{-# LANGUAGE Trustworthy #-} {-# LANGUAGE CPP , GHCForeignImportPrim , NoImplicitPrelude , MagicHash , UnboxedTuples , UnliftedFFITypes #-} {-# LANGUAGE CApiFFI #-} -- We believe we could deorphan this module, by moving lots of things -- around, but we haven't got there yet: {-# OPTIONS_GHC -Wno-orphans #-} {-# OPTIONS_HADDOCK hide #-} ----------------------------------------------------------------------------- -- | -- Module : GHC.Float -- Copyright : (c) The University of Glasgow 1994-2002 -- Portions obtained from hbc (c) Lennart Augusstson -- License : see libraries/base/LICENSE -- -- Maintainer : cvs-ghc@haskell.org -- Stability : internal -- Portability : non-portable (GHC Extensions) -- -- The types 'Float' and 'Double', the classes 'Floating' and 'RealFloat' and -- casting between Word32 and Float and Word64 and Double. -- ----------------------------------------------------------------------------- #include "ieee-flpt.h" #include "MachDeps.h" module GHC.Float ( module GHC.Float , Float(..), Double(..), Float#, Double# , double2Int, int2Double, float2Int, int2Float -- * Monomorphic equality operators -- | See GHC.Classes#matching_overloaded_methods_in_rules , eqFloat, eqDouble ) where import Data.Maybe import Data.Bits import GHC.Base import GHC.List import GHC.Enum import GHC.Show import GHC.Num import GHC.Real import GHC.Word import GHC.Arr import GHC.Float.RealFracMethods import GHC.Float.ConversionUtils import GHC.Integer.Logarithms ( integerLogBase# ) import GHC.Integer.Logarithms.Internals infixr 8 ** ------------------------------------------------------------------------ -- Standard numeric classes ------------------------------------------------------------------------ -- | Trigonometric and hyperbolic functions and related functions. -- -- The Haskell Report defines no laws for 'Floating'. However, '(+)', '(*)' -- and 'exp' are customarily expected to define an exponential field and have -- the following properties: -- -- * @exp (a + b)@ = @exp a * exp b -- * @exp (fromInteger 0)@ = @fromInteger 1@ class (Fractional a) => Floating a where pi :: a exp, log, sqrt :: a -> a (**), logBase :: a -> a -> a sin, cos, tan :: a -> a asin, acos, atan :: a -> a sinh, cosh, tanh :: a -> a asinh, acosh, atanh :: a -> a -- | @'log1p' x@ computes @'log' (1 + x)@, but provides more precise -- results for small (absolute) values of @x@ if possible. -- -- @since 4.9.0.0 log1p :: a -> a -- | @'expm1' x@ computes @'exp' x - 1@, but provides more precise -- results for small (absolute) values of @x@ if possible. -- -- @since 4.9.0.0 expm1 :: a -> a -- | @'log1pexp' x@ computes @'log' (1 + 'exp' x)@, but provides more -- precise results if possible. -- -- Examples: -- -- * if @x@ is a large negative number, @'log' (1 + 'exp' x)@ will be -- imprecise for the reasons given in 'log1p'. -- -- * if @'exp' x@ is close to @-1@, @'log' (1 + 'exp' x)@ will be -- imprecise for the reasons given in 'expm1'. -- -- @since 4.9.0.0 log1pexp :: a -> a -- | @'log1mexp' x@ computes @'log' (1 - 'exp' x)@, but provides more -- precise results if possible. -- -- Examples: -- -- * if @x@ is a large negative number, @'log' (1 - 'exp' x)@ will be -- imprecise for the reasons given in 'log1p'. -- -- * if @'exp' x@ is close to @1@, @'log' (1 - 'exp' x)@ will be -- imprecise for the reasons given in 'expm1'. -- -- @since 4.9.0.0 log1mexp :: a -> a {-# INLINE (**) #-} {-# INLINE logBase #-} {-# INLINE sqrt #-} {-# INLINE tan #-} {-# INLINE tanh #-} x ** y = exp (log x * y) logBase x y = log y / log x sqrt x = x ** 0.5 tan x = sin x / cos x tanh x = sinh x / cosh x {-# INLINE log1p #-} {-# INLINE expm1 #-} {-# INLINE log1pexp #-} {-# INLINE log1mexp #-} log1p x = log (1 + x) expm1 x = exp x - 1 log1pexp x = log1p (exp x) log1mexp x = log1p (negate (exp x)) -- | Efficient, machine-independent access to the components of a -- floating-point number. class (RealFrac a, Floating a) => RealFloat a where -- | a constant function, returning the radix of the representation -- (often @2@) floatRadix :: a -> Integer -- | a constant function, returning the number of digits of -- 'floatRadix' in the significand floatDigits :: a -> Int -- | a constant function, returning the lowest and highest values -- the exponent may assume floatRange :: a -> (Int,Int) -- | The function 'decodeFloat' applied to a real floating-point -- number returns the significand expressed as an 'Integer' and an -- appropriately scaled exponent (an 'Int'). If @'decodeFloat' x@ -- yields @(m,n)@, then @x@ is equal in value to @m*b^^n@, where @b@ -- is the floating-point radix, and furthermore, either @m@ and @n@ -- are both zero or else @b^(d-1) <= 'abs' m < b^d@, where @d@ is -- the value of @'floatDigits' x@. -- In particular, @'decodeFloat' 0 = (0,0)@. If the type -- contains a negative zero, also @'decodeFloat' (-0.0) = (0,0)@. -- /The result of/ @'decodeFloat' x@ /is unspecified if either of/ -- @'isNaN' x@ /or/ @'isInfinite' x@ /is/ 'True'. decodeFloat :: a -> (Integer,Int) -- | 'encodeFloat' performs the inverse of 'decodeFloat' in the -- sense that for finite @x@ with the exception of @-0.0@, -- @'uncurry' 'encodeFloat' ('decodeFloat' x) = x@. -- @'encodeFloat' m n@ is one of the two closest representable -- floating-point numbers to @m*b^^n@ (or @±Infinity@ if overflow -- occurs); usually the closer, but if @m@ contains too many bits, -- the result may be rounded in the wrong direction. encodeFloat :: Integer -> Int -> a -- | 'exponent' corresponds to the second component of 'decodeFloat'. -- @'exponent' 0 = 0@ and for finite nonzero @x@, -- @'exponent' x = snd ('decodeFloat' x) + 'floatDigits' x@. -- If @x@ is a finite floating-point number, it is equal in value to -- @'significand' x * b ^^ 'exponent' x@, where @b@ is the -- floating-point radix. -- The behaviour is unspecified on infinite or @NaN@ values. exponent :: a -> Int -- | The first component of 'decodeFloat', scaled to lie in the open -- interval (@-1@,@1@), either @0.0@ or of absolute value @>= 1\/b@, -- where @b@ is the floating-point radix. -- The behaviour is unspecified on infinite or @NaN@ values. significand :: a -> a -- | multiplies a floating-point number by an integer power of the radix scaleFloat :: Int -> a -> a -- | 'True' if the argument is an IEEE \"not-a-number\" (NaN) value isNaN :: a -> Bool -- | 'True' if the argument is an IEEE infinity or negative infinity isInfinite :: a -> Bool -- | 'True' if the argument is too small to be represented in -- normalized format isDenormalized :: a -> Bool -- | 'True' if the argument is an IEEE negative zero isNegativeZero :: a -> Bool -- | 'True' if the argument is an IEEE floating point number isIEEE :: a -> Bool -- | a version of arctangent taking two real floating-point arguments. -- For real floating @x@ and @y@, @'atan2' y x@ computes the angle -- (from the positive x-axis) of the vector from the origin to the -- point @(x,y)@. @'atan2' y x@ returns a value in the range [@-pi@, -- @pi@]. It follows the Common Lisp semantics for the origin when -- signed zeroes are supported. @'atan2' y 1@, with @y@ in a type -- that is 'RealFloat', should return the same value as @'atan' y@. -- A default definition of 'atan2' is provided, but implementors -- can provide a more accurate implementation. atan2 :: a -> a -> a exponent x = if m == 0 then 0 else n + floatDigits x where (m,n) = decodeFloat x significand x = encodeFloat m (negate (floatDigits x)) where (m,_) = decodeFloat x scaleFloat 0 x = x scaleFloat k x | isFix = x | otherwise = encodeFloat m (n + clamp b k) where (m,n) = decodeFloat x (l,h) = floatRange x d = floatDigits x b = h - l + 4*d -- n+k may overflow, which would lead -- to wrong results, hence we clamp the -- scaling parameter. -- If n + k would be larger than h, -- n + clamp b k must be too, simliar -- for smaller than l - d. -- Add a little extra to keep clear -- from the boundary cases. isFix = x == 0 || isNaN x || isInfinite x 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) || (x < 0 && isNegativeZero y) || (isNegativeZero x && isNegativeZero y) = -atan2 (-y) x | y == 0 && (x < 0 || isNegativeZero x) = pi -- must be after the previous test on zero y | x==0 && y==0 = y -- must be after the other double zero tests | otherwise = x + y -- x or y is a NaN, return a NaN (via +) ------------------------------------------------------------------------ -- Float ------------------------------------------------------------------------ -- | @since 2.01 -- Note that due to the presence of @NaN@, not all elements of 'Float' have an -- additive inverse. -- -- >>> 0/0 + (negate 0/0 :: Float) -- NaN -- -- Also note that due to the presence of -0, `Float`'s 'Num' instance doesn't -- have an additive identity -- -- >>> 0 + (-0 :: Float) -- 0.0 instance Num Float where (+) x y = plusFloat x y (-) x y = minusFloat x y negate x = negateFloat x (*) x y = timesFloat x y abs x = fabsFloat x signum x | x > 0 = 1 | x < 0 = negateFloat 1 | otherwise = x -- handles 0.0, (-0.0), and NaN {-# INLINE fromInteger #-} fromInteger i = F# (floatFromInteger i) -- | @since 2.01 instance Real Float where toRational (F# x#) = case decodeFloat_Int# x# of (# m#, e# #) | isTrue# (e# >=# 0#) -> (smallInteger m# `shiftLInteger` e#) :% 1 | isTrue# ((int2Word# m# `and#` 1##) `eqWord#` 0##) -> case elimZerosInt# m# (negateInt# e#) of (# n, d# #) -> n :% shiftLInteger 1 d# | otherwise -> smallInteger m# :% shiftLInteger 1 (negateInt# e#) -- | @since 2.01 -- Note that due to the presence of @NaN@, not all elements of 'Float' have an -- multiplicative inverse. -- -- >>> 0/0 * (recip 0/0 :: Float) -- NaN instance Fractional Float where (/) x y = divideFloat x y {-# INLINE fromRational #-} fromRational (n:%d) = rationalToFloat n d recip x = 1.0 / x rationalToFloat :: Integer -> Integer -> Float {-# NOINLINE [1] rationalToFloat #-} rationalToFloat n 0 | n == 0 = 0/0 | n < 0 = (-1)/0 | otherwise = 1/0 rationalToFloat n d | n == 0 = encodeFloat 0 0 | n < 0 = -(fromRat'' minEx mantDigs (-n) d) | otherwise = fromRat'' minEx mantDigs n d where minEx = FLT_MIN_EXP mantDigs = FLT_MANT_DIG -- RULES for Integer and Int {-# RULES "properFraction/Float->Integer" properFraction = properFractionFloatInteger "truncate/Float->Integer" truncate = truncateFloatInteger "floor/Float->Integer" floor = floorFloatInteger "ceiling/Float->Integer" ceiling = ceilingFloatInteger "round/Float->Integer" round = roundFloatInteger "properFraction/Float->Int" properFraction = properFractionFloatInt "truncate/Float->Int" truncate = float2Int "floor/Float->Int" floor = floorFloatInt "ceiling/Float->Int" ceiling = ceilingFloatInt "round/Float->Int" round = roundFloatInt #-} -- | @since 2.01 instance RealFrac Float where -- ceiling, floor, and truncate are all small {-# INLINE [1] ceiling #-} {-# INLINE [1] floor #-} {-# INLINE [1] truncate #-} -- We assume that FLT_RADIX is 2 so that we can use more efficient code #if FLT_RADIX != 2 #error FLT_RADIX must be 2 #endif properFraction (F# x#) = case decodeFloat_Int# x# of (# m#, n# #) -> let m = I# m# n = I# n# in if n >= 0 then (fromIntegral m * (2 ^ n), 0.0) else let i = if m >= 0 then m `shiftR` negate n else negate (negate m `shiftR` negate n) f = m - (i `shiftL` negate n) in (fromIntegral i, encodeFloat (fromIntegral f) n) truncate x = case properFraction x of (n,_) -> n round x = case properFraction x of (n,r) -> let m = if r < 0.0 then n - 1 else n + 1 half_down = abs r - 0.5 in case (compare half_down 0.0) of LT -> n EQ -> if even n then n else m GT -> m ceiling x = case properFraction x of (n,r) -> if r > 0.0 then n + 1 else n floor x = case properFraction x of (n,r) -> if r < 0.0 then n - 1 else n -- | @since 2.01 instance Floating Float where pi = 3.141592653589793238 exp x = expFloat x log x = logFloat x sqrt x = sqrtFloat x sin x = sinFloat x cos x = cosFloat x tan x = tanFloat x asin x = asinFloat x acos x = acosFloat x atan x = atanFloat x sinh x = sinhFloat x cosh x = coshFloat x tanh x = tanhFloat x (**) x y = powerFloat x y logBase x y = log y / log x asinh x | x > huge = log 2 + log x | x < 0 = -asinh (-x) | otherwise = log (x + sqrt (1 + x*x)) where huge = 1e10 acosh x = log (x + (x+1.0) * sqrt ((x-1.0)/(x+1.0))) atanh x = 0.5 * log ((1.0+x) / (1.0-x)) log1p = log1pFloat expm1 = expm1Float log1mexp a | a <= log 2 = log (negate (expm1Float a)) | otherwise = log1pFloat (negate (exp a)) {-# INLINE log1mexp #-} log1pexp a | a <= 18 = log1pFloat (exp a) | a <= 100 = a + exp (negate a) | otherwise = a {-# INLINE log1pexp #-} -- | @since 2.01 instance RealFloat Float where floatRadix _ = FLT_RADIX -- from float.h floatDigits _ = FLT_MANT_DIG -- ditto floatRange _ = (FLT_MIN_EXP, FLT_MAX_EXP) -- ditto decodeFloat (F# f#) = case decodeFloat_Int# f# of (# i, e #) -> (smallInteger i, I# e) encodeFloat i (I# e) = F# (encodeFloatInteger i e) exponent x = case decodeFloat x of (m,n) -> if m == 0 then 0 else n + floatDigits x significand x = case decodeFloat x of (m,_) -> encodeFloat m (negate (floatDigits x)) scaleFloat 0 x = x scaleFloat k x | isFix = x | otherwise = case decodeFloat x of (m,n) -> encodeFloat m (n + clamp bf k) where bf = FLT_MAX_EXP - (FLT_MIN_EXP) + 4*FLT_MANT_DIG isFix = x == 0 || isFloatFinite x == 0 isNaN x = 0 /= isFloatNaN x isInfinite x = 0 /= isFloatInfinite x isDenormalized x = 0 /= isFloatDenormalized x isNegativeZero x = 0 /= isFloatNegativeZero x isIEEE _ = True -- | @since 2.01 instance Show Float where showsPrec x = showSignedFloat showFloat x showList = showList__ (showsPrec 0) ------------------------------------------------------------------------ -- Double ------------------------------------------------------------------------ -- | @since 2.01 -- Note that due to the presence of @NaN@, not all elements of 'Double' have an -- additive inverse. -- -- >>> 0/0 + (negate 0/0 :: Double) -- NaN -- -- Also note that due to the presence of -0, `Double`'s 'Num' instance doesn't -- have an additive identity -- -- >>> 0 + (-0 :: Double) -- 0.0 instance Num Double where (+) x y = plusDouble x y (-) x y = minusDouble x y negate x = negateDouble x (*) x y = timesDouble x y abs x = fabsDouble x signum x | x > 0 = 1 | x < 0 = negateDouble 1 | otherwise = x -- handles 0.0, (-0.0), and NaN {-# INLINE fromInteger #-} fromInteger i = D# (doubleFromInteger i) -- | @since 2.01 instance Real Double where toRational (D# x#) = case decodeDoubleInteger x# of (# m, e# #) | isTrue# (e# >=# 0#) -> shiftLInteger m e# :% 1 | isTrue# ((integerToWord m `and#` 1##) `eqWord#` 0##) -> case elimZerosInteger m (negateInt# e#) of (# n, d# #) -> n :% shiftLInteger 1 d# | otherwise -> m :% shiftLInteger 1 (negateInt# e#) -- | @since 2.01 -- Note that due to the presence of @NaN@, not all elements of 'Double' have an -- multiplicative inverse. -- -- >>> 0/0 * (recip 0/0 :: Double) -- NaN instance Fractional Double where (/) x y = divideDouble x y {-# INLINE fromRational #-} fromRational (n:%d) = rationalToDouble n d recip x = 1.0 / x rationalToDouble :: Integer -> Integer -> Double {-# NOINLINE [1] rationalToDouble #-} rationalToDouble n 0 | n == 0 = 0/0 | n < 0 = (-1)/0 | otherwise = 1/0 rationalToDouble n d | n == 0 = encodeFloat 0 0 | n < 0 = -(fromRat'' minEx mantDigs (-n) d) | otherwise = fromRat'' minEx mantDigs n d where minEx = DBL_MIN_EXP mantDigs = DBL_MANT_DIG -- | @since 2.01 instance Floating Double where pi = 3.141592653589793238 exp x = expDouble x log x = logDouble x sqrt x = sqrtDouble x sin x = sinDouble x cos x = cosDouble x tan x = tanDouble x asin x = asinDouble x acos x = acosDouble x atan x = atanDouble x sinh x = sinhDouble x cosh x = coshDouble x tanh x = tanhDouble x (**) x y = powerDouble x y logBase x y = log y / log x asinh x | x > huge = log 2 + log x | x < 0 = -asinh (-x) | otherwise = log (x + sqrt (1 + x*x)) where huge = 1e20 acosh x = log (x + (x+1.0) * sqrt ((x-1.0)/(x+1.0))) atanh x = 0.5 * log ((1.0+x) / (1.0-x)) log1p = log1pDouble expm1 = expm1Double log1mexp a | a <= log 2 = log (negate (expm1Double a)) | otherwise = log1pDouble (negate (exp a)) {-# INLINE log1mexp #-} log1pexp a | a <= 18 = log1pDouble (exp a) | a <= 100 = a + exp (negate a) | otherwise = a {-# INLINE log1pexp #-} -- RULES for Integer and Int {-# RULES "properFraction/Double->Integer" properFraction = properFractionDoubleInteger "truncate/Double->Integer" truncate = truncateDoubleInteger "floor/Double->Integer" floor = floorDoubleInteger "ceiling/Double->Integer" ceiling = ceilingDoubleInteger "round/Double->Integer" round = roundDoubleInteger "properFraction/Double->Int" properFraction = properFractionDoubleInt "truncate/Double->Int" truncate = double2Int "floor/Double->Int" floor = floorDoubleInt "ceiling/Double->Int" ceiling = ceilingDoubleInt "round/Double->Int" round = roundDoubleInt #-} -- | @since 2.01 instance RealFrac Double where -- ceiling, floor, and truncate are all small {-# INLINE [1] ceiling #-} {-# INLINE [1] floor #-} {-# INLINE [1] truncate #-} properFraction x = case (decodeFloat x) of { (m,n) -> if n >= 0 then (fromInteger m * 2 ^ n, 0.0) else case (quotRem m (2^(negate n))) of { (w,r) -> (fromInteger w, encodeFloat r n) } } truncate x = case properFraction x of (n,_) -> n round x = case properFraction x of (n,r) -> let m = if r < 0.0 then n - 1 else n + 1 half_down = abs r - 0.5 in case (compare half_down 0.0) of LT -> n EQ -> if even n then n else m GT -> m ceiling x = case properFraction x of (n,r) -> if r > 0.0 then n + 1 else n floor x = case properFraction x of (n,r) -> if r < 0.0 then n - 1 else n -- | @since 2.01 instance RealFloat Double where floatRadix _ = FLT_RADIX -- from float.h floatDigits _ = DBL_MANT_DIG -- ditto floatRange _ = (DBL_MIN_EXP, DBL_MAX_EXP) -- ditto decodeFloat (D# x#) = case decodeDoubleInteger x# of (# i, j #) -> (i, I# j) encodeFloat i (I# j) = D# (encodeDoubleInteger i j) exponent x = case decodeFloat x of (m,n) -> if m == 0 then 0 else n + floatDigits x significand x = case decodeFloat x of (m,_) -> encodeFloat m (negate (floatDigits x)) scaleFloat 0 x = x scaleFloat k x | isFix = x | otherwise = case decodeFloat x of (m,n) -> encodeFloat m (n + clamp bd k) where bd = DBL_MAX_EXP - (DBL_MIN_EXP) + 4*DBL_MANT_DIG isFix = x == 0 || isDoubleFinite x == 0 isNaN x = 0 /= isDoubleNaN x isInfinite x = 0 /= isDoubleInfinite x isDenormalized x = 0 /= isDoubleDenormalized x isNegativeZero x = 0 /= isDoubleNegativeZero x isIEEE _ = True -- | @since 2.01 instance Show Double where showsPrec x = showSignedFloat showFloat x showList = showList__ (showsPrec 0) ------------------------------------------------------------------------ -- Enum instances ------------------------------------------------------------------------ {- The @Enum@ instances for Floats and Doubles are slightly unusual. The @toEnum@ function truncates numbers to Int. The definitions of @enumFrom@ and @enumFromThen@ allow floats to be used in arithmetic series: [0,0.1 .. 1.0]. However, roundoff errors make these somewhat dubious. This example may have either 10 or 11 elements, depending on how 0.1 is represented. 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 1.2 default methods (back in the days when Enum had Ord as a superclass) for these (@numericEnumFromTo@ and @numericEnumFromThenTo@ below.) -} -- | @since 2.01 instance Enum Float where succ x = x + 1 pred x = x - 1 toEnum = int2Float fromEnum = fromInteger . truncate -- may overflow enumFrom = numericEnumFrom enumFromTo = numericEnumFromTo enumFromThen = numericEnumFromThen enumFromThenTo = numericEnumFromThenTo -- | @since 2.01 instance Enum Double where succ x = x + 1 pred x = x - 1 toEnum = int2Double fromEnum = fromInteger . truncate -- may overflow enumFrom = numericEnumFrom enumFromTo = numericEnumFromTo enumFromThen = numericEnumFromThen enumFromThenTo = numericEnumFromThenTo ------------------------------------------------------------------------ -- Printing floating point ------------------------------------------------------------------------ -- | 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. showFloat :: (RealFloat a) => a -> ShowS showFloat x = showString (formatRealFloat FFGeneric Nothing x) -- These are the format types. This type is not exported. data FFFormat = FFExponent | FFFixed | FFGeneric -- This is just a compatibility stub, as the "alt" argument formerly -- didn't exist. formatRealFloat :: (RealFloat a) => FFFormat -> Maybe Int -> a -> String formatRealFloat fmt decs x = formatRealFloatAlt fmt decs False x formatRealFloatAlt :: (RealFloat a) => FFFormat -> Maybe Int -> Bool -> a -> String formatRealFloatAlt fmt decs alt x | isNaN x = "NaN" | 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 base = 10 doFmt format (is, e) = let ds = map intToDigit is in case format of FFGeneric -> doFmt (if e < 0 || e > 7 then FFExponent else FFFixed) (is,e) FFExponent -> case decs of Nothing -> let show_e' = show (e-1) in case ds of "0" -> "0.0e0" [d] -> d : ".0e" ++ show_e' (d:ds') -> d : '.' : ds' ++ "e" ++ show_e' [] -> errorWithoutStackTrace "formatRealFloat/doFmt/FFExponent: []" Just 0 -> -- handle this case specifically since we need to omit the -- decimal point as well (#15115) case is of [0] -> "0e0" _ -> let (ei,is') = roundTo base 1 is d:_ = map intToDigit (if ei > 0 then init is' else is') in d : 'e' : show (e-1+ei) Just dec -> let dec' = max dec 1 in case is of [0] -> '0' :'.' : take dec' (repeat '0') ++ "e0" _ -> let (ei,is') = roundTo base (dec'+1) is (d:ds') = map intToDigit (if ei > 0 then init is' else is') in d:'.':ds' ++ 'e':show (e-1+ei) FFFixed -> let mk0 ls = case ls of { "" -> "0" ; _ -> ls} in case decs of Nothing | e <= 0 -> "0." ++ replicate (-e) '0' ++ ds | otherwise -> let f 0 s rs = mk0 (reverse s) ++ '.':mk0 rs f n s "" = f (n-1) ('0':s) "" f n s (r:rs) = f (n-1) (r:s) rs in f e "" ds Just dec -> let dec' = max dec 0 in if e >= 0 then let (ei,is') = roundTo base (dec' + e) is (ls,rs) = splitAt (e+ei) (map intToDigit is') in mk0 ls ++ (if null rs && not alt then "" else '.':rs) else let (ei,is') = roundTo base dec' (replicate (-e) 0 ++ is) d:ds' = map intToDigit (if ei > 0 then is' else 0:is') in d : (if null ds' && not alt then "" else '.':ds') roundTo :: Int -> Int -> [Int] -> (Int,[Int]) roundTo base d is = case f d True is of x@(0,_) -> x (1,xs) -> (1, 1:xs) _ -> errorWithoutStackTrace "roundTo: bad Value" where b2 = base `quot` 2 f n _ [] = (0, replicate n 0) f 0 e (x:xs) | x == b2 && e && all (== 0) xs = (0, []) -- Round to even when at exactly half the base | otherwise = (if x >= b2 then 1 else 0, []) f n _ (i:xs) | i' == base = (1,0:ds) | otherwise = (0,i':ds) where (c,ds) = f (n-1) (even i) xs i' = c + i -- Based on "Printing Floating-Point Numbers Quickly and Accurately" -- by R.G. Burger and R.K. Dybvig in PLDI 96. -- 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. -- 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@ floatToDigits :: (RealFloat a) => Integer -> a -> ([Int], Int) floatToDigits _ 0 = ([0], 0) floatToDigits base x = let (f0, e0) = decodeFloat x (minExp0, _) = floatRange x p = floatDigits x b = floatRadix 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) = let n = minExp - e0 in if n > 0 then (f0 `quot` (expt b n), e0+n) else (f0, e0) (r, s, mUp, mDn) = if e >= 0 then let be = expt b e in if f == expt b (p-1) then (f*be*b*2, 2*b, be*b, be) -- according to Burger and Dybvig else (f*be*2, 2, be, be) else if e > minExp && f == expt b (p-1) then (f*b*2, expt b (-e+1)*2, b, 1) else (f*2, expt b (-e)*2, 1, 1) k :: Int k = let k0 :: Int k0 = if b == 2 && base == 10 then -- logBase 10 2 is very slightly larger than 8651/28738 -- (about 5.3558e-10), so if log x >= 0, the approximation -- k1 is too small, hence we add one and need one fixup step less. -- If log x < 0, the approximation errs rather on the high side. -- That is usually more than compensated for by ignoring the -- fractional part of logBase 2 x, but when x is a power of 1/2 -- or slightly larger and the exponent is a multiple of the -- denominator of the rational approximation to logBase 10 2, -- k1 is larger than logBase 10 x. If k1 > 1 + logBase 10 x, -- we get a leading zero-digit we don't want. -- With the approximation 3/10, this happened for -- 0.5^1030, 0.5^1040, ..., 0.5^1070 and values close above. -- The approximation 8651/28738 guarantees k1 < 1 + logBase 10 x -- for IEEE-ish floating point types with exponent fields -- <= 17 bits and mantissae of several thousand bits, earlier -- convergents to logBase 10 2 would fail for long double. -- Using quot instead of div is a little faster and requires -- fewer fixup steps for negative lx. let lx = p - 1 + e0 k1 = (lx * 8651) `quot` 28738 in if lx >= 0 then k1 + 1 else k1 else -- f :: Integer, log :: Float -> Float, -- ceiling :: Float -> Int ceiling ((log (fromInteger (f+1) :: Float) + fromIntegral e * log (fromInteger b)) / log (fromInteger base)) --WAS: fromInt e * log (fromInteger b)) fixup n = if n >= 0 then if r + mUp <= expt base n * s then n else fixup (n+1) else if expt base (-n) * (r + mUp) <= s then n else fixup (n+1) in fixup k0 gen ds rn sN mUpN mDnN = let (dn, rn') = (rn * base) `quotRem` sN mUpN' = mUpN * base mDnN' = mDnN * base in case (rn' < mDnN', rn' + mUpN' > sN) of (True, False) -> dn : ds (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 = if k >= 0 then gen [] r (s * expt base k) mUp mDn else let bk = expt base (-k) in gen [] (r * bk) s (mUp * bk) (mDn * bk) in (map fromIntegral (reverse rds), k) ------------------------------------------------------------------------ -- Converting from a Rational to a RealFloa ------------------------------------------------------------------------ {- [In response to a request for documentation of how fromRational works, Joe Fasel writes:] A quite reasonable request! This code was added to the Prelude just before the 1.2 release, when Lennart, working with an early version of hbi, noticed that (read . show) was not the identity for floating-point numbers. (There was a one-bit error about half the time.) The original version of the conversion function was in fact simply a floating-point divide, as you suggest above. The new version is, I grant you, somewhat denser. Unfortunately, Joe's code doesn't work! Here's an example: main = putStr (shows (1.82173691287639817263897126389712638972163e-300::Double) "\n") This program prints 0.0000000000000000 instead of 1.8217369128763981e-300 Here's Joe's code: \begin{pseudocode} fromRat :: (RealFloat a) => Rational -> a fromRat x = x' where x' = f e -- 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 -- floating-point number we construct will again be e. If -- not, one more iteration is needed. f e = if e' == e then y else f e' where y = encodeFloat (round (x * (1 % b)^^e)) e (_,e') = decodeFloat y b = floatRadix x' -- We obtain a trial exponent by doing a floating-point -- division of x's numerator by its denominator. The -- result of this division may not itself be the ultimate -- result, because of an accumulation of three rounding -- errors. (s,e) = decodeFloat (fromInteger (numerator x) `asTypeOf` x' / fromInteger (denominator x)) \end{pseudocode} Now, here's Lennart's code (which works): -} -- | Converts a 'Rational' value into any type in class 'RealFloat'. {-# RULES "fromRat/Float" fromRat = (fromRational :: Rational -> Float) "fromRat/Double" fromRat = (fromRational :: Rational -> Double) #-} {-# NOINLINE [1] fromRat #-} fromRat :: (RealFloat a) => Rational -> a -- Deal with special cases first, delegating the real work to fromRat' fromRat (n :% 0) | n > 0 = 1/0 -- +Infinity | n < 0 = -1/0 -- -Infinity | otherwise = 0/0 -- NaN fromRat (n :% d) | n > 0 = fromRat' (n :% d) | n < 0 = - fromRat' ((-n) :% d) | otherwise = encodeFloat 0 0 -- Zero -- Conversion process: -- Scale the rational number by the RealFloat base until -- it lies in the range of the mantissa (as used by decodeFloat/encodeFloat). -- Then round the rational to an Integer and encode it with the exponent -- that we got from the scaling. -- To speed up the scaling process we compute the log2 of the number to get -- a first guess of the exponent. fromRat' :: (RealFloat a) => Rational -> a -- Invariant: argument is strictly positive fromRat' x = r where b = floatRadix r p = floatDigits r (minExp0, _) = floatRange r minExp = minExp0 - p -- the real minimum exponent xMax = toRational (expt b p) p0 = (integerLogBase b (numerator x) - integerLogBase b (denominator x) - p) `max` minExp -- if x = n/d and ln = integerLogBase b n, ld = integerLogBase b d, -- then b^(ln-ld-1) < x < b^(ln-ld+1) f = if p0 < 0 then 1 :% expt b (-p0) else expt b p0 :% 1 x0 = x / f -- if ln - ld >= minExp0, then b^(p-1) < x0 < b^(p+1), so there's at most -- one scaling step needed, otherwise, x0 < b^p and no scaling is needed (x', p') = if x0 >= xMax then (x0 / toRational b, p0+1) else (x0, p0) r = encodeFloat (round x') p' -- Exponentiation with a cache for the most common numbers. minExpt, maxExpt :: Int minExpt = 0 maxExpt = 1100 expt :: Integer -> Int -> Integer expt base n = if base == 2 && n >= minExpt && n <= maxExpt then expts!n else if base == 10 && n <= maxExpt10 then expts10!n else base^n expts :: Array Int Integer expts = array (minExpt,maxExpt) [(n,2^n) | n <- [minExpt .. maxExpt]] maxExpt10 :: Int maxExpt10 = 324 expts10 :: Array Int Integer expts10 = array (minExpt,maxExpt10) [(n,10^n) | n <- [minExpt .. maxExpt10]] -- Compute the (floor of the) log of i in base b. -- Simplest way would be just divide i by b until it's smaller then b, but that would -- be very slow! We are just slightly more clever, except for base 2, where -- we take advantage of the representation of Integers. -- The general case could be improved by a lookup table for -- approximating the result by integerLog2 i / integerLog2 b. integerLogBase :: Integer -> Integer -> Int integerLogBase b i | i < b = 0 | b == 2 = I# (integerLog2# i) | otherwise = I# (integerLogBase# b i) {- Unfortunately, the old conversion code was awfully slow due to a) a slow integer logarithm b) repeated calculation of gcd's For the case of Rational's coming from a Float or Double via toRational, we can exploit the fact that the denominator is a power of two, which for these brings a huge speedup since we need only shift and add instead of division. The below is an adaption of fromRat' for the conversion to Float or Double exploiting the known floatRadix and avoiding divisions as much as possible. -} {-# SPECIALISE fromRat'' :: Int -> Int -> Integer -> Integer -> Float, Int -> Int -> Integer -> Integer -> Double #-} fromRat'' :: RealFloat a => Int -> Int -> Integer -> Integer -> a -- Invariant: n and d strictly positive fromRat'' minEx@(I# me#) mantDigs@(I# md#) n d = case integerLog2IsPowerOf2# d of (# ld#, pw# #) | isTrue# (pw# ==# 0#) -> case integerLog2# n of ln# | isTrue# (ln# >=# (ld# +# me# -# 1#)) -> -- this means n/d >= 2^(minEx-1), i.e. we are guaranteed to get -- a normalised number, round to mantDigs bits if isTrue# (ln# <# md#) then encodeFloat n (I# (negateInt# ld#)) else let n' = n `shiftR` (I# (ln# +# 1# -# md#)) n'' = case roundingMode# n (ln# -# md#) of 0# -> n' 2# -> n' + 1 _ -> case fromInteger n' .&. (1 :: Int) of 0 -> n' _ -> n' + 1 in encodeFloat n'' (I# (ln# -# ld# +# 1# -# md#)) | otherwise -> -- n/d < 2^(minEx-1), a denorm or rounded to 2^(minEx-1) -- the exponent for encoding is always minEx-mantDigs -- so we must shift right by (minEx-mantDigs) - (-ld) case ld# +# (me# -# md#) of ld'# | isTrue# (ld'# <=# 0#) -> -- we would shift left, so we don't shift encodeFloat n (I# ((me# -# md#) -# ld'#)) | isTrue# (ld'# <=# ln#) -> let n' = n `shiftR` (I# ld'#) in case roundingMode# n (ld'# -# 1#) of 0# -> encodeFloat n' (minEx - mantDigs) 1# -> if fromInteger n' .&. (1 :: Int) == 0 then encodeFloat n' (minEx-mantDigs) else encodeFloat (n' + 1) (minEx-mantDigs) _ -> encodeFloat (n' + 1) (minEx-mantDigs) | isTrue# (ld'# ># (ln# +# 1#)) -> encodeFloat 0 0 -- result of shift < 0.5 | otherwise -> -- first bit of n shifted to 0.5 place case integerLog2IsPowerOf2# n of (# _, 0# #) -> encodeFloat 0 0 -- round to even (# _, _ #) -> encodeFloat 1 (minEx - mantDigs) | otherwise -> let ln = I# (integerLog2# n) ld = I# ld# -- 2^(ln-ld-1) < n/d < 2^(ln-ld+1) p0 = max minEx (ln - ld) (n', d') | p0 < mantDigs = (n `shiftL` (mantDigs - p0), d) | p0 == mantDigs = (n, d) | otherwise = (n, d `shiftL` (p0 - mantDigs)) -- if ln-ld < minEx, then n'/d' < 2^mantDigs, else -- 2^(mantDigs-1) < n'/d' < 2^(mantDigs+1) and we -- may need one scaling step scale p a b | (b `shiftL` mantDigs) <= a = (p+1, a, b `shiftL` 1) | otherwise = (p, a, b) (p', n'', d'') = scale (p0-mantDigs) n' d' -- n''/d'' < 2^mantDigs and p' == minEx-mantDigs or n''/d'' >= 2^(mantDigs-1) rdq = case n'' `quotRem` d'' of (q,r) -> case compare (r `shiftL` 1) d'' of LT -> q EQ -> if fromInteger q .&. (1 :: Int) == 0 then q else q+1 GT -> q+1 in encodeFloat rdq p' ------------------------------------------------------------------------ -- Floating point numeric primops ------------------------------------------------------------------------ -- Definitions of the boxed PrimOps; these will be -- used in the case of partial applications, etc. plusFloat, minusFloat, timesFloat, divideFloat :: Float -> Float -> Float plusFloat (F# x) (F# y) = F# (plusFloat# x y) minusFloat (F# x) (F# y) = F# (minusFloat# x y) timesFloat (F# x) (F# y) = F# (timesFloat# x y) divideFloat (F# x) (F# y) = F# (divideFloat# x y) negateFloat :: Float -> Float negateFloat (F# x) = F# (negateFloat# x) gtFloat, geFloat, ltFloat, leFloat :: Float -> Float -> Bool gtFloat (F# x) (F# y) = isTrue# (gtFloat# x y) geFloat (F# x) (F# y) = isTrue# (geFloat# x y) ltFloat (F# x) (F# y) = isTrue# (ltFloat# x y) leFloat (F# x) (F# y) = isTrue# (leFloat# x y) expFloat, logFloat, sqrtFloat, fabsFloat :: Float -> Float sinFloat, cosFloat, tanFloat :: Float -> Float asinFloat, acosFloat, atanFloat :: Float -> Float sinhFloat, coshFloat, tanhFloat :: Float -> Float expFloat (F# x) = F# (expFloat# x) logFloat (F# x) = F# (logFloat# x) sqrtFloat (F# x) = F# (sqrtFloat# x) fabsFloat (F# x) = F# (fabsFloat# x) sinFloat (F# x) = F# (sinFloat# x) cosFloat (F# x) = F# (cosFloat# x) tanFloat (F# x) = F# (tanFloat# x) asinFloat (F# x) = F# (asinFloat# x) acosFloat (F# x) = F# (acosFloat# x) atanFloat (F# x) = F# (atanFloat# x) sinhFloat (F# x) = F# (sinhFloat# x) coshFloat (F# x) = F# (coshFloat# x) tanhFloat (F# x) = F# (tanhFloat# x) powerFloat :: Float -> Float -> Float powerFloat (F# x) (F# y) = F# (powerFloat# x y) -- definitions of the boxed PrimOps; these will be -- used in the case of partial applications, etc. plusDouble, minusDouble, timesDouble, divideDouble :: Double -> Double -> Double plusDouble (D# x) (D# y) = D# (x +## y) minusDouble (D# x) (D# y) = D# (x -## y) timesDouble (D# x) (D# y) = D# (x *## y) divideDouble (D# x) (D# y) = D# (x /## y) negateDouble :: Double -> Double negateDouble (D# x) = D# (negateDouble# x) gtDouble, geDouble, leDouble, ltDouble :: Double -> Double -> Bool gtDouble (D# x) (D# y) = isTrue# (x >## y) geDouble (D# x) (D# y) = isTrue# (x >=## y) ltDouble (D# x) (D# y) = isTrue# (x <## y) leDouble (D# x) (D# y) = isTrue# (x <=## y) double2Float :: Double -> Float double2Float (D# x) = F# (double2Float# x) float2Double :: Float -> Double float2Double (F# x) = D# (float2Double# x) expDouble, logDouble, sqrtDouble, fabsDouble :: Double -> Double sinDouble, cosDouble, tanDouble :: Double -> Double asinDouble, acosDouble, atanDouble :: Double -> Double sinhDouble, coshDouble, tanhDouble :: Double -> Double expDouble (D# x) = D# (expDouble# x) logDouble (D# x) = D# (logDouble# x) sqrtDouble (D# x) = D# (sqrtDouble# x) fabsDouble (D# x) = D# (fabsDouble# x) sinDouble (D# x) = D# (sinDouble# x) cosDouble (D# x) = D# (cosDouble# x) tanDouble (D# x) = D# (tanDouble# x) asinDouble (D# x) = D# (asinDouble# x) acosDouble (D# x) = D# (acosDouble# x) atanDouble (D# x) = D# (atanDouble# x) sinhDouble (D# x) = D# (sinhDouble# x) coshDouble (D# x) = D# (coshDouble# x) tanhDouble (D# x) = D# (tanhDouble# x) powerDouble :: Double -> Double -> Double powerDouble (D# x) (D# y) = D# (x **## y) foreign import ccall unsafe "isFloatNaN" isFloatNaN :: Float -> Int foreign import ccall unsafe "isFloatInfinite" isFloatInfinite :: Float -> Int foreign import ccall unsafe "isFloatDenormalized" isFloatDenormalized :: Float -> Int foreign import ccall unsafe "isFloatNegativeZero" isFloatNegativeZero :: Float -> Int foreign import ccall unsafe "isFloatFinite" isFloatFinite :: Float -> Int foreign import ccall unsafe "isDoubleNaN" isDoubleNaN :: Double -> Int foreign import ccall unsafe "isDoubleInfinite" isDoubleInfinite :: Double -> Int foreign import ccall unsafe "isDoubleDenormalized" isDoubleDenormalized :: Double -> Int foreign import ccall unsafe "isDoubleNegativeZero" isDoubleNegativeZero :: Double -> Int foreign import ccall unsafe "isDoubleFinite" isDoubleFinite :: Double -> Int ------------------------------------------------------------------------ -- libm imports for extended floating ------------------------------------------------------------------------ foreign import capi unsafe "math.h log1p" log1pDouble :: Double -> Double foreign import capi unsafe "math.h expm1" expm1Double :: Double -> Double foreign import capi unsafe "math.h log1pf" log1pFloat :: Float -> Float foreign import capi unsafe "math.h expm1f" expm1Float :: Float -> Float ------------------------------------------------------------------------ -- Coercion rules ------------------------------------------------------------------------ word2Double :: Word -> Double word2Double (W# w) = D# (word2Double# w) word2Float :: Word -> Float word2Float (W# w) = F# (word2Float# w) {-# RULES "fromIntegral/Int->Float" fromIntegral = int2Float "fromIntegral/Int->Double" fromIntegral = int2Double "fromIntegral/Word->Float" fromIntegral = word2Float "fromIntegral/Word->Double" fromIntegral = word2Double "realToFrac/Float->Float" realToFrac = id :: Float -> Float "realToFrac/Float->Double" realToFrac = float2Double "realToFrac/Double->Float" realToFrac = double2Float "realToFrac/Double->Double" realToFrac = id :: Double -> Double "realToFrac/Int->Double" realToFrac = int2Double -- See Note [realToFrac int-to-float] "realToFrac/Int->Float" realToFrac = int2Float -- ..ditto #-} {- Note [realToFrac int-to-float] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 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 "Add RULES for realToFrac from Int". -} -- Utils showSignedFloat :: (RealFloat a) => (a -> ShowS) -- ^ a function that can show unsigned values -> Int -- ^ the precedence of the enclosing context -> a -- ^ the value to show -> ShowS showSignedFloat showPos p x | x < 0 || isNegativeZero x = showParen (p > 6) (showChar '-' . showPos (-x)) | otherwise = showPos x {- We need to prevent over/underflow of the exponent in encodeFloat when called from scaleFloat, hence we clamp the scaling parameter. We must have a large enough range to cover the maximum difference of exponents returned by decodeFloat. -} clamp :: Int -> Int -> Int clamp bd k = max (-bd) (min bd k) {- Note [Casting from integral to floating point types] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ To implement something like `reinterpret_cast` from C++ to go from a floating-point type to an integral type one might niavely think that the following should work: cast :: Float -> Word32 cast (F# f#) = W32# (unsafeCoerce# f#) Unfortunately that is not the case, because all the `unsafeCoerce#` does is tell the compiler that the types have changed. When one does the above cast and tries to operate on the resulting `Word32` the code generator will generate code that performs an integer/word operation on a floating-point register, which results in a compile error. The correct way of implementing `reinterpret_cast` to implement a primpop, but that requires a unique implementation for all supported archetectures. The next best solution is to write the value from the source register to memory and then read it from memory into the destination register and the best way to do that is using CMM. -} -- | @'castWord32ToFloat' w@ does a bit-for-bit copy from an integral value -- to a floating-point value. -- -- @since 4.10.0.0 {-# INLINE castWord32ToFloat #-} castWord32ToFloat :: Word32 -> Float castWord32ToFloat (W32# w#) = F# (stgWord32ToFloat w#) foreign import prim "stg_word32ToFloatzh" stgWord32ToFloat :: Word# -> Float# -- | @'castFloatToWord32' f@ does a bit-for-bit copy from a floating-point value -- to an integral value. -- -- @since 4.10.0.0 {-# INLINE castFloatToWord32 #-} castFloatToWord32 :: Float -> Word32 castFloatToWord32 (F# f#) = W32# (stgFloatToWord32 f#) foreign import prim "stg_floatToWord32zh" stgFloatToWord32 :: Float# -> Word# -- | @'castWord64ToDouble' w@ does a bit-for-bit copy from an integral value -- to a floating-point value. -- -- @since 4.10.0.0 {-# INLINE castWord64ToDouble #-} castWord64ToDouble :: Word64 -> Double castWord64ToDouble (W64# w) = D# (stgWord64ToDouble w) foreign import prim "stg_word64ToDoublezh" #if WORD_SIZE_IN_BITS == 64 stgWord64ToDouble :: Word# -> Double# #else stgWord64ToDouble :: Word64# -> Double# #endif -- | @'castFloatToWord32' f@ does a bit-for-bit copy from a floating-point value -- to an integral value. -- -- @since 4.10.0.0 {-# INLINE castDoubleToWord64 #-} castDoubleToWord64 :: Double -> Word64 castDoubleToWord64 (D# d#) = W64# (stgDoubleToWord64 d#) foreign import prim "stg_doubleToWord64zh" #if WORD_SIZE_IN_BITS == 64 stgDoubleToWord64 :: Double# -> Word# #else stgDoubleToWord64 :: Double# -> Word64# #endif