--- /dev/null
+/*****************************************************************************/
+/* */
+/* 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. */
+/* */
+/* */
+/* Several geometric predicates are defined. Their parameters are all */
+/* points. Each point is an array of two or three floating-point */
+/* numbers. The geometric predicates, described in the papers, are */
+/* */
+/* orient2d(pa, pb, pc) */
+/* orient2dfast(pa, pb, pc) */
+/* orient3d(pa, pb, pc, pd) */
+/* orient3dfast(pa, pb, pc, pd) */
+/* incircle(pa, pb, pc, pd) */
+/* incirclefast(pa, pb, pc, pd) */
+/* insphere(pa, pb, pc, pd, pe) */
+/* inspherefast(pa, pb, pc, pd, pe) */
+/* */
+/* Those with suffix "fast" are approximate, non-robust versions. Those */
+/* without the suffix are adaptive precision, robust versions. There */
+/* are also versions with the suffices "exact" and "slow", which are */
+/* non-adaptive, exact arithmetic versions, which I use only for timings */
+/* in my arithmetic papers. */
+/* */
+/* */
+/* An expansion is represented by an array of floating-point numbers, */
+/* sorted from smallest to largest magnitude (possibly with interspersed */
+/* zeros). The length of each expansion is stored as a separate integer, */
+/* and each arithmetic function returns an integer which is the length */
+/* of the expansion it created. */
+/* */
+/* Several arithmetic functions are defined. Their parameters are */
+/* */
+/* e, f Input expansions */
+/* elen, flen Lengths of input expansions (must be >= 1) */
+/* h Output expansion */
+/* b Input scalar */
+/* */
+/* The arithmetic functions are */
+/* */
+/* grow_expansion(elen, e, b, h) */
+/* grow_expansion_zeroelim(elen, e, b, h) */
+/* expansion_sum(elen, e, flen, f, h) */
+/* expansion_sum_zeroelim1(elen, e, flen, f, h) */
+/* expansion_sum_zeroelim2(elen, e, flen, f, h) */
+/* fast_expansion_sum(elen, e, flen, f, h) */
+/* fast_expansion_sum_zeroelim(elen, e, flen, f, h) */
+/* linear_expansion_sum(elen, e, flen, f, h) */
+/* linear_expansion_sum_zeroelim(elen, e, flen, f, h) */
+/* scale_expansion(elen, e, b, h) */
+/* scale_expansion_zeroelim(elen, e, b, h) */
+/* compress(elen, e, h) */
+/* */
+/* All of these are described in the long version of the paper; some are */
+/* described in the short version. All return an integer that is the */
+/* length of h. Those with suffix _zeroelim perform zero elimination, */
+/* and are recommended over their counterparts. The procedure */
+/* fast_expansion_sum_zeroelim() (or linear_expansion_sum_zeroelim() on */
+/* processors that do not use the round-to-even tiebreaking rule) is */
+/* recommended over expansion_sum_zeroelim(). Each procedure has a */
+/* little note next to it (in the code below) that tells you whether or */
+/* not the output expansion may be the same array as one of the input */
+/* expansions. */
+/* */
+/* */
+/* If you look around below, you'll also find macros for a bunch of */
+/* simple unrolled arithmetic operations, and procedures for printing */
+/* expansions (commented out because they don't work with all C */
+/* compilers) and for generating random floating-point numbers whose */
+/* significand bits are all random. Most of the macros have undocumented */
+/* requirements that certain of their parameters should not be the same */
+/* variable; for safety, better to make sure all the parameters are */
+/* distinct variables. Feel free to send email to jrs@cs.cmu.edu if you */
+/* have questions. */
+/* */
+/*****************************************************************************/
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <sys/time.h>
+
+/* 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*/
+
+#define REAL double /* float or double */
+#define REALPRINT doubleprint
+#define REALRAND doublerand
+#define NARROWRAND narrowdoublerand
+#define UNIFORMRAND uniformdoublerand
+
+/* 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 */
+/* roundoff 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 roundoff 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 = (REAL) (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 = (REAL) (a - b); \
+ Fast_Two_Diff_Tail(a, b, x, y)
+
+#define Two_Sum_Tail(a, b, x, y) \
+ bvirt = (REAL) (x - a); \
+ avirt = x - bvirt; \
+ bround = b - bvirt; \
+ around = a - avirt; \
+ y = around + bround
+
+#define Two_Sum(a, b, x, y) \
+ x = (REAL) (a + b); \
+ Two_Sum_Tail(a, b, x, y)
+
+#define Two_Diff_Tail(a, b, x, y) \
+ bvirt = (REAL) (a - x); \
+ avirt = x + bvirt; \
+ bround = bvirt - b; \
+ around = a - avirt; \
+ y = around + bround
+
+#define Two_Diff(a, b, x, y) \
+ x = (REAL) (a - b); \
+ Two_Diff_Tail(a, b, x, y)
+
+#define Split(a, ahi, alo) \
+ c = (REAL) (splitter * a); \
+ abig = (REAL) (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 = (REAL) (a * b); \
+ Two_Product_Tail(a, b, x, y)
+
+/* Two_Product_Presplit() is Two_Product() where one of the inputs has */
+/* already been split. Avoids redundant splitting. */
+
+#define Two_Product_Presplit(a, b, bhi, blo, x, y) \
+ x = (REAL) (a * b); \
+ Split(a, ahi, alo); \
+ err1 = x - (ahi * bhi); \
+ err2 = err1 - (alo * bhi); \
+ err3 = err2 - (ahi * blo); \
+ y = (alo * blo) - err3
+
+/* Two_Product_2Presplit() is Two_Product() where both of the inputs have */
+/* already been split. Avoids redundant splitting. */
+
+#define Two_Product_2Presplit(a, ahi, alo, b, bhi, blo, x, y) \
+ x = (REAL) (a * b); \
+ err1 = x - (ahi * bhi); \
+ err2 = err1 - (alo * bhi); \
+ err3 = err2 - (ahi * blo); \
+ y = (alo * blo) - err3
+
+/* Square() can be done more quickly than Two_Product(). */
+
+#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 = (REAL) (a * a); \
+ Square_Tail(a, x, y)
+
+/* Macros for summing expansions of various fixed lengths. These are all */
+/* unrolled versions of Expansion_Sum(). */
+
+#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)
+
+/* Macros for multiplying expansions of various fixed lengths. */
+
+#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)
+
+/* An expansion of length two can be squared more quickly than finding the */
+/* product of two different expansions of length two, and the result is */
+/* guaranteed to have no more than six (rather than eight) components. */
+
+#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 REAL splitter; /* = 2^ceiling(p / 2) + 1. Used to split floats in half. */
+static REAL epsilon; /* = 2^(-p). Used to estimate roundoff errors. */
+/* A set of coefficients used to calculate maximum roundoff errors. */
+static REAL resulterrbound;
+static REAL ccwerrboundA, ccwerrboundB, ccwerrboundC;
+static REAL o3derrboundA, o3derrboundB, o3derrboundC;
+static REAL iccerrboundA, iccerrboundB, iccerrboundC;
+static REAL isperrboundA, isperrboundB, isperrboundC;
+
+/*****************************************************************************/
+/* */
+/* doubleprint() Print the bit representation of a double. */
+/* */
+/* Useful for debugging exact arithmetic routines. */
+/* */
+/*****************************************************************************/
+
+/*
+void doubleprint(number)
+double number;
+{
+ unsigned long long no;
+ unsigned long long sign, expo;
+ int exponent;
+ int i, bottomi;
+
+ no = *(unsigned long long *) &number;
+ sign = no & 0x8000000000000000ll;
+ expo = (no >> 52) & 0x7ffll;
+ exponent = (int) expo;
+ exponent = exponent - 1023;
+ if (sign) {
+ printf("-");
+ } else {
+ printf(" ");
+ }
+ if (exponent == -1023) {
+ printf(
+ "0.0000000000000000000000000000000000000000000000000000_ ( )");
+ } else {
+ printf("1.");
+ bottomi = -1;
+ for (i = 0; i < 52; i++) {
+ if (no & 0x0008000000000000ll) {
+ printf("1");
+ bottomi = i;
+ } else {
+ printf("0");
+ }
+ no <<= 1;
+ }
+ printf("_%d (%d)", exponent, exponent - 1 - bottomi);
+ }
+}
+*/
+
+/*****************************************************************************/
+/* */
+/* floatprint() Print the bit representation of a float. */
+/* */
+/* Useful for debugging exact arithmetic routines. */
+/* */
+/*****************************************************************************/
+
+/*
+void floatprint(number)
+float number;
+{
+ unsigned no;
+ unsigned sign, expo;
+ int exponent;
+ int i, bottomi;
+
+ no = *(unsigned *) &number;
+ sign = no & 0x80000000;
+ expo = (no >> 23) & 0xff;
+ exponent = (int) expo;
+ exponent = exponent - 127;
+ if (sign) {
+ printf("-");
+ } else {
+ printf(" ");
+ }
+ if (exponent == -127) {
+ printf("0.00000000000000000000000_ ( )");
+ } else {
+ printf("1.");
+ bottomi = -1;
+ for (i = 0; i < 23; i++) {
+ if (no & 0x00400000) {
+ printf("1");
+ bottomi = i;
+ } else {
+ printf("0");
+ }
+ no <<= 1;
+ }
+ printf("_%3d (%3d)", exponent, exponent - 1 - bottomi);
+ }
+}
+*/
+
+/*****************************************************************************/
+/* */
+/* expansion_print() Print the bit representation of an expansion. */
+/* */
+/* Useful for debugging exact arithmetic routines. */
+/* */
+/*****************************************************************************/
+
+/*
+void expansion_print(elen, e)
+int elen;
+REAL *e;
+{
+ int i;
+
+ for (i = elen - 1; i >= 0; i--) {
+ REALPRINT(e[i]);
+ if (i > 0) {
+ printf(" +\n");
+ } else {
+ printf("\n");
+ }
+ }
+}
+*/
+
+/*****************************************************************************/
+/* */
+/* doublerand() Generate a double with random 53-bit significand and a */
+/* random exponent in [0, 511]. */
+/* */
+/*****************************************************************************/
+
+double doublerand()
+{
+ double result;
+ double expo;
+ long a, b, c;
+ long i;
+
+ a = random();
+ b = random();
+ c = random();
+ result = (double) (a - 1073741824) * 8388608.0 + (double) (b >> 8);
+ for (i = 512, expo = 2; i <= 131072; i *= 2, expo = expo * expo) {
+ if (c & i) {
+ result *= expo;
+ }
+ }
+ return result;
+}
+
+/*****************************************************************************/
+/* */
+/* narrowdoublerand() Generate a double with random 53-bit significand */
+/* and a random exponent in [0, 7]. */
+/* */
+/*****************************************************************************/
+
+double narrowdoublerand()
+{
+ double result;
+ double expo;
+ long a, b, c;
+ long i;
+
+ a = random();
+ b = random();
+ c = random();
+ result = (double) (a - 1073741824) * 8388608.0 + (double) (b >> 8);
+ for (i = 512, expo = 2; i <= 2048; i *= 2, expo = expo * expo) {
+ if (c & i) {
+ result *= expo;
+ }
+ }
+ return result;
+}
+
+/*****************************************************************************/
+/* */
+/* uniformdoublerand() Generate a double with random 53-bit significand. */
+/* */
+/*****************************************************************************/
+
+double uniformdoublerand()
+{
+ double result;
+ long a, b;
+
+ a = random();
+ b = random();
+ result = (double) (a - 1073741824) * 8388608.0 + (double) (b >> 8);
+ return result;
+}
+
+/*****************************************************************************/
+/* */
+/* floatrand() Generate a float with random 24-bit significand and a */
+/* random exponent in [0, 63]. */
+/* */
+/*****************************************************************************/
+
+float floatrand()
+{
+ float result;
+ float expo;
+ long a, c;
+ long i;
+
+ a = random();
+ c = random();
+ result = (float) ((a - 1073741824) >> 6);
+ for (i = 512, expo = 2; i <= 16384; i *= 2, expo = expo * expo) {
+ if (c & i) {
+ result *= expo;
+ }
+ }
+ return result;
+}
+
+/*****************************************************************************/
+/* */
+/* narrowfloatrand() Generate a float with random 24-bit significand and */
+/* a random exponent in [0, 7]. */
+/* */
+/*****************************************************************************/
+
+float narrowfloatrand()
+{
+ float result;
+ float expo;
+ long a, c;
+ long i;
+
+ a = random();
+ c = random();
+ result = (float) ((a - 1073741824) >> 6);
+ for (i = 512, expo = 2; i <= 2048; i *= 2, expo = expo * expo) {
+ if (c & i) {
+ result *= expo;
+ }
+ }
+ return result;
+}
+
+/*****************************************************************************/
+/* */
+/* uniformfloatrand() Generate a float with random 24-bit significand. */
+/* */
+/*****************************************************************************/
+
+float uniformfloatrand()
+{
+ float result;
+ long a;
+
+ a = random();
+ result = (float) ((a - 1073741824) >> 6);
+ return result;
+}
+
+/*****************************************************************************/
+/* */
+/* 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 roundoff */
+/* error. It is used for floating-point error analysis. */
+/* */
+/* `splitter' is used to split floating-point numbers into two half- */
+/* length significands 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()
+{
+ REAL half;
+ REAL 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 roundoff. (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 ((check != 1.0) && (check != 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;
+}
+
+/*****************************************************************************/
+/* */
+/* grow_expansion() Add a scalar to an expansion. */
+/* */
+/* Sets h = e + b. See the long version of my paper for details. */
+/* */
+/* Maintains the nonoverlapping property. If round-to-even is used (as */
+/* with IEEE 754), maintains the strongly nonoverlapping and nonadjacent */
+/* properties as well. (That is, if e has one of these properties, so */
+/* will h.) */
+/* */
+/*****************************************************************************/
+
+int grow_expansion(elen, e, b, h) /* e and h can be the same. */
+int elen;
+REAL *e;
+REAL b;
+REAL *h;
+{
+ REAL Q;
+ INEXACT REAL Qnew;
+ int eindex;
+ REAL enow;
+ INEXACT REAL bvirt;
+ REAL avirt, bround, around;
+
+ Q = b;
+ for (eindex = 0; eindex < elen; eindex++) {
+ enow = e[eindex];
+ Two_Sum(Q, enow, Qnew, h[eindex]);
+ Q = Qnew;
+ }
+ h[eindex] = Q;
+ return eindex + 1;
+}
+
+/*****************************************************************************/
+/* */
+/* grow_expansion_zeroelim() Add a scalar to an expansion, eliminating */
+/* zero components from the output expansion. */
+/* */
+/* Sets h = e + b. See the long version of my paper for details. */
+/* */
+/* Maintains the nonoverlapping property. If round-to-even is used (as */
+/* with IEEE 754), maintains the strongly nonoverlapping and nonadjacent */
+/* properties as well. (That is, if e has one of these properties, so */
+/* will h.) */
+/* */
+/*****************************************************************************/
+
+int grow_expansion_zeroelim(elen, e, b, h) /* e and h can be the same. */
+int elen;
+REAL *e;
+REAL b;
+REAL *h;
+{
+ REAL Q, hh;
+ INEXACT REAL Qnew;
+ int eindex, hindex;
+ REAL enow;
+ INEXACT REAL bvirt;
+ REAL avirt, bround, around;
+
+ hindex = 0;
+ Q = b;
+ for (eindex = 0; eindex < elen; eindex++) {
+ enow = e[eindex];
+ Two_Sum(Q, enow, Qnew, hh);
+ Q = Qnew;
+ if (hh != 0.0) {
+ h[hindex++] = hh;
+ }
+ }
+ if ((Q != 0.0) || (hindex == 0)) {
+ h[hindex++] = Q;
+ }
+ return hindex;
+}
+
+/*****************************************************************************/
+/* */
+/* expansion_sum() Sum two expansions. */
+/* */
+/* Sets h = e + f. See the long version of my paper for details. */
+/* */
+/* Maintains the nonoverlapping property. If round-to-even is used (as */
+/* with IEEE 754), maintains the nonadjacent property as well. (That is, */
+/* if e has one of these properties, so will h.) Does NOT maintain the */
+/* strongly nonoverlapping property. */
+/* */
+/*****************************************************************************/
+
+int expansion_sum(elen, e, flen, f, h)
+/* e and h can be the same, but f and h cannot. */
+int elen;
+REAL *e;
+int flen;
+REAL *f;
+REAL *h;
+{
+ REAL Q;
+ INEXACT REAL Qnew;
+ int findex, hindex, hlast;
+ REAL hnow;
+ INEXACT REAL bvirt;
+ REAL avirt, bround, around;
+
+ Q = f[0];
+ for (hindex = 0; hindex < elen; hindex++) {
+ hnow = e[hindex];
+ Two_Sum(Q, hnow, Qnew, h[hindex]);
+ Q = Qnew;
+ }
+ h[hindex] = Q;
+ hlast = hindex;
+ for (findex = 1; findex < flen; findex++) {
+ Q = f[findex];
+ for (hindex = findex; hindex <= hlast; hindex++) {
+ hnow = h[hindex];
+ Two_Sum(Q, hnow, Qnew, h[hindex]);
+ Q = Qnew;
+ }
+ h[++hlast] = Q;
+ }
+ return hlast + 1;
+}
+
+/*****************************************************************************/
+/* */
+/* expansion_sum_zeroelim1() Sum two expansions, eliminating zero */
+/* components from the output expansion. */
+/* */
+/* Sets h = e + f. See the long version of my paper for details. */
+/* */
+/* Maintains the nonoverlapping property. If round-to-even is used (as */
+/* with IEEE 754), maintains the nonadjacent property as well. (That is, */
+/* if e has one of these properties, so will h.) Does NOT maintain the */
+/* strongly nonoverlapping property. */
+/* */
+/*****************************************************************************/
+
+int expansion_sum_zeroelim1(elen, e, flen, f, h)
+/* e and h can be the same, but f and h cannot. */
+int elen;
+REAL *e;
+int flen;
+REAL *f;
+REAL *h;
+{
+ REAL Q;
+ INEXACT REAL Qnew;
+ int index, findex, hindex, hlast;
+ REAL hnow;
+ INEXACT REAL bvirt;
+ REAL avirt, bround, around;
+
+ Q = f[0];
+ for (hindex = 0; hindex < elen; hindex++) {
+ hnow = e[hindex];
+ Two_Sum(Q, hnow, Qnew, h[hindex]);
+ Q = Qnew;
+ }
+ h[hindex] = Q;
+ hlast = hindex;
+ for (findex = 1; findex < flen; findex++) {
+ Q = f[findex];
+ for (hindex = findex; hindex <= hlast; hindex++) {
+ hnow = h[hindex];
+ Two_Sum(Q, hnow, Qnew, h[hindex]);
+ Q = Qnew;
+ }
+ h[++hlast] = Q;
+ }
+ hindex = -1;
+ for (index = 0; index <= hlast; index++) {
+ hnow = h[index];
+ if (hnow != 0.0) {
+ h[++hindex] = hnow;
+ }
+ }
+ if (hindex == -1) {
+ return 1;
+ } else {
+ return hindex + 1;
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* expansion_sum_zeroelim2() Sum two expansions, eliminating zero */
+/* components from the output expansion. */
+/* */
+/* Sets h = e + f. See the long version of my paper for details. */
+/* */
+/* Maintains the nonoverlapping property. If round-to-even is used (as */
+/* with IEEE 754), maintains the nonadjacent property as well. (That is, */
+/* if e has one of these properties, so will h.) Does NOT maintain the */
+/* strongly nonoverlapping property. */
+/* */
+/*****************************************************************************/
+
+int expansion_sum_zeroelim2(elen, e, flen, f, h)
+/* e and h can be the same, but f and h cannot. */
+int elen;
+REAL *e;
+int flen;
+REAL *f;
+REAL *h;
+{
+ REAL Q, hh;
+ INEXACT REAL Qnew;
+ int eindex, findex, hindex, hlast;
+ REAL enow;
+ INEXACT REAL bvirt;
+ REAL avirt, bround, around;
+
+ hindex = 0;
+ Q = f[0];
+ for (eindex = 0; eindex < elen; eindex++) {
+ enow = e[eindex];
+ Two_Sum(Q, enow, Qnew, hh);
+ Q = Qnew;
+ if (hh != 0.0) {
+ h[hindex++] = hh;
+ }
+ }
+ h[hindex] = Q;
+ hlast = hindex;
+ for (findex = 1; findex < flen; findex++) {
+ hindex = 0;
+ Q = f[findex];
+ for (eindex = 0; eindex <= hlast; eindex++) {
+ enow = h[eindex];
+ Two_Sum(Q, enow, Qnew, hh);
+ Q = Qnew;
+ if (hh != 0) {
+ h[hindex++] = hh;
+ }
+ }
+ h[hindex] = Q;
+ hlast = hindex;
+ }
+ return hlast + 1;
+}
+
+/*****************************************************************************/
+/* */
+/* fast_expansion_sum() Sum two expansions. */
+/* */
+/* Sets h = e + f. See the long version of my paper for details. */
+/* */
+/* If round-to-even is used (as with IEEE 754), maintains the strongly */
+/* nonoverlapping property. (That is, if e is strongly nonoverlapping, h */
+/* will be also.) Does NOT maintain the nonoverlapping or nonadjacent */
+/* properties. */
+/* */
+/*****************************************************************************/
+
+int fast_expansion_sum(elen, e, flen, f, h) /* h cannot be e or f. */
+int elen;
+REAL *e;
+int flen;
+REAL *f;
+REAL *h;
+{
+ REAL Q;
+ INEXACT REAL Qnew;
+ INEXACT REAL bvirt;
+ REAL avirt, bround, around;
+ int eindex, findex, hindex;
+ REAL 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, h[0]);
+ enow = e[++eindex];
+ } else {
+ Fast_Two_Sum(fnow, Q, Qnew, h[0]);
+ fnow = f[++findex];
+ }
+ Q = Qnew;
+ hindex = 1;
+ while ((eindex < elen) && (findex < flen)) {
+ if ((fnow > enow) == (fnow > -enow)) {
+ Two_Sum(Q, enow, Qnew, h[hindex]);
+ enow = e[++eindex];
+ } else {
+ Two_Sum(Q, fnow, Qnew, h[hindex]);
+ fnow = f[++findex];
+ }
+ Q = Qnew;
+ hindex++;
+ }
+ }
+ while (eindex < elen) {
+ Two_Sum(Q, enow, Qnew, h[hindex]);
+ enow = e[++eindex];
+ Q = Qnew;
+ hindex++;
+ }
+ while (findex < flen) {
+ Two_Sum(Q, fnow, Qnew, h[hindex]);
+ fnow = f[++findex];
+ Q = Qnew;
+ hindex++;
+ }
+ h[hindex] = Q;
+ return hindex + 1;
+}
+
+/*****************************************************************************/
+/* */
+/* 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. */
+/* */
+/* If round-to-even is used (as with IEEE 754), maintains the strongly */
+/* nonoverlapping property. (That is, if e is strongly nonoverlapping, h */
+/* will be also.) Does NOT maintain the nonoverlapping or nonadjacent */
+/* properties. */
+/* */
+/*****************************************************************************/
+
+int fast_expansion_sum_zeroelim(elen, e, flen, f, h) /* h cannot be e or f. */
+int elen;
+REAL *e;
+int flen;
+REAL *f;
+REAL *h;
+{
+ REAL Q;
+ INEXACT REAL Qnew;
+ INEXACT REAL hh;
+ INEXACT REAL bvirt;
+ REAL avirt, bround, around;
+ int eindex, findex, hindex;
+ REAL 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;
+}
+
+/*****************************************************************************/
+/* */
+/* linear_expansion_sum() Sum two expansions. */
+/* */
+/* Sets h = e + f. See either version of my paper for details. */
+/* */
+/* Maintains the nonoverlapping property. (That is, if e is */
+/* nonoverlapping, h will be also.) */
+/* */
+/*****************************************************************************/
+
+int linear_expansion_sum(elen, e, flen, f, h) /* h cannot be e or f. */
+int elen;
+REAL *e;
+int flen;
+REAL *f;
+REAL *h;
+{
+ REAL Q, q;
+ INEXACT REAL Qnew;
+ INEXACT REAL R;
+ INEXACT REAL bvirt;
+ REAL avirt, bround, around;
+ int eindex, findex, hindex;
+ REAL enow, fnow;
+ REAL g0;
+
+ enow = e[0];
+ fnow = f[0];
+ eindex = findex = 0;
+ if ((fnow > enow) == (fnow > -enow)) {
+ g0 = enow;
+ enow = e[++eindex];
+ } else {
+ g0 = fnow;
+ fnow = f[++findex];
+ }
+ if ((eindex < elen) && ((findex >= flen)
+ || ((fnow > enow) == (fnow > -enow)))) {
+ Fast_Two_Sum(enow, g0, Qnew, q);
+ enow = e[++eindex];
+ } else {
+ Fast_Two_Sum(fnow, g0, Qnew, q);
+ fnow = f[++findex];
+ }
+ Q = Qnew;
+ for (hindex = 0; hindex < elen + flen - 2; hindex++) {
+ if ((eindex < elen) && ((findex >= flen)
+ || ((fnow > enow) == (fnow > -enow)))) {
+ Fast_Two_Sum(enow, q, R, h[hindex]);
+ enow = e[++eindex];
+ } else {
+ Fast_Two_Sum(fnow, q, R, h[hindex]);
+ fnow = f[++findex];
+ }
+ Two_Sum(Q, R, Qnew, q);
+ Q = Qnew;
+ }
+ h[hindex] = q;
+ h[hindex + 1] = Q;
+ return hindex + 2;
+}
+
+/*****************************************************************************/
+/* */
+/* linear_expansion_sum_zeroelim() Sum two expansions, eliminating zero */
+/* components from the output expansion. */
+/* */
+/* Sets h = e + f. See either version of my paper for details. */
+/* */
+/* Maintains the nonoverlapping property. (That is, if e is */
+/* nonoverlapping, h will be also.) */
+/* */
+/*****************************************************************************/
+
+int linear_expansion_sum_zeroelim(elen, e, flen, f, h)/* h cannot be e or f. */
+int elen;
+REAL *e;
+int flen;
+REAL *f;
+REAL *h;
+{
+ REAL Q, q, hh;
+ INEXACT REAL Qnew;
+ INEXACT REAL R;
+ INEXACT REAL bvirt;
+ REAL avirt, bround, around;
+ int eindex, findex, hindex;
+ int count;
+ REAL enow, fnow;
+ REAL g0;
+
+ enow = e[0];
+ fnow = f[0];
+ eindex = findex = 0;
+ hindex = 0;
+ if ((fnow > enow) == (fnow > -enow)) {
+ g0 = enow;
+ enow = e[++eindex];
+ } else {
+ g0 = fnow;
+ fnow = f[++findex];
+ }
+ if ((eindex < elen) && ((findex >= flen)
+ || ((fnow > enow) == (fnow > -enow)))) {
+ Fast_Two_Sum(enow, g0, Qnew, q);
+ enow = e[++eindex];
+ } else {
+ Fast_Two_Sum(fnow, g0, Qnew, q);
+ fnow = f[++findex];
+ }
+ Q = Qnew;
+ for (count = 2; count < elen + flen; count++) {
+ if ((eindex < elen) && ((findex >= flen)
+ || ((fnow > enow) == (fnow > -enow)))) {
+ Fast_Two_Sum(enow, q, R, hh);
+ enow = e[++eindex];
+ } else {
+ Fast_Two_Sum(fnow, q, R, hh);
+ fnow = f[++findex];
+ }
+ Two_Sum(Q, R, Qnew, q);
+ Q = Qnew;
+ if (hh != 0) {
+ h[hindex++] = hh;
+ }
+ }
+ if (q != 0) {
+ h[hindex++] = q;
+ }
+ if ((Q != 0.0) || (hindex == 0)) {
+ h[hindex++] = Q;
+ }
+ return hindex;
+}
+
+/*****************************************************************************/
+/* */
+/* scale_expansion() Multiply an expansion by a scalar. */
+/* */
+/* Sets h = be. See either version of my paper for details. */
+/* */
+/* Maintains the nonoverlapping property. If round-to-even is used (as */
+/* with IEEE 754), maintains the strongly nonoverlapping and nonadjacent */
+/* properties as well. (That is, if e has one of these properties, so */
+/* will h.) */
+/* */
+/*****************************************************************************/
+
+int scale_expansion(elen, e, b, h) /* e and h cannot be the same. */
+int elen;
+REAL *e;
+REAL b;
+REAL *h;
+{
+ INEXACT REAL Q;
+ INEXACT REAL sum;
+ INEXACT REAL product1;
+ REAL product0;
+ int eindex, hindex;
+ REAL enow;
+ INEXACT REAL bvirt;
+ REAL avirt, bround, around;
+ INEXACT REAL c;
+ INEXACT REAL abig;
+ REAL ahi, alo, bhi, blo;
+ REAL err1, err2, err3;
+
+ Split(b, bhi, blo);
+ Two_Product_Presplit(e[0], b, bhi, blo, Q, h[0]);
+ hindex = 1;
+ for (eindex = 1; eindex < elen; eindex++) {
+ enow = e[eindex];
+ Two_Product_Presplit(enow, b, bhi, blo, product1, product0);
+ Two_Sum(Q, product0, sum, h[hindex]);
+ hindex++;
+ Two_Sum(product1, sum, Q, h[hindex]);
+ hindex++;
+ }
+ h[hindex] = Q;
+ return elen + elen;
+}
+
+/*****************************************************************************/
+/* */
+/* 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. */
+/* */
+/* Maintains the nonoverlapping property. If round-to-even is used (as */
+/* with IEEE 754), maintains the strongly nonoverlapping and nonadjacent */
+/* properties as well. (That is, if e has one of these properties, so */
+/* will h.) */
+/* */
+/*****************************************************************************/
+
+int scale_expansion_zeroelim(elen, e, b, h) /* e and h cannot be the same. */
+int elen;
+REAL *e;
+REAL b;
+REAL *h;
+{
+ INEXACT REAL Q, sum;
+ REAL hh;
+ INEXACT REAL product1;
+ REAL product0;
+ int eindex, hindex;
+ REAL enow;
+ INEXACT REAL bvirt;
+ REAL avirt, bround, around;
+ INEXACT REAL c;
+ INEXACT REAL abig;
+ REAL ahi, alo, bhi, blo;
+ REAL 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;
+}
+
+/*****************************************************************************/
+/* */
+/* compress() Compress an expansion. */
+/* */
+/* See the long version of my paper for details. */
+/* */
+/* Maintains the nonoverlapping property. If round-to-even is used (as */
+/* with IEEE 754), then any nonoverlapping expansion is converted to a */
+/* nonadjacent expansion. */
+/* */
+/*****************************************************************************/
+
+int compress(elen, e, h) /* e and h may be the same. */
+int elen;
+REAL *e;
+REAL *h;
+{
+ REAL Q, q;
+ INEXACT REAL Qnew;
+ int eindex, hindex;
+ INEXACT REAL bvirt;
+ REAL enow, hnow;
+ int top, bottom;
+
+ bottom = elen - 1;
+ Q = e[bottom];
+ for (eindex = elen - 2; eindex >= 0; eindex--) {
+ enow = e[eindex];
+ Fast_Two_Sum(Q, enow, Qnew, q);
+ if (q != 0) {
+ h[bottom--] = Qnew;
+ Q = q;
+ } else {
+ Q = Qnew;
+ }
+ }
+ top = 0;
+ for (hindex = bottom + 1; hindex < elen; hindex++) {
+ hnow = h[hindex];
+ Fast_Two_Sum(hnow, Q, Qnew, q);
+ if (q != 0) {
+ h[top++] = q;
+ }
+ Q = Qnew;
+ }
+ h[top] = Q;
+ return top + 1;
+}
+
+/*****************************************************************************/
+/* */
+/* estimate() Produce a one-word estimate of an expansion's value. */
+/* */
+/* See either version of my paper for details. */
+/* */
+/*****************************************************************************/
+
+REAL estimate(elen, e)
+int elen;
+REAL *e;
+{
+ REAL Q;
+ int eindex;
+
+ Q = e[0];
+ for (eindex = 1; eindex < elen; eindex++) {
+ Q += e[eindex];
+ }
+ return Q;
+}
+
+/*****************************************************************************/
+/* */
+/* orient2dfast() Approximate 2D orientation test. Nonrobust. */
+/* orient2dexact() Exact 2D orientation test. Robust. */
+/* orient2dslow() Another exact 2D orientation test. 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 collinear. The */
+/* result is also a rough approximation of twice the signed */
+/* area of the triangle defined by the three points. */
+/* */
+/* Only the first and last routine should be used; the middle two are for */
+/* timings. */
+/* */
+/* The last three use 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 collinear or */
+/* nearly so. */
+/* */
+/*****************************************************************************/
+
+REAL orient2dfast(pa, pb, pc)
+REAL *pa;
+REAL *pb;
+REAL *pc;
+{
+ REAL 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;
+}
+
+REAL orient2dexact(pa, pb, pc)
+REAL *pa;
+REAL *pb;
+REAL *pc;
+{
+ INEXACT REAL axby1, axcy1, bxcy1, bxay1, cxay1, cxby1;
+ REAL axby0, axcy0, bxcy0, bxay0, cxay0, cxby0;
+ REAL aterms[4], bterms[4], cterms[4];
+ INEXACT REAL aterms3, bterms3, cterms3;
+ REAL v[8], w[12];
+ int vlength, wlength;
+
+ INEXACT REAL bvirt;
+ REAL avirt, bround, around;
+ INEXACT REAL c;
+ INEXACT REAL abig;
+ REAL ahi, alo, bhi, blo;
+ REAL err1, err2, err3;
+ INEXACT REAL _i, _j;
+ REAL _0;
+
+ Two_Product(pa[0], pb[1], axby1, axby0);
+ Two_Product(pa[0], pc[1], axcy1, axcy0);
+ Two_Two_Diff(axby1, axby0, axcy1, axcy0,
+ aterms3, aterms[2], aterms[1], aterms[0]);
+ aterms[3] = aterms3;
+
+ Two_Product(pb[0], pc[1], bxcy1, bxcy0);
+ Two_Product(pb[0], pa[1], bxay1, bxay0);
+ Two_Two_Diff(bxcy1, bxcy0, bxay1, bxay0,
+ bterms3, bterms[2], bterms[1], bterms[0]);
+ bterms[3] = bterms3;
+
+ Two_Product(pc[0], pa[1], cxay1, cxay0);
+ Two_Product(pc[0], pb[1], cxby1, cxby0);
+ Two_Two_Diff(cxay1, cxay0, cxby1, cxby0,
+ cterms3, cterms[2], cterms[1], cterms[0]);
+ cterms[3] = cterms3;
+
+ vlength = fast_expansion_sum_zeroelim(4, aterms, 4, bterms, v);
+ wlength = fast_expansion_sum_zeroelim(vlength, v, 4, cterms, w);
+
+ return w[wlength - 1];
+}
+
+REAL orient2dslow(pa, pb, pc)
+REAL *pa;
+REAL *pb;
+REAL *pc;
+{
+ INEXACT REAL acx, acy, bcx, bcy;
+ REAL acxtail, acytail;
+ REAL bcxtail, bcytail;
+ REAL negate, negatetail;
+ REAL axby[8], bxay[8];
+ INEXACT REAL axby7, bxay7;
+ REAL deter[16];
+ int deterlen;
+
+ INEXACT REAL bvirt;
+ REAL avirt, bround, around;
+ INEXACT REAL c;
+ INEXACT REAL abig;
+ REAL a0hi, a0lo, a1hi, a1lo, bhi, blo;
+ REAL err1, err2, err3;
+ INEXACT REAL _i, _j, _k, _l, _m, _n;
+ REAL _0, _1, _2;
+
+ Two_Diff(pa[0], pc[0], acx, acxtail);
+ Two_Diff(pa[1], pc[1], acy, acytail);
+ Two_Diff(pb[0], pc[0], bcx, bcxtail);
+ Two_Diff(pb[1], pc[1], bcy, bcytail);
+
+ Two_Two_Product(acx, acxtail, bcy, bcytail,
+ axby7, axby[6], axby[5], axby[4],
+ axby[3], axby[2], axby[1], axby[0]);
+ axby[7] = axby7;
+ negate = -acy;
+ negatetail = -acytail;
+ Two_Two_Product(bcx, bcxtail, negate, negatetail,
+ bxay7, bxay[6], bxay[5], bxay[4],
+ bxay[3], bxay[2], bxay[1], bxay[0]);
+ bxay[7] = bxay7;
+
+ deterlen = fast_expansion_sum_zeroelim(8, axby, 8, bxay, deter);
+
+ return deter[deterlen - 1];
+}
+
+REAL orient2dadapt(pa, pb, pc, detsum)
+REAL *pa;
+REAL *pb;
+REAL *pc;
+REAL detsum;
+{
+ INEXACT REAL acx, acy, bcx, bcy;
+ REAL acxtail, acytail, bcxtail, bcytail;
+ INEXACT REAL detleft, detright;
+ REAL detlefttail, detrighttail;
+ REAL det, errbound;
+ REAL B[4], C1[8], C2[12], D[16];
+ INEXACT REAL B3;
+ int C1length, C2length, Dlength;
+ REAL u[4];
+ INEXACT REAL u3;
+ INEXACT REAL s1, t1;
+ REAL s0, t0;
+
+ INEXACT REAL bvirt;
+ REAL avirt, bround, around;
+ INEXACT REAL c;
+ INEXACT REAL abig;
+ REAL ahi, alo, bhi, blo;
+ REAL err1, err2, err3;
+ INEXACT REAL _i, _j;
+ REAL _0;
+
+ acx = (REAL) (pa[0] - pc[0]);
+ bcx = (REAL) (pb[0] - pc[0]);
+ acy = (REAL) (pa[1] - pc[1]);
+ bcy = (REAL) (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]);
+}
+
+REAL orient2d(pa, pb, pc)
+REAL *pa;
+REAL *pb;
+REAL *pc;
+{
+ REAL detleft, detright, det;
+ REAL 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;
+ } else {
+ detsum = detleft + detright;
+ }
+ } else if (detleft < 0.0) {
+ if (detright >= 0.0) {
+ return det;
+ } else {
+ 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. Nonrobust. */
+/* orient3dexact() Exact 3D orientation test. Robust. */
+/* orient3dslow() Another exact 3D orientation test. 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 */
+/* coplanar. The result is also a rough approximation of six */
+/* times the signed volume of the tetrahedron defined by the */
+/* four points. */
+/* */
+/* Only the first and last routine should be used; the middle two are for */
+/* timings. */
+/* */
+/* The last three use 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 coplanar or */
+/* nearly so. */
+/* */
+/*****************************************************************************/
+
+REAL orient3dfast(pa, pb, pc, pd)
+REAL *pa;
+REAL *pb;
+REAL *pc;
+REAL *pd;
+{
+ REAL adx, bdx, cdx;
+ REAL ady, bdy, cdy;
+ REAL 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);
+}
+
+REAL orient3dexact(pa, pb, pc, pd)
+REAL *pa;
+REAL *pb;
+REAL *pc;
+REAL *pd;
+{
+ INEXACT REAL axby1, bxcy1, cxdy1, dxay1, axcy1, bxdy1;
+ INEXACT REAL bxay1, cxby1, dxcy1, axdy1, cxay1, dxby1;
+ REAL axby0, bxcy0, cxdy0, dxay0, axcy0, bxdy0;
+ REAL bxay0, cxby0, dxcy0, axdy0, cxay0, dxby0;
+ REAL ab[4], bc[4], cd[4], da[4], ac[4], bd[4];
+ REAL temp8[8];
+ int templen;
+ REAL abc[12], bcd[12], cda[12], dab[12];
+ int abclen, bcdlen, cdalen, dablen;
+ REAL adet[24], bdet[24], cdet[24], ddet[24];
+ int alen, blen, clen, dlen;
+ REAL abdet[48], cddet[48];
+ int ablen, cdlen;
+ REAL deter[96];
+ int deterlen;
+ int i;
+
+ INEXACT REAL bvirt;
+ REAL avirt, bround, around;
+ INEXACT REAL c;
+ INEXACT REAL abig;
+ REAL ahi, alo, bhi, blo;
+ REAL err1, err2, err3;
+ INEXACT REAL _i, _j;
+ REAL _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], 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(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]);
+
+ templen = fast_expansion_sum_zeroelim(4, cd, 4, da, temp8);
+ cdalen = fast_expansion_sum_zeroelim(templen, temp8, 4, ac, cda);
+ templen = fast_expansion_sum_zeroelim(4, da, 4, ab, temp8);
+ dablen = fast_expansion_sum_zeroelim(templen, temp8, 4, bd, dab);
+ for (i = 0; i < 4; i++) {
+ bd[i] = -bd[i];
+ ac[i] = -ac[i];
+ }
+ templen = fast_expansion_sum_zeroelim(4, ab, 4, bc, temp8);
+ abclen = fast_expansion_sum_zeroelim(templen, temp8, 4, ac, abc);
+ templen = fast_expansion_sum_zeroelim(4, bc, 4, cd, temp8);
+ bcdlen = fast_expansion_sum_zeroelim(templen, temp8, 4, bd, bcd);
+
+ alen = scale_expansion_zeroelim(bcdlen, bcd, pa[2], adet);
+ blen = scale_expansion_zeroelim(cdalen, cda, -pb[2], bdet);
+ clen = scale_expansion_zeroelim(dablen, dab, pc[2], cdet);
+ dlen = scale_expansion_zeroelim(abclen, abc, -pd[2], ddet);
+
+ ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
+ cdlen = fast_expansion_sum_zeroelim(clen, cdet, dlen, ddet, cddet);
+ deterlen = fast_expansion_sum_zeroelim(ablen, abdet, cdlen, cddet, deter);
+
+ return deter[deterlen - 1];
+}
+
+REAL orient3dslow(pa, pb, pc, pd)
+REAL *pa;
+REAL *pb;
+REAL *pc;
+REAL *pd;
+{
+ INEXACT REAL adx, ady, adz, bdx, bdy, bdz, cdx, cdy, cdz;
+ REAL adxtail, adytail, adztail;
+ REAL bdxtail, bdytail, bdztail;
+ REAL cdxtail, cdytail, cdztail;
+ REAL negate, negatetail;
+ INEXACT REAL axby7, bxcy7, axcy7, bxay7, cxby7, cxay7;
+ REAL axby[8], bxcy[8], axcy[8], bxay[8], cxby[8], cxay[8];
+ REAL temp16[16], temp32[32], temp32t[32];
+ int temp16len, temp32len, temp32tlen;
+ REAL adet[64], bdet[64], cdet[64];
+ int alen, blen, clen;
+ REAL abdet[128];
+ int ablen;
+ REAL deter[192];
+ int deterlen;
+
+ INEXACT REAL bvirt;
+ REAL avirt, bround, around;
+ INEXACT REAL c;
+ INEXACT REAL abig;
+ REAL a0hi, a0lo, a1hi, a1lo, bhi, blo;
+ REAL err1, err2, err3;
+ INEXACT REAL _i, _j, _k, _l, _m, _n;
+ REAL _0, _1, _2;
+
+ Two_Diff(pa[0], pd[0], adx, adxtail);
+ Two_Diff(pa[1], pd[1], ady, adytail);
+ Two_Diff(pa[2], pd[2], adz, adztail);
+ Two_Diff(pb[0], pd[0], bdx, bdxtail);
+ Two_Diff(pb[1], pd[1], bdy, bdytail);
+ Two_Diff(pb[2], pd[2], bdz, bdztail);
+ Two_Diff(pc[0], pd[0], cdx, cdxtail);
+ Two_Diff(pc[1], pd[1], cdy, cdytail);
+ Two_Diff(pc[2], pd[2], cdz, cdztail);
+
+ Two_Two_Product(adx, adxtail, bdy, bdytail,
+ axby7, axby[6], axby[5], axby[4],
+ axby[3], axby[2], axby[1], axby[0]);
+ axby[7] = axby7;
+ negate = -ady;
+ negatetail = -adytail;
+ Two_Two_Product(bdx, bdxtail, negate, negatetail,
+ bxay7, bxay[6], bxay[5], bxay[4],
+ bxay[3], bxay[2], bxay[1], bxay[0]);
+ bxay[7] = bxay7;
+ Two_Two_Product(bdx, bdxtail, cdy, cdytail,
+ bxcy7, bxcy[6], bxcy[5], bxcy[4],
+ bxcy[3], bxcy[2], bxcy[1], bxcy[0]);
+ bxcy[7] = bxcy7;
+ negate = -bdy;
+ negatetail = -bdytail;
+ Two_Two_Product(cdx, cdxtail, negate, negatetail,
+ cxby7, cxby[6], cxby[5], cxby[4],
+ cxby[3], cxby[2], cxby[1], cxby[0]);
+ cxby[7] = cxby7;
+ Two_Two_Product(cdx, cdxtail, ady, adytail,
+ cxay7, cxay[6], cxay[5], cxay[4],
+ cxay[3], cxay[2], cxay[1], cxay[0]);
+ cxay[7] = cxay7;
+ negate = -cdy;
+ negatetail = -cdytail;
+ Two_Two_Product(adx, adxtail, negate, negatetail,
+ axcy7, axcy[6], axcy[5], axcy[4],
+ axcy[3], axcy[2], axcy[1], axcy[0]);
+ axcy[7] = axcy7;
+
+ temp16len = fast_expansion_sum_zeroelim(8, bxcy, 8, cxby, temp16);
+ temp32len = scale_expansion_zeroelim(temp16len, temp16, adz, temp32);
+ temp32tlen = scale_expansion_zeroelim(temp16len, temp16, adztail, temp32t);
+ alen = fast_expansion_sum_zeroelim(temp32len, temp32, temp32tlen, temp32t,
+ adet);
+
+ temp16len = fast_expansion_sum_zeroelim(8, cxay, 8, axcy, temp16);
+ temp32len = scale_expansion_zeroelim(temp16len, temp16, bdz, temp32);
+ temp32tlen = scale_expansion_zeroelim(temp16len, temp16, bdztail, temp32t);
+ blen = fast_expansion_sum_zeroelim(temp32len, temp32, temp32tlen, temp32t,
+ bdet);
+
+ temp16len = fast_expansion_sum_zeroelim(8, axby, 8, bxay, temp16);
+ temp32len = scale_expansion_zeroelim(temp16len, temp16, cdz, temp32);
+ temp32tlen = scale_expansion_zeroelim(temp16len, temp16, cdztail, temp32t);
+ clen = fast_expansion_sum_zeroelim(temp32len, temp32, temp32tlen, temp32t,
+ cdet);
+
+ ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
+ deterlen = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, deter);
+
+ return deter[deterlen - 1];
+}
+
+REAL orient3dadapt(pa, pb, pc, pd, permanent)
+REAL *pa;
+REAL *pb;
+REAL *pc;
+REAL *pd;
+REAL permanent;
+{
+ INEXACT REAL adx, bdx, cdx, ady, bdy, cdy, adz, bdz, cdz;
+ REAL det, errbound;
+
+ INEXACT REAL bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1;
+ REAL bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0;
+ REAL bc[4], ca[4], ab[4];
+ INEXACT REAL bc3, ca3, ab3;
+ REAL adet[8], bdet[8], cdet[8];
+ int alen, blen, clen;
+ REAL abdet[16];
+ int ablen;
+ REAL *finnow, *finother, *finswap;
+ REAL fin1[192], fin2[192];
+ int finlength;
+
+ REAL adxtail, bdxtail, cdxtail;
+ REAL adytail, bdytail, cdytail;
+ REAL adztail, bdztail, cdztail;
+ INEXACT REAL at_blarge, at_clarge;
+ INEXACT REAL bt_clarge, bt_alarge;
+ INEXACT REAL ct_alarge, ct_blarge;
+ REAL 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 REAL bdxt_cdy1, cdxt_bdy1, cdxt_ady1;
+ INEXACT REAL adxt_cdy1, adxt_bdy1, bdxt_ady1;
+ REAL bdxt_cdy0, cdxt_bdy0, cdxt_ady0;
+ REAL adxt_cdy0, adxt_bdy0, bdxt_ady0;
+ INEXACT REAL bdyt_cdx1, cdyt_bdx1, cdyt_adx1;
+ INEXACT REAL adyt_cdx1, adyt_bdx1, bdyt_adx1;
+ REAL bdyt_cdx0, cdyt_bdx0, cdyt_adx0;
+ REAL adyt_cdx0, adyt_bdx0, bdyt_adx0;
+ REAL bct[8], cat[8], abt[8];
+ int bctlen, catlen, abtlen;
+ INEXACT REAL bdxt_cdyt1, cdxt_bdyt1, cdxt_adyt1;
+ INEXACT REAL adxt_cdyt1, adxt_bdyt1, bdxt_adyt1;
+ REAL bdxt_cdyt0, cdxt_bdyt0, cdxt_adyt0;
+ REAL adxt_cdyt0, adxt_bdyt0, bdxt_adyt0;
+ REAL u[4], v[12], w[16];
+ INEXACT REAL u3;
+ int vlength, wlength;
+ REAL negate;
+
+ INEXACT REAL bvirt;
+ REAL avirt, bround, around;
+ INEXACT REAL c;
+ INEXACT REAL abig;
+ REAL ahi, alo, bhi, blo;
+ REAL err1, err2, err3;
+ INEXACT REAL _i, _j, _k;
+ REAL _0;
+
+ adx = (REAL) (pa[0] - pd[0]);
+ bdx = (REAL) (pb[0] - pd[0]);
+ cdx = (REAL) (pc[0] - pd[0]);
+ ady = (REAL) (pa[1] - pd[1]);
+ bdy = (REAL) (pb[1] - pd[1]);
+ cdy = (REAL) (pc[1] - pd[1]);
+ adz = (REAL) (pa[2] - pd[2]);
+ bdz = (REAL) (pb[2] - pd[2]);
+ cdz = (REAL) (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];
+}
+
+REAL orient3d(pa, pb, pc, pd)
+REAL *pa;
+REAL *pb;
+REAL *pc;
+REAL *pd;
+{
+ REAL adx, bdx, cdx, ady, bdy, cdy, adz, bdz, cdz;
+ REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady;
+ REAL det;
+ REAL 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. Nonrobust. */
+/* incircleexact() Exact 2D incircle test. Robust. */
+/* incircleslow() Another exact 2D incircle test. Robust. */
+/* incircle() Adaptive exact 2D incircle test. Robust. */
+/* */
+/* 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 cocircular.*/
+/* The points pa, pb, and pc must be in counterclockwise */
+/* order, or the sign of the result will be reversed. */
+/* */
+/* Only the first and last routine should be used; the middle two are for */
+/* timings. */
+/* */
+/* The last three use 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 cocircular or */
+/* nearly so. */
+/* */
+/*****************************************************************************/
+
+REAL incirclefast(pa, pb, pc, pd)
+REAL *pa;
+REAL *pb;
+REAL *pc;
+REAL *pd;
+{
+ REAL adx, ady, bdx, bdy, cdx, cdy;
+ REAL abdet, bcdet, cadet;
+ REAL 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;
+}
+
+REAL incircleexact(pa, pb, pc, pd)
+REAL *pa;
+REAL *pb;
+REAL *pc;
+REAL *pd;
+{
+ INEXACT REAL axby1, bxcy1, cxdy1, dxay1, axcy1, bxdy1;
+ INEXACT REAL bxay1, cxby1, dxcy1, axdy1, cxay1, dxby1;
+ REAL axby0, bxcy0, cxdy0, dxay0, axcy0, bxdy0;
+ REAL bxay0, cxby0, dxcy0, axdy0, cxay0, dxby0;
+ REAL ab[4], bc[4], cd[4], da[4], ac[4], bd[4];
+ REAL temp8[8];
+ int templen;
+ REAL abc[12], bcd[12], cda[12], dab[12];
+ int abclen, bcdlen, cdalen, dablen;
+ REAL det24x[24], det24y[24], det48x[48], det48y[48];
+ int xlen, ylen;
+ REAL adet[96], bdet[96], cdet[96], ddet[96];
+ int alen, blen, clen, dlen;
+ REAL abdet[192], cddet[192];
+ int ablen, cdlen;
+ REAL deter[384];
+ int deterlen;
+ int i;
+
+ INEXACT REAL bvirt;
+ REAL avirt, bround, around;
+ INEXACT REAL c;
+ INEXACT REAL abig;
+ REAL ahi, alo, bhi, blo;
+ REAL err1, err2, err3;
+ INEXACT REAL _i, _j;
+ REAL _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], 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(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]);
+
+ templen = fast_expansion_sum_zeroelim(4, cd, 4, da, temp8);
+ cdalen = fast_expansion_sum_zeroelim(templen, temp8, 4, ac, cda);
+ templen = fast_expansion_sum_zeroelim(4, da, 4, ab, temp8);
+ dablen = fast_expansion_sum_zeroelim(templen, temp8, 4, bd, dab);
+ for (i = 0; i < 4; i++) {
+ bd[i] = -bd[i];
+ ac[i] = -ac[i];
+ }
+ templen = fast_expansion_sum_zeroelim(4, ab, 4, bc, temp8);
+ abclen = fast_expansion_sum_zeroelim(templen, temp8, 4, ac, abc);
+ templen = fast_expansion_sum_zeroelim(4, bc, 4, cd, temp8);
+ bcdlen = fast_expansion_sum_zeroelim(templen, temp8, 4, bd, bcd);
+
+ xlen = scale_expansion_zeroelim(bcdlen, bcd, pa[0], det24x);
+ xlen = scale_expansion_zeroelim(xlen, det24x, pa[0], det48x);
+ ylen = scale_expansion_zeroelim(bcdlen, bcd, pa[1], det24y);
+ ylen = scale_expansion_zeroelim(ylen, det24y, pa[1], det48y);
+ alen = fast_expansion_sum_zeroelim(xlen, det48x, ylen, det48y, adet);
+
+ xlen = scale_expansion_zeroelim(cdalen, cda, pb[0], det24x);
+ xlen = scale_expansion_zeroelim(xlen, det24x, -pb[0], det48x);
+ ylen = scale_expansion_zeroelim(cdalen, cda, pb[1], det24y);
+ ylen = scale_expansion_zeroelim(ylen, det24y, -pb[1], det48y);
+ blen = fast_expansion_sum_zeroelim(xlen, det48x, ylen, det48y, bdet);
+
+ xlen = scale_expansion_zeroelim(dablen, dab, pc[0], det24x);
+ xlen = scale_expansion_zeroelim(xlen, det24x, pc[0], det48x);
+ ylen = scale_expansion_zeroelim(dablen, dab, pc[1], det24y);
+ ylen = scale_expansion_zeroelim(ylen, det24y, pc[1], det48y);
+ clen = fast_expansion_sum_zeroelim(xlen, det48x, ylen, det48y, cdet);
+
+ xlen = scale_expansion_zeroelim(abclen, abc, pd[0], det24x);
+ xlen = scale_expansion_zeroelim(xlen, det24x, -pd[0], det48x);
+ ylen = scale_expansion_zeroelim(abclen, abc, pd[1], det24y);
+ ylen = scale_expansion_zeroelim(ylen, det24y, -pd[1], det48y);
+ dlen = fast_expansion_sum_zeroelim(xlen, det48x, ylen, det48y, ddet);
+
+ ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
+ cdlen = fast_expansion_sum_zeroelim(clen, cdet, dlen, ddet, cddet);
+ deterlen = fast_expansion_sum_zeroelim(ablen, abdet, cdlen, cddet, deter);
+
+ return deter[deterlen - 1];
+}
+
+REAL incircleslow(pa, pb, pc, pd)
+REAL *pa;
+REAL *pb;
+REAL *pc;
+REAL *pd;
+{
+ INEXACT REAL adx, bdx, cdx, ady, bdy, cdy;
+ REAL adxtail, bdxtail, cdxtail;
+ REAL adytail, bdytail, cdytail;
+ REAL negate, negatetail;
+ INEXACT REAL axby7, bxcy7, axcy7, bxay7, cxby7, cxay7;
+ REAL axby[8], bxcy[8], axcy[8], bxay[8], cxby[8], cxay[8];
+ REAL temp16[16];
+ int temp16len;
+ REAL detx[32], detxx[64], detxt[32], detxxt[64], detxtxt[64];
+ int xlen, xxlen, xtlen, xxtlen, xtxtlen;
+ REAL x1[128], x2[192];
+ int x1len, x2len;
+ REAL dety[32], detyy[64], detyt[32], detyyt[64], detytyt[64];
+ int ylen, yylen, ytlen, yytlen, ytytlen;
+ REAL y1[128], y2[192];
+ int y1len, y2len;
+ REAL adet[384], bdet[384], cdet[384], abdet[768], deter[1152];
+ int alen, blen, clen, ablen, deterlen;
+ int i;
+
+ INEXACT REAL bvirt;
+ REAL avirt, bround, around;
+ INEXACT REAL c;
+ INEXACT REAL abig;
+ REAL a0hi, a0lo, a1hi, a1lo, bhi, blo;
+ REAL err1, err2, err3;
+ INEXACT REAL _i, _j, _k, _l, _m, _n;
+ REAL _0, _1, _2;
+
+ Two_Diff(pa[0], pd[0], adx, adxtail);
+ Two_Diff(pa[1], pd[1], ady, adytail);
+ Two_Diff(pb[0], pd[0], bdx, bdxtail);
+ Two_Diff(pb[1], pd[1], bdy, bdytail);
+ Two_Diff(pc[0], pd[0], cdx, cdxtail);
+ Two_Diff(pc[1], pd[1], cdy, cdytail);
+
+ Two_Two_Product(adx, adxtail, bdy, bdytail,
+ axby7, axby[6], axby[5], axby[4],
+ axby[3], axby[2], axby[1], axby[0]);
+ axby[7] = axby7;
+ negate = -ady;
+ negatetail = -adytail;
+ Two_Two_Product(bdx, bdxtail, negate, negatetail,
+ bxay7, bxay[6], bxay[5], bxay[4],
+ bxay[3], bxay[2], bxay[1], bxay[0]);
+ bxay[7] = bxay7;
+ Two_Two_Product(bdx, bdxtail, cdy, cdytail,
+ bxcy7, bxcy[6], bxcy[5], bxcy[4],
+ bxcy[3], bxcy[2], bxcy[1], bxcy[0]);
+ bxcy[7] = bxcy7;
+ negate = -bdy;
+ negatetail = -bdytail;
+ Two_Two_Product(cdx, cdxtail, negate, negatetail,
+ cxby7, cxby[6], cxby[5], cxby[4],
+ cxby[3], cxby[2], cxby[1], cxby[0]);
+ cxby[7] = cxby7;
+ Two_Two_Product(cdx, cdxtail, ady, adytail,
+ cxay7, cxay[6], cxay[5], cxay[4],
+ cxay[3], cxay[2], cxay[1], cxay[0]);
+ cxay[7] = cxay7;
+ negate = -cdy;
+ negatetail = -cdytail;
+ Two_Two_Product(adx, adxtail, negate, negatetail,
+ axcy7, axcy[6], axcy[5], axcy[4],
+ axcy[3], axcy[2], axcy[1], axcy[0]);
+ axcy[7] = axcy7;
+
+
+ temp16len = fast_expansion_sum_zeroelim(8, bxcy, 8, cxby, temp16);
+
+ xlen = scale_expansion_zeroelim(temp16len, temp16, adx, detx);
+ xxlen = scale_expansion_zeroelim(xlen, detx, adx, detxx);
+ xtlen = scale_expansion_zeroelim(temp16len, temp16, adxtail, detxt);
+ xxtlen = scale_expansion_zeroelim(xtlen, detxt, adx, detxxt);
+ for (i = 0; i < xxtlen; i++) {
+ detxxt[i] *= 2.0;
+ }
+ xtxtlen = scale_expansion_zeroelim(xtlen, detxt, adxtail, detxtxt);
+ x1len = fast_expansion_sum_zeroelim(xxlen, detxx, xxtlen, detxxt, x1);
+ x2len = fast_expansion_sum_zeroelim(x1len, x1, xtxtlen, detxtxt, x2);
+
+ ylen = scale_expansion_zeroelim(temp16len, temp16, ady, dety);
+ yylen = scale_expansion_zeroelim(ylen, dety, ady, detyy);
+ ytlen = scale_expansion_zeroelim(temp16len, temp16, adytail, detyt);
+ yytlen = scale_expansion_zeroelim(ytlen, detyt, ady, detyyt);
+ for (i = 0; i < yytlen; i++) {
+ detyyt[i] *= 2.0;
+ }
+ ytytlen = scale_expansion_zeroelim(ytlen, detyt, adytail, detytyt);
+ y1len = fast_expansion_sum_zeroelim(yylen, detyy, yytlen, detyyt, y1);
+ y2len = fast_expansion_sum_zeroelim(y1len, y1, ytytlen, detytyt, y2);
+
+ alen = fast_expansion_sum_zeroelim(x2len, x2, y2len, y2, adet);
+
+
+ temp16len = fast_expansion_sum_zeroelim(8, cxay, 8, axcy, temp16);
+
+ xlen = scale_expansion_zeroelim(temp16len, temp16, bdx, detx);
+ xxlen = scale_expansion_zeroelim(xlen, detx, bdx, detxx);
+ xtlen = scale_expansion_zeroelim(temp16len, temp16, bdxtail, detxt);
+ xxtlen = scale_expansion_zeroelim(xtlen, detxt, bdx, detxxt);
+ for (i = 0; i < xxtlen; i++) {
+ detxxt[i] *= 2.0;
+ }
+ xtxtlen = scale_expansion_zeroelim(xtlen, detxt, bdxtail, detxtxt);
+ x1len = fast_expansion_sum_zeroelim(xxlen, detxx, xxtlen, detxxt, x1);
+ x2len = fast_expansion_sum_zeroelim(x1len, x1, xtxtlen, detxtxt, x2);
+
+ ylen = scale_expansion_zeroelim(temp16len, temp16, bdy, dety);
+ yylen = scale_expansion_zeroelim(ylen, dety, bdy, detyy);
+ ytlen = scale_expansion_zeroelim(temp16len, temp16, bdytail, detyt);
+ yytlen = scale_expansion_zeroelim(ytlen, detyt, bdy, detyyt);
+ for (i = 0; i < yytlen; i++) {
+ detyyt[i] *= 2.0;
+ }
+ ytytlen = scale_expansion_zeroelim(ytlen, detyt, bdytail, detytyt);
+ y1len = fast_expansion_sum_zeroelim(yylen, detyy, yytlen, detyyt, y1);
+ y2len = fast_expansion_sum_zeroelim(y1len, y1, ytytlen, detytyt, y2);
+
+ blen = fast_expansion_sum_zeroelim(x2len, x2, y2len, y2, bdet);
+
+
+ temp16len = fast_expansion_sum_zeroelim(8, axby, 8, bxay, temp16);
+
+ xlen = scale_expansion_zeroelim(temp16len, temp16, cdx, detx);
+ xxlen = scale_expansion_zeroelim(xlen, detx, cdx, detxx);
+ xtlen = scale_expansion_zeroelim(temp16len, temp16, cdxtail, detxt);
+ xxtlen = scale_expansion_zeroelim(xtlen, detxt, cdx, detxxt);
+ for (i = 0; i < xxtlen; i++) {
+ detxxt[i] *= 2.0;
+ }
+ xtxtlen = scale_expansion_zeroelim(xtlen, detxt, cdxtail, detxtxt);
+ x1len = fast_expansion_sum_zeroelim(xxlen, detxx, xxtlen, detxxt, x1);
+ x2len = fast_expansion_sum_zeroelim(x1len, x1, xtxtlen, detxtxt, x2);
+
+ ylen = scale_expansion_zeroelim(temp16len, temp16, cdy, dety);
+ yylen = scale_expansion_zeroelim(ylen, dety, cdy, detyy);
+ ytlen = scale_expansion_zeroelim(temp16len, temp16, cdytail, detyt);
+ yytlen = scale_expansion_zeroelim(ytlen, detyt, cdy, detyyt);
+ for (i = 0; i < yytlen; i++) {
+ detyyt[i] *= 2.0;
+ }
+ ytytlen = scale_expansion_zeroelim(ytlen, detyt, cdytail, detytyt);
+ y1len = fast_expansion_sum_zeroelim(yylen, detyy, yytlen, detyyt, y1);
+ y2len = fast_expansion_sum_zeroelim(y1len, y1, ytytlen, detytyt, y2);
+
+ clen = fast_expansion_sum_zeroelim(x2len, x2, y2len, y2, cdet);
+
+ ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
+ deterlen = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, deter);
+
+ return deter[deterlen - 1];
+}
+
+REAL incircleadapt(pa, pb, pc, pd, permanent)
+REAL *pa;
+REAL *pb;
+REAL *pc;
+REAL *pd;
+REAL permanent;
+{
+ INEXACT REAL adx, bdx, cdx, ady, bdy, cdy;
+ REAL det, errbound;
+
+ INEXACT REAL bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1;
+ REAL bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0;
+ REAL bc[4], ca[4], ab[4];
+ INEXACT REAL bc3, ca3, ab3;
+ REAL axbc[8], axxbc[16], aybc[8], ayybc[16], adet[32];
+ int axbclen, axxbclen, aybclen, ayybclen, alen;
+ REAL bxca[8], bxxca[16], byca[8], byyca[16], bdet[32];
+ int bxcalen, bxxcalen, bycalen, byycalen, blen;
+ REAL cxab[8], cxxab[16], cyab[8], cyyab[16], cdet[32];
+ int cxablen, cxxablen, cyablen, cyyablen, clen;
+ REAL abdet[64];
+ int ablen;
+ REAL fin1[1152], fin2[1152];
+ REAL *finnow, *finother, *finswap;
+ int finlength;
+
+ REAL adxtail, bdxtail, cdxtail, adytail, bdytail, cdytail;
+ INEXACT REAL adxadx1, adyady1, bdxbdx1, bdybdy1, cdxcdx1, cdycdy1;
+ REAL adxadx0, adyady0, bdxbdx0, bdybdy0, cdxcdx0, cdycdy0;
+ REAL aa[4], bb[4], cc[4];
+ INEXACT REAL aa3, bb3, cc3;
+ INEXACT REAL ti1, tj1;
+ REAL ti0, tj0;
+ REAL u[4], v[4];
+ INEXACT REAL u3, v3;
+ REAL temp8[8], temp16a[16], temp16b[16], temp16c[16];
+ REAL temp32a[32], temp32b[32], temp48[48], temp64[64];
+ int temp8len, temp16alen, temp16blen, temp16clen;
+ int temp32alen, temp32blen, temp48len, temp64len;
+ REAL axtbb[8], axtcc[8], aytbb[8], aytcc[8];
+ int axtbblen, axtcclen, aytbblen, aytcclen;
+ REAL bxtaa[8], bxtcc[8], bytaa[8], bytcc[8];
+ int bxtaalen, bxtcclen, bytaalen, bytcclen;
+ REAL cxtaa[8], cxtbb[8], cytaa[8], cytbb[8];
+ int cxtaalen, cxtbblen, cytaalen, cytbblen;
+ REAL axtbc[8], aytbc[8], bxtca[8], bytca[8], cxtab[8], cytab[8];
+ int axtbclen, aytbclen, bxtcalen, bytcalen, cxtablen, cytablen;
+ REAL axtbct[16], aytbct[16], bxtcat[16], bytcat[16], cxtabt[16], cytabt[16];
+ int axtbctlen, aytbctlen, bxtcatlen, bytcatlen, cxtabtlen, cytabtlen;
+ REAL axtbctt[8], aytbctt[8], bxtcatt[8];
+ REAL bytcatt[8], cxtabtt[8], cytabtt[8];
+ int axtbcttlen, aytbcttlen, bxtcattlen, bytcattlen, cxtabttlen, cytabttlen;
+ REAL abt[8], bct[8], cat[8];
+ int abtlen, bctlen, catlen;
+ REAL abtt[4], bctt[4], catt[4];
+ int abttlen, bcttlen, cattlen;
+ INEXACT REAL abtt3, bctt3, catt3;
+ REAL negate;
+
+ INEXACT REAL bvirt;
+ REAL avirt, bround, around;
+ INEXACT REAL c;
+ INEXACT REAL abig;
+ REAL ahi, alo, bhi, blo;
+ REAL err1, err2, err3;
+ INEXACT REAL _i, _j;
+ REAL _0;
+
+ adx = (REAL) (pa[0] - pd[0]);
+ bdx = (REAL) (pb[0] - pd[0]);
+ cdx = (REAL) (pc[0] - pd[0]);
+ ady = (REAL) (pa[1] - pd[1]);
+ bdy = (REAL) (pb[1] - pd[1]);
+ cdy = (REAL) (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];
+}
+
+REAL incircle(pa, pb, pc, pd)
+REAL *pa;
+REAL *pb;
+REAL *pc;
+REAL *pd;
+{
+ REAL adx, bdx, cdx, ady, bdy, cdy;
+ REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady;
+ REAL alift, blift, clift;
+ REAL det;
+ REAL 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. Nonrobust. */
+/* insphereexact() Exact 3D insphere test. Robust. */
+/* insphereslow() Another exact 3D insphere test. 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 */
+/* cospherical. 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. */
+/* */
+/* Only the first and last routine should be used; the middle two are for */
+/* timings. */
+/* */
+/* The last three use 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 cospherical or */
+/* nearly so. */
+/* */
+/*****************************************************************************/
+
+REAL inspherefast(pa, pb, pc, pd, pe)
+REAL *pa;
+REAL *pb;
+REAL *pc;
+REAL *pd;
+REAL *pe;
+{
+ REAL aex, bex, cex, dex;
+ REAL aey, bey, cey, dey;
+ REAL aez, bez, cez, dez;
+ REAL alift, blift, clift, dlift;
+ REAL ab, bc, cd, da, ac, bd;
+ REAL 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);
+}
+
+REAL insphereexact(pa, pb, pc, pd, pe)
+REAL *pa;
+REAL *pb;
+REAL *pc;
+REAL *pd;
+REAL *pe;
+{
+ INEXACT REAL axby1, bxcy1, cxdy1, dxey1, exay1;
+ INEXACT REAL bxay1, cxby1, dxcy1, exdy1, axey1;
+ INEXACT REAL axcy1, bxdy1, cxey1, dxay1, exby1;
+ INEXACT REAL cxay1, dxby1, excy1, axdy1, bxey1;
+ REAL axby0, bxcy0, cxdy0, dxey0, exay0;
+ REAL bxay0, cxby0, dxcy0, exdy0, axey0;
+ REAL axcy0, bxdy0, cxey0, dxay0, exby0;
+ REAL cxay0, dxby0, excy0, axdy0, bxey0;
+ REAL ab[4], bc[4], cd[4], de[4], ea[4];
+ REAL ac[4], bd[4], ce[4], da[4], eb[4];
+ REAL temp8a[8], temp8b[8], temp16[16];
+ int temp8alen, temp8blen, temp16len;
+ REAL abc[24], bcd[24], cde[24], dea[24], eab[24];
+ REAL abd[24], bce[24], cda[24], deb[24], eac[24];
+ int abclen, bcdlen, cdelen, dealen, eablen;
+ int abdlen, bcelen, cdalen, deblen, eaclen;
+ REAL temp48a[48], temp48b[48];
+ int temp48alen, temp48blen;
+ REAL abcd[96], bcde[96], cdea[96], deab[96], eabc[96];
+ int abcdlen, bcdelen, cdealen, deablen, eabclen;
+ REAL temp192[192];
+ REAL det384x[384], det384y[384], det384z[384];
+ int xlen, ylen, zlen;
+ REAL detxy[768];
+ int xylen;
+ REAL adet[1152], bdet[1152], cdet[1152], ddet[1152], edet[1152];
+ int alen, blen, clen, dlen, elen;
+ REAL abdet[2304], cddet[2304], cdedet[3456];
+ int ablen, cdlen;
+ REAL deter[5760];
+ int deterlen;
+ int i;
+
+ INEXACT REAL bvirt;
+ REAL avirt, bround, around;
+ INEXACT REAL c;
+ INEXACT REAL abig;
+ REAL ahi, alo, bhi, blo;
+ REAL err1, err2, err3;
+ INEXACT REAL _i, _j;
+ REAL _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];
+}
+
+REAL insphereslow(pa, pb, pc, pd, pe)
+REAL *pa;
+REAL *pb;
+REAL *pc;
+REAL *pd;
+REAL *pe;
+{
+ INEXACT REAL aex, bex, cex, dex, aey, bey, cey, dey, aez, bez, cez, dez;
+ REAL aextail, bextail, cextail, dextail;
+ REAL aeytail, beytail, ceytail, deytail;
+ REAL aeztail, beztail, ceztail, deztail;
+ REAL negate, negatetail;
+ INEXACT REAL axby7, bxcy7, cxdy7, dxay7, axcy7, bxdy7;
+ INEXACT REAL bxay7, cxby7, dxcy7, axdy7, cxay7, dxby7;
+ REAL axby[8], bxcy[8], cxdy[8], dxay[8], axcy[8], bxdy[8];
+ REAL bxay[8], cxby[8], dxcy[8], axdy[8], cxay[8], dxby[8];
+ REAL ab[16], bc[16], cd[16], da[16], ac[16], bd[16];
+ int ablen, bclen, cdlen, dalen, aclen, bdlen;
+ REAL temp32a[32], temp32b[32], temp64a[64], temp64b[64], temp64c[64];
+ int temp32alen, temp32blen, temp64alen, temp64blen, temp64clen;
+ REAL temp128[128], temp192[192];
+ int temp128len, temp192len;
+ REAL detx[384], detxx[768], detxt[384], detxxt[768], detxtxt[768];
+ int xlen, xxlen, xtlen, xxtlen, xtxtlen;
+ REAL x1[1536], x2[2304];
+ int x1len, x2len;
+ REAL dety[384], detyy[768], detyt[384], detyyt[768], detytyt[768];
+ int ylen, yylen, ytlen, yytlen, ytytlen;
+ REAL y1[1536], y2[2304];
+ int y1len, y2len;
+ REAL detz[384], detzz[768], detzt[384], detzzt[768], detztzt[768];
+ int zlen, zzlen, ztlen, zztlen, ztztlen;
+ REAL z1[1536], z2[2304];
+ int z1len, z2len;
+ REAL detxy[4608];
+ int xylen;
+ REAL adet[6912], bdet[6912], cdet[6912], ddet[6912];
+ int alen, blen, clen, dlen;
+ REAL abdet[13824], cddet[13824], deter[27648];
+ int deterlen;
+ int i;
+
+ INEXACT REAL bvirt;
+ REAL avirt, bround, around;
+ INEXACT REAL c;
+ INEXACT REAL abig;
+ REAL a0hi, a0lo, a1hi, a1lo, bhi, blo;
+ REAL err1, err2, err3;
+ INEXACT REAL _i, _j, _k, _l, _m, _n;
+ REAL _0, _1, _2;
+
+ Two_Diff(pa[0], pe[0], aex, aextail);
+ Two_Diff(pa[1], pe[1], aey, aeytail);
+ Two_Diff(pa[2], pe[2], aez, aeztail);
+ Two_Diff(pb[0], pe[0], bex, bextail);
+ Two_Diff(pb[1], pe[1], bey, beytail);
+ Two_Diff(pb[2], pe[2], bez, beztail);
+ Two_Diff(pc[0], pe[0], cex, cextail);
+ Two_Diff(pc[1], pe[1], cey, ceytail);
+ Two_Diff(pc[2], pe[2], cez, ceztail);
+ Two_Diff(pd[0], pe[0], dex, dextail);
+ Two_Diff(pd[1], pe[1], dey, deytail);
+ Two_Diff(pd[2], pe[2], dez, deztail);
+
+ Two_Two_Product(aex, aextail, bey, beytail,
+ axby7, axby[6], axby[5], axby[4],
+ axby[3], axby[2], axby[1], axby[0]);
+ axby[7] = axby7;
+ negate = -aey;
+ negatetail = -aeytail;
+ Two_Two_Product(bex, bextail, negate, negatetail,
+ bxay7, bxay[6], bxay[5], bxay[4],
+ bxay[3], bxay[2], bxay[1], bxay[0]);
+ bxay[7] = bxay7;
+ ablen = fast_expansion_sum_zeroelim(8, axby, 8, bxay, ab);
+ Two_Two_Product(bex, bextail, cey, ceytail,
+ bxcy7, bxcy[6], bxcy[5], bxcy[4],
+ bxcy[3], bxcy[2], bxcy[1], bxcy[0]);
+ bxcy[7] = bxcy7;
+ negate = -bey;
+ negatetail = -beytail;
+ Two_Two_Product(cex, cextail, negate, negatetail,
+ cxby7, cxby[6], cxby[5], cxby[4],
+ cxby[3], cxby[2], cxby[1], cxby[0]);
+ cxby[7] = cxby7;
+ bclen = fast_expansion_sum_zeroelim(8, bxcy, 8, cxby, bc);
+ Two_Two_Product(cex, cextail, dey, deytail,
+ cxdy7, cxdy[6], cxdy[5], cxdy[4],
+ cxdy[3], cxdy[2], cxdy[1], cxdy[0]);
+ cxdy[7] = cxdy7;
+ negate = -cey;
+ negatetail = -ceytail;
+ Two_Two_Product(dex, dextail, negate, negatetail,
+ dxcy7, dxcy[6], dxcy[5], dxcy[4],
+ dxcy[3], dxcy[2], dxcy[1], dxcy[0]);
+ dxcy[7] = dxcy7;
+ cdlen = fast_expansion_sum_zeroelim(8, cxdy, 8, dxcy, cd);
+ Two_Two_Product(dex, dextail, aey, aeytail,
+ dxay7, dxay[6], dxay[5], dxay[4],
+ dxay[3], dxay[2], dxay[1], dxay[0]);
+ dxay[7] = dxay7;
+ negate = -dey;
+ negatetail = -deytail;
+ Two_Two_Product(aex, aextail, negate, negatetail,
+ axdy7, axdy[6], axdy[5], axdy[4],
+ axdy[3], axdy[2], axdy[1], axdy[0]);
+ axdy[7] = axdy7;
+ dalen = fast_expansion_sum_zeroelim(8, dxay, 8, axdy, da);
+ Two_Two_Product(aex, aextail, cey, ceytail,
+ axcy7, axcy[6], axcy[5], axcy[4],
+ axcy[3], axcy[2], axcy[1], axcy[0]);
+ axcy[7] = axcy7;
+ negate = -aey;
+ negatetail = -aeytail;
+ Two_Two_Product(cex, cextail, negate, negatetail,
+ cxay7, cxay[6], cxay[5], cxay[4],
+ cxay[3], cxay[2], cxay[1], cxay[0]);
+ cxay[7] = cxay7;
+ aclen = fast_expansion_sum_zeroelim(8, axcy, 8, cxay, ac);
+ Two_Two_Product(bex, bextail, dey, deytail,
+ bxdy7, bxdy[6], bxdy[5], bxdy[4],
+ bxdy[3], bxdy[2], bxdy[1], bxdy[0]);
+ bxdy[7] = bxdy7;
+ negate = -bey;
+ negatetail = -beytail;
+ Two_Two_Product(dex, dextail, negate, negatetail,
+ dxby7, dxby[6], dxby[5], dxby[4],
+ dxby[3], dxby[2], dxby[1], dxby[0]);
+ dxby[7] = dxby7;
+ bdlen = fast_expansion_sum_zeroelim(8, bxdy, 8, dxby, bd);
+
+ temp32alen = scale_expansion_zeroelim(cdlen, cd, -bez, temp32a);
+ temp32blen = scale_expansion_zeroelim(cdlen, cd, -beztail, temp32b);
+ temp64alen = fast_expansion_sum_zeroelim(temp32alen, temp32a,
+ temp32blen, temp32b, temp64a);
+ temp32alen = scale_expansion_zeroelim(bdlen, bd, cez, temp32a);
+ temp32blen = scale_expansion_zeroelim(bdlen, bd, ceztail, temp32b);
+ temp64blen = fast_expansion_sum_zeroelim(temp32alen, temp32a,
+ temp32blen, temp32b, temp64b);
+ temp32alen = scale_expansion_zeroelim(bclen, bc, -dez, temp32a);
+ temp32blen = scale_expansion_zeroelim(bclen, bc, -deztail, temp32b);
+ temp64clen = fast_expansion_sum_zeroelim(temp32alen, temp32a,
+ temp32blen, temp32b, temp64c);
+ temp128len = fast_expansion_sum_zeroelim(temp64alen, temp64a,
+ temp64blen, temp64b, temp128);
+ temp192len = fast_expansion_sum_zeroelim(temp64clen, temp64c,
+ temp128len, temp128, temp192);
+ xlen = scale_expansion_zeroelim(temp192len, temp192, aex, detx);
+ xxlen = scale_expansion_zeroelim(xlen, detx, aex, detxx);
+ xtlen = scale_expansion_zeroelim(temp192len, temp192, aextail, detxt);
+ xxtlen = scale_expansion_zeroelim(xtlen, detxt, aex, detxxt);
+ for (i = 0; i < xxtlen; i++) {
+ detxxt[i] *= 2.0;
+ }
+ xtxtlen = scale_expansion_zeroelim(xtlen, detxt, aextail, detxtxt);
+ x1len = fast_expansion_sum_zeroelim(xxlen, detxx, xxtlen, detxxt, x1);
+ x2len = fast_expansion_sum_zeroelim(x1len, x1, xtxtlen, detxtxt, x2);
+ ylen = scale_expansion_zeroelim(temp192len, temp192, aey, dety);
+ yylen = scale_expansion_zeroelim(ylen, dety, aey, detyy);
+ ytlen = scale_expansion_zeroelim(temp192len, temp192, aeytail, detyt);
+ yytlen = scale_expansion_zeroelim(ytlen, detyt, aey, detyyt);
+ for (i = 0; i < yytlen; i++) {
+ detyyt[i] *= 2.0;
+ }
+ ytytlen = scale_expansion_zeroelim(ytlen, detyt, aeytail, detytyt);
+ y1len = fast_expansion_sum_zeroelim(yylen, detyy, yytlen, detyyt, y1);
+ y2len = fast_expansion_sum_zeroelim(y1len, y1, ytytlen, detytyt, y2);
+ zlen = scale_expansion_zeroelim(temp192len, temp192, aez, detz);
+ zzlen = scale_expansion_zeroelim(zlen, detz, aez, detzz);
+ ztlen = scale_expansion_zeroelim(temp192len, temp192, aeztail, detzt);
+ zztlen = scale_expansion_zeroelim(ztlen, detzt, aez, detzzt);
+ for (i = 0; i < zztlen; i++) {
+ detzzt[i] *= 2.0;
+ }
+ ztztlen = scale_expansion_zeroelim(ztlen, detzt, aeztail, detztzt);
+ z1len = fast_expansion_sum_zeroelim(zzlen, detzz, zztlen, detzzt, z1);
+ z2len = fast_expansion_sum_zeroelim(z1len, z1, ztztlen, detztzt, z2);
+ xylen = fast_expansion_sum_zeroelim(x2len, x2, y2len, y2, detxy);
+ alen = fast_expansion_sum_zeroelim(z2len, z2, xylen, detxy, adet);
+
+ temp32alen = scale_expansion_zeroelim(dalen, da, cez, temp32a);
+ temp32blen = scale_expansion_zeroelim(dalen, da, ceztail, temp32b);
+ temp64alen = fast_expansion_sum_zeroelim(temp32alen, temp32a,
+ temp32blen, temp32b, temp64a);
+ temp32alen = scale_expansion_zeroelim(aclen, ac, dez, temp32a);
+ temp32blen = scale_expansion_zeroelim(aclen, ac, deztail, temp32b);
+ temp64blen = fast_expansion_sum_zeroelim(temp32alen, temp32a,
+ temp32blen, temp32b, temp64b);
+ temp32alen = scale_expansion_zeroelim(cdlen, cd, aez, temp32a);
+ temp32blen = scale_expansion_zeroelim(cdlen, cd, aeztail, temp32b);
+ temp64clen = fast_expansion_sum_zeroelim(temp32alen, temp32a,
+ temp32blen, temp32b, temp64c);
+ temp128len = fast_expansion_sum_zeroelim(temp64alen, temp64a,
+ temp64blen, temp64b, temp128);
+ temp192len = fast_expansion_sum_zeroelim(temp64clen, temp64c,
+ temp128len, temp128, temp192);
+ xlen = scale_expansion_zeroelim(temp192len, temp192, bex, detx);
+ xxlen = scale_expansion_zeroelim(xlen, detx, bex, detxx);
+ xtlen = scale_expansion_zeroelim(temp192len, temp192, bextail, detxt);
+ xxtlen = scale_expansion_zeroelim(xtlen, detxt, bex, detxxt);
+ for (i = 0; i < xxtlen; i++) {
+ detxxt[i] *= 2.0;
+ }
+ xtxtlen = scale_expansion_zeroelim(xtlen, detxt, bextail, detxtxt);
+ x1len = fast_expansion_sum_zeroelim(xxlen, detxx, xxtlen, detxxt, x1);
+ x2len = fast_expansion_sum_zeroelim(x1len, x1, xtxtlen, detxtxt, x2);
+ ylen = scale_expansion_zeroelim(temp192len, temp192, bey, dety);
+ yylen = scale_expansion_zeroelim(ylen, dety, bey, detyy);
+ ytlen = scale_expansion_zeroelim(temp192len, temp192, beytail, detyt);
+ yytlen = scale_expansion_zeroelim(ytlen, detyt, bey, detyyt);
+ for (i = 0; i < yytlen; i++) {
+ detyyt[i] *= 2.0;
+ }
+ ytytlen = scale_expansion_zeroelim(ytlen, detyt, beytail, detytyt);
+ y1len = fast_expansion_sum_zeroelim(yylen, detyy, yytlen, detyyt, y1);
+ y2len = fast_expansion_sum_zeroelim(y1len, y1, ytytlen, detytyt, y2);
+ zlen = scale_expansion_zeroelim(temp192len, temp192, bez, detz);
+ zzlen = scale_expansion_zeroelim(zlen, detz, bez, detzz);
+ ztlen = scale_expansion_zeroelim(temp192len, temp192, beztail, detzt);
+ zztlen = scale_expansion_zeroelim(ztlen, detzt, bez, detzzt);
+ for (i = 0; i < zztlen; i++) {
+ detzzt[i] *= 2.0;
+ }
+ ztztlen = scale_expansion_zeroelim(ztlen, detzt, beztail, detztzt);
+ z1len = fast_expansion_sum_zeroelim(zzlen, detzz, zztlen, detzzt, z1);
+ z2len = fast_expansion_sum_zeroelim(z1len, z1, ztztlen, detztzt, z2);
+ xylen = fast_expansion_sum_zeroelim(x2len, x2, y2len, y2, detxy);
+ blen = fast_expansion_sum_zeroelim(z2len, z2, xylen, detxy, bdet);
+
+ temp32alen = scale_expansion_zeroelim(ablen, ab, -dez, temp32a);
+ temp32blen = scale_expansion_zeroelim(ablen, ab, -deztail, temp32b);
+ temp64alen = fast_expansion_sum_zeroelim(temp32alen, temp32a,
+ temp32blen, temp32b, temp64a);
+ temp32alen = scale_expansion_zeroelim(bdlen, bd, -aez, temp32a);
+ temp32blen = scale_expansion_zeroelim(bdlen, bd, -aeztail, temp32b);
+ temp64blen = fast_expansion_sum_zeroelim(temp32alen, temp32a,
+ temp32blen, temp32b, temp64b);
+ temp32alen = scale_expansion_zeroelim(dalen, da, -bez, temp32a);
+ temp32blen = scale_expansion_zeroelim(dalen, da, -beztail, temp32b);
+ temp64clen = fast_expansion_sum_zeroelim(temp32alen, temp32a,
+ temp32blen, temp32b, temp64c);
+ temp128len = fast_expansion_sum_zeroelim(temp64alen, temp64a,
+ temp64blen, temp64b, temp128);
+ temp192len = fast_expansion_sum_zeroelim(temp64clen, temp64c,
+ temp128len, temp128, temp192);
+ xlen = scale_expansion_zeroelim(temp192len, temp192, cex, detx);
+ xxlen = scale_expansion_zeroelim(xlen, detx, cex, detxx);
+ xtlen = scale_expansion_zeroelim(temp192len, temp192, cextail, detxt);
+ xxtlen = scale_expansion_zeroelim(xtlen, detxt, cex, detxxt);
+ for (i = 0; i < xxtlen; i++) {
+ detxxt[i] *= 2.0;
+ }
+ xtxtlen = scale_expansion_zeroelim(xtlen, detxt, cextail, detxtxt);
+ x1len = fast_expansion_sum_zeroelim(xxlen, detxx, xxtlen, detxxt, x1);
+ x2len = fast_expansion_sum_zeroelim(x1len, x1, xtxtlen, detxtxt, x2);
+ ylen = scale_expansion_zeroelim(temp192len, temp192, cey, dety);
+ yylen = scale_expansion_zeroelim(ylen, dety, cey, detyy);
+ ytlen = scale_expansion_zeroelim(temp192len, temp192, ceytail, detyt);
+ yytlen = scale_expansion_zeroelim(ytlen, detyt, cey, detyyt);
+ for (i = 0; i < yytlen; i++) {
+ detyyt[i] *= 2.0;
+ }
+ ytytlen = scale_expansion_zeroelim(ytlen, detyt, ceytail, detytyt);
+ y1len = fast_expansion_sum_zeroelim(yylen, detyy, yytlen, detyyt, y1);
+ y2len = fast_expansion_sum_zeroelim(y1len, y1, ytytlen, detytyt, y2);
+ zlen = scale_expansion_zeroelim(temp192len, temp192, cez, detz);
+ zzlen = scale_expansion_zeroelim(zlen, detz, cez, detzz);
+ ztlen = scale_expansion_zeroelim(temp192len, temp192, ceztail, detzt);
+ zztlen = scale_expansion_zeroelim(ztlen, detzt, cez, detzzt);
+ for (i = 0; i < zztlen; i++) {
+ detzzt[i] *= 2.0;
+ }
+ ztztlen = scale_expansion_zeroelim(ztlen, detzt, ceztail, detztzt);
+ z1len = fast_expansion_sum_zeroelim(zzlen, detzz, zztlen, detzzt, z1);
+ z2len = fast_expansion_sum_zeroelim(z1len, z1, ztztlen, detztzt, z2);
+ xylen = fast_expansion_sum_zeroelim(x2len, x2, y2len, y2, detxy);
+ clen = fast_expansion_sum_zeroelim(z2len, z2, xylen, detxy, cdet);
+
+ temp32alen = scale_expansion_zeroelim(bclen, bc, aez, temp32a);
+ temp32blen = scale_expansion_zeroelim(bclen, bc, aeztail, temp32b);
+ temp64alen = fast_expansion_sum_zeroelim(temp32alen, temp32a,
+ temp32blen, temp32b, temp64a);
+ temp32alen = scale_expansion_zeroelim(aclen, ac, -bez, temp32a);
+ temp32blen = scale_expansion_zeroelim(aclen, ac, -beztail, temp32b);
+ temp64blen = fast_expansion_sum_zeroelim(temp32alen, temp32a,
+ temp32blen, temp32b, temp64b);
+ temp32alen = scale_expansion_zeroelim(ablen, ab, cez, temp32a);
+ temp32blen = scale_expansion_zeroelim(ablen, ab, ceztail, temp32b);
+ temp64clen = fast_expansion_sum_zeroelim(temp32alen, temp32a,
+ temp32blen, temp32b, temp64c);
+ temp128len = fast_expansion_sum_zeroelim(temp64alen, temp64a,
+ temp64blen, temp64b, temp128);
+ temp192len = fast_expansion_sum_zeroelim(temp64clen, temp64c,
+ temp128len, temp128, temp192);
+ xlen = scale_expansion_zeroelim(temp192len, temp192, dex, detx);
+ xxlen = scale_expansion_zeroelim(xlen, detx, dex, detxx);
+ xtlen = scale_expansion_zeroelim(temp192len, temp192, dextail, detxt);
+ xxtlen = scale_expansion_zeroelim(xtlen, detxt, dex, detxxt);
+ for (i = 0; i < xxtlen; i++) {
+ detxxt[i] *= 2.0;
+ }
+ xtxtlen = scale_expansion_zeroelim(xtlen, detxt, dextail, detxtxt);
+ x1len = fast_expansion_sum_zeroelim(xxlen, detxx, xxtlen, detxxt, x1);
+ x2len = fast_expansion_sum_zeroelim(x1len, x1, xtxtlen, detxtxt, x2);
+ ylen = scale_expansion_zeroelim(temp192len, temp192, dey, dety);
+ yylen = scale_expansion_zeroelim(ylen, dety, dey, detyy);
+ ytlen = scale_expansion_zeroelim(temp192len, temp192, deytail, detyt);
+ yytlen = scale_expansion_zeroelim(ytlen, detyt, dey, detyyt);
+ for (i = 0; i < yytlen; i++) {
+ detyyt[i] *= 2.0;
+ }
+ ytytlen = scale_expansion_zeroelim(ytlen, detyt, deytail, detytyt);
+ y1len = fast_expansion_sum_zeroelim(yylen, detyy, yytlen, detyyt, y1);
+ y2len = fast_expansion_sum_zeroelim(y1len, y1, ytytlen, detytyt, y2);
+ zlen = scale_expansion_zeroelim(temp192len, temp192, dez, detz);
+ zzlen = scale_expansion_zeroelim(zlen, detz, dez, detzz);
+ ztlen = scale_expansion_zeroelim(temp192len, temp192, deztail, detzt);
+ zztlen = scale_expansion_zeroelim(ztlen, detzt, dez, detzzt);
+ for (i = 0; i < zztlen; i++) {
+ detzzt[i] *= 2.0;
+ }
+ ztztlen = scale_expansion_zeroelim(ztlen, detzt, deztail, detztzt);
+ z1len = fast_expansion_sum_zeroelim(zzlen, detzz, zztlen, detzzt, z1);
+ z2len = fast_expansion_sum_zeroelim(z1len, z1, ztztlen, detztzt, z2);
+ xylen = fast_expansion_sum_zeroelim(x2len, x2, y2len, y2, detxy);
+ dlen = fast_expansion_sum_zeroelim(z2len, z2, xylen, detxy, ddet);
+
+ ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
+ cdlen = fast_expansion_sum_zeroelim(clen, cdet, dlen, ddet, cddet);
+ deterlen = fast_expansion_sum_zeroelim(ablen, abdet, cdlen, cddet, deter);
+
+ return deter[deterlen - 1];
+}
+
+REAL insphereadapt(pa, pb, pc, pd, pe, permanent)
+REAL *pa;
+REAL *pb;
+REAL *pc;
+REAL *pd;
+REAL *pe;
+REAL permanent;
+{
+ INEXACT REAL aex, bex, cex, dex, aey, bey, cey, dey, aez, bez, cez, dez;
+ REAL det, errbound;
+
+ INEXACT REAL aexbey1, bexaey1, bexcey1, cexbey1;
+ INEXACT REAL cexdey1, dexcey1, dexaey1, aexdey1;
+ INEXACT REAL aexcey1, cexaey1, bexdey1, dexbey1;
+ REAL aexbey0, bexaey0, bexcey0, cexbey0;
+ REAL cexdey0, dexcey0, dexaey0, aexdey0;
+ REAL aexcey0, cexaey0, bexdey0, dexbey0;
+ REAL ab[4], bc[4], cd[4], da[4], ac[4], bd[4];
+ INEXACT REAL ab3, bc3, cd3, da3, ac3, bd3;
+ REAL abeps, bceps, cdeps, daeps, aceps, bdeps;
+ REAL temp8a[8], temp8b[8], temp8c[8], temp16[16], temp24[24], temp48[48];
+ int temp8alen, temp8blen, temp8clen, temp16len, temp24len, temp48len;
+ REAL xdet[96], ydet[96], zdet[96], xydet[192];
+ int xlen, ylen, zlen, xylen;
+ REAL adet[288], bdet[288], cdet[288], ddet[288];
+ int alen, blen, clen, dlen;
+ REAL abdet[576], cddet[576];
+ int ablen, cdlen;
+ REAL fin1[1152];
+ int finlength;
+
+ REAL aextail, bextail, cextail, dextail;
+ REAL aeytail, beytail, ceytail, deytail;
+ REAL aeztail, beztail, ceztail, deztail;
+
+ INEXACT REAL bvirt;
+ REAL avirt, bround, around;
+ INEXACT REAL c;
+ INEXACT REAL abig;
+ REAL ahi, alo, bhi, blo;
+ REAL err1, err2, err3;
+ INEXACT REAL _i, _j;
+ REAL _0;
+
+ aex = (REAL) (pa[0] - pe[0]);
+ bex = (REAL) (pb[0] - pe[0]);
+ cex = (REAL) (pc[0] - pe[0]);
+ dex = (REAL) (pd[0] - pe[0]);
+ aey = (REAL) (pa[1] - pe[1]);
+ bey = (REAL) (pb[1] - pe[1]);
+ cey = (REAL) (pc[1] - pe[1]);
+ dey = (REAL) (pd[1] - pe[1]);
+ aez = (REAL) (pa[2] - pe[2]);
+ bez = (REAL) (pb[2] - pe[2]);
+ cez = (REAL) (pc[2] - pe[2]);
+ dez = (REAL) (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);
+}
+
+REAL insphere(pa, pb, pc, pd, pe)
+REAL *pa;
+REAL *pb;
+REAL *pc;
+REAL *pd;
+REAL *pe;
+{
+ REAL aex, bex, cex, dex;
+ REAL aey, bey, cey, dey;
+ REAL aez, bez, cez, dez;
+ REAL aexbey, bexaey, bexcey, cexbey, cexdey, dexcey, dexaey, aexdey;
+ REAL aexcey, cexaey, bexdey, dexbey;
+ REAL alift, blift, clift, dlift;
+ REAL ab, bc, cd, da, ac, bd;
+ REAL abc, bcd, cda, dab;
+ REAL aezplus, bezplus, cezplus, dezplus;
+ REAL aexbeyplus, bexaeyplus, bexceyplus, cexbeyplus;
+ REAL cexdeyplus, dexceyplus, dexaeyplus, aexdeyplus;
+ REAL aexceyplus, cexaeyplus, bexdeyplus, dexbeyplus;
+ REAL det;
+ REAL 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);
+}
+
+static int init = 0;
+
+#include<predicates.h>
+
+JNIEXPORT jint JNICALL Java_org_ibex_graphics_Predicates_side
+(JNIEnv *jni, jclass jc, jdouble x1, jdouble y1, jdouble x2, jdouble y2, jdouble x3, jdouble y3) {
+ double p1[2];
+ double p2[2];
+ double p3[2];
+ if (init==0) {
+ init = 1;
+ exactinit();
+ }
+ p1[0] = x1;
+ p2[0] = x2;
+ p3[0] = x3;
+ p1[1] = y1;
+ p2[1] = y2;
+ p3[1] = y3;
+ double ret = orient2d(p1, p2, p3);
+ return ret > 0 ? 1 : ret < 0 ? -1 : 0;
+}
+JNIEXPORT jint JNICALL Java_org_ibex_graphics_Predicates_incircle
+(JNIEnv *jni, jclass jc, jdouble x1, jdouble y1, jdouble x2, jdouble y2, jdouble x3, jdouble y3, jdouble x4, jdouble y4) {
+ double p1[2];
+ double p2[2];
+ double p3[2];
+ double p4[2];
+ if (init==0) {
+ init = 1;
+ exactinit();
+ }
+ p1[0] = x1;
+ p2[0] = x2;
+ p3[0] = x3;
+ p4[0] = x4;
+ p1[1] = y1;
+ p2[1] = y2;
+ p3[1] = y3;
+ p4[1] = y4;
+ if (orient2d(p1, p2, p3)<0) {
+ p2[0] = x3;
+ p3[0] = x2;
+ p2[1] = y3;
+ p3[1] = y2;
+ }
+ if (orient2d(p1, p2, p3)<0) printf("error!!!\n");
+ double ret = incircle(p1, p2, p3, p4);
+ return ret > 0 ? 1 : ret < 0 ? -1 : 0;
+}
+
projects / org.ibex.core.git / commitdiff