Sound.SC3.UGen.Math

Non-standard mathematical classes and class instances.

Documentation

dinf :: UGen

Pseudo-infinite constant UGen.

sc3_true :: Num n => n

True is conventionally 1. The test to determine true is > 0.

sc3_false :: Num n => n

False is conventionally 0.

sc3_not :: (Ord n, Num n) => n -> n

Lifted not.

sc3_not sc3_true == sc3_false
sc3_not sc3_false == sc3_true

sc3_bool :: Num n => Bool -> n

Translate Bool to sc3_true and sc3_false.

sc3_comparison :: Num n => (n -> n -> Bool) -> n -> n -> n

Lift comparison function.

sc3_eq :: (Num n, Eq n) => n -> n -> n

Lifted ==.

sc3_neq :: (Num n, Eq n) => n -> n -> n

Lifted /=.

sc3_lt :: (Num n, Ord n) => n -> n -> n

Lifted <.

sc3_lte :: (Num n, Ord n) => n -> n -> n

Lifted <=.

sc3_gt :: (Num n, Ord n) => n -> n -> n

Lifted >.

sc3_gte :: (Num n, Ord n) => n -> n -> n

Lifted >=.

roundTo_ :: (RealFrac n, Ord n) => n -> n -> n

Variant of SC3 roundTo function.

let r = [0,0,0.25,0.25,0.5,0.5,0.5,0.75,0.75,1,1]
in map (`roundTo_` 0.25) [0,0.1 .. 1] == r

sc3_round_to :: (RealFrac n, Ord n) => n -> n -> n

sc3_idiv :: RealFrac n => n -> n -> n

binop_hs_tbl :: (Real n, Floating n, RealFrac n, Ord n) => [(Binary, n -> n -> n)]

Association table for Binary to haskell function implementing operator.

binop_special_hs :: (Real n, RealFrac n, Floating n, Ord n) => Int -> Maybe (n -> n -> n)

lookup binop_hs_tbl via toEnum.

uop_hs_tbl :: (RealFrac n, Floating n, Ord n) => [(Unary, n -> n)]

Association table for Unary to haskell function implementing operator.

uop_special_hs :: (RealFrac n, Floating n, Ord n) => Int -> Maybe (n -> n)

lookup uop_hs_tbl via toEnum.

class (Eq a, Num a) => EqE a where

Variant on Eq class, result is of the same type as the values compared.

Minimal complete definition

Nothing

Methods

(==*) :: a -> a -> a

(/=*) :: a -> a -> a

Instances

EqE Double

EqE Float

EqE Int

EqE Int32

EqE Int64

EqE Integer

EqE UGen

class (Ord a, Num a) => OrdE a where

Variant on Ord class, result is of the same type as the values compared.

Minimal complete definition

Nothing

Methods

(<*) :: a -> a -> a

(<=*) :: a -> a -> a

(>*) :: a -> a -> a

(>=*) :: a -> a -> a

Instances

OrdE Double

OrdE Float

OrdE Int

OrdE Int32

OrdE Int64

OrdE Integer

OrdE UGen

sc3_properFraction :: (RealFrac t, Num t) => t -> (t, t)

sc3_truncate :: (RealFrac a, Num a) => a -> a

sc3_round :: (RealFrac a, Num a) => a -> a

sc3_ceiling :: (RealFrac a, Num a) => a -> a

sc3_floor :: (RealFrac a, Num a) => a -> a

class RealFrac a => RealFracE a where

Variant of RealFrac with non Integral results.

Minimal complete definition

Nothing

Methods

properFractionE :: a -> (a, a)

truncateE :: a -> a

roundE :: a -> a

ceilingE :: a -> a

floorE :: a -> a

Instances

RealFracE Double

RealFracE Float

RealFracE UGen

roundTo :: UGen -> UGen -> UGen

UGen form or roundTo_.

ceil :: UGen -> UGen

UGen form of ceilingE.

midiCPS' :: Floating a => a -> a

Floating form of midiCPS.

cpsMIDI' :: Floating a => a -> a

Floating form of cpsMIDI.

cpsOct' :: Floating a => a -> a

ampDb' :: Floating a => a -> a

dbAmp' :: Floating a => a -> a

cubed' :: Num a => a -> a

midiRatio' :: Floating a => a -> a

octCPS' :: Floating a => a -> a

ratioMIDI' :: Floating a => a -> a

squared' :: Num a => a -> a

class (Floating a, Ord a) => UnaryOp a where

Unary operator class.

map (floor . (* 1e4) . dbAmp) [-90,-60,-30,0] == [0,10,316,10000]

Minimal complete definition

Nothing

Methods

ampDb :: a -> a

asFloat :: a -> a

asInt :: a -> a

cpsMIDI :: a -> a

cpsOct :: a -> a

cubed :: a -> a

dbAmp :: a -> a

distort :: a -> a

frac :: a -> a

isNil :: a -> a

log10 :: a -> a

log2 :: a -> a

midiCPS :: a -> a

midiRatio :: a -> a

notE :: a -> a

notNil :: a -> a

octCPS :: a -> a

ramp_ :: a -> a

ratioMIDI :: a -> a

softClip :: a -> a

squared :: a -> a

Instances

UnaryOp Double

UnaryOp Float

UnaryOp UGen

difSqr' :: Num a => a -> a -> a

hypotx' :: (Ord a, Floating a) => a -> a -> a

class (Floating a, RealFrac a, Ord a) => BinaryOp a where

Binary operator class.

Minimal complete definition

Nothing

Methods

absDif :: a -> a -> a

amClip :: a -> a -> a

atan2E :: a -> a -> a

clip2 :: a -> a -> a

difSqr :: a -> a -> a

excess :: a -> a -> a

exprandRange :: a -> a -> a

fill :: a -> a -> a

firstArg :: a -> a -> a

fold2 :: a -> a -> a

gcdE :: a -> a -> a

hypot :: a -> a -> a

hypotx :: a -> a -> a

iDiv :: a -> a -> a

lcmE :: a -> a -> a

modE :: a -> a -> a

randRange :: a -> a -> a

ring1 :: a -> a -> a

ring2 :: a -> a -> a

ring3 :: a -> a -> a

ring4 :: a -> a -> a

roundUp :: a -> a -> a

scaleNeg :: a -> a -> a

sqrDif :: a -> a -> a

sqrSum :: a -> a -> a

sumSqr :: a -> a -> a

thresh :: a -> a -> a

trunc :: a -> a -> a

wrap2 :: a -> a -> a

Instances

BinaryOp Double

BinaryOp Float

BinaryOp UGen

fmod_f32 :: Float -> Float -> Float

The SC3 % operator is the 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

1.5 `fmod_f32` 1.2 -- ~= 0.3
(-1.5) `fmod_f32` 1.2 -- ~= 0.9
1.5 `fmod_f32` (-1.2) -- ~= -0.9
(-1.5) `fmod_f32` (-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 `fmod_f32` 1.5 -- ~= 1.2
(-1.2) `fmod_f32` 1.5 -- ~= 0.3
1.2 `fmod_f32` (-1.5) -- ~= -0.3
(-1.2) `fmod_f32` (-1.5) -- ~= -1.2

class Num a => TernaryOp a where

Ternary operator class.

Minimal complete definition

Nothing

Methods

mul_add :: a -> a -> a -> a

Instances

TernaryOp Double

TernaryOp Float

TernaryOp UGen

wrap' :: RealFracE n => n -> n -> n -> n

Wrap k to within range (i,j), ie. AbstractFunction.wrap.

> [5,6].wrap(0,5) == [5,0]
map (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 (wrap' 5 10) [3..12] == [9,10,5,6,7,8,9,10,5,6]

genericWrap :: (Ord a, Num a) => a -> a -> a -> a

Generic variant of wrap'.

> [5,6].wrap(0,5) == [5,0]
map (genericWrap 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 (genericWrap (5::Integer) 10) [3..12] == [9,10,5,6,7,8,9,10,5,6]

wrap_ :: RealFracE n => n -> n -> n -> n

Variant of wrap' with SC3 argument ordering.

map (\n -> wrap_ n 5 10) [3..12] == map (wrap' 5 10) [3..12]

foldToRange :: (Ord a, Num a) => a -> a -> a -> a

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]

fold_ :: (Ord a, Num a) => a -> a -> a -> a

Variant of foldToRange with SC3 argument ordering.

clip' :: Ord a => a -> a -> a -> a

Clip k to within range (i,j),

map (clip' 5 10) [3..12] == [5,5,5,6,7,8,9,10,10,10]

clip_ :: Ord a => a -> a -> a -> a

Variant of clip' with SC3 argument ordering.

hypot_ :: Floating a => a -> a -> a

linLin_muladd :: Fractional t => t -> t -> t -> t -> (t, t)

Calculate multiplier and add values for linLin transform.

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 :: (Fractional a, TernaryOp a) => a -> a -> a -> a -> a -> a

Map from one linear range to another linear range.

linlin' :: Fractional a => a -> a -> a -> a -> a -> a

Variant without TernaryOp constraint.

urange :: (Fractional a, TernaryOp a) => a -> a -> a -> a

Scale uni-polar (0,1) input to linear (l,r) range

map (urange 3 4) [0,0.5,1] == [3,3.5,4]

urange' :: Fractional a => a -> a -> a -> a

Variant without TernaryOp constraint.

range_muladd :: Fractional t => t -> t -> (t, t)

Calculate multiplier and add values for range transform.

range_muladd 3 4 == (0.5,3.5)

range :: (Fractional a, TernaryOp a) => a -> a -> a -> a

Scale bi-polar (-1,1) input to linear (l,r) range. Note that the argument order is not the same as linLin.

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]

range' :: Fractional a => a -> a -> a -> a

Variant without TernaryOp constraint.