https://github.com/nearform/node-cephes

Implementation of special functions and distributions mathematical functions from the cephes library.
https://github.com/nearform/node-cephes

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Implementation of special functions and distributions mathematical functions from the cephes library.

• Host: GitHub
• URL: https://github.com/nearform/node-cephes
• Owner: nearform
• License: other
• Created: 2018-08-27T09:40:56.000Z (about 6 years ago)
• Default Branch: master
• Last Pushed: 2024-06-17T02:21:59.000Z (5 months ago)
• Last Synced: 2024-10-01T23:05:44.841Z (about 1 month ago)
• Topics: hacktoberfest
• Language: C
• Homepage:
• Size: 501 KB
• Stars: 117
• Watchers: 99
• Forks: 9
• Open Issues: 2
• Metadata Files:
  • Readme: README.md
  • Contributing: CONTRIBUTING.md
  • License: LICENSE

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README

        
# node-cephes

This is a WebAssembly packaging of the [cephes library](http://www.netlib.org/cephes/).

The cephes library contains C implementations of most

[special functions](https://en.wikipedia.org/wiki/Special_functions),

[distributions](https://en.wikipedia.org/wiki/Probability_distribution),

and other hard-to-implement mathematical functions.

_Note that there are a few cephes functions that are not exposed here, as some

of them are quite hard to make consumable in JavaScript using WebAssembly. Feel

free to send a pull request if you need one of them._

## Install

```

npm install cephes

```

If you are looking on GitHub, you will notice some files are missing. These

are statically built from the cephes library. See the

[CONTRIBUTING.md](CONTRIBUTING.md) file, for how to build them.

## Usage

Cephes is a WebAssembly module but is very small and fast to compile, as it

doesn't depend on any runtime libraries. In Node.js it is therefore compiled

synchronously and all you need to do is require the module.

```js

const cephes = require('cephes'); // Node.js

```

In the browser, it is, for good practice, compiled asynchronously. You must

therefore wait for the `.compiled` promise to be resolved.

```js

const cephes = require('cephes'); // Browser

await cephes.compiled;

```

Note that the `.compiled` promise is also available in Node.js, but it is

simply a dummy promise that resolves immediately.

### The JavaScript interface

There are three variations of functions to be aware of:

#### 1. Plain numeric function

These don't require anything special.

```js

const value = cephes.zeta(2, 1);

```

#### 2. Functions that return more than one value

In C, these functions return a primary value and then return extra value

using pointer arguments. In JavaScript this is implemented as a function

that returns an array of length 2. The first element is the primary returned

value, the second is an object of the extra returned values.

```js

const [value, {ai, aip, bi, bip}] = cephes.airy(-1);

```

#### 3. Functions that consumes an array

Some functions consumes an array of values, these must be `TypedArrays` of

the appropriate type. These functions will typically also require a variation

of `.length` value as a parameter, like you would do in C. Be aware, that in

some cases it may not be exactly the `.length` of the `TypedArray`, but may be

one less or one more. Check the specific function documentation to be sure.

```js

const arrayInput = new Float64Array([2.2, 3.3, 4.4]);

const value = ephes.polevl(1.1, arrayInput, arrayInput.length - 1);

```

## Table of Content

  Function

  Description

  Documentation

  

    Arithmetic and Algebraic

  

  

    signbit(x)

    Returns the sign bit

    c-doc  •  js-doc

  

    isnan(x)

    Check if Not-A-Number

    c-doc  •  js-doc

  

    isfinite(x)

    Check if finite

    c-doc  •  js-doc

  

    cbrt(x)

    Cube root

    c-doc  •  js-doc

  

    polevl(x, coef, N)

    Evaluate polynomial

    c-doc  •  js-doc

  

    chbevl(x, array, n)

    Evaluate Chebyshev series

    c-doc  •  js-doc

  

    round(x)

    Round to nearest integer value

    c-doc  •  js-doc

  

    frexp(x)

    Extract exponent

    c-doc  •  js-doc

  

    ldexp(x, pw2)

    Add integer to exponent

    c-doc  •  js-doc

  

    Exponential and Trigonometric

  

  

    expx2(x, sign)

    Exponential of squared argument

    c-doc  •  js-doc

  

    radian(d, m, s)

    Degrees, minutes, seconds to radians

    c-doc  •  js-doc

  

    sincos(x, flg)

    Circular sine and cosine of argument in degrees

    c-doc  •  js-doc

  

    cot(x)

    Circular cotangent

    c-doc  •  js-doc

  

    cotdg(x)

    Circular cotangent of argument in degrees

    c-doc  •  js-doc

  

    log1p(x)

    Relative error approximations for log(1 + x)

    c-doc  •  js-doc

  

    expm1(x)

    Relative error approximations for exp(x) - 1

    c-doc  •  js-doc

  

    cosm1(x)

    Relative error approximations for cos(x) - 1

    c-doc  •  js-doc

  

    acos(x)

    Arc cosine

    c-doc  •  js-doc

  

    acosh(x)

    Arc hyperbolic cosine

    c-doc  •  js-doc

  

    asinh(xx)

    Arc hyperbolic sine

    c-doc  •  js-doc

  

    atanh(x)

    Arc hyperbolic tangent

    c-doc  •  js-doc

  

    asin(x)

    Arcsine

    c-doc  •  js-doc

  

    atan(x)

    Arctangent

    c-doc  •  js-doc

  

    atan2(y, x)

    Quadrant correct arctangent

    c-doc  •  js-doc

  

    cos(x)

    Cosine

    c-doc  •  js-doc

  

    cosdg(x)

    Cosine of arg in degrees

    c-doc  •  js-doc

  

    exp(x)

    Exponential, base e

    c-doc  •  js-doc

  

    exp2(x)

    Exponential, base 2

    c-doc  •  js-doc

  

    exp10(x)

    Exponential, base 10

    c-doc  •  js-doc

  

    cosh(x)

    Hyperbolic cosine

    c-doc  •  js-doc

  

    sinh(x)

    Hyperbolic sine

    c-doc  •  js-doc

  

    tanh(x)

    Hyperbolic tangent

    c-doc  •  js-doc

  

    log(x)

    Logarithm, base e

    c-doc  •  js-doc

  

    log2(x)

    Logarithm, base 2

    c-doc  •  js-doc

  

    log10(x)

    Logarithm, base 10

    c-doc  •  js-doc

  

    pow(x, y)

    Power

    c-doc  •  js-doc

  

    powi(x, nn)

    Integer Power

    c-doc  •  js-doc

  

    sin(x)

    Sine

    c-doc  •  js-doc

  

    sindg(x)

    Sine of arg in degrees

    c-doc  •  js-doc

  

    tan(x)

    Tangent

    c-doc  •  js-doc

  

    tandg(x)

    Tangent of arg in degrees

    c-doc  •  js-doc

  

    Exponential integral

  

  

    ei(x)

    Exponential integral

    c-doc  •  js-doc

  

    expn(n, x)

    Exponential integral

    c-doc  •  js-doc

  

    shichi(x)

    Hyperbolic cosine integral

    c-doc  •  js-doc

  

    sici(x)

    Cosine integral

    c-doc  •  js-doc

  

    Gamma

  

  

    lbeta(a, b)

    Natural log of |beta|.

    c-doc  •  js-doc

  

    beta(a, b)

    Beta

    c-doc  •  js-doc

  

    fac(i)

    Factorial

    c-doc  •  js-doc

  

    gamma(x)

    Gamma

    c-doc  •  js-doc

  

    lgam(x)

    Logarithm of gamma function

    c-doc  •  js-doc

  

    incbet(aa, bb, xx)

    Incomplete beta integral

    c-doc  •  js-doc

  

    incbi(aa, bb, yy0)

    Inverse beta integral

    c-doc  •  js-doc

  

    igam(a, x)

    Incomplete gamma integral

    c-doc  •  js-doc

  

    igamc(a, x)

    Complemented gamma integral

    c-doc  •  js-doc

  

    igami(a, y0)

    Inverse gamma integral

    c-doc  •  js-doc

  

    psi(x)

    Psi (digamma) function

    c-doc  •  js-doc

  

    rgamma(x)

    Reciprocal Gamma

    c-doc  •  js-doc

  

    Error function

  

  

    erf(x)

    Error function

    c-doc  •  js-doc

  

    erfc(a)

    Complemented error function

    c-doc  •  js-doc

  

    dawsn(xx)

    Dawson's integral

    c-doc  •  js-doc

  

    fresnl(xxa)

    Fresnel integral

    c-doc  •  js-doc

  

    Bessel

  

  

    airy(x)

    Airy

    c-doc  •  js-doc

  

    j0(x)

    Bessel, order 0

    c-doc  •  js-doc

  

    j1(x)

    Bessel, order 1

    c-doc  •  js-doc

  

    jn(n, x)

    Bessel, order n

    c-doc  •  js-doc

  

    jv(n, x)

    Bessel, noninteger order

    c-doc  •  js-doc

  

    y0(x)

    Bessel, second kind, order 0

    c-doc  •  js-doc

  

    y1(x)

    Bessel, second kind, order 1

    c-doc  •  js-doc

  

    yn(n, x)

    Bessel, second kind, order n

    c-doc  •  js-doc

  

    yv(v, x)

    Bessel, noninteger order

    c-doc  •  js-doc

  

    i0(x)

    Modified Bessel, order 0

    c-doc  •  js-doc

  

    i0e(x)

    Exponentially scaled i0

    c-doc  •  js-doc

  

    i1(x)

    Modified Bessel, order 1

    c-doc  •  js-doc

  

    i1e(x)

    Exponentially scaled i1

    c-doc  •  js-doc

  

    iv(v, x)

    Modified Bessel, nonint. order

    c-doc  •  js-doc

  

    k0(x)

    Mod. Bessel, 3rd kind, order 0

    c-doc  •  js-doc

  

    k0e(x)

    Exponentially scaled k0

    c-doc  •  js-doc

  

    k1(x)

    Mod. Bessel, 3rd kind, order 1

    c-doc  •  js-doc

  

    k1e(x)

    Exponentially scaled k1

    c-doc  •  js-doc

  

    kn(nn, x)

    Mod. Bessel, 3rd kind, order n

    c-doc  •  js-doc

  

    Hypergeometric

  

  

    hyperg(a, b, x)

    Confluent hypergeometric

    c-doc  •  js-doc

  

    hyp2f1(a, b, c, x)

    Gauss hypergeometric function

    c-doc  •  js-doc

  

    Elliptic

  

  

    ellpe(x)

    Complete elliptic integral

    c-doc  •  js-doc

  

    ellie(phi, m)

    Incomplete elliptic integral

    c-doc  •  js-doc

  

    ellpk(x)

    Complete elliptic integral

    c-doc  •  js-doc

  

    ellik(phi, m)

    Incomplete elliptic integral

    c-doc  •  js-doc

  

    ellpj(u, m)

    Jacobian elliptic function

    c-doc  •  js-doc

  

    Probability

  

  

    btdtr(a, b, x)

    Beta distribution

    c-doc  •  js-doc

  

    smirnov(n, e)

    Exact Smirnov statistic, for one-sided test.

    c-doc  •  js-doc

  

    kolmogorov(y)

    Kolmogorov's limiting distribution of two-sided test.

    c-doc  •  js-doc

  

    smirnovi(n, p)

    Functional inverse of Smirnov distribution.

    c-doc  •  js-doc

  

    kolmogi(p)

    Functional inverse of Kolmogorov statistic for two-sided test.

    c-doc  •  js-doc

  

    nbdtri(k, n, p)

    Inverse Negative binomial distribution

    c-doc  •  js-doc

  

    stdtri(k, p)

    Functional inverse of Student's t distribution

    c-doc  •  js-doc

  

    bdtr(k, n, p)

    Binomial distribution

    c-doc  •  js-doc

  

    bdtrc(k, n, p)

    Complemented binomial

    c-doc  •  js-doc

  

    bdtri(k, n, y)

    Inverse binomial

    c-doc  •  js-doc

  

    chdtr(df, x)

    Chi square distribution

    c-doc  •  js-doc

  

    chdtrc(df, x)

    Complemented Chi square

    c-doc  •  js-doc

  

    chdtri(df, y)

    Inverse Chi square

    c-doc  •  js-doc

  

    fdtr(ia, ib, x)

    F distribution

    c-doc  •  js-doc

  

    fdtrc(ia, ib, x)

    Complemented F

    c-doc  •  js-doc

  

    fdtri(ia, ib, y)

    Inverse F distribution

    c-doc  •  js-doc

  

    gdtr(a, b, x)

    Gamma distribution

    c-doc  •  js-doc

  

    gdtrc(a, b, x)

    Complemented gamma

    c-doc  •  js-doc

  

    nbdtr(k, n, p)

    Negative binomial distribution

    c-doc  •  js-doc

  

    nbdtrc(k, n, p)

    Complemented negative binomial

    c-doc  •  js-doc

  

    ndtr(a)

    Normal distribution

    c-doc  •  js-doc

  

    ndtri(y0)

    Inverse normal distribution

    c-doc  •  js-doc

  

    pdtr(k, m)

    Poisson distribution

    c-doc  •  js-doc

  

    pdtrc(k, m)

    Complemented Poisson

    c-doc  •  js-doc

  

    pdtri(k, y)

    Inverse Poisson distribution

    c-doc  •  js-doc

  

    stdtr(k, t)

    Student's t distribution

    c-doc  •  js-doc

  

    Miscellaneous

  

  

    plancki(w, T)

    Integral of Planck's black body radiation formula

    c-doc  •  js-doc

  

    planckc(w, T)

    Complemented Planck radiation integral

    c-doc  •  js-doc

  

    planckd(w, T)

    Planck's black body radiation formula

    c-doc  •  js-doc

  

    planckw(T)

    Wavelength, w, of maximum radiation at given temperature T.

    c-doc  •  js-doc

  

    spence(x)

    Dilogarithm

    c-doc  •  js-doc

  

    zetac(x)

    Riemann Zeta function

    c-doc  •  js-doc

  

    zeta(x, q)

    Two argument zeta function

    c-doc  •  js-doc

  

    struve(v, x)

    Struve function

    c-doc  •  js-doc

  

    Polynomials and Power Series

  

  

    p1evl(x, coef, N)

    Evaluate polynomial when coefficient of x is 1.0.

    c-doc  •  js-doc

  

    polylog(n, x)

    The polylogarithm of order n

    c-doc  •  js-doc

## Documentation

### Arithmetic and Algebraic

#### int = cephes.signbit(x: double)

`signbit` is the "Returns the sign bit". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#signbit.

```js

const ret = cephes.signbit(x);

```

#### int = cephes.isnan(x: double)

`isnan` is the "Check if Not-A-Number". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#isnan.

```js

const ret = cephes.isnan(x);

```

#### int = cephes.isfinite(x: double)

`isfinite` is the "Check if finite". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#isfinite.

```js

const ret = cephes.isfinite(x);

```

#### double = cephes.cbrt(x: double)

`cbrt` is the "Cube root". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#cbrt.

```js

const ret = cephes.cbrt(x);

```

#### double = cephes.polevl(x: double, coef: Float64Array, N: int)

`polevl` is the "Evaluate polynomial". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#polevl.

```js

const ret = cephes.polevl(x, new Float64Array(coef), N);

```

#### double = cephes.chbevl(x: double, array: Float64Array, n: int)

`chbevl` is the "Evaluate Chebyshev series". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#chbevl.

```js

const ret = cephes.chbevl(x, new Float64Array(array), n);

```

#### double = cephes.round(x: double)

`round` is the "Round to nearest integer value". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#round.

```js

const ret = cephes.round(x);

```

#### [double, extra] = cephes.frexp(x: double)

`frexp` is the "Extract exponent". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#frexp.

```js

const [ret, extra] = cephes.frexp(x);

```

The `extra` object contains the following values: 

```js

const {

  pw2: int

} = extra;

```

#### double = cephes.ldexp(x: double, pw2: int)

`ldexp` is the "Add integer to exponent". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#ldexp.

```js

const ret = cephes.ldexp(x, pw2);

```

### Exponential and Trigonometric

#### double = cephes.expx2(x: double, sign: int)

`expx2` is the "Exponential of squared argument". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#expx2.

```js

const ret = cephes.expx2(x, sign);

```

#### double = cephes.radian(d: double, m: double, s: double)

`radian` is the "Degrees, minutes, seconds to radians". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#radian.

```js

const ret = cephes.radian(d, m, s);

```

#### [int, extra] = cephes.sincos(x: double, flg: int)

`sincos` is the "Circular sine and cosine of argument in degrees". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#sincos.

```js

const [ret, extra] = cephes.sincos(x, flg);

```

The `extra` object contains the following values: 

```js

const {

  s: double,

  c: double

} = extra;

```

#### double = cephes.cot(x: double)

`cot` is the "Circular cotangent". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#cot.

```js

const ret = cephes.cot(x);

```

#### double = cephes.cotdg(x: double)

`cotdg` is the "Circular cotangent of argument in degrees". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#cotdg.

```js

const ret = cephes.cotdg(x);

```

#### double = cephes.log1p(x: double)

`log1p` is the "Relative error approximations for log(1 + x)". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#log1p.

```js

const ret = cephes.log1p(x);

```

#### double = cephes.expm1(x: double)

`expm1` is the "Relative error approximations for exp(x) - 1". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#expm1.

```js

const ret = cephes.expm1(x);

```

#### double = cephes.cosm1(x: double)

`cosm1` is the "Relative error approximations for cos(x) - 1". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#cosm1.

```js

const ret = cephes.cosm1(x);

```

#### double = cephes.acos(x: double)

`acos` is the "Arc cosine". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#acos.

```js

const ret = cephes.acos(x);

```

#### double = cephes.acosh(x: double)

`acosh` is the "Arc hyperbolic cosine". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#acosh.

```js

const ret = cephes.acosh(x);

```

#### double = cephes.asinh(xx: double)

`asinh` is the "Arc hyperbolic sine". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#asinh.

```js

const ret = cephes.asinh(xx);

```

#### double = cephes.atanh(x: double)

`atanh` is the "Arc hyperbolic tangent". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#atanh.

```js

const ret = cephes.atanh(x);

```

#### double = cephes.asin(x: double)

`asin` is the "Arcsine". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#asin.

```js

const ret = cephes.asin(x);

```

#### double = cephes.atan(x: double)

`atan` is the "Arctangent". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#atan.

```js

const ret = cephes.atan(x);

```

#### double = cephes.atan2(y: double, x: double)

`atan2` is the "Quadrant correct arctangent". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#atan2.

```js

const ret = cephes.atan2(y, x);

```

#### double = cephes.cos(x: double)

`cos` is the "Cosine". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#cos.

```js

const ret = cephes.cos(x);

```

#### double = cephes.cosdg(x: double)

`cosdg` is the "Cosine of arg in degrees". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#cosdg.

```js

const ret = cephes.cosdg(x);

```

#### double = cephes.exp(x: double)

`exp` is the "Exponential, base e". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#exp.

```js

const ret = cephes.exp(x);

```

#### double = cephes.exp2(x: double)

`exp2` is the "Exponential, base 2". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#exp2.

```js

const ret = cephes.exp2(x);

```

#### double = cephes.exp10(x: double)

`exp10` is the "Exponential, base 10". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#exp10.

```js

const ret = cephes.exp10(x);

```

#### double = cephes.cosh(x: double)

`cosh` is the "Hyperbolic cosine". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#cosh.

```js

const ret = cephes.cosh(x);

```

#### double = cephes.sinh(x: double)

`sinh` is the "Hyperbolic sine". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#sinh.

```js

const ret = cephes.sinh(x);

```

#### double = cephes.tanh(x: double)

`tanh` is the "Hyperbolic tangent". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#tanh.

```js

const ret = cephes.tanh(x);

```

#### double = cephes.log(x: double)

`log` is the "Logarithm, base e". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#log.

```js

const ret = cephes.log(x);

```

#### double = cephes.log2(x: double)

`log2` is the "Logarithm, base 2". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#log2.

```js

const ret = cephes.log2(x);

```

#### double = cephes.log10(x: double)

`log10` is the "Logarithm, base 10". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#log10.

```js

const ret = cephes.log10(x);

```

#### double = cephes.pow(x: double, y: double)

`pow` is the "Power". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#pow.

```js

const ret = cephes.pow(x, y);

```

#### double = cephes.powi(x: double, nn: int)

`powi` is the "Integer Power". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#powi.

```js

const ret = cephes.powi(x, nn);

```

#### double = cephes.sin(x: double)

`sin` is the "Sine". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#sin.

```js

const ret = cephes.sin(x);

```

#### double = cephes.sindg(x: double)

`sindg` is the "Sine of arg in degrees". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#sindg.

```js

const ret = cephes.sindg(x);

```

#### double = cephes.tan(x: double)

`tan` is the "Tangent". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#tan.

```js

const ret = cephes.tan(x);

```

#### double = cephes.tandg(x: double)

`tandg` is the "Tangent of arg in degrees". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#tandg.

```js

const ret = cephes.tandg(x);

```

### Exponential integral

#### double = cephes.ei(x: double)

`ei` is the "Exponential integral". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#ei.

```js

const ret = cephes.ei(x);

```

#### double = cephes.expn(n: int, x: double)

`expn` is the "Exponential integral". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#expn.

```js

const ret = cephes.expn(n, x);

```

#### [int, extra] = cephes.shichi(x: double)

`shichi` is the "Hyperbolic cosine integral". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#shichi.

```js

const [ret, extra] = cephes.shichi(x);

```

The `extra` object contains the following values: 

```js

const {

  si: double,

  ci: double

} = extra;

```

#### [int, extra] = cephes.sici(x: double)

`sici` is the "Cosine integral". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#sici.

```js

const [ret, extra] = cephes.sici(x);

```

The `extra` object contains the following values: 

```js

const {

  si: double,

  ci: double

} = extra;

```

### Gamma

#### double = cephes.lbeta(a: double, b: double)

`lbeta` is the "Natural log of |beta|.". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#lbeta.

```js

const ret = cephes.lbeta(a, b);

```

#### double = cephes.beta(a: double, b: double)

`beta` is the "Beta". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#beta.

```js

const ret = cephes.beta(a, b);

```

#### double = cephes.fac(i: int)

`fac` is the "Factorial". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#fac.

```js

const ret = cephes.fac(i);

```

#### double = cephes.gamma(x: double)

`gamma` is the "Gamma". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#gamma.

```js

const ret = cephes.gamma(x);

```

#### double = cephes.lgam(x: double)

`lgam` is the "Logarithm of gamma function". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#lgam.

```js

const ret = cephes.lgam(x);

```

#### double = cephes.incbet(aa: double, bb: double, xx: double)

`incbet` is the "Incomplete beta integral". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#incbet.

```js

const ret = cephes.incbet(aa, bb, xx);

```

#### double = cephes.incbi(aa: double, bb: double, yy0: double)

`incbi` is the "Inverse beta integral". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#incbi.

```js

const ret = cephes.incbi(aa, bb, yy0);

```

#### double = cephes.igam(a: double, x: double)

`igam` is the "Incomplete gamma integral". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#igam.

```js

const ret = cephes.igam(a, x);

```

#### double = cephes.igamc(a: double, x: double)

`igamc` is the "Complemented gamma integral". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#igamc.

```js

const ret = cephes.igamc(a, x);

```

#### double = cephes.igami(a: double, y0: double)

`igami` is the "Inverse gamma integral". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#igami.

```js

const ret = cephes.igami(a, y0);

```

#### double = cephes.psi(x: double)

`psi` is the "Psi (digamma) function". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#psi.

```js

const ret = cephes.psi(x);

```

#### double = cephes.rgamma(x: double)

`rgamma` is the "Reciprocal Gamma". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#rgamma.

```js

const ret = cephes.rgamma(x);

```

### Error function

#### double = cephes.erf(x: double)

`erf` is the "Error function". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#erf.

```js

const ret = cephes.erf(x);

```

#### double = cephes.erfc(a: double)

`erfc` is the "Complemented error function". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#erfc.

```js

const ret = cephes.erfc(a);

```

#### double = cephes.dawsn(xx: double)

`dawsn` is the "Dawson's integral". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#dawsn.

```js

const ret = cephes.dawsn(xx);

```

#### [int, extra] = cephes.fresnl(xxa: double)

`fresnl` is the "Fresnel integral". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#fresnl.

```js

const [ret, extra] = cephes.fresnl(xxa);

```

The `extra` object contains the following values: 

```js

const {

  ssa: double,

  cca: double

} = extra;

```

### Bessel

#### [int, extra] = cephes.airy(x: double)

`airy` is the "Airy". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#airy.

```js

const [ret, extra] = cephes.airy(x);

```

The `extra` object contains the following values: 

```js

const {

  ai: double,

  aip: double,

  bi: double,

  bip: double

} = extra;

```

#### double = cephes.j0(x: double)

`j0` is the "Bessel, order 0". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#j0.

```js

const ret = cephes.j0(x);

```

#### double = cephes.j1(x: double)

`j1` is the "Bessel, order 1". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#j1.

```js

const ret = cephes.j1(x);

```

#### double = cephes.jn(n: int, x: double)

`jn` is the "Bessel, order n". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#jn.

```js

const ret = cephes.jn(n, x);

```

#### double = cephes.jv(n: double, x: double)

`jv` is the "Bessel, noninteger order". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#jv.

```js

const ret = cephes.jv(n, x);

```

#### double = cephes.y0(x: double)

`y0` is the "Bessel, second kind, order 0". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#y0.

```js

const ret = cephes.y0(x);

```

#### double = cephes.y1(x: double)

`y1` is the "Bessel, second kind, order 1". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#y1.

```js

const ret = cephes.y1(x);

```

#### double = cephes.yn(n: int, x: double)

`yn` is the "Bessel, second kind, order n". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#yn.

```js

const ret = cephes.yn(n, x);

```

#### double = cephes.yv(v: double, x: double)

`yv` is the "Bessel, noninteger order". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#yv.

```js

const ret = cephes.yv(v, x);

```

#### double = cephes.i0(x: double)

`i0` is the "Modified Bessel, order 0". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#i0.

```js

const ret = cephes.i0(x);

```

#### double = cephes.i0e(x: double)

`i0e` is the "Exponentially scaled i0". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#i0e.

```js

const ret = cephes.i0e(x);

```

#### double = cephes.i1(x: double)

`i1` is the "Modified Bessel, order 1". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#i1.

```js

const ret = cephes.i1(x);

```

#### double = cephes.i1e(x: double)

`i1e` is the "Exponentially scaled i1". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#i1e.

```js

const ret = cephes.i1e(x);

```

#### double = cephes.iv(v: double, x: double)

`iv` is the "Modified Bessel, nonint. order". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#iv.

```js

const ret = cephes.iv(v, x);

```

#### double = cephes.k0(x: double)

`k0` is the "Mod. Bessel, 3rd kind, order 0". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#k0.

```js

const ret = cephes.k0(x);

```

#### double = cephes.k0e(x: double)

`k0e` is the "Exponentially scaled k0". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#k0e.

```js

const ret = cephes.k0e(x);

```

#### double = cephes.k1(x: double)

`k1` is the "Mod. Bessel, 3rd kind, order 1". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#k1.

```js

const ret = cephes.k1(x);

```

#### double = cephes.k1e(x: double)

`k1e` is the "Exponentially scaled k1". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#k1e.

```js

const ret = cephes.k1e(x);

```

#### double = cephes.kn(nn: int, x: double)

`kn` is the "Mod. Bessel, 3rd kind, order n". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#kn.

```js

const ret = cephes.kn(nn, x);

```

### Hypergeometric

#### double = cephes.hyperg(a: double, b: double, x: double)

`hyperg` is the "Confluent hypergeometric". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#hyperg.

```js

const ret = cephes.hyperg(a, b, x);

```

#### double = cephes.hyp2f1(a: double, b: double, c: double, x: double)

`hyp2f1` is the "Gauss hypergeometric function". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#hyp2f1.

```js

const ret = cephes.hyp2f1(a, b, c, x);

```

### Elliptic

#### double = cephes.ellpe(x: double)

`ellpe` is the "Complete elliptic integral". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#ellpe.

```js

const ret = cephes.ellpe(x);

```

#### double = cephes.ellie(phi: double, m: double)

`ellie` is the "Incomplete elliptic integral". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#ellie.

```js

const ret = cephes.ellie(phi, m);

```

#### double = cephes.ellpk(x: double)

`ellpk` is the "Complete elliptic integral". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#ellpk.

```js

const ret = cephes.ellpk(x);

```

#### double = cephes.ellik(phi: double, m: double)

`ellik` is the "Incomplete elliptic integral". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#ellik.

```js

const ret = cephes.ellik(phi, m);

```

#### [int, extra] = cephes.ellpj(u: double, m: double)

`ellpj` is the "Jacobian elliptic function". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#ellpj.

```js

const [ret, extra] = cephes.ellpj(u, m);

```

The `extra` object contains the following values: 

```js

const {

  sn: double,

  cn: double,

  dn: double,

  ph: double

} = extra;

```

### Probability

#### double = cephes.btdtr(a: double, b: double, x: double)

`btdtr` is the "Beta distribution". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#btdtr.

```js

const ret = cephes.btdtr(a, b, x);

```

#### double = cephes.smirnov(n: int, e: double)

`smirnov` is the "Exact Smirnov statistic, for one-sided test.". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#smirnov.

```js

const ret = cephes.smirnov(n, e);

```

#### double = cephes.kolmogorov(y: double)

`kolmogorov` is the "Kolmogorov's limiting distribution of two-sided test.". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#kolmogorov.

```js

const ret = cephes.kolmogorov(y);

```

#### double = cephes.smirnovi(n: int, p: double)

`smirnovi` is the "Functional inverse of Smirnov distribution.". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#smirnovi.

```js

const ret = cephes.smirnovi(n, p);

```

#### double = cephes.kolmogi(p: double)

`kolmogi` is the "Functional inverse of Kolmogorov statistic for two-sided test.". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#kolmogi.

```js

const ret = cephes.kolmogi(p);

```

#### double = cephes.nbdtri(k: int, n: int, p: double)

`nbdtri` is the "Inverse Negative binomial distribution". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#nbdtri.

```js

const ret = cephes.nbdtri(k, n, p);

```

#### double = cephes.stdtri(k: int, p: double)

`stdtri` is the "Functional inverse of Student's t distribution". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#stdtri.

```js

const ret = cephes.stdtri(k, p);

```

#### double = cephes.bdtr(k: int, n: int, p: double)

`bdtr` is the "Binomial distribution". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#bdtr.

```js

const ret = cephes.bdtr(k, n, p);

```

#### double = cephes.bdtrc(k: int, n: int, p: double)

`bdtrc` is the "Complemented binomial". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#bdtrc.

```js

const ret = cephes.bdtrc(k, n, p);

```

#### double = cephes.bdtri(k: int, n: int, y: double)

`bdtri` is the "Inverse binomial". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#bdtri.

```js

const ret = cephes.bdtri(k, n, y);

```

#### double = cephes.chdtr(df: double, x: double)

`chdtr` is the "Chi square distribution". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#chdtr.

```js

const ret = cephes.chdtr(df, x);

```

#### double = cephes.chdtrc(df: double, x: double)

`chdtrc` is the "Complemented Chi square". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#chdtrc.

```js

const ret = cephes.chdtrc(df, x);

```

#### double = cephes.chdtri(df: double, y: double)

`chdtri` is the "Inverse Chi square". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#chdtri.

```js

const ret = cephes.chdtri(df, y);

```

#### double = cephes.fdtr(ia: int, ib: int, x: double)

`fdtr` is the "F distribution". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#fdtr.

```js

const ret = cephes.fdtr(ia, ib, x);

```

#### double = cephes.fdtrc(ia: int, ib: int, x: double)

`fdtrc` is the "Complemented F". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#fdtrc.

```js

const ret = cephes.fdtrc(ia, ib, x);

```

#### double = cephes.fdtri(ia: int, ib: int, y: double)

`fdtri` is the "Inverse F distribution". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#fdtri.

```js

const ret = cephes.fdtri(ia, ib, y);

```

#### double = cephes.gdtr(a: double, b: double, x: double)

`gdtr` is the "Gamma distribution". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#gdtr.

```js

const ret = cephes.gdtr(a, b, x);

```

#### double = cephes.gdtrc(a: double, b: double, x: double)

`gdtrc` is the "Complemented gamma". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#gdtrc.

```js

const ret = cephes.gdtrc(a, b, x);

```

#### double = cephes.nbdtr(k: int, n: int, p: double)

`nbdtr` is the "Negative binomial distribution". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#nbdtr.

```js

const ret = cephes.nbdtr(k, n, p);

```

#### double = cephes.nbdtrc(k: int, n: int, p: double)

`nbdtrc` is the "Complemented negative binomial". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#nbdtrc.

```js

const ret = cephes.nbdtrc(k, n, p);

```

#### double = cephes.ndtr(a: double)

`ndtr` is the "Normal distribution". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#ndtr.

```js

const ret = cephes.ndtr(a);

```

#### double = cephes.ndtri(y0: double)

`ndtri` is the "Inverse normal distribution". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#ndtri.

```js

const ret = cephes.ndtri(y0);

```

#### double = cephes.pdtr(k: int, m: double)

`pdtr` is the "Poisson distribution". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#pdtr.

```js

const ret = cephes.pdtr(k, m);

```

#### double = cephes.pdtrc(k: int, m: double)

`pdtrc` is the "Complemented Poisson". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#pdtrc.

```js

const ret = cephes.pdtrc(k, m);

```

#### double = cephes.pdtri(k: int, y: double)

`pdtri` is the "Inverse Poisson distribution". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#pdtri.

```js

const ret = cephes.pdtri(k, y);

```

#### double = cephes.stdtr(k: int, t: double)

`stdtr` is the "Student's t distribution". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#stdtr.

```js

const ret = cephes.stdtr(k, t);

```

### Miscellaneous

#### double = cephes.plancki(w: double, T: double)

`plancki` is the "Integral of Planck's black body radiation formula". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#plancki.

```js

const ret = cephes.plancki(w, T);

```

#### double = cephes.planckc(w: double, T: double)

`planckc` is the "Complemented Planck radiation integral". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#planckc.

```js

const ret = cephes.planckc(w, T);

```

#### double = cephes.planckd(w: double, T: double)

`planckd` is the "Planck's black body radiation formula". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#planckd.

```js

const ret = cephes.planckd(w, T);

```

#### double = cephes.planckw(T: double)

`planckw` is the "Wavelength, w, of maximum radiation at given temperature T.". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#planckw.

```js

const ret = cephes.planckw(T);

```

#### double = cephes.spence(x: double)

`spence` is the "Dilogarithm". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#spence.

```js

const ret = cephes.spence(x);

```

#### double = cephes.zetac(x: double)

`zetac` is the "Riemann Zeta function". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#zetac.

```js

const ret = cephes.zetac(x);

```

#### double = cephes.zeta(x: double, q: double)

`zeta` is the "Two argument zeta function". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#zeta.

```js

const ret = cephes.zeta(x, q);

```

#### double = cephes.struve(v: double, x: double)

`struve` is the "Struve function". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#struve.

```js

const ret = cephes.struve(v, x);

```

### Polynomials and Power Series

#### double = cephes.p1evl(x: double, coef: Float64Array, N: int)

`p1evl` is the "Evaluate polynomial when coefficient of x is 1.0.". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#p1evl.

```js

const ret = cephes.p1evl(x, new Float64Array(coef), N);

```

#### double = cephes.polylog(n: int, x: double)

`polylog` is the "The polylogarithm of order n". You can read the full documentation at http://www.netlib.org/cephes/doubldoc.html#polylog.

```js

const ret = cephes.polylog(n, x);

```

## LICENSE

The cephes library, that this module wraps, can be found at

http://www.netlib.org/cephes/. The cephes library from the NetLib website,

doesn't have any license. However, the author Stephen Moshier, has kindly given

permission for it to be included in a BSD-licensed package.

Please see the [LICENSE](LICENSE) file, for all the details.