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Your reply has been successfully submitted. About UrbanPro. I am a Student I am a Tutor. Please enter your full name. Please enter institute name. Please enter your email address. Please enter a pincode or area name. Please enter city name. 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. 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 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. Not all approximations that have 1 ulp accuracy will automatically meet the monotonicity requirements.

Since: JDK1. Method Summary Methods Modifier and Type Method and Description static double abs double a Returns the absolute value of a double value. Methods inherited from class java. Object clone , equals , finalize , getClass , hashCode , notify , notifyAll , toString , wait , wait , wait Field Detail E public static final double E The double value that is closer than any other to e , the base of the natural logarithms.

See Also: Constant Field Values PI public static final double PI The double value that is closer than any other to pi , the ratio of the circumference of a circle to its diameter.

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.

Parameters: a - an angle, in radians. Returns: the sine of the argument. Returns: the cosine of the argument. Returns: the tangent of the argument. Special cases: If the argument is NaN or its absolute value is greater than 1, then the result is NaN. Parameters: a - the value whose arc sine is to be returned. Returns: the arc sine of the argument. Special case: If the argument is NaN or its absolute value is greater than 1, then the result is NaN.

Parameters: a - the value whose arc cosine is to be returned. Returns: the arc cosine of the argument. Parameters: a - the value whose arc tangent is to be returned. Returns: the arc tangent of the argument. The conversion from degrees to radians is generally inexact. Parameters: angdeg - an angle, in degrees Returns: the measurement of the angle angdeg in radians.

Since: 1. The conversion from radians to degrees is generally inexact; users should not expect cos toRadians Parameters: angrad - an angle, in radians Returns: the measurement of the angle angrad in degrees. If the argument is positive infinity, then the result is positive infinity.

If the argument is negative infinity, then the result is positive zero. Parameters: a - the exponent to raise e to. Returns: the value e a , where e is the base of the natural logarithms. If the argument is positive zero or negative zero, then the result is negative infinity. Parameters: a - a value Returns: the value ln a , the natural logarithm of a. If the argument is equal to 10 n for integer n , then the result is n.

Parameters: a - a value Returns: the base 10 logarithm of a. If the argument is positive zero or negative zero, then the result is the same as the argument. Otherwise, the result is the double value closest to the true mathematical square root of the argument value. Parameters: a - a value. Returns: the positive square root of a.

If the argument is NaN or less than zero, the result is NaN. If the argument is infinite, then the result is an infinity with the same sign as the argument. Returns: the cube root of a. 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. Parameters: f1 - the dividend. Returns: the remainder when f1 is divided by f2. 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 Note that the value of Math.

Returns: the smallest closest to negative infinity floating-point value that is greater than or equal to the argument and is equal to a mathematical integer. Returns: the largest closest to positive infinity floating-point value that less than or equal to the argument and is equal to a mathematical integer.

If two double values that are mathematical integers are equally close, the result is the integer value that is even. Parameters: a - a double value. Returns: the closest floating-point value to a that is equal to a mathematical integer.

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 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 double value closest to - pi.

The computed result must be within 2 ulps of the exact result. Parameters: y - the ordinate coordinate x - the abscissa coordinate Returns: the theta component of the point r , theta in polar coordinates that corresponds to the point x , y in Cartesian coordinates.

Special cases: If the second argument is positive or negative zero, then the result is 1. If the second argument is 1. 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 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. Parameters: a - the base. Returns: the value a b. 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 Integer.

If the argument is positive infinity or any value greater than or equal to the value of Integer. Parameters: a - a floating-point value to be rounded to an integer. Returns: the value of the argument rounded to the nearest int value. See Also: Integer. If the argument is negative infinity or any value less than or equal to the value of Long.

If the argument is positive infinity or any value greater than or equal to the value of Long. Parameters: a - a floating-point value to be rounded to a long. Returns: the value of the argument rounded to the nearest long value. See Also: Long. 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 new java. 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.

Returns: a pseudorandom double greater than or equal to 0. See Also: Random. 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. Parameters: a - the argument whose absolute value is to be determined Returns: the absolute value of the argument. Note that if the argument is equal to the value of Long.

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: Float. In other words, the result is the same as the value of the expression: Double. That is, the result is the argument closer to the value of Integer.

If the arguments have the same value, the result is that same value. Parameters: a - an argument. Returns: the larger of a and b.

That is, the result is the argument closer to the value of Long. That is, the result is the argument closer to positive infinity. 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.

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