Numeric

Odds and ends, mostly functions for reading and showing RealFloat-like kind of values.

Showing

showSigned

Arguments

:: Real a

=> (a -> ShowS)

a function that can show unsigned values

-> Int

the precedence of the enclosing context

-> a

the value to show

-> ShowS

Converts a possibly-negative Real value to a string.

showIntAtBase :: Integral a => a -> (Int -> Char) -> a -> ShowS

Shows a non-negative Integral number using the base specified by the first argument, and the character representation specified by the second.

showInt :: Integral a => a -> ShowS

Show non-negative Integral numbers in base 10.

showBin :: Integral a => a -> ShowS

Show non-negative Integral numbers in base 2.

showHex :: Integral a => a -> ShowS

Show non-negative Integral numbers in base 16.

showOct :: Integral a => a -> ShowS

Show non-negative Integral numbers in base 8.

showEFloat :: RealFloat a => Maybe Int -> a -> ShowS

Show a signed RealFloat value using scientific (exponential) notation (e.g. 2.45e2, 1.5e-3).

In the call showEFloat digs val, if digs is Nothing, the value is shown to full precision; if digs is Just d, then at most d digits after the decimal point are shown.

showFFloat :: RealFloat a => Maybe Int -> a -> ShowS

Show a signed RealFloat value using standard decimal notation (e.g. 245000, 0.0015).

In the call showFFloat digs val, if digs is Nothing, the value is shown to full precision; if digs is Just d, then at most d digits after the decimal point are shown.

showGFloat :: RealFloat a => Maybe Int -> a -> ShowS

Show a signed RealFloat value using standard decimal notation for arguments whose absolute value lies between 0.1 and 9,999,999, and scientific notation otherwise.

In the call showGFloat digs val, if digs is Nothing, the value is shown to full precision; if digs is Just d, then at most d digits after the decimal point are shown.

showFFloatAlt :: RealFloat a => Maybe Int -> a -> ShowS

Show a signed RealFloat value using standard decimal notation (e.g. 245000, 0.0015).

This behaves as showFFloat, except that a decimal point is always guaranteed, even if not needed.

Since: base-4.7.0.0

showGFloatAlt :: RealFloat a => Maybe Int -> a -> ShowS

Show a signed RealFloat value using standard decimal notation for arguments whose absolute value lies between 0.1 and 9,999,999, and scientific notation otherwise.

This behaves as showFFloat, except that a decimal point is always guaranteed, even if not needed.

Since: base-4.7.0.0

showFloat :: RealFloat a => a -> ShowS

Show a signed RealFloat value to full precision using standard decimal notation for arguments whose absolute value lies between 0.1 and 9,999,999, and scientific notation otherwise.

showHFloat :: RealFloat a => a -> ShowS

Show a floating-point value in the hexadecimal format, similar to the %a specifier in C's printf.

>>> showHFloat (212.21 :: Double) ""
"0x1.a86b851eb851fp7"
>>> showHFloat (-12.76 :: Float) ""
"-0x1.9851ecp3"
>>> showHFloat (-0 :: Double) ""
"-0x0p+0"

floatToDigits :: RealFloat a => Integer -> a -> ([Int], Int)

floatToDigits takes a base and a non-negative RealFloat number, and returns a list of digits and an exponent. In particular, if x>=0, and

floatToDigits base x = ([d1,d2,...,dn], e)

then

1. n >= 1

2. x = 0.d1d2...dn * (base**e)

3. 0 <= di <= base-1

Reading

NB: readInt is the 'dual' of showIntAtBase, and readDec is the `dual' of showInt. The inconsistent naming is a historical accident.

readSigned :: Real a => ReadS a -> ReadS a

Reads a signed Real value, given a reader for an unsigned value.

readInt

Arguments

:: Num a

=> a

the base

-> (Char -> Bool)

a predicate distinguishing valid digits in this base

-> (Char -> Int)

a function converting a valid digit character to an Int

-> ReadS a

Reads an unsigned integral value in an arbitrary base.

readBin :: (Eq a, Num a) => ReadS a

Read an unsigned number in binary notation.

>>> readBin "10011"
[(19,"")]

readDec :: (Eq a, Num a) => ReadS a

Read an unsigned number in decimal notation.

>>> readDec "0644"
[(644,"")]

readOct :: (Eq a, Num a) => ReadS a

Read an unsigned number in octal notation.

>>> readOct "0644"
[(420,"")]

readHex :: (Eq a, Num a) => ReadS a

Read an unsigned number in hexadecimal notation. Both upper or lower case letters are allowed.

>>> readHex "deadbeef"
[(3735928559,"")]

readFloat :: RealFrac a => ReadS a

Reads an unsigned RealFrac value, expressed in decimal scientific notation.

lexDigits :: ReadS String

Reads a non-empty string of decimal digits.

Miscellaneous

fromRat :: RealFloat a => Rational -> a

Converts a Rational value into any type in class RealFloat.

class Fractional a => Floating a where

Trigonometric and hyperbolic functions and related functions.

The Haskell Report defines no laws for Floating. However, (+), (*) and exp are customarily expected to define an exponential field and have the following properties:

• exp (a + b) = exp a * exp b
• exp (fromInteger 0) = fromInteger 1

Minimal complete definition

pi, exp, log, sin, cos, asin, acos, atan, sinh, cosh, asinh, acosh, atanh

Methods

pi :: a

exp :: a -> a

log :: a -> a

sqrt :: a -> a

(**) :: a -> a -> a infixr 8

logBase :: a -> a -> a

sin :: a -> a

cos :: a -> a

tan :: a -> a

asin :: a -> a

acos :: a -> a

atan :: a -> a

sinh :: a -> a

cosh :: a -> a

tanh :: a -> a

asinh :: a -> a

acosh :: a -> a

atanh :: a -> a

log1p :: a -> a

log1p x computes log (1 + x), but provides more precise results for small (absolute) values of x if possible.

Since: base-4.9.0.0

expm1 :: a -> a

expm1 x computes exp x - 1, but provides more precise results for small (absolute) values of x if possible.

Since: base-4.9.0.0

log1pexp :: a -> a

log1pexp x computes log (1 + exp x), but provides more precise results if possible.

Examples:

• if x is a large negative number, log (1 + exp x) will be imprecise for the reasons given in log1p.
• if exp x is close to -1, log (1 + exp x) will be imprecise for the reasons given in expm1.

Since: base-4.9.0.0

log1mexp :: a -> a

log1mexp x computes log (1 - exp x), but provides more precise results if possible.

Examples:

• if x is a large negative number, log (1 - exp x) will be imprecise for the reasons given in log1p.
• if exp x is close to 1, log (1 - exp x) will be imprecise for the reasons given in expm1.

Since: base-4.9.0.0

Instances

Floating CDouble

Defined in Foreign.C.Types

Methods

pi :: CDouble

exp :: CDouble -> CDouble

log :: CDouble -> CDouble

sqrt :: CDouble -> CDouble

(**) :: CDouble -> CDouble -> CDouble

logBase :: CDouble -> CDouble -> CDouble

sin :: CDouble -> CDouble

cos :: CDouble -> CDouble

tan :: CDouble -> CDouble

asin :: CDouble -> CDouble

acos :: CDouble -> CDouble

atan :: CDouble -> CDouble

sinh :: CDouble -> CDouble

cosh :: CDouble -> CDouble

tanh :: CDouble -> CDouble

asinh :: CDouble -> CDouble

acosh :: CDouble -> CDouble

atanh :: CDouble -> CDouble

log1p :: CDouble -> CDouble

expm1 :: CDouble -> CDouble

log1pexp :: CDouble -> CDouble

log1mexp :: CDouble -> CDouble

Floating CFloat

Defined in Foreign.C.Types

Methods

pi :: CFloat

exp :: CFloat -> CFloat

log :: CFloat -> CFloat

sqrt :: CFloat -> CFloat

(**) :: CFloat -> CFloat -> CFloat

logBase :: CFloat -> CFloat -> CFloat

sin :: CFloat -> CFloat

cos :: CFloat -> CFloat

tan :: CFloat -> CFloat

asin :: CFloat -> CFloat

acos :: CFloat -> CFloat

atan :: CFloat -> CFloat

sinh :: CFloat -> CFloat

cosh :: CFloat -> CFloat

tanh :: CFloat -> CFloat

asinh :: CFloat -> CFloat

acosh :: CFloat -> CFloat

atanh :: CFloat -> CFloat

log1p :: CFloat -> CFloat

expm1 :: CFloat -> CFloat

log1pexp :: CFloat -> CFloat

log1mexp :: CFloat -> CFloat

Floating Double

Since: base-2.1

Defined in GHC.Float

Methods

pi :: Double

exp :: Double -> Double

log :: Double -> Double

sqrt :: Double -> Double

(**) :: Double -> Double -> Double

logBase :: Double -> Double -> Double

sin :: Double -> Double

cos :: Double -> Double

tan :: Double -> Double

asin :: Double -> Double

acos :: Double -> Double

atan :: Double -> Double

sinh :: Double -> Double

cosh :: Double -> Double

tanh :: Double -> Double

asinh :: Double -> Double

acosh :: Double -> Double

atanh :: Double -> Double

log1p :: Double -> Double

expm1 :: Double -> Double

log1pexp :: Double -> Double

log1mexp :: Double -> Double

Floating Float

Since: base-2.1

Defined in GHC.Float

Methods

pi :: Float

exp :: Float -> Float

log :: Float -> Float

sqrt :: Float -> Float

(**) :: Float -> Float -> Float

logBase :: Float -> Float -> Float

sin :: Float -> Float

cos :: Float -> Float

tan :: Float -> Float

asin :: Float -> Float

acos :: Float -> Float

atan :: Float -> Float

sinh :: Float -> Float

cosh :: Float -> Float

tanh :: Float -> Float

asinh :: Float -> Float

acosh :: Float -> Float

atanh :: Float -> Float

log1p :: Float -> Float

expm1 :: Float -> Float

log1pexp :: Float -> Float

log1mexp :: Float -> Float

RealFloat a => Floating (Complex a)

Since: base-2.1

Defined in Data.Complex

Methods

pi :: Complex a

exp :: Complex a -> Complex a

log :: Complex a -> Complex a

sqrt :: Complex a -> Complex a

(**) :: Complex a -> Complex a -> Complex a

logBase :: Complex a -> Complex a -> Complex a

sin :: Complex a -> Complex a

cos :: Complex a -> Complex a

tan :: Complex a -> Complex a

asin :: Complex a -> Complex a

acos :: Complex a -> Complex a

atan :: Complex a -> Complex a

sinh :: Complex a -> Complex a

cosh :: Complex a -> Complex a

tanh :: Complex a -> Complex a

asinh :: Complex a -> Complex a

acosh :: Complex a -> Complex a

atanh :: Complex a -> Complex a

log1p :: Complex a -> Complex a

expm1 :: Complex a -> Complex a

log1pexp :: Complex a -> Complex a

log1mexp :: Complex a -> Complex a

Floating a => Floating (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

pi :: Identity a

exp :: Identity a -> Identity a

log :: Identity a -> Identity a

sqrt :: Identity a -> Identity a

(**) :: Identity a -> Identity a -> Identity a

logBase :: Identity a -> Identity a -> Identity a

sin :: Identity a -> Identity a

cos :: Identity a -> Identity a

tan :: Identity a -> Identity a

asin :: Identity a -> Identity a

acos :: Identity a -> Identity a

atan :: Identity a -> Identity a

sinh :: Identity a -> Identity a

cosh :: Identity a -> Identity a

tanh :: Identity a -> Identity a

asinh :: Identity a -> Identity a

acosh :: Identity a -> Identity a

atanh :: Identity a -> Identity a

log1p :: Identity a -> Identity a

expm1 :: Identity a -> Identity a

log1pexp :: Identity a -> Identity a

log1mexp :: Identity a -> Identity a

Floating a => Floating (Down a)

Since: base-4.14.0.0

Defined in Data.Ord

Methods

pi :: Down a

exp :: Down a -> Down a

log :: Down a -> Down a

sqrt :: Down a -> Down a

(**) :: Down a -> Down a -> Down a

logBase :: Down a -> Down a -> Down a

sin :: Down a -> Down a

cos :: Down a -> Down a

tan :: Down a -> Down a

asin :: Down a -> Down a

acos :: Down a -> Down a

atan :: Down a -> Down a

sinh :: Down a -> Down a

cosh :: Down a -> Down a

tanh :: Down a -> Down a

asinh :: Down a -> Down a

acosh :: Down a -> Down a

atanh :: Down a -> Down a

log1p :: Down a -> Down a

expm1 :: Down a -> Down a

log1pexp :: Down a -> Down a

log1mexp :: Down a -> Down a

Floating a => Floating (Op a b)

Defined in Data.Functor.Contravariant

Methods

pi :: Op a b

exp :: Op a b -> Op a b

log :: Op a b -> Op a b

sqrt :: Op a b -> Op a b

(**) :: Op a b -> Op a b -> Op a b

logBase :: Op a b -> Op a b -> Op a b

sin :: Op a b -> Op a b

cos :: Op a b -> Op a b

tan :: Op a b -> Op a b

asin :: Op a b -> Op a b

acos :: Op a b -> Op a b

atan :: Op a b -> Op a b

sinh :: Op a b -> Op a b

cosh :: Op a b -> Op a b

tanh :: Op a b -> Op a b

asinh :: Op a b -> Op a b

acosh :: Op a b -> Op a b

atanh :: Op a b -> Op a b

log1p :: Op a b -> Op a b

expm1 :: Op a b -> Op a b

log1pexp :: Op a b -> Op a b

log1mexp :: Op a b -> Op a b

Floating a => Floating (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

pi :: Const a b

exp :: Const a b -> Const a b

log :: Const a b -> Const a b

sqrt :: Const a b -> Const a b

(**) :: Const a b -> Const a b -> Const a b

logBase :: Const a b -> Const a b -> Const a b

sin :: Const a b -> Const a b

cos :: Const a b -> Const a b

tan :: Const a b -> Const a b

asin :: Const a b -> Const a b

acos :: Const a b -> Const a b

atan :: Const a b -> Const a b

sinh :: Const a b -> Const a b

cosh :: Const a b -> Const a b

tanh :: Const a b -> Const a b

asinh :: Const a b -> Const a b

acosh :: Const a b -> Const a b

atanh :: Const a b -> Const a b

log1p :: Const a b -> Const a b

expm1 :: Const a b -> Const a b

log1pexp :: Const a b -> Const a b

log1mexp :: Const a b -> Const a b