| 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 | Safe |
| Language | Haskell2010 |
Numeric
Contents
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 :: a -> a
- log :: a -> a
- sqrt :: a -> a
- (**) :: a -> a -> a
- 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
- expm1 :: a -> a
- log1pexp :: a -> a
- log1mexp :: a -> a
Showing
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.
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 valdigs is Nothing,
the value is shown to full precision; if digs is Just dd 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 valdigs is Nothing,
the value is shown to full precision; if digs is Just dd 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 valdigs is Nothing,
the value is shown to full precision; if digs is Just dd 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"
Since: base-4.11.0.0
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.
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 |
| -> 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.
Miscellaneous
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 bexp (fromInteger 0)=fromInteger 1
Minimal complete definition
pi, exp, log, sin, cos, asin, acos, atan, sinh, cosh, asinh, acosh, atanh
Methods
(**) :: a -> a -> a infixr 8 Source #
logBase :: a -> a -> a Source #
log1p xlog (1 + x)x if possible.
Since: base-4.9.0.0
expm1 xexp x - 1x if possible.
Since: base-4.9.0.0