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。
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); }
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