C++库文件 <cmath> (math.h)

约定不等于承诺〃 2022-05-08 03:48 124阅读 0赞

1、三角函数 Trigonometric functions

1.1、 cos() 函数

/* cos example */
    #include <stdio.h>      /* printf */
    #include <math.h>       /* cos */
    #define PI 3.14159265
    int main ()
    {
      double param, result;
      param = 60.0;
      result = cos ( param * PI / 180.0 );
      printf ("The cosine of %f degrees is %f.\n", param, result );
      return 0;
    }

1.2 sin() 正弦函数

/* sin example */
    #include <stdio.h>      /* printf */
    #include <math.h>       /* sin */
    
    #define PI 3.14159265
    
    int main ()
    {
      double param, result;
      param = 30.0;
      result = sin (param*PI/180);
      printf ("The sine of %f degrees is %f.\n", param, result );
      return 0;
    }

1.3、 tan() 正切函数

/* tan example */
    #include <stdio.h>      /* printf */
    #include <math.h>       /* tan */
    
    #define PI 3.14159265
    
    int main ()
    {
      double param, result;
      param = 45.0;
      result = tan ( param * PI / 180.0 );
      printf ("The tangent of %f degrees is %f.\n", param, result );
      return 0;
    }

1.4、 acos() 反余弦函数

/* acos example */
    #include <stdio.h>      /* printf */
    #include <math.h>       /* acos */
    
    #define PI 3.14159265
    
    int main ()
    {
      double param, result;
      param = 0.5;
      result = acos (param) * 180.0 / PI;
      printf ("The arc cosine of %f is %f degrees.\n", param, result);
      return 0;
    }

1.5、asin() 反正弦函数

/* asin example */
    #include <stdio.h>      /* printf */
    #include <math.h>       /* asin */
    
    #define PI 3.14159265
    
    int main ()
    {
      double param, result;
      param = 0.5;
      result = asin (param) * 180.0 / PI;
      printf ("The arc sine of %f is %f degrees\n", param, result);
      return 0;
    }

1.6、atan() 反正切函数

/* atan example */
    #include <stdio.h>      /* printf */
    #include <math.h>       /* atan */
    
    #define PI 3.14159265
    
    int main ()
    {
      double param, result;
      param = 1.0;
      result = atan (param) * 180 / PI;
      printf ("The arc tangent of %f is %f degrees\n", param, result );
      return 0;
    }

1.7、atan2() 带两个参数的反正切函数

/* atan2 example */
    #include <stdio.h>      /* printf */
    #include <math.h>       /* atan2 */
    
    #define PI 3.14159265
    
    int main ()
    {
      double x, y, result;
      x = -10.0;
      y = 10.0;
      result = atan2 (y,x) * 180 / PI;
      printf ("The arc tangent for (x=%f, y=%f) is %f degrees\n", x, y, result );
      return 0;
    }

2、双曲函数 Hyperbolic functions

2.1、双曲余弦函数

/* cosh example */
    #include <stdio.h>      /* printf */
    #include <math.h>       /* cosh, log */
    
    int main ()
    {
      double param, result;
      param = log(2.0);
      result = cosh (param);
      printf ("The hyperbolic cosine of %f is %f.\n", param, result );
      return 0;
    }

2.2、双曲正弦函数

/* sinh example */
    #include <stdio.h>      /* printf */
    #include <math.h>       /* sinh, log */
    
    int main ()
    {
      double param, result;
      param = log(2.0);
      result = sinh (param);
      printf ("The hyperbolic sine of %f is %f.\n", param, result );
      return 0;
    }

2.3、双曲正切函数

/* tanh example */
    #include <stdio.h>      /* printf */
    #include <math.h>       /* tanh, log */
    
    int main ()
    {
      double param, result;
      param = log(2.0);
      result = tanh (param);
      printf ("The hyperbolic tangent of %f is %f.\n", param, result);
      return 0;
    }

3、指数函数与对数函数 Exponential and logarithmic functions

3.1、**exp ()** 指数函数，以 **e** 为底数

/* exp example */
    #include <stdio.h>      /* printf */
    #include <math.h>       /* exp */
    
    int main ()
    {
      double param, result;
      param = 5.0;
      result = exp (param);
      printf ("The exponential value of %f is %f.\n", param, result );
      return 0;
    }

3.2、**frexp(param，n)** 二进制浮点数表示方法 **x=param\*2^n**

/* frexp example */
    #include <stdio.h>      /* printf */
    #include <math.h>       /* frexp */
    
    int main ()
    {
      double param, result;
      int n;
    
      param = 8.0;
      result = frexp (param , &n);
      printf ("%f = %f * 2^%d\n", param, result, n);
      return 0;
    }

3.3、**log(x)** x的自然对数 (Natural logarithm of x)

/* log example */
    #include <stdio.h>      /* printf */
    #include <math.h>       /* log */
    
    int main ()
    {
      double param, result;
      param = 5.5;
      result = log (param);
      printf ("log(%f) = %f\n", param, result );
      return 0;
    }

3.4、**log10()** 常用对数，**以10为底** ( Common logarithm of x )

/* log10 example */
    #include <stdio.h>      /* printf */
    #include <math.h>       /* log10 */
    
    int main ()
    {
      double param, result;
      param = 1000.0;
      result = log10 (param);
      printf ("log10(%f) = %f\n", param, result );
      return 0;
    }

3.5、**modf()** 返回x的小数部分，其符号与x相同 ，但是参数中可以添加整数部分的变量( The fractional part of x, with the same sign)

/* modf example */
    #include <stdio.h>      /* printf */
    #include <math.h>       /* modf */
    
    int main ()
    {
      double param, fractpart, intpart;
    
      param = 3.14159265;
      fractpart = modf (param , &intpart);
      printf ("%f = %f + %f \n", param, intpart, fractpart);
      return 0;
    }

3.6、**exp2()** 返回2的x次方，2 raised to the power of x.

/* exp2 example */
    #include <stdio.h>      /* printf */
    #include <math.h>       /* exp2 */
    
    int main ()
    {
      double param, result;
      param = 8.0;
      result = exp2 (param);
      printf ("2 ^ %f = %f.\n", param, result );
      return 0;
    }

3.7、**log2()** x的二进制对数( The binary logarithm of x)

/* log2 example */
    #include <stdio.h>      /* printf */
    #include <math.h>       /* log2 */
    
    int main ()
    {
      double param, result;
      param = 1024.0;
      result = log2 (param);
      printf ("log2 (%f) = %f.\n", param, result );
      return 0;
    }

4、幂函数 Power functions

4.1、**pow(base, power)** 幂函数 The result of raising **base** to the **power** exponent

/* pow example */
    #include <stdio.h>      /* printf */
    #include <math.h>       /* pow */
    
    int main ()
    {
      printf ("7 ^ 3 = %f\n", pow (7.0, 3.0) );
      printf ("4.73 ^ 12 = %f\n", pow (4.73, 12.0) );
      printf ("32.01 ^ 1.54 = %f\n", pow (32.01, 1.54) );
      return 0;
    }

4.2、**sqrt(x)** 计算x的平方根

/* sqrt example */
    #include <stdio.h>      /* printf */
    #include <math.h>       /* sqrt */
    
    int main ()
    {
      double param, result;
      param = 1024.0;
      result = sqrt (param);
      printf ("sqrt(%f) = %f\n", param, result );
      return 0;
    }

4.3、**cbrt(x)** 计算x的立方根

/* cbrt example */
    #include <stdio.h>      /* printf */
    #include <math.h>       /* cbrt */
    
    int main ()
    {
      double param, result;
      param = 27.0;
      result = cbrt (param);
      printf ("cbrt (%f) = %f\n", param, result);
      return 0;
    }

4.4、**hypot(x,y)** 计算直角三角形的斜边 ( The square root of (x^2+y^2) )

/* hypot example */
    #include <stdio.h>      /* printf */
    #include <math.h>       /* hypot */
    
    int main ()
    {
      double leg_x, leg_y, result;
      leg_x = 3;
      leg_y = 4;
      result = hypot (leg_x, leg_y);
      printf ("%f, %f and %f form a right-angled triangle.\n",leg_x,leg_y,result);
      return 0;
    }

5、误差与伽马函数 Error and gamma functions

5.1、**误差函数erf(x)**  
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/* erf example */
    #include <stdio.h>      /* printf */
    #include <math.h>       /* erf */
    
    int main ()
    {
      double param, result;
      param = 1.0;
      result = erf (param);
      printf ("erf (%f) = %f\n", param, result );
      return 0;
    }

5.2、**余差函数erfc(x)** erfc(x) = 1-erf(x) 误差函数的补函数  
![这里写图片描述][SouthEast 1]

/* erfc example */
    #include <stdio.h>      /* printf */
    #include <math.h>       /* erfc */
    
    int main ()
    {
      double param, result;
      param = 1.0;
      result = erfc (param);
      printf ("erfc(%f) = %f\n", param, result );
      return 0;
    }

5.3、**tgamma(x)** 伽马函数 ( the gamma function )  
![这里写图片描述][SouthEast 2]

/* tgamma example */
    #include <stdio.h>      /* printf */
    #include <math.h>       /* tgamma */
    
    int main ()
    {
      double param, result;
      param = 0.5;
      result = tgamma (param);
      printf ("tgamma(%f) = %f\n", param, result );
      return 0;
    }

5.4、**lgamma(x)** log伽马函数 ( log-gamma function )  
![这里写图片描述][SouthEast 3]

/* lgamma example */
    #include <stdio.h>      /* printf */
    #include <math.h>       /* lgamma */
    
    int main ()
    {
      double param, result;
      param = 0.5;
      result = lgamma (param);
      printf ("lgamma(%f) = %f\n", param, result );
      return 0;
    }

6、四舍五入与余数函数Rounding and remainder functions

6.1、**ceil(x)** x上取整函数

/* ceil example */
    #include <stdio.h>      /* printf */
    #include <math.h>       /* ceil */
    
    int main ()
    {
      printf ( "ceil of 2.3 is %.1f\n", ceil(2.3) );
      printf ( "ceil of 3.8 is %.1f\n", ceil(3.8) );
      printf ( "ceil of -2.3 is %.1f\n", ceil(-2.3) );
      printf ( "ceil of -3.8 is %.1f\n", ceil(-3.8) );
      return 0;
    }

6.2、**floor(x)** x的下取整函数

/* floor example */
    #include <stdio.h>      /* printf */
    #include <math.h>       /* floor */
    
    int main ()
    {
      printf ( "floor of 2.3 is %.1lf\n", floor (2.3) );
      printf ( "floor of 3.8 is %.1lf\n", floor (3.8) );
      printf ( "floor of -2.3 is %.1lf\n", floor (-2.3) );
      printf ( "floor of -3.8 is %.1lf\n", floor (-3.8) );
      return 0;
    }

6.3、**fmod(y, x)** y/x的余数

/* fmod example */
    #include <stdio.h>      /* printf */
    #include <math.h>       /* fmod */
    
    int main ()
    {
      printf ( "fmod of 5.3 / 2 is %f\n", fmod (5.3,2) );
      printf ( "fmod of 18.5 / 4.2 is %f\n", fmod (18.5,4.2) );
      return 0;
    }

6.4、**round(x)** x的四舍五入值  
![这里写图片描述][SouthEast 4]

/* round vs floor vs ceil vs trunc */
    #include <stdio.h>      /* printf */
    #include <math.h>       /* round, floor, ceil, trunc */
    
    int main ()
    {
      const char * format = "%.1f \t%.1f \t%.1f \t%.1f \t%.1f\n";
      printf ("value\tround\tfloor\tceil\ttrunc\n");
      printf ("-----\t-----\t-----\t----\t-----\n");
      printf (format, 2.3,round( 2.3),floor( 2.3),ceil( 2.3),trunc( 2.3));
      printf (format, 3.8,round( 3.8),floor( 3.8),ceil( 3.8),trunc( 3.8));
      printf (format, 5.5,round( 5.5),floor( 5.5),ceil( 5.5),trunc( 5.5));
      printf (format,-2.3,round(-2.3),floor(-2.3),ceil(-2.3),trunc(-2.3));
      printf (format,-3.8,round(-3.8),floor(-3.8),ceil(-3.8),trunc(-3.8));
      printf (format,-5.5,round(-5.5),floor(-5.5),ceil(-5.5),trunc(-5.5));
      return 0;
    }

7、绝对值、最小、最大 Absolute、Minimum, maximum

7.1、**fabs(x)** x的绝对值函数

/* fabs example */
    #include <stdio.h>      /* printf */
    #include <math.h>       /* fabs */
    
    int main ()
    {
      printf ("The absolute value of 3.1416 is %f\n", fabs (3.1416) );
      printf ("The absolute value of -10.6 is %f\n", fabs (-10.6) );
      return 0;
    }

7.2、**abs(x)** x的绝对值

// cmath's abs example
    #include <iostream>     // std::cout
    #include <cmath>        // std::abs
    
    int main ()
    {
      std::cout << "abs (3.1416) = " << std::abs (3.1416) << '\n';
      std::cout << "abs (-10.6)  = " << std::abs (-10.6) << '\n';
      return 0;
    }

7.3、**fmax(x, y)** 两个参数中的最大值 (The maximum numeric value of its arguments. Values among which the function selects a maximum )

/* fmax example */
    #include <stdio.h>      /* printf */
    #include <math.h>       /* fmax */
    
    int main ()
    {
      printf ("fmax (100.0, 1.0) = %f\n", fmax(100.0,1.0));
      printf ("fmax (-100.0, 1.0) = %f\n", fmax(-100.0,1.0));
      printf ("fmax (-100.0, -1.0) = %f\n", fmax(-100.0,-1.0));
      return 0;
    }

7.4、**fmin(x, y)** 两个参数中的最小值

/* fmin example */
    #include <stdio.h>      /* printf */
    #include <math.h>       /* fmin */
    
    int main ()
    {
      printf ("fmin (100.0, 1.0) = %f\n", fmin(100.0,1.0));
      printf ("fmin (-100.0, 1.0) = %f\n", fmin(-100.0,1.0));
      printf ("fmin (-100.0, -1.0) = %f\n", fmin(-100.0,-1.0));
      return 0;
    }

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[SouthEast]: /images/20220508/131b19dfe7d94e86a00cd037b0aa2745.png
[SouthEast 1]: /images/20220508/af3eac2bd2fb4d099a7bf6a183af3def.png
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