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Class: SmallInteger

Inheritance:

   Object
   |
   +--Magnitude
      |
      +--ArithmeticValue
         |
         +--Number
            |
            +--Integer
               |
               +--SmallInteger
Package:
stx:libbasic
Category:
Magnitude-Numbers
Version:
rev: 1.322 date: 2019/07/09 12:26:08
user: sr
file: SmallInteger.st directory: libbasic
module: stx stc-classLibrary: libbasic
Author:
Claus Gittinger

Description:


SmallIntegers are Integers in the range of at least +/- 2^30
i.e. 31 bits, but this is not a guaranteed:
    on an alpha or x86_64, 63 bits are used, if the system was configured for 64bit mode.
    under the Schteam-VM, 64 bits are used (i.e. a full long integer)

These are no real objects - they have no instances (not even storage !)
and cannot be subclassed.
The reason is to save both storage and runtime by not boxing and
garbage collecting SmallIntegers in the system.
SmallInts are marked by having the TAG_INT
bit set, in contrast to all other objects which do not.
Since this knowledge is hardwired into the system (and there is no
class-field stored with SmallIntegers) there can be no subclass of
SmallInteger (sorry).

If you really need this kind of thing, create a subclass of Integer,
with an instance variable holding the value.

Because the range and sharing of SmallIntegers is different among implementations
(both in different dialects, and in different architectures within the Smalltalk/X family),
you should not depend on the identity of two integers with the same value.
For portable code, when comparing integers, use #'=' and #'~=' (instead of #'==' / #'~~'),
unless you are comparing very small integers in the -1024 .. 0 .. 1024 range.

Related information:

    Number
    Float
    Fraction
    FixedPoint
    LargeInteger

Class protocol:

bit mask constants
o  bitMaskFor: index
return a bitmask for the index's bit (index starts at 1)

class initialization
o  initialize

constants
o  maxBits
return the number of bits in instances of me.
For very special uses only - not constant across implementations

usage example(s): 

     SmallInteger maxBits

o  maxBytes
return the number of bytes in instances of me.
For very special uses only - not constant across implementations.
Notice: this is inlined by the compiler(s) as a constant,
therefore, a query like 'SmallInteger maxBytes == 8'
costs nothing; it is compiled in as a constant.

usage example(s): 

     SmallInteger maxBytes

o  maxVal
return the largest Integer representable as SmallInteger.
For very special uses only - not constant across implementations

usage example(s): 

     SmallInteger maxVal

o  minVal
return the smallest Integer representable as SmallInteger.
For very special uses only - not constant across implementations

usage example(s): 

     SmallInteger minVal

instance creation
o  basicNew
catch instance creation
- SmallIntegers cannot be created with new

o  basicNew: size
catch instance creation
- SmallIntegers cannot be created with new

o  fastFromString: aString at: startIndex
return the next SmallInteger from the string starting at startIndex.
No spaces are skipped.
Raises an error, if the index is out of bounds,
Returns garbage if the argument string is not a valid integer.

This is a specially tuned entry (using a low-level C-call to atol).
It has been added to allow high speed string decomposition into
numbers, especially for mass-data (reading millions of numbers).

usage example(s): 

     SmallInteger fastFromString:'hello12345' at:6
     SmallInteger fastFromString:'12345' at:1
     SmallInteger fastFromString:'12345' at:2
     SmallInteger fastFromString:'12345' at:3
     SmallInteger fastFromString:'12345' at:4
     SmallInteger fastFromString:'12345' at:5
     SmallInteger fastFromString:'12345' at:6
     SmallInteger fastFromString:'12345' at:0

     Time millisecondsToRun:[
        1000000 timesRepeat:[
            SmallInteger readFrom:'12345'
        ]
     ]

usage example(s): 

     Time millisecondsToRun:[
        1000000 timesRepeat:[
            SmallInteger fastFromString:'12345' at:1
        ]
     ]

queries
o  canBeSubclassed
return true, if it's allowed to create subclasses of the receiver.
Return false here - since it is NOT possible for SmallInteger
(due to the tagged representation of SmallIntegers)

o  hasImmediateInstances
return true if this class has immediate instances
i.e. if the instances are represented in the pointer itself and
no real object header/storage is used for the object.
Redefined from Behavior

o  isBuiltInClass
return true if this class is known by the run-time-system.
Here, true is returned.

Instance protocol:

arithmetic
o  * aNumber
return the product of the receiver and the argument

usage example(s): 

	3 * (1/2)
	6 * (1/2)
	6 * (-1/2)

o  + aNumber
return the sum of the receiver's value and the argument's value

o  - aNumber
return the difference of the receiver's value and the argument's value

o  / aNumber
return the quotient of the receiver's value and the argument's value

usage example(s): 

     8 / 4
     9 / 4
     9 // 4
     9 quo:4

     -8 / 4
     -9 / 4
     -9 // 4
     -9 quo:4

o  // aNumber
return the integer part of the quotient of the receiver's value
and the argument's value.
The result is truncated toward negative infinity
and will be negative, if the operands signs differ.
The following is always true:
(receiver // aNumber) * aNumber + (receiver \\ aNumber) = receiver

Be careful with negative results: 9 // 4 -> 2, while -9 // 4 -> -3.
Especially surprising (because of truncation toward negative infinity):
-1 // 10 -> -1 (because -(1/10) is truncated towards next smaller integer, which is -1.
-10 // 3 -> -4 (because -(10/3) is truncated towards next smaller integer, which is -4.

See #quo: which truncates toward zero and returns -2 in the above case
and #rem: which is the corresponding remainder.

usage example(s): 

     9 // 4     ~~ 2 ifTrue:[self halt].
     -9 // 4    ~~ -3 ifTrue:[self halt].
     9 // -4    ~~ -3 ifTrue:[self halt].
     -9 // -4   ~~ 2 ifTrue:[self halt].
     1 // 2     ~~ 0 ifTrue:[self halt].
     -1 // 2    ~~ -1 ifTrue:[self halt].
     1 // -2    ~~ -1 ifTrue:[self halt].
     -1 // -2   ~~ 0 ifTrue:[self halt].

     -7 // (4/3)
     -7 quo: (4/3)

     7 // (-4/3)
     7 quo: (-4/3)

     10000 // 3600000 ~~ 0 ifTrue:[self halt].
     12 // (1 / 1000000000000000000)
     12 // (1 / 100000000000000)
     12 // 0.00000000000001s

     9 quo:4   => 2
     -9 quo:4  => -2
     9 quo:-4  => -2
     -9 quo:-4 => 2

o  \\ aNumber
Answer the integer remainder m defined by division with truncation toward
negative infinity.
m < |aNumber| AND there is an integer k with (k * aNumber + m) = self

The returned remainder has the same sign as aNumber.
The following is always true:
(receiver // aNumber) * aNumber + (receiver \\ aNumber) = receiver

Be careful with negative results: 9 // 4 -> 2, while -9 // 4 -> -3.
Especially surprising:
-1 \\ 10 -> 9 (because -(1/10) is truncated towards next smaller integer, which is -1,
and -1 multiplied by 10 gives -10, so we have to add 9 to get the original -1).
-10 \\ 3 -> 2 (because -(10/3) is truncated towards next smaller integer, which is -4,
and -4 * 4 gives -12, so we need to add 2 to get the original -10.

See #rem: which is the corresponding remainder for division via #quo:.

Redefined here for speed.

usage example(s): 

     9 \\ 4  == 1 ifFalse:[self halt].
     -9 \\ 4 == 3 ifFalse:[self halt].
     9 \\ -4 == -3 ifFalse:[self halt].
     -9 \\ -4 == -1 ifFalse:[self halt].
     (9 rem:4) == 1 ifFalse:[self halt].
     (-9 rem:4) == -1 ifFalse:[self halt].
     1000 \\ 3600000 == 1000 ifFalse:[self halt]

o  abs
return the absolute value of the receiver
reimplemented here for speed

o  negated
return the negative value of the receiver
reimplemented here for speed

o  quo: aNumber
return the integer part of the quotient of the receiver's value
and the argument's value. The result is truncated towards zero
and negative, if the operands signs differ..
The following is always true:
(receiver quo: aNumber) * aNumber + (receiver rem: aNumber) = receiver
For positive results, this is the same as #//,
for negative results, the remainder is ignored.
I.e.: '9 // 4 = 2' and '-9 // 4 = -3'
in contrast: '9 quo: 4 = 2' and '-9 quo: 4 = -2'

usage example(s): 

     9 // 4
     -9 // 4
     9 quo:4
     -9 quo:4

     -7 // (4/3)
     -7 quo: (4/3)

     7 // (-4/3)
     7 quo: (-4/3)

o  sqrt
return the square root value of the receiver
reimplemented here for speed

usage example(s): 

	2 sqrt
	-2 sqrt

bit operators
o  bitAnd: anInteger
return the bitwise-and of the receiver and the argument, anInteger

usage example(s): 

(2r001010100 bitAnd:2r00001111) radixPrintStringRadix:2

o  bitClear: anInteger
return the bitwise-and of the receiver and the complement of the argument, anInteger,
returning the receiver with bits of the argument cleared.
(i.e. the same as self bitAnd:aMaskInteger bitInvert).
The method's name may be misleading: the receiver is not changed,
but a new number is returned. Should be named #withBitCleared:

usage example(s): 

     (2r001010100 bitClear:2r00001111) radixPrintStringRadix:2
     (2r111111111 bitClear:2r00001000) radixPrintStringRadix:2

     (2r001010100 bitAnd:2r00001111 bitInvert) radixPrintStringRadix:2

o  bitCount
return the number of 1-bits in the receiver

usage example(s): 

     16rAA bitCount
     
     TimeDuration toRun:[
        1 to:10000000 do:[:n |
            n bitCount
        ].
     ] 

     AL1: 967ms 958ms 971ms 930ms
     AL2: 900ms 872ms 877ms 870ms

     AL3: 879ms 849ms 831ms 849ms 
     AL4: 858ms 852ms 846ms 810ms
     AL5: 830ms 843ms 835ms 845ms

     Mac PB2012/2.6Ghz I7
     AL3: 855ms 885ms 859ms 878ms 844ms
     AL5: 877ms 877ms 846ms 890ms 853ms
     
     1 to:1000000 do:[:n |
        self assert:(n bitCount = ((n printStringRadix:2) occurrencesOf:$1))
     ].

     #( 16r00000000
        16r00010000 16r00100000 16r01000000 16r10000000
        16r00020000 16r00200000 16r02000000 16r20000000
        16r00040000 16r00400000 16r04000000 16r40000000
        16r00080000 16r00800000 16r08000000 16r80000000

        16rFFFFFFFF 16r7FFFFFFF 16r3FFFFFFF 16r1FFFFFFF
        16rEEEEEEEE 16r7EEEEEEE 16r3EEEEEEE 16r1EEEEEEE
        16rDDDDDDDD 16r7DDDDDDD 16r3DDDDDDD 16r1DDDDDDD
        16rCCCCCCCC 16r7CCCCCCC 16r3CCCCCCC 16r1CCCCCCC

        16r8000000000010000 16r8000000000100000 16r8000000001000000 16r8000000010000000
        16r8000000000020000 16r8000000000200000 16r8000000002000000 16r8000000020000000
        16r8000000000040000 16r8000000000400000 16r8000000004000000 16r8000000040000000
        16r8000000000080000 16r8000000000800000 16r8000000008000000 16r8000000080000000

        16r80000000FFFFFFFF 16r800000007FFFFFFF 16r800000003FFFFFFF 16r800000001FFFFFFF
        16r80000000EEEEEEEE 16r800000007EEEEEEE 16r800000003EEEEEEE 16r800000001EEEEEEE
        16r80000000DDDDDDDD 16r800000007DDDDDDD 16r800000003DDDDDDD 16r800000001DDDDDDD
        16r80000000CCCCCCCC 16r800000007CCCCCCC 16r800000003CCCCCCC 16r800000001CCCCCCC

        16rFFFFFFFFFFFFFFFF 16r7FFFFFFFFFFFFFFF 16r3FFFFFFFFFFFFFFF 16r1FFFFFFFFFFFFFFF
     ) do:[:n |
        self assert:(n bitCount = ((n printStringRadix:2) occurrencesOf:$1))
     ]

     1 to:10000000 do:[:n |
        (n bitCount)
     ]

o  bitDeinterleave: n
extract count integers from an n-way Morton number as a vector;
This is the inverse operation from bitInterleave: - see comment there.
i.e. if count is 3,
and the receiver's bits are
cN bN aN ... c2 b2 a2 c1 b1 a1 c0 b0 a0
then the result will be a vector containing the numbers a,b,c with bits:
aN ... a2 a1 a0
bN ... b2 b1 b0
cN ... c2 c1 c0.

usage example(s): 

     (2r1100 bitInterleaveWith:2r1001) bitDeinterleave:2 -> #(12 9)
     (197 bitInterleaveWith:144) bitDeinterleave:2 -> #(197 144)

     (197 bitInterleaveWith:144 and:62) bitDeinterleave:3 -> #(197 144 62)

     |a b|
     (0 to:31) do:[:bitA |
	 a := 1 << bitA.
	 (0 to:31) do:[:bitB |
	    b := 1 << bitB.
	    self assert:( (a bitInterleaveWith:b) bitDeinterleave:2 ) = {a . b }
	 ].
     ].

     |a b c|
     (0 to:31) do:[:bitA |
	 a := 1 << bitA.
	 (0 to:31) do:[:bitB |
	     b := 1 << bitB.
	     (0 to:31) do:[:bitC |
		 c := 1 << bitC.
		 self assert:( (a bitInterleaveWith:b and:c) bitDeinterleave:3 ) = {a . b . c}
	     ].
	 ].
     ].

o  bitInterleaveWith: anInteger
generate a Morton number (-> https://en.wikipedia.org/wiki/Morton_number_(number_theory))
by interleaving bits of the receiver
(at even positions if counting from 1) with bits of the argument (at odd bit positions).
Thus, if the bits of the receiver are
aN ... a2 a1 a0
and those of the argument are:
bN ... b2 b1 b0
the result is
bN aN ... b2 a2 b1 a1 b0 a0.

Morton numbers are great to linearize 2D coordinates
eg. to sort 2D points by distances

usage example(s): 

     (2r1100 bitInterleaveWith:2r1001) printStringRadix:2 -> '11 01 00 10'
     (2r11000101 bitInterleaveWith:2r10010000) printStringRadix:2'1101001000010001 -> '11 01 00 10 00 01 00 01'

     |a b|
     (0 to:31) do:[:bitA |
	 a := 1 << bitA.
	 (0 to:31) do:[:bitB |
	    b := 1 << bitB.
	    self assert:( (a bitInterleaveWith:b) bitDeinterleave:2 ) = {a . b }
	 ].
     ].

o  bitInvert
return the value of the receiver with all bits inverted.
The method's name may be misleading: the receiver is not changed,
but a new number is returned. Could be named #withBitsInverted

o  bitInvertByte
return a new integer, where the low 8 bits are masked and complemented.
This returns an unsigned version of what bitInvert would return.
(i.e. same as self bitInvert bitAnd:16rFF)

usage example(s): 

     16r7f bitInvert
     16r7f bitInvertByte

     16r80 bitInvert
     16r80 bitInvertByte

     16rff bitInvert
     16rff bitInvertByte

o  bitOr: anInteger
return the bitwise-or of the receiver and the argument, anInteger

usage example(s): 

     (2r000000100 bitOr:2r00000011) radixPrintStringRadix:2
     (0 bitOr:16r20000000) hexPrintString
     (0 bitOr:16r40000000) hexPrintString
     (0 bitOr:16r80000000) hexPrintString

o  bitReversed
swap (i.e. reverse) bits in an integer
i.e. a.b.c.d....x.y.z -> z.y.x...b.a.d.c.
Warning:
do not use this without care: it depends on the machine's
word size; i.e. a 64bit machine will return a different result as a 32bit machine.
Better use one of the bitReversedXX methods.
This my vanish or be replaced by something better

usage example(s): 

     2r1001 bitReversed printStringRadix:2
     2r100111010011 bitReversed printStringRadix:2
     -1 bitReversed printStringRadix:2

o  bitReversed16
swap (i.e. reverse) the low 16 bits in an integer
the high bits are ignored and clear in the result
i.e. xxx.a.b.c.d....x.y.z -> 000.z.y.x...b.a.d.c.

usage example(s): 

     2r1001 bitReversed16 printStringRadix:2
     2r100111010011 bitReversed16 printStringRadix:2
     16r1ABCD bitReversed16 printStringRadix:2
     -1 bitReversed16 printStringRadix:2

o  bitReversed32
swap (i.e. reverse) the low 32 bits in an integer
the high bits are ignored and clear in the result
i.e. xxx.a.b.c.d....x.y.z -> 000.z.y.x...b.a.d.c.

usage example(s): 

     2r1001 bitReversed32 printStringRadix:2
     2r100111010011 bitReversed32 printStringRadix:2
     -1 bitReversed32 printStringRadix:2

o  bitReversed64
swap (i.e. reverse) the low 64 bits in an integer
the high bits are ignored and clear in the result
i.e. xxx.a.b.c.d....x.y.z -> 000.z.y.x...b.a.d.c.

usage example(s): 

     2r1001 bitReversed64 printStringRadix:2
     2r100111010011 bitReversed64 printStringRadix:2
     -1 bitReversed64 printStringRadix:2

o  bitReversed8
swap (i.e. reverse) the low 8 bits in an integer
the high bits are ignored and clear in the result
i.e. xxx.a.b.c.d....x.y.z -> 000.z.y.x...b.a.d.c.

usage example(s): 

     2r1001 bitReversed8 printStringRadix:2
     2r10011101 bitReversed8 printStringRadix:2
     2r111110011101 bitReversed8 printStringRadix:2
     16r1234 bitReversed8 printStringRadix:2
     -1 bitReversed8 printStringRadix:2

o  bitShift: shiftCount
return the value of the receiver shifted by shiftCount bits;
leftShift if shiftCount > 0; rightShift otherwise.
Notice: the result of bitShift: on negative receivers is not
defined in the language standard (since the implementation
is free to choose any internal representation for integers).
However, ST/X preserves the sign;
i.e. it is an arithmetic shift as long as you stay within the
number of bits supported by the platform.

usage example(s): 

       16 bitShift:-1
       16 bitShift:-2
       16 bitShift:-63
       
       -16 bitShift:-1
       -16 bitShift:-2
       -16 bitShift:-63

         4 rightShift:-2
        -4 rightShift:-2
        -4 rightShift:63

o  bitTest: aMask
return true, if any bit from aMask is set in the receiver.
I.e. true, if the bitwise-AND of the receiver and the argument, anInteger
is non-0, false otherwise.

usage example(s): 

     2r10001 bitTest:2r00001
     2r10001 bitTest:2r00010
     2r10001 bitTest:2r00100
     2r10001 bitTest:2r01000
     2r10001 bitTest:2r10000
     2r10001 bitTest:2r10001
     2r10001 bitTest:2r10010

o  bitXor: anInteger
return the bitwise-exclusive-or of the receiver and the argument, anInteger

o  highBit
return the bitIndex of the highest bit set.
The returned bitIndex starts at 1 for the least significant bit.
Returns 0 if no bit is set.
Notice for negative numbers, the returned value is undefined (actually: nonsense),
because for 2's complement representation, conceptionally all high bits are 1.
But because we use a sign-magnitude representation for large integers,
you'll get the high bit of the absolute magnitude for numbers above the SmallInteger
range, in contrast to the highbit of the negative number if within the SmallInt range.

usage example(s): 

     2r0 highBit
     2r1 highBit
     2r10 highBit
     2r100 highBit
     2r1000 highBit
     2r100000000000 highBit

     ((0 to:64) collect:[:s | 1 bitShift:s])
        collect:[:n | n highBit]

     (((0 to:64) collect:[:s | 1 bitShift:s])
        collect:[:n | n highBit]) = (1 to:65)

usage example(s): 

     Time millisecondsToRun:[
        1000000 timesRepeat:[
            2r1 highBit
        ]
     ]

usage example(s): 

     Time millisecondsToRun:[
        1000000 timesRepeat:[
            2r1111 highBit
        ]
     ]

usage example(s): 

     Time millisecondsToRun:[
        1000000 timesRepeat:[
            2r11111111111111 highBit
        ]
     ]

usage example(s): 

     Time millisecondsToRun:[
        1000000 timesRepeat:[
            2r11111111111111111111111111 highBit
        ]
     ]

usage example(s): 

     2r000100 highBit
     2r010100 highBit
     2r000001 highBit
     0 highBit
     SmallInteger maxVal highBit

o  lowBit
return the bitIndex of the lowest bit set. The returned bitIndex
starts at 1 for the least significant bit.
Returns 0 if no bit is set.

usage example(s): 

     0 lowBit
     2r0001 lowBit
     2r0010 lowBit
     2r0100 lowBit
     2r1000 lowBit

     2r000100 lowBit
     2r010010 lowBit
     2r100001 lowBit
     16r1000 lowBit
     16r1000000 lowBit
     16r1000000000000000 lowBit

     Time millisecondsToRun:[
	1000000 timesRepeat:[
	    2r1000 lowBit
	]
     ]

     Time millisecondsToRun:[
	1000000 timesRepeat:[
	    2r11110000000 lowBit
	]
     ]

     Time millisecondsToRun:[
	1000000 timesRepeat:[
	    2r1000000000000 lowBit
	]
     ]

     Time millisecondsToRun:[
	1000000 timesRepeat:[
	    2r1000000000000000000000000000 lowBit
	]
     ]

o  rightShift: shiftCount
return the value of the receiver shifted by shiftCount bits;
right shift if shiftCount > 0; left shift otherwise.
Notice: the result of bitShift: on negative receivers is not
defined in the language standard (since the implementation
is free to choose any internal representation for integers).
However, ST/X preserves the sign,
i.e. it is an arithmetic shift as long as you stay within the
number of bits supported by the platform.

usage example(s): 

        16 rightShift:1
        16 rightShift:2
        16 rightShift:63

       -16 rightShift:1
       -16 rightShift:2
       -16 rightShift:63

        1 rightShift:-2
       -1 rightShift:-2

         4 rightShift:-2
        -4 rightShift:-2
        -4 rightShift:63

bit operators - indexed
o  bitAt: anIntegerIndex
return the value of the index's bit (index starts at 1) as 0 or 1.
Notice: the result of bitAt: on negative receivers is not
defined in the language standard (since the implementation
is free to choose any internal representation for integers)

usage example(s): 

     16r000000001 bitAt:0 -> error
     16r000000001 bitAt:1
     16r000000001 bitAt:2
     16r000008000 bitAt:16
     16r000800000 bitAt:24
     16r008000000 bitAt:28
     16r010000000 bitAt:29
     16r020000000 bitAt:30
     16r040000000 bitAt:31
     16r080000000 bitAt:32
     16r100000000 bitAt:33

o  clearBit: anInteger
return a new integer where the specified bit is off.
Bits are counted from 1 starting with the least significant.
The method's name may be misleading: the receiver is not changed,
but a new number is returned. Should be named #withBitCleared:

usage example(s): 

     (16r401 clearBit:1     ) hexPrintString
     (16r401 clearBit:0     ) hexPrintString
     (16r3fffffff clearBit:1) hexPrintString
     (16r3fffffff clearBit:29) hexPrintString
     (16r3fffffff clearBit:30) hexPrintString
     (16r3fffffff clearBit:31) hexPrintString
     (16r3fffffff bitAt:29) hexPrintString
     (16r3fffffff bitAt:30) hexPrintString
     (16r3fffffff bitAt:31) hexPrintString
     (16r40000001 clearBit:1) hexPrintString
     (16rF0000001 clearBit:29) hexPrintString
     (16rF0000001 clearBit:30) hexPrintString
     (16rF0000001 clearBit:31) hexPrintString
     (16rF0000001 clearBit:32) hexPrintString
     (16r1F0000001 clearBit:33) hexPrintString

o  invertBit: anInteger
return a new number where the specified bit is inverted.
Bits are counted from 1 starting with the least significant.
The method's name may be misleading: the receiver is not changed,
but a new number is returned. Should be named #withBitInverted:

usage example(s): 

     (16r401 invertBit:2     ) hexPrintString
     (16r401 invertBit:1     ) hexPrintString
     (16r30000000 invertBit:1) hexPrintString
     (16r40000000 invertBit:0) hexPrintString
     (16r0 invertBit:29) hexPrintString
     (16r0 invertBit:30) hexPrintString
     (16r0 invertBit:31) hexPrintString
     (16r0 invertBit:32) hexPrintString
     (16r0 invertBit:33) hexPrintString
     (16r0 invertBit:100) hexPrintString

o  setBit: anInteger
return a new integer where the specified bit is on.
Bits are counted from 1 starting with the least significant.
The method's name may be misleading: the receiver is not changed,
but a new number is returned. Should be named #withBitSet:

usage example(s): 

     (16r401 setBit:2     ) hexPrintString
     (16r30000000 setBit:1) hexPrintString
     (16r40000000 setBit:0) hexPrintString
     (16r0 setBit:29) hexPrintString
     (16r0 setBit:30) hexPrintString
     (16r0 setBit:31) hexPrintString
     (16r0 setBit:32) hexPrintString
     (16r0 setBit:33) hexPrintString
     (16r0 setBit:100) hexPrintString

byte access
o  byteSwapped
lsb -> msb;
i.e. a.b.c.d -> d.c.b.a

usage example(s): 

     16r11223344 byteSwapped hexPrintString
     16r44332211 byteSwapped hexPrintString

o  byteSwapped16
for 16bit values only:
lsb -> msb;
i.e. a.b -> b.a

usage example(s): 

     16r1122 byteSwapped16 hexPrintString
     16r2211 byteSwapped16 hexPrintString
     16r332211 byteSwapped16 hexPrintString

o  byteSwapped32
for 32bit values only:
lsb -> msb;
i.e. a.b.c.d -> d.c.b.a

usage example(s): 

     16r11223344 byteSwapped32 hexPrintString
     16r44332211 byteSwapped32 hexPrintString

o  byteSwapped64
for 64bit values only:
lsb -> msb;
i.e. a.b.c.d.e.f.g.h -> h.g.f.e.d.c.b.a

usage example(s): 

     16r11223344 byteSwapped64 hexPrintString
     16r44332211 byteSwapped64 hexPrintString

o  digitAt: index
return 8 bits of value, starting at byte index

usage example(s): 

     (16r12345678 digitAt:1) printStringRadix:16
     (16r12345678 digitAt:3) printStringRadix:16
     (16r12345678 digitAt:15) printStringRadix:16
     (16r12345678 digitAt:0) printStringRadix:16
     (16r12345678 digitAt:-10) printStringRadix:16

o  digitByteAt: index
return 8 bits of my signed value, starting at byte index.
For positive receivers, this is the same as #digitAt:;
for negative ones, the actual bit representation is returned.

usage example(s): 

     (10 digitByteAt:1) printStringRadix:16
     (10 digitByteAt:3) printStringRadix:16
     (-10 digitByteAt:1) printStringRadix:16
     (-10 digitByteAt:3) printStringRadix:16

o  digitBytes
return a byteArray filled with the receiver's bits
(8 bits of the absolute value per element),
least significant byte is first

usage example(s): 

      16r12 digitBytes hexPrintString
      16r1234 digitBytes hexPrintString
      16r12345678 digitBytes hexPrintString

o  digitBytesMSB
return a byteArray filled with the receiver's bits
(8 bits of the absolute value per element),
most significant byte is first

usage example(s): 

      16r12 digitBytesMSB hexPrintString
      16r1234 digitBytesMSB hexPrintString
      16r12345678 digitBytesMSB hexPrintString

o  digitLength
return the number of bytes needed for the unsigned binary representation of the receiver.
For negative receivers, the result is not defined by the language standard.
ST/X returns the digitLength of its absolute value.

usage example(s): 

     16rFF00000000000000 digitLength
     16r-FF00000000000000 digitLength

     16rFF000000 digitLength
     16rFF0000 digitLength
     16rFF00 digitLength
     16rFF digitLength
     16r-FF000000 digitLength
     16r-FF0000 digitLength
     16r-FF00 digitLength
     16r-FF digitLength

o  swapBytes
swap bytes pair-wise in a positive integer
i.e. a.b.c.d -> b.a.d.c.
The name may be misleading; actually a new integer is returned,
and the receiver is not modified.

Redefined here for speed.
Swapping of negative integers is undefined and therefore not supported.
This case is handled in the superclass.

usage example(s): 

     -1 swapBytes hexPrintString
     16r11223344 swapBytes hexPrintString
     16r44332211 swapBytes hexPrintString
     self maxVal swapBytes hexPrintString
     self maxVal swapBytes swapBytes hexPrintString
     16r1122334455667788 swapBytes hexPrintString
     16r11223344556677889900 swapBytes hexPrintString

catching messages
o  basicAt: index
catch indexed access - report an error
defined here since basicAt: in Object omits the SmallInteger check.

o  basicAt: index put: anObject
catch indexed access - report an error
defined here since basicAt:put: in Object omits the SmallInteger check.

o  basicSize
return the number of indexed instvars - SmallIntegers have none.
Defined here since basicSize in Object omits the SmallInteger check.

o  size
return the number of indexed instvars - SmallIntegers have none.

coercing & converting
o  asCharacter
Return a character with the receiver as ascii (actually: unicode) value

o  asFloat
return a Float with same value as the receiver.
Redefined for performance (machine can do it faster)

o  asLargeInteger
return a LargeInteger with same value as receiver.
Not for general use:
Notice, that this returns an unnormalized large int (i.e. a large with a smallint value),
which are normally not present in the system, and not handled correctly by many functions.
This exists only as a helper for some algorithms and converters

o  asShortFloat
return a ShortFloat with same value as receiver.
Redefined for performance (machine can do it faster)

o  asUnsignedInt
return an integer representing my unsigned INT value.
Notice, that the returned integer's size
depends heavily on the underlying INT size;
You will get 16rFFFFFFFF on 32bit machines,
but 16rFFFFFFFFFFFFFFFF on 64 bit machines.
So use this only for printing or certain bit operations (emulating C semantics).

usage example(s): 

     -1 asUnsignedInt hexPrintString -> 'FFFFFFFFFFFFFFFF'
     16r-8000 asUnsignedInt hexPrintString -> ''FFFFFFFFFFFF8000''

o  codePoint
for compatibility with Characters.
(Allows for integers to be stored into U16/U32 strings)

o  generality
return the generality value - see ArithmeticValue>>retry:coercing:

o  signExtended24BitValue
return a smallInteger from sign-extending the 24'th bit.
May be useful for communication interfaces

usage example(s): 

     16rFFFFFF signExtended24BitValue
     16r800000 signExtended24BitValue
     16r7FFFFF signExtended24BitValue

o  signExtendedByteValue
return a smallInteger from sign-extending the 8'th bit.
May be useful for communication interfaces

usage example(s): 

     16rFF signExtendedByteValue
     16r80 signExtendedByteValue
     16r7F signExtendedByteValue

o  signExtendedLongValue
return a smallInteger from sign-extending the 32'th bit.
May be useful for communication interfaces

usage example(s): 

     16rFFFFFFFF signExtendedLongValue -> -1
     16r80000000 signExtendedLongValue -> -2147483648
     16r7FFFFFFF signExtendedLongValue -> 2147483647

o  signExtendedShortValue
return a smallInteger from sign-extending the 16'th bit.
May be useful for communication interfaces

usage example(s): 

     16rFFFF signExtendedShortValue
     16r8000 signExtendedShortValue
     16r7FFF signExtendedShortValue

comparing
o  < aNumber
return true, if the argument is greater than the receiver

usage example(s): 

^ self retry:#< coercing:aNumber

o  <= aNumber
return true, if the argument is greater or equal

o  = aNumber
return true, if the argument represents the same numeric value
as the receiver, false otherwise

o  > aNumber
return true, if the argument is less than the receiver

o  >= aNumber
return true, if the argument is less or equal

o  hash
return an integer useful for hashing on value

o  hashMultiply
used in some squeak code to generate an alternative hash value for integers

usage example(s): 

     1 hashMultiply
     2 hashMultiply
     3 hashMultiply
     100 hashMultiply

o  identityHash
return an integer useful for hashing on identity

o  max: aNumber
return the receiver or the argument, whichever is greater

o  min: aNumber
return the receiver or the argument, whichever is smaller

o  ~= aNumber
return true, if the arguments value is not equal to mine

copying
o  deepCopy
return a deep copy of myself
- reimplemented here since smallintegers are unique

o  deepCopyUsing: aDictionary postCopySelector: postCopySelector
return a deep copy of myself
- reimplemented here since smallintegers are unique

o  shallowCopy
return a shallow copy of myself
- reimplemented here since smallintegers are unique

o  simpleDeepCopy
return a deep copy of myself
- reimplemented here since smallintegers are unique

inspecting
o  inspectorExtraAttributes
( an extension from the stx:libtool package )
extra (pseudo instvar) entries to be shown in an inspector.

iteration
o  timesRepeat: aBlock
evaluate the argument, aBlock self times.
Reimplemented as primitive for speed

o  to: stop by: incr do: aBlock
reimplemented as primitive for speed

usage example(s): 

     1 to:10 by:3 do:[:i | i printNewline]

o  to: stop do: aBlock
evaluate aBlock for every integer between (and including) the receiver
and the argument, stop.
Reimplemented as primitive for speed

usage example(s): 

     1 to:10 do:[:i | i printNewline]

misc math
o  bernoulli
returns the nth Bernoulli number.
The series runs this:
1, 1/2, 1/6, 0, -1/30, 0, 1/42, 0, -1/30, 0, 5/66, 0, -691/2730, etc

Uses a table of the first 20 even bernoulli numbers.
So bernoulli(42) will fail for now.
Used with taylor series for tan

usage example(s): 

     0 bernoulli
     1 bernoulli
     2 bernoulli
     3 bernoulli
     4 bernoulli
     5 bernoulli
     6 bernoulli
     8 bernoulli
     38 bernoulli
     40 bernoulli
     41 bernoulli
     42 bernoulli

o  divMod: aNumber
return an array filled with
(self // aNumber) and (self \\ aNumber).
The returned remainder has the same sign as aNumber.
The following is always true:
(receiver // something) * something + (receiver \\ something) = receiver

Be careful with negative results: 9 // 4 -> 2, while -9 // 4 -> -3.
Especially surprising:
-1 \\ 10 -> 9 (because -(1/10) is truncated towards next smaller integer, which is -1,
and -1 multiplied by 10 gives -10, so we have to add 9 to get the original -1).
-10 \\ 3 -> 2 (because -(10/3) is truncated towards next smaller integer, which is -4,
and -4 * 4 gives -12, so we need to add 2 to get the original -10.

This is redefined here for more performance

usage example(s): 

     10 // 3           -> 3
     10 \\ 3           -> 1

     10 // -3          -> -4
     10 \\ -3          -> -2

     -10 // 3          -> -4
     -10 \\ 3          -> 2

     -10 // -3         -> 3
     -10 \\ -3         -> -1

     -78 \\ 10         2
     -78 // 10         -8

     10 divMod:3       -> #(3 1)   because 3*3 + 1 = 10
     10 divMod:-3      -> #(-4 -2) because -4*-3 + (-2) = 10
     -10 divMod:3      -> #(-4 2)  because -4*3 + 2 = -10
     -10 divMod:-3     -> #(3 -1)  because -3*3 + (-1) = -10

     1000000000000000000000 divMod:3   -> #(333333333333333333333 1)
     1000000000000000000000 divMod:-3  -> #(-333333333333333333334 -2)
     -1000000000000000000000 divMod:3  -> #(-333333333333333333334 2)
     -1000000000000000000000 divMod:-3 -> #(333333333333333333333 -1)
     100 factorial divMod:103

o  gcd: anInteger
return the greatest common divisor (Euclid's algorithm).
This has been redefined here for more speed since due to the
use of gcd in Fraction code, it has become time-critical for
some code. (thanx to MessageTally)

usage example(s): 

     45 gcd:30 15
     -45 gcd:30 15
     45 gcd:-30 -15
     -45 gcd:-30 -15

o  gcd_helper: anInteger
same as gcd - see knuth & Integer>>gcd:

o  integerLog10
return the truncation of log10 of the receiver.
The same as (self log:10) floor.
Stupid implementation, which is used to find out the number of digits needed
to print a number/and for conversion to a LargeInteger.
Implemented that way, to allow for tiny systems (PDAs) without a Float class
(i.e. without log).

usage example(s): 

      99 integerLog10
      100 integerLog10
      101 integerLog10
      (101 log:10) floor
      120 integerLog10

      -1 integerLog10
      0 integerLog10
      Number trapInfinity:[ 0 integerLog10 ]

o  intlog10
return the truncation of log10 of the receiver.
The same as (self log:10) floor.
Stupid implementation, which is used to find out the number of digits needed
to print a number/and for conversion to a LargeInteger.
Implemented that way, to allow for tiny systems (PDAs) without a Float class
(i.e. without log).

** This is an obsolete interface - do not use it (it may vanish in future versions) **

printing & storing
o  asBCD
return an integer which represents the BCD encoded value of the receiver;
that is: each digit of its decimal representation is placed into a nibble
of the result. (aka 162 -> 0x162). The BCD hex string looks like the original decimal.
This conversion is useful for some communication protocols,
or control systems, which represent numbers this way...

usage example(s): 

      99999999 asBCD hexPrintString
      12812345 asBCD hexPrintString
      128123 asBCD hexPrintString
      128901 asBCD hexPrintString
      12890 asBCD hexPrintString
      1289 asBCD hexPrintString
      999 asBCD hexPrintString
      256 asBCD hexPrintString
      255 asBCD hexPrintString
      128 asBCD hexPrintString
      162 asBCD hexPrintString

      999999999 asBCD hexPrintString
      128123456 asBCD hexPrintString

o  printOn: aStream
append my printstring (base 10) to aStream.

I use #printString instead of #printOn: as basic print mechanism.

o  printOn: aStream base: base showRadix: showRadix
append a string representation of the receiver in the specified numberBase to aStream
(if showRadix is true, with initial XXr)
The base argument should be between 2 and 36.

o  printString
return my printstring (base 10)

usage example(s): 

since this was heavily used in some applications,
     here is an exception to the rule of basing printString
     upon the printOn: method.

usage example(s): 

     1234 printString
     0    printString
     -100 printString

    Time millisecondsToRun:[ 1000000 timesRepeat:[ 123456789012 printString ]] 180 180 180 170 180
    Time millisecondsToRun:[ 1000000 timesRepeat:[ 12345678 printString ]]     140 150 140 150 140
    Time millisecondsToRun:[ 1000000 timesRepeat:[ 1234 printString ]]         130 140 130 130 130
    Time millisecondsToRun:[ 1000000 timesRepeat:[ 12 printString ]]           130 120 120 120 110
    Time millisecondsToRun:[ 1000000 timesRepeat:[ 5 printString ]]            110 110 100 110 90
    Time millisecondsToRun:[ 1000000 timesRepeat:[ 0 printString ]]             60

o  printStringRadix: base
return my printstring (optimized for bases 16, 10 and 8).
Print digits > 0 as uppercase chars if base > 0,
as lowercase chars if base < 0.

usage example(s): 

      127 printStringRadix:16
      127 printStringRadix:-16
      -127 printStringRadix:16
      -127 printStringRadix:-16
      123 printStringRadix:12
      123 printStringRadix:10
      123 printStringRadix:8
      123 printStringRadix:3
      123 printStringRadix:2
      123 printStringRadix:1
      35 printStringRadix:36
      123 printStringRadix:37

      -127 printStringRadix:16
      -123 printStringRadix:12
      -123 printStringRadix:10
      -123 printStringRadix:8
      -123 printStringRadix:3
      -123 printStringRadix:2

      16r3FFFFFFF printStringRadix:16
      16r7FFFFFFF printStringRadix:16
      16rFFFFFFFF printStringRadix:16
      16r3FFFFFFFFFFFFFFF printStringRadix:16
      16r7FFFFFFFFFFFFFFF printStringRadix:16
      16rFFFFFFFFFFFFFFFF printStringRadix:16

      16r-3FFFFFFF printStringRadix:16
      16r-40000000 printStringRadix:16
      16r-7FFFFFFF printStringRadix:16
      16r-80000000 printStringRadix:16
      16r-FFFFFFFF printStringRadix:16
      16r-3FFFFFFFFFFFFFFF printStringRadix:16
      16r-7FFFFFFFFFFFFFFF printStringRadix:16
      16r-FFFFFFFFFFFFFFFF printStringRadix:16
      16r-4000000000000000 printStringRadix:16
      16r-8000000000000000 printStringRadix:16

o  printfPrintString: formatString
non-standard, but sometimes useful.
return a printed representation of the receiver
as specified by formatString, which is defined by the C-function 'printf'.
No checking for string overrun - the resulting string
must be shorter than 256 chars or else ...

Notice that a conversion may not be portable; for example,
to correctly convert an int on a 64-bit alpha, a %ld is required,
on 64bit mingw or visualc, %lld is required,
while other systems may be happy with a %d.
You cannot use lld unconditionally, because some (old) c printfs do not support it!)
Use at your own risk (if at all).

This method is NONSTANDARD and may be removed without notice;
it is provided to allow special conversions in very special situations.
WARNNG: this goes directly to the C-printf function and may therefore be inherently unsafe.
Please use the printf: method, which is safe as it is completely implemented in Smalltalk.

usage example(s): 

	123 printfPrintString:'%%d -> %d'
	123 printfPrintString:'%%6d -> %6d'
	123 printfPrintString:'%%x -> %x'
	123 printfPrintString:'%%4x -> %4x'
	123 printfPrintString:'%%04x -> %04x'

private
o  numberOfDigits: n8BitDigits
initialize the instance to store n8BitDigits.
It is a no-op for SmallIntegers.

o  numberOfDigits: n8BitDigits sign: sign
private: for protocol completeness with LargeIntegers.
Returns a smallInteger with my absValue and the sign of the argument.
The method's name may be misleading: the receiver is not changed,
but a new number is returned.

special modulo arithmetic
o  plus32: aNumber
return the sum of the receiver and the argument, as SmallInteger.
The argument must be another SmallInteger.
If the result overflows the 32 bit range, the value modulo 16rFFFFFFFF is returned.
This is of course not always correct, but allows for C/Java behavior to be emulated.

usage example(s): 

     16r7FFFFFFF + 1          2147483648
     16r7FFFFFFF plus32: 1

o  plus: aNumber
return the sum of the receiver and the argument, as SmallInteger.
The argument must be another SmallInteger.
If the result overflows the smallInteger range, the value modulo the
smallInteger range is returned (i.e. the low bits of the sum).
This is of course not always correct, but some code does a modulo anyway
and can therefore speed things up by not going through LargeIntegers.

usage example(s): 

	5 plus:-1
	5 plus:1
	1 plus:-5
	self maxVal plus:1
	self maxVal + 1

o  subtract: aNumber
return the difference of the receiver and the argument, as SmallInteger.
The argument must be another SmallInteger.
If the result overflows the smallInteger range, the value modulo the
smallInteger range is returned (i.e. the low bits of the sum).
This is of course not always correct, but some code does a modulo anyway
and can therefore speed things up by not going through LargeIntegers.

usage example(s): 

	-1 subtract:5
	5 subtract:1
	1 subtract:-5
	self minVal subtract:1
	self minVal - 1

o  times: aNumber
return the product of the receiver and the argument, as SmallInteger.
The argument must be another SmallInteger.
If the result overflows the smallInteger range, the value modulo the
smallInteger range is returned (i.e. the low bits of the product).
This is of course not always correct, but some code does a modulo anyway
and can therefore speed things up by not going through LargeIntegers.

usage example(s): 

	5 times:-1
	5 times:1
	self maxVal-1 times:2
	self maxVal-1 times:-2
	self maxVal-1 * 2  bitAnd:16r3fffffff

special modulo bit operators
o  bitInvert32
return the value of the receiver with all bits inverted in 32bit signed int space
(changes the sign)

usage example(s): 

     1 bitInvert32
     16r40000000 bitInvert32
     16r80000000 bitInvert32

o  bitRotate32: shiftCount
return the value of the receiver rotated by shiftCount bits,
but only within 32 bits, rotating left for positive, right for negative counts.
Rotates through the sign bit.
Useful for crypt algorithms, or to emulate C/Java semantics.

o  bitShift32: shiftCount
return the value of the receiver shifted by shiftCount bits,
but only within 32 bits, shifting into/out-of the sign bit.
May be useful for communication interfaces, to create ST-numbers
from a signed 32bit int value given as individual bytes,
or to emulate C/Java semantics.

usage example(s): 

     128 bitShift:24
     128 bitShift32:24

     1 bitShift:31
     1 bitShift32:31

o  bitXor32: aNumber
return the xor of the receiver and the argument.
The argument must be another SmallInteger or a 4-byte LargeInteger.
If the result overflows the 32 bit range, the value modulo 16rFFFFFFFF is returned.
This is of course not always correct, but allows for C/Java behavior to be emulated.

usage example(s): 

     16r7FFFFFFF bitXor: 16r80000000          4294967295
     16r7FFFFFFF bitXor32: 16r80000000

o  unsignedBitShift32: shiftCount
return the value of the receiver shifted by shiftCount bits,
but only within 32 unsigned bits.
May be useful for communication interfaces, to create ST-numbers
from an unsigned 32bit int value given as individual byte,
or to emulate C/Java semantics.

usage example(s): 

     128 unsignedBitShift:24
     128 unsignedBitShift32:24

     1 unsignedBitShift:31
     1 unsignedBitShift32:31

     -1 unsignedBitShift32:-1
     -1 unsignedBitShift32:1

testing
o  between: min and: max
return true if the receiver is greater than or equal to the argument min
and less than or equal to the argument max.
- reimplemented here for speed

o  even
return true, if the receiver is even

o  isImmediate
return true if I am an immediate object
i.e. I am represented in the pointer itself and
no real object header/storage is used by me.

o  isPowerOfTwo
return true, if the receiver is a power of 2

usage example(s): 

     0 isPowerOfTwo
     1 isPowerOfTwo
     2 isPowerOfTwo
     3 isPowerOfTwo
     4 isPowerOfTwo
     5 isPowerOfTwo
     16r8000000000000000 isPowerOfTwo
     16r8000000000000001 isPowerOfTwo
     16r40000000 isPowerOfTwo
     16r80000000 isPowerOfTwo
     16r100000000 isPowerOfTwo

     10000 factorial isPowerOfTwo
     |n| n := 10000 factorial. Time millisecondsToRun:[10000 timesRepeat:[ n isPowerOfTwo]]

o  negative
return true, if the receiver is less than zero
reimplemented here for speed

o  nextPowerOf2
return the power of 2 at or above the receiver.
Useful for padding.
Notice, that for a powerOf2, the receiver is returned.
Also notice, that (because it is used for padding),
0 is returned for zero.

usage example(s): 

     0 nextPowerOf2
     1 nextPowerOf2
     2 nextPowerOf2
     3 nextPowerOf2
     4 nextPowerOf2
     5 nextPowerOf2
     6 nextPowerOf2
     7 nextPowerOf2
     8 nextPowerOf2
     9 nextPowerOf2

     22 nextPowerOf2
     32 nextPowerOf2
     16rFFFF nextPowerOf2 = 16r10000
     16rFFFFFFFF nextPowerOf2 = 16r100000000
     16r1FFFFFFFFFFFFFFF nextPowerOf2 = 16r2000000000000000
     16r3FFFFFFFFFFFFFFF nextPowerOf2 = 16r4000000000000000
     16r7FFFFFFFFFFFFFFF nextPowerOf2 = 16r8000000000000000
     16rFFFFFFFFFFFFFFFF nextPowerOf2 = 16r10000000000000000
     10 factorial nextPowerOf2
     20 factorial nextPowerOf2
     100 factorial nextPowerOf2

o  odd
return true, if the receiver is odd

o  parityOdd
return true, if an odd number of bits are set in the receiver, false otherwise.
(i.e. true for odd parity)
Undefined for negative values (smalltalk does not require the machine to use 2's complement)

usage example(s): 

	self assert:
	 (((0 to:255) collect:[:i | i parityOdd ifTrue:1 ifFalse:0])
	    asByteArray collect:[:c | c + $0 asciiValue]) asString
	 =
	    '0110100110010110100101100110100110010110011010010110100110010110100101100110100101101001100101100110100110010110100101100110100110010110011010010110100110010110011010011001011010010110011010010110100110010110100101100110100110010110011010010110100110010110'

	self assert:(16r0FFFFFFF parityOdd = 16r0FFFFFFF bitCount odd).
	self assert:(16r1FFFFFFF parityOdd = 16r1FFFFFFF bitCount odd).
	self assert:(16r3FFFFFFF parityOdd = 16r3FFFFFFF bitCount odd).
	self assert:(16r7FFFFFFF parityOdd = 16r7FFFFFFF bitCount odd).
	self assert:(16rFFFFFFFF parityOdd = 16rFFFFFFFF bitCount odd).
	self assert:(16r3FFFFFFFFFFFFFFF parityOdd = 16r3FFFFFFFFFFFFFFF bitCount odd).
	self assert:(16r7FFFFFFFFFFFFFFF parityOdd = 16r7FFFFFFFFFFFFFFF bitCount odd).
	self assert:(16rFFFFFFFFFFFFFFFF parityOdd = 16rFFFFFFFFFFFFFFFF bitCount odd).

o  positive
return true, if the receiver is greater or equal to zero (not negative)
reimplemented here for speed

o  sign
return the sign of the receiver (-1, 0 or 1).
reimplemented here for speed

usage example(s): 

     -5 sign
     -1 sign
     0 sign
     1 sign
     5 sign

o  strictlyPositive
return true, if the receiver is greater than zero
reimplemented here for speed

usage example(s): 

     0 strictlyPositive
     1 strictlyPositive
     -1 strictlyPositive


ST/X 7.2.0.0; WebServer 1.670 at bd0aa1f87cdd.unknown:8081; Fri, 08 Dec 2023 03:16:40 GMT