C语言中的浮点数组

Question

我正在开发一个代码，其中我必须一次在文本文件中加载存储在每一行中的浮点值...我使用fscanf（）将这些数据中的每一个加载到浮点数组中...但是我发现浮点以不同的方式存储，示例407.18存储为407.179993，414.35存储为414.350006 ...现在我被困住了，因为将数字以它们在文件中的形式存储是绝对重要的，但在这里看来即使本质上是相同的，也各不相同。...我如何获取数字以原始形式存储？

Answer 1

If it's absolutely important that the numbers be stored in the form they were in the file, don't use floating-point values . Not all fractional base-10 values can be represented exactly in binary.

For details, you should consult the article "What Every Computer Scientist Should Know About Floating-Point Arithmetic" [PDF link].

You should store the numbers in string form or as scaled integers.

Answer 2

What you see is correct since floating point cannot exactly represent many real numbers. This is a must-read: What Every Computer Scientist Should Know About Floating-Point Arithmetic

Answer 3

The C++ float and double types are represented as IEEE floating point numbers. There are binary floating point numbers, not decimals. They don't have infinite precision, and even relatively 'simple' decimal values will change when converted to binary floating point and back.

Languages that focus on money (COBOL and PL/I, eg) have decimal data types that use slower representations that don't have this problem. There are libraries for this purpose in C or C++, or you can use scaled integers if you don't need too much range.

Answer 4

sfactor, A bit of clarification: you state "...absolutely important that the numbers be stored in the form they were in the file" - what 'form' is this? I'm assuming a display form?! Here's the deal: If you store in the file 407.18, but it is displayed as 407.179993 - this is totally normal and expected. When you construct your sprintf or whatever formatted print you are using, you must instruct it to limit the precision after the decimal point. This should do the trick:

#include <stdio.h>
void main(void);
void main()
{
   printf("%.2f",407.179993);
}

Answer 5

You might want to take a look at an existing library that implements floating point with controlled rounding. I have used MPFR . It is fast and open source. If you are working with money then a different library would be better.

Answer 6

There is a lot of different ways to store numbers - each with their strenghts and weaknesses.

In your case floating point numbers are not the best choice because they don't represent most real numbers exactly .

Scaled integers is a case of the common design idiom: separate representation from the presentation.

Decide on how many digits you want after the decimal point, eg. 2 digits as in 123,45. You should then internaly represent the number as the integer 12345. Whenever you display the value to the user you should insert a decimal point at the relevant spot.

Short InformIT article on Scaled Integers by Danny Kalev

Before going overboard on scaled integers do inspect the domain of your problem closely to assert that the "slack" in the floating point numbers is significant enough to warrent using scaled integers.