Class: FixedPoint

• Inheritance
• Description
• Related information
• Class protocol
  • coercing & converting
  • constants
  • instance creation
  • printing control
  • queries
• Instance protocol
  • accessing
  • arithmetic
  • coercing & converting
  • double dispatching
  • mathematical functions
  • printing & storing
  • private
  • testing
  • truncation & rounding
• Examples

Inheritance:

   Object
   |
   +--Magnitude
      |
      +--ArithmeticValue
         |
         +--Number
            |
            +--Fraction
               |
               +--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

Description:

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

Related information:

    Number
    Fraction
    Integer
    Float
    ShortFloat
    LongFloat
    Complex

Class protocol:

 coerce: aNumber

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

 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

 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

 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

 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

usage example(s):

^ self numerator:n denominator:d scale:(d log max:n log) ceiling

usage example(s):

self numerator:123 denominator:100

 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.

 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'

 readFrom: aStringOrStream decimalPointCharacters: decimalPointCharacters onError: exceptionBlock

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']

 printTruncated

return the PrintTruncated flag, which controls printing.
See the description in the documentation for details

 printTruncated: aBoolean

set the PrintTruncated flag, which controls printing.
See the description in the documentation for details

 exponentCharacter

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

Instance protocol:

 epsilon

(2 asFixedPoint:4) epsilon
(2 asFixedPoint:100) epsilon
(2 asFixedPoint:1000) epsilon

 scale

return the number of places of significance that is carried by the receiver.

 * 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.

 + 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)

 - aNumber

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.

 / aNumber

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.

 negated

redefined from Fraction to preserve scale

 reciprocal

redefined from Fraction to preserve scale

 asFixedPoint

return the receiver as a fixedPoint number
- that's the receiver itself

 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

 asFraction

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

 asIntegerIfPossible

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

 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:

 differenceFromFixedPoint: aFixedPoint

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.

 differenceFromFraction: aFraction

sent when a fraction is asked to subtract the receiver.
The result has my scale.
Redefined here to preserve the scale.

 differenceFromInteger: anInteger

sent when an integer does not know how to subtract the receiver.
The result has my scale.
Redefined here to preserve the scale.

 productFromFixedPoint: aFixedPoint

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.

 productFromFraction: aFraction

sent when a fraction is asked to multiply the receiver.
The result has my scale.
Redefined here to preserve the scale.

 productFromInteger: anInteger

sent when an integer does not know how to multiply the receiver.
Redefined here to preserve the scale.

 quotientFromFixedPoint: aFixedPoint

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.

 quotientFromFraction: aFraction

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.

 quotientFromInteger: anInteger

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.

 sumFromFixedPoint: aFixedPoint

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.

 sumFromFraction: aFraction

sent when a fraction is asked to add the receiver.
The result has my scale.
Redefined here to preserve the scale.

 sumFromInteger: anInteger

sent when an integer does not know how to add the receiver.
The result has my scale.
Redefined here to preserve the scale.

 sqrt

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

 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

 printOn: aStream

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)

 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

 printTruncatedOn: aStream

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

 storeOn: aStream

notice: we MUST preserve the full internal precision when storing/reloading

 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

 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).

 scale: newScale

set the scale.

 setNumerator: nInteger denominator: d scale: s

initialize the instance variables.
Assumes that the fraction as specified by numerator and denominator
is already reduced.

 setNumerator: nInteger scale: s

initialize the instance variables, given an integer

 setScale: newScale

initialize the scale instance variables.

 isFixedPoint

return true, if the receiver is some kind of fixedPoint number;
true is returned here - the method is redefined from Object.

 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

 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

Examples:

     |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).

     |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).

     |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).

     |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).

     |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).