38 Numeric
Date: 2010-07-20 13:11:00

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## Chapter 38
Numeric

module Numeric (
showSigned, showIntAtBase, showInt, showHex, showOct, showEFloat,
showFFloat, showGFloat, showFloat, floatToDigits, readSigned, readInt,
readDec, readOct, readHex, readFloat, lexDigits, fromRat
) where

### 38.1 Showing

showSigned

  :: | 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.

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.

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.

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

### 38.2 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

  :: | 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 :: Num a => ReadS a

  Read an unsigned number in decimal notation.

readOct :: Num a => ReadS a

  Read an unsigned number in octal notation.

readHex :: Num a => ReadS a

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

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.

### 38.3 Miscellaneous

fromRat :: RealFloat a => Rational -> a

  Converts a Rational value into any type in class RealFloat.

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