比较 IEEE 浮点数和双精度数的相等性 [英] Comparing IEEE floats and doubles for equality

问题描述

比较 IEEE 浮点数和双精度数是否相等的最佳方法是什么?我听说过几种方法，但我想看看社区是怎么想的.

What is the best method for comparing IEEE floats and doubles for equality? I have heard of several methods, but I wanted to see what the community thought.

推荐答案

我认为最好的方法是比较 ULP.

The best approach I think is to compare ULPs.

bool is_nan(float f)
{
    return (*reinterpret_cast<unsigned __int32*>(&f) & 0x7f800000) == 0x7f800000 && (*reinterpret_cast<unsigned __int32*>(&f) & 0x007fffff) != 0;
}

bool is_finite(float f)
{
    return (*reinterpret_cast<unsigned __int32*>(&f) & 0x7f800000) != 0x7f800000;
}

// if this symbol is defined, NaNs are never equal to anything (as is normal in IEEE floating point)
// if this symbol is not defined, NaNs are hugely different from regular numbers, but might be equal to each other
#define UNEQUAL_NANS 1
// if this symbol is defined, infinites are never equal to finite numbers (as they're unimaginably greater)
// if this symbol is not defined, infinities are 1 ULP away from +/- FLT_MAX
#define INFINITE_INFINITIES 1

// test whether two IEEE floats are within a specified number of representable values of each other
// This depends on the fact that IEEE floats are properly ordered when treated as signed magnitude integers
bool equal_float(float lhs, float rhs, unsigned __int32 max_ulp_difference)
{
#ifdef UNEQUAL_NANS
    if(is_nan(lhs) || is_nan(rhs))
    {
        return false;
    }
#endif
#ifdef INFINITE_INFINITIES
    if((is_finite(lhs) && !is_finite(rhs)) || (!is_finite(lhs) && is_finite(rhs)))
    {
        return false;
    }
#endif
    signed __int32 left(*reinterpret_cast<signed __int32*>(&lhs));
    // transform signed magnitude ints into 2s complement signed ints
    if(left < 0)
    {
        left = 0x80000000 - left;
    }
    signed __int32 right(*reinterpret_cast<signed __int32*>(&rhs));
    // transform signed magnitude ints into 2s complement signed ints
    if(right < 0)
    {
        right = 0x80000000 - right;
    }
    if(static_cast<unsigned __int32>(std::abs(left - right)) <= max_ulp_difference)
    {
        return true;
    }
    return false;
}

类似的技术可用于双打.诀窍是转换浮点数，使它们有序(就像整数一样)，然后看看它们有多大不同.

A similar technique can be used for doubles. The trick is to convert the floats so that they're ordered (as if integers) and then just see how different they are.

我不知道为什么这个该死的东西会搞砸我的下划线.哦，也许这只是预览的人工制品.那就可以了.

I have no idea why this damn thing is screwing up my underscores. Oh, perhaps that is just an artefact of the preview. That's OK then.

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