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debugging/02_day/valgrind/valgrind-3.11.0/perf/fbench.c
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// This small program does some raytracing. It tests Valgrind's handling of
// FP operations. It apparently does a lot of trigonometry operations.
// Licensing: This program is closely based on the one of the same name from
// http://www.fourmilab.ch/. The front page of that site says:
//
// "Except for a few clearly-marked exceptions, all the material on this
// site is in the public domain and may be used in any manner without
// permission, restriction, attribution, or compensation."
/* This program can be used in two ways. If INTRIG is undefined, sin,
cos, tan, etc, will be used as supplied by <math.h>. If it is
defined, then the program calculates all this stuff from first
principles (so to speak) and does not use the libc facilities. For
benchmarking purposes it seems better to avoid the libc stuff, so
that the inner loops (sin, sqrt) present a workload independent of
libc implementations on different platforms. Hence: */
#define INTRIG 1
/*
John Walker's Floating Point Benchmark, derived from...
Marinchip Interactive Lens Design System
John Walker December 1980
By John Walker
http://www.fourmilab.ch/
This program may be used, distributed, and modified freely as
long as the origin information is preserved.
This is a complete optical design raytracing algorithm,
stripped of its user interface and recast into portable C. It
not only determines execution speed on an extremely floating
point (including trig function) intensive real-world
application, it checks accuracy on an algorithm that is
exquisitely sensitive to errors. The performance of this
program is typically far more sensitive to changes in the
efficiency of the trigonometric library routines than the
average floating point program.
The benchmark may be compiled in two modes. If the symbol
INTRIG is defined, built-in trigonometric and square root
routines will be used for all calculations. Timings made with
INTRIG defined reflect the machine's basic floating point
performance for the arithmetic operators. If INTRIG is not
defined, the system library <math.h> functions are used.
Results with INTRIG not defined reflect the system's library
performance and/or floating point hardware support for trig
functions and square root. Results with INTRIG defined are a
good guide to general floating point performance, while
results with INTRIG undefined indicate the performance of an
application which is math function intensive.
Special note regarding errors in accuracy: this program has
generated numbers identical to the last digit it formats and
checks on the following machines, floating point
architectures, and languages:
Marinchip 9900 QBASIC IBM 370 double-precision (REAL * 8) format
IBM PC / XT / AT Lattice C IEEE 64 bit, 80 bit temporaries
High C same, in line 80x87 code
BASICA "Double precision"
Quick BASIC IEEE double precision, software routines
Sun 3 C IEEE 64 bit, 80 bit temporaries,
in-line 68881 code, in-line FPA code.
MicroVAX II C Vax "G" format floating point
Macintosh Plus MPW C SANE floating point, IEEE 64 bit format
implemented in ROM.
Inaccuracies reported by this program should be taken VERY
SERIOUSLY INDEED, as the program has been demonstrated to be
invariant under changes in floating point format, as long as
the format is a recognised double precision format. If you
encounter errors, please remember that they are just as likely
to be in the floating point editing library or the
trigonometric libraries as in the low level operator code.
The benchmark assumes that results are basically reliable, and
only tests the last result computed against the reference. If
you're running on a suspect system you can compile this
program with ACCURACY defined. This will generate a version
which executes as an infinite loop, performing the ray trace
and checking the results on every pass. All incorrect results
will be reported.
Representative timings are given below. All have been
normalised as if run for 1000 iterations.
Time in seconds Computer, Compiler, and notes
Normal INTRIG
3466.00 4031.00 Commodore 128, 2 Mhz 8510 with software floating
point. Abacus Software/Data-Becker Super-C 128,
version 3.00, run in fast (2 Mhz) mode. Note:
the results generated by this system differed
from the reference results in the 8th to 10th
decimal place.
3290.00 IBM PC/AT 6 Mhz, Microsoft/IBM BASICA version A3.00.
Run with the "/d" switch, software floating point.
2131.50 IBM PC/AT 6 Mhz, Lattice C version 2.14, small model.
This version of Lattice compiles subroutine
calls which either do software floating point
or use the 80x87. The machine on which I ran
this had an 80287, but the results were so bad
I wonder if it was being used.
1598.00 Macintosh Plus, MPW C, SANE Software floating point.
1582.13 Marinchip 9900 2 Mhz, QBASIC compiler with software
floating point. This was a QBASIC version of the
program which contained the identical algorithm.
404.00 IBM PC/AT 6 Mhz, Microsoft QuickBASIC version 2.0.
Software floating point.
165.15 IBM PC/AT 6 Mhz, Metaware High C version 1.3, small
model. This was compiled to call subroutines for
floating point, and the machine contained an 80287
which was used by the subroutines.
143.20 Macintosh II, MPW C, SANE calls. I was unable to
determine whether SANE was using the 68881 chip or
not.
121.80 Sun 3/160 16 Mhz, Sun C. Compiled with -fsoft switch
which executes floating point in software.
78.78 110.11 IBM RT PC (Model 6150). IBM AIX 1.0 C compiler
with -O switch.
75.2 254.0 Microsoft Quick C 1.0, in-line 8087 instructions,
compiled with 80286 optimisation on. (Switches
were -Ol -FPi87-G2 -AS). Small memory model.
69.50 IBM PC/AT 6Mhz, Borland Turbo BASIC 1.0. Compiled
in "8087 required" mode to generate in-line
code for the math coprocessor.
66.96 IBM PC/AT 6Mhz, Microsoft QuickBASIC 4.0. This
release of QuickBASIC compiles code for the
80287 math coprocessor.
66.36 206.35 IBM PC/AT 6Mhz, Metaware High C version 1.3, small
model. This was compiled with in-line code for the
80287 math coprocessor. Trig functions still call
library routines.
63.07 220.43 IBM PC/AT, 6Mhz, Borland Turbo C, in-line 8087 code,
small model, word alignment, no stack checking,
8086 code mode.
17.18 Apollo DN-3000, 12 Mhz 68020 with 68881, compiled
with in-line code for the 68881 coprocessor.
According to Apollo, the library routines are chosen
at runtime based on coprocessor presence. Since the
coprocessor was present, the library is supposed to
use in-line floating point code.
15.55 27.56 VAXstation II GPX. Compiled and executed under
VAX/VMS C.
15.14 37.93 Macintosh II, Unix system V. Green Hills 68020
Unix compiler with in-line code for the 68881
coprocessor (-O -ZI switches).
12.69 Sun 3/160 16 Mhz, Sun C. Compiled with -fswitch,
which calls a subroutine to select the fastest
floating point processor. This was using the 68881.
11.74 26.73 Compaq Deskpro 386, 16 Mhz 80386 with 16 Mhz 80387.
Metaware High C version 1.3, compiled with in-line
for the math coprocessor (but not optimised for the
80386/80387). Trig functions still call library
routines.
8.43 30.49 Sun 3/160 16 Mhz, Sun C. Compiled with -f68881,
generating in-line MC68881 instructions. Trig
functions still call library routines.
6.29 25.17 Sun 3/260 25 Mhz, Sun C. Compiled with -f68881,
generating in-line MC68881 instructions. Trig
functions still call library routines.
4.57 Sun 3/260 25 Mhz, Sun FORTRAN 77. Compiled with
-O -f68881, generating in-line MC68881 instructions.
Trig functions are compiled in-line. This used
the FORTRAN 77 version of the program, FBFORT77.F.
4.00 14.20 Sun386i/25 Mhz model 250, Sun C compiler.
4.00 14.00 Sun386i/25 Mhz model 250, Metaware C.
3.10 12.00 Compaq 386/387 25 Mhz running SCO Xenix 2.
Compiled with Metaware HighC 386, optimized
for 386.
3.00 12.00 Compaq 386/387 25MHZ optimized for 386/387.
2.96 5.17 Sun 4/260, Sparc RISC processor. Sun C,
compiled with the -O2 switch for global
optimisation.
2.47 COMPAQ 486/25, secondary cache disabled, High C,
486/387, inline f.p., small memory model.
2.20 3.40 Data General Motorola 88000, 16 Mhz, Gnu C.
1.56 COMPAQ 486/25, 128K secondary cache, High C, 486/387,
inline f.p., small memory model.
0.66 1.50 DEC Pmax, Mips processor.
0.63 0.91 Sun SparcStation 2, Sun C (SunOS 4.1.1) with
-O4 optimisation and "/usr/lib/libm.il" inline
floating point.
0.60 1.07 Intel 860 RISC processor, 33 Mhz, Greenhills
C compiler.
0.40 0.90 Dec 3MAX, MIPS 3000 processor, -O4.
0.31 0.90 IBM RS/6000, -O.
0.1129 0.2119 Dell Dimension XPS P133c, Pentium 133 MHz,
Windows 95, Microsoft Visual C 5.0.
0.0883 0.2166 Silicon Graphics Indigo<67>, MIPS R4400,
175 Mhz, "-O3".
0.0351 0.0561 Dell Dimension XPS R100, Pentium II 400 MHz,
Windows 98, Microsoft Visual C 5.0.
0.0312 0.0542 Sun Ultra 2, UltraSPARC V9, 300 MHz, Solaris
2.5.1.
0.00862 0.01074 Dell Inspiron 9100, Pentium 4, 3.4 GHz, gcc -O3.
*/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#ifndef INTRIG
#include <math.h>
#endif
#define cot(x) (1.0 / tan(x))
#define TRUE 1
#define FALSE 0
#define max_surfaces 10
/* Local variables */
/* static char tbfr[132]; */
static short current_surfaces;
static short paraxial;
static double clear_aperture;
static double aberr_lspher;
static double aberr_osc;
static double aberr_lchrom;
static double max_lspher;
static double max_osc;
static double max_lchrom;
static double radius_of_curvature;
static double object_distance;
static double ray_height;
static double axis_slope_angle;
static double from_index;
static double to_index;
static double spectral_line[9];
static double s[max_surfaces][5];
static double od_sa[2][2];
static char outarr[8][80]; /* Computed output of program goes here */
int itercount; /* The iteration counter for the main loop
in the program is made global so that
the compiler should not be allowed to
optimise out the loop over the ray
tracing code. */
#ifndef ITERATIONS
#define ITERATIONS /*1000*/ /*500000*/ 80000
#endif
int niter = ITERATIONS; /* Iteration counter */
static char *refarr[] = { /* Reference results. These happen to
be derived from a run on Microsoft
Quick BASIC on the IBM PC/AT. */
" Marginal ray 47.09479120920 0.04178472683",
" Paraxial ray 47.08372160249 0.04177864821",
"Longitudinal spherical aberration: -0.01106960671",
" (Maximum permissible): 0.05306749907",
"Offense against sine condition (coma): 0.00008954761",
" (Maximum permissible): 0.00250000000",
"Axial chromatic aberration: 0.00448229032",
" (Maximum permissible): 0.05306749907"
};
/* The test case used in this program is the design for a 4 inch
achromatic telescope objective used as the example in Wyld's
classic work on ray tracing by hand, given in Amateur Telescope
Making, Volume 3. */
static double testcase[4][4] = {
{27.05, 1.5137, 63.6, 0.52},
{-16.68, 1, 0, 0.138},
{-16.68, 1.6164, 36.7, 0.38},
{-78.1, 1, 0, 0}
};
/* Internal trig functions (used only if INTRIG is defined). These
standard functions may be enabled to obtain timings that reflect
the machine's floating point performance rather than the speed of
its trig function evaluation. */
#ifdef INTRIG
/* The following definitions should keep you from getting intro trouble
with compilers which don't let you redefine intrinsic functions. */
#define sin I_sin
#define cos I_cos
#define tan I_tan
#define sqrt I_sqrt
#define atan I_atan
#define atan2 I_atan2
#define asin I_asin
#define fabs(x) ((x < 0.0) ? -x : x)
#define pic 3.1415926535897932
/* Commonly used constants */
static double pi = pic,
twopi =pic * 2.0,
piover4 = pic / 4.0,
fouroverpi = 4.0 / pic,
piover2 = pic / 2.0;
/* Coefficients for ATAN evaluation */
static double atanc[] = {
0.0,
0.4636476090008061165,
0.7853981633974483094,
0.98279372324732906714,
1.1071487177940905022,
1.1902899496825317322,
1.2490457723982544262,
1.2924966677897852673,
1.3258176636680324644
};
/* aint(x) Return integer part of number. Truncates towards 0 */
double aint(x)
double x;
{
long l;
/* Note that this routine cannot handle the full floating point
number range. This function should be in the machine-dependent
floating point library! */
l = x;
if ((int)(-0.5) != 0 && l < 0 )
l++;
x = l;
return x;
}
/* sin(x) Return sine, x in radians */
static double sin(x)
double x;
{
int sign;
double y, r, z;
x = (((sign= (x < 0.0)) != 0) ? -x: x);
if (x > twopi)
x -= (aint(x / twopi) * twopi);
if (x > pi) {
x -= pi;
sign = !sign;
}
if (x > piover2)
x = pi - x;
if (x < piover4) {
y = x * fouroverpi;
z = y * y;
r = y * (((((((-0.202253129293E-13 * z + 0.69481520350522E-11) * z -
0.17572474176170806E-8) * z + 0.313361688917325348E-6) * z -
0.365762041821464001E-4) * z + 0.249039457019271628E-2) * z -
0.0807455121882807815) * z + 0.785398163397448310);
} else {
y = (piover2 - x) * fouroverpi;
z = y * y;
r = ((((((-0.38577620372E-12 * z + 0.11500497024263E-9) * z -
0.2461136382637005E-7) * z + 0.359086044588581953E-5) * z -
0.325991886926687550E-3) * z + 0.0158543442438154109) * z -
0.308425137534042452) * z + 1.0;
}
return sign ? -r : r;
}
/* cos(x) Return cosine, x in radians, by identity */
static double cos(x)
double x;
{
x = (x < 0.0) ? -x : x;
if (x > twopi) /* Do range reduction here to limit */
x = x - (aint(x / twopi) * twopi); /* roundoff on add of PI/2 */
return sin(x + piover2);
}
/* tan(x) Return tangent, x in radians, by identity */
static double tan(x)
double x;
{
return sin(x) / cos(x);
}
/* sqrt(x) Return square root. Initial guess, then Newton-
Raphson refinement */
double sqrt(x)
double x;
{
double c, cl, y;
int n;
if (x == 0.0)
return 0.0;
if (x < 0.0) {
fprintf(stderr,
"\nGood work! You tried to take the square root of %g",
x);
fprintf(stderr,
"\nunfortunately, that is too complex for me to handle.\n");
exit(1);
}
y = (0.154116 + 1.893872 * x) / (1.0 + 1.047988 * x);
c = (y - x / y) / 2.0;
cl = 0.0;
for (n = 50; c != cl && n--;) {
y = y - c;
cl = c;
c = (y - x / y) / 2.0;
}
return y;
}
/* atan(x) Return arctangent in radians,
range -pi/2 to pi/2 */
static double atan(x)
double x;
{
int sign, l, y;
double a, b, z;
x = (((sign = (x < 0.0)) != 0) ? -x : x);
l = 0;
if (x >= 4.0) {
l = -1;
x = 1.0 / x;
y = 0;
goto atl;
} else {
if (x < 0.25) {
y = 0;
goto atl;
}
}
y = aint(x / 0.5);
z = y * 0.5;
x = (x - z) / (x * z + 1);
atl:
z = x * x;
b = ((((893025.0 * z + 49116375.0) * z + 425675250.0) * z +
1277025750.0) * z + 1550674125.0) * z + 654729075.0;
a = (((13852575.0 * z + 216602100.0) * z + 891080190.0) * z +
1332431100.0) * z + 654729075.0;
a = (a / b) * x + atanc[y];
if (l)
a=piover2 - a;
return sign ? -a : a;
}
/* atan2(y,x) Return arctangent in radians of y/x,
range -pi to pi */
static double atan2(y, x)
double y, x;
{
double temp;
if (x == 0.0) {
if (y == 0.0) /* Special case: atan2(0,0) = 0 */
return 0.0;
else if (y > 0)
return piover2;
else
return -piover2;
}
temp = atan(y / x);
if (x < 0.0) {
if (y >= 0.0)
temp += pic;
else
temp -= pic;
}
return temp;
}
/* asin(x) Return arcsine in radians of x */
static double asin(x)
double x;
{
if (fabs(x)>1.0) {
fprintf(stderr,
"\nInverse trig functions lose much of their gloss when");
fprintf(stderr,
"\ntheir arguments are greater than 1, such as the");
fprintf(stderr,
"\nvalue %g you passed.\n", x);
exit(1);
}
return atan2(x, sqrt(1 - x * x));
}
#endif
/* Calculate passage through surface
If the variable PARAXIAL is true, the trace through the
surface will be done using the paraxial approximations.
Otherwise, the normal trigonometric trace will be done.
This routine takes the following inputs:
RADIUS_OF_CURVATURE Radius of curvature of surface
being crossed. If 0, surface is
plane.
OBJECT_DISTANCE Distance of object focus from
lens vertex. If 0, incoming
rays are parallel and
the following must be specified:
RAY_HEIGHT Height of ray from axis. Only
relevant if OBJECT.DISTANCE == 0
AXIS_SLOPE_ANGLE Angle incoming ray makes with axis
at intercept
FROM_INDEX Refractive index of medium being left
TO_INDEX Refractive index of medium being
entered.
The outputs are the following variables:
OBJECT_DISTANCE Distance from vertex to object focus
after refraction.
AXIS_SLOPE_ANGLE Angle incoming ray makes with axis
at intercept after refraction.
*/
static void transit_surface() {
double iang, /* Incidence angle */
rang, /* Refraction angle */
iang_sin, /* Incidence angle sin */
rang_sin, /* Refraction angle sin */
old_axis_slope_angle, sagitta;
if (paraxial) {
if (radius_of_curvature != 0.0) {
if (object_distance == 0.0) {
axis_slope_angle = 0.0;
iang_sin = ray_height / radius_of_curvature;
} else
iang_sin = ((object_distance -
radius_of_curvature) / radius_of_curvature) *
axis_slope_angle;
rang_sin = (from_index / to_index) *
iang_sin;
old_axis_slope_angle = axis_slope_angle;
axis_slope_angle = axis_slope_angle +
iang_sin - rang_sin;
if (object_distance != 0.0)
ray_height = object_distance * old_axis_slope_angle;
object_distance = ray_height / axis_slope_angle;
return;
}
object_distance = object_distance * (to_index / from_index);
axis_slope_angle = axis_slope_angle * (from_index / to_index);
return;
}
if (radius_of_curvature != 0.0) {
if (object_distance == 0.0) {
axis_slope_angle = 0.0;
iang_sin = ray_height / radius_of_curvature;
} else {
iang_sin = ((object_distance -
radius_of_curvature) / radius_of_curvature) *
sin(axis_slope_angle);
}
iang = asin(iang_sin);
rang_sin = (from_index / to_index) *
iang_sin;
old_axis_slope_angle = axis_slope_angle;
axis_slope_angle = axis_slope_angle +
iang - asin(rang_sin);
sagitta = sin((old_axis_slope_angle + iang) / 2.0);
sagitta = 2.0 * radius_of_curvature*sagitta*sagitta;
object_distance = ((radius_of_curvature * sin(
old_axis_slope_angle + iang)) *
cot(axis_slope_angle)) + sagitta;
return;
}
rang = -asin((from_index / to_index) *
sin(axis_slope_angle));
object_distance = object_distance * ((to_index *
cos(-rang)) / (from_index *
cos(axis_slope_angle)));
axis_slope_angle = -rang;
}
/* Perform ray trace in specific spectral line */
static void trace_line(line, ray_h)
int line;
double ray_h;
{
int i;
object_distance = 0.0;
ray_height = ray_h;
from_index = 1.0;
for (i = 1; i <= current_surfaces; i++) {
radius_of_curvature = s[i][1];
to_index = s[i][2];
if (to_index > 1.0)
to_index = to_index + ((spectral_line[4] -
spectral_line[line]) /
(spectral_line[3] - spectral_line[6])) * ((s[i][2] - 1.0) /
s[i][3]);
transit_surface();
from_index = to_index;
if (i < current_surfaces)
object_distance = object_distance - s[i][4];
}
}
/* Initialise when called the first time */
int main(argc, argv)
int argc;
char *argv[];
{
int i, j, k, errors;
double od_fline, od_cline;
#ifdef ACCURACY
long passes;
#endif
spectral_line[1] = 7621.0; /* A */
spectral_line[2] = 6869.955; /* B */
spectral_line[3] = 6562.816; /* C */
spectral_line[4] = 5895.944; /* D */
spectral_line[5] = 5269.557; /* E */
spectral_line[6] = 4861.344; /* F */
spectral_line[7] = 4340.477; /* G'*/
spectral_line[8] = 3968.494; /* H */
/* Process the number of iterations argument, if one is supplied. */
if (argc > 1) {
niter = atoi(argv[1]);
if (*argv[1] == '-' || niter < 1) {
printf("This is John Walker's floating point accuracy and\n");
printf("performance benchmark program. You call it with\n");
printf("\nfbench <itercount>\n\n");
printf("where <itercount> is the number of iterations\n");
printf("to be executed. Archival timings should be made\n");
printf("with the iteration count set so that roughly five\n");
printf("minutes of execution is timed.\n");
exit(0);
}
}
/* Load test case into working array */
clear_aperture = 4.0;
current_surfaces = 4;
for (i = 0; i < current_surfaces; i++)
for (j = 0; j < 4; j++)
s[i + 1][j + 1] = testcase[i][j];
#ifdef ACCURACY
printf("Beginning execution of floating point accuracy test...\n");
passes = 0;
#else
printf("Ready to begin John Walker's floating point accuracy\n");
printf("and performance benchmark. %d iterations will be made.\n\n",
niter);
printf("\nMeasured run time in seconds should be divided by %.f\n", niter / 1000.0);
printf("to normalise for reporting results. For archival results,\n");
printf("adjust iteration count so the benchmark runs about five minutes.\n\n");
//printf("Press return to begin benchmark:");
//gets(tbfr);
#endif
/* Perform ray trace the specified number of times. */
#ifdef ACCURACY
while (TRUE) {
passes++;
if ((passes % 100L) == 0) {
printf("Pass %ld.\n", passes);
}
#else
for (itercount = 0; itercount < niter; itercount++) {
#endif
for (paraxial = 0; paraxial <= 1; paraxial++) {
/* Do main trace in D light */
trace_line(4, clear_aperture / 2.0);
od_sa[paraxial][0] = object_distance;
od_sa[paraxial][1] = axis_slope_angle;
}
paraxial = FALSE;
/* Trace marginal ray in C */
trace_line(3, clear_aperture / 2.0);
od_cline = object_distance;
/* Trace marginal ray in F */
trace_line(6, clear_aperture / 2.0);
od_fline = object_distance;
aberr_lspher = od_sa[1][0] - od_sa[0][0];
aberr_osc = 1.0 - (od_sa[1][0] * od_sa[1][1]) /
(sin(od_sa[0][1]) * od_sa[0][0]);
aberr_lchrom = od_fline - od_cline;
max_lspher = sin(od_sa[0][1]);
/* D light */
max_lspher = 0.0000926 / (max_lspher * max_lspher);
max_osc = 0.0025;
max_lchrom = max_lspher;
#ifndef ACCURACY
}
//printf("Stop the timer:\007");
//gets(tbfr);
#endif
/* Now evaluate the accuracy of the results from the last ray trace */
sprintf(outarr[0], "%15s %21.11f %14.11f",
"Marginal ray", od_sa[0][0], od_sa[0][1]);
sprintf(outarr[1], "%15s %21.11f %14.11f",
"Paraxial ray", od_sa[1][0], od_sa[1][1]);
sprintf(outarr[2],
"Longitudinal spherical aberration: %16.11f",
aberr_lspher);
sprintf(outarr[3],
" (Maximum permissible): %16.11f",
max_lspher);
sprintf(outarr[4],
"Offense against sine condition (coma): %16.11f",
aberr_osc);
sprintf(outarr[5],
" (Maximum permissible): %16.11f",
max_osc);
sprintf(outarr[6],
"Axial chromatic aberration: %16.11f",
aberr_lchrom);
sprintf(outarr[7],
" (Maximum permissible): %16.11f",
max_lchrom);
/* Now compare the edited results with the master values from
reference executions of this program. */
errors = 0;
for (i = 0; i < 8; i++) {
if (strcmp(outarr[i], refarr[i]) != 0) {
#ifdef ACCURACY
printf("\nError in pass %ld for results on line %d...\n",
passes, i + 1);
#else
printf("\nError in results on line %d...\n", i + 1);
#endif
printf("Expected: \"%s\"\n", refarr[i]);
printf("Received: \"%s\"\n", outarr[i]);
printf("(Errors) ");
k = strlen(refarr[i]);
for (j = 0; j < k; j++) {
printf("%c", refarr[i][j] == outarr[i][j] ? ' ' : '^');
if (refarr[i][j] != outarr[i][j])
errors++;
}
printf("\n");
}
}
#ifdef ACCURACY
}
#else
if (errors > 0) {
printf("\n%d error%s in results. This is VERY SERIOUS.\n",
errors, errors > 1 ? "s" : "");
} else
printf("\nNo errors in results.\n");
#endif
return 0;
}
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