Package net.jafama

Class StrictFastMath


  • public final class StrictFastMath
    extends Object
    Strict versions of FastMath methods. Cf. README.txt for more info.
    • Field Summary

      Fields 
      Modifier and Type Field Description
      static double E
      Closest double approximation of e.
      static double PI
      Closest double approximation of pi, which is inferior to mathematical pi: pi ~= 3.14159265358979323846...
      static double PI_SUP
      High double approximation of pi, which is further from pi than the low approximation PI: pi ~= 3.14159265358979323846...
    • Method Summary

      All Methods Static Methods Concrete Methods 
      Modifier and Type Method Description
      static double abs​(double a)  
      static float abs​(float a)  
      static int abs​(int value)  
      static long abs​(long value)  
      static double acos​(double value)  
      static double acosh​(double value)
      Some properties of acosh(x) = log(x + sqrt(x^2 - 1)): 1) defined on [1,+Infinity[ 2) result in ]0,+Infinity[ (by convention, since cosh(x) = cosh(-x)) 3) acosh(1) = 0 4) acosh(1+epsilon) ~= log(1 + sqrt(2*epsilon)) ~= sqrt(2*epsilon) 5) lim(acosh(x),x->+Infinity) = +Infinity (y increasing logarithmically slower than x)
      static double acosh1p​(double value)
      Much more accurate than acosh(1+value), for arguments (and results) close to zero.
      static double acosInRange​(double value)
      If value is not NaN and is outside [-1,1] range, closest value in this range is used.
      static int addBounded​(int a, int b)  
      static long addBounded​(long a, long b)  
      static int addExact​(int a, int b)  
      static long addExact​(long a, long b)  
      static double asin​(double value)  
      static double asinh​(double value)
      Some properties of asinh(x) = log(x + sqrt(x^2 + 1)) 1) defined on ]-Infinity,+Infinity[ 2) result in ]-Infinity,+Infinity[ 3) asinh(x) = -asinh(-x) (implies asinh(0) = 0) 4) asinh(epsilon) ~= epsilon 5) lim(asinh(x),x->+Infinity) = +Infinity (y increasing logarithmically slower than x)
      static double asinInRange​(double value)
      If value is not NaN and is outside [-1,1] range, closest value in this range is used.
      static double atan​(double value)  
      static double atan2​(double y, double x)
      For special values for which multiple conventions could be adopted, behaves like StrictMath.atan2(double,double).
      static double atanh​(double value)
      Some properties of atanh(x) = log((1+x)/(1-x))/2: 1) defined on ]-1,1[ 2) result in ]-Infinity,+Infinity[ 3) atanh(-1) = -Infinity (by continuity) 4) atanh(1) = +Infinity (by continuity) 5) atanh(epsilon) ~= epsilon 6) lim(atanh(x),x->1) = +Infinity
      static double cbrt​(double value)  
      static double ceil​(double value)  
      static float ceil​(float value)  
      static int ceilToInt​(double value)  
      static double copySign​(double magnitude, double sign)
      A sign of NaN is interpreted as positive.
      static float copySign​(float magnitude, float sign)
      A sign of NaN is interpreted as positive.
      static double cos​(double angle)  
      static double cosh​(double value)
      Some properties of cosh(x) = (exp(x)+exp(-x))/2: 1) defined on ]-Infinity,+Infinity[ 2) result in [1,+Infinity[ 3) cosh(0) = 1 4) cosh(x) = cosh(-x) 5) lim(cosh(x),x->+Infinity) = +Infinity (y increasing exponentially faster than x) 6) reaches +Infinity (double overflow) for x >= 710.475860073944, i.e.
      static double coshm1​(double value)
      Much more accurate than cosh(value)-1, for arguments (and results) close to zero.
      static double cosQuick​(double angle)
      Quick cos, with accuracy of about 1.6e-3 (PI/) for |angle| < 6588397.0 (Integer.MAX_VALUE * (2*PI/)), and no accuracy at all for larger values.
      static int decrementBounded​(int value)  
      static long decrementBounded​(long value)  
      static int decrementExact​(int value)  
      static long decrementExact​(long value)  
      static double exp​(double value)  
      static double expm1​(double value)
      Much more accurate than exp(value)-1, for arguments (and results) close to zero.
      static double expQuick​(double value)
      Quick exp, with a max relative error of about 2.94e-2 for |value| < 700.0 or so, and no accuracy at all outside this range.
      static double floor​(double value)  
      static float floor​(float value)  
      static int floorDiv​(int x, int y)
      Returns the largest int <= dividend/divisor.
      static long floorDiv​(long x, int y)
      Returns the largest long <= dividend/divisor.
      static long floorDiv​(long x, long y)
      Returns the largest long <= dividend/divisor.
      static int floorMod​(int x, int y)
      Returns the floor modulus, which is "x - floorDiv(x,y) * y", has the same sign as y, and is in ]-abs(y),abs(y)[.
      static int floorMod​(long x, int y)
      Returns the floor modulus, which is "x - floorDiv(x,y) * y", has the same sign as y, and is in ]-abs(y),abs(y)[.
      static long floorMod​(long x, long y)
      Returns the floor modulus, which is "x - floorDiv(x,y) * y", has the same sign as y, and is in ]-abs(y),abs(y)[.
      static int floorToInt​(double value)  
      static int getExponent​(double value)  
      static int getExponent​(float value)  
      static double hypot​(double x, double y)  
      static double hypot​(double x, double y, double z)  
      static double IEEEremainder​(double f1, double f2)  
      static int incrementBounded​(int value)  
      static long incrementBounded​(long value)  
      static int incrementExact​(int value)  
      static long incrementExact​(long value)  
      static void initTables()
      Ensures that all look-up tables are initialized - otherwise they are initialized lazily.
      static double invSqrtQuick​(double value)
      Quick inverse of square root, with a max relative error of about 3.44e-2 for values in [Double.MIN_NORMAL,Double.MAX_VALUE], and worse accuracy outside this range.
      static boolean isInClockwiseDomain​(double startAngRad, double angSpanRad, double angRad)
      NB: Since 2*Math.PI < 2*PI, a span of 2*Math.PI does not mean full angular range.
      static boolean isNaNOrInfinite​(double value)  
      static boolean isNaNOrInfinite​(float value)  
      static double log​(double value)  
      static double log10​(double value)  
      static double log1p​(double value)
      Much more accurate than log(1+value), for arguments (and results) close to zero.
      static int log2​(int value)  
      static int log2​(long value)  
      static double logQuick​(double value)
      Quick log, with a max relative error of about 1.9e-3 for values in ]Double.MIN_NORMAL,+Infinity[, and worse accuracy outside this range.
      static double max​(double a, double b)  
      static float max​(float a, float b)  
      static int max​(int a, int b)  
      static long max​(long a, long b)  
      static double min​(double a, double b)  
      static float min​(float a, float b)  
      static int min​(int a, int b)  
      static long min​(long a, long b)  
      static int multiplyBounded​(int a, int b)  
      static long multiplyBounded​(long a, int b)  
      static long multiplyBounded​(long a, long b)  
      static int multiplyExact​(int a, int b)  
      static long multiplyExact​(long a, int b)  
      static long multiplyExact​(long a, long b)  
      static long multiplyFull​(int x, int y)  
      static long multiplyHigh​(long x, long y)  
      static int negateBounded​(int value)  
      static long negateBounded​(long value)  
      static int negateExact​(int value)  
      static long negateExact​(long value)  
      static double nextAfter​(double start, double direction)
      If both arguments are +-0.0, direction is returned.
      static float nextAfter​(float start, double direction)
      If both arguments are +-0.0(f), (float)direction is returned.
      static double nextDown​(double start)
      Semantically equivalent to nextAfter(start,Double.NEGATIVE_INFINITY).
      static float nextDown​(float start)
      Semantically equivalent to nextAfter(start,Double.NEGATIVE_INFINITY).
      static double nextUp​(double start)
      Semantically equivalent to nextAfter(start,Double.POSITIVE_INFINITY).
      static float nextUp​(float start)
      Semantically equivalent to nextAfter(start,Double.POSITIVE_INFINITY).
      static double normalizeMinusHalfPiHalfPi​(double angle)  
      static double normalizeMinusHalfPiHalfPiFast​(double angle)
      Not accurate for large values.
      static double normalizeMinusPiPi​(double angle)  
      static double normalizeMinusPiPiFast​(double angle)
      Not accurate for large values.
      static double normalizeZeroTwoPi​(double angle)  
      static double normalizeZeroTwoPiFast​(double angle)
      Not accurate for large values.
      static double pow​(double value, double power)
      1e-13ish accuracy or better on whole double range.
      static double pow2​(double value)  
      static float pow2​(float value)  
      static int pow2​(int value)  
      static long pow2​(long value)  
      static double pow3​(double value)  
      static float pow3​(float value)  
      static int pow3​(int value)  
      static long pow3​(long value)  
      static double powFast​(double value, int power)
      This treatment is somehow accurate for low values of |power|, and for |power*getExponent(value)| < 1023 or so (to stay away from double extreme magnitudes (large and small)).
      static double powQuick​(double value, double power)
      Quick pow, with a max relative error of about 1e-2 for value >= Double.MIN_NORMAL and 1e-10 < |value^power| < 1e10, of about 6e-2 for value >= Double.MIN_NORMAL and 1e-40 < |value^power| < 1e40, and worse accuracy otherwise.
      static double random()  
      static double remainder​(double dividend, double divisor)
      Returns dividend - divisor * n, where n is the mathematical integer closest to dividend/divisor.
      static double rint​(double value)  
      static float rint​(float value)  
      static long round​(double value)
      Might have different semantics than StrictMath.round(double), see bugs 6430675 and 8010430.
      static int round​(float value)
      Might have different semantics than StrictMath.round(float), see bugs 6430675 and 8010430.
      static long roundEven​(double value)  
      static int roundEven​(float value)  
      static int roundEvenToInt​(double value)  
      static int roundToInt​(double value)  
      static double scalb​(double value, int scaleFactor)
      Precision may be lost if the result is subnormal.
      static float scalb​(float value, int scaleFactor)
      Precision may be lost if the result is subnormal.
      static long signFromBit​(double value)  
      static int signFromBit​(float value)  
      static double signum​(double value)  
      static float signum​(float value)  
      static double sin​(double angle)  
      static double sinAndCos​(double angle, DoubleWrapper cosine)
      Computes sine and cosine together.
      static double sinh​(double value)
      Some properties of sinh(x) = (exp(x)-exp(-x))/2: 1) defined on ]-Infinity,+Infinity[ 2) result in ]-Infinity,+Infinity[ 3) sinh(x) = -sinh(-x) (implies sinh(0) = 0) 4) sinh(epsilon) ~= epsilon 5) lim(sinh(x),x->+Infinity) = +Infinity (y increasing exponentially faster than x) 6) reaches +Infinity (double overflow) for x >= 710.475860073944, i.e.
      static double sinhAndCosh​(double value, DoubleWrapper hcosine)
      Computes hyperbolic sine and hyperbolic cosine together.
      static double sinQuick​(double angle)
      Quick sin, with accuracy of about 1.6e-3 (PI/) for |angle| < 6588395.0 (Integer.MAX_VALUE * (2*PI/) - 2) (- 2 due to removing PI/2 before using cosine tab), and no accuracy at all for larger values.
      static double sqrt​(double value)  
      static double sqrtQuick​(double value)
      Quick sqrt, with with a max relative error of about 3.41e-2 for values in [Double.MIN_NORMAL,Double.MAX_VALUE], and worse accuracy outside this range.
      static int subtractBounded​(int a, int b)  
      static long subtractBounded​(long a, long b)  
      static int subtractExact​(int a, int b)  
      static long subtractExact​(long a, long b)  
      static double tan​(double angle)
      Can have very bad relative error near +-PI/2, but of the same magnitude than the relative delta between StrictMath.tan(PI/2) and StrictMath.tan(nextDown(PI/2)).
      static double tanh​(double value)
      Some properties of tanh(x) = sinh(x)/cosh(x) = (exp(2*x)-1)/(exp(2*x)+1): 1) defined on ]-Infinity,+Infinity[ 2) result in ]-1,1[ 3) tanh(x) = -tanh(-x) (implies tanh(0) = 0) 4) tanh(epsilon) ~= epsilon 5) lim(tanh(x),x->+Infinity) = 1 6) reaches 1 (double loss of precision) for x = 19.061547465398498
      static double toDegrees​(boolean sign, int degrees, int minutes, double seconds)  
      static double toDegrees​(double angrad)
      Gives same result as StrictMath.toDegrees for some particular values like Math.PI/2, Math.PI or 2*Math.PI, but is faster (no division).
      static boolean toDMS​(double angrad, IntWrapper degrees, IntWrapper minutes, DoubleWrapper seconds)  
      static int toInt​(long value)  
      static int toIntExact​(long value)  
      static double toRadians​(boolean sign, int degrees, int minutes, double seconds)  
      static double toRadians​(double angdeg)
      Gives same result as StrictMath.toRadians for some particular values like 90.0, 180.0 or 360.0, but is faster (no division).
      static double toRange​(double min, double max, double value)  
      static float toRange​(float min, float max, float value)  
      static int toRange​(int min, int max, int value)  
      static long toRange​(long min, long max, long value)  
      static double twoPow​(int power)
      Returns the exact result, provided it's in double range, i.e.
      static double ulp​(double value)
      The ULP (Unit in the Last Place) is the distance to the next value larger in magnitude.
      static float ulp​(float value)
      The ULP (Unit in the Last Place) is the distance to the next value larger in magnitude.
    • Field Detail

      • PI

        public static final double PI
        Closest double approximation of pi, which is inferior to mathematical pi: pi ~= 3.14159265358979323846... PI ~= 3.141592653589793
        See Also:
        Constant Field Values
      • PI_SUP

        public static final double PI_SUP
        High double approximation of pi, which is further from pi than the low approximation PI: pi ~= 3.14159265358979323846... PI ~= 3.141592653589793 PI_SUP ~= 3.1415926535897936
    • Method Detail

      • sin

        public static double sin​(double angle)
        Parameters:
        angle - Angle in radians.
        Returns:
        Angle sine.
      • sinQuick

        public static double sinQuick​(double angle)
        Quick sin, with accuracy of about 1.6e-3 (PI/) for |angle| < 6588395.0 (Integer.MAX_VALUE * (2*PI/) - 2) (- 2 due to removing PI/2 before using cosine tab), and no accuracy at all for larger values.
        Parameters:
        angle - Angle in radians.
        Returns:
        Angle sine.
      • cos

        public static double cos​(double angle)
        Parameters:
        angle - Angle in radians.
        Returns:
        Angle cosine.
      • cosQuick

        public static double cosQuick​(double angle)
        Quick cos, with accuracy of about 1.6e-3 (PI/) for |angle| < 6588397.0 (Integer.MAX_VALUE * (2*PI/)), and no accuracy at all for larger values.
        Parameters:
        angle - Angle in radians.
        Returns:
        Angle cosine.
      • sinAndCos

        public static double sinAndCos​(double angle,
                                       DoubleWrapper cosine)
        Computes sine and cosine together.
        Parameters:
        angle - Angle in radians.
        cosine - (out) Angle cosine.
        Returns:
        Angle sine.
      • tan

        public static double tan​(double angle)
        Can have very bad relative error near +-PI/2, but of the same magnitude than the relative delta between StrictMath.tan(PI/2) and StrictMath.tan(nextDown(PI/2)).
        Parameters:
        angle - Angle in radians.
        Returns:
        Angle tangent.
      • asin

        public static double asin​(double value)
        Parameters:
        value - Value in [-1,1].
        Returns:
        Value arcsine, in radians, in [-PI/2,PI/2].
      • asinInRange

        public static double asinInRange​(double value)
        If value is not NaN and is outside [-1,1] range, closest value in this range is used.
        Parameters:
        value - Value in [-1,1].
        Returns:
        Value arcsine, in radians, in [-PI/2,PI/2].
      • acos

        public static double acos​(double value)
        Parameters:
        value - Value in [-1,1].
        Returns:
        Value arccosine, in radians, in [0,PI].
      • acosInRange

        public static double acosInRange​(double value)
        If value is not NaN and is outside [-1,1] range, closest value in this range is used.
        Parameters:
        value - Value in [-1,1].
        Returns:
        Value arccosine, in radians, in [0,PI].
      • atan

        public static double atan​(double value)
        Parameters:
        value - A double value.
        Returns:
        Value arctangent, in radians, in [-PI/2,PI/2].
      • atan2

        public static double atan2​(double y,
                                   double x)
        For special values for which multiple conventions could be adopted, behaves like StrictMath.atan2(double,double).
        Parameters:
        y - Coordinate on y axis.
        x - Coordinate on x axis.
        Returns:
        Angle from x axis positive side to (x,y) position, in radians, in [-PI,PI]. Angle measure is positive when going from x axis to y axis (positive sides).
      • toRadians

        public static double toRadians​(double angdeg)
        Gives same result as StrictMath.toRadians for some particular values like 90.0, 180.0 or 360.0, but is faster (no division).
        Parameters:
        angdeg - Angle value in degrees.
        Returns:
        Angle value in radians.
      • toDegrees

        public static double toDegrees​(double angrad)
        Gives same result as StrictMath.toDegrees for some particular values like Math.PI/2, Math.PI or 2*Math.PI, but is faster (no division).
        Parameters:
        angrad - Angle value in radians.
        Returns:
        Angle value in degrees.
      • toRadians

        public static double toRadians​(boolean sign,
                                       int degrees,
                                       int minutes,
                                       double seconds)
        Parameters:
        sign - Sign of the angle: true for positive, false for negative.
        degrees - Degrees, in [0,180].
        minutes - Minutes, in [0,59].
        seconds - Seconds, in [0.0,60.0[.
        Returns:
        Angle in radians.
      • toDegrees

        public static double toDegrees​(boolean sign,
                                       int degrees,
                                       int minutes,
                                       double seconds)
        Parameters:
        sign - Sign of the angle: true for positive, false for negative.
        degrees - Degrees, in [0,180].
        minutes - Minutes, in [0,59].
        seconds - Seconds, in [0.0,60.0[.
        Returns:
        Angle in degrees.
      • toDMS

        public static boolean toDMS​(double angrad,
                                    IntWrapper degrees,
                                    IntWrapper minutes,
                                    DoubleWrapper seconds)
        Parameters:
        angrad - Angle in radians.
        degrees - (out) Degrees, in [0,180].
        minutes - (out) Minutes, in [0,59].
        seconds - (out) Seconds, in [0.0,60.0[.
        Returns:
        true if the resulting angle in [-180deg,180deg] is positive, false if it is negative.
      • isInClockwiseDomain

        public static boolean isInClockwiseDomain​(double startAngRad,
                                                  double angSpanRad,
                                                  double angRad)
        NB: Since 2*Math.PI < 2*PI, a span of 2*Math.PI does not mean full angular range. ex.: isInClockwiseDomain(0.0, 2*Math.PI, -1e-20) returns false. ---> For full angular range, use a span > 2*Math.PI, like 2*PI_SUP constant of this class.
        Parameters:
        startAngRad - An angle, in radians.
        angSpanRad - An angular span, >= 0.0, in radians.
        angRad - An angle, in radians.
        Returns:
        true if angRad is in the clockwise angular domain going from startAngRad, over angSpanRad, extremities included, false otherwise.
      • sinh

        public static double sinh​(double value)
        Some properties of sinh(x) = (exp(x)-exp(-x))/2: 1) defined on ]-Infinity,+Infinity[ 2) result in ]-Infinity,+Infinity[ 3) sinh(x) = -sinh(-x) (implies sinh(0) = 0) 4) sinh(epsilon) ~= epsilon 5) lim(sinh(x),x->+Infinity) = +Infinity (y increasing exponentially faster than x) 6) reaches +Infinity (double overflow) for x >= 710.475860073944, i.e. a bit further than exp(x)
        Parameters:
        value - A double value.
        Returns:
        Value hyperbolic sine.
      • cosh

        public static double cosh​(double value)
        Some properties of cosh(x) = (exp(x)+exp(-x))/2: 1) defined on ]-Infinity,+Infinity[ 2) result in [1,+Infinity[ 3) cosh(0) = 1 4) cosh(x) = cosh(-x) 5) lim(cosh(x),x->+Infinity) = +Infinity (y increasing exponentially faster than x) 6) reaches +Infinity (double overflow) for x >= 710.475860073944, i.e. a bit further than exp(x)
        Parameters:
        value - A double value.
        Returns:
        Value hyperbolic cosine.
      • coshm1

        public static double coshm1​(double value)
        Much more accurate than cosh(value)-1, for arguments (and results) close to zero. coshm1(-0.0) = -0.0, for homogeneity with acosh1p(-0.0) = -0.0.
        Parameters:
        value - A double value.
        Returns:
        Value hyperbolic cosine, minus 1.
      • sinhAndCosh

        public static double sinhAndCosh​(double value,
                                         DoubleWrapper hcosine)
        Computes hyperbolic sine and hyperbolic cosine together.
        Parameters:
        value - A double value.
        hcosine - (out) Value hyperbolic cosine.
        Returns:
        Value hyperbolic sine.
      • tanh

        public static double tanh​(double value)
        Some properties of tanh(x) = sinh(x)/cosh(x) = (exp(2*x)-1)/(exp(2*x)+1): 1) defined on ]-Infinity,+Infinity[ 2) result in ]-1,1[ 3) tanh(x) = -tanh(-x) (implies tanh(0) = 0) 4) tanh(epsilon) ~= epsilon 5) lim(tanh(x),x->+Infinity) = 1 6) reaches 1 (double loss of precision) for x = 19.061547465398498
        Parameters:
        value - A double value.
        Returns:
        Value hyperbolic tangent.
      • asinh

        public static double asinh​(double value)
        Some properties of asinh(x) = log(x + sqrt(x^2 + 1)) 1) defined on ]-Infinity,+Infinity[ 2) result in ]-Infinity,+Infinity[ 3) asinh(x) = -asinh(-x) (implies asinh(0) = 0) 4) asinh(epsilon) ~= epsilon 5) lim(asinh(x),x->+Infinity) = +Infinity (y increasing logarithmically slower than x)
        Parameters:
        value - A double value.
        Returns:
        Value hyperbolic arcsine.
      • acosh

        public static double acosh​(double value)
        Some properties of acosh(x) = log(x + sqrt(x^2 - 1)): 1) defined on [1,+Infinity[ 2) result in ]0,+Infinity[ (by convention, since cosh(x) = cosh(-x)) 3) acosh(1) = 0 4) acosh(1+epsilon) ~= log(1 + sqrt(2*epsilon)) ~= sqrt(2*epsilon) 5) lim(acosh(x),x->+Infinity) = +Infinity (y increasing logarithmically slower than x)
        Parameters:
        value - A double value.
        Returns:
        Value hyperbolic arccosine.
      • acosh1p

        public static double acosh1p​(double value)
        Much more accurate than acosh(1+value), for arguments (and results) close to zero. acosh1p(-0.0) = -0.0, for homogeneity with sqrt(-0.0) = -0.0, which looks about the same near 0.
        Parameters:
        value - A double value.
        Returns:
        Hyperbolic arccosine of (1+value).
      • atanh

        public static double atanh​(double value)
        Some properties of atanh(x) = log((1+x)/(1-x))/2: 1) defined on ]-1,1[ 2) result in ]-Infinity,+Infinity[ 3) atanh(-1) = -Infinity (by continuity) 4) atanh(1) = +Infinity (by continuity) 5) atanh(epsilon) ~= epsilon 6) lim(atanh(x),x->1) = +Infinity
        Parameters:
        value - A double value.
        Returns:
        Value hyperbolic arctangent.
      • exp

        public static double exp​(double value)
        Parameters:
        value - A double value.
        Returns:
        e^value.
      • expQuick

        public static double expQuick​(double value)
        Quick exp, with a max relative error of about 2.94e-2 for |value| < 700.0 or so, and no accuracy at all outside this range. Derived from a note by Nicol N. Schraudolph, IDSIA, 1998.
        Parameters:
        value - A double value.
        Returns:
        e^value.
      • expm1

        public static double expm1​(double value)
        Much more accurate than exp(value)-1, for arguments (and results) close to zero.
        Parameters:
        value - A double value.
        Returns:
        e^value-1.
      • log

        public static double log​(double value)
        Parameters:
        value - A double value.
        Returns:
        Value logarithm (base e).
      • logQuick

        public static double logQuick​(double value)
        Quick log, with a max relative error of about 1.9e-3 for values in ]Double.MIN_NORMAL,+Infinity[, and worse accuracy outside this range.
        Parameters:
        value - A double value, in ]0,+Infinity[ (strictly positive and finite).
        Returns:
        Value logarithm (base e).
      • log10

        public static double log10​(double value)
        Parameters:
        value - A double value.
        Returns:
        Value logarithm (base 10).
      • log1p

        public static double log1p​(double value)
        Much more accurate than log(1+value), for arguments (and results) close to zero.
        Parameters:
        value - A double value.
        Returns:
        Logarithm (base e) of (1+value).
      • pow

        public static double pow​(double value,
                                 double power)
        1e-13ish accuracy or better on whole double range.
        Parameters:
        value - A double value.
        power - A power.
        Returns:
        value^power.
      • powQuick

        public static double powQuick​(double value,
                                      double power)
        Quick pow, with a max relative error of about 1e-2 for value >= Double.MIN_NORMAL and 1e-10 < |value^power| < 1e10, of about 6e-2 for value >= Double.MIN_NORMAL and 1e-40 < |value^power| < 1e40, and worse accuracy otherwise.
        Parameters:
        value - A double value, in ]0,+Infinity[ (strictly positive and finite).
        power - A double value.
        Returns:
        value^power.
      • powFast

        public static double powFast​(double value,
                                     int power)
        This treatment is somehow accurate for low values of |power|, and for |power*getExponent(value)| < 1023 or so (to stay away from double extreme magnitudes (large and small)).
        Parameters:
        value - A double value.
        power - A power.
        Returns:
        value^power.
      • pow2

        public static float pow2​(float value)
        Parameters:
        value - A float value.
        Returns:
        value*value.
      • pow2

        public static double pow2​(double value)
        Parameters:
        value - A double value.
        Returns:
        value*value.
      • pow3

        public static float pow3​(float value)
        Parameters:
        value - A float value.
        Returns:
        value*value*value.
      • pow3

        public static double pow3​(double value)
        Parameters:
        value - A double value.
        Returns:
        value*value*value.
      • sqrt

        public static double sqrt​(double value)
        Parameters:
        value - A double value.
        Returns:
        Value square root.
      • sqrtQuick

        public static double sqrtQuick​(double value)
        Quick sqrt, with with a max relative error of about 3.41e-2 for values in [Double.MIN_NORMAL,Double.MAX_VALUE], and worse accuracy outside this range.
        Parameters:
        value - A double value.
        Returns:
        Value square root.
      • invSqrtQuick

        public static double invSqrtQuick​(double value)
        Quick inverse of square root, with a max relative error of about 3.44e-2 for values in [Double.MIN_NORMAL,Double.MAX_VALUE], and worse accuracy outside this range. This implementation uses zero step of Newton's method. Here are the max relative errors on [Double.MIN_NORMAL,Double.MAX_VALUE] depending on number of steps, if you want to copy-paste this code and use your own number: n=0: about 3.44e-2 n=1: about 1.75e-3 n=2: about 4.6e-6 n=3: about 3.17e-11 n=4: about 3.92e-16 n=5: about 3.03e-16
        Parameters:
        value - A double value.
        Returns:
        Inverse of value square root.
      • cbrt

        public static double cbrt​(double value)
        Parameters:
        value - A double value.
        Returns:
        Value cubic root.
      • hypot

        public static double hypot​(double x,
                                   double y)
        Returns:
        sqrt(x^2+y^2) without intermediate overflow or underflow.
      • hypot

        public static double hypot​(double x,
                                   double y,
                                   double z)
        Returns:
        sqrt(x^2+y^2+z^2) without intermediate overflow or underflow.
      • floor

        public static float floor​(float value)
        Parameters:
        value - A float value.
        Returns:
        Floor of value.
      • floor

        public static double floor​(double value)
        Parameters:
        value - A double value.
        Returns:
        Floor of value.
      • ceil

        public static float ceil​(float value)
        Parameters:
        value - A float value.
        Returns:
        Ceiling of value.
      • ceil

        public static double ceil​(double value)
        Parameters:
        value - A double value.
        Returns:
        Ceiling of value.
      • round

        public static int round​(float value)
        Might have different semantics than StrictMath.round(float), see bugs 6430675 and 8010430.
        Parameters:
        value - A double value.
        Returns:
        Value rounded to nearest int, choosing superior int in case two are equally close (i.e. rounding-up).
      • round

        public static long round​(double value)
        Might have different semantics than StrictMath.round(double), see bugs 6430675 and 8010430.
        Parameters:
        value - A double value.
        Returns:
        Value rounded to nearest long, choosing superior long in case two are equally close (i.e. rounding-up).
      • roundEven

        public static int roundEven​(float value)
        Parameters:
        value - A float value.
        Returns:
        Value rounded to nearest int, choosing even int in case two are equally close.
      • roundEven

        public static long roundEven​(double value)
        Parameters:
        value - A double value.
        Returns:
        Value rounded to nearest long, choosing even long in case two are equally close.
      • rint

        public static float rint​(float value)
        Parameters:
        value - A float value.
        Returns:
        The float mathematical integer closest to the specified value, choosing even one if two are equally close, or respectively NaN, +-Infinity or +-0.0f if the value is any of these.
      • rint

        public static double rint​(double value)
        Parameters:
        value - A double value.
        Returns:
        The double mathematical integer closest to the specified value, choosing even one if two are equally close, or respectively NaN, +-Infinity or +-0.0 if the value is any of these.
      • floorToInt

        public static int floorToInt​(double value)
        Parameters:
        value - A double value.
        Returns:
        Floor of value as int, or closest int if floor is out of int range, or 0 if value is NaN.
      • ceilToInt

        public static int ceilToInt​(double value)
        Parameters:
        value - A double value.
        Returns:
        Ceiling of value as int, or closest int if ceiling is out of int range, or 0 if value is NaN.
      • roundToInt

        public static int roundToInt​(double value)
        Parameters:
        value - A double value.
        Returns:
        Value rounded to nearest int, choosing superior int in case two are equally close (i.e. rounding-up).
      • roundEvenToInt

        public static int roundEvenToInt​(double value)
        Parameters:
        value - A double value.
        Returns:
        Value rounded to nearest int, choosing even int in case two are equally close.
      • toRange

        public static float toRange​(float min,
                                    float max,
                                    float value)
        Parameters:
        min - A float value.
        max - A float value.
        value - A float value.
        Returns:
        min if value < min, max if value > max, value otherwise.
      • toRange

        public static double toRange​(double min,
                                     double max,
                                     double value)
        Parameters:
        min - A double value.
        max - A double value.
        value - A double value.
        Returns:
        min if value < min, max if value > max, value otherwise.
      • remainder

        public static double remainder​(double dividend,
                                       double divisor)
        Returns dividend - divisor * n, where n is the mathematical integer closest to dividend/divisor. If dividend/divisor is equally close to surrounding integers, we choose n to be the integer of smallest magnitude, which makes this treatment differ from StrictMath.IEEEremainder(double,double), where n is chosen to be the even integer. Note that the choice of n is not done considering the double approximation of dividend/divisor, because it could cause result to be outside [-|divisor|/2,|divisor|/2] range. The practical effect is that if multiple results would be possible, we always choose the result that is the closest to (and has the same sign as) the dividend. Ex. : - for (-3.0,2.0), this method returns -1.0, whereas StrictMath.IEEEremainder returns 1.0. - for (-5.0,2.0), both this method and StrictMath.IEEEremainder return -1.0. If the remainder is zero, its sign is the same as the sign of the first argument. If either argument is NaN, or the first argument is infinite, or the second argument is positive zero or negative zero, then the result is NaN. If the first argument is finite and the second argument is infinite, then the result is the same as the first argument. NB: - Modulo operator (%) returns a value in ]-|divisor|,|divisor|[, which sign is the same as dividend. - As for modulo operator, the sign of the divisor has no effect on the result. - On some architecture, % operator has been observed to return NaN for some subnormal values of divisor, when dividend exponent is 1023, which impacts the correctness of this method.
        Parameters:
        dividend - Dividend.
        divisor - Divisor.
        Returns:
        Remainder of dividend/divisor, i.e. a value in [-|divisor|/2,|divisor|/2].
      • normalizeMinusPiPi

        public static double normalizeMinusPiPi​(double angle)
        Parameters:
        angle - Angle in radians.
        Returns:
        The same angle, in radians, but in [-PI,PI].
      • normalizeMinusPiPiFast

        public static double normalizeMinusPiPiFast​(double angle)
        Not accurate for large values.
        Parameters:
        angle - Angle in radians.
        Returns:
        The same angle, in radians, but in [-PI,PI].
      • normalizeZeroTwoPi

        public static double normalizeZeroTwoPi​(double angle)
        Parameters:
        angle - Angle in radians.
        Returns:
        The same angle, in radians, but in [0,2*PI].
      • normalizeZeroTwoPiFast

        public static double normalizeZeroTwoPiFast​(double angle)
        Not accurate for large values.
        Parameters:
        angle - Angle in radians.
        Returns:
        The same angle, in radians, but in [0,2*PI].
      • normalizeMinusHalfPiHalfPi

        public static double normalizeMinusHalfPiHalfPi​(double angle)
        Parameters:
        angle - Angle in radians.
        Returns:
        Angle value modulo PI, in radians, in [-PI/2,PI/2].
      • normalizeMinusHalfPiHalfPiFast

        public static double normalizeMinusHalfPiHalfPiFast​(double angle)
        Not accurate for large values.
        Parameters:
        angle - Angle in radians.
        Returns:
        Angle value modulo PI, in radians, in [-PI/2,PI/2].
      • isNaNOrInfinite

        public static boolean isNaNOrInfinite​(float value)
        Parameters:
        value - A float value.
        Returns:
        true if the specified value is NaN or +-Infinity, false otherwise.
      • isNaNOrInfinite

        public static boolean isNaNOrInfinite​(double value)
        Parameters:
        value - A double value.
        Returns:
        true if the specified value is NaN or +-Infinity, false otherwise.
      • getExponent

        public static int getExponent​(float value)
        Parameters:
        value - A float value.
        Returns:
        Value unbiased exponent.
      • getExponent

        public static int getExponent​(double value)
        Parameters:
        value - A double value.
        Returns:
        Value unbiased exponent.
      • signum

        public static float signum​(float value)
        Parameters:
        value - A float value.
        Returns:
        -1.0f if the specified value is < 0, 1.0f if it is > 0, and the value itself if it is NaN or +-0.0f.
      • signum

        public static double signum​(double value)
        Parameters:
        value - A double value.
        Returns:
        -1.0 if the specified value is < 0, 1.0 if it is > 0, and the value itself if it is NaN or +-0.0.
      • signFromBit

        public static int signFromBit​(float value)
        Parameters:
        value - A float value.
        Returns:
        -1 if sign bit is 1, 1 if sign bit is 0.
      • signFromBit

        public static long signFromBit​(double value)
        Parameters:
        value - A double value.
        Returns:
        -1 if sign bit is 1, 1 if sign bit is 0.
      • copySign

        public static float copySign​(float magnitude,
                                     float sign)
        A sign of NaN is interpreted as positive.
        Parameters:
        magnitude - A float value.
        sign - A float value.
        Returns:
        A value with the magnitude of the first argument, and the sign of the second argument.
      • copySign

        public static double copySign​(double magnitude,
                                      double sign)
        A sign of NaN is interpreted as positive.
        Parameters:
        magnitude - A double value.
        sign - A double value.
        Returns:
        A value with the magnitude of the first argument, and the sign of the second argument.
      • ulp

        public static float ulp​(float value)
        The ULP (Unit in the Last Place) is the distance to the next value larger in magnitude.
        Parameters:
        value - A float value.
        Returns:
        The size of an ulp of the specified value, or Float.MIN_VALUE if it is +-0.0f, or +Infinity if it is +-Infinity, or NaN if it is NaN.
      • ulp

        public static double ulp​(double value)
        The ULP (Unit in the Last Place) is the distance to the next value larger in magnitude.
        Parameters:
        value - A double value.
        Returns:
        The size of an ulp of the specified value, or Double.MIN_VALUE if it is +-0.0, or +Infinity if it is +-Infinity, or NaN if it is NaN.
      • nextAfter

        public static float nextAfter​(float start,
                                      double direction)
        If both arguments are +-0.0(f), (float)direction is returned. If both arguments are +Infinity or -Infinity, respectively +Infinity or -Infinity is returned.
        Parameters:
        start - A float value.
        direction - A double value.
        Returns:
        The float adjacent to start towards direction, considering that +(-)Float.MIN_VALUE is adjacent to +(-)0.0f, and that +(-)Float.MAX_VALUE is adjacent to +(-)Infinity, or NaN if any argument is NaN.
      • nextAfter

        public static double nextAfter​(double start,
                                       double direction)
        If both arguments are +-0.0, direction is returned. If both arguments are +Infinity or -Infinity, respectively +Infinity or -Infinity is returned.
        Parameters:
        start - A double value.
        direction - A double value.
        Returns:
        The double adjacent to start towards direction, considering that +(-)Double.MIN_VALUE is adjacent to +(-)0.0, and that +(-)Double.MAX_VALUE is adjacent to +(-)Infinity, or NaN if any argument is NaN.
      • nextDown

        public static float nextDown​(float start)
        Semantically equivalent to nextAfter(start,Double.NEGATIVE_INFINITY).
      • nextDown

        public static double nextDown​(double start)
        Semantically equivalent to nextAfter(start,Double.NEGATIVE_INFINITY).
      • nextUp

        public static float nextUp​(float start)
        Semantically equivalent to nextAfter(start,Double.POSITIVE_INFINITY).
      • nextUp

        public static double nextUp​(double start)
        Semantically equivalent to nextAfter(start,Double.POSITIVE_INFINITY).
      • scalb

        public static float scalb​(float value,
                                  int scaleFactor)
        Precision may be lost if the result is subnormal.
        Parameters:
        value - A float value.
        scaleFactor - An int value.
        Returns:
        value * 2^scaleFactor, or a value equivalent to the specified one if it is NaN, +-Infinity or +-0.0f.
      • scalb

        public static double scalb​(double value,
                                   int scaleFactor)
        Precision may be lost if the result is subnormal.
        Parameters:
        value - A double value.
        scaleFactor - An int value.
        Returns:
        value * 2^scaleFactor, or a value equivalent to the specified one if it is NaN, +-Infinity or +-0.0.
      • abs

        public static float abs​(float a)
      • abs

        public static double abs​(double a)
      • min

        public static float min​(float a,
                                float b)
      • min

        public static double min​(double a,
                                 double b)
      • max

        public static float max​(float a,
                                float b)
      • max

        public static double max​(double a,
                                 double b)
      • IEEEremainder

        public static double IEEEremainder​(double f1,
                                           double f2)
      • random

        public static double random()
      • initTables

        public static void initTables()
        Ensures that all look-up tables are initialized - otherwise they are initialized lazily.
      • log2

        public static int log2​(int value)
        Parameters:
        value - An integer value in [1,Integer.MAX_VALUE].
        Returns:
        The integer part of the logarithm, in base 2, of the specified value, i.e. a result in [0,30]
        Throws:
        IllegalArgumentException - if the specified value is <= 0.
      • log2

        public static int log2​(long value)
        Parameters:
        value - An integer value in [1,Long.MAX_VALUE].
        Returns:
        The integer part of the logarithm, in base 2, of the specified value, i.e. a result in [0,62]
        Throws:
        IllegalArgumentException - if the specified value is <= 0.
      • twoPow

        public static double twoPow​(int power)
        Returns the exact result, provided it's in double range, i.e. if power is in [-1074,1023].
        Parameters:
        power - An int power.
        Returns:
        2^power as a double, or +-Infinity in case of overflow.
      • pow2

        public static int pow2​(int value)
        Parameters:
        value - An int value.
        Returns:
        value*value.
      • pow2

        public static long pow2​(long value)
        Parameters:
        value - A long value.
        Returns:
        value*value.
      • pow3

        public static int pow3​(int value)
        Parameters:
        value - An int value.
        Returns:
        value*value*value.
      • pow3

        public static long pow3​(long value)
        Parameters:
        value - A long value.
        Returns:
        value*value*value.
      • abs

        public static int abs​(int value)
        Parameters:
        value - An int value.
        Returns:
        The absolute value, except if value is Integer.MIN_VALUE, for which it returns Integer.MIN_VALUE.
      • abs

        public static long abs​(long value)
        Parameters:
        value - A long value.
        Returns:
        The absolute value, except if value is Long.MIN_VALUE, for which it returns Long.MIN_VALUE.
      • toIntExact

        public static int toIntExact​(long value)
        Parameters:
        value - A long value.
        Returns:
        The specified value as int.
        Throws:
        ArithmeticException - if the specified value is not in [Integer.MIN_VALUE,Integer.MAX_VALUE] range.
      • toInt

        public static int toInt​(long value)
        Parameters:
        value - A long value.
        Returns:
        The closest int value in [Integer.MIN_VALUE,Integer.MAX_VALUE] range.
      • toRange

        public static int toRange​(int min,
                                  int max,
                                  int value)
        Parameters:
        min - An int value.
        max - An int value.
        value - An int value.
        Returns:
        minValue if value < minValue, maxValue if value > maxValue, value otherwise.
      • toRange

        public static long toRange​(long min,
                                   long max,
                                   long value)
        Parameters:
        min - A long value.
        max - A long value.
        value - A long value.
        Returns:
        min if value < min, max if value > max, value otherwise.
      • incrementExact

        public static int incrementExact​(int value)
        Parameters:
        value - An int value.
        Returns:
        The argument incremented by one.
        Throws:
        ArithmeticException - if the mathematical result is not in int range.
      • incrementExact

        public static long incrementExact​(long value)
        Parameters:
        value - A long value.
        Returns:
        The argument incremented by one.
        Throws:
        ArithmeticException - if the mathematical result is not in long range.
      • incrementBounded

        public static int incrementBounded​(int value)
        Parameters:
        value - An int value.
        Returns:
        The argument incremented by one, or the argument if the mathematical result is not in int range.
      • incrementBounded

        public static long incrementBounded​(long value)
        Parameters:
        value - A long value.
        Returns:
        The argument incremented by one, or the argument if the mathematical result is not in long range.
      • decrementExact

        public static int decrementExact​(int value)
        Parameters:
        value - An int value.
        Returns:
        The argument decremented by one.
        Throws:
        ArithmeticException - if the mathematical result is not in int range.
      • decrementExact

        public static long decrementExact​(long value)
        Parameters:
        value - A long value.
        Returns:
        The argument decremented by one.
        Throws:
        ArithmeticException - if the mathematical result is not in long range.
      • decrementBounded

        public static int decrementBounded​(int value)
        Parameters:
        value - An int value.
        Returns:
        The argument decremented by one, or the argument if the mathematical result is not in int range.
      • decrementBounded

        public static long decrementBounded​(long value)
        Parameters:
        value - A long value.
        Returns:
        The argument decremented by one, or the argument if the mathematical result is not in long range.
      • negateExact

        public static int negateExact​(int value)
        Parameters:
        value - An int value.
        Returns:
        The argument negated.
        Throws:
        ArithmeticException - if the mathematical result is not in int range.
      • negateExact

        public static long negateExact​(long value)
        Parameters:
        value - A long value.
        Returns:
        The argument negated.
        Throws:
        ArithmeticException - if the mathematical result is not in long range.
      • negateBounded

        public static int negateBounded​(int value)
        Parameters:
        value - An int value.
        Returns:
        The argument negated, or Integer.MAX_VALUE if the argument is Integer.MIN_VALUE.
      • negateBounded

        public static long negateBounded​(long value)
        Parameters:
        value - A long value.
        Returns:
        The argument negated, or Long.MAX_VALUE if the argument is Long.MIN_VALUE.
      • addExact

        public static int addExact​(int a,
                                   int b)
        Parameters:
        a - An int value.
        b - An int value.
        Returns:
        The mathematical result of a+b.
        Throws:
        ArithmeticException - if the mathematical result of a+b is not in [Integer.MIN_VALUE,Integer.MAX_VALUE] range.
      • addExact

        public static long addExact​(long a,
                                    long b)
        Parameters:
        a - A long value.
        b - A long value.
        Returns:
        The mathematical result of a+b.
        Throws:
        ArithmeticException - if the mathematical result of a+b is not in [Long.MIN_VALUE,Long.MAX_VALUE] range.
      • addBounded

        public static int addBounded​(int a,
                                     int b)
        Parameters:
        a - An int value.
        b - An int value.
        Returns:
        The int value of [Integer.MIN_VALUE,Integer.MAX_VALUE] range which is the closest to mathematical result of a+b.
      • addBounded

        public static long addBounded​(long a,
                                      long b)
        Parameters:
        a - A long value.
        b - A long value.
        Returns:
        The long value of [Long.MIN_VALUE,Long.MAX_VALUE] range which is the closest to mathematical result of a+b.
      • subtractExact

        public static int subtractExact​(int a,
                                        int b)
        Parameters:
        a - An int value.
        b - An int value.
        Returns:
        The mathematical result of a-b.
        Throws:
        ArithmeticException - if the mathematical result of a-b is not in [Integer.MIN_VALUE,Integer.MAX_VALUE] range.
      • subtractExact

        public static long subtractExact​(long a,
                                         long b)
        Parameters:
        a - A long value.
        b - A long value.
        Returns:
        The mathematical result of a-b.
        Throws:
        ArithmeticException - if the mathematical result of a-b is not in [Long.MIN_VALUE,Long.MAX_VALUE] range.
      • subtractBounded

        public static int subtractBounded​(int a,
                                          int b)
        Parameters:
        a - An int value.
        b - An int value.
        Returns:
        The int value of [Integer.MIN_VALUE,Integer.MAX_VALUE] range which is the closest to mathematical result of a-b.
      • subtractBounded

        public static long subtractBounded​(long a,
                                           long b)
        Parameters:
        a - A long value.
        b - A long value.
        Returns:
        The long value of [Long.MIN_VALUE,Long.MAX_VALUE] range which is the closest to mathematical result of a-b.
      • multiplyExact

        public static int multiplyExact​(int a,
                                        int b)
        Parameters:
        a - An int value.
        b - An int value.
        Returns:
        The mathematical result of a*b.
        Throws:
        ArithmeticException - if the mathematical result of a*b is not in [Integer.MIN_VALUE,Integer.MAX_VALUE] range.
      • multiplyExact

        public static long multiplyExact​(long a,
                                         int b)
        Parameters:
        a - A long value.
        b - An int value.
        Returns:
        The mathematical result of a*b.
        Throws:
        ArithmeticException - if the mathematical result of a*b is not in [Long.MIN_VALUE,Long.MAX_VALUE] range.
      • multiplyExact

        public static long multiplyExact​(long a,
                                         long b)
        Parameters:
        a - A long value.
        b - A long value.
        Returns:
        The mathematical result of a*b.
        Throws:
        ArithmeticException - if the mathematical result of a*b is not in [Long.MIN_VALUE,Long.MAX_VALUE] range.
      • multiplyBounded

        public static int multiplyBounded​(int a,
                                          int b)
        Parameters:
        a - An int value.
        b - An int value.
        Returns:
        The int value of [Integer.MIN_VALUE,Integer.MAX_VALUE] range which is the closest to mathematical result of a*b.
      • multiplyBounded

        public static long multiplyBounded​(long a,
                                           int b)
        Parameters:
        a - A long value.
        b - An int value.
        Returns:
        The long value of [Long.MIN_VALUE,Long.MAX_VALUE] range which is the closest to mathematical result of a*b.
      • multiplyBounded

        public static long multiplyBounded​(long a,
                                           long b)
        Parameters:
        a - A long value.
        b - A long value.
        Returns:
        The long value of [Long.MIN_VALUE,Long.MAX_VALUE] range which is the closest to mathematical result of a*b.
      • multiplyFull

        public static long multiplyFull​(int x,
                                        int y)
        Parameters:
        x - An int value.
        y - An int value.
        Returns:
        The mathematical product as a long.
      • multiplyHigh

        public static long multiplyHigh​(long x,
                                        long y)
        Parameters:
        x - A long value.
        y - A long value.
        Returns:
        The most significant 64 bits of the 128-bit product of two 64-bit factors.
      • floorDiv

        public static int floorDiv​(int x,
                                   int y)
        Returns the largest int <= dividend/divisor. Unlike "/" operator, which rounds towards 0, this division rounds towards -Infinity (which give different result when the exact result is negative).
        Parameters:
        x - The dividend.
        y - The divisor.
        Returns:
        The largest int <= dividend/divisor, unless dividend is Integer.MIN_VALUE and divisor is -1, in which case Integer.MIN_VALUE is returned.
        Throws:
        ArithmeticException - if the divisor is zero.
      • floorDiv

        public static long floorDiv​(long x,
                                    int y)
        Returns the largest long <= dividend/divisor. Unlike "/" operator, which rounds towards 0, this division rounds towards -Infinity (which give different result when the exact result is negative).
        Parameters:
        x - The dividend.
        y - The divisor.
        Returns:
        The largest long <= dividend/divisor, unless dividend is Long.MIN_VALUE and divisor is -1, in which case Long.MIN_VALUE is returned.
        Throws:
        ArithmeticException - if the divisor is zero.
      • floorDiv

        public static long floorDiv​(long x,
                                    long y)
        Returns the largest long <= dividend/divisor. Unlike "/" operator, which rounds towards 0, this division rounds towards -Infinity (which give different result when the exact result is negative).
        Parameters:
        x - The dividend.
        y - The divisor.
        Returns:
        The largest long <= dividend/divisor, unless dividend is Long.MIN_VALUE and divisor is -1, in which case Long.MIN_VALUE is returned.
        Throws:
        ArithmeticException - if the divisor is zero.
      • floorMod

        public static int floorMod​(int x,
                                   int y)
        Returns the floor modulus, which is "x - floorDiv(x,y) * y", has the same sign as y, and is in ]-abs(y),abs(y)[. The relationship between floorMod and floorDiv is the same than between "%" and "/".
        Parameters:
        x - The dividend.
        y - The divisor.
        Returns:
        The floor modulus, i.e. "x - (floorDiv(x, y) * y)".
        Throws:
        ArithmeticException - if the divisor is zero.
      • floorMod

        public static int floorMod​(long x,
                                   int y)
        Returns the floor modulus, which is "x - floorDiv(x,y) * y", has the same sign as y, and is in ]-abs(y),abs(y)[. The relationship between floorMod and floorDiv is the same than between "%" and "/".
        Parameters:
        x - The dividend.
        y - The divisor.
        Returns:
        The floor modulus, i.e. "x - (floorDiv(x, y) * y)".
        Throws:
        ArithmeticException - if the divisor is zero.
      • floorMod

        public static long floorMod​(long x,
                                    long y)
        Returns the floor modulus, which is "x - floorDiv(x,y) * y", has the same sign as y, and is in ]-abs(y),abs(y)[. The relationship between floorMod and floorDiv is the same than between "%" and "/".
        Parameters:
        x - The dividend.
        y - The divisor.
        Returns:
        The floor modulus, i.e. "x - (floorDiv(x, y) * y)".
        Throws:
        ArithmeticException - if the divisor is zero.
      • min

        public static int min​(int a,
                              int b)
      • min

        public static long min​(long a,
                               long b)
      • max

        public static int max​(int a,
                              int b)
      • max

        public static long max​(long a,
                               long b)