Rework the math library tests per the glibc math test code, with

many unsupported tests disabled for the moment.
 -Erik

1 files changed, 0 insertions, 3550 deletions

diff --git a/test/math/eparanoi.c b/test/math/eparanoi.c
deleted file mode 100644
index 84cab73f8..000000000
--- a/test/math/eparanoi.c
+++ /dev/null
@@ -1,3550 +0,0 @@
-/* paranoia.c arithmetic tester
- *
- * This is an implementation of the PARANOIA program.  It substitutes
- * subroutine calls for ALL floating point arithmetic operations.
- * This permits you to substitute your own experimental versions of
- * arithmetic routines.  It also defeats compiler optimizations,
- * so for native arithmetic you can be pretty sure you are testing
- * the arithmetic and not the compiler.
- *
- * This version of PARANOIA omits the display of division by zero.
- * It also omits the test for extra precise subexpressions, since
- * they cannot occur in this context.  Otherwise it includes all the
- * tests of the 27 Jan 86 distribution, plus a few additional tests.
- * Commentary has been reduced to a minimum in order to make the program
- * smaller.
- *
- * The original PARANOIA program, written by W. Kahan, C version
- * by Thos Sumner and David Gay, can be downloaded free from the
- * Internet NETLIB.  An MSDOS disk can be obtained for $15 from:
- *   Richard Karpinski
- *   6521 Raymond Street
- *   Oakland, CA 94609
- *
- * Steve Moshier, 28 Oct 88
- * last rev: 23 May 92
- */
-
-#define DEBUG 0
-
-/* To use the native arithmetic of the computer, define NATIVE
- * to be 1.  To use your own supplied arithmetic routines, NATIVE is 0.
- */
-#define NATIVE 0
-
-/* gcc real.c interface */
-#define L128DOUBLE 0
-
-#include <stdio.h>
-
-
-
-
-/* Data structure of floating point number.  If NATIVE was
- * selected above, you can define LDOUBLE 1 to test 80-bit long double
- * precision or define it 0 to test 64-bit double precision.
-*/
-#define LDOUBLE 0
-#if NATIVE
-
-#define NE 1
-#if LDOUBLE
-#define FSIZE long double
-#define FLOAT(x) FSIZE x[NE]
-static FSIZE eone[NE] = {1.0L};	/* The constant 1.0 */
-#define ZSQRT sqrtl
-#define ZLOG logl
-#define ZFLOOR floorl
-#define ZPOW powl
-long double sqrtl(), logl(), floorl(), powl();
-#define FSETUP einit
-#else /* not LDOUBLE */
-#define FSIZE double
-#define FLOAT(x) FSIZE x[NE]
-static FSIZE eone[NE] = {1.0};	/* The constant 1.0 */
-#define ZSQRT sqrt
-#define ZLOG log
-#define ZFLOOR floor
-#define ZPOW pow
-double sqrt(), log(), floor(), pow();
-/* Coprocessor initialization,
- * defeat underflow trap or what have you.
- * This is required mainly on i386 and 68K processors.
- */
-#define FSETUP dprec
-#endif /* double, not LDOUBLE */
-
-#else /* not NATIVE */
-
-/* Setup for extended double type.
- * Put NE = 10 for real.c operating with TFmode support (16-byte reals)
- * Put NE = 6 for real.c operating with XFmode support (10- or 12-byte reals)
- * The value of NE must agree with that in ehead.h, if ieee.c is used.
- */
-#define NE 6
-#define FSIZE unsigned short
-#define FLOAT(x) unsigned short x[NE]
-extern unsigned short eone[];
-#define FSETUP einit
-
-/* default for FSETUP */
-/*
-einit()
-{}
-*/
-
-error(s)
-char *s;
-{
-printf( "error: %s\n", s );
-}
-
-#endif	/* not NATIVE */
-
-
-
-#if L128DOUBLE
-/* real.c interface */
-
-#undef FSETUP
-#define FSETUP efsetup
-
-FLOAT(enone);
-
-#define ONE enone
-
-/* Use emov to convert from widest type to widest type, ... */
-/*
-#define ENTOE emov
-#define ETOEN emov
-*/
-
-/*                 ... else choose e24toe, e53toe, etc. */
-#define ENTOE e64toe
-#define ETOEN etoe64
-#define NNBITS 64
-
-#define NIBITS ((NE-1)*16)
-extern int rndprc;
-
-efsetup()
-{
-rndprc = NNBITS;
-ETOEN(eone, enone);
-}
-
-add(a,b,c)
-FLOAT(a);
-FLOAT(b);
-FLOAT(c);
-{
-unsigned short aa[10], bb[10], cc[10];
-
-ENTOE(a,aa);
-ENTOE(b,bb);
-eadd(aa,bb,cc);
-ETOEN(cc,c);
-}
-
-sub(a,b,c)
-FLOAT(a);
-FLOAT(b);
-FLOAT(c);
-{
-unsigned short aa[10], bb[10], cc[10];
-
-ENTOE(a,aa);
-ENTOE(b,bb);
-esub(aa,bb,cc);
-ETOEN(cc,c);
-}
-
-mul(a,b,c)
-FLOAT(a);
-FLOAT(b);
-FLOAT(c);
-{
-unsigned short aa[10], bb[10], cc[10];
-
-ENTOE(a,aa);
-ENTOE(b,bb);
-emul(aa,bb,cc);
-ETOEN(cc,c);
-}
-
-div(a,b,c)
-FLOAT(a);
-FLOAT(b);
-FLOAT(c);
-{
-unsigned short aa[10], bb[10], cc[10];
-
-ENTOE(a,aa);
-ENTOE(b,bb);
-ediv(aa,bb,cc);
-ETOEN(cc,c);
-}
-
-int cmp(a,b)
-FLOAT(a);
-FLOAT(b);
-{
-unsigned short aa[10], bb[10];
-int c;
-int ecmp();
-
-ENTOE(a,aa);
-ENTOE(b,bb);
-c = ecmp(aa,bb);
-return(c);
-}
-
-mov(a,b)
-FLOAT(a);
-FLOAT(b);
-{
-int i;
-
-for( i=0; i<NE; i++ )
-	b[i] = a[i];
-}
-
-
-neg(a)
-FLOAT(a);
-{
-unsigned short aa[10];
-
-ENTOE(a,aa);
-eneg(aa);
-ETOEN(aa,a);
-}
-
-clear(a)
-FLOAT(a);
-{
-int i;
-
-for( i=0; i<NE; i++ )
-	a[i] = 0;
-}
-
-FABS(a)
-FLOAT(a);
-{
-unsigned short aa[10];
-
-ENTOE(a,aa);
-eabs(aa);
-ETOEN(aa,a);
-}
-
-FLOOR(a,b)
-FLOAT(a);
-FLOAT(b);
-{
-unsigned short aa[10], bb[10];
-
-ENTOE(a,aa);
-efloor(aa,bb);
-ETOEN(bb,b);
-}
-
-LOG(a,b)
-FLOAT(a);
-FLOAT(b);
-{
-unsigned short aa[10], bb[10];
-int rndsav;
-
-ENTOE(a,aa);
-rndsav = rndprc;
-rndprc = NIBITS;
-elog(aa,bb);
-rndprc = rndsav;
-ETOEN(bb,b);
-}
-
-POW(a,b,c)
-FLOAT(a);
-FLOAT(b);
-FLOAT(c);
-{
-unsigned short aa[10], bb[10], cc[10];
-int rndsav;
-
-ENTOE(a,aa);
-ENTOE(b,bb);
-rndsav = rndprc;
-rndprc = NIBITS;
-epow(aa,bb,cc);
-rndprc = rndsav;
-ETOEN(cc,c);
-}
-
-SQRT(a,b)
-FLOAT(a);
-FLOAT(b);
-{
-unsigned short aa[10], bb[10];
-
-ENTOE(a,aa);
-esqrt(aa,bb);
-ETOEN(bb,b);
-}
-
-FTOL(x,ip,f)
-FLOAT(x);
-long *ip;
-FLOAT(f);
-{
-unsigned short xx[10], ff[10];
-
-ENTOE(x,xx);
-eifrac(xx,ip,ff);
-ETOEN(ff,f);
-}
-
-LTOF(ip,x)
-long *ip;
-FLOAT(x);
-{
-unsigned short xx[10];
-ltoe(ip,xx);
-ETOEN(xx,x);
-}
-
-TOASC(a,b,c)
-FLOAT(a);
-int b;
-char *c;
-{
-unsigned short xx[10];
-
-ENTOE(a,xx);
-etoasc(xx,b,c);
-}
-
-#else /* not L128DOUBLE */
-
-#define ONE eone
-
-/* Note all arguments of operation subroutines are pointers. */
-/* c = b + a */
-#define add(a,b,c) eadd(a,b,c)
-/* c = b - a */
-#define sub(a,b,c) esub(a,b,c)
-/* c = b * a */
-#define mul(a,b,c) emul(a,b,c)
-/* c = b / a */
-#define div(a,b,c) ediv(a,b,c)
-/* 1 if a>b, 0 if a==b, -1 if a<b */
-#define cmp(a,b) ecmp(a,b)
-/* b = a */
-#define mov(a,b) emov(a,b)
-/* a = -a */
-#define neg(a) eneg(a)
-/* a = 0 */
-#define clear(a) eclear(a)
-
-#define FABS(x) eabs(x)
-#define FLOOR(x,y) efloor(x,y)
-#define LOG(x,y) elog(x,y)
-#define POW(x,y,z) epow(x,y,z)
-#define SQRT(x,y) esqrt(x,y)
-
-/* x = &FLOAT input, i = &long integer part, f = &FLOAT fractional part */
-#define FTOL(x,i,f) eifrac(x,i,f)
-
-/* i = &long integer input, x = &FLOAT output */
-#define LTOF(i,x) ltoe(i,x)
-
-/* Convert FLOAT a to decimal ASCII string with b digits */
-#define TOASC(a,b,c) etoasc(a,b,c)
-#endif /* not L128DOUBLE */
-
-
-
-/* The following subroutines are implementations of the above
- * named functions, using the native or default arithmetic.
- */
-#if NATIVE
-eadd(a,b,c)
-FSIZE *a, *b, *c;
-{
-*c = *b + *a;
-}
-
-esub(a,b,c)
-FSIZE *a, *b, *c;
-{
-*c = *b - *a;
-}
-
-emul(a,b,c)
-FSIZE *a, *b, *c;
-{
-*c = (*b) * (*a);
-}
-
-ediv(a,b,c)
-FSIZE *a, *b, *c;
-{
-*c = (*b) / (*a);
-}
-
-
-/* Important note: comparison can be done by subracting
- * or by a compare instruction that may or may not be
- * equivalent to subtracting.
- */
-ecmp(a,b)
-FSIZE *a, *b;
-{
-if( (*a) > (*b) )
-	return( 1 );
-if( (*a) < (*b) )
-	return( -1 );
-if( (*a) != (*b) )
-	goto cmpf;
-if( (*a) == (*b) )
-	return( 0 );
-cmpf:
-printf( "Compare fails\n" );
-return(0);
-}
-
-
-emov( a, b )
-FSIZE *a, *b;
-{
-*b = *a;
-}
-
-eneg( a )
-FSIZE *a;
-{
-*a = -(*a);
-}
-
-eclear(a)
-FSIZE *a;
-{
-*a = 0.0;
-}
-
-eabs(x)
-FSIZE *x;
-{
-if( (*x) < 0.0 )
-	*x = -(*x);
-}
-
-efloor(x,y)
-FSIZE *x, *y;
-{
-
-*y = (FSIZE )ZFLOOR( *x );
-}
-
-elog(x,y)
-FSIZE *x, *y;
-{
-
-*y = (FSIZE )ZLOG( *x );
-}
-
-epow(x,y,z)
-FSIZE *x, *y, *z;
-{
-
-*z = (FSIZE )ZPOW( *x, *y );
-}
-
-esqrt(x,y)
-FSIZE *x, *y;
-{
-
-*y = (FSIZE )ZSQRT( *x );
-}
-
-
-eifrac(x,i,f)
-FSIZE *x;
-long *i;
-FSIZE *f;
-{
-FSIZE y;
-
-y = (FSIZE )ZFLOOR( *x );
-if( y < 0.0 )
-	{
-	*f = y - *x;
-	*i = -y;
-	}
-else
-	{
-	*f = *x - y;
-	*i = y;
-	}
-}
-
-
-ltoe(i,x)
-long *i;
-FSIZE *x;
-{
-*x = *i;
-}
-
-
-etoasc(a,str,n)
-FSIZE *a;
-char *str;
-int n;
-{
-double x;
-
-x = (double )(*a);
-sprintf( str, " %.17e ", x );
-}
-
-/* default for FSETUP */
-einit()
-{}
-
-#endif	/* NATIVE */
-
-
-
-
-FLOAT(Radix);
-FLOAT(BInvrse);
-FLOAT(RadixD2);
-FLOAT(BMinusU2);
-/*Small floating point constants.*/
-FLOAT(Zero);
-FLOAT(Half);
-FLOAT(One);
-FLOAT(Two);
-FLOAT(Three);
-FLOAT(Four);
-FLOAT(Five);
-FLOAT(Six);
-FLOAT(Eight);
-FLOAT(Nine);
-FLOAT(Ten);
-FLOAT(TwentySeven);
-FLOAT(ThirtyTwo);
-FLOAT(TwoForty);
-FLOAT(MinusOne );
-FLOAT(OneAndHalf);
-
-/*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 */
-FLOAT(AInvrse);
-FLOAT(A1);
-FLOAT(C);
-FLOAT(CInvrse);
-FLOAT(D);
-FLOAT(FourD);
-FLOAT(E0);
-FLOAT(E1);
-FLOAT(Exp2);
-FLOAT(E3);
-FLOAT(MinSqEr);
-FLOAT(SqEr);
-FLOAT(MaxSqEr);
-FLOAT(E9);
-FLOAT(Third);
-FLOAT(F6);
-FLOAT(F9);
-FLOAT(H);
-FLOAT(HInvrse);
-FLOAT(StickyBit);
-FLOAT(J);
-FLOAT(MyZero);
-FLOAT(Precision);
-FLOAT(Q);
-FLOAT(Q9);
-FLOAT(R);
-FLOAT(Random9);
-FLOAT(T);
-FLOAT(Underflow);
-FLOAT(S);
-FLOAT(OneUlp);
-FLOAT(UfThold);
-FLOAT(U1);
-FLOAT(U2);
-FLOAT(V);
-FLOAT(V0);
-FLOAT(V9);
-FLOAT(W);
-FLOAT(X);
-FLOAT(X1);
-FLOAT(X2);
-FLOAT(X8);
-FLOAT(Random1);
-FLOAT(Y);
-FLOAT(YY1);
-FLOAT(Y2);
-FLOAT(Random2);
-FLOAT(Z);
-FLOAT(PseudoZero);
-FLOAT(Z1);
-FLOAT(Z2);
-FLOAT(Z9);
-static FLOAT(t);
-FLOAT(t2);
-FLOAT(Sqarg);
-int ErrCnt[4];
-int fpecount;
-int Milestone;
-int PageNo;
-int I, M, N, N1, stkflg;
-Guard GMult, GDiv, GAddSub;
-Rounding RMult, RDiv, RAddSub, RSqrt;
-int Break, Done, NotMonot, Monot, Anomaly, IEEE;
-int SqRWrng, UfNGrad;
-int k, k2;
-int Indx;
-char ch[8];
-
-long lngint, lng2; /* intermediate for conversion between int and FLOAT */
-
-/* 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 */
-
-
-show( x )
-short x[];
-{
-int i;
-char s[80];
-
-/* Number of 16-bit groups to display */
-#if NATIVE
-#if LDOUBLE
-#define NPRT (sizeof( long double )/2)
-#else
-#define NPRT (sizeof( double )/2)
-#endif
-#else
-#define NPRT NE
-#endif
-
-TOASC( x, s, 70 );
-printf( "%s\n", s );
-for( i=0; i<NPRT; i++ )
-	printf( "%04x ", x[i] & 0xffff );
-printf( "\n" );
-}
-
-/* define NOSIGNAL */
-#ifndef NOSIGNAL
-#include <signal.h>
-#endif
-#include <setjmp.h>
-jmp_buf ovfl_buf;
-/*typedef int (*Sig_type)();*/
-typedef void (*Sig_type)();
-Sig_type sigsave;
-
-/* Floating point exception receiver */
-void sigfpe()
-{
-fpecount++;
-printf( "\n* * * FLOATING-POINT ERROR * * *\n" );
-/* reinitialize the floating point unit */
-FSETUP();
-fflush(stdout);
-if( sigsave )
-	{
-#ifndef NOSIGNAL
-	signal( SIGFPE, sigsave );
-#endif
-	sigsave = 0;
-	longjmp( ovfl_buf, 1 );
-	}
-abort();
-}
-
-
-main()
-{
-
-/* Do coprocessor or other initializations */
-FSETUP();
-
-printf(
- "This version of paranoia omits test for extra precise subexpressions\n" );
-printf( "and includes a few additional tests.\n" );
-
-clear(Zero);
-printf( "0 = " );
-show( Zero );
-mov( ONE, One);
-printf( "1 = " );
-show( One );
-add( One, One, Two );
-printf( "1+1 = " );
-show( Two );
-add( Two, One, Three );
-add( Three, One, Four );
-add( Four, One, Five );
-add( Five, One, Six );
-add( Four, Four, Eight );
-mul( Three, Three, Nine );
-add( Nine, One, Ten );
-mul( Nine, Three, TwentySeven );
-mul( Four, Eight, ThirtyTwo );
-mul( Four, Five, t );
-mul( t, Three, t );
-mul( t, Four, TwoForty );
-mov( One, MinusOne );
-neg( MinusOne );
-div( Two, One, Half );
-add( One, Half, OneAndHalf );
-ErrCnt[Failure] = 0;
-ErrCnt[Serious] = 0;
-ErrCnt[Defect] = 0;
-ErrCnt[Flaw] = 0;
-PageNo = 1;
-#ifndef NOSIGNAL
-signal( SIGFPE, sigfpe );
-#endif
-printf("Program is now RUNNING tests on small integers:\n");
-
-add( Zero, Zero, t );
-if( cmp( t, Zero ) != 0)
-	{
-	printf( "0+0 != 0\n" );
-	ErrCnt[Failure] += 1;
-	}
-sub( One, One, t );
-if( cmp( t, Zero ) != 0 )
-	{
-	printf( "1-1 != 0\n" );
-	ErrCnt[Failure] += 1;
-	}
-if( cmp( One, Zero ) <= 0 )
-	{
-	printf( "1 <= 0\n" );
-	ErrCnt[Failure] += 1;
-	}
-add( One, One, t );
-if( cmp( t, Two ) != 0 )
-	{
-	printf( "1+1 != 2\n" );
-	ErrCnt[Failure] += 1;
-	}
-mov( Zero, Z );
-neg( Z );
-FLOOR( Z, t );
-if( cmp(t,Zero) != 0 )
-	{
-	ErrCnt[Serious] += 1;
-	printf( "FLOOR(-0) should equal 0, is = " );
-	show( t );
-	}
-if( cmp(Z, Zero) != 0)
-	{
-	ErrCnt[Failure] += 1;
-	printf("Comparison alleges that -0.0 is Non-zero!\n");
-	}
-else
-	{
-	div( TwoForty, One, U1 ); /* U1 = 0.001 */
-	mov( One, Radix );
-	TstPtUf();
-	}
-add( Two, One, t );
-if( cmp( t, Three ) != 0 )
-	{
-	printf( "2+1 != 3\n" );
-	ErrCnt[Failure] += 1;
-	}
-add( Three, One, t );
-if( cmp( t, Four ) != 0 )
-	{
-	printf( "3+1 != 4\n" );
-	ErrCnt[Failure] += 1;
-	}
-mov( Two, t );
-neg( t );
-mul( Two, t, t );
-add( Four, t, t );
-if( cmp( t, Zero ) != 0 )
-	{
-	printf( "4+2*(-2) != 0\n" );
-	ErrCnt[Failure] += 1;
-	}
-sub( Three, Four, t );
-sub( One, t, t );
-if( cmp( t, Zero ) != 0 )
-	{
-	printf( "4-3-1 != 0\n" );
-	ErrCnt[Failure] += 1;
-	}
-	sub( One, Zero, t );
-if( cmp( t, MinusOne ) != 0 )
-	{
-	printf( "-1 != 0-1\n" );
-	ErrCnt[Failure] += 1;
-	}
-add( One, MinusOne, t );
-if( cmp( t, Zero ) != 0 )
-	{
-	printf( "1+(-1) != 0\n" );
-	ErrCnt[Failure] += 1;
-	}
-mov( One, t );
-FABS( t );
-add( MinusOne, t, t );
-if( cmp( t, Zero ) != 0 )
-	{
-	printf( "-1+abs(1) != 0\n" );
-	ErrCnt[Failure] += 1;
-	}
-mul( MinusOne, MinusOne, t );
-add( MinusOne, t, t );
-if( cmp( t, Zero ) != 0 )
-	{
-	printf( "-1+(-1)*(-1) != 0\n" );
-	ErrCnt[Failure] += 1;
-	}
-add( Half, MinusOne, t );
-add( Half, t, t );
-if( cmp( t, Zero ) != 0 )
-	{
-	printf( "1/2 + (-1) + 1/2 != 0\n" );
-	ErrCnt[Failure] += 1;
-	}
-Milestone = 10;
-mul( Three, Three, t );
-if( cmp( t, Nine ) != 0 )
-	{
-	printf( "3*3 != 9\n" );
-	ErrCnt[Failure] += 1;
-	}
-mul( Nine, Three, t );
-if( cmp( t, TwentySeven ) != 0 )
-	{
-	printf( "3*9 != 27\n" );
-	ErrCnt[Failure] += 1;
-	}
-add( Four, Four, t );
-if( cmp( t, Eight ) != 0 )
-	{
-	printf( "4+4 != 8\n" );
-	ErrCnt[Failure] += 1;
-	}
-mul( Eight, Four, t );
-if( cmp( t, ThirtyTwo ) != 0 )
-	{
-	printf( "8*4 != 32\n" );
-	ErrCnt[Failure] += 1;
-	}
-sub( TwentySeven, ThirtyTwo, t );
-sub( Four, t, t );
-sub( One, t, t );
-if( cmp( t, Zero ) != 0 )
-	{
-	printf( "32-27-4-1 != 0\n" );
-	ErrCnt[Failure] += 1;
-	}
-add( Four, One, t );
-if( cmp( t, Five ) != 0 )
-	{
-	printf( "4+1 != 5\n" );
-	ErrCnt[Failure] += 1;
-	}
-mul( Four, Five, t );
-mul( Three, t, t );
-mul( Four, t, t );
-if( cmp( t, TwoForty ) != 0 )
-	{
-	printf( "4*5*3*4 != 240\n" );
-	ErrCnt[Failure] += 1;
-	}
-div( Three, TwoForty, t );
-mul( Four, Four, t2 );
-mul( Five, t2, t2 );
-sub( t2, t2, t );
-if( cmp( t, Zero ) != 0 )
-	{
-	printf( "240/3 - 4*4*5 != 0\n" );
-	ErrCnt[Failure] += 1;
-	}
-div( Four, TwoForty, t );
-mul( Five, Three, t2 );
-mul( Four, t2, t2 );
-sub( t2, t, t );
-if( cmp( t, Zero ) != 0 )
-	{
-	printf( "240/4 - 5*3*4 != 0\n" );
-	ErrCnt[Failure] += 1;
-	}
-div( Five, TwoForty, t );
-mul( Four, Three, t2 );
-mul( Four, t2, t2 );
-sub( t2, t, t );
-if( cmp( t, Zero ) != 0 )
-	{
-	printf( "240/5 - 4*3*4 != 0\n" );
-	ErrCnt[Failure] += 1;
-	}
-if(ErrCnt[Failure] == 0)
-	{
-printf("-1, 0, 1/2, 1, 2, 3, 4, 5, 9, 27, 32 & 240 are O.K.\n\n");
-	}
-printf("Searching for Radix and Precision.\n");
-mov( One, W );
-do
-	{
-	add( W, W, W );
-	add( W, One, Y );
-	sub( W, Y, Z );
-	sub( One, Z, Y );
-	mov( Y, t );
-	FABS(t);
-	add( MinusOne, t, t );
-	k = cmp( t, Zero );
-	}
-while( k < 0 );
-/*.. now W is just big enough that |((W+1)-W)-1| >= 1 ...*/
-mov( Zero, Precision );
-mov( One, Y );
-do
-	{
-	add( W, Y, Radix );
-	add( Y, Y, Y );
-	sub( W, Radix, Radix );
-	k = cmp( Radix, Zero );
-	}
-while( k == 0);
-
-if( cmp(Radix, Two) < 0 )
-	mov( One, Radix );
-printf("Radix = " );
-show( Radix );
-if( cmp(Radix, One) != 0)
-	{
-	mov( One, W );
-	do
-		{
-		add( One, Precision, Precision );
-		mul( W, Radix, W );
-		add( W, One, Y );
-		sub( W, Y, t );
-		k = cmp( t, One );
-		}
-	while( k == 0 );
-	}
-/* now W == Radix^Precision is barely too big to satisfy (W+1)-W == 1 */
-div( W, One, U1 );
-mul( Radix, U1, U2 );
-printf( "Closest relative separation found is U 1 = " );
-show( U1 );
-printf( "Recalculating radix and precision." );
-	
-/*save old values*/
-mov( Radix, E0 );
-mov( U1, E1 );
-mov( U2, E9 );
-mov( Precision, E3 );
-	
-div( Three, Four, X );
-sub( One, X, Third );
-sub( Third, Half, F6 );
-add( F6, F6, X );
-sub( Third, X, X );
-FABS( X );
-if( cmp(X, U2) < 0 )
-	mov( U2, X );
-	
-/*... now X = (unknown no.) ulps of 1+...*/
-do
-	{
-	mov( X, U2 );
-/* Y = Half * U2 + ThirtyTwo * U2 * U2; */
-	mul( ThirtyTwo, U2, t );
-	mul( t, U2, t );
-	mul( Half, U2, Y );
-	add( t, Y, Y );
-	add( One, Y, Y );
-	sub( One, Y, X );
-	k = cmp( U2, X );
-	k2 = cmp( X, Zero );
-	}
-while ( ! ((k <= 0) || (k2 <= 0)));
-	
-/*... now U2 == 1 ulp of 1 + ... */
-div( Three, Two, X );
-sub( Half, X, F6 );
-add( F6, F6, Third );
-sub( Half, Third, X );
-add( F6, X, X );
-FABS( X );
-if( cmp(X, U1) < 0 )
-	mov( U1, X );
-	
-/*... now  X == (unknown no.) ulps of 1 -... */
-do
-	{
-	mov( X, U1 );
- /* Y = Half * U1 + ThirtyTwo * U1 * U1;*/
-	mul( ThirtyTwo, U1, t );
-	mul( U1, t, t );
-	mul( Half, U1, Y );
-	add( t, Y, Y );
-	sub( Y, Half, Y );
-	add( Half, Y, X );
-	sub( X, Half, Y );
-	add( Half, Y, X );
-	k = cmp( U1, X );
-	k2 = cmp( X, Zero );
-	} while ( ! ((k <= 0) || (k2 <= 0)));
-/*... now U1 == 1 ulp of 1 - ... */
-if( cmp( U1, E1 ) == 0 )
-	printf("confirms closest relative separation U1 .\n");
-else
-	{
-	printf("gets better closest relative separation U1 = " );
-	show( U1 );
-	}
-div( U1, One, W );
-sub( U1, Half, F9 );
-add( F9, Half, F9 );
-div( U1, U2, t );
-div( TwoForty, One, t2 );
-add( t2, t, t );
-FLOOR( t, Radix );
-if( cmp(Radix, E0) == 0 )
-	printf("Radix confirmed.\n");
-else
-	{
-	printf("MYSTERY: recalculated Radix = " );
-	show( Radix );
-	mov( E0, Radix );
-	}
-add( Eight, Eight, t );
-if( cmp( Radix, t ) > 0 )
-	{
-	printf( "Radix is too big: roundoff problems\n" );
-	ErrCnt[Defect] += 1;
-	}
-k = 1;
-if( cmp( Radix, Two ) == 0 )
-	k = 0;
-if( cmp( Radix, Ten ) == 0 )
-	k = 0;
-if( cmp( Radix, One ) == 0 )
-	k = 0;
-if( k != 0 )
-	{
-	printf( "Radix is not as good as 2 or 10\n" );
-	ErrCnt[Flaw] += 1;
-	}
-/*=============================================*/
-Milestone = 20;
-/*=============================================*/
-sub( Half, F9, t );
-if( cmp( t, Half ) >= 0 )
-	{
-	printf( "(1-U1)-1/2 < 1/2 is FALSE, prog. fails?\n" );
-	ErrCnt[Failure] += 1;
-	}
-mov( F9, X );
-I = 1;
-sub( Half, X, Y );
-sub( Half, Y, Z );
-if( (cmp( X, One ) == 0) && (cmp( Z, Zero) != 0) )
-	{
-	printf( "Comparison is fuzzy ,X=1 but X-1/2-1/2 != 0\n" );
-	ErrCnt[Failure] += 1;
-	}
-add( One, U2, X );
-I = 0;
-/*=============================================*/
-Milestone = 25;
-/*=============================================*/
-/*... BMinusU2 = nextafter(Radix, 0) */
-
-sub( One, Radix, BMinusU2 );
-sub( U2, BMinusU2, t );
-add( One, t, BMinusU2 );
-/* Purify Integers */
-if( cmp(Radix,One) != 0 )
-	{
-/*X = - TwoForty * LOG(U1) / LOG(Radix);*/
-	LOG( U1, X );
-	LOG( Radix, t );
-	div( t, X, X );
-	mul( TwoForty, X, X );
-	neg( X );	
-
-	add( Half, X, Y );
-	FLOOR( Y, Y );
-	sub( Y, X, t );
-	FABS( t );
-	mul( Four, t, t );
-	if( cmp( t, One ) < 0 )
-		mov( Y, X );
-	div( TwoForty, X, Precision );
-	add( Half, Precision, Y );
-	FLOOR( Y, Y );
-	sub( Y, Precision, t );
-	FABS( t );
-	mul( TwoForty, t, t );
-	if( cmp( t, Half ) < 0 )
-		mov( Y, Precision );
-	}
-FLOOR( Precision, t );
-if( (cmp( Precision, t ) != 0) || (cmp( Radix, One ) == 0) )
-	{
-	printf("Precision cannot be characterized by an Integer number\n");
-	printf("of significant digits but, by itself, this is a minor flaw.\n");
-	}
-if( cmp(Radix, One) == 0 ) 
-	printf("logarithmic encoding has precision characterized solely by U1.\n");
-else
-	{
-	printf("The number of significant digits of the Radix is " );
-	show( Precision );
-	}
-mul( U2, Nine, t );
-mul( Nine, t, t );
-mul( TwoForty, t, t );
-if( cmp( t, One ) >= 0 )
-	{
-	printf( "Precision worse than 5 decimal figures\n" );
-	ErrCnt[Serious] += 1;
-	}
-/*=============================================*/
-Milestone = 30;
-/*=============================================*/
-/* Test for extra-precise subepressions has been deleted. */
-Milestone = 35;
-/*=============================================*/
-if( cmp(Radix,Two) >= 0 )
-	{
-	mul( Radix, Radix, t );
-	div( t, W, X );
-	add( X, One, Y );
-	sub( X, Y, Z );
-	add( Z, U2, T );
-	sub( Z, T, X );
-	if( cmp( X, U2 ) != 0 )
-		{
-		printf( "Subtraction is not normalized X=Y,X+Z != Y+Z!\n" );
-		ErrCnt[Failure] += 1;
-		}
-	if( cmp(X,U2) == 0 )
-	 printf("Subtraction appears to be normalized, as it should be.");
-	}
-
-printf("\nChecking for guard digit in *, /, and -.\n");
-mul( F9, One, Y );
-mul( One, F9, Z );
-sub( Half, F9, X );
-sub( Half, Y, Y );
-sub( X, Y, Y );
-sub( Half, Z, Z );
-sub( X, Z, Z );
-add( One, U2, X );
-mul( X, Radix, T );
-mul( Radix, X, R );
-sub( Radix, T, X );
-mul( Radix, U2, t );
-sub( t, X, X );
-sub( Radix, R, T );
-mul( Radix, U2, t );
-sub( t, T, T );
-sub( One, Radix, t );
-mul( t, X, X );
-sub( One, Radix, t );
-mul( t, T, T );
-
-k = cmp(X,Zero);
-k |= cmp(Y,Zero);
-k |= cmp(Z,Zero);
-k |= cmp(T,Zero);
-if( k == 0 )
-	GMult = Yes;
-else
-	{
-	GMult = No;
-	ErrCnt[Serious] += 1;
-	printf( "* lacks a Guard Digit, so 1*X != X\n" );
-	}
-mul( Radix, U2, Z );
-add( One, Z, X );
-add( X, Z, Y );
-mul( X, X, t );
-sub( t, Y, Y );
-FABS( Y );
-sub( U2, Y, Y );
-sub( U2, One, X );
-sub( U2, X, Z );
-mul( X, X, t );
-sub( t, Z, Z );
-FABS( Z );
-sub( U1, Z, Z );
-if( (cmp(Y,Zero) > 0) || (cmp(Z,Zero) > 0) )
-	{
-	ErrCnt[Failure] += 1;
-	printf( "* gets too many final digits wrong.\n" );
-	}
-sub( U2, One, Y );
-add( One, U2, X );
-div( Y, One, Z );
-sub( X, Z, Y );
-div( Three, One, X );
-div( Nine, Three, Z );
-sub( Z, X, X );
-div( TwentySeven, Nine, T );
-sub( T, Z, Z );
-k = cmp( X, Zero );
-k |= cmp( Y, Zero );
-k |= cmp( Z, Zero );
-if( k )
-	{
-	ErrCnt[Defect] += 1;
-printf( "Division lacks a Guard Digit, so error can exceed 1 ulp\n" );
-printf( "or  1/3  and  3/9  and  9/27 may disagree\n" );
-	}
-div( One, F9, Y );
-sub( Half, F9, X );
-sub( Half, Y, Y );
-sub( X, Y, Y );
-add( One, U2, X );
-div( One, X, T );
-sub( X, T, X );
-k = cmp( X, Zero );
-k |= cmp( Y, Zero );
-k |= cmp( Z, Zero );
-if( k == 0 )
-	GDiv = Yes;
-else
-	{
-	GDiv = No;
-	ErrCnt[Serious] += 1;
-	printf( "Division lacks a Guard Digit, so X/1 != X\n" );
-	}
-add( One, U2, X );
-div( X, One, X );
-sub( Half, X, Y );
-sub( Half, Y, Y );
-if( cmp(Y,Zero) >= 0 )
-	{
-	ErrCnt[Serious] += 1;
-	printf( "Computed value of 1/1.000..1 >= 1\n" );
-	}
-sub( U2, One, X );
-mul( Radix, U2, Y );
-add( One, Y, Y );
-mul( X, Radix, Z );
-mul( Y, Radix, T );
-div( Radix, Z, R );
-div( Radix, T, StickyBit );
-sub( X, R, X );
-sub( Y, StickyBit, Y );
-k = cmp( X, Zero );
-k |= cmp( Y, Zero );
-if( k )
-	{
-	ErrCnt[Failure] += 1;
-	printf( "* and/or / gets too many last digits wrong\n" );
-	}
-sub( U1, One, Y );
-sub( F9, One, X );
-sub( Y, One, Y );
-sub( U2, Radix, T );
-sub( BMinusU2, Radix, Z );
-sub( T, Radix, T );
-k = cmp( X, U1 );
-k |= cmp( Y, U1 );
-k |= cmp( Z, U2 );
-k |= cmp( T, U2 );
-if( k == 0 )
-	GAddSub = Yes;
-else
-	{
-	GAddSub = No;
-	ErrCnt[Serious] += 1;
-	printf( "- lacks Guard Digit, so cancellation is obscured\n" );
-	}
-sub( One, F9, t );
-if( (cmp(F9,One) != 0) && (cmp(t,Zero) >= 0) )
-	{
-	ErrCnt[Serious] += 1;
-	printf("comparison alleges  (1-U1) < 1  although\n");
-	printf("  subtration 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;
-/*=============================================*/
-printf("Checking rounding on multiply, divide and add/subtract.\n");
-RMult = Other;
-RDiv = Other;
-RAddSub = Other;
-div( Two, Radix, RadixD2 );
-mov( Two, A1 );
-Done = False;
-do
-	{
-	mov( Radix, AInvrse );
-	do
-		{
-		mov( AInvrse, X );
-		div( A1, AInvrse, AInvrse );
-		FLOOR( AInvrse, t );
-		k = cmp( t, AInvrse );
-		}
-	while( ! (k != 0 ) );
-	k = cmp( X, One );
-	k2 = cmp( A1, Three );
-	Done = (k == 0) || (k2 > 0);
-	if(! Done)
-		add( Nine, One, A1 );
-	}
-while( ! (Done));
-if( cmp(X, One) == 0 )
-	mov( Radix, A1 );
-div( A1, One, AInvrse );
-mov( A1, X );
-mov( AInvrse, Y );
-Done = False;
-do
-	{
-	mul( X, Y, Z );
-	sub( Half, Z, Z );
-	if( cmp( Z, Half ) != 0 )
-		{
-		ErrCnt[Failure] += 1;
-		printf( "X * (1/X) differs from 1\n" );
-		}
-	k = cmp( X, Radix );
-	Done = (k == 0);
-	mov( Radix, X );
-	div( X, One, Y );
-	}
-while( ! (Done));
-
-add( One, U2, Y2 );
-sub( U2, One, YY1 );
-sub( U2, OneAndHalf, X );
-add( OneAndHalf, U2, Y );
-sub( U2, X, Z );
-mul( Z, Y2, Z );
-mul( Y, YY1, T );
-sub( X, Z, Z );
-sub( X, T, T );
-mul( X, Y2, X );
-add( Y, U2, Y );
-mul( Y, YY1, Y );
-sub( OneAndHalf, X, X );
-sub( OneAndHalf, Y, Y );
-k = cmp( X, Zero );
-k |= cmp( Y, Zero );
-k |= cmp( Z, Zero );
-if( cmp( T, Zero ) > 0 )
-	k = 1;
-if( k == 0 )
-	{
-	add( OneAndHalf, U2, X );
-	mul( X, Y2, X );
-	sub( U2, OneAndHalf, Y );
-	sub( U2, Y, Y );
-	add( OneAndHalf, U2, Z );
-	add( U2, Z, Z );
-	sub( U2, OneAndHalf, T );
-	mul( T, YY1, T );
-	add( Z, U2, t );
-	sub( t, X, X );
-	mul( Y, YY1, StickyBit );
-	mul( Z, Y2, S );
-	sub( Y, T, T );
-	sub( Y, U2, Y );
-	add( StickyBit, Y, Y );
-/* Z = S - (Z + U2 + U2); */
-	add( Z, U2, t );
-	add( t, U2, t );
-	sub( t, S, Z );
-	add( Y2, U2, t );
-	mul( t, YY1, StickyBit );
-	mul( Y2, YY1, YY1 );
-	sub( Y2, StickyBit, StickyBit );
-	sub( Half, YY1, YY1 );
-	k = cmp( X, Zero );
-	k |= cmp( Y, Zero );
-	k |= cmp( Z, Zero );
-	k |= cmp( T, Zero );
-	k |= cmp( StickyBit, Zero );
-	k |= cmp( YY1, Half );
-	if( k == 0 )
-		{
-		RMult = Rounded;
-		printf("Multiplication appears to round correctly.\n");
-		}
-	else
-		{
-		add( X, U2, t );
-		k = cmp( t, Zero );
-		if( cmp( Y, Zero ) >= 0 )
-			k |= 1;
-		add( Z, U2, t );
-		k |= cmp( t, Zero );
-		if( cmp( T, Zero ) >= 0 )
-			k |= 1;
-		add( StickyBit, U2, t );
-		k |= cmp( t, Zero );
-		if( cmp(YY1, Half) >= 0 )
-			k |= 1;
-		if( k == 0 )
-			{
-			printf("Multiplication appears to chop.\n");
-			}
-		else
-			{
-		printf("* is neither chopped nor correctly rounded.\n");
-			}
-		if( (RMult == Rounded) && (GMult == No) )
-			printf("Multiplication has inconsistent result");
-		}
-	}
-else
-	printf("* is neither chopped nor correctly rounded.\n");
-
-/*=============================================*/
-Milestone = 45;
-/*=============================================*/
-add( One, U2, Y2 );
-sub( U2, One, YY1 );
-add( OneAndHalf, U2, Z );
-add( Z, U2, Z );
-div( Y2, Z, X );
-sub( U2, OneAndHalf, T );
-sub( U2, T, T );
-sub( U2, T, Y );
-div( YY1, Y, Y );
-add( Z, U2, Z );
-div( Y2, Z, Z );
-sub( OneAndHalf, X, X );
-sub( T, Y, Y );
-div( YY1, T, T );
-add( OneAndHalf, U2, t );
-sub( t, Z, Z );
-sub( OneAndHalf, U2, t );
-add( t, T, T );
-k = 0;
-if( cmp( X, Zero ) > 0 )
-	k = 1;
-if( cmp( Y, Zero ) > 0 )
-	k = 1;
-if( cmp( Z, Zero ) > 0 )
-	k = 1;
-if( cmp( T, Zero ) > 0 )
-	k = 1;
-if( k == 0 )
-	{
-	div( Y2, OneAndHalf, X );
-	sub( U2, OneAndHalf, Y );
-	add( U2, OneAndHalf, Z );
-	sub( Y, X, X );
-	div( YY1, OneAndHalf, T );
-	div( YY1, Y, Y );
-	add( Z, U2, t );
-	sub( t, T, T );
-	sub( Z, Y, Y );
-	div( Y2, Z, Z );
-	add( Y2, U2, YY1 );
-	div( Y2, YY1, YY1 );
-	sub( OneAndHalf, Z, Z );
-	sub( Y2, YY1, Y2 );
-	sub( U1, F9, YY1 );
-	div( F9, YY1, YY1 );
-	k = cmp( X, Zero );
-	k |= cmp( Y, Zero );
-	k |= cmp( Z, Zero );
-	k |= cmp( T, Zero );
-	k |= cmp( Y2, Zero );
-	sub( Half, YY1, t );
-	sub( Half, F9, t2 );
-	k |= cmp( t, t2 );
-	if( k == 0 )
-		{
-		RDiv = Rounded;
-		printf("Division appears to round correctly.\n");
-		if(GDiv == No)
-			printf("Division test inconsistent\n");
-		}
-	else
-		{
-		k = 0;
-		if( cmp( X, Zero ) >= 0 )
-			k = 1;
-		if( cmp( Y, Zero ) >= 0 )
-			k = 1;
-		if( cmp( Z, Zero ) >= 0 )
-			k = 1;
-		if( cmp( T, Zero ) >= 0 )
-			k = 1;
-		if( cmp( Y, Zero ) >= 0 )
-			k = 1;
-		sub( Half, YY1, t );
-		sub( Half, F9, t2 );
-		if( cmp( t, t2 ) >= 0 )
-			k = 1;
-		if( k == 0 )
-			{
-			RDiv = Chopped;
-			printf("Division appears to chop.\n");
-			}
-		}
-	}
-if(RDiv == Other)
-	printf("/ is neither chopped nor correctly rounded.\n");
-div( Radix, One, BInvrse );
-mul( BInvrse, Radix, t );
-sub( Half, t, t );
-if( cmp( t, Half ) != 0 )
-	{
-	ErrCnt[Failure] += 1;
-	printf( "Radix * ( 1 / Radix ) differs from 1\n" );
-	}
-
-Milestone = 50;
-/*=============================================*/
-add( F9, U1, t );
-sub( Half, t, t );
-k = cmp( t, Half );
-add( BMinusU2, U2, t );
-sub( One, t, t );
-sub( One, Radix, t2 );
-k |= cmp( t, t2 );
-if( k != 0 )
-	{
-	ErrCnt[Failure] += 1;
-	printf( "Incomplete carry-propagation in Addition\n" );
-	}
-mul( U1, U1, X );
-sub( X, One, X );
-sub( U2, One, Y );
-mul( U2, Y, Y );
-add( One, Y, Y );
-sub( Half, F9, Z );
-sub( Half, X, X );
-sub( Z, X, X );
-sub( One, Y, Y );
-if( (cmp(X,Zero) == 0) && (cmp(Y,Zero) == 0) )
-	{
-	RAddSub = Chopped;
-	printf("Add/Subtract appears to be chopped.\n");
-	}
-if(GAddSub == Yes)
-	{
-	add( Half, U2, X );
-	mul( X, U2, X );
-	sub( U2, Half, Y );
-	mul( Y, U2, Y );
-	add( One, X, X );
-	add( One, Y, Y );
-	add( One, U2, t );
-	sub( X, t, X );
-	sub( Y, One, Y );
-	k = cmp(X,Zero);
-	if( k )
-		printf( "1+U2-[u2(1/2+U2)+1] != 0\n" );
-	k2 = cmp(Y,Zero);
-	if( k2 )
-		printf( "1-[U2(1/2-U2)+1] != 0\n" );
-	k |= k2;
-	if( k == 0 )
-		{
-		add( Half, U2, X );
-		mul( X, U1, X );
-		sub( U2, Half, Y );
-		mul( Y, U1, Y );
-		sub( X, One, X );
-		sub( Y, One, Y );
-		sub( X, F9, X );
-		sub( Y, One, Y );
-		k = cmp(X,Zero);
-		if( k )
-			printf( "F9-[1-U1(1/2+U2)] != 0\n" );
-		k2 = cmp(Y,Zero);
-		if( k2 )
-			printf( "1-[1-U1(1/2-U2)] != 0\n" );
-		k |= k2;
-		if( k == 0 )
-			{
-			RAddSub = Rounded;
-		printf("Addition/Subtraction appears to round correctly.\n");
-			if(GAddSub == No)
-				printf( "Add/Subtract test inconsistent\n");
-			}
-		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");
-
-mov( One, S );
-add( One, Half, X );
-mul( Half, X, X );
-add( One, X, X );
-add( One, U2, Y );
-mul( Y, Half, Y );
-sub( Y, X, Z );
-sub( X, Y, T );
-add( Z, T, StickyBit );
-if( cmp(StickyBit, Zero) != 0 )
-	{
-	mov( Zero, S );
-	ErrCnt[Flaw] += 1;
-	printf( "(X - Y) + (Y - X) is non zero!\n" );
-	}
-mov( Zero, StickyBit );
-FLOOR( RadixD2, t );
-k2 = cmp( t, RadixD2 );
-k = 1;
-if( (GMult == Yes) && (GDiv == Yes) && (GAddSub == Yes)
-	&& (RMult == Rounded) && (RDiv == Rounded)
-	&& (RAddSub == Rounded) && (k2 == 0) )
-	{
-	printf("Checking for sticky bit.\n");
-	k = 0;
-	add( Half, U1, X );
-	mul( X, U2, X );
-	mul( Half, U2, Y );
-	add( One, Y, Z );
-	add( One, X, T );
-	sub( One, Z, t );
-	sub( One, T, t2 );
-	if( cmp(t,Zero) > 0 )
-		{
-		k = 1;
-		printf( "[1+(1/2)U2]-1 > 0\n" );
-		}
-	if( cmp(t2,U2) < 0 )
-		{
-		k = 1;
-		printf( "[1+U2(1/2+U1)]-1 < U2\n" );
-		}
-	add( T, Y, Z );
-	sub( X, Z, Y );
-	sub( T, Z, t );
-	sub( T, Y, t2 );
-	if( cmp(t,U2) < 0 )
-		{
-		k = 1;
-		printf( "[[1+U2(1/2+U1)]+(1/2)U2]-[1+U2(1/2+U1)] < U2\n" );
-		}
-	if( cmp(t2,Zero) != 0 )
-		{
-		k = 1;
-		printf( "(1/2)U2-[1+U2(1/2+U1)] != 0\n" );
-		}
-	add( Half, U1, X );
-	mul( X, U1, X );
-	mul( Half, U1, Y );
-	sub( Y, One, Z );
-	sub( X, One, T );
-	sub( One, Z, t );
-	sub( F9, T, t2 );
-	if( cmp(t,Zero) != 0 )
-		{
-		k = 1;
-		printf( "(1-(1/2)U1)-1 != 0\n" );
-		}
-	if( cmp(t2,Zero) != 0 )
-		{
-		k = 1;
-		printf( "[1-U1(1/2+U1)]-F9 != 0\n" );
-		}
-	sub( U1, Half, Z );
-	mul( Z, U1, Z );
-	sub( Z, F9, T );
-	sub( Y, F9, Q );
-	sub( F9, T, t );
-	if( cmp( t, Zero ) != 0 )
-		{
-		k = 1;
-		printf( "[F9-U1(1/2-U1)]-F9 != 0\n" );
-		}
-	sub( U1, F9, t );
-	sub( Q, t, t );
-	if( cmp( t, Zero ) != 0 )
-		{
-		k = 1;
-		printf( "(F9-U1)-(F9-(1/2)U1) != 0\n" );
-		}
-	add( One, U2, Z );
-	mul( Z, OneAndHalf, Z );
-	add( OneAndHalf, U2, T );
-	sub( Z, T, T );
-	add( U2, T, T );
-	div( Radix, Half, X );
-	add( One, X, X );
-	mul( Radix, U2, Y );
-	add( One, Y, Y );
-	mul( X, Y, Z );
-	if( cmp( T, Zero ) != 0 )
-		{
-		k = 1;
-		printf( "(3/2+U2)-3/2(1+U2)+U2 != 0\n" );
-		}
-	mul( Radix, U2, t );
-	add( X, t, t );
-	sub( Z, t, t );
-	if( cmp( t, Zero ) != 0 )
-		{
-		k = 1;
-	printf( "(1+1/2Radix)+Radix*U2-[1+1/(2Radix)][1+Radix*U2] != 0\n" );
-		}
-	if( cmp(Radix, Two) != 0 )
-		{
-		add( Two, U2, X );
-		div( Two, X, Y );
-		sub( One, Y, t );
-		if( cmp( t, Zero) != 0 )
-			k = 1;
-		}
-	}
-if( k == 0 )
-	{
-	printf("Sticky bit apparently used correctly.\n");
-	mov( One, StickyBit );
-	}
-else
-	{
-	printf("Sticky bit used incorrectly or not at all.\n");
-	}
-
-if( GMult == No || GDiv == No || GAddSub == No ||
-		RMult == Other || RDiv == Other || RAddSub == Other)
-	{
-	ErrCnt[Flaw] += 1;
- printf("lack(s) of guard digits or failure(s) to correctly round or chop\n");
-printf( "(noted above) count as one flaw in the final tally below\n" );
-	}
-/*=============================================*/
-Milestone = 60;
-/*=============================================*/
-printf("\n");
-printf("Does Multiplication commute?  ");
-printf("Testing on %d random pairs.\n", NoTrials);
-SQRT( Three, Random9 );
-mov( Third, Random1 );
-I = 1;
-do
-	{
-	Random();
-	mov( Random1, X );
-	Random();
-	mov( Random1, Y );
-	mul( Y, X, Z9 );
-	mul( X, Y, Z );
-	sub( Z9, Z, Z9 );
-	I = I + 1;
-	}
-while ( ! ((I > NoTrials) || (cmp(Z9,Zero) != 0)));
-if(I == NoTrials)
-	{
-	div( Three, Half, t );
-	add( One, t, Random1 );
-	add( U2, U1, t );
-	add( t, One, Random2 );
-	mul( Random1, Random2, Z );
-	mul( Random2, Random1, Y );
-/* Z9 = (One + Half / Three) * ((U2 + U1) + One) - (One + Half /
- *			Three) * ((U2 + U1) + One);
- */
-	div( Three, Half, t2 );
-	add( One, t2, t2 );
-	add( U2, U1, t );
-	add( t, One, t );
-	mul( t2, t, Z9 );
-	mul( t2, t, t );
-	sub( t, Z9, Z9 );
-	}
-if(! ((I == NoTrials) || (cmp(Z9,Zero) == 0)))
-	{
-	ErrCnt[Defect] += 1;
-	printf( "X * Y == Y * X trial fails.\n");
-	}
-else
-	{
-	printf("     No failures found in %d integer pairs.\n", NoTrials);
-	}
-/*=============================================*/
-Milestone = 70;
-/*=============================================*/
-sqtest();
-Milestone = 90;
-pow1test();
-
-Milestone = 110;
-
-printf("Seeking Underflow thresholds UfThold and E0.\n");
-mov( U1, D );
-FLOOR( Precision, t );
-if( cmp(Precision, t) != 0 )
-	{
-	mov( BInvrse, D );
-	mov( Precision, X );
-	do
-		{
-		mul( D, BInvrse, D );
-		sub( One, X, X );
-		}
-	while( cmp(X, Zero) > 0 );
-	}
-mov( One, Y );
-mov( D, Z );
-/* ... D is power of 1/Radix < 1. */
-sigsave = sigfpe;
-if( setjmp(ovfl_buf) )
-	goto under0;
-do
-	{
-	mov( Y, C );
-	mov( Z, Y );
-	mul( Y, Y, Z );
-	add( Z, Z, t );
-	}
-while( (cmp(Y,Z) > 0) && (cmp(t,Z) > 0) );
-
-under0:
-sigsave = 0;
-
-mov( C, Y );
-mul( Y, D, Z );
-sigsave = sigfpe;
-if( setjmp(ovfl_buf) )
-	goto under1;
-do
-	{
-	mov( Y, C );
-	mov( Z, Y );
-	mul( Y, D, Z );
-	add( Z, Z, t );
-	}
-while( (cmp(Y,Z) > 0) && (cmp(t,Z) > 0) );
-
-under1:
-sigsave = 0;
-
-if( cmp(Radix,Two) < 0 )
-	mov( Two, HInvrse );
-else
-	mov( Radix, HInvrse );
-div( HInvrse, One, H );
-/* ... 1/HInvrse == H == Min(1/Radix, 1/2) */
-div( C, One, CInvrse );
-mov( C, E0 );
-mul( E0, H, Z );
-/* ...1/Radix^(BIG Integer) << 1 << CInvrse == 1/C */
-sigsave = sigfpe;
-if( setjmp(ovfl_buf) )
-	goto under2;
-do
-	{
-	mov( E0, Y );
-	mov( Z, E0 );
-	mul( E0, H, Z );
-	add( Z, Z, t );
-	}
-while( (cmp(E0,Z) > 0) && (cmp(t,Z) > 0) );
-
-under2:
-sigsave = 0;
-
-mov( E0, UfThold );
-mov( Zero, E1 );
-mov( Zero, Q );
-mov( U2, E9 );
-add( One, E9, S );
-mul( C, S, D );
-if( cmp(D,C) <= 0 )
-	{
-	mul( Radix, U2, E9 );
-	add( One, E9, S );
-	mul( C, S, D );
-	if( cmp(D, C) <= 0 )
-		{
-		ErrCnt[Failure] += 1;
-		printf( "multiplication gets too many last digits wrong.\n" );
-		mov( E0, Underflow );
-		mov( Zero, YY1 );
-		mov( Z, PseudoZero );
-		}
-	}
-else
-	{
-	mov( D, Underflow );
-	mul( Underflow, H, PseudoZero );
-	mov( Zero, UfThold );
-	do
-		{
-		mov( Underflow, YY1 );
-		mov( PseudoZero, Underflow );
-		add( E1, E1, t );
-		if( cmp(t, E1) <= 0)
-			{
-			mul( Underflow, HInvrse, Y2 );
-			sub( Y2, YY1, E1 );
-			FABS( E1 );
-			mov( YY1, Q );
-			if( (cmp( UfThold, Zero ) == 0)
-				&& (cmp(YY1, Y2) != 0) )
-				mov( YY1, UfThold );
-			}
-		mul( PseudoZero, H, PseudoZero );
-		add( PseudoZero, PseudoZero, t );
-		}
-	while( (cmp(Underflow, PseudoZero) > 0)
-		&& (cmp(t, PseudoZero) > 0) );
-	}
-/* Comment line 4530 .. 4560 */
-if( cmp(PseudoZero, Zero) != 0 )
-	{
-	printf("\n");
-	mov(PseudoZero, Z );
-/* ... Test PseudoZero for "phoney- zero" violates */
-/* ... PseudoZero < Underflow or PseudoZero < PseudoZero + PseudoZero
-		   ... */
-	if( cmp(PseudoZero, Zero) <= 0 )
-		{
-		ErrCnt[Failure] += 1;
-		printf("Positive expressions can underflow to an\n");
-		printf("allegedly negative value\n");
-		printf("PseudoZero that prints out as: " );
-		show( PseudoZero );
-		mov( PseudoZero, X );
-		neg( X );
-		if( cmp(X, Zero) <= 0 )
-			{
-			printf("But -PseudoZero, which should be\n");
-			printf("positive, isn't; it prints out as " );
-			show( X );
-			}
-		}
-	else
-		{
-		ErrCnt[Flaw] += 1;
-		printf( "Underflow can stick at an allegedly positive\n");
-		printf("value PseudoZero that prints out as " );
-		show( PseudoZero );
-		}
-/*	TstPtUf();*/
-	}
-
-/*=============================================*/
-Milestone = 120;
-/*=============================================*/
-mul( CInvrse, Y, t );
-mul( CInvrse, YY1, t2 );
-if( cmp(t,t2) > 0 )
-	{
-	mul( H, S, S );
-	mov( Underflow, E0 );
-	}
-if(! ((cmp(E1,Zero) == 0) || (cmp(E1,E0) == 0)) )
-	{
-	ErrCnt[Defect] += 1;
-	if( cmp(E1,E0) < 0 )
-		{
-		printf("Products underflow at a higher");
-		printf(" threshold than differences.\n");
-		if( cmp(PseudoZero,Zero) == 0 ) 
-			mov( E1, E0 );
-		}
-	else
-		{
-		printf("Difference underflows at a higher");
-		printf(" threshold than products.\n");
-		}
-	}
-printf("Smallest strictly positive number found is E0 = " );
-show( E0 );
-mov( E0, Z );
-TstPtUf();
-mov( E0, Underflow );
-if(N == 1)
-	mov( Y, Underflow );
-I = 4;
-if( cmp(E1,Zero) == 0 )
-	I = 3;
-if( cmp( UfThold,Zero) == 0 )
-	I = I - 2;
-UfNGrad = True;
-switch(I)
-	{
-	case 1:
-	mov( Underflow, UfThold );
-	mul( CInvrse, Q, t );
-	mul( CInvrse, Y, t2 );
-	mul( t2, S, t2 );
-	if( cmp( t, t2 ) != 0 )
-		{
-		mov( Y, UfThold );
-		ErrCnt[Failure] += 1;
-		printf( "Either accuracy deteriorates as numbers\n");
-		printf("approach a threshold = " );
-		show( UfThold );
-		printf(" coming down from " );
-		show( C );
-	printf(" or else multiplication gets too many last digits wrong.\n");
-		}
-	break;
-	
-	case	2:
-	ErrCnt[Failure] += 1;
-	printf( "Underflow confuses Comparison which alleges that\n");
-	printf("Q == Y while denying that |Q - Y| == 0; these values\n");
-	printf("print out as Q = " );
-	show( Q );
-	printf( ", Y = " );
-	show( Y );
-	sub( Y2, Q, t );
-	FABS(t);
-	printf ("|Q - Y| = " );
-	show( t );
-	mov( Q, UfThold );
-	break;
-	
-	case 3:
-	mov( X, X );
-	break;
-	
-	case 4:
-	div( E9, E1, t );
-	sub( t, UfThold, t );
-	FABS(t);
-	if( (cmp(Q,UfThold) == 0) && (cmp(E1,E0) == 0)
-		&& (cmp(t,E1) <= 0) )
-		{
-		UfNGrad = False;
-		printf("Underflow is gradual; it incurs Absolute Error =\n");
-		printf("(roundoff in UfThold) < E0.\n");
-		mul( E0, CInvrse, Y );
-		add( OneAndHalf, U2, t );
-		mul( Y, t, Y );
-		add( One, U2, X );
-		mul( CInvrse, X, X );
-		div( X, Y, t );
-		IEEE = (cmp(t,E0) == 0);
-		if( IEEE == 0 )
-			{
-		printf( "((CInvrse E0) (1.5+U2)) / (CInvrse (1+U2)) != E0\n" );
-			printf( "CInvrse = " );
-			show( CInvrse );
-			printf( "E0 = " );
-			show( E0 );
-			printf( "U2 = " );
-			show( U2 );
-			printf( "X = " );
-			show(X);
-			printf( "Y = " );
-			show(Y);
-			printf( "Y/X = " );
-			show(t);
-			}
-		}
-	}
-if(UfNGrad)
-	{
-	printf("\n");
-	div( UfThold, Underflow, R );
-	SQRT( R, R );
-	if( cmp(R,H) <= 0)
-		{
-		mul( R, UfThold, Z );
-/* X = Z * (One + R * H * (One + H));*/
-		add( One, H, X );
-		mul( H, X, X );
-		mul( R, X, X );
-		add( One, X, X );
-		mul( Z, X, X );
-		}
-	else
-		{
-		mov( UfThold, Z );
-/*X = Z * (One + H * H * (One + H));*/
-		add( One, H, X );
-		mul( H, X, X );
-		mul( H, X, X );
-		add( One, X, X );
-		mul( Z, X, X );
-		}
-	sub( Z, X, t );
-/*	if(! ((cmp(X,Z) == 0) || (cmp(t,Zero) != 0)) )*/
-	if( (cmp(X,Z) != 0) && (cmp(t,Zero) == 0) )
-		{
-/*		ErrCnt[Flaw] += 1;*/
-		ErrCnt[Serious] += 1;
-		printf("X = " );
-		show( X );
-		printf( "\tis not equal to Z = " );
-		show( Z );
-/*		sub( Z, X, Z9 );*/
-		printf("yet X - Z yields " );
-		show( t );
-		printf("which compares equal to " );
-		show( Zero );
-		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");
-		printf("X / Z = 1 + " );
-		div( Z, X, t );
-		sub( Half, t, t );
-		sub( Half, t, t );
-		show(t);
-		}
-	}
-printf("The Underflow threshold is " );
-show( UfThold );
-printf( "below which calculation may suffer larger Relative error than" );
-printf( " merely roundoff.\n");
-mul( U1, U1, Y2 );
-mul( Y2, Y2, Y );
-mul( Y, U1, Y2 );
-if( cmp( Y2,UfThold) <= 0 )
-	{
-	if( cmp(Y,E0) > 0 )
-		{
-		ErrCnt[Defect] += 1;
-		I = 5;
-		}
-	else
-		{
-		ErrCnt[Serious] += 1;
-		I = 4;
-		}
-	printf("Range is too narrow; U1^%d Underflows.\n", I);
-	}
-Milestone = 130;
-
-/*Y = - FLOOR(Half - TwoForty * LOG(UfThold) / LOG(HInvrse)) / TwoForty;*/
-LOG( UfThold, Y );
-LOG( HInvrse, t );
-div( t, Y, Y );
-mul( TwoForty, Y, Y );
-sub( Y, Half, Y );
-FLOOR( Y, Y );
-div( TwoForty, Y, Y );
-neg(Y);
-sub( One, Y, Y2 ); /* ***** changed from Y2 = Y + Y */
-printf("Since underflow occurs below the threshold\n");
-printf("UfThold = " ); 
-show( HInvrse );
-printf( "\tto the power  " );
-show( Y );
-printf( "only underflow should afflict the expression " );
-show( HInvrse );
-printf( "\tto the power  " );
-show( Y2 );
-POW( HInvrse, Y2, V9 );
-printf("Actually calculating yields: " );
-show( V9 );
-add( Radix, Radix, t );
-add( t, E9, t );
-mul( t, UfThold, t );
-if( (cmp(V9,Zero) < 0) || (cmp(V9,t) > 0) )
-	{
-	ErrCnt[Serious] += 1;
-	printf( "this is not between 0 and underflow\n");
-	printf("   threshold = " );
-	show( UfThold );
-	}
-else
-	{
-	add( One, E9, t );
-	mul( UfThold, t, t );
-	if( cmp(V9,t) <= 0 )
-		printf("This computed value is O.K.\n");
-	else
-		{
-		ErrCnt[Defect] += 1;
-		printf( "this is not between 0 and underflow\n");
-		printf("   threshold = " );
-		show( UfThold );
-		}
-	}
-
-Milestone = 140;
-
-pow2test();
-	
-/*=============================================*/
-Milestone = 160;
-/*=============================================*/
-Pause();
-printf("Searching for Overflow threshold:\n");
-printf("This may generate an error.\n");
-sigsave = sigfpe;
-I = 0;
-mov( CInvrse, Y ); /* a large power of 2 */
-neg(Y);
-mul( HInvrse, Y, V9 ); /* HInvrse = 2 */
-if (setjmp(ovfl_buf))
-	goto overflow;
-do
-	{
-	mov( Y, V );
-	mov( V9, Y );
-	mul( HInvrse, Y, V9 );
-	}
-while( cmp(V9,Y) < 0 ); /* V9 = 2 * Y */
-I = 1;
-
-overflow:
-
-show( HInvrse );
-printf( "\ttimes " );
-show( Y );
-printf( "\tequals " );
-show( V9 );
-
-mov( V9, Z );
-printf("Can `Z = -Y' overflow?\n");
-printf("Trying it on Y = " );
-show(Y);
-mov( Y, V9 );
-neg( V9 );
-mov( V9, V0 );
-sub( Y, V, t );
-add( V, V0, t2 );
-if( cmp(t,t2) == 0 )
-	printf("Seems O.K.\n");
-else
-	{
-	printf("finds a Flaw, -(-Y) differs from Y.\n");
-	printf( "V-Y=t:" );
-	show(V);
-	show(Y);
-	show(t);
-	printf( "V+V0=t2:" );
-	show(V);
-	show(V0);
-	show(t2);
-	ErrCnt[Flaw] += 1;
-	}
-if( (cmp(Z, Y) != 0) && (I != 0) )
-	{
-	ErrCnt[Serious] += 1;
-	printf("overflow past " );
-	show( Y );
-	printf( "\tshrinks to " );
-	show( Z );
-	printf( "= Y * " );
-	show( HInvrse );
-	}
-/*Y = V * (HInvrse * U2 - HInvrse);*/
-mul( HInvrse, U2, Y );
-sub( HInvrse, Y, Y );
-mul( V, Y, Y );
-/*Z = Y + ((One - HInvrse) * U2) * V;*/
-sub( HInvrse, One, Z );
-mul( Z, U2, Z );
-mul( Z, V, Z );
-add( Y, Z, Z );
-if( cmp(Z,V0) < 0 )
-	mov( Z, Y );
-if( cmp(Y,V0) < 0)
-	mov( Y, V );
-sub( V, V0, t );
-if( cmp(t,V0) < 0 )
-	mov( V0, V );
-printf("Overflow threshold is V  = " );
-show( V );
-if(I)
-	{
-	printf("Overflow saturates at V0 = " );
-	show( V0 );
-	}
-else
-printf("There is no saturation value because the system traps on overflow.\n");
-
-mul( V, One, V9 );
-printf("No Overflow should be signaled for V * 1 = " );
-show( V9 );
-div( One, V, V9 );
-	printf("                           nor for V / 1 = " );
-	show( V9 );
-	printf("Any overflow signal separating this * from the one\n");
-	printf("above is a DEFECT.\n");
-/*=============================================*/
-Milestone = 170;
-/*=============================================*/
-mov( V, t );
-neg( t );
-k = 0;
-if( cmp(t,V) >= 0 )
-	k = 1;
-mov( V0, t );
-neg( t );
-if( cmp(t,V0) >= 0 )
-	k = 1;
-mov( UfThold, t );
-neg(t);
-if( cmp(t,V) >= 0 )
-	k = 1;
-if( cmp(UfThold,V) >= 0 )
-	k = 1;
-if( k != 0 )
-	{
-	ErrCnt[Failure] += 1;
-	printf( "Comparisons involving +-");
-	show( V );
-	show( V0 );
-	show( UfThold );
-	printf("are confused by Overflow." );
-	}
-/*=============================================*/
-Milestone = 175;
-/*=============================================*/
-printf("\n");
-for(Indx = 1; Indx <= 3; ++Indx) {
-	switch(Indx)
-		{
-		case 1: mov(UfThold, Z); break;
-		case 2: mov( E0, Z); break;
-		case 3: mov(PseudoZero, Z); break;
-		}
-if( cmp(Z, Zero) != 0 )
-	{
-	SQRT( Z, V9 );
-	mul( V9, V9, Y );
-	mul( Radix, E9, t );
-	sub( t, One, t );
-	div( t, Y, t );
-	add( One, Radix, t2 );
-	add( t2, E9, t2 );
-	mul( t2, Z, t2 );
-	if( (cmp(t,Z) < 0) || (cmp(Y,t2) > 0) )
-		{
-		if( cmp(V9,U1) > 0 )
-			ErrCnt[Serious] += 1;
-		else
-			ErrCnt[Defect] += 1;
-		printf("Comparison alleges that what prints as Z = " );
-		show( Z );
-		printf(" is too far from sqrt(Z) ^ 2 = " );
-		show( Y );
-		}
-	}
-}
-
-Milestone = 180;
-
-for(Indx = 1; Indx <= 2; ++Indx)
-	{
-	if(Indx == 1)
-		mov( V, Z );
-	else
-		mov( V0, Z );
-	SQRT( Z, V9 );
-	mul( Radix, E9, X );
-	sub( X, One, X );
-	mul( X, V9, X );
-	mul( V9, X, V9 );
-	mul( Two, Radix, t );
-	mul( t, E9, t );
-	sub( t, One, t );
-	mul( t, Z, t );
-	if( (cmp(V9,t) < 0) || (cmp(V9,Z) > 0) )
-		{
-		mov( V9, Y );
-		if( cmp(X,W) <  0 )
-			ErrCnt[Serious] += 1;
-		else
-			ErrCnt[Defect] += 1;
-		printf("Comparison alleges that Z = " );
-		show( Z );
-		printf(" is too far from sqrt(Z) ^ 2 :" );
-		show( Y );
-		}
-	}
-
-Milestone = 190;
-
-Pause();
-mul( UfThold, V, X ); 
-mul( Radix, Radix, Y );
-mul( X, Y, t );
-if( (cmp(t,One) < 0) || (cmp(X,Y) > 0) )
-	{
-	mul( X, Y, t );
-	div( U1, Y, t2 );
-	if( (cmp(t,U1) < 0) || (cmp(X,t2) > 0) )
-		{
-		ErrCnt[Defect] += 1;
-		printf( "Badly " );
-		}
-	else
-		{
-		ErrCnt[Flaw] += 1;
-		}
-	printf(" unbalanced range; UfThold * V = " );
-	show( X );
-	printf( "\tis too far from 1.\n");
-	}
-Milestone = 200;
-
-for(Indx = 1; Indx <= 5; ++Indx)
-	{
-	mov( F9, X );
-	switch(Indx)
-		{
-		case 2: add( One, U2, X ); break;
-		case 3: mov( V, X ); break;
-		case 4: mov(UfThold,X); break;
-		case 5: mov(Radix,X);
-		}
-	mov( X, Y );
-
-	sigsave = sigfpe;
-	if (setjmp(ovfl_buf))
-		{
-		printf("  X / X  traps when X = " );
-		show( X );
-		}
-	else
-		{
-/*V9 = (Y / X - Half) - Half;*/
-		div( X, Y, t );
-		sub( Half, t, t );
-		sub( Half, t, V9 );
-		if( cmp(V9,Zero) == 0 )
-			continue;
-		mov( U1, t );
-		neg(t);
-		if( (cmp(V9,t) == 0) && (Indx < 5) )
-			{
-			ErrCnt[Flaw] += 1;
-			}
-		else
-			{
-			ErrCnt[Serious] += 1;
-			}
-		printf("  X / X differs from 1 when X = " );
-		show( X );
-		printf("  instead, X / X - 1/2 - 1/2 = " );
-		show( V9 );
-		}
-	}
-
-	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("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 {
-			k = 0;
-			if( cmp( Radix, Two ) == 0 )
-				k = 1;
-			if( cmp( Radix, Ten ) == 0 )
-				k = 1;
-			if( (cmp(StickyBit,One) >= 0) && (k == 1) )
-				{
-				printf("Rounding appears to conform to ");
-				printf("the proposed IEEE standard P");
-				k = 0;
-				k |= cmp( Radix, Two );
-				mul( Four, Three, t );
-				mul( t, Two, t );
-				sub( t, Precision, t );
-				sub( TwentySeven, Precision, t2 );
-				sub( TwentySeven, t2, t2 );
-				add( t2, One, t2 );
-				mul( t2, t, t );
-				if( (cmp(Radix,Two) == 0)
-					&& (cmp(t,Zero) == 0) )
-					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");
-	}
-
-
-/* Random */
-/*  Random computes
-     X = (Random1 + Random9)^5
-     Random1 = X - FLOOR(X) + 0.000005 * X;
-   and returns the new value of Random1
-*/
-
-
-static int randflg = 0;
-FLOAT(C5em6);
-
-Random()
-{
-
-if( randflg == 0 )
-	{
-	mov( Six, t );
-	neg(t);
-	POW( Ten, t, t );
-	mul( Five, t, C5em6 );
-	randflg = 1;
-	}
-add( Random1, Random9, t );
-mul( t, t, t2 );
-mul( t2, t2, t2 );
-mul( t, t2, t );
-FLOOR(t, t2 );
-sub( t2, t, t2 );
-mul( t, C5em6, t );
-add( t, t2, Random1 );
-/*return(Random1);*/
-}
-
-/* SqXMinX */
-
-SqXMinX( ErrKind )
-int ErrKind;
-{
-mul( X, BInvrse, t2 );
-sub( t2, X, t );
-/*SqEr = ((SQRT(X * X) - XB) - XA) / OneUlp;*/
-mul( X, X, Sqarg );
-SQRT( Sqarg, SqEr );
-sub( t2, SqEr, SqEr );
-sub( t, SqEr, SqEr );
-div( OneUlp, SqEr, SqEr );
-if( cmp(SqEr,Zero) != 0)
-	{
-	Showsq( 0 );
-	add( J, One, J );
-	ErrCnt[ErrKind] += 1;
-	printf("sqrt of " );
-	mul( X, X, t );
-	show( t );
-	printf( "minus " );
-	show( X );
-	printf( "equals " );
-	mul( OneUlp, SqEr, t );
-	show( t );
-	printf("\tinstead of correct value 0 .\n");
-	}
-}
-
-/* NewD */
-
-NewD()
-{
-mul( Z1, Q, X );
-/*X = FLOOR(Half - X / Radix) * Radix + X;*/
-div( Radix, X, t );
-sub( t, Half, t );
-FLOOR( t, t );
-mul( t, Radix, t );
-add( t, X, X );
-/*Q = (Q - X * Z) / Radix + X * X * (D / Radix);*/
-mul( X, Z, t );
-sub( t, Q, t );
-div( Radix, t, t );
-div( Radix, D, t2 );
-mul( X, t2, t2 );
-mul( X, t2, t2 );
-add( t, t2, Q );
-/*Z = Z - Two * X * D;*/
-mul( Two, X, t );
-mul( t, D, t );
-sub( t, Z, Z );
-
-if( cmp(Z,Zero) <= 0)
-	{
-	neg(Z);
-	neg(Z1);
-	}
-mul( Radix, D, D );
-}
-
-/* SR3750 */
-
-SR3750()
-{
-sub( Radix, X, t );
-sub( Radix, Z2, t2 );
-k = 0;
-if( cmp(t,t2) < 0 )
-	k = 1;
-sub( Z2, X, t );
-sub( Z2, W, t2 );
-if( cmp(t,t2) > 0 )
-	k = 1;
-/*if (! ((X - Radix < Z2 - Radix) || (X - Z2 > W - Z2))) {*/
-if( k == 0 )
-	{
-	I = I + 1;
-	mul( X, D, X2 );
-	mov( X2, Sqarg );
-	SQRT( X2, X2 );
-/*Y2 = (X2 - Z2) - (Y - Z2);*/
-	sub( Z2, X2, Y2 );
-	sub( Z2, Y, t );
-	sub( t, Y2, Y2 );
-	sub( Half, Y, X2 );
-	div( X2, X8, X2 );
-	mul( Half, X2, t );
-	mul( t, X2, t );
-	sub( t, X2, X2 );
-/*SqEr = (Y2 + Half) + (Half - X2);*/
-	add( Y2, Half, SqEr );
-	sub( X2, Half, t );
-	add( t, SqEr, SqEr );
-	Showsq( -1 );
-	sub( X2, Y2, SqEr );
-	Showsq( 1 );
-	}
-}
-
-/* IsYeqX */
-
-IsYeqX()
-{
-if( cmp(Y,X) != 0 )
-	{
-	if (N <= 0)
-		{
-		if( (cmp(Z,Zero) == 0) && (cmp(Q,Zero) <= 0) )
-			printf("WARNING:  computing\n");
-		else
-			{
-			ErrCnt[Defect] += 1;
-			printf( "computing\n");
-			}
-		show( Z );
-		printf( "\tto the power " );
-		show( Q );
-		printf("\tyielded " );
-		show( Y );
-		printf("\twhich compared unequal to correct " );
-		show( X );
-		sub( X, Y, t );
-		printf("\t\tthey differ by " );
-		show( t );
-		}
-	N = N + 1; /* ... count discrepancies. */
-	}
-}
-
-/* SR3980 */
-
-SR3980()
-{
-long li;
-
-do
-	{
-/*Q = (FLOAT) I;*/
-	li = I;
-	LTOF( &li, Q );
-	POW( Z, Q, Y );
-	IsYeqX();
-	if(++I > M)
-		break;
-	mul( Z, X, X );
-	}
-while( cmp(X,W) < 0 );
-}
-
-/* PrintIfNPositive */
-
-PrintIfNPositive()
-{
-if(N > 0)
-	printf("Similar discrepancies have occurred %d times.\n", N);
-}
-
-
-/* TstPtUf */
-
-TstPtUf()
-{
-N = 0;
-if( cmp(Z,Zero) != 0)
-	{
-	printf( "Z = " );
-	show(Z);
-	printf("Since comparison denies Z = 0, evaluating ");
-	printf("(Z + Z) / Z should be safe.\n");
-	sigsave = sigfpe;
-	if (setjmp(ovfl_buf))
-		goto very_serious;
-	add( Z, Z, Q9 );
-	div( Z, Q9, Q9 );
-	printf("What the machine gets for (Z + Z) / Z is " );
-	show( Q9 );
-	sub( Two, Q9, t );
-	FABS(t);
-	mul( Radix, U2, t2 );
-	if( cmp(t,t2) < 0 )
-		{
-		printf("This is O.K., provided Over/Underflow");
-		printf(" has NOT just been signaled.\n");
-		}
-	else
-		{
-		if( (cmp(Q9,One) < 0) || (cmp(Q9,Two) > 0) )
-			{
-very_serious:
-			N = 1;
-			ErrCnt [Serious] = ErrCnt [Serious] + 1;
-			printf("This is a VERY SERIOUS DEFECT!\n");
-			}
-		else
-			{
-			N = 1;
-			ErrCnt[Defect] += 1;
-			printf("This is a DEFECT!\n");
-			}
-		}
-	mul( Z, One, V9 );
-	mov( V9, Random1 );
-	mul( One, Z, V9 );
-	mov( V9, Random2 );
-	div( One, Z, V9 );
-	if( (cmp(Z,Random1) == 0) && (cmp(Z,Random2) == 0)
-		&& (cmp(Z,V9) == 0) )
-		{
-		if (N > 0)
-			Pause();
-		}
-	else
-		{
-		N = 1;
-		ErrCnt[Defect] += 1;
-		printf( "What prints as Z = ");
-		show( Z );
-		printf( "\tcompares different from " );
-		if( cmp(Z,Random1) != 0)
-			{
-			printf("Z * 1 = " );
-			show( Random1 );
-			}
-		if( (cmp(Z,Random2) != 0)
-			|| (cmp(Random2,Random1) != 0) )
-			{
-			printf("1 * Z == " );
-			show( Random2 );
-			}
-		if( cmp(Z,V9) != 0 )
-			{
-			printf("Z / 1 = " );
-			show( V9 );
-			}
-		if( cmp(Random2,Random1) != 0 )
-			{
-			ErrCnt[Defect] += 1;
-			printf( "Multiplication does not commute!\n");
-			printf("\tComparison alleges that 1 * Z = " );
-			show(Random2);
-			printf("\tdiffers from Z * 1 = " );
-			show(Random1);
-			}
-		Pause();
-		}
-	}
-}
-
-Pause()
-{
-}
-
-Sign( x, y )
-FSIZE *x, *y;
-{
-
-if( cmp( x, Zero ) < 0 )
-	{
-	mov( One, y );
-	neg( y );
-	}
-else
-	{
-	mov( One, y );
-	}
-}
-
-sqtest()
-{
-printf("\nRunning test of square root(x).\n");
-
-RSqrt = Other;
-k = 0;
-SQRT( Zero, t );
-k |= cmp( Zero, t );
-mov( Zero, t );
-neg(t);
-SQRT( t, t2 );
-k |= cmp( t, t2 );
-SQRT( One, t );
-k |= cmp( One, t );
-if( k != 0 )
- 	{
-	ErrCnt[Failure] += 1;
-	printf( "Square root of 0.0, -0.0 or 1.0 wrong\n");
-	}
-mov( Zero, MinSqEr );
-mov( Zero, MaxSqEr );
-mov( Zero, J );
-mov( Radix, X );
-mov( U2, OneUlp );
-SqXMinX( Serious );
-mov( BInvrse, X );
-mul( BInvrse, U1, OneUlp );
-SqXMinX( Serious );
-mov( U1, X );
-mul( U1, U1, OneUlp );
-SqXMinX( Serious );
-if( cmp(J,Zero) != 0)
-	Pause();
-printf("Testing if sqrt(X * X) == X for %d Integers X.\n", NoTrials);
-mov( Zero, J );
-mov( Two, X );
-mov( Radix, Y );
-if( cmp(Radix,One) != 0 )
-	{
-	lngint = NoTrials;
-	LTOF( &lngint, t );
-	FTOL( t, &lng2, X );
-	if( lngint != lng2 )
-		{
-		printf( "Integer conversion error\n" );
-		exit(1);
-		}
-	do
-		{
-		mov( Y, X );
-		mul( Radix, Y, Y );
-		sub( X, Y, t2 );
-		}
-	while( ! (cmp(t2,t) >= 0) );
-	}
-mul( X, U2, OneUlp );
-I = 1;
-while(I < 10)
-	{
-	add( X, One, X );
-	SqXMinX( Defect );
-	if( cmp(J,Zero) > 0 )
-		break;
-	I = I + 1;
-	}
-printf("Test for sqrt monotonicity.\n");
-I = - 1;
-mov( BMinusU2, X );
-mov( Radix, Y );
-mul( Radix, U2, Z );
-add( Radix, Z, Z );
-NotMonot = False;
-Monot = False;
-while( ! (NotMonot || Monot))
-	{
-	I = I + 1;
-	SQRT(X, X);
-	SQRT(Y,Q);
-	SQRT(Z,Z);
-	if( (cmp(X,Q) > 0) || (cmp(Q,Z) > 0) )
-		NotMonot = True;
-	else
-		{
-		add( Q, Half, Q );
-		FLOOR( Q, Q );
-		mul( Q, Q, t );
-		if( (I > 0) || (cmp(Radix,t) == 0) )
-			Monot = True;
-		else if (I > 0)
-			{
-			if(I > 1)
-				Monot = True;
-			else
-				{
-				mul( Y, BInvrse, Y );
-				sub( U1, Y, X );
-				add( Y, U1, Z );
-				}
-			}
-		else
-			{
-			mov( Q, Y );
-			sub( U2, Y, X );
-			add( Y, U2, Z );
-			}
-		}
-	}
-if( Monot )
-	printf("sqrt has passed a test for Monotonicity.\n");
-else
-	{
-	ErrCnt[Defect] += 1;
-	printf("sqrt(X) is non-monotonic for X near " );
-	show(Y);
-	}
-/*=============================================*/
-Milestone = 80;
-/*=============================================*/
-add( MinSqEr, Half, MinSqEr );
-sub( Half, MaxSqEr, MaxSqEr);
-/*Y = (SQRT(One + U2) - One) / U2;*/
-add( One, U2, Sqarg );
-SQRT( Sqarg, Y );
-sub( One, Y, Y );
-div( U2, Y, Y );
-/*SqEr = (Y - One) + U2 / Eight;*/
-sub( One, Y, t );
-div( Eight, U2, SqEr );
-add( t, SqEr, SqEr );
-Showsq( 1 );
-div( Eight, U2, SqEr );
-add( Y, SqEr, SqEr );
-Showsq( -1 );
-/*Y = ((SQRT(F9) - U2) - (One - U2)) / U1;*/
-mov( F9, Sqarg );
-SQRT( Sqarg, Y );
-sub( U2, Y, Y );
-sub( U2, One, t );
-sub( t, Y, Y );
-div( U1, Y, Y );
-div( Eight, U1, SqEr );
-add( Y, SqEr, SqEr );
-Showsq( 1 );
-/*SqEr = (Y + One) + U1 / Eight;*/
-div( Eight, U1, t );
-add( Y, One, SqEr );
-add( SqEr, t, SqEr );
-Showsq( -1 );
-mov( U2, OneUlp );
-mov( OneUlp, X );
-for( Indx = 1; Indx <= 3; ++Indx)
-	{
-/*Y = SQRT((X + U1 + X) + F9);*/
-	add( X, U1, Y );
-	add( Y, X, Y );
-	add( Y, F9, Y );
-	mov( Y, Sqarg );
-	SQRT( Sqarg, Y );
-/*Y = ((Y - U2) - ((One - U2) + X)) / OneUlp;*/
-	sub( U2, One, t );
-	add( t, X, t );
-	sub( U2, Y, Y );
-	sub( t, Y, Y );
-	div( OneUlp, Y, Y );
-/*Z = ((U1 - X) + F9) * Half * X * X / OneUlp;*/
-	sub( X, U1, t );
-	add( t, F9, t );
-	mul( t, Half, t );
-	mul( t, X, t );
-	mul( t, X, t );
-	div( OneUlp, t, Z );
-	add( Y, Half, SqEr );
-	add( SqEr, Z, SqEr );
-	Showsq( -1 );
-	sub( Half, Y, SqEr );
-	add( SqEr, Z, SqEr );
-	Showsq( 1 );
-	if(((Indx == 1) || (Indx == 3))) 
-		{
-/*X = OneUlp * Sign (X) * FLOOR(Eight / (Nine * SQRT(OneUlp)));*/
-		mov( OneUlp, Sqarg );
-		SQRT( Sqarg, t );
-		mul( Nine, t, t );
-		div( t, Eight, t );
-		FLOOR( t, t );
-		Sign( X, t2 );
-		mul( t2, t, t );
-		mul( OneUlp, t, X );
-		}
-	else
-		{
-		mov( U1, OneUlp );
-		mov( OneUlp, X );
-		neg( X );
-		}
-	}
-/*=============================================*/
-Milestone = 85;
-/*=============================================*/
-SqRWrng = False;
-Anomaly = False;
-if( cmp(Radix,One) != 0 )
-	{
-	printf("Testing whether sqrt is rounded or chopped.\n");
-/*D = FLOOR(Half + POW(Radix, One + Precision - FLOOR(Precision)));*/
-	FLOOR( Precision, t2 );
-	add( One, Precision, t );
-	sub( t2, t, t );
-	POW( Radix, t, D );
-	add( Half, D, D );
-	FLOOR( D, D );
-/* ... == Radix^(1 + fract) if (Precision == Integer + fract. */
-	div( Radix, D, X );
-	div( A1, D, Y );
-	FLOOR( X, t );
-	FLOOR( Y, t2 );
-	if( (cmp(X,t) != 0) || (cmp(Y,t2) != 0) )
-		{
-		Anomaly = True;
-		printf( "Anomaly 1\n" );
-		}
-	else
-		{
-		mov( Zero, X );
-		mov( X, Z2 );
-		mov( One, Y );
-		mov( Y, Y2 );
-		sub( One, Radix, Z1 );
-		mul( Four, D, FourD );
-		do
-			{
-			if( cmp(Y2,Z2) >0 )
-				{
-				mov( Radix, Q );
-				mov( Y, YY1 );
-				do
-					{
-/*X1 = FABS(Q + FLOOR(Half - Q / YY1) * YY1);*/
-					div( YY1, Q, t );
-					sub( t, Half, t );
-					FLOOR( t, t );
-					mul( t, YY1, t );
-					add( Q, t, X1 );
-					FABS( X1 );
-					mov( YY1, Q );
-					mov( X1, YY1 );
-					}
-				while( ! (cmp(X1,Zero) <= 0) );
-				if( cmp(Q,One) <= 0 )
-					{
-					mov( Y2, Z2 );
-					mov( Y, Z );
-					}
-				}
-			add( Y, Two, Y );
-			add( X, Eight, X );
-			add( Y2, X, Y2 );
-			if( cmp(Y2,FourD) >= 0 )
-				sub( FourD, Y2, Y2 );
-			}
-		while( ! (cmp(Y,D) >= 0) );
-		sub( Z2, FourD, X8 );
-		mul( Z, Z, Q );
-		add( X8, Q, Q );
-		div( FourD, Q, Q );
-		div( Eight, X8, X8 );
-		FLOOR( Q, t );
-		if( cmp(Q,t) != 0 )
-			{
-			Anomaly = True;
-			printf( "Anomaly 2\n" );
-			}
-		else
-			{
-			Break = False;
-			do
-				{
-				mul( Z1, Z, X );
-/*X = X - FLOOR(X / Radix) * Radix;*/
-				div( Radix, X, t );
-				FLOOR( t, t );
-				mul( t, Radix, t );
-				sub( t, X, X );
-				if( cmp(X,One) == 0 ) 
-					Break = True;
-				else
-					sub( One, Z1, Z1 );
-				}
-			while( ! (Break || (cmp(Z1,Zero) <= 0)) );
-			if( (cmp(Z1,Zero) <= 0) && (! Break))
-				{
-				printf( "Anomaly 3\n" );
-				Anomaly = True;
-				}
-			else
-				{
-				if( cmp(Z1,RadixD2) > 0)
-					sub( Radix, Z1, Z1 );
-				do
-					{
-					NewD();
-					mul( U2, D, t );
-					}
-				while( ! (cmp(t,F9) >= 0) );
-				mul( D, Radix, t );
-				sub( D, t, t );
-				sub( D, W, t2 );
-				if (cmp(t,t2) != 0 )
-					{
-					printf( "Anomaly 4\n" );
-					Anomaly = True;
-					}
-				else
-					{
-					mov( D, Z2 );
-					I = 0;
-					add( One, Z, t );
-					mul( t, Half, t );
-					add( D, t, Y );
-					add( D, Z, X );
-					add( X, Q, X );
-					SR3750();
-					sub( Z, One, t );
-					mul( t, Half, t );
-					add( D, t, Y );
-					add( Y, D, Y );
-					sub( Z, D, X );
-					add( X, D, X );
-					add( X, Q, t );
-					add( t, X, X );
-					SR3750();
-					NewD();
-					sub( Z2, D, t );
-					sub( Z2, W, t2 );
-					if(cmp(t,t2) != 0 )
-						{
-						printf( "Anomaly 5\n" );
-						Anomaly = True;
-						}
-					else
-						{
-/*Y = (D - Z2) + (Z2 + (One - Z) * Half);*/
-						sub( Z, One, t );
-						mul( t, Half, t );
-						add( Z2, t, t );
-						sub( Z2, D, Y );
-						add( Y, t, Y );
-/*X = (D - Z2) + (Z2 - Z + Q);*/
-						sub( Z, Z2, t );
-						add( t, Q, t );
-						sub( Z2, D, X );
-						add( X, t, X );
-						SR3750();
-						add( One, Z, Y );
-						mul( Y, Half, Y );
-						mov( Q, X );
-						SR3750();
-						if(I == 0)
-							{
-							printf( "Anomaly 6\n" );
-							Anomaly = True;
-							}
-						}
-					}
-				}
-			}
-		}
-	if ((I == 0) || Anomaly)
-		{
-		ErrCnt[Failure] += 1;
-		printf( "Anomalous arithmetic with Integer < \n");
-		printf("Radix^Precision = " );
-		show( W );
-		printf(" fails test whether sqrt rounds or chops.\n");
-		SqRWrng = True;
-		}
-	}
-if(! Anomaly)
-	{
-	if(! ((cmp(MinSqEr,Zero) < 0) || (cmp(MaxSqEr,Zero) > 0))) {
-	RSqrt = Rounded;
-	printf("Square root appears to be correctly rounded.\n");
-	}
-	else
-		{
-		k = 0;
-		add( MaxSqEr, U2, t );
-		sub( Half, U2, t2 );
-		if( cmp(t,t2) > 0 )
-			k = 1;
-		if( cmp( MinSqEr, Half ) > 0 )
-			k = 1;
-		add( MinSqEr, Radix, t );
-		if( cmp( t, Half ) < 0 )
-			k = 1;
-		if( k == 1 )
-			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 " );
-	sub( Half, MinSqEr, t );
-	show( t );
-	printf("\tto " );
-	add( Half, MaxSqEr, t );
-	show( t );
-	printf( "ulps.\n" );
-	sub( MinSqEr, MaxSqEr, t );
-	mul( Radix, Radix, t2 );
-	if( cmp( t, t2 ) >= 0 )
-		{
-		ErrCnt[Serious] += 1;
-		printf( "sqrt gets too many last digits wrong\n");
-		}
-	}
-}
-
-Showsq( arg )
-int arg;
-{
-
-k = 0;
-if( arg <= 0 )
-	{
-	if( cmp(SqEr,MinSqEr) < 0 )
-		{
-		k = 1;
-		mov( SqEr, MinSqEr );
-		}
-	}
-if( arg >= 0 )
-	{
-	if( cmp(SqEr,MaxSqEr) > 0 )
-		{
-		k = 2;
-		mov( SqEr, MaxSqEr );
-		}
-	}
-#if DEBUG
-if( k != 0 )
-	{
-	printf( "Square root of " );
-	show( arg );
-	printf( "\tis in error by " );
-	show( SqEr );
-	}
-#endif
-}
-
-
-pow1test()
-{
-
-/*=============================================*/
-Milestone = 90;
-/*=============================================*/
-Pause();
-printf("Testing powers Z^i for small Integers Z and i.\n");
-N = 0;
-/* ... test powers of zero. */
-I = 0;
-mov( Zero, Z );
-neg(Z);
-M = 3;
-Break = False;
-do
-	{
-	mov( One, X );
-	SR3980();
-	if(I <= 10)
-		{
-		I = 1023;
-		SR3980();
-		}
-	if( cmp(Z,MinusOne) == 0 )
-		Break = True;
-	else
-		{
-		mov( MinusOne, Z );
-		PrintIfNPositive();
-		N = 0;
-/* .. if(-1)^N is invalid, replace MinusOne by One. */
-		I = - 4;
-		}
-	}
-while( ! Break );
-PrintIfNPositive();
-N1 = N;
-N = 0;
-mov( A1, Z );
-/*M = FLOOR(Two * LOG(W) / LOG(A1));*/
-LOG( W, t );
-mul( Two, t, t );
-FLOOR( t, t );
-LOG( A1, t2 );
-div( t2, t, t );
-FTOL( t, &lngint, t2 );
-M = lngint;
-Break = False;
-do
-	{
-	mov( Z, X );
-	I = 1;
-	SR3980();
-	if( cmp(Z,AInvrse) == 0 )
-		Break = True;
-	else
-		 mov( AInvrse, Z );
-	}
-while( ! (Break) );
-/*=============================================*/
-Milestone = 100;
-/*=============================================*/
-/*  Powers of Radix have been tested, */
-/*         next try a few primes     */
-
-M = NoTrials;
-
-mov( Three, Z );
-do
-	{
-	mov( Z, X );
-	I = 1;
-	SR3980();
-	do
-		{
-		add( Z, Two, Z );
-		div( Three, Z, t );
-		FLOOR( t, t );
-		mul( Three, t, t );
-		}
-	while( cmp(t,Z) == 0 );
-	mul( Eight, Three, t );
-	}
-while( cmp(Z,t) < 0 );
-
-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");
-}
-
-
-
-pow2test()
-{
-printf("\n");
-/* ...calculate Exp2 == exp(2) == 7.38905 60989 30650 22723 04275-... */
-mov( Zero, X );
-mov( Two, t2 ); /*I = 2;*/
-
-mul( Two, Three, Y );
-mov( Zero, Q );
-N = 0;
-do
-	{
-	mov( X, Z );
-	add( t2, One, t2 ); /*I = I + 1;*/
-	add( t2, t2, t );
-	div( t, Y, Y ); /*Y = Y / (I + I);*/
-	add( Y, Q, R );
-	add( Z, R, X );
-	sub( X, Z, Q );
-	add( Q, R, Q );
-	}
-while( cmp(X,Z) > 0 );
-
-/*Z = (OneAndHalf + One / Eight) + X / (OneAndHalf * ThirtyTwo);*/
-div( Eight, One, t );
-add( OneAndHalf, t, Z );
-mul( OneAndHalf, ThirtyTwo, t );
-div( t, X, t );
-add( Z, t, Z );
-mul( Z, Z, X );
-mul( X, X, Exp2 );
-mov( F9, X );
-sub( U1, X, Y );
-printf("Testing X^((X + 1) / (X - 1)) vs. exp(2) = " );
-show( Exp2 );
-printf( "\tas X -> 1.\n" );
-for(I = 1;;)
-	{
-	sub( BInvrse, X, Z );
-/*Z = (X + One) / (Z - (One - BInvrse));*/
-	add( X, One, t2 );
-	sub( BInvrse, One, t );
-	sub( t, Z, t );
-	div( t, t2, Z );
-	POW( X, Z, Sqarg );
-	sub( Exp2, Sqarg, Q );
-	mov( Q, t );
-	FABS( t );
-	mul( TwoForty, U2, t2 );
-	if( cmp( t, t2 ) > 0 )
-		{
-		N = 1;
-		sub( BInvrse, X, V9 );
-		sub( BInvrse, One, t );
-		sub( t, V9, V9 );
-		ErrCnt[Defect] += 1;
-		printf( "Calculated " );
-		show( Sqarg );
-		printf(" for \t(1 + " );
-		show( V9 );
-		printf( "\tto the power " );
-		show( Z );
-		printf("\tdiffers from correct value by " );
-		show( Q );
-		printf("\tThis much error may spoil financial\n");
-		printf("\tcalculations involving tiny interest rates.\n");
-		break;
-		}
-	else
-		{
-		sub( X, Y, Z );
-		mul( Z, Two, Z );
-		add( Z, Y, Z );
-		mov( Y, X );
-		mov( Z, Y );
-		sub( F9, X, Z );
-		mul( Z, Z, Z );
-		add( Z, One, Z );
-		if( (cmp(Z,One) > 0) && (I < NoTrials) )
-			I++;
-		else
-			{
-			if( cmp(X,One) > 0 )
-				{
-				if(N == 0)
-					printf("Accuracy seems adequate.\n");
-				break;
-				}
-			else
-				{
-				add( One, U2, X );
-				add( U2, U2, Y );
-				add( X, Y, Y );
-				I = 1;
-				}
-			}
-		}
-	}
-/*=============================================*/
-Milestone = 150;
-/*=============================================*/
-printf("Testing powers Z^Q at four nearly extreme values.\n");
-N = 0;
-mov( A1, Z );
-/*Q = FLOOR(Half - LOG(C) / LOG(A1));*/
-LOG( C, t );
-LOG( A1, t2 );
-div( t2, t, t );
-sub( t, Half, t );
-FLOOR( t, Q );
-Break = False;
-do
-	{
-	mov( CInvrse, X );
-	POW( Z, Q, Y );
-	IsYeqX();
-	neg(Q);
-	mov( C, X );
-	POW( Z, Q, Y );
-	IsYeqX();
-	if( cmp(Z,One) < 0 )
-		Break = True;
-	else
-		mov( AInvrse, Z );
-	}
-while( ! (Break));
-PrintIfNPositive();
-if(N == 0)
-	printf(" ... no discrepancies found.\n");
-printf("\n");
-}