是否有一个C/C++函数来安全地处理除零？

Question

根据两个其他值v1和v2远离零的距离,我们想要对两个值w1和w2进行一种加权平均的情况...例如:

• 如果v1为零,它根本没有加权,所以我们返回w2
• 如果v2为零,它根本没有加权,所以我们返回w1
• 如果两个值都等于零,我们进行平均值并返回(w1 + w2)/ 2

我继承了以下代码:

float calcWeightedAverage(v1,v2,w1,w2)
{
  v1=fabs(v1);
  v2=fabs(v2);
  return (v1/(v1+v2))*w1 + (v2/(v1+v2)*w2);
}

对于一些背景,v1和v2表示两个不同旋钮的转动距离,它们各自的合成效果的加权仅取决于它们转动多少,而不是转向哪个方向.

显然,这有一个问题v1==v2==0,因为我们最终会结束return (0/0)*w1 + (0/0)*w2而你却做不到 0/0.在v1==v2==0数学上对声音进行特殊测试是非常糟糕的,即使用浮点数做练习也不错.

所以我想知道是否

• 有一个标准的库函数来处理这个问题
• 有一个更整洁的数学表示

Answer 1

You're trying to implement this mathematical function:

F(x, y) = (W1 * |x| + W2 * |y|) / (|x| + |y|)

This function is discontinuous at the point x = 0, y = 0. Unfortunately, as R. stated in a comment, the discontinuity is not removable - there is no sensible value to use at this point.

This is because the "sensible value" changes depending on the path you take to get to x = 0, y = 0. For example, consider following the path F(0, r) from r = R1 to r = 0 (this is equivalent to having the X knob at zero, and smoothly adjusting the Y knob down from R1 to 0). The value of F(x, y) will be constant at W2 until you get to the discontinuity.

Now consider following F(r, 0) (keeping the Y knob at zero and adjusting the X knob smoothly down to zero) - the output will be constant at W1 until you get to the discontinuity.

Now consider following F(r, r) (keeping both knobs at the same value, and adjusting them down simulatneously to zero). The output here will be constant at W1 + W2 / 2 until you go to the discontinuity.

This implies that any value between W1 and W2 is equally valid as the output at x = 0, y = 0. There's no sensible way to choose between them. (And further, always choosing 0 as the output is completely wrong - the output is otherwise bounded to be on the interval W1..W2 (ie, for any path you approach the discontinuity along, the limit of F() is always within that interval), and 0 might not even lie in this interval!)

You can "fix" the problem by adjusting the function slightly - add a constant (eg 1.0) to both v1 and v2 after the fabs(). This will make it so that the minimum contribution of each knob can't be zero - just "close to zero" (the constant defines how close).

It may be tempting to define this constant as "a very small number", but that will just cause the output to change wildly as the knobs are manipulated close to their zero points, which is probably undesirable.