测试浮点数相等 [英] Testing floating point numbers equality

问题描述

我在Windows 7（32位）下使用MinGW中的gfortran来编译Fortran代码。这是文件 testequal.f 中包含的最小代码：

 程序testequal 
 real * 8 a1，a2 
 
 a1 = 0.3d0 
 a2 = 0.7d0 
 
写（*，*）1.d0 $ b * b写（*，*）a1 + a2 
写（*，*）a1 + a2.eq.1.0 
写（*，*）a1 + a2.eq.1.d0 
 
  

与

<$ p $输出为： gfortran testequal.f -std = legacy


/ p>

  1.0000000000000000 
 1.0000000000000000 
 F 
 F 
  

但我期望两个布尔值都是 T （true）。这里有什么问题？

解决方案

极少数例外情况下，请不要比较浮点数以确保相等。有限精度浮点运算的规则与实数运算的规则不尽相同。比较数字与宽容，例如，如果（abs（sum - 1.0）

I am using gfortran in MinGW under Windows 7 (32bit) to compile Fortran code. Here is the minimal code contained in the file testequal.f:

      program testequal
      real*8 a1, a2

      a1 = 0.3d0
      a2 = 0.7d0

      write(*,*) 1.d0
      write(*,*) a1+a2
      write(*,*) a1+a2.eq.1.0
      write(*,*) a1+a2.eq.1.d0
      end

Compiled with

gfortran testequal.f -std=legacy

the output is:

1.0000000000000000
1.0000000000000000
F
F

But I expect the two booleans to be both T (true). What is the problem here?

解决方案

With rare exceptions, don't compare floating point numbers for exact equality. The rules of finite-precision floating point arithmetic are not the same are the rules of real number arithmetic. Compare numbers with a tolerance, e.g.,

sum = a1 + a2
if ( abs (sum - 1.0) < 1.0D-5 ) ...

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