Data.FormatN

Text formatting of Doubles.

In particular, the library provides functionality to calculate and display a fixed number of significant figures for a variety of different number formatting styles.

Some similar libraries that may be better suited for different use cases include:

Flexible formatters. These libraries provide more flexibility around formatting options, but do not have a concept of significance:

• Text.Printf and Numeric in base.
• Formatting
• vformat: A Python str.format() like formatter

text-format has similar functionality but is not native haskell and I wanted to do some tweaking to defaults. It's probably safer and faster.

rounded seems to be much more about doing computation taking rounding into account, compared with the much simpler task of pretty printing a number.

This library could have just provided an ability to compute a significant figure version of a number and then use these other libraries, but the round trip (from Double to SigFig to Double) introduces errors (eg the least significant figure goes from being a '4' to a '3999999' via float maths).

formatn is used in the chart-svg library to automate consistent number formatting across different scales.

Usage

>>> import Data.FormatN
>>> xs = [(-1),0,1,1.01,1.02,1.1,1.2]
>>> fixed (Just 2) <$> xs
["-1.00","0.00","1.00","1.01","1.02","1.10","1.20"]
>>> decimal (Just 2) <$> xs
["-1.0","0.0","1.0","1.0","1.0","1.1","1.2"]
>>> decimal (Just 3) . (1e-3*) <$> xs
["-0.00100","0.00","0.00100","0.00101","0.00102","0.00110","0.00120"]
>>> comma (Just 3) . (1e3*) <$> xs
["-1,000","0.00","1,000","1,010","1,020","1,100","1,200"]

formats is useful when you want a consistent textual style across a list of numbers:

>>> formats True False (const DecimalStyle) (Just 2) $ (1e-3*) <$> xs
["-0.0010"," 0.0000"," 0.0010"," 0.0010"," 0.0010"," 0.0011"," 0.0012"]

Using significant figures actually changes numbers - numbers that were slightly different end up being (and looking like) the same. distinguish increases the number of significant figures to compensate for this effect.

>>> distinguish 4 True False (const DecimalStyle) (Just 2) xs
["-1.00"," 0.00"," 1.00"," 1.01"," 1.02"," 1.10"," 1.20"]

SigFig

data SigFig

Decomposition of a Double into the components that are needed to determine significant figure formatting.

Eliding type changes, the relationship between a Double and a SigFig is:

\[ x == sign * figures * 10^{exponent} \]

Constructors

SigFig

Fields

• sfSign :: SigFigSign

  sign

• sfFigures :: Integer

  significant figures expressed as an Integer

• sfExponent :: Int

  the power of 10 exponent given figures.

Instances

Show SigFig

Defined in Data.FormatN

Methods

showsPrec :: Int -> SigFig -> ShowS

show :: SigFig -> String

showList :: [SigFig] -> ShowS

Eq SigFig

Defined in Data.FormatN

Methods

(==) :: SigFig -> SigFig -> Bool

(/=) :: SigFig -> SigFig -> Bool

data SigFigSign

Sign component

Constructors

SigFigNeg

SigFigPos

Instances

Show SigFigSign

Defined in Data.FormatN

Methods

showsPrec :: Int -> SigFigSign -> ShowS

show :: SigFigSign -> String

showList :: [SigFigSign] -> ShowS

Eq SigFigSign

Defined in Data.FormatN

Methods

(==) :: SigFigSign -> SigFigSign -> Bool

(/=) :: SigFigSign -> SigFigSign -> Bool

toSigFig :: Maybe Int -> Double -> SigFig

convert from a Double to a SigFig

>>> toSigFig (Just 2) 1234
SigFig {sfSign = SigFigPos, sfFigures = 12, sfExponent = 2}

toSigFig Nothing . fromSigFig <==> id
toSigFig (Just x) . fromSigFig . toSigFig (Just x) <==> toSigFig (Just x)

\x -> let (SigFig s fs e) = toSigFig Nothing x in let x' = ((if (s==SigFigNeg) then (-1.0) else 1.0) * fromIntegral fs * 10.0**fromIntegral e) in (x==0 || abs (x/x'-1) < 1e-6)

Checks for a valid number of significant figures and turns it off on a silly number.

>>> toSigFig Nothing 1234
SigFig {sfSign = SigFigPos, sfFigures = 1234, sfExponent = 0}

>>> toSigFig (Just (-3)) 1234
SigFig {sfSign = SigFigPos, sfFigures = 1234, sfExponent = 0}

fromSigFig :: SigFig -> Double

convert from a SigFig to a Double

>>> fromSigFig (SigFig SigFigPos 12 2)
1200.0

isZero :: SigFig -> Bool

Note that zero can still be represented in a SigFig way, so that we can distinguish between something that starts off as zero, and something that ends up as zero via rounding.

>>> isZero (SigFig SigFigPos 0 (-3))
True

incSigFig :: Int -> SigFig -> SigFig

increase significant figures

>>> incSigFig 1 (SigFig SigFigPos 1 0)
SigFig {sfSign = SigFigPos, sfFigures = 10, sfExponent = -1}

decSigFig :: Int -> SigFig -> Maybe SigFig

decrease significant figures, if possible.

>>> decSigFig 1 (SigFig SigFigPos 100 0)
Just (SigFig {sfSign = SigFigPos, sfFigures = 10, sfExponent = 1})

>>> decSigFig 1 (SigFig SigFigPos 123 0)
Nothing

Format Styles

data FormatStyle

Data type representing styles of formatting

Constructors

DecimalStyle

1000 1 0.001

ExponentStyle (Maybe Int)

1e3 1e0 1e-3

CommaStyle

1,000 1 0.001

FixedStyle Int

1. 00 1.00 0.00

PercentStyle

100,000% 100% 0.1%

DollarStyle

$1,000 $1 $0.001

Instances

Show FormatStyle

Defined in Data.FormatN

Methods

showsPrec :: Int -> FormatStyle -> ShowS

show :: FormatStyle -> String

showList :: [FormatStyle] -> ShowS

Eq FormatStyle

Defined in Data.FormatN

Methods

(==) :: FormatStyle -> FormatStyle -> Bool

(/=) :: FormatStyle -> FormatStyle -> Bool

Ord FormatStyle

Defined in Data.FormatN

Methods

compare :: FormatStyle -> FormatStyle -> Ordering

(<) :: FormatStyle -> FormatStyle -> Bool

(<=) :: FormatStyle -> FormatStyle -> Bool

(>) :: FormatStyle -> FormatStyle -> Bool

(>=) :: FormatStyle -> FormatStyle -> Bool

max :: FormatStyle -> FormatStyle -> FormatStyle

min :: FormatStyle -> FormatStyle -> FormatStyle

precStyle :: Double -> FormatStyle

DecimalStyle between 0.001 and a million and ExponentStyle outside this range.

commaPrecStyle :: Double -> FormatStyle

CommaStyle above a thousand but below a million, DecimalStyle between 0.001 and a thousand and ExponentStyle outside this range.

data FStyle

Data type representing styles of formatting dependent on the number

Constructors

FSDecimal

FSExponent (Maybe Int)

FSComma

FSFixed Int

FSPercent

FSDollar

FSPrec

FSCommaPrec

FSNone

Instances

Show FStyle

Defined in Data.FormatN

Methods

showsPrec :: Int -> FStyle -> ShowS

show :: FStyle -> String

showList :: [FStyle] -> ShowS

Eq FStyle

Defined in Data.FormatN

Methods

(==) :: FStyle -> FStyle -> Bool

(/=) :: FStyle -> FStyle -> Bool

Ord FStyle

Defined in Data.FormatN

Methods

compare :: FStyle -> FStyle -> Ordering

(<) :: FStyle -> FStyle -> Bool

(<=) :: FStyle -> FStyle -> Bool

(>) :: FStyle -> FStyle -> Bool

(>=) :: FStyle -> FStyle -> Bool

max :: FStyle -> FStyle -> FStyle

min :: FStyle -> FStyle -> FStyle

SigFig formatters

fixedSF :: Maybe Int -> SigFig -> Text

expt format for a SigFig

exptSF :: SigFig -> Text

expt format for a SigFig

exptSFWith :: Maybe Int -> SigFig -> Text

expt format for a SigFig, with an exponent override

>>> exptSFWith (Just 1) (toSigFig (Just 1) 1)
"0.1e1"
>>> exptSFWith (Just 0) (toSigFig (Just 1) 1)
"1e0"
>>> exptSFWith (Just (-1)) (toSigFig (Just 1) 1)
"10e-1"

decimalSF :: SigFig -> Text

decimal format for a SigFig

commaSF :: SigFig -> Text

comma format for a SigFig

dollarSF :: (SigFig -> Text) -> SigFig -> Text

dollar format for a SigFig

percentSF :: (SigFig -> Text) -> SigFig -> Text

percent format for a SigFig

formatSF :: FormatStyle -> SigFig -> Text

format a SigFig according to a style

>>> formatSF CommaStyle (toSigFig (Just 2) 1234)
"1,200"
>>> formatSF CommaStyle (SigFig SigFigPos 0 1)
"0"
>>> formatSF CommaStyle (SigFig SigFigPos 0 (-1))
"0.0"

Double formatters

format :: FormatStyle -> Maybe Int -> Double -> Text

format a number according to a FormatStyle and significant figures

>>> format CommaStyle (Just 2) 1234
"1,200"

formatOrShow :: FormatStyle -> Maybe Int -> Double -> Text

Format with the shorter of show and a style.

>>> format (ExponentStyle Nothing) Nothing 0
"0e0"
>>> formatOrShow (ExponentStyle Nothing) Nothing 0
"0"

fixed :: Maybe Int -> Double -> Text

Format to x decimal places with no significant figure rounding.

>>> fixed (Just 2) 100
"100.00"
>>> fixed (Just 2) 0.001
"0.00"

expt :: Maybe Int -> Double -> Text

Format in exponential style, maybe with significant figure rounding.

>>> expt Nothing 1245
"1.245e3"
>>> expt (Just 3) 1245
"1.24e3"
>>> expt (Just 3) 0.1245
"1.24e-1"
>>> expt (Just 2) 0
"0.0e0"

exptWith :: Maybe Int -> Maybe Int -> Double -> Text

Format in exponential style, with the suggested exponent.

>>> exptWith (Just 2) Nothing 1245
"12.45e2"
>>> exptWith (Just 6) (Just 3) 1245
"0.00124e6"

decimal :: Maybe Int -> Double -> Text

Format in decimal style, and maybe round to n significant figures.

>>> decimal Nothing 1.2345e-2
"0.012345"
>>> decimal (Just 2) 0.012345
"0.012"
>>> decimal (Just 2) 12345
"12000"

prec :: Maybe Int -> Double -> Text

Format between 0.001 and 1000000 using decimal style and exponential style outside this range.

>>> prec (Just 2) 0.00234
"0.0023"
>>> prec (Just 2) 0.000023
"2.3e-5"
>>> prec (Just 2) 123
"120"
>>> prec (Just 2) 123456
"120000"
>>> prec (Just 2) 1234567
"1.2e6"

comma :: Maybe Int -> Double -> Text

Format with US-style commas

>>> comma (Just 3) 1234567
"1,230,000"

commaPrec :: Maybe Int -> Double -> Text

Format using comma separators for numbers above 1,000 but below 1 million, otherwise use prec style.

>>> commaPrec (Just 3) 1234
"1,230"
>>> commaPrec (Just 3) 1234567
"1.23e6"

dollar :: (SigFig -> Text) -> Maybe Int -> Double -> Text

Adjust format to dollar style.

>>> dollar commaSF (Just 3) 1234
"$1,230"
>>> dollar (fixedSF (Just 2)) (Just 2) 0.01234
"$0.01"

percent :: (SigFig -> Text) -> Maybe Int -> Double -> Text

Adjust format to a percent.

>>> percent commaSF (Just 3) 0.1234
"12.3%"
>>> percent decimalSF (Just 1) 0.1234
"10%"

List Modifiers

majorityStyle :: (Double -> FormatStyle) -> [Double] -> FormatStyle

Compute the majority (modal) FormatStyle so a list of numbers can all have the same formatting

Also equalises the exponent to the majority for exponent style.

>>> commaPrecStyle <$> [0,5e6,1e7,2e7]
[CommaStyle,ExponentStyle (Just 6),ExponentStyle (Just 7),ExponentStyle (Just 7)]
>>> majorityStyle commaPrecStyle [0,5e6,1e7,2e7]
ExponentStyle (Just 7)

formats

Arguments

:: Bool

left pad to the largest text length

-> Bool

Try and reduce excess right-hand zeros

-> (Double -> FormatStyle)

style

-> Maybe Int

significant figures requested

-> [Double]

list of numbers

-> [Text]

Consistently format a list of numbers,using the minimum number of decimal places or minimum exponent.

>>> formats True True precStyle (Just 1) [0,0.5,1,2]
["0.0","0.5","1.0","2.0"]

Note how the presence of 0.5 in the example above changes the format of all numbers. Without it:

>>> formats True True precStyle (Just 1) [0,1,2]
["0","1","2"]

>>> formats False True precStyle (Just 1) $ ((-1)*) <$> [0,0.5,1,2]
["0.0","-0.5","-1.0","-2.0"]
>>> formats True True commaPrecStyle (Just 1) $ ((-1000)*) <$> [0,0.5,1,2]
["     0","  -500","-1,000","-2,000"]
>>> formats True True commaPrecStyle (Just 1) $ ((1e6)*) <$> [0,0.5,1,2]
["        0","  500,000","1,000,000","2,000,000"]
>>> formats True True commaPrecStyle (Just 1) $ ((1e6)*) <$> [0.9,2,3]
["0.9e6","2.0e6","3.0e6"]
>>> formats True True commaPrecStyle (Just 1) $ ((1e-6)*) <$> [0,0.5,1,2]
["0.0e-6","0.5e-6","1.0e-6","2.0e-6"]
>>> formats True True commaPrecStyle (Just 1) $ ((1e-3)*) <$> [0,0.5,1,2]
["0.0000","0.0005","0.0010","0.0020"]
>>> formats True False (const (ExponentStyle Nothing)) (Just 2) [0..4]
["0.0e0","1.0e0","2.0e0","3.0e0","4.0e0"]
>>> formats True True (const (ExponentStyle Nothing)) (Just 2) [0..4]
["0e0","1e0","2e0","3e0","4e0"]

formatsSF

Arguments

:: Maybe Int

significant figures requested

-> [Double]

list of numbers

-> [SigFig]

Consistently convert a list of numbers to SigFigs, using the minimum natural exponent of the list.

decSigFigs :: [SigFig] -> [SigFig]

Decrease the SigFig figure of a list of SigFigs without loss of precision, if possible. This has the effect of removing right zeros in decimal representations.

lpads :: [Text] -> [Text]

Add spaces to the left of a text representation so that all elements have the same length.

distinguish

Arguments

:: Int

maximum number of iterations

-> Bool

left pad to the largest text length

-> Bool

try and reduce excess right zero pads

-> (Double -> FormatStyle)

style

-> Maybe Int

significant figures requested

-> [Double]

list of numbers

-> [Text]

Provide formatted text for a list of numbers so that they are just distinguished.

For example, distinguish 4 commaPrecStyle (Just 2) means use as much significant figures as is needed for the numbers to be distinguished on rendering (up to 4+2=6), but with at least 2 significant figures.

The difference between this and formats can be seen in these examples:

>>> formats True True commaPrecStyle (Just 2) [0,1,1.01,1.02,1.1,1.2]
["0.0","1.0","1.0","1.0","1.1","1.2"]
>>> distinguish 4 True True commaPrecStyle (Just 2) [0,1,1.01,1.02,1.1,1.2]
["0.00","1.00","1.01","1.02","1.10","1.20"]

A common occurence is that significant figures being increased to enable textual uniqueness results in excess right zeros (after a decimal place). Consider:

>>> formats True False commaPrecStyle (Just 1) [0, 0.5, 1, 1.5, 2]
["0.0","0.5","1.0","2.0","2.0"]

Note that formats seeks With 1.5 rounding up to 2, the distinguish algorithm will increase the number of sigfigs to 2:

>>> distinguish 4 True False commaPrecStyle (Just 1) [0, 0.5, 1, 1.5, 2]
["0.00","0.50","1.00","1.50","2.00"]

The format can be simplified further by removing the excess right zeros from each formatted number:

>>> distinguish 4 True True commaPrecStyle (Just 2) [0, 0.5, 1, 1.5, 2]
["0.0","0.5","1.0","1.5","2.0"]

FormatN

data FormatN

Wrapper for the various formatting options.

>>> defaultFormatN
FormatN {fstyle = FSCommaPrec, sigFigs = Just 2, maxDistinguishIterations = 4, addLPad = True, cutRightZeros = True}

Constructors

FormatN

Fields

• fstyle :: FStyle
• sigFigs :: Maybe Int
• maxDistinguishIterations :: Int
• addLPad :: Bool
• cutRightZeros :: Bool

Instances

Generic FormatN

Defined in Data.FormatN

Associated Types

type Rep FormatN :: Type -> Type

Methods

from :: FormatN -> Rep FormatN x

to :: Rep FormatN x -> FormatN

Show FormatN

Defined in Data.FormatN

Methods

showsPrec :: Int -> FormatN -> ShowS

show :: FormatN -> String

showList :: [FormatN] -> ShowS

Eq FormatN

Defined in Data.FormatN

Methods

(==) :: FormatN -> FormatN -> Bool

(/=) :: FormatN -> FormatN -> Bool

type Rep FormatN

Defined in Data.FormatN

type Rep FormatN = D1 ('MetaData "FormatN" "Data.FormatN" "formatn-0.3.0.1-LVR3e3Pxxa85EhLYKcOmHS" 'False) (C1 ('MetaCons "FormatN" 'PrefixI 'True) ((S1 ('MetaSel ('Just "fstyle") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedStrict) (Rec0 FStyle) :*: S1 ('MetaSel ('Just "sigFigs") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedStrict) (Rec0 (Maybe Int))) :*: (S1 ('MetaSel ('Just "maxDistinguishIterations") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedStrict) (Rec0 Int) :*: (S1 ('MetaSel ('Just "addLPad") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedStrict) (Rec0 Bool) :*: S1 ('MetaSel ('Just "cutRightZeros") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedStrict) (Rec0 Bool)))))

defaultFormatN :: FormatN

The official FormatN

formatN :: FormatN -> Double -> Text

run a FormatN

>>> formatN defaultFormatN 1234
"1,200"

formatNs :: FormatN -> [Double] -> [Text]

Consistently format a list of numbers via using distinguish.

>>> formatNs defaultFormatN [0,1,1.01,1.02,1.1,1.2]
["0.00","1.00","1.01","1.02","1.10","1.20"]