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 => a -> (Int -> Char) -> a -> ShowS
showInt :: Integral a => a -> ShowS
showBin :: Integral a => a -> ShowS
showHex :: Integral a => a -> ShowS
showOct :: Integral 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
showHFloat :: 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
readBin :: (Eq a, Num a) => 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
- pi :: a
- exp, log, sqrt :: a -> a
- (**), logBase :: a -> a -> a
- sin, cos, tan :: a -> a
- asin, acos, atan :: a -> a
- sinh, cosh, tanh :: a -> a
- asinh, acosh, atanh :: a -> a
- log1p :: a -> a
- expm1 :: a -> a
- log1pexp :: a -> a
- log1mexp :: a -> a

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 => 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.

showBin :: Integral a => a -> ShowS Source #

Show non-negative Integral numbers in base 2.

showHex :: Integral a => a -> ShowS Source #

Show non-negative Integral numbers in base 16.

showOct :: Integral 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: base-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: base-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.

showHFloat :: RealFloat a => a -> ShowS Source #

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) 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

```
n >= 1
```
```
x = 0.d1d2...dn * (base**e)
```
```
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.

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

Read an unsigned number in binary notation.

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

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

Read an unsigned number in decimal notation.

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

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

Read an unsigned number in octal notation.

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

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

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

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

readFloat :: RealFrac a => ReadS a Source #

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

Note that this function takes time linear in the magnitude of its input which can scale exponentially with input size (e.g. "1e100000000" is a very large number while having a very small textual form). For this reason, users should take care to avoid using this function on untrusted input. Users needing to parse floating point values (e.g. Float ) are encouraged to instead use read, which does not suffer from this issue.

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.

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 Source #

exp :: a -> a Source #

log :: a -> a Source #

sqrt :: a -> a Source #

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

logBase :: a -> a -> a Source #

sin :: a -> a Source #

cos :: a -> a Source #

tan :: a -> a Source #

asin :: a -> a Source #

acos :: a -> a Source #

atan :: a -> a Source #

sinh :: a -> a Source #

cosh :: a -> a Source #

tanh :: a -> a Source #

asinh :: a -> a Source #

acosh :: a -> a Source #

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: base-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: base-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: base-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 .