/*****************************************************************************/
/* */
/* 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 */
/*
[email protected] */
/* */
/* 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
[email protected] if you */
/* have questions. */
/* */
/*****************************************************************************/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <cfloat>
#include "predicates.h"
/* FPU control. We MUST have only double precision (not extended precision) */
#include "rounding.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)
/* 2^(-p), where p=DBL_MANT_DIG. Used to estimate roundoff errors. */
static const REAL epsilon=0.5*DBL_EPSILON;
/* 2^ceiling(p/2) + 1. Used to split floats in half. */
static const REAL splitter=sqrt((DBL_MANT_DIG % 2 ? 2.0 : 1.0)/epsilon)+1.0;
/* A set of coefficients used to calculate maximum roundoff errors. */
const REAL resulterrbound=(3.0 + 8.0 * epsilon) * epsilon;
const REAL ccwerrboundA=(3.0 + 16.0 * epsilon) * epsilon;
const REAL ccwerrboundB=(2.0 + 12.0 * epsilon) * epsilon;
const REAL ccwerrboundC=(9.0 + 64.0 * epsilon) * epsilon * epsilon;
const REAL o3derrboundA=(7.0 + 56.0 * epsilon) * epsilon;
const REAL o3derrboundB=(3.0 + 28.0 * epsilon) * epsilon;
const REAL o3derrboundC=(26.0 + 288.0 * epsilon) * epsilon * epsilon;
const REAL iccerrboundA=(10.0 + 96.0 * epsilon) * epsilon;
const REAL iccerrboundB=(4.0 + 48.0 * epsilon) * epsilon;
const REAL iccerrboundC=(44.0 + 576.0 * epsilon) * epsilon * epsilon;
const REAL isperrboundA=(16.0 + 224.0 * epsilon) * epsilon;
const REAL isperrboundB=(5.0 + 72.0 * epsilon) * epsilon;
const REAL isperrboundC=(71.0 + 1408.0 * epsilon) * epsilon * epsilon;
/*****************************************************************************/
/* */
/* 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]. */
/* */
/*****************************************************************************/
/*
static 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]. */
/* */
/*****************************************************************************/
/*
static 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. */
/* */
/*****************************************************************************/
/*
static 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]. */
/* */
/*****************************************************************************/
/*
static 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]. */
/* */
/*****************************************************************************/
/*
static 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. */
/* */
/*****************************************************************************/
/*
static float uniformfloatrand()
{
float result;
long a;
a = random();
result = (float) ((a - 1073741824) >> 6);
return result;
}
*/
/*****************************************************************************/
/* */
/* 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. */
/* */
/*****************************************************************************/
static int fast_expansion_sum_zeroelim(int elen, const REAL *e,
int flen, const REAL *f, REAL *h)
/* h cannot be e or f. */
{
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;
}
/*****************************************************************************/
/* */
/* 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.) */
/* */
/*****************************************************************************/
static int scale_expansion_zeroelim(int elen, const REAL *e, REAL b, REAL *h)
/* e and h cannot be the same. */
{
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;
}
/*****************************************************************************/
/* */
/* estimate() Produce a one-word estimate of an expansion's value. */
/* */
/* See either version of my paper for details. */
/* */
/*****************************************************************************/
static REAL estimate(int elen, const 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 orient2dadapt(const REAL *pa, const REAL *pb, const REAL *pc, const 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(const REAL *pa, const REAL *pb, const REAL *pc)
{
REAL detleft, detright, det;
REAL detsum, errbound;
REAL orient;
FPU_ROUND_DOUBLE;
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) {
FPU_RESTORE;
return det;
} else {
detsum = detleft + detright;
}
} else if (detleft < 0.0) {
if (detright >= 0.0) {
FPU_RESTORE;
return det;
} else {
detsum = -detleft - detright;
}
} else {
FPU_RESTORE;
return det;
}
errbound = ccwerrboundA * detsum;
if ((det >= errbound) || (-det >= errbound)) {
FPU_RESTORE;
return det;
}
orient = orient2dadapt(pa, pb, pc, detsum);
FPU_RESTORE;
return orient;
}
REAL orient2d(const REAL ax, const REAL ay, const REAL bx, const REAL by,
const REAL cx, const REAL cy)
{
REAL detleft, detright, det;
REAL detsum, errbound;
REAL orient;
FPU_ROUND_DOUBLE;
detleft = (ax - cx) * (by - cy);
detright = (ay - cy) * (bx - cx);
det = detleft - detright;
if (detleft > 0.0) {
if (detright <= 0.0) {
FPU_RESTORE;
return det;
} else {
detsum = detleft + detright;
}
} else if (detleft < 0.0) {
if (detright >= 0.0) {
FPU_RESTORE;
return det;
} else {
detsum = -detleft - detright;
}
} else {
FPU_RESTORE;
return det;
}
errbound = ccwerrboundA * detsum;
if ((det >= errbound) || (-det >= errbound)) {
FPU_RESTORE;
return det;
}
REAL pa[]={ax,ay};
REAL pb[]={bx,by};
REAL pc[]={cx,cy};
orient = orient2dadapt(pa, pb, pc, detsum);
FPU_RESTORE;
return orient;
}
/*****************************************************************************/
/* */
/* 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. */
/* */
/*****************************************************************************/
static REAL orient3dadapt(const REAL *pa, const REAL *pb, const REAL *pc, const 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(const REAL *pa, const REAL *pb, const REAL *pc, const REAL *pd)
{
REAL adx, bdx, cdx, ady, bdy, cdy, adz, bdz, cdz;
REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady;
REAL det;
REAL permanent, errbound;
REAL orient;
FPU_ROUND_DOUBLE;
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)) {
FPU_RESTORE;
return det;
}
orient = orient3dadapt(pa, pb, pc, pd, permanent);
FPU_RESTORE;
return orient;
}
/*****************************************************************************/
/* */
/* 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. */
/* */
/*****************************************************************************/
static REAL incircleadapt(const REAL *pa, const REAL *pb, const REAL *pc, const 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 = 0, aytbclen = 0;
int bxtcalen = 0, bytcalen = 0;
int cxtablen = 0, cytablen = 0;
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(const REAL *pa, const REAL *pb, const REAL *pc, const 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;
REAL inc;
FPU_ROUND_DOUBLE;
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)) {
FPU_RESTORE;
return det;
}
inc = incircleadapt(pa, pb, pc, pd, permanent);
FPU_RESTORE;
return inc;
}
REAL incircle(REAL ax, REAL ay, REAL bx, REAL by, REAL cx, REAL cy, REAL dx,
REAL dy)
{
REAL adx, bdx, cdx, ady, bdy, cdy;
REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady;
REAL alift, blift, clift;
REAL det;
REAL permanent, errbound;
REAL inc;
FPU_ROUND_DOUBLE;
adx = ax - dx;
bdx = bx - dx;
cdx = cx - dx;
ady = ay - dy;
bdy = by - dy;
cdy = cy - dy;
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)) {
FPU_RESTORE;
return det;
}
REAL pa[]={ax,ay};
REAL pb[]={bx,by};
REAL pc[]={cx,cy};
REAL pd[]={dx,dy};
inc = incircleadapt(pa, pb, pc, pd, permanent);
FPU_RESTORE;
return inc;
}
/*****************************************************************************/
/* */
/* 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. */
/* */
/*****************************************************************************/
static REAL insphereexact(const REAL *pa, const REAL *pb, const REAL *pc, const REAL *pd, const 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];
}
static REAL insphereadapt(const REAL *pa, const REAL *pb, const REAL *pc, const REAL *pd, const 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(const REAL *pa, const REAL *pb, const REAL *pc, const REAL *pd, const 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;
REAL ins;
FPU_ROUND_DOUBLE;
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)) {
FPU_RESTORE;
return det;
}
ins = insphereadapt(pa, pb, pc, pd, pe, permanent);
FPU_RESTORE;
return ins;
}
