summaryrefslogtreecommitdiffstats
path: root/testsuites/samples/paranoia
diff options
context:
space:
mode:
authorJoel Sherrill <joel.sherrill@OARcorp.com>1995-05-11 17:39:37 +0000
committerJoel Sherrill <joel.sherrill@OARcorp.com>1995-05-11 17:39:37 +0000
commitac7d5ef06a6d6e8d84abbd1f0b82162725f98326 (patch)
tree9304cf759a73f2a1c6fd3191948f00e870af3787 /testsuites/samples/paranoia
downloadrtems-ac7d5ef06a6d6e8d84abbd1f0b82162725f98326.tar.bz2
Initial revision
Diffstat (limited to 'testsuites/samples/paranoia')
-rw-r--r--testsuites/samples/paranoia/init.c43
-rw-r--r--testsuites/samples/paranoia/paranoia.c2300
-rw-r--r--testsuites/samples/paranoia/paranoia.doc13
-rw-r--r--testsuites/samples/paranoia/system.h30
4 files changed, 2386 insertions, 0 deletions
diff --git a/testsuites/samples/paranoia/init.c b/testsuites/samples/paranoia/init.c
new file mode 100644
index 0000000000..4e9c9cde09
--- /dev/null
+++ b/testsuites/samples/paranoia/init.c
@@ -0,0 +1,43 @@
+/* Init
+ *
+ * This routine is the initialization task for this test program.
+ * It is called from init_exec and has the responsibility for creating
+ * and starting the tasks that make up the test. If the time of day
+ * clock is required for the test, it should also be set to a known
+ * value by this function.
+ *
+ * Input parameters: NONE
+ *
+ * Output parameters: NONE
+ *
+ * COPYRIGHT (c) 1989, 1990, 1991, 1992, 1993, 1994.
+ * On-Line Applications Research Corporation (OAR).
+ * All rights assigned to U.S. Government, 1994.
+ *
+ * This material may be reproduced by or for the U.S. Government pursuant
+ * to the copyright license under the clause at DFARS 252.227-7013. This
+ * notice must appear in all copies of this file and its derivatives.
+ *
+ * $Id$
+ */
+
+#include "system.h"
+#undef EXTERN
+#define EXTERN
+#include "conftbl.h"
+#include "gvar.h"
+#include "libcsupport.h"
+
+extern int paranoia(int, char **);
+
+char *args[2] = { "paranoia", 0 };
+
+rtems_task Init(
+ rtems_task_argument ignored
+)
+{
+ printf( "\n\n*** PARANOIA TEST ***\n" );
+ paranoia(1, args);
+ printf( "*** END OF PARANOIA TEST ***\n" );
+ exit( 0 );
+}
diff --git a/testsuites/samples/paranoia/paranoia.c b/testsuites/samples/paranoia/paranoia.c
new file mode 100644
index 0000000000..64ebdc7e5e
--- /dev/null
+++ b/testsuites/samples/paranoia/paranoia.c
@@ -0,0 +1,2300 @@
+/*
+ * RTEMS RCS Id: $Id$
+ *
+ * A C version of Kahan's Floating Point Test "Paranoia"
+ *
+ * Thos Sumner, UCSF, Feb. 1985
+ * David Gay, BTL, Jan. 1986
+ *
+ * This is a rewrite from the Pascal version by
+ *
+ * B. A. Wichmann, 18 Jan. 1985
+ *
+ * (and does NOT exhibit good C programming style).
+ *
+ * Sun May 16 18:21:51 MDT 1993 Jeffrey Wheat (cassidy@cygnus.com)
+ * Removed KR_headers defines, removed ANSI prototyping
+ * Cleaned up and reformated code. Added special CYGNUS
+ * "verbose" mode type messages (-DCYGNUS).
+ * Note: This code is VERY NASTY.
+ *
+ * Adjusted to use Standard C headers 19 Jan. 1992 (dmg);
+ * compile with -DKR_headers or insert
+ * #define KR_headers
+ * at the beginning if you have an old-style C compiler.
+ *
+ * (C) Apr 19 1983 in BASIC version by:
+ * Professor W. M. Kahan,
+ * 567 Evans Hall
+ * Electrical Engineering & Computer Science Dept.
+ * University of California
+ * Berkeley, California 94720
+ * USA
+ *
+ * converted to Pascal by:
+ * B. A. Wichmann
+ * National Physical Laboratory
+ * Teddington Middx
+ * TW11 OLW
+ * UK
+ *
+ * converted to C by:
+ *
+ * David M. Gay and Thos Sumner
+ * AT&T Bell Labs Computer Center, Rm. U-76
+ * 600 Mountain Avenue University of California
+ * Murray Hill, NJ 07974 San Francisco, CA 94143
+ * USA USA
+ *
+ * with simultaneous corrections to the Pascal source (reflected
+ * in the Pascal source available over netlib).
+ * [A couple of bug fixes from dgh = sun!dhough incorporated 31 July 1986.]
+ *
+ * Reports of results on various systems from all the versions
+ * of Paranoia are being collected by Richard Karpinski at the
+ * same address as Thos Sumner. This includes sample outputs,
+ * bug reports, and criticisms.
+ *
+ * You may copy this program freely if you acknowledge its source.
+ * Comments on the Pascal version to NPL, please.
+ *
+ *
+ * The C version catches signals from floating-point exceptions.
+ * If signal(SIGFPE,...) is unavailable in your environment, you may
+ * #define NOSIGNAL to comment out the invocations of signal.
+ *
+ * This source file is too big for some C compilers, but may be split
+ * into pieces. Comments containing "SPLIT" suggest convenient places
+ * for this splitting. At the end of these comments is an "ed script"
+ * (for the UNIX(tm) editor ed) that will do this splitting.
+ *
+ * By #defining SINGLE_PRECISION when you compile this source, you may
+ * obtain a single-precision C version of Paranoia.
+ *
+ * The following is from the introductory commentary from Wichmann's work:
+ *
+ * The BASIC program of Kahan is written in Microsoft BASIC using many
+ * facilities which have no exact analogy in Pascal. The Pascal
+ * version below cannot therefore be exactly the same. Rather than be
+ * a minimal transcription of the BASIC program, the Pascal coding
+ * follows the conventional style of block-structured languages. Hence
+ * the Pascal version could be useful in producing versions in other
+ * structured languages.
+ *
+ * Rather than use identifiers of minimal length (which therefore have
+ * little mnemonic significance), the Pascal version uses meaningful
+ * identifiers as follows [Note: A few changes have been made for C]:
+ *
+ *
+ * BASIC C BASIC C BASIC C
+ *
+ * A J S StickyBit
+ * A1 AInverse J0 NoErrors T
+ * B Radix [Failure] T0 Underflow
+ * B1 BInverse J1 NoErrors T2 ThirtyTwo
+ * B2 RadixD2 [SeriousDefect] T5 OneAndHalf
+ * B9 BMinusU2 J2 NoErrors T7 TwentySeven
+ * C [Defect] T8 TwoForty
+ * C1 CInverse J3 NoErrors U OneUlp
+ * D [Flaw] U0 UnderflowThreshold
+ * D4 FourD K PageNo U1
+ * E0 L Milestone U2
+ * E1 M V
+ * E2 Exp2 N V0
+ * E3 N1 V8
+ * E5 MinSqEr O Zero V9
+ * E6 SqEr O1 One W
+ * E7 MaxSqEr O2 Two X
+ * E8 O3 Three X1
+ * E9 O4 Four X8
+ * F1 MinusOne O5 Five X9 Random1
+ * F2 Half O8 Eight Y
+ * F3 Third O9 Nine Y1
+ * F6 P Precision Y2
+ * F9 Q Y9 Random2
+ * G1 GMult Q8 Z
+ * G2 GDiv Q9 Z0 PseudoZero
+ * G3 GAddSub R Z1
+ * H R1 RMult Z2
+ * H1 HInverse R2 RDiv Z9
+ * I R3 RAddSub
+ * IO NoTrials R4 RSqrt
+ * I3 IEEE R9 Random9
+ *
+ * SqRWrng
+ *
+ * All the variables in BASIC are true variables and in consequence,
+ * the program is more difficult to follow since the "constants" must
+ * be determined (the glossary is very helpful). The Pascal version
+ * uses Real constants, but checks are added to ensure that the values
+ * are correctly converted by the compiler.
+ *
+ * The major textual change to the Pascal version apart from the
+ * identifiersis that named procedures are used, inserting parameters
+ * wherehelpful. New procedures are also introduced. The
+ * correspondence is as follows:
+ *
+ *
+ * BASIC Pascal
+ * lines
+ *
+ * 90- 140 Pause
+ * 170- 250 Instructions
+ * 380- 460 Heading
+ * 480- 670 Characteristics
+ * 690- 870 History
+ * 2940-2950 Random
+ * 3710-3740 NewD
+ * 4040-4080 DoesYequalX
+ * 4090-4110 PrintIfNPositive
+ * 4640-4850 TestPartialUnderflow
+ *
+*/
+
+#include <stdio.h>
+#include <string.h>
+
+/*
+ * To compile this on host using only libm from newlib (and using host libc)
+ * do:
+ * gcc -g -DNEED_REENT -DCYGNUS paranoia.c .../newlib-1.6/newlib/libm.a
+ */
+
+#ifdef NEED_REENT
+#include "reent.h"
+struct _reent libm_reent = _REENT_INIT(libm_reent);
+struct _reent *_impure_ptr = &libm_reent;
+#endif
+
+#ifndef NOSIGNAL
+#include <signal.h>
+#include <setjmp.h>
+#else /* NOSIGNAL */
+#define longjmp(e,v)
+#define setjmp(e) 0
+#define jmp_buf int
+#endif /* NOSIGNAL */
+
+#ifdef SINGLE_PRECISION
+#define FLOAT float
+#define FABS(x) (float)fabs((double)(x))
+#define FLOOR(x) (float)floor((double)(x))
+#define LOG(x) (float)log((double)(x))
+#define POW(x,y) (float)pow((double)(x),(double)(y))
+#define SQRT(x) (float)sqrt((double)(x))
+#else /* !SINGLE_PRECISION */
+#define FLOAT double
+#define FABS(x) fabs(x)
+#define FLOOR(x) floor(x)
+#define LOG(x) log(x)
+#define POW(x,y) pow(x,y)
+#define SQRT(x) sqrt(x)
+#endif /* SINGLE_PRECISION */
+
+jmp_buf ovfl_buf;
+extern double fabs (), floor (), log (), pow (), sqrt ();
+extern void exit ();
+typedef void (*Sig_type) ();
+FLOAT Sign (), Random ();
+extern void BadCond ();
+extern void SqXMinX ();
+extern void TstCond ();
+extern void notify ();
+extern int read ();
+extern void Characteristics ();
+extern void Heading ();
+extern void History ();
+extern void Instructions ();
+extern void IsYeqX ();
+extern void NewD ();
+extern void Pause ();
+extern void PrintIfNPositive ();
+extern void SR3750 ();
+extern void SR3980 ();
+extern void TstPtUf ();
+
+Sig_type sigsave;
+
+#define KEYBOARD 0
+
+FLOAT Radix, BInvrse, RadixD2, BMinusU2;
+
+/*Small floating point constants.*/
+FLOAT Zero = 0.0;
+FLOAT Half = 0.5;
+FLOAT One = 1.0;
+FLOAT Two = 2.0;
+FLOAT Three = 3.0;
+FLOAT Four = 4.0;
+FLOAT Five = 5.0;
+FLOAT Eight = 8.0;
+FLOAT Nine = 9.0;
+FLOAT TwentySeven = 27.0;
+FLOAT ThirtyTwo = 32.0;
+FLOAT TwoForty = 240.0;
+FLOAT MinusOne = -1.0;
+FLOAT OneAndHalf = 1.5;
+
+/*Integer constants*/
+int NoTrials = 20; /*Number of tests for commutativity. */
+#define False 0
+#define True 1
+
+/*
+ * Definitions for declared types
+ * Guard == (Yes, No);
+ * Rounding == (Chopped, Rounded, Other);
+ * Message == packed array [1..40] of char;
+ * Class == (Flaw, Defect, Serious, Failure);
+ */
+#define Yes 1
+#define No 0
+#define Chopped 2
+#define Rounded 1
+#define Other 0
+#define Flaw 3
+#define Defect 2
+#define Serious 1
+#define Failure 0
+typedef int Guard, Rounding, Class;
+typedef char Message;
+
+/* Declarations of Variables */
+int Indx;
+char ch[8];
+FLOAT AInvrse, A1;
+FLOAT C, CInvrse;
+FLOAT D, FourD;
+FLOAT E0, E1, Exp2, E3, MinSqEr;
+FLOAT SqEr, MaxSqEr, E9;
+FLOAT Third;
+FLOAT F6, F9;
+FLOAT H, HInvrse;
+int I;
+FLOAT StickyBit, J;
+FLOAT MyZero;
+FLOAT Precision;
+FLOAT Q, Q9;
+FLOAT R, Random9;
+FLOAT T, Underflow, S;
+FLOAT OneUlp, UfThold, U1, U2;
+FLOAT V, V0, V9;
+FLOAT W;
+FLOAT X, X1, X2, X8, Random1;
+FLOAT Y, Y1, Y2, Random2;
+FLOAT Z, PseudoZero, Z1, Z2, Z9;
+int ErrCnt[4];
+int fpecount;
+int Milestone;
+int PageNo;
+int M, N, N1;
+Guard GMult, GDiv, GAddSub;
+Rounding RMult, RDiv, RAddSub, RSqrt;
+int Break, Done, NotMonot, Monot, Anomaly, IEEE, SqRWrng, UfNGrad;
+
+/* Computed constants.
+ * U1 gap below 1.0, i.e, 1.0 - U1 is next number below 1.0
+ * U2 gap above 1.0, i.e, 1.0 + U2 is next number above 1.0
+ */
+
+int batchmode; /* global batchmode test */
+
+/* program name and version variables and macro */
+char *temp;
+char *program_name;
+char *program_vers;
+
+#ifndef VERSION
+#define VERSION "1.1 [cygnus]"
+#endif /* VERSION */
+
+#define basename(cp) ((temp=(char *)strrchr((cp), '/')) ? temp+1 : (cp))
+
+#ifndef BATCHMODE
+# ifdef CYGNUS
+# define BATCHMODE
+# endif
+#endif
+
+/* floating point exception receiver */
+void
+_sigfpe (x)
+int x;
+{
+ fpecount++;
+ printf ("\n* * * FLOATING-POINT ERROR %d * * *\n", x);
+ fflush (stdout);
+ if (sigsave) {
+#ifndef NOSIGNAL
+ signal (SIGFPE, sigsave);
+#endif /* NOSIGNAL */
+ sigsave = 0;
+ longjmp (ovfl_buf, 1);
+ }
+ exit (1);
+}
+
+#ifdef NOMAIN
+#define main paranoia
+#endif
+
+int
+main (argc, argv)
+int argc;
+char **argv;
+{
+ /* First two assignments use integer right-hand sides. */
+ Zero = 0;
+ One = 1;
+ Two = One + One;
+ Three = Two + One;
+ Four = Three + One;
+ Five = Four + One;
+ Eight = Four + Four;
+ Nine = Three * Three;
+ TwentySeven = Nine * Three;
+ ThirtyTwo = Four * Eight;
+ TwoForty = Four * Five * Three * Four;
+ MinusOne = -One;
+ Half = One / Two;
+ OneAndHalf = One + Half;
+ ErrCnt[Failure] = 0;
+ ErrCnt[Serious] = 0;
+ ErrCnt[Defect] = 0;
+ ErrCnt[Flaw] = 0;
+ PageNo = 1;
+
+#ifdef BATCHMODE
+ batchmode = 1; /* run test in batchmode? */
+#else /* !BATCHMODE */
+ batchmode = 0; /* run test interactively */
+#endif /* BATCHMODE */
+
+ program_name = basename (argv[0]);
+ program_vers = VERSION;
+
+ printf ("%s version %s\n", program_name, program_vers);
+
+ /*=============================================*/
+ Milestone = 0;
+ /*=============================================*/
+#ifndef NOSIGNAL
+ signal (SIGFPE, _sigfpe);
+#endif
+
+ if (!batchmode) {
+ Instructions ();
+ Pause ();
+ Heading ();
+ Instructions ();
+ Pause ();
+ Heading ();
+ Pause ();
+ Characteristics ();
+ Pause ();
+ History ();
+ Pause ();
+ }
+
+ /*=============================================*/
+ Milestone = 7;
+ /*=============================================*/
+ printf ("Program is now RUNNING tests on small integers:\n");
+ TstCond (Failure, (Zero + Zero == Zero) && (One - One == Zero)
+ && (One > Zero) && (One + One == Two),
+ "0+0 != 0, 1-1 != 0, 1 <= 0, or 1+1 != 2");
+ Z = -Zero;
+ if (Z != 0.0) {
+ ErrCnt[Failure] = ErrCnt[Failure] + 1;
+ printf ("Comparison alleges that -0.0 is Non-zero!\n");
+ U1 = 0.001;
+ Radix = 1;
+ TstPtUf ();
+ }
+ TstCond (Failure, (Three == Two + One) && (Four == Three + One)
+ && (Four + Two * (-Two) == Zero)
+ && (Four - Three - One == Zero),
+ "3 != 2+1, 4 != 3+1, 4+2*(-2) != 0, or 4-3-1 != 0");
+ TstCond (Failure, (MinusOne == (0 - One))
+ && (MinusOne + One == Zero) && (One + MinusOne == Zero)
+ && (MinusOne + FABS (One) == Zero)
+ && (MinusOne + MinusOne * MinusOne == Zero),
+ "-1+1 != 0, (-1)+abs(1) != 0, or -1+(-1)*(-1) != 0");
+ TstCond (Failure, Half + MinusOne + Half == Zero,
+ "1/2 + (-1) + 1/2 != 0");
+ /*=============================================*/
+ Milestone = 10;
+ /*=============================================*/
+ TstCond (Failure, (Nine == Three * Three)
+ && (TwentySeven == Nine * Three) && (Eight == Four + Four)
+ && (ThirtyTwo == Eight * Four)
+ && (ThirtyTwo - TwentySeven - Four - One == Zero),
+ "9 != 3*3, 27 != 9*3, 32 != 8*4, or 32-27-4-1 != 0");
+ TstCond (Failure, (Five == Four + One) &&
+ (TwoForty == Four * Five * Three * Four)
+ && (TwoForty / Three - Four * Four * Five == Zero)
+ && (TwoForty / Four - Five * Three * Four == Zero)
+ && (TwoForty / Five - Four * Three * Four == Zero),
+ "5 != 4+1, 240/3 != 80, 240/4 != 60, or 240/5 != 48");
+ if (ErrCnt[Failure] == 0) {
+ printf ("-1, 0, 1/2, 1, 2, 3, 4, 5, 9, 27, 32 & 240 are O.K.\n");
+ printf ("\n");
+ }
+ printf ("Searching for Radix and Precision.\n");
+ W = One;
+ do {
+ W = W + W;
+ Y = W + One;
+ Z = Y - W;
+ Y = Z - One;
+ }
+ while (MinusOne + FABS (Y) < Zero);
+ /*.. now W is just big enough that |((W+1)-W)-1| >= 1 ...*/
+ Precision = Zero;
+ Y = One;
+ do {
+ Radix = W + Y;
+ Y = Y + Y;
+ Radix = Radix - W;
+ }
+ while (Radix == Zero);
+ if (Radix < Two)
+ Radix = One;
+ printf ("Radix = %f .\n", Radix);
+ if (Radix != 1) {
+ W = One;
+ do {
+ Precision = Precision + One;
+ W = W * Radix;
+ Y = W + One;
+ }
+ while ((Y - W) == One);
+ }
+ /*... now W == Radix^Precision is barely too big to satisfy (W+1)-W == 1
+ ...*/
+ U1 = One / W;
+ U2 = Radix * U1;
+ printf ("Closest relative separation found is U1 = %.7e .\n\n", U1);
+ printf ("Recalculating radix and precision\n ");
+
+ /*save old values*/
+ E0 = Radix;
+ E1 = U1;
+ E9 = U2;
+ E3 = Precision;
+
+ X = Four / Three;
+ Third = X - One;
+ F6 = Half - Third;
+ X = F6 + F6;
+ X = FABS (X - Third);
+ if (X < U2)
+ X = U2;
+
+ /*... now X = (unknown no.) ulps of 1+...*/
+ do {
+ U2 = X;
+ Y = Half * U2 + ThirtyTwo * U2 * U2;
+ Y = One + Y;
+ X = Y - One;
+ }
+ while (!((U2 <= X) || (X <= Zero)));
+
+ /*... now U2 == 1 ulp of 1 + ... */
+ X = Two / Three;
+ F6 = X - Half;
+ Third = F6 + F6;
+ X = Third - Half;
+ X = FABS (X + F6);
+ if (X < U1)
+ X = U1;
+
+ /*... now X == (unknown no.) ulps of 1 -... */
+ do {
+ U1 = X;
+ Y = Half * U1 + ThirtyTwo * U1 * U1;
+ Y = Half - Y;
+ X = Half + Y;
+ Y = Half - X;
+ X = Half + Y;
+ }
+ while (!((U1 <= X) || (X <= Zero)));
+ /*... now U1 == 1 ulp of 1 - ... */
+ if (U1 == E1)
+ printf ("confirms closest relative separation U1 .\n");
+ else
+ printf ("gets better closest relative separation U1 = %.7e .\n", U1);
+ W = One / U1;
+ F9 = (Half - U1) + Half;
+ Radix = FLOOR (0.01 + U2 / U1);
+ if (Radix == E0)
+ printf ("Radix confirmed.\n");
+ else
+ printf ("MYSTERY: recalculated Radix = %.7e .\n", Radix);
+ TstCond (Defect, Radix <= Eight + Eight,
+ "Radix is too big: roundoff problems");
+ TstCond (Flaw, (Radix == Two) || (Radix == 10)
+ || (Radix == One), "Radix is not as good as 2 or 10");
+ /*=============================================*/
+ Milestone = 20;
+ /*=============================================*/
+ TstCond (Failure, F9 - Half < Half,
+ "(1-U1)-1/2 < 1/2 is FALSE, prog. fails?");
+ X = F9;
+ I = 1;
+ Y = X - Half;
+ Z = Y - Half;
+ TstCond (Failure, (X != One)
+ || (Z == Zero), "Comparison is fuzzy,X=1 but X-1/2-1/2 != 0");
+ X = One + U2;
+ I = 0;
+ /*=============================================*/
+ Milestone = 25;
+ /*=============================================*/
+ /*... BMinusU2 = nextafter(Radix, 0) */
+ BMinusU2 = Radix - One;
+ BMinusU2 = (BMinusU2 - U2) + One;
+ /* Purify Integers */
+ if (Radix != One) {
+ X = -TwoForty * LOG (U1) / LOG (Radix);
+ Y = FLOOR (Half + X);
+ if (FABS (X - Y) * Four < One)
+ X = Y;
+ Precision = X / TwoForty;
+ Y = FLOOR (Half + Precision);
+ if (FABS (Precision - Y) * TwoForty < Half)
+ Precision = Y;
+ }
+ if ((Precision != FLOOR (Precision)) || (Radix == One)) {
+ printf ("Precision cannot be characterized by an Integer number\n");
+ printf ("of significant digits but, by itself, this is a minor flaw.\n");
+ }
+ if (Radix == One)
+ printf ("logarithmic encoding has precision characterized solely by U1.\n");
+ else
+ printf ("The number of significant digits of the Radix is %f .\n",
+ Precision);
+ TstCond (Serious, U2 * Nine * Nine * TwoForty < One,
+ "Precision worse than 5 decimal figures ");
+ /*=============================================*/
+ Milestone = 30;
+ /*=============================================*/
+ /* Test for extra-precise subepressions */
+ X = FABS (((Four / Three - One) - One / Four) * Three - One / Four);
+ do {
+ Z2 = X;
+ X = (One + (Half * Z2 + ThirtyTwo * Z2 * Z2)) - One;
+ }
+ while (!((Z2 <= X) || (X <= Zero)));
+ X = Y = Z = FABS ((Three / Four - Two / Three) * Three - One / Four);
+ do {
+ Z1 = Z;
+ Z = (One / Two - ((One / Two - (Half * Z1 + ThirtyTwo * Z1 * Z1))
+ + One / Two)) + One / Two;
+ }
+ while (!((Z1 <= Z) || (Z <= Zero)));
+ do {
+ do {
+ Y1 = Y;
+ Y = (Half - ((Half - (Half * Y1 + ThirtyTwo * Y1 * Y1)) + Half
+ )) + Half;
+ }
+ while (!((Y1 <= Y) || (Y <= Zero)));
+ X1 = X;
+ X = ((Half * X1 + ThirtyTwo * X1 * X1) - F9) + F9;
+ }
+ while (!((X1 <= X) || (X <= Zero)));
+ if ((X1 != Y1) || (X1 != Z1)) {
+ BadCond (Serious, "Disagreements among the values X1, Y1, Z1,\n");
+ printf ("respectively %.7e, %.7e, %.7e,\n", X1, Y1, Z1);
+ printf ("are symptoms of inconsistencies introduced\n");
+ printf ("by extra-precise evaluation of arithmetic subexpressions.\n");
+ notify ("Possibly some part of this");
+ if ((X1 == U1) || (Y1 == U1) || (Z1 == U1))
+ printf (
+ "That feature is not tested further by this program.\n");
+ } else {
+ if ((Z1 != U1) || (Z2 != U2)) {
+ if ((Z1 >= U1) || (Z2 >= U2)) {
+ BadCond (Failure, "");
+ notify ("Precision");
+ printf ("\tU1 = %.7e, Z1 - U1 = %.7e\n", U1, Z1 - U1);
+ printf ("\tU2 = %.7e, Z2 - U2 = %.7e\n", U2, Z2 - U2);
+ } else {
+ if ((Z1 <= Zero) || (Z2 <= Zero)) {
+ printf ("Because of unusual Radix = %f", Radix);
+ printf (", or exact rational arithmetic a result\n");
+ printf ("Z1 = %.7e, or Z2 = %.7e ", Z1, Z2);
+ notify ("of an\nextra-precision");
+ }
+ if (Z1 != Z2 || Z1 > Zero) {
+ X = Z1 / U1;
+ Y = Z2 / U2;
+ if (Y > X)
+ X = Y;
+ Q = -LOG (X);
+ printf ("Some subexpressions appear to be calculated extra\n");
+ printf ("precisely with about %g extra B-digits, i.e.\n",
+ (Q / LOG (Radix)));
+ printf ("roughly %g extra significant decimals.\n",
+ Q / LOG (10.));
+ }
+ printf ("That feature is not tested further by this program.\n");
+ }
+ }
+ }
+ Pause ();
+ /*=============================================*/
+ Milestone = 35;
+ /*=============================================*/
+ if (Radix >= Two) {
+ X = W / (Radix * Radix);
+ Y = X + One;
+ Z = Y - X;
+ T = Z + U2;
+ X = T - Z;
+ TstCond (Failure, X == U2,
+ "Subtraction is not normalized X=Y,X+Z != Y+Z!");
+ if (X == U2)
+ printf (
+ "Subtraction appears to be normalized, as it should be.");
+ }
+ printf ("\nChecking for guard digit in *, /, and -.\n");
+ Y = F9 * One;
+ Z = One * F9;
+ X = F9 - Half;
+ Y = (Y - Half) - X;
+ Z = (Z - Half) - X;
+ X = One + U2;
+ T = X * Radix;
+ R = Radix * X;
+ X = T - Radix;
+ X = X - Radix * U2;
+ T = R - Radix;
+ T = T - Radix * U2;
+ X = X * (Radix - One);
+ T = T * (Radix - One);
+ if ((X == Zero) && (Y == Zero) && (Z == Zero) && (T == Zero))
+ GMult = Yes;
+ else {
+ GMult = No;
+ TstCond (Serious, False,
+ "* lacks a Guard Digit, so 1*X != X");
+ }
+ Z = Radix * U2;
+ X = One + Z;
+ Y = FABS ((X + Z) - X * X) - U2;
+ X = One - U2;
+ Z = FABS ((X - U2) - X * X) - U1;
+ TstCond (Failure, (Y <= Zero)
+ && (Z <= Zero), "* gets too many final digits wrong.\n");
+ Y = One - U2;
+ X = One + U2;
+ Z = One / Y;
+ Y = Z - X;
+ X = One / Three;
+ Z = Three / Nine;
+ X = X - Z;
+ T = Nine / TwentySeven;
+ Z = Z - T;
+ TstCond (Defect, X == Zero && Y == Zero && Z == Zero,
+ "Division lacks a Guard Digit, so error can exceed 1 ulp\n\
+or 1/3 and 3/9 and 9/27 may disagree");
+ Y = F9 / One;
+ X = F9 - Half;
+ Y = (Y - Half) - X;
+ X = One + U2;
+ T = X / One;
+ X = T - X;
+ if ((X == Zero) && (Y == Zero) && (Z == Zero))
+ GDiv = Yes;
+ else {
+ GDiv = No;
+ TstCond (Serious, False,
+ "Division lacks a Guard Digit, so X/1 != X");
+ }
+ X = One / (One + U2);
+ Y = X - Half - Half;
+ TstCond (Serious, Y < Zero,
+ "Computed value of 1/1.000..1 >= 1");
+ X = One - U2;
+ Y = One + Radix * U2;
+ Z = X * Radix;
+ T = Y * Radix;
+ R = Z / Radix;
+ StickyBit = T / Radix;
+ X = R - X;
+ Y = StickyBit - Y;
+ TstCond (Failure, X == Zero && Y == Zero,
+ "* and/or / gets too many last digits wrong");
+ Y = One - U1;
+ X = One - F9;
+ Y = One - Y;
+ T = Radix - U2;
+ Z = Radix - BMinusU2;
+ T = Radix - T;
+ if ((X == U1) && (Y == U1) && (Z == U2) && (T == U2))
+ GAddSub = Yes;
+ else {
+ GAddSub = No;
+ TstCond (Serious, False,
+ "- lacks Guard Digit, so cancellation is obscured");
+ }
+ if (F9 != One && F9 - One >= Zero) {
+ BadCond (Serious, "comparison alleges (1-U1) < 1 although\n");
+ printf (" subtraction yields (1-U1) - 1 = 0 , thereby vitiating\n");
+ printf (" such precautions against division by zero as\n");
+ printf (" ... if (X == 1.0) {.....} else {.../(X-1.0)...}\n");
+ }
+ if (GMult == Yes && GDiv == Yes && GAddSub == Yes)
+ printf (
+ " *, /, and - appear to have guard digits, as they should.\n");
+ /*=============================================*/
+ Milestone = 40;
+ /*=============================================*/
+ Pause ();
+ printf ("Checking rounding on multiply, divide and add/subtract.\n");
+ RMult = Other;
+ RDiv = Other;
+ RAddSub = Other;
+ RadixD2 = Radix / Two;
+ A1 = Two;
+ Done = False;
+ do {
+ AInvrse = Radix;
+ do {
+ X = AInvrse;
+ AInvrse = AInvrse / A1;
+ }
+ while (!(FLOOR (AInvrse) != AInvrse));
+ Done = (X == One) || (A1 > Three);
+ if (!Done)
+ A1 = Nine + One;
+ }
+ while (!(Done));
+ if (X == One)
+ A1 = Radix;
+ AInvrse = One / A1;
+ X = A1;
+ Y = AInvrse;
+ Done = False;
+ do {
+ Z = X * Y - Half;
+ TstCond (Failure, Z == Half,
+ "X * (1/X) differs from 1");
+ Done = X == Radix;
+ X = Radix;
+ Y = One / X;
+ }
+ while (!(Done));
+ Y2 = One + U2;
+ Y1 = One - U2;
+ X = OneAndHalf - U2;
+ Y = OneAndHalf + U2;
+ Z = (X - U2) * Y2;
+ T = Y * Y1;
+ Z = Z - X;
+ T = T - X;
+ X = X * Y2;
+ Y = (Y + U2) * Y1;
+ X = X - OneAndHalf;
+ Y = Y - OneAndHalf;
+ if ((X == Zero) && (Y == Zero) && (Z == Zero) && (T <= Zero)) {
+ X = (OneAndHalf + U2) * Y2;
+ Y = OneAndHalf - U2 - U2;
+ Z = OneAndHalf + U2 + U2;
+ T = (OneAndHalf - U2) * Y1;
+ X = X - (Z + U2);
+ StickyBit = Y * Y1;
+ S = Z * Y2;
+ T = T - Y;
+ Y = (U2 - Y) + StickyBit;
+ Z = S - (Z + U2 + U2);
+ StickyBit = (Y2 + U2) * Y1;
+ Y1 = Y2 * Y1;
+ StickyBit = StickyBit - Y2;
+ Y1 = Y1 - Half;
+ if ((X == Zero) && (Y == Zero) && (Z == Zero) && (T == Zero)
+ && (StickyBit == Zero) && (Y1 == Half)) {
+ RMult = Rounded;
+ printf ("Multiplication appears to round correctly.\n");
+ } else if ((X + U2 == Zero) && (Y < Zero) && (Z + U2 == Zero)
+ && (T < Zero) && (StickyBit + U2 == Zero)
+ && (Y1 < Half)) {
+ RMult = Chopped;
+ printf ("Multiplication appears to chop.\n");
+ } else
+ printf ("* is neither chopped nor correctly rounded.\n");
+ if ((RMult == Rounded) && (GMult == No))
+ notify ("Multiplication");
+ } else
+ printf ("* is neither chopped nor correctly rounded.\n");
+ /*=============================================*/
+ Milestone = 45;
+ /*=============================================*/
+ Y2 = One + U2;
+ Y1 = One - U2;
+ Z = OneAndHalf + U2 + U2;
+ X = Z / Y2;
+ T = OneAndHalf - U2 - U2;
+ Y = (T - U2) / Y1;
+ Z = (Z + U2) / Y2;
+ X = X - OneAndHalf;
+ Y = Y - T;
+ T = T / Y1;
+ Z = Z - (OneAndHalf + U2);
+ T = (U2 - OneAndHalf) + T;
+ if (!((X > Zero) || (Y > Zero) || (Z > Zero) || (T > Zero))) {
+ X = OneAndHalf / Y2;
+ Y = OneAndHalf - U2;
+ Z = OneAndHalf + U2;
+ X = X - Y;
+ T = OneAndHalf / Y1;
+ Y = Y / Y1;
+ T = T - (Z + U2);
+ Y = Y - Z;
+ Z = Z / Y2;
+ Y1 = (Y2 + U2) / Y2;
+ Z = Z - OneAndHalf;
+ Y2 = Y1 - Y2;
+ Y1 = (F9 - U1) / F9;
+ if ((X == Zero) && (Y == Zero) && (Z == Zero) && (T == Zero)
+ && (Y2 == Zero) && (Y2 == Zero)
+ && (Y1 - Half == F9 - Half)) {
+ RDiv = Rounded;
+ printf ("Division appears to round correctly.\n");
+ if (GDiv == No)
+ notify ("Division");
+ } else if ((X < Zero) && (Y < Zero) && (Z < Zero) && (T < Zero)
+ && (Y2 < Zero) && (Y1 - Half < F9 - Half)) {
+ RDiv = Chopped;
+ printf ("Division appears to chop.\n");
+ }
+ }
+ if (RDiv == Other)
+ printf ("/ is neither chopped nor correctly rounded.\n");
+ BInvrse = One / Radix;
+ TstCond (Failure, (BInvrse * Radix - Half == Half),
+ "Radix * ( 1 / Radix ) differs from 1");
+ /*=============================================*/
+ Milestone = 50;
+ /*=============================================*/
+ TstCond (Failure, ((F9 + U1) - Half == Half)
+ && ((BMinusU2 + U2) - One == Radix - One),
+ "Incomplete carry-propagation in Addition");
+ X = One - U1 * U1;
+ Y = One + U2 * (One - U2);
+ Z = F9 - Half;
+ X = (X - Half) - Z;
+ Y = Y - One;
+ if ((X == Zero) && (Y == Zero)) {
+ RAddSub = Chopped;
+ printf ("Add/Subtract appears to be chopped.\n");
+ }
+ if (GAddSub == Yes) {
+ X = (Half + U2) * U2;
+ Y = (Half - U2) * U2;
+ X = One + X;
+ Y = One + Y;
+ X = (One + U2) - X;
+ Y = One - Y;
+ if ((X == Zero) && (Y == Zero)) {
+ X = (Half + U2) * U1;
+ Y = (Half - U2) * U1;
+ X = One - X;
+ Y = One - Y;
+ X = F9 - X;
+ Y = One - Y;
+ if ((X == Zero) && (Y == Zero)) {
+ RAddSub = Rounded;
+ printf ("Addition/Subtraction appears to round correctly.\n");
+ if (GAddSub == No)
+ notify ("Add/Subtract");
+ } else
+ printf ("Addition/Subtraction neither rounds nor chops.\n");
+ } else
+ printf ("Addition/Subtraction neither rounds nor chops.\n");
+ } else
+ printf ("Addition/Subtraction neither rounds nor chops.\n");
+ S = One;
+ X = One + Half * (One + Half);
+ Y = (One + U2) * Half;
+ Z = X - Y;
+ T = Y - X;
+ StickyBit = Z + T;
+ if (StickyBit != Zero) {
+ S = Zero;
+ BadCond (Flaw, "(X - Y) + (Y - X) is non zero!\n");
+ }
+ StickyBit = Zero;
+ if ((GMult == Yes) && (GDiv == Yes) && (GAddSub == Yes)
+ && (RMult == Rounded) && (RDiv == Rounded)
+ && (RAddSub == Rounded) && (FLOOR (RadixD2) == RadixD2)) {
+ printf ("Checking for sticky bit.\n");
+ X = (Half + U1) * U2;
+ Y = Half * U2;
+ Z = One + Y;
+ T = One + X;
+ if ((Z - One <= Zero) && (T - One >= U2)) {
+ Z = T + Y;
+ Y = Z - X;
+ if ((Z - T >= U2) && (Y - T == Zero)) {
+ X = (Half + U1) * U1;
+ Y = Half * U1;
+ Z = One - Y;
+ T = One - X;
+ if ((Z - One == Zero) && (T - F9 == Zero)) {
+ Z = (Half - U1) * U1;
+ T = F9 - Z;
+ Q = F9 - Y;
+ if ((T - F9 == Zero) && (F9 - U1 - Q == Zero)) {
+ Z = (One + U2) * OneAndHalf;
+ T = (OneAndHalf + U2) - Z + U2;
+ X = One + Half / Radix;
+ Y = One + Radix * U2;
+ Z = X * Y;
+ if (T == Zero && X + Radix * U2 - Z == Zero) {
+ if (Radix != Two) {
+ X = Two + U2;
+ Y = X / Two;
+ if ((Y - One == Zero))
+ StickyBit = S;
+ } else
+ StickyBit = S;
+ }
+ }
+ }
+ }
+ }
+ }
+ if (StickyBit == One)
+ printf ("Sticky bit apparently used correctly.\n");
+ else
+ printf ("Sticky bit used incorrectly or not at all.\n");
+ TstCond (Flaw, !(GMult == No || GDiv == No || GAddSub == No ||
+ RMult == Other || RDiv == Other || RAddSub == Other),
+ "lack(s) of guard digits or failure(s) to correctly round or chop\n\
+(noted above) count as one flaw in the final tally below");
+ /*=============================================*/
+ Milestone = 60;
+ /*=============================================*/
+ printf ("\n");
+ printf ("Does Multiplication commute? ");
+ printf ("Testing on %d random pairs.\n", NoTrials);
+ Random9 = SQRT (3.0);
+ Random1 = Third;
+ I = 1;
+ do {
+ X = Random ();
+ Y = Random ();
+ Z9 = Y * X;
+ Z = X * Y;
+ Z9 = Z - Z9;
+ I = I + 1;
+ }
+ while (!((I > NoTrials) || (Z9 != Zero)));
+ if (I == NoTrials) {
+ Random1 = One + Half / Three;
+ Random2 = (U2 + U1) + One;
+ Z = Random1 * Random2;
+ Y = Random2 * Random1;
+ Z9 = (One + Half / Three) * ((U2 + U1) + One) - (One + Half /
+ Three) * ((U2 + U1) + One);
+ }
+ if (!((I == NoTrials) || (Z9 == Zero)))
+ BadCond (Defect, "X * Y == Y * X trial fails.\n");
+ else
+ printf (" No failures found in %d integer pairs.\n", NoTrials);
+ /*=============================================*/
+ Milestone = 70;
+ /*=============================================*/
+ printf ("\nRunning test of square root(x).\n");
+ TstCond (Failure, (Zero == SQRT (Zero))
+ && (-Zero == SQRT (-Zero))
+ && (One == SQRT (One)), "Square root of 0.0, -0.0 or 1.0 wrong");
+ MinSqEr = Zero;
+ MaxSqEr = Zero;
+ J = Zero;
+ X = Radix;
+ OneUlp = U2;
+ SqXMinX (Serious);
+ X = BInvrse;
+ OneUlp = BInvrse * U1;
+ SqXMinX (Serious);
+ X = U1;
+ OneUlp = U1 * U1;
+ SqXMinX (Serious);
+ if (J != Zero)
+ Pause ();
+ printf ("Testing if sqrt(X * X) == X for %d Integers X.\n", NoTrials);
+ J = Zero;
+ X = Two;
+ Y = Radix;
+ if ((Radix != One))
+ do {
+ X = Y;
+ Y = Radix * Y;
+ }
+ while (!((Y - X >= NoTrials)));
+ OneUlp = X * U2;
+ I = 1;
+ while (I <= NoTrials) {
+ X = X + One;
+ SqXMinX (Defect);
+ if (J > Zero)
+ break;
+ I = I + 1;
+ }
+ printf ("Test for sqrt monotonicity.\n");
+ I = -1;
+ X = BMinusU2;
+ Y = Radix;
+ Z = Radix + Radix * U2;
+ NotMonot = False;
+ Monot = False;
+ while (!(NotMonot || Monot)) {
+ I = I + 1;
+ X = SQRT (X);
+ Q = SQRT (Y);
+ Z = SQRT (Z);
+ if ((X > Q) || (Q > Z))
+ NotMonot = True;
+ else {
+ Q = FLOOR (Q + Half);
+ if ((I > 0) || (Radix == Q * Q))
+ Monot = True;
+ else if (I > 0) {
+ if (I > 1)
+ Monot = True;
+ else {
+ Y = Y * BInvrse;
+ X = Y - U1;
+ Z = Y + U1;
+ }
+ } else {
+ Y = Q;
+ X = Y - U2;
+ Z = Y + U2;
+ }
+ }
+ }
+ if (Monot)
+ printf ("sqrt has passed a test for Monotonicity.\n");
+ else {
+ BadCond (Defect, "");
+ printf ("sqrt(X) is non-monotonic for X near %.7e .\n", Y);
+ }
+ /*=============================================*/
+ Milestone = 80;
+ /*=============================================*/
+ MinSqEr = MinSqEr + Half;
+ MaxSqEr = MaxSqEr - Half;
+ Y = (SQRT (One + U2) - One) / U2;
+ SqEr = (Y - One) + U2 / Eight;
+ if (SqEr > MaxSqEr)
+ MaxSqEr = SqEr;
+ SqEr = Y + U2 / Eight;
+ if (SqEr < MinSqEr)
+ MinSqEr = SqEr;
+ Y = ((SQRT (F9) - U2) - (One - U2)) / U1;
+ SqEr = Y + U1 / Eight;
+ if (SqEr > MaxSqEr)
+ MaxSqEr = SqEr;
+ SqEr = (Y + One) + U1 / Eight;
+ if (SqEr < MinSqEr)
+ MinSqEr = SqEr;
+ OneUlp = U2;
+ X = OneUlp;
+ for (Indx = 1; Indx <= 3; ++Indx) {
+ Y = SQRT ((X + U1 + X) + F9);
+ Y = ((Y - U2) - ((One - U2) + X)) / OneUlp;
+ Z = ((U1 - X) + F9) * Half * X * X / OneUlp;
+ SqEr = (Y + Half) + Z;
+ if (SqEr < MinSqEr)
+ MinSqEr = SqEr;
+ SqEr = (Y - Half) + Z;
+ if (SqEr > MaxSqEr)
+ MaxSqEr = SqEr;
+ if (((Indx == 1) || (Indx == 3)))
+ X = OneUlp * Sign (X) * FLOOR (Eight / (Nine * SQRT (OneUlp)));
+ else {
+ OneUlp = U1;
+ X = -OneUlp;
+ }
+ }
+ /*=============================================*/
+ Milestone = 85;
+ /*=============================================*/
+ SqRWrng = False;
+ Anomaly = False;
+ RSqrt = Other; /* ~dgh */
+ if (Radix != One) {
+ printf ("Testing whether sqrt is rounded or chopped.\n");
+ D = FLOOR (Half + POW (Radix, One + Precision - FLOOR (Precision)));
+ /* ... == Radix^(1 + fract) if (Precision == Integer + fract. */
+ X = D / Radix;
+ Y = D / A1;
+ if ((X != FLOOR (X)) || (Y != FLOOR (Y))) {
+ Anomaly = True;
+ } else {
+ X = Zero;
+ Z2 = X;
+ Y = One;
+ Y2 = Y;
+ Z1 = Radix - One;
+ FourD = Four * D;
+ do {
+ if (Y2 > Z2) {
+ Q = Radix;
+ Y1 = Y;
+ do {
+ X1 = FABS (Q + FLOOR (Half - Q / Y1) * Y1);
+ Q = Y1;
+ Y1 = X1;
+ }
+ while (!(X1 <= Zero));
+ if (Q <= One) {
+ Z2 = Y2;
+ Z = Y;
+ }
+ }
+ Y = Y + Two;
+ X = X + Eight;
+ Y2 = Y2 + X;
+ if (Y2 >= FourD)
+ Y2 = Y2 - FourD;
+ }
+ while (!(Y >= D));
+ X8 = FourD - Z2;
+ Q = (X8 + Z * Z) / FourD;
+ X8 = X8 / Eight;
+ if (Q != FLOOR (Q))
+ Anomaly = True;
+ else {
+ Break = False;
+ do {
+ X = Z1 * Z;
+ X = X - FLOOR (X / Radix) * Radix;
+ if (X == One)
+ Break = True;
+ else
+ Z1 = Z1 - One;
+ }
+ while (!(Break || (Z1 <= Zero)));
+ if ((Z1 <= Zero) && (!Break))
+ Anomaly = True;
+ else {
+ if (Z1 > RadixD2)
+ Z1 = Z1 - Radix;
+ do {
+ NewD ();
+ }
+ while (!(U2 * D >= F9));
+ if (D * Radix - D != W - D)
+ Anomaly = True;
+ else {
+ Z2 = D;
+ I = 0;
+ Y = D + (One + Z) * Half;
+ X = D + Z + Q;
+ SR3750 ();
+ Y = D + (One - Z) * Half + D;
+ X = D - Z + D;
+ X = X + Q + X;
+ SR3750 ();
+ NewD ();
+ if (D - Z2 != W - Z2)
+ Anomaly = True;
+ else {
+ Y = (D - Z2) + (Z2 + (One - Z) * Half);
+ X = (D - Z2) + (Z2 - Z + Q);
+ SR3750 ();
+ Y = (One + Z) * Half;
+ X = Q;
+ SR3750 ();
+ if (I == 0)
+ Anomaly = True;
+ }
+ }
+ }
+ }
+ }
+ if ((I == 0) || Anomaly) {
+ BadCond (Failure, "Anomalous arithmetic with Integer < ");
+ printf ("Radix^Precision = %.7e\n", W);
+ printf (" fails test whether sqrt rounds or chops.\n");
+ SqRWrng = True;
+ }
+ }
+ if (!Anomaly) {
+ if (!((MinSqEr < Zero) || (MaxSqEr > Zero))) {
+ RSqrt = Rounded;
+ printf ("Square root appears to be correctly rounded.\n");
+ } else {
+ if ((MaxSqEr + U2 > U2 - Half) || (MinSqEr > Half)
+ || (MinSqEr + Radix < Half))
+ SqRWrng = True;
+ else {
+ RSqrt = Chopped;
+ printf ("Square root appears to be chopped.\n");
+ }
+ }
+ }
+ if (SqRWrng) {
+ printf ("Square root is neither chopped nor correctly rounded.\n");
+ printf ("Observed errors run from %.7e ", MinSqEr - Half);
+ printf ("to %.7e ulps.\n", Half + MaxSqEr);
+ TstCond (Serious, MaxSqEr - MinSqEr < Radix * Radix,
+ "sqrt gets too many last digits wrong");
+ }
+ /*=============================================*/
+ Milestone = 90;
+ /*=============================================*/
+ Pause ();
+ printf ("Testing powers Z^i for small Integers Z and i.\n");
+ N = 0;
+ /* ... test powers of zero. */
+ I = 0;
+ Z = -Zero;
+ M = 3;
+ Break = False;
+ do {
+ X = One;
+ SR3980 ();
+ if (I <= 10) {
+ I = 1023;
+ SR3980 ();
+ }
+ if (Z == MinusOne)
+ Break = True;
+ else {
+ Z = MinusOne;
+ /* .. if(-1)^N is invalid, replace MinusOne by One. */
+ I = -4;
+ }
+ }
+ while (!Break);
+ PrintIfNPositive ();
+ N1 = N;
+ N = 0;
+ Z = A1;
+ M = (int) FLOOR (Two * LOG (W) / LOG (A1));
+ Break = False;
+ do {
+ X = Z;
+ I = 1;
+ SR3980 ();
+ if (Z == AInvrse)
+ Break = True;
+ else
+ Z = AInvrse;
+ }
+ while (!(Break));
+ /*=============================================*/
+ Milestone = 100;
+ /*=============================================*/
+ /* Powers of Radix have been tested, */
+ /* next try a few primes */
+ M = NoTrials;
+ Z = Three;
+ do {
+ X = Z;
+ I = 1;
+ SR3980 ();
+ do {
+ Z = Z + Two;
+ }
+ while (Three * FLOOR (Z / Three) == Z);
+ }
+ while (Z < Eight * Three);
+ if (N > 0) {
+ printf ("Errors like this may invalidate financial calculations\n");
+ printf ("\tinvolving interest rates.\n");
+ }
+ PrintIfNPositive ();
+ N += N1;
+ if (N == 0)
+ printf ("... no discrepancies found.\n");
+ if (N > 0)
+ Pause ();
+ else
+ printf ("\n");
+ /*=============================================*/
+ Milestone = 110;
+ /*=============================================*/
+ printf ("Seeking Underflow thresholds UfThold and E0.\n");
+ D = U1;
+ if (Precision != FLOOR (Precision)) {
+ D = BInvrse;
+ X = Precision;
+ do {
+ D = D * BInvrse;
+ X = X - One;
+ }
+ while (X > Zero);
+ }
+ Y = One;
+ Z = D;
+ /* ... D is power of 1/Radix < 1. */
+ do {
+ C = Y;
+ Y = Z;
+ Z = Y * Y;
+ }
+ while ((Y > Z) && (Z + Z > Z));
+ Y = C;
+ Z = Y * D;
+ do {
+ C = Y;
+ Y = Z;
+ Z = Y * D;
+ }
+ while ((Y > Z) && (Z + Z > Z));
+ if (Radix < Two)
+ HInvrse = Two;
+ else
+ HInvrse = Radix;
+ H = One / HInvrse;
+ /* ... 1/HInvrse == H == Min(1/Radix, 1/2) */
+ CInvrse = One / C;
+ E0 = C;
+ Z = E0 * H;
+ /* ...1/Radix^(BIG Integer) << 1 << CInvrse == 1/C */
+ do {
+ Y = E0;
+ E0 = Z;
+ Z = E0 * H;
+ }
+ while ((E0 > Z) && (Z + Z > Z));
+ UfThold = E0;
+ E1 = Zero;
+ Q = Zero;
+ E9 = U2;
+ S = One + E9;
+ D = C * S;
+ if (D <= C) {
+ E9 = Radix * U2;
+ S = One + E9;
+ D = C * S;
+ if (D <= C) {
+ BadCond (Failure, "multiplication gets too many last digits wrong.\n");
+ Underflow = E0;
+ Y1 = Zero;
+ PseudoZero = Z;
+ Pause ();
+ }
+ } else {
+ Underflow = D;
+ PseudoZero = Underflow * H;
+ UfThold = Zero;
+ do {
+ Y1 = Underflow;
+ Underflow = PseudoZero;
+ if (E1 + E1 <= E1) {
+ Y2 = Underflow * HInvrse;
+ E1 = FABS (Y1 - Y2);
+ Q = Y1;
+ if ((UfThold == Zero) && (Y1 != Y2))
+ UfThold = Y1;
+ }
+ PseudoZero = PseudoZero * H;
+ }
+ while ((Underflow > PseudoZero)
+ && (PseudoZero + PseudoZero > PseudoZero));
+ }
+ /* Comment line 4530 .. 4560 */
+ if (PseudoZero != Zero) {
+ printf ("\n");
+ Z = PseudoZero;
+ /* ... Test PseudoZero for "phoney- zero" violates */
+ /* ... PseudoZero < Underflow or PseudoZero < PseudoZero + PseudoZero
+ ... */
+ if (PseudoZero <= Zero) {
+ BadCond (Failure, "Positive expressions can underflow to an\n");
+ printf ("allegedly negative value\n");
+ printf ("PseudoZero that prints out as: %g .\n", PseudoZero);
+ X = -PseudoZero;
+ if (X <= Zero) {
+ printf ("But -PseudoZero, which should be\n");
+ printf ("positive, isn't; it prints out as %g .\n", X);
+ }
+ } else {
+ BadCond (Flaw, "Underflow can stick at an allegedly positive\n");
+ printf ("value PseudoZero that prints out as %g .\n", PseudoZero);
+ }
+ TstPtUf ();
+ }
+ /*=============================================*/
+ Milestone = 120;
+ /*=============================================*/
+ if (CInvrse * Y > CInvrse * Y1) {
+ S = H * S;
+ E0 = Underflow;
+ }
+ if (!((E1 == Zero) || (E1 == E0))) {
+ BadCond (Defect, "");
+ if (E1 < E0) {
+ printf ("Products underflow at a higher");
+ printf (" threshold than differences.\n");
+ if (PseudoZero == Zero)
+ E0 = E1;
+ } else {
+ printf ("Difference underflows at a higher");
+ printf (" threshold than products.\n");
+ }
+ }
+ printf ("Smallest strictly positive number found is E0 = %g .\n", E0);
+ Z = E0;
+ TstPtUf ();
+ Underflow = E0;
+ if (N == 1)
+ Underflow = Y;
+ I = 4;
+ if (E1 == Zero)
+ I = 3;
+ if (UfThold == Zero)
+ I = I - 2;
+ UfNGrad = True;
+ switch (I) {
+ case 1:
+ UfThold = Underflow;
+ if ((CInvrse * Q) != ((CInvrse * Y) * S)) {
+ UfThold = Y;
+ BadCond (Failure, "Either accuracy deteriorates as numbers\n");
+ printf ("approach a threshold = %.17e\n", UfThold);;
+ printf (" coming down from %.17e\n", C);
+ printf (" or else multiplication gets too many last digits wrong.\n");
+ }
+ Pause ();
+ break;
+
+ case 2:
+ BadCond (Failure, "Underflow confuses Comparison, which alleges that\n");
+ printf ("Q == Y while denying that |Q - Y| == 0; these values\n");
+ printf ("print out as Q = %.17e, Y = %.17e .\n", Q, Y2);
+ printf ("|Q - Y| = %.17e .\n", FABS (Q - Y2));
+ UfThold = Q;
+ break;
+
+ case 3:
+ X = X;
+ break;
+
+ case 4:
+ if ((Q == UfThold) && (E1 == E0)
+ && (FABS (UfThold - E1 / E9) <= E1)) {
+ UfNGrad = False;
+ printf ("Underflow is gradual; it incurs Absolute Error =\n");
+ printf ("(roundoff in UfThold) < E0.\n");
+ Y = E0 * CInvrse;
+ Y = Y * (OneAndHalf + U2);
+ X = CInvrse * (One + U2);
+ Y = Y / X;
+ IEEE = (Y == E0);
+ }
+ }
+ if (UfNGrad) {
+ printf ("\n");
+ sigsave = _sigfpe;
+ if (setjmp (ovfl_buf)) {
+ printf ("Underflow / UfThold failed!\n");
+ R = H + H;
+ } else
+ R = SQRT (Underflow / UfThold);
+ sigsave = 0;
+ if (R <= H) {
+ Z = R * UfThold;
+ X = Z * (One + R * H * (One + H));
+ } else {
+ Z = UfThold;
+ X = Z * (One + H * H * (One + H));
+ }
+ if (!((X == Z) || (X - Z != Zero))) {
+ BadCond (Flaw, "");
+ printf ("X = %.17e\n\tis not equal to Z = %.17e .\n", X, Z);
+ Z9 = X - Z;
+ printf ("yet X - Z yields %.17e .\n", Z9);
+ printf (" Should this NOT signal Underflow, ");
+ printf ("this is a SERIOUS DEFECT\nthat causes ");
+ printf ("confusion when innocent statements like\n");;
+ printf (" if (X == Z) ... else");
+ printf (" ... (f(X) - f(Z)) / (X - Z) ...\n");
+ printf ("encounter Division by Zero although actually\n");
+ sigsave = _sigfpe;
+ if (setjmp (ovfl_buf))
+ printf ("X / Z fails!\n");
+ else
+ printf ("X / Z = 1 + %g .\n", (X / Z - Half) - Half);
+ sigsave = 0;
+ }
+ }
+ printf ("The Underflow threshold is %.17e, %s\n", UfThold,
+ " below which");
+ printf ("calculation may suffer larger Relative error than ");
+ printf ("merely roundoff.\n");
+ Y2 = U1 * U1;
+ Y = Y2 * Y2;
+ Y2 = Y * U1;
+ if (Y2 <= UfThold) {
+ if (Y > E0) {
+ BadCond (Defect, "");
+ I = 5;
+ } else {
+ BadCond (Serious, "");
+ I = 4;
+ }
+ printf ("Range is too narrow; U1^%d Underflows.\n", I);
+ }
+ /*=============================================*/
+ Milestone = 130;
+ /*=============================================*/
+ Y = -FLOOR (Half - TwoForty * LOG (UfThold) / LOG (HInvrse)) / TwoForty;
+ Y2 = Y + Y;
+ printf ("Since underflow occurs below the threshold\n");
+ printf ("UfThold = (%.17e) ^ (%.17e)\nonly underflow ", HInvrse, Y);
+ printf ("should afflict the expression\n\t(%.17e) ^ (%.17e);\n",
+ HInvrse, Y2);
+ printf ("actually calculating yields:");
+ if (setjmp (ovfl_buf)) {
+ sigsave = 0;
+ BadCond (Serious, "trap on underflow.\n");
+ } else {
+ sigsave = _sigfpe;
+ V9 = POW (HInvrse, Y2);
+ sigsave = 0;
+ printf (" %.17e .\n", V9);
+ if (!((V9 >= Zero) && (V9 <= (Radix + Radix + E9) * UfThold))) {
+ BadCond (Serious, "this is not between 0 and underflow\n");
+ printf (" threshold = %.17e .\n", UfThold);
+ } else if (!(V9 > UfThold * (One + E9)))
+ printf ("This computed value is O.K.\n");
+ else {
+ BadCond (Defect, "this is not between 0 and underflow\n");
+ printf (" threshold = %.17e .\n", UfThold);
+ }
+ }
+ /*=============================================*/
+ Milestone = 140;
+ /*=============================================*/
+ printf ("\n");
+ /* ...calculate Exp2 == exp(2) == 7.389056099... */
+ X = Zero;
+ I = 2;
+ Y = Two * Three;
+ Q = Zero;
+ N = 0;
+ do {
+ Z = X;
+ I = I + 1;
+ Y = Y / (I + I);
+ R = Y + Q;
+ X = Z + R;
+ Q = (Z - X) + R;
+ }
+ while (X > Z);
+ Z = (OneAndHalf + One / Eight) + X / (OneAndHalf * ThirtyTwo);
+ X = Z * Z;
+ Exp2 = X * X;
+ X = F9;
+ Y = X - U1;
+ printf ("Testing X^((X + 1) / (X - 1)) vs. exp(2) = %.17e as X -> 1.\n",
+ Exp2);
+ for (I = 1;;) {
+ Z = X - BInvrse;
+ Z = (X + One) / (Z - (One - BInvrse));
+ Q = POW (X, Z) - Exp2;
+ if (FABS (Q) > TwoForty * U2) {
+ N = 1;
+ V9 = (X - BInvrse) - (One - BInvrse);
+ BadCond (Defect, "Calculated");
+ printf (" %.17e for\n", POW (X, Z));
+ printf ("\t(1 + (%.17e) ^ (%.17e);\n", V9, Z);
+ printf ("\tdiffers from correct value by %.17e .\n", Q);
+ printf ("\tThis much error may spoil financial\n");
+ printf ("\tcalculations involving tiny interest rates.\n");
+ break;
+ } else {
+ Z = (Y - X) * Two + Y;
+ X = Y;
+ Y = Z;
+ Z = One + (X - F9) * (X - F9);
+ if (Z > One && I < NoTrials)
+ I++;
+ else {
+ if (X > One) {
+ if (N == 0)
+ printf ("Accuracy seems adequate.\n");
+ break;
+ } else {
+ X = One + U2;
+ Y = U2 + U2;
+ Y += X;
+ I = 1;
+ }
+ }
+ }
+ }
+ /*=============================================*/
+ Milestone = 150;
+ /*=============================================*/
+ printf ("Testing powers Z^Q at four nearly extreme values.\n");
+ N = 0;
+ Z = A1;
+ Q = FLOOR (Half - LOG (C) / LOG (A1));
+ Break = False;
+ do {
+ X = CInvrse;
+ Y = POW (Z, Q);
+ IsYeqX ();
+ Q = -Q;
+ X = C;
+ Y = POW (Z, Q);
+ IsYeqX ();
+ if (Z < One)
+ Break = True;
+ else
+ Z = AInvrse;
+ }
+ while (!(Break));
+ PrintIfNPositive ();
+ if (N == 0)
+ printf (" ... no discrepancies found.\n");
+ printf ("\n");
+
+ /*=============================================*/
+ Milestone = 160;
+ /*=============================================*/
+ Pause ();
+ printf ("Searching for Overflow threshold:\n");
+ printf ("This may generate an error.\n");
+ Y = -CInvrse;
+ V9 = HInvrse * Y;
+ sigsave = _sigfpe;
+ if (setjmp (ovfl_buf)) {
+ I = 0;
+ V9 = Y;
+ goto overflow;
+ }
+ do {
+ V = Y;
+ Y = V9;
+ V9 = HInvrse * Y;
+ }
+ while (V9 < Y);
+ I = 1;
+ overflow:
+ sigsave = 0;
+ Z = V9;
+ printf ("Can `Z = -Y' overflow?\n");
+ printf ("Trying it on Y = %.17e .\n", Y);
+ V9 = -Y;
+ V0 = V9;
+ if (V - Y == V + V0)
+ printf ("Seems O.K.\n");
+ else {
+ printf ("finds a ");
+ BadCond (Flaw, "-(-Y) differs from Y.\n");
+ }
+ if (Z != Y) {
+ BadCond (Serious, "");
+ printf ("overflow past %.17e\n\tshrinks to %.17e .\n", Y, Z);
+ }
+ if (I) {
+ Y = V * (HInvrse * U2 - HInvrse);
+ Z = Y + ((One - HInvrse) * U2) * V;
+ if (Z < V0)
+ Y = Z;
+ if (Y < V0)
+ V = Y;
+ if (V0 - V < V0)
+ V = V0;
+ } else {
+ V = Y * (HInvrse * U2 - HInvrse);
+ V = V + ((One - HInvrse) * U2) * Y;
+ }
+ printf ("Overflow threshold is V = %.17e .\n", V);
+ if (I)
+ printf ("Overflow saturates at V0 = %.17e .\n", V0);
+ else
+ printf ("There is no saturation value because \
+the system traps on overflow.\n");
+ V9 = V * One;
+ printf ("No Overflow should be signaled for V * 1 = %.17e\n", V9);
+ V9 = V / One;
+ printf (" nor for V / 1 = %.17e .\n", V9);
+ printf ("Any overflow signal separating this * from the one\n");
+ printf ("above is a DEFECT.\n");
+ /*=============================================*/
+ Milestone = 170;
+ /*=============================================*/
+ if (!(-V < V && -V0 < V0 && -UfThold < V && UfThold < V)) {
+ BadCond (Failure, "Comparisons involving ");
+ printf ("+-%g, +-%g\nand +-%g are confused by Overflow.",
+ V, V0, UfThold);
+ }
+ /*=============================================*/
+ Milestone = 175;
+ /*=============================================*/
+ printf ("\n");
+ for (Indx = 1; Indx <= 3; ++Indx) {
+ switch (Indx) {
+ case 1:
+ Z = UfThold;
+ break;
+ case 2:
+ Z = E0;
+ break;
+ case 3:
+ Z = PseudoZero;
+ break;
+ }
+ if (Z != Zero) {
+ V9 = SQRT (Z);
+ Y = V9 * V9;
+ if (Y / (One - Radix * E9) < Z
+ || Y > (One + Radix * E9) * Z) { /* dgh: + E9 --> * E9 */
+ if (V9 > U1)
+ BadCond (Serious, "");
+ else
+ BadCond (Defect, "");
+ printf ("Comparison alleges that what prints as Z = %.17e\n", Z);
+ printf (" is too far from sqrt(Z) ^ 2 = %.17e .\n", Y);
+ }
+ }
+ }
+ /*=============================================*/
+ Milestone = 180;
+ /*=============================================*/
+ for (Indx = 1; Indx <= 2; ++Indx) {
+ if (Indx == 1)
+ Z = V;
+ else
+ Z = V0;
+ V9 = SQRT (Z);
+ X = (One - Radix * E9) * V9;
+ V9 = V9 * X;
+ if (((V9 < (One - Two * Radix * E9) * Z) || (V9 > Z))) {
+ Y = V9;
+ if (X < W)
+ BadCond (Serious, "");
+ else
+ BadCond (Defect, "");
+ printf ("Comparison alleges that Z = %17e\n", Z);
+ printf (" is too far from sqrt(Z) ^ 2 (%.17e) .\n", Y);
+ }
+ }
+ /*=============================================*/
+ Milestone = 190;
+ /*=============================================*/
+ Pause ();
+ X = UfThold * V;
+ Y = Radix * Radix;
+ if (X * Y < One || X > Y) {
+ if (X * Y < U1 || X > Y / U1)
+ BadCond (Defect, "Badly");
+ else
+ BadCond (Flaw, "");
+
+ printf (" unbalanced range; UfThold * V = %.17e\n\t%s\n",
+ X, "is too far from 1.\n");
+ }
+ /*=============================================*/
+ Milestone = 200;
+ /*=============================================*/
+ for (Indx = 1; Indx <= 5; ++Indx) {
+ X = F9;
+ switch (Indx) {
+ case 2:
+ X = One + U2;
+ break;
+ case 3:
+ X = V;
+ break;
+ case 4:
+ X = UfThold;
+ break;
+ case 5:
+ X = Radix;
+ }
+ Y = X;
+ sigsave = _sigfpe;
+ if (setjmp (ovfl_buf))
+ printf (" X / X traps when X = %g\n", X);
+ else {
+ V9 = (Y / X - Half) - Half;
+ if (V9 == Zero)
+ continue;
+ if (V9 == -U1 && Indx < 5)
+ BadCond (Flaw, "");
+ else
+ BadCond (Serious, "");
+ printf (" X / X differs from 1 when X = %.17e\n", X);
+ printf (" instead, X / X - 1/2 - 1/2 = %.17e .\n", V9);
+ }
+ sigsave = 0;
+ }
+ /*=============================================*/
+ Milestone = 210;
+ /*=============================================*/
+ MyZero = Zero;
+ printf ("\n");
+ printf ("What message and/or values does Division by Zero produce?\n");
+#ifndef BATCHMODE
+ printf ("This can interupt your program. You can ");
+ printf ("skip this part if you wish.\n");
+ printf ("Do you wish to compute 1 / 0? ");
+ fflush (stdout);
+ read (KEYBOARD, ch, 8);
+ if ((ch[0] == 'Y') || (ch[0] == 'y')) {
+#endif /* !BATCHMODE */
+ sigsave = _sigfpe;
+ printf (" Trying to compute 1 / 0 produces ...");
+ if (!setjmp (ovfl_buf))
+ printf (" %.7e .\n", One / MyZero);
+ sigsave = 0;
+#ifndef BATCHMODE
+ } else
+ printf ("O.K.\n");
+ printf ("\nDo you wish to compute 0 / 0? ");
+ fflush (stdout);
+ read (KEYBOARD, ch, 80);
+ if ((ch[0] == 'Y') || (ch[0] == 'y')) {
+#endif /* !BATCHMODE */
+ sigsave = _sigfpe;
+ printf ("\n Trying to compute 0 / 0 produces ...");
+ if (!setjmp (ovfl_buf))
+ printf (" %.7e .\n", Zero / MyZero);
+ sigsave = 0;
+#ifndef BATCHMODE
+ } else
+ printf ("O.K.\n");
+#endif /* !BATCHMODE */
+ /*=============================================*/
+ Milestone = 220;
+ /*=============================================*/
+
+ Pause ();
+ printf ("\n");
+ {
+ static char *msg[] =
+ {
+ "FAILUREs encountered =",
+ "SERIOUS DEFECTs discovered =",
+ "DEFECTs discovered =",
+ "FLAWs discovered ="};
+ int i;
+ for (i = 0; i < 4; i++)
+ if (ErrCnt[i])
+ printf ("The number of %-29s %d.\n",
+ msg[i], ErrCnt[i]);
+ }
+
+ printf ("\n");
+ if ((ErrCnt[Failure] + ErrCnt[Serious] + ErrCnt[Defect]
+ + ErrCnt[Flaw]) > 0) {
+ if ((ErrCnt[Failure] + ErrCnt[Serious] + ErrCnt[
+ Defect] == 0) && (ErrCnt[Flaw] > 0)) {
+ printf ("The arithmetic diagnosed seems ");
+ printf ("Satisfactory though flawed.\n");
+ }
+ if ((ErrCnt[Failure] + ErrCnt[Serious] == 0)
+ && (ErrCnt[Defect] > 0)) {
+ printf ("The arithmetic diagnosed may be Acceptable\n");
+ printf ("despite inconvenient Defects.\n");
+ }
+ if ((ErrCnt[Failure] + ErrCnt[Serious]) > 0) {
+ printf ("The arithmetic diagnosed has ");
+ printf ("unacceptable Serious Defects.\n");
+ }
+ if (ErrCnt[Failure] > 0) {
+ printf ("Potentially fatal FAILURE may have spoiled this");
+ printf (" program's subsequent diagnoses.\n");
+ }
+ } else {
+
+ printf ("No failures, defects nor flaws have been discovered.\n");
+ if (!((RMult == Rounded) && (RDiv == Rounded)
+ && (RAddSub == Rounded) && (RSqrt == Rounded)))
+ printf ("The arithmetic diagnosed seems Satisfactory.\n");
+ else {
+ if (StickyBit >= One &&
+ (Radix - Two) * (Radix - Nine - One) == Zero) {
+ printf ("Rounding appears to conform to ");
+ printf ("the proposed IEEE standard P");
+ if ((Radix == Two) &&
+ ((Precision - Four * Three * Two) *
+ (Precision - TwentySeven -
+ TwentySeven + One) == Zero))
+ printf ("754");
+ else
+ printf ("854");
+ if (IEEE)
+ printf (".\n");
+ else {
+ printf (",\nexcept for possibly Double Rounding");
+ printf (" during Gradual Underflow.\n");
+ }
+ }
+ printf ("The arithmetic diagnosed appears to be Excellent!\n");
+ }
+ }
+
+ if (fpecount)
+ printf ("\nA total of %d floating point exceptions were registered.\n",
+ fpecount);
+ printf ("END OF TEST.\n");
+ return 0;
+}
+
+FLOAT
+Sign (X)
+ FLOAT X;
+{
+ return X >= 0. ? 1.0 : -1.0;
+}
+
+void
+Pause ()
+{
+#ifndef BATCHMODE
+ char ch[8];
+
+ printf ("\nTo continue, press RETURN");
+ fflush (stdout);
+ read (KEYBOARD, ch, 8);
+#endif /* !BATCHMODE */
+#ifndef CYGNUS
+ printf ("\nDiagnosis resumes after milestone Number %d", Milestone);
+ printf (" Page: %d\n\n", PageNo);
+ ++Milestone;
+ ++PageNo;
+#endif /* !CYGNUS */
+}
+
+void
+TstCond (K, Valid, T)
+ int K, Valid;
+ char *T;
+{
+#ifdef CYGNUS
+ printf ("TEST: %s\n", T);
+#endif /* CYGNUS */
+ if (!Valid) {
+ BadCond (K, T);
+ printf (".\n");
+ }
+#ifdef CYGNUS
+ printf ("PASS: %s\n", T);
+#endif /* CYGNUS */
+}
+
+void
+BadCond (K, T)
+ int K;
+ char *T;
+{
+ static char *msg[] =
+ {"FAILURE", "SERIOUS DEFECT", "DEFECT", "FLAW"};
+
+ ErrCnt[K] = ErrCnt[K] + 1;
+#ifndef CYGNUS
+ printf ("%s: %s", msg[K], T);
+#else
+ printf ("ERROR: Severity: %s: %s", msg[K], T);
+#endif /* CYGNUS */
+}
+
+/*
+ * Random computes
+ * X = (Random1 + Random9)^5
+ * Random1 = X - FLOOR(X) + 0.000005 * X;
+ * and returns the new value of Random1
+*/
+FLOAT
+Random ()
+{
+ FLOAT X, Y;
+
+ X = Random1 + Random9;
+ Y = X * X;
+ Y = Y * Y;
+ X = X * Y;
+ Y = X - FLOOR (X);
+ Random1 = Y + X * 0.000005;
+ return (Random1);
+}
+
+void
+SqXMinX (ErrKind)
+ int ErrKind;
+{
+ FLOAT XA, XB;
+
+ XB = X * BInvrse;
+ XA = X - XB;
+ SqEr = ((SQRT (X * X) - XB) - XA) / OneUlp;
+ if (SqEr != Zero) {
+ if (SqEr < MinSqEr)
+ MinSqEr = SqEr;
+ if (SqEr > MaxSqEr)
+ MaxSqEr = SqEr;
+ J = J + 1.0;
+ BadCond (ErrKind, "\n");
+ printf ("sqrt( %.17e) - %.17e = %.17e\n", X * X, X, OneUlp * SqEr);
+ printf ("\tinstead of correct value 0 .\n");
+ }
+}
+
+void
+NewD ()
+{
+ X = Z1 * Q;
+ X = FLOOR (Half - X / Radix) * Radix + X;
+ Q = (Q - X * Z) / Radix + X * X * (D / Radix);
+ Z = Z - Two * X * D;
+ if (Z <= Zero) {
+ Z = -Z;
+ Z1 = -Z1;
+ }
+ D = Radix * D;
+}
+
+void
+SR3750 ()
+{
+ if (!((X - Radix < Z2 - Radix) || (X - Z2 > W - Z2))) {
+ I = I + 1;
+ X2 = SQRT (X * D);
+ Y2 = (X2 - Z2) - (Y - Z2);
+ X2 = X8 / (Y - Half);
+ X2 = X2 - Half * X2 * X2;
+ SqEr = (Y2 + Half) + (Half - X2);
+ if (SqEr < MinSqEr)
+ MinSqEr = SqEr;
+ SqEr = Y2 - X2;
+ if (SqEr > MaxSqEr)
+ MaxSqEr = SqEr;
+ }
+}
+
+void
+IsYeqX ()
+{
+ if (Y != X) {
+ if (N <= 0) {
+ if (Z == Zero && Q <= Zero)
+ printf ("WARNING: computing\n");
+ else
+ BadCond (Defect, "computing\n");
+ printf ("\t(%.17e) ^ (%.17e)\n", Z, Q);
+ printf ("\tyielded %.17e;\n", Y);
+ printf ("\twhich compared unequal to correct %.17e ;\n",
+ X);
+ printf ("\t\tthey differ by %.17e .\n", Y - X);
+ }
+ N = N + 1; /* ... count discrepancies. */
+ }
+}
+
+void
+SR3980 ()
+{
+ do {
+ Q = (FLOAT) I;
+ Y = POW (Z, Q);
+ IsYeqX ();
+ if (++I > M)
+ break;
+ X = Z * X;
+ }
+ while (X < W);
+}
+
+void
+PrintIfNPositive ()
+{
+ if (N > 0)
+ printf ("Similar discrepancies have occurred %d times.\n", N);
+}
+
+void
+TstPtUf ()
+{
+ N = 0;
+ if (Z != Zero) {
+ printf ("Since comparison denies Z = 0, evaluating ");
+ printf ("(Z + Z) / Z should be safe.\n");
+ sigsave = _sigfpe;
+ if (setjmp (ovfl_buf))
+ goto very_serious;
+ Q9 = (Z + Z) / Z;
+ printf ("What the machine gets for (Z + Z) / Z is %.17e .\n",
+ Q9);
+ if (FABS (Q9 - Two) < Radix * U2) {
+ printf ("This is O.K., provided Over/Underflow");
+ printf (" has NOT just been signaled.\n");
+ } else {
+ if ((Q9 < One) || (Q9 > Two)) {
+ very_serious:
+ N = 1;
+ ErrCnt[Serious] = ErrCnt[Serious] + 1;
+ printf ("This is a VERY SERIOUS DEFECT!\n");
+ } else {
+ N = 1;
+ ErrCnt[Defect] = ErrCnt[Defect] + 1;
+ printf ("This is a DEFECT!\n");
+ }
+ }
+ sigsave = 0;
+ V9 = Z * One;
+ Random1 = V9;
+ V9 = One * Z;
+ Random2 = V9;
+ V9 = Z / One;
+ if ((Z == Random1) && (Z == Random2) && (Z == V9)) {
+ if (N > 0)
+ Pause ();
+ } else {
+ N = 1;
+ BadCond (Defect, "What prints as Z = ");
+ printf ("%.17e\n\tcompares different from ", Z);
+ if (Z != Random1)
+ printf ("Z * 1 = %.17e ", Random1);
+ if (!((Z == Random2)
+ || (Random2 == Random1)))
+ printf ("1 * Z == %g\n", Random2);
+ if (!(Z == V9))
+ printf ("Z / 1 = %.17e\n", V9);
+ if (Random2 != Random1) {
+ ErrCnt[Defect] = ErrCnt[Defect] + 1;
+ BadCond (Defect, "Multiplication does not commute!\n");
+ printf ("\tComparison alleges that 1 * Z = %.17e\n",
+ Random2);
+ printf ("\tdiffers from Z * 1 = %.17e\n", Random1);
+ }
+ Pause ();
+ }
+ }
+}
+
+void
+notify (s)
+ char *s;
+{
+ printf ("%s test appears to be inconsistent...\n", s);
+ printf (" PLEASE NOTIFY KARPINKSI!\n");
+}
+
+void
+msglist (s)
+ char **s;
+{
+ while (*s)
+ printf ("%s\n", *s++);
+}
+
+void
+Instructions ()
+{
+ static char *instr[] =
+ {
+ "Lest this program stop prematurely, i.e. before displaying\n",
+ " `END OF TEST',\n",
+ "try to persuade the computer NOT to terminate execution when an",
+ "error like Over/Underflow or Division by Zero occurs, but rather",
+ "to persevere with a surrogate value after, perhaps, displaying some",
+ "warning. If persuasion avails naught, don't despair but run this",
+ "program anyway to see how many milestones it passes, and then",
+ "amend it to make further progress.\n",
+ "Answer questions with Y, y, N or n (unless otherwise indicated).\n",
+ 0};
+
+ msglist (instr);
+}
+
+void
+Heading ()
+{
+ static char *head[] =
+ {
+ "Users are invited to help debug and augment this program so it will",
+ "cope with unanticipated and newly uncovered arithmetic pathologies.\n",
+ "Please send suggestions and interesting results to",
+ "\tRichard Karpinski",
+ "\tComputer Center U-76",
+ "\tUniversity of California",
+ "\tSan Francisco, CA 94143-0704, USA\n",
+ "In doing so, please include the following information:",
+#ifdef SINGLE_PRECISION
+ "\tPrecision:\tsingle;",
+#else /* !SINGLE_PRECISION */
+ "\tPrecision:\tdouble;",
+#endif /* SINGLE_PRECISION */
+ "\tVersion:\t10 February 1989;",
+ "\tComputer:\n",
+ "\tCompiler:\n",
+ "\tOptimization level:\n",
+ "\tOther relevant compiler options:",
+ 0};
+
+ msglist (head);
+}
+
+void
+Characteristics ()
+{
+ static char *chars[] =
+ {
+ "Running this program should reveal these characteristics:",
+ " Radix = 1, 2, 4, 8, 10, 16, 100, 256 ...",
+ " Precision = number of significant digits carried.",
+ " U2 = Radix/Radix^Precision = One Ulp",
+ "\t(OneUlpnit in the Last Place) of 1.000xxx .",
+ " U1 = 1/Radix^Precision = One Ulp of numbers a little less than 1.0 .",
+ " Adequacy of guard digits for Mult., Div. and Subt.",
+ " Whether arithmetic is chopped, correctly rounded, or something else",
+ "\tfor Mult., Div., Add/Subt. and Sqrt.",
+ " Whether a Sticky Bit used correctly for rounding.",
+ " UnderflowThreshold = an underflow threshold.",
+ " E0 and PseudoZero tell whether underflow is abrupt, gradual, or fuzzy.",
+ " V = an overflow threshold, roughly.",
+ " V0 tells, roughly, whether Infinity is represented.",
+ " Comparisions are checked for consistency with subtraction",
+ "\tand for contamination with pseudo-zeros.",
+ " Sqrt is tested. Y^X is not tested.",
+ " Extra-precise subexpressions are revealed but NOT YET tested.",
+ " Decimal-Binary conversion is NOT YET tested for accuracy.",
+ 0};
+
+ msglist (chars);
+}
+
+void
+History ()
+{ /* History */
+ /* Converted from Brian Wichmann's Pascal version to C by Thos Sumner,
+ with further massaging by David M. Gay. */
+
+ static char *hist[] =
+ {
+ "The program attempts to discriminate among",
+ " FLAWs, like lack of a sticky bit,",
+ " Serious DEFECTs, like lack of a guard digit, and",
+ " FAILUREs, like 2+2 == 5 .",
+ "Failures may confound subsequent diagnoses.\n",
+ "The diagnostic capabilities of this program go beyond an earlier",
+ "program called `MACHAR', which can be found at the end of the",
+ "book `Software Manual for the Elementary Functions' (1980) by",
+ "W. J. Cody and W. Waite. Although both programs try to discover",
+ "the Radix, Precision and range (over/underflow thresholds)",
+ "of the arithmetic, this program tries to cope with a wider variety",
+ "of pathologies, and to say how well the arithmetic is implemented.",
+ "\nThe program is based upon a conventional radix representation for",
+ "floating-point numbers, but also allows logarithmic encoding",
+ "as used by certain early WANG machines.\n",
+ "BASIC version of this program (C) 1983 by Prof. W. M. Kahan;",
+ "see source comments for more history.",
+ 0};
+
+ msglist (hist);
+}
diff --git a/testsuites/samples/paranoia/paranoia.doc b/testsuites/samples/paranoia/paranoia.doc
new file mode 100644
index 0000000000..0de40191c6
--- /dev/null
+++ b/testsuites/samples/paranoia/paranoia.doc
@@ -0,0 +1,13 @@
+#
+# $Id$
+#
+# COPYRIGHT (c) 1989, 1990, 1991, 1992, 1993, 1994.
+# On-Line Applications Research Corporation (OAR).
+# All rights assigned to U.S. Government, 1994.
+#
+# This material may be reproduced by or for the U.S. Government pursuant
+# to the copyright license under the clause at DFARS 252.227-7013. This
+# notice must appear in all copies of this file and its derivatives.
+#
+
+
diff --git a/testsuites/samples/paranoia/system.h b/testsuites/samples/paranoia/system.h
new file mode 100644
index 0000000000..88e60beb9a
--- /dev/null
+++ b/testsuites/samples/paranoia/system.h
@@ -0,0 +1,30 @@
+/* system.h
+ *
+ * This include file contains information that is included in every
+ * function in the test set.
+ *
+ * COPYRIGHT (c) 1989, 1990, 1991, 1992, 1993, 1994.
+ * On-Line Applications Research Corporation (OAR).
+ * All rights assigned to U.S. Government, 1994.
+ *
+ * This material may be reproduced by or for the U.S. Government pursuant
+ * to the copyright license under the clause at DFARS 252.227-7013. This
+ * notice must appear in all copies of this file and its derivatives.
+ *
+ * $Id$
+ */
+
+#include <rtems.h>
+#include "stdio.h"
+
+/* Miscellaneous */
+
+#define EXTERN extern /* external definition */
+
+/* macros */
+
+/* structures */
+
+#include "gvar.h"
+
+/* end of include file */