static inline A0_n asin(const A0_n a0_n)
{
const A0 a0 = { a0_n };
typedef typename meta::scalar_of<A0>::type sA0;
A0 x = nt2::abs(a0);
const A0 pio4 = Pio_4<A0>();
const bA0 small= lt(x, Sqrteps<A0>());
const A0 morebits = double_constant<A0, 0xbc91a62633145c07ll>();
const A0 ct1 = double_constant<A0, 0x3fe4000000000000ll>();
A0 zz1 = oneminus(x);
const A0 vp = zz1*horner< NT2_HORNER_COEFF_T(sA0, 5,
(0x3f684fc3988e9f08ll,
0xbfe2079259f9290fll,
0x401bdff5baf33e6all,
0xc03991aaac01ab68ll,
0x403c896240f3081dll)
)>(zz1)/
horner< NT2_HORNER_COEFF_T(sA0, 5,
(0x3ff0000000000000ll,
0xc035f2a2b6bf5d8cll,
0x40626219af6a7f42ll,
0xc077fe08959063eell,
0x40756709b0b644bell)
)>(zz1);
zz1 = sqrt(zz1+zz1);
A0 z = pio4-zz1;
zz1 = fma(zz1, vp, morebits);
z = z-zz1;
zz1 = z+pio4;
A0 zz2 = sqr(a0);
z = zz2*horner< NT2_HORNER_COEFF_T(sA0, 6,
(0x3f716b9b0bd48ad3ll,
0xbfe34341333e5c16ll,
0x4015c74b178a2dd9ll,
0xc0304331de27907bll,
0x40339007da779259ll,
0xc020656c06ceafd5ll)
)>(zz2)/
horner< NT2_HORNER_COEFF_T(sA0, 6,
(0x3ff0000000000000ll,
0xc02d7b590b5e0eabll,
0x40519fc025fe9054ll,
0xc06265bb6d3576d7ll,
0x4061705684ffbf9dll,
0xc04898220a3607acll)
)>(zz2);
zz2 = x*z+x;
return if_nan_else( gt(x, One<A0>())
, b_xor ( select( small
, x
, select( gt(x, ct1)
, zz1
, zz2
)
)
, bitofsign(a0)
)
);
}
static inline A0_n acos(const A0_n a0_n)
{
const A0 a0 = { a0_n };
const A0 as = { asin( sqrt(Half<A0>() - Half<A0>()*a0) )};
A0 z1 = Two<A0>() * as;
const A0 as1 = {asin(a0)};
A0 z2 = ((Pio_4<A0>() - as1)+double_constant<A0, 0x3c91a62633145c07ll>())+ Pio_4<A0>();
return if_nan_else( gt(abs(a0),One<A0>()), sel( gt(a0,Half<A0>()), z1, z2));
}
static inline A0 log2(const A0& a0)
{
A0 x, fe, x2, y;
kernel_log(a0, fe, x, x2, y);
y = madd(Mhalf<A0>(),x2, y);
// multiply log of fraction by log2(e)
A0 z = madd(x,single_constant<A0, 0x3ee2a8ed>(),mul(y,single_constant<A0, 0x3ee2a8ed>()));// 0.44269504088896340735992
A0 z1 = ((z+y)+x)+fe;
A0 y1 = a0-rec(abs(a0)); // trick to reduce selection testing
return seladd(is_inf(y1),if_nan_else(logical_or(is_ltz(a0), is_nan(a0)), z1),y1);
}
static inline A0 log(const A0& a0)
{
A0 x, fe, x2, y;
kernel_log(a0, fe, x, x2, y);
y = madd(fe, single_constant<A0, 0xb95e8083>(), y);
y = madd(Mhalf<A0>(), x2, y);
A0 z = x + y;
A0 y1 = a0-rec(abs(a0));// trick to reduce selection testing
A0 y2 = madd(single_constant<A0, 0x3f318000>(), fe, z);
y2 = if_nan_else(logical_or(is_ltz(a0), is_nan(a0)), y2);
return seladd(is_inf(y1), y2, y1);
}
static inline A0 log10(const A0& a0)
{
A0 x, fe, x2, y;
kernel_log(a0, fe, x, x2, y);
y = amul(y, -Half<A0>(), x2);
// multiply log of fraction by log10(e) and base 2 exponent by log10(2)
A0 z = mul(x+y, single_constant<A0, 0x3a37b152>());//7.00731903251827651129E-4f // log10(e)lo
z = amul(z, y, single_constant<A0, 0x3ede0000>()); //4.3359375E-1f // log10(e)hi
z = amul(z, x, single_constant<A0, 0x3ede0000>());
z = amul(z, fe, single_constant<A0, 0x39826a14>());//3.0078125E-1f // log10(2)hi
z = amul(z, fe, single_constant<A0, 0x3e9a0000>());//2.48745663981195213739E-4f // log10(2)lo
A0 y1 = a0-rec(abs(a0)); // trick to reduce selection testing perhaps bad TODO
return seladd(is_inf(y1), if_nan_else(logical_or(is_ltz(a0), is_nan(a0)), z),y1);
}
// compute exp(ax)
static inline A0 expa(const A0& a0)
{
A0 hi, lo, x;
A0 k = reduc_t::reduce(a0, hi, lo, x);
A0 c = reduc_t::approx(x);
bA0 ge = reduc_t::isgemaxlog(a0);
bA0 le = reduc_t::isleminlog(a0);
A0 z = nt2::if_zero_else(le,
finalize_t::finalize(a0, x, c, k, hi, lo)
);
#ifdef BOOST_SIMD_NO_INVALIDS
return z;
#else
return if_nan_else(is_nan(a0), nt2::if_else(ge, nt2::Inf<A0>(), z));
#endif
}
