static inline A0 asin(const A0& a0)
{
A0 sign, x, z;
// bf::tie(sign, x) = sign_and_abs(a0);
x = nt2::abs(a0);
sign = bitofsign(a0);
if ((x < single_constant<A0,0x38d1b717>())) return a0;
if ((x > One<A0>())) return Nan<A0>();
bool bx_larger_05 = (x > Half<A0>());
if (bx_larger_05)
{
z = Half<A0>()*oneminus(x);
x = sqrt(z);
}
else
{
z = sqr(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);
if(bx_larger_05)
{
z1 = z1+z1;
z1 = Pio_2<A0>()-z1;
}
return b_xor(z1, sign);
}
static inline A0 finalize(const A0& a0, const A0& x,
const A0& c, const A0 & k,
const A0& ,const A0& )
{
A0 y = oneminus(((-(x*c)/(Two<A0>()-c))-x));
return fast_ldexp(y, fast_toint(k));
}
result_type operator()(A0& yi, A1& inputs) const
{
yi.resize(inputs.extent());
const child0 & x = boost::proto::child_c<0>(inputs);
if (numel(x) <= 1)
BOOST_ASSERT_MSG(numel(x) > 1, "Interpolation requires at least two sample points in each dimension.");
else
{
BOOST_ASSERT_MSG(issorted(x, 'a'), "for 'linear' interpolation x values must be sorted in ascending order");
const child1 & y = boost::proto::child_c<1>(inputs);
BOOST_ASSERT_MSG(numel(x) == numel(y), "The grid vectors do not define a grid of points that match the given values.");
const child2 & xi = boost::proto::child_c<2>(inputs);
bool extrap = false;
value_type extrapval = Nan<value_type>();
choices(inputs, extrap, extrapval, N1());
table<index_type> index = bsearch (x, xi);
table<value_type> dx = xi-x(index);
yi = fma(oneminus(dx), y(index), dx*y(oneplus(index)));
value_type b = value_type(x(begin_));
value_type e = value_type(x(end_));
if (!extrap) yi = nt2::if_else(nt2::logical_or(boost::simd::is_nge(xi, b),
boost::simd::is_nle(xi, e)), extrapval, yi);
}
return yi;
}
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);
}
static inline A0 finalize(const A0&, const A0& x,
const A0& c, const A0 & k,
const A0& hi,const A0& lo)
{
A0 y = oneminus(((lo-(x*c)/(Two<A0>()-c))-hi));
return fast_ldexp(y, toint(k));
}
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_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 acos(const A0& a0)
{
if (a0 < Mhalf<A0>())
return Pi<A0>()-asin( nt2::sqrt(oneplus(a0)*Half<A0>()))*Two<A0>();
else if (a0 > Half<A0>())
return asin( nt2::sqrt(oneminus(a0)*Half<A0>()))*Two<A0>();
return (Pio_2<A0>()-asin(a0));
}
static inline A0 finalize(const A0& a0, const A0& x,
const A0& c, const A0 & k,
const A0& ,const A0& )
{
details::ignore_unused(a0);
A0 y = oneminus(((-(x*c)/(Two<A0>()-c))-x));
return fast_ldexp(y, toint(k));
}
static inline A0 finalize(const A0& a0, const A0& x,
const A0& c, const A0 & k,
const A0& ,const A0& )
{
A0 y = oneminus(((-(x*c)/(Two<A0>()-c))-x));
y = fast_ldexp(y, fast_toint(k));
// adjust for 2^n n flint
return where(isflint(a0), round(y), y);
}
static inline A0 finalize(const A0& a0, const A0& x,
const A0& c, const A0 & k,
const A0& ,const A0& )
{
A0 y = oneminus(((-(x*c)/(Two<A0>()-c))-x));
y = fast_ldexp(y, toint(k));
// adjust for 2^n n flint
return sel(b_and(is_gtz(a0), is_flint(a0)), round2even(y), y);
}
static inline A0 cos_eval(const A0& z)
{
const A0 y = horner< NT2_HORNER_COEFF_T(stype, 7, (0x3da8ff831ad9b219ll,
0xbe21eea7c1e514d4ll,
0x3e927e4f8e06d9a5ll,
0xbefa01a019ddbcd9ll,
0x3f56c16c16c15d47ll,
0xbfa5555555555551ll,
0x3fe0000000000000ll) ) > (z);
return oneminus(y*z);
}
static inline A0 asin(const A0& a0)
{
A0 x = nt2::abs(a0);
if ((x > One<A0>())) return Nan<A0>();
if ((x < Sqrteps<A0>())) return a0;
A0 zz;
if((x > double_constant<double,0x3fe4000000000000ll> ())) //0.625;
{
zz = oneminus(x);
const A0 vp = zz*horner< NT2_HORNER_COEFF_T(stype, 5,
(0x3f684fc3988e9f08ll,
0xbfe2079259f9290fll,
0x401bdff5baf33e6all,
0xc03991aaac01ab68ll,
0x403c896240f3081dll)
)>(zz)/
horner< NT2_HORNER_COEFF_T(stype, 5,
(0x3ff0000000000000ll,
0xc035f2a2b6bf5d8cll,
0x40626219af6a7f42ll,
0xc077fe08959063eell,
0x40756709b0b644bell)
)>(zz);
zz = sqrt(zz+zz);
A0 z = Pio_4<A0>()-zz;
zz = madd(zz, vp, double_constant<double,0xbc91a62633145c07ll>());
z = z-zz;
zz = z+Pio_4<A0>();
}
else
{
zz = sqr(x);
A0 z = zz*horner< NT2_HORNER_COEFF_T(stype, 6,
(0x3f716b9b0bd48ad3ll,
0xbfe34341333e5c16ll,
0x4015c74b178a2dd9ll,
0xc0304331de27907bll,
0x40339007da779259ll,
0xc020656c06ceafd5ll)
)>(zz)/
horner< NT2_HORNER_COEFF_T(stype, 6,
(0x3ff0000000000000ll,
0xc02d7b590b5e0eabll,
0x40519fc025fe9054ll,
0xc06265bb6d3576d7ll,
0x4061705684ffbf9dll,
0xc04898220a3607acll)
)>(zz);
zz = x*z+x;
}
return b_xor(bitofsign(a0), zz);
}
BOOST_FORCEINLINE static void conf_bounds(const A0& a0, A1& a1,
const M2x2 pcov,
const value_type& normz,
Out0 & p)
{
typedef typename boost::proto::result_of::child_c<A1&,1>::type Out1;
typedef typename boost::proto::result_of::child_c<A1&,2>::type Out2;
// NT2_DISPLAY(a0.extent()); NT2_DISPLAY(a1.extent());
p.resize(a0.extent());
const In0& x = boost::proto::child_c<0>(a0);
// NT2_DISPLAY(x);
const In1& a = boost::proto::child_c<1>(a0);
// NT2_DISPLAY(a);
const In2& b = boost::proto::child_c<2>(a0);
// NT2_DISPLAY(b);
BOOST_AUTO_TPL(z, x/b);
// NT2_DISPLAY(z);
// NT2_DISPLAY(nt2::gammainc(z, a));
// NT2_DISPLAY(size(p));
p = nt2::exp(z); //nt2::gammainc(z, a);
// NT2_DISPLAY(p);
// Out0& p = boost::proto::child_c<0>(a1);
// NT2_DISPLAY(p);
BOOST_AUTO_TPL(itp, (p/nt2::oneminus(p)));
// NT2_DISPLAY(itp);
BOOST_AUTO_TPL(dp, nt2::rec(p*oneminus(p))); // derivative of logit(p) w.r.t. p
// NT2_DISPLAY(dp);
BOOST_AUTO_TPL(da, dgammainc(z,a)*dp); // dlogitp/da = dp/da * dlogitp/dp
// NT2_DISPLAY(da);
BOOST_AUTO_TPL(db, -nt2::exp(a*nt2::log(z)-z-nt2::gammaln(a)-nt2::log(b))* dp); // dlogitp/db = dp/db * dlogitp/dp
// NT2_DISPLAY(db);
BOOST_AUTO_TPL(varLogitp, pcov(1,1)*sqr(da) + (Two<value_type>()*pcov(1,2)*da + pcov(2,2)*db)*db);
// NT2_DISPLAY(varLogitp);
// NT2_DISPLAY(normz);
BOOST_AUTO_TPL(exp_halfwidth, nt2::exp(normz*nt2::sqrt(varLogitp)));
// NT2_DISPLAY(exp_halfwidth);
Out1 & plo = boost::proto::child_c<1>(a1);
Out2 & pup = boost::proto::child_c<2>(a1);
plo.resize(a0.extent());
pup.resize(a0.extent());
// std::cout << "1" << std::endl;
plo = itp*exp_halfwidth;
// std::cout << "2" << std::endl;
pup = itp/exp_halfwidth;
// std::cout << "3" << std::endl;
plo /= nt2::oneplus(plo);
// std::cout << "4" << std::endl;
pup /= nt2::oneplus(pup);
// std::cout << "5" << std::endl;
}
static inline A0 acos(const A0& a0)
{
A0 x = abs(a0);
A0 z2 = asin(a0);
A0 isgtxh = gt(x, Half<A0>());
if (any(isgtxh))
{
A0 z1 = asin(sqrt(oneminus(x)*Half<A0>()))*Two<A0>();
z2 = select(isgtxh, z1, z2);
}
z2 = select(lt(a0, -Half<A0>()), Pi<A0>()-z2, z2);
return select(isgtxh, z2, Pio_2<A0>()-z2);
// return Pi_o_2<A0>()-asin(a0);
}
static inline A0_n acos(const A0_n a0_n)
{
const A0 a0 = { a0_n };
A0 x = nt2::abs(a0);
A0 z2 = {asin(a0)};
bA0 isgtxh = gt(x, Half<A0>());
if (nt2::any(isgtxh))
{
const A0 as = {asin(sqrt(oneminus(x)*Half<A0>()))};
const A0 z1 = as*Two<A0>();
z2 = select(isgtxh, z1, z2);
}
z2 = select(lt(a0, -Half<A0>()), Pi<A0>()-z2, z2);
return select(isgtxh, z2, Pio_2<A0>()-z2);
}
