#include "ieee-flpt.h"
#include "MachDeps.h"
#if WORD_SIZE_IN_BITS == 32
# define WSHIFT 5
# define MMASK 31
#elif WORD_SIZE_IN_BITS == 64
# define WSHIFT 6
# define MMASK 63
#else
# error unsupported WORD_SIZE_IN_BITS
#endif
module GHC.Float
( module GHC.Float
, Float(..), Double(..), Float#, Double#
, double2Int, int2Double, float2Int, int2Float
, eqFloat, eqDouble
) where
import Data.Maybe
import GHC.Base
import GHC.Bits
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.Num.BigNat
infixr 8 **
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 :: a -> a
expm1 :: a -> a
log1pexp :: a -> a
log1mexp :: a -> a
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
log1p x = log (1 + x)
expm1 x = exp x 1
log1pexp x = log1p (exp x)
log1mexp x = log1p (negate (exp x))
log1mexpOrd :: (Ord a, Floating a) => a -> a
log1mexpOrd a
| a > (log 2) = log (negate (expm1 a))
| otherwise = log1p (negate (exp a))
class (RealFrac a, Floating a) => RealFloat a where
floatRadix :: a -> Integer
floatDigits :: a -> Int
floatRange :: a -> (Int,Int)
decodeFloat :: a -> (Integer,Int)
encodeFloat :: Integer -> Int -> a
exponent :: a -> Int
significand :: a -> a
scaleFloat :: Int -> a -> a
isNaN :: a -> Bool
isInfinite :: a -> Bool
isDenormalized :: a -> Bool
isNegativeZero :: a -> Bool
isIEEE :: a -> Bool
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
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
| x==0 && y==0 = y
| otherwise = x + y
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
fromInteger i = F# (integerToFloat# i)
integerToFloat# :: Integer -> Float#
integerToFloat# (IS i) = int2Float# i
integerToFloat# i@(IP _) = case integerToBinaryFloat' i of
F# x -> x
integerToFloat# (IN bn) = case integerToBinaryFloat' (IP bn) of
F# x -> negateFloat# x
naturalToFloat# :: Natural -> Float#
naturalToFloat# (NS w) = word2Float# w
naturalToFloat# (NB b) = case integerToBinaryFloat' (IP b) of
F# x -> x
instance Real Float where
toRational (F# x#) =
case decodeFloat_Int# x# of
(# m#, e# #)
| isTrue# (e# >=# 0#) ->
(IS m# `integerShiftL#` int2Word# e#) :% 1
| isTrue# ((int2Word# m# `and#` 1##) `eqWord#` 0##) ->
case elimZerosInt# m# (negateInt# e#) of
(# n, d# #) -> n :% integerShiftL# 1 (int2Word# d#)
| otherwise ->
IS m# :% integerShiftL# 1 (int2Word# (negateInt# e#))
instance Fractional Float where
(/) x y = divideFloat x y
fromRational (n:%d) = rationalToFloat n d
recip x = 1.0 / x
rationalToFloat :: Integer -> Integer -> Float
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
instance RealFrac Float where
#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
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 = asinhFloat x
acosh x = acoshFloat x
atanh x = atanhFloat x
log1p = log1pFloat
expm1 = expm1Float
log1mexp x = log1mexpOrd x
log1pexp a
| a <= 18 = log1pFloat (exp a)
| a <= 100 = a + exp (negate a)
| otherwise = a
instance RealFloat Float where
floatRadix _ = FLT_RADIX
floatDigits _ = FLT_MANT_DIG
floatRange _ = (FLT_MIN_EXP, FLT_MAX_EXP)
decodeFloat (F# f#) = case decodeFloat_Int# f# of
(# i, e #) -> (IS i, I# e)
encodeFloat i (I# e) = F# (integerEncodeFloat# 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
instance Show Float where
showsPrec x = showSignedFloat showFloat x
showList = showList__ (showsPrec 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
fromInteger i = D# (integerToDouble# i)
integerToDouble# :: Integer -> Double#
integerToDouble# (IS i) = int2Double# i
integerToDouble# i@(IP _) = case integerToBinaryFloat' i of
D# x -> x
integerToDouble# (IN bn) = case integerToBinaryFloat' (IP bn) of
D# x -> negateDouble# x
naturalToDouble# :: Natural -> Double#
naturalToDouble# (NS w) = word2Double# w
naturalToDouble# (NB b) = case integerToBinaryFloat' (IP b) of
D# x -> x
instance Real Double where
toRational (D# x#) =
case integerDecodeDouble# x# of
(# m, e# #)
| isTrue# (e# >=# 0#) ->
integerShiftL# m (int2Word# e#) :% 1
| isTrue# ((integerToWord# m `and#` 1##) `eqWord#` 0##) ->
case elimZerosInteger m (negateInt# e#) of
(# n, d# #) -> n :% integerShiftL# 1 (int2Word# d#)
| otherwise ->
m :% integerShiftL# 1 (int2Word# (negateInt# e#))
instance Fractional Double where
(/) x y = divideDouble x y
fromRational (n:%d) = rationalToDouble n d
recip x = 1.0 / x
rationalToDouble :: Integer -> Integer -> Double
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
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 = asinhDouble x
acosh x = acoshDouble x
atanh x = atanhDouble x
log1p = log1pDouble
expm1 = expm1Double
log1mexp x = log1mexpOrd x
log1pexp a
| a <= 18 = log1pDouble (exp a)
| a <= 100 = a + exp (negate a)
| otherwise = a
instance RealFrac Double where
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
instance RealFloat Double where
floatRadix _ = FLT_RADIX
floatDigits _ = DBL_MANT_DIG
floatRange _ = (DBL_MIN_EXP, DBL_MAX_EXP)
decodeFloat (D# x#)
= case integerDecodeDouble# x# of
(# i, j #) -> (i, I# j)
encodeFloat i (I# j) = D# (integerEncodeDouble# 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
instance Show Double where
showsPrec x = showSignedFloat showFloat x
showList = showList__ (showsPrec 0)
instance Enum Float where
succ x = x + 1
pred x = x 1
toEnum = int2Float
fromEnum = fromInteger . truncate
enumFrom = numericEnumFrom
enumFromTo = numericEnumFromTo
enumFromThen = numericEnumFromThen
enumFromThenTo = numericEnumFromThenTo
instance Enum Double where
succ x = x + 1
pred x = x 1
toEnum = int2Double
fromEnum = fromInteger . truncate
enumFrom = numericEnumFrom
enumFromTo = numericEnumFromTo
enumFromThen = numericEnumFromThen
enumFromThenTo = numericEnumFromThenTo
showFloat :: (RealFloat a) => a -> ShowS
showFloat x = showString (formatRealFloat FFGeneric Nothing x)
data FFFormat = FFExponent | FFFixed | FFGeneric
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 (e1) in
case ds of
"0" -> "0.0e0"
[d] -> d : ".0e" ++ show_e'
(d:ds') -> d : '.' : ds' ++ "e" ++ show_e'
[] -> errorWithoutStackTrace "formatRealFloat/doFmt/FFExponent: []"
Just d | d <= 0 ->
case is of
[0] -> "0e0"
_ ->
let
(ei,is') = roundTo base 1 is
n:_ = map intToDigit (if ei > 0 then init is' else is')
in n : 'e' : show (e1+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 (e1+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 (n1) ('0':s) ""
f n s (r:rs) = f (n1) (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, [])
| 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 (n1) (even i) xs
i' = c + i
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
(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 (p1) then
(f*be*b*2, 2*b, be*b, be)
else
(f*be*2, 2, be, be)
else
if e > minExp && f == expt b (p1) 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
let lx = p 1 + e0
k1 = (lx * 8651) `quot` 28738
in if lx >= 0 then k1 + 1 else k1
else
ceiling ((log (fromInteger (f+1) :: Float) +
fromIntegral e * log (fromInteger b)) /
log (fromInteger base))
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)
integerToBinaryFloat' :: RealFloat a => Integer -> a
integerToBinaryFloat' n = result
where
mantDigs = floatDigits result
k = I# (word2Int# (integerLog2# n))
result = if k < mantDigs then
encodeFloat n 0
else
let !e@(I# e#) = k mantDigs + 1
q = n `unsafeShiftR` e
n' = case roundingMode# n (e# -# 1#) of
0# -> q
1# -> if integerToInt q .&. 1 == 0 then
q
else
q + 1
_ -> q + 1
in encodeFloat n' e
fromRat :: (RealFloat a) => Rational -> a
fromRat (n :% 0) | n > 0 = 1/0
| n < 0 = 1/0
| otherwise = 0/0
fromRat (n :% d) | n > 0 = fromRat' (n :% d)
| n < 0 = fromRat' ((n) :% d)
| otherwise = encodeFloat 0 0
fromRat' :: (RealFloat a) => Rational -> a
fromRat' x = r
where b = floatRadix r
p = floatDigits r
(minExp0, _) = floatRange r
minExp = minExp0 p
xMax = toRational (expt b p)
ln = I# (word2Int# (integerLogBase# b (numerator x)))
ld = I# (word2Int# (integerLogBase# b (denominator x)))
p0 = (ln ld p) `max` minExp
f = if p0 < 0 then 1 :% expt b (p0) else expt b p0 :% 1
x0 = x / f
(x', p') = if x0 >= xMax then (x0 / toRational b, p0+1) else (x0, p0)
r = encodeFloat (round x') p'
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]]
fromRat'' :: RealFloat a => Int -> Int -> Integer -> Integer -> a
fromRat'' minEx@(I# me#) mantDigs@(I# md#) n d =
case integerIsPowerOf2# d of
(# | ldw# #) ->
let ld# = word2Int# ldw#
in case word2Int# (integerLog2# n) of
ln# | isTrue# (ln# >=# (ld# +# me# -# 1#)) ->
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 ->
case ld# +# (me# -# md#) of
ld'# | isTrue# (ld'# <=# 0#) ->
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' (minExmantDigs)
else encodeFloat (n' + 1) (minExmantDigs)
_ -> encodeFloat (n' + 1) (minExmantDigs)
| isTrue# (ld'# ># (ln# +# 1#)) -> encodeFloat 0 0
| otherwise ->
case integerIsPowerOf2# n of
(# | _ #) -> encodeFloat 0 0
(# (# #) | #) -> encodeFloat 1 (minEx mantDigs)
(# (# #) | #) ->
let ln = I# (word2Int# (integerLog2# n))
ld = I# (word2Int# (integerLog2# d))
p0 = max minEx (ln ld)
(n', d')
| p0 < mantDigs = (n `shiftL` (mantDigs p0), d)
| p0 == mantDigs = (n, d)
| otherwise = (n, d `shiftL` (p0 mantDigs))
scale p a b
| (b `shiftL` mantDigs) <= a = (p+1, a, b `shiftL` 1)
| otherwise = (p, a, b)
(p', n'', d'') = scale (p0mantDigs) n' d'
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'
roundingMode# :: Integer -> Int# -> Int#
roundingMode# (IS i#) t =
let
k = int2Word# i# `and#` ((uncheckedShiftL# 2## t) `minusWord#` 1##)
c = uncheckedShiftL# 1## t
in if isTrue# (c `gtWord#` k)
then 0#
else if isTrue# (c `ltWord#` k)
then 2#
else 1#
roundingMode# (IN bn) t = roundingMode# (IP bn) t
roundingMode# (IP bn) t =
let
j = word2Int# (int2Word# t `and#` MMASK##)
k = uncheckedIShiftRA# t WSHIFT#
r = bigNatIndex# bn k `and#` ((uncheckedShiftL# 2## j) `minusWord#` 1##)
c = uncheckedShiftL# 1## j
test i = if isTrue# (i <# 0#)
then 1#
else case bigNatIndex# bn i of
0## -> test (i -# 1#)
_ -> 2#
in if isTrue# (c `gtWord#` r)
then 0#
else if isTrue# (c `ltWord#` r)
then 2#
else test (k -# 1#)
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, expm1Float :: Float -> Float
logFloat, log1pFloat, sqrtFloat, fabsFloat :: Float -> Float
sinFloat, cosFloat, tanFloat :: Float -> Float
asinFloat, acosFloat, atanFloat :: Float -> Float
sinhFloat, coshFloat, tanhFloat :: Float -> Float
asinhFloat, acoshFloat, atanhFloat :: Float -> Float
expFloat (F# x) = F# (expFloat# x)
expm1Float (F# x) = F# (expm1Float# x)
logFloat (F# x) = F# (logFloat# x)
log1pFloat (F# x) = F# (log1pFloat# 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)
asinhFloat (F# x) = F# (asinhFloat# x)
acoshFloat (F# x) = F# (acoshFloat# x)
atanhFloat (F# x) = F# (atanhFloat# x)
powerFloat :: Float -> Float -> Float
powerFloat (F# x) (F# y) = F# (powerFloat# x y)
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, expm1Double :: Double -> Double
logDouble, log1pDouble, sqrtDouble, fabsDouble :: Double -> Double
sinDouble, cosDouble, tanDouble :: Double -> Double
asinDouble, acosDouble, atanDouble :: Double -> Double
sinhDouble, coshDouble, tanhDouble :: Double -> Double
asinhDouble, acoshDouble, atanhDouble :: Double -> Double
expDouble (D# x) = D# (expDouble# x)
expm1Double (D# x) = D# (expm1Double# x)
logDouble (D# x) = D# (logDouble# x)
log1pDouble (D# x) = D# (log1pDouble# 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)
asinhDouble (D# x) = D# (asinhDouble# x)
acoshDouble (D# x) = D# (acoshDouble# x)
atanhDouble (D# x) = D# (atanhDouble# 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
word2Double :: Word -> Double
word2Double (W# w) = D# (word2Double# w)
word2Float :: Word -> Float
word2Float (W# w) = F# (word2Float# w)
showSignedFloat :: (RealFloat a)
=> (a -> ShowS)
-> Int
-> a
-> ShowS
showSignedFloat showPos p x
| x < 0 || isNegativeZero x
= showParen (p > 6) (showChar '-' . showPos (x))
| otherwise = showPos x
clamp :: Int -> Int -> Int
clamp bd k = max (bd) (min bd k)
castWord32ToFloat :: Word32 -> Float
castWord32ToFloat (W32# w#) = F# (stgWord32ToFloat w#)
foreign import prim "stg_word32ToFloatzh"
stgWord32ToFloat :: Word32# -> Float#
castFloatToWord32 :: Float -> Word32
castFloatToWord32 (F# f#) = W32# (stgFloatToWord32 f#)
foreign import prim "stg_floatToWord32zh"
stgFloatToWord32 :: Float# -> Word32#
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
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