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public final class: Math [javadoc | source]
java.lang.Object
   java.lang.Math
The class {@code Math} contains methods for performing basic numeric operations such as the elementary exponential, logarithm, square root, and trigonometric functions.

Unlike some of the numeric methods of class {@code StrictMath}, all implementations of the equivalent functions of class {@code Math} are not defined to return the bit-for-bit same results. This relaxation permits better-performing implementations where strict reproducibility is not required.

By default many of the {@code Math} methods simply call the equivalent method in {@code StrictMath} for their implementation. Code generators are encouraged to use platform-specific native libraries or microprocessor instructions, where available, to provide higher-performance implementations of {@code Math} methods. Such higher-performance implementations still must conform to the specification for {@code Math}.

The quality of implementation specifications concern two properties, accuracy of the returned result and monotonicity of the method. Accuracy of the floating-point {@code Math} methods is measured in terms of ulps, units in the last place. For a given floating-point format, an ulp of a specific real number value is the distance between the two floating-point values bracketing that numerical value. When discussing the accuracy of a method as a whole rather than at a specific argument, the number of ulps cited is for the worst-case error at any argument. If a method always has an error less than 0.5 ulps, the method always returns the floating-point number nearest the exact result; such a method is correctly rounded. A correctly rounded method is generally the best a floating-point approximation can be; however, it is impractical for many floating-point methods to be correctly rounded. Instead, for the {@code Math} class, a larger error bound of 1 or 2 ulps is allowed for certain methods. Informally, with a 1 ulp error bound, when the exact result is a representable number, the exact result should be returned as the computed result; otherwise, either of the two floating-point values which bracket the exact result may be returned. For exact results large in magnitude, one of the endpoints of the bracket may be infinite. Besides accuracy at individual arguments, maintaining proper relations between the method at different arguments is also important. Therefore, most methods with more than 0.5 ulp errors are required to be semi-monotonic: whenever the mathematical function is non-decreasing, so is the floating-point approximation, likewise, whenever the mathematical function is non-increasing, so is the floating-point approximation. Not all approximations that have 1 ulp accuracy will automatically meet the monotonicity requirements.

Field Summary
public static final  double E    The {@code double} value that is closer than any other to e, the base of the natural logarithms. 
public static final  double PI    The {@code double} value that is closer than any other to pi, the ratio of the circumference of a circle to its diameter. 
Method from java.lang.Math Summary:
IEEEremainder,   abs,   abs,   abs,   abs,   acos,   asin,   atan,   atan2,   cbrt,   ceil,   copySign,   copySign,   cos,   cosh,   exp,   expm1,   floor,   getExponent,   getExponent,   hypot,   log,   log10,   log1p,   max,   max,   max,   max,   min,   min,   min,   min,   nextAfter,   nextAfter,   nextUp,   nextUp,   pow,   random,   rint,   round,   round,   scalb,   scalb,   signum,   signum,   sin,   sinh,   sqrt,   tan,   tanh,   toDegrees,   toRadians,   ulp,   ulp
Methods from java.lang.Object:
clone,   equals,   finalize,   getClass,   hashCode,   notify,   notifyAll,   toString,   wait,   wait,   wait
Method from java.lang.Math Detail:
 public static double IEEEremainder(double f1,
    double f2) 
    Computes the remainder operation on two arguments as prescribed by the IEEE 754 standard. The remainder value is mathematically equal to f1 - f2 × n, where n is the mathematical integer closest to the exact mathematical value of the quotient {@code f1/f2}, and if two mathematical integers are equally close to {@code f1/f2}, then n is the integer that is even. If the remainder is zero, its sign is the same as the sign of the first argument. Special cases:
    • 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.
 public static int abs(int a) 
    Returns the absolute value of an {@code int} value. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned.

    Note that if the argument is equal to the value of Integer#MIN_VALUE , the most negative representable {@code int} value, the result is that same value, which is negative.

 public static long abs(long a) 
    Returns the absolute value of a {@code long} value. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned.

    Note that if the argument is equal to the value of Long#MIN_VALUE , the most negative representable {@code long} value, the result is that same value, which is negative.

 public static float abs(float a) 
    Returns the absolute value of a {@code float} value. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned. Special cases:
    • If the argument is positive zero or negative zero, the result is positive zero.
    • If the argument is infinite, the result is positive infinity.
    • If the argument is NaN, the result is NaN.
    In other words, the result is the same as the value of the expression:

    {@code Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))}

 public static double abs(double a) 
    Returns the absolute value of a {@code double} value. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned. Special cases:
    • If the argument is positive zero or negative zero, the result is positive zero.
    • If the argument is infinite, the result is positive infinity.
    • If the argument is NaN, the result is NaN.
    In other words, the result is the same as the value of the expression:

    {@code Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1)}

 public static double acos(double a) 
    Returns the arc cosine of a value; the returned angle is in the range 0.0 through pi. Special case:
    • If the argument is NaN or its absolute value is greater than 1, then the result is NaN.

    The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

 public static double asin(double a) 
    Returns the arc sine of a value; the returned angle is in the range -pi/2 through pi/2. Special cases:
    • If the argument is NaN or its absolute value is greater than 1, then the result is NaN.
    • If the argument is zero, then the result is a zero with the same sign as the argument.

    The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

 public static double atan(double a) 
    Returns the arc tangent of a value; the returned angle is in the range -pi/2 through pi/2. Special cases:
    • If the argument is NaN, then the result is NaN.
    • If the argument is zero, then the result is a zero with the same sign as the argument.

    The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

 public static double atan2(double y,
    double x) 
    Returns the angle theta from the conversion of rectangular coordinates ({@code x}, {@code y}) to polar coordinates (r, theta). This method computes the phase theta by computing an arc tangent of {@code y/x} in the range of -pi to pi. Special cases:
    • If either argument is NaN, then the result is NaN.
    • If the first argument is positive zero and the second argument is positive, or the first argument is positive and finite and the second argument is positive infinity, then the result is positive zero.
    • If the first argument is negative zero and the second argument is positive, or the first argument is negative and finite and the second argument is positive infinity, then the result is negative zero.
    • If the first argument is positive zero and the second argument is negative, or the first argument is positive and finite and the second argument is negative infinity, then the result is the {@code double} value closest to pi.
    • If the first argument is negative zero and the second argument is negative, or the first argument is negative and finite and the second argument is negative infinity, then the result is the {@code double} value closest to -pi.
    • If the first argument is positive and the second argument is positive zero or negative zero, or the first argument is positive infinity and the second argument is finite, then the result is the {@code double} value closest to pi/2.
    • If the first argument is negative and the second argument is positive zero or negative zero, or the first argument is negative infinity and the second argument is finite, then the result is the {@code double} value closest to -pi/2.
    • If both arguments are positive infinity, then the result is the {@code double} value closest to pi/4.
    • If the first argument is positive infinity and the second argument is negative infinity, then the result is the {@code double} value closest to 3*pi/4.
    • If the first argument is negative infinity and the second argument is positive infinity, then the result is the {@code double} value closest to -pi/4.
    • If both arguments are negative infinity, then the result is the {@code double} value closest to -3*pi/4.

    The computed result must be within 2 ulps of the exact result. Results must be semi-monotonic.

 public static double cbrt(double a) 
    Returns the cube root of a {@code double} value. For positive finite {@code x}, {@code cbrt(-x) == -cbrt(x)}; that is, the cube root of a negative value is the negative of the cube root of that value's magnitude. Special cases:
    • If the argument is NaN, then the result is NaN.
    • If the argument is infinite, then the result is an infinity with the same sign as the argument.
    • If the argument is zero, then the result is a zero with the same sign as the argument.

    The computed result must be within 1 ulp of the exact result.

 public static double ceil(double a) 
    Returns the smallest (closest to negative infinity) {@code double} value that is greater than or equal to the argument and is equal to a mathematical integer. Special cases:
    • If the argument value is already equal to a mathematical integer, then the result is the same as the argument.
    • If the argument is NaN or an infinity or positive zero or negative zero, then the result is the same as the argument.
    • If the argument value is less than zero but greater than -1.0, then the result is negative zero.
    Note that the value of {@code Math.ceil(x)} is exactly the value of {@code -Math.floor(-x)}.
 public static double copySign(double magnitude,
    double sign) 
    Returns the first floating-point argument with the sign of the second floating-point argument. Note that unlike the StrictMath.copySign method, this method does not require NaN {@code sign} arguments to be treated as positive values; implementations are permitted to treat some NaN arguments as positive and other NaN arguments as negative to allow greater performance.
 public static float copySign(float magnitude,
    float sign) 
    Returns the first floating-point argument with the sign of the second floating-point argument. Note that unlike the StrictMath.copySign method, this method does not require NaN {@code sign} arguments to be treated as positive values; implementations are permitted to treat some NaN arguments as positive and other NaN arguments as negative to allow greater performance.
 public static double cos(double a) 
    Returns the trigonometric cosine of an angle. Special cases:
    • If the argument is NaN or an infinity, then the result is NaN.

    The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

 public static double cosh(double x) 
    Returns the hyperbolic cosine of a {@code double} value. The hyperbolic cosine of x is defined to be (ex + e-x)/2 where e is {@linkplain Math#E Euler's number}.

    Special cases:

    • If the argument is NaN, then the result is NaN.
    • If the argument is infinite, then the result is positive infinity.
    • If the argument is zero, then the result is {@code 1.0}.

    The computed result must be within 2.5 ulps of the exact result.

 public static double exp(double a) 
    Returns Euler's number e raised to the power of a {@code double} value. Special cases:
    • If the argument is NaN, the result is NaN.
    • If the argument is positive infinity, then the result is positive infinity.
    • If the argument is negative infinity, then the result is positive zero.

    The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

 public static double expm1(double x) 
    Returns ex -1. Note that for values of x near 0, the exact sum of {@code expm1(x)} + 1 is much closer to the true result of ex than {@code exp(x)}.

    Special cases:

    • If the argument is NaN, the result is NaN.
    • If the argument is positive infinity, then the result is positive infinity.
    • If the argument is negative infinity, then the result is -1.0.
    • If the argument is zero, then the result is a zero with the same sign as the argument.

    The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic. The result of {@code expm1} for any finite input must be greater than or equal to {@code -1.0}. Note that once the exact result of e{@code x} - 1 is within 1/2 ulp of the limit value -1, {@code -1.0} should be returned.

 public static double floor(double a) 
    Returns the largest (closest to positive infinity) {@code double} value that is less than or equal to the argument and is equal to a mathematical integer. Special cases:
    • If the argument value is already equal to a mathematical integer, then the result is the same as the argument.
    • If the argument is NaN or an infinity or positive zero or negative zero, then the result is the same as the argument.
 public static int getExponent(float f) 
    Returns the unbiased exponent used in the representation of a {@code float}. Special cases:
 public static int getExponent(double d) 
    Returns the unbiased exponent used in the representation of a {@code double}. Special cases:
 public static double hypot(double x,
    double y) 
    Returns sqrt(x2 +y2) without intermediate overflow or underflow.

    Special cases:

    • If either argument is infinite, then the result is positive infinity.
    • If either argument is NaN and neither argument is infinite, then the result is NaN.

    The computed result must be within 1 ulp of the exact result. If one parameter is held constant, the results must be semi-monotonic in the other parameter.

 public static double log(double a) 
    Returns the natural logarithm (base e) of a {@code double} value. Special cases:
    • If the argument is NaN or less than zero, then the result is NaN.
    • If the argument is positive infinity, then the result is positive infinity.
    • If the argument is positive zero or negative zero, then the result is negative infinity.

    The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

 public static double log10(double a) 
    Returns the base 10 logarithm of a {@code double} value. Special cases:
    • If the argument is NaN or less than zero, then the result is NaN.
    • If the argument is positive infinity, then the result is positive infinity.
    • If the argument is positive zero or negative zero, then the result is negative infinity.
    • If the argument is equal to 10n for integer n, then the result is n.

    The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

 public static double log1p(double x) 
    Returns the natural logarithm of the sum of the argument and 1. Note that for small values {@code x}, the result of {@code log1p(x)} is much closer to the true result of ln(1 + {@code x}) than the floating-point evaluation of {@code log(1.0+x)}.

    Special cases:

    • If the argument is NaN or less than -1, then the result is NaN.
    • If the argument is positive infinity, then the result is positive infinity.
    • If the argument is negative one, then the result is negative infinity.
    • If the argument is zero, then the result is a zero with the same sign as the argument.

    The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

 public static int max(int a,
    int b) 
    Returns the greater of two {@code int} values. That is, the result is the argument closer to the value of Integer#MAX_VALUE . If the arguments have the same value, the result is that same value.
 public static long max(long a,
    long b) 
    Returns the greater of two {@code long} values. That is, the result is the argument closer to the value of Long#MAX_VALUE . If the arguments have the same value, the result is that same value.
 public static float max(float a,
    float b) 
    Returns the greater of two {@code float} values. That is, the result is the argument closer to positive infinity. If the arguments have the same value, the result is that same value. If either value is NaN, then the result is NaN. Unlike the numerical comparison operators, this method considers negative zero to be strictly smaller than positive zero. If one argument is positive zero and the other negative zero, the result is positive zero.
 public static double max(double a,
    double b) 
    Returns the greater of two {@code double} values. That is, the result is the argument closer to positive infinity. If the arguments have the same value, the result is that same value. If either value is NaN, then the result is NaN. Unlike the numerical comparison operators, this method considers negative zero to be strictly smaller than positive zero. If one argument is positive zero and the other negative zero, the result is positive zero.
 public static int min(int a,
    int b) 
    Returns the smaller of two {@code int} values. That is, the result the argument closer to the value of Integer#MIN_VALUE . If the arguments have the same value, the result is that same value.
 public static long min(long a,
    long b) 
    Returns the smaller of two {@code long} values. That is, the result is the argument closer to the value of Long#MIN_VALUE . If the arguments have the same value, the result is that same value.
 public static float min(float a,
    float b) 
    Returns the smaller of two {@code float} values. That is, the result is the value closer to negative infinity. If the arguments have the same value, the result is that same value. If either value is NaN, then the result is NaN. Unlike the numerical comparison operators, this method considers negative zero to be strictly smaller than positive zero. If one argument is positive zero and the other is negative zero, the result is negative zero.
 public static double min(double a,
    double b) 
    Returns the smaller of two {@code double} values. That is, the result is the value closer to negative infinity. If the arguments have the same value, the result is that same value. If either value is NaN, then the result is NaN. Unlike the numerical comparison operators, this method considers negative zero to be strictly smaller than positive zero. If one argument is positive zero and the other is negative zero, the result is negative zero.
 public static double nextAfter(double start,
    double direction) 
    Returns the floating-point number adjacent to the first argument in the direction of the second argument. If both arguments compare as equal the second argument is returned.

    Special cases:

    • If either argument is a NaN, then NaN is returned.
    • If both arguments are signed zeros, {@code direction} is returned unchanged (as implied by the requirement of returning the second argument if the arguments compare as equal).
    • If {@code start} is ±Double#MIN_VALUE and {@code direction} has a value such that the result should have a smaller magnitude, then a zero with the same sign as {@code start} is returned.
    • If {@code start} is infinite and {@code direction} has a value such that the result should have a smaller magnitude, Double#MAX_VALUE with the same sign as {@code start} is returned.
    • If {@code start} is equal to ± Double#MAX_VALUE and {@code direction} has a value such that the result should have a larger magnitude, an infinity with same sign as {@code start} is returned.
 public static float nextAfter(float start,
    double direction) 
    Returns the floating-point number adjacent to the first argument in the direction of the second argument. If both arguments compare as equal a value equivalent to the second argument is returned.

    Special cases:

    • If either argument is a NaN, then NaN is returned.
    • If both arguments are signed zeros, a value equivalent to {@code direction} is returned.
    • If {@code start} is ±Float#MIN_VALUE and {@code direction} has a value such that the result should have a smaller magnitude, then a zero with the same sign as {@code start} is returned.
    • If {@code start} is infinite and {@code direction} has a value such that the result should have a smaller magnitude, Float#MAX_VALUE with the same sign as {@code start} is returned.
    • If {@code start} is equal to ± Float#MAX_VALUE and {@code direction} has a value such that the result should have a larger magnitude, an infinity with same sign as {@code start} is returned.
 public static double nextUp(double d) 
    Returns the floating-point value adjacent to {@code d} in the direction of positive infinity. This method is semantically equivalent to {@code nextAfter(d, Double.POSITIVE_INFINITY)}; however, a {@code nextUp} implementation may run faster than its equivalent {@code nextAfter} call.

    Special Cases:

    • If the argument is NaN, the result is NaN.
    • If the argument is positive infinity, the result is positive infinity.
    • If the argument is zero, the result is Double#MIN_VALUE
 public static float nextUp(float f) 
    Returns the floating-point value adjacent to {@code f} in the direction of positive infinity. This method is semantically equivalent to {@code nextAfter(f, Float.POSITIVE_INFINITY)}; however, a {@code nextUp} implementation may run faster than its equivalent {@code nextAfter} call.

    Special Cases:

    • If the argument is NaN, the result is NaN.
    • If the argument is positive infinity, the result is positive infinity.
    • If the argument is zero, the result is Float#MIN_VALUE
 public static double pow(double a,
    double b) 
    Returns the value of the first argument raised to the power of the second argument. Special cases:
    • If the second argument is positive or negative zero, then the result is 1.0.
    • If the second argument is 1.0, then the result is the same as the first argument.
    • If the second argument is NaN, then the result is NaN.
    • If the first argument is NaN and the second argument is nonzero, then the result is NaN.
    • If
      • the absolute value of the first argument is greater than 1 and the second argument is positive infinity, or
      • the absolute value of the first argument is less than 1 and the second argument is negative infinity,
      then the result is positive infinity.
    • If
      • the absolute value of the first argument is greater than 1 and the second argument is negative infinity, or
      • the absolute value of the first argument is less than 1 and the second argument is positive infinity,
      then the result is positive zero.
    • If the absolute value of the first argument equals 1 and the second argument is infinite, then the result is NaN.
    • If
      • the first argument is positive zero and the second argument is greater than zero, or
      • the first argument is positive infinity and the second argument is less than zero,
      then the result is positive zero.
    • If
      • the first argument is positive zero and the second argument is less than zero, or
      • the first argument is positive infinity and the second argument is greater than zero,
      then the result is positive infinity.
    • If
      • the first argument is negative zero and the second argument is greater than zero but not a finite odd integer, or
      • the first argument is negative infinity and the second argument is less than zero but not a finite odd integer,
      then the result is positive zero.
    • If
      • the first argument is negative zero and the second argument is a positive finite odd integer, or
      • the first argument is negative infinity and the second argument is a negative finite odd integer,
      then the result is negative zero.
    • If
      • the first argument is negative zero and the second argument is less than zero but not a finite odd integer, or
      • the first argument is negative infinity and the second argument is greater than zero but not a finite odd integer,
      then the result is positive infinity.
    • If
      • the first argument is negative zero and the second argument is a negative finite odd integer, or
      • the first argument is negative infinity and the second argument is a positive finite odd integer,
      then the result is negative infinity.
    • If the first argument is finite and less than zero
      • if the second argument is a finite even integer, the result is equal to the result of raising the absolute value of the first argument to the power of the second argument
      • if the second argument is a finite odd integer, the result is equal to the negative of the result of raising the absolute value of the first argument to the power of the second argument
      • if the second argument is finite and not an integer, then the result is NaN.
    • If both arguments are integers, then the result is exactly equal to the mathematical result of raising the first argument to the power of the second argument if that result can in fact be represented exactly as a {@code double} value.

    (In the foregoing descriptions, a floating-point value is considered to be an integer if and only if it is finite and a fixed point of the method ceil or, equivalently, a fixed point of the method floor . A value is a fixed point of a one-argument method if and only if the result of applying the method to the value is equal to the value.)

    The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

 public static double random() 
    Returns a {@code double} value with a positive sign, greater than or equal to {@code 0.0} and less than {@code 1.0}. Returned values are chosen pseudorandomly with (approximately) uniform distribution from that range.

    When this method is first called, it creates a single new pseudorandom-number generator, exactly as if by the expression

    {@code new java.util.Random()}
    This new pseudorandom-number generator is used thereafter for all calls to this method and is used nowhere else.

    This method is properly synchronized to allow correct use by more than one thread. However, if many threads need to generate pseudorandom numbers at a great rate, it may reduce contention for each thread to have its own pseudorandom-number generator.

 public static double rint(double a) 
    Returns the {@code double} value that is closest in value to the argument and is equal to a mathematical integer. If two {@code double} values that are mathematical integers are equally close, the result is the integer value that is even. Special cases:
    • If the argument value is already equal to a mathematical integer, then the result is the same as the argument.
    • If the argument is NaN or an infinity or positive zero or negative zero, then the result is the same as the argument.
 public static int round(float a) 
    Returns the closest {@code int} to the argument, with ties rounding up.

    Special cases:

    • If the argument is NaN, the result is 0.
    • If the argument is negative infinity or any value less than or equal to the value of {@code Integer.MIN_VALUE}, the result is equal to the value of {@code Integer.MIN_VALUE}.
    • If the argument is positive infinity or any value greater than or equal to the value of {@code Integer.MAX_VALUE}, the result is equal to the value of {@code Integer.MAX_VALUE}.
 public static long round(double a) 
    Returns the closest {@code long} to the argument, with ties rounding up.

    Special cases:

    • If the argument is NaN, the result is 0.
    • If the argument is negative infinity or any value less than or equal to the value of {@code Long.MIN_VALUE}, the result is equal to the value of {@code Long.MIN_VALUE}.
    • If the argument is positive infinity or any value greater than or equal to the value of {@code Long.MAX_VALUE}, the result is equal to the value of {@code Long.MAX_VALUE}.
 public static double scalb(double d,
    int scaleFactor) 
    Return {@code d} × 2{@code scaleFactor} rounded as if performed by a single correctly rounded floating-point multiply to a member of the double value set. See the Java Language Specification for a discussion of floating-point value sets. If the exponent of the result is between Double#MIN_EXPONENT and Double#MAX_EXPONENT , the answer is calculated exactly. If the exponent of the result would be larger than {@code Double.MAX_EXPONENT}, an infinity is returned. Note that if the result is subnormal, precision may be lost; that is, when {@code scalb(x, n)} is subnormal, {@code scalb(scalb(x, n), -n)} may not equal x. When the result is non-NaN, the result has the same sign as {@code d}.

    Special cases:

    • If the first argument is NaN, NaN is returned.
    • If the first argument is infinite, then an infinity of the same sign is returned.
    • If the first argument is zero, then a zero of the same sign is returned.
 public static float scalb(float f,
    int scaleFactor) 
    Return {@code f} × 2{@code scaleFactor} rounded as if performed by a single correctly rounded floating-point multiply to a member of the float value set. See the Java Language Specification for a discussion of floating-point value sets. If the exponent of the result is between Float#MIN_EXPONENT and Float#MAX_EXPONENT , the answer is calculated exactly. If the exponent of the result would be larger than {@code Float.MAX_EXPONENT}, an infinity is returned. Note that if the result is subnormal, precision may be lost; that is, when {@code scalb(x, n)} is subnormal, {@code scalb(scalb(x, n), -n)} may not equal x. When the result is non-NaN, the result has the same sign as {@code f}.

    Special cases:

    • If the first argument is NaN, NaN is returned.
    • If the first argument is infinite, then an infinity of the same sign is returned.
    • If the first argument is zero, then a zero of the same sign is returned.
 public static double signum(double d) 
    Returns the signum function of the argument; zero if the argument is zero, 1.0 if the argument is greater than zero, -1.0 if the argument is less than zero.

    Special Cases:

    • If the argument is NaN, then the result is NaN.
    • If the argument is positive zero or negative zero, then the result is the same as the argument.
 public static float signum(float f) 
    Returns the signum function of the argument; zero if the argument is zero, 1.0f if the argument is greater than zero, -1.0f if the argument is less than zero.

    Special Cases:

    • If the argument is NaN, then the result is NaN.
    • If the argument is positive zero or negative zero, then the result is the same as the argument.
 public static double sin(double a) 
    Returns the trigonometric sine of an angle. Special cases:
    • If the argument is NaN or an infinity, then the result is NaN.
    • If the argument is zero, then the result is a zero with the same sign as the argument.

    The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

 public static double sinh(double x) 
    Returns the hyperbolic sine of a {@code double} value. The hyperbolic sine of x is defined to be (ex - e-x)/2 where e is {@linkplain Math#E Euler's number}.

    Special cases:

    • If the argument is NaN, then the result is NaN.
    • If the argument is infinite, then the result is an infinity with the same sign as the argument.
    • If the argument is zero, then the result is a zero with the same sign as the argument.

    The computed result must be within 2.5 ulps of the exact result.

 public static double sqrt(double a) 
    Returns the correctly rounded positive square root of a {@code double} value. Special cases:
    • If the argument is NaN or less than zero, then the result is NaN.
    • If the argument is positive infinity, then the result is positive infinity.
    • If the argument is positive zero or negative zero, then the result is the same as the argument.
    Otherwise, the result is the {@code double} value closest to the true mathematical square root of the argument value.
 public static double tan(double a) 
    Returns the trigonometric tangent of an angle. Special cases:
    • If the argument is NaN or an infinity, then the result is NaN.
    • If the argument is zero, then the result is a zero with the same sign as the argument.

    The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

 public static double tanh(double x) 
    Returns the hyperbolic tangent of a {@code double} value. The hyperbolic tangent of x is defined to be (ex - e-x)/(ex + e-x), in other words, {@linkplain Math#sinh sinh(x)}/{@linkplain Math#cosh cosh(x)}. Note that the absolute value of the exact tanh is always less than 1.

    Special cases:

    • If the argument is NaN, then the result is NaN.
    • If the argument is zero, then the result is a zero with the same sign as the argument.
    • If the argument is positive infinity, then the result is {@code +1.0}.
    • If the argument is negative infinity, then the result is {@code -1.0}.

    The computed result must be within 2.5 ulps of the exact result. The result of {@code tanh} for any finite input must have an absolute value less than or equal to 1. Note that once the exact result of tanh is within 1/2 of an ulp of the limit value of ±1, correctly signed ±{@code 1.0} should be returned.

 public static double toDegrees(double angrad) 
    Converts an angle measured in radians to an approximately equivalent angle measured in degrees. The conversion from radians to degrees is generally inexact; users should not expect {@code cos(toRadians(90.0))} to exactly equal {@code 0.0}.
 public static double toRadians(double angdeg) 
    Converts an angle measured in degrees to an approximately equivalent angle measured in radians. The conversion from degrees to radians is generally inexact.
 public static double ulp(double d) 
    Returns the size of an ulp of the argument. An ulp of a {@code double} value is the positive distance between this floating-point value and the {@code double} value next larger in magnitude. Note that for non-NaN x, ulp(-x) == ulp(x).

    Special Cases:

    • If the argument is NaN, then the result is NaN.
    • If the argument is positive or negative infinity, then the result is positive infinity.
    • If the argument is positive or negative zero, then the result is {@code Double.MIN_VALUE}.
    • If the argument is ±{@code Double.MAX_VALUE}, then the result is equal to 2971.
 public static float ulp(float f) 
    Returns the size of an ulp of the argument. An ulp of a {@code float} value is the positive distance between this floating-point value and the {@code float} value next larger in magnitude. Note that for non-NaN x, ulp(-x) == ulp(x).

    Special Cases:

    • If the argument is NaN, then the result is NaN.
    • If the argument is positive or negative infinity, then the result is positive infinity.
    • If the argument is positive or negative zero, then the result is {@code Float.MIN_VALUE}.
    • If the argument is ±{@code Float.MAX_VALUE}, then the result is equal to 2104.