gnu.math
Class IntNum

java.lang.Object
  java.lang.Number
      gnu.math.Numeric
          gnu.math.Quantity
              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

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

Fields inherited from class gnu.math.Numeric

CEILING, FLOOR, ROUND, TRUNCATE

Constructor Summary

IntNum()

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

Method Summary

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()
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 {# code this} or {#code 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)
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()
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) Return a (possibly-shared) IntNum with a given long value.
static IntNum	makeU(long value) Make an IntNum from an unsigned 64-bit 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)
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(java.lang.String s)
static IntNum	valueOf(java.lang.String s, int radix)
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, compare, divide, equals, infinity, isExact, make, rationalize, times, toExact

Methods inherited from class gnu.math.RealNum

abs, add, compareTo, divide, exp, im, log, max, min, re, rneg, sin, sqrt, times, toExactInt, toExactInt, toInt, toScaledInt, toScaledInt, toScaledInt, toStringDecimal, toStringScientific, toStringScientific, toStringScientific, toStringScientific

Methods inherited from class gnu.math.Complex

add, addReversed, angle, compare, divide, divReversed, doubleImagValue, doubleRealValue, equals, imMinusOne, imOne, make, make, mulReversed, neg, number, polar, polar, power, times

Methods inherited from class gnu.math.Quantity

add, compare, compareReversed, dimensions, divide, imValue, make, make, make, reValue, times, unit

Methods inherited from class gnu.math.Numeric

add, 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

make

public static IntNum make(int value)

Return a (possibly-shared) IntNum with a given int value.

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.

make

public static IntNum make(long value)

Return a (possibly-shared) IntNum with a given long value.

makeU

public static IntNum makeU(long value)

Make an IntNum from an unsigned 64-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)

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 {# code this} or {#code 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)

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)

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 Complex

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

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 Complex

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