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>();
const A0 tanpio8 = double_constant<A0, 0x3fda827999fcef31ll>();
const A0 a0 = {a0_n};
const A0 x = nt2::abs(a0);
const bA0 flag1 = lt(x, tan3pio8);
const bA0 flag2 = logical_and(ge(x, tanpio8), flag1);
A0 yy = if_zero_else(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+if_zero_else(flag1, morebits);
return yy + z;
}
static inline A0_n asin(const A0_n a0_n)
{
const A0 a0 = { a0_n };
A0 sign, x;
x = nt2::abs(a0);
sign = bitofsign(a0);
const bA0 x_smaller_1e_4 = lt(x, single_constant<A0, 0x38d1b717>()); //1.0e-4f;
const bA0 x_larger_05 = gt(x, Half<A0>());
const bA0 x_else = logical_or(x_smaller_1e_4, x_larger_05);
A0 a = if_else_zero(x_smaller_1e_4, x);
const A0 b = if_else_zero(x_larger_05, Half<A0>()*oneminus(x));
A0 z = b_or(b_or(if_zero_else(x_else, sqr(x)), a), b);
x = if_zero_else(x_else, x);
a = if_else_zero(x_larger_05, sqrt(z));
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);
}
template < class AA0 > static inline AA0 branch2(const AA0 & a0)
{
typedef typename meta::scalar_of<AA0>::type sAA0;
AA0 q = rec(a0);
AA0 w = sqrt(q);
AA0 p3 = w *
horner< NT2_HORNER_COEFF_T(sAA0, 8,
(0xbd8c100e,
0x3e3ef887,
0xbe5ba616,
0x3df54214,
0xbb69539e,
0xbd4b8bc1,
0xb6612dc2,
0x3f4c422a
) ) > (q);
w = sqr(q);
AA0 xn = q*
horner< NT2_HORNER_COEFF_T(sAA0, 8,
(0x4201aee0,
0xc2113945,
0x418c7f6a,
0xc09f3306,
0x3f8040aa,
0xbe46a57f,
0x3d84ed6e,
0xbdffff97
) ) > (w)-Pio_4<AA0>();
return if_zero_else(eq(a0, Inf<AA0>()), p3*nt2::sin(xn+a0));
}
template < class AA0 > static inline AA0 branch2(const AA0 & x)
{
typedef typename meta::scalar_of<AA0>::type stype;
AA0 q = rec(x);
AA0 w = sqrt(q);
AA0 p3 = w *
horner< NT2_HORNER_COEFF_T(stype, 8,
(0x3d8d98f9,
0xbe69f6b3,
0x3ea0ad85,
0xbe574699,
0x3bb21b25,
0x3e18ec50,
0x36a6f7c5,
0x3f4c4229
) ) > (q);
w = sqr(q);
AA0 xn = q*
horner< NT2_HORNER_COEFF_T(stype, 8,
(0xc233e16d,
0x424af04a,
0xc1c6dca7,
0x40e72299,
0xbfc5bd69,
0x3eb364d9,
0xbe27bad7,
0x3ebfffdd
) ) > (w)-single_constant<AA0,0x4016cbe4 > ();
return if_zero_else(eq(x, Inf<AA0>()), p3*cos(xn+x));
}
static inline A0_n kernel_atan(const A0_n a0_n)
{
const A0 a0 = {a0_n};
const A0 x = nt2::abs(a0);
//here x is positive
const bA0 flag1 = lt(x, single_constant<A0, 0x401a827a>()); //tan3pio8);
const bA0 flag2 = logical_and(ge(x, single_constant<A0, 0x3ed413cd>()), flag1);
A0 yy = if_zero_else(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>());
const A0 z2 = madd(z, single_constant<A0, 0x3e4c925f>(),single_constant<A0, 0xbeaaaa2a>());
z1 = madd(z1, sqr(z), z2);
return add(yy, madd(xx, mul( z1, z), xx));
}
BOOST_FORCEINLINE static void conf_bounds(const A0& a0, A1& a1,
const value_type& alpha )
{
typedef nt2::memory::container<tag::table_, value_type, nt2::_2D> semantic;
NT2_AS_TERMINAL_IN(semantic, pcov, boost::proto::child_c<3>(a0));
const In0& x = boost::proto::child_c<0>(a0);
const In1& mu = boost::proto::child_c<1>(a0);
const In2& sigma = boost::proto::child_c<2>(a0);
auto z = (log(if_zero_else(is_lez(x), x))-mu)/sigma;
// this is [1, x0]*pcov*[1; x0]
auto zvar = fma(fma(pcov(2,2), z, Two<value_type>()*pcov(1,2)), z, pcov(1,1));
BOOST_ASSERT_MSG(nt2::globalall(nt2::is_gez(zvar)), "Covariance matrix must be positive");
value_type normz = -nt2::norminv(alpha*nt2::Half<value_type>());
auto halfwidth = normz*nt2::sqrt(zvar)/sigma;
boost::proto::child_c<0>(a1) = Half<value_type>()*nt2::erfc(-Sqrt_2o_2<value_type>()*z);
boost::proto::child_c<1>(a1) = Half<value_type>()*nt2::erfc(-Sqrt_2o_2<value_type>()*(z-halfwidth));
boost::proto::child_c<2>(a1) = Half<value_type>()*nt2::erfc(-Sqrt_2o_2<value_type>()*(z+halfwidth));
}
