Update mathh.h

Author: Mandywualmighty

arc_design_contest/2018/XDU_Autofollowing_suitcase/src/mathh.h

@@ -22,9 +22,9 @@ double asr1(double a, double b, double eps, double A,int flag);
 
 
 
-double pow1(double a,int n)//实数的整数次幂，快速幂
+double pow1(double a,int n)
 {
-    if(n<0) return 1/pow1(a,-n);//n为负时的处理
+    if(n<0) return 1/pow1(a,-n);
     double res = 1.0;
     while(n)
     {
@@ -36,17 +36,17 @@ double asr1(double a, double b, double eps, double A,int flag);
 }
 
 
-double F11(double x)//为了使用定积分计算lnx
+double F11(double x)
 {
     return 1/x;
 }
 
-double F21(double x)//为了使用定积分计算arcsinx
+double F21(double x)
 {
     return 1/sqrt1(1-x*x);
 }
 
-double simpson1(double a, double b,int flag)//辛普森积分公式
+double simpson1(double a, double b,int flag)
 {
     double c = a + (b-a)/2;
     if(flag==1)
@@ -55,15 +55,15 @@ double asr1(double a, double b, double eps, double A,int flag);
         return (F21(a)+4*F21(c)+F21(b))*(b-a)/6;
 }
 
-double asr1(double a, double b, double eps, double A,int flag)//辛普森积分公式的自适应过程
+double asr1(double a, double b, double eps, double A,int flag)
 {
     double c = a + (b-a)/2;
     double L = simpson1(a, c,flag), R = simpson1(c, b,flag);
     if(fabs(L+R-A) <= 15*eps) return L+R+(L+R-A)/15.0;
     return asr1(a, c, eps/2, L,flag) + asr1(c, b, eps/2, R,flag);
 }
 
-double asr11(double a, double b, double eps,int flag)//辛普森积分主体函数
+double asr11(double a, double b, double eps,int flag)
 {
     return asr1(a, b, eps, simpson1(a, b,flag),flag);
 }
@@ -88,9 +88,9 @@ double sin1(double x)
     {
         x*=-1;
         fl*=-1;
-    }//处理区间
+    }//处理区间
     if(x>PI/4) return cos1(PI/2-x);
-    else return fl*(x - pow1(x,3)/6 + pow1(x,5)/120 - pow1(x,7)/5040 +pow1(x,9)/362880);//泰勒公式
+    else return fl*(x - pow1(x,3)/6 + pow1(x,5)/120 - pow1(x,7)/5040 +pow1(x,9)/362880);
 }
 
 double cos1(double x)
@@ -108,49 +108,49 @@ double cos1(double x)
     {
         x += PI;
         fl *= -1;
-    }//处理区间
+    }
     if(x>PI/4) return sin1(PI/2-x);
-    else return fl*(1 - pow1(x,2)/2 + pow1(x,4)/24 - pow1(x,6)/720 + pow1(x,8)/40320);//泰勒公式
+    else return fl*(1 - pow1(x,2)/2 + pow1(x,4)/24 - pow1(x,6)/720 + pow1(x,8)/40320);
 }
 
 double tan1(double x)
 {
     if(x>PI || x<-PI) x -= (int)(x/(PI))*PI;
     if(x>PI/2) x -= PI;
-    if(x<-PI/2) x += PI;//处理区间
-    return x + pow1(x,3)/3 + pow1(x,5)*2/15 + pow1(x,7)*17/315 + pow1(x,9)*62/2835;//泰勒公式
+    if(x<-PI/2) x += PI;
+    return x + pow1(x,3)/3 + pow1(x,5)*2/15 + pow1(x,7)*17/315 + pow1(x,9)*62/2835;
 }
 
 double asin1(double x)
 {
     if(fabs(x)>1) return -1;
     double fl = 1.0;
     if(x<0) {fl*=-1;x*=-1;}
-    if(fabs(x-1)<1e-7) return PI/2;//x为正负1时特判
-    return (fl*asr11(0,x,1e-8,2));//主体积分过程
+    if(fabs(x-1)<1e-7) return PI/2;
+    return (fl*asr11(0,x,1e-8,2));
     //return x + pow(x,3)/6 + pow(x,5)*3/40 +pow(x,7)*5/112 + pow(x,9)*35/1152 + pow(x,11)*315/1408;
 }
 
 double acos1(double x)
 {
     if(fabs(x)>1) return -1;
-    return PI/2 - asin1(x);//简单公式的应用
+    return PI/2 - asin1(x);
 }
 
 double atan1(double x)
 {
     if(x<0) return -atan1(-x);
     if(x>1) return PI/2 - atan1(1/x);
-    if(x>1e-3) return 2*atan1((sqrt1(1+x*x)-1)/x);//递推地缩小自变量，使之接近0，保证泰勒公式的精度
-    return x - pow1(x,3)/3 + pow1(x,5)/5 - pow1(x,7)/7 + pow1(x,9)/9;//泰勒公式
+    if(x>1e-3) return 2*atan1((sqrt1(1+x*x)-1)/x);
+    return x - pow1(x,3)/3 + pow1(x,5)/5 - pow1(x,7)/7 + pow1(x,9)/9;
 }
 
 
 double sqrt1(double x)
 {
-    if(x>100) return 10.0*sqrt1(x/100);//缩小自变量值
-    double t = x/8 + 0.5 + 2*x/(4+x);//迭代两次之后的结果
-    int c = 10;//迭代十次
+    if(x>100) return 10.0*sqrt1(x/100);
+    double t = x/8 + 0.5 + 2*x/(4+x);
+    int c = 10;
     while(c--)
     {
         t = (t+x/t)/2;