Package cds.healpix.common.math

Class HackersDelight

  • public final class HackersDelight
extends java.lang.Object
    Utility class which takes its name from the book "Hacker's Delight" by Henry S. Warren. Jr. We also uses the "Bit Twiddling Hacks" page by Sean Eron Anderson from Standford.
    Author:
    F.-X Pineau

    • Field Summary

      Fields 
      Modifier and Type Field Description
      static long BUT_EXPONENT_BIT_MASK
      Bit mask to isolate all but the sign bit of a long or double.
      static long BUT_SIGN_BIT_MASK_L
      Bit mask to isolate all but the sign bit of a long or double.
      static long EXPONENT_BITS_MASK
      Bit mask to isolate the sign bit of a long or double.
      static int SIGN_BIT_MASK_I
      Bit mask to isolate the sign bit of an int or a float.
      static long SIGN_BIT_MASK_L
      Bit mask to isolate the sign bit of a long or double.

    • Constructor Summary

      Constructors 
      Constructor Description
      HackersDelight()  

    • Method Summary

      All Methods Static Methods Concrete Methods 
      Modifier and Type Method Description
      static double abs​(double x)  
      static int abs​(int x)  
      static long abs​(long x)  
      static int doz​(int x, int y)
      Doz stands for "difference or zero" (see p.
      static long doz​(long x, long y)
      Doz stands for "difference or zero" (see p.
      static int floorInt​(double a)  
      static int floorIntN​(double a)  
      static int floorIntP​(double a)  
      static long floorLong​(double a)  
      static long floorLongN​(double a)  
      static long floorLongP​(double a)  
      static long flp2​(long x)
      Round down to the next power of 2 (see HD Fig.
      static double fromBits​(long doubleBits)  
      static double halfOf​(double x)  
      static boolean isPowOf2​(int x)
      Determines if an integer is a power of two, exact solution.
      static boolean isPowOf2Fast​(int x)
      Determines if an integer is a power of two, including 0.
      static void main​(java.lang.String[] args)  
      static int max​(int x, int y)
      Returns the greater of two values.
      static long max​(long x, long y)
      Returns the greater of two values.
      static int min​(int x, int y)
      Returns the smaller of two values.
      static long min​(long x, long y)
      Returns the smaller of two values.
      static int nlz​(int x)
      Branch-free version of Integer.numberOfLeadingZeros(int) (also taken from the HD).
      static long toBits​(double x)  

      • Methods inherited from class java.lang.Object

        equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

    • Field Detail

      • SIGN_BIT_MASK_I

        public static final int SIGN_BIT_MASK_I
        Bit mask to isolate the sign bit of an int or a float.
        See Also:
        Constant Field Values

      • SIGN_BIT_MASK_L

        public static final long SIGN_BIT_MASK_L
        Bit mask to isolate the sign bit of a long or double.
        See Also:
        Constant Field Values

      • BUT_SIGN_BIT_MASK_L

        public static final long BUT_SIGN_BIT_MASK_L
        Bit mask to isolate all but the sign bit of a long or double.
        See Also:
        Constant Field Values

      • EXPONENT_BITS_MASK

        public static final long EXPONENT_BITS_MASK
        Bit mask to isolate the sign bit of a long or double.
        See Also:
        Constant Field Values

      • BUT_EXPONENT_BIT_MASK

        public static final long BUT_EXPONENT_BIT_MASK
        Bit mask to isolate all but the sign bit of a long or double.
        See Also:
        Constant Field Values

    • Constructor Detail

      • HackersDelight

        public HackersDelight()

    • Method Detail

      • isPowOf2

        public static boolean isPowOf2​(int x)
        Determines if an integer is a power of two, exact solution. From the "Bit Twiddling Hacks" web page of Sean Eron Anderson, slightly modified.
        Parameters:
        x - the argument
        Returns:
        true if the argument is a power of 2 and is different from 0.

      • isPowOf2Fast

        public static boolean isPowOf2Fast​(int x)
        Determines if an integer is a power of two, including 0. From the "Bit Twiddling Hacks" web page of Sean Eron Anderson, slightly modified.
        Parameters:
        x - the argument
        Returns:
        if the argument is a power of 2 OR if it is 0 (which is not a power of 2). For an exact solution (excluding 0), isPowOf2(int).

      • flp2

        public static long flp2​(long x)
        Round down to the next power of 2 (see HD Fig. 3-1).
        Parameters:
        x - the argument
        Returns:
        round down to the next power of 2

      • halfOf

        public static double halfOf​(double x)

      • toBits

        public static long toBits​(double x)

      • fromBits

        public static double fromBits​(long doubleBits)

      • abs

        public static int abs​(int x)

      • abs

        public static long abs​(long x)

      • abs

        public static double abs​(double x)

      • floorIntP

        public static int floorIntP​(double a)

      • floorIntN

        public static int floorIntN​(double a)

      • floorInt

        public static int floorInt​(double a)

      • floorLongP

        public static long floorLongP​(double a)

      • floorLongN

        public static long floorLongN​(double a)

      • floorLong

        public static long floorLong​(double a)

      • doz

        public static int doz​(int x,
                      int y)
        Doz stands for "difference or zero" (see p. 37 of HD). It returns 0 if x > y, else returns x - y, so it can be replace by (x - y) > 0 ? x - y : 0
        Parameters:
        x - an argument
        y - another argument
        Returns:
        0 if x > y, else returns x - y.

      • doz

        public static long doz​(long x,
                       long y)
        Doz stands for "difference or zero" (see p. 37 of HD). It returns 0 if x > y, else returns x - y, so it can be replace by (x - y) > 0 ? x - y : 0
        Parameters:
        x - an argument
        y - another argument
        Returns:
        0 if x > y, else returns x - y.

      • min

        public static int min​(int x,
                      int y)
        Returns the smaller of two values.
        Parameters:
        x - an argument
        y - another argument
        Returns:
        the smaller of two values.

      • min

        public static long min​(long x,
                       long y)
        Returns the smaller of two values.
        Parameters:
        x - an argument
        y - another argument
        Returns:
        the smaller of two values.

      • max

        public static int max​(int x,
                      int y)
        Returns the greater of two values.
        Parameters:
        x - an argument
        y - another argument
        Returns:
        the greater of two values.

      • max

        public static long max​(long x,
                       long y)
        Returns the greater of two values.
        Parameters:
        x - an argument
        y - another argument
        Returns:
        the greater of two values.

      • nlz

        public static int nlz​(int x)
        Branch-free version of Integer.numberOfLeadingZeros(int) (also taken from the HD). See "Number of leading zeros, branch-free binary search" in HD.
        Parameters:
        x - the argument
        Returns:
        the number of leading zeros in the given argument.

      • main

        public static void main​(java.lang.String[] args)