目录
iOS数学公式都定义在<math.h>文件中，引用关系是Foundation.h <- CoreFoundation.h <- math.h,所以一般情况下不需要单独引入<math.h>即可调用相关的数学函数。
一般情况下，同一个数学函数有多个，根据需要选择，有些是重载的，有些是xxx和xxx2这样的形式。
常用数学函数
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 exp (double);求取自然数e的幂
double sqrt (double);开平方
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）;计算以x为底数的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
5 取整
double ceil (double); 取上整
double floor (double); 取下整
6 绝对值
double fabs (double);求绝对值
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)
常见应用代码示例
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)
角度转弧度，弧度转角度
//弧度转角度
#define Radians_To_Degrees(radians) ((radians) * (180.0 / M_PI))
//角度转弧度
#define Degrees_To_Radians(angle) ((angle) / 180.0 * M_PI)
eg:计算三角形的三个点
CGFloat R = 200 ;
CGFloat oirin_y = 100 ;
CGPoint point0 = CGPointMake(self.view.frame.size.width/2.0, 0+oirin_y);
CGPoint point1 = CGPointMake(self.view.frame.size.width/2.0 - R/2.0, cos(Degrees_To_Radians(30))*R + oirin_y);
CGPoint point2 = CGPointMake(self.view.frame.size.width/2.0 + R/2.0, cos(Degrees_To_Radians(30))*R + oirin_y);
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
附完整头文件内容
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 <math.h> */
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);
更多信息请直接参考math.h文件。