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// -*-C++-*-
#ifndef MATHFUNCS_ASIN_H
#define MATHFUNCS_ASIN_H
#include "mathfuncs_base.h"
#include <cmath>
namespace vecmathlib {
namespace {
template <typename realvec_t> realvec_t mulsign(realvec_t x, realvec_t y) {
typedef typename realvec_t::real_t real_t;
typedef typename realvec_t::intvec_t intvec_t;
typedef intvec_t IV;
typedef floatprops<real_t> FP;
intvec_t value = as_int(x);
intvec_t sign = as_int(y) & IV(FP::signbit_mask);
return as_float(value ^ sign);
}
// Note: the order of arguments is y, x, as is convention for atan2
template <typename realvec_t> realvec_t atan2k(realvec_t y, realvec_t x) {
// Algorithm taken from SLEEF 2.80
typedef typename realvec_t::real_t real_t;
typedef typename realvec_t::boolvec_t boolvec_t;
typedef realvec_t RV;
realvec_t q = RV(0.0);
q = ifthen(signbit(x), RV(-2.0), q);
x = fabs(x);
boolvec_t cond = y > x;
realvec_t x0 = x;
realvec_t y0 = y;
x = ifthen(cond, y0, x0);
y = ifthen(cond, -x0, y0);
q += ifthen(cond, RV(1.0), RV(0.0));
realvec_t s = y / x;
realvec_t t = s * s;
realvec_t u;
switch (sizeof(real_t)) {
default:
__builtin_unreachable();
case sizeof(float):
u = RV(0.00282363896258175373077393f);
u = mad(u, t, RV(-0.0159569028764963150024414f));
u = mad(u, t, RV(0.0425049886107444763183594f));
u = mad(u, t, RV(-0.0748900920152664184570312f));
u = mad(u, t, RV(0.106347933411598205566406f));
u = mad(u, t, RV(-0.142027363181114196777344f));
u = mad(u, t, RV(0.199926957488059997558594f));
u = mad(u, t, RV(-0.333331018686294555664062f));
break;
case sizeof(double):
u = RV(-1.88796008463073496563746e-05);
u = mad(u, t, RV(0.000209850076645816976906797));
u = mad(u, t, RV(-0.00110611831486672482563471));
u = mad(u, t, RV(0.00370026744188713119232403));
u = mad(u, t, RV(-0.00889896195887655491740809));
u = mad(u, t, RV(0.016599329773529201970117));
u = mad(u, t, RV(-0.0254517624932312641616861));
u = mad(u, t, RV(0.0337852580001353069993897));
u = mad(u, t, RV(-0.0407629191276836500001934));
u = mad(u, t, RV(0.0466667150077840625632675));
u = mad(u, t, RV(-0.0523674852303482457616113));
u = mad(u, t, RV(0.0587666392926673580854313));
u = mad(u, t, RV(-0.0666573579361080525984562));
u = mad(u, t, RV(0.0769219538311769618355029));
u = mad(u, t, RV(-0.090908995008245008229153));
u = mad(u, t, RV(0.111111105648261418443745));
u = mad(u, t, RV(-0.14285714266771329383765));
u = mad(u, t, RV(0.199999999996591265594148));
u = mad(u, t, RV(-0.333333333333311110369124));
break;
}
t = mad(u, t * s, s);
t = mad(q, RV(M_PI_2), t);
return t;
}
}
template <typename realvec_t>
realvec_t mathfuncs<realvec_t>::vml_asin(realvec_t d) {
// Algorithm taken from SLEEF 2.80
return mulsign(atan2k(fabs(d), sqrt((RV(1.0) + d) * (RV(1.0) - d))), d);
}
template <typename realvec_t>
realvec_t mathfuncs<realvec_t>::vml_acos(realvec_t d) {
// Algorithm taken from SLEEF 2.80
return (mulsign(atan2k(sqrt((RV(1.0) + d) * (RV(1.0) - d)), fabs(d)), d) +
ifthen(d < RV(0.0), RV(M_PI), RV(0.0)));
}
template <typename realvec_t>
realvec_t mathfuncs<realvec_t>::vml_atan(realvec_t s) {
// Algorithm taken from SLEEF 2.80
realvec_t q1 = s;
s = fabs(s);
boolvec_t q0 = s > RV(1.0);
s = ifthen(q0, rcp(s), s);
realvec_t t = s * s;
realvec_t u;
switch (sizeof(real_t)) {
default:
__builtin_unreachable();
case sizeof(float):
u = RV(0.00282363896258175373077393f);
u = mad(u, t, RV(-0.0159569028764963150024414f));
u = mad(u, t, RV(0.0425049886107444763183594f));
u = mad(u, t, RV(-0.0748900920152664184570312f));
u = mad(u, t, RV(0.106347933411598205566406f));
u = mad(u, t, RV(-0.142027363181114196777344f));
u = mad(u, t, RV(0.199926957488059997558594f));
u = mad(u, t, RV(-0.333331018686294555664062f));
break;
case sizeof(double):
u = RV(-1.88796008463073496563746e-05);
u = mad(u, t, RV(0.000209850076645816976906797));
u = mad(u, t, RV(-0.00110611831486672482563471));
u = mad(u, t, RV(0.00370026744188713119232403));
u = mad(u, t, RV(-0.00889896195887655491740809));
u = mad(u, t, RV(0.016599329773529201970117));
u = mad(u, t, RV(-0.0254517624932312641616861));
u = mad(u, t, RV(0.0337852580001353069993897));
u = mad(u, t, RV(-0.0407629191276836500001934));
u = mad(u, t, RV(0.0466667150077840625632675));
u = mad(u, t, RV(-0.0523674852303482457616113));
u = mad(u, t, RV(0.0587666392926673580854313));
u = mad(u, t, RV(-0.0666573579361080525984562));
u = mad(u, t, RV(0.0769219538311769618355029));
u = mad(u, t, RV(-0.090908995008245008229153));
u = mad(u, t, RV(0.111111105648261418443745));
u = mad(u, t, RV(-0.14285714266771329383765));
u = mad(u, t, RV(0.199999999996591265594148));
u = mad(u, t, RV(-0.333333333333311110369124));
break;
}
t = s + s * (t * u);
t = ifthen(q0, RV(M_PI_2) - t, t);
t = copysign(t, q1);
return t;
}
// Note: the order of arguments is y, x, as is convention for atan2
template <typename realvec_t>
realvec_t mathfuncs<realvec_t>::vml_atan2(realvec_t y, realvec_t x) {
// Algorithm taken from SLEEF 2.80
realvec_t r = atan2k(fabs(y), x);
r = mulsign(r, x);
r = ifthen(isinf(x) || x == RV(0.0),
ifthen(isinf(x), RV(M_PI_2) - copysign(RV(M_PI_2), x), RV(M_PI_2)),
r);
r = ifthen(isinf(y),
ifthen(isinf(x), RV(M_PI_2) - copysign(RV(M_PI_4), x), RV(M_PI_2)),
r);
r = ifthen(y == RV(0.0), ifthen(signbit(x), RV(M_PI), RV(0.0)), r);
const real_t nan = std::numeric_limits<real_t>::quiet_NaN();
return ifthen(isnan(x) || isnan(y), RV(nan), mulsign(r, y));
}
}; // namespace vecmathlib
#endif // #ifndef MATHFUNCS_ASIN_H
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