[project @ 2002-02-12 15:17:13 by simonmar]

[ghc-hetmet.git] / ghc / lib / std / Ratio.lhs

diff --git a/ghc/lib/std/Ratio.lhs b/ghc/lib/std/Ratio.lhs
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-% ------------------------------------------------------------------------------
-% $Id: Ratio.lhs,v 1.7 2000/06/30 13:39:36 simonmar Exp $
-%
-% (c) The University of Glasgow, 1994-2000
-%
-
-\section[Ratio]{Module @Ratio@}
-
-Standard functions on rational numbers
-
-\begin{code}
-module 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
-
-    -- Ratio instances: 
-    --   (Integral a) => Eq   (Ratio a)
-    --   (Integral a) => Ord  (Ratio a)
-    --   (Integral a) => Num  (Ratio a)
-    --   (Integral a) => Real (Ratio a)
-    --   (Integral a) => Fractional (Ratio a)
-    --   (Integral a) => RealFrac (Ratio a)
-    --   (Integral a) => Enum    (Ratio a)
-    --   (Read a, Integral a) => Read (Ratio a)
-    --   (Integral a) => Show    (Ratio a)
-    --
-    -- Implementation checked wrt. Haskell 98 lib report, 1/99.
-
-  ) where
-\end{code}
-
-
-#ifndef __HUGS__
-
-\begin{code}
-import Prelude         -- To generate the dependencies
-import PrelReal                -- The basic defns for Ratio
-\end{code}
-
-%*********************************************************
-%*                                                     *
-\subsection{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
-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.
-
-\begin{code}
-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''
-
-\end{code}
-
-#else
-
-\begin{code}
--- Hugs already has this functionally inside its prelude
-\end{code}
-
-#endif
-
-
-