Numeric

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

Showing

showSigned Source

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"

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

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

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