Float angle != angle什麼時候爲true？

[TOC]

看到一段代碼，頓時就呆了

if (angle != angle)
    {
        return XMQuaternionIdentity();
    }

這樣寫的用意到底是啥呢？

源代碼

代碼很好理解，就是求兩個向量的四元數表示的旋轉角度

DirectX::XMVECTOR SimStarMan::QuaternionFromToRotation(const XMVECTOR& from, const XMVECTOR& to)
{
    XMVECTOR quatRet;
    XMVECTOR axis, fromN, toN;
    float angle;
    fromN = XMVector3Normalize(from);
    toN = XMVector3Normalize(to);
    const XMVECTOR epsilon = XMLoadFloat3(&XMFLOAT3(0.00001f, 0.00001f, 0.00001f));

    if (XMVector3NearEqual(fromN, toN, epsilon))
    {
        return XMQuaternionIdentity();
    }
    axis = XMVector3Cross(fromN, toN);
    axis = XMVector3Normalize(axis);
    angle = acosf(XMVectorGetX(XMVector3Dot(fromN, toN)));
    if (angle != angle)
    {
        return XMQuaternionIdentity();
    }
    quatRet = XMQuaternionRotationAxis(axis, angle);
    quatRet = XMQuaternionNormalize(quatRet);
    return quatRet;
}

探究

NAN

參考[2]中解釋了，說IEEE標準規定，NaN和任何數比較都是false，所以只有當angle爲NaN的時候， angle != angle才爲true

float a = acos(2);
cout << "a = " << a << endl;    // a = nan
cout << (a != a) << endl;         // 1

向量可能有問題

比如某個向量是無限長，正如 XMVector3Normalize 文檔提到的一樣[3]

For a vector of length 0, this function returns a zero vector. For a vector with infinite length, it returns a vector of QNaN.

acosf會出現Nan的情況

如果輸入範圍有問題，那麼結果就會出現NaN，第二條提到了[4]

If no errors occur, the arc cosine of arg (arccos(arg)) in the range [0 ; π], is returned.

If a domain error occurs, an implementation-defined value is returned (NaN where supported).

If a range error occurs due to underflow, the correct result (after rounding) is returned.

如何寫更優雅？

參考[2]中有個評論是這麼回答的：

This answer should be updated since std::isnan is now part of the C++11 standard and support has spread out. std::isnan was implemented in Visual Studio starting with Visual Studio 2013.

所以，上面的寫法是不是寫成下面這樣，會更加清晰明瞭：

// old
angle ! = angle
// new
std::isnan(angle)

至此，這個問題算是清楚了，那麼NaN到底是如何定義的呢？

NaN定義

參考[5][6]

IEEE 754 floating point numbers can represent positive or negative infinity, and NaN (not a number).

小結：

NaN在運算中得結果始終都是NaN，不像infinity有可能算出來一個正常值，比如 4/∞ = 0
NaN的浮點數IEEE表示是一個範圍，節碼都是1，所以尾數表示的範圍都是NaN

Positive infinity is represented by the bit pattern X'7F80 0000'.
Negative infinity is represented by the bit pattern X'FF80 0000'.
A signaling NaN (NANS) is represented by any bit pattern between X'7F80 0001' and X'7FBF FFFF' or between X'FF80 0001' and X'FFBF FFFF'.
A quiet NaN (NANQ) is represented by any bit pattern between X'7FC0 0000' and X'7FFF FFFF' or between X'FFC0 0000' and X'FFFF FFFF'.

     31
     |
     | 30    23 22                    0
     | |      | |                     |
-----+-+------+-+---------------------+
qnan 0 11111111 10000000000000000000000
snan 0 11111111 01000000000000000000000
 inf 0 11111111 00000000000000000000000
-inf 1 11111111 00000000000000000000000
-----+-+------+-+---------------------+
     | |      | |                     |
     | +------+ +---------------------+
     |    |               |
     |    v               v
     | exponent        fraction
     |
     v
     sign