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js8call/.svn/pristine/e1/e1d4aec3b05a54a568933dfe9495f3c5f1d8575d.svn-base

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Initial Commit
2018-02-08 21:28:33 -05:00
// (C) Copyright John Maddock 2006.
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
#ifndef BOOST_MATH_SF_ERF_INV_HPP
#define BOOST_MATH_SF_ERF_INV_HPP
#ifdef _MSC_VER
#pragma once
#pragma warning(push)
#pragma warning(disable:4127) // Conditional expression is constant
#pragma warning(disable:4702) // Unreachable code: optimization warning
#endif
namespace boost{ namespace math{
namespace detail{
//
// The inverse erf and erfc functions share a common implementation,
// this version is for 80-bit long double's and smaller:
//
template <class T, class Policy>
T erf_inv_imp(const T& p, const T& q, const Policy&, const boost::mpl::int_<64>*)
{
BOOST_MATH_STD_USING // for ADL of std names.
T result = 0;
if(p <= 0.5)
{
//
// Evaluate inverse erf using the rational approximation:
//
// x = p(p+10)(Y+R(p))
//
// Where Y is a constant, and R(p) is optimised for a low
// absolute error compared to |Y|.
//
// double: Max error found: 2.001849e-18
// long double: Max error found: 1.017064e-20
// Maximum Deviation Found (actual error term at infinite precision) 8.030e-21
//
static const float Y = 0.0891314744949340820313f;
static const T P[] = {
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[] = {
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);
result = g * Y + g * r;
}
else if(q >= 0.25)
{
//
// Rational approximation for 0.5 > q >= 0.25
//
// x = sqrt(-2*log(q)) / (Y + R(q))
//
// Where Y is a constant, and R(q) is optimised for a low
// absolute error compared to Y.
//
// double : Max error found: 7.403372e-17
// long double : Max error found: 6.084616e-20
// Maximum Deviation Found (error term) 4.811e-20
//
static const float Y = 2.249481201171875f;
static const T P[] = {
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[] = {
BOOST_MATH_BIG_CONSTANT(T, 64, 1.0),
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 - 0.25f;
T r = tools::evaluate_polynomial(P, xs) / tools::evaluate_polynomial(Q, xs);
result = g / (Y + r);
}
else
{
//
// For q < 0.25 we have a series of rational approximations all
// of the general form:
//
// let: x = sqrt(-log(q))
//
// Then the result is given by:
//
// x(Y+R(x-B))
//
// where Y is a constant, B is the lowest value of x for which
// the approximation is valid, and R(x-B) is optimised for a low
// absolute error compared to Y.
//
// Note that almost all code will really go through the first
// or maybe second approximation. After than we're dealing with very
// small input values indeed: 80 and 128 bit long double's go all the
// way down to ~ 1e-5000 so the "tail" is rather long...
//
T x = sqrt(-log(q));
if(x < 3)
{
// Max error found: 1.089051e-20
static const float Y = 0.807220458984375f;
static const T P[] = {
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[] = {
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 - 1.125f;
T R = tools::evaluate_polynomial(P, xs) / tools::evaluate_polynomial(Q, xs);
result = Y * x + R * x;
}
else if(x < 6)
{
// Max error found: 8.389174e-21
static const float Y = 0.93995571136474609375f;
static const T P[] = {
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[] = {
BOOST_MATH_BIG_CONSTANT(T, 64, 1.0),
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);
result = Y * x + R * x;
}
else if(x < 18)
{
// Max error found: 1.481312e-19
static const float Y = 0.98362827301025390625f;
static const T P[] = {
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[] = {
BOOST_MATH_BIG_CONSTANT(T, 64, 1.0),
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);
result = Y * x + R * x;
}
else if(x < 44)
{
// Max error found: 5.697761e-20
static const float Y = 0.99714565277099609375f;
static const T P[] = {
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[] = {
BOOST_MATH_BIG_CONSTANT(T, 64, 1.0),
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);
result = Y * x + R * x;
}
else
{
// Max error found: 1.279746e-20
static const float Y = 0.99941349029541015625f;
static const T P[] = {
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[] = {
BOOST_MATH_BIG_CONSTANT(T, 64, 1.0),
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);
result = Y * x + R * x;
}
}
return result;
}
template <class T, class Policy>
struct erf_roots
{
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 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:
T target;
int sign;
};
template <class T, class Policy>
T erf_inv_imp(const T& p, const T& q, const Policy& pol, const boost::mpl::int_<0>*)
{
//
// Generic version, get a guess that's accurate to 64-bits (10^-19)
//
T guess = erf_inv_imp(p, q, pol, static_cast<mpl::int_<64> const*>(0));
T result;
//
// If T has more bit's than 64 in it's mantissa then we need to iterate,
// otherwise we can just return the result:
//
if(policies::digits<T, Policy>() > 64)
{
boost::uintmax_t max_iter = policies::get_max_root_iterations<Policy>();
if(p <= 0.5)
{
result = tools::halley_iterate(detail::erf_roots<typename remove_cv<T>::type, Policy>(p, 1), guess, static_cast<T>(0), tools::max_value<T>(), (policies::digits<T, Policy>() * 2) / 3, max_iter);
}
else
{
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<T>("boost::math::erf_inv<%1%>", max_iter, pol);
}
else
{
result = guess;
}
return result;
}
template <class T, class Policy>
struct erf_inv_initializer
{
struct init
{
init()
{
do_init();
}
static bool is_value_non_zero(T);
static void do_init()
{
// If std::numeric_limits<T>::digits is zero, we must not call
// our inituialization code here as the precision presumably
// varies at runtime, and will not have been set yet.
if(std::numeric_limits<T>::digits)
{
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());
// These following initializations must not be called if
// type T can not hold the relevant values without
// underflow to zero. We check this at runtime because
// some tools such as valgrind silently change the precision
// of T at runtime, and numeric_limits basically lies!
if(is_value_non_zero(static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-130))))
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(is_value_non_zero(static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-800))))
boost::math::erfc_inv(static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-800)), Policy());
if(is_value_non_zero(static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-900))))
boost::math::erfc_inv(static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-900)), Policy());
#else
if(is_value_non_zero(static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 64, 1e-800))))
boost::math::erfc_inv(static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 64, 1e-800)), Policy());
if(is_value_non_zero(static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 64, 1e-900))))
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;
template <class T, class Policy>
bool erf_inv_initializer<T, Policy>::init::is_value_non_zero(T v)
{
// This needs to be non-inline to detect whether v is non zero at runtime
// rather than at compile time, only relevant when running under valgrind
// which changes long double's to double's on the fly.
return v != 0;
}
} // 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:
//
static const char* function = "boost::math::erfc_inv<%1%>(%1%, %1%)";
if((z < 0) || (z > 2))
return policies::raise_domain_error<result_type>(function, "Argument outside range [0,2] in inverse erfc function (got p=%1%).", z, pol);
if(z == 0)
return policies::raise_overflow_error<result_type>(function, 0, pol);
if(z == 2)
return -policies::raise_overflow_error<result_type>(function, 0, pol);
//
// Normalise the input, so it's in the range [0,1], we will
// negate the result if z is outside that range. This is a simple
// application of the erfc reflection formula: erfc(-z) = 2 - erfc(z)
//
result_type p, q, s;
if(z > 1)
{
q = 2 - z;
p = 1 - q;
s = -1;
}
else
{
p = 1 - z;
q = z;
s = 1;
}
//
// A bit of meta-programming to figure out which implementation
// to use, based on the number of bits in the mantissa of T:
//
typedef typename policies::precision<result_type, Policy>::type precision_type;
typedef typename mpl::if_<
mpl::or_<mpl::less_equal<precision_type, mpl::int_<0> >, mpl::greater<precision_type, mpl::int_<64> > >,
mpl::int_<0>,
mpl::int_<64>
>::type tag_type;
//
// Likewise use internal promotion, so we evaluate at a higher
// precision internally if it's appropriate:
//
typedef typename policies::evaluation<result_type, Policy>::type eval_type;
typedef typename policies::normalise<
Policy,
policies::promote_float<false>,
policies::promote_double<false>,
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:
//
return s * policies::checked_narrowing_cast<result_type, forwarding_policy>(
detail::erf_inv_imp(static_cast<eval_type>(p), static_cast<eval_type>(q), forwarding_policy(), static_cast<tag_type const*>(0)), function);
}
template <class T, class Policy>
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:
//
static const char* function = "boost::math::erf_inv<%1%>(%1%, %1%)";
if((z < -1) || (z > 1))
return policies::raise_domain_error<result_type>(function, "Argument outside range [-1, 1] in inverse erf function (got p=%1%).", z, pol);
if(z == 1)
return policies::raise_overflow_error<result_type>(function, 0, pol);
if(z == -1)
return -policies::raise_overflow_error<result_type>(function, 0, pol);
if(z == 0)
return 0;
//
// Normalise the input, so it's in the range [0,1], we will
// negate the result if z is outside that range. This is a simple
// application of the erf reflection formula: erf(-z) = -erf(z)
//
result_type p, q, s;
if(z < 0)
{
p = -z;
q = 1 - p;
s = -1;
}
else
{
p = z;
q = 1 - z;
s = 1;
}
//
// A bit of meta-programming to figure out which implementation
// to use, based on the number of bits in the mantissa of T:
//
typedef typename policies::precision<result_type, Policy>::type precision_type;
typedef typename mpl::if_<
mpl::or_<mpl::less_equal<precision_type, mpl::int_<0> >, mpl::greater<precision_type, mpl::int_<64> > >,
mpl::int_<0>,
mpl::int_<64>
>::type tag_type;
//
// Likewise use internal promotion, so we evaluate at a higher
// precision internally if it's appropriate:
//
typedef typename policies::evaluation<result_type, Policy>::type eval_type;
typedef typename policies::normalise<
Policy,
policies::promote_float<false>,
policies::promote_double<false>,
policies::discrete_quantile<>,
policies::assert_undefined<> >::type forwarding_policy;
//
// Likewise use internal promotion, so we evaluate at a higher
// 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:
//
return s * policies::checked_narrowing_cast<result_type, forwarding_policy>(
detail::erf_inv_imp(static_cast<eval_type>(p), static_cast<eval_type>(q), forwarding_policy(), static_cast<tag_type const*>(0)), function);
}
template <class T>
inline typename tools::promote_args<T>::type erfc_inv(T z)
{
return erfc_inv(z, policies::policy<>());
}
template <class T>
inline typename tools::promote_args<T>::type erf_inv(T z)
{
return erf_inv(z, policies::policy<>());
}
} // namespace math
} // namespace boost
#ifdef _MSC_VER
#pragma warning(pop)
#endif
#endif // BOOST_MATH_SF_ERF_INV_HPP
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