MachineArithmetic (rings 2.5.7 API)

java.lang.Object
- cc.redberry.rings.poly.MachineArithmetic

```
public final class MachineArithmetic
extends Object
```
Helper methods for arithmetic with machine numbers.

Since:

1.0

Field Summary

Fields
Modifier and Type	Field and Description
`static BigInteger`	`b_MAX_SUPPORTED_MODULUS` Max supported modulus
`static long`	`MAX_SUPPORTED_MODULUS` Max supported modulus which fits into machine word
`static int`	`MAX_SUPPORTED_MODULUS_BITS` Max supported modulus bits which fits into machine word

Method Summary

All Methods Static Methods Concrete Methods
Modifier and Type	Method and Description
`static boolean`	`fits31bitWord(long val)` Returns true if `val` fits into 32-bit machine word (unsigned) and false otherwise
`static boolean`	`fits32bitWord(long val)` Returns true if `val` fits into 32-bit machine word (unsigned) and false otherwise
`static long`	`gcd(int... integers)` Returns the greatest common an array of integers
`static long`	`gcd(int[] integers, int from, int to)` Returns the greatest common an array of integers
`static int`	`gcd(int p, int q)` Computes the greatest common divisor of the absolute value of two numbers, using a modified version of the "binary gcd" method.
`static long`	`gcd(long... integers)` Returns the greatest common an array of longs
`static long`	`gcd(long[] integers, int from, int to)` Returns the greatest common an array of longs
`static long`	`gcd(long p, long q)` Returns the greatest common divisor of two longs.
`static long[]`	`gcdExtended(long a, long b)` Runs extended Euclidean algorithm to compute `[gcd(a,b), x, y]` such that `x * a + y * b = gcd(a, b)`
`static boolean`	`isOverflowAdd(long x, long y)` Tests whether the addition of `x + y` will cause long overflow
`static boolean`	`isOverflowMultiply(long x, long y)` Tests whether the multiplication of `x*y` will cause long overflow
`static int`	`lcm(int a, int b)` Returns the least common multiple of two integers
`static long`	`lcm(long a, long b)` Returns the least common multiple of two longs
`static long`	`mod(long num, long modulus)` Delegates to `Math.floorMod(long, long)`
`static long`	`modInverse(long num, long modulus)` Returns a solution of congruence `num * x = 1 mod modulus`
`static long[]`	`perfectPowerDecomposition(long n)` Tests whether `n` is a perfect power `n == a^b` and returns `{a, b}` if so and `null` otherwise
`static long`	`powMod(long base, long exponent, long modulus)` Returns `base` in a power of non-negative `e` modulo `modulus`
`static long`	`powModSigned(long base, long exponent, cc.redberry.libdivide4j.FastDivision.Magic magic)` Returns `base` in a power of non-negative `e` modulo `magic.modulus`
`static long`	`powModUnsigned(long base, long exponent, cc.redberry.libdivide4j.FastDivision.Magic magic)` Returns `base` in a power of non-negative `e` modulo `magic.modulus`
`static long`	`safeAdd(long x, long y)` Delegates to `Math.addExact(long, long)`
`static long`	`safeMultiply(long x, long y)` Delegates to `Math.multiplyExact(long, long)`
`static long`	`safeMultiply(long x, long y, long z)` Delegates to `Math.multiplyExact(long, long)`
`static long`	`safeNegate(long x)` Delegates to `Math.negateExact(long)`
`static long`	`safePow(long base, long exponent)` Returns `base` in a power of `e` (non negative)
`static long`	`safeSubtract(long a, long b)` Delegates to `Math.subtractExact(long, long)`
`static int`	`safeToInt(long value)` Casts `long` to signed `int` throwing exception in case of overflow.
`static long`	`symMod(long value, long modulus)` Returns `value mod modulus` in the symmetric representation (`-modulus/2 <= result <= modulus/2`)
`static long`	`unsafePow(long base, long exponent)` Returns `base` in a power of `e` (non negative)

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Field Detail
  - MAX_SUPPORTED_MODULUS_BITS
```
public static final int MAX_SUPPORTED_MODULUS_BITS
```
    Max supported modulus bits which fits into machine word
    
    See Also:
    
    Constant Field Values
  - MAX_SUPPORTED_MODULUS
```
public static final long MAX_SUPPORTED_MODULUS
```
    Max supported modulus which fits into machine word
    
    See Also:
    
    Constant Field Values
  - b_MAX_SUPPORTED_MODULUS
```
public static final BigInteger b_MAX_SUPPORTED_MODULUS
```
    Max supported modulus
- Method Detail
  - fits32bitWord
```
public static boolean fits32bitWord(long val)
```
    Returns true if val fits into 32-bit machine word (unsigned) and false otherwise
    
    Parameters:
    
    val - the value
    
    Returns:
    
    true if val fits into 32-bit machine word (unsigned) and false otherwise
  - fits31bitWord
```
public static boolean fits31bitWord(long val)
```
    Returns true if val fits into 32-bit machine word (unsigned) and false otherwise
    
    Parameters:
    
    val - the value
    
    Returns:
    
    true if val fits into 32-bit machine word (unsigned) and false otherwise
  - safeMultiply
```
public static long safeMultiply(long x,
                                long y)
```
    Delegates to Math.multiplyExact(long, long)
    
    Throws:
    
    ArithmeticException - if the result overflows a long
  - safeMultiply
```
public static long safeMultiply(long x,
                                long y,
                                long z)
```
    Delegates to Math.multiplyExact(long, long)
    
    Throws:
    
    ArithmeticException - if the result overflows a long
  - safeAdd
```
public static long safeAdd(long x,
                           long y)
```
    Delegates to Math.addExact(long, long)
    
    Throws:
    
    ArithmeticException - if the result overflows a long
  - safeSubtract
```
public static long safeSubtract(long a,
                                long b)
```
    Delegates to Math.subtractExact(long, long)
    
    Throws:
    
    ArithmeticException - if the result overflows a long
  - safeNegate
```
public static long safeNegate(long x)
```
    Delegates to Math.negateExact(long)
    
    Throws:
    
    ArithmeticException - if the result overflows a long
  - isOverflowMultiply
```
public static boolean isOverflowMultiply(long x,
                                         long y)
```
    Tests whether the multiplication of x*y will cause long overflow
  - isOverflowAdd
```
public static boolean isOverflowAdd(long x,
                                    long y)
```
    Tests whether the addition of x + y will cause long overflow
  - safePow
```
public static long safePow(long base,
                           long exponent)
```
    Returns base in a power of e (non negative)
    
    Parameters:
    
    base - base
    
    exponent - exponent (non negative)
    
    Returns:
    
    base in a power of e
    
    Throws:
    
    ArithmeticException - if the result overflows a long
  - unsafePow
```
public static long unsafePow(long base,
                             long exponent)
```
    Returns base in a power of e (non negative)
    
    Parameters:
    
    base - base
    
    exponent - exponent (non negative)
    
    Returns:
    
    base in a power of e
  - gcd
```
public static long gcd(long p,
                       long q)
```
    Returns the greatest common divisor of two longs.
    
    Parameters:
    
    p - a long
    
    q - a long
    
    Returns:
    
    greatest common divisor of a and b
  - gcd
```
public static int gcd(int p,
                      int q)
```
    Computes the greatest common divisor of the absolute value of two numbers, using a modified version of the "binary gcd" method. See Knuth 4.5.2 algorithm B. The algorithm is due to Josef Stein (1961).
    Special cases:
    - The invocations gcd(Integer.MIN_VALUE, Integer.MIN_VALUE), gcd(Integer.MIN_VALUE, 0) and gcd(0, Integer.MIN_VALUE) throw an ArithmeticException, because the result would be 2^31, which is too large for an int value.
    - The result of gcd(x, x), gcd(0, x) and gcd(x, 0) is the absolute value of x, except for the special cases above.
    - The invocation gcd(0, 0) is the only one which returns 0.
    Parameters:
    
    p - Number.
    
    q - Number.
    
    Returns:
    
    the greatest common divisor (never negative).
  - gcdExtended
```
public static long[] gcdExtended(long a,
                                 long b)
```
    Runs extended Euclidean algorithm to compute [gcd(a,b), x, y] such that x * a + y * b = gcd(a, b)
    
    Parameters:
    
    a - a long
    
    b - a long
    
    Returns:
    
    array of [gcd(a,b), x, y] such that x * a + y * b = gcd(a, b)
  - lcm
```
public static long lcm(long a,
                       long b)
```
    Returns the least common multiple of two longs
    
    Parameters:
    
    a - a long
    
    b - a long
    
    Returns:
    
    least common multiple of a and b
    
    Throws:
    
    ArithmeticException - if the result overflows a long
  - lcm
```
public static int lcm(int a,
                      int b)
```
    Returns the least common multiple of two integers
    
    Parameters:
    
    a - a number
    
    b - a number
    
    Returns:
    
    least common multiple of a and b
  - gcd
```
public static long gcd(long[] integers,
                       int from,
                       int to)
```
    Returns the greatest common an array of longs
    
    Parameters:
    
    integers - array of longs
    
    from - from position (inclusive)
    
    to - to position (exclusive)
    
    Returns:
    
    greatest common divisor of array
  - gcd
```
public static long gcd(long... integers)
```
    Returns the greatest common an array of longs
    
    Parameters:
    
    integers - array of longs
    
    Returns:
    
    greatest common divisor of array
  - gcd
```
public static long gcd(int[] integers,
                       int from,
                       int to)
```
    Returns the greatest common an array of integers
    
    Parameters:
    
    integers - array of integers
    
    from - from position (inclusive)
    
    to - to position (exclusive)
    
    Returns:
    
    greatest common divisor of array
  - gcd
```
public static long gcd(int... integers)
```
    Returns the greatest common an array of integers
    
    Parameters:
    
    integers - array of integers
    
    Returns:
    
    greatest common divisor of array
  - mod
```
public static long mod(long num,
                       long modulus)
```
    Delegates to Math.floorMod(long, long)
  - symMod
```
public static long symMod(long value,
                          long modulus)
```
    Returns value mod modulus in the symmetric representation (-modulus/2 <= result <= modulus/2)
    
    Parameters:
    
    value - a long
    
    modulus - modulus
    
    Returns:
    
    value mod modulus in the symmetric representation (-modulus/2 <= result <= modulus/2)
  - modInverse
```
public static long modInverse(long num,
                              long modulus)
```
    Returns a solution of congruence num * x = 1 mod modulus
    
    Parameters:
    
    num - base
    
    modulus - modulus
    
    Returns:
    
    a^(-1) mod p
    
    Throws:
    
    IllegalArgumentException - a and modulus are not coprime
  - safeToInt
```
public static int safeToInt(long value)
```
    Casts long to signed int throwing exception in case of overflow.
    
    Parameters:
    
    value - the long
    
    Returns:
    
    int value
    
    Throws:
    
    ArithmeticException - if the result overflows a long
  - powMod
```
public static long powMod(long base,
                          long exponent,
                          long modulus)
```
    Returns base in a power of non-negative e modulo modulus
    
    Parameters:
    
    base - the base
    
    exponent - the non-negative exponent
    
    modulus - the modulus
    
    Returns:
    
    base in a power of e
  - powModSigned
```
public static long powModSigned(long base,
                                long exponent,
                                cc.redberry.libdivide4j.FastDivision.Magic magic)
```
    Returns base in a power of non-negative e modulo magic.modulus
    
    Parameters:
    
    base - the base
    
    exponent - the non-negative exponent
    
    magic - magic modulus
    
    Returns:
    
    base in a power of e
  - powModUnsigned
```
public static long powModUnsigned(long base,
                                  long exponent,
                                  cc.redberry.libdivide4j.FastDivision.Magic magic)
```
    Returns base in a power of non-negative e modulo magic.modulus
    
    Parameters:
    
    base - the base
    
    exponent - the non-negative exponent
    
    magic - magic modulus
    
    Returns:
    
    base in a power of e
  - perfectPowerDecomposition
```
public static long[] perfectPowerDecomposition(long n)
```
    Tests whether n is a perfect power n == a^b and returns {a, b} if so and null otherwise
    
    Parameters:
    
    n - the number
    
    Returns:
    
    array {a, b} so that n = a^b or null is n is not a perfect power

Class MachineArithmetic

Field Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

MAX_SUPPORTED_MODULUS_BITS

MAX_SUPPORTED_MODULUS

b_MAX_SUPPORTED_MODULUS

Method Detail

fits32bitWord

fits31bitWord

safeMultiply

safeMultiply

safeAdd

safeSubtract

safeNegate

isOverflowMultiply

isOverflowAdd

safePow

unsafePow

gcd

gcd

gcdExtended

lcm

lcm

gcd

gcd

gcd

gcd

mod

symMod

modInverse

safeToInt

powMod

powModSigned

powModUnsigned

perfectPowerDecomposition