/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

package org.apache.commons.math.random;

import java.io.Serializable;
import java.security.MessageDigest;
import java.security.SecureRandom;
import java.security.NoSuchAlgorithmException;
import java.security.NoSuchProviderException;
import java.util.Collection;

import org.apache.commons.math.MathRuntimeException;
import org.apache.commons.math.util.MathUtils;

/**
 * Implements the {@link RandomData} interface using a {@link RandomGenerator}
 * instance to generate non-secure data and a {@link java.security.SecureRandom}
 * instance to provide data for the <code>nextSecureXxx</code> methods. If no
 * <code>RandomGenerator</code> is provided in the constructor, the default is
 * to use a generator based on {@link java.util.Random}. To plug in a different
 * implementation, either implement <code>RandomGenerator</code> directly or
 * extend {@link AbstractRandomGenerator}.
 * <p>
 * Supports reseeding the underlying pseudo-random number generator (PRNG). The
 * <code>SecurityProvider</code> and <code>Algorithm</code> used by the
 * <code>SecureRandom</code> instance can also be reset.
 * </p>
 * <p>
 * For details on the default PRNGs, see {@link java.util.Random} and
 * {@link java.security.SecureRandom}.
 * </p>
 * <p>
 * <strong>Usage Notes</strong>:
 * <ul>
 * <li>
 * Instance variables are used to maintain <code>RandomGenerator</code> and
 * <code>SecureRandom</code> instances used in data generation. Therefore, to
 * generate a random sequence of values or strings, you should use just
 * <strong>one</strong> <code>RandomDataImpl</code> instance repeatedly.</li>
 * <li>
 * The "secure" methods are *much* slower. These should be used only when a
 * cryptographically secure random sequence is required. A secure random
 * sequence is a sequence of pseudo-random values which, in addition to being
 * well-dispersed (so no subsequence of values is an any more likely than other
 * subsequence of the the same length), also has the additional property that
 * knowledge of values generated up to any point in the sequence does not make
 * it any easier to predict subsequent values.</li>
 * <li>
 * When a new <code>RandomDataImpl</code> is created, the underlying random
 * number generators are <strong>not</strong> intialized. If you do not
 * explicitly seed the default non-secure generator, it is seeded with the
 * current time in milliseconds on first use. The same holds for the secure
 * generator. If you provide a <code>RandomGenerator</code> to the constructor,
 * however, this generator is not reseeded by the constructor nor is it reseeded
 * on first use.</li>
 * <li>
 * The <code>reSeed</code> and <code>reSeedSecure</code> methods delegate to the
 * corresponding methods on the underlying <code>RandomGenerator</code> and
 * <code>SecureRandom</code> instances. Therefore, <code>reSeed(long)</code>
 * fully resets the initial state of the non-secure random number generator (so
 * that reseeding with a specific value always results in the same subsequent
 * random sequence); whereas reSeedSecure(long) does <strong>not</strong>
 * reinitialize the secure random number generator (so secure sequences started
 * with calls to reseedSecure(long) won't be identical).</li>
 * <li>
 * This implementation is not synchronized.
 * </ul>
 * </p>
 * 
 * @version $Revision$ $Date$
 */
public class RandomDataImpl implements RandomData, Serializable {

    /** Serializable version identifier */
    private static final long serialVersionUID = -626730818244969716L;

    /** underlying random number generator */
    private RandomGenerator rand = null;

    /** underlying secure random number generator */
    private SecureRandom secRand = null;

    /**
     * Construct a RandomDataImpl.
     */
    public RandomDataImpl() {
    }

    /**
     * Construct a RandomDataImpl using the supplied {@link RandomGenerator} as
     * the source of (non-secure) random data.
     * 
     * @param rand
     *            the source of (non-secure) random data
     * @since 1.1
     */
    public RandomDataImpl(RandomGenerator rand) {
        super();
        this.rand = rand;
    }

    /**
     * {@inheritDoc}
     * <p>
     * <strong>Algorithm Description:</strong> hex strings are generated using a
     * 2-step process.
     * <ol>
     * <li>
     * len/2+1 binary bytes are generated using the underlying Random</li>
     * <li>
     * Each binary byte is translated into 2 hex digits</li>
     * </ol>
     * </p>
     * 
     * @param len
     *            the desired string length.
     * @return the random string.
     */
    public String nextHexString(int len) {
        if (len <= 0) {
            throw MathRuntimeException.createIllegalArgumentException(
                  "length must be positive ({0})", len);
        }

        // Get a random number generator
        RandomGenerator ran = getRan();

        // Initialize output buffer
        StringBuffer outBuffer = new StringBuffer();

        // Get int(len/2)+1 random bytes
        byte[] randomBytes = new byte[(len / 2) + 1];
        ran.nextBytes(randomBytes);

        // Convert each byte to 2 hex digits
        for (int i = 0; i < randomBytes.length; i++) {
            Integer c = Integer.valueOf(randomBytes[i]);

            /*
             * Add 128 to byte value to make interval 0-255 before doing hex
             * conversion. This guarantees <= 2 hex digits from toHexString()
             * toHexString would otherwise add 2^32 to negative arguments.
             */
            String hex = Integer.toHexString(c.intValue() + 128);

            // Make sure we add 2 hex digits for each byte
            if (hex.length() == 1) {
                hex = "0" + hex;
            }
            outBuffer.append(hex);
        }
        return outBuffer.toString().substring(0, len);
    }

    /**
     * Generate a random int value uniformly distributed between
     * <code>lower</code> and <code>upper</code>, inclusive.
     * 
     * @param lower
     *            the lower bound.
     * @param upper
     *            the upper bound.
     * @return the random integer.
     */
    public int nextInt(int lower, int upper) {
        if (lower >= upper) {
            throw MathRuntimeException.createIllegalArgumentException(
                    "upper bound ({0}) must be greater than lower bound ({1})",
                    upper, lower);
        }
        RandomGenerator rand = getRan();
        double r = rand.nextDouble();
        return (int) ((r * upper) + ((1.0 - r) * lower) + r);
    }

    /**
     * Generate a random long value uniformly distributed between
     * <code>lower</code> and <code>upper</code>, inclusive.
     * 
     * @param lower
     *            the lower bound.
     * @param upper
     *            the upper bound.
     * @return the random integer.
     */
    public long nextLong(long lower, long upper) {
        if (lower >= upper) {
            throw MathRuntimeException.createIllegalArgumentException(
                  "upper bound ({0}) must be greater than lower bound ({1})",
                  upper, lower);
        }
        RandomGenerator rand = getRan();
        double r = rand.nextDouble();
        return (long) ((r * upper) + ((1.0 - r) * lower) + r);
    }

    /**
     * {@inheritDoc}
     * <p>
     * <strong>Algorithm Description:</strong> hex strings are generated in
     * 40-byte segments using a 3-step process.
     * <ol>
     * <li>
     * 20 random bytes are generated using the underlying
     * <code>SecureRandom</code>.</li>
     * <li>
     * SHA-1 hash is applied to yield a 20-byte binary digest.</li>
     * <li>
     * Each byte of the binary digest is converted to 2 hex digits.</li>
     * </ol>
     * </p>
     * 
     * @param len
     *            the length of the generated string
     * @return the random string
     */
    public String nextSecureHexString(int len) {
        if (len <= 0) {
            throw MathRuntimeException.createIllegalArgumentException(
                  "length must be positive ({0})", len);
        }

        // Get SecureRandom and setup Digest provider
        SecureRandom secRan = getSecRan();
        MessageDigest alg = null;
        try {
            alg = MessageDigest.getInstance("SHA-1");
        } catch (NoSuchAlgorithmException ex) {
            return null; // gulp FIXME? -- this *should* never fail.
        }
        alg.reset();

        // Compute number of iterations required (40 bytes each)
        int numIter = (len / 40) + 1;

        StringBuffer outBuffer = new StringBuffer();
        for (int iter = 1; iter < numIter + 1; iter++) {
            byte[] randomBytes = new byte[40];
            secRan.nextBytes(randomBytes);
            alg.update(randomBytes);

            // Compute hash -- will create 20-byte binary hash
            byte hash[] = alg.digest();

            // Loop over the hash, converting each byte to 2 hex digits
            for (int i = 0; i < hash.length; i++) {
                Integer c = Integer.valueOf(hash[i]);

                /*
                 * Add 128 to byte value to make interval 0-255 This guarantees
                 * <= 2 hex digits from toHexString() toHexString would
                 * otherwise add 2^32 to negative arguments
                 */
                String hex = Integer.toHexString(c.intValue() + 128);

                // Keep strings uniform length -- guarantees 40 bytes
                if (hex.length() == 1) {
                    hex = "0" + hex;
                }
                outBuffer.append(hex);
            }
        }
        return outBuffer.toString().substring(0, len);
    }

    /**
     * Generate a random int value uniformly distributed between
     * <code>lower</code> and <code>upper</code>, inclusive. This algorithm uses
     * a secure random number generator.
     * 
     * @param lower
     *            the lower bound.
     * @param upper
     *            the upper bound.
     * @return the random integer.
     */
    public int nextSecureInt(int lower, int upper) {
        if (lower >= upper) {
            throw MathRuntimeException.createIllegalArgumentException(
                  "upper bound ({0}) must be greater than lower bound ({1})",
                  upper, lower);
        }
        SecureRandom sec = getSecRan();
        return lower + (int) (sec.nextDouble() * (upper - lower + 1));
    }

    /**
     * Generate a random long value uniformly distributed between
     * <code>lower</code> and <code>upper</code>, inclusive. This algorithm uses
     * a secure random number generator.
     * 
     * @param lower
     *            the lower bound.
     * @param upper
     *            the upper bound.
     * @return the random integer.
     */
    public long nextSecureLong(long lower, long upper) {
        if (lower >= upper) {
            throw MathRuntimeException.createIllegalArgumentException(
                  "upper bound ({0}) must be greater than lower bound ({1})",
                  upper, lower);
        }
        SecureRandom sec = getSecRan();
        return lower + (long) (sec.nextDouble() * (upper - lower + 1));
    }

    /**
     * {@inheritDoc}
     * <p>
     * <strong>Algorithm Description</strong>: For small means, uses simulation
     * of a Poisson process using Uniform deviates, as described <a
     * href="http://irmi.epfl.ch/cmos/Pmmi/interactive/rng7.htm"> here.</a>
     * </p>
     * <p>
     * The Poisson process (and hence value returned) is bounded by 1000 * mean.
     * </p>
     * 
     * <p>
     * For large means, uses a reject method as described in <a
     * href="http://cg.scs.carleton.ca/~luc/rnbookindex.html">Non-Uniform Random
     * Variate Generation</a>
     * </p>
     * 
     * <p>
     * References:
     * <ul>
     * <li>Devroye, Luc. (1986). <i>Non-Uniform Random Variate Generation</i>.
     * New York, NY. Springer-Verlag</li>
     * </ul>
     * </p>
     * 
     * @param mean
     *            mean of the Poisson distribution.
     * @return the random Poisson value.
     */
    public long nextPoisson(double mean) {
        if (mean <= 0) {
            throw MathRuntimeException.createIllegalArgumentException(
                  "the Poisson mean must be positive ({0})", mean);
        }

        RandomGenerator rand = getRan();

        double pivot = 6.0;
        if (mean < pivot) {
            double p = Math.exp(-mean);
            long n = 0;
            double r = 1.0d;
            double rnd = 1.0d;

            while (n < 1000 * mean) {
                rnd = rand.nextDouble();
                r = r * rnd;
                if (r >= p) {
                    n++;
                } else {
                    return n;
                }
            }
            return n;
        } else {
            double mu = Math.floor(mean);
            double delta = Math.floor(pivot + (mu - pivot) / 2.0); // integer
            // between 6
            // and mean
            double mu2delta = 2.0 * mu + delta;
            double muDeltaHalf = mu + delta / 2.0;
            double logMeanMu = Math.log(mean / mu);

            double muFactorialLog = MathUtils.factorialLog((int) mu);

            double c1 = Math.sqrt(Math.PI * mu / 2.0);
            double c2 = c1 +
                        Math.sqrt(Math.PI * muDeltaHalf /
                                  (2.0 * Math.exp(1.0 / mu2delta)));
            double c3 = c2 + 2.0;
            double c4 = c3 + Math.exp(1.0 / 78.0);
            double c = c4 + 2.0 / delta * mu2delta *
                       Math.exp(-delta / mu2delta * (1.0 + delta / 2.0));

            double y = 0.0;
            double x = 0.0;
            double w = Double.POSITIVE_INFINITY;

            boolean accept = false;
            while (!accept) {
                double u = nextUniform(0.0, c);
                double e = nextExponential(mean);

                if (u <= c1) {
                    double z = nextGaussian(0.0, 1.0);
                    y = -Math.abs(z) * Math.sqrt(mu) - 1.0;
                    x = Math.floor(y);
                    w = -z * z / 2.0 - e - x * logMeanMu;
                    if (x < -mu) {
                        w = Double.POSITIVE_INFINITY;
                    }
                } else if (c1 < u && u <= c2) {
                    double z = nextGaussian(0.0, 1.0);
                    y = 1.0 + Math.abs(z) * Math.sqrt(muDeltaHalf);
                    x = Math.ceil(y);
                    w = (-y * y + 2.0 * y) / mu2delta - e - x * logMeanMu;
                    if (x > delta) {
                        w = Double.POSITIVE_INFINITY;
                    }
                } else if (c2 < u && u <= c3) {
                    x = 0.0;
                    w = -e;
                } else if (c3 < u && u <= c4) {
                    x = 1.0;
                    w = -e - logMeanMu;
                } else if (c4 < u) {
                    double v = nextExponential(mean);
                    y = delta + v * 2.0 / delta * mu2delta;
                    x = Math.ceil(y);
                    w = -delta / mu2delta * (1.0 + y / 2.0) - e - x * logMeanMu;
                }
                accept = (w <= x * Math.log(mu) -
                         MathUtils.factorialLog((int) (mu + x)) /
                         muFactorialLog);
            }
            // cast to long is acceptable because both x and mu are whole
            // numbers.
            return (long) (x + mu);
        }
    }

    /**
     * Generate a random value from a Normal (a.k.a. Gaussian) distribution with
     * the given mean, <code>mu</code> and the given standard deviation,
     * <code>sigma</code>.
     * 
     * @param mu
     *            the mean of the distribution
     * @param sigma
     *            the standard deviation of the distribution
     * @return the random Normal value
     */
    public double nextGaussian(double mu, double sigma) {
        if (sigma <= 0) {
            throw MathRuntimeException.createIllegalArgumentException(
                  "standard deviation must be positive ({0})", sigma);
        }
        RandomGenerator rand = getRan();
        return sigma * rand.nextGaussian() + mu;
    }

    /**
     * Returns a random value from an Exponential distribution with the given
     * mean.
     * <p>
     * <strong>Algorithm Description</strong>: Uses the <a
     * href="http://www.jesus.ox.ac.uk/~clifford/a5/chap1/node5.html"> Inversion
     * Method</a> to generate exponentially distributed random values from
     * uniform deviates.
     * </p>
     * 
     * @param mean
     *            the mean of the distribution
     * @return the random Exponential value
     */
    public double nextExponential(double mean) {
        if (mean < 0.0) {
            throw MathRuntimeException.createIllegalArgumentException(
                  "mean must be positive ({0})", mean);
        }
        RandomGenerator rand = getRan();
        double unif = rand.nextDouble();
        while (unif == 0.0d) {
            unif = rand.nextDouble();
        }
        return -mean * Math.log(unif);
    }

    /**
     * {@inheritDoc}
     * <p>
     * <strong>Algorithm Description</strong>: scales the output of
     * Random.nextDouble(), but rejects 0 values (i.e., will generate another
     * random double if Random.nextDouble() returns 0). This is necessary to
     * provide a symmetric output interval (both endpoints excluded).
     * </p>
     * 
     * @param lower
     *            the lower bound.
     * @param upper
     *            the upper bound.
     * @return a uniformly distributed random value from the interval (lower,
     *         upper)
     */
    public double nextUniform(double lower, double upper) {
        if (lower >= upper) {
            throw MathRuntimeException.createIllegalArgumentException(
                  "upper bound ({0}) must be greater than lower bound ({1})",
                  upper, lower);
        }
        RandomGenerator rand = getRan();

        // ensure nextDouble() isn't 0.0
        double u = rand.nextDouble();
        while (u <= 0.0) {
            u = rand.nextDouble();
        }

        return lower + u * (upper - lower);
    }

    /**
     * Returns the RandomGenerator used to generate non-secure random data.
     * <p>
     * Creates and initializes a default generator if null.
     * </p>
     * 
     * @return the Random used to generate random data
     * @since 1.1
     */
    private RandomGenerator getRan() {
        if (rand == null) {
            rand = new JDKRandomGenerator();
            rand.setSeed(System.currentTimeMillis());
        }
        return rand;
    }

    /**
     * Returns the SecureRandom used to generate secure random data.
     * <p>
     * Creates and initializes if null.
     * </p>
     * 
     * @return the SecureRandom used to generate secure random data
     */
    private SecureRandom getSecRan() {
        if (secRand == null) {
            secRand = new SecureRandom();
            secRand.setSeed(System.currentTimeMillis());
        }
        return secRand;
    }

    /**
     * Reseeds the random number generator with the supplied seed.
     * <p>
     * Will create and initialize if null.
     * </p>
     * 
     * @param seed
     *            the seed value to use
     */
    public void reSeed(long seed) {
        if (rand == null) {
            rand = new JDKRandomGenerator();
        }
        rand.setSeed(seed);
    }

    /**
     * Reseeds the secure random number generator with the current time in
     * milliseconds.
     * <p>
     * Will create and initialize if null.
     * </p>
     */
    public void reSeedSecure() {
        if (secRand == null) {
            secRand = new SecureRandom();
        }
        secRand.setSeed(System.currentTimeMillis());
    }

    /**
     * Reseeds the secure random number generator with the supplied seed.
     * <p>
     * Will create and initialize if null.
     * </p>
     * 
     * @param seed
     *            the seed value to use
     */
    public void reSeedSecure(long seed) {
        if (secRand == null) {
            secRand = new SecureRandom();
        }
        secRand.setSeed(seed);
    }

    /**
     * Reseeds the random number generator with the current time in
     * milliseconds.
     */
    public void reSeed() {
        if (rand == null) {
            rand = new JDKRandomGenerator();
        }
        rand.setSeed(System.currentTimeMillis());
    }

    /**
     * Sets the PRNG algorithm for the underlying SecureRandom instance using
     * the Security Provider API. The Security Provider API is defined in <a
     * href =
     * "http://java.sun.com/j2se/1.3/docs/guide/security/CryptoSpec.html#AppA">
     * Java Cryptography Architecture API Specification & Reference.</a>
     * <p>
     * <strong>USAGE NOTE:</strong> This method carries <i>significant</i>
     * overhead and may take several seconds to execute.
     * </p>
     * 
     * @param algorithm
     *            the name of the PRNG algorithm
     * @param provider
     *            the name of the provider
     * @throws NoSuchAlgorithmException
     *             if the specified algorithm is not available
     * @throws NoSuchProviderException
     *             if the specified provider is not installed
     */
    public void setSecureAlgorithm(String algorithm, String provider)
            throws NoSuchAlgorithmException, NoSuchProviderException {
        secRand = SecureRandom.getInstance(algorithm, provider);
    }

    /**
     * Generates an integer array of length <code>k</code> whose entries are
     * selected randomly, without repetition, from the integers
     * <code>0 through n-1</code> (inclusive).
     * <p>
     * Generated arrays represent permutations of <code>n</code> taken
     * <code>k</code> at a time.
     * </p>
     * <p>
     * <strong>Preconditions:</strong>
     * <ul>
     * <li> <code>k <= n</code></li>
     * <li> <code>n > 0</code></li>
     * </ul>
     * If the preconditions are not met, an IllegalArgumentException is thrown.
     * </p>
     * <p>
     * Uses a 2-cycle permutation shuffle. The shuffling process is described <a
     * href="http://www.maths.abdn.ac.uk/~igc/tch/mx4002/notes/node83.html">
     * here</a>.
     * </p>
     * 
     * @param n
     *            domain of the permutation (must be positive)
     * @param k
     *            size of the permutation (must satisfy 0 < k <= n).
     * @return the random permutation as an int array
     */
    public int[] nextPermutation(int n, int k) {
        if (k > n) {
            throw MathRuntimeException.createIllegalArgumentException(
                  "permutation k ({0}) exceeds n ({1})", k, n);
        }
        if (k == 0) {
            throw MathRuntimeException.createIllegalArgumentException(
                  "permutation k ({0}) must be positive", k);
        }

        int[] index = getNatural(n);
        shuffle(index, n - k);
        int[] result = new int[k];
        for (int i = 0; i < k; i++) {
            result[i] = index[n - i - 1];
        }

        return result;
    }

    /**
     * Uses a 2-cycle permutation shuffle to generate a random permutation.
     * <strong>Algorithm Description</strong>: Uses a 2-cycle permutation
     * shuffle to generate a random permutation of <code>c.size()</code> and
     * then returns the elements whose indexes correspond to the elements of the
     * generated permutation. This technique is described, and proven to
     * generate random samples, <a
     * href="http://www.maths.abdn.ac.uk/~igc/tch/mx4002/notes/node83.html">
     * here</a>
     * 
     * @param c
     *            Collection to sample from.
     * @param k
     *            sample size.
     * @return the random sample.
     */
    public Object[] nextSample(Collection<?> c, int k) {
        int len = c.size();
        if (k > len) {
            throw MathRuntimeException.createIllegalArgumentException(
                  "sample size ({0}) exceeds collection size ({1})");
        }
        if (k <= 0) {
            throw MathRuntimeException.createIllegalArgumentException(
                  "sample size must be positive ({0})", k);
        }

        Object[] objects = c.toArray();
        int[] index = nextPermutation(len, k);
        Object[] result = new Object[k];
        for (int i = 0; i < k; i++) {
            result[i] = objects[index[i]];
        }
        return result;
    }

    // ------------------------Private methods----------------------------------

    /**
     * Uses a 2-cycle permutation shuffle to randomly re-order the last elements
     * of list.
     * 
     * @param list
     *            list to be shuffled
     * @param end
     *            element past which shuffling begins
     */
    private void shuffle(int[] list, int end) {
        int target = 0;
        for (int i = list.length - 1; i >= end; i--) {
            if (i == 0) {
                target = 0;
            } else {
                target = nextInt(0, i);
            }
            int temp = list[target];
            list[target] = list[i];
            list[i] = temp;
        }
    }

    /**
     * Returns an array representing n.
     * 
     * @param n
     *            the natural number to represent
     * @return array with entries = elements of n
     */
    private int[] getNatural(int n) {
        int[] natural = new int[n];
        for (int i = 0; i < n; i++) {
            natural[i] = i;
        }
        return natural;
    }

}
