integer - data - string to numeric stata

Simular variables int con byte o short

Question

Como sabes, no hay una variable int en JavaCard 2.2.x. Necesito variables enteras para el applet que estoy desarrollando.

Quiero saber cómo simular una variable int y su aritmética usando byte y variables short .

Answer 1

int variables int son opcionales en Java Card 2.2, por lo que puede haber una variable int . Sin embargo, muchas implementaciones no molestan, probablemente porque ninguna de las llamadas API maneja enteros. Lo mismo vale para la clase javacardx.framework.math.BigNumber . Si tienes suerte, está presente, aunque solo te ayudará con la suma y la multiplicación (pero puede implementarse usando funciones nativas, lo que lo haría mucho más rápido).

Tenga en cuenta que si solo necesita las funciones con moderación, es mejor que use algunas variables short locales y las use para realizar los cálculos en línea. Esto tiene la ventaja de que tiene un rendimiento mucho mejor. Como no es posible devolver más de una variable (y los argumentos de Java pasan por valor) es difícil devolver dos valores por valor.

Puede tomar algunas sugerencias de, por ejemplo, las implementaciones de Java BigInteger que utilizan matrices long para representar enteros de tamaño arbitrario. Un problema es que los operadores normales devuelven una nueva instancia cada vez que son llamados. Esta no es una buena opción en Java Card, ya que se crearán nuevas instancias en la memoria persistente. Por lo tanto, es más fácil crear combinados

Answer 2

Respuesta especial de Navidad.

Completamente probado usando pruebas unitarias, pero aún solo en Java SE.

Necesita algo de trabajo para crear instancias de la matriz de respaldo.

Algunos códigos aún se pueden optimizar alineando el operando de la izquierda.

Tenga en cuenta que este código utiliza *= lugar de * ya que no es una buena idea crear instancias de objetos durante el tiempo de ejecución de Java Card (se crean en la memoria persistente).

Eliminó todos los comentarios de JavaDoc, ya que de lo contrario no se ajustaría al tamaño máximo de publicación.

/**
 * Free for use by all, please keep this line and the author line intact.
 * 
 * @author Maarten Bodewes
 */
public final class JCInteger {

    private static final short BYTE_SIZE = 8;
    private static final short SHORT_SIZE = 16;
    private static final short INTEGER_SIZE = 32;

    private static final short HIGH = 0;
    private static final short LOW = 1;

    private final short[] values;

    private JCInteger(final byte memoryType) {

        // TODO this should be backed by an array in RAM, using JCSystem.makeTransientByteArray()
        // using either JCSystem.CLEAR_ON_RESET or JCSystem.CLEAR_ON_DESELECT

        values = new short[(short) 2];
    }

    public static JCInteger createInstance(final byte memoryType) {
        return new JCInteger(memoryType);
    }

    public JCInteger assign(final JCInteger rightHandOperand) {
        values[HIGH] = rightHandOperand.values[HIGH];
        values[LOW] = rightHandOperand.values[LOW];
        return this;
    }

    public JCInteger assign(final short high, final short low) {
        values[HIGH] = high;
        values[LOW] = low;
        return this;
    }

    public JCInteger assignSigned(final short signedValue) {
        if (signedValue >= 0) {
            values[HIGH] = (short) 0x0000;
        } else {
            values[HIGH] = (short) 0xFFFF;
        }
        values[LOW] = signedValue;
        return this;
    }

    public JCInteger assignUnsigned(final short unsignedValue) {
        values[HIGH] = (short) 0x0000;
        values[LOW] = unsignedValue;
        return this;
    }

    public short getHigh() {
        // no pun intended
        return values[HIGH];
    }

    public short getLow() {
        return values[LOW];
    }

    public short[] getBackingShortArray() {
        return values;
    }

    public JCInteger negate() {

        // basically invert, then increase, note that -Integer.MIN_VALUE = Integer.MIN_VALUE (as it is in Java) 
        values[HIGH] = (short)~values[HIGH];
        values[LOW] = (short)~values[LOW];
        increment();
        return this;
    }

    public JCInteger increment() {
        values[LOW]++;
        if (values[LOW] == 0) {
            values[HIGH]++;
        }
        return this;
    }

    public JCInteger decrement() {
        values[LOW]--;
        if (values[LOW] == -1) {
            values[HIGH]--;
        }
        return this;
    }

    public JCInteger add(final JCInteger y) {
        addUnsignedLow(y.values[LOW]);
        values[HIGH] += y.values[HIGH];
        return this;
    }

    public JCInteger subtract(final JCInteger y) {
        // subtracts by adding the negated i
        // negation is identical to invert + increase
        // however the increase is performed to the result of adding the inverted value

        // invert
        final short xlInv = (short) ~y.values[LOW];
        final short xhInv = (short) ~y.values[HIGH];

        // add
        addUnsignedLow(xlInv);
        values[HIGH] += xhInv;

        // increase
        increment();
        return this;
    }

    public JCInteger multiply(JCInteger y) {
        // uses the fact that:
        // x * y =
        // (x1 * 2 ^ 16 + x0) * (y1 * 2 ^ 16 + y0) =
        // (x1 * y1 * 2 ^ 32) + x1 * y0 * 2 ^ 16 + x0 * y1 * 2 ^ 16 + x0 * y0 =
        // x1 * y0 * 2 ^ 16 + x0 * y1 * 2 ^ 16 + x0 * y0 (because anything * 2 ^ 32 overflows all the bits) =
        // x1 * y0 * 2 ^ 16 + x0 * y1 * 2 ^ 16 + z1 | z0 (where z1 = high 16 bits of x0 * y* and z0 is the low part) =
        // r1 | r0 where r1 = x1 * y0 + x0 * y1 + z1 and r0 = z0
        // r1 is only 16 bits so x1 * y0 and x0 * y0 may overflow, as may the additions, hopefully leaving the sign
        // bit correctly set

        boolean xPositive = this.isPositive();
        if (!xPositive) {
            this.negate();
        }

        final short xh = this.values[HIGH];
        final short xl = this.values[LOW];

        short yh = y.values[HIGH];
        short yl = y.values[LOW];

        // --- if signed then negate y ---
        final boolean yPositive;
        if ((yh & 0x8000) == 0) {
            yPositive = true;
        } else {
            // negation (complement then increase)
            yh = (short) ~yh;
            yl = (short) ~yl;
            yl++;
            if (yl == 0) {
                yh++;
            }
            yPositive = false;
        }

        // calculates z1 and z0 and stores it in the current values
        multiplyUnsigned(xl, yl, values);

        // perform the calculation for the high parts
        values[HIGH] += (short) (xh * yl + xl * yh);

        // make sure we return a correctly signed value
        if ((xPositive && !yPositive) || (!xPositive && yPositive)) {
            this.negate();
        }

        return this;
    }

    public JCInteger divide(JCInteger y) {

        // --- pre-calculations on y ---

        // put y in yh and yl
        short yh = y.values[HIGH];
        short yl = y.values[LOW];

        if (yh == 0 && yl == 0) {
            // division by zero
            throw new ArithmeticException();
        }

        final boolean yPositive;
        if ((yh & 0x8000) == 0) {
            yPositive = true;
        } else {
            // negation (complement then increase)
            yh = (short) ~yh;
            yl = (short) ~yl;
            yl++;
            if (yl == 0) {
                yh++;
            }
            yPositive = false;
        }

        final short divisorSize = (short) (INTEGER_SIZE - numberOfLeadingZeros(yh, yl));

        // --- pre-calculations on x ---

        final boolean xPositive = this.isPositive();
        if (!xPositive) {
            this.negate();
        }
        final short dividentSize = (short) (INTEGER_SIZE - numberOfLeadingZeros());

        // --- setup the maximum number of shifts ---

        final short maxShifts = (short) (dividentSize - divisorSize); 

        // --- slightly superfluous check if divisor is higher than dividend ---

        if (maxShifts < 0) {
            // return 0, no division can be performed
            values[HIGH] = 0;
            values[LOW] = 0;
            return this;
        }

        // --- shift divisor left until the highest bit is aligned with the highest bit of the dividend ---

        if (maxShifts <= JCInteger.SHORT_SIZE) {
            yh = (short) (((yl & 0xFFFF) >>> (SHORT_SIZE - maxShifts)) | (yh << maxShifts));  
            yl <<= maxShifts;
        } else {
            yh = (short) (yl << (maxShifts - SHORT_SIZE));
            yl = 0;
        }

        short rh = 0, rl = 0;
        for (short i = maxShifts; i >= 0; i--) {
            final short xho = values[HIGH];
            final short xlo = values[LOW];

            // --- subtract (add complement and increment does the job) ---

            // add complement
            addUnsignedLow((short) ~yl);
            values[HIGH] += (short) ~yh;

            // increase to create subtraction
            increment();

            if (isPositive()) {
                // --- we have subtracted y * 2 ^ n, so include 2 ^ n to the result ---
                if (i >= SHORT_SIZE) {
                    rh |= 1 << (i - SHORT_SIZE);
                } else {
                    rl |= 1 << i;
                }
            } else {
                // --- we could not subtract, so restore ---
                values[HIGH] = xho;
                values[LOW] = xlo;
            }

            // --- shift right by 1 ---
            // first do low shift as high shift changes value
            yl = (short) ((yh << (JCInteger.SHORT_SIZE - 1)) | ((yl & 0xFFFF) >>> 1));
            yh = (short) ((yh & 0xFFFF) >>> 1);  
        }

        values[HIGH] = rh;
        values[LOW] = rl;

        // make sure we return a correctly signed value (may mess up sign bit on overflows?)
        if ((xPositive && !yPositive) || (!xPositive && yPositive)) {
            this.negate();
        }

        return this;
    }

    public JCInteger remainder(JCInteger y) {

        // --- pre-calculations on y ---

        // put y in yh and yl
        short yh = y.values[HIGH];
        short yl = y.values[LOW];

        if (yh == 0 && yl == 0) {
            // division by zero
            throw new ArithmeticException();
        }

        if ((yh & 0x8000) != 0) {
            // negation (complement then increase)
            yh = (short) ~yh;
            yl = (short) ~yl;
            yl++;
            if (yl == 0) {
                yh++;
            }
        }

        final short divisorSize = (short) (INTEGER_SIZE - numberOfLeadingZeros(yh, yl));

        // --- pre-calculations on x ---

        final boolean xPositive = this.isPositive();
        if (!xPositive) {
            this.negate();
        }
        final short dividentSize = (short) (INTEGER_SIZE - numberOfLeadingZeros());

        // --- setup the maximum number of shifts ---

        final short maxShifts = (short) (dividentSize - divisorSize); 

        // --- slightly superfluous check if divisor is higher than dividend ---

        if (maxShifts < 0) {
            if (!xPositive) {
                return this.negate();
            }
            return this;
        }

        // --- shift divisor left until the highest bit is aligned with the highest bit of the dividend ---

        if (maxShifts <= JCInteger.SHORT_SIZE) {
            yh = (short) (((yl & 0xFFFF) >>> (SHORT_SIZE - maxShifts)) | (yh << maxShifts));  
            yl <<= maxShifts;
        } else {
            yh = (short) (yl << (maxShifts - SHORT_SIZE));
            yl = 0;
        }

        for (short i = maxShifts; i >= 0; i--) {
            final short xho = values[HIGH];
            final short xlo = values[LOW];

            // --- subtract (add complement and increment does the job) ---

            // add complement
            addUnsignedLow((short) ~yl);
            values[HIGH] += (short) ~yh;

            // increase to create subtraction
            increment();

            if (!isPositive()) {
                values[HIGH] = xho;
                values[LOW] = xlo;
            }

            // --- shift right by 1 ---
            // first do low shift as high shift changes value
            yl = (short) ((yh << (JCInteger.SHORT_SIZE - 1)) | ((yl & 0xFFFF) >>> 1));
            yh = (short) ((yh & 0xFFFF) >>> 1);  
        }

        if (!xPositive) {
            negate();
        }

        return this;
    }

    public JCInteger leftShift(short shiftDistance) {
        shiftDistance = (short) (shiftDistance & 0x1F);
        if (shiftDistance == 0) {
            return this;
        }

        final short low = values[LOW];
        final short high = values[HIGH];

        // TODO test if we can do without if on Java Card (is integer value calculated? cannot really be.
        if (shiftDistance < SHORT_SIZE) {
            values[HIGH] = (short) (((low & 0xFFFF) >>> (SHORT_SIZE - shiftDistance)) | (high << shiftDistance));  
            values[LOW] <<= shiftDistance;
        } else {
            values[HIGH] = (short) (low << (shiftDistance - SHORT_SIZE));
            values[LOW] = 0;
        }

        return this;
    }

    public JCInteger signedRightShift(short shiftDistance) {
        shiftDistance = (short) (shiftDistance & 0x1F);
        if (shiftDistance == 0) {
            return this;
        }

        final short low = values[LOW];
        final short high = values[HIGH];

        if (shiftDistance < SHORT_SIZE) {
            values[HIGH] = (short) (high >>> shiftDistance);  
            values[LOW] = (short) ((high << (SHORT_SIZE - shiftDistance)) | ((low & 0xFFFF) >>> shiftDistance));
        } else {
            if ((high & 0x8000) == 0) {
                values[HIGH] = 0;
                values[LOW] = (short) ((high & 0xFFFF) >>> (shiftDistance - SHORT_SIZE));
            } else {
                values[HIGH] = (short) 0xFFFF;
                values[LOW] = (short) (high >>> (shiftDistance - SHORT_SIZE));
            }
        }

        return this;
    }

    public JCInteger unsignedRightShift(short shiftDistance) {
        shiftDistance = (short) (shiftDistance & 0x1F);
        if (shiftDistance == 0) {
            return this;
        }

        final short low = values[LOW];
        final short high = values[HIGH];

        if (shiftDistance < SHORT_SIZE) {
            values[HIGH] = (short) ((high & 0xFFFF) >>> shiftDistance);  
            values[LOW] = (short) ((high << (SHORT_SIZE - shiftDistance)) | ((low & 0xFFFF) >>> shiftDistance));
        } else {
            values[HIGH] = 0;
            values[LOW] = (short) ((high & 0xFFFF) >>> (shiftDistance - SHORT_SIZE));
        }

        return this;
    }

    public JCInteger complement() {
        this.values[HIGH] = (short) ~this.values[HIGH];
        this.values[LOW] = (short) ~this.values[LOW];
        return this;
    }

    public JCInteger xor(final JCInteger y) {
        this.values[HIGH] ^= y.values[HIGH];
        this.values[LOW] ^= y.values[LOW];
        return this;
    }

    public JCInteger and(final JCInteger y) {
        this.values[HIGH] &= y.values[HIGH];
        this.values[LOW] &= y.values[LOW];
        return this;
    }

    public JCInteger or(final JCInteger y) {
        this.values[HIGH] |= y.values[HIGH];
        this.values[LOW] |= y.values[LOW];
        return this;
    }

    public short signum() {
        if (values[HIGH] == 0 && values[LOW] == 0) {
            return 0;
        }

        // get sign bit (>>> 15) negate, -1 for neg, 0 for pos, then times 2 (<< 2) which leaves -2 for neg 0 for pos
        // and finally add 1, to get the result -1 or 1 for negative and positive, respectively
        return (short) ((-((values[HIGH] >>> 15) & 1) * 2) + 1);
    }

    public short numberOfLeadingZeros() {
        short t = values[HIGH];

        if (t != 0) {
            for (short i = 0; i < SHORT_SIZE; i++) {
                if (t < 0) {
                    return i;
                }
                t <<= 1;
            }
        }

        t = values[LOW];

        if (t != 0) {
            for (short i = SHORT_SIZE; i < INTEGER_SIZE; i++) {
                if (t < 0) {
                    return i;
                }
                t <<= 1;
            }
        }

        return INTEGER_SIZE;
    }

    public short compareTo(JCInteger anotherInteger) {
        final short xh = values[HIGH];
        final short yh = anotherInteger.values[HIGH];

        if (xh < yh) {
            return -1;
        } else if (xh > yh) {
            return 1;
        }

        // --- xh == yh ---

        final short xl = values[LOW];
        final short yl = anotherInteger.values[LOW];

        // TODO think of better way than four ifs
        if (xl < 0 && yl >= 0) {
            return 1;
        } else if (xl >= 0 && yl < 0) {
            return -1;
        } else if (xl > yl) {
            return 1;
        } else if (xl < yl) {
            return -1;
        }

        return 0;
    }

    public boolean equals(Object obj) {

        if (!(obj instanceof JCInteger)) {
            return false;
        }

        final JCInteger otherInt = (JCInteger) obj;
        return values[HIGH] == otherInt.values[HIGH]
                && values[LOW] == otherInt.values[LOW];
    }

    public short encode(final byte[] bArray, short bOff) {
        // use javacard.framework.Util.setShort() instead
        bArray[bOff++] = (byte) (values[HIGH] >>> BYTE_SIZE);
        bArray[bOff++] = (byte) (values[HIGH] & 0xFF);
        bArray[bOff++] = (byte) (values[LOW] >>> BYTE_SIZE);
        bArray[bOff++] = (byte) (values[LOW] & 0xFF);
        return bOff;
    }

    public JCInteger decode(final byte[] bArray, short bOff) {
        values[HIGH] = (short) ((bArray[bOff++] << BYTE_SIZE) | (bArray[bOff++] & 0xFF)); 
        values[LOW] = (short) ((bArray[bOff++] << BYTE_SIZE) | (bArray[bOff++] & 0xFF));
        return this;
    }

    private boolean isPositive() {
        return (values[HIGH] & 0x8000) == 0;
    }

    private void addUnsignedLow(final short yl) {
        final short xl = values[LOW];
        values[HIGH] += carryOnUnsignedAddition(xl, yl);
        values[LOW] = (short) (xl + yl);
    }

    private static short carryOnUnsignedAddition(final short x, final short y) {
        // implementation without any conditionals on the highest bits of x, y and r = x + y
        final short r = (short) (x + y);
        // uses only the sign bit on the variables including the result to see if carry will happen
        return (short) ((((x & y) | (x & ~y & ~r) | (~x & y & ~r)) >>> 15) & 1);
    }

    private static short[] multiplyUnsigned(short x, short y, short[] r) {

        // uses the fact that:
        // x * y =
        // (x1 * 2 ^ 8 + x0) * (y1 * 2 ^ 8 + y0) =
        // (x1 * y1 * 2 ^ 16) + x1 * y0 * 2 ^ 8 + x0 * y1 * 2 ^ 8 + x0 * y0 

        final short x1 = (short) ((x >>> BYTE_SIZE) & 0xFF);
        final short x0 = (short) (x & 0xFF);

        final short y1 = (short) ((y >>> BYTE_SIZE) & 0xFF);
        final short y0 = (short) (y & 0xFF);

        // TODO check uppiest bit of rh and rl

        // calculate z2 * 2 ^ (2 * 8) = x1 * y1 * 2 ^ (2 * 8) = x1 * y1 << 16,
        // store it as partial result in rh
        short rh = (short) (x1 * y1);

        // calculate z0 = x0 * y0
        short rl = (short) (x0 * y0);

        short toAdd, result;

        // calculate x1 * y0* 2 ^ 8
        short x1y0 = (short) (x1 * y0);
        rh += (x1y0 >>> 8) & 0xFF;
        toAdd = (short) ((x1y0 << 8) & 0xFF00);
        result = (short) (rl + toAdd);
        rh += carryOnUnsignedAddition(rl, toAdd);
        rl = result;

        // calculate x0 * y1* 2 ^ 8
        short x0y1 = (short) (x0 * y1);
        rh += (x0y1 >>> 8) & 0xFF;
        toAdd = (short) ((x0y1 << 8) & 0xFF00);
        result = (short) (rl + toAdd);
        rh += carryOnUnsignedAddition(rl, toAdd);
        rl = result;

        r[HIGH] = rh;
        r[LOW] = rl;
        return r;
    }

    private static short numberOfLeadingZeros(short ih, short il) {

        if (ih != 0) {
            for (short i = 0; i < SHORT_SIZE; i++) {
                if (ih < 0) {
                    return i;
                }
                ih <<= 1;
            }
        }

        if (il != 0) {
            for (short i = SHORT_SIZE; i < INTEGER_SIZE; i++) {
                if (il < 0) {
                    return i;
                }
                il <<= 1;
            }
        }

        return INTEGER_SIZE;
    }
}