paranoia.c

RTEMS (Real-Time Executive for Multiprocessor Systems) is a free open source real-time operating sys

        V = V + ((One - HInvrse) * U2) * Y;
    }
    printf ("Overflow threshold is V  = %.17e .\n", V);
    if (I)
        printf ("Overflow saturates at V0 = %.17e .\n", V0);
    else
        printf ("There is no saturation value because \
the system traps on overflow.\n");
    V9 = V * One;
    printf ("No Overflow should be signaled for V * 1 = %.17e\n", V9);
    V9 = V / One;
    printf ("                           nor for V / 1 = %.17e .\n", V9);
    printf ("Any overflow signal separating this * from the one\n");
    printf ("above is a DEFECT.\n");
    /*=============================================*/
    Milestone = 170;
    /*=============================================*/
    if (!(-V < V && -V0 < V0 && -UfThold < V && UfThold < V)) {
        BadCond (Failure, "Comparisons involving ");
        printf ("+-%g, +-%g\nand +-%g are confused by Overflow.",
            V, V0, UfThold);
    }
    /*=============================================*/
    Milestone = 175;
    /*=============================================*/
    printf ("\n");
    for (Indx = 1; Indx <= 3; ++Indx) {
        switch (Indx) {
        case 1:
            Z = UfThold;
            break;
        case 2:
            Z = E0;
            break;
        case 3:
            Z = PseudoZero;
            break;
        }
        if (Z != Zero) {
            V9 = SQRT (Z);
            Y = V9 * V9;
            if (Y / (One - Radix * E9) < Z
                || Y > (One + Radix * E9) * Z) {        /* dgh: + E9 --> * E9 */
                if (V9 > U1)
                    BadCond (Serious, "");
                else
                    BadCond (Defect, "");
                printf ("Comparison alleges that what prints as Z = %.17e\n", Z);
                printf (" is too far from sqrt(Z) ^ 2 = %.17e .\n", Y);
            }
        }
    }
    /*=============================================*/
    Milestone = 180;
    /*=============================================*/
    for (Indx = 1; Indx <= 2; ++Indx) {
        if (Indx == 1)
            Z = V;
        else
            Z = V0;
        V9 = SQRT (Z);
        X = (One - Radix * E9) * V9;
        V9 = V9 * X;
        if (((V9 < (One - Two * Radix * E9) * Z) || (V9 > Z))) {
            Y = V9;
            if (X < WVar)
                BadCond (Serious, "");
            else
                BadCond (Defect, "");
            printf ("Comparison alleges that Z = %17e\n", Z);
            printf (" is too far from sqrt(Z) ^ 2 (%.17e) .\n", Y);
        }
    }
    /*=============================================*/
    Milestone = 190;
    /*=============================================*/
    Pause ();
    X = UfThold * V;
    Y = Radix * Radix;
    if (X * Y < One || X > Y) {
        if (X * Y < U1 || X > Y / U1)
            BadCond (Defect, "Badly");
        else
            BadCond (Flaw, "");

        printf (" unbalanced range; UfThold * V = %.17e\n\t%s\n",
            X, "is too far from 1.\n");
    }
    /*=============================================*/
    Milestone = 200;
    /*=============================================*/
    for (Indx = 1; Indx <= 5; ++Indx) {
        X = F9;
        switch (Indx) {
        case 2:
            X = One + U2;
            break;
        case 3:
            X = V;
            break;
        case 4:
            X = UfThold;
            break;
        case 5:
            X = Radix;
        }
        Y = X;
        sigsave = _sigfpe;
        if (setjmp (ovfl_buf))
            printf ("  X / X  traps when X = %g\n", X);
        else {
            V9 = (Y / X - Half) - Half;
            if (V9 == Zero)
                continue;
            if (V9 == -U1 && Indx < 5)
                BadCond (Flaw, "");
            else
                BadCond (Serious, "");
            printf ("  X / X differs from 1 when X = %.17e\n", X);
            printf ("  instead, X / X - 1/2 - 1/2 = %.17e .\n", V9);
        }
        sigsave = 0;
    }
    /*=============================================*/
    Milestone = 210;
    /*=============================================*/
    MyZero = Zero;
    printf ("\n");
    printf ("What message and/or values does Division by Zero produce?\n");
#ifndef BATCHMODE
    printf ("This can interupt your program.  You can ");
    printf ("skip this part if you wish.\n");
    printf ("Do you wish to compute 1 / 0? ");
    fflush (stdout);
    read (KEYBOARD, ch, 8);
    if ((ch[0] == 'Y') || (ch[0] == 'y')) {
#endif /* !BATCHMODE */
        sigsave = _sigfpe;
        printf ("    Trying to compute 1 / 0 produces ...");
        if (!setjmp (ovfl_buf))
            printf ("  %.7e .\n", One / MyZero);
        sigsave = 0;
#ifndef BATCHMODE
    } else
        printf ("O.K.\n");
    printf ("\nDo you wish to compute 0 / 0? ");
    fflush (stdout);
    read (KEYBOARD, ch, 80);
    if ((ch[0] == 'Y') || (ch[0] == 'y')) {
#endif /* !BATCHMODE */
        sigsave = _sigfpe;
        printf ("\n    Trying to compute 0 / 0 produces ...");
        if (!setjmp (ovfl_buf))
            printf ("  %.7e .\n", Zero / MyZero);
        sigsave = 0;
#ifndef BATCHMODE
    } else
        printf ("O.K.\n");
#endif /* !BATCHMODE */
    /*=============================================*/
    Milestone = 220;
    /*=============================================*/

    Pause ();
    printf ("\n");
    {
        static char *msg[] =
        {
            "FAILUREs  encountered =",
            "SERIOUS DEFECTs  discovered =",
            "DEFECTs  discovered =",
            "FLAWs  discovered ="};
        int     i;
        for (i = 0; i < 4; i++)
            if (ErrCnt[i])
                printf ("The number of  %-29s %d.\n",
                    msg[i], ErrCnt[i]);
    }

    printf ("\n");
    if ((ErrCnt[Failure] + ErrCnt[Serious] + ErrCnt[Defect]
            + ErrCnt[Flaw]) > 0) {
        if ((ErrCnt[Failure] + ErrCnt[Serious] + ErrCnt[
                    Defect] == 0) && (ErrCnt[Flaw] > 0)) {
            printf ("The arithmetic diagnosed seems ");
            printf ("Satisfactory though flawed.\n");
        }
        if ((ErrCnt[Failure] + ErrCnt[Serious] == 0)
            && (ErrCnt[Defect] > 0)) {
            printf ("The arithmetic diagnosed may be Acceptable\n");
            printf ("despite inconvenient Defects.\n");
        }
        if ((ErrCnt[Failure] + ErrCnt[Serious]) > 0) {
            printf ("The arithmetic diagnosed has ");
            printf ("unacceptable Serious Defects.\n");
        }
        if (ErrCnt[Failure] > 0) {
            printf ("Potentially fatal FAILURE may have spoiled this");
            printf (" program's subsequent diagnoses.\n");
        }
    } else {

        printf ("No failures, defects nor flaws have been discovered.\n");
        if (!((RMult == Rounded) && (RDiv == Rounded)
                && (RAddSub == Rounded) && (RSqrt == Rounded)))
            printf ("The arithmetic diagnosed seems Satisfactory.\n");
        else {
            if (StickyBit >= One &&
                (Radix - Two) * (Radix - Nine - One) == Zero) {
                printf ("Rounding appears to conform to ");
                printf ("the proposed IEEE standard P");
                if ((Radix == Two) &&
                    ((Precision - Four * Three * Two) *
                        (Precision - TwentySeven -
                            TwentySeven + One) == Zero))
                    printf ("754");
                else
                    printf ("854");
                if (IEEE)
                    printf (".\n");
                else {
                    printf (",\nexcept for possibly Double Rounding");
                    printf (" during Gradual Underflow.\n");
                }
            }
            printf ("The arithmetic diagnosed appears to be Excellent!\n");
        }
    }

    if (fpecount)
        printf ("\nA total of %d floating point exceptions were registered.\n",
            fpecount);
    printf ("END OF TEST.\n");
    return 0;
}

FLOAT
Sign (X)
     FLOAT   X;
{
    return X >= 0. ? 1.0 : -1.0;
}

void
Pause ()
{
#ifndef BATCHMODE
    char    ch[8];

    printf ("\nTo continue, press RETURN");
    fflush (stdout);
    read (KEYBOARD, ch, 8);
#endif /* !BATCHMODE */
#ifndef CYGNUS
    printf ("\nDiagnosis resumes after milestone Number %d", Milestone);
    printf ("          Page: %d\n\n", PageNo);
    ++Milestone;
    ++PageNo;
#endif /* !CYGNUS */
}

void
TstCond (K, Valid, T)
     int     K, Valid;
     char   *T;
{
#ifdef CYGNUS
    printf ("TEST: %s\n", T);
#endif /* CYGNUS */
    if (!Valid) {
        BadCond (K, T);
        printf (".\n");
    }
#ifdef CYGNUS
    printf ("PASS: %s\n", T);
#endif /* CYGNUS */
}

void
BadCond (K, T)
     int     K;
     char   *T;
{
    static char *msg[] =
    {"FAILURE", "SERIOUS DEFECT", "DEFECT", "FLAW"};

    ErrCnt[K] = ErrCnt[K] + 1;
#ifndef CYGNUS
    printf ("%s:  %s", msg[K], T);
#else
    printf ("ERROR: Severity: %s:  %s", msg[K], T);
#endif /* CYGNUS */
}

/*
 * Random computes
 *     X = (Random1 + Random9)^5
 *     Random1 = X - FLOOR(X) + 0.000005 * X;
 *   and returns the new value of Random1
*/
FLOAT
Random ()
{
    FLOAT   X, Y;

    X = Random1 + Random9;
    Y = X * X;
    Y = Y * Y;
    X = X * Y;
    Y = X - FLOOR (X);
    Random1 = Y + X * 0.000005;
    return (Random1);
}

void
SqXMinX (ErrKind)
     int     ErrKind;
{
    FLOAT   XA, XB;

    XB = X * BInvrse;
    XA = X - XB;
    SqEr = ((SQRT (X * X) - XB) - XA) / OneUlp;
    if (SqEr != Zero) {
        if (SqEr < MinSqEr)
            MinSqEr = SqEr;
        if (SqEr > MaxSqEr)
            MaxSqEr = SqEr;
        J = J + 1.0;
        BadCond (ErrKind, "\n");
        printf ("sqrt( %.17e) - %.17e  = %.17e\n", X * X, X, OneUlp * SqEr);
        printf ("\tinstead of correct value 0 .\n");
    }
}

void
NewD ()
{
    X = Z1 * Q;
    X = FLOOR (Half - X / Radix) * Radix + X;
    Q = (Q - X * Z) / Radix + X * X * (D / Radix);
    Z = Z - Two * X * D;
    if (Z <= Zero) {
        Z = -Z;
        Z1 = -Z1;
    }
    D = Radix * D;
}

void
SR3750 ()
{
    if (!((X - Radix < Z2 - Radix) || (X - Z2 > WVar - Z2))) {
        I = I + 1;
        X2 = SQRT (X * D);
        Y2 = (X2 - Z2) - (Y - Z2);
        X2 = X8 / (Y - Half);
        X2 = X2 - Half * X2 * X2;
        SqEr = (Y2 + Half) + (Half - X2);
        if (SqEr < MinSqEr)
            MinSqEr = SqEr;
        SqEr = Y2 - X2;
        if (SqEr > MaxSqEr)
            MaxSqEr = SqEr;
    }
}

void
IsYeqX ()
{
    if (Y != X) {
        if (N <= 0) {
            if (Z == Zero && Q <= Zero)
                printf ("WARNING:  computing\n");
            else
                BadCond (Defect, "computing\n");
            printf ("\t(%.17e) ^ (%.17e)\n", Z, Q);
            printf ("\tyielded %.17e;\n", Y);
            printf ("\twhich compared unequal to correct %.17e ;\n",
                X);
            printf ("\t\tthey differ by %.17e .\n", Y - X);
        }
        N = N + 1;              /* ... count discrepancies. */
    }
}

void
SR3980 ()
{
    do {
        Q = (FLOAT) I;
        Y = POW (Z, Q);
        IsYeqX ();
        if (++I > M)
            break;
        X = Z * X;
    }
    while (X < WVar);
}

void
PrintIfNPositive ()
{
    if (N > 0)
        printf ("Similar discrepancies have occurred %d times.\n", N);
}

void
TstPtUf ()
{
    N = 0;
    if (Z != Zero) {
        printf ("Since comparison denies Z = 0, evaluating ");
        printf ("(Z + Z) / Z should be safe.\n");
        sigsave = _sigfpe;
        if (setjmp (ovfl_buf))
            goto very_serious;
        Q9 = (Z + Z) / Z;
        printf ("What the machine gets for (Z + Z) / Z is  %.17e .\n",
            Q9);
        if (FABS (Q9 - Two) < Radix * U2) {
            printf ("This is O.K., provided Over/Underflow");
            printf (" has NOT just been signaled.\n");
        } else {
            if ((Q9 < One) || (Q9 > Two)) {
              very_serious: