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Class: FixedPoint
Object
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+--Magnitude
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+--ArithmeticValue
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+--Number
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+--Fraction
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+--FixedPoint
- Package:
- stx:libbasic
- Category:
- Magnitude-Numbers
- Version:
- rev:
1.57
date: 2017/07/03 15:36:25
- user: cg
- file: FixedPoint.st directory: libbasic
- module: stx stc-classLibrary: libbasic
- Author:
- Jan Steinman, Bytesmiths
- adapted, modified & enhanced by Claus Gittinger
This class implements infinite precision fixed-point numbers,
which internally hold exact (fractional) results, but print themself with
a limited number of digits after the decimal point (rounded).
NOTICE:
it seems that squeak prints these truncated,
whereas ST/X prints them rounded.
This behavior should probably be controllable by providing
a subclass (RoundedFixedPoint ?) which redefines the printOn: method.
(it is now controlled by a classVar, which is of course not a thread-safe
solution).
These can be used in computation, where rounding errors should not accumulate,
but only a limited precision is required for the final result.
(i.e. business applications)
It doesn't really do anything too interesting except creating instances,
converting, and printing, since its superclass Fraction does all the work.
Test:
'123456789012345678901234567890.123456789' asFixedPoint * 1000000000
-> 123456789012345678901234567890123456789'
Notes: 1) The current implementation does not convert arbitrarily-based
String representations, which shouldn't be too much a problem
for financial types.
2) the implementation is a hack - it has not been optimized for speed
in particular.
Mixed mode arithmetic:
fix op fix -> fix, scale is max. of operands
fix op fraction -> fix; scale is fix's scale
fix op integer -> fix; scale is fix's scale
fix op float -> float
Number
Fraction
Integer
Float
ShortFloat
LongFloat
Complex
coercing & converting
-
coerce: aNumber
-
convert the argument aNumber into an instance of the receiver's class and return it.
constants
-
e
-
e with roughly 26 valid digits...
usage example(s):
E := nil.
self e
-> 2.7182818284590452353602875
wolfram:
2.718281828459045235360287471352662497757247093699959574966...
self e squared
self e reciprocal
1 / self e
self e * 1000000000000000000000000000000000000000000
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-
pi
-
pi with roughly 26 valid digits...
usage example(s):
Pi := nil.
self pi
-> 3.1415926535897932384626434
wolfram:
-> 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904...
self pi squared
self pi reciprocal
1 / self pi
self pi * 1000000000000000000000000000000000000000000
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-
pi1000
-
pi with roughly 1000 valid digits...
usage example(s):
Pi_1000 := nil.
self pi1000
-> 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989
wolfram:
-> 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904...
self pi1000 squared
self pi1000 reciprocal
(self pi1000 - self pi) asFloat
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instance creation
-
numerator: n denominator: d
-
redefined to block the inherited instance creation method from fraction.
Raises an error - you must give a scale or provide a power-of-10 denominator
usage example(s):
use #numerator:denominator:scale
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usage example(s):
^ self numerator:n denominator:d scale:(d log max:n log) ceiling
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usage example(s):
self numerator:123 denominator:100
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-
numerator: n denominator: d scale: s
-
create and return a new fixedPoint instances with the given scale
(post decimal digits when printed). Assume its already reduced.
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readFrom: aStringOrStream
-
return the next FixedPoint from the (character-)stream aStream.
NOTICE:
This behaves different from the default readFrom:, in returning
0 (instead of raising an error) in case no number can be read.
It is unclear, if this is the correct behavior (ST-80 does this)
- depending on the upcoming ANSI standard, this may change.
usage example(s):
FixedPoint readFrom:'.456'
FixedPoint readFrom:'123.456'
FixedPoint readFrom:'123.'
FixedPoint readFrom:'3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632788'
FixedPoint readFrom:(ReadStream on:'foobar')
FixedPoint readFrom:(ReadStream on:'foobar') onError:nil
FixedPoint readFrom:'0b1234' onError:nil
FixedPoint readFrom:'1'
FixedPoint readFrom:'2'
FixedPoint readFrom:'1.5'
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-
readFrom: aStringOrStream decimalPointCharacters: decimalPointCharacters onError: exceptionBlock
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return an instance of me as described on the string or stream, aStringOrStream.
If an error occurs during conversion, return the result from evaluating exceptionBlock
usage example(s):
FixedPoint readFrom:'1.00'
FixedPoint readFrom:'123.456'
FixedPoint readFrom:'123,456' decimalPointCharacters:','
FixedPoint readFrom:'-123.456'
FixedPoint readFrom:'123'
FixedPoint readFrom:'-123'
-- notice the difference between readFromString and readFrom:
FixedPoint readFromString:'-123.abcd' onError:[47.5]
FixedPoint readFromString:'-1a.bcd' onError:[47.5]
FixedPoint readFromString:'foot' onError:['bad fixedpoint']
FixedPoint readFromString:'0b1234' onError:['bad fixedpoint']
-- readFrom only reads what can be read, leaving the stream at the end:
FixedPoint readFrom:'-123.abcd' onError:[47.5]
FixedPoint readFrom:'-1a.bcd' onError:[47.5]
FixedPoint readFrom:'foot' onError:['bad fixedpoint']
FixedPoint readFrom:'0b1234' onError:['bad fixedpoint']
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printing control
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printTruncated
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return the PrintTruncated flag, which controls printing.
See the description in the documentation for details
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printTruncated: aBoolean
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set the PrintTruncated flag, which controls printing.
See the description in the documentation for details
queries
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exponentCharacter
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return the character used to print between mantissa an exponent.
Also used by the scanner when reading numbers.
accessing
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epsilon
-
(2 asFixedPoint:4) epsilon
(2 asFixedPoint:100) epsilon
(2 asFixedPoint:1000) epsilon
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scale
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return the number of places of significance that is carried by the receiver.
arithmetic
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* aNumber
-
return the product of the receiver and the argument.
Redefined to care for the scale if the argument is another fixPoint number.
The result's scale is the maximum of the receiver's scale and the argument's scale.
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+ aNumber
-
return the sum of the receiver and the argument, aNumber.
Redefined to care for the scale if the argument is another fixPoint number.
The result's scale will be the maximum of the receiver's and the argument's scale.
usage example(s):
((1/3) asFixedPoint:2) + 1
((1/3) asFixedPoint:2) + (1/3)
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-
- aNumber
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return the difference of the receiver and the argument, aNumber.
Redefined to care for the scale if the argument is another fixPoint number.
The result's scale is the maximum of the receiver's scale and the argument's scale.
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/ aNumber
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return the quotient of the receiver and the argument, aNumber.
Redefined to care for the scale if the argument is another fixPoint number.
The result's scale is the maximum of the receiver's scale and the argument's scale.
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negated
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redefined from Fraction to preserve scale
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reciprocal
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redefined from Fraction to preserve scale
coercing & converting
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asFixedPoint
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return the receiver as a fixedPoint number
- that's the receiver itself
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asFixedPoint: newScale
-
return a fixedPoint with the same value as the receiver,
and newScale number of valid decimal digits
usage example(s):
'12345.12345' asFixedPoint:2
(FixedPoint fromString:'12345.12345') asFixedPoint:2
((FixedPoint fromString:'0.33333333')
+
(FixedPoint fromString:'0.33333333')
) asFixedPoint:2
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-
asFraction
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return the receiver as a fraction
usage example(s):
(FixedPoint fromString:'0.2')
(FixedPoint fromString:'0.2') asFraction
(FixedPoint fromString:'0.2') asFloat
(FixedPoint fromString:'0.2') asShortFloat
(FixedPoint fromString:'0.2') asInteger
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-
asIntegerIfPossible
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if the receiver can be represented as an integer without loosing precision,
return that integer. Otherwise, return the receiver.
Useful for printing / string conversion
usage example(s):
1.2345s3 asIntegerIfPossible
12.345s3 asIntegerIfPossible
123.45s3 asIntegerIfPossible
1234.5s3 asIntegerIfPossible
12345.0s3 asIntegerIfPossible
12345s3 asIntegerIfPossible
1.2345s3 asInteger
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coerce: aNumber
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convert the argument aNumber into an instance of the receiver's class and return it.
-
generality
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return the generality value - see ArithmeticValue>>retry:coercing:
double dispatching
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differenceFromFixedPoint: aFixedPoint
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sent when a fixedPoint is asked to subtract the receiver.
The result has the higher scale of the two operands.
Redefined here to compute the scale.
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differenceFromFraction: aFraction
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sent when a fraction is asked to subtract the receiver.
The result has my scale.
Redefined here to preserve the scale.
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differenceFromInteger: anInteger
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sent when an integer does not know how to subtract the receiver.
The result has my scale.
Redefined here to preserve the scale.
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productFromFixedPoint: aFixedPoint
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sent when a fixedPoint is asked to multiply the receiver.
The result has the higher scale of the two operands.
Redefined here to compute the scale.
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productFromFraction: aFraction
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sent when a fraction is asked to multiply the receiver.
The result has my scale.
Redefined here to preserve the scale.
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productFromInteger: anInteger
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sent when an integer does not know how to multiply the receiver.
Redefined here to preserve the scale.
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quotientFromFixedPoint: aFixedPoint
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sent when a fixedPoint is asked to divide by the receiver.
The result has the higher scale of the two operands.
Redefined here to compute the scale.
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quotientFromFraction: aFraction
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Return the quotient of the argument, aFraction and the receiver.
Sent when aFraction does not know how to divide by the receiver.
Redefined here to preserve the scale.
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quotientFromInteger: anInteger
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Return the quotient of the argument, anInteger and the receiver.
Sent when anInteger does not know how to divide by the receiver.
Redefined here to preserve the scale.
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sumFromFixedPoint: aFixedPoint
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sent when a fixedPoint is asked to add by the receiver.
The result has the higher scale of the two operands.
Redefined here to compute the scale.
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sumFromFraction: aFraction
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sent when a fraction is asked to add the receiver.
The result has my scale.
Redefined here to preserve the scale.
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sumFromInteger: anInteger
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sent when an integer does not know how to add the receiver.
The result has my scale.
Redefined here to preserve the scale.
mathematical functions
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sqrt
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compute the square root, using the Newton method.
The approximated return value has an error less than
the receiver's last digit, as specified in the scale.
usage example(s):
(2 asFixedPoint:4) sqrt
(2 asFixedPoint:100) sqrt
(2 asFixedPoint:1000) sqrt
(10 asFixedPoint:100) sqrt
(100 asFixedPoint:100) sqrt
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printing & storing
-
printDecimalOn: aStream roundToScale: roundToScale truncateToScale: truncateToScale
-
common helper for printing (with round or truncate)
and storing (neither rounding, nor truncating)
usage example(s):
((FixedPoint fromString:'0.66666666') withScale:2)
printDecimalOn:Transcript roundToScale:false truncateToScale:false
((FixedPoint fromString:'0.66666666') withScale:2)
printDecimalOn:Transcript roundToScale:true truncateToScale:false
((FixedPoint fromString:'0.66666666') withScale:2)
printDecimalOn:Transcript roundToScale:false truncateToScale:true
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-
printOn: aStream
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append to the argument, aStream, a printed representation of the receiver.
For printout, only scale post-decimal digits are printed
(By default, the printout is rounded to that many digits)
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printRoundedOn: aStream
-
append to the argument, aStream, a printed representation of the receiver.
For printout, only scale post-decimal digits are printed,
the printout is rounded to that many digits
usage example(s):
((FixedPoint fromString:'0.66666666') withScale:2) printRoundedOn:Transcript
((FixedPoint fromString:'0.66666666') withScale:2) printTruncatedOn:Transcript
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-
printTruncatedOn: aStream
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append to the argument, aStream, a printed representation of the receiver.
For printout, only scale post-decimal digits are printed,
the printout is truncated to that many digits
usage example(s):
((FixedPoint fromString:'0.66666666') withScale:2) printRoundedOn:Transcript
((FixedPoint fromString:'0.66666666') withScale:2) printTruncatedOn:Transcript
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-
storeOn: aStream
-
notice: we MUST preserve the full internal precision when storing/reloading
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storeString
-
((FixedPoint fromString:'0.66666666') ) storeString
((FixedPoint fromString:'0.66666666') withScale:2 ) storeString
((FixedPoint fromString:'1.5') ) storeString
((FixedPoint fromString:'1.5') withScale:2 ) storeString
((FixedPoint fromString:'1.5') withScale:1 ) storeString
((FixedPoint fromString:'1.5') withScale:0 ) storeString
private
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reduced
-
reduce the receiver; divide the numerator and denominator by their
greatest common divisor; if the result is integral, return an Integer.
Otherwise, return the normalized receiver.
CAVEAT: bad name; should be called reduce, as it has a side effect
(i.e. this is destructive wrt. the instance values).
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scale: newScale
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set the scale.
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setNumerator: nInteger denominator: d scale: s
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initialize the instance variables.
Assumes that the fraction as specified by numerator and denominator
is already reduced.
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setNumerator: nInteger scale: s
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initialize the instance variables, given an integer
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setScale: newScale
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initialize the scale instance variables.
testing
-
isFixedPoint
-
return true, if the receiver is some kind of fixedPoint number;
true is returned here - the method is redefined from Object.
truncation & rounding
-
roundedToScale
-
return the receiver rounded to my scale
(i.e. return a number which has the value which is shown when printing)
usage example(s):
((2/3) asFixedPoint:2)
((2/3) asFixedPoint:2) rounded
((2/3) asFixedPoint:2) roundedToScale
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-
truncatedToScale
-
return the receiver truncated towards zero to my scale
usage example(s):
((2/3) asFixedPoint:2)
((2/3) asFixedPoint:2) truncated
((2/3) asFixedPoint:2) truncatedToScale
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|a b r|
a := (FixedPoint fromString:'123.456').
b := '1.10' asFixedPoint.
r := a + b.
Transcript showCR:r.
Transcript showCR:(r withScale:2).
Transcript showCR:(r withScale:1).
Transcript showCR:(r rounded).
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|a b r|
a := (FixedPoint fromString:'0.9999999').
b := 0.0000001 asFixedPoint.
r := a + b.
Transcript showCR:r.
Transcript showCR:(r withScale:2).
Transcript showCR:(r withScale:1).
Transcript showCR:(r rounded).
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|a b r|
a := (FixedPoint fromString:'0.9999998').
b := (FixedPoint fromString:'0.0000001').
r := a + b.
Transcript showCR:r.
Transcript showCR:(r withScale:2).
Transcript showCR:(r withScale:1).
Transcript showCR:(r rounded).
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|a b r|
a := (FixedPoint fromString:'1.0').
b := (FixedPoint fromString:'0.0000001').
r := a + b.
Transcript showCR:r.
Transcript showCR:(r withScale:2).
Transcript showCR:(r withScale:1).
Transcript showCR:(r rounded).
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|a b r|
a := (FixedPoint fromString:'0.99').
b := (FixedPoint fromString:'0.0000001').
r := a + b.
Transcript showCR:r.
Transcript showCR:(r withScale:2).
Transcript showCR:(r withScale:1).
Transcript showCR:(r rounded).
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