Package org.apfloat

Class ApintMath

java.lang.Object

org.apfloat.ApintMath

public class ApintMath
extends java.lang.Object

Various mathematical functions for arbitrary precision integers.

Version:

1.14.0

Field Summary

Fields

Modifier and Type	Field	Description
private static java.util.Random	RANDOM

Constructor Summary

Constructors

Modifier	Constructor	Description
private	ApintMath()

Method Summary

Modifier and Type	Method	Description
static Apint	abs(Apint x)	Absolute value.
static Apint	binomial(long n, long k)	Binomial coefficient.
static Apint	binomial(long n, long k, int radix)	Binomial coefficient.
static Apint	binomial(Apint n, Apint k)	Binomial coefficient.
static Apint[]	cbrt(Apint x)	Cube root and remainder.
static Apint	copySign(Apint x, Apint y)	Copy sign from one argument to another.
static Apint[]	div(Apint x, Apint y)	Quotient and remainder.
static Apint	doubleFactorial(long n)	Double factorial function.
static Apint	doubleFactorial(long n, int radix)	Double factorial function.
static Apint	factorial(long n)	Factorial function.
static Apint	factorial(long n, int radix)	Factorial function.
static Apint	gcd(Apint a, Apint b)	Greatest common divisor.
static Apint	lcm(Apint a, Apint b)	Least common multiple.
static Apint	max(Apint x, Apint y)	Returns the greater of the two values.
static Apint	min(Apint x, Apint y)	Returns the smaller of the two values.
private static Apint	modInverse(Apint a, Apint m)
static Apint	modMultiply(Apint a, Apint b, Apint m)	Modular multiplication.
private static Apint	modMultiply(Apint x1, Apint x2, Apint y, Apfloat inverseY)
static Apint	modPow(Apint a, Apint b, Apint m)	Modular power.
static Apint	negate(Apint x)	Deprecated. Use Apint.negate().
private static Apint	pochhammer(long n, long m, int radix)
private static Apint	pochhammer(Apint n, Apint m)
static Apint	pow(Apint x, long n)	Integer power.
private static Apint	powXMinus1(Apint pow, Apint x, long n)
private static Apint	powXPlus1(Apint pow, Apint x, long n)
static Apint	product(Apint... x)	Product of numbers.
static Apint	random(long digits)	Generates a random number.
static Apint	random(long digits, int radix)	Generates a random number.
static Apint[]	root(Apint x, long n)	Positive integer root and remainder.
static Apint	scale(Apint x, long scale)	Multiply by a power of the radix.
static Apint[]	sqrt(Apint x)	Square root and remainder.
static Apint	sum(Apint... x)	Sum of numbers.

Methods inherited from class java.lang.Object

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

Field Detail

RANDOM

private static final java.util.Random RANDOM

Constructor Detail

ApintMath

private ApintMath()

Method Detail

pow

public static Apint pow(Apint x,
                        long n)
                 throws java.lang.ArithmeticException,
                        ApfloatRuntimeException

Integer power.

Parameters:

x - Base of the power operator.

n - Exponent of the power operator.

Returns:

x to the n:th power, that is xn.

Throws:

java.lang.ArithmeticException - If both x and n are zero.

ApfloatRuntimeException

sqrt

public static Apint[] sqrt(Apint x)
                    throws java.lang.ArithmeticException,
                           ApfloatRuntimeException

Square root and remainder.

Parameters:

x - The argument.

Returns:

An array of two apints: [q, r], where q2 + r = x.

Throws:

java.lang.ArithmeticException - If x is negative.

ApfloatRuntimeException

cbrt

public static Apint[] cbrt(Apint x)
                    throws ApfloatRuntimeException

Cube root and remainder.

Parameters:

x - The argument.

Returns:

An array of two apints: [q, r], where q3 + r = x.

Throws:

ApfloatRuntimeException

root

public static Apint[] root(Apint x,
                           long n)
                    throws java.lang.ArithmeticException,
                           ApfloatRuntimeException

Positive integer root and remainder.

Returns the n:th root of x, that is x1/n, rounded towards zero.

Parameters:

x - The argument.

n - Which root to take.

Returns:

An array of two apints: [q, r], where qn + r = x.

Throws:

java.lang.ArithmeticException - If n and x are zero, or x is negative and n is even.

ApfloatRuntimeException

powXMinus1

private static Apint powXMinus1(Apint pow,
                                Apint x,
                                long n)
                         throws ApfloatRuntimeException

Throws:

ApfloatRuntimeException

powXPlus1

private static Apint powXPlus1(Apint pow,
                               Apint x,
                               long n)
                        throws ApfloatRuntimeException

Throws:

ApfloatRuntimeException

negate

@Deprecated
public static Apint negate(Apint x)
                    throws ApfloatRuntimeException

Deprecated.

Use Apint.negate().

Returns an apint whose value is -x.

Parameters:

x - The argument.

Returns:

-x.

Throws:

ApfloatRuntimeException

abs

public static Apint abs(Apint x)
                 throws ApfloatRuntimeException

Absolute value.

Parameters:

x - The argument.

Returns:

Absolute value of x.

Throws:

ApfloatRuntimeException

copySign

public static Apint copySign(Apint x,
                             Apint y)
                      throws ApfloatRuntimeException

Copy sign from one argument to another.

Parameters:

x - The value whose sign is to be adjusted.

y - The value whose sign is to be used.

Returns:

x with its sign changed to match the sign of y.

Throws:

ApfloatRuntimeException

Since:

1.1

scale

public static Apint scale(Apint x,
                          long scale)
                   throws ApfloatRuntimeException

Multiply by a power of the radix. Any rounding will occur towards zero.

Parameters:

x - The argument.

scale - The scaling factor.

Returns:

x * x.radix()scale.

Throws:

ApfloatRuntimeException

div

public static Apint[] div(Apint x,
                          Apint y)
                   throws java.lang.ArithmeticException,
                          ApfloatRuntimeException

Quotient and remainder.

Parameters:

x - The dividend.

y - The divisor.

Returns:

An array of two apints: [quotient, remainder], that is [x / y, x % y].

Throws:

java.lang.ArithmeticException - In case the divisor is zero.

ApfloatRuntimeException

gcd

public static Apint gcd(Apint a,
                        Apint b)
                 throws ApfloatRuntimeException

Greatest common divisor. This method returns a positive number even if one of a and b is negative.

Parameters:

a - First argument.

b - Second argument.

Returns:

Greatest common divisor of a and b.

Throws:

ApfloatRuntimeException

lcm

public static Apint lcm(Apint a,
                        Apint b)
                 throws ApfloatRuntimeException

Least common multiple. This method returns a positive number even if one of a and b is negative.

Parameters:

a - First argument.

b - Second argument.

Returns:

Least common multiple of a and b.

Throws:

ApfloatRuntimeException

modMultiply

public static Apint modMultiply(Apint a,
                                Apint b,
                                Apint m)
                         throws ApfloatRuntimeException

Modular multiplication. Returns a * b % m

Parameters:

a - First argument.

b - Second argument.

m - Modulus.

Returns:

a * b mod m

Throws:

ApfloatRuntimeException

modMultiply

private static Apint modMultiply(Apint x1,
                                 Apint x2,
                                 Apint y,
                                 Apfloat inverseY)
                          throws ApfloatRuntimeException

Throws:

ApfloatRuntimeException

modPow

public static Apint modPow(Apint a,
                           Apint b,
                           Apint m)
                    throws java.lang.ArithmeticException,
                           ApfloatRuntimeException

Modular power.

Parameters:

a - Base.

b - Exponent.

m - Modulus.

Returns:

ab mod m

Throws:

java.lang.ArithmeticException - If the exponent is negative but the GCD of a and m is not 1 and the modular inverse does not exist.

ApfloatRuntimeException

modInverse

private static Apint modInverse(Apint a,
                                Apint m)
                         throws java.lang.ArithmeticException,
                                ApfloatRuntimeException

Throws:

java.lang.ArithmeticException

ApfloatRuntimeException

factorial

public static Apint factorial(long n)
                       throws java.lang.ArithmeticException,
                              java.lang.NumberFormatException,
                              ApfloatRuntimeException

Factorial function. Uses the default radix.

Parameters:

n - The number whose factorial is to be calculated. Should be non-negative.

Returns:

n!

Throws:

java.lang.ArithmeticException - If n is negative.

java.lang.NumberFormatException - If the default radix is not valid.

ApfloatRuntimeException

Since:

1.1

factorial

public static Apint factorial(long n,
                              int radix)
                       throws java.lang.ArithmeticException,
                              java.lang.NumberFormatException,
                              ApfloatRuntimeException

Factorial function. Returns a number in the specified radix.

Parameters:

n - The number whose factorial is to be calculated. Should be non-negative.

radix - The radix to use.

Returns:

n!

Throws:

java.lang.ArithmeticException - If n is negative.

java.lang.NumberFormatException - If the radix is not valid.

ApfloatRuntimeException

Since:

1.1

doubleFactorial

public static Apint doubleFactorial(long n)
                             throws java.lang.ArithmeticException,
                                    java.lang.NumberFormatException,
                                    ApfloatRuntimeException

Double factorial function. Uses the default radix.

Parameters:

n - The number whose double factorial is to be calculated. Should be non-negative.

Returns:

n!!

Throws:

java.lang.ArithmeticException - If n is negative.

java.lang.NumberFormatException - If the default radix is not valid.

ApfloatRuntimeException

Since:

1.14.0

doubleFactorial

public static Apint doubleFactorial(long n,
                                    int radix)
                             throws java.lang.ArithmeticException,
                                    java.lang.NumberFormatException,
                                    ApfloatRuntimeException

Double factorial function. Returns a number in the specified radix.

Parameters:

n - The number whose double factorial is to be calculated. Should be non-negative.

radix - The radix to use.

Returns:

n!!

Throws:

java.lang.ArithmeticException - If n is negative.

java.lang.NumberFormatException - If the radix is not valid.

ApfloatRuntimeException

Since:

1.14.0

binomial

public static Apint binomial(long n,
                             long k)
                      throws ApfloatRuntimeException

Binomial coefficient. Uses the default radix.

Parameters:

n - The first argument.

k - The second argument.

Returns:

$\left(\genfrac{}{}{0ex}{}{n}{k}\right)$

Throws:

ApfloatRuntimeException

Since:

1.11.0

binomial

public static Apint binomial(long n,
                             long k,
                             int radix)
                      throws java.lang.NumberFormatException,
                             ApfloatRuntimeException

Binomial coefficient. Uses the specified radix.

Parameters:

n - The first argument.

k - The second argument.

radix - The radix.

Returns:

$\left(\genfrac{}{}{0ex}{}{n}{k}\right)$

Throws:

java.lang.NumberFormatException - If the radix is not valid.

ApfloatRuntimeException

Since:

1.11.0

binomial

public static Apint binomial(Apint n,
                             Apint k)
                      throws ApfloatRuntimeException

Binomial coefficient.

Parameters:

n - The first argument.

k - The second argument.

Returns:

$\left(\genfrac{}{}{0ex}{}{n}{k}\right)$

Throws:

ApfloatRuntimeException

Since:

1.11.0

pochhammer

private static Apint pochhammer(long n,
                                long m,
                                int radix)

pochhammer

private static Apint pochhammer(Apint n,
                                Apint m)

product

public static Apint product(Apint... x)
                     throws ApfloatRuntimeException

Product of numbers. This method may perform significantly better than simply multiplying the numbers sequentially.

If there are no arguments, the return value is 1.

Parameters:

x - The argument(s).

Returns:

The product of the given numbers.

Throws:

ApfloatRuntimeException

Since:

1.3

sum

public static Apint sum(Apint... x)
                 throws ApfloatRuntimeException

Sum of numbers.

If there are no arguments, the return value is 0.

Parameters:

x - The argument(s).

Returns:

The sum of the given numbers.

Throws:

ApfloatRuntimeException

Since:

1.3

random

public static Apint random(long digits)

Generates a random number. Uses the default radix. Returned values are chosen pseudorandomly with (approximately) uniform distribution from the range 0 ≤ x < radixdigits. The generated random numbers may have leading zeros and may thus not always have exactly the requested number of digis.

Parameters:

digits - Maximum number of digits in the number.

Returns:

A random number, uniformly distributed between 0 ≤ x < radixdigits.

Throws:

java.lang.NumberFormatException - If the default radix is not valid.

java.lang.IllegalArgumentException - In case the number of specified digits is invalid.

Since:

1.9.0

random

public static Apint random(long digits,
                           int radix)

Generates a random number. Returned values are chosen pseudorandomly with (approximately) uniform distribution from the range 0 ≤ x < radixdigits. The generated random numbers may have leading zeros and may thus not always have exactly the requested number of digis.

Parameters:

digits - Maximum number of digits in the number.

radix - The radix in which the number should be generated.

Returns:

A random number, uniformly distributed between 0 ≤ x < radixdigits, in base radix.

Throws:

java.lang.NumberFormatException - If the radix is not valid.

java.lang.IllegalArgumentException - In case the number of specified digits is invalid.

Since:

1.9.0

max

public static Apint max(Apint x,
                        Apint y)

Returns the greater of the two values.

Parameters:

x - An argument.

y - Another argument.

Returns:

The greater of the two values.

Since:

1.9.0

min

public static Apint min(Apint x,
                        Apint y)

Returns the smaller of the two values.

Parameters:

x - An argument.

y - Another argument.

Returns:

The smaller of the two values.

Since:

1.9.0