Floating Point Math

Your language isn't broken, it's doing floating point math. Computers can only natively store integers, so they need some way of representing decimal numbers. This representation comes with some degree of inaccuracy. That's why, more often than not, .1 + .2 != .3.

Why does this happen?

It's actually pretty simple. When you have a base 10 system (like ours), it can only express fractions that use a prime factor of the base. The prime factors of 10 are 2 and 5. So 1/2, 1/4, 1/5, 1/8, and 1/10 can all be expressed cleanly because the denominators all use prime factors of 10. In contrast, 1/3, 1/6, and 1/7 are all repeating decimals because their denominators use a prime factor of 3 or 7. In binary (or base 2), the only prime factor is 2. So you can only express fractions cleanly which only contain 2 as a prime factor. In binary, 1/2, 1/4, 1/8 would all be expressed cleanly as decimals. While, 1/5 or 1/10 would be repeating decimals. So 0.1 and 0.2 (1/10 and 1/5) while clean decimals in a base 10 system, are repeating decimals in the base 2 system the computer is operating in. When you do math on these repeating decimals, you end up with leftovers which carry over when you convert the computer's base 2 (binary) number into a more human readable base 10 number.

Below are some examples of sending .1 + .2 to standard output in a variety of languages.

read more: | wikipedia | IEEE 754 | Stack Overflow | What Every Computer Scientist Should Know About Floating-Point Arithmetic

Language Code Result
ABAP 
WRITE / CONV f( '.1' + '.2' ).

And

WRITE / CONV decfloat16( '.1' + '.2' ).

0.30000000000000004

And

0.3
Ada 
with Ada.Text_IO; use Ada.Text_IO;

procedure Sum is

  A : Float := 0.1;

  B : Float := 0.2;

  C : Float := A + B;

begin

  Put_Line(Float'Image(C));

  Put_Line(Float'Image(0.1 + 0.2));

end Sum;

3.00000E-01

3.00000E-01
APL 
0.1 + 0.2

0.30000000000000004
AutoHotkey 
MsgBox, % 0.1 + 0.2

0.300000
awk 
echo | awk '{ print 0.1 + 0.2 }'

0.3
bc 
0.1 + 0.2

0.3
C 
#include<stdio.h>

int main(int argc, char** argv) {

    printf("%.17f\n", .1+.2);

    return 0;

}

0.30000000000000004
Clojure 
(+ 0.1 0.2)

0.30000000000000004

Clojure supports arbitrary precision and ratios. (+ 0.1M 0.2M) returns 0.3M, while (+ 1/10 2/10) returns 3/10.
ColdFusion 
<cfset foo = .1 + .2>

<cfoutput>#foo#</cfoutput>

0.3
Common Lisp 
(+ .1 .2)

And

(+ 1/10 2/10)

And

(+ 0.1d0 0.2d0)

And

(- 1.2 1.0)

0.3

And

3/10

And

0.30000000000000004d0

And

0.20000005

CL’s spec doesn’t actually even require radix 2 floats (let alone specifically 32-bit singles and 64-bit doubles), but the high-performance implementations all seem to use IEEE floats with the usual sizes. This was tested on SBCL and ECL in particular.
C++ 
#include <iomanip>

std::cout << std::setprecision(17) << 0.1 + 0.2

0.30000000000000004
Crystal 
puts 0.1 + 0.2

And

puts 0.1_f32 + 0.2_f32

0.30000000000000004

And

0.3
C# 
Console.WriteLine("{0:R}", .1 + .2);

And

Console.WriteLine("{0:R}", .1m + .2m);

0.30000000000000004

And

0.3

C# has support for 128-bit decimal numbers, with 28-29 significant digits of precision. Their range, however, is smaller than that of both the single and double precision floating point types. Decimal literals are denoted with the m suffix.
D 
import std.stdio;

void main(string[] args) {

  writefln("%.17f", .1+.2);

  writefln("%.17f", .1f+.2f);

  writefln("%.17f", .1L+.2L);

}

0.29999999999999999

0.30000001192092896

0.30000000000000000
Dart 
print(.1 + .2);

0.30000000000000004
dc 
0.1 0.2 + p

.3
Delphi XE5 
writeln(0.1 + 0.2);

3.00000000000000E-0001
Elixir 
IO.puts(0.1 + 0.2)

0.30000000000000004
Elm 
0.1 + 0.2

0.30000000000000004
elvish 
+ .1 .2

0.30000000000000004

elvish uses Go’s double for numerical operations.
Emacs Lisp 
(+ .1 .2)

0.30000000000000004
Erlang 
io:format("~w~n", [0.1 + 0.2]).

0.30000000000000004
FORTRAN 
program FLOATMATHTEST

  real(kind=4) :: x4, y4

  real(kind=8) :: x8, y8

  real(kind=16) :: x16, y16

  ! REAL literals are single precision, use _8 or _16

  ! if the literal should be wider.

  x4 = .1; x8 = .1_8; x16 = .1_16

  y4 = .2; y8 = .2_8; y16 = .2_16

  write (*,*) x4 + y4, x8 + y8, x16 + y16

end

0.300000012

0.30000000000000004

0.300000000000000000000000000000000039
Gforth 
0.1e 0.2e f+ f.

0.3
GHC (Haskell) 
* 0.1 + 0.2 :: Double

And

* 0.1 + 0.2 :: Float

* 0.30000000000000004

And

* 0.3

Haskell supports rational numbers. To get the math right, 0.1 + 0.2 :: Rational returns 3 % 10, which is exactly 0.3.
Go 
package main

import "fmt"

func main() {

  fmt.Println(.1 + .2)

  var a float64 = .1

  var b float64 = .2

  fmt.Println(a + b)

  fmt.Printf("%.54f\n", .1 + .2)

}

0.3

0.30000000000000004

0.299999999999999988897769753748434595763683319091796875

Go numeric constants have arbitrary precision.
Groovy 
println 0.1 + 0.2

0.3

Literal decimal values in Groovy are instances of java.math.BigDecimal
Hugs (Haskell) 
0.1 + 0.2

0.3
Io 
(0.1 + 0.2) print

0.3
Java 
System.out.println(.1 + .2);

And

System.out.println(.1F + .2F);

0.30000000000000004

And

0.3

Java has built-in support for arbitrary precision numbers using the BigDecimal class.
JavaScript 
console.log(.1 + .2);

0.30000000000000004

The decimal.js library provides an arbitrary-precision Decimal type for JavaScript.
Julia 
.1 + .2

0.30000000000000004

Julia has built-in rational numbers support and also a built-in arbitrary-precision BigFloat data type. To get the math right, 1//10 + 2//10 returns 3//10.
K (Kona) 
0.1 + 0.2

0.3
Lua 
print(.1 + .2)

And

print(string.format("%0.17f", 0.1 + 0.2))

0.3

And

0.30000000000000004
Mathematica 
0.1 + 0.2

0.3

Mathematica has a fairly thorough internal mechanism for dealing with numerical precision and supports arbitrary precision.
Matlab 
0.1 + 0.2

And

sprintf('%.17f',0.1+0.2)

0.3

And

0.30000000000000004
MySQL 
SELECT .1 + .2;

0.3
Nim 
echo(0.1 + 0.2)

0.3
Objective-C 
#import <Foundation/Foundation.h>

int main(int argc, const char * argv[]) {

  @autoreleasepool {

    NSLog(@"%.17f\n", .1+.2);

  }

  return 0;

}

0.30000000000000004
OCaml 
0.1 +. 0.2;;

float = 0.300000000000000044
Perl 5 
perl -E 'say 0.1+0.2'

And

perl -e 'printf q{%.17f}, 0.1+0.2'

0.3

And

0.30000000000000004
Perl 6 
perl6 -e 'say 0.1+0.2'

And

perl6 -e 'say (0.1+0.2).base(10, 17)'

And

perl6 -e 'say 1/10+2/10'

And

perl6 -e 'say (0.1.Num + 0.2.Num).base(10, 17)'

0.3

And

0.3

And

0.3

And

0.30000000000000004

Perl 6, unlike Perl 5, uses rationals by default, so .1 is stored something like { numerator => 1, denominator => 10 }. To actually trigger the behavior, you must force the numbers to be of type Num (double in C terms) and use the base function instead of the sprintf or fmt functions (since those functions have a bug that limits the precision of the output).
PHP 
echo .1 + .2;

var_dump(.1 + .2);

0.3 float(0.30000000000000004441)

PHP echo converts 0.30000000000000004441 to a string and shortens it to “0.3”. To achieve the desired floating point result, adjust the precision ini setting: ini_set(“precision”, 17).
PicoLisp 
[load "frac.min.l"]  # https://gist.github.com/6016d743c4c124a1c04fc12accf7ef17

And

[println (+ (/ 1 10) (/ 2 10))]

(/ 3 10)

You must load file “frac.min.l”.
Postgres 
SELECT select 0.1::float + 0.2::float;

0.3
Powershell 
PS C:\>0.1 + 0.2

0.3
Prolog (SWI-Prolog) 
?- X is 0.1 + 0.2.

X = 0.30000000000000004.
Pyret 
0.1 + 0.2

And

~0.1 + ~0.2

0.3

And

~0.30000000000000004

Pyret has built-in support for both rational numbers and floating points. Numbers written normally are assumed to be exact. In contrast, RoughNums are represented by floating points, and are written with a ~ in front, to indicate that they are not precise answers. (The ~ is meant to visually evoke hand-waving.) Therefore, a user who sees a computation produce ~0.30000000000000004knows to treat the value with skepticism. RoughNums also cannot be compared directly for equality; they can only be compared up to a given tolerance.
Python 2 
print(.1 + .2)

And

.1 + .2

And

float(decimal.Decimal(".1") + decimal.Decimal(".2"))

And

float(fractions.Fraction('0.1') + fractions.Fraction('0.2'))

0.3

And

0.30000000000000004

And

0.3

And

0.3

Python 2’s “print” statement converts 0.30000000000000004 to a string and shortens it to “0.3”. To achieve the desired floating point result, use print(repr(.1 + .2)). This was fixed in Python 3 (see below).
Python 3 
print(.1 + .2)

And

.1 + .2

And

float(decimal.Decimal('.1') + decimal.Decimal('.2'))

And

float(fractions.Fraction('0.1') + fractions.Fraction('0.2'))

0.30000000000000004

And

0.30000000000000004

And

0.3

And

0.3

Python (both 2 and 3) supports decimal arithmetic with the decimal module, and true rational numbers with the fractions module.
R 
print(.1+.2)

And

print(.1+.2, digits=18)

0.3

And

0.30000000000000004
Racket (PLT Scheme) 
(+ .1 .2)

And

(+ 1/10 2/10)

0.30000000000000004

And

3/10
Ruby 
puts 0.1 + 0.2

And

puts 1/10r + 2/10r

0.30000000000000004

And

3/10

Ruby supports rational numbers in syntax with version 2.1 and newer directly. For older versions use Rational.

Ruby also has a library specifically for decimals: BigDecimal.
Rust 
extern crate num;

use num::rational::Ratio;

fn main() {

    println!("{}", 0.1 + 0.2);

    println!("1/10 + 2/10 = {}", Ratio::new(1, 10) + Ratio::new(2, 10));

}

0.30000000000000004

And

1/10 + 2/10 = 3/10

Rust has rational number support from the num crate.
SageMath 
.1 + .2

And

RDF(.1) + RDF(.2)

And

RBF('.1') + RBF('.2')

And

QQ('1/10') + QQ('2/10')

0.3

And

0.30000000000000004

And

[“0.300000000000000 +/- 1.64e-16”]

And

3/10

SageMath supports various fields for arithmetic: Arbitrary Precision Real Numbers, RealDoubleField, Ball Arithmetic, Rational Numbers, etc.
scala 
scala -e 'println(0.1 + 0.2)'

And

scala -e 'println(0.1F + 0.2F)'

And

scala -e 'println(BigDecimal("0.1") + BigDecimal("0.2"))'

0.30000000000000004

And

0.3

And

0.3
Smalltalk 
0.1 + 0.2.

0.30000000000000004
Swift 
0.1 + 0.2

And

NSString(format: "%.17f", 0.1 + 0.2)

0.3

And

0.30000000000000004
TCL 
puts [expr .1 + .2]

0.30000000000000004
Turbo Pascal 7.0 
writeln(0.1 + 0.2);

3.0000000000E-01
Vala 
static int main(string[] args) {

  stdout.printf("%.17f\n", 0.1 + 0.2);

  return 0;

}

0.30000000000000004
Visual Basic 6 
a# = 0.1 + 0.2: b# = 0.3

Debug.Print Format(a - b, "0." & String(16, "0"))

Debug.Print a = b

0.0000000000000001

False

Appending the identifier type character # to any identifier forces it to Double.
WebAssembly (WAST) 
(func $add_f32 (result f32)

    f32.const 0.1

    f32.const 0.2

    f32.add)

(export "add_f32" (func $add_f32))

And

(func $add_f64 (result f64)

    f64.const 0.1

    f64.const 0.2

    f64.add)

(export "add_f64" (func $add_f64))

0.30000001192092896

And

0.30000000000000004

https://webassembly.studio/?f=r739k6d6q4t
zsh 
echo "$((.1+.2))"

0.30000000000000004

I am Erik Wiffin. You can contact me at: erik.wiffin.com or erik.wiffin@gmail.com.

This project is on github. If you think this page could be improved, send me a pull request.

Floating Point Math的更多相关文章

  1. Brief Tour of the Standard Library

    10.1. Operating System Interface The os module provides dozens of functions for interacting with the ...

  2. Awk by Example--转载

    原文地址: http://www.funtoo.org/Awk_by_Example,_Part_1?ref=dzone http://www.funtoo.org/Awk_by_Example,_P ...

  3. C++ QUICK REFERENCE

    C++ string 用法详解 字符串分割(C++)  C++ QUICK REFERENCE Matt Mahoney, mmahoney@cs.fit.edu DECLARATIONS enum ...

  4. net programming guid

    Beej's Guide to Network Programming Using Internet Sockets Brian "Beej Jorgensen" Hallbeej ...

  5. VS2012下基于Glut 矩阵变换示例程序：

    也可以使用我们自己的矩阵运算来实现OpenGL下的glTranslatef相应的旋转变换.需要注意的是OpenGL下的矩阵是列优先存储的. 示例通过矩阵运算使得圆柱或者甜圈自动绕Y轴旋转,可以单击鼠标 ...

  6. [Python] 01 - Number

    故事背景 一.大纲 如下,chapter4 是个概览,之后才是具体讲解. 二. 编译过程 Ref: http://www.dsf.unica.it/~fiore/LearningPython.pdf

  7. JavaScript-Tool：Moment.js

    ylbtech-JavaScript-Tool:Moment.js Parse, validate, manipulate, and display dates and times in JavaSc ...

  8. Delphi 64与32位的差异

    Delphi 64与32位的差异   最近,Delphi推出了64位预览版本, 我做为一个忠实的Delphier, 看到这消息后,第一时间学习,并写下这个做为以后的参考资料. 相同点: 在Delphi ...

  9. [Python] 01 - Number and Matrix

    故事背景 一.大纲 如下,chapter4 是个概览,之后才是具体讲解. 二. 编译过程 Ref: http://www.dsf.unica.it/~fiore/LearningPython.pdf

随机推荐

  1. PHP手册在7.1迁移页面给出了替代方案,就是用OpenSSL取代MCrypt.

    /**  * [AesSecurity aes加密,支持PHP7.1]  */ class AesSecurity {     /**      * [encrypt aes加密]      * @p ...

  2. MySQL数据库入门备份数据库

    MySQL数据库入门——备份数据库   一提到数据,大家神经都会很紧张,数据的类型有很多种,但是总归一点,数据很重要,非常重要,因此,日常的数据备份工作就成了运维工作的重点中的重点的重点....... ...

  3. SQL 基础语句整理

    SQL教程 SELECT 语句 SELECT * FROM 表名称 DISTINCT 语句 SELECT DISTINCT 列名称 FROM 表名称 SELECT LastName,FirstName ...

  4. JSP的9大内置对象和4打作用域对象

    一.9大内置对象 二.4大内置作用域对象

  5. urlencode编/解码

    from urllib.parse import urlencode, quote, unquote # urlencode方法参数是字典 body = { "content": ...

  6. jsp-TagLib标签库

    <%@ page contentType="text/html;charset=UTF-8" language="java" %> <%@ t ...

  7. 76. Minimum Window Substring (JAVA)

    Given a string S and a string T, find the minimum window in S which will contain all the characters ...

  8. sed 的用法

    sed 的语法: sed `样式命令` 文件 意思是:如果文件中的某一行符合”样式”,就执行指定的 sed 命令,如删除(d)或替换(s) “样式”使用一对//含括,表示寻找的意思.也可以指定数据行的 ...

  9. Java学习01-使用maven插件tomcat搭建web maven项目

    我使用社区版的IDEA,社区版的没有tomcat插件,只能使用maven插件进行tomcat的使用了,下面进入正题 一.pom.xml配置tomcat插件 <build> <fina ...

  10. CSS3参数matrix(n,n,n,n,n,n)定义 2D 转换，使用六个值的矩阵。那这六个值分别代表了什么参数？

    matrix( a, b, c, d, e, f );a 水平缩放b 水平倾斜c 垂直倾斜d 垂直缩放e 水平移动f 垂直移动