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README.md
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 Algebraicsignbit(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.
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