Numeric

base-4.9.0.0: Basic libraries

Copyright | (c) The University of Glasgow 2002
License | BSD-style (see the file libraries/base/LICENSE)
Maintainer | libraries@haskell.org
Stability | provisional
Portability | portable
Safe Haskell | Trustworthy
Language | Haskell2010

Numeric

Contents

- Showing
- Reading
- Miscellaneous

Description

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

Synopsis

- showSigned :: Real a => (a -> ShowS) -> Int -> a -> ShowS
- showIntAtBase :: (Integral a, Show a) => a -> (Int -> Char) -> a -> ShowS
- showInt :: Integral a => a -> ShowS
- showHex :: (Integral a, Show a) => a -> ShowS
- showOct :: (Integral a, Show a) => a -> ShowS
- showEFloat :: RealFloat a => Maybe Int -> a -> ShowS
- showFFloat :: RealFloat a => Maybe Int -> a -> ShowS
- showGFloat :: RealFloat a => Maybe Int -> a -> ShowS
- showFFloatAlt :: RealFloat a => Maybe Int -> a -> ShowS
- showGFloatAlt :: RealFloat a => Maybe Int -> a -> ShowS
- showFloat :: RealFloat a => a -> ShowS
- floatToDigits :: RealFloat a => Integer -> a -> ([Int], Int)
- readSigned :: Real a => ReadS a -> ReadS a
- readInt :: Num a => a -> (Char -> Bool) -> (Char -> Int) -> ReadS a
- readDec :: (Eq a, Num a) => ReadS a
- readOct :: (Eq a, Num a) => ReadS a
- readHex :: (Eq a, Num a) => ReadS a
- readFloat :: RealFrac a => ReadS a
- lexDigits :: ReadS String
- fromRat :: RealFloat a => Rational -> a
- class Fractional a => Floating a where

# Showing

showSigned Source

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, Show a) => a -> (Int -> Char) -> a -> ShowS Source

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 Source

Show non-negative `Integral` numbers in base 10.

showHex :: (Integral a, Show a) => a -> ShowS Source

Show non-negative `Integral` numbers in base 16.

showOct :: (Integral a, Show a) => a -> ShowS Source

Show non-negative `Integral` numbers in base 8.

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

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 Source

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 Source

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 Source

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: 4.7.0.0

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

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: 4.7.0.0

showFloat :: RealFloat a => a -> ShowS Source

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.

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

`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 Source

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

readInt Source

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.

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

Read an unsigned number in decimal notation.

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

Read an unsigned number in octal notation.

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

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

readFloat :: RealFrac a => ReadS a Source

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

lexDigits :: ReadS String Source

Reads a non-empty string of decimal digits.

# Miscellaneous

fromRat :: RealFloat a => Rational -> a Source

Converts a `Rational` value into any type in class `RealFloat`.

class Fractional a => Floating a where Source

Trigonometric and hyperbolic functions and related functions.

Minimal complete definition

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

Methods

pi :: a Source

exp, log, sqrt :: a -> a Source

(**), logBase :: a -> a -> a infixr 8 Source

sin, cos, tan :: a -> a Source

asin, acos, atan :: a -> a Source

sinh, cosh, tanh :: a -> a Source

asinh, acosh, atanh :: a -> a Source

log1p :: a -> a Source

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

Since: 4.9.0.0

expm1 :: a -> a Source

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

Since: 4.9.0.0

log1pexp :: a -> a Source

``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: 4.9.0.0

log1mexp :: a -> a Source

``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: 4.9.0.0

Instances

Floating Double |
Methods pi :: Double Source exp :: Double -> Double Source log :: Double -> Double Source sqrt :: Double -> Double Source (**) :: Double -> Double -> Double Source logBase :: Double -> Double -> Double Source sin :: Double -> Double Source cos :: Double -> Double Source tan :: Double -> Double Source asin :: Double -> Double Source acos :: Double -> Double Source atan :: Double -> Double Source sinh :: Double -> Double Source cosh :: Double -> Double Source tanh :: Double -> Double Source asinh :: Double -> Double Source acosh :: Double -> Double Source atanh :: Double -> Double Source log1p :: Double -> Double Source expm1 :: Double -> Double Source log1pexp :: Double -> Double Source log1mexp :: Double -> Double Source
Floating Float |
Methods pi :: Float Source exp :: Float -> Float Source log :: Float -> Float Source sqrt :: Float -> Float Source (**) :: Float -> Float -> Float Source logBase :: Float -> Float -> Float Source sin :: Float -> Float Source cos :: Float -> Float Source tan :: Float -> Float Source asin :: Float -> Float Source acos :: Float -> Float Source atan :: Float -> Float Source sinh :: Float -> Float Source cosh :: Float -> Float Source tanh :: Float -> Float Source asinh :: Float -> Float Source acosh :: Float -> Float Source atanh :: Float -> Float Source log1p :: Float -> Float Source expm1 :: Float -> Float Source log1pexp :: Float -> Float Source log1mexp :: Float -> Float Source
Floating CDouble |
Methods pi :: CDouble Source exp :: CDouble -> CDouble Source log :: CDouble -> CDouble Source sqrt :: CDouble -> CDouble Source (**) :: CDouble -> CDouble -> CDouble Source logBase :: CDouble -> CDouble -> CDouble Source sin :: CDouble -> CDouble Source cos :: CDouble -> CDouble Source tan :: CDouble -> CDouble Source asin :: CDouble -> CDouble Source acos :: CDouble -> CDouble Source atan :: CDouble -> CDouble Source sinh :: CDouble -> CDouble Source cosh :: CDouble -> CDouble Source tanh :: CDouble -> CDouble Source asinh :: CDouble -> CDouble Source acosh :: CDouble -> CDouble Source atanh :: CDouble -> CDouble Source log1p :: CDouble -> CDouble Source expm1 :: CDouble -> CDouble Source log1pexp :: CDouble -> CDouble Source log1mexp :: CDouble -> CDouble Source
Floating CFloat |
Methods pi :: CFloat Source exp :: CFloat -> CFloat Source log :: CFloat -> CFloat Source sqrt :: CFloat -> CFloat Source (**) :: CFloat -> CFloat -> CFloat Source logBase :: CFloat -> CFloat -> CFloat Source sin :: CFloat -> CFloat Source cos :: CFloat -> CFloat Source tan :: CFloat -> CFloat Source asin :: CFloat -> CFloat Source acos :: CFloat -> CFloat Source atan :: CFloat -> CFloat Source sinh :: CFloat -> CFloat Source cosh :: CFloat -> CFloat Source tanh :: CFloat -> CFloat Source asinh :: CFloat -> CFloat Source acosh :: CFloat -> CFloat Source atanh :: CFloat -> CFloat Source log1p :: CFloat -> CFloat Source expm1 :: CFloat -> CFloat Source log1pexp :: CFloat -> CFloat Source log1mexp :: CFloat -> CFloat Source
RealFloat a => Floating (Complex a) |
Methods pi :: Complex a Source exp :: Complex a -> Complex a Source log :: Complex a -> Complex a Source sqrt :: Complex a -> Complex a Source (**) :: Complex a -> Complex a -> Complex a Source logBase :: Complex a -> Complex a -> Complex a Source sin :: Complex a -> Complex a Source cos :: Complex a -> Complex a Source tan :: Complex a -> Complex a Source asin :: Complex a -> Complex a Source acos :: Complex a -> Complex a Source atan :: Complex a -> Complex a Source sinh :: Complex a -> Complex a Source cosh :: Complex a -> Complex a Source tanh :: Complex a -> Complex a Source asinh :: Complex a -> Complex a Source acosh :: Complex a -> Complex a Source atanh :: Complex a -> Complex a Source log1p :: Complex a -> Complex a Source expm1 :: Complex a -> Complex a Source log1pexp :: Complex a -> Complex a Source log1mexp :: Complex a -> Complex a Source