I'd like to
take more digits of the Prelude
Prelude> take 4 $ show pi "3.14"
Prelude> take 17 $ show pi "3.141592653589793" Prelude> take 170 $ show pi "3.141592653589793"
pi constant just stored this truncated? Is there an option in show to print to string more digits?
pi is a method of the
class Fractional a => Floating a where pi :: a ...
pi is polymorphic, and it is up to the implementor of the instance to define it appropriately.
The most common instances are
Double which have limited precision:
Prelude> pi :: Float 3.1415927 Prelude> pi :: Double 3.141592653589793
but nothing is stopping you from using other packages, like
long-double which gives a few more bits on some systems:
Numeric.LongDouble> pi :: LongDouble 3.1415926535897932385
rounded which gives arbitrarily many bits of precision via the MPFR software implementation:
Numeric.Rounded> pi :: Rounded TowardNearest 100 3.1415926535897932384626433832793 Numeric.Rounded> pi :: Rounded TowardNearest 500 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081283
numbers package provides a pure-Haskell implementation of constructive (exact) real numbers, which can be shown to as many digits as desired:
Data.Number.CReal> showCReal 100 pi "3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117068"
You can also have lower precision with the
half package, maybe interoperable with GPU:
Numeric.Half> pi :: Half 3.140625
When you evaluate
pi without giving a specific type, the interpreter's defaulting rules come into play.
Each defaultable variable is replaced by the first type in the default list that is an instance of all the ambiguous variable’s classes. ... If no default declaration is given in a module then it assumed to be:
default (Integer, Double)-- https://www.haskell.org/onlinereport/haskell2010/haskellch4.html#x10-790004.3.4
Prelude> :t pi pi :: Floating a => a
Integer is not
Double is, so the ambiguous type gets resolved by defaulting to
Double. You can get more information by enabling
Prelude> :set -Wtype-defaults Prelude> pi <interactive>:2:1: warning: [-Wtype-defaults] • Defaulting the following constraints to type ‘Double’ (Show a0) arising from a use of ‘print’ at <interactive>:2:1-2 (Floating a0) arising from a use of ‘it’ at <interactive>:2:1-2 • In a stmt of an interactive GHCi command: print it 3.141592653589793
(Note: I wrote the
long-double package and am the current maintainer of