-- | Common math functions.
module Sound.Sc3.Common.Math where

import qualified Data.Fixed {- base -}
import Data.Maybe {- base -}
import Data.Ratio {- base -}
import qualified Numeric {- base -}

import qualified Sound.Sc3.Common.Base as Common.Base {- hsc3 -}

-- | Half pi.
--
-- > half_pi == 1.5707963267948966
half_pi :: Floating a => a
half_pi :: forall a. Floating a => a
half_pi = forall a. Floating a => a
pi forall a. Fractional a => a -> a -> a
/ a
2

-- | Two pi.
--
-- > two_pi == 6.283185307179586
two_pi :: Floating n => n
two_pi :: forall a. Floating a => a
two_pi = n
2 forall a. Num a => a -> a -> a
* forall a. Floating a => a
pi

-- | 'abs' of '(-)'.
absdif :: Num a => a -> a -> a
absdif :: forall a. Num a => a -> a -> a
absdif a
i a
j = forall a. Num a => a -> a
abs (a
j forall a. Num a => a -> a -> a
- a
i)

-- | SC3 MulAdd type signature, arguments in SC3 order of input, multiply, add.
type SC3_MulAdd t = t -> t -> t -> t

-- | Ordinary (un-optimised) multiply-add, see also mulAdd Ugen.
--
-- > sc3_mul_add 2 3 4 == 2 * 3 + 4
-- > map (\x -> sc3_mul_add x 2 3) [1,5] == [5,13] && map (\x -> sc3_mul_add x 3 2) [1,5] == [5,17]
sc3_mul_add :: Num t => SC3_MulAdd t
sc3_mul_add :: forall t. Num t => SC3_MulAdd t
sc3_mul_add t
i t
m t
a = t
i forall a. Num a => a -> a -> a
* t
m forall a. Num a => a -> a -> a
+ t
a

-- | Ordinary Haskell order (un-optimised) multiply-add.
--
-- > mul_add 3 4 2 == 2 * 3 + 4
-- > map (mul_add 2 3) [1,5] == [5,13] && map (mul_add 3 4) [1,5] == [7,19]
mul_add :: Num t => t -> t -> t -> t
mul_add :: forall t. Num t => SC3_MulAdd t
mul_add t
m t
a = (forall a. Num a => a -> a -> a
+ t
a) forall b c a. (b -> c) -> (a -> b) -> a -> c
. (forall a. Num a => a -> a -> a
* t
m)

-- | 'uncurry' 'mul_add'
--
-- > mul_add_hs (3,4) 2 == 2 * 3 + 4
mul_add_hs :: Num t => (t,t) -> t -> t
mul_add_hs :: forall t. Num t => (t, t) -> t -> t
mul_add_hs = forall a b c. (a -> b -> c) -> (a, b) -> c
uncurry forall t. Num t => SC3_MulAdd t
mul_add

-- | 'fromInteger' of 'truncate'.
sc3_truncate :: RealFrac a => a -> a
sc3_truncate :: forall a. RealFrac a => a -> a
sc3_truncate = forall a. Num a => Integer -> a
fromInteger forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a b. (RealFrac a, Integral b) => a -> b
truncate

-- | 'fromInteger' of 'round'.
sc3_round :: RealFrac a => a -> a
sc3_round :: forall a. RealFrac a => a -> a
sc3_round = forall a. Num a => Integer -> a
fromInteger forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a b. (RealFrac a, Integral b) => a -> b
round

-- | 'fromInteger' of 'ceiling'.
sc3_ceiling :: RealFrac a => a -> a
sc3_ceiling :: forall a. RealFrac a => a -> a
sc3_ceiling = forall a. Num a => Integer -> a
fromInteger forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a b. (RealFrac a, Integral b) => a -> b
ceiling

-- | 'fromInteger' of 'floor'.
sc3_floor :: RealFrac a => a -> a
sc3_floor :: forall a. RealFrac a => a -> a
sc3_floor = forall a. Num a => Integer -> a
fromInteger forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a b. (RealFrac a, Integral b) => a -> b
floor

-- | Variant of @SC3@ @roundTo@ function.
--
-- > sc3_round_to (2/3) 0.25 == 0.75
--
-- > let r = [0,0,0.25,0.25,0.5,0.5,0.5,0.75,0.75,1,1]
-- > map (`sc3_round_to` 0.25) [0,0.1 .. 1] == r
-- > map (`sc3_round_to` 5.0) [100.0 .. 110.0]
sc3_round_to :: RealFrac n => n -> n -> n
sc3_round_to :: forall n. RealFrac n => n -> n -> n
sc3_round_to n
a n
b = if n
b forall a. Eq a => a -> a -> Bool
== n
0 then n
a else forall a. RealFrac a => a -> a
sc3_floor ((n
a forall a. Fractional a => a -> a -> a
/ n
b) forall a. Num a => a -> a -> a
+ n
0.5) forall a. Num a => a -> a -> a
* n
b

-- | 'fromInteger' of 'div' of 'floor'.
sc3_idiv :: RealFrac n => n -> n -> n
sc3_idiv :: forall n. RealFrac n => n -> n -> n
sc3_idiv n
a n
b = forall a. Num a => Integer -> a
fromInteger (forall a b. (RealFrac a, Integral b) => a -> b
floor n
a forall a. Integral a => a -> a -> a
`div` forall a b. (RealFrac a, Integral b) => a -> b
floor n
b)

{- | 'sc3_lcm'

Least common multiple. This definition extends the usual definition
and returns a negative number if any of the operands is negative. This
makes it consistent with the lattice-theoretical interpretation and
its idempotency, commutative, associative, absorption laws.

> lcm 4 6 == 12
> lcm 1 1 == 1
> lcm 1624 26 == 21112
> lcm 1624 (-26) /= (-21112)
> lcm (-1624) (-26) /= (-21112)
> lcm 513 (gcd 513 44) == 513
-}
sc3_lcm :: t -> t -> t
sc3_lcm :: forall t. t -> t -> t
sc3_lcm = forall a. HasCallStack => [Char] -> a
error [Char]
"sc3_lcm: undefined"

{- | 'sc3_gcd'

Greatest common divisor. This definition extends the usual
definition and returns a negative number if both operands are
negative. This makes it consistent with the lattice-theoretical
interpretation and its idempotency, commutative, associative,
absorption laws. <https://www.jsoftware.com/papers/eem/gcd.htm>

> gcd 4 6 == 2
> gcd 0 1 == 1
> gcd 1024 256 == 256
> gcd 1024 (-256) == 256
> gcd (-1024) (-256) /= (-256)
> gcd (-1024) (lcm (-1024) 256) /= (-1024)
> gcd 66 54 * lcm 66 54 == 66 * 54

-}
sc3_gcd :: t -> t -> t
sc3_gcd :: forall t. t -> t -> t
sc3_gcd = forall a. HasCallStack => [Char] -> a
error [Char]
"sc3_gcd: undefined"

{- | The SC3 @%@ Ugen operator is the 'Data.Fixed.mod'' function.

> > 1.5 % 1.2 // ~= 0.3
> > -1.5 % 1.2 // ~= 0.9
> > 1.5 % -1.2 // ~= -0.9
> > -1.5 % -1.2 // ~= -0.3

> let (%) = sc3_mod
> 1.5 % 1.2 ~= 0.3
> (-1.5) % 1.2 ~= 0.9
> 1.5 % (-1.2) ~= -0.9
> (-1.5) % (-1.2) ~= -0.3

> > 1.2 % 1.5 // ~= 1.2
> > -1.2 % 1.5 // ~= 0.3
> > 1.2 % -1.5 // ~= -0.3
> > -1.2 % -1.5 // ~= -1.2

> 1.2 % 1.5 ~= 1.2
> (-1.2) % 1.5 ~= 0.3
> 1.2 % (-1.5) ~= -0.3
> (-1.2) % (-1.5) ~= -1.2

> map (\n -> sc3_mod n 12.0) [-1.0,12.25,15.0] == [11.0,0.25,3.0]
-}
sc3_mod :: RealFrac n => n -> n -> n
sc3_mod :: forall n. RealFrac n => n -> n -> n
sc3_mod = forall a. Real a => a -> a -> a
Data.Fixed.mod'

-- | Type specialised 'sc3_mod'.
fmod_f32 :: Float -> Float -> Float
fmod_f32 :: Float -> Float -> Float
fmod_f32 = forall n. RealFrac n => n -> n -> n
sc3_mod

-- | Type specialised 'sc3_mod'.
fmod_f64 :: Double -> Double -> Double
fmod_f64 :: Double -> Double -> Double
fmod_f64 = forall n. RealFrac n => n -> n -> n
sc3_mod

-- | @SC3@ clip function.  Clip /n/ to within range /(i,j)/.  'clip' is a 'Ugen'.
--
-- > map (\n -> sc3_clip n 5 10) [3..12] == [5,5,5,6,7,8,9,10,10,10]
sc3_clip :: Ord a => a -> a -> a -> a
sc3_clip :: forall a. Ord a => a -> a -> a -> a
sc3_clip a
n a
i a
j = if a
n forall a. Ord a => a -> a -> Bool
< a
i then a
i else if a
n forall a. Ord a => a -> a -> Bool
> a
j then a
j else a
n

-- | Variant of 'sc3_clip' with haskell argument structure.
--
-- > map (clip_hs (5,10)) [3..12] == [5,5,5,6,7,8,9,10,10,10]
clip_hs :: (Ord a) => (a,a) -> a -> a
clip_hs :: forall a. Ord a => (a, a) -> a -> a
clip_hs (a
i,a
j) a
n = forall a. Ord a => a -> a -> a -> a
sc3_clip a
n a
i a
j

-- | Fractional modulo, alternate implementation.
--
-- > map (\n -> sc3_mod_alt n 12.0) [-1.0,12.25,15.0] == [11.0,0.25,3.0]
sc3_mod_alt :: RealFrac a => a -> a -> a
sc3_mod_alt :: forall n. RealFrac n => n -> n -> n
sc3_mod_alt a
n a
hi =
    let lo :: a
lo = a
0.0
    in if a
n forall a. Ord a => a -> a -> Bool
>= a
lo Bool -> Bool -> Bool
&& a
n forall a. Ord a => a -> a -> Bool
< a
hi
       then a
n
       else if a
hi forall a. Eq a => a -> a -> Bool
== a
lo
            then a
lo
            else a
n forall a. Num a => a -> a -> a
- a
hi forall a. Num a => a -> a -> a
* forall a. RealFrac a => a -> a
sc3_floor (a
n forall a. Fractional a => a -> a -> a
/ a
hi)

{- | Wrap function that is /non-inclusive/ at right edge, ie. the Wrap Ugen rule.

> map (sc3_wrap_ni 0 5) [4,5,6] == [4,0,1]
> map (sc3_wrap_ni 5 10) [3..12] == [8,9,5,6,7,8,9,5,6,7]
> Sound.Sc3.Plot.plot_fn_r1_ln (sc3_wrap_ni (-1) 1) (-2,2)

-}
sc3_wrap_ni :: RealFrac a => a -> a -> a -> a
sc3_wrap_ni :: forall a. RealFrac a => a -> a -> a -> a
sc3_wrap_ni a
lo a
hi a
n = forall n. RealFrac n => n -> n -> n
sc3_mod (a
n forall a. Num a => a -> a -> a
- a
lo) (a
hi forall a. Num a => a -> a -> a
- a
lo) forall a. Num a => a -> a -> a
+ a
lo

{- | sc_wrap::int

> > [5,6].wrap(0,5) == [5,0]
> map (wrap_hs_int (0,5)) [5,6] == [5,0]

> > [9,10,5,6,7,8,9,10,5,6].wrap(5,10) == [9,10,5,6,7,8,9,10,5,6]
> map (wrap_hs_int (5,10)) [3..12] == [9,10,5,6,7,8,9,10,5,6]
-}
wrap_hs_int :: Integral a => (a, a) -> a -> a
wrap_hs_int :: forall a. Integral a => (a, a) -> a -> a
wrap_hs_int (a
i,a
j) a
n = ((a
n forall a. Num a => a -> a -> a
- a
i) forall a. Integral a => a -> a -> a
`mod` (a
j forall a. Num a => a -> a -> a
- a
i forall a. Num a => a -> a -> a
+ a
1)) forall a. Num a => a -> a -> a
+ a
i

{- | Wrap /n/ to within range /(i,j)/, ie. @AbstractFunction.wrap@,
ie. /inclusive/ at right edge.  'wrap' is a 'Ugen', hence prime.

> > [5.0,6.0].wrap(0.0,5.0) == [0.0,1.0]
> map (wrap_hs (0,5)) [5,6] == [0,1]
> map (wrap_hs (5,10)) [3..12] == [8,9,5,6,7,8,9,5,6,7]

> Sound.Sc3.Plot.plot_fn_r1_ln (wrap_hs (-1,1)) (-2,2)

-}
wrap_hs :: RealFrac n => (n,n) -> n -> n
wrap_hs :: forall n. RealFrac n => (n, n) -> n -> n
wrap_hs (n
i,n
j) n
n =
    let r :: n
r = n
j forall a. Num a => a -> a -> a
- n
i -- + 1
        n' :: n
n' = if n
n forall a. Ord a => a -> a -> Bool
>= n
j then n
n forall a. Num a => a -> a -> a
- n
r else if n
n forall a. Ord a => a -> a -> Bool
< n
i then n
n forall a. Num a => a -> a -> a
+ n
r else n
n
    in if n
n' forall a. Ord a => a -> a -> Bool
>= n
i Bool -> Bool -> Bool
&& n
n' forall a. Ord a => a -> a -> Bool
< n
j
       then n
n'
       else n
n' forall a. Num a => a -> a -> a
- n
r forall a. Num a => a -> a -> a
* forall a. RealFrac a => a -> a
sc3_floor ((n
n' forall a. Num a => a -> a -> a
- n
i) forall a. Fractional a => a -> a -> a
/ n
r)

-- | Variant of 'wrap_hs' with @SC3@ argument ordering.
--
-- > map (\n -> sc3_wrap n 5 10) [3..12] == map (wrap_hs (5,10)) [3..12]
sc3_wrap :: RealFrac n => n -> n -> n -> n
sc3_wrap :: forall a. RealFrac a => a -> a -> a -> a
sc3_wrap n
a n
b n
c = forall n. RealFrac n => (n, n) -> n -> n
wrap_hs (n
b,n
c) n
a

{- | Generic variant of 'wrap''.

> > [5,6].wrap(0,5) == [5,0]
> map (generic_wrap (0,5)) [5,6] == [5,0]

> > [9,10,5,6,7,8,9,10,5,6].wrap(5,10) == [9,10,5,6,7,8,9,10,5,6]
> map (generic_wrap (5::Integer,10)) [3..12] == [9,10,5,6,7,8,9,10,5,6]
-}
generic_wrap :: (Ord a, Num a) => (a,a) -> a -> a
generic_wrap :: forall a. (Ord a, Num a) => (a, a) -> a -> a
generic_wrap (a
l,a
r) a
n =
    let d :: a
d = a
r forall a. Num a => a -> a -> a
- a
l forall a. Num a => a -> a -> a
+ a
1
        f :: a -> a
f = forall a. (Ord a, Num a) => (a, a) -> a -> a
generic_wrap (a
l,a
r)
    in if a
n forall a. Ord a => a -> a -> Bool
< a
l
       then a -> a
f (a
n forall a. Num a => a -> a -> a
+ a
d)
       else if a
n forall a. Ord a => a -> a -> Bool
> a
r then a -> a
f (a
n forall a. Num a => a -> a -> a
- a
d) else a
n

-- | Given sample-rate /sr/ and bin-count /n/ calculate frequency of /i/th bin.
--
-- > bin_to_freq 44100 2048 32 == 689.0625
bin_to_freq :: (Fractional n, Integral i) => n -> i -> i -> n
bin_to_freq :: forall n i. (Fractional n, Integral i) => n -> i -> i -> n
bin_to_freq n
sr i
n i
i = forall a b. (Integral a, Num b) => a -> b
fromIntegral i
i forall a. Num a => a -> a -> a
* n
sr forall a. Fractional a => a -> a -> a
/ forall a b. (Integral a, Num b) => a -> b
fromIntegral i
n

-- | Fractional midi note number to cycles per second.
--
-- > map (floor . midi_to_cps) [0,24,69,120,127] == [8,32,440,8372,12543]
-- > map (floor . midi_to_cps) [-36,138] == [1,23679]
-- > map (floor . midi_to_cps) [69.0,69.25 .. 70.0] == [440,446,452,459,466]
midi_to_cps :: Floating a => a -> a
midi_to_cps :: forall a. Floating a => a -> a
midi_to_cps a
i = a
440.0 forall a. Num a => a -> a -> a
* (a
2.0 forall a. Floating a => a -> a -> a
** ((a
i forall a. Num a => a -> a -> a
- a
69.0) forall a. Num a => a -> a -> a
* (a
1.0 forall a. Fractional a => a -> a -> a
/ a
12.0)))

-- | Cycles per second to fractional midi note number.
--
-- > map (round . cps_to_midi) [8,32,440,8372,12543] == [0,24,69,120,127]
-- > map (round . cps_to_midi) [1,24000] == [-36,138]
cps_to_midi :: Floating a => a -> a
cps_to_midi :: forall a. Floating a => a -> a
cps_to_midi a
a = (forall a. Floating a => a -> a -> a
logBase a
2 (a
a forall a. Num a => a -> a -> a
* (a
1.0 forall a. Fractional a => a -> a -> a
/ a
440.0)) forall a. Num a => a -> a -> a
* a
12.0) forall a. Num a => a -> a -> a
+ a
69.0

-- | Cycles per second to linear octave (4.75 = A4 = 440).
--
-- > map (cps_to_oct . midi_to_cps) [60,63,69] == [4.0,4.25,4.75]
cps_to_oct :: Floating a => a -> a
cps_to_oct :: forall a. Floating a => a -> a
cps_to_oct a
a = forall a. Floating a => a -> a -> a
logBase a
2 (a
a forall a. Num a => a -> a -> a
* (a
1.0 forall a. Fractional a => a -> a -> a
/ a
440.0)) forall a. Num a => a -> a -> a
+ a
4.75

-- | Linear octave to cycles per second.
--
-- > > [4.0,4.25,4.75].octcps.cpsmidi == [60,63,69]
-- > map (cps_to_midi . oct_to_cps) [4.0,4.25,4.75] == [60,63,69]
oct_to_cps :: Floating a => a -> a
oct_to_cps :: forall a. Floating a => a -> a
oct_to_cps a
a = a
440.0 forall a. Num a => a -> a -> a
* (a
2.0 forall a. Floating a => a -> a -> a
** (a
a forall a. Num a => a -> a -> a
- a
4.75))

-- | Degree, scale and steps per octave to key.
degree_to_key :: RealFrac a => [a] -> a -> a -> a
degree_to_key :: forall a. RealFrac a => [a] -> a -> a -> a
degree_to_key [a]
s a
n a
d =
    let l :: Int
l = forall (t :: * -> *) a. Foldable t => t a -> Int
length [a]
s
        d' :: Int
d' = forall a b. (RealFrac a, Integral b) => a -> b
round a
d
        a :: a
a = (a
d forall a. Num a => a -> a -> a
- forall a b. (Integral a, Num b) => a -> b
fromIntegral Int
d') forall a. Num a => a -> a -> a
* a
10.0 forall a. Num a => a -> a -> a
* (a
n forall a. Fractional a => a -> a -> a
/ a
12.0)
    in (a
n forall a. Num a => a -> a -> a
* forall a b. (Integral a, Num b) => a -> b
fromIntegral (Int
d' forall a. Integral a => a -> a -> a
`div` Int
l)) forall a. Num a => a -> a -> a
+ forall t. [Char] -> [t] -> Int -> t
Common.Base.at_with_error_message [Char]
"degree_to_key" [a]
s (Int
d' forall a. Integral a => a -> a -> a
`mod` Int
l) forall a. Num a => a -> a -> a
+ a
a

{- | One-indexed piano key number (for standard 88 key piano) to midi note number.

> map pianokey_to_midi [1,49,88] == [21,69,108]
-}
pianokey_to_midi :: Num n => n -> n
pianokey_to_midi :: forall a. Num a => a -> a
pianokey_to_midi = forall a. Num a => a -> a -> a
(+) n
20

{- | Piano key to hertz (ba.pianokey2hz in Faust).
     This is useful as a more musical gamut than midi note numbers.
     Ie. if x is in (0,1) then pianokey_to_cps of (x * 88) is in (26,4168)

> map (round . pianokey_to_cps) [0,1,40,49,88] == [26,28,262,440,4186]
> map (round . midi_to_cps) [0,60,69,127] == [8,262,440,12544]
-}
pianokey_to_cps :: Floating n => n -> n
pianokey_to_cps :: forall a. Floating a => a -> a
pianokey_to_cps = forall a. Floating a => a -> a
midi_to_cps forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. Num a => a -> a
pianokey_to_midi

-- | Linear amplitude to decibels.
--
-- > map (round . amp_to_db) [0.01,0.05,0.0625,0.125,0.25,0.5] == [-40,-26,-24,-18,-12,-6]
amp_to_db :: Floating a => a -> a
amp_to_db :: forall a. Floating a => a -> a
amp_to_db = (forall a. Num a => a -> a -> a
* a
20) forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. Floating a => a -> a -> a
logBase a
10

{- | Decibels to linear amplitude.

map (floor . (* 100). db_to_amp) [-40,-26,-24,-18,-12,-6] == [01,05,06,12,25,50]

let amp = map (2 **) [0 .. 15]
let db = [0,-6 .. -90]
map (round . ampDb . (/) 1) amp == db
map (round . amp_to_db . (/) 1) amp == db
 zip amp db

db_to_amp (-3) == 0.7079457843841379
amp_to_db 0.7079457843841379 == -3
-}
db_to_amp :: Floating a => a -> a
db_to_amp :: forall a. Floating a => a -> a
db_to_amp = (a
10 forall a. Floating a => a -> a -> a
**) forall b c a. (b -> c) -> (a -> b) -> a -> c
.  (forall a. Num a => a -> a -> a
* a
0.05)

-- | Fractional midi note interval to frequency multiplier.
--
-- > map midi_to_ratio [-12,0,7,12] == [0.5,1,1.4983070768766815,2]
midi_to_ratio :: Floating a => a -> a
midi_to_ratio :: forall a. Floating a => a -> a
midi_to_ratio a
a = a
2.0 forall a. Floating a => a -> a -> a
** (a
a forall a. Num a => a -> a -> a
* (a
1.0 forall a. Fractional a => a -> a -> a
/ a
12.0))

-- | Inverse of 'midi_to_ratio'.
--
-- > map ratio_to_midi [3/2,2] == [7.019550008653875,12]
ratio_to_midi :: Floating a => a -> a
ratio_to_midi :: forall a. Floating a => a -> a
ratio_to_midi a
a = a
12.0 forall a. Num a => a -> a -> a
* forall a. Floating a => a -> a -> a
logBase a
2 a
a

-- | /sr/ = sample rate, /r/ = cycle (two-pi), /cps/ = frequency
--
-- > cps_to_incr 48000 128 375 == 1
-- > cps_to_incr 48000 two_pi 458.3662361046586 == 6e-2
cps_to_incr :: Fractional a => a -> a -> a -> a
cps_to_incr :: forall a. Fractional a => a -> a -> a -> a
cps_to_incr a
sr a
r a
cps = (a
r forall a. Fractional a => a -> a -> a
/ a
sr) forall a. Num a => a -> a -> a
* a
cps

-- | Inverse of 'cps_to_incr'.
--
-- > incr_to_cps 48000 128 1 == 375
incr_to_cps :: Fractional a => a -> a -> a -> a
incr_to_cps :: forall a. Fractional a => a -> a -> a -> a
incr_to_cps a
sr a
r a
ic = a
ic forall a. Fractional a => a -> a -> a
/ (a
r forall a. Fractional a => a -> a -> a
/ a
sr)

-- | Pan2 function, identity is linear, sqrt is equal power.
pan2_f :: Fractional t => (t -> t) -> t -> t -> (t, t)
pan2_f :: forall t. Fractional t => (t -> t) -> t -> t -> (t, t)
pan2_f t -> t
f t
p t
q =
    let q' :: t
q' = (t
q forall a. Fractional a => a -> a -> a
/ t
2) forall a. Num a => a -> a -> a
+ t
0.5
    in (t
p forall a. Num a => a -> a -> a
* t -> t
f (t
1 forall a. Num a => a -> a -> a
- t
q'),t
p forall a. Num a => a -> a -> a
* t -> t
f t
q')

-- | Linear pan.
--
-- > map (lin_pan2 1) [-1,-0.5,0,0.5,1] == [(1,0),(0.75,0.25),(0.5,0.5),(0.25,0.75),(0,1)]
lin_pan2 :: Fractional t => t -> t -> (t, t)
lin_pan2 :: forall t. Fractional t => t -> t -> (t, t)
lin_pan2 = forall t. Fractional t => (t -> t) -> t -> t -> (t, t)
pan2_f forall a. a -> a
id

-- | Equal power pan.
--
-- > map (eq_pan2 1) [-1,-0.5,0,0.5,1]
eq_pan2 :: Floating t => t -> t -> (t, t)
eq_pan2 :: forall t. Floating t => t -> t -> (t, t)
eq_pan2 = forall t. Fractional t => (t -> t) -> t -> t -> (t, t)
pan2_f forall a. Floating a => a -> a
sqrt

-- | 'fromInteger' of 'properFraction'.
sc3_properFraction :: RealFrac t => t -> (t,t)
sc3_properFraction :: forall t. RealFrac t => t -> (t, t)
sc3_properFraction t
a =
    let (Integer
p,t
q) = forall a b. (RealFrac a, Integral b) => a -> (b, a)
properFraction t
a
    in (forall a. Num a => Integer -> a
fromInteger Integer
p,t
q)

-- | a^2 - b^2.
sc3_dif_sqr :: Num a => a -> a -> a
sc3_dif_sqr :: forall a. Num a => a -> a -> a
sc3_dif_sqr a
a a
b = (a
a forall a. Num a => a -> a -> a
* a
a) forall a. Num a => a -> a -> a
- (a
b forall a. Num a => a -> a -> a
* a
b)

-- | Euclidean distance function ('sqrt' of sum of squares).
sc3_hypot :: Floating a => a -> a -> a
sc3_hypot :: forall a. Floating a => a -> a -> a
sc3_hypot a
x a
y = forall a. Floating a => a -> a
sqrt (a
x forall a. Num a => a -> a -> a
* a
x forall a. Num a => a -> a -> a
+ a
y forall a. Num a => a -> a -> a
* a
y)

-- | Sc3 hypotenuse approximation function.
sc3_hypotx :: (Ord a, Floating a) => a -> a -> a
sc3_hypotx :: forall a. (Ord a, Floating a) => a -> a -> a
sc3_hypotx a
x a
y = forall a. Num a => a -> a
abs a
x forall a. Num a => a -> a -> a
+ forall a. Num a => a -> a
abs a
y forall a. Num a => a -> a -> a
- ((forall a. Floating a => a -> a
sqrt a
2 forall a. Num a => a -> a -> a
- a
1) forall a. Num a => a -> a -> a
* forall a. Ord a => a -> a -> a
min (forall a. Num a => a -> a
abs a
x) (forall a. Num a => a -> a
abs a
y))

-- | Fold /k/ to within range /(i,j)/, ie. @AbstractFunction.fold@
--
-- > map (foldToRange 5 10) [3..12] == [7,6,5,6,7,8,9,10,9,8]
foldToRange :: (Ord a,Num a) => a -> a -> a -> a
foldToRange :: forall a. (Ord a, Num a) => a -> a -> a -> a
foldToRange a
i a
j =
    let f :: a -> a
f a
n = if a
n forall a. Ord a => a -> a -> Bool
> a
j
              then a -> a
f (a
j forall a. Num a => a -> a -> a
- (a
n forall a. Num a => a -> a -> a
- a
j))
              else if a
n forall a. Ord a => a -> a -> Bool
< a
i
                   then a -> a
f (a
i forall a. Num a => a -> a -> a
- (a
n forall a. Num a => a -> a -> a
- a
i))
                   else a
n
    in a -> a
f

-- | Variant of 'foldToRange' with @SC3@ argument ordering.
sc3_fold :: (Ord a,Num a) => a -> a -> a -> a
sc3_fold :: forall a. (Ord a, Num a) => a -> a -> a -> a
sc3_fold a
n a
i a
j = forall a. (Ord a, Num a) => a -> a -> a -> a
foldToRange a
i a
j a
n

-- | SC3 distort operator.
sc3_distort :: Fractional n => n -> n
sc3_distort :: forall n. Fractional n => n -> n
sc3_distort n
x = n
x forall a. Fractional a => a -> a -> a
/ (n
1 forall a. Num a => a -> a -> a
+ forall a. Num a => a -> a
abs n
x)

-- | SC3 softclip operator.
sc3_softclip :: (Ord n, Fractional n) => n -> n
sc3_softclip :: forall n. (Ord n, Fractional n) => n -> n
sc3_softclip n
x = let x' :: n
x' = forall a. Num a => a -> a
abs n
x in if n
x' forall a. Ord a => a -> a -> Bool
<= n
0.5 then n
x else (n
x' forall a. Num a => a -> a -> a
- n
0.25) forall a. Fractional a => a -> a -> a
/ n
x

-- * Bool

-- | True is conventionally 1.  The test to determine true is @> 0@.
sc3_true :: Num n => n
sc3_true :: forall n. Num n => n
sc3_true = n
1

-- | False is conventionally 0.  The test to determine true is @<= 0@.
sc3_false :: Num n => n
sc3_false :: forall n. Num n => n
sc3_false = n
0

-- | Lifted 'not'.
--
-- > sc3_not sc3_true == sc3_false
-- > sc3_not sc3_false == sc3_true
sc3_not :: (Ord n,Num n) => n -> n
sc3_not :: forall n. (Ord n, Num n) => n -> n
sc3_not = forall n. Num n => Bool -> n
sc3_bool forall b c a. (b -> c) -> (a -> b) -> a -> c
. (forall a. Ord a => a -> a -> Bool
<= n
0)

-- | Translate 'Bool' to 'sc3_true' and 'sc3_false'.
sc3_bool :: Num n => Bool -> n
sc3_bool :: forall n. Num n => Bool -> n
sc3_bool Bool
b = if Bool
b then forall n. Num n => n
sc3_true else forall n. Num n => n
sc3_false

-- | Lift comparison function.
sc3_comparison :: Num n => (n -> n -> Bool) -> n -> n -> n
sc3_comparison :: forall n. Num n => (n -> n -> Bool) -> n -> n -> n
sc3_comparison n -> n -> Bool
f n
p n
q = forall n. Num n => Bool -> n
sc3_bool (n -> n -> Bool
f n
p n
q)

-- * Eq

-- | Lifted '=='.
sc3_eq :: (Num n, Eq n) => n -> n -> n
sc3_eq :: forall n. (Num n, Eq n) => n -> n -> n
sc3_eq = forall n. Num n => (n -> n -> Bool) -> n -> n -> n
sc3_comparison forall a. Eq a => a -> a -> Bool
(==)

-- | Lifted '/='.
sc3_neq :: (Num n, Eq n) => n -> n -> n
sc3_neq :: forall n. (Num n, Eq n) => n -> n -> n
sc3_neq = forall n. Num n => (n -> n -> Bool) -> n -> n -> n
sc3_comparison forall a. Eq a => a -> a -> Bool
(/=)

-- * Ord

-- | Lifted '<'.
sc3_lt :: (Num n, Ord n) => n -> n -> n
sc3_lt :: forall n. (Num n, Ord n) => n -> n -> n
sc3_lt = forall n. Num n => (n -> n -> Bool) -> n -> n -> n
sc3_comparison forall a. Ord a => a -> a -> Bool
(<)

-- | Lifted '<='.
sc3_lte :: (Num n, Ord n) => n -> n -> n
sc3_lte :: forall n. (Num n, Ord n) => n -> n -> n
sc3_lte = forall n. Num n => (n -> n -> Bool) -> n -> n -> n
sc3_comparison forall a. Ord a => a -> a -> Bool
(<=)

-- | Lifted '>'.
sc3_gt :: (Num n, Ord n) => n -> n -> n
sc3_gt :: forall n. (Num n, Ord n) => n -> n -> n
sc3_gt = forall n. Num n => (n -> n -> Bool) -> n -> n -> n
sc3_comparison forall a. Ord a => a -> a -> Bool
(>)

-- | Lifted '>='.
sc3_gte :: (Num n, Ord n) => n -> n -> n
sc3_gte :: forall n. (Num n, Ord n) => n -> n -> n
sc3_gte = forall n. Num n => (n -> n -> Bool) -> n -> n -> n
sc3_comparison forall a. Ord a => a -> a -> Bool
(>=)

-- * Clip Rule

-- | Enumeration of clipping rules.
data Clip_Rule = Clip_None | Clip_Left | Clip_Right | Clip_Both
                 deriving (Int -> Clip_Rule
Clip_Rule -> Int
Clip_Rule -> [Clip_Rule]
Clip_Rule -> Clip_Rule
Clip_Rule -> Clip_Rule -> [Clip_Rule]
Clip_Rule -> Clip_Rule -> Clip_Rule -> [Clip_Rule]
forall a.
(a -> a)
-> (a -> a)
-> (Int -> a)
-> (a -> Int)
-> (a -> [a])
-> (a -> a -> [a])
-> (a -> a -> [a])
-> (a -> a -> a -> [a])
-> Enum a
enumFromThenTo :: Clip_Rule -> Clip_Rule -> Clip_Rule -> [Clip_Rule]
$cenumFromThenTo :: Clip_Rule -> Clip_Rule -> Clip_Rule -> [Clip_Rule]
enumFromTo :: Clip_Rule -> Clip_Rule -> [Clip_Rule]
$cenumFromTo :: Clip_Rule -> Clip_Rule -> [Clip_Rule]
enumFromThen :: Clip_Rule -> Clip_Rule -> [Clip_Rule]
$cenumFromThen :: Clip_Rule -> Clip_Rule -> [Clip_Rule]
enumFrom :: Clip_Rule -> [Clip_Rule]
$cenumFrom :: Clip_Rule -> [Clip_Rule]
fromEnum :: Clip_Rule -> Int
$cfromEnum :: Clip_Rule -> Int
toEnum :: Int -> Clip_Rule
$ctoEnum :: Int -> Clip_Rule
pred :: Clip_Rule -> Clip_Rule
$cpred :: Clip_Rule -> Clip_Rule
succ :: Clip_Rule -> Clip_Rule
$csucc :: Clip_Rule -> Clip_Rule
Enum,Clip_Rule
forall a. a -> a -> Bounded a
maxBound :: Clip_Rule
$cmaxBound :: Clip_Rule
minBound :: Clip_Rule
$cminBound :: Clip_Rule
Bounded)

-- | Clip a value that is expected to be within an input range to an output range,
--   according to a rule.
--
-- > let f r = map (\x -> apply_clip_rule r 0 1 (-1) 1 x) [-1,0,0.5,1,2]
-- > in map f [minBound .. maxBound]
apply_clip_rule :: Ord n => Clip_Rule -> n -> n -> n -> n -> n -> Maybe n
apply_clip_rule :: forall n. Ord n => Clip_Rule -> n -> n -> n -> n -> n -> Maybe n
apply_clip_rule Clip_Rule
clip_rule n
sl n
sr n
dl n
dr n
x =
    case Clip_Rule
clip_rule of
      Clip_Rule
Clip_None -> forall a. Maybe a
Nothing
      Clip_Rule
Clip_Left -> if n
x forall a. Ord a => a -> a -> Bool
<= n
sl then forall a. a -> Maybe a
Just n
dl else forall a. Maybe a
Nothing
      Clip_Rule
Clip_Right -> if n
x forall a. Ord a => a -> a -> Bool
>= n
sr then forall a. a -> Maybe a
Just n
dr else forall a. Maybe a
Nothing
      Clip_Rule
Clip_Both -> if n
x forall a. Ord a => a -> a -> Bool
<= n
sl then forall a. a -> Maybe a
Just n
dl else if n
x forall a. Ord a => a -> a -> Bool
>= n
sr then forall a. a -> Maybe a
Just n
dr else forall a. Maybe a
Nothing

-- * LinLin

-- | Scale uni-polar (0,1) input to linear (l,r) range.
urange_ma :: Fractional a => SC3_MulAdd a -> a -> a -> a -> a
urange_ma :: forall a. Fractional a => SC3_MulAdd a -> SC3_MulAdd a
urange_ma SC3_MulAdd a
mul_add_f a
l a
r a
i = SC3_MulAdd a
mul_add_f a
i (a
r forall a. Num a => a -> a -> a
- a
l) a
l

-- | Scale (0,1) input to linear (l,r) range. u = uni-polar.
--
-- > map (urange 3 4) [0,0.5,1] == [3,3.5,4]
urange :: Fractional a => a -> a -> a -> a
urange :: forall a. Fractional a => a -> a -> a -> a
urange = forall a. Fractional a => SC3_MulAdd a -> SC3_MulAdd a
urange_ma forall t. Num t => SC3_MulAdd t
sc3_mul_add

-- | Calculate multiplier and add values for (-1,1) 'range' transform.
--
-- > range_muladd 3 4 == (0.5,3.5)
range_muladd :: Fractional t => t -> t -> (t,t)
range_muladd :: forall t. Fractional t => t -> t -> (t, t)
range_muladd = forall t. Fractional t => t -> t -> t -> t -> (t, t)
linlin_muladd (-t
1) t
1

-- | Scale bi-polar (-1,1) input to linear (l,r) range.  Note that the
-- argument order is not the same as 'linLin'.
range_ma :: Fractional a => SC3_MulAdd a -> a -> a -> a -> a
range_ma :: forall a. Fractional a => SC3_MulAdd a -> SC3_MulAdd a
range_ma SC3_MulAdd a
mul_add_f a
l a
r a
i =
  let (a
m,a
a) = forall t. Fractional t => t -> t -> (t, t)
range_muladd a
l a
r
  in SC3_MulAdd a
mul_add_f a
i a
m a
a

-- | Scale (-1,1) input to linear (l,r) range.  Note that the argument
-- order is not the same as 'linlin'. Note also that the various range
-- Ugen methods at sclang select mul-add values given the output range
-- of the Ugen, ie LFPulse.range selects a (0,1) input range.
--
-- > map (range 3 4) [-1,0,1] == [3,3.5,4]
-- > map (\x -> let (m,a) = linlin_muladd (-1) 1 3 4 in x * m + a) [-1,0,1] == [3,3.5,4]
range :: Fractional a => a -> a -> a -> a
range :: forall a. Fractional a => a -> a -> a -> a
range = forall a. Fractional a => SC3_MulAdd a -> SC3_MulAdd a
range_ma forall t. Num t => SC3_MulAdd t
sc3_mul_add

-- | 'uncurry' 'range'
range_hs :: Fractional a => (a,a) -> a -> a
range_hs :: forall a. Fractional a => (a, a) -> a -> a
range_hs = forall a b c. (a -> b -> c) -> (a, b) -> c
uncurry forall a. Fractional a => a -> a -> a -> a
range

-- | 'flip' 'range_hs'.  This allows cases such as osc `in_range` (0,1)
in_range :: Fractional a => a -> (a,a) -> a
in_range :: forall a. Fractional a => a -> (a, a) -> a
in_range = forall a b c. (a -> b -> c) -> b -> a -> c
flip forall a. Fractional a => (a, a) -> a -> a
range_hs

-- | Calculate multiplier and add values for 'linlin' transform.
--   Inputs are: input-min input-max output-min output-max
--
-- > range_muladd 3 4 == (0.5,3.5)
-- > linlin_muladd (-1) 1 3 4 == (0.5,3.5)
-- > linlin_muladd 0 1 3 4 == (1,3)
-- > linlin_muladd (-1) 1 0 1 == (0.5,0.5)
-- > linlin_muladd (-0.3) 1 (-1) 1
linlin_muladd :: Fractional t => t -> t -> t -> t -> (t,t)
linlin_muladd :: forall t. Fractional t => t -> t -> t -> t -> (t, t)
linlin_muladd t
sl t
sr t
dl t
dr =
    let m :: t
m = (t
dr forall a. Num a => a -> a -> a
- t
dl) forall a. Fractional a => a -> a -> a
/ (t
sr forall a. Num a => a -> a -> a
- t
sl)
        a :: t
a = t
dl forall a. Num a => a -> a -> a
- (t
m forall a. Num a => a -> a -> a
* t
sl)
    in (t
m,t
a)

-- | Map from one linear range to another linear range.
--
-- > linlin_ma hs_muladd 5 0 10 (-1) 1 == 0
linlin_ma :: Fractional a => SC3_MulAdd a -> a -> a -> a -> a -> a -> a
linlin_ma :: forall a. Fractional a => SC3_MulAdd a -> a -> a -> SC3_MulAdd a
linlin_ma SC3_MulAdd a
mul_add_f a
i a
sl a
sr a
dl a
dr =
  let (a
m,a
a) = forall t. Fractional t => t -> t -> t -> t -> (t, t)
linlin_muladd a
sl a
sr a
dl a
dr
  in SC3_MulAdd a
mul_add_f a
i a
m a
a

-- | 'linLin' with a more typical haskell argument structure, ranges as pairs and input last.
--
-- > map (linlin_hs (0,127) (-0.5,0.5)) [0,63.5,127] == [-0.5,0.0,0.5]
linlin_hs :: Fractional a => (a, a) -> (a, a) -> a -> a
linlin_hs :: forall a. Fractional a => (a, a) -> (a, a) -> a -> a
linlin_hs (a
sl,a
sr) (a
dl,a
dr) = let (a
m,a
a) = forall t. Fractional t => t -> t -> t -> t -> (t, t)
linlin_muladd a
sl a
sr a
dl a
dr in (forall a. Num a => a -> a -> a
+ a
a) forall b c a. (b -> c) -> (a -> b) -> a -> c
. (forall a. Num a => a -> a -> a
* a
m)

{- | Map from one linear range to another linear range.

> r = [0,0.125,0.25,0.375,0.5,0.625,0.75,0.875,1]
> map (\i -> sc3_linlin i (-1) 1 0 1) [-1,-0.75 .. 1] == r

-}
sc3_linlin :: Fractional a => a -> a -> a -> a -> a -> a
sc3_linlin :: forall a. Fractional a => a -> a -> a -> a -> a -> a
sc3_linlin a
i a
sl a
sr a
dl a
dr = forall a. Fractional a => (a, a) -> (a, a) -> a -> a
linlin_hs (a
sl,a
sr) (a
dl,a
dr) a
i

-- | Given enumeration from /dst/ that is in the same relation as /n/ is from /src/.
--
-- > linlin _enum_plain 'a' 'A' 'e' == 'E'
-- > linlin_enum_plain 0 (-50) 16 == -34
-- > linlin_enum_plain 0 (-50) (-1) == -51
linlin_enum_plain :: (Enum t,Enum u) => t -> u -> t -> u
linlin_enum_plain :: forall t u. (Enum t, Enum u) => t -> u -> t -> u
linlin_enum_plain t
src u
dst t
n = forall a. Enum a => Int -> a
toEnum (forall a. Enum a => a -> Int
fromEnum u
dst forall a. Num a => a -> a -> a
+ (forall a. Enum a => a -> Int
fromEnum t
n forall a. Num a => a -> a -> a
- forall a. Enum a => a -> Int
fromEnum t
src))

-- | Variant of 'linlin_enum_plain' that requires /src/ and /dst/ ranges to be of equal size,
-- and for /n/ to lie in /src/.
--
-- > linlin_enum (0,100) (-50,50) 0x10 == Just (-34)
-- > linlin_enum (-50,50) (0,100) (-34) == Just 0x10
-- > linlin_enum (0,100) (-50,50) (-1) == Nothing
linlin_enum :: (Enum t,Enum u) => (t,t) -> (u,u) -> t -> Maybe u
linlin_enum :: forall t u. (Enum t, Enum u) => (t, t) -> (u, u) -> t -> Maybe u
linlin_enum (t
l,t
r) (u
l',u
r') t
n =
    if forall a. Enum a => a -> Int
fromEnum t
n forall a. Ord a => a -> a -> Bool
>= forall a. Enum a => a -> Int
fromEnum t
l Bool -> Bool -> Bool
&& forall a. Enum a => a -> Int
fromEnum t
r forall a. Num a => a -> a -> a
- forall a. Enum a => a -> Int
fromEnum t
l forall a. Eq a => a -> a -> Bool
== forall a. Enum a => a -> Int
fromEnum u
r' forall a. Num a => a -> a -> a
- forall a. Enum a => a -> Int
fromEnum u
l'
    then forall a. a -> Maybe a
Just (forall t u. (Enum t, Enum u) => t -> u -> t -> u
linlin_enum_plain t
l u
l' t
n)
    else forall a. Maybe a
Nothing

-- | Erroring variant.
linlin_enum_err :: (Enum t,Enum u) => (t,t) -> (u,u) -> t -> u
linlin_enum_err :: forall t u. (Enum t, Enum u) => (t, t) -> (u, u) -> t -> u
linlin_enum_err (t, t)
src (u, u)
dst = forall a. a -> Maybe a -> a
fromMaybe (forall a. HasCallStack => [Char] -> a
error [Char]
"linlin_enum") forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall t u. (Enum t, Enum u) => (t, t) -> (u, u) -> t -> Maybe u
linlin_enum (t, t)
src (u, u)
dst

-- | Variant of 'linlin' that requires /src/ and /dst/ ranges to be of
-- equal size, thus with constraint of 'Num' and 'Eq' instead of
-- 'Fractional'.
--
-- > linlin_eq (0,100) (-50,50) 0x10 == Just (-34)
-- > linlin_eq (-50,50) (0,100) (-34) == Just 0x10
linlin_eq :: (Eq a, Num a) => (a,a) -> (a,a) -> a -> Maybe a
linlin_eq :: forall a. (Eq a, Num a) => (a, a) -> (a, a) -> a -> Maybe a
linlin_eq (a
l,a
r) (a
l',a
r') a
n =
    let d :: a
d = a
r forall a. Num a => a -> a -> a
- a
l
        d' :: a
d' = a
r' forall a. Num a => a -> a -> a
- a
l'
    in if a
d forall a. Eq a => a -> a -> Bool
== a
d' then forall a. a -> Maybe a
Just (a
l' forall a. Num a => a -> a -> a
+ (a
n forall a. Num a => a -> a -> a
- a
l)) else forall a. Maybe a
Nothing

-- | Erroring variant.
linlin_eq_err :: (Eq a,Num a) => (a,a) -> (a,a) -> a -> a
linlin_eq_err :: forall a. (Eq a, Num a) => (a, a) -> (a, a) -> a -> a
linlin_eq_err (a, a)
src (a, a)
dst = forall a. a -> Maybe a -> a
fromMaybe (forall a. HasCallStack => [Char] -> a
error [Char]
"linlin_eq") forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. (Eq a, Num a) => (a, a) -> (a, a) -> a -> Maybe a
linlin_eq (a, a)
src (a, a)
dst

-- * LinExp

{- | Linear to exponential range conversion.
     Rule is as at linExp Ugen, haskell manner argument ordering.
     Destination values must be nonzero and have the same sign.

> map (floor . linexp_hs (1,2) (10,100)) [0,1,1.5,2,3] == [1,10,31,100,1000]
> map (floor . linexp_hs (-2,2) (1,100)) [-3,-2,-1,0,1,2,3] == [0,1,3,10,31,100,316]

-}
linexp_hs :: Floating a => (a,a) -> (a,a) -> a -> a
linexp_hs :: forall a. Floating a => (a, a) -> (a, a) -> a -> a
linexp_hs (a
in_l,a
in_r) (a
out_l,a
out_r) a
x =
    let rt :: a
rt = a
out_r forall a. Fractional a => a -> a -> a
/ a
out_l
        rn :: a
rn = a
1.0 forall a. Fractional a => a -> a -> a
/ (a
in_r forall a. Num a => a -> a -> a
- a
in_l)
        rr :: a
rr = a
rn forall a. Num a => a -> a -> a
* forall a. Num a => a -> a
negate a
in_l
    in a
out_l forall a. Num a => a -> a -> a
* (a
rt forall a. Floating a => a -> a -> a
** (a
x forall a. Num a => a -> a -> a
* a
rn forall a. Num a => a -> a -> a
+ a
rr))

-- | Variant of 'linexp_hs' with argument ordering as at 'linExp' Ugen.
--
-- > map (\i -> lin_exp i 1 2 1 3) [1,1.1 .. 2]
-- > map (\i -> floor (lin_exp i 1 2 10 100)) [0,1,1.5,2,3]
lin_exp :: Floating a => a -> a -> a -> a -> a -> a
lin_exp :: forall a. Floating a => a -> a -> a -> a -> a -> a
lin_exp a
x a
in_l a
in_r a
out_l a
out_r = forall a. Floating a => (a, a) -> (a, a) -> a -> a
linexp_hs (a
in_l,a
in_r) (a
out_l,a
out_r) a
x

-- | @SimpleNumber.linexp@ shifts from linear to exponential ranges.
--
-- > map (sc3_linexp 1 2 1 3) [1,1.1 .. 2]
--
-- > > [1,1.5,2].collect({|i| i.linexp(1,2,10,100).floor}) == [10,31,100]
-- > map (floor . sc3_linexp 1 2 10 100) [0,1,1.5,2,3] == [10,10,31,100,100]
sc3_linexp :: (Ord a, Floating a) => a -> a -> a -> a -> a -> a
sc3_linexp :: forall a. (Ord a, Floating a) => a -> a -> a -> a -> a -> a
sc3_linexp a
src_l a
src_r a
dst_l a
dst_r a
x =
    case forall n. Ord n => Clip_Rule -> n -> n -> n -> n -> n -> Maybe n
apply_clip_rule Clip_Rule
Clip_Both a
src_l a
src_r a
dst_l a
dst_r a
x of
      Just a
r -> a
r
      Maybe a
Nothing -> ((a
dst_r forall a. Fractional a => a -> a -> a
/ a
dst_l) forall a. Floating a => a -> a -> a
** ((a
x forall a. Num a => a -> a -> a
- a
src_l) forall a. Fractional a => a -> a -> a
/ (a
src_r forall a. Num a => a -> a -> a
- a
src_l))) forall a. Num a => a -> a -> a
* a
dst_l

-- | @SimpleNumber.explin@ is the inverse of linexp.
--
-- > map (sc3_explin 10 100 1 2) [10,10,31,100,100]
sc3_explin :: (Ord a, Floating a) => a -> a -> a -> a -> a -> a
sc3_explin :: forall a. (Ord a, Floating a) => a -> a -> a -> a -> a -> a
sc3_explin a
src_l a
src_r a
dst_l a
dst_r a
x =
  forall a. a -> Maybe a -> a
fromMaybe
  (forall a. Floating a => a -> a -> a
logBase (a
src_r forall a. Fractional a => a -> a -> a
/ a
src_l) (a
x forall a. Fractional a => a -> a -> a
/ a
src_l) forall a. Num a => a -> a -> a
* (a
dst_r forall a. Num a => a -> a -> a
- a
dst_l) forall a. Num a => a -> a -> a
+ a
dst_l)
  (forall n. Ord n => Clip_Rule -> n -> n -> n -> n -> n -> Maybe n
apply_clip_rule Clip_Rule
Clip_Both a
src_l a
src_r a
dst_l a
dst_r a
x)

-- * ExpExp

-- | Translate from one exponential range to another.
--
-- > map (sc3_expexp 0.1 10 4.3 100) [1 .. 10]
sc3_expexp :: (Ord a, Floating a) => a -> a -> a -> a -> a -> a
sc3_expexp :: forall a. (Ord a, Floating a) => a -> a -> a -> a -> a -> a
sc3_expexp a
src_l a
src_r a
dst_l a
dst_r a
x =
  forall a. a -> Maybe a -> a
fromMaybe
  ((a
dst_r forall a. Fractional a => a -> a -> a
/ a
dst_l) forall a. Floating a => a -> a -> a
** forall a. Floating a => a -> a -> a
logBase (a
src_r forall a. Fractional a => a -> a -> a
/ a
src_l) (a
x forall a. Fractional a => a -> a -> a
/ a
src_l) forall a. Num a => a -> a -> a
* a
dst_l)
  (forall n. Ord n => Clip_Rule -> n -> n -> n -> n -> n -> Maybe n
apply_clip_rule Clip_Rule
Clip_Both a
src_l a
src_r a
dst_l a
dst_r a
x)

-- * LinCurve

{- | Map /x/ from an assumed linear input range (src_l,src_r) to an
exponential curve output range (dst_l,dst_r). 'curve' is like the
parameter in Env.  Unlike with linexp, the output range may include
zero.

> > (0..10).lincurve(0,10,-4.3,100,-3).round == [-4,24,45,61,72,81,87,92,96,98,100]

> let f = round . sc3_lincurve (-3) 0 10 (-4.3) 100
> in map f [0 .. 10] == [-4,24,45,61,72,81,87,92,96,98,100]

> import Sound.Sc3.Plot {- hsc3-plot -}
> plotTable (map (\c-> map (sc3_lincurve c 0 1 (-1) 1) [0,0.01 .. 1]) [-6,-4 .. 6])

-}
sc3_lincurve :: (Ord a, Floating a) => a -> a -> a -> a -> a -> a -> a
sc3_lincurve :: forall a. (Ord a, Floating a) => a -> a -> a -> a -> a -> a -> a
sc3_lincurve a
curve a
src_l a
src_r a
dst_l a
dst_r a
x =
    case forall n. Ord n => Clip_Rule -> n -> n -> n -> n -> n -> Maybe n
apply_clip_rule Clip_Rule
Clip_Both a
src_l a
src_r a
dst_l a
dst_r a
x of
      Just a
r -> a
r
      Maybe a
Nothing ->
          if forall a. Num a => a -> a
abs a
curve forall a. Ord a => a -> a -> Bool
< a
0.001
          then forall a. Fractional a => (a, a) -> (a, a) -> a -> a
linlin_hs (a
src_l,a
src_r) (a
dst_l,a
dst_r) a
x
          else let grow :: a
grow = forall a. Floating a => a -> a
exp a
curve
                   a :: a
a = (a
dst_r forall a. Num a => a -> a -> a
- a
dst_l) forall a. Fractional a => a -> a -> a
/ (a
1.0 forall a. Num a => a -> a -> a
- a
grow)
                   b :: a
b = a
dst_l forall a. Num a => a -> a -> a
+ a
a
                   scaled :: a
scaled = (a
x forall a. Num a => a -> a -> a
- a
src_l) forall a. Fractional a => a -> a -> a
/ (a
src_r forall a. Num a => a -> a -> a
- a
src_l)
               in a
b forall a. Num a => a -> a -> a
- (a
a forall a. Num a => a -> a -> a
* (a
grow forall a. Floating a => a -> a -> a
** a
scaled))

-- | Inverse of 'sc3_lincurve'.
--
-- > let f = round . sc3_curvelin (-3) (-4.3) 100 0 10
-- > in map f [-4,24,45,61,72,81,87,92,96,98,100] == [0..10]
sc3_curvelin :: (Ord a, Floating a) => a -> a -> a -> a -> a -> a -> a
sc3_curvelin :: forall a. (Ord a, Floating a) => a -> a -> a -> a -> a -> a -> a
sc3_curvelin a
curve a
src_l a
src_r a
dst_l a
dst_r a
x =
    case forall n. Ord n => Clip_Rule -> n -> n -> n -> n -> n -> Maybe n
apply_clip_rule Clip_Rule
Clip_Both a
src_l a
src_r a
dst_l a
dst_r a
x of
      Just a
r -> a
r
      Maybe a
Nothing ->
          if forall a. Num a => a -> a
abs a
curve forall a. Ord a => a -> a -> Bool
< a
0.001
          then forall a. Fractional a => (a, a) -> (a, a) -> a -> a
linlin_hs (a
src_l,a
src_r) (a
dst_l,a
dst_r) a
x
          else let grow :: a
grow = forall a. Floating a => a -> a
exp a
curve
                   a :: a
a = (a
src_r forall a. Num a => a -> a -> a
- a
src_l) forall a. Fractional a => a -> a -> a
/ (a
1.0 forall a. Num a => a -> a -> a
- a
grow)
                   b :: a
b = a
src_l forall a. Num a => a -> a -> a
+ a
a
               in forall a. Floating a => a -> a
log ((a
b forall a. Num a => a -> a -> a
- a
x) forall a. Fractional a => a -> a -> a
/ a
a) forall a. Num a => a -> a -> a
* (a
dst_r forall a. Num a => a -> a -> a
- a
dst_l) forall a. Fractional a => a -> a -> a
/ a
curve forall a. Num a => a -> a -> a
+ a
dst_l

-- * PP

-- | Removes all but the last trailing zero from floating point string.
double_pp_rm0 :: String -> String
double_pp_rm0 :: [Char] -> [Char]
double_pp_rm0 =
    let rev_f :: ([a] -> [a]) -> [a] -> [a]
rev_f [a] -> [a]
f = forall a. [a] -> [a]
reverse forall b c a. (b -> c) -> (a -> b) -> a -> c
. [a] -> [a]
f forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. [a] -> [a]
reverse
        remv :: [Char] -> [Char]
remv [Char]
l = case [Char]
l of
                   Char
'0':Char
'.':[Char]
_ -> [Char]
l
                   Char
'0':[Char]
l' -> [Char] -> [Char]
remv [Char]
l'
                   [Char]
_ -> [Char]
l
    in forall {a} {a}. ([a] -> [a]) -> [a] -> [a]
rev_f [Char] -> [Char]
remv

-- | The default show is odd, 0.05 shows as 5.0e-2.
--
-- > unwords (map (double_pp 4) [0.0001,0.001,0.01,0.1,1.0]) == "0.0001 0.001 0.01 0.1 1.0"
double_pp :: Int -> Double -> String
double_pp :: Int -> Double -> [Char]
double_pp Int
k Double
n = [Char] -> [Char]
double_pp_rm0 (forall a. RealFloat a => Maybe Int -> a -> [Char] -> [Char]
Numeric.showFFloat (forall a. a -> Maybe a
Just Int
k) Double
n [Char]
"")

-- | Print as integer if integral, else as real.
--
-- > unwords (map (real_pp 5) [0.0001,0.001,0.01,0.1,1.0]) == "0.0001 0.001 0.01 0.1 1"
real_pp :: Int -> Double -> String
real_pp :: Int -> Double -> [Char]
real_pp Int
k Double
n =
    let r :: Rational
r = forall a. Real a => a -> Rational
toRational Double
n
    in if forall a. Ratio a -> a
denominator Rational
r forall a. Eq a => a -> a -> Bool
== Integer
1 then forall a. Show a => a -> [Char]
show (forall a. Ratio a -> a
numerator Rational
r) else Int -> Double -> [Char]
double_pp Int
k Double
n

-- * Parser

-- | Type-specialised 'Text.Read.readMaybe'.
parse_double :: String -> Maybe Double
parse_double :: [Char] -> Maybe Double
parse_double = forall a. Read a => [Char] -> Maybe a
Common.Base.reads_exact

-- * Optimiser

-- | Non-specialised optimised sum function (3 & 4 element adders).
sum_opt_f :: Num t => (t -> t -> t -> t) -> (t -> t -> t -> t -> t) -> [t] -> t
sum_opt_f :: forall t.
Num t =>
(t -> t -> t -> t) -> (t -> t -> t -> t -> t) -> [t] -> t
sum_opt_f t -> t -> t -> t
f3 t -> t -> t -> t -> t
f4 =
  let recur :: [t] -> t
recur [t]
l =
        case [t]
l of
          t
p:t
q:t
r:t
s:[t]
l' -> [t] -> t
recur (t -> t -> t -> t -> t
f4 t
p t
q t
r t
s forall a. a -> [a] -> [a]
: [t]
l')
          t
p:t
q:t
r:[t]
l' -> [t] -> t
recur (t -> t -> t -> t
f3 t
p t
q t
r forall a. a -> [a] -> [a]
: [t]
l')
          [t]
_ -> forall (t :: * -> *) a. (Foldable t, Num a) => t a -> a
sum [t]
l
  in [t] -> t
recur

-- * Sin

{- | Taylor approximation of sin, (-pi, pi).

> import Sound.Sc3.Plot
> let xs = [-pi, -pi + 0.05 .. pi] in plot_p1_ln [map sin_taylor_approximation xs, map sin xs]
> let xs = [-pi, -pi + 0.05 .. pi] in plot_p1_ln [map (\x -> sin_taylor_approximation x - sin x) xs]
-}
sin_taylor_approximation :: Floating a => a -> a
sin_taylor_approximation :: forall a. Floating a => a -> a
sin_taylor_approximation a
x = a
x forall a. Num a => a -> a -> a
- (a
x forall a. Floating a => a -> a -> a
** a
3) forall a. Fractional a => a -> a -> a
/ (a
3 forall a. Num a => a -> a -> a
* a
2) forall a. Num a => a -> a -> a
+ (a
x forall a. Floating a => a -> a -> a
** a
5) forall a. Fractional a => a -> a -> a
/ (a
5 forall a. Num a => a -> a -> a
* a
4 forall a. Num a => a -> a -> a
* a
3 forall a. Num a => a -> a -> a
* a
2) forall a. Num a => a -> a -> a
- (a
x forall a. Floating a => a -> a -> a
** a
7) forall a. Fractional a => a -> a -> a
/ (a
7 forall a. Num a => a -> a -> a
* a
6 forall a. Num a => a -> a -> a
* a
5 forall a. Num a => a -> a -> a
* a
4 forall a. Num a => a -> a -> a
* a
3 forall a. Num a => a -> a -> a
* a
2) forall a. Num a => a -> a -> a
+ (a
x forall a. Floating a => a -> a -> a
** a
9) forall a. Fractional a => a -> a -> a
/ (a
9 forall a. Num a => a -> a -> a
* a
8 forall a. Num a => a -> a -> a
* a
7 forall a. Num a => a -> a -> a
* a
6 forall a. Num a => a -> a -> a
* a
5 forall a. Num a => a -> a -> a
* a
4 forall a. Num a => a -> a -> a
* a
3 forall a. Num a => a -> a -> a
* a
2)

{- | Bhaskara approximation of sin, (0, pi).

> import Sound.Sc3.Plot
> let xs = [0, 0.05 .. pi] in plot_p1_ln [map sin_bhaskara_approximation xs, map sin xs]
> let xs = [0, 0.05 .. pi] in plot_p1_ln [map (\x -> sin_bhaskara_approximation x - sin x) xs]
-}
sin_bhaskara_approximation :: Floating a => a -> a
sin_bhaskara_approximation :: forall a. Floating a => a -> a
sin_bhaskara_approximation a
x = (a
16 forall a. Num a => a -> a -> a
* a
x forall a. Num a => a -> a -> a
* (forall a. Floating a => a
pi forall a. Num a => a -> a -> a
- a
x)) forall a. Fractional a => a -> a -> a
/ ((a
5 forall a. Num a => a -> a -> a
* forall a. Floating a => a
pi forall a. Num a => a -> a -> a
* forall a. Floating a => a
pi) forall a. Num a => a -> a -> a
- (a
4 forall a. Num a => a -> a -> a
* a
x forall a. Num a => a -> a -> a
* (forall a. Floating a => a
pi forall a. Num a => a -> a -> a
- a
x)))

{- | Robin Green, robin_green@playstation.sony.com, (-pi, pi)

> import Sound.Sc3.Plot
> let xs = [-pi, -pi + 0.05 .. pi] in plot_p1_ln [map sin_green_approximation xs, map sin xs]
> let xs = [-pi, -pi + 0.05 .. pi] in plot_p1_ln [map (\x -> sin_green_approximation x - sin x) xs]
-}
sin_green_approximation :: Floating a => a -> a
sin_green_approximation :: forall a. Floating a => a -> a
sin_green_approximation a
x = a
x forall a. Num a => a -> a -> a
- (a
0.166666546 forall a. Num a => a -> a -> a
* (a
x forall a. Floating a => a -> a -> a
** a
3)) forall a. Num a => a -> a -> a
+ (a
0.00833216076 forall a. Num a => a -> a -> a
* (a
x forall a. Floating a => a -> a -> a
** a
5)) forall a. Num a => a -> a -> a
- (a
0.000195152832 forall a. Num a => a -> a -> a
* (a
x forall a. Floating a => a -> a -> a
** a
7))

{- | Paul Adenot, (-pi, pi)

> import Sound.Sc3.Plot
> let xs = [-pi, -pi + 0.05 .. pi] in plot_p1_ln [map sin_adenot_approximation xs, map sin xs]
> let xs = [-pi, -pi + 0.05 .. pi] in plot_p1_ln [map (\x -> sin_adenot_approximation x - sin x) xs]
-}
sin_adenot_approximation :: Floating a => a -> a
sin_adenot_approximation :: forall a. Floating a => a -> a
sin_adenot_approximation a
x = a
0.391969947653056 forall a. Num a => a -> a -> a
* a
x forall a. Num a => a -> a -> a
* (forall a. Floating a => a
pi forall a. Num a => a -> a -> a
- forall a. Num a => a -> a
abs a
x)

{- Anthony C. Robin, (0, 45).
Simple Trigonometric Approximations, The Mathematical Gazette, Vol. 79, No. 485 (Jul., 1995), pp. 385-387.

> import Sound.Sc3.Plot
> degrees_to_radians = (* pi) . (/ 180)
> let xs = [0, 0.05 .. 45] in plot_p1_ln [map sin_robin_approximation xs, map (sin . degrees_to_radians) xs]
> let xs = [0, 0.05 .. 45] in plot_p1_ln [map (\x -> sin_robin_approximation x - sin (degrees_to_radians x)) xs]
-}
sin_robin_approximation :: Floating a => a -> a
sin_robin_approximation :: forall a. Floating a => a -> a
sin_robin_approximation a
x = let c :: a
c = a
x forall a. Num a => a -> a -> a
* a
0.01 in a
c forall a. Num a => a -> a -> a
* (a
2 forall a. Num a => a -> a -> a
- a
c)