package java.lang;
import java.util.Random;
public final class Math {
/**
* The {@code double} value that is closer than any other to e, the base of the natural
* logarithms.
*/
public static final double E = 2.7182818284590452354;
/**
* The {@code double} value that is closer than any other to pi, the ratio of the
* circumference of a circle to its diameter.
*/
public static final double PI = 3.14159265358979323846;
/**
* 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)}
*
* @param a
* the argument whose absolute value is to be determined
* @return the absolute value of the argument.
*/
public static double abs(double a) {
throw new RuntimeException();
}
/**
* 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))}
*
* @param a
* the argument whose absolute value is to be determined
* @return the absolute value of the argument.
*/
public static float abs(float a) {
throw new RuntimeException();
}
/**
* 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 {@link Integer#MIN_VALUE}, the most negative
* representable {@code int} value, the result is that same value, which is negative.
*
* @param a
* the argument whose absolute value is to be determined
* @return the absolute value of the argument.
*/
public static int abs(int a) {
throw new RuntimeException();
}
/**
* 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 {@link Long#MIN_VALUE}, the most negative
* representable {@code long} value, the result is that same value, which is negative.
*
* @param a
* the argument whose absolute value is to be determined
* @return the absolute value of the argument.
*/
public static long abs(long a) {
throw new RuntimeException();
}
/**
* 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.
*
* @param a
* the value whose arc cosine is to be returned.
* @return the arc cosine of the argument.
*/
public static double acos(double a) {
throw new RuntimeException();
}
/**
* 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.
*
* @param a
* the value whose arc sine is to be returned.
* @return the arc sine of the argument.
*/
public static double asin(double a) {
throw new RuntimeException();
}
/**
* 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.
*
* @param a
* the value whose arc tangent is to be returned.
* @return the arc tangent of the argument.
*/
public static double atan(double a) {
throw new RuntimeException();
}
/**
* 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.
*
* @param y
* the ordinate coordinate
* @param x
* the abscissa coordinate
* @return the theta component of the point (r, theta) in polar
* coordinates that corresponds to the point (x, y) in Cartesian
* coordinates.
*/
public static double atan2(double y, double x) {
throw new RuntimeException();
}
/**
* 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.
*
* @param a
* a value.
* @return the cube root of {@code a}.
*/
public static double cbrt(double a) {
throw new RuntimeException();
}
/**
* 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)}.
*
* @param a
* a value.
* @return 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.
*/
public static double ceil(double a) {
throw new RuntimeException();
}
/**
* Returns the first floating-point argument with the sign of the second floating-point argument.
*
* @param magnitude
* the parameter providing the magnitude of the result
* @param sign
* the parameter providing the sign of the result
* @return a value with the magnitude of {@code magnitude} and the sign of {@code sign}.
*/
public static double copySign(double magnitude, double sign) {
throw new RuntimeException();
}
/**
* Returns the first floating-point argument with the sign of the second floating-point argument.
*
* @param magnitude
* the parameter providing the magnitude of the result
* @param sign
* the parameter providing the sign of the result
* @return a value with the magnitude of {@code magnitude} and the sign of {@code sign}.
*/
public static float copySign(float magnitude, float sign) {
throw new RuntimeException();
}
/**
* 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.
*
* @param a
* an angle, in radians.
* @return the cosine of the argument.
*/
public static double cos(double a) {
throw new RuntimeException();
}
/**
* 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.
*
* @param x
* The number whose hyperbolic cosine is to be returned.
* @return The hyperbolic cosine of {@code x}.
*/
public static double cosh(double x) {
throw new RuntimeException();
}
/**
* 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.
*
* @param a
* the exponent to raise e to.
* @return the value e{@code a}, where e is the base of the natural
* logarithms.
*/
public static double exp(double a) {
throw new RuntimeException();
}
/**
* 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.
*
* @param x
* the exponent to raise e to in the computation of e{@code x}
* -1.
* @return the value e{@code x} - 1.
*/
public static double expm1(double x) {
throw new RuntimeException();
}
/**
* 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.
*
*
* @param a
* a value.
* @return the largest (closest to positive infinity) floating-point value that less than or equal
* to the argument and is equal to a mathematical integer.
*/
public static double floor(double a) {
throw new RuntimeException();
}
/**
* Returns the unbiased exponent used in the representation of a {@code double}. Special cases:
*
*
* - If the argument is NaN or infinite, then the result is {@link Double#MAX_EXPONENT} + 1.
*
- If the argument is zero or subnormal, then the result is {@link Double#MIN_EXPONENT} -1.
*
*
* @param d
* a {@code double} value
* @return the unbiased exponent of the argument
*/
public static int getExponent(double d) {
throw new RuntimeException();
}
/**
* Returns the unbiased exponent used in the representation of a {@code float}. Special cases:
*
*
* - If the argument is NaN or infinite, then the result is {@link Float#MAX_EXPONENT} + 1.
*
- If the argument is zero or subnormal, then the result is {@link Float#MIN_EXPONENT} -1.
*
*
* @param f
* a {@code float} value
* @return the unbiased exponent of the argument
*/
public static int getExponent(float f) {
throw new RuntimeException();
}
/**
* 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.
*
* @param x
* a value
* @param y
* a value
* @return sqrt(x2 +y2) without intermediate overflow or
* underflow
*/
public static double hypot(double x, double y) {
throw new RuntimeException();
}
/**
* 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.
*
*
* @param f1
* the dividend.
* @param f2
* the divisor.
* @return the remainder when {@code f1} is divided by {@code f2}.
*/
public static double IEEEremainder(double f1, double f2) {
throw new RuntimeException();
}
/**
* 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.
*
* @param a
* a value
* @return the value ln {@code a}, the natural logarithm of {@code a}.
*/
public static double log(double a) {
throw new RuntimeException();
}
/**
* 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.
*
* @param a
* a value
* @return the base 10 logarithm of {@code a}.
*/
public static double log10(double a) {
throw new RuntimeException();
}
/**
* 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.
*
* @param x
* a value
* @return the value ln({@code x} + 1), the natural log of {@code x} + 1
*/
public static double log1p(double x) {
throw new RuntimeException();
}
/**
* 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.
*
* @param a
* an argument.
* @param b
* another argument.
* @return the larger of {@code a} and {@code b}.
*/
public static double max(double a, double b) {
throw new RuntimeException();
}
/**
* 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.
*
* @param a
* an argument.
* @param b
* another argument.
* @return the larger of {@code a} and {@code b}.
*/
public static float max(float a, float b) {
throw new RuntimeException();
}
/**
* Returns the greater of two {@code int} values. That is, the result is the argument closer to the
* value of {@link Integer#MAX_VALUE}. If the arguments have the same value, the result is that same
* value.
*
* @param a
* an argument.
* @param b
* another argument.
* @return the larger of {@code a} and {@code b}.
*/
public static int max(int a, int b) {
throw new RuntimeException();
}
/**
* Returns the greater of two {@code long} values. That is, the result is the argument closer to the
* value of {@link Long#MAX_VALUE}. If the arguments have the same value, the result is that same
* value.
*
* @param a
* an argument.
* @param b
* another argument.
* @return the larger of {@code a} and {@code b}.
*/
public static long max(long a, long b) {
throw new RuntimeException();
}
/**
* 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.
*
* @param a
* an argument.
* @param b
* another argument.
* @return the smaller of {@code a} and {@code b}.
*/
public static double min(double a, double b) {
throw new RuntimeException();
}
/**
* 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.
*
* @param a
* an argument.
* @param b
* another argument.
* @return the smaller of {@code a} and {@code b}.
*/
public static float min(float a, float b) {
throw new RuntimeException();
}
/**
* Returns the smaller of two {@code int} values. That is, the result the argument closer to the
* value of {@link Integer#MIN_VALUE}. If the arguments have the same value, the result is that same
* value.
*
* @param a
* an argument.
* @param b
* another argument.
* @return the smaller of {@code a} and {@code b}.
*/
public static int min(int a, int b) {
throw new RuntimeException();
}
/**
* Returns the smaller of two {@code long} values. That is, the result is the argument closer to the
* value of {@link Long#MIN_VALUE}. If the arguments have the same value, the result is that same
* value.
*
* @param a
* an argument.
* @param b
* another argument.
* @return the smaller of {@code a} and {@code b}.
*/
public static long min(long a, long b) {
throw new RuntimeException();
}
/**
* 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 ±{@link 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, {@link Double#MAX_VALUE} with the same sign as {@code start} is
* returned.
*
*
- If {@code start} is equal to ± {@link 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.
*
*
* @param start
* starting floating-point value
* @param direction
* value indicating which of {@code start}'s neighbors or {@code start} should be returned
* @return The floating-point number adjacent to {@code start} in the direction of
* {@code direction}.
*/
public static double nextAfter(double start, double direction) {
throw new RuntimeException();
}
/**
* 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 ±{@link 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, {@link Float#MAX_VALUE} with the same sign as {@code start} is
* returned.
*
*
- If {@code start} is equal to ± {@link 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.
*
*
* @param start
* starting floating-point value
* @param direction
* value indicating which of {@code start}'s neighbors or {@code start} should be returned
* @return The floating-point number adjacent to {@code start} in the direction of
* {@code direction}.
*/
public static float nextAfter(float start, double direction) {
throw new RuntimeException();
}
/**
* 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 {@link Double#MIN_VALUE}
*
*
*
* @param d
* starting floating-point value
* @return The adjacent floating-point value closer to positive infinity.
*/
public static double nextUp(double d) {
throw new RuntimeException();
}
/**
* 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 {@link Float#MIN_VALUE}
*
*
*
* @param f
* starting floating-point value
* @return The adjacent floating-point value closer to positive infinity.
*/
public static float nextUp(float f) {
throw new RuntimeException();
}
/**
* 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 {@link #ceil ceil} or, equivalently, a fixed
* point of the method {@link #floor 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.
*
* @param a
* the base.
* @param b
* the exponent.
* @return the value {@code a}{@code b}.
*/
public static double pow(double a, double b) {
throw new RuntimeException();
}
/**
* 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.
*
* @return a pseudorandom {@code double} greater than or equal to {@code 0.0} and less than
* {@code 1.0}.
* @see Random#nextDouble()
*/
public static double random() {
throw new RuntimeException();
}
/**
* 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.
*
*
* @param a
* a {@code double} value.
* @return the closest floating-point value to {@code a} that is equal to a mathematical integer.
*/
public static double rint(double a) {
throw new RuntimeException();
}
/**
* 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}.
*
*
* @param a
* a floating-point value to be rounded to a {@code long}.
* @return the value of the argument rounded to the nearest {@code long} value.
* @see java.lang.Long#MAX_VALUE
* @see java.lang.Long#MIN_VALUE
*/
public static long round(double a) {
throw new RuntimeException();
}
/**
* 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}.
*
*
* @param a
* a floating-point value to be rounded to an integer.
* @return the value of the argument rounded to the nearest {@code int} value.
* @see java.lang.Integer#MAX_VALUE
* @see java.lang.Integer#MIN_VALUE
*/
public static int round(float a) {
throw new RuntimeException();
}
/**
* 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 {@link Double#MIN_EXPONENT} and {@link 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.
*
*
* @param d
* number to be scaled by a power of two.
* @param scaleFactor
* power of 2 used to scale {@code d}
* @return {@code d} × 2{@code scaleFactor}
*/
public static double scalb(double d, int scaleFactor) {
throw new RuntimeException();
}
/**
* 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 {@link Float#MIN_EXPONENT} and {@link 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.
*
*
* @param f
* number to be scaled by a power of two.
* @param scaleFactor
* power of 2 used to scale {@code f}
* @return {@code f} × 2{@code scaleFactor}
*/
public static float scalb(float f, int scaleFactor) {
throw new RuntimeException();
}
/**
* 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.
*
*
* @param d
* the floating-point value whose signum is to be returned
* @return the signum function of the argument
*/
public static double signum(double d) {
throw new RuntimeException();
}
/**
* 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.
*
*
* @param f
* the floating-point value whose signum is to be returned
* @return the signum function of the argument
*/
public static float signum(float f) {
throw new RuntimeException();
}
/**
* 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.
*
* @param a
* an angle, in radians.
* @return the sine of the argument.
*/
public static double sin(double a) {
throw new RuntimeException();
}
/**
* 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.
*
* @param x
* The number whose hyperbolic sine is to be returned.
* @return The hyperbolic sine of {@code x}.
*/
public static double sinh(double x) {
throw new RuntimeException();
}
/**
* 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.
*
* @param a
* a value.
* @return the positive square root of {@code a}. If the argument is NaN or less than zero, the
* result is NaN.
*/
public static double sqrt(double a) {
throw new RuntimeException();
}
/**
* 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.
*
* @param a
* an angle, in radians.
* @return the tangent of the argument.
*/
public static double tan(double a) {
throw new RuntimeException();
}
/**
* 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.
*
* @param x
* The number whose hyperbolic tangent is to be returned.
* @return The hyperbolic tangent of {@code x}.
*/
public static double tanh(double x) {
throw new RuntimeException();
}
/**
* 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}.
*
* @param angrad
* an angle, in radians
* @return the measurement of the angle {@code angrad} in degrees.
*/
public static double toDegrees(double angrad) {
throw new RuntimeException();
}
/**
* Converts an angle measured in degrees to an approximately equivalent angle measured in radians.
* The conversion from degrees to radians is generally inexact.
*
* @param angdeg
* an angle, in degrees
* @return the measurement of the angle {@code angdeg} in radians.
*/
public static double toRadians(double angdeg) {
throw new RuntimeException();
}
/**
* 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.
*
*
* @param d
* the floating-point value whose ulp is to be returned
* @return the size of an ulp of the argument
*/
public static double ulp(double d) {
throw new RuntimeException();
}
/**
* 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.
*
*
* @param f
* the floating-point value whose ulp is to be returned
* @return the size of an ulp of the argument
*/
public static float ulp(float f) {
throw new RuntimeException();
}
}
/**
* 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.
*/