plume

Class MathMDE

java.lang.Object

plume.MathMDE

Deprecated.

use org.plumelib.util.MathPlume

@Deprecated
public final class MathMDE
extends java.lang.Object

Mathematical utilities.

Method Summary

Modifier and Type	Method and Description
static int	bitwiseAnd(int x, int y) Deprecated. Returns x & y, the bitwise and of its arguments.
static long	bitwiseAnd(long x, long y) Deprecated. Returns x & y, the bitwise and of its arguments.
static int	bitwiseComplement(int a) Deprecated. Returns ~a, the bitwise complement of its argument.
static long	bitwiseComplement(long a) Deprecated. Returns ~a, the bitwise complement of its argument.
static int	bitwiseOr(int x, int y) Deprecated. Returns x | y, the bitwise or of its arguments.
static long	bitwiseOr(long x, long y) Deprecated. Returns x | y, the bitwise or of its arguments.
static int	bitwiseXor(int x, int y) Deprecated. Returns x ^ y, the bitwise xor of its arguments.
static long	bitwiseXor(long x, long y) Deprecated. Returns x ^ y, the bitwise xor of its arguments.
static double	div(double x, double y) Deprecated. Divides its arguments.
static int	div(int x, int y) Deprecated. Divides its arguments.
static long	div(long x, long y) Deprecated. Divides its arguments.
static double	gcd_differences(double[] a) Deprecated. Return the gcd (greatest common divisor) of the differences between the elements of double array a.
static int	gcd_differences(int[] a) Deprecated. Return the gcd (greatest common divisor) of the differences between the elements of int array a.
static long	gcd_differences(long[] a) Deprecated. Return the gcd (greatest common divisor) of the differences between the elements of long array a.
static double	gcd(double[] a) Deprecated. Return the greatest common divisor of the elements of double array a.
static double	gcd(double a, double b) Deprecated. Return the greatest common divisor of the two arguments.
static int	gcd(int[] a) Deprecated. Return the greatest common divisor of the elements of int array a.
static int	gcd(int a, int b) Deprecated. Return the greatest common divisor of the two arguments.
static long	gcd(long[] a) Deprecated. Return the greatest common divisor of the elements of long array a.
static long	gcd(long a, long b) Deprecated. Return the greatest common divisor of the two arguments.
static int	logicalAnd(int x, int y) Deprecated. Returns the logical and of its arguments.
static long	logicalAnd(long x, long y) Deprecated. Returns the logical and of its arguments.
static int	logicalOr(int x, int y) Deprecated. Returns the logical or of its arguments.
static long	logicalOr(long x, long y) Deprecated. Returns the logical or of its arguments.
static int	logicalXor(int x, int y) Deprecated. Returns the logical xor of its arguments.
static long	logicalXor(long x, long y) Deprecated. Returns the logical xor of its arguments.
static int	lshift(int x, int y) Deprecated. Returns x << y, the left-shift operation applied to its arguments.
static long	lshift(long x, long y) Deprecated. Returns x << y, the left-shift operation applied to its arguments.
static int[]	missing_numbers(int[] nums) Deprecated. Return an array containing all the numbers not in its argument array (which must be non-empty) but in the argument's range; that is, bigger than its argument's minimum value and smaller than its argument's maximum value.
static long[]	missing_numbers(long[] nums) Deprecated. Return an array containing all the numbers not in its argument array (which must be non-empty) but in the argument's range; that is, bigger than its argument's minimum value and smaller than its argument's maximum value.
static int	mod_positive(int x, int y) Deprecated. Return z such that (z == x mod y) && (0 <= z < abs(y)).
static long	mod_positive(long x, long y) Deprecated. Return z such that (z == x mod y) && (0 <= z < abs(y)).
static int	mod(int x, int y) Deprecated. Returns x % y, the modulus operation applied to its arguments.
static long	mod(long x, long y) Deprecated. Returns x % y, the modulus operation applied to its arguments.
static int[]	modulus_int(java.util.Iterator<java.lang.Integer> itor) Deprecated. The iterator produces Integer values.
static long[]	modulus_long(java.util.Iterator<java.lang.Long> itor) Deprecated. The iterator produces Long values.
static int[]	modulus_strict_int(java.util.Iterator<java.lang.Integer> itor, boolean nonstrict_ends) Deprecated. The iterator produces Integer values.
static long[]	modulus_strict_long(java.util.Iterator<java.lang.Long> itor, boolean nonstrict_ends) Deprecated. The iterator produces Long values.
static int[]	modulus_strict(int[] nums, boolean nonstrict_ends) Deprecated. Return an array of two integers (r,m) such that each number in NUMS is equal to r (mod m).
static long[]	modulus_strict(long[] nums, boolean nonstrict_ends) Deprecated. Return an array of two integers (r,m) such that each number in NUMS is equal to r (mod m).
static int[]	modulus(int[] nums) Deprecated. Return an array of two integers (r,m) such that each number in NUMS is equal to r (mod m).
static long[]	modulus(long[] nums) Deprecated. Return an array of two integers (r,m) such that each number in NUMS is equal to r (mod m).
static double	mul(double x, double y) Deprecated. Multiplies its arguments.
static int	mul(int x, int y) Deprecated. Multiplies its arguments.
static long	mul(long x, long y) Deprecated. Multiplies its arguments.
static double	negate(double a) Deprecated. Negates its argument.
static int	negate(int a) Deprecated. Negates its argument.
static long	negate(long a) Deprecated. Negates its argument.
static int[]	nonmodulus_nonstrict(int[] nums) Deprecated. Return a tuple of (r,m) where no number in NUMS is equal to r (mod m) but for every number in NUMS, at least one is equal to every non-r remainder.
static long[]	nonmodulus_nonstrict(long[] nums) Deprecated. Return a tuple of (r,m) where no number in NUMS is equal to r (mod m) but for every number in NUMS, at least one is equal to every non-r remainder.
static int[]	nonmodulus_strict_int(java.util.Iterator<java.lang.Integer> nums) Deprecated. Return a tuple of (r,m) where no number in NUMS is equal to r (mod m) but all missing numbers in their range are.
static long[]	nonmodulus_strict_long(java.util.Iterator<java.lang.Long> nums) Deprecated. Return a tuple of (r,m) where no number in NUMS is equal to r (mod m) but all missing numbers in their range are.
static int[]	nonmodulus_strict(int[] nums) Deprecated. Return a tuple of (r,m) where no number in NUMS is equal to r (mod m) but all missing numbers in their range are.
static long[]	nonmodulus_strict(long[] nums) Deprecated. Return a tuple of (r,m) where no number in NUMS is equal to r (mod m) but all missing numbers in their range are.
static int	pow(int base, int expt) Deprecated. Returns of value of the first argument raised to the power of the second argument.
static long	pow(long base, long expt) Deprecated. Returns of value of the first argument raised to the power of the second argument.
static int	rshiftSigned(int x, int y) Deprecated. Returns x >> y, the signed right-shift operation applied to its arguments.
static long	rshiftSigned(long x, long y) Deprecated. Returns x >> y, the signed right-shift operation applied to its arguments.
static int	rshiftUnsigned(int x, int y) Deprecated. Returns x >>> y, the unsigned right-shift operation applied to its arguments.
static long	rshiftUnsigned(long x, long y) Deprecated. Returns x >>> y, the unsigned right-shift operation applied to its arguments.
static int	sign(int a) Deprecated. Returns the sign of its argument.

Methods inherited from class java.lang.Object

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

Method Detail

negate

public static int negate(int a)

Deprecated.

Negates its argument.

Parameters:

a - value to negate

Returns:

negative of a

negate

public static long negate(long a)

Deprecated.

Negates its argument.

Parameters:

a - value to negate

Returns:

negative of a

negate

public static double negate(double a)

Deprecated.

Negates its argument.

Parameters:

a - value to negate

Returns:

negative of a

bitwiseComplement

public static int bitwiseComplement(int a)

Deprecated.

Returns ~a, the bitwise complement of its argument.

Parameters:

a - value to bitwise-complement

Returns:

~a, the bitwise complement of a

bitwiseComplement

public static long bitwiseComplement(long a)

Deprecated.

Returns ~a, the bitwise complement of its argument.

Parameters:

a - value to bitwise-complement

Returns:

~a, the bitwise complement of a

mul

public static int mul(int x,
                      int y)

Deprecated.

Multiplies its arguments.

Parameters:

x - first multiplicand

y - second multiplicand

Returns:

x * y

mul

public static long mul(long x,
                       long y)

Deprecated.

Multiplies its arguments.

Parameters:

x - first multiplicand

y - second multiplicand

Returns:

x * y

mul

public static double mul(double x,
                         double y)

Deprecated.

Multiplies its arguments.

Parameters:

x - first multiplicand

y - second multiplicand

Returns:

x * y

div

public static int div(int x,
                      int y)

Deprecated.

Divides its arguments.

Parameters:

x - dividend

y - divisor

Returns:

x / y

div

public static long div(long x,
                       long y)

Deprecated.

Divides its arguments.

Parameters:

x - dividend

y - divisor

Returns:

x / y

div

public static double div(double x,
                         double y)

Deprecated.

Divides its arguments.

Parameters:

x - dividend

y - divisor

Returns:

x / y

mod

public static int mod(int x,
                      int y)

Deprecated.

Returns x % y, the modulus operation applied to its arguments.

Parameters:

x - valued to be modded

y - modulus

Returns:

x % y

mod

public static long mod(long x,
                       long y)

Deprecated.

Returns x % y, the modulus operation applied to its arguments.

Parameters:

x - valued to be modded

y - modulus

Returns:

x % y

lshift

public static int lshift(int x,
                         int y)

Deprecated.

Returns x << y, the left-shift operation applied to its arguments.

Parameters:

x - valued to be left-shifted

y - magnitude of the left-shift

Returns:

x << y

lshift

public static long lshift(long x,
                          long y)

Deprecated.

Returns x << y, the left-shift operation applied to its arguments.

Parameters:

x - valued to be left-shifted

y - magnitude of the left-shift

Returns:

x << y

rshiftSigned

public static int rshiftSigned(int x,
                               int y)

Deprecated.

Returns x >> y, the signed right-shift operation applied to its arguments.

Parameters:

x - valued to be right-shifted

y - magnitude of the right-shift

Returns:

x >> y

rshiftSigned

public static long rshiftSigned(long x,
                                long y)

Deprecated.

Returns x >> y, the signed right-shift operation applied to its arguments.

Parameters:

x - valued to be right-shifted

y - magnitude of the right-shift

Returns:

x >> y

rshiftUnsigned

public static int rshiftUnsigned(int x,
                                 int y)

Deprecated.

Returns x >>> y, the unsigned right-shift operation applied to its arguments.

Parameters:

x - valued to be right-shifted

y - magnitude of the right-shift

Returns:

x >>> y

rshiftUnsigned

public static long rshiftUnsigned(long x,
                                  long y)

Deprecated.

Returns x >>> y, the unsigned right-shift operation applied to its arguments.

Parameters:

x - valued to be right-shifted

y - magnitude of the right-shift

Returns:

x >>> y

bitwiseAnd

public static int bitwiseAnd(int x,
                             int y)

Deprecated.

Returns x & y, the bitwise and of its arguments.

Parameters:

x - first operand

y - second operand

Returns:

x & y

bitwiseAnd

public static long bitwiseAnd(long x,
                              long y)

Deprecated.

Returns x & y, the bitwise and of its arguments.

Parameters:

x - first operand

y - second operand

Returns:

x & y

logicalAnd

public static int logicalAnd(int x,
                             int y)

Deprecated.

Returns the logical and of its arguments. The result is always 0 or 1.

Parameters:

x - first operand

y - second operand

Returns:

the logical and of x and y; the result is always 0 or 1

logicalAnd

public static long logicalAnd(long x,
                              long y)

Deprecated.

Returns the logical and of its arguments. The result is always 0 or 1.

Parameters:

x - first operand

y - second operand

Returns:

the logical and of x and y; the result is always 0 or 1

bitwiseXor

public static int bitwiseXor(int x,
                             int y)

Deprecated.

Returns x ^ y, the bitwise xor of its arguments.

Parameters:

x - first operand

y - second operand

Returns:

x ^ y

bitwiseXor

public static long bitwiseXor(long x,
                              long y)

Deprecated.

Returns x ^ y, the bitwise xor of its arguments.

Parameters:

x - first operand

y - second operand

Returns:

x ^ y

logicalXor

public static int logicalXor(int x,
                             int y)

Deprecated.

Returns the logical xor of its arguments. The result is always 0 or 1.

Parameters:

x - first operand

y - second operand

Returns:

the logical xor of x and y; the result is always 0 or 1

logicalXor

public static long logicalXor(long x,
                              long y)

Deprecated.

Returns the logical xor of its arguments. The result is always 0 or 1.

Parameters:

x - first operand

y - second operand

Returns:

the logical xor of x and y; the result is always 0 or 1

bitwiseOr

public static int bitwiseOr(int x,
                            int y)

Deprecated.

Returns x | y, the bitwise or of its arguments.

Parameters:

x - first operand

y - second operand

Returns:

x | y

bitwiseOr

public static long bitwiseOr(long x,
                             long y)

Deprecated.

Returns x | y, the bitwise or of its arguments.

Parameters:

x - first operand

y - second operand

Returns:

x | y

logicalOr

public static int logicalOr(int x,
                            int y)

Deprecated.

Returns the logical or of its arguments. The result is always 0 or 1.

Parameters:

x - first operand

y - second operand

Returns:

the logical or of x and y; the result is always 0 or 1

logicalOr

public static long logicalOr(long x,
                             long y)

Deprecated.

Returns the logical or of its arguments. The result is always 0 or 1.

Parameters:

x - first operand

y - second operand

Returns:

the logical or of x and y; the result is always 0 or 1

sign

public static int sign(int a)

Deprecated.

Returns the sign of its argument. The result is always -1, 0, or 1.

Parameters:

a - value to have its sign taken

Returns:

the sign of a: -1, 0, or 1

pow

public static int pow(int base,
                      int expt)
               throws java.lang.ArithmeticException

Deprecated.

Returns of value of the first argument raised to the power of the second argument. The arguments are integers.

Parameters:

base - the base

expt - the exponent

Returns:

base to the expt power

Throws:

java.lang.ArithmeticException

See Also:

Math.pow(double, double)

pow

public static long pow(long base,
                       long expt)
                throws java.lang.ArithmeticException

Deprecated.

Returns of value of the first argument raised to the power of the second argument.

Parameters:

base - the base

expt - the exponent

Returns:

base to the expt power

Throws:

java.lang.ArithmeticException

See Also:

Math.pow(double, double)

gcd

public static int gcd(int a,
                      int b)

Deprecated.

Return the greatest common divisor of the two arguments.

Parameters:

a - first operand

b - second operand

Returns:

greatest common divisor of a and b

gcd

public static int gcd(int[] a)

Deprecated.

Return the greatest common divisor of the elements of int array a.

Parameters:

a - array of operands

Returns:

greatest common divisor of the elements of a

gcd_differences

public static int gcd_differences(int[] a)

Deprecated.

Return the gcd (greatest common divisor) of the differences between the elements of int array a.

Parameters:

a - array of operands

Returns:

greatest common divisor of the differences between the elements of a

gcd

public static long gcd(long a,
                       long b)

Deprecated.

Return the greatest common divisor of the two arguments.

Parameters:

a - first operand

b - second operand

Returns:

greatest common divisor of a and b

gcd

public static long gcd(long[] a)

Deprecated.

Return the greatest common divisor of the elements of long array a.

Parameters:

a - array of operands

Returns:

greatest common divisor of the elements of a

gcd_differences

public static long gcd_differences(long[] a)

Deprecated.

Return the gcd (greatest common divisor) of the differences between the elements of long array a.

Parameters:

a - array of operands

Returns:

greatest common divisor of the differences between the elements of a

gcd

public static double gcd(double a,
                         double b)

Deprecated.

Return the greatest common divisor of the two arguments.

Parameters:

a - first operand

b - second operand

Returns:

greatest common divisor of a and b

gcd

public static double gcd(double[] a)

Deprecated.

Return the greatest common divisor of the elements of double array a.

Parameters:

a - array of operands

Returns:

greatest common divisor of the elements of a

gcd_differences

public static double gcd_differences(double[] a)

Deprecated.

Return the gcd (greatest common divisor) of the differences between the elements of double array a.

Parameters:

a - array of operands

Returns:

greatest common divisor of the differences between the elements of a

mod_positive

public static int mod_positive(int x,
                               int y)

Deprecated.

Return z such that (z == x mod y) && (0 <= z < abs(y)). This should really be named mod_nonnegative rather than mod_positive.

Parameters:

x - value to be modded

y - modulus

Returns:

x % y, where the result is constrained to be non-negative

modulus

public static int[] modulus(int[] nums)

Deprecated.

Return an array of two integers (r,m) such that each number in NUMS is equal to r (mod m). The largest possible modulus is used, and the trivial constraint that all integers are equal to 0 mod 1 is not returned (null is returned instead). Also, return null if the array is less than 3 elements long.

Parameters:

nums - array of operands

Returns:

an array of two integers (r,m) such that each number in NUMS is equal to r (mod m), or null if no such exists or the iterator contains fewer than 3 elements

modulus_int

public static int[] modulus_int(java.util.Iterator<java.lang.Integer> itor)

Deprecated.

The iterator produces Integer values. This can be more efficient than modulus(int[]) if the int[] doesn't already exist, because this does not necessarily examine every value produced by its iterator.

Parameters:

itor - iterator of operands

Returns:

an array of two integers (r,m) such that each number in itor is equal to r (mod m), or null if no such exists or the iterator contains fewer than 3 elements

See Also:

modulus(int[])

modulus_strict

public static int[] modulus_strict(int[] nums,
                                   boolean nonstrict_ends)

Deprecated.

Return an array of two integers (r,m) such that each number in NUMS is equal to r (mod m). The largest possible modulus is used, and the trivial constraint that all integers are equal to 0 mod 1 is not returned (null is returned instead).

This "_strict" version requires its input to be sorted, and no element may be missing.

This "_strict" version differs from the regular modulus by requiring that the argument be dense: that is, every pair of numbers in the argument array is separated by exactly the modulus.

The endpoints can be treated in two different ways: Either exactly like other numbers in the input, or they can merely be checked for the condition without the strict density requirement.

Parameters:

nums - array of operands

nonstrict_ends - whether endpoints are NOT subject to the strict density requirement

Returns:

an array of two integers (r,m) such that each number in NUMS is equal to r (mod m), or null if no such exists or the array contains fewer than 3 elements

modulus_strict_int

public static int[] modulus_strict_int(java.util.Iterator<java.lang.Integer> itor,
                                       boolean nonstrict_ends)

Deprecated.

The iterator produces Integer values. This can be more efficient than modulus(int[]) if the int[] doesn't already exist, because this does not necessarily examine every value produced by its iterator.

For documentation, see modulus_strict(int[], boolean).

Parameters:

itor - iterator of operands

nonstrict_ends - whether endpoints are NOT subject to the strict density requirement

Returns:

an array of two integers (r,m) such that each number in NUMS is equal to r (mod m), or null if no such exists or the iterator contains fewer than 3 elements

See Also:

modulus_strict(int[], boolean)

mod_positive

public static long mod_positive(long x,
                                long y)

Deprecated.

Return z such that (z == x mod y) && (0 <= z < abs(y)). This should really be named mod_nonnegative rather than mod_positive.

Parameters:

x - value to be modded

y - modulus

Returns:

x % y, where the result is constrained to be non-negative

modulus

public static long[] modulus(long[] nums)

Deprecated.

Return an array of two integers (r,m) such that each number in NUMS is equal to r (mod m). The largest possible modulus is used, and the trivial constraint that all integers are equal to 0 mod 1 is not returned (null is returned instead). Also, return null if the array is less than 3 elements long.

Parameters:

nums - array of operands

Returns:

an array of two integers (r,m) such that each number in NUMS is equal to r (mod m), or null if no such exists or the iterator contains fewer than 3 elements

modulus_long

public static long[] modulus_long(java.util.Iterator<java.lang.Long> itor)

Deprecated.

The iterator produces Long values. This can be more efficient than modulus(long[]) if the long[] doesn't already exist, because this does not necessarily examine every value produced by its iterator.

Parameters:

itor - iterator of operands

Returns:

an array of two integers (r,m) such that each number in itor is equal to r (mod m), or null if no such exists or the iterator contains fewer than 3 elements

See Also:

modulus(long[])

modulus_strict

public static long[] modulus_strict(long[] nums,
                                    boolean nonstrict_ends)

Deprecated.

Return an array of two integers (r,m) such that each number in NUMS is equal to r (mod m). The largest possible modulus is used, and the trivial constraint that all integers are equal to 0 mod 1 is not returned (null is returned instead).

This "_strict" version requires its input to be sorted, and no element may be missing.

This "_strict" version differs from the regular modulus by requiring that the argument be dense: that is, every pair of numbers in the argument array is separated by exactly the modulus.

The endpoints can be treated in two different ways: Either exactly like other numbers in the input, or they can merely be checked for the condition without the strict density requirement.

Parameters:

nums - array of operands

nonstrict_ends - whether endpoints are NOT subject to the strict density requirement

Returns:

an array of two integers (r,m) such that each number in NUMS is equal to r (mod m), or null if no such exists or the array contains fewer than 3 elements

modulus_strict_long

public static long[] modulus_strict_long(java.util.Iterator<java.lang.Long> itor,
                                         boolean nonstrict_ends)

Deprecated.

The iterator produces Long values. This can be more efficient than modulus(long[]) if the long[] doesn't already exist, because this does not necessarily examine every value produced by its iterator.

For documentation, see modulus_strict(long[], boolean).

Parameters:

itor - iterator of operands

nonstrict_ends - whether endpoints are NOT subject to the strict density requirement

Returns:

an array of two integers (r,m) such that each number in NUMS is equal to r (mod m), or null if no such exists or the iterator contains fewer than 3 elements

See Also:

modulus_strict(int[], boolean)

missing_numbers

public static int[] missing_numbers(int[] nums)

Deprecated.

Return an array containing all the numbers not in its argument array (which must be non-empty) but in the argument's range; that is, bigger than its argument's minimum value and smaller than its argument's maximum value. The result contains no duplicates and is in order.

Parameters:

nums - numbers to be excluded; length > 0; may contain duplicates

Returns:

the set: [min(nums)..max(nums)] - nums

nonmodulus_strict

public static int[] nonmodulus_strict(int[] nums)

Deprecated.

Return a tuple of (r,m) where no number in NUMS is equal to r (mod m) but all missing numbers in their range are. Returns null if the input array has 0 length.

Parameters:

nums - the list of operands

Returns:

a (remainder, modulus) pair that fails to match elements of nums

nonmodulus_strict_int

public static int[] nonmodulus_strict_int(java.util.Iterator<java.lang.Integer> nums)

Deprecated.

Return a tuple of (r,m) where no number in NUMS is equal to r (mod m) but all missing numbers in their range are.

Parameters:

nums - the list of operands

Returns:

a (remainder, modulus) pair that fails to match elements of nums

nonmodulus_nonstrict

public static int[] nonmodulus_nonstrict(int[] nums)

Deprecated.

Return a tuple of (r,m) where no number in NUMS is equal to r (mod m) but for every number in NUMS, at least one is equal to every non-r remainder. The modulus is chosen as small as possible, but no greater than half the range of the input numbers (else null is returned).

Parameters:

nums - the list of operands

Returns:

a (remainder, modulus) pair that fails to match elements of nums

missing_numbers

public static long[] missing_numbers(long[] nums)

Deprecated.

Return an array containing all the numbers not in its argument array (which must be non-empty) but in the argument's range; that is, bigger than its argument's minimum value and smaller than its argument's maximum value. The result contains no duplicates and is in order.

Parameters:

nums - numbers to be excluded; length > 0; may contain duplicates

Returns:

the set: [min(nums)..max(nums)] - nums

nonmodulus_strict

public static long[] nonmodulus_strict(long[] nums)

Deprecated.

Return a tuple of (r,m) where no number in NUMS is equal to r (mod m) but all missing numbers in their range are. Returns null if the input array has 0 length.

Parameters:

nums - the list of operands

Returns:

a (remainder, modulus) pair that fails to match elements of nums

nonmodulus_strict_long

public static long[] nonmodulus_strict_long(java.util.Iterator<java.lang.Long> nums)

Deprecated.

Return a tuple of (r,m) where no number in NUMS is equal to r (mod m) but all missing numbers in their range are.

Parameters:

nums - the list of operands

Returns:

a (remainder, modulus) pair that fails to match elements of nums

nonmodulus_nonstrict

public static long[] nonmodulus_nonstrict(long[] nums)

Deprecated.

Return a tuple of (r,m) where no number in NUMS is equal to r (mod m) but for every number in NUMS, at least one is equal to every non-r remainder. The modulus is chosen as small as possible, but no greater than half the range of the input numbers (else null is returned).

Parameters:

nums - the list of operands

Returns:

a (remainder, modulus) pair that fails to match elements of nums