package com.j2medev.chapter5;/** * @name FixedPoint * @brief fixed point math operations class * @author sunyuzhe   <sunyuzhe@hotmail.com> * @version 1.16 */public final class FixedPoint{        /////////////////////////////////////////////////////////        /// Variables                                         ///        /////////////////////////////////////////////////////////        /** Public */                public static final int FIX_SHIFT = 16;                public static final int FIX_UNIT = (1<<FIX_SHIFT);                public static final int FIX_FRACMASK = (FIX_UNIT-1);                public static final int FIX_INTMASK = (~FIX_FRACMASK);                /*                  * angle constants with fixed shift of 16                 * PI = 3.1416                 * HALFPI = 1.5708                 */                public static final int FIXED_PI = 205887;                public static final int FIXED_HALFPI = 102943;                public static final int FIXED_QUARTERPI = 51471;        /** Private */                private static byte[] gP = new byte[21];                private static byte[] gA = new byte[21];                private static StringBuffer gB = new StringBuffer(23);        /////////////////////////////////////////////////////////        /// Methods        /////////////////////////////////////////////////////////        /**        * @brief converts fixed-point back to integer        * @param x fixed-point value        * @return converted integer value        */        public static final int toInt(int x) {                return x>>FIX_SHIFT;        }/// ~func        /**        * @brief converts integer value to fixed-point        * @param x integer value        * @return converted fixed-point value        */        public static final int toFix(int x) {                return x<<FIX_SHIFT;        }/// ~func        /**        * @brief multiplies fixed-point values x & y each by other        * @param x fixed-point value        * @param y fixed-point value        * @return multiplication value        */        public static final int Mul(int x, int y) {                return ((int) (((long) x * (long) y) >> FIX_SHIFT));        }/// END FUNC        /**        * @brief multiplies fixed-point values x & y each by other        * @param x fixed-point value        * @param y fixed-point value        * @return multiplication value in long type        */        public static final long lMul(int x, int y) {                return ((((long) x * (long) y) >> FIX_SHIFT));        }/// END FUNC        /**        * @name MulFixedPoint        * @brief multiplies fixed-point values x & y each by other        * @param x fixed-point value        * @param y fixed-point value        * @return multiplication value        */        public static final long MulFixedPoint(long x, long y)        {                return (long) x * (long) y;        }/// END FUNC        /**        * @brief calculates fixed-point division x by y        * @param x fixed-point divided value        * @param y fixed-point divisor value        * @return fixed-point calculated division x by y        */        public static final int Div(int x, int y) {                return (int) (((((long) x) << FIX_SHIFT << FIX_SHIFT) / y) >> FIX_SHIFT);        }/// ~func        /**         * @name Sqrt         * @brief returns square root of x         * @author Stellars Henson         * @param x value to calculate sqrt from         * @return FixedPoint sqrt value         */        public static final int Sqrt( int x ) {                /* prepare environment */                /* Fixedpoint sqrt table size */                long index = FIX_SQRT.length;                long dx, dy, darg;                long value = 0;                long arg_left = 0;                long arg_right = 0;                long left, right;                /* special circumstances */                if( x==0 )                        return 0;                /* find index, start from highest mask - the youngest 8-th octet */                     if( (x & 0xf0000000) != 0 )                        index = index - 1*(15) + ((x & 0xf0000000)>>28) - 1;                else if( (x & 0x0f000000) != 0 )                        index = index - 2*(15) + ((x & 0x0f000000)>>24) - 1;                else if( (x & 0x00f00000) != 0 )                        index = index - 3*(15) + ((x & 0x00f00000)>>20) - 1;                else if( (x & 0x000f0000) != 0 )                        index = index - 4*(15) + ((x & 0x000f0000)>>16) - 1;                else if( (x & 0x0000f000) != 0 )                        index = index - 5*(15) + ((x & 0x0000f000)>>12) - 1;                else if( (x & 0x00000f00) != 0 )                        index = index - 6*(15) + ((x & 0x00000f00)>>8) - 1;                else if( (x & 0x000000f0) != 0 )                        index = index - 7*(15) + ((x & 0x000000f0)>>4) - 1;                else if( (x & 0x0000000f) != 0 )                        index = index - 8*(15) + ((x & 0x0000000f)>>0) - 1;                /* linearize sqrt value between neighbours */                arg_left = FIX_SQRT[(int)index][0];                arg_right = FIX_SQRT[(int)index+1][0];                left = FIX_SQRT[(int)index][1];                right = FIX_SQRT[(int)index+1][1];                darg = (arg_right-arg_left);                dy = (right-left);                dx = (x - arg_left);                /* signs */                dx = (dx<0) ? -dx : dx;                dy = (dy<0) ? -dy : dy;                darg = (darg<0) ? -darg : darg;                /* linearization */                value = (long)Div( (int)dy, (int)darg );                value = left + lMul( (int)value, (int)dx );                /* rescale to fixedpoint answer */                value = value>>8;                /* while index found, calculate sqrt */                return( (int)value );        }/// END FUNC        /**         * @name lSqrt         * @brief returns square root of x         * @author Stellars Henson         * @param x value to calculate sqrt from         * @return long FixedPoint sqrt value         */        public static final long lSqrt( long x ) {                /* prepare environment */                /* Fixedpoint sqrt table size */                long index = FIX_SQRT.length;                long dx, dy, darg;                long value = 0;                long arg_left = 0;                long arg_right = 0;                long left, right;                /* special circumstances */                if( x==0 )                        return 0;                /* find index, start from highest mask - the youngest 8-th octet */                     if( (x & 0xf0000000) != 0 )                        index = index - 1*(15) + ((x & 0xf0000000)>>28) - 1;                else if( (x & 0x0f000000) != 0 )                        index = index - 2*(15) + ((x & 0x0f000000)>>24) - 1;                else if( (x & 0x00f00000) != 0 )                        index = index - 3*(15) + ((x & 0x00f00000)>>20) - 1;                else if( (x & 0x000f0000) != 0 )                        index = index - 4*(15) + ((x & 0x000f0000)>>16) - 1;                else if( (x & 0x0000f000) != 0 )                        index = index - 5*(15) + ((x & 0x0000f000)>>12) - 1;                else if( (x & 0x00000f00) != 0 )                        index = index - 6*(15) + ((x & 0x00000f00)>>8) - 1;                else if( (x & 0x000000f0) != 0 )                        index = index - 7*(15) + ((x & 0x000000f0)>>4) - 1;                else if( (x & 0x0000000f) != 0 )                        index = index - 8*(15) + ((x & 0x0000000f)>>0) - 1;                /* linearize sqrt value between neighbours */                arg_left = FIX_SQRT[(int)index][0];                arg_right = FIX_SQRT[(int)index+1][0];                left = FIX_SQRT[(int)index][1];                right = FIX_SQRT[(int)index+1][1];                darg = (arg_right-arg_left);                dy = (right-left);                dx = (x - arg_left);                /* signs */                dx = (dx<0) ? -dx : dx;                dy = (dy<0) ? -dy : dy;                darg = (darg<0) ? -darg : darg;                /* linearization */                value = (long)Div( (int)dy, (int)darg );                value = left + lMul( (int)value, (int)dx );                /* rescale to fixedpoint answer */                value = value>>8;                /* while index found, calculate sqrt */                return( value );        }/// END FUNC        /**        * @brief rounds given fixed-point number to nearest integer value        * @param n fixed-point value        * @return nearest integer value        */        public static final int round(int n)        {                if (n > 0) {                        if ((n & (FIX_UNIT>>1)) != 0)                                return (((n+FIX_UNIT)>>FIX_SHIFT)<<FIX_SHIFT);                        else                                return (((n)>>FIX_SHIFT)<<FIX_SHIFT);                }// ~if                else {