Float angle != angle什么时候为true?
2012 年 12 月 1 日
[TOC]
看到一段代码,顿时就呆了
看到一段代码,顿时就呆了
if (angle != angle) { return XMQuaternionIdentity(); }
这样写的用意到底是啥呢?
源代码
代码很好理解,就是求两个向量的四元数表示的旋转角度
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
参考[2]中解释了,说IEEE标准规定,NaN和任何数比较都是false,所以只有当angle为NaN的时候, angle != angle才为true
float a = acos(2); cout << "a = " << a << endl; // a = nan cout << (a != a) << endl; // 1
向量可能有问题
比如某个向量是无限长,正如 XMVector3Normalize
文档提到的一样[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会出现Nan的情况
如果输入范围有问题,那么结果就会出现NaN,第二条提到了[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.
如何写更优雅?
参考[2]中有个评论是这么回答的:
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,上面的写法是不是写成下面这样,会更加清晰明了:
// old angle ! = angle // new std::isnan(angle)
至此,这个问题算是清楚了,那么NaN到底是如何定义的呢?
NaN定义
参考[5][6]
IEEE 754 floating point numbers can represent positive or negative infinity, and NaN (not a number).
小结:
- NaN在运算中得结果始终都是NaN,不像infinity有可能算出来一个正常值,比如 4/∞ = 0
- NaN的浮点数IEEE表示是一个范围,节码都是1,所以尾数表示的范围都是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
参考
[1] When is a float variable not equal to itself
[2] Checking if a double (or float) is NaN in C++
[7] IEEE User’s Guide
[8] What is difference between quiet NaN and signaling NaN?