Javascript Float Rounding Error
Contents |
here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site About Us Learn more about Stack Overflow the company Business Learn more javascript floating point error example about hiring developers or posting ads with us Stack Overflow Questions Jobs Documentation Tags Users
Javascript Decimal Data Type
Badges Ask Question x Dismiss Join the Stack Overflow Community Stack Overflow is a community of 4.7 million programmers, just like you, helping javascript toprecision each other. Join them; it only takes a minute: Sign up Avoiding problems with JavaScript's weird decimal calculations up vote 9 down vote favorite 2 I just read on MDN that one of the quirks of JS's handling
Javascript Decimal Precision
of numbers due to everything being "double-precision 64-bit format IEEE 754 values" is that when you do something like .2 + .1 you get 0.30000000000000004 (that's what the article reads, but I get 0.29999999999999993 in Firefox). Therefore: (.2 + .1) * 10 == 3 evaluates to false. This seems like it would be very problematic. So what can be done to avoid bugs due to the imprecise decimal calculations in JS? I've noticed that if you do javascript integer precision 1.2 + 1.1 you get the right answer. So should you just avoid any kind of math that involves values less than 1? Because that seems very impractical. Are there any other dangers to doing math in JS? Edit: I understand that many decimal fractions can't be stored as binary, but the way most other languages I've encountered appear to deal with the error (like JS handles numbers greater than 1) seems more intuitive, so I'm not used to this, which is why I want to see how other programmers deal with these calculations. javascript math decimal share|improve this question edited Feb 18 '11 at 5:39 asked Feb 18 '11 at 5:06 Lèse majesté 5,70512134 3 Floating point numbers almost never perfectly compare to other numbers, in any language. –deceze Feb 18 '11 at 5:08 Rounding is your friend. –mellamokb Feb 18 '11 at 5:08 @mellamokb: So you would have to multiply everything by a power of 10 and then round to the nearest integer? –Lèse majesté Feb 18 '11 at 5:22 @deceze: PHP, MySQL, Perl, VB, and most languages I've used in the past have never had any problem with these types of calculations. –Lèse majesté Feb 18 '11 at 5:24 2 @Lèse $ php -r 'var_dump((0.1 + 0.2) * 10 == 3);' → bool(false) :) –deceze Feb
Know About Floating Points What Every JavaScript Developer Should Know About Floating Points By Xuanyi Chew At some point in a JavaScript developer's career, she will come across strange bugs - basic mathematics that
Floating Point Rounding Error
do not seem to make sense. And at some point or another, she will
Javascript Int To Float
be told that numbers in JavaScript are actually floating points. Any attempts to understand floating points or why they act floating point arithmetic so strangely will eventually lead to a long and a difficult-to-read article. The goal of this article is to make floating points simple for JavaScript developers. This article assumes the reader is familiar with http://stackoverflow.com/questions/5037839/avoiding-problems-with-javascripts-weird-decimal-calculations base-2 (binary) representations of base-10 (decimal) numbers (i.e. 1 is written as 1b, 2 is 10b, 3 is 11b, 4 is 100b… etc). To even further clarify things, in this article, the word “decimal” mostly refers to the decimal representation of numbers (for example: 2.718) in the machine. The word “binary” in this article refers to a machine representation. Written representations will be referred to as “base-10″ and “base-2″ respectively. https://modernweb.com/2014/02/17/what-every-javascript-developer-should-know-about-floating-points/ Floating Points To figure out what a floating point is, we first start with the idea that there are many kinds of numbers, which we will go through. We call 1 an integer - it is a whole number with no fractional values in it. ½ is what's called a fraction. It implies that the whole number 1 is being divided into 2. The concept of fractions is a very important one in deriving floating points. 0.5 is commonly known as a decimal number. However, a very important distinction needs to be made - 0.5 is actually the decimal (base-10) representation of the fraction ½. This is how ½ is represented when written as a base-10 number - for this article, we will call it the dot notation. We call 0.5 a finite representation because the numbers in the representation for the fraction are finite - there are no more numbers after 5 in 0.5. An infinite representation would for example be 0.3333... when representing ⅓. Again, this idea will be important later on in our discussion. There exists another way of representing numbers other than as whole numbers, fractions or decimal notations. You might have actually seen it before. It looks som
by David Goldberg, published in the March, 1991 issue of Computing Surveys. Copyright 1991, Association for Computing Machinery, Inc., reprinted by permission. Abstract https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html Floating-point arithmetic is considered an esoteric subject by many people. This http://www.jacklmoore.com/notes/rounding-in-javascript/ is rather surprising because floating-point is ubiquitous in computer systems. Almost every language has a floating-point datatype; computers from PCs to supercomputers have floating-point accelerators; most compilers will be called upon to compile floating-point algorithms from time to time; and virtually every operating system must floating point respond to floating-point exceptions such as overflow. This paper presents a tutorial on those aspects of floating-point that have a direct impact on designers of computer systems. It begins with background on floating-point representation and rounding error, continues with a discussion of the IEEE floating-point standard, and concludes with numerous examples of how computer builders can better javascript float rounding support floating-point. Categories and Subject Descriptors: (Primary) C.0 [Computer Systems Organization]: General -- instruction set design; D.3.4 [Programming Languages]: Processors -- compilers, optimization; G.1.0 [Numerical Analysis]: General -- computer arithmetic, error analysis, numerical algorithms (Secondary) D.2.1 [Software Engineering]: Requirements/Specifications -- languages; D.3.4 Programming Languages]: Formal Definitions and Theory -- semantics; D.4.1 Operating Systems]: Process Management -- synchronization. General Terms: Algorithms, Design, Languages Additional Key Words and Phrases: Denormalized number, exception, floating-point, floating-point standard, gradual underflow, guard digit, NaN, overflow, relative error, rounding error, rounding mode, ulp, underflow. Introduction Builders of computer systems often need information about floating-point arithmetic. There are, however, remarkably few sources of detailed information about it. One of the few books on the subject, Floating-Point Computation by Pat Sterbenz, is long out of print. This paper is a tutorial on those aspects of floating-point arithmetic (floating-point hereafter) that have a direct connection to systems building. It consists of three loosely connected parts. The first section, Rounding Error, discusses the implications of using different roundi
decimal places, then we have to handle that ourselves. This post doesn't get into the details of floating-point arithmetic, but the short of it is most programming languages use a binary floating-point representation which can only approximate many decimal fractions. This results in rounding errors for the most common approaches to rounding in JavaScript. Rounding Errors The most common solutions for rounding to a decimal place is to either use Number.prototype.toFixed(), or multiply the float by some power of 10 in order to leverage Math.round(). Both of these work, except sometimes a decimal of 5 is rounded down instead of up. Number((1.005).toFixed(2)); // 1 instead of 1.01 Math.round(1.005*100)/100; // 1 instead of 1.01 A Better Solution The rounding problem can be avoided by using numbers represented in exponential notation: Number(Math.round(1.005+'e2')+'e-2'); // 1.01 And to abstract that into something more usable: function round(value, decimals) { return Number(Math.round(value+'e'+decimals)+'e-'+decimals); } round(1.005, 2); // 1.01 Hey,Follow me on Twitter and Github, that's where I'm most active these days. I welcome email (), but I'm afraid I no longer have time to answer personal r