+{-# LANGUAGE CPP #-}
+
-----------------------------------------------------------------------------
---
+-- |
-- Module : Data.Ratio
-- Copyright : (c) The University of Glasgow 2001
--- License : BSD-style (see the file libraries/core/LICENSE)
+-- License : BSD-style (see the file libraries/base/LICENSE)
--
-- Maintainer : libraries@haskell.org
--- Stability : provisional
+-- Stability : stable
-- Portability : portable
--
--- $Id: Ratio.hs,v 1.1 2001/06/28 14:15:02 simonmar Exp $
---
-- Standard functions on rational numbers
--
-----------------------------------------------------------------------------
module Data.Ratio
( Ratio
, Rational
- , (%) -- :: (Integral a) => a -> a -> Ratio a
- , numerator -- :: (Integral a) => Ratio a -> a
- , denominator -- :: (Integral a) => Ratio a -> a
- , approxRational -- :: (RealFrac a) => a -> a -> Rational
+ , (%) -- :: (Integral a) => a -> a -> Ratio a
+ , numerator -- :: (Integral a) => Ratio a -> a
+ , denominator -- :: (Integral a) => Ratio a -> a
+ , approxRational -- :: (RealFrac a) => a -> a -> Rational
-- Ratio instances:
-- (Integral a) => Eq (Ratio a)
-- (Integral a) => Real (Ratio a)
-- (Integral a) => Fractional (Ratio a)
-- (Integral a) => RealFrac (Ratio a)
- -- (Integral a) => Enum (Ratio a)
+ -- (Integral a) => Enum (Ratio a)
-- (Read a, Integral a) => Read (Ratio a)
- -- (Integral a) => Show (Ratio a)
+ -- (Integral a) => Show (Ratio a)
) where
import Prelude
#ifdef __GLASGOW_HASKELL__
-import GHC.Real -- The basic defns for Ratio
+import GHC.Real -- The basic defns for Ratio
#endif
+#ifdef __HUGS__
+import Hugs.Prelude(Ratio(..), (%), numerator, denominator)
+#endif
+
+#ifdef __NHC__
+import Ratio (Ratio(..), (%), numerator, denominator, approxRational)
+#else
+
-- -----------------------------------------------------------------------------
-- approxRational
--- @approxRational@, applied to two real fractional numbers x and epsilon,
--- returns the simplest rational number within epsilon of x. A rational
--- number n%d in reduced form is said to be simpler than another n'%d' if
--- abs n <= abs n' && d <= d'. Any real interval contains a unique
--- simplest rational; here, for simplicity, we assume a closed rational
+-- | 'approxRational', applied to two real fractional numbers @x@ and @epsilon@,
+-- returns the simplest rational number within @epsilon@ of @x@.
+-- A rational number @y@ is said to be /simpler/ than another @y'@ if
+--
+-- * @'abs' ('numerator' y) <= 'abs' ('numerator' y')@, and
+--
+-- * @'denominator' y <= 'denominator' y'@.
+--
+-- Any real interval contains a unique simplest rational;
+-- in particular, note that @0\/1@ is the simplest rational of all.
+
+-- Implementation details: Here, for simplicity, we assume a closed rational
-- interval. If such an interval includes at least one whole number, then
-- the simplest rational is the absolutely least whole number. Otherwise,
-- the bounds are of the form q%1 + r%d and q%1 + r'%d', where abs r < d
-- and abs r' < d', and the simplest rational is q%1 + the reciprocal of
-- the simplest rational between d'%r' and d%r.
-approxRational :: (RealFrac a) => a -> a -> Rational
-approxRational rat eps = simplest (rat-eps) (rat+eps)
- where simplest x y | y < x = simplest y x
- | x == y = xr
- | x > 0 = simplest' n d n' d'
- | y < 0 = - simplest' (-n') d' (-n) d
- | otherwise = 0 :% 1
- where xr = toRational x
- n = numerator xr
- d = denominator xr
- nd' = toRational y
- n' = numerator nd'
- d' = denominator nd'
-
- simplest' n d n' d' -- assumes 0 < n%d < n'%d'
- | r == 0 = q :% 1
- | q /= q' = (q+1) :% 1
- | otherwise = (q*n''+d'') :% n''
- where (q,r) = quotRem n d
- (q',r') = quotRem n' d'
- nd'' = simplest' d' r' d r
- n'' = numerator nd''
- d'' = denominator nd''
+approxRational :: (RealFrac a) => a -> a -> Rational
+approxRational rat eps = simplest (rat-eps) (rat+eps)
+ where simplest x y | y < x = simplest y x
+ | x == y = xr
+ | x > 0 = simplest' n d n' d'
+ | y < 0 = - simplest' (-n') d' (-n) d
+ | otherwise = 0 :% 1
+ where xr = toRational x
+ n = numerator xr
+ d = denominator xr
+ nd' = toRational y
+ n' = numerator nd'
+ d' = denominator nd'
+ simplest' n d n' d' -- assumes 0 < n%d < n'%d'
+ | r == 0 = q :% 1
+ | q /= q' = (q+1) :% 1
+ | otherwise = (q*n''+d'') :% n''
+ where (q,r) = quotRem n d
+ (q',r') = quotRem n' d'
+ nd'' = simplest' d' r' d r
+ n'' = numerator nd''
+ d'' = denominator nd''
+#endif
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