Safe Haskell | Safe |
---|---|
Language | Haskell98 |
Common math functions.
Synopsis
- half_pi :: Floating a => a
- two_pi :: Floating n => n
- mul_add_hs :: Num a => a -> a -> a -> a
- sc3_truncate :: RealFrac a => a -> a
- sc3_round :: RealFrac a => a -> a
- sc3_ceiling :: RealFrac a => a -> a
- sc3_floor :: RealFrac a => a -> a
- sc3_round_to :: RealFrac n => n -> n -> n
- sc3_idiv :: RealFrac n => n -> n -> n
- sc3_mod :: RealFrac n => n -> n -> n
- fmod_f32 :: Float -> Float -> Float
- fmod_f64 :: Double -> Double -> Double
- sc3_clip :: Ord a => a -> a -> a -> a
- clip_hs :: Ord a => (a, a) -> a -> a
- sc3_mod_alt :: RealFrac a => a -> a -> a
- sc3_wrap_ni :: RealFrac a => a -> a -> a -> a
- wrap_hs :: RealFrac n => (n, n) -> n -> n
- sc3_wrap :: RealFrac n => n -> n -> n -> n
- generic_wrap :: (Ord a, Num a) => (a, a) -> a -> a
- bin_to_freq :: (Fractional n, Integral i) => n -> i -> i -> n
- midi_to_cps :: Floating a => a -> a
- cps_to_midi :: Floating a => a -> a
- cps_to_oct :: Floating a => a -> a
- oct_to_cps :: Floating a => a -> a
- degree_to_key :: RealFrac a => [a] -> a -> a -> a
- amp_to_db :: Floating a => a -> a
- db_to_amp :: Floating a => a -> a
- midi_to_ratio :: Floating a => a -> a
- ratio_to_midi :: Floating a => a -> a
- cps_to_incr :: Fractional a => a -> a -> a -> a
- incr_to_cps :: Fractional a => a -> a -> a -> a
- pan2_f :: Fractional t => (t -> t) -> t -> t -> (t, t)
- lin_pan2 :: Fractional t => t -> t -> (t, t)
- eq_pan2 :: Floating t => t -> t -> (t, t)
- sc3_properFraction :: RealFrac t => t -> (t, t)
- sc3_dif_sqr :: Num a => a -> a -> a
- sc3_hypot :: Floating a => a -> a -> a
- sc3_hypotx :: (Ord a, Floating a) => a -> a -> a
- foldToRange :: (Ord a, Num a) => a -> a -> a -> a
- sc3_fold :: (Ord a, Num a) => a -> a -> a -> a
- sc3_distort :: Fractional n => n -> n
- sc3_softclip :: (Ord n, Fractional n) => n -> n
- sc3_true :: Num n => n
- sc3_false :: Num n => n
- sc3_not :: (Ord n, Num n) => n -> n
- sc3_bool :: Num n => Bool -> n
- sc3_comparison :: Num n => (n -> n -> Bool) -> n -> n -> n
- sc3_eq :: (Num n, Eq n) => n -> n -> n
- sc3_neq :: (Num n, Eq n) => n -> n -> n
- sc3_lt :: (Num n, Ord n) => n -> n -> n
- sc3_lte :: (Num n, Ord n) => n -> n -> n
- sc3_gt :: (Num n, Ord n) => n -> n -> n
- sc3_gte :: (Num n, Ord n) => n -> n -> n
- data Clip_Rule
- apply_clip_rule :: Ord n => Clip_Rule -> n -> n -> n -> n -> n -> Maybe n
- urange :: Fractional a => a -> a -> a -> a
- range_muladd :: Fractional t => t -> t -> (t, t)
- range :: Fractional a => a -> a -> a -> a
- range_hs :: Fractional a => (a, a) -> a -> a
- linlin_muladd :: Fractional t => t -> t -> t -> t -> (t, t)
- linlin_hs :: Fractional a => (a, a) -> (a, a) -> a -> a
- sc3_linlin :: Fractional a => a -> a -> a -> a -> a -> a
- linlin_enum_plain :: (Enum t, Enum u) => t -> u -> t -> u
- linlin_enum :: (Enum t, Enum u) => (t, t) -> (u, u) -> t -> Maybe u
- linlin_enum_err :: (Enum t, Enum u) => (t, t) -> (u, u) -> t -> u
- linlin_eq :: (Eq a, Num a) => (a, a) -> (a, a) -> a -> Maybe a
- linlin_eq_err :: (Eq a, Num a) => (a, a) -> (a, a) -> a -> a
- linexp_hs :: Floating a => (a, a) -> (a, a) -> a -> a
- lin_exp :: Floating a => a -> a -> a -> a -> a -> a
- sc3_linexp :: (Ord a, Floating a) => a -> a -> a -> a -> a -> a
- sc3_explin :: (Ord a, Floating a) => a -> a -> a -> a -> a -> a
- sc3_expexp :: (Ord a, Floating a) => a -> a -> a -> a -> a -> a
- sc3_lincurve :: (Ord a, Floating a) => a -> a -> a -> a -> a -> a -> a
- sc3_curvelin :: (Ord a, Floating a) => a -> a -> a -> a -> a -> a -> a
- double_pp :: Int -> Double -> String
- real_pp :: Double -> String
- parse_double :: String -> Maybe Double
Documentation
mul_add_hs :: Num a => a -> a -> a -> a Source #
Multiply and add, ordinary haskell argument order.
See also mul_add
of the MulAdd
class.
map (mul_add_hs 2 3) [1,2] == [5,7] && map (mul_add_hs 3 4) [1,2] == [7,10]
sc3_truncate :: RealFrac a => a -> a Source #
fromInteger
of truncate
.
sc3_ceiling :: RealFrac a => a -> a Source #
fromInteger
of ceiling
.
sc3_round_to :: RealFrac n => n -> n -> n Source #
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
sc3_mod :: RealFrac n => n -> n -> n Source #
The SC3 %
UGen 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
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_clip :: Ord a => a -> a -> a -> a Source #
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]
clip_hs :: Ord a => (a, a) -> a -> a Source #
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]
sc3_mod_alt :: RealFrac a => a -> a -> a Source #
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_wrap_ni :: RealFrac a => a -> a -> a -> a Source #
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]
wrap_hs :: RealFrac n => (n, n) -> n -> n Source #
Wrap n to within range (i,j), ie. AbstractFunction.wrap
,
ie. inclusive at right edge. wrap
is a UGen
, hence prime.
> [5,6].wrap(0,5) == [5,0] map (wrap_hs (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 (5,10)) [3..12] == [9,10,5,6,7,8,9,10,5,6]
sc3_wrap :: RealFrac n => n -> n -> n -> n Source #
Variant of wrap_hs
with SC3
argument ordering.
map (\n -> sc3_wrap n 5 10) [3..12] == map (wrap_hs (5,10)) [3..12]
generic_wrap :: (Ord a, Num a) => (a, a) -> a -> a Source #
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]
bin_to_freq :: (Fractional n, Integral i) => n -> i -> i -> n Source #
Given sample-rate sr and bin-count n calculate frequency of ith bin.
bin_to_freq 44100 2048 32 == 689.0625
midi_to_cps :: Floating a => a -> a Source #
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]
cps_to_midi :: Floating a => a -> a Source #
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_oct :: Floating a => a -> a Source #
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]
oct_to_cps :: Floating a => a -> a Source #
Linear octave to cycles per second.
map (cps_to_midi . oct_to_cps) [4.0,4.25,4.75] == [60,63,69]
degree_to_key :: RealFrac a => [a] -> a -> a -> a Source #
Degree, scale and steps per octave to key.
amp_to_db :: Floating a => a -> a Source #
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]
db_to_amp :: Floating a => a -> a Source #
Decibels to linear amplitude.
map (floor . (* 100). db_to_amp) [-40,-26,-24,-18,-12,-6] == [01,05,06,12,25,50]
midi_to_ratio :: Floating a => a -> a Source #
Fractional midi note interval to frequency multiplier.
map midi_to_ratio [0,7,12] == [1,1.4983070768766815,2]
ratio_to_midi :: Floating a => a -> a Source #
Inverse of midi_to_ratio
.
map ratio_to_midi [3/2,2] == [7.019550008653875,12]
cps_to_incr :: Fractional a => a -> a -> a -> a Source #
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
incr_to_cps :: Fractional a => a -> a -> a -> a Source #
Inverse of cps_to_incr
.
incr_to_cps 48000 128 1 == 375
pan2_f :: Fractional t => (t -> t) -> t -> t -> (t, t) Source #
Pan2 function, identity is linear, sqrt is equal power.
lin_pan2 :: Fractional t => t -> t -> (t, t) Source #
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)]
sc3_properFraction :: RealFrac t => t -> (t, t) Source #
sc3_dif_sqr :: Num a => a -> a -> a Source #
a^2 - b^2.
sc3_hypot :: Floating a => a -> a -> a Source #
Euclidean distance function (sqrt
of sum of squares).
sc3_hypotx :: (Ord a, Floating a) => a -> a -> a Source #
SC3 hypotenuse approximation function.
foldToRange :: (Ord a, Num a) => a -> a -> a -> a Source #
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]
sc3_fold :: (Ord a, Num a) => a -> a -> a -> a Source #
Variant of foldToRange
with SC3
argument ordering.
sc3_distort :: Fractional n => n -> n Source #
SC3 distort operator.
sc3_softclip :: (Ord n, Fractional n) => n -> n Source #
SC3 softclip operator.
Bool
sc3_not :: (Ord n, Num n) => n -> n Source #
Lifted not
.
sc3_not sc3_true == sc3_false sc3_not sc3_false == sc3_true
sc3_comparison :: Num n => (n -> n -> Bool) -> n -> n -> n Source #
Lift comparison function.
Eq
Ord
Clip Rule
Enumeration of clipping rules.
Instances
Bounded Clip_Rule Source # | |
Enum Clip_Rule Source # | |
Defined in Sound.SC3.Common.Math succ :: Clip_Rule -> Clip_Rule # pred :: Clip_Rule -> Clip_Rule # fromEnum :: Clip_Rule -> Int # enumFrom :: Clip_Rule -> [Clip_Rule] # enumFromThen :: Clip_Rule -> Clip_Rule -> [Clip_Rule] # enumFromTo :: Clip_Rule -> Clip_Rule -> [Clip_Rule] # enumFromThenTo :: Clip_Rule -> Clip_Rule -> Clip_Rule -> [Clip_Rule] # |
apply_clip_rule :: Ord n => Clip_Rule -> n -> n -> n -> n -> n -> Maybe n Source #
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]
LinLin
urange :: Fractional a => a -> a -> a -> a Source #
Scale uni-polar (0,1) input to linear (l,r) range
map (urange 3 4) [0,0.5,1] == [3,3.5,4]
range_muladd :: Fractional t => t -> t -> (t, t) Source #
Calculate multiplier and add values for range
transform.
range_muladd 3 4 == (0.5,3.5)
range :: Fractional a => a -> a -> a -> a Source #
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] == [3,3.5,4]
range_hs :: Fractional a => (a, a) -> a -> a Source #
Tuple variant of range
.
linlin_muladd :: Fractional t => t -> t -> t -> t -> (t, t) Source #
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_muladd (-0.3) 1 (-1) 1
linlin_hs :: Fractional a => (a, a) -> (a, a) -> a -> a Source #
sc3_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]
sc3_linlin :: Fractional a => a -> a -> a -> a -> a -> a Source #
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
linlin_enum_plain :: (Enum t, Enum u) => t -> u -> t -> u Source #
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 :: (Enum t, Enum u) => (t, t) -> (u, u) -> t -> Maybe u Source #
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_err :: (Enum t, Enum u) => (t, t) -> (u, u) -> t -> u Source #
Erroring variant.
linlin_eq :: (Eq a, Num a) => (a, a) -> (a, a) -> a -> Maybe a Source #
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_err :: (Eq a, Num a) => (a, a) -> (a, a) -> a -> a Source #
Erroring variant.
LinExp
linexp_hs :: Floating a => (a, a) -> (a, a) -> a -> a Source #
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]
lin_exp :: Floating a => a -> a -> a -> a -> a -> a Source #
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]
sc3_linexp :: (Ord a, Floating a) => a -> a -> a -> a -> a -> a Source #
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_explin :: (Ord a, Floating a) => a -> a -> a -> a -> a -> a Source #
SimpleNumber.explin
is the inverse of linexp.
map (sc3_explin 10 100 1 2) [10,10,31,100,100]
ExpExp
sc3_expexp :: (Ord a, Floating a) => a -> a -> a -> a -> a -> a Source #
Translate from one exponential range to another.
map (sc3_expexp 0.1 10 4.3 100) [1.. 10]
LinCurve
sc3_lincurve :: (Ord a, Floating a) => a -> a -> a -> a -> a -> a -> a Source #
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 plotTable (map (\c-> map (sc3_lincurve c 0 1 (-1) 1) [0,0.01 .. 1]) [-6,-4 .. 6])
sc3_curvelin :: (Ord a, Floating a) => a -> a -> a -> a -> a -> a -> a Source #
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]
PP
double_pp :: Int -> Double -> String Source #
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"
real_pp :: Double -> String Source #
Print as integer if integral, else as real.
unwords (map real_pp [0.0001,0.001,0.01,0.1,1.0]) == "0.0001 0.001 0.01 0.1 1"