Mathpublic final class Math extends Object The class 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
StrictMath , all implementations of the equivalent
functions of class Math are not defined to return the
bitforbit same results. This relaxation permits
betterperforming implementations where strict reproducibility is
not required.
By default many of the Math methods simply call
the equivalent method in StrictMath for their
implementation. Code generators are encouraged to use
platformspecific native libraries or microprocessor instructions,
where available, to provide higherperformance implementations of
Math methods. Such higherperformance
implementations still must conform to the specification for
Math .
The quality of implementation specifications concern two
properties, accuracy of the returned result and monotonicity of the
method. Accuracy of the floatingpoint Math methods
is measured in terms of ulps, units in the last place. For
a given floatingpoint format, an ulp of a specific real number
value is the distance between the two floatingpoint 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 worstcase error at any argument. If a
method always has an error less than 0.5 ulps, the method always
returns the floatingpoint number nearest the exact result; such a
method is correctly rounded. A correctly rounded method is
generally the best a floatingpoint approximation can be; however,
it is impractical for many floatingpoint 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 floatingpoint 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 semimonotonic: whenever the mathematical
function is nondecreasing, so is the floatingpoint approximation,
likewise, whenever the mathematical function is nonincreasing, so
is the floatingpoint approximation. Not all approximations that
have 1 ulp accuracy will automatically meet the monotonicity
requirements. 
Fields Summary 

public static final double  EThe double value that is closer than any other to
e, the base of the natural logarithms.  public static final double  PIThe double value that is closer than any other to
pi, the ratio of the circumference of a circle to its
diameter.  private static Random  randomNumberGenerator  private static long  negativeZeroFloatBits  private static long  negativeZeroDoubleBits 
Constructors Summary 

private Math()Don't let anyone instantiate this class.

Methods Summary 

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 f1/f2 , and if two
mathematical integers are equally close to 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.
return StrictMath.IEEEremainder(f1, f2); // delegate to StrictMath
 public static int  abs(int a)Returns the absolute value of an 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
int value, the result is that same value, which is
negative.
return (a < 0) ? a : a;
 public static long  abs(long a)Returns the absolute value of a 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
long value, the result is that same value, which
is negative.
return (a < 0) ? a : a;
 public static float  abs(float a)Returns the absolute value of a 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:
Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))
return (a <= 0.0F) ? 0.0F  a : a;
 public static double  abs(double a)Returns the absolute value of a 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:
Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1)
return (a <= 0.0D) ? 0.0D  a : a;
 public static double  acos(double a)Returns the arc cosine of an angle, in the range of 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 semimonotonic.
return StrictMath.acos(a); // default impl. delegates to StrictMath
 public static double  asin(double a)Returns the arc sine of an angle, in the range of 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 semimonotonic.
return StrictMath.asin(a); // default impl. delegates to StrictMath
 public static double  atan(double a)Returns the arc tangent of an angle, in the range of 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 semimonotonic.
return StrictMath.atan(a); // default impl. delegates to StrictMath
 public static double  atan2(double y, double x)Converts rectangular coordinates (x , y )
to polar (r, theta).
This method computes the phase theta by computing an arc tangent
of 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
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.
 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
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
double value closest to pi/2.
 If both arguments are positive infinity, then the result is the
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
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
double value
closest to pi/4.
 If both arguments are negative infinity, then the result is the
double value closest to 3*pi/4.
The computed result must be within 2 ulps of the exact result.
Results must be semimonotonic.
return StrictMath.atan2(y, x); // default impl. delegates to StrictMath
 public static double  cbrt(double a)Returns the cube root of a double value. For
positive finite x , 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.
return StrictMath.cbrt(a);
 public static double  ceil(double a)Returns the smallest (closest to negative infinity)
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 Math.ceil(x) is exactly the
value of Math.floor(x) .
return StrictMath.ceil(a); // default impl. delegates to StrictMath
 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 semimonotonic.
return StrictMath.cos(a); // default impl. delegates to StrictMath
 public static double  cosh(double x)Returns the hyperbolic cosine of a double value.
The hyperbolic cosine of x is defined to be
(e^{x} + 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
1.0 .
The computed result must be within 2.5 ulps of the exact result.
return StrictMath.cosh(x);
 public static double  exp(double a)Returns Euler's number e raised to the power of a
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 semimonotonic.
return StrictMath.exp(a); // default impl. delegates to StrictMath
 public static double  expm1(double x)Returns e^{x} 1. Note that for values of
x near 0, the exact sum of
expm1(x) + 1 is much closer to the true
result of e^{x} than 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 semimonotonic. The result of
expm1 for any finite input must be greater than or
equal to 1.0 . Note that once the exact result of
e^{x}  1 is within 1/2
ulp of the limit value 1, 1.0 should be
returned.
return StrictMath.expm1(x);
 public static double  floor(double a)Returns the largest (closest to positive infinity)
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.
return StrictMath.floor(a); // default impl. delegates to StrictMath
 public static double  hypot(double x, double y)Returns sqrt(x^{2} +y^{2})
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
semimonotonic in the other parameter.
return StrictMath.hypot(x, y);
 private static synchronized void  initRNG()
if (randomNumberGenerator == null)
randomNumberGenerator = new Random();
 public static double  log(double a)Returns the natural logarithm (base e) of a 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 semimonotonic.
return StrictMath.log(a); // default impl. delegates to StrictMath
 public static double  log10(double a)Returns the base 10 logarithm of a 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 10^{n} for
integer n, then the result is n.
The computed result must be within 1 ulp of the exact result.
Results must be semimonotonic.
return StrictMath.log10(a); // default impl. delegates to StrictMath
 public static double  log1p(double x)Returns the natural logarithm of the sum of the argument and 1.
Note that for small values x , the result of
log1p(x) is much closer to the true result of ln(1
+ x ) than the floatingpoint evaluation of
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 semimonotonic.
return StrictMath.log1p(x);
 public static int  max(int a, int b)Returns the greater of two 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.
return (a >= b) ? a : b;
 public static long  max(long a, long b)Returns the greater of two 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.
return (a >= b) ? a : b;
 public static float  max(float a, float b)Returns the greater of two 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.
if (a != a) return a; // a is NaN
if ((a == 0.0f) && (b == 0.0f)
&& (Float.floatToIntBits(a) == negativeZeroFloatBits)) {
return b;
}
return (a >= b) ? a : b;
 public static double  max(double a, double b)Returns the greater of two 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.
if (a != a) return a; // a is NaN
if ((a == 0.0d) && (b == 0.0d)
&& (Double.doubleToLongBits(a) == negativeZeroDoubleBits)) {
return b;
}
return (a >= b) ? a : b;
 public static int  min(int a, int b)Returns the smaller of two 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.
return (a <= b) ? a : b;
 public static long  min(long a, long b)Returns the smaller of two 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.
return (a <= b) ? a : b;
 public static float  min(float a, float b)Returns the smaller of two 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.
if (a != a) return a; // a is NaN
if ((a == 0.0f) && (b == 0.0f)
&& (Float.floatToIntBits(b) == negativeZeroFloatBits)) {
return b;
}
return (a <= b) ? a : b;
 public static double  min(double a, double b)Returns the smaller of two 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.
if (a != a) return a; // a is NaN
if ((a == 0.0d) && (b == 0.0d)
&& (Double.doubleToLongBits(b) == negativeZeroDoubleBits)) {
return b;
}
return (a <= b) ? a : b;
 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
double value.
(In the foregoing descriptions, a floatingpoint 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 oneargument
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 semimonotonic.
return StrictMath.pow(a, b); // default impl. delegates to StrictMath
 public static double  random()Returns a double value with a positive sign, greater
than or equal to 0.0 and less than 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
pseudorandomnumber generator, exactly as if by the expression
new java.util.Random This
new pseudorandomnumber 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 pseudorandomnumber generator.
if (randomNumberGenerator == null) initRNG();
return randomNumberGenerator.nextDouble();
 public static double  rint(double a)Returns the double value that is closest in value
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. 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.
return StrictMath.rint(a); // default impl. delegates to StrictMath
 public static int  round(float a)Returns the closest int to the argument. The
result is rounded to an integer by adding 1/2, taking the
floor of the result, and casting the result to type int .
In other words, the result is equal to the value of the expression:
(int)Math.floor(a + 0.5f)
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.MIN_VALUE , the result is
equal to the value of Integer.MIN_VALUE .
 If the argument is positive infinity or any value greater than or
equal to the value of
Integer.MAX_VALUE , the result is
equal to the value of Integer.MAX_VALUE .
return (int)floor(a + 0.5f);
 public static long  round(double a)Returns the closest long to the argument. The result
is rounded to an integer by adding 1/2, taking the floor of the
result, and casting the result to type long . In other
words, the result is equal to the value of the expression:
(long)Math.floor(a + 0.5d)
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
Long.MIN_VALUE , the result is
equal to the value of Long.MIN_VALUE .
 If the argument is positive infinity or any value greater than or
equal to the value of
Long.MAX_VALUE , the result is
equal to the value of Long.MAX_VALUE .
return (long)floor(a + 0.5d);
 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.
return sun.misc.FpUtils.signum(d);
 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.
return sun.misc.FpUtils.signum(f);
 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 semimonotonic.
return StrictMath.sin(a); // default impl. delegates to StrictMath
 public static double  sinh(double x)Returns the hyperbolic sine of a double value.
The hyperbolic sine of x is defined to be
(e^{x}  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.
return StrictMath.sinh(x);
 public static double  sqrt(double a)Returns the correctly rounded positive square root of a
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 double value closest to
the true mathematical square root of the argument value.
return StrictMath.sqrt(a); // default impl. delegates to StrictMath
// Note that hardware sqrt instructions
// frequently can be directly used by JITs
// and should be much faster than doing
// Math.sqrt in software.
 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 semimonotonic.
return StrictMath.tan(a); // default impl. delegates to StrictMath
 public static double  tanh(double x)Returns the hyperbolic tangent of a double value.
The hyperbolic tangent of x is defined to be
(e^{x}  e^{x})/(e^{x} + 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
+1.0 .
 If the argument is negative infinity, then the result is
1.0 .
The computed result must be within 2.5 ulps of the exact result.
The result of 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 ±1.0 should
be returned.
return StrictMath.tanh(x);
 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 cos(toRadians(90.0)) to exactly
equal 0.0 .
return angrad * 180.0 / PI;
 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.
return angdeg / 180.0 * PI;
 public static double  ulp(double d)Returns the size of an ulp of the argument. An ulp of a
double value is the positive distance between this
floatingpoint value and the double value next
larger in magnitude. Note that for nonNaN 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
Double.MIN_VALUE .
 If the argument is ±
Double.MAX_VALUE , then
the result is equal to 2^{971}.
return sun.misc.FpUtils.ulp(d);
 public static float  ulp(float f)Returns the size of an ulp of the argument. An ulp of a
float value is the positive distance between this
floatingpoint value and the float value next
larger in magnitude. Note that for nonNaN 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
Float.MIN_VALUE .
 If the argument is ±
Float.MAX_VALUE , then
the result is equal to 2^{104}.
return sun.misc.FpUtils.ulp(f);

