StrictMathpublic final class StrictMath extends Object The class StrictMath contains methods for performing basic
numeric operations such as the elementary exponential, logarithm,
square root, and trigonometric functions.
To help ensure portability of Java programs, the definitions of
some of the numeric functions in this package require that they
produce the same results as certain published algorithms. These
algorithms are available from the wellknown network library
netlib as the package "Freely Distributable Math
Library," fdlibm . These
algorithms, which are written in the C programming language, are
then to be understood as executed with all floatingpoint
operations following the rules of Java floatingpoint arithmetic.
The Java math library is defined with respect to
fdlibm version 5.3. Where fdlibm provides
more than one definition for a function (such as
acos ), use the "IEEE 754 core function" version
(residing in a file whose name begins with the letter
e ). The methods which require fdlibm
semantics are sin , cos , tan ,
asin , acos , atan ,
exp , log , log10 ,
cbrt , atan2 , pow ,
sinh , cosh , tanh ,
hypot , expm1 , and log1p . 
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 StrictMath()Don't let anyone instantiate this class.

Methods Summary 

public static native 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.
 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 native 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.
 public static native 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.
 public static native 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.
 public static native 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.
 public static native 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.
 public static native 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 StrictMath.ceil(x) is exactly the
value of StrictMath.floor(x) .
 public static native 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.
 public static native 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 .
 public static native 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.
 public static native 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.
 public static native 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.
 public static native 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.
 private static synchronized void  initRNG()
if (randomNumberGenerator == null)
randomNumberGenerator = new Random();
 public static native 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.
 public static native 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.
 public static native 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.
 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 native 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.)
 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 pseudorandom number 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 to the value of the argument, 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.
/*
* If the absolute value of a is not less than 2^52, it
* is either a finite integer (the double format does not have
* enough significand bits for a number that large to have any
* fractional portion), an infinity, or a NaN. In any of
* these cases, rint of the argument is the argument.
*
* Otherwise, the sum (twoToThe52 + a ) will properly round
* away any fractional portion of a since ulp(twoToThe52) ==
* 1.0; subtracting out twoToThe52 from this sum will then be
* exact and leave the rounded integer portion of a.
*
* This method does *not* need to be declared strictfp to get
* fully reproducible results. Whether or not a method is
* declared strictfp can only make a difference in the
* returned result if some operation would overflow or
* underflow with strictfp semantics. The operation
* (twoToThe52 + a ) cannot overflow since large values of a
* are screened out; the add cannot underflow since twoToThe52
* is too large. The subtraction ((twoToThe52 + a ) 
* twoToThe52) will be exact as discussed above and thus
* cannot overflow or meaningfully underflow. Finally, the
* last multiply in the return statement is by plus or minus
* 1.0, which is exact too.
*/
double twoToThe52 = (double)(1L << 52); // 2^52
double sign = FpUtils.rawCopySign(1.0, a); // preserve sign info
a = Math.abs(a);
if (a < twoToThe52) { // E_min <= ilogb(a) <= 51
a = ((twoToThe52 + a )  twoToThe52);
}
return sign * a; // restore original sign
 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 native 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.
 public static native 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.
 public static native 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.
 public static native 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.
 public static native 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 .
 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);

