subtract exponents in JavaScript

Question

Out of interest and not real life demands: Is it somehow possible to subtract exponents of two numbers in JavaScript? Because the result of 1e+29 * 1e-3 (or 1e+29 / 1e+3) is the unprecise number 9.999999999999999e+25 even though the correct result 1e+26 can be expressed in JavaScript.

You might find this question interesting: http://stackoverflow.com/questions/9383593/extracting-the-exponent-and-mantissa-of-a-javascript-number — Abraham P, Feb 23 '13 at 00:38

score 0 · Answer 1 · answered Feb 23 '13 at 01:06

There must be cleaner ways of doing it, but one option would be to convert your number to a string, operate on it, and then convert it back to a number:

function exp_add(num,exp) {
    var split = num.toExponential().split('e');
    var exponent = parseInt(split[1],10);
    exponent += exp;
    return parseFloat(split[0] + "e" + exponent);
}

Working example at jsFiddle.

score 0 · Answer 2 · answered Feb 23 '13 at 01:13

You could use Math.log(1e29)/Math.LN10, however that yields 28.999999999999993. Base 2 is just inexact for these numbers. So our last resort is Number.prototype.toString, which correctly yields "1e29". How can we use that now?

function toExp(num) {
    return num.toExponential().split("e").map(Number);
    // num.toString() only works for num <= 1e-6 and num >= 1e21
}
function fromExp(exp) {
    return exp[0] * Math.pow(10, exp[1]);
// or:     parseFloat(exp[0]+"e"+exp[1]);
}

function expMultiply(a, b) {
    return [ a[0]*b[0], a[1]+b[1] ];
}
function expDivide(a, b) {
    return [ a[0]/b[0], a[1]-b[1] ];
}

> fromExp(expMultiply(toExp(1e29), toExp(1e-3)))
1e+26
> fromExp(expDivide(toExp(1e29), toExp(1e3)))
1e+26

score 0 · Answer 3 · answered Feb 23 '13 at 01:16

You will naturally see this as a result of floating point division, especially when one number is much smaller than the other. But, if the numbers have the same base, maybe you should just store their exponents. Otherwise, you can use the logarithm:

( Math.log(1e29) + Math.log(1e-3) ) / Math.LN10
> 25.999999999999993

You may want to just round that result to a few decimal places to take care of the inaccuracy and obtain the result in base 10.

subtract exponents in JavaScript

3 Answers3