static inline A0_n kernel_atan(const A0_n a0_n)
{
typedef typename meta::scalar_of<A0>::type sA0;
const A0 tan3pio8 = double_constant<A0, 0x4003504f333f9de6ll>();
// static const A0 Twothird = double_constant<A0, 0x3fe51eb851eb851fll>();
const A0 tanpio8 = double_constant<A0, 0x3fda827999fcef31ll>();
A0 x = { a0_n };
const A0 flag1 = lt(x, tan3pio8); //tan3pio8
const A0 flag2 = b_and(ge(x, tanpio8), flag1); //tanpio8
A0 yy = b_notand(flag1, Pio_2<A0>());
yy = select(flag2, Pio_4<A0>(), yy);
A0 xx = select(flag1, x, -rec(x));
xx = select(flag2, minusone(x)/oneplus(x),xx);
A0 z = sqr(xx);
z = z*horner< NT2_HORNER_COEFF_T(sA0, 5,
(0xbfec007fa1f72594ll,
0xc03028545b6b807all,
0xc052c08c36880273ll,
0xc05eb8bf2d05ba25ll,
0xc0503669fd28ec8ell)
)>(z)/
horner< NT2_HORNER_COEFF_T(sA0, 6,
(0x3ff0000000000000ll,
0x4038dbc45b14603cll,
0x4064a0dd43b8fa25ll,
0x407b0e18d2e2be3bll,
0x407e563f13b049eall,
0x4068519efbbd62ecll)
)>(z);
z = fma(xx, z, xx);
const A0 morebits = double_constant<A0, 0x3c91a62633145c07ll>();
z = seladd(flag2, z, mul(Half<A0>(), morebits));
z = z+b_notand(flag1, morebits);
return yy + z;
}
static inline A0 asin(const A0& a0)
{
A0 sign, x;
// bf::tie(sign, x) = sign_and_abs(a0);
x = abs(a0);
sign = bitofsign(a0);
A0 x_smaller_1e_4 = lt(x, single_constant<A0, 0x38d1b717>()); //1.0e-4f;
A0 x_larger_05 = gt(x, Half<A0>());
A0 x_else = b_or(x_smaller_1e_4, x_larger_05);
A0 a = b_and(x, x_smaller_1e_4);
A0 b = b_and(Half<A0>()*oneminus(x), x_larger_05);
A0 z = b_or(b_or(b_notand(x_else, sqr(x)), a), b);
x = b_notand(x_else, x);
a = b_and(sqrt(z), x_larger_05);
x = b_or(a, x);
A0 z1 = madd(z, single_constant<A0, 0x3d2cb352>(), single_constant<A0, 0x3cc617e3>());
z1 = madd(z1, z, single_constant<A0, 0x3d3a3ec7>());
z1 = madd(z1, z, single_constant<A0, 0x3d9980f6>());
z1 = madd(z1, z, single_constant<A0, 0x3e2aaae4>());
z1 = madd(z1, z*x, x);
z = select(x_smaller_1e_4, z, z1);
z1 = z+z;
z1 = Pio_2<A0>()-z1;
z = select(x_larger_05, z1, z);
return b_xor(z, sign);
}
static inline A0 atan(const A0& a0)
{
A0 x, sign;
x = nt2::abs(a0);
sign = bitofsign(a0);
// bf::tie(sign, x) = sign_and_abs(a0);
const A0 flag1 = lt(x, single_constant<A0, 0x401a827a>()); //tan3pio8);
const A0 flag2 = b_and(ge(x, single_constant<A0, 0x3ed413cd>()), flag1);
A0 yy = b_notand(flag1, Pio_2<A0>());
yy = select(flag2, Pio_4<A0>(), yy);
A0 xx = select(flag1, x, -rec(x));
xx = select(flag2, (minusone(x)/oneplus(x)),xx);
const A0 z = sqr(xx);
A0 z1 = madd(z, single_constant<A0, 0x3da4f0d1>(),single_constant<A0, 0xbe0e1b85>());
A0 z2 = madd(z, single_constant<A0, 0x3e4c925f>(),single_constant<A0, 0xbeaaaa2a>());
z1 = madd(z1, sqr(z), z2);
yy = add(yy, madd(xx, mul( z1, z), xx));
return b_xor(yy, sign);
}