Client side complex numbers in JavaScript.

complex.min.js

/*
    complex.js
        Client-side complex numbers in JavaScript
    Licensed under the GNU General Public License (https://pommicket.github.io/LICENSE.txt)
*/
var complex={};complex.i=[0,1];complex.logi=[0,.682188177];complex.PI=[Math.PI,0];complex.E=[Math.E,0];complex.lnAccuracy=20;complex.re=function(a){return a[0]};complex.im=function(a){return a[1]};complex.reToC=function(a){return[a,0]};complex.reC=function(a){return complex.reToC(complex.re(a))};complex.imC=function(a){return complex.reToC(complex.im(a))};complex.show=function(a){var im=complex.im(a);var re=complex.re(a);if(im==1&&re==0)return"i";if(im==0)return re.toString();if(im==1)return re+" + i";if(re==0)return im+"i";return re+" + "+im+"i"};complex.add=function(a,b){return[complex.re(a)+complex.re(b),complex.im(a)+complex.im(b)]};complex.neg=function(a){return[-complex.re(a),-complex.im(a)]};complex.sub=function(a,b){return complex.add(a,complex.neg(b))};complex.mult=function(a,b){var a_Re,a_Im,b_Re,b_Im;a_Re=complex.re(a);a_Im=complex.im(a);b_Re=complex.re(b);b_Im=complex.im(b);return[a_Re*b_Re-a_Im*b_Im,a_Re*b_Im+a_Im*b_Re]};complex.recip=function(a){var re=complex.re(a);var im=complex.im(a);var divBy=re*re+im*im;return[re/divBy,-im/divBy]};complex.div=function(a,b){return complex.mult(a,complex.recip(b))};complex.exp=function(a){var re=complex.re(a);var im=complex.im(a);var expRe=Math.exp(re);return[expRe*Math.cos(im),expRe*Math.sin(im)]};complex.theta=function(a){return Math.atan(complex.im(a)/complex.re(a))};complex.abs=function(a){var re=complex.re(a);var im=complex.im(a);return Math.sqrt(re*re+im*im)};complex.polar=function(a){return[complex.abs(a),complex.theta(a)]};complex.arg=function(a){var x=complex.re(a);var y=complex.im(a);var theta=complex.theta(a);if(x>0)return theta;if(x<0&&y>=0)return theta+Math.PI;if(x<0&&y<0)return theta-Math.PI;if(x==0&&y>0)return Math.PI/2;if(x==0&&y<0)return-Math.PI/2;return 1/0};complex.ln=function(a){return[Math.log(complex.abs(a)),complex.arg(a)]};complex.log=function(base,a){return complex.div(complex.ln(a),complex.ln(base))};complex.pow=function(a,b){return complex.exp(complex.mult(b,complex.ln(a)))};complex.sin=function(a){var ia=complex.mult(complex.i,a);return complex.mult([0,.5],complex.sub(complex.exp(complex.neg(ia)),complex.exp(ia)))};complex.cos=function(a){return complex.sin(complex.sub(complex.reToC(Math.PI/2),a))};complex.tan=function(a){return complex.div(complex.sin(a),complex.cos(a))};complex.sqrt=function(a){return complex.pow(a,complex.reToC(.5))};complex.sinh=function(a){return complex.mult([.5,0],complex.sub(complex.exp(a),complex.exp(complex.neg(a))))};complex.cosh=function(a){return complex.mult([.5,0],complex.add(complex.exp(a),complex.exp(complex.neg(a))))};complex.tanh=function(a){return complex.div(complex.sinh(a),complex.cosh(a))};complex.rpn=function(s){var tokens=s.split(" ");return function(x){var token;var stack=[];for(var i=0;i<tokens.length;i++){token=tokens[i];switch(token){case"":break;case"+":stack.push(complex.add(stack.pop(),stack.pop()));break;case"*":stack.push(complex.mult(stack.pop(),stack.pop()));break;case"-":var val2=stack.pop();var val1=stack.pop();stack.push(complex.sub(val1,val2));break;case"/":var val2=stack.pop();var val1=stack.pop();stack.push(complex.div(val1,val2));break;case"^":var val2=stack.pop();var val1=stack.pop();stack.push(complex.pow(val1,val2));break;case"log":var val2=stack.pop();var val1=stack.pop();stack.push(complex.log(val1,val2));break;case"sqrt":stack.push(complex.sqrt(stack.pop()));break;case"ln":stack.push(complex.ln(stack.pop()));break;case"exp":stack.push(complex.exp(stack.pop()));break;case"sin":stack.push(complex.sin(stack.pop()));break;case"cos":stack.push(complex.cos(stack.pop()));break;case"tan":stack.push(complex.tan(stack.pop()));break;case"sinh":stack.push(complex.sinh(stack.pop()));break;case"cosh":stack.push(complex.cosh(stack.pop()));break;case"tanh":stack.push(complex.tanh(stack.pop()));break;case"re":stack.push(complex.reC(stack.pop()));break;case"im":stack.push(complex.imC(stack.pop()));break;case"abs":stack.push(complex.reToC(complex.abs(stack.pop())));break;case"x":stack.push(x);break;case"i":stack.push(complex.i);break;case"-i":stack.push(complex.neg(complex.i));break;case"e":stack.push(complex.E);break;case"pi":stack.push(complex.PI);break;case"r":stack.push(complex.reToC(complex.abs(stack.pop())));break;case"theta":stack.push(complex.reToC(complex.theta(stack.pop())));break;default:if(token[token.length-1]=="i"){stack.push([0,parseFloat(token.substring(0,token.length-1))])}else{stack.push(complex.reToC(parseFloat(token)))}}}return stack.pop()}};