[C++]直接访问float变量内存的类，addEpison和subEpison、almostEqual约等于，及浮点数排序函数。从此忘记0.000001 再也不要使用FLT

本文主要是介绍[C++]直接访问float变量内存的类，addEpison和subEpison、almostEqual约等于，及浮点数排序函数。从此忘记0.000001 再也不要使用FLT_EPSILON！，希望对大家解决编程问题提供一定的参考价值，需要的开发者们随着小编来一起学习吧！

探究浮点数奥秘，这里给出一个直接访问float变量内存的类，二进制兼容float，
并给出addEpison和subEpison两个函数
而这两个函数，是模糊比较所需要的方法的基础。

//负数时随着内存值int变大，浮点值绝对值越大
// 80000000   →→→ bf800000  →  ff7fffff  ff800000  ff800001 ffffffff
//    -0       渐变     -1    渐变   -MAX    -INF       -Nan      -Nan
// 
// 正数时随着内存值int变大，浮点值绝对值越大
// 00000000   →→→ 3f800000  →  ff7fffff  7f7fffff  7f800001 7fffffff
//    +0       渐变     +1    渐变   +MAX    +INF       +Nan      +Nan//从负到正遍历浮点数的方法：  ff800000 -> 80000000, 00000000 -> 7f7fffff
//                              -INF         -0        +0         +INFstruct Float
{union{struct{unsigned int Mantissa : 23;unsigned int Exponent : 8;unsigned int Sign : 1;};struct {unsigned int withoutSign : 31;unsigned int : 1;};int _memoryInt = 0;float _float;};operator float&() { return _float; }operator const float&() const { return _float; }operator float() const { return _float; }Float() = default;Float(float f) : _memoryInt((int&)f){}bool equalZero() { return withoutSign == 0; }bool isNan() { return Exponent == 0xFF && Mantissa != 0; }//是正无穷大bool isINF_P() { return _memoryInt == 0x7F800000; }//是负无穷大bool isINF_N() { return _memoryInt == 0xFF800000; }//是无穷大bool isINF_PN() { return (_memoryInt & 0x7F800000) == 0x7F800000; }//非数值void makeNan() { _memoryInt = 0x7FFFFFFF; } //正Nan中内存值最大的//正无穷大void makeINF_P() { _memoryInt = 0x7F800000; }//负无穷大void makeINF_N() { _memoryInt = 0xFF800000; }void makeMax()      { _memoryInt = 0x7F7FFFFF; }void makeMax_N()    { _memoryInt = 0xFF7FFFFF; }void makeMin()      { _memoryInt = 0x00800000; }    //最小值1.1754943510e-38(0x00800000), 次小值1.175494491e-38(0x00800001)void makeMin_N()    { _memoryInt = 0x80800000; }void makeTrueMin() { _memoryInt = 0x00000001; }     //最小值1.4012984643e-45F(0x00000001)，次小值2.803e-45  2.8025969286496341e-45 (0x00800002)void makeTrueMin_N() { _memoryInt = 0x80000001; }//增加一个极小值，使得比当前值大；+max,+/-INF,+/-Nan不受影响void addEpison(){if ((unsigned int)_memoryInt >= 0xFF800000u) return; //负无穷大，负Nanif (_memoryInt >= 0x7F7FFFFF) return; //正最大值，正无穷大，正Nanif (_memoryInt == 0x80000000)   //负0_memoryInt = 0x00000001;    //TrueMinelse{_memoryInt += 1 - ((_memoryInt<0)<<1);}}//减少一个极小值，是的比当前值小void subEpison() {if ((unsigned int)_memoryInt >= 0xFF800000u) return; //负最大值，负无穷大，负Nanif (_memoryInt >= 0x7F800000) return; //正无穷大，正Nanif (_memoryInt == 0x00000000)   //正0_memoryInt = 0x80000001;    //TrueNegMinelse{_memoryInt -= 1 - ((_memoryInt < 0) << 1);}}bool almostEqual(const Float& other, unsigned int episonCount) const{if (((unsigned int)_memoryInt >= 0xFF800000u) || (_memoryInt >= 0x7F800000)|| ((unsigned int)other._memoryInt >= 0xFF800000u) || (other._memoryInt >= 0x7F800000))return _float == other._float; //无穷大，Nanint absA = _memoryInt < 0 ? 0x80000000 - _memoryInt : _memoryInt;int absB = other._memoryInt < 0 ? 0x80000000 - other._memoryInt : other._memoryInt;return (episonCount + unsigned int(absA - absB)) <= (episonCount << 1);}
};

    Float a = 1.f / 3;Float b = 0.5f - 1.f / 6;a += a;b += b;{bool test = a == b;puts(test ? "true" : "false");  //false}{bool test = a.almostEqual(b, 1); //一个精度差距？puts(test ? "true" : "false");  //true}{Float A = a;A.addEpison(); //手动增加一个精度差距bool test = A.almostEqual(b, 1); //一个精度差距？puts(test ? "true" : "false");  //false}{Float A = a;A.addEpison(); //手动增加一个精度差距bool test = A.almostEqual(b, 2); //二个精度差距？puts(test ? "true" : "false");  //true}{Float x1 = a, x2 = a;x1.addEpison();x2.subEpison();bool test2 = a == b || x1 == b || x2 == b;puts(test2 ? "true" : "false"); //true}

下面给出一个浮点数排序函数，使用他能正确使包含无穷大、Nan的浮点数组成功排序

[](float a, float b) {bool isnanA = isnan(a), isnanB = isnan(b);if (isnanA || isnanB){if (!isnanB){return ((int&)a & 0x80000000) != 0;}if (!isnanA){return ((int&)b & 0x80000000) == 0; }if (((int&)a < 0) != ((int&)b < 0))return (int&)a < (int&)b;else //两nan符号相同return (((int&)a & 0x7FFFFF) < ((int&)b & 0x7FFFFF)) != ((int&)a < 0);}if ((int&)a == (int&)b)return false;else if (a < b)return true;else if (b < a)return false;elsereturn (int&)a < (int&)b;}