blender-archive/source/blender/blenlib/intern/math_boolean.cc

/*
 * This program is free software; you can redistribute it and/or
 * modify it under the terms of the GNU General Public License
 * as published by the Free Software Foundation; either version 2
 * of the License, or (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software Foundation,
 * Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
 */

/** \file
 * \ingroup bli
 */

#include "BLI_double2.hh"
#include "BLI_double3.hh"
#include "BLI_float2.hh"
#include "BLI_float3.hh"
#include "BLI_hash.hh"
#include "BLI_math_boolean.hh"
#include "BLI_math_mpq.hh"
#include "BLI_mpq2.hh"
#include "BLI_mpq3.hh"
#include "BLI_span.hh"
#include "BLI_utildefines.h"

namespace blender {

#ifdef WITH_GMP
int orient2d(const mpq2 &a, const mpq2 &b, const mpq2 &c)
{
  mpq_class detleft = (a[0] - c[0]) * (b[1] - c[1]);
  mpq_class detright = (a[1] - c[1]) * (b[0] - c[0]);
  mpq_class det = detleft - detright;
  return sgn(det);
}

int incircle(const mpq2 &a, const mpq2 &b, const mpq2 &c, const mpq2 &d)
{
  mpq_class adx = a[0] - d[0];
  mpq_class bdx = b[0] - d[0];
  mpq_class cdx = c[0] - d[0];
  mpq_class ady = a[1] - d[1];
  mpq_class bdy = b[1] - d[1];
  mpq_class cdy = c[1] - d[1];

  mpq_class bdxcdy = bdx * cdy;
  mpq_class cdxbdy = cdx * bdy;
  mpq_class alift = adx * adx + ady * ady;

  mpq_class cdxady = cdx * ady;
  mpq_class adxcdy = adx * cdy;
  mpq_class blift = bdx * bdx + bdy * bdy;

  mpq_class adxbdy = adx * bdy;
  mpq_class bdxady = bdx * ady;
  mpq_class clift = cdx * cdx + cdy * cdy;

  mpq_class det = alift * (bdxcdy - cdxbdy) + blift * (cdxady - adxcdy) +
                  clift * (adxbdy - bdxady);
  return sgn(det);
}

int orient3d(const mpq3 &a, const mpq3 &b, const mpq3 &c, const mpq3 &d)
{
  mpq_class adx = a[0] - d[0];
  mpq_class bdx = b[0] - d[0];
  mpq_class cdx = c[0] - d[0];
  mpq_class ady = a[1] - d[1];
  mpq_class bdy = b[1] - d[1];
  mpq_class cdy = c[1] - d[1];
  mpq_class adz = a[2] - d[2];
  mpq_class bdz = b[2] - d[2];
  mpq_class cdz = c[2] - d[2];

  mpq_class bdxcdy = bdx * cdy;
  mpq_class cdxbdy = cdx * bdy;

  mpq_class cdxady = cdx * ady;
  mpq_class adxcdy = adx * cdy;

  mpq_class adxbdy = adx * bdy;
  mpq_class bdxady = bdx * ady;

  mpq_class det = adz * (bdxcdy - cdxbdy) + bdz * (cdxady - adxcdy) + cdz * (adxbdy - bdxady);
  return sgn(det);
}
#endif /* WITH_GMP */

/**
 * For double versions of orient and incircle functions, use robust predicates
 * that give exact answers for double inputs.
 * First, encapsulate functions from Jonathan Shewchuk's implementation.
 * After this name-space, see the implementation of the double3 primitives.
 */
namespace robust_pred {

/* Using Shewchuk's file here, edited to removed unneeded functions,
 * change REAL to double everywhere, added const to some arguments,
 * and to export only the following declared non-static functions.
 *
 * Since this is C++, an instantiated singleton class is used to make
 * sure that #exactinit() is called once.
 * (Because it's undefined when this is called in initialization of all modules,
 * other modules shouldn't use these functions in initialization.)
 */

void exactinit();
double orient2dfast(const double *pa, const double *pb, const double *pc);
double orient2d(const double *pa, const double *pb, const double *pc);
double orient3dfast(const double *pa, const double *pb, const double *pc, const double *pd);
double orient3d(const double *pa, const double *pb, const double *pc, const double *pd);
double incirclefast(const double *pa, const double *pb, const double *pc, const double *pd);
double incircle(const double *pa, const double *pb, const double *pc, const double *pd);
double inspherefast(
    const double *pa, const double *pb, const double *pc, const double *pd, const double *pe);
double insphere(
    const double *pa, const double *pb, const double *pc, const double *pd, const double *pe);

class RobustInitCaller {
 public:
  RobustInitCaller()
  {
    exactinit();
  }
};

static RobustInitCaller init_caller;

/* Routines for Arbitrary Precision Floating-point Arithmetic
 * and Fast Robust Geometric Predicates
 * (predicates.c)
 *
 * May 18, 1996
 *
 * Placed in the public domain by
 * Jonathan Richard Shewchuk
 * School of Computer Science
 * Carnegie Mellon University
 * 5000 Forbes Avenue
 * Pittsburgh, Pennsylvania  15213-3891
 * <jrs@cs.cmu.edu>
 *
 * This file contains C implementation of algorithms for exact addition
 * and multiplication of floating-point numbers, and predicates for
 * robustly performing the orientation and incircle tests used in
 * computational geometry.  The algorithms and underlying theory are
 * described in Jonathan Richard Shewchuk.  "Adaptive Precision Floating-
 * Point Arithmetic and Fast Robust Geometric Predicates."  Technical
 * Report CMU-CS-96-140, School of Computer Science, Carnegie Mellon
 * University, Pittsburgh, Pennsylvania, May 1996.  (Submitted to
 * Discrete & Computational Geometry.)
 *
 * This file, the paper listed above, and other information are available
 * from the Web page http://www.cs.cmu.edu/~quake/robust.html .
 *
 *
 * Using this code:
 *
 * First, read the short or long version of the paper (from the Web page above).
 *
 * Be sure to call #exactinit() once, before calling any of the arithmetic
 * functions or geometric predicates.  Also be sure to turn on the
 * optimizer when compiling this file.
 */

/* On some machines, the exact arithmetic routines might be defeated by the
 * use of internal extended precision floating-point registers.  Sometimes
 * this problem can be fixed by defining certain values to be volatile,
 * thus forcing them to be stored to memory and rounded off.  This isn't
 * a great solution, though, as it slows the arithmetic down.
 *
 * To try this out, write "#define INEXACT volatile" below.  Normally,
 * however, INEXACT should be defined to be nothing.  ("#define INEXACT".)
 */

#define INEXACT /* Nothing */
/* #define INEXACT volatile */

/* Which of the following two methods of finding the absolute values is
 * fastest is compiler-dependent.  A few compilers can inline and optimize
 * the fabs() call; but most will incur the overhead of a function call,
 * which is disastrously slow.  A faster way on IEEE machines might be to
 * mask the appropriate bit, but that's difficult to do in C.
 */

#define Absolute(a) ((a) >= 0.0 ? (a) : -(a))
/* #define Absolute(a)  fabs(a) */

/* Many of the operations are broken up into two pieces, a main part that
 * performs an approximate operation, and a "tail" that computes the
 * round-off error of that operation.
 *
 * The operations Fast_Two_Sum(), Fast_Two_Diff(), Two_Sum(), Two_Diff(),
 * Split(), and Two_Product() are all implemented as described in the
 * reference.  Each of these macros requires certain variables to be
 * defined in the calling routine.  The variables `bvirt', `c', `abig',
 * `_i', `_j', `_k', `_l', `_m', and `_n' are declared `INEXACT' because
 * they store the result of an operation that may incur round-off error.
 * The input parameter `x' (or the highest numbered `x_' parameter) must
 * also be declared `INEXACT'.
 */

#define Fast_Two_Sum_Tail(a, b, x, y) \
  bvirt = x - a; \
  y = b - bvirt

#define Fast_Two_Sum(a, b, x, y) \
  x = (double)(a + b); \
  Fast_Two_Sum_Tail(a, b, x, y)

#define Fast_Two_Diff_Tail(a, b, x, y) \
  bvirt = a - x; \
  y = bvirt - b

#define Fast_Two_Diff(a, b, x, y) \
  x = (double)(a - b); \
  Fast_Two_Diff_Tail(a, b, x, y)

#define Two_Sum_Tail(a, b, x, y) \
  bvirt = (double)(x - a); \
  avirt = x - bvirt; \
  bround = b - bvirt; \
  around = a - avirt; \
  y = around + bround

#define Two_Sum(a, b, x, y) \
  x = (double)(a + b); \
  Two_Sum_Tail(a, b, x, y)

#define Two_Diff_Tail(a, b, x, y) \
  bvirt = (double)(a - x); \
  avirt = x + bvirt; \
  bround = bvirt - b; \
  around = a - avirt; \
  y = around + bround

#define Two_Diff(a, b, x, y) \
  x = (double)(a - b); \
  Two_Diff_Tail(a, b, x, y)

#define Split(a, ahi, alo) \
  c = (double)(splitter * a); \
  abig = (double)(c - a); \
  ahi = c - abig; \
  alo = a - ahi

#define Two_Product_Tail(a, b, x, y) \
  Split(a, ahi, alo); \
  Split(b, bhi, blo); \
  err1 = x - (ahi * bhi); \
  err2 = err1 - (alo * bhi); \
  err3 = err2 - (ahi * blo); \
  y = (alo * blo) - err3

#define Two_Product(a, b, x, y) \
  x = (double)(a * b); \
  Two_Product_Tail(a, b, x, y)

#define Two_Product_Presplit(a, b, bhi, blo, x, y) \
  x = (double)(a * b); \
  Split(a, ahi, alo); \
  err1 = x - (ahi * bhi); \
  err2 = err1 - (alo * bhi); \
  err3 = err2 - (ahi * blo); \
  y = (alo * blo) - err3

#define Two_Product_2Presplit(a, ahi, alo, b, bhi, blo, x, y) \
  x = (double)(a * b); \
  err1 = x - (ahi * bhi); \
  err2 = err1 - (alo * bhi); \
  err3 = err2 - (ahi * blo); \
  y = (alo * blo) - err3

#define Square_Tail(a, x, y) \
  Split(a, ahi, alo); \
  err1 = x - (ahi * ahi); \
  err3 = err1 - ((ahi + ahi) * alo); \
  y = (alo * alo) - err3

#define Square(a, x, y) \
  x = (double)(a * a); \
  Square_Tail(a, x, y)

#define Two_One_Sum(a1, a0, b, x2, x1, x0) \
  Two_Sum(a0, b, _i, x0); \
  Two_Sum(a1, _i, x2, x1)

#define Two_One_Diff(a1, a0, b, x2, x1, x0) \
  Two_Diff(a0, b, _i, x0); \
  Two_Sum(a1, _i, x2, x1)

#define Two_Two_Sum(a1, a0, b1, b0, x3, x2, x1, x0) \
  Two_One_Sum(a1, a0, b0, _j, _0, x0); \
  Two_One_Sum(_j, _0, b1, x3, x2, x1)

#define Two_Two_Diff(a1, a0, b1, b0, x3, x2, x1, x0) \
  Two_One_Diff(a1, a0, b0, _j, _0, x0); \
  Two_One_Diff(_j, _0, b1, x3, x2, x1)

#define Four_One_Sum(a3, a2, a1, a0, b, x4, x3, x2, x1, x0) \
  Two_One_Sum(a1, a0, b, _j, x1, x0); \
  Two_One_Sum(a3, a2, _j, x4, x3, x2)

#define Four_Two_Sum(a3, a2, a1, a0, b1, b0, x5, x4, x3, x2, x1, x0) \
  Four_One_Sum(a3, a2, a1, a0, b0, _k, _2, _1, _0, x0); \
  Four_One_Sum(_k, _2, _1, _0, b1, x5, x4, x3, x2, x1)

#define Four_Four_Sum(a3, a2, a1, a0, b4, b3, b1, b0, x7, x6, x5, x4, x3, x2, x1, x0) \
  Four_Two_Sum(a3, a2, a1, a0, b1, b0, _l, _2, _1, _0, x1, x0); \
  Four_Two_Sum(_l, _2, _1, _0, b4, b3, x7, x6, x5, x4, x3, x2)

#define Eight_One_Sum(a7, a6, a5, a4, a3, a2, a1, a0, b, x8, x7, x6, x5, x4, x3, x2, x1, x0) \
  Four_One_Sum(a3, a2, a1, a0, b, _j, x3, x2, x1, x0); \
  Four_One_Sum(a7, a6, a5, a4, _j, x8, x7, x6, x5, x4)

#define Eight_Two_Sum( \
    a7, a6, a5, a4, a3, a2, a1, a0, b1, b0, x9, x8, x7, x6, x5, x4, x3, x2, x1, x0) \
  Eight_One_Sum(a7, a6, a5, a4, a3, a2, a1, a0, b0, _k, _6, _5, _4, _3, _2, _1, _0, x0); \
  Eight_One_Sum(_k, _6, _5, _4, _3, _2, _1, _0, b1, x9, x8, x7, x6, x5, x4, x3, x2, x1)

#define Eight_Four_Sum(a7, \
                       a6, \
                       a5, \
                       a4, \
                       a3, \
                       a2, \
                       a1, \
                       a0, \
                       b4, \
                       b3, \
                       b1, \
                       b0, \
                       x11, \
                       x10, \
                       x9, \
                       x8, \
                       x7, \
                       x6, \
                       x5, \
                       x4, \
                       x3, \
                       x2, \
                       x1, \
                       x0) \
  Eight_Two_Sum(a7, a6, a5, a4, a3, a2, a1, a0, b1, b0, _l, _6, _5, _4, _3, _2, _1, _0, x1, x0); \
  Eight_Two_Sum(_l, _6, _5, _4, _3, _2, _1, _0, b4, b3, x11, x10, x9, x8, x7, x6, x5, x4, x3, x2)

#define Two_One_Product(a1, a0, b, x3, x2, x1, x0) \
  Split(b, bhi, blo); \
  Two_Product_Presplit(a0, b, bhi, blo, _i, x0); \
  Two_Product_Presplit(a1, b, bhi, blo, _j, _0); \
  Two_Sum(_i, _0, _k, x1); \
  Fast_Two_Sum(_j, _k, x3, x2)

#define Four_One_Product(a3, a2, a1, a0, b, x7, x6, x5, x4, x3, x2, x1, x0) \
  Split(b, bhi, blo); \
  Two_Product_Presplit(a0, b, bhi, blo, _i, x0); \
  Two_Product_Presplit(a1, b, bhi, blo, _j, _0); \
  Two_Sum(_i, _0, _k, x1); \
  Fast_Two_Sum(_j, _k, _i, x2); \
  Two_Product_Presplit(a2, b, bhi, blo, _j, _0); \
  Two_Sum(_i, _0, _k, x3); \
  Fast_Two_Sum(_j, _k, _i, x4); \
  Two_Product_Presplit(a3, b, bhi, blo, _j, _0); \
  Two_Sum(_i, _0, _k, x5); \
  Fast_Two_Sum(_j, _k, x7, x6)

#define Two_Two_Product(a1, a0, b1, b0, x7, x6, x5, x4, x3, x2, x1, x0) \
  Split(a0, a0hi, a0lo); \
  Split(b0, bhi, blo); \
  Two_Product_2Presplit(a0, a0hi, a0lo, b0, bhi, blo, _i, x0); \
  Split(a1, a1hi, a1lo); \
  Two_Product_2Presplit(a1, a1hi, a1lo, b0, bhi, blo, _j, _0); \
  Two_Sum(_i, _0, _k, _1); \
  Fast_Two_Sum(_j, _k, _l, _2); \
  Split(b1, bhi, blo); \
  Two_Product_2Presplit(a0, a0hi, a0lo, b1, bhi, blo, _i, _0); \
  Two_Sum(_1, _0, _k, x1); \
  Two_Sum(_2, _k, _j, _1); \
  Two_Sum(_l, _j, _m, _2); \
  Two_Product_2Presplit(a1, a1hi, a1lo, b1, bhi, blo, _j, _0); \
  Two_Sum(_i, _0, _n, _0); \
  Two_Sum(_1, _0, _i, x2); \
  Two_Sum(_2, _i, _k, _1); \
  Two_Sum(_m, _k, _l, _2); \
  Two_Sum(_j, _n, _k, _0); \
  Two_Sum(_1, _0, _j, x3); \
  Two_Sum(_2, _j, _i, _1); \
  Two_Sum(_l, _i, _m, _2); \
  Two_Sum(_1, _k, _i, x4); \
  Two_Sum(_2, _i, _k, x5); \
  Two_Sum(_m, _k, x7, x6)

#define Two_Square(a1, a0, x5, x4, x3, x2, x1, x0) \
  Square(a0, _j, x0); \
  _0 = a0 + a0; \
  Two_Product(a1, _0, _k, _1); \
  Two_One_Sum(_k, _1, _j, _l, _2, x1); \
  Square(a1, _j, _1); \
  Two_Two_Sum(_j, _1, _l, _2, x5, x4, x3, x2)

static double splitter; /* = 2^ceiling(p / 2) + 1.  Used to split floats in half. */
static double epsilon;  /* = 2^(-p).  Used to estimate round-off errors. */
/* A set of coefficients used to calculate maximum round-off errors. */
static double resulterrbound;
static double ccwerrboundA, ccwerrboundB, ccwerrboundC;
static double o3derrboundA, o3derrboundB, o3derrboundC;
static double iccerrboundA, iccerrboundB, iccerrboundC;
static double isperrboundA, isperrboundB, isperrboundC;

/**
 *  exactinit()   Initialize the variables used for exact arithmetic.
 *
 *  `epsilon' is the largest power of two such that 1.0 + epsilon = 1.0 in
 *  floating-point arithmetic.  `epsilon' bounds the relative round-off
 *  error.  It is used for floating-point error analysis.
 *
 *  `splitter' is used to split floating-point numbers into two half-length
 *  significant for exact multiplication.
 *
 *  I imagine that a highly optimizing compiler might be too smart for its
 *  own good, and somehow cause this routine to fail, if it pretends that
 *  floating-point arithmetic is too much like real arithmetic.
 *
 *  Don't change this routine unless you fully understand it.
 */

void exactinit()
{
  double half;
  double check, lastcheck;
  int every_other;

  every_other = 1;
  half = 0.5;
  epsilon = 1.0;
  splitter = 1.0;
  check = 1.0;
  /* Repeatedly divide `epsilon' by two until it is too small to add to
   * one without causing round-off.  (Also check if the sum is equal to
   * the previous sum, for machines that round up instead of using exact
   * rounding.  Not that this library will work on such machines anyway. */
  do {
    lastcheck = check;
    epsilon *= half;
    if (every_other) {
      splitter *= 2.0;
    }
    every_other = !every_other;
    check = 1.0 + epsilon;
  } while (!ELEM(check, 1.0, lastcheck));
  splitter += 1.0;

  /* Error bounds for orientation and #incircle tests. */
  resulterrbound = (3.0 + 8.0 * epsilon) * epsilon;
  ccwerrboundA = (3.0 + 16.0 * epsilon) * epsilon;
  ccwerrboundB = (2.0 + 12.0 * epsilon) * epsilon;
  ccwerrboundC = (9.0 + 64.0 * epsilon) * epsilon * epsilon;
  o3derrboundA = (7.0 + 56.0 * epsilon) * epsilon;
  o3derrboundB = (3.0 + 28.0 * epsilon) * epsilon;
  o3derrboundC = (26.0 + 288.0 * epsilon) * epsilon * epsilon;
  iccerrboundA = (10.0 + 96.0 * epsilon) * epsilon;
  iccerrboundB = (4.0 + 48.0 * epsilon) * epsilon;
  iccerrboundC = (44.0 + 576.0 * epsilon) * epsilon * epsilon;
  isperrboundA = (16.0 + 224.0 * epsilon) * epsilon;
  isperrboundB = (5.0 + 72.0 * epsilon) * epsilon;
  isperrboundC = (71.0 + 1408.0 * epsilon) * epsilon * epsilon;
}

/**
 * fast_expansion_sum_zeroelim()    Sum two expansions, eliminating zero
 *                                  components from the output expansion.
 *
 *  Sets h = e + f.  See the long version of my paper for details.
 * h cannot be e or f.
 */
static int fast_expansion_sum_zeroelim(
    int elen, const double *e, int flen, const double *f, double *h)
{
  double Q;
  INEXACT double Qnew;
  INEXACT double hh;
  INEXACT double bvirt;
  double avirt, bround, around;
  int eindex, findex, hindex;
  double enow, fnow;

  enow = e[0];
  fnow = f[0];
  eindex = findex = 0;
  if ((fnow > enow) == (fnow > -enow)) {
    Q = enow;
    enow = e[++eindex];
  }
  else {
    Q = fnow;
    fnow = f[++findex];
  }
  hindex = 0;
  if ((eindex < elen) && (findex < flen)) {
    if ((fnow > enow) == (fnow > -enow)) {
      Fast_Two_Sum(enow, Q, Qnew, hh);
      enow = e[++eindex];
    }
    else {
      Fast_Two_Sum(fnow, Q, Qnew, hh);
      fnow = f[++findex];
    }
    Q = Qnew;
    if (hh != 0.0) {
      h[hindex++] = hh;
    }
    while ((eindex < elen) && (findex < flen)) {
      if ((fnow > enow) == (fnow > -enow)) {
        Two_Sum(Q, enow, Qnew, hh);
        enow = e[++eindex];
      }
      else {
        Two_Sum(Q, fnow, Qnew, hh);
        fnow = f[++findex];
      }
      Q = Qnew;
      if (hh != 0.0) {
        h[hindex++] = hh;
      }
    }
  }
  while (eindex < elen) {
    Two_Sum(Q, enow, Qnew, hh);
    enow = e[++eindex];
    Q = Qnew;
    if (hh != 0.0) {
      h[hindex++] = hh;
    }
  }
  while (findex < flen) {
    Two_Sum(Q, fnow, Qnew, hh);
    fnow = f[++findex];
    Q = Qnew;
    if (hh != 0.0) {
      h[hindex++] = hh;
    }
  }
  if ((Q != 0.0) || (hindex == 0)) {
    h[hindex++] = Q;
  }
  return hindex;
}

/*  scale_expansion_zeroelim()   Multiply an expansion by a scalar,
 *                               eliminating zero components from the
 *                               output expansion.
 *
 *  Sets h = be.  See either version of my paper for details.
 *  e and h cannot be the same.
 */
static int scale_expansion_zeroelim(int elen, const double *e, double b, double *h)
{
  INEXACT double Q, sum;
  double hh;
  INEXACT double product1;
  double product0;
  int eindex, hindex;
  double enow;
  INEXACT double bvirt;
  double avirt, bround, around;
  INEXACT double c;
  INEXACT double abig;
  double ahi, alo, bhi, blo;
  double err1, err2, err3;

  Split(b, bhi, blo);
  Two_Product_Presplit(e[0], b, bhi, blo, Q, hh);
  hindex = 0;
  if (hh != 0) {
    h[hindex++] = hh;
  }
  for (eindex = 1; eindex < elen; eindex++) {
    enow = e[eindex];
    Two_Product_Presplit(enow, b, bhi, blo, product1, product0);
    Two_Sum(Q, product0, sum, hh);
    if (hh != 0) {
      h[hindex++] = hh;
    }
    Fast_Two_Sum(product1, sum, Q, hh);
    if (hh != 0) {
      h[hindex++] = hh;
    }
  }
  if ((Q != 0.0) || (hindex == 0)) {
    h[hindex++] = Q;
  }
  return hindex;
}

/*  estimate()   Produce a one-word estimate of an expansion's value. */
static double estimate(int elen, const double *e)
{
  double Q;
  int eindex;

  Q = e[0];
  for (eindex = 1; eindex < elen; eindex++) {
    Q += e[eindex];
  }
  return Q;
}

/**
 * orient2dfast()   Approximate 2D orientation test.  Non-robust.
 * orient2d()    Adaptive exact 2D orientation test.  Robust.
 *               Return a positive value if the points pa, pb, and pc occur
 *               in counterclockwise order; a negative value if they occur
 *               in clockwise order; and zero if they are co-linear.  The
 *               result is also a rough approximation of twice the signed
 *               area of the triangle defined by the three points.
 *
 * The second uses exact arithmetic to ensure a correct answer.  The
 * result returned is the determinant of a matrix.  In orient2d() only,
 * this determinant is computed adaptively, in the sense that exact
 * arithmetic is used only to the degree it is needed to ensure that the
 * returned value has the correct sign.  Hence, orient2d() is usually quite
 * fast, but will run more slowly when the input points are co-linear or
 * nearly so.
 */

double orient2dfast(const double *pa, const double *pb, const double *pc)
{
  double acx, bcx, acy, bcy;

  acx = pa[0] - pc[0];
  bcx = pb[0] - pc[0];
  acy = pa[1] - pc[1];
  bcy = pb[1] - pc[1];
  return acx * bcy - acy * bcx;
}

static double orient2dadapt(const double *pa, const double *pb, const double *pc, double detsum)
{
  INEXACT double acx, acy, bcx, bcy;
  double acxtail, acytail, bcxtail, bcytail;
  INEXACT double detleft, detright;
  double detlefttail, detrighttail;
  double det, errbound;
  double B[4], C1[8], C2[12], D[16];
  INEXACT double B3;
  int C1length, C2length, Dlength;
  double u[4];
  INEXACT double u3;
  INEXACT double s1, t1;
  double s0, t0;

  INEXACT double bvirt;
  double avirt, bround, around;
  INEXACT double c;
  INEXACT double abig;
  double ahi, alo, bhi, blo;
  double err1, err2, err3;
  INEXACT double _i, _j;
  double _0;

  acx = (double)(pa[0] - pc[0]);
  bcx = (double)(pb[0] - pc[0]);
  acy = (double)(pa[1] - pc[1]);
  bcy = (double)(pb[1] - pc[1]);

  Two_Product(acx, bcy, detleft, detlefttail);
  Two_Product(acy, bcx, detright, detrighttail);

  Two_Two_Diff(detleft, detlefttail, detright, detrighttail, B3, B[2], B[1], B[0]);
  B[3] = B3;

  det = estimate(4, B);
  errbound = ccwerrboundB * detsum;
  if ((det >= errbound) || (-det >= errbound)) {
    return det;
  }

  Two_Diff_Tail(pa[0], pc[0], acx, acxtail);
  Two_Diff_Tail(pb[0], pc[0], bcx, bcxtail);
  Two_Diff_Tail(pa[1], pc[1], acy, acytail);
  Two_Diff_Tail(pb[1], pc[1], bcy, bcytail);

  if ((acxtail == 0.0) && (acytail == 0.0) && (bcxtail == 0.0) && (bcytail == 0.0)) {
    return det;
  }

  errbound = ccwerrboundC * detsum + resulterrbound * Absolute(det);
  det += (acx * bcytail + bcy * acxtail) - (acy * bcxtail + bcx * acytail);
  if ((det >= errbound) || (-det >= errbound)) {
    return det;
  }

  Two_Product(acxtail, bcy, s1, s0);
  Two_Product(acytail, bcx, t1, t0);
  Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
  u[3] = u3;
  C1length = fast_expansion_sum_zeroelim(4, B, 4, u, C1);

  Two_Product(acx, bcytail, s1, s0);
  Two_Product(acy, bcxtail, t1, t0);
  Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
  u[3] = u3;
  C2length = fast_expansion_sum_zeroelim(C1length, C1, 4, u, C2);

  Two_Product(acxtail, bcytail, s1, s0);
  Two_Product(acytail, bcxtail, t1, t0);
  Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
  u[3] = u3;
  Dlength = fast_expansion_sum_zeroelim(C2length, C2, 4, u, D);

  return (D[Dlength - 1]);
}

double orient2d(const double *pa, const double *pb, const double *pc)
{
  double detleft, detright, det;
  double detsum, errbound;

  detleft = (pa[0] - pc[0]) * (pb[1] - pc[1]);
  detright = (pa[1] - pc[1]) * (pb[0] - pc[0]);
  det = detleft - detright;

  if (detleft > 0.0) {
    if (detright <= 0.0) {
      return det;
    }
    detsum = detleft + detright;
  }
  else if (detleft < 0.0) {
    if (detright >= 0.0) {
      return det;
    }
    detsum = -detleft - detright;
  }
  else {
    return det;
  }

  errbound = ccwerrboundA * detsum;
  if ((det >= errbound) || (-det >= errbound)) {
    return det;
  }

  return orient2dadapt(pa, pb, pc, detsum);
}

/**
 * orient3dfast()   Approximate 3D orientation test.  Non-robust.
 * orient3d()    Adaptive exact 3D orientation test.  Robust.
 *
 *               Return a positive value if the point pd lies below the
 *               plane passing through pa, pb, and pc; "below" is defined so
 *               that pa, pb, and pc appear in counterclockwise order when
 *               viewed from above the plane.  Returns a negative value if
 *               pd lies above the plane.  Returns zero if the points are
 *               co-planar.  The result is also a rough approximation of six
 *               times the signed volume of the tetrahedron defined by the
 *               four points.
 *
 * The second uses exact arithmetic to ensure a correct answer.  The
 * result returned is the determinant of a matrix.  In orient3d() only,
 * this determinant is computed adaptively, in the sense that exact
 * arithmetic is used only to the degree it is needed to ensure that the
 * returned value has the correct sign.  Hence, orient3d() is usually quite
 * fast, but will run more slowly when the input points are co-planar or
 * nearly so.
 */

double orient3dfast(const double *pa, const double *pb, const double *pc, const double *pd)
{
  double adx, bdx, cdx;
  double ady, bdy, cdy;
  double adz, bdz, cdz;

  adx = pa[0] - pd[0];
  bdx = pb[0] - pd[0];
  cdx = pc[0] - pd[0];
  ady = pa[1] - pd[1];
  bdy = pb[1] - pd[1];
  cdy = pc[1] - pd[1];
  adz = pa[2] - pd[2];
  bdz = pb[2] - pd[2];
  cdz = pc[2] - pd[2];

  return adx * (bdy * cdz - bdz * cdy) + bdx * (cdy * adz - cdz * ady) +
         cdx * (ady * bdz - adz * bdy);
}

/**
 * \note since this code comes from an external source, prefer not to break it
 * up to fix this clang-tidy warning.
 */
/* NOLINTNEXTLINE: readability-function-size */
static double orient3dadapt(
    const double *pa, const double *pb, const double *pc, const double *pd, double permanent)
{
  INEXACT double adx, bdx, cdx, ady, bdy, cdy, adz, bdz, cdz;
  double det, errbound;

  INEXACT double bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1;
  double bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0;
  double bc[4], ca[4], ab[4];
  INEXACT double bc3, ca3, ab3;
  double adet[8], bdet[8], cdet[8];
  int alen, blen, clen;
  double abdet[16];
  int ablen;
  double *finnow, *finother, *finswap;
  double fin1[192], fin2[192];
  int finlength;

  double adxtail, bdxtail, cdxtail;
  double adytail, bdytail, cdytail;
  double adztail, bdztail, cdztail;
  INEXACT double at_blarge, at_clarge;
  INEXACT double bt_clarge, bt_alarge;
  INEXACT double ct_alarge, ct_blarge;
  double at_b[4], at_c[4], bt_c[4], bt_a[4], ct_a[4], ct_b[4];
  int at_blen, at_clen, bt_clen, bt_alen, ct_alen, ct_blen;
  INEXACT double bdxt_cdy1, cdxt_bdy1, cdxt_ady1;
  INEXACT double adxt_cdy1, adxt_bdy1, bdxt_ady1;
  double bdxt_cdy0, cdxt_bdy0, cdxt_ady0;
  double adxt_cdy0, adxt_bdy0, bdxt_ady0;
  INEXACT double bdyt_cdx1, cdyt_bdx1, cdyt_adx1;
  INEXACT double adyt_cdx1, adyt_bdx1, bdyt_adx1;
  double bdyt_cdx0, cdyt_bdx0, cdyt_adx0;
  double adyt_cdx0, adyt_bdx0, bdyt_adx0;
  double bct[8], cat[8], abt[8];
  int bctlen, catlen, abtlen;
  INEXACT double bdxt_cdyt1, cdxt_bdyt1, cdxt_adyt1;
  INEXACT double adxt_cdyt1, adxt_bdyt1, bdxt_adyt1;
  double bdxt_cdyt0, cdxt_bdyt0, cdxt_adyt0;
  double adxt_cdyt0, adxt_bdyt0, bdxt_adyt0;
  double u[4], v[12], w[16];
  INEXACT double u3;
  int vlength, wlength;
  double negate;

  INEXACT double bvirt;
  double avirt, bround, around;
  INEXACT double c;
  INEXACT double abig;
  double ahi, alo, bhi, blo;
  double err1, err2, err3;
  INEXACT double _i, _j, _k;
  double _0;

  adx = (double)(pa[0] - pd[0]);
  bdx = (double)(pb[0] - pd[0]);
  cdx = (double)(pc[0] - pd[0]);
  ady = (double)(pa[1] - pd[1]);
  bdy = (double)(pb[1] - pd[1]);
  cdy = (double)(pc[1] - pd[1]);
  adz = (double)(pa[2] - pd[2]);
  bdz = (double)(pb[2] - pd[2]);
  cdz = (double)(pc[2] - pd[2]);

  Two_Product(bdx, cdy, bdxcdy1, bdxcdy0);
  Two_Product(cdx, bdy, cdxbdy1, cdxbdy0);
  Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]);
  bc[3] = bc3;
  alen = scale_expansion_zeroelim(4, bc, adz, adet);

  Two_Product(cdx, ady, cdxady1, cdxady0);
  Two_Product(adx, cdy, adxcdy1, adxcdy0);
  Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]);
  ca[3] = ca3;
  blen = scale_expansion_zeroelim(4, ca, bdz, bdet);

  Two_Product(adx, bdy, adxbdy1, adxbdy0);
  Two_Product(bdx, ady, bdxady1, bdxady0);
  Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]);
  ab[3] = ab3;
  clen = scale_expansion_zeroelim(4, ab, cdz, cdet);

  ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
  finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1);

  det = estimate(finlength, fin1);
  errbound = o3derrboundB * permanent;
  if ((det >= errbound) || (-det >= errbound)) {
    return det;
  }

  Two_Diff_Tail(pa[0], pd[0], adx, adxtail);
  Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail);
  Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail);
  Two_Diff_Tail(pa[1], pd[1], ady, adytail);
  Two_Diff_Tail(pb[1], pd[1], bdy, bdytail);
  Two_Diff_Tail(pc[1], pd[1], cdy, cdytail);
  Two_Diff_Tail(pa[2], pd[2], adz, adztail);
  Two_Diff_Tail(pb[2], pd[2], bdz, bdztail);
  Two_Diff_Tail(pc[2], pd[2], cdz, cdztail);

  if ((adxtail == 0.0) && (bdxtail == 0.0) && (cdxtail == 0.0) && (adytail == 0.0) &&
      (bdytail == 0.0) && (cdytail == 0.0) && (adztail == 0.0) && (bdztail == 0.0) &&
      (cdztail == 0.0)) {
    return det;
  }

  errbound = o3derrboundC * permanent + resulterrbound * Absolute(det);
  det += (adz * ((bdx * cdytail + cdy * bdxtail) - (bdy * cdxtail + cdx * bdytail)) +
          adztail * (bdx * cdy - bdy * cdx)) +
         (bdz * ((cdx * adytail + ady * cdxtail) - (cdy * adxtail + adx * cdytail)) +
          bdztail * (cdx * ady - cdy * adx)) +
         (cdz * ((adx * bdytail + bdy * adxtail) - (ady * bdxtail + bdx * adytail)) +
          cdztail * (adx * bdy - ady * bdx));
  if ((det >= errbound) || (-det >= errbound)) {
    return det;
  }

  finnow = fin1;
  finother = fin2;

  if (adxtail == 0.0) {
    if (adytail == 0.0) {
      at_b[0] = 0.0;
      at_blen = 1;
      at_c[0] = 0.0;
      at_clen = 1;
    }
    else {
      negate = -adytail;
      Two_Product(negate, bdx, at_blarge, at_b[0]);
      at_b[1] = at_blarge;
      at_blen = 2;
      Two_Product(adytail, cdx, at_clarge, at_c[0]);
      at_c[1] = at_clarge;
      at_clen = 2;
    }
  }
  else {
    if (adytail == 0.0) {
      Two_Product(adxtail, bdy, at_blarge, at_b[0]);
      at_b[1] = at_blarge;
      at_blen = 2;
      negate = -adxtail;
      Two_Product(negate, cdy, at_clarge, at_c[0]);
      at_c[1] = at_clarge;
      at_clen = 2;
    }
    else {
      Two_Product(adxtail, bdy, adxt_bdy1, adxt_bdy0);
      Two_Product(adytail, bdx, adyt_bdx1, adyt_bdx0);
      Two_Two_Diff(
          adxt_bdy1, adxt_bdy0, adyt_bdx1, adyt_bdx0, at_blarge, at_b[2], at_b[1], at_b[0]);
      at_b[3] = at_blarge;
      at_blen = 4;
      Two_Product(adytail, cdx, adyt_cdx1, adyt_cdx0);
      Two_Product(adxtail, cdy, adxt_cdy1, adxt_cdy0);
      Two_Two_Diff(
          adyt_cdx1, adyt_cdx0, adxt_cdy1, adxt_cdy0, at_clarge, at_c[2], at_c[1], at_c[0]);
      at_c[3] = at_clarge;
      at_clen = 4;
    }
  }
  if (bdxtail == 0.0) {
    if (bdytail == 0.0) {
      bt_c[0] = 0.0;
      bt_clen = 1;
      bt_a[0] = 0.0;
      bt_alen = 1;
    }
    else {
      negate = -bdytail;
      Two_Product(negate, cdx, bt_clarge, bt_c[0]);
      bt_c[1] = bt_clarge;
      bt_clen = 2;
      Two_Product(bdytail, adx, bt_alarge, bt_a[0]);
      bt_a[1] = bt_alarge;
      bt_alen = 2;
    }
  }
  else {
    if (bdytail == 0.0) {
      Two_Product(bdxtail, cdy, bt_clarge, bt_c[0]);
      bt_c[1] = bt_clarge;
      bt_clen = 2;
      negate = -bdxtail;
      Two_Product(negate, ady, bt_alarge, bt_a[0]);
      bt_a[1] = bt_alarge;
      bt_alen = 2;
    }
    else {
      Two_Product(bdxtail, cdy, bdxt_cdy1, bdxt_cdy0);
      Two_Product(bdytail, cdx, bdyt_cdx1, bdyt_cdx0);
      Two_Two_Diff(
          bdxt_cdy1, bdxt_cdy0, bdyt_cdx1, bdyt_cdx0, bt_clarge, bt_c[2], bt_c[1], bt_c[0]);
      bt_c[3] = bt_clarge;
      bt_clen = 4;
      Two_Product(bdytail, adx, bdyt_adx1, bdyt_adx0);
      Two_Product(bdxtail, ady, bdxt_ady1, bdxt_ady0);
      Two_Two_Diff(
          bdyt_adx1, bdyt_adx0, bdxt_ady1, bdxt_ady0, bt_alarge, bt_a[2], bt_a[1], bt_a[0]);
      bt_a[3] = bt_alarge;
      bt_alen = 4;
    }
  }
  if (cdxtail == 0.0) {
    if (cdytail == 0.0) {
      ct_a[0] = 0.0;
      ct_alen = 1;
      ct_b[0] = 0.0;
      ct_blen = 1;
    }
    else {
      negate = -cdytail;
      Two_Product(negate, adx, ct_alarge, ct_a[0]);
      ct_a[1] = ct_alarge;
      ct_alen = 2;
      Two_Product(cdytail, bdx, ct_blarge, ct_b[0]);
      ct_b[1] = ct_blarge;
      ct_blen = 2;
    }
  }
  else {
    if (cdytail == 0.0) {
      Two_Product(cdxtail, ady, ct_alarge, ct_a[0]);
      ct_a[1] = ct_alarge;
      ct_alen = 2;
      negate = -cdxtail;
      Two_Product(negate, bdy, ct_blarge, ct_b[0]);
      ct_b[1] = ct_blarge;
      ct_blen = 2;
    }
    else {
      Two_Product(cdxtail, ady, cdxt_ady1, cdxt_ady0);
      Two_Product(cdytail, adx, cdyt_adx1, cdyt_adx0);
      Two_Two_Diff(
          cdxt_ady1, cdxt_ady0, cdyt_adx1, cdyt_adx0, ct_alarge, ct_a[2], ct_a[1], ct_a[0]);
      ct_a[3] = ct_alarge;
      ct_alen = 4;
      Two_Product(cdytail, bdx, cdyt_bdx1, cdyt_bdx0);
      Two_Product(cdxtail, bdy, cdxt_bdy1, cdxt_bdy0);
      Two_Two_Diff(
          cdyt_bdx1, cdyt_bdx0, cdxt_bdy1, cdxt_bdy0, ct_blarge, ct_b[2], ct_b[1], ct_b[0]);
      ct_b[3] = ct_blarge;
      ct_blen = 4;
    }
  }

  bctlen = fast_expansion_sum_zeroelim(bt_clen, bt_c, ct_blen, ct_b, bct);
  wlength = scale_expansion_zeroelim(bctlen, bct, adz, w);
  finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w, finother);
  finswap = finnow;
  finnow = finother;
  finother = finswap;

  catlen = fast_expansion_sum_zeroelim(ct_alen, ct_a, at_clen, at_c, cat);
  wlength = scale_expansion_zeroelim(catlen, cat, bdz, w);
  finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w, finother);
  finswap = finnow;
  finnow = finother;
  finother = finswap;

  abtlen = fast_expansion_sum_zeroelim(at_blen, at_b, bt_alen, bt_a, abt);
  wlength = scale_expansion_zeroelim(abtlen, abt, cdz, w);
  finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w, finother);
  finswap = finnow;
  finnow = finother;
  finother = finswap;

  if (adztail != 0.0) {
    vlength = scale_expansion_zeroelim(4, bc, adztail, v);
    finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v, finother);
    finswap = finnow;
    finnow = finother;
    finother = finswap;
  }
  if (bdztail != 0.0) {
    vlength = scale_expansion_zeroelim(4, ca, bdztail, v);
    finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v, finother);
    finswap = finnow;
    finnow = finother;
    finother = finswap;
  }
  if (cdztail != 0.0) {
    vlength = scale_expansion_zeroelim(4, ab, cdztail, v);
    finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v, finother);
    finswap = finnow;
    finnow = finother;
    finother = finswap;
  }

  if (adxtail != 0.0) {
    if (bdytail != 0.0) {
      Two_Product(adxtail, bdytail, adxt_bdyt1, adxt_bdyt0);
      Two_One_Product(adxt_bdyt1, adxt_bdyt0, cdz, u3, u[2], u[1], u[0]);
      u[3] = u3;
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, finother);
      finswap = finnow;
      finnow = finother;
      finother = finswap;
      if (cdztail != 0.0) {
        Two_One_Product(adxt_bdyt1, adxt_bdyt0, cdztail, u3, u[2], u[1], u[0]);
        u[3] = u3;
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, finother);
        finswap = finnow;
        finnow = finother;
        finother = finswap;
      }
    }
    if (cdytail != 0.0) {
      negate = -adxtail;
      Two_Product(negate, cdytail, adxt_cdyt1, adxt_cdyt0);
      Two_One_Product(adxt_cdyt1, adxt_cdyt0, bdz, u3, u[2], u[1], u[0]);
      u[3] = u3;
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, finother);
      finswap = finnow;
      finnow = finother;
      finother = finswap;
      if (bdztail != 0.0) {
        Two_One_Product(adxt_cdyt1, adxt_cdyt0, bdztail, u3, u[2], u[1], u[0]);
        u[3] = u3;
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, finother);
        finswap = finnow;
        finnow = finother;
        finother = finswap;
      }
    }
  }
  if (bdxtail != 0.0) {
    if (cdytail != 0.0) {
      Two_Product(bdxtail, cdytail, bdxt_cdyt1, bdxt_cdyt0);
      Two_One_Product(bdxt_cdyt1, bdxt_cdyt0, adz, u3, u[2], u[1], u[0]);
      u[3] = u3;
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, finother);
      finswap = finnow;
      finnow = finother;
      finother = finswap;
      if (adztail != 0.0) {
        Two_One_Product(bdxt_cdyt1, bdxt_cdyt0, adztail, u3, u[2], u[1], u[0]);
        u[3] = u3;
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, finother);
        finswap = finnow;
        finnow = finother;
        finother = finswap;
      }
    }
    if (adytail != 0.0) {
      negate = -bdxtail;
      Two_Product(negate, adytail, bdxt_adyt1, bdxt_adyt0);
      Two_One_Product(bdxt_adyt1, bdxt_adyt0, cdz, u3, u[2], u[1], u[0]);
      u[3] = u3;
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, finother);
      finswap = finnow;
      finnow = finother;
      finother = finswap;
      if (cdztail != 0.0) {
        Two_One_Product(bdxt_adyt1, bdxt_adyt0, cdztail, u3, u[2], u[1], u[0]);
        u[3] = u3;
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, finother);
        finswap = finnow;
        finnow = finother;
        finother = finswap;
      }
    }
  }
  if (cdxtail != 0.0) {
    if (adytail != 0.0) {
      Two_Product(cdxtail, adytail, cdxt_adyt1, cdxt_adyt0);
      Two_One_Product(cdxt_adyt1, cdxt_adyt0, bdz, u3, u[2], u[1], u[0]);
      u[3] = u3;
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, finother);
      finswap = finnow;
      finnow = finother;
      finother = finswap;
      if (bdztail != 0.0) {
        Two_One_Product(cdxt_adyt1, cdxt_adyt0, bdztail, u3, u[2], u[1], u[0]);
        u[3] = u3;
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, finother);
        finswap = finnow;
        finnow = finother;
        finother = finswap;
      }
    }
    if (bdytail != 0.0) {
      negate = -cdxtail;
      Two_Product(negate, bdytail, cdxt_bdyt1, cdxt_bdyt0);
      Two_One_Product(cdxt_bdyt1, cdxt_bdyt0, adz, u3, u[2], u[1], u[0]);
      u[3] = u3;
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, finother);
      finswap = finnow;
      finnow = finother;
      finother = finswap;
      if (adztail != 0.0) {
        Two_One_Product(cdxt_bdyt1, cdxt_bdyt0, adztail, u3, u[2], u[1], u[0]);
        u[3] = u3;
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, finother);
        finswap = finnow;
        finnow = finother;
        finother = finswap;
      }
    }
  }

  if (adztail != 0.0) {
    wlength = scale_expansion_zeroelim(bctlen, bct, adztail, w);
    finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w, finother);
    finswap = finnow;
    finnow = finother;
    finother = finswap;
  }
  if (bdztail != 0.0) {
    wlength = scale_expansion_zeroelim(catlen, cat, bdztail, w);
    finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w, finother);
    finswap = finnow;
    finnow = finother;
    finother = finswap;
  }
  if (cdztail != 0.0) {
    wlength = scale_expansion_zeroelim(abtlen, abt, cdztail, w);
    finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w, finother);
    finswap = finnow;
    finnow = finother;
    finother = finswap;
  }

  return finnow[finlength - 1];
}

double orient3d(const double *pa, const double *pb, const double *pc, const double *pd)
{
  double adx, bdx, cdx, ady, bdy, cdy, adz, bdz, cdz;
  double bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady;
  double det;
  double permanent, errbound;

  adx = pa[0] - pd[0];
  bdx = pb[0] - pd[0];
  cdx = pc[0] - pd[0];
  ady = pa[1] - pd[1];
  bdy = pb[1] - pd[1];
  cdy = pc[1] - pd[1];
  adz = pa[2] - pd[2];
  bdz = pb[2] - pd[2];
  cdz = pc[2] - pd[2];

  bdxcdy = bdx * cdy;
  cdxbdy = cdx * bdy;

  cdxady = cdx * ady;
  adxcdy = adx * cdy;

  adxbdy = adx * bdy;
  bdxady = bdx * ady;

  det = adz * (bdxcdy - cdxbdy) + bdz * (cdxady - adxcdy) + cdz * (adxbdy - bdxady);

  permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * Absolute(adz) +
              (Absolute(cdxady) + Absolute(adxcdy)) * Absolute(bdz) +
              (Absolute(adxbdy) + Absolute(bdxady)) * Absolute(cdz);
  errbound = o3derrboundA * permanent;
  if ((det > errbound) || (-det > errbound)) {
    return det;
  }

  return orient3dadapt(pa, pb, pc, pd, permanent);
}

/**
 *  incirclefast()   Approximate 2D incircle test.  Non-robust.
 *  incircle()
 *
 *               Return a positive value if the point pd lies inside the
 *               circle passing through pa, pb, and pc; a negative value if
 *               it lies outside; and zero if the four points are co-circular.
 *               The points pa, pb, and pc must be in counterclockwise
 *               order, or the sign of the result will be reversed.
 *
 *  The second uses exact arithmetic to ensure a correct answer.  The
 *  result returned is the determinant of a matrix.  In incircle() only,
 *  this determinant is computed adaptively, in the sense that exact
 *  arithmetic is used only to the degree it is needed to ensure that the
 *  returned value has the correct sign.  Hence, incircle() is usually quite
 *  fast, but will run more slowly when the input points are co-circular or
 *  nearly so.
 */

double incirclefast(const double *pa, const double *pb, const double *pc, const double *pd)
{
  double adx, ady, bdx, bdy, cdx, cdy;
  double abdet, bcdet, cadet;
  double alift, blift, clift;

  adx = pa[0] - pd[0];
  ady = pa[1] - pd[1];
  bdx = pb[0] - pd[0];
  bdy = pb[1] - pd[1];
  cdx = pc[0] - pd[0];
  cdy = pc[1] - pd[1];

  abdet = adx * bdy - bdx * ady;
  bcdet = bdx * cdy - cdx * bdy;
  cadet = cdx * ady - adx * cdy;
  alift = adx * adx + ady * ady;
  blift = bdx * bdx + bdy * bdy;
  clift = cdx * cdx + cdy * cdy;

  return alift * bcdet + blift * cadet + clift * abdet;
}

/**
 * \note since this code comes from an external source, prefer not to break it
 * up to fix this clang-tidy warning.
 */
/* NOLINTNEXTLINE: readability-function-size */
static double incircleadapt(
    const double *pa, const double *pb, const double *pc, const double *pd, double permanent)
{
  INEXACT double adx, bdx, cdx, ady, bdy, cdy;
  double det, errbound;

  INEXACT double bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1;
  double bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0;
  double bc[4], ca[4], ab[4];
  INEXACT double bc3, ca3, ab3;
  double axbc[8], axxbc[16], aybc[8], ayybc[16], adet[32];
  int axbclen, axxbclen, aybclen, ayybclen, alen;
  double bxca[8], bxxca[16], byca[8], byyca[16], bdet[32];
  int bxcalen, bxxcalen, bycalen, byycalen, blen;
  double cxab[8], cxxab[16], cyab[8], cyyab[16], cdet[32];
  int cxablen, cxxablen, cyablen, cyyablen, clen;
  double abdet[64];
  int ablen;
  double fin1[1152], fin2[1152];
  double *finnow, *finother, *finswap;
  int finlength;

  double adxtail, bdxtail, cdxtail, adytail, bdytail, cdytail;
  INEXACT double adxadx1, adyady1, bdxbdx1, bdybdy1, cdxcdx1, cdycdy1;
  double adxadx0, adyady0, bdxbdx0, bdybdy0, cdxcdx0, cdycdy0;
  double aa[4], bb[4], cc[4];
  INEXACT double aa3, bb3, cc3;
  INEXACT double ti1, tj1;
  double ti0, tj0;
  double u[4], v[4];
  INEXACT double u3, v3;
  double temp8[8], temp16a[16], temp16b[16], temp16c[16];
  double temp32a[32], temp32b[32], temp48[48], temp64[64];
  int temp8len, temp16alen, temp16blen, temp16clen;
  int temp32alen, temp32blen, temp48len, temp64len;
  double axtbb[8], axtcc[8], aytbb[8], aytcc[8];
  int axtbblen, axtcclen, aytbblen, aytcclen;
  double bxtaa[8], bxtcc[8], bytaa[8], bytcc[8];
  int bxtaalen, bxtcclen, bytaalen, bytcclen;
  double cxtaa[8], cxtbb[8], cytaa[8], cytbb[8];
  int cxtaalen, cxtbblen, cytaalen, cytbblen;
  double axtbc[8], aytbc[8], bxtca[8], bytca[8], cxtab[8], cytab[8];
  int axtbclen, aytbclen, bxtcalen, bytcalen, cxtablen, cytablen;
  double axtbct[16], aytbct[16], bxtcat[16], bytcat[16], cxtabt[16], cytabt[16];
  int axtbctlen, aytbctlen, bxtcatlen, bytcatlen, cxtabtlen, cytabtlen;
  double axtbctt[8], aytbctt[8], bxtcatt[8];
  double bytcatt[8], cxtabtt[8], cytabtt[8];
  int axtbcttlen, aytbcttlen, bxtcattlen, bytcattlen, cxtabttlen, cytabttlen;
  double abt[8], bct[8], cat[8];
  int abtlen, bctlen, catlen;
  double abtt[4], bctt[4], catt[4];
  int abttlen, bcttlen, cattlen;
  INEXACT double abtt3, bctt3, catt3;
  double negate;

  INEXACT double bvirt;
  double avirt, bround, around;
  INEXACT double c;
  INEXACT double abig;
  double ahi, alo, bhi, blo;
  double err1, err2, err3;
  INEXACT double _i, _j;
  double _0;

  adx = (double)(pa[0] - pd[0]);
  bdx = (double)(pb[0] - pd[0]);
  cdx = (double)(pc[0] - pd[0]);
  ady = (double)(pa[1] - pd[1]);
  bdy = (double)(pb[1] - pd[1]);
  cdy = (double)(pc[1] - pd[1]);

  Two_Product(bdx, cdy, bdxcdy1, bdxcdy0);
  Two_Product(cdx, bdy, cdxbdy1, cdxbdy0);
  Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]);
  bc[3] = bc3;
  axbclen = scale_expansion_zeroelim(4, bc, adx, axbc);
  axxbclen = scale_expansion_zeroelim(axbclen, axbc, adx, axxbc);
  aybclen = scale_expansion_zeroelim(4, bc, ady, aybc);
  ayybclen = scale_expansion_zeroelim(aybclen, aybc, ady, ayybc);
  alen = fast_expansion_sum_zeroelim(axxbclen, axxbc, ayybclen, ayybc, adet);

  Two_Product(cdx, ady, cdxady1, cdxady0);
  Two_Product(adx, cdy, adxcdy1, adxcdy0);
  Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]);
  ca[3] = ca3;
  bxcalen = scale_expansion_zeroelim(4, ca, bdx, bxca);
  bxxcalen = scale_expansion_zeroelim(bxcalen, bxca, bdx, bxxca);
  bycalen = scale_expansion_zeroelim(4, ca, bdy, byca);
  byycalen = scale_expansion_zeroelim(bycalen, byca, bdy, byyca);
  blen = fast_expansion_sum_zeroelim(bxxcalen, bxxca, byycalen, byyca, bdet);

  Two_Product(adx, bdy, adxbdy1, adxbdy0);
  Two_Product(bdx, ady, bdxady1, bdxady0);
  Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]);
  ab[3] = ab3;
  cxablen = scale_expansion_zeroelim(4, ab, cdx, cxab);
  cxxablen = scale_expansion_zeroelim(cxablen, cxab, cdx, cxxab);
  cyablen = scale_expansion_zeroelim(4, ab, cdy, cyab);
  cyyablen = scale_expansion_zeroelim(cyablen, cyab, cdy, cyyab);
  clen = fast_expansion_sum_zeroelim(cxxablen, cxxab, cyyablen, cyyab, cdet);

  ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
  finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1);

  det = estimate(finlength, fin1);
  errbound = iccerrboundB * permanent;
  if ((det >= errbound) || (-det >= errbound)) {
    return det;
  }

  Two_Diff_Tail(pa[0], pd[0], adx, adxtail);
  Two_Diff_Tail(pa[1], pd[1], ady, adytail);
  Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail);
  Two_Diff_Tail(pb[1], pd[1], bdy, bdytail);
  Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail);
  Two_Diff_Tail(pc[1], pd[1], cdy, cdytail);
  if ((adxtail == 0.0) && (bdxtail == 0.0) && (cdxtail == 0.0) && (adytail == 0.0) &&
      (bdytail == 0.0) && (cdytail == 0.0)) {
    return det;
  }

  errbound = iccerrboundC * permanent + resulterrbound * Absolute(det);
  det += ((adx * adx + ady * ady) *
              ((bdx * cdytail + cdy * bdxtail) - (bdy * cdxtail + cdx * bdytail)) +
          2.0 * (adx * adxtail + ady * adytail) * (bdx * cdy - bdy * cdx)) +
         ((bdx * bdx + bdy * bdy) *
              ((cdx * adytail + ady * cdxtail) - (cdy * adxtail + adx * cdytail)) +
          2.0 * (bdx * bdxtail + bdy * bdytail) * (cdx * ady - cdy * adx)) +
         ((cdx * cdx + cdy * cdy) *
              ((adx * bdytail + bdy * adxtail) - (ady * bdxtail + bdx * adytail)) +
          2.0 * (cdx * cdxtail + cdy * cdytail) * (adx * bdy - ady * bdx));
  if ((det >= errbound) || (-det >= errbound)) {
    return det;
  }

  finnow = fin1;
  finother = fin2;

  if ((bdxtail != 0.0) || (bdytail != 0.0) || (cdxtail != 0.0) || (cdytail != 0.0)) {
    Square(adx, adxadx1, adxadx0);
    Square(ady, adyady1, adyady0);
    Two_Two_Sum(adxadx1, adxadx0, adyady1, adyady0, aa3, aa[2], aa[1], aa[0]);
    aa[3] = aa3;
  }
  if ((cdxtail != 0.0) || (cdytail != 0.0) || (adxtail != 0.0) || (adytail != 0.0)) {
    Square(bdx, bdxbdx1, bdxbdx0);
    Square(bdy, bdybdy1, bdybdy0);
    Two_Two_Sum(bdxbdx1, bdxbdx0, bdybdy1, bdybdy0, bb3, bb[2], bb[1], bb[0]);
    bb[3] = bb3;
  }
  if ((adxtail != 0.0) || (adytail != 0.0) || (bdxtail != 0.0) || (bdytail != 0.0)) {
    Square(cdx, cdxcdx1, cdxcdx0);
    Square(cdy, cdycdy1, cdycdy0);
    Two_Two_Sum(cdxcdx1, cdxcdx0, cdycdy1, cdycdy0, cc3, cc[2], cc[1], cc[0]);
    cc[3] = cc3;
  }

  if (adxtail != 0.0) {
    axtbclen = scale_expansion_zeroelim(4, bc, adxtail, axtbc);
    temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, 2.0 * adx, temp16a);

    axtcclen = scale_expansion_zeroelim(4, cc, adxtail, axtcc);
    temp16blen = scale_expansion_zeroelim(axtcclen, axtcc, bdy, temp16b);

    axtbblen = scale_expansion_zeroelim(4, bb, adxtail, axtbb);
    temp16clen = scale_expansion_zeroelim(axtbblen, axtbb, -cdy, temp16c);

    temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32a);
    temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, temp32alen, temp32a, temp48);
    finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother);
    finswap = finnow;
    finnow = finother;
    finother = finswap;
  }
  if (adytail != 0.0) {
    aytbclen = scale_expansion_zeroelim(4, bc, adytail, aytbc);
    temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, 2.0 * ady, temp16a);

    aytbblen = scale_expansion_zeroelim(4, bb, adytail, aytbb);
    temp16blen = scale_expansion_zeroelim(aytbblen, aytbb, cdx, temp16b);

    aytcclen = scale_expansion_zeroelim(4, cc, adytail, aytcc);
    temp16clen = scale_expansion_zeroelim(aytcclen, aytcc, -bdx, temp16c);

    temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32a);
    temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, temp32alen, temp32a, temp48);
    finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother);
    finswap = finnow;
    finnow = finother;
    finother = finswap;
  }
  if (bdxtail != 0.0) {
    bxtcalen = scale_expansion_zeroelim(4, ca, bdxtail, bxtca);
    temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, 2.0 * bdx, temp16a);

    bxtaalen = scale_expansion_zeroelim(4, aa, bdxtail, bxtaa);
    temp16blen = scale_expansion_zeroelim(bxtaalen, bxtaa, cdy, temp16b);

    bxtcclen = scale_expansion_zeroelim(4, cc, bdxtail, bxtcc);
    temp16clen = scale_expansion_zeroelim(bxtcclen, bxtcc, -ady, temp16c);

    temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32a);
    temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, temp32alen, temp32a, temp48);
    finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother);
    finswap = finnow;
    finnow = finother;
    finother = finswap;
  }
  if (bdytail != 0.0) {
    bytcalen = scale_expansion_zeroelim(4, ca, bdytail, bytca);
    temp16alen = scale_expansion_zeroelim(bytcalen, bytca, 2.0 * bdy, temp16a);

    bytcclen = scale_expansion_zeroelim(4, cc, bdytail, bytcc);
    temp16blen = scale_expansion_zeroelim(bytcclen, bytcc, adx, temp16b);

    bytaalen = scale_expansion_zeroelim(4, aa, bdytail, bytaa);
    temp16clen = scale_expansion_zeroelim(bytaalen, bytaa, -cdx, temp16c);

    temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32a);
    temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, temp32alen, temp32a, temp48);
    finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother);
    finswap = finnow;
    finnow = finother;
    finother = finswap;
  }
  if (cdxtail != 0.0) {
    cxtablen = scale_expansion_zeroelim(4, ab, cdxtail, cxtab);
    temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, 2.0 * cdx, temp16a);

    cxtbblen = scale_expansion_zeroelim(4, bb, cdxtail, cxtbb);
    temp16blen = scale_expansion_zeroelim(cxtbblen, cxtbb, ady, temp16b);

    cxtaalen = scale_expansion_zeroelim(4, aa, cdxtail, cxtaa);
    temp16clen = scale_expansion_zeroelim(cxtaalen, cxtaa, -bdy, temp16c);

    temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32a);
    temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, temp32alen, temp32a, temp48);
    finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother);
    finswap = finnow;
    finnow = finother;
    finother = finswap;
  }
  if (cdytail != 0.0) {
    cytablen = scale_expansion_zeroelim(4, ab, cdytail, cytab);
    temp16alen = scale_expansion_zeroelim(cytablen, cytab, 2.0 * cdy, temp16a);

    cytaalen = scale_expansion_zeroelim(4, aa, cdytail, cytaa);
    temp16blen = scale_expansion_zeroelim(cytaalen, cytaa, bdx, temp16b);

    cytbblen = scale_expansion_zeroelim(4, bb, cdytail, cytbb);
    temp16clen = scale_expansion_zeroelim(cytbblen, cytbb, -adx, temp16c);

    temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32a);
    temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, temp32alen, temp32a, temp48);
    finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother);
    finswap = finnow;
    finnow = finother;
    finother = finswap;
  }

  if ((adxtail != 0.0) || (adytail != 0.0)) {
    if ((bdxtail != 0.0) || (bdytail != 0.0) || (cdxtail != 0.0) || (cdytail != 0.0)) {
      Two_Product(bdxtail, cdy, ti1, ti0);
      Two_Product(bdx, cdytail, tj1, tj0);
      Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
      u[3] = u3;
      negate = -bdy;
      Two_Product(cdxtail, negate, ti1, ti0);
      negate = -bdytail;
      Two_Product(cdx, negate, tj1, tj0);
      Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
      v[3] = v3;
      bctlen = fast_expansion_sum_zeroelim(4, u, 4, v, bct);

      Two_Product(bdxtail, cdytail, ti1, ti0);
      Two_Product(cdxtail, bdytail, tj1, tj0);
      Two_Two_Diff(ti1, ti0, tj1, tj0, bctt3, bctt[2], bctt[1], bctt[0]);
      bctt[3] = bctt3;
      bcttlen = 4;
    }
    else {
      bct[0] = 0.0;
      bctlen = 1;
      bctt[0] = 0.0;
      bcttlen = 1;
    }

    if (adxtail != 0.0) {
      temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, adxtail, temp16a);
      axtbctlen = scale_expansion_zeroelim(bctlen, bct, adxtail, axtbct);
      temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, 2.0 * adx, temp32a);
      temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp32alen, temp32a, temp48);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother);
      finswap = finnow;
      finnow = finother;
      finother = finswap;
      if (bdytail != 0.0) {
        temp8len = scale_expansion_zeroelim(4, cc, adxtail, temp8);
        temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail, temp16a);
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, temp16a, finother);
        finswap = finnow;
        finnow = finother;
        finother = finswap;
      }
      if (cdytail != 0.0) {
        temp8len = scale_expansion_zeroelim(4, bb, -adxtail, temp8);
        temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail, temp16a);
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, temp16a, finother);
        finswap = finnow;
        finnow = finother;
        finother = finswap;
      }

      temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, adxtail, temp32a);
      axtbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adxtail, axtbctt);
      temp16alen = scale_expansion_zeroelim(axtbcttlen, axtbctt, 2.0 * adx, temp16a);
      temp16blen = scale_expansion_zeroelim(axtbcttlen, axtbctt, adxtail, temp16b);
      temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32b);
      temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, temp32blen, temp32b, temp64);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, temp64, finother);
      finswap = finnow;
      finnow = finother;
      finother = finswap;
    }
    if (adytail != 0.0) {
      temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, adytail, temp16a);
      aytbctlen = scale_expansion_zeroelim(bctlen, bct, adytail, aytbct);
      temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, 2.0 * ady, temp32a);
      temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp32alen, temp32a, temp48);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother);
      finswap = finnow;
      finnow = finother;
      finother = finswap;

      temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, adytail, temp32a);
      aytbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adytail, aytbctt);
      temp16alen = scale_expansion_zeroelim(aytbcttlen, aytbctt, 2.0 * ady, temp16a);
      temp16blen = scale_expansion_zeroelim(aytbcttlen, aytbctt, adytail, temp16b);
      temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32b);
      temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, temp32blen, temp32b, temp64);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, temp64, finother);
      finswap = finnow;
      finnow = finother;
      finother = finswap;
    }
  }
  if ((bdxtail != 0.0) || (bdytail != 0.0)) {
    if ((cdxtail != 0.0) || (cdytail != 0.0) || (adxtail != 0.0) || (adytail != 0.0)) {
      Two_Product(cdxtail, ady, ti1, ti0);
      Two_Product(cdx, adytail, tj1, tj0);
      Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
      u[3] = u3;
      negate = -cdy;
      Two_Product(adxtail, negate, ti1, ti0);
      negate = -cdytail;
      Two_Product(adx, negate, tj1, tj0);
      Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
      v[3] = v3;
      catlen = fast_expansion_sum_zeroelim(4, u, 4, v, cat);

      Two_Product(cdxtail, adytail, ti1, ti0);
      Two_Product(adxtail, cdytail, tj1, tj0);
      Two_Two_Diff(ti1, ti0, tj1, tj0, catt3, catt[2], catt[1], catt[0]);
      catt[3] = catt3;
      cattlen = 4;
    }
    else {
      cat[0] = 0.0;
      catlen = 1;
      catt[0] = 0.0;
      cattlen = 1;
    }

    if (bdxtail != 0.0) {
      temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, bdxtail, temp16a);
      bxtcatlen = scale_expansion_zeroelim(catlen, cat, bdxtail, bxtcat);
      temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, 2.0 * bdx, temp32a);
      temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp32alen, temp32a, temp48);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother);
      finswap = finnow;
      finnow = finother;
      finother = finswap;
      if (cdytail != 0.0) {
        temp8len = scale_expansion_zeroelim(4, aa, bdxtail, temp8);
        temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail, temp16a);
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, temp16a, finother);
        finswap = finnow;
        finnow = finother;
        finother = finswap;
      }
      if (adytail != 0.0) {
        temp8len = scale_expansion_zeroelim(4, cc, -bdxtail, temp8);
        temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail, temp16a);
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, temp16a, finother);
        finswap = finnow;
        finnow = finother;
        finother = finswap;
      }

      temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, bdxtail, temp32a);
      bxtcattlen = scale_expansion_zeroelim(cattlen, catt, bdxtail, bxtcatt);
      temp16alen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, 2.0 * bdx, temp16a);
      temp16blen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, bdxtail, temp16b);
      temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32b);
      temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, temp32blen, temp32b, temp64);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, temp64, finother);
      finswap = finnow;
      finnow = finother;
      finother = finswap;
    }
    if (bdytail != 0.0) {
      temp16alen = scale_expansion_zeroelim(bytcalen, bytca, bdytail, temp16a);
      bytcatlen = scale_expansion_zeroelim(catlen, cat, bdytail, bytcat);
      temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, 2.0 * bdy, temp32a);
      temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp32alen, temp32a, temp48);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother);
      finswap = finnow;
      finnow = finother;
      finother = finswap;

      temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, bdytail, temp32a);
      bytcattlen = scale_expansion_zeroelim(cattlen, catt, bdytail, bytcatt);
      temp16alen = scale_expansion_zeroelim(bytcattlen, bytcatt, 2.0 * bdy, temp16a);
      temp16blen = scale_expansion_zeroelim(bytcattlen, bytcatt, bdytail, temp16b);
      temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32b);
      temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, temp32blen, temp32b, temp64);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, temp64, finother);
      finswap = finnow;
      finnow = finother;
      finother = finswap;
    }
  }
  if ((cdxtail != 0.0) || (cdytail != 0.0)) {
    if ((adxtail != 0.0) || (adytail != 0.0) || (bdxtail != 0.0) || (bdytail != 0.0)) {
      Two_Product(adxtail, bdy, ti1, ti0);
      Two_Product(adx, bdytail, tj1, tj0);
      Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
      u[3] = u3;
      negate = -ady;
      Two_Product(bdxtail, negate, ti1, ti0);
      negate = -adytail;
      Two_Product(bdx, negate, tj1, tj0);
      Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
      v[3] = v3;
      abtlen = fast_expansion_sum_zeroelim(4, u, 4, v, abt);

      Two_Product(adxtail, bdytail, ti1, ti0);
      Two_Product(bdxtail, adytail, tj1, tj0);
      Two_Two_Diff(ti1, ti0, tj1, tj0, abtt3, abtt[2], abtt[1], abtt[0]);
      abtt[3] = abtt3;
      abttlen = 4;
    }
    else {
      abt[0] = 0.0;
      abtlen = 1;
      abtt[0] = 0.0;
      abttlen = 1;
    }

    if (cdxtail != 0.0) {
      temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, cdxtail, temp16a);
      cxtabtlen = scale_expansion_zeroelim(abtlen, abt, cdxtail, cxtabt);
      temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, 2.0 * cdx, temp32a);
      temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp32alen, temp32a, temp48);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother);
      finswap = finnow;
      finnow = finother;
      finother = finswap;
      if (adytail != 0.0) {
        temp8len = scale_expansion_zeroelim(4, bb, cdxtail, temp8);
        temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail, temp16a);
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, temp16a, finother);
        finswap = finnow;
        finnow = finother;
        finother = finswap;
      }
      if (bdytail != 0.0) {
        temp8len = scale_expansion_zeroelim(4, aa, -cdxtail, temp8);
        temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail, temp16a);
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, temp16a, finother);
        finswap = finnow;
        finnow = finother;
        finother = finswap;
      }

      temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, cdxtail, temp32a);
      cxtabttlen = scale_expansion_zeroelim(abttlen, abtt, cdxtail, cxtabtt);
      temp16alen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, 2.0 * cdx, temp16a);
      temp16blen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, cdxtail, temp16b);
      temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32b);
      temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, temp32blen, temp32b, temp64);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, temp64, finother);
      finswap = finnow;
      finnow = finother;
      finother = finswap;
    }
    if (cdytail != 0.0) {
      temp16alen = scale_expansion_zeroelim(cytablen, cytab, cdytail, temp16a);
      cytabtlen = scale_expansion_zeroelim(abtlen, abt, cdytail, cytabt);
      temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, 2.0 * cdy, temp32a);
      temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp32alen, temp32a, temp48);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother);
      finswap = finnow;
      finnow = finother;
      finother = finswap;

      temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, cdytail, temp32a);
      cytabttlen = scale_expansion_zeroelim(abttlen, abtt, cdytail, cytabtt);
      temp16alen = scale_expansion_zeroelim(cytabttlen, cytabtt, 2.0 * cdy, temp16a);
      temp16blen = scale_expansion_zeroelim(cytabttlen, cytabtt, cdytail, temp16b);
      temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32b);
      temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, temp32blen, temp32b, temp64);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, temp64, finother);
      finswap = finnow;
      finnow = finother;
      finother = finswap;
    }
  }

  return finnow[finlength - 1];
}

double incircle(const double *pa, const double *pb, const double *pc, const double *pd)
{
  double adx, bdx, cdx, ady, bdy, cdy;
  double bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady;
  double alift, blift, clift;
  double det;
  double permanent, errbound;

  adx = pa[0] - pd[0];
  bdx = pb[0] - pd[0];
  cdx = pc[0] - pd[0];
  ady = pa[1] - pd[1];
  bdy = pb[1] - pd[1];
  cdy = pc[1] - pd[1];

  bdxcdy = bdx * cdy;
  cdxbdy = cdx * bdy;
  alift = adx * adx + ady * ady;

  cdxady = cdx * ady;
  adxcdy = adx * cdy;
  blift = bdx * bdx + bdy * bdy;

  adxbdy = adx * bdy;
  bdxady = bdx * ady;
  clift = cdx * cdx + cdy * cdy;

  det = alift * (bdxcdy - cdxbdy) + blift * (cdxady - adxcdy) + clift * (adxbdy - bdxady);

  permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * alift +
              (Absolute(cdxady) + Absolute(adxcdy)) * blift +
              (Absolute(adxbdy) + Absolute(bdxady)) * clift;
  errbound = iccerrboundA * permanent;
  if ((det > errbound) || (-det > errbound)) {
    return det;
  }

  return incircleadapt(pa, pb, pc, pd, permanent);
}

/**
 *  inspherefast()   Approximate 3D insphere test.  Non-robust.
 *  insphere()   Adaptive exact 3D insphere test.  Robust.
 *
 *               Return a positive value if the point pe lies inside the
 *               sphere passing through pa, pb, pc, and pd; a negative value
 *               if it lies outside; and zero if the five points are
 *               co-spherical.  The points pa, pb, pc, and pd must be ordered
 *               so that they have a positive orientation (as defined by
 *               orient3d()), or the sign of the result will be reversed.
 *
 *  The second uses exact arithmetic to ensure a correct answer.  The
 *  result returned is the determinant of a matrix.  In insphere() only,
 *  this determinant is computed adaptively, in the sense that exact
 *  arithmetic is used only to the degree it is needed to ensure that the
 *  returned value has the correct sign.  Hence, insphere() is usually quite
 *  fast, but will run more slowly when the input points are co-spherical or
 *  nearly so.
 */

double inspherefast(
    const double *pa, const double *pb, const double *pc, const double *pd, const double *pe)
{
  double aex, bex, cex, dex;
  double aey, bey, cey, dey;
  double aez, bez, cez, dez;
  double alift, blift, clift, dlift;
  double ab, bc, cd, da, ac, bd;
  double abc, bcd, cda, dab;

  aex = pa[0] - pe[0];
  bex = pb[0] - pe[0];
  cex = pc[0] - pe[0];
  dex = pd[0] - pe[0];
  aey = pa[1] - pe[1];
  bey = pb[1] - pe[1];
  cey = pc[1] - pe[1];
  dey = pd[1] - pe[1];
  aez = pa[2] - pe[2];
  bez = pb[2] - pe[2];
  cez = pc[2] - pe[2];
  dez = pd[2] - pe[2];

  ab = aex * bey - bex * aey;
  bc = bex * cey - cex * bey;
  cd = cex * dey - dex * cey;
  da = dex * aey - aex * dey;

  ac = aex * cey - cex * aey;
  bd = bex * dey - dex * bey;

  abc = aez * bc - bez * ac + cez * ab;
  bcd = bez * cd - cez * bd + dez * bc;
  cda = cez * da + dez * ac + aez * cd;
  dab = dez * ab + aez * bd + bez * da;

  alift = aex * aex + aey * aey + aez * aez;
  blift = bex * bex + bey * bey + bez * bez;
  clift = cex * cex + cey * cey + cez * cez;
  dlift = dex * dex + dey * dey + dez * dez;

  return (dlift * abc - clift * dab) + (blift * cda - alift * bcd);
}

static double insphereexact(
    const double *pa, const double *pb, const double *pc, const double *pd, const double *pe)
{
  INEXACT double axby1, bxcy1, cxdy1, dxey1, exay1;
  INEXACT double bxay1, cxby1, dxcy1, exdy1, axey1;
  INEXACT double axcy1, bxdy1, cxey1, dxay1, exby1;
  INEXACT double cxay1, dxby1, excy1, axdy1, bxey1;
  double axby0, bxcy0, cxdy0, dxey0, exay0;
  double bxay0, cxby0, dxcy0, exdy0, axey0;
  double axcy0, bxdy0, cxey0, dxay0, exby0;
  double cxay0, dxby0, excy0, axdy0, bxey0;
  double ab[4], bc[4], cd[4], de[4], ea[4];
  double ac[4], bd[4], ce[4], da[4], eb[4];
  double temp8a[8], temp8b[8], temp16[16];
  int temp8alen, temp8blen, temp16len;
  double abc[24], bcd[24], cde[24], dea[24], eab[24];
  double abd[24], bce[24], cda[24], deb[24], eac[24];
  int abclen, bcdlen, cdelen, dealen, eablen;
  int abdlen, bcelen, cdalen, deblen, eaclen;
  double temp48a[48], temp48b[48];
  int temp48alen, temp48blen;
  double abcd[96], bcde[96], cdea[96], deab[96], eabc[96];
  int abcdlen, bcdelen, cdealen, deablen, eabclen;
  double temp192[192];
  double det384x[384], det384y[384], det384z[384];
  int xlen, ylen, zlen;
  double detxy[768];
  int xylen;
  double adet[1152], bdet[1152], cdet[1152], ddet[1152], edet[1152];
  int alen, blen, clen, dlen, elen;
  double abdet[2304], cddet[2304], cdedet[3456];
  int ablen, cdlen;
  double deter[5760];
  int deterlen;
  int i;

  INEXACT double bvirt;
  double avirt, bround, around;
  INEXACT double c;
  INEXACT double abig;
  double ahi, alo, bhi, blo;
  double err1, err2, err3;
  INEXACT double _i, _j;
  double _0;

  Two_Product(pa[0], pb[1], axby1, axby0);
  Two_Product(pb[0], pa[1], bxay1, bxay0);
  Two_Two_Diff(axby1, axby0, bxay1, bxay0, ab[3], ab[2], ab[1], ab[0]);

  Two_Product(pb[0], pc[1], bxcy1, bxcy0);
  Two_Product(pc[0], pb[1], cxby1, cxby0);
  Two_Two_Diff(bxcy1, bxcy0, cxby1, cxby0, bc[3], bc[2], bc[1], bc[0]);

  Two_Product(pc[0], pd[1], cxdy1, cxdy0);
  Two_Product(pd[0], pc[1], dxcy1, dxcy0);
  Two_Two_Diff(cxdy1, cxdy0, dxcy1, dxcy0, cd[3], cd[2], cd[1], cd[0]);

  Two_Product(pd[0], pe[1], dxey1, dxey0);
  Two_Product(pe[0], pd[1], exdy1, exdy0);
  Two_Two_Diff(dxey1, dxey0, exdy1, exdy0, de[3], de[2], de[1], de[0]);

  Two_Product(pe[0], pa[1], exay1, exay0);
  Two_Product(pa[0], pe[1], axey1, axey0);
  Two_Two_Diff(exay1, exay0, axey1, axey0, ea[3], ea[2], ea[1], ea[0]);

  Two_Product(pa[0], pc[1], axcy1, axcy0);
  Two_Product(pc[0], pa[1], cxay1, cxay0);
  Two_Two_Diff(axcy1, axcy0, cxay1, cxay0, ac[3], ac[2], ac[1], ac[0]);

  Two_Product(pb[0], pd[1], bxdy1, bxdy0);
  Two_Product(pd[0], pb[1], dxby1, dxby0);
  Two_Two_Diff(bxdy1, bxdy0, dxby1, dxby0, bd[3], bd[2], bd[1], bd[0]);

  Two_Product(pc[0], pe[1], cxey1, cxey0);
  Two_Product(pe[0], pc[1], excy1, excy0);
  Two_Two_Diff(cxey1, cxey0, excy1, excy0, ce[3], ce[2], ce[1], ce[0]);

  Two_Product(pd[0], pa[1], dxay1, dxay0);
  Two_Product(pa[0], pd[1], axdy1, axdy0);
  Two_Two_Diff(dxay1, dxay0, axdy1, axdy0, da[3], da[2], da[1], da[0]);

  Two_Product(pe[0], pb[1], exby1, exby0);
  Two_Product(pb[0], pe[1], bxey1, bxey0);
  Two_Two_Diff(exby1, exby0, bxey1, bxey0, eb[3], eb[2], eb[1], eb[0]);

  temp8alen = scale_expansion_zeroelim(4, bc, pa[2], temp8a);
  temp8blen = scale_expansion_zeroelim(4, ac, -pb[2], temp8b);
  temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp8blen, temp8b, temp16);
  temp8alen = scale_expansion_zeroelim(4, ab, pc[2], temp8a);
  abclen = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp16len, temp16, abc);

  temp8alen = scale_expansion_zeroelim(4, cd, pb[2], temp8a);
  temp8blen = scale_expansion_zeroelim(4, bd, -pc[2], temp8b);
  temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp8blen, temp8b, temp16);
  temp8alen = scale_expansion_zeroelim(4, bc, pd[2], temp8a);
  bcdlen = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp16len, temp16, bcd);

  temp8alen = scale_expansion_zeroelim(4, de, pc[2], temp8a);
  temp8blen = scale_expansion_zeroelim(4, ce, -pd[2], temp8b);
  temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp8blen, temp8b, temp16);
  temp8alen = scale_expansion_zeroelim(4, cd, pe[2], temp8a);
  cdelen = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp16len, temp16, cde);

  temp8alen = scale_expansion_zeroelim(4, ea, pd[2], temp8a);
  temp8blen = scale_expansion_zeroelim(4, da, -pe[2], temp8b);
  temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp8blen, temp8b, temp16);
  temp8alen = scale_expansion_zeroelim(4, de, pa[2], temp8a);
  dealen = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp16len, temp16, dea);

  temp8alen = scale_expansion_zeroelim(4, ab, pe[2], temp8a);
  temp8blen = scale_expansion_zeroelim(4, eb, -pa[2], temp8b);
  temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp8blen, temp8b, temp16);
  temp8alen = scale_expansion_zeroelim(4, ea, pb[2], temp8a);
  eablen = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp16len, temp16, eab);

  temp8alen = scale_expansion_zeroelim(4, bd, pa[2], temp8a);
  temp8blen = scale_expansion_zeroelim(4, da, pb[2], temp8b);
  temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp8blen, temp8b, temp16);
  temp8alen = scale_expansion_zeroelim(4, ab, pd[2], temp8a);
  abdlen = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp16len, temp16, abd);

  temp8alen = scale_expansion_zeroelim(4, ce, pb[2], temp8a);
  temp8blen = scale_expansion_zeroelim(4, eb, pc[2], temp8b);
  temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp8blen, temp8b, temp16);
  temp8alen = scale_expansion_zeroelim(4, bc, pe[2], temp8a);
  bcelen = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp16len, temp16, bce);

  temp8alen = scale_expansion_zeroelim(4, da, pc[2], temp8a);
  temp8blen = scale_expansion_zeroelim(4, ac, pd[2], temp8b);
  temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp8blen, temp8b, temp16);
  temp8alen = scale_expansion_zeroelim(4, cd, pa[2], temp8a);
  cdalen = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp16len, temp16, cda);

  temp8alen = scale_expansion_zeroelim(4, eb, pd[2], temp8a);
  temp8blen = scale_expansion_zeroelim(4, bd, pe[2], temp8b);
  temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp8blen, temp8b, temp16);
  temp8alen = scale_expansion_zeroelim(4, de, pb[2], temp8a);
  deblen = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp16len, temp16, deb);

  temp8alen = scale_expansion_zeroelim(4, ac, pe[2], temp8a);
  temp8blen = scale_expansion_zeroelim(4, ce, pa[2], temp8b);
  temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp8blen, temp8b, temp16);
  temp8alen = scale_expansion_zeroelim(4, ea, pc[2], temp8a);
  eaclen = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp16len, temp16, eac);

  temp48alen = fast_expansion_sum_zeroelim(cdelen, cde, bcelen, bce, temp48a);
  temp48blen = fast_expansion_sum_zeroelim(deblen, deb, bcdlen, bcd, temp48b);
  for (i = 0; i < temp48blen; i++) {
    temp48b[i] = -temp48b[i];
  }
  bcdelen = fast_expansion_sum_zeroelim(temp48alen, temp48a, temp48blen, temp48b, bcde);
  xlen = scale_expansion_zeroelim(bcdelen, bcde, pa[0], temp192);
  xlen = scale_expansion_zeroelim(xlen, temp192, pa[0], det384x);
  ylen = scale_expansion_zeroelim(bcdelen, bcde, pa[1], temp192);
  ylen = scale_expansion_zeroelim(ylen, temp192, pa[1], det384y);
  zlen = scale_expansion_zeroelim(bcdelen, bcde, pa[2], temp192);
  zlen = scale_expansion_zeroelim(zlen, temp192, pa[2], det384z);
  xylen = fast_expansion_sum_zeroelim(xlen, det384x, ylen, det384y, detxy);
  alen = fast_expansion_sum_zeroelim(xylen, detxy, zlen, det384z, adet);

  temp48alen = fast_expansion_sum_zeroelim(dealen, dea, cdalen, cda, temp48a);
  temp48blen = fast_expansion_sum_zeroelim(eaclen, eac, cdelen, cde, temp48b);
  for (i = 0; i < temp48blen; i++) {
    temp48b[i] = -temp48b[i];
  }
  cdealen = fast_expansion_sum_zeroelim(temp48alen, temp48a, temp48blen, temp48b, cdea);
  xlen = scale_expansion_zeroelim(cdealen, cdea, pb[0], temp192);
  xlen = scale_expansion_zeroelim(xlen, temp192, pb[0], det384x);
  ylen = scale_expansion_zeroelim(cdealen, cdea, pb[1], temp192);
  ylen = scale_expansion_zeroelim(ylen, temp192, pb[1], det384y);
  zlen = scale_expansion_zeroelim(cdealen, cdea, pb[2], temp192);
  zlen = scale_expansion_zeroelim(zlen, temp192, pb[2], det384z);
  xylen = fast_expansion_sum_zeroelim(xlen, det384x, ylen, det384y, detxy);
  blen = fast_expansion_sum_zeroelim(xylen, detxy, zlen, det384z, bdet);

  temp48alen = fast_expansion_sum_zeroelim(eablen, eab, deblen, deb, temp48a);
  temp48blen = fast_expansion_sum_zeroelim(abdlen, abd, dealen, dea, temp48b);
  for (i = 0; i < temp48blen; i++) {
    temp48b[i] = -temp48b[i];
  }
  deablen = fast_expansion_sum_zeroelim(temp48alen, temp48a, temp48blen, temp48b, deab);
  xlen = scale_expansion_zeroelim(deablen, deab, pc[0], temp192);
  xlen = scale_expansion_zeroelim(xlen, temp192, pc[0], det384x);
  ylen = scale_expansion_zeroelim(deablen, deab, pc[1], temp192);
  ylen = scale_expansion_zeroelim(ylen, temp192, pc[1], det384y);
  zlen = scale_expansion_zeroelim(deablen, deab, pc[2], temp192);
  zlen = scale_expansion_zeroelim(zlen, temp192, pc[2], det384z);
  xylen = fast_expansion_sum_zeroelim(xlen, det384x, ylen, det384y, detxy);
  clen = fast_expansion_sum_zeroelim(xylen, detxy, zlen, det384z, cdet);

  temp48alen = fast_expansion_sum_zeroelim(abclen, abc, eaclen, eac, temp48a);
  temp48blen = fast_expansion_sum_zeroelim(bcelen, bce, eablen, eab, temp48b);
  for (i = 0; i < temp48blen; i++) {
    temp48b[i] = -temp48b[i];
  }
  eabclen = fast_expansion_sum_zeroelim(temp48alen, temp48a, temp48blen, temp48b, eabc);
  xlen = scale_expansion_zeroelim(eabclen, eabc, pd[0], temp192);
  xlen = scale_expansion_zeroelim(xlen, temp192, pd[0], det384x);
  ylen = scale_expansion_zeroelim(eabclen, eabc, pd[1], temp192);
  ylen = scale_expansion_zeroelim(ylen, temp192, pd[1], det384y);
  zlen = scale_expansion_zeroelim(eabclen, eabc, pd[2], temp192);
  zlen = scale_expansion_zeroelim(zlen, temp192, pd[2], det384z);
  xylen = fast_expansion_sum_zeroelim(xlen, det384x, ylen, det384y, detxy);
  dlen = fast_expansion_sum_zeroelim(xylen, detxy, zlen, det384z, ddet);

  temp48alen = fast_expansion_sum_zeroelim(bcdlen, bcd, abdlen, abd, temp48a);
  temp48blen = fast_expansion_sum_zeroelim(cdalen, cda, abclen, abc, temp48b);
  for (i = 0; i < temp48blen; i++) {
    temp48b[i] = -temp48b[i];
  }
  abcdlen = fast_expansion_sum_zeroelim(temp48alen, temp48a, temp48blen, temp48b, abcd);
  xlen = scale_expansion_zeroelim(abcdlen, abcd, pe[0], temp192);
  xlen = scale_expansion_zeroelim(xlen, temp192, pe[0], det384x);
  ylen = scale_expansion_zeroelim(abcdlen, abcd, pe[1], temp192);
  ylen = scale_expansion_zeroelim(ylen, temp192, pe[1], det384y);
  zlen = scale_expansion_zeroelim(abcdlen, abcd, pe[2], temp192);
  zlen = scale_expansion_zeroelim(zlen, temp192, pe[2], det384z);
  xylen = fast_expansion_sum_zeroelim(xlen, det384x, ylen, det384y, detxy);
  elen = fast_expansion_sum_zeroelim(xylen, detxy, zlen, det384z, edet);

  ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
  cdlen = fast_expansion_sum_zeroelim(clen, cdet, dlen, ddet, cddet);
  cdelen = fast_expansion_sum_zeroelim(cdlen, cddet, elen, edet, cdedet);
  deterlen = fast_expansion_sum_zeroelim(ablen, abdet, cdelen, cdedet, deter);

  return deter[deterlen - 1];
}

static double insphereadapt(const double *pa,
                            const double *pb,
                            const double *pc,
                            const double *pd,
                            const double *pe,
                            double permanent)
{
  INEXACT double aex, bex, cex, dex, aey, bey, cey, dey, aez, bez, cez, dez;
  double det, errbound;

  INEXACT double aexbey1, bexaey1, bexcey1, cexbey1;
  INEXACT double cexdey1, dexcey1, dexaey1, aexdey1;
  INEXACT double aexcey1, cexaey1, bexdey1, dexbey1;
  double aexbey0, bexaey0, bexcey0, cexbey0;
  double cexdey0, dexcey0, dexaey0, aexdey0;
  double aexcey0, cexaey0, bexdey0, dexbey0;
  double ab[4], bc[4], cd[4], da[4], ac[4], bd[4];
  INEXACT double ab3, bc3, cd3, da3, ac3, bd3;
  double abeps, bceps, cdeps, daeps, aceps, bdeps;
  double temp8a[8], temp8b[8], temp8c[8], temp16[16], temp24[24], temp48[48];
  int temp8alen, temp8blen, temp8clen, temp16len, temp24len, temp48len;
  double xdet[96], ydet[96], zdet[96], xydet[192];
  int xlen, ylen, zlen, xylen;
  double adet[288], bdet[288], cdet[288], ddet[288];
  int alen, blen, clen, dlen;
  double abdet[576], cddet[576];
  int ablen, cdlen;
  double fin1[1152];
  int finlength;

  double aextail, bextail, cextail, dextail;
  double aeytail, beytail, ceytail, deytail;
  double aeztail, beztail, ceztail, deztail;

  INEXACT double bvirt;
  double avirt, bround, around;
  INEXACT double c;
  INEXACT double abig;
  double ahi, alo, bhi, blo;
  double err1, err2, err3;
  INEXACT double _i, _j;
  double _0;

  aex = (double)(pa[0] - pe[0]);
  bex = (double)(pb[0] - pe[0]);
  cex = (double)(pc[0] - pe[0]);
  dex = (double)(pd[0] - pe[0]);
  aey = (double)(pa[1] - pe[1]);
  bey = (double)(pb[1] - pe[1]);
  cey = (double)(pc[1] - pe[1]);
  dey = (double)(pd[1] - pe[1]);
  aez = (double)(pa[2] - pe[2]);
  bez = (double)(pb[2] - pe[2]);
  cez = (double)(pc[2] - pe[2]);
  dez = (double)(pd[2] - pe[2]);

  Two_Product(aex, bey, aexbey1, aexbey0);
  Two_Product(bex, aey, bexaey1, bexaey0);
  Two_Two_Diff(aexbey1, aexbey0, bexaey1, bexaey0, ab3, ab[2], ab[1], ab[0]);
  ab[3] = ab3;

  Two_Product(bex, cey, bexcey1, bexcey0);
  Two_Product(cex, bey, cexbey1, cexbey0);
  Two_Two_Diff(bexcey1, bexcey0, cexbey1, cexbey0, bc3, bc[2], bc[1], bc[0]);
  bc[3] = bc3;

  Two_Product(cex, dey, cexdey1, cexdey0);
  Two_Product(dex, cey, dexcey1, dexcey0);
  Two_Two_Diff(cexdey1, cexdey0, dexcey1, dexcey0, cd3, cd[2], cd[1], cd[0]);
  cd[3] = cd3;

  Two_Product(dex, aey, dexaey1, dexaey0);
  Two_Product(aex, dey, aexdey1, aexdey0);
  Two_Two_Diff(dexaey1, dexaey0, aexdey1, aexdey0, da3, da[2], da[1], da[0]);
  da[3] = da3;

  Two_Product(aex, cey, aexcey1, aexcey0);
  Two_Product(cex, aey, cexaey1, cexaey0);
  Two_Two_Diff(aexcey1, aexcey0, cexaey1, cexaey0, ac3, ac[2], ac[1], ac[0]);
  ac[3] = ac3;

  Two_Product(bex, dey, bexdey1, bexdey0);
  Two_Product(dex, bey, dexbey1, dexbey0);
  Two_Two_Diff(bexdey1, bexdey0, dexbey1, dexbey0, bd3, bd[2], bd[1], bd[0]);
  bd[3] = bd3;

  temp8alen = scale_expansion_zeroelim(4, cd, bez, temp8a);
  temp8blen = scale_expansion_zeroelim(4, bd, -cez, temp8b);
  temp8clen = scale_expansion_zeroelim(4, bc, dez, temp8c);
  temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp8blen, temp8b, temp16);
  temp24len = fast_expansion_sum_zeroelim(temp8clen, temp8c, temp16len, temp16, temp24);
  temp48len = scale_expansion_zeroelim(temp24len, temp24, aex, temp48);
  xlen = scale_expansion_zeroelim(temp48len, temp48, -aex, xdet);
  temp48len = scale_expansion_zeroelim(temp24len, temp24, aey, temp48);
  ylen = scale_expansion_zeroelim(temp48len, temp48, -aey, ydet);
  temp48len = scale_expansion_zeroelim(temp24len, temp24, aez, temp48);
  zlen = scale_expansion_zeroelim(temp48len, temp48, -aez, zdet);
  xylen = fast_expansion_sum_zeroelim(xlen, xdet, ylen, ydet, xydet);
  alen = fast_expansion_sum_zeroelim(xylen, xydet, zlen, zdet, adet);

  temp8alen = scale_expansion_zeroelim(4, da, cez, temp8a);
  temp8blen = scale_expansion_zeroelim(4, ac, dez, temp8b);
  temp8clen = scale_expansion_zeroelim(4, cd, aez, temp8c);
  temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp8blen, temp8b, temp16);
  temp24len = fast_expansion_sum_zeroelim(temp8clen, temp8c, temp16len, temp16, temp24);
  temp48len = scale_expansion_zeroelim(temp24len, temp24, bex, temp48);
  xlen = scale_expansion_zeroelim(temp48len, temp48, bex, xdet);
  temp48len = scale_expansion_zeroelim(temp24len, temp24, bey, temp48);
  ylen = scale_expansion_zeroelim(temp48len, temp48, bey, ydet);
  temp48len = scale_expansion_zeroelim(temp24len, temp24, bez, temp48);
  zlen = scale_expansion_zeroelim(temp48len, temp48, bez, zdet);
  xylen = fast_expansion_sum_zeroelim(xlen, xdet, ylen, ydet, xydet);
  blen = fast_expansion_sum_zeroelim(xylen, xydet, zlen, zdet, bdet);

  temp8alen = scale_expansion_zeroelim(4, ab, dez, temp8a);
  temp8blen = scale_expansion_zeroelim(4, bd, aez, temp8b);
  temp8clen = scale_expansion_zeroelim(4, da, bez, temp8c);
  temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp8blen, temp8b, temp16);
  temp24len = fast_expansion_sum_zeroelim(temp8clen, temp8c, temp16len, temp16, temp24);
  temp48len = scale_expansion_zeroelim(temp24len, temp24, cex, temp48);
  xlen = scale_expansion_zeroelim(temp48len, temp48, -cex, xdet);
  temp48len = scale_expansion_zeroelim(temp24len, temp24, cey, temp48);
  ylen = scale_expansion_zeroelim(temp48len, temp48, -cey, ydet);
  temp48len = scale_expansion_zeroelim(temp24len, temp24, cez, temp48);
  zlen = scale_expansion_zeroelim(temp48len, temp48, -cez, zdet);
  xylen = fast_expansion_sum_zeroelim(xlen, xdet, ylen, ydet, xydet);
  clen = fast_expansion_sum_zeroelim(xylen, xydet, zlen, zdet, cdet);

  temp8alen = scale_expansion_zeroelim(4, bc, aez, temp8a);
  temp8blen = scale_expansion_zeroelim(4, ac, -bez, temp8b);
  temp8clen = scale_expansion_zeroelim(4, ab, cez, temp8c);
  temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp8blen, temp8b, temp16);
  temp24len = fast_expansion_sum_zeroelim(temp8clen, temp8c, temp16len, temp16, temp24);
  temp48len = scale_expansion_zeroelim(temp24len, temp24, dex, temp48);
  xlen = scale_expansion_zeroelim(temp48len, temp48, dex, xdet);
  temp48len = scale_expansion_zeroelim(temp24len, temp24, dey, temp48);
  ylen = scale_expansion_zeroelim(temp48len, temp48, dey, ydet);
  temp48len = scale_expansion_zeroelim(temp24len, temp24, dez, temp48);
  zlen = scale_expansion_zeroelim(temp48len, temp48, dez, zdet);
  xylen = fast_expansion_sum_zeroelim(xlen, xdet, ylen, ydet, xydet);
  dlen = fast_expansion_sum_zeroelim(xylen, xydet, zlen, zdet, ddet);

  ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
  cdlen = fast_expansion_sum_zeroelim(clen, cdet, dlen, ddet, cddet);
  finlength = fast_expansion_sum_zeroelim(ablen, abdet, cdlen, cddet, fin1);

  det = estimate(finlength, fin1);
  errbound = isperrboundB * permanent;
  if ((det >= errbound) || (-det >= errbound)) {
    return det;
  }

  Two_Diff_Tail(pa[0], pe[0], aex, aextail);
  Two_Diff_Tail(pa[1], pe[1], aey, aeytail);
  Two_Diff_Tail(pa[2], pe[2], aez, aeztail);
  Two_Diff_Tail(pb[0], pe[0], bex, bextail);
  Two_Diff_Tail(pb[1], pe[1], bey, beytail);
  Two_Diff_Tail(pb[2], pe[2], bez, beztail);
  Two_Diff_Tail(pc[0], pe[0], cex, cextail);
  Two_Diff_Tail(pc[1], pe[1], cey, ceytail);
  Two_Diff_Tail(pc[2], pe[2], cez, ceztail);
  Two_Diff_Tail(pd[0], pe[0], dex, dextail);
  Two_Diff_Tail(pd[1], pe[1], dey, deytail);
  Two_Diff_Tail(pd[2], pe[2], dez, deztail);
  if ((aextail == 0.0) && (aeytail == 0.0) && (aeztail == 0.0) && (bextail == 0.0) &&
      (beytail == 0.0) && (beztail == 0.0) && (cextail == 0.0) && (ceytail == 0.0) &&
      (ceztail == 0.0) && (dextail == 0.0) && (deytail == 0.0) && (deztail == 0.0)) {
    return det;
  }

  errbound = isperrboundC * permanent + resulterrbound * Absolute(det);
  abeps = (aex * beytail + bey * aextail) - (aey * bextail + bex * aeytail);
  bceps = (bex * ceytail + cey * bextail) - (bey * cextail + cex * beytail);
  cdeps = (cex * deytail + dey * cextail) - (cey * dextail + dex * ceytail);
  daeps = (dex * aeytail + aey * dextail) - (dey * aextail + aex * deytail);
  aceps = (aex * ceytail + cey * aextail) - (aey * cextail + cex * aeytail);
  bdeps = (bex * deytail + dey * bextail) - (bey * dextail + dex * beytail);
  det +=
      (((bex * bex + bey * bey + bez * bez) * ((cez * daeps + dez * aceps + aez * cdeps) +
                                               (ceztail * da3 + deztail * ac3 + aeztail * cd3)) +
        (dex * dex + dey * dey + dez * dez) * ((aez * bceps - bez * aceps + cez * abeps) +
                                               (aeztail * bc3 - beztail * ac3 + ceztail * ab3))) -
       ((aex * aex + aey * aey + aez * aez) * ((bez * cdeps - cez * bdeps + dez * bceps) +
                                               (beztail * cd3 - ceztail * bd3 + deztail * bc3)) +
        (cex * cex + cey * cey + cez * cez) * ((dez * abeps + aez * bdeps + bez * daeps) +
                                               (deztail * ab3 + aeztail * bd3 + beztail * da3)))) +
      2.0 *
          (((bex * bextail + bey * beytail + bez * beztail) * (cez * da3 + dez * ac3 + aez * cd3) +
            (dex * dextail + dey * deytail + dez * deztail) *
                (aez * bc3 - bez * ac3 + cez * ab3)) -
           ((aex * aextail + aey * aeytail + aez * aeztail) * (bez * cd3 - cez * bd3 + dez * bc3) +
            (cex * cextail + cey * ceytail + cez * ceztail) *
                (dez * ab3 + aez * bd3 + bez * da3)));
  if ((det >= errbound) || (-det >= errbound)) {
    return det;
  }

  return insphereexact(pa, pb, pc, pd, pe);
}

double insphere(
    const double *pa, const double *pb, const double *pc, const double *pd, const double *pe)
{
  double aex, bex, cex, dex;
  double aey, bey, cey, dey;
  double aez, bez, cez, dez;
  double aexbey, bexaey, bexcey, cexbey, cexdey, dexcey, dexaey, aexdey;
  double aexcey, cexaey, bexdey, dexbey;
  double alift, blift, clift, dlift;
  double ab, bc, cd, da, ac, bd;
  double abc, bcd, cda, dab;
  double aezplus, bezplus, cezplus, dezplus;
  double aexbeyplus, bexaeyplus, bexceyplus, cexbeyplus;
  double cexdeyplus, dexceyplus, dexaeyplus, aexdeyplus;
  double aexceyplus, cexaeyplus, bexdeyplus, dexbeyplus;
  double det;
  double permanent, errbound;

  aex = pa[0] - pe[0];
  bex = pb[0] - pe[0];
  cex = pc[0] - pe[0];
  dex = pd[0] - pe[0];
  aey = pa[1] - pe[1];
  bey = pb[1] - pe[1];
  cey = pc[1] - pe[1];
  dey = pd[1] - pe[1];
  aez = pa[2] - pe[2];
  bez = pb[2] - pe[2];
  cez = pc[2] - pe[2];
  dez = pd[2] - pe[2];

  aexbey = aex * bey;
  bexaey = bex * aey;
  ab = aexbey - bexaey;
  bexcey = bex * cey;
  cexbey = cex * bey;
  bc = bexcey - cexbey;
  cexdey = cex * dey;
  dexcey = dex * cey;
  cd = cexdey - dexcey;
  dexaey = dex * aey;
  aexdey = aex * dey;
  da = dexaey - aexdey;

  aexcey = aex * cey;
  cexaey = cex * aey;
  ac = aexcey - cexaey;
  bexdey = bex * dey;
  dexbey = dex * bey;
  bd = bexdey - dexbey;

  abc = aez * bc - bez * ac + cez * ab;
  bcd = bez * cd - cez * bd + dez * bc;
  cda = cez * da + dez * ac + aez * cd;
  dab = dez * ab + aez * bd + bez * da;

  alift = aex * aex + aey * aey + aez * aez;
  blift = bex * bex + bey * bey + bez * bez;
  clift = cex * cex + cey * cey + cez * cez;
  dlift = dex * dex + dey * dey + dez * dez;

  det = (dlift * abc - clift * dab) + (blift * cda - alift * bcd);

  aezplus = Absolute(aez);
  bezplus = Absolute(bez);
  cezplus = Absolute(cez);
  dezplus = Absolute(dez);
  aexbeyplus = Absolute(aexbey);
  bexaeyplus = Absolute(bexaey);
  bexceyplus = Absolute(bexcey);
  cexbeyplus = Absolute(cexbey);
  cexdeyplus = Absolute(cexdey);
  dexceyplus = Absolute(dexcey);
  dexaeyplus = Absolute(dexaey);
  aexdeyplus = Absolute(aexdey);
  aexceyplus = Absolute(aexcey);
  cexaeyplus = Absolute(cexaey);
  bexdeyplus = Absolute(bexdey);
  dexbeyplus = Absolute(dexbey);
  permanent = ((cexdeyplus + dexceyplus) * bezplus + (dexbeyplus + bexdeyplus) * cezplus +
               (bexceyplus + cexbeyplus) * dezplus) *
                  alift +
              ((dexaeyplus + aexdeyplus) * cezplus + (aexceyplus + cexaeyplus) * dezplus +
               (cexdeyplus + dexceyplus) * aezplus) *
                  blift +
              ((aexbeyplus + bexaeyplus) * dezplus + (bexdeyplus + dexbeyplus) * aezplus +
               (dexaeyplus + aexdeyplus) * bezplus) *
                  clift +
              ((bexceyplus + cexbeyplus) * aezplus + (cexaeyplus + aexceyplus) * bezplus +
               (aexbeyplus + bexaeyplus) * cezplus) *
                  dlift;
  errbound = isperrboundA * permanent;
  if ((det > errbound) || (-det > errbound)) {
    return det;
  }

  return insphereadapt(pa, pb, pc, pd, pe, permanent);
}

} /* namespace robust_pred */

static int sgn(double x)
{
  return (x > 0) ? 1 : ((x < 0) ? -1 : 0);
}

int orient2d(const double2 &a, const double2 &b, const double2 &c)
{
  return sgn(blender::robust_pred::orient2d(a, b, c));
}

int orient2d_fast(const double2 &a, const double2 &b, const double2 &c)
{
  return sgn(blender::robust_pred::orient2dfast(a, b, c));
}

int incircle(const double2 &a, const double2 &b, const double2 &c, const double2 &d)
{
  return sgn(robust_pred::incircle(a, b, c, d));
}

int incircle_fast(const double2 &a, const double2 &b, const double2 &c, const double2 &d)
{
  return sgn(robust_pred::incirclefast(a, b, c, d));
}

int orient3d(const double3 &a, const double3 &b, const double3 &c, const double3 &d)
{
  return sgn(robust_pred::orient3d(a, b, c, d));
}

int orient3d_fast(const double3 &a, const double3 &b, const double3 &c, const double3 &d)
{
  return sgn(robust_pred::orient3dfast(a, b, c, d));
}

int insphere(
    const double3 &a, const double3 &b, const double3 &c, const double3 &d, const double3 &e)
{
  return sgn(robust_pred::insphere(a, b, c, d, e));
}

int insphere_fast(
    const double3 &a, const double3 &b, const double3 &c, const double3 &d, const double3 &e)
{
  return sgn(robust_pred::inspherefast(a, b, c, d, e));
}

}  // namespace blender