64_to_floatx80(
make_float64(0x3FC5555555554A54), status),
status); /* A2+S*A4 */
fp2 = floatx80_mul(fp2, fp1, status); /* S*(A3+S*A5) */
fp3 = floatx80_mul(fp3, fp1, status); /* S*(A2+S*A4) */
fp2 = floatx80_add(fp2, float64_to_floatx80(
make_float64(0x3FE0000000000000), status),
status); /* A1+S*(A3+S*A5) */
fp3 = floatx80_mul(fp3, fp0, status); /* R*S*(A2+S*A4) */
fp2 = floatx80_mul(fp2, fp1, status); /* S*(A1+S*(A3+S*A5)) */
fp0 = floatx80_add(fp0, fp3, status); /* R+R*S*(A2+S*A4) */
fp0 = floatx80_add(fp0, fp2, status); /* EXP(R) - 1 */
fp0 = floatx80_mul(fp0, fact1, status);
fp0 = floatx80_add(fp0, fact2, status);
fp0 = floatx80_add(fp0, fact1, status);
status->float_rounding_mode = user_rnd_mode;
status->floatx80_rounding_precision = user_rnd_prec;
a = floatx80_mul(fp0, adjfact, status);
float_raise(float_flag_inexact, status);
return a;
}
}
/*
* 10 to x
*/
floatx80 floatx80_tentox(floatx80 a, float_status *status)
{
bool 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, UINT64_C(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, UINT64_C(0x935D8DDDAAA8AC17)); /* LOG10 */
fp0 = floatx80_mul(fp0, fp2, status); /* R */
/* EXPR */
fp1 = floatx80_mul(fp0, fp0, status); /* S = R*R */
fp2 = float64_to_floatx80(make_float64(0x3F56C16D6F7BD0B2),
status); /* A5 */
fp3 = float64_to_floatx80(make_float64(0x3F811112302C712C),
status); /* A4 */
fp2 = floatx80_mul(fp2, fp1, status); /* S*A5 */
fp3 = floatx80_mul(fp3, fp1, status); /* S*A4 */
fp2 = floatx80_add(fp2, float64_to_floatx80(
make_float64(0x3FA5555555554CC1), status),
status); /* A3+S*A5 */
fp3 = floatx80_add(fp3, float64_to_floatx80(
make_float64(0x3FC5555555554A54), status),
status); /* A2+S*A4 */
fp2 = floatx80_mul(fp2, fp1, status); /* S*(A3+S*A5) */
fp3 = floatx80_mul(fp3, fp1, status); /* S*(A2+S*A4) */
fp2 = floatx80_add(fp2, float64_to_floatx80(
make_float64(0x3FE0000000000000), status),
status); /* A1+S*(A3+S*A5) */
fp3 = floatx80_mul(fp3, fp0, status); /* R*S*(A2+S*A4) */
fp2 = floatx80_mul(fp2, fp1, status); /* S*(A1+S*(A3+S*A5)) */
fp0 = floatx80_add(fp0, fp3, status); /* R+R*S*(A2+S*A4) */
fp0 = floatx80_add(fp0, fp2, status); /* EXP(R) - 1 */
fp0 = floatx80_mul(fp0, fact1, status);
fp0 = floatx80_add(fp0, fact2, status);
fp0 = floatx80_add(fp0, fact1, status);
status->float_rounding_mode = user_rnd_mode;
status->floatx80_rounding_precision = user_rnd_prec;
a = floatx80_mul(fp0, adjfact, status);
float_raise(float_flag_inexact, status);
return a;
}
}
/*
* Tangent
*/
floatx80 floatx80_tan(floatx80 a, float_status *status)
{
bool 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;
bool 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,
UINT64_C(0xC90FDAA200000000));
twopi2 = packFloatx80(aSign ^ 1, 0x7FDC,
UINT64_C(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 = true;
} else {
l = xExp - 27;
endflag = false;
}
invtwopi = packFloatx80(0, 0x3FFE - l,
UINT64_C(0xA2F9836E4E44152A)); /* INVTWOPI */
twopi1 = packFloatx80(0, 0x3FFF + l, UINT64_C(0xC90FDAA200000000));
twopi2 = packFloatx80(0, 0x3FDD + l, UINT64_C(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) {
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, UINT64_C(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, UINT64_C(0xD23CD68415D95FA1));
fp3 = floatx80_add(fp3, fp4, status); /* Q2+S(Q3+SQ4) */
fp4 = packFloatx80(1, 0x3FFC, UINT64_C(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, UINT64_C(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, UINT64_C(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, UINT64_C(0xD23CD68415D95FA1));
fp3 = floatx80_add(fp3, fp4, status); /* Q2+S(Q3+SQ4) */
fp4 = packFloatx80(1, 0x3FFC, UINT64_C(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, UINT64_C(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;
}
}
}
/*
* Sine
*/
floatx80 floatx80_sin(floatx80 a, float_status *status)
{
bool 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;
bool 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,
UINT64_C(0xC90FDAA200000000));
twopi2 = packFloatx80(aSign ^ 1, 0x7FDC,
UINT64_C(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 = true;
} else {
l = xExp - 27;
endflag = false;
}
invtwopi = packFloatx80(0, 0x3FFE - l,
UINT64_C(0xA2F9836E4E44152A)); /* INVTWOPI */
twopi1 = packFloatx80(0, 0x3FFF + l, UINT64_C(0xC90FDAA200000000));
twopi2 = packFloatx80(0, 0x3FDD + l, UINT64_C(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) {
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;
/* SINTINY */
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 */
sincont:
if (n & 1) {
/* 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);
if ((n >> 1) & 1) {
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, UINT64_C(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, UINT64_C(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);
xSign ^= (n >> 1) & 1; /* X IS NOW R'= SGN*R */
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, UINT64_C(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, UINT64_C(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;
}
}
}
/*
* Cosine
*/
floatx80 floatx80_cos(floatx80 a, float_status *status)
{
bool 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;
bool 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(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,
UINT64_C(0xC90FDAA200000000));
twopi2 = packFloatx80(aSign ^ 1, 0x7FDC,
UINT64_C(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 = true;
} else {
l = xExp - 27;
endflag = false;
}
invtwopi = packFloatx80(0, 0x3FFE - l,
UINT64_C(0xA2F9836E4E44152A)); /* INVTWOPI */
twopi1 = packFloatx80(0, 0x3FFF + l, UINT64_C(0xC90FDAA200000000));
twopi2 = packFloatx80(0, 0x3FDD + l, UINT64_C(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) {
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;
/* COSTINY */
a = floatx80_sub(fp0, float32_to_floatx80(
make_float32(0x00800000), status),
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 */
sincont:
if ((n + 1) & 1) {
/* 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);
if (((n + 1) >> 1) & 1) {
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, UINT64_C(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, UINT64_C(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);
xSign ^= ((n + 1) >> 1) & 1; /* X IS NOW R'= SGN*R */
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, UINT64_C(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, UINT64_C(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;
}
}
}
/*
* Arc tangent
*/
floatx80 floatx80_atan(floatx80 a, float_status *status)
{
bool 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 &= UINT64_C(0xF800000000000000);
aSig |= UINT64_C(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;
}
}
/*
* Arc sine
*/
floatx80 floatx80_asin(floatx80 a, float_status *status)
{
bool 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;
}
/*
* Arc cosine
*/
floatx80 floatx80_acos(floatx80 a, float_status *status)
{
bool 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;
}
/*
* Hyperbolic arc tangent
*/
floatx80 floatx80_atanh(floatx80 a, float_status *status)
{
bool 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;
}
/*
* e to x minus 1
*/
floatx80 floatx80_etoxm1(floatx80 a, float_status *status)
{
bool 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, UINT64_C(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, UINT64_C(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)
{
bool 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;
}
}
/*
* Hyperbolic sine
*/
floatx80 floatx80_sinh(floatx80 a, float_status *status)
{
bool 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;
}
}
/*
* 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;
}