Add in some math lib tests

test/math/Makefile

@@ -0,0 +1,71 @@
+# Unix makefile for ieetst, eparanoi.
+# Set LARGEMEM 1 in qcalc.h for 32-bit memory addresses.
+# Define computer type and/or endianness in mconf.h.
+#
+# Configure eparanoi.c for desired arithmetic test;
+# also define appropriate version of setprec.o, or use a stub that
+# does no FPU setup.  To test native arithmetic, eparanoi uses
+# the system libraries only; compile simply by `cc eparanoi.c -lm'.
+#
+
+TESTDIR=../
+include $(TESTDIR)/Rules.mak
+
+
+#CC = gcc
+#CFLAGS= -O
+INCS= mconf.h ehead.h
+OBJS = ieee.o econst.o eexp.o elog.o epow.o etanh.o etodec.o mtherr.o #setprec.o
+TARGETS=ieetst eparanoi
+
+all: $(TARGETS)
+
+ieetst: ieetst.o $(OBJS) drand.o $(INCS)
+	$(CC) -o ieetst ieetst.o $(OBJS) drand.o -lc -lm
+
+eparanoi: eparanoi.o $(OBJS) $(INCS)
+	$(CC) -o eparanoi  eparanoi.o $(OBJS) -lc -lm
+
+#setprec.o: setprec.387
+#	as -o setprec.o setprec.387
+
+#setprec.o: setprec.688
+#	as -o setprec.o setprec.688
+
+ieee.o: ieee.c $(INCS)
+	$(CC) $(CFLAGS) -c ieee.c
+
+econst.o: econst.c $(INCS)
+	$(CC) $(CFLAGS) -c econst.c
+
+elog.o: elog.c $(INCS)
+	$(CC) $(CFLAGS) -c elog.c
+
+eexp.o: eexp.c $(INCS)
+	$(CC) $(CFLAGS) -c eexp.c
+
+etanh.o: etanh.c $(INCS)
+	$(CC) $(CFLAGS) -c etanh.c
+
+epow.o: epow.c $(INCS)
+	$(CC) $(CFLAGS) -c epow.c
+
+mtherr.o: mtherr.c $(INCS)
+	$(CC) $(CFLAGS) -c mtherr.c
+
+ieetst.o: ieetst.c $(INCS)
+	$(CC) $(CFLAGS) -c ieetst.c
+
+drand.o: drand.c $(INCS)
+	$(CC) $(CFLAGS) -c drand.c
+
+etodec.o: etodec.c $(INCS)
+	$(CC) $(CFLAGS) -c etodec.c
+
+eparanoi.o: eparanoi.c $(INCS)
+	$(CC) $(CFLAGS) -c eparanoi.c
+
+clean:
+	rm -f *.[oa] *~ core $(TARGETS)
+
+

test/math/drand.c

@@ -0,0 +1,158 @@
+/*							drand.c
+ *
+ *	Pseudorandom number generator
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double y, drand();
+ *
+ * drand( &y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Yields a random number 1.0 <= y < 2.0.
+ *
+ * The three-generator congruential algorithm by Brian
+ * Wichmann and David Hill (BYTE magazine, March, 1987,
+ * pp 127-8) is used. The period, given by them, is
+ * 6953607871644.
+ *
+ * Versions invoked by the different arithmetic compile
+ * time options DEC, IBMPC, and MIEEE, produce
+ * approximately the same sequences, differing only in the
+ * least significant bits of the numbers. The UNK option
+ * implements the algorithm as recommended in the BYTE
+ * article.  It may be used on all computers. However,
+ * the low order bits of a double precision number may
+ * not be adequately random, and may vary due to arithmetic
+ * implementation details on different computers.
+ *
+ * The other compile options generate an additional random
+ * integer that overwrites the low order bits of the double
+ * precision number.  This reduces the period by a factor of
+ * two but tends to overcome the problems mentioned.
+ *
+ */
+
+
+
+#include "mconf.h"
+
+
+/*  Three-generator random number algorithm
+ * of Brian Wichmann and David Hill
+ * BYTE magazine, March, 1987 pp 127-8
+ *
+ * The period, given by them, is (p-1)(q-1)(r-1)/4 = 6.95e12.
+ */
+
+static int sx = 1;
+static int sy = 10000;
+static int sz = 3000;
+
+static union {
+ double d;
+ unsigned short s[4];
+} unkans;
+
+/* This function implements the three
+ * congruential generators.
+ */
+ 
+int ranwh()
+{
+int r, s;
+
+/*  sx = sx * 171 mod 30269 */
+r = sx/177;
+s = sx - 177 * r;
+sx = 171 * s - 2 * r;
+if( sx < 0 )
+	sx += 30269;
+
+
+/* sy = sy * 172 mod 30307 */
+r = sy/176;
+s = sy - 176 * r;
+sy = 172 * s - 35 * r;
+if( sy < 0 )
+	sy += 30307;
+
+/* sz = 170 * sz mod 30323 */
+r = sz/178;
+s = sz - 178 * r;
+sz = 170 * s - 63 * r;
+if( sz < 0 )
+	sz += 30323;
+/* The results are in static sx, sy, sz. */
+return 0;
+}
+
+/*	drand.c
+ *
+ * Random double precision floating point number between 1 and 2.
+ *
+ * C callable:
+ *	drand( &x );
+ */
+
+int drand( a )
+double *a;
+{
+unsigned short r;
+#ifdef DEC
+unsigned short s, t;
+#endif
+
+/* This algorithm of Wichmann and Hill computes a floating point
+ * result:
+ */
+ranwh();
+unkans.d = sx/30269.0  +  sy/30307.0  +  sz/30323.0;
+r = unkans.d;
+unkans.d -= r;
+unkans.d += 1.0;
+
+/* if UNK option, do nothing further.
+ * Otherwise, make a random 16 bit integer
+ * to overwrite the least significant word
+ * of unkans.
+ */
+#ifdef UNK
+/* do nothing */
+#else
+ranwh();
+r = sx * sy + sz;
+#endif
+
+#ifdef DEC
+/* To make the numbers as similar as possible
+ * in all arithmetics, the random integer has
+ * to be inserted 3 bits higher up in a DEC number.
+ * An alternative would be put it 3 bits lower down
+ * in all the other number types.
+ */
+s = unkans.s[2];
+t = s & 07;	/* save these bits to put in at the bottom */
+s &= 0177770;
+s |= (r >> 13) & 07;
+unkans.s[2] = s;
+t |= r << 3;
+unkans.s[3] = t;
+#endif
+
+#ifdef IBMPC
+unkans.s[0] = r;
+#endif
+
+#ifdef MIEEE
+unkans.s[3] = r;
+#endif
+
+*a = unkans.d;
+return 0;
+}

test/math/econst.c

@@ -0,0 +1,96 @@
+/*							econst.c	*/
+/*  e type constants used by high precision check routines */
+
+#include "ehead.h"
+
+
+#if NE == 10
+/* 0.0 */
+unsigned short ezero[NE] =
+ {0x0000, 0x0000, 0x0000, 0x0000,
+  0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,};
+
+/* 5.0E-1 */
+unsigned short ehalf[NE] =
+ {0x0000, 0x0000, 0x0000, 0x0000,
+  0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x3ffe,};
+
+/* 1.0E0 */
+unsigned short eone[NE] =
+ {0x0000, 0x0000, 0x0000, 0x0000,
+  0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x3fff,};
+
+/* 2.0E0 */
+unsigned short etwo[NE] =
+ {0x0000, 0x0000, 0x0000, 0x0000,
+  0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x4000,};
+
+/* 3.2E1 */
+unsigned short e32[NE] =
+ {0x0000, 0x0000, 0x0000, 0x0000,
+  0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x4004,};
+
+/* 6.93147180559945309417232121458176568075500134360255E-1 */
+unsigned short elog2[NE] =
+ {0x40f3, 0xf6af, 0x03f2, 0xb398,
+  0xc9e3, 0x79ab, 0150717, 0013767, 0130562, 0x3ffe,};
+
+/* 1.41421356237309504880168872420969807856967187537695E0 */
+unsigned short esqrt2[NE] =
+ {0x1d6f, 0xbe9f, 0x754a, 0x89b3,
+  0x597d, 0x6484, 0174736, 0171463, 0132404, 0x3fff,};
+
+/* 3.14159265358979323846264338327950288419716939937511E0 */
+unsigned short epi[NE] =
+ {0x2902, 0x1cd1, 0x80dc, 0x628b,
+  0xc4c6, 0xc234, 0020550, 0155242, 0144417, 0040000,};
+  
+/* 5.7721566490153286060651209008240243104215933593992E-1 */
+unsigned short eeul[NE] = {
+0xd1be,0xc7a4,0076660,0063743,0111704,0x3ffe,};
+
+#else
+
+/* 0.0 */
+unsigned short ezero[NE] = {
+0, 0000000,0000000,0000000,0000000,0000000,};
+/* 5.0E-1 */
+unsigned short ehalf[NE] = {
+0, 0000000,0000000,0000000,0100000,0x3ffe,};
+/* 1.0E0 */
+unsigned short eone[NE] = {
+0, 0000000,0000000,0000000,0100000,0x3fff,};
+/* 2.0E0 */
+unsigned short etwo[NE] = {
+0, 0000000,0000000,0000000,0100000,0040000,};
+/* 3.2E1 */
+unsigned short e32[NE] = {
+0, 0000000,0000000,0000000,0100000,0040004,};
+/* 6.93147180559945309417232121458176568075500134360255E-1 */
+unsigned short elog2[NE] = {
+0xc9e4,0x79ab,0150717,0013767,0130562,0x3ffe,};
+/* 1.41421356237309504880168872420969807856967187537695E0 */
+unsigned short esqrt2[NE] = {
+0x597e,0x6484,0174736,0171463,0132404,0x3fff,};
+/* 2/sqrt(PI) =
+ * 1.12837916709551257389615890312154517168810125865800E0 */
+unsigned short eoneopi[NE] = {
+0x71d5,0x688d,0012333,0135202,0110156,0x3fff,};
+/* 3.14159265358979323846264338327950288419716939937511E0 */
+unsigned short epi[NE] = {
+0xc4c6,0xc234,0020550,0155242,0144417,0040000,};
+/* 5.7721566490153286060651209008240243104215933593992E-1 */
+unsigned short eeul[NE] = {
+0xd1be,0xc7a4,0076660,0063743,0111704,0x3ffe,};
+#endif
+extern unsigned short ezero[];
+extern unsigned short ehalf[];
+extern unsigned short eone[];
+extern unsigned short etwo[];
+extern unsigned short e32[];
+extern unsigned short elog2[];
+extern unsigned short esqrt2[];
+extern unsigned short eoneopi[];
+extern unsigned short epi[];
+extern unsigned short eeul[];
+

test/math/eexp.c

@@ -0,0 +1,77 @@
+/*							xexp.c		*/
+/* exponential function check routine */
+/* by Stephen L. Moshier. */
+
+
+#include "ehead.h"
+
+/*
+extern int powinited;
+extern short maxposint[], maxnegint[];
+*/
+
+void eexp( x, y )
+unsigned short *x, *y;
+{
+unsigned short num[NE], den[NE], x2[NE];
+long i;
+unsigned short sign, expchk;
+
+/* range reduction theory: x = i + f, 0<=f<1;
+ * e**x = e**i * e**f 
+ * e**i = 2**(i/log 2).
+ * Let i/log2 = i1 + f1, 0<=f1<1.
+ * Then e**i = 2**i1 * 2**f1, so
+ * e**x = 2**i1 * e**(log 2 * f1) * e**f.
+ */
+/*
+if( powinited == 0 )
+	initpow();
+*/
+if( ecmp(x, ezero) == 0 )
+	{
+	emov( eone, y );
+	return;
+	}
+emov(x, x2);
+expchk = x2[NE-1];
+sign = expchk & 0x8000;
+x2[NE-1] &= 0x7fff;
+
+/* Test for excessively large argument */
+expchk &= 0x7fff;
+if( expchk > (EXONE + 15) )
+	{
+	eclear( y );
+	if( sign == 0 )
+		einfin( y );
+	return;
+	}
+
+eifrac( x2, &i, num );		/* x = i + f		*/
+
+if( i != 0 )
+ {
+ ltoe( &i, den );		/* floating point i	*/
+ ediv( elog2, den, den );	/* i/log 2		*/
+ eifrac( den, &i, den );	/* i/log 2  =  i1 + f1	*/
+ emul( elog2, den, den );	/* log 2 * f1		*/
+ eadd( den, num, x2 );		/* log 2 * f1  + f	*/
+ }
+
+/*x2[NE-1] -= 1;*/
+eldexp( x2, -1L, x2 ); /* divide by 2 */
+etanh( x2, x2 );	/* tanh( x/2 )			*/
+eadd( x2, eone, num );	/* 1 + tanh			*/
+eneg( x2 );
+eadd( x2, eone, den );	/* 1 - tanh			*/
+ediv( den, num, y );	/* (1 + tanh)/(1 - tanh)	*/
+
+/*y[NE-1] += i;*/
+if( sign )
+	{
+	ediv( y, eone, y );
+	i = -i;
+	}
+eldexp( y, i, y );	/* multiply by 2**i */
+}

test/math/ehead.h

@@ -0,0 +1,42 @@
+
+/* Include file for extended precision arithmetic programs.
+ */
+
+/* Number of 16 bit words in external x type format */
+#define NE 6
+
+/* Number of 16 bit words in internal format */
+#define NI (NE+3)
+
+/* Array offset to exponent */
+#define E 1
+
+/* Array offset to high guard word */
+#define M 2
+
+/* Number of bits of precision */
+#define NBITS ((NI-4)*16)
+
+/* Maximum number of decimal digits in ASCII conversion
+ * = NBITS*log10(2)
+ */
+#define NDEC (NBITS*8/27)
+
+/* The exponent of 1.0 */
+#define EXONE (0x3fff)
+
+void eadd(), esub(), emul(), ediv();
+int ecmp(), enormlz(), eshift();
+void eshup1(), eshup8(), eshup6(), eshdn1(), eshdn8(), eshdn6();
+void eabs(), eneg(), emov(), eclear(), einfin(), efloor();
+void eldexp(), efrexp(), eifrac(), ltoe();
+void esqrt(), elog(), eexp(), etanh(), epow();
+void asctoe(), asctoe24(), asctoe53(), asctoe64();
+void etoasc(), e24toasc(), e53toasc(), e64toasc();
+void etoe64(), etoe53(), etoe24(), e64toe(), e53toe(), e24toe();
+void mtherr();
+extern unsigned short ezero[], ehalf[], eone[], etwo[];
+extern unsigned short elog2[], esqrt2[];
+
+
+/* by Stephen L. Moshier. */

test/math/elog.c

@@ -0,0 +1,92 @@
+/*						xlog.c	*/
+/* natural logarithm */
+/* by Stephen L. Moshier. */
+
+#include "mconf.h"
+#include "ehead.h"
+
+
+
+void elog( x, y )
+unsigned short *x, *y;
+{
+unsigned short xx[NE], z[NE], a[NE], b[NE], t[NE], qj[NE];
+long ex;
+int fex;
+
+
+if( x[NE-1] & (unsigned short )0x8000 )
+	{
+	eclear(y);
+	mtherr( "elog", DOMAIN );
+	return;
+	}
+if( ecmp( x, ezero ) == 0 )
+	{
+	einfin( y );
+	eneg(y);
+	mtherr( "elog", SING );
+	return;
+	}
+if( ecmp( x, eone ) == 0 )
+	{
+	eclear( y );
+	return;
+	}
+
+/* range reduction: log x = log( 2**ex * m ) = ex * log2 + log m */
+efrexp( x, &fex, xx );
+/*
+emov(x, xx );
+ex = xx[NX-1] & 0x7fff;
+ex -= 0x3ffe;
+xx[NX-1] = 0x3ffe;
+*/
+
+/* Adjust range to 1/sqrt(2), sqrt(2) */
+esqrt2[NE-1] -= 1;
+if( ecmp( xx, esqrt2 ) < 0 )
+	{
+	fex -= 1;
+	emul( xx, etwo, xx );
+	}
+esqrt2[NE-1] += 1;
+
+esub( eone, xx, a );
+if( a[NE-1] == 0 )
+	{
+	eclear( y );
+	goto logdon;
+	}
+eadd( eone, xx, b );
+ediv( b, a, y );	/* store (x-1)/(x+1) in y */
+
+emul( y, y, z );
+
+emov( eone, a );
+emov( eone, b );
+emov( eone, qj );
+do
+	{
+	eadd( etwo, qj, qj );	/* 2 * i + 1		*/
+	emul( z, a, a );
+	ediv( qj, a, t );
+	eadd( t, b, b );
+	}
+while( ((b[NE-1] & 0x7fff) - (t[NE-1] & 0x7fff)) < NBITS );
+
+
+emul( b, y, y );
+emul( y, etwo, y );
+
+logdon:
+
+/* now add log of 2**ex */
+if( fex != 0 )
+	{
+	ex = fex;
+	ltoe( &ex, b );
+	emul( elog2, b, b );
+	eadd( b, y, y );
+	}
+}

test/math/eparanoi.c

@@ -0,0 +1,3550 @@
+/* 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");
+}

test/math/epow.c

@@ -0,0 +1,215 @@
+/*						epow.c	*/
+/*  power function: z = x**y */
+/*  by Stephen L. Moshier. */
+
+
+#include "ehead.h"
+#define MAXPOS ((long) (((unsigned long) ~(0L)) >> 1))
+#define MAXNEG (-MAXPOS)
+/* #define MAXNEG (-MAXPOS - 1L) */
+
+extern int rndprc;
+void epowi();
+static void epowr();
+
+
+/* Run-time determination of largest integers */
+
+int powinited = 0;
+unsigned short maxposint[NE], maxnegint[NE];
+
+void initpow()
+{
+long li;
+
+li = MAXPOS;
+ltoe( &li, maxposint );
+li = MAXNEG;
+ltoe( &li, maxnegint );
+powinited = 1;
+}
+
+
+
+
+void epow( x, y, z )
+unsigned short *x, *y, *z;
+{
+unsigned short w[NE];
+int rndsav;
+long li;
+
+if( powinited == 0 )
+	initpow();
+
+/* Check for integer power. */
+
+efloor( y, w );
+if( (ecmp(y,w) == 0)
+   && (ecmp(maxposint,w) >= 0)
+   && (ecmp(w,maxnegint) >= 0) )
+	{
+	eifrac( y, &li, w );
+	epowi( x, y, z );
+	return;
+	}
+epowr( x, y, z );
+}
+
+
+
+
+/* y is integer valued. */
+
+void epowi( x, y, z )
+unsigned short x[], y[], z[];
+{
+unsigned short w[NE];
+long li, lx;
+unsigned long lu;
+int rndsav;
+unsigned short signx;
+/* unsigned short signy; */
+
+if( powinited == 0 )
+	initpow();
+
+rndsav = rndprc;
+
+if( (ecmp(y,maxposint) > 0) || (ecmp(maxnegint,y) > 0) )
+	{
+	epowr( x, y, z );
+	return;
+	}
+
+eifrac( y, &li, w );
+if( li < 0 )
+	lx = -li;
+else
+	lx = li;
+
+/*
+if( (x[NE-1] & (unsigned short )0x7fff) == 0 )
+*/
+
+if( ecmp( x, ezero) == 0 )
+	{
+	if( li == 0 )
+		{
+		emov( eone, z );
+		return;
+		}
+	else if( li < 0 )
+		{
+		einfin( z );
+		return;
+		}
+	else
+		{
+		eclear( z );
+		return;
+		}
+	}
+
+if( li == 0L )
+	{
+	emov( eone, z );
+	return;
+	}
+
+emov( x, w );
+signx = w[NE-1] & (unsigned short )0x8000;
+w[NE-1] &= (unsigned short )0x7fff;
+
+/* Overflow detection */
+/*
+lx = li * (w[NE-1] - 0x3fff);
+if( lx > 16385L )
+	{
+	einfin( z );
+	mtherr( "epowi", OVERFLOW );
+	goto done;
+	}
+if( lx < -16450L )
+	{
+	eclear( z );
+	return;
+	}
+*/
+rndprc = NBITS;
+
+if( li < 0 )
+	{
+	lu = (unsigned int )( -li );
+/*	signy = 0xffff;*/
+	ediv( w, eone, w );
+	}
+else
+	{
+	lu = (unsigned int )li;
+/*	signy = 0;*/
+	}
+
+/* First bit of the power */
+if( lu & 1 )
+	{
+	emov( w, z );
+	}	
+else
+	{
+	emov( eone, z );
+	signx = 0;
+	}
+
+
+lu >>= 1;
+while( lu != 0L )
+	{
+	emul( w, w, w );	/* arg to the 2-to-the-kth power */
+	if( lu & 1L )	/* if that bit is set, then include in product */
+		emul( w, z, z );
+	lu >>= 1;
+	}
+
+
+done:
+
+if( signx )
+	eneg( z ); /* odd power of negative number */
+
+/*
+if( signy )
+  	{
+  	if( ecmp( z, ezero ) != 0 )
+ 		{
+		ediv( z, eone, z );
+		}
+	else
+		{
+		einfin( z );
+		printf( "epowi OVERFLOW\n" );
+		}
+	}
+*/
+rndprc = rndsav;
+emul( eone, z, z );
+}
+
+
+
+/* z = exp( y * log(x) ) */
+
+static void epowr( x, y, z )
+unsigned short *x, *y, *z;
+{
+unsigned short w[NE];
+int rndsav;
+
+rndsav = rndprc;
+rndprc = NBITS;
+elog( x, w );
+emul( y, w, w );
+eexp( w, z );
+rndprc = rndsav;
+emul( eone, z, z );
+}

test/math/etanh.c

@@ -0,0 +1,52 @@
+/*							xtanh.c		*/
+/* hyperbolic tangent check routine */
+/* this subroutine is used by the exponential function routine */
+/* by Stephen L. Moshier. */
+
+
+
+#include "ehead.h"
+
+
+void etanh( x, y )
+unsigned short *x, *y;
+{
+unsigned short e[NE], r[NE], j[NE], xx[NE], m2[NE];
+short i, n;
+long lj;
+
+emov( x, r );
+r[NE-1] &= (unsigned short )0x7fff;
+if( ecmp(r, eone) >= 0 )
+	{
+/* tanh(x) = (exp(x) - exp(-x)) / (exp(x) + exp(-x))
+ * Note eexp() calls xtanh, but with an argument less than (1 + log 2)/2.
+ */
+	eexp( r, e );
+	ediv( e, eone, r );
+	esub( r, e, xx );
+	eadd( r, e, j );
+	ediv( j, xx, y );
+	return;
+	}
+
+emov( etwo, m2 );
+eneg( m2 );
+
+n = NBITS/8;	/* Number of terms to do in the continued fraction */
+lj = 2 * n + 1;
+ltoe( &lj, j );
+
+emov( j, e );
+emul( x, x, xx );
+
+/* continued fraction */
+for( i=0; i<n; i++)
+	{
+	ediv( e, xx, r );
+	eadd( m2, j, j );
+	eadd( r, j, e );
+	}
+
+ediv( e, x, y );
+}

test/math/etodec.c

@@ -0,0 +1,181 @@
+#include "ehead.h"
+void emovi(), emovo(), ecleaz(), eshdn8(), emdnorm();
+void todec();
+/*
+;	convert DEC double precision to e type
+;	double d;
+;	short e[NE];
+;	dectoe( &d, e );
+*/
+void dectoe( d, e )
+unsigned short *d;
+unsigned short *e;
+{
+unsigned short y[NI];
+register unsigned short r, *p;
+
+ecleaz(y);		/* start with a zero */
+p = y;			/* point to our number */
+r = *d;			/* get DEC exponent word */
+if( *d & (unsigned int )0x8000 )
+	*p = 0xffff;	/* fill in our sign */
+++p;			/* bump pointer to our exponent word */
+r &= 0x7fff;		/* strip the sign bit */
+if( r == 0 )		/* answer = 0 if high order DEC word = 0 */
+	goto done;
+
+
+r >>= 7;	/* shift exponent word down 7 bits */
+r += EXONE - 0201;	/* subtract DEC exponent offset */
+			/* add our e type exponent offset */
+*p++ = r;	/* to form our exponent */
+
+r = *d++;	/* now do the high order mantissa */
+r &= 0177;	/* strip off the DEC exponent and sign bits */
+r |= 0200;	/* the DEC understood high order mantissa bit */
+*p++ = r;	/* put result in our high guard word */
+
+*p++ = *d++;	/* fill in the rest of our mantissa */
+*p++ = *d++;
+*p = *d;
+
+eshdn8(y);	/* shift our mantissa down 8 bits */
+done:
+emovo( y, e );
+}
+
+
+
+/*
+;	convert e type to DEC double precision
+;	double d;
+;	short e[NE];
+;	etodec( e, &d );
+*/
+#if 0
+static unsigned short decbit[NI] = {0,0,0,0,0,0,0200,0};
+void etodec( x, d )
+unsigned short *x, *d;
+{
+unsigned short xi[NI];
+register unsigned short r;
+int i, j;
+
+emovi( x, xi );
+*d = 0;
+if( xi[0] != 0 )
+	*d = 0100000;
+r = xi[E];
+if( r < (EXONE - 128) )
+	goto zout;
+i = xi[M+4];
+if( (i & 0200) != 0 )
+	{
+	if( (i & 0377) == 0200 )
+		{
+		if( (i & 0400) != 0 )
+			{
+		/* check all less significant bits */
+			for( j=M+5; j<NI; j++ )
+				{
+				if( xi[j] != 0 )
+					goto yesrnd;
+				}
+			}
+		goto nornd;
+		}
+yesrnd:
+	eaddm( decbit, xi );
+	r -= enormlz(xi);
+	}
+
+nornd:
+
+r -= EXONE;
+r += 0201;
+if( r < 0 )
+	{
+zout:
+	*d++ = 0;
+	*d++ = 0;
+	*d++ = 0;
+	*d++ = 0;
+	return;
+	}
+if( r >= 0377 )
+	{
+	*d++ = 077777;
+	*d++ = -1;
+	*d++ = -1;
+	*d++ = -1;
+	return;
+	}
+r &= 0377;
+r <<= 7;
+eshup8( xi );
+xi[M] &= 0177;
+r |= xi[M];
+*d++ |= r;
+*d++ = xi[M+1];
+*d++ = xi[M+2];
+*d++ = xi[M+3];
+}
+#else
+
+extern int rndprc;
+
+void etodec( x, d )
+unsigned short *x, *d;
+{
+unsigned short xi[NI];
+long exp;
+int rndsav;
+
+emovi( x, xi );
+exp = (long )xi[E] - (EXONE - 0201); /* adjust exponent for offsets */
+/* round off to nearest or even */
+rndsav = rndprc;
+rndprc = 56;
+emdnorm( xi, 0, 0, exp, 64 );
+rndprc = rndsav;
+todec( xi, d );
+}
+
+void todec( x, y )
+unsigned short *x, *y;
+{
+unsigned short i;
+unsigned short *p;
+
+p = x;
+*y = 0;
+if( *p++ )
+	*y = 0100000;
+i = *p++;
+if( i == 0 )
+	{
+	*y++ = 0;
+	*y++ = 0;
+	*y++ = 0;
+	*y++ = 0;
+	return;
+	}
+if( i > 0377 )
+	{
+	*y++ |= 077777;
+	*y++ = 0xffff;
+	*y++ = 0xffff;
+	*y++ = 0xffff;
+	return;
+	}
+i &= 0377;
+i <<= 7;
+eshup8( x );
+x[M] &= 0177;
+i |= x[M];
+*y++ |= i;
+*y++ = x[M+1];
+*y++ = x[M+2];
+*y++ = x[M+3];
+}
+#endif

test/math/ieee.c

@@ -0,0 +1,4119 @@
+/*							ieee.c
+ *
+ *    Extended precision IEEE binary floating point arithmetic routines
+ *
+ * Numbers are stored in C language as arrays of 16-bit unsigned
+ * short integers.  The arguments of the routines are pointers to
+ * the arrays.
+ *
+ *
+ * External e type data structure, simulates Intel 8087 chip
+ * temporary real format but possibly with a larger significand:
+ *
+ *	NE-1 significand words	(least significant word first,
+ *				 most significant bit is normally set)
+ *	exponent		(value = EXONE for 1.0,
+ *				top bit is the sign)
+ *
+ *
+ * Internal data structure of a number (a "word" is 16 bits):
+ *
+ * ei[0]	sign word	(0 for positive, 0xffff for negative)
+ * ei[1]	biased exponent	(value = EXONE for the number 1.0)
+ * ei[2]	high guard word	(always zero after normalization)
+ * ei[3]
+ * to ei[NI-2]	significand	(NI-4 significand words,
+ *				 most significant word first,
+ *				 most significant bit is set)
+ * ei[NI-1]	low guard word	(0x8000 bit is rounding place)
+ *
+ *
+ *
+ *		Routines for external format numbers
+ *
+ *	asctoe( string, e )	ASCII string to extended double e type
+ *	asctoe64( string, &d )	ASCII string to long double
+ *	asctoe53( string, &d )	ASCII string to double
+ *	asctoe24( string, &f )	ASCII string to single
+ *	asctoeg( string, e, prec ) ASCII string to specified precision
+ *	e24toe( &f, e )		IEEE single precision to e type
+ *	e53toe( &d, e )		IEEE double precision to e type
+ *	e64toe( &d, e )		IEEE long double precision to e type
+ *	eabs(e)			absolute value
+ *	eadd( a, b, c )		c = b + a
+ *	eclear(e)		e = 0
+ *	ecmp (a, b)		Returns 1 if a > b, 0 if a == b,
+ *				-1 if a < b, -2 if either a or b is a NaN.
+ *	ediv( a, b, c )		c = b / a
+ *	efloor( a, b )		truncate to integer, toward -infinity
+ *	efrexp( a, exp, s )	extract exponent and significand
+ *	eifrac( e, &l, frac )   e to long integer and e type fraction
+ *	euifrac( e, &l, frac )  e to unsigned long integer and e type fraction
+ *	einfin( e )		set e to infinity, leaving its sign alone
+ *	eldexp( a, n, b )	multiply by 2**n
+ *	emov( a, b )		b = a
+ *	emul( a, b, c )		c = b * a
+ *	eneg(e)			e = -e
+ *	eround( a, b )		b = nearest integer value to a
+ *	esub( a, b, c )		c = b - a
+ *	e24toasc( &f, str, n )	single to ASCII string, n digits after decimal
+ *	e53toasc( &d, str, n )	double to ASCII string, n digits after decimal
+ *	e64toasc( &d, str, n )	long double to ASCII string
+ *	etoasc( e, str, n )	e to ASCII string, n digits after decimal
+ *	etoe24( e, &f )		convert e type to IEEE single precision
+ *	etoe53( e, &d )		convert e type to IEEE double precision
+ *	etoe64( e, &d )		convert e type to IEEE long double precision
+ *	ltoe( &l, e )		long (32 bit) integer to e type
+ *	ultoe( &l, e )		unsigned long (32 bit) integer to e type
+ *      eisneg( e )             1 if sign bit of e != 0, else 0
+ *      eisinf( e )             1 if e has maximum exponent (non-IEEE)
+ *				or is infinite (IEEE)
+ *      eisnan( e )             1 if e is a NaN
+ *	esqrt( a, b )		b = square root of a
+ *
+ *
+ *		Routines for internal format numbers
+ *
+ *	eaddm( ai, bi )		add significands, bi = bi + ai
+ *	ecleaz(ei)		ei = 0
+ *	ecleazs(ei)		set ei = 0 but leave its sign alone
+ *	ecmpm( ai, bi )		compare significands, return 1, 0, or -1
+ *	edivm( ai, bi )		divide  significands, bi = bi / ai
+ *	emdnorm(ai,l,s,exp)	normalize and round off
+ *	emovi( a, ai )		convert external a to internal ai
+ *	emovo( ai, a )		convert internal ai to external a
+ *	emovz( ai, bi )		bi = ai, low guard word of bi = 0
+ *	emulm( ai, bi )		multiply significands, bi = bi * ai
+ *	enormlz(ei)		left-justify the significand
+ *	eshdn1( ai )		shift significand and guards down 1 bit
+ *	eshdn8( ai )		shift down 8 bits
+ *	eshdn6( ai )		shift down 16 bits
+ *	eshift( ai, n )		shift ai n bits up (or down if n < 0)
+ *	eshup1( ai )		shift significand and guards up 1 bit
+ *	eshup8( ai )		shift up 8 bits
+ *	eshup6( ai )		shift up 16 bits
+ *	esubm( ai, bi )		subtract significands, bi = bi - ai
+ *
+ *
+ * The result is always normalized and rounded to NI-4 word precision
+ * after each arithmetic operation.
+ *
+ * Exception flags are NOT fully supported.
+ *
+ * Define INFINITY in mconf.h for support of infinity; otherwise a
+ * saturation arithmetic is implemented.
+ *
+ * Define NANS for support of Not-a-Number items; otherwise the
+ * arithmetic will never produce a NaN output, and might be confused
+ * by a NaN input.
+ * If NaN's are supported, the output of ecmp(a,b) is -2 if
+ * either a or b is a NaN. This means asking if(ecmp(a,b) < 0)
+ * may not be legitimate. Use if(ecmp(a,b) == -1) for less-than
+ * if in doubt.
+ * Signaling NaN's are NOT supported; they are treated the same
+ * as quiet NaN's.
+ *
+ * Denormals are always supported here where appropriate (e.g., not
+ * for conversion to DEC numbers).
+ */
+
+/*
+ * Revision history:
+ *
+ *  5 Jan 84	PDP-11 assembly language version
+ *  2 Mar 86	fixed bug in asctoq()
+ *  6 Dec 86	C language version
+ * 30 Aug 88	100 digit version, improved rounding
+ * 15 May 92    80-bit long double support
+ *
+ * Author:  S. L. Moshier.
+ */
+
+#include <stdio.h>
+/* #include "\usr\include\stdio.h" */
+#include "ehead.h"
+#include "mconf.h"
+
+/* Change UNK into something else. */
+#ifdef UNK
+#undef UNK
+#define IBMPC 1
+#endif
+
+/* NaN's require infinity support. */
+#ifdef NANS
+#ifndef INFINITY
+#define INFINITY
+#endif
+#endif
+
+/* This handles 64-bit long ints. */
+#define LONGBITS (8 * sizeof(long))
+
+/* Control register for rounding precision.
+ * This can be set to 80 (if NE=6), 64, 56, 53, or 24 bits.
+ */
+int rndprc = NBITS;
+extern int rndprc;
+
+void eaddm(), esubm(), emdnorm(), asctoeg(), enan();
+static void toe24(), toe53(), toe64(), toe113();
+void eremain(), einit(), eiremain();
+int ecmpm(), edivm(), emulm(), eisneg(), eisinf();
+void emovi(), emovo(), emovz(), ecleaz(), eadd1();
+void etodec(), todec(), dectoe();
+int eisnan(), eiisnan();
+
+
+
+void einit()
+{
+}
+
+/*
+; Clear out entire external format number.
+;
+; unsigned short x[];
+; eclear( x );
+*/
+
+void eclear( x )
+register unsigned short *x;
+{
+register int i;
+
+for( i=0; i<NE; i++ )
+	*x++ = 0;
+}
+
+
+
+/* Move external format number from a to b.
+ *
+ * emov( a, b );
+ */
+
+void emov( a, b )
+register unsigned short *a, *b;
+{
+register int i;
+
+for( i=0; i<NE; i++ )
+	*b++ = *a++;
+}
+
+
+/*
+;	Absolute value of external format number
+;
+;	short x[NE];
+;	eabs( x );
+*/
+
+void eabs(x)
+unsigned short x[];	/* x is the memory address of a short */
+{
+
+x[NE-1] &= 0x7fff; /* sign is top bit of last word of external format */
+}
+
+
+
+
+/*
+;	Negate external format number
+;
+;	unsigned short x[NE];
+;	eneg( x );
+*/
+
+void eneg(x)
+unsigned short x[];
+{
+
+#ifdef NANS
+if( eisnan(x) )
+	return;
+#endif
+x[NE-1] ^= 0x8000; /* Toggle the sign bit */
+}
+
+
+
+/* Return 1 if external format number is negative,
+ * else return zero.
+ */
+int eisneg(x)
+unsigned short x[];
+{
+
+#ifdef NANS
+if( eisnan(x) )
+	return( 0 );
+#endif
+if( x[NE-1] & 0x8000 )
+	return( 1 );
+else
+	return( 0 );
+}
+
+
+/* Return 1 if external format number has maximum possible exponent,
+ * else return zero.
+ */
+int eisinf(x)
+unsigned short x[];
+{
+
+if( (x[NE-1] & 0x7fff) == 0x7fff )
+	{
+#ifdef NANS
+	if( eisnan(x) )
+		return( 0 );
+#endif
+	return( 1 );
+	}
+else
+	return( 0 );
+}
+
+/* Check if e-type number is not a number.
+ */
+int eisnan(x)
+unsigned short x[];
+{
+
+#ifdef NANS
+int i;
+/* NaN has maximum exponent */
+if( (x[NE-1] & 0x7fff) != 0x7fff )
+	return (0);
+/* ... and non-zero significand field. */
+for( i=0; i<NE-1; i++ )
+	{
+	if( *x++ != 0 )
+		return (1);
+	}
+#endif
+return (0);
+}
+
+/*
+; Fill entire number, including exponent and significand, with
+; largest possible number.  These programs implement a saturation
+; value that is an ordinary, legal number.  A special value
+; "infinity" may also be implemented; this would require tests
+; for that value and implementation of special rules for arithmetic
+; operations involving inifinity.
+*/
+
+void einfin(x)
+register unsigned short *x;
+{
+register int i;
+
+#ifdef INFINITY
+for( i=0; i<NE-1; i++ )
+	*x++ = 0;
+*x |= 32767;
+#else
+for( i=0; i<NE-1; i++ )
+	*x++ = 0xffff;
+*x |= 32766;
+if( rndprc < NBITS )
+	{
+	if (rndprc == 113)
+		{
+		*(x - 9) = 0;
+		*(x - 8) = 0;
+		}
+	if( rndprc == 64 )
+		{
+		*(x-5) = 0;
+		}
+	if( rndprc == 53 )
+		{
+		*(x-4) = 0xf800;
+		}
+	else
+		{
+		*(x-4) = 0;
+		*(x-3) = 0;
+		*(x-2) = 0xff00;
+		}
+	}
+#endif
+}
+
+
+
+/* Move in external format number,
+ * converting it to internal format.
+ */
+void emovi( a, b )
+unsigned short *a, *b;
+{
+register unsigned short *p, *q;
+int i;
+
+q = b;
+p = a + (NE-1);	/* point to last word of external number */
+/* get the sign bit */
+if( *p & 0x8000 )
+	*q++ = 0xffff;
+else
+	*q++ = 0;
+/* get the exponent */
+*q = *p--;
+*q++ &= 0x7fff;	/* delete the sign bit */
+#ifdef INFINITY
+if( (*(q-1) & 0x7fff) == 0x7fff )
+	{
+#ifdef NANS
+	if( eisnan(a) )
+		{
+		*q++ = 0;
+		for( i=3; i<NI; i++ )
+			*q++ = *p--;
+		return;
+		}
+#endif
+	for( i=2; i<NI; i++ )
+		*q++ = 0;
+	return;
+	}
+#endif
+/* clear high guard word */
+*q++ = 0;
+/* move in the significand */
+for( i=0; i<NE-1; i++ )
+	*q++ = *p--;
+/* clear low guard word */
+*q = 0;
+}
+
+
+/* Move internal format number out,
+ * converting it to external format.
+ */
+void emovo( a, b )
+unsigned short *a, *b;
+{
+register unsigned short *p, *q;
+unsigned short i;
+
+p = a;
+q = b + (NE-1); /* point to output exponent */
+/* combine sign and exponent */
+i = *p++;
+if( i )
+	*q-- = *p++ | 0x8000;
+else
+	*q-- = *p++;
+#ifdef INFINITY
+if( *(p-1) == 0x7fff )
+	{
+#ifdef NANS
+	if( eiisnan(a) )
+		{
+		enan( b, NBITS );
+		return;
+		}
+#endif
+	einfin(b);
+	return;
+	}
+#endif
+/* skip over guard word */
+++p;
+/* move the significand */
+for( i=0; i<NE-1; i++ )
+	*q-- = *p++;
+}
+
+
+
+
+/* Clear out internal format number.
+ */
+
+void ecleaz( xi )
+register unsigned short *xi;
+{
+register int i;
+
+for( i=0; i<NI; i++ )
+	*xi++ = 0;
+}
+
+/* same, but don't touch the sign. */
+
+void ecleazs( xi )
+register unsigned short *xi;
+{
+register int i;
+
+++xi;
+for(i=0; i<NI-1; i++)
+	*xi++ = 0;
+}
+
+
+
+
+/* Move internal format number from a to b.
+ */
+void emovz( a, b )
+register unsigned short *a, *b;
+{
+register int i;
+
+for( i=0; i<NI-1; i++ )
+	*b++ = *a++;
+/* clear low guard word */
+*b = 0;
+}
+
+/* Return nonzero if internal format number is a NaN.
+ */
+
+int eiisnan (x)
+unsigned short x[];
+{
+int i;
+
+if( (x[E] & 0x7fff) == 0x7fff )
+	{
+	for( i=M+1; i<NI; i++ )
+		{
+		if( x[i] != 0 )
+			return(1);
+		}
+	}
+return(0);
+}
+
+#ifdef INFINITY
+/* Return nonzero if internal format number is infinite. */
+
+static int 
+eiisinf (x)
+     unsigned short x[];
+{
+
+#ifdef NANS
+  if (eiisnan (x))
+    return (0);
+#endif
+  if ((x[E] & 0x7fff) == 0x7fff)
+    return (1);
+  return (0);
+}
+#endif
+
+/*
+;	Compare significands of numbers in internal format.
+;	Guard words are included in the comparison.
+;
+;	unsigned short a[NI], b[NI];
+;	cmpm( a, b );
+;
+;	for the significands:
+;	returns	+1 if a > b
+;		 0 if a == b
+;		-1 if a < b
+*/
+int ecmpm( a, b )
+register unsigned short *a, *b;
+{
+int i;
+
+a += M; /* skip up to significand area */
+b += M;
+for( i=M; i<NI; i++ )
+	{
+	if( *a++ != *b++ )
+		goto difrnt;
+	}
+return(0);
+
+difrnt:
+if( *(--a) > *(--b) )
+	return(1);
+else
+	return(-1);
+}
+
+
+/*
+;	Shift significand down by 1 bit
+*/
+
+void eshdn1(x)
+register unsigned short *x;
+{
+register unsigned short bits;
+int i;
+
+x += M;	/* point to significand area */
+
+bits = 0;
+for( i=M; i<NI; i++ )
+	{
+	if( *x & 1 )
+		bits |= 1;
+	*x >>= 1;
+	if( bits & 2 )
+		*x |= 0x8000;
+	bits <<= 1;
+	++x;
+	}	
+}
+
+
+
+/*
+;	Shift significand up by 1 bit
+*/
+
+void eshup1(x)
+register unsigned short *x;
+{
+register unsigned short bits;
+int i;
+
+x += NI-1;
+bits = 0;
+
+for( i=M; i<NI; i++ )
+	{
+	if( *x & 0x8000 )
+		bits |= 1;
+	*x <<= 1;
+	if( bits & 2 )
+		*x |= 1;
+	bits <<= 1;
+	--x;
+	}
+}
+
+
+
+/*
+;	Shift significand down by 8 bits
+*/
+
+void eshdn8(x)
+register unsigned short *x;
+{
+register unsigned short newbyt, oldbyt;
+int i;
+
+x += M;
+oldbyt = 0;
+for( i=M; i<NI; i++ )
+	{
+	newbyt = *x << 8;
+	*x >>= 8;
+	*x |= oldbyt;
+	oldbyt = newbyt;
+	++x;
+	}
+}
+
+/*
+;	Shift significand up by 8 bits
+*/
+
+void eshup8(x)
+register unsigned short *x;
+{
+int i;
+register unsigned short newbyt, oldbyt;
+
+x += NI-1;
+oldbyt = 0;
+
+for( i=M; i<NI; i++ )
+	{
+	newbyt = *x >> 8;
+	*x <<= 8;
+	*x |= oldbyt;
+	oldbyt = newbyt;
+	--x;
+	}
+}
+
+/*
+;	Shift significand up by 16 bits
+*/
+
+void eshup6(x)
+register unsigned short *x;
+{
+int i;
+register unsigned short *p;
+
+p = x + M;
+x += M + 1;
+
+for( i=M; i<NI-1; i++ )
+	*p++ = *x++;
+
+*p = 0;
+}
+
+/*
+;	Shift significand down by 16 bits
+*/
+
+void eshdn6(x)
+register unsigned short *x;
+{
+int i;
+register unsigned short *p;
+
+x += NI-1;
+p = x + 1;
+
+for( i=M; i<NI-1; i++ )
+	*(--p) = *(--x);
+
+*(--p) = 0;
+}
+
+/*
+;	Add significands
+;	x + y replaces y
+*/
+
+void eaddm( x, y )
+unsigned short *x, *y;
+{
+register unsigned long a;
+int i;
+unsigned int carry;
+
+x += NI-1;
+y += NI-1;
+carry = 0;
+for( i=M; i<NI; i++ )
+	{
+	a = (unsigned long )(*x) + (unsigned long )(*y) + carry;
+	if( a & 0x10000 )
+		carry = 1;
+	else
+		carry = 0;
+	*y = (unsigned short )a;
+	--x;
+	--y;
+	}
+}
+
+/*
+;	Subtract significands
+;	y - x replaces y
+*/
+
+void esubm( x, y )
+unsigned short *x, *y;
+{
+unsigned long a;
+int i;
+unsigned int carry;
+
+x += NI-1;
+y += NI-1;
+carry = 0;
+for( i=M; i<NI; i++ )
+	{
+	a = (unsigned long )(*y) - (unsigned long )(*x) - carry;
+	if( a & 0x10000 )
+		carry = 1;
+	else
+		carry = 0;
+	*y = (unsigned short )a;
+	--x;
+	--y;
+	}
+}
+
+
+/* Divide significands */
+
+static unsigned short equot[NI] = {0}; /* was static */
+
+#if 0
+int edivm( den, num )
+unsigned short den[], num[];
+{
+int i;
+register unsigned short *p, *q;
+unsigned short j;
+
+p = &equot[0];
+*p++ = num[0];
+*p++ = num[1];
+
+for( i=M; i<NI; i++ )
+	{
+	*p++ = 0;
+	}
+
+/* Use faster compare and subtraction if denominator
+ * has only 15 bits of significance.
+ */
+p = &den[M+2];
+if( *p++ == 0 )
+	{
+	for( i=M+3; i<NI; i++ )
+		{
+		if( *p++ != 0 )
+			goto fulldiv;
+		}
+	if( (den[M+1] & 1) != 0 )
+		goto fulldiv;
+	eshdn1(num);
+	eshdn1(den);
+
+	p = &den[M+1];
+	q = &num[M+1];
+
+	for( i=0; i<NBITS+2; i++ )
+		{
+		if( *p <= *q )
+			{
+			*q -= *p;
+			j = 1;
+			}
+		else
+			{
+			j = 0;
+			}
+		eshup1(equot);
+		equot[NI-2] |= j;
+		eshup1(num);
+		}
+	goto divdon;
+	}
+
+/* The number of quotient bits to calculate is
+ * NBITS + 1 scaling guard bit + 1 roundoff bit.
+ */
+fulldiv:
+
+p = &equot[NI-2];
+for( i=0; i<NBITS+2; i++ )
+	{
+	if( ecmpm(den,num) <= 0 )
+		{
+		esubm(den, num);
+		j = 1;	/* quotient bit = 1 */
+		}
+	else
+		j = 0;
+	eshup1(equot);
+	*p |= j;
+	eshup1(num);
+	}
+
+divdon:
+
+eshdn1( equot );
+eshdn1( equot );
+
+/* test for nonzero remainder after roundoff bit */
+p = &num[M];
+j = 0;
+for( i=M; i<NI; i++ )
+	{
+	j |= *p++;
+	}
+if( j )
+	j = 1;
+
+
+for( i=0; i<NI; i++ )
+	num[i] = equot[i];
+return( (int )j );
+}
+
+/* Multiply significands */
+int emulm( a, b )
+unsigned short a[], b[];
+{
+unsigned short *p, *q;
+int i, j, k;
+
+equot[0] = b[0];
+equot[1] = b[1];
+for( i=M; i<NI; i++ )
+	equot[i] = 0;
+
+p = &a[NI-2];
+k = NBITS;
+while( *p == 0 ) /* significand is not supposed to be all zero */
+	{
+	eshdn6(a);
+	k -= 16;
+	}
+if( (*p & 0xff) == 0 )
+	{
+	eshdn8(a);
+	k -= 8;
+	}
+
+q = &equot[NI-1];
+j = 0;
+for( i=0; i<k; i++ )
+	{
+	if( *p & 1 )
+		eaddm(b, equot);
+/* remember if there were any nonzero bits shifted out */
+	if( *q & 1 )
+		j |= 1;
+	eshdn1(a);
+	eshdn1(equot);
+	}
+
+for( i=0; i<NI; i++ )
+	b[i] = equot[i];
+
+/* return flag for lost nonzero bits */
+return(j);
+}
+
+#else
+
+/* Multiply significand of e-type number b
+by 16-bit quantity a, e-type result to c. */
+
+void m16m( a, b, c )
+unsigned short a;
+unsigned short b[], c[];
+{
+register unsigned short *pp;
+register unsigned long carry;
+unsigned short *ps;
+unsigned short p[NI];
+unsigned long aa, m;
+int i;
+
+aa = a;
+pp = &p[NI-2];
+*pp++ = 0;
+*pp = 0;
+ps = &b[NI-1];
+
+for( i=M+1; i<NI; i++ )
+	{
+	if( *ps == 0 )
+		{
+		--ps;
+		--pp;
+		*(pp-1) = 0;
+		}
+	else
+		{
+		m = (unsigned long) aa * *ps--;
+		carry = (m & 0xffff) + *pp;
+		*pp-- = (unsigned short )carry;
+		carry = (carry >> 16) + (m >> 16) + *pp;
+		*pp = (unsigned short )carry;
+		*(pp-1) = carry >> 16;
+		}
+	}
+for( i=M; i<NI; i++ )
+	c[i] = p[i];
+}
+
+
+/* Divide significands. Neither the numerator nor the denominator
+is permitted to have its high guard word nonzero.  */
+
+
+int edivm( den, num )
+unsigned short den[], num[];
+{
+int i;
+register unsigned short *p;
+unsigned long tnum;
+unsigned short j, tdenm, tquot;
+unsigned short tprod[NI+1];
+
+p = &equot[0];
+*p++ = num[0];
+*p++ = num[1];
+
+for( i=M; i<NI; i++ )
+	{
+	*p++ = 0;
+	}
+eshdn1( num );
+tdenm = den[M+1];
+for( i=M; i<NI; i++ )
+	{
+	/* Find trial quotient digit (the radix is 65536). */
+	tnum = (((unsigned long) num[M]) << 16) + num[M+1];
+
+	/* Do not execute the divide instruction if it will overflow. */
+        if( (tdenm * 0xffffL) < tnum )
+		tquot = 0xffff;
+	else
+		tquot = tnum / tdenm;
+
+		/* Prove that the divide worked. */
+/*
+	tcheck = (unsigned long )tquot * tdenm;
+	if( tnum - tcheck > tdenm )
+		tquot = 0xffff;
+*/
+	/* Multiply denominator by trial quotient digit. */
+	m16m( tquot, den, tprod );
+	/* The quotient digit may have been overestimated. */
+	if( ecmpm( tprod, num ) > 0 )
+		{
+		tquot -= 1;
+		esubm( den, tprod );
+		if( ecmpm( tprod, num ) > 0 )
+			{
+			tquot -= 1;
+			esubm( den, tprod );
+			}
+		}
+/*
+	if( ecmpm( tprod, num ) > 0 )
+		{
+		eshow( "tprod", tprod );
+		eshow( "num  ", num );
+		printf( "tnum = %08lx, tden = %04x, tquot = %04x\n",
+			 tnum, den[M+1], tquot );
+		}
+*/
+	esubm( tprod, num );
+/*
+	if( ecmpm( num, den ) >= 0 )
+		{
+		eshow( "num  ", num );
+		eshow( "den  ", den );
+		printf( "tnum = %08lx, tden = %04x, tquot = %04x\n",
+			 tnum, den[M+1], tquot );
+		}
+*/
+	equot[i] = tquot;
+	eshup6(num);
+	}
+/* test for nonzero remainder after roundoff bit */
+p = &num[M];
+j = 0;
+for( i=M; i<NI; i++ )
+	{
+	j |= *p++;
+	}
+if( j )
+	j = 1;
+
+for( i=0; i<NI; i++ )
+	num[i] = equot[i];
+
+return( (int )j );
+}
+
+
+
+/* Multiply significands */
+int emulm( a, b )
+unsigned short a[], b[];
+{
+unsigned short *p, *q;
+unsigned short pprod[NI];
+unsigned short j;
+int i;
+
+equot[0] = b[0];
+equot[1] = b[1];
+for( i=M; i<NI; i++ )
+	equot[i] = 0;
+
+j = 0;
+p = &a[NI-1];
+q = &equot[NI-1];
+for( i=M+1; i<NI; i++ )
+	{
+	if( *p == 0 )
+		{
+		--p;
+		}
+	else
+		{
+		m16m( *p--, b, pprod );
+		eaddm(pprod, equot);
+		}
+	j |= *q;
+	eshdn6(equot);
+	}
+
+for( i=0; i<NI; i++ )
+	b[i] = equot[i];
+
+/* return flag for lost nonzero bits */
+return( (int)j );
+}
+
+
+/*
+eshow(str, x)
+char *str;
+unsigned short *x;
+{
+int i;
+
+printf( "%s ", str );
+for( i=0; i<NI; i++ )
+	printf( "%04x ", *x++ );
+printf( "\n" );
+}
+*/
+#endif
+
+
+
+/*
+ * Normalize and round off.
+ *
+ * The internal format number to be rounded is "s".
+ * Input "lost" indicates whether the number is exact.
+ * This is the so-called sticky bit.
+ *
+ * Input "subflg" indicates whether the number was obtained
+ * by a subtraction operation.  In that case if lost is nonzero
+ * then the number is slightly smaller than indicated.
+ *
+ * Input "exp" is the biased exponent, which may be negative.
+ * the exponent field of "s" is ignored but is replaced by
+ * "exp" as adjusted by normalization and rounding.
+ *
+ * Input "rcntrl" is the rounding control.
+ */
+
+static int rlast = -1;
+static int rw = 0;
+static unsigned short rmsk = 0;
+static unsigned short rmbit = 0;
+static unsigned short rebit = 0;
+static int re = 0;
+static unsigned short rbit[NI] = {0,0,0,0,0,0,0,0};
+
+void emdnorm( s, lost, subflg, exp, rcntrl )
+unsigned short s[];
+int lost;
+int subflg;
+long exp;
+int rcntrl;
+{
+int i, j;
+unsigned short r;
+
+/* Normalize */
+j = enormlz( s );
+
+/* a blank significand could mean either zero or infinity. */
+#ifndef INFINITY
+if( j > NBITS )
+	{
+	ecleazs( s );
+	return;
+	}
+#endif
+exp -= j;
+#ifndef INFINITY
+if( exp >= 32767L )
+	goto overf;
+#else
+if( (j > NBITS) && (exp < 32767L) )
+	{
+	ecleazs( s );
+	return;
+	}
+#endif
+if( exp < 0L )
+	{
+	if( exp > (long )(-NBITS-1) )
+		{
+		j = (int )exp;
+		i = eshift( s, j );
+		if( i )
+			lost = 1;
+		}
+	else
+		{
+		ecleazs( s );
+		return;
+		}
+	}
+/* Round off, unless told not to by rcntrl. */
+if( rcntrl == 0 )
+	goto mdfin;
+/* Set up rounding parameters if the control register changed. */
+if( rndprc != rlast )
+	{
+	ecleaz( rbit );
+	switch( rndprc )
+		{
+		default:
+		case NBITS:
+			rw = NI-1; /* low guard word */
+			rmsk = 0xffff;
+			rmbit = 0x8000;
+			rebit = 1;
+			re = rw - 1;
+			break;
+		case 113:
+			rw = 10;
+			rmsk = 0x7fff;
+			rmbit = 0x4000;
+			rebit = 0x8000;
+			re = rw;
+			break;
+		case 64:
+			rw = 7;
+			rmsk = 0xffff;
+			rmbit = 0x8000;
+			rebit = 1;
+			re = rw-1;
+			break;
+/* For DEC arithmetic */
+		case 56:
+			rw = 6;
+			rmsk = 0xff;
+			rmbit = 0x80;
+			rebit = 0x100;
+			re = rw;
+			break;
+		case 53:
+			rw = 6;
+			rmsk = 0x7ff;
+			rmbit = 0x0400;
+			rebit = 0x800;
+			re = rw;
+			break;
+		case 24:
+			rw = 4;
+			rmsk = 0xff;
+			rmbit = 0x80;
+			rebit = 0x100;
+			re = rw;
+			break;
+		}
+	rbit[re] = rebit;
+	rlast = rndprc;
+	}
+
+/* Shift down 1 temporarily if the data structure has an implied
+ * most significant bit and the number is denormal.
+ * For rndprc = 64 or NBITS, there is no implied bit.
+ * But Intel long double denormals lose one bit of significance even so.
+ */
+#if IBMPC
+if( (exp <= 0) && (rndprc != NBITS) )
+#else
+if( (exp <= 0) && (rndprc != 64) && (rndprc != NBITS) )
+#endif
+	{
+	lost |= s[NI-1] & 1;
+	eshdn1(s);
+	}
+/* Clear out all bits below the rounding bit,
+ * remembering in r if any were nonzero.
+ */
+r = s[rw] & rmsk;
+if( rndprc < NBITS )
+	{
+	i = rw + 1;
+	while( i < NI )
+		{
+		if( s[i] )
+			r |= 1;
+		s[i] = 0;
+		++i;
+		}
+	}
+s[rw] &= ~rmsk;
+if( (r & rmbit) != 0 )
+	{
+	if( r == rmbit )
+		{
+		if( lost == 0 )
+			{ /* round to even */
+			if( (s[re] & rebit) == 0 )
+				goto mddone;
+			}
+		else
+			{
+			if( subflg != 0 )
+				goto mddone;
+			}
+		}
+	eaddm( rbit, s );
+	}
+mddone:
+#if IBMPC
+if( (exp <= 0) && (rndprc != NBITS) )
+#else
+if( (exp <= 0) && (rndprc != 64) && (rndprc != NBITS) )
+#endif
+	{
+	eshup1(s);
+	}
+if( s[2] != 0 )
+	{ /* overflow on roundoff */
+	eshdn1(s);
+	exp += 1;
+	}
+mdfin:
+s[NI-1] = 0;
+if( exp >= 32767L )
+	{
+#ifndef INFINITY
+overf:
+#endif
+#ifdef INFINITY
+	s[1] = 32767;
+	for( i=2; i<NI-1; i++ )
+		s[i] = 0;
+#else
+	s[1] = 32766;
+	s[2] = 0;
+	for( i=M+1; i<NI-1; i++ )
+		s[i] = 0xffff;
+	s[NI-1] = 0;
+	if( (rndprc < 64) || (rndprc == 113) )
+		{
+		s[rw] &= ~rmsk;
+		if( rndprc == 24 )
+			{
+			s[5] = 0;
+			s[6] = 0;
+			}
+		}
+#endif
+	return;
+	}
+if( exp < 0 )
+	s[1] = 0;
+else
+	s[1] = (unsigned short )exp;
+}
+
+
+
+/*
+;	Subtract external format numbers.
+;
+;	unsigned short a[NE], b[NE], c[NE];
+;	esub( a, b, c );	 c = b - a
+*/
+
+static int subflg = 0;
+
+void esub( a, b, c )
+unsigned short *a, *b, *c;
+{
+
+#ifdef NANS
+if( eisnan(a) )
+	{
+	emov (a, c);
+	return;
+	}
+if( eisnan(b) )
+	{
+	emov(b,c);
+	return;
+	}
+/* Infinity minus infinity is a NaN.
+ * Test for subtracting infinities of the same sign.
+ */
+if( eisinf(a) && eisinf(b) && ((eisneg (a) ^ eisneg (b)) == 0))
+	{
+	mtherr( "esub", DOMAIN );
+	enan( c, NBITS );
+	return;
+	}
+#endif
+subflg = 1;
+eadd1( a, b, c );
+}
+
+
+/*
+;	Add.
+;
+;	unsigned short a[NE], b[NE], c[NE];
+;	eadd( a, b, c );	 c = b + a
+*/
+void eadd( a, b, c )
+unsigned short *a, *b, *c;
+{
+
+#ifdef NANS
+/* NaN plus anything is a NaN. */
+if( eisnan(a) )
+	{
+	emov(a,c);
+	return;
+	}
+if( eisnan(b) )
+	{
+	emov(b,c);
+	return;
+	}
+/* Infinity minus infinity is a NaN.
+ * Test for adding infinities of opposite signs.
+ */
+if( eisinf(a) && eisinf(b)
+	&& ((eisneg(a) ^ eisneg(b)) != 0) )
+	{
+	mtherr( "eadd", DOMAIN );
+	enan( c, NBITS );
+	return;
+	}
+#endif
+subflg = 0;
+eadd1( a, b, c );
+}
+
+void eadd1( a, b, c )
+unsigned short *a, *b, *c;
+{
+unsigned short ai[NI], bi[NI], ci[NI];
+int i, lost, j, k;
+long lt, lta, ltb;
+
+#ifdef INFINITY
+if( eisinf(a) )
+	{
+	emov(a,c);
+	if( subflg )
+		eneg(c);
+	return;
+	}
+if( eisinf(b) )
+	{
+	emov(b,c);
+	return;
+	}
+#endif
+emovi( a, ai );
+emovi( b, bi );
+if( subflg )
+	ai[0] = ~ai[0];
+
+/* compare exponents */
+lta = ai[E];
+ltb = bi[E];
+lt = lta - ltb;
+if( lt > 0L )
+	{	/* put the larger number in bi */
+	emovz( bi, ci );
+	emovz( ai, bi );
+	emovz( ci, ai );
+	ltb = bi[E];
+	lt = -lt;
+	}
+lost = 0;
+if( lt != 0L )
+	{
+	if( lt < (long )(-NBITS-1) )
+		goto done;	/* answer same as larger addend */
+	k = (int )lt;
+	lost = eshift( ai, k ); /* shift the smaller number down */
+	}
+else
+	{
+/* exponents were the same, so must compare significands */
+	i = ecmpm( ai, bi );
+	if( i == 0 )
+		{ /* the numbers are identical in magnitude */
+		/* if different signs, result is zero */
+		if( ai[0] != bi[0] )
+			{
+			eclear(c);
+			return;
+			}
+		/* if same sign, result is double */
+		/* double denomalized tiny number */
+		if( (bi[E] == 0) && ((bi[3] & 0x8000) == 0) )
+			{
+			eshup1( bi );
+			goto done;
+			}
+		/* add 1 to exponent unless both are zero! */
+		for( j=1; j<NI-1; j++ )
+			{
+			if( bi[j] != 0 )
+				{
+/* This could overflow, but let emovo take care of that. */
+				ltb += 1;
+				break;
+				}
+			}
+		bi[E] = (unsigned short )ltb;
+		goto done;
+		}
+	if( i > 0 )
+		{	/* put the larger number in bi */
+		emovz( bi, ci );
+		emovz( ai, bi );
+		emovz( ci, ai );
+		}
+	}
+if( ai[0] == bi[0] )
+	{
+	eaddm( ai, bi );
+	subflg = 0;
+	}
+else
+	{
+	esubm( ai, bi );
+	subflg = 1;
+	}
+emdnorm( bi, lost, subflg, ltb, 64 );
+
+done:
+emovo( bi, c );
+}
+
+
+
+/*
+;	Divide.
+;
+;	unsigned short a[NE], b[NE], c[NE];
+;	ediv( a, b, c );	c = b / a
+*/
+void ediv( a, b, c )
+unsigned short *a, *b, *c;
+{
+unsigned short ai[NI], bi[NI];
+int i;
+long lt, lta, ltb;
+
+#ifdef NANS
+/* Return any NaN input. */
+if( eisnan(a) )
+	{
+	emov(a,c);
+	return;
+	}
+if( eisnan(b) )
+	{
+	emov(b,c);
+	return;
+	}
+/* Zero over zero, or infinity over infinity, is a NaN. */
+if( ((ecmp(a,ezero) == 0) && (ecmp(b,ezero) == 0))
+	|| (eisinf (a) && eisinf (b)) )
+	{
+	mtherr( "ediv", DOMAIN );
+	enan( c, NBITS );
+	return;
+	}
+#endif
+/* Infinity over anything else is infinity. */
+#ifdef INFINITY
+if( eisinf(b) )
+	{
+	if( eisneg(a) ^ eisneg(b) )
+		*(c+(NE-1)) = 0x8000;
+	else
+		*(c+(NE-1)) = 0;
+	einfin(c);
+	return;
+	}
+if( eisinf(a) )
+	{
+	eclear(c);
+	return;
+	}
+#endif
+emovi( a, ai );
+emovi( b, bi );
+lta = ai[E];
+ltb = bi[E];
+if( bi[E] == 0 )
+	{ /* See if numerator is zero. */
+	for( i=1; i<NI-1; i++ )
+		{
+		if( bi[i] != 0 )
+			{
+			ltb -= enormlz( bi );
+			goto dnzro1;
+			}
+		}
+	eclear(c);
+	return;
+	}
+dnzro1:
+
+if( ai[E] == 0 )
+	{	/* possible divide by zero */
+	for( i=1; i<NI-1; i++ )
+		{
+		if( ai[i] != 0 )
+			{
+			lta -= enormlz( ai );
+			goto dnzro2;
+			}
+		}
+	if( ai[0] == bi[0] )
+		*(c+(NE-1)) = 0;
+	else
+		*(c+(NE-1)) = 0x8000;
+	einfin(c);
+	mtherr( "ediv", SING );
+	return;
+	}
+dnzro2:
+
+i = edivm( ai, bi );
+/* calculate exponent */
+lt = ltb - lta + EXONE;
+emdnorm( bi, i, 0, lt, 64 );
+/* set the sign */
+if( ai[0] == bi[0] )
+	bi[0] = 0;
+else
+	bi[0] = 0Xffff;
+emovo( bi, c );
+}
+
+
+
+/*
+;	Multiply.
+;
+;	unsigned short a[NE], b[NE], c[NE];
+;	emul( a, b, c );	c = b * a
+*/
+void emul( a, b, c )
+unsigned short *a, *b, *c;
+{
+unsigned short ai[NI], bi[NI];
+int i, j;
+long lt, lta, ltb;
+
+#ifdef NANS
+/* NaN times anything is the same NaN. */
+if( eisnan(a) )
+	{
+	emov(a,c);
+	return;
+	}
+if( eisnan(b) )
+	{
+	emov(b,c);
+	return;
+	}
+/* Zero times infinity is a NaN. */
+if( (eisinf(a) && (ecmp(b,ezero) == 0))
+	|| (eisinf(b) && (ecmp(a,ezero) == 0)) )
+	{
+	mtherr( "emul", DOMAIN );
+	enan( c, NBITS );
+	return;
+	}
+#endif
+/* Infinity times anything else is infinity. */
+#ifdef INFINITY
+if( eisinf(a) || eisinf(b) )
+	{
+	if( eisneg(a) ^ eisneg(b) )
+		*(c+(NE-1)) = 0x8000;
+	else
+		*(c+(NE-1)) = 0;
+	einfin(c);
+	return;
+	}
+#endif
+emovi( a, ai );
+emovi( b, bi );
+lta = ai[E];
+ltb = bi[E];
+if( ai[E] == 0 )
+	{
+	for( i=1; i<NI-1; i++ )
+		{
+		if( ai[i] != 0 )
+			{
+			lta -= enormlz( ai );
+			goto mnzer1;
+			}
+		}
+	eclear(c);
+	return;
+	}
+mnzer1:
+
+if( bi[E] == 0 )
+	{
+	for( i=1; i<NI-1; i++ )
+		{
+		if( bi[i] != 0 )
+			{
+			ltb -= enormlz( bi );
+			goto mnzer2;
+			}
+		}
+	eclear(c);
+	return;
+	}
+mnzer2:
+
+/* Multiply significands */
+j = emulm( ai, bi );
+/* calculate exponent */
+lt = lta + ltb - (EXONE - 1);
+emdnorm( bi, j, 0, lt, 64 );
+/* calculate sign of product */
+if( ai[0] == bi[0] )
+	bi[0] = 0;
+else
+	bi[0] = 0xffff;
+emovo( bi, c );
+}
+
+
+
+
+/*
+; Convert IEEE double precision to e type
+;	double d;
+;	unsigned short x[N+2];
+;	e53toe( &d, x );
+*/
+void e53toe( pe, y )
+unsigned short *pe, *y;
+{
+#ifdef DEC
+
+dectoe( pe, y ); /* see etodec.c */
+
+#else
+
+register unsigned short r;
+register unsigned short *p, *e;
+unsigned short yy[NI];
+int denorm, k;
+
+e = pe;
+denorm = 0;	/* flag if denormalized number */
+ecleaz(yy);
+#ifdef IBMPC
+e += 3;
+#endif
+r = *e;
+yy[0] = 0;
+if( r & 0x8000 )
+	yy[0] = 0xffff;
+yy[M] = (r & 0x0f) | 0x10;
+r &= ~0x800f;	/* strip sign and 4 significand bits */
+#ifdef INFINITY
+if( r == 0x7ff0 )
+	{
+#ifdef NANS
+#ifdef IBMPC
+	if( ((pe[3] & 0xf) != 0) || (pe[2] != 0)
+		|| (pe[1] != 0) || (pe[0] != 0) )
+		{
+		enan( y, NBITS );
+		return;
+		}
+#else
+	if( ((pe[0] & 0xf) != 0) || (pe[1] != 0)
+		 || (pe[2] != 0) || (pe[3] != 0) )
+		{
+		enan( y, NBITS );
+		return;
+		}
+#endif
+#endif  /* NANS */
+	eclear( y );
+	einfin( y );
+	if( yy[0] )
+		eneg(y);
+	return;
+	}
+#endif
+r >>= 4;
+/* If zero exponent, then the significand is denormalized.
+ * So, take back the understood high significand bit. */ 
+if( r == 0 )
+	{
+	denorm = 1;
+	yy[M] &= ~0x10;
+	}
+r += EXONE - 01777;
+yy[E] = r;
+p = &yy[M+1];
+#ifdef IBMPC
+*p++ = *(--e);
+*p++ = *(--e);
+*p++ = *(--e);
+#endif
+#ifdef MIEEE
+++e;
+*p++ = *e++;
+*p++ = *e++;
+*p++ = *e++;
+#endif
+(void )eshift( yy, -5 );
+if( denorm )
+	{ /* if zero exponent, then normalize the significand */
+	if( (k = enormlz(yy)) > NBITS )
+		ecleazs(yy);
+	else
+		yy[E] -= (unsigned short )(k-1);
+	}
+emovo( yy, y );
+#endif /* not DEC */
+}
+
+void e64toe( pe, y )
+unsigned short *pe, *y;
+{
+unsigned short yy[NI];
+unsigned short *p, *q, *e;
+int i;
+
+e = pe;
+p = yy;
+for( i=0; i<NE-5; i++ )
+	*p++ = 0;
+#ifdef IBMPC
+for( i=0; i<5; i++ )
+	*p++ = *e++;
+#endif
+#ifdef DEC
+for( i=0; i<5; i++ )
+	*p++ = *e++;
+#endif
+#ifdef MIEEE
+p = &yy[0] + (NE-1);
+*p-- = *e++;
+++e;
+for( i=0; i<4; i++ )
+	*p-- = *e++;
+#endif
+
+#ifdef IBMPC
+/* For Intel long double, shift denormal significand up 1
+   -- but only if the top significand bit is zero.  */
+if((yy[NE-1] & 0x7fff) == 0 && (yy[NE-2] & 0x8000) == 0)
+  {
+    unsigned short temp[NI+1];
+    emovi(yy, temp);
+    eshup1(temp);
+    emovo(temp,y);
+    return;
+  }
+#endif
+#ifdef INFINITY
+/* Point to the exponent field.  */
+p = &yy[NE-1];
+if( *p == 0x7fff )
+	{
+#ifdef NANS
+#ifdef IBMPC
+	for( i=0; i<4; i++ )
+		{
+		if((i != 3 && pe[i] != 0)
+		   /* Check for Intel long double infinity pattern.  */
+		   || (i == 3 && pe[i] != 0x8000))
+			{
+			enan( y, NBITS );
+			return;
+			}
+		}
+#else
+	for( i=1; i<=4; i++ )
+		{
+		if( pe[i] != 0 )
+			{
+			enan( y, NBITS );
+			return;
+			}
+		}
+#endif
+#endif /* NANS */
+	eclear( y );
+	einfin( y );
+	if( *p & 0x8000 )
+		eneg(y);
+	return;
+	}
+#endif
+p = yy;
+q = y;
+for( i=0; i<NE; i++ )
+	*q++ = *p++;
+}
+
+void e113toe(pe,y)
+unsigned short *pe, *y;
+{
+register unsigned short r;
+unsigned short *e, *p;
+unsigned short yy[NI];
+int denorm, i;
+
+e = pe;
+denorm = 0;
+ecleaz(yy);
+#ifdef IBMPC
+e += 7;
+#endif
+r = *e;
+yy[0] = 0;
+if( r & 0x8000 )
+	yy[0] = 0xffff;
+r &= 0x7fff;
+#ifdef INFINITY
+if( r == 0x7fff )
+	{
+#ifdef NANS
+#ifdef IBMPC
+	for( i=0; i<7; i++ )
+		{
+		if( pe[i] != 0 )
+			{
+			enan( y, NBITS );
+			return;
+			}
+		}
+#else
+	for( i=1; i<8; i++ )
+		{
+		if( pe[i] != 0 )
+			{
+			enan( y, NBITS );
+			return;
+			}
+		}
+#endif
+#endif /* NANS */
+	eclear( y );
+	einfin( y );
+	if( *e & 0x8000 )
+		eneg(y);
+	return;
+	}
+#endif  /* INFINITY */
+yy[E] = r;
+p = &yy[M + 1];
+#ifdef IBMPC
+for( i=0; i<7; i++ )
+	*p++ = *(--e);
+#endif
+#ifdef MIEEE
+++e;
+for( i=0; i<7; i++ )
+	*p++ = *e++;
+#endif
+/* If denormal, remove the implied bit; else shift down 1. */
+if( r == 0 )
+	{
+	yy[M] = 0;
+	}
+else
+	{
+	yy[M] = 1;
+	eshift( yy, -1 );
+	}
+emovo(yy,y);
+}
+
+
+/*
+; Convert IEEE single precision to e type
+;	float d;
+;	unsigned short x[N+2];
+;	dtox( &d, x );
+*/
+void e24toe( pe, y )
+unsigned short *pe, *y;
+{
+register unsigned short r;
+register unsigned short *p, *e;
+unsigned short yy[NI];
+int denorm, k;
+
+e = pe;
+denorm = 0;	/* flag if denormalized number */
+ecleaz(yy);
+#ifdef IBMPC
+e += 1;
+#endif
+#ifdef DEC
+e += 1;
+#endif
+r = *e;
+yy[0] = 0;
+if( r & 0x8000 )
+	yy[0] = 0xffff;
+yy[M] = (r & 0x7f) | 0200;
+r &= ~0x807f;	/* strip sign and 7 significand bits */
+#ifdef INFINITY
+if( r == 0x7f80 )
+	{
+#ifdef NANS
+#ifdef MIEEE
+	if( ((pe[0] & 0x7f) != 0) || (pe[1] != 0) )
+		{
+		enan( y, NBITS );
+		return;
+		}
+#else
+	if( ((pe[1] & 0x7f) != 0) || (pe[0] != 0) )
+		{
+		enan( y, NBITS );
+		return;
+		}
+#endif
+#endif  /* NANS */
+	eclear( y );
+	einfin( y );
+	if( yy[0] )
+		eneg(y);
+	return;
+	}
+#endif
+r >>= 7;
+/* If zero exponent, then the significand is denormalized.
+ * So, take back the understood high significand bit. */ 
+if( r == 0 )
+	{
+	denorm = 1;
+	yy[M] &= ~0200;
+	}
+r += EXONE - 0177;
+yy[E] = r;
+p = &yy[M+1];
+#ifdef IBMPC
+*p++ = *(--e);
+#endif
+#ifdef DEC
+*p++ = *(--e);
+#endif
+#ifdef MIEEE
+++e;
+*p++ = *e++;
+#endif
+(void )eshift( yy, -8 );
+if( denorm )
+	{ /* if zero exponent, then normalize the significand */
+	if( (k = enormlz(yy)) > NBITS )
+		ecleazs(yy);
+	else
+		yy[E] -= (unsigned short )(k-1);
+	}
+emovo( yy, y );
+}
+
+void etoe113(x,e)
+unsigned short *x, *e;
+{
+unsigned short xi[NI];
+long exp;
+int rndsav;
+
+#ifdef NANS
+if( eisnan(x) )
+	{
+	enan( e, 113 );
+	return;
+	}
+#endif
+emovi( x, xi );
+exp = (long )xi[E];
+#ifdef INFINITY
+if( eisinf(x) )
+	goto nonorm;
+#endif
+/* round off to nearest or even */
+rndsav = rndprc;
+rndprc = 113;
+emdnorm( xi, 0, 0, exp, 64 );
+rndprc = rndsav;
+nonorm:
+toe113 (xi, e);
+}
+
+/* move out internal format to ieee long double */
+static void toe113(a,b)
+unsigned short *a, *b;
+{
+register unsigned short *p, *q;
+unsigned short i;
+
+#ifdef NANS
+if( eiisnan(a) )
+	{
+	enan( b, 113 );
+	return;
+	}
+#endif
+p = a;
+#ifdef MIEEE
+q = b;
+#else
+q = b + 7;			/* point to output exponent */
+#endif
+
+/* If not denormal, delete the implied bit. */
+if( a[E] != 0 )
+	{
+	eshup1 (a);
+	}
+/* combine sign and exponent */
+i = *p++;
+#ifdef MIEEE
+if( i )
+	*q++ = *p++ | 0x8000;
+else
+	*q++ = *p++;
+#else
+if( i )
+	*q-- = *p++ | 0x8000;
+else
+	*q-- = *p++;
+#endif
+/* skip over guard word */
+++p;
+/* move the significand */
+#ifdef MIEEE
+for (i = 0; i < 7; i++)
+	*q++ = *p++;
+#else
+for (i = 0; i < 7; i++)
+	*q-- = *p++;
+#endif
+}
+
+
+void etoe64( x, e )
+unsigned short *x, *e;
+{
+unsigned short xi[NI];
+long exp;
+int rndsav;
+
+#ifdef NANS
+if( eisnan(x) )
+	{
+	enan( e, 64 );
+	return;
+	}
+#endif
+emovi( x, xi );
+exp = (long )xi[E]; /* adjust exponent for offset */
+#ifdef INFINITY
+if( eisinf(x) )
+	goto nonorm;
+#endif
+/* round off to nearest or even */
+rndsav = rndprc;
+rndprc = 64;
+emdnorm( xi, 0, 0, exp, 64 );
+rndprc = rndsav;
+nonorm:
+toe64( xi, e );
+}
+
+/* move out internal format to ieee long double */
+static void toe64( a, b )
+unsigned short *a, *b;
+{
+register unsigned short *p, *q;
+unsigned short i;
+
+#ifdef NANS
+if( eiisnan(a) )
+	{
+	enan( b, 64 );
+	return;
+	}
+#endif
+#ifdef IBMPC
+/* Shift Intel denormal significand down 1.  */
+if( a[E] == 0 )
+  eshdn1(a);
+#endif
+p = a;
+#ifdef MIEEE
+q = b;
+#else
+q = b + 4; /* point to output exponent */
+#if 1
+/* NOTE: if data type is 96 bits wide, clear the last word here. */
+*(q+1)= 0;
+#endif
+#endif
+
+/* combine sign and exponent */
+i = *p++;
+#ifdef MIEEE
+if( i )
+	*q++ = *p++ | 0x8000;
+else
+	*q++ = *p++;
+*q++ = 0;
+#else
+if( i )
+	*q-- = *p++ | 0x8000;
+else
+	*q-- = *p++;
+#endif
+/* skip over guard word */
+++p;
+/* move the significand */
+#ifdef MIEEE
+for( i=0; i<4; i++ )
+	*q++ = *p++;
+#else
+#ifdef INFINITY
+if (eiisinf (a))
+        {
+	/* Intel long double infinity.  */
+	*q-- = 0x8000;
+	*q-- = 0;
+	*q-- = 0;
+	*q = 0;
+	return;
+	}
+#endif
+for( i=0; i<4; i++ )
+	*q-- = *p++;
+#endif
+}
+
+
+/*
+; e type to IEEE double precision
+;	double d;
+;	unsigned short x[NE];
+;	etoe53( x, &d );
+*/
+
+#ifdef DEC
+
+void etoe53( x, e )
+unsigned short *x, *e;
+{
+etodec( x, e ); /* see etodec.c */
+}
+
+static void toe53( x, y )
+unsigned short *x, *y;
+{
+todec( x, y );
+}
+
+#else
+
+void etoe53( x, e )
+unsigned short *x, *e;
+{
+unsigned short xi[NI];
+long exp;
+int rndsav;
+
+#ifdef NANS
+if( eisnan(x) )
+	{
+	enan( e, 53 );
+	return;
+	}
+#endif
+emovi( x, xi );
+exp = (long )xi[E] - (EXONE - 0x3ff); /* adjust exponent for offsets */
+#ifdef INFINITY
+if( eisinf(x) )
+	goto nonorm;
+#endif
+/* round off to nearest or even */
+rndsav = rndprc;
+rndprc = 53;
+emdnorm( xi, 0, 0, exp, 64 );
+rndprc = rndsav;
+nonorm:
+toe53( xi, e );
+}
+
+
+static void toe53( x, y )
+unsigned short *x, *y;
+{
+unsigned short i;
+unsigned short *p;
+
+
+#ifdef NANS
+if( eiisnan(x) )
+	{
+	enan( y, 53 );
+	return;
+	}
+#endif
+p = &x[0];
+#ifdef IBMPC
+y += 3;
+#endif
+*y = 0;	/* output high order */
+if( *p++ )
+	*y = 0x8000;	/* output sign bit */
+
+i = *p++;
+if( i >= (unsigned int )2047 )
+	{	/* Saturate at largest number less than infinity. */
+#ifdef INFINITY
+	*y |= 0x7ff0;
+#ifdef IBMPC
+	*(--y) = 0;
+	*(--y) = 0;
+	*(--y) = 0;
+#endif
+#ifdef MIEEE
+	++y;
+	*y++ = 0;
+	*y++ = 0;
+	*y++ = 0;
+#endif
+#else
+	*y |= (unsigned short )0x7fef;
+#ifdef IBMPC
+	*(--y) = 0xffff;
+	*(--y) = 0xffff;
+	*(--y) = 0xffff;
+#endif
+#ifdef MIEEE
+	++y;
+	*y++ = 0xffff;
+	*y++ = 0xffff;
+	*y++ = 0xffff;
+#endif
+#endif
+	return;
+	}
+if( i == 0 )
+	{
+	(void )eshift( x, 4 );
+	}
+else
+	{
+	i <<= 4;
+	(void )eshift( x, 5 );
+	}
+i |= *p++ & (unsigned short )0x0f;	/* *p = xi[M] */
+*y |= (unsigned short )i; /* high order output already has sign bit set */
+#ifdef IBMPC
+*(--y) = *p++;
+*(--y) = *p++;
+*(--y) = *p;
+#endif
+#ifdef MIEEE
+++y;
+*y++ = *p++;
+*y++ = *p++;
+*y++ = *p++;
+#endif
+}
+
+#endif /* not DEC */
+
+
+
+/*
+; e type to IEEE single precision
+;	float d;
+;	unsigned short x[N+2];
+;	xtod( x, &d );
+*/
+void etoe24( x, e )
+unsigned short *x, *e;
+{
+long exp;
+unsigned short xi[NI];
+int rndsav;
+
+#ifdef NANS
+if( eisnan(x) )
+	{
+	enan( e, 24 );
+	return;
+	}
+#endif
+emovi( x, xi );
+exp = (long )xi[E] - (EXONE - 0177); /* adjust exponent for offsets */
+#ifdef INFINITY
+if( eisinf(x) )
+	goto nonorm;
+#endif
+/* round off to nearest or even */
+rndsav = rndprc;
+rndprc = 24;
+emdnorm( xi, 0, 0, exp, 64 );
+rndprc = rndsav;
+nonorm:
+toe24( xi, e );
+}
+
+static void toe24( x, y )
+unsigned short *x, *y;
+{
+unsigned short i;
+unsigned short *p;
+
+#ifdef NANS
+if( eiisnan(x) )
+	{
+	enan( y, 24 );
+	return;
+	}
+#endif
+p = &x[0];
+#ifdef IBMPC
+y += 1;
+#endif
+#ifdef DEC
+y += 1;
+#endif
+*y = 0;	/* output high order */
+if( *p++ )
+	*y = 0x8000;	/* output sign bit */
+
+i = *p++;
+if( i >= 255 )
+	{	/* Saturate at largest number less than infinity. */
+#ifdef INFINITY
+	*y |= (unsigned short )0x7f80;
+#ifdef IBMPC
+	*(--y) = 0;
+#endif
+#ifdef DEC
+	*(--y) = 0;
+#endif
+#ifdef MIEEE
+	++y;
+	*y = 0;
+#endif
+#else
+	*y |= (unsigned short )0x7f7f;
+#ifdef IBMPC
+	*(--y) = 0xffff;
+#endif
+#ifdef DEC
+	*(--y) = 0xffff;
+#endif
+#ifdef MIEEE
+	++y;
+	*y = 0xffff;
+#endif
+#endif
+	return;
+	}
+if( i == 0 )
+	{
+	(void )eshift( x, 7 );
+	}
+else
+	{
+	i <<= 7;
+	(void )eshift( x, 8 );
+	}
+i |= *p++ & (unsigned short )0x7f;	/* *p = xi[M] */
+*y |= i;	/* high order output already has sign bit set */
+#ifdef IBMPC
+*(--y) = *p;
+#endif
+#ifdef DEC
+*(--y) = *p;
+#endif
+#ifdef MIEEE
+++y;
+*y = *p;
+#endif
+}
+
+
+/* Compare two e type numbers.
+ *
+ * unsigned short a[NE], b[NE];
+ * ecmp( a, b );
+ *
+ *  returns +1 if a > b
+ *           0 if a == b
+ *          -1 if a < b
+ *          -2 if either a or b is a NaN.
+ */
+int ecmp( a, b )
+unsigned short *a, *b;
+{
+unsigned short ai[NI], bi[NI];
+register unsigned short *p, *q;
+register int i;
+int msign;
+
+#ifdef NANS
+if (eisnan (a)  || eisnan (b))
+	return( -2 );
+#endif
+emovi( a, ai );
+p = ai;
+emovi( b, bi );
+q = bi;
+
+if( *p != *q )
+	{ /* the signs are different */
+/* -0 equals + 0 */
+	for( i=1; i<NI-1; i++ )
+		{
+		if( ai[i] != 0 )
+			goto nzro;
+		if( bi[i] != 0 )
+			goto nzro;
+		}
+	return(0);
+nzro:
+	if( *p == 0 )
+		return( 1 );
+	else
+		return( -1 );
+	}
+/* both are the same sign */
+if( *p == 0 )
+	msign = 1;
+else
+	msign = -1;
+i = NI-1;
+do
+	{
+	if( *p++ != *q++ )
+		{
+		goto diff;
+		}
+	}
+while( --i > 0 );
+
+return(0);	/* equality */
+
+
+
+diff:
+
+if( *(--p) > *(--q) )
+	return( msign );		/* p is bigger */
+else
+	return( -msign );	/* p is littler */
+}
+
+
+
+
+/* Find nearest integer to x = floor( x + 0.5 )
+ *
+ * unsigned short x[NE], y[NE]
+ * eround( x, y );
+ */
+void eround( x, y )
+unsigned short *x, *y;
+{
+
+eadd( ehalf, x, y );
+efloor( y, y );
+}
+
+
+
+
+/*
+; convert long (32-bit) integer to e type
+;
+;	long l;
+;	unsigned short x[NE];
+;	ltoe( &l, x );
+; note &l is the memory address of l
+*/
+void ltoe( lp, y )
+long *lp;	/* lp is the memory address of a long integer */
+unsigned short *y;	/* y is the address of a short */
+{
+unsigned short yi[NI];
+unsigned long ll;
+int k;
+
+ecleaz( yi );
+if( *lp < 0 )
+	{
+	ll =  (unsigned long )( -(*lp) ); /* make it positive */
+	yi[0] = 0xffff; /* put correct sign in the e type number */
+	}
+else
+	{
+	ll = (unsigned long )( *lp );
+	}
+/* move the long integer to yi significand area */
+if( sizeof(long) == 8 )
+	{
+	yi[M] = (unsigned short) (ll >> (LONGBITS - 16));
+	yi[M + 1] = (unsigned short) (ll >> (LONGBITS - 32));
+	yi[M + 2] = (unsigned short) (ll >> 16);
+	yi[M + 3] = (unsigned short) ll;
+	yi[E] = EXONE + 47; /* exponent if normalize shift count were 0 */
+	}
+else
+	{
+	yi[M] = (unsigned short )(ll >> 16); 
+	yi[M+1] = (unsigned short )ll;
+	yi[E] = EXONE + 15; /* exponent if normalize shift count were 0 */
+	}
+if( (k = enormlz( yi )) > NBITS ) /* normalize the significand */
+	ecleaz( yi );	/* it was zero */
+else
+	yi[E] -= (unsigned short )k; /* subtract shift count from exponent */
+emovo( yi, y );	/* output the answer */
+}
+
+/*
+; convert unsigned long (32-bit) integer to e type
+;
+;	unsigned long l;
+;	unsigned short x[NE];
+;	ltox( &l, x );
+; note &l is the memory address of l
+*/
+void ultoe( lp, y )
+unsigned long *lp; /* lp is the memory address of a long integer */
+unsigned short *y;	/* y is the address of a short */
+{
+unsigned short yi[NI];
+unsigned long ll;
+int k;
+
+ecleaz( yi );
+ll = *lp;
+
+/* move the long integer to ayi significand area */
+if( sizeof(long) == 8 )
+	{
+	yi[M] = (unsigned short) (ll >> (LONGBITS - 16));
+	yi[M + 1] = (unsigned short) (ll >> (LONGBITS - 32));
+	yi[M + 2] = (unsigned short) (ll >> 16);
+	yi[M + 3] = (unsigned short) ll;
+	yi[E] = EXONE + 47; /* exponent if normalize shift count were 0 */
+	}
+else
+	{
+	yi[M] = (unsigned short )(ll >> 16); 
+	yi[M+1] = (unsigned short )ll;
+	yi[E] = EXONE + 15; /* exponent if normalize shift count were 0 */
+	}
+if( (k = enormlz( yi )) > NBITS ) /* normalize the significand */
+	ecleaz( yi );	/* it was zero */
+else
+	yi[E] -= (unsigned short )k; /* subtract shift count from exponent */
+emovo( yi, y );	/* output the answer */
+}
+
+
+/*
+;	Find long integer and fractional parts
+
+;	long i;
+;	unsigned short x[NE], frac[NE];
+;	xifrac( x, &i, frac );
+ 
+  The integer output has the sign of the input.  The fraction is
+  the positive fractional part of abs(x).
+*/
+void eifrac( x, i, frac )
+unsigned short *x;
+long *i;
+unsigned short *frac;
+{
+unsigned short xi[NI];
+int j, k;
+unsigned long ll;
+
+emovi( x, xi );
+k = (int )xi[E] - (EXONE - 1);
+if( k <= 0 )
+	{
+/* if exponent <= 0, integer = 0 and real output is fraction */
+	*i = 0L;
+	emovo( xi, frac );
+	return;
+	}
+if( k > (8 * sizeof(long) - 1) )
+	{
+/*
+;	long integer overflow: output large integer
+;	and correct fraction
+*/
+	j = 8 * sizeof(long) - 1;
+	if( xi[0] )
+		*i = (long) ((unsigned long) 1) << j;
+	else
+		*i = (long) (((unsigned long) (~(0L))) >> 1);
+	(void )eshift( xi, k );
+	}
+if( k > 16 )
+	{
+/*
+  Shift more than 16 bits: shift up k-16 mod 16
+  then shift by 16's.
+*/
+	j = k - ((k >> 4) << 4);
+	eshift (xi, j);
+	ll = xi[M];
+	k -= j;
+	do
+		{
+		eshup6 (xi);
+		ll = (ll << 16) | xi[M];
+		}
+	while ((k -= 16) > 0);
+	*i = ll;
+	if (xi[0])
+		*i = -(*i);
+	}
+else
+	{
+/* shift not more than 16 bits */
+	eshift( xi, k );
+	*i = (long )xi[M] & 0xffff;
+	if( xi[0] )
+		*i = -(*i);
+	}
+xi[0] = 0;
+xi[E] = EXONE - 1;
+xi[M] = 0;
+if( (k = enormlz( xi )) > NBITS )
+	ecleaz( xi );
+else
+	xi[E] -= (unsigned short )k;
+
+emovo( xi, frac );
+}
+
+
+/*
+;	Find unsigned long integer and fractional parts
+
+;	unsigned long i;
+;	unsigned short x[NE], frac[NE];
+;	xifrac( x, &i, frac );
+
+  A negative e type input yields integer output = 0
+  but correct fraction.
+*/
+void euifrac( x, i, frac )
+unsigned short *x;
+unsigned long *i;
+unsigned short *frac;
+{
+unsigned short xi[NI];
+int j, k;
+unsigned long ll;
+
+emovi( x, xi );
+k = (int )xi[E] - (EXONE - 1);
+if( k <= 0 )
+	{
+/* if exponent <= 0, integer = 0 and argument is fraction */
+	*i = 0L;
+	emovo( xi, frac );
+	return;
+	}
+if( k > (8 * sizeof(long)) )
+	{
+/*
+;	long integer overflow: output large integer
+;	and correct fraction
+*/
+	*i = ~(0L);
+	(void )eshift( xi, k );
+	}
+else if( k > 16 )
+	{
+/*
+  Shift more than 16 bits: shift up k-16 mod 16
+  then shift up by 16's.
+*/
+	j = k - ((k >> 4) << 4);
+	eshift (xi, j);
+	ll = xi[M];
+	k -= j;
+	do
+		{
+		eshup6 (xi);
+		ll = (ll << 16) | xi[M];
+		}
+	while ((k -= 16) > 0);
+	*i = ll;
+	}
+else
+	{
+/* shift not more than 16 bits */
+	eshift( xi, k );
+	*i = (long )xi[M] & 0xffff;
+	}
+
+if( xi[0] )  /* A negative value yields unsigned integer 0. */
+	*i = 0L;
+
+xi[0] = 0;
+xi[E] = EXONE - 1;
+xi[M] = 0;
+if( (k = enormlz( xi )) > NBITS )
+	ecleaz( xi );
+else
+	xi[E] -= (unsigned short )k;
+
+emovo( xi, frac );
+}
+
+
+
+/*
+;	Shift significand
+;
+;	Shifts significand area up or down by the number of bits
+;	given by the variable sc.
+*/
+int eshift( x, sc )
+unsigned short *x;
+int sc;
+{
+unsigned short lost;
+unsigned short *p;
+
+if( sc == 0 )
+	return( 0 );
+
+lost = 0;
+p = x + NI-1;
+
+if( sc < 0 )
+	{
+	sc = -sc;
+	while( sc >= 16 )
+		{
+		lost |= *p;	/* remember lost bits */
+		eshdn6(x);
+		sc -= 16;
+		}
+
+	while( sc >= 8 )
+		{
+		lost |= *p & 0xff;
+		eshdn8(x);
+		sc -= 8;
+		}
+
+	while( sc > 0 )
+		{
+		lost |= *p & 1;
+		eshdn1(x);
+		sc -= 1;
+		}
+	}
+else
+	{
+	while( sc >= 16 )
+		{
+		eshup6(x);
+		sc -= 16;
+		}
+
+	while( sc >= 8 )
+		{
+		eshup8(x);
+		sc -= 8;
+		}
+
+	while( sc > 0 )
+		{
+		eshup1(x);
+		sc -= 1;
+		}
+	}
+if( lost )
+	lost = 1;
+return( (int )lost );
+}
+
+
+
+/*
+;	normalize
+;
+; Shift normalizes the significand area pointed to by argument
+; shift count (up = positive) is returned.
+*/
+int enormlz(x)
+unsigned short x[];
+{
+register unsigned short *p;
+int sc;
+
+sc = 0;
+p = &x[M];
+if( *p != 0 )
+	goto normdn;
+++p;
+if( *p & 0x8000 )
+	return( 0 );	/* already normalized */
+while( *p == 0 )
+	{
+	eshup6(x);
+	sc += 16;
+/* With guard word, there are NBITS+16 bits available.
+ * return true if all are zero.
+ */
+	if( sc > NBITS )
+		return( sc );
+	}
+/* see if high byte is zero */
+while( (*p & 0xff00) == 0 )
+	{
+	eshup8(x);
+	sc += 8;
+	}
+/* now shift 1 bit at a time */
+while( (*p  & 0x8000) == 0)
+	{
+	eshup1(x);
+	sc += 1;
+	if( sc > (NBITS+16) )
+		{
+		mtherr( "enormlz", UNDERFLOW );
+		return( sc );
+		}
+	}
+return( sc );
+
+/* Normalize by shifting down out of the high guard word
+   of the significand */
+normdn:
+
+if( *p & 0xff00 )
+	{
+	eshdn8(x);
+	sc -= 8;
+	}
+while( *p != 0 )
+	{
+	eshdn1(x);
+	sc -= 1;
+
+	if( sc < -NBITS )
+		{
+		mtherr( "enormlz", OVERFLOW );
+		return( sc );
+		}
+	}
+return( sc );
+}
+
+
+
+
+/* Convert e type number to decimal format ASCII string.
+ * The constants are for 64 bit precision.
+ */
+
+#define NTEN 12
+#define MAXP 4096
+
+#if NE == 10
+static unsigned short etens[NTEN + 1][NE] =
+{
+  {0x6576, 0x4a92, 0x804a, 0x153f,
+   0xc94c, 0x979a, 0x8a20, 0x5202, 0xc460, 0x7525,},	/* 10**4096 */
+  {0x6a32, 0xce52, 0x329a, 0x28ce,
+   0xa74d, 0x5de4, 0xc53d, 0x3b5d, 0x9e8b, 0x5a92,},	/* 10**2048 */
+  {0x526c, 0x50ce, 0xf18b, 0x3d28,
+   0x650d, 0x0c17, 0x8175, 0x7586, 0xc976, 0x4d48,},
+  {0x9c66, 0x58f8, 0xbc50, 0x5c54,
+   0xcc65, 0x91c6, 0xa60e, 0xa0ae, 0xe319, 0x46a3,},
+  {0x851e, 0xeab7, 0x98fe, 0x901b,
+   0xddbb, 0xde8d, 0x9df9, 0xebfb, 0xaa7e, 0x4351,},
+  {0x0235, 0x0137, 0x36b1, 0x336c,
+   0xc66f, 0x8cdf, 0x80e9, 0x47c9, 0x93ba, 0x41a8,},
+  {0x50f8, 0x25fb, 0xc76b, 0x6b71,
+   0x3cbf, 0xa6d5, 0xffcf, 0x1f49, 0xc278, 0x40d3,},
+  {0x0000, 0x0000, 0x0000, 0x0000,
+   0xf020, 0xb59d, 0x2b70, 0xada8, 0x9dc5, 0x4069,},
+  {0x0000, 0x0000, 0x0000, 0x0000,
+   0x0000, 0x0000, 0x0400, 0xc9bf, 0x8e1b, 0x4034,},
+  {0x0000, 0x0000, 0x0000, 0x0000,
+   0x0000, 0x0000, 0x0000, 0x2000, 0xbebc, 0x4019,},
+  {0x0000, 0x0000, 0x0000, 0x0000,
+   0x0000, 0x0000, 0x0000, 0x0000, 0x9c40, 0x400c,},
+  {0x0000, 0x0000, 0x0000, 0x0000,
+   0x0000, 0x0000, 0x0000, 0x0000, 0xc800, 0x4005,},
+  {0x0000, 0x0000, 0x0000, 0x0000,
+   0x0000, 0x0000, 0x0000, 0x0000, 0xa000, 0x4002,},	/* 10**1 */
+};
+
+static unsigned short emtens[NTEN + 1][NE] =
+{
+  {0x2030, 0xcffc, 0xa1c3, 0x8123,
+   0x2de3, 0x9fde, 0xd2ce, 0x04c8, 0xa6dd, 0x0ad8,},	/* 10**-4096 */
+  {0x8264, 0xd2cb, 0xf2ea, 0x12d4,
+   0x4925, 0x2de4, 0x3436, 0x534f, 0xceae, 0x256b,},	/* 10**-2048 */
+  {0xf53f, 0xf698, 0x6bd3, 0x0158,
+   0x87a6, 0xc0bd, 0xda57, 0x82a5, 0xa2a6, 0x32b5,},
+  {0xe731, 0x04d4, 0xe3f2, 0xd332,
+   0x7132, 0xd21c, 0xdb23, 0xee32, 0x9049, 0x395a,},
+  {0xa23e, 0x5308, 0xfefb, 0x1155,
+   0xfa91, 0x1939, 0x637a, 0x4325, 0xc031, 0x3cac,},
+  {0xe26d, 0xdbde, 0xd05d, 0xb3f6,
+   0xac7c, 0xe4a0, 0x64bc, 0x467c, 0xddd0, 0x3e55,},
+  {0x2a20, 0x6224, 0x47b3, 0x98d7,
+   0x3f23, 0xe9a5, 0xa539, 0xea27, 0xa87f, 0x3f2a,},
+  {0x0b5b, 0x4af2, 0xa581, 0x18ed,
+   0x67de, 0x94ba, 0x4539, 0x1ead, 0xcfb1, 0x3f94,},
+  {0xbf71, 0xa9b3, 0x7989, 0xbe68,
+   0x4c2e, 0xe15b, 0xc44d, 0x94be, 0xe695, 0x3fc9,},
+  {0x3d4d, 0x7c3d, 0x36ba, 0x0d2b,
+   0xfdc2, 0xcefc, 0x8461, 0x7711, 0xabcc, 0x3fe4,},
+  {0xc155, 0xa4a8, 0x404e, 0x6113,
+   0xd3c3, 0x652b, 0xe219, 0x1758, 0xd1b7, 0x3ff1,},
+  {0xd70a, 0x70a3, 0x0a3d, 0xa3d7,
+   0x3d70, 0xd70a, 0x70a3, 0x0a3d, 0xa3d7, 0x3ff8,},
+  {0xcccd, 0xcccc, 0xcccc, 0xcccc,
+   0xcccc, 0xcccc, 0xcccc, 0xcccc, 0xcccc, 0x3ffb,},	/* 10**-1 */
+};
+#else
+static unsigned short etens[NTEN+1][NE] = {
+{0xc94c,0x979a,0x8a20,0x5202,0xc460,0x7525,},/* 10**4096 */
+{0xa74d,0x5de4,0xc53d,0x3b5d,0x9e8b,0x5a92,},/* 10**2048 */
+{0x650d,0x0c17,0x8175,0x7586,0xc976,0x4d48,},
+{0xcc65,0x91c6,0xa60e,0xa0ae,0xe319,0x46a3,},
+{0xddbc,0xde8d,0x9df9,0xebfb,0xaa7e,0x4351,},
+{0xc66f,0x8cdf,0x80e9,0x47c9,0x93ba,0x41a8,},
+{0x3cbf,0xa6d5,0xffcf,0x1f49,0xc278,0x40d3,},
+{0xf020,0xb59d,0x2b70,0xada8,0x9dc5,0x4069,},
+{0x0000,0x0000,0x0400,0xc9bf,0x8e1b,0x4034,},
+{0x0000,0x0000,0x0000,0x2000,0xbebc,0x4019,},
+{0x0000,0x0000,0x0000,0x0000,0x9c40,0x400c,},
+{0x0000,0x0000,0x0000,0x0000,0xc800,0x4005,},
+{0x0000,0x0000,0x0000,0x0000,0xa000,0x4002,}, /* 10**1 */
+};
+
+static unsigned short emtens[NTEN+1][NE] = {
+{0x2de4,0x9fde,0xd2ce,0x04c8,0xa6dd,0x0ad8,}, /* 10**-4096 */
+{0x4925,0x2de4,0x3436,0x534f,0xceae,0x256b,}, /* 10**-2048 */
+{0x87a6,0xc0bd,0xda57,0x82a5,0xa2a6,0x32b5,},
+{0x7133,0xd21c,0xdb23,0xee32,0x9049,0x395a,},
+{0xfa91,0x1939,0x637a,0x4325,0xc031,0x3cac,},
+{0xac7d,0xe4a0,0x64bc,0x467c,0xddd0,0x3e55,},
+{0x3f24,0xe9a5,0xa539,0xea27,0xa87f,0x3f2a,},
+{0x67de,0x94ba,0x4539,0x1ead,0xcfb1,0x3f94,},
+{0x4c2f,0xe15b,0xc44d,0x94be,0xe695,0x3fc9,},
+{0xfdc2,0xcefc,0x8461,0x7711,0xabcc,0x3fe4,},
+{0xd3c3,0x652b,0xe219,0x1758,0xd1b7,0x3ff1,},
+{0x3d71,0xd70a,0x70a3,0x0a3d,0xa3d7,0x3ff8,},
+{0xcccd,0xcccc,0xcccc,0xcccc,0xcccc,0x3ffb,}, /* 10**-1 */
+};
+#endif
+
+void e24toasc( x, string, ndigs )
+unsigned short x[];
+char *string;
+int ndigs;
+{
+unsigned short w[NI];
+
+e24toe( x, w );
+etoasc( w, string, ndigs );
+}
+
+
+void e53toasc( x, string, ndigs )
+unsigned short x[];
+char *string;
+int ndigs;
+{
+unsigned short w[NI];
+
+e53toe( x, w );
+etoasc( w, string, ndigs );
+}
+
+
+void e64toasc( x, string, ndigs )
+unsigned short x[];
+char *string;
+int ndigs;
+{
+unsigned short w[NI];
+
+e64toe( x, w );
+etoasc( w, string, ndigs );
+}
+
+void e113toasc (x, string, ndigs)
+unsigned short x[];
+char *string;
+int ndigs;
+{
+unsigned short w[NI];
+
+e113toe (x, w);
+etoasc (w, string, ndigs);
+}
+
+
+void etoasc( x, string, ndigs )
+unsigned short x[];
+char *string;
+int ndigs;
+{
+long digit;
+unsigned short y[NI], t[NI], u[NI], w[NI];
+unsigned short *p, *r, *ten;
+unsigned short sign;
+int i, j, k, expon, rndsav;
+char *s, *ss;
+unsigned short m;
+
+rndsav = rndprc;
+#ifdef NANS
+if( eisnan(x) )
+	{
+	sprintf( string, " NaN " );
+	goto bxit;
+	}
+#endif
+rndprc = NBITS;		/* set to full precision */
+emov( x, y ); /* retain external format */
+if( y[NE-1] & 0x8000 )
+	{
+	sign = 0xffff;
+	y[NE-1] &= 0x7fff;
+	}
+else
+	{
+	sign = 0;
+	}
+expon = 0;
+ten = &etens[NTEN][0];
+emov( eone, t );
+/* Test for zero exponent */
+if( y[NE-1] == 0 )
+	{
+	for( k=0; k<NE-1; k++ )
+		{
+		if( y[k] != 0 )
+			goto tnzro; /* denormalized number */
+		}
+	goto isone; /* legal all zeros */
+	}
+tnzro:
+
+/* Test for infinity.
+ */
+if( y[NE-1] == 0x7fff )
+	{
+	if( sign )
+		sprintf( string, " -Infinity " );
+	else
+		sprintf( string, " Infinity " );
+	goto bxit;
+	}
+
+/* Test for exponent nonzero but significand denormalized.
+ * This is an error condition.
+ */
+if( (y[NE-1] != 0) && ((y[NE-2] & 0x8000) == 0) )
+	{
+	mtherr( "etoasc", DOMAIN );
+	sprintf( string, "NaN" );
+	goto bxit;
+	}
+
+/* Compare to 1.0 */
+i = ecmp( eone, y );
+if( i == 0 )
+	goto isone;
+
+if( i < 0 )
+	{ /* Number is greater than 1 */
+/* Convert significand to an integer and strip trailing decimal zeros. */
+	emov( y, u );
+	u[NE-1] = EXONE + NBITS - 1;
+
+	p = &etens[NTEN-4][0];
+	m = 16;
+do
+	{
+	ediv( p, u, t );
+	efloor( t, w );
+	for( j=0; j<NE-1; j++ )
+		{
+		if( t[j] != w[j] )
+			goto noint;
+		}
+	emov( t, u );
+	expon += (int )m;
+noint:
+	p += NE;
+	m >>= 1;
+	}
+while( m != 0 );
+
+/* Rescale from integer significand */
+	u[NE-1] += y[NE-1] - (unsigned int )(EXONE + NBITS - 1);
+	emov( u, y );
+/* Find power of 10 */
+	emov( eone, t );
+	m = MAXP;
+	p = &etens[0][0];
+	while( ecmp( ten, u ) <= 0 )
+		{
+		if( ecmp( p, u ) <= 0 )
+			{
+			ediv( p, u, u );
+			emul( p, t, t );
+			expon += (int )m;
+			}
+		m >>= 1;
+		if( m == 0 )
+			break;
+		p += NE;
+		}
+	}
+else
+	{ /* Number is less than 1.0 */
+/* Pad significand with trailing decimal zeros. */
+	if( y[NE-1] == 0 )
+		{
+		while( (y[NE-2] & 0x8000) == 0 )
+			{
+			emul( ten, y, y );
+			expon -= 1;
+			}
+		}
+	else
+		{
+		emovi( y, w );
+		for( i=0; i<NDEC+1; i++ )
+			{
+			if( (w[NI-1] & 0x7) != 0 )
+				break;
+/* multiply by 10 */
+			emovz( w, u );
+			eshdn1( u );
+			eshdn1( u );
+			eaddm( w, u );
+			u[1] += 3;
+			while( u[2] != 0 )
+				{
+				eshdn1(u);
+				u[1] += 1;
+				}
+			if( u[NI-1] != 0 )
+				break;
+			if( eone[NE-1] <= u[1] )
+				break;
+			emovz( u, w );
+			expon -= 1;
+			}
+		emovo( w, y );
+		}
+	k = -MAXP;
+	p = &emtens[0][0];
+	r = &etens[0][0];
+	emov( y, w );
+	emov( eone, t );
+	while( ecmp( eone, w ) > 0 )
+		{
+		if( ecmp( p, w ) >= 0 )
+			{
+			emul( r, w, w );
+			emul( r, t, t );
+			expon += k;
+			}
+		k /= 2;
+		if( k == 0 )
+			break;
+		p += NE;
+		r += NE;
+		}
+	ediv( t, eone, t );
+	}
+isone:
+/* Find the first (leading) digit. */
+emovi( t, w );
+emovz( w, t );
+emovi( y, w );
+emovz( w, y );
+eiremain( t, y );
+digit = equot[NI-1];
+while( (digit == 0) && (ecmp(y,ezero) != 0) )
+	{
+	eshup1( y );
+	emovz( y, u );
+	eshup1( u );
+	eshup1( u );
+	eaddm( u, y );
+	eiremain( t, y );
+	digit = equot[NI-1];
+	expon -= 1;
+	}
+s = string;
+if( sign )
+	*s++ = '-';
+else
+	*s++ = ' ';
+/* Examine number of digits requested by caller. */
+if( ndigs < 0 )
+	ndigs = 0;
+if( ndigs > NDEC )
+	ndigs = NDEC;
+if( digit == 10 )
+	{
+	*s++ = '1';
+	*s++ = '.';
+	if( ndigs > 0 )
+		{
+		*s++ = '0';
+		ndigs -= 1;
+		}
+	expon += 1;
+	}
+else
+	{
+	*s++ = (char )digit + '0';
+	*s++ = '.';
+	}
+/* Generate digits after the decimal point. */
+for( k=0; k<=ndigs; k++ )
+	{
+/* multiply current number by 10, without normalizing */
+	eshup1( y );
+	emovz( y, u );
+	eshup1( u );
+	eshup1( u );
+	eaddm( u, y );
+	eiremain( t, y );
+	*s++ = (char )equot[NI-1] + '0';
+	}
+digit = equot[NI-1];
+--s;
+ss = s;
+/* round off the ASCII string */
+if( digit > 4 )
+	{
+/* Test for critical rounding case in ASCII output. */
+	if( digit == 5 )
+		{
+		emovo( y, t );
+		if( ecmp(t,ezero) != 0 )
+			goto roun;	/* round to nearest */
+		if( (*(s-1) & 1) == 0 )
+			goto doexp;	/* round to even */
+		}
+/* Round up and propagate carry-outs */
+roun:
+	--s;
+	k = *s & 0x7f;
+/* Carry out to most significant digit? */
+	if( k == '.' )
+		{
+		--s;
+		k = *s;
+		k += 1;
+		*s = (char )k;
+/* Most significant digit carries to 10? */
+		if( k > '9' )
+			{
+			expon += 1;
+			*s = '1';
+			}
+		goto doexp;
+		}
+/* Round up and carry out from less significant digits */
+	k += 1;
+	*s = (char )k;
+	if( k > '9' )
+		{
+		*s = '0';
+		goto roun;
+		}
+	}
+doexp:
+/*
+if( expon >= 0 )
+	sprintf( ss, "e+%d", expon );
+else
+	sprintf( ss, "e%d", expon );
+*/
+	sprintf( ss, "E%d", expon );
+bxit:
+rndprc = rndsav;
+}
+
+
+
+
+/*
+;								ASCTOQ
+;		ASCTOQ.MAC		LATEST REV: 11 JAN 84
+;					SLM, 3 JAN 78
+;
+;	Convert ASCII string to quadruple precision floating point
+;
+;		Numeric input is free field decimal number
+;		with max of 15 digits with or without 
+;		decimal point entered as ASCII from teletype.
+;	Entering E after the number followed by a second
+;	number causes the second number to be interpreted
+;	as a power of 10 to be multiplied by the first number
+;	(i.e., "scientific" notation).
+;
+;	Usage:
+;		asctoq( string, q );
+*/
+
+/* ASCII to single */
+void asctoe24( s, y )
+char *s;
+unsigned short *y;
+{
+asctoeg( s, y, 24 );
+}
+
+
+/* ASCII to double */
+void asctoe53( s, y )
+char *s;
+unsigned short *y;
+{
+#ifdef DEC
+asctoeg( s, y, 56 );
+#else
+asctoeg( s, y, 53 );
+#endif
+}
+
+
+/* ASCII to long double */
+void asctoe64( s, y )
+char *s;
+unsigned short *y;
+{
+asctoeg( s, y, 64 );
+}
+
+/* ASCII to 128-bit long double */
+void asctoe113 (s, y)
+char *s;
+unsigned short *y;
+{
+asctoeg( s, y, 113 );
+}
+
+/* ASCII to super double */
+void asctoe( s, y )
+char *s;
+unsigned short *y;
+{
+asctoeg( s, y, NBITS );
+}
+
+/* Space to make a copy of the input string: */
+static char lstr[82] = {0};
+
+void asctoeg( ss, y, oprec )
+char *ss;
+unsigned short *y;
+int oprec;
+{
+unsigned short yy[NI], xt[NI], tt[NI];
+int esign, decflg, sgnflg, nexp, exp, prec, lost;
+int k, trail, c, rndsav;
+long lexp;
+unsigned short nsign, *p;
+char *sp, *s;
+
+/* Copy the input string. */
+s = ss;
+while( *s == ' ' ) /* skip leading spaces */
+	++s;
+sp = lstr;
+for( k=0; k<79; k++ )
+	{
+	if( (*sp++ = *s++) == '\0' )
+		break;
+	}
+*sp = '\0';
+s = lstr;
+
+rndsav = rndprc;
+rndprc = NBITS; /* Set to full precision */
+lost = 0;
+nsign = 0;
+decflg = 0;
+sgnflg = 0;
+nexp = 0;
+exp = 0;
+prec = 0;
+ecleaz( yy );
+trail = 0;
+
+nxtcom:
+k = *s - '0';
+if( (k >= 0) && (k <= 9) )
+	{
+/* Ignore leading zeros */
+	if( (prec == 0) && (decflg == 0) && (k == 0) )
+		goto donchr;
+/* Identify and strip trailing zeros after the decimal point. */
+	if( (trail == 0) && (decflg != 0) )
+		{
+		sp = s;
+		while( (*sp >= '0') && (*sp <= '9') )
+			++sp;
+/* Check for syntax error */
+		c = *sp & 0x7f;
+		if( (c != 'e') && (c != 'E') && (c != '\0')
+			&& (c != '\n') && (c != '\r') && (c != ' ')
+			&& (c != ',') )
+			goto error;
+		--sp;
+		while( *sp == '0' )
+			*sp-- = 'z';
+		trail = 1;
+		if( *s == 'z' )
+			goto donchr;
+		}
+/* If enough digits were given to more than fill up the yy register,
+ * continuing until overflow into the high guard word yy[2]
+ * guarantees that there will be a roundoff bit at the top
+ * of the low guard word after normalization.
+ */
+	if( yy[2] == 0 )
+		{
+		if( decflg )
+			nexp += 1; /* count digits after decimal point */
+		eshup1( yy );	/* multiply current number by 10 */
+		emovz( yy, xt );
+		eshup1( xt );
+		eshup1( xt );
+		eaddm( xt, yy );
+		ecleaz( xt );
+		xt[NI-2] = (unsigned short )k;
+		eaddm( xt, yy );
+		}
+	else
+		{
+		/* Mark any lost non-zero digit.  */
+		lost |= k;
+		/* Count lost digits before the decimal point.  */
+		if (decflg == 0)
+		        nexp -= 1;
+		}
+	prec += 1;
+	goto donchr;
+	}
+
+switch( *s )
+	{
+	case 'z':
+		break;
+	case 'E':
+	case 'e':
+		goto expnt;
+	case '.':	/* decimal point */
+		if( decflg )
+			goto error;
+		++decflg;
+		break;
+	case '-':
+		nsign = 0xffff;
+		if( sgnflg )
+			goto error;
+		++sgnflg;
+		break;
+	case '+':
+		if( sgnflg )
+			goto error;
+		++sgnflg;
+		break;
+	case ',':
+	case ' ':
+	case '\0':
+	case '\n':
+	case '\r':
+		goto daldone;
+	case 'i':
+	case 'I':
+		goto infinite;
+	default:
+	error:
+#ifdef NANS
+		enan( yy, NI*16 );
+#else
+		mtherr( "asctoe", DOMAIN );
+		ecleaz(yy);
+#endif
+		goto aexit;
+	}
+donchr:
+++s;
+goto nxtcom;
+
+/* Exponent interpretation */
+expnt:
+
+esign = 1;
+exp = 0;
+++s;
+/* check for + or - */
+if( *s == '-' )
+	{
+	esign = -1;
+	++s;
+	}
+if( *s == '+' )
+	++s;
+while( (*s >= '0') && (*s <= '9') )
+	{
+	exp *= 10;
+	exp += *s++ - '0';
+	if (exp > 4977)
+		{
+		if (esign < 0)
+			goto zero;
+		else
+			goto infinite;
+		}
+	}
+if( esign < 0 )
+	exp = -exp;
+if( exp > 4932 )
+	{
+infinite:
+	ecleaz(yy);
+	yy[E] = 0x7fff;  /* infinity */
+	goto aexit;
+	}
+if( exp < -4977 )
+	{
+zero:
+	ecleaz(yy);
+	goto aexit;
+	}
+
+daldone:
+nexp = exp - nexp;
+/* Pad trailing zeros to minimize power of 10, per IEEE spec. */
+while( (nexp > 0) && (yy[2] == 0) )
+	{
+	emovz( yy, xt );
+	eshup1( xt );
+	eshup1( xt );
+	eaddm( yy, xt );
+	eshup1( xt );
+	if( xt[2] != 0 )
+		break;
+	nexp -= 1;
+	emovz( xt, yy );
+	}
+if( (k = enormlz(yy)) > NBITS )
+	{
+	ecleaz(yy);
+	goto aexit;
+	}
+lexp = (EXONE - 1 + NBITS) - k;
+emdnorm( yy, lost, 0, lexp, 64 );
+/* convert to external format */
+
+
+/* Multiply by 10**nexp.  If precision is 64 bits,
+ * the maximum relative error incurred in forming 10**n
+ * for 0 <= n <= 324 is 8.2e-20, at 10**180.
+ * For 0 <= n <= 999, the peak relative error is 1.4e-19 at 10**947.
+ * For 0 >= n >= -999, it is -1.55e-19 at 10**-435.
+ */
+lexp = yy[E];
+if( nexp == 0 )
+	{
+	k = 0;
+	goto expdon;
+	}
+esign = 1;
+if( nexp < 0 )
+	{
+	nexp = -nexp;
+	esign = -1;
+	if( nexp > 4096 )
+		{ /* Punt.  Can't handle this without 2 divides. */
+		emovi( etens[0], tt );
+		lexp -= tt[E];
+		k = edivm( tt, yy );
+		lexp += EXONE;
+		nexp -= 4096;
+		}
+	}
+p = &etens[NTEN][0];
+emov( eone, xt );
+exp = 1;
+do
+	{
+	if( exp & nexp )
+		emul( p, xt, xt );
+	p -= NE;
+	exp = exp + exp;
+	}
+while( exp <= MAXP );
+
+emovi( xt, tt );
+if( esign < 0 )
+	{
+	lexp -= tt[E];
+	k = edivm( tt, yy );
+	lexp += EXONE;
+	}
+else
+	{
+	lexp += tt[E];
+	k = emulm( tt, yy );
+	lexp -= EXONE - 1;
+	}
+
+expdon:
+
+/* Round and convert directly to the destination type */
+if( oprec == 53 )
+	lexp -= EXONE - 0x3ff;
+else if( oprec == 24 )
+	lexp -= EXONE - 0177;
+#ifdef DEC
+else if( oprec == 56 )
+	lexp -= EXONE - 0201;
+#endif
+rndprc = oprec;
+emdnorm( yy, k, 0, lexp, 64 );
+
+aexit:
+
+rndprc = rndsav;
+yy[0] = nsign;
+switch( oprec )
+	{
+#ifdef DEC
+	case 56:
+		todec( yy, y ); /* see etodec.c */
+		break;
+#endif
+	case 53:
+		toe53( yy, y );
+		break;
+	case 24:
+		toe24( yy, y );
+		break;
+	case 64:
+		toe64( yy, y );
+		break;
+	case 113:
+		toe113( yy, y );
+		break;
+	case NBITS:
+		emovo( yy, y );
+		break;
+	}
+}
+
+
+ 
+/* y = largest integer not greater than x
+ * (truncated toward minus infinity)
+ *
+ * unsigned short x[NE], y[NE]
+ *
+ * efloor( x, y );
+ */
+static unsigned short bmask[] = {
+0xffff,
+0xfffe,
+0xfffc,
+0xfff8,
+0xfff0,
+0xffe0,
+0xffc0,
+0xff80,
+0xff00,
+0xfe00,
+0xfc00,
+0xf800,
+0xf000,
+0xe000,
+0xc000,
+0x8000,
+0x0000,
+};
+
+void efloor( x, y )
+unsigned short x[], y[];
+{
+register unsigned short *p;
+int e, expon, i;
+unsigned short f[NE];
+
+emov( x, f ); /* leave in external format */
+expon = (int )f[NE-1];
+e = (expon & 0x7fff) - (EXONE - 1);
+if( e <= 0 )
+	{
+	eclear(y);
+	goto isitneg;
+	}
+/* number of bits to clear out */
+e = NBITS - e;
+emov( f, y );
+if( e <= 0 )
+	return;
+
+p = &y[0];
+while( e >= 16 )
+	{
+	*p++ = 0;
+	e -= 16;
+	}
+/* clear the remaining bits */
+*p &= bmask[e];
+/* truncate negatives toward minus infinity */
+isitneg:
+
+if( (unsigned short )expon & (unsigned short )0x8000 )
+	{
+	for( i=0; i<NE-1; i++ )
+		{
+		if( f[i] != y[i] )
+			{
+			esub( eone, y, y );
+			break;
+			}
+		}
+	}
+}
+
+
+/* unsigned short x[], s[];
+ * long *exp;
+ *
+ * efrexp( x, exp, s );
+ *
+ * Returns s and exp such that  s * 2**exp = x and .5 <= s < 1.
+ * For example, 1.1 = 0.55 * 2**1
+ * Handles denormalized numbers properly using long integer exp.
+ */
+void efrexp( x, exp, s )
+unsigned short x[];
+long *exp;
+unsigned short s[];
+{
+unsigned short xi[NI];
+long li;
+
+emovi( x, xi );
+li = (long )((short )xi[1]);
+
+if( li == 0 )
+	{
+	li -= enormlz( xi );
+	}
+xi[1] = 0x3ffe;
+emovo( xi, s );
+*exp = li - 0x3ffe;
+}
+
+
+
+/* unsigned short x[], y[];
+ * long pwr2;
+ *
+ * eldexp( x, pwr2, y );
+ *
+ * Returns y = x * 2**pwr2.
+ */
+void eldexp( x, pwr2, y )
+unsigned short x[];
+long pwr2;
+unsigned short y[];
+{
+unsigned short xi[NI];
+long li;
+int i;
+
+emovi( x, xi );
+li = xi[1];
+li += pwr2;
+i = 0;
+emdnorm( xi, i, i, li, 64 );
+emovo( xi, y );
+}
+
+
+/* c = remainder after dividing b by a
+ * Least significant integer quotient bits left in equot[].
+ */
+void eremain( a, b, c )
+unsigned short a[], b[], c[];
+{
+unsigned short den[NI], num[NI];
+
+#ifdef NANS
+if( eisinf(b) || (ecmp(a,ezero) == 0) || eisnan(a) || eisnan(b))
+	{
+	enan( c, NBITS );
+	return;
+	}
+#endif
+if( ecmp(a,ezero) == 0 )
+	{
+	mtherr( "eremain", SING );
+	eclear( c );
+	return;
+	}
+emovi( a, den );
+emovi( b, num );
+eiremain( den, num );
+/* Sign of remainder = sign of quotient */
+if( a[0] == b[0] )
+	num[0] = 0;
+else
+	num[0] = 0xffff;
+emovo( num, c );
+}
+
+
+void eiremain( den, num )
+unsigned short den[], num[];
+{
+long ld, ln;
+unsigned short j;
+
+ld = den[E];
+ld -= enormlz( den );
+ln = num[E];
+ln -= enormlz( num );
+ecleaz( equot );
+while( ln >= ld )
+	{
+	if( ecmpm(den,num) <= 0 )
+		{
+		esubm(den, num);
+		j = 1;
+		}
+	else
+		{
+		j = 0;
+		}
+	eshup1(equot);
+	equot[NI-1] |= j;
+	eshup1(num);
+	ln -= 1;
+	}
+emdnorm( num, 0, 0, ln, 0 );
+}
+
+/* NaN bit patterns
+ */
+#ifdef MIEEE
+unsigned short nan113[8] = {
+  0x7fff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff};
+unsigned short nan64[6] = {0x7fff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff};
+unsigned short nan53[4] = {0x7fff, 0xffff, 0xffff, 0xffff};
+unsigned short nan24[2] = {0x7fff, 0xffff};
+#endif
+
+#ifdef IBMPC
+unsigned short nan113[8] = {0, 0, 0, 0, 0, 0, 0xc000, 0xffff};
+unsigned short nan64[6] = {0, 0, 0, 0xc000, 0xffff, 0};
+unsigned short nan53[4] = {0, 0, 0, 0xfff8};
+unsigned short nan24[2] = {0, 0xffc0};
+#endif
+
+
+void enan (nan, size)
+unsigned short *nan;
+int size;
+{
+int i, n;
+unsigned short *p;
+
+switch( size )
+	{
+#ifndef DEC
+	case 113:
+	n = 8;
+	p = nan113;
+	break;
+
+	case 64:
+	n = 6;
+	p = nan64;
+	break;
+
+	case 53:
+	n = 4;
+	p = nan53;
+	break;
+
+	case 24:
+	n = 2;
+	p = nan24;
+	break;
+
+	case NBITS:
+	for( i=0; i<NE-2; i++ )
+		*nan++ = 0;
+	*nan++ = 0xc000;
+	*nan++ = 0x7fff;
+	return;
+
+	case NI*16:
+	*nan++ = 0;
+	*nan++ = 0x7fff;
+	*nan++ = 0;
+	*nan++ = 0xc000;
+	for( i=4; i<NI; i++ )
+		*nan++ = 0;
+	return;
+#endif
+	default:
+	mtherr( "enan", DOMAIN );
+	return;
+	}
+for (i=0; i < n; i++)
+	*nan++ = *p++;
+}
+
+
+
+/* Longhand square root. */
+
+static int esqinited = 0;
+static unsigned short sqrndbit[NI];
+
+void esqrt( x, y )
+short *x, *y;
+{
+unsigned short temp[NI], num[NI], sq[NI], xx[NI];
+int i, j, k, n, nlups;
+long m, exp;
+
+if( esqinited == 0 )
+	{
+	ecleaz( sqrndbit );
+	sqrndbit[NI-2] = 1;
+	esqinited = 1;
+	}
+/* Check for arg <= 0 */
+i = ecmp( x, ezero );
+if( i <= 0 )
+	{
+#ifdef NANS
+	if (i == -2)
+		{
+		enan (y, NBITS);
+		return;
+		}
+#endif
+	eclear(y);
+	if( i < 0 )
+		mtherr( "esqrt", DOMAIN );
+	return;
+	}
+
+#ifdef INFINITY
+if( eisinf(x) )
+	{
+	eclear(y);
+	einfin(y);
+	return;
+	}
+#endif
+/* Bring in the arg and renormalize if it is denormal. */
+emovi( x, xx );
+m = (long )xx[1]; /* local long word exponent */
+if( m == 0 )
+	m -= enormlz( xx );
+
+/* Divide exponent by 2 */
+m -= 0x3ffe;
+exp = (unsigned short )( (m / 2) + 0x3ffe );
+
+/* Adjust if exponent odd */
+if( (m & 1) != 0 )
+	{
+	if( m > 0 )
+		exp += 1;
+	eshdn1( xx );
+	}
+
+ecleaz( sq );
+ecleaz( num );
+n = 8; /* get 8 bits of result per inner loop */
+nlups = rndprc;
+j = 0;
+
+while( nlups > 0 )
+	{
+/* bring in next word of arg */
+	if( j < NE )
+		num[NI-1] = xx[j+3];
+/* Do additional bit on last outer loop, for roundoff. */
+	if( nlups <= 8 )
+		n = nlups + 1;
+	for( i=0; i<n; i++ )
+		{
+/* Next 2 bits of arg */
+		eshup1( num );
+		eshup1( num );
+/* Shift up answer */
+		eshup1( sq );
+/* Make trial divisor */
+		for( k=0; k<NI; k++ )
+			temp[k] = sq[k];
+		eshup1( temp );
+		eaddm( sqrndbit, temp );
+/* Subtract and insert answer bit if it goes in */
+		if( ecmpm( temp, num ) <= 0 )
+			{
+			esubm( temp, num );
+			sq[NI-2] |= 1;
+			}
+		}
+	nlups -= n;
+	j += 1;
+	}
+
+/* Adjust for extra, roundoff loop done. */
+exp += (NBITS - 1) - rndprc;
+
+/* Sticky bit = 1 if the remainder is nonzero. */
+k = 0;
+for( i=3; i<NI; i++ )
+	k |= (int )num[i];
+
+/* Renormalize and round off. */
+emdnorm( sq, k, 0, exp, 64 );
+emovo( sq, y );
+}

test/math/ieetst.c

@@ -0,0 +1,850 @@
+/* Floating point to ASCII input and output string test program.
+ *
+ * Numbers in the native machine data structure are converted
+ * to e type, then to and from decimal ASCII strings.  Native
+ * printf() and scanf() functions are also used to produce
+ * and read strings.  The resulting e type binary values
+ * are compared, with diagnostic printouts of any discrepancies.
+ *
+ * Steve Moshier, 16 Dec 88
+ * last revision: 16 May 92
+ */
+
+#include "ehead.h"
+#include "mconf.h"
+
+/* Include tests of 80-bit long double precision: */
+#define LDOUBLE 0
+/* Abort subtest after getting this many errors: */
+#define MAXERR 5
+/* Number of random arguments to try (set as large as you have
+ * patience for): */
+#define NRAND 100
+/* Perform internal consistency test: */
+#define CHKINTERNAL 0
+
+static unsigned short fullp[NE], rounded[NE];
+float prec24, sprec24, ssprec24;
+double prec53, sprec53, ssprec53;
+#if LDOUBLE
+long double prec64, sprec64, ssprec64;
+#endif
+
+static unsigned short rprint[NE], rscan[NE];
+static unsigned short q1[NE], q2[NE], q5[NE];
+static unsigned short e1[NE], e2[NE], e3[NE];
+static double d1, d2;
+static int errprint = 0;
+static int errscan = 0;
+static int identerr = 0;
+static int errtot = 0;
+static int count = 0;
+static char str0[80], str1[80], str2[80], str3[80];
+static unsigned short eten[NE], maxm[NE];
+
+int m, n, k2, mprec, SPREC;
+
+char *Ten = "10.0";
+char tformat[10];
+char *format24 = "%.8e";
+#ifdef DEC
+char *format53 = "%.17e";
+#else
+char *format53 = "%.16e";
+#endif
+char *fformat24 = "%e";
+char *fformat53 = "%le";
+char *pct = "%";
+char *quo = "\042";
+#if LDOUBLE
+char *format64 = "%.20Le";
+char *fformat64 = "%Le";
+#endif
+char *format;
+char *fformat;
+char *toomany = "Too many errors; aborting this test.\n";
+
+static int mnrflag;
+static int etrflag;
+void chkit(), printerr(), mnrand(), etrand(), shownoncrit();
+void chkid(), pvec();
+
+main()
+{
+int i, iprec;
+
+printf( "Steve Moshier's printf/scanf tester, version 0.2.\n\n" );
+#ifdef DEC
+ /* DEC PDP-11/VAX single precision not yet implemented */
+for( iprec = 1; iprec<2; iprec++ )
+#else
+for( iprec = 0; iprec<3; iprec++ )
+#endif
+	{
+	errscan = 0;
+	identerr = 0;
+	errprint = 0;
+	eclear( rprint );
+	eclear( rscan );
+
+switch( iprec )
+	{
+	case 0:
+		SPREC = 8; /* # digits after the decimal point */
+		mprec = 24; /* # bits in the significand */
+		m = 9; /* max # decimal digits for correct rounding */
+		n = 13; /* max power of ten for correct rounding */
+		k2 = -125; /* underflow beyond 2^-k2 */
+		format = format24; /* printf format string */
+		fformat = fformat24; /* scanf format string */
+		mnrflag = 1; /* sets interval for random numbers */
+		etrflag = 1;
+		printf( "Testing FLOAT precision.\n" );
+		break;
+
+	case 1:
+#ifdef DEC
+		SPREC = 17;
+		mprec = 56;
+		m = 17;
+		n = 27;
+		k2 = -125;
+		format = format53;
+		fformat = fformat53;
+		mnrflag = 2;
+		etrflag = 1;
+		printf( "Testing DEC DOUBLE precision.\n" );
+		break;
+#else
+		SPREC = 16;
+		mprec = 53;
+		m = 17;
+		n = 27;
+		k2 = -1021;
+		format = format53;
+		fformat = fformat53;
+		mnrflag = 2;
+		etrflag = 2;
+		printf( "Testing DOUBLE precision.\n" );
+		break;
+#endif
+	case 2:
+#if LDOUBLE
+		SPREC = 20;
+		mprec = 64;
+		m = 20;
+		n = 34;
+		k2 = -16382;
+		format = format64;
+		fformat = fformat64;
+		mnrflag = 3;
+		etrflag = 3;
+		printf( "Testing LONG DOUBLE precision.\n" );
+		break;
+#else
+		goto nodenorm;
+#endif
+	}
+
+	asctoe( Ten, eten );
+/* 10^m - 1 */
+	d2 = m;
+	e53toe( &d2, e1 );
+	epow( eten, e1, maxm );
+	esub( eone, maxm, maxm );
+
+/* test 1 */
+	printf( "1. Checking 10^n - 1 for n = %d to %d.\n", -m, m );
+	emov( eone, q5 );
+	for( count=0; count<=m; count++ )
+		{
+		esub( eone, q5, fullp );
+		chkit( 1 );
+		ediv( q5, eone, q2 );
+		esub( eone, q2, fullp );
+		chkit( 1 );
+		emul( eten, q5, q5 );
+		if( errtot >= MAXERR )
+			{
+			printf( "%s", toomany );
+			goto end1;
+			}
+		}
+end1:
+	printerr();
+
+
+/* test 2 */
+	printf( "2. Checking powers of 10 from 10^-%d to 10^%d.\n", n, n );
+	emov( eone, q5 );
+	for( count=0; count<=n; count++ )
+		{
+		emov( q5, fullp );
+		chkit( 2 );
+		ediv( q5, eone, fullp );
+		chkit( 2 );
+		emul( eten, q5, q5 );
+		if( errtot >= MAXERR )
+			{
+			printf( "%s", toomany );
+			goto end2;
+			}
+		}
+end2:
+	printerr();
+
+/* test 3 */
+	printf( "3. Checking (10^%d-1)*10^n from n = -%d to %d.\n", m, n, n );
+	emov( eone, q5 );
+	for( count= -n; count<=n; count++ )
+		{
+		emul( maxm, q5, fullp );
+		chkit( 3 );
+		emov( q5, fullp );
+		ediv( fullp, eone, fullp );
+		emul( maxm, fullp, fullp );
+		chkit( 3 );
+		emul( eten, q5, q5 );
+		if( errtot >= MAXERR )
+			{
+			printf( "%s", toomany );
+			goto end3;
+			}
+		}
+end3:
+	printerr();
+
+
+
+/* test 4 */
+	printf( "4. Checking powers of 2 from 2^-24 to 2^+56.\n" );
+	d1 = -24.0;
+	e53toe( &d1, q1 );
+	epow( etwo, q1, q5 );
+
+	for( count = -24; count <= 56; count++ )
+		{
+		emov( q5, fullp );
+		chkit( 4 );
+		emul( etwo, q5, q5 );
+		if( errtot >= MAXERR )
+			{
+			printf( "%s", toomany );
+			goto end4;
+			}
+		}
+end4:
+	printerr();
+
+
+/* test 5 */
+	printf( "5. Checking 2^n - 1 for n = 0 to %d.\n", mprec );
+	emov( eone, q5 );
+	for( count=0; count<=mprec; count++ )
+		{
+		esub( eone, q5, fullp );
+		chkit( 5 );
+		emul( etwo, q5, q5 );
+		if( errtot >= MAXERR )
+			{
+			printf( "%s", toomany );
+			goto end5;
+			}
+		}
+end5:
+	printerr();
+
+/* test 6 */
+	printf( "6. Checking 2^n + 1 for n = 0 to %d.\n", mprec );
+	emov( eone, q5 );
+	for( count=0; count<=mprec; count++ )
+		{
+		eadd( eone, q5, fullp );
+		chkit( 6 );
+		emul( etwo, q5, q5 );
+		if( errtot >= MAXERR )
+			{
+			printf( "%s", toomany );
+			goto end6;
+			}
+		}
+end6:
+	printerr();
+
+/* test 7 */
+	printf(
+	 "7. Checking %d values M * 10^N with random integer M and N,\n",
+	 NRAND );
+	printf("  1 <= M <= 10^%d - 1  and  -%d <= N <= +%d.\n", m, n, n );
+	for( i=0; i<NRAND; i++ )
+		{
+		mnrand( fullp );
+		chkit( 7 );
+		if( errtot >= MAXERR )
+			{
+			printf( "%s", toomany );
+			goto end7;
+			}
+		}
+end7:
+	printerr();
+
+/* test 8 */
+	printf("8. Checking critical rounding cases.\n" );
+	for( i=0; i<20; i++ )
+		{
+		mnrand( fullp );
+		eabs( fullp );
+		if( ecmp( fullp, eone ) < 0 )
+			ediv( fullp, eone, fullp );
+		efloor( fullp, fullp );
+		eadd( ehalf, fullp, fullp );
+		chkit( 8 );
+		if( errtot >= MAXERR )
+			{
+			printf( "%s", toomany );
+			goto end8;
+			}
+		}
+end8:
+	printerr();
+
+
+
+/* test 9 */
+	printf("9. Testing on %d random non-denormal values.\n", NRAND );
+	for( i=0; i<NRAND; i++ )
+		{
+		etrand( fullp );
+		chkit( 9 );
+		}
+	printerr();
+	shownoncrit();
+
+/* test 10 */
+	printf(
+	"Do you want to check denormal numbers in this precision ? (y/n) " );
+	gets( str0 );
+	if( str0[0] != 'y' )
+		goto nodenorm;
+
+	printf( "10. Checking denormal numbers.\n" );
+
+/* Form 2^-starting power */
+	d1 = k2;
+	e53toe( &d1, q1 );
+	epow( etwo, q1, e1 );
+
+/* Find 2^-mprec less than starting power */
+	d1 = -mprec + 4;
+	e53toe( &d1, q1 );
+	epow( etwo, q1, e3 );
+	emul( e1, e3, e3 );
+	emov( e3, e2 );
+	ediv( etwo, e2, e2 );
+
+	while( ecmp(e1,e2) != 0 )
+		{
+		eadd( e1, e2, fullp );
+		switch( mprec )
+			{
+#if LDOUBLE
+			case 64:
+			etoe64( e1, &sprec64 );
+			e64toe( &sprec64, q1 );
+			etoe64( fullp, &prec64 );
+			e64toe( &prec64, q2 );
+			break;
+#endif
+#ifdef DEC
+			case 56:
+#endif
+			case 53:
+			etoe53( e1, &sprec53 );
+			e53toe( &sprec53, q1 );
+			etoe53( fullp, &prec53 );
+			e53toe( &prec53, q2 );
+			break;
+
+			case 24:
+			etoe24( e1, &sprec24 );
+			e24toe( &sprec24, q1 );
+			etoe24( fullp, &prec24 );
+			e24toe( &prec24, q2 );
+			break;
+			}
+		if( ecmp( q2, ezero ) == 0 )
+			goto maxden;
+		chkit(10);
+		if( ecmp(q1,q2) == 0 )
+			{
+			ediv( etwo, e1, e1 );
+			emov( e3, e2 );
+			}
+		if( errtot >= MAXERR )
+			{
+			printf( "%s", toomany );
+			goto maxden;
+			}
+		ediv( etwo, e2, e2 );
+		}
+maxden:
+	printerr();
+nodenorm:
+	printf( "\n" );
+	} /* loop on precision */
+printf( "End of test.\n" );
+}
+
+#if CHKINTERNAL
+long double xprec64;
+double xprec53;
+float xprec24;
+
+/* Check binary -> printf -> scanf -> binary identity
+ * of internal routines
+ */
+void chkinternal( ref, tst, string )
+unsigned short ref[], tst[];
+char *string;
+{
+
+if( ecmp(ref,tst) != 0 )
+	{
+	printf( "internal identity compare error!\n" );
+	chkid( ref, tst, string );
+	}
+}
+#endif
+
+
+/* Check binary -> printf -> scanf -> binary identity
+ */
+void chkid( print, scan, string )
+unsigned short print[], scan[];
+char *string;
+{
+/* Test printf-scanf identity */
+if( ecmp( print, scan ) != 0 )
+	{
+	pvec( print, NE );
+	printf( " ->printf-> %s ->scanf->\n", string );
+	pvec( scan, NE );
+	printf( " is not an identity.\n" );
+	++identerr;
+	}
+}
+
+
+/* Check scanf result
+ */
+void chkscan( ref, tst, string )
+unsigned short ref[], tst[];
+char *string;
+{
+/* Test scanf()  */
+if( ecmp( ref, tst ) != 0 )
+	{
+	printf( "scanf(%s) -> ", string );
+	pvec( tst, NE );
+	printf( "\n should be    " );
+	pvec( ref, NE );
+	printf( ".\n" );
+	++errscan;
+	++errtot;
+	}
+}
+
+
+/* Test printf() result
+ */
+void chkprint( ref, tst, string ) 
+unsigned short ref[], tst[];
+char *string;
+{
+if( ecmp(ref, tst) != 0 )
+	{
+	printf( "printf( ");
+	pvec( ref, NE );
+	printf( ") -> %s\n", string );
+	printf( "      = " );
+	pvec( tst, NE );
+	printf( ".\n" );
+	++errprint;
+	++errtot;
+	}
+}
+
+
+/* Print array of n 16-bit shorts
+ */
+void pvec( x, n )
+unsigned short x[];
+int n;
+{
+int i;
+
+for( i=0; i<n; i++ )
+	{
+	printf( "%04x ", x[i] );
+	}
+}
+
+/* Measure worst case printf rounding error
+ */
+void cmpprint( ref, tst )
+unsigned short ref[], tst[];
+{
+unsigned short e[NE];
+
+if( ecmp( ref, ezero ) != 0 )
+	{
+	esub( ref, tst, e );
+	ediv( ref, e, e );
+	eabs( e );
+	if( ecmp( e, rprint ) > 0 )
+		emov( e, rprint );
+	}
+}
+
+/* Measure worst case scanf rounding error
+ */
+void cmpscan( ref, tst )
+unsigned short ref[], tst[];
+{
+unsigned short er[NE];
+
+if( ecmp( ref, ezero ) != 0 )
+	{
+	esub( ref, tst, er );
+	ediv( ref, er, er );
+	eabs( er );
+	if( ecmp( er, rscan ) > 0 )
+		emov( er, rscan );
+	if( ecmp( er, ehalf ) > 0 )
+		{
+		etoasc( tst, str1, 21 );
+		printf( "Bad error: scanf(%s) = %s !\n", str0, str1 );
+		}
+	}
+}
+
+/* Check rounded-down decimal string output of printf
+ */
+void cmptrunc( ref, tst )
+unsigned short ref[], tst[];
+{
+if( ecmp( ref, tst ) != 0 )
+	{
+	printf( "printf(%s%s%s, %s) -> %s\n", quo, tformat, quo, str1, str2 );
+	printf( "should be      %s .\n", str3 );
+	errprint += 1;
+	}
+}
+
+
+void shownoncrit()
+{
+
+etoasc( rprint, str0, 3 );
+printf( "Maximum relative printf error found = %s .\n", str0 );
+etoasc( rscan, str0, 3 );
+printf( "Maximum relative scanf error found = %s .\n", str0 );
+}
+
+
+
+/* Produce arguments and call comparison subroutines.
+ */
+void chkit( testno )
+int testno;
+{
+unsigned short t[NE], u[NE], v[NE];
+int j;
+
+switch( mprec )
+	{
+#if LDOUBLE
+	case 64:
+		etoe64( fullp, &prec64 );
+		e64toe( &prec64, rounded );
+#if CHKINTERNAL
+		e64toasc( &prec64, str1, SPREC );
+		asctoe64( str1, &xprec64 );
+		e64toe( &xprec64, t );
+		chkinternal( rounded, t, str1 );
+#endif
+/* check printf and scanf */
+		sprintf( str2, format, prec64 );
+		sscanf( str2, fformat, &sprec64 );
+		e64toe( &sprec64, u );
+		chkid( rounded, u, str2 );
+		asctoe64( str2, &ssprec64 );
+		e64toe( &ssprec64, v );
+		chkscan( v, u, str2 );
+		chkprint( rounded, v, str2 );
+		if( testno < 8 )
+			break;
+/* rounding error measurement */
+		etoasc( fullp, str0, 24 );
+		etoe64( fullp, &ssprec64 );
+		e64toe( &ssprec64, u );
+		sprintf( str2, format, ssprec64 );
+		asctoe( str2, t );
+		cmpprint( u, t );
+		sscanf( str0, fformat, &sprec64 );
+		e64toe( &sprec64, t );
+		cmpscan( fullp, t );
+		if( testno < 8 )
+			break;
+/* strings rounded to less than maximum precision */
+		e64toasc( &ssprec64, str1, 24 );
+		for( j=SPREC-1; j>0; j-- )		
+			{
+			e64toasc( &ssprec64, str3, j );
+			asctoe( str3, v );
+			sprintf( tformat, "%s.%dLe", pct, j );
+			sprintf( str2, tformat, ssprec64 );
+			asctoe( str2, t );
+			cmptrunc( v, t );
+			}
+		break;
+#endif
+#ifdef DEC
+	case 56:
+#endif
+	case 53:
+		etoe53( fullp, &prec53 );
+		e53toe( &prec53, rounded );
+#if CHKINTERNAL
+		e53toasc( &prec53, str1, SPREC );
+		asctoe53( str1, &xprec53 );
+		e53toe( &xprec53, t );
+		chkinternal( rounded, t, str1 );
+#endif
+		sprintf( str2, format, prec53 );
+		sscanf( str2, fformat, &sprec53 );
+		e53toe( &sprec53, u );
+		chkid( rounded, u, str2 );
+		asctoe53( str2, &ssprec53 );
+		e53toe( &ssprec53, v );
+		chkscan( v, u, str2 );
+		chkprint( rounded, v, str2 );
+		if( testno < 8 )
+			break;
+/* rounding error measurement */
+		etoasc( fullp, str0, 24 );
+		etoe53( fullp, &ssprec53 );
+		e53toe( &ssprec53, u );
+		sprintf( str2, format, ssprec53 );
+		asctoe( str2, t );
+		cmpprint( u, t );
+		sscanf( str0, fformat, &sprec53 );
+		e53toe( &sprec53, t );
+		cmpscan( fullp, t );
+		if( testno < 8 )
+			break;
+		e53toasc( &ssprec53, str1, 24 );
+		for( j=SPREC-1; j>0; j-- )		
+			{
+			e53toasc( &ssprec53, str3, j );
+			asctoe( str3, v );
+			sprintf( tformat, "%s.%de", pct, j );
+			sprintf( str2, tformat, ssprec53 );
+			asctoe( str2, t );
+			cmptrunc( v, t );
+			}
+		break;
+
+	case 24:
+		etoe24( fullp, &prec24 );
+		e24toe( &prec24, rounded );
+#if CHKINTERNAL
+		e24toasc( &prec24, str1, SPREC );
+		asctoe24( str1, &xprec24 );
+		e24toe( &xprec24, t );
+		chkinternal( rounded, t, str1 );
+#endif
+		sprintf( str2, format, prec24 );
+		sscanf( str2, fformat, &sprec24 );
+		e24toe( &sprec24, u );
+		chkid( rounded, u, str2 );
+		asctoe24( str2, &ssprec24 );
+		e24toe( &ssprec24, v );
+		chkscan( v, u, str2 );
+		chkprint( rounded, v, str2 );
+		if( testno < 8 )
+			break;
+/* rounding error measurement */
+		etoasc( fullp, str0, 24 );
+		etoe24( fullp, &ssprec24 );
+		e24toe( &ssprec24, u );
+		sprintf( str2, format, ssprec24 );
+		asctoe( str2, t );
+		cmpprint( u, t );
+		sscanf( str0, fformat, &sprec24 );
+		e24toe( &sprec24, t );
+		cmpscan( fullp, t );
+/*
+		if( testno < 8 )
+			break;
+*/
+		e24toasc( &ssprec24, str1, 24 );
+		for( j=SPREC-1; j>0; j-- )		
+			{
+			e24toasc( &ssprec24, str3, j );
+			asctoe( str3, v );
+			sprintf( tformat, "%s.%de", pct, j );
+			sprintf( str2, tformat, ssprec24 );
+			asctoe( str2, t );
+			cmptrunc( v, t );
+			}
+		break;
+	}
+}
+
+
+void printerr()
+{
+if( (errscan == 0) && (identerr == 0) && (errprint == 0) )
+	printf( "No errors found.\n" );
+else
+	{
+	printf( "%d binary -> decimal errors found.\n", errprint );
+	printf( "%d decimal -> binary errors found.\n", errscan );
+	}
+errscan = 0;	/* reset for next test */
+identerr = 0;
+errprint = 0;
+errtot = 0;
+}
+
+
+/* Random number generator
+ * in the range M * 10^N, where 1 <= M <= 10^17 - 1
+ * and -27 <= N <= +27.  Test values of M are logarithmically distributed
+ * random integers; test values of N are uniformly distributed random integers.
+ */
+
+static char *fwidth = "1.036163291797320557783096e1"; /* log(sqrt(10^9-1)) */
+static char *dwidth = "1.957197329044938830915E1"; /* log(sqrt(10^17-1)) */
+static char *ldwidth = "2.302585092994045684017491e1"; /* log(sqrt(10^20-1)) */
+
+static char *a13 = "13.0";
+static char *a27 = "27.0";
+static char *a34 = "34.0";
+static char *a10m13 = "1.0e-13";
+static unsigned short LOW[ NE ], WIDTH[NE], e27[NE], e10m13[NE];
+
+
+void mnrand( erand )
+unsigned short erand[];
+{
+unsigned short ea[NE], em[NE], en[NE], ex[NE];
+double x, a;
+
+if( mnrflag )
+	{
+	if( mnrflag == 3 )
+		{
+		asctoe( ldwidth, WIDTH );
+		asctoe( a34, e27 );
+		}
+	if( mnrflag == 2 )
+		{
+		asctoe( dwidth, WIDTH );
+		asctoe( a27, e27 );
+		}
+	if( mnrflag == 1 )
+		{
+		asctoe( fwidth, WIDTH );
+		asctoe( a13, e27 );
+		}
+	asctoe( a10m13, e10m13 );
+	mnrflag = 0;
+	}
+drand( &x );
+e53toe( &x, ex ); /* x = WIDTH *  ( x - 1.0 )  +  LOW; */
+esub( eone, ex, ex );
+emul( WIDTH, ex, ex );
+eexp( ex, ex );   /* x = exp(x); */
+
+drand( &a );
+e53toe( &a, ea );
+emul( ea, ex, ea );  /* a = 1.0e-13 * x * a; */
+emul( e10m13, ea, ea );
+eabs( ea );
+eadd( ea, ex, ex );	/* add fuzz */
+emul( ex, ex, ex );	/* square it, to get range to 10^17 - 1 */
+efloor( ex, em ); /* this is M */
+
+/* Random power of 10 */
+drand( &a );
+e53toe( &a, ex );
+esub( eone, ex, ex ); /* y3 = 54.0 *  ( y3 - 1.0 ) + 0.5; */
+emul( e27, ex, ex );
+eadd( ex, ex, ex );
+eadd( ehalf, ex, ex );
+efloor( ex, ex ); /* y3 = floor( y3 ) - 27.0; */
+esub( e27, ex, en ); /* this is N */
+epow( eten, en, ex );
+emul( ex, em, erand );
+}
+
+/* -ln 2^16382 */
+char *ldemin = "-1.1355137111933024058873097E4";
+char *ldewid =  "2.2710274223866048117746193E4";
+/* -ln 2^1022 */
+char *demin  = "-7.0839641853226410622441123E2";
+char *dewid  =  "1.4167928370645282124488225E3";
+/* -ln 2^125 */
+char *femin  = "-8.6643397569993163677154015E1";
+char *fewid  =  "1.7328679513998632735430803E2";
+
+void etrand( erand )
+unsigned short erand[];
+{
+unsigned short ea[NE], ex[NE];
+double x, a;
+
+if( etrflag )
+	{
+	if( etrflag == 3 )
+		{
+		asctoe( ldemin, LOW );
+		asctoe( ldewid, WIDTH );
+		asctoe( a34, e27 );
+		}
+	if( etrflag == 2 )
+		{
+		asctoe( demin, LOW );
+		asctoe( dewid, WIDTH );
+		asctoe( a27, e27 );
+		}
+	if( etrflag == 1 )
+		{
+		asctoe( femin, LOW );
+		asctoe( fewid, WIDTH );
+		asctoe( a13, e27 );
+		}
+	asctoe( a10m13, e10m13 );
+	etrflag = 0;
+	}
+drand( &x );
+e53toe( &x, ex ); /* x = WIDTH *  ( x - 1.0 )  +  LOW; */
+esub( eone, ex, ex );
+emul( WIDTH, ex, ex );
+eadd( LOW, ex, ex );
+eexp( ex, ex );   /* x = exp(x); */
+
+/* add fuzz
+ */
+drand( &a );
+e53toe( &a, ea );
+emul( ea, ex, ea );  /* a = 1.0e-13 * x * a; */
+emul( e10m13, ea, ea );
+if( ecmp( ex, ezero ) > 0 )
+	eneg( ea );
+eadd( ea, ex, erand );
+}
+

test/math/ieetst.doc

@@ -0,0 +1,132 @@
+
+                  ieetst, version 0.2
+
+   This software tests the numerical accuracy of floating point
+binary <-> decimal string conversion, as done by your C language
+library functions printf() and scanf(), for compliance with the
+IEEE arithmetic standards ANSI/IEEE Std 754-1985 and ANSI/IEEE
+Std 854-1987.  The test covers 32-bit float, 64-bit double, and
+80-bit long double precision conversions to and from decimal
+ASCII strings.
+
+   The test program checks for proper implementation of the
+following specifications of the standards:
+
+   (1) correctly rounded conversions of numbers of the form M *
+   10^N, where M and N are integers such that, in double precision,
+   for example, |M| < 10^17, |N| <= 27.
+
+   (2) binary -> decimal -> binary conversions to be an identity
+   if a sufficiently large number of decimal digits is requested.
+
+   (3) correctly rounded decimal outputs of less than the maximum
+   number of digits
+
+   (4) The maximum observed conversion error of numbers outside the
+   domain covered by (1) is reported by the test program; it is
+   not supposed to exceed 0.97 ulp.
+
+There are 10 separate tests.  Tests 1 through 6 use values near
+2^n and 10^n.  Test 7 addresses item (1) above.  Test 8 checks
+the rounding of exact half-integer numbers. Test 9 is for item
+(4) above.  Test 10 checks denormal numbers.  Tests 8 through 10
+address item (3) using printf formats that produce outputs of 1,
+2, 3, ... digits after the decimal point.  All tests check, when
+appropriate, that the binary output of scanf is the same as the
+binary input to printf, item (2).
+
+Example error messages:
+
+   0000 0000 0000 1000 8000 3f80 ->printf-> 5.87748296e-39 ->scanf->
+   0000 0000 0000 0000 8000 3f6e  is not an identity.
+
+   scanf(-9.9999900000000003e-01) -> 0000 4800 085f ef39 ffff bffe 
+   should be 0000 5000 085f ef39 ffff bffe .
+
+   printf("%.14e",  6.13592315154256467968352E-3) -> 6.13592315154257e-03
+   should be       6.13592315154256E-3 .
+
+Binary values are displayed as four-digit hex groups in the
+little-endian format of the internal reference arithmetic. The
+least significant 16-bit word is first, the exponent is last.
+
+   The design of the test program requires knowing the binary
+data structure of the floating point format under test.  For
+configuration, check the .h files carefully. All the programs
+need to be told via mconf.h if the numeric format is
+little-endian (IBMPC) or big-endian (MIEEE).  If your system
+supports an 80-bit long double precision data type, define
+LDOUBLE 1 in ieetst.c; otherwise define LDOUBLE 0.  A provision
+for DEC PDP-11/VAX numbers is implemented (double precision
+only).  Conversions for other data structures can be added by
+analogy to the ifdefs for DEC.
+
+   Most of the tests rely on comparison with the results of a
+portable reference arithmetic, contained in the file ieee.c. 
+This is configured for an 80-bit significand, to have enough
+precision to satisfy the conversion requirements of IEEE 854 for
+the extended double format of IEEE 754.  The reference arithmetic
+includes binary <--> ASCII conversion routines and single <-->
+double <--> extended double conversions.  A strictly rounded
+square root function is given in esqrt.c.  Additional functions
+are provided by elog.c, eexp.c, etanh.c, epow.c, all of which
+call on ieee.c for their arithmetic.  Some of the ANSI C
+functions are supplied in ieee.c; for example, efloor(),
+efrexp(), eldexp(). The functions and the reference arithmetic
+are described further in the book _Methods and Programs for
+Mathematical Functions_ (Prentice-Hall or Simon & Schuster
+International, 1989), by S. L. Moshier.
+
+   As an aid in diagnosis, a calculator program, ecalc.c, is
+supplied.  It uses ieee.c for its arithmetic. Documentation for
+the calculator's user interface is in the file calc100.doc
+(calc100 is a fuller featured 100-digit version of ecalc).  The
+calculator needs to be told by qcalc.h if addresses are 32 bits
+long (define LARGEMEM 1) or 16 bits long (define LARGEMEM 0).
+
+   Because the source code of ieee.c is included here, a version
+of W. Kahan's PARANOIA is also provided; this has been heavily
+modified by substituting subroutine calls to ieee.c in place of
+all arithmetic operators.  It is important that you use PARANOIA
+to check the arithmetic after any modifications you may make to
+ieee.c.
+
+   Several systems have been tested with the initial version of
+ieetst.  Sun 4 (SPARC) passes; DEC VMS C has only a small flaw;
+Microsoft flunks; ATT SysVR2 (Motorola) flunks even worse.
+
+
+   Files:
+
+calc100.doc     calculator documentaton
+descrip.mms     part of VAX VMS makefile
+drand.c         random number generator
+ecalc.c         calculator
+ecalc.opt       part of VAX VMS makefile
+econst.c        constants for reference arithmetic
+eexp.c          reference exponential function
+ehead.h         declarations for reference arithmetic routines
+elog.c          reference logarithm
+eparanoi.c      floating point arithmetic tester
+eparanoi.opt    part of VAX VMS makefile
+epow.c          reference exponentiation
+esqrt.c         reference square root
+etanh.c         reference hyperbolic tangent
+etodec.c        conversions to and from DEC double precision format
+ieee.c          the reference arithmetic
+ieetst.c        printf/scanf tester
+ieetst.doc      this file
+ieetst.mak      Microsoft make file
+ieetst.opt      part of VAX VMS makefile
+makefile        Unix make file
+mconf.h         definitions for arithmetic format
+mtherr.c        common error reporter
+qcalc.h         definitions for calculator
+
+
+This software may be copied freely.
+
+-- Steve Moshier
+
+v0.1   July, 1992
+v0.2   January, 1993

test/math/mconf.h

@@ -0,0 +1,108 @@
+/*							mconf.h
+ *
+ *	Common include file for math routines
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * #include "mconf.h"
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * This file contains definitions for error codes that are
+ * passed to the common error handling routine mtherr()
+ * (which see).
+ *
+ * The file also includes a conditional assembly definition
+ * for the type of computer arithmetic (IEEE, DEC, Motorola
+ * IEEE, or UNKnown).
+ *
+ * For Digital Equipment PDP-11 and VAX computers, certain
+ * IBM systems, and others that use numbers with a 56-bit
+ * significand, the symbol DEC should be defined.  In this
+ * mode, most floating point constants are given as arrays
+ * of octal integers to eliminate decimal to binary conversion
+ * errors that might be introduced by the compiler.
+ *
+ * For computers, such as IBM PC, that follow the IEEE 
+ * Standard for Binary Floating Point Arithmetic (ANSI/IEEE
+ * Std 754-1985), the symbol IBMPC should be defined.  These
+ * numbers have 53-bit significands.  In this mode, constants
+ * are provided as arrays of hexadecimal 16 bit integers.
+ *
+ * To accommodate other types of computer arithmetic, all
+ * constants are also provided in a normal decimal radix
+ * which one can hope are correctly converted to a suitable
+ * format by the available C language compiler.  To invoke
+ * this mode, the symbol UNK is defined.
+ *
+ * An important difference among these modes is a predefined
+ * set of machine arithmetic constants for each.  The numbers
+ * MACHEP (the machine roundoff error), MAXNUM (largest number
+ * represented), and several other parameters are preset by
+ * the configuration symbol.  Check the file const.c to
+ * ensure that these values are correct for your computer.
+ *
+ */
+
+/*
+Cephes Math Library Release 2.0:  April, 1987
+by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+
+/* Constant definitions for math error conditions
+ */
+
+#define DOMAIN		1	/* argument domain error */
+#define SING		2	/* argument singularity */
+#define OVERFLOW	3	/* overflow range error */
+#define UNDERFLOW	4	/* underflow range error */
+#define TLOSS		5	/* total loss of precision */
+#define PLOSS		6	/* partial loss of precision */
+
+#define EDOM		33
+#define ERANGE		34
+
+/*
+typedef struct
+	{
+	double r;
+	double i;
+	}cmplx;
+*/
+
+/* Type of computer arithmetic */
+
+/* PDP-11, Pro350, VAX:
+ */
+/*define DEC 1*/
+
+/* Intel IEEE, low order words come first:
+ */
+#define IBMPC 1
+
+/* Motorola IEEE, high order words come first
+ * (Sun workstation):
+ */
+/*define MIEEE 1*/
+
+/* UNKnown arithmetic, invokes coefficients given in
+ * normal decimal format.  Beware of range boundary
+ * problems (MACHEP, MAXLOG, etc. in const.c) and
+ * roundoff problems in pow.c:
+ */
+ /*define UNK 1*/
+
+/* Define to ask for infinity support, else undefine. */
+#define INFINITY
+
+/* Define to ask for Not-a-Number support, else undefine. */
+#define NANS
+
+/* Define to support denormal numbers, else undefine. */
+#define DENORMAL

test/math/mtherr.c

@@ -0,0 +1,96 @@
+/*							mtherr.c
+ *
+ *	Library common error handling routine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * char *fctnam;
+ * int code;
+ * void mtherr();
+ *
+ * mtherr( fctnam, code );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * This routine may be called to report one of the following
+ * error conditions (in the include file mconf.h).
+ *  
+ *   Mnemonic        Value          Significance
+ *
+ *    DOMAIN            1       argument domain error
+ *    SING              2       function singularity
+ *    OVERFLOW          3       overflow range error
+ *    UNDERFLOW         4       underflow range error
+ *    TLOSS             5       total loss of precision
+ *    PLOSS             6       partial loss of precision
+ *    EDOM             33       Unix domain error code
+ *    ERANGE           34       Unix range error code
+ *
+ * The default version of the file prints the function name,
+ * passed to it by the pointer fctnam, followed by the
+ * error condition.  The display is directed to the standard
+ * output device.  The routine then returns to the calling
+ * program.  Users may wish to modify the program to abort by
+ * calling exit() under severe error conditions such as domain
+ * errors.
+ *
+ * Since all error conditions pass control to this function,
+ * the display may be easily changed, eliminated, or directed
+ * to an error logging device.
+ *
+ * SEE ALSO:
+ *
+ * mconf.h
+ *
+ */
+
+/*
+Cephes Math Library Release 2.0:  April, 1987
+by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include "mconf.h"
+
+/* Notice: the order of appearance of the following
+ * messages is bound to the error codes defined
+ * in mconf.h.
+ */
+static char *ermsg[7] = {
+"unknown",      /* error code 0 */
+"domain",       /* error code 1 */
+"singularity",  /* et seq.      */
+"overflow",
+"underflow",
+"total loss of precision",
+"partial loss of precision"
+};
+
+
+
+void mtherr( name, code )
+char *name;
+int code;
+{
+
+/* Display string passed by calling program,
+ * which is supposed to be the name of the
+ * function in which the error occurred:
+ */
+printf( "\n%s ", name );
+
+/* Display error message defined
+ * by the code argument.
+ */
+if( (code <= 0) || (code >= 6) )
+	code = 0;
+printf( "%s error\n", ermsg[code] );
+
+/* Return to calling
+ * program
+ */
+}