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Documentation of class 'ShortFloat':

Class: ShortFloat

Inheritance
Description
Related information
Class protocol
Instance protocol

Inheritance:

   Object
   |
   +--Magnitude
      |
      +--ArithmeticValue
         |
         +--Number
            |
            +--LimitedPrecisionReal
               |
               +--ShortFloat

Package:: stx:libbasic

Category:: Magnitude-Numbers

Version:: rev: 1.195 date: 2019/07/22 18:15:55; user: cg; file: ShortFloat.st directory: libbasic; module: stx stc-classLibrary: libbasic

Author:: Claus Gittinger

Description:

ShortFloats represent rational numbers with limited precision.
They use the C-compiler's 'float' format, which is usually the IEEE single float format.

In contrast to Floats (which use the C-compiler's 64bit 'double' format),
ShortFloats give you 32 bit floats.

Notice, that ST/X Floats are what Doubles are in ST-80 and ShortFloats are
ST-80's Floats respectively. The reason was to make ST/X's floats compatible
to bothe VisualWorks and other Smalltalks, which use C-doubles for the Float class
(i.e. VisualST and V'Age).
Thus, STX's Float precision is not worse than that of other ST's.

WARNING:
The layout of shortFloat instances is known by the runtime system and the compiler;
you may not add instance variables here.
Also, subclassing is complicated by the fact, that the VM creates floats/shortFloats,
and does some of its float-checks by an identity compare with the ShortFloat-class.
(i.e. your subclasses instances may not be recognized as float-like objects,
thus mixed mode arithmetic will always coerce them, effectively slowing things down).
This may be changed, to use a flag bit in the class.

Mixed mode arithmetic:
shortFloat op shortFloat -> shortFloat
shortFloat op fix -> shortFloat
shortFloat op fraction -> shortFloat
shortFloat op integer -> shortFloat
shortFloat op longFloat -> longFloat
shortFloat op float -> float
shortFloat op complex -> complex

Representation:
32bit single precision IEEE floats
23 bit mantissa + 1 hidden bit, providing a precision of 24bits,
8 bit exponent,
6 decimal digits (approx.)

Range and Precision of Storage Formats: see LimitedPrecisionReal >> documentation

Related information:

    Number
    Float
    LongFloat
    Fraction
    FixedPoint
    Integer
    Complex
    FloatArray
    DoubleArray

Class protocol:

accessing

defaultPrintFormat
defaultPrintFormat: aString

binary storage

readBinaryIEEESingleFrom: aStream: read a float value from the binary stream, aStream,
interpreting the next bytes as an IEEE formatted 4-byte float.
The bytes are read in the native byte order (i.e.lsb on intel)
readBinaryIEEESingleFrom: aStream MSB: msbFirst: read a float value from the binary stream, aStream,
interpreting the next bytes as an IEEE formatted 4-byte float.
The bytes are read in the soecified byte order
readBinaryIEEESingleFrom: aStream into: aBasicNewShortFloat: read a float value from the binary stream, aStream,
interpreting the next bytes as an IEEE formatted 4-byte float.
The bytes are read in the native byte order (i.e.lsb on intel)
readBinaryIEEESingleFrom: aStream into: aBasicNewShortFloat MSB: msb: read a float value from the binary stream, aStream,
interpreting the next bytes as an IEEE formatted 4-byte float.
If msb is true, the stream bytes are most-significant-first.
storeBinaryIEEESingle: aFloat on: aStream: store aFloat as an IEEE formatted 4-byte float
onto the binary stream, aStream.
The bytes are written in the native byte order (i.e.lsb on intel)
storeBinaryIEEESingle: aFloat on: aStream MSB: msb: store aFloat as an IEEE formatted 4-byte float
onto the binary stream, aStream.
If msb is true, the stream bytes are written most-significant-first.

class initialization

initialize

print 7 valid digits

usage example(s):

     self initialize

coercing & converting

coerce: aNumber: convert the argument aNumber into an instance of the receiver's class and return it.

constants

NaN

return a shortFloat which represents not-a-Number (i.e. an invalid number)

usage example(s):

     self NaN

e

return the constant e as ShortFloat

emax

Answer the maximum exponent for this representation.

emin

Answer the minimum exponent for this representation.

infinity

return a shortFloat which represents positive infinity (for my instances)

ln10

return the natural logarithm of 10 as a shortFloat

usage example(s):

     self ln10

negativeInfinity

return a shortFloat which represents negative infinity (for my instances).
Warning: do not compare equal against infinities;
instead, check using isFinite or isInfinite

pi

return the constant pi as ShortFloat

unity

return the neutral element for multiplication (1.0) as ShortFloat

zero

return the neutral element for addition (0.0) as ShortFloat

instance creation

basicNew

return a new shortFloat - here we return 0.0
- shortFloats are usually NOT created this way ...
Its implemented here to allow things like binary store & load
of shortFloats. (but even this support will go away eventually, its not
a good idea to store the bits of a float - the reader might have a
totally different representation - so floats will eventually be
binary stored in a device independent format.

fastFromString: aString at: startIndex

return the next ShortFloat from the string starting at startIndex.
No spaces are skipped.
Raises an exception, if the startIndex is not valid.
Returns garbage if the argument string is not a valid float number.

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

usage example(s):

     ShortFloat fastFromString:'123.45' at:1
     ShortFloat fastFromString:'123.45' at:2
     ShortFloat fastFromString:'123.45E4' at:1
     ShortFloat fastFromString:'hello123.45E4' at:6
     ShortFloat fastFromString:'12345' at:1
     ShortFloat fastFromString:'12345' at:2
     ShortFloat fastFromString:'12345' at:3
     ShortFloat fastFromString:'12345' at:4
     ShortFloat fastFromString:'12345' at:5
     ShortFloat fastFromString:'12345' at:6
     ShortFloat fastFromString:'12345' at:0
     ShortFloat fastFromString:'hello123.45E4' at:1

usage example(s):

     Time millisecondsToRun:[
        1000000 timesRepeat:[
            ShortFloat fastFromString:'123.45' at:1
        ]
     ]

fromIEEE32Bit: anInteger

creates a float, given the four native float bytes as an integer

usage example(s):

	ShortFloat fromIEEE32Bit:(#[64 73 15 219] asInteger)

queries

defaultPrintPrecision

return the number of decimal digits printed by default

usage example(s):

     ShortFloat defaultPrintPrecision
     Float defaultPrintPrecision
     LongFloat defaultPrintPrecision

epsilon

return the maximum relative spacing of instances of mySelf
(i.e. the value-delta of the least significant bit)

usage example(s):

     self epsilon

exponentCharacter

return the character used to print between mantissa an exponent.
Also used by the scanner when reading numbers.

isBuiltInClass

return true if this class is known by the run-time-system.
Here, true is returned for myself, false for subclasses.

numBitsInExponent

answer the number of bits in the exponent
This is an IEEE float, where 8 bits are available:
seeeeeee emmmmmmm mmmmmmmm mmmmmmmm

usage example(s):

     1.0 asShortFloat numBitsInExponent

numBitsInMantissa

answer the number of bits in the mantissa.
This is an IEEE float, where 23 bits (the hidden one is not counted here) are available:
seeeeeee emmmmmmm mmmmmmmm mmmmmmmm

precision

answer the precision (the number of bits in the mantissa) of a ShortFloat (in bits)
This is an IEEE float, where only the fraction from the normalized mantissa is stored
and so there is a hidden bit and the mantissa is actually represented by 24 binary digits
(although only 23 are needed in the binary representation)

usage example(s):

     self numBitsInMantissa + 1
     self precision

radix

answer the radix of a ShortFloat's exponent
This is an IEEE float, which is represented as binary

Instance protocol:

arithmetic

* aNumber

return the product of the receiver and the argument.

+ aNumber

return the sum of the receiver and the argument, aNumber

- aNumber

return the difference of the receiver and the argument, aNumber

/ aNumber

return the quotient of the receiver and the argument, aNumber

abs

return the absolute value of the receiver
reimplemented here for speed

usage example(s):

     3.0 asShortFloat abs
     -3.0 asShortFloat abs

negated

return myself negated

rem: aNumber

return the floating point remainder of the receiver and the argument, aNumber

uncheckedDivide: aNumber

return the quotient of the receiver and the argument, aNumber.
Do not check for divide by zero (return NaN or Infinity).
This operation is provided for emulators of other languages/semantics,
where no exception is raised for these results (i.e. Java).
It is only defined if the argument's type is the same as the receiver's.

usage example(s):

      0.0 asShortFloat uncheckedDivide:0
      1.0 asShortFloat uncheckedDivide:0.0

coercing & converting

asFloat

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

usage example(s):

     1.0 asShortFloat asFloat

asInteger

return an integer with same value - might truncate

usage example(s):

     12345.0 asShortFloat asInteger
     1e15 asShortFloat asInteger

asLongFloat

return a LongFloat with same value as the receiver

asQuadFloat

return a QuadFloat with same value as the receiver

asShortFloat

return a ShortFloat with same value as the receiver - that's me

coerce: aNumber

convert the argument aNumber into an instance of the receiver's class and return it.

generality

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

comparing

< aNumber

return true, if the argument is greater

<= aNumber

return true, if the argument is greater or equal

= aNumber

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

> aNumber

return true, if the argument is less

>= aNumber

return true, if the argument is less or equal

hash

return a number for hashing; redefined, since floats compare
by numeric value (i.e. 3.0 = 3), therefore 3.0 hash must be the same
as 3 hash.

usage example(s):

     1.2345 hash
     1.2345 asShortFloat hash
     1.0 hash
     1.0 asShortFloat hash
     0.5 asShortFloat hash
     0.25 asShortFloat hash
     0.5 hash
     0.25 hash

isAlmostEqualTo: aNumber nEpsilon: nE

return true, if the argument, aNumber represents almost the same numeric value
as the receiver, false otherwise.

nE is the number of minimal float distances, that the numbers may differ and
still be considered equal.

For background information why floats need this
read: http://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/

usage example(s):

        67329.234 asShortFloat isAlmostEqualTo:67329.23401 asShortFloat nEpsilon:1
        1.0 asShortFloat isAlmostEqualTo:1.0000001 asShortFloat nEpsilon:1
        1.0 asShortFloat isAlmostEqualTo:1.0000001  nEpsilon:1
        1.0 asShortFloat isAlmostEqualTo:-1.0 nEpsilon:1
        1.0 asShortFloat isAlmostEqualTo:1 nEpsilon:1
        0.0 asShortFloat isAlmostEqualTo:0.0000001 asShortFloat nEpsilon:1
        0.0 asShortFloat isAlmostEqualTo:0.000001 asShortFloat nEpsilon:1
        0.0 asShortFloat isAlmostEqualTo:self epsilon nEpsilon:1
        0.0 asShortFloat - 1.192093e-07 asShortFloat

~= aNumber

return true, if the arguments value are not equal

copying

deepCopy: return a deep copy of myself
- because storing into floats is not recommended/allowed, its ok to return the receiver
deepCopyUsing: aDictionary postCopySelector: postCopySelector: return a deep copy of myself
- because storing into floats is not recommended/allowed, its ok to return the receiver
shallowCopy: return a shallow copy of the receiver
simpleDeepCopy: return a deep copy of the receiver
- because storing into floats is not recommended/allowed, its ok to return the receiver

mathematical functions

fastInverseSqrt

return a rough but fast approximation of (1 / self sqrt).
The error is some 1%, which is ok for many 3D computations or physics simulations.
Do not use this for now: it is non-portable and probably not speeding things up
much, unless inlined into the sender code.
The code is here as a reminder and might be later used as a hint for the inliner
(to speed up 3D computations, for example).
see: http://betterexplained.com/articles/understanding-quakes-fast-inverse-square-root/

usage example(s):

     10.0 asShortFloat fastInverseSqrt
     (1 / 10.0 asShortFloat sqrt)

ln

return the natural logarithm of the receiver.
Raises an exception, if the receiver is less or equal to zero.

usage example(s):

     0 asFloat ln
     Number trapInfinity:[ 0 asFloat ln ]

     10 asFloat ln       2.30258509299405
     10 asShortFloat ln  2.302585
     10 asLongFloat ln   2.302585092994045684
     10 asQDouble ln     2.30258509299404568402

     50 asFloat ln       3.91202300542815
     50 asShortFloat ln  3.912023
     50 asLongFloat ln   3.912023005428146059
     50 asQDouble ln     3.91202300542814605862

log10

return the base-10 logarithm of the receiver.
Raises an exception, if the receiver is less or equal to zero.

usage example(s):

     0 asShortFloat log10
     Number trapInfinity:[ 0 asShortFloat log10 ]

     10 asFloat log10       1.0
     10 asShortFloat log10  1.0
     10 asLongFloat log10   1.0
     10 asQDouble log10     1.00000000000000000000000000000000000000000

     50 asFloat log10       1.69897000433602
     50 asShortFloat log10  1.69897
     50 asLongFloat log10   1.698970004336018805
     50 asQDouble log10     1.69897000433601880478626110527550697323181

printing & storing

printOn: aStream

append a printed representation of the receiver to
the argument, aStream.

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

printString

return a printed representation of the receiver
LimitedPrecisonReal and its subclasses use #printString instead of
#printOn: as basic print mechanism.

usage example(s):

	1.234 asShortFloat printString.
	1.0 asShortFloat printString.
	1e10 asShortFloat printString.
	1.2e3 asShortFloat printString.
	1.2e30 asShortFloat printString.
	(1.0 uncheckedDivide:0) asShortFloat printString.
	(0.0 uncheckedDivide:0) asShortFloat printString.
	self pi printString.

	self pi printString.
	DefaultPrintFormat := '.3'.
	self pi printString.
	DefaultPrintFormat := '.7'.

	DecimalPointCharacterForPrinting := $,.
	1.234 asShortFloat printString.
	1.0 asShortFloat printString.
	1e10 asShortFloat printString.
	1.2e3 asShortFloat printString.
	1.2e30 asShortFloat printString.
	(1.0 uncheckedDivide:0) asShortFloat printString.
	(0.0 uncheckedDivide:0) asShortFloat printString.
	DecimalPointCharacterForPrinting := $.

printStringWithFormat: format

return a printed representation of the receiver;
fmt must be of the form: .nn, where nn is the number of digits.
To print 6 valid digits, use printStringWithFormat:'.6'
For Floats, the default used in printString, is 15 (because its a double);
for ShortFloats, it is 6 (because it is a float)

printfPrintString: formatString

non-standard: return a printed representation of the receiver
as specified by formatString, which is defined by printf.

If you use this, be aware, that the format string must be correct and something like %f.
Also, the resulting string may not be longer than 255 bytes -
since that's the (static) size of the buffer.

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

usage example(s):

ShortFloat pi printfPrintString:'%%lg -> %lg'

usage example(s):

ShortFloat pi printfPrintString:'%%lf -> %lf'

usage example(s):

ShortFloat pi printfPrintString:'%%7.5lg -> %7.5lg'

usage example(s):

ShortFloat pi printfPrintString:'%%G -> %G'

usage example(s):

ShortFloat pi printfPrintString:'%%F -> %F'

usage example(s):

ShortFloat pi printfPrintString:'%%7.5G -> %7.5G'

usage example(s):

ShortFloat pi printfPrintString:'%%7.5F -> %7.5F'

storeOn: aStream

append a printed representation of the receiver to
the argument, aStream.

I use #storeString instead of #storeOn: as basic store mechanism.

storeString

return a printed representation of the receiver;
all valid digits are printed.
LimitedPrecisonReal and its subclasses use #storeString instead of
#storeOn: as basic print mechanism.

usage example(s):

	0.1 asShortFloat storeString
	((Array new:10 withAll:0.1 asShortFloat) inject:0 into:[:v :sumSoFar| sumSoFar + v]) storeString
	1.0 asShortFloat storeString
	1.234 asShortFloat storeString
	1e10 asShortFloat storeString
	1.2e3 asShortFloat storeString
	1.2e30 asShortFloat storeString
	Float pi asShortFloat storeString
	(1.0 uncheckedDivide:0) asShortFloat storeString
	(0.0 uncheckedDivide:0) asShortFloat storeString

     notice that the storeString is NOT affected by DecimalPointCharacterForPrinting:

	DecimalPointCharacterForPrinting := $,.
	1.234 asShortFloat storeString.
	1.0 asShortFloat storeString.
	1e10 asShortFloat storeString.
	1.2e3 asShortFloat storeString.
	1.2e30 asShortFloat storeString.
	(1.0 uncheckedDivide:0) asShortFloat storeString.
	(0.0 uncheckedDivide:0) asShortFloat storeString.
	DecimalPointCharacterForPrinting := $.

private accessing

basicAt: index: return an internal byte of the float.
The value returned here depends on byte order, float representation etc.
Therefore, this method should be used strictly private.

Notice:
the need to redefine this method here is due to the
inability of many machines to store floats in non-double aligned memory.
Therefore, on some machines, the first 4 bytes of a float are left unused,
and the actual float is stored at index 5 .. 12.
To hide this at one place, this method knows about that, and returns
values as if this filler wasnt present.
basicAt: index put: value: set an internal byte of the float.
The value to be stored here depends on byte order, float representation etc.
Therefore, this method should be used strictly private.

Notice:
the need to redefine this method here is due to the
inability of many machines to store floats in non-double aligned memory.
Therefore, on some machines, the first 4 bytes of a float are left unused,
and the actual float is stored at index 5 .. 12.
To hide this at one place, this method knows about that, and returns
values as if this filler wasnt present.

private-accessing

byteAt: index
byteAt: index put: newByte

queries

nextFloat: count

answer the next float count places after (or before if count is negative) myself

usage example(s):

     (1.0 asShortFloat nextFloat:2) storeString
     (67329.234 asShortFloat nextFloat:1) storeString
     ShortFloat NaN nextFloat:100000
     ShortFloat infinity nextFloat:100000

special access

exponent

extract a normalized float's exponent.
The returned value depends on the float-representation of
the underlying machine and is therefore highly unportable.
This is not for general use.
This assumes that the mantissa is normalized to
0.5 .. 1.0 and the float's value is mantissa * 2^exp

usage example(s):

     4.0 asShortFloat exponent
     2.0 asShortFloat exponent
     1.0 asShortFloat exponent
     0.5 asShortFloat exponent
     0.25 asShortFloat exponent
     0.00000011111 asShortFloat exponent

mantissa

extract a normalized float's mantissa.
The returned value depends on the float-representation of
the underlying machine and is therefore highly unportable.
This is not for general use.
This assumes that the mantissa is normalized to
0.5 .. 1.0 and the float's value is mantissa * 2^exp

usage example(s):

     1.0 asShortFloat exponent
     1.0 asShortFloat mantissa
     1e1000 asShortFloat mantissa

     0.5 asShortFloat exponent
     0.5 asShortFloat mantissa

     0.25 asShortFloat exponent
     0.25 asShortFloat mantissa

     0.00000011111 asShortFloat exponent
     0.00000011111 asShortFloat mantissa

testing

isFinite

return true, if the receiver is a finite float
i.e. not NaN and not infinite.

usage example(s):

	1.0 asShortFloat isFinite
	(0.0 asShortFloat uncheckedDivide: 0.0) isFinite
	(1.0 asShortFloat uncheckedDivide: 0.0) isFinite

isNaN

return true, if the receiver is an invalid float (NaN - not a number).
These are not created by ST/X float operations (they raise an exception);
however, inline C-code could produce them ...

usage example(s):

     1.0 asShortFloat isNaN
     (0.0 asShortFloat uncheckedDivide: 0.0) isNaN
     (0.0 asShortFloat uncheckedDivide: 0.0 asShortFloat) isNaN

isNegativeZero

many systems have two float.Pnt zeros

usage example(s):

     0.0 asShortFloat isNegativeZero
     -0.0 asShortFloat isNegativeZero

isZero

return true, if the receiver is zero

negative

return true if the receiver is less than zero.
-0.0 is positive for now.

usage example(s):

	0.0 asShortFloat negative
	-0.0 asShortFloat negative
	1.0 asShortFloat negative
	-1.0 asShortFloat negative
	(1.0 uncheckedDivide: 0.0) asShortFloat negative
	(-1.0 uncheckedDivide: 0.0) asShortFloat negative

numberOfBits

return the size (in bits) of the real;
typically, 32 is returned here,
but who knows ...

usage example(s):

     1.2 numberOfBits
     1.2 asShortFloat numberOfBits

positive

return true if the receiver is greater or equal to zero (not negative)
0.0 and -0.0 are positive for now.

usage example(s):

	0.0 asShortFloat positive
	-0.0 asShortFloat positive
	1.0 asShortFloat positive
	-1.0 asShortFloat positive
	(1.0 uncheckedDivide: 0.0) asShortFloat positive
	(-1.0 uncheckedDivide: 0.0) asShortFloat positive

strictlyPositive

return true if the receiver is greater than zero

truncation & rounding

ceiling

return the smallest integer which is greater or equal to the receiver.

usage example(s):

     0.5 asShortFloat ceiling
     -0.5 asShortFloat ceiling

ceilingAsFloat

return the smallest integer-valued float greater or equal to the receiver.
This is much like #ceiling, but avoids a (possibly expensive) conversion
of the result to an integer.
It may be useful, if the result is to be further used in another float-operation.

usage example(s):

     0.5 asShortFloat ceilingAsFloat
     -0.5 asShortFloat ceilingAsFloat
     -1.5 asShortFloat ceilingAsFloat

floor

return the integer nearest the receiver towards negative infinity.

usage example(s):

     0.5 asShortFloat floor
     -0.5 asShortFloat floor

floorAsFloat

return the float which represents the next lower
integer nearest the receiver towards negative infinity.
Much like floor, but returns a float result - useful if the result
will be used in another float operation, to avoid costy int-conversion.

usage example(s):

     0.5 asShortFloat floorAsFloat
     -0.5 asShortFloat floorAsFloat

fractionPart

extract the after-decimal fraction part.
such that (self truncated + self fractionPart) = self

usage example(s):

     1.6 asShortFloat fractionPart + 1.6 asShortFloat truncated
     -1.6 asShortFloat fractionPart + -1.6 asShortFloat truncated

     1.0 asShortFloat fractionPart
     0.5 asShortFloat fractionPart
     0.25 asShortFloat fractionPart
     3.14159 asShortFloat fractionPart
     12345673.14159 asShortFloat fractionPart
     123456731231231231.14159 asShortFloat fractionPart

rounded

return the receiver rounded to the nearest integer

usage example(s):

     0.4 asShortFloat rounded
     0.5 asShortFloat rounded
     0.6 asShortFloat rounded
     -0.4 asShortFloat rounded
     -0.5 asShortFloat rounded
     -0.6 asShortFloat rounded
     1e32 asShortFloat rounded

roundedAsFloat

return the receiver rounded to the nearest integer as a float.
This is much like #rounded, but avoids a (possibly expensive) conversion
of the result to an integer.
It may be useful, if the result is to be further used in another float-operation.

usage example(s):

     0.4 asShortFloat rounded
     0.5 asShortFloat rounded
     0.6 asShortFloat rounded
     -0.4 asShortFloat rounded
     -0.5 asShortFloat rounded
     -0.6 asShortFloat rounded

     0.4 asShortFloat roundedAsFloat
     0.5 asShortFloat roundedAsFloat
     0.6 asShortFloat roundedAsFloat
     -0.4 asShortFloat roundedAsFloat
     -0.5 asShortFloat roundedAsFloat
     -0.6 asShortFloat roundedAsFloat

truncated

return the receiver truncated towards zero as an integer

usage example(s):

     0.5 asShortFloat truncated
     -0.5 asShortFloat truncated
     0.5 asShortFloat truncatedAsFloat
     -0.5 asShortFloat truncatedAsFloat

truncatedAsFloat

return the receiver truncated towards zero as a float.
This is much like #truncated, but avoids a (possibly expensive) conversion
of the result to an integer.
It may be useful, if the result is to be further used in another
float-operation.

usage example(s):

     0.5 asShortFloat truncated
     -0.5 asShortFloat truncated
     0.5 asShortFloat truncatedAsFloat
     -0.5 asShortFloat truncatedAsFloat

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