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/*
将浮点数x分解成整数部分和小数部分。
返回小数部分，将整数部分存入* iptr所指内存中。
*/
double my_modf01(double x, double *iptr)
{
double ret = fmod(x,1.0);
*iptr = x - ret;
return ret;
}//这个函数算法比较简单，也容易让人理解。
//下面的这个函数理解起来就有点困难了。
typedef struct
{
unsigned int mantissal:32;
unsigned int mantissah:20;
unsigned int exponent:11;
unsigned int sign:1;
}double_t;//这个结构体在IEEE.h定义。
double my_modf02(double x, double *y)
{
double_t * z = (double_t *)&x;
double_t * iptr = (double_t *)y;
int j0;
unsigned int i;
j0 = z->exponent - 0x3ff; /* exponent of x */
if(j0<20)
{/* integer part in high x */
if(j0<0)
{ /* |x|<1 */
*y = 0.0;
iptr->sign = z->sign;
return x;
}
else
{
if ( z->mantissah == 0 && z->mantissal == 0 )
{
*y = x;
return 0.0;
}
i = (0x000fffff)>>j0;
iptr->sign = z->sign;
iptr->exponent = z->exponent;
iptr->mantissah = z->mantissah&(~i);
iptr->mantissal = 0;
if ( x == *y )
{
x = 0.0;
z->sign = iptr->sign;
return x;
}
return x - *y;
}
}
else if (j0>51)
{ /* no fraction part */
*y = x;
if ( isnan(x) || isinf(x) )
return x;
x = 0.0;
z->sign = iptr->sign;
return x;
}
else
{ /* fraction part in low x */
i = ((unsigned)(0xffffffff))>>(j0-20);
iptr->sign = z->sign;
iptr->exponent = z->exponent;
iptr->mantissah = z->mantissah;
iptr->mantissal = z->mantissal&(~i);
if ( x == *y )
{
x = 0.0;
z->sign = iptr->sign;
return x;
}
return x - *y;
}
}
//下面是两个要用到的函数
int isnan(double d)
{
union
{
unsigned long long l;
double d;
} u;
u.d=d;
return (u.l==0x7FF8000000000000ll || u.l==0x7FF0000000000000ll || u.l==0xfff8000000000000ll);
}
int isinf(double d)
{
union
{
unsigned long long l;
double d;
} u;
u.d=d;
return (u.l==0x7FF0000000000000ll?1:u.l==0xFFF0000000000000ll?-1:0);
}
int main()
{
double x,y;
x = 12345678901.1234567;
printf("%f = (%f) + (%f) \n",x,y,modf(x,&y));
printf("%f = (%f) + (%f) \n",x,y,my_modf01(x,&y));
printf("%f = (%f) + (%f) \n",x,y,my_modf02(x,&y));
printf("\n******************************************\n");
printf("%f = (%f) + (%f) \n",-x,y,modf(-x,&y));
printf("%f = (%f) + (%f) \n",-x,y,my_modf01(-x,&y));
printf("%f = (%f) + (%f) \n",-x,y,my_modf02(-x,&y));
system("pause");
return 0;
}
【C语言库函数源代码】
【本程序在Dev C++ 4.9.9.2 下编译通过】
/*
hypot函数对于给定的直角三角形的两个直角边，
求其斜边的长度。
*/
//一般的常规算法：
double my_hypot01(double x, double y)
{
double hypotenuse;
x = fabs(x);
y = fabs(y);
if (x < y)
{
double temp = x;
x = y;
y = temp;
}
if (x == 0.)
return 0.;
else
{
hypotenuse = y/x;
return x*sqrt(1.+hypotenuse*hypotenuse);
}
}
#define __SQRT_DBL_MAX 1.3e+154
#define __SQRT_DBL_MIN 2.3e-162
double my_hypot02(double x, double y)
{
double ratio;
double r, t, s, p, q;
x = fabs(x), y = fabs(y);
if (x < y)
{
double temp = x;
x = y;
y = temp;
}//保持x 是两个直角边中较长的边，y是较短的边。
if (y == 0.)
return x;
/*
主要考虑的是当x很大而y很小，那么它们的平方和将会造成
丢失小数的现象。首先要判断y是否是太小，x是不是太大。
如果出现这种情况则用，第一个公式来处理。其他的则用
这样可以让求出的斜边更加精确一些。
*/
if ((ratio = y / x) > __SQRT_DBL_MIN && x < __SQRT_DBL_MAX)
return x * sqrt(1. + ratio*ratio);
else
{//使用3次迭代是增加精确度。
r = ratio*ratio, p = x, q = y;
do
{
t = 4.+ r;
if (t == 4.)
break;
s = r / t;
p += 2. * s * p;
q *= s;
r = (q / p) * (q / p);
} while (1);
return p;
}
}
struct complex
{
double x;
double y;
}
double cabs(struct complex x)
{
return hypot(z.x,z.y);
}//hypot 函数的封装（这里不再举调用的例子了。）
# define DBL_MAX 1.79769313486231e+308
# define DBL_MIN 2.22507385850721e-308
int main(void)
{
printf("hypot(3, 4) =%25.17e\n",hypot(3., 4.));
printf("hypot(3*10^150,4*10^150) =%25.17g\n",hypot(3.e+150, 4.e+150));
printf("hypot(3*10^306,4*10^306) =%25.17g\n",hypot(3.e+306, 4.e+306));
printf("hypot(3*10^-320,4*10^-320) =%25.17g\n",hypot(3.e-320, 4.e-320));
printf("hypot(0.7*DBL_MAX,0.7*DBL_MAX) =%25.17g\n",hypot(0.7*DBL_MAX,0.7*DBL_MAX));
printf("hypot(DBL_MAX, 1.0) =%25.17g\n",hypot(DBL_MAX, 1.0));
printf("hypot(1.0, DBL_MAX) =%25.17g\n",hypot(1.0, DBL_MAX));
printf("hypot(0.0, DBL_MAX) =%25.17g\n",hypot(0.0, DBL_MAX));
printf("\n************************************************************\n");
printf("hypot(3, 4) =%25.17e\n",my_hypot01(3., 4.));
printf("hypot(3*10^150,4*10^150) =%25.17g\n",my_hypot01(3.e+150, 4.e+150));
printf("hypot(3*10^306,4*10^306) =%25.17g\n",my_hypot01(3.e+306, 4.e+306));
printf("hypot(3*10^-320,4*10^-320) =%25.17g\n",my_hypot01(3.e-320, 4.e-320));
printf("hypot(0.7*DBL_MAX,0.7*DBL_MAX) =%25.17g\n",my_hypot01(0.7*DBL_MAX,0.7*DBL_MAX));
printf("hypot(DBL_MAX, 1.0) =%25.17g\n",my_hypot01(DBL_MAX, 1.0));
printf("hypot(1.0, DBL_MAX) =%25.17g\n",my_hypot01(1.0, DBL_MAX));
printf("hypot(0.0, DBL_MAX) =%25.17g\n",my_hypot01(0.0, DBL_MAX));
printf("\n************************************************************\n");
printf("hypot(3, 4) =%25.17e\n",my_hypot02(3., 4.));
printf("hypot(3*10^150,4*10^150) =%25.17g\n",my_hypot02(3.e+150, 4.e+150));
printf("hypot(3*10^306,4*10^306) =%25.17g\n",my_hypot02(3.e+306, 4.e+306));
printf("hypot(3*10^-320,4*10^-320) =%25.17g\n",my_hypot02(3.e-320, 4.e-320));
printf("hypot(0.7*DBL_MAX,0.7*DBL_MAX) =%25.17g\n",my_hypot02(0.7*DBL_MAX,0.7*DBL_MAX));
printf("hypot(DBL_MAX, 1.0) =%25.17g\n",my_hypot02(DBL_MAX, 1.0));
printf("hypot(1.0, DBL_MAX) =%25.17g\n",my_hypot02(1.0, DBL_MAX));
printf("hypot(0.0, DBL_MAX) =%25.17g\n",my_hypot02(0.0, DBL_MAX));
system("pause");
return 0;
}
int abs(int n);
返回整型变量的绝对值。
In addition to the prototype already specified for this function,
ANSI-C++ standard incorporates an overloaded version:
long abs (long n );
with the same functionality as labs.
///////////////////////////////////////////////////////////////////////////
long labs(long n);
///////////////////////////////////////////////////////////////////////////
double fabs(double x);
///////////////////////////////////////////////////////////////////////////
double sin(double x);
ANSI-C++增加了float和double重载的版本
///////////////////////////////////////////////////////////////////////////
double cos(double x);
ANSI-C++增加了float和double重载的版本
/* cos example */
#include
#include
#define PI 3.14159265
int main ()
{
double param, result;
param = 45;
result = cos (param*PI/180);
printf ("Cosine of %lf degrees is %lf\n", param, result );
return 0;
}
Output:
Cosine of 45.000000 degrees is 0.707107
///////////////////////////////////////////////////////////////////////////
double tan(double x);
ANSI-C++ adds float and double overloaded versions of this function,
with the same bahavior but being both, parameter and result, of one of
these types
///////////////////////////////////////////////////////////////////////////
double asin(double x);
计算反三角 x在－1和＋1之间。
ANSI-C++ adds float and double overloaded versions of this function,
with the same bahavior but being both, parameter and result, of one of
these types.
///////////////////////////////////////////////////////////////////////////
double acos(double x);
计算反三角 x在－1和＋1之间。
ANSI-C++ adds float and double overloaded versions of this function,
with the same bahavior but being both, parameter and result, of one of
these types.
///////////////////////////////////////////////////////////////////////////
double atan(double x);
计算反三角。
ANSI-C++ adds float and double overloaded versions of this function,
with the same bahavior but being both, parameter and result, of one of
these types.
///////////////////////////////////////////////////////////////////////////
double atan2(double y,double x);
计算角度。根据y/x得到结果范围为－PI到PI
///////////////////////////////////////////////////////////////////////////
double atof(const char * string);
使用浮点数代表的字符串。数字，符号和E和e都作为有效数字的一部分。
格式通常为[whitespaces][+|-][nnnn][.nnn][e|E[+|-]nnnn]
如果发生错误返回0.0
/* atof example: sines calculator */
#include
#include
int main ()
{
double n,m;
double pi=3.1415926535;
char szInput [256];
printf ( "Enter degrees: " );
gets ( szInput );
n = atof ( szInput );
m = sin (n*pi/180);
printf ( "sine of %f degrees is %f\n" , n, m );
return 0;
}
Output:
Enter degrees: 45
sine of 45.000000 degrees is 0.707101
///////////////////////////////////////////////////////////////////////////
double ceil(double x);
返回大于或等于x的最小的整数。
ANSI-C++ adds float and double overloaded versions of this function,
with the same bahavior but being both, parameter and result, of one of
these types
/* ceil example */
#include
#include
int main ()
{
printf ("ceil of 2.3 is %.1lf\n", ceil (2.3) );
printf ("ceil of 3.8 is %.1lf\n", ceil (3.8) );
printf ("ceil of -2.3 is %.1lf\n", ceil (-2.3) );
printf ("ceil of -3.8 is %.1lf\n", ceil (-3.8) );
return 0;
}
Output:
ceil of 2.3 is 3.0
ceil of 3.8 is 4.0
ceil of -2.3 is -2.0
ceil of -3.8 is -3.0
///////////////////////////////////////////////////////////////////////////
double floor(double x);
返回小于或等于x的最大整数。
ANSI-C++ adds float and double overloaded versions of this function,
with the same bahavior but being both, parameter and result, of one of
these types
///////////////////////////////////////////////////////////////////////////
double fmod(double x,double y);
返回x/y的余
ANSI-C++ adds float and double overloaded versions of this function,
with the same bahavior but being both, parameter and result, of one of
these types
/* fmod example */
#include
#include
int main ()
{
printf ("fmod of 5.3 / 2 is %lf\n", fmod (5.3,2) );
printf ("fmod of 18.5 / 4.2 is %lf\n", fmod (18.5,4.2) );
return 0;
}
Output:
fmod of 5.3 / 2 is 1.300000
fmod of 18.5 / 4.2 is 1.700000
///////////////////////////////////////////////////////////////////////////
double exp(double x);
返回x的自然指数。
ANSI-C++ adds float and double overloaded versions of this function,
with the same bahavior but being both, parameter and result, of one of
these types
/* exp example */
#include
#include
int main ()
{
double param, result;
param = 5;
result = exp (param);
printf ("Exponential of %lf is %lf\n", param, result );
return 0;
}
///////////////////////////////////////////////////////////////////////////
double ldexp(double x,int exp);
根据给定的指数和尾数得到 x * 2^exp
ANSI-C++ adds float and double overloaded versions of this function,
with the same bahavior but being both, parameter x and return value, of
one of these types.
/* ldexp example */
#include
#include
int main ()
{
double param, result;
int n;
param = 0.95;
n = 4;
result = ldexp (param , n);
printf ("%f * 2^%d = %f\n", param, n, result);
return 0;
}
Output:
0.950000 * 2^4 = 15.200000
///////////////////////////////////////////////////////////////////////////
double frexp(double x,int * exp);
余数(在0.5到1之间)和指数(一个整数)的计算值。x = mantissa * 2^exponent
mantissa是被返回的值。
/* frexp example */
#include
#include
int main ()
{
double param, result;
int n;
param = 15.2;
result = frexp (param , &n);
printf ("%f * 2^%d = %f\n", result, n, param);
return 0;
}
Output:
0.950000 * 2^4 = 15.200000
///////////////////////////////////////////////////////////////////////////
double modf(double x,double * ipart);
将x分解为两部分。整数部分存储在ipart，小数部分作为返回值
ANSI-C++ adds float and double overloaded versions of this function,
with the same bahavior but being both, parameter x and return value, of
one of these types.
/* modf example */
#include
#include
int main ()
{
double param, fractpart, intpart;
param = 3.14159265;
fractpart = modf (param , &intpart);
printf ("%lf = %lf + %lf \n", param, intpart, fractpart);
return 0;
}
Output:
3.141593 = 3.000000 + 0.141593
///////////////////////////////////////////////////////////////////////////
double log(double x);
返回x的自然对数。
ANSI-C++ adds float and double overloaded versions of this function, with
the same bahavior but being both, parameter and result, of one of these
types
/* log example */
#include
#include
int main ()
{
double param, result;
param = 5.5;
result = log (param);
printf ("ln(%lf) = %lf\n", param, result );
return 0;
}
Output:
ln(5.500000) = 1.704748
///////////////////////////////////////////////////////////////////////////
double log10(double x);
ANSI-C++ adds float and double overloaded versions of this function, with
the same bahavior but being both, parameter and result, of one of these
types.
///////////////////////////////////////////////////////////////////////////
double pow(double x,double y);
返回x^y
ANSI-C++ adds float and double overloaded versions of this function, with
the same bahavior but being all of them, parameters and return value, of
one of these types
///////////////////////////////////////////////////////////////////////////
double aqrt(double x);
返回x的平方根。
ANSI-C++ adds float and double overloaded versions of this function, with
the same bahavior but being both, parameter and result, of one of these
types
///////////////////////////////////////////////////////////////////////////
double sinh(double x);
返回x的双曲正弦
ANSI-C++ adds float and double overloaded versions of this function, with
the same bahavior but being both, parameter and result, of one of these
types
* sinh example */
#include
#include
#define PI 3.14159265
int main ()
{
double param, result;
param = 45;
result = cosh (param*PI/180);
printf ("Hyperbolic sine of %lf degrees is %lf\n", param, result );
return 0;
}
Output:
Hyperbolic sine of 45.000000 degrees is 0.868671
///////////////////////////////////////////////////////////////////////////
double cosh(double x);
计算x的双曲余弦
ANSI-C++ adds float and double overloaded versions of this function, with
the same bahavior but being both, parameter and result, of one of these
types
/* cosh example */
#include
#include
#define PI 3.14159265
int main ()
{
double param, result;
param = 45;
result = cosh (param*PI/180);
printf ("Hyperbolic cosine of %lf degrees is %lf\n", param, result );
return 0;
}
Output:
Hyperbolic cosine of 45.000000 degrees is 1.324609
///////////////////////////////////////////////////////////////////////////
double tanh(double x);
计算x的双曲正切
ANSI-C++ adds float and double overloaded versions of this function, with
the same bahavior but being both, parameter and result, of one of these
types
/* tanh example */
#include
#include
#define PI 3.14159265
int main ()
{
double param, result;
param = 45;
result = tanh (param*PI/180);
printf ("Hyperbolic tangent of %lf degrees is %lf\n", param, result );
return 0;
}
Output:
Hyperbolic tangent of 45.000000 degrees is 0.655794
1.int abs(int x)
这函数呢,就是求整数x的绝对值.返回的是计算出来的结果.其中有一个函数,double fabs(double x),这也是求绝对值的函数,作用不止止用于整数哦.
2.double exp(double x)
这是求e的x次方的值,也就是e^x.
3.double pow(double x,double y)
求的是x的y次方的值,就是x^y.说起这个函数,我就记得以前大学时候的一件事.那时候老师让我们写一个计数器程序,结果用到x的y次方的时候,很多同学都写成:int n=x^y;当然结果是错误的了.这就是对库函数不熟悉所造成的.
4.int rand(void)
这是随机函数,产生的是从-90到32767的随机值,用这函数的时候记得要给随机种子哦,要不得出的不是真正的随机数.产生随机种子可以用srand((unsigned int)time(NULL));这就是由时间产生的随机种子了.
5.double sqrt(double x)
这个大家应该很熟悉吧?经常用到的开方函数了.没什么好说的呵呵.
6.double floor(double x)
求出的是不大于x的最大的整数.
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