//
static const float Y = 0.0891314744949340820313f;
static const T P[] = {
- -0.000508781949658280665617L,
- -0.00836874819741736770379L,
- 0.0334806625409744615033L,
- -0.0126926147662974029034L,
- -0.0365637971411762664006L,
- 0.0219878681111168899165L,
- 0.00822687874676915743155L,
- -0.00538772965071242932965L
+ BOOST_MATH_BIG_CONSTANT(T, 64, -0.000508781949658280665617),
+ BOOST_MATH_BIG_CONSTANT(T, 64, -0.00836874819741736770379),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.0334806625409744615033),
+ BOOST_MATH_BIG_CONSTANT(T, 64, -0.0126926147662974029034),
+ BOOST_MATH_BIG_CONSTANT(T, 64, -0.0365637971411762664006),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.0219878681111168899165),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.00822687874676915743155),
+ BOOST_MATH_BIG_CONSTANT(T, 64, -0.00538772965071242932965)
};
static const T Q[] = {
- 1,
- -0.970005043303290640362L,
- -1.56574558234175846809L,
- 1.56221558398423026363L,
- 0.662328840472002992063L,
- -0.71228902341542847553L,
- -0.0527396382340099713954L,
- 0.0795283687341571680018L,
- -0.00233393759374190016776L,
- 0.000886216390456424707504L
+ BOOST_MATH_BIG_CONSTANT(T, 64, 1.0),
+ BOOST_MATH_BIG_CONSTANT(T, 64, -0.970005043303290640362),
+ BOOST_MATH_BIG_CONSTANT(T, 64, -1.56574558234175846809),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 1.56221558398423026363),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.662328840472002992063),
+ BOOST_MATH_BIG_CONSTANT(T, 64, -0.71228902341542847553),
+ BOOST_MATH_BIG_CONSTANT(T, 64, -0.0527396382340099713954),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.0795283687341571680018),
+ BOOST_MATH_BIG_CONSTANT(T, 64, -0.00233393759374190016776),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.000886216390456424707504)
};
T g = p * (p + 10);
T r = tools::evaluate_polynomial(P, p) / tools::evaluate_polynomial(Q, p);
//
static const float Y = 2.249481201171875f;
static const T P[] = {
- -0.202433508355938759655L,
- 0.105264680699391713268L,
- 8.37050328343119927838L,
- 17.6447298408374015486L,
- -18.8510648058714251895L,
- -44.6382324441786960818L,
- 17.445385985570866523L,
- 21.1294655448340526258L,
- -3.67192254707729348546L
+ BOOST_MATH_BIG_CONSTANT(T, 64, -0.202433508355938759655),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.105264680699391713268),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 8.37050328343119927838),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 17.6447298408374015486),
+ BOOST_MATH_BIG_CONSTANT(T, 64, -18.8510648058714251895),
+ BOOST_MATH_BIG_CONSTANT(T, 64, -44.6382324441786960818),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 17.445385985570866523),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 21.1294655448340526258),
+ BOOST_MATH_BIG_CONSTANT(T, 64, -3.67192254707729348546)
};
static const T Q[] = {
- 1L,
- 6.24264124854247537712L,
- 3.9713437953343869095L,
- -28.6608180499800029974L,
- -20.1432634680485188801L,
- 48.5609213108739935468L,
- 10.8268667355460159008L,
- -22.6436933413139721736L,
- 1.72114765761200282724L
+ BOOST_MATH_BIG_CONSTANT(T, 64, 1),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 6.24264124854247537712),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 3.9713437953343869095),
+ BOOST_MATH_BIG_CONSTANT(T, 64, -28.6608180499800029974),
+ BOOST_MATH_BIG_CONSTANT(T, 64, -20.1432634680485188801),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 48.5609213108739935468),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 10.8268667355460159008),
+ BOOST_MATH_BIG_CONSTANT(T, 64, -22.6436933413139721736),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 1.72114765761200282724)
};
T g = sqrt(-2 * log(q));
T xs = q - 0.25;
// Max error found: 1.089051e-20
static const float Y = 0.807220458984375f;
static const T P[] = {
- -0.131102781679951906451L,
- -0.163794047193317060787L,
- 0.117030156341995252019L,
- 0.387079738972604337464L,
- 0.337785538912035898924L,
- 0.142869534408157156766L,
- 0.0290157910005329060432L,
- 0.00214558995388805277169L,
- -0.679465575181126350155e-6L,
- 0.285225331782217055858e-7L,
- -0.681149956853776992068e-9L
+ BOOST_MATH_BIG_CONSTANT(T, 64, -0.131102781679951906451),
+ BOOST_MATH_BIG_CONSTANT(T, 64, -0.163794047193317060787),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.117030156341995252019),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.387079738972604337464),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.337785538912035898924),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.142869534408157156766),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.0290157910005329060432),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.00214558995388805277169),
+ BOOST_MATH_BIG_CONSTANT(T, 64, -0.679465575181126350155e-6),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.285225331782217055858e-7),
+ BOOST_MATH_BIG_CONSTANT(T, 64, -0.681149956853776992068e-9)
};
static const T Q[] = {
- 1,
- 3.46625407242567245975L,
- 5.38168345707006855425L,
- 4.77846592945843778382L,
- 2.59301921623620271374L,
- 0.848854343457902036425L,
- 0.152264338295331783612L,
- 0.01105924229346489121L
+ BOOST_MATH_BIG_CONSTANT(T, 64, 1.0),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 3.46625407242567245975),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 5.38168345707006855425),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 4.77846592945843778382),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 2.59301921623620271374),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.848854343457902036425),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.152264338295331783612),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.01105924229346489121)
};
T xs = x - 1.125;
T R = tools::evaluate_polynomial(P, xs) / tools::evaluate_polynomial(Q, xs);
// Max error found: 8.389174e-21
static const float Y = 0.93995571136474609375f;
static const T P[] = {
- -0.0350353787183177984712L,
- -0.00222426529213447927281L,
- 0.0185573306514231072324L,
- 0.00950804701325919603619L,
- 0.00187123492819559223345L,
- 0.000157544617424960554631L,
- 0.460469890584317994083e-5L,
- -0.230404776911882601748e-9L,
- 0.266339227425782031962e-11L
+ BOOST_MATH_BIG_CONSTANT(T, 64, -0.0350353787183177984712),
+ BOOST_MATH_BIG_CONSTANT(T, 64, -0.00222426529213447927281),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.0185573306514231072324),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.00950804701325919603619),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.00187123492819559223345),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.000157544617424960554631),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.460469890584317994083e-5),
+ BOOST_MATH_BIG_CONSTANT(T, 64, -0.230404776911882601748e-9),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.266339227425782031962e-11)
};
static const T Q[] = {
- 1L,
- 1.3653349817554063097L,
- 0.762059164553623404043L,
- 0.220091105764131249824L,
- 0.0341589143670947727934L,
- 0.00263861676657015992959L,
- 0.764675292302794483503e-4L
+ BOOST_MATH_BIG_CONSTANT(T, 64, 1),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 1.3653349817554063097),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.762059164553623404043),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.220091105764131249824),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.0341589143670947727934),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.00263861676657015992959),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.764675292302794483503e-4)
};
T xs = x - 3;
T R = tools::evaluate_polynomial(P, xs) / tools::evaluate_polynomial(Q, xs);
// Max error found: 1.481312e-19
static const float Y = 0.98362827301025390625f;
static const T P[] = {
- -0.0167431005076633737133L,
- -0.00112951438745580278863L,
- 0.00105628862152492910091L,
- 0.000209386317487588078668L,
- 0.149624783758342370182e-4L,
- 0.449696789927706453732e-6L,
- 0.462596163522878599135e-8L,
- -0.281128735628831791805e-13L,
- 0.99055709973310326855e-16L
+ BOOST_MATH_BIG_CONSTANT(T, 64, -0.0167431005076633737133),
+ BOOST_MATH_BIG_CONSTANT(T, 64, -0.00112951438745580278863),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.00105628862152492910091),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.000209386317487588078668),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.149624783758342370182e-4),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.449696789927706453732e-6),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.462596163522878599135e-8),
+ BOOST_MATH_BIG_CONSTANT(T, 64, -0.281128735628831791805e-13),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.99055709973310326855e-16)
};
static const T Q[] = {
- 1L,
- 0.591429344886417493481L,
- 0.138151865749083321638L,
- 0.0160746087093676504695L,
- 0.000964011807005165528527L,
- 0.275335474764726041141e-4L,
- 0.282243172016108031869e-6L
+ BOOST_MATH_BIG_CONSTANT(T, 64, 1),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.591429344886417493481),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.138151865749083321638),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.0160746087093676504695),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.000964011807005165528527),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.275335474764726041141e-4),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.282243172016108031869e-6)
};
T xs = x - 6;
T R = tools::evaluate_polynomial(P, xs) / tools::evaluate_polynomial(Q, xs);
// Max error found: 5.697761e-20
static const float Y = 0.99714565277099609375f;
static const T P[] = {
- -0.0024978212791898131227L,
- -0.779190719229053954292e-5L,
- 0.254723037413027451751e-4L,
- 0.162397777342510920873e-5L,
- 0.396341011304801168516e-7L,
- 0.411632831190944208473e-9L,
- 0.145596286718675035587e-11L,
- -0.116765012397184275695e-17L
+ BOOST_MATH_BIG_CONSTANT(T, 64, -0.0024978212791898131227),
+ BOOST_MATH_BIG_CONSTANT(T, 64, -0.779190719229053954292e-5),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.254723037413027451751e-4),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.162397777342510920873e-5),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.396341011304801168516e-7),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.411632831190944208473e-9),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.145596286718675035587e-11),
+ BOOST_MATH_BIG_CONSTANT(T, 64, -0.116765012397184275695e-17)
};
static const T Q[] = {
- 1L,
- 0.207123112214422517181L,
- 0.0169410838120975906478L,
- 0.000690538265622684595676L,
- 0.145007359818232637924e-4L,
- 0.144437756628144157666e-6L,
- 0.509761276599778486139e-9L
+ BOOST_MATH_BIG_CONSTANT(T, 64, 1),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.207123112214422517181),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.0169410838120975906478),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.000690538265622684595676),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.145007359818232637924e-4),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.144437756628144157666e-6),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.509761276599778486139e-9)
};
T xs = x - 18;
T R = tools::evaluate_polynomial(P, xs) / tools::evaluate_polynomial(Q, xs);
// Max error found: 1.279746e-20
static const float Y = 0.99941349029541015625f;
static const T P[] = {
- -0.000539042911019078575891L,
- -0.28398759004727721098e-6L,
- 0.899465114892291446442e-6L,
- 0.229345859265920864296e-7L,
- 0.225561444863500149219e-9L,
- 0.947846627503022684216e-12L,
- 0.135880130108924861008e-14L,
- -0.348890393399948882918e-21L
+ BOOST_MATH_BIG_CONSTANT(T, 64, -0.000539042911019078575891),
+ BOOST_MATH_BIG_CONSTANT(T, 64, -0.28398759004727721098e-6),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.899465114892291446442e-6),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.229345859265920864296e-7),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.225561444863500149219e-9),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.947846627503022684216e-12),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.135880130108924861008e-14),
+ BOOST_MATH_BIG_CONSTANT(T, 64, -0.348890393399948882918e-21)
};
static const T Q[] = {
- 1L,
- 0.0845746234001899436914L,
- 0.00282092984726264681981L,
- 0.468292921940894236786e-4L,
- 0.399968812193862100054e-6L,
- 0.161809290887904476097e-8L,
- 0.231558608310259605225e-11L
+ BOOST_MATH_BIG_CONSTANT(T, 64, 1),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.0845746234001899436914),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.00282092984726264681981),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.468292921940894236786e-4),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.399968812193862100054e-6),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.161809290887904476097e-8),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.231558608310259605225e-11)
};
T xs = x - 44;
T R = tools::evaluate_polynomial(P, xs) / tools::evaluate_polynomial(Q, xs);
template <class T, class Policy>
struct erf_roots
{
- std::tr1::tuple<T,T,T> operator()(const T& guess)
+ boost::math::tuple<T,T,T> operator()(const T& guess)
{
BOOST_MATH_STD_USING
T derivative = sign * (2 / sqrt(constants::pi<T>())) * exp(-(guess * guess));
T derivative2 = -2 * guess * derivative;
- return std::tr1::make_tuple(((sign > 0) ? boost::math::erf(guess, Policy()) : boost::math::erfc(guess, Policy())) - target, derivative, derivative2);
+ return boost::math::make_tuple(((sign > 0) ? static_cast<T>(boost::math::erf(guess, Policy()) - target) : static_cast<T>(boost::math::erfc(guess, Policy())) - target), derivative, derivative2);
}
erf_roots(T z, int s) : target(z), sign(s) {}
private:
{
result = tools::halley_iterate(detail::erf_roots<typename remove_cv<T>::type, Policy>(q, -1), guess, static_cast<T>(0), tools::max_value<T>(), (policies::digits<T, Policy>() * 2) / 3, max_iter);
}
- policies::check_root_iterations("boost::math::erf_inv<%1%>", max_iter, pol);
+ policies::check_root_iterations<T>("boost::math::erf_inv<%1%>", max_iter, pol);
}
else
{
return result;
}
+template <class T, class Policy>
+struct erf_inv_initializer
+{
+ struct init
+ {
+ init()
+ {
+ do_init();
+ }
+ static void do_init()
+ {
+ boost::math::erf_inv(static_cast<T>(0.25), Policy());
+ boost::math::erf_inv(static_cast<T>(0.55), Policy());
+ boost::math::erf_inv(static_cast<T>(0.95), Policy());
+ boost::math::erfc_inv(static_cast<T>(1e-15), Policy());
+ if(static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-130)) != 0)
+ boost::math::erfc_inv(static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-130)), Policy());
+
+ // Some compilers choke on constants that would underflow, even in code that isn't instantiated
+ // so try and filter these cases out in the preprocessor:
+#if LDBL_MAX_10_EXP >= 800
+ if(static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-800)) != 0)
+ boost::math::erfc_inv(static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-800)), Policy());
+ if(static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-900)) != 0)
+ boost::math::erfc_inv(static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-900)), Policy());
+#else
+ if(static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 64, 1e-800)) != 0)
+ boost::math::erfc_inv(static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 64, 1e-800)), Policy());
+ if(static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 64, 1e-900)) != 0)
+ boost::math::erfc_inv(static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 64, 1e-900)), Policy());
+#endif
+ }
+ void force_instantiate()const{}
+ };
+ static const init initializer;
+ static void force_instantiate()
+ {
+ initializer.force_instantiate();
+ }
+};
+
+template <class T, class Policy>
+const typename erf_inv_initializer<T, Policy>::init erf_inv_initializer<T, Policy>::initializer;
+
} // namespace detail
template <class T, class Policy>
typename tools::promote_args<T>::type erfc_inv(T z, const Policy& pol)
{
typedef typename tools::promote_args<T>::type result_type;
+
//
// Begin by testing for domain errors, and other special cases:
//
policies::discrete_quantile<>,
policies::assert_undefined<> >::type forwarding_policy;
+ detail::erf_inv_initializer<eval_type, forwarding_policy>::force_instantiate();
+
//
// And get the result, negating where required:
//
typename tools::promote_args<T>::type erf_inv(T z, const Policy& pol)
{
typedef typename tools::promote_args<T>::type result_type;
+
//
// Begin by testing for domain errors, and other special cases:
//
// precision internally if it's appropriate:
//
typedef typename policies::evaluation<result_type, Policy>::type eval_type;
+
+ detail::erf_inv_initializer<eval_type, forwarding_policy>::force_instantiate();
//
// And get the result, negating where required:
//
projects / rsem.git / blobdiff