IntNum

java.lang.Object
- java.lang.Number
- - gnu.math.Numeric
  - - gnu.math.Quantity
    - - gnu.math.Quaternion
      - gnu.math.Complex
        
        gnu.math.RealNum
        
        gnu.math.RatNum
        
        gnu.math.IntNum

All Implemented Interfaces:

java.io.Externalizable, java.io.Serializable, java.lang.Comparable

Direct Known Subclasses:

XInteger
```
public class IntNum
extends RatNum
implements java.io.Externalizable
```
A class for infinite-precision integers.

See Also:

Serialized Form

Field Summary

Fields
Modifier and Type Field and Description

int ival
All integers are stored in 2's-complement form.

int[] words
- Fields inherited from class gnu.math.RatNum
  ten_exp_9
- Fields inherited from class gnu.math.Numeric
  CEILING, FLOOR, NONNEG_MOD, ROUND, TRUNCATE

Fields
Modifier and Type	Field and Description
`int`	`ival` All integers are stored in 2's-complement form.
`int[]`	`words`

Constructor Summary

Constructors
Constructor and Description

IntNum()

IntNum(int value)
Create a new (non-shared) IntNum, and initialize to an int.

Constructors
Constructor and Description
`IntNum()`
`IntNum(int value)` Create a new (non-shared) IntNum, and initialize to an int.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`static IntNum`	`abs(IntNum x)`
`static IntNum`	`add(int x, int y)` Add two ints, yielding an IntNum.
`static IntNum`	`add(IntNum x, int y)` Add an IntNum and an int, yielding a new IntNum.
`static IntNum`	`add(IntNum x, IntNum y)` Add two IntNums, yielding their sum as another IntNum.
`static IntNum`	`add(IntNum x, IntNum y, int k)` Add two IntNums, yielding their sum as another IntNum.
`Numeric`	`add(java.lang.Object y, int k)` Return this + k * obj.
`static IntNum`	`alloc(int nwords)` Allocate a new non-shared IntNum.
`java.math.BigDecimal`	`asBigDecimal()`
`java.math.BigInteger`	`asBigInteger()`
`static IntNum`	`asIntNumOrNull(java.lang.Object value)`
`IntNum`	`canonicalize()`
`static int`	`compare(IntNum x, IntNum y)` Return -1, 0, or 1, depending on which value is greater.
`static int`	`compare(IntNum x, long y)` Return -1, 0, or 1, depending on which value is greater.
`int`	`compare(java.lang.Object obj)` Return an integer for which of `this` or `obj` is larger.
`IntNum`	`denominator()`
`Numeric`	`div(java.lang.Object y)`
`static void`	`divide(IntNum x, IntNum y, IntNum quotient, IntNum remainder, int rounding_mode)` Divide two integers, yielding quotient and remainder.
`static void`	`divide(long x, long y, IntNum quotient, IntNum remainder, int rounding_mode)`
`double`	`doubleValue()` The value of the real component, as a double.
`static boolean`	`equals(IntNum x, IntNum y)`
`boolean`	`equals(java.lang.Object obj)`
`void`	`format(int radix, java.lang.StringBuffer buffer)`
`void`	`format(int radix, java.lang.StringBuilder buffer)`
`static int`	`gcd(int a, int b)` Calculate Greatest Common Divisor for non-negative ints.
`static IntNum`	`gcd(IntNum x, IntNum y)`
`void`	`getAbsolute(int[] words)` Copy the abolute value of this into an array of words.
`int`	`hashCode()`
`boolean`	`inIntRange()` Does this value fit in a signed 32-bit `int`?
`boolean`	`inLongRange()` Does this value fit in a signed 64-bit `long`?
`boolean`	`inRange(long lo, long hi)` Is this integer both `>= lo` and `<= hi`?.
`int`	`intLength()` Calculates `ceiling(log2(this < 0 ? -this : this+1))`.
`int`	`intValue()`
`static int`	`intValue(java.lang.Object obj)` Cast an Object to an int.
`boolean`	`isMinusOne()`
`boolean`	`isNegative()`
`boolean`	`isOdd()`
`boolean`	`isOne()`
`boolean`	`isZero()`
`static IntNum`	`lcm(IntNum x, IntNum y)`
`long`	`longValue()`
`static IntNum`	`make(int value)` Return a (possibly-shared) IntNum with a given int value.
`static IntNum`	`make(int[] words)`
`static IntNum`	`make(int[] words, int len)` Make a canonicalized IntNum from an array of words.
`static IntNum`	`make(long value)`
`static IntNum`	`minusOne()` Return the IntNum for -1.
`static IntNum`	`modulo(IntNum x, IntNum y)`
`Numeric`	`mul(java.lang.Object y)`
`Numeric`	`neg()`
`static IntNum`	`neg(IntNum x)`
`static boolean`	`negate(int[] dest, int[] src, int len)` Set dest[0:len-1] to the negation of src[0:len-1].
`IntNum`	`numerator()`
`static IntNum`	`one()`
`Numeric`	`power(IntNum y)` Return this raised to an integer power.
`static IntNum`	`power(IntNum x, int y)` Calculate the integral power of an IntNum.
`static IntNum`	`quotient(IntNum x, IntNum y)`
`static IntNum`	`quotient(IntNum x, IntNum y, int rounding_mode)`
`void`	`readExternal(java.io.ObjectInput in)`
`java.lang.Object`	`readResolve()`
`void`	`realloc(int nwords)` Change words.length to nwords.
`static IntNum`	`remainder(IntNum x, IntNum y)`
`static IntNum`	`remainder(IntNum x, IntNum y, int rounding_mode)`
`double`	`roundToDouble(int exp, boolean neg, boolean remainder)` Convert a semi-processed IntNum to double.
`void`	`set(int y)` Destructively set the value of this to an int.
`void`	`set(int[] words, int length)` Destructively set the value of this to the given words.
`void`	`set(IntNum y)` Destructively set the value of this to that of y.
`void`	`set(long y)` Destructively set the value of this to a long.
`void`	`setAdd(int y)` Destructively add an int to this.
`void`	`setAdd(IntNum x, int y)` Set this to the sum of x and y.
`void`	`setNegative()` Destructively negate this.
`void`	`setNegative(IntNum x)` Destructively set this to the negative of x.
`static IntNum`	`shift(IntNum x, int count)`
`int`	`sign()` Return 1 if `>0`; 0 if `==0`; -1 if `<0`; -2 if `NaN`.
`static IntNum`	`sub(IntNum x, IntNum y)` Subtract two IntNums, yielding their sum as another IntNum.
`static IntNum`	`ten()`
`static IntNum`	`times(int x, int y)` Multiply two ints, yielding an IntNum.
`static IntNum`	`times(IntNum x, int y)`
`static IntNum`	`times(IntNum x, IntNum y)`
`IntNum`	`toExactInt(int rounding_mode)` Converts to an exact integer, with specified rounding mode.
`RealNum`	`toInt(int rounding_mode)` Converts a real to an integer, according to a specified rounding mode.
`java.lang.String`	`toString(int radix)`
`static IntNum`	`valueOf(byte[] digits, int byte_len, boolean negative, int radix)`
`static IntNum`	`valueOf(char[] buf, int offset, int length, int radix, boolean negative)`
`static IntNum`	`valueOf(int value)` Return a (possibly-shared) IntNum with a given int value.
`static IntNum`	`valueOf(long value)` Return a (possibly-shared) IntNum with a given long value.
`static IntNum`	`valueOf(java.lang.String s)`
`static IntNum`	`valueOf(java.lang.String s, int radix)`
`static IntNum`	`valueOfUnsigned(int value)` Make an IntNum from an unsigned 32-bit value.
`static IntNum`	`valueOfUnsigned(long value)` Make an IntNum from an unsigned 64-bit value.
`static int`	`wordsNeeded(int[] words, int len)` Calculate how many words are significant in words[0:len-1].
`void`	`writeExternal(java.io.ObjectOutput out)`
`static IntNum`	`zero()`

Methods inherited from class gnu.math.RatNum
add, asRatNumOrNull, classifyFinite, compare, divide, equals, infinity, isExact, make, neg, rationalize, rneg, times, toExact, valueOf

Methods inherited from class gnu.math.RealNum
abs, add, angle, asRealNumOrNull, compareTo, conjugate, cos, divide, exp, im, isReal, log, max, min, re, sin, sqrt, tan, times, toExactInt, toExactInt, toInexact, toInt, toScaledInt, toScaledInt, toScaledInt, toStringDecimal, toStringScientific, toStringScientific, toStringScientific, toStringScientific, unitQuaternion, unitVector, vectorPart

Methods inherited from class gnu.math.Complex
add, addReversed, colatitude, compare, complexPart, divide, divReversed, equals, imMinusOne, imOne, jm, km, longitude, make, make, mulReversed, neg, polar, polar, power, times

Methods inherited from class gnu.math.Quaternion
add, compare, divide, doubleImagValue, doubleJmagValue, doubleKmagValue, doubleRealValue, equals, jmMinusOne, jmOne, kmMinusOne, kmOne, make, make, neg, number, polar, polar, power, times

Methods inherited from class gnu.math.Quantity
add, compare, compareReversed, dimensions, divide, imValue, jmValue, kmValue, make, make, make, reValue, times, unit

Methods inherited from class gnu.math.Numeric
add, asNumericOrNull, div_inv, floatValue, geq, grt, mul_ident, sub, toString

Methods inherited from class java.lang.Number
byteValue, shortValue

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

Field Detail
- ival
```
public int ival
```
  All integers are stored in 2's-complement form. If words == null, the ival is the value of this IntNum. Otherwise, the first ival elements of words make the value of this IntNum, stored in little-endian order, 2's-complement form.
- words
```
public int[] words
```

Constructor Detail
- IntNum
```
public IntNum()
```
- IntNum
```
public IntNum(int value)
```
  Create a new (non-shared) IntNum, and initialize to an int.
  
  Parameters:
  
  value - the initial value

Method Detail

zero
```
public static final IntNum zero()
```

one
```
public static final IntNum one()
```

ten
```
public static final IntNum ten()
```

minusOne
```
public static IntNum minusOne()
```
Return the IntNum for -1.

asIntNumOrNull

public static IntNum asIntNumOrNull(java.lang.Object value)

alloc
```
public static IntNum alloc(int nwords)
```
Allocate a new non-shared IntNum.

Parameters:

nwords - number of words to allocate

realloc
```
public void realloc(int nwords)
```
Change words.length to nwords. We allow words.length to be upto nwords+2 without reallocating.

numerator
```
public final IntNum numerator()
```
Specified by:

numerator in class RatNum

denominator
```
public final IntNum denominator()
```
Specified by:

denominator in class RatNum

isNegative
```
public final boolean isNegative()
```
Specified by:

isNegative in class RealNum

sign
```
public int sign()
```
Description copied from class: RealNum

Return 1 if >0; 0 if ==0; -1 if <0; -2 if NaN.

Specified by:

sign in class RealNum

compare

public static int compare(IntNum x,
                          IntNum y)

Return -1, 0, or 1, depending on which value is greater.

compare

public static int compare(IntNum x,
                          long y)

Return -1, 0, or 1, depending on which value is greater.

compare
```
public int compare(java.lang.Object obj)
```
Description copied from class: Numeric

Return an integer for which of this or obj is larger. Return 1 if this>obj; 0 if this==obj; -1 if this<obj; -2 if this!=obj otherwise (for example if either is NaN); -3 if not comparable (incompatible types).

Overrides:

compare in class Complex

isOdd
```
public final boolean isOdd()
```

isZero
```
public final boolean isZero()
```
Overrides:

isZero in class RatNum

isOne
```
public final boolean isOne()
```

isMinusOne
```
public final boolean isMinusOne()
```

wordsNeeded
```
public static int wordsNeeded(int[] words,
                              int len)
```
Calculate how many words are significant in words[0:len-1]. Returns the least value x such that x>0 && words[0:x-1]==words[0:len-1], when words is viewed as a 2's complement integer.

canonicalize
```
public IntNum canonicalize()
```

add

public static final IntNum add(int x,
                               int y)

Add two ints, yielding an IntNum.

add

public static IntNum add(IntNum x,
                         int y)

Add an IntNum and an int, yielding a new IntNum.

setAdd

public void setAdd(IntNum x,
                   int y)

Set this to the sum of x and y. OK if x==this.

setAdd
```
public final void setAdd(int y)
```
Destructively add an int to this.

set
```
public final void set(int y)
```
Destructively set the value of this to an int.

set
```
public final void set(long y)
```
Destructively set the value of this to a long.

set
```
public final void set(int[] words,
                      int length)
```
Destructively set the value of this to the given words. The words array is reused, not copied.

set
```
public final void set(IntNum y)
```
Destructively set the value of this to that of y.

add

public static IntNum add(IntNum x,
                         IntNum y)

Add two IntNums, yielding their sum as another IntNum.

sub

public static IntNum sub(IntNum x,
                         IntNum y)

Subtract two IntNums, yielding their sum as another IntNum.

add

public static IntNum add(IntNum x,
                         IntNum y,
                         int k)

Add two IntNums, yielding their sum as another IntNum.

times

public static final IntNum times(int x,
                                 int y)

Multiply two ints, yielding an IntNum.

times

public static final IntNum times(IntNum x,
                                 int y)

times

public static final IntNum times(IntNum x,
                                 IntNum y)

divide

public static void divide(long x,
                          long y,
                          IntNum quotient,
                          IntNum remainder,
                          int rounding_mode)

divide
```
public static void divide(IntNum x,
                          IntNum y,
                          IntNum quotient,
                          IntNum remainder,
                          int rounding_mode)
```
Divide two integers, yielding quotient and remainder.

Parameters:

x - the numerator in the division

y - the denominator in the division

quotient - is set to the quotient of the result (iff quotient!=null)

remainder - is set to the remainder of the result (iff remainder!=null)

rounding_mode - one of FLOOR, CEILING, TRUNCATE, or ROUND.

quotient

public static IntNum quotient(IntNum x,
                              IntNum y,
                              int rounding_mode)

quotient

public static IntNum quotient(IntNum x,
                              IntNum y)

toExactInt
```
public IntNum toExactInt(int rounding_mode)
```
Description copied from class: RealNum

Converts to an exact integer, with specified rounding mode.

Overrides:

toExactInt in class RatNum

toInt
```
public RealNum toInt(int rounding_mode)
```
Description copied from class: RealNum

Converts a real to an integer, according to a specified rounding mode. Note an inexact argument gives an inexact result, following Scheme. See also toExactInt.

Overrides:

toInt in class RatNum

remainder

public static IntNum remainder(IntNum x,
                               IntNum y,
                               int rounding_mode)

remainder

public static IntNum remainder(IntNum x,
                               IntNum y)

modulo

public static IntNum modulo(IntNum x,
                            IntNum y)

power
```
public Numeric power(IntNum y)
```
Description copied from class: Numeric

Return this raised to an integer power. Implemented by repeated squaring and multiplication. If y < 0, returns div_inv of the result.

Overrides:

power in class RatNum

power
```
public static IntNum power(IntNum x,
                           int y)
```
Calculate the integral power of an IntNum.

Parameters:

x - the value (base) to exponentiate

y - the exponent (must be non-negative)

gcd

public static final int gcd(int a,
                            int b)

Calculate Greatest Common Divisor for non-negative ints.

gcd

public static IntNum gcd(IntNum x,
                         IntNum y)

lcm

public static IntNum lcm(IntNum x,
                         IntNum y)

shift

public static IntNum shift(IntNum x,
                           int count)

format

public void format(int radix,
                   java.lang.StringBuffer buffer)

format

public void format(int radix,
                   java.lang.StringBuilder buffer)

toString

public java.lang.String toString(int radix)

Overrides:: toString in class Complex

intValue
```
public int intValue()
```
Overrides:

intValue in class Numeric

intValue
```
public static int intValue(java.lang.Object obj)
```
Cast an Object to an int. The Object must (currently) be an IntNum.

longValue
```
public long longValue()
```
Overrides:

longValue in class Quaternion

hashCode
```
public int hashCode()
```
Overrides:

hashCode in class java.lang.Object

equals

public static boolean equals(IntNum x,
                             IntNum y)

equals

public boolean equals(java.lang.Object obj)

Overrides:: equals in class RatNum

make
```
public static IntNum make(int value)
```
Return a (possibly-shared) IntNum with a given int value.

valueOfUnsigned
```
public static IntNum valueOfUnsigned(long value)
```
Make an IntNum from an unsigned 64-bit value.

valueOfUnsigned
```
public static IntNum valueOfUnsigned(int value)
```
Make an IntNum from an unsigned 32-bit value.

make
```
public static IntNum make(int[] words,
                          int len)
```
Make a canonicalized IntNum from an array of words. The array may be reused (without copying).

make

public static IntNum make(int[] words)

make

public static IntNum make(long value)

valueOf
```
public static IntNum valueOf(int value)
```
Return a (possibly-shared) IntNum with a given int value.

valueOf
```
public static IntNum valueOf(long value)
```
Return a (possibly-shared) IntNum with a given long value.

valueOf

public static IntNum valueOf(char[] buf,
                             int offset,
                             int length,
                             int radix,
                             boolean negative)

valueOf

public static IntNum valueOf(java.lang.String s,
                             int radix)
                      throws java.lang.NumberFormatException

Throws:: java.lang.NumberFormatException

valueOf

public static IntNum valueOf(byte[] digits,
                             int byte_len,
                             boolean negative,
                             int radix)

valueOf

public static IntNum valueOf(java.lang.String s)
                      throws java.lang.NumberFormatException

Throws:: java.lang.NumberFormatException

doubleValue
```
public double doubleValue()
```
Description copied from class: Quantity

The value of the real component, as a double. This is relative to the unit().dims - i.e. unit()/doubleValue() is factored in.

Overrides:

doubleValue in class Quaternion

roundToDouble
```
public double roundToDouble(int exp,
                            boolean neg,
                            boolean remainder)
```
Convert a semi-processed IntNum to double. Number must be non-negative. Multiplies by a power of two, applies sign, and converts to double, with the usual java rounding.

Parameters:

exp - power of two, positive or negative, by which to multiply

neg - true if negative

remainder - true if the IntNum is the result of a truncating division that had non-zero remainder. To ensure proper rounding in this case, the IntNum must have at least 54 bits.

add
```
public Numeric add(java.lang.Object y,
                   int k)
```
Description copied from class: Numeric

Return this + k * obj.

Specified by:

add in class RealNum

mul

public Numeric mul(java.lang.Object y)

Specified by:: mul in class RealNum

div

public Numeric div(java.lang.Object y)

Specified by:: div in class RealNum

getAbsolute
```
public void getAbsolute(int[] words)
```
Copy the abolute value of this into an array of words. Assumes words.length >= (this.words == null ? 1 : this.ival). Result is zero-extended, but need not be a valid 2's complement number.

negate
```
public static boolean negate(int[] dest,
                             int[] src,
                             int len)
```
Set dest[0:len-1] to the negation of src[0:len-1]. Return true if overflow (i.e. if src is -2**(32*len-1)). Ok for src==dest.

setNegative
```
public void setNegative(IntNum x)
```
Destructively set this to the negative of x. It is OK if x==this.

setNegative
```
public final void setNegative()
```
Destructively negate this.

abs
```
public static IntNum abs(IntNum x)
```

neg
```
public static IntNum neg(IntNum x)
```

neg
```
public Numeric neg()
```
Overrides:

neg in class Complex

intLength
```
public int intLength()
```
Calculates ceiling(log2(this < 0 ? -this : this+1)). See Common Lisp: the Language, 2nd ed, p. 361.

writeExternal

public void writeExternal(java.io.ObjectOutput out)
                   throws java.io.IOException

Specified by:: writeExternal in interface java.io.Externalizable
Throws:: java.io.IOException

readExternal

public void readExternal(java.io.ObjectInput in)
                  throws java.io.IOException,
                         java.lang.ClassNotFoundException

Specified by:: readExternal in interface java.io.Externalizable
Throws:: java.io.IOException; java.lang.ClassNotFoundException

readResolve

public java.lang.Object readResolve()
                             throws java.io.ObjectStreamException

Throws:: java.io.ObjectStreamException

asBigInteger

public java.math.BigInteger asBigInteger()

asBigDecimal
```
public java.math.BigDecimal asBigDecimal()
```
Overrides:

asBigDecimal in class RealNum

inRange

public boolean inRange(long lo,
                       long hi)

Is this integer both >= lo and <= hi?.

inIntRange
```
public boolean inIntRange()
```
Does this value fit in a signed 32-bit int?

inLongRange
```
public boolean inLongRange()
```
Does this value fit in a signed 64-bit long?

Class IntNum

Field Summary

Fields inherited from class gnu.math.RatNum

Fields inherited from class gnu.math.Numeric

Constructor Summary

Method Summary

Methods inherited from class gnu.math.RatNum

Methods inherited from class gnu.math.RealNum

Methods inherited from class gnu.math.Complex

Methods inherited from class gnu.math.Quaternion

Methods inherited from class gnu.math.Quantity

Methods inherited from class gnu.math.Numeric

Methods inherited from class java.lang.Number

Methods inherited from class java.lang.Object

Field Detail

ival

words

Constructor Detail

IntNum

IntNum

Method Detail

zero

one

ten

minusOne

asIntNumOrNull

alloc

realloc

numerator

denominator

isNegative

sign

compare

compare

compare

isOdd

isZero

isOne

isMinusOne

wordsNeeded

canonicalize

add

add

setAdd

setAdd

set

set

set

set

add

sub

add

times

times

times

divide

divide

quotient

quotient

toExactInt

toInt

remainder

remainder

modulo

power

power

gcd

gcd

lcm

shift

format

format

toString

intValue

intValue

longValue

hashCode

equals

equals

make