Javascript Libraries for Numerical computation

Below is a list of powerful JavaScript libraries for numerical calculation. These libraries work on top of the build in Math, Array and String function generally available in any browser. Furthermore, it automatically accepts some of the JavaScript extension and only provide a function if this is not available in the current browser version. There is several different libraries available.

The first library is a library for Complex arithmetic that runs on top of the Math library. It also extend the basic Math libraries with Hyperbolic functions as well as Gamma and Beta functions if not available in the current browser.
The second library extend the build in floating point arithmetic with arbitrary precisions functions.
The third library extend complex arithmetic to also work on Arbitrary precision numbers.
The fourth library is a Polynomial class library that works on polynomial arithmetic and zeros for polynomials.
The fifth library is a library for fraction arithmetic. It supports both regular Javascript Numbers, but also the new type BigInt.

Complex - Javascript library
JavaScript Complex Class Library contains several methods to handle complex arithmetic and complex functions.

Complex arithmetic: +,-,*,/,conj(),real(),imag(),
Complex functions: arg(),norm(),polar(),negate(),abs(),log(),log10(),exp(),pow(),sqrt()
Complex comparison: equal(),notequal()
Complex trigonometric: sin(),cos(),tan(),asin(),acos(),atan(),atan2()
Complex hyperbolic: sinh(),cosh(),tanh(),asinh(),acosh(),atanh()
Complex special function: gamma(), lgamma(), beta()
Other functions: toString(), toExponential(), toFixed(), toPrecision(), valueOf(), parseComplex()

Download Library ver 1.14
Download User Manual...

Example: Evaluate a polynomial at a complex point z. this.c[] contains the coefficients of the polynomial

//Evaluate f(z). z can be a complex number or real number.
//Polynomial can be either with complex or real coefficients
Polynomial.prototype.value=function(z)
{ var i, fz;
// Polynomial evaluation Real point Complex point
// Real coefficients Real Complex
// Complex coefficients Complex Complex
if(this.isReal()) // Evaluate f(z). Horner. Real coefficients only
{
if(z instanceof Complex)
{// Real coefficients and complex z
var p,q,s,r,t;
p=-2.0*z.real(); q=z.norm(); s=0; r=this.c[0];
for(i=1;i<this.c.length-1;i++) { t=this.c[i]-p*r-q*s; s=r; r=t; }
fz=new Complex(this.c[this.c.length-1]+z.real()*r-q*s, z.imag()*r);
return fz; // Return Complex
}
else
{// Real coefficients and real z
fz=this.c[0];
for(i=1;i<this.c.length;i++) fz=fz*z+this.c[i];
return fz; // Return real;
}
}
else // Evaluate a polynomial complex coefficients, at a real or complex number z using Horner,
// return complex function value
{var zz;
fz=Complex(this.c[0]); zz=Complex(z);
for(i=1;i<this.c.length;i++) {fz=Complex.add(Complex.mul(fz,zz),Complex(this.c[i]));}
return fz; // return Complex
}
}

October
2018
New Tool

BigFloat - Arbitrary precision Javascript library
JavaScript BigFloat Class Library. This arbitrary precision library is a full implementation of arbitrary precision library that contains all relevant functions available with arbitrary precision. Compare to other libraries like bigfloat (Smaller case), or BigNumber this libraries contains more than just the arithmetic operators, abs() and sqrt(). Furthermore, the number of decimal precisions can be controlled per BigFloat variable and not just a global constant setting. This mean you can mix freely variable with different decimal precisions and round mode. Making it ideal for a BigFloat interval class to be available later. Also the BigFloat constant PI, LN2, LN10 or E is available in arbitrary precision.

BigFloat arithmetic: add(),sub(),mul(),div(),minus(),floor(),ceil()
BigFloat functions: abs(),log(),log10(),exp(),pow(),sqrt()
BigFloat comparison: equal(), notequal(), less(), lessequal(), greater(), greatereual()
BigFloat trigonometric: sin(),cos(),tan(),asin(),acos(),atan(),atan2()
BigFloat hyperbolic: sinh(),cosh(),tanh(),asinh(),acosh(),atanh()
BigFloat Special function: gamma(), lgamma(), beta(), erf()
BigFloat constant: PI(),LN2(),LN10(),E()

Download Library ver 1.26
Download User Manual...

Example:

function PolynomialBigFloat(coeff,x)
// coeff is an BigFloat Array of polynomial coefficients,
// x is a BigFloat number of the real point for evaluation
{var i,fz;
fz=new BigFloat(oeff[0],x.precision()); // Do the evaluation using the same precision as x
for(i=1;i < coeff.length; i++)
fz.assign(BigFloat.add(BigFloat.mul(fz,x),coeff[i]));
return fz; // Return real;
}

There is also a small web tool where you can see how different multiplication algorithm works for arbitrary precision using this Javascript library. It support a number of different methods, see below:

Karatsuba (2 way splitting).
Toom-cook3 (3 way splitting).
Schönhage-Strassen with Linear convolution.
Fast Fourier Multiplication.
School Book multiplication.

Click Here for the multiplication calculator

Revised
October
2019
New Tool

ComplexBigFloat - Complex Arbitrary precision Javascript library
JavaScript Complex Class Library for arbitrary precision math (BigFloat library) contains several methods to handle complex arithmetic and complex functions. Similar to the Complex library using the build in floating point type

Complex arithmetic: +,-,*,/,conj(),real(),imag(),
Complex functions: arg(),norm(),polar(),negate(),abs(),log(),log10(),exp(),pow(),sqrt()
Complex comparison: equal(),notequal()
Complex trigonometric: sin(),cos(),tan(),asin(),acos(),atan(),atan2()
Complex hyperbolic: sinh(),cosh(),tanh(),asinh(),acosh(),atanh()
Complex special function: gamma(), lgamma(), beta()
Other functions: toString(), toExponential(), toFixed(), toPrecision()

Download Library ver 1.01
Download User Manual...

December
2019
New Tool

Polynomial Arithmetic - Polynomial Arithmetic Javascript library
JavaScript Polynomial Class Library for Polynomial Arithmetic.

Polynomial arithmetic: +,-,*,/,rem
Polynomial functions: deflate(),compositedeflate(),derivative(),value(),pow(),zeros()
Polynomial other functions: array(),join(), degree(),getcoeff(),setcoeff(),isComplex(),isReal(),normalize(),scale(),shift(),simplify(),monic()
Other functions: toString(), toExponential(), toFixed(), toPrecision()

Download Library ver 1.26
Download User Manual...

Example:

// Find the zeros and reconstruct the error polynomial from the zeros
var pp=new Polynomial(),i,px,solutions;
pp=parsePolynomial("x^3-2x+1");
solution=pp.zeros();
for(i=pp.degree();i>0;i--)
{
var px=new Polynomial(1,solutions[i].negate());
if(i==pp.degree()) pp.px=px; else pp.px=Polynomial.mul(pp.px,px);
}

February
2020
New Tool

Fraction Arihtmetic - Fraction Arithmetic Javascript library
JavaScript Fraction Class Library for Fraction Arithmetic.

Fraction arithmetic: +,-,*,/,
Fraction functions: ,abs(),gcd(),typeof(),whole(),reduce(),negate(),inverse()
Fraction comparison: equal(),notequal(),greater(),greaterequal(),less(),lessequal()
Other functions: toString(), toExponential(), toFixed(), toPrecision(), parseFraction()

Download Library ver 1.0
Download User Manual...

Example:

// Example of using continuous fraction for finding π.
function pi(i) // i is the number of iterations
{var cf=Fraction(0);
for(;i>0;--i)
{cf=Fraction.add(cf,Fraction(i*2+1));
cf=Fraction.div(Fraction(i*i),cf);}
return Fraction.div(Fraction(4),Fraction.add(cf,Fraction(1)));}
var cf=pit(10);

February
2020
New Tool

Interval Arihtmetic - Interval Arithmetic Javascript library
JavaScript Interval Class Library for Interval Arithmetic.

Interval arithmetic: +,-,*,/,
Interval functions: ,abs(),log(),log10(),exp(),pow(),sqrt()
Interval comparison: equal(),notequal(),less(),lessequal(),greater(),greaterequal()
Interval trigonometric: sin(),cos(),tan(),asin(),acos(),atan(),atan2()
Interval hyperbolic: sinh(),cosh(),tanh(),asinh(),acosh(),atanh()
Interval logical: interior(),precedes(),intersection(),union(),subset()
Other functions: toString(), toExponential(), toFixed(), toPrecision(),parseInterval(),center(),width(),isEmpty(),in()

Download Library ver 1.10
Download User Manual...

Example:

// Example of using interval arithmetic to calculate the result of exp(x).
{var low,high,t;
function intervalexp(x)
{var i,k,sign=1,isum,ix,ixp,ifac,idelta;
if(x<0) {x=-x; sign=-1;}
// Argument reduction
for(k=0;x>0.5 &&k<=16;++k) x*=0.5;
ix=Interval(x); ixp=Interval(1); isum=Interval(1); ifac=Interval(1);
for(i=1;;++i)
{
ifac=Interval.mul(ifac,Interval(i));
ixp=Interval.mul(ixp,ix);
idelta=Interval.div(ixp,ifac);
if(isum.center()+idelta.center()==isum.center()) break;
isum=Interval.add(isum,idelta);
}
// Reverse reduction
for(;k>0;--k) isum=Interval.mul(isum,isum);
if(sign<0) {isum=Interval.div(Interval(1),isum);}
return isum;
}
alert(intervalexp(1.5).toString());

June
2021