Big Numbers

For calculations with an arbitrary precision, math.js supports BigNumber. BigNumber is powered by the the library bignumber.js.

A big number can be created using the function bignumber:

math.bignumber('2.3e+500'); // BigNumber, 2.3e+500

Most functions can determine the type of output from the type of input: a number as input will return a number as output, a bignumber as input returns a bignumber as output. Functions which cannot determine the type of output from the input (for example math.eval) use the default number type number, which can be configured when instantiating math.js. To configure the use of big numbers instead of numbers by default, configure math.js like:

var mathjs = require('mathjs'),
    math = mathjs({
      number: 'bignumber', // Default type of number: 'number' (default) or 'bignumber'
      decimals: 20         // Number decimal places behind the dot for big numbers
    });

// use math
math.eval('0.1 + 0.2'); // BigNumber, 0.3

Important: BigNumber is not supported by the following functions: exp, gcd, lcm, log, log10, xgcd, arg, random, acos, asin, atan, atan2, cos, cot, csc, sec, sin, tan. These functions will downgrade BigNumber to Number, and return a Number.

Calculations with BigNumber are much slower than calculations with Number, but they can be executed with an arbitrary precision. By using a higher precision, it is less likely that round-off errors occur:

// round-off errors with numbers
math.add(0.1, 0.2);                                     // Number, 0.30000000000000004
math.divide(0.3, 0.2);                                  // Number, 1.4999999999999998

// no round-off errors with big numbers :)
math.add(math.bignumber(0.1), math.bignumber(0.2));     // BigNumber, 0.3
math.divide(math.bignumber(0.3), math.bignumber(0.2));  // BigNumber, 1.5

The default precision for BigNumber is 20 digits. This is a global setting in the underlying BigNumber library, which can be changed by configuring BigNumber:

BigNumber.config({DECIMAL_PLACES: 32});

Important: To work with small numbers, DECIMAL_PLACES must be configured sufficiently large.

Big numbers can be converted to numbers and vice versa using the functions number and bignumber. When converting a big number to a number, the high precision of the will be lost. When a BigNumber is too large to be represented as Number, it will be initialized as Infinity.

// converting numbers and bignumbers
var a = math.number(0.3);                         // Number, 0.3
var b = math.bignumber(a);                        // BigNumber, 0.3
var c = math.number(b);                           // Number, 0.3

// exceeding the maximum of a number
var d = math.bignumber('1.2e500');                // BigNumber, 1.2e+500
var e = math.number(d);                           // Number, Infinity

// loosing precision when converting to number
var f = math.bignumber('0.2222222222222222222');  // BigNumber, 0.2222222222222222222
var g = math.number(f);                           // Number,    0.2222222222222222

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Big Numbers

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