node-cephes
This is a WebAssembly packaging of the cephes library. The cephes library contains C implementations of most special functions, distributions, 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 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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
const [ret, extra] = cephes.frexp(x);
The extra
object contains the following values:
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.
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.
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.
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.
const [ret, extra] = cephes.sincos(x, flg);
The extra
object contains the following values:
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
const [ret, extra] = cephes.shichi(x);
The extra
object contains the following values:
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.
const [ret, extra] = cephes.sici(x);
The extra
object contains the following values:
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
const [ret, extra] = cephes.fresnl(xxa);
The extra
object contains the following values:
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.
const [ret, extra] = cephes.airy(x);
The extra
object contains the following values:
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
const [ret, extra] = cephes.ellpj(u, m);
The extra
object contains the following values:
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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 file, for all the details.