integer(3) UNIX System V (Nov 25, 1998) integer(3)
Integer
Inherits from:
CAObject
Maturity Index:
Relatively mature
Class Description
An integer (alias BigInt ) is an array of digits, each digit
is a value of type DIGIT declared as unsigned short int .
So, abstractly, the integer is expressed base USHRT_MAX + 1,
which is a power of two. (USHRT_MAX is defined in the ANSI
header file limits.h) The most significant (or leading )
digit is never zero; the last digit is the least significant
digit of the integer. There are methods to count, access,
insert or remove digits. Besides the normal elementary
arithmetical operations, Integer also supports
multiplication, division etc. by digits. For input and
output, integers are in decimal representation.
Method types
Creation
* new
* str:
* int:
* factorial:
* fibonacci:
* copy
* deepCopy
* clear
Identity
* hash
* isEqual:
* numDigits
* isDigit
Inserting and Removing Digits
* insertDigit:
* removeDigit
Accessing Digits
* digitAt:
* lastDigit
* leadingDigit
String Value
* str
* str:
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integer(3) UNIX System V (Nov 25, 1998) integer(3)
Coercion
* asNumerical
* asModp:
* digitValue
* digitValue:
* ulongValue
* ulongValue:
* intValue
* intValue:
* doubleValue
* floatValue
Comparing
* sign
* compare:
Addition
* zero
* isZero
* isOpposite:
* negate
* double
* add:
* subtract:
* addDigit:
* subtractDigit:
Multiplication
* one
* minusOne
* isOne
* isMinusOne
* square
* multiply:
* multiplyDigit:
* inverse
Division
* divide:
* divideDigit:
* quotientDigit:
* remainder:quotient:
* quotientDigit:remainder:
* remainderDigit:
Parity
* isEven
* isOdd
Greatest Common Divisor
* gcd:
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integer(3) UNIX System V (Nov 25, 1998) integer(3)
Printing
* printsLeadingSign
* printOn:
Methods
new
+ new
Returns a new integer equal to zero. The instance method
zero returns a cheap copy of a shared, zero integer object.
See also:
- zero
str:
+ str :(STR) aString
Returns a new integer from the decimal representation
aString , or returns nil if aString doesn't contain decimal
characters (with optional unary minus sign).
int:
+ int :(int) intValue
Returns a new integer with value equal to intValue .
factorial:
+ factorial :(int) n
Returns a new integer object that is the n -th factorial.
fibonacci:
+ fibonacci :(int) n
Returns a new object that is the n -th Fibonacci number.
(Not implemented).
copy
- copy
Makes a copy of the digits.
deepCopy
- deepCopy
For integer objects, deepCopy is equivalent to copy .
clear
- clear
Frees the array of digits of the integer object.
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integer(3) UNIX System V (Nov 25, 1998) integer(3)
numDigits
- ( int ) numDigits
Returns the number of DIGIT's in the integer. Returns zero
if the integer is zero. The leading digit of an integer is
at position numDigits minus one.
isDigit
- ( BOOL ) isDigit
Whether the integer consists of a single digit. If the
integer is zero, this method returns NO. The method ignores
the sign of the integer.
See also:
digitValue
insertDigit:
- insertDigit :(DIGIT) d
Inserts d as last digit, shifting the other digits one
position up. The method doesn't insert anything if both the
integer and d are equal to zero. To insert a digit, the
integer must not be a cheap copy of another integer object.
removeDigit
- ( DIGIT ) removeDigit
Removes and returns the last digit, shifting the other
digits one position down. The method returns zero if the
integer is equal to zero. To remove a digit, the integer
must not be a cheap copy of another integer object.
digitAt:
- ( DIGIT ) digitAt :(int) i
Returns the digit at position i . The leading digit is
position numDigits minus one. The last digit is at position
zero. Returns 0 if the index is less than zero or equal to
or greater than numDigits.
lastDigit
- ( DIGIT ) lastDigit
Returns the least significant digit of the integer, the
digit at position 0. Returns 0 if the integer is zero.
leadingDigit
- ( DIGIT ) leadingDigit
Returns the most significant digit of the integer, the digit
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integer(3) UNIX System V (Nov 25, 1998) integer(3)
at position numDigits minus one. The leading digit of a
nonzero integer is never zero. The method returns 0 if the
integer is zero.
str
- ( STR ) str
Returns the decimal representation of the integer as a
NULL-terminated string of characters. The string is
automatically disposed off when freeing the integer, or when
modifying the integer with methods that work destructively
on the integer such as removeDigit or insertDigit: .
str:
- str :(STR) aString
Returns a new integer from the decimal representation
aString , or returns nil if aString doesn't contain decimal
characters (with optional unary minus sign).
asNumerical
- asNumerical
Returns a new instance of the Float class whose float value
is equal to that of the integer.
See also:
floatValue
asModp:
- asModp :(unsigned short) p
Returns a new instance of the IntegerModp class whose value
is equal to that of the integer modulo p (with p a small
prime number). Negative integers are mapped to the opposite
(mod p ) of their absolute value.
See also:
IntegerModp
digitValue
- ( DIGIT ) digitValue
Equivalent to lastDigit . This method ignores the sign of
the integer i.e., for a negative integer that consists of
just one digit, it returns the absolute value of the
integer.
digitValue:
- digitValue :(DIGIT) aValue
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integer(3) UNIX System V (Nov 25, 1998) integer(3)
Returns a new (positive) integer object, with value equal to
aValue .
ulongValue
- ( unsigned long ) ulongValue
Returns the two last digits of the integer as an unsigned
long value.
ulongValue:
- ulongValue :(unsigned long) aValue
Returns a (positive) integer with value as unsigned long
equal to aValue .
intValue
- ( int ) intValue
Returns the value of the integer as int value, if possible.
If the integer is too large to represented as int , the
method returns INT_MIN or INT_MAX depending on the sign of
the integer.
intValue:
- intValue :(int) aValue
Returns a new integer with value equal to aValue .
doubleValue
- ( double ) doubleValue
Returns the integer as a floating-point double value, if
possible. If the integer is too big to be represented as
double , the method returns DBL_MIN or DBL_MAX depending on
the sign of the integer.
floatValue
- ( float ) floatValue
Returns the integer as a floating-point float value, if
possible. If the integer is too big to be represented as
float , the method returns FLT_MIN or FLT_MAX depending on
the sign of the integer.
zero
- zero
Returns a cheap copy of a shared integer instance with value
equal to zero.
addDigit:
- addDigit :(DIGIT) d
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integer(3) UNIX System V (Nov 25, 1998) integer(3)
Returns a new integer that is the sum of the integer self
and the digit d .
subtractDigit:
- subtractDigit :(DIGIT) d
Returns a new integer that is the equal to the integer self
minus the digit d .
one
- one
Returns a cheap copy of a shared integer instance with value
equal to one.
minusOne
- minusOne
Returns a cheap copy of the integer minus one.
multiplyDigit:
- multiplyDigit :(DIGIT) d
Returns the product of the integer and the digit d (the
product is a new object).
inverse
- inverse
Returns nil , except if the integer is one or minus one, in
which case the method returns a cheap copy of the object
itself.
divide:
- divide : b
Returns the exact quotient on division by b . Returns nil
if the divisor b is zero or if the division is not exact
(when the remainder is not zero).
See also:
quotient:
divideDigit:
- divideDigit :(DIGIT) b
Returns the exact quotient on division by the digit b .
Returns nil if the divisor b is zero or if the division is
not exact (when the remainder is not zero).
quotientDigit:
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integer(3) UNIX System V (Nov 25, 1998) integer(3)
- quotientDigit :(DIGIT) b
Returns the quotient on division by the digit b ; the
division need not necessarily be exact. Returns nil if b is
equal to zero.
remainder:quotient:
- remainder : b quotient :(id *) q
Returns the remainder and, if a non-NULL pointer is passed
for q , the quotient on division of the dividend self by a
divisor b . Both remainder and quotient are new integer
objects. The remainder is signed i.e., its sign is the same
as the sign of the dividend; the relation dividend ==
quotient
divisor + remainder holds for all integers.
quotientDigit:remainder:
- quotientDigit :(DIGIT) d remainder :(DIGIT *) r
Returns the quotient and, if a non-NULL pointer is passed
along for r , the unsigned remainder on division by a digit
d ; the relation dividend == quotient
divisor + remainder does not hold if the dividend is
negative.
remainderDigit:
- ( DIGIT ) remainderDigit :(DIGIT) d
Returns the unsigned remainder on division by a digit d
i.e., the sign of the object is ignored. The divisor d
shouldn't be equal to zero.
isEven
- ( BOOL ) isEven
Whether the integer is even i.e., zero or divisible by two.
isOdd
- ( BOOL ) isOdd
Whether the integer is odd i.e., not divisible by two.
gcd:
- gcd : b
Returns a new (non-negative) integer, the greatest common
divisor of the two integers, computed by the Euclidean
algorithm. If one of the integers is zero, the method
returns a cheap copy of the other object.
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integer(3) UNIX System V (Nov 25, 1998) integer(3)
printsLeadingSign
- ( BOOL ) printsLeadingSign
Returns YES if the integer is negative.
printOn:
- printOn :(IOD) aFile
Prints the integer in decimal representation to aFile .
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