/*
 * 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.math3.util;

import java.io.PrintStream;

import org.apache.commons.math3.exception.DimensionMismatchException;

/** Class used to compute the classical functions tables.
 * @version $Id: FastMathCalc.java 1416643 2012-12-03 19:37:14Z tn $
 * @since 3.0
 */
class FastMathCalc {

    /**
     * 0x40000000 - used to split a double into two parts, both with the low order bits cleared.
     * Equivalent to 2^30.
     */
    private static final long HEX_40000000 = 0x40000000L; // 1073741824L

    /** Factorial table, for Taylor series expansions. 0!, 1!, 2!, ... 19! */
    private static final double FACT[] = new double[]
        {
        +1.0d,                        // 0
        +1.0d,                        // 1
        +2.0d,                        // 2
        +6.0d,                        // 3
        +24.0d,                       // 4
        +120.0d,                      // 5
        +720.0d,                      // 6
        +5040.0d,                     // 7
        +40320.0d,                    // 8
        +362880.0d,                   // 9
        +3628800.0d,                  // 10
        +39916800.0d,                 // 11
        +479001600.0d,                // 12
        +6227020800.0d,               // 13
        +87178291200.0d,              // 14
        +1307674368000.0d,            // 15
        +20922789888000.0d,           // 16
        +355687428096000.0d,          // 17
        +6402373705728000.0d,         // 18
        +121645100408832000.0d,       // 19
        };

    /** Coefficients for slowLog. */
    private static final double LN_SPLIT_COEF[][] = {
        {2.0, 0.0},
        {0.6666666269302368, 3.9736429850260626E-8},
        {0.3999999761581421, 2.3841857910019882E-8},
        {0.2857142686843872, 1.7029898543501842E-8},
        {0.2222222089767456, 1.3245471311735498E-8},
        {0.1818181574344635, 2.4384203044354907E-8},
        {0.1538461446762085, 9.140260083262505E-9},
        {0.13333332538604736, 9.220590270857665E-9},
        {0.11764700710773468, 1.2393345855018391E-8},
        {0.10526403784751892, 8.251545029714408E-9},
        {0.0952233225107193, 1.2675934823758863E-8},
        {0.08713622391223907, 1.1430250008909141E-8},
        {0.07842259109020233, 2.404307984052299E-9},
        {0.08371849358081818, 1.176342548272881E-8},
        {0.030589580535888672, 1.2958646899018938E-9},
        {0.14982303977012634, 1.225743062930824E-8},
    };

    /** Table start declaration. */
    private static final String TABLE_START_DECL = "    {";

    /** Table end declaration. */
    private static final String TABLE_END_DECL   = "    };";

    /**
     * Private Constructor.
     */
    private FastMathCalc() {
    }

    /** Build the sine and cosine tables.
     * @param SINE_TABLE_A table of the most significant part of the sines
     * @param SINE_TABLE_B table of the least significant part of the sines
     * @param COSINE_TABLE_A table of the most significant part of the cosines
     * @param COSINE_TABLE_B table of the most significant part of the cosines
     * @param SINE_TABLE_LEN length of the tables
     * @param TANGENT_TABLE_A table of the most significant part of the tangents
     * @param TANGENT_TABLE_B table of the most significant part of the tangents
     */
    @SuppressWarnings("unused")
    private static void buildSinCosTables(double[] SINE_TABLE_A, double[] SINE_TABLE_B,
                                          double[] COSINE_TABLE_A, double[] COSINE_TABLE_B,
                                          int SINE_TABLE_LEN, double[] TANGENT_TABLE_A, double[] TANGENT_TABLE_B) {
        final double result[] = new double[2];

        /* Use taylor series for 0 <= x <= 6/8 */
        for (int i = 0; i < 7; i++) {
            double x = i / 8.0;

            slowSin(x, result);
            SINE_TABLE_A[i] = result[0];
            SINE_TABLE_B[i] = result[1];

            slowCos(x, result);
            COSINE_TABLE_A[i] = result[0];
            COSINE_TABLE_B[i] = result[1];
        }

        /* Use angle addition formula to complete table to 13/8, just beyond pi/2 */
        for (int i = 7; i < SINE_TABLE_LEN; i++) {
            double xs[] = new double[2];
            double ys[] = new double[2];
            double as[] = new double[2];
            double bs[] = new double[2];
            double temps[] = new double[2];

            if ( (i & 1) == 0) {
                // Even, use double angle
                xs[0] = SINE_TABLE_A[i/2];
                xs[1] = SINE_TABLE_B[i/2];
                ys[0] = COSINE_TABLE_A[i/2];
                ys[1] = COSINE_TABLE_B[i/2];

                /* compute sine */
                splitMult(xs, ys, result);
                SINE_TABLE_A[i] = result[0] * 2.0;
                SINE_TABLE_B[i] = result[1] * 2.0;

                /* Compute cosine */
                splitMult(ys, ys, as);
                splitMult(xs, xs, temps);
                temps[0] = -temps[0];
                temps[1] = -temps[1];
                splitAdd(as, temps, result);
                COSINE_TABLE_A[i] = result[0];
                COSINE_TABLE_B[i] = result[1];
            } else {
                xs[0] = SINE_TABLE_A[i/2];
                xs[1] = SINE_TABLE_B[i/2];
                ys[0] = COSINE_TABLE_A[i/2];
                ys[1] = COSINE_TABLE_B[i/2];
                as[0] = SINE_TABLE_A[i/2+1];
                as[1] = SINE_TABLE_B[i/2+1];
                bs[0] = COSINE_TABLE_A[i/2+1];
                bs[1] = COSINE_TABLE_B[i/2+1];

                /* compute sine */
                splitMult(xs, bs, temps);
                splitMult(ys, as, result);
                splitAdd(result, temps, result);
                SINE_TABLE_A[i] = result[0];
                SINE_TABLE_B[i] = result[1];

                /* Compute cosine */
                splitMult(ys, bs, result);
                splitMult(xs, as, temps);
                temps[0] = -temps[0];
                temps[1] = -temps[1];
                splitAdd(result, temps, result);
                COSINE_TABLE_A[i] = result[0];
                COSINE_TABLE_B[i] = result[1];
            }
        }

        /* Compute tangent = sine/cosine */
        for (int i = 0; i < SINE_TABLE_LEN; i++) {
            double xs[] = new double[2];
            double ys[] = new double[2];
            double as[] = new double[2];

            as[0] = COSINE_TABLE_A[i];
            as[1] = COSINE_TABLE_B[i];

            splitReciprocal(as, ys);

            xs[0] = SINE_TABLE_A[i];
            xs[1] = SINE_TABLE_B[i];

            splitMult(xs, ys, as);

            TANGENT_TABLE_A[i] = as[0];
            TANGENT_TABLE_B[i] = as[1];
        }

    }

    /**
     *  For x between 0 and pi/4 compute cosine using Talor series
     *  cos(x) = 1 - x^2/2! + x^4/4! ...
     * @param x number from which cosine is requested
     * @param result placeholder where to put the result in extended precision
     * (may be null)
     * @return cos(x)
     */
    static double slowCos(final double x, final double result[]) {

        final double xs[] = new double[2];
        final double ys[] = new double[2];
        final double facts[] = new double[2];
        final double as[] = new double[2];
        split(x, xs);
        ys[0] = ys[1] = 0.0;

        for (int i = FACT.length-1; i >= 0; i--) {
            splitMult(xs, ys, as);
            ys[0] = as[0]; ys[1] = as[1];

            if ( (i & 1) != 0) { // skip odd entries
                continue;
            }

            split(FACT[i], as);
            splitReciprocal(as, facts);

            if ( (i & 2) != 0 ) { // alternate terms are negative
                facts[0] = -facts[0];
                facts[1] = -facts[1];
            }

            splitAdd(ys, facts, as);
            ys[0] = as[0]; ys[1] = as[1];
        }

        if (result != null) {
            result[0] = ys[0];
            result[1] = ys[1];
        }

        return ys[0] + ys[1];
    }

    /**
     * For x between 0 and pi/4 compute sine using Taylor expansion:
     * sin(x) = x - x^3/3! + x^5/5! - x^7/7! ...
     * @param x number from which sine is requested
     * @param result placeholder where to put the result in extended precision
     * (may be null)
     * @return sin(x)
     */
    static double slowSin(final double x, final double result[]) {
        final double xs[] = new double[2];
        final double ys[] = new double[2];
        final double facts[] = new double[2];
        final double as[] = new double[2];
        split(x, xs);
        ys[0] = ys[1] = 0.0;

        for (int i = FACT.length-1; i >= 0; i--) {
            splitMult(xs, ys, as);
            ys[0] = as[0]; ys[1] = as[1];

            if ( (i & 1) == 0) { // Ignore even numbers
                continue;
            }

            split(FACT[i], as);
            splitReciprocal(as, facts);

            if ( (i & 2) != 0 ) { // alternate terms are negative
                facts[0] = -facts[0];
                facts[1] = -facts[1];
            }

            splitAdd(ys, facts, as);
            ys[0] = as[0]; ys[1] = as[1];
        }

        if (result != null) {
            result[0] = ys[0];
            result[1] = ys[1];
        }

        return ys[0] + ys[1];
    }


    /**
     *  For x between 0 and 1, returns exp(x), uses extended precision
     *  @param x argument of exponential
     *  @param result placeholder where to place exp(x) split in two terms
     *  for extra precision (i.e. exp(x) = result[0] + result[1]
     *  @return exp(x)
     */
    static double slowexp(final double x, final double result[]) {
        final double xs[] = new double[2];
        final double ys[] = new double[2];
        final double facts[] = new double[2];
        final double as[] = new double[2];
        split(x, xs);
        ys[0] = ys[1] = 0.0;

        for (int i = FACT.length-1; i >= 0; i--) {
            splitMult(xs, ys, as);
            ys[0] = as[0];
            ys[1] = as[1];

            split(FACT[i], as);
            splitReciprocal(as, facts);

            splitAdd(ys, facts, as);
            ys[0] = as[0];
            ys[1] = as[1];
        }

        if (result != null) {
            result[0] = ys[0];
            result[1] = ys[1];
        }

        return ys[0] + ys[1];
    }

    /** Compute split[0], split[1] such that their sum is equal to d,
     * and split[0] has its 30 least significant bits as zero.
     * @param d number to split
     * @param split placeholder where to place the result
     */
    private static void split(final double d, final double split[]) {
        if (d < 8e298 && d > -8e298) {
            final double a = d * HEX_40000000;
            split[0] = (d + a) - a;
            split[1] = d - split[0];
        } else {
            final double a = d * 9.31322574615478515625E-10;
            split[0] = (d + a - d) * HEX_40000000;
            split[1] = d - split[0];
        }
    }

    /** Recompute a split.
     * @param a input/out array containing the split, changed
     * on output
     */
    private static void resplit(final double a[]) {
        final double c = a[0] + a[1];
        final double d = -(c - a[0] - a[1]);

        if (c < 8e298 && c > -8e298) { // MAGIC NUMBER
            double z = c * HEX_40000000;
            a[0] = (c + z) - z;
            a[1] = c - a[0] + d;
        } else {
            double z = c * 9.31322574615478515625E-10;
            a[0] = (c + z - c) * HEX_40000000;
            a[1] = c - a[0] + d;
        }
    }

    /** Multiply two numbers in split form.
     * @param a first term of multiplication
     * @param b second term of multiplication
     * @param ans placeholder where to put the result
     */
    private static void splitMult(double a[], double b[], double ans[]) {
        ans[0] = a[0] * b[0];
        ans[1] = a[0] * b[1] + a[1] * b[0] + a[1] * b[1];

        /* Resplit */
        resplit(ans);
    }

    /** Add two numbers in split form.
     * @param a first term of addition
     * @param b second term of addition
     * @param ans placeholder where to put the result
     */
    private static void splitAdd(final double a[], final double b[], final double ans[]) {
        ans[0] = a[0] + b[0];
        ans[1] = a[1] + b[1];

        resplit(ans);
    }

    /** Compute the reciprocal of in.  Use the following algorithm.
     *  in = c + d.
     *  want to find x + y such that x+y = 1/(c+d) and x is much
     *  larger than y and x has several zero bits on the right.
     *
     *  Set b = 1/(2^22),  a = 1 - b.  Thus (a+b) = 1.
     *  Use following identity to compute (a+b)/(c+d)
     *
     *  (a+b)/(c+d)  =   a/c   +    (bc - ad) / (c^2 + cd)
     *  set x = a/c  and y = (bc - ad) / (c^2 + cd)
     *  This will be close to the right answer, but there will be
     *  some rounding in the calculation of X.  So by carefully
     *  computing 1 - (c+d)(x+y) we can compute an error and
     *  add that back in.   This is done carefully so that terms
     *  of similar size are subtracted first.
     *  @param in initial number, in split form
     *  @param result placeholder where to put the result
     */
    static void splitReciprocal(final double in[], final double result[]) {
        final double b = 1.0/4194304.0;
        final double a = 1.0 - b;

        if (in[0] == 0.0) {
            in[0] = in[1];
            in[1] = 0.0;
        }

        result[0] = a / in[0];
        result[1] = (b*in[0]-a*in[1]) / (in[0]*in[0] + in[0]*in[1]);

        if (result[1] != result[1]) { // can happen if result[1] is NAN
            result[1] = 0.0;
        }

        /* Resplit */
        resplit(result);

        for (int i = 0; i < 2; i++) {
            /* this may be overkill, probably once is enough */
            double err = 1.0 - result[0] * in[0] - result[0] * in[1] -
            result[1] * in[0] - result[1] * in[1];
            /*err = 1.0 - err; */
            err = err * (result[0] + result[1]);
            /*printf("err = %16e\n", err); */
            result[1] += err;
        }
    }

    /** Compute (a[0] + a[1]) * (b[0] + b[1]) in extended precision.
     * @param a first term of the multiplication
     * @param b second term of the multiplication
     * @param result placeholder where to put the result
     */
    private static void quadMult(final double a[], final double b[], final double result[]) {
        final double xs[] = new double[2];
        final double ys[] = new double[2];
        final double zs[] = new double[2];

        /* a[0] * b[0] */
        split(a[0], xs);
        split(b[0], ys);
        splitMult(xs, ys, zs);

        result[0] = zs[0];
        result[1] = zs[1];

        /* a[0] * b[1] */
        split(b[1], ys);
        splitMult(xs, ys, zs);

        double tmp = result[0] + zs[0];
        result[1] = result[1] - (tmp - result[0] - zs[0]);
        result[0] = tmp;
        tmp = result[0] + zs[1];
        result[1] = result[1] - (tmp - result[0] - zs[1]);
        result[0] = tmp;

        /* a[1] * b[0] */
        split(a[1], xs);
        split(b[0], ys);
        splitMult(xs, ys, zs);

        tmp = result[0] + zs[0];
        result[1] = result[1] - (tmp - result[0] - zs[0]);
        result[0] = tmp;
        tmp = result[0] + zs[1];
        result[1] = result[1] - (tmp - result[0] - zs[1]);
        result[0] = tmp;

        /* a[1] * b[0] */
        split(a[1], xs);
        split(b[1], ys);
        splitMult(xs, ys, zs);

        tmp = result[0] + zs[0];
        result[1] = result[1] - (tmp - result[0] - zs[0]);
        result[0] = tmp;
        tmp = result[0] + zs[1];
        result[1] = result[1] - (tmp - result[0] - zs[1]);
        result[0] = tmp;
    }

    /** Compute exp(p) for a integer p in extended precision.
     * @param p integer whose exponential is requested
     * @param result placeholder where to put the result in extended precision
     * @return exp(p) in standard precision (equal to result[0] + result[1])
     */
    static double expint(int p, final double result[]) {
        //double x = M_E;
        final double xs[] = new double[2];
        final double as[] = new double[2];
        final double ys[] = new double[2];
        //split(x, xs);
        //xs[1] = (double)(2.7182818284590452353602874713526625L - xs[0]);
        //xs[0] = 2.71827697753906250000;
        //xs[1] = 4.85091998273542816811e-06;
        //xs[0] = Double.longBitsToDouble(0x4005bf0800000000L);
        //xs[1] = Double.longBitsToDouble(0x3ed458a2bb4a9b00L);

        /* E */
        xs[0] = 2.718281828459045;
        xs[1] = 1.4456468917292502E-16;

        split(1.0, ys);

        while (p > 0) {
            if ((p & 1) != 0) {
                quadMult(ys, xs, as);
                ys[0] = as[0]; ys[1] = as[1];
            }

            quadMult(xs, xs, as);
            xs[0] = as[0]; xs[1] = as[1];

            p >>= 1;
        }

        if (result != null) {
            result[0] = ys[0];
            result[1] = ys[1];

            resplit(result);
        }

        return ys[0] + ys[1];
    }
    /** xi in the range of [1, 2].
     *                                3        5        7
     *      x+1           /          x        x        x          \
     *  ln ----- =   2 *  |  x  +   ----  +  ----  +  ---- + ...  |
     *      1-x           \          3        5        7          /
     *
     * So, compute a Remez approximation of the following function
     *
     *  ln ((sqrt(x)+1)/(1-sqrt(x)))  /  x
     *
     * This will be an even function with only positive coefficents.
     * x is in the range [0 - 1/3].
     *
     * Transform xi for input to the above function by setting
     * x = (xi-1)/(xi+1).   Input to the polynomial is x^2, then
     * the result is multiplied by x.
     * @param xi number from which log is requested
     * @return log(xi)
     */
    static double[] slowLog(double xi) {
        double x[] = new double[2];
        double x2[] = new double[2];
        double y[] = new double[2];
        double a[] = new double[2];

        split(xi, x);

        /* Set X = (x-1)/(x+1) */
        x[0] += 1.0;
        resplit(x);
        splitReciprocal(x, a);
        x[0] -= 2.0;
        resplit(x);
        splitMult(x, a, y);
        x[0] = y[0];
        x[1] = y[1];

        /* Square X -> X2*/
        splitMult(x, x, x2);


        //x[0] -= 1.0;
        //resplit(x);

        y[0] = LN_SPLIT_COEF[LN_SPLIT_COEF.length-1][0];
        y[1] = LN_SPLIT_COEF[LN_SPLIT_COEF.length-1][1];

        for (int i = LN_SPLIT_COEF.length-2; i >= 0; i--) {
            splitMult(y, x2, a);
            y[0] = a[0];
            y[1] = a[1];
            splitAdd(y, LN_SPLIT_COEF[i], a);
            y[0] = a[0];
            y[1] = a[1];
        }

        splitMult(y, x, a);
        y[0] = a[0];
        y[1] = a[1];

        return y;
    }


    /**
     * Print an array.
     * @param out text output stream where output should be printed
     * @param name array name
     * @param expectedLen expected length of the array
     * @param array2d array data
     */
    static void printarray(PrintStream out, String name, int expectedLen, double[][] array2d) {
        out.println(name);
        checkLen(expectedLen, array2d.length);
        out.println(TABLE_START_DECL + " ");
        int i = 0;
        for(double[] array : array2d) { // "double array[]" causes PMD parsing error
            out.print("        {");
            for(double d : array) { // assume inner array has very few entries
                out.printf("%-25.25s", format(d)); // multiple entries per line
            }
            out.println("}, // " + i++);
        }
        out.println(TABLE_END_DECL);
    }

    /**
     * Print an array.
     * @param out text output stream where output should be printed
     * @param name array name
     * @param expectedLen expected length of the array
     * @param array array data
     */
    static void printarray(PrintStream out, String name, int expectedLen, double[] array) {
        out.println(name + "=");
        checkLen(expectedLen, array.length);
        out.println(TABLE_START_DECL);
        for(double d : array){
            out.printf("        %s%n", format(d)); // one entry per line
        }
        out.println(TABLE_END_DECL);
    }

    /** Format a double.
     * @param d double number to format
     * @return formatted number
     */
    static String format(double d) {
        if (d != d) {
            return "Double.NaN,";
        } else {
            return ((d >= 0) ? "+" : "") + Double.toString(d) + "d,";
        }
    }

    /**
     * Check two lengths are equal.
     * @param expectedLen expected length
     * @param actual actual length
     * @exception DimensionMismatchException if the two lengths are not equal
     */
    private static void checkLen(int expectedLen, int actual)
        throws DimensionMismatchException {
        if (expectedLen != actual) {
            throw new DimensionMismatchException(actual, expectedLen);
        }
    }

}
