SimpleNumber:
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SimpleNumber : Number : Magnitude : Object

one-dimensional value
Subclasses: Float, Integer

Description

Base class for numbers which can be represented by a single one dimensional value.

Most of the Unary and Binary operations are also implemented by UnaryOpUGen and BinaryOpUGen, so you can get more examples by looking at the help for those.

Class Methods

SimpleNumber.new

allocates a new SimpleNumber.

Inherited class methods

Instance Methods

math support

+(aNumber, adverb)

Addition

-(aNumber, adverb)

Subtraction

*(aNumber, adverb)

Multiplication

/(aNumber, adverb)

Division

%(that)

From superclass: Object

Modulo

.mod(aNumber, adverb)

Modulo

.div(aNumber, adverb)

Integer Division

**(that)

From superclass: Object

Exponentiation

!=(aNumber, adverb)

Is not

>(aNumber, adverb)

greater than

<(aNumber, adverb)

greater than

>=(aNumber, adverb)

greater or equal than

<=(aNumber, adverb)

smaller or equal than

.lcm(aNumber, adverb)

Least common multiple

.gcd(aNumber, adverb)

Greatest common divisor

.round(aNumber: 1.0, adverb)

Round to multiple of aNumber

.roundUp(aNumber: 1.0, adverb)

Round up to a multiple of aNumber. For roundDown use trunc.

.trunc(aNumber: 1.0, adverb)

Truncate to multiple of aNumber (e.g. it rounds numbers down to a multiple of aNumber).

.softRound(resolution: 1.0, margin: 0.05, strength: 1.0)

Rounds the value to a multiple of resolution. By using margin and strength you can control which values will be rounded, and by how much.

Conceptually this is the equivalent of MIDI quantization in a DAW/MIDI sequencer. In particular it allows a certain sloppiness close to the resolution value.

Note: this method expects values >= 0.

Arguments:

resolution

Round this value to a multiple of resolution. E.g. if you chose 1, then all values would be rounded to the nearest integer.

margin

Values that are within ±margin from a multiple of resolution will be left as they are.

E.g. if you chose a resolution value of 0.5 and a margin of 0.01, then the values 0.501 and 0.499 would be left as they are, but the value 0.502 would become 0.5.

This should be a value between 0 and resolution.

strength

Determines the degree to which this number will be changed.

If strength is 1, then this function will return the nearest resolution. If it is 0, then value of this number will be left unchanged.

E.g. If the resolution was 1 and strength was 0.5, then the value 0.6 would become 0.8.

Discussion:

.snap(resolution: 1.0, margin: 0.05, strength: 1.0)

Rounds the values margin distance from resolution to a multiple of resolution. By using margin and strength you can control when values will be rounded, and by how much.

Conceptually this is the equivalent of 'snap' in a graphics program. Values within a certain distance (margin) from a grid line are snapped to it. All other values are unchanged.

Note: this method expects values >= 0.

Arguments:

resolution

Snap this value to a multiple of resolution. E.g. if you chose 1, then all values would be rounded to the nearest integer.

margin

Only values that are greater ±margin from a multiple of resolution value will be changed. Values that are less than margin will be unchanged.

E.g. if you chose a resolution value of 0.5 and a margin of 0.01, then the values 0.501 and 0.499 would be snapped to 0.5, but the value 0.502 would be unchanged.

This should be a value between 0 and resolution.

strength

Determines the degree to which this number will be changed.

If strength is 1, then this function will return the nearest resolution. If it is 0, then value of this number will be left unchanged.

E.g. If the resolution was 1 and strength was 0.5, then the value 0.6 would become 0.8.

Discussion:

.thresh(aNumber, adverb)

.min(aNumber, adverb)

Minimum

.max(aNumber: 0.0, adverb)

Maximum

.wrap2(aNumber: 1, adverb)

.atan2(aNumber, adverb)

Arctangent of (this/aNumber)

.hypot(aNumber, adverb)

Square root of the sum of the squares.

.log

Returns:

Base e logarithm.

.log2

Returns:

Base 2 logarithm.

.log10

Returns:

Base 10 logarithm.

.neg

Returns:

negation

.abs

Returns:

absolute value.

.sign

Returns:

Answer -1 if negative, +1 if positive or 0 if zero.

.ceil

Returns:

next larger integer.

.floor

Returns:

next smaller integer

.sin

Sine

.cos

Cosine

.tan

Tangent

.asin

Arcsine

.acos

Arccosine

.atan

Arctangent

.sinh

Hyperbolic sine

.cosh

Hyperbolic cosine

.tanh

Hyperbolic tangent

.frac

fractional part

.squared

the square of the number

.cubed

the cube of the number

.sqrt

the square root of the number.

.exp

e to the power of the receiver.

.reciprocal

1 / this

.pow(aNumber, adverb)

this to the power of aNumber

.fold2(aNumber: 1, adverb)

the folded value, a bitwise or with aNumber

.previousPowerOf(base)

the number relative to this that is the previous power of aNumber

.nextPowerOf(base)

the next power of aNumber

.nextPowerOfTwo

Returns:

the number relative to this that is the next power of 2

.nextPowerOfThree

the next power of three

.hash

Returns:

a hash value

<!(that)

From superclass: Object

Returns:

the receiver. aNumber is ignored.

&(that)

From superclass: Object

Bitwise And

|(that)

From superclass: Object

Bitwise Or

.bitXor(aNumber, adverb)

Bitwise Exclusive Or

.bitHammingDistance(aNumber, adverb)

Binary Hamming distance: the count of bits that are not the same in the two numbers

.bitTest(bit)

Returns:

true if bit at index aNumber is set.

.bitNot

Returns:

ones complement

<<(that)

From superclass: Object

Binary shift left.

>>(that)

From superclass: Object

Binary shift right.

+>>(that)

From superclass: Object

Unsigned binary shift right.

.rightShift(aNumber: 1, adverb)

Returns:

performs a binary right shift

.unsignedRightShift(aNumber, adverb)

Returns:

performs an unsigned right shift

.leftShift(aNumber: 1, adverb)

Returns:

performs a binary left shift

.bitOr(aNumber, adverb)

Returns:

performs a bitwise or with aNumber

.bitAnd(aNumber, adverb)

Returns:

performs a bitwise and with aNumber

.ring1(aNumber, adverb)

(a * b) + a

.ring2(aNumber, adverb)

((a*b) + a + b)

.ring3(aNumber, adverb)

(a * a *b)

.ring4(aNumber, adverb)

((a*a *b) - (a*b*b))

.difsqr(aNumber, adverb)

(a*a) - (b*b)

.sumsqr(aNumber, adverb)

(a*a) + (b*b)

.sqrdif(aNumber, adverb)

(a - b) ** 2

.sqrsum(aNumber, adverb)

(a + b) ** 2

.absdif(aNumber, adverb)

(a - b).abs

.moddif(aNumber: 0.0, mod: 1.0)

On a circle, there are two distances between two points. This operator returns the smaller value of the two.

.amclip(aNumber, adverb)

0 when b <= 0, a*b when b > 0

.scaleneg(aNumber, adverb)

a * b when a < 0, otherwise a.

.clip2(aNumber: 1, adverb)

clips receiver to +/- aNumber

.excess(aNumber: 1, adverb)

Returns the difference of the receiver and its clipped form.

Discussion:

.madd(mul, add)

testing

.isPositive

Answer if the number is >= 0.

.isNegative

Answer if the number is < 0.

.isStrictlyPositive

Answer if the number is > 0.

.booleanValue

Returns:

true, if strictly positive ( > 0), otherwise false (see Boolean)

.isNaN

==(aNumber, adverb)

conversion

.asFraction(denominator: 100, fasterBetter: true)

Arguments:

denominator
fasterBetter

if true, asFraction may find a much closer approximation and do it faster.

Returns:

an array of denominator and divisor of the nearest and smallest fraction

.asAudioRateInput

Converts this into an audiorate input.

.asTimeString(precision: 0.001, maxDays: 365, dropDaysIfPossible: true)

Produces a time string in the format ddd:hh:mm:ss.sss, interpreting the receiver as time in seconds. See String: -asSecs for the inverse function.

Arguments:

precision

accuracy of the millisecond format; the string will always be formatted with 3 decimal places for milliseconds. Minimum value: 0.001.

maxDays

maximum number of days

dropDaysIfPossible

a Boolean. If set to true, and the number of days in the formatted string would be 0, that section is instead ommitted and the string is formatted as hh:mm:ss.sss.

Discussion:

.asPoint

Returns:

this as Point. x = y = this.

.asComplex

Returns:

this as Point. x = y = this.

.asWarp(spec)

Arguments:

spec

a ControlSpec

Returns:

this as CurveWarp according to spec.

.asFloat

Returns:

this as Float

.asRect

Returns:

a Rect with x = y = w = h = this.

.asBoolean

Returns:

this as a Boolean. this > 0

.asQuant

Returns:

the values as Quant

.asInteger

Returns:

this as Integer

timing

.wait

within a routine, yield the number so that the clock can wait for this many beats. Outside a Routine, this trows an error (see also Routine for details).

Discussion:

Create a routine by a function fork

.waitUntil

like wait, only specify a time (measured in beats of the current thread's clock). Outside a Routine, this trows an error (see also Routine for details).

.sleep

make the current thread sleep, until woken up by re-scheduling. Outside a Routine, this trows an error (see also Routine for details).

.nextTimeOnGrid(clock)

Arguments:

clock

Returns:

the next possible multiple of the clock's beats.

.schedBundleArrayOnClock(clock, bundleArray, lag: 0, server, latency)

series and arrays

.nearestInList(list)

Returns:

the value in the list closest to this

Discussion:

.nearestInScale(scale, stepsPerOctave: 12)

Arguments:

scale

an array of SimpleNumbers each treated as a step in the octave.

stepsPerOctave

12 by default

Returns:

the value in the collection closest to this, assuming an octave repeating table of note values.

Discussion:

.series(second, last)

return an arithmetic series from this over second to last.

Discussion:

This is used in the shortcuts:

If second is nil, it is one magnitude step towards last (1 or -1). Examples:

.seriesIter(second, last)

Returns:

a Routine that iterates over the numbers from this to last.

Discussion:

Since this is a lazy operation, last may be inf, generating an endless series (see also List Comprehensions)

windowing

.rectWindow

Returns:

a value for a rectangular window function between 0 and 1.

.hanWindow

Returns:

a value for a hanning window function between 0 and 1.

.welWindow

Returns:

a value for a welsh window function between 0 and 1.

.triWindow

Returns:

a value for a triangle window function between 0 and 1.

mapping

.distort

a nonlinear distortion function.

.softclip

Distortion with a perfectly linear region from -0.5 to +0.5

.scurve

Map receiver in the onto an S-curve.

Discussion:

.ramp

Map receiver onto a ramp starting at 0.

Discussion:

.magnitude

Returns:

absolute value (see Polar, Complex)

.angle

Returns:

angle of receiver conceived as Polar or Complex number.

.degreeToKey(scale, stepsPerOctave: 12)

Arguments:

scale

an array of SimpleNumbers each treated as a step in the octave.

stepsPerOctave

12 is the standard chromatic scale.

Discussion:

the value is truncated to an integer and used as an index into an octave repeating table of note values. Indices wrap around the table and shift octaves as they do.

.keyToDegree(scale, stepsPerOctave: 12)

inverse of degreeToKey.

Arguments:

scale

an array of SimpleNumbers each treated as a step in the octave.

stepsPerOctave

12 is the standard chromatic scale.

Discussion:

.gaussCurve(a: 1.0, b: 0.0, c: 1.0)

map the receiver onto a gauss function.

Discussion:

Uses the formula:

Example code

.equalWithPrecision(that, precision: 0.0001, relativePrecision: 0)

Arguments:

that

the number to compare with within precision

precision

The absolute precision, independent of the value compared

relativePrecision

The precision relative to the larger absolute of the values compared.

Returns:

true if receiver is closer to that than precision.

Discussion:

.quantize(quantum: 1.0, tolerance: 0.05, strength: 1.0)

From extension in /usr/local/share/SuperCollider/SCClassLibrary/deprecated/3.10/deprecated-3.10.sc

Deprecated. Round the receiver to the quantum. If you're looking for MIDI quantization type features use SimpleNumber#-softRound

Arguments:

quantum

amount.

tolerance

allowed tolerance.

strength

Determines how much the value is allowed to differ in the tolerance range.

Discussion:

.linlin(inMin, inMax, outMin, outMax, clip: 'minmax')

map the receiver from an assumed linear input range to a linear output range. If the input exceeds the assumed input range, the behaviour is specified by the clip argument.

Arguments:

inMin

assumed input minimum

inMax

assumed input maximum

outMin

output minimum

outMax

output maximum

clip

nil (don't clip) \max (clip ceiling) \min (clip floor) \minmax (clip both - this is default).

Discussion:

.linexp(inMin, inMax, outMin, outMax, clip: 'minmax')

map the receiver from an assumed linear input range (inMin..inMax) to an exponential output range (outMin..outMax). The output range must not include zero. If the input exceeds the input range, the following behaviours are specified by the clip argument.

Arguments:

inMin

assumed input minimum

inMax

assumed input maximum

outMin

output minimum

outMax

output maximum

clip

nil (don't clip) \max (clip ceiling) \min (clip floor) \minmax (clip both - this is default).

Discussion:

.explin(inMin, inMax, outMin, outMax, clip: 'minmax')

map the receiver from an assumed exponential input range (inMin..inMax) to a linear output range (outMin..outMax). If the input exceeds the assumed input range. The input range must not include zero. If the input exceeds the input range, the following behaviours are specified by the clip argument.

Arguments:

inMin

assumed input minimum

inMax

assumed input maximum

outMin

output minimum

outMax

output maximum

clip

nil (don't clip) \max (clip ceiling) \min (clip floor) \minmax (clip both - this is default).

Discussion:

.expexp(inMin, inMax, outMin, outMax, clip: 'minmax')

map the receiver from an assumed exponential input range (inMin..inMax) to an exponential output range (outMin..outMax). If the input exceeds the assumed input range. Both input range and output range must not include zero. If the input exceeds the input range, the following behaviours are specified by the clip argument.

Arguments:

inMin

assumed input minimum

inMax

assumed input maximum

outMin

output minimum

outMax

output maximum

clip

nil (don't clip) \max (clip ceiling) \min (clip floor) \minmax (clip both - this is default).

Discussion:

.lincurve(inMin: 0, inMax: 1, outMin: 0, outMax: 1, curve: -4, clip: 'minmax')

map the receiver from an assumed linear input range (inMin..inMax) to an exponential curve output range (outMin..outMax). A curve is like the curve parameter in Env. Unlike with linexp, the output range may include zero. If the input exceeds the input range, the following behaviours are specified by the clip argument.

Arguments:

inMin

assumed input minimum

inMax

assumed input maximum

outMin

output minimum

outMax

output maximum

curve

0 (linear) <0 (concave, negatively curved) >0 (convex, positively curved)

clip

nil (don't clip) \max (clip ceiling) \min (clip floor) \minmax (clip both - this is default).

Discussion:

.curvelin(inMin: 0, inMax: 1, outMin: 0, outMax: 1, curve: -4, clip: 'minmax')

map the receiver from an assumed curve-exponential input range (inMin..inMax) to a linear output range (outMin..outMax). If the input exceeds the assumed input range. A curve is like the curve parameter in Env. Unlike with explin, the input range may include zero. If the input exceeds the input range, the following behaviours are specified by the clip argument.

Arguments:

inMin

assumed input minimum

inMax

assumed input maximum

outMin

output minimum

outMax

output maximum

curve

0 (linear) <0 (concave, negatively curved) >0 (convex, positively curved)

clip

nil (don't clip) \max (clip ceiling) \min (clip floor) \minmax (clip both - this is default).

Discussion:

.bilin(inCenter, inMin, inMax, outCenter, outMin, outMax, clip: 'minmax')

map the receiver from two assumed linear input ranges (inMin..inCenter) and (inCenter..inMax) to two linear output ranges (outMin..outCenter) and (outCenter..outMax). If the input exceeds the input range, the following behaviours are specified by the clip argument.

Arguments:

inCenter
inMin

assumed input minimum

inMax

assumed input maximum

outCenter
outMin

output minimum

outMax

output maximum

clip

nil (don't clip) \max (clip ceiling) \min (clip floor) \minmax (clip both - this is default).

Discussion:

.biexp(inCenter, inMin, inMax, outCenter, outMin, outMax, clip: 'minmax')

map the receiver from two assumed exponential input ranges (inMin..inCenter) and (inCenter..inMax) to two linear output ranges (outMin..outCenter) and (outCenter..outMax). The input range must not include zero. If the input exceeds the input range, the following behaviours are specified by the clip argument.

Arguments:

inCenter
inMin

assumed input minimum

inMax

assumed input maximum

outCenter
outMin

output minimum

outMax

output maximum

clip

nil (don't clip) \max (clip ceiling) \min (clip floor) \minmax (clip both - this is default).

Discussion:

.lcurve(a: 1.0, m: 0.0, n: 1.0, tau: 1.0)

map the receiver onto an L-curve.

Discussion:

Uses the formula

This is used for smoothing values and limiting them to a range.

.degrad

Returns:

converts degree to radian

.raddeg

Returns:

converts radian to degree

.midicps

Convert MIDI note to cycles per second

Returns:

cycles per second

.cpsmidi

Convert cycles per second to MIDI note.

Returns:

midi note

.midiratio

Convert an interval in semitones to a ratio.

Returns:

a ratio

.ratiomidi

Convert a ratio to an interval in semitones.

Returns:

an interval in semitones

.ampdb

Convert a linear amplitude to decibels.

.dbamp

Convert a decibels to a linear amplitude.

.octcps

Convert decimal octaves to cycles per second.

.cpsoct

Convert cycles per second to decimal octaves.

streams

.storeOn(stream)

stores this on the given stream

.printOn(stream)

prints this on the given stream

random

.coin

Let x be the receiver clipped to the range [0, 1]. With probability x, return true. With probability 1 - x, return false.

.rand

Returns:

Random number from zero up to the receiver, exclusive.

.rand2

Returns:

a random number from -this to +this.

.rrand(aNumber, adverb)

Arguments:

aNumber

the upper limit

adverb

Returns:

a random number in the interval ]a, b[.

Discussion:

If both a and b are Integer then the result will be an Integer.

.linrand

Returns:

a linearly distributed random number from zero to this.

.bilinrand

Returns:

Bilateral linearly distributed random number from -this to +this.

.sum3rand

This was suggested by Larry Polansky as a poor man's gaussian.

Returns:

A random number from -this to +this that is the result of summing three uniform random generators to yield a bell-like distribution.

.exprand(aNumber, adverb)

an exponentially distributed random number in the interval ]a, b[. This is always a Float. (Note that the distribution of numbers is not exactly an exponential distribution, since that would be unbounded: we might call it a logarithmic uniform distribution.)

Arguments:

aNumber

the upper limit

adverb

.gauss(standardDeviation)

a gaussian distributed random number.

Arguments:

standardDeviation

the upper limit

Discussion:

Always returns a Float.

.partition(parts: 2, min: 1)

randomly partition a number into parts of at least min size.

Arguments:

parts

number of parts

min

the minimum size

Discussion:

UGen Compatibility Methods

Some methods to ease the development of generic ugen code.

.lag

.lag2

.lag3

.lagud

.lag2ud

.lag3ud

.slew

.varlag

Returns:

this

misc

.isValidUGenInput

Returns:

false if receiver cannot be used in UGen.

Special Functions

A variety of Special Functions are supplied by the Boost C++ library. The library's online documentation serves as the primary reference for the following functions. The methods here match closely with those found in the source library, as do argument names.

Below you'll find descriptions of the functions and their bounds, but for visualizing the functions, have a look in Tour of Special Functions.

WARNING: Many of the functions are only valid in certain numerical ranges. For the most part, error handling happens in the underlying boost functions. While these errors are often obtuse, you'll usually find a useful message at the end of the error regarding proper ranges and the erroneous value supplied. Refer to the online documentation for more detailed descriptions, and the Tour of Special Functions for plots showing ranges and asymptotes.

Number Series

Take a tour of Number Series.

.bernouliB2n

Returns the (2*n)th Bernoulli number.

Because all odd numbered Bernoulli numbers are zero (apart from B(1) which is -1/2) the interface will only return the even numbered Bernoulli numbers.

.tangentT2n

Returns a single tangent number at i. Also called a zag function.

Gamma Functions

Take a tour of Gamma Functions.

.tgamma

Returns the "true gamma" of value z.

.tgamma1pm1

Returns gamma(dz + 1) - 1.

.lgamma

Returns the natural logarithm of the gamma function.

.digamma

Returns the digamma or psi function of z.

Digamma is defined as the logarithmic derivative of the gamma function.

.trigamma

Returns the trigamma function of z.

Trigamma is defined as the derivative of the digamma function.

.polygamma(z)

Returns the polygamma function of z.

Polygamma is defined as the n'th derivative of the digamma function.

.tgammaRatio(b)

Returns the ratio of gamma functions tgamma(a) / tgamma(b).

.tgammaDeltaRatio(delta)

Returns the ratio of gamma functions tgamma(a) / tgamma(a+delta).

.gammaP(z)

Returns the normalised lower incomplete gamma function.

Requires a > 0 and z >= 0.

.gammaQ(z)

Returns the normalised upper incomplete gamma function.

Requires a > 0 and z >= 0.

.tgammaLower(z)

Returns the full (non-normalised) lower incomplete gamma function.

Requires a > 0 and z >= 0.

.tgammaUpper(z)

Returns the full (non-normalised) upper incomplete gamma function.

Requires a > 0 and z >= 0.

.gammaPInv(p)

Returns a value such that p = gamma_p(a, x).

Requires a > 0 and 1 >= p,q >= 0.

.gammaQInv(q)

Returns a value x such that q = gamma_q(a, x).

Requires a > 0 and 1 >= p,q >= 0.

.gammaPInvA(p)

Returns a value such that p = gamma_p(a, x).

Requires x > 0 and 1 >= p,q >= 0.

.gammaQInvA(q)

Returns a value x such that q = gamma_q(a, x).

Requires x > 0 and 1 >= p,q >= 0.

.gammaPDerivative(x)

Implements the partial derivative with respect to x of the incomplete gamma function (lower).

.gammaQDerivative(x)

Implements the partial derivative with respect to x of the incomplete gamma function (upper).

Factorials and Binomial Coefficients

Take a tour of Factorials and Binomial Coefficients.

.factorial

Returns i!.

WARNING: factorial will overflow if i > 170

.doubleFactorial

Returns i!!.

For even i, i !! = i(i-2)(i-4)(i-6) ... (4)(2).

For odd i, i !! = i(i-2)(i-4)(i-6) ... (3)(1).

.risingFactorial(i)

Returns the rising factorial of x and i:

x(x+1)(x+2)(x+3)...(x+i-1)

Both x and i can be negative as well as positive.

.fallingFactorial(i)

Returns the falling factorial of x and i:

x(x-1)(x-2)(x-3)...(x-i+1)

This function is only defined for positive i. Argument x can be either positive or negative.

.binomialCoefficient(k)

Requires k <= n.

Beta Functions

Take a tour of Beta Functions.

.beta(b)

The beta function is defined by: tgamma(a)*tgamma(b) / tgamma(a+b).

.ibeta(b, x)

Returns the normalised incomplete beta function of a, b and x.

Require 0 <= x <= 1, a,b >= 0, and in addition that not both a and b are zero.

.ibetaC(b, x)

Returns the normalised complement of the incomplete beta function of a, b and x.

Require 0 <= x <= 1, a,b >= 0, and in addition that not both a and b are zero.

.betaFull(b, x)

Returns the full (non-normalised) incomplete beta function of a, b and x.

Require 0 <= x <= 1, and a,b > 0.

.betaFullC(b, x)

Returns the full (non-normalised) complement of the incomplete beta function of a, b and x.

Require 0 <= x <= 1, and a,b > 0.

.ibetaInv(b, p)

Returns a value x such that: p = ibeta(a, b, x).

Requires a,b > 0 and 0 <= p <= 1.

.ibetaCInv(b, q)

Returns a value x such that: q = ibetaC(a, b, x).

Requires a,b > 0 and 0 <= q <= 1.

.ibetaInvA(x, p)

Returns a value a such that: p = ibeta(a, b, x).

Requires b > 0, 0 < x < 1, and 0 <= p <= 1.

.ibetaCInvA(x, q)

Returns a value a such that: q = ibetaC(a, b, x).

Requires b > 0, 0 < x < 1, and 0 <= q <= 1.

.ibetaInvB(x, p)

Returns a value b such that: p = ibeta(a, b, x).

Requires a > 0, 0 < x < 1, and 0 <= p <= 1.

.ibetaCInvB(x, q)

Returns a value b such that: q = ibetaC(a, b, x).

Requires a > 0, 0 < x < 1, and 0 <= q <= 1.

.ibetaDerivative(b, x)

Returns the partial derivative with respect to x of the incomplete beta function ibeta(a,b,x).

Error Functions

Take a tour of Error Functions.

.erf

Returns the error function of z.

.erfC

Returns the complement of the error function of z.

.erfInv

Returns the inverse error function of z, that is a value x such that:

p = erf(x).

.erfCInv

Returns the inverse of the complement of the error function of z, that is a value x such that:

p = erfC(x)

Polynomials

Take a tour of Polynomials.

.legendreP(x)

Returns the Legendre Polynomial of the first kind.

Requires -1 <= x <= 1.

.legendrePPrime(x)

Returns the derivatives of the Legendre polynomials.

.legendrePZeros

Since the Legendre polynomials are alternatively even and odd, only the non-negative zeros are returned. For the odd Legendre polynomials, the first zero is always zero. The rest of the zeros are returned in increasing order.

.legendrePAssoc(m, x)

Returns the associated Legendre polynomial of the first kind.

Requires -1 <= x <= 1.

.legendreQ(x)

Returns the value of the Legendre polynomial that is the second solution to the Legendre differential equation.

Requires -1 <= x <= 1.

.laguerre(x)

Returns the value of the Laguerre Polynomial of order n at point x.

.laguerreAssoc(m, x)

Returns the Associated Laguerre polynomial of degree of dgree n and order m at point x.

.hermite(x)

Returns the value of the Hermite Polynomial of order n at point x.

.chebyshevT(x)

Returns the Chebyshev polynomials of the first kind.

.chebyshevU(x)

Returns the Chebyshev polynomials of the second kind.

.chebyshevTPrime(x)

Returns the derivatives of the Chebyshev polynomials of the first kind.

.chebyshevTZeros

Returns the roots (zeros) of the n-th Chebyshev polynomial of the first kind.

.sphericalHarmonic(m, theta, phi)

Returns the (Complex) value of the Spherical Harmonic.

theta is taken as the polar (colatitudinal) coordinate within [0, pi], and phi as the azimuthal (longitudinal) coordinate within [0,2pi].

See boost documentation for further information, including a note about the Condon-Shortley phase term of (-1)^m.

.sphericalHarmonicR(m, theta, phi)

Returns the real part of the Spherical Harmonic.

.sphericalHarmonicI(m, theta, phi)

Returns the imaginary part of the Spherical Harmonic.

Bessel Functions

Take a tour of Bessel Functions.

.cylBesselJ(x)

Returns the result of the Bessel functions of the first kind.

The functions return the result of domain_error whenever the result is undefined or complex. This occurs when x < 0 and v is not an integer, or when x == 0 and v != 0.

.cylNeumann(x)

Returns the result of the Bessel functions of the second kind.

The functions return the result of domain_error whenever the result is undefined or complex. This occurs when x <= 0.

.cylBesselJZero(index)

Returns a single zero or root of the Bessel function of the first kind.

index is a 1-based index of zero of the cylindrical Bessel function of order v.

.cylNeumannZero(index)

Returns a single zero or root of the Neumann function (Bessel function of the second kind).

index is a 1-based index of zero of the cylindrical Neumann function of order v.

.cylBesselI(x)

Returns the result of the modified Bessel functions of the first kind.

.cylBesselK(x)

Returns the result of the modified Bessel functions of the second kind.

Requires x > 0.

.sphBessel(x)

Returns the result of the spherical Bessel functions of the first kind.

Requires x > 0.

.sphNeumann(x)

Returns the result of the spherical Bessel functions of the first kind.

Requires x > 0.

.cylBesselJPrime(x)

Returns the first derivative with respect to x of the corresponding Bessel function.

.cylNeumannPrime(x)

Returns the first derivative with respect to x of the corresponding Neumann function.

Requires x > 0.

.cylBesselIPrime(x)

Returns the first derivative with respect to x of the corresponding Bessel function.

.cylBesselKPrime(x)

Returns the first derivative with respect to x of the corresponding Bessel function.

Requires x > 0.

.sphBesselPrime(x)

Returns the first derivative with respect to x of the corresponding Bessel function.

Requires x > 0.

.sphNeumannPrime(x)

Returns the first derivative with respect to x of the corresponding Neumann function.

Requires x > 0.

Hankel Functions

Take a tour of Hankel Functions.

.cylHankel1(x)

Returns the result of the Hankel functions of the first kind.

.cylHankel2(x)

Returns the result of the Hankel functions of the second kind.

.sphHankel1(x)

Returns the result of the spherical Hankel functions of the first kind.

.sphHankel2(x)

Returns the result of the spherical Hankel functions of the second kind.

Airy Functions

Take a tour of Airy Functions.

.airyAi

Returns the result of the Airy function Ai at x.

.airyBi

Returns the result of the Airy function Bi at x.

.airyAiPrime

Returns the derivative of the Airy function Ai at x.

.airyBiPrime

Returns the derivative of the Airy function Bi at x.

.airyAiZero

Returns the mth zero or root of the Airy Ai function. The Airy Ai function has an infinite number of zeros on the negative real axis.

m is 1-based.

.airyBiZero

Returns the mth zero or root (1-based) of the Airy Bi function. The Airy Bi function has an infinite number of zeros on the negative real axis.

m is 1-based.

Elliptic Integrals

Take a tour of Elliptic Integrals.

.ellintRf(y, z)

Returns Carlson's Elliptic Integral RF.

Requires that x,y >= 0, with at most one of them zero, and that z >= 0.

.ellintRd(y, z)

Returns Carlson's Elliptic Integral RD.

Requires that x,y >= 0, with at most one of them zero, and that z >= 0.

.ellintRj(y, z, p)

Returns Carlson's Elliptic Integral RJ.

Requires that x,y,z >= 0, with at most one of them zero, and that p != 0.

.ellintRc(y)

Returns Carlson's Elliptic Integral RC.

Requires that x >= 0, with at most one of them zero, and that y != 0.

.ellintRg(y, z)

Returns Carlson's Elliptic Integral RG.

Requires that x,y >= 0.

.ellint1(phi)

Returns the incomplete elliptic integral of the first kind, Legendre form.

Requires -1 <= k <= 1.

.ellint1C

Returns the complete elliptic integral of the first kind, Legendre form.

Requires -1 <= k <= 1.

.ellint2(phi)

Returns the incomplete elliptic integral of the second kind, Legendre form.

Requires -1 <= k <= 1.

.ellint2C

Returns the complete elliptic integral of the second kind, Legendre form.

Requires -1 <= k <= 1.

.ellint3(n, phi)

Returns the incomplete elliptic integral of the third kind, Legendre form.

Requires -1 <= k <= 1 and n < 1/sin^2(phi).

.ellint3C(n)

Returns the complete elliptic integral of the third kind, Legendre form.

Requires -1 <= k <= 1 and n < 1.

.ellintD(phi)

Returns the incomplete elliptic integral D(phi, k), Legendre form.

Requires -1 <= k <= 1.

.ellintDC

Returns the complete elliptic integral D(phi, k), Legendre form.

Requires -1 <= k <= 1.

.jacobiZeta(phi)

Returns the result of the Jacobi Zeta Function.

Requires -1 <= k <= 1.

.heumanLambda(phi)

Returns the result of the Heuman Lambda Function.

Requires -1 <= k <= 1.

Jacobi Elliptic Functions

Like all elliptic functions, these can be parameterised in a number of ways:

This implementation takes the elliptic modulus k as the parameter. In addition the variable u is used to express an amplitude φ. All take the elliptic modulus as the first argument - this is for alignment with the Elliptic Integrals.

Take a tour of Jacobi Elliptic Functions.

.jacobiCd(u)

.jacobiCn(u)

.jacobiCs(u)

.jacobiDc(u)

.jacobiDn(u)

.jacobiDs(u)

.jacobiNc(u)

.jacobiNd(u)

.jacobiNs(u)

.jacobiSc(u)

.jacobiSd(u)

.jacobiSn(u)

Zeta Functions

Take a tour of Zeta Functions.

.zeta

Returns the zeta function of z.

Requires z != 1.

Exponential Integrals

Take a tour of Exponential Integrals.

.expintEn(z)

Returns the exponential integral En of z.

Requires that when n == 1, z !=0.

.expintEi

Returns the exponential integral of z.

Requires z != 0.

Basic Functions

Take a tour of Basic Functions.

.sinPi

Returns sin(x * π).

.cosPi

Returns cos(x * π).

.log1p

Returns the natural logarithm of x+1.

.expm1

Returns e^x - 1.

.cbrt

Returns the cube root of x.

.sqrt1pm1

Returns sqrt(1+x) - 1.

.powm1(y)

Returns x^y - 1.

Sinus Cardinal (Sinc) and Hyperbolic Sinus Cardinal Functions

Take a tour of Sinus Cardinal (Sinc) and Hyperbolic Sinus Cardinal Functions.

.sincPi

Returns the Sinus Cardinal of x. Also known as the "sinc" function.

sincPi(x) = sin(x) / x

.sinhcPi

Returns the Hyperbolic Sinus Cardinal of x.

sinhcPi(x) = sinh(x) / x

Inverse Hyperbolic Functions

Take a tour of Inverse Hyperbolic Functions.

.asinh

Returns the reciprocal of the hyperbolic sine function at x.

.acosh

Returns the reciprocal of the hyperbolic cosine function at x.

Requires x >= 1.

.atanh

Returns the reciprocal of the hyperbolic sine function at x.

Requires -1 < x < 1.

Owen's T Function

Take a tour of Owen's T Function.

.owensT(a)

Returns the Owens T function of h and a.

Inherited instance methods

Undocumented instance methods

.asBufWithValues

.asEvent

From extension in /usr/local/share/SuperCollider/SCClassLibrary/Common/Streams/Rest.sc

.asMIDIInPortUID

From extension in /usr/local/share/SuperCollider/SCClassLibrary/Common/Control/asMIDIPort.sc

.asSize

From extension in /usr/local/share/SuperCollider/SCClassLibrary/Common/Geometry/Size.sc

.asTimeStringLJP

From extension in /usr/local/share/SuperCollider/Extensions/SC3plugins/LoopBufUGens/classes/LJP Classes/Extensions/SimpleNumber-asTimeString.sc

.betarand(val2: 1, prob1: 1, prob2: 1)

From extension in /usr/local/share/SuperCollider/Extensions/SC3plugins/LoopBufUGens/classes/LJP Classes/ProbabilityDistributions.sc

.binaryValue

.buildForProxy(proxy, channelOffset: 0)

From extension in /usr/local/share/SuperCollider/SCClassLibrary/JITLib/ProxySpace/wrapForNodeProxy.sc

.calcPVRecSize(frameSize, hop, sampleRate)

From extension in /usr/local/share/SuperCollider/Extensions/SC3plugins/JoshUGens/classes/JoshPV.sc

.cauchy(spread: 1.0)

From extension in /usr/local/share/SuperCollider/Extensions/SC3plugins/LoopBufUGens/classes/LJP Classes/ProbabilityDistributions.sc

.delta

From extension in /usr/local/share/SuperCollider/SCClassLibrary/Common/Streams/Rest.sc

.firstArg(aNumber, adverb)

.gaussian(dev: 1)

From extension in /usr/local/share/SuperCollider/Extensions/SC3plugins/LoopBufUGens/classes/LJP Classes/ProbabilityDistributions.sc

.guiClass

From extension in /usr/local/share/SuperCollider/SCClassLibrary/Common/GUI/tools/guicrucial/gui.sc

.hypotApx(aNumber, adverb)

.linrrand(val2: 1.0)

From extension in /usr/local/share/SuperCollider/Extensions/SC3plugins/LoopBufUGens/classes/LJP Classes/ProbabilityDistributions.sc

.logistic(spread: 1)

From extension in /usr/local/share/SuperCollider/Extensions/SC3plugins/LoopBufUGens/classes/LJP Classes/ProbabilityDistributions.sc

.midinote

From extension in /usr/local/share/SuperCollider/Extensions/SC3plugins/LoopBufUGens/classes/LJP Classes/Extensions/midinote.sc

.numChannels

.pareto(shape: 1)

From extension in /usr/local/share/SuperCollider/Extensions/SC3plugins/LoopBufUGens/classes/LJP Classes/ProbabilityDistributions.sc

.performBinaryOpOnComplex(aSelector, aComplex, adverb)

.performBinaryOpOnSignal(aSelector, aSignal, adverb)

.performBinaryOpOnSimpleNumber(aSelector, aNumber, adverb)

.playAndDelta

.poisson

From extension in /usr/local/share/SuperCollider/Extensions/SC3plugins/LoopBufUGens/classes/LJP Classes/ProbabilityDistributions.sc

.poll(trig: 10, label, trigid: -1)

.proxyControlClass

From extension in /usr/local/share/SuperCollider/SCClassLibrary/JITLib/ProxySpace/wrapForNodeProxy.sc

.rate

.weibull(spread, shape: 1)

From extension in /usr/local/share/SuperCollider/Extensions/SC3plugins/LoopBufUGens/classes/LJP Classes/ProbabilityDistributions.sc

.writeInputSpec(file, synth)

.writeInputSpecOld(file, synth)

From extension in /usr/local/share/SuperCollider/SCClassLibrary/Common/Audio/SynthDefOld.sc