tools/detail/rational_horner3_11.hpp

0001 //  (C) Copyright John Maddock 2007.
0002 //  Use, modification and distribution are subject to the
0003 //  Boost Software License, Version 1.0. (See accompanying file
0004 //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
0005 //
0006 //  This file is machine generated, do not edit by hand
0007
0008 // Polynomial evaluation using second order Horners rule
0009 #ifndef BOOST_MATH_TOOLS_RAT_EVAL_11_HPP
0010 #define BOOST_MATH_TOOLS_RAT_EVAL_11_HPP
0011
0012 namespace boost{ namespace math{ namespace tools{ namespace detail{
0013
0014 template <class T, class U, class V>
0015 inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
0016 {
0017    return static_cast<V>(0);
0018 }
0019
0020 template <class T, class U, class V>
0021 inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
0022 {
0023    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
0024 }
0025
0026 template <class T, class U, class V>
0027 inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
0028 {
0029    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
0030 }
0031
0032 template <class T, class U, class V>
0033 inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
0034 {
0035    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
0036 }
0037
0038 template <class T, class U, class V>
0039 inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
0040 {
0041    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
0042 }
0043
0044 template <class T, class U, class V>
0045 inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
0046 {
0047    if(x <= 1)
0048    {
0049       V x2 = x * x;
0050       V t[4];
0051       t[0] = a[4] * x2 + a[2];
0052       t[1] = a[3] * x2 + a[1];
0053       t[2] = b[4] * x2 + b[2];
0054       t[3] = b[3] * x2 + b[1];
0055       t[0] *= x2;
0056       t[2] *= x2;
0057       t[0] += static_cast<V>(a[0]);
0058       t[2] += static_cast<V>(b[0]);
0059       t[1] *= x;
0060       t[3] *= x;
0061       return (t[0] + t[1]) / (t[2] + t[3]);
0062    }
0063    else
0064    {
0065       V z = 1 / x;
0066       V z2 = 1 / (x * x);
0067       V t[4];
0068       t[0] = a[0] * z2 + a[2];
0069       t[1] = a[1] * z2 + a[3];
0070       t[2] = b[0] * z2 + b[2];
0071       t[3] = b[1] * z2 + b[3];
0072       t[0] *= z2;
0073       t[2] *= z2;
0074       t[0] += static_cast<V>(a[4]);
0075       t[2] += static_cast<V>(b[4]);
0076       t[1] *= z;
0077       t[3] *= z;
0078       return (t[0] + t[1]) / (t[2] + t[3]);
0079    }
0080 }
0081
0082 template <class T, class U, class V>
0083 inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
0084 {
0085    if(x <= 1)
0086    {
0087       V x2 = x * x;
0088       V t[4];
0089       t[0] = a[5] * x2 + a[3];
0090       t[1] = a[4] * x2 + a[2];
0091       t[2] = b[5] * x2 + b[3];
0092       t[3] = b[4] * x2 + b[2];
0093       t[0] *= x2;
0094       t[1] *= x2;
0095       t[2] *= x2;
0096       t[3] *= x2;
0097       t[0] += static_cast<V>(a[1]);
0098       t[1] += static_cast<V>(a[0]);
0099       t[2] += static_cast<V>(b[1]);
0100       t[3] += static_cast<V>(b[0]);
0101       t[0] *= x;
0102       t[2] *= x;
0103       return (t[0] + t[1]) / (t[2] + t[3]);
0104    }
0105    else
0106    {
0107       V z = 1 / x;
0108       V z2 = 1 / (x * x);
0109       V t[4];
0110       t[0] = a[0] * z2 + a[2];
0111       t[1] = a[1] * z2 + a[3];
0112       t[2] = b[0] * z2 + b[2];
0113       t[3] = b[1] * z2 + b[3];
0114       t[0] *= z2;
0115       t[1] *= z2;
0116       t[2] *= z2;
0117       t[3] *= z2;
0118       t[0] += static_cast<V>(a[4]);
0119       t[1] += static_cast<V>(a[5]);
0120       t[2] += static_cast<V>(b[4]);
0121       t[3] += static_cast<V>(b[5]);
0122       t[0] *= z;
0123       t[2] *= z;
0124       return (t[0] + t[1]) / (t[2] + t[3]);
0125    }
0126 }
0127
0128 template <class T, class U, class V>
0129 inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
0130 {
0131    if(x <= 1)
0132    {
0133       V x2 = x * x;
0134       V t[4];
0135       t[0] = a[6] * x2 + a[4];
0136       t[1] = a[5] * x2 + a[3];
0137       t[2] = b[6] * x2 + b[4];
0138       t[3] = b[5] * x2 + b[3];
0139       t[0] *= x2;
0140       t[1] *= x2;
0141       t[2] *= x2;
0142       t[3] *= x2;
0143       t[0] += static_cast<V>(a[2]);
0144       t[1] += static_cast<V>(a[1]);
0145       t[2] += static_cast<V>(b[2]);
0146       t[3] += static_cast<V>(b[1]);
0147       t[0] *= x2;
0148       t[2] *= x2;
0149       t[0] += static_cast<V>(a[0]);
0150       t[2] += static_cast<V>(b[0]);
0151       t[1] *= x;
0152       t[3] *= x;
0153       return (t[0] + t[1]) / (t[2] + t[3]);
0154    }
0155    else
0156    {
0157       V z = 1 / x;
0158       V z2 = 1 / (x * x);
0159       V t[4];
0160       t[0] = a[0] * z2 + a[2];
0161       t[1] = a[1] * z2 + a[3];
0162       t[2] = b[0] * z2 + b[2];
0163       t[3] = b[1] * z2 + b[3];
0164       t[0] *= z2;
0165       t[1] *= z2;
0166       t[2] *= z2;
0167       t[3] *= z2;
0168       t[0] += static_cast<V>(a[4]);
0169       t[1] += static_cast<V>(a[5]);
0170       t[2] += static_cast<V>(b[4]);
0171       t[3] += static_cast<V>(b[5]);
0172       t[0] *= z2;
0173       t[2] *= z2;
0174       t[0] += static_cast<V>(a[6]);
0175       t[2] += static_cast<V>(b[6]);
0176       t[1] *= z;
0177       t[3] *= z;
0178       return (t[0] + t[1]) / (t[2] + t[3]);
0179    }
0180 }
0181
0182 template <class T, class U, class V>
0183 inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
0184 {
0185    if(x <= 1)
0186    {
0187       V x2 = x * x;
0188       V t[4];
0189       t[0] = a[7] * x2 + a[5];
0190       t[1] = a[6] * x2 + a[4];
0191       t[2] = b[7] * x2 + b[5];
0192       t[3] = b[6] * x2 + b[4];
0193       t[0] *= x2;
0194       t[1] *= x2;
0195       t[2] *= x2;
0196       t[3] *= x2;
0197       t[0] += static_cast<V>(a[3]);
0198       t[1] += static_cast<V>(a[2]);
0199       t[2] += static_cast<V>(b[3]);
0200       t[3] += static_cast<V>(b[2]);
0201       t[0] *= x2;
0202       t[1] *= x2;
0203       t[2] *= x2;
0204       t[3] *= x2;
0205       t[0] += static_cast<V>(a[1]);
0206       t[1] += static_cast<V>(a[0]);
0207       t[2] += static_cast<V>(b[1]);
0208       t[3] += static_cast<V>(b[0]);
0209       t[0] *= x;
0210       t[2] *= x;
0211       return (t[0] + t[1]) / (t[2] + t[3]);
0212    }
0213    else
0214    {
0215       V z = 1 / x;
0216       V z2 = 1 / (x * x);
0217       V t[4];
0218       t[0] = a[0] * z2 + a[2];
0219       t[1] = a[1] * z2 + a[3];
0220       t[2] = b[0] * z2 + b[2];
0221       t[3] = b[1] * z2 + b[3];
0222       t[0] *= z2;
0223       t[1] *= z2;
0224       t[2] *= z2;
0225       t[3] *= z2;
0226       t[0] += static_cast<V>(a[4]);
0227       t[1] += static_cast<V>(a[5]);
0228       t[2] += static_cast<V>(b[4]);
0229       t[3] += static_cast<V>(b[5]);
0230       t[0] *= z2;
0231       t[1] *= z2;
0232       t[2] *= z2;
0233       t[3] *= z2;
0234       t[0] += static_cast<V>(a[6]);
0235       t[1] += static_cast<V>(a[7]);
0236       t[2] += static_cast<V>(b[6]);
0237       t[3] += static_cast<V>(b[7]);
0238       t[0] *= z;
0239       t[2] *= z;
0240       return (t[0] + t[1]) / (t[2] + t[3]);
0241    }
0242 }
0243
0244 template <class T, class U, class V>
0245 inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
0246 {
0247    if(x <= 1)
0248    {
0249       V x2 = x * x;
0250       V t[4];
0251       t[0] = a[8] * x2 + a[6];
0252       t[1] = a[7] * x2 + a[5];
0253       t[2] = b[8] * x2 + b[6];
0254       t[3] = b[7] * x2 + b[5];
0255       t[0] *= x2;
0256       t[1] *= x2;
0257       t[2] *= x2;
0258       t[3] *= x2;
0259       t[0] += static_cast<V>(a[4]);
0260       t[1] += static_cast<V>(a[3]);
0261       t[2] += static_cast<V>(b[4]);
0262       t[3] += static_cast<V>(b[3]);
0263       t[0] *= x2;
0264       t[1] *= x2;
0265       t[2] *= x2;
0266       t[3] *= x2;
0267       t[0] += static_cast<V>(a[2]);
0268       t[1] += static_cast<V>(a[1]);
0269       t[2] += static_cast<V>(b[2]);
0270       t[3] += static_cast<V>(b[1]);
0271       t[0] *= x2;
0272       t[2] *= x2;
0273       t[0] += static_cast<V>(a[0]);
0274       t[2] += static_cast<V>(b[0]);
0275       t[1] *= x;
0276       t[3] *= x;
0277       return (t[0] + t[1]) / (t[2] + t[3]);
0278    }
0279    else
0280    {
0281       V z = 1 / x;
0282       V z2 = 1 / (x * x);
0283       V t[4];
0284       t[0] = a[0] * z2 + a[2];
0285       t[1] = a[1] * z2 + a[3];
0286       t[2] = b[0] * z2 + b[2];
0287       t[3] = b[1] * z2 + b[3];
0288       t[0] *= z2;
0289       t[1] *= z2;
0290       t[2] *= z2;
0291       t[3] *= z2;
0292       t[0] += static_cast<V>(a[4]);
0293       t[1] += static_cast<V>(a[5]);
0294       t[2] += static_cast<V>(b[4]);
0295       t[3] += static_cast<V>(b[5]);
0296       t[0] *= z2;
0297       t[1] *= z2;
0298       t[2] *= z2;
0299       t[3] *= z2;
0300       t[0] += static_cast<V>(a[6]);
0301       t[1] += static_cast<V>(a[7]);
0302       t[2] += static_cast<V>(b[6]);
0303       t[3] += static_cast<V>(b[7]);
0304       t[0] *= z2;
0305       t[2] *= z2;
0306       t[0] += static_cast<V>(a[8]);
0307       t[2] += static_cast<V>(b[8]);
0308       t[1] *= z;
0309       t[3] *= z;
0310       return (t[0] + t[1]) / (t[2] + t[3]);
0311    }
0312 }
0313
0314 template <class T, class U, class V>
0315 inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
0316 {
0317    if(x <= 1)
0318    {
0319       V x2 = x * x;
0320       V t[4];
0321       t[0] = a[9] * x2 + a[7];
0322       t[1] = a[8] * x2 + a[6];
0323       t[2] = b[9] * x2 + b[7];
0324       t[3] = b[8] * x2 + b[6];
0325       t[0] *= x2;
0326       t[1] *= x2;
0327       t[2] *= x2;
0328       t[3] *= x2;
0329       t[0] += static_cast<V>(a[5]);
0330       t[1] += static_cast<V>(a[4]);
0331       t[2] += static_cast<V>(b[5]);
0332       t[3] += static_cast<V>(b[4]);
0333       t[0] *= x2;
0334       t[1] *= x2;
0335       t[2] *= x2;
0336       t[3] *= x2;
0337       t[0] += static_cast<V>(a[3]);
0338       t[1] += static_cast<V>(a[2]);
0339       t[2] += static_cast<V>(b[3]);
0340       t[3] += static_cast<V>(b[2]);
0341       t[0] *= x2;
0342       t[1] *= x2;
0343       t[2] *= x2;
0344       t[3] *= x2;
0345       t[0] += static_cast<V>(a[1]);
0346       t[1] += static_cast<V>(a[0]);
0347       t[2] += static_cast<V>(b[1]);
0348       t[3] += static_cast<V>(b[0]);
0349       t[0] *= x;
0350       t[2] *= x;
0351       return (t[0] + t[1]) / (t[2] + t[3]);
0352    }
0353    else
0354    {
0355       V z = 1 / x;
0356       V z2 = 1 / (x * x);
0357       V t[4];
0358       t[0] = a[0] * z2 + a[2];
0359       t[1] = a[1] * z2 + a[3];
0360       t[2] = b[0] * z2 + b[2];
0361       t[3] = b[1] * z2 + b[3];
0362       t[0] *= z2;
0363       t[1] *= z2;
0364       t[2] *= z2;
0365       t[3] *= z2;
0366       t[0] += static_cast<V>(a[4]);
0367       t[1] += static_cast<V>(a[5]);
0368       t[2] += static_cast<V>(b[4]);
0369       t[3] += static_cast<V>(b[5]);
0370       t[0] *= z2;
0371       t[1] *= z2;
0372       t[2] *= z2;
0373       t[3] *= z2;
0374       t[0] += static_cast<V>(a[6]);
0375       t[1] += static_cast<V>(a[7]);
0376       t[2] += static_cast<V>(b[6]);
0377       t[3] += static_cast<V>(b[7]);
0378       t[0] *= z2;
0379       t[1] *= z2;
0380       t[2] *= z2;
0381       t[3] *= z2;
0382       t[0] += static_cast<V>(a[8]);
0383       t[1] += static_cast<V>(a[9]);
0384       t[2] += static_cast<V>(b[8]);
0385       t[3] += static_cast<V>(b[9]);
0386       t[0] *= z;
0387       t[2] *= z;
0388       return (t[0] + t[1]) / (t[2] + t[3]);
0389    }
0390 }
0391
0392 template <class T, class U, class V>
0393 inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
0394 {
0395    if(x <= 1)
0396    {
0397       V x2 = x * x;
0398       V t[4];
0399       t[0] = a[10] * x2 + a[8];
0400       t[1] = a[9] * x2 + a[7];
0401       t[2] = b[10] * x2 + b[8];
0402       t[3] = b[9] * x2 + b[7];
0403       t[0] *= x2;
0404       t[1] *= x2;
0405       t[2] *= x2;
0406       t[3] *= x2;
0407       t[0] += static_cast<V>(a[6]);
0408       t[1] += static_cast<V>(a[5]);
0409       t[2] += static_cast<V>(b[6]);
0410       t[3] += static_cast<V>(b[5]);
0411       t[0] *= x2;
0412       t[1] *= x2;
0413       t[2] *= x2;
0414       t[3] *= x2;
0415       t[0] += static_cast<V>(a[4]);
0416       t[1] += static_cast<V>(a[3]);
0417       t[2] += static_cast<V>(b[4]);
0418       t[3] += static_cast<V>(b[3]);
0419       t[0] *= x2;
0420       t[1] *= x2;
0421       t[2] *= x2;
0422       t[3] *= x2;
0423       t[0] += static_cast<V>(a[2]);
0424       t[1] += static_cast<V>(a[1]);
0425       t[2] += static_cast<V>(b[2]);
0426       t[3] += static_cast<V>(b[1]);
0427       t[0] *= x2;
0428       t[2] *= x2;
0429       t[0] += static_cast<V>(a[0]);
0430       t[2] += static_cast<V>(b[0]);
0431       t[1] *= x;
0432       t[3] *= x;
0433       return (t[0] + t[1]) / (t[2] + t[3]);
0434    }
0435    else
0436    {
0437       V z = 1 / x;
0438       V z2 = 1 / (x * x);
0439       V t[4];
0440       t[0] = a[0] * z2 + a[2];
0441       t[1] = a[1] * z2 + a[3];
0442       t[2] = b[0] * z2 + b[2];
0443       t[3] = b[1] * z2 + b[3];
0444       t[0] *= z2;
0445       t[1] *= z2;
0446       t[2] *= z2;
0447       t[3] *= z2;
0448       t[0] += static_cast<V>(a[4]);
0449       t[1] += static_cast<V>(a[5]);
0450       t[2] += static_cast<V>(b[4]);
0451       t[3] += static_cast<V>(b[5]);
0452       t[0] *= z2;
0453       t[1] *= z2;
0454       t[2] *= z2;
0455       t[3] *= z2;
0456       t[0] += static_cast<V>(a[6]);
0457       t[1] += static_cast<V>(a[7]);
0458       t[2] += static_cast<V>(b[6]);
0459       t[3] += static_cast<V>(b[7]);
0460       t[0] *= z2;
0461       t[1] *= z2;
0462       t[2] *= z2;
0463       t[3] *= z2;
0464       t[0] += static_cast<V>(a[8]);
0465       t[1] += static_cast<V>(a[9]);
0466       t[2] += static_cast<V>(b[8]);
0467       t[3] += static_cast<V>(b[9]);
0468       t[0] *= z2;
0469       t[2] *= z2;
0470       t[0] += static_cast<V>(a[10]);
0471       t[2] += static_cast<V>(b[10]);
0472       t[1] *= z;
0473       t[3] *= z;
0474       return (t[0] + t[1]) / (t[2] + t[3]);
0475    }
0476 }
0477
0478
0479 }}}} // namespaces
0480
0481 #endif // include guard
0482