JavaScript Notes: Precision Woes

The problem is "a lack of precision"

While JavaScript is quickly becoming the lingua franca of the web, this general purpose language contains built-in limitations which restrict its use to simple applications. For example, I recently (2012) attempted to write a Diffie-Hellman Key-Exchange Demo in JavaScript but detected problems during testing which I traced to a lack of mathematical precision. Check out these comparisons:

JavaScript	Math.pow(7,18)	1,628,413,597,910,449	correct
Calculator	7^18	1,628,413,597,910,449	correct
JavaScript	Math.pow(7,19)	11,398,895,185,373,144	incorrect
Calculator	7^19	11,398,895,185,373,143	correct
JavaScript	Math.pow(7,20)	79,792,266,297,612,000	incorrect
Calculator	7^20	79,792,266,297,612,001	correct
JavaScript	Math.pow(7,21)	558,545,864,083,284,030	incorrect
Calculator	7^21	558,545,864,083,284,007	correct

• Many junior programmers think this problem is related to internal rounding but it is actually a limitation due to float-point math.
• Many seasoned programmers are surprised to learn that all JavaScript numbers (floating point or not) are stored in 64-bit floating point format (similar to JAVA's double) and there are no official alternative data types. Without an official integer data type, divisions may produce a fractional result.
• The only way to fix this in your JavaScript programs is to engage an external library
• References:
  • http://www.crockford.com/javascript/survey.html
  • http://www.hunlock.com/blogs/The_Complete_Javascript_Number_Reference
• JavaScript workarounds:
  • https://github.com/iriscouch/bigdecimal.js (Big Decimal)
  • https://github.com/silentmatt/javascript-biginteger/ (Big Integer)
  • http://www-cs-students.stanford.edu/~tjw/jsbn/ (Big Number)
• Other workarounds:
  • for client side software, switch to JAVA (you will still need to get a library capable of processing very large integers)
  • for server side software:
    • switch to PERL (see:  below)
    • switch to Python (see: my solution on another page)

PERL Workaround

Legend:	<sr> = system response
	<ur> = user response

<sr>	$
<ur>	type bigint_demo.pl
	#
	#       title: bigint_demo.pl
	#
	use bigint;             # use bigint after this point
	$x = 7 ** 19;           # x = 7^19
	printf("%s\n",$x);      # "%s" because other formats bomb
<sr>	$
<ur>	perl bigint_demo.pl
<sr>	11398895185373143	! correct
<ur>	$

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Neil Rieck
Waterloo, Ontario, Canada.