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October 16, 2016 20:54
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Client-side complex numbers in JavaScript
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/* | |
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, 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]; | |
} | |
// Create a complex number from a real number | |
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, 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(0.5)); | |
} | |
complex.sinh = function (a) | |
{ | |
return complex.mult([0.5, 0], complex.sub(complex.exp(a), complex.exp(complex.neg(a)))); | |
} | |
complex.cosh = function (a) | |
{ | |
return complex.mult([0.5, 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) | |
{ | |
// complex.rpn :: String -> (Complex -> Complex) | |
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(); | |
}; | |
} |
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