Objective-C中的数学函数math.h

数学函数库，一些数学计算的公式的具体实现是放在math.h里，具体有：

/******************************************************************
 *                        Math Functions                          *
 ******************************************************************/

extern float acosf(float);
extern double acos(double);
extern long double acosl(long double);

extern float asinf(float);
extern double asin(double);
extern long double asinl(long double);
    
extern float atanf(float);
extern double atan(double);
extern long double atanl(long double);
    
extern float atan2f(float, float);
extern double atan2(double, double);
extern long double atan2l(long double, long double);
    
extern float cosf(float);
extern double cos(double);
extern long double cosl(long double);
    
extern float sinf(float);
extern double sin(double);
extern long double sinl(long double);
    
extern float tanf(float);
extern double tan(double);
extern long double tanl(long double);
    
extern float acoshf(float);
extern double acosh(double);
extern long double acoshl(long double);
    
extern float asinhf(float);
extern double asinh(double);
extern long double asinhl(long double);
    
extern float atanhf(float);
extern double atanh(double);
extern long double atanhl(long double);
    
extern float coshf(float);
extern double cosh(double);
extern long double coshl(long double);
    
extern float sinhf(float);
extern double sinh(double);
extern long double sinhl(long double);
    
extern float tanhf(float);
extern double tanh(double);
extern long double tanhl(long double);
    
extern float expf(float);
extern double exp(double);
extern long double expl(long double);

extern float exp2f(float);
extern double exp2(double); 
extern long double exp2l(long double); 

extern float expm1f(float);
extern double expm1(double); 
extern long double expm1l(long double); 

extern float logf(float);
extern double log(double);
extern long double logl(long double);

extern float log10f(float);
extern double log10(double);
extern long double log10l(long double);

extern float log2f(float);
extern double log2(double);
extern long double log2l(long double);

extern float log1pf(float);
extern double log1p(double);
extern long double log1pl(long double);

extern float logbf(float);
extern double logb(double);
extern long double logbl(long double);

extern float modff(float, float *);
extern double modf(double, double *);
extern long double modfl(long double, long double *);

extern float ldexpf(float, int);
extern double ldexp(double, int);
extern long double ldexpl(long double, int);

extern float frexpf(float, int *);
extern double frexp(double, int *);
extern long double frexpl(long double, int *);

extern int ilogbf(float);
extern int ilogb(double);
extern int ilogbl(long double);

extern float scalbnf(float, int);
extern double scalbn(double, int);
extern long double scalbnl(long double, int);

extern float scalblnf(float, long int);
extern double scalbln(double, long int);
extern long double scalblnl(long double, long int);

extern float fabsf(float);
extern double fabs(double);
extern long double fabsl(long double);

extern float cbrtf(float);
extern double cbrt(double);
extern long double cbrtl(long double);

extern float hypotf(float, float);
extern double hypot(double, double);
extern long double hypotl(long double, long double);

extern float powf(float, float);
extern double pow(double, double);
extern long double powl(long double, long double);

extern float sqrtf(float);
extern double sqrt(double);
extern long double sqrtl(long double);

extern float erff(float);
extern double erf(double);
extern long double erfl(long double);

extern float erfcf(float);
extern double erfc(double);
extern long double erfcl(long double);

/*  lgammaf, lgamma, and lgammal are not thread-safe. The thread-safe
    variants lgammaf_r, lgamma_r, and lgammal_r are made available if
    you define the _REENTRANT symbol before including                 */
extern float lgammaf(float);
extern double lgamma(double);
extern long double lgammal(long double);

extern float tgammaf(float);
extern double tgamma(double);
extern long double tgammal(long double);

extern float ceilf(float);
extern double ceil(double);
extern long double ceill(long double);

extern float floorf(float);
extern double floor(double);
extern long double floorl(long double);

extern float nearbyintf(float);
extern double nearbyint(double);
extern long double nearbyintl(long double);

extern float rintf(float);
extern double rint(double);
extern long double rintl(long double);

extern long int lrintf(float);
extern long int lrint(double);
extern long int lrintl(long double);

extern float roundf(float);
extern double round(double);
extern long double roundl(long double);

extern long int lroundf(float);
extern long int lround(double);
extern long int lroundl(long double);
    
/*  long long is not part of C90. Make sure you are passing -std=c99 or
    -std=gnu99 or higher if you need these functions returning long longs     */
#if !(__DARWIN_NO_LONG_LONG)
extern long long int llrintf(float);
extern long long int llrint(double);
extern long long int llrintl(long double);

extern long long int llroundf(float);
extern long long int llround(double);
extern long long int llroundl(long double);
#endif /* !(__DARWIN_NO_LONG_LONG) */

extern float truncf(float);
extern double trunc(double);
extern long double truncl(long double);

extern float fmodf(float, float);
extern double fmod(double, double);
extern long double fmodl(long double, long double);

extern float remainderf(float, float);
extern double remainder(double, double);
extern long double remainderl(long double, long double);

extern float remquof(float, float, int *);
extern double remquo(double, double, int *);
extern long double remquol(long double, long double, int *);

extern float copysignf(float, float);
extern double copysign(double, double);
extern long double copysignl(long double, long double);

extern float nanf(const char *);
extern double nan(const char *);
extern long double nanl(const char *);

extern float nextafterf(float, float);
extern double nextafter(double, double);
extern long double nextafterl(long double, long double);

extern double nexttoward(double, long double);
extern float nexttowardf(float, long double);
extern long double nexttowardl(long double, long double);

extern float fdimf(float, float);
extern double fdim(double, double);
extern long double fdiml(long double, long double);

extern float fmaxf(float, float);
extern double fmax(double, double);
extern long double fmaxl(long double, long double);

extern float fminf(float, float);
extern double fmin(double, double);
extern long double fminl(long double, long double);

extern float fmaf(float, float, float);
extern double fma(double, double, double);
extern long double fmal(long double, long double, long double);

#define isgreater(x, y) __builtin_isgreater((x),(y))
#define isgreaterequal(x, y) __builtin_isgreaterequal((x),(y))
#define isless(x, y) __builtin_isless((x),(y))
#define islessequal(x, y) __builtin_islessequal((x),(y))
#define islessgreater(x, y) __builtin_islessgreater((x),(y))
#define isunordered(x, y) __builtin_isunordered((x),(y))

常用函数：

1、 三角函数
double sin(double);正弦
double cos(double);余弦
double tan(double);正切

2 、反三角函数
double asin (double); 结果介于[-PI/2,PI/2]
double acos (double); 结果介于[0,PI]
double atan (double); 反正切（主值），结果介于[-PI/2,PI/2]
double atan2 (double,double); 反正切（整圆值），结果介于[-PI,PI]

3 、双曲三角函数
double sinh (double);
double cosh (double);
double tanh (double);

4 、指数与对数
double frexp(double value,int *exp);这是一个将value值拆分成小数部分f和（以2为底的）指数部分exp，并返回小数部分f，即f*2^exp。其中f取值在0.5~1.0范围或者0。
double ldexp(double x,int exp);这个函数刚好跟上面那个frexp函数功能相反，它的返回值是x*2^exp
double modf(double value,double *iptr);拆分value值，返回它的小数部分，iptr指向整数部分。
double log (double); 以e为底的对数
double log10 (double);以10为底的对数
double pow(double x,double y);计算x的y次幂
float powf(float x,float y); 功能与pow一致，只是输入与输出皆为浮点数
double exp (double);求取自然数e的幂
double sqrt (double);开平方

5 、取整
double ceil (double); 取上整，返回不比x小的最小整数
double floor (double); 取下整，返回不比x大的最大整数，即[高斯函数](http://baike.baidu.com/view/856844.htm)[x]

6 、绝对值
int abs(int i); 求整型的绝对值
double fabs (double);求实型的绝对值
double cabs(struct complex znum);求复数的绝对值

7 、标准化浮点数
double frexp (double f,int *p); 标准化浮点数，f = x * 2^p，已知f求x,p (x介于[0.5,1])
double ldexp (double x,int p); 与frexp相反，已知x,p求f

8 、取整与取余
double modf (double,double*); 将参数的整数部分通过指针回传，返回小数部分
double fmod (double,double); 返回两参数相除的余数

9 、其他
double hypot(double x,double y);已知直角三角形两个直角边长度，求斜边长度
double ldexp(double x,int exponent);计算x*（2的exponent次幂）
double poly(double x,int degree,double coeffs []);计算多项式
int matherr(struct exception *e);数学错误计算处理程序
source: 《C & C++ Code Capsules》

10、取绝对值　　　
int abs(int i);                   // 处理int类型的取绝对值
double fabs(double i); //处理double类型的取绝对值
float fabsf(float i);           /处理float类型的取绝对值

11、取随机数
Objective-C 没有提供相关的函数生成随机数，不过C供了rand(), srand(), random(), srandom()， arc4random()，randomize()几个函数。要引用头文件#include
其中，random()和randomize()函数的使用的方法分别与rand()和srand()函数的使用方法对应类似。 arc4random()不用seed
1）   srand((unsigned)time(0));  //不加这句每次产生的随机数不变         int i = rand() % 5;      
2）   srandom(time(0));         int i = random() % 5;
3）   int i = arc4random() % 5 ;
注：rand()和random()实际并不是一个真正的伪随机数发生器，在使用之前需要先初始化随机种子，否则每次生成的随机数一样。 arc4random() 是一个真正的伪随机算法，不需要生成随机种子，因为第一次调用的时候就会自动生成。而且范围是rand()的两倍。在iPhone中，RAND_MAX是 0x7fffffff (2147483647)，而arc4random()返回的最大值则是 0x100000000 (4294967296)。
精确度比较：arc4random()  >  random()  >  rand()。
常用方法：arc4random
1）获取一个随机整数范围在：[0,100)包括0，不包括100 int x = arc4random() % 100;
2） 获取一个随机数范围在：[500,1000），包括500，不包括1000 int y = (arc4random() % 501) + 500;
3）获取一个随机整数，范围在[from,to），包括from，不包括to -(int)getRandomNumber:(int)from to:(int)to {     return (int)(from + (arc4random() % (to – from + 1))); //+1,result is [from to]; else is [from, to)!!!!!!! }

数学常量：

#define M_E         2.71828182845904523536028747135266250   // e
#define M_LOG2E     1.44269504088896340735992468100189214   // log 2e
#define M_LOG10E    0.434294481903251827651128918916605082  // log 10e
#define M_LN2       0.693147180559945309417232121458176568  // log e2
#define M_LN10      2.30258509299404568401799145468436421   // log e10
#define M_PI        3.14159265358979323846264338327950288   // pi
#define M_PI_2      1.57079632679489661923132169163975144   // pi/2
#define M_PI_4      0.785398163397448309615660845819875721  // pi/4
#define M_1_PI      0.318309886183790671537767526745028724  // 1/pi
#define M_2_PI      0.636619772367581343075535053490057448  // 2/pi
#define M_2_SQRTPI  1.12837916709551257389615890312154517   // 2/sqrt(pi)
#define M_SQRT2     1.41421356237309504880168872420969808   // sqrt(2)
#define M_SQRT1_2   0.707106781186547524400844362104849039  // 1/sqrt(2)

常用函数：

//指数运算
NSLog(@"%.f", pow(3,2) ); //result 9
NSLog(@"%.f", pow(3,3) ); //result 27

//开平方运算
NSLog(@"%.f", sqrt(16) ); //result 4
NSLog(@"%.f", sqrt(81) ); //result 9

//上舍入
NSLog(@"res: %.f", ceil(3.000000000001)); //result 4
NSLog(@"res: %.f", ceil(3.00)); //result 3

//下舍入
NSLog(@"res: %.f", floor(3.000000000001)); //result 3
NSLog(@"res: %.f", floor(3.9999999)); //result 3

//四舍五入
NSLog(@"res: %.f", round(3.5)); //result 4
NSLog(@"res: %.f", round(3.46)); //result 3
NSLog(@"res: %.f", round(-3.5)); //NB: this one returns -4

//最小值
NSLog(@"res: %.f", fmin(5,10)); //result 5

//最大值
NSLog(@"res: %.f", fmax(5,10)); //result 10

//绝对值
NSLog(@"res: %.f", fabs(10)); //result 10
NSLog(@"res: %.f", fabs(-10)); //result 10

NSArray * arr = [NSArray arrayWithObjects:@"10",@"50",@"9", nil];
NSInteger max = [[arr valueForKeyPath:@"@max.intValue"] integerValue];
max = max;//50
//另一种思路，在一些情况下可以很快获取，同样去最小值用min,要比循环方便多了，如果数组中放的是其他对象也可以用@max.property尽心筛选，不过类型都是NSNumber,没测试过其他类型

iOS开发

rand() ----随机数
abs() / labs() ----整数绝对值
fabs() / fabsf() / fabsl() ----浮点数绝对值
floor() / floorf() / floorl() ----向下取整
ceil() / ceilf() / ceill() ----向上取整
round() / roundf() / roundl() ----四舍五入
sqrt() / sqrtf() / sqrtl() ----求平方根
fmax() / fmaxf() / fmaxl() ----求最大值
fmin() / fminf() / fminl() ----求最小值
hypot() / hypotf() / hypotl() ----求直角三角形斜边的长度
fmod() / fmodf() / fmodl() ----求两数整除后的余数
modf() / modff() / modfl() ----浮点数分解为整数和小数
frexp() / frexpf() / frexpl() ----浮点数分解尾数和二为底的指数
sin() / sinf() / sinl() ----求正弦值
sinh() / sinhf() / sinhl() ----求双曲正弦值
cos() / cosf() / cosl() ----求余弦值
cosh() / coshf() / coshl() ----求双曲余弦值
tan() / tanf() / tanl() ----求正切值
tanh() / tanhf() / tanhl() ----求双曲正切值
asin() / asinf() / asinl() ----求反正弦值
asinh() / asinhf() / asinhl() ----求反双曲正弦值
acos() / acosf() / acosl() ----求反余弦值
acosh() / acoshf() / acoshl() ----求反双曲余弦值
atan() / atanf() / atanl() ----求反正切值
atan2() / atan2f() / atan2l() ----求坐标值的反正切值
atanh() / atanhf() / atanhl() ----求反双曲正切值

输出语法

%@                   对象
%d, %i               整数
%u                    无符整形
%f                     浮点/双字
%x, %X              二进制整数
%o                    八进制整数
%zu size_t
%p                    指针
%e                    浮点/双字 （科学计算）
%g                    浮点/双字
%s C                字符串
%.*s                  Pascal字符串
%c                    字符
%C                    unichar
%lld                   64位长整数（long long）
%llu                   无符64位长整数
%Lf                    64位双字

结构体输出
NSStringFromCGPoint
NSStringFromCGSize
NSStringFromCGRect
NSStringFromCGAffineTransform
NSStringFromUIEdgeInsets
例如：
NSLog(@"rect1: %@", NSStringFromCGRect(rect1));