2
{-# OPTIONS_GHC -XNoImplicitPrelude #-}
3
-- We believe we could deorphan this module, by moving lots of things
4
-- around, but we haven't got there yet:
5
{-# OPTIONS_GHC -fno-warn-orphans #-}
6
{-# OPTIONS_HADDOCK hide #-}
7
-----------------------------------------------------------------------------
10
-- Copyright : (c) The University of Glasgow 1994-2002
11
-- License : see libraries/base/LICENSE
13
-- Maintainer : cvs-ghc@haskell.org
14
-- Stability : internal
15
-- Portability : non-portable (GHC Extensions)
17
-- The types 'Float' and 'Double', and the classes 'Floating' and 'RealFloat'.
19
-----------------------------------------------------------------------------
21
#include "ieee-flpt.h"
24
module GHC.Float( module GHC.Float, Float(..), Double(..), Float#, Double# )
41
%*********************************************************
43
\subsection{Standard numeric classes}
45
%*********************************************************
48
-- | Trigonometric and hyperbolic functions and related functions.
50
-- Minimal complete definition:
51
-- 'pi', 'exp', 'log', 'sin', 'cos', 'sinh', 'cosh',
52
-- 'asin', 'acos', 'atan', 'asinh', 'acosh' and 'atanh'
53
class (Fractional a) => Floating a where
55
exp, log, sqrt :: a -> a
56
(**), logBase :: a -> a -> a
57
sin, cos, tan :: a -> a
58
asin, acos, atan :: a -> a
59
sinh, cosh, tanh :: a -> a
60
asinh, acosh, atanh :: a -> a
63
{-# INLINE logBase #-}
67
x ** y = exp (log x * y)
68
logBase x y = log y / log x
71
tanh x = sinh x / cosh x
73
-- | Efficient, machine-independent access to the components of a
74
-- floating-point number.
76
-- Minimal complete definition:
77
-- all except 'exponent', 'significand', 'scaleFloat' and 'atan2'
78
class (RealFrac a, Floating a) => RealFloat a where
79
-- | a constant function, returning the radix of the representation
81
floatRadix :: a -> Integer
82
-- | a constant function, returning the number of digits of
83
-- 'floatRadix' in the significand
84
floatDigits :: a -> Int
85
-- | a constant function, returning the lowest and highest values
86
-- the exponent may assume
87
floatRange :: a -> (Int,Int)
88
-- | The function 'decodeFloat' applied to a real floating-point
89
-- number returns the significand expressed as an 'Integer' and an
90
-- appropriately scaled exponent (an 'Int'). If @'decodeFloat' x@
91
-- yields @(m,n)@, then @x@ is equal in value to @m*b^^n@, where @b@
92
-- is the floating-point radix, and furthermore, either @m@ and @n@
93
-- are both zero or else @b^(d-1) <= m < b^d@, where @d@ is the value
94
-- of @'floatDigits' x@. In particular, @'decodeFloat' 0 = (0,0)@.
95
decodeFloat :: a -> (Integer,Int)
96
-- | 'encodeFloat' performs the inverse of 'decodeFloat'
97
encodeFloat :: Integer -> Int -> a
98
-- | the second component of 'decodeFloat'.
100
-- | the first component of 'decodeFloat', scaled to lie in the open
101
-- interval (@-1@,@1@)
102
significand :: a -> a
103
-- | multiplies a floating-point number by an integer power of the radix
104
scaleFloat :: Int -> a -> a
105
-- | 'True' if the argument is an IEEE \"not-a-number\" (NaN) value
107
-- | 'True' if the argument is an IEEE infinity or negative infinity
108
isInfinite :: a -> Bool
109
-- | 'True' if the argument is too small to be represented in
111
isDenormalized :: a -> Bool
112
-- | 'True' if the argument is an IEEE negative zero
113
isNegativeZero :: a -> Bool
114
-- | 'True' if the argument is an IEEE floating point number
116
-- | a version of arctangent taking two real floating-point arguments.
117
-- For real floating @x@ and @y@, @'atan2' y x@ computes the angle
118
-- (from the positive x-axis) of the vector from the origin to the
119
-- point @(x,y)@. @'atan2' y x@ returns a value in the range [@-pi@,
120
-- @pi@]. It follows the Common Lisp semantics for the origin when
121
-- signed zeroes are supported. @'atan2' y 1@, with @y@ in a type
122
-- that is 'RealFloat', should return the same value as @'atan' y@.
123
-- A default definition of 'atan2' is provided, but implementors
124
-- can provide a more accurate implementation.
128
exponent x = if m == 0 then 0 else n + floatDigits x
129
where (m,n) = decodeFloat x
131
significand x = encodeFloat m (negate (floatDigits x))
132
where (m,_) = decodeFloat x
134
scaleFloat k x = encodeFloat m (n + clamp b k)
135
where (m,n) = decodeFloat x
139
-- n+k may overflow, which would lead
140
-- to wrong results, hence we clamp the
141
-- scaling parameter.
142
-- If n + k would be larger than h,
143
-- n + clamp b k must be too, simliar
144
-- for smaller than l - d.
145
-- Add a little extra to keep clear
146
-- from the boundary cases.
150
| x == 0 && y > 0 = pi/2
151
| x < 0 && y > 0 = pi + atan (y/x)
152
|(x <= 0 && y < 0) ||
153
(x < 0 && isNegativeZero y) ||
154
(isNegativeZero x && isNegativeZero y)
156
| y == 0 && (x < 0 || isNegativeZero x)
157
= pi -- must be after the previous test on zero y
158
| x==0 && y==0 = y -- must be after the other double zero tests
159
| otherwise = x + y -- x or y is a NaN, return a NaN (via +)
163
%*********************************************************
165
\subsection{Type @Float@}
167
%*********************************************************
170
instance Num Float where
171
(+) x y = plusFloat x y
172
(-) x y = minusFloat x y
173
negate x = negateFloat x
174
(*) x y = timesFloat x y
176
| otherwise = negateFloat x
177
signum x | x == 0.0 = 0
179
| otherwise = negate 1
181
{-# INLINE fromInteger #-}
182
fromInteger i = F# (floatFromInteger i)
184
instance Real Float where
185
toRational x = (m%1)*(b%1)^^n
186
where (m,n) = decodeFloat x
189
instance Fractional Float where
190
(/) x y = divideFloat x y
191
fromRational x = fromRat x
194
{-# RULES "truncate/Float->Int" truncate = float2Int #-}
195
instance RealFrac Float where
197
{-# SPECIALIZE properFraction :: Float -> (Int, Float) #-}
198
{-# SPECIALIZE round :: Float -> Int #-}
200
{-# SPECIALIZE properFraction :: Float -> (Integer, Float) #-}
201
{-# SPECIALIZE round :: Float -> Integer #-}
203
-- ceiling, floor, and truncate are all small
204
{-# INLINE ceiling #-}
206
{-# INLINE truncate #-}
208
-- We assume that FLT_RADIX is 2 so that we can use more efficient code
210
#error FLT_RADIX must be 2
212
properFraction (F# x#)
213
= case decodeFloat_Int# x# of
219
then (fromIntegral m * (2 ^ n), 0.0)
220
else let i = if m >= 0 then m `shiftR` negate n
221
else negate (negate m `shiftR` negate n)
222
f = m - (i `shiftL` negate n)
223
in (fromIntegral i, encodeFloat (fromIntegral f) n)
225
truncate x = case properFraction x of
228
round x = case properFraction x of
230
m = if r < 0.0 then n - 1 else n + 1
231
half_down = abs r - 0.5
233
case (compare half_down 0.0) of
235
EQ -> if even n then n else m
238
ceiling x = case properFraction x of
239
(n,r) -> if r > 0.0 then n + 1 else n
241
floor x = case properFraction x of
242
(n,r) -> if r < 0.0 then n - 1 else n
244
instance Floating Float where
245
pi = 3.141592653589793238
258
(**) x y = powerFloat x y
259
logBase x y = log y / log x
261
asinh x = log (x + sqrt (1.0+x*x))
262
acosh x = log (x + (x+1.0) * sqrt ((x-1.0)/(x+1.0)))
263
atanh x = 0.5 * log ((1.0+x) / (1.0-x))
265
instance RealFloat Float where
266
floatRadix _ = FLT_RADIX -- from float.h
267
floatDigits _ = FLT_MANT_DIG -- ditto
268
floatRange _ = (FLT_MIN_EXP, FLT_MAX_EXP) -- ditto
270
decodeFloat (F# f#) = case decodeFloat_Int# f# of
271
(# i, e #) -> (smallInteger i, I# e)
273
encodeFloat i (I# e) = F# (encodeFloatInteger i e)
275
exponent x = case decodeFloat x of
276
(m,n) -> if m == 0 then 0 else n + floatDigits x
278
significand x = case decodeFloat x of
279
(m,_) -> encodeFloat m (negate (floatDigits x))
281
scaleFloat k x = case decodeFloat x of
282
(m,n) -> encodeFloat m (n + clamp bf k)
283
where bf = FLT_MAX_EXP - (FLT_MIN_EXP) + 4*FLT_MANT_DIG
285
isNaN x = 0 /= isFloatNaN x
286
isInfinite x = 0 /= isFloatInfinite x
287
isDenormalized x = 0 /= isFloatDenormalized x
288
isNegativeZero x = 0 /= isFloatNegativeZero x
291
instance Show Float where
292
showsPrec x = showSignedFloat showFloat x
293
showList = showList__ (showsPrec 0)
296
%*********************************************************
298
\subsection{Type @Double@}
300
%*********************************************************
303
instance Num Double where
304
(+) x y = plusDouble x y
305
(-) x y = minusDouble x y
306
negate x = negateDouble x
307
(*) x y = timesDouble x y
309
| otherwise = negateDouble x
310
signum x | x == 0.0 = 0
312
| otherwise = negate 1
314
{-# INLINE fromInteger #-}
315
fromInteger i = D# (doubleFromInteger i)
318
instance Real Double where
319
toRational x = (m%1)*(b%1)^^n
320
where (m,n) = decodeFloat x
323
instance Fractional Double where
324
(/) x y = divideDouble x y
325
fromRational x = fromRat x
328
instance Floating Double where
329
pi = 3.141592653589793238
332
sqrt x = sqrtDouble x
336
asin x = asinDouble x
337
acos x = acosDouble x
338
atan x = atanDouble x
339
sinh x = sinhDouble x
340
cosh x = coshDouble x
341
tanh x = tanhDouble x
342
(**) x y = powerDouble x y
343
logBase x y = log y / log x
345
asinh x = log (x + sqrt (1.0+x*x))
346
acosh x = log (x + (x+1.0) * sqrt ((x-1.0)/(x+1.0)))
347
atanh x = 0.5 * log ((1.0+x) / (1.0-x))
349
{-# RULES "truncate/Double->Int" truncate = double2Int #-}
350
instance RealFrac Double where
352
{-# SPECIALIZE properFraction :: Double -> (Int, Double) #-}
353
{-# SPECIALIZE round :: Double -> Int #-}
355
{-# SPECIALIZE properFraction :: Double -> (Integer, Double) #-}
356
{-# SPECIALIZE round :: Double -> Integer #-}
358
-- ceiling, floor, and truncate are all small
359
{-# INLINE ceiling #-}
361
{-# INLINE truncate #-}
364
= case (decodeFloat x) of { (m,n) ->
365
let b = floatRadix x in
367
(fromInteger m * fromInteger b ^ n, 0.0)
369
case (quotRem m (b^(negate n))) of { (w,r) ->
370
(fromInteger w, encodeFloat r n)
374
truncate x = case properFraction x of
377
round x = case properFraction x of
379
m = if r < 0.0 then n - 1 else n + 1
380
half_down = abs r - 0.5
382
case (compare half_down 0.0) of
384
EQ -> if even n then n else m
387
ceiling x = case properFraction x of
388
(n,r) -> if r > 0.0 then n + 1 else n
390
floor x = case properFraction x of
391
(n,r) -> if r < 0.0 then n - 1 else n
393
instance RealFloat Double where
394
floatRadix _ = FLT_RADIX -- from float.h
395
floatDigits _ = DBL_MANT_DIG -- ditto
396
floatRange _ = (DBL_MIN_EXP, DBL_MAX_EXP) -- ditto
399
= case decodeDoubleInteger x# of
400
(# i, j #) -> (i, I# j)
402
encodeFloat i (I# j) = D# (encodeDoubleInteger i j)
404
exponent x = case decodeFloat x of
405
(m,n) -> if m == 0 then 0 else n + floatDigits x
407
significand x = case decodeFloat x of
408
(m,_) -> encodeFloat m (negate (floatDigits x))
410
scaleFloat k x = case decodeFloat x of
411
(m,n) -> encodeFloat m (n + clamp bd k)
412
where bd = DBL_MAX_EXP - (DBL_MIN_EXP) + 4*DBL_MANT_DIG
414
isNaN x = 0 /= isDoubleNaN x
415
isInfinite x = 0 /= isDoubleInfinite x
416
isDenormalized x = 0 /= isDoubleDenormalized x
417
isNegativeZero x = 0 /= isDoubleNegativeZero x
420
instance Show Double where
421
showsPrec x = showSignedFloat showFloat x
422
showList = showList__ (showsPrec 0)
425
%*********************************************************
427
\subsection{@Enum@ instances}
429
%*********************************************************
431
The @Enum@ instances for Floats and Doubles are slightly unusual.
432
The @toEnum@ function truncates numbers to Int. The definitions
433
of @enumFrom@ and @enumFromThen@ allow floats to be used in arithmetic
434
series: [0,0.1 .. 1.0]. However, roundoff errors make these somewhat
435
dubious. This example may have either 10 or 11 elements, depending on
436
how 0.1 is represented.
438
NOTE: The instances for Float and Double do not make use of the default
439
methods for @enumFromTo@ and @enumFromThenTo@, as these rely on there being
440
a `non-lossy' conversion to and from Ints. Instead we make use of the
441
1.2 default methods (back in the days when Enum had Ord as a superclass)
442
for these (@numericEnumFromTo@ and @numericEnumFromThenTo@ below.)
445
instance Enum Float where
449
fromEnum = fromInteger . truncate -- may overflow
450
enumFrom = numericEnumFrom
451
enumFromTo = numericEnumFromTo
452
enumFromThen = numericEnumFromThen
453
enumFromThenTo = numericEnumFromThenTo
455
instance Enum Double where
459
fromEnum = fromInteger . truncate -- may overflow
460
enumFrom = numericEnumFrom
461
enumFromTo = numericEnumFromTo
462
enumFromThen = numericEnumFromThen
463
enumFromThenTo = numericEnumFromThenTo
467
%*********************************************************
469
\subsection{Printing floating point}
471
%*********************************************************
475
-- | Show a signed 'RealFloat' value to full precision
476
-- using standard decimal notation for arguments whose absolute value lies
477
-- between @0.1@ and @9,999,999@, and scientific notation otherwise.
478
showFloat :: (RealFloat a) => a -> ShowS
479
showFloat x = showString (formatRealFloat FFGeneric Nothing x)
481
-- These are the format types. This type is not exported.
483
data FFFormat = FFExponent | FFFixed | FFGeneric
485
formatRealFloat :: (RealFloat a) => FFFormat -> Maybe Int -> a -> String
486
formatRealFloat fmt decs x
488
| isInfinite x = if x < 0 then "-Infinity" else "Infinity"
489
| x < 0 || isNegativeZero x = '-':doFmt fmt (floatToDigits (toInteger base) (-x))
490
| otherwise = doFmt fmt (floatToDigits (toInteger base) x)
494
doFmt format (is, e) =
495
let ds = map intToDigit is in
498
doFmt (if e < 0 || e > 7 then FFExponent else FFFixed)
503
let show_e' = show (e-1) in
506
[d] -> d : ".0e" ++ show_e'
507
(d:ds') -> d : '.' : ds' ++ "e" ++ show_e'
508
[] -> error "formatRealFloat/doFmt/FFExponent: []"
510
let dec' = max dec 1 in
512
[0] -> '0' :'.' : take dec' (repeat '0') ++ "e0"
515
(ei,is') = roundTo base (dec'+1) is
516
(d:ds') = map intToDigit (if ei > 0 then init is' else is')
518
d:'.':ds' ++ 'e':show (e-1+ei)
521
mk0 ls = case ls of { "" -> "0" ; _ -> ls}
525
| e <= 0 -> "0." ++ replicate (-e) '0' ++ ds
528
f 0 s rs = mk0 (reverse s) ++ '.':mk0 rs
529
f n s "" = f (n-1) ('0':s) ""
530
f n s (r:rs) = f (n-1) (r:s) rs
534
let dec' = max dec 0 in
537
(ei,is') = roundTo base (dec' + e) is
538
(ls,rs) = splitAt (e+ei) (map intToDigit is')
540
mk0 ls ++ (if null rs then "" else '.':rs)
543
(ei,is') = roundTo base dec' (replicate (-e) 0 ++ is)
544
d:ds' = map intToDigit (if ei > 0 then is' else 0:is')
546
d : (if null ds' then "" else '.':ds')
549
roundTo :: Int -> Int -> [Int] -> (Int,[Int])
554
_ -> error "roundTo: bad Value"
558
f n [] = (0, replicate n 0)
559
f 0 (x:_) = (if x >= b2 then 1 else 0, [])
561
| i' == base = (1,0:ds)
562
| otherwise = (0,i':ds)
567
-- Based on "Printing Floating-Point Numbers Quickly and Accurately"
568
-- by R.G. Burger and R.K. Dybvig in PLDI 96.
569
-- This version uses a much slower logarithm estimator. It should be improved.
571
-- | 'floatToDigits' takes a base and a non-negative 'RealFloat' number,
572
-- and returns a list of digits and an exponent.
573
-- In particular, if @x>=0@, and
575
-- > floatToDigits base x = ([d1,d2,...,dn], e)
581
-- (2) @x = 0.d1d2...dn * (base**e)@
583
-- (3) @0 <= di <= base-1@
585
floatToDigits :: (RealFloat a) => Integer -> a -> ([Int], Int)
586
floatToDigits _ 0 = ([0], 0)
587
floatToDigits base x =
589
(f0, e0) = decodeFloat x
590
(minExp0, _) = floatRange x
593
minExp = minExp0 - p -- the real minimum exponent
594
-- Haskell requires that f be adjusted so denormalized numbers
595
-- will have an impossibly low exponent. Adjust for this.
597
let n = minExp - e0 in
598
if n > 0 then (f0 `div` (b^n), e0+n) else (f0, e0)
603
(f*be*b*2, 2*b, be*b, b)
607
if e > minExp && f == b^(p-1) then
608
(f*b*2, b^(-e+1)*2, b, 1)
610
(f*2, b^(-e)*2, 1, 1)
616
if b == 2 && base == 10 then
617
-- logBase 10 2 is slightly bigger than 3/10 so
618
-- the following will err on the low side. Ignoring
619
-- the fraction will make it err even more.
620
-- Haskell promises that p-1 <= logBase b f < p.
621
(p - 1 + e0) * 3 `div` 10
623
-- f :: Integer, log :: Float -> Float,
624
-- ceiling :: Float -> Int
625
ceiling ((log (fromInteger (f+1) :: Float) +
626
fromIntegral e * log (fromInteger b)) /
627
log (fromInteger base))
628
--WAS: fromInt e * log (fromInteger b))
632
if r + mUp <= expt base n * s then n else fixup (n+1)
634
if expt base (-n) * (r + mUp) <= s then n else fixup (n+1)
638
gen ds rn sN mUpN mDnN =
640
(dn, rn') = (rn * base) `divMod` sN
644
case (rn' < mDnN', rn' + mUpN' > sN) of
645
(True, False) -> dn : ds
646
(False, True) -> dn+1 : ds
647
(True, True) -> if rn' * 2 < sN then dn : ds else dn+1 : ds
648
(False, False) -> gen (dn:ds) rn' sN mUpN' mDnN'
652
gen [] r (s * expt base k) mUp mDn
654
let bk = expt base (-k) in
655
gen [] (r * bk) s (mUp * bk) (mDn * bk)
657
(map fromIntegral (reverse rds), k)
662
%*********************************************************
664
\subsection{Converting from a Rational to a RealFloat
666
%*********************************************************
668
[In response to a request for documentation of how fromRational works,
669
Joe Fasel writes:] A quite reasonable request! This code was added to
670
the Prelude just before the 1.2 release, when Lennart, working with an
671
early version of hbi, noticed that (read . show) was not the identity
672
for floating-point numbers. (There was a one-bit error about half the
673
time.) The original version of the conversion function was in fact
674
simply a floating-point divide, as you suggest above. The new version
675
is, I grant you, somewhat denser.
677
Unfortunately, Joe's code doesn't work! Here's an example:
679
main = putStr (shows (1.82173691287639817263897126389712638972163e-300::Double) "\n")
684
1.8217369128763981e-300
689
fromRat :: (RealFloat a) => Rational -> a
693
-- If the exponent of the nearest floating-point number to x
694
-- is e, then the significand is the integer nearest xb^(-e),
695
-- where b is the floating-point radix. We start with a good
696
-- guess for e, and if it is correct, the exponent of the
697
-- floating-point number we construct will again be e. If
698
-- not, one more iteration is needed.
700
f e = if e' == e then y else f e'
701
where y = encodeFloat (round (x * (1 % b)^^e)) e
702
(_,e') = decodeFloat y
705
-- We obtain a trial exponent by doing a floating-point
706
-- division of x's numerator by its denominator. The
707
-- result of this division may not itself be the ultimate
708
-- result, because of an accumulation of three rounding
711
(s,e) = decodeFloat (fromInteger (numerator x) `asTypeOf` x'
712
/ fromInteger (denominator x))
715
Now, here's Lennart's code (which works)
718
-- | Converts a 'Rational' value into any type in class 'RealFloat'.
719
{-# SPECIALISE fromRat :: Rational -> Double,
720
Rational -> Float #-}
721
fromRat :: (RealFloat a) => Rational -> a
723
-- Deal with special cases first, delegating the real work to fromRat'
724
fromRat (n :% 0) | n > 0 = 1/0 -- +Infinity
725
| n < 0 = -1/0 -- -Infinity
726
| otherwise = 0/0 -- NaN
728
fromRat (n :% d) | n > 0 = fromRat' (n :% d)
729
| n < 0 = - fromRat' ((-n) :% d)
730
| otherwise = encodeFloat 0 0 -- Zero
732
-- Conversion process:
733
-- Scale the rational number by the RealFloat base until
734
-- it lies in the range of the mantissa (as used by decodeFloat/encodeFloat).
735
-- Then round the rational to an Integer and encode it with the exponent
736
-- that we got from the scaling.
737
-- To speed up the scaling process we compute the log2 of the number to get
738
-- a first guess of the exponent.
740
fromRat' :: (RealFloat a) => Rational -> a
741
-- Invariant: argument is strictly positive
743
where b = floatRadix r
745
(minExp0, _) = floatRange r
746
minExp = minExp0 - p -- the real minimum exponent
747
xMin = toRational (expt b (p-1))
748
xMax = toRational (expt b p)
749
p0 = (integerLogBase b (numerator x) - integerLogBase b (denominator x) - p) `max` minExp
750
f = if p0 < 0 then 1 % expt b (-p0) else expt b p0 % 1
751
(x', p') = scaleRat (toRational b) minExp xMin xMax p0 (x / f)
752
r = encodeFloat (round x') p'
754
-- Scale x until xMin <= x < xMax, or p (the exponent) <= minExp.
755
scaleRat :: Rational -> Int -> Rational -> Rational -> Int -> Rational -> (Rational, Int)
756
scaleRat b minExp xMin xMax p x
757
| p <= minExp = (x, p)
758
| x >= xMax = scaleRat b minExp xMin xMax (p+1) (x/b)
759
| x < xMin = scaleRat b minExp xMin xMax (p-1) (x*b)
762
-- Exponentiation with a cache for the most common numbers.
763
minExpt, maxExpt :: Int
767
expt :: Integer -> Int -> Integer
769
if base == 2 && n >= minExpt && n <= maxExpt then
774
expts :: Array Int Integer
775
expts = array (minExpt,maxExpt) [(n,2^n) | n <- [minExpt .. maxExpt]]
777
-- Compute the (floor of the) log of i in base b.
778
-- Simplest way would be just divide i by b until it's smaller then b, but that would
779
-- be very slow! We are just slightly more clever.
780
integerLogBase :: Integer -> Integer -> Int
783
| otherwise = doDiv (i `div` (b^l)) l
785
-- Try squaring the base first to cut down the number of divisions.
786
l = 2 * integerLogBase (b*b) i
788
doDiv :: Integer -> Int -> Int
791
| otherwise = doDiv (x `div` b) (y+1)
796
%*********************************************************
798
\subsection{Floating point numeric primops}
800
%*********************************************************
802
Definitions of the boxed PrimOps; these will be
803
used in the case of partial applications, etc.
806
plusFloat, minusFloat, timesFloat, divideFloat :: Float -> Float -> Float
807
plusFloat (F# x) (F# y) = F# (plusFloat# x y)
808
minusFloat (F# x) (F# y) = F# (minusFloat# x y)
809
timesFloat (F# x) (F# y) = F# (timesFloat# x y)
810
divideFloat (F# x) (F# y) = F# (divideFloat# x y)
812
negateFloat :: Float -> Float
813
negateFloat (F# x) = F# (negateFloat# x)
815
gtFloat, geFloat, eqFloat, neFloat, ltFloat, leFloat :: Float -> Float -> Bool
816
gtFloat (F# x) (F# y) = gtFloat# x y
817
geFloat (F# x) (F# y) = geFloat# x y
818
eqFloat (F# x) (F# y) = eqFloat# x y
819
neFloat (F# x) (F# y) = neFloat# x y
820
ltFloat (F# x) (F# y) = ltFloat# x y
821
leFloat (F# x) (F# y) = leFloat# x y
823
float2Int :: Float -> Int
824
float2Int (F# x) = I# (float2Int# x)
826
int2Float :: Int -> Float
827
int2Float (I# x) = F# (int2Float# x)
829
expFloat, logFloat, sqrtFloat :: Float -> Float
830
sinFloat, cosFloat, tanFloat :: Float -> Float
831
asinFloat, acosFloat, atanFloat :: Float -> Float
832
sinhFloat, coshFloat, tanhFloat :: Float -> Float
833
expFloat (F# x) = F# (expFloat# x)
834
logFloat (F# x) = F# (logFloat# x)
835
sqrtFloat (F# x) = F# (sqrtFloat# x)
836
sinFloat (F# x) = F# (sinFloat# x)
837
cosFloat (F# x) = F# (cosFloat# x)
838
tanFloat (F# x) = F# (tanFloat# x)
839
asinFloat (F# x) = F# (asinFloat# x)
840
acosFloat (F# x) = F# (acosFloat# x)
841
atanFloat (F# x) = F# (atanFloat# x)
842
sinhFloat (F# x) = F# (sinhFloat# x)
843
coshFloat (F# x) = F# (coshFloat# x)
844
tanhFloat (F# x) = F# (tanhFloat# x)
846
powerFloat :: Float -> Float -> Float
847
powerFloat (F# x) (F# y) = F# (powerFloat# x y)
849
-- definitions of the boxed PrimOps; these will be
850
-- used in the case of partial applications, etc.
852
plusDouble, minusDouble, timesDouble, divideDouble :: Double -> Double -> Double
853
plusDouble (D# x) (D# y) = D# (x +## y)
854
minusDouble (D# x) (D# y) = D# (x -## y)
855
timesDouble (D# x) (D# y) = D# (x *## y)
856
divideDouble (D# x) (D# y) = D# (x /## y)
858
negateDouble :: Double -> Double
859
negateDouble (D# x) = D# (negateDouble# x)
861
gtDouble, geDouble, eqDouble, neDouble, leDouble, ltDouble :: Double -> Double -> Bool
862
gtDouble (D# x) (D# y) = x >## y
863
geDouble (D# x) (D# y) = x >=## y
864
eqDouble (D# x) (D# y) = x ==## y
865
neDouble (D# x) (D# y) = x /=## y
866
ltDouble (D# x) (D# y) = x <## y
867
leDouble (D# x) (D# y) = x <=## y
869
double2Int :: Double -> Int
870
double2Int (D# x) = I# (double2Int# x)
872
int2Double :: Int -> Double
873
int2Double (I# x) = D# (int2Double# x)
875
double2Float :: Double -> Float
876
double2Float (D# x) = F# (double2Float# x)
878
float2Double :: Float -> Double
879
float2Double (F# x) = D# (float2Double# x)
881
expDouble, logDouble, sqrtDouble :: Double -> Double
882
sinDouble, cosDouble, tanDouble :: Double -> Double
883
asinDouble, acosDouble, atanDouble :: Double -> Double
884
sinhDouble, coshDouble, tanhDouble :: Double -> Double
885
expDouble (D# x) = D# (expDouble# x)
886
logDouble (D# x) = D# (logDouble# x)
887
sqrtDouble (D# x) = D# (sqrtDouble# x)
888
sinDouble (D# x) = D# (sinDouble# x)
889
cosDouble (D# x) = D# (cosDouble# x)
890
tanDouble (D# x) = D# (tanDouble# x)
891
asinDouble (D# x) = D# (asinDouble# x)
892
acosDouble (D# x) = D# (acosDouble# x)
893
atanDouble (D# x) = D# (atanDouble# x)
894
sinhDouble (D# x) = D# (sinhDouble# x)
895
coshDouble (D# x) = D# (coshDouble# x)
896
tanhDouble (D# x) = D# (tanhDouble# x)
898
powerDouble :: Double -> Double -> Double
899
powerDouble (D# x) (D# y) = D# (x **## y)
903
foreign import ccall unsafe "isFloatNaN" isFloatNaN :: Float -> Int
904
foreign import ccall unsafe "isFloatInfinite" isFloatInfinite :: Float -> Int
905
foreign import ccall unsafe "isFloatDenormalized" isFloatDenormalized :: Float -> Int
906
foreign import ccall unsafe "isFloatNegativeZero" isFloatNegativeZero :: Float -> Int
909
foreign import ccall unsafe "isDoubleNaN" isDoubleNaN :: Double -> Int
910
foreign import ccall unsafe "isDoubleInfinite" isDoubleInfinite :: Double -> Int
911
foreign import ccall unsafe "isDoubleDenormalized" isDoubleDenormalized :: Double -> Int
912
foreign import ccall unsafe "isDoubleNegativeZero" isDoubleNegativeZero :: Double -> Int
915
%*********************************************************
917
\subsection{Coercion rules}
919
%*********************************************************
923
"fromIntegral/Int->Float" fromIntegral = int2Float
924
"fromIntegral/Int->Double" fromIntegral = int2Double
925
"realToFrac/Float->Float" realToFrac = id :: Float -> Float
926
"realToFrac/Float->Double" realToFrac = float2Double
927
"realToFrac/Double->Float" realToFrac = double2Float
928
"realToFrac/Double->Double" realToFrac = id :: Double -> Double
929
"realToFrac/Int->Double" realToFrac = int2Double -- See Note [realToFrac int-to-float]
930
"realToFrac/Int->Float" realToFrac = int2Float -- ..ditto
934
Note [realToFrac int-to-float]
935
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
936
Don found that the RULES for realToFrac/Int->Double and simliarly
937
Float made a huge difference to some stream-fusion programs. Here's
940
import Data.Array.Vector
945
let c = replicateU n (2::Double)
946
a = mapU realToFrac (enumFromToU 0 (n-1) ) :: UArr Double
947
print (sumU (zipWithU (*) c a))
949
Without the RULE we get this loop body:
951
case $wtoRational sc_sY4 of ww_aM7 { (# ww1_aM9, ww2_aMa #) ->
952
case $wfromRat ww1_aM9 ww2_aMa of tpl_X1P { D# ipv_sW3 ->
956
(+## sc2_sY6 (*## 2.0 ipv_sW3))
963
(+## sc2_sXV (*## 2.0 (int2Double# sc_sXT)))
965
The running time of the program goes from 120 seconds to 0.198 seconds
966
with the native backend, and 0.143 seconds with the C backend.
968
A few more details in Trac #2251, and the patch message
969
"Add RULES for realToFrac from Int".
971
%*********************************************************
975
%*********************************************************
978
showSignedFloat :: (RealFloat a)
979
=> (a -> ShowS) -- ^ a function that can show unsigned values
980
-> Int -- ^ the precedence of the enclosing context
981
-> a -- ^ the value to show
983
showSignedFloat showPos p x
984
| x < 0 || isNegativeZero x
985
= showParen (p > 6) (showChar '-' . showPos (-x))
986
| otherwise = showPos x
989
We need to prevent over/underflow of the exponent in encodeFloat when
990
called from scaleFloat, hence we clamp the scaling parameter.
991
We must have a large enough range to cover the maximum difference of
992
exponents returned by decodeFloat.
994
clamp :: Int -> Int -> Int
995
clamp bd k = max (-bd) (min bd k)
added
removed
libraries/base/GHC/Float.lhs
