-- Module : GHC.Float
-- Copyright : (c) The University of Glasgow 1994-2002
-- License : see libraries/base/LICENSE
---
+--
-- Maintainer : cvs-ghc@haskell.org
-- Stability : internal
-- Portability : non-portable (GHC Extensions)
atan2 y x
| x > 0 = atan (y/x)
| x == 0 && y > 0 = pi/2
- | x < 0 && y > 0 = pi + atan (y/x)
+ | x < 0 && y > 0 = pi + atan (y/x)
|(x <= 0 && y < 0) ||
(x < 0 && isNegativeZero y) ||
(isNegativeZero x && isNegativeZero y)
instance Show Float where
showsPrec x = showSignedFloat showFloat x
- showList = showList__ (showsPrec 0)
+ showList = showList__ (showsPrec 0)
\end{code}
%*********************************************************
instance Show Double where
showsPrec x = showSignedFloat showFloat x
- showList = showList__ (showsPrec 0)
+ showList = showList__ (showsPrec 0)
\end{code}
%*********************************************************
NOTE: The instances for Float and Double do not make use of the default
methods for @enumFromTo@ and @enumFromThenTo@, as these rely on there being
-a `non-lossy' conversion to and from Ints. Instead we make use of the
+a `non-lossy' conversion to and from Ints. Instead we make use of the
1.2 default methods (back in the days when Enum had Ord as a superclass)
for these (@numericEnumFromTo@ and @numericEnumFromThenTo@ below.)
\begin{code}
-- | Show a signed 'RealFloat' value to full precision
--- using standard decimal notation for arguments whose absolute value lies
+-- using standard decimal notation for arguments whose absolute value lies
-- between @0.1@ and @9,999,999@, and scientific notation otherwise.
showFloat :: (RealFloat a) => a -> ShowS
showFloat x = showString (formatRealFloat FFGeneric Nothing x)
| isInfinite x = if x < 0 then "-Infinity" else "Infinity"
| x < 0 || isNegativeZero x = '-':doFmt fmt (floatToDigits (toInteger base) (-x))
| otherwise = doFmt fmt (floatToDigits (toInteger base) x)
- where
+ where
base = 10
doFmt format (is, e) =
-- This version uses a much slower logarithm estimator. It should be improved.
-- | 'floatToDigits' takes a base and a non-negative 'RealFloat' number,
--- and returns a list of digits and an exponent.
+-- and returns a list of digits and an exponent.
-- In particular, if @x>=0@, and
--
-- > floatToDigits base x = ([d1,d2,...,dn], e)
floatToDigits :: (RealFloat a) => Integer -> a -> ([Int], Int)
floatToDigits _ 0 = ([0], 0)
floatToDigits base x =
- let
+ let
(f0, e0) = decodeFloat x
(minExp0, _) = floatRange x
p = floatDigits x
minExp = minExp0 - p -- the real minimum exponent
-- Haskell requires that f be adjusted so denormalized numbers
-- will have an impossibly low exponent. Adjust for this.
- (f, e) =
+ (f, e) =
let n = minExp - e0 in
if n > 0 then (f0 `div` (b^n), e0+n) else (f0, e0)
(r, s, mUp, mDn) =
(f*2, b^(-e)*2, 1, 1)
k :: Int
k =
- let
+ let
k0 :: Int
k0 =
if b == 2 && base == 10 then
-- Haskell promises that p-1 <= logBase b f < p.
(p - 1 + e0) * 3 `div` 10
else
- -- f :: Integer, log :: Float -> Float,
+ -- f :: Integer, log :: Float -> Float,
-- ceiling :: Float -> Int
ceiling ((log (fromInteger (f+1) :: Float) +
fromIntegral e * log (fromInteger b)) /
(False, True) -> dn+1 : ds
(True, True) -> if rn' * 2 < sN then dn : ds else dn+1 : ds
(False, False) -> gen (dn:ds) rn' sN mUpN' mDnN'
-
- rds =
+
+ rds =
if k >= 0 then
gen [] r (s * expt base k) mUp mDn
else
fromRat x = x'
where x' = f e
--- If the exponent of the nearest floating-point number to x
+-- If the exponent of the nearest floating-point number to x
-- is e, then the significand is the integer nearest xb^(-e),
-- where b is the floating-point radix. We start with a good
-- guess for e, and if it is correct, the exponent of the
-- Scale x until xMin <= x < xMax, or p (the exponent) <= minExp.
scaleRat :: Rational -> Int -> Rational -> Rational -> Int -> Rational -> (Rational, Int)
-scaleRat b minExp xMin xMax p x
+scaleRat b minExp xMin xMax p x
| p <= minExp = (x, p)
| x >= xMax = scaleRat b minExp xMin xMax (p+1) (x/b)
| x < xMin = scaleRat b minExp xMin xMax (p-1) (x*b)
Don found that the RULES for realToFrac/Int->Double and simliarly
Float made a huge difference to some stream-fusion programs. Here's
an example
-
+
import Data.Array.Vector
-
+
n = 40000000
-
+
main = do
let c = replicateU n (2::Double)
a = mapU realToFrac (enumFromToU 0 (n-1) ) :: UArr Double
print (sumU (zipWithU (*) c a))
-
+
Without the RULE we get this loop body:
-
+
case $wtoRational sc_sY4 of ww_aM7 { (# ww1_aM9, ww2_aMa #) ->
case $wfromRat ww1_aM9 ww2_aMa of tpl_X1P { D# ipv_sW3 ->
Main.$s$wfold
(+# sc_sY4 1)
(+# wild_X1i 1)
(+## sc2_sY6 (*## 2.0 ipv_sW3))
-
+
And with the rule:
-
+
Main.$s$wfold
(+# sc_sXT 1)
(+# wild_X1h 1)
(+## sc2_sXV (*## 2.0 (int2Double# sc_sXT)))
-
+
The running time of the program goes from 120 seconds to 0.198 seconds
with the native backend, and 0.143 seconds with the C backend.
-
-A few more details in Trac #2251, and the patch message
+
+A few more details in Trac #2251, and the patch message
"Add RULES for realToFrac from Int".
%*********************************************************
projects / ghc-base.git / blobdiff