diff options
Diffstat (limited to 'libraries/base/GHC/Float.hs')
| -rw-r--r-- | libraries/base/GHC/Float.hs | 75 |
1 files changed, 67 insertions, 8 deletions
diff --git a/libraries/base/GHC/Float.hs b/libraries/base/GHC/Float.hs index c534bafa07..9296978bd4 100644 --- a/libraries/base/GHC/Float.hs +++ b/libraries/base/GHC/Float.hs @@ -64,6 +64,13 @@ infixr 8 ** ------------------------------------------------------------------------ -- | 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 @@ -159,7 +166,7 @@ class (RealFrac a, Floating a) => RealFloat a where 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@. + -- @'Prelude.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, @@ -245,7 +252,18 @@ class (RealFrac a, Floating a) => RealFloat a where ------------------------------------------------------------------------ -- | @since 2.01 -instance Num Float where +-- 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 @@ -272,6 +290,11 @@ instance Real Float where 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 #-} @@ -367,9 +390,9 @@ instance Floating Float where (**) x y = powerFloat x y logBase x y = log y / log x - asinh x = log (x + sqrt (1.0+x*x)) - 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)) + asinh x = asinhFloat x + acosh x = acoshFloat x + atanh x = atanhFloat x log1p = log1pFloat expm1 = expm1Float @@ -425,6 +448,17 @@ instance Show Float where ------------------------------------------------------------------------ -- | @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 @@ -454,6 +488,11 @@ instance Real Double where 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 #-} @@ -492,9 +531,9 @@ instance Floating Double where (**) x y = powerDouble x y logBase x y = log y / log x - asinh x = log (x + sqrt (1.0+x*x)) - 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)) + asinh x = asinhDouble x + acosh x = acoshDouble x + atanh x = atanhDouble x log1p = log1pDouble expm1 = expm1Double @@ -682,6 +721,18 @@ formatRealFloatAlt fmt decs alt x [d] -> d : ".0e" ++ show_e' (d:ds') -> d : '.' : ds' ++ "e" ++ show_e' [] -> errorWithoutStackTrace "formatRealFloat/doFmt/FFExponent: []" + Just d | d <= 0 -> + -- handle this case specifically since we need to omit the + -- decimal point as well (#15115). + -- Note that this handles negative precisions as well for consistency + -- (see #15509). + 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 (e-1+ei) Just dec -> let dec' = max dec 1 in case is of @@ -1092,6 +1143,7 @@ expFloat, logFloat, 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) logFloat (F# x) = F# (logFloat# x) sqrtFloat (F# x) = F# (sqrtFloat# x) @@ -1105,6 +1157,9 @@ 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) @@ -1137,6 +1192,7 @@ expDouble, logDouble, 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) logDouble (D# x) = D# (logDouble# x) sqrtDouble (D# x) = D# (sqrtDouble# x) @@ -1150,6 +1206,9 @@ 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) |