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hatari 2.2.0
/*============================================================================
This C source file is an extension to the SoftFloat IEC/IEEE Floating-point
Arithmetic Package, Release 2a.
Written by Andreas Grabher for Previous, NeXT Computer Emulator.
=============================================================================*/
#include <stdint.h>
#include <stdlib.h>
#include "softfloat.h"
#include "softfloat-specialize.h"
#include "softfloat_fpsp_tables.h"
/*----------------------------------------------------------------------------
| Algorithms for transcendental functions supported by MC68881 and MC68882
| mathematical coprocessors. The functions are derived from FPSP library.
*----------------------------------------------------------------------------*/
#define pi_sig LIT64(0xc90fdaa22168c235)
#define pi_sig0 LIT64(0xc90fdaa22168c234)
#define pi_sig1 LIT64(0xc4c6628b80dc1cd1)
#define pi_exp 0x4000
#define piby2_exp 0x3FFF
#define piby4_exp 0x3FFE
#define one_exp 0x3FFF
#define one_sig LIT64(0x8000000000000000)
#define SET_PREC \
int8_t user_rnd_mode, user_rnd_prec; \
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
#define RESET_PREC \
status->float_rounding_mode = user_rnd_mode; \
status->floatx80_rounding_precision = user_rnd_prec
/*----------------------------------------------------------------------------
| 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);
}
/*----------------------------------------------------------------------------
| Arc cosine
*----------------------------------------------------------------------------*/
floatx80 floatx80_acos(floatx80 a, float_status *status)
{
flag aSign;
int32_t aExp;
uint64_t aSig;
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
SET_PREC;
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)))
RESET_PREC;
a = floatx80_add(fp0, fp0, status); // 2 * ATAN(SQRT((1-X)/(1+X)))
float_raise(float_flag_inexact, status);
return a;
}
/*----------------------------------------------------------------------------
| Arc sine
*----------------------------------------------------------------------------*/
floatx80 floatx80_asin(floatx80 a, float_status *status)
{
flag aSign;
int32_t aExp;
uint64_t aSig;
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
SET_PREC;
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))
RESET_PREC;
a = floatx80_atan(fp0, status); // ATAN(X/SQRT((1+X)*(1-X)))
float_raise(float_flag_inexact, status);
return a;
}
/*----------------------------------------------------------------------------
| Arc tangent
*----------------------------------------------------------------------------*/
floatx80 floatx80_atan(floatx80 a, float_status *status)
{
flag aSign;
int32_t aExp;
uint64_t aSig;
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);
SET_PREC;
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);
RESET_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(LIT64(0xBFB70BF398539E6A), status); // C5
fp2 = float64_to_floatx80(LIT64(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(LIT64(0xBFC24924827107B8), status), status); // C3+Z*C5
fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(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(LIT64(0xBFD5555555555536), status), status); // C1+Z*(C3+Z*C5)
fp0 = floatx80_mul(fp0, xsave, status); // X'*Y
fp1 = floatx80_add(fp1, fp2, status); // [Y*(C2+Z*C4)]+[C1+Z*(C3+Z*C5)]
fp0 = floatx80_mul(fp0, fp1, status); // X'*Y*([B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))]) ??
fp0 = floatx80_add(fp0, xsave, status);
fp1 = packFloatx80(aSign, piby2_exp, pi_sig);
RESET_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)
RESET_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(LIT64(0x3FB344447F876989), status); // B6
fp3 = float64_to_floatx80(LIT64(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(LIT64(0x3FBC71C646940220), status), status); // B4+Z*B6
fp3 = floatx80_add(fp3, float64_to_floatx80(LIT64(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(LIT64(0x3FC9999999998FA9), status), status); // B2+Z*(B4+Z*B6)
fp1 = floatx80_add(fp1, float64_to_floatx80(LIT64(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
fp1 = floatx80_add(fp1, fp2, status); // [B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))]
fp0 = floatx80_mul(fp0, fp1, status); // X*Y*([B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))])
RESET_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(LIT64(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(LIT64(0x4002AC6934A26DB3), status), status); // A2+V*(A3+V)
fp1 = floatx80_mul(fp1, float64_to_floatx80(LIT64(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)
RESET_PREC;
a = floatx80_add(fp0, fp3, status); // ATAN(X)
float_raise(float_flag_inexact, status);
return a;
}
}
/*----------------------------------------------------------------------------
| Hyperbolic arc tangent
*----------------------------------------------------------------------------*/
floatx80 floatx80_atanh(floatx80 a, float_status *status)
{
flag aSign;
int32_t aExp;
uint64_t aSig;
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, 0x7FFF, floatx80_default_infinity_low);
} else { // |X| > 1
float_raise(float_flag_invalid, status);
return floatx80_default_nan(status);
}
} // |X| < 1
SET_PREC;
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)
RESET_PREC;
a = floatx80_mul(fp0, fp2, status); // ATANH(X) = SIGN(X) * (1/2) * LOG1P(Z)
float_raise(float_flag_inexact, status);
return a;
}
/*----------------------------------------------------------------------------
| Cosine
*----------------------------------------------------------------------------*/
floatx80 floatx80_cos(floatx80 a, float_status *status)
{
flag aSign, xSign;
int32_t aExp, xExp;
uint64_t aSig, xSig;
int32_t compact, l, n, j;
floatx80 fp0, fp1, fp2, fp3, fp4, fp5, x, invtwopi, twopi1, twopi2;
float32 posneg1, twoto63;
flag adjn, 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);
}
adjn = 1;
SET_PREC;
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));
twoto63 = 0x5F000000;
twoto63 |= xSign ? 0x80000000 : 0x00000000; // SIGN(INARG)*2^63 IN SGL
fp2 = floatx80_mul(fp0, invtwopi, status);
fp2 = floatx80_add(fp2, float32_to_floatx80(twoto63, status), status); // THE FRACTIONAL 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(0x3F800000, status); // 1
RESET_PREC;
if (adjn) {
// COSTINY
a = floatx80_sub(fp0, float32_to_floatx80(0x00800000, status), status);
} else {
// SINTINY
a = floatx80_move(a, status);
}
float_raise(float_flag_inexact, status);
return a;
}
} else {
fp1 = floatx80_mul(fp0, float64_to_floatx80(LIT64(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 + adjn) & 1) {
// COSPOLY
fp0 = floatx80_mul(fp0, fp0, status); // FP0 IS S
fp1 = floatx80_mul(fp0, fp0, status); // FP1 IS T
fp2 = float64_to_floatx80(LIT64(0x3D2AC4D0D6011EE3), status); // B8
fp3 = float64_to_floatx80(LIT64(0xBDA9396F9F45AC19), status); // B7
xSign = extractFloatx80Sign(fp0); // X IS S
xExp = extractFloatx80Exp(fp0);
xSig = extractFloatx80Frac(fp0);
if (((n + adjn) >> 1) & 1) {
xSign ^= 1;
posneg1 = 0xBF800000; // -1
} else {
xSign ^= 0;
posneg1 = 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(LIT64(0x3E21EED90612C972), status), status); // B6+TB8
fp3 = floatx80_add(fp3, float64_to_floatx80(LIT64(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(LIT64(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(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);
RESET_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 + adjn) >> 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(LIT64(0xBD6AAA77CCC994F5), status); // A7
fp2 = float64_to_floatx80(LIT64(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(LIT64(0xBE5AE6452A118AE4), status), status); // A5+T*A7
fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(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(LIT64(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'
RESET_PREC;
a = floatx80_add(fp0, x, status);
float_raise(float_flag_inexact, status);
return a;
}
}
}
/*----------------------------------------------------------------------------
| Hyperbolic cosine
*----------------------------------------------------------------------------*/
floatx80 floatx80_cosh(floatx80 a, float_status *status)
{
flag aSign;
int32_t aExp;
uint64_t aSig;
int32_t compact;
floatx80 fp0, fp1;
aSig = extractFloatx80Frac(a);
aExp = extractFloatx80Exp(a);
aSign = extractFloatx80Sign(a);
if (aExp == 0x7FFF) {
if ((uint64_t) (aSig<<1)) return propagateFloatx80NaNOneArg(a, status);
return packFloatx80(0, aExp, aSig);
}
if (aExp == 0 && aSig == 0) {
return packFloatx80(0, one_exp, one_sig);
}
SET_PREC;
compact = floatx80_make_compact(aExp, aSig);
if (compact > 0x400CB167) {
if (compact > 0x400CB2B3) {
RESET_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(LIT64(0x40C62D38D3D64634), status), status);
fp0 = floatx80_sub(fp0, float64_to_floatx80(LIT64(0x3D6F90AEB1E75CC7), status), status);
fp0 = floatx80_etox(fp0, status);
fp1 = packFloatx80(0, 0x7FFB, one_sig);
RESET_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(0x3F000000, status), status); // (1/2)*EXP(|X|)
fp1 = float32_to_floatx80(0x3E800000, status); // 1/4
fp1 = floatx80_div(fp1, fp0, status); // 1/(2*EXP(|X|))
RESET_PREC;
a = floatx80_add(fp0, fp1, status);
float_raise(float_flag_inexact, status);
return a;
}
/*----------------------------------------------------------------------------
| e to x
*----------------------------------------------------------------------------*/
floatx80 floatx80_etox(floatx80 a, float_status *status)
{
flag aSign;
int32_t aExp;
uint64_t aSig;
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 a;
}
if (aExp == 0 && aSig == 0) {
return packFloatx80(0, one_exp, one_sig);
}
SET_PREC;
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(0x42B8AA3B, status), status); // 64/log2 * X
adjflag = 0;
n = floatx80_to_int32(fp0, status); // int(64/log2*X)
fp0 = int32_to_floatx80(n);
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(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(0x3AB60B70, status); // A5
fp2 = floatx80_mul(fp2, fp1, status); // fp2 is S*A5
fp3 = floatx80_mul(float32_to_floatx80(0x3C088895, status), fp1, status); // fp3 is S*A4
fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(0x3FA5555555554431), status), status); // fp2 is A3+S*A5
fp3 = floatx80_add(fp3, float64_to_floatx80(LIT64(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(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);
}
RESET_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
RESET_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(0x42B8AA3B, status), status); // 64/log2 * X
adjflag = 1;
n = floatx80_to_int32(fp0, status); // int(64/log2*X)
fp0 = int32_to_floatx80(n);
j = n & 0x3F; // J = N mod 64
k = 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
k--;
}
m1 = k / 2; // NOTE: this is really arithmetic right shift by 1
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)
RESET_PREC;
a = floatx80_add(a, float32_to_floatx80(0x3F800000, status), status); // 1 + X
float_raise(float_flag_inexact, status);
return a;
}
}
/*----------------------------------------------------------------------------
| e to x minus 1
*----------------------------------------------------------------------------*/
floatx80 floatx80_etoxm1(floatx80 a, float_status *status)
{
flag aSign;
int32_t aExp;
uint64_t aSig;
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 a;
}
if (aExp == 0 && aSig == 0) {
return packFloatx80(aSign, 0, 0);
}
SET_PREC;
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(0x42B8AA3B, status), status); // 64/log2 * X
n = floatx80_to_int32(fp0, status); // int(64/log2*X)
fp0 = int32_to_floatx80(n);
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(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(0x3950097B, status); // A6
fp2 = floatx80_mul(fp2, fp1, status); // fp2 is S*A6
fp3 = floatx80_mul(float32_to_floatx80(0x3AB60B6A, status), fp1, status); // fp3 is S*A5
fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(0x3F81111111174385), status), status); // fp2 IS A4+S*A6
fp3 = floatx80_add(fp3, float64_to_floatx80(LIT64(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(LIT64(0x3FC5555555555555), status), status); // fp2 IS A2+S*(A4+S*A6)
fp3 = floatx80_add(fp3, float32_to_floatx80(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);
RESET_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(0xBF800000, status); // -1
RESET_PREC;
a = floatx80_add(fp0, float32_to_floatx80(0x00800000, status), status); // -1 + 2^(-126)
float_raise(float_flag_inexact, status);
return a;
} else {
RESET_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(0x2F30CAA8, status); // B12
fp1 = floatx80_mul(fp1, fp0, status); // S * B12
fp2 = float32_to_floatx80(0x310F8290, status); // B11
fp1 = floatx80_add(fp1, float32_to_floatx80(0x32D73220, status), status); // B10
fp2 = floatx80_mul(fp2, fp0, status);
fp1 = floatx80_mul(fp1, fp0, status);
fp2 = floatx80_add(fp2, float32_to_floatx80(0x3493F281, status), status); // B9
fp1 = floatx80_add(fp1, float64_to_floatx80(LIT64(0x3EC71DE3A5774682), status), status); // B8
fp2 = floatx80_mul(fp2, fp0, status);
fp1 = floatx80_mul(fp1, fp0, status);
fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(0x3EFA01A019D7CB68), status), status); // B7
fp1 = floatx80_add(fp1, float64_to_floatx80(LIT64(0x3F2A01A01A019DF3), status), status); // B6
fp2 = floatx80_mul(fp2, fp0, status);
fp1 = floatx80_mul(fp1, fp0, status);
fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(0x3F56C16C16C170E2), status), status); // B5
fp1 = floatx80_add(fp1, float64_to_floatx80(LIT64(0x3F81111111111111), status), status); // B4
fp2 = floatx80_mul(fp2, fp0, status);
fp1 = floatx80_mul(fp1, fp0, status);
fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(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(0x3F000000, status), status); // S*B1
fp1 = floatx80_add(fp1, fp2, status); // Q
fp0 = floatx80_add(fp0, fp1, status); // S*B1+Q
RESET_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(LIT64(0x48B0000000000000), status), status);
fp0 = floatx80_add(fp0, sc, status);
RESET_PREC;
a = floatx80_mul(fp0, float64_to_floatx80(LIT64(0x3730000000000000), status), status);
} else {
RESET_PREC;
a = floatx80_add(fp0, sc, status);
}
float_raise(float_flag_inexact, status);
return a;
}
}
}
/*----------------------------------------------------------------------------
| Log base 10
*----------------------------------------------------------------------------*/
floatx80 floatx80_log10(floatx80 a, float_status *status)
{
flag aSign;
int32_t aExp;
uint64_t aSig;
floatx80 fp0, fp1;
aSig = extractFloatx80Frac(a);
aExp = extractFloatx80Exp(a);
aSign = extractFloatx80Sign(a);
if (aExp == 0x7FFF) {
if ((uint64_t) (aSig<<1)) return propagateFloatx80NaNOneArg(a, status);
if (aSign == 0)
return a;
}
if (aExp == 0 && aSig == 0) {
float_raise(float_flag_divbyzero, status);
return packFloatx80(1, 0x7FFF, floatx80_default_infinity_low);
}
if (aSign) {
float_raise(float_flag_invalid, status);
return floatx80_default_nan(status);
}
SET_PREC;
fp0 = floatx80_logn(a, status);
fp1 = packFloatx80(0, 0x3FFD, LIT64(0xDE5BD8A937287195)); // INV_L10
RESET_PREC;
a = floatx80_mul(fp0, fp1, status); // LOGN(X)*INV_L10
float_raise(float_flag_inexact, status);
return a;
}
/*----------------------------------------------------------------------------
| Log base 2
*----------------------------------------------------------------------------*/
floatx80 floatx80_log2(floatx80 a, float_status *status)
{
flag aSign;
int32_t aExp;
uint64_t aSig;
floatx80 fp0, fp1;
aSig = extractFloatx80Frac(a);
aExp = extractFloatx80Exp(a);
aSign = extractFloatx80Sign(a);
if (aExp == 0x7FFF) {
if ((uint64_t) (aSig<<1)) return propagateFloatx80NaNOneArg(a, status);
if (aSign == 0)
return a;
}
if (aExp == 0) {
if (aSig == 0) {
float_raise(float_flag_divbyzero, status);
return packFloatx80(1, 0x7FFF, floatx80_default_infinity_low);
}
normalizeFloatx80Subnormal(aSig, &aExp, &aSig);
}
if (aSign) {
float_raise(float_flag_invalid, status);
return floatx80_default_nan(status);
}
SET_PREC;
if (aSig == one_sig) { // X is 2^k
RESET_PREC;
a = int32_to_floatx80(aExp-0x3FFF);
} else {
fp0 = floatx80_logn(a, status);
fp1 = packFloatx80(0, 0x3FFF, LIT64(0xB8AA3B295C17F0BC)); // INV_L2
RESET_PREC;
a = floatx80_mul(fp0, fp1, status); // LOGN(X)*INV_L2
}
float_raise(float_flag_inexact, status);
return a;
}
/*----------------------------------------------------------------------------
| Log base e
*----------------------------------------------------------------------------*/
floatx80 floatx80_logn(floatx80 a, float_status *status)
{
flag aSign;
int32_t aExp;
uint64_t aSig, fSig;
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)) return propagateFloatx80NaNOneArg(a, status);
if (aSign == 0)
return a;
}
adjk = 0;
if (aExp == 0) {
if (aSig == 0) { // zero
float_raise(float_flag_divbyzero, status);
return packFloatx80(1, 0x7FFF, floatx80_default_infinity_low);
}
#if 1
if ((aSig & one_sig) == 0) { // denormal
normalizeFloatx80Subnormal(aSig, &aExp, &aSig);
adjk = -100;
aExp += 100;
a = packFloatx80(aSign, aExp, aSig);
}
#else
normalizeFloatx80Subnormal(aSig, &aExp, &aSig);
#endif
}
if (aSign) {
float_raise(float_flag_invalid, status);
return floatx80_default_nan(status);
}
SET_PREC;
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);
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(LIT64(0x3FC2499AB5E4040B), status), status); // V*A6
fp2 = floatx80_mul(fp2, float64_to_floatx80(LIT64(0xBFC555B5848CB7DB), status), status); // V*A5
fp1 = floatx80_add(fp1, float64_to_floatx80(LIT64(0x3FC99999987D8730), status), status); // A4+V*A6
fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(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(LIT64(0x3FD55555555555A4), status), status); // A2+V*(A4+V*A6)
fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(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)
RESET_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(0x3F800000, status), status); // FP1 IS X-1
fp0 = floatx80_add(fp0, float32_to_floatx80(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(LIT64(0x3F175496ADD7DAD6), status); // B5
fp2 = float64_to_floatx80(LIT64(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(LIT64(0x3F624924928BCCFF), status), status); // B3+W*B5
fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(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(LIT64(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)] )
RESET_PREC;
a = floatx80_add(fp0, saveu, status);
float_raise(float_flag_inexact, status);
return a;
}
}
/*----------------------------------------------------------------------------
| Log base e of x plus 1
*----------------------------------------------------------------------------*/
floatx80 floatx80_lognp1(floatx80 a, float_status *status)
{
flag aSign;
int32_t aExp;
uint64_t aSig, fSig;
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)) return propagateFloatx80NaNOneArg(a, status);
if (aSign) {
float_raise(float_flag_invalid, status);
return floatx80_default_nan(status);
}
return a;
}
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, 0x7FFF, floatx80_default_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);
}
SET_PREC;
compact = floatx80_make_compact(aExp, aSig);
fp0 = a; // Z
fp1 = a;
fp0 = floatx80_add(fp0, float32_to_floatx80(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);
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(LIT64(0x3FC2499AB5E4040B), status), status); // V*A6
fp2 = floatx80_mul(fp2, float64_to_floatx80(LIT64(0xBFC555B5848CB7DB), status), status); // V*A5
fp1 = floatx80_add(fp1, float64_to_floatx80(LIT64(0x3FC99999987D8730), status), status); // A4+V*A6
fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(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(LIT64(0x3FD55555555555A4), status), status); // A2+V*(A4+V*A6)
fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(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)
RESET_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(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(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(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(LIT64(0x3F175496ADD7DAD6), status); // B5
fp2 = float64_to_floatx80(LIT64(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(LIT64(0x3F624924928BCCFF), status), status); // B3+W*B5
fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(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(LIT64(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)] )
RESET_PREC;
a = floatx80_add(fp0, saveu, status);
float_raise(float_flag_inexact, status);
return a;
}
}
/*----------------------------------------------------------------------------
| Sine
*----------------------------------------------------------------------------*/
floatx80 floatx80_sin(floatx80 a, float_status *status)
{
flag aSign, xSign;
int32_t aExp, xExp;
uint64_t aSig, xSig;
int32_t compact, l, n, j;
floatx80 fp0, fp1, fp2, fp3, fp4, fp5, x, invtwopi, twopi1, twopi2;
float32 posneg1, twoto63;
flag adjn, 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);
}
adjn = 0;
SET_PREC;
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));
twoto63 = 0x5F000000;
twoto63 |= xSign ? 0x80000000 : 0x00000000; // SIGN(INARG)*2^63 IN SGL
fp2 = floatx80_mul(fp0, invtwopi, status);
fp2 = floatx80_add(fp2, float32_to_floatx80(twoto63, status), status); // THE FRACTIONAL 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(0x3F800000, status); // 1
RESET_PREC;
if (adjn) {
// COSTINY
a = floatx80_sub(fp0, float32_to_floatx80(0x00800000, status), status);
} else {
// SINTINY
a = floatx80_move(a, status);
}
float_raise(float_flag_inexact, status);
return a;
}
} else {
fp1 = floatx80_mul(fp0, float64_to_floatx80(LIT64(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 + adjn) & 1) {
// COSPOLY
fp0 = floatx80_mul(fp0, fp0, status); // FP0 IS S
fp1 = floatx80_mul(fp0, fp0, status); // FP1 IS T
fp2 = float64_to_floatx80(LIT64(0x3D2AC4D0D6011EE3), status); // B8
fp3 = float64_to_floatx80(LIT64(0xBDA9396F9F45AC19), status); // B7
xSign = extractFloatx80Sign(fp0); // X IS S
xExp = extractFloatx80Exp(fp0);
xSig = extractFloatx80Frac(fp0);
if (((n + adjn) >> 1) & 1) {
xSign ^= 1;
posneg1 = 0xBF800000; // -1
} else {
xSign ^= 0;
posneg1 = 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(LIT64(0x3E21EED90612C972), status), status); // B6+TB8
fp3 = floatx80_add(fp3, float64_to_floatx80(LIT64(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(LIT64(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(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);
RESET_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 + adjn) >> 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(LIT64(0xBD6AAA77CCC994F5), status); // A7
fp2 = float64_to_floatx80(LIT64(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(LIT64(0xBE5AE6452A118AE4), status), status); // A5+T*A7
fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(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(LIT64(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'
RESET_PREC;
a = floatx80_add(fp0, x, status);
float_raise(float_flag_inexact, status);
return a;
}
}
}
/*----------------------------------------------------------------------------
| Hyperbolic sine
*----------------------------------------------------------------------------*/
floatx80 floatx80_sinh(floatx80 a, float_status *status)
{
flag aSign;
int32_t aExp;
uint64_t aSig;
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 a;
}
if (aExp == 0 && aSig == 0) {
return packFloatx80(aSign, 0, 0);
}
SET_PREC;
compact = floatx80_make_compact(aExp, aSig);
if (compact > 0x400CB167) {
// SINHBIG
if (compact > 0x400CB2B3) {
RESET_PREC;
return roundAndPackFloatx80(status->floatx80_rounding_precision, aSign, 0x8000, aSig, 0, status);
} else {
fp0 = floatx80_abs(a, status); // Y = |X|
fp0 = floatx80_sub(fp0, float64_to_floatx80(LIT64(0x40C62D38D3D64634), status), status); // (|X|-16381LOG2_LEAD)
fp0 = floatx80_sub(fp0, float64_to_floatx80(LIT64(0x3D6F90AEB1E75CC7), status), status); // |X| - 16381 LOG2, ACCURATE
fp0 = floatx80_etox(fp0, status);
fp2 = packFloatx80(aSign, 0x7FFB, one_sig);
RESET_PREC;
a = floatx80_mul(fp0, fp2, status);
float_raise(float_flag_inexact, status);
return a;
}
} else { // |X| < 16380 LOG2
fp0 = floatx80_abs(a, status); // Y = |X|
fp0 = floatx80_etoxm1(fp0, status); // FP0 IS Z = EXPM1(Y)
fp1 = floatx80_add(fp0, float32_to_floatx80(0x3F800000, status), status); // 1+Z
fp2 = fp0;
fp0 = floatx80_div(fp0, fp1, status); // Z/(1+Z)
fp0 = floatx80_add(fp0, fp2, status);
fact = 0x3F000000;
fact |= aSign ? 0x80000000 : 0x00000000;
RESET_PREC;
a = floatx80_mul(fp0, float32_to_floatx80(fact, status), status);
float_raise(float_flag_inexact, status);
return a;
}
}
/*----------------------------------------------------------------------------
| Tangent
*----------------------------------------------------------------------------*/
floatx80 floatx80_tan(floatx80 a, float_status *status)
{
flag aSign, xSign;
int32_t aExp, xExp;
uint64_t aSig, xSig;
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);
}
SET_PREC;
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));
twoto63 = 0x5F000000;
twoto63 |= xSign ? 0x80000000 : 0x00000000; // SIGN(INARG)*2^63 IN SGL
fp2 = floatx80_mul(fp0, invtwopi, status);
fp2 = floatx80_add(fp2, float32_to_floatx80(twoto63, status), status); // THE FRACTIONAL 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 {
RESET_PREC;
a = floatx80_move(a, status);
float_raise(float_flag_inexact, status);
return a;
}
} else {
fp1 = floatx80_mul(fp0, float64_to_floatx80(LIT64(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(LIT64(0x3EA0B759F50F8688), status); // Q4
fp2 = float64_to_floatx80(LIT64(0xBEF2BAA5A8924F04), status); // P3
fp3 = floatx80_mul(fp3, fp0, status); // SQ4
fp2 = floatx80_mul(fp2, fp0, status); // SP3
fp3 = floatx80_add(fp3, float64_to_floatx80(LIT64(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(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);
RESET_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(LIT64(0x3EA0B759F50F8688), status); // Q4
fp2 = float64_to_floatx80(LIT64(0xBEF2BAA5A8924F04), status); // P3
fp3 = floatx80_mul(fp3, fp1, status); // SQ4
fp2 = floatx80_mul(fp2, fp1, status); // SP3
fp3 = floatx80_add(fp3, float64_to_floatx80(LIT64(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(0x3F800000, status), status); // 1+S(Q1+S(Q2+S(Q3+SQ4)))
RESET_PREC;
a = floatx80_div(fp0, fp1, 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;
int32_t compact;
floatx80 fp0, fp1;
float32 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);
}
SET_PREC;
compact = floatx80_make_compact(aExp, aSig);
if (compact < 0x3FD78000 || compact > 0x3FFFDDCE) {
// TANHBORS
if (compact < 0x3FFF8000) {
// TANHSM
RESET_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(sign, status);
sign &= 0x80000000;
sign ^= 0x80800000; // -SIGN(X)*EPS
RESET_PREC;
a = floatx80_add(fp0, float32_to_floatx80(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(0x3F800000, status), status); // EXP(Y)+1
sign = aSign ? 0x80000000 : 0x00000000;
fp1 = floatx80_div(float32_to_floatx80(sign^0xC0000000, status), fp0, status); // -SIGN(X)*2 / [EXP(Y)+1]
fp0 = float32_to_floatx80(sign | 0x3F800000, status); // SIGN
RESET_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(0x40000000, status), status); // Z+2
vSign = extractFloatx80Sign(fp1);
vExp = extractFloatx80Exp(fp1);
vSig = extractFloatx80Frac(fp1);
fp1 = packFloatx80(vSign ^ aSign, vExp, vSig);
RESET_PREC;
a = floatx80_div(fp0, fp1, 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;
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 a;
}
if (aExp == 0 && aSig == 0) {
return packFloatx80(0, one_exp, one_sig);
}
SET_PREC;
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
RESET_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)
RESET_PREC;
a = floatx80_add(fp0, float32_to_floatx80(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(LIT64(0x406A934F0979A371), status), status); // X*64*LOG10/LOG2
n = floatx80_to_int32(fp1, status); // N=INT(X*64*LOG10/LOG2)
fp1 = int32_to_floatx80(n);
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(LIT64(0x3F734413509F8000), status), status); // N*(LOG2/64LOG10)_LEAD
fp3 = packFloatx80(1, 0x3FCD, LIT64(0xC0219DC1DA994FD2));
fp2 = floatx80_mul(fp2, fp3, status); // N*(LOG2/64LOG10)_TRAIL
fp0 = floatx80_sub(fp0, fp1, status); // X - N L_LEAD
fp0 = floatx80_sub(fp0, fp2, status); // X - N L_TRAIL
fp2 = packFloatx80(0, 0x4000, LIT64(0x935D8DDDAAA8AC17)); // LOG10
fp0 = floatx80_mul(fp0, fp2, status); // R
// EXPR
fp1 = floatx80_mul(fp0, fp0, status); // S = R*R
fp2 = float64_to_floatx80(LIT64(0x3F56C16D6F7BD0B2), status); // A5
fp3 = float64_to_floatx80(LIT64(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(LIT64(0x3FA5555555554CC1), status), status); // A3+S*A5
fp3 = floatx80_add(fp3, float64_to_floatx80(LIT64(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(LIT64(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);
RESET_PREC;
a = floatx80_mul(fp0, adjfact, status);
float_raise(float_flag_inexact, status);
return a;
}
}
/*----------------------------------------------------------------------------
| 2 to x
*----------------------------------------------------------------------------*/
floatx80 floatx80_twotox(floatx80 a, float_status *status)
{
flag aSign;
int32_t aExp;
uint64_t aSig;
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 a;
}
if (aExp == 0 && aSig == 0) {
return packFloatx80(0, one_exp, one_sig);
}
SET_PREC;
fp0 = a;
compact = floatx80_make_compact(aExp, aSig);
if (compact < 0x3FB98000 || compact > 0x400D80C0) { // |X| > 16480 or |X| < 2^(-70)
if (compact > 0x3FFF8000) { // |X| > 16480
RESET_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)
RESET_PREC;;
a = floatx80_add(fp0, float32_to_floatx80(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(0x42800000, status), status); // X * 64
n = floatx80_to_int32(fp1, status);
fp1 = int32_to_floatx80(n);
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(0x3C800000, status), status); // (1/64)*N
fp0 = floatx80_sub(fp0, fp1, status); // X - (1/64)*INT(64 X)
fp2 = packFloatx80(0, 0x3FFE, LIT64(0xB17217F7D1CF79AC)); // LOG2
fp0 = floatx80_mul(fp0, fp2, status); // R
// EXPR
fp1 = floatx80_mul(fp0, fp0, status); // S = R*R
fp2 = float64_to_floatx80(LIT64(0x3F56C16D6F7BD0B2), status); // A5
fp3 = float64_to_floatx80(LIT64(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(LIT64(0x3FA5555555554CC1), status), status); // A3+S*A5
fp3 = floatx80_add(fp3, float64_to_floatx80(LIT64(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(LIT64(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);
RESET_PREC;
a = floatx80_mul(fp0, adjfact, status);
float_raise(float_flag_inexact, status);
return a;
}
}
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