各种浮动值的epsilon

FLT_MIN常量最接近零。 如何获得最接近some number数值？

举个例子：

 float nearest_to_1000 = 1000.0f + epsilon; // epsilon must be the smallest value satisfying condition: // nearest_to_1000 > 1000.0f 

我更喜欢不使用特殊function的数字公式。

Answer 1

警告：在处理另一个答案时，在此代码中发现了错误。 我希望稍后更新。 与此同时，它失败了一些涉及次正规的值。

C在头文件中为此提供了一个函数。 nextafterf(x, INFINITY)是x之后的下一个可表示的值，朝向INFINITY的方向。

但是，如果您愿意自己做：

假设IEEE 754，以下内容返回您寻找的epsilon，单精度（浮点）。

 #include  #include  /* Return the ULP of q. This was inspired by Algorithm 3.5 in Siegfried M. Rump, Takeshi Ogita, and Shin'ichi Oishi, "Accurate Floating-Point Summation", _Technical Report 05.12_, Faculty for Information and Communication Sciences, Hamburg University of Technology, November 13, 2005. */ float ULP(float q) { // SmallestPositive is the smallest positive floating-point number. static const float SmallestPositive = FLT_EPSILON * FLT_MIN; /* Scale is .75 ULP, so multiplying it by any significand in [1, 2) yields something in [.75 ULP, 1.5 ULP) (even with rounding). */ static const float Scale = 0.75 * FLT_EPSILON; q = fabs(q); return fmax(SmallestPositive, q - (q - q * Scale)); } 

以下内容返回传递值后浮点数中可表示的下一个值（将-0和+ 0视为相同）。

 #include  #include  /* Return the next floating-point value after the finite value q. This was inspired by Algorithm 3.5 in Siegfried M. Rump, Takeshi Ogita, and Shin'ichi Oishi, "Accurate Floating-Point Summation", _Technical Report 05.12_, Faculty for Information and Communication Sciences, Hamburg University of Technology, November 13, 2005. */ float NextAfter(float q) { // SmallestPositive is the smallest positive floating-point number. static const float SmallestPositive = FLT_EPSILON * FLT_MIN; /* Scale is .625 ULP, so multiplying it by any significand in [1, 2) yields something in [.625 ULP, 1.25 ULP]. */ static const float Scale = 0.625 * FLT_EPSILON; return q + fmax(SmallestPositive, fabs(q)*Scale); }