C
数值 | Numerics

clogl

clogf, clog, clogl

在头文件中定义
float complex clogf( float complex z (1)(since C99)
double complex clog( double complex z (2)(since C99)
long double complex clogl( long double complex z (3)(since C99)
Defined in header <tgmath.h>
#define log( z )(4)(since C99)

1-3)计算沿着负实轴的分支切割的复数自然(base- e)对数z

4)类型 - 通用宏:如果z有类型long double complexclogl被调用。如果z有类型double complexclog称为,如果z有类型float complexclogf称为。如果z是真实的或整数,则宏调用相应的实函数(logfloglogl)。如果z是虚构的,则调用相应的复数版本。

参数

z-复杂的论点

返回值

如果没有出现错误,则复数自然对数z返回,在沿虚轴的间隔-iπ,+iπ中的条带范围内,并且在实轴上数学上无界。

错误处理和特殊值

报告的错误与math_errhandling一致。

如果实现支持IEEE浮点运算,

  • 考虑到虚部的符号,该功能在分支切割上是连续的

笔记

具有极坐标分量(r,θ)的复数z的自然对数等于ln r + i(θ+2nπ),其中主值ln r +iθ

#include <stdio.h> #include <math.h> #include <complex.h> int main(void) { double complex z = clog(I // r = 1, θ = pi/2 printf("2*log(i) = %.1f%+fi\n", creal(2*z), cimag(2*z) double complex z2 = clog(sqrt(2)/2 + sqrt(2)/2*I // r = 1, θ = pi/4 printf("4*log(sqrt(2)/2+sqrt(2)i/2) = %.1f%+fi\n", creal(4*z2), cimag(4*z2) double complex z3 = clog(-1 // r = 1, θ = pi printf("log(-1+0i) = %.1f%+fi\n", creal(z3), cimag(z3) double complex z4 = clog(conj(-1) // or clog(CMPLX(-1, -0.0)) in C11 printf("log(-1-0i) (the other side of the cut) = %.1f%+fi\n", creal(z4), cimag(z4) }

输出:

2*log(i) = 0.0+3.141593i 4*log(sqrt(2)/2+sqrt(2)i/2) = 0.0+3.141593i log(-1+0i) = 0.0+3.141593i log(-1-0i) (the other side of the cut) = 0.0-3.141593i

参考

  • C11标准(ISO / IEC 9899:2011):