Package org.hipparchus.util

Class FastMath

java.lang.Object

org.hipparchus.util.FastMath

public class FastMath
extends Object

Faster, more accurate, portable alternative to Math and StrictMath for large scale computation.

FastMath is a drop-in replacement for both Math and StrictMath. This means that for any method in Math (say Math.sin(x) or Math.cbrt(y)), user can directly change the class and use the methods as is (using FastMath.sin(x) or FastMath.cbrt(y) in the previous example).

FastMath speed is achieved by relying heavily on optimizing compilers to native code present in many JVMs today and use of large tables. The larger tables are lazily initialized on first use, so that the setup time does not penalize methods that don't need them.

Note that FastMath is extensively used inside Hipparchus, so by calling some algorithms, the overhead when the the tables need to be initialized will occur regardless of the end-user calling FastMath methods directly or not. Performance figures for a specific JVM and hardware can be evaluated by running the FastMathTestPerformance tests in the test directory of the source distribution.

FastMath accuracy should be mostly independent of the JVM as it relies only on IEEE-754 basic operations and on embedded tables. Almost all operations are accurate to about 0.5 ulp throughout the domain range. This statement, of course is only a rough global observed behavior, it is not a guarantee for every double numbers input (see William Kahan's Table Maker's Dilemma).

FastMath additionally implements the following methods not found in Math/StrictMath:

• asinh(double)
• acosh(double)
• atanh(double)

The following methods are found in Math/StrictMath since 1.6 only, they are provided by FastMath even in 1.5 Java virtual machines

• copySign(double, double)
• getExponent(double)
• nextAfter(double,double)
• nextUp(double)
• scalb(double, int)
• copySign(float, float)
• getExponent(float)
• nextAfter(float,double)
• nextUp(float)
• scalb(float, int)

Field Summary

Fields

Modifier and Type	Field	Description
static final double	E	Napier's constant e, base of the natural logarithm.
static final double	PI	Archimede's constant PI, ratio of circle circumference to diameter.

Method Summary

Modifier and Type	Method	Description
static double	abs(double x)	Absolute value.
static float	abs(float x)	Absolute value.
static int	abs(int x)	Absolute value.
static long	abs(long x)	Absolute value.
static <T extends CalculusFieldElement<T>> T	abs(T x)	Absolute value.
static int	absExact(int x)	Absolute value.
static long	absExact(long x)	Absolute value.
static double	acos(double x)	Compute the arc cosine of a number.
static <T extends CalculusFieldElement<T>> T	acos(T x)	Compute the arc cosine of a number.
static double	acosh(double a)	Compute the inverse hyperbolic cosine of a number.
static <T extends CalculusFieldElement<T>> T	acosh(T a)	Compute the inverse hyperbolic cosine of a number.
static int	addExact(int a, int b)	Add two numbers, detecting overflows.
static long	addExact(long a, long b)	Add two numbers, detecting overflows.
static double	asin(double x)	Compute the arc sine of a number.
static <T extends CalculusFieldElement<T>> T	asin(T x)	Compute the arc sine of a number.
static double	asinh(double a)	Compute the inverse hyperbolic sine of a number.
static <T extends CalculusFieldElement<T>> T	asinh(T a)	Compute the inverse hyperbolic sine of a number.
static double	atan(double x)	Arctangent function
static <T extends CalculusFieldElement<T>> T	atan(T x)	Arctangent function
static double	atan2(double y, double x)	Two arguments arctangent function
static <T extends CalculusFieldElement<T>> T	atan2(T y, T x)	Two arguments arctangent function
static double	atanh(double a)	Compute the inverse hyperbolic tangent of a number.
static <T extends CalculusFieldElement<T>> T	atanh(T a)	Compute the inverse hyperbolic tangent of a number.
static double	cbrt(double x)	Compute the cubic root of a number.
static <T extends CalculusFieldElement<T>> T	cbrt(T x)	Compute the cubic root of a number.
static double	ceil(double x)	Get the smallest whole number larger than x.
static <T extends CalculusFieldElement<T>> T	ceil(T x)	Get the smallest whole number larger than x.
static int	ceilDiv(int a, int b)	Finds q such that a = q b + r with b < r <= 0 if b > 0 and 0 <= r < b if b < 0.
static long	ceilDiv(long a, int b)	Finds q such that a = q b + r with b < r <= 0 if b > 0 and 0 <= r < b if b < 0.
static long	ceilDiv(long a, long b)	Finds q such that a = q b + r with b < r <= 0 if b > 0 and 0 <= r < b if b < 0.
static int	ceilDivExact(int a, int b)	Finds q such that a = q b + r with b < r <= 0 if b > 0 and 0 <= r < b if b < 0.
static long	ceilDivExact(long a, long b)	Finds q such that a = q b + r with b < r <= 0 if b > 0 and 0 <= r < b if b < 0.
static int	ceilMod(int a, int b)	Finds r such that a = q b + r with b < r <= 0 if b > 0 and 0 <= r < b if b < 0.
static int	ceilMod(long a, int b)	Finds r such that a = q b + r with b < r <= 0 if b > 0 and 0 <= r < b if b < 0.
static long	ceilMod(long a, long b)	Finds r such that a = q b + r with b < r <= 0 if b > 0 and 0 <= r < b if b < 0.
static double	clamp(double value, double inf, double sup)	Clamp a value within an interval.
static float	clamp(float value, float inf, float sup)	Clamp a value within an interval.
static int	clamp(int value, int inf, int sup)	Clamp a value within an interval.
static int	clamp(long value, int inf, int sup)	Clamp a value within an interval.
static long	clamp(long value, long inf, long sup)	Clamp a value within an interval.
static double	copySign(double magnitude, double sign)	Returns the first argument with the sign of the second argument.
static float	copySign(float magnitude, float sign)	Returns the first argument with the sign of the second argument.
static <T extends CalculusFieldElement<T>> T	copySign(T magnitude, double sign)	Returns the first argument with the sign of the second argument.
static <T extends CalculusFieldElement<T>> T	copySign(T magnitude, T sign)	Returns the first argument with the sign of the second argument.
static double	cos(double x)	Cosine function.
static <T extends CalculusFieldElement<T>> T	cos(T x)	Cosine function.
static double	cosh(double x)	Compute the hyperbolic cosine of a number.
static <T extends CalculusFieldElement<T>> T	cosh(T x)	Compute the hyperbolic cosine of a number.
static int	decrementExact(int n)	Decrement a number, detecting overflows.
static long	decrementExact(long n)	Decrement a number, detecting overflows.
static int	divideExact(int x, int y)	Divide two integers, checking for overflow.
static long	divideExact(long x, long y)	Divide two long integers, checking for overflow.
static double	exp(double x)	Exponential function.
static <T extends CalculusFieldElement<T>> T	exp(T x)	Exponential function.
static double	expm1(double x)	Compute exp(x) - 1
static <T extends CalculusFieldElement<T>> T	expm1(T x)	Compute exp(x) - 1
static double	floor(double x)	Get the largest whole number smaller than x.
static <T extends CalculusFieldElement<T>> T	floor(T x)	Get the largest whole number smaller than x.
static int	floorDiv(int a, int b)	Finds q such that a = q b + r with 0 <= r < b if b > 0 and b < r <= 0 if b < 0.
static long	floorDiv(long a, int b)	Finds q such that a = q b + r with 0 <= r < b if b > 0 and b < r <= 0 if b < 0.
static long	floorDiv(long a, long b)	Finds q such that a = q b + r with 0 <= r < b if b > 0 and b < r <= 0 if b < 0.
static int	floorDivExact(int a, int b)	Finds q such that a = q b + r with 0 <= r < b if b > 0 and b < r <= 0 if b < 0.
static long	floorDivExact(long a, long b)	Finds q such that a = q b + r with 0 <= r < b if b > 0 and b < r <= 0 if b < 0.
static int	floorMod(int a, int b)	Finds r such that a = q b + r with 0 <= r < b if b > 0 and b < r <= 0 if b < 0.
static int	floorMod(long a, int b)	Finds r such that a = q b + r with 0 <= r < b if b > 0 and b < r <= 0 if b < 0.
static long	floorMod(long a, long b)	Finds r such that a = q b + r with 0 <= r < b if b > 0 and b < r <= 0 if b < 0.
static double	fma(double a, double b, double c)	Compute Fused-multiply-add operation a * b + c.
static float	fma(float a, float b, float c)	Compute Fused-multiply-add operation a * b + c.
static int	getExponent(double d)	Return the exponent of a double number, removing the bias.
static int	getExponent(float f)	Return the exponent of a float number, removing the bias.
static double	hypot(double x, double y)	Returns the hypotenuse of a triangle with sides x and y - sqrt(x2 +y2) avoiding intermediate overflow or underflow.
static <T extends CalculusFieldElement<T>> T	hypot(T x, T y)	Returns the hypotenuse of a triangle with sides x and y - sqrt(x2 +y2) avoiding intermediate overflow or underflow.
static double	IEEEremainder(double dividend, double divisor)	Computes the remainder as prescribed by the IEEE 754 standard.
static <T extends CalculusFieldElement<T>> T	IEEEremainder(T dividend, double divisor)	Computes the remainder as prescribed by the IEEE 754 standard.
static <T extends CalculusFieldElement<T>> T	IEEEremainder(T dividend, T divisor)	Computes the remainder as prescribed by the IEEE 754 standard.
static int	incrementExact(int n)	Increment a number, detecting overflows.
static long	incrementExact(long n)	Increment a number, detecting overflows.
static double	log(double x)	Natural logarithm.
static double	log(double base, double x)	Computes the logarithm in a given base.
static <T extends CalculusFieldElement<T>> T	log(T x)	Natural logarithm.
static double	log10(double x)	Compute the base 10 logarithm.
static <T extends CalculusFieldElement<T>> T	log10(T x)	Compute the base 10 logarithm.
static double	log1p(double x)	Computes log(1 + x).
static <T extends CalculusFieldElement<T>> T	log1p(T x)	Computes log(1 + x).
static double	max(double a, double b)	Compute the maximum of two values
static float	max(float a, float b)	Compute the maximum of two values
static int	max(int a, int b)	Compute the maximum of two values
static long	max(long a, long b)	Compute the maximum of two values
static <T extends CalculusFieldElement<T>> T	max(T a, double b)	Compute the maximum of two values
static <T extends CalculusFieldElement<T>> T	max(T a, T b)	Compute the maximum of two values
static double	min(double a, double b)	Compute the minimum of two values
static float	min(float a, float b)	Compute the minimum of two values
static int	min(int a, int b)	Compute the minimum of two values
static long	min(long a, long b)	Compute the minimum of two values
static <T extends CalculusFieldElement<T>> T	min(T a, double b)	Compute the minimum of two values
static <T extends CalculusFieldElement<T>> T	min(T a, T b)	Compute the minimum of two values
static int	multiplyExact(int a, int b)	Multiply two numbers, detecting overflows.
static long	multiplyExact(long a, int b)	Multiply two numbers, detecting overflows.
static long	multiplyExact(long a, long b)	Multiply two numbers, detecting overflows.
static long	multiplyFull(int a, int b)	Multiply two integers and give an exact result without overflow.
static long	multiplyHigh(long a, long b)	Multiply two long integers and give the 64 most significant bits of the result.
static int	negateExact(int x)	Negates the argument.
static long	negateExact(long x)	Negates the argument.
static double	nextAfter(double d, double direction)	Get the next machine representable number after a number, moving in the direction of another number.
static float	nextAfter(float f, double direction)	Get the next machine representable number after a number, moving in the direction of another number.
static double	nextDown(double a)	Compute next number towards negative infinity.
static float	nextDown(float a)	Compute next number towards negative infinity.
static double	nextUp(double a)	Compute next number towards positive infinity.
static float	nextUp(float a)	Compute next number towards positive infinity.
static <T extends CalculusFieldElement<T>> double	norm(T x)	Norm.
static double	pow(double x, double y)	Power function.
static double	pow(double d, int e)	Raise a double to an int power.
static double	pow(double d, long e)	Raise a double to a long power.
static <T extends CalculusFieldElement<T>> T	pow(T x, double y)	Power function.
static <T extends CalculusFieldElement<T>> T	pow(T d, int e)	Raise a double to an int power.
static <T extends CalculusFieldElement<T>> T	pow(T x, T y)	Power function.
static double	random()	Returns a pseudo-random number between 0.0 and 1.0.
static double	rint(double x)	Get the whole number that is the nearest to x, or the even one if x is exactly half way between two integers.
static <T extends CalculusFieldElement<T>> T	rint(T x)	Get the whole number that is the nearest to x, or the even one if x is exactly half way between two integers.
static long	round(double x)	Get the closest long to x.
static int	round(float x)	Get the closest int to x.
static <T extends CalculusFieldElement<T>> long	round(T x)	Get the closest long to x.
static double	scalb(double d, int n)	Multiply a double number by a power of 2.
static float	scalb(float f, int n)	Multiply a float number by a power of 2.
static <T extends CalculusFieldElement<T>> T	scalb(T d, int n)	Multiply a double number by a power of 2.
static <T extends CalculusFieldElement<T>> T	sign(T a)	Compute the sign of a number.
static double	signum(double a)	Compute the signum of a number.
static float	signum(float a)	Compute the signum of a number.
static double	sin(double x)	Sine function.
static <T extends CalculusFieldElement<T>> T	sin(T x)	Sine function.
static SinCos	sinCos(double x)	Combined Sine and Cosine function.
static <T extends CalculusFieldElement<T>> FieldSinCos<T>	sinCos(T x)	Combined Sine and Cosine function.
static double	sinh(double x)	Compute the hyperbolic sine of a number.
static <T extends CalculusFieldElement<T>> T	sinh(T x)	Compute the hyperbolic sine of a number.
static SinhCosh	sinhCosh(double x)	Combined hyperbolic sine and hyperbolic cosine function.
static <T extends CalculusFieldElement<T>> FieldSinhCosh<T>	sinhCosh(T x)	Combined hyperbolic sine and hyperbolic cosine function.
static double	sqrt(double a)	Compute the square root of a number.
static <T extends CalculusFieldElement<T>> T	sqrt(T a)	Compute the square root of a number.
static int	subtractExact(int a, int b)	Subtract two numbers, detecting overflows.
static long	subtractExact(long a, long b)	Subtract two numbers, detecting overflows.
static double	tan(double x)	Tangent function.
static <T extends CalculusFieldElement<T>> T	tan(T x)	Tangent function.
static double	tanh(double x)	Compute the hyperbolic tangent of a number.
static <T extends CalculusFieldElement<T>> T	tanh(T x)	Compute the hyperbolic tangent of a number.
static double	toDegrees(double x)	Convert radians to degrees, with error of less than 0.5 ULP
static <T extends CalculusFieldElement<T>> T	toDegrees(T x)	Convert radians to degrees, with error of less than 0.5 ULP
static int	toIntExact(long n)	Convert a long to interger, detecting overflows
static double	toRadians(double x)	Convert degrees to radians, with error of less than 0.5 ULP
static <T extends CalculusFieldElement<T>> T	toRadians(T x)	Convert degrees to radians, with error of less than 0.5 ULP
static double	ulp(double x)	Compute least significant bit (Unit in Last Position) for a number.
static float	ulp(float x)	Compute least significant bit (Unit in Last Position) for a number.
static <T extends CalculusFieldElement<T>> T	ulp(T x)	Compute least significant bit (Unit in Last Position) for a number.
static long	unsignedMultiplyHigh(long a, long b)	Multiply two long unsigned integers and give the 64 most significant bits of the unsigned result.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Details

PI

public static final double PI

Archimede's constant PI, ratio of circle circumference to diameter.

See Also:

• Constant Field Values

E

public static final double E

Napier's constant e, base of the natural logarithm.

See Also:

• Constant Field Values

Method Details

sqrt

public static double sqrt(double a)

Compute the square root of a number.

Note: this implementation currently delegates to Math.sqrt(double)

Parameters:

a - number on which evaluation is done

Returns:

square root of a

cosh

public static double cosh(double x)

Compute the hyperbolic cosine of a number.

Parameters:

x - number on which evaluation is done

Returns:

hyperbolic cosine of x

sinh

public static double sinh(double x)

Compute the hyperbolic sine of a number.

Parameters:

x - number on which evaluation is done

Returns:

hyperbolic sine of x

sinhCosh

public static SinhCosh sinhCosh(double x)

Combined hyperbolic sine and hyperbolic cosine function.

Parameters:

x - Argument.

Returns:

[sinh(x), cosh(x)]

sinhCosh

public static <T extends CalculusFieldElement<T>>
FieldSinhCosh<T> sinhCosh(T x)

Combined hyperbolic sine and hyperbolic cosine function.

Type Parameters:

T - the type of the field element

Parameters:

x - Argument.

Returns:

[sinh(x), cosh(x)]

tanh

public static double tanh(double x)

Compute the hyperbolic tangent of a number.

Parameters:

x - number on which evaluation is done

Returns:

hyperbolic tangent of x

acosh

public static double acosh(double a)

Compute the inverse hyperbolic cosine of a number.

Parameters:

a - number on which evaluation is done

Returns:

inverse hyperbolic cosine of a

asinh

public static double asinh(double a)

Compute the inverse hyperbolic sine of a number.

Parameters:

a - number on which evaluation is done

Returns:

inverse hyperbolic sine of a

atanh

public static double atanh(double a)

Compute the inverse hyperbolic tangent of a number.

Parameters:

a - number on which evaluation is done

Returns:

inverse hyperbolic tangent of a

signum

public static double signum(double a)

Compute the signum of a number. The signum is -1 for negative numbers, +1 for positive numbers and 0 otherwise

Parameters:

a - number on which evaluation is done

Returns:

-1.0, -0.0, +0.0, +1.0 or NaN depending on sign of a

signum

public static float signum(float a)

Compute the signum of a number. The signum is -1 for negative numbers, +1 for positive numbers and 0 otherwise

Parameters:

a - number on which evaluation is done

Returns:

-1.0, -0.0, +0.0, +1.0 or NaN depending on sign of a

nextUp

public static double nextUp(double a)

Compute next number towards positive infinity.

Parameters:

a - number to which neighbor should be computed

Returns:

neighbor of a towards positive infinity

nextUp

public static float nextUp(float a)

Compute next number towards positive infinity.

Parameters:

a - number to which neighbor should be computed

Returns:

neighbor of a towards positive infinity

nextDown

public static double nextDown(double a)

Compute next number towards negative infinity.

Parameters:

a - number to which neighbor should be computed

Returns:

neighbor of a towards negative infinity

nextDown

public static float nextDown(float a)

Compute next number towards negative infinity.

Parameters:

a - number to which neighbor should be computed

Returns:

neighbor of a towards negative infinity

clamp

public static int clamp(int value,
 int inf,
 int sup)

Clamp a value within an interval.

Parameters:

value - value to clamp

inf - lower bound of the clamping interval

sup - upper bound of the clamping interval

Returns:

value clamped within [inf; sup], or value if already within bounds.

Since:

3.0

clamp

public static long clamp(long value,
 long inf,
 long sup)

Clamp a value within an interval.

Parameters:

value - value to clamp

inf - lower bound of the clamping interval

sup - upper bound of the clamping interval

Returns:

value clamped within [inf; sup], or value if already within bounds.

Since:

3.0

clamp

public static int clamp(long value,
 int inf,
 int sup)

Clamp a value within an interval.

Parameters:

value - value to clamp

inf - lower bound of the clamping interval

sup - upper bound of the clamping interval

Returns:

value clamped within [inf; sup], or value if already within bounds.

Since:

3.0

clamp

public static float clamp(float value,
 float inf,
 float sup)

Clamp a value within an interval.

This method assumes -0.0 is below +0.0

Parameters:

value - value to clamp

inf - lower bound of the clamping interval

sup - upper bound of the clamping interval

Returns:

value clamped within [inf; sup], or value if already within bounds.

Since:

3.0

clamp

public static double clamp(double value,
 double inf,
 double sup)

Clamp a value within an interval.

This method assumes -0.0 is below +0.0

Parameters:

value - value to clamp

inf - lower bound of the clamping interval

sup - upper bound of the clamping interval

Returns:

value clamped within [inf; sup], or value if already within bounds.

Since:

3.0

random

public static double random()

Returns a pseudo-random number between 0.0 and 1.0.

Note: this implementation currently delegates to Math.random()

Returns:

a random number between 0.0 and 1.0

exp

public static double exp(double x)

Exponential function. Computes exp(x), function result is nearly rounded. It will be correctly rounded to the theoretical value for 99.9% of input values, otherwise it will have a 1 ULP error. Method: Lookup intVal = exp(int(x)) Lookup fracVal = exp(int(x-int(x) / 1024.0) * 1024.0 ); Compute z as the exponential of the remaining bits by a polynomial minus one exp(x) = intVal * fracVal * (1 + z) Accuracy: Calculation is done with 63 bits of precision, so result should be correctly rounded for 99.9% of input values, with less than 1 ULP error otherwise.

Parameters:

x - a double

Returns:

double e^x

expm1

public static double expm1(double x)

Compute exp(x) - 1

Parameters:

x - number to compute shifted exponential

Returns:

exp(x) - 1

log

public static double log(double x)

Natural logarithm.

Parameters:

x - a double

Returns:

log(x)

log1p

public static double log1p(double x)

Computes log(1 + x).

Parameters:

x - Number.

Returns:

log(1 + x).

log10

public static double log10(double x)

Compute the base 10 logarithm.

Parameters:

x - a number

Returns:

log10(x)

log

public static double log(double base,
 double x)

Computes the logarithm in a given base. Returns NaN if either argument is negative. If base is 0 and x is positive, 0 is returned. If base is positive and x is 0, Double.NEGATIVE_INFINITY is returned. If both arguments are 0, the result is NaN.

Parameters:

base - Base of the logarithm, must be greater than 0.

x - Argument, must be greater than 0.

Returns:

the value of the logarithm, i.e. the number y such that basey = x.

pow

public static double pow(double x,
 double y)

Power function. Compute x^y.

Parameters:

x - a double

y - a double

Returns:

double

pow

public static double pow(double d,
 int e)

Raise a double to an int power.

Parameters:

d - Number to raise.

e - Exponent.

Returns:

d^e

pow

public static double pow(double d,
 long e)

Raise a double to a long power.

Parameters:

d - Number to raise.

e - Exponent.

Returns:

d^e

sin

public static double sin(double x)

Sine function.

Parameters:

x - Argument.

Returns:

sin(x)

cos

public static double cos(double x)

Cosine function.

Parameters:

x - Argument.

Returns:

cos(x)

sinCos

public static SinCos sinCos(double x)

Combined Sine and Cosine function.

Parameters:

x - Argument.

Returns:

[sin(x), cos(x)]

sinCos

public static <T extends CalculusFieldElement<T>>
FieldSinCos<T> sinCos(T x)

Combined Sine and Cosine function.

Type Parameters:

T - the type of the field element

Parameters:

x - Argument.

Returns:

[sin(x), cos(x)]

Since:

1.4

tan

public static double tan(double x)

Tangent function.

Parameters:

x - Argument.

Returns:

tan(x)

atan

public static double atan(double x)

Arctangent function

Parameters:

x - a number

Returns:

atan(x)

atan2

public static double atan2(double y,
 double x)

Two arguments arctangent function

Parameters:

y - ordinate

x - abscissa

Returns:

phase angle of point (x,y) between -PI and PI

asin

public static double asin(double x)

Compute the arc sine of a number.

Parameters:

x - number on which evaluation is done

Returns:

arc sine of x

acos

public static double acos(double x)

Compute the arc cosine of a number.

Parameters:

x - number on which evaluation is done

Returns:

arc cosine of x

cbrt

public static double cbrt(double x)

Compute the cubic root of a number.

Parameters:

x - number on which evaluation is done

Returns:

cubic root of x

toRadians

public static double toRadians(double x)

Convert degrees to radians, with error of less than 0.5 ULP

Parameters:

x - angle in degrees

Returns:

x converted into radians

toDegrees

public static double toDegrees(double x)

Convert radians to degrees, with error of less than 0.5 ULP

Parameters:

x - angle in radians

Returns:

x converted into degrees

abs

public static int abs(int x)

Absolute value.

Parameters:

x - number from which absolute value is requested

Returns:

abs(x)

abs

public static long abs(long x)

Absolute value.

Parameters:

x - number from which absolute value is requested

Returns:

abs(x)

absExact

public static int absExact(int x)

Absolute value.

Parameters:

x - number from which absolute value is requested

Returns:

abs(x), or throws an exception for Integer.MIN_VALUE

Since:

2.0

absExact

public static long absExact(long x)

Absolute value.

Parameters:

x - number from which absolute value is requested

Returns:

abs(x), or throws an exception for Long.MIN_VALUE

Since:

2.0

abs

public static float abs(float x)

Absolute value.

Parameters:

x - number from which absolute value is requested

Returns:

abs(x)

Since:

2.0

abs

public static double abs(double x)

Absolute value.

Parameters:

x - number from which absolute value is requested

Returns:

abs(x)

negateExact

public static int negateExact(int x)

Negates the argument.

Parameters:

x - number from which opposite value is requested

Returns:

-x, or throws an exception for Integer.MIN_VALUE

Since:

2.0

negateExact

public static long negateExact(long x)

Negates the argument.

Parameters:

x - number from which opposite value is requested

Returns:

-x, or throws an exception for Long.MIN_VALUE

Since:

2.0

ulp

public static double ulp(double x)

Compute least significant bit (Unit in Last Position) for a number.

Parameters:

x - number from which ulp is requested

Returns:

ulp(x)

ulp

public static float ulp(float x)

Compute least significant bit (Unit in Last Position) for a number.

Parameters:

x - number from which ulp is requested

Returns:

ulp(x)

scalb

public static double scalb(double d,
 int n)

Multiply a double number by a power of 2.

Parameters:

d - number to multiply

n - power of 2

Returns:

d × 2ⁿ

scalb

public static float scalb(float f,
 int n)

Multiply a float number by a power of 2.

Parameters:

f - number to multiply

n - power of 2

Returns:

f × 2ⁿ

nextAfter

public static double nextAfter(double d,
 double direction)

Get the next machine representable number after a number, moving in the direction of another number.

The ordering is as follows (increasing):

• -INFINITY
• -MAX_VALUE
• -MIN_VALUE
• -0.0
• +0.0
• +MIN_VALUE
• +MAX_VALUE
• +INFINITY

If arguments compare equal, then the second argument is returned.

If direction is greater than d, the smallest machine representable number strictly greater than d is returned; if less, then the largest representable number strictly less than d is returned.

If d is infinite and direction does not bring it back to finite numbers, it is returned unchanged.

Parameters:

d - base number

direction - (the only important thing is whether direction is greater or smaller than d)

Returns:

the next machine representable number in the specified direction

nextAfter

public static float nextAfter(float f,
 double direction)

Get the next machine representable number after a number, moving in the direction of another number.

* The ordering is as follows (increasing):

• -INFINITY
• -MAX_VALUE
• -MIN_VALUE
• -0.0
• +0.0
• +MIN_VALUE
• +MAX_VALUE
• +INFINITY

If arguments compare equal, then the second argument is returned.

If direction is greater than f, the smallest machine representable number strictly greater than f is returned; if less, then the largest representable number strictly less than f is returned.

If f is infinite and direction does not bring it back to finite numbers, it is returned unchanged.

Parameters:

f - base number

direction - (the only important thing is whether direction is greater or smaller than f)

Returns:

the next machine representable number in the specified direction

floor

public static double floor(double x)

Get the largest whole number smaller than x.

Parameters:

x - number from which floor is requested

Returns:

a double number f such that f is an integer f <= x < f + 1.0

ceil

public static double ceil(double x)

Get the smallest whole number larger than x.

Parameters:

x - number from which ceil is requested

Returns:

a double number c such that c is an integer c - 1.0 < x <= c

rint

public static double rint(double x)

Get the whole number that is the nearest to x, or the even one if x is exactly half way between two integers.

Parameters:

x - number from which nearest whole number is requested

Returns:

a double number r such that r is an integer r - 0.5 <= x <= r + 0.5

round

public static long round(double x)

Get the closest long to x.

Parameters:

x - number from which closest long is requested

Returns:

closest long to x

round

public static int round(float x)

Get the closest int to x.

Parameters:

x - number from which closest int is requested

Returns:

closest int to x

min

public static int min(int a,
 int b)

Compute the minimum of two values

Parameters:

a - first value

b - second value

Returns:

a if a is lesser or equal to b, b otherwise

min

public static long min(long a,
 long b)

Compute the minimum of two values

Parameters:

a - first value

b - second value

Returns:

a if a is lesser or equal to b, b otherwise

min

public static float min(float a,
 float b)

Compute the minimum of two values

Parameters:

a - first value

b - second value

Returns:

a if a is lesser or equal to b, b otherwise

min

public static double min(double a,
 double b)

Compute the minimum of two values

Parameters:

a - first value

b - second value

Returns:

a if a is lesser or equal to b, b otherwise

max

public static int max(int a,
 int b)

Compute the maximum of two values

Parameters:

a - first value

b - second value

Returns:

b if a is lesser or equal to b, a otherwise

max

public static long max(long a,
 long b)

Compute the maximum of two values

Parameters:

a - first value

b - second value

Returns:

b if a is lesser or equal to b, a otherwise

max

public static float max(float a,
 float b)

Compute the maximum of two values

Parameters:

a - first value

b - second value

Returns:

b if a is lesser or equal to b, a otherwise

max

public static double max(double a,
 double b)

Compute the maximum of two values

Parameters:

a - first value

b - second value

Returns:

b if a is lesser or equal to b, a otherwise

hypot

public static double hypot(double x,
 double y)

Returns the hypotenuse of a triangle with sides x and y - sqrt(x² +y²)
avoiding intermediate overflow or underflow.

• If either argument is infinite, then the result is positive infinity.
• else, if either argument is NaN then the result is NaN.

Parameters:

x - a value

y - a value

Returns:

sqrt(x² +y²)

IEEEremainder

public static double IEEEremainder(double dividend,
 double divisor)

Computes the remainder as prescribed by the IEEE 754 standard.

The remainder value is mathematically equal to x - y*n where n is the mathematical integer closest to the exact mathematical value of the quotient x/y. If two mathematical integers are equally close to x/y then n is the integer that is even.

• If either operand is NaN, the result is NaN.
• If the result is not NaN, the sign of the result equals the sign of the dividend.
• If the dividend is an infinity, or the divisor is a zero, or both, the result is NaN.
• If the dividend is finite and the divisor is an infinity, the result equals the dividend.
• If the dividend is a zero and the divisor is finite, the result equals the dividend.

Parameters:

dividend - the number to be divided

divisor - the number by which to divide

Returns:

the remainder, rounded

toIntExact

public static int toIntExact(long n)
                      throws MathRuntimeException

Convert a long to interger, detecting overflows

Parameters:

n - number to convert to int

Returns:

integer with same valie as n if no overflows occur

Throws:

MathRuntimeException - if n cannot fit into an int

incrementExact

public static int incrementExact(int n)
                          throws MathRuntimeException

Increment a number, detecting overflows.

Parameters:

n - number to increment

Returns:

n+1 if no overflows occur

Throws:

MathRuntimeException - if an overflow occurs

incrementExact

public static long incrementExact(long n)
                           throws MathRuntimeException

Increment a number, detecting overflows.

Parameters:

n - number to increment

Returns:

n+1 if no overflows occur

Throws:

MathRuntimeException - if an overflow occurs

decrementExact

public static int decrementExact(int n)
                          throws MathRuntimeException

Decrement a number, detecting overflows.

Parameters:

n - number to decrement

Returns:

n-1 if no overflows occur

Throws:

MathRuntimeException - if an overflow occurs

decrementExact

public static long decrementExact(long n)
                           throws MathRuntimeException

Decrement a number, detecting overflows.

Parameters:

n - number to decrement

Returns:

n-1 if no overflows occur

Throws:

MathRuntimeException - if an overflow occurs

addExact

public static int addExact(int a,
 int b)
                    throws MathRuntimeException

Add two numbers, detecting overflows.

Parameters:

a - first number to add

b - second number to add

Returns:

a+b if no overflows occur

Throws:

MathRuntimeException - if an overflow occurs

addExact

public static long addExact(long a,
 long b)
                     throws MathRuntimeException

Add two numbers, detecting overflows.

Parameters:

a - first number to add

b - second number to add

Returns:

a+b if no overflows occur

Throws:

MathRuntimeException - if an overflow occurs

subtractExact

public static int subtractExact(int a,
 int b)

Subtract two numbers, detecting overflows.

Parameters:

a - first number

b - second number to subtract from a

Returns:

a-b if no overflows occur

Throws:

MathRuntimeException - if an overflow occurs

subtractExact

public static long subtractExact(long a,
 long b)

Subtract two numbers, detecting overflows.

Parameters:

a - first number

b - second number to subtract from a

Returns:

a-b if no overflows occur

Throws:

MathRuntimeException - if an overflow occurs

multiplyExact

public static int multiplyExact(int a,
 int b)

Multiply two numbers, detecting overflows.

Parameters:

a - first number to multiply

b - second number to multiply

Returns:

a*b if no overflows occur

Throws:

MathRuntimeException - if an overflow occurs

multiplyExact

public static long multiplyExact(long a,
 int b)

Multiply two numbers, detecting overflows.

Parameters:

a - first number to multiply

b - second number to multiply

Returns:

a*b if no overflows occur

Throws:

MathRuntimeException - if an overflow occurs

Since:

1.3

multiplyExact

public static long multiplyExact(long a,
 long b)

Multiply two numbers, detecting overflows.

Parameters:

a - first number to multiply

b - second number to multiply

Returns:

a*b if no overflows occur

Throws:

MathRuntimeException - if an overflow occurs

multiplyFull

public static long multiplyFull(int a,
 int b)

Multiply two integers and give an exact result without overflow.

Parameters:

a - first factor

b - second factor

Returns:

a * b exactly

Since:

1.3

multiplyHigh

public static long multiplyHigh(long a,
 long b)

Multiply two long integers and give the 64 most significant bits of the result.

Beware that as Java primitive long are always considered to be signed, there are some intermediate values a and b for which a * b exceeds Long.MAX_VALUE but this method will still return 0l. This happens for example for a = 2³¹ and b = 2³² as a * b = 2⁶³ = Long.MAX_VALUE + 1, so it exceeds the max value for a long, but still fits in 64 bits, so this method correctly returns 0l in this case, but multiplication result would be considered negative (and in fact equal to Long.MIN_VALUE

Parameters:

a - first factor

b - second factor

Returns:

a * b / 2⁶⁴

Since:

1.3

unsignedMultiplyHigh

public static long unsignedMultiplyHigh(long a,
 long b)

Multiply two long unsigned integers and give the 64 most significant bits of the unsigned result.

Beware that as Java primitive long are always considered to be signed, there are some intermediate values a and b for which a * b exceeds Long.MAX_VALUE but this method will still return 0l. This happens for example for a = 2³¹ and b = 2³² as a * b = 2⁶³ = Long.MAX_VALUE + 1, so it exceeds the max value for a long, but still fits in 64 bits, so this method correctly returns 0l in this case, but multiplication result would be considered negative (and in fact equal to Long.MIN_VALUE

Parameters:

a - first factor

b - second factor

Returns:

a * b / 2⁶⁴

Since:

3.0

divideExact

public static int divideExact(int x,
 int y)

Divide two integers, checking for overflow.

Parameters:

x - dividend

y - divisor

Returns:

x / y

Throws:

MathRuntimeException - if an overflow occurs

Since:

3.0

divideExact

public static long divideExact(long x,
 long y)

Divide two long integers, checking for overflow.

Parameters:

x - dividend

y - divisor

Returns:

x / y

Throws:

MathRuntimeException - if an overflow occurs

Since:

3.0

ceilDiv

public static int ceilDiv(int a,
 int b)
                   throws MathRuntimeException

Finds q such that a = q b + r with b < r <= 0 if b > 0 and 0 <= r < b if b < 0.

This methods returns the same value as integer division when a and b are opposite signs, but returns a different value when they are same (i.e. q is positive).

Parameters:

a - dividend

b - divisor

Returns:

q such that a = q b + r with b < r <= 0 if b > 0 and 0 <= r < b if b < 0

Throws:

MathRuntimeException - if b == 0

Since:

3.0

ceilDivExact

public static int ceilDivExact(int a,
 int b)
                        throws MathRuntimeException

Finds q such that a = q b + r with b < r <= 0 if b > 0 and 0 <= r < b if b < 0.

This methods returns the same value as integer division when a and b are opposite signs, but returns a different value when they are same (i.e. q is positive).

Parameters:

a - dividend

b - divisor

Returns:

q such that a = q b + r with b < r <= 0 if b > 0 and 0 <= r < b if b < 0

Throws:

MathRuntimeException - if b == 0 or if a == Integer.MIN_VALUE and b = -1

Since:

3.0

ceilDiv

public static long ceilDiv(long a,
 long b)
                    throws MathRuntimeException

Finds q such that a = q b + r with b < r <= 0 if b > 0 and 0 <= r < b if b < 0.

This methods returns the same value as integer division when a and b are opposite signs, but returns a different value when they are same (i.e. q is positive).

Parameters:

a - dividend

b - divisor

Returns:

q such that a = q b + r with b < r <= 0 if b > 0 and 0 <= r < b if b < 0

Throws:

MathRuntimeException - if b == 0

Since:

3.0

ceilDivExact

public static long ceilDivExact(long a,
 long b)
                         throws MathRuntimeException

Finds q such that a = q b + r with b < r <= 0 if b > 0 and 0 <= r < b if b < 0.

This methods returns the same value as integer division when a and b are opposite signs, but returns a different value when they are same (i.e. q is positive).

Parameters:

a - dividend

b - divisor

Returns:

q such that a = q b + r with b < r <= 0 if b > 0 and 0 <= r < b if b < 0

Throws:

MathRuntimeException - if b == 0 or if a == Long.MIN_VALUE and b = -1

Since:

3.0

ceilDiv

public static long ceilDiv(long a,
 int b)
                    throws MathRuntimeException

Finds q such that a = q b + r with b < r <= 0 if b > 0 and 0 <= r < b if b < 0.

This methods returns the same value as integer division when a and b are opposite signs, but returns a different value when they are same (i.e. q is positive).

Parameters:

a - dividend

b - divisor

Returns:

q such that a = q b + r with b < r <= 0 if b > 0 and 0 <= r < b if b < 0

Throws:

MathRuntimeException - if b == 0

Since:

3.0

ceilMod

public static int ceilMod(int a,
 int b)
                   throws MathRuntimeException

Finds r such that a = q b + r with b < r <= 0 if b > 0 and 0 <= r < b if b < 0.

This methods returns the same value as integer modulo when a and b are opposite signs, but returns a different value when they are same (i.e. q is positive).

Parameters:

a - dividend

b - divisor

Returns:

r such that a = q b + r with b < r <= 0 if b > 0 and 0 <= r < b if b < 0

Throws:

MathRuntimeException - if b == 0

Since:

3.0

ceilMod

public static int ceilMod(long a,
 int b)
                   throws MathRuntimeException

Finds r such that a = q b + r with b < r <= 0 if b > 0 and 0 <= r < b if b < 0.

This methods returns the same value as integer modulo when a and b are opposite signs, but returns a different value when they are same (i.e. q is positive).

Parameters:

a - dividend

b - divisor

Returns:

r such that a = q b + r with b < r <= 0 if b > 0 and 0 <= r < b if b < 0

Throws:

MathRuntimeException - if b == 0

Since:

3.0

ceilMod

public static long ceilMod(long a,
 long b)
                    throws MathRuntimeException

Finds r such that a = q b + r with b < r <= 0 if b > 0 and 0 <= r < b if b < 0.

This methods returns the same value as integer modulo when a and b are opposite signs, but returns a different value when they are same (i.e. q is positive).

Parameters:

a - dividend

b - divisor

Returns:

r such that a = q b + r with b < r <= 0 if b > 0 and 0 <= r < b if b < 0

Throws:

MathRuntimeException - if b == 0

Since:

3.0

floorDiv

public static int floorDiv(int a,
 int b)
                    throws MathRuntimeException

Finds q such that a = q b + r with 0 <= r < b if b > 0 and b < r <= 0 if b < 0.

This methods returns the same value as integer division when a and b are same signs, but returns a different value when they are opposite (i.e. q is negative).

Parameters:

a - dividend

b - divisor

Returns:

q such that a = q b + r with 0 <= r < b if b > 0 and b < r <= 0 if b < 0

Throws:

MathRuntimeException - if b == 0

See Also:

• floorMod(int, int)

floorDivExact

public static int floorDivExact(int a,
 int b)
                         throws MathRuntimeException

Finds q such that a = q b + r with 0 <= r < b if b > 0 and b < r <= 0 if b < 0.

This methods returns the same value as integer division when a and b are same signs, but returns a different value when they are opposite (i.e. q is negative).

Parameters:

a - dividend

b - divisor

Returns:

q such that a = q b + r with 0 <= r < b if b > 0 and b < r <= 0 if b < 0

Throws:

MathRuntimeException - if b == 0 or if a == Integer.MIN_VALUE and b = -1

Since:

3.0

See Also:

• floorMod(int, int)

floorDiv

public static long floorDiv(long a,
 int b)
                     throws MathRuntimeException

Finds q such that a = q b + r with 0 <= r < b if b > 0 and b < r <= 0 if b < 0.

This methods returns the same value as integer division when a and b are same signs, but returns a different value when they are opposite (i.e. q is negative).

Parameters:

a - dividend

b - divisor

Returns:

q such that a = q b + r with 0 <= r < b if b > 0 and b < r <= 0 if b < 0

Throws:

MathRuntimeException - if b == 0

Since:

1.3

See Also:

• floorMod(long, int)

floorDiv

public static long floorDiv(long a,
 long b)
                     throws MathRuntimeException

Finds q such that a = q b + r with 0 <= r < b if b > 0 and b < r <= 0 if b < 0.

This methods returns the same value as integer division when a and b are same signs, but returns a different value when they are opposite (i.e. q is negative).

Parameters:

a - dividend

b - divisor

Returns:

q such that a = q b + r with 0 <= r < b if b > 0 and b < r <= 0 if b < 0

Throws:

MathRuntimeException - if b == 0

See Also:

• floorMod(long, long)

floorDivExact

public static long floorDivExact(long a,
 long b)
                          throws MathRuntimeException

Finds q such that a = q b + r with 0 <= r < b if b > 0 and b < r <= 0 if b < 0.

This methods returns the same value as integer division when a and b are same signs, but returns a different value when they are opposite (i.e. q is negative).

Parameters:

a - dividend

b - divisor

Returns:

q such that a = q b + r with 0 <= r < b if b > 0 and b < r <= 0 if b < 0

Throws:

MathRuntimeException - if b == 0 or if a == Long.MIN_VALUE and b = -1

Since:

3.0

See Also:

• floorMod(long, long)

floorMod

public static int floorMod(int a,
 int b)
                    throws MathRuntimeException

Finds r such that a = q b + r with 0 <= r < b if b > 0 and b < r <= 0 if b < 0.

This methods returns the same value as integer modulo when a and b are same signs, but returns a different value when they are opposite (i.e. q is negative).

Parameters:

a - dividend

b - divisor

Returns:

r such that a = q b + r with 0 <= r < b if b > 0 and b < r <= 0 if b < 0

Throws:

MathRuntimeException - if b == 0

See Also:

• floorDiv(int, int)

floorMod

public static int floorMod(long a,
 int b)

Finds r such that a = q b + r with 0 <= r < b if b > 0 and b < r <= 0 if b < 0.

This methods returns the same value as integer modulo when a and b are same signs, but returns a different value when they are opposite (i.e. q is negative).

Parameters:

a - dividend

b - divisor

Returns:

r such that a = q b + r with 0 <= r < b if b > 0 and b < r <= 0 if b < 0

Throws:

MathRuntimeException - if b == 0

Since:

1.3

See Also:

• floorDiv(long, int)

floorMod

public static long floorMod(long a,
 long b)

Finds r such that a = q b + r with 0 <= r < b if b > 0 and b < r <= 0 if b < 0.

This methods returns the same value as integer modulo when a and b are same signs, but returns a different value when they are opposite (i.e. q is negative).

Parameters:

a - dividend

b - divisor

Returns:

r such that a = q b + r with 0 <= r < b if b > 0 and b < r <= 0 if b < 0

Throws:

MathRuntimeException - if b == 0

See Also:

• floorDiv(long, long)

copySign

public static double copySign(double magnitude,
 double sign)

Returns the first argument with the sign of the second argument. A NaN sign argument is treated as positive.

Parameters:

magnitude - the value to return

sign - the sign for the returned value

Returns:

the magnitude with the same sign as the sign argument

copySign

public static float copySign(float magnitude,
 float sign)

Returns the first argument with the sign of the second argument. A NaN sign argument is treated as positive.

Parameters:

magnitude - the value to return

sign - the sign for the returned value

Returns:

the magnitude with the same sign as the sign argument

getExponent

public static int getExponent(double d)

Return the exponent of a double number, removing the bias.

For double numbers of the form 2^x, the unbiased exponent is exactly x.

Parameters:

d - number from which exponent is requested

Returns:

exponent for d in IEEE754 representation, without bias

getExponent

public static int getExponent(float f)

Return the exponent of a float number, removing the bias.

For float numbers of the form 2^x, the unbiased exponent is exactly x.

Parameters:

f - number from which exponent is requested

Returns:

exponent for d in IEEE754 representation, without bias

fma

public static double fma(double a,
 double b,
 double c)

Compute Fused-multiply-add operation a * b + c.

This method was introduced in the regular Math and StrictMath methods with Java 9, and then added to Hipparchus for consistency. However, a more general method was available in Hipparchus that also allow to repeat this computation across several terms: MathArrays.linearCombination(double[], double[]). The linear combination method should probably be preferred in most cases.

Parameters:

a - first factor

b - second factor

c - additive term

Returns:

a * b + c, using extended precision in the multiplication

Since:

1.3

See Also:

• MathArrays.linearCombination(double[], double[])
• MathArrays.linearCombination(double, double, double, double)
• MathArrays.linearCombination(double, double, double, double, double, double)
• MathArrays.linearCombination(double, double, double, double, double, double, double, double)

fma

public static float fma(float a,
 float b,
 float c)

Compute Fused-multiply-add operation a * b + c.

This method was introduced in the regular Math and StrictMath methods with Java 9, and then added to Hipparchus for consistency. However, a more general method was available in Hipparchus that also allow to repeat this computation across several terms: MathArrays.linearCombination(double[], double[]). The linear combination method should probably be preferred in most cases.

Parameters:

a - first factor

b - second factor

c - additive term

Returns:

a * b + c, using extended precision in the multiplication

See Also:

• MathArrays.linearCombination(double[], double[])
• MathArrays.linearCombination(double, double, double, double)
• MathArrays.linearCombination(double, double, double, double, double, double)
• MathArrays.linearCombination(double, double, double, double, double, double, double, double)

sqrt

public static <T extends CalculusFieldElement<T>> T sqrt(T a)

Compute the square root of a number.

Type Parameters:

T - the type of the field element

Parameters:

a - number on which evaluation is done

Returns:

square root of a

Since:

1.3

cosh

public static <T extends CalculusFieldElement<T>> T cosh(T x)

Compute the hyperbolic cosine of a number.

Type Parameters:

T - the type of the field element

Parameters:

x - number on which evaluation is done

Returns:

hyperbolic cosine of x

Since:

1.3

sinh

public static <T extends CalculusFieldElement<T>> T sinh(T x)

Compute the hyperbolic sine of a number.

Type Parameters:

T - the type of the field element

Parameters:

x - number on which evaluation is done

Returns:

hyperbolic sine of x

Since:

1.3

tanh

public static <T extends CalculusFieldElement<T>> T tanh(T x)

Compute the hyperbolic tangent of a number.

Type Parameters:

T - the type of the field element

Parameters:

x - number on which evaluation is done

Returns:

hyperbolic tangent of x

Since:

1.3

acosh

public static <T extends CalculusFieldElement<T>> T acosh(T a)

Compute the inverse hyperbolic cosine of a number.

Type Parameters:

T - the type of the field element

Parameters:

a - number on which evaluation is done

Returns:

inverse hyperbolic cosine of a

Since:

1.3

asinh

public static <T extends CalculusFieldElement<T>> T asinh(T a)

Compute the inverse hyperbolic sine of a number.

Type Parameters:

T - the type of the field element

Parameters:

a - number on which evaluation is done

Returns:

inverse hyperbolic sine of a

Since:

1.3

atanh

public static <T extends CalculusFieldElement<T>> T atanh(T a)

Compute the inverse hyperbolic tangent of a number.

Type Parameters:

T - the type of the field element

Parameters:

a - number on which evaluation is done

Returns:

inverse hyperbolic tangent of a

Since:

1.3

sign

public static <T extends CalculusFieldElement<T>> T sign(T a)

Compute the sign of a number. The sign is -1 for negative numbers, +1 for positive numbers and 0 otherwise, for Complex number, it is extended on the unit circle (equivalent to z/|z|, with special handling for 0 and NaN)

Type Parameters:

T - the type of the field element

Parameters:

a - number on which evaluation is done

Returns:

-1.0, -0.0, +0.0, +1.0 or NaN depending on sign of a

Since:

2.0

exp

public static <T extends CalculusFieldElement<T>> T exp(T x)

Exponential function. Computes exp(x), function result is nearly rounded. It will be correctly rounded to the theoretical value for 99.9% of input values, otherwise it will have a 1 ULP error. Method: Lookup intVal = exp(int(x)) Lookup fracVal = exp(int(x-int(x) / 1024.0) * 1024.0 ); Compute z as the exponential of the remaining bits by a polynomial minus one exp(x) = intVal * fracVal * (1 + z) Accuracy: Calculation is done with 63 bits of precision, so result should be correctly rounded for 99.9% of input values, with less than 1 ULP error otherwise.

Type Parameters:

T - the type of the field element

Parameters:

x - a double

Returns:

double e^x

Since:

1.3

expm1

public static <T extends CalculusFieldElement<T>> T expm1(T x)

Compute exp(x) - 1

Type Parameters:

T - the type of the field element

Parameters:

x - number to compute shifted exponential

Returns:

exp(x) - 1

Since:

1.3

log

public static <T extends CalculusFieldElement<T>> T log(T x)

Natural logarithm.

Type Parameters:

T - the type of the field element

Parameters:

x - a double

Returns:

log(x)

Since:

1.3

log1p

public static <T extends CalculusFieldElement<T>> T log1p(T x)

Computes log(1 + x).

Type Parameters:

T - the type of the field element

Parameters:

x - Number.

Returns:

log(1 + x).

Since:

1.3

log10

public static <T extends CalculusFieldElement<T>> T log10(T x)

Compute the base 10 logarithm.

Type Parameters:

T - the type of the field element

Parameters:

x - a number

Returns:

log10(x)

Since:

1.3

pow

public static <T extends CalculusFieldElement<T>> T pow(T x,
 T y)

Power function. Compute x^y.

Type Parameters:

T - the type of the field element

Parameters:

x - a double

y - a double

Returns:

x^y

Since:

1.3

pow

public static <T extends CalculusFieldElement<T>> T pow(T x,
 double y)

Power function. Compute x^y.

Type Parameters:

T - the type of the field element

Parameters:

x - a double

y - a double

Returns:

x^y

Since:

1.7

pow

public static <T extends CalculusFieldElement<T>> T pow(T d,
 int e)

Raise a double to an int power.

Type Parameters:

T - the type of the field element

Parameters:

d - Number to raise.

e - Exponent.

Returns:

d^e

Since:

1.3

sin

public static <T extends CalculusFieldElement<T>> T sin(T x)

Sine function.

Type Parameters:

T - the type of the field element

Parameters:

x - Argument.

Returns:

sin(x)

Since:

1.3

cos

public static <T extends CalculusFieldElement<T>> T cos(T x)

Cosine function.

Type Parameters:

T - the type of the field element

Parameters:

x - Argument.

Returns:

cos(x)

Since:

1.3

tan

public static <T extends CalculusFieldElement<T>> T tan(T x)

Tangent function.

Type Parameters:

T - the type of the field element

Parameters:

x - Argument.

Returns:

tan(x)

Since:

1.3

atan

public static <T extends CalculusFieldElement<T>> T atan(T x)

Arctangent function

Type Parameters:

T - the type of the field element

Parameters:

x - a number

Returns:

atan(x)

Since:

1.3

atan2

public static <T extends CalculusFieldElement<T>> T atan2(T y,
 T x)

Two arguments arctangent function

Type Parameters:

T - the type of the field element

Parameters:

y - ordinate

x - abscissa

Returns:

phase angle of point (x,y) between -PI and PI

Since:

1.3

asin

public static <T extends CalculusFieldElement<T>> T asin(T x)

Compute the arc sine of a number.

Type Parameters:

T - the type of the field element

Parameters:

x - number on which evaluation is done

Returns:

arc sine of x

Since:

1.3

acos

public static <T extends CalculusFieldElement<T>> T acos(T x)

Compute the arc cosine of a number.

Type Parameters:

T - the type of the field element

Parameters:

x - number on which evaluation is done

Returns:

arc cosine of x

Since:

1.3

cbrt

public static <T extends CalculusFieldElement<T>> T cbrt(T x)

Compute the cubic root of a number.

Type Parameters:

T - the type of the field element

Parameters:

x - number on which evaluation is done

Returns:

cubic root of x

Since:

1.3

norm

public static <T extends CalculusFieldElement<T>>
double norm(T x)

Norm.

Type Parameters:

T - the type of the field element

Parameters:

x - number from which norm is requested

Returns:

norm(x)

Since:

2.0

abs

public static <T extends CalculusFieldElement<T>> T abs(T x)

Absolute value.

Type Parameters:

T - the type of the field element

Parameters:

x - number from which absolute value is requested

Returns:

abs(x)

Since:

2.0

toRadians

public static <T extends CalculusFieldElement<T>> T toRadians(T x)

Convert degrees to radians, with error of less than 0.5 ULP

Type Parameters:

T - the type of the field element

Parameters:

x - angle in degrees

Returns:

x converted into radians

toDegrees

public static <T extends CalculusFieldElement<T>> T toDegrees(T x)

Convert radians to degrees, with error of less than 0.5 ULP

Type Parameters:

T - the type of the field element

Parameters:

x - angle in radians

Returns:

x converted into degrees

scalb

public static <T extends CalculusFieldElement<T>> T scalb(T d,
 int n)

Multiply a double number by a power of 2.

Type Parameters:

T - the type of the field element

Parameters:

d - number to multiply

n - power of 2

Returns:

d × 2ⁿ

Since:

1.3

ulp

public static <T extends CalculusFieldElement<T>> T ulp(T x)

Compute least significant bit (Unit in Last Position) for a number.

Type Parameters:

T - the type of the field element

Parameters:

x - number from which ulp is requested

Returns:

ulp(x)

Since:

2.0

floor

public static <T extends CalculusFieldElement<T>> T floor(T x)

Get the largest whole number smaller than x.

Type Parameters:

T - the type of the field element

Parameters:

x - number from which floor is requested

Returns:

a double number f such that f is an integer f <= x < f + 1.0

Since:

1.3

ceil

public static <T extends CalculusFieldElement<T>> T ceil(T x)

Get the smallest whole number larger than x.

Type Parameters:

T - the type of the field element

Parameters:

x - number from which ceil is requested

Returns:

a double number c such that c is an integer c - 1.0 < x <= c

Since:

1.3

rint

public static <T extends CalculusFieldElement<T>> T rint(T x)

Get the whole number that is the nearest to x, or the even one if x is exactly half way between two integers.

Type Parameters:

T - the type of the field element

Parameters:

x - number from which nearest whole number is requested

Returns:

a double number r such that r is an integer r - 0.5 <= x <= r + 0.5

Since:

1.3

round

public static <T extends CalculusFieldElement<T>>
long round(T x)

Get the closest long to x.

Type Parameters:

T - the type of the field element

Parameters:

x - number from which closest long is requested

Returns:

closest long to x

Since:

1.3

min

public static <T extends CalculusFieldElement<T>> T min(T a,
 T b)

Compute the minimum of two values

Type Parameters:

T - the type of the field element

Parameters:

a - first value

b - second value

Returns:

a if a is lesser or equal to b, b otherwise

Since:

1.3

min

public static <T extends CalculusFieldElement<T>> T min(T a,
 double b)

Compute the minimum of two values

Type Parameters:

T - the type of the field element

Parameters:

a - first value

b - second value

Returns:

a if a is lesser or equal to b, b otherwise

Since:

1.3

max

public static <T extends CalculusFieldElement<T>> T max(T a,
 T b)

Compute the maximum of two values

Type Parameters:

T - the type of the field element

Parameters:

a - first value

b - second value

Returns:

b if a is lesser or equal to b, a otherwise

Since:

1.3

max

public static <T extends CalculusFieldElement<T>> T max(T a,
 double b)

Compute the maximum of two values

Type Parameters:

T - the type of the field element

Parameters:

a - first value

b - second value

Returns:

b if a is lesser or equal to b, a otherwise

Since:

1.3

hypot

public static <T extends CalculusFieldElement<T>> T hypot(T x,
 T y)

Returns the hypotenuse of a triangle with sides x and y - sqrt(x² +y²)
avoiding intermediate overflow or underflow.

• If either argument is infinite, then the result is positive infinity.
• else, if either argument is NaN then the result is NaN.

Type Parameters:

T - the type of the field element

Parameters:

x - a value

y - a value

Returns:

sqrt(x² +y²)

Since:

1.3

IEEEremainder

public static <T extends CalculusFieldElement<T>> T IEEEremainder(T dividend,
 double divisor)

Computes the remainder as prescribed by the IEEE 754 standard.

The remainder value is mathematically equal to x - y*n where n is the mathematical integer closest to the exact mathematical value of the quotient x/y. If two mathematical integers are equally close to x/y then n is the integer that is even.

• If either operand is NaN, the result is NaN.
• If the result is not NaN, the sign of the result equals the sign of the dividend.
• If the dividend is an infinity, or the divisor is a zero, or both, the result is NaN.
• If the dividend is finite and the divisor is an infinity, the result equals the dividend.
• If the dividend is a zero and the divisor is finite, the result equals the dividend.

Type Parameters:

T - the type of the field element

Parameters:

dividend - the number to be divided

divisor - the number by which to divide

Returns:

the remainder, rounded

Since:

1.3

IEEEremainder

public static <T extends CalculusFieldElement<T>> T IEEEremainder(T dividend,
 T divisor)

Computes the remainder as prescribed by the IEEE 754 standard.

The remainder value is mathematically equal to x - y*n where n is the mathematical integer closest to the exact mathematical value of the quotient x/y. If two mathematical integers are equally close to x/y then n is the integer that is even.

• If either operand is NaN, the result is NaN.
• If the result is not NaN, the sign of the result equals the sign of the dividend.
• If the dividend is an infinity, or the divisor is a zero, or both, the result is NaN.
• If the dividend is finite and the divisor is an infinity, the result equals the dividend.
• If the dividend is a zero and the divisor is finite, the result equals the dividend.

Type Parameters:

T - the type of the field element

Parameters:

dividend - the number to be divided

divisor - the number by which to divide

Returns:

the remainder, rounded

Since:

1.3

copySign

public static <T extends CalculusFieldElement<T>> T copySign(T magnitude,
 T sign)

Returns the first argument with the sign of the second argument. A NaN sign argument is treated as positive.

Type Parameters:

T - the type of the field element

Parameters:

magnitude - the value to return

sign - the sign for the returned value

Returns:

the magnitude with the same sign as the sign argument

Since:

1.3

copySign

public static <T extends CalculusFieldElement<T>> T copySign(T magnitude,
 double sign)

Returns the first argument with the sign of the second argument. A NaN sign argument is treated as positive.

Type Parameters:

T - the type of the field element

Parameters:

magnitude - the value to return

sign - the sign for the returned value

Returns:

the magnitude with the same sign as the sign argument

Since:

1.3