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在头文件<math.h>中定义



float       atanhf( float arg );

(1)

(since C99)

double      atanh( double arg );

(2)

(since C99)

long double atanhl( long double arg );

(3)

(since C99)

Defined in header <tgmath.h>



#define atanh( arg )

(4)

(since C99)

1-3）计算的反双曲正切值arg。

4）类型 - 通用宏：如果参数具有类型long double，atanhl则被调用。否则，如果参数具有整数类型或类型double，atanh则调用该参数。否则，atanhf被调用。如果参数是复杂的，则宏调用相应的复变函数（catanhf，catanh，catanhl）。

参数

arg

-

浮点值代表双曲线区域的面积

返回值

如果没有错误发生，则arg（tanh-1）的反双曲正切值

（arg）或artanh（arg））。

如果发生域错误，则返回实现定义的值（NaN，如果支持）。

如果发生极错误±HUGE_VAL，±HUGE_VALF或±HUGE_VALL返回（用正确的符号）。

如果由于下溢而发生范围错误，则返回正确的结果（舍入后）。

错误处理

按照math_errhandling中的指定报告错误。

如果参数不在区间-1，+1上，则会发生范围错误。

如果参数为±1，则会发生极点错误。

如果实现支持IEEE浮点运算（IEC 60559），

  • 如果参数为±0，则不加修改地返回

  • 如果参数为±1，则返回并FE_DIVBYZERO提高±∞ 。

  • 如果| arg |> 1，则NaN返回并FE_INVALID升高。

  • 如果参数是NaN，则返回NaN

笔记

尽管C标准将该函数命名为“双曲正切”，但双曲函数的反函数是区域函数。他们的论点是双曲线领域，而不是弧线。正确的名称是“反双曲正切”（由POSIX使用）或“区域双曲线正切”。

POSIX指定在发生下溢时，arg未经修改就返回，如果不支持，则返回不大于DBL_MIN，FLT_MIN和LDBL_MIN的实现定义值。

例

#include <stdio.h>#include <math.h>#include <float.h>#include <errno.h>#include <fenv.h>#pragma STDC FENV_ACCESS ON
int main(void){    printf("atanh(0) = %f\natanh(-0) = %f\n", atanh(0), atanh(-0.0));    printf("atanh(0.9) = %f\n", atanh(0.9));    //error handling
    errno = 0; feclearexcept(FE_ALL_EXCEPT);    printf("atanh(-1) = %f\n", atanh(-1));    if(errno == ERANGE) perror("    errno == ERANGE");    if(fetestexcept(FE_DIVBYZERO)) puts("    FE_DIVBYZERO raised");}

可能的输出：

atanh(0) = 0.000000atanh(-0) = -0.000000atanh(0.9) = 1.472219atanh(-1) = -inf
    errno == ERANGE: Numerical result out of range
    FE_DIVBYZERO raised

参考

  • C11标准（ISO / IEC 9899：2011）：

    • 7.12.5.3 atanh函数（p：241）

    • 7.25类型通用数学<tgmath.h>（p：373-375）

    • F.10.2.3 atanh函数（p：520）

  • C99标准（ISO / IEC 9899：1999）：

    • 7.12.5.3 atanh函数（p：221-222）

    • 7.22类型通用数学<tgmath.h>（p：335-337）

    • F.9.2.3 atanh函数（p：457）

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