ceph/src/boost/boost/math/tools/detail/rational_horner3_13.hpp

   1 //  (C) Copyright John Maddock 2007.
   2 //  Use, modification and distribution are subject to the
   3 //  Boost Software License, Version 1.0. (See accompanying file
   4 //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
   5 //
   6 //  This file is machine generated, do not edit by hand
   7
   8 // Polynomial evaluation using second order Horners rule
   9 #ifndef BOOST_MATH_TOOLS_RAT_EVAL_13_HPP
  10 #define BOOST_MATH_TOOLS_RAT_EVAL_13_HPP
  11
  12 namespace boost{ namespace math{ namespace tools{ namespace detail{
  13
  14 template <class T, class U, class V>
  15 inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
  16 {
  17    return static_cast<V>(0);
  18 }
  19
  20 template <class T, class U, class V>
  21 inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
  22 {
  23    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
  24 }
  25
  26 template <class T, class U, class V>
  27 inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
  28 {
  29    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
  30 }
  31
  32 template <class T, class U, class V>
  33 inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
  34 {
  35    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
  36 }
  37
  38 template <class T, class U, class V>
  39 inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
  40 {
  41    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]));
  42 }
  43
  44 template <class T, class U, class V>
  45 inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
  46 {
  47    if(x <= 1)
  48    {
  49       V x2 = x * x;
  50       V t[4];
  51       t[0] = a[4] * x2 + a[2];
  52       t[1] = a[3] * x2 + a[1];
  53       t[2] = b[4] * x2 + b[2];
  54       t[3] = b[3] * x2 + b[1];
  55       t[0] *= x2;
  56       t[2] *= x2;
  57       t[0] += static_cast<V>(a[0]);
  58       t[2] += static_cast<V>(b[0]);
  59       t[1] *= x;
  60       t[3] *= x;
  61       return (t[0] + t[1]) / (t[2] + t[3]);
  62    }
  63    else
  64    {
  65       V z = 1 / x;
  66       V z2 = 1 / (x * x);
  67       V t[4];
  68       t[0] = a[0] * z2 + a[2];
  69       t[1] = a[1] * z2 + a[3];
  70       t[2] = b[0] * z2 + b[2];
  71       t[3] = b[1] * z2 + b[3];
  72       t[0] *= z2;
  73       t[2] *= z2;
  74       t[0] += static_cast<V>(a[4]);
  75       t[2] += static_cast<V>(b[4]);
  76       t[1] *= z;
  77       t[3] *= z;
  78       return (t[0] + t[1]) / (t[2] + t[3]);
  79    }
  80 }
  81
  82 template <class T, class U, class V>
  83 inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
  84 {
  85    if(x <= 1)
  86    {
  87       V x2 = x * x;
  88       V t[4];
  89       t[0] = a[5] * x2 + a[3];
  90       t[1] = a[4] * x2 + a[2];
  91       t[2] = b[5] * x2 + b[3];
  92       t[3] = b[4] * x2 + b[2];
  93       t[0] *= x2;
  94       t[1] *= x2;
  95       t[2] *= x2;
  96       t[3] *= x2;
  97       t[0] += static_cast<V>(a[1]);
  98       t[1] += static_cast<V>(a[0]);
  99       t[2] += static_cast<V>(b[1]);
 100       t[3] += static_cast<V>(b[0]);
 101       t[0] *= x;
 102       t[2] *= x;
 103       return (t[0] + t[1]) / (t[2] + t[3]);
 104    }
 105    else
 106    {
 107       V z = 1 / x;
 108       V z2 = 1 / (x * x);
 109       V t[4];
 110       t[0] = a[0] * z2 + a[2];
 111       t[1] = a[1] * z2 + a[3];
 112       t[2] = b[0] * z2 + b[2];
 113       t[3] = b[1] * z2 + b[3];
 114       t[0] *= z2;
 115       t[1] *= z2;
 116       t[2] *= z2;
 117       t[3] *= z2;
 118       t[0] += static_cast<V>(a[4]);
 119       t[1] += static_cast<V>(a[5]);
 120       t[2] += static_cast<V>(b[4]);
 121       t[3] += static_cast<V>(b[5]);
 122       t[0] *= z;
 123       t[2] *= z;
 124       return (t[0] + t[1]) / (t[2] + t[3]);
 125    }
 126 }
 127
 128 template <class T, class U, class V>
 129 inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 130 {
 131    if(x <= 1)
 132    {
 133       V x2 = x * x;
 134       V t[4];
 135       t[0] = a[6] * x2 + a[4];
 136       t[1] = a[5] * x2 + a[3];
 137       t[2] = b[6] * x2 + b[4];
 138       t[3] = b[5] * x2 + b[3];
 139       t[0] *= x2;
 140       t[1] *= x2;
 141       t[2] *= x2;
 142       t[3] *= x2;
 143       t[0] += static_cast<V>(a[2]);
 144       t[1] += static_cast<V>(a[1]);
 145       t[2] += static_cast<V>(b[2]);
 146       t[3] += static_cast<V>(b[1]);
 147       t[0] *= x2;
 148       t[2] *= x2;
 149       t[0] += static_cast<V>(a[0]);
 150       t[2] += static_cast<V>(b[0]);
 151       t[1] *= x;
 152       t[3] *= x;
 153       return (t[0] + t[1]) / (t[2] + t[3]);
 154    }
 155    else
 156    {
 157       V z = 1 / x;
 158       V z2 = 1 / (x * x);
 159       V t[4];
 160       t[0] = a[0] * z2 + a[2];
 161       t[1] = a[1] * z2 + a[3];
 162       t[2] = b[0] * z2 + b[2];
 163       t[3] = b[1] * z2 + b[3];
 164       t[0] *= z2;
 165       t[1] *= z2;
 166       t[2] *= z2;
 167       t[3] *= z2;
 168       t[0] += static_cast<V>(a[4]);
 169       t[1] += static_cast<V>(a[5]);
 170       t[2] += static_cast<V>(b[4]);
 171       t[3] += static_cast<V>(b[5]);
 172       t[0] *= z2;
 173       t[2] *= z2;
 174       t[0] += static_cast<V>(a[6]);
 175       t[2] += static_cast<V>(b[6]);
 176       t[1] *= z;
 177       t[3] *= z;
 178       return (t[0] + t[1]) / (t[2] + t[3]);
 179    }
 180 }
 181
 182 template <class T, class U, class V>
 183 inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 184 {
 185    if(x <= 1)
 186    {
 187       V x2 = x * x;
 188       V t[4];
 189       t[0] = a[7] * x2 + a[5];
 190       t[1] = a[6] * x2 + a[4];
 191       t[2] = b[7] * x2 + b[5];
 192       t[3] = b[6] * x2 + b[4];
 193       t[0] *= x2;
 194       t[1] *= x2;
 195       t[2] *= x2;
 196       t[3] *= x2;
 197       t[0] += static_cast<V>(a[3]);
 198       t[1] += static_cast<V>(a[2]);
 199       t[2] += static_cast<V>(b[3]);
 200       t[3] += static_cast<V>(b[2]);
 201       t[0] *= x2;
 202       t[1] *= x2;
 203       t[2] *= x2;
 204       t[3] *= x2;
 205       t[0] += static_cast<V>(a[1]);
 206       t[1] += static_cast<V>(a[0]);
 207       t[2] += static_cast<V>(b[1]);
 208       t[3] += static_cast<V>(b[0]);
 209       t[0] *= x;
 210       t[2] *= x;
 211       return (t[0] + t[1]) / (t[2] + t[3]);
 212    }
 213    else
 214    {
 215       V z = 1 / x;
 216       V z2 = 1 / (x * x);
 217       V t[4];
 218       t[0] = a[0] * z2 + a[2];
 219       t[1] = a[1] * z2 + a[3];
 220       t[2] = b[0] * z2 + b[2];
 221       t[3] = b[1] * z2 + b[3];
 222       t[0] *= z2;
 223       t[1] *= z2;
 224       t[2] *= z2;
 225       t[3] *= z2;
 226       t[0] += static_cast<V>(a[4]);
 227       t[1] += static_cast<V>(a[5]);
 228       t[2] += static_cast<V>(b[4]);
 229       t[3] += static_cast<V>(b[5]);
 230       t[0] *= z2;
 231       t[1] *= z2;
 232       t[2] *= z2;
 233       t[3] *= z2;
 234       t[0] += static_cast<V>(a[6]);
 235       t[1] += static_cast<V>(a[7]);
 236       t[2] += static_cast<V>(b[6]);
 237       t[3] += static_cast<V>(b[7]);
 238       t[0] *= z;
 239       t[2] *= z;
 240       return (t[0] + t[1]) / (t[2] + t[3]);
 241    }
 242 }
 243
 244 template <class T, class U, class V>
 245 inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 246 {
 247    if(x <= 1)
 248    {
 249       V x2 = x * x;
 250       V t[4];
 251       t[0] = a[8] * x2 + a[6];
 252       t[1] = a[7] * x2 + a[5];
 253       t[2] = b[8] * x2 + b[6];
 254       t[3] = b[7] * x2 + b[5];
 255       t[0] *= x2;
 256       t[1] *= x2;
 257       t[2] *= x2;
 258       t[3] *= x2;
 259       t[0] += static_cast<V>(a[4]);
 260       t[1] += static_cast<V>(a[3]);
 261       t[2] += static_cast<V>(b[4]);
 262       t[3] += static_cast<V>(b[3]);
 263       t[0] *= x2;
 264       t[1] *= x2;
 265       t[2] *= x2;
 266       t[3] *= x2;
 267       t[0] += static_cast<V>(a[2]);
 268       t[1] += static_cast<V>(a[1]);
 269       t[2] += static_cast<V>(b[2]);
 270       t[3] += static_cast<V>(b[1]);
 271       t[0] *= x2;
 272       t[2] *= x2;
 273       t[0] += static_cast<V>(a[0]);
 274       t[2] += static_cast<V>(b[0]);
 275       t[1] *= x;
 276       t[3] *= x;
 277       return (t[0] + t[1]) / (t[2] + t[3]);
 278    }
 279    else
 280    {
 281       V z = 1 / x;
 282       V z2 = 1 / (x * x);
 283       V t[4];
 284       t[0] = a[0] * z2 + a[2];
 285       t[1] = a[1] * z2 + a[3];
 286       t[2] = b[0] * z2 + b[2];
 287       t[3] = b[1] * z2 + b[3];
 288       t[0] *= z2;
 289       t[1] *= z2;
 290       t[2] *= z2;
 291       t[3] *= z2;
 292       t[0] += static_cast<V>(a[4]);
 293       t[1] += static_cast<V>(a[5]);
 294       t[2] += static_cast<V>(b[4]);
 295       t[3] += static_cast<V>(b[5]);
 296       t[0] *= z2;
 297       t[1] *= z2;
 298       t[2] *= z2;
 299       t[3] *= z2;
 300       t[0] += static_cast<V>(a[6]);
 301       t[1] += static_cast<V>(a[7]);
 302       t[2] += static_cast<V>(b[6]);
 303       t[3] += static_cast<V>(b[7]);
 304       t[0] *= z2;
 305       t[2] *= z2;
 306       t[0] += static_cast<V>(a[8]);
 307       t[2] += static_cast<V>(b[8]);
 308       t[1] *= z;
 309       t[3] *= z;
 310       return (t[0] + t[1]) / (t[2] + t[3]);
 311    }
 312 }
 313
 314 template <class T, class U, class V>
 315 inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 316 {
 317    if(x <= 1)
 318    {
 319       V x2 = x * x;
 320       V t[4];
 321       t[0] = a[9] * x2 + a[7];
 322       t[1] = a[8] * x2 + a[6];
 323       t[2] = b[9] * x2 + b[7];
 324       t[3] = b[8] * x2 + b[6];
 325       t[0] *= x2;
 326       t[1] *= x2;
 327       t[2] *= x2;
 328       t[3] *= x2;
 329       t[0] += static_cast<V>(a[5]);
 330       t[1] += static_cast<V>(a[4]);
 331       t[2] += static_cast<V>(b[5]);
 332       t[3] += static_cast<V>(b[4]);
 333       t[0] *= x2;
 334       t[1] *= x2;
 335       t[2] *= x2;
 336       t[3] *= x2;
 337       t[0] += static_cast<V>(a[3]);
 338       t[1] += static_cast<V>(a[2]);
 339       t[2] += static_cast<V>(b[3]);
 340       t[3] += static_cast<V>(b[2]);
 341       t[0] *= x2;
 342       t[1] *= x2;
 343       t[2] *= x2;
 344       t[3] *= x2;
 345       t[0] += static_cast<V>(a[1]);
 346       t[1] += static_cast<V>(a[0]);
 347       t[2] += static_cast<V>(b[1]);
 348       t[3] += static_cast<V>(b[0]);
 349       t[0] *= x;
 350       t[2] *= x;
 351       return (t[0] + t[1]) / (t[2] + t[3]);
 352    }
 353    else
 354    {
 355       V z = 1 / x;
 356       V z2 = 1 / (x * x);
 357       V t[4];
 358       t[0] = a[0] * z2 + a[2];
 359       t[1] = a[1] * z2 + a[3];
 360       t[2] = b[0] * z2 + b[2];
 361       t[3] = b[1] * z2 + b[3];
 362       t[0] *= z2;
 363       t[1] *= z2;
 364       t[2] *= z2;
 365       t[3] *= z2;
 366       t[0] += static_cast<V>(a[4]);
 367       t[1] += static_cast<V>(a[5]);
 368       t[2] += static_cast<V>(b[4]);
 369       t[3] += static_cast<V>(b[5]);
 370       t[0] *= z2;
 371       t[1] *= z2;
 372       t[2] *= z2;
 373       t[3] *= z2;
 374       t[0] += static_cast<V>(a[6]);
 375       t[1] += static_cast<V>(a[7]);
 376       t[2] += static_cast<V>(b[6]);
 377       t[3] += static_cast<V>(b[7]);
 378       t[0] *= z2;
 379       t[1] *= z2;
 380       t[2] *= z2;
 381       t[3] *= z2;
 382       t[0] += static_cast<V>(a[8]);
 383       t[1] += static_cast<V>(a[9]);
 384       t[2] += static_cast<V>(b[8]);
 385       t[3] += static_cast<V>(b[9]);
 386       t[0] *= z;
 387       t[2] *= z;
 388       return (t[0] + t[1]) / (t[2] + t[3]);
 389    }
 390 }
 391
 392 template <class T, class U, class V>
 393 inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 394 {
 395    if(x <= 1)
 396    {
 397       V x2 = x * x;
 398       V t[4];
 399       t[0] = a[10] * x2 + a[8];
 400       t[1] = a[9] * x2 + a[7];
 401       t[2] = b[10] * x2 + b[8];
 402       t[3] = b[9] * x2 + b[7];
 403       t[0] *= x2;
 404       t[1] *= x2;
 405       t[2] *= x2;
 406       t[3] *= x2;
 407       t[0] += static_cast<V>(a[6]);
 408       t[1] += static_cast<V>(a[5]);
 409       t[2] += static_cast<V>(b[6]);
 410       t[3] += static_cast<V>(b[5]);
 411       t[0] *= x2;
 412       t[1] *= x2;
 413       t[2] *= x2;
 414       t[3] *= x2;
 415       t[0] += static_cast<V>(a[4]);
 416       t[1] += static_cast<V>(a[3]);
 417       t[2] += static_cast<V>(b[4]);
 418       t[3] += static_cast<V>(b[3]);
 419       t[0] *= x2;
 420       t[1] *= x2;
 421       t[2] *= x2;
 422       t[3] *= x2;
 423       t[0] += static_cast<V>(a[2]);
 424       t[1] += static_cast<V>(a[1]);
 425       t[2] += static_cast<V>(b[2]);
 426       t[3] += static_cast<V>(b[1]);
 427       t[0] *= x2;
 428       t[2] *= x2;
 429       t[0] += static_cast<V>(a[0]);
 430       t[2] += static_cast<V>(b[0]);
 431       t[1] *= x;
 432       t[3] *= x;
 433       return (t[0] + t[1]) / (t[2] + t[3]);
 434    }
 435    else
 436    {
 437       V z = 1 / x;
 438       V z2 = 1 / (x * x);
 439       V t[4];
 440       t[0] = a[0] * z2 + a[2];
 441       t[1] = a[1] * z2 + a[3];
 442       t[2] = b[0] * z2 + b[2];
 443       t[3] = b[1] * z2 + b[3];
 444       t[0] *= z2;
 445       t[1] *= z2;
 446       t[2] *= z2;
 447       t[3] *= z2;
 448       t[0] += static_cast<V>(a[4]);
 449       t[1] += static_cast<V>(a[5]);
 450       t[2] += static_cast<V>(b[4]);
 451       t[3] += static_cast<V>(b[5]);
 452       t[0] *= z2;
 453       t[1] *= z2;
 454       t[2] *= z2;
 455       t[3] *= z2;
 456       t[0] += static_cast<V>(a[6]);
 457       t[1] += static_cast<V>(a[7]);
 458       t[2] += static_cast<V>(b[6]);
 459       t[3] += static_cast<V>(b[7]);
 460       t[0] *= z2;
 461       t[1] *= z2;
 462       t[2] *= z2;
 463       t[3] *= z2;
 464       t[0] += static_cast<V>(a[8]);
 465       t[1] += static_cast<V>(a[9]);
 466       t[2] += static_cast<V>(b[8]);
 467       t[3] += static_cast<V>(b[9]);
 468       t[0] *= z2;
 469       t[2] *= z2;
 470       t[0] += static_cast<V>(a[10]);
 471       t[2] += static_cast<V>(b[10]);
 472       t[1] *= z;
 473       t[3] *= z;
 474       return (t[0] + t[1]) / (t[2] + t[3]);
 475    }
 476 }
 477
 478 template <class T, class U, class V>
 479 inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 480 {
 481    if(x <= 1)
 482    {
 483       V x2 = x * x;
 484       V t[4];
 485       t[0] = a[11] * x2 + a[9];
 486       t[1] = a[10] * x2 + a[8];
 487       t[2] = b[11] * x2 + b[9];
 488       t[3] = b[10] * x2 + b[8];
 489       t[0] *= x2;
 490       t[1] *= x2;
 491       t[2] *= x2;
 492       t[3] *= x2;
 493       t[0] += static_cast<V>(a[7]);
 494       t[1] += static_cast<V>(a[6]);
 495       t[2] += static_cast<V>(b[7]);
 496       t[3] += static_cast<V>(b[6]);
 497       t[0] *= x2;
 498       t[1] *= x2;
 499       t[2] *= x2;
 500       t[3] *= x2;
 501       t[0] += static_cast<V>(a[5]);
 502       t[1] += static_cast<V>(a[4]);
 503       t[2] += static_cast<V>(b[5]);
 504       t[3] += static_cast<V>(b[4]);
 505       t[0] *= x2;
 506       t[1] *= x2;
 507       t[2] *= x2;
 508       t[3] *= x2;
 509       t[0] += static_cast<V>(a[3]);
 510       t[1] += static_cast<V>(a[2]);
 511       t[2] += static_cast<V>(b[3]);
 512       t[3] += static_cast<V>(b[2]);
 513       t[0] *= x2;
 514       t[1] *= x2;
 515       t[2] *= x2;
 516       t[3] *= x2;
 517       t[0] += static_cast<V>(a[1]);
 518       t[1] += static_cast<V>(a[0]);
 519       t[2] += static_cast<V>(b[1]);
 520       t[3] += static_cast<V>(b[0]);
 521       t[0] *= x;
 522       t[2] *= x;
 523       return (t[0] + t[1]) / (t[2] + t[3]);
 524    }
 525    else
 526    {
 527       V z = 1 / x;
 528       V z2 = 1 / (x * x);
 529       V t[4];
 530       t[0] = a[0] * z2 + a[2];
 531       t[1] = a[1] * z2 + a[3];
 532       t[2] = b[0] * z2 + b[2];
 533       t[3] = b[1] * z2 + b[3];
 534       t[0] *= z2;
 535       t[1] *= z2;
 536       t[2] *= z2;
 537       t[3] *= z2;
 538       t[0] += static_cast<V>(a[4]);
 539       t[1] += static_cast<V>(a[5]);
 540       t[2] += static_cast<V>(b[4]);
 541       t[3] += static_cast<V>(b[5]);
 542       t[0] *= z2;
 543       t[1] *= z2;
 544       t[2] *= z2;
 545       t[3] *= z2;
 546       t[0] += static_cast<V>(a[6]);
 547       t[1] += static_cast<V>(a[7]);
 548       t[2] += static_cast<V>(b[6]);
 549       t[3] += static_cast<V>(b[7]);
 550       t[0] *= z2;
 551       t[1] *= z2;
 552       t[2] *= z2;
 553       t[3] *= z2;
 554       t[0] += static_cast<V>(a[8]);
 555       t[1] += static_cast<V>(a[9]);
 556       t[2] += static_cast<V>(b[8]);
 557       t[3] += static_cast<V>(b[9]);
 558       t[0] *= z2;
 559       t[1] *= z2;
 560       t[2] *= z2;
 561       t[3] *= z2;
 562       t[0] += static_cast<V>(a[10]);
 563       t[1] += static_cast<V>(a[11]);
 564       t[2] += static_cast<V>(b[10]);
 565       t[3] += static_cast<V>(b[11]);
 566       t[0] *= z;
 567       t[2] *= z;
 568       return (t[0] + t[1]) / (t[2] + t[3]);
 569    }
 570 }
 571
 572 template <class T, class U, class V>
 573 inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 574 {
 575    if(x <= 1)
 576    {
 577       V x2 = x * x;
 578       V t[4];
 579       t[0] = a[12] * x2 + a[10];
 580       t[1] = a[11] * x2 + a[9];
 581       t[2] = b[12] * x2 + b[10];
 582       t[3] = b[11] * x2 + b[9];
 583       t[0] *= x2;
 584       t[1] *= x2;
 585       t[2] *= x2;
 586       t[3] *= x2;
 587       t[0] += static_cast<V>(a[8]);
 588       t[1] += static_cast<V>(a[7]);
 589       t[2] += static_cast<V>(b[8]);
 590       t[3] += static_cast<V>(b[7]);
 591       t[0] *= x2;
 592       t[1] *= x2;
 593       t[2] *= x2;
 594       t[3] *= x2;
 595       t[0] += static_cast<V>(a[6]);
 596       t[1] += static_cast<V>(a[5]);
 597       t[2] += static_cast<V>(b[6]);
 598       t[3] += static_cast<V>(b[5]);
 599       t[0] *= x2;
 600       t[1] *= x2;
 601       t[2] *= x2;
 602       t[3] *= x2;
 603       t[0] += static_cast<V>(a[4]);
 604       t[1] += static_cast<V>(a[3]);
 605       t[2] += static_cast<V>(b[4]);
 606       t[3] += static_cast<V>(b[3]);
 607       t[0] *= x2;
 608       t[1] *= x2;
 609       t[2] *= x2;
 610       t[3] *= x2;
 611       t[0] += static_cast<V>(a[2]);
 612       t[1] += static_cast<V>(a[1]);
 613       t[2] += static_cast<V>(b[2]);
 614       t[3] += static_cast<V>(b[1]);
 615       t[0] *= x2;
 616       t[2] *= x2;
 617       t[0] += static_cast<V>(a[0]);
 618       t[2] += static_cast<V>(b[0]);
 619       t[1] *= x;
 620       t[3] *= x;
 621       return (t[0] + t[1]) / (t[2] + t[3]);
 622    }
 623    else
 624    {
 625       V z = 1 / x;
 626       V z2 = 1 / (x * x);
 627       V t[4];
 628       t[0] = a[0] * z2 + a[2];
 629       t[1] = a[1] * z2 + a[3];
 630       t[2] = b[0] * z2 + b[2];
 631       t[3] = b[1] * z2 + b[3];
 632       t[0] *= z2;
 633       t[1] *= z2;
 634       t[2] *= z2;
 635       t[3] *= z2;
 636       t[0] += static_cast<V>(a[4]);
 637       t[1] += static_cast<V>(a[5]);
 638       t[2] += static_cast<V>(b[4]);
 639       t[3] += static_cast<V>(b[5]);
 640       t[0] *= z2;
 641       t[1] *= z2;
 642       t[2] *= z2;
 643       t[3] *= z2;
 644       t[0] += static_cast<V>(a[6]);
 645       t[1] += static_cast<V>(a[7]);
 646       t[2] += static_cast<V>(b[6]);
 647       t[3] += static_cast<V>(b[7]);
 648       t[0] *= z2;
 649       t[1] *= z2;
 650       t[2] *= z2;
 651       t[3] *= z2;
 652       t[0] += static_cast<V>(a[8]);
 653       t[1] += static_cast<V>(a[9]);
 654       t[2] += static_cast<V>(b[8]);
 655       t[3] += static_cast<V>(b[9]);
 656       t[0] *= z2;
 657       t[1] *= z2;
 658       t[2] *= z2;
 659       t[3] *= z2;
 660       t[0] += static_cast<V>(a[10]);
 661       t[1] += static_cast<V>(a[11]);
 662       t[2] += static_cast<V>(b[10]);
 663       t[3] += static_cast<V>(b[11]);
 664       t[0] *= z2;
 665       t[2] *= z2;
 666       t[0] += static_cast<V>(a[12]);
 667       t[2] += static_cast<V>(b[12]);
 668       t[1] *= z;
 669       t[3] *= z;
 670       return (t[0] + t[1]) / (t[2] + t[3]);
 671    }
 672 }
 673
 674
 675 }}}} // namespaces
 676
 677 #endif // include guard
 678